CoCalc -- 3613.sagews

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K.<z>=NumberField(x^2+x+1)
for p in prime_range(1,100):
    p, K. factor(p), p%3

(2, Fractional ideal (2), 2)
(3, (Fractional ideal (-2*z - 1))^2, 0)
(5, Fractional ideal (5), 2)
(7, (Fractional ideal (z + 3)) * (Fractional ideal (-z + 2)), 1)
(11, Fractional ideal (11), 2)
(13, (Fractional ideal (z - 3)) * (Fractional ideal (z + 4)), 1)
(17, Fractional ideal (17), 2)
(19, (Fractional ideal (5*z + 3)) * (Fractional ideal (-5*z - 2)), 1)
(23, Fractional ideal (23), 2)
(29, Fractional ideal (29), 2)
(31, (Fractional ideal (6*z + 1)) * (Fractional ideal (-6*z - 5)), 1)
(37, (Fractional ideal (-7*z - 3)) * (Fractional ideal (-7*z - 4)), 1)
(41, Fractional ideal (41), 2)
(43, (Fractional ideal (7*z + 1)) * (Fractional ideal (-7*z - 6)), 1)
(47, Fractional ideal (47), 2)
(53, Fractional ideal (53), 2)
(59, Fractional ideal (59), 2)
(61, (Fractional ideal (-9*z - 4)) * (Fractional ideal (-9*z - 5)), 1)
(67, (Fractional ideal (9*z + 2)) * (Fractional ideal (9*z + 7)), 1)
(71, Fractional ideal (71), 2)
(73, (Fractional ideal (9*z + 1)) * (Fractional ideal (-9*z - 8)), 1)
(79, (Fractional ideal (10*z + 3)) * (Fractional ideal (10*z + 7)), 1)
(83, Fractional ideal (83), 2)
(89, Fractional ideal (89), 2)
(97, (Fractional ideal (-11*z - 8)) * (Fractional ideal (-11*z - 3)), 1)

K.<z>=NumberField(x^2-5)
for p in prime_range(1,100):
    p, K. factor(p), p%5

(2, Fractional ideal (2), 2)
(3, Fractional ideal (3), 3)
(5, (Fractional ideal (z))^2, 0)
(7, Fractional ideal (7), 2)
(11, (Fractional ideal (-3/2*z + 1/2)) * (Fractional ideal (-3/2*z - 1/2)), 1)
(13, Fractional ideal (13), 3)
(17, Fractional ideal (17), 2)
(19, (Fractional ideal (-2*z - 1)) * (Fractional ideal (-2*z + 1)), 4)
(23, Fractional ideal (23), 3)
(29, (Fractional ideal (-1/2*z + 11/2)) * (Fractional ideal (1/2*z + 11/2)), 4)
(31, (Fractional ideal (5/2*z + 1/2)) * (Fractional ideal (5/2*z - 1/2)), 1)
(37, Fractional ideal (37), 2)
(41, (Fractional ideal (1/2*z - 13/2)) * (Fractional ideal (1/2*z + 13/2)), 1)
(43, Fractional ideal (43), 3)
(47, Fractional ideal (47), 2)
(53, Fractional ideal (53), 3)
(59, (Fractional ideal (7/2*z + 3/2)) * (Fractional ideal (7/2*z - 3/2)), 4)
(61, (Fractional ideal (7/2*z + 1/2)) * (Fractional ideal (7/2*z - 1/2)), 1)
(67, Fractional ideal (67), 2)
(71, (Fractional ideal (1/2*z - 17/2)) * (Fractional ideal (1/2*z + 17/2)), 1)
(73, Fractional ideal (73), 3)
(79, (Fractional ideal (-4*z + 1)) * (Fractional ideal (-4*z - 1)), 4)
(83, Fractional ideal (83), 3)
(89, (Fractional ideal (1/2*z + 19/2)) * (Fractional ideal (1/2*z - 19/2)), 4)
(97, Fractional ideal (97), 2)

K.<z>=NumberField(x^2-2)
for p in prime_range(1,100):
    p, K. factor(p), p%8

(2, (Fractional ideal (z))^2, 2)
(3, Fractional ideal (3), 3)
(5, Fractional ideal (5), 5)
(7, (Fractional ideal (2*z - 1)) * (Fractional ideal (2*z + 1)), 7)
(11, Fractional ideal (11), 3)
(13, Fractional ideal (13), 5)
(17, (Fractional ideal (-3*z + 1)) * (Fractional ideal (3*z + 1)), 1)
(19, Fractional ideal (19), 3)
(23, (Fractional ideal (-z + 5)) * (Fractional ideal (z + 5)), 7)
(29, Fractional ideal (29), 5)
(31, (Fractional ideal (4*z - 1)) * (Fractional ideal (-4*z - 1)), 7)
(37, Fractional ideal (37), 5)
(41, (Fractional ideal (-2*z + 7)) * (Fractional ideal (2*z + 7)), 1)
(43, Fractional ideal (43), 3)
(47, (Fractional ideal (z - 7)) * (Fractional ideal (z + 7)), 7)
(53, Fractional ideal (53), 5)
(59, Fractional ideal (59), 3)
(61, Fractional ideal (61), 5)
(67, Fractional ideal (67), 3)
(71, (Fractional ideal (-6*z - 1)) * (Fractional ideal (6*z - 1)), 7)
(73, (Fractional ideal (-2*z + 9)) * (Fractional ideal (2*z + 9)), 1)
(79, (Fractional ideal (z - 9)) * (Fractional ideal (z + 9)), 7)
(83, Fractional ideal (83), 3)
(89, (Fractional ideal (-7*z + 3)) * (Fractional ideal (-7*z - 3)), 1)
(97, (Fractional ideal (-7*z - 1)) * (Fractional ideal (7*z - 1)), 1)

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_2.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("Zm9yIG0gaW4gcmFuZ2UgKDEsMjApCiAgICBmb3IgbiBpbiByYW5nZSAoMSwyMCkKICAgICAgICBwcmludCBnY2QoRihtKSxGKG4pKQ=="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single')
  File "", line 1, in <module>
    
  File "/tmp/tmpGWBQo7/___code___.py", line 3
    for m in range (_sage_const_1 ,_sage_const_20 )
                                                  ^
SyntaxError: invalid syntax