Basic properties
Modulus: | \(4012\) | |
Conductor: | \(4012\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(232\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4012.bj
\(\chi_{4012}(15,\cdot)\) \(\chi_{4012}(19,\cdot)\) \(\chi_{4012}(87,\cdot)\) \(\chi_{4012}(127,\cdot)\) \(\chi_{4012}(223,\cdot)\) \(\chi_{4012}(263,\cdot)\) \(\chi_{4012}(287,\cdot)\) \(\chi_{4012}(315,\cdot)\) \(\chi_{4012}(331,\cdot)\) \(\chi_{4012}(359,\cdot)\) \(\chi_{4012}(383,\cdot)\) \(\chi_{4012}(399,\cdot)\) \(\chi_{4012}(491,\cdot)\) \(\chi_{4012}(535,\cdot)\) \(\chi_{4012}(559,\cdot)\) \(\chi_{4012}(631,\cdot)\) \(\chi_{4012}(671,\cdot)\) \(\chi_{4012}(695,\cdot)\) \(\chi_{4012}(723,\cdot)\) \(\chi_{4012}(831,\cdot)\) \(\chi_{4012}(835,\cdot)\) \(\chi_{4012}(875,\cdot)\) \(\chi_{4012}(971,\cdot)\) \(\chi_{4012}(995,\cdot)\) \(\chi_{4012}(1039,\cdot)\) \(\chi_{4012}(1079,\cdot)\) \(\chi_{4012}(1103,\cdot)\) \(\chi_{4012}(1107,\cdot)\) \(\chi_{4012}(1147,\cdot)\) \(\chi_{4012}(1199,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{232})$ |
Fixed field: | Number field defined by a degree 232 polynomial (not computed) |
Values on generators
\((2007,3777,3129)\) → \((-1,e\left(\frac{5}{8}\right),e\left(\frac{20}{29}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 4012 }(1079, a) \) | \(-1\) | \(1\) | \(e\left(\frac{141}{232}\right)\) | \(e\left(\frac{61}{232}\right)\) | \(e\left(\frac{183}{232}\right)\) | \(e\left(\frac{25}{116}\right)\) | \(e\left(\frac{27}{232}\right)\) | \(e\left(\frac{31}{58}\right)\) | \(e\left(\frac{101}{116}\right)\) | \(e\left(\frac{53}{116}\right)\) | \(e\left(\frac{23}{58}\right)\) | \(e\left(\frac{51}{232}\right)\) |