Basic properties
Modulus: | \(4012\) | |
Conductor: | \(1003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(232\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1003}(53,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4012.bi
\(\chi_{4012}(9,\cdot)\) \(\chi_{4012}(25,\cdot)\) \(\chi_{4012}(49,\cdot)\) \(\chi_{4012}(53,\cdot)\) \(\chi_{4012}(121,\cdot)\) \(\chi_{4012}(145,\cdot)\) \(\chi_{4012}(189,\cdot)\) \(\chi_{4012}(213,\cdot)\) \(\chi_{4012}(253,\cdot)\) \(\chi_{4012}(257,\cdot)\) \(\chi_{4012}(281,\cdot)\) \(\chi_{4012}(321,\cdot)\) \(\chi_{4012}(389,\cdot)\) \(\chi_{4012}(417,\cdot)\) \(\chi_{4012}(433,\cdot)\) \(\chi_{4012}(461,\cdot)\) \(\chi_{4012}(501,\cdot)\) \(\chi_{4012}(525,\cdot)\) \(\chi_{4012}(529,\cdot)\) \(\chi_{4012}(553,\cdot)\) \(\chi_{4012}(593,\cdot)\) \(\chi_{4012}(597,\cdot)\) \(\chi_{4012}(661,\cdot)\) \(\chi_{4012}(665,\cdot)\) \(\chi_{4012}(729,\cdot)\) \(\chi_{4012}(733,\cdot)\) \(\chi_{4012}(757,\cdot)\) \(\chi_{4012}(841,\cdot)\) \(\chi_{4012}(933,\cdot)\) \(\chi_{4012}(961,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{232})$ |
Fixed field: | Number field defined by a degree 232 polynomial (not computed) |
Values on generators
\((2007,3777,3129)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{11}{29}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 4012 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{195}{232}\right)\) | \(e\left(\frac{151}{232}\right)\) | \(e\left(\frac{105}{232}\right)\) | \(e\left(\frac{79}{116}\right)\) | \(e\left(\frac{141}{232}\right)\) | \(e\left(\frac{33}{58}\right)\) | \(e\left(\frac{57}{116}\right)\) | \(e\left(\frac{77}{116}\right)\) | \(e\left(\frac{17}{58}\right)\) | \(e\left(\frac{189}{232}\right)\) |