Basic properties
| Modulus: | \(1175\) | |
| Conductor: | \(235\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(92\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{235}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1175.r
\(\chi_{1175}(43,\cdot)\) \(\chi_{1175}(57,\cdot)\) \(\chi_{1175}(82,\cdot)\) \(\chi_{1175}(107,\cdot)\) \(\chi_{1175}(132,\cdot)\) \(\chi_{1175}(182,\cdot)\) \(\chi_{1175}(193,\cdot)\) \(\chi_{1175}(207,\cdot)\) \(\chi_{1175}(218,\cdot)\) \(\chi_{1175}(232,\cdot)\) \(\chi_{1175}(257,\cdot)\) \(\chi_{1175}(268,\cdot)\) \(\chi_{1175}(293,\cdot)\) \(\chi_{1175}(368,\cdot)\) \(\chi_{1175}(407,\cdot)\) \(\chi_{1175}(443,\cdot)\) \(\chi_{1175}(468,\cdot)\) \(\chi_{1175}(493,\cdot)\) \(\chi_{1175}(532,\cdot)\) \(\chi_{1175}(543,\cdot)\) \(\chi_{1175}(557,\cdot)\) \(\chi_{1175}(593,\cdot)\) \(\chi_{1175}(607,\cdot)\) \(\chi_{1175}(668,\cdot)\) \(\chi_{1175}(693,\cdot)\) \(\chi_{1175}(718,\cdot)\) \(\chi_{1175}(743,\cdot)\) \(\chi_{1175}(757,\cdot)\) \(\chi_{1175}(782,\cdot)\) \(\chi_{1175}(793,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{92})$ |
| Fixed field: | Number field defined by a degree 92 polynomial |
Values on generators
\((377,851)\) → \((-i,e\left(\frac{13}{46}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 1175 }(43, a) \) | \(1\) | \(1\) | \(e\left(\frac{77}{92}\right)\) | \(e\left(\frac{83}{92}\right)\) | \(e\left(\frac{31}{46}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{73}{92}\right)\) | \(e\left(\frac{47}{92}\right)\) | \(e\left(\frac{37}{46}\right)\) | \(e\left(\frac{45}{46}\right)\) | \(e\left(\frac{53}{92}\right)\) | \(e\left(\frac{33}{92}\right)\) |