Basic properties
| Modulus: | \(1175\) | |
| Conductor: | \(1175\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(460\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1175.w
\(\chi_{1175}(13,\cdot)\) \(\chi_{1175}(22,\cdot)\) \(\chi_{1175}(23,\cdot)\) \(\chi_{1175}(33,\cdot)\) \(\chi_{1175}(38,\cdot)\) \(\chi_{1175}(52,\cdot)\) \(\chi_{1175}(58,\cdot)\) \(\chi_{1175}(62,\cdot)\) \(\chi_{1175}(67,\cdot)\) \(\chi_{1175}(73,\cdot)\) \(\chi_{1175}(77,\cdot)\) \(\chi_{1175}(78,\cdot)\) \(\chi_{1175}(87,\cdot)\) \(\chi_{1175}(88,\cdot)\) \(\chi_{1175}(92,\cdot)\) \(\chi_{1175}(113,\cdot)\) \(\chi_{1175}(117,\cdot)\) \(\chi_{1175}(123,\cdot)\) \(\chi_{1175}(127,\cdot)\) \(\chi_{1175}(133,\cdot)\) \(\chi_{1175}(137,\cdot)\) \(\chi_{1175}(138,\cdot)\) \(\chi_{1175}(152,\cdot)\) \(\chi_{1175}(163,\cdot)\) \(\chi_{1175}(167,\cdot)\) \(\chi_{1175}(172,\cdot)\) \(\chi_{1175}(198,\cdot)\) \(\chi_{1175}(203,\cdot)\) \(\chi_{1175}(208,\cdot)\) \(\chi_{1175}(217,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{460})$ |
| Fixed field: | Number field defined by a degree 460 polynomial (not computed) |
Values on generators
\((377,851)\) → \((e\left(\frac{19}{20}\right),e\left(\frac{11}{46}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 1175 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{117}{460}\right)\) | \(e\left(\frac{199}{460}\right)\) | \(e\left(\frac{117}{230}\right)\) | \(e\left(\frac{79}{115}\right)\) | \(e\left(\frac{37}{92}\right)\) | \(e\left(\frac{351}{460}\right)\) | \(e\left(\frac{199}{230}\right)\) | \(e\left(\frac{201}{230}\right)\) | \(e\left(\frac{433}{460}\right)\) | \(e\left(\frac{313}{460}\right)\) |