Basic properties
| Modulus: | \(705\) | |
| 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 \(\chi_{235}(22,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 705.x
\(\chi_{705}(13,\cdot)\) \(\chi_{705}(22,\cdot)\) \(\chi_{705}(43,\cdot)\) \(\chi_{705}(52,\cdot)\) \(\chi_{705}(58,\cdot)\) \(\chi_{705}(67,\cdot)\) \(\chi_{705}(73,\cdot)\) \(\chi_{705}(82,\cdot)\) \(\chi_{705}(88,\cdot)\) \(\chi_{705}(127,\cdot)\) \(\chi_{705}(133,\cdot)\) \(\chi_{705}(163,\cdot)\) \(\chi_{705}(172,\cdot)\) \(\chi_{705}(193,\cdot)\) \(\chi_{705}(208,\cdot)\) \(\chi_{705}(217,\cdot)\) \(\chi_{705}(223,\cdot)\) \(\chi_{705}(232,\cdot)\) \(\chi_{705}(268,\cdot)\) \(\chi_{705}(292,\cdot)\) \(\chi_{705}(313,\cdot)\) \(\chi_{705}(322,\cdot)\) \(\chi_{705}(352,\cdot)\) \(\chi_{705}(358,\cdot)\) \(\chi_{705}(367,\cdot)\) \(\chi_{705}(373,\cdot)\) \(\chi_{705}(433,\cdot)\) \(\chi_{705}(442,\cdot)\) \(\chi_{705}(463,\cdot)\) \(\chi_{705}(493,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{92})$ |
| Fixed field: | Number field defined by a degree 92 polynomial |
Values on generators
\((236,142,616)\) → \((1,i,e\left(\frac{25}{46}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 705 }(22, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{92}\right)\) | \(e\left(\frac{3}{46}\right)\) | \(e\left(\frac{59}{92}\right)\) | \(e\left(\frac{9}{92}\right)\) | \(e\left(\frac{37}{46}\right)\) | \(e\left(\frac{67}{92}\right)\) | \(e\left(\frac{31}{46}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{87}{92}\right)\) | \(e\left(\frac{22}{23}\right)\) |