Basic properties
| Modulus: | \(946\) | |
| Conductor: | \(473\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{473}(57,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 946.bd
\(\chi_{946}(13,\cdot)\) \(\chi_{946}(17,\cdot)\) \(\chi_{946}(57,\cdot)\) \(\chi_{946}(83,\cdot)\) \(\chi_{946}(95,\cdot)\) \(\chi_{946}(101,\cdot)\) \(\chi_{946}(117,\cdot)\) \(\chi_{946}(139,\cdot)\) \(\chi_{946}(167,\cdot)\) \(\chi_{946}(189,\cdot)\) \(\chi_{946}(195,\cdot)\) \(\chi_{946}(239,\cdot)\) \(\chi_{946}(255,\cdot)\) \(\chi_{946}(271,\cdot)\) \(\chi_{946}(281,\cdot)\) \(\chi_{946}(283,\cdot)\) \(\chi_{946}(315,\cdot)\) \(\chi_{946}(325,\cdot)\) \(\chi_{946}(359,\cdot)\) \(\chi_{946}(369,\cdot)\) \(\chi_{946}(425,\cdot)\) \(\chi_{946}(447,\cdot)\) \(\chi_{946}(453,\cdot)\) \(\chi_{946}(497,\cdot)\) \(\chi_{946}(513,\cdot)\) \(\chi_{946}(525,\cdot)\) \(\chi_{946}(541,\cdot)\) \(\chi_{946}(547,\cdot)\) \(\chi_{946}(569,\cdot)\) \(\chi_{946}(611,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((431,89)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{10}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 946 }(57, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{105}\right)\) | \(e\left(\frac{32}{105}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{58}{105}\right)\) | \(e\left(\frac{71}{210}\right)\) | \(e\left(\frac{61}{105}\right)\) | \(e\left(\frac{209}{210}\right)\) | \(e\left(\frac{73}{210}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{13}{21}\right)\) |