Basic properties
| Modulus: | \(946\) | |
| Conductor: | \(473\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(105\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{473}(411,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 946.bc
\(\chi_{946}(9,\cdot)\) \(\chi_{946}(15,\cdot)\) \(\chi_{946}(25,\cdot)\) \(\chi_{946}(31,\cdot)\) \(\chi_{946}(53,\cdot)\) \(\chi_{946}(81,\cdot)\) \(\chi_{946}(103,\cdot)\) \(\chi_{946}(169,\cdot)\) \(\chi_{946}(181,\cdot)\) \(\chi_{946}(185,\cdot)\) \(\chi_{946}(203,\cdot)\) \(\chi_{946}(225,\cdot)\) \(\chi_{946}(229,\cdot)\) \(\chi_{946}(267,\cdot)\) \(\chi_{946}(273,\cdot)\) \(\chi_{946}(289,\cdot)\) \(\chi_{946}(311,\cdot)\) \(\chi_{946}(339,\cdot)\) \(\chi_{946}(357,\cdot)\) \(\chi_{946}(361,\cdot)\) \(\chi_{946}(367,\cdot)\) \(\chi_{946}(401,\cdot)\) \(\chi_{946}(411,\cdot)\) \(\chi_{946}(427,\cdot)\) \(\chi_{946}(443,\cdot)\) \(\chi_{946}(445,\cdot)\) \(\chi_{946}(455,\cdot)\) \(\chi_{946}(487,\cdot)\) \(\chi_{946}(511,\cdot)\) \(\chi_{946}(531,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 105 polynomial (not computed) |
Values on generators
\((431,89)\) → \((e\left(\frac{1}{5}\right),e\left(\frac{20}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 946 }(411, a) \) | \(1\) | \(1\) | \(e\left(\frac{58}{105}\right)\) | \(e\left(\frac{64}{105}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{11}{105}\right)\) | \(e\left(\frac{71}{105}\right)\) | \(e\left(\frac{17}{105}\right)\) | \(e\left(\frac{104}{105}\right)\) | \(e\left(\frac{73}{105}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{5}{21}\right)\) |