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 \(\chi_{473}(19,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 946.bf
\(\chi_{946}(19,\cdot)\) \(\chi_{946}(29,\cdot)\) \(\chi_{946}(61,\cdot)\) \(\chi_{946}(63,\cdot)\) \(\chi_{946}(73,\cdot)\) \(\chi_{946}(105,\cdot)\) \(\chi_{946}(149,\cdot)\) \(\chi_{946}(205,\cdot)\) \(\chi_{946}(227,\cdot)\) \(\chi_{946}(233,\cdot)\) \(\chi_{946}(249,\cdot)\) \(\chi_{946}(261,\cdot)\) \(\chi_{946}(277,\cdot)\) \(\chi_{946}(321,\cdot)\) \(\chi_{946}(327,\cdot)\) \(\chi_{946}(347,\cdot)\) \(\chi_{946}(349,\cdot)\) \(\chi_{946}(413,\cdot)\) \(\chi_{946}(415,\cdot)\) \(\chi_{946}(435,\cdot)\) \(\chi_{946}(459,\cdot)\) \(\chi_{946}(491,\cdot)\) \(\chi_{946}(501,\cdot)\) \(\chi_{946}(503,\cdot)\) \(\chi_{946}(519,\cdot)\) \(\chi_{946}(535,\cdot)\) \(\chi_{946}(545,\cdot)\) \(\chi_{946}(579,\cdot)\) \(\chi_{946}(585,\cdot)\) \(\chi_{946}(589,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((431,89)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{19}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 946 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{179}{210}\right)\) | \(e\left(\frac{107}{210}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{74}{105}\right)\) | \(e\left(\frac{163}{210}\right)\) | \(e\left(\frac{38}{105}\right)\) | \(e\left(\frac{187}{210}\right)\) | \(e\left(\frac{52}{105}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{5}{21}\right)\) |