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 \(\chi_{473}(71,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 946.be
\(\chi_{946}(3,\cdot)\) \(\chi_{946}(5,\cdot)\) \(\chi_{946}(69,\cdot)\) \(\chi_{946}(71,\cdot)\) \(\chi_{946}(91,\cdot)\) \(\chi_{946}(115,\cdot)\) \(\chi_{946}(119,\cdot)\) \(\chi_{946}(141,\cdot)\) \(\chi_{946}(147,\cdot)\) \(\chi_{946}(157,\cdot)\) \(\chi_{946}(159,\cdot)\) \(\chi_{946}(163,\cdot)\) \(\chi_{946}(191,\cdot)\) \(\chi_{946}(201,\cdot)\) \(\chi_{946}(235,\cdot)\) \(\chi_{946}(245,\cdot)\) \(\chi_{946}(291,\cdot)\) \(\chi_{946}(313,\cdot)\) \(\chi_{946}(335,\cdot)\) \(\chi_{946}(377,\cdot)\) \(\chi_{946}(399,\cdot)\) \(\chi_{946}(405,\cdot)\) \(\chi_{946}(421,\cdot)\) \(\chi_{946}(433,\cdot)\) \(\chi_{946}(449,\cdot)\) \(\chi_{946}(493,\cdot)\) \(\chi_{946}(499,\cdot)\) \(\chi_{946}(521,\cdot)\) \(\chi_{946}(577,\cdot)\) \(\chi_{946}(587,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((431,89)\) → \((e\left(\frac{2}{5}\right),e\left(\frac{5}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 946 }(71, a) \) | \(-1\) | \(1\) | \(e\left(\frac{67}{210}\right)\) | \(e\left(\frac{121}{210}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{67}{105}\right)\) | \(e\left(\frac{22}{105}\right)\) | \(e\left(\frac{94}{105}\right)\) | \(e\left(\frac{13}{105}\right)\) | \(e\left(\frac{97}{210}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{19}{21}\right)\) |