Basic properties
| Modulus: | \(8624\) | |
| Conductor: | \(4312\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4312}(2259,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8624.gx
\(\chi_{8624}(103,\cdot)\) \(\chi_{8624}(311,\cdot)\) \(\chi_{8624}(647,\cdot)\) \(\chi_{8624}(663,\cdot)\) \(\chi_{8624}(775,\cdot)\) \(\chi_{8624}(983,\cdot)\) \(\chi_{8624}(1335,\cdot)\) \(\chi_{8624}(1543,\cdot)\) \(\chi_{8624}(1655,\cdot)\) \(\chi_{8624}(1879,\cdot)\) \(\chi_{8624}(1895,\cdot)\) \(\chi_{8624}(2007,\cdot)\) \(\chi_{8624}(2215,\cdot)\) \(\chi_{8624}(2231,\cdot)\) \(\chi_{8624}(2887,\cdot)\) \(\chi_{8624}(3111,\cdot)\) \(\chi_{8624}(3127,\cdot)\) \(\chi_{8624}(3239,\cdot)\) \(\chi_{8624}(3447,\cdot)\) \(\chi_{8624}(3463,\cdot)\) \(\chi_{8624}(3799,\cdot)\) \(\chi_{8624}(4007,\cdot)\) \(\chi_{8624}(4119,\cdot)\) \(\chi_{8624}(4359,\cdot)\) \(\chi_{8624}(4471,\cdot)\) \(\chi_{8624}(4679,\cdot)\) \(\chi_{8624}(4695,\cdot)\) \(\chi_{8624}(5031,\cdot)\) \(\chi_{8624}(5239,\cdot)\) \(\chi_{8624}(5351,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((5391,6469,7745,3137)\) → \((-1,-1,e\left(\frac{29}{42}\right),e\left(\frac{1}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 8624 }(103, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{210}\right)\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{61}{105}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{13}{210}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{68}{105}\right)\) | \(e\left(\frac{61}{70}\right)\) |