Basic properties
| Modulus: | \(8619\) | |
| Conductor: | \(2873\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(624\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2873}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8619.fn
\(\chi_{8619}(7,\cdot)\) \(\chi_{8619}(97,\cdot)\) \(\chi_{8619}(163,\cdot)\) \(\chi_{8619}(175,\cdot)\) \(\chi_{8619}(184,\cdot)\) \(\chi_{8619}(193,\cdot)\) \(\chi_{8619}(232,\cdot)\) \(\chi_{8619}(292,\cdot)\) \(\chi_{8619}(301,\cdot)\) \(\chi_{8619}(379,\cdot)\) \(\chi_{8619}(397,\cdot)\) \(\chi_{8619}(436,\cdot)\) \(\chi_{8619}(466,\cdot)\) \(\chi_{8619}(496,\cdot)\) \(\chi_{8619}(622,\cdot)\) \(\chi_{8619}(643,\cdot)\) \(\chi_{8619}(670,\cdot)\) \(\chi_{8619}(760,\cdot)\) \(\chi_{8619}(838,\cdot)\) \(\chi_{8619}(847,\cdot)\) \(\chi_{8619}(856,\cdot)\) \(\chi_{8619}(895,\cdot)\) \(\chi_{8619}(955,\cdot)\) \(\chi_{8619}(964,\cdot)\) \(\chi_{8619}(1042,\cdot)\) \(\chi_{8619}(1060,\cdot)\) \(\chi_{8619}(1099,\cdot)\) \(\chi_{8619}(1129,\cdot)\) \(\chi_{8619}(1159,\cdot)\) \(\chi_{8619}(1285,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{624})$ |
| Fixed field: | Number field defined by a degree 624 polynomial (not computed) |
Values on generators
\((5747,5917,2536)\) → \((1,e\left(\frac{107}{156}\right),e\left(\frac{11}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(19\) |
| \( \chi_{ 8619 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{97}{312}\right)\) | \(e\left(\frac{97}{156}\right)\) | \(e\left(\frac{127}{208}\right)\) | \(e\left(\frac{595}{624}\right)\) | \(e\left(\frac{97}{104}\right)\) | \(e\left(\frac{575}{624}\right)\) | \(e\left(\frac{287}{624}\right)\) | \(e\left(\frac{55}{208}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{5}{24}\right)\) |