Basic properties
| Modulus: | \(2535\) | |
| Conductor: | \(845\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{845}(549,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2535.ck
\(\chi_{2535}(94,\cdot)\) \(\chi_{2535}(139,\cdot)\) \(\chi_{2535}(289,\cdot)\) \(\chi_{2535}(334,\cdot)\) \(\chi_{2535}(679,\cdot)\) \(\chi_{2535}(724,\cdot)\) \(\chi_{2535}(874,\cdot)\) \(\chi_{2535}(919,\cdot)\) \(\chi_{2535}(1069,\cdot)\) \(\chi_{2535}(1114,\cdot)\) \(\chi_{2535}(1264,\cdot)\) \(\chi_{2535}(1309,\cdot)\) \(\chi_{2535}(1459,\cdot)\) \(\chi_{2535}(1504,\cdot)\) \(\chi_{2535}(1654,\cdot)\) \(\chi_{2535}(1699,\cdot)\) \(\chi_{2535}(1849,\cdot)\) \(\chi_{2535}(1894,\cdot)\) \(\chi_{2535}(2044,\cdot)\) \(\chi_{2535}(2089,\cdot)\) \(\chi_{2535}(2239,\cdot)\) \(\chi_{2535}(2284,\cdot)\) \(\chi_{2535}(2434,\cdot)\) \(\chi_{2535}(2479,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1691,1522,1861)\) → \((1,-1,e\left(\frac{19}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 2535 }(2239, a) \) | \(1\) | \(1\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) |