Basic properties
| Modulus: | \(2535\) | |
| Conductor: | \(845\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{845}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2535.cr
\(\chi_{2535}(7,\cdot)\) \(\chi_{2535}(28,\cdot)\) \(\chi_{2535}(37,\cdot)\) \(\chi_{2535}(58,\cdot)\) \(\chi_{2535}(202,\cdot)\) \(\chi_{2535}(223,\cdot)\) \(\chi_{2535}(232,\cdot)\) \(\chi_{2535}(253,\cdot)\) \(\chi_{2535}(397,\cdot)\) \(\chi_{2535}(448,\cdot)\) \(\chi_{2535}(592,\cdot)\) \(\chi_{2535}(613,\cdot)\) \(\chi_{2535}(622,\cdot)\) \(\chi_{2535}(643,\cdot)\) \(\chi_{2535}(787,\cdot)\) \(\chi_{2535}(808,\cdot)\) \(\chi_{2535}(817,\cdot)\) \(\chi_{2535}(838,\cdot)\) \(\chi_{2535}(982,\cdot)\) \(\chi_{2535}(1003,\cdot)\) \(\chi_{2535}(1012,\cdot)\) \(\chi_{2535}(1177,\cdot)\) \(\chi_{2535}(1198,\cdot)\) \(\chi_{2535}(1207,\cdot)\) \(\chi_{2535}(1228,\cdot)\) \(\chi_{2535}(1372,\cdot)\) \(\chi_{2535}(1393,\cdot)\) \(\chi_{2535}(1402,\cdot)\) \(\chi_{2535}(1423,\cdot)\) \(\chi_{2535}(1567,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1691,1522,1861)\) → \((1,i,e\left(\frac{107}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 2535 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{101}{156}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{61}{156}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) |