Basic properties
| Modulus: | \(1455\) | |
| Conductor: | \(485\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(96\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{485}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1455.di
\(\chi_{1455}(7,\cdot)\) \(\chi_{1455}(13,\cdot)\) \(\chi_{1455}(37,\cdot)\) \(\chi_{1455}(82,\cdot)\) \(\chi_{1455}(112,\cdot)\) \(\chi_{1455}(118,\cdot)\) \(\chi_{1455}(157,\cdot)\) \(\chi_{1455}(187,\cdot)\) \(\chi_{1455}(208,\cdot)\) \(\chi_{1455}(223,\cdot)\) \(\chi_{1455}(232,\cdot)\) \(\chi_{1455}(268,\cdot)\) \(\chi_{1455}(427,\cdot)\) \(\chi_{1455}(508,\cdot)\) \(\chi_{1455}(553,\cdot)\) \(\chi_{1455}(568,\cdot)\) \(\chi_{1455}(592,\cdot)\) \(\chi_{1455}(622,\cdot)\) \(\chi_{1455}(658,\cdot)\) \(\chi_{1455}(763,\cdot)\) \(\chi_{1455}(793,\cdot)\) \(\chi_{1455}(802,\cdot)\) \(\chi_{1455}(847,\cdot)\) \(\chi_{1455}(868,\cdot)\) \(\chi_{1455}(1027,\cdot)\) \(\chi_{1455}(1057,\cdot)\) \(\chi_{1455}(1108,\cdot)\) \(\chi_{1455}(1123,\cdot)\) \(\chi_{1455}(1222,\cdot)\) \(\chi_{1455}(1363,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{96})$ |
| Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((971,292,781)\) → \((1,i,e\left(\frac{31}{96}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 1455 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{48}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{25}{96}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{37}{48}\right)\) | \(e\left(\frac{79}{96}\right)\) | \(e\left(\frac{47}{96}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{95}{96}\right)\) | \(e\left(\frac{21}{32}\right)\) |