Basic properties
| Modulus: | \(405\) | |
| Conductor: | \(405\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(108\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 405.w
\(\chi_{405}(7,\cdot)\) \(\chi_{405}(13,\cdot)\) \(\chi_{405}(22,\cdot)\) \(\chi_{405}(43,\cdot)\) \(\chi_{405}(52,\cdot)\) \(\chi_{405}(58,\cdot)\) \(\chi_{405}(67,\cdot)\) \(\chi_{405}(88,\cdot)\) \(\chi_{405}(97,\cdot)\) \(\chi_{405}(103,\cdot)\) \(\chi_{405}(112,\cdot)\) \(\chi_{405}(133,\cdot)\) \(\chi_{405}(142,\cdot)\) \(\chi_{405}(148,\cdot)\) \(\chi_{405}(157,\cdot)\) \(\chi_{405}(178,\cdot)\) \(\chi_{405}(187,\cdot)\) \(\chi_{405}(193,\cdot)\) \(\chi_{405}(202,\cdot)\) \(\chi_{405}(223,\cdot)\) \(\chi_{405}(232,\cdot)\) \(\chi_{405}(238,\cdot)\) \(\chi_{405}(247,\cdot)\) \(\chi_{405}(268,\cdot)\) \(\chi_{405}(277,\cdot)\) \(\chi_{405}(283,\cdot)\) \(\chi_{405}(292,\cdot)\) \(\chi_{405}(313,\cdot)\) \(\chi_{405}(322,\cdot)\) \(\chi_{405}(328,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((326,82)\) → \((e\left(\frac{4}{27}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 405 }(13, a) \) | \(-1\) | \(1\) | \(e\left(\frac{97}{108}\right)\) | \(e\left(\frac{43}{54}\right)\) | \(e\left(\frac{13}{108}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{25}{27}\right)\) | \(e\left(\frac{47}{108}\right)\) | \(e\left(\frac{1}{54}\right)\) | \(e\left(\frac{16}{27}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{11}{18}\right)\) |