Basic properties
| Modulus: | \(675\) | |
| Conductor: | \(675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | 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 675.bj
\(\chi_{675}(13,\cdot)\) \(\chi_{675}(22,\cdot)\) \(\chi_{675}(52,\cdot)\) \(\chi_{675}(58,\cdot)\) \(\chi_{675}(67,\cdot)\) \(\chi_{675}(88,\cdot)\) \(\chi_{675}(97,\cdot)\) \(\chi_{675}(103,\cdot)\) \(\chi_{675}(112,\cdot)\) \(\chi_{675}(133,\cdot)\) \(\chi_{675}(142,\cdot)\) \(\chi_{675}(148,\cdot)\) \(\chi_{675}(178,\cdot)\) \(\chi_{675}(187,\cdot)\) \(\chi_{675}(202,\cdot)\) \(\chi_{675}(223,\cdot)\) \(\chi_{675}(238,\cdot)\) \(\chi_{675}(247,\cdot)\) \(\chi_{675}(277,\cdot)\) \(\chi_{675}(283,\cdot)\) \(\chi_{675}(292,\cdot)\) \(\chi_{675}(313,\cdot)\) \(\chi_{675}(322,\cdot)\) \(\chi_{675}(328,\cdot)\) \(\chi_{675}(337,\cdot)\) \(\chi_{675}(358,\cdot)\) \(\chi_{675}(367,\cdot)\) \(\chi_{675}(373,\cdot)\) \(\chi_{675}(403,\cdot)\) \(\chi_{675}(412,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((326,352)\) → \((e\left(\frac{7}{9}\right),e\left(\frac{17}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 675 }(22, a) \) | \(-1\) | \(1\) | \(e\left(\frac{113}{180}\right)\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{67}{180}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{19}{30}\right)\) |