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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 675.bi
\(\chi_{675}(2,\cdot)\) \(\chi_{675}(23,\cdot)\) \(\chi_{675}(38,\cdot)\) \(\chi_{675}(47,\cdot)\) \(\chi_{675}(77,\cdot)\) \(\chi_{675}(83,\cdot)\) \(\chi_{675}(92,\cdot)\) \(\chi_{675}(113,\cdot)\) \(\chi_{675}(122,\cdot)\) \(\chi_{675}(128,\cdot)\) \(\chi_{675}(137,\cdot)\) \(\chi_{675}(158,\cdot)\) \(\chi_{675}(167,\cdot)\) \(\chi_{675}(173,\cdot)\) \(\chi_{675}(203,\cdot)\) \(\chi_{675}(212,\cdot)\) \(\chi_{675}(227,\cdot)\) \(\chi_{675}(248,\cdot)\) \(\chi_{675}(263,\cdot)\) \(\chi_{675}(272,\cdot)\) \(\chi_{675}(302,\cdot)\) \(\chi_{675}(308,\cdot)\) \(\chi_{675}(317,\cdot)\) \(\chi_{675}(338,\cdot)\) \(\chi_{675}(347,\cdot)\) \(\chi_{675}(353,\cdot)\) \(\chi_{675}(362,\cdot)\) \(\chi_{675}(383,\cdot)\) \(\chi_{675}(392,\cdot)\) \(\chi_{675}(398,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((326,352)\) → \((e\left(\frac{11}{18}\right),e\left(\frac{3}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 675 }(158, a) \) | \(1\) | \(1\) | \(e\left(\frac{137}{180}\right)\) | \(e\left(\frac{47}{90}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{133}{180}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{1}{30}\right)\) |