Basic properties
| Modulus: | \(675\) | |
| Conductor: | \(675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | 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.bg
\(\chi_{675}(4,\cdot)\) \(\chi_{675}(34,\cdot)\) \(\chi_{675}(79,\cdot)\) \(\chi_{675}(94,\cdot)\) \(\chi_{675}(139,\cdot)\) \(\chi_{675}(169,\cdot)\) \(\chi_{675}(184,\cdot)\) \(\chi_{675}(214,\cdot)\) \(\chi_{675}(229,\cdot)\) \(\chi_{675}(259,\cdot)\) \(\chi_{675}(304,\cdot)\) \(\chi_{675}(319,\cdot)\) \(\chi_{675}(364,\cdot)\) \(\chi_{675}(394,\cdot)\) \(\chi_{675}(409,\cdot)\) \(\chi_{675}(439,\cdot)\) \(\chi_{675}(454,\cdot)\) \(\chi_{675}(484,\cdot)\) \(\chi_{675}(529,\cdot)\) \(\chi_{675}(544,\cdot)\) \(\chi_{675}(589,\cdot)\) \(\chi_{675}(619,\cdot)\) \(\chi_{675}(634,\cdot)\) \(\chi_{675}(664,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((326,352)\) → \((e\left(\frac{8}{9}\right),e\left(\frac{1}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 675 }(304, a) \) | \(1\) | \(1\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) |