Basic properties
| Modulus: | \(837\) | |
| Conductor: | \(837\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 837.cl
\(\chi_{837}(52,\cdot)\) \(\chi_{837}(106,\cdot)\) \(\chi_{837}(115,\cdot)\) \(\chi_{837}(148,\cdot)\) \(\chi_{837}(220,\cdot)\) \(\chi_{837}(229,\cdot)\) \(\chi_{837}(259,\cdot)\) \(\chi_{837}(265,\cdot)\) \(\chi_{837}(331,\cdot)\) \(\chi_{837}(385,\cdot)\) \(\chi_{837}(394,\cdot)\) \(\chi_{837}(427,\cdot)\) \(\chi_{837}(499,\cdot)\) \(\chi_{837}(508,\cdot)\) \(\chi_{837}(538,\cdot)\) \(\chi_{837}(544,\cdot)\) \(\chi_{837}(610,\cdot)\) \(\chi_{837}(664,\cdot)\) \(\chi_{837}(673,\cdot)\) \(\chi_{837}(706,\cdot)\) \(\chi_{837}(778,\cdot)\) \(\chi_{837}(787,\cdot)\) \(\chi_{837}(817,\cdot)\) \(\chi_{837}(823,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((218,406)\) → \((e\left(\frac{5}{9}\right),e\left(\frac{17}{30}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 837 }(673, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{28}{45}\right)\) |