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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 837.ce
\(\chi_{837}(65,\cdot)\) \(\chi_{837}(74,\cdot)\) \(\chi_{837}(104,\cdot)\) \(\chi_{837}(110,\cdot)\) \(\chi_{837}(176,\cdot)\) \(\chi_{837}(230,\cdot)\) \(\chi_{837}(239,\cdot)\) \(\chi_{837}(272,\cdot)\) \(\chi_{837}(344,\cdot)\) \(\chi_{837}(353,\cdot)\) \(\chi_{837}(383,\cdot)\) \(\chi_{837}(389,\cdot)\) \(\chi_{837}(455,\cdot)\) \(\chi_{837}(509,\cdot)\) \(\chi_{837}(518,\cdot)\) \(\chi_{837}(551,\cdot)\) \(\chi_{837}(623,\cdot)\) \(\chi_{837}(632,\cdot)\) \(\chi_{837}(662,\cdot)\) \(\chi_{837}(668,\cdot)\) \(\chi_{837}(734,\cdot)\) \(\chi_{837}(788,\cdot)\) \(\chi_{837}(797,\cdot)\) \(\chi_{837}(830,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((218,406)\) → \((e\left(\frac{1}{18}\right),e\left(\frac{7}{30}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 837 }(110, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{90}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{7}{90}\right)\) | \(e\left(\frac{28}{45}\right)\) |