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.ch
\(\chi_{837}(23,\cdot)\) \(\chi_{837}(29,\cdot)\) \(\chi_{837}(77,\cdot)\) \(\chi_{837}(122,\cdot)\) \(\chi_{837}(182,\cdot)\) \(\chi_{837}(209,\cdot)\) \(\chi_{837}(263,\cdot)\) \(\chi_{837}(275,\cdot)\) \(\chi_{837}(302,\cdot)\) \(\chi_{837}(308,\cdot)\) \(\chi_{837}(356,\cdot)\) \(\chi_{837}(401,\cdot)\) \(\chi_{837}(461,\cdot)\) \(\chi_{837}(488,\cdot)\) \(\chi_{837}(542,\cdot)\) \(\chi_{837}(554,\cdot)\) \(\chi_{837}(581,\cdot)\) \(\chi_{837}(587,\cdot)\) \(\chi_{837}(635,\cdot)\) \(\chi_{837}(680,\cdot)\) \(\chi_{837}(740,\cdot)\) \(\chi_{837}(767,\cdot)\) \(\chi_{837}(821,\cdot)\) \(\chi_{837}(833,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((218,406)\) → \((e\left(\frac{7}{18}\right),e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 837 }(209, a) \) | \(1\) | \(1\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{43}{45}\right)\) |