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
\((218,406)\) → \((e\left(\frac{11}{18}\right),e\left(\frac{1}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 837 }(833, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{2}{45}\right)\) |