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.ck
\(\chi_{837}(58,\cdot)\) \(\chi_{837}(85,\cdot)\) \(\chi_{837}(139,\cdot)\) \(\chi_{837}(151,\cdot)\) \(\chi_{837}(178,\cdot)\) \(\chi_{837}(184,\cdot)\) \(\chi_{837}(232,\cdot)\) \(\chi_{837}(277,\cdot)\) \(\chi_{837}(337,\cdot)\) \(\chi_{837}(364,\cdot)\) \(\chi_{837}(418,\cdot)\) \(\chi_{837}(430,\cdot)\) \(\chi_{837}(457,\cdot)\) \(\chi_{837}(463,\cdot)\) \(\chi_{837}(511,\cdot)\) \(\chi_{837}(556,\cdot)\) \(\chi_{837}(616,\cdot)\) \(\chi_{837}(643,\cdot)\) \(\chi_{837}(697,\cdot)\) \(\chi_{837}(709,\cdot)\) \(\chi_{837}(736,\cdot)\) \(\chi_{837}(742,\cdot)\) \(\chi_{837}(790,\cdot)\) \(\chi_{837}(835,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((218,406)\) → \((e\left(\frac{4}{9}\right),e\left(\frac{9}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 837 }(364, a) \) | \(-1\) | \(1\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{41}{90}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{8}{45}\right)\) |