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.cj
\(\chi_{837}(13,\cdot)\) \(\chi_{837}(22,\cdot)\) \(\chi_{837}(34,\cdot)\) \(\chi_{837}(43,\cdot)\) \(\chi_{837}(79,\cdot)\) \(\chi_{837}(166,\cdot)\) \(\chi_{837}(238,\cdot)\) \(\chi_{837}(241,\cdot)\) \(\chi_{837}(292,\cdot)\) \(\chi_{837}(301,\cdot)\) \(\chi_{837}(313,\cdot)\) \(\chi_{837}(322,\cdot)\) \(\chi_{837}(358,\cdot)\) \(\chi_{837}(445,\cdot)\) \(\chi_{837}(517,\cdot)\) \(\chi_{837}(520,\cdot)\) \(\chi_{837}(571,\cdot)\) \(\chi_{837}(580,\cdot)\) \(\chi_{837}(592,\cdot)\) \(\chi_{837}(601,\cdot)\) \(\chi_{837}(637,\cdot)\) \(\chi_{837}(724,\cdot)\) \(\chi_{837}(796,\cdot)\) \(\chi_{837}(799,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((218,406)\) → \((e\left(\frac{1}{9}\right),e\left(\frac{17}{30}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 837 }(301, a) \) | \(-1\) | \(1\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{11}{90}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{38}{45}\right)\) |