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.ci
\(\chi_{837}(14,\cdot)\) \(\chi_{837}(20,\cdot)\) \(\chi_{837}(50,\cdot)\) \(\chi_{837}(59,\cdot)\) \(\chi_{837}(131,\cdot)\) \(\chi_{837}(164,\cdot)\) \(\chi_{837}(173,\cdot)\) \(\chi_{837}(227,\cdot)\) \(\chi_{837}(293,\cdot)\) \(\chi_{837}(299,\cdot)\) \(\chi_{837}(329,\cdot)\) \(\chi_{837}(338,\cdot)\) \(\chi_{837}(410,\cdot)\) \(\chi_{837}(443,\cdot)\) \(\chi_{837}(452,\cdot)\) \(\chi_{837}(506,\cdot)\) \(\chi_{837}(572,\cdot)\) \(\chi_{837}(578,\cdot)\) \(\chi_{837}(608,\cdot)\) \(\chi_{837}(617,\cdot)\) \(\chi_{837}(689,\cdot)\) \(\chi_{837}(722,\cdot)\) \(\chi_{837}(731,\cdot)\) \(\chi_{837}(785,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((218,406)\) → \((e\left(\frac{11}{18}\right),e\left(\frac{8}{15}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 837 }(617, a) \) | \(-1\) | \(1\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{11}{90}\right)\) | \(e\left(\frac{29}{45}\right)\) |