Basic properties
| Modulus: | \(837\) | |
| Conductor: | \(837\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(45\) | 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.cb
\(\chi_{837}(76,\cdot)\) \(\chi_{837}(112,\cdot)\) \(\chi_{837}(121,\cdot)\) \(\chi_{837}(133,\cdot)\) \(\chi_{837}(142,\cdot)\) \(\chi_{837}(193,\cdot)\) \(\chi_{837}(196,\cdot)\) \(\chi_{837}(268,\cdot)\) \(\chi_{837}(355,\cdot)\) \(\chi_{837}(391,\cdot)\) \(\chi_{837}(400,\cdot)\) \(\chi_{837}(412,\cdot)\) \(\chi_{837}(421,\cdot)\) \(\chi_{837}(472,\cdot)\) \(\chi_{837}(475,\cdot)\) \(\chi_{837}(547,\cdot)\) \(\chi_{837}(634,\cdot)\) \(\chi_{837}(670,\cdot)\) \(\chi_{837}(679,\cdot)\) \(\chi_{837}(691,\cdot)\) \(\chi_{837}(700,\cdot)\) \(\chi_{837}(751,\cdot)\) \(\chi_{837}(754,\cdot)\) \(\chi_{837}(826,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((218,406)\) → \((e\left(\frac{5}{9}\right),e\left(\frac{7}{15}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 837 }(754, a) \) | \(1\) | \(1\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{1}{45}\right)\) |