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.ca
\(\chi_{837}(7,\cdot)\) \(\chi_{837}(40,\cdot)\) \(\chi_{837}(49,\cdot)\) \(\chi_{837}(103,\cdot)\) \(\chi_{837}(169,\cdot)\) \(\chi_{837}(175,\cdot)\) \(\chi_{837}(205,\cdot)\) \(\chi_{837}(214,\cdot)\) \(\chi_{837}(286,\cdot)\) \(\chi_{837}(319,\cdot)\) \(\chi_{837}(328,\cdot)\) \(\chi_{837}(382,\cdot)\) \(\chi_{837}(448,\cdot)\) \(\chi_{837}(454,\cdot)\) \(\chi_{837}(484,\cdot)\) \(\chi_{837}(493,\cdot)\) \(\chi_{837}(565,\cdot)\) \(\chi_{837}(598,\cdot)\) \(\chi_{837}(607,\cdot)\) \(\chi_{837}(661,\cdot)\) \(\chi_{837}(727,\cdot)\) \(\chi_{837}(733,\cdot)\) \(\chi_{837}(763,\cdot)\) \(\chi_{837}(772,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((218,406)\) → \((e\left(\frac{7}{9}\right),e\left(\frac{4}{15}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 837 }(454, a) \) | \(1\) | \(1\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{32}{45}\right)\) |