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.cc
\(\chi_{837}(4,\cdot)\) \(\chi_{837}(16,\cdot)\) \(\chi_{837}(70,\cdot)\) \(\chi_{837}(97,\cdot)\) \(\chi_{837}(157,\cdot)\) \(\chi_{837}(202,\cdot)\) \(\chi_{837}(250,\cdot)\) \(\chi_{837}(256,\cdot)\) \(\chi_{837}(283,\cdot)\) \(\chi_{837}(295,\cdot)\) \(\chi_{837}(349,\cdot)\) \(\chi_{837}(376,\cdot)\) \(\chi_{837}(436,\cdot)\) \(\chi_{837}(481,\cdot)\) \(\chi_{837}(529,\cdot)\) \(\chi_{837}(535,\cdot)\) \(\chi_{837}(562,\cdot)\) \(\chi_{837}(574,\cdot)\) \(\chi_{837}(628,\cdot)\) \(\chi_{837}(655,\cdot)\) \(\chi_{837}(715,\cdot)\) \(\chi_{837}(760,\cdot)\) \(\chi_{837}(808,\cdot)\) \(\chi_{837}(814,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((218,406)\) → \((e\left(\frac{1}{9}\right),e\left(\frac{1}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 837 }(760, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{29}{45}\right)\) |