Basic properties
| Modulus: | \(950\) | |
| Conductor: | \(475\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(45\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{475}(61,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 950.bc
\(\chi_{950}(61,\cdot)\) \(\chi_{950}(81,\cdot)\) \(\chi_{950}(111,\cdot)\) \(\chi_{950}(131,\cdot)\) \(\chi_{950}(161,\cdot)\) \(\chi_{950}(271,\cdot)\) \(\chi_{950}(291,\cdot)\) \(\chi_{950}(321,\cdot)\) \(\chi_{950}(441,\cdot)\) \(\chi_{950}(461,\cdot)\) \(\chi_{950}(481,\cdot)\) \(\chi_{950}(491,\cdot)\) \(\chi_{950}(511,\cdot)\) \(\chi_{950}(541,\cdot)\) \(\chi_{950}(631,\cdot)\) \(\chi_{950}(671,\cdot)\) \(\chi_{950}(681,\cdot)\) \(\chi_{950}(731,\cdot)\) \(\chi_{950}(821,\cdot)\) \(\chi_{950}(841,\cdot)\) \(\chi_{950}(861,\cdot)\) \(\chi_{950}(871,\cdot)\) \(\chi_{950}(891,\cdot)\) \(\chi_{950}(921,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((77,401)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{1}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 950 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{22}{45}\right)\) |