Basic properties
| Modulus: | \(475\) | |
| Conductor: | \(475\) | 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 475.bh
\(\chi_{475}(14,\cdot)\) \(\chi_{475}(29,\cdot)\) \(\chi_{475}(34,\cdot)\) \(\chi_{475}(59,\cdot)\) \(\chi_{475}(79,\cdot)\) \(\chi_{475}(89,\cdot)\) \(\chi_{475}(109,\cdot)\) \(\chi_{475}(129,\cdot)\) \(\chi_{475}(154,\cdot)\) \(\chi_{475}(184,\cdot)\) \(\chi_{475}(204,\cdot)\) \(\chi_{475}(219,\cdot)\) \(\chi_{475}(269,\cdot)\) \(\chi_{475}(279,\cdot)\) \(\chi_{475}(314,\cdot)\) \(\chi_{475}(319,\cdot)\) \(\chi_{475}(344,\cdot)\) \(\chi_{475}(364,\cdot)\) \(\chi_{475}(394,\cdot)\) \(\chi_{475}(409,\cdot)\) \(\chi_{475}(414,\cdot)\) \(\chi_{475}(439,\cdot)\) \(\chi_{475}(459,\cdot)\) \(\chi_{475}(469,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((77,401)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{13}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 475 }(269, a) \) | \(-1\) | \(1\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{32}{45}\right)\) |