Basic properties
| Modulus: | \(475\) | |
| Conductor: | \(475\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | 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 475.bi
\(\chi_{475}(2,\cdot)\) \(\chi_{475}(3,\cdot)\) \(\chi_{475}(13,\cdot)\) \(\chi_{475}(22,\cdot)\) \(\chi_{475}(33,\cdot)\) \(\chi_{475}(48,\cdot)\) \(\chi_{475}(52,\cdot)\) \(\chi_{475}(53,\cdot)\) \(\chi_{475}(67,\cdot)\) \(\chi_{475}(72,\cdot)\) \(\chi_{475}(78,\cdot)\) \(\chi_{475}(97,\cdot)\) \(\chi_{475}(98,\cdot)\) \(\chi_{475}(108,\cdot)\) \(\chi_{475}(117,\cdot)\) \(\chi_{475}(127,\cdot)\) \(\chi_{475}(128,\cdot)\) \(\chi_{475}(147,\cdot)\) \(\chi_{475}(148,\cdot)\) \(\chi_{475}(162,\cdot)\) \(\chi_{475}(167,\cdot)\) \(\chi_{475}(173,\cdot)\) \(\chi_{475}(192,\cdot)\) \(\chi_{475}(203,\cdot)\) \(\chi_{475}(212,\cdot)\) \(\chi_{475}(222,\cdot)\) \(\chi_{475}(223,\cdot)\) \(\chi_{475}(238,\cdot)\) \(\chi_{475}(242,\cdot)\) \(\chi_{475}(262,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((77,401)\) → \((e\left(\frac{11}{20}\right),e\left(\frac{11}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 475 }(148, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{180}\right)\) | \(e\left(\frac{143}{180}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{91}{180}\right)\) |