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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 475.bj
\(\chi_{475}(17,\cdot)\) \(\chi_{475}(23,\cdot)\) \(\chi_{475}(28,\cdot)\) \(\chi_{475}(42,\cdot)\) \(\chi_{475}(47,\cdot)\) \(\chi_{475}(62,\cdot)\) \(\chi_{475}(63,\cdot)\) \(\chi_{475}(73,\cdot)\) \(\chi_{475}(92,\cdot)\) \(\chi_{475}(112,\cdot)\) \(\chi_{475}(123,\cdot)\) \(\chi_{475}(137,\cdot)\) \(\chi_{475}(138,\cdot)\) \(\chi_{475}(142,\cdot)\) \(\chi_{475}(158,\cdot)\) \(\chi_{475}(177,\cdot)\) \(\chi_{475}(187,\cdot)\) \(\chi_{475}(188,\cdot)\) \(\chi_{475}(213,\cdot)\) \(\chi_{475}(233,\cdot)\) \(\chi_{475}(237,\cdot)\) \(\chi_{475}(252,\cdot)\) \(\chi_{475}(253,\cdot)\) \(\chi_{475}(263,\cdot)\) \(\chi_{475}(272,\cdot)\) \(\chi_{475}(283,\cdot)\) \(\chi_{475}(302,\cdot)\) \(\chi_{475}(308,\cdot)\) \(\chi_{475}(313,\cdot)\) \(\chi_{475}(327,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((77,401)\) → \((e\left(\frac{17}{20}\right),e\left(\frac{8}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 475 }(347, a) \) | \(-1\) | \(1\) | \(e\left(\frac{133}{180}\right)\) | \(e\left(\frac{91}{180}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{107}{180}\right)\) |