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.bf
\(\chi_{475}(21,\cdot)\) \(\chi_{475}(41,\cdot)\) \(\chi_{475}(71,\cdot)\) \(\chi_{475}(86,\cdot)\) \(\chi_{475}(91,\cdot)\) \(\chi_{475}(116,\cdot)\) \(\chi_{475}(136,\cdot)\) \(\chi_{475}(146,\cdot)\) \(\chi_{475}(166,\cdot)\) \(\chi_{475}(181,\cdot)\) \(\chi_{475}(186,\cdot)\) \(\chi_{475}(211,\cdot)\) \(\chi_{475}(231,\cdot)\) \(\chi_{475}(241,\cdot)\) \(\chi_{475}(261,\cdot)\) \(\chi_{475}(281,\cdot)\) \(\chi_{475}(306,\cdot)\) \(\chi_{475}(336,\cdot)\) \(\chi_{475}(356,\cdot)\) \(\chi_{475}(371,\cdot)\) \(\chi_{475}(421,\cdot)\) \(\chi_{475}(431,\cdot)\) \(\chi_{475}(466,\cdot)\) \(\chi_{475}(471,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((77,401)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{1}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 475 }(211, a) \) | \(-1\) | \(1\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{43}{90}\right)\) |