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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 475.bg
\(\chi_{475}(4,\cdot)\) \(\chi_{475}(9,\cdot)\) \(\chi_{475}(44,\cdot)\) \(\chi_{475}(54,\cdot)\) \(\chi_{475}(104,\cdot)\) \(\chi_{475}(119,\cdot)\) \(\chi_{475}(139,\cdot)\) \(\chi_{475}(169,\cdot)\) \(\chi_{475}(194,\cdot)\) \(\chi_{475}(214,\cdot)\) \(\chi_{475}(234,\cdot)\) \(\chi_{475}(244,\cdot)\) \(\chi_{475}(264,\cdot)\) \(\chi_{475}(289,\cdot)\) \(\chi_{475}(294,\cdot)\) \(\chi_{475}(309,\cdot)\) \(\chi_{475}(329,\cdot)\) \(\chi_{475}(339,\cdot)\) \(\chi_{475}(359,\cdot)\) \(\chi_{475}(384,\cdot)\) \(\chi_{475}(389,\cdot)\) \(\chi_{475}(404,\cdot)\) \(\chi_{475}(434,\cdot)\) \(\chi_{475}(454,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((77,401)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{1}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 475 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{13}{90}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{41}{90}\right)\) |