Basic properties
| Modulus: | \(475\) | |
| Conductor: | \(475\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(45\) | 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.bc
\(\chi_{475}(6,\cdot)\) \(\chi_{475}(16,\cdot)\) \(\chi_{475}(36,\cdot)\) \(\chi_{475}(61,\cdot)\) \(\chi_{475}(66,\cdot)\) \(\chi_{475}(81,\cdot)\) \(\chi_{475}(111,\cdot)\) \(\chi_{475}(131,\cdot)\) \(\chi_{475}(156,\cdot)\) \(\chi_{475}(161,\cdot)\) \(\chi_{475}(196,\cdot)\) \(\chi_{475}(206,\cdot)\) \(\chi_{475}(256,\cdot)\) \(\chi_{475}(271,\cdot)\) \(\chi_{475}(291,\cdot)\) \(\chi_{475}(321,\cdot)\) \(\chi_{475}(346,\cdot)\) \(\chi_{475}(366,\cdot)\) \(\chi_{475}(386,\cdot)\) \(\chi_{475}(396,\cdot)\) \(\chi_{475}(416,\cdot)\) \(\chi_{475}(441,\cdot)\) \(\chi_{475}(446,\cdot)\) \(\chi_{475}(461,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((77,401)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{4}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 475 }(446, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{28}{45}\right)\) |