Basic properties
Modulus: | \(9025\) | |
Conductor: | \(475\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{475}(127,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9025.bu
\(\chi_{9025}(127,\cdot)\) \(\chi_{9025}(262,\cdot)\) \(\chi_{9025}(333,\cdot)\) \(\chi_{9025}(477,\cdot)\) \(\chi_{9025}(488,\cdot)\) \(\chi_{9025}(623,\cdot)\) \(\chi_{9025}(838,\cdot)\) \(\chi_{9025}(1777,\cdot)\) \(\chi_{9025}(2067,\cdot)\) \(\chi_{9025}(2112,\cdot)\) \(\chi_{9025}(2138,\cdot)\) \(\chi_{9025}(2428,\cdot)\) \(\chi_{9025}(2473,\cdot)\) \(\chi_{9025}(3187,\cdot)\) \(\chi_{9025}(3548,\cdot)\) \(\chi_{9025}(3737,\cdot)\) \(\chi_{9025}(3872,\cdot)\) \(\chi_{9025}(3917,\cdot)\) \(\chi_{9025}(4087,\cdot)\) \(\chi_{9025}(4098,\cdot)\) \(\chi_{9025}(4233,\cdot)\) \(\chi_{9025}(4278,\cdot)\) \(\chi_{9025}(4448,\cdot)\) \(\chi_{9025}(4992,\cdot)\) \(\chi_{9025}(5353,\cdot)\) \(\chi_{9025}(5387,\cdot)\) \(\chi_{9025}(5542,\cdot)\) \(\chi_{9025}(5677,\cdot)\) \(\chi_{9025}(5722,\cdot)\) \(\chi_{9025}(5748,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{180})$ |
Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((5777,3251)\) → \((e\left(\frac{1}{20}\right),e\left(\frac{5}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 9025 }(127, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{180}\right)\) | \(e\left(\frac{173}{180}\right)\) | \(e\left(\frac{59}{90}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{83}{90}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{61}{180}\right)\) |