Basic properties
Modulus: | \(8100\) | |
Conductor: | \(675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(45\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{675}(331,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8100.cf
\(\chi_{8100}(181,\cdot)\) \(\chi_{8100}(361,\cdot)\) \(\chi_{8100}(721,\cdot)\) \(\chi_{8100}(1261,\cdot)\) \(\chi_{8100}(1441,\cdot)\) \(\chi_{8100}(1981,\cdot)\) \(\chi_{8100}(2341,\cdot)\) \(\chi_{8100}(2521,\cdot)\) \(\chi_{8100}(2881,\cdot)\) \(\chi_{8100}(3061,\cdot)\) \(\chi_{8100}(3421,\cdot)\) \(\chi_{8100}(3961,\cdot)\) \(\chi_{8100}(4141,\cdot)\) \(\chi_{8100}(4681,\cdot)\) \(\chi_{8100}(5041,\cdot)\) \(\chi_{8100}(5221,\cdot)\) \(\chi_{8100}(5581,\cdot)\) \(\chi_{8100}(5761,\cdot)\) \(\chi_{8100}(6121,\cdot)\) \(\chi_{8100}(6661,\cdot)\) \(\chi_{8100}(6841,\cdot)\) \(\chi_{8100}(7381,\cdot)\) \(\chi_{8100}(7741,\cdot)\) \(\chi_{8100}(7921,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((4051,6401,7777)\) → \((1,e\left(\frac{8}{9}\right),e\left(\frac{2}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 8100 }(181, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{32}{45}\right)\) |