Basic properties
| Modulus: | \(132300\) | |
| Conductor: | \(132300\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(630\) | 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 132300.bcj
\(\chi_{132300}(131,\cdot)\) \(\chi_{132300}(731,\cdot)\) \(\chi_{132300}(3911,\cdot)\) \(\chi_{132300}(4511,\cdot)\) \(\chi_{132300}(5171,\cdot)\) \(\chi_{132300}(5771,\cdot)\) \(\chi_{132300}(6431,\cdot)\) \(\chi_{132300}(7031,\cdot)\) \(\chi_{132300}(7691,\cdot)\) \(\chi_{132300}(8291,\cdot)\) \(\chi_{132300}(11471,\cdot)\) \(\chi_{132300}(12071,\cdot)\) \(\chi_{132300}(12731,\cdot)\) \(\chi_{132300}(13331,\cdot)\) \(\chi_{132300}(13991,\cdot)\) \(\chi_{132300}(14591,\cdot)\) \(\chi_{132300}(16511,\cdot)\) \(\chi_{132300}(17111,\cdot)\) \(\chi_{132300}(17771,\cdot)\) \(\chi_{132300}(18371,\cdot)\) \(\chi_{132300}(20291,\cdot)\) \(\chi_{132300}(20891,\cdot)\) \(\chi_{132300}(22811,\cdot)\) \(\chi_{132300}(23411,\cdot)\) \(\chi_{132300}(24071,\cdot)\) \(\chi_{132300}(24671,\cdot)\) \(\chi_{132300}(25331,\cdot)\) \(\chi_{132300}(25931,\cdot)\) \(\chi_{132300}(26591,\cdot)\) \(\chi_{132300}(27191,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{315})$ |
| Fixed field: | Number field defined by a degree 630 polynomial (not computed) |
Values on generators
\((66151,122501,15877,54001)\) → \((-1,e\left(\frac{11}{18}\right),e\left(\frac{2}{5}\right),e\left(\frac{41}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 132300 }(131, a) \) | \(-1\) | \(1\) | \(e\left(\frac{281}{315}\right)\) | \(e\left(\frac{443}{630}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{226}{315}\right)\) | \(e\left(\frac{619}{630}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{53}{105}\right)\) | \(e\left(\frac{199}{315}\right)\) | \(e\left(\frac{101}{126}\right)\) |