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.bcb
\(\chi_{132300}(59,\cdot)\) \(\chi_{132300}(1319,\cdot)\) \(\chi_{132300}(1559,\cdot)\) \(\chi_{132300}(2819,\cdot)\) \(\chi_{132300}(3839,\cdot)\) \(\chi_{132300}(4079,\cdot)\) \(\chi_{132300}(5339,\cdot)\) \(\chi_{132300}(6359,\cdot)\) \(\chi_{132300}(7619,\cdot)\) \(\chi_{132300}(8879,\cdot)\) \(\chi_{132300}(9119,\cdot)\) \(\chi_{132300}(10139,\cdot)\) \(\chi_{132300}(10379,\cdot)\) \(\chi_{132300}(11639,\cdot)\) \(\chi_{132300}(12659,\cdot)\) \(\chi_{132300}(13919,\cdot)\) \(\chi_{132300}(14159,\cdot)\) \(\chi_{132300}(15179,\cdot)\) \(\chi_{132300}(15419,\cdot)\) \(\chi_{132300}(16439,\cdot)\) \(\chi_{132300}(17939,\cdot)\) \(\chi_{132300}(18959,\cdot)\) \(\chi_{132300}(20459,\cdot)\) \(\chi_{132300}(21479,\cdot)\) \(\chi_{132300}(21719,\cdot)\) \(\chi_{132300}(22739,\cdot)\) \(\chi_{132300}(22979,\cdot)\) \(\chi_{132300}(24239,\cdot)\) \(\chi_{132300}(25259,\cdot)\) \(\chi_{132300}(26519,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{315})$ |
| Fixed field: | Number field defined by a degree 630 polynomial (not computed) |
Values on generators
\((66151,122501,15877,54001)\) → \((-1,e\left(\frac{17}{18}\right),e\left(\frac{7}{10}\right),e\left(\frac{19}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 132300 }(6359, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{315}\right)\) | \(e\left(\frac{247}{315}\right)\) | \(e\left(\frac{121}{210}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{491}{630}\right)\) | \(e\left(\frac{307}{630}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{202}{315}\right)\) | \(e\left(\frac{31}{63}\right)\) |