Basic properties
| Modulus: | \(132300\) | |
| Conductor: | \(1323\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1323}(542,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 132300.tl
\(\chi_{132300}(101,\cdot)\) \(\chi_{132300}(12101,\cdot)\) \(\chi_{132300}(12701,\cdot)\) \(\chi_{132300}(18401,\cdot)\) \(\chi_{132300}(19001,\cdot)\) \(\chi_{132300}(24701,\cdot)\) \(\chi_{132300}(25301,\cdot)\) \(\chi_{132300}(31001,\cdot)\) \(\chi_{132300}(31601,\cdot)\) \(\chi_{132300}(37301,\cdot)\) \(\chi_{132300}(37901,\cdot)\) \(\chi_{132300}(43601,\cdot)\) \(\chi_{132300}(44201,\cdot)\) \(\chi_{132300}(56201,\cdot)\) \(\chi_{132300}(56801,\cdot)\) \(\chi_{132300}(62501,\cdot)\) \(\chi_{132300}(63101,\cdot)\) \(\chi_{132300}(68801,\cdot)\) \(\chi_{132300}(69401,\cdot)\) \(\chi_{132300}(75101,\cdot)\) \(\chi_{132300}(75701,\cdot)\) \(\chi_{132300}(81401,\cdot)\) \(\chi_{132300}(82001,\cdot)\) \(\chi_{132300}(87701,\cdot)\) \(\chi_{132300}(88301,\cdot)\) \(\chi_{132300}(100301,\cdot)\) \(\chi_{132300}(100901,\cdot)\) \(\chi_{132300}(106601,\cdot)\) \(\chi_{132300}(107201,\cdot)\) \(\chi_{132300}(112901,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((66151,122501,15877,54001)\) → \((1,e\left(\frac{1}{18}\right),1,e\left(\frac{1}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 132300 }(44201, a) \) | \(1\) | \(1\) | \(e\left(\frac{85}{126}\right)\) | \(e\left(\frac{29}{126}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(-1\) | \(e\left(\frac{65}{126}\right)\) | \(e\left(\frac{61}{126}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{19}{63}\right)\) | \(e\left(\frac{23}{63}\right)\) |