Basic properties
| Modulus: | \(114075\) | |
| Conductor: | \(8775\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{8775}(23,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 114075.pr
\(\chi_{114075}(23,\cdot)\) \(\chi_{114075}(992,\cdot)\) \(\chi_{114075}(2513,\cdot)\) \(\chi_{114075}(7628,\cdot)\) \(\chi_{114075}(8597,\cdot)\) \(\chi_{114075}(13712,\cdot)\) \(\chi_{114075}(15233,\cdot)\) \(\chi_{114075}(16202,\cdot)\) \(\chi_{114075}(17723,\cdot)\) \(\chi_{114075}(21317,\cdot)\) \(\chi_{114075}(22838,\cdot)\) \(\chi_{114075}(25328,\cdot)\) \(\chi_{114075}(28922,\cdot)\) \(\chi_{114075}(31412,\cdot)\) \(\chi_{114075}(32933,\cdot)\) \(\chi_{114075}(36527,\cdot)\) \(\chi_{114075}(38048,\cdot)\) \(\chi_{114075}(39017,\cdot)\) \(\chi_{114075}(40538,\cdot)\) \(\chi_{114075}(45653,\cdot)\) \(\chi_{114075}(46622,\cdot)\) \(\chi_{114075}(51737,\cdot)\) \(\chi_{114075}(53258,\cdot)\) \(\chi_{114075}(54227,\cdot)\) \(\chi_{114075}(55748,\cdot)\) \(\chi_{114075}(59342,\cdot)\) \(\chi_{114075}(60863,\cdot)\) \(\chi_{114075}(63353,\cdot)\) \(\chi_{114075}(66947,\cdot)\) \(\chi_{114075}(69437,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((105626,9127,113401)\) → \((e\left(\frac{11}{18}\right),e\left(\frac{11}{20}\right),e\left(\frac{5}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 114075 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{179}{180}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{103}{180}\right)\) |