Basic properties
| Modulus: | \(9408\) | |
| Conductor: | \(1568\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(168\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1568}(1083,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9408.fs
\(\chi_{9408}(103,\cdot)\) \(\chi_{9408}(199,\cdot)\) \(\chi_{9408}(439,\cdot)\) \(\chi_{9408}(535,\cdot)\) \(\chi_{9408}(775,\cdot)\) \(\chi_{9408}(871,\cdot)\) \(\chi_{9408}(1111,\cdot)\) \(\chi_{9408}(1447,\cdot)\) \(\chi_{9408}(1543,\cdot)\) \(\chi_{9408}(1879,\cdot)\) \(\chi_{9408}(2119,\cdot)\) \(\chi_{9408}(2215,\cdot)\) \(\chi_{9408}(2455,\cdot)\) \(\chi_{9408}(2551,\cdot)\) \(\chi_{9408}(2791,\cdot)\) \(\chi_{9408}(2887,\cdot)\) \(\chi_{9408}(3127,\cdot)\) \(\chi_{9408}(3223,\cdot)\) \(\chi_{9408}(3463,\cdot)\) \(\chi_{9408}(3799,\cdot)\) \(\chi_{9408}(3895,\cdot)\) \(\chi_{9408}(4231,\cdot)\) \(\chi_{9408}(4471,\cdot)\) \(\chi_{9408}(4567,\cdot)\) \(\chi_{9408}(4807,\cdot)\) \(\chi_{9408}(4903,\cdot)\) \(\chi_{9408}(5143,\cdot)\) \(\chi_{9408}(5239,\cdot)\) \(\chi_{9408}(5479,\cdot)\) \(\chi_{9408}(5575,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{168})$ |
| Fixed field: | Number field defined by a degree 168 polynomial (not computed) |
Values on generators
\((1471,6469,3137,4609)\) → \((-1,e\left(\frac{1}{8}\right),1,e\left(\frac{29}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 9408 }(103, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{168}\right)\) | \(e\left(\frac{125}{168}\right)\) | \(e\left(\frac{37}{56}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{45}{56}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{37}{168}\right)\) |