Basic properties
| Modulus: | \(6422\) | |
| Conductor: | \(3211\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3211}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6422.cw
\(\chi_{6422}(31,\cdot)\) \(\chi_{6422}(255,\cdot)\) \(\chi_{6422}(369,\cdot)\) \(\chi_{6422}(411,\cdot)\) \(\chi_{6422}(525,\cdot)\) \(\chi_{6422}(749,\cdot)\) \(\chi_{6422}(863,\cdot)\) \(\chi_{6422}(905,\cdot)\) \(\chi_{6422}(1019,\cdot)\) \(\chi_{6422}(1243,\cdot)\) \(\chi_{6422}(1357,\cdot)\) \(\chi_{6422}(1399,\cdot)\) \(\chi_{6422}(1513,\cdot)\) \(\chi_{6422}(1737,\cdot)\) \(\chi_{6422}(1851,\cdot)\) \(\chi_{6422}(1893,\cdot)\) \(\chi_{6422}(2007,\cdot)\) \(\chi_{6422}(2231,\cdot)\) \(\chi_{6422}(2345,\cdot)\) \(\chi_{6422}(2387,\cdot)\) \(\chi_{6422}(2501,\cdot)\) \(\chi_{6422}(2725,\cdot)\) \(\chi_{6422}(2839,\cdot)\) \(\chi_{6422}(2881,\cdot)\) \(\chi_{6422}(2995,\cdot)\) \(\chi_{6422}(3219,\cdot)\) \(\chi_{6422}(3333,\cdot)\) \(\chi_{6422}(3375,\cdot)\) \(\chi_{6422}(3489,\cdot)\) \(\chi_{6422}(3713,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((4903,4733)\) → \((e\left(\frac{7}{52}\right),e\left(\frac{5}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 6422 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{85}{156}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{11}{156}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{145}{156}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{78}\right)\) |