Basic properties
| Modulus: | \(5915\) | |
| Conductor: | \(5915\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5915.gv
\(\chi_{5915}(82,\cdot)\) \(\chi_{5915}(173,\cdot)\) \(\chi_{5915}(283,\cdot)\) \(\chi_{5915}(537,\cdot)\) \(\chi_{5915}(628,\cdot)\) \(\chi_{5915}(647,\cdot)\) \(\chi_{5915}(738,\cdot)\) \(\chi_{5915}(1083,\cdot)\) \(\chi_{5915}(1102,\cdot)\) \(\chi_{5915}(1193,\cdot)\) \(\chi_{5915}(1447,\cdot)\) \(\chi_{5915}(1538,\cdot)\) \(\chi_{5915}(1557,\cdot)\) \(\chi_{5915}(1648,\cdot)\) \(\chi_{5915}(1902,\cdot)\) \(\chi_{5915}(1993,\cdot)\) \(\chi_{5915}(2012,\cdot)\) \(\chi_{5915}(2103,\cdot)\) \(\chi_{5915}(2357,\cdot)\) \(\chi_{5915}(2448,\cdot)\) \(\chi_{5915}(2467,\cdot)\) \(\chi_{5915}(2812,\cdot)\) \(\chi_{5915}(2903,\cdot)\) \(\chi_{5915}(2922,\cdot)\) \(\chi_{5915}(3013,\cdot)\) \(\chi_{5915}(3267,\cdot)\) \(\chi_{5915}(3377,\cdot)\) \(\chi_{5915}(3468,\cdot)\) \(\chi_{5915}(3722,\cdot)\) \(\chi_{5915}(3813,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((2367,5071,1016)\) → \((i,e\left(\frac{5}{6}\right),e\left(\frac{43}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(16\) | \(17\) |
| \( \chi_{ 5915 }(82, a) \) | \(1\) | \(1\) | \(e\left(\frac{73}{156}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{137}{156}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{89}{156}\right)\) |