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.ho
\(\chi_{5915}(67,\cdot)\) \(\chi_{5915}(163,\cdot)\) \(\chi_{5915}(193,\cdot)\) \(\chi_{5915}(422,\cdot)\) \(\chi_{5915}(522,\cdot)\) \(\chi_{5915}(618,\cdot)\) \(\chi_{5915}(648,\cdot)\) \(\chi_{5915}(877,\cdot)\) \(\chi_{5915}(977,\cdot)\) \(\chi_{5915}(1073,\cdot)\) \(\chi_{5915}(1332,\cdot)\) \(\chi_{5915}(1528,\cdot)\) \(\chi_{5915}(1558,\cdot)\) \(\chi_{5915}(1787,\cdot)\) \(\chi_{5915}(1887,\cdot)\) \(\chi_{5915}(1983,\cdot)\) \(\chi_{5915}(2013,\cdot)\) \(\chi_{5915}(2242,\cdot)\) \(\chi_{5915}(2342,\cdot)\) \(\chi_{5915}(2438,\cdot)\) \(\chi_{5915}(2468,\cdot)\) \(\chi_{5915}(2697,\cdot)\) \(\chi_{5915}(2797,\cdot)\) \(\chi_{5915}(2893,\cdot)\) \(\chi_{5915}(2923,\cdot)\) \(\chi_{5915}(3152,\cdot)\) \(\chi_{5915}(3252,\cdot)\) \(\chi_{5915}(3348,\cdot)\) \(\chi_{5915}(3378,\cdot)\) \(\chi_{5915}(3607,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((2367,5071,1016)\) → \((i,e\left(\frac{2}{3}\right),e\left(\frac{37}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(16\) | \(17\) |
| \( \chi_{ 5915 }(67, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{101}{156}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{73}{156}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{85}{156}\right)\) |