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.fx
\(\chi_{5915}(2,\cdot)\) \(\chi_{5915}(32,\cdot)\) \(\chi_{5915}(128,\cdot)\) \(\chi_{5915}(228,\cdot)\) \(\chi_{5915}(457,\cdot)\) \(\chi_{5915}(487,\cdot)\) \(\chi_{5915}(583,\cdot)\) \(\chi_{5915}(683,\cdot)\) \(\chi_{5915}(912,\cdot)\) \(\chi_{5915}(942,\cdot)\) \(\chi_{5915}(1038,\cdot)\) \(\chi_{5915}(1138,\cdot)\) \(\chi_{5915}(1367,\cdot)\) \(\chi_{5915}(1397,\cdot)\) \(\chi_{5915}(1493,\cdot)\) \(\chi_{5915}(1593,\cdot)\) \(\chi_{5915}(1822,\cdot)\) \(\chi_{5915}(1852,\cdot)\) \(\chi_{5915}(2048,\cdot)\) \(\chi_{5915}(2307,\cdot)\) \(\chi_{5915}(2403,\cdot)\) \(\chi_{5915}(2503,\cdot)\) \(\chi_{5915}(2732,\cdot)\) \(\chi_{5915}(2762,\cdot)\) \(\chi_{5915}(2858,\cdot)\) \(\chi_{5915}(2958,\cdot)\) \(\chi_{5915}(3187,\cdot)\) \(\chi_{5915}(3217,\cdot)\) \(\chi_{5915}(3313,\cdot)\) \(\chi_{5915}(3413,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((2367,5071,1016)\) → \((i,e\left(\frac{1}{3}\right),e\left(\frac{1}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(16\) | \(17\) |
| \( \chi_{ 5915 }(2, a) \) | \(1\) | \(1\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{137}{156}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{125}{156}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{155}{156}\right)\) | \(e\left(\frac{113}{156}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{27}{52}\right)\) |