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.ha
\(\chi_{5915}(17,\cdot)\) \(\chi_{5915}(108,\cdot)\) \(\chi_{5915}(257,\cdot)\) \(\chi_{5915}(348,\cdot)\) \(\chi_{5915}(472,\cdot)\) \(\chi_{5915}(563,\cdot)\) \(\chi_{5915}(712,\cdot)\) \(\chi_{5915}(803,\cdot)\) \(\chi_{5915}(927,\cdot)\) \(\chi_{5915}(1018,\cdot)\) \(\chi_{5915}(1167,\cdot)\) \(\chi_{5915}(1258,\cdot)\) \(\chi_{5915}(1382,\cdot)\) \(\chi_{5915}(1473,\cdot)\) \(\chi_{5915}(1622,\cdot)\) \(\chi_{5915}(1928,\cdot)\) \(\chi_{5915}(2077,\cdot)\) \(\chi_{5915}(2168,\cdot)\) \(\chi_{5915}(2292,\cdot)\) \(\chi_{5915}(2383,\cdot)\) \(\chi_{5915}(2532,\cdot)\) \(\chi_{5915}(2623,\cdot)\) \(\chi_{5915}(2747,\cdot)\) \(\chi_{5915}(2838,\cdot)\) \(\chi_{5915}(2987,\cdot)\) \(\chi_{5915}(3078,\cdot)\) \(\chi_{5915}(3202,\cdot)\) \(\chi_{5915}(3293,\cdot)\) \(\chi_{5915}(3442,\cdot)\) \(\chi_{5915}(3533,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((2367,5071,1016)\) → \((i,e\left(\frac{1}{6}\right),e\left(\frac{73}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(16\) | \(17\) |
| \( \chi_{ 5915 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{151}{156}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{1}{156}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{3}{52}\right)\) |