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.gp
\(\chi_{5915}(48,\cdot)\) \(\chi_{5915}(237,\cdot)\) \(\chi_{5915}(328,\cdot)\) \(\chi_{5915}(412,\cdot)\) \(\chi_{5915}(503,\cdot)\) \(\chi_{5915}(692,\cdot)\) \(\chi_{5915}(783,\cdot)\) \(\chi_{5915}(958,\cdot)\) \(\chi_{5915}(1147,\cdot)\) \(\chi_{5915}(1238,\cdot)\) \(\chi_{5915}(1322,\cdot)\) \(\chi_{5915}(1413,\cdot)\) \(\chi_{5915}(1602,\cdot)\) \(\chi_{5915}(1693,\cdot)\) \(\chi_{5915}(1777,\cdot)\) \(\chi_{5915}(1868,\cdot)\) \(\chi_{5915}(2057,\cdot)\) \(\chi_{5915}(2148,\cdot)\) \(\chi_{5915}(2232,\cdot)\) \(\chi_{5915}(2323,\cdot)\) \(\chi_{5915}(2603,\cdot)\) \(\chi_{5915}(2687,\cdot)\) \(\chi_{5915}(2778,\cdot)\) \(\chi_{5915}(2967,\cdot)\) \(\chi_{5915}(3058,\cdot)\) \(\chi_{5915}(3142,\cdot)\) \(\chi_{5915}(3422,\cdot)\) \(\chi_{5915}(3513,\cdot)\) \(\chi_{5915}(3597,\cdot)\) \(\chi_{5915}(3688,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((2367,5071,1016)\) → \((-i,-1,e\left(\frac{32}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(16\) | \(17\) |
\( \chi_{ 5915 }(48, a) \) | \(1\) | \(1\) | \(e\left(\frac{89}{156}\right)\) | \(e\left(\frac{77}{156}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{7}{156}\right)\) |