Basic properties
Modulus: | \(5915\) | |
Conductor: | \(5915\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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.ga
\(\chi_{5915}(18,\cdot)\) \(\chi_{5915}(177,\cdot)\) \(\chi_{5915}(242,\cdot)\) \(\chi_{5915}(473,\cdot)\) \(\chi_{5915}(632,\cdot)\) \(\chi_{5915}(697,\cdot)\) \(\chi_{5915}(863,\cdot)\) \(\chi_{5915}(928,\cdot)\) \(\chi_{5915}(1087,\cdot)\) \(\chi_{5915}(1152,\cdot)\) \(\chi_{5915}(1318,\cdot)\) \(\chi_{5915}(1383,\cdot)\) \(\chi_{5915}(1542,\cdot)\) \(\chi_{5915}(1607,\cdot)\) \(\chi_{5915}(1773,\cdot)\) \(\chi_{5915}(1838,\cdot)\) \(\chi_{5915}(1997,\cdot)\) \(\chi_{5915}(2062,\cdot)\) \(\chi_{5915}(2228,\cdot)\) \(\chi_{5915}(2293,\cdot)\) \(\chi_{5915}(2452,\cdot)\) \(\chi_{5915}(2517,\cdot)\) \(\chi_{5915}(2683,\cdot)\) \(\chi_{5915}(2748,\cdot)\) \(\chi_{5915}(2907,\cdot)\) \(\chi_{5915}(3138,\cdot)\) \(\chi_{5915}(3203,\cdot)\) \(\chi_{5915}(3362,\cdot)\) \(\chi_{5915}(3427,\cdot)\) \(\chi_{5915}(3593,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((2367,5071,1016)\) → \((-i,e\left(\frac{2}{3}\right),e\left(\frac{31}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(16\) | \(17\) |
\( \chi_{ 5915 }(18, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{131}{156}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{11}{156}\right)\) | \(e\left(\frac{31}{156}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{71}{156}\right)\) |