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.gv
\(\chi_{5915}(82,\cdot)\) \(\chi_{5915}(173,\cdot)\) \(\chi_{5915}(283,\cdot)\) \(\chi_{5915}(537,\cdot)\) \(\chi_{5915}(628,\cdot)\) \(\chi_{5915}(647,\cdot)\) \(\chi_{5915}(738,\cdot)\) \(\chi_{5915}(1083,\cdot)\) \(\chi_{5915}(1102,\cdot)\) \(\chi_{5915}(1193,\cdot)\) \(\chi_{5915}(1447,\cdot)\) \(\chi_{5915}(1538,\cdot)\) \(\chi_{5915}(1557,\cdot)\) \(\chi_{5915}(1648,\cdot)\) \(\chi_{5915}(1902,\cdot)\) \(\chi_{5915}(1993,\cdot)\) \(\chi_{5915}(2012,\cdot)\) \(\chi_{5915}(2103,\cdot)\) \(\chi_{5915}(2357,\cdot)\) \(\chi_{5915}(2448,\cdot)\) \(\chi_{5915}(2467,\cdot)\) \(\chi_{5915}(2812,\cdot)\) \(\chi_{5915}(2903,\cdot)\) \(\chi_{5915}(2922,\cdot)\) \(\chi_{5915}(3013,\cdot)\) \(\chi_{5915}(3267,\cdot)\) \(\chi_{5915}(3377,\cdot)\) \(\chi_{5915}(3468,\cdot)\) \(\chi_{5915}(3722,\cdot)\) \(\chi_{5915}(3813,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((2367,5071,1016)\) → \((i,e\left(\frac{1}{6}\right),e\left(\frac{59}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(16\) | \(17\) |
\( \chi_{ 5915 }(647, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{156}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{61}{156}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{133}{156}\right)\) |