Basic properties
Modulus: | \(5915\) | |
Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1183}(461,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5915.gg
\(\chi_{5915}(6,\cdot)\) \(\chi_{5915}(41,\cdot)\) \(\chi_{5915}(76,\cdot)\) \(\chi_{5915}(111,\cdot)\) \(\chi_{5915}(461,\cdot)\) \(\chi_{5915}(496,\cdot)\) \(\chi_{5915}(531,\cdot)\) \(\chi_{5915}(566,\cdot)\) \(\chi_{5915}(916,\cdot)\) \(\chi_{5915}(951,\cdot)\) \(\chi_{5915}(986,\cdot)\) \(\chi_{5915}(1021,\cdot)\) \(\chi_{5915}(1406,\cdot)\) \(\chi_{5915}(1476,\cdot)\) \(\chi_{5915}(1826,\cdot)\) \(\chi_{5915}(1861,\cdot)\) \(\chi_{5915}(1896,\cdot)\) \(\chi_{5915}(1931,\cdot)\) \(\chi_{5915}(2281,\cdot)\) \(\chi_{5915}(2316,\cdot)\) \(\chi_{5915}(2351,\cdot)\) \(\chi_{5915}(2386,\cdot)\) \(\chi_{5915}(2736,\cdot)\) \(\chi_{5915}(2771,\cdot)\) \(\chi_{5915}(2806,\cdot)\) \(\chi_{5915}(2841,\cdot)\) \(\chi_{5915}(3191,\cdot)\) \(\chi_{5915}(3226,\cdot)\) \(\chi_{5915}(3261,\cdot)\) \(\chi_{5915}(3296,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((2367,5071,1016)\) → \((1,-1,e\left(\frac{53}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(16\) | \(17\) |
\( \chi_{ 5915 }(461, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{156}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{151}{156}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{155}{156}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{4}{39}\right)\) |