Basic properties
Modulus: | \(5915\) | |
Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1183}(51,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5915.ff
\(\chi_{5915}(51,\cdot)\) \(\chi_{5915}(116,\cdot)\) \(\chi_{5915}(571,\cdot)\) \(\chi_{5915}(961,\cdot)\) \(\chi_{5915}(1026,\cdot)\) \(\chi_{5915}(1416,\cdot)\) \(\chi_{5915}(1481,\cdot)\) \(\chi_{5915}(1871,\cdot)\) \(\chi_{5915}(1936,\cdot)\) \(\chi_{5915}(2326,\cdot)\) \(\chi_{5915}(2391,\cdot)\) \(\chi_{5915}(2781,\cdot)\) \(\chi_{5915}(2846,\cdot)\) \(\chi_{5915}(3236,\cdot)\) \(\chi_{5915}(3301,\cdot)\) \(\chi_{5915}(3691,\cdot)\) \(\chi_{5915}(3756,\cdot)\) \(\chi_{5915}(4146,\cdot)\) \(\chi_{5915}(4211,\cdot)\) \(\chi_{5915}(4601,\cdot)\) \(\chi_{5915}(4666,\cdot)\) \(\chi_{5915}(5056,\cdot)\) \(\chi_{5915}(5121,\cdot)\) \(\chi_{5915}(5511,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2367,5071,1016)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{19}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(16\) | \(17\) |
\( \chi_{ 5915 }(51, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) |