Basic properties
Modulus: | \(5915\) | |
Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1183}(81,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5915.ef
\(\chi_{5915}(81,\cdot)\) \(\chi_{5915}(536,\cdot)\) \(\chi_{5915}(646,\cdot)\) \(\chi_{5915}(1101,\cdot)\) \(\chi_{5915}(1446,\cdot)\) \(\chi_{5915}(1556,\cdot)\) \(\chi_{5915}(1901,\cdot)\) \(\chi_{5915}(2011,\cdot)\) \(\chi_{5915}(2356,\cdot)\) \(\chi_{5915}(2466,\cdot)\) \(\chi_{5915}(2811,\cdot)\) \(\chi_{5915}(2921,\cdot)\) \(\chi_{5915}(3266,\cdot)\) \(\chi_{5915}(3376,\cdot)\) \(\chi_{5915}(3721,\cdot)\) \(\chi_{5915}(3831,\cdot)\) \(\chi_{5915}(4176,\cdot)\) \(\chi_{5915}(4286,\cdot)\) \(\chi_{5915}(4631,\cdot)\) \(\chi_{5915}(4741,\cdot)\) \(\chi_{5915}(5086,\cdot)\) \(\chi_{5915}(5196,\cdot)\) \(\chi_{5915}(5541,\cdot)\) \(\chi_{5915}(5651,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | 39.39.253721406991290895924770503111827676888647505643788160579278763946491805765758913183386148271215912203961.1 |
Values on generators
\((2367,5071,1016)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{7}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(16\) | \(17\) |
\( \chi_{ 5915 }(81, a) \) | \(1\) | \(1\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{34}{39}\right)\) |