Basic properties
Modulus: | \(5915\) | |
Conductor: | \(845\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{845}(134,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5915.fk
\(\chi_{5915}(134,\cdot)\) \(\chi_{5915}(309,\cdot)\) \(\chi_{5915}(589,\cdot)\) \(\chi_{5915}(764,\cdot)\) \(\chi_{5915}(1044,\cdot)\) \(\chi_{5915}(1219,\cdot)\) \(\chi_{5915}(1674,\cdot)\) \(\chi_{5915}(1954,\cdot)\) \(\chi_{5915}(2129,\cdot)\) \(\chi_{5915}(2409,\cdot)\) \(\chi_{5915}(2584,\cdot)\) \(\chi_{5915}(2864,\cdot)\) \(\chi_{5915}(3039,\cdot)\) \(\chi_{5915}(3319,\cdot)\) \(\chi_{5915}(3494,\cdot)\) \(\chi_{5915}(3774,\cdot)\) \(\chi_{5915}(3949,\cdot)\) \(\chi_{5915}(4229,\cdot)\) \(\chi_{5915}(4404,\cdot)\) \(\chi_{5915}(4684,\cdot)\) \(\chi_{5915}(4859,\cdot)\) \(\chi_{5915}(5139,\cdot)\) \(\chi_{5915}(5314,\cdot)\) \(\chi_{5915}(5594,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2367,5071,1016)\) → \((-1,1,e\left(\frac{19}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(16\) | \(17\) |
\( \chi_{ 5915 }(134, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{5}{78}\right)\) |