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 \(\chi_{845}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5915.fc
\(\chi_{5915}(29,\cdot)\) \(\chi_{5915}(204,\cdot)\) \(\chi_{5915}(659,\cdot)\) \(\chi_{5915}(939,\cdot)\) \(\chi_{5915}(1114,\cdot)\) \(\chi_{5915}(1394,\cdot)\) \(\chi_{5915}(1569,\cdot)\) \(\chi_{5915}(1849,\cdot)\) \(\chi_{5915}(2024,\cdot)\) \(\chi_{5915}(2304,\cdot)\) \(\chi_{5915}(2479,\cdot)\) \(\chi_{5915}(2759,\cdot)\) \(\chi_{5915}(2934,\cdot)\) \(\chi_{5915}(3214,\cdot)\) \(\chi_{5915}(3389,\cdot)\) \(\chi_{5915}(3669,\cdot)\) \(\chi_{5915}(3844,\cdot)\) \(\chi_{5915}(4124,\cdot)\) \(\chi_{5915}(4299,\cdot)\) \(\chi_{5915}(4579,\cdot)\) \(\chi_{5915}(5034,\cdot)\) \(\chi_{5915}(5209,\cdot)\) \(\chi_{5915}(5489,\cdot)\) \(\chi_{5915}(5664,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2367,5071,1016)\) → \((-1,1,e\left(\frac{10}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(16\) | \(17\) |
| \( \chi_{ 5915 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{73}{78}\right)\) |