Basic properties
| Modulus: | \(845\) | |
| Conductor: | \(845\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 845.bh
\(\chi_{845}(4,\cdot)\) \(\chi_{845}(49,\cdot)\) \(\chi_{845}(69,\cdot)\) \(\chi_{845}(114,\cdot)\) \(\chi_{845}(134,\cdot)\) \(\chi_{845}(179,\cdot)\) \(\chi_{845}(199,\cdot)\) \(\chi_{845}(244,\cdot)\) \(\chi_{845}(264,\cdot)\) \(\chi_{845}(309,\cdot)\) \(\chi_{845}(329,\cdot)\) \(\chi_{845}(374,\cdot)\) \(\chi_{845}(394,\cdot)\) \(\chi_{845}(439,\cdot)\) \(\chi_{845}(459,\cdot)\) \(\chi_{845}(504,\cdot)\) \(\chi_{845}(524,\cdot)\) \(\chi_{845}(569,\cdot)\) \(\chi_{845}(589,\cdot)\) \(\chi_{845}(634,\cdot)\) \(\chi_{845}(719,\cdot)\) \(\chi_{845}(764,\cdot)\) \(\chi_{845}(784,\cdot)\) \(\chi_{845}(829,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((677,171)\) → \((-1,e\left(\frac{1}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(14\) |
| \( \chi_{ 845 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{5}{13}\right)\) |