Basic properties
| Modulus: | \(845\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(16,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 845.y
\(\chi_{845}(16,\cdot)\) \(\chi_{845}(61,\cdot)\) \(\chi_{845}(81,\cdot)\) \(\chi_{845}(126,\cdot)\) \(\chi_{845}(211,\cdot)\) \(\chi_{845}(256,\cdot)\) \(\chi_{845}(276,\cdot)\) \(\chi_{845}(321,\cdot)\) \(\chi_{845}(341,\cdot)\) \(\chi_{845}(386,\cdot)\) \(\chi_{845}(406,\cdot)\) \(\chi_{845}(451,\cdot)\) \(\chi_{845}(471,\cdot)\) \(\chi_{845}(516,\cdot)\) \(\chi_{845}(536,\cdot)\) \(\chi_{845}(581,\cdot)\) \(\chi_{845}(601,\cdot)\) \(\chi_{845}(646,\cdot)\) \(\chi_{845}(666,\cdot)\) \(\chi_{845}(711,\cdot)\) \(\chi_{845}(731,\cdot)\) \(\chi_{845}(776,\cdot)\) \(\chi_{845}(796,\cdot)\) \(\chi_{845}(841,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((677,171)\) → \((1,e\left(\frac{1}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(14\) |
| \( \chi_{ 845 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{10}{13}\right)\) |