Basic properties
| Modulus: | \(507\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(82,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 507.t
\(\chi_{507}(4,\cdot)\) \(\chi_{507}(10,\cdot)\) \(\chi_{507}(43,\cdot)\) \(\chi_{507}(49,\cdot)\) \(\chi_{507}(82,\cdot)\) \(\chi_{507}(88,\cdot)\) \(\chi_{507}(121,\cdot)\) \(\chi_{507}(127,\cdot)\) \(\chi_{507}(160,\cdot)\) \(\chi_{507}(166,\cdot)\) \(\chi_{507}(199,\cdot)\) \(\chi_{507}(205,\cdot)\) \(\chi_{507}(238,\cdot)\) \(\chi_{507}(244,\cdot)\) \(\chi_{507}(277,\cdot)\) \(\chi_{507}(283,\cdot)\) \(\chi_{507}(322,\cdot)\) \(\chi_{507}(355,\cdot)\) \(\chi_{507}(394,\cdot)\) \(\chi_{507}(400,\cdot)\) \(\chi_{507}(433,\cdot)\) \(\chi_{507}(439,\cdot)\) \(\chi_{507}(472,\cdot)\) \(\chi_{507}(478,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((170,340)\) → \((1,e\left(\frac{43}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 507 }(82, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) |