Basic properties
| Modulus: | \(507\) | |
| 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 \(\chi_{169}(3,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 507.q
\(\chi_{507}(16,\cdot)\) \(\chi_{507}(55,\cdot)\) \(\chi_{507}(61,\cdot)\) \(\chi_{507}(94,\cdot)\) \(\chi_{507}(100,\cdot)\) \(\chi_{507}(133,\cdot)\) \(\chi_{507}(139,\cdot)\) \(\chi_{507}(172,\cdot)\) \(\chi_{507}(178,\cdot)\) \(\chi_{507}(211,\cdot)\) \(\chi_{507}(217,\cdot)\) \(\chi_{507}(250,\cdot)\) \(\chi_{507}(256,\cdot)\) \(\chi_{507}(289,\cdot)\) \(\chi_{507}(295,\cdot)\) \(\chi_{507}(328,\cdot)\) \(\chi_{507}(334,\cdot)\) \(\chi_{507}(367,\cdot)\) \(\chi_{507}(373,\cdot)\) \(\chi_{507}(406,\cdot)\) \(\chi_{507}(412,\cdot)\) \(\chi_{507}(445,\cdot)\) \(\chi_{507}(451,\cdot)\) \(\chi_{507}(490,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((170,340)\) → \((1,e\left(\frac{31}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 507 }(172, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) |