Basic properties
| Modulus: | \(507\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(34,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 507.r
\(\chi_{507}(31,\cdot)\) \(\chi_{507}(34,\cdot)\) \(\chi_{507}(73,\cdot)\) \(\chi_{507}(109,\cdot)\) \(\chi_{507}(112,\cdot)\) \(\chi_{507}(148,\cdot)\) \(\chi_{507}(151,\cdot)\) \(\chi_{507}(187,\cdot)\) \(\chi_{507}(190,\cdot)\) \(\chi_{507}(226,\cdot)\) \(\chi_{507}(229,\cdot)\) \(\chi_{507}(265,\cdot)\) \(\chi_{507}(304,\cdot)\) \(\chi_{507}(307,\cdot)\) \(\chi_{507}(343,\cdot)\) \(\chi_{507}(346,\cdot)\) \(\chi_{507}(382,\cdot)\) \(\chi_{507}(385,\cdot)\) \(\chi_{507}(421,\cdot)\) \(\chi_{507}(424,\cdot)\) \(\chi_{507}(460,\cdot)\) \(\chi_{507}(463,\cdot)\) \(\chi_{507}(499,\cdot)\) \(\chi_{507}(502,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((170,340)\) → \((1,e\left(\frac{49}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 507 }(34, a) \) | \(-1\) | \(1\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{15}{26}\right)\) |