Basic properties
| Modulus: | \(507\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(2,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 507.w
\(\chi_{507}(7,\cdot)\) \(\chi_{507}(28,\cdot)\) \(\chi_{507}(37,\cdot)\) \(\chi_{507}(46,\cdot)\) \(\chi_{507}(58,\cdot)\) \(\chi_{507}(67,\cdot)\) \(\chi_{507}(76,\cdot)\) \(\chi_{507}(85,\cdot)\) \(\chi_{507}(97,\cdot)\) \(\chi_{507}(106,\cdot)\) \(\chi_{507}(115,\cdot)\) \(\chi_{507}(124,\cdot)\) \(\chi_{507}(136,\cdot)\) \(\chi_{507}(145,\cdot)\) \(\chi_{507}(154,\cdot)\) \(\chi_{507}(163,\cdot)\) \(\chi_{507}(175,\cdot)\) \(\chi_{507}(184,\cdot)\) \(\chi_{507}(193,\cdot)\) \(\chi_{507}(202,\cdot)\) \(\chi_{507}(214,\cdot)\) \(\chi_{507}(223,\cdot)\) \(\chi_{507}(232,\cdot)\) \(\chi_{507}(241,\cdot)\) \(\chi_{507}(253,\cdot)\) \(\chi_{507}(262,\cdot)\) \(\chi_{507}(271,\cdot)\) \(\chi_{507}(280,\cdot)\) \(\chi_{507}(292,\cdot)\) \(\chi_{507}(301,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((170,340)\) → \((1,e\left(\frac{1}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 507 }(340, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{156}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{107}{156}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{103}{156}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{73}{78}\right)\) |