Basic properties
Modulus: | \(668\) | |
Conductor: | \(668\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 668.h
\(\chi_{668}(15,\cdot)\) \(\chi_{668}(23,\cdot)\) \(\chi_{668}(35,\cdot)\) \(\chi_{668}(39,\cdot)\) \(\chi_{668}(43,\cdot)\) \(\chi_{668}(51,\cdot)\) \(\chi_{668}(55,\cdot)\) \(\chi_{668}(59,\cdot)\) \(\chi_{668}(67,\cdot)\) \(\chi_{668}(71,\cdot)\) \(\chi_{668}(79,\cdot)\) \(\chi_{668}(83,\cdot)\) \(\chi_{668}(91,\cdot)\) \(\chi_{668}(95,\cdot)\) \(\chi_{668}(103,\cdot)\) \(\chi_{668}(111,\cdot)\) \(\chi_{668}(119,\cdot)\) \(\chi_{668}(123,\cdot)\) \(\chi_{668}(131,\cdot)\) \(\chi_{668}(135,\cdot)\) \(\chi_{668}(139,\cdot)\) \(\chi_{668}(143,\cdot)\) \(\chi_{668}(151,\cdot)\) \(\chi_{668}(155,\cdot)\) \(\chi_{668}(159,\cdot)\) \(\chi_{668}(163,\cdot)\) \(\chi_{668}(187,\cdot)\) \(\chi_{668}(207,\cdot)\) \(\chi_{668}(219,\cdot)\) \(\chi_{668}(227,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((335,5)\) → \((-1,e\left(\frac{101}{166}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 668 }(575, a) \) | \(1\) | \(1\) | \(e\left(\frac{115}{166}\right)\) | \(e\left(\frac{101}{166}\right)\) | \(e\left(\frac{49}{166}\right)\) | \(e\left(\frac{32}{83}\right)\) | \(e\left(\frac{89}{166}\right)\) | \(e\left(\frac{111}{166}\right)\) | \(e\left(\frac{25}{83}\right)\) | \(e\left(\frac{41}{166}\right)\) | \(e\left(\frac{131}{166}\right)\) | \(e\left(\frac{82}{83}\right)\) |