Basic properties
Modulus: | \(490\) | |
Conductor: | \(245\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{245}(108,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 490.w
\(\chi_{490}(3,\cdot)\) \(\chi_{490}(17,\cdot)\) \(\chi_{490}(33,\cdot)\) \(\chi_{490}(47,\cdot)\) \(\chi_{490}(73,\cdot)\) \(\chi_{490}(87,\cdot)\) \(\chi_{490}(103,\cdot)\) \(\chi_{490}(143,\cdot)\) \(\chi_{490}(157,\cdot)\) \(\chi_{490}(173,\cdot)\) \(\chi_{490}(187,\cdot)\) \(\chi_{490}(213,\cdot)\) \(\chi_{490}(243,\cdot)\) \(\chi_{490}(257,\cdot)\) \(\chi_{490}(283,\cdot)\) \(\chi_{490}(297,\cdot)\) \(\chi_{490}(327,\cdot)\) \(\chi_{490}(353,\cdot)\) \(\chi_{490}(367,\cdot)\) \(\chi_{490}(383,\cdot)\) \(\chi_{490}(397,\cdot)\) \(\chi_{490}(437,\cdot)\) \(\chi_{490}(453,\cdot)\) \(\chi_{490}(467,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((197,101)\) → \((-i,e\left(\frac{13}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
\( \chi_{ 490 }(353, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{1}{6}\right)\) |