Basic properties
Modulus: | \(916\) | |
Conductor: | \(916\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(76\) | 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 916.s
\(\chi_{916}(115,\cdot)\) \(\chi_{916}(123,\cdot)\) \(\chi_{916}(143,\cdot)\) \(\chi_{916}(175,\cdot)\) \(\chi_{916}(195,\cdot)\) \(\chi_{916}(199,\cdot)\) \(\chi_{916}(207,\cdot)\) \(\chi_{916}(227,\cdot)\) \(\chi_{916}(231,\cdot)\) \(\chi_{916}(251,\cdot)\) \(\chi_{916}(259,\cdot)\) \(\chi_{916}(263,\cdot)\) \(\chi_{916}(283,\cdot)\) \(\chi_{916}(315,\cdot)\) \(\chi_{916}(335,\cdot)\) \(\chi_{916}(343,\cdot)\) \(\chi_{916}(471,\cdot)\) \(\chi_{916}(479,\cdot)\) \(\chi_{916}(551,\cdot)\) \(\chi_{916}(559,\cdot)\) \(\chi_{916}(567,\cdot)\) \(\chi_{916}(599,\cdot)\) \(\chi_{916}(603,\cdot)\) \(\chi_{916}(635,\cdot)\) \(\chi_{916}(655,\cdot)\) \(\chi_{916}(679,\cdot)\) \(\chi_{916}(695,\cdot)\) \(\chi_{916}(719,\cdot)\) \(\chi_{916}(739,\cdot)\) \(\chi_{916}(771,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{76})$ |
Fixed field: | Number field defined by a degree 76 polynomial |
Values on generators
\((459,693)\) → \((-1,e\left(\frac{61}{76}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 916 }(251, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{38}\right)\) | \(e\left(\frac{25}{38}\right)\) | \(e\left(\frac{29}{76}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{69}{76}\right)\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{13}{38}\right)\) | \(e\left(\frac{63}{76}\right)\) |