Basic properties
| Modulus: | \(916\) | |
| Conductor: | \(229\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(76\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{229}(21,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 916.r
\(\chi_{916}(13,\cdot)\) \(\chi_{916}(21,\cdot)\) \(\chi_{916}(93,\cdot)\) \(\chi_{916}(101,\cdot)\) \(\chi_{916}(109,\cdot)\) \(\chi_{916}(141,\cdot)\) \(\chi_{916}(145,\cdot)\) \(\chi_{916}(177,\cdot)\) \(\chi_{916}(197,\cdot)\) \(\chi_{916}(221,\cdot)\) \(\chi_{916}(237,\cdot)\) \(\chi_{916}(261,\cdot)\) \(\chi_{916}(281,\cdot)\) \(\chi_{916}(313,\cdot)\) \(\chi_{916}(317,\cdot)\) \(\chi_{916}(349,\cdot)\) \(\chi_{916}(357,\cdot)\) \(\chi_{916}(365,\cdot)\) \(\chi_{916}(437,\cdot)\) \(\chi_{916}(445,\cdot)\) \(\chi_{916}(573,\cdot)\) \(\chi_{916}(581,\cdot)\) \(\chi_{916}(601,\cdot)\) \(\chi_{916}(633,\cdot)\) \(\chi_{916}(653,\cdot)\) \(\chi_{916}(657,\cdot)\) \(\chi_{916}(665,\cdot)\) \(\chi_{916}(685,\cdot)\) \(\chi_{916}(689,\cdot)\) \(\chi_{916}(709,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{76})$ |
| Fixed field: | Number field defined by a degree 76 polynomial |
Values on generators
\((459,693)\) → \((1,e\left(\frac{29}{76}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 916 }(21, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{15}{38}\right)\) | \(e\left(\frac{63}{76}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{31}{38}\right)\) | \(e\left(\frac{49}{76}\right)\) | \(e\left(\frac{29}{38}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{15}{76}\right)\) |