Basic properties
| Modulus: | \(916\) | |
| Conductor: | \(229\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(228\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{229}(41,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 916.x
\(\chi_{916}(29,\cdot)\) \(\chi_{916}(41,\cdot)\) \(\chi_{916}(65,\cdot)\) \(\chi_{916}(69,\cdot)\) \(\chi_{916}(73,\cdot)\) \(\chi_{916}(77,\cdot)\) \(\chi_{916}(105,\cdot)\) \(\chi_{916}(113,\cdot)\) \(\chi_{916}(117,\cdot)\) \(\chi_{916}(133,\cdot)\) \(\chi_{916}(137,\cdot)\) \(\chi_{916}(157,\cdot)\) \(\chi_{916}(189,\cdot)\) \(\chi_{916}(201,\cdot)\) \(\chi_{916}(205,\cdot)\) \(\chi_{916}(253,\cdot)\) \(\chi_{916}(257,\cdot)\) \(\chi_{916}(269,\cdot)\) \(\chi_{916}(301,\cdot)\) \(\chi_{916}(321,\cdot)\) \(\chi_{916}(325,\cdot)\) \(\chi_{916}(341,\cdot)\) \(\chi_{916}(345,\cdot)\) \(\chi_{916}(353,\cdot)\) \(\chi_{916}(381,\cdot)\) \(\chi_{916}(385,\cdot)\) \(\chi_{916}(389,\cdot)\) \(\chi_{916}(393,\cdot)\) \(\chi_{916}(417,\cdot)\) \(\chi_{916}(429,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{228})$ |
| Fixed field: | Number field defined by a degree 228 polynomial (not computed) |
Values on generators
\((459,693)\) → \((1,e\left(\frac{59}{228}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 916 }(41, a) \) | \(-1\) | \(1\) | \(e\left(\frac{47}{57}\right)\) | \(e\left(\frac{41}{114}\right)\) | \(e\left(\frac{157}{228}\right)\) | \(e\left(\frac{37}{57}\right)\) | \(e\left(\frac{35}{38}\right)\) | \(e\left(\frac{21}{76}\right)\) | \(e\left(\frac{7}{38}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{39}{76}\right)\) |