Basic properties
| Modulus: | \(2656\) | |
| Conductor: | \(332\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(82\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{332}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2656.v
\(\chi_{2656}(31,\cdot)\) \(\chi_{2656}(63,\cdot)\) \(\chi_{2656}(95,\cdot)\) \(\chi_{2656}(127,\cdot)\) \(\chi_{2656}(191,\cdot)\) \(\chi_{2656}(287,\cdot)\) \(\chi_{2656}(319,\cdot)\) \(\chi_{2656}(383,\cdot)\) \(\chi_{2656}(479,\cdot)\) \(\chi_{2656}(575,\cdot)\) \(\chi_{2656}(607,\cdot)\) \(\chi_{2656}(671,\cdot)\) \(\chi_{2656}(863,\cdot)\) \(\chi_{2656}(895,\cdot)\) \(\chi_{2656}(991,\cdot)\) \(\chi_{2656}(1023,\cdot)\) \(\chi_{2656}(1055,\cdot)\) \(\chi_{2656}(1119,\cdot)\) \(\chi_{2656}(1183,\cdot)\) \(\chi_{2656}(1439,\cdot)\) \(\chi_{2656}(1503,\cdot)\) \(\chi_{2656}(1535,\cdot)\) \(\chi_{2656}(1663,\cdot)\) \(\chi_{2656}(1759,\cdot)\) \(\chi_{2656}(1791,\cdot)\) \(\chi_{2656}(1855,\cdot)\) \(\chi_{2656}(1887,\cdot)\) \(\chi_{2656}(1919,\cdot)\) \(\chi_{2656}(2015,\cdot)\) \(\chi_{2656}(2079,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{41})$ |
| Fixed field: | Number field defined by a degree 82 polynomial |
Values on generators
\((831,997,417)\) → \((-1,1,e\left(\frac{19}{41}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 2656 }(31, a) \) | \(-1\) | \(1\) | \(e\left(\frac{71}{82}\right)\) | \(e\left(\frac{21}{41}\right)\) | \(e\left(\frac{17}{82}\right)\) | \(e\left(\frac{30}{41}\right)\) | \(e\left(\frac{51}{82}\right)\) | \(e\left(\frac{28}{41}\right)\) | \(e\left(\frac{31}{82}\right)\) | \(e\left(\frac{39}{41}\right)\) | \(e\left(\frac{23}{82}\right)\) | \(e\left(\frac{3}{41}\right)\) |