Basic properties
| Modulus: | \(664\) | |
| Conductor: | \(664\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(82\) | 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 664.j
\(\chi_{664}(19,\cdot)\) \(\chi_{664}(35,\cdot)\) \(\chi_{664}(43,\cdot)\) \(\chi_{664}(67,\cdot)\) \(\chi_{664}(91,\cdot)\) \(\chi_{664}(107,\cdot)\) \(\chi_{664}(115,\cdot)\) \(\chi_{664}(139,\cdot)\) \(\chi_{664}(155,\cdot)\) \(\chi_{664}(163,\cdot)\) \(\chi_{664}(171,\cdot)\) \(\chi_{664}(179,\cdot)\) \(\chi_{664}(211,\cdot)\) \(\chi_{664}(219,\cdot)\) \(\chi_{664}(251,\cdot)\) \(\chi_{664}(267,\cdot)\) \(\chi_{664}(283,\cdot)\) \(\chi_{664}(291,\cdot)\) \(\chi_{664}(299,\cdot)\) \(\chi_{664}(307,\cdot)\) \(\chi_{664}(315,\cdot)\) \(\chi_{664}(323,\cdot)\) \(\chi_{664}(347,\cdot)\) \(\chi_{664}(371,\cdot)\) \(\chi_{664}(379,\cdot)\) \(\chi_{664}(387,\cdot)\) \(\chi_{664}(403,\cdot)\) \(\chi_{664}(411,\cdot)\) \(\chi_{664}(435,\cdot)\) \(\chi_{664}(467,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{41})$ |
| Fixed field: | Number field defined by a degree 82 polynomial |
Values on generators
\((167,333,417)\) → \((-1,-1,e\left(\frac{39}{82}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 664 }(643, a) \) | \(1\) | \(1\) | \(e\left(\frac{10}{41}\right)\) | \(e\left(\frac{14}{41}\right)\) | \(e\left(\frac{25}{82}\right)\) | \(e\left(\frac{20}{41}\right)\) | \(e\left(\frac{17}{41}\right)\) | \(e\left(\frac{5}{41}\right)\) | \(e\left(\frac{24}{41}\right)\) | \(e\left(\frac{26}{41}\right)\) | \(e\left(\frac{29}{82}\right)\) | \(e\left(\frac{45}{82}\right)\) |