Basic properties
| Modulus: | \(821\) | |
| Conductor: | \(821\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(41\) | 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 821.g
\(\chi_{821}(28,\cdot)\) \(\chi_{821}(35,\cdot)\) \(\chi_{821}(42,\cdot)\) \(\chi_{821}(63,\cdot)\) \(\chi_{821}(88,\cdot)\) \(\chi_{821}(106,\cdot)\) \(\chi_{821}(110,\cdot)\) \(\chi_{821}(122,\cdot)\) \(\chi_{821}(132,\cdot)\) \(\chi_{821}(159,\cdot)\) \(\chi_{821}(165,\cdot)\) \(\chi_{821}(166,\cdot)\) \(\chi_{821}(183,\cdot)\) \(\chi_{821}(198,\cdot)\) \(\chi_{821}(249,\cdot)\) \(\chi_{821}(284,\cdot)\) \(\chi_{821}(297,\cdot)\) \(\chi_{821}(347,\cdot)\) \(\chi_{821}(355,\cdot)\) \(\chi_{821}(362,\cdot)\) \(\chi_{821}(404,\cdot)\) \(\chi_{821}(412,\cdot)\) \(\chi_{821}(426,\cdot)\) \(\chi_{821}(434,\cdot)\) \(\chi_{821}(463,\cdot)\) \(\chi_{821}(505,\cdot)\) \(\chi_{821}(515,\cdot)\) \(\chi_{821}(543,\cdot)\) \(\chi_{821}(548,\cdot)\) \(\chi_{821}(563,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{41})$ |
| Fixed field: | Number field defined by a degree 41 polynomial |
Values on generators
\(2\) → \(e\left(\frac{21}{41}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 821 }(618, a) \) | \(1\) | \(1\) | \(e\left(\frac{21}{41}\right)\) | \(e\left(\frac{3}{41}\right)\) | \(e\left(\frac{1}{41}\right)\) | \(e\left(\frac{2}{41}\right)\) | \(e\left(\frac{24}{41}\right)\) | \(e\left(\frac{24}{41}\right)\) | \(e\left(\frac{22}{41}\right)\) | \(e\left(\frac{6}{41}\right)\) | \(e\left(\frac{23}{41}\right)\) | \(e\left(\frac{35}{41}\right)\) |