Basic properties
| Modulus: | \(40310\) | |
| Conductor: | \(20155\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(644\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{20155}(33,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 40310.fd
\(\chi_{40310}(33,\cdot)\) \(\chi_{40310}(187,\cdot)\) \(\chi_{40310}(353,\cdot)\) \(\chi_{40310}(383,\cdot)\) \(\chi_{40310}(477,\cdot)\) \(\chi_{40310}(643,\cdot)\) \(\chi_{40310}(937,\cdot)\) \(\chi_{40310}(1057,\cdot)\) \(\chi_{40310}(1327,\cdot)\) \(\chi_{40310}(1543,\cdot)\) \(\chi_{40310}(1773,\cdot)\) \(\chi_{40310}(2093,\cdot)\) \(\chi_{40310}(2703,\cdot)\) \(\chi_{40310}(2913,\cdot)\) \(\chi_{40310}(2933,\cdot)\) \(\chi_{40310}(2967,\cdot)\) \(\chi_{40310}(2993,\cdot)\) \(\chi_{40310}(3257,\cdot)\) \(\chi_{40310}(3647,\cdot)\) \(\chi_{40310}(3717,\cdot)\) \(\chi_{40310}(3747,\cdot)\) \(\chi_{40310}(3763,\cdot)\) \(\chi_{40310}(3837,\cdot)\) \(\chi_{40310}(4093,\cdot)\) \(\chi_{40310}(4383,\cdot)\) \(\chi_{40310}(5137,\cdot)\) \(\chi_{40310}(5387,\cdot)\) \(\chi_{40310}(5503,\cdot)\) \(\chi_{40310}(5693,\cdot)\) \(\chi_{40310}(5747,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{644})$ |
| Fixed field: | Number field defined by a degree 644 polynomial (not computed) |
Values on generators
\((24187,19461,16821)\) → \((-i,e\left(\frac{1}{14}\right),e\left(\frac{39}{46}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 40310 }(33, a) \) | \(1\) | \(1\) | \(e\left(\frac{237}{644}\right)\) | \(e\left(\frac{643}{644}\right)\) | \(e\left(\frac{237}{322}\right)\) | \(e\left(\frac{71}{322}\right)\) | \(e\left(\frac{513}{644}\right)\) | \(e\left(\frac{89}{92}\right)\) | \(e\left(\frac{277}{322}\right)\) | \(e\left(\frac{59}{161}\right)\) | \(e\left(\frac{367}{644}\right)\) | \(e\left(\frac{67}{644}\right)\) |