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 \(\chi_{20155}(63,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 40310.fe
\(\chi_{40310}(63,\cdot)\) \(\chi_{40310}(183,\cdot)\) \(\chi_{40310}(323,\cdot)\) \(\chi_{40310}(357,\cdot)\) \(\chi_{40310}(497,\cdot)\) \(\chi_{40310}(613,\cdot)\) \(\chi_{40310}(647,\cdot)\) \(\chi_{40310}(747,\cdot)\) \(\chi_{40310}(963,\cdot)\) \(\chi_{40310}(1037,\cdot)\) \(\chi_{40310}(1053,\cdot)\) \(\chi_{40310}(1367,\cdot)\) \(\chi_{40310}(1733,\cdot)\) \(\chi_{40310}(1907,\cdot)\) \(\chi_{40310}(1923,\cdot)\) \(\chi_{40310}(2023,\cdot)\) \(\chi_{40310}(2197,\cdot)\) \(\chi_{40310}(2353,\cdot)\) \(\chi_{40310}(2557,\cdot)\) \(\chi_{40310}(2677,\cdot)\) \(\chi_{40310}(2963,\cdot)\) \(\chi_{40310}(3137,\cdot)\) \(\chi_{40310}(3183,\cdot)\) \(\chi_{40310}(3203,\cdot)\) \(\chi_{40310}(3427,\cdot)\) \(\chi_{40310}(3833,\cdot)\) \(\chi_{40310}(3937,\cdot)\) \(\chi_{40310}(3957,\cdot)\) \(\chi_{40310}(4037,\cdot)\) \(\chi_{40310}(4227,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{644})$ |
| Fixed field: | Number field defined by a degree 644 polynomial (not computed) |
Values on generators
\((24187,19461,16821)\) → \((-i,e\left(\frac{11}{14}\right),e\left(\frac{22}{23}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 40310 }(63, a) \) | \(-1\) | \(1\) | \(e\left(\frac{255}{644}\right)\) | \(e\left(\frac{3}{644}\right)\) | \(e\left(\frac{255}{322}\right)\) | \(e\left(\frac{109}{322}\right)\) | \(e\left(\frac{393}{644}\right)\) | \(e\left(\frac{55}{92}\right)\) | \(e\left(\frac{148}{161}\right)\) | \(e\left(\frac{129}{322}\right)\) | \(e\left(\frac{509}{644}\right)\) | \(e\left(\frac{121}{644}\right)\) |