Basic properties
Modulus: | \(40310\) | |
Conductor: | \(4031\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(966\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{4031}(51,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 40310.fp
\(\chi_{40310}(51,\cdot)\) \(\chi_{40310}(71,\cdot)\) \(\chi_{40310}(121,\cdot)\) \(\chi_{40310}(361,\cdot)\) \(\chi_{40310}(441,\cdot)\) \(\chi_{40310}(941,\cdot)\) \(\chi_{40310}(961,\cdot)\) \(\chi_{40310}(1211,\cdot)\) \(\chi_{40310}(1281,\cdot)\) \(\chi_{40310}(1401,\cdot)\) \(\chi_{40310}(1811,\cdot)\) \(\chi_{40310}(1831,\cdot)\) \(\chi_{40310}(1861,\cdot)\) \(\chi_{40310}(1981,\cdot)\) \(\chi_{40310}(2101,\cdot)\) \(\chi_{40310}(2151,\cdot)\) \(\chi_{40310}(2271,\cdot)\) \(\chi_{40310}(2391,\cdot)\) \(\chi_{40310}(2441,\cdot)\) \(\chi_{40310}(2661,\cdot)\) \(\chi_{40310}(2761,\cdot)\) \(\chi_{40310}(2851,\cdot)\) \(\chi_{40310}(3141,\cdot)\) \(\chi_{40310}(3341,\cdot)\) \(\chi_{40310}(3721,\cdot)\) \(\chi_{40310}(3921,\cdot)\) \(\chi_{40310}(4151,\cdot)\) \(\chi_{40310}(4181,\cdot)\) \(\chi_{40310}(4211,\cdot)\) \(\chi_{40310}(4591,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{483})$ |
Fixed field: | Number field defined by a degree 966 polynomial (not computed) |
Values on generators
\((24187,19461,16821)\) → \((1,e\left(\frac{13}{14}\right),e\left(\frac{5}{69}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 40310 }(51, a) \) | \(1\) | \(1\) | \(e\left(\frac{593}{966}\right)\) | \(e\left(\frac{370}{483}\right)\) | \(e\left(\frac{110}{483}\right)\) | \(e\left(\frac{697}{966}\right)\) | \(e\left(\frac{170}{483}\right)\) | \(e\left(\frac{35}{138}\right)\) | \(e\left(\frac{751}{966}\right)\) | \(e\left(\frac{367}{966}\right)\) | \(e\left(\frac{85}{161}\right)\) | \(e\left(\frac{271}{322}\right)\) |