Basic properties
| Modulus: | \(40310\) | |
| Conductor: | \(4031\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(483\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4031}(81,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 40310.ey
\(\chi_{40310}(81,\cdot)\) \(\chi_{40310}(471,\cdot)\) \(\chi_{40310}(741,\cdot)\) \(\chi_{40310}(761,\cdot)\) \(\chi_{40310}(951,\cdot)\) \(\chi_{40310}(1011,\cdot)\) \(\chi_{40310}(1051,\cdot)\) \(\chi_{40310}(1271,\cdot)\) \(\chi_{40310}(1441,\cdot)\) \(\chi_{40310}(2171,\cdot)\) \(\chi_{40310}(2401,\cdot)\) \(\chi_{40310}(2481,\cdot)\) \(\chi_{40310}(2601,\cdot)\) \(\chi_{40310}(2791,\cdot)\) \(\chi_{40310}(3041,\cdot)\) \(\chi_{40310}(3371,\cdot)\) \(\chi_{40310}(3561,\cdot)\) \(\chi_{40310}(3621,\cdot)\) \(\chi_{40310}(3661,\cdot)\) \(\chi_{40310}(4051,\cdot)\) \(\chi_{40310}(4201,\cdot)\) \(\chi_{40310}(4221,\cdot)\) \(\chi_{40310}(4241,\cdot)\) \(\chi_{40310}(4431,\cdot)\) \(\chi_{40310}(4461,\cdot)\) \(\chi_{40310}(4531,\cdot)\) \(\chi_{40310}(4751,\cdot)\) \(\chi_{40310}(5011,\cdot)\) \(\chi_{40310}(5041,\cdot)\) \(\chi_{40310}(5071,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{483})$ |
| Fixed field: | Number field defined by a degree 483 polynomial (not computed) |
Values on generators
\((24187,19461,16821)\) → \((1,e\left(\frac{5}{7}\right),e\left(\frac{13}{69}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 40310 }(81, a) \) | \(1\) | \(1\) | \(e\left(\frac{143}{483}\right)\) | \(e\left(\frac{479}{483}\right)\) | \(e\left(\frac{286}{483}\right)\) | \(e\left(\frac{85}{483}\right)\) | \(e\left(\frac{442}{483}\right)\) | \(e\left(\frac{11}{69}\right)\) | \(e\left(\frac{445}{483}\right)\) | \(e\left(\frac{139}{483}\right)\) | \(e\left(\frac{60}{161}\right)\) | \(e\left(\frac{143}{161}\right)\) |