Basic properties
| Modulus: | \(7220\) | |
| Conductor: | \(1444\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(114\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1444}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7220.cd
\(\chi_{7220}(31,\cdot)\) \(\chi_{7220}(331,\cdot)\) \(\chi_{7220}(411,\cdot)\) \(\chi_{7220}(711,\cdot)\) \(\chi_{7220}(1091,\cdot)\) \(\chi_{7220}(1171,\cdot)\) \(\chi_{7220}(1471,\cdot)\) \(\chi_{7220}(1551,\cdot)\) \(\chi_{7220}(1851,\cdot)\) \(\chi_{7220}(1931,\cdot)\) \(\chi_{7220}(2231,\cdot)\) \(\chi_{7220}(2311,\cdot)\) \(\chi_{7220}(2611,\cdot)\) \(\chi_{7220}(2691,\cdot)\) \(\chi_{7220}(2991,\cdot)\) \(\chi_{7220}(3071,\cdot)\) \(\chi_{7220}(3371,\cdot)\) \(\chi_{7220}(3451,\cdot)\) \(\chi_{7220}(3751,\cdot)\) \(\chi_{7220}(3831,\cdot)\) \(\chi_{7220}(4131,\cdot)\) \(\chi_{7220}(4211,\cdot)\) \(\chi_{7220}(4511,\cdot)\) \(\chi_{7220}(4591,\cdot)\) \(\chi_{7220}(4891,\cdot)\) \(\chi_{7220}(4971,\cdot)\) \(\chi_{7220}(5271,\cdot)\) \(\chi_{7220}(5351,\cdot)\) \(\chi_{7220}(5651,\cdot)\) \(\chi_{7220}(5731,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((3611,5777,6861)\) → \((-1,1,e\left(\frac{101}{114}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 7220 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{57}\right)\) | \(e\left(\frac{15}{38}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{33}{38}\right)\) | \(e\left(\frac{55}{114}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{5}{114}\right)\) | \(e\left(\frac{97}{114}\right)\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{7}{114}\right)\) |