Basic properties
| Modulus: | \(7220\) | |
| Conductor: | \(7220\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(228\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7220.ci
\(\chi_{7220}(7,\cdot)\) \(\chi_{7220}(83,\cdot)\) \(\chi_{7220}(87,\cdot)\) \(\chi_{7220}(163,\cdot)\) \(\chi_{7220}(387,\cdot)\) \(\chi_{7220}(463,\cdot)\) \(\chi_{7220}(467,\cdot)\) \(\chi_{7220}(543,\cdot)\) \(\chi_{7220}(767,\cdot)\) \(\chi_{7220}(843,\cdot)\) \(\chi_{7220}(847,\cdot)\) \(\chi_{7220}(923,\cdot)\) \(\chi_{7220}(1147,\cdot)\) \(\chi_{7220}(1223,\cdot)\) \(\chi_{7220}(1227,\cdot)\) \(\chi_{7220}(1303,\cdot)\) \(\chi_{7220}(1527,\cdot)\) \(\chi_{7220}(1603,\cdot)\) \(\chi_{7220}(1607,\cdot)\) \(\chi_{7220}(1683,\cdot)\) \(\chi_{7220}(1907,\cdot)\) \(\chi_{7220}(1983,\cdot)\) \(\chi_{7220}(1987,\cdot)\) \(\chi_{7220}(2063,\cdot)\) \(\chi_{7220}(2287,\cdot)\) \(\chi_{7220}(2363,\cdot)\) \(\chi_{7220}(2367,\cdot)\) \(\chi_{7220}(2443,\cdot)\) \(\chi_{7220}(2667,\cdot)\) \(\chi_{7220}(2743,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{228})$ |
| Fixed field: | Number field defined by a degree 228 polynomial (not computed) |
Values on generators
\((3611,5777,6861)\) → \((-1,i,e\left(\frac{25}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 7220 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{228}\right)\) | \(e\left(\frac{41}{76}\right)\) | \(e\left(\frac{49}{114}\right)\) | \(e\left(\frac{9}{38}\right)\) | \(e\left(\frac{11}{228}\right)\) | \(e\left(\frac{85}{228}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{65}{228}\right)\) | \(e\left(\frac{49}{76}\right)\) | \(e\left(\frac{109}{114}\right)\) |