Basic properties
| Modulus: | \(7220\) | |
| Conductor: | \(7220\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(76\) | 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.bv
\(\chi_{7220}(267,\cdot)\) \(\chi_{7220}(343,\cdot)\) \(\chi_{7220}(647,\cdot)\) \(\chi_{7220}(1027,\cdot)\) \(\chi_{7220}(1103,\cdot)\) \(\chi_{7220}(1407,\cdot)\) \(\chi_{7220}(1483,\cdot)\) \(\chi_{7220}(1787,\cdot)\) \(\chi_{7220}(1863,\cdot)\) \(\chi_{7220}(2243,\cdot)\) \(\chi_{7220}(2547,\cdot)\) \(\chi_{7220}(2623,\cdot)\) \(\chi_{7220}(2927,\cdot)\) \(\chi_{7220}(3003,\cdot)\) \(\chi_{7220}(3307,\cdot)\) \(\chi_{7220}(3383,\cdot)\) \(\chi_{7220}(3687,\cdot)\) \(\chi_{7220}(3763,\cdot)\) \(\chi_{7220}(4067,\cdot)\) \(\chi_{7220}(4143,\cdot)\) \(\chi_{7220}(4447,\cdot)\) \(\chi_{7220}(4523,\cdot)\) \(\chi_{7220}(4827,\cdot)\) \(\chi_{7220}(4903,\cdot)\) \(\chi_{7220}(5207,\cdot)\) \(\chi_{7220}(5283,\cdot)\) \(\chi_{7220}(5587,\cdot)\) \(\chi_{7220}(5663,\cdot)\) \(\chi_{7220}(5967,\cdot)\) \(\chi_{7220}(6043,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{76})$ |
| Fixed field: | Number field defined by a degree 76 polynomial |
Values on generators
\((3611,5777,6861)\) → \((-1,i,e\left(\frac{11}{19}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 7220 }(267, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{76}\right)\) | \(e\left(\frac{45}{76}\right)\) | \(e\left(\frac{17}{38}\right)\) | \(e\left(\frac{21}{38}\right)\) | \(e\left(\frac{17}{76}\right)\) | \(e\left(\frac{7}{76}\right)\) | \(e\left(\frac{6}{19}\right)\) | \(e\left(\frac{59}{76}\right)\) | \(e\left(\frac{13}{76}\right)\) | \(e\left(\frac{13}{38}\right)\) |