Basic properties
| Modulus: | \(7360\) | |
| Conductor: | \(3680\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(88\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3680}(1579,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7360.es
\(\chi_{7360}(199,\cdot)\) \(\chi_{7360}(359,\cdot)\) \(\chi_{7360}(839,\cdot)\) \(\chi_{7360}(999,\cdot)\) \(\chi_{7360}(1079,\cdot)\) \(\chi_{7360}(1239,\cdot)\) \(\chi_{7360}(1399,\cdot)\) \(\chi_{7360}(1479,\cdot)\) \(\chi_{7360}(1719,\cdot)\) \(\chi_{7360}(1799,\cdot)\) \(\chi_{7360}(2039,\cdot)\) \(\chi_{7360}(2199,\cdot)\) \(\chi_{7360}(2679,\cdot)\) \(\chi_{7360}(2839,\cdot)\) \(\chi_{7360}(2919,\cdot)\) \(\chi_{7360}(3079,\cdot)\) \(\chi_{7360}(3239,\cdot)\) \(\chi_{7360}(3319,\cdot)\) \(\chi_{7360}(3559,\cdot)\) \(\chi_{7360}(3639,\cdot)\) \(\chi_{7360}(3879,\cdot)\) \(\chi_{7360}(4039,\cdot)\) \(\chi_{7360}(4519,\cdot)\) \(\chi_{7360}(4679,\cdot)\) \(\chi_{7360}(4759,\cdot)\) \(\chi_{7360}(4919,\cdot)\) \(\chi_{7360}(5079,\cdot)\) \(\chi_{7360}(5159,\cdot)\) \(\chi_{7360}(5399,\cdot)\) \(\chi_{7360}(5479,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{88})$ |
| Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((1151,5061,4417,6721)\) → \((-1,e\left(\frac{5}{8}\right),-1,e\left(\frac{17}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
| \( \chi_{ 7360 }(199, a) \) | \(1\) | \(1\) | \(e\left(\frac{21}{88}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{51}{88}\right)\) | \(e\left(\frac{61}{88}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{41}{88}\right)\) | \(e\left(\frac{15}{88}\right)\) | \(e\left(\frac{63}{88}\right)\) | \(e\left(\frac{69}{88}\right)\) |