Basic properties
| Modulus: | \(7360\) | |
| Conductor: | \(736\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(88\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{736}(563,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7360.ep
\(\chi_{7360}(471,\cdot)\) \(\chi_{7360}(631,\cdot)\) \(\chi_{7360}(711,\cdot)\) \(\chi_{7360}(871,\cdot)\) \(\chi_{7360}(1031,\cdot)\) \(\chi_{7360}(1111,\cdot)\) \(\chi_{7360}(1351,\cdot)\) \(\chi_{7360}(1431,\cdot)\) \(\chi_{7360}(1671,\cdot)\) \(\chi_{7360}(1831,\cdot)\) \(\chi_{7360}(2311,\cdot)\) \(\chi_{7360}(2471,\cdot)\) \(\chi_{7360}(2551,\cdot)\) \(\chi_{7360}(2711,\cdot)\) \(\chi_{7360}(2871,\cdot)\) \(\chi_{7360}(2951,\cdot)\) \(\chi_{7360}(3191,\cdot)\) \(\chi_{7360}(3271,\cdot)\) \(\chi_{7360}(3511,\cdot)\) \(\chi_{7360}(3671,\cdot)\) \(\chi_{7360}(4151,\cdot)\) \(\chi_{7360}(4311,\cdot)\) \(\chi_{7360}(4391,\cdot)\) \(\chi_{7360}(4551,\cdot)\) \(\chi_{7360}(4711,\cdot)\) \(\chi_{7360}(4791,\cdot)\) \(\chi_{7360}(5031,\cdot)\) \(\chi_{7360}(5111,\cdot)\) \(\chi_{7360}(5351,\cdot)\) \(\chi_{7360}(5511,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{88})$ |
| Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((1151,5061,4417,6721)\) → \((-1,e\left(\frac{7}{8}\right),1,e\left(\frac{9}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
| \( \chi_{ 7360 }(471, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{88}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{49}{88}\right)\) | \(e\left(\frac{75}{88}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{67}{88}\right)\) | \(e\left(\frac{61}{88}\right)\) | \(e\left(\frac{1}{88}\right)\) | \(e\left(\frac{87}{88}\right)\) |