Basic properties
| Modulus: | \(7360\) | |
| Conductor: | \(7360\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(176\) | 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 7360.fn
\(\chi_{7360}(37,\cdot)\) \(\chi_{7360}(333,\cdot)\) \(\chi_{7360}(493,\cdot)\) \(\chi_{7360}(517,\cdot)\) \(\chi_{7360}(573,\cdot)\) \(\chi_{7360}(677,\cdot)\) \(\chi_{7360}(733,\cdot)\) \(\chi_{7360}(757,\cdot)\) \(\chi_{7360}(893,\cdot)\) \(\chi_{7360}(917,\cdot)\) \(\chi_{7360}(973,\cdot)\) \(\chi_{7360}(1077,\cdot)\) \(\chi_{7360}(1157,\cdot)\) \(\chi_{7360}(1213,\cdot)\) \(\chi_{7360}(1293,\cdot)\) \(\chi_{7360}(1397,\cdot)\) \(\chi_{7360}(1477,\cdot)\) \(\chi_{7360}(1533,\cdot)\) \(\chi_{7360}(1693,\cdot)\) \(\chi_{7360}(1717,\cdot)\) \(\chi_{7360}(1877,\cdot)\) \(\chi_{7360}(2173,\cdot)\) \(\chi_{7360}(2333,\cdot)\) \(\chi_{7360}(2357,\cdot)\) \(\chi_{7360}(2413,\cdot)\) \(\chi_{7360}(2517,\cdot)\) \(\chi_{7360}(2573,\cdot)\) \(\chi_{7360}(2597,\cdot)\) \(\chi_{7360}(2733,\cdot)\) \(\chi_{7360}(2757,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{176})$ |
| Fixed field: | Number field defined by a degree 176 polynomial (not computed) |
Values on generators
\((1151,5061,4417,6721)\) → \((1,e\left(\frac{9}{16}\right),i,e\left(\frac{21}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
| \( \chi_{ 7360 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{125}{176}\right)\) | \(e\left(\frac{1}{88}\right)\) | \(e\left(\frac{37}{88}\right)\) | \(e\left(\frac{71}{176}\right)\) | \(e\left(\frac{97}{176}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{133}{176}\right)\) | \(e\left(\frac{127}{176}\right)\) | \(e\left(\frac{23}{176}\right)\) | \(e\left(\frac{153}{176}\right)\) |