Basic properties
| Modulus: | \(7744\) | |
| Conductor: | \(7744\) | 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 7744.co
\(\chi_{7744}(45,\cdot)\) \(\chi_{7744}(133,\cdot)\) \(\chi_{7744}(221,\cdot)\) \(\chi_{7744}(309,\cdot)\) \(\chi_{7744}(397,\cdot)\) \(\chi_{7744}(573,\cdot)\) \(\chi_{7744}(661,\cdot)\) \(\chi_{7744}(749,\cdot)\) \(\chi_{7744}(837,\cdot)\) \(\chi_{7744}(925,\cdot)\) \(\chi_{7744}(1013,\cdot)\) \(\chi_{7744}(1101,\cdot)\) \(\chi_{7744}(1189,\cdot)\) \(\chi_{7744}(1277,\cdot)\) \(\chi_{7744}(1365,\cdot)\) \(\chi_{7744}(1541,\cdot)\) \(\chi_{7744}(1629,\cdot)\) \(\chi_{7744}(1717,\cdot)\) \(\chi_{7744}(1805,\cdot)\) \(\chi_{7744}(1893,\cdot)\) \(\chi_{7744}(1981,\cdot)\) \(\chi_{7744}(2069,\cdot)\) \(\chi_{7744}(2157,\cdot)\) \(\chi_{7744}(2245,\cdot)\) \(\chi_{7744}(2333,\cdot)\) \(\chi_{7744}(2509,\cdot)\) \(\chi_{7744}(2597,\cdot)\) \(\chi_{7744}(2685,\cdot)\) \(\chi_{7744}(2773,\cdot)\) \(\chi_{7744}(2861,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{176})$ |
| Fixed field: | Number field defined by a degree 176 polynomial (not computed) |
Values on generators
\((5567,4357,6657)\) → \((1,e\left(\frac{7}{16}\right),e\left(\frac{3}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 7744 }(45, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{109}{176}\right)\) | \(e\left(\frac{25}{88}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{19}{176}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{123}{176}\right)\) | \(e\left(\frac{105}{176}\right)\) | \(e\left(\frac{19}{88}\right)\) |