Basic properties
| Modulus: | \(7744\) | |
| Conductor: | \(7744\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(880\) | 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.cz
\(\chi_{7744}(5,\cdot)\) \(\chi_{7744}(37,\cdot)\) \(\chi_{7744}(53,\cdot)\) \(\chi_{7744}(69,\cdot)\) \(\chi_{7744}(93,\cdot)\) \(\chi_{7744}(125,\cdot)\) \(\chi_{7744}(141,\cdot)\) \(\chi_{7744}(157,\cdot)\) \(\chi_{7744}(181,\cdot)\) \(\chi_{7744}(213,\cdot)\) \(\chi_{7744}(229,\cdot)\) \(\chi_{7744}(301,\cdot)\) \(\chi_{7744}(317,\cdot)\) \(\chi_{7744}(333,\cdot)\) \(\chi_{7744}(357,\cdot)\) \(\chi_{7744}(389,\cdot)\) \(\chi_{7744}(405,\cdot)\) \(\chi_{7744}(421,\cdot)\) \(\chi_{7744}(445,\cdot)\) \(\chi_{7744}(477,\cdot)\) \(\chi_{7744}(509,\cdot)\) \(\chi_{7744}(533,\cdot)\) \(\chi_{7744}(581,\cdot)\) \(\chi_{7744}(597,\cdot)\) \(\chi_{7744}(621,\cdot)\) \(\chi_{7744}(653,\cdot)\) \(\chi_{7744}(669,\cdot)\) \(\chi_{7744}(685,\cdot)\) \(\chi_{7744}(709,\cdot)\) \(\chi_{7744}(741,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{880})$ |
| Fixed field: | Number field defined by a degree 880 polynomial (not computed) |
Values on generators
\((5567,4357,6657)\) → \((1,e\left(\frac{1}{16}\right),e\left(\frac{37}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 7744 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{743}{880}\right)\) | \(e\left(\frac{147}{440}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{777}{880}\right)\) | \(e\left(\frac{51}{220}\right)\) | \(e\left(\frac{157}{220}\right)\) | \(e\left(\frac{241}{880}\right)\) | \(e\left(\frac{127}{176}\right)\) | \(e\left(\frac{85}{88}\right)\) |