Basic properties
| Modulus: | \(7744\) | |
| Conductor: | \(704\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{704}(403,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7744.bx
\(\chi_{7744}(403,\cdot)\) \(\chi_{7744}(475,\cdot)\) \(\chi_{7744}(699,\cdot)\) \(\chi_{7744}(723,\cdot)\) \(\chi_{7744}(1371,\cdot)\) \(\chi_{7744}(1443,\cdot)\) \(\chi_{7744}(1667,\cdot)\) \(\chi_{7744}(1691,\cdot)\) \(\chi_{7744}(2339,\cdot)\) \(\chi_{7744}(2411,\cdot)\) \(\chi_{7744}(2635,\cdot)\) \(\chi_{7744}(2659,\cdot)\) \(\chi_{7744}(3307,\cdot)\) \(\chi_{7744}(3379,\cdot)\) \(\chi_{7744}(3603,\cdot)\) \(\chi_{7744}(3627,\cdot)\) \(\chi_{7744}(4275,\cdot)\) \(\chi_{7744}(4347,\cdot)\) \(\chi_{7744}(4571,\cdot)\) \(\chi_{7744}(4595,\cdot)\) \(\chi_{7744}(5243,\cdot)\) \(\chi_{7744}(5315,\cdot)\) \(\chi_{7744}(5539,\cdot)\) \(\chi_{7744}(5563,\cdot)\) \(\chi_{7744}(6211,\cdot)\) \(\chi_{7744}(6283,\cdot)\) \(\chi_{7744}(6507,\cdot)\) \(\chi_{7744}(6531,\cdot)\) \(\chi_{7744}(7179,\cdot)\) \(\chi_{7744}(7251,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((5567,4357,6657)\) → \((-1,e\left(\frac{7}{16}\right),e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 7744 }(403, a) \) | \(1\) | \(1\) | \(e\left(\frac{33}{80}\right)\) | \(e\left(\frac{19}{80}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{21}{80}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) |