Basic properties
| Modulus: | \(1275\) | |
| Conductor: | \(1275\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | 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 1275.cp
\(\chi_{1275}(11,\cdot)\) \(\chi_{1275}(41,\cdot)\) \(\chi_{1275}(56,\cdot)\) \(\chi_{1275}(71,\cdot)\) \(\chi_{1275}(116,\cdot)\) \(\chi_{1275}(131,\cdot)\) \(\chi_{1275}(146,\cdot)\) \(\chi_{1275}(266,\cdot)\) \(\chi_{1275}(296,\cdot)\) \(\chi_{1275}(311,\cdot)\) \(\chi_{1275}(371,\cdot)\) \(\chi_{1275}(386,\cdot)\) \(\chi_{1275}(431,\cdot)\) \(\chi_{1275}(521,\cdot)\) \(\chi_{1275}(566,\cdot)\) \(\chi_{1275}(581,\cdot)\) \(\chi_{1275}(641,\cdot)\) \(\chi_{1275}(656,\cdot)\) \(\chi_{1275}(686,\cdot)\) \(\chi_{1275}(806,\cdot)\) \(\chi_{1275}(821,\cdot)\) \(\chi_{1275}(836,\cdot)\) \(\chi_{1275}(881,\cdot)\) \(\chi_{1275}(896,\cdot)\) \(\chi_{1275}(911,\cdot)\) \(\chi_{1275}(941,\cdot)\) \(\chi_{1275}(1031,\cdot)\) \(\chi_{1275}(1061,\cdot)\) \(\chi_{1275}(1091,\cdot)\) \(\chi_{1275}(1136,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((851,52,751)\) → \((-1,e\left(\frac{2}{5}\right),e\left(\frac{5}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(19\) | \(22\) |
| \( \chi_{ 1275 }(56, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{7}{80}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{29}{80}\right)\) |