Basic properties
| Modulus: | \(704\) | |
| Conductor: | \(704\) | 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 704.bk
\(\chi_{704}(19,\cdot)\) \(\chi_{704}(35,\cdot)\) \(\chi_{704}(51,\cdot)\) \(\chi_{704}(83,\cdot)\) \(\chi_{704}(107,\cdot)\) \(\chi_{704}(123,\cdot)\) \(\chi_{704}(139,\cdot)\) \(\chi_{704}(171,\cdot)\) \(\chi_{704}(195,\cdot)\) \(\chi_{704}(211,\cdot)\) \(\chi_{704}(227,\cdot)\) \(\chi_{704}(259,\cdot)\) \(\chi_{704}(283,\cdot)\) \(\chi_{704}(299,\cdot)\) \(\chi_{704}(315,\cdot)\) \(\chi_{704}(347,\cdot)\) \(\chi_{704}(371,\cdot)\) \(\chi_{704}(387,\cdot)\) \(\chi_{704}(403,\cdot)\) \(\chi_{704}(435,\cdot)\) \(\chi_{704}(459,\cdot)\) \(\chi_{704}(475,\cdot)\) \(\chi_{704}(491,\cdot)\) \(\chi_{704}(523,\cdot)\) \(\chi_{704}(547,\cdot)\) \(\chi_{704}(563,\cdot)\) \(\chi_{704}(579,\cdot)\) \(\chi_{704}(611,\cdot)\) \(\chi_{704}(635,\cdot)\) \(\chi_{704}(651,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((639,133,321)\) → \((-1,e\left(\frac{3}{16}\right),e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 704 }(579, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) |