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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 704.bl
\(\chi_{704}(3,\cdot)\) \(\chi_{704}(27,\cdot)\) \(\chi_{704}(59,\cdot)\) \(\chi_{704}(75,\cdot)\) \(\chi_{704}(91,\cdot)\) \(\chi_{704}(115,\cdot)\) \(\chi_{704}(147,\cdot)\) \(\chi_{704}(163,\cdot)\) \(\chi_{704}(179,\cdot)\) \(\chi_{704}(203,\cdot)\) \(\chi_{704}(235,\cdot)\) \(\chi_{704}(251,\cdot)\) \(\chi_{704}(267,\cdot)\) \(\chi_{704}(291,\cdot)\) \(\chi_{704}(323,\cdot)\) \(\chi_{704}(339,\cdot)\) \(\chi_{704}(355,\cdot)\) \(\chi_{704}(379,\cdot)\) \(\chi_{704}(411,\cdot)\) \(\chi_{704}(427,\cdot)\) \(\chi_{704}(443,\cdot)\) \(\chi_{704}(467,\cdot)\) \(\chi_{704}(499,\cdot)\) \(\chi_{704}(515,\cdot)\) \(\chi_{704}(531,\cdot)\) \(\chi_{704}(555,\cdot)\) \(\chi_{704}(587,\cdot)\) \(\chi_{704}(603,\cdot)\) \(\chi_{704}(619,\cdot)\) \(\chi_{704}(643,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((639,133,321)\) → \((-1,e\left(\frac{9}{16}\right),e\left(\frac{3}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 704 }(603, a) \) | \(-1\) | \(1\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{3}{80}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{19}{80}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) |