Basic properties
| Modulus: | \(723\) | |
| Conductor: | \(241\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{241}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 723.bi
\(\chi_{723}(28,\cdot)\) \(\chi_{723}(43,\cdot)\) \(\chi_{723}(73,\cdot)\) \(\chi_{723}(85,\cdot)\) \(\chi_{723}(103,\cdot)\) \(\chi_{723}(124,\cdot)\) \(\chi_{723}(136,\cdot)\) \(\chi_{723}(139,\cdot)\) \(\chi_{723}(148,\cdot)\) \(\chi_{723}(184,\cdot)\) \(\chi_{723}(208,\cdot)\) \(\chi_{723}(220,\cdot)\) \(\chi_{723}(262,\cdot)\) \(\chi_{723}(274,\cdot)\) \(\chi_{723}(298,\cdot)\) \(\chi_{723}(334,\cdot)\) \(\chi_{723}(343,\cdot)\) \(\chi_{723}(346,\cdot)\) \(\chi_{723}(358,\cdot)\) \(\chi_{723}(379,\cdot)\) \(\chi_{723}(397,\cdot)\) \(\chi_{723}(409,\cdot)\) \(\chi_{723}(439,\cdot)\) \(\chi_{723}(454,\cdot)\) \(\chi_{723}(499,\cdot)\) \(\chi_{723}(505,\cdot)\) \(\chi_{723}(508,\cdot)\) \(\chi_{723}(583,\cdot)\) \(\chi_{723}(622,\cdot)\) \(\chi_{723}(697,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((242,7)\) → \((1,e\left(\frac{73}{80}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 723 }(43, a) \) | \(-1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(-i\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{71}{80}\right)\) | \(e\left(\frac{23}{80}\right)\) | \(-1\) |