Basic properties
| Modulus: | \(723\) | |
| Conductor: | \(241\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(240\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{241}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 723.bm
\(\chi_{723}(7,\cdot)\) \(\chi_{723}(13,\cdot)\) \(\chi_{723}(31,\cdot)\) \(\chi_{723}(34,\cdot)\) \(\chi_{723}(37,\cdot)\) \(\chi_{723}(46,\cdot)\) \(\chi_{723}(52,\cdot)\) \(\chi_{723}(55,\cdot)\) \(\chi_{723}(70,\cdot)\) \(\chi_{723}(109,\cdot)\) \(\chi_{723}(112,\cdot)\) \(\chi_{723}(127,\cdot)\) \(\chi_{723}(142,\cdot)\) \(\chi_{723}(157,\cdot)\) \(\chi_{723}(163,\cdot)\) \(\chi_{723}(172,\cdot)\) \(\chi_{723}(175,\cdot)\) \(\chi_{723}(190,\cdot)\) \(\chi_{723}(199,\cdot)\) \(\chi_{723}(202,\cdot)\) \(\chi_{723}(280,\cdot)\) \(\chi_{723}(283,\cdot)\) \(\chi_{723}(292,\cdot)\) \(\chi_{723}(307,\cdot)\) \(\chi_{723}(310,\cdot)\) \(\chi_{723}(319,\cdot)\) \(\chi_{723}(325,\cdot)\) \(\chi_{723}(340,\cdot)\) \(\chi_{723}(355,\cdot)\) \(\chi_{723}(370,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{240})$ |
| Fixed field: | Number field defined by a degree 240 polynomial (not computed) |
Values on generators
\((242,7)\) → \((1,e\left(\frac{47}{240}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 723 }(13, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{47}{240}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{43}{48}\right)\) | \(e\left(\frac{49}{240}\right)\) | \(e\left(\frac{97}{240}\right)\) | \(e\left(\frac{5}{6}\right)\) |