Basic properties
Modulus: | \(723\) | |
Conductor: | \(723\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(240\) | 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 723.bn
\(\chi_{723}(14,\cdot)\) \(\chi_{723}(35,\cdot)\) \(\chi_{723}(56,\cdot)\) \(\chi_{723}(62,\cdot)\) \(\chi_{723}(68,\cdot)\) \(\chi_{723}(71,\cdot)\) \(\chi_{723}(74,\cdot)\) \(\chi_{723}(86,\cdot)\) \(\chi_{723}(92,\cdot)\) \(\chi_{723}(95,\cdot)\) \(\chi_{723}(104,\cdot)\) \(\chi_{723}(110,\cdot)\) \(\chi_{723}(131,\cdot)\) \(\chi_{723}(137,\cdot)\) \(\chi_{723}(146,\cdot)\) \(\chi_{723}(149,\cdot)\) \(\chi_{723}(155,\cdot)\) \(\chi_{723}(167,\cdot)\) \(\chi_{723}(170,\cdot)\) \(\chi_{723}(173,\cdot)\) \(\chi_{723}(179,\cdot)\) \(\chi_{723}(185,\cdot)\) \(\chi_{723}(206,\cdot)\) \(\chi_{723}(227,\cdot)\) \(\chi_{723}(248,\cdot)\) \(\chi_{723}(254,\cdot)\) \(\chi_{723}(272,\cdot)\) \(\chi_{723}(275,\cdot)\) \(\chi_{723}(278,\cdot)\) \(\chi_{723}(287,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{240})$ |
Fixed field: | Number field defined by a degree 240 polynomial (not computed) |
Values on generators
\((242,7)\) → \((-1,e\left(\frac{191}{240}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 723 }(14, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{191}{240}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{19}{48}\right)\) | \(e\left(\frac{97}{240}\right)\) | \(e\left(\frac{121}{240}\right)\) | \(e\left(\frac{5}{6}\right)\) |