Basic properties
| Modulus: | \(723\) | |
| Conductor: | \(723\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | 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 723.bl
\(\chi_{723}(20,\cdot)\) \(\chi_{723}(29,\cdot)\) \(\chi_{723}(50,\cdot)\) \(\chi_{723}(53,\cdot)\) \(\chi_{723}(59,\cdot)\) \(\chi_{723}(77,\cdot)\) \(\chi_{723}(80,\cdot)\) \(\chi_{723}(161,\cdot)\) \(\chi_{723}(164,\cdot)\) \(\chi_{723}(182,\cdot)\) \(\chi_{723}(188,\cdot)\) \(\chi_{723}(191,\cdot)\) \(\chi_{723}(212,\cdot)\) \(\chi_{723}(221,\cdot)\) \(\chi_{723}(290,\cdot)\) \(\chi_{723}(308,\cdot)\) \(\chi_{723}(374,\cdot)\) \(\chi_{723}(407,\cdot)\) \(\chi_{723}(410,\cdot)\) \(\chi_{723}(437,\cdot)\) \(\chi_{723}(464,\cdot)\) \(\chi_{723}(470,\cdot)\) \(\chi_{723}(479,\cdot)\) \(\chi_{723}(485,\cdot)\) \(\chi_{723}(494,\cdot)\) \(\chi_{723}(500,\cdot)\) \(\chi_{723}(527,\cdot)\) \(\chi_{723}(554,\cdot)\) \(\chi_{723}(557,\cdot)\) \(\chi_{723}(590,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((242,7)\) → \((-1,e\left(\frac{77}{120}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 723 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(i\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{19}{120}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{2}{3}\right)\) |