Basic properties
| Modulus: | \(221760\) | |
| Conductor: | \(110880\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{110880}(109987,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 221760.dsc
\(\chi_{221760}(103,\cdot)\) \(\chi_{221760}(3127,\cdot)\) \(\chi_{221760}(25063,\cdot)\) \(\chi_{221760}(28087,\cdot)\) \(\chi_{221760}(30343,\cdot)\) \(\chi_{221760}(33367,\cdot)\) \(\chi_{221760}(35143,\cdot)\) \(\chi_{221760}(40423,\cdot)\) \(\chi_{221760}(58327,\cdot)\) \(\chi_{221760}(63607,\cdot)\) \(\chi_{221760}(68407,\cdot)\) \(\chi_{221760}(73687,\cdot)\) \(\chi_{221760}(75463,\cdot)\) \(\chi_{221760}(80743,\cdot)\) \(\chi_{221760}(105703,\cdot)\) \(\chi_{221760}(108727,\cdot)\) \(\chi_{221760}(110983,\cdot)\) \(\chi_{221760}(114007,\cdot)\) \(\chi_{221760}(135943,\cdot)\) \(\chi_{221760}(138967,\cdot)\) \(\chi_{221760}(141223,\cdot)\) \(\chi_{221760}(144247,\cdot)\) \(\chi_{221760}(146023,\cdot)\) \(\chi_{221760}(151303,\cdot)\) \(\chi_{221760}(169207,\cdot)\) \(\chi_{221760}(174487,\cdot)\) \(\chi_{221760}(179287,\cdot)\) \(\chi_{221760}(184567,\cdot)\) \(\chi_{221760}(186343,\cdot)\) \(\chi_{221760}(191623,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((48511,124741,98561,133057,190081,141121)\) → \((-1,e\left(\frac{3}{8}\right),e\left(\frac{2}{3}\right),i,e\left(\frac{1}{6}\right),e\left(\frac{3}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 221760 }(68407, a) \) | \(-1\) | \(1\) | \(e\left(\frac{97}{120}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{59}{120}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{19}{120}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{11}{20}\right)\) |