Basic properties
| Modulus: | \(1476\) | |
| Conductor: | \(1476\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1476.cl
\(\chi_{1476}(7,\cdot)\) \(\chi_{1476}(67,\cdot)\) \(\chi_{1476}(151,\cdot)\) \(\chi_{1476}(175,\cdot)\) \(\chi_{1476}(211,\cdot)\) \(\chi_{1476}(259,\cdot)\) \(\chi_{1476}(391,\cdot)\) \(\chi_{1476}(403,\cdot)\) \(\chi_{1476}(427,\cdot)\) \(\chi_{1476}(439,\cdot)\) \(\chi_{1476}(463,\cdot)\) \(\chi_{1476}(475,\cdot)\) \(\chi_{1476}(499,\cdot)\) \(\chi_{1476}(511,\cdot)\) \(\chi_{1476}(643,\cdot)\) \(\chi_{1476}(691,\cdot)\) \(\chi_{1476}(727,\cdot)\) \(\chi_{1476}(751,\cdot)\) \(\chi_{1476}(835,\cdot)\) \(\chi_{1476}(895,\cdot)\) \(\chi_{1476}(931,\cdot)\) \(\chi_{1476}(967,\cdot)\) \(\chi_{1476}(1003,\cdot)\) \(\chi_{1476}(1051,\cdot)\) \(\chi_{1476}(1159,\cdot)\) \(\chi_{1476}(1183,\cdot)\) \(\chi_{1476}(1195,\cdot)\) \(\chi_{1476}(1219,\cdot)\) \(\chi_{1476}(1327,\cdot)\) \(\chi_{1476}(1375,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((739,821,1441)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{39}{40}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 1476 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{11}{120}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{59}{120}\right)\) | \(e\left(\frac{2}{15}\right)\) |