Basic properties
| Modulus: | \(1476\) | |
| Conductor: | \(369\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{369}(65,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1476.ck
\(\chi_{1476}(29,\cdot)\) \(\chi_{1476}(65,\cdot)\) \(\chi_{1476}(101,\cdot)\) \(\chi_{1476}(149,\cdot)\) \(\chi_{1476}(257,\cdot)\) \(\chi_{1476}(281,\cdot)\) \(\chi_{1476}(293,\cdot)\) \(\chi_{1476}(317,\cdot)\) \(\chi_{1476}(425,\cdot)\) \(\chi_{1476}(473,\cdot)\) \(\chi_{1476}(509,\cdot)\) \(\chi_{1476}(545,\cdot)\) \(\chi_{1476}(581,\cdot)\) \(\chi_{1476}(641,\cdot)\) \(\chi_{1476}(725,\cdot)\) \(\chi_{1476}(749,\cdot)\) \(\chi_{1476}(785,\cdot)\) \(\chi_{1476}(833,\cdot)\) \(\chi_{1476}(965,\cdot)\) \(\chi_{1476}(977,\cdot)\) \(\chi_{1476}(1001,\cdot)\) \(\chi_{1476}(1013,\cdot)\) \(\chi_{1476}(1037,\cdot)\) \(\chi_{1476}(1049,\cdot)\) \(\chi_{1476}(1073,\cdot)\) \(\chi_{1476}(1085,\cdot)\) \(\chi_{1476}(1217,\cdot)\) \(\chi_{1476}(1265,\cdot)\) \(\chi_{1476}(1301,\cdot)\) \(\chi_{1476}(1325,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((739,821,1441)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{13}{40}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 1476 }(65, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{49}{120}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{13}{30}\right)\) |