Basic properties
| Modulus: | \(2704\) | |
| Conductor: | \(676\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{676}(123,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2704.cq
\(\chi_{2704}(15,\cdot)\) \(\chi_{2704}(63,\cdot)\) \(\chi_{2704}(111,\cdot)\) \(\chi_{2704}(175,\cdot)\) \(\chi_{2704}(223,\cdot)\) \(\chi_{2704}(271,\cdot)\) \(\chi_{2704}(383,\cdot)\) \(\chi_{2704}(431,\cdot)\) \(\chi_{2704}(479,\cdot)\) \(\chi_{2704}(527,\cdot)\) \(\chi_{2704}(591,\cdot)\) \(\chi_{2704}(639,\cdot)\) \(\chi_{2704}(687,\cdot)\) \(\chi_{2704}(735,\cdot)\) \(\chi_{2704}(799,\cdot)\) \(\chi_{2704}(847,\cdot)\) \(\chi_{2704}(895,\cdot)\) \(\chi_{2704}(943,\cdot)\) \(\chi_{2704}(1007,\cdot)\) \(\chi_{2704}(1055,\cdot)\) \(\chi_{2704}(1151,\cdot)\) \(\chi_{2704}(1215,\cdot)\) \(\chi_{2704}(1311,\cdot)\) \(\chi_{2704}(1359,\cdot)\) \(\chi_{2704}(1423,\cdot)\) \(\chi_{2704}(1471,\cdot)\) \(\chi_{2704}(1519,\cdot)\) \(\chi_{2704}(1567,\cdot)\) \(\chi_{2704}(1631,\cdot)\) \(\chi_{2704}(1679,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((2367,677,1185)\) → \((-1,1,e\left(\frac{53}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 2704 }(799, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{133}{156}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{77}{156}\right)\) | \(e\left(\frac{107}{156}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{2}{3}\right)\) |