Basic properties
| Modulus: | \(2704\) | |
| Conductor: | \(676\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{676}(47,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2704.ci
\(\chi_{2704}(31,\cdot)\) \(\chi_{2704}(47,\cdot)\) \(\chi_{2704}(255,\cdot)\) \(\chi_{2704}(447,\cdot)\) \(\chi_{2704}(463,\cdot)\) \(\chi_{2704}(655,\cdot)\) \(\chi_{2704}(671,\cdot)\) \(\chi_{2704}(863,\cdot)\) \(\chi_{2704}(879,\cdot)\) \(\chi_{2704}(1071,\cdot)\) \(\chi_{2704}(1087,\cdot)\) \(\chi_{2704}(1279,\cdot)\) \(\chi_{2704}(1295,\cdot)\) \(\chi_{2704}(1487,\cdot)\) \(\chi_{2704}(1503,\cdot)\) \(\chi_{2704}(1695,\cdot)\) \(\chi_{2704}(1711,\cdot)\) \(\chi_{2704}(1903,\cdot)\) \(\chi_{2704}(1919,\cdot)\) \(\chi_{2704}(2111,\cdot)\) \(\chi_{2704}(2319,\cdot)\) \(\chi_{2704}(2335,\cdot)\) \(\chi_{2704}(2527,\cdot)\) \(\chi_{2704}(2543,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((2367,677,1185)\) → \((-1,1,e\left(\frac{21}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 2704 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(-i\) | \(e\left(\frac{15}{52}\right)\) | \(1\) |