Basic properties
| Modulus: | \(7098\) | |
| Conductor: | \(507\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{507}(86,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.cv
\(\chi_{7098}(281,\cdot)\) \(\chi_{7098}(785,\cdot)\) \(\chi_{7098}(827,\cdot)\) \(\chi_{7098}(1331,\cdot)\) \(\chi_{7098}(1373,\cdot)\) \(\chi_{7098}(1877,\cdot)\) \(\chi_{7098}(1919,\cdot)\) \(\chi_{7098}(2423,\cdot)\) \(\chi_{7098}(2969,\cdot)\) \(\chi_{7098}(3011,\cdot)\) \(\chi_{7098}(3515,\cdot)\) \(\chi_{7098}(3557,\cdot)\) \(\chi_{7098}(4061,\cdot)\) \(\chi_{7098}(4103,\cdot)\) \(\chi_{7098}(4607,\cdot)\) \(\chi_{7098}(4649,\cdot)\) \(\chi_{7098}(5153,\cdot)\) \(\chi_{7098}(5195,\cdot)\) \(\chi_{7098}(5699,\cdot)\) \(\chi_{7098}(5741,\cdot)\) \(\chi_{7098}(6245,\cdot)\) \(\chi_{7098}(6287,\cdot)\) \(\chi_{7098}(6791,\cdot)\) \(\chi_{7098}(6833,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((4733,5071,6931)\) → \((-1,1,e\left(\frac{41}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 7098 }(4649, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(i\) | \(1\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{27}{52}\right)\) |