Basic properties
| Modulus: | \(7098\) | |
| Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1183}(61,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.db
\(\chi_{7098}(61,\cdot)\) \(\chi_{7098}(367,\cdot)\) \(\chi_{7098}(607,\cdot)\) \(\chi_{7098}(913,\cdot)\) \(\chi_{7098}(1153,\cdot)\) \(\chi_{7098}(1459,\cdot)\) \(\chi_{7098}(1699,\cdot)\) \(\chi_{7098}(2245,\cdot)\) \(\chi_{7098}(2551,\cdot)\) \(\chi_{7098}(2791,\cdot)\) \(\chi_{7098}(3097,\cdot)\) \(\chi_{7098}(3337,\cdot)\) \(\chi_{7098}(3643,\cdot)\) \(\chi_{7098}(3883,\cdot)\) \(\chi_{7098}(4189,\cdot)\) \(\chi_{7098}(4429,\cdot)\) \(\chi_{7098}(4735,\cdot)\) \(\chi_{7098}(4975,\cdot)\) \(\chi_{7098}(5281,\cdot)\) \(\chi_{7098}(5521,\cdot)\) \(\chi_{7098}(5827,\cdot)\) \(\chi_{7098}(6067,\cdot)\) \(\chi_{7098}(6373,\cdot)\) \(\chi_{7098}(6919,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((4733,5071,6931)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{35}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 7098 }(61, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{61}{78}\right)\) |