Basic properties
| Modulus: | \(7098\) | |
| Conductor: | \(3549\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3549}(95,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.dt
\(\chi_{7098}(95,\cdot)\) \(\chi_{7098}(569,\cdot)\) \(\chi_{7098}(641,\cdot)\) \(\chi_{7098}(1115,\cdot)\) \(\chi_{7098}(1187,\cdot)\) \(\chi_{7098}(1661,\cdot)\) \(\chi_{7098}(1733,\cdot)\) \(\chi_{7098}(2207,\cdot)\) \(\chi_{7098}(2279,\cdot)\) \(\chi_{7098}(2753,\cdot)\) \(\chi_{7098}(2825,\cdot)\) \(\chi_{7098}(3299,\cdot)\) \(\chi_{7098}(3371,\cdot)\) \(\chi_{7098}(3845,\cdot)\) \(\chi_{7098}(3917,\cdot)\) \(\chi_{7098}(4391,\cdot)\) \(\chi_{7098}(4463,\cdot)\) \(\chi_{7098}(4937,\cdot)\) \(\chi_{7098}(5009,\cdot)\) \(\chi_{7098}(5483,\cdot)\) \(\chi_{7098}(6029,\cdot)\) \(\chi_{7098}(6101,\cdot)\) \(\chi_{7098}(6575,\cdot)\) \(\chi_{7098}(6647,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((4733,5071,6931)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{37}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 7098 }(95, a) \) | \(-1\) | \(1\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{32}{39}\right)\) |