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 \(\chi_{3549}(1343,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.dz
\(\chi_{7098}(251,\cdot)\) \(\chi_{7098}(335,\cdot)\) \(\chi_{7098}(797,\cdot)\) \(\chi_{7098}(881,\cdot)\) \(\chi_{7098}(1343,\cdot)\) \(\chi_{7098}(1427,\cdot)\) \(\chi_{7098}(1889,\cdot)\) \(\chi_{7098}(1973,\cdot)\) \(\chi_{7098}(2435,\cdot)\) \(\chi_{7098}(2519,\cdot)\) \(\chi_{7098}(2981,\cdot)\) \(\chi_{7098}(3611,\cdot)\) \(\chi_{7098}(4073,\cdot)\) \(\chi_{7098}(4157,\cdot)\) \(\chi_{7098}(4619,\cdot)\) \(\chi_{7098}(4703,\cdot)\) \(\chi_{7098}(5165,\cdot)\) \(\chi_{7098}(5249,\cdot)\) \(\chi_{7098}(5711,\cdot)\) \(\chi_{7098}(5795,\cdot)\) \(\chi_{7098}(6257,\cdot)\) \(\chi_{7098}(6341,\cdot)\) \(\chi_{7098}(6803,\cdot)\) \(\chi_{7098}(6887,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((4733,5071,6931)\) → \((-1,-1,e\left(\frac{7}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 7098 }(1343, a) \) | \(1\) | \(1\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{49}{78}\right)\) |