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 \(\chi_{1183}(753,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.df
\(\chi_{7098}(25,\cdot)\) \(\chi_{7098}(415,\cdot)\) \(\chi_{7098}(571,\cdot)\) \(\chi_{7098}(961,\cdot)\) \(\chi_{7098}(1117,\cdot)\) \(\chi_{7098}(1507,\cdot)\) \(\chi_{7098}(1663,\cdot)\) \(\chi_{7098}(2053,\cdot)\) \(\chi_{7098}(2209,\cdot)\) \(\chi_{7098}(2599,\cdot)\) \(\chi_{7098}(2755,\cdot)\) \(\chi_{7098}(3145,\cdot)\) \(\chi_{7098}(3301,\cdot)\) \(\chi_{7098}(3691,\cdot)\) \(\chi_{7098}(3847,\cdot)\) \(\chi_{7098}(4237,\cdot)\) \(\chi_{7098}(4783,\cdot)\) \(\chi_{7098}(4939,\cdot)\) \(\chi_{7098}(5329,\cdot)\) \(\chi_{7098}(5485,\cdot)\) \(\chi_{7098}(5875,\cdot)\) \(\chi_{7098}(6031,\cdot)\) \(\chi_{7098}(6577,\cdot)\) \(\chi_{7098}(6967,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((4733,5071,6931)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{9}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 7098 }(5485, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{11}{26}\right)\) |