Basic properties
| Modulus: | \(7098\) | |
| Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1183}(235,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.ct
\(\chi_{7098}(79,\cdot)\) \(\chi_{7098}(235,\cdot)\) \(\chi_{7098}(625,\cdot)\) \(\chi_{7098}(781,\cdot)\) \(\chi_{7098}(1171,\cdot)\) \(\chi_{7098}(1327,\cdot)\) \(\chi_{7098}(1717,\cdot)\) \(\chi_{7098}(1873,\cdot)\) \(\chi_{7098}(2263,\cdot)\) \(\chi_{7098}(2419,\cdot)\) \(\chi_{7098}(2809,\cdot)\) \(\chi_{7098}(2965,\cdot)\) \(\chi_{7098}(3355,\cdot)\) \(\chi_{7098}(3511,\cdot)\) \(\chi_{7098}(3901,\cdot)\) \(\chi_{7098}(4447,\cdot)\) \(\chi_{7098}(4603,\cdot)\) \(\chi_{7098}(4993,\cdot)\) \(\chi_{7098}(5149,\cdot)\) \(\chi_{7098}(5539,\cdot)\) \(\chi_{7098}(5695,\cdot)\) \(\chi_{7098}(6241,\cdot)\) \(\chi_{7098}(6631,\cdot)\) \(\chi_{7098}(6787,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((4733,5071,6931)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{6}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 7098 }(235, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{3}{13}\right)\) |