Basic properties
| Modulus: | \(7098\) | |
| Conductor: | \(507\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{507}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.dw
\(\chi_{7098}(29,\cdot)\) \(\chi_{7098}(113,\cdot)\) \(\chi_{7098}(575,\cdot)\) \(\chi_{7098}(659,\cdot)\) \(\chi_{7098}(1121,\cdot)\) \(\chi_{7098}(1751,\cdot)\) \(\chi_{7098}(2213,\cdot)\) \(\chi_{7098}(2297,\cdot)\) \(\chi_{7098}(2759,\cdot)\) \(\chi_{7098}(2843,\cdot)\) \(\chi_{7098}(3305,\cdot)\) \(\chi_{7098}(3389,\cdot)\) \(\chi_{7098}(3851,\cdot)\) \(\chi_{7098}(3935,\cdot)\) \(\chi_{7098}(4397,\cdot)\) \(\chi_{7098}(4481,\cdot)\) \(\chi_{7098}(4943,\cdot)\) \(\chi_{7098}(5027,\cdot)\) \(\chi_{7098}(5489,\cdot)\) \(\chi_{7098}(5573,\cdot)\) \(\chi_{7098}(6035,\cdot)\) \(\chi_{7098}(6119,\cdot)\) \(\chi_{7098}(6581,\cdot)\) \(\chi_{7098}(6665,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((4733,5071,6931)\) → \((-1,1,e\left(\frac{10}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 7098 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{23}{78}\right)\) |