Basic properties
| Modulus: | \(7098\) | |
| Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1183}(109,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.ef
\(\chi_{7098}(109,\cdot)\) \(\chi_{7098}(151,\cdot)\) \(\chi_{7098}(499,\cdot)\) \(\chi_{7098}(541,\cdot)\) \(\chi_{7098}(655,\cdot)\) \(\chi_{7098}(697,\cdot)\) \(\chi_{7098}(1045,\cdot)\) \(\chi_{7098}(1087,\cdot)\) \(\chi_{7098}(1201,\cdot)\) \(\chi_{7098}(1243,\cdot)\) \(\chi_{7098}(1633,\cdot)\) \(\chi_{7098}(1747,\cdot)\) \(\chi_{7098}(2137,\cdot)\) \(\chi_{7098}(2179,\cdot)\) \(\chi_{7098}(2293,\cdot)\) \(\chi_{7098}(2335,\cdot)\) \(\chi_{7098}(2683,\cdot)\) \(\chi_{7098}(2725,\cdot)\) \(\chi_{7098}(2839,\cdot)\) \(\chi_{7098}(2881,\cdot)\) \(\chi_{7098}(3229,\cdot)\) \(\chi_{7098}(3271,\cdot)\) \(\chi_{7098}(3385,\cdot)\) \(\chi_{7098}(3427,\cdot)\) \(\chi_{7098}(3775,\cdot)\) \(\chi_{7098}(3931,\cdot)\) \(\chi_{7098}(3973,\cdot)\) \(\chi_{7098}(4321,\cdot)\) \(\chi_{7098}(4363,\cdot)\) \(\chi_{7098}(4477,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((4733,5071,6931)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{19}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 7098 }(109, a) \) | \(-1\) | \(1\) | \(e\left(\frac{97}{156}\right)\) | \(e\left(\frac{47}{156}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{53}{156}\right)\) | \(e\left(\frac{79}{156}\right)\) | \(e\left(\frac{3}{52}\right)\) |