Basic properties
| Modulus: | \(7098\) | |
| Conductor: | \(3549\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3549}(59,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.ep
\(\chi_{7098}(59,\cdot)\) \(\chi_{7098}(227,\cdot)\) \(\chi_{7098}(509,\cdot)\) \(\chi_{7098}(605,\cdot)\) \(\chi_{7098}(635,\cdot)\) \(\chi_{7098}(773,\cdot)\) \(\chi_{7098}(1055,\cdot)\) \(\chi_{7098}(1151,\cdot)\) \(\chi_{7098}(1181,\cdot)\) \(\chi_{7098}(1319,\cdot)\) \(\chi_{7098}(1697,\cdot)\) \(\chi_{7098}(1727,\cdot)\) \(\chi_{7098}(1865,\cdot)\) \(\chi_{7098}(2147,\cdot)\) \(\chi_{7098}(2243,\cdot)\) \(\chi_{7098}(2273,\cdot)\) \(\chi_{7098}(2411,\cdot)\) \(\chi_{7098}(2693,\cdot)\) \(\chi_{7098}(2789,\cdot)\) \(\chi_{7098}(2819,\cdot)\) \(\chi_{7098}(2957,\cdot)\) \(\chi_{7098}(3239,\cdot)\) \(\chi_{7098}(3335,\cdot)\) \(\chi_{7098}(3365,\cdot)\) \(\chi_{7098}(3503,\cdot)\) \(\chi_{7098}(3785,\cdot)\) \(\chi_{7098}(3881,\cdot)\) \(\chi_{7098}(3911,\cdot)\) \(\chi_{7098}(4049,\cdot)\) \(\chi_{7098}(4331,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((4733,5071,6931)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{35}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 7098 }(59, a) \) | \(-1\) | \(1\) | \(e\left(\frac{55}{156}\right)\) | \(e\left(\frac{43}{156}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(1\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{137}{156}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{11}{156}\right)\) |