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 \(\chi_{3549}(821,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.eb
\(\chi_{7098}(137,\cdot)\) \(\chi_{7098}(275,\cdot)\) \(\chi_{7098}(305,\cdot)\) \(\chi_{7098}(401,\cdot)\) \(\chi_{7098}(683,\cdot)\) \(\chi_{7098}(821,\cdot)\) \(\chi_{7098}(851,\cdot)\) \(\chi_{7098}(947,\cdot)\) \(\chi_{7098}(1229,\cdot)\) \(\chi_{7098}(1367,\cdot)\) \(\chi_{7098}(1397,\cdot)\) \(\chi_{7098}(1493,\cdot)\) \(\chi_{7098}(1775,\cdot)\) \(\chi_{7098}(1913,\cdot)\) \(\chi_{7098}(1943,\cdot)\) \(\chi_{7098}(2039,\cdot)\) \(\chi_{7098}(2321,\cdot)\) \(\chi_{7098}(2459,\cdot)\) \(\chi_{7098}(2489,\cdot)\) \(\chi_{7098}(2585,\cdot)\) \(\chi_{7098}(2867,\cdot)\) \(\chi_{7098}(3005,\cdot)\) \(\chi_{7098}(3035,\cdot)\) \(\chi_{7098}(3413,\cdot)\) \(\chi_{7098}(3551,\cdot)\) \(\chi_{7098}(3581,\cdot)\) \(\chi_{7098}(3677,\cdot)\) \(\chi_{7098}(3959,\cdot)\) \(\chi_{7098}(4097,\cdot)\) \(\chi_{7098}(4127,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((4733,5071,6931)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{49}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 7098 }(821, a) \) | \(1\) | \(1\) | \(e\left(\frac{155}{156}\right)\) | \(e\left(\frac{29}{156}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(1\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{145}{156}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{31}{156}\right)\) |