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 \(\chi_{3549}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.ed
\(\chi_{7098}(5,\cdot)\) \(\chi_{7098}(47,\cdot)\) \(\chi_{7098}(395,\cdot)\) \(\chi_{7098}(551,\cdot)\) \(\chi_{7098}(593,\cdot)\) \(\chi_{7098}(941,\cdot)\) \(\chi_{7098}(983,\cdot)\) \(\chi_{7098}(1097,\cdot)\) \(\chi_{7098}(1139,\cdot)\) \(\chi_{7098}(1487,\cdot)\) \(\chi_{7098}(1529,\cdot)\) \(\chi_{7098}(1643,\cdot)\) \(\chi_{7098}(1685,\cdot)\) \(\chi_{7098}(2033,\cdot)\) \(\chi_{7098}(2075,\cdot)\) \(\chi_{7098}(2189,\cdot)\) \(\chi_{7098}(2231,\cdot)\) \(\chi_{7098}(2579,\cdot)\) \(\chi_{7098}(2621,\cdot)\) \(\chi_{7098}(2735,\cdot)\) \(\chi_{7098}(2777,\cdot)\) \(\chi_{7098}(3125,\cdot)\) \(\chi_{7098}(3167,\cdot)\) \(\chi_{7098}(3323,\cdot)\) \(\chi_{7098}(3671,\cdot)\) \(\chi_{7098}(3713,\cdot)\) \(\chi_{7098}(3827,\cdot)\) \(\chi_{7098}(3869,\cdot)\) \(\chi_{7098}(4217,\cdot)\) \(\chi_{7098}(4259,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((4733,5071,6931)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{3}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 7098 }(5, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{156}\right)\) | \(e\left(\frac{121}{156}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{7}{156}\right)\) | \(e\left(\frac{59}{156}\right)\) | \(e\left(\frac{47}{52}\right)\) |