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 \(\chi_{3549}(41,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.ee
\(\chi_{7098}(41,\cdot)\) \(\chi_{7098}(167,\cdot)\) \(\chi_{7098}(293,\cdot)\) \(\chi_{7098}(461,\cdot)\) \(\chi_{7098}(713,\cdot)\) \(\chi_{7098}(839,\cdot)\) \(\chi_{7098}(1007,\cdot)\) \(\chi_{7098}(1133,\cdot)\) \(\chi_{7098}(1259,\cdot)\) \(\chi_{7098}(1385,\cdot)\) \(\chi_{7098}(1553,\cdot)\) \(\chi_{7098}(1679,\cdot)\) \(\chi_{7098}(1805,\cdot)\) \(\chi_{7098}(1931,\cdot)\) \(\chi_{7098}(2099,\cdot)\) \(\chi_{7098}(2225,\cdot)\) \(\chi_{7098}(2351,\cdot)\) \(\chi_{7098}(2477,\cdot)\) \(\chi_{7098}(2645,\cdot)\) \(\chi_{7098}(2771,\cdot)\) \(\chi_{7098}(2897,\cdot)\) \(\chi_{7098}(3191,\cdot)\) \(\chi_{7098}(3317,\cdot)\) \(\chi_{7098}(3443,\cdot)\) \(\chi_{7098}(3569,\cdot)\) \(\chi_{7098}(3863,\cdot)\) \(\chi_{7098}(3989,\cdot)\) \(\chi_{7098}(4115,\cdot)\) \(\chi_{7098}(4283,\cdot)\) \(\chi_{7098}(4409,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((4733,5071,6931)\) → \((-1,-1,e\left(\frac{85}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 7098 }(41, a) \) | \(-1\) | \(1\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{97}{156}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{43}{156}\right)\) | \(e\left(\frac{49}{156}\right)\) |