Basic properties
| Modulus: | \(7098\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(85,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.eh
\(\chi_{7098}(85,\cdot)\) \(\chi_{7098}(253,\cdot)\) \(\chi_{7098}(379,\cdot)\) \(\chi_{7098}(505,\cdot)\) \(\chi_{7098}(631,\cdot)\) \(\chi_{7098}(799,\cdot)\) \(\chi_{7098}(1051,\cdot)\) \(\chi_{7098}(1177,\cdot)\) \(\chi_{7098}(1345,\cdot)\) \(\chi_{7098}(1471,\cdot)\) \(\chi_{7098}(1597,\cdot)\) \(\chi_{7098}(1723,\cdot)\) \(\chi_{7098}(1891,\cdot)\) \(\chi_{7098}(2017,\cdot)\) \(\chi_{7098}(2143,\cdot)\) \(\chi_{7098}(2269,\cdot)\) \(\chi_{7098}(2437,\cdot)\) \(\chi_{7098}(2563,\cdot)\) \(\chi_{7098}(2689,\cdot)\) \(\chi_{7098}(2815,\cdot)\) \(\chi_{7098}(2983,\cdot)\) \(\chi_{7098}(3109,\cdot)\) \(\chi_{7098}(3235,\cdot)\) \(\chi_{7098}(3529,\cdot)\) \(\chi_{7098}(3655,\cdot)\) \(\chi_{7098}(3781,\cdot)\) \(\chi_{7098}(3907,\cdot)\) \(\chi_{7098}(4201,\cdot)\) \(\chi_{7098}(4327,\cdot)\) \(\chi_{7098}(4453,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((4733,5071,6931)\) → \((1,1,e\left(\frac{155}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 7098 }(85, a) \) | \(-1\) | \(1\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{53}{156}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{5}{156}\right)\) | \(e\left(\frac{71}{156}\right)\) |