Basic properties
| Modulus: | \(8112\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(120,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8112.ds
\(\chi_{8112}(289,\cdot)\) \(\chi_{8112}(913,\cdot)\) \(\chi_{8112}(1153,\cdot)\) \(\chi_{8112}(1537,\cdot)\) \(\chi_{8112}(1777,\cdot)\) \(\chi_{8112}(2161,\cdot)\) \(\chi_{8112}(2401,\cdot)\) \(\chi_{8112}(2785,\cdot)\) \(\chi_{8112}(3025,\cdot)\) \(\chi_{8112}(3409,\cdot)\) \(\chi_{8112}(3649,\cdot)\) \(\chi_{8112}(4273,\cdot)\) \(\chi_{8112}(4657,\cdot)\) \(\chi_{8112}(4897,\cdot)\) \(\chi_{8112}(5281,\cdot)\) \(\chi_{8112}(5521,\cdot)\) \(\chi_{8112}(5905,\cdot)\) \(\chi_{8112}(6145,\cdot)\) \(\chi_{8112}(6529,\cdot)\) \(\chi_{8112}(6769,\cdot)\) \(\chi_{8112}(7153,\cdot)\) \(\chi_{8112}(7393,\cdot)\) \(\chi_{8112}(7777,\cdot)\) \(\chi_{8112}(8017,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((5071,6085,2705,3889)\) → \((1,1,1,e\left(\frac{34}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8112 }(289, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{5}{39}\right)\) |