Basic properties
| Modulus: | \(9295\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(56,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9295.eb
\(\chi_{9295}(56,\cdot)\) \(\chi_{9295}(166,\cdot)\) \(\chi_{9295}(771,\cdot)\) \(\chi_{9295}(881,\cdot)\) \(\chi_{9295}(1486,\cdot)\) \(\chi_{9295}(1596,\cdot)\) \(\chi_{9295}(2201,\cdot)\) \(\chi_{9295}(2311,\cdot)\) \(\chi_{9295}(2916,\cdot)\) \(\chi_{9295}(3026,\cdot)\) \(\chi_{9295}(3631,\cdot)\) \(\chi_{9295}(4346,\cdot)\) \(\chi_{9295}(4456,\cdot)\) \(\chi_{9295}(5061,\cdot)\) \(\chi_{9295}(5171,\cdot)\) \(\chi_{9295}(5776,\cdot)\) \(\chi_{9295}(5886,\cdot)\) \(\chi_{9295}(6491,\cdot)\) \(\chi_{9295}(6601,\cdot)\) \(\chi_{9295}(7206,\cdot)\) \(\chi_{9295}(7316,\cdot)\) \(\chi_{9295}(8031,\cdot)\) \(\chi_{9295}(8636,\cdot)\) \(\chi_{9295}(8746,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((7437,4226,6931)\) → \((1,1,e\left(\frac{55}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(14\) | \(16\) |
| \( \chi_{ 9295 }(56, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{32}{39}\right)\) |