Basic properties
| Modulus: | \(9295\) | |
| 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 \(\chi_{169}(107,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9295.cy
\(\chi_{9295}(276,\cdot)\) \(\chi_{9295}(386,\cdot)\) \(\chi_{9295}(1101,\cdot)\) \(\chi_{9295}(1706,\cdot)\) \(\chi_{9295}(1816,\cdot)\) \(\chi_{9295}(2421,\cdot)\) \(\chi_{9295}(2531,\cdot)\) \(\chi_{9295}(3136,\cdot)\) \(\chi_{9295}(3246,\cdot)\) \(\chi_{9295}(3851,\cdot)\) \(\chi_{9295}(3961,\cdot)\) \(\chi_{9295}(4566,\cdot)\) \(\chi_{9295}(4676,\cdot)\) \(\chi_{9295}(5281,\cdot)\) \(\chi_{9295}(5391,\cdot)\) \(\chi_{9295}(5996,\cdot)\) \(\chi_{9295}(6711,\cdot)\) \(\chi_{9295}(6821,\cdot)\) \(\chi_{9295}(7426,\cdot)\) \(\chi_{9295}(7536,\cdot)\) \(\chi_{9295}(8141,\cdot)\) \(\chi_{9295}(8251,\cdot)\) \(\chi_{9295}(8856,\cdot)\) \(\chi_{9295}(8966,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((7437,4226,6931)\) → \((1,1,e\left(\frac{25}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(14\) | \(16\) |
| \( \chi_{ 9295 }(276, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{22}{39}\right)\) |