Basic properties
| Modulus: | \(9295\) | |
| Conductor: | \(845\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{845}(199,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9295.ec
\(\chi_{9295}(199,\cdot)\) \(\chi_{9295}(309,\cdot)\) \(\chi_{9295}(914,\cdot)\) \(\chi_{9295}(1024,\cdot)\) \(\chi_{9295}(1629,\cdot)\) \(\chi_{9295}(1739,\cdot)\) \(\chi_{9295}(2454,\cdot)\) \(\chi_{9295}(3059,\cdot)\) \(\chi_{9295}(3169,\cdot)\) \(\chi_{9295}(3774,\cdot)\) \(\chi_{9295}(3884,\cdot)\) \(\chi_{9295}(4489,\cdot)\) \(\chi_{9295}(4599,\cdot)\) \(\chi_{9295}(5204,\cdot)\) \(\chi_{9295}(5314,\cdot)\) \(\chi_{9295}(5919,\cdot)\) \(\chi_{9295}(6029,\cdot)\) \(\chi_{9295}(6634,\cdot)\) \(\chi_{9295}(6744,\cdot)\) \(\chi_{9295}(7349,\cdot)\) \(\chi_{9295}(8064,\cdot)\) \(\chi_{9295}(8174,\cdot)\) \(\chi_{9295}(8779,\cdot)\) \(\chi_{9295}(8889,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((7437,4226,6931)\) → \((-1,1,e\left(\frac{67}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(14\) | \(16\) |
| \( \chi_{ 9295 }(199, a) \) | \(1\) | \(1\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{17}{39}\right)\) |