Basic properties
| Modulus: | \(9295\) | |
| Conductor: | \(1859\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(130\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1859}(181,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9295.ei
\(\chi_{9295}(181,\cdot)\) \(\chi_{9295}(246,\cdot)\) \(\chi_{9295}(311,\cdot)\) \(\chi_{9295}(636,\cdot)\) \(\chi_{9295}(896,\cdot)\) \(\chi_{9295}(961,\cdot)\) \(\chi_{9295}(1026,\cdot)\) \(\chi_{9295}(1611,\cdot)\) \(\chi_{9295}(1676,\cdot)\) \(\chi_{9295}(1741,\cdot)\) \(\chi_{9295}(2066,\cdot)\) \(\chi_{9295}(2326,\cdot)\) \(\chi_{9295}(2391,\cdot)\) \(\chi_{9295}(2456,\cdot)\) \(\chi_{9295}(2781,\cdot)\) \(\chi_{9295}(3106,\cdot)\) \(\chi_{9295}(3171,\cdot)\) \(\chi_{9295}(3496,\cdot)\) \(\chi_{9295}(3756,\cdot)\) \(\chi_{9295}(3821,\cdot)\) \(\chi_{9295}(4211,\cdot)\) \(\chi_{9295}(4471,\cdot)\) \(\chi_{9295}(4536,\cdot)\) \(\chi_{9295}(4601,\cdot)\) \(\chi_{9295}(4926,\cdot)\) \(\chi_{9295}(5186,\cdot)\) \(\chi_{9295}(5251,\cdot)\) \(\chi_{9295}(5316,\cdot)\) \(\chi_{9295}(5641,\cdot)\) \(\chi_{9295}(5901,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{65})$ |
| Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((7437,4226,6931)\) → \((1,e\left(\frac{2}{5}\right),e\left(\frac{21}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(14\) | \(16\) |
| \( \chi_{ 9295 }(181, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{130}\right)\) | \(e\left(\frac{23}{65}\right)\) | \(e\left(\frac{27}{65}\right)\) | \(e\left(\frac{73}{130}\right)\) | \(e\left(\frac{29}{130}\right)\) | \(e\left(\frac{81}{130}\right)\) | \(e\left(\frac{46}{65}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{28}{65}\right)\) | \(e\left(\frac{54}{65}\right)\) |