Basic properties
| Modulus: | \(9295\) | |
| Conductor: | \(845\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{845}(232,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9295.em
\(\chi_{9295}(232,\cdot)\) \(\chi_{9295}(353,\cdot)\) \(\chi_{9295}(397,\cdot)\) \(\chi_{9295}(903,\cdot)\) \(\chi_{9295}(947,\cdot)\) \(\chi_{9295}(1068,\cdot)\) \(\chi_{9295}(1112,\cdot)\) \(\chi_{9295}(1618,\cdot)\) \(\chi_{9295}(1662,\cdot)\) \(\chi_{9295}(1783,\cdot)\) \(\chi_{9295}(1827,\cdot)\) \(\chi_{9295}(2333,\cdot)\) \(\chi_{9295}(2377,\cdot)\) \(\chi_{9295}(2498,\cdot)\) \(\chi_{9295}(2542,\cdot)\) \(\chi_{9295}(3048,\cdot)\) \(\chi_{9295}(3092,\cdot)\) \(\chi_{9295}(3213,\cdot)\) \(\chi_{9295}(3257,\cdot)\) \(\chi_{9295}(3763,\cdot)\) \(\chi_{9295}(3928,\cdot)\) \(\chi_{9295}(3972,\cdot)\) \(\chi_{9295}(4478,\cdot)\) \(\chi_{9295}(4522,\cdot)\) \(\chi_{9295}(4687,\cdot)\) \(\chi_{9295}(5193,\cdot)\) \(\chi_{9295}(5237,\cdot)\) \(\chi_{9295}(5358,\cdot)\) \(\chi_{9295}(5402,\cdot)\) \(\chi_{9295}(5908,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((7437,4226,6931)\) → \((i,1,e\left(\frac{43}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(14\) | \(16\) |
| \( \chi_{ 9295 }(232, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{145}{156}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{71}{156}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{4}{39}\right)\) |