Basic properties
| Modulus: | \(7803\) | |
| Conductor: | \(289\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(136\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{289}(9,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7803.bm
\(\chi_{7803}(298,\cdot)\) \(\chi_{7803}(325,\cdot)\) \(\chi_{7803}(406,\cdot)\) \(\chi_{7803}(433,\cdot)\) \(\chi_{7803}(784,\cdot)\) \(\chi_{7803}(865,\cdot)\) \(\chi_{7803}(892,\cdot)\) \(\chi_{7803}(1216,\cdot)\) \(\chi_{7803}(1243,\cdot)\) \(\chi_{7803}(1324,\cdot)\) \(\chi_{7803}(1351,\cdot)\) \(\chi_{7803}(1675,\cdot)\) \(\chi_{7803}(1702,\cdot)\) \(\chi_{7803}(1783,\cdot)\) \(\chi_{7803}(1810,\cdot)\) \(\chi_{7803}(2134,\cdot)\) \(\chi_{7803}(2161,\cdot)\) \(\chi_{7803}(2242,\cdot)\) \(\chi_{7803}(2269,\cdot)\) \(\chi_{7803}(2593,\cdot)\) \(\chi_{7803}(2620,\cdot)\) \(\chi_{7803}(2701,\cdot)\) \(\chi_{7803}(2728,\cdot)\) \(\chi_{7803}(3052,\cdot)\) \(\chi_{7803}(3079,\cdot)\) \(\chi_{7803}(3160,\cdot)\) \(\chi_{7803}(3187,\cdot)\) \(\chi_{7803}(3511,\cdot)\) \(\chi_{7803}(3538,\cdot)\) \(\chi_{7803}(3619,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{136})$ |
| Fixed field: | Number field defined by a degree 136 polynomial (not computed) |
Values on generators
\((2891,2026)\) → \((1,e\left(\frac{1}{136}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 7803 }(298, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{68}\right)\) | \(e\left(\frac{27}{34}\right)\) | \(e\left(\frac{93}{136}\right)\) | \(e\left(\frac{19}{136}\right)\) | \(e\left(\frac{13}{68}\right)\) | \(e\left(\frac{11}{136}\right)\) | \(e\left(\frac{23}{136}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{73}{136}\right)\) | \(e\left(\frac{10}{17}\right)\) |