Basic properties
| Modulus: | \(4235\) | |
| Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{121}(2,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4235.cr
\(\chi_{4235}(106,\cdot)\) \(\chi_{4235}(211,\cdot)\) \(\chi_{4235}(281,\cdot)\) \(\chi_{4235}(316,\cdot)\) \(\chi_{4235}(491,\cdot)\) \(\chi_{4235}(666,\cdot)\) \(\chi_{4235}(701,\cdot)\) \(\chi_{4235}(876,\cdot)\) \(\chi_{4235}(981,\cdot)\) \(\chi_{4235}(1051,\cdot)\) \(\chi_{4235}(1261,\cdot)\) \(\chi_{4235}(1366,\cdot)\) \(\chi_{4235}(1436,\cdot)\) \(\chi_{4235}(1471,\cdot)\) \(\chi_{4235}(1646,\cdot)\) \(\chi_{4235}(1751,\cdot)\) \(\chi_{4235}(1821,\cdot)\) \(\chi_{4235}(1856,\cdot)\) \(\chi_{4235}(2031,\cdot)\) \(\chi_{4235}(2136,\cdot)\) \(\chi_{4235}(2206,\cdot)\) \(\chi_{4235}(2241,\cdot)\) \(\chi_{4235}(2416,\cdot)\) \(\chi_{4235}(2521,\cdot)\) \(\chi_{4235}(2591,\cdot)\) \(\chi_{4235}(2626,\cdot)\) \(\chi_{4235}(2801,\cdot)\) \(\chi_{4235}(2906,\cdot)\) \(\chi_{4235}(2976,\cdot)\) \(\chi_{4235}(3011,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((2542,1816,2906)\) → \((1,1,e\left(\frac{1}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(12\) | \(13\) | \(16\) | \(17\) |
| \( \chi_{ 4235 }(2906, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{110}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{89}{110}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{49}{110}\right)\) |