Basic properties
| Modulus: | \(4235\) | |
| Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(55\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{121}(36,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4235.cf
\(\chi_{4235}(36,\cdot)\) \(\chi_{4235}(71,\cdot)\) \(\chi_{4235}(141,\cdot)\) \(\chi_{4235}(246,\cdot)\) \(\chi_{4235}(421,\cdot)\) \(\chi_{4235}(456,\cdot)\) \(\chi_{4235}(526,\cdot)\) \(\chi_{4235}(631,\cdot)\) \(\chi_{4235}(806,\cdot)\) \(\chi_{4235}(841,\cdot)\) \(\chi_{4235}(911,\cdot)\) \(\chi_{4235}(1016,\cdot)\) \(\chi_{4235}(1191,\cdot)\) \(\chi_{4235}(1226,\cdot)\) \(\chi_{4235}(1296,\cdot)\) \(\chi_{4235}(1401,\cdot)\) \(\chi_{4235}(1611,\cdot)\) \(\chi_{4235}(1681,\cdot)\) \(\chi_{4235}(1786,\cdot)\) \(\chi_{4235}(1961,\cdot)\) \(\chi_{4235}(1996,\cdot)\) \(\chi_{4235}(2171,\cdot)\) \(\chi_{4235}(2346,\cdot)\) \(\chi_{4235}(2381,\cdot)\) \(\chi_{4235}(2451,\cdot)\) \(\chi_{4235}(2556,\cdot)\) \(\chi_{4235}(2731,\cdot)\) \(\chi_{4235}(2766,\cdot)\) \(\chi_{4235}(2836,\cdot)\) \(\chi_{4235}(2941,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 55 polynomial |
Values on generators
\((2542,1816,2906)\) → \((1,1,e\left(\frac{34}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(12\) | \(13\) | \(16\) | \(17\) |
| \( \chi_{ 4235 }(36, a) \) | \(1\) | \(1\) | \(e\left(\frac{34}{55}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{24}{55}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{16}{55}\right)\) |