Basic properties
| Modulus: | \(4235\) | |
| Conductor: | \(605\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{605}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4235.cx
\(\chi_{4235}(29,\cdot)\) \(\chi_{4235}(134,\cdot)\) \(\chi_{4235}(204,\cdot)\) \(\chi_{4235}(414,\cdot)\) \(\chi_{4235}(519,\cdot)\) \(\chi_{4235}(589,\cdot)\) \(\chi_{4235}(624,\cdot)\) \(\chi_{4235}(799,\cdot)\) \(\chi_{4235}(904,\cdot)\) \(\chi_{4235}(974,\cdot)\) \(\chi_{4235}(1009,\cdot)\) \(\chi_{4235}(1184,\cdot)\) \(\chi_{4235}(1289,\cdot)\) \(\chi_{4235}(1359,\cdot)\) \(\chi_{4235}(1394,\cdot)\) \(\chi_{4235}(1569,\cdot)\) \(\chi_{4235}(1674,\cdot)\) \(\chi_{4235}(1744,\cdot)\) \(\chi_{4235}(1779,\cdot)\) \(\chi_{4235}(1954,\cdot)\) \(\chi_{4235}(2059,\cdot)\) \(\chi_{4235}(2129,\cdot)\) \(\chi_{4235}(2164,\cdot)\) \(\chi_{4235}(2444,\cdot)\) \(\chi_{4235}(2549,\cdot)\) \(\chi_{4235}(2724,\cdot)\) \(\chi_{4235}(2829,\cdot)\) \(\chi_{4235}(2899,\cdot)\) \(\chi_{4235}(2934,\cdot)\) \(\chi_{4235}(3109,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((2542,1816,2906)\) → \((-1,1,e\left(\frac{17}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(12\) | \(13\) | \(16\) | \(17\) |
| \( \chi_{ 4235 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{83}{110}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{34}{55}\right)\) | \(e\left(\frac{4}{55}\right)\) |