Basic properties
| Modulus: | \(43120\) | |
| Conductor: | \(4312\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4312}(2227,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 43120.rl
\(\chi_{43120}(71,\cdot)\) \(\chi_{43120}(631,\cdot)\) \(\chi_{43120}(1191,\cdot)\) \(\chi_{43120}(3991,\cdot)\) \(\chi_{43120}(6231,\cdot)\) \(\chi_{43120}(6791,\cdot)\) \(\chi_{43120}(10151,\cdot)\) \(\chi_{43120}(12391,\cdot)\) \(\chi_{43120}(12951,\cdot)\) \(\chi_{43120}(13511,\cdot)\) \(\chi_{43120}(16311,\cdot)\) \(\chi_{43120}(18551,\cdot)\) \(\chi_{43120}(19671,\cdot)\) \(\chi_{43120}(22471,\cdot)\) \(\chi_{43120}(24711,\cdot)\) \(\chi_{43120}(25271,\cdot)\) \(\chi_{43120}(25831,\cdot)\) \(\chi_{43120}(28631,\cdot)\) \(\chi_{43120}(31431,\cdot)\) \(\chi_{43120}(31991,\cdot)\) \(\chi_{43120}(37031,\cdot)\) \(\chi_{43120}(37591,\cdot)\) \(\chi_{43120}(38151,\cdot)\) \(\chi_{43120}(40951,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((5391,32341,34497,42241,11761)\) → \((-1,-1,1,e\left(\frac{4}{7}\right),e\left(\frac{2}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 43120 }(71, a) \) | \(-1\) | \(1\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{41}{70}\right)\) |