Basic properties
| Modulus: | \(4410\) | |
| Conductor: | \(2205\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2205}(47,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4410.eo
\(\chi_{4410}(47,\cdot)\) \(\chi_{4410}(173,\cdot)\) \(\chi_{4410}(437,\cdot)\) \(\chi_{4410}(563,\cdot)\) \(\chi_{4410}(677,\cdot)\) \(\chi_{4410}(1067,\cdot)\) \(\chi_{4410}(1193,\cdot)\) \(\chi_{4410}(1307,\cdot)\) \(\chi_{4410}(1433,\cdot)\) \(\chi_{4410}(1823,\cdot)\) \(\chi_{4410}(1937,\cdot)\) \(\chi_{4410}(2063,\cdot)\) \(\chi_{4410}(2327,\cdot)\) \(\chi_{4410}(2453,\cdot)\) \(\chi_{4410}(2693,\cdot)\) \(\chi_{4410}(2957,\cdot)\) \(\chi_{4410}(3083,\cdot)\) \(\chi_{4410}(3197,\cdot)\) \(\chi_{4410}(3323,\cdot)\) \(\chi_{4410}(3587,\cdot)\) \(\chi_{4410}(3713,\cdot)\) \(\chi_{4410}(3827,\cdot)\) \(\chi_{4410}(3953,\cdot)\) \(\chi_{4410}(4217,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((3431,2647,1081)\) → \((e\left(\frac{1}{6}\right),i,e\left(\frac{5}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 4410 }(47, a) \) | \(-1\) | \(1\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{11}{84}\right)\) |