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 \(\chi_{2205}(1123,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4410.ej
\(\chi_{4410}(103,\cdot)\) \(\chi_{4410}(367,\cdot)\) \(\chi_{4410}(493,\cdot)\) \(\chi_{4410}(733,\cdot)\) \(\chi_{4410}(997,\cdot)\) \(\chi_{4410}(1123,\cdot)\) \(\chi_{4410}(1237,\cdot)\) \(\chi_{4410}(1363,\cdot)\) \(\chi_{4410}(1627,\cdot)\) \(\chi_{4410}(1753,\cdot)\) \(\chi_{4410}(1867,\cdot)\) \(\chi_{4410}(1993,\cdot)\) \(\chi_{4410}(2257,\cdot)\) \(\chi_{4410}(2497,\cdot)\) \(\chi_{4410}(2623,\cdot)\) \(\chi_{4410}(2887,\cdot)\) \(\chi_{4410}(3013,\cdot)\) \(\chi_{4410}(3127,\cdot)\) \(\chi_{4410}(3517,\cdot)\) \(\chi_{4410}(3643,\cdot)\) \(\chi_{4410}(3757,\cdot)\) \(\chi_{4410}(3883,\cdot)\) \(\chi_{4410}(4273,\cdot)\) \(\chi_{4410}(4387,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((3431,2647,1081)\) → \((e\left(\frac{2}{3}\right),-i,e\left(\frac{31}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 4410 }(1123, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(-1\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{29}{84}\right)\) |