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 \(\chi_{2205}(428,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4410.ec
\(\chi_{4410}(113,\cdot)\) \(\chi_{4410}(407,\cdot)\) \(\chi_{4410}(533,\cdot)\) \(\chi_{4410}(617,\cdot)\) \(\chi_{4410}(743,\cdot)\) \(\chi_{4410}(1037,\cdot)\) \(\chi_{4410}(1163,\cdot)\) \(\chi_{4410}(1247,\cdot)\) \(\chi_{4410}(1793,\cdot)\) \(\chi_{4410}(1877,\cdot)\) \(\chi_{4410}(2003,\cdot)\) \(\chi_{4410}(2297,\cdot)\) \(\chi_{4410}(2423,\cdot)\) \(\chi_{4410}(2507,\cdot)\) \(\chi_{4410}(2633,\cdot)\) \(\chi_{4410}(2927,\cdot)\) \(\chi_{4410}(3053,\cdot)\) \(\chi_{4410}(3263,\cdot)\) \(\chi_{4410}(3557,\cdot)\) \(\chi_{4410}(3683,\cdot)\) \(\chi_{4410}(3767,\cdot)\) \(\chi_{4410}(3893,\cdot)\) \(\chi_{4410}(4187,\cdot)\) \(\chi_{4410}(4397,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((3431,2647,1081)\) → \((e\left(\frac{5}{6}\right),-i,e\left(\frac{2}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 4410 }(2633, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(-1\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{25}{84}\right)\) |