Basic properties
Modulus: | \(4410\) | |
Conductor: | \(735\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{735}(32,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4410.ef
\(\chi_{4410}(53,\cdot)\) \(\chi_{4410}(107,\cdot)\) \(\chi_{4410}(233,\cdot)\) \(\chi_{4410}(683,\cdot)\) \(\chi_{4410}(737,\cdot)\) \(\chi_{4410}(1187,\cdot)\) \(\chi_{4410}(1313,\cdot)\) \(\chi_{4410}(1367,\cdot)\) \(\chi_{4410}(1493,\cdot)\) \(\chi_{4410}(1817,\cdot)\) \(\chi_{4410}(1943,\cdot)\) \(\chi_{4410}(1997,\cdot)\) \(\chi_{4410}(2123,\cdot)\) \(\chi_{4410}(2447,\cdot)\) \(\chi_{4410}(2573,\cdot)\) \(\chi_{4410}(2753,\cdot)\) \(\chi_{4410}(3077,\cdot)\) \(\chi_{4410}(3257,\cdot)\) \(\chi_{4410}(3383,\cdot)\) \(\chi_{4410}(3707,\cdot)\) \(\chi_{4410}(3833,\cdot)\) \(\chi_{4410}(3887,\cdot)\) \(\chi_{4410}(4013,\cdot)\) \(\chi_{4410}(4337,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((3431,2647,1081)\) → \((-1,i,e\left(\frac{2}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 4410 }(3707, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{9}{28}\right)\) |