Basic properties
| Modulus: | \(1470\) | |
| 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 \(\chi_{735}(47,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1470.bs
\(\chi_{1470}(17,\cdot)\) \(\chi_{1470}(47,\cdot)\) \(\chi_{1470}(143,\cdot)\) \(\chi_{1470}(173,\cdot)\) \(\chi_{1470}(257,\cdot)\) \(\chi_{1470}(353,\cdot)\) \(\chi_{1470}(383,\cdot)\) \(\chi_{1470}(437,\cdot)\) \(\chi_{1470}(467,\cdot)\) \(\chi_{1470}(563,\cdot)\) \(\chi_{1470}(593,\cdot)\) \(\chi_{1470}(647,\cdot)\) \(\chi_{1470}(677,\cdot)\) \(\chi_{1470}(773,\cdot)\) \(\chi_{1470}(857,\cdot)\) \(\chi_{1470}(887,\cdot)\) \(\chi_{1470}(983,\cdot)\) \(\chi_{1470}(1013,\cdot)\) \(\chi_{1470}(1067,\cdot)\) \(\chi_{1470}(1193,\cdot)\) \(\chi_{1470}(1223,\cdot)\) \(\chi_{1470}(1277,\cdot)\) \(\chi_{1470}(1307,\cdot)\) \(\chi_{1470}(1433,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((491,1177,1081)\) → \((-1,i,e\left(\frac{5}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 1470 }(47, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{13}{28}\right)\) |