Basic properties
| Modulus: | \(3136\) | |
| Conductor: | \(784\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{784}(437,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3136.cm
\(\chi_{3136}(17,\cdot)\) \(\chi_{3136}(145,\cdot)\) \(\chi_{3136}(241,\cdot)\) \(\chi_{3136}(369,\cdot)\) \(\chi_{3136}(465,\cdot)\) \(\chi_{3136}(593,\cdot)\) \(\chi_{3136}(689,\cdot)\) \(\chi_{3136}(817,\cdot)\) \(\chi_{3136}(1041,\cdot)\) \(\chi_{3136}(1137,\cdot)\) \(\chi_{3136}(1265,\cdot)\) \(\chi_{3136}(1361,\cdot)\) \(\chi_{3136}(1585,\cdot)\) \(\chi_{3136}(1713,\cdot)\) \(\chi_{3136}(1809,\cdot)\) \(\chi_{3136}(1937,\cdot)\) \(\chi_{3136}(2033,\cdot)\) \(\chi_{3136}(2161,\cdot)\) \(\chi_{3136}(2257,\cdot)\) \(\chi_{3136}(2385,\cdot)\) \(\chi_{3136}(2609,\cdot)\) \(\chi_{3136}(2705,\cdot)\) \(\chi_{3136}(2833,\cdot)\) \(\chi_{3136}(2929,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,197,1473)\) → \((1,i,e\left(\frac{31}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 3136 }(241, a) \) | \(-1\) | \(1\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{13}{42}\right)\) |