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 \(\chi_{784}(11,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3136.cp
\(\chi_{3136}(207,\cdot)\) \(\chi_{3136}(303,\cdot)\) \(\chi_{3136}(431,\cdot)\) \(\chi_{3136}(527,\cdot)\) \(\chi_{3136}(751,\cdot)\) \(\chi_{3136}(879,\cdot)\) \(\chi_{3136}(975,\cdot)\) \(\chi_{3136}(1103,\cdot)\) \(\chi_{3136}(1199,\cdot)\) \(\chi_{3136}(1327,\cdot)\) \(\chi_{3136}(1423,\cdot)\) \(\chi_{3136}(1551,\cdot)\) \(\chi_{3136}(1775,\cdot)\) \(\chi_{3136}(1871,\cdot)\) \(\chi_{3136}(1999,\cdot)\) \(\chi_{3136}(2095,\cdot)\) \(\chi_{3136}(2319,\cdot)\) \(\chi_{3136}(2447,\cdot)\) \(\chi_{3136}(2543,\cdot)\) \(\chi_{3136}(2671,\cdot)\) \(\chi_{3136}(2767,\cdot)\) \(\chi_{3136}(2895,\cdot)\) \(\chi_{3136}(2991,\cdot)\) \(\chi_{3136}(3119,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,197,1473)\) → \((-1,i,e\left(\frac{20}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 3136 }(207, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{31}{42}\right)\) |