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 \(\chi_{784}(669,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3136.cn
\(\chi_{3136}(81,\cdot)\) \(\chi_{3136}(305,\cdot)\) \(\chi_{3136}(401,\cdot)\) \(\chi_{3136}(529,\cdot)\) \(\chi_{3136}(625,\cdot)\) \(\chi_{3136}(849,\cdot)\) \(\chi_{3136}(977,\cdot)\) \(\chi_{3136}(1073,\cdot)\) \(\chi_{3136}(1201,\cdot)\) \(\chi_{3136}(1297,\cdot)\) \(\chi_{3136}(1425,\cdot)\) \(\chi_{3136}(1521,\cdot)\) \(\chi_{3136}(1649,\cdot)\) \(\chi_{3136}(1873,\cdot)\) \(\chi_{3136}(1969,\cdot)\) \(\chi_{3136}(2097,\cdot)\) \(\chi_{3136}(2193,\cdot)\) \(\chi_{3136}(2417,\cdot)\) \(\chi_{3136}(2545,\cdot)\) \(\chi_{3136}(2641,\cdot)\) \(\chi_{3136}(2769,\cdot)\) \(\chi_{3136}(2865,\cdot)\) \(\chi_{3136}(2993,\cdot)\) \(\chi_{3136}(3089,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,197,1473)\) → \((1,-i,e\left(\frac{2}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 3136 }(81, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{1}{42}\right)\) |