Basic properties
Modulus: | \(784\) | |
Conductor: | \(784\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 784.bs
\(\chi_{784}(5,\cdot)\) \(\chi_{784}(45,\cdot)\) \(\chi_{784}(61,\cdot)\) \(\chi_{784}(101,\cdot)\) \(\chi_{784}(157,\cdot)\) \(\chi_{784}(173,\cdot)\) \(\chi_{784}(213,\cdot)\) \(\chi_{784}(229,\cdot)\) \(\chi_{784}(269,\cdot)\) \(\chi_{784}(285,\cdot)\) \(\chi_{784}(341,\cdot)\) \(\chi_{784}(381,\cdot)\) \(\chi_{784}(397,\cdot)\) \(\chi_{784}(437,\cdot)\) \(\chi_{784}(453,\cdot)\) \(\chi_{784}(493,\cdot)\) \(\chi_{784}(549,\cdot)\) \(\chi_{784}(565,\cdot)\) \(\chi_{784}(605,\cdot)\) \(\chi_{784}(621,\cdot)\) \(\chi_{784}(661,\cdot)\) \(\chi_{784}(677,\cdot)\) \(\chi_{784}(733,\cdot)\) \(\chi_{784}(773,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((687,197,689)\) → \((1,-i,e\left(\frac{31}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 784 }(45, a) \) | \(-1\) | \(1\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{13}{42}\right)\) |