Basic properties
Modulus: | \(688\) | |
Conductor: | \(688\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 688.bv
\(\chi_{688}(13,\cdot)\) \(\chi_{688}(53,\cdot)\) \(\chi_{688}(101,\cdot)\) \(\chi_{688}(109,\cdot)\) \(\chi_{688}(117,\cdot)\) \(\chi_{688}(181,\cdot)\) \(\chi_{688}(189,\cdot)\) \(\chi_{688}(197,\cdot)\) \(\chi_{688}(229,\cdot)\) \(\chi_{688}(253,\cdot)\) \(\chi_{688}(325,\cdot)\) \(\chi_{688}(341,\cdot)\) \(\chi_{688}(357,\cdot)\) \(\chi_{688}(397,\cdot)\) \(\chi_{688}(445,\cdot)\) \(\chi_{688}(453,\cdot)\) \(\chi_{688}(461,\cdot)\) \(\chi_{688}(525,\cdot)\) \(\chi_{688}(533,\cdot)\) \(\chi_{688}(541,\cdot)\) \(\chi_{688}(573,\cdot)\) \(\chi_{688}(597,\cdot)\) \(\chi_{688}(669,\cdot)\) \(\chi_{688}(685,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((431,517,433)\) → \((1,-i,e\left(\frac{16}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 688 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{5}{28}\right)\) |