Basic properties
Modulus: | \(633\) | |
Conductor: | \(633\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(210\) | 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 633.be
\(\chi_{633}(20,\cdot)\) \(\chi_{633}(44,\cdot)\) \(\chi_{633}(47,\cdot)\) \(\chi_{633}(53,\cdot)\) \(\chi_{633}(56,\cdot)\) \(\chi_{633}(59,\cdot)\) \(\chi_{633}(62,\cdot)\) \(\chi_{633}(80,\cdot)\) \(\chi_{633}(95,\cdot)\) \(\chi_{633}(119,\cdot)\) \(\chi_{633}(170,\cdot)\) \(\chi_{633}(176,\cdot)\) \(\chi_{633}(182,\cdot)\) \(\chi_{633}(194,\cdot)\) \(\chi_{633}(209,\cdot)\) \(\chi_{633}(215,\cdot)\) \(\chi_{633}(227,\cdot)\) \(\chi_{633}(248,\cdot)\) \(\chi_{633}(257,\cdot)\) \(\chi_{633}(260,\cdot)\) \(\chi_{633}(263,\cdot)\) \(\chi_{633}(281,\cdot)\) \(\chi_{633}(314,\cdot)\) \(\chi_{633}(347,\cdot)\) \(\chi_{633}(350,\cdot)\) \(\chi_{633}(365,\cdot)\) \(\chi_{633}(374,\cdot)\) \(\chi_{633}(383,\cdot)\) \(\chi_{633}(419,\cdot)\) \(\chi_{633}(428,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((212,424)\) → \((-1,e\left(\frac{67}{105}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 633 }(20, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{210}\right)\) | \(e\left(\frac{29}{105}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{73}{105}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{58}{105}\right)\) |