Basic properties
Modulus: | \(683\) | |
Conductor: | \(683\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(682\) | 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 683.h
\(\chi_{683}(5,\cdot)\) \(\chi_{683}(6,\cdot)\) \(\chi_{683}(7,\cdot)\) \(\chi_{683}(11,\cdot)\) \(\chi_{683}(13,\cdot)\) \(\chi_{683}(15,\cdot)\) \(\chi_{683}(17,\cdot)\) \(\chi_{683}(18,\cdot)\) \(\chi_{683}(20,\cdot)\) \(\chi_{683}(21,\cdot)\) \(\chi_{683}(23,\cdot)\) \(\chi_{683}(24,\cdot)\) \(\chi_{683}(28,\cdot)\) \(\chi_{683}(31,\cdot)\) \(\chi_{683}(33,\cdot)\) \(\chi_{683}(38,\cdot)\) \(\chi_{683}(39,\cdot)\) \(\chi_{683}(41,\cdot)\) \(\chi_{683}(43,\cdot)\) \(\chi_{683}(44,\cdot)\) \(\chi_{683}(45,\cdot)\) \(\chi_{683}(47,\cdot)\) \(\chi_{683}(50,\cdot)\) \(\chi_{683}(51,\cdot)\) \(\chi_{683}(52,\cdot)\) \(\chi_{683}(54,\cdot)\) \(\chi_{683}(58,\cdot)\) \(\chi_{683}(60,\cdot)\) \(\chi_{683}(63,\cdot)\) \(\chi_{683}(68,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{341})$ |
Fixed field: | Number field defined by a degree 682 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{265}{682}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 683 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{7}{31}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{265}{682}\right)\) | \(e\left(\frac{371}{682}\right)\) | \(e\left(\frac{661}{682}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{14}{31}\right)\) | \(e\left(\frac{241}{341}\right)\) | \(e\left(\frac{195}{682}\right)\) |