Basic properties
Modulus: | \(309\) | |
Conductor: | \(309\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(102\) | 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 309.o
\(\chi_{309}(5,\cdot)\) \(\chi_{309}(11,\cdot)\) \(\chi_{309}(20,\cdot)\) \(\chi_{309}(35,\cdot)\) \(\chi_{309}(44,\cdot)\) \(\chi_{309}(53,\cdot)\) \(\chi_{309}(62,\cdot)\) \(\chi_{309}(65,\cdot)\) \(\chi_{309}(71,\cdot)\) \(\chi_{309}(74,\cdot)\) \(\chi_{309}(77,\cdot)\) \(\chi_{309}(86,\cdot)\) \(\chi_{309}(101,\cdot)\) \(\chi_{309}(143,\cdot)\) \(\chi_{309}(146,\cdot)\) \(\chi_{309}(170,\cdot)\) \(\chi_{309}(173,\cdot)\) \(\chi_{309}(188,\cdot)\) \(\chi_{309}(191,\cdot)\) \(\chi_{309}(212,\cdot)\) \(\chi_{309}(218,\cdot)\) \(\chi_{309}(227,\cdot)\) \(\chi_{309}(251,\cdot)\) \(\chi_{309}(254,\cdot)\) \(\chi_{309}(257,\cdot)\) \(\chi_{309}(260,\cdot)\) \(\chi_{309}(281,\cdot)\) \(\chi_{309}(284,\cdot)\) \(\chi_{309}(290,\cdot)\) \(\chi_{309}(293,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((104,211)\) → \((-1,e\left(\frac{97}{102}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 309 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{102}\right)\) | \(e\left(\frac{35}{51}\right)\) | \(e\left(\frac{23}{51}\right)\) | \(e\left(\frac{41}{51}\right)\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{27}{34}\right)\) | \(e\left(\frac{26}{51}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{5}{34}\right)\) | \(e\left(\frac{19}{51}\right)\) |