Basic properties
Modulus: | \(618\) | |
Conductor: | \(309\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(102\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{309}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 618.p
\(\chi_{618}(5,\cdot)\) \(\chi_{618}(11,\cdot)\) \(\chi_{618}(35,\cdot)\) \(\chi_{618}(53,\cdot)\) \(\chi_{618}(65,\cdot)\) \(\chi_{618}(71,\cdot)\) \(\chi_{618}(77,\cdot)\) \(\chi_{618}(101,\cdot)\) \(\chi_{618}(143,\cdot)\) \(\chi_{618}(173,\cdot)\) \(\chi_{618}(191,\cdot)\) \(\chi_{618}(227,\cdot)\) \(\chi_{618}(251,\cdot)\) \(\chi_{618}(257,\cdot)\) \(\chi_{618}(281,\cdot)\) \(\chi_{618}(293,\cdot)\) \(\chi_{618}(305,\cdot)\) \(\chi_{618}(329,\cdot)\) \(\chi_{618}(353,\cdot)\) \(\chi_{618}(371,\cdot)\) \(\chi_{618}(383,\cdot)\) \(\chi_{618}(395,\cdot)\) \(\chi_{618}(455,\cdot)\) \(\chi_{618}(479,\cdot)\) \(\chi_{618}(497,\cdot)\) \(\chi_{618}(521,\cdot)\) \(\chi_{618}(527,\cdot)\) \(\chi_{618}(563,\cdot)\) \(\chi_{618}(569,\cdot)\) \(\chi_{618}(593,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((413,211)\) → \((-1,e\left(\frac{1}{102}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 618 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{26}{51}\right)\) | \(e\left(\frac{2}{51}\right)\) | \(e\left(\frac{5}{51}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{19}{102}\right)\) | \(e\left(\frac{40}{51}\right)\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{1}{51}\right)\) | \(e\left(\frac{35}{102}\right)\) | \(e\left(\frac{19}{34}\right)\) |