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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 309.n
\(\chi_{309}(2,\cdot)\) \(\chi_{309}(17,\cdot)\) \(\chi_{309}(26,\cdot)\) \(\chi_{309}(29,\cdot)\) \(\chi_{309}(32,\cdot)\) \(\chi_{309}(38,\cdot)\) \(\chi_{309}(41,\cdot)\) \(\chi_{309}(50,\cdot)\) \(\chi_{309}(59,\cdot)\) \(\chi_{309}(68,\cdot)\) \(\chi_{309}(83,\cdot)\) \(\chi_{309}(92,\cdot)\) \(\chi_{309}(98,\cdot)\) \(\chi_{309}(107,\cdot)\) \(\chi_{309}(110,\cdot)\) \(\chi_{309}(119,\cdot)\) \(\chi_{309}(122,\cdot)\) \(\chi_{309}(128,\cdot)\) \(\chi_{309}(131,\cdot)\) \(\chi_{309}(152,\cdot)\) \(\chi_{309}(155,\cdot)\) \(\chi_{309}(158,\cdot)\) \(\chi_{309}(161,\cdot)\) \(\chi_{309}(185,\cdot)\) \(\chi_{309}(194,\cdot)\) \(\chi_{309}(200,\cdot)\) \(\chi_{309}(221,\cdot)\) \(\chi_{309}(224,\cdot)\) \(\chi_{309}(239,\cdot)\) \(\chi_{309}(242,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((104,211)\) → \((-1,e\left(\frac{29}{51}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 309 }(155, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{102}\right)\) | \(e\left(\frac{2}{51}\right)\) | \(e\left(\frac{7}{102}\right)\) | \(e\left(\frac{14}{51}\right)\) | \(e\left(\frac{19}{34}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{19}{102}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{27}{34}\right)\) | \(e\left(\frac{4}{51}\right)\) |