Basic properties
| Modulus: | \(309\) | |
| Conductor: | \(103\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(102\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{103}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 309.p
\(\chi_{309}(40,\cdot)\) \(\chi_{309}(43,\cdot)\) \(\chi_{309}(67,\cdot)\) \(\chi_{309}(70,\cdot)\) \(\chi_{309}(85,\cdot)\) \(\chi_{309}(88,\cdot)\) \(\chi_{309}(109,\cdot)\) \(\chi_{309}(115,\cdot)\) \(\chi_{309}(124,\cdot)\) \(\chi_{309}(148,\cdot)\) \(\chi_{309}(151,\cdot)\) \(\chi_{309}(154,\cdot)\) \(\chi_{309}(157,\cdot)\) \(\chi_{309}(178,\cdot)\) \(\chi_{309}(181,\cdot)\) \(\chi_{309}(187,\cdot)\) \(\chi_{309}(190,\cdot)\) \(\chi_{309}(199,\cdot)\) \(\chi_{309}(202,\cdot)\) \(\chi_{309}(211,\cdot)\) \(\chi_{309}(217,\cdot)\) \(\chi_{309}(226,\cdot)\) \(\chi_{309}(241,\cdot)\) \(\chi_{309}(250,\cdot)\) \(\chi_{309}(259,\cdot)\) \(\chi_{309}(268,\cdot)\) \(\chi_{309}(271,\cdot)\) \(\chi_{309}(277,\cdot)\) \(\chi_{309}(280,\cdot)\) \(\chi_{309}(283,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((104,211)\) → \((1,e\left(\frac{1}{102}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 309 }(211, a) \) | \(-1\) | \(1\) | \(e\left(\frac{22}{51}\right)\) | \(e\left(\frac{44}{51}\right)\) | \(e\left(\frac{1}{102}\right)\) | \(e\left(\frac{2}{51}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{61}{102}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{37}{51}\right)\) |