Basic properties
| Modulus: | \(338130\) | |
| Conductor: | \(33813\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(102\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{33813}(101,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 338130.bez
\(\chi_{338130}(101,\cdot)\) \(\chi_{338130}(5711,\cdot)\) \(\chi_{338130}(19991,\cdot)\) \(\chi_{338130}(25601,\cdot)\) \(\chi_{338130}(45491,\cdot)\) \(\chi_{338130}(59771,\cdot)\) \(\chi_{338130}(65381,\cdot)\) \(\chi_{338130}(79661,\cdot)\) \(\chi_{338130}(85271,\cdot)\) \(\chi_{338130}(99551,\cdot)\) \(\chi_{338130}(105161,\cdot)\) \(\chi_{338130}(119441,\cdot)\) \(\chi_{338130}(125051,\cdot)\) \(\chi_{338130}(139331,\cdot)\) \(\chi_{338130}(144941,\cdot)\) \(\chi_{338130}(159221,\cdot)\) \(\chi_{338130}(164831,\cdot)\) \(\chi_{338130}(179111,\cdot)\) \(\chi_{338130}(184721,\cdot)\) \(\chi_{338130}(199001,\cdot)\) \(\chi_{338130}(218891,\cdot)\) \(\chi_{338130}(224501,\cdot)\) \(\chi_{338130}(238781,\cdot)\) \(\chi_{338130}(244391,\cdot)\) \(\chi_{338130}(258671,\cdot)\) \(\chi_{338130}(264281,\cdot)\) \(\chi_{338130}(278561,\cdot)\) \(\chi_{338130}(284171,\cdot)\) \(\chi_{338130}(298451,\cdot)\) \(\chi_{338130}(304061,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((262991,67627,104041,145081)\) → \((e\left(\frac{1}{6}\right),1,e\left(\frac{5}{6}\right),e\left(\frac{9}{34}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 338130 }(101, a) \) | \(-1\) | \(1\) | \(e\left(\frac{44}{51}\right)\) | \(e\left(\frac{3}{34}\right)\) | \(e\left(\frac{89}{102}\right)\) | \(e\left(\frac{10}{51}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{11}{51}\right)\) | \(e\left(\frac{50}{51}\right)\) | \(e\left(\frac{95}{102}\right)\) | \(e\left(\frac{8}{51}\right)\) | \(e\left(\frac{7}{51}\right)\) |