Basic properties
| Modulus: | \(206\) | |
| 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 \(\chi_{103}(96,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 206.h
\(\chi_{206}(5,\cdot)\) \(\chi_{206}(11,\cdot)\) \(\chi_{206}(21,\cdot)\) \(\chi_{206}(35,\cdot)\) \(\chi_{206}(43,\cdot)\) \(\chi_{206}(45,\cdot)\) \(\chi_{206}(51,\cdot)\) \(\chi_{206}(53,\cdot)\) \(\chi_{206}(65,\cdot)\) \(\chi_{206}(67,\cdot)\) \(\chi_{206}(71,\cdot)\) \(\chi_{206}(75,\cdot)\) \(\chi_{206}(77,\cdot)\) \(\chi_{206}(85,\cdot)\) \(\chi_{206}(87,\cdot)\) \(\chi_{206}(99,\cdot)\) \(\chi_{206}(101,\cdot)\) \(\chi_{206}(109,\cdot)\) \(\chi_{206}(115,\cdot)\) \(\chi_{206}(123,\cdot)\) \(\chi_{206}(143,\cdot)\) \(\chi_{206}(147,\cdot)\) \(\chi_{206}(151,\cdot)\) \(\chi_{206}(157,\cdot)\) \(\chi_{206}(165,\cdot)\) \(\chi_{206}(173,\cdot)\) \(\chi_{206}(177,\cdot)\) \(\chi_{206}(181,\cdot)\) \(\chi_{206}(187,\cdot)\) \(\chi_{206}(189,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{55}{102}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 206 }(199, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{55}{102}\right)\) | \(e\left(\frac{8}{51}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{91}{102}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{29}{51}\right)\) | \(e\left(\frac{38}{51}\right)\) | \(e\left(\frac{7}{51}\right)\) | \(e\left(\frac{19}{102}\right)\) |