Basic properties
| Modulus: | \(618\) | |
| Conductor: | \(103\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(51\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{103}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 618.m
\(\chi_{618}(7,\cdot)\) \(\chi_{618}(19,\cdot)\) \(\chi_{618}(25,\cdot)\) \(\chi_{618}(49,\cdot)\) \(\chi_{618}(55,\cdot)\) \(\chi_{618}(91,\cdot)\) \(\chi_{618}(97,\cdot)\) \(\chi_{618}(121,\cdot)\) \(\chi_{618}(139,\cdot)\) \(\chi_{618}(163,\cdot)\) \(\chi_{618}(223,\cdot)\) \(\chi_{618}(235,\cdot)\) \(\chi_{618}(247,\cdot)\) \(\chi_{618}(265,\cdot)\) \(\chi_{618}(289,\cdot)\) \(\chi_{618}(313,\cdot)\) \(\chi_{618}(325,\cdot)\) \(\chi_{618}(337,\cdot)\) \(\chi_{618}(361,\cdot)\) \(\chi_{618}(367,\cdot)\) \(\chi_{618}(391,\cdot)\) \(\chi_{618}(427,\cdot)\) \(\chi_{618}(445,\cdot)\) \(\chi_{618}(475,\cdot)\) \(\chi_{618}(517,\cdot)\) \(\chi_{618}(541,\cdot)\) \(\chi_{618}(547,\cdot)\) \(\chi_{618}(553,\cdot)\) \(\chi_{618}(565,\cdot)\) \(\chi_{618}(583,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 51 polynomial |
Values on generators
\((413,211)\) → \((1,e\left(\frac{2}{51}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 618 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{51}\right)\) | \(e\left(\frac{8}{51}\right)\) | \(e\left(\frac{20}{51}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{38}{51}\right)\) | \(e\left(\frac{7}{51}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{4}{51}\right)\) | \(e\left(\frac{19}{51}\right)\) | \(e\left(\frac{4}{17}\right)\) |