Basic properties
| Modulus: | \(1309\) | |
| Conductor: | \(1309\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | 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 1309.cs
\(\chi_{1309}(6,\cdot)\) \(\chi_{1309}(41,\cdot)\) \(\chi_{1309}(62,\cdot)\) \(\chi_{1309}(90,\cdot)\) \(\chi_{1309}(139,\cdot)\) \(\chi_{1309}(160,\cdot)\) \(\chi_{1309}(167,\cdot)\) \(\chi_{1309}(216,\cdot)\) \(\chi_{1309}(244,\cdot)\) \(\chi_{1309}(398,\cdot)\) \(\chi_{1309}(447,\cdot)\) \(\chi_{1309}(503,\cdot)\) \(\chi_{1309}(524,\cdot)\) \(\chi_{1309}(601,\cdot)\) \(\chi_{1309}(622,\cdot)\) \(\chi_{1309}(657,\cdot)\) \(\chi_{1309}(734,\cdot)\) \(\chi_{1309}(755,\cdot)\) \(\chi_{1309}(776,\cdot)\) \(\chi_{1309}(811,\cdot)\) \(\chi_{1309}(853,\cdot)\) \(\chi_{1309}(860,\cdot)\) \(\chi_{1309}(930,\cdot)\) \(\chi_{1309}(1014,\cdot)\) \(\chi_{1309}(1042,\cdot)\) \(\chi_{1309}(1091,\cdot)\) \(\chi_{1309}(1119,\cdot)\) \(\chi_{1309}(1161,\cdot)\) \(\chi_{1309}(1168,\cdot)\) \(\chi_{1309}(1196,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1123,596,309)\) → \((-1,e\left(\frac{3}{10}\right),e\left(\frac{11}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 1309 }(41, a) \) | \(-1\) | \(1\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{47}{80}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{11}{80}\right)\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{11}{20}\right)\) |