Basic properties
| Modulus: | \(2550\) | |
| Conductor: | \(425\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{425}(73,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2550.cs
\(\chi_{2550}(73,\cdot)\) \(\chi_{2550}(133,\cdot)\) \(\chi_{2550}(367,\cdot)\) \(\chi_{2550}(397,\cdot)\) \(\chi_{2550}(403,\cdot)\) \(\chi_{2550}(487,\cdot)\) \(\chi_{2550}(517,\cdot)\) \(\chi_{2550}(583,\cdot)\) \(\chi_{2550}(853,\cdot)\) \(\chi_{2550}(877,\cdot)\) \(\chi_{2550}(913,\cdot)\) \(\chi_{2550}(997,\cdot)\) \(\chi_{2550}(1027,\cdot)\) \(\chi_{2550}(1153,\cdot)\) \(\chi_{2550}(1363,\cdot)\) \(\chi_{2550}(1387,\cdot)\) \(\chi_{2550}(1417,\cdot)\) \(\chi_{2550}(1423,\cdot)\) \(\chi_{2550}(1537,\cdot)\) \(\chi_{2550}(1603,\cdot)\) \(\chi_{2550}(1663,\cdot)\) \(\chi_{2550}(1873,\cdot)\) \(\chi_{2550}(1897,\cdot)\) \(\chi_{2550}(1927,\cdot)\) \(\chi_{2550}(1933,\cdot)\) \(\chi_{2550}(2017,\cdot)\) \(\chi_{2550}(2047,\cdot)\) \(\chi_{2550}(2113,\cdot)\) \(\chi_{2550}(2173,\cdot)\) \(\chi_{2550}(2383,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((851,1327,751)\) → \((1,e\left(\frac{11}{20}\right),e\left(\frac{5}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 2550 }(73, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{13}{80}\right)\) | \(e\left(\frac{17}{80}\right)\) | \(e\left(\frac{21}{80}\right)\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{7}{8}\right)\) |