Basic properties
Modulus: | \(2550\) | |
Conductor: | \(1275\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1275}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2550.cp
\(\chi_{2550}(29,\cdot)\) \(\chi_{2550}(209,\cdot)\) \(\chi_{2550}(269,\cdot)\) \(\chi_{2550}(329,\cdot)\) \(\chi_{2550}(419,\cdot)\) \(\chi_{2550}(479,\cdot)\) \(\chi_{2550}(539,\cdot)\) \(\chi_{2550}(719,\cdot)\) \(\chi_{2550}(779,\cdot)\) \(\chi_{2550}(809,\cdot)\) \(\chi_{2550}(839,\cdot)\) \(\chi_{2550}(929,\cdot)\) \(\chi_{2550}(959,\cdot)\) \(\chi_{2550}(989,\cdot)\) \(\chi_{2550}(1229,\cdot)\) \(\chi_{2550}(1289,\cdot)\) \(\chi_{2550}(1319,\cdot)\) \(\chi_{2550}(1439,\cdot)\) \(\chi_{2550}(1469,\cdot)\) \(\chi_{2550}(1559,\cdot)\) \(\chi_{2550}(1739,\cdot)\) \(\chi_{2550}(1829,\cdot)\) \(\chi_{2550}(1859,\cdot)\) \(\chi_{2550}(1979,\cdot)\) \(\chi_{2550}(2009,\cdot)\) \(\chi_{2550}(2069,\cdot)\) \(\chi_{2550}(2309,\cdot)\) \(\chi_{2550}(2339,\cdot)\) \(\chi_{2550}(2369,\cdot)\) \(\chi_{2550}(2459,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((851,1327,751)\) → \((-1,e\left(\frac{1}{10}\right),e\left(\frac{13}{16}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 2550 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{63}{80}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{63}{80}\right)\) | \(e\left(\frac{21}{80}\right)\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{1}{8}\right)\) |