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 \(\chi_{1275}(11,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2550.cr
\(\chi_{2550}(11,\cdot)\) \(\chi_{2550}(41,\cdot)\) \(\chi_{2550}(71,\cdot)\) \(\chi_{2550}(131,\cdot)\) \(\chi_{2550}(311,\cdot)\) \(\chi_{2550}(371,\cdot)\) \(\chi_{2550}(431,\cdot)\) \(\chi_{2550}(521,\cdot)\) \(\chi_{2550}(581,\cdot)\) \(\chi_{2550}(641,\cdot)\) \(\chi_{2550}(821,\cdot)\) \(\chi_{2550}(881,\cdot)\) \(\chi_{2550}(911,\cdot)\) \(\chi_{2550}(941,\cdot)\) \(\chi_{2550}(1031,\cdot)\) \(\chi_{2550}(1061,\cdot)\) \(\chi_{2550}(1091,\cdot)\) \(\chi_{2550}(1331,\cdot)\) \(\chi_{2550}(1391,\cdot)\) \(\chi_{2550}(1421,\cdot)\) \(\chi_{2550}(1541,\cdot)\) \(\chi_{2550}(1571,\cdot)\) \(\chi_{2550}(1661,\cdot)\) \(\chi_{2550}(1841,\cdot)\) \(\chi_{2550}(1931,\cdot)\) \(\chi_{2550}(1961,\cdot)\) \(\chi_{2550}(2081,\cdot)\) \(\chi_{2550}(2111,\cdot)\) \(\chi_{2550}(2171,\cdot)\) \(\chi_{2550}(2411,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((851,1327,751)\) → \((-1,e\left(\frac{4}{5}\right),e\left(\frac{7}{16}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 2550 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{29}{80}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{69}{80}\right)\) | \(e\left(\frac{63}{80}\right)\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{7}{8}\right)\) |