Basic properties
Modulus: | \(2805\) | |
Conductor: | \(561\) | 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 \(\chi_{561}(71,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2805.fd
\(\chi_{2805}(71,\cdot)\) \(\chi_{2805}(146,\cdot)\) \(\chi_{2805}(311,\cdot)\) \(\chi_{2805}(401,\cdot)\) \(\chi_{2805}(521,\cdot)\) \(\chi_{2805}(566,\cdot)\) \(\chi_{2805}(581,\cdot)\) \(\chi_{2805}(641,\cdot)\) \(\chi_{2805}(686,\cdot)\) \(\chi_{2805}(806,\cdot)\) \(\chi_{2805}(896,\cdot)\) \(\chi_{2805}(911,\cdot)\) \(\chi_{2805}(1061,\cdot)\) \(\chi_{2805}(1076,\cdot)\) \(\chi_{2805}(1136,\cdot)\) \(\chi_{2805}(1346,\cdot)\) \(\chi_{2805}(1391,\cdot)\) \(\chi_{2805}(1406,\cdot)\) \(\chi_{2805}(1571,\cdot)\) \(\chi_{2805}(1676,\cdot)\) \(\chi_{2805}(1796,\cdot)\) \(\chi_{2805}(1841,\cdot)\) \(\chi_{2805}(1901,\cdot)\) \(\chi_{2805}(1961,\cdot)\) \(\chi_{2805}(2051,\cdot)\) \(\chi_{2805}(2171,\cdot)\) \(\chi_{2805}(2216,\cdot)\) \(\chi_{2805}(2336,\cdot)\) \(\chi_{2805}(2561,\cdot)\) \(\chi_{2805}(2621,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1871,562,1531,496)\) → \((-1,1,e\left(\frac{2}{5}\right),e\left(\frac{1}{16}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(19\) | \(23\) | \(26\) |
\( \chi_{ 2805 }(71, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{39}{80}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{21}{80}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{17}{40}\right)\) |