Basic properties
Modulus: | \(2805\) | |
Conductor: | \(935\) | 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 \(\chi_{935}(79,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2805.fe
\(\chi_{2805}(79,\cdot)\) \(\chi_{2805}(139,\cdot)\) \(\chi_{2805}(184,\cdot)\) \(\chi_{2805}(244,\cdot)\) \(\chi_{2805}(469,\cdot)\) \(\chi_{2805}(589,\cdot)\) \(\chi_{2805}(634,\cdot)\) \(\chi_{2805}(754,\cdot)\) \(\chi_{2805}(844,\cdot)\) \(\chi_{2805}(904,\cdot)\) \(\chi_{2805}(964,\cdot)\) \(\chi_{2805}(1009,\cdot)\) \(\chi_{2805}(1129,\cdot)\) \(\chi_{2805}(1234,\cdot)\) \(\chi_{2805}(1399,\cdot)\) \(\chi_{2805}(1414,\cdot)\) \(\chi_{2805}(1459,\cdot)\) \(\chi_{2805}(1669,\cdot)\) \(\chi_{2805}(1729,\cdot)\) \(\chi_{2805}(1744,\cdot)\) \(\chi_{2805}(1894,\cdot)\) \(\chi_{2805}(1909,\cdot)\) \(\chi_{2805}(1999,\cdot)\) \(\chi_{2805}(2119,\cdot)\) \(\chi_{2805}(2164,\cdot)\) \(\chi_{2805}(2224,\cdot)\) \(\chi_{2805}(2239,\cdot)\) \(\chi_{2805}(2284,\cdot)\) \(\chi_{2805}(2404,\cdot)\) \(\chi_{2805}(2494,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1871,562,1531,496)\) → \((1,-1,e\left(\frac{1}{10}\right),e\left(\frac{7}{16}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(19\) | \(23\) | \(26\) |
\( \chi_{ 2805 }(79, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{1}{80}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{3}{40}\right)\) |