Basic properties
Modulus: | \(2624\) | |
Conductor: | \(2624\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2624.en
\(\chi_{2624}(115,\cdot)\) \(\chi_{2624}(203,\cdot)\) \(\chi_{2624}(251,\cdot)\) \(\chi_{2624}(267,\cdot)\) \(\chi_{2624}(307,\cdot)\) \(\chi_{2624}(323,\cdot)\) \(\chi_{2624}(371,\cdot)\) \(\chi_{2624}(459,\cdot)\) \(\chi_{2624}(771,\cdot)\) \(\chi_{2624}(859,\cdot)\) \(\chi_{2624}(907,\cdot)\) \(\chi_{2624}(923,\cdot)\) \(\chi_{2624}(963,\cdot)\) \(\chi_{2624}(979,\cdot)\) \(\chi_{2624}(1027,\cdot)\) \(\chi_{2624}(1115,\cdot)\) \(\chi_{2624}(1427,\cdot)\) \(\chi_{2624}(1515,\cdot)\) \(\chi_{2624}(1563,\cdot)\) \(\chi_{2624}(1579,\cdot)\) \(\chi_{2624}(1619,\cdot)\) \(\chi_{2624}(1635,\cdot)\) \(\chi_{2624}(1683,\cdot)\) \(\chi_{2624}(1771,\cdot)\) \(\chi_{2624}(2083,\cdot)\) \(\chi_{2624}(2171,\cdot)\) \(\chi_{2624}(2219,\cdot)\) \(\chi_{2624}(2235,\cdot)\) \(\chi_{2624}(2275,\cdot)\) \(\chi_{2624}(2291,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((575,1477,129)\) → \((-1,e\left(\frac{15}{16}\right),e\left(\frac{9}{20}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 2624 }(115, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{1}{80}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{39}{80}\right)\) |