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.ef
\(\chi_{2624}(69,\cdot)\) \(\chi_{2624}(341,\cdot)\) \(\chi_{2624}(421,\cdot)\) \(\chi_{2624}(477,\cdot)\) \(\chi_{2624}(485,\cdot)\) \(\chi_{2624}(509,\cdot)\) \(\chi_{2624}(557,\cdot)\) \(\chi_{2624}(589,\cdot)\) \(\chi_{2624}(709,\cdot)\) \(\chi_{2624}(1013,\cdot)\) \(\chi_{2624}(1085,\cdot)\) \(\chi_{2624}(1101,\cdot)\) \(\chi_{2624}(1237,\cdot)\) \(\chi_{2624}(1277,\cdot)\) \(\chi_{2624}(1293,\cdot)\) \(\chi_{2624}(1301,\cdot)\) \(\chi_{2624}(1381,\cdot)\) \(\chi_{2624}(1653,\cdot)\) \(\chi_{2624}(1733,\cdot)\) \(\chi_{2624}(1789,\cdot)\) \(\chi_{2624}(1797,\cdot)\) \(\chi_{2624}(1821,\cdot)\) \(\chi_{2624}(1869,\cdot)\) \(\chi_{2624}(1901,\cdot)\) \(\chi_{2624}(2021,\cdot)\) \(\chi_{2624}(2325,\cdot)\) \(\chi_{2624}(2397,\cdot)\) \(\chi_{2624}(2413,\cdot)\) \(\chi_{2624}(2549,\cdot)\) \(\chi_{2624}(2589,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((575,1477,129)\) → \((1,e\left(\frac{1}{16}\right),e\left(\frac{11}{40}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 2624 }(69, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{11}{80}\right)\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{53}{80}\right)\) |