Basic properties
Modulus: | \(2624\) | |
Conductor: | \(2624\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2624.ed
\(\chi_{2624}(5,\cdot)\) \(\chi_{2624}(21,\cdot)\) \(\chi_{2624}(61,\cdot)\) \(\chi_{2624}(77,\cdot)\) \(\chi_{2624}(125,\cdot)\) \(\chi_{2624}(213,\cdot)\) \(\chi_{2624}(525,\cdot)\) \(\chi_{2624}(613,\cdot)\) \(\chi_{2624}(661,\cdot)\) \(\chi_{2624}(677,\cdot)\) \(\chi_{2624}(717,\cdot)\) \(\chi_{2624}(733,\cdot)\) \(\chi_{2624}(781,\cdot)\) \(\chi_{2624}(869,\cdot)\) \(\chi_{2624}(1181,\cdot)\) \(\chi_{2624}(1269,\cdot)\) \(\chi_{2624}(1317,\cdot)\) \(\chi_{2624}(1333,\cdot)\) \(\chi_{2624}(1373,\cdot)\) \(\chi_{2624}(1389,\cdot)\) \(\chi_{2624}(1437,\cdot)\) \(\chi_{2624}(1525,\cdot)\) \(\chi_{2624}(1837,\cdot)\) \(\chi_{2624}(1925,\cdot)\) \(\chi_{2624}(1973,\cdot)\) \(\chi_{2624}(1989,\cdot)\) \(\chi_{2624}(2029,\cdot)\) \(\chi_{2624}(2045,\cdot)\) \(\chi_{2624}(2093,\cdot)\) \(\chi_{2624}(2181,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((575,1477,129)\) → \((1,e\left(\frac{1}{16}\right),e\left(\frac{11}{20}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 2624 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{13}{80}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{41}{80}\right)\) |