LMFDB - Dirichlet character orbit 6025.ht

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6025, base_ring=CyclotomicField(80)) M = H._module chi = DirichletCharacter(H, M([76,7])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(213,6025)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$6025$
Conductor:	$6025$	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)

Related number fields

Field of values:	$\Q(\zeta_{80})$
Fixed field:	Number field defined by a degree 80 polynomial

First 31 of 32 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{6025}(213,\cdot)$	$1$	$1$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{13}{80}\right)$
$\chi_{6025}(508,\cdot)$	$1$	$1$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{21}{80}\right)$
$\chi_{6025}(1278,\cdot)$	$1$	$1$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{49}{80}\right)$
$\chi_{6025}(1353,\cdot)$	$1$	$1$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{29}{80}\right)$
$\chi_{6025}(1827,\cdot)$	$1$	$1$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{47}{80}\right)$
$\chi_{6025}(2433,\cdot)$	$1$	$1$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{1}{80}\right)$
$\chi_{6025}(2438,\cdot)$	$1$	$1$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{53}{80}\right)$
$\chi_{6025}(2467,\cdot)$	$1$	$1$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{51}{80}\right)$
$\chi_{6025}(2503,\cdot)$	$1$	$1$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{69}{80}\right)$
$\chi_{6025}(2548,\cdot)$	$1$	$1$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{37}{80}\right)$
$\chi_{6025}(2578,\cdot)$	$1$	$1$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{9}{80}\right)$
$\chi_{6025}(2672,\cdot)$	$1$	$1$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{79}{80}\right)$
$\chi_{6025}(2752,\cdot)$	$1$	$1$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{7}{80}\right)$
$\chi_{6025}(3048,\cdot)$	$1$	$1$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{57}{80}\right)$
$\chi_{6025}(3238,\cdot)$	$1$	$1$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{73}{80}\right)$
$\chi_{6025}(3272,\cdot)$	$1$	$1$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{19}{80}\right)$
$\chi_{6025}(3317,\cdot)$	$1$	$1$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{11}{80}\right)$
$\chi_{6025}(3833,\cdot)$	$1$	$1$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{41}{80}\right)$
$\chi_{6025}(4423,\cdot)$	$1$	$1$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{17}{80}\right)$
$\chi_{6025}(4462,\cdot)$	$1$	$1$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{43}{80}\right)$
$\chi_{6025}(4562,\cdot)$	$1$	$1$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{63}{80}\right)$
$\chi_{6025}(4777,\cdot)$	$1$	$1$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{27}{80}\right)$
$\chi_{6025}(4837,\cdot)$	$1$	$1$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{23}{80}\right)$
$\chi_{6025}(4922,\cdot)$	$1$	$1$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{59}{80}\right)$
$\chi_{6025}(4923,\cdot)$	$1$	$1$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{77}{80}\right)$
$\chi_{6025}(4937,\cdot)$	$1$	$1$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{3}{80}\right)$
$\chi_{6025}(5438,\cdot)$	$1$	$1$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{33}{80}\right)$
$\chi_{6025}(5522,\cdot)$	$1$	$1$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{39}{80}\right)$
$\chi_{6025}(5758,\cdot)$	$1$	$1$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{61}{80}\right)$
$\chi_{6025}(5817,\cdot)$	$1$	$1$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{71}{80}\right)$
$\chi_{6025}(5827,\cdot)$	$1$	$1$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{67}{80}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\(\chi_{6025}(213,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{13}{80}\right)\)
\(\chi_{6025}(508,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{21}{80}\right)\)
\(\chi_{6025}(1278,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{49}{80}\right)\)
\(\chi_{6025}(1353,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{29}{80}\right)\)
\(\chi_{6025}(1827,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{47}{80}\right)\)
\(\chi_{6025}(2433,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{1}{80}\right)\)
\(\chi_{6025}(2438,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{53}{80}\right)\)
\(\chi_{6025}(2467,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{51}{80}\right)\)
\(\chi_{6025}(2503,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{69}{80}\right)\)
\(\chi_{6025}(2548,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{37}{80}\right)\)
\(\chi_{6025}(2578,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{9}{80}\right)\)
\(\chi_{6025}(2672,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{79}{80}\right)\)
\(\chi_{6025}(2752,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{7}{80}\right)\)
\(\chi_{6025}(3048,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{57}{80}\right)\)
\(\chi_{6025}(3238,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{73}{80}\right)\)
\(\chi_{6025}(3272,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{19}{80}\right)\)
\(\chi_{6025}(3317,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{11}{80}\right)\)
\(\chi_{6025}(3833,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{41}{80}\right)\)
\(\chi_{6025}(4423,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{17}{80}\right)\)
\(\chi_{6025}(4462,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{43}{80}\right)\)
\(\chi_{6025}(4562,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{63}{80}\right)\)
\(\chi_{6025}(4777,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{27}{80}\right)\)
\(\chi_{6025}(4837,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{23}{80}\right)\)
\(\chi_{6025}(4922,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{59}{80}\right)\)
\(\chi_{6025}(4923,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{77}{80}\right)\)
\(\chi_{6025}(4937,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{3}{80}\right)\)
\(\chi_{6025}(5438,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{33}{80}\right)\)
\(\chi_{6025}(5522,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{39}{80}\right)\)
\(\chi_{6025}(5758,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{61}{80}\right)\)
\(\chi_{6025}(5817,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{71}{80}\right)\)
\(\chi_{6025}(5827,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{67}{80}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 31 of 32 characters in Galois orbit

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	6025.ht
Modulus	$6025$
Conductor	$6025$
Order	$80$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(6025\)
Conductor:	\(6025\)	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)