LMFDB - Group of Dirichlet characters of modulus 4025

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4025)

pari: g = idealstar(,4025,2)

Character group

sage: G.order() pari: g.no
Order	=	2640
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{660}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{4025}(2577,\cdot)$, $\chi_{4025}(1151,\cdot)$, $\chi_{4025}(3501,\cdot)$

First 32 of 2640 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$2$	$3$	$4$	$6$	$8$	$9$	$11$	$12$	$13$	$16$
$\chi_{4025}(1,\cdot)$	4025.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4025}(2,\cdot)$	4025.dq	660	yes	$-1$	$1$	$e\left(\frac{593}{660}\right)$	$e\left(\frac{91}{660}\right)$	$e\left(\frac{263}{330}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{91}{330}\right)$	$e\left(\frac{157}{165}\right)$	$e\left(\frac{617}{660}\right)$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{98}{165}\right)$
$\chi_{4025}(3,\cdot)$	4025.do	660	yes	$1$	$1$	$e\left(\frac{91}{660}\right)$	$e\left(\frac{167}{660}\right)$	$e\left(\frac{91}{330}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{91}{220}\right)$	$e\left(\frac{167}{330}\right)$	$e\left(\frac{134}{165}\right)$	$e\left(\frac{349}{660}\right)$	$e\left(\frac{73}{220}\right)$	$e\left(\frac{91}{165}\right)$
$\chi_{4025}(4,\cdot)$	4025.dm	330	yes	$1$	$1$	$e\left(\frac{263}{330}\right)$	$e\left(\frac{91}{330}\right)$	$e\left(\frac{98}{165}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{91}{165}\right)$	$e\left(\frac{149}{165}\right)$	$e\left(\frac{287}{330}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{31}{165}\right)$
$\chi_{4025}(6,\cdot)$	4025.cw	110	yes	$-1$	$1$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{8}{55}\right)$
$\chi_{4025}(8,\cdot)$	4025.dg	220	no	$-1$	$1$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{91}{220}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{43}{55}\right)$
$\chi_{4025}(9,\cdot)$	4025.dm	330	yes	$1$	$1$	$e\left(\frac{91}{330}\right)$	$e\left(\frac{167}{330}\right)$	$e\left(\frac{91}{165}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{19}{330}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{17}{165}\right)$
$\chi_{4025}(11,\cdot)$	4025.dh	330	yes	$-1$	$1$	$e\left(\frac{157}{165}\right)$	$e\left(\frac{134}{165}\right)$	$e\left(\frac{149}{165}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{49}{330}\right)$	$e\left(\frac{118}{165}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{133}{165}\right)$
$\chi_{4025}(12,\cdot)$	4025.do	660	yes	$1$	$1$	$e\left(\frac{617}{660}\right)$	$e\left(\frac{349}{660}\right)$	$e\left(\frac{287}{330}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{19}{330}\right)$	$e\left(\frac{118}{165}\right)$	$e\left(\frac{263}{660}\right)$	$e\left(\frac{171}{220}\right)$	$e\left(\frac{122}{165}\right)$
$\chi_{4025}(13,\cdot)$	4025.de	220	yes	$1$	$1$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{73}{220}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{171}{220}\right)$	$e\left(\frac{101}{220}\right)$	$e\left(\frac{49}{55}\right)$
$\chi_{4025}(16,\cdot)$	4025.dc	165	yes	$1$	$1$	$e\left(\frac{98}{165}\right)$	$e\left(\frac{91}{165}\right)$	$e\left(\frac{31}{165}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{17}{165}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{122}{165}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{62}{165}\right)$
$\chi_{4025}(17,\cdot)$	4025.dp	660	yes	$-1$	$1$	$e\left(\frac{409}{660}\right)$	$e\left(\frac{533}{660}\right)$	$e\left(\frac{79}{330}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{189}{220}\right)$	$e\left(\frac{203}{330}\right)$	$e\left(\frac{307}{330}\right)$	$e\left(\frac{31}{660}\right)$	$e\left(\frac{67}{220}\right)$	$e\left(\frac{79}{165}\right)$
$\chi_{4025}(18,\cdot)$	4025.cz	132	no	$-1$	$1$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{23}{33}\right)$
$\chi_{4025}(19,\cdot)$	4025.dl	330	yes	$1$	$1$	$e\left(\frac{307}{330}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{142}{165}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{287}{330}\right)$	$e\left(\frac{149}{165}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{119}{165}\right)$
$\chi_{4025}(22,\cdot)$	4025.bj	20	no	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{4025}(24,\cdot)$	4025.r	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$
$\chi_{4025}(26,\cdot)$	4025.cp	66	no	$-1$	$1$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{16}{33}\right)$
$\chi_{4025}(27,\cdot)$	4025.de	220	yes	$1$	$1$	$e\left(\frac{91}{220}\right)$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{129}{220}\right)$	$e\left(\frac{219}{220}\right)$	$e\left(\frac{36}{55}\right)$
$\chi_{4025}(29,\cdot)$	4025.cs	110	no	$1$	$1$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{52}{55}\right)$
$\chi_{4025}(31,\cdot)$	4025.di	330	yes	$-1$	$1$	$e\left(\frac{46}{165}\right)$	$e\left(\frac{109}{330}\right)$	$e\left(\frac{92}{165}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{109}{165}\right)$	$e\left(\frac{86}{165}\right)$	$e\left(\frac{293}{330}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{19}{165}\right)$
$\chi_{4025}(32,\cdot)$	4025.cz	132	no	$-1$	$1$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{32}{33}\right)$
$\chi_{4025}(33,\cdot)$	4025.dp	660	yes	$-1$	$1$	$e\left(\frac{59}{660}\right)$	$e\left(\frac{43}{660}\right)$	$e\left(\frac{59}{330}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{43}{330}\right)$	$e\left(\frac{317}{330}\right)$	$e\left(\frac{161}{660}\right)$	$e\left(\frac{57}{220}\right)$	$e\left(\frac{59}{165}\right)$
$\chi_{4025}(34,\cdot)$	4025.ct	110	yes	$1$	$1$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{4}{55}\right)$
$\chi_{4025}(36,\cdot)$	4025.cf	55	no	$1$	$1$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{16}{55}\right)$
$\chi_{4025}(37,\cdot)$	4025.dr	660	yes	$1$	$1$	$e\left(\frac{17}{660}\right)$	$e\left(\frac{499}{660}\right)$	$e\left(\frac{17}{330}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{17}{220}\right)$	$e\left(\frac{169}{330}\right)$	$e\left(\frac{41}{330}\right)$	$e\left(\frac{533}{660}\right)$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{17}{165}\right)$
$\chi_{4025}(38,\cdot)$	4025.dp	660	yes	$-1$	$1$	$e\left(\frac{547}{660}\right)$	$e\left(\frac{119}{660}\right)$	$e\left(\frac{217}{330}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{107}{220}\right)$	$e\left(\frac{119}{330}\right)$	$e\left(\frac{271}{330}\right)$	$e\left(\frac{553}{660}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{52}{165}\right)$
$\chi_{4025}(39,\cdot)$	4025.dm	330	yes	$1$	$1$	$e\left(\frac{119}{330}\right)$	$e\left(\frac{193}{330}\right)$	$e\left(\frac{119}{165}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{28}{165}\right)$	$e\left(\frac{122}{165}\right)$	$e\left(\frac{101}{330}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{73}{165}\right)$
$\chi_{4025}(41,\cdot)$	4025.cw	110	yes	$-1$	$1$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{9}{55}\right)$
$\chi_{4025}(43,\cdot)$	4025.cc	44	no	$1$	$1$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{4025}(44,\cdot)$	4025.dn	330	yes	$-1$	$1$	$e\left(\frac{247}{330}\right)$	$e\left(\frac{29}{330}\right)$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{29}{165}\right)$	$e\left(\frac{17}{330}\right)$	$e\left(\frac{193}{330}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{164}{165}\right)$
$\chi_{4025}(47,\cdot)$	4025.cj	60	no	$1$	$1$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{4025}(48,\cdot)$	4025.de	220	yes	$1$	$1$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{43}{220}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{51}{55}\right)$

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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 $\F_{q}$

Modulus	$4025$
Structure	\(C_{2}\times C_{2}\times C_{660}\)
Order	$2640$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)	\(16\)
\(\chi_{4025}(1,\cdot)\)	4025.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4025}(2,\cdot)\)	4025.dq	660	yes	\(-1\)	\(1\)	\(e\left(\frac{593}{660}\right)\)	\(e\left(\frac{91}{660}\right)\)	\(e\left(\frac{263}{330}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{91}{330}\right)\)	\(e\left(\frac{157}{165}\right)\)	\(e\left(\frac{617}{660}\right)\)	\(e\left(\frac{49}{220}\right)\)	\(e\left(\frac{98}{165}\right)\)
\(\chi_{4025}(3,\cdot)\)	4025.do	660	yes	\(1\)	\(1\)	\(e\left(\frac{91}{660}\right)\)	\(e\left(\frac{167}{660}\right)\)	\(e\left(\frac{91}{330}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{91}{220}\right)\)	\(e\left(\frac{167}{330}\right)\)	\(e\left(\frac{134}{165}\right)\)	\(e\left(\frac{349}{660}\right)\)	\(e\left(\frac{73}{220}\right)\)	\(e\left(\frac{91}{165}\right)\)
\(\chi_{4025}(4,\cdot)\)	4025.dm	330	yes	\(1\)	\(1\)	\(e\left(\frac{263}{330}\right)\)	\(e\left(\frac{91}{330}\right)\)	\(e\left(\frac{98}{165}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{91}{165}\right)\)	\(e\left(\frac{149}{165}\right)\)	\(e\left(\frac{287}{330}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{31}{165}\right)\)
\(\chi_{4025}(6,\cdot)\)	4025.cw	110	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{8}{55}\right)\)
\(\chi_{4025}(8,\cdot)\)	4025.dg	220	no	\(-1\)	\(1\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{91}{220}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{19}{220}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{43}{55}\right)\)
\(\chi_{4025}(9,\cdot)\)	4025.dm	330	yes	\(1\)	\(1\)	\(e\left(\frac{91}{330}\right)\)	\(e\left(\frac{167}{330}\right)\)	\(e\left(\frac{91}{165}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{19}{330}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{17}{165}\right)\)
\(\chi_{4025}(11,\cdot)\)	4025.dh	330	yes	\(-1\)	\(1\)	\(e\left(\frac{157}{165}\right)\)	\(e\left(\frac{134}{165}\right)\)	\(e\left(\frac{149}{165}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{49}{330}\right)\)	\(e\left(\frac{118}{165}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{133}{165}\right)\)
\(\chi_{4025}(12,\cdot)\)	4025.do	660	yes	\(1\)	\(1\)	\(e\left(\frac{617}{660}\right)\)	\(e\left(\frac{349}{660}\right)\)	\(e\left(\frac{287}{330}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{19}{330}\right)\)	\(e\left(\frac{118}{165}\right)\)	\(e\left(\frac{263}{660}\right)\)	\(e\left(\frac{171}{220}\right)\)	\(e\left(\frac{122}{165}\right)\)
\(\chi_{4025}(13,\cdot)\)	4025.de	220	yes	\(1\)	\(1\)	\(e\left(\frac{49}{220}\right)\)	\(e\left(\frac{73}{220}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{171}{220}\right)\)	\(e\left(\frac{101}{220}\right)\)	\(e\left(\frac{49}{55}\right)\)
\(\chi_{4025}(16,\cdot)\)	4025.dc	165	yes	\(1\)	\(1\)	\(e\left(\frac{98}{165}\right)\)	\(e\left(\frac{91}{165}\right)\)	\(e\left(\frac{31}{165}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{17}{165}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{122}{165}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{62}{165}\right)\)
\(\chi_{4025}(17,\cdot)\)	4025.dp	660	yes	\(-1\)	\(1\)	\(e\left(\frac{409}{660}\right)\)	\(e\left(\frac{533}{660}\right)\)	\(e\left(\frac{79}{330}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{189}{220}\right)\)	\(e\left(\frac{203}{330}\right)\)	\(e\left(\frac{307}{330}\right)\)	\(e\left(\frac{31}{660}\right)\)	\(e\left(\frac{67}{220}\right)\)	\(e\left(\frac{79}{165}\right)\)
\(\chi_{4025}(18,\cdot)\)	4025.cz	132	no	\(-1\)	\(1\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{23}{33}\right)\)
\(\chi_{4025}(19,\cdot)\)	4025.dl	330	yes	\(1\)	\(1\)	\(e\left(\frac{307}{330}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{142}{165}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{287}{330}\right)\)	\(e\left(\frac{149}{165}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{119}{165}\right)\)
\(\chi_{4025}(22,\cdot)\)	4025.bj	20	no	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{4025}(24,\cdot)\)	4025.r	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{4025}(26,\cdot)\)	4025.cp	66	no	\(-1\)	\(1\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{16}{33}\right)\)
\(\chi_{4025}(27,\cdot)\)	4025.de	220	yes	\(1\)	\(1\)	\(e\left(\frac{91}{220}\right)\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{129}{220}\right)\)	\(e\left(\frac{219}{220}\right)\)	\(e\left(\frac{36}{55}\right)\)
\(\chi_{4025}(29,\cdot)\)	4025.cs	110	no	\(1\)	\(1\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{52}{55}\right)\)
\(\chi_{4025}(31,\cdot)\)	4025.di	330	yes	\(-1\)	\(1\)	\(e\left(\frac{46}{165}\right)\)	\(e\left(\frac{109}{330}\right)\)	\(e\left(\frac{92}{165}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{109}{165}\right)\)	\(e\left(\frac{86}{165}\right)\)	\(e\left(\frac{293}{330}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{19}{165}\right)\)
\(\chi_{4025}(32,\cdot)\)	4025.cz	132	no	\(-1\)	\(1\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{32}{33}\right)\)
\(\chi_{4025}(33,\cdot)\)	4025.dp	660	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{660}\right)\)	\(e\left(\frac{43}{660}\right)\)	\(e\left(\frac{59}{330}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{43}{330}\right)\)	\(e\left(\frac{317}{330}\right)\)	\(e\left(\frac{161}{660}\right)\)	\(e\left(\frac{57}{220}\right)\)	\(e\left(\frac{59}{165}\right)\)
\(\chi_{4025}(34,\cdot)\)	4025.ct	110	yes	\(1\)	\(1\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)
\(\chi_{4025}(36,\cdot)\)	4025.cf	55	no	\(1\)	\(1\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)
\(\chi_{4025}(37,\cdot)\)	4025.dr	660	yes	\(1\)	\(1\)	\(e\left(\frac{17}{660}\right)\)	\(e\left(\frac{499}{660}\right)\)	\(e\left(\frac{17}{330}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{17}{220}\right)\)	\(e\left(\frac{169}{330}\right)\)	\(e\left(\frac{41}{330}\right)\)	\(e\left(\frac{533}{660}\right)\)	\(e\left(\frac{201}{220}\right)\)	\(e\left(\frac{17}{165}\right)\)
\(\chi_{4025}(38,\cdot)\)	4025.dp	660	yes	\(-1\)	\(1\)	\(e\left(\frac{547}{660}\right)\)	\(e\left(\frac{119}{660}\right)\)	\(e\left(\frac{217}{330}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{107}{220}\right)\)	\(e\left(\frac{119}{330}\right)\)	\(e\left(\frac{271}{330}\right)\)	\(e\left(\frac{553}{660}\right)\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{52}{165}\right)\)
\(\chi_{4025}(39,\cdot)\)	4025.dm	330	yes	\(1\)	\(1\)	\(e\left(\frac{119}{330}\right)\)	\(e\left(\frac{193}{330}\right)\)	\(e\left(\frac{119}{165}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{28}{165}\right)\)	\(e\left(\frac{122}{165}\right)\)	\(e\left(\frac{101}{330}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{73}{165}\right)\)
\(\chi_{4025}(41,\cdot)\)	4025.cw	110	yes	\(-1\)	\(1\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{9}{55}\right)\)
\(\chi_{4025}(43,\cdot)\)	4025.cc	44	no	\(1\)	\(1\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{4025}(44,\cdot)\)	4025.dn	330	yes	\(-1\)	\(1\)	\(e\left(\frac{247}{330}\right)\)	\(e\left(\frac{29}{330}\right)\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{29}{165}\right)\)	\(e\left(\frac{17}{330}\right)\)	\(e\left(\frac{193}{330}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{164}{165}\right)\)
\(\chi_{4025}(47,\cdot)\)	4025.cj	60	no	\(1\)	\(1\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{4025}(48,\cdot)\)	4025.de	220	yes	\(1\)	\(1\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{43}{220}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{49}{220}\right)\)	\(e\left(\frac{51}{55}\right)\)

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