LMFDB - Group of Dirichlet characters of modulus 9075

sage:H = DirichletGroup(9075)

pari:g = idealstar(,9075,2)

Character group

sage:G.order() pari:g.no
Order	=	4400
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{10}\times C_{220}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{9075}(3026,\cdot)$, $\chi_{9075}(727,\cdot)$, $\chi_{9075}(5326,\cdot)$

First 32 of 4400 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	$-1$	$1$	$2$	$4$	$7$	$8$	$13$	$14$	$16$	$17$	$19$	$23$
$\chi_{9075}(1,\cdot)$	9075.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{9075}(2,\cdot)$	9075.gc	220	yes	$-1$	$1$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{69}{220}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{191}{220}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{151}{220}\right)$
$\chi_{9075}(4,\cdot)$	9075.eh	110	no	$1$	$1$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{41}{110}\right)$
$\chi_{9075}(7,\cdot)$	9075.fx	220	no	$1$	$1$	$e\left(\frac{69}{220}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{207}{220}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{9}{44}\right)$
$\chi_{9075}(8,\cdot)$	9075.gc	220	yes	$-1$	$1$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{207}{220}\right)$	$e\left(\frac{7}{220}\right)$	$e\left(\frac{133}{220}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{173}{220}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{13}{220}\right)$
$\chi_{9075}(13,\cdot)$	9075.gh	220	no	$1$	$1$	$e\left(\frac{191}{220}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{133}{220}\right)$	$e\left(\frac{173}{220}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{159}{220}\right)$
$\chi_{9075}(14,\cdot)$	9075.fd	110	yes	$-1$	$1$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{49}{55}\right)$
$\chi_{9075}(16,\cdot)$	9075.dx	55	no	$1$	$1$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{41}{55}\right)$
$\chi_{9075}(17,\cdot)$	9075.gd	220	yes	$-1$	$1$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{173}{220}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{171}{220}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{183}{220}\right)$
$\chi_{9075}(19,\cdot)$	9075.fg	110	no	$-1$	$1$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{79}{110}\right)$
$\chi_{9075}(23,\cdot)$	9075.gb	220	yes	$1$	$1$	$e\left(\frac{151}{220}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{13}{220}\right)$	$e\left(\frac{159}{220}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{183}{220}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{21}{220}\right)$
$\chi_{9075}(26,\cdot)$	9075.eq	110	no	$-1$	$1$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{9075}(28,\cdot)$	9075.gi	220	no	$1$	$1$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{127}{220}\right)$
$\chi_{9075}(29,\cdot)$	9075.eo	110	yes	$1$	$1$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{23}{55}\right)$
$\chi_{9075}(31,\cdot)$	9075.ds	55	no	$1$	$1$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{7}{55}\right)$
$\chi_{9075}(32,\cdot)$	9075.do	44	no	$-1$	$1$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{19}{44}\right)$
$\chi_{9075}(34,\cdot)$	9075.eu	110	no	$1$	$1$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{57}{110}\right)$
$\chi_{9075}(37,\cdot)$	9075.fs	220	no	$-1$	$1$	$e\left(\frac{183}{220}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{149}{220}\right)$
$\chi_{9075}(38,\cdot)$	9075.fy	220	yes	$1$	$1$	$e\left(\frac{47}{220}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{141}{220}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{89}{220}\right)$
$\chi_{9075}(41,\cdot)$	9075.dz	110	yes	$1$	$1$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{37}{110}\right)$
$\chi_{9075}(43,\cdot)$	9075.dq	44	no	$1$	$1$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{44}\right)$
$\chi_{9075}(46,\cdot)$	9075.ej	110	no	$-1$	$1$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{43}{55}\right)$
$\chi_{9075}(47,\cdot)$	9075.fo	220	yes	$1$	$1$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{107}{220}\right)$	$e\left(\frac{159}{220}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{47}{220}\right)$
$\chi_{9075}(49,\cdot)$	9075.ei	110	no	$1$	$1$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{9075}(52,\cdot)$	9075.fw	220	no	$1$	$1$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{21}{220}\right)$
$\chi_{9075}(53,\cdot)$	9075.fz	220	yes	$1$	$1$	$e\left(\frac{179}{220}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{97}{220}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{177}{220}\right)$
$\chi_{9075}(56,\cdot)$	9075.ec	110	yes	$-1$	$1$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{29}{110}\right)$
$\chi_{9075}(58,\cdot)$	9075.fr	220	no	$-1$	$1$	$e\left(\frac{69}{220}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{207}{220}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{23}{220}\right)$
$\chi_{9075}(59,\cdot)$	9075.fd	110	yes	$-1$	$1$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{31}{55}\right)$
$\chi_{9075}(61,\cdot)$	9075.ed	110	no	$-1$	$1$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{9}{55}\right)$
$\chi_{9075}(62,\cdot)$	9075.gd	220	yes	$-1$	$1$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{173}{220}\right)$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{23}{220}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{179}{220}\right)$
$\chi_{9075}(64,\cdot)$	9075.eh	110	no	$1$	$1$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{13}{110}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$9075$
Structure	\(C_{2}\times C_{10}\times C_{220}\)
Order	$4400$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)	\(23\)
\(\chi_{9075}(1,\cdot)\)	9075.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{9075}(2,\cdot)\)	9075.gc	220	yes	\(-1\)	\(1\)	\(e\left(\frac{123}{220}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{69}{220}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{191}{220}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{151}{220}\right)\)
\(\chi_{9075}(4,\cdot)\)	9075.eh	110	no	\(1\)	\(1\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{41}{110}\right)\)
\(\chi_{9075}(7,\cdot)\)	9075.fx	220	no	\(1\)	\(1\)	\(e\left(\frac{69}{220}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{207}{220}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{9}{44}\right)\)
\(\chi_{9075}(8,\cdot)\)	9075.gc	220	yes	\(-1\)	\(1\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{207}{220}\right)\)	\(e\left(\frac{7}{220}\right)\)	\(e\left(\frac{133}{220}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{173}{220}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{13}{220}\right)\)
\(\chi_{9075}(13,\cdot)\)	9075.gh	220	no	\(1\)	\(1\)	\(e\left(\frac{191}{220}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{133}{220}\right)\)	\(e\left(\frac{173}{220}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{159}{220}\right)\)
\(\chi_{9075}(14,\cdot)\)	9075.fd	110	yes	\(-1\)	\(1\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)
\(\chi_{9075}(16,\cdot)\)	9075.dx	55	no	\(1\)	\(1\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)
\(\chi_{9075}(17,\cdot)\)	9075.gd	220	yes	\(-1\)	\(1\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{173}{220}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{171}{220}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{183}{220}\right)\)
\(\chi_{9075}(19,\cdot)\)	9075.fg	110	no	\(-1\)	\(1\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{79}{110}\right)\)
\(\chi_{9075}(23,\cdot)\)	9075.gb	220	yes	\(1\)	\(1\)	\(e\left(\frac{151}{220}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{13}{220}\right)\)	\(e\left(\frac{159}{220}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{183}{220}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{21}{220}\right)\)
\(\chi_{9075}(26,\cdot)\)	9075.eq	110	no	\(-1\)	\(1\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{9075}(28,\cdot)\)	9075.gi	220	no	\(1\)	\(1\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{201}{220}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{123}{220}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{127}{220}\right)\)
\(\chi_{9075}(29,\cdot)\)	9075.eo	110	yes	\(1\)	\(1\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{23}{55}\right)\)
\(\chi_{9075}(31,\cdot)\)	9075.ds	55	no	\(1\)	\(1\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{7}{55}\right)\)
\(\chi_{9075}(32,\cdot)\)	9075.do	44	no	\(-1\)	\(1\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{19}{44}\right)\)
\(\chi_{9075}(34,\cdot)\)	9075.eu	110	no	\(1\)	\(1\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{57}{110}\right)\)
\(\chi_{9075}(37,\cdot)\)	9075.fs	220	no	\(-1\)	\(1\)	\(e\left(\frac{183}{220}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{123}{220}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{149}{220}\right)\)
\(\chi_{9075}(38,\cdot)\)	9075.fy	220	yes	\(1\)	\(1\)	\(e\left(\frac{47}{220}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{21}{220}\right)\)	\(e\left(\frac{141}{220}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{89}{220}\right)\)
\(\chi_{9075}(41,\cdot)\)	9075.dz	110	yes	\(1\)	\(1\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{37}{110}\right)\)
\(\chi_{9075}(43,\cdot)\)	9075.dq	44	no	\(1\)	\(1\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{44}\right)\)
\(\chi_{9075}(46,\cdot)\)	9075.ej	110	no	\(-1\)	\(1\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{43}{55}\right)\)
\(\chi_{9075}(47,\cdot)\)	9075.fo	220	yes	\(1\)	\(1\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{107}{220}\right)\)	\(e\left(\frac{159}{220}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{47}{220}\right)\)
\(\chi_{9075}(49,\cdot)\)	9075.ei	110	no	\(1\)	\(1\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{9075}(52,\cdot)\)	9075.fw	220	no	\(1\)	\(1\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{21}{220}\right)\)
\(\chi_{9075}(53,\cdot)\)	9075.fz	220	yes	\(1\)	\(1\)	\(e\left(\frac{179}{220}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{97}{220}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{177}{220}\right)\)
\(\chi_{9075}(56,\cdot)\)	9075.ec	110	yes	\(-1\)	\(1\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{29}{110}\right)\)
\(\chi_{9075}(58,\cdot)\)	9075.fr	220	no	\(-1\)	\(1\)	\(e\left(\frac{69}{220}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{207}{220}\right)\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{213}{220}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{23}{220}\right)\)
\(\chi_{9075}(59,\cdot)\)	9075.fd	110	yes	\(-1\)	\(1\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)
\(\chi_{9075}(61,\cdot)\)	9075.ed	110	no	\(-1\)	\(1\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{9}{55}\right)\)
\(\chi_{9075}(62,\cdot)\)	9075.gd	220	yes	\(-1\)	\(1\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{173}{220}\right)\)	\(e\left(\frac{49}{220}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{23}{220}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{179}{220}\right)\)
\(\chi_{9075}(64,\cdot)\)	9075.eh	110	no	\(1\)	\(1\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{13}{110}\right)\)

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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.