Properties

Modulus 69696
Structure \(C_{2640}\times C_{2}\times C_{2}\times C_{2}\)
Order 21120

Learn more about

Show commands for: Pari/GP / SageMath

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(69696)
 
pari: g = idealstar(,69696,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 21120
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2640}\times C_{2}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{69696}(35213,\cdot)$, $\chi_{69696}(2177,\cdot)$, $\chi_{69696}(40897,\cdot)$, $\chi_{69696}(67519,\cdot)$

First 37 of 21120 characters

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

order primitive 1 5 7 13 17 19 23 25 29 31 35 37 41 43 47 49 53 59 61 65 67 71 73 79 83 85 89 91 95 97
\(\chi_{69696}(1,\cdot)\) 1 no 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
\(\chi_{69696}(5,\cdot)\) 2640 yes 1 \(e\left(\frac{29}{2640}\right)\) \(e\left(\frac{881}{1320}\right)\) \(e\left(\frac{1451}{2640}\right)\) \(e\left(\frac{47}{220}\right)\) \(e\left(\frac{241}{880}\right)\) \(e\left(\frac{35}{264}\right)\) \(e\left(\frac{29}{1320}\right)\) \(e\left(\frac{2527}{2640}\right)\) \(e\left(\frac{7}{330}\right)\) \(e\left(\frac{597}{880}\right)\) \(e\left(\frac{719}{880}\right)\) \(e\left(\frac{679}{1320}\right)\) \(e\left(\frac{509}{528}\right)\) \(e\left(\frac{337}{660}\right)\) \(e\left(\frac{221}{660}\right)\) \(e\left(\frac{107}{880}\right)\) \(e\left(\frac{1997}{2640}\right)\) \(e\left(\frac{2239}{2640}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{67}{528}\right)\) \(e\left(\frac{159}{440}\right)\) \(e\left(\frac{117}{440}\right)\) \(e\left(\frac{109}{660}\right)\) \(e\left(\frac{2059}{2640}\right)\) \(e\left(\frac{593}{2640}\right)\) \(e\left(\frac{87}{88}\right)\) \(e\left(\frac{191}{880}\right)\) \(e\left(\frac{47}{165}\right)\) \(e\left(\frac{17}{330}\right)\)
\(\chi_{69696}(7,\cdot)\) 1320 no 1 \(e\left(\frac{881}{1320}\right)\) \(e\left(\frac{569}{660}\right)\) \(e\left(\frac{179}{1320}\right)\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{69}{440}\right)\) \(e\left(\frac{5}{132}\right)\) \(e\left(\frac{221}{660}\right)\) \(e\left(\frac{823}{1320}\right)\) \(e\left(\frac{101}{330}\right)\) \(e\left(\frac{233}{440}\right)\) \(e\left(\frac{131}{440}\right)\) \(e\left(\frac{361}{660}\right)\) \(e\left(\frac{233}{264}\right)\) \(e\left(\frac{149}{165}\right)\) \(e\left(\frac{239}{330}\right)\) \(e\left(\frac{383}{440}\right)\) \(e\left(\frac{653}{1320}\right)\) \(e\left(\frac{631}{1320}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{19}{264}\right)\) \(e\left(\frac{161}{220}\right)\) \(e\left(\frac{23}{220}\right)\) \(e\left(\frac{91}{330}\right)\) \(e\left(\frac{511}{1320}\right)\) \(e\left(\frac{377}{1320}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{439}{440}\right)\) \(e\left(\frac{136}{165}\right)\) \(e\left(\frac{158}{165}\right)\)
\(\chi_{69696}(13,\cdot)\) 2640 yes 1 \(e\left(\frac{1451}{2640}\right)\) \(e\left(\frac{179}{1320}\right)\) \(e\left(\frac{1229}{2640}\right)\) \(e\left(\frac{53}{220}\right)\) \(e\left(\frac{679}{880}\right)\) \(e\left(\frac{17}{264}\right)\) \(e\left(\frac{131}{1320}\right)\) \(e\left(\frac{673}{2640}\right)\) \(e\left(\frac{43}{330}\right)\) \(e\left(\frac{603}{880}\right)\) \(e\left(\frac{1}{880}\right)\) \(e\left(\frac{1201}{1320}\right)\) \(e\left(\frac{251}{528}\right)\) \(e\left(\frac{373}{660}\right)\) \(e\left(\frac{179}{660}\right)\) \(e\left(\frac{13}{880}\right)\) \(e\left(\frac{2603}{2640}\right)\) \(e\left(\frac{601}{2640}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{157}{528}\right)\) \(e\left(\frac{301}{440}\right)\) \(e\left(\frac{263}{440}\right)\) \(e\left(\frac{481}{660}\right)\) \(e\left(\frac{1381}{2640}\right)\) \(e\left(\frac{2087}{2640}\right)\) \(e\left(\frac{85}{88}\right)\) \(e\left(\frac{529}{880}\right)\) \(e\left(\frac{53}{165}\right)\) \(e\left(\frac{293}{330}\right)\)
\(\chi_{69696}(17,\cdot)\) 220 no 1 \(e\left(\frac{47}{220}\right)\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{53}{220}\right)\) \(e\left(\frac{18}{55}\right)\) \(e\left(\frac{49}{220}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{47}{110}\right)\) \(e\left(\frac{71}{220}\right)\) \(e\left(\frac{17}{55}\right)\) \(e\left(\frac{183}{220}\right)\) \(e\left(\frac{101}{220}\right)\) \(e\left(\frac{27}{110}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{17}{110}\right)\) \(e\left(\frac{13}{55}\right)\) \(e\left(\frac{103}{220}\right)\) \(e\left(\frac{111}{220}\right)\) \(e\left(\frac{177}{220}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{48}{55}\right)\) \(e\left(\frac{54}{55}\right)\) \(e\left(\frac{29}{110}\right)\) \(e\left(\frac{147}{220}\right)\) \(e\left(\frac{119}{220}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{189}{220}\right)\) \(e\left(\frac{24}{55}\right)\) \(e\left(\frac{2}{55}\right)\)
\(\chi_{69696}(19,\cdot)\) 880 no 1 \(e\left(\frac{241}{880}\right)\) \(e\left(\frac{69}{440}\right)\) \(e\left(\frac{679}{880}\right)\) \(e\left(\frac{49}{220}\right)\) \(e\left(\frac{167}{880}\right)\) \(e\left(\frac{39}{88}\right)\) \(e\left(\frac{241}{440}\right)\) \(e\left(\frac{563}{880}\right)\) \(e\left(\frac{49}{55}\right)\) \(e\left(\frac{379}{880}\right)\) \(e\left(\frac{553}{880}\right)\) \(e\left(\frac{211}{440}\right)\) \(e\left(\frac{9}{176}\right)\) \(e\left(\frac{153}{220}\right)\) \(e\left(\frac{69}{220}\right)\) \(e\left(\frac{149}{880}\right)\) \(e\left(\frac{73}{880}\right)\) \(e\left(\frac{491}{880}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{47}{176}\right)\) \(e\left(\frac{353}{440}\right)\) \(e\left(\frac{239}{440}\right)\) \(e\left(\frac{41}{220}\right)\) \(e\left(\frac{391}{880}\right)\) \(e\left(\frac{437}{880}\right)\) \(e\left(\frac{13}{88}\right)\) \(e\left(\frac{817}{880}\right)\) \(e\left(\frac{51}{110}\right)\) \(e\left(\frac{73}{110}\right)\)
\(\chi_{69696}(23,\cdot)\) 264 no 1 \(e\left(\frac{35}{264}\right)\) \(e\left(\frac{5}{132}\right)\) \(e\left(\frac{17}{264}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{39}{88}\right)\) \(e\left(\frac{61}{132}\right)\) \(e\left(\frac{35}{132}\right)\) \(e\left(\frac{73}{264}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{15}{88}\right)\) \(e\left(\frac{53}{88}\right)\) \(e\left(\frac{7}{132}\right)\) \(e\left(\frac{31}{264}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{29}{88}\right)\) \(e\left(\frac{239}{264}\right)\) \(e\left(\frac{85}{264}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{113}{264}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{241}{264}\right)\) \(e\left(\frac{83}{264}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{9}{88}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{8}{33}\right)\)
\(\chi_{69696}(25,\cdot)\) 1320 no 1 \(e\left(\frac{29}{1320}\right)\) \(e\left(\frac{221}{660}\right)\) \(e\left(\frac{131}{1320}\right)\) \(e\left(\frac{47}{110}\right)\) \(e\left(\frac{241}{440}\right)\) \(e\left(\frac{35}{132}\right)\) \(e\left(\frac{29}{660}\right)\) \(e\left(\frac{1207}{1320}\right)\) \(e\left(\frac{7}{165}\right)\) \(e\left(\frac{157}{440}\right)\) \(e\left(\frac{279}{440}\right)\) \(e\left(\frac{19}{660}\right)\) \(e\left(\frac{245}{264}\right)\) \(e\left(\frac{7}{330}\right)\) \(e\left(\frac{221}{330}\right)\) \(e\left(\frac{107}{440}\right)\) \(e\left(\frac{677}{1320}\right)\) \(e\left(\frac{919}{1320}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{67}{264}\right)\) \(e\left(\frac{159}{220}\right)\) \(e\left(\frac{117}{220}\right)\) \(e\left(\frac{109}{330}\right)\) \(e\left(\frac{739}{1320}\right)\) \(e\left(\frac{593}{1320}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{191}{440}\right)\) \(e\left(\frac{94}{165}\right)\) \(e\left(\frac{17}{165}\right)\)
\(\chi_{69696}(29,\cdot)\) 2640 yes 1 \(e\left(\frac{2527}{2640}\right)\) \(e\left(\frac{823}{1320}\right)\) \(e\left(\frac{673}{2640}\right)\) \(e\left(\frac{71}{220}\right)\) \(e\left(\frac{563}{880}\right)\) \(e\left(\frac{73}{264}\right)\) \(e\left(\frac{1207}{1320}\right)\) \(e\left(\frac{941}{2640}\right)\) \(e\left(\frac{41}{330}\right)\) \(e\left(\frac{511}{880}\right)\) \(e\left(\frac{597}{880}\right)\) \(e\left(\frac{17}{1320}\right)\) \(e\left(\frac{247}{528}\right)\) \(e\left(\frac{371}{660}\right)\) \(e\left(\frac{163}{660}\right)\) \(e\left(\frac{281}{880}\right)\) \(e\left(\frac{1231}{2640}\right)\) \(e\left(\frac{1517}{2640}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{449}{528}\right)\) \(e\left(\frac{397}{440}\right)\) \(e\left(\frac{371}{440}\right)\) \(e\left(\frac{497}{660}\right)\) \(e\left(\frac{1217}{2640}\right)\) \(e\left(\frac{739}{2640}\right)\) \(e\left(\frac{13}{88}\right)\) \(e\left(\frac{773}{880}\right)\) \(e\left(\frac{197}{330}\right)\) \(e\left(\frac{241}{330}\right)\)
\(\chi_{69696}(31,\cdot)\) 330 no 1 \(e\left(\frac{7}{330}\right)\) \(e\left(\frac{101}{330}\right)\) \(e\left(\frac{43}{330}\right)\) \(e\left(\frac{17}{55}\right)\) \(e\left(\frac{49}{55}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{7}{165}\right)\) \(e\left(\frac{41}{330}\right)\) \(e\left(\frac{133}{330}\right)\) \(e\left(\frac{18}{55}\right)\) \(e\left(\frac{37}{110}\right)\) \(e\left(\frac{107}{165}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{149}{330}\right)\) \(e\left(\frac{101}{165}\right)\) \(e\left(\frac{41}{110}\right)\) \(e\left(\frac{113}{165}\right)\) \(e\left(\frac{17}{330}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{109}{110}\right)\) \(e\left(\frac{51}{55}\right)\) \(e\left(\frac{293}{330}\right)\) \(e\left(\frac{1}{165}\right)\) \(e\left(\frac{109}{330}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{24}{55}\right)\) \(e\left(\frac{301}{330}\right)\) \(e\left(\frac{79}{165}\right)\)
\(\chi_{69696}(35,\cdot)\) 880 no 1 \(e\left(\frac{597}{880}\right)\) \(e\left(\frac{233}{440}\right)\) \(e\left(\frac{603}{880}\right)\) \(e\left(\frac{183}{220}\right)\) \(e\left(\frac{379}{880}\right)\) \(e\left(\frac{15}{88}\right)\) \(e\left(\frac{157}{440}\right)\) \(e\left(\frac{511}{880}\right)\) \(e\left(\frac{18}{55}\right)\) \(e\left(\frac{183}{880}\right)\) \(e\left(\frac{101}{880}\right)\) \(e\left(\frac{27}{440}\right)\) \(e\left(\frac{149}{176}\right)\) \(e\left(\frac{91}{220}\right)\) \(e\left(\frac{13}{220}\right)\) \(e\left(\frac{873}{880}\right)\) \(e\left(\frac{221}{880}\right)\) \(e\left(\frac{287}{880}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{35}{176}\right)\) \(e\left(\frac{41}{440}\right)\) \(e\left(\frac{163}{440}\right)\) \(e\left(\frac{97}{220}\right)\) \(e\left(\frac{147}{880}\right)\) \(e\left(\frac{449}{880}\right)\) \(e\left(\frac{5}{88}\right)\) \(e\left(\frac{189}{880}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{1}{110}\right)\)
\(\chi_{69696}(37,\cdot)\) 880 no 1 \(e\left(\frac{719}{880}\right)\) \(e\left(\frac{131}{440}\right)\) \(e\left(\frac{1}{880}\right)\) \(e\left(\frac{101}{220}\right)\) \(e\left(\frac{553}{880}\right)\) \(e\left(\frac{53}{88}\right)\) \(e\left(\frac{279}{440}\right)\) \(e\left(\frac{597}{880}\right)\) \(e\left(\frac{37}{110}\right)\) \(e\left(\frac{101}{880}\right)\) \(e\left(\frac{87}{880}\right)\) \(e\left(\frac{289}{440}\right)\) \(e\left(\frac{151}{176}\right)\) \(e\left(\frac{37}{220}\right)\) \(e\left(\frac{131}{220}\right)\) \(e\left(\frac{251}{880}\right)\) \(e\left(\frac{687}{880}\right)\) \(e\left(\frac{269}{880}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{153}{176}\right)\) \(e\left(\frac{227}{440}\right)\) \(e\left(\frac{221}{440}\right)\) \(e\left(\frac{199}{220}\right)\) \(e\left(\frac{9}{880}\right)\) \(e\left(\frac{243}{880}\right)\) \(e\left(\frac{3}{88}\right)\) \(e\left(\frac{263}{880}\right)\) \(e\left(\frac{49}{110}\right)\) \(e\left(\frac{27}{110}\right)\)
\(\chi_{69696}(41,\cdot)\) 1320 no 1 \(e\left(\frac{679}{1320}\right)\) \(e\left(\frac{361}{660}\right)\) \(e\left(\frac{1201}{1320}\right)\) \(e\left(\frac{27}{110}\right)\) \(e\left(\frac{211}{440}\right)\) \(e\left(\frac{7}{132}\right)\) \(e\left(\frac{19}{660}\right)\) \(e\left(\frac{17}{1320}\right)\) \(e\left(\frac{107}{165}\right)\) \(e\left(\frac{27}{440}\right)\) \(e\left(\frac{289}{440}\right)\) \(e\left(\frac{149}{660}\right)\) \(e\left(\frac{247}{264}\right)\) \(e\left(\frac{136}{165}\right)\) \(e\left(\frac{31}{330}\right)\) \(e\left(\frac{17}{440}\right)\) \(e\left(\frac{967}{1320}\right)\) \(e\left(\frac{989}{1320}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{53}{264}\right)\) \(e\left(\frac{199}{220}\right)\) \(e\left(\frac{217}{220}\right)\) \(e\left(\frac{67}{165}\right)\) \(e\left(\frac{29}{1320}\right)\) \(e\left(\frac{1003}{1320}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{201}{440}\right)\) \(e\left(\frac{164}{165}\right)\) \(e\left(\frac{142}{165}\right)\)
\(\chi_{69696}(43,\cdot)\) 528 yes 1 \(e\left(\frac{509}{528}\right)\) \(e\left(\frac{233}{264}\right)\) \(e\left(\frac{251}{528}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{9}{176}\right)\) \(e\left(\frac{31}{264}\right)\) \(e\left(\frac{245}{264}\right)\) \(e\left(\frac{247}{528}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{149}{176}\right)\) \(e\left(\frac{151}{176}\right)\) \(e\left(\frac{247}{264}\right)\) \(e\left(\frac{217}{528}\right)\) \(e\left(\frac{25}{132}\right)\) \(e\left(\frac{101}{132}\right)\) \(e\left(\frac{27}{176}\right)\) \(e\left(\frac{485}{528}\right)\) \(e\left(\frac{463}{528}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{527}{528}\right)\) \(e\left(\frac{87}{88}\right)\) \(e\left(\frac{25}{88}\right)\) \(e\left(\frac{97}{132}\right)\) \(e\left(\frac{235}{528}\right)\) \(e\left(\frac{449}{528}\right)\) \(e\left(\frac{23}{88}\right)\) \(e\left(\frac{63}{176}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{23}{66}\right)\)
\(\chi_{69696}(47,\cdot)\) 660 no 1 \(e\left(\frac{337}{660}\right)\) \(e\left(\frac{149}{165}\right)\) \(e\left(\frac{373}{660}\right)\) \(e\left(\frac{17}{110}\right)\) \(e\left(\frac{153}{220}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{7}{330}\right)\) \(e\left(\frac{371}{660}\right)\) \(e\left(\frac{149}{330}\right)\) \(e\left(\frac{91}{220}\right)\) \(e\left(\frac{37}{220}\right)\) \(e\left(\frac{136}{165}\right)\) \(e\left(\frac{25}{132}\right)\) \(e\left(\frac{161}{165}\right)\) \(e\left(\frac{133}{165}\right)\) \(e\left(\frac{151}{220}\right)\) \(e\left(\frac{391}{660}\right)\) \(e\left(\frac{17}{660}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{23}{132}\right)\) \(e\left(\frac{27}{110}\right)\) \(e\left(\frac{51}{110}\right)\) \(e\left(\frac{229}{330}\right)\) \(e\left(\frac{497}{660}\right)\) \(e\left(\frac{439}{660}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{103}{220}\right)\) \(e\left(\frac{34}{165}\right)\) \(e\left(\frac{122}{165}\right)\)
\(\chi_{69696}(49,\cdot)\) 660 no 1 \(e\left(\frac{221}{660}\right)\) \(e\left(\frac{239}{330}\right)\) \(e\left(\frac{179}{660}\right)\) \(e\left(\frac{13}{55}\right)\) \(e\left(\frac{69}{220}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{221}{330}\right)\) \(e\left(\frac{163}{660}\right)\) \(e\left(\frac{101}{165}\right)\) \(e\left(\frac{13}{220}\right)\) \(e\left(\frac{131}{220}\right)\) \(e\left(\frac{31}{330}\right)\) \(e\left(\frac{101}{132}\right)\) \(e\left(\frac{133}{165}\right)\) \(e\left(\frac{74}{165}\right)\) \(e\left(\frac{163}{220}\right)\) \(e\left(\frac{653}{660}\right)\) \(e\left(\frac{631}{660}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{19}{132}\right)\) \(e\left(\frac{51}{110}\right)\) \(e\left(\frac{23}{110}\right)\) \(e\left(\frac{91}{165}\right)\) \(e\left(\frac{511}{660}\right)\) \(e\left(\frac{377}{660}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{219}{220}\right)\) \(e\left(\frac{107}{165}\right)\) \(e\left(\frac{151}{165}\right)\)
\(\chi_{69696}(53,\cdot)\) 880 no 1 \(e\left(\frac{107}{880}\right)\) \(e\left(\frac{383}{440}\right)\) \(e\left(\frac{13}{880}\right)\) \(e\left(\frac{103}{220}\right)\) \(e\left(\frac{149}{880}\right)\) \(e\left(\frac{29}{88}\right)\) \(e\left(\frac{107}{440}\right)\) \(e\left(\frac{281}{880}\right)\) \(e\left(\frac{41}{110}\right)\) \(e\left(\frac{873}{880}\right)\) \(e\left(\frac{251}{880}\right)\) \(e\left(\frac{17}{440}\right)\) \(e\left(\frac{27}{176}\right)\) \(e\left(\frac{151}{220}\right)\) \(e\left(\frac{163}{220}\right)\) \(e\left(\frac{183}{880}\right)\) \(e\left(\frac{571}{880}\right)\) \(e\left(\frac{857}{880}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{53}{176}\right)\) \(e\left(\frac{91}{440}\right)\) \(e\left(\frac{233}{440}\right)\) \(e\left(\frac{167}{220}\right)\) \(e\left(\frac{557}{880}\right)\) \(e\left(\frac{519}{880}\right)\) \(e\left(\frac{83}{88}\right)\) \(e\left(\frac{779}{880}\right)\) \(e\left(\frac{16}{55}\right)\) \(e\left(\frac{21}{110}\right)\)
\(\chi_{69696}(59,\cdot)\) 2640 yes 1 \(e\left(\frac{1997}{2640}\right)\) \(e\left(\frac{653}{1320}\right)\) \(e\left(\frac{2603}{2640}\right)\) \(e\left(\frac{111}{220}\right)\) \(e\left(\frac{73}{880}\right)\) \(e\left(\frac{239}{264}\right)\) \(e\left(\frac{677}{1320}\right)\) \(e\left(\frac{1231}{2640}\right)\) \(e\left(\frac{113}{165}\right)\) \(e\left(\frac{221}{880}\right)\) \(e\left(\frac{687}{880}\right)\) \(e\left(\frac{967}{1320}\right)\) \(e\left(\frac{485}{528}\right)\) \(e\left(\frac{391}{660}\right)\) \(e\left(\frac{653}{660}\right)\) \(e\left(\frac{571}{880}\right)\) \(e\left(\frac{101}{2640}\right)\) \(e\left(\frac{607}{2640}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{235}{528}\right)\) \(e\left(\frac{427}{440}\right)\) \(e\left(\frac{61}{440}\right)\) \(e\left(\frac{7}{660}\right)\) \(e\left(\frac{547}{2640}\right)\) \(e\left(\frac{689}{2640}\right)\) \(e\left(\frac{7}{88}\right)\) \(e\left(\frac{423}{880}\right)\) \(e\left(\frac{277}{330}\right)\) \(e\left(\frac{101}{330}\right)\)
\(\chi_{69696}(61,\cdot)\) 2640 yes 1 \(e\left(\frac{2239}{2640}\right)\) \(e\left(\frac{631}{1320}\right)\) \(e\left(\frac{601}{2640}\right)\) \(e\left(\frac{177}{220}\right)\) \(e\left(\frac{491}{880}\right)\) \(e\left(\frac{85}{264}\right)\) \(e\left(\frac{919}{1320}\right)\) \(e\left(\frac{1517}{2640}\right)\) \(e\left(\frac{17}{330}\right)\) \(e\left(\frac{287}{880}\right)\) \(e\left(\frac{269}{880}\right)\) \(e\left(\frac{989}{1320}\right)\) \(e\left(\frac{463}{528}\right)\) \(e\left(\frac{17}{660}\right)\) \(e\left(\frac{631}{660}\right)\) \(e\left(\frac{857}{880}\right)\) \(e\left(\frac{607}{2640}\right)\) \(e\left(\frac{629}{2640}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{521}{528}\right)\) \(e\left(\frac{9}{440}\right)\) \(e\left(\frac{347}{440}\right)\) \(e\left(\frac{29}{660}\right)\) \(e\left(\frac{1889}{2640}\right)\) \(e\left(\frac{1723}{2640}\right)\) \(e\left(\frac{73}{88}\right)\) \(e\left(\frac{621}{880}\right)\) \(e\left(\frac{67}{165}\right)\) \(e\left(\frac{277}{330}\right)\)
\(\chi_{69696}(65,\cdot)\) 66 no 1 \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{31}{33}\right)\)
\(\chi_{69696}(67,\cdot)\) 528 yes 1 \(e\left(\frac{67}{528}\right)\) \(e\left(\frac{19}{264}\right)\) \(e\left(\frac{157}{528}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{47}{176}\right)\) \(e\left(\frac{113}{264}\right)\) \(e\left(\frac{67}{264}\right)\) \(e\left(\frac{449}{528}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{35}{176}\right)\) \(e\left(\frac{153}{176}\right)\) \(e\left(\frac{53}{264}\right)\) \(e\left(\frac{527}{528}\right)\) \(e\left(\frac{23}{132}\right)\) \(e\left(\frac{19}{132}\right)\) \(e\left(\frac{53}{176}\right)\) \(e\left(\frac{235}{528}\right)\) \(e\left(\frac{521}{528}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{337}{528}\right)\) \(e\left(\frac{73}{88}\right)\) \(e\left(\frac{67}{88}\right)\) \(e\left(\frac{113}{132}\right)\) \(e\left(\frac{269}{528}\right)\) \(e\left(\frac{487}{528}\right)\) \(e\left(\frac{81}{88}\right)\) \(e\left(\frac{65}{176}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{37}{66}\right)\)
\(\chi_{69696}(71,\cdot)\) 440 no 1 \(e\left(\frac{159}{440}\right)\) \(e\left(\frac{161}{220}\right)\) \(e\left(\frac{301}{440}\right)\) \(e\left(\frac{48}{55}\right)\) \(e\left(\frac{353}{440}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{159}{220}\right)\) \(e\left(\frac{397}{440}\right)\) \(e\left(\frac{109}{110}\right)\) \(e\left(\frac{41}{440}\right)\) \(e\left(\frac{227}{440}\right)\) \(e\left(\frac{199}{220}\right)\) \(e\left(\frac{87}{88}\right)\) \(e\left(\frac{27}{110}\right)\) \(e\left(\frac{51}{110}\right)\) \(e\left(\frac{91}{440}\right)\) \(e\left(\frac{427}{440}\right)\) \(e\left(\frac{9}{440}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{73}{88}\right)\) \(e\left(\frac{127}{220}\right)\) \(e\left(\frac{81}{220}\right)\) \(e\left(\frac{2}{55}\right)\) \(e\left(\frac{69}{440}\right)\) \(e\left(\frac{103}{440}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{183}{440}\right)\) \(e\left(\frac{9}{55}\right)\) \(e\left(\frac{42}{55}\right)\)
\(\chi_{69696}(73,\cdot)\) 440 no 1 \(e\left(\frac{117}{440}\right)\) \(e\left(\frac{23}{220}\right)\) \(e\left(\frac{263}{440}\right)\) \(e\left(\frac{54}{55}\right)\) \(e\left(\frac{239}{440}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{117}{220}\right)\) \(e\left(\frac{371}{440}\right)\) \(e\left(\frac{51}{55}\right)\) \(e\left(\frac{163}{440}\right)\) \(e\left(\frac{221}{440}\right)\) \(e\left(\frac{217}{220}\right)\) \(e\left(\frac{25}{88}\right)\) \(e\left(\frac{51}{110}\right)\) \(e\left(\frac{23}{110}\right)\) \(e\left(\frac{233}{440}\right)\) \(e\left(\frac{61}{440}\right)\) \(e\left(\frac{347}{440}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{67}{88}\right)\) \(e\left(\frac{81}{220}\right)\) \(e\left(\frac{153}{220}\right)\) \(e\left(\frac{16}{55}\right)\) \(e\left(\frac{167}{440}\right)\) \(e\left(\frac{109}{440}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{309}{440}\right)\) \(e\left(\frac{89}{110}\right)\) \(e\left(\frac{6}{55}\right)\)
\(\chi_{69696}(79,\cdot)\) 660 no 1 \(e\left(\frac{109}{660}\right)\) \(e\left(\frac{91}{330}\right)\) \(e\left(\frac{481}{660}\right)\) \(e\left(\frac{29}{110}\right)\) \(e\left(\frac{41}{220}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{109}{330}\right)\) \(e\left(\frac{497}{660}\right)\) \(e\left(\frac{293}{330}\right)\) \(e\left(\frac{97}{220}\right)\) \(e\left(\frac{199}{220}\right)\) \(e\left(\frac{67}{165}\right)\) \(e\left(\frac{97}{132}\right)\) \(e\left(\frac{229}{330}\right)\) \(e\left(\frac{91}{165}\right)\) \(e\left(\frac{167}{220}\right)\) \(e\left(\frac{7}{660}\right)\) \(e\left(\frac{29}{660}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{113}{132}\right)\) \(e\left(\frac{2}{55}\right)\) \(e\left(\frac{16}{55}\right)\) \(e\left(\frac{74}{165}\right)\) \(e\left(\frac{479}{660}\right)\) \(e\left(\frac{283}{660}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{1}{220}\right)\) \(e\left(\frac{58}{165}\right)\) \(e\left(\frac{14}{165}\right)\)
\(\chi_{69696}(83,\cdot)\) 2640 yes 1 \(e\left(\frac{2059}{2640}\right)\) \(e\left(\frac{511}{1320}\right)\) \(e\left(\frac{1381}{2640}\right)\) \(e\left(\frac{147}{220}\right)\) \(e\left(\frac{391}{880}\right)\) \(e\left(\frac{241}{264}\right)\) \(e\left(\frac{739}{1320}\right)\) \(e\left(\frac{1217}{2640}\right)\) \(e\left(\frac{1}{165}\right)\) \(e\left(\frac{147}{880}\right)\) \(e\left(\frac{9}{880}\right)\) \(e\left(\frac{29}{1320}\right)\) \(e\left(\frac{235}{528}\right)\) \(e\left(\frac{497}{660}\right)\) \(e\left(\frac{511}{660}\right)\) \(e\left(\frac{557}{880}\right)\) \(e\left(\frac{547}{2640}\right)\) \(e\left(\frac{1889}{2640}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{269}{528}\right)\) \(e\left(\frac{69}{440}\right)\) \(e\left(\frac{167}{440}\right)\) \(e\left(\frac{479}{660}\right)\) \(e\left(\frac{989}{2640}\right)\) \(e\left(\frac{1183}{2640}\right)\) \(e\left(\frac{17}{88}\right)\) \(e\left(\frac{801}{880}\right)\) \(e\left(\frac{37}{165}\right)\) \(e\left(\frac{217}{330}\right)\)
\(\chi_{69696}(85,\cdot)\) 2640 yes 1 \(e\left(\frac{593}{2640}\right)\) \(e\left(\frac{377}{1320}\right)\) \(e\left(\frac{2087}{2640}\right)\) \(e\left(\frac{119}{220}\right)\) \(e\left(\frac{437}{880}\right)\) \(e\left(\frac{83}{264}\right)\) \(e\left(\frac{593}{1320}\right)\) \(e\left(\frac{739}{2640}\right)\) \(e\left(\frac{109}{330}\right)\) \(e\left(\frac{449}{880}\right)\) \(e\left(\frac{243}{880}\right)\) \(e\left(\frac{1003}{1320}\right)\) \(e\left(\frac{449}{528}\right)\) \(e\left(\frac{439}{660}\right)\) \(e\left(\frac{377}{660}\right)\) \(e\left(\frac{519}{880}\right)\) \(e\left(\frac{689}{2640}\right)\) \(e\left(\frac{1723}{2640}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{487}{528}\right)\) \(e\left(\frac{103}{440}\right)\) \(e\left(\frac{109}{440}\right)\) \(e\left(\frac{283}{660}\right)\) \(e\left(\frac{1183}{2640}\right)\) \(e\left(\frac{2021}{2640}\right)\) \(e\left(\frac{63}{88}\right)\) \(e\left(\frac{67}{880}\right)\) \(e\left(\frac{119}{165}\right)\) \(e\left(\frac{29}{330}\right)\)
\(\chi_{69696}(89,\cdot)\) 88 no 1 \(e\left(\frac{87}{88}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{85}{88}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{13}{88}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{13}{88}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{5}{88}\right)\) \(e\left(\frac{3}{88}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{23}{88}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{83}{88}\right)\) \(e\left(\frac{7}{88}\right)\) \(e\left(\frac{73}{88}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{81}{88}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{17}{88}\right)\) \(e\left(\frac{63}{88}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{3}{88}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{69696}(91,\cdot)\) 880 no 1 \(e\left(\frac{191}{880}\right)\) \(e\left(\frac{439}{440}\right)\) \(e\left(\frac{529}{880}\right)\) \(e\left(\frac{189}{220}\right)\) \(e\left(\frac{817}{880}\right)\) \(e\left(\frac{9}{88}\right)\) \(e\left(\frac{191}{440}\right)\) \(e\left(\frac{773}{880}\right)\) \(e\left(\frac{24}{55}\right)\) \(e\left(\frac{189}{880}\right)\) \(e\left(\frac{263}{880}\right)\) \(e\left(\frac{201}{440}\right)\) \(e\left(\frac{63}{176}\right)\) \(e\left(\frac{103}{220}\right)\) \(e\left(\frac{219}{220}\right)\) \(e\left(\frac{779}{880}\right)\) \(e\left(\frac{423}{880}\right)\) \(e\left(\frac{621}{880}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{65}{176}\right)\) \(e\left(\frac{183}{440}\right)\) \(e\left(\frac{309}{440}\right)\) \(e\left(\frac{1}{220}\right)\) \(e\left(\frac{801}{880}\right)\) \(e\left(\frac{67}{880}\right)\) \(e\left(\frac{3}{88}\right)\) \(e\left(\frac{527}{880}\right)\) \(e\left(\frac{8}{55}\right)\) \(e\left(\frac{93}{110}\right)\)
\(\chi_{69696}(95,\cdot)\) 330 no 1 \(e\left(\frac{47}{165}\right)\) \(e\left(\frac{136}{165}\right)\) \(e\left(\frac{53}{165}\right)\) \(e\left(\frac{24}{55}\right)\) \(e\left(\frac{51}{110}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{94}{165}\right)\) \(e\left(\frac{197}{330}\right)\) \(e\left(\frac{301}{330}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{49}{110}\right)\) \(e\left(\frac{164}{165}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{34}{165}\right)\) \(e\left(\frac{107}{165}\right)\) \(e\left(\frac{16}{55}\right)\) \(e\left(\frac{277}{330}\right)\) \(e\left(\frac{67}{165}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{9}{55}\right)\) \(e\left(\frac{89}{110}\right)\) \(e\left(\frac{58}{165}\right)\) \(e\left(\frac{37}{165}\right)\) \(e\left(\frac{119}{165}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{8}{55}\right)\) \(e\left(\frac{247}{330}\right)\) \(e\left(\frac{118}{165}\right)\)
\(\chi_{69696}(97,\cdot)\) 330 no 1 \(e\left(\frac{17}{330}\right)\) \(e\left(\frac{158}{165}\right)\) \(e\left(\frac{293}{330}\right)\) \(e\left(\frac{2}{55}\right)\) \(e\left(\frac{73}{110}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{17}{165}\right)\) \(e\left(\frac{241}{330}\right)\) \(e\left(\frac{79}{165}\right)\) \(e\left(\frac{1}{110}\right)\) \(e\left(\frac{27}{110}\right)\) \(e\left(\frac{142}{165}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{122}{165}\right)\) \(e\left(\frac{151}{165}\right)\) \(e\left(\frac{21}{110}\right)\) \(e\left(\frac{101}{330}\right)\) \(e\left(\frac{277}{330}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{42}{55}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{14}{165}\right)\) \(e\left(\frac{217}{330}\right)\) \(e\left(\frac{29}{330}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{93}{110}\right)\) \(e\left(\frac{118}{165}\right)\) \(e\left(\frac{74}{165}\right)\)
\(\chi_{69696}(101,\cdot)\) 2640 yes 1 \(e\left(\frac{1381}{2640}\right)\) \(e\left(\frac{829}{1320}\right)\) \(e\left(\frac{139}{2640}\right)\) \(e\left(\frac{133}{220}\right)\) \(e\left(\frac{689}{880}\right)\) \(e\left(\frac{19}{264}\right)\) \(e\left(\frac{61}{1320}\right)\) \(e\left(\frac{1583}{2640}\right)\) \(e\left(\frac{83}{330}\right)\) \(e\left(\frac{133}{880}\right)\) \(e\left(\frac{71}{880}\right)\) \(e\left(\frac{131}{1320}\right)\) \(e\left(\frac{397}{528}\right)\) \(e\left(\frac{413}{660}\right)\) \(e\left(\frac{169}{660}\right)\) \(e\left(\frac{483}{880}\right)\) \(e\left(\frac{1333}{2640}\right)\) \(e\left(\frac{431}{2640}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{59}{528}\right)\) \(e\left(\frac{31}{440}\right)\) \(e\left(\frac{193}{440}\right)\) \(e\left(\frac{491}{660}\right)\) \(e\left(\frac{1691}{2640}\right)\) \(e\left(\frac{337}{2640}\right)\) \(e\left(\frac{7}{88}\right)\) \(e\left(\frac{599}{880}\right)\) \(e\left(\frac{101}{330}\right)\) \(e\left(\frac{13}{330}\right)\)
\(\chi_{69696}(103,\cdot)\) 1320 no 1 \(e\left(\frac{1141}{1320}\right)\) \(e\left(\frac{559}{660}\right)\) \(e\left(\frac{739}{1320}\right)\) \(e\left(\frac{93}{110}\right)\) \(e\left(\frac{189}{440}\right)\) \(e\left(\frac{73}{132}\right)\) \(e\left(\frac{481}{660}\right)\) \(e\left(\frac{743}{1320}\right)\) \(e\left(\frac{181}{330}\right)\) \(e\left(\frac{313}{440}\right)\) \(e\left(\frac{311}{440}\right)\) \(e\left(\frac{611}{660}\right)\) \(e\left(\frac{49}{264}\right)\) \(e\left(\frac{4}{165}\right)\) \(e\left(\frac{229}{330}\right)\) \(e\left(\frac{83}{440}\right)\) \(e\left(\frac{1033}{1320}\right)\) \(e\left(\frac{791}{1320}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{119}{264}\right)\) \(e\left(\frac{1}{220}\right)\) \(e\left(\frac{173}{220}\right)\) \(e\left(\frac{133}{165}\right)\) \(e\left(\frac{1151}{1320}\right)\) \(e\left(\frac{937}{1320}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{179}{440}\right)\) \(e\left(\frac{97}{330}\right)\) \(e\left(\frac{43}{165}\right)\)
\(\chi_{69696}(107,\cdot)\) 880 no 1 \(e\left(\frac{611}{880}\right)\) \(e\left(\frac{279}{440}\right)\) \(e\left(\frac{29}{880}\right)\) \(e\left(\frac{69}{220}\right)\) \(e\left(\frac{637}{880}\right)\) \(e\left(\frac{41}{88}\right)\) \(e\left(\frac{171}{440}\right)\) \(e\left(\frac{153}{880}\right)\) \(e\left(\frac{14}{55}\right)\) \(e\left(\frac{289}{880}\right)\) \(e\left(\frac{323}{880}\right)\) \(e\left(\frac{21}{440}\right)\) \(e\left(\frac{67}{176}\right)\) \(e\left(\frac{193}{220}\right)\) \(e\left(\frac{59}{220}\right)\) \(e\left(\frac{239}{880}\right)\) \(e\left(\frac{123}{880}\right)\) \(e\left(\frac{761}{880}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{37}{176}\right)\) \(e\left(\frac{423}{440}\right)\) \(e\left(\frac{29}{440}\right)\) \(e\left(\frac{51}{220}\right)\) \(e\left(\frac{261}{880}\right)\) \(e\left(\frac{7}{880}\right)\) \(e\left(\frac{43}{88}\right)\) \(e\left(\frac{587}{880}\right)\) \(e\left(\frac{23}{55}\right)\) \(e\left(\frac{13}{110}\right)\)
\(\chi_{69696}(109,\cdot)\) 176 no 1 \(e\left(\frac{173}{176}\right)\) \(e\left(\frac{53}{88}\right)\) \(e\left(\frac{123}{176}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{83}{176}\right)\) \(e\left(\frac{35}{88}\right)\) \(e\left(\frac{85}{88}\right)\) \(e\left(\frac{39}{176}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{103}{176}\right)\) \(e\left(\frac{53}{176}\right)\) \(e\left(\frac{39}{88}\right)\) \(e\left(\frac{113}{176}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{161}{176}\right)\) \(e\left(\frac{109}{176}\right)\) \(e\left(\frac{175}{176}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{23}{176}\right)\) \(e\left(\frac{25}{88}\right)\) \(e\left(\frac{35}{88}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{51}{176}\right)\) \(e\left(\frac{145}{176}\right)\) \(e\left(\frac{85}{88}\right)\) \(e\left(\frac{53}{176}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{21}{22}\right)\)
\(\chi_{69696}(113,\cdot)\) 660 no 1 \(e\left(\frac{287}{660}\right)\) \(e\left(\frac{173}{330}\right)\) \(e\left(\frac{443}{660}\right)\) \(e\left(\frac{37}{110}\right)\) \(e\left(\frac{113}{220}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{287}{330}\right)\) \(e\left(\frac{361}{660}\right)\) \(e\left(\frac{2}{165}\right)\) \(e\left(\frac{211}{220}\right)\) \(e\left(\frac{87}{220}\right)\) \(e\left(\frac{131}{165}\right)\) \(e\left(\frac{101}{132}\right)\) \(e\left(\frac{167}{330}\right)\) \(e\left(\frac{8}{165}\right)\) \(e\left(\frac{141}{220}\right)\) \(e\left(\frac{191}{660}\right)\) \(e\left(\frac{367}{660}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{19}{132}\right)\) \(e\left(\frac{31}{55}\right)\) \(e\left(\frac{1}{110}\right)\) \(e\left(\frac{157}{165}\right)\) \(e\left(\frac{577}{660}\right)\) \(e\left(\frac{509}{660}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{43}{220}\right)\) \(e\left(\frac{313}{330}\right)\) \(e\left(\frac{52}{165}\right)\)
\(\chi_{69696}(115,\cdot)\) 2640 yes 1 \(e\left(\frac{379}{2640}\right)\) \(e\left(\frac{931}{1320}\right)\) \(e\left(\frac{1621}{2640}\right)\) \(e\left(\frac{87}{220}\right)\) \(e\left(\frac{631}{880}\right)\) \(e\left(\frac{157}{264}\right)\) \(e\left(\frac{379}{1320}\right)\) \(e\left(\frac{617}{2640}\right)\) \(e\left(\frac{151}{165}\right)\) \(e\left(\frac{747}{880}\right)\) \(e\left(\frac{369}{880}\right)\) \(e\left(\frac{749}{1320}\right)\) \(e\left(\frac{43}{528}\right)\) \(e\left(\frac{467}{660}\right)\) \(e\left(\frac{271}{660}\right)\) \(e\left(\frac{397}{880}\right)\) \(e\left(\frac{1747}{2640}\right)\) \(e\left(\frac{449}{2640}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{293}{528}\right)\) \(e\left(\frac{409}{440}\right)\) \(e\left(\frac{27}{440}\right)\) \(e\left(\frac{389}{660}\right)\) \(e\left(\frac{1829}{2640}\right)\) \(e\left(\frac{1423}{2640}\right)\) \(e\left(\frac{37}{88}\right)\) \(e\left(\frac{281}{880}\right)\) \(e\left(\frac{142}{165}\right)\) \(e\left(\frac{97}{330}\right)\)
\(\chi_{69696}(119,\cdot)\) 1320 no 1 \(e\left(\frac{1163}{1320}\right)\) \(e\left(\frac{317}{660}\right)\) \(e\left(\frac{497}{1320}\right)\) \(e\left(\frac{52}{55}\right)\) \(e\left(\frac{167}{440}\right)\) \(e\left(\frac{29}{132}\right)\) \(e\left(\frac{503}{660}\right)\) \(e\left(\frac{1249}{1320}\right)\) \(e\left(\frac{203}{330}\right)\) \(e\left(\frac{159}{440}\right)\) \(e\left(\frac{333}{440}\right)\) \(e\left(\frac{523}{660}\right)\) \(e\left(\frac{203}{264}\right)\) \(e\left(\frac{19}{330}\right)\) \(e\left(\frac{317}{330}\right)\) \(e\left(\frac{149}{440}\right)\) \(e\left(\frac{1319}{1320}\right)\) \(e\left(\frac{373}{1320}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{229}{264}\right)\) \(e\left(\frac{133}{220}\right)\) \(e\left(\frac{19}{220}\right)\) \(e\left(\frac{89}{165}\right)\) \(e\left(\frac{73}{1320}\right)\) \(e\left(\frac{1091}{1320}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{377}{440}\right)\) \(e\left(\frac{43}{165}\right)\) \(e\left(\frac{164}{165}\right)\)