# Properties

 Modulus 10009 Structure $$C_{10008}$$ Order 10008

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(10009)

pari: g = idealstar(,10009,2)

## Character group

 sage: G.order()  pari: g.no Order = 10008 sage: H.invariants()  pari: g.cyc Structure = $$C_{10008}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{10009}(11,\cdot)$

## First 37 of 10008 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 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
$$\chi_{10009}(1,\cdot)$$ 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
$$\chi_{10009}(2,\cdot)$$ 1668 Yes 1 $$e\left(\frac{89}{278}\right)$$ $$e\left(\frac{79}{834}\right)$$ $$e\left(\frac{89}{139}\right)$$ $$e\left(\frac{199}{417}\right)$$ $$e\left(\frac{173}{417}\right)$$ $$e\left(\frac{447}{556}\right)$$ $$e\left(\frac{267}{278}\right)$$ $$e\left(\frac{79}{417}\right)$$ $$e\left(\frac{665}{834}\right)$$ $$e\left(\frac{167}{1668}\right)$$ $$e\left(\frac{613}{834}\right)$$ $$e\left(\frac{83}{278}\right)$$ $$e\left(\frac{69}{556}\right)$$ $$e\left(\frac{159}{278}\right)$$ $$e\left(\frac{39}{139}\right)$$ $$e\left(\frac{797}{834}\right)$$ $$e\left(\frac{425}{834}\right)$$ $$e\left(\frac{235}{556}\right)$$ $$e\left(\frac{49}{417}\right)$$ $$e\left(\frac{1499}{1668}\right)$$ $$e\left(\frac{701}{1668}\right)$$ $$e\left(\frac{749}{834}\right)$$ $$e\left(\frac{23}{417}\right)$$ $$e\left(\frac{398}{417}\right)$$ $$e\left(\frac{86}{139}\right)$$ $$e\left(\frac{79}{278}\right)$$ $$e\left(\frac{247}{556}\right)$$ $$e\left(\frac{71}{417}\right)$$ $$e\left(\frac{124}{139}\right)$$
$$\chi_{10009}(3,\cdot)$$ 5004 Yes 1 $$e\left(\frac{79}{834}\right)$$ $$e\left(\frac{67}{2502}\right)$$ $$e\left(\frac{79}{417}\right)$$ $$e\left(\frac{211}{1251}\right)$$ $$e\left(\frac{152}{1251}\right)$$ $$e\left(\frac{429}{556}\right)$$ $$e\left(\frac{79}{278}\right)$$ $$e\left(\frac{67}{1251}\right)$$ $$e\left(\frac{659}{2502}\right)$$ $$e\left(\frac{2063}{5004}\right)$$ $$e\left(\frac{541}{2502}\right)$$ $$e\left(\frac{461}{834}\right)$$ $$e\left(\frac{1445}{1668}\right)$$ $$e\left(\frac{163}{834}\right)$$ $$e\left(\frac{158}{417}\right)$$ $$e\left(\frac{1985}{2502}\right)$$ $$e\left(\frac{371}{2502}\right)$$ $$e\left(\frac{1255}{1668}\right)$$ $$e\left(\frac{448}{1251}\right)$$ $$e\left(\frac{3995}{5004}\right)$$ $$e\left(\frac{2537}{5004}\right)$$ $$e\left(\frac{1427}{2502}\right)$$ $$e\left(\frac{389}{1251}\right)$$ $$e\left(\frac{422}{1251}\right)$$ $$e\left(\frac{90}{139}\right)$$ $$e\left(\frac{67}{834}\right)$$ $$e\left(\frac{1603}{1668}\right)$$ $$e\left(\frac{530}{1251}\right)$$ $$e\left(\frac{121}{417}\right)$$
$$\chi_{10009}(4,\cdot)$$ 834 Yes 1 $$e\left(\frac{89}{139}\right)$$ $$e\left(\frac{79}{417}\right)$$ $$e\left(\frac{39}{139}\right)$$ $$e\left(\frac{398}{417}\right)$$ $$e\left(\frac{346}{417}\right)$$ $$e\left(\frac{169}{278}\right)$$ $$e\left(\frac{128}{139}\right)$$ $$e\left(\frac{158}{417}\right)$$ $$e\left(\frac{248}{417}\right)$$ $$e\left(\frac{167}{834}\right)$$ $$e\left(\frac{196}{417}\right)$$ $$e\left(\frac{83}{139}\right)$$ $$e\left(\frac{69}{278}\right)$$ $$e\left(\frac{20}{139}\right)$$ $$e\left(\frac{78}{139}\right)$$ $$e\left(\frac{380}{417}\right)$$ $$e\left(\frac{8}{417}\right)$$ $$e\left(\frac{235}{278}\right)$$ $$e\left(\frac{98}{417}\right)$$ $$e\left(\frac{665}{834}\right)$$ $$e\left(\frac{701}{834}\right)$$ $$e\left(\frac{332}{417}\right)$$ $$e\left(\frac{46}{417}\right)$$ $$e\left(\frac{379}{417}\right)$$ $$e\left(\frac{33}{139}\right)$$ $$e\left(\frac{79}{139}\right)$$ $$e\left(\frac{247}{278}\right)$$ $$e\left(\frac{142}{417}\right)$$ $$e\left(\frac{109}{139}\right)$$
$$\chi_{10009}(5,\cdot)$$ 2502 Yes 1 $$e\left(\frac{199}{417}\right)$$ $$e\left(\frac{211}{1251}\right)$$ $$e\left(\frac{398}{417}\right)$$ $$e\left(\frac{134}{1251}\right)$$ $$e\left(\frac{808}{1251}\right)$$ $$e\left(\frac{127}{278}\right)$$ $$e\left(\frac{60}{139}\right)$$ $$e\left(\frac{422}{1251}\right)$$ $$e\left(\frac{731}{1251}\right)$$ $$e\left(\frac{1829}{2502}\right)$$ $$e\left(\frac{154}{1251}\right)$$ $$e\left(\frac{95}{417}\right)$$ $$e\left(\frac{779}{834}\right)$$ $$e\left(\frac{115}{417}\right)$$ $$e\left(\frac{379}{417}\right)$$ $$e\left(\frac{239}{1251}\right)$$ $$e\left(\frac{1019}{1251}\right)$$ $$e\left(\frac{691}{834}\right)$$ $$e\left(\frac{77}{1251}\right)$$ $$e\left(\frac{1565}{2502}\right)$$ $$e\left(\frac{521}{2502}\right)$$ $$e\left(\frac{797}{1251}\right)$$ $$e\left(\frac{751}{1251}\right)$$ $$e\left(\frac{268}{1251}\right)$$ $$e\left(\frac{98}{139}\right)$$ $$e\left(\frac{211}{417}\right)$$ $$e\left(\frac{343}{834}\right)$$ $$e\left(\frac{52}{1251}\right)$$ $$e\left(\frac{314}{417}\right)$$
$$\chi_{10009}(6,\cdot)$$ 1251 Yes 1 $$e\left(\frac{173}{417}\right)$$ $$e\left(\frac{152}{1251}\right)$$ $$e\left(\frac{346}{417}\right)$$ $$e\left(\frac{808}{1251}\right)$$ $$e\left(\frac{671}{1251}\right)$$ $$e\left(\frac{80}{139}\right)$$ $$e\left(\frac{34}{139}\right)$$ $$e\left(\frac{304}{1251}\right)$$ $$e\left(\frac{76}{1251}\right)$$ $$e\left(\frac{641}{1251}\right)$$ $$e\left(\frac{1190}{1251}\right)$$ $$e\left(\frac{355}{417}\right)$$ $$e\left(\frac{413}{417}\right)$$ $$e\left(\frac{320}{417}\right)$$ $$e\left(\frac{275}{417}\right)$$ $$e\left(\frac{937}{1251}\right)$$ $$e\left(\frac{823}{1251}\right)$$ $$e\left(\frac{73}{417}\right)$$ $$e\left(\frac{595}{1251}\right)$$ $$e\left(\frac{872}{1251}\right)$$ $$e\left(\frac{1160}{1251}\right)$$ $$e\left(\frac{586}{1251}\right)$$ $$e\left(\frac{458}{1251}\right)$$ $$e\left(\frac{365}{1251}\right)$$ $$e\left(\frac{37}{139}\right)$$ $$e\left(\frac{152}{417}\right)$$ $$e\left(\frac{169}{417}\right)$$ $$e\left(\frac{743}{1251}\right)$$ $$e\left(\frac{76}{417}\right)$$
$$\chi_{10009}(7,\cdot)$$ 1112 Yes 1 $$e\left(\frac{447}{556}\right)$$ $$e\left(\frac{429}{556}\right)$$ $$e\left(\frac{169}{278}\right)$$ $$e\left(\frac{127}{278}\right)$$ $$e\left(\frac{80}{139}\right)$$ $$e\left(\frac{121}{1112}\right)$$ $$e\left(\frac{229}{556}\right)$$ $$e\left(\frac{151}{278}\right)$$ $$e\left(\frac{145}{556}\right)$$ $$e\left(\frac{467}{1112}\right)$$ $$e\left(\frac{211}{556}\right)$$ $$e\left(\frac{117}{556}\right)$$ $$e\left(\frac{1015}{1112}\right)$$ $$e\left(\frac{127}{556}\right)$$ $$e\left(\frac{30}{139}\right)$$ $$e\left(\frac{63}{556}\right)$$ $$e\left(\frac{193}{556}\right)$$ $$e\left(\frac{693}{1112}\right)$$ $$e\left(\frac{9}{139}\right)$$ $$e\left(\frac{979}{1112}\right)$$ $$e\left(\frac{249}{1112}\right)$$ $$e\left(\frac{17}{556}\right)$$ $$e\left(\frac{51}{278}\right)$$ $$e\left(\frac{127}{139}\right)$$ $$e\left(\frac{2}{139}\right)$$ $$e\left(\frac{175}{556}\right)$$ $$e\left(\frac{797}{1112}\right)$$ $$e\left(\frac{118}{139}\right)$$ $$e\left(\frac{9}{278}\right)$$
$$\chi_{10009}(8,\cdot)$$ 556 Yes 1 $$e\left(\frac{267}{278}\right)$$ $$e\left(\frac{79}{278}\right)$$ $$e\left(\frac{128}{139}\right)$$ $$e\left(\frac{60}{139}\right)$$ $$e\left(\frac{34}{139}\right)$$ $$e\left(\frac{229}{556}\right)$$ $$e\left(\frac{245}{278}\right)$$ $$e\left(\frac{79}{139}\right)$$ $$e\left(\frac{109}{278}\right)$$ $$e\left(\frac{167}{556}\right)$$ $$e\left(\frac{57}{278}\right)$$ $$e\left(\frac{249}{278}\right)$$ $$e\left(\frac{207}{556}\right)$$ $$e\left(\frac{199}{278}\right)$$ $$e\left(\frac{117}{139}\right)$$ $$e\left(\frac{241}{278}\right)$$ $$e\left(\frac{147}{278}\right)$$ $$e\left(\frac{149}{556}\right)$$ $$e\left(\frac{49}{139}\right)$$ $$e\left(\frac{387}{556}\right)$$ $$e\left(\frac{145}{556}\right)$$ $$e\left(\frac{193}{278}\right)$$ $$e\left(\frac{23}{139}\right)$$ $$e\left(\frac{120}{139}\right)$$ $$e\left(\frac{119}{139}\right)$$ $$e\left(\frac{237}{278}\right)$$ $$e\left(\frac{185}{556}\right)$$ $$e\left(\frac{71}{139}\right)$$ $$e\left(\frac{94}{139}\right)$$
$$\chi_{10009}(9,\cdot)$$ 2502 Yes 1 $$e\left(\frac{79}{417}\right)$$ $$e\left(\frac{67}{1251}\right)$$ $$e\left(\frac{158}{417}\right)$$ $$e\left(\frac{422}{1251}\right)$$ $$e\left(\frac{304}{1251}\right)$$ $$e\left(\frac{151}{278}\right)$$ $$e\left(\frac{79}{139}\right)$$ $$e\left(\frac{134}{1251}\right)$$ $$e\left(\frac{659}{1251}\right)$$ $$e\left(\frac{2063}{2502}\right)$$ $$e\left(\frac{541}{1251}\right)$$ $$e\left(\frac{44}{417}\right)$$ $$e\left(\frac{611}{834}\right)$$ $$e\left(\frac{163}{417}\right)$$ $$e\left(\frac{316}{417}\right)$$ $$e\left(\frac{734}{1251}\right)$$ $$e\left(\frac{371}{1251}\right)$$ $$e\left(\frac{421}{834}\right)$$ $$e\left(\frac{896}{1251}\right)$$ $$e\left(\frac{1493}{2502}\right)$$ $$e\left(\frac{35}{2502}\right)$$ $$e\left(\frac{176}{1251}\right)$$ $$e\left(\frac{778}{1251}\right)$$ $$e\left(\frac{844}{1251}\right)$$ $$e\left(\frac{41}{139}\right)$$ $$e\left(\frac{67}{417}\right)$$ $$e\left(\frac{769}{834}\right)$$ $$e\left(\frac{1060}{1251}\right)$$ $$e\left(\frac{242}{417}\right)$$
$$\chi_{10009}(10,\cdot)$$ 5004 Yes 1 $$e\left(\frac{665}{834}\right)$$ $$e\left(\frac{659}{2502}\right)$$ $$e\left(\frac{248}{417}\right)$$ $$e\left(\frac{731}{1251}\right)$$ $$e\left(\frac{76}{1251}\right)$$ $$e\left(\frac{145}{556}\right)$$ $$e\left(\frac{109}{278}\right)$$ $$e\left(\frac{659}{1251}\right)$$ $$e\left(\frac{955}{2502}\right)$$ $$e\left(\frac{4159}{5004}\right)$$ $$e\left(\frac{2147}{2502}\right)$$ $$e\left(\frac{439}{834}\right)$$ $$e\left(\frac{97}{1668}\right)$$ $$e\left(\frac{707}{834}\right)$$ $$e\left(\frac{79}{417}\right)$$ $$e\left(\frac{367}{2502}\right)$$ $$e\left(\frac{811}{2502}\right)$$ $$e\left(\frac{419}{1668}\right)$$ $$e\left(\frac{224}{1251}\right)$$ $$e\left(\frac{2623}{5004}\right)$$ $$e\left(\frac{3145}{5004}\right)$$ $$e\left(\frac{1339}{2502}\right)$$ $$e\left(\frac{820}{1251}\right)$$ $$e\left(\frac{211}{1251}\right)$$ $$e\left(\frac{45}{139}\right)$$ $$e\left(\frac{659}{834}\right)$$ $$e\left(\frac{1427}{1668}\right)$$ $$e\left(\frac{265}{1251}\right)$$ $$e\left(\frac{269}{417}\right)$$
$$\chi_{10009}(11,\cdot)$$ 10008 Yes 1 $$e\left(\frac{167}{1668}\right)$$ $$e\left(\frac{2063}{5004}\right)$$ $$e\left(\frac{167}{834}\right)$$ $$e\left(\frac{1829}{2502}\right)$$ $$e\left(\frac{641}{1251}\right)$$ $$e\left(\frac{467}{1112}\right)$$ $$e\left(\frac{167}{556}\right)$$ $$e\left(\frac{2063}{2502}\right)$$ $$e\left(\frac{4159}{5004}\right)$$ $$e\left(\frac{1}{10008}\right)$$ $$e\left(\frac{3065}{5004}\right)$$ $$e\left(\frac{1249}{1668}\right)$$ $$e\left(\frac{1735}{3336}\right)$$ $$e\left(\frac{239}{1668}\right)$$ $$e\left(\frac{167}{417}\right)$$ $$e\left(\frac{3985}{5004}\right)$$ $$e\left(\frac{4627}{5004}\right)$$ $$e\left(\frac{341}{3336}\right)$$ $$e\left(\frac{1165}{1251}\right)$$ $$e\left(\frac{8329}{10008}\right)$$ $$e\left(\frac{1003}{10008}\right)$$ $$e\left(\frac{4579}{5004}\right)$$ $$e\left(\frac{1783}{2502}\right)$$ $$e\left(\frac{578}{1251}\right)$$ $$e\left(\frac{118}{139}\right)$$ $$e\left(\frac{395}{1668}\right)$$ $$e\left(\frac{2069}{3336}\right)$$ $$e\left(\frac{803}{1251}\right)$$ $$e\left(\frac{203}{834}\right)$$
$$\chi_{10009}(12,\cdot)$$ 5004 Yes 1 $$e\left(\frac{613}{834}\right)$$ $$e\left(\frac{541}{2502}\right)$$ $$e\left(\frac{196}{417}\right)$$ $$e\left(\frac{154}{1251}\right)$$ $$e\left(\frac{1190}{1251}\right)$$ $$e\left(\frac{211}{556}\right)$$ $$e\left(\frac{57}{278}\right)$$ $$e\left(\frac{541}{1251}\right)$$ $$e\left(\frac{2147}{2502}\right)$$ $$e\left(\frac{3065}{5004}\right)$$ $$e\left(\frac{1717}{2502}\right)$$ $$e\left(\frac{125}{834}\right)$$ $$e\left(\frac{191}{1668}\right)$$ $$e\left(\frac{283}{834}\right)$$ $$e\left(\frac{392}{417}\right)$$ $$e\left(\frac{1763}{2502}\right)$$ $$e\left(\frac{419}{2502}\right)$$ $$e\left(\frac{997}{1668}\right)$$ $$e\left(\frac{742}{1251}\right)$$ $$e\left(\frac{2981}{5004}\right)$$ $$e\left(\frac{1739}{5004}\right)$$ $$e\left(\frac{917}{2502}\right)$$ $$e\left(\frac{527}{1251}\right)$$ $$e\left(\frac{308}{1251}\right)$$ $$e\left(\frac{123}{139}\right)$$ $$e\left(\frac{541}{834}\right)$$ $$e\left(\frac{1417}{1668}\right)$$ $$e\left(\frac{956}{1251}\right)$$ $$e\left(\frac{31}{417}\right)$$
$$\chi_{10009}(13,\cdot)$$ 1668 Yes 1 $$e\left(\frac{83}{278}\right)$$ $$e\left(\frac{461}{834}\right)$$ $$e\left(\frac{83}{139}\right)$$ $$e\left(\frac{95}{417}\right)$$ $$e\left(\frac{355}{417}\right)$$ $$e\left(\frac{117}{556}\right)$$ $$e\left(\frac{249}{278}\right)$$ $$e\left(\frac{44}{417}\right)$$ $$e\left(\frac{439}{834}\right)$$ $$e\left(\frac{1249}{1668}\right)$$ $$e\left(\frac{125}{834}\right)$$ $$e\left(\frac{143}{278}\right)$$ $$e\left(\frac{283}{556}\right)$$ $$e\left(\frac{217}{278}\right)$$ $$e\left(\frac{27}{139}\right)$$ $$e\left(\frac{787}{834}\right)$$ $$e\left(\frac{337}{834}\right)$$ $$e\left(\frac{13}{556}\right)$$ $$e\left(\frac{344}{417}\right)$$ $$e\left(\frac{1273}{1668}\right)$$ $$e\left(\frac{79}{1668}\right)$$ $$e\left(\frac{433}{834}\right)$$ $$e\left(\frac{187}{417}\right)$$ $$e\left(\frac{190}{417}\right)$$ $$e\left(\frac{113}{139}\right)$$ $$e\left(\frac{183}{278}\right)$$ $$e\left(\frac{449}{556}\right)$$ $$e\left(\frac{124}{417}\right)$$ $$e\left(\frac{11}{139}\right)$$
$$\chi_{10009}(14,\cdot)$$ 3336 Yes 1 $$e\left(\frac{69}{556}\right)$$ $$e\left(\frac{1445}{1668}\right)$$ $$e\left(\frac{69}{278}\right)$$ $$e\left(\frac{779}{834}\right)$$ $$e\left(\frac{413}{417}\right)$$ $$e\left(\frac{1015}{1112}\right)$$ $$e\left(\frac{207}{556}\right)$$ $$e\left(\frac{611}{834}\right)$$ $$e\left(\frac{97}{1668}\right)$$ $$e\left(\frac{1735}{3336}\right)$$ $$e\left(\frac{191}{1668}\right)$$ $$e\left(\frac{283}{556}\right)$$ $$e\left(\frac{41}{1112}\right)$$ $$e\left(\frac{445}{556}\right)$$ $$e\left(\frac{69}{139}\right)$$ $$e\left(\frac{115}{1668}\right)$$ $$e\left(\frac{1429}{1668}\right)$$ $$e\left(\frac{51}{1112}\right)$$ $$e\left(\frac{76}{417}\right)$$ $$e\left(\frac{2599}{3336}\right)$$ $$e\left(\frac{2149}{3336}\right)$$ $$e\left(\frac{1549}{1668}\right)$$ $$e\left(\frac{199}{834}\right)$$ $$e\left(\frac{362}{417}\right)$$ $$e\left(\frac{88}{139}\right)$$ $$e\left(\frac{333}{556}\right)$$ $$e\left(\frac{179}{1112}\right)$$ $$e\left(\frac{8}{417}\right)$$ $$e\left(\frac{257}{278}\right)$$
$$\chi_{10009}(15,\cdot)$$ 1668 Yes 1 $$e\left(\frac{159}{278}\right)$$ $$e\left(\frac{163}{834}\right)$$ $$e\left(\frac{20}{139}\right)$$ $$e\left(\frac{115}{417}\right)$$ $$e\left(\frac{320}{417}\right)$$ $$e\left(\frac{127}{556}\right)$$ $$e\left(\frac{199}{278}\right)$$ $$e\left(\frac{163}{417}\right)$$ $$e\left(\frac{707}{834}\right)$$ $$e\left(\frac{239}{1668}\right)$$ $$e\left(\frac{283}{834}\right)$$ $$e\left(\frac{217}{278}\right)$$ $$e\left(\frac{445}{556}\right)$$ $$e\left(\frac{131}{278}\right)$$ $$e\left(\frac{40}{139}\right)$$ $$e\left(\frac{821}{834}\right)$$ $$e\left(\frac{803}{834}\right)$$ $$e\left(\frac{323}{556}\right)$$ $$e\left(\frac{175}{417}\right)$$ $$e\left(\frac{707}{1668}\right)$$ $$e\left(\frac{1193}{1668}\right)$$ $$e\left(\frac{173}{834}\right)$$ $$e\left(\frac{380}{417}\right)$$ $$e\left(\frac{230}{417}\right)$$ $$e\left(\frac{49}{139}\right)$$ $$e\left(\frac{163}{278}\right)$$ $$e\left(\frac{207}{556}\right)$$ $$e\left(\frac{194}{417}\right)$$ $$e\left(\frac{6}{139}\right)$$
$$\chi_{10009}(16,\cdot)$$ 417 Yes 1 $$e\left(\frac{39}{139}\right)$$ $$e\left(\frac{158}{417}\right)$$ $$e\left(\frac{78}{139}\right)$$ $$e\left(\frac{379}{417}\right)$$ $$e\left(\frac{275}{417}\right)$$ $$e\left(\frac{30}{139}\right)$$ $$e\left(\frac{117}{139}\right)$$ $$e\left(\frac{316}{417}\right)$$ $$e\left(\frac{79}{417}\right)$$ $$e\left(\frac{167}{417}\right)$$ $$e\left(\frac{392}{417}\right)$$ $$e\left(\frac{27}{139}\right)$$ $$e\left(\frac{69}{139}\right)$$ $$e\left(\frac{40}{139}\right)$$ $$e\left(\frac{17}{139}\right)$$ $$e\left(\frac{343}{417}\right)$$ $$e\left(\frac{16}{417}\right)$$ $$e\left(\frac{96}{139}\right)$$ $$e\left(\frac{196}{417}\right)$$ $$e\left(\frac{248}{417}\right)$$ $$e\left(\frac{284}{417}\right)$$ $$e\left(\frac{247}{417}\right)$$ $$e\left(\frac{92}{417}\right)$$ $$e\left(\frac{341}{417}\right)$$ $$e\left(\frac{66}{139}\right)$$ $$e\left(\frac{19}{139}\right)$$ $$e\left(\frac{108}{139}\right)$$ $$e\left(\frac{284}{417}\right)$$ $$e\left(\frac{79}{139}\right)$$
$$\chi_{10009}(17,\cdot)$$ 5004 Yes 1 $$e\left(\frac{797}{834}\right)$$ $$e\left(\frac{1985}{2502}\right)$$ $$e\left(\frac{380}{417}\right)$$ $$e\left(\frac{239}{1251}\right)$$ $$e\left(\frac{937}{1251}\right)$$ $$e\left(\frac{63}{556}\right)$$ $$e\left(\frac{241}{278}\right)$$ $$e\left(\frac{734}{1251}\right)$$ $$e\left(\frac{367}{2502}\right)$$ $$e\left(\frac{3985}{5004}\right)$$ $$e\left(\frac{1763}{2502}\right)$$ $$e\left(\frac{787}{834}\right)$$ $$e\left(\frac{115}{1668}\right)$$ $$e\left(\frac{821}{834}\right)$$ $$e\left(\frac{343}{417}\right)$$ $$e\left(\frac{31}{2502}\right)$$ $$e\left(\frac{1357}{2502}\right)$$ $$e\left(\frac{1133}{1668}\right)$$ $$e\left(\frac{128}{1251}\right)$$ $$e\left(\frac{4537}{5004}\right)$$ $$e\left(\frac{3763}{5004}\right)$$ $$e\left(\frac{229}{2502}\right)$$ $$e\left(\frac{826}{1251}\right)$$ $$e\left(\frac{478}{1251}\right)$$ $$e\left(\frac{125}{139}\right)$$ $$e\left(\frac{317}{834}\right)$$ $$e\left(\frac{41}{1668}\right)$$ $$e\left(\frac{1045}{1251}\right)$$ $$e\left(\frac{392}{417}\right)$$
$$\chi_{10009}(18,\cdot)$$ 5004 Yes 1 $$e\left(\frac{425}{834}\right)$$ $$e\left(\frac{371}{2502}\right)$$ $$e\left(\frac{8}{417}\right)$$ $$e\left(\frac{1019}{1251}\right)$$ $$e\left(\frac{823}{1251}\right)$$ $$e\left(\frac{193}{556}\right)$$ $$e\left(\frac{147}{278}\right)$$ $$e\left(\frac{371}{1251}\right)$$ $$e\left(\frac{811}{2502}\right)$$ $$e\left(\frac{4627}{5004}\right)$$ $$e\left(\frac{419}{2502}\right)$$ $$e\left(\frac{337}{834}\right)$$ $$e\left(\frac{1429}{1668}\right)$$ $$e\left(\frac{803}{834}\right)$$ $$e\left(\frac{16}{417}\right)$$ $$e\left(\frac{1357}{2502}\right)$$ $$e\left(\frac{2017}{2502}\right)$$ $$e\left(\frac{1547}{1668}\right)$$ $$e\left(\frac{1043}{1251}\right)$$ $$e\left(\frac{2479}{5004}\right)$$ $$e\left(\frac{2173}{5004}\right)$$ $$e\left(\frac{97}{2502}\right)$$ $$e\left(\frac{847}{1251}\right)$$ $$e\left(\frac{787}{1251}\right)$$ $$e\left(\frac{127}{139}\right)$$ $$e\left(\frac{371}{834}\right)$$ $$e\left(\frac{611}{1668}\right)$$ $$e\left(\frac{22}{1251}\right)$$ $$e\left(\frac{197}{417}\right)$$
$$\chi_{10009}(19,\cdot)$$ 3336 Yes 1 $$e\left(\frac{235}{556}\right)$$ $$e\left(\frac{1255}{1668}\right)$$ $$e\left(\frac{235}{278}\right)$$ $$e\left(\frac{691}{834}\right)$$ $$e\left(\frac{73}{417}\right)$$ $$e\left(\frac{693}{1112}\right)$$ $$e\left(\frac{149}{556}\right)$$ $$e\left(\frac{421}{834}\right)$$ $$e\left(\frac{419}{1668}\right)$$ $$e\left(\frac{341}{3336}\right)$$ $$e\left(\frac{997}{1668}\right)$$ $$e\left(\frac{13}{556}\right)$$ $$e\left(\frac{51}{1112}\right)$$ $$e\left(\frac{323}{556}\right)$$ $$e\left(\frac{96}{139}\right)$$ $$e\left(\frac{1133}{1668}\right)$$ $$e\left(\frac{1547}{1668}\right)$$ $$e\left(\frac{633}{1112}\right)$$ $$e\left(\frac{281}{417}\right)$$ $$e\left(\frac{1253}{3336}\right)$$ $$e\left(\frac{1751}{3336}\right)$$ $$e\left(\frac{191}{1668}\right)$$ $$e\left(\frac{17}{834}\right)$$ $$e\left(\frac{274}{417}\right)$$ $$e\left(\frac{62}{139}\right)$$ $$e\left(\frac{143}{556}\right)$$ $$e\left(\frac{521}{1112}\right)$$ $$e\left(\frac{271}{417}\right)$$ $$e\left(\frac{1}{278}\right)$$
$$\chi_{10009}(20,\cdot)$$ 1251 Yes 1 $$e\left(\frac{49}{417}\right)$$ $$e\left(\frac{448}{1251}\right)$$ $$e\left(\frac{98}{417}\right)$$ $$e\left(\frac{77}{1251}\right)$$ $$e\left(\frac{595}{1251}\right)$$ $$e\left(\frac{9}{139}\right)$$ $$e\left(\frac{49}{139}\right)$$ $$e\left(\frac{896}{1251}\right)$$ $$e\left(\frac{224}{1251}\right)$$ $$e\left(\frac{1165}{1251}\right)$$ $$e\left(\frac{742}{1251}\right)$$ $$e\left(\frac{344}{417}\right)$$ $$e\left(\frac{76}{417}\right)$$ $$e\left(\frac{175}{417}\right)$$ $$e\left(\frac{196}{417}\right)$$ $$e\left(\frac{128}{1251}\right)$$ $$e\left(\frac{1043}{1251}\right)$$ $$e\left(\frac{281}{417}\right)$$ $$e\left(\frac{371}{1251}\right)$$ $$e\left(\frac{529}{1251}\right)$$ $$e\left(\frac{61}{1251}\right)$$ $$e\left(\frac{542}{1251}\right)$$ $$e\left(\frac{889}{1251}\right)$$ $$e\left(\frac{154}{1251}\right)$$ $$e\left(\frac{131}{139}\right)$$ $$e\left(\frac{31}{417}\right)$$ $$e\left(\frac{125}{417}\right)$$ $$e\left(\frac{478}{1251}\right)$$ $$e\left(\frac{224}{417}\right)$$
$$\chi_{10009}(21,\cdot)$$ 10008 Yes 1 $$e\left(\frac{1499}{1668}\right)$$ $$e\left(\frac{3995}{5004}\right)$$ $$e\left(\frac{665}{834}\right)$$ $$e\left(\frac{1565}{2502}\right)$$ $$e\left(\frac{872}{1251}\right)$$ $$e\left(\frac{979}{1112}\right)$$ $$e\left(\frac{387}{556}\right)$$ $$e\left(\frac{1493}{2502}\right)$$ $$e\left(\frac{2623}{5004}\right)$$ $$e\left(\frac{8329}{10008}\right)$$ $$e\left(\frac{2981}{5004}\right)$$ $$e\left(\frac{1273}{1668}\right)$$ $$e\left(\frac{2599}{3336}\right)$$ $$e\left(\frac{707}{1668}\right)$$ $$e\left(\frac{248}{417}\right)$$ $$e\left(\frac{4537}{5004}\right)$$ $$e\left(\frac{2479}{5004}\right)$$ $$e\left(\frac{1253}{3336}\right)$$ $$e\left(\frac{529}{1251}\right)$$ $$e\left(\frac{6793}{10008}\right)$$ $$e\left(\frac{7315}{10008}\right)$$ $$e\left(\frac{3007}{5004}\right)$$ $$e\left(\frac{1237}{2502}\right)$$ $$e\left(\frac{314}{1251}\right)$$ $$e\left(\frac{92}{139}\right)$$ $$e\left(\frac{659}{1668}\right)$$ $$e\left(\frac{2261}{3336}\right)$$ $$e\left(\frac{341}{1251}\right)$$ $$e\left(\frac{269}{834}\right)$$
$$\chi_{10009}(22,\cdot)$$ 10008 Yes 1 $$e\left(\frac{701}{1668}\right)$$ $$e\left(\frac{2537}{5004}\right)$$ $$e\left(\frac{701}{834}\right)$$ $$e\left(\frac{521}{2502}\right)$$ $$e\left(\frac{1160}{1251}\right)$$ $$e\left(\frac{249}{1112}\right)$$ $$e\left(\frac{145}{556}\right)$$ $$e\left(\frac{35}{2502}\right)$$ $$e\left(\frac{3145}{5004}\right)$$ $$e\left(\frac{1003}{10008}\right)$$ $$e\left(\frac{1739}{5004}\right)$$ $$e\left(\frac{79}{1668}\right)$$ $$e\left(\frac{2149}{3336}\right)$$ $$e\left(\frac{1193}{1668}\right)$$ $$e\left(\frac{284}{417}\right)$$ $$e\left(\frac{3763}{5004}\right)$$ $$e\left(\frac{2173}{5004}\right)$$ $$e\left(\frac{1751}{3336}\right)$$ $$e\left(\frac{61}{1251}\right)$$ $$e\left(\frac{7315}{10008}\right)$$ $$e\left(\frac{5209}{10008}\right)$$ $$e\left(\frac{4069}{5004}\right)$$ $$e\left(\frac{1921}{2502}\right)$$ $$e\left(\frac{521}{1251}\right)$$ $$e\left(\frac{65}{139}\right)$$ $$e\left(\frac{869}{1668}\right)$$ $$e\left(\frac{215}{3336}\right)$$ $$e\left(\frac{1016}{1251}\right)$$ $$e\left(\frac{113}{834}\right)$$
$$\chi_{10009}(23,\cdot)$$ 5004 Yes 1 $$e\left(\frac{749}{834}\right)$$ $$e\left(\frac{1427}{2502}\right)$$ $$e\left(\frac{332}{417}\right)$$ $$e\left(\frac{797}{1251}\right)$$ $$e\left(\frac{586}{1251}\right)$$ $$e\left(\frac{17}{556}\right)$$ $$e\left(\frac{193}{278}\right)$$ $$e\left(\frac{176}{1251}\right)$$ $$e\left(\frac{1339}{2502}\right)$$ $$e\left(\frac{4579}{5004}\right)$$ $$e\left(\frac{917}{2502}\right)$$ $$e\left(\frac{433}{834}\right)$$ $$e\left(\frac{1549}{1668}\right)$$ $$e\left(\frac{173}{834}\right)$$ $$e\left(\frac{247}{417}\right)$$ $$e\left(\frac{229}{2502}\right)$$ $$e\left(\frac{97}{2502}\right)$$ $$e\left(\frac{191}{1668}\right)$$ $$e\left(\frac{542}{1251}\right)$$ $$e\left(\frac{3007}{5004}\right)$$ $$e\left(\frac{4069}{5004}\right)$$ $$e\left(\frac{481}{2502}\right)$$ $$e\left(\frac{331}{1251}\right)$$ $$e\left(\frac{343}{1251}\right)$$ $$e\left(\frac{58}{139}\right)$$ $$e\left(\frac{593}{834}\right)$$ $$e\left(\frac{1379}{1668}\right)$$ $$e\left(\frac{496}{1251}\right)$$ $$e\left(\frac{44}{417}\right)$$
$$\chi_{10009}(24,\cdot)$$ 2502 Yes 1 $$e\left(\frac{23}{417}\right)$$ $$e\left(\frac{389}{1251}\right)$$ $$e\left(\frac{46}{417}\right)$$ $$e\left(\frac{751}{1251}\right)$$ $$e\left(\frac{458}{1251}\right)$$ $$e\left(\frac{51}{278}\right)$$ $$e\left(\frac{23}{139}\right)$$ $$e\left(\frac{778}{1251}\right)$$ $$e\left(\frac{820}{1251}\right)$$ $$e\left(\frac{1783}{2502}\right)$$ $$e\left(\frac{527}{1251}\right)$$ $$e\left(\frac{187}{417}\right)$$ $$e\left(\frac{199}{834}\right)$$ $$e\left(\frac{380}{417}\right)$$ $$e\left(\frac{92}{417}\right)$$ $$e\left(\frac{826}{1251}\right)$$ $$e\left(\frac{847}{1251}\right)$$ $$e\left(\frac{17}{834}\right)$$ $$e\left(\frac{889}{1251}\right)$$ $$e\left(\frac{1237}{2502}\right)$$ $$e\left(\frac{1921}{2502}\right)$$ $$e\left(\frac{331}{1251}\right)$$ $$e\left(\frac{596}{1251}\right)$$ $$e\left(\frac{251}{1251}\right)$$ $$e\left(\frac{70}{139}\right)$$ $$e\left(\frac{389}{417}\right)$$ $$e\left(\frac{245}{834}\right)$$ $$e\left(\frac{1169}{1251}\right)$$ $$e\left(\frac{403}{417}\right)$$
$$\chi_{10009}(25,\cdot)$$ 1251 Yes 1 $$e\left(\frac{398}{417}\right)$$ $$e\left(\frac{422}{1251}\right)$$ $$e\left(\frac{379}{417}\right)$$ $$e\left(\frac{268}{1251}\right)$$ $$e\left(\frac{365}{1251}\right)$$ $$e\left(\frac{127}{139}\right)$$ $$e\left(\frac{120}{139}\right)$$ $$e\left(\frac{844}{1251}\right)$$ $$e\left(\frac{211}{1251}\right)$$ $$e\left(\frac{578}{1251}\right)$$ $$e\left(\frac{308}{1251}\right)$$ $$e\left(\frac{190}{417}\right)$$ $$e\left(\frac{362}{417}\right)$$ $$e\left(\frac{230}{417}\right)$$ $$e\left(\frac{341}{417}\right)$$ $$e\left(\frac{478}{1251}\right)$$ $$e\left(\frac{787}{1251}\right)$$ $$e\left(\frac{274}{417}\right)$$ $$e\left(\frac{154}{1251}\right)$$ $$e\left(\frac{314}{1251}\right)$$ $$e\left(\frac{521}{1251}\right)$$ $$e\left(\frac{343}{1251}\right)$$ $$e\left(\frac{251}{1251}\right)$$ $$e\left(\frac{536}{1251}\right)$$ $$e\left(\frac{57}{139}\right)$$ $$e\left(\frac{5}{417}\right)$$ $$e\left(\frac{343}{417}\right)$$ $$e\left(\frac{104}{1251}\right)$$ $$e\left(\frac{211}{417}\right)$$
$$\chi_{10009}(26,\cdot)$$ 139 Yes 1 $$e\left(\frac{86}{139}\right)$$ $$e\left(\frac{90}{139}\right)$$ $$e\left(\frac{33}{139}\right)$$ $$e\left(\frac{98}{139}\right)$$ $$e\left(\frac{37}{139}\right)$$ $$e\left(\frac{2}{139}\right)$$ $$e\left(\frac{119}{139}\right)$$ $$e\left(\frac{41}{139}\right)$$ $$e\left(\frac{45}{139}\right)$$ $$e\left(\frac{118}{139}\right)$$ $$e\left(\frac{123}{139}\right)$$ $$e\left(\frac{113}{139}\right)$$ $$e\left(\frac{88}{139}\right)$$ $$e\left(\frac{49}{139}\right)$$ $$e\left(\frac{66}{139}\right)$$ $$e\left(\frac{125}{139}\right)$$ $$e\left(\frac{127}{139}\right)$$ $$e\left(\frac{62}{139}\right)$$ $$e\left(\frac{131}{139}\right)$$ $$e\left(\frac{92}{139}\right)$$ $$e\left(\frac{65}{139}\right)$$ $$e\left(\frac{58}{139}\right)$$ $$e\left(\frac{70}{139}\right)$$ $$e\left(\frac{57}{139}\right)$$ $$e\left(\frac{60}{139}\right)$$ $$e\left(\frac{131}{139}\right)$$ $$e\left(\frac{35}{139}\right)$$ $$e\left(\frac{65}{139}\right)$$ $$e\left(\frac{135}{139}\right)$$
$$\chi_{10009}(27,\cdot)$$ 1668 Yes 1 $$e\left(\frac{79}{278}\right)$$ $$e\left(\frac{67}{834}\right)$$ $$e\left(\frac{79}{139}\right)$$ $$e\left(\frac{211}{417}\right)$$ $$e\left(\frac{152}{417}\right)$$ $$e\left(\frac{175}{556}\right)$$ $$e\left(\frac{237}{278}\right)$$ $$e\left(\frac{67}{417}\right)$$ $$e\left(\frac{659}{834}\right)$$ $$e\left(\frac{395}{1668}\right)$$ $$e\left(\frac{541}{834}\right)$$ $$e\left(\frac{183}{278}\right)$$ $$e\left(\frac{333}{556}\right)$$ $$e\left(\frac{163}{278}\right)$$ $$e\left(\frac{19}{139}\right)$$ $$e\left(\frac{317}{834}\right)$$ $$e\left(\frac{371}{834}\right)$$ $$e\left(\frac{143}{556}\right)$$ $$e\left(\frac{31}{417}\right)$$ $$e\left(\frac{659}{1668}\right)$$ $$e\left(\frac{869}{1668}\right)$$ $$e\left(\frac{593}{834}\right)$$ $$e\left(\frac{389}{417}\right)$$ $$e\left(\frac{5}{417}\right)$$ $$e\left(\frac{131}{139}\right)$$ $$e\left(\frac{67}{278}\right)$$ $$e\left(\frac{491}{556}\right)$$ $$e\left(\frac{113}{417}\right)$$ $$e\left(\frac{121}{139}\right)$$
$$\chi_{10009}(28,\cdot)$$ 3336 Yes 1 $$e\left(\frac{247}{556}\right)$$ $$e\left(\frac{1603}{1668}\right)$$ $$e\left(\frac{247}{278}\right)$$ $$e\left(\frac{343}{834}\right)$$ $$e\left(\frac{169}{417}\right)$$ $$e\left(\frac{797}{1112}\right)$$ $$e\left(\frac{185}{556}\right)$$ $$e\left(\frac{769}{834}\right)$$ $$e\left(\frac{1427}{1668}\right)$$ $$e\left(\frac{2069}{3336}\right)$$ $$e\left(\frac{1417}{1668}\right)$$ $$e\left(\frac{449}{556}\right)$$ $$e\left(\frac{179}{1112}\right)$$ $$e\left(\frac{207}{556}\right)$$ $$e\left(\frac{108}{139}\right)$$ $$e\left(\frac{41}{1668}\right)$$ $$e\left(\frac{611}{1668}\right)$$ $$e\left(\frac{521}{1112}\right)$$ $$e\left(\frac{125}{417}\right)$$ $$e\left(\frac{2261}{3336}\right)$$ $$e\left(\frac{215}{3336}\right)$$ $$e\left(\frac{1379}{1668}\right)$$ $$e\left(\frac{245}{834}\right)$$ $$e\left(\frac{343}{417}\right)$$ $$e\left(\frac{35}{139}\right)$$ $$e\left(\frac{491}{556}\right)$$ $$e\left(\frac{673}{1112}\right)$$ $$e\left(\frac{79}{417}\right)$$ $$e\left(\frac{227}{278}\right)$$
$$\chi_{10009}(29,\cdot)$$ 1251 Yes 1 $$e\left(\frac{71}{417}\right)$$ $$e\left(\frac{530}{1251}\right)$$ $$e\left(\frac{142}{417}\right)$$ $$e\left(\frac{52}{1251}\right)$$ $$e\left(\frac{743}{1251}\right)$$ $$e\left(\frac{118}{139}\right)$$ $$e\left(\frac{71}{139}\right)$$ $$e\left(\frac{1060}{1251}\right)$$ $$e\left(\frac{265}{1251}\right)$$ $$e\left(\frac{803}{1251}\right)$$ $$e\left(\frac{956}{1251}\right)$$ $$e\left(\frac{124}{417}\right)$$ $$e\left(\frac{8}{417}\right)$$ $$e\left(\frac{194}{417}\right)$$ $$e\left(\frac{284}{417}\right)$$ $$e\left(\frac{1045}{1251}\right)$$ $$e\left(\frac{22}{1251}\right)$$ $$e\left(\frac{271}{417}\right)$$ $$e\left(\frac{478}{1251}\right)$$ $$e\left(\frac{341}{1251}\right)$$ $$e\left(\frac{1016}{1251}\right)$$ $$e\left(\frac{496}{1251}\right)$$ $$e\left(\frac{1169}{1251}\right)$$ $$e\left(\frac{104}{1251}\right)$$ $$e\left(\frac{65}{139}\right)$$ $$e\left(\frac{113}{417}\right)$$ $$e\left(\frac{79}{417}\right)$$ $$e\left(\frac{599}{1251}\right)$$ $$e\left(\frac{265}{417}\right)$$
$$\chi_{10009}(30,\cdot)$$ 834 Yes 1 $$e\left(\frac{124}{139}\right)$$ $$e\left(\frac{121}{417}\right)$$ $$e\left(\frac{109}{139}\right)$$ $$e\left(\frac{314}{417}\right)$$ $$e\left(\frac{76}{417}\right)$$ $$e\left(\frac{9}{278}\right)$$ $$e\left(\frac{94}{139}\right)$$ $$e\left(\frac{242}{417}\right)$$ $$e\left(\frac{269}{417}\right)$$ $$e\left(\frac{203}{834}\right)$$ $$e\left(\frac{31}{417}\right)$$ $$e\left(\frac{11}{139}\right)$$ $$e\left(\frac{257}{278}\right)$$ $$e\left(\frac{6}{139}\right)$$ $$e\left(\frac{79}{139}\right)$$ $$e\left(\frac{392}{417}\right)$$ $$e\left(\frac{197}{417}\right)$$ $$e\left(\frac{1}{278}\right)$$ $$e\left(\frac{224}{417}\right)$$ $$e\left(\frac{269}{834}\right)$$ $$e\left(\frac{113}{834}\right)$$ $$e\left(\frac{44}{417}\right)$$ $$e\left(\frac{403}{417}\right)$$ $$e\left(\frac{211}{417}\right)$$ $$e\left(\frac{135}{139}\right)$$ $$e\left(\frac{121}{139}\right)$$ $$e\left(\frac{227}{278}\right)$$ $$e\left(\frac{265}{417}\right)$$ $$e\left(\frac{130}{139}\right)$$
$$\chi_{10009}(31,\cdot)$$ 10008 Yes 1 $$e\left(\frac{437}{1668}\right)$$ $$e\left(\frac{3221}{5004}\right)$$ $$e\left(\frac{437}{834}\right)$$ $$e\left(\frac{2339}{2502}\right)$$ $$e\left(\frac{1133}{1251}\right)$$ $$e\left(\frac{969}{1112}\right)$$ $$e\left(\frac{437}{556}\right)$$ $$e\left(\frac{719}{2502}\right)$$ $$e\left(\frac{985}{5004}\right)$$ $$e\left(\frac{3019}{10008}\right)$$ $$e\left(\frac{839}{5004}\right)$$ $$e\left(\frac{1051}{1668}\right)$$ $$e\left(\frac{445}{3336}\right)$$ $$e\left(\frac{965}{1668}\right)$$ $$e\left(\frac{20}{417}\right)$$ $$e\left(\frac{1099}{5004}\right)$$ $$e\left(\frac{2749}{5004}\right)$$ $$e\left(\frac{1991}{3336}\right)$$ $$e\left(\frac{574}{1251}\right)$$ $$e\left(\frac{5155}{10008}\right)$$ $$e\left(\frac{5641}{10008}\right)$$ $$e\left(\frac{2953}{5004}\right)$$ $$e\left(\frac{1075}{2502}\right)$$ $$e\left(\frac{1088}{1251}\right)$$ $$e\left(\frac{124}{139}\right)$$ $$e\left(\frac{1553}{1668}\right)$$ $$e\left(\frac{1319}{3336}\right)$$ $$e\left(\frac{1070}{1251}\right)$$ $$e\left(\frac{701}{834}\right)$$
$$\chi_{10009}(32,\cdot)$$ 1668 Yes 1 $$e\left(\frac{167}{278}\right)$$ $$e\left(\frac{395}{834}\right)$$ $$e\left(\frac{28}{139}\right)$$ $$e\left(\frac{161}{417}\right)$$ $$e\left(\frac{31}{417}\right)$$ $$e\left(\frac{11}{556}\right)$$ $$e\left(\frac{223}{278}\right)$$ $$e\left(\frac{395}{417}\right)$$ $$e\left(\frac{823}{834}\right)$$ $$e\left(\frac{835}{1668}\right)$$ $$e\left(\frac{563}{834}\right)$$ $$e\left(\frac{137}{278}\right)$$ $$e\left(\frac{345}{556}\right)$$ $$e\left(\frac{239}{278}\right)$$ $$e\left(\frac{56}{139}\right)$$ $$e\left(\frac{649}{834}\right)$$ $$e\left(\frac{457}{834}\right)$$ $$e\left(\frac{63}{556}\right)$$ $$e\left(\frac{245}{417}\right)$$ $$e\left(\frac{823}{1668}\right)$$ $$e\left(\frac{169}{1668}\right)$$ $$e\left(\frac{409}{834}\right)$$ $$e\left(\frac{115}{417}\right)$$ $$e\left(\frac{322}{417}\right)$$ $$e\left(\frac{13}{139}\right)$$ $$e\left(\frac{117}{278}\right)$$ $$e\left(\frac{123}{556}\right)$$ $$e\left(\frac{355}{417}\right)$$ $$e\left(\frac{64}{139}\right)$$
$$\chi_{10009}(33,\cdot)$$ 10008 Yes 1 $$e\left(\frac{325}{1668}\right)$$ $$e\left(\frac{2197}{5004}\right)$$ $$e\left(\frac{325}{834}\right)$$ $$e\left(\frac{2251}{2502}\right)$$ $$e\left(\frac{793}{1251}\right)$$ $$e\left(\frac{213}{1112}\right)$$ $$e\left(\frac{325}{556}\right)$$ $$e\left(\frac{2197}{2502}\right)$$ $$e\left(\frac{473}{5004}\right)$$ $$e\left(\frac{4127}{10008}\right)$$ $$e\left(\frac{4147}{5004}\right)$$ $$e\left(\frac{503}{1668}\right)$$ $$e\left(\frac{1289}{3336}\right)$$ $$e\left(\frac{565}{1668}\right)$$ $$e\left(\frac{325}{417}\right)$$ $$e\left(\frac{2951}{5004}\right)$$ $$e\left(\frac{365}{5004}\right)$$ $$e\left(\frac{2851}{3336}\right)$$ $$e\left(\frac{362}{1251}\right)$$ $$e\left(\frac{6311}{10008}\right)$$ $$e\left(\frac{6077}{10008}\right)$$ $$e\left(\frac{2429}{5004}\right)$$ $$e\left(\frac{59}{2502}\right)$$ $$e\left(\frac{1000}{1251}\right)$$ $$e\left(\frac{69}{139}\right)$$ $$e\left(\frac{529}{1668}\right)$$ $$e\left(\frac{1939}{3336}\right)$$ $$e\left(\frac{82}{1251}\right)$$ $$e\left(\frac{445}{834}\right)$$
$$\chi_{10009}(34,\cdot)$$ 2502 Yes 1 $$e\left(\frac{115}{417}\right)$$ $$e\left(\frac{1111}{1251}\right)$$ $$e\left(\frac{230}{417}\right)$$ $$e\left(\frac{836}{1251}\right)$$ $$e\left(\frac{205}{1251}\right)$$ $$e\left(\frac{255}{278}\right)$$ $$e\left(\frac{115}{139}\right)$$ $$e\left(\frac{971}{1251}\right)$$ $$e\left(\frac{1181}{1251}\right)$$ $$e\left(\frac{2243}{2502}\right)$$ $$e\left(\frac{550}{1251}\right)$$ $$e\left(\frac{101}{417}\right)$$ $$e\left(\frac{161}{834}\right)$$ $$e\left(\frac{232}{417}\right)$$ $$e\left(\frac{43}{417}\right)$$ $$e\left(\frac{1211}{1251}\right)$$ $$e\left(\frac{65}{1251}\right)$$ $$e\left(\frac{85}{834}\right)$$ $$e\left(\frac{275}{1251}\right)$$ $$e\left(\frac{2015}{2502}\right)$$ $$e\left(\frac{431}{2502}\right)$$ $$e\left(\frac{1238}{1251}\right)$$ $$e\left(\frac{895}{1251}\right)$$ $$e\left(\frac{421}{1251}\right)$$ $$e\left(\frac{72}{139}\right)$$ $$e\left(\frac{277}{417}\right)$$ $$e\left(\frac{391}{834}\right)$$ $$e\left(\frac{7}{1251}\right)$$ $$e\left(\frac{347}{417}\right)$$
$$\chi_{10009}(35,\cdot)$$ 10008 Yes 1 $$e\left(\frac{469}{1668}\right)$$ $$e\left(\frac{4705}{5004}\right)$$ $$e\left(\frac{469}{834}\right)$$ $$e\left(\frac{1411}{2502}\right)$$ $$e\left(\frac{277}{1251}\right)$$ $$e\left(\frac{629}{1112}\right)$$ $$e\left(\frac{469}{556}\right)$$ $$e\left(\frac{2203}{2502}\right)$$ $$e\left(\frac{4229}{5004}\right)$$ $$e\left(\frac{1511}{10008}\right)$$ $$e\left(\frac{2515}{5004}\right)$$ $$e\left(\frac{731}{1668}\right)$$ $$e\left(\frac{2825}{3336}\right)$$ $$e\left(\frac{841}{1668}\right)$$ $$e\left(\frac{52}{417}\right)$$ $$e\left(\frac{1523}{5004}\right)$$ $$e\left(\frac{809}{5004}\right)$$ $$e\left(\frac{1507}{3336}\right)$$ $$e\left(\frac{158}{1251}\right)$$ $$e\left(\frac{5063}{10008}\right)$$ $$e\left(\frac{4325}{10008}\right)$$ $$e\left(\frac{3341}{5004}\right)$$ $$e\left(\frac{1961}{2502}\right)$$ $$e\left(\frac{160}{1251}\right)$$ $$e\left(\frac{100}{139}\right)$$ $$e\left(\frac{1369}{1668}\right)$$ $$e\left(\frac{427}{3336}\right)$$ $$e\left(\frac{1114}{1251}\right)$$ $$e\left(\frac{655}{834}\right)$$
$$\chi_{10009}(36,\cdot)$$ 1251 Yes 1 $$e\left(\frac{346}{417}\right)$$ $$e\left(\frac{304}{1251}\right)$$ $$e\left(\frac{275}{417}\right)$$ $$e\left(\frac{365}{1251}\right)$$ $$e\left(\frac{91}{1251}\right)$$ $$e\left(\frac{21}{139}\right)$$ $$e\left(\frac{68}{139}\right)$$ $$e\left(\frac{608}{1251}\right)$$ $$e\left(\frac{152}{1251}\right)$$ $$e\left(\frac{31}{1251}\right)$$ $$e\left(\frac{1129}{1251}\right)$$ $$e\left(\frac{293}{417}\right)$$ $$e\left(\frac{409}{417}\right)$$ $$e\left(\frac{223}{417}\right)$$ $$e\left(\frac{133}{417}\right)$$ $$e\left(\frac{623}{1251}\right)$$ $$e\left(\frac{395}{1251}\right)$$ $$e\left(\frac{146}{417}\right)$$ $$e\left(\frac{1190}{1251}\right)$$ $$e\left(\frac{493}{1251}\right)$$ $$e\left(\frac{1069}{1251}\right)$$ $$e\left(\frac{1172}{1251}\right)$$ $$e\left(\frac{916}{1251}\right)$$ $$e\left(\frac{730}{1251}\right)$$ $$e\left(\frac{74}{139}\right)$$ $$e\left(\frac{304}{417}\right)$$ $$e\left(\frac{338}{417}\right)$$ $$e\left(\frac{235}{1251}\right)$$ $$e\left(\frac{152}{417}\right)$$
$$\chi_{10009}(37,\cdot)$$ 10008 Yes 1 $$e\left(\frac{569}{1668}\right)$$ $$e\left(\frac{2045}{5004}\right)$$ $$e\left(\frac{569}{834}\right)$$ $$e\left(\frac{1847}{2502}\right)$$ $$e\left(\frac{938}{1251}\right)$$ $$e\left(\frac{609}{1112}\right)$$ $$e\left(\frac{13}{556}\right)$$ $$e\left(\frac{2045}{2502}\right)$$ $$e\left(\frac{397}{5004}\right)$$ $$e\left(\frac{5347}{10008}\right)$$ $$e\left(\frac{455}{5004}\right)$$ $$e\left(\frac{1399}{1668}\right)$$ $$e\left(\frac{2965}{3336}\right)$$ $$e\left(\frac{245}{1668}\right)$$ $$e\left(\frac{152}{417}\right)$$ $$e\left(\frac{763}{5004}\right)$$ $$e\left(\frac{793}{5004}\right)$$ $$e\left(\frac{1871}{3336}\right)$$ $$e\left(\frac{526}{1251}\right)$$ $$e\left(\frac{9571}{10008}\right)$$ $$e\left(\frac{8761}{10008}\right)$$ $$e\left(\frac{4345}{5004}\right)$$ $$e\left(\frac{1081}{2502}\right)$$ $$e\left(\frac{596}{1251}\right)$$ $$e\left(\frac{25}{139}\right)$$ $$e\left(\frac{377}{1668}\right)$$ $$e\left(\frac{767}{3336}\right)$$ $$e\left(\frac{209}{1251}\right)$$ $$e\left(\frac{407}{834}\right)$$