Normalized defining polynomial
\( x^{43} - x^{42} - 84 x^{41} + 79 x^{40} + 3160 x^{39} - 2786 x^{38} - 70521 x^{37} + 58076 x^{36} + \cdots - 1 \)
Invariants
| Degree: | $43$ |
| |
| Signature: | $(43, 0)$ |
| |
| Discriminant: |
\(995\!\cdots\!529\)
\(\medspace = 173^{42}\)
|
| |
| Root discriminant: | \(153.46\) |
| |
| Galois root discriminant: | $173^{42/43}\approx 153.46117507511823$ | ||
| Ramified primes: |
\(173\)
|
| |
| Discriminant root field: | \(\Q\) | ||
| $\Aut(K/\Q)$ $=$ $\Gal(K/\Q)$: | $C_{43}$ |
| |
| This field is Galois and abelian over $\Q$. | |||
| Conductor: | \(173\) | ||
| Dirichlet character group: | $\lbrace$$\chi_{173}(1,·)$, $\chi_{173}(132,·)$, $\chi_{173}(133,·)$, $\chi_{173}(6,·)$, $\chi_{173}(135,·)$, $\chi_{173}(136,·)$, $\chi_{173}(10,·)$, $\chi_{173}(139,·)$, $\chi_{173}(140,·)$, $\chi_{173}(14,·)$, $\chi_{173}(16,·)$, $\chi_{173}(148,·)$, $\chi_{173}(149,·)$, $\chi_{173}(22,·)$, $\chi_{173}(23,·)$, $\chi_{173}(152,·)$, $\chi_{173}(29,·)$, $\chi_{173}(158,·)$, $\chi_{173}(160,·)$, $\chi_{173}(36,·)$, $\chi_{173}(169,·)$, $\chi_{173}(43,·)$, $\chi_{173}(47,·)$, $\chi_{173}(51,·)$, $\chi_{173}(52,·)$, $\chi_{173}(57,·)$, $\chi_{173}(60,·)$, $\chi_{173}(138,·)$, $\chi_{173}(81,·)$, $\chi_{173}(83,·)$, $\chi_{173}(84,·)$, $\chi_{173}(142,·)$, $\chi_{173}(164,·)$, $\chi_{173}(95,·)$, $\chi_{173}(96,·)$, $\chi_{173}(100,·)$, $\chi_{173}(106,·)$, $\chi_{173}(109,·)$, $\chi_{173}(117,·)$, $\chi_{173}(118,·)$, $\chi_{173}(119,·)$, $\chi_{173}(124,·)$, $\chi_{173}(85,·)$$\rbrace$ | ||
| This is not a CM field. | |||
| This field has no CM subfields. | |||
Integral basis (with respect to field generator \(a\))
$1$, $a$, $a^{2}$, $a^{3}$, $a^{4}$, $a^{5}$, $a^{6}$, $a^{7}$, $a^{8}$, $a^{9}$, $a^{10}$, $a^{11}$, $a^{12}$, $a^{13}$, $a^{14}$, $a^{15}$, $a^{16}$, $a^{17}$, $a^{18}$, $a^{19}$, $a^{20}$, $a^{21}$, $a^{22}$, $a^{23}$, $a^{24}$, $a^{25}$, $a^{26}$, $a^{27}$, $a^{28}$, $a^{29}$, $a^{30}$, $a^{31}$, $a^{32}$, $a^{33}$, $a^{34}$, $a^{35}$, $a^{36}$, $a^{37}$, $a^{38}$, $a^{39}$, $\frac{1}{439}a^{40}-\frac{195}{439}a^{39}+\frac{16}{439}a^{38}-\frac{89}{439}a^{37}+\frac{194}{439}a^{36}-\frac{161}{439}a^{35}+\frac{42}{439}a^{34}-\frac{201}{439}a^{33}+\frac{152}{439}a^{32}-\frac{191}{439}a^{31}-\frac{35}{439}a^{30}+\frac{123}{439}a^{29}-\frac{153}{439}a^{28}-\frac{215}{439}a^{27}-\frac{140}{439}a^{26}+\frac{90}{439}a^{25}+\frac{84}{439}a^{24}+\frac{105}{439}a^{23}-\frac{49}{439}a^{22}+\frac{57}{439}a^{21}-\frac{173}{439}a^{20}+\frac{202}{439}a^{19}-\frac{27}{439}a^{18}-\frac{150}{439}a^{17}+\frac{79}{439}a^{16}+\frac{71}{439}a^{15}-\frac{33}{439}a^{14}+\frac{14}{439}a^{13}+\frac{134}{439}a^{12}+\frac{215}{439}a^{11}+\frac{76}{439}a^{10}+\frac{100}{439}a^{9}+\frac{187}{439}a^{8}+\frac{93}{439}a^{7}+\frac{143}{439}a^{6}-\frac{46}{439}a^{5}-\frac{79}{439}a^{4}+\frac{195}{439}a^{3}-\frac{139}{439}a^{2}-\frac{10}{439}a+\frac{66}{439}$, $\frac{1}{393729808938589}a^{41}+\frac{118184672889}{393729808938589}a^{40}-\frac{175419443235213}{393729808938589}a^{39}+\frac{140439653559240}{393729808938589}a^{38}+\frac{169328219003484}{393729808938589}a^{37}-\frac{17816338841554}{393729808938589}a^{36}-\frac{16660852818608}{393729808938589}a^{35}-\frac{92365897316206}{393729808938589}a^{34}-\frac{174069904687629}{393729808938589}a^{33}+\frac{74511950628496}{393729808938589}a^{32}+\frac{122586483809914}{393729808938589}a^{31}+\frac{158635369124277}{393729808938589}a^{30}-\frac{13848889877657}{393729808938589}a^{29}+\frac{140347423553191}{393729808938589}a^{28}-\frac{112968103160742}{393729808938589}a^{27}+\frac{153430105794647}{393729808938589}a^{26}-\frac{72736226978788}{393729808938589}a^{25}+\frac{168180617028682}{393729808938589}a^{24}-\frac{87525194788406}{393729808938589}a^{23}-\frac{187336522664663}{393729808938589}a^{22}+\frac{9276296544652}{393729808938589}a^{21}+\frac{2641420354443}{393729808938589}a^{20}+\frac{88456071253694}{393729808938589}a^{19}-\frac{175525679316799}{393729808938589}a^{18}-\frac{126527970694928}{393729808938589}a^{17}-\frac{126898159483620}{393729808938589}a^{16}-\frac{143143684221711}{393729808938589}a^{15}-\frac{145220588297682}{393729808938589}a^{14}-\frac{54014514099111}{393729808938589}a^{13}+\frac{134045097322187}{393729808938589}a^{12}+\frac{69303068603000}{393729808938589}a^{11}+\frac{32621135966434}{393729808938589}a^{10}+\frac{151443163986127}{393729808938589}a^{9}-\frac{115549570362463}{393729808938589}a^{8}+\frac{1028061930698}{393729808938589}a^{7}-\frac{25514004847786}{393729808938589}a^{6}+\frac{28879785465430}{393729808938589}a^{5}-\frac{178641133299543}{393729808938589}a^{4}+\frac{112500866236428}{393729808938589}a^{3}+\frac{179231976728897}{393729808938589}a^{2}+\frac{36082084950171}{393729808938589}a-\frac{179213920964281}{393729808938589}$, $\frac{1}{35\cdots 59}a^{42}+\frac{31\cdots 08}{35\cdots 59}a^{41}+\frac{19\cdots 53}{35\cdots 59}a^{40}+\frac{14\cdots 12}{35\cdots 59}a^{39}+\frac{53\cdots 95}{35\cdots 59}a^{38}-\frac{54\cdots 40}{35\cdots 59}a^{37}-\frac{93\cdots 58}{35\cdots 59}a^{36}-\frac{99\cdots 83}{35\cdots 59}a^{35}-\frac{53\cdots 34}{35\cdots 59}a^{34}-\frac{28\cdots 99}{35\cdots 59}a^{33}+\frac{10\cdots 32}{35\cdots 59}a^{32}+\frac{17\cdots 59}{35\cdots 59}a^{31}-\frac{11\cdots 91}{35\cdots 59}a^{30}+\frac{16\cdots 31}{35\cdots 59}a^{29}-\frac{61\cdots 65}{35\cdots 59}a^{28}+\frac{66\cdots 97}{35\cdots 59}a^{27}-\frac{44\cdots 94}{35\cdots 59}a^{26}+\frac{14\cdots 32}{35\cdots 59}a^{25}-\frac{16\cdots 34}{35\cdots 59}a^{24}-\frac{79\cdots 47}{35\cdots 59}a^{23}-\frac{51\cdots 53}{35\cdots 59}a^{22}+\frac{72\cdots 98}{35\cdots 59}a^{21}-\frac{23\cdots 80}{35\cdots 59}a^{20}-\frac{59\cdots 85}{35\cdots 59}a^{19}-\frac{15\cdots 59}{35\cdots 59}a^{18}-\frac{10\cdots 06}{35\cdots 59}a^{17}+\frac{25\cdots 57}{35\cdots 59}a^{16}-\frac{14\cdots 21}{35\cdots 59}a^{15}+\frac{94\cdots 99}{35\cdots 59}a^{14}+\frac{48\cdots 50}{35\cdots 59}a^{13}-\frac{12\cdots 39}{35\cdots 59}a^{12}-\frac{31\cdots 50}{35\cdots 59}a^{11}+\frac{11\cdots 03}{35\cdots 59}a^{10}+\frac{15\cdots 80}{35\cdots 59}a^{9}-\frac{26\cdots 03}{35\cdots 59}a^{8}-\frac{14\cdots 15}{35\cdots 59}a^{7}+\frac{12\cdots 05}{35\cdots 59}a^{6}+\frac{65\cdots 22}{35\cdots 59}a^{5}+\frac{13\cdots 72}{35\cdots 59}a^{4}+\frac{69\cdots 46}{35\cdots 59}a^{3}+\frac{69\cdots 40}{35\cdots 59}a^{2}-\frac{11\cdots 04}{35\cdots 59}a+\frac{36\cdots 96}{35\cdots 59}$
| Monogenic: | No | |
| Index: | $1$ | |
| Inessential primes: | None |
Class group and class number
| Ideal class group: | Trivial group, which has order $1$ (assuming GRH) |
| |
| Narrow class group: | Trivial group, which has order $1$ (assuming GRH) |
|
Unit group
| Rank: | $42$ |
| |
| Torsion generator: |
\( -1 \)
(order $2$)
|
| |
| Fundamental units: |
$\frac{46\cdots 16}{35\cdots 59}a^{42}-\frac{48\cdots 69}{35\cdots 59}a^{41}-\frac{39\cdots 39}{35\cdots 59}a^{40}+\frac{38\cdots 99}{35\cdots 59}a^{39}+\frac{14\cdots 26}{35\cdots 59}a^{38}-\frac{13\cdots 76}{35\cdots 59}a^{37}-\frac{33\cdots 13}{35\cdots 59}a^{36}+\frac{28\cdots 22}{35\cdots 59}a^{35}+\frac{48\cdots 75}{35\cdots 59}a^{34}-\frac{38\cdots 44}{35\cdots 59}a^{33}-\frac{50\cdots 38}{35\cdots 59}a^{32}+\frac{37\cdots 46}{35\cdots 59}a^{31}+\frac{37\cdots 71}{35\cdots 59}a^{30}-\frac{25\cdots 34}{35\cdots 59}a^{29}-\frac{20\cdots 04}{35\cdots 59}a^{28}+\frac{13\cdots 47}{35\cdots 59}a^{27}+\frac{86\cdots 34}{35\cdots 59}a^{26}-\frac{49\cdots 82}{35\cdots 59}a^{25}-\frac{26\cdots 85}{35\cdots 59}a^{24}+\frac{13\cdots 77}{35\cdots 59}a^{23}+\frac{60\cdots 49}{35\cdots 59}a^{22}-\frac{28\cdots 86}{35\cdots 59}a^{21}-\frac{10\cdots 23}{35\cdots 59}a^{20}+\frac{43\cdots 48}{35\cdots 59}a^{19}+\frac{12\cdots 24}{35\cdots 59}a^{18}-\frac{47\cdots 94}{35\cdots 59}a^{17}-\frac{11\cdots 80}{35\cdots 59}a^{16}+\frac{37\cdots 56}{35\cdots 59}a^{15}+\frac{68\cdots 01}{35\cdots 59}a^{14}-\frac{20\cdots 94}{35\cdots 59}a^{13}-\frac{28\cdots 11}{35\cdots 59}a^{12}+\frac{73\cdots 73}{35\cdots 59}a^{11}+\frac{78\cdots 78}{35\cdots 59}a^{10}-\frac{17\cdots 01}{35\cdots 59}a^{9}-\frac{13\cdots 49}{35\cdots 59}a^{8}+\frac{24\cdots 32}{35\cdots 59}a^{7}+\frac{11\cdots 08}{35\cdots 59}a^{6}-\frac{18\cdots 93}{35\cdots 59}a^{5}-\frac{44\cdots 62}{35\cdots 59}a^{4}+\frac{67\cdots 55}{35\cdots 59}a^{3}+\frac{24\cdots 96}{35\cdots 59}a^{2}-\frac{21\cdots 44}{35\cdots 59}a-\frac{86\cdots 96}{35\cdots 59}$, $\frac{14\cdots 17}{35\cdots 59}a^{42}-\frac{15\cdots 49}{35\cdots 59}a^{41}-\frac{12\cdots 71}{35\cdots 59}a^{40}+\frac{12\cdots 32}{35\cdots 59}a^{39}+\frac{45\cdots 88}{35\cdots 59}a^{38}-\frac{43\cdots 04}{35\cdots 59}a^{37}-\frac{10\cdots 72}{35\cdots 59}a^{36}+\frac{91\cdots 29}{35\cdots 59}a^{35}+\frac{14\cdots 53}{35\cdots 59}a^{34}-\frac{12\cdots 21}{35\cdots 59}a^{33}-\frac{15\cdots 26}{35\cdots 59}a^{32}+\frac{12\cdots 82}{35\cdots 59}a^{31}+\frac{11\cdots 07}{35\cdots 59}a^{30}-\frac{85\cdots 92}{35\cdots 59}a^{29}-\frac{63\cdots 79}{35\cdots 59}a^{28}+\frac{43\cdots 69}{35\cdots 59}a^{27}+\frac{26\cdots 21}{35\cdots 59}a^{26}-\frac{16\cdots 27}{35\cdots 59}a^{25}-\frac{80\cdots 99}{35\cdots 59}a^{24}+\frac{46\cdots 69}{35\cdots 59}a^{23}+\frac{18\cdots 76}{35\cdots 59}a^{22}-\frac{97\cdots 53}{35\cdots 59}a^{21}-\frac{88\cdots 99}{10\cdots 97}a^{20}+\frac{14\cdots 82}{35\cdots 59}a^{19}+\frac{37\cdots 11}{35\cdots 59}a^{18}-\frac{16\cdots 39}{35\cdots 59}a^{17}-\frac{33\cdots 32}{35\cdots 59}a^{16}+\frac{13\cdots 81}{35\cdots 59}a^{15}+\frac{20\cdots 31}{35\cdots 59}a^{14}-\frac{71\cdots 48}{35\cdots 59}a^{13}-\frac{84\cdots 17}{35\cdots 59}a^{12}+\frac{26\cdots 53}{35\cdots 59}a^{11}+\frac{23\cdots 59}{35\cdots 59}a^{10}-\frac{60\cdots 59}{35\cdots 59}a^{9}-\frac{38\cdots 31}{35\cdots 59}a^{8}+\frac{85\cdots 66}{35\cdots 59}a^{7}+\frac{33\cdots 79}{35\cdots 59}a^{6}-\frac{66\cdots 84}{35\cdots 59}a^{5}-\frac{11\cdots 71}{35\cdots 59}a^{4}+\frac{23\cdots 62}{35\cdots 59}a^{3}+\frac{32\cdots 85}{35\cdots 59}a^{2}-\frac{11\cdots 55}{35\cdots 59}a-\frac{18\cdots 32}{35\cdots 59}$, $\frac{45\cdots 78}{35\cdots 59}a^{42}-\frac{49\cdots 74}{35\cdots 59}a^{41}-\frac{38\cdots 86}{35\cdots 59}a^{40}+\frac{39\cdots 22}{35\cdots 59}a^{39}+\frac{14\cdots 47}{35\cdots 59}a^{38}-\frac{13\cdots 73}{35\cdots 59}a^{37}-\frac{31\cdots 97}{35\cdots 59}a^{36}+\frac{29\cdots 60}{35\cdots 59}a^{35}+\frac{47\cdots 04}{35\cdots 59}a^{34}-\frac{40\cdots 82}{35\cdots 59}a^{33}-\frac{48\cdots 53}{35\cdots 59}a^{32}+\frac{39\cdots 83}{35\cdots 59}a^{31}+\frac{36\cdots 22}{35\cdots 59}a^{30}-\frac{27\cdots 04}{35\cdots 59}a^{29}-\frac{20\cdots 10}{35\cdots 59}a^{28}+\frac{14\cdots 70}{35\cdots 59}a^{27}+\frac{82\cdots 18}{35\cdots 59}a^{26}-\frac{53\cdots 03}{35\cdots 59}a^{25}-\frac{25\cdots 75}{35\cdots 59}a^{24}+\frac{15\cdots 80}{35\cdots 59}a^{23}+\frac{57\cdots 63}{35\cdots 59}a^{22}-\frac{31\cdots 48}{35\cdots 59}a^{21}-\frac{97\cdots 28}{35\cdots 59}a^{20}+\frac{48\cdots 02}{35\cdots 59}a^{19}+\frac{11\cdots 32}{35\cdots 59}a^{18}-\frac{53\cdots 79}{35\cdots 59}a^{17}-\frac{10\cdots 44}{35\cdots 59}a^{16}+\frac{42\cdots 34}{35\cdots 59}a^{15}+\frac{64\cdots 82}{35\cdots 59}a^{14}-\frac{23\cdots 10}{35\cdots 59}a^{13}-\frac{27\cdots 85}{35\cdots 59}a^{12}+\frac{87\cdots 78}{35\cdots 59}a^{11}+\frac{73\cdots 94}{35\cdots 59}a^{10}-\frac{20\cdots 66}{35\cdots 59}a^{9}-\frac{12\cdots 72}{35\cdots 59}a^{8}+\frac{30\cdots 98}{35\cdots 59}a^{7}+\frac{11\cdots 65}{35\cdots 59}a^{6}-\frac{24\cdots 52}{35\cdots 59}a^{5}-\frac{42\cdots 15}{35\cdots 59}a^{4}+\frac{89\cdots 53}{35\cdots 59}a^{3}+\frac{25\cdots 09}{35\cdots 59}a^{2}-\frac{54\cdots 09}{35\cdots 59}a-\frac{17\cdots 64}{35\cdots 59}$, $\frac{85\cdots 30}{35\cdots 59}a^{42}-\frac{92\cdots 80}{35\cdots 59}a^{41}-\frac{71\cdots 15}{35\cdots 59}a^{40}+\frac{73\cdots 40}{35\cdots 59}a^{39}+\frac{27\cdots 75}{35\cdots 59}a^{38}-\frac{26\cdots 85}{35\cdots 59}a^{37}-\frac{60\cdots 05}{35\cdots 59}a^{36}+\frac{54\cdots 05}{35\cdots 59}a^{35}+\frac{89\cdots 80}{35\cdots 59}a^{34}-\frac{75\cdots 20}{35\cdots 59}a^{33}-\frac{92\cdots 70}{35\cdots 59}a^{32}+\frac{72\cdots 40}{35\cdots 59}a^{31}+\frac{69\cdots 75}{35\cdots 59}a^{30}-\frac{50\cdots 80}{35\cdots 59}a^{29}-\frac{38\cdots 95}{35\cdots 59}a^{28}+\frac{26\cdots 85}{35\cdots 59}a^{27}+\frac{15\cdots 20}{35\cdots 59}a^{26}-\frac{98\cdots 85}{35\cdots 59}a^{25}-\frac{47\cdots 25}{35\cdots 59}a^{24}+\frac{27\cdots 75}{35\cdots 59}a^{23}+\frac{10\cdots 55}{35\cdots 59}a^{22}-\frac{57\cdots 55}{35\cdots 59}a^{21}-\frac{18\cdots 25}{35\cdots 59}a^{20}+\frac{87\cdots 85}{35\cdots 59}a^{19}+\frac{22\cdots 55}{35\cdots 59}a^{18}-\frac{97\cdots 15}{35\cdots 59}a^{17}-\frac{19\cdots 00}{35\cdots 59}a^{16}+\frac{76\cdots 90}{35\cdots 59}a^{15}+\frac{12\cdots 90}{35\cdots 59}a^{14}-\frac{41\cdots 85}{35\cdots 59}a^{13}-\frac{50\cdots 95}{35\cdots 59}a^{12}+\frac{15\cdots 55}{35\cdots 59}a^{11}+\frac{13\cdots 95}{35\cdots 59}a^{10}-\frac{35\cdots 15}{35\cdots 59}a^{9}-\frac{23\cdots 80}{35\cdots 59}a^{8}+\frac{48\cdots 55}{35\cdots 59}a^{7}+\frac{20\cdots 70}{35\cdots 59}a^{6}-\frac{37\cdots 89}{35\cdots 59}a^{5}-\frac{77\cdots 75}{35\cdots 59}a^{4}+\frac{13\cdots 05}{35\cdots 59}a^{3}+\frac{44\cdots 60}{35\cdots 59}a^{2}-\frac{65\cdots 10}{35\cdots 59}a-\frac{18\cdots 80}{35\cdots 59}$, $\frac{12\cdots 86}{35\cdots 59}a^{42}-\frac{13\cdots 64}{35\cdots 59}a^{41}-\frac{10\cdots 86}{35\cdots 59}a^{40}+\frac{10\cdots 65}{35\cdots 59}a^{39}+\frac{39\cdots 10}{35\cdots 59}a^{38}-\frac{37\cdots 41}{35\cdots 59}a^{37}-\frac{89\cdots 92}{35\cdots 59}a^{36}+\frac{79\cdots 50}{35\cdots 59}a^{35}+\frac{13\cdots 98}{35\cdots 59}a^{34}-\frac{10\cdots 81}{35\cdots 59}a^{33}-\frac{13\cdots 75}{35\cdots 59}a^{32}+\frac{10\cdots 65}{35\cdots 59}a^{31}+\frac{10\cdots 33}{35\cdots 59}a^{30}-\frac{73\cdots 77}{35\cdots 59}a^{29}-\frac{56\cdots 27}{35\cdots 59}a^{28}+\frac{37\cdots 17}{35\cdots 59}a^{27}+\frac{23\cdots 52}{35\cdots 59}a^{26}-\frac{14\cdots 18}{35\cdots 59}a^{25}-\frac{71\cdots 74}{35\cdots 59}a^{24}+\frac{39\cdots 35}{35\cdots 59}a^{23}+\frac{16\cdots 77}{35\cdots 59}a^{22}-\frac{82\cdots 47}{35\cdots 59}a^{21}-\frac{27\cdots 28}{35\cdots 59}a^{20}+\frac{12\cdots 95}{35\cdots 59}a^{19}+\frac{33\cdots 85}{35\cdots 59}a^{18}-\frac{13\cdots 88}{35\cdots 59}a^{17}-\frac{29\cdots 91}{35\cdots 59}a^{16}+\frac{10\cdots 62}{35\cdots 59}a^{15}+\frac{18\cdots 38}{35\cdots 59}a^{14}-\frac{59\cdots 70}{35\cdots 59}a^{13}-\frac{76\cdots 37}{35\cdots 59}a^{12}+\frac{21\cdots 86}{35\cdots 59}a^{11}+\frac{20\cdots 69}{35\cdots 59}a^{10}-\frac{50\cdots 86}{35\cdots 59}a^{9}-\frac{34\cdots 17}{35\cdots 59}a^{8}+\frac{70\cdots 94}{35\cdots 59}a^{7}+\frac{30\cdots 04}{35\cdots 59}a^{6}-\frac{54\cdots 55}{35\cdots 59}a^{5}-\frac{10\cdots 16}{35\cdots 59}a^{4}+\frac{19\cdots 83}{35\cdots 59}a^{3}+\frac{22\cdots 86}{35\cdots 59}a^{2}-\frac{64\cdots 47}{35\cdots 59}a-\frac{70\cdots 78}{35\cdots 59}$, $\frac{18\cdots 58}{35\cdots 59}a^{42}-\frac{22\cdots 06}{35\cdots 59}a^{41}-\frac{15\cdots 40}{35\cdots 59}a^{40}+\frac{18\cdots 66}{35\cdots 59}a^{39}+\frac{59\cdots 53}{35\cdots 59}a^{38}-\frac{65\cdots 92}{35\cdots 59}a^{37}-\frac{13\cdots 89}{35\cdots 59}a^{36}+\frac{13\cdots 48}{35\cdots 59}a^{35}+\frac{19\cdots 93}{35\cdots 59}a^{34}-\frac{19\cdots 08}{35\cdots 59}a^{33}-\frac{20\cdots 49}{35\cdots 59}a^{32}+\frac{18\cdots 12}{35\cdots 59}a^{31}+\frac{14\cdots 88}{35\cdots 59}a^{30}-\frac{13\cdots 72}{35\cdots 59}a^{29}-\frac{82\cdots 44}{35\cdots 59}a^{28}+\frac{68\cdots 27}{35\cdots 59}a^{27}+\frac{33\cdots 40}{35\cdots 59}a^{26}-\frac{26\cdots 27}{35\cdots 59}a^{25}-\frac{10\cdots 55}{35\cdots 59}a^{24}+\frac{74\cdots 24}{35\cdots 59}a^{23}+\frac{23\cdots 73}{35\cdots 59}a^{22}-\frac{15\cdots 32}{35\cdots 59}a^{21}-\frac{38\cdots 57}{35\cdots 59}a^{20}+\frac{24\cdots 08}{35\cdots 59}a^{19}+\frac{46\cdots 21}{35\cdots 59}a^{18}-\frac{27\cdots 57}{35\cdots 59}a^{17}-\frac{40\cdots 36}{35\cdots 59}a^{16}+\frac{22\cdots 64}{35\cdots 59}a^{15}+\frac{24\cdots 31}{35\cdots 59}a^{14}-\frac{12\cdots 58}{35\cdots 59}a^{13}-\frac{97\cdots 35}{35\cdots 59}a^{12}+\frac{48\cdots 15}{35\cdots 59}a^{11}+\frac{25\cdots 77}{35\cdots 59}a^{10}-\frac{11\cdots 61}{35\cdots 59}a^{9}-\frac{38\cdots 00}{35\cdots 59}a^{8}+\frac{17\cdots 01}{35\cdots 59}a^{7}+\frac{28\cdots 48}{35\cdots 59}a^{6}-\frac{14\cdots 25}{35\cdots 59}a^{5}-\frac{44\cdots 69}{35\cdots 59}a^{4}+\frac{50\cdots 69}{35\cdots 59}a^{3}-\frac{72\cdots 47}{81\cdots 81}a^{2}-\frac{10\cdots 22}{35\cdots 59}a+\frac{58\cdots 46}{35\cdots 59}$, $\frac{13\cdots 78}{35\cdots 59}a^{42}-\frac{14\cdots 52}{35\cdots 59}a^{41}-\frac{11\cdots 13}{35\cdots 59}a^{40}+\frac{11\cdots 84}{35\cdots 59}a^{39}+\frac{42\cdots 81}{35\cdots 59}a^{38}-\frac{41\cdots 83}{35\cdots 59}a^{37}-\frac{94\cdots 65}{35\cdots 59}a^{36}+\frac{86\cdots 11}{35\cdots 59}a^{35}+\frac{13\cdots 56}{35\cdots 59}a^{34}-\frac{11\cdots 63}{35\cdots 59}a^{33}-\frac{14\cdots 96}{35\cdots 59}a^{32}+\frac{11\cdots 82}{35\cdots 59}a^{31}+\frac{10\cdots 38}{35\cdots 59}a^{30}-\frac{80\cdots 30}{35\cdots 59}a^{29}-\frac{59\cdots 56}{35\cdots 59}a^{28}+\frac{41\cdots 91}{35\cdots 59}a^{27}+\frac{24\cdots 29}{35\cdots 59}a^{26}-\frac{15\cdots 28}{35\cdots 59}a^{25}-\frac{74\cdots 77}{35\cdots 59}a^{24}+\frac{44\cdots 89}{35\cdots 59}a^{23}+\frac{17\cdots 74}{35\cdots 59}a^{22}-\frac{91\cdots 80}{35\cdots 59}a^{21}-\frac{28\cdots 99}{35\cdots 59}a^{20}+\frac{14\cdots 34}{35\cdots 59}a^{19}+\frac{35\cdots 56}{35\cdots 59}a^{18}-\frac{15\cdots 41}{35\cdots 59}a^{17}-\frac{30\cdots 05}{35\cdots 59}a^{16}+\frac{12\cdots 32}{35\cdots 59}a^{15}+\frac{18\cdots 13}{35\cdots 59}a^{14}-\frac{67\cdots 52}{35\cdots 59}a^{13}-\frac{78\cdots 63}{35\cdots 59}a^{12}+\frac{24\cdots 32}{35\cdots 59}a^{11}+\frac{21\cdots 33}{35\cdots 59}a^{10}-\frac{57\cdots 80}{35\cdots 59}a^{9}-\frac{34\cdots 24}{35\cdots 59}a^{8}+\frac{80\cdots 69}{35\cdots 59}a^{7}+\frac{30\cdots 59}{35\cdots 59}a^{6}-\frac{62\cdots 20}{35\cdots 59}a^{5}-\frac{10\cdots 32}{35\cdots 59}a^{4}+\frac{22\cdots 72}{35\cdots 59}a^{3}+\frac{27\cdots 71}{35\cdots 59}a^{2}-\frac{99\cdots 45}{35\cdots 59}a-\frac{14\cdots 81}{35\cdots 59}$, $\frac{22\cdots 88}{35\cdots 59}a^{42}-\frac{20\cdots 32}{35\cdots 59}a^{41}-\frac{19\cdots 00}{35\cdots 59}a^{40}+\frac{16\cdots 80}{35\cdots 59}a^{39}+\frac{71\cdots 10}{35\cdots 59}a^{38}-\frac{56\cdots 78}{35\cdots 59}a^{37}-\frac{16\cdots 26}{35\cdots 59}a^{36}+\frac{11\cdots 14}{35\cdots 59}a^{35}+\frac{23\cdots 98}{35\cdots 59}a^{34}-\frac{15\cdots 90}{35\cdots 59}a^{33}-\frac{24\cdots 66}{35\cdots 59}a^{32}+\frac{15\cdots 54}{35\cdots 59}a^{31}+\frac{18\cdots 60}{35\cdots 59}a^{30}-\frac{10\cdots 00}{35\cdots 59}a^{29}-\frac{10\cdots 00}{35\cdots 59}a^{28}+\frac{51\cdots 94}{35\cdots 59}a^{27}+\frac{42\cdots 64}{35\cdots 59}a^{26}-\frac{19\cdots 26}{35\cdots 59}a^{25}-\frac{13\cdots 84}{35\cdots 59}a^{24}+\frac{51\cdots 74}{35\cdots 59}a^{23}+\frac{30\cdots 02}{35\cdots 59}a^{22}-\frac{10\cdots 44}{35\cdots 59}a^{21}-\frac{51\cdots 68}{35\cdots 59}a^{20}+\frac{15\cdots 32}{35\cdots 59}a^{19}+\frac{63\cdots 00}{35\cdots 59}a^{18}-\frac{15\cdots 12}{35\cdots 59}a^{17}-\frac{56\cdots 22}{35\cdots 59}a^{16}+\frac{11\cdots 26}{35\cdots 59}a^{15}+\frac{35\cdots 46}{35\cdots 59}a^{14}-\frac{59\cdots 56}{35\cdots 59}a^{13}-\frac{15\cdots 78}{35\cdots 59}a^{12}+\frac{19\cdots 54}{35\cdots 59}a^{11}+\frac{43\cdots 72}{35\cdots 59}a^{10}-\frac{39\cdots 60}{35\cdots 59}a^{9}-\frac{75\cdots 75}{35\cdots 59}a^{8}+\frac{44\cdots 56}{35\cdots 59}a^{7}+\frac{73\cdots 54}{35\cdots 59}a^{6}-\frac{26\cdots 44}{35\cdots 59}a^{5}-\frac{33\cdots 12}{35\cdots 59}a^{4}+\frac{87\cdots 66}{35\cdots 59}a^{3}+\frac{52\cdots 74}{35\cdots 59}a^{2}-\frac{98\cdots 88}{35\cdots 59}a-\frac{16\cdots 54}{35\cdots 59}$, $\frac{37\cdots 02}{35\cdots 59}a^{42}-\frac{42\cdots 17}{35\cdots 59}a^{41}-\frac{31\cdots 82}{35\cdots 59}a^{40}+\frac{33\cdots 94}{35\cdots 59}a^{39}+\frac{11\cdots 68}{35\cdots 59}a^{38}-\frac{12\cdots 30}{35\cdots 59}a^{37}-\frac{25\cdots 21}{35\cdots 59}a^{36}+\frac{25\cdots 64}{35\cdots 59}a^{35}+\frac{38\cdots 31}{35\cdots 59}a^{34}-\frac{35\cdots 82}{35\cdots 59}a^{33}-\frac{39\cdots 47}{35\cdots 59}a^{32}+\frac{34\cdots 12}{35\cdots 59}a^{31}+\frac{29\cdots 54}{35\cdots 59}a^{30}-\frac{23\cdots 68}{35\cdots 59}a^{29}-\frac{16\cdots 05}{35\cdots 59}a^{28}+\frac{12\cdots 40}{35\cdots 59}a^{27}+\frac{66\cdots 13}{35\cdots 59}a^{26}-\frac{46\cdots 14}{35\cdots 59}a^{25}-\frac{20\cdots 07}{35\cdots 59}a^{24}+\frac{13\cdots 21}{35\cdots 59}a^{23}+\frac{45\cdots 43}{35\cdots 59}a^{22}-\frac{27\cdots 27}{35\cdots 59}a^{21}-\frac{76\cdots 37}{35\cdots 59}a^{20}+\frac{42\cdots 42}{35\cdots 59}a^{19}+\frac{93\cdots 40}{35\cdots 59}a^{18}-\frac{47\cdots 46}{35\cdots 59}a^{17}-\frac{80\cdots 68}{35\cdots 59}a^{16}+\frac{37\cdots 70}{35\cdots 59}a^{15}+\frac{49\cdots 14}{35\cdots 59}a^{14}-\frac{20\cdots 38}{35\cdots 59}a^{13}-\frac{20\cdots 16}{35\cdots 59}a^{12}+\frac{76\cdots 02}{35\cdots 59}a^{11}+\frac{53\cdots 09}{35\cdots 59}a^{10}-\frac{17\cdots 61}{35\cdots 59}a^{9}-\frac{88\cdots 41}{35\cdots 59}a^{8}+\frac{25\cdots 03}{35\cdots 59}a^{7}+\frac{79\cdots 04}{35\cdots 59}a^{6}-\frac{19\cdots 88}{35\cdots 59}a^{5}-\frac{30\cdots 60}{35\cdots 59}a^{4}+\frac{63\cdots 35}{35\cdots 59}a^{3}+\frac{19\cdots 91}{35\cdots 59}a^{2}-\frac{33\cdots 61}{35\cdots 59}a-\frac{93\cdots 40}{35\cdots 59}$, $\frac{50\cdots 64}{35\cdots 59}a^{42}-\frac{52\cdots 04}{35\cdots 59}a^{41}-\frac{42\cdots 72}{35\cdots 59}a^{40}+\frac{41\cdots 24}{35\cdots 59}a^{39}+\frac{15\cdots 74}{35\cdots 59}a^{38}-\frac{14\cdots 74}{35\cdots 59}a^{37}-\frac{35\cdots 36}{35\cdots 59}a^{36}+\frac{30\cdots 26}{35\cdots 59}a^{35}+\frac{52\cdots 68}{35\cdots 59}a^{34}-\frac{42\cdots 10}{35\cdots 59}a^{33}-\frac{54\cdots 24}{35\cdots 59}a^{32}+\frac{41\cdots 70}{35\cdots 59}a^{31}+\frac{40\cdots 20}{35\cdots 59}a^{30}-\frac{28\cdots 84}{35\cdots 59}a^{29}-\frac{22\cdots 36}{35\cdots 59}a^{28}+\frac{14\cdots 74}{35\cdots 59}a^{27}+\frac{91\cdots 60}{35\cdots 59}a^{26}-\frac{55\cdots 44}{35\cdots 59}a^{25}-\frac{28\cdots 48}{35\cdots 59}a^{24}+\frac{15\cdots 72}{35\cdots 59}a^{23}+\frac{64\cdots 32}{35\cdots 59}a^{22}-\frac{32\cdots 68}{35\cdots 59}a^{21}-\frac{10\cdots 02}{35\cdots 59}a^{20}+\frac{48\cdots 96}{35\cdots 59}a^{19}+\frac{13\cdots 06}{35\cdots 59}a^{18}-\frac{53\cdots 08}{35\cdots 59}a^{17}-\frac{11\cdots 04}{35\cdots 59}a^{16}+\frac{41\cdots 48}{35\cdots 59}a^{15}+\frac{72\cdots 42}{35\cdots 59}a^{14}-\frac{22\cdots 08}{35\cdots 59}a^{13}-\frac{30\cdots 96}{35\cdots 59}a^{12}+\frac{81\cdots 26}{35\cdots 59}a^{11}+\frac{82\cdots 46}{35\cdots 59}a^{10}-\frac{18\cdots 34}{35\cdots 59}a^{9}-\frac{13\cdots 42}{35\cdots 59}a^{8}+\frac{25\cdots 34}{35\cdots 59}a^{7}+\frac{12\cdots 02}{35\cdots 59}a^{6}-\frac{19\cdots 74}{35\cdots 59}a^{5}-\frac{46\cdots 93}{35\cdots 59}a^{4}+\frac{68\cdots 16}{35\cdots 59}a^{3}+\frac{28\cdots 80}{35\cdots 59}a^{2}-\frac{31\cdots 70}{35\cdots 59}a-\frac{10\cdots 20}{35\cdots 59}$, $a$, $\frac{14\cdots 50}{35\cdots 59}a^{42}-\frac{15\cdots 24}{35\cdots 59}a^{41}-\frac{12\cdots 60}{35\cdots 59}a^{40}+\frac{12\cdots 24}{35\cdots 59}a^{39}+\frac{45\cdots 32}{35\cdots 59}a^{38}-\frac{42\cdots 32}{35\cdots 59}a^{37}-\frac{10\cdots 80}{35\cdots 59}a^{36}+\frac{89\cdots 16}{35\cdots 59}a^{35}+\frac{14\cdots 50}{35\cdots 59}a^{34}-\frac{12\cdots 82}{35\cdots 59}a^{33}-\frac{15\cdots 54}{35\cdots 59}a^{32}+\frac{12\cdots 48}{35\cdots 59}a^{31}+\frac{11\cdots 20}{35\cdots 59}a^{30}-\frac{83\cdots 92}{35\cdots 59}a^{29}-\frac{64\cdots 48}{35\cdots 59}a^{28}+\frac{42\cdots 50}{35\cdots 59}a^{27}+\frac{26\cdots 98}{35\cdots 59}a^{26}-\frac{16\cdots 34}{35\cdots 59}a^{25}-\frac{80\cdots 54}{35\cdots 59}a^{24}+\frac{45\cdots 34}{35\cdots 59}a^{23}+\frac{18\cdots 52}{35\cdots 59}a^{22}-\frac{94\cdots 76}{35\cdots 59}a^{21}-\frac{30\cdots 24}{35\cdots 59}a^{20}+\frac{14\cdots 70}{35\cdots 59}a^{19}+\frac{38\cdots 30}{35\cdots 59}a^{18}-\frac{15\cdots 72}{35\cdots 59}a^{17}-\frac{33\cdots 01}{35\cdots 59}a^{16}+\frac{12\cdots 30}{35\cdots 59}a^{15}+\frac{20\cdots 26}{35\cdots 59}a^{14}-\frac{67\cdots 22}{35\cdots 59}a^{13}-\frac{86\cdots 62}{35\cdots 59}a^{12}+\frac{24\cdots 74}{35\cdots 59}a^{11}+\frac{23\cdots 28}{35\cdots 59}a^{10}-\frac{57\cdots 14}{35\cdots 59}a^{9}-\frac{38\cdots 02}{35\cdots 59}a^{8}+\frac{79\cdots 80}{35\cdots 59}a^{7}+\frac{34\cdots 88}{35\cdots 59}a^{6}-\frac{61\cdots 98}{35\cdots 59}a^{5}-\frac{12\cdots 00}{35\cdots 59}a^{4}+\frac{21\cdots 30}{35\cdots 59}a^{3}+\frac{31\cdots 72}{35\cdots 59}a^{2}-\frac{79\cdots 74}{35\cdots 59}a-\frac{10\cdots 32}{35\cdots 59}$, $\frac{98\cdots 86}{35\cdots 59}a^{42}-\frac{73\cdots 10}{35\cdots 59}a^{41}-\frac{82\cdots 50}{35\cdots 59}a^{40}+\frac{13\cdots 00}{81\cdots 81}a^{39}+\frac{31\cdots 74}{35\cdots 59}a^{38}-\frac{19\cdots 68}{35\cdots 59}a^{37}-\frac{70\cdots 62}{35\cdots 59}a^{36}+\frac{40\cdots 90}{35\cdots 59}a^{35}+\frac{10\cdots 02}{35\cdots 59}a^{34}-\frac{53\cdots 10}{35\cdots 59}a^{33}-\frac{10\cdots 21}{35\cdots 59}a^{32}+\frac{50\cdots 88}{35\cdots 59}a^{31}+\frac{82\cdots 22}{35\cdots 59}a^{30}-\frac{33\cdots 66}{35\cdots 59}a^{29}-\frac{46\cdots 58}{35\cdots 59}a^{28}+\frac{16\cdots 36}{35\cdots 59}a^{27}+\frac{19\cdots 48}{35\cdots 59}a^{26}-\frac{58\cdots 98}{35\cdots 59}a^{25}-\frac{59\cdots 52}{35\cdots 59}a^{24}+\frac{15\cdots 12}{35\cdots 59}a^{23}+\frac{13\cdots 90}{35\cdots 59}a^{22}-\frac{29\cdots 50}{35\cdots 59}a^{21}-\frac{23\cdots 22}{35\cdots 59}a^{20}+\frac{41\cdots 92}{35\cdots 59}a^{19}+\frac{30\cdots 02}{35\cdots 59}a^{18}-\frac{42\cdots 44}{35\cdots 59}a^{17}-\frac{27\cdots 12}{35\cdots 59}a^{16}+\frac{30\cdots 94}{35\cdots 59}a^{15}+\frac{17\cdots 32}{35\cdots 59}a^{14}-\frac{15\cdots 66}{35\cdots 59}a^{13}-\frac{78\cdots 38}{35\cdots 59}a^{12}+\frac{53\cdots 12}{35\cdots 59}a^{11}+\frac{22\cdots 10}{35\cdots 59}a^{10}-\frac{12\cdots 84}{35\cdots 59}a^{9}-\frac{41\cdots 86}{35\cdots 59}a^{8}+\frac{21\cdots 94}{35\cdots 59}a^{7}+\frac{42\cdots 82}{35\cdots 59}a^{6}-\frac{21\cdots 10}{35\cdots 59}a^{5}-\frac{20\cdots 18}{35\cdots 59}a^{4}+\frac{12\cdots 98}{35\cdots 59}a^{3}+\frac{32\cdots 06}{35\cdots 59}a^{2}-\frac{19\cdots 70}{35\cdots 59}a-\frac{11\cdots 98}{35\cdots 59}$, $\frac{39\cdots 59}{35\cdots 59}a^{42}-\frac{49\cdots 57}{35\cdots 59}a^{41}-\frac{33\cdots 71}{35\cdots 59}a^{40}+\frac{39\cdots 32}{35\cdots 59}a^{39}+\frac{12\cdots 49}{35\cdots 59}a^{38}-\frac{14\cdots 34}{35\cdots 59}a^{37}-\frac{27\cdots 12}{35\cdots 59}a^{36}+\frac{29\cdots 82}{35\cdots 59}a^{35}+\frac{40\cdots 68}{35\cdots 59}a^{34}-\frac{41\cdots 04}{35\cdots 59}a^{33}-\frac{41\cdots 47}{35\cdots 59}a^{32}+\frac{40\cdots 69}{35\cdots 59}a^{31}+\frac{30\cdots 91}{35\cdots 59}a^{30}-\frac{28\cdots 64}{35\cdots 59}a^{29}-\frac{16\cdots 79}{35\cdots 59}a^{28}+\frac{14\cdots 99}{35\cdots 59}a^{27}+\frac{67\cdots 60}{35\cdots 59}a^{26}-\frac{55\cdots 49}{35\cdots 59}a^{25}-\frac{20\cdots 24}{35\cdots 59}a^{24}+\frac{15\cdots 32}{35\cdots 59}a^{23}+\frac{44\cdots 06}{35\cdots 59}a^{22}-\frac{32\cdots 91}{35\cdots 59}a^{21}-\frac{71\cdots 08}{35\cdots 59}a^{20}+\frac{50\cdots 92}{35\cdots 59}a^{19}+\frac{83\cdots 06}{35\cdots 59}a^{18}-\frac{55\cdots 84}{35\cdots 59}a^{17}-\frac{67\cdots 04}{35\cdots 59}a^{16}+\frac{43\cdots 85}{35\cdots 59}a^{15}+\frac{36\cdots 94}{35\cdots 59}a^{14}-\frac{22\cdots 74}{35\cdots 59}a^{13}-\frac{12\cdots 60}{35\cdots 59}a^{12}+\frac{80\cdots 88}{35\cdots 59}a^{11}+\frac{21\cdots 11}{35\cdots 59}a^{10}-\frac{17\cdots 00}{35\cdots 59}a^{9}-\frac{68\cdots 33}{35\cdots 59}a^{8}+\frac{20\cdots 64}{35\cdots 59}a^{7}-\frac{39\cdots 63}{35\cdots 59}a^{6}-\frac{11\cdots 48}{35\cdots 59}a^{5}+\frac{57\cdots 89}{35\cdots 59}a^{4}+\frac{16\cdots 31}{35\cdots 59}a^{3}-\frac{23\cdots 81}{35\cdots 59}a^{2}+\frac{85\cdots 19}{35\cdots 59}a+\frac{94\cdots 53}{35\cdots 59}$, $\frac{14\cdots 99}{35\cdots 59}a^{42}-\frac{12\cdots 40}{35\cdots 59}a^{41}-\frac{12\cdots 96}{35\cdots 59}a^{40}+\frac{94\cdots 97}{35\cdots 59}a^{39}+\frac{47\cdots 77}{35\cdots 59}a^{38}-\frac{32\cdots 92}{35\cdots 59}a^{37}-\frac{10\cdots 74}{35\cdots 59}a^{36}+\frac{67\cdots 21}{35\cdots 59}a^{35}+\frac{15\cdots 99}{35\cdots 59}a^{34}-\frac{90\cdots 11}{35\cdots 59}a^{33}-\frac{16\cdots 12}{35\cdots 59}a^{32}+\frac{85\cdots 61}{35\cdots 59}a^{31}+\frac{12\cdots 76}{35\cdots 59}a^{30}-\frac{57\cdots 95}{35\cdots 59}a^{29}-\frac{68\cdots 01}{35\cdots 59}a^{28}+\frac{28\cdots 44}{35\cdots 59}a^{27}+\frac{28\cdots 40}{35\cdots 59}a^{26}-\frac{10\cdots 91}{35\cdots 59}a^{25}-\frac{87\cdots 31}{35\cdots 59}a^{24}+\frac{27\cdots 47}{35\cdots 59}a^{23}+\frac{20\cdots 96}{35\cdots 59}a^{22}-\frac{54\cdots 31}{35\cdots 59}a^{21}-\frac{34\cdots 35}{35\cdots 59}a^{20}+\frac{78\cdots 79}{35\cdots 59}a^{19}+\frac{42\cdots 77}{35\cdots 59}a^{18}-\frac{81\cdots 15}{35\cdots 59}a^{17}-\frac{38\cdots 68}{35\cdots 59}a^{16}+\frac{60\cdots 56}{35\cdots 59}a^{15}+\frac{24\cdots 00}{35\cdots 59}a^{14}-\frac{31\cdots 56}{35\cdots 59}a^{13}-\frac{10\cdots 25}{35\cdots 59}a^{12}+\frac{11\cdots 79}{35\cdots 59}a^{11}+\frac{28\cdots 77}{35\cdots 59}a^{10}-\frac{26\cdots 52}{35\cdots 59}a^{9}-\frac{48\cdots 55}{35\cdots 59}a^{8}+\frac{39\cdots 66}{35\cdots 59}a^{7}+\frac{42\cdots 24}{35\cdots 59}a^{6}-\frac{37\cdots 08}{35\cdots 59}a^{5}-\frac{13\cdots 57}{35\cdots 59}a^{4}+\frac{18\cdots 45}{35\cdots 59}a^{3}-\frac{56\cdots 99}{35\cdots 59}a^{2}-\frac{62\cdots 21}{35\cdots 59}a+\frac{21\cdots 75}{35\cdots 59}$, $\frac{12\cdots 46}{35\cdots 59}a^{42}-\frac{12\cdots 84}{35\cdots 59}a^{41}-\frac{10\cdots 64}{35\cdots 59}a^{40}+\frac{98\cdots 42}{35\cdots 59}a^{39}+\frac{37\cdots 46}{35\cdots 59}a^{38}-\frac{34\cdots 29}{35\cdots 59}a^{37}-\frac{84\cdots 47}{35\cdots 59}a^{36}+\frac{72\cdots 69}{35\cdots 59}a^{35}+\frac{12\cdots 34}{35\cdots 59}a^{34}-\frac{10\cdots 61}{35\cdots 59}a^{33}-\frac{12\cdots 79}{35\cdots 59}a^{32}+\frac{96\cdots 98}{35\cdots 59}a^{31}+\frac{97\cdots 07}{35\cdots 59}a^{30}-\frac{67\cdots 73}{35\cdots 59}a^{29}-\frac{53\cdots 87}{35\cdots 59}a^{28}+\frac{34\cdots 34}{35\cdots 59}a^{27}+\frac{22\cdots 19}{35\cdots 59}a^{26}-\frac{12\cdots 54}{35\cdots 59}a^{25}-\frac{67\cdots 76}{35\cdots 59}a^{24}+\frac{35\cdots 74}{35\cdots 59}a^{23}+\frac{15\cdots 57}{35\cdots 59}a^{22}-\frac{74\cdots 07}{35\cdots 59}a^{21}-\frac{26\cdots 26}{35\cdots 59}a^{20}+\frac{11\cdots 44}{35\cdots 59}a^{19}+\frac{32\cdots 32}{35\cdots 59}a^{18}-\frac{12\cdots 83}{35\cdots 59}a^{17}-\frac{28\cdots 96}{35\cdots 59}a^{16}+\frac{95\cdots 88}{35\cdots 59}a^{15}+\frac{17\cdots 35}{35\cdots 59}a^{14}-\frac{51\cdots 52}{35\cdots 59}a^{13}-\frac{73\cdots 44}{35\cdots 59}a^{12}+\frac{18\cdots 98}{35\cdots 59}a^{11}+\frac{19\cdots 05}{35\cdots 59}a^{10}-\frac{41\cdots 78}{35\cdots 59}a^{9}-\frac{33\cdots 83}{35\cdots 59}a^{8}+\frac{56\cdots 92}{35\cdots 59}a^{7}+\frac{30\cdots 41}{35\cdots 59}a^{6}-\frac{41\cdots 05}{35\cdots 59}a^{5}-\frac{11\cdots 05}{35\cdots 59}a^{4}+\frac{15\cdots 28}{35\cdots 59}a^{3}+\frac{74\cdots 51}{35\cdots 59}a^{2}-\frac{69\cdots 43}{35\cdots 59}a-\frac{14\cdots 91}{35\cdots 59}$, $\frac{24\cdots 08}{35\cdots 59}a^{42}-\frac{26\cdots 34}{35\cdots 59}a^{41}-\frac{20\cdots 12}{35\cdots 59}a^{40}+\frac{20\cdots 98}{35\cdots 59}a^{39}+\frac{78\cdots 35}{35\cdots 59}a^{38}-\frac{73\cdots 37}{35\cdots 59}a^{37}-\frac{17\cdots 96}{35\cdots 59}a^{36}+\frac{15\cdots 23}{35\cdots 59}a^{35}+\frac{25\cdots 42}{35\cdots 59}a^{34}-\frac{21\cdots 59}{35\cdots 59}a^{33}-\frac{26\cdots 74}{35\cdots 59}a^{32}+\frac{20\cdots 73}{35\cdots 59}a^{31}+\frac{20\cdots 60}{35\cdots 59}a^{30}-\frac{14\cdots 60}{35\cdots 59}a^{29}-\frac{11\cdots 24}{35\cdots 59}a^{28}+\frac{72\cdots 09}{35\cdots 59}a^{27}+\frac{45\cdots 98}{35\cdots 59}a^{26}-\frac{27\cdots 24}{35\cdots 59}a^{25}-\frac{14\cdots 62}{35\cdots 59}a^{24}+\frac{77\cdots 96}{35\cdots 59}a^{23}+\frac{31\cdots 76}{35\cdots 59}a^{22}-\frac{15\cdots 70}{35\cdots 59}a^{21}-\frac{53\cdots 05}{35\cdots 59}a^{20}+\frac{24\cdots 46}{35\cdots 59}a^{19}+\frac{66\cdots 45}{35\cdots 59}a^{18}-\frac{26\cdots 72}{35\cdots 59}a^{17}-\frac{58\cdots 00}{35\cdots 59}a^{16}+\frac{20\cdots 78}{35\cdots 59}a^{15}+\frac{35\cdots 29}{35\cdots 59}a^{14}-\frac{11\cdots 90}{35\cdots 59}a^{13}-\frac{15\cdots 76}{35\cdots 59}a^{12}+\frac{40\cdots 81}{35\cdots 59}a^{11}+\frac{41\cdots 53}{35\cdots 59}a^{10}-\frac{92\cdots 49}{35\cdots 59}a^{9}-\frac{68\cdots 75}{35\cdots 59}a^{8}+\frac{12\cdots 59}{35\cdots 59}a^{7}+\frac{61\cdots 07}{35\cdots 59}a^{6}-\frac{95\cdots 43}{35\cdots 59}a^{5}-\frac{23\cdots 42}{35\cdots 59}a^{4}+\frac{34\cdots 36}{35\cdots 59}a^{3}+\frac{13\cdots 24}{35\cdots 59}a^{2}-\frac{15\cdots 23}{35\cdots 59}a-\frac{44\cdots 16}{35\cdots 59}$, $\frac{39\cdots 44}{35\cdots 59}a^{42}-\frac{40\cdots 66}{35\cdots 59}a^{41}-\frac{32\cdots 14}{35\cdots 59}a^{40}+\frac{31\cdots 54}{35\cdots 59}a^{39}+\frac{12\cdots 05}{35\cdots 59}a^{38}-\frac{11\cdots 63}{35\cdots 59}a^{37}-\frac{27\cdots 05}{35\cdots 59}a^{36}+\frac{23\cdots 07}{35\cdots 59}a^{35}+\frac{40\cdots 19}{35\cdots 59}a^{34}-\frac{32\cdots 09}{35\cdots 59}a^{33}-\frac{42\cdots 83}{35\cdots 59}a^{32}+\frac{31\cdots 77}{35\cdots 59}a^{31}+\frac{31\cdots 50}{35\cdots 59}a^{30}-\frac{21\cdots 46}{35\cdots 59}a^{29}-\frac{17\cdots 48}{35\cdots 59}a^{28}+\frac{10\cdots 57}{35\cdots 59}a^{27}+\frac{72\cdots 52}{35\cdots 59}a^{26}-\frac{41\cdots 43}{35\cdots 59}a^{25}-\frac{22\cdots 98}{35\cdots 59}a^{24}+\frac{11\cdots 21}{35\cdots 59}a^{23}+\frac{50\cdots 73}{35\cdots 59}a^{22}-\frac{23\cdots 00}{35\cdots 59}a^{21}-\frac{85\cdots 88}{35\cdots 59}a^{20}+\frac{35\cdots 18}{35\cdots 59}a^{19}+\frac{10\cdots 22}{35\cdots 59}a^{18}-\frac{38\cdots 22}{35\cdots 59}a^{17}-\frac{92\cdots 25}{35\cdots 59}a^{16}+\frac{29\cdots 37}{35\cdots 59}a^{15}+\frac{56\cdots 55}{35\cdots 59}a^{14}-\frac{15\cdots 94}{35\cdots 59}a^{13}-\frac{23\cdots 11}{35\cdots 59}a^{12}+\frac{54\cdots 95}{35\cdots 59}a^{11}+\frac{65\cdots 68}{35\cdots 59}a^{10}-\frac{11\cdots 40}{35\cdots 59}a^{9}-\frac{11\cdots 44}{35\cdots 59}a^{8}+\frac{15\cdots 96}{35\cdots 59}a^{7}+\frac{10\cdots 05}{35\cdots 59}a^{6}-\frac{10\cdots 46}{35\cdots 59}a^{5}-\frac{40\cdots 26}{35\cdots 59}a^{4}+\frac{35\cdots 17}{35\cdots 59}a^{3}+\frac{40\cdots 53}{35\cdots 59}a^{2}-\frac{14\cdots 82}{35\cdots 59}a-\frac{19\cdots 97}{35\cdots 59}$, $\frac{81\cdots 25}{35\cdots 59}a^{42}-\frac{83\cdots 30}{35\cdots 59}a^{41}-\frac{68\cdots 54}{35\cdots 59}a^{40}+\frac{65\cdots 84}{35\cdots 59}a^{39}+\frac{25\cdots 34}{35\cdots 59}a^{38}-\frac{23\cdots 05}{35\cdots 59}a^{37}-\frac{57\cdots 50}{35\cdots 59}a^{36}+\frac{48\cdots 20}{35\cdots 59}a^{35}+\frac{84\cdots 17}{35\cdots 59}a^{34}-\frac{67\cdots 28}{35\cdots 59}a^{33}-\frac{88\cdots 09}{35\cdots 59}a^{32}+\frac{64\cdots 23}{35\cdots 59}a^{31}+\frac{66\cdots 36}{35\cdots 59}a^{30}-\frac{44\cdots 83}{35\cdots 59}a^{29}-\frac{36\cdots 48}{35\cdots 59}a^{28}+\frac{22\cdots 07}{35\cdots 59}a^{27}+\frac{15\cdots 74}{35\cdots 59}a^{26}-\frac{85\cdots 41}{35\cdots 59}a^{25}-\frac{46\cdots 33}{35\cdots 59}a^{24}+\frac{23\cdots 82}{35\cdots 59}a^{23}+\frac{10\cdots 63}{35\cdots 59}a^{22}-\frac{49\cdots 94}{35\cdots 59}a^{21}-\frac{17\cdots 32}{35\cdots 59}a^{20}+\frac{74\cdots 47}{35\cdots 59}a^{19}+\frac{22\cdots 13}{35\cdots 59}a^{18}-\frac{81\cdots 44}{35\cdots 59}a^{17}-\frac{19\cdots 87}{35\cdots 59}a^{16}+\frac{63\cdots 13}{35\cdots 59}a^{15}+\frac{12\cdots 35}{35\cdots 59}a^{14}-\frac{34\cdots 66}{35\cdots 59}a^{13}-\frac{52\cdots 47}{35\cdots 59}a^{12}+\frac{12\cdots 11}{35\cdots 59}a^{11}+\frac{14\cdots 56}{35\cdots 59}a^{10}-\frac{28\cdots 45}{35\cdots 59}a^{9}-\frac{24\cdots 16}{35\cdots 59}a^{8}+\frac{39\cdots 90}{35\cdots 59}a^{7}+\frac{22\cdots 91}{35\cdots 59}a^{6}-\frac{31\cdots 70}{35\cdots 59}a^{5}-\frac{25\cdots 06}{10\cdots 97}a^{4}+\frac{12\cdots 01}{35\cdots 59}a^{3}+\frac{48\cdots 55}{35\cdots 59}a^{2}-\frac{52\cdots 41}{35\cdots 59}a-\frac{16\cdots 92}{35\cdots 59}$, $\frac{64\cdots 00}{35\cdots 59}a^{42}-\frac{67\cdots 24}{35\cdots 59}a^{41}-\frac{54\cdots 04}{35\cdots 59}a^{40}+\frac{53\cdots 22}{35\cdots 59}a^{39}+\frac{20\cdots 02}{35\cdots 59}a^{38}-\frac{18\cdots 27}{35\cdots 59}a^{37}-\frac{45\cdots 35}{35\cdots 59}a^{36}+\frac{39\cdots 10}{35\cdots 59}a^{35}+\frac{67\cdots 91}{35\cdots 59}a^{34}-\frac{54\cdots 06}{35\cdots 59}a^{33}-\frac{69\cdots 09}{35\cdots 59}a^{32}+\frac{52\cdots 38}{35\cdots 59}a^{31}+\frac{52\cdots 39}{35\cdots 59}a^{30}-\frac{36\cdots 96}{35\cdots 59}a^{29}-\frac{28\cdots 23}{35\cdots 59}a^{28}+\frac{18\cdots 35}{35\cdots 59}a^{27}+\frac{11\cdots 10}{35\cdots 59}a^{26}-\frac{70\cdots 16}{35\cdots 59}a^{25}-\frac{36\cdots 79}{35\cdots 59}a^{24}+\frac{19\cdots 19}{35\cdots 59}a^{23}+\frac{82\cdots 06}{35\cdots 59}a^{22}-\frac{40\cdots 47}{35\cdots 59}a^{21}-\frac{13\cdots 50}{35\cdots 59}a^{20}+\frac{61\cdots 12}{35\cdots 59}a^{19}+\frac{17\cdots 78}{35\cdots 59}a^{18}-\frac{67\cdots 04}{35\cdots 59}a^{17}-\frac{15\cdots 30}{35\cdots 59}a^{16}+\frac{52\cdots 33}{35\cdots 59}a^{15}+\frac{93\cdots 16}{35\cdots 59}a^{14}-\frac{27\cdots 69}{35\cdots 59}a^{13}-\frac{38\cdots 10}{35\cdots 59}a^{12}+\frac{10\cdots 75}{35\cdots 59}a^{11}+\frac{10\cdots 09}{35\cdots 59}a^{10}-\frac{22\cdots 87}{35\cdots 59}a^{9}-\frac{17\cdots 96}{35\cdots 59}a^{8}+\frac{30\cdots 52}{35\cdots 59}a^{7}+\frac{15\cdots 35}{35\cdots 59}a^{6}-\frac{23\cdots 54}{35\cdots 59}a^{5}-\frac{58\cdots 25}{35\cdots 59}a^{4}+\frac{82\cdots 63}{35\cdots 59}a^{3}+\frac{31\cdots 69}{35\cdots 59}a^{2}-\frac{41\cdots 39}{35\cdots 59}a-\frac{64\cdots 98}{35\cdots 59}$, $\frac{24\cdots 97}{35\cdots 59}a^{42}-\frac{25\cdots 85}{35\cdots 59}a^{41}-\frac{20\cdots 20}{35\cdots 59}a^{40}+\frac{19\cdots 61}{35\cdots 59}a^{39}+\frac{75\cdots 51}{35\cdots 59}a^{38}-\frac{70\cdots 74}{35\cdots 59}a^{37}-\frac{16\cdots 98}{35\cdots 59}a^{36}+\frac{14\cdots 53}{35\cdots 59}a^{35}+\frac{25\cdots 12}{35\cdots 59}a^{34}-\frac{20\cdots 08}{35\cdots 59}a^{33}-\frac{25\cdots 53}{35\cdots 59}a^{32}+\frac{19\cdots 88}{35\cdots 59}a^{31}+\frac{19\cdots 44}{35\cdots 59}a^{30}-\frac{13\cdots 72}{35\cdots 59}a^{29}-\frac{10\cdots 16}{35\cdots 59}a^{28}+\frac{69\cdots 98}{35\cdots 59}a^{27}+\frac{44\cdots 70}{35\cdots 59}a^{26}-\frac{26\cdots 69}{35\cdots 59}a^{25}-\frac{13\cdots 32}{35\cdots 59}a^{24}+\frac{72\cdots 68}{35\cdots 59}a^{23}+\frac{30\cdots 10}{35\cdots 59}a^{22}-\frac{15\cdots 37}{35\cdots 59}a^{21}-\frac{51\cdots 35}{35\cdots 59}a^{20}+\frac{22\cdots 65}{35\cdots 59}a^{19}+\frac{63\cdots 18}{35\cdots 59}a^{18}-\frac{25\cdots 74}{35\cdots 59}a^{17}-\frac{56\cdots 13}{35\cdots 59}a^{16}+\frac{19\cdots 19}{35\cdots 59}a^{15}+\frac{34\cdots 02}{35\cdots 59}a^{14}-\frac{10\cdots 90}{35\cdots 59}a^{13}-\frac{14\cdots 87}{35\cdots 59}a^{12}+\frac{38\cdots 10}{35\cdots 59}a^{11}+\frac{39\cdots 39}{35\cdots 59}a^{10}-\frac{87\cdots 16}{35\cdots 59}a^{9}-\frac{66\cdots 73}{35\cdots 59}a^{8}+\frac{11\cdots 52}{35\cdots 59}a^{7}+\frac{59\cdots 15}{35\cdots 59}a^{6}-\frac{90\cdots 96}{35\cdots 59}a^{5}-\frac{22\cdots 40}{35\cdots 59}a^{4}+\frac{32\cdots 25}{35\cdots 59}a^{3}+\frac{12\cdots 53}{35\cdots 59}a^{2}-\frac{13\cdots 16}{35\cdots 59}a-\frac{42\cdots 54}{35\cdots 59}$, $\frac{11\cdots 03}{35\cdots 59}a^{42}-\frac{12\cdots 11}{35\cdots 59}a^{41}-\frac{99\cdots 63}{35\cdots 59}a^{40}+\frac{97\cdots 92}{35\cdots 59}a^{39}+\frac{37\cdots 24}{35\cdots 59}a^{38}-\frac{34\cdots 44}{35\cdots 59}a^{37}-\frac{83\cdots 91}{35\cdots 59}a^{36}+\frac{72\cdots 74}{35\cdots 59}a^{35}+\frac{12\cdots 41}{35\cdots 59}a^{34}-\frac{99\cdots 38}{35\cdots 59}a^{33}-\frac{12\cdots 01}{35\cdots 59}a^{32}+\frac{96\cdots 92}{35\cdots 59}a^{31}+\frac{95\cdots 49}{35\cdots 59}a^{30}-\frac{66\cdots 11}{35\cdots 59}a^{29}-\frac{52\cdots 34}{35\cdots 59}a^{28}+\frac{34\cdots 03}{35\cdots 59}a^{27}+\frac{21\cdots 51}{35\cdots 59}a^{26}-\frac{12\cdots 29}{35\cdots 59}a^{25}-\frac{66\cdots 89}{35\cdots 59}a^{24}+\frac{35\cdots 69}{35\cdots 59}a^{23}+\frac{15\cdots 68}{35\cdots 59}a^{22}-\frac{74\cdots 99}{35\cdots 59}a^{21}-\frac{25\cdots 81}{35\cdots 59}a^{20}+\frac{11\cdots 90}{35\cdots 59}a^{19}+\frac{31\cdots 75}{35\cdots 59}a^{18}-\frac{12\cdots 02}{35\cdots 59}a^{17}-\frac{27\cdots 77}{35\cdots 59}a^{16}+\frac{96\cdots 89}{35\cdots 59}a^{15}+\frac{17\cdots 26}{35\cdots 59}a^{14}-\frac{51\cdots 04}{35\cdots 59}a^{13}-\frac{71\cdots 35}{35\cdots 59}a^{12}+\frac{18\cdots 38}{35\cdots 59}a^{11}+\frac{19\cdots 50}{35\cdots 59}a^{10}-\frac{42\cdots 49}{35\cdots 59}a^{9}-\frac{32\cdots 82}{35\cdots 59}a^{8}+\frac{58\cdots 59}{35\cdots 59}a^{7}+\frac{29\cdots 14}{35\cdots 59}a^{6}-\frac{43\cdots 01}{35\cdots 59}a^{5}-\frac{10\cdots 05}{35\cdots 59}a^{4}+\frac{15\cdots 44}{35\cdots 59}a^{3}+\frac{57\cdots 11}{35\cdots 59}a^{2}-\frac{53\cdots 32}{35\cdots 59}a-\frac{17\cdots 22}{35\cdots 59}$, $\frac{17\cdots 18}{35\cdots 59}a^{42}-\frac{20\cdots 07}{35\cdots 59}a^{41}-\frac{14\cdots 98}{35\cdots 59}a^{40}+\frac{16\cdots 79}{35\cdots 59}a^{39}+\frac{55\cdots 64}{35\cdots 59}a^{38}-\frac{58\cdots 06}{35\cdots 59}a^{37}-\frac{12\cdots 29}{35\cdots 59}a^{36}+\frac{12\cdots 29}{35\cdots 59}a^{35}+\frac{18\cdots 26}{35\cdots 59}a^{34}-\frac{17\cdots 43}{35\cdots 59}a^{33}-\frac{18\cdots 36}{35\cdots 59}a^{32}+\frac{16\cdots 28}{35\cdots 59}a^{31}+\frac{14\cdots 15}{35\cdots 59}a^{30}-\frac{11\cdots 02}{35\cdots 59}a^{29}-\frac{77\cdots 73}{35\cdots 59}a^{28}+\frac{61\cdots 29}{35\cdots 59}a^{27}+\frac{31\cdots 51}{35\cdots 59}a^{26}-\frac{23\cdots 27}{35\cdots 59}a^{25}-\frac{97\cdots 86}{35\cdots 59}a^{24}+\frac{66\cdots 50}{35\cdots 59}a^{23}+\frac{22\cdots 38}{35\cdots 59}a^{22}-\frac{14\cdots 82}{35\cdots 59}a^{21}-\frac{37\cdots 55}{35\cdots 59}a^{20}+\frac{22\cdots 85}{35\cdots 59}a^{19}+\frac{45\cdots 64}{35\cdots 59}a^{18}-\frac{24\cdots 92}{35\cdots 59}a^{17}-\frac{39\cdots 51}{35\cdots 59}a^{16}+\frac{20\cdots 00}{35\cdots 59}a^{15}+\frac{24\cdots 31}{35\cdots 59}a^{14}-\frac{11\cdots 97}{35\cdots 59}a^{13}-\frac{10\cdots 95}{35\cdots 59}a^{12}+\frac{43\cdots 55}{35\cdots 59}a^{11}+\frac{27\cdots 78}{35\cdots 59}a^{10}-\frac{10\cdots 42}{35\cdots 59}a^{9}-\frac{45\cdots 57}{35\cdots 59}a^{8}+\frac{16\cdots 39}{35\cdots 59}a^{7}+\frac{41\cdots 77}{35\cdots 59}a^{6}-\frac{13\cdots 13}{35\cdots 59}a^{5}-\frac{16\cdots 37}{35\cdots 59}a^{4}+\frac{50\cdots 87}{35\cdots 59}a^{3}+\frac{11\cdots 99}{35\cdots 59}a^{2}-\frac{33\cdots 30}{35\cdots 59}a-\frac{12\cdots 20}{35\cdots 59}$, $\frac{26\cdots 69}{35\cdots 59}a^{42}-\frac{54\cdots 70}{35\cdots 59}a^{41}-\frac{16\cdots 11}{35\cdots 59}a^{40}+\frac{45\cdots 19}{35\cdots 59}a^{39}+\frac{33\cdots 80}{35\cdots 59}a^{38}-\frac{16\cdots 83}{35\cdots 59}a^{37}-\frac{77\cdots 38}{35\cdots 59}a^{36}+\frac{37\cdots 48}{35\cdots 59}a^{35}-\frac{10\cdots 26}{35\cdots 59}a^{34}-\frac{54\cdots 43}{35\cdots 59}a^{33}+\frac{24\cdots 21}{35\cdots 59}a^{32}+\frac{55\cdots 89}{35\cdots 59}a^{31}-\frac{30\cdots 14}{35\cdots 59}a^{30}-\frac{41\cdots 38}{35\cdots 59}a^{29}+\frac{24\cdots 71}{35\cdots 59}a^{28}+\frac{22\cdots 98}{35\cdots 59}a^{27}-\frac{13\cdots 61}{35\cdots 59}a^{26}-\frac{90\cdots 80}{35\cdots 59}a^{25}+\frac{56\cdots 32}{35\cdots 59}a^{24}+\frac{27\cdots 63}{35\cdots 59}a^{23}-\frac{16\cdots 58}{35\cdots 59}a^{22}-\frac{60\cdots 36}{35\cdots 59}a^{21}+\frac{36\cdots 35}{35\cdots 59}a^{20}+\frac{97\cdots 65}{35\cdots 59}a^{19}-\frac{56\cdots 01}{35\cdots 59}a^{18}-\frac{11\cdots 88}{35\cdots 59}a^{17}+\frac{63\cdots 94}{35\cdots 59}a^{16}+\frac{94\cdots 88}{35\cdots 59}a^{15}-\frac{49\cdots 46}{35\cdots 59}a^{14}-\frac{53\cdots 61}{35\cdots 59}a^{13}+\frac{26\cdots 84}{35\cdots 59}a^{12}+\frac{19\cdots 21}{35\cdots 59}a^{11}-\frac{89\cdots 54}{35\cdots 59}a^{10}-\frac{44\cdots 52}{35\cdots 59}a^{9}+\frac{18\cdots 24}{35\cdots 59}a^{8}+\frac{58\cdots 86}{35\cdots 59}a^{7}-\frac{19\cdots 52}{35\cdots 59}a^{6}-\frac{35\cdots 28}{35\cdots 59}a^{5}+\frac{88\cdots 81}{35\cdots 59}a^{4}+\frac{48\cdots 43}{35\cdots 59}a^{3}-\frac{14\cdots 12}{35\cdots 59}a^{2}+\frac{26\cdots 78}{35\cdots 59}a+\frac{52\cdots 69}{35\cdots 59}$, $\frac{12\cdots 81}{35\cdots 59}a^{42}-\frac{13\cdots 23}{35\cdots 59}a^{41}-\frac{10\cdots 27}{35\cdots 59}a^{40}+\frac{10\cdots 40}{35\cdots 59}a^{39}+\frac{40\cdots 66}{35\cdots 59}a^{38}-\frac{37\cdots 10}{35\cdots 59}a^{37}-\frac{90\cdots 27}{35\cdots 59}a^{36}+\frac{78\cdots 38}{35\cdots 59}a^{35}+\frac{13\cdots 49}{35\cdots 59}a^{34}-\frac{10\cdots 22}{35\cdots 59}a^{33}-\frac{13\cdots 37}{35\cdots 59}a^{32}+\frac{10\cdots 42}{35\cdots 59}a^{31}+\frac{10\cdots 09}{35\cdots 59}a^{30}-\frac{72\cdots 23}{35\cdots 59}a^{29}-\frac{57\cdots 32}{35\cdots 59}a^{28}+\frac{36\cdots 23}{35\cdots 59}a^{27}+\frac{23\cdots 45}{35\cdots 59}a^{26}-\frac{13\cdots 49}{35\cdots 59}a^{25}-\frac{72\cdots 57}{35\cdots 59}a^{24}+\frac{39\cdots 55}{35\cdots 59}a^{23}+\frac{16\cdots 32}{35\cdots 59}a^{22}-\frac{80\cdots 15}{35\cdots 59}a^{21}-\frac{27\cdots 73}{35\cdots 59}a^{20}+\frac{12\cdots 14}{35\cdots 59}a^{19}+\frac{34\cdots 86}{35\cdots 59}a^{18}-\frac{13\cdots 54}{35\cdots 59}a^{17}-\frac{30\cdots 39}{35\cdots 59}a^{16}+\frac{10\cdots 95}{35\cdots 59}a^{15}+\frac{18\cdots 80}{35\cdots 59}a^{14}-\frac{56\cdots 88}{35\cdots 59}a^{13}-\frac{78\cdots 12}{35\cdots 59}a^{12}+\frac{20\cdots 32}{35\cdots 59}a^{11}+\frac{21\cdots 84}{35\cdots 59}a^{10}-\frac{46\cdots 83}{35\cdots 59}a^{9}-\frac{36\cdots 12}{35\cdots 59}a^{8}+\frac{64\cdots 19}{35\cdots 59}a^{7}+\frac{33\cdots 66}{35\cdots 59}a^{6}-\frac{49\cdots 71}{35\cdots 59}a^{5}-\frac{12\cdots 50}{35\cdots 59}a^{4}+\frac{17\cdots 41}{35\cdots 59}a^{3}+\frac{94\cdots 45}{35\cdots 59}a^{2}-\frac{92\cdots 01}{35\cdots 59}a-\frac{40\cdots 56}{35\cdots 59}$, $\frac{14\cdots 77}{35\cdots 59}a^{42}-\frac{15\cdots 76}{35\cdots 59}a^{41}-\frac{12\cdots 82}{35\cdots 59}a^{40}+\frac{12\cdots 28}{35\cdots 59}a^{39}+\frac{46\cdots 54}{35\cdots 59}a^{38}-\frac{43\cdots 80}{35\cdots 59}a^{37}-\frac{10\cdots 88}{35\cdots 59}a^{36}+\frac{89\cdots 24}{35\cdots 59}a^{35}+\frac{15\cdots 95}{35\cdots 59}a^{34}-\frac{12\cdots 43}{35\cdots 59}a^{33}-\frac{16\cdots 03}{35\cdots 59}a^{32}+\frac{11\cdots 06}{35\cdots 59}a^{31}+\frac{12\cdots 32}{35\cdots 59}a^{30}-\frac{83\cdots 94}{35\cdots 59}a^{29}-\frac{66\cdots 32}{35\cdots 59}a^{28}+\frac{42\cdots 95}{35\cdots 59}a^{27}+\frac{27\cdots 07}{35\cdots 59}a^{26}-\frac{15\cdots 09}{35\cdots 59}a^{25}-\frac{83\cdots 51}{35\cdots 59}a^{24}+\frac{44\cdots 87}{35\cdots 59}a^{23}+\frac{19\cdots 60}{35\cdots 59}a^{22}-\frac{92\cdots 00}{35\cdots 59}a^{21}-\frac{32\cdots 54}{35\cdots 59}a^{20}+\frac{13\cdots 37}{35\cdots 59}a^{19}+\frac{39\cdots 25}{35\cdots 59}a^{18}-\frac{15\cdots 14}{35\cdots 59}a^{17}-\frac{35\cdots 28}{35\cdots 59}a^{16}+\frac{11\cdots 79}{35\cdots 59}a^{15}+\frac{21\cdots 89}{35\cdots 59}a^{14}-\frac{64\cdots 93}{35\cdots 59}a^{13}-\frac{91\cdots 87}{35\cdots 59}a^{12}+\frac{23\cdots 97}{35\cdots 59}a^{11}+\frac{25\cdots 98}{35\cdots 59}a^{10}-\frac{53\cdots 01}{35\cdots 59}a^{9}-\frac{42\cdots 47}{35\cdots 59}a^{8}+\frac{73\cdots 12}{35\cdots 59}a^{7}+\frac{38\cdots 82}{35\cdots 59}a^{6}-\frac{56\cdots 93}{35\cdots 59}a^{5}-\frac{14\cdots 94}{35\cdots 59}a^{4}+\frac{20\cdots 31}{35\cdots 59}a^{3}+\frac{10\cdots 24}{35\cdots 59}a^{2}-\frac{10\cdots 15}{35\cdots 59}a-\frac{43\cdots 02}{35\cdots 59}$, $\frac{22\cdots 62}{35\cdots 59}a^{42}-\frac{25\cdots 10}{35\cdots 59}a^{41}-\frac{18\cdots 75}{35\cdots 59}a^{40}+\frac{20\cdots 38}{35\cdots 59}a^{39}+\frac{69\cdots 74}{35\cdots 59}a^{38}-\frac{72\cdots 91}{35\cdots 59}a^{37}-\frac{15\cdots 09}{35\cdots 59}a^{36}+\frac{15\cdots 30}{35\cdots 59}a^{35}+\frac{22\cdots 34}{35\cdots 59}a^{34}-\frac{21\cdots 04}{35\cdots 59}a^{33}-\frac{23\cdots 53}{35\cdots 59}a^{32}+\frac{20\cdots 60}{35\cdots 59}a^{31}+\frac{17\cdots 26}{35\cdots 59}a^{30}-\frac{14\cdots 64}{35\cdots 59}a^{29}-\frac{97\cdots 57}{35\cdots 59}a^{28}+\frac{74\cdots 64}{35\cdots 59}a^{27}+\frac{39\cdots 54}{35\cdots 59}a^{26}-\frac{28\cdots 24}{35\cdots 59}a^{25}-\frac{12\cdots 19}{35\cdots 59}a^{24}+\frac{80\cdots 96}{35\cdots 59}a^{23}+\frac{27\cdots 08}{35\cdots 59}a^{22}-\frac{16\cdots 80}{35\cdots 59}a^{21}-\frac{45\cdots 74}{35\cdots 59}a^{20}+\frac{26\cdots 99}{35\cdots 59}a^{19}+\frac{55\cdots 31}{35\cdots 59}a^{18}-\frac{29\cdots 92}{35\cdots 59}a^{17}-\frac{47\cdots 90}{35\cdots 59}a^{16}+\frac{23\cdots 48}{35\cdots 59}a^{15}+\frac{28\cdots 34}{35\cdots 59}a^{14}-\frac{13\cdots 53}{35\cdots 59}a^{13}-\frac{11\cdots 62}{35\cdots 59}a^{12}+\frac{48\cdots 55}{35\cdots 59}a^{11}+\frac{29\cdots 50}{35\cdots 59}a^{10}-\frac{11\cdots 82}{35\cdots 59}a^{9}-\frac{45\cdots 70}{35\cdots 59}a^{8}+\frac{17\cdots 89}{35\cdots 59}a^{7}+\frac{33\cdots 31}{35\cdots 59}a^{6}-\frac{13\cdots 97}{35\cdots 59}a^{5}-\frac{54\cdots 86}{35\cdots 59}a^{4}+\frac{49\cdots 73}{35\cdots 59}a^{3}-\frac{31\cdots 64}{35\cdots 59}a^{2}-\frac{14\cdots 99}{35\cdots 59}a+\frac{64\cdots 59}{35\cdots 59}$, $\frac{11\cdots 20}{35\cdots 59}a^{42}-\frac{12\cdots 45}{35\cdots 59}a^{41}-\frac{10\cdots 10}{35\cdots 59}a^{40}+\frac{10\cdots 15}{35\cdots 59}a^{39}+\frac{37\cdots 50}{35\cdots 59}a^{38}-\frac{35\cdots 10}{35\cdots 59}a^{37}-\frac{84\cdots 75}{35\cdots 59}a^{36}+\frac{75\cdots 95}{35\cdots 59}a^{35}+\frac{12\cdots 20}{35\cdots 59}a^{34}-\frac{10\cdots 25}{35\cdots 59}a^{33}-\frac{12\cdots 80}{35\cdots 59}a^{32}+\frac{10\cdots 35}{35\cdots 59}a^{31}+\frac{96\cdots 55}{35\cdots 59}a^{30}-\frac{70\cdots 95}{35\cdots 59}a^{29}-\frac{53\cdots 45}{35\cdots 59}a^{28}+\frac{35\cdots 85}{35\cdots 59}a^{27}+\frac{21\cdots 80}{35\cdots 59}a^{26}-\frac{13\cdots 61}{35\cdots 59}a^{25}-\frac{66\cdots 70}{35\cdots 59}a^{24}+\frac{38\cdots 05}{35\cdots 59}a^{23}+\frac{15\cdots 95}{35\cdots 59}a^{22}-\frac{79\cdots 25}{35\cdots 59}a^{21}-\frac{25\cdots 70}{35\cdots 59}a^{20}+\frac{12\cdots 55}{35\cdots 59}a^{19}+\frac{31\cdots 10}{35\cdots 59}a^{18}-\frac{13\cdots 05}{35\cdots 59}a^{17}-\frac{27\cdots 60}{35\cdots 59}a^{16}+\frac{10\cdots 75}{35\cdots 59}a^{15}+\frac{17\cdots 65}{35\cdots 59}a^{14}-\frac{57\cdots 75}{35\cdots 59}a^{13}-\frac{71\cdots 00}{35\cdots 59}a^{12}+\frac{20\cdots 85}{35\cdots 59}a^{11}+\frac{19\cdots 65}{35\cdots 59}a^{10}-\frac{48\cdots 75}{35\cdots 59}a^{9}-\frac{32\cdots 25}{35\cdots 59}a^{8}+\frac{68\cdots 20}{35\cdots 59}a^{7}+\frac{29\cdots 35}{35\cdots 59}a^{6}-\frac{52\cdots 50}{35\cdots 59}a^{5}-\frac{11\cdots 25}{35\cdots 59}a^{4}+\frac{18\cdots 10}{35\cdots 59}a^{3}+\frac{63\cdots 35}{35\cdots 59}a^{2}-\frac{84\cdots 20}{35\cdots 59}a-\frac{25\cdots 50}{35\cdots 59}$, $\frac{24\cdots 61}{35\cdots 59}a^{42}-\frac{18\cdots 74}{35\cdots 59}a^{41}-\frac{20\cdots 40}{35\cdots 59}a^{40}+\frac{14\cdots 25}{35\cdots 59}a^{39}+\frac{78\cdots 53}{35\cdots 59}a^{38}-\frac{48\cdots 31}{35\cdots 59}a^{37}-\frac{17\cdots 12}{35\cdots 59}a^{36}+\frac{98\cdots 58}{35\cdots 59}a^{35}+\frac{26\cdots 99}{35\cdots 59}a^{34}-\frac{13\cdots 33}{35\cdots 59}a^{33}-\frac{27\cdots 03}{35\cdots 59}a^{32}+\frac{12\cdots 96}{35\cdots 59}a^{31}+\frac{20\cdots 53}{35\cdots 59}a^{30}-\frac{80\cdots 25}{35\cdots 59}a^{29}-\frac{11\cdots 29}{35\cdots 59}a^{28}+\frac{39\cdots 11}{35\cdots 59}a^{27}+\frac{47\cdots 17}{35\cdots 59}a^{26}-\frac{13\cdots 36}{35\cdots 59}a^{25}-\frac{14\cdots 15}{35\cdots 59}a^{24}+\frac{36\cdots 98}{35\cdots 59}a^{23}+\frac{34\cdots 62}{35\cdots 59}a^{22}-\frac{69\cdots 09}{35\cdots 59}a^{21}-\frac{59\cdots 78}{35\cdots 59}a^{20}+\frac{96\cdots 88}{35\cdots 59}a^{19}+\frac{74\cdots 53}{35\cdots 59}a^{18}-\frac{96\cdots 44}{35\cdots 59}a^{17}-\frac{67\cdots 16}{35\cdots 59}a^{16}+\frac{68\cdots 69}{35\cdots 59}a^{15}+\frac{43\cdots 32}{35\cdots 59}a^{14}-\frac{34\cdots 90}{35\cdots 59}a^{13}-\frac{18\cdots 28}{35\cdots 59}a^{12}+\frac{12\cdots 59}{35\cdots 59}a^{11}+\frac{53\cdots 36}{35\cdots 59}a^{10}-\frac{29\cdots 87}{35\cdots 59}a^{9}-\frac{93\cdots 97}{35\cdots 59}a^{8}+\frac{47\cdots 19}{35\cdots 59}a^{7}+\frac{88\cdots 83}{35\cdots 59}a^{6}-\frac{46\cdots 52}{35\cdots 59}a^{5}-\frac{33\cdots 48}{35\cdots 59}a^{4}+\frac{62\cdots 74}{10\cdots 97}a^{3}+\frac{17\cdots 54}{35\cdots 59}a^{2}+\frac{83\cdots 37}{35\cdots 59}a+\frac{26\cdots 08}{35\cdots 59}$, $\frac{28\cdots 32}{35\cdots 59}a^{42}-\frac{29\cdots 27}{35\cdots 59}a^{41}-\frac{23\cdots 37}{35\cdots 59}a^{40}+\frac{23\cdots 55}{35\cdots 59}a^{39}+\frac{88\cdots 58}{35\cdots 59}a^{38}-\frac{83\cdots 41}{35\cdots 59}a^{37}-\frac{19\cdots 65}{35\cdots 59}a^{36}+\frac{17\cdots 35}{35\cdots 59}a^{35}+\frac{29\cdots 54}{35\cdots 59}a^{34}-\frac{24\cdots 53}{35\cdots 59}a^{33}-\frac{30\cdots 83}{35\cdots 59}a^{32}+\frac{23\cdots 84}{35\cdots 59}a^{31}+\frac{22\cdots 43}{35\cdots 59}a^{30}-\frac{16\cdots 18}{35\cdots 59}a^{29}-\frac{12\cdots 28}{35\cdots 59}a^{28}+\frac{82\cdots 63}{35\cdots 59}a^{27}+\frac{51\cdots 85}{35\cdots 59}a^{26}-\frac{31\cdots 77}{35\cdots 59}a^{25}-\frac{15\cdots 29}{35\cdots 59}a^{24}+\frac{87\cdots 14}{35\cdots 59}a^{23}+\frac{35\cdots 04}{35\cdots 59}a^{22}-\frac{18\cdots 44}{35\cdots 59}a^{21}-\frac{60\cdots 77}{35\cdots 59}a^{20}+\frac{27\cdots 42}{35\cdots 59}a^{19}+\frac{74\cdots 85}{35\cdots 59}a^{18}-\frac{30\cdots 38}{35\cdots 59}a^{17}-\frac{65\cdots 85}{35\cdots 59}a^{16}+\frac{23\cdots 10}{35\cdots 59}a^{15}+\frac{40\cdots 91}{35\cdots 59}a^{14}-\frac{12\cdots 28}{35\cdots 59}a^{13}-\frac{16\cdots 87}{35\cdots 59}a^{12}+\frac{46\cdots 72}{35\cdots 59}a^{11}+\frac{46\cdots 28}{35\cdots 59}a^{10}-\frac{10\cdots 86}{35\cdots 59}a^{9}-\frac{76\cdots 65}{35\cdots 59}a^{8}+\frac{14\cdots 12}{35\cdots 59}a^{7}+\frac{69\cdots 77}{35\cdots 59}a^{6}-\frac{11\cdots 28}{35\cdots 59}a^{5}-\frac{25\cdots 89}{35\cdots 59}a^{4}+\frac{40\cdots 96}{35\cdots 59}a^{3}+\frac{13\cdots 78}{35\cdots 59}a^{2}-\frac{18\cdots 39}{35\cdots 59}a-\frac{48\cdots 63}{35\cdots 59}$, $\frac{54\cdots 81}{35\cdots 59}a^{42}-\frac{58\cdots 59}{35\cdots 59}a^{41}-\frac{45\cdots 53}{35\cdots 59}a^{40}+\frac{46\cdots 31}{35\cdots 59}a^{39}+\frac{17\cdots 93}{35\cdots 59}a^{38}-\frac{16\cdots 25}{35\cdots 59}a^{37}-\frac{38\cdots 23}{35\cdots 59}a^{36}+\frac{34\cdots 39}{35\cdots 59}a^{35}+\frac{56\cdots 74}{35\cdots 59}a^{34}-\frac{47\cdots 16}{35\cdots 59}a^{33}-\frac{58\cdots 00}{35\cdots 59}a^{32}+\frac{46\cdots 09}{35\cdots 59}a^{31}+\frac{43\cdots 54}{35\cdots 59}a^{30}-\frac{32\cdots 85}{35\cdots 59}a^{29}-\frac{24\cdots 72}{35\cdots 59}a^{28}+\frac{16\cdots 03}{35\cdots 59}a^{27}+\frac{99\cdots 41}{35\cdots 59}a^{26}-\frac{62\cdots 36}{35\cdots 59}a^{25}-\frac{30\cdots 38}{35\cdots 59}a^{24}+\frac{17\cdots 26}{35\cdots 59}a^{23}+\frac{69\cdots 86}{35\cdots 59}a^{22}-\frac{36\cdots 62}{35\cdots 59}a^{21}-\frac{11\cdots 49}{35\cdots 59}a^{20}+\frac{55\cdots 71}{35\cdots 59}a^{19}+\frac{14\cdots 35}{35\cdots 59}a^{18}-\frac{61\cdots 46}{35\cdots 59}a^{17}-\frac{12\cdots 59}{35\cdots 59}a^{16}+\frac{47\cdots 71}{35\cdots 59}a^{15}+\frac{77\cdots 80}{35\cdots 59}a^{14}-\frac{26\cdots 06}{35\cdots 59}a^{13}-\frac{32\cdots 67}{35\cdots 59}a^{12}+\frac{94\cdots 80}{35\cdots 59}a^{11}+\frac{87\cdots 67}{35\cdots 59}a^{10}-\frac{22\cdots 68}{35\cdots 59}a^{9}-\frac{14\cdots 96}{35\cdots 59}a^{8}+\frac{30\cdots 43}{35\cdots 59}a^{7}+\frac{12\cdots 79}{35\cdots 59}a^{6}-\frac{23\cdots 62}{35\cdots 59}a^{5}-\frac{38\cdots 02}{35\cdots 59}a^{4}+\frac{81\cdots 94}{35\cdots 59}a^{3}-\frac{15\cdots 46}{35\cdots 59}a^{2}-\frac{22\cdots 60}{35\cdots 59}a+\frac{76\cdots 48}{35\cdots 59}$, $\frac{39\cdots 59}{35\cdots 59}a^{42}-\frac{41\cdots 79}{35\cdots 59}a^{41}-\frac{32\cdots 21}{35\cdots 59}a^{40}+\frac{32\cdots 20}{35\cdots 59}a^{39}+\frac{12\cdots 15}{35\cdots 59}a^{38}-\frac{11\cdots 64}{35\cdots 59}a^{37}-\frac{27\cdots 39}{35\cdots 59}a^{36}+\frac{24\cdots 57}{35\cdots 59}a^{35}+\frac{40\cdots 09}{35\cdots 59}a^{34}-\frac{33\cdots 77}{35\cdots 59}a^{33}-\frac{42\cdots 70}{35\cdots 59}a^{32}+\frac{32\cdots 86}{35\cdots 59}a^{31}+\frac{31\cdots 75}{35\cdots 59}a^{30}-\frac{22\cdots 93}{35\cdots 59}a^{29}-\frac{17\cdots 05}{35\cdots 59}a^{28}+\frac{11\cdots 44}{35\cdots 59}a^{27}+\frac{71\cdots 72}{35\cdots 59}a^{26}-\frac{43\cdots 61}{35\cdots 59}a^{25}-\frac{21\cdots 72}{35\cdots 59}a^{24}+\frac{12\cdots 66}{35\cdots 59}a^{23}+\frac{49\cdots 11}{35\cdots 59}a^{22}-\frac{25\cdots 89}{35\cdots 59}a^{21}-\frac{83\cdots 27}{35\cdots 59}a^{20}+\frac{38\cdots 68}{35\cdots 59}a^{19}+\frac{10\cdots 09}{35\cdots 59}a^{18}-\frac{42\cdots 62}{35\cdots 59}a^{17}-\frac{90\cdots 36}{35\cdots 59}a^{16}+\frac{33\cdots 73}{35\cdots 59}a^{15}+\frac{55\cdots 60}{35\cdots 59}a^{14}-\frac{18\cdots 77}{35\cdots 59}a^{13}-\frac{23\cdots 33}{35\cdots 59}a^{12}+\frac{65\cdots 44}{35\cdots 59}a^{11}+\frac{63\cdots 33}{35\cdots 59}a^{10}-\frac{43\cdots 30}{10\cdots 97}a^{9}-\frac{10\cdots 57}{35\cdots 59}a^{8}+\frac{20\cdots 81}{35\cdots 59}a^{7}+\frac{95\cdots 01}{35\cdots 59}a^{6}-\frac{15\cdots 29}{35\cdots 59}a^{5}-\frac{35\cdots 33}{35\cdots 59}a^{4}+\frac{55\cdots 87}{35\cdots 59}a^{3}+\frac{19\cdots 09}{35\cdots 59}a^{2}-\frac{25\cdots 19}{35\cdots 59}a-\frac{75\cdots 07}{35\cdots 59}$, $\frac{31\cdots 34}{35\cdots 59}a^{42}-\frac{33\cdots 12}{35\cdots 59}a^{41}-\frac{26\cdots 55}{35\cdots 59}a^{40}+\frac{26\cdots 43}{35\cdots 59}a^{39}+\frac{98\cdots 28}{35\cdots 59}a^{38}-\frac{94\cdots 31}{35\cdots 59}a^{37}-\frac{21\cdots 78}{35\cdots 59}a^{36}+\frac{19\cdots 11}{35\cdots 59}a^{35}+\frac{32\cdots 18}{35\cdots 59}a^{34}-\frac{27\cdots 29}{35\cdots 59}a^{33}-\frac{33\cdots 54}{35\cdots 59}a^{32}+\frac{26\cdots 98}{35\cdots 59}a^{31}+\frac{25\cdots 10}{35\cdots 59}a^{30}-\frac{18\cdots 21}{35\cdots 59}a^{29}-\frac{13\cdots 72}{35\cdots 59}a^{28}+\frac{94\cdots 80}{35\cdots 59}a^{27}+\frac{56\cdots 48}{35\cdots 59}a^{26}-\frac{35\cdots 72}{35\cdots 59}a^{25}-\frac{17\cdots 52}{35\cdots 59}a^{24}+\frac{10\cdots 48}{35\cdots 59}a^{23}+\frac{39\cdots 53}{35\cdots 59}a^{22}-\frac{20\cdots 20}{35\cdots 59}a^{21}-\frac{66\cdots 83}{35\cdots 59}a^{20}+\frac{31\cdots 12}{35\cdots 59}a^{19}+\frac{82\cdots 56}{35\cdots 59}a^{18}-\frac{35\cdots 24}{35\cdots 59}a^{17}-\frac{72\cdots 53}{35\cdots 59}a^{16}+\frac{27\cdots 94}{35\cdots 59}a^{15}+\frac{44\cdots 22}{35\cdots 59}a^{14}-\frac{15\cdots 77}{35\cdots 59}a^{13}-\frac{18\cdots 41}{35\cdots 59}a^{12}+\frac{54\cdots 25}{35\cdots 59}a^{11}+\frac{50\cdots 27}{35\cdots 59}a^{10}-\frac{12\cdots 31}{35\cdots 59}a^{9}-\frac{83\cdots 95}{35\cdots 59}a^{8}+\frac{17\cdots 65}{35\cdots 59}a^{7}+\frac{74\cdots 53}{35\cdots 59}a^{6}-\frac{13\cdots 76}{35\cdots 59}a^{5}-\frac{27\cdots 16}{35\cdots 59}a^{4}+\frac{48\cdots 95}{35\cdots 59}a^{3}+\frac{11\cdots 93}{35\cdots 59}a^{2}-\frac{21\cdots 40}{35\cdots 59}a-\frac{51\cdots 96}{35\cdots 59}$, $\frac{13\cdots 50}{35\cdots 59}a^{42}-\frac{14\cdots 32}{35\cdots 59}a^{41}-\frac{11\cdots 06}{35\cdots 59}a^{40}+\frac{11\cdots 23}{35\cdots 59}a^{39}+\frac{43\cdots 93}{35\cdots 59}a^{38}-\frac{40\cdots 15}{35\cdots 59}a^{37}-\frac{97\cdots 20}{35\cdots 59}a^{36}+\frac{84\cdots 59}{35\cdots 59}a^{35}+\frac{14\cdots 59}{35\cdots 59}a^{34}-\frac{11\cdots 30}{35\cdots 59}a^{33}-\frac{14\cdots 57}{35\cdots 59}a^{32}+\frac{11\cdots 41}{35\cdots 59}a^{31}+\frac{11\cdots 31}{35\cdots 59}a^{30}-\frac{78\cdots 84}{35\cdots 59}a^{29}-\frac{61\cdots 20}{35\cdots 59}a^{28}+\frac{39\cdots 42}{35\cdots 59}a^{27}+\frac{25\cdots 12}{35\cdots 59}a^{26}-\frac{15\cdots 81}{35\cdots 59}a^{25}-\frac{77\cdots 69}{35\cdots 59}a^{24}+\frac{42\cdots 01}{35\cdots 59}a^{23}+\frac{17\cdots 92}{35\cdots 59}a^{22}-\frac{87\cdots 89}{35\cdots 59}a^{21}-\frac{29\cdots 24}{35\cdots 59}a^{20}+\frac{13\cdots 73}{35\cdots 59}a^{19}+\frac{36\cdots 43}{35\cdots 59}a^{18}-\frac{14\cdots 32}{35\cdots 59}a^{17}-\frac{32\cdots 12}{35\cdots 59}a^{16}+\frac{11\cdots 30}{35\cdots 59}a^{15}+\frac{20\cdots 62}{35\cdots 59}a^{14}-\frac{61\cdots 40}{35\cdots 59}a^{13}-\frac{84\cdots 54}{35\cdots 59}a^{12}+\frac{22\cdots 00}{35\cdots 59}a^{11}+\frac{23\cdots 37}{35\cdots 59}a^{10}-\frac{50\cdots 09}{35\cdots 59}a^{9}-\frac{38\cdots 24}{35\cdots 59}a^{8}+\frac{69\cdots 72}{35\cdots 59}a^{7}+\frac{35\cdots 07}{35\cdots 59}a^{6}-\frac{52\cdots 37}{35\cdots 59}a^{5}-\frac{13\cdots 01}{35\cdots 59}a^{4}+\frac{18\cdots 27}{35\cdots 59}a^{3}+\frac{11\cdots 85}{35\cdots 59}a^{2}-\frac{89\cdots 01}{35\cdots 59}a-\frac{40\cdots 60}{35\cdots 59}$, $\frac{25\cdots 86}{35\cdots 59}a^{42}-\frac{27\cdots 31}{35\cdots 59}a^{41}-\frac{21\cdots 40}{35\cdots 59}a^{40}+\frac{21\cdots 10}{35\cdots 59}a^{39}+\frac{80\cdots 14}{35\cdots 59}a^{38}-\frac{76\cdots 26}{35\cdots 59}a^{37}-\frac{18\cdots 05}{35\cdots 59}a^{36}+\frac{15\cdots 22}{35\cdots 59}a^{35}+\frac{26\cdots 46}{35\cdots 59}a^{34}-\frac{22\cdots 32}{35\cdots 59}a^{33}-\frac{27\cdots 75}{35\cdots 59}a^{32}+\frac{21\cdots 26}{35\cdots 59}a^{31}+\frac{20\cdots 31}{35\cdots 59}a^{30}-\frac{14\cdots 41}{35\cdots 59}a^{29}-\frac{11\cdots 66}{35\cdots 59}a^{28}+\frac{75\cdots 09}{35\cdots 59}a^{27}+\frac{46\cdots 11}{35\cdots 59}a^{26}-\frac{28\cdots 57}{35\cdots 59}a^{25}-\frac{14\cdots 19}{35\cdots 59}a^{24}+\frac{80\cdots 26}{35\cdots 59}a^{23}+\frac{32\cdots 51}{35\cdots 59}a^{22}-\frac{16\cdots 56}{35\cdots 59}a^{21}-\frac{55\cdots 46}{35\cdots 59}a^{20}+\frac{25\cdots 54}{35\cdots 59}a^{19}+\frac{67\cdots 57}{35\cdots 59}a^{18}-\frac{27\cdots 04}{35\cdots 59}a^{17}-\frac{59\cdots 24}{35\cdots 59}a^{16}+\frac{21\cdots 48}{35\cdots 59}a^{15}+\frac{36\cdots 31}{35\cdots 59}a^{14}-\frac{11\cdots 29}{35\cdots 59}a^{13}-\frac{15\cdots 76}{35\cdots 59}a^{12}+\frac{42\cdots 17}{35\cdots 59}a^{11}+\frac{41\cdots 43}{35\cdots 59}a^{10}-\frac{98\cdots 99}{35\cdots 59}a^{9}-\frac{69\cdots 70}{35\cdots 59}a^{8}+\frac{13\cdots 33}{35\cdots 59}a^{7}+\frac{62\cdots 65}{35\cdots 59}a^{6}-\frac{10\cdots 40}{35\cdots 59}a^{5}-\frac{23\cdots 15}{35\cdots 59}a^{4}+\frac{36\cdots 59}{35\cdots 59}a^{3}+\frac{12\cdots 48}{35\cdots 59}a^{2}-\frac{16\cdots 67}{35\cdots 59}a-\frac{44\cdots 03}{35\cdots 59}$, $\frac{50\cdots 43}{35\cdots 59}a^{42}-\frac{53\cdots 59}{35\cdots 59}a^{41}-\frac{42\cdots 45}{35\cdots 59}a^{40}+\frac{42\cdots 17}{35\cdots 59}a^{39}+\frac{15\cdots 20}{35\cdots 59}a^{38}-\frac{15\cdots 06}{35\cdots 59}a^{37}-\frac{35\cdots 50}{35\cdots 59}a^{36}+\frac{31\cdots 15}{35\cdots 59}a^{35}+\frac{52\cdots 45}{35\cdots 59}a^{34}-\frac{43\cdots 49}{35\cdots 59}a^{33}-\frac{53\cdots 10}{35\cdots 59}a^{32}+\frac{42\cdots 66}{35\cdots 59}a^{31}+\frac{40\cdots 35}{35\cdots 59}a^{30}-\frac{29\cdots 98}{35\cdots 59}a^{29}-\frac{22\cdots 16}{35\cdots 59}a^{28}+\frac{15\cdots 72}{35\cdots 59}a^{27}+\frac{91\cdots 55}{35\cdots 59}a^{26}-\frac{56\cdots 66}{35\cdots 59}a^{25}-\frac{28\cdots 74}{35\cdots 59}a^{24}+\frac{15\cdots 15}{35\cdots 59}a^{23}+\frac{63\cdots 77}{35\cdots 59}a^{22}-\frac{33\cdots 48}{35\cdots 59}a^{21}-\frac{10\cdots 11}{35\cdots 59}a^{20}+\frac{50\cdots 55}{35\cdots 59}a^{19}+\frac{13\cdots 42}{35\cdots 59}a^{18}-\frac{55\cdots 22}{35\cdots 59}a^{17}-\frac{11\cdots 15}{35\cdots 59}a^{16}+\frac{43\cdots 38}{35\cdots 59}a^{15}+\frac{71\cdots 74}{35\cdots 59}a^{14}-\frac{23\cdots 22}{35\cdots 59}a^{13}-\frac{29\cdots 15}{35\cdots 59}a^{12}+\frac{86\cdots 31}{35\cdots 59}a^{11}+\frac{80\cdots 21}{35\cdots 59}a^{10}-\frac{19\cdots 37}{35\cdots 59}a^{9}-\frac{13\cdots 38}{35\cdots 59}a^{8}+\frac{27\cdots 18}{35\cdots 59}a^{7}+\frac{11\cdots 10}{35\cdots 59}a^{6}-\frac{21\cdots 57}{35\cdots 59}a^{5}-\frac{34\cdots 94}{35\cdots 59}a^{4}+\frac{73\cdots 67}{35\cdots 59}a^{3}-\frac{17\cdots 69}{35\cdots 59}a^{2}-\frac{16\cdots 49}{35\cdots 59}a+\frac{88\cdots 94}{35\cdots 59}$, $\frac{20\cdots 29}{35\cdots 59}a^{42}-\frac{21\cdots 80}{35\cdots 59}a^{41}-\frac{16\cdots 57}{35\cdots 59}a^{40}+\frac{16\cdots 62}{35\cdots 59}a^{39}+\frac{63\cdots 93}{35\cdots 59}a^{38}-\frac{59\cdots 43}{35\cdots 59}a^{37}-\frac{14\cdots 43}{35\cdots 59}a^{36}+\frac{12\cdots 19}{35\cdots 59}a^{35}+\frac{20\cdots 60}{35\cdots 59}a^{34}-\frac{17\cdots 29}{35\cdots 59}a^{33}-\frac{21\cdots 74}{35\cdots 59}a^{32}+\frac{16\cdots 58}{35\cdots 59}a^{31}+\frac{16\cdots 95}{35\cdots 59}a^{30}-\frac{11\cdots 76}{35\cdots 59}a^{29}-\frac{89\cdots 52}{35\cdots 59}a^{28}+\frac{59\cdots 34}{35\cdots 59}a^{27}+\frac{36\cdots 49}{35\cdots 59}a^{26}-\frac{22\cdots 16}{35\cdots 59}a^{25}-\frac{11\cdots 38}{35\cdots 59}a^{24}+\frac{62\cdots 57}{35\cdots 59}a^{23}+\frac{25\cdots 66}{35\cdots 59}a^{22}-\frac{12\cdots 28}{35\cdots 59}a^{21}-\frac{43\cdots 67}{35\cdots 59}a^{20}+\frac{19\cdots 82}{35\cdots 59}a^{19}+\frac{52\cdots 38}{35\cdots 59}a^{18}-\frac{21\cdots 24}{35\cdots 59}a^{17}-\frac{46\cdots 48}{35\cdots 59}a^{16}+\frac{16\cdots 00}{35\cdots 59}a^{15}+\frac{28\cdots 77}{35\cdots 59}a^{14}-\frac{91\cdots 11}{35\cdots 59}a^{13}-\frac{11\cdots 01}{35\cdots 59}a^{12}+\frac{33\cdots 62}{35\cdots 59}a^{11}+\frac{32\cdots 35}{35\cdots 59}a^{10}-\frac{76\cdots 81}{35\cdots 59}a^{9}-\frac{54\cdots 79}{35\cdots 59}a^{8}+\frac{10\cdots 06}{35\cdots 59}a^{7}+\frac{48\cdots 35}{35\cdots 59}a^{6}-\frac{79\cdots 75}{35\cdots 59}a^{5}-\frac{17\cdots 37}{35\cdots 59}a^{4}+\frac{28\cdots 81}{35\cdots 59}a^{3}+\frac{97\cdots 02}{35\cdots 59}a^{2}-\frac{13\cdots 93}{35\cdots 59}a-\frac{36\cdots 14}{35\cdots 59}$, $\frac{36\cdots 38}{35\cdots 59}a^{42}-\frac{38\cdots 51}{35\cdots 59}a^{41}-\frac{30\cdots 56}{35\cdots 59}a^{40}+\frac{30\cdots 80}{35\cdots 59}a^{39}+\frac{11\cdots 73}{35\cdots 59}a^{38}-\frac{10\cdots 13}{35\cdots 59}a^{37}-\frac{25\cdots 96}{35\cdots 59}a^{36}+\frac{22\cdots 98}{35\cdots 59}a^{35}+\frac{38\cdots 33}{35\cdots 59}a^{34}-\frac{31\cdots 87}{35\cdots 59}a^{33}-\frac{39\cdots 51}{35\cdots 59}a^{32}+\frac{29\cdots 81}{35\cdots 59}a^{31}+\frac{29\cdots 26}{35\cdots 59}a^{30}-\frac{20\cdots 32}{35\cdots 59}a^{29}-\frac{16\cdots 38}{35\cdots 59}a^{28}+\frac{10\cdots 73}{35\cdots 59}a^{27}+\frac{67\cdots 45}{35\cdots 59}a^{26}-\frac{40\cdots 09}{35\cdots 59}a^{25}-\frac{20\cdots 78}{35\cdots 59}a^{24}+\frac{11\cdots 53}{35\cdots 59}a^{23}+\frac{46\cdots 94}{35\cdots 59}a^{22}-\frac{23\cdots 18}{35\cdots 59}a^{21}-\frac{79\cdots 49}{35\cdots 59}a^{20}+\frac{35\cdots 98}{35\cdots 59}a^{19}+\frac{97\cdots 00}{35\cdots 59}a^{18}-\frac{38\cdots 10}{35\cdots 59}a^{17}-\frac{85\cdots 60}{35\cdots 59}a^{16}+\frac{30\cdots 96}{35\cdots 59}a^{15}+\frac{52\cdots 35}{35\cdots 59}a^{14}-\frac{16\cdots 83}{35\cdots 59}a^{13}-\frac{22\cdots 82}{35\cdots 59}a^{12}+\frac{58\cdots 93}{35\cdots 59}a^{11}+\frac{60\cdots 27}{35\cdots 59}a^{10}-\frac{13\cdots 28}{35\cdots 59}a^{9}-\frac{10\cdots 87}{35\cdots 59}a^{8}+\frac{18\cdots 58}{35\cdots 59}a^{7}+\frac{91\cdots 29}{35\cdots 59}a^{6}-\frac{13\cdots 87}{35\cdots 59}a^{5}-\frac{34\cdots 40}{35\cdots 59}a^{4}+\frac{48\cdots 96}{35\cdots 59}a^{3}+\frac{21\cdots 95}{35\cdots 59}a^{2}-\frac{22\cdots 50}{35\cdots 59}a-\frac{72\cdots 00}{35\cdots 59}$, $\frac{14\cdots 34}{35\cdots 59}a^{42}-\frac{15\cdots 52}{35\cdots 59}a^{41}-\frac{12\cdots 67}{35\cdots 59}a^{40}+\frac{12\cdots 78}{35\cdots 59}a^{39}+\frac{46\cdots 21}{35\cdots 59}a^{38}-\frac{44\cdots 64}{35\cdots 59}a^{37}-\frac{10\cdots 19}{35\cdots 59}a^{36}+\frac{21\cdots 93}{81\cdots 81}a^{35}+\frac{15\cdots 24}{35\cdots 59}a^{34}-\frac{12\cdots 15}{35\cdots 59}a^{33}-\frac{15\cdots 35}{35\cdots 59}a^{32}+\frac{12\cdots 35}{35\cdots 59}a^{31}+\frac{11\cdots 28}{35\cdots 59}a^{30}-\frac{87\cdots 76}{35\cdots 59}a^{29}-\frac{65\cdots 71}{35\cdots 59}a^{28}+\frac{44\cdots 43}{35\cdots 59}a^{27}+\frac{26\cdots 94}{35\cdots 59}a^{26}-\frac{16\cdots 84}{35\cdots 59}a^{25}-\frac{82\cdots 28}{35\cdots 59}a^{24}+\frac{47\cdots 80}{35\cdots 59}a^{23}+\frac{18\cdots 62}{35\cdots 59}a^{22}-\frac{99\cdots 20}{35\cdots 59}a^{21}-\frac{31\cdots 51}{35\cdots 59}a^{20}+\frac{15\cdots 85}{35\cdots 59}a^{19}+\frac{38\cdots 00}{35\cdots 59}a^{18}-\frac{16\cdots 95}{35\cdots 59}a^{17}-\frac{34\cdots 22}{35\cdots 59}a^{16}+\frac{13\cdots 80}{35\cdots 59}a^{15}+\frac{21\cdots 09}{35\cdots 59}a^{14}-\frac{72\cdots 47}{35\cdots 59}a^{13}-\frac{87\cdots 70}{35\cdots 59}a^{12}+\frac{26\cdots 50}{35\cdots 59}a^{11}+\frac{23\cdots 43}{35\cdots 59}a^{10}-\frac{61\cdots 77}{35\cdots 59}a^{9}-\frac{39\cdots 58}{35\cdots 59}a^{8}+\frac{85\cdots 36}{35\cdots 59}a^{7}+\frac{35\cdots 22}{35\cdots 59}a^{6}-\frac{66\cdots 90}{35\cdots 59}a^{5}-\frac{12\cdots 80}{35\cdots 59}a^{4}+\frac{23\cdots 11}{35\cdots 59}a^{3}+\frac{54\cdots 04}{35\cdots 59}a^{2}-\frac{10\cdots 06}{35\cdots 59}a-\frac{17\cdots 05}{35\cdots 59}$, $\frac{14\cdots 85}{35\cdots 59}a^{42}-\frac{15\cdots 60}{35\cdots 59}a^{41}-\frac{12\cdots 29}{35\cdots 59}a^{40}+\frac{12\cdots 70}{35\cdots 59}a^{39}+\frac{46\cdots 86}{35\cdots 59}a^{38}-\frac{42\cdots 30}{35\cdots 59}a^{37}-\frac{10\cdots 22}{35\cdots 59}a^{36}+\frac{89\cdots 98}{35\cdots 59}a^{35}+\frac{15\cdots 80}{35\cdots 59}a^{34}-\frac{12\cdots 38}{35\cdots 59}a^{33}-\frac{15\cdots 83}{35\cdots 59}a^{32}+\frac{11\cdots 97}{35\cdots 59}a^{31}+\frac{11\cdots 46}{35\cdots 59}a^{30}-\frac{83\cdots 01}{35\cdots 59}a^{29}-\frac{65\cdots 36}{35\cdots 59}a^{28}+\frac{42\cdots 92}{35\cdots 59}a^{27}+\frac{26\cdots 09}{35\cdots 59}a^{26}-\frac{15\cdots 51}{35\cdots 59}a^{25}-\frac{82\cdots 59}{35\cdots 59}a^{24}+\frac{44\cdots 78}{35\cdots 59}a^{23}+\frac{18\cdots 21}{35\cdots 59}a^{22}-\frac{92\cdots 37}{35\cdots 59}a^{21}-\frac{31\cdots 88}{35\cdots 59}a^{20}+\frac{14\cdots 57}{35\cdots 59}a^{19}+\frac{38\cdots 05}{35\cdots 59}a^{18}-\frac{15\cdots 44}{35\cdots 59}a^{17}-\frac{34\cdots 91}{35\cdots 59}a^{16}+\frac{11\cdots 20}{35\cdots 59}a^{15}+\frac{21\cdots 27}{35\cdots 59}a^{14}-\frac{64\cdots 98}{35\cdots 59}a^{13}-\frac{88\cdots 76}{35\cdots 59}a^{12}+\frac{23\cdots 49}{35\cdots 59}a^{11}+\frac{24\cdots 58}{35\cdots 59}a^{10}-\frac{53\cdots 25}{35\cdots 59}a^{9}-\frac{40\cdots 17}{35\cdots 59}a^{8}+\frac{72\cdots 37}{35\cdots 59}a^{7}+\frac{36\cdots 44}{35\cdots 59}a^{6}-\frac{54\cdots 54}{35\cdots 59}a^{5}-\frac{13\cdots 20}{35\cdots 59}a^{4}+\frac{19\cdots 49}{35\cdots 59}a^{3}+\frac{71\cdots 23}{35\cdots 59}a^{2}-\frac{74\cdots 90}{35\cdots 59}a-\frac{22\cdots 10}{35\cdots 59}$, $\frac{10\cdots 29}{35\cdots 59}a^{42}-\frac{10\cdots 20}{35\cdots 59}a^{41}-\frac{84\cdots 11}{35\cdots 59}a^{40}+\frac{82\cdots 37}{35\cdots 59}a^{39}+\frac{31\cdots 52}{35\cdots 59}a^{38}-\frac{29\cdots 77}{35\cdots 59}a^{37}-\frac{70\cdots 79}{35\cdots 59}a^{36}+\frac{61\cdots 26}{35\cdots 59}a^{35}+\frac{10\cdots 79}{35\cdots 59}a^{34}-\frac{84\cdots 31}{35\cdots 59}a^{33}-\frac{10\cdots 82}{35\cdots 59}a^{32}+\frac{81\cdots 01}{35\cdots 59}a^{31}+\frac{81\cdots 51}{35\cdots 59}a^{30}-\frac{56\cdots 75}{35\cdots 59}a^{29}-\frac{44\cdots 96}{35\cdots 59}a^{28}+\frac{28\cdots 29}{35\cdots 59}a^{27}+\frac{18\cdots 60}{35\cdots 59}a^{26}-\frac{10\cdots 76}{35\cdots 59}a^{25}-\frac{56\cdots 56}{35\cdots 59}a^{24}+\frac{30\cdots 22}{35\cdots 59}a^{23}+\frac{12\cdots 51}{35\cdots 59}a^{22}-\frac{63\cdots 86}{35\cdots 59}a^{21}-\frac{21\cdots 60}{35\cdots 59}a^{20}+\frac{95\cdots 64}{35\cdots 59}a^{19}+\frac{26\cdots 32}{35\cdots 59}a^{18}-\frac{10\cdots 30}{35\cdots 59}a^{17}-\frac{23\cdots 68}{35\cdots 59}a^{16}+\frac{82\cdots 46}{35\cdots 59}a^{15}+\frac{14\cdots 90}{35\cdots 59}a^{14}-\frac{44\cdots 41}{35\cdots 59}a^{13}-\frac{61\cdots 20}{35\cdots 59}a^{12}+\frac{16\cdots 34}{35\cdots 59}a^{11}+\frac{16\cdots 72}{35\cdots 59}a^{10}-\frac{37\cdots 67}{35\cdots 59}a^{9}-\frac{27\cdots 35}{35\cdots 59}a^{8}+\frac{52\cdots 21}{35\cdots 59}a^{7}+\frac{25\cdots 94}{35\cdots 59}a^{6}-\frac{41\cdots 97}{35\cdots 59}a^{5}-\frac{91\cdots 32}{35\cdots 59}a^{4}+\frac{15\cdots 50}{35\cdots 59}a^{3}+\frac{38\cdots 61}{35\cdots 59}a^{2}-\frac{71\cdots 31}{35\cdots 59}a-\frac{12\cdots 46}{35\cdots 59}$, $\frac{41\cdots 89}{35\cdots 59}a^{42}-\frac{44\cdots 32}{35\cdots 59}a^{41}-\frac{34\cdots 36}{35\cdots 59}a^{40}+\frac{34\cdots 22}{35\cdots 59}a^{39}+\frac{13\cdots 82}{35\cdots 59}a^{38}-\frac{12\cdots 16}{35\cdots 59}a^{37}-\frac{29\cdots 50}{35\cdots 59}a^{36}+\frac{25\cdots 70}{35\cdots 59}a^{35}+\frac{43\cdots 17}{35\cdots 59}a^{34}-\frac{35\cdots 02}{35\cdots 59}a^{33}-\frac{44\cdots 08}{35\cdots 59}a^{32}+\frac{34\cdots 07}{35\cdots 59}a^{31}+\frac{33\cdots 45}{35\cdots 59}a^{30}-\frac{24\cdots 37}{35\cdots 59}a^{29}-\frac{18\cdots 08}{35\cdots 59}a^{28}+\frac{12\cdots 80}{35\cdots 59}a^{27}+\frac{76\cdots 91}{35\cdots 59}a^{26}-\frac{46\cdots 50}{35\cdots 59}a^{25}-\frac{23\cdots 03}{35\cdots 59}a^{24}+\frac{13\cdots 69}{35\cdots 59}a^{23}+\frac{53\cdots 09}{35\cdots 59}a^{22}-\frac{27\cdots 24}{35\cdots 59}a^{21}-\frac{89\cdots 03}{35\cdots 59}a^{20}+\frac{41\cdots 55}{35\cdots 59}a^{19}+\frac{11\cdots 88}{35\cdots 59}a^{18}-\frac{45\cdots 70}{35\cdots 59}a^{17}-\frac{97\cdots 51}{35\cdots 59}a^{16}+\frac{35\cdots 19}{35\cdots 59}a^{15}+\frac{59\cdots 49}{35\cdots 59}a^{14}-\frac{19\cdots 63}{35\cdots 59}a^{13}-\frac{25\cdots 79}{35\cdots 59}a^{12}+\frac{69\cdots 32}{35\cdots 59}a^{11}+\frac{68\cdots 85}{35\cdots 59}a^{10}-\frac{16\cdots 65}{35\cdots 59}a^{9}-\frac{11\cdots 95}{35\cdots 59}a^{8}+\frac{22\cdots 58}{35\cdots 59}a^{7}+\frac{10\cdots 45}{35\cdots 59}a^{6}-\frac{16\cdots 46}{35\cdots 59}a^{5}-\frac{37\cdots 71}{35\cdots 59}a^{4}+\frac{60\cdots 94}{35\cdots 59}a^{3}+\frac{20\cdots 54}{35\cdots 59}a^{2}-\frac{27\cdots 51}{35\cdots 59}a-\frac{79\cdots 79}{35\cdots 59}$
|
| |
| Regulator: | \( 2657880348049265700000000000000000 \) (assuming GRH) |
| |
| Unit signature rank: | \( 43 \) (assuming GRH) |
Class number formula
\[ \begin{aligned}\lim_{s\to 1} (s-1)\zeta_K(s) =\mathstrut & \frac{2^{r_1}\cdot (2\pi)^{r_2}\cdot R\cdot h}{w\cdot\sqrt{|D|}}\cr \approx\mathstrut &\frac{2^{43}\cdot(2\pi)^{0}\cdot 2657880348049265700000000000000000 \cdot 1}{2\cdot\sqrt{9952594992767664919302480397055915291864099597331865326873171797085952964991380209309055259529}}\cr\approx \mathstrut & 0.117172872887188 \end{aligned}\] (assuming GRH)
Galois group
| A cyclic group of order 43 |
| The 43 conjugacy class representatives for $C_{43}$ |
| Character table for $C_{43}$ |
Intermediate fields
| The extension is primitive: there are no intermediate fields between this field and $\Q$. |
Frobenius cycle types
| $p$ | $2$ | $3$ | $5$ | $7$ | $11$ | $13$ | $17$ | $19$ | $23$ | $29$ | $31$ | $37$ | $41$ | $43$ | $47$ | $53$ | $59$ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Cycle type | $43$ | $43$ | $43$ | $43$ | $43$ | $43$ | $43$ | $43$ | $43$ | $43$ | $43$ | $43$ | $43$ | $43$ | $43$ | $43$ | $43$ |
Cycle lengths which are repeated in a cycle type are indicated by exponents.
Local algebras for ramified primes
| $p$ | Label | Polynomial | $e$ | $f$ | $c$ | Galois group | Slope content |
|---|---|---|---|---|---|---|---|
|
\(173\)
| Deg $43$ | $43$ | $1$ | $42$ |