# Properties

 Label 441.4.e Level $441$ Weight $4$ Character orbit 441.e Rep. character $\chi_{441}(226,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $96$ Newform subspaces $26$ Sturm bound $224$ Trace bound $13$

# Learn more about

## Defining parameters

 Level: $$N$$ $$=$$ $$441 = 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 441.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$26$$ Sturm bound: $$224$$ Trace bound: $$13$$ Distinguishing $$T_p$$: $$2$$, $$5$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(441, [\chi])$$.

Total New Old
Modular forms 368 104 264
Cusp forms 304 96 208
Eisenstein series 64 8 56

## Trace form

 $$96q + q^{2} - 193q^{4} - 15q^{5} + 102q^{8} + O(q^{10})$$ $$96q + q^{2} - 193q^{4} - 15q^{5} + 102q^{8} - 10q^{10} - 29q^{11} - 172q^{13} - 741q^{16} - 111q^{17} + 53q^{19} + 816q^{20} + 372q^{22} + 41q^{23} - 825q^{25} - 438q^{26} - 784q^{29} + 19q^{31} - 1327q^{32} - 1404q^{34} + 407q^{37} + 252q^{38} + 612q^{40} + 1908q^{41} + 1504q^{43} + 548q^{44} + 922q^{46} - 285q^{47} - 2234q^{50} + 276q^{52} - 2299q^{53} - 2978q^{55} - 3314q^{58} - 1023q^{59} + 731q^{61} + 4224q^{62} + 6578q^{64} + 378q^{65} + 1017q^{67} - 2112q^{68} - 2312q^{71} + 1987q^{73} - 3138q^{74} + 192q^{76} + 351q^{79} - 276q^{80} + 2224q^{82} + 4176q^{83} - 3118q^{85} + 546q^{86} - 2760q^{88} - 2343q^{89} + 4768q^{92} - 3570q^{94} - 57q^{95} - 5300q^{97} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(441, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
441.4.e.a $$2$$ $$26.020$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-7})$$ $$-5$$ $$0$$ $$0$$ $$0$$ $$q-5\zeta_{6}q^{2}+(-17+17\zeta_{6})q^{4}+45q^{8}+\cdots$$
441.4.e.b $$2$$ $$26.020$$ $$\Q(\sqrt{-3})$$ None $$-3$$ $$0$$ $$-18$$ $$0$$ $$q-3\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-18\zeta_{6}q^{5}+\cdots$$
441.4.e.c $$2$$ $$26.020$$ $$\Q(\sqrt{-3})$$ None $$-3$$ $$0$$ $$3$$ $$0$$ $$q-3\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+3\zeta_{6}q^{5}+\cdots$$
441.4.e.d $$2$$ $$26.020$$ $$\Q(\sqrt{-3})$$ None $$-3$$ $$0$$ $$18$$ $$0$$ $$q-3\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+18\zeta_{6}q^{5}+\cdots$$
441.4.e.e $$2$$ $$26.020$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$-16$$ $$0$$ $$q-\zeta_{6}q^{2}+(7-7\zeta_{6})q^{4}-2^{4}\zeta_{6}q^{5}+\cdots$$
441.4.e.f $$2$$ $$26.020$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$-12$$ $$0$$ $$q-\zeta_{6}q^{2}+(7-7\zeta_{6})q^{4}-12\zeta_{6}q^{5}+\cdots$$
441.4.e.g $$2$$ $$26.020$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$12$$ $$0$$ $$q-\zeta_{6}q^{2}+(7-7\zeta_{6})q^{4}+12\zeta_{6}q^{5}+\cdots$$
441.4.e.h $$2$$ $$26.020$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$16$$ $$0$$ $$q-\zeta_{6}q^{2}+(7-7\zeta_{6})q^{4}+2^{4}\zeta_{6}q^{5}+\cdots$$
441.4.e.i $$2$$ $$26.020$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+(8-8\zeta_{6})q^{4}-70q^{13}-2^{6}\zeta_{6}q^{16}+\cdots$$
441.4.e.j $$2$$ $$26.020$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+(8-8\zeta_{6})q^{4}+70q^{13}-2^{6}\zeta_{6}q^{16}+\cdots$$
441.4.e.k $$2$$ $$26.020$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$-7$$ $$0$$ $$q+2\zeta_{6}q^{2}+(4-4\zeta_{6})q^{4}-7\zeta_{6}q^{5}+\cdots$$
441.4.e.l $$2$$ $$26.020$$ $$\Q(\sqrt{-3})$$ None $$4$$ $$0$$ $$-18$$ $$0$$ $$q+4\zeta_{6}q^{2}+(-8+8\zeta_{6})q^{4}-18\zeta_{6}q^{5}+\cdots$$
441.4.e.m $$2$$ $$26.020$$ $$\Q(\sqrt{-3})$$ None $$4$$ $$0$$ $$-4$$ $$0$$ $$q+4\zeta_{6}q^{2}+(-8+8\zeta_{6})q^{4}-4\zeta_{6}q^{5}+\cdots$$
441.4.e.n $$2$$ $$26.020$$ $$\Q(\sqrt{-3})$$ None $$4$$ $$0$$ $$4$$ $$0$$ $$q+4\zeta_{6}q^{2}+(-8+8\zeta_{6})q^{4}+4\zeta_{6}q^{5}+\cdots$$
441.4.e.o $$2$$ $$26.020$$ $$\Q(\sqrt{-3})$$ None $$4$$ $$0$$ $$18$$ $$0$$ $$q+4\zeta_{6}q^{2}+(-8+8\zeta_{6})q^{4}+18\zeta_{6}q^{5}+\cdots$$
441.4.e.p $$4$$ $$26.020$$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None $$-3$$ $$0$$ $$-6$$ $$0$$ $$q+(-1-\beta _{1}-\beta _{3})q^{2}+(7\beta _{1}-3\beta _{2}+\cdots)q^{4}+\cdots$$
441.4.e.q $$4$$ $$26.020$$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None $$-3$$ $$0$$ $$6$$ $$0$$ $$q+(-1-\beta _{1}-\beta _{3})q^{2}+(7\beta _{1}-3\beta _{2}+\cdots)q^{4}+\cdots$$
441.4.e.r $$4$$ $$26.020$$ $$\Q(\sqrt{-3}, \sqrt{19})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+11\beta _{2}q^{4}+2\beta _{1}q^{5}+3\beta _{3}q^{8}+\cdots$$
441.4.e.s $$4$$ $$26.020$$ $$\Q(\sqrt{-3}, \sqrt{19})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+11\beta _{2}q^{4}-2\beta _{1}q^{5}+3\beta _{3}q^{8}+\cdots$$
441.4.e.t $$4$$ $$26.020$$ $$\Q(\sqrt{-3}, \sqrt{7})$$ $$\Q(\sqrt{-7})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{2}q^{4}-9\beta _{3}q^{8}+(-10\beta _{1}+\cdots)q^{11}+\cdots$$
441.4.e.u $$4$$ $$26.020$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$2$$ $$0$$ $$-20$$ $$0$$ $$q+(1+\beta _{1}+\beta _{2})q^{2}+(2\beta _{1}-5\beta _{2}+2\beta _{3})q^{4}+\cdots$$
441.4.e.v $$4$$ $$26.020$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$2$$ $$0$$ $$20$$ $$0$$ $$q+(1+\beta _{1}+\beta _{2})q^{2}+(2\beta _{1}-5\beta _{2}+2\beta _{3})q^{4}+\cdots$$
441.4.e.w $$6$$ $$26.020$$ 6.0.9924270768.1 None $$1$$ $$0$$ $$-11$$ $$0$$ $$q+\beta _{1}q^{2}+(-8+\beta _{1}+\beta _{2}+8\beta _{4}+\beta _{5})q^{4}+\cdots$$
441.4.e.x $$8$$ $$26.020$$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}+\beta _{3})q^{2}+(-2-2\beta _{2}-\beta _{6})q^{4}+\cdots$$
441.4.e.y $$8$$ $$26.020$$ 8.0.$$\cdots$$.19 None $$2$$ $$0$$ $$0$$ $$0$$ $$q+(1-\beta _{2}+\beta _{6})q^{2}+(-8-8\beta _{1}+\beta _{6}+\cdots)q^{4}+\cdots$$
441.4.e.z $$16$$ $$26.020$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{2}+(-9+9\beta _{2}+\beta _{7})q^{4}-\beta _{6}q^{5}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(441, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(441, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(7, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(49, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(147, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$1 + 5 T + 17 T^{2} + 40 T^{3} + 64 T^{4}$$)($$1 + 3 T + T^{2} + 24 T^{3} + 64 T^{4}$$)($$1 + 3 T + T^{2} + 24 T^{3} + 64 T^{4}$$)($$1 + 3 T + T^{2} + 24 T^{3} + 64 T^{4}$$)($$1 + T - 7 T^{2} + 8 T^{3} + 64 T^{4}$$)($$1 + T - 7 T^{2} + 8 T^{3} + 64 T^{4}$$)($$1 + T - 7 T^{2} + 8 T^{3} + 64 T^{4}$$)($$1 + T - 7 T^{2} + 8 T^{3} + 64 T^{4}$$)($$1 - 8 T^{2} + 64 T^{4}$$)($$1 - 8 T^{2} + 64 T^{4}$$)($$1 - 2 T - 4 T^{2} - 16 T^{3} + 64 T^{4}$$)($$1 - 4 T + 8 T^{2} - 32 T^{3} + 64 T^{4}$$)($$1 - 4 T + 8 T^{2} - 32 T^{3} + 64 T^{4}$$)($$1 - 4 T + 8 T^{2} - 32 T^{3} + 64 T^{4}$$)($$1 - 4 T + 8 T^{2} - 32 T^{3} + 64 T^{4}$$)($$1 + 3 T + 5 T^{2} - 36 T^{3} - 120 T^{4} - 288 T^{5} + 320 T^{6} + 1536 T^{7} + 4096 T^{8}$$)($$1 + 3 T + 5 T^{2} - 36 T^{3} - 120 T^{4} - 288 T^{5} + 320 T^{6} + 1536 T^{7} + 4096 T^{8}$$)($$1 + 3 T^{2} - 55 T^{4} + 192 T^{6} + 4096 T^{8}$$)($$1 + 3 T^{2} - 55 T^{4} + 192 T^{6} + 4096 T^{8}$$)($$1 - 9 T^{2} + 17 T^{4} - 576 T^{6} + 4096 T^{8}$$)($$1 - 2 T - 11 T^{2} + 2 T^{3} + 129 T^{4} + 16 T^{5} - 704 T^{6} - 1024 T^{7} + 4096 T^{8}$$)($$1 - 2 T - 11 T^{2} + 2 T^{3} + 129 T^{4} + 16 T^{5} - 704 T^{6} - 1024 T^{7} + 4096 T^{8}$$)($$1 - T + T^{2} + 20 T^{3} - 10 T^{4} - 64 T^{5} + 1060 T^{6} - 512 T^{7} - 640 T^{8} + 10240 T^{9} + 4096 T^{10} - 32768 T^{11} + 262144 T^{12}$$)($$1 - 13 T^{2} + 47 T^{4} + 78 T^{6} - 28 T^{8} + 4992 T^{10} + 192512 T^{12} - 3407872 T^{14} + 16777216 T^{16}$$)($$( 1 - T + T^{2} + 16 T^{3} - 72 T^{4} + 128 T^{5} + 64 T^{6} - 512 T^{7} + 4096 T^{8} )^{2}$$)($$( 1 + T^{2} + 33 T^{4} - 160 T^{6} - 3136 T^{8} - 10240 T^{10} + 135168 T^{12} + 262144 T^{14} + 16777216 T^{16} )^{2}$$)
$3$ 1
$5$ ($$1 - 125 T^{2} + 15625 T^{4}$$)($$1 + 18 T + 199 T^{2} + 2250 T^{3} + 15625 T^{4}$$)($$1 - 3 T - 116 T^{2} - 375 T^{3} + 15625 T^{4}$$)($$1 - 18 T + 199 T^{2} - 2250 T^{3} + 15625 T^{4}$$)($$1 + 16 T + 131 T^{2} + 2000 T^{3} + 15625 T^{4}$$)($$1 + 12 T + 19 T^{2} + 1500 T^{3} + 15625 T^{4}$$)($$1 - 12 T + 19 T^{2} - 1500 T^{3} + 15625 T^{4}$$)($$1 - 16 T + 131 T^{2} - 2000 T^{3} + 15625 T^{4}$$)($$1 - 125 T^{2} + 15625 T^{4}$$)($$1 - 125 T^{2} + 15625 T^{4}$$)($$1 + 7 T - 76 T^{2} + 875 T^{3} + 15625 T^{4}$$)($$1 + 18 T + 199 T^{2} + 2250 T^{3} + 15625 T^{4}$$)($$1 + 4 T - 109 T^{2} + 500 T^{3} + 15625 T^{4}$$)($$1 - 4 T - 109 T^{2} - 500 T^{3} + 15625 T^{4}$$)($$1 - 18 T + 199 T^{2} - 2250 T^{3} + 15625 T^{4}$$)($$1 + 6 T - 166 T^{2} - 288 T^{3} + 20679 T^{4} - 36000 T^{5} - 2593750 T^{6} + 11718750 T^{7} + 244140625 T^{8}$$)($$1 - 6 T - 166 T^{2} + 288 T^{3} + 20679 T^{4} + 36000 T^{5} - 2593750 T^{6} - 11718750 T^{7} + 244140625 T^{8}$$)($$1 - 174 T^{2} + 14651 T^{4} - 2718750 T^{6} + 244140625 T^{8}$$)($$1 - 174 T^{2} + 14651 T^{4} - 2718750 T^{6} + 244140625 T^{8}$$)($$( 1 - 125 T^{2} + 15625 T^{4} )^{2}$$)($$1 + 20 T + 148 T^{2} + 40 T^{3} - 2121 T^{4} + 5000 T^{5} + 2312500 T^{6} + 39062500 T^{7} + 244140625 T^{8}$$)($$1 - 20 T + 148 T^{2} - 40 T^{3} - 2121 T^{4} - 5000 T^{5} + 2312500 T^{6} - 39062500 T^{7} + 244140625 T^{8}$$)($$1 + 11 T - 62 T^{2} - 1015 T^{3} - 6040 T^{4} - 54313 T^{5} + 121696 T^{6} - 6789125 T^{7} - 94375000 T^{8} - 1982421875 T^{9} - 15136718750 T^{10} + 335693359375 T^{11} + 3814697265625 T^{12}$$)($$1 - 67 T^{2} - 13939 T^{4} + 859074 T^{6} + 25309934 T^{8} + 13423031250 T^{10} - 3403076171875 T^{12} - 255584716796875 T^{14} + 59604644775390625 T^{16}$$)($$1 - 314 T^{2} + 50562 T^{4} - 5270176 T^{6} + 522562031 T^{8} - 82346500000 T^{10} + 12344238281250 T^{12} - 1197814941406250 T^{14} + 59604644775390625 T^{16}$$)($$( 1 - 116 T^{2} - 18594 T^{4} - 92800 T^{6} + 572811875 T^{8} - 1450000000 T^{10} - 4539550781250 T^{12} - 442504882812500 T^{14} + 59604644775390625 T^{16} )^{2}$$)
$7$ 1
$11$ ($$1 + 68 T + 3293 T^{2} + 90508 T^{3} + 1771561 T^{4}$$)($$1 + 36 T - 35 T^{2} + 47916 T^{3} + 1771561 T^{4}$$)($$1 + 15 T - 1106 T^{2} + 19965 T^{3} + 1771561 T^{4}$$)($$1 + 36 T - 35 T^{2} + 47916 T^{3} + 1771561 T^{4}$$)($$1 + 8 T - 1267 T^{2} + 10648 T^{3} + 1771561 T^{4}$$)($$1 - 20 T - 931 T^{2} - 26620 T^{3} + 1771561 T^{4}$$)($$1 - 20 T - 931 T^{2} - 26620 T^{3} + 1771561 T^{4}$$)($$1 + 8 T - 1267 T^{2} + 10648 T^{3} + 1771561 T^{4}$$)($$1 - 1331 T^{2} + 1771561 T^{4}$$)($$1 - 1331 T^{2} + 1771561 T^{4}$$)($$1 + 5 T - 1306 T^{2} + 6655 T^{3} + 1771561 T^{4}$$)($$1 + 50 T + 1169 T^{2} + 66550 T^{3} + 1771561 T^{4}$$)($$1 - 62 T + 2513 T^{2} - 82522 T^{3} + 1771561 T^{4}$$)($$1 - 62 T + 2513 T^{2} - 82522 T^{3} + 1771561 T^{4}$$)($$1 + 50 T + 1169 T^{2} + 66550 T^{3} + 1771561 T^{4}$$)($$1 + 6 T - 1210 T^{2} - 8496 T^{3} - 266961 T^{4} - 11308176 T^{5} - 2143588810 T^{6} + 14147686146 T^{7} + 3138428376721 T^{8}$$)($$1 + 6 T - 1210 T^{2} - 8496 T^{3} - 266961 T^{4} - 11308176 T^{5} - 2143588810 T^{6} + 14147686146 T^{7} + 3138428376721 T^{8}$$)($$1 - 762 T^{2} - 1190917 T^{4} - 1349929482 T^{6} + 3138428376721 T^{8}$$)($$1 - 762 T^{2} - 1190917 T^{4} - 1349929482 T^{6} + 3138428376721 T^{8}$$)($$1 - 1962 T^{2} + 2077883 T^{4} - 3475802682 T^{6} + 3138428376721 T^{8}$$)($$1 + 20 T - 1210 T^{2} - 21040 T^{3} + 288139 T^{4} - 28004240 T^{5} - 2143588810 T^{6} + 47158953820 T^{7} + 3138428376721 T^{8}$$)($$1 + 20 T - 1210 T^{2} - 21040 T^{3} + 288139 T^{4} - 28004240 T^{5} - 2143588810 T^{6} + 47158953820 T^{7} + 3138428376721 T^{8}$$)($$1 - 35 T - 1400 T^{2} + 113593 T^{3} - 198940 T^{4} - 87110135 T^{5} + 3928586038 T^{6} - 115943589685 T^{7} - 352434345340 T^{8} + 267846352063763 T^{9} - 4393799727409400 T^{10} - 146203685929547785 T^{11} + 5559917313492231481 T^{12}$$)($$1 - 1387 T^{2} + 1086569 T^{4} + 3753113814 T^{6} - 5845598670130 T^{8} + 6648870061443654 T^{10} + 3410118982865360249 T^{12} -$$$$77\!\cdots\!47$$$$T^{14} +$$$$98\!\cdots\!41$$$$T^{16}$$)($$( 1 - 50 T - 202 T^{2} - 2000 T^{3} + 2201743 T^{4} - 2662000 T^{5} - 357855322 T^{6} - 117897384550 T^{7} + 3138428376721 T^{8} )^{2}$$)($$( 1 - 2976 T^{2} + 3122386 T^{4} - 6520618368 T^{6} + 14052541944243 T^{8} - 11551673196632448 T^{10} + 9799384825476376306 T^{12} -$$$$16\!\cdots\!56$$$$T^{14} +$$$$98\!\cdots\!41$$$$T^{16} )^{2}$$)
$13$ ($$( 1 + 2197 T^{2} )^{2}$$)($$( 1 + 34 T + 2197 T^{2} )^{2}$$)($$( 1 - 64 T + 2197 T^{2} )^{2}$$)($$( 1 - 34 T + 2197 T^{2} )^{2}$$)($$( 1 + 28 T + 2197 T^{2} )^{2}$$)($$( 1 - 84 T + 2197 T^{2} )^{2}$$)($$( 1 + 84 T + 2197 T^{2} )^{2}$$)($$( 1 - 28 T + 2197 T^{2} )^{2}$$)($$( 1 + 70 T + 2197 T^{2} )^{2}$$)($$( 1 - 70 T + 2197 T^{2} )^{2}$$)($$( 1 - 14 T + 2197 T^{2} )^{2}$$)($$( 1 - 36 T + 2197 T^{2} )^{2}$$)($$( 1 + 62 T + 2197 T^{2} )^{2}$$)($$( 1 - 62 T + 2197 T^{2} )^{2}$$)($$( 1 + 36 T + 2197 T^{2} )^{2}$$)($$( 1 + 16 T + 2406 T^{2} + 35152 T^{3} + 4826809 T^{4} )^{2}$$)($$( 1 - 16 T + 2406 T^{2} - 35152 T^{3} + 4826809 T^{4} )^{2}$$)($$( 1 - 82 T + 2197 T^{2} )^{4}$$)($$( 1 + 82 T + 2197 T^{2} )^{4}$$)($$( 1 + 2197 T^{2} )^{4}$$)($$( 1 + 104 T + 5848 T^{2} + 228488 T^{3} + 4826809 T^{4} )^{2}$$)($$( 1 - 104 T + 5848 T^{2} - 228488 T^{3} + 4826809 T^{4} )^{2}$$)($$( 1 + 62 T + 7016 T^{2} + 253976 T^{3} + 15414152 T^{4} + 299262158 T^{5} + 10604499373 T^{6} )^{2}$$)($$( 1 + 51 T + 4996 T^{2} + 112047 T^{3} + 4826809 T^{4} )^{4}$$)($$( 1 + 5554 T^{2} + 17209282 T^{4} + 26808097186 T^{6} + 23298085122481 T^{8} )^{2}$$)($$( 1 + 3520 T^{2} + 5818162 T^{4} + 16990367680 T^{6} + 23298085122481 T^{8} )^{4}$$)
$17$ ($$1 - 4913 T^{2} + 24137569 T^{4}$$)($$1 - 42 T - 3149 T^{2} - 206346 T^{3} + 24137569 T^{4}$$)($$1 + 84 T + 2143 T^{2} + 412692 T^{3} + 24137569 T^{4}$$)($$1 + 42 T - 3149 T^{2} + 206346 T^{3} + 24137569 T^{4}$$)($$1 + 54 T - 1997 T^{2} + 265302 T^{3} + 24137569 T^{4}$$)($$1 - 96 T + 4303 T^{2} - 471648 T^{3} + 24137569 T^{4}$$)($$1 + 96 T + 4303 T^{2} + 471648 T^{3} + 24137569 T^{4}$$)($$1 - 54 T - 1997 T^{2} - 265302 T^{3} + 24137569 T^{4}$$)($$1 - 4913 T^{2} + 24137569 T^{4}$$)($$1 - 4913 T^{2} + 24137569 T^{4}$$)($$1 - 21 T - 4472 T^{2} - 103173 T^{3} + 24137569 T^{4}$$)($$1 + 126 T + 10963 T^{2} + 619038 T^{3} + 24137569 T^{4}$$)($$1 - 84 T + 2143 T^{2} - 412692 T^{3} + 24137569 T^{4}$$)($$1 + 84 T + 2143 T^{2} + 412692 T^{3} + 24137569 T^{4}$$)($$1 - 126 T + 10963 T^{2} - 619038 T^{3} + 24137569 T^{4}$$)($$1 - 6 T - 9742 T^{2} + 288 T^{3} + 71294847 T^{4} + 1414944 T^{5} - 235148197198 T^{6} - 711527258982 T^{7} + 582622237229761 T^{8}$$)($$1 + 6 T - 9742 T^{2} - 288 T^{3} + 71294847 T^{4} - 1414944 T^{5} - 235148197198 T^{6} + 711527258982 T^{7} + 582622237229761 T^{8}$$)($$1 - 3670 T^{2} - 10668669 T^{4} - 88584878230 T^{6} + 582622237229761 T^{8}$$)($$1 - 3670 T^{2} - 10668669 T^{4} - 88584878230 T^{6} + 582622237229761 T^{8}$$)($$( 1 - 4913 T^{2} + 24137569 T^{4} )^{2}$$)($$1 + 116 T + 4316 T^{2} - 79576 T^{3} - 6707297 T^{4} - 390956888 T^{5} + 104177747804 T^{6} + 13756193673652 T^{7} + 582622237229761 T^{8}$$)($$1 - 116 T + 4316 T^{2} + 79576 T^{3} - 6707297 T^{4} + 390956888 T^{5} + 104177747804 T^{6} - 13756193673652 T^{7} + 582622237229761 T^{8}$$)($$1 + 48 T - 10035 T^{2} - 125232 T^{3} + 74409318 T^{4} - 234420432 T^{5} - 437742983351 T^{6} - 1151707582416 T^{7} + 1796060047467942 T^{8} - 14850996949472304 T^{9} - 5846614150600651635 T^{10} +$$$$13\!\cdots\!64$$$$T^{11} +$$$$14\!\cdots\!09$$$$T^{12}$$)($$1 - 4256 T^{2} - 33515774 T^{4} - 14275356032 T^{6} + 1645746688812355 T^{8} - 344572391221966208 T^{10} -$$$$19\!\cdots\!14$$$$T^{12} -$$$$59\!\cdots\!04$$$$T^{14} +$$$$33\!\cdots\!21$$$$T^{16}$$)($$1 - 5088 T^{2} + 14421310 T^{4} + 187282685952 T^{6} - 1076010335607741 T^{8} + 4520548754671730688 T^{10} +$$$$84\!\cdots\!10$$$$T^{12} -$$$$71\!\cdots\!92$$$$T^{14} +$$$$33\!\cdots\!21$$$$T^{16}$$)($$( 1 - 9156 T^{2} + 34006030 T^{4} - 14202494208 T^{6} - 123470262255309 T^{8} - 342813683917700352 T^{10} +$$$$19\!\cdots\!30$$$$T^{12} -$$$$12\!\cdots\!04$$$$T^{14} +$$$$33\!\cdots\!21$$$$T^{16} )^{2}$$)
$19$ ($$1 - 6859 T^{2} + 47045881 T^{4}$$)($$1 - 124 T + 8517 T^{2} - 850516 T^{3} + 47045881 T^{4}$$)($$1 + 16 T - 6603 T^{2} + 109744 T^{3} + 47045881 T^{4}$$)($$1 + 124 T + 8517 T^{2} + 850516 T^{3} + 47045881 T^{4}$$)($$1 + 110 T + 5241 T^{2} + 754490 T^{3} + 47045881 T^{4}$$)($$1 - 12 T - 6715 T^{2} - 82308 T^{3} + 47045881 T^{4}$$)($$1 + 12 T - 6715 T^{2} + 82308 T^{3} + 47045881 T^{4}$$)($$1 - 110 T + 5241 T^{2} - 754490 T^{3} + 47045881 T^{4}$$)($$( 1 - 107 T + 6859 T^{2} )( 1 + 163 T + 6859 T^{2} )$$)($$( 1 - 163 T + 6859 T^{2} )( 1 + 107 T + 6859 T^{2} )$$)($$1 - 49 T - 4458 T^{2} - 336091 T^{3} + 47045881 T^{4}$$)($$1 + 72 T - 1675 T^{2} + 493848 T^{3} + 47045881 T^{4}$$)($$1 + 100 T + 3141 T^{2} + 685900 T^{3} + 47045881 T^{4}$$)($$1 - 100 T + 3141 T^{2} - 685900 T^{3} + 47045881 T^{4}$$)($$1 - 72 T - 1675 T^{2} - 493848 T^{3} + 47045881 T^{4}$$)($$1 - 64 T - 2438 T^{2} + 459776 T^{3} - 32447189 T^{4} + 3153603584 T^{5} - 114697857878 T^{6} - 20652012657856 T^{7} + 2213314919066161 T^{8}$$)($$1 + 64 T - 2438 T^{2} - 459776 T^{3} - 32447189 T^{4} - 3153603584 T^{5} - 114697857878 T^{6} + 20652012657856 T^{7} + 2213314919066161 T^{8}$$)($$( 1 - 20 T - 6459 T^{2} - 137180 T^{3} + 47045881 T^{4} )^{2}$$)($$( 1 + 20 T - 6459 T^{2} + 137180 T^{3} + 47045881 T^{4} )^{2}$$)($$( 1 - 6859 T^{2} + 47045881 T^{4} )^{2}$$)($$1 - 192 T + 14898 T^{2} - 1583616 T^{3} + 182609099 T^{4} - 10862022144 T^{5} + 700889535138 T^{6} - 61956037973568 T^{7} + 2213314919066161 T^{8}$$)($$1 + 192 T + 14898 T^{2} + 1583616 T^{3} + 182609099 T^{4} + 10862022144 T^{5} + 700889535138 T^{6} + 61956037973568 T^{7} + 2213314919066161 T^{8}$$)($$1 + 202 T + 7946 T^{2} + 627636 T^{3} + 247297462 T^{4} + 17185599794 T^{5} + 349471935958 T^{6} + 117876028987046 T^{7} + 11634326968854022 T^{8} + 202530415883220444 T^{9} + 17587000346899715306 T^{10} +$$$$30\!\cdots\!98$$$$T^{11} +$$$$10\!\cdots\!41$$$$T^{12}$$)($$( 1 - 111 T + 1361 T^{2} + 306138 T^{3} - 11434020 T^{4} + 2099800542 T^{5} + 64029444041 T^{6} - 35818334453469 T^{7} + 2213314919066161 T^{8} )^{2}$$)($$1 - 12690 T^{2} + 28454938 T^{4} - 488430486000 T^{6} + 7788364400899983 T^{8} - 22978642521128166000 T^{10} +$$$$62\!\cdots\!18$$$$T^{12} -$$$$13\!\cdots\!90$$$$T^{14} +$$$$48\!\cdots\!21$$$$T^{16}$$)($$( 1 - 4356 T^{2} - 79768406 T^{4} - 20261411280 T^{6} + 6644210001103587 T^{8} - 953215943970937680 T^{10} -$$$$17\!\cdots\!66$$$$T^{12} -$$$$45\!\cdots\!96$$$$T^{14} +$$$$48\!\cdots\!21$$$$T^{16} )^{2}$$)
$23$ ($$1 + 40 T - 10567 T^{2} + 486680 T^{3} + 148035889 T^{4}$$)($$1 - 12167 T^{2} + 148035889 T^{4}$$)($$1 + 84 T - 5111 T^{2} + 1022028 T^{3} + 148035889 T^{4}$$)($$1 - 12167 T^{2} + 148035889 T^{4}$$)($$1 - 48 T - 9863 T^{2} - 584016 T^{3} + 148035889 T^{4}$$)($$1 + 176 T + 18809 T^{2} + 2141392 T^{3} + 148035889 T^{4}$$)($$1 + 176 T + 18809 T^{2} + 2141392 T^{3} + 148035889 T^{4}$$)($$1 - 48 T - 9863 T^{2} - 584016 T^{3} + 148035889 T^{4}$$)($$1 - 12167 T^{2} + 148035889 T^{4}$$)($$1 - 12167 T^{2} + 148035889 T^{4}$$)($$1 + 159 T + 13114 T^{2} + 1934553 T^{3} + 148035889 T^{4}$$)($$1 - 14 T - 11971 T^{2} - 170338 T^{3} + 148035889 T^{4}$$)($$1 + 42 T - 10403 T^{2} + 511014 T^{3} + 148035889 T^{4}$$)($$1 + 42 T - 10403 T^{2} + 511014 T^{3} + 148035889 T^{4}$$)($$1 - 14 T - 11971 T^{2} - 170338 T^{3} + 148035889 T^{4}$$)($$1 - 6 T - 7834 T^{2} + 98784 T^{3} - 86537001 T^{4} + 1201904928 T^{5} - 1159713154426 T^{6} - 10806915968778 T^{7} + 21914624432020321 T^{8}$$)($$1 - 6 T - 7834 T^{2} + 98784 T^{3} - 86537001 T^{4} + 1201904928 T^{5} - 1159713154426 T^{6} - 10806915968778 T^{7} + 21914624432020321 T^{8}$$)($$1 - 7234 T^{2} - 95705133 T^{4} - 1070891621026 T^{6} + 21914624432020321 T^{8}$$)($$1 - 7234 T^{2} - 95705133 T^{4} - 1070891621026 T^{6} + 21914624432020321 T^{8}$$)($$1 + 22734 T^{2} + 368798867 T^{4} + 3365447900526 T^{6} + 21914624432020321 T^{8}$$)($$1 - 28 T - 22178 T^{2} + 38416 T^{3} + 369678627 T^{4} + 467407472 T^{5} - 3283139946242 T^{6} - 50432274520964 T^{7} + 21914624432020321 T^{8}$$)($$1 - 28 T - 22178 T^{2} + 38416 T^{3} + 369678627 T^{4} + 467407472 T^{5} - 3283139946242 T^{6} - 50432274520964 T^{7} + 21914624432020321 T^{8}$$)($$1 - 216 T + 10827 T^{2} - 387864 T^{3} + 53856198 T^{4} + 24653558952 T^{5} - 5413409425505 T^{6} + 299959851768984 T^{7} + 7972650149090022 T^{8} - 698602275885685032 T^{9} +$$$$23\!\cdots\!67$$$$T^{10} -$$$$57\!\cdots\!12$$$$T^{11} +$$$$32\!\cdots\!69$$$$T^{12}$$)($$1 - 8216 T^{2} + 118915282 T^{4} + 2854931863264 T^{6} - 29264182010625629 T^{8} +$$$$42\!\cdots\!96$$$$T^{10} +$$$$26\!\cdots\!22$$$$T^{12} -$$$$26\!\cdots\!04$$$$T^{14} +$$$$48\!\cdots\!41$$$$T^{16}$$)($$( 1 - 176 T - 62 T^{2} - 1179904 T^{3} + 438436563 T^{4} - 14355891968 T^{5} - 9178225118 T^{6} - 317002868417488 T^{7} + 21914624432020321 T^{8} )^{2}$$)($$( 1 - 42656 T^{2} + 1068581538 T^{4} - 19403404789120 T^{6} + 272659097396223779 T^{8} -$$$$28\!\cdots\!80$$$$T^{10} +$$$$23\!\cdots\!98$$$$T^{12} -$$$$13\!\cdots\!64$$$$T^{14} +$$$$48\!\cdots\!41$$$$T^{16} )^{2}$$)
$29$ ($$( 1 - 166 T + 24389 T^{2} )^{2}$$)($$( 1 + 102 T + 24389 T^{2} )^{2}$$)($$( 1 - 297 T + 24389 T^{2} )^{2}$$)($$( 1 + 102 T + 24389 T^{2} )^{2}$$)($$( 1 - 110 T + 24389 T^{2} )^{2}$$)($$( 1 + 58 T + 24389 T^{2} )^{2}$$)($$( 1 + 58 T + 24389 T^{2} )^{2}$$)($$( 1 - 110 T + 24389 T^{2} )^{2}$$)($$( 1 + 24389 T^{2} )^{2}$$)($$( 1 + 24389 T^{2} )^{2}$$)($$( 1 + 58 T + 24389 T^{2} )^{2}$$)($$( 1 + 158 T + 24389 T^{2} )^{2}$$)($$( 1 - 10 T + 24389 T^{2} )^{2}$$)($$( 1 - 10 T + 24389 T^{2} )^{2}$$)($$( 1 + 158 T + 24389 T^{2} )^{2}$$)($$( 1 - 252 T + 56446 T^{2} - 6146028 T^{3} + 594823321 T^{4} )^{2}$$)($$( 1 - 252 T + 56446 T^{2} - 6146028 T^{3} + 594823321 T^{4} )^{2}$$)($$( 1 - 10806 T^{2} + 594823321 T^{4} )^{2}$$)($$( 1 - 10806 T^{2} + 594823321 T^{4} )^{2}$$)($$( 1 - 21222 T^{2} + 594823321 T^{4} )^{2}$$)($$( 1 + 296 T + 62994 T^{2} + 7219144 T^{3} + 594823321 T^{4} )^{2}$$)($$( 1 + 296 T + 62994 T^{2} + 7219144 T^{3} + 594823321 T^{4} )^{2}$$)($$( 1 + 53 T + 52695 T^{2} + 3410210 T^{3} + 1285178355 T^{4} + 31525636013 T^{5} + 14507145975869 T^{6} )^{2}$$)($$( 1 + 59371 T^{2} + 1802370044 T^{4} + 35315255391091 T^{6} + 353814783205469041 T^{8} )^{2}$$)($$( 1 + 130 T + 49818 T^{2} + 3170570 T^{3} + 594823321 T^{4} )^{4}$$)($$( 1 + 44468 T^{2} + 996014662 T^{4} + 26450603438228 T^{6} + 353814783205469041 T^{8} )^{4}$$)
$31$ ($$1 - 29791 T^{2} + 887503681 T^{4}$$)($$1 - 160 T - 4191 T^{2} - 4766560 T^{3} + 887503681 T^{4}$$)($$1 + 253 T + 34218 T^{2} + 7537123 T^{3} + 887503681 T^{4}$$)($$1 + 160 T - 4191 T^{2} + 4766560 T^{3} + 887503681 T^{4}$$)($$1 - 12 T - 29647 T^{2} - 357492 T^{3} + 887503681 T^{4}$$)($$1 + 264 T + 39905 T^{2} + 7864824 T^{3} + 887503681 T^{4}$$)($$1 - 264 T + 39905 T^{2} - 7864824 T^{3} + 887503681 T^{4}$$)($$1 + 12 T - 29647 T^{2} + 357492 T^{3} + 887503681 T^{4}$$)($$( 1 + 19 T + 29791 T^{2} )( 1 + 289 T + 29791 T^{2} )$$)($$( 1 - 289 T + 29791 T^{2} )( 1 - 19 T + 29791 T^{2} )$$)($$1 - 147 T - 8182 T^{2} - 4379277 T^{3} + 887503681 T^{4}$$)($$1 + 36 T - 28495 T^{2} + 1072476 T^{3} + 887503681 T^{4}$$)($$1 - 48 T - 27487 T^{2} - 1429968 T^{3} + 887503681 T^{4}$$)($$1 + 48 T - 27487 T^{2} + 1429968 T^{3} + 887503681 T^{4}$$)($$1 - 36 T - 28495 T^{2} - 1072476 T^{3} + 887503681 T^{4}$$)($$1 - 40 T + 15490 T^{2} + 2938880 T^{3} - 742237181 T^{4} + 87552174080 T^{5} + 13747432018690 T^{6} - 1057584886426840 T^{7} + 787662783788549761 T^{8}$$)($$1 + 40 T + 15490 T^{2} - 2938880 T^{3} - 742237181 T^{4} - 87552174080 T^{5} + 13747432018690 T^{6} + 1057584886426840 T^{7} + 787662783788549761 T^{8}$$)($$( 1 + 156 T - 5455 T^{2} + 4647396 T^{3} + 887503681 T^{4} )^{2}$$)($$( 1 - 156 T - 5455 T^{2} - 4647396 T^{3} + 887503681 T^{4} )^{2}$$)($$( 1 - 29791 T^{2} + 887503681 T^{4} )^{2}$$)($$1 + 104 T - 46470 T^{2} - 238784 T^{3} + 2071962659 T^{4} - 7113614144 T^{5} - 41242296056070 T^{6} + 2749720704709784 T^{7} + 787662783788549761 T^{8}$$)($$1 - 104 T - 46470 T^{2} + 238784 T^{3} + 2071962659 T^{4} + 7113614144 T^{5} - 41242296056070 T^{6} - 2749720704709784 T^{7} + 787662783788549761 T^{8}$$)($$1 + 95 T - 70347 T^{2} - 3756594 T^{3} + 3398738767 T^{4} + 83374434539 T^{5} - 110906046363338 T^{6} + 2483807779351349 T^{7} + 3016393166469901327 T^{8} - 99322925971043714574 T^{9} -$$$$55\!\cdots\!67$$$$T^{10} +$$$$22\!\cdots\!45$$$$T^{11} +$$$$69\!\cdots\!41$$$$T^{12}$$)($$( 1 - 110 T - 31207 T^{2} + 1790250 T^{3} + 627521468 T^{4} + 53333337750 T^{5} - 27696327372967 T^{6} - 2908358437673810 T^{7} + 787662783788549761 T^{8} )^{2}$$)($$1 - 19060 T^{2} + 373250298 T^{4} + 34021605583600 T^{6} - 1109978980966458157 T^{8} +$$$$30\!\cdots\!00$$$$T^{10} +$$$$29\!\cdots\!78$$$$T^{12} -$$$$13\!\cdots\!60$$$$T^{14} +$$$$62\!\cdots\!21$$$$T^{16}$$)($$( 1 - 99700 T^{2} + 5723391738 T^{4} - 243436582730000 T^{6} + 8171014984493980883 T^{8} -$$$$21\!\cdots\!00$$$$T^{10} +$$$$45\!\cdots\!18$$$$T^{12} -$$$$69\!\cdots\!00$$$$T^{14} +$$$$62\!\cdots\!21$$$$T^{16} )^{2}$$)
$37$ ($$1 + 450 T + 151847 T^{2} + 22793850 T^{3} + 2565726409 T^{4}$$)($$1 + 398 T + 107751 T^{2} + 20159894 T^{3} + 2565726409 T^{4}$$)($$1 - 316 T + 49203 T^{2} - 16006348 T^{3} + 2565726409 T^{4}$$)($$1 + 398 T + 107751 T^{2} + 20159894 T^{3} + 2565726409 T^{4}$$)($$1 - 246 T + 9863 T^{2} - 12460638 T^{3} + 2565726409 T^{4}$$)($$1 + 258 T + 15911 T^{2} + 13068474 T^{3} + 2565726409 T^{4}$$)($$1 + 258 T + 15911 T^{2} + 13068474 T^{3} + 2565726409 T^{4}$$)($$1 - 246 T + 9863 T^{2} - 12460638 T^{3} + 2565726409 T^{4}$$)($$( 1 - 323 T + 50653 T^{2} )( 1 + 433 T + 50653 T^{2} )$$)($$( 1 - 323 T + 50653 T^{2} )( 1 + 433 T + 50653 T^{2} )$$)($$1 + 219 T - 2692 T^{2} + 11093007 T^{3} + 2565726409 T^{4}$$)($$1 - 162 T - 24409 T^{2} - 8205786 T^{3} + 2565726409 T^{4}$$)($$1 - 246 T + 9863 T^{2} - 12460638 T^{3} + 2565726409 T^{4}$$)($$1 - 246 T + 9863 T^{2} - 12460638 T^{3} + 2565726409 T^{4}$$)($$1 - 162 T - 24409 T^{2} - 8205786 T^{3} + 2565726409 T^{4}$$)($$1 - 248 T - 36710 T^{2} + 766816 T^{3} + 3964901275 T^{4} + 38841530848 T^{5} - 94187816474390 T^{6} - 32230511469179096 T^{7} + 6582952005840035281 T^{8}$$)($$1 - 248 T - 36710 T^{2} + 766816 T^{3} + 3964901275 T^{4} + 38841530848 T^{5} - 94187816474390 T^{6} - 32230511469179096 T^{7} + 6582952005840035281 T^{8}$$)($$( 1 + 186 T - 16057 T^{2} + 9421458 T^{3} + 2565726409 T^{4} )^{2}$$)($$( 1 + 186 T - 16057 T^{2} + 9421458 T^{3} + 2565726409 T^{4} )^{2}$$)($$( 1 - 450 T + 151847 T^{2} - 22793850 T^{3} + 2565726409 T^{4} )^{2}$$)($$1 - 248 T - 50570 T^{2} - 2670464 T^{3} + 6879492955 T^{4} - 135267012992 T^{5} - 129748784503130 T^{6} - 32230511469179096 T^{7} + 6582952005840035281 T^{8}$$)($$1 - 248 T - 50570 T^{2} - 2670464 T^{3} + 6879492955 T^{4} - 135267012992 T^{5} - 129748784503130 T^{6} - 32230511469179096 T^{7} + 6582952005840035281 T^{8}$$)($$1 + 262 T - 97404 T^{2} - 9678072 T^{3} + 12194182072 T^{4} + 680381910454 T^{5} - 605701122868778 T^{6} + 34463384910226462 T^{7} + 31286934978284739448 T^{8} -$$$$12\!\cdots\!44$$$$T^{9} -$$$$64\!\cdots\!24$$$$T^{10} +$$$$87\!\cdots\!66$$$$T^{11} +$$$$16\!\cdots\!29$$$$T^{12}$$)($$( 1 - 187 T - 44923 T^{2} + 4004418 T^{3} + 2045720498 T^{4} + 202835784954 T^{5} - 115260127471507 T^{6} - 24302845341679399 T^{7} + 6582952005840035281 T^{8} )^{2}$$)($$( 1 + 106 T - 92294 T^{2} + 235744 T^{3} + 7583597383 T^{4} + 11941140832 T^{5} - 236801153192246 T^{6} + 13775944418278162 T^{7} + 6582952005840035281 T^{8} )^{2}$$)($$( 1 + 16 T - 8810 T^{2} - 1475840 T^{3} - 2496501221 T^{4} - 74755723520 T^{5} - 22604049663290 T^{6} + 2079387836721232 T^{7} + 6582952005840035281 T^{8} )^{4}$$)
$41$ ($$( 1 + 68921 T^{2} )^{2}$$)($$( 1 - 318 T + 68921 T^{2} )^{2}$$)($$( 1 - 360 T + 68921 T^{2} )^{2}$$)($$( 1 + 318 T + 68921 T^{2} )^{2}$$)($$( 1 - 182 T + 68921 T^{2} )^{2}$$)($$( 1 + 68921 T^{2} )^{2}$$)($$( 1 + 68921 T^{2} )^{2}$$)($$( 1 + 182 T + 68921 T^{2} )^{2}$$)($$( 1 + 68921 T^{2} )^{2}$$)($$( 1 + 68921 T^{2} )^{2}$$)($$( 1 - 350 T + 68921 T^{2} )^{2}$$)($$( 1 + 270 T + 68921 T^{2} )^{2}$$)($$( 1 - 248 T + 68921 T^{2} )^{2}$$)($$( 1 + 248 T + 68921 T^{2} )^{2}$$)($$( 1 - 270 T + 68921 T^{2} )^{2}$$)($$( 1 + 450 T + 175642 T^{2} + 31014450 T^{3} + 4750104241 T^{4} )^{2}$$)($$( 1 - 450 T + 175642 T^{2} - 31014450 T^{3} + 4750104241 T^{4} )^{2}$$)($$( 1 + 110406 T^{2} + 4750104241 T^{4} )^{2}$$)($$( 1 + 110406 T^{2} + 4750104241 T^{4} )^{2}$$)($$( 1 + 68921 T^{2} )^{4}$$)($$( 1 - 20 T + 42020 T^{2} - 1378420 T^{3} + 4750104241 T^{4} )^{2}$$)($$( 1 + 20 T + 42020 T^{2} + 1378420 T^{3} + 4750104241 T^{4} )^{2}$$)($$( 1 - 244 T + 187983 T^{2} - 33933832 T^{3} + 12955976343 T^{4} - 1159025434804 T^{5} + 327381934393961 T^{6} )^{2}$$)($$( 1 + 85540 T^{2} + 8435951270 T^{4} + 406323916775140 T^{6} + 22563490300366186081 T^{8} )^{2}$$)($$( 1 + 208848 T^{2} + 19595539298 T^{4} + 992049770524368 T^{6} + 22563490300366186081 T^{8} )^{2}$$)($$( 1 + 42420 T^{2} + 6386007458 T^{4} + 201499421903220 T^{6} + 22563490300366186081 T^{8} )^{4}$$)
$43$ ($$( 1 + 180 T + 79507 T^{2} )^{2}$$)($$( 1 + 268 T + 79507 T^{2} )^{2}$$)($$( 1 - 26 T + 79507 T^{2} )^{2}$$)($$( 1 + 268 T + 79507 T^{2} )^{2}$$)($$( 1 - 128 T + 79507 T^{2} )^{2}$$)($$( 1 - 156 T + 79507 T^{2} )^{2}$$)($$( 1 - 156 T + 79507 T^{2} )^{2}$$)($$( 1 - 128 T + 79507 T^{2} )^{2}$$)($$( 1 + 520 T + 79507 T^{2} )^{2}$$)($$( 1 + 520 T + 79507 T^{2} )^{2}$$)($$( 1 + 124 T + 79507 T^{2} )^{2}$$)($$( 1 + 324 T + 79507 T^{2} )^{2}$$)($$( 1 - 68 T + 79507 T^{2} )^{2}$$)($$( 1 - 68 T + 79507 T^{2} )^{2}$$)($$( 1 + 324 T + 79507 T^{2} )^{2}$$)($$( 1 - 376 T + 161526 T^{2} - 29894632 T^{3} + 6321363049 T^{4} )^{2}$$)($$( 1 - 376 T + 161526 T^{2} - 29894632 T^{3} + 6321363049 T^{4} )^{2}$$)($$( 1 - 164 T + 79507 T^{2} )^{4}$$)($$( 1 - 164 T + 79507 T^{2} )^{4}$$)($$( 1 - 180 T + 79507 T^{2} )^{4}$$)($$( 1 + 720 T + 268614 T^{2} + 57245040 T^{3} + 6321363049 T^{4} )^{2}$$)($$( 1 + 720 T + 268614 T^{2} + 57245040 T^{3} + 6321363049 T^{4} )^{2}$$)($$( 1 - 360 T + 166158 T^{2} - 38975294 T^{3} + 13210724106 T^{4} - 2275690697640 T^{5} + 502592611936843 T^{6} )^{2}$$)($$( 1 + 419 T + 167730 T^{2} + 33313433 T^{3} + 6321363049 T^{4} )^{4}$$)($$( 1 - 270 T + 97614 T^{2} - 21466890 T^{3} + 6321363049 T^{4} )^{4}$$)($$( 1 - 540 T + 167814 T^{2} - 42933780 T^{3} + 6321363049 T^{4} )^{8}$$)
$47$ ($$1 - 103823 T^{2} + 10779215329 T^{4}$$)($$1 - 240 T - 46223 T^{2} - 24917520 T^{3} + 10779215329 T^{4}$$)($$1 - 30 T - 102923 T^{2} - 3114690 T^{3} + 10779215329 T^{4}$$)($$1 + 240 T - 46223 T^{2} + 24917520 T^{3} + 10779215329 T^{4}$$)($$1 + 324 T + 1153 T^{2} + 33638652 T^{3} + 10779215329 T^{4}$$)($$1 - 408 T + 62641 T^{2} - 42359784 T^{3} + 10779215329 T^{4}$$)($$1 + 408 T + 62641 T^{2} + 42359784 T^{3} + 10779215329 T^{4}$$)($$1 - 324 T + 1153 T^{2} - 33638652 T^{3} + 10779215329 T^{4}$$)($$1 - 103823 T^{2} + 10779215329 T^{4}$$)($$1 - 103823 T^{2} + 10779215329 T^{4}$$)($$1 + 525 T + 171802 T^{2} + 54507075 T^{3} + 10779215329 T^{4}$$)($$1 - 72 T - 98639 T^{2} - 7475256 T^{3} + 10779215329 T^{4}$$)($$1 - 324 T + 1153 T^{2} - 33638652 T^{3} + 10779215329 T^{4}$$)($$1 + 324 T + 1153 T^{2} + 33638652 T^{3} + 10779215329 T^{4}$$)($$1 + 72 T - 98639 T^{2} + 7475256 T^{3} + 10779215329 T^{4}$$)($$1 - 12 T - 141646 T^{2} + 790272 T^{3} + 9310238259 T^{4} + 82048409856 T^{5} - 1526832734491534 T^{6} - 13429565677233204 T^{7} +$$$$11\!\cdots\!41$$$$T^{8}$$)($$1 + 12 T - 141646 T^{2} - 790272 T^{3} + 9310238259 T^{4} - 82048409856 T^{5} - 1526832734491534 T^{6} + 13429565677233204 T^{7} +$$$$11\!\cdots\!41$$$$T^{8}$$)($$1 + 13970 T^{2} - 10584054429 T^{4} + 150585638146130 T^{6} +$$$$11\!\cdots\!41$$$$T^{8}$$)($$1 + 13970 T^{2} - 10584054429 T^{4} + 150585638146130 T^{6} +$$$$11\!\cdots\!41$$$$T^{8}$$)($$( 1 - 103823 T^{2} + 10779215329 T^{4} )^{2}$$)($$1 - 96 T - 75734 T^{2} + 11778816 T^{3} - 4519545597 T^{4} + 1222912013568 T^{5} - 816353093726486 T^{6} - 107436525417865632 T^{7} +$$$$11\!\cdots\!41$$$$T^{8}$$)($$1 + 96 T - 75734 T^{2} - 11778816 T^{3} - 4519545597 T^{4} - 1222912013568 T^{5} - 816353093726486 T^{6} + 107436525417865632 T^{7} +$$$$11\!\cdots\!41$$$$T^{8}$$)($$1 - 210 T - 20853 T^{2} + 83809446 T^{3} - 12756928590 T^{4} - 2596137940074 T^{5} + 3698984470026571 T^{6} - 269538829352302902 T^{7} -$$$$13\!\cdots\!10$$$$T^{8} +$$$$93\!\cdots\!82$$$$T^{9} -$$$$24\!\cdots\!73$$$$T^{10} -$$$$25\!\cdots\!30$$$$T^{11} +$$$$12\!\cdots\!89$$$$T^{12}$$)($$1 - 279692 T^{2} + 37152412138 T^{4} - 5458685013243056 T^{6} +$$$$72\!\cdots\!79$$$$T^{8} -$$$$58\!\cdots\!24$$$$T^{10} +$$$$43\!\cdots\!58$$$$T^{12} -$$$$35\!\cdots\!88$$$$T^{14} +$$$$13\!\cdots\!81$$$$T^{16}$$)($$1 - 228052 T^{2} + 17880021370 T^{4} - 2866445491787152 T^{6} +$$$$48\!\cdots\!99$$$$T^{8} -$$$$30\!\cdots\!08$$$$T^{10} +$$$$20\!\cdots\!70$$$$T^{12} -$$$$28\!\cdots\!28$$$$T^{14} +$$$$13\!\cdots\!81$$$$T^{16}$$)($$( 1 - 80164 T^{2} - 7810995302 T^{4} + 586894148427440 T^{6} + 17238037152042764179 T^{8} +$$$$63\!\cdots\!60$$$$T^{10} -$$$$90\!\cdots\!82$$$$T^{12} -$$$$10\!\cdots\!96$$$$T^{14} +$$$$13\!\cdots\!81$$$$T^{16} )^{2}$$)
$53$ ($$1 - 590 T + 199223 T^{2} - 87837430 T^{3} + 22164361129 T^{4}$$)($$1 + 498 T + 99127 T^{2} + 74140746 T^{3} + 22164361129 T^{4}$$)($$1 - 363 T - 17108 T^{2} - 54042351 T^{3} + 22164361129 T^{4}$$)($$1 + 498 T + 99127 T^{2} + 74140746 T^{3} + 22164361129 T^{4}$$)($$1 + 162 T - 122633 T^{2} + 24118074 T^{3} + 22164361129 T^{4}$$)($$1 + 722 T + 372407 T^{2} + 107489194 T^{3} + 22164361129 T^{4}$$)($$1 + 722 T + 372407 T^{2} + 107489194 T^{3} + 22164361129 T^{4}$$)($$1 + 162 T - 122633 T^{2} + 24118074 T^{3} + 22164361129 T^{4}$$)($$1 - 148877 T^{2} + 22164361129 T^{4}$$)($$1 - 148877 T^{2} + 22164361129 T^{4}$$)($$1 - 303 T - 57068 T^{2} - 45109731 T^{3} + 22164361129 T^{4}$$)($$1 + 22 T - 148393 T^{2} + 3275294 T^{3} + 22164361129 T^{4}$$)($$1 - 258 T - 82313 T^{2} - 38410266 T^{3} + 22164361129 T^{4}$$)($$1 - 258 T - 82313 T^{2} - 38410266 T^{3} + 22164361129 T^{4}$$)($$1 + 22 T - 148393 T^{2} + 3275294 T^{3} + 22164361129 T^{4}$$)($$1 + 1104 T + 616586 T^{2} + 336141504 T^{3} + 159062942139 T^{4} + 50043738691008 T^{5} + 13666234771085594 T^{6} + 3642939005349554832 T^{7} +$$$$49\!\cdots\!41$$$$T^{8}$$)($$1 + 1104 T + 616586 T^{2} + 336141504 T^{3} + 159062942139 T^{4} + 50043738691008 T^{5} + 13666234771085594 T^{6} + 3642939005349554832 T^{7} +$$$$49\!\cdots\!41$$$$T^{8}$$)($$1 - 273130 T^{2} + 52435635771 T^{4} - 6053751955163770 T^{6} +$$$$49\!\cdots\!41$$$$T^{8}$$)($$1 - 273130 T^{2} + 52435635771 T^{4} - 6053751955163770 T^{6} +$$$$49\!\cdots\!41$$$$T^{8}$$)($$1 - 50346 T^{2} - 19629641413 T^{4} - 1115886925400634 T^{6} +$$$$49\!\cdots\!41$$$$T^{8}$$)($$1 - 268 T + 15314 T^{2} + 64653392 T^{3} - 29663922677 T^{4} + 9625403040784 T^{5} + 339425026329506 T^{6} - 884336642602971644 T^{7} +$$$$49\!\cdots\!41$$$$T^{8}$$)($$1 - 268 T + 15314 T^{2} + 64653392 T^{3} - 29663922677 T^{4} + 9625403040784 T^{5} + 339425026329506 T^{6} - 884336642602971644 T^{7} +$$$$49\!\cdots\!41$$$$T^{8}$$)($$1 - 393 T - 211446 T^{2} + 23899125 T^{3} + 46453564620 T^{4} + 3425920762143 T^{5} - 9724787230272680 T^{6} + 510040805305563411 T^{7} +$$$$10\!\cdots\!80$$$$T^{8} +$$$$78\!\cdots\!25$$$$T^{9} -$$$$10\!\cdots\!86$$$$T^{10} -$$$$28\!\cdots\!01$$$$T^{11} +$$$$10\!\cdots\!89$$$$T^{12}$$)($$1 - 574307 T^{2} + 203127896557 T^{4} - 47306765339926238 T^{6} +$$$$82\!\cdots\!02$$$$T^{8} -$$$$10\!\cdots\!02$$$$T^{10} +$$$$99\!\cdots\!37$$$$T^{12} -$$$$62\!\cdots\!23$$$$T^{14} +$$$$24\!\cdots\!81$$$$T^{16}$$)($$( 1 - 8 T - 276646 T^{2} + 168352 T^{3} + 54394534843 T^{4} + 25063740704 T^{5} - 6131681848893334 T^{6} - 26398108734417064 T^{7} +$$$$49\!\cdots\!41$$$$T^{8} )^{2}$$)($$( 1 - 462132 T^{2} + 115859058586 T^{4} - 24667776438964560 T^{6} +$$$$43\!\cdots\!07$$$$T^{8} -$$$$54\!\cdots\!40$$$$T^{10} +$$$$56\!\cdots\!26$$$$T^{12} -$$$$50\!\cdots\!48$$$$T^{14} +$$$$24\!\cdots\!81$$$$T^{16} )^{2}$$)
$59$ ($$1 - 205379 T^{2} + 42180533641 T^{4}$$)($$1 + 132 T - 187955 T^{2} + 27110028 T^{3} + 42180533641 T^{4}$$)($$1 - 15 T - 205154 T^{2} - 3080685 T^{3} + 42180533641 T^{4}$$)($$1 - 132 T - 187955 T^{2} - 27110028 T^{3} + 42180533641 T^{4}$$)($$1 + 810 T + 450721 T^{2} + 166356990 T^{3} + 42180533641 T^{4}$$)($$1 + 492 T + 36685 T^{2} + 101046468 T^{3} + 42180533641 T^{4}$$)($$1 - 492 T + 36685 T^{2} - 101046468 T^{3} + 42180533641 T^{4}$$)($$1 - 810 T + 450721 T^{2} - 166356990 T^{3} + 42180533641 T^{4}$$)($$1 - 205379 T^{2} + 42180533641 T^{4}$$)($$1 - 205379 T^{2} + 42180533641 T^{4}$$)($$1 - 105 T - 194354 T^{2} - 21564795 T^{3} + 42180533641 T^{4}$$)($$1 + 468 T + 13645 T^{2} + 96117372 T^{3} + 42180533641 T^{4}$$)($$1 - 120 T - 190979 T^{2} - 24645480 T^{3} + 42180533641 T^{4}$$)($$1 + 120 T - 190979 T^{2} + 24645480 T^{3} + 42180533641 T^{4}$$)($$1 - 468 T + 13645 T^{2} - 96117372 T^{3} + 42180533641 T^{4}$$)($$1 + 804 T + 265802 T^{2} - 24235776 T^{3} - 30073788309 T^{4} - 4977519439104 T^{5} + 11211670202845082 T^{6} + 6965048638198570956 T^{7} +$$$$17\!\cdots\!81$$$$T^{8}$$)($$1 - 804 T + 265802 T^{2} + 24235776 T^{3} - 30073788309 T^{4} + 4977519439104 T^{5} + 11211670202845082 T^{6} - 6965048638198570956 T^{7} +$$$$17\!\cdots\!81$$$$T^{8}$$)($$1 - 386134 T^{2} + 106918932315 T^{4} - 16287338176933894 T^{6} +$$$$17\!\cdots\!81$$$$T^{8}$$)($$1 - 386134 T^{2} + 106918932315 T^{4} - 16287338176933894 T^{6} +$$$$17\!\cdots\!81$$$$T^{8}$$)($$( 1 - 205379 T^{2} + 42180533641 T^{4} )^{2}$$)($$1 - 616 T - 24014 T^{2} + 4489408 T^{3} + 42675213435 T^{4} + 922030125632 T^{5} - 1012923334854974 T^{6} - 5336405424291442424 T^{7} +$$$$17\!\cdots\!81$$$$T^{8}$$)($$1 + 616 T - 24014 T^{2} - 4489408 T^{3} + 42675213435 T^{4} - 922030125632 T^{5} - 1012923334854974 T^{6} + 5336405424291442424 T^{7} +$$$$17\!\cdots\!81$$$$T^{8}$$)($$1 + 1143 T + 557208 T^{2} + 118327563 T^{3} - 14314666608 T^{4} - 27063102119841 T^{5} - 16891447327378130 T^{6} - 5558192850270824739 T^{7} -$$$$60\!\cdots\!28$$$$T^{8} +$$$$10\!\cdots\!57$$$$T^{9} +$$$$99\!\cdots\!48$$$$T^{10} +$$$$41\!\cdots\!57$$$$T^{11} +$$$$75\!\cdots\!21$$$$T^{12}$$)($$1 - 615851 T^{2} + 202986056233 T^{4} - 56612306828303786 T^{6} +$$$$13\!\cdots\!02$$$$T^{8} -$$$$23\!\cdots\!26$$$$T^{10} +$$$$36\!\cdots\!73$$$$T^{12} -$$$$46\!\cdots\!71$$$$T^{14} +$$$$31\!\cdots\!61$$$$T^{16}$$)($$1 - 632162 T^{2} + 222723302586 T^{4} - 58503068402380912 T^{6} +$$$$12\!\cdots\!79$$$$T^{8} -$$$$24\!\cdots\!92$$$$T^{10} +$$$$39\!\cdots\!66$$$$T^{12} -$$$$47\!\cdots\!02$$$$T^{14} +$$$$31\!\cdots\!61$$$$T^{16}$$)($$( 1 - 590420 T^{2} + 179680625322 T^{4} - 49922422154834320 T^{6} +$$$$12\!\cdots\!03$$$$T^{8} -$$$$21\!\cdots\!20$$$$T^{10} +$$$$31\!\cdots\!82$$$$T^{12} -$$$$44\!\cdots\!20$$$$T^{14} +$$$$31\!\cdots\!61$$$$T^{16} )^{2}$$)
$61$ ($$1 - 226981 T^{2} + 51520374361 T^{4}$$)($$1 + 398 T - 68577 T^{2} + 90338438 T^{3} + 51520374361 T^{4}$$)($$1 + 118 T - 213057 T^{2} + 26783758 T^{3} + 51520374361 T^{4}$$)($$1 - 398 T - 68577 T^{2} - 90338438 T^{3} + 51520374361 T^{4}$$)($$1 + 488 T + 11163 T^{2} + 110766728 T^{3} + 51520374361 T^{4}$$)($$1 + 492 T + 15083 T^{2} + 111674652 T^{3} + 51520374361 T^{4}$$)($$1 - 492 T + 15083 T^{2} - 111674652 T^{3} + 51520374361 T^{4}$$)($$1 - 488 T + 11163 T^{2} - 110766728 T^{3} + 51520374361 T^{4}$$)($$( 1 - 719 T + 226981 T^{2} )( 1 + 901 T + 226981 T^{2} )$$)($$( 1 - 901 T + 226981 T^{2} )( 1 + 719 T + 226981 T^{2} )$$)($$1 + 413 T - 56412 T^{2} + 93743153 T^{3} + 51520374361 T^{4}$$)($$1 - 792 T + 400283 T^{2} - 179768952 T^{3} + 51520374361 T^{4}$$)($$1 + 622 T + 159903 T^{2} + 141182182 T^{3} + 51520374361 T^{4}$$)($$1 - 622 T + 159903 T^{2} - 141182182 T^{3} + 51520374361 T^{4}$$)($$1 + 792 T + 400283 T^{2} + 179768952 T^{3} + 51520374361 T^{4}$$)($$1 + 428 T - 242702 T^{2} - 12016528 T^{3} + 88279223131 T^{4} - 2727523541968 T^{5} - 12504097898163422 T^{6} + 5005094527733012348 T^{7} +$$$$26\!\cdots\!21$$$$T^{8}$$)($$1 - 428 T - 242702 T^{2} + 12016528 T^{3} + 88279223131 T^{4} + 2727523541968 T^{5} - 12504097898163422 T^{6} - 5005094527733012348 T^{7} +$$$$26\!\cdots\!21$$$$T^{8}$$)($$( 1 + 790 T + 397119 T^{2} + 179314990 T^{3} + 51520374361 T^{4} )^{2}$$)($$( 1 - 790 T + 397119 T^{2} - 179314990 T^{3} + 51520374361 T^{4} )^{2}$$)($$( 1 - 226981 T^{2} + 51520374361 T^{4} )^{2}$$)($$1 - 16 T - 453752 T^{2} - 736 T^{3} + 154544782567 T^{4} - 167058016 T^{5} - 23377472907052472 T^{6} - 187106337485346256 T^{7} +$$$$26\!\cdots\!21$$$$T^{8}$$)($$1 + 16 T - 453752 T^{2} + 736 T^{3} + 154544782567 T^{4} + 167058016 T^{5} - 23377472907052472 T^{6} + 187106337485346256 T^{7} +$$$$26\!\cdots\!21$$$$T^{8}$$)($$1 + 70 T - 335143 T^{2} + 129510330 T^{3} + 42145697866 T^{4} - 25171752927730 T^{5} - 316289217432887 T^{6} - 5713509651289083130 T^{7} +$$$$21\!\cdots\!26$$$$T^{8} +$$$$15\!\cdots\!30$$$$T^{9} -$$$$88\!\cdots\!03$$$$T^{10} +$$$$42\!\cdots\!70$$$$T^{11} +$$$$13\!\cdots\!81$$$$T^{12}$$)($$( 1 - 666 T - 19198 T^{2} - 5855472 T^{3} + 61942105719 T^{4} - 1329080890032 T^{5} - 989088146982478 T^{6} - 7788301297827537906 T^{7} +$$$$26\!\cdots\!21$$$$T^{8} )^{2}$$)($$1 - 547658 T^{2} + 149331839266 T^{4} - 26044805552482208 T^{6} +$$$$45\!\cdots\!79$$$$T^{8} -$$$$13\!\cdots\!88$$$$T^{10} +$$$$39\!\cdots\!86$$$$T^{12} -$$$$74\!\cdots\!98$$$$T^{14} +$$$$70\!\cdots\!41$$$$T^{16}$$)($$( 1 - 162080 T^{2} + 51803982478 T^{4} + 20839404361984000 T^{6} -$$$$33\!\cdots\!37$$$$T^{8} +$$$$10\!\cdots\!00$$$$T^{10} +$$$$13\!\cdots\!38$$$$T^{12} -$$$$22\!\cdots\!80$$$$T^{14} +$$$$70\!\cdots\!41$$$$T^{16} )^{2}$$)
$67$ ($$1 - 740 T + 246837 T^{2} - 222564620 T^{3} + 90458382169 T^{4}$$)($$1 + 92 T - 292299 T^{2} + 27670196 T^{3} + 90458382169 T^{4}$$)($$1 - 370 T - 163863 T^{2} - 111282310 T^{3} + 90458382169 T^{4}$$)($$1 + 92 T - 292299 T^{2} + 27670196 T^{3} + 90458382169 T^{4}$$)($$1 + 244 T - 241227 T^{2} + 73386172 T^{3} + 90458382169 T^{4}$$)($$1 + 412 T - 131019 T^{2} + 123914356 T^{3} + 90458382169 T^{4}$$)($$1 + 412 T - 131019 T^{2} + 123914356 T^{3} + 90458382169 T^{4}$$)($$1 + 244 T - 241227 T^{2} + 73386172 T^{3} + 90458382169 T^{4}$$)($$( 1 - 1007 T + 300763 T^{2} )( 1 + 127 T + 300763 T^{2} )$$)($$( 1 - 1007 T + 300763 T^{2} )( 1 + 127 T + 300763 T^{2} )$$)($$1 + 415 T - 128538 T^{2} + 124816645 T^{3} + 90458382169 T^{4}$$)($$1 + 232 T - 246939 T^{2} + 69777016 T^{3} + 90458382169 T^{4}$$)($$1 + 904 T + 516453 T^{2} + 271889752 T^{3} + 90458382169 T^{4}$$)($$1 + 904 T + 516453 T^{2} + 271889752 T^{3} + 90458382169 T^{4}$$)($$1 + 232 T - 246939 T^{2} + 69777016 T^{3} + 90458382169 T^{4}$$)($$1 + 148 T - 418886 T^{2} - 23788928 T^{3} + 97249529179 T^{4} - 7154829352064 T^{5} - 37891749873243734 T^{6} + 4026567090651652156 T^{7} +$$$$81\!\cdots\!61$$$$T^{8}$$)($$1 + 148 T - 418886 T^{2} - 23788928 T^{3} + 97249529179 T^{4} - 7154829352064 T^{5} - 37891749873243734 T^{6} + 4026567090651652156 T^{7} +$$$$81\!\cdots\!61$$$$T^{8}$$)($$( 1 - 44 T - 298827 T^{2} - 13233572 T^{3} + 90458382169 T^{4} )^{2}$$)($$( 1 - 44 T - 298827 T^{2} - 13233572 T^{3} + 90458382169 T^{4} )^{2}$$)($$( 1 - 740 T + 246837 T^{2} - 222564620 T^{3} + 90458382169 T^{4} )^{2}$$)($$1 - 144 T - 36822 T^{2} + 78331392 T^{3} - 93382080373 T^{4} + 23559184452096 T^{5} - 3330858548226918 T^{6} - 3917740953066472368 T^{7} +$$$$81\!\cdots\!61$$$$T^{8}$$)($$1 - 144 T - 36822 T^{2} + 78331392 T^{3} - 93382080373 T^{4} + 23559184452096 T^{5} - 3330858548226918 T^{6} - 3917740953066472368 T^{7} +$$$$81\!\cdots\!61$$$$T^{8}$$)($$1 - 628 T - 202942 T^{2} + 436381932 T^{3} - 77667044702 T^{4} - 73528811914784 T^{5} + 76060129771959310 T^{6} - 22114746057926180192 T^{7} -$$$$70\!\cdots\!38$$$$T^{8} +$$$$11\!\cdots\!04$$$$T^{9} -$$$$16\!\cdots\!62$$$$T^{10} -$$$$15\!\cdots\!04$$$$T^{11} +$$$$74\!\cdots\!09$$$$T^{12}$$)($$( 1 + 945 T + 85661 T^{2} + 194516910 T^{3} + 292789368252 T^{4} + 58503489402330 T^{5} + 7748755474978709 T^{6} + 25710175004498724915 T^{7} +$$$$81\!\cdots\!61$$$$T^{8} )^{2}$$)($$( 1 - 972 T + 200922 T^{2} - 138350592 T^{3} + 178716222683 T^{4} - 41610739101696 T^{5} + 18175079062159818 T^{6} - 26444751433198688484 T^{7} +$$$$81\!\cdots\!61$$$$T^{8} )^{2}$$)($$( 1 - 345126 T^{2} + 28653573707 T^{4} - 31219539604458294 T^{6} +$$$$81\!\cdots\!61$$$$T^{8} )^{4}$$)
$71$ ($$( 1 + 688 T + 357911 T^{2} )^{2}$$)($$( 1 - 720 T + 357911 T^{2} )^{2}$$)($$( 1 - 342 T + 357911 T^{2} )^{2}$$)($$( 1 - 720 T + 357911 T^{2} )^{2}$$)($$( 1 - 768 T + 357911 T^{2} )^{2}$$)($$( 1 + 296 T + 357911 T^{2} )^{2}$$)($$( 1 + 296 T + 357911 T^{2} )^{2}$$)($$( 1 - 768 T + 357911 T^{2} )^{2}$$)($$( 1 + 357911 T^{2} )^{2}$$)($$( 1 + 357911 T^{2} )^{2}$$)($$( 1 - 432 T + 357911 T^{2} )^{2}$$)($$( 1 - 734 T + 357911 T^{2} )^{2}$$)($$( 1 - 678 T + 357911 T^{2} )^{2}$$)($$( 1 - 678 T + 357911 T^{2} )^{2}$$)($$( 1 - 734 T + 357911 T^{2} )^{2}$$)($$( 1 + 954 T + 930526 T^{2} + 341447094 T^{3} + 128100283921 T^{4} )^{2}$$)($$( 1 + 954 T + 930526 T^{2} + 341447094 T^{3} + 128100283921 T^{4} )^{2}$$)($$( 1 + 518146 T^{2} + 128100283921 T^{4} )^{2}$$)($$( 1 + 518146 T^{2} + 128100283921 T^{4} )^{2}$$)($$( 1 - 242478 T^{2} + 128100283921 T^{4} )^{2}$$)($$( 1 + 988 T + 852210 T^{2} + 353616068 T^{3} + 128100283921 T^{4} )^{2}$$)($$( 1 + 988 T + 852210 T^{2} + 353616068 T^{3} + 128100283921 T^{4} )^{2}$$)($$( 1 + 318 T + 742929 T^{2} + 256167372 T^{3} + 265902461319 T^{4} + 40735890286878 T^{5} + 45848500718449031 T^{6} )^{2}$$)($$( 1 + 874364 T^{2} + 392544633894 T^{4} + 112006276650301244 T^{6} +$$$$16\!\cdots\!41$$$$T^{8} )^{2}$$)($$( 1 + 1124 T + 1018926 T^{2} + 402291964 T^{3} + 128100283921 T^{4} )^{4}$$)($$( 1 + 472256 T^{2} + 269755485790 T^{4} + 60496127683395776 T^{6} +$$$$16\!\cdots\!41$$$$T^{8} )^{4}$$)
$73$ ($$1 - 389017 T^{2} + 151334226289 T^{4}$$)($$1 - 502 T - 137013 T^{2} - 195286534 T^{3} + 151334226289 T^{4}$$)($$1 - 362 T - 257973 T^{2} - 140824154 T^{3} + 151334226289 T^{4}$$)($$1 + 502 T - 137013 T^{2} + 195286534 T^{3} + 151334226289 T^{4}$$)($$1 + 702 T + 103787 T^{2} + 273089934 T^{3} + 151334226289 T^{4}$$)($$1 - 240 T - 331417 T^{2} - 93364080 T^{3} + 151334226289 T^{4}$$)($$1 + 240 T - 331417 T^{2} + 93364080 T^{3} + 151334226289 T^{4}$$)($$1 - 702 T + 103787 T^{2} - 273089934 T^{3} + 151334226289 T^{4}$$)($$( 1 + 271 T + 389017 T^{2} )( 1 + 919 T + 389017 T^{2} )$$)($$( 1 - 919 T + 389017 T^{2} )( 1 - 271 T + 389017 T^{2} )$$)($$1 + 1113 T + 849752 T^{2} + 432975921 T^{3} + 151334226289 T^{4}$$)($$1 - 180 T - 356617 T^{2} - 70023060 T^{3} + 151334226289 T^{4}$$)($$1 - 642 T + 23147 T^{2} - 249748914 T^{3} + 151334226289 T^{4}$$)($$1 + 642 T + 23147 T^{2} + 249748914 T^{3} + 151334226289 T^{4}$$)($$1 + 180 T - 356617 T^{2} + 70023060 T^{3} + 151334226289 T^{4}$$)($$1 - 1072 T + 85906 T^{2} - 305781568 T^{3} + 532173766867 T^{4} - 118954228238656 T^{5} + 13000518043582834 T^{6} - 63110340951263202736 T^{7} +$$$$22\!\cdots\!21$$$$T^{8}$$)($$1 + 1072 T + 85906 T^{2} + 305781568 T^{3} + 532173766867 T^{4} + 118954228238656 T^{5} + 13000518043582834 T^{6} + 63110340951263202736 T^{7} +$$$$22\!\cdots\!21$$$$T^{8}$$)($$( 1 + 126 T - 373141 T^{2} + 49016142 T^{3} + 151334226289 T^{4} )^{2}$$)($$( 1 - 126 T - 373141 T^{2} - 49016142 T^{3} + 151334226289 T^{4} )^{2}$$)($$( 1 - 389017 T^{2} + 151334226289 T^{4} )^{2}$$)($$1 - 104 T - 448320 T^{2} + 33165392 T^{3} + 55264032335 T^{4} + 12901901299664 T^{5} - 67846160329884480 T^{6} - 6122645017659862952 T^{7} +$$$$22\!\cdots\!21$$$$T^{8}$$)($$1 + 104 T - 448320 T^{2} - 33165392 T^{3} + 55264032335 T^{4} - 12901901299664 T^{5} - 67846160329884480 T^{6} + 6122645017659862952 T^{7} +$$$$22\!\cdots\!21$$$$T^{8}$$)($$1 - 988 T - 186552 T^{2} + 102237300 T^{3} + 281568890272 T^{4} + 16988127696596 T^{5} - 164639785652996186 T^{6} + 6608670472146686132 T^{7} +$$$$42\!\cdots\!08$$$$T^{8} +$$$$60\!\cdots\!00$$$$T^{9} -$$$$42\!\cdots\!92$$$$T^{10} -$$$$88\!\cdots\!16$$$$T^{11} +$$$$34\!\cdots\!69$$$$T^{12}$$)($$( 1 - 875 T - 201451 T^{2} - 165411750 T^{3} + 486060622862 T^{4} - 64347982749750 T^{5} - 30486431220145339 T^{6} - 51512638369734423875 T^{7} +$$$$22\!\cdots\!21$$$$T^{8} )^{2}$$)($$1 - 1279312 T^{2} + 931531176990 T^{4} - 514845763213402112 T^{6} +$$$$22\!\cdots\!79$$$$T^{8} -$$$$77\!\cdots\!68$$$$T^{10} +$$$$21\!\cdots\!90$$$$T^{12} -$$$$44\!\cdots\!28$$$$T^{14} +$$$$52\!\cdots\!41$$$$T^{16}$$)($$( 1 - 1020400 T^{2} + 494889934878 T^{4} - 248628391103897600 T^{6} +$$$$11\!\cdots\!63$$$$T^{8} -$$$$37\!\cdots\!00$$$$T^{10} +$$$$11\!\cdots\!38$$$$T^{12} -$$$$35\!\cdots\!00$$$$T^{14} +$$$$52\!\cdots\!41$$$$T^{16} )^{2}$$)
$79$ ($$1 - 1384 T + 1422417 T^{2} - 682365976 T^{3} + 243087455521 T^{4}$$)($$1 - 1024 T + 555537 T^{2} - 504871936 T^{3} + 243087455521 T^{4}$$)($$1 + 467 T - 274950 T^{2} + 230249213 T^{3} + 243087455521 T^{4}$$)($$1 - 1024 T + 555537 T^{2} - 504871936 T^{3} + 243087455521 T^{4}$$)($$1 + 440 T - 299439 T^{2} + 216937160 T^{3} + 243087455521 T^{4}$$)($$1 + 776 T + 109137 T^{2} + 382598264 T^{3} + 243087455521 T^{4}$$)($$1 + 776 T + 109137 T^{2} + 382598264 T^{3} + 243087455521 T^{4}$$)($$1 + 440 T - 299439 T^{2} + 216937160 T^{3} + 243087455521 T^{4}$$)($$( 1 - 503 T + 493039 T^{2} )( 1 + 1387 T + 493039 T^{2} )$$)($$( 1 - 503 T + 493039 T^{2} )( 1 + 1387 T + 493039 T^{2} )$$)($$1 - 103 T - 482430 T^{2} - 50783017 T^{3} + 243087455521 T^{4}$$)($$1 + 236 T - 437343 T^{2} + 116357204 T^{3} + 243087455521 T^{4}$$)($$1 + 740 T + 54561 T^{2} + 364848860 T^{3} + 243087455521 T^{4}$$)($$1 + 740 T + 54561 T^{2} + 364848860 T^{3} + 243087455521 T^{4}$$)($$1 + 236 T - 437343 T^{2} + 116357204 T^{3} + 243087455521 T^{4}$$)($$1 - 572 T - 574478 T^{2} + 48285952 T^{3} + 408592434547 T^{4} + 23806857488128 T^{5} - 139648395272793038 T^{6} - 68555112902057678468 T^{7} +$$$$59\!\cdots\!41$$$$T^{8}$$)($$1 - 572 T - 574478 T^{2} + 48285952 T^{3} + 408592434547 T^{4} + 23806857488128 T^{5} - 139648395272793038 T^{6} - 68555112902057678468 T^{7} +$$$$59\!\cdots\!41$$$$T^{8}$$)($$( 1 - 712 T + 13905 T^{2} - 351043768 T^{3} + 243087455521 T^{4} )^{2}$$)($$( 1 - 712 T + 13905 T^{2} - 351043768 T^{3} + 243087455521 T^{4} )^{2}$$)($$( 1 - 1384 T + 1422417 T^{2} - 682365976 T^{3} + 243087455521 T^{4} )^{2}$$)($$1 - 944 T - 206334 T^{2} - 105154048 T^{3} + 521988143075 T^{4} - 51845046671872 T^{5} - 50157207047470014 T^{6} -$$$$11\!\cdots\!36$$$$T^{7} +$$$$59\!\cdots\!41$$$$T^{8}$$)($$1 - 944 T - 206334 T^{2} - 105154048 T^{3} + 521988143075 T^{4} - 51845046671872 T^{5} - 50157207047470014 T^{6} -$$$$11\!\cdots\!36$$$$T^{7} +$$$$59\!\cdots\!41$$$$T^{8}$$)($$1 + 861 T - 479895 T^{2} - 258646666 T^{3} + 325257480351 T^{4} - 27564282842211 T^{5} - 246706047980056146 T^{6} - 13590266448240869229 T^{7} +$$$$79\!\cdots\!71$$$$T^{8} -$$$$30\!\cdots\!54$$$$T^{9} -$$$$28\!\cdots\!95$$$$T^{10} +$$$$25\!\cdots\!39$$$$T^{11} +$$$$14\!\cdots\!61$$$$T^{12}$$)($$( 1 + 4 T - 900953 T^{2} - 340436 T^{3} + 568649794816 T^{4} - 167848225004 T^{5} - 219010372314011513 T^{6} + 479406383930473276 T^{7} +$$$$59\!\cdots\!41$$$$T^{8} )^{2}$$)($$( 1 - 524 T - 205806 T^{2} + 264984704 T^{3} - 147697266061 T^{4} + 130647793475456 T^{5} - 50028856870954926 T^{6} - 62802236294891999156 T^{7} +$$$$59\!\cdots\!41$$$$T^{8} )^{2}$$)($$( 1 + 1348 T + 502386 T^{2} + 443006720 T^{3} + 589492824947 T^{4} + 218419590222080 T^{5} + 122123734429373106 T^{6} +$$$$16\!\cdots\!12$$$$T^{7} +$$$$59\!\cdots\!41$$$$T^{8} )^{4}$$)
$83$ ($$( 1 + 571787 T^{2} )^{2}$$)($$( 1 - 204 T + 571787 T^{2} )^{2}$$)($$( 1 - 477 T + 571787 T^{2} )^{2}$$)($$( 1 + 204 T + 571787 T^{2} )^{2}$$)($$( 1 + 1302 T + 571787 T^{2} )^{2}$$)($$( 1 - 924 T + 571787 T^{2} )^{2}$$)($$( 1 + 924 T + 571787 T^{2} )^{2}$$)($$( 1 - 1302 T + 571787 T^{2} )^{2}$$)($$( 1 + 571787 T^{2} )^{2}$$)($$( 1 + 571787 T^{2} )^{2}$$)($$( 1 - 1092 T + 571787 T^{2} )^{2}$$)($$( 1 - 36 T + 571787 T^{2} )^{2}$$)($$( 1 + 468 T + 571787 T^{2} )^{2}$$)($$( 1 - 468 T + 571787 T^{2} )^{2}$$)($$( 1 + 36 T + 571787 T^{2} )^{2}$$)($$( 1 - 1944 T + 1957030 T^{2} - 1111553928 T^{3} + 326940373369 T^{4} )^{2}$$)($$( 1 + 1944 T + 1957030 T^{2} + 1111553928 T^{3} + 326940373369 T^{4} )^{2}$$)($$( 1 - 1001450 T^{2} + 326940373369 T^{4} )^{2}$$)($$( 1 - 1001450 T^{2} + 326940373369 T^{4} )^{2}$$)($$( 1 + 571787 T^{2} )^{4}$$)($$( 1 - 1016 T + 1388838 T^{2} - 580935592 T^{3} + 326940373369 T^{4} )^{2}$$)($$( 1 + 1016 T + 1388838 T^{2} + 580935592 T^{3} + 326940373369 T^{4} )^{2}$$)($$( 1 - 519 T + 1583745 T^{2} - 545598870 T^{3} + 905564802315 T^{4} - 169682053778511 T^{5} + 186940255267540403 T^{6} )^{2}$$)($$( 1 + 1482323 T^{2} + 1051851285456 T^{4} + 484631235073456187 T^{6} +$$$$10\!\cdots\!61$$$$T^{8} )^{2}$$)($$( 1 + 2275682 T^{2} + 1948536513034 T^{4} + 744012322749112658 T^{6} +$$$$10\!\cdots\!61$$$$T^{8} )^{2}$$)($$( 1 + 367916 T^{2} + 118793240278 T^{4} + 120286594408429004 T^{6} +$$$$10\!\cdots\!61$$$$T^{8} )^{4}$$)
$89$ ($$1 - 704969 T^{2} + 496981290961 T^{4}$$)($$1 - 354 T - 579653 T^{2} - 249559026 T^{3} + 496981290961 T^{4}$$)($$1 + 906 T + 115867 T^{2} + 638701914 T^{3} + 496981290961 T^{4}$$)($$1 + 354 T - 579653 T^{2} + 249559026 T^{3} + 496981290961 T^{4}$$)($$1 + 730 T - 172069 T^{2} + 514627370 T^{3} + 496981290961 T^{4}$$)($$1 - 744 T - 151433 T^{2} - 524496936 T^{3} + 496981290961 T^{4}$$)($$1 + 744 T - 151433 T^{2} + 524496936 T^{3} + 496981290961 T^{4}$$)($$1 - 730 T - 172069 T^{2} - 514627370 T^{3} + 496981290961 T^{4}$$)($$1 - 704969 T^{2} + 496981290961 T^{4}$$)($$1 - 704969 T^{2} + 496981290961 T^{4}$$)($$1 - 329 T - 596728 T^{2} - 231934801 T^{3} + 496981290961 T^{4}$$)($$1 + 234 T - 650213 T^{2} + 164962746 T^{3} + 496981290961 T^{4}$$)($$1 - 200 T - 664969 T^{2} - 140993800 T^{3} + 496981290961 T^{4}$$)($$1 + 200 T - 664969 T^{2} + 140993800 T^{3} + 496981290961 T^{4}$$)($$1 - 234 T - 650213 T^{2} - 164962746 T^{3} + 496981290961 T^{4}$$)($$1 + 366 T - 1022134 T^{2} - 92908368 T^{3} + 745127969775 T^{4} - 65497519280592 T^{5} - 507981474855130774 T^{6} +$$$$12\!\cdots\!94$$$$T^{7} +$$$$24\!\cdots\!21$$$$T^{8}$$)($$1 - 366 T - 1022134 T^{2} + 92908368 T^{3} + 745127969775 T^{4} + 65497519280592 T^{5} - 507981474855130774 T^{6} -$$$$12\!\cdots\!94$$$$T^{7} +$$$$24\!\cdots\!21$$$$T^{8}$$)($$1 + 709626 T^{2} + 6587768915 T^{4} + 352670845579490586 T^{6} +$$$$24\!\cdots\!21$$$$T^{8}$$)($$1 + 709626 T^{2} + 6587768915 T^{4} + 352670845579490586 T^{6} +$$$$24\!\cdots\!21$$$$T^{8}$$)($$( 1 - 704969 T^{2} + 496981290961 T^{4} )^{2}$$)($$1 - 388 T - 1067188 T^{2} + 74575928 T^{3} + 879761079727 T^{4} + 52573717386232 T^{5} - 530372469938087668 T^{6} -$$$$13\!\cdots\!92$$$$T^{7} +$$$$24\!\cdots\!21$$$$T^{8}$$)($$1 + 388 T - 1067188 T^{2} - 74575928 T^{3} + 879761079727 T^{4} - 52573717386232 T^{5} - 530372469938087668 T^{6} +$$$$13\!\cdots\!92$$$$T^{7} +$$$$24\!\cdots\!21$$$$T^{8}$$)($$1 + 1766 T + 725929 T^{2} - 728159446 T^{3} - 335534377858 T^{4} + 846551335831238 T^{5} + 1249625385561159997 T^{6} +$$$$59\!\cdots\!22$$$$T^{7} -$$$$16\!\cdots\!38$$$$T^{8} -$$$$25\!\cdots\!14$$$$T^{9} +$$$$17\!\cdots\!09$$$$T^{10} +$$$$30\!\cdots\!34$$$$T^{11} +$$$$12\!\cdots\!81$$$$T^{12}$$)($$1 - 627904 T^{2} - 652647550942 T^{4} - 33246513557593344 T^{6} +$$$$65\!\cdots\!67$$$$T^{8} -$$$$16\!\cdots\!84$$$$T^{10} -$$$$16\!\cdots\!82$$$$T^{12} -$$$$77\!\cdots\!24$$$$T^{14} +$$$$61\!\cdots\!41$$$$T^{16}$$)($$1 + 804000 T^{2} - 70725036962 T^{4} - 222564522147840000 T^{6} -$$$$53\!\cdots\!77$$$$T^{8} -$$$$11\!\cdots\!00$$$$T^{10} -$$$$17\!\cdots\!02$$$$T^{12} +$$$$98\!\cdots\!00$$$$T^{14} +$$$$61\!\cdots\!41$$$$T^{16}$$)($$( 1 - 2588100 T^{2} + 4029765216622 T^{4} - 4333860957429273600 T^{6} +$$$$35\!\cdots\!63$$$$T^{8} -$$$$21\!\cdots\!00$$$$T^{10} +$$$$99\!\cdots\!62$$$$T^{12} -$$$$31\!\cdots\!00$$$$T^{14} +$$$$61\!\cdots\!41$$$$T^{16} )^{2}$$)
$97$ ($$( 1 + 912673 T^{2} )^{2}$$)($$( 1 + 286 T + 912673 T^{2} )^{2}$$)($$( 1 + 503 T + 912673 T^{2} )^{2}$$)($$( 1 - 286 T + 912673 T^{2} )^{2}$$)($$( 1 + 294 T + 912673 T^{2} )^{2}$$)($$( 1 - 168 T + 912673 T^{2} )^{2}$$)($$( 1 + 168 T + 912673 T^{2} )^{2}$$)($$( 1 - 294 T + 912673 T^{2} )^{2}$$)($$( 1 + 1330 T + 912673 T^{2} )^{2}$$)($$( 1 - 1330 T + 912673 T^{2} )^{2}$$)($$( 1 - 882 T + 912673 T^{2} )^{2}$$)($$( 1 + 468 T + 912673 T^{2} )^{2}$$)($$( 1 + 1266 T + 912673 T^{2} )^{2}$$)($$( 1 - 1266 T + 912673 T^{2} )^{2}$$)($$( 1 - 468 T + 912673 T^{2} )^{2}$$)($$( 1 + 808 T + 903054 T^{2} + 737439784 T^{3} + 832972004929 T^{4} )^{2}$$)($$( 1 - 808 T + 903054 T^{2} - 737439784 T^{3} + 832972004929 T^{4} )^{2}$$)($$( 1 - 798 T + 912673 T^{2} )^{4}$$)($$( 1 + 798 T + 912673 T^{2} )^{4}$$)($$( 1 + 912673 T^{2} )^{4}$$)($$( 1 + 488 T + 1167280 T^{2} + 445384424 T^{3} + 832972004929 T^{4} )^{2}$$)($$( 1 - 488 T + 1167280 T^{2} - 445384424 T^{3} + 832972004929 T^{4} )^{2}$$)($$( 1 + 19 T + 2168419 T^{2} - 10094878 T^{3} + 1979057473987 T^{4} + 15826468093651 T^{5} + 760231058654565217 T^{6} )^{2}$$)($$( 1 + 1505 T + 1992044 T^{2} + 1373572865 T^{3} + 832972004929 T^{4} )^{4}$$)($$( 1 + 567808 T^{2} + 211724872834 T^{4} + 472968168174725632 T^{6} +$$$$69\!\cdots\!41$$$$T^{8} )^{2}$$)($$( 1 + 2268304 T^{2} + 2510084445826 T^{4} + 1889433730668470416 T^{6} +$$$$69\!\cdots\!41$$$$T^{8} )^{4}$$)
show more
show less