Properties

Label 1.40.a.a.1.2
Level $1$
Weight $40$
Character 1.1
Self dual yes
Analytic conductor $9.634$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 40 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(9.63395513897\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: \(\mathbb{Q}[x]/(x^{3} - \cdots)\)
Defining polynomial: \(x^{3} - 175630027 x - 142249227846\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{10}\cdot 3^{5}\cdot 5\cdot 13 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-812.996\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+241488. q^{2} -3.14962e9 q^{3} -4.91439e11 q^{4} +5.36221e13 q^{5} -7.60595e14 q^{6} +1.82084e16 q^{7} -2.51436e17 q^{8} +5.86757e18 q^{9} +O(q^{10})\) \(q+241488. q^{2} -3.14962e9 q^{3} -4.91439e11 q^{4} +5.36221e13 q^{5} -7.60595e14 q^{6} +1.82084e16 q^{7} -2.51436e17 q^{8} +5.86757e18 q^{9} +1.29491e19 q^{10} +2.56889e20 q^{11} +1.54785e21 q^{12} -2.93238e21 q^{13} +4.39709e21 q^{14} -1.68890e23 q^{15} +2.09453e23 q^{16} -9.89190e22 q^{17} +1.41695e24 q^{18} +1.24548e25 q^{19} -2.63520e25 q^{20} -5.73494e25 q^{21} +6.20355e25 q^{22} -1.86286e26 q^{23} +7.91928e26 q^{24} +1.05635e27 q^{25} -7.08133e26 q^{26} -5.71661e27 q^{27} -8.94830e27 q^{28} +1.31775e28 q^{29} -4.07848e28 q^{30} +1.89026e29 q^{31} +1.88809e29 q^{32} -8.09103e29 q^{33} -2.38877e28 q^{34} +9.76371e29 q^{35} -2.88356e30 q^{36} +3.22957e30 q^{37} +3.00769e30 q^{38} +9.23588e30 q^{39} -1.34825e31 q^{40} -2.27011e31 q^{41} -1.38492e31 q^{42} +5.36582e31 q^{43} -1.26245e32 q^{44} +3.14632e32 q^{45} -4.49858e31 q^{46} +1.87430e32 q^{47} -6.59698e32 q^{48} -5.78000e32 q^{49} +2.55095e32 q^{50} +3.11557e32 q^{51} +1.44109e33 q^{52} -3.22443e32 q^{53} -1.38049e33 q^{54} +1.37749e34 q^{55} -4.57823e33 q^{56} -3.92280e34 q^{57} +3.18220e33 q^{58} +1.01307e34 q^{59} +8.29990e34 q^{60} -8.66378e34 q^{61} +4.56473e34 q^{62} +1.06839e35 q^{63} -6.95530e34 q^{64} -1.57240e35 q^{65} -1.95389e35 q^{66} -5.98696e33 q^{67} +4.86127e34 q^{68} +5.86730e35 q^{69} +2.35782e35 q^{70} +5.02476e35 q^{71} -1.47532e36 q^{72} +1.14062e36 q^{73} +7.79901e35 q^{74} -3.32709e36 q^{75} -6.12079e36 q^{76} +4.67752e36 q^{77} +2.23035e36 q^{78} +7.78268e36 q^{79} +1.12313e37 q^{80} -5.77348e36 q^{81} -5.48205e36 q^{82} -4.09909e37 q^{83} +2.81838e37 q^{84} -5.30425e36 q^{85} +1.29578e37 q^{86} -4.15041e37 q^{87} -6.45911e37 q^{88} +2.04808e38 q^{89} +7.59797e37 q^{90} -5.33937e37 q^{91} +9.15483e37 q^{92} -5.95359e38 q^{93} +4.52621e37 q^{94} +6.67854e38 q^{95} -5.94676e38 q^{96} -2.29267e38 q^{97} -1.39580e38 q^{98} +1.50731e39 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 548856q^{2} + 1109442852q^{3} + 272078981184q^{4} + 17426916500490q^{5} + 1529727847867296q^{6} - 17996297718635544q^{7} + 255044243806133760q^{8} + 8305879902078677391q^{9} + O(q^{10}) \) \( 3q + 548856q^{2} + 1109442852q^{3} + 272078981184q^{4} + 17426916500490q^{5} + 1529727847867296q^{6} - 17996297718635544q^{7} + 255044243806133760q^{8} + 8305879902078677391q^{9} + 90373081165367671440q^{10} + \)\(66\!\cdots\!76\)\(q^{11} + \)\(36\!\cdots\!96\)\(q^{12} + \)\(31\!\cdots\!62\)\(q^{13} - \)\(63\!\cdots\!72\)\(q^{14} - \)\(17\!\cdots\!20\)\(q^{15} - \)\(35\!\cdots\!72\)\(q^{16} + \)\(89\!\cdots\!06\)\(q^{17} + \)\(87\!\cdots\!72\)\(q^{18} + \)\(92\!\cdots\!80\)\(q^{19} - \)\(14\!\cdots\!80\)\(q^{20} - \)\(19\!\cdots\!44\)\(q^{21} - \)\(12\!\cdots\!48\)\(q^{22} + \)\(30\!\cdots\!72\)\(q^{23} + \)\(16\!\cdots\!40\)\(q^{24} + \)\(18\!\cdots\!25\)\(q^{25} + \)\(28\!\cdots\!96\)\(q^{26} - \)\(11\!\cdots\!60\)\(q^{27} - \)\(41\!\cdots\!12\)\(q^{28} - \)\(24\!\cdots\!30\)\(q^{29} + \)\(10\!\cdots\!80\)\(q^{30} + \)\(30\!\cdots\!16\)\(q^{31} - \)\(56\!\cdots\!64\)\(q^{32} - \)\(15\!\cdots\!16\)\(q^{33} - \)\(16\!\cdots\!12\)\(q^{34} - \)\(11\!\cdots\!60\)\(q^{35} + \)\(18\!\cdots\!48\)\(q^{36} + \)\(75\!\cdots\!06\)\(q^{37} + \)\(24\!\cdots\!40\)\(q^{38} + \)\(22\!\cdots\!92\)\(q^{39} - \)\(32\!\cdots\!00\)\(q^{40} + \)\(23\!\cdots\!86\)\(q^{41} - \)\(19\!\cdots\!28\)\(q^{42} + \)\(16\!\cdots\!92\)\(q^{43} - \)\(45\!\cdots\!72\)\(q^{44} + \)\(58\!\cdots\!30\)\(q^{45} - \)\(24\!\cdots\!04\)\(q^{46} + \)\(20\!\cdots\!56\)\(q^{47} - \)\(17\!\cdots\!28\)\(q^{48} + \)\(36\!\cdots\!79\)\(q^{49} - \)\(26\!\cdots\!00\)\(q^{50} + \)\(78\!\cdots\!76\)\(q^{51} + \)\(37\!\cdots\!76\)\(q^{52} + \)\(58\!\cdots\!02\)\(q^{53} + \)\(79\!\cdots\!80\)\(q^{54} - \)\(49\!\cdots\!20\)\(q^{55} - \)\(62\!\cdots\!80\)\(q^{56} - \)\(46\!\cdots\!20\)\(q^{57} + \)\(25\!\cdots\!60\)\(q^{58} - \)\(56\!\cdots\!60\)\(q^{59} + \)\(12\!\cdots\!40\)\(q^{60} + \)\(39\!\cdots\!26\)\(q^{61} + \)\(26\!\cdots\!32\)\(q^{62} - \)\(17\!\cdots\!28\)\(q^{63} - \)\(16\!\cdots\!76\)\(q^{64} - \)\(26\!\cdots\!20\)\(q^{65} - \)\(28\!\cdots\!68\)\(q^{66} - \)\(14\!\cdots\!44\)\(q^{67} - \)\(13\!\cdots\!12\)\(q^{68} + \)\(15\!\cdots\!92\)\(q^{69} - \)\(48\!\cdots\!60\)\(q^{70} + \)\(38\!\cdots\!96\)\(q^{71} - \)\(16\!\cdots\!80\)\(q^{72} - \)\(18\!\cdots\!78\)\(q^{73} - \)\(50\!\cdots\!92\)\(q^{74} - \)\(43\!\cdots\!00\)\(q^{75} - \)\(73\!\cdots\!60\)\(q^{76} + \)\(56\!\cdots\!52\)\(q^{77} + \)\(93\!\cdots\!44\)\(q^{78} + \)\(13\!\cdots\!20\)\(q^{79} + \)\(26\!\cdots\!40\)\(q^{80} - \)\(18\!\cdots\!37\)\(q^{81} + \)\(50\!\cdots\!72\)\(q^{82} - \)\(20\!\cdots\!68\)\(q^{83} - \)\(72\!\cdots\!32\)\(q^{84} - \)\(10\!\cdots\!60\)\(q^{85} + \)\(17\!\cdots\!96\)\(q^{86} - \)\(73\!\cdots\!80\)\(q^{87} + \)\(69\!\cdots\!20\)\(q^{88} + \)\(20\!\cdots\!10\)\(q^{89} + \)\(93\!\cdots\!80\)\(q^{90} - \)\(16\!\cdots\!44\)\(q^{91} + \)\(26\!\cdots\!56\)\(q^{92} - \)\(16\!\cdots\!56\)\(q^{93} - \)\(11\!\cdots\!32\)\(q^{94} + \)\(72\!\cdots\!00\)\(q^{95} - \)\(14\!\cdots\!24\)\(q^{96} + \)\(17\!\cdots\!06\)\(q^{97} + \)\(22\!\cdots\!08\)\(q^{98} + \)\(10\!\cdots\!72\)\(q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 241488. 0.325694 0.162847 0.986651i \(-0.447932\pi\)
0.162847 + 0.986651i \(0.447932\pi\)
\(3\) −3.14962e9 −1.56457 −0.782283 0.622923i \(-0.785945\pi\)
−0.782283 + 0.622923i \(0.785945\pi\)
\(4\) −4.91439e11 −0.893923
\(5\) 5.36221e13 1.25727 0.628636 0.777700i \(-0.283614\pi\)
0.628636 + 0.777700i \(0.283614\pi\)
\(6\) −7.60595e14 −0.509571
\(7\) 1.82084e16 0.603752 0.301876 0.953347i \(-0.402387\pi\)
0.301876 + 0.953347i \(0.402387\pi\)
\(8\) −2.51436e17 −0.616840
\(9\) 5.86757e18 1.44787
\(10\) 1.29491e19 0.409486
\(11\) 2.56889e20 1.26645 0.633225 0.773968i \(-0.281731\pi\)
0.633225 + 0.773968i \(0.281731\pi\)
\(12\) 1.54785e21 1.39860
\(13\) −2.93238e21 −0.556319 −0.278160 0.960535i \(-0.589724\pi\)
−0.278160 + 0.960535i \(0.589724\pi\)
\(14\) 4.39709e21 0.196639
\(15\) −1.68890e23 −1.96709
\(16\) 2.09453e23 0.693022
\(17\) −9.89190e22 −0.100352 −0.0501759 0.998740i \(-0.515978\pi\)
−0.0501759 + 0.998740i \(0.515978\pi\)
\(18\) 1.41695e24 0.471563
\(19\) 1.24548e25 1.44425 0.722125 0.691763i \(-0.243166\pi\)
0.722125 + 0.691763i \(0.243166\pi\)
\(20\) −2.63520e25 −1.12390
\(21\) −5.73494e25 −0.944611
\(22\) 6.20355e25 0.412476
\(23\) −1.86286e26 −0.520580 −0.260290 0.965531i \(-0.583818\pi\)
−0.260290 + 0.965531i \(0.583818\pi\)
\(24\) 7.91928e26 0.965087
\(25\) 1.05635e27 0.580732
\(26\) −7.08133e26 −0.181190
\(27\) −5.71661e27 −0.700721
\(28\) −8.94830e27 −0.539708
\(29\) 1.31775e28 0.400932 0.200466 0.979701i \(-0.435754\pi\)
0.200466 + 0.979701i \(0.435754\pi\)
\(30\) −4.07848e28 −0.640669
\(31\) 1.89026e29 1.56663 0.783317 0.621623i \(-0.213526\pi\)
0.783317 + 0.621623i \(0.213526\pi\)
\(32\) 1.88809e29 0.842553
\(33\) −8.09103e29 −1.98145
\(34\) −2.38877e28 −0.0326840
\(35\) 9.76371e29 0.759081
\(36\) −2.88356e30 −1.29428
\(37\) 3.22957e30 0.849593 0.424797 0.905289i \(-0.360346\pi\)
0.424797 + 0.905289i \(0.360346\pi\)
\(38\) 3.00769e30 0.470384
\(39\) 9.23588e30 0.870399
\(40\) −1.34825e31 −0.775536
\(41\) −2.27011e31 −0.806793 −0.403397 0.915025i \(-0.632171\pi\)
−0.403397 + 0.915025i \(0.632171\pi\)
\(42\) −1.38492e31 −0.307654
\(43\) 5.36582e31 0.753357 0.376679 0.926344i \(-0.377066\pi\)
0.376679 + 0.926344i \(0.377066\pi\)
\(44\) −1.26245e32 −1.13211
\(45\) 3.14632e32 1.82036
\(46\) −4.49858e31 −0.169550
\(47\) 1.87430e32 0.464442 0.232221 0.972663i \(-0.425401\pi\)
0.232221 + 0.972663i \(0.425401\pi\)
\(48\) −6.59698e32 −1.08428
\(49\) −5.78000e32 −0.635483
\(50\) 2.55095e32 0.189141
\(51\) 3.11557e32 0.157007
\(52\) 1.44109e33 0.497307
\(53\) −3.22443e32 −0.0767490 −0.0383745 0.999263i \(-0.512218\pi\)
−0.0383745 + 0.999263i \(0.512218\pi\)
\(54\) −1.38049e33 −0.228221
\(55\) 1.37749e34 1.59227
\(56\) −4.57823e33 −0.372419
\(57\) −3.92280e34 −2.25962
\(58\) 3.18220e33 0.130581
\(59\) 1.01307e34 0.297870 0.148935 0.988847i \(-0.452415\pi\)
0.148935 + 0.988847i \(0.452415\pi\)
\(60\) 8.29990e34 1.75842
\(61\) −8.66378e34 −1.32977 −0.664884 0.746947i \(-0.731519\pi\)
−0.664884 + 0.746947i \(0.731519\pi\)
\(62\) 4.56473e34 0.510244
\(63\) 1.06839e35 0.874155
\(64\) −6.95530e34 −0.418607
\(65\) −1.57240e35 −0.699445
\(66\) −1.95389e35 −0.645345
\(67\) −5.98696e33 −0.0147485 −0.00737424 0.999973i \(-0.502347\pi\)
−0.00737424 + 0.999973i \(0.502347\pi\)
\(68\) 4.86127e34 0.0897069
\(69\) 5.86730e35 0.814482
\(70\) 2.35782e35 0.247228
\(71\) 5.02476e35 0.399556 0.199778 0.979841i \(-0.435978\pi\)
0.199778 + 0.979841i \(0.435978\pi\)
\(72\) −1.47532e36 −0.893104
\(73\) 1.14062e36 0.527651 0.263826 0.964570i \(-0.415016\pi\)
0.263826 + 0.964570i \(0.415016\pi\)
\(74\) 7.79901e35 0.276708
\(75\) −3.32709e36 −0.908594
\(76\) −6.12079e36 −1.29105
\(77\) 4.67752e36 0.764622
\(78\) 2.23035e36 0.283484
\(79\) 7.78268e36 0.771615 0.385808 0.922579i \(-0.373923\pi\)
0.385808 + 0.922579i \(0.373923\pi\)
\(80\) 1.12313e37 0.871317
\(81\) −5.77348e36 −0.351544
\(82\) −5.48205e36 −0.262768
\(83\) −4.09909e37 −1.55119 −0.775594 0.631232i \(-0.782550\pi\)
−0.775594 + 0.631232i \(0.782550\pi\)
\(84\) 2.81838e37 0.844410
\(85\) −5.30425e36 −0.126170
\(86\) 1.29578e37 0.245364
\(87\) −4.15041e37 −0.627286
\(88\) −6.45911e37 −0.781197
\(89\) 2.04808e38 1.98720 0.993600 0.112954i \(-0.0360312\pi\)
0.993600 + 0.112954i \(0.0360312\pi\)
\(90\) 7.59797e37 0.592883
\(91\) −5.33937e37 −0.335879
\(92\) 9.15483e37 0.465358
\(93\) −5.95359e38 −2.45110
\(94\) 4.52621e37 0.151266
\(95\) 6.67854e38 1.81581
\(96\) −5.94676e38 −1.31823
\(97\) −2.29267e38 −0.415234 −0.207617 0.978210i \(-0.566571\pi\)
−0.207617 + 0.978210i \(0.566571\pi\)
\(98\) −1.39580e38 −0.206973
\(99\) 1.50731e39 1.83365
\(100\) −5.19130e38 −0.519130
\(101\) 1.29569e39 1.06717 0.533587 0.845745i \(-0.320844\pi\)
0.533587 + 0.845745i \(0.320844\pi\)
\(102\) 7.52373e37 0.0511364
\(103\) −2.69807e39 −1.51610 −0.758049 0.652198i \(-0.773847\pi\)
−0.758049 + 0.652198i \(0.773847\pi\)
\(104\) 7.37304e38 0.343160
\(105\) −3.07520e39 −1.18763
\(106\) −7.78659e37 −0.0249967
\(107\) 1.69252e39 0.452430 0.226215 0.974077i \(-0.427365\pi\)
0.226215 + 0.974077i \(0.427365\pi\)
\(108\) 2.80937e39 0.626391
\(109\) 1.65572e39 0.308439 0.154220 0.988037i \(-0.450714\pi\)
0.154220 + 0.988037i \(0.450714\pi\)
\(110\) 3.32648e39 0.518594
\(111\) −1.01719e40 −1.32924
\(112\) 3.81379e39 0.418414
\(113\) 1.65677e40 1.52839 0.764193 0.644988i \(-0.223137\pi\)
0.764193 + 0.644988i \(0.223137\pi\)
\(114\) −9.47308e39 −0.735947
\(115\) −9.98905e39 −0.654510
\(116\) −6.47593e39 −0.358403
\(117\) −1.72059e40 −0.805478
\(118\) 2.44645e39 0.0970145
\(119\) −1.80115e39 −0.0605877
\(120\) 4.24649e40 1.21338
\(121\) 2.48471e40 0.603895
\(122\) −2.09220e40 −0.433098
\(123\) 7.15000e40 1.26228
\(124\) −9.28946e40 −1.40045
\(125\) −4.08946e40 −0.527134
\(126\) 2.58003e40 0.284707
\(127\) 1.00910e41 0.954473 0.477236 0.878775i \(-0.341639\pi\)
0.477236 + 0.878775i \(0.341639\pi\)
\(128\) −1.20595e41 −0.978891
\(129\) −1.69003e41 −1.17868
\(130\) −3.79716e40 −0.227805
\(131\) 3.37684e40 0.174470 0.0872348 0.996188i \(-0.472197\pi\)
0.0872348 + 0.996188i \(0.472197\pi\)
\(132\) 3.97625e41 1.77126
\(133\) 2.26782e41 0.871969
\(134\) −1.44578e39 −0.00480350
\(135\) −3.06537e41 −0.880997
\(136\) 2.48718e40 0.0619011
\(137\) −5.27644e41 −1.13839 −0.569193 0.822204i \(-0.692744\pi\)
−0.569193 + 0.822204i \(0.692744\pi\)
\(138\) 1.41688e41 0.265272
\(139\) 6.43985e41 1.04734 0.523669 0.851922i \(-0.324563\pi\)
0.523669 + 0.851922i \(0.324563\pi\)
\(140\) −4.79827e41 −0.678560
\(141\) −5.90335e41 −0.726650
\(142\) 1.21342e41 0.130133
\(143\) −7.53295e41 −0.704551
\(144\) 1.22898e42 1.00341
\(145\) 7.06604e41 0.504081
\(146\) 2.75447e41 0.171853
\(147\) 1.82048e42 0.994256
\(148\) −1.58714e42 −0.759471
\(149\) 1.12323e42 0.471341 0.235671 0.971833i \(-0.424271\pi\)
0.235671 + 0.971833i \(0.424271\pi\)
\(150\) −8.03452e41 −0.295924
\(151\) −3.59308e42 −1.16256 −0.581281 0.813703i \(-0.697448\pi\)
−0.581281 + 0.813703i \(0.697448\pi\)
\(152\) −3.13159e42 −0.890871
\(153\) −5.80414e41 −0.145296
\(154\) 1.12956e42 0.249033
\(155\) 1.01360e43 1.96968
\(156\) −4.53887e42 −0.778070
\(157\) −2.11217e42 −0.319659 −0.159829 0.987145i \(-0.551094\pi\)
−0.159829 + 0.987145i \(0.551094\pi\)
\(158\) 1.87942e42 0.251311
\(159\) 1.01557e42 0.120079
\(160\) 1.01243e43 1.05932
\(161\) −3.39196e42 −0.314301
\(162\) −1.39422e42 −0.114496
\(163\) −5.72434e42 −0.416934 −0.208467 0.978029i \(-0.566847\pi\)
−0.208467 + 0.978029i \(0.566847\pi\)
\(164\) 1.11562e43 0.721211
\(165\) −4.33859e43 −2.49122
\(166\) −9.89879e42 −0.505213
\(167\) 3.34941e43 1.52054 0.760268 0.649610i \(-0.225068\pi\)
0.760268 + 0.649610i \(0.225068\pi\)
\(168\) 1.44197e43 0.582674
\(169\) −1.91849e43 −0.690509
\(170\) −1.28091e42 −0.0410927
\(171\) 7.30795e43 2.09108
\(172\) −2.63697e43 −0.673444
\(173\) −3.41377e43 −0.778636 −0.389318 0.921103i \(-0.627289\pi\)
−0.389318 + 0.921103i \(0.627289\pi\)
\(174\) −1.00227e43 −0.204303
\(175\) 1.92343e43 0.350618
\(176\) 5.38062e43 0.877678
\(177\) −3.19080e43 −0.466037
\(178\) 4.94586e43 0.647220
\(179\) −1.44182e44 −1.69151 −0.845757 0.533569i \(-0.820851\pi\)
−0.845757 + 0.533569i \(0.820851\pi\)
\(180\) −1.54622e44 −1.62727
\(181\) 3.88244e43 0.366752 0.183376 0.983043i \(-0.441297\pi\)
0.183376 + 0.983043i \(0.441297\pi\)
\(182\) −1.28939e43 −0.109394
\(183\) 2.72877e44 2.08051
\(184\) 4.68390e43 0.321114
\(185\) 1.73176e44 1.06817
\(186\) −1.43772e44 −0.798310
\(187\) −2.54112e43 −0.127091
\(188\) −9.21106e43 −0.415175
\(189\) −1.04090e44 −0.423062
\(190\) 1.61279e44 0.591400
\(191\) −1.72164e44 −0.569889 −0.284945 0.958544i \(-0.591975\pi\)
−0.284945 + 0.958544i \(0.591975\pi\)
\(192\) 2.19066e44 0.654939
\(193\) −6.30991e44 −1.70473 −0.852365 0.522947i \(-0.824832\pi\)
−0.852365 + 0.522947i \(0.824832\pi\)
\(194\) −5.53651e43 −0.135239
\(195\) 4.95248e44 1.09433
\(196\) 2.84052e44 0.568073
\(197\) −1.00595e45 −1.82173 −0.910865 0.412705i \(-0.864584\pi\)
−0.910865 + 0.412705i \(0.864584\pi\)
\(198\) 3.63998e44 0.597211
\(199\) 1.18780e45 1.76648 0.883242 0.468918i \(-0.155356\pi\)
0.883242 + 0.468918i \(0.155356\pi\)
\(200\) −2.65603e44 −0.358219
\(201\) 1.88567e43 0.0230750
\(202\) 3.12894e44 0.347572
\(203\) 2.39940e44 0.242064
\(204\) −1.53112e44 −0.140352
\(205\) −1.21728e45 −1.01436
\(206\) −6.51551e44 −0.493784
\(207\) −1.09305e45 −0.753731
\(208\) −6.14195e44 −0.385542
\(209\) 3.19950e45 1.82907
\(210\) −7.42623e44 −0.386805
\(211\) −3.02479e43 −0.0143611 −0.00718054 0.999974i \(-0.502286\pi\)
−0.00718054 + 0.999974i \(0.502286\pi\)
\(212\) 1.58461e44 0.0686078
\(213\) −1.58261e45 −0.625132
\(214\) 4.08724e44 0.147354
\(215\) 2.87727e45 0.947175
\(216\) 1.43736e45 0.432233
\(217\) 3.44184e45 0.945859
\(218\) 3.99836e44 0.100457
\(219\) −3.59254e45 −0.825545
\(220\) −6.76955e45 −1.42337
\(221\) 2.90068e44 0.0558277
\(222\) −2.45640e45 −0.432928
\(223\) −6.62720e45 −1.07000 −0.535002 0.844851i \(-0.679689\pi\)
−0.535002 + 0.844851i \(0.679689\pi\)
\(224\) 3.43790e45 0.508694
\(225\) 6.19818e45 0.840824
\(226\) 4.00090e45 0.497787
\(227\) −5.09742e45 −0.581897 −0.290948 0.956739i \(-0.593971\pi\)
−0.290948 + 0.956739i \(0.593971\pi\)
\(228\) 1.92782e46 2.01993
\(229\) −5.09087e45 −0.489778 −0.244889 0.969551i \(-0.578752\pi\)
−0.244889 + 0.969551i \(0.578752\pi\)
\(230\) −2.41223e45 −0.213170
\(231\) −1.47324e46 −1.19630
\(232\) −3.31329e45 −0.247311
\(233\) 2.36093e46 1.62048 0.810239 0.586100i \(-0.199337\pi\)
0.810239 + 0.586100i \(0.199337\pi\)
\(234\) −4.15502e45 −0.262340
\(235\) 1.00504e46 0.583930
\(236\) −4.97864e45 −0.266273
\(237\) −2.45125e46 −1.20724
\(238\) −4.34956e44 −0.0197331
\(239\) −1.68674e46 −0.705162 −0.352581 0.935781i \(-0.614696\pi\)
−0.352581 + 0.935781i \(0.614696\pi\)
\(240\) −3.53744e46 −1.36323
\(241\) 3.12678e46 1.11113 0.555565 0.831473i \(-0.312502\pi\)
0.555565 + 0.831473i \(0.312502\pi\)
\(242\) 6.00028e45 0.196685
\(243\) 4.13512e46 1.25074
\(244\) 4.25773e46 1.18871
\(245\) −3.09936e46 −0.798975
\(246\) 1.72664e46 0.411118
\(247\) −3.65222e46 −0.803464
\(248\) −4.75278e46 −0.966362
\(249\) 1.29106e47 2.42694
\(250\) −9.87555e45 −0.171684
\(251\) −6.69718e46 −1.07710 −0.538548 0.842595i \(-0.681027\pi\)
−0.538548 + 0.842595i \(0.681027\pi\)
\(252\) −5.25048e46 −0.781427
\(253\) −4.78548e46 −0.659288
\(254\) 2.43686e46 0.310866
\(255\) 1.67064e46 0.197401
\(256\) 9.11500e45 0.0997878
\(257\) −3.87410e46 −0.393074 −0.196537 0.980496i \(-0.562970\pi\)
−0.196537 + 0.980496i \(0.562970\pi\)
\(258\) −4.08122e46 −0.383889
\(259\) 5.88051e46 0.512944
\(260\) 7.72741e46 0.625250
\(261\) 7.73197e46 0.580498
\(262\) 8.15465e45 0.0568238
\(263\) −5.89846e45 −0.0381594 −0.0190797 0.999818i \(-0.506074\pi\)
−0.0190797 + 0.999818i \(0.506074\pi\)
\(264\) 2.03438e47 1.22223
\(265\) −1.72901e46 −0.0964944
\(266\) 5.47650e46 0.283995
\(267\) −6.45068e47 −3.10911
\(268\) 2.94223e45 0.0131840
\(269\) 8.99725e46 0.374921 0.187461 0.982272i \(-0.439974\pi\)
0.187461 + 0.982272i \(0.439974\pi\)
\(270\) −7.40249e46 −0.286936
\(271\) 1.93454e47 0.697711 0.348855 0.937177i \(-0.386570\pi\)
0.348855 + 0.937177i \(0.386570\pi\)
\(272\) −2.07189e46 −0.0695461
\(273\) 1.68170e47 0.525505
\(274\) −1.27420e47 −0.370766
\(275\) 2.71363e47 0.735468
\(276\) −2.88342e47 −0.728084
\(277\) −5.39283e47 −1.26900 −0.634500 0.772923i \(-0.718794\pi\)
−0.634500 + 0.772923i \(0.718794\pi\)
\(278\) 1.55514e47 0.341112
\(279\) 1.10912e48 2.26828
\(280\) −2.45495e47 −0.468231
\(281\) 3.42772e47 0.609862 0.304931 0.952374i \(-0.401367\pi\)
0.304931 + 0.952374i \(0.401367\pi\)
\(282\) −1.42559e47 −0.236666
\(283\) 8.61731e47 1.33517 0.667584 0.744534i \(-0.267328\pi\)
0.667584 + 0.744534i \(0.267328\pi\)
\(284\) −2.46937e47 −0.357172
\(285\) −2.10349e48 −2.84096
\(286\) −1.81911e47 −0.229468
\(287\) −4.13350e47 −0.487104
\(288\) 1.10785e48 1.21991
\(289\) −9.61861e47 −0.989929
\(290\) 1.70636e47 0.164176
\(291\) 7.22104e47 0.649661
\(292\) −5.60548e47 −0.471679
\(293\) 1.93492e48 1.52316 0.761578 0.648073i \(-0.224425\pi\)
0.761578 + 0.648073i \(0.224425\pi\)
\(294\) 4.39624e47 0.323823
\(295\) 5.43232e47 0.374503
\(296\) −8.12030e47 −0.524063
\(297\) −1.46853e48 −0.887428
\(298\) 2.71246e47 0.153513
\(299\) 5.46260e47 0.289609
\(300\) 1.63506e48 0.812213
\(301\) 9.77027e47 0.454841
\(302\) −8.67684e47 −0.378640
\(303\) −4.08094e48 −1.66966
\(304\) 2.60870e48 1.00090
\(305\) −4.64571e48 −1.67188
\(306\) −1.40163e47 −0.0473222
\(307\) −1.51569e48 −0.480188 −0.240094 0.970750i \(-0.577178\pi\)
−0.240094 + 0.970750i \(0.577178\pi\)
\(308\) −2.29872e48 −0.683514
\(309\) 8.49790e48 2.37204
\(310\) 2.44771e48 0.641515
\(311\) 1.19146e48 0.293260 0.146630 0.989191i \(-0.453157\pi\)
0.146630 + 0.989191i \(0.453157\pi\)
\(312\) −2.32223e48 −0.536897
\(313\) −4.44520e47 −0.0965555 −0.0482778 0.998834i \(-0.515373\pi\)
−0.0482778 + 0.998834i \(0.515373\pi\)
\(314\) −5.10064e47 −0.104111
\(315\) 5.72893e48 1.09905
\(316\) −3.82472e48 −0.689765
\(317\) −1.03382e48 −0.175303 −0.0876516 0.996151i \(-0.527936\pi\)
−0.0876516 + 0.996151i \(0.527936\pi\)
\(318\) 2.45248e47 0.0391091
\(319\) 3.38515e48 0.507761
\(320\) −3.72958e48 −0.526303
\(321\) −5.33082e48 −0.707857
\(322\) −8.19117e47 −0.102366
\(323\) −1.23202e48 −0.144933
\(324\) 2.83732e48 0.314253
\(325\) −3.09760e48 −0.323073
\(326\) −1.38236e48 −0.135793
\(327\) −5.21489e48 −0.482574
\(328\) 5.70788e48 0.497663
\(329\) 3.41280e48 0.280408
\(330\) −1.04772e49 −0.811375
\(331\) 6.53650e48 0.477199 0.238599 0.971118i \(-0.423312\pi\)
0.238599 + 0.971118i \(0.423312\pi\)
\(332\) 2.01445e49 1.38664
\(333\) 1.89497e49 1.23010
\(334\) 8.08841e48 0.495230
\(335\) −3.21033e47 −0.0185429
\(336\) −1.20120e49 −0.654636
\(337\) −2.75713e49 −1.41799 −0.708996 0.705213i \(-0.750852\pi\)
−0.708996 + 0.705213i \(0.750852\pi\)
\(338\) −4.63292e48 −0.224895
\(339\) −5.21821e49 −2.39126
\(340\) 2.60672e48 0.112786
\(341\) 4.85586e49 1.98406
\(342\) 1.76478e49 0.681054
\(343\) −2.70857e49 −0.987427
\(344\) −1.34916e49 −0.464701
\(345\) 3.14617e49 1.02402
\(346\) −8.24383e48 −0.253597
\(347\) 1.59040e48 0.0462468 0.0231234 0.999733i \(-0.492639\pi\)
0.0231234 + 0.999733i \(0.492639\pi\)
\(348\) 2.03967e49 0.560745
\(349\) −4.30840e49 −1.12001 −0.560003 0.828491i \(-0.689200\pi\)
−0.560003 + 0.828491i \(0.689200\pi\)
\(350\) 4.64485e48 0.114194
\(351\) 1.67633e49 0.389825
\(352\) 4.85029e49 1.06705
\(353\) 4.31576e49 0.898361 0.449181 0.893441i \(-0.351716\pi\)
0.449181 + 0.893441i \(0.351716\pi\)
\(354\) −7.70539e48 −0.151786
\(355\) 2.69439e49 0.502350
\(356\) −1.00651e50 −1.77640
\(357\) 5.67295e48 0.0947935
\(358\) −3.48181e49 −0.550916
\(359\) −2.80608e49 −0.420492 −0.210246 0.977648i \(-0.567427\pi\)
−0.210246 + 0.977648i \(0.567427\pi\)
\(360\) −7.91097e49 −1.12287
\(361\) 8.07537e49 1.08586
\(362\) 9.37562e48 0.119449
\(363\) −7.82591e49 −0.944834
\(364\) 2.62398e49 0.300250
\(365\) 6.11627e49 0.663401
\(366\) 6.58963e49 0.677610
\(367\) 8.06624e49 0.786472 0.393236 0.919438i \(-0.371356\pi\)
0.393236 + 0.919438i \(0.371356\pi\)
\(368\) −3.90181e49 −0.360773
\(369\) −1.33200e50 −1.16813
\(370\) 4.18200e49 0.347897
\(371\) −5.87115e48 −0.0463374
\(372\) 2.92583e50 2.19110
\(373\) −2.09254e50 −1.48714 −0.743571 0.668657i \(-0.766870\pi\)
−0.743571 + 0.668657i \(0.766870\pi\)
\(374\) −6.13649e48 −0.0413927
\(375\) 1.28803e50 0.824736
\(376\) −4.71267e49 −0.286486
\(377\) −3.86413e49 −0.223046
\(378\) −2.51365e49 −0.137789
\(379\) 3.48223e49 0.181298 0.0906489 0.995883i \(-0.471106\pi\)
0.0906489 + 0.995883i \(0.471106\pi\)
\(380\) −3.28210e50 −1.62320
\(381\) −3.17830e50 −1.49334
\(382\) −4.15754e49 −0.185610
\(383\) 6.27597e49 0.266259 0.133130 0.991099i \(-0.457497\pi\)
0.133130 + 0.991099i \(0.457497\pi\)
\(384\) 3.79828e50 1.53154
\(385\) 2.50819e50 0.961338
\(386\) −1.52377e50 −0.555221
\(387\) 3.14843e50 1.09076
\(388\) 1.12671e50 0.371187
\(389\) −2.37857e50 −0.745245 −0.372623 0.927983i \(-0.621541\pi\)
−0.372623 + 0.927983i \(0.621541\pi\)
\(390\) 1.19596e50 0.356416
\(391\) 1.84272e49 0.0522412
\(392\) 1.45330e50 0.391991
\(393\) −1.06358e50 −0.272969
\(394\) −2.42924e50 −0.593327
\(395\) 4.17324e50 0.970130
\(396\) −7.40753e50 −1.63915
\(397\) −1.69815e50 −0.357734 −0.178867 0.983873i \(-0.557243\pi\)
−0.178867 + 0.983873i \(0.557243\pi\)
\(398\) 2.86840e50 0.575334
\(399\) −7.14277e50 −1.36425
\(400\) 2.21255e50 0.402460
\(401\) 1.06858e51 1.85136 0.925681 0.378306i \(-0.123493\pi\)
0.925681 + 0.378306i \(0.123493\pi\)
\(402\) 4.55365e48 0.00751539
\(403\) −5.54294e50 −0.871549
\(404\) −6.36754e50 −0.953971
\(405\) −3.09586e50 −0.441986
\(406\) 5.79426e49 0.0788388
\(407\) 8.29640e50 1.07597
\(408\) −7.83367e49 −0.0968483
\(409\) 1.58478e50 0.186794 0.0933972 0.995629i \(-0.470227\pi\)
0.0933972 + 0.995629i \(0.470227\pi\)
\(410\) −2.93959e50 −0.330371
\(411\) 1.66188e51 1.78108
\(412\) 1.32594e51 1.35528
\(413\) 1.84464e50 0.179840
\(414\) −2.63957e50 −0.245486
\(415\) −2.19802e51 −1.95026
\(416\) −5.53658e50 −0.468729
\(417\) −2.02831e51 −1.63863
\(418\) 7.72641e50 0.595717
\(419\) −2.13326e50 −0.156989 −0.0784947 0.996915i \(-0.525011\pi\)
−0.0784947 + 0.996915i \(0.525011\pi\)
\(420\) 1.51128e51 1.06165
\(421\) −1.07542e51 −0.721232 −0.360616 0.932714i \(-0.617434\pi\)
−0.360616 + 0.932714i \(0.617434\pi\)
\(422\) −7.30450e48 −0.00467732
\(423\) 1.09976e51 0.672451
\(424\) 8.10737e49 0.0473419
\(425\) −1.04493e50 −0.0582776
\(426\) −3.82181e50 −0.203602
\(427\) −1.57753e51 −0.802851
\(428\) −8.31774e50 −0.404438
\(429\) 2.37259e51 1.10232
\(430\) 6.94825e50 0.308489
\(431\) 3.49435e51 1.48272 0.741360 0.671108i \(-0.234181\pi\)
0.741360 + 0.671108i \(0.234181\pi\)
\(432\) −1.19736e51 −0.485615
\(433\) 2.34196e51 0.907956 0.453978 0.891013i \(-0.350005\pi\)
0.453978 + 0.891013i \(0.350005\pi\)
\(434\) 8.31163e50 0.308061
\(435\) −2.22554e51 −0.788668
\(436\) −8.13685e50 −0.275721
\(437\) −2.32016e51 −0.751847
\(438\) −8.67553e50 −0.268875
\(439\) 1.54147e51 0.456960 0.228480 0.973549i \(-0.426624\pi\)
0.228480 + 0.973549i \(0.426624\pi\)
\(440\) −3.46351e51 −0.982177
\(441\) −3.39145e51 −0.920096
\(442\) 7.00477e49 0.0181828
\(443\) −6.02650e51 −1.49690 −0.748449 0.663192i \(-0.769201\pi\)
−0.748449 + 0.663192i \(0.769201\pi\)
\(444\) 4.99889e51 1.18824
\(445\) 1.09822e52 2.49845
\(446\) −1.60039e51 −0.348494
\(447\) −3.53774e51 −0.737445
\(448\) −1.26645e51 −0.252735
\(449\) 8.31046e51 1.58789 0.793947 0.607987i \(-0.208023\pi\)
0.793947 + 0.607987i \(0.208023\pi\)
\(450\) 1.49678e51 0.273852
\(451\) −5.83167e51 −1.02176
\(452\) −8.14203e51 −1.36626
\(453\) 1.13168e52 1.81891
\(454\) −1.23096e51 −0.189520
\(455\) −2.86309e51 −0.422291
\(456\) 9.86332e51 1.39383
\(457\) −7.27855e51 −0.985551 −0.492776 0.870156i \(-0.664018\pi\)
−0.492776 + 0.870156i \(0.664018\pi\)
\(458\) −1.22938e51 −0.159518
\(459\) 5.65481e50 0.0703187
\(460\) 4.90901e51 0.585082
\(461\) −1.09767e51 −0.125402 −0.0627008 0.998032i \(-0.519971\pi\)
−0.0627008 + 0.998032i \(0.519971\pi\)
\(462\) −3.55770e51 −0.389629
\(463\) −8.46883e51 −0.889189 −0.444595 0.895732i \(-0.646652\pi\)
−0.444595 + 0.895732i \(0.646652\pi\)
\(464\) 2.76006e51 0.277855
\(465\) −3.19244e52 −3.08170
\(466\) 5.70136e51 0.527780
\(467\) 1.69800e52 1.50751 0.753753 0.657158i \(-0.228242\pi\)
0.753753 + 0.657158i \(0.228242\pi\)
\(468\) 8.45567e51 0.720035
\(469\) −1.09013e50 −0.00890443
\(470\) 2.42705e51 0.190183
\(471\) 6.65255e51 0.500127
\(472\) −2.54723e51 −0.183738
\(473\) 1.37842e52 0.954089
\(474\) −5.91947e51 −0.393192
\(475\) 1.31566e52 0.838722
\(476\) 8.85157e50 0.0541608
\(477\) −1.89195e51 −0.111123
\(478\) −4.07327e51 −0.229667
\(479\) 2.99013e51 0.161863 0.0809314 0.996720i \(-0.474211\pi\)
0.0809314 + 0.996720i \(0.474211\pi\)
\(480\) −3.18878e52 −1.65737
\(481\) −9.47031e51 −0.472645
\(482\) 7.55078e51 0.361889
\(483\) 1.06834e52 0.491745
\(484\) −1.22109e52 −0.539836
\(485\) −1.22938e52 −0.522061
\(486\) 9.98580e51 0.407357
\(487\) −1.46011e52 −0.572232 −0.286116 0.958195i \(-0.592364\pi\)
−0.286116 + 0.958195i \(0.592364\pi\)
\(488\) 2.17839e52 0.820254
\(489\) 1.80295e52 0.652321
\(490\) −7.48457e51 −0.260222
\(491\) −1.53063e52 −0.511426 −0.255713 0.966753i \(-0.582310\pi\)
−0.255713 + 0.966753i \(0.582310\pi\)
\(492\) −3.51379e52 −1.12838
\(493\) −1.30350e51 −0.0402343
\(494\) −8.81966e51 −0.261684
\(495\) 8.08254e52 2.30540
\(496\) 3.95920e52 1.08571
\(497\) 9.14926e51 0.241233
\(498\) 3.11775e52 0.790440
\(499\) −4.30786e51 −0.105027 −0.0525135 0.998620i \(-0.516723\pi\)
−0.0525135 + 0.998620i \(0.516723\pi\)
\(500\) 2.00972e52 0.471217
\(501\) −1.05494e53 −2.37898
\(502\) −1.61729e52 −0.350804
\(503\) −7.62462e52 −1.59090 −0.795449 0.606020i \(-0.792765\pi\)
−0.795449 + 0.606020i \(0.792765\pi\)
\(504\) −2.68631e52 −0.539214
\(505\) 6.94778e52 1.34173
\(506\) −1.15563e52 −0.214726
\(507\) 6.04253e52 1.08035
\(508\) −4.95914e52 −0.853225
\(509\) 4.36698e51 0.0723078 0.0361539 0.999346i \(-0.488489\pi\)
0.0361539 + 0.999346i \(0.488489\pi\)
\(510\) 4.03439e51 0.0642923
\(511\) 2.07689e52 0.318571
\(512\) 6.84989e52 1.01139
\(513\) −7.11993e52 −1.01202
\(514\) −9.35547e51 −0.128022
\(515\) −1.44676e53 −1.90615
\(516\) 8.30548e52 1.05365
\(517\) 4.81487e52 0.588192
\(518\) 1.42007e52 0.167063
\(519\) 1.07521e53 1.21823
\(520\) 3.95358e52 0.431445
\(521\) −2.72686e51 −0.0286634 −0.0143317 0.999897i \(-0.504562\pi\)
−0.0143317 + 0.999897i \(0.504562\pi\)
\(522\) 1.86718e52 0.189065
\(523\) 3.45861e52 0.337379 0.168690 0.985669i \(-0.446046\pi\)
0.168690 + 0.985669i \(0.446046\pi\)
\(524\) −1.65951e52 −0.155962
\(525\) −6.05808e52 −0.548566
\(526\) −1.42441e51 −0.0124283
\(527\) −1.86982e52 −0.157215
\(528\) −1.69469e53 −1.37319
\(529\) −9.33493e52 −0.728997
\(530\) −4.17534e51 −0.0314277
\(531\) 5.94428e52 0.431277
\(532\) −1.11449e53 −0.779473
\(533\) 6.65682e52 0.448835
\(534\) −1.55776e53 −1.01262
\(535\) 9.07568e52 0.568827
\(536\) 1.50534e51 0.00909746
\(537\) 4.54117e53 2.64649
\(538\) 2.17273e52 0.122110
\(539\) −1.48482e53 −0.804807
\(540\) 1.50644e53 0.787544
\(541\) −1.10485e53 −0.557129 −0.278565 0.960417i \(-0.589859\pi\)
−0.278565 + 0.960417i \(0.589859\pi\)
\(542\) 4.67167e52 0.227240
\(543\) −1.22282e53 −0.573809
\(544\) −1.86768e52 −0.0845518
\(545\) 8.87832e52 0.387792
\(546\) 4.06110e52 0.171154
\(547\) −1.77885e52 −0.0723413 −0.0361706 0.999346i \(-0.511516\pi\)
−0.0361706 + 0.999346i \(0.511516\pi\)
\(548\) 2.59305e53 1.01763
\(549\) −5.08354e53 −1.92533
\(550\) 6.55310e52 0.239538
\(551\) 1.64123e53 0.579046
\(552\) −1.47525e53 −0.502405
\(553\) 1.41710e53 0.465865
\(554\) −1.30230e53 −0.413306
\(555\) −5.45440e53 −1.67122
\(556\) −3.16480e53 −0.936240
\(557\) 3.89141e53 1.11155 0.555777 0.831332i \(-0.312421\pi\)
0.555777 + 0.831332i \(0.312421\pi\)
\(558\) 2.67839e53 0.738766
\(559\) −1.57346e53 −0.419107
\(560\) 2.04504e53 0.526060
\(561\) 8.00356e52 0.198842
\(562\) 8.27752e52 0.198629
\(563\) −4.03186e53 −0.934528 −0.467264 0.884118i \(-0.654760\pi\)
−0.467264 + 0.884118i \(0.654760\pi\)
\(564\) 2.90114e53 0.649570
\(565\) 8.88397e53 1.92160
\(566\) 2.08097e53 0.434857
\(567\) −1.05126e53 −0.212246
\(568\) −1.26341e53 −0.246462
\(569\) −6.36680e52 −0.120014 −0.0600070 0.998198i \(-0.519112\pi\)
−0.0600070 + 0.998198i \(0.519112\pi\)
\(570\) −5.07967e53 −0.925285
\(571\) −6.36424e53 −1.12032 −0.560160 0.828384i \(-0.689260\pi\)
−0.560160 + 0.828384i \(0.689260\pi\)
\(572\) 3.70199e53 0.629814
\(573\) 5.42250e53 0.891630
\(574\) −9.98190e52 −0.158647
\(575\) −1.96782e53 −0.302317
\(576\) −4.08107e53 −0.606088
\(577\) −9.29606e53 −1.33466 −0.667330 0.744762i \(-0.732563\pi\)
−0.667330 + 0.744762i \(0.732563\pi\)
\(578\) −2.32278e53 −0.322414
\(579\) 1.98738e54 2.66716
\(580\) −3.47253e53 −0.450610
\(581\) −7.46376e53 −0.936533
\(582\) 1.74379e53 0.211591
\(583\) −8.28319e52 −0.0971988
\(584\) −2.86794e53 −0.325476
\(585\) −9.22618e53 −1.01270
\(586\) 4.67260e53 0.496083
\(587\) 6.03454e52 0.0619728 0.0309864 0.999520i \(-0.490135\pi\)
0.0309864 + 0.999520i \(0.490135\pi\)
\(588\) −8.94656e53 −0.888788
\(589\) 2.35428e54 2.26261
\(590\) 1.31184e53 0.121974
\(591\) 3.16835e54 2.85022
\(592\) 6.76443e53 0.588787
\(593\) −1.41264e54 −1.18977 −0.594886 0.803810i \(-0.702803\pi\)
−0.594886 + 0.803810i \(0.702803\pi\)
\(594\) −3.54633e53 −0.289030
\(595\) −9.65816e52 −0.0761752
\(596\) −5.51998e53 −0.421343
\(597\) −3.74113e54 −2.76378
\(598\) 1.31915e53 0.0943239
\(599\) −1.17608e54 −0.813979 −0.406990 0.913433i \(-0.633421\pi\)
−0.406990 + 0.913433i \(0.633421\pi\)
\(600\) 8.36550e53 0.560457
\(601\) −1.78335e53 −0.115660 −0.0578300 0.998326i \(-0.518418\pi\)
−0.0578300 + 0.998326i \(0.518418\pi\)
\(602\) 2.35940e53 0.148139
\(603\) −3.51289e52 −0.0213539
\(604\) 1.76578e54 1.03924
\(605\) 1.33236e54 0.759260
\(606\) −9.85497e53 −0.543800
\(607\) −1.82763e54 −0.976582 −0.488291 0.872681i \(-0.662380\pi\)
−0.488291 + 0.872681i \(0.662380\pi\)
\(608\) 2.35158e54 1.21686
\(609\) −7.55721e53 −0.378725
\(610\) −1.12188e54 −0.544522
\(611\) −5.49616e53 −0.258378
\(612\) 2.85238e53 0.129884
\(613\) 1.27061e54 0.560446 0.280223 0.959935i \(-0.409592\pi\)
0.280223 + 0.959935i \(0.409592\pi\)
\(614\) −3.66020e53 −0.156395
\(615\) 3.83398e54 1.58703
\(616\) −1.17610e54 −0.471650
\(617\) 1.76693e54 0.686530 0.343265 0.939239i \(-0.388467\pi\)
0.343265 + 0.939239i \(0.388467\pi\)
\(618\) 2.05214e54 0.772559
\(619\) −2.12154e54 −0.773897 −0.386948 0.922101i \(-0.626471\pi\)
−0.386948 + 0.922101i \(0.626471\pi\)
\(620\) −4.98121e54 −1.76075
\(621\) 1.06492e54 0.364781
\(622\) 2.87723e53 0.0955130
\(623\) 3.72922e54 1.19978
\(624\) 1.93448e54 0.603205
\(625\) −4.11434e54 −1.24348
\(626\) −1.07346e53 −0.0314476
\(627\) −1.00772e55 −2.86170
\(628\) 1.03801e54 0.285750
\(629\) −3.19466e53 −0.0852583
\(630\) 1.38347e54 0.357954
\(631\) 4.38932e54 1.10109 0.550547 0.834804i \(-0.314419\pi\)
0.550547 + 0.834804i \(0.314419\pi\)
\(632\) −1.95684e54 −0.475963
\(633\) 9.52695e52 0.0224689
\(634\) −2.49655e53 −0.0570953
\(635\) 5.41103e54 1.20003
\(636\) −4.99093e53 −0.107341
\(637\) 1.69491e54 0.353532
\(638\) 8.17471e53 0.165375
\(639\) 2.94831e54 0.578505
\(640\) −6.46656e54 −1.23073
\(641\) 8.28753e54 1.53001 0.765004 0.644025i \(-0.222737\pi\)
0.765004 + 0.644025i \(0.222737\pi\)
\(642\) −1.28733e54 −0.230545
\(643\) −1.96493e54 −0.341376 −0.170688 0.985325i \(-0.554599\pi\)
−0.170688 + 0.985325i \(0.554599\pi\)
\(644\) 1.66694e54 0.280961
\(645\) −9.06230e54 −1.48192
\(646\) −2.97517e53 −0.0472039
\(647\) 8.12153e54 1.25027 0.625136 0.780516i \(-0.285044\pi\)
0.625136 + 0.780516i \(0.285044\pi\)
\(648\) 1.45166e54 0.216846
\(649\) 2.60247e54 0.377237
\(650\) −7.48033e53 −0.105223
\(651\) −1.08405e55 −1.47986
\(652\) 2.81317e54 0.372707
\(653\) −1.31229e55 −1.68741 −0.843707 0.536804i \(-0.819632\pi\)
−0.843707 + 0.536804i \(0.819632\pi\)
\(654\) −1.25933e54 −0.157172
\(655\) 1.81073e54 0.219356
\(656\) −4.75482e54 −0.559126
\(657\) 6.69269e54 0.763970
\(658\) 8.24148e53 0.0913273
\(659\) −1.11571e55 −1.20029 −0.600146 0.799890i \(-0.704891\pi\)
−0.600146 + 0.799890i \(0.704891\pi\)
\(660\) 2.13215e55 2.22696
\(661\) −3.62687e54 −0.367793 −0.183897 0.982946i \(-0.558871\pi\)
−0.183897 + 0.982946i \(0.558871\pi\)
\(662\) 1.57848e54 0.155421
\(663\) −9.13603e53 −0.0873462
\(664\) 1.03066e55 0.956835
\(665\) 1.21605e55 1.09630
\(666\) 4.57613e54 0.400636
\(667\) −2.45478e54 −0.208717
\(668\) −1.64603e55 −1.35924
\(669\) 2.08732e55 1.67409
\(670\) −7.75256e52 −0.00603930
\(671\) −2.22563e55 −1.68408
\(672\) −1.08281e55 −0.795885
\(673\) −1.86876e54 −0.133432 −0.0667159 0.997772i \(-0.521252\pi\)
−0.0667159 + 0.997772i \(0.521252\pi\)
\(674\) −6.65812e54 −0.461832
\(675\) −6.03872e54 −0.406931
\(676\) 9.42823e54 0.617262
\(677\) 1.48956e55 0.947498 0.473749 0.880660i \(-0.342900\pi\)
0.473749 + 0.880660i \(0.342900\pi\)
\(678\) −1.26013e55 −0.778821
\(679\) −4.17457e54 −0.250698
\(680\) 1.33368e54 0.0778265
\(681\) 1.60549e55 0.910416
\(682\) 1.17263e55 0.646198
\(683\) 9.58075e54 0.513093 0.256546 0.966532i \(-0.417415\pi\)
0.256546 + 0.966532i \(0.417415\pi\)
\(684\) −3.59142e55 −1.86927
\(685\) −2.82934e55 −1.43126
\(686\) −6.54087e54 −0.321599
\(687\) 1.60343e55 0.766291
\(688\) 1.12389e55 0.522093
\(689\) 9.45523e53 0.0426970
\(690\) 7.59763e54 0.333519
\(691\) 1.23084e54 0.0525267 0.0262634 0.999655i \(-0.491639\pi\)
0.0262634 + 0.999655i \(0.491639\pi\)
\(692\) 1.67766e55 0.696041
\(693\) 2.74457e55 1.10707
\(694\) 3.84062e53 0.0150623
\(695\) 3.45319e55 1.31679
\(696\) 1.04356e55 0.386935
\(697\) 2.24557e54 0.0809633
\(698\) −1.04043e55 −0.364779
\(699\) −7.43605e55 −2.53535
\(700\) −9.45250e54 −0.313426
\(701\) −4.60890e55 −1.48627 −0.743133 0.669144i \(-0.766661\pi\)
−0.743133 + 0.669144i \(0.766661\pi\)
\(702\) 4.04812e54 0.126964
\(703\) 4.02237e55 1.22702
\(704\) −1.78674e55 −0.530145
\(705\) −3.16550e55 −0.913597
\(706\) 1.04220e55 0.292591
\(707\) 2.35924e55 0.644308
\(708\) 1.56808e55 0.416602
\(709\) −4.42017e54 −0.114245 −0.0571226 0.998367i \(-0.518193\pi\)
−0.0571226 + 0.998367i \(0.518193\pi\)
\(710\) 6.50661e54 0.163613
\(711\) 4.56654e55 1.11720
\(712\) −5.14961e55 −1.22578
\(713\) −3.52128e55 −0.815558
\(714\) 1.36995e54 0.0308737
\(715\) −4.03933e55 −0.885812
\(716\) 7.08565e55 1.51208
\(717\) 5.31259e55 1.10327
\(718\) −6.77634e54 −0.136952
\(719\) 4.79691e55 0.943514 0.471757 0.881729i \(-0.343620\pi\)
0.471757 + 0.881729i \(0.343620\pi\)
\(720\) 6.59006e55 1.26155
\(721\) −4.91274e55 −0.915348
\(722\) 1.95010e55 0.353657
\(723\) −9.84817e55 −1.73844
\(724\) −1.90799e55 −0.327848
\(725\) 1.39200e55 0.232834
\(726\) −1.88986e55 −0.307727
\(727\) 1.02822e56 1.62991 0.814956 0.579523i \(-0.196761\pi\)
0.814956 + 0.579523i \(0.196761\pi\)
\(728\) 1.34251e55 0.207184
\(729\) −1.06843e56 −1.60531
\(730\) 1.47700e55 0.216066
\(731\) −5.30781e54 −0.0756008
\(732\) −1.34102e56 −1.85982
\(733\) −5.77006e55 −0.779207 −0.389603 0.920983i \(-0.627388\pi\)
−0.389603 + 0.920983i \(0.627388\pi\)
\(734\) 1.94790e55 0.256149
\(735\) 9.76181e55 1.25005
\(736\) −3.51724e55 −0.438616
\(737\) −1.53798e54 −0.0186782
\(738\) −3.21663e55 −0.380454
\(739\) 1.40056e56 1.61337 0.806686 0.590980i \(-0.201259\pi\)
0.806686 + 0.590980i \(0.201259\pi\)
\(740\) −8.51057e55 −0.954861
\(741\) 1.15031e56 1.25707
\(742\) −1.41781e54 −0.0150918
\(743\) 7.96262e54 0.0825609 0.0412804 0.999148i \(-0.486856\pi\)
0.0412804 + 0.999148i \(0.486856\pi\)
\(744\) 1.49695e56 1.51194
\(745\) 6.02299e55 0.592604
\(746\) −5.05324e55 −0.484354
\(747\) −2.40517e56 −2.24592
\(748\) 1.24881e55 0.113609
\(749\) 3.08181e55 0.273156
\(750\) 3.11042e55 0.268612
\(751\) −8.79022e55 −0.739641 −0.369821 0.929103i \(-0.620581\pi\)
−0.369821 + 0.929103i \(0.620581\pi\)
\(752\) 3.92578e55 0.321868
\(753\) 2.10936e56 1.68519
\(754\) −9.33140e54 −0.0726450
\(755\) −1.92669e56 −1.46166
\(756\) 5.11540e55 0.378185
\(757\) −6.05512e54 −0.0436268 −0.0218134 0.999762i \(-0.506944\pi\)
−0.0218134 + 0.999762i \(0.506944\pi\)
\(758\) 8.40915e54 0.0590477
\(759\) 1.50725e56 1.03150
\(760\) −1.67922e56 −1.12007
\(761\) −2.67473e56 −1.73892 −0.869458 0.494008i \(-0.835532\pi\)
−0.869458 + 0.494008i \(0.835532\pi\)
\(762\) −7.67520e55 −0.486371
\(763\) 3.01479e55 0.186221
\(764\) 8.46080e55 0.509437
\(765\) −3.11230e55 −0.182677
\(766\) 1.51557e55 0.0867191
\(767\) −2.97071e55 −0.165711
\(768\) −2.87088e55 −0.156125
\(769\) 3.07792e55 0.163190 0.0815951 0.996666i \(-0.473999\pi\)
0.0815951 + 0.996666i \(0.473999\pi\)
\(770\) 6.05697e55 0.313102
\(771\) 1.22019e56 0.614991
\(772\) 3.10094e56 1.52390
\(773\) 7.39678e55 0.354440 0.177220 0.984171i \(-0.443290\pi\)
0.177220 + 0.984171i \(0.443290\pi\)
\(774\) 7.60307e55 0.355255
\(775\) 1.99676e56 0.909794
\(776\) 5.76459e55 0.256133
\(777\) −1.85214e56 −0.802535
\(778\) −5.74396e55 −0.242722
\(779\) −2.82738e56 −1.16521
\(780\) −2.43384e56 −0.978245
\(781\) 1.29081e56 0.506018
\(782\) 4.44995e54 0.0170146
\(783\) −7.53305e55 −0.280942
\(784\) −1.21064e56 −0.440404
\(785\) −1.13259e56 −0.401898
\(786\) −2.56841e55 −0.0889046
\(787\) −3.95231e56 −1.33458 −0.667289 0.744799i \(-0.732545\pi\)
−0.667289 + 0.744799i \(0.732545\pi\)
\(788\) 4.94362e56 1.62849
\(789\) 1.85779e55 0.0597030
\(790\) 1.00779e56 0.315966
\(791\) 3.01671e56 0.922767
\(792\) −3.78993e56 −1.13107
\(793\) 2.54055e56 0.739776
\(794\) −4.10082e55 −0.116512
\(795\) 5.44572e55 0.150972
\(796\) −5.83734e56 −1.57910
\(797\) −1.36161e56 −0.359432 −0.179716 0.983719i \(-0.557518\pi\)
−0.179716 + 0.983719i \(0.557518\pi\)
\(798\) −1.72489e56 −0.444330
\(799\) −1.85404e55 −0.0466076
\(800\) 1.99447e56 0.489298
\(801\) 1.20172e57 2.87721
\(802\) 2.58049e56 0.602978
\(803\) 2.93014e56 0.668244
\(804\) −9.26690e54 −0.0206273
\(805\) −1.81884e56 −0.395162
\(806\) −1.33855e56 −0.283858
\(807\) −2.83379e56 −0.586590
\(808\) −3.25783e56 −0.658275
\(809\) 5.42801e56 1.07064 0.535321 0.844649i \(-0.320191\pi\)
0.535321 + 0.844649i \(0.320191\pi\)
\(810\) −7.47613e55 −0.143952
\(811\) −8.54286e56 −1.60582 −0.802910 0.596100i \(-0.796716\pi\)
−0.802910 + 0.596100i \(0.796716\pi\)
\(812\) −1.17916e56 −0.216387
\(813\) −6.09306e56 −1.09162
\(814\) 2.00348e56 0.350436
\(815\) −3.06952e56 −0.524199
\(816\) 6.52566e55 0.108809
\(817\) 6.68303e56 1.08804
\(818\) 3.82704e55 0.0608379
\(819\) −3.13291e56 −0.486309
\(820\) 5.98221e56 0.906759
\(821\) −2.83593e56 −0.419763 −0.209882 0.977727i \(-0.567308\pi\)
−0.209882 + 0.977727i \(0.567308\pi\)
\(822\) 4.01323e56 0.580088
\(823\) −7.79009e56 −1.09963 −0.549814 0.835287i \(-0.685301\pi\)
−0.549814 + 0.835287i \(0.685301\pi\)
\(824\) 6.78392e56 0.935190
\(825\) −8.54693e56 −1.15069
\(826\) 4.45458e55 0.0585728
\(827\) 2.44580e56 0.314097 0.157049 0.987591i \(-0.449802\pi\)
0.157049 + 0.987591i \(0.449802\pi\)
\(828\) 5.37166e56 0.673778
\(829\) −1.26495e56 −0.154974 −0.0774871 0.996993i \(-0.524690\pi\)
−0.0774871 + 0.996993i \(0.524690\pi\)
\(830\) −5.30795e56 −0.635190
\(831\) 1.69854e57 1.98543
\(832\) 2.03956e56 0.232879
\(833\) 5.71751e55 0.0637719
\(834\) −4.89812e56 −0.533693
\(835\) 1.79602e57 1.91173
\(836\) −1.57236e57 −1.63505
\(837\) −1.08059e57 −1.09777
\(838\) −5.15156e55 −0.0511305
\(839\) 1.05147e57 1.01962 0.509809 0.860287i \(-0.329716\pi\)
0.509809 + 0.860287i \(0.329716\pi\)
\(840\) 7.73216e56 0.732579
\(841\) −9.06598e56 −0.839253
\(842\) −2.59700e56 −0.234901
\(843\) −1.07960e57 −0.954170
\(844\) 1.48650e55 0.0128377
\(845\) −1.02874e57 −0.868157
\(846\) 2.65579e56 0.219013
\(847\) 4.52425e56 0.364603
\(848\) −6.75366e55 −0.0531888
\(849\) −2.71413e57 −2.08896
\(850\) −2.52337e55 −0.0189807
\(851\) −6.01623e56 −0.442281
\(852\) 7.77757e56 0.558820
\(853\) 2.14388e57 1.50555 0.752775 0.658278i \(-0.228715\pi\)
0.752775 + 0.658278i \(0.228715\pi\)
\(854\) −3.80955e56 −0.261484
\(855\) 3.91868e57 2.62906
\(856\) −4.25562e56 −0.279077
\(857\) 1.76630e57 1.13224 0.566119 0.824323i \(-0.308444\pi\)
0.566119 + 0.824323i \(0.308444\pi\)
\(858\) 5.72952e56 0.359018
\(859\) −1.41212e57 −0.864978 −0.432489 0.901639i \(-0.642365\pi\)
−0.432489 + 0.901639i \(0.642365\pi\)
\(860\) −1.41400e57 −0.846702
\(861\) 1.30190e57 0.762106
\(862\) 8.43842e56 0.482913
\(863\) −2.76506e57 −1.54702 −0.773508 0.633787i \(-0.781500\pi\)
−0.773508 + 0.633787i \(0.781500\pi\)
\(864\) −1.07935e57 −0.590395
\(865\) −1.83053e57 −0.978958
\(866\) 5.65553e56 0.295716
\(867\) 3.02950e57 1.54881
\(868\) −1.69146e57 −0.845525
\(869\) 1.99928e57 0.977212
\(870\) −5.37440e56 −0.256865
\(871\) 1.75560e55 0.00820487
\(872\) −4.16307e56 −0.190258
\(873\) −1.34524e57 −0.601204
\(874\) −5.60289e56 −0.244872
\(875\) −7.44623e56 −0.318258
\(876\) 1.76551e57 0.737974
\(877\) −7.42378e56 −0.303482 −0.151741 0.988420i \(-0.548488\pi\)
−0.151741 + 0.988420i \(0.548488\pi\)
\(878\) 3.72247e56 0.148829
\(879\) −6.09427e57 −2.38308
\(880\) 2.88520e57 1.10348
\(881\) 6.13623e56 0.229547 0.114773 0.993392i \(-0.463386\pi\)
0.114773 + 0.993392i \(0.463386\pi\)
\(882\) −8.18994e56 −0.299670
\(883\) 2.47374e57 0.885361 0.442681 0.896679i \(-0.354028\pi\)
0.442681 + 0.896679i \(0.354028\pi\)
\(884\) −1.42551e56 −0.0499057
\(885\) −1.71097e57 −0.585936
\(886\) −1.45533e57 −0.487531
\(887\) 4.04554e57 1.32576 0.662882 0.748724i \(-0.269333\pi\)
0.662882 + 0.748724i \(0.269333\pi\)
\(888\) 2.55759e57 0.819932
\(889\) 1.83741e57 0.576265
\(890\) 2.65208e57 0.813731
\(891\) −1.48314e57 −0.445213
\(892\) 3.25687e57 0.956501
\(893\) 2.33441e57 0.670770
\(894\) −8.54321e56 −0.240182
\(895\) −7.73132e57 −2.12669
\(896\) −2.19583e57 −0.591008
\(897\) −1.72051e57 −0.453112
\(898\) 2.00687e57 0.517168
\(899\) 2.49088e57 0.628114
\(900\) −3.04603e57 −0.751632
\(901\) 3.18957e55 0.00770191
\(902\) −1.40828e57 −0.332783
\(903\) −3.07727e57 −0.711630
\(904\) −4.16572e57 −0.942770
\(905\) 2.08185e57 0.461107
\(906\) 2.73288e57 0.592407
\(907\) 1.91109e57 0.405452 0.202726 0.979236i \(-0.435020\pi\)
0.202726 + 0.979236i \(0.435020\pi\)
\(908\) 2.50507e57 0.520171
\(909\) 7.60256e57 1.54513
\(910\) −6.91400e56 −0.137538
\(911\) −6.02986e57 −1.17408 −0.587041 0.809557i \(-0.699707\pi\)
−0.587041 + 0.809557i \(0.699707\pi\)
\(912\) −8.21642e57 −1.56597
\(913\) −1.05301e58 −1.96450
\(914\) −1.75768e57 −0.320988
\(915\) 1.46322e58 2.61577
\(916\) 2.50185e57 0.437824
\(917\) 6.14867e56 0.105336
\(918\) 1.36557e56 0.0229024
\(919\) 6.23642e57 1.02396 0.511980 0.858997i \(-0.328912\pi\)
0.511980 + 0.858997i \(0.328912\pi\)
\(920\) 2.51161e57 0.403728
\(921\) 4.77384e57 0.751286
\(922\) −2.65073e56 −0.0408426
\(923\) −1.47345e57 −0.222281
\(924\) 7.24010e57 1.06940
\(925\) 3.41154e57 0.493386
\(926\) −2.04512e57 −0.289604
\(927\) −1.58311e58 −2.19511
\(928\) 2.48802e57 0.337807
\(929\) 4.25561e57 0.565790 0.282895 0.959151i \(-0.408705\pi\)
0.282895 + 0.959151i \(0.408705\pi\)
\(930\) −7.70936e57 −1.00369
\(931\) −7.19888e57 −0.917796
\(932\) −1.16026e58 −1.44858
\(933\) −3.75266e57 −0.458825
\(934\) 4.10047e57 0.490986
\(935\) −1.36260e57 −0.159787
\(936\) 4.32619e57 0.496851
\(937\) 1.14088e58 1.28327 0.641637 0.767008i \(-0.278255\pi\)
0.641637 + 0.767008i \(0.278255\pi\)
\(938\) −2.63252e55 −0.00290012
\(939\) 1.40007e57 0.151068
\(940\) −4.93917e57 −0.521988
\(941\) −2.33700e57 −0.241914 −0.120957 0.992658i \(-0.538596\pi\)
−0.120957 + 0.992658i \(0.538596\pi\)
\(942\) 1.60651e57 0.162889
\(943\) 4.22890e57 0.420000
\(944\) 2.12191e57 0.206430
\(945\) −5.58153e57 −0.531904
\(946\) 3.32871e57 0.310741
\(947\) −4.94229e56 −0.0451964 −0.0225982 0.999745i \(-0.507194\pi\)
−0.0225982 + 0.999745i \(0.507194\pi\)
\(948\) 1.20464e58 1.07918
\(949\) −3.34474e57 −0.293542
\(950\) 3.17716e57 0.273167
\(951\) 3.25615e57 0.274274
\(952\) 4.52874e56 0.0373729
\(953\) 1.48078e56 0.0119723 0.00598617 0.999982i \(-0.498095\pi\)
0.00598617 + 0.999982i \(0.498095\pi\)
\(954\) −4.56884e56 −0.0361920
\(955\) −9.23178e57 −0.716506
\(956\) 8.28930e57 0.630361
\(957\) −1.06619e58 −0.794426
\(958\) 7.22079e56 0.0527178
\(959\) −9.60753e57 −0.687304
\(960\) 1.17468e58 0.823436
\(961\) 2.11725e58 1.45434
\(962\) −2.28696e57 −0.153938
\(963\) 9.93101e57 0.655059
\(964\) −1.53662e58 −0.993264
\(965\) −3.38351e58 −2.14331
\(966\) 2.57991e57 0.160159
\(967\) −6.58500e57 −0.400627 −0.200313 0.979732i \(-0.564196\pi\)
−0.200313 + 0.979732i \(0.564196\pi\)
\(968\) −6.24746e57 −0.372507
\(969\) 3.88039e57 0.226758
\(970\) −2.96880e57 −0.170032
\(971\) 4.39314e57 0.246604 0.123302 0.992369i \(-0.460652\pi\)
0.123302 + 0.992369i \(0.460652\pi\)
\(972\) −2.03216e58 −1.11806
\(973\) 1.17259e58 0.632333
\(974\) −3.52600e57 −0.186373
\(975\) 9.75628e57 0.505469
\(976\) −1.81466e58 −0.921558
\(977\) 2.41520e58 1.20229 0.601144 0.799141i \(-0.294712\pi\)
0.601144 + 0.799141i \(0.294712\pi\)
\(978\) 4.35391e57 0.212457
\(979\) 5.26129e58 2.51669
\(980\) 1.52315e58 0.714222
\(981\) 9.71504e57 0.446580
\(982\) −3.69630e57 −0.166568
\(983\) 7.73253e57 0.341608 0.170804 0.985305i \(-0.445364\pi\)
0.170804 + 0.985305i \(0.445364\pi\)
\(984\) −1.79777e58 −0.778626
\(985\) −5.39411e58 −2.29041
\(986\) −3.14780e56 −0.0131041
\(987\) −1.07490e58 −0.438717
\(988\) 1.79485e58 0.718235
\(989\) −9.99576e57 −0.392183
\(990\) 1.95183e58 0.750856
\(991\) −2.62440e58 −0.989904 −0.494952 0.868920i \(-0.664814\pi\)
−0.494952 + 0.868920i \(0.664814\pi\)
\(992\) 3.56897e58 1.31997
\(993\) −2.05875e58 −0.746609
\(994\) 2.20944e57 0.0785682
\(995\) 6.36926e58 2.22095
\(996\) −6.34477e58 −2.16950
\(997\) −2.17628e58 −0.729726 −0.364863 0.931061i \(-0.618884\pi\)
−0.364863 + 0.931061i \(0.618884\pi\)
\(998\) −1.04029e57 −0.0342067
\(999\) −1.84622e58 −0.595328
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1.40.a.a.1.2 3
3.2 odd 2 9.40.a.b.1.2 3
4.3 odd 2 16.40.a.c.1.3 3
5.2 odd 4 25.40.b.a.24.4 6
5.3 odd 4 25.40.b.a.24.3 6
5.4 even 2 25.40.a.a.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.40.a.a.1.2 3 1.1 even 1 trivial
9.40.a.b.1.2 3 3.2 odd 2
16.40.a.c.1.3 3 4.3 odd 2
25.40.a.a.1.2 3 5.4 even 2
25.40.b.a.24.3 6 5.3 odd 4
25.40.b.a.24.4 6 5.2 odd 4