Properties

Label 1.68.a.a.1.4
Level 1
Weight 68
Character 1.1
Self dual yes
Analytic conductor 28.429
Analytic rank 0
Dimension 5
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 68 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(28.4290351930\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
Defining polynomial: \(x^{5} - x^{4} - 939384011925257456 x^{3} + 31046449413968483513911200 x^{2} + 156793504704482691874379743265203200 x + 20916736226052669578405116700517591609696000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{40}\cdot 3^{15}\cdot 5^{4}\cdot 7^{2}\cdot 11\cdot 13\cdot 17 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-3.05046e8\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+8.43209e9 q^{2} +1.56682e16 q^{3} -7.64738e19 q^{4} +3.83370e23 q^{5} +1.32115e26 q^{6} -1.75533e27 q^{7} -1.88919e30 q^{8} +1.52782e32 q^{9} +O(q^{10})\) \(q+8.43209e9 q^{2} +1.56682e16 q^{3} -7.64738e19 q^{4} +3.83370e23 q^{5} +1.32115e26 q^{6} -1.75533e27 q^{7} -1.88919e30 q^{8} +1.52782e32 q^{9} +3.23261e33 q^{10} +1.38749e35 q^{11} -1.19820e36 q^{12} -6.45579e36 q^{13} -1.48011e37 q^{14} +6.00670e39 q^{15} -4.64430e39 q^{16} -8.51154e40 q^{17} +1.28827e42 q^{18} -5.19929e42 q^{19} -2.93178e43 q^{20} -2.75028e43 q^{21} +1.16995e45 q^{22} +2.49803e45 q^{23} -2.96001e46 q^{24} +7.92100e46 q^{25} -5.44359e46 q^{26} +9.41218e47 q^{27} +1.34237e47 q^{28} +1.20701e49 q^{29} +5.06491e49 q^{30} -6.23103e49 q^{31} +2.39634e50 q^{32} +2.17395e51 q^{33} -7.17701e50 q^{34} -6.72941e50 q^{35} -1.16838e52 q^{36} +3.56231e51 q^{37} -4.38409e52 q^{38} -1.01150e53 q^{39} -7.24259e53 q^{40} +4.51579e53 q^{41} -2.31906e53 q^{42} +6.41012e54 q^{43} -1.06107e55 q^{44} +5.85719e55 q^{45} +2.10636e55 q^{46} -1.03805e56 q^{47} -7.27676e55 q^{48} -4.15297e56 q^{49} +6.67906e56 q^{50} -1.33360e57 q^{51} +4.93699e56 q^{52} -9.61057e57 q^{53} +7.93644e57 q^{54} +5.31924e58 q^{55} +3.31615e57 q^{56} -8.14632e58 q^{57} +1.01776e59 q^{58} -4.77326e58 q^{59} -4.59355e59 q^{60} -2.98642e58 q^{61} -5.25406e59 q^{62} -2.68182e59 q^{63} +2.70600e60 q^{64} -2.47496e60 q^{65} +1.83309e61 q^{66} -2.03266e61 q^{67} +6.50909e60 q^{68} +3.91395e61 q^{69} -5.67430e60 q^{70} -6.57721e61 q^{71} -2.88634e62 q^{72} -1.20026e62 q^{73} +3.00377e61 q^{74} +1.24107e63 q^{75} +3.97609e62 q^{76} -2.43551e62 q^{77} -8.52909e62 q^{78} +2.11502e63 q^{79} -1.78049e63 q^{80} +5.82859e62 q^{81} +3.80776e63 q^{82} -3.25858e64 q^{83} +2.10324e63 q^{84} -3.26307e64 q^{85} +5.40507e64 q^{86} +1.89115e65 q^{87} -2.62124e65 q^{88} +6.19321e64 q^{89} +4.93884e65 q^{90} +1.13320e64 q^{91} -1.91034e65 q^{92} -9.76287e65 q^{93} -8.75297e65 q^{94} -1.99325e66 q^{95} +3.75463e66 q^{96} -9.58970e65 q^{97} -3.50182e66 q^{98} +2.11984e67 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q + 5554901256q^{2} + 3443360269119372q^{3} + \)\(35\!\cdots\!40\)\(q^{4} + \)\(33\!\cdots\!50\)\(q^{5} + \)\(14\!\cdots\!60\)\(q^{6} + \)\(33\!\cdots\!56\)\(q^{7} + \)\(32\!\cdots\!80\)\(q^{8} + \)\(27\!\cdots\!85\)\(q^{9} + O(q^{10}) \) \( 5q + 5554901256q^{2} + 3443360269119372q^{3} + \)\(35\!\cdots\!40\)\(q^{4} + \)\(33\!\cdots\!50\)\(q^{5} + \)\(14\!\cdots\!60\)\(q^{6} + \)\(33\!\cdots\!56\)\(q^{7} + \)\(32\!\cdots\!80\)\(q^{8} + \)\(27\!\cdots\!85\)\(q^{9} - \)\(52\!\cdots\!00\)\(q^{10} + \)\(20\!\cdots\!60\)\(q^{11} - \)\(20\!\cdots\!24\)\(q^{12} + \)\(17\!\cdots\!02\)\(q^{13} + \)\(29\!\cdots\!80\)\(q^{14} - \)\(93\!\cdots\!00\)\(q^{15} + \)\(18\!\cdots\!80\)\(q^{16} + \)\(75\!\cdots\!06\)\(q^{17} - \)\(10\!\cdots\!68\)\(q^{18} + \)\(39\!\cdots\!00\)\(q^{19} - \)\(15\!\cdots\!00\)\(q^{20} - \)\(17\!\cdots\!40\)\(q^{21} + \)\(18\!\cdots\!32\)\(q^{22} - \)\(41\!\cdots\!68\)\(q^{23} - \)\(13\!\cdots\!00\)\(q^{24} + \)\(17\!\cdots\!75\)\(q^{25} + \)\(21\!\cdots\!60\)\(q^{26} + \)\(18\!\cdots\!20\)\(q^{27} + \)\(14\!\cdots\!48\)\(q^{28} + \)\(18\!\cdots\!50\)\(q^{29} + \)\(18\!\cdots\!00\)\(q^{30} + \)\(36\!\cdots\!60\)\(q^{31} + \)\(15\!\cdots\!96\)\(q^{32} + \)\(24\!\cdots\!84\)\(q^{33} + \)\(78\!\cdots\!80\)\(q^{34} + \)\(45\!\cdots\!00\)\(q^{35} - \)\(38\!\cdots\!20\)\(q^{36} - \)\(56\!\cdots\!94\)\(q^{37} - \)\(31\!\cdots\!80\)\(q^{38} - \)\(71\!\cdots\!80\)\(q^{39} - \)\(18\!\cdots\!00\)\(q^{40} + \)\(11\!\cdots\!10\)\(q^{41} + \)\(28\!\cdots\!92\)\(q^{42} + \)\(65\!\cdots\!92\)\(q^{43} + \)\(49\!\cdots\!80\)\(q^{44} + \)\(99\!\cdots\!50\)\(q^{45} + \)\(79\!\cdots\!60\)\(q^{46} - \)\(12\!\cdots\!44\)\(q^{47} - \)\(19\!\cdots\!68\)\(q^{48} - \)\(77\!\cdots\!35\)\(q^{49} - \)\(39\!\cdots\!00\)\(q^{50} - \)\(33\!\cdots\!40\)\(q^{51} + \)\(67\!\cdots\!16\)\(q^{52} + \)\(10\!\cdots\!22\)\(q^{53} + \)\(19\!\cdots\!00\)\(q^{54} + \)\(66\!\cdots\!00\)\(q^{55} + \)\(16\!\cdots\!00\)\(q^{56} - \)\(92\!\cdots\!60\)\(q^{57} - \)\(61\!\cdots\!20\)\(q^{58} - \)\(30\!\cdots\!00\)\(q^{59} - \)\(13\!\cdots\!00\)\(q^{60} - \)\(11\!\cdots\!90\)\(q^{61} - \)\(21\!\cdots\!28\)\(q^{62} - \)\(20\!\cdots\!68\)\(q^{63} + \)\(63\!\cdots\!40\)\(q^{64} + \)\(17\!\cdots\!00\)\(q^{65} + \)\(27\!\cdots\!20\)\(q^{66} - \)\(11\!\cdots\!44\)\(q^{67} + \)\(81\!\cdots\!48\)\(q^{68} + \)\(35\!\cdots\!20\)\(q^{69} - \)\(26\!\cdots\!00\)\(q^{70} - \)\(11\!\cdots\!40\)\(q^{71} - \)\(74\!\cdots\!40\)\(q^{72} - \)\(30\!\cdots\!18\)\(q^{73} + \)\(92\!\cdots\!80\)\(q^{74} + \)\(21\!\cdots\!00\)\(q^{75} + \)\(20\!\cdots\!00\)\(q^{76} + \)\(50\!\cdots\!32\)\(q^{77} + \)\(61\!\cdots\!64\)\(q^{78} + \)\(29\!\cdots\!00\)\(q^{79} - \)\(15\!\cdots\!00\)\(q^{80} - \)\(11\!\cdots\!95\)\(q^{81} - \)\(17\!\cdots\!08\)\(q^{82} - \)\(47\!\cdots\!88\)\(q^{83} - \)\(52\!\cdots\!20\)\(q^{84} - \)\(39\!\cdots\!00\)\(q^{85} + \)\(49\!\cdots\!60\)\(q^{86} + \)\(35\!\cdots\!60\)\(q^{87} + \)\(43\!\cdots\!60\)\(q^{88} - \)\(11\!\cdots\!50\)\(q^{89} + \)\(47\!\cdots\!00\)\(q^{90} + \)\(23\!\cdots\!60\)\(q^{91} - \)\(98\!\cdots\!44\)\(q^{92} - \)\(18\!\cdots\!36\)\(q^{93} - \)\(49\!\cdots\!20\)\(q^{94} - \)\(20\!\cdots\!00\)\(q^{95} - \)\(22\!\cdots\!40\)\(q^{96} + \)\(28\!\cdots\!06\)\(q^{97} + \)\(12\!\cdots\!08\)\(q^{98} + \)\(16\!\cdots\!20\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 8.43209e9 0.694114 0.347057 0.937844i \(-0.387181\pi\)
0.347057 + 0.937844i \(0.387181\pi\)
\(3\) 1.56682e16 1.62726 0.813628 0.581386i \(-0.197489\pi\)
0.813628 + 0.581386i \(0.197489\pi\)
\(4\) −7.64738e19 −0.518206
\(5\) 3.83370e23 1.47273 0.736365 0.676584i \(-0.236541\pi\)
0.736365 + 0.676584i \(0.236541\pi\)
\(6\) 1.32115e26 1.12950
\(7\) −1.75533e27 −0.0858172 −0.0429086 0.999079i \(-0.513662\pi\)
−0.0429086 + 0.999079i \(0.513662\pi\)
\(8\) −1.88919e30 −1.05381
\(9\) 1.52782e32 1.64796
\(10\) 3.23261e33 1.02224
\(11\) 1.38749e35 1.80126 0.900630 0.434587i \(-0.143106\pi\)
0.900630 + 0.434587i \(0.143106\pi\)
\(12\) −1.19820e36 −0.843254
\(13\) −6.45579e36 −0.311062 −0.155531 0.987831i \(-0.549709\pi\)
−0.155531 + 0.987831i \(0.549709\pi\)
\(14\) −1.48011e37 −0.0595669
\(15\) 6.00670e39 2.39651
\(16\) −4.64430e39 −0.213256
\(17\) −8.51154e40 −0.512825 −0.256412 0.966567i \(-0.582541\pi\)
−0.256412 + 0.966567i \(0.582541\pi\)
\(18\) 1.28827e42 1.14387
\(19\) −5.19929e42 −0.754568 −0.377284 0.926098i \(-0.623142\pi\)
−0.377284 + 0.926098i \(0.623142\pi\)
\(20\) −2.93178e43 −0.763178
\(21\) −2.75028e43 −0.139646
\(22\) 1.16995e45 1.25028
\(23\) 2.49803e45 0.602164 0.301082 0.953598i \(-0.402652\pi\)
0.301082 + 0.953598i \(0.402652\pi\)
\(24\) −2.96001e46 −1.71481
\(25\) 7.92100e46 1.16893
\(26\) −5.44359e46 −0.215913
\(27\) 9.41218e47 1.05440
\(28\) 1.34237e47 0.0444710
\(29\) 1.20701e49 1.23417 0.617087 0.786895i \(-0.288313\pi\)
0.617087 + 0.786895i \(0.288313\pi\)
\(30\) 5.06491e49 1.66345
\(31\) −6.23103e49 −0.682249 −0.341124 0.940018i \(-0.610808\pi\)
−0.341124 + 0.940018i \(0.610808\pi\)
\(32\) 2.39634e50 0.905784
\(33\) 2.17395e51 2.93111
\(34\) −7.17701e50 −0.355959
\(35\) −6.72941e50 −0.126386
\(36\) −1.16838e52 −0.853984
\(37\) 3.56231e51 0.103986 0.0519929 0.998647i \(-0.483443\pi\)
0.0519929 + 0.998647i \(0.483443\pi\)
\(38\) −4.38409e52 −0.523756
\(39\) −1.01150e53 −0.506178
\(40\) −7.24259e53 −1.55197
\(41\) 4.51579e53 0.423131 0.211565 0.977364i \(-0.432144\pi\)
0.211565 + 0.977364i \(0.432144\pi\)
\(42\) −2.31906e53 −0.0969305
\(43\) 6.41012e54 1.21807 0.609036 0.793143i \(-0.291557\pi\)
0.609036 + 0.793143i \(0.291557\pi\)
\(44\) −1.06107e55 −0.933424
\(45\) 5.85719e55 2.42700
\(46\) 2.10636e55 0.417970
\(47\) −1.03805e56 −1.00217 −0.501085 0.865398i \(-0.667066\pi\)
−0.501085 + 0.865398i \(0.667066\pi\)
\(48\) −7.27676e55 −0.347022
\(49\) −4.15297e56 −0.992635
\(50\) 6.67906e56 0.811373
\(51\) −1.33360e57 −0.834497
\(52\) 4.93699e56 0.161194
\(53\) −9.61057e57 −1.65771 −0.828853 0.559466i \(-0.811006\pi\)
−0.828853 + 0.559466i \(0.811006\pi\)
\(54\) 7.93644e57 0.731872
\(55\) 5.31924e58 2.65277
\(56\) 3.31615e57 0.0904348
\(57\) −8.14632e58 −1.22787
\(58\) 1.01776e59 0.856657
\(59\) −4.77326e58 −0.226607 −0.113303 0.993560i \(-0.536143\pi\)
−0.113303 + 0.993560i \(0.536143\pi\)
\(60\) −4.59355e59 −1.24189
\(61\) −2.98642e58 −0.0464088 −0.0232044 0.999731i \(-0.507387\pi\)
−0.0232044 + 0.999731i \(0.507387\pi\)
\(62\) −5.25406e59 −0.473558
\(63\) −2.68182e59 −0.141423
\(64\) 2.70600e60 0.841973
\(65\) −2.47496e60 −0.458111
\(66\) 1.83309e61 2.03452
\(67\) −2.03266e61 −1.36320 −0.681599 0.731726i \(-0.738715\pi\)
−0.681599 + 0.731726i \(0.738715\pi\)
\(68\) 6.50909e60 0.265749
\(69\) 3.91395e61 0.979874
\(70\) −5.67430e60 −0.0877259
\(71\) −6.57721e61 −0.632247 −0.316123 0.948718i \(-0.602381\pi\)
−0.316123 + 0.948718i \(0.602381\pi\)
\(72\) −2.88634e62 −1.73663
\(73\) −1.20026e62 −0.454944 −0.227472 0.973785i \(-0.573046\pi\)
−0.227472 + 0.973785i \(0.573046\pi\)
\(74\) 3.00377e61 0.0721780
\(75\) 1.24107e63 1.90215
\(76\) 3.97609e62 0.391022
\(77\) −2.43551e62 −0.154579
\(78\) −8.52909e62 −0.351345
\(79\) 2.11502e63 0.568599 0.284299 0.958736i \(-0.408239\pi\)
0.284299 + 0.958736i \(0.408239\pi\)
\(80\) −1.78049e63 −0.314068
\(81\) 5.82859e62 0.0678134
\(82\) 3.80776e63 0.293701
\(83\) −3.25858e64 −1.67461 −0.837303 0.546740i \(-0.815869\pi\)
−0.837303 + 0.546740i \(0.815869\pi\)
\(84\) 2.10324e63 0.0723657
\(85\) −3.26307e64 −0.755253
\(86\) 5.40507e64 0.845480
\(87\) 1.89115e65 2.00832
\(88\) −2.62124e65 −1.89818
\(89\) 6.19321e64 0.307150 0.153575 0.988137i \(-0.450921\pi\)
0.153575 + 0.988137i \(0.450921\pi\)
\(90\) 4.93884e65 1.68461
\(91\) 1.13320e64 0.0266945
\(92\) −1.91034e65 −0.312045
\(93\) −9.76287e65 −1.11019
\(94\) −8.75297e65 −0.695620
\(95\) −1.99325e66 −1.11127
\(96\) 3.75463e66 1.47394
\(97\) −9.58970e65 −0.266043 −0.133022 0.991113i \(-0.542468\pi\)
−0.133022 + 0.991113i \(0.542468\pi\)
\(98\) −3.50182e66 −0.689002
\(99\) 2.11984e67 2.96841
\(100\) −6.05749e66 −0.605749
\(101\) −1.60525e67 −1.15021 −0.575104 0.818080i \(-0.695038\pi\)
−0.575104 + 0.818080i \(0.695038\pi\)
\(102\) −1.12450e67 −0.579236
\(103\) 4.02418e67 1.49496 0.747481 0.664284i \(-0.231263\pi\)
0.747481 + 0.664284i \(0.231263\pi\)
\(104\) 1.21962e67 0.327800
\(105\) −1.05437e67 −0.205662
\(106\) −8.10373e67 −1.15064
\(107\) −7.96494e67 −0.825707 −0.412853 0.910798i \(-0.635468\pi\)
−0.412853 + 0.910798i \(0.635468\pi\)
\(108\) −7.19785e67 −0.546395
\(109\) −1.26408e67 −0.0704673 −0.0352336 0.999379i \(-0.511218\pi\)
−0.0352336 + 0.999379i \(0.511218\pi\)
\(110\) 4.48523e68 1.84132
\(111\) 5.58148e67 0.169212
\(112\) 8.15228e66 0.0183010
\(113\) 4.43655e68 0.739465 0.369732 0.929138i \(-0.379449\pi\)
0.369732 + 0.929138i \(0.379449\pi\)
\(114\) −6.86906e68 −0.852284
\(115\) 9.57669e68 0.886825
\(116\) −9.23042e68 −0.639557
\(117\) −9.86326e68 −0.512618
\(118\) −4.02486e68 −0.157291
\(119\) 1.49406e68 0.0440092
\(120\) −1.13478e70 −2.52546
\(121\) 1.33179e70 2.24454
\(122\) −2.51817e68 −0.0322130
\(123\) 7.07541e69 0.688542
\(124\) 4.76510e69 0.353546
\(125\) 4.38859e69 0.248794
\(126\) −2.26133e69 −0.0981639
\(127\) −3.09560e70 −1.03115 −0.515574 0.856845i \(-0.672421\pi\)
−0.515574 + 0.856845i \(0.672421\pi\)
\(128\) −1.25466e70 −0.321359
\(129\) 1.00435e71 1.98211
\(130\) −2.08691e70 −0.317981
\(131\) −6.24988e70 −0.736687 −0.368343 0.929690i \(-0.620075\pi\)
−0.368343 + 0.929690i \(0.620075\pi\)
\(132\) −1.66250e71 −1.51892
\(133\) 9.12646e69 0.0647549
\(134\) −1.71396e71 −0.946215
\(135\) 3.60835e71 1.55284
\(136\) 1.60799e71 0.540419
\(137\) 9.38159e69 0.0246682 0.0123341 0.999924i \(-0.496074\pi\)
0.0123341 + 0.999924i \(0.496074\pi\)
\(138\) 3.30028e71 0.680144
\(139\) 6.21722e71 1.00601 0.503003 0.864285i \(-0.332228\pi\)
0.503003 + 0.864285i \(0.332228\pi\)
\(140\) 5.14623e70 0.0654938
\(141\) −1.62644e72 −1.63079
\(142\) −5.54596e71 −0.438851
\(143\) −8.95738e71 −0.560304
\(144\) −7.09564e71 −0.351437
\(145\) 4.62730e72 1.81760
\(146\) −1.01207e72 −0.315783
\(147\) −6.50693e72 −1.61527
\(148\) −2.72423e71 −0.0538861
\(149\) 2.36862e72 0.373900 0.186950 0.982369i \(-0.440140\pi\)
0.186950 + 0.982369i \(0.440140\pi\)
\(150\) 1.04649e73 1.32031
\(151\) 4.21606e72 0.425774 0.212887 0.977077i \(-0.431713\pi\)
0.212887 + 0.977077i \(0.431713\pi\)
\(152\) 9.82245e72 0.795169
\(153\) −1.30041e73 −0.845115
\(154\) −2.05365e72 −0.107295
\(155\) −2.38879e73 −1.00477
\(156\) 7.73535e72 0.262305
\(157\) 2.28213e73 0.624744 0.312372 0.949960i \(-0.398876\pi\)
0.312372 + 0.949960i \(0.398876\pi\)
\(158\) 1.78340e73 0.394672
\(159\) −1.50580e74 −2.69751
\(160\) 9.18686e73 1.33398
\(161\) −4.38486e72 −0.0516760
\(162\) 4.91473e72 0.0470702
\(163\) −1.50864e74 −1.17571 −0.587854 0.808967i \(-0.700027\pi\)
−0.587854 + 0.808967i \(0.700027\pi\)
\(164\) −3.45340e73 −0.219269
\(165\) 8.33427e74 4.31673
\(166\) −2.74767e74 −1.16237
\(167\) 2.98109e73 0.103127 0.0515637 0.998670i \(-0.483579\pi\)
0.0515637 + 0.998670i \(0.483579\pi\)
\(168\) 5.19580e73 0.147161
\(169\) −3.89052e74 −0.903240
\(170\) −2.75145e74 −0.524231
\(171\) −7.94355e74 −1.24350
\(172\) −4.90206e74 −0.631212
\(173\) 5.87795e74 0.623277 0.311639 0.950201i \(-0.399122\pi\)
0.311639 + 0.950201i \(0.399122\pi\)
\(174\) 1.59464e75 1.39400
\(175\) −1.39040e74 −0.100315
\(176\) −6.44395e74 −0.384129
\(177\) −7.47881e74 −0.368747
\(178\) 5.22217e74 0.213197
\(179\) 2.89879e75 0.980935 0.490467 0.871460i \(-0.336826\pi\)
0.490467 + 0.871460i \(0.336826\pi\)
\(180\) −4.47921e75 −1.25769
\(181\) 7.66482e75 1.78760 0.893798 0.448469i \(-0.148031\pi\)
0.893798 + 0.448469i \(0.148031\pi\)
\(182\) 9.55529e73 0.0185290
\(183\) −4.67916e74 −0.0755191
\(184\) −4.71925e75 −0.634565
\(185\) 1.36568e75 0.153143
\(186\) −8.23214e75 −0.770600
\(187\) −1.18097e76 −0.923731
\(188\) 7.93839e75 0.519331
\(189\) −1.65215e75 −0.0904854
\(190\) −1.68073e76 −0.771351
\(191\) 4.40959e75 0.169739 0.0848693 0.996392i \(-0.472953\pi\)
0.0848693 + 0.996392i \(0.472953\pi\)
\(192\) 4.23980e76 1.37010
\(193\) 3.04412e76 0.826592 0.413296 0.910597i \(-0.364377\pi\)
0.413296 + 0.910597i \(0.364377\pi\)
\(194\) −8.08613e75 −0.184664
\(195\) −3.87780e76 −0.745463
\(196\) 3.17593e76 0.514390
\(197\) −6.11000e76 −0.834492 −0.417246 0.908793i \(-0.637005\pi\)
−0.417246 + 0.908793i \(0.637005\pi\)
\(198\) 1.78747e77 2.06041
\(199\) 6.76401e76 0.658607 0.329303 0.944224i \(-0.393186\pi\)
0.329303 + 0.944224i \(0.393186\pi\)
\(200\) −1.49643e77 −1.23183
\(201\) −3.18480e77 −2.21827
\(202\) −1.35356e77 −0.798375
\(203\) −2.11869e76 −0.105913
\(204\) 1.01985e77 0.432442
\(205\) 1.73122e77 0.623158
\(206\) 3.39322e77 1.03767
\(207\) 3.81652e77 0.992342
\(208\) 2.99827e76 0.0663359
\(209\) −7.21399e77 −1.35917
\(210\) −8.89058e76 −0.142752
\(211\) 4.61607e77 0.632136 0.316068 0.948737i \(-0.397637\pi\)
0.316068 + 0.948737i \(0.397637\pi\)
\(212\) 7.34957e77 0.859034
\(213\) −1.03053e78 −1.02883
\(214\) −6.71611e77 −0.573134
\(215\) 2.45745e78 1.79389
\(216\) −1.77814e78 −1.11113
\(217\) 1.09375e77 0.0585487
\(218\) −1.06589e77 −0.0489123
\(219\) −1.88058e78 −0.740311
\(220\) −4.06782e78 −1.37468
\(221\) 5.49487e77 0.159521
\(222\) 4.70636e77 0.117452
\(223\) 5.73226e78 1.23059 0.615295 0.788297i \(-0.289037\pi\)
0.615295 + 0.788297i \(0.289037\pi\)
\(224\) −4.20637e77 −0.0777318
\(225\) 1.21018e79 1.92636
\(226\) 3.74094e78 0.513272
\(227\) −1.30879e79 −1.54883 −0.774414 0.632680i \(-0.781955\pi\)
−0.774414 + 0.632680i \(0.781955\pi\)
\(228\) 6.22980e78 0.636292
\(229\) −1.09438e79 −0.965342 −0.482671 0.875802i \(-0.660333\pi\)
−0.482671 + 0.875802i \(0.660333\pi\)
\(230\) 8.07515e78 0.615557
\(231\) −3.81599e78 −0.251540
\(232\) −2.28026e79 −1.30058
\(233\) 2.12939e79 1.05155 0.525777 0.850622i \(-0.323775\pi\)
0.525777 + 0.850622i \(0.323775\pi\)
\(234\) −8.31680e78 −0.355815
\(235\) −3.97959e79 −1.47593
\(236\) 3.65029e78 0.117429
\(237\) 3.31384e79 0.925256
\(238\) 1.25980e78 0.0305474
\(239\) 3.58283e77 0.00754912 0.00377456 0.999993i \(-0.498799\pi\)
0.00377456 + 0.999993i \(0.498799\pi\)
\(240\) −2.78969e79 −0.511070
\(241\) 9.84113e79 1.56846 0.784231 0.620469i \(-0.213058\pi\)
0.784231 + 0.620469i \(0.213058\pi\)
\(242\) 1.12298e80 1.55796
\(243\) −7.81275e79 −0.944048
\(244\) 2.28382e78 0.0240494
\(245\) −1.59212e80 −1.46188
\(246\) 5.96605e79 0.477926
\(247\) 3.35655e79 0.234718
\(248\) 1.17716e80 0.718959
\(249\) −5.10559e80 −2.72501
\(250\) 3.70050e79 0.172691
\(251\) 2.75351e80 1.12413 0.562065 0.827093i \(-0.310007\pi\)
0.562065 + 0.827093i \(0.310007\pi\)
\(252\) 2.05089e79 0.0732865
\(253\) 3.46600e80 1.08465
\(254\) −2.61024e80 −0.715733
\(255\) −5.11263e80 −1.22899
\(256\) −5.05128e80 −1.06503
\(257\) 4.62111e80 0.855041 0.427520 0.904006i \(-0.359387\pi\)
0.427520 + 0.904006i \(0.359387\pi\)
\(258\) 8.46875e80 1.37581
\(259\) −6.25303e78 −0.00892377
\(260\) 1.89269e80 0.237396
\(261\) 1.84408e81 2.03387
\(262\) −5.26995e80 −0.511344
\(263\) 2.15218e81 1.83806 0.919031 0.394184i \(-0.128973\pi\)
0.919031 + 0.394184i \(0.128973\pi\)
\(264\) −4.10700e81 −3.08883
\(265\) −3.68441e81 −2.44135
\(266\) 7.69552e79 0.0449472
\(267\) 9.70361e80 0.499812
\(268\) 1.55445e81 0.706418
\(269\) −1.18612e81 −0.475803 −0.237901 0.971289i \(-0.576460\pi\)
−0.237901 + 0.971289i \(0.576460\pi\)
\(270\) 3.04259e81 1.07785
\(271\) −2.43922e81 −0.763448 −0.381724 0.924276i \(-0.624669\pi\)
−0.381724 + 0.924276i \(0.624669\pi\)
\(272\) 3.95302e80 0.109363
\(273\) 1.77552e80 0.0434388
\(274\) 7.91064e79 0.0171225
\(275\) 1.09904e82 2.10555
\(276\) −2.99314e81 −0.507777
\(277\) −4.94623e81 −0.743365 −0.371682 0.928360i \(-0.621219\pi\)
−0.371682 + 0.928360i \(0.621219\pi\)
\(278\) 5.24242e81 0.698283
\(279\) −9.51986e81 −1.12432
\(280\) 1.27131e81 0.133186
\(281\) 1.83232e82 1.70349 0.851746 0.523955i \(-0.175544\pi\)
0.851746 + 0.523955i \(0.175544\pi\)
\(282\) −1.37143e82 −1.13195
\(283\) −5.08970e81 −0.373119 −0.186559 0.982444i \(-0.559734\pi\)
−0.186559 + 0.982444i \(0.559734\pi\)
\(284\) 5.02984e81 0.327634
\(285\) −3.12306e82 −1.80833
\(286\) −7.55295e81 −0.388915
\(287\) −7.92670e80 −0.0363119
\(288\) 3.66117e82 1.49270
\(289\) −2.03026e82 −0.737011
\(290\) 3.90178e82 1.26162
\(291\) −1.50253e82 −0.432920
\(292\) 9.17881e81 0.235755
\(293\) 4.16071e82 0.953020 0.476510 0.879169i \(-0.341902\pi\)
0.476510 + 0.879169i \(0.341902\pi\)
\(294\) −5.48671e82 −1.12118
\(295\) −1.82992e82 −0.333730
\(296\) −6.72989e81 −0.109581
\(297\) 1.30594e83 1.89924
\(298\) 1.99724e82 0.259529
\(299\) −1.61268e82 −0.187310
\(300\) −9.49096e82 −0.985708
\(301\) −1.12519e82 −0.104531
\(302\) 3.55502e82 0.295535
\(303\) −2.51513e83 −1.87168
\(304\) 2.41471e82 0.160916
\(305\) −1.14490e82 −0.0683477
\(306\) −1.09651e83 −0.586606
\(307\) −7.74779e82 −0.371572 −0.185786 0.982590i \(-0.559483\pi\)
−0.185786 + 0.982590i \(0.559483\pi\)
\(308\) 1.86253e82 0.0801038
\(309\) 6.30514e83 2.43268
\(310\) −2.01425e83 −0.697423
\(311\) 5.78665e83 1.79868 0.899341 0.437248i \(-0.144047\pi\)
0.899341 + 0.437248i \(0.144047\pi\)
\(312\) 1.91092e83 0.533414
\(313\) −4.31694e83 −1.08253 −0.541266 0.840851i \(-0.682055\pi\)
−0.541266 + 0.840851i \(0.682055\pi\)
\(314\) 1.92432e83 0.433644
\(315\) −1.02813e83 −0.208278
\(316\) −1.61743e83 −0.294651
\(317\) −9.02240e83 −1.47855 −0.739276 0.673402i \(-0.764832\pi\)
−0.739276 + 0.673402i \(0.764832\pi\)
\(318\) −1.26970e84 −1.87238
\(319\) 1.67471e84 2.22307
\(320\) 1.03740e84 1.24000
\(321\) −1.24796e84 −1.34364
\(322\) −3.69735e82 −0.0358690
\(323\) 4.42539e83 0.386961
\(324\) −4.45735e82 −0.0351413
\(325\) −5.11364e83 −0.363611
\(326\) −1.27210e84 −0.816075
\(327\) −1.98058e83 −0.114668
\(328\) −8.53120e83 −0.445899
\(329\) 1.82213e83 0.0860035
\(330\) 7.02753e84 2.99630
\(331\) −1.45028e84 −0.558744 −0.279372 0.960183i \(-0.590126\pi\)
−0.279372 + 0.960183i \(0.590126\pi\)
\(332\) 2.49196e84 0.867791
\(333\) 5.44256e83 0.171365
\(334\) 2.51369e83 0.0715821
\(335\) −7.79262e84 −2.00762
\(336\) 1.27731e83 0.0297804
\(337\) 1.36629e83 0.0288365 0.0144183 0.999896i \(-0.495410\pi\)
0.0144183 + 0.999896i \(0.495410\pi\)
\(338\) −3.28052e84 −0.626951
\(339\) 6.95125e84 1.20330
\(340\) 2.49539e84 0.391377
\(341\) −8.64552e84 −1.22891
\(342\) −6.69808e84 −0.863129
\(343\) 1.46337e84 0.171002
\(344\) −1.21099e85 −1.28361
\(345\) 1.50049e85 1.44309
\(346\) 4.95634e84 0.432625
\(347\) 3.52969e84 0.279704 0.139852 0.990172i \(-0.455337\pi\)
0.139852 + 0.990172i \(0.455337\pi\)
\(348\) −1.44624e85 −1.04072
\(349\) 2.68026e85 1.75196 0.875980 0.482347i \(-0.160216\pi\)
0.875980 + 0.482347i \(0.160216\pi\)
\(350\) −1.17240e84 −0.0696297
\(351\) −6.07631e84 −0.327983
\(352\) 3.32491e85 1.63155
\(353\) −1.77646e82 −0.000792688 0 −0.000396344 1.00000i \(-0.500126\pi\)
−0.000396344 1.00000i \(0.500126\pi\)
\(354\) −6.30621e84 −0.255952
\(355\) −2.52150e85 −0.931129
\(356\) −4.73618e84 −0.159167
\(357\) 2.34091e84 0.0716142
\(358\) 2.44429e85 0.680880
\(359\) −7.24629e85 −1.83845 −0.919225 0.393732i \(-0.871184\pi\)
−0.919225 + 0.393732i \(0.871184\pi\)
\(360\) −1.10653e86 −2.55759
\(361\) −2.04453e85 −0.430627
\(362\) 6.46304e85 1.24079
\(363\) 2.08667e86 3.65244
\(364\) −8.66604e83 −0.0138333
\(365\) −4.60143e85 −0.670010
\(366\) −3.94551e84 −0.0524188
\(367\) −9.89279e85 −1.19952 −0.599758 0.800182i \(-0.704736\pi\)
−0.599758 + 0.800182i \(0.704736\pi\)
\(368\) −1.16016e85 −0.128415
\(369\) 6.89930e85 0.697303
\(370\) 1.15156e85 0.106299
\(371\) 1.68697e85 0.142260
\(372\) 7.46603e85 0.575309
\(373\) −2.64810e84 −0.0186504 −0.00932521 0.999957i \(-0.502968\pi\)
−0.00932521 + 0.999957i \(0.502968\pi\)
\(374\) −9.95806e85 −0.641174
\(375\) 6.87611e85 0.404851
\(376\) 1.96108e86 1.05610
\(377\) −7.79218e85 −0.383905
\(378\) −1.39311e85 −0.0628072
\(379\) −3.32517e86 −1.37215 −0.686073 0.727533i \(-0.740667\pi\)
−0.686073 + 0.727533i \(0.740667\pi\)
\(380\) 1.52431e86 0.575870
\(381\) −4.85024e86 −1.67794
\(382\) 3.71821e85 0.117818
\(383\) −6.25868e85 −0.181687 −0.0908435 0.995865i \(-0.528956\pi\)
−0.0908435 + 0.995865i \(0.528956\pi\)
\(384\) −1.96581e86 −0.522933
\(385\) −9.33702e85 −0.227653
\(386\) 2.56683e86 0.573749
\(387\) 9.79348e86 2.00733
\(388\) 7.33361e85 0.137865
\(389\) 6.09926e86 1.05188 0.525939 0.850522i \(-0.323714\pi\)
0.525939 + 0.850522i \(0.323714\pi\)
\(390\) −3.26980e86 −0.517436
\(391\) −2.12621e86 −0.308805
\(392\) 7.84575e86 1.04605
\(393\) −9.79240e86 −1.19878
\(394\) −5.15201e86 −0.579233
\(395\) 8.10834e86 0.837393
\(396\) −1.62112e87 −1.53825
\(397\) 1.14304e87 0.996736 0.498368 0.866966i \(-0.333933\pi\)
0.498368 + 0.866966i \(0.333933\pi\)
\(398\) 5.70347e86 0.457148
\(399\) 1.42995e86 0.105373
\(400\) −3.67875e86 −0.249282
\(401\) −1.93243e87 −1.20439 −0.602196 0.798348i \(-0.705707\pi\)
−0.602196 + 0.798348i \(0.705707\pi\)
\(402\) −2.68546e87 −1.53973
\(403\) 4.02262e86 0.212222
\(404\) 1.22759e87 0.596045
\(405\) 2.23451e86 0.0998709
\(406\) −1.78650e86 −0.0735159
\(407\) 4.94269e86 0.187306
\(408\) 2.51943e87 0.879400
\(409\) 4.40444e87 1.41632 0.708158 0.706054i \(-0.249526\pi\)
0.708158 + 0.706054i \(0.249526\pi\)
\(410\) 1.45978e87 0.432542
\(411\) 1.46992e86 0.0401415
\(412\) −3.07744e87 −0.774698
\(413\) 8.37864e85 0.0194467
\(414\) 3.21813e87 0.688798
\(415\) −1.24924e88 −2.46624
\(416\) −1.54703e87 −0.281755
\(417\) 9.74124e87 1.63703
\(418\) −6.08290e87 −0.943420
\(419\) 9.02411e87 1.29192 0.645958 0.763373i \(-0.276458\pi\)
0.645958 + 0.763373i \(0.276458\pi\)
\(420\) 8.06319e86 0.106575
\(421\) −1.07202e88 −1.30843 −0.654215 0.756308i \(-0.727001\pi\)
−0.654215 + 0.756308i \(0.727001\pi\)
\(422\) 3.89231e87 0.438774
\(423\) −1.58596e88 −1.65154
\(424\) 1.81562e88 1.74690
\(425\) −6.74199e87 −0.599458
\(426\) −8.68950e87 −0.714123
\(427\) 5.24214e85 0.00398268
\(428\) 6.09109e87 0.427886
\(429\) −1.40346e88 −0.911758
\(430\) 2.07214e88 1.24516
\(431\) 7.24337e87 0.402673 0.201336 0.979522i \(-0.435472\pi\)
0.201336 + 0.979522i \(0.435472\pi\)
\(432\) −4.37130e87 −0.224856
\(433\) −7.28174e86 −0.0346649 −0.0173325 0.999850i \(-0.505517\pi\)
−0.0173325 + 0.999850i \(0.505517\pi\)
\(434\) 9.22261e86 0.0406394
\(435\) 7.25012e88 2.95771
\(436\) 9.66691e86 0.0365166
\(437\) −1.29880e88 −0.454373
\(438\) −1.58572e88 −0.513860
\(439\) 1.22243e88 0.366998 0.183499 0.983020i \(-0.441258\pi\)
0.183499 + 0.983020i \(0.441258\pi\)
\(440\) −1.00491e89 −2.79551
\(441\) −6.34497e88 −1.63582
\(442\) 4.63333e87 0.110725
\(443\) 2.48797e88 0.551215 0.275608 0.961270i \(-0.411121\pi\)
0.275608 + 0.961270i \(0.411121\pi\)
\(444\) −4.26837e87 −0.0876865
\(445\) 2.37429e88 0.452349
\(446\) 4.83350e88 0.854169
\(447\) 3.71119e88 0.608431
\(448\) −4.74991e87 −0.0722557
\(449\) −1.29903e89 −1.83386 −0.916931 0.399046i \(-0.869341\pi\)
−0.916931 + 0.399046i \(0.869341\pi\)
\(450\) 1.02044e89 1.33711
\(451\) 6.26564e88 0.762169
\(452\) −3.39280e88 −0.383195
\(453\) 6.60578e88 0.692842
\(454\) −1.10358e89 −1.07506
\(455\) 4.34437e87 0.0393138
\(456\) 1.53900e89 1.29394
\(457\) 1.20530e89 0.941681 0.470841 0.882218i \(-0.343951\pi\)
0.470841 + 0.882218i \(0.343951\pi\)
\(458\) −9.22796e88 −0.670057
\(459\) −8.01122e88 −0.540721
\(460\) −7.32365e88 −0.459558
\(461\) −2.20679e88 −0.128760 −0.0643800 0.997925i \(-0.520507\pi\)
−0.0643800 + 0.997925i \(0.520507\pi\)
\(462\) −3.21768e88 −0.174597
\(463\) 1.20440e89 0.607867 0.303934 0.952693i \(-0.401700\pi\)
0.303934 + 0.952693i \(0.401700\pi\)
\(464\) −5.60570e88 −0.263195
\(465\) −3.74279e89 −1.63502
\(466\) 1.79552e89 0.729898
\(467\) −2.22415e89 −0.841491 −0.420745 0.907179i \(-0.638231\pi\)
−0.420745 + 0.907179i \(0.638231\pi\)
\(468\) 7.54281e88 0.265642
\(469\) 3.56799e88 0.116986
\(470\) −3.35563e89 −1.02446
\(471\) 3.57568e89 1.01662
\(472\) 9.01760e88 0.238800
\(473\) 8.89401e89 2.19406
\(474\) 2.79426e89 0.642232
\(475\) −4.11836e89 −0.882040
\(476\) −1.14256e88 −0.0228058
\(477\) −1.46832e90 −2.73184
\(478\) 3.02108e87 0.00523995
\(479\) 3.75550e89 0.607335 0.303667 0.952778i \(-0.401789\pi\)
0.303667 + 0.952778i \(0.401789\pi\)
\(480\) 1.43941e90 2.17072
\(481\) −2.29976e88 −0.0323461
\(482\) 8.29813e89 1.08869
\(483\) −6.87027e88 −0.0840901
\(484\) −1.01847e90 −1.16313
\(485\) −3.67641e89 −0.391810
\(486\) −6.58779e89 −0.655276
\(487\) 3.60986e89 0.335174 0.167587 0.985857i \(-0.446403\pi\)
0.167587 + 0.985857i \(0.446403\pi\)
\(488\) 5.64191e88 0.0489060
\(489\) −2.36375e90 −1.91318
\(490\) −1.34249e90 −1.01471
\(491\) 9.21555e89 0.650566 0.325283 0.945617i \(-0.394540\pi\)
0.325283 + 0.945617i \(0.394540\pi\)
\(492\) −5.41083e89 −0.356807
\(493\) −1.02735e90 −0.632915
\(494\) 2.83028e89 0.162921
\(495\) 8.12682e90 4.37166
\(496\) 2.89388e89 0.145494
\(497\) 1.15452e89 0.0542577
\(498\) −4.30508e90 −1.89147
\(499\) 2.88968e90 1.18708 0.593542 0.804803i \(-0.297729\pi\)
0.593542 + 0.804803i \(0.297729\pi\)
\(500\) −3.35612e89 −0.128926
\(501\) 4.67082e89 0.167815
\(502\) 2.32178e90 0.780273
\(503\) −3.03767e90 −0.955021 −0.477511 0.878626i \(-0.658461\pi\)
−0.477511 + 0.878626i \(0.658461\pi\)
\(504\) 5.06647e89 0.149033
\(505\) −6.15405e90 −1.69395
\(506\) 2.92256e90 0.752873
\(507\) −6.09573e90 −1.46980
\(508\) 2.36732e90 0.534347
\(509\) 6.10246e90 1.28961 0.644806 0.764346i \(-0.276938\pi\)
0.644806 + 0.764346i \(0.276938\pi\)
\(510\) −4.31102e90 −0.853058
\(511\) 2.10685e89 0.0390420
\(512\) −2.40774e90 −0.417894
\(513\) −4.89367e90 −0.795614
\(514\) 3.89656e90 0.593495
\(515\) 1.54275e91 2.20167
\(516\) −7.68062e90 −1.02714
\(517\) −1.44029e91 −1.80517
\(518\) −5.27261e88 −0.00619411
\(519\) 9.20966e90 1.01423
\(520\) 4.67567e90 0.482761
\(521\) −1.36791e91 −1.32433 −0.662163 0.749360i \(-0.730362\pi\)
−0.662163 + 0.749360i \(0.730362\pi\)
\(522\) 1.55495e91 1.41174
\(523\) 7.08965e90 0.603695 0.301848 0.953356i \(-0.402397\pi\)
0.301848 + 0.953356i \(0.402397\pi\)
\(524\) 4.77951e90 0.381756
\(525\) −2.17849e90 −0.163237
\(526\) 1.81474e91 1.27582
\(527\) 5.30356e90 0.349874
\(528\) −1.00965e91 −0.625077
\(529\) −1.09692e91 −0.637399
\(530\) −3.10673e91 −1.69458
\(531\) −7.29266e90 −0.373439
\(532\) −6.97935e89 −0.0335564
\(533\) −2.91530e90 −0.131620
\(534\) 8.18218e90 0.346926
\(535\) −3.05352e91 −1.21604
\(536\) 3.84009e91 1.43655
\(537\) 4.54187e91 1.59623
\(538\) −1.00015e91 −0.330261
\(539\) −5.76222e91 −1.78799
\(540\) −2.75944e91 −0.804693
\(541\) −6.80713e90 −0.186576 −0.0932879 0.995639i \(-0.529738\pi\)
−0.0932879 + 0.995639i \(0.529738\pi\)
\(542\) −2.05677e91 −0.529919
\(543\) 1.20094e92 2.90888
\(544\) −2.03966e91 −0.464509
\(545\) −4.84611e90 −0.103779
\(546\) 1.49714e90 0.0301514
\(547\) 7.97357e91 1.51035 0.755174 0.655524i \(-0.227552\pi\)
0.755174 + 0.655524i \(0.227552\pi\)
\(548\) −7.17445e89 −0.0127832
\(549\) −4.56269e90 −0.0764799
\(550\) 9.26717e91 1.46149
\(551\) −6.27557e91 −0.931268
\(552\) −7.39419e91 −1.03260
\(553\) −3.71255e90 −0.0487955
\(554\) −4.17071e91 −0.515980
\(555\) 2.13977e91 0.249203
\(556\) −4.75455e91 −0.521319
\(557\) −6.17265e91 −0.637269 −0.318634 0.947878i \(-0.603224\pi\)
−0.318634 + 0.947878i \(0.603224\pi\)
\(558\) −8.02723e91 −0.780405
\(559\) −4.13824e91 −0.378896
\(560\) 3.12534e90 0.0269525
\(561\) −1.85036e92 −1.50315
\(562\) 1.54503e92 1.18242
\(563\) 2.12849e92 1.53476 0.767379 0.641194i \(-0.221560\pi\)
0.767379 + 0.641194i \(0.221560\pi\)
\(564\) 1.24380e92 0.845085
\(565\) 1.70084e92 1.08903
\(566\) −4.29169e91 −0.258987
\(567\) −1.02311e90 −0.00581956
\(568\) 1.24256e92 0.666267
\(569\) −2.23483e92 −1.12975 −0.564876 0.825176i \(-0.691076\pi\)
−0.564876 + 0.825176i \(0.691076\pi\)
\(570\) −2.63339e92 −1.25518
\(571\) −4.99687e91 −0.224589 −0.112294 0.993675i \(-0.535820\pi\)
−0.112294 + 0.993675i \(0.535820\pi\)
\(572\) 6.85005e91 0.290353
\(573\) 6.90901e91 0.276208
\(574\) −6.68387e90 −0.0252046
\(575\) 1.97869e92 0.703890
\(576\) 4.13426e92 1.38754
\(577\) −1.98229e92 −0.627736 −0.313868 0.949467i \(-0.601625\pi\)
−0.313868 + 0.949467i \(0.601625\pi\)
\(578\) −1.71193e92 −0.511569
\(579\) 4.76957e92 1.34508
\(580\) −3.53867e92 −0.941894
\(581\) 5.71988e91 0.143710
\(582\) −1.26695e92 −0.300496
\(583\) −1.33346e93 −2.98596
\(584\) 2.26751e92 0.479424
\(585\) −3.78128e92 −0.754949
\(586\) 3.50835e92 0.661504
\(587\) 1.77753e92 0.316548 0.158274 0.987395i \(-0.449407\pi\)
0.158274 + 0.987395i \(0.449407\pi\)
\(588\) 4.97609e92 0.837044
\(589\) 3.23969e92 0.514803
\(590\) −1.54301e92 −0.231647
\(591\) −9.57324e92 −1.35793
\(592\) −1.65445e91 −0.0221756
\(593\) 1.10546e93 1.40026 0.700132 0.714014i \(-0.253125\pi\)
0.700132 + 0.714014i \(0.253125\pi\)
\(594\) 1.10118e93 1.31829
\(595\) 5.72776e91 0.0648137
\(596\) −1.81137e92 −0.193758
\(597\) 1.05979e93 1.07172
\(598\) −1.35982e92 −0.130015
\(599\) 2.74758e92 0.248400 0.124200 0.992257i \(-0.460364\pi\)
0.124200 + 0.992257i \(0.460364\pi\)
\(600\) −2.34463e93 −2.00450
\(601\) 1.24095e93 1.00337 0.501683 0.865052i \(-0.332714\pi\)
0.501683 + 0.865052i \(0.332714\pi\)
\(602\) −9.48768e91 −0.0725567
\(603\) −3.10553e93 −2.24650
\(604\) −3.22418e92 −0.220639
\(605\) 5.10570e93 3.30560
\(606\) −2.12078e93 −1.29916
\(607\) −1.85465e93 −1.07508 −0.537541 0.843238i \(-0.680647\pi\)
−0.537541 + 0.843238i \(0.680647\pi\)
\(608\) −1.24593e93 −0.683475
\(609\) −3.31960e92 −0.172348
\(610\) −9.65393e91 −0.0474411
\(611\) 6.70146e92 0.311738
\(612\) 9.94469e92 0.437944
\(613\) −9.71814e92 −0.405189 −0.202594 0.979263i \(-0.564937\pi\)
−0.202594 + 0.979263i \(0.564937\pi\)
\(614\) −6.53301e92 −0.257913
\(615\) 2.71250e93 1.01404
\(616\) 4.60114e92 0.162897
\(617\) −5.79595e93 −1.94344 −0.971722 0.236129i \(-0.924121\pi\)
−0.971722 + 0.236129i \(0.924121\pi\)
\(618\) 5.31655e93 1.68856
\(619\) 1.80658e93 0.543527 0.271764 0.962364i \(-0.412393\pi\)
0.271764 + 0.962364i \(0.412393\pi\)
\(620\) 1.82680e93 0.520677
\(621\) 2.35119e93 0.634920
\(622\) 4.87936e93 1.24849
\(623\) −1.08711e92 −0.0263587
\(624\) 4.69773e92 0.107945
\(625\) −3.68503e93 −0.802528
\(626\) −3.64008e93 −0.751400
\(627\) −1.13030e94 −2.21172
\(628\) −1.74523e93 −0.323747
\(629\) −3.03208e92 −0.0533265
\(630\) −8.66928e92 −0.144569
\(631\) 1.24799e94 1.97346 0.986731 0.162366i \(-0.0519124\pi\)
0.986731 + 0.162366i \(0.0519124\pi\)
\(632\) −3.99567e93 −0.599194
\(633\) 7.23253e93 1.02865
\(634\) −7.60777e93 −1.02628
\(635\) −1.18676e94 −1.51860
\(636\) 1.15154e94 1.39787
\(637\) 2.68107e93 0.308771
\(638\) 1.41213e94 1.54306
\(639\) −1.00488e94 −1.04192
\(640\) −4.80997e93 −0.473275
\(641\) −1.46544e94 −1.36843 −0.684217 0.729279i \(-0.739856\pi\)
−0.684217 + 0.729279i \(0.739856\pi\)
\(642\) −1.05229e94 −0.932636
\(643\) −1.83843e93 −0.154661 −0.0773305 0.997006i \(-0.524640\pi\)
−0.0773305 + 0.997006i \(0.524640\pi\)
\(644\) 3.35327e92 0.0267788
\(645\) 3.85037e94 2.91912
\(646\) 3.73153e93 0.268595
\(647\) 1.37225e94 0.937867 0.468933 0.883234i \(-0.344638\pi\)
0.468933 + 0.883234i \(0.344638\pi\)
\(648\) −1.10113e93 −0.0714623
\(649\) −6.62287e93 −0.408177
\(650\) −4.31187e93 −0.252388
\(651\) 1.71370e93 0.0952737
\(652\) 1.15371e94 0.609259
\(653\) 9.27456e93 0.465266 0.232633 0.972565i \(-0.425266\pi\)
0.232633 + 0.972565i \(0.425266\pi\)
\(654\) −1.67005e93 −0.0795928
\(655\) −2.39602e94 −1.08494
\(656\) −2.09727e93 −0.0902352
\(657\) −1.83377e94 −0.749730
\(658\) 1.53643e93 0.0596962
\(659\) −3.82564e94 −1.41268 −0.706339 0.707874i \(-0.749655\pi\)
−0.706339 + 0.707874i \(0.749655\pi\)
\(660\) −6.37353e94 −2.23696
\(661\) 3.63043e94 1.21118 0.605590 0.795777i \(-0.292937\pi\)
0.605590 + 0.795777i \(0.292937\pi\)
\(662\) −1.22289e94 −0.387832
\(663\) 8.60945e93 0.259581
\(664\) 6.15608e94 1.76471
\(665\) 3.49881e93 0.0953665
\(666\) 4.58921e93 0.118946
\(667\) 3.01513e94 0.743175
\(668\) −2.27975e93 −0.0534412
\(669\) 8.98139e94 2.00248
\(670\) −6.57081e94 −1.39352
\(671\) −4.14364e93 −0.0835944
\(672\) −6.59060e93 −0.126490
\(673\) −8.84206e94 −1.61454 −0.807270 0.590182i \(-0.799056\pi\)
−0.807270 + 0.590182i \(0.799056\pi\)
\(674\) 1.15207e93 0.0200158
\(675\) 7.45539e94 1.23252
\(676\) 2.97523e94 0.468065
\(677\) 2.44389e94 0.365899 0.182949 0.983122i \(-0.441436\pi\)
0.182949 + 0.983122i \(0.441436\pi\)
\(678\) 5.86136e94 0.835225
\(679\) 1.68331e93 0.0228311
\(680\) 6.16456e94 0.795891
\(681\) −2.05063e95 −2.52034
\(682\) −7.28998e94 −0.853002
\(683\) −4.41098e94 −0.491408 −0.245704 0.969345i \(-0.579019\pi\)
−0.245704 + 0.969345i \(0.579019\pi\)
\(684\) 6.07473e94 0.644388
\(685\) 3.59662e93 0.0363296
\(686\) 1.23393e94 0.118695
\(687\) −1.71470e95 −1.57086
\(688\) −2.97705e94 −0.259761
\(689\) 6.20439e94 0.515650
\(690\) 1.26523e95 1.00167
\(691\) 7.50986e94 0.566392 0.283196 0.959062i \(-0.408605\pi\)
0.283196 + 0.959062i \(0.408605\pi\)
\(692\) −4.49509e94 −0.322986
\(693\) −3.72101e94 −0.254740
\(694\) 2.97627e94 0.194147
\(695\) 2.38350e95 1.48158
\(696\) −3.57275e95 −2.11638
\(697\) −3.84363e94 −0.216992
\(698\) 2.26002e95 1.21606
\(699\) 3.33636e95 1.71115
\(700\) 1.06329e94 0.0519837
\(701\) −1.61698e95 −0.753617 −0.376808 0.926291i \(-0.622978\pi\)
−0.376808 + 0.926291i \(0.622978\pi\)
\(702\) −5.12360e94 −0.227658
\(703\) −1.85215e94 −0.0784644
\(704\) 3.75456e95 1.51661
\(705\) −6.23528e95 −2.40171
\(706\) −1.49793e92 −0.000550215 0
\(707\) 2.81774e94 0.0987076
\(708\) 5.71933e94 0.191087
\(709\) 2.05667e95 0.655413 0.327707 0.944780i \(-0.393724\pi\)
0.327707 + 0.944780i \(0.393724\pi\)
\(710\) −2.12616e95 −0.646309
\(711\) 3.23135e95 0.937028
\(712\) −1.17002e95 −0.323677
\(713\) −1.55653e95 −0.410826
\(714\) 1.97388e94 0.0497084
\(715\) −3.43399e95 −0.825177
\(716\) −2.21681e95 −0.508327
\(717\) 5.61363e93 0.0122844
\(718\) −6.11014e95 −1.27609
\(719\) 2.35820e95 0.470070 0.235035 0.971987i \(-0.424479\pi\)
0.235035 + 0.971987i \(0.424479\pi\)
\(720\) −2.72026e95 −0.517572
\(721\) −7.06375e94 −0.128293
\(722\) −1.72396e95 −0.298904
\(723\) 1.54192e96 2.55229
\(724\) −5.86157e95 −0.926344
\(725\) 9.56069e95 1.44267
\(726\) 1.75950e96 2.53521
\(727\) 4.63503e95 0.637750 0.318875 0.947797i \(-0.396695\pi\)
0.318875 + 0.947797i \(0.396695\pi\)
\(728\) −2.14084e94 −0.0281309
\(729\) −1.27815e96 −1.60402
\(730\) −3.87997e95 −0.465063
\(731\) −5.45600e95 −0.624658
\(732\) 3.57833e94 0.0391344
\(733\) 1.41477e96 1.47809 0.739047 0.673654i \(-0.235276\pi\)
0.739047 + 0.673654i \(0.235276\pi\)
\(734\) −8.34170e95 −0.832600
\(735\) −2.49456e96 −2.37886
\(736\) 5.98613e95 0.545430
\(737\) −2.82031e96 −2.45548
\(738\) 5.81755e95 0.484008
\(739\) 2.00156e96 1.59141 0.795703 0.605688i \(-0.207102\pi\)
0.795703 + 0.605688i \(0.207102\pi\)
\(740\) −1.04439e95 −0.0793597
\(741\) 5.25910e95 0.381946
\(742\) 1.42247e95 0.0987444
\(743\) −6.29529e95 −0.417725 −0.208863 0.977945i \(-0.566976\pi\)
−0.208863 + 0.977945i \(0.566976\pi\)
\(744\) 1.84439e96 1.16993
\(745\) 9.08059e95 0.550654
\(746\) −2.23290e94 −0.0129455
\(747\) −4.97851e96 −2.75968
\(748\) 9.03133e95 0.478683
\(749\) 1.39811e95 0.0708598
\(750\) 5.79800e95 0.281013
\(751\) 4.41895e95 0.204824 0.102412 0.994742i \(-0.467344\pi\)
0.102412 + 0.994742i \(0.467344\pi\)
\(752\) 4.82104e95 0.213719
\(753\) 4.31423e96 1.82925
\(754\) −6.57044e95 −0.266474
\(755\) 1.61631e96 0.627050
\(756\) 1.26346e95 0.0468901
\(757\) −5.26073e96 −1.86782 −0.933908 0.357513i \(-0.883625\pi\)
−0.933908 + 0.357513i \(0.883625\pi\)
\(758\) −2.80381e96 −0.952425
\(759\) 5.43058e96 1.76501
\(760\) 3.76563e96 1.17107
\(761\) 2.28223e96 0.679161 0.339581 0.940577i \(-0.389715\pi\)
0.339581 + 0.940577i \(0.389715\pi\)
\(762\) −4.08977e96 −1.16468
\(763\) 2.21888e94 0.00604730
\(764\) −3.37218e95 −0.0879596
\(765\) −4.98537e96 −1.24463
\(766\) −5.27738e95 −0.126111
\(767\) 3.08152e95 0.0704888
\(768\) −7.91443e96 −1.73308
\(769\) −3.29099e95 −0.0689913 −0.0344956 0.999405i \(-0.510982\pi\)
−0.0344956 + 0.999405i \(0.510982\pi\)
\(770\) −7.87306e95 −0.158017
\(771\) 7.24043e96 1.39137
\(772\) −2.32795e96 −0.428345
\(773\) −1.15830e96 −0.204084 −0.102042 0.994780i \(-0.532538\pi\)
−0.102042 + 0.994780i \(0.532538\pi\)
\(774\) 8.25795e96 1.39332
\(775\) −4.93560e96 −0.797504
\(776\) 1.81168e96 0.280358
\(777\) −9.79734e94 −0.0145213
\(778\) 5.14295e96 0.730123
\(779\) −2.34789e96 −0.319281
\(780\) 2.96550e96 0.386304
\(781\) −9.12584e96 −1.13884
\(782\) −1.79284e96 −0.214346
\(783\) 1.13606e97 1.30131
\(784\) 1.92876e96 0.211685
\(785\) 8.74901e96 0.920080
\(786\) −8.25704e96 −0.832088
\(787\) −8.38013e96 −0.809277 −0.404639 0.914477i \(-0.632603\pi\)
−0.404639 + 0.914477i \(0.632603\pi\)
\(788\) 4.67254e96 0.432439
\(789\) 3.37206e97 2.99100
\(790\) 6.83703e96 0.581246
\(791\) −7.78760e95 −0.0634588
\(792\) −4.00478e97 −3.12813
\(793\) 1.92797e95 0.0144360
\(794\) 9.63823e96 0.691848
\(795\) −5.77279e97 −3.97271
\(796\) −5.17269e96 −0.341294
\(797\) 1.06380e97 0.672988 0.336494 0.941686i \(-0.390759\pi\)
0.336494 + 0.941686i \(0.390759\pi\)
\(798\) 1.20575e96 0.0731407
\(799\) 8.83544e96 0.513938
\(800\) 1.89814e97 1.05880
\(801\) 9.46208e96 0.506171
\(802\) −1.62944e97 −0.835985
\(803\) −1.66535e97 −0.819473
\(804\) 2.43554e97 1.14952
\(805\) −1.68102e96 −0.0761048
\(806\) 3.39191e96 0.147306
\(807\) −1.85843e97 −0.774253
\(808\) 3.03262e97 1.21210
\(809\) 4.90920e97 1.88250 0.941250 0.337711i \(-0.109653\pi\)
0.941250 + 0.337711i \(0.109653\pi\)
\(810\) 1.88416e96 0.0693217
\(811\) 2.45004e97 0.864917 0.432458 0.901654i \(-0.357646\pi\)
0.432458 + 0.901654i \(0.357646\pi\)
\(812\) 1.62024e96 0.0548849
\(813\) −3.82180e97 −1.24232
\(814\) 4.16772e96 0.130011
\(815\) −5.78366e97 −1.73150
\(816\) 6.19365e96 0.177961
\(817\) −3.33281e97 −0.919117
\(818\) 3.71387e97 0.983085
\(819\) 1.73133e96 0.0439915
\(820\) −1.32393e97 −0.322924
\(821\) −2.49187e97 −0.583485 −0.291742 0.956497i \(-0.594235\pi\)
−0.291742 + 0.956497i \(0.594235\pi\)
\(822\) 1.23945e96 0.0278627
\(823\) 2.64932e97 0.571794 0.285897 0.958260i \(-0.407708\pi\)
0.285897 + 0.958260i \(0.407708\pi\)
\(824\) −7.60244e97 −1.57540
\(825\) 1.72198e98 3.42627
\(826\) 7.06495e95 0.0134982
\(827\) 2.19369e97 0.402477 0.201238 0.979542i \(-0.435503\pi\)
0.201238 + 0.979542i \(0.435503\pi\)
\(828\) −2.91864e97 −0.514238
\(829\) −8.91046e97 −1.50773 −0.753864 0.657030i \(-0.771812\pi\)
−0.753864 + 0.657030i \(0.771812\pi\)
\(830\) −1.05337e98 −1.71185
\(831\) −7.74983e97 −1.20964
\(832\) −1.74694e97 −0.261906
\(833\) 3.53481e97 0.509048
\(834\) 8.21391e97 1.13628
\(835\) 1.14286e97 0.151879
\(836\) 5.51681e97 0.704332
\(837\) −5.86476e97 −0.719362
\(838\) 7.60921e97 0.896737
\(839\) 1.07395e98 1.21607 0.608035 0.793910i \(-0.291958\pi\)
0.608035 + 0.793910i \(0.291958\pi\)
\(840\) 1.99191e97 0.216728
\(841\) 5.00404e97 0.523185
\(842\) −9.03933e97 −0.908199
\(843\) 2.87091e98 2.77202
\(844\) −3.53008e97 −0.327577
\(845\) −1.49151e98 −1.33023
\(846\) −1.33729e98 −1.14636
\(847\) −2.33774e97 −0.192620
\(848\) 4.46344e97 0.353516
\(849\) −7.97463e97 −0.607159
\(850\) −5.68491e97 −0.416092
\(851\) 8.89875e96 0.0626165
\(852\) 7.88082e97 0.533145
\(853\) −2.41773e97 −0.157259 −0.0786295 0.996904i \(-0.525054\pi\)
−0.0786295 + 0.996904i \(0.525054\pi\)
\(854\) 4.42022e95 0.00276443
\(855\) −3.04532e98 −1.83134
\(856\) 1.50473e98 0.870136
\(857\) 1.45082e97 0.0806780 0.0403390 0.999186i \(-0.487156\pi\)
0.0403390 + 0.999186i \(0.487156\pi\)
\(858\) −1.18341e98 −0.632864
\(859\) 2.11191e98 1.08619 0.543093 0.839672i \(-0.317253\pi\)
0.543093 + 0.839672i \(0.317253\pi\)
\(860\) −1.87930e98 −0.929605
\(861\) −1.24197e97 −0.0590887
\(862\) 6.10768e97 0.279501
\(863\) −2.19104e98 −0.964470 −0.482235 0.876042i \(-0.660175\pi\)
−0.482235 + 0.876042i \(0.660175\pi\)
\(864\) 2.25548e98 0.955056
\(865\) 2.25343e98 0.917919
\(866\) −6.14003e96 −0.0240614
\(867\) −3.18104e98 −1.19930
\(868\) −8.36432e96 −0.0303403
\(869\) 2.93457e98 1.02419
\(870\) 6.11337e98 2.05298
\(871\) 1.31224e98 0.424040
\(872\) 2.38809e97 0.0742590
\(873\) −1.46513e98 −0.438429
\(874\) −1.09516e98 −0.315387
\(875\) −7.70342e96 −0.0213508
\(876\) 1.43815e98 0.383634
\(877\) −6.51102e98 −1.67172 −0.835858 0.548946i \(-0.815029\pi\)
−0.835858 + 0.548946i \(0.815029\pi\)
\(878\) 1.03077e98 0.254738
\(879\) 6.51906e98 1.55081
\(880\) −2.47042e98 −0.565719
\(881\) −6.96595e98 −1.53563 −0.767817 0.640670i \(-0.778657\pi\)
−0.767817 + 0.640670i \(0.778657\pi\)
\(882\) −5.35013e98 −1.13545
\(883\) −1.65040e98 −0.337215 −0.168607 0.985683i \(-0.553927\pi\)
−0.168607 + 0.985683i \(0.553927\pi\)
\(884\) −4.20214e97 −0.0826645
\(885\) −2.86715e98 −0.543064
\(886\) 2.09788e98 0.382606
\(887\) 5.98960e98 1.05186 0.525929 0.850529i \(-0.323718\pi\)
0.525929 + 0.850529i \(0.323718\pi\)
\(888\) −1.05445e98 −0.178316
\(889\) 5.43380e97 0.0884902
\(890\) 2.00202e98 0.313982
\(891\) 8.08715e97 0.122150
\(892\) −4.38368e98 −0.637699
\(893\) 5.39714e98 0.756206
\(894\) 3.12931e98 0.422321
\(895\) 1.11131e99 1.44465
\(896\) 2.20233e97 0.0275781
\(897\) −2.52676e98 −0.304802
\(898\) −1.09535e99 −1.27291
\(899\) −7.52088e98 −0.842014
\(900\) −9.25472e98 −0.998250
\(901\) 8.18008e98 0.850113
\(902\) 5.28325e98 0.529032
\(903\) −1.76296e98 −0.170099
\(904\) −8.38149e98 −0.779253
\(905\) 2.93846e99 2.63265
\(906\) 5.57006e98 0.480911
\(907\) 1.20263e99 1.00067 0.500333 0.865833i \(-0.333211\pi\)
0.500333 + 0.865833i \(0.333211\pi\)
\(908\) 1.00088e99 0.802612
\(909\) −2.45252e99 −1.89550
\(910\) 3.66321e97 0.0272882
\(911\) −5.27192e98 −0.378532 −0.189266 0.981926i \(-0.560611\pi\)
−0.189266 + 0.981926i \(0.560611\pi\)
\(912\) 3.78340e98 0.261852
\(913\) −4.52126e99 −3.01640
\(914\) 1.01632e99 0.653634
\(915\) −1.79385e98 −0.111219
\(916\) 8.36917e98 0.500247
\(917\) 1.09706e98 0.0632204
\(918\) −6.75513e98 −0.375322
\(919\) −1.45226e98 −0.0777993 −0.0388997 0.999243i \(-0.512385\pi\)
−0.0388997 + 0.999243i \(0.512385\pi\)
\(920\) −1.80922e99 −0.934543
\(921\) −1.21394e99 −0.604642
\(922\) −1.86079e98 −0.0893741
\(923\) 4.24611e98 0.196668
\(924\) 2.91823e98 0.130349
\(925\) 2.82171e98 0.121553
\(926\) 1.01556e99 0.421929
\(927\) 6.14820e99 2.46364
\(928\) 2.89240e99 1.11789
\(929\) −1.56446e99 −0.583227 −0.291614 0.956536i \(-0.594192\pi\)
−0.291614 + 0.956536i \(0.594192\pi\)
\(930\) −3.15596e99 −1.13489
\(931\) 2.15925e99 0.749011
\(932\) −1.62842e99 −0.544922
\(933\) 9.06662e99 2.92692
\(934\) −1.87543e99 −0.584090
\(935\) −4.52749e99 −1.36041
\(936\) 1.86336e99 0.540201
\(937\) −4.36725e99 −1.22161 −0.610804 0.791782i \(-0.709154\pi\)
−0.610804 + 0.791782i \(0.709154\pi\)
\(938\) 3.00856e98 0.0812015
\(939\) −6.76385e99 −1.76156
\(940\) 3.04334e99 0.764835
\(941\) −5.74065e99 −1.39222 −0.696111 0.717934i \(-0.745088\pi\)
−0.696111 + 0.717934i \(0.745088\pi\)
\(942\) 3.01505e99 0.705649
\(943\) 1.12806e99 0.254794
\(944\) 2.21685e98 0.0483252
\(945\) −6.33384e98 −0.133261
\(946\) 7.49951e99 1.52293
\(947\) 1.46937e99 0.288010 0.144005 0.989577i \(-0.454002\pi\)
0.144005 + 0.989577i \(0.454002\pi\)
\(948\) −2.53422e99 −0.479473
\(949\) 7.74861e98 0.141516
\(950\) −3.47264e99 −0.612236
\(951\) −1.41364e100 −2.40598
\(952\) −2.82256e98 −0.0463772
\(953\) 3.58980e99 0.569453 0.284727 0.958609i \(-0.408097\pi\)
0.284727 + 0.958609i \(0.408097\pi\)
\(954\) −1.23810e100 −1.89620
\(955\) 1.69051e99 0.249979
\(956\) −2.73992e97 −0.00391200
\(957\) 2.62397e100 3.61750
\(958\) 3.16667e99 0.421559
\(959\) −1.64678e97 −0.00211696
\(960\) 1.62541e100 2.01779
\(961\) −4.45873e99 −0.534536
\(962\) −1.93918e98 −0.0224519
\(963\) −1.21690e100 −1.36073
\(964\) −7.52588e99 −0.812787
\(965\) 1.16702e100 1.21735
\(966\) −5.79307e98 −0.0583681
\(967\) 1.01618e100 0.988969 0.494484 0.869187i \(-0.335357\pi\)
0.494484 + 0.869187i \(0.335357\pi\)
\(968\) −2.51601e100 −2.36531
\(969\) 6.93377e99 0.629685
\(970\) −3.09998e99 −0.271960
\(971\) −6.18477e99 −0.524179 −0.262089 0.965044i \(-0.584412\pi\)
−0.262089 + 0.965044i \(0.584412\pi\)
\(972\) 5.97470e99 0.489211
\(973\) −1.09133e99 −0.0863326
\(974\) 3.04387e99 0.232649
\(975\) −8.01212e99 −0.591688
\(976\) 1.38698e98 0.00989696
\(977\) 9.04350e99 0.623546 0.311773 0.950157i \(-0.399077\pi\)
0.311773 + 0.950157i \(0.399077\pi\)
\(978\) −1.99314e100 −1.32796
\(979\) 8.59305e99 0.553257
\(980\) 1.21756e100 0.757557
\(981\) −1.93128e99 −0.116127
\(982\) 7.77064e99 0.451567
\(983\) −9.29144e99 −0.521844 −0.260922 0.965360i \(-0.584026\pi\)
−0.260922 + 0.965360i \(0.584026\pi\)
\(984\) −1.33668e100 −0.725591
\(985\) −2.34239e100 −1.22898
\(986\) −8.66269e99 −0.439315
\(987\) 2.85494e99 0.139950
\(988\) −2.56688e99 −0.121632
\(989\) 1.60126e100 0.733479
\(990\) 6.85261e100 3.03443
\(991\) −3.03921e100 −1.30105 −0.650524 0.759485i \(-0.725451\pi\)
−0.650524 + 0.759485i \(0.725451\pi\)
\(992\) −1.49317e100 −0.617970
\(993\) −2.27231e100 −0.909219
\(994\) 9.73499e98 0.0376610
\(995\) 2.59312e100 0.969950
\(996\) 3.90444e100 1.41212
\(997\) 2.16012e100 0.755422 0.377711 0.925924i \(-0.376711\pi\)
0.377711 + 0.925924i \(0.376711\pi\)
\(998\) 2.43661e100 0.823971
\(999\) 3.35291e99 0.109642
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 1.68.a.a.1.4 5
3.2 odd 2 9.68.a.a.1.2 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.68.a.a.1.4 5 1.1 even 1 trivial
9.68.a.a.1.2 5 3.2 odd 2