Properties

Label 8042.2.a.c.1.15
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 0
Dimension 86
CM No

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Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(0\)
Dimension: \(86\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-2.17138 q^{3}\) \(+1.00000 q^{4}\) \(+3.37288 q^{5}\) \(+2.17138 q^{6}\) \(+0.0526160 q^{7}\) \(-1.00000 q^{8}\) \(+1.71488 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-2.17138 q^{3}\) \(+1.00000 q^{4}\) \(+3.37288 q^{5}\) \(+2.17138 q^{6}\) \(+0.0526160 q^{7}\) \(-1.00000 q^{8}\) \(+1.71488 q^{9}\) \(-3.37288 q^{10}\) \(-3.41347 q^{11}\) \(-2.17138 q^{12}\) \(+0.293411 q^{13}\) \(-0.0526160 q^{14}\) \(-7.32379 q^{15}\) \(+1.00000 q^{16}\) \(-1.08333 q^{17}\) \(-1.71488 q^{18}\) \(+4.94043 q^{19}\) \(+3.37288 q^{20}\) \(-0.114249 q^{21}\) \(+3.41347 q^{22}\) \(+4.89351 q^{23}\) \(+2.17138 q^{24}\) \(+6.37629 q^{25}\) \(-0.293411 q^{26}\) \(+2.79048 q^{27}\) \(+0.0526160 q^{28}\) \(-1.82864 q^{29}\) \(+7.32379 q^{30}\) \(+8.89349 q^{31}\) \(-1.00000 q^{32}\) \(+7.41194 q^{33}\) \(+1.08333 q^{34}\) \(+0.177467 q^{35}\) \(+1.71488 q^{36}\) \(+3.24810 q^{37}\) \(-4.94043 q^{38}\) \(-0.637107 q^{39}\) \(-3.37288 q^{40}\) \(-5.40286 q^{41}\) \(+0.114249 q^{42}\) \(+0.278980 q^{43}\) \(-3.41347 q^{44}\) \(+5.78409 q^{45}\) \(-4.89351 q^{46}\) \(-4.56043 q^{47}\) \(-2.17138 q^{48}\) \(-6.99723 q^{49}\) \(-6.37629 q^{50}\) \(+2.35231 q^{51}\) \(+0.293411 q^{52}\) \(-6.10135 q^{53}\) \(-2.79048 q^{54}\) \(-11.5132 q^{55}\) \(-0.0526160 q^{56}\) \(-10.7275 q^{57}\) \(+1.82864 q^{58}\) \(+6.43470 q^{59}\) \(-7.32379 q^{60}\) \(-1.07070 q^{61}\) \(-8.89349 q^{62}\) \(+0.0902303 q^{63}\) \(+1.00000 q^{64}\) \(+0.989640 q^{65}\) \(-7.41194 q^{66}\) \(-1.46666 q^{67}\) \(-1.08333 q^{68}\) \(-10.6257 q^{69}\) \(-0.177467 q^{70}\) \(-0.917589 q^{71}\) \(-1.71488 q^{72}\) \(+9.92543 q^{73}\) \(-3.24810 q^{74}\) \(-13.8453 q^{75}\) \(+4.94043 q^{76}\) \(-0.179603 q^{77}\) \(+0.637107 q^{78}\) \(+7.70598 q^{79}\) \(+3.37288 q^{80}\) \(-11.2038 q^{81}\) \(+5.40286 q^{82}\) \(+6.94011 q^{83}\) \(-0.114249 q^{84}\) \(-3.65392 q^{85}\) \(-0.278980 q^{86}\) \(+3.97067 q^{87}\) \(+3.41347 q^{88}\) \(-5.52579 q^{89}\) \(-5.78409 q^{90}\) \(+0.0154381 q^{91}\) \(+4.89351 q^{92}\) \(-19.3111 q^{93}\) \(+4.56043 q^{94}\) \(+16.6634 q^{95}\) \(+2.17138 q^{96}\) \(+9.29685 q^{97}\) \(+6.99723 q^{98}\) \(-5.85371 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 12q^{12} \) \(\mathstrut +\mathstrut 45q^{13} \) \(\mathstrut -\mathstrut 35q^{14} \) \(\mathstrut +\mathstrut 17q^{15} \) \(\mathstrut +\mathstrut 86q^{16} \) \(\mathstrut +\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 72q^{18} \) \(\mathstrut +\mathstrut 47q^{19} \) \(\mathstrut -\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut -\mathstrut 12q^{24} \) \(\mathstrut +\mathstrut 112q^{25} \) \(\mathstrut -\mathstrut 45q^{26} \) \(\mathstrut +\mathstrut 51q^{27} \) \(\mathstrut +\mathstrut 35q^{28} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut -\mathstrut 17q^{30} \) \(\mathstrut +\mathstrut 24q^{31} \) \(\mathstrut -\mathstrut 86q^{32} \) \(\mathstrut +\mathstrut 43q^{33} \) \(\mathstrut -\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 42q^{35} \) \(\mathstrut +\mathstrut 72q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 47q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut -\mathstrut 15q^{42} \) \(\mathstrut +\mathstrut 72q^{43} \) \(\mathstrut +\mathstrut 13q^{44} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut +\mathstrut 12q^{48} \) \(\mathstrut +\mathstrut 89q^{49} \) \(\mathstrut -\mathstrut 112q^{50} \) \(\mathstrut +\mathstrut 56q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut -\mathstrut 7q^{53} \) \(\mathstrut -\mathstrut 51q^{54} \) \(\mathstrut +\mathstrut 48q^{55} \) \(\mathstrut -\mathstrut 35q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 17q^{60} \) \(\mathstrut +\mathstrut 31q^{61} \) \(\mathstrut -\mathstrut 24q^{62} \) \(\mathstrut +\mathstrut 98q^{63} \) \(\mathstrut +\mathstrut 86q^{64} \) \(\mathstrut -\mathstrut 9q^{65} \) \(\mathstrut -\mathstrut 43q^{66} \) \(\mathstrut +\mathstrut 157q^{67} \) \(\mathstrut +\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut q^{69} \) \(\mathstrut -\mathstrut 42q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 72q^{72} \) \(\mathstrut +\mathstrut 74q^{73} \) \(\mathstrut -\mathstrut 61q^{74} \) \(\mathstrut +\mathstrut 76q^{75} \) \(\mathstrut +\mathstrut 47q^{76} \) \(\mathstrut -\mathstrut 13q^{77} \) \(\mathstrut -\mathstrut 20q^{78} \) \(\mathstrut +\mathstrut 57q^{79} \) \(\mathstrut -\mathstrut 4q^{80} \) \(\mathstrut +\mathstrut 34q^{81} \) \(\mathstrut +\mathstrut 16q^{82} \) \(\mathstrut +\mathstrut 65q^{83} \) \(\mathstrut +\mathstrut 15q^{84} \) \(\mathstrut +\mathstrut 102q^{85} \) \(\mathstrut -\mathstrut 72q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 91q^{91} \) \(\mathstrut +\mathstrut 6q^{92} \) \(\mathstrut +\mathstrut 57q^{93} \) \(\mathstrut -\mathstrut 11q^{94} \) \(\mathstrut -\mathstrut 13q^{95} \) \(\mathstrut -\mathstrut 12q^{96} \) \(\mathstrut +\mathstrut 64q^{97} \) \(\mathstrut -\mathstrut 89q^{98} \) \(\mathstrut +\mathstrut 56q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.17138 −1.25365 −0.626823 0.779162i \(-0.715645\pi\)
−0.626823 + 0.779162i \(0.715645\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.37288 1.50840 0.754198 0.656647i \(-0.228026\pi\)
0.754198 + 0.656647i \(0.228026\pi\)
\(6\) 2.17138 0.886461
\(7\) 0.0526160 0.0198870 0.00994349 0.999951i \(-0.496835\pi\)
0.00994349 + 0.999951i \(0.496835\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.71488 0.571627
\(10\) −3.37288 −1.06660
\(11\) −3.41347 −1.02920 −0.514601 0.857430i \(-0.672060\pi\)
−0.514601 + 0.857430i \(0.672060\pi\)
\(12\) −2.17138 −0.626823
\(13\) 0.293411 0.0813777 0.0406888 0.999172i \(-0.487045\pi\)
0.0406888 + 0.999172i \(0.487045\pi\)
\(14\) −0.0526160 −0.0140622
\(15\) −7.32379 −1.89099
\(16\) 1.00000 0.250000
\(17\) −1.08333 −0.262745 −0.131372 0.991333i \(-0.541938\pi\)
−0.131372 + 0.991333i \(0.541938\pi\)
\(18\) −1.71488 −0.404202
\(19\) 4.94043 1.13341 0.566706 0.823920i \(-0.308218\pi\)
0.566706 + 0.823920i \(0.308218\pi\)
\(20\) 3.37288 0.754198
\(21\) −0.114249 −0.0249312
\(22\) 3.41347 0.727755
\(23\) 4.89351 1.02037 0.510184 0.860065i \(-0.329577\pi\)
0.510184 + 0.860065i \(0.329577\pi\)
\(24\) 2.17138 0.443231
\(25\) 6.37629 1.27526
\(26\) −0.293411 −0.0575427
\(27\) 2.79048 0.537027
\(28\) 0.0526160 0.00994349
\(29\) −1.82864 −0.339570 −0.169785 0.985481i \(-0.554307\pi\)
−0.169785 + 0.985481i \(0.554307\pi\)
\(30\) 7.32379 1.33713
\(31\) 8.89349 1.59732 0.798659 0.601784i \(-0.205543\pi\)
0.798659 + 0.601784i \(0.205543\pi\)
\(32\) −1.00000 −0.176777
\(33\) 7.41194 1.29025
\(34\) 1.08333 0.185789
\(35\) 0.177467 0.0299975
\(36\) 1.71488 0.285814
\(37\) 3.24810 0.533984 0.266992 0.963699i \(-0.413970\pi\)
0.266992 + 0.963699i \(0.413970\pi\)
\(38\) −4.94043 −0.801443
\(39\) −0.637107 −0.102019
\(40\) −3.37288 −0.533298
\(41\) −5.40286 −0.843785 −0.421892 0.906646i \(-0.638634\pi\)
−0.421892 + 0.906646i \(0.638634\pi\)
\(42\) 0.114249 0.0176290
\(43\) 0.278980 0.0425441 0.0212720 0.999774i \(-0.493228\pi\)
0.0212720 + 0.999774i \(0.493228\pi\)
\(44\) −3.41347 −0.514601
\(45\) 5.78409 0.862241
\(46\) −4.89351 −0.721509
\(47\) −4.56043 −0.665207 −0.332604 0.943067i \(-0.607927\pi\)
−0.332604 + 0.943067i \(0.607927\pi\)
\(48\) −2.17138 −0.313411
\(49\) −6.99723 −0.999605
\(50\) −6.37629 −0.901744
\(51\) 2.35231 0.329389
\(52\) 0.293411 0.0406888
\(53\) −6.10135 −0.838086 −0.419043 0.907967i \(-0.637634\pi\)
−0.419043 + 0.907967i \(0.637634\pi\)
\(54\) −2.79048 −0.379736
\(55\) −11.5132 −1.55244
\(56\) −0.0526160 −0.00703111
\(57\) −10.7275 −1.42090
\(58\) 1.82864 0.240113
\(59\) 6.43470 0.837727 0.418864 0.908049i \(-0.362429\pi\)
0.418864 + 0.908049i \(0.362429\pi\)
\(60\) −7.32379 −0.945497
\(61\) −1.07070 −0.137089 −0.0685445 0.997648i \(-0.521836\pi\)
−0.0685445 + 0.997648i \(0.521836\pi\)
\(62\) −8.89349 −1.12947
\(63\) 0.0902303 0.0113679
\(64\) 1.00000 0.125000
\(65\) 0.989640 0.122750
\(66\) −7.41194 −0.912347
\(67\) −1.46666 −0.179181 −0.0895905 0.995979i \(-0.528556\pi\)
−0.0895905 + 0.995979i \(0.528556\pi\)
\(68\) −1.08333 −0.131372
\(69\) −10.6257 −1.27918
\(70\) −0.177467 −0.0212114
\(71\) −0.917589 −0.108898 −0.0544489 0.998517i \(-0.517340\pi\)
−0.0544489 + 0.998517i \(0.517340\pi\)
\(72\) −1.71488 −0.202101
\(73\) 9.92543 1.16168 0.580842 0.814017i \(-0.302724\pi\)
0.580842 + 0.814017i \(0.302724\pi\)
\(74\) −3.24810 −0.377584
\(75\) −13.8453 −1.59872
\(76\) 4.94043 0.566706
\(77\) −0.179603 −0.0204677
\(78\) 0.637107 0.0721382
\(79\) 7.70598 0.866990 0.433495 0.901156i \(-0.357280\pi\)
0.433495 + 0.901156i \(0.357280\pi\)
\(80\) 3.37288 0.377099
\(81\) −11.2038 −1.24487
\(82\) 5.40286 0.596646
\(83\) 6.94011 0.761776 0.380888 0.924621i \(-0.375618\pi\)
0.380888 + 0.924621i \(0.375618\pi\)
\(84\) −0.114249 −0.0124656
\(85\) −3.65392 −0.396323
\(86\) −0.278980 −0.0300832
\(87\) 3.97067 0.425701
\(88\) 3.41347 0.363878
\(89\) −5.52579 −0.585732 −0.292866 0.956153i \(-0.594609\pi\)
−0.292866 + 0.956153i \(0.594609\pi\)
\(90\) −5.78409 −0.609696
\(91\) 0.0154381 0.00161836
\(92\) 4.89351 0.510184
\(93\) −19.3111 −2.00247
\(94\) 4.56043 0.470372
\(95\) 16.6634 1.70963
\(96\) 2.17138 0.221615
\(97\) 9.29685 0.943952 0.471976 0.881611i \(-0.343541\pi\)
0.471976 + 0.881611i \(0.343541\pi\)
\(98\) 6.99723 0.706827
\(99\) −5.85371 −0.588320
\(100\) 6.37629 0.637629
\(101\) −5.28666 −0.526042 −0.263021 0.964790i \(-0.584719\pi\)
−0.263021 + 0.964790i \(0.584719\pi\)
\(102\) −2.35231 −0.232913
\(103\) 2.54577 0.250842 0.125421 0.992104i \(-0.459972\pi\)
0.125421 + 0.992104i \(0.459972\pi\)
\(104\) −0.293411 −0.0287713
\(105\) −0.385349 −0.0376062
\(106\) 6.10135 0.592616
\(107\) −10.2676 −0.992607 −0.496304 0.868149i \(-0.665310\pi\)
−0.496304 + 0.868149i \(0.665310\pi\)
\(108\) 2.79048 0.268514
\(109\) 19.4556 1.86351 0.931756 0.363084i \(-0.118276\pi\)
0.931756 + 0.363084i \(0.118276\pi\)
\(110\) 11.5132 1.09774
\(111\) −7.05284 −0.669426
\(112\) 0.0526160 0.00497175
\(113\) −10.1419 −0.954073 −0.477037 0.878883i \(-0.658289\pi\)
−0.477037 + 0.878883i \(0.658289\pi\)
\(114\) 10.7275 1.00473
\(115\) 16.5052 1.53912
\(116\) −1.82864 −0.169785
\(117\) 0.503166 0.0465177
\(118\) −6.43470 −0.592363
\(119\) −0.0570003 −0.00522521
\(120\) 7.32379 0.668567
\(121\) 0.651811 0.0592556
\(122\) 1.07070 0.0969366
\(123\) 11.7317 1.05781
\(124\) 8.89349 0.798659
\(125\) 4.64206 0.415198
\(126\) −0.0902303 −0.00803835
\(127\) −8.09666 −0.718462 −0.359231 0.933249i \(-0.616961\pi\)
−0.359231 + 0.933249i \(0.616961\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −0.605771 −0.0533352
\(130\) −0.989640 −0.0867972
\(131\) −14.9833 −1.30910 −0.654550 0.756018i \(-0.727142\pi\)
−0.654550 + 0.756018i \(0.727142\pi\)
\(132\) 7.41194 0.645127
\(133\) 0.259946 0.0225401
\(134\) 1.46666 0.126700
\(135\) 9.41193 0.810050
\(136\) 1.08333 0.0928944
\(137\) 20.2771 1.73239 0.866195 0.499707i \(-0.166559\pi\)
0.866195 + 0.499707i \(0.166559\pi\)
\(138\) 10.6257 0.904516
\(139\) 18.8107 1.59551 0.797753 0.602985i \(-0.206022\pi\)
0.797753 + 0.602985i \(0.206022\pi\)
\(140\) 0.177467 0.0149987
\(141\) 9.90242 0.833934
\(142\) 0.917589 0.0770024
\(143\) −1.00155 −0.0837540
\(144\) 1.71488 0.142907
\(145\) −6.16778 −0.512207
\(146\) −9.92543 −0.821434
\(147\) 15.1936 1.25315
\(148\) 3.24810 0.266992
\(149\) 10.8116 0.885720 0.442860 0.896591i \(-0.353964\pi\)
0.442860 + 0.896591i \(0.353964\pi\)
\(150\) 13.8453 1.13047
\(151\) −1.73171 −0.140925 −0.0704623 0.997514i \(-0.522447\pi\)
−0.0704623 + 0.997514i \(0.522447\pi\)
\(152\) −4.94043 −0.400721
\(153\) −1.85778 −0.150192
\(154\) 0.179603 0.0144729
\(155\) 29.9966 2.40939
\(156\) −0.637107 −0.0510094
\(157\) 6.56378 0.523847 0.261923 0.965089i \(-0.415643\pi\)
0.261923 + 0.965089i \(0.415643\pi\)
\(158\) −7.70598 −0.613055
\(159\) 13.2483 1.05066
\(160\) −3.37288 −0.266649
\(161\) 0.257477 0.0202920
\(162\) 11.2038 0.880256
\(163\) −4.01375 −0.314381 −0.157191 0.987568i \(-0.550244\pi\)
−0.157191 + 0.987568i \(0.550244\pi\)
\(164\) −5.40286 −0.421892
\(165\) 24.9996 1.94621
\(166\) −6.94011 −0.538657
\(167\) 16.5924 1.28396 0.641980 0.766722i \(-0.278113\pi\)
0.641980 + 0.766722i \(0.278113\pi\)
\(168\) 0.114249 0.00881452
\(169\) −12.9139 −0.993378
\(170\) 3.65392 0.280243
\(171\) 8.47225 0.647889
\(172\) 0.278980 0.0212720
\(173\) −9.23659 −0.702245 −0.351122 0.936330i \(-0.614200\pi\)
−0.351122 + 0.936330i \(0.614200\pi\)
\(174\) −3.97067 −0.301016
\(175\) 0.335495 0.0253610
\(176\) −3.41347 −0.257300
\(177\) −13.9722 −1.05021
\(178\) 5.52579 0.414175
\(179\) −4.66307 −0.348534 −0.174267 0.984698i \(-0.555756\pi\)
−0.174267 + 0.984698i \(0.555756\pi\)
\(180\) 5.78409 0.431120
\(181\) −5.89517 −0.438184 −0.219092 0.975704i \(-0.570310\pi\)
−0.219092 + 0.975704i \(0.570310\pi\)
\(182\) −0.0154381 −0.00114435
\(183\) 2.32489 0.171861
\(184\) −4.89351 −0.360754
\(185\) 10.9554 0.805459
\(186\) 19.3111 1.41596
\(187\) 3.69790 0.270418
\(188\) −4.56043 −0.332604
\(189\) 0.146824 0.0106799
\(190\) −16.6634 −1.20889
\(191\) 22.8960 1.65670 0.828348 0.560214i \(-0.189281\pi\)
0.828348 + 0.560214i \(0.189281\pi\)
\(192\) −2.17138 −0.156706
\(193\) −13.8039 −0.993626 −0.496813 0.867858i \(-0.665496\pi\)
−0.496813 + 0.867858i \(0.665496\pi\)
\(194\) −9.29685 −0.667475
\(195\) −2.14888 −0.153885
\(196\) −6.99723 −0.499802
\(197\) −6.71073 −0.478120 −0.239060 0.971005i \(-0.576839\pi\)
−0.239060 + 0.971005i \(0.576839\pi\)
\(198\) 5.85371 0.416005
\(199\) −20.9027 −1.48175 −0.740876 0.671642i \(-0.765589\pi\)
−0.740876 + 0.671642i \(0.765589\pi\)
\(200\) −6.37629 −0.450872
\(201\) 3.18467 0.224630
\(202\) 5.28666 0.371968
\(203\) −0.0962159 −0.00675303
\(204\) 2.35231 0.164695
\(205\) −18.2232 −1.27276
\(206\) −2.54577 −0.177372
\(207\) 8.39179 0.583270
\(208\) 0.293411 0.0203444
\(209\) −16.8640 −1.16651
\(210\) 0.385349 0.0265916
\(211\) −12.4346 −0.856035 −0.428018 0.903770i \(-0.640788\pi\)
−0.428018 + 0.903770i \(0.640788\pi\)
\(212\) −6.10135 −0.419043
\(213\) 1.99243 0.136519
\(214\) 10.2676 0.701879
\(215\) 0.940965 0.0641733
\(216\) −2.79048 −0.189868
\(217\) 0.467940 0.0317658
\(218\) −19.4556 −1.31770
\(219\) −21.5519 −1.45634
\(220\) −11.5132 −0.776222
\(221\) −0.317860 −0.0213816
\(222\) 7.05284 0.473356
\(223\) 3.58277 0.239920 0.119960 0.992779i \(-0.461723\pi\)
0.119960 + 0.992779i \(0.461723\pi\)
\(224\) −0.0526160 −0.00351556
\(225\) 10.9346 0.728973
\(226\) 10.1419 0.674632
\(227\) 3.29537 0.218721 0.109361 0.994002i \(-0.465120\pi\)
0.109361 + 0.994002i \(0.465120\pi\)
\(228\) −10.7275 −0.710448
\(229\) 4.79651 0.316962 0.158481 0.987362i \(-0.449340\pi\)
0.158481 + 0.987362i \(0.449340\pi\)
\(230\) −16.5052 −1.08832
\(231\) 0.389987 0.0256593
\(232\) 1.82864 0.120056
\(233\) −5.26170 −0.344705 −0.172353 0.985035i \(-0.555137\pi\)
−0.172353 + 0.985035i \(0.555137\pi\)
\(234\) −0.503166 −0.0328930
\(235\) −15.3818 −1.00340
\(236\) 6.43470 0.418864
\(237\) −16.7326 −1.08690
\(238\) 0.0570003 0.00369478
\(239\) 15.1773 0.981736 0.490868 0.871234i \(-0.336680\pi\)
0.490868 + 0.871234i \(0.336680\pi\)
\(240\) −7.32379 −0.472748
\(241\) 10.6380 0.685252 0.342626 0.939472i \(-0.388684\pi\)
0.342626 + 0.939472i \(0.388684\pi\)
\(242\) −0.651811 −0.0419000
\(243\) 15.9563 1.02360
\(244\) −1.07070 −0.0685445
\(245\) −23.6008 −1.50780
\(246\) −11.7317 −0.747983
\(247\) 1.44958 0.0922344
\(248\) −8.89349 −0.564737
\(249\) −15.0696 −0.954998
\(250\) −4.64206 −0.293589
\(251\) 5.44235 0.343518 0.171759 0.985139i \(-0.445055\pi\)
0.171759 + 0.985139i \(0.445055\pi\)
\(252\) 0.0902303 0.00568397
\(253\) −16.7039 −1.05016
\(254\) 8.09666 0.508029
\(255\) 7.93405 0.496849
\(256\) 1.00000 0.0625000
\(257\) 24.5266 1.52993 0.764963 0.644074i \(-0.222757\pi\)
0.764963 + 0.644074i \(0.222757\pi\)
\(258\) 0.605771 0.0377137
\(259\) 0.170902 0.0106193
\(260\) 0.989640 0.0613749
\(261\) −3.13591 −0.194108
\(262\) 14.9833 0.925674
\(263\) 8.42086 0.519253 0.259626 0.965709i \(-0.416401\pi\)
0.259626 + 0.965709i \(0.416401\pi\)
\(264\) −7.41194 −0.456174
\(265\) −20.5791 −1.26416
\(266\) −0.259946 −0.0159383
\(267\) 11.9986 0.734301
\(268\) −1.46666 −0.0895905
\(269\) −8.95887 −0.546232 −0.273116 0.961981i \(-0.588054\pi\)
−0.273116 + 0.961981i \(0.588054\pi\)
\(270\) −9.41193 −0.572792
\(271\) −2.18160 −0.132523 −0.0662614 0.997802i \(-0.521107\pi\)
−0.0662614 + 0.997802i \(0.521107\pi\)
\(272\) −1.08333 −0.0656862
\(273\) −0.0335220 −0.00202885
\(274\) −20.2771 −1.22498
\(275\) −21.7653 −1.31250
\(276\) −10.6257 −0.639590
\(277\) −1.57566 −0.0946724 −0.0473362 0.998879i \(-0.515073\pi\)
−0.0473362 + 0.998879i \(0.515073\pi\)
\(278\) −18.8107 −1.12819
\(279\) 15.2513 0.913071
\(280\) −0.177467 −0.0106057
\(281\) 4.90892 0.292841 0.146421 0.989222i \(-0.453225\pi\)
0.146421 + 0.989222i \(0.453225\pi\)
\(282\) −9.90242 −0.589680
\(283\) 20.2031 1.20095 0.600475 0.799644i \(-0.294978\pi\)
0.600475 + 0.799644i \(0.294978\pi\)
\(284\) −0.917589 −0.0544489
\(285\) −36.1826 −2.14327
\(286\) 1.00155 0.0592230
\(287\) −0.284277 −0.0167803
\(288\) −1.71488 −0.101050
\(289\) −15.8264 −0.930965
\(290\) 6.16778 0.362185
\(291\) −20.1870 −1.18338
\(292\) 9.92543 0.580842
\(293\) −30.9205 −1.80640 −0.903198 0.429224i \(-0.858787\pi\)
−0.903198 + 0.429224i \(0.858787\pi\)
\(294\) −15.1936 −0.886111
\(295\) 21.7035 1.26362
\(296\) −3.24810 −0.188792
\(297\) −9.52522 −0.552709
\(298\) −10.8116 −0.626299
\(299\) 1.43581 0.0830351
\(300\) −13.8453 −0.799361
\(301\) 0.0146788 0.000846073 0
\(302\) 1.73171 0.0996488
\(303\) 11.4793 0.659470
\(304\) 4.94043 0.283353
\(305\) −3.61134 −0.206785
\(306\) 1.85778 0.106202
\(307\) 23.4009 1.33556 0.667779 0.744360i \(-0.267245\pi\)
0.667779 + 0.744360i \(0.267245\pi\)
\(308\) −0.179603 −0.0102339
\(309\) −5.52782 −0.314467
\(310\) −29.9966 −1.70369
\(311\) 23.3127 1.32194 0.660972 0.750411i \(-0.270144\pi\)
0.660972 + 0.750411i \(0.270144\pi\)
\(312\) 0.637107 0.0360691
\(313\) 19.4779 1.10096 0.550478 0.834849i \(-0.314445\pi\)
0.550478 + 0.834849i \(0.314445\pi\)
\(314\) −6.56378 −0.370415
\(315\) 0.304336 0.0171474
\(316\) 7.70598 0.433495
\(317\) −14.2608 −0.800969 −0.400484 0.916304i \(-0.631158\pi\)
−0.400484 + 0.916304i \(0.631158\pi\)
\(318\) −13.2483 −0.742930
\(319\) 6.24203 0.349486
\(320\) 3.37288 0.188549
\(321\) 22.2949 1.24438
\(322\) −0.257477 −0.0143486
\(323\) −5.35209 −0.297798
\(324\) −11.2038 −0.622435
\(325\) 1.87088 0.103778
\(326\) 4.01375 0.222301
\(327\) −42.2456 −2.33618
\(328\) 5.40286 0.298323
\(329\) −0.239952 −0.0132290
\(330\) −24.9996 −1.37618
\(331\) −15.5598 −0.855245 −0.427622 0.903957i \(-0.640649\pi\)
−0.427622 + 0.903957i \(0.640649\pi\)
\(332\) 6.94011 0.380888
\(333\) 5.57010 0.305240
\(334\) −16.5924 −0.907896
\(335\) −4.94686 −0.270276
\(336\) −0.114249 −0.00623281
\(337\) 30.5380 1.66351 0.831756 0.555141i \(-0.187336\pi\)
0.831756 + 0.555141i \(0.187336\pi\)
\(338\) 12.9139 0.702424
\(339\) 22.0220 1.19607
\(340\) −3.65392 −0.198162
\(341\) −30.3577 −1.64396
\(342\) −8.47225 −0.458127
\(343\) −0.736479 −0.0397661
\(344\) −0.278980 −0.0150416
\(345\) −35.8390 −1.92951
\(346\) 9.23659 0.496562
\(347\) 22.7161 1.21946 0.609732 0.792607i \(-0.291277\pi\)
0.609732 + 0.792607i \(0.291277\pi\)
\(348\) 3.97067 0.212850
\(349\) 2.98906 0.160001 0.0800005 0.996795i \(-0.474508\pi\)
0.0800005 + 0.996795i \(0.474508\pi\)
\(350\) −0.335495 −0.0179330
\(351\) 0.818757 0.0437020
\(352\) 3.41347 0.181939
\(353\) 18.2499 0.971342 0.485671 0.874142i \(-0.338575\pi\)
0.485671 + 0.874142i \(0.338575\pi\)
\(354\) 13.9722 0.742613
\(355\) −3.09491 −0.164261
\(356\) −5.52579 −0.292866
\(357\) 0.123769 0.00655056
\(358\) 4.66307 0.246451
\(359\) −27.0261 −1.42638 −0.713191 0.700970i \(-0.752751\pi\)
−0.713191 + 0.700970i \(0.752751\pi\)
\(360\) −5.78409 −0.304848
\(361\) 5.40781 0.284622
\(362\) 5.89517 0.309843
\(363\) −1.41533 −0.0742855
\(364\) 0.0154381 0.000809178 0
\(365\) 33.4772 1.75228
\(366\) −2.32489 −0.121524
\(367\) −13.0432 −0.680851 −0.340425 0.940272i \(-0.610571\pi\)
−0.340425 + 0.940272i \(0.610571\pi\)
\(368\) 4.89351 0.255092
\(369\) −9.26527 −0.482331
\(370\) −10.9554 −0.569545
\(371\) −0.321029 −0.0166670
\(372\) −19.3111 −1.00124
\(373\) 19.5704 1.01332 0.506659 0.862147i \(-0.330880\pi\)
0.506659 + 0.862147i \(0.330880\pi\)
\(374\) −3.69790 −0.191214
\(375\) −10.0797 −0.520511
\(376\) 4.56043 0.235186
\(377\) −0.536544 −0.0276334
\(378\) −0.146824 −0.00755180
\(379\) 17.7294 0.910700 0.455350 0.890313i \(-0.349514\pi\)
0.455350 + 0.890313i \(0.349514\pi\)
\(380\) 16.6634 0.854817
\(381\) 17.5809 0.900697
\(382\) −22.8960 −1.17146
\(383\) −35.3338 −1.80548 −0.902738 0.430192i \(-0.858446\pi\)
−0.902738 + 0.430192i \(0.858446\pi\)
\(384\) 2.17138 0.110808
\(385\) −0.605780 −0.0308734
\(386\) 13.8039 0.702599
\(387\) 0.478418 0.0243194
\(388\) 9.29685 0.471976
\(389\) −13.8339 −0.701404 −0.350702 0.936487i \(-0.614057\pi\)
−0.350702 + 0.936487i \(0.614057\pi\)
\(390\) 2.14888 0.108813
\(391\) −5.30126 −0.268096
\(392\) 6.99723 0.353414
\(393\) 32.5345 1.64115
\(394\) 6.71073 0.338082
\(395\) 25.9913 1.30776
\(396\) −5.85371 −0.294160
\(397\) −5.42374 −0.272210 −0.136105 0.990694i \(-0.543458\pi\)
−0.136105 + 0.990694i \(0.543458\pi\)
\(398\) 20.9027 1.04776
\(399\) −0.564440 −0.0282574
\(400\) 6.37629 0.318815
\(401\) −21.3314 −1.06524 −0.532621 0.846354i \(-0.678793\pi\)
−0.532621 + 0.846354i \(0.678793\pi\)
\(402\) −3.18467 −0.158837
\(403\) 2.60945 0.129986
\(404\) −5.28666 −0.263021
\(405\) −37.7891 −1.87776
\(406\) 0.0962159 0.00477512
\(407\) −11.0873 −0.549577
\(408\) −2.35231 −0.116457
\(409\) −1.57475 −0.0778665 −0.0389333 0.999242i \(-0.512396\pi\)
−0.0389333 + 0.999242i \(0.512396\pi\)
\(410\) 18.2232 0.899978
\(411\) −44.0292 −2.17180
\(412\) 2.54577 0.125421
\(413\) 0.338569 0.0166599
\(414\) −8.39179 −0.412434
\(415\) 23.4081 1.14906
\(416\) −0.293411 −0.0143857
\(417\) −40.8452 −2.00020
\(418\) 16.8640 0.824846
\(419\) 12.1007 0.591158 0.295579 0.955318i \(-0.404487\pi\)
0.295579 + 0.955318i \(0.404487\pi\)
\(420\) −0.385349 −0.0188031
\(421\) 18.2144 0.887717 0.443859 0.896097i \(-0.353609\pi\)
0.443859 + 0.896097i \(0.353609\pi\)
\(422\) 12.4346 0.605308
\(423\) −7.82060 −0.380251
\(424\) 6.10135 0.296308
\(425\) −6.90760 −0.335068
\(426\) −1.99243 −0.0965337
\(427\) −0.0563360 −0.00272629
\(428\) −10.2676 −0.496304
\(429\) 2.17475 0.104998
\(430\) −0.940965 −0.0453774
\(431\) 31.0681 1.49650 0.748248 0.663419i \(-0.230895\pi\)
0.748248 + 0.663419i \(0.230895\pi\)
\(432\) 2.79048 0.134257
\(433\) 13.2693 0.637684 0.318842 0.947808i \(-0.396706\pi\)
0.318842 + 0.947808i \(0.396706\pi\)
\(434\) −0.467940 −0.0224618
\(435\) 13.3926 0.642126
\(436\) 19.4556 0.931756
\(437\) 24.1760 1.15650
\(438\) 21.5519 1.02979
\(439\) 22.5930 1.07831 0.539153 0.842208i \(-0.318744\pi\)
0.539153 + 0.842208i \(0.318744\pi\)
\(440\) 11.5132 0.548872
\(441\) −11.9994 −0.571401
\(442\) 0.317860 0.0151191
\(443\) 10.0573 0.477838 0.238919 0.971039i \(-0.423207\pi\)
0.238919 + 0.971039i \(0.423207\pi\)
\(444\) −7.05284 −0.334713
\(445\) −18.6378 −0.883516
\(446\) −3.58277 −0.169649
\(447\) −23.4761 −1.11038
\(448\) 0.0526160 0.00248587
\(449\) −21.1930 −1.00016 −0.500080 0.865979i \(-0.666696\pi\)
−0.500080 + 0.865979i \(0.666696\pi\)
\(450\) −10.9346 −0.515461
\(451\) 18.4425 0.868425
\(452\) −10.1419 −0.477037
\(453\) 3.76020 0.176670
\(454\) −3.29537 −0.154659
\(455\) 0.0520709 0.00244112
\(456\) 10.7275 0.502363
\(457\) −17.9721 −0.840700 −0.420350 0.907362i \(-0.638093\pi\)
−0.420350 + 0.907362i \(0.638093\pi\)
\(458\) −4.79651 −0.224126
\(459\) −3.02299 −0.141101
\(460\) 16.5052 0.769559
\(461\) 24.1633 1.12540 0.562698 0.826663i \(-0.309763\pi\)
0.562698 + 0.826663i \(0.309763\pi\)
\(462\) −0.389987 −0.0181438
\(463\) 28.9577 1.34578 0.672890 0.739742i \(-0.265053\pi\)
0.672890 + 0.739742i \(0.265053\pi\)
\(464\) −1.82864 −0.0848926
\(465\) −65.1340 −3.02052
\(466\) 5.26170 0.243743
\(467\) 33.3211 1.54192 0.770958 0.636885i \(-0.219778\pi\)
0.770958 + 0.636885i \(0.219778\pi\)
\(468\) 0.503166 0.0232589
\(469\) −0.0771698 −0.00356337
\(470\) 15.3818 0.709508
\(471\) −14.2524 −0.656718
\(472\) −6.43470 −0.296181
\(473\) −0.952291 −0.0437864
\(474\) 16.7326 0.768554
\(475\) 31.5016 1.44539
\(476\) −0.0570003 −0.00261260
\(477\) −10.4631 −0.479073
\(478\) −15.1773 −0.694192
\(479\) −1.90854 −0.0872034 −0.0436017 0.999049i \(-0.513883\pi\)
−0.0436017 + 0.999049i \(0.513883\pi\)
\(480\) 7.32379 0.334284
\(481\) 0.953028 0.0434544
\(482\) −10.6380 −0.484546
\(483\) −0.559080 −0.0254390
\(484\) 0.651811 0.0296278
\(485\) 31.3571 1.42385
\(486\) −15.9563 −0.723793
\(487\) 7.65935 0.347078 0.173539 0.984827i \(-0.444480\pi\)
0.173539 + 0.984827i \(0.444480\pi\)
\(488\) 1.07070 0.0484683
\(489\) 8.71537 0.394123
\(490\) 23.6008 1.06618
\(491\) 0.234956 0.0106034 0.00530172 0.999986i \(-0.498312\pi\)
0.00530172 + 0.999986i \(0.498312\pi\)
\(492\) 11.7317 0.528904
\(493\) 1.98101 0.0892204
\(494\) −1.44958 −0.0652196
\(495\) −19.7438 −0.887419
\(496\) 8.89349 0.399329
\(497\) −0.0482799 −0.00216565
\(498\) 15.0696 0.675285
\(499\) −7.08820 −0.317312 −0.158656 0.987334i \(-0.550716\pi\)
−0.158656 + 0.987334i \(0.550716\pi\)
\(500\) 4.64206 0.207599
\(501\) −36.0284 −1.60963
\(502\) −5.44235 −0.242904
\(503\) −0.149938 −0.00668542 −0.00334271 0.999994i \(-0.501064\pi\)
−0.00334271 + 0.999994i \(0.501064\pi\)
\(504\) −0.0902303 −0.00401918
\(505\) −17.8312 −0.793480
\(506\) 16.7039 0.742578
\(507\) 28.0410 1.24534
\(508\) −8.09666 −0.359231
\(509\) 29.7847 1.32018 0.660091 0.751185i \(-0.270518\pi\)
0.660091 + 0.751185i \(0.270518\pi\)
\(510\) −7.93405 −0.351325
\(511\) 0.522237 0.0231024
\(512\) −1.00000 −0.0441942
\(513\) 13.7861 0.608673
\(514\) −24.5266 −1.08182
\(515\) 8.58656 0.378369
\(516\) −0.605771 −0.0266676
\(517\) 15.5669 0.684632
\(518\) −0.170902 −0.00750900
\(519\) 20.0561 0.880366
\(520\) −0.989640 −0.0433986
\(521\) −2.44679 −0.107196 −0.0535979 0.998563i \(-0.517069\pi\)
−0.0535979 + 0.998563i \(0.517069\pi\)
\(522\) 3.13591 0.137255
\(523\) 20.1564 0.881378 0.440689 0.897660i \(-0.354734\pi\)
0.440689 + 0.897660i \(0.354734\pi\)
\(524\) −14.9833 −0.654550
\(525\) −0.728487 −0.0317938
\(526\) −8.42086 −0.367167
\(527\) −9.63454 −0.419687
\(528\) 7.41194 0.322563
\(529\) 0.946438 0.0411495
\(530\) 20.5791 0.893899
\(531\) 11.0348 0.478868
\(532\) 0.259946 0.0112701
\(533\) −1.58526 −0.0686652
\(534\) −11.9986 −0.519229
\(535\) −34.6314 −1.49724
\(536\) 1.46666 0.0633501
\(537\) 10.1253 0.436938
\(538\) 8.95887 0.386244
\(539\) 23.8849 1.02879
\(540\) 9.41193 0.405025
\(541\) 5.29232 0.227534 0.113767 0.993507i \(-0.463708\pi\)
0.113767 + 0.993507i \(0.463708\pi\)
\(542\) 2.18160 0.0937078
\(543\) 12.8006 0.549328
\(544\) 1.08333 0.0464472
\(545\) 65.6215 2.81092
\(546\) 0.0335220 0.00143461
\(547\) −7.44203 −0.318198 −0.159099 0.987263i \(-0.550859\pi\)
−0.159099 + 0.987263i \(0.550859\pi\)
\(548\) 20.2771 0.866195
\(549\) −1.83612 −0.0783639
\(550\) 21.7653 0.928076
\(551\) −9.03427 −0.384873
\(552\) 10.6257 0.452258
\(553\) 0.405458 0.0172418
\(554\) 1.57566 0.0669435
\(555\) −23.7884 −1.00976
\(556\) 18.8107 0.797753
\(557\) −8.07540 −0.342166 −0.171083 0.985257i \(-0.554727\pi\)
−0.171083 + 0.985257i \(0.554727\pi\)
\(558\) −15.2513 −0.645638
\(559\) 0.0818559 0.00346214
\(560\) 0.177467 0.00749936
\(561\) −8.02955 −0.339008
\(562\) −4.90892 −0.207070
\(563\) 42.8489 1.80587 0.902933 0.429782i \(-0.141409\pi\)
0.902933 + 0.429782i \(0.141409\pi\)
\(564\) 9.90242 0.416967
\(565\) −34.2075 −1.43912
\(566\) −20.2031 −0.849199
\(567\) −0.589501 −0.0247567
\(568\) 0.917589 0.0385012
\(569\) −17.8550 −0.748521 −0.374261 0.927324i \(-0.622103\pi\)
−0.374261 + 0.927324i \(0.622103\pi\)
\(570\) 36.1826 1.51552
\(571\) −23.9931 −1.00408 −0.502039 0.864845i \(-0.667417\pi\)
−0.502039 + 0.864845i \(0.667417\pi\)
\(572\) −1.00155 −0.0418770
\(573\) −49.7159 −2.07691
\(574\) 0.284277 0.0118655
\(575\) 31.2024 1.30123
\(576\) 1.71488 0.0714534
\(577\) −20.7860 −0.865331 −0.432666 0.901554i \(-0.642427\pi\)
−0.432666 + 0.901554i \(0.642427\pi\)
\(578\) 15.8264 0.658292
\(579\) 29.9735 1.24565
\(580\) −6.16778 −0.256103
\(581\) 0.365161 0.0151494
\(582\) 20.1870 0.836777
\(583\) 20.8268 0.862559
\(584\) −9.92543 −0.410717
\(585\) 1.69712 0.0701671
\(586\) 30.9205 1.27732
\(587\) 26.8652 1.10884 0.554422 0.832236i \(-0.312939\pi\)
0.554422 + 0.832236i \(0.312939\pi\)
\(588\) 15.1936 0.626575
\(589\) 43.9376 1.81042
\(590\) −21.7035 −0.893517
\(591\) 14.5715 0.599393
\(592\) 3.24810 0.133496
\(593\) −13.2738 −0.545088 −0.272544 0.962143i \(-0.587865\pi\)
−0.272544 + 0.962143i \(0.587865\pi\)
\(594\) 9.52522 0.390825
\(595\) −0.192255 −0.00788168
\(596\) 10.8116 0.442860
\(597\) 45.3876 1.85759
\(598\) −1.43581 −0.0587147
\(599\) 5.62060 0.229651 0.114826 0.993386i \(-0.463369\pi\)
0.114826 + 0.993386i \(0.463369\pi\)
\(600\) 13.8453 0.565233
\(601\) 2.97529 0.121365 0.0606823 0.998157i \(-0.480672\pi\)
0.0606823 + 0.998157i \(0.480672\pi\)
\(602\) −0.0146788 −0.000598264 0
\(603\) −2.51515 −0.102425
\(604\) −1.73171 −0.0704623
\(605\) 2.19848 0.0893809
\(606\) −11.4793 −0.466316
\(607\) 16.1148 0.654078 0.327039 0.945011i \(-0.393949\pi\)
0.327039 + 0.945011i \(0.393949\pi\)
\(608\) −4.94043 −0.200361
\(609\) 0.208921 0.00846591
\(610\) 3.61134 0.146219
\(611\) −1.33808 −0.0541330
\(612\) −1.85778 −0.0750961
\(613\) −11.3163 −0.457059 −0.228530 0.973537i \(-0.573392\pi\)
−0.228530 + 0.973537i \(0.573392\pi\)
\(614\) −23.4009 −0.944382
\(615\) 39.5694 1.59559
\(616\) 0.179603 0.00723643
\(617\) 10.1319 0.407894 0.203947 0.978982i \(-0.434623\pi\)
0.203947 + 0.978982i \(0.434623\pi\)
\(618\) 5.52782 0.222362
\(619\) −21.7799 −0.875408 −0.437704 0.899119i \(-0.644208\pi\)
−0.437704 + 0.899119i \(0.644208\pi\)
\(620\) 29.9966 1.20469
\(621\) 13.6552 0.547965
\(622\) −23.3127 −0.934756
\(623\) −0.290745 −0.0116485
\(624\) −0.637107 −0.0255047
\(625\) −16.2244 −0.648975
\(626\) −19.4779 −0.778494
\(627\) 36.6182 1.46239
\(628\) 6.56378 0.261923
\(629\) −3.51875 −0.140302
\(630\) −0.304336 −0.0121250
\(631\) 8.62936 0.343529 0.171765 0.985138i \(-0.445053\pi\)
0.171765 + 0.985138i \(0.445053\pi\)
\(632\) −7.70598 −0.306527
\(633\) 27.0003 1.07316
\(634\) 14.2608 0.566370
\(635\) −27.3090 −1.08373
\(636\) 13.2483 0.525331
\(637\) −2.05307 −0.0813455
\(638\) −6.24203 −0.247124
\(639\) −1.57356 −0.0622490
\(640\) −3.37288 −0.133325
\(641\) −47.1639 −1.86286 −0.931431 0.363919i \(-0.881439\pi\)
−0.931431 + 0.363919i \(0.881439\pi\)
\(642\) −22.2949 −0.879908
\(643\) −6.38361 −0.251745 −0.125872 0.992046i \(-0.540173\pi\)
−0.125872 + 0.992046i \(0.540173\pi\)
\(644\) 0.257477 0.0101460
\(645\) −2.04319 −0.0804506
\(646\) 5.35209 0.210575
\(647\) −0.534438 −0.0210109 −0.0105055 0.999945i \(-0.503344\pi\)
−0.0105055 + 0.999945i \(0.503344\pi\)
\(648\) 11.2038 0.440128
\(649\) −21.9647 −0.862190
\(650\) −1.87088 −0.0733818
\(651\) −1.01607 −0.0398231
\(652\) −4.01375 −0.157191
\(653\) 27.1867 1.06390 0.531949 0.846776i \(-0.321460\pi\)
0.531949 + 0.846776i \(0.321460\pi\)
\(654\) 42.2456 1.65193
\(655\) −50.5370 −1.97464
\(656\) −5.40286 −0.210946
\(657\) 17.0209 0.664050
\(658\) 0.239952 0.00935429
\(659\) 18.3397 0.714414 0.357207 0.934025i \(-0.383729\pi\)
0.357207 + 0.934025i \(0.383729\pi\)
\(660\) 24.9996 0.973107
\(661\) −14.5315 −0.565208 −0.282604 0.959237i \(-0.591198\pi\)
−0.282604 + 0.959237i \(0.591198\pi\)
\(662\) 15.5598 0.604749
\(663\) 0.690194 0.0268049
\(664\) −6.94011 −0.269329
\(665\) 0.876764 0.0339995
\(666\) −5.57010 −0.215837
\(667\) −8.94848 −0.346487
\(668\) 16.5924 0.641980
\(669\) −7.77955 −0.300775
\(670\) 4.94686 0.191114
\(671\) 3.65481 0.141092
\(672\) 0.114249 0.00440726
\(673\) −4.44013 −0.171154 −0.0855771 0.996332i \(-0.527273\pi\)
−0.0855771 + 0.996332i \(0.527273\pi\)
\(674\) −30.5380 −1.17628
\(675\) 17.7929 0.684848
\(676\) −12.9139 −0.496689
\(677\) 10.9973 0.422659 0.211329 0.977415i \(-0.432221\pi\)
0.211329 + 0.977415i \(0.432221\pi\)
\(678\) −22.0220 −0.845749
\(679\) 0.489163 0.0187724
\(680\) 3.65392 0.140121
\(681\) −7.15549 −0.274199
\(682\) 30.3577 1.16246
\(683\) 17.4871 0.669124 0.334562 0.942374i \(-0.391412\pi\)
0.334562 + 0.942374i \(0.391412\pi\)
\(684\) 8.47225 0.323945
\(685\) 68.3921 2.61313
\(686\) 0.736479 0.0281189
\(687\) −10.4150 −0.397359
\(688\) 0.278980 0.0106360
\(689\) −1.79021 −0.0682014
\(690\) 35.8390 1.36437
\(691\) −9.77547 −0.371877 −0.185938 0.982561i \(-0.559532\pi\)
−0.185938 + 0.982561i \(0.559532\pi\)
\(692\) −9.23659 −0.351122
\(693\) −0.307999 −0.0116999
\(694\) −22.7161 −0.862292
\(695\) 63.4463 2.40665
\(696\) −3.97067 −0.150508
\(697\) 5.85305 0.221700
\(698\) −2.98906 −0.113138
\(699\) 11.4251 0.432138
\(700\) 0.335495 0.0126805
\(701\) 11.8508 0.447597 0.223799 0.974635i \(-0.428154\pi\)
0.223799 + 0.974635i \(0.428154\pi\)
\(702\) −0.818757 −0.0309020
\(703\) 16.0470 0.605223
\(704\) −3.41347 −0.128650
\(705\) 33.3996 1.25790
\(706\) −18.2499 −0.686843
\(707\) −0.278163 −0.0104614
\(708\) −13.9722 −0.525106
\(709\) 3.49044 0.131086 0.0655431 0.997850i \(-0.479122\pi\)
0.0655431 + 0.997850i \(0.479122\pi\)
\(710\) 3.09491 0.116150
\(711\) 13.2148 0.495596
\(712\) 5.52579 0.207088
\(713\) 43.5204 1.62985
\(714\) −0.123769 −0.00463194
\(715\) −3.37811 −0.126334
\(716\) −4.66307 −0.174267
\(717\) −32.9556 −1.23075
\(718\) 27.0261 1.00860
\(719\) 32.1353 1.19844 0.599222 0.800583i \(-0.295477\pi\)
0.599222 + 0.800583i \(0.295477\pi\)
\(720\) 5.78409 0.215560
\(721\) 0.133948 0.00498849
\(722\) −5.40781 −0.201258
\(723\) −23.0991 −0.859063
\(724\) −5.89517 −0.219092
\(725\) −11.6600 −0.433040
\(726\) 1.41533 0.0525278
\(727\) 18.5752 0.688918 0.344459 0.938801i \(-0.388062\pi\)
0.344459 + 0.938801i \(0.388062\pi\)
\(728\) −0.0154381 −0.000572176 0
\(729\) −1.03571 −0.0383596
\(730\) −33.4772 −1.23905
\(731\) −0.302226 −0.0111782
\(732\) 2.32489 0.0859306
\(733\) −29.9659 −1.10681 −0.553407 0.832911i \(-0.686673\pi\)
−0.553407 + 0.832911i \(0.686673\pi\)
\(734\) 13.0432 0.481434
\(735\) 51.2462 1.89025
\(736\) −4.89351 −0.180377
\(737\) 5.00641 0.184413
\(738\) 9.26527 0.341059
\(739\) −16.7066 −0.614563 −0.307281 0.951619i \(-0.599419\pi\)
−0.307281 + 0.951619i \(0.599419\pi\)
\(740\) 10.9554 0.402729
\(741\) −3.14758 −0.115629
\(742\) 0.321029 0.0117853
\(743\) 0.334126 0.0122579 0.00612894 0.999981i \(-0.498049\pi\)
0.00612894 + 0.999981i \(0.498049\pi\)
\(744\) 19.3111 0.707980
\(745\) 36.4662 1.33602
\(746\) −19.5704 −0.716524
\(747\) 11.9015 0.435452
\(748\) 3.69790 0.135209
\(749\) −0.540241 −0.0197400
\(750\) 10.0797 0.368057
\(751\) −15.6295 −0.570329 −0.285165 0.958479i \(-0.592048\pi\)
−0.285165 + 0.958479i \(0.592048\pi\)
\(752\) −4.56043 −0.166302
\(753\) −11.8174 −0.430650
\(754\) 0.536544 0.0195398
\(755\) −5.84085 −0.212570
\(756\) 0.146824 0.00533993
\(757\) 28.6649 1.04184 0.520922 0.853604i \(-0.325588\pi\)
0.520922 + 0.853604i \(0.325588\pi\)
\(758\) −17.7294 −0.643962
\(759\) 36.2704 1.31653
\(760\) −16.6634 −0.604447
\(761\) 2.00984 0.0728568 0.0364284 0.999336i \(-0.488402\pi\)
0.0364284 + 0.999336i \(0.488402\pi\)
\(762\) −17.5809 −0.636889
\(763\) 1.02368 0.0370597
\(764\) 22.8960 0.828348
\(765\) −6.26605 −0.226549
\(766\) 35.3338 1.27666
\(767\) 1.88802 0.0681723
\(768\) −2.17138 −0.0783529
\(769\) −18.7370 −0.675674 −0.337837 0.941205i \(-0.609695\pi\)
−0.337837 + 0.941205i \(0.609695\pi\)
\(770\) 0.605780 0.0218308
\(771\) −53.2565 −1.91799
\(772\) −13.8039 −0.496813
\(773\) 52.7636 1.89777 0.948887 0.315617i \(-0.102211\pi\)
0.948887 + 0.315617i \(0.102211\pi\)
\(774\) −0.478418 −0.0171964
\(775\) 56.7075 2.03699
\(776\) −9.29685 −0.333738
\(777\) −0.371093 −0.0133129
\(778\) 13.8339 0.495968
\(779\) −26.6924 −0.956356
\(780\) −2.14888 −0.0769423
\(781\) 3.13217 0.112078
\(782\) 5.30126 0.189573
\(783\) −5.10278 −0.182359
\(784\) −6.99723 −0.249901
\(785\) 22.1388 0.790168
\(786\) −32.5345 −1.16047
\(787\) 36.2565 1.29240 0.646202 0.763167i \(-0.276356\pi\)
0.646202 + 0.763167i \(0.276356\pi\)
\(788\) −6.71073 −0.239060
\(789\) −18.2849 −0.650959
\(790\) −25.9913 −0.924729
\(791\) −0.533629 −0.0189736
\(792\) 5.85371 0.208002
\(793\) −0.314156 −0.0111560
\(794\) 5.42374 0.192481
\(795\) 44.6850 1.58481
\(796\) −20.9027 −0.740876
\(797\) −44.3874 −1.57228 −0.786141 0.618047i \(-0.787924\pi\)
−0.786141 + 0.618047i \(0.787924\pi\)
\(798\) 0.564440 0.0199810
\(799\) 4.94043 0.174780
\(800\) −6.37629 −0.225436
\(801\) −9.47608 −0.334821
\(802\) 21.3314 0.753240
\(803\) −33.8802 −1.19561
\(804\) 3.18467 0.112315
\(805\) 0.868438 0.0306084
\(806\) −2.60945 −0.0919140
\(807\) 19.4531 0.684781
\(808\) 5.28666 0.185984
\(809\) −20.7123 −0.728205 −0.364103 0.931359i \(-0.618624\pi\)
−0.364103 + 0.931359i \(0.618624\pi\)
\(810\) 37.7891 1.32777
\(811\) 24.0203 0.843468 0.421734 0.906720i \(-0.361422\pi\)
0.421734 + 0.906720i \(0.361422\pi\)
\(812\) −0.0962159 −0.00337652
\(813\) 4.73708 0.166137
\(814\) 11.0873 0.388610
\(815\) −13.5379 −0.474211
\(816\) 2.35231 0.0823473
\(817\) 1.37828 0.0482199
\(818\) 1.57475 0.0550599
\(819\) 0.0264746 0.000925097 0
\(820\) −18.2232 −0.636381
\(821\) −11.9459 −0.416916 −0.208458 0.978031i \(-0.566844\pi\)
−0.208458 + 0.978031i \(0.566844\pi\)
\(822\) 44.0292 1.53570
\(823\) −0.528155 −0.0184103 −0.00920516 0.999958i \(-0.502930\pi\)
−0.00920516 + 0.999958i \(0.502930\pi\)
\(824\) −2.54577 −0.0886860
\(825\) 47.2607 1.64541
\(826\) −0.338569 −0.0117803
\(827\) −32.2798 −1.12248 −0.561240 0.827653i \(-0.689676\pi\)
−0.561240 + 0.827653i \(0.689676\pi\)
\(828\) 8.39179 0.291635
\(829\) 22.0972 0.767469 0.383734 0.923443i \(-0.374638\pi\)
0.383734 + 0.923443i \(0.374638\pi\)
\(830\) −23.4081 −0.812508
\(831\) 3.42136 0.118686
\(832\) 0.293411 0.0101722
\(833\) 7.58028 0.262641
\(834\) 40.8452 1.41435
\(835\) 55.9641 1.93672
\(836\) −16.8640 −0.583254
\(837\) 24.8171 0.857803
\(838\) −12.1007 −0.418012
\(839\) 16.9642 0.585670 0.292835 0.956163i \(-0.405401\pi\)
0.292835 + 0.956163i \(0.405401\pi\)
\(840\) 0.385349 0.0132958
\(841\) −25.6561 −0.884692
\(842\) −18.2144 −0.627711
\(843\) −10.6591 −0.367119
\(844\) −12.4346 −0.428018
\(845\) −43.5570 −1.49841
\(846\) 7.82060 0.268878
\(847\) 0.0342957 0.00117842
\(848\) −6.10135 −0.209521
\(849\) −43.8685 −1.50556
\(850\) 6.90760 0.236929
\(851\) 15.8946 0.544860
\(852\) 1.99243 0.0682596
\(853\) −21.2802 −0.728620 −0.364310 0.931278i \(-0.618695\pi\)
−0.364310 + 0.931278i \(0.618695\pi\)
\(854\) 0.0563360 0.00192778
\(855\) 28.5758 0.977273
\(856\) 10.2676 0.350940
\(857\) 33.7329 1.15229 0.576147 0.817346i \(-0.304555\pi\)
0.576147 + 0.817346i \(0.304555\pi\)
\(858\) −2.17475 −0.0742447
\(859\) 5.42159 0.184982 0.0924911 0.995714i \(-0.470517\pi\)
0.0924911 + 0.995714i \(0.470517\pi\)
\(860\) 0.940965 0.0320866
\(861\) 0.617273 0.0210366
\(862\) −31.0681 −1.05818
\(863\) −13.6631 −0.465097 −0.232548 0.972585i \(-0.574706\pi\)
−0.232548 + 0.972585i \(0.574706\pi\)
\(864\) −2.79048 −0.0949339
\(865\) −31.1539 −1.05926
\(866\) −13.2693 −0.450910
\(867\) 34.3651 1.16710
\(868\) 0.467940 0.0158829
\(869\) −26.3042 −0.892308
\(870\) −13.3926 −0.454051
\(871\) −0.430335 −0.0145813
\(872\) −19.4556 −0.658851
\(873\) 15.9430 0.539589
\(874\) −24.1760 −0.817766
\(875\) 0.244247 0.00825704
\(876\) −21.5519 −0.728170
\(877\) −17.9992 −0.607788 −0.303894 0.952706i \(-0.598287\pi\)
−0.303894 + 0.952706i \(0.598287\pi\)
\(878\) −22.5930 −0.762478
\(879\) 67.1402 2.26458
\(880\) −11.5132 −0.388111
\(881\) 14.3527 0.483554 0.241777 0.970332i \(-0.422270\pi\)
0.241777 + 0.970332i \(0.422270\pi\)
\(882\) 11.9994 0.404042
\(883\) −1.20679 −0.0406117 −0.0203058 0.999794i \(-0.506464\pi\)
−0.0203058 + 0.999794i \(0.506464\pi\)
\(884\) −0.317860 −0.0106908
\(885\) −47.1264 −1.58414
\(886\) −10.0573 −0.337883
\(887\) 42.0093 1.41053 0.705267 0.708942i \(-0.250827\pi\)
0.705267 + 0.708942i \(0.250827\pi\)
\(888\) 7.05284 0.236678
\(889\) −0.426014 −0.0142880
\(890\) 18.6378 0.624740
\(891\) 38.2440 1.28122
\(892\) 3.58277 0.119960
\(893\) −22.5305 −0.753953
\(894\) 23.4761 0.785157
\(895\) −15.7279 −0.525727
\(896\) −0.0526160 −0.00175778
\(897\) −3.11769 −0.104097
\(898\) 21.1930 0.707220
\(899\) −16.2630 −0.542402
\(900\) 10.9346 0.364486
\(901\) 6.60975 0.220203
\(902\) −18.4425 −0.614069
\(903\) −0.0318733 −0.00106068
\(904\) 10.1419 0.337316
\(905\) −19.8837 −0.660955
\(906\) −3.76020 −0.124924
\(907\) 58.8286 1.95337 0.976685 0.214675i \(-0.0688693\pi\)
0.976685 + 0.214675i \(0.0688693\pi\)
\(908\) 3.29537 0.109361
\(909\) −9.06600 −0.300700
\(910\) −0.0520709 −0.00172613
\(911\) −9.36336 −0.310222 −0.155111 0.987897i \(-0.549573\pi\)
−0.155111 + 0.987897i \(0.549573\pi\)
\(912\) −10.7275 −0.355224
\(913\) −23.6899 −0.784021
\(914\) 17.9721 0.594464
\(915\) 7.84158 0.259235
\(916\) 4.79651 0.158481
\(917\) −0.788364 −0.0260341
\(918\) 3.02299 0.0997736
\(919\) −28.0614 −0.925659 −0.462830 0.886447i \(-0.653166\pi\)
−0.462830 + 0.886447i \(0.653166\pi\)
\(920\) −16.5052 −0.544160
\(921\) −50.8121 −1.67432
\(922\) −24.1633 −0.795775
\(923\) −0.269231 −0.00886185
\(924\) 0.389987 0.0128296
\(925\) 20.7108 0.680967
\(926\) −28.9577 −0.951611
\(927\) 4.36569 0.143388
\(928\) 1.82864 0.0600281
\(929\) 40.8244 1.33941 0.669703 0.742629i \(-0.266421\pi\)
0.669703 + 0.742629i \(0.266421\pi\)
\(930\) 65.1340 2.13583
\(931\) −34.5693 −1.13296
\(932\) −5.26170 −0.172353
\(933\) −50.6208 −1.65725
\(934\) −33.3211 −1.09030
\(935\) 12.4726 0.407897
\(936\) −0.503166 −0.0164465
\(937\) 2.41784 0.0789873 0.0394936 0.999220i \(-0.487426\pi\)
0.0394936 + 0.999220i \(0.487426\pi\)
\(938\) 0.0771698 0.00251968
\(939\) −42.2939 −1.38021
\(940\) −15.3818 −0.501698
\(941\) −9.50988 −0.310013 −0.155007 0.987913i \(-0.549540\pi\)
−0.155007 + 0.987913i \(0.549540\pi\)
\(942\) 14.2524 0.464370
\(943\) −26.4389 −0.860971
\(944\) 6.43470 0.209432
\(945\) 0.495218 0.0161095
\(946\) 0.952291 0.0309617
\(947\) −23.0342 −0.748511 −0.374255 0.927326i \(-0.622102\pi\)
−0.374255 + 0.927326i \(0.622102\pi\)
\(948\) −16.7326 −0.543449
\(949\) 2.91223 0.0945351
\(950\) −31.5016 −1.02205
\(951\) 30.9657 1.00413
\(952\) 0.0570003 0.00184739
\(953\) 43.4618 1.40786 0.703932 0.710267i \(-0.251426\pi\)
0.703932 + 0.710267i \(0.251426\pi\)
\(954\) 10.4631 0.338756
\(955\) 77.2254 2.49895
\(956\) 15.1773 0.490868
\(957\) −13.5538 −0.438132
\(958\) 1.90854 0.0616621
\(959\) 1.06690 0.0344520
\(960\) −7.32379 −0.236374
\(961\) 48.0941 1.55142
\(962\) −0.953028 −0.0307269
\(963\) −17.6077 −0.567402
\(964\) 10.6380 0.342626
\(965\) −46.5588 −1.49878
\(966\) 0.559080 0.0179881
\(967\) 25.3324 0.814636 0.407318 0.913286i \(-0.366464\pi\)
0.407318 + 0.913286i \(0.366464\pi\)
\(968\) −0.651811 −0.0209500
\(969\) 11.6214 0.373333
\(970\) −31.3571 −1.00682
\(971\) −24.8363 −0.797035 −0.398517 0.917161i \(-0.630475\pi\)
−0.398517 + 0.917161i \(0.630475\pi\)
\(972\) 15.9563 0.511799
\(973\) 0.989746 0.0317298
\(974\) −7.65935 −0.245421
\(975\) −4.06238 −0.130100
\(976\) −1.07070 −0.0342723
\(977\) −12.7607 −0.408252 −0.204126 0.978945i \(-0.565435\pi\)
−0.204126 + 0.978945i \(0.565435\pi\)
\(978\) −8.71537 −0.278687
\(979\) 18.8621 0.602836
\(980\) −23.6008 −0.753900
\(981\) 33.3641 1.06524
\(982\) −0.234956 −0.00749776
\(983\) −5.46648 −0.174353 −0.0871767 0.996193i \(-0.527784\pi\)
−0.0871767 + 0.996193i \(0.527784\pi\)
\(984\) −11.7317 −0.373991
\(985\) −22.6345 −0.721194
\(986\) −1.98101 −0.0630884
\(987\) 0.521026 0.0165844
\(988\) 1.44958 0.0461172
\(989\) 1.36519 0.0434106
\(990\) 19.7438 0.627500
\(991\) 25.6486 0.814756 0.407378 0.913260i \(-0.366443\pi\)
0.407378 + 0.913260i \(0.366443\pi\)
\(992\) −8.89349 −0.282369
\(993\) 33.7862 1.07217
\(994\) 0.0482799 0.00153135
\(995\) −70.5021 −2.23507
\(996\) −15.0696 −0.477499
\(997\) 61.2966 1.94128 0.970641 0.240534i \(-0.0773227\pi\)
0.970641 + 0.240534i \(0.0773227\pi\)
\(998\) 7.08820 0.224373
\(999\) 9.06373 0.286764
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 \(a_p\))