Properties

Label 8018.2.a.j.1.8
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 0
Dimension 47
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(0\)
Dimension: \(47\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-2.28341 q^{3}\) \(+1.00000 q^{4}\) \(+4.33431 q^{5}\) \(-2.28341 q^{6}\) \(-0.955796 q^{7}\) \(+1.00000 q^{8}\) \(+2.21398 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-2.28341 q^{3}\) \(+1.00000 q^{4}\) \(+4.33431 q^{5}\) \(-2.28341 q^{6}\) \(-0.955796 q^{7}\) \(+1.00000 q^{8}\) \(+2.21398 q^{9}\) \(+4.33431 q^{10}\) \(-5.13031 q^{11}\) \(-2.28341 q^{12}\) \(-0.223732 q^{13}\) \(-0.955796 q^{14}\) \(-9.89701 q^{15}\) \(+1.00000 q^{16}\) \(+2.89292 q^{17}\) \(+2.21398 q^{18}\) \(-1.00000 q^{19}\) \(+4.33431 q^{20}\) \(+2.18248 q^{21}\) \(-5.13031 q^{22}\) \(-3.30652 q^{23}\) \(-2.28341 q^{24}\) \(+13.7862 q^{25}\) \(-0.223732 q^{26}\) \(+1.79481 q^{27}\) \(-0.955796 q^{28}\) \(-0.0537792 q^{29}\) \(-9.89701 q^{30}\) \(-1.90761 q^{31}\) \(+1.00000 q^{32}\) \(+11.7146 q^{33}\) \(+2.89292 q^{34}\) \(-4.14271 q^{35}\) \(+2.21398 q^{36}\) \(-2.29313 q^{37}\) \(-1.00000 q^{38}\) \(+0.510873 q^{39}\) \(+4.33431 q^{40}\) \(+0.965538 q^{41}\) \(+2.18248 q^{42}\) \(-5.82516 q^{43}\) \(-5.13031 q^{44}\) \(+9.59606 q^{45}\) \(-3.30652 q^{46}\) \(+9.69579 q^{47}\) \(-2.28341 q^{48}\) \(-6.08645 q^{49}\) \(+13.7862 q^{50}\) \(-6.60574 q^{51}\) \(-0.223732 q^{52}\) \(+10.8683 q^{53}\) \(+1.79481 q^{54}\) \(-22.2363 q^{55}\) \(-0.955796 q^{56}\) \(+2.28341 q^{57}\) \(-0.0537792 q^{58}\) \(+4.27122 q^{59}\) \(-9.89701 q^{60}\) \(+1.64689 q^{61}\) \(-1.90761 q^{62}\) \(-2.11611 q^{63}\) \(+1.00000 q^{64}\) \(-0.969724 q^{65}\) \(+11.7146 q^{66}\) \(-11.7055 q^{67}\) \(+2.89292 q^{68}\) \(+7.55016 q^{69}\) \(-4.14271 q^{70}\) \(+6.06103 q^{71}\) \(+2.21398 q^{72}\) \(+3.78080 q^{73}\) \(-2.29313 q^{74}\) \(-31.4796 q^{75}\) \(-1.00000 q^{76}\) \(+4.90353 q^{77}\) \(+0.510873 q^{78}\) \(+9.19955 q^{79}\) \(+4.33431 q^{80}\) \(-10.7402 q^{81}\) \(+0.965538 q^{82}\) \(+16.2278 q^{83}\) \(+2.18248 q^{84}\) \(+12.5388 q^{85}\) \(-5.82516 q^{86}\) \(+0.122800 q^{87}\) \(-5.13031 q^{88}\) \(+15.5406 q^{89}\) \(+9.59606 q^{90}\) \(+0.213842 q^{91}\) \(-3.30652 q^{92}\) \(+4.35586 q^{93}\) \(+9.69579 q^{94}\) \(-4.33431 q^{95}\) \(-2.28341 q^{96}\) \(+12.7256 q^{97}\) \(-6.08645 q^{98}\) \(-11.3584 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 17q^{11} \) \(\mathstrut +\mathstrut 10q^{12} \) \(\mathstrut +\mathstrut 27q^{13} \) \(\mathstrut +\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 47q^{16} \) \(\mathstrut +\mathstrut 16q^{17} \) \(\mathstrut +\mathstrut 69q^{18} \) \(\mathstrut -\mathstrut 47q^{19} \) \(\mathstrut +\mathstrut 15q^{20} \) \(\mathstrut +\mathstrut 26q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 86q^{25} \) \(\mathstrut +\mathstrut 27q^{26} \) \(\mathstrut +\mathstrut 43q^{27} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 10q^{30} \) \(\mathstrut +\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut 47q^{32} \) \(\mathstrut +\mathstrut 18q^{33} \) \(\mathstrut +\mathstrut 16q^{34} \) \(\mathstrut +\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut 69q^{36} \) \(\mathstrut +\mathstrut 78q^{37} \) \(\mathstrut -\mathstrut 47q^{38} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut +\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 53q^{41} \) \(\mathstrut +\mathstrut 26q^{42} \) \(\mathstrut +\mathstrut 47q^{43} \) \(\mathstrut +\mathstrut 17q^{44} \) \(\mathstrut +\mathstrut 23q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 93q^{49} \) \(\mathstrut +\mathstrut 86q^{50} \) \(\mathstrut +\mathstrut 28q^{51} \) \(\mathstrut +\mathstrut 27q^{52} \) \(\mathstrut +\mathstrut 43q^{53} \) \(\mathstrut +\mathstrut 43q^{54} \) \(\mathstrut +\mathstrut 23q^{55} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 58q^{58} \) \(\mathstrut +\mathstrut 3q^{59} \) \(\mathstrut +\mathstrut 10q^{60} \) \(\mathstrut +\mathstrut 12q^{61} \) \(\mathstrut +\mathstrut 21q^{62} \) \(\mathstrut -\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 47q^{64} \) \(\mathstrut +\mathstrut 62q^{65} \) \(\mathstrut +\mathstrut 18q^{66} \) \(\mathstrut +\mathstrut 68q^{67} \) \(\mathstrut +\mathstrut 16q^{68} \) \(\mathstrut +\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 24q^{70} \) \(\mathstrut -\mathstrut 13q^{71} \) \(\mathstrut +\mathstrut 69q^{72} \) \(\mathstrut +\mathstrut 35q^{73} \) \(\mathstrut +\mathstrut 78q^{74} \) \(\mathstrut +\mathstrut 22q^{75} \) \(\mathstrut -\mathstrut 47q^{76} \) \(\mathstrut +\mathstrut 26q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut +\mathstrut 15q^{80} \) \(\mathstrut +\mathstrut 123q^{81} \) \(\mathstrut +\mathstrut 53q^{82} \) \(\mathstrut +\mathstrut 23q^{83} \) \(\mathstrut +\mathstrut 26q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut +\mathstrut 47q^{86} \) \(\mathstrut +\mathstrut 39q^{87} \) \(\mathstrut +\mathstrut 17q^{88} \) \(\mathstrut +\mathstrut 24q^{89} \) \(\mathstrut +\mathstrut 23q^{90} \) \(\mathstrut +\mathstrut 49q^{91} \) \(\mathstrut +\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 91q^{93} \) \(\mathstrut +\mathstrut 16q^{94} \) \(\mathstrut -\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut +\mathstrut 88q^{97} \) \(\mathstrut +\mathstrut 93q^{98} \) \(\mathstrut +\mathstrut 26q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.28341 −1.31833 −0.659165 0.751999i \(-0.729090\pi\)
−0.659165 + 0.751999i \(0.729090\pi\)
\(4\) 1.00000 0.500000
\(5\) 4.33431 1.93836 0.969180 0.246352i \(-0.0792321\pi\)
0.969180 + 0.246352i \(0.0792321\pi\)
\(6\) −2.28341 −0.932200
\(7\) −0.955796 −0.361257 −0.180628 0.983551i \(-0.557813\pi\)
−0.180628 + 0.983551i \(0.557813\pi\)
\(8\) 1.00000 0.353553
\(9\) 2.21398 0.737993
\(10\) 4.33431 1.37063
\(11\) −5.13031 −1.54685 −0.773423 0.633890i \(-0.781457\pi\)
−0.773423 + 0.633890i \(0.781457\pi\)
\(12\) −2.28341 −0.659165
\(13\) −0.223732 −0.0620522 −0.0310261 0.999519i \(-0.509877\pi\)
−0.0310261 + 0.999519i \(0.509877\pi\)
\(14\) −0.955796 −0.255447
\(15\) −9.89701 −2.55540
\(16\) 1.00000 0.250000
\(17\) 2.89292 0.701637 0.350819 0.936443i \(-0.385903\pi\)
0.350819 + 0.936443i \(0.385903\pi\)
\(18\) 2.21398 0.521840
\(19\) −1.00000 −0.229416
\(20\) 4.33431 0.969180
\(21\) 2.18248 0.476256
\(22\) −5.13031 −1.09379
\(23\) −3.30652 −0.689458 −0.344729 0.938702i \(-0.612029\pi\)
−0.344729 + 0.938702i \(0.612029\pi\)
\(24\) −2.28341 −0.466100
\(25\) 13.7862 2.75724
\(26\) −0.223732 −0.0438775
\(27\) 1.79481 0.345412
\(28\) −0.955796 −0.180628
\(29\) −0.0537792 −0.00998654 −0.00499327 0.999988i \(-0.501589\pi\)
−0.00499327 + 0.999988i \(0.501589\pi\)
\(30\) −9.89701 −1.80694
\(31\) −1.90761 −0.342617 −0.171308 0.985217i \(-0.554799\pi\)
−0.171308 + 0.985217i \(0.554799\pi\)
\(32\) 1.00000 0.176777
\(33\) 11.7146 2.03925
\(34\) 2.89292 0.496132
\(35\) −4.14271 −0.700246
\(36\) 2.21398 0.368996
\(37\) −2.29313 −0.376989 −0.188494 0.982074i \(-0.560361\pi\)
−0.188494 + 0.982074i \(0.560361\pi\)
\(38\) −1.00000 −0.162221
\(39\) 0.510873 0.0818052
\(40\) 4.33431 0.685314
\(41\) 0.965538 0.150792 0.0753958 0.997154i \(-0.475978\pi\)
0.0753958 + 0.997154i \(0.475978\pi\)
\(42\) 2.18248 0.336764
\(43\) −5.82516 −0.888328 −0.444164 0.895945i \(-0.646499\pi\)
−0.444164 + 0.895945i \(0.646499\pi\)
\(44\) −5.13031 −0.773423
\(45\) 9.59606 1.43050
\(46\) −3.30652 −0.487520
\(47\) 9.69579 1.41428 0.707138 0.707076i \(-0.249986\pi\)
0.707138 + 0.707076i \(0.249986\pi\)
\(48\) −2.28341 −0.329582
\(49\) −6.08645 −0.869493
\(50\) 13.7862 1.94966
\(51\) −6.60574 −0.924989
\(52\) −0.223732 −0.0310261
\(53\) 10.8683 1.49287 0.746437 0.665456i \(-0.231763\pi\)
0.746437 + 0.665456i \(0.231763\pi\)
\(54\) 1.79481 0.244243
\(55\) −22.2363 −2.99835
\(56\) −0.955796 −0.127724
\(57\) 2.28341 0.302446
\(58\) −0.0537792 −0.00706155
\(59\) 4.27122 0.556066 0.278033 0.960572i \(-0.410318\pi\)
0.278033 + 0.960572i \(0.410318\pi\)
\(60\) −9.89701 −1.27770
\(61\) 1.64689 0.210862 0.105431 0.994427i \(-0.466378\pi\)
0.105431 + 0.994427i \(0.466378\pi\)
\(62\) −1.90761 −0.242267
\(63\) −2.11611 −0.266605
\(64\) 1.00000 0.125000
\(65\) −0.969724 −0.120280
\(66\) 11.7146 1.44197
\(67\) −11.7055 −1.43006 −0.715028 0.699096i \(-0.753586\pi\)
−0.715028 + 0.699096i \(0.753586\pi\)
\(68\) 2.89292 0.350819
\(69\) 7.55016 0.908933
\(70\) −4.14271 −0.495149
\(71\) 6.06103 0.719312 0.359656 0.933085i \(-0.382894\pi\)
0.359656 + 0.933085i \(0.382894\pi\)
\(72\) 2.21398 0.260920
\(73\) 3.78080 0.442509 0.221255 0.975216i \(-0.428985\pi\)
0.221255 + 0.975216i \(0.428985\pi\)
\(74\) −2.29313 −0.266571
\(75\) −31.4796 −3.63495
\(76\) −1.00000 −0.114708
\(77\) 4.90353 0.558809
\(78\) 0.510873 0.0578450
\(79\) 9.19955 1.03503 0.517515 0.855674i \(-0.326857\pi\)
0.517515 + 0.855674i \(0.326857\pi\)
\(80\) 4.33431 0.484590
\(81\) −10.7402 −1.19336
\(82\) 0.965538 0.106626
\(83\) 16.2278 1.78123 0.890616 0.454756i \(-0.150273\pi\)
0.890616 + 0.454756i \(0.150273\pi\)
\(84\) 2.18248 0.238128
\(85\) 12.5388 1.36003
\(86\) −5.82516 −0.628143
\(87\) 0.122800 0.0131656
\(88\) −5.13031 −0.546893
\(89\) 15.5406 1.64730 0.823652 0.567095i \(-0.191933\pi\)
0.823652 + 0.567095i \(0.191933\pi\)
\(90\) 9.59606 1.01151
\(91\) 0.213842 0.0224168
\(92\) −3.30652 −0.344729
\(93\) 4.35586 0.451682
\(94\) 9.69579 1.00004
\(95\) −4.33431 −0.444690
\(96\) −2.28341 −0.233050
\(97\) 12.7256 1.29209 0.646045 0.763299i \(-0.276422\pi\)
0.646045 + 0.763299i \(0.276422\pi\)
\(98\) −6.08645 −0.614825
\(99\) −11.3584 −1.14156
\(100\) 13.7862 1.37862
\(101\) 17.0356 1.69510 0.847551 0.530714i \(-0.178076\pi\)
0.847551 + 0.530714i \(0.178076\pi\)
\(102\) −6.60574 −0.654066
\(103\) −10.5631 −1.04081 −0.520407 0.853918i \(-0.674220\pi\)
−0.520407 + 0.853918i \(0.674220\pi\)
\(104\) −0.223732 −0.0219388
\(105\) 9.45952 0.923155
\(106\) 10.8683 1.05562
\(107\) −3.59047 −0.347104 −0.173552 0.984825i \(-0.555524\pi\)
−0.173552 + 0.984825i \(0.555524\pi\)
\(108\) 1.79481 0.172706
\(109\) 4.87950 0.467372 0.233686 0.972312i \(-0.424921\pi\)
0.233686 + 0.972312i \(0.424921\pi\)
\(110\) −22.2363 −2.12015
\(111\) 5.23617 0.496996
\(112\) −0.955796 −0.0903142
\(113\) −8.29563 −0.780388 −0.390194 0.920733i \(-0.627592\pi\)
−0.390194 + 0.920733i \(0.627592\pi\)
\(114\) 2.28341 0.213861
\(115\) −14.3315 −1.33642
\(116\) −0.0537792 −0.00499327
\(117\) −0.495339 −0.0457941
\(118\) 4.27122 0.393198
\(119\) −2.76504 −0.253471
\(120\) −9.89701 −0.903470
\(121\) 15.3201 1.39273
\(122\) 1.64689 0.149102
\(123\) −2.20472 −0.198793
\(124\) −1.90761 −0.171308
\(125\) 38.0821 3.40617
\(126\) −2.11611 −0.188518
\(127\) 19.3439 1.71649 0.858247 0.513237i \(-0.171554\pi\)
0.858247 + 0.513237i \(0.171554\pi\)
\(128\) 1.00000 0.0883883
\(129\) 13.3012 1.17111
\(130\) −0.969724 −0.0850505
\(131\) 9.20602 0.804334 0.402167 0.915566i \(-0.368257\pi\)
0.402167 + 0.915566i \(0.368257\pi\)
\(132\) 11.7146 1.01963
\(133\) 0.955796 0.0828780
\(134\) −11.7055 −1.01120
\(135\) 7.77926 0.669532
\(136\) 2.89292 0.248066
\(137\) −16.3335 −1.39547 −0.697734 0.716357i \(-0.745808\pi\)
−0.697734 + 0.716357i \(0.745808\pi\)
\(138\) 7.55016 0.642713
\(139\) 9.81016 0.832087 0.416043 0.909345i \(-0.363416\pi\)
0.416043 + 0.909345i \(0.363416\pi\)
\(140\) −4.14271 −0.350123
\(141\) −22.1395 −1.86448
\(142\) 6.06103 0.508631
\(143\) 1.14782 0.0959852
\(144\) 2.21398 0.184498
\(145\) −0.233095 −0.0193575
\(146\) 3.78080 0.312901
\(147\) 13.8979 1.14628
\(148\) −2.29313 −0.188494
\(149\) 0.990937 0.0811808 0.0405904 0.999176i \(-0.487076\pi\)
0.0405904 + 0.999176i \(0.487076\pi\)
\(150\) −31.4796 −2.57030
\(151\) 10.4306 0.848827 0.424414 0.905468i \(-0.360480\pi\)
0.424414 + 0.905468i \(0.360480\pi\)
\(152\) −1.00000 −0.0811107
\(153\) 6.40487 0.517803
\(154\) 4.90353 0.395137
\(155\) −8.26816 −0.664115
\(156\) 0.510873 0.0409026
\(157\) −8.84405 −0.705832 −0.352916 0.935655i \(-0.614810\pi\)
−0.352916 + 0.935655i \(0.614810\pi\)
\(158\) 9.19955 0.731877
\(159\) −24.8168 −1.96810
\(160\) 4.33431 0.342657
\(161\) 3.16036 0.249071
\(162\) −10.7402 −0.843832
\(163\) 0.889463 0.0696681 0.0348340 0.999393i \(-0.488910\pi\)
0.0348340 + 0.999393i \(0.488910\pi\)
\(164\) 0.965538 0.0753958
\(165\) 50.7747 3.95281
\(166\) 16.2278 1.25952
\(167\) 7.07473 0.547459 0.273729 0.961807i \(-0.411743\pi\)
0.273729 + 0.961807i \(0.411743\pi\)
\(168\) 2.18248 0.168382
\(169\) −12.9499 −0.996150
\(170\) 12.5388 0.961683
\(171\) −2.21398 −0.169307
\(172\) −5.82516 −0.444164
\(173\) −2.39066 −0.181758 −0.0908792 0.995862i \(-0.528968\pi\)
−0.0908792 + 0.995862i \(0.528968\pi\)
\(174\) 0.122800 0.00930945
\(175\) −13.1768 −0.996073
\(176\) −5.13031 −0.386712
\(177\) −9.75297 −0.733078
\(178\) 15.5406 1.16482
\(179\) 8.08589 0.604368 0.302184 0.953250i \(-0.402284\pi\)
0.302184 + 0.953250i \(0.402284\pi\)
\(180\) 9.59606 0.715248
\(181\) 0.291984 0.0217030 0.0108515 0.999941i \(-0.496546\pi\)
0.0108515 + 0.999941i \(0.496546\pi\)
\(182\) 0.213842 0.0158511
\(183\) −3.76053 −0.277986
\(184\) −3.30652 −0.243760
\(185\) −9.93915 −0.730741
\(186\) 4.35586 0.319387
\(187\) −14.8416 −1.08532
\(188\) 9.69579 0.707138
\(189\) −1.71547 −0.124782
\(190\) −4.33431 −0.314444
\(191\) −16.3318 −1.18172 −0.590862 0.806772i \(-0.701212\pi\)
−0.590862 + 0.806772i \(0.701212\pi\)
\(192\) −2.28341 −0.164791
\(193\) −22.2848 −1.60410 −0.802048 0.597260i \(-0.796256\pi\)
−0.802048 + 0.597260i \(0.796256\pi\)
\(194\) 12.7256 0.913646
\(195\) 2.21428 0.158568
\(196\) −6.08645 −0.434747
\(197\) −7.01787 −0.500003 −0.250001 0.968245i \(-0.580431\pi\)
−0.250001 + 0.968245i \(0.580431\pi\)
\(198\) −11.3584 −0.807206
\(199\) −8.26753 −0.586069 −0.293035 0.956102i \(-0.594665\pi\)
−0.293035 + 0.956102i \(0.594665\pi\)
\(200\) 13.7862 0.974832
\(201\) 26.7285 1.88529
\(202\) 17.0356 1.19862
\(203\) 0.0514019 0.00360771
\(204\) −6.60574 −0.462494
\(205\) 4.18494 0.292289
\(206\) −10.5631 −0.735967
\(207\) −7.32058 −0.508815
\(208\) −0.223732 −0.0155130
\(209\) 5.13031 0.354871
\(210\) 9.45952 0.652769
\(211\) −1.00000 −0.0688428
\(212\) 10.8683 0.746437
\(213\) −13.8398 −0.948291
\(214\) −3.59047 −0.245439
\(215\) −25.2480 −1.72190
\(216\) 1.79481 0.122121
\(217\) 1.82329 0.123773
\(218\) 4.87950 0.330482
\(219\) −8.63313 −0.583373
\(220\) −22.2363 −1.49917
\(221\) −0.647241 −0.0435381
\(222\) 5.23617 0.351429
\(223\) 20.6508 1.38288 0.691441 0.722433i \(-0.256976\pi\)
0.691441 + 0.722433i \(0.256976\pi\)
\(224\) −0.955796 −0.0638618
\(225\) 30.5224 2.03483
\(226\) −8.29563 −0.551817
\(227\) 7.68360 0.509979 0.254989 0.966944i \(-0.417928\pi\)
0.254989 + 0.966944i \(0.417928\pi\)
\(228\) 2.28341 0.151223
\(229\) −29.6585 −1.95989 −0.979945 0.199269i \(-0.936143\pi\)
−0.979945 + 0.199269i \(0.936143\pi\)
\(230\) −14.3315 −0.944990
\(231\) −11.1968 −0.736694
\(232\) −0.0537792 −0.00353078
\(233\) 2.77318 0.181677 0.0908385 0.995866i \(-0.471045\pi\)
0.0908385 + 0.995866i \(0.471045\pi\)
\(234\) −0.495339 −0.0323813
\(235\) 42.0245 2.74138
\(236\) 4.27122 0.278033
\(237\) −21.0064 −1.36451
\(238\) −2.76504 −0.179231
\(239\) −5.22141 −0.337745 −0.168872 0.985638i \(-0.554013\pi\)
−0.168872 + 0.985638i \(0.554013\pi\)
\(240\) −9.89701 −0.638850
\(241\) −2.31966 −0.149422 −0.0747111 0.997205i \(-0.523803\pi\)
−0.0747111 + 0.997205i \(0.523803\pi\)
\(242\) 15.3201 0.984811
\(243\) 19.1400 1.22783
\(244\) 1.64689 0.105431
\(245\) −26.3806 −1.68539
\(246\) −2.20472 −0.140568
\(247\) 0.223732 0.0142357
\(248\) −1.90761 −0.121133
\(249\) −37.0548 −2.34825
\(250\) 38.0821 2.40852
\(251\) 17.6215 1.11226 0.556130 0.831095i \(-0.312286\pi\)
0.556130 + 0.831095i \(0.312286\pi\)
\(252\) −2.11611 −0.133303
\(253\) 16.9635 1.06649
\(254\) 19.3439 1.21374
\(255\) −28.6313 −1.79296
\(256\) 1.00000 0.0625000
\(257\) −18.0907 −1.12847 −0.564233 0.825616i \(-0.690828\pi\)
−0.564233 + 0.825616i \(0.690828\pi\)
\(258\) 13.3012 0.828099
\(259\) 2.19177 0.136190
\(260\) −0.969724 −0.0601398
\(261\) −0.119066 −0.00737000
\(262\) 9.20602 0.568750
\(263\) −5.52366 −0.340603 −0.170302 0.985392i \(-0.554474\pi\)
−0.170302 + 0.985392i \(0.554474\pi\)
\(264\) 11.7146 0.720985
\(265\) 47.1065 2.89373
\(266\) 0.955796 0.0586036
\(267\) −35.4857 −2.17169
\(268\) −11.7055 −0.715028
\(269\) 22.3892 1.36509 0.682546 0.730843i \(-0.260873\pi\)
0.682546 + 0.730843i \(0.260873\pi\)
\(270\) 7.77926 0.473431
\(271\) 21.1723 1.28613 0.643063 0.765813i \(-0.277663\pi\)
0.643063 + 0.765813i \(0.277663\pi\)
\(272\) 2.89292 0.175409
\(273\) −0.488291 −0.0295527
\(274\) −16.3335 −0.986745
\(275\) −70.7275 −4.26503
\(276\) 7.55016 0.454466
\(277\) 30.5060 1.83293 0.916464 0.400117i \(-0.131031\pi\)
0.916464 + 0.400117i \(0.131031\pi\)
\(278\) 9.81016 0.588374
\(279\) −4.22341 −0.252849
\(280\) −4.14271 −0.247574
\(281\) 0.299543 0.0178692 0.00893461 0.999960i \(-0.497156\pi\)
0.00893461 + 0.999960i \(0.497156\pi\)
\(282\) −22.1395 −1.31839
\(283\) 6.89607 0.409929 0.204964 0.978769i \(-0.434292\pi\)
0.204964 + 0.978769i \(0.434292\pi\)
\(284\) 6.06103 0.359656
\(285\) 9.89701 0.586249
\(286\) 1.14782 0.0678718
\(287\) −0.922857 −0.0544745
\(288\) 2.21398 0.130460
\(289\) −8.63099 −0.507705
\(290\) −0.233095 −0.0136878
\(291\) −29.0579 −1.70340
\(292\) 3.78080 0.221255
\(293\) 10.4173 0.608586 0.304293 0.952578i \(-0.401580\pi\)
0.304293 + 0.952578i \(0.401580\pi\)
\(294\) 13.8979 0.810542
\(295\) 18.5128 1.07786
\(296\) −2.29313 −0.133286
\(297\) −9.20794 −0.534299
\(298\) 0.990937 0.0574035
\(299\) 0.739776 0.0427824
\(300\) −31.4796 −1.81748
\(301\) 5.56766 0.320915
\(302\) 10.4306 0.600212
\(303\) −38.8992 −2.23470
\(304\) −1.00000 −0.0573539
\(305\) 7.13812 0.408727
\(306\) 6.40487 0.366142
\(307\) −24.1824 −1.38016 −0.690080 0.723733i \(-0.742425\pi\)
−0.690080 + 0.723733i \(0.742425\pi\)
\(308\) 4.90353 0.279404
\(309\) 24.1199 1.37214
\(310\) −8.26816 −0.469600
\(311\) 4.73300 0.268384 0.134192 0.990955i \(-0.457156\pi\)
0.134192 + 0.990955i \(0.457156\pi\)
\(312\) 0.510873 0.0289225
\(313\) 9.38214 0.530310 0.265155 0.964206i \(-0.414577\pi\)
0.265155 + 0.964206i \(0.414577\pi\)
\(314\) −8.84405 −0.499099
\(315\) −9.17188 −0.516777
\(316\) 9.19955 0.517515
\(317\) 16.9015 0.949282 0.474641 0.880179i \(-0.342578\pi\)
0.474641 + 0.880179i \(0.342578\pi\)
\(318\) −24.8168 −1.39166
\(319\) 0.275904 0.0154476
\(320\) 4.33431 0.242295
\(321\) 8.19853 0.457597
\(322\) 3.16036 0.176120
\(323\) −2.89292 −0.160967
\(324\) −10.7402 −0.596680
\(325\) −3.08442 −0.171093
\(326\) 0.889463 0.0492628
\(327\) −11.1419 −0.616150
\(328\) 0.965538 0.0533129
\(329\) −9.26719 −0.510917
\(330\) 50.7747 2.79506
\(331\) 3.06898 0.168686 0.0843432 0.996437i \(-0.473121\pi\)
0.0843432 + 0.996437i \(0.473121\pi\)
\(332\) 16.2278 0.890616
\(333\) −5.07695 −0.278215
\(334\) 7.07473 0.387112
\(335\) −50.7353 −2.77197
\(336\) 2.18248 0.119064
\(337\) 12.0774 0.657898 0.328949 0.944348i \(-0.393306\pi\)
0.328949 + 0.944348i \(0.393306\pi\)
\(338\) −12.9499 −0.704384
\(339\) 18.9424 1.02881
\(340\) 12.5388 0.680013
\(341\) 9.78662 0.529975
\(342\) −2.21398 −0.119718
\(343\) 12.5080 0.675367
\(344\) −5.82516 −0.314071
\(345\) 32.7247 1.76184
\(346\) −2.39066 −0.128523
\(347\) −30.2646 −1.62469 −0.812345 0.583177i \(-0.801809\pi\)
−0.812345 + 0.583177i \(0.801809\pi\)
\(348\) 0.122800 0.00658278
\(349\) −0.577196 −0.0308966 −0.0154483 0.999881i \(-0.504918\pi\)
−0.0154483 + 0.999881i \(0.504918\pi\)
\(350\) −13.1768 −0.704330
\(351\) −0.401557 −0.0214335
\(352\) −5.13031 −0.273446
\(353\) −32.8742 −1.74972 −0.874860 0.484376i \(-0.839047\pi\)
−0.874860 + 0.484376i \(0.839047\pi\)
\(354\) −9.75297 −0.518365
\(355\) 26.2704 1.39429
\(356\) 15.5406 0.823652
\(357\) 6.31374 0.334159
\(358\) 8.08589 0.427353
\(359\) −22.0424 −1.16336 −0.581678 0.813419i \(-0.697604\pi\)
−0.581678 + 0.813419i \(0.697604\pi\)
\(360\) 9.59606 0.505757
\(361\) 1.00000 0.0526316
\(362\) 0.291984 0.0153463
\(363\) −34.9820 −1.83608
\(364\) 0.213842 0.0112084
\(365\) 16.3872 0.857743
\(366\) −3.76053 −0.196566
\(367\) 28.0980 1.46670 0.733352 0.679849i \(-0.237955\pi\)
0.733352 + 0.679849i \(0.237955\pi\)
\(368\) −3.30652 −0.172365
\(369\) 2.13768 0.111283
\(370\) −9.93915 −0.516712
\(371\) −10.3879 −0.539311
\(372\) 4.35586 0.225841
\(373\) 32.0311 1.65851 0.829255 0.558871i \(-0.188765\pi\)
0.829255 + 0.558871i \(0.188765\pi\)
\(374\) −14.8416 −0.767440
\(375\) −86.9572 −4.49045
\(376\) 9.69579 0.500022
\(377\) 0.0120321 0.000619687 0
\(378\) −1.71547 −0.0882344
\(379\) −37.9753 −1.95066 −0.975331 0.220749i \(-0.929150\pi\)
−0.975331 + 0.220749i \(0.929150\pi\)
\(380\) −4.33431 −0.222345
\(381\) −44.1701 −2.26291
\(382\) −16.3318 −0.835606
\(383\) 7.68475 0.392672 0.196336 0.980537i \(-0.437096\pi\)
0.196336 + 0.980537i \(0.437096\pi\)
\(384\) −2.28341 −0.116525
\(385\) 21.2534 1.08317
\(386\) −22.2848 −1.13427
\(387\) −12.8968 −0.655580
\(388\) 12.7256 0.646045
\(389\) 30.6879 1.55594 0.777968 0.628304i \(-0.216251\pi\)
0.777968 + 0.628304i \(0.216251\pi\)
\(390\) 2.21428 0.112125
\(391\) −9.56552 −0.483749
\(392\) −6.08645 −0.307412
\(393\) −21.0212 −1.06038
\(394\) −7.01787 −0.353555
\(395\) 39.8737 2.00626
\(396\) −11.3584 −0.570781
\(397\) −11.9920 −0.601860 −0.300930 0.953646i \(-0.597297\pi\)
−0.300930 + 0.953646i \(0.597297\pi\)
\(398\) −8.26753 −0.414414
\(399\) −2.18248 −0.109261
\(400\) 13.7862 0.689310
\(401\) −3.28872 −0.164231 −0.0821154 0.996623i \(-0.526168\pi\)
−0.0821154 + 0.996623i \(0.526168\pi\)
\(402\) 26.7285 1.33310
\(403\) 0.426794 0.0212601
\(404\) 17.0356 0.847551
\(405\) −46.5515 −2.31316
\(406\) 0.0514019 0.00255103
\(407\) 11.7645 0.583144
\(408\) −6.60574 −0.327033
\(409\) 29.2267 1.44517 0.722584 0.691283i \(-0.242954\pi\)
0.722584 + 0.691283i \(0.242954\pi\)
\(410\) 4.18494 0.206679
\(411\) 37.2962 1.83969
\(412\) −10.5631 −0.520407
\(413\) −4.08242 −0.200883
\(414\) −7.32058 −0.359787
\(415\) 70.3363 3.45267
\(416\) −0.223732 −0.0109694
\(417\) −22.4007 −1.09696
\(418\) 5.13031 0.250932
\(419\) 35.5644 1.73744 0.868718 0.495307i \(-0.164945\pi\)
0.868718 + 0.495307i \(0.164945\pi\)
\(420\) 9.45952 0.461578
\(421\) −18.5289 −0.903045 −0.451523 0.892260i \(-0.649119\pi\)
−0.451523 + 0.892260i \(0.649119\pi\)
\(422\) −1.00000 −0.0486792
\(423\) 21.4663 1.04373
\(424\) 10.8683 0.527811
\(425\) 39.8825 1.93458
\(426\) −13.8398 −0.670543
\(427\) −1.57409 −0.0761755
\(428\) −3.59047 −0.173552
\(429\) −2.62094 −0.126540
\(430\) −25.2480 −1.21757
\(431\) 24.6150 1.18566 0.592830 0.805327i \(-0.298010\pi\)
0.592830 + 0.805327i \(0.298010\pi\)
\(432\) 1.79481 0.0863529
\(433\) −38.2251 −1.83698 −0.918491 0.395441i \(-0.870592\pi\)
−0.918491 + 0.395441i \(0.870592\pi\)
\(434\) 1.82329 0.0875205
\(435\) 0.532253 0.0255196
\(436\) 4.87950 0.233686
\(437\) 3.30652 0.158173
\(438\) −8.63313 −0.412507
\(439\) 4.87452 0.232648 0.116324 0.993211i \(-0.462889\pi\)
0.116324 + 0.993211i \(0.462889\pi\)
\(440\) −22.2363 −1.06008
\(441\) −13.4753 −0.641680
\(442\) −0.647241 −0.0307861
\(443\) 36.7284 1.74502 0.872509 0.488598i \(-0.162492\pi\)
0.872509 + 0.488598i \(0.162492\pi\)
\(444\) 5.23617 0.248498
\(445\) 67.3579 3.19307
\(446\) 20.6508 0.977845
\(447\) −2.26272 −0.107023
\(448\) −0.955796 −0.0451571
\(449\) 14.8606 0.701316 0.350658 0.936504i \(-0.385958\pi\)
0.350658 + 0.936504i \(0.385958\pi\)
\(450\) 30.5224 1.43884
\(451\) −4.95351 −0.233252
\(452\) −8.29563 −0.390194
\(453\) −23.8173 −1.11903
\(454\) 7.68360 0.360609
\(455\) 0.926858 0.0434518
\(456\) 2.28341 0.106931
\(457\) −34.4174 −1.60998 −0.804990 0.593288i \(-0.797829\pi\)
−0.804990 + 0.593288i \(0.797829\pi\)
\(458\) −29.6585 −1.38585
\(459\) 5.19225 0.242354
\(460\) −14.3315 −0.668209
\(461\) −12.0352 −0.560533 −0.280267 0.959922i \(-0.590423\pi\)
−0.280267 + 0.959922i \(0.590423\pi\)
\(462\) −11.1968 −0.520921
\(463\) 13.7270 0.637949 0.318974 0.947763i \(-0.396662\pi\)
0.318974 + 0.947763i \(0.396662\pi\)
\(464\) −0.0537792 −0.00249664
\(465\) 18.8796 0.875522
\(466\) 2.77318 0.128465
\(467\) 16.6043 0.768355 0.384178 0.923259i \(-0.374485\pi\)
0.384178 + 0.923259i \(0.374485\pi\)
\(468\) −0.495339 −0.0228970
\(469\) 11.1881 0.516618
\(470\) 42.0245 1.93845
\(471\) 20.1946 0.930519
\(472\) 4.27122 0.196599
\(473\) 29.8848 1.37411
\(474\) −21.0064 −0.964855
\(475\) −13.7862 −0.632555
\(476\) −2.76504 −0.126736
\(477\) 24.0622 1.10173
\(478\) −5.22141 −0.238822
\(479\) −35.6304 −1.62800 −0.813998 0.580867i \(-0.802714\pi\)
−0.813998 + 0.580867i \(0.802714\pi\)
\(480\) −9.89701 −0.451735
\(481\) 0.513048 0.0233930
\(482\) −2.31966 −0.105657
\(483\) −7.21641 −0.328358
\(484\) 15.3201 0.696366
\(485\) 55.1567 2.50454
\(486\) 19.1400 0.868206
\(487\) −27.0689 −1.22661 −0.613304 0.789847i \(-0.710160\pi\)
−0.613304 + 0.789847i \(0.710160\pi\)
\(488\) 1.64689 0.0745511
\(489\) −2.03101 −0.0918455
\(490\) −26.3806 −1.19175
\(491\) 20.6028 0.929791 0.464896 0.885365i \(-0.346092\pi\)
0.464896 + 0.885365i \(0.346092\pi\)
\(492\) −2.20472 −0.0993966
\(493\) −0.155579 −0.00700693
\(494\) 0.223732 0.0100662
\(495\) −49.2308 −2.21276
\(496\) −1.90761 −0.0856542
\(497\) −5.79311 −0.259857
\(498\) −37.0548 −1.66046
\(499\) 19.1318 0.856459 0.428229 0.903670i \(-0.359138\pi\)
0.428229 + 0.903670i \(0.359138\pi\)
\(500\) 38.0821 1.70308
\(501\) −16.1545 −0.721731
\(502\) 17.6215 0.786487
\(503\) 19.4783 0.868493 0.434246 0.900794i \(-0.357015\pi\)
0.434246 + 0.900794i \(0.357015\pi\)
\(504\) −2.11611 −0.0942591
\(505\) 73.8373 3.28572
\(506\) 16.9635 0.754119
\(507\) 29.5701 1.31325
\(508\) 19.3439 0.858247
\(509\) 15.6613 0.694174 0.347087 0.937833i \(-0.387171\pi\)
0.347087 + 0.937833i \(0.387171\pi\)
\(510\) −28.6313 −1.26782
\(511\) −3.61367 −0.159860
\(512\) 1.00000 0.0441942
\(513\) −1.79481 −0.0792429
\(514\) −18.0907 −0.797945
\(515\) −45.7837 −2.01747
\(516\) 13.3012 0.585555
\(517\) −49.7424 −2.18767
\(518\) 2.19177 0.0963008
\(519\) 5.45887 0.239618
\(520\) −0.969724 −0.0425252
\(521\) 24.7153 1.08280 0.541398 0.840766i \(-0.317895\pi\)
0.541398 + 0.840766i \(0.317895\pi\)
\(522\) −0.119066 −0.00521137
\(523\) 31.4808 1.37656 0.688280 0.725445i \(-0.258366\pi\)
0.688280 + 0.725445i \(0.258366\pi\)
\(524\) 9.20602 0.402167
\(525\) 30.0881 1.31315
\(526\) −5.52366 −0.240843
\(527\) −5.51857 −0.240393
\(528\) 11.7146 0.509813
\(529\) −12.0669 −0.524648
\(530\) 47.1065 2.04618
\(531\) 9.45640 0.410373
\(532\) 0.955796 0.0414390
\(533\) −0.216022 −0.00935695
\(534\) −35.4857 −1.53562
\(535\) −15.5622 −0.672812
\(536\) −11.7055 −0.505601
\(537\) −18.4634 −0.796756
\(538\) 22.3892 0.965266
\(539\) 31.2254 1.34497
\(540\) 7.77926 0.334766
\(541\) −16.1161 −0.692887 −0.346444 0.938071i \(-0.612611\pi\)
−0.346444 + 0.938071i \(0.612611\pi\)
\(542\) 21.1723 0.909429
\(543\) −0.666719 −0.0286117
\(544\) 2.89292 0.124033
\(545\) 21.1493 0.905935
\(546\) −0.488291 −0.0208969
\(547\) −16.4297 −0.702485 −0.351242 0.936285i \(-0.614241\pi\)
−0.351242 + 0.936285i \(0.614241\pi\)
\(548\) −16.3335 −0.697734
\(549\) 3.64618 0.155615
\(550\) −70.7275 −3.01583
\(551\) 0.0537792 0.00229107
\(552\) 7.55016 0.321356
\(553\) −8.79289 −0.373912
\(554\) 30.5060 1.29608
\(555\) 22.6952 0.963357
\(556\) 9.81016 0.416043
\(557\) −40.4682 −1.71469 −0.857347 0.514739i \(-0.827889\pi\)
−0.857347 + 0.514739i \(0.827889\pi\)
\(558\) −4.22341 −0.178791
\(559\) 1.30328 0.0551227
\(560\) −4.14271 −0.175062
\(561\) 33.8895 1.43082
\(562\) 0.299543 0.0126354
\(563\) 8.20347 0.345735 0.172868 0.984945i \(-0.444697\pi\)
0.172868 + 0.984945i \(0.444697\pi\)
\(564\) −22.1395 −0.932241
\(565\) −35.9558 −1.51267
\(566\) 6.89607 0.289864
\(567\) 10.2655 0.431109
\(568\) 6.06103 0.254315
\(569\) 22.1725 0.929520 0.464760 0.885437i \(-0.346141\pi\)
0.464760 + 0.885437i \(0.346141\pi\)
\(570\) 9.89701 0.414540
\(571\) −36.4729 −1.52634 −0.763172 0.646195i \(-0.776359\pi\)
−0.763172 + 0.646195i \(0.776359\pi\)
\(572\) 1.14782 0.0479926
\(573\) 37.2922 1.55790
\(574\) −0.922857 −0.0385193
\(575\) −45.5844 −1.90100
\(576\) 2.21398 0.0922491
\(577\) 4.67388 0.194576 0.0972881 0.995256i \(-0.468983\pi\)
0.0972881 + 0.995256i \(0.468983\pi\)
\(578\) −8.63099 −0.359002
\(579\) 50.8855 2.11473
\(580\) −0.233095 −0.00967876
\(581\) −15.5105 −0.643482
\(582\) −29.0579 −1.20449
\(583\) −55.7577 −2.30925
\(584\) 3.78080 0.156451
\(585\) −2.14695 −0.0887654
\(586\) 10.4173 0.430335
\(587\) −0.250896 −0.0103556 −0.00517780 0.999987i \(-0.501648\pi\)
−0.00517780 + 0.999987i \(0.501648\pi\)
\(588\) 13.8979 0.573140
\(589\) 1.90761 0.0786017
\(590\) 18.5128 0.762160
\(591\) 16.0247 0.659169
\(592\) −2.29313 −0.0942472
\(593\) 32.7873 1.34641 0.673207 0.739454i \(-0.264916\pi\)
0.673207 + 0.739454i \(0.264916\pi\)
\(594\) −9.20794 −0.377806
\(595\) −11.9845 −0.491319
\(596\) 0.990937 0.0405904
\(597\) 18.8782 0.772633
\(598\) 0.739776 0.0302517
\(599\) −15.4877 −0.632812 −0.316406 0.948624i \(-0.602476\pi\)
−0.316406 + 0.948624i \(0.602476\pi\)
\(600\) −31.4796 −1.28515
\(601\) 21.1575 0.863031 0.431516 0.902106i \(-0.357979\pi\)
0.431516 + 0.902106i \(0.357979\pi\)
\(602\) 5.56766 0.226921
\(603\) −25.9158 −1.05537
\(604\) 10.4306 0.424414
\(605\) 66.4018 2.69962
\(606\) −38.8992 −1.58017
\(607\) 3.06005 0.124204 0.0621018 0.998070i \(-0.480220\pi\)
0.0621018 + 0.998070i \(0.480220\pi\)
\(608\) −1.00000 −0.0405554
\(609\) −0.117372 −0.00475615
\(610\) 7.13812 0.289014
\(611\) −2.16926 −0.0877589
\(612\) 6.40487 0.258902
\(613\) −18.4730 −0.746117 −0.373059 0.927808i \(-0.621691\pi\)
−0.373059 + 0.927808i \(0.621691\pi\)
\(614\) −24.1824 −0.975921
\(615\) −9.55594 −0.385333
\(616\) 4.90353 0.197569
\(617\) 18.4812 0.744026 0.372013 0.928227i \(-0.378668\pi\)
0.372013 + 0.928227i \(0.378668\pi\)
\(618\) 24.1199 0.970247
\(619\) −19.8455 −0.797659 −0.398829 0.917025i \(-0.630583\pi\)
−0.398829 + 0.917025i \(0.630583\pi\)
\(620\) −8.26816 −0.332057
\(621\) −5.93459 −0.238147
\(622\) 4.73300 0.189776
\(623\) −14.8537 −0.595100
\(624\) 0.510873 0.0204513
\(625\) 96.1285 3.84514
\(626\) 9.38214 0.374986
\(627\) −11.7146 −0.467837
\(628\) −8.84405 −0.352916
\(629\) −6.63386 −0.264509
\(630\) −9.17188 −0.365416
\(631\) 0.596367 0.0237410 0.0118705 0.999930i \(-0.496221\pi\)
0.0118705 + 0.999930i \(0.496221\pi\)
\(632\) 9.19955 0.365939
\(633\) 2.28341 0.0907576
\(634\) 16.9015 0.671244
\(635\) 83.8424 3.32718
\(636\) −24.8168 −0.984050
\(637\) 1.36174 0.0539540
\(638\) 0.275904 0.0109231
\(639\) 13.4190 0.530847
\(640\) 4.33431 0.171328
\(641\) −16.1306 −0.637121 −0.318560 0.947903i \(-0.603199\pi\)
−0.318560 + 0.947903i \(0.603199\pi\)
\(642\) 8.19853 0.323570
\(643\) 39.1153 1.54256 0.771278 0.636498i \(-0.219618\pi\)
0.771278 + 0.636498i \(0.219618\pi\)
\(644\) 3.16036 0.124536
\(645\) 57.6517 2.27003
\(646\) −2.89292 −0.113821
\(647\) −19.0893 −0.750478 −0.375239 0.926928i \(-0.622439\pi\)
−0.375239 + 0.926928i \(0.622439\pi\)
\(648\) −10.7402 −0.421916
\(649\) −21.9127 −0.860149
\(650\) −3.08442 −0.120981
\(651\) −4.16331 −0.163173
\(652\) 0.889463 0.0348340
\(653\) 21.4411 0.839056 0.419528 0.907742i \(-0.362196\pi\)
0.419528 + 0.907742i \(0.362196\pi\)
\(654\) −11.1419 −0.435684
\(655\) 39.9017 1.55909
\(656\) 0.965538 0.0376979
\(657\) 8.37061 0.326569
\(658\) −9.26719 −0.361273
\(659\) 4.82406 0.187919 0.0939593 0.995576i \(-0.470048\pi\)
0.0939593 + 0.995576i \(0.470048\pi\)
\(660\) 50.7747 1.97640
\(661\) 20.1301 0.782969 0.391484 0.920185i \(-0.371962\pi\)
0.391484 + 0.920185i \(0.371962\pi\)
\(662\) 3.06898 0.119279
\(663\) 1.47792 0.0573976
\(664\) 16.2278 0.629761
\(665\) 4.14271 0.160647
\(666\) −5.07695 −0.196728
\(667\) 0.177822 0.00688530
\(668\) 7.07473 0.273729
\(669\) −47.1544 −1.82309
\(670\) −50.7353 −1.96008
\(671\) −8.44904 −0.326172
\(672\) 2.18248 0.0841909
\(673\) 18.7453 0.722577 0.361288 0.932454i \(-0.382337\pi\)
0.361288 + 0.932454i \(0.382337\pi\)
\(674\) 12.0774 0.465204
\(675\) 24.7436 0.952383
\(676\) −12.9499 −0.498075
\(677\) 29.3705 1.12880 0.564399 0.825502i \(-0.309108\pi\)
0.564399 + 0.825502i \(0.309108\pi\)
\(678\) 18.9424 0.727477
\(679\) −12.1631 −0.466777
\(680\) 12.5388 0.480842
\(681\) −17.5448 −0.672320
\(682\) 9.78662 0.374749
\(683\) −10.0911 −0.386125 −0.193062 0.981186i \(-0.561842\pi\)
−0.193062 + 0.981186i \(0.561842\pi\)
\(684\) −2.21398 −0.0846536
\(685\) −70.7945 −2.70492
\(686\) 12.5080 0.477557
\(687\) 67.7227 2.58378
\(688\) −5.82516 −0.222082
\(689\) −2.43159 −0.0926361
\(690\) 32.7247 1.24581
\(691\) 0.478655 0.0182089 0.00910445 0.999959i \(-0.497102\pi\)
0.00910445 + 0.999959i \(0.497102\pi\)
\(692\) −2.39066 −0.0908792
\(693\) 10.8563 0.412397
\(694\) −30.2646 −1.14883
\(695\) 42.5202 1.61288
\(696\) 0.122800 0.00465473
\(697\) 2.79323 0.105801
\(698\) −0.577196 −0.0218472
\(699\) −6.33231 −0.239510
\(700\) −13.1768 −0.498036
\(701\) −51.6805 −1.95194 −0.975972 0.217895i \(-0.930081\pi\)
−0.975972 + 0.217895i \(0.930081\pi\)
\(702\) −0.401557 −0.0151558
\(703\) 2.29313 0.0864872
\(704\) −5.13031 −0.193356
\(705\) −95.9593 −3.61404
\(706\) −32.8742 −1.23724
\(707\) −16.2825 −0.612367
\(708\) −9.75297 −0.366539
\(709\) −34.8782 −1.30988 −0.654940 0.755681i \(-0.727306\pi\)
−0.654940 + 0.755681i \(0.727306\pi\)
\(710\) 26.2704 0.985910
\(711\) 20.3676 0.763845
\(712\) 15.5406 0.582410
\(713\) 6.30756 0.236220
\(714\) 6.31374 0.236286
\(715\) 4.97498 0.186054
\(716\) 8.08589 0.302184
\(717\) 11.9226 0.445259
\(718\) −22.0424 −0.822617
\(719\) −44.3798 −1.65509 −0.827544 0.561400i \(-0.810263\pi\)
−0.827544 + 0.561400i \(0.810263\pi\)
\(720\) 9.59606 0.357624
\(721\) 10.0962 0.376001
\(722\) 1.00000 0.0372161
\(723\) 5.29673 0.196988
\(724\) 0.291984 0.0108515
\(725\) −0.741411 −0.0275353
\(726\) −34.9820 −1.29831
\(727\) −28.5440 −1.05864 −0.529319 0.848423i \(-0.677552\pi\)
−0.529319 + 0.848423i \(0.677552\pi\)
\(728\) 0.213842 0.00792553
\(729\) −11.4838 −0.425324
\(730\) 16.3872 0.606516
\(731\) −16.8517 −0.623284
\(732\) −3.76053 −0.138993
\(733\) −38.2904 −1.41429 −0.707143 0.707070i \(-0.750016\pi\)
−0.707143 + 0.707070i \(0.750016\pi\)
\(734\) 28.0980 1.03712
\(735\) 60.2377 2.22190
\(736\) −3.30652 −0.121880
\(737\) 60.0529 2.21208
\(738\) 2.13768 0.0786891
\(739\) −4.86293 −0.178886 −0.0894429 0.995992i \(-0.528509\pi\)
−0.0894429 + 0.995992i \(0.528509\pi\)
\(740\) −9.93915 −0.365370
\(741\) −0.510873 −0.0187674
\(742\) −10.3879 −0.381350
\(743\) −0.793285 −0.0291028 −0.0145514 0.999894i \(-0.504632\pi\)
−0.0145514 + 0.999894i \(0.504632\pi\)
\(744\) 4.35586 0.159694
\(745\) 4.29503 0.157358
\(746\) 32.0311 1.17274
\(747\) 35.9280 1.31454
\(748\) −14.8416 −0.542662
\(749\) 3.43176 0.125394
\(750\) −86.9572 −3.17523
\(751\) 4.93314 0.180013 0.0900065 0.995941i \(-0.471311\pi\)
0.0900065 + 0.995941i \(0.471311\pi\)
\(752\) 9.69579 0.353569
\(753\) −40.2372 −1.46633
\(754\) 0.0120321 0.000438185 0
\(755\) 45.2093 1.64533
\(756\) −1.71547 −0.0623912
\(757\) −39.2225 −1.42557 −0.712783 0.701385i \(-0.752566\pi\)
−0.712783 + 0.701385i \(0.752566\pi\)
\(758\) −37.9753 −1.37933
\(759\) −38.7347 −1.40598
\(760\) −4.33431 −0.157222
\(761\) 35.6627 1.29277 0.646387 0.763010i \(-0.276279\pi\)
0.646387 + 0.763010i \(0.276279\pi\)
\(762\) −44.1701 −1.60012
\(763\) −4.66381 −0.168841
\(764\) −16.3318 −0.590862
\(765\) 27.7607 1.00369
\(766\) 7.68475 0.277661
\(767\) −0.955611 −0.0345051
\(768\) −2.28341 −0.0823956
\(769\) −32.0463 −1.15562 −0.577810 0.816172i \(-0.696092\pi\)
−0.577810 + 0.816172i \(0.696092\pi\)
\(770\) 21.2534 0.765919
\(771\) 41.3085 1.48769
\(772\) −22.2848 −0.802048
\(773\) −36.0321 −1.29598 −0.647992 0.761647i \(-0.724391\pi\)
−0.647992 + 0.761647i \(0.724391\pi\)
\(774\) −12.8968 −0.463565
\(775\) −26.2987 −0.944677
\(776\) 12.7256 0.456823
\(777\) −5.00471 −0.179543
\(778\) 30.6879 1.10021
\(779\) −0.965538 −0.0345940
\(780\) 2.21428 0.0792840
\(781\) −31.0950 −1.11267
\(782\) −9.56552 −0.342062
\(783\) −0.0965235 −0.00344947
\(784\) −6.08645 −0.217373
\(785\) −38.3328 −1.36816
\(786\) −21.0212 −0.749800
\(787\) −15.8706 −0.565726 −0.282863 0.959160i \(-0.591284\pi\)
−0.282863 + 0.959160i \(0.591284\pi\)
\(788\) −7.01787 −0.250001
\(789\) 12.6128 0.449027
\(790\) 39.8737 1.41864
\(791\) 7.92893 0.281920
\(792\) −11.3584 −0.403603
\(793\) −0.368462 −0.0130845
\(794\) −11.9920 −0.425579
\(795\) −107.564 −3.81489
\(796\) −8.26753 −0.293035
\(797\) −20.3226 −0.719862 −0.359931 0.932979i \(-0.617200\pi\)
−0.359931 + 0.932979i \(0.617200\pi\)
\(798\) −2.18248 −0.0772589
\(799\) 28.0492 0.992308
\(800\) 13.7862 0.487416
\(801\) 34.4067 1.21570
\(802\) −3.28872 −0.116129
\(803\) −19.3967 −0.684494
\(804\) 26.7285 0.942643
\(805\) 13.6980 0.482790
\(806\) 0.426794 0.0150332
\(807\) −51.1238 −1.79964
\(808\) 17.0356 0.599309
\(809\) −19.0189 −0.668669 −0.334334 0.942454i \(-0.608512\pi\)
−0.334334 + 0.942454i \(0.608512\pi\)
\(810\) −46.5515 −1.63565
\(811\) −14.8294 −0.520730 −0.260365 0.965510i \(-0.583843\pi\)
−0.260365 + 0.965510i \(0.583843\pi\)
\(812\) 0.0514019 0.00180385
\(813\) −48.3452 −1.69554
\(814\) 11.7645 0.412345
\(815\) 3.85520 0.135042
\(816\) −6.60574 −0.231247
\(817\) 5.82516 0.203796
\(818\) 29.2267 1.02189
\(819\) 0.473443 0.0165434
\(820\) 4.18494 0.146144
\(821\) 14.0275 0.489562 0.244781 0.969578i \(-0.421284\pi\)
0.244781 + 0.969578i \(0.421284\pi\)
\(822\) 37.2962 1.30086
\(823\) 28.2974 0.986386 0.493193 0.869920i \(-0.335830\pi\)
0.493193 + 0.869920i \(0.335830\pi\)
\(824\) −10.5631 −0.367983
\(825\) 161.500 5.62271
\(826\) −4.08242 −0.142046
\(827\) 14.4380 0.502057 0.251029 0.967980i \(-0.419231\pi\)
0.251029 + 0.967980i \(0.419231\pi\)
\(828\) −7.32058 −0.254408
\(829\) 44.2391 1.53649 0.768244 0.640157i \(-0.221131\pi\)
0.768244 + 0.640157i \(0.221131\pi\)
\(830\) 70.3363 2.44141
\(831\) −69.6578 −2.41640
\(832\) −0.223732 −0.00775652
\(833\) −17.6076 −0.610069
\(834\) −22.4007 −0.775671
\(835\) 30.6640 1.06117
\(836\) 5.13031 0.177435
\(837\) −3.42380 −0.118344
\(838\) 35.5644 1.22855
\(839\) −8.61764 −0.297514 −0.148757 0.988874i \(-0.547527\pi\)
−0.148757 + 0.988874i \(0.547527\pi\)
\(840\) 9.45952 0.326385
\(841\) −28.9971 −0.999900
\(842\) −18.5289 −0.638549
\(843\) −0.683980 −0.0235575
\(844\) −1.00000 −0.0344214
\(845\) −56.1290 −1.93090
\(846\) 21.4663 0.738025
\(847\) −14.6428 −0.503134
\(848\) 10.8683 0.373219
\(849\) −15.7466 −0.540421
\(850\) 39.8825 1.36796
\(851\) 7.58230 0.259918
\(852\) −13.8398 −0.474145
\(853\) 43.5815 1.49220 0.746101 0.665833i \(-0.231924\pi\)
0.746101 + 0.665833i \(0.231924\pi\)
\(854\) −1.57409 −0.0538642
\(855\) −9.59606 −0.328178
\(856\) −3.59047 −0.122720
\(857\) 7.04546 0.240668 0.120334 0.992733i \(-0.461603\pi\)
0.120334 + 0.992733i \(0.461603\pi\)
\(858\) −2.62094 −0.0894774
\(859\) −14.2081 −0.484774 −0.242387 0.970180i \(-0.577930\pi\)
−0.242387 + 0.970180i \(0.577930\pi\)
\(860\) −25.2480 −0.860950
\(861\) 2.10726 0.0718154
\(862\) 24.6150 0.838389
\(863\) −22.7307 −0.773763 −0.386882 0.922129i \(-0.626448\pi\)
−0.386882 + 0.922129i \(0.626448\pi\)
\(864\) 1.79481 0.0610607
\(865\) −10.3619 −0.352313
\(866\) −38.2251 −1.29894
\(867\) 19.7081 0.669323
\(868\) 1.82329 0.0618863
\(869\) −47.1965 −1.60103
\(870\) 0.532253 0.0180451
\(871\) 2.61890 0.0887381
\(872\) 4.87950 0.165241
\(873\) 28.1743 0.953554
\(874\) 3.30652 0.111845
\(875\) −36.3987 −1.23050
\(876\) −8.63313 −0.291687
\(877\) 35.8319 1.20996 0.604979 0.796241i \(-0.293182\pi\)
0.604979 + 0.796241i \(0.293182\pi\)
\(878\) 4.87452 0.164507
\(879\) −23.7871 −0.802317
\(880\) −22.2363 −0.749586
\(881\) 8.59293 0.289503 0.144752 0.989468i \(-0.453762\pi\)
0.144752 + 0.989468i \(0.453762\pi\)
\(882\) −13.4753 −0.453736
\(883\) 20.6165 0.693799 0.346899 0.937902i \(-0.387235\pi\)
0.346899 + 0.937902i \(0.387235\pi\)
\(884\) −0.647241 −0.0217691
\(885\) −42.2724 −1.42097
\(886\) 36.7284 1.23391
\(887\) 47.8875 1.60790 0.803952 0.594694i \(-0.202727\pi\)
0.803952 + 0.594694i \(0.202727\pi\)
\(888\) 5.23617 0.175715
\(889\) −18.4888 −0.620095
\(890\) 67.3579 2.25784
\(891\) 55.1007 1.84594
\(892\) 20.6508 0.691441
\(893\) −9.69579 −0.324457
\(894\) −2.26272 −0.0756767
\(895\) 35.0467 1.17148
\(896\) −0.955796 −0.0319309
\(897\) −1.68922 −0.0564013
\(898\) 14.8606 0.495906
\(899\) 0.102590 0.00342156
\(900\) 30.5224 1.01741
\(901\) 31.4411 1.04746
\(902\) −4.95351 −0.164934
\(903\) −12.7133 −0.423071
\(904\) −8.29563 −0.275909
\(905\) 1.26555 0.0420682
\(906\) −23.8173 −0.791277
\(907\) −7.85610 −0.260857 −0.130429 0.991458i \(-0.541635\pi\)
−0.130429 + 0.991458i \(0.541635\pi\)
\(908\) 7.68360 0.254989
\(909\) 37.7164 1.25097
\(910\) 0.926858 0.0307251
\(911\) 31.2631 1.03579 0.517897 0.855443i \(-0.326715\pi\)
0.517897 + 0.855443i \(0.326715\pi\)
\(912\) 2.28341 0.0756114
\(913\) −83.2536 −2.75529
\(914\) −34.4174 −1.13843
\(915\) −16.2993 −0.538837
\(916\) −29.6585 −0.979945
\(917\) −8.79908 −0.290571
\(918\) 5.19225 0.171370
\(919\) −34.9245 −1.15205 −0.576027 0.817431i \(-0.695398\pi\)
−0.576027 + 0.817431i \(0.695398\pi\)
\(920\) −14.3315 −0.472495
\(921\) 55.2184 1.81951
\(922\) −12.0352 −0.396357
\(923\) −1.35605 −0.0446349
\(924\) −11.1968 −0.368347
\(925\) −31.6136 −1.03945
\(926\) 13.7270 0.451098
\(927\) −23.3865 −0.768113
\(928\) −0.0537792 −0.00176539
\(929\) 40.7402 1.33664 0.668321 0.743873i \(-0.267013\pi\)
0.668321 + 0.743873i \(0.267013\pi\)
\(930\) 18.8796 0.619088
\(931\) 6.08645 0.199475
\(932\) 2.77318 0.0908385
\(933\) −10.8074 −0.353818
\(934\) 16.6043 0.543309
\(935\) −64.3280 −2.10375
\(936\) −0.495339 −0.0161907
\(937\) 26.8862 0.878333 0.439167 0.898406i \(-0.355274\pi\)
0.439167 + 0.898406i \(0.355274\pi\)
\(938\) 11.1881 0.365304
\(939\) −21.4233 −0.699123
\(940\) 42.0245 1.37069
\(941\) −22.0354 −0.718334 −0.359167 0.933273i \(-0.616939\pi\)
−0.359167 + 0.933273i \(0.616939\pi\)
\(942\) 20.1946 0.657976
\(943\) −3.19257 −0.103965
\(944\) 4.27122 0.139017
\(945\) −7.43539 −0.241873
\(946\) 29.8848 0.971640
\(947\) −18.9954 −0.617266 −0.308633 0.951181i \(-0.599871\pi\)
−0.308633 + 0.951181i \(0.599871\pi\)
\(948\) −21.0064 −0.682256
\(949\) −0.845887 −0.0274587
\(950\) −13.7862 −0.447284
\(951\) −38.5931 −1.25147
\(952\) −2.76504 −0.0896156
\(953\) −16.2966 −0.527899 −0.263949 0.964537i \(-0.585025\pi\)
−0.263949 + 0.964537i \(0.585025\pi\)
\(954\) 24.0622 0.779041
\(955\) −70.7869 −2.29061
\(956\) −5.22141 −0.168872
\(957\) −0.630002 −0.0203651
\(958\) −35.6304 −1.15117
\(959\) 15.6115 0.504122
\(960\) −9.89701 −0.319425
\(961\) −27.3610 −0.882614
\(962\) 0.513048 0.0165413
\(963\) −7.94922 −0.256160
\(964\) −2.31966 −0.0747111
\(965\) −96.5892 −3.10932
\(966\) −7.21641 −0.232184
\(967\) 2.68153 0.0862323 0.0431161 0.999070i \(-0.486271\pi\)
0.0431161 + 0.999070i \(0.486271\pi\)
\(968\) 15.3201 0.492405
\(969\) 6.60574 0.212207
\(970\) 55.1567 1.77098
\(971\) 47.4001 1.52114 0.760571 0.649255i \(-0.224919\pi\)
0.760571 + 0.649255i \(0.224919\pi\)
\(972\) 19.1400 0.613915
\(973\) −9.37651 −0.300597
\(974\) −27.0689 −0.867343
\(975\) 7.04301 0.225557
\(976\) 1.64689 0.0527156
\(977\) −42.5792 −1.36223 −0.681114 0.732177i \(-0.738504\pi\)
−0.681114 + 0.732177i \(0.738504\pi\)
\(978\) −2.03101 −0.0649446
\(979\) −79.7283 −2.54813
\(980\) −26.3806 −0.842696
\(981\) 10.8031 0.344917
\(982\) 20.6028 0.657462
\(983\) −27.2983 −0.870681 −0.435340 0.900266i \(-0.643372\pi\)
−0.435340 + 0.900266i \(0.643372\pi\)
\(984\) −2.20472 −0.0702840
\(985\) −30.4176 −0.969186
\(986\) −0.155579 −0.00495465
\(987\) 21.1608 0.673557
\(988\) 0.223732 0.00711787
\(989\) 19.2610 0.612465
\(990\) −49.2308 −1.56466
\(991\) −60.9292 −1.93548 −0.967740 0.251951i \(-0.918928\pi\)
−0.967740 + 0.251951i \(0.918928\pi\)
\(992\) −1.90761 −0.0605667
\(993\) −7.00776 −0.222384
\(994\) −5.79311 −0.183746
\(995\) −35.8340 −1.13601
\(996\) −37.0548 −1.17413
\(997\) −3.25619 −0.103125 −0.0515623 0.998670i \(-0.516420\pi\)
−0.0515623 + 0.998670i \(0.516420\pi\)
\(998\) 19.1318 0.605608
\(999\) −4.11574 −0.130216
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 \(a_p\))