Properties

Label 8020.2.a.c.1.3
Level 8020
Weight 2
Character 8020.1
Self dual Yes
Analytic conductor 64.040
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

Level: \( N \) = \( 8020 = 2^{2} \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8020.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0400224211\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 8020.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.59496 q^{3}\) \(-1.00000 q^{5}\) \(+1.42420 q^{7}\) \(+3.73381 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.59496 q^{3}\) \(-1.00000 q^{5}\) \(+1.42420 q^{7}\) \(+3.73381 q^{9}\) \(+3.63795 q^{11}\) \(-2.47890 q^{13}\) \(+2.59496 q^{15}\) \(+4.00900 q^{17}\) \(+0.503905 q^{19}\) \(-3.69573 q^{21}\) \(-8.01771 q^{23}\) \(+1.00000 q^{25}\) \(-1.90422 q^{27}\) \(-1.71938 q^{29}\) \(-6.28565 q^{31}\) \(-9.44032 q^{33}\) \(-1.42420 q^{35}\) \(+5.09212 q^{37}\) \(+6.43265 q^{39}\) \(+1.37887 q^{41}\) \(+7.23723 q^{43}\) \(-3.73381 q^{45}\) \(+7.49079 q^{47}\) \(-4.97167 q^{49}\) \(-10.4032 q^{51}\) \(-7.78413 q^{53}\) \(-3.63795 q^{55}\) \(-1.30761 q^{57}\) \(-5.83373 q^{59}\) \(-9.44664 q^{61}\) \(+5.31768 q^{63}\) \(+2.47890 q^{65}\) \(+9.06165 q^{67}\) \(+20.8056 q^{69}\) \(-9.23923 q^{71}\) \(-7.53548 q^{73}\) \(-2.59496 q^{75}\) \(+5.18115 q^{77}\) \(-10.3976 q^{79}\) \(-6.26008 q^{81}\) \(+6.25543 q^{83}\) \(-4.00900 q^{85}\) \(+4.46173 q^{87}\) \(+2.74123 q^{89}\) \(-3.53044 q^{91}\) \(+16.3110 q^{93}\) \(-0.503905 q^{95}\) \(+9.29500 q^{97}\) \(+13.5834 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 3q^{13} \) \(\mathstrut -\mathstrut 3q^{15} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut +\mathstrut 28q^{25} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut -\mathstrut 37q^{29} \) \(\mathstrut -\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 2q^{33} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut -\mathstrut 3q^{37} \) \(\mathstrut -\mathstrut 19q^{39} \) \(\mathstrut -\mathstrut 30q^{41} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut -\mathstrut 17q^{45} \) \(\mathstrut -\mathstrut 15q^{47} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 2q^{55} \) \(\mathstrut -\mathstrut 22q^{57} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut -\mathstrut 33q^{61} \) \(\mathstrut -\mathstrut 20q^{63} \) \(\mathstrut -\mathstrut 3q^{65} \) \(\mathstrut +\mathstrut 19q^{67} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut -\mathstrut 42q^{77} \) \(\mathstrut -\mathstrut 29q^{79} \) \(\mathstrut -\mathstrut 36q^{81} \) \(\mathstrut +\mathstrut 14q^{83} \) \(\mathstrut +\mathstrut 10q^{85} \) \(\mathstrut -\mathstrut 32q^{87} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 7q^{91} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 39q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.59496 −1.49820 −0.749100 0.662457i \(-0.769514\pi\)
−0.749100 + 0.662457i \(0.769514\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 1.42420 0.538295 0.269148 0.963099i \(-0.413258\pi\)
0.269148 + 0.963099i \(0.413258\pi\)
\(8\) 0 0
\(9\) 3.73381 1.24460
\(10\) 0 0
\(11\) 3.63795 1.09688 0.548441 0.836189i \(-0.315222\pi\)
0.548441 + 0.836189i \(0.315222\pi\)
\(12\) 0 0
\(13\) −2.47890 −0.687523 −0.343762 0.939057i \(-0.611701\pi\)
−0.343762 + 0.939057i \(0.611701\pi\)
\(14\) 0 0
\(15\) 2.59496 0.670016
\(16\) 0 0
\(17\) 4.00900 0.972327 0.486163 0.873868i \(-0.338396\pi\)
0.486163 + 0.873868i \(0.338396\pi\)
\(18\) 0 0
\(19\) 0.503905 0.115604 0.0578018 0.998328i \(-0.481591\pi\)
0.0578018 + 0.998328i \(0.481591\pi\)
\(20\) 0 0
\(21\) −3.69573 −0.806474
\(22\) 0 0
\(23\) −8.01771 −1.67181 −0.835904 0.548876i \(-0.815056\pi\)
−0.835904 + 0.548876i \(0.815056\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −1.90422 −0.366467
\(28\) 0 0
\(29\) −1.71938 −0.319282 −0.159641 0.987175i \(-0.551034\pi\)
−0.159641 + 0.987175i \(0.551034\pi\)
\(30\) 0 0
\(31\) −6.28565 −1.12894 −0.564468 0.825455i \(-0.690919\pi\)
−0.564468 + 0.825455i \(0.690919\pi\)
\(32\) 0 0
\(33\) −9.44032 −1.64335
\(34\) 0 0
\(35\) −1.42420 −0.240733
\(36\) 0 0
\(37\) 5.09212 0.837139 0.418569 0.908185i \(-0.362532\pi\)
0.418569 + 0.908185i \(0.362532\pi\)
\(38\) 0 0
\(39\) 6.43265 1.03005
\(40\) 0 0
\(41\) 1.37887 0.215343 0.107672 0.994187i \(-0.465661\pi\)
0.107672 + 0.994187i \(0.465661\pi\)
\(42\) 0 0
\(43\) 7.23723 1.10367 0.551834 0.833954i \(-0.313928\pi\)
0.551834 + 0.833954i \(0.313928\pi\)
\(44\) 0 0
\(45\) −3.73381 −0.556604
\(46\) 0 0
\(47\) 7.49079 1.09264 0.546322 0.837575i \(-0.316028\pi\)
0.546322 + 0.837575i \(0.316028\pi\)
\(48\) 0 0
\(49\) −4.97167 −0.710238
\(50\) 0 0
\(51\) −10.4032 −1.45674
\(52\) 0 0
\(53\) −7.78413 −1.06923 −0.534617 0.845095i \(-0.679544\pi\)
−0.534617 + 0.845095i \(0.679544\pi\)
\(54\) 0 0
\(55\) −3.63795 −0.490540
\(56\) 0 0
\(57\) −1.30761 −0.173197
\(58\) 0 0
\(59\) −5.83373 −0.759487 −0.379744 0.925092i \(-0.623988\pi\)
−0.379744 + 0.925092i \(0.623988\pi\)
\(60\) 0 0
\(61\) −9.44664 −1.20952 −0.604759 0.796408i \(-0.706731\pi\)
−0.604759 + 0.796408i \(0.706731\pi\)
\(62\) 0 0
\(63\) 5.31768 0.669965
\(64\) 0 0
\(65\) 2.47890 0.307470
\(66\) 0 0
\(67\) 9.06165 1.10706 0.553528 0.832830i \(-0.313281\pi\)
0.553528 + 0.832830i \(0.313281\pi\)
\(68\) 0 0
\(69\) 20.8056 2.50470
\(70\) 0 0
\(71\) −9.23923 −1.09649 −0.548247 0.836316i \(-0.684705\pi\)
−0.548247 + 0.836316i \(0.684705\pi\)
\(72\) 0 0
\(73\) −7.53548 −0.881961 −0.440981 0.897517i \(-0.645369\pi\)
−0.440981 + 0.897517i \(0.645369\pi\)
\(74\) 0 0
\(75\) −2.59496 −0.299640
\(76\) 0 0
\(77\) 5.18115 0.590447
\(78\) 0 0
\(79\) −10.3976 −1.16982 −0.584912 0.811096i \(-0.698871\pi\)
−0.584912 + 0.811096i \(0.698871\pi\)
\(80\) 0 0
\(81\) −6.26008 −0.695564
\(82\) 0 0
\(83\) 6.25543 0.686622 0.343311 0.939222i \(-0.388451\pi\)
0.343311 + 0.939222i \(0.388451\pi\)
\(84\) 0 0
\(85\) −4.00900 −0.434838
\(86\) 0 0
\(87\) 4.46173 0.478348
\(88\) 0 0
\(89\) 2.74123 0.290570 0.145285 0.989390i \(-0.453590\pi\)
0.145285 + 0.989390i \(0.453590\pi\)
\(90\) 0 0
\(91\) −3.53044 −0.370091
\(92\) 0 0
\(93\) 16.3110 1.69137
\(94\) 0 0
\(95\) −0.503905 −0.0516995
\(96\) 0 0
\(97\) 9.29500 0.943764 0.471882 0.881662i \(-0.343575\pi\)
0.471882 + 0.881662i \(0.343575\pi\)
\(98\) 0 0
\(99\) 13.5834 1.36518
\(100\) 0 0
\(101\) 6.15352 0.612298 0.306149 0.951984i \(-0.400959\pi\)
0.306149 + 0.951984i \(0.400959\pi\)
\(102\) 0 0
\(103\) −0.805067 −0.0793256 −0.0396628 0.999213i \(-0.512628\pi\)
−0.0396628 + 0.999213i \(0.512628\pi\)
\(104\) 0 0
\(105\) 3.69573 0.360666
\(106\) 0 0
\(107\) −10.3717 −1.00267 −0.501337 0.865252i \(-0.667158\pi\)
−0.501337 + 0.865252i \(0.667158\pi\)
\(108\) 0 0
\(109\) 4.02337 0.385369 0.192684 0.981261i \(-0.438281\pi\)
0.192684 + 0.981261i \(0.438281\pi\)
\(110\) 0 0
\(111\) −13.2138 −1.25420
\(112\) 0 0
\(113\) 12.5686 1.18236 0.591178 0.806541i \(-0.298663\pi\)
0.591178 + 0.806541i \(0.298663\pi\)
\(114\) 0 0
\(115\) 8.01771 0.747655
\(116\) 0 0
\(117\) −9.25575 −0.855695
\(118\) 0 0
\(119\) 5.70961 0.523399
\(120\) 0 0
\(121\) 2.23465 0.203150
\(122\) 0 0
\(123\) −3.57811 −0.322627
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 1.98446 0.176092 0.0880461 0.996116i \(-0.471938\pi\)
0.0880461 + 0.996116i \(0.471938\pi\)
\(128\) 0 0
\(129\) −18.7803 −1.65351
\(130\) 0 0
\(131\) −0.828022 −0.0723446 −0.0361723 0.999346i \(-0.511517\pi\)
−0.0361723 + 0.999346i \(0.511517\pi\)
\(132\) 0 0
\(133\) 0.717659 0.0622289
\(134\) 0 0
\(135\) 1.90422 0.163889
\(136\) 0 0
\(137\) 12.2403 1.04576 0.522879 0.852407i \(-0.324858\pi\)
0.522879 + 0.852407i \(0.324858\pi\)
\(138\) 0 0
\(139\) 19.0082 1.61225 0.806125 0.591745i \(-0.201561\pi\)
0.806125 + 0.591745i \(0.201561\pi\)
\(140\) 0 0
\(141\) −19.4383 −1.63700
\(142\) 0 0
\(143\) −9.01811 −0.754132
\(144\) 0 0
\(145\) 1.71938 0.142787
\(146\) 0 0
\(147\) 12.9013 1.06408
\(148\) 0 0
\(149\) −21.1851 −1.73555 −0.867775 0.496958i \(-0.834450\pi\)
−0.867775 + 0.496958i \(0.834450\pi\)
\(150\) 0 0
\(151\) 16.4754 1.34075 0.670375 0.742023i \(-0.266133\pi\)
0.670375 + 0.742023i \(0.266133\pi\)
\(152\) 0 0
\(153\) 14.9689 1.21016
\(154\) 0 0
\(155\) 6.28565 0.504876
\(156\) 0 0
\(157\) −6.53892 −0.521863 −0.260931 0.965357i \(-0.584030\pi\)
−0.260931 + 0.965357i \(0.584030\pi\)
\(158\) 0 0
\(159\) 20.1995 1.60193
\(160\) 0 0
\(161\) −11.4188 −0.899927
\(162\) 0 0
\(163\) −5.21914 −0.408795 −0.204397 0.978888i \(-0.565523\pi\)
−0.204397 + 0.978888i \(0.565523\pi\)
\(164\) 0 0
\(165\) 9.44032 0.734928
\(166\) 0 0
\(167\) 21.5110 1.66457 0.832286 0.554346i \(-0.187031\pi\)
0.832286 + 0.554346i \(0.187031\pi\)
\(168\) 0 0
\(169\) −6.85505 −0.527312
\(170\) 0 0
\(171\) 1.88149 0.143881
\(172\) 0 0
\(173\) 15.3570 1.16757 0.583786 0.811907i \(-0.301571\pi\)
0.583786 + 0.811907i \(0.301571\pi\)
\(174\) 0 0
\(175\) 1.42420 0.107659
\(176\) 0 0
\(177\) 15.1383 1.13786
\(178\) 0 0
\(179\) −0.883490 −0.0660351 −0.0330176 0.999455i \(-0.510512\pi\)
−0.0330176 + 0.999455i \(0.510512\pi\)
\(180\) 0 0
\(181\) 0.683182 0.0507805 0.0253903 0.999678i \(-0.491917\pi\)
0.0253903 + 0.999678i \(0.491917\pi\)
\(182\) 0 0
\(183\) 24.5136 1.81210
\(184\) 0 0
\(185\) −5.09212 −0.374380
\(186\) 0 0
\(187\) 14.5845 1.06653
\(188\) 0 0
\(189\) −2.71198 −0.197267
\(190\) 0 0
\(191\) 16.2944 1.17902 0.589512 0.807760i \(-0.299320\pi\)
0.589512 + 0.807760i \(0.299320\pi\)
\(192\) 0 0
\(193\) 17.1368 1.23353 0.616767 0.787146i \(-0.288442\pi\)
0.616767 + 0.787146i \(0.288442\pi\)
\(194\) 0 0
\(195\) −6.43265 −0.460651
\(196\) 0 0
\(197\) 0.178606 0.0127251 0.00636256 0.999980i \(-0.497975\pi\)
0.00636256 + 0.999980i \(0.497975\pi\)
\(198\) 0 0
\(199\) 7.07367 0.501439 0.250720 0.968060i \(-0.419333\pi\)
0.250720 + 0.968060i \(0.419333\pi\)
\(200\) 0 0
\(201\) −23.5146 −1.65859
\(202\) 0 0
\(203\) −2.44874 −0.171868
\(204\) 0 0
\(205\) −1.37887 −0.0963044
\(206\) 0 0
\(207\) −29.9366 −2.08074
\(208\) 0 0
\(209\) 1.83318 0.126804
\(210\) 0 0
\(211\) −7.17620 −0.494030 −0.247015 0.969012i \(-0.579450\pi\)
−0.247015 + 0.969012i \(0.579450\pi\)
\(212\) 0 0
\(213\) 23.9754 1.64277
\(214\) 0 0
\(215\) −7.23723 −0.493575
\(216\) 0 0
\(217\) −8.95200 −0.607701
\(218\) 0 0
\(219\) 19.5543 1.32135
\(220\) 0 0
\(221\) −9.93792 −0.668497
\(222\) 0 0
\(223\) −8.11856 −0.543659 −0.271829 0.962345i \(-0.587629\pi\)
−0.271829 + 0.962345i \(0.587629\pi\)
\(224\) 0 0
\(225\) 3.73381 0.248921
\(226\) 0 0
\(227\) 8.82846 0.585966 0.292983 0.956118i \(-0.405352\pi\)
0.292983 + 0.956118i \(0.405352\pi\)
\(228\) 0 0
\(229\) −14.3450 −0.947946 −0.473973 0.880539i \(-0.657181\pi\)
−0.473973 + 0.880539i \(0.657181\pi\)
\(230\) 0 0
\(231\) −13.4449 −0.884607
\(232\) 0 0
\(233\) −18.5730 −1.21676 −0.608378 0.793648i \(-0.708179\pi\)
−0.608378 + 0.793648i \(0.708179\pi\)
\(234\) 0 0
\(235\) −7.49079 −0.488645
\(236\) 0 0
\(237\) 26.9814 1.75263
\(238\) 0 0
\(239\) −28.3897 −1.83638 −0.918188 0.396145i \(-0.870348\pi\)
−0.918188 + 0.396145i \(0.870348\pi\)
\(240\) 0 0
\(241\) −7.16168 −0.461324 −0.230662 0.973034i \(-0.574089\pi\)
−0.230662 + 0.973034i \(0.574089\pi\)
\(242\) 0 0
\(243\) 21.9573 1.40856
\(244\) 0 0
\(245\) 4.97167 0.317628
\(246\) 0 0
\(247\) −1.24913 −0.0794802
\(248\) 0 0
\(249\) −16.2326 −1.02870
\(250\) 0 0
\(251\) 4.47845 0.282677 0.141339 0.989961i \(-0.454859\pi\)
0.141339 + 0.989961i \(0.454859\pi\)
\(252\) 0 0
\(253\) −29.1680 −1.83378
\(254\) 0 0
\(255\) 10.4032 0.651474
\(256\) 0 0
\(257\) −8.09408 −0.504895 −0.252447 0.967611i \(-0.581235\pi\)
−0.252447 + 0.967611i \(0.581235\pi\)
\(258\) 0 0
\(259\) 7.25217 0.450628
\(260\) 0 0
\(261\) −6.41986 −0.397380
\(262\) 0 0
\(263\) −18.5791 −1.14564 −0.572820 0.819682i \(-0.694150\pi\)
−0.572820 + 0.819682i \(0.694150\pi\)
\(264\) 0 0
\(265\) 7.78413 0.478176
\(266\) 0 0
\(267\) −7.11339 −0.435332
\(268\) 0 0
\(269\) −5.47249 −0.333664 −0.166832 0.985985i \(-0.553354\pi\)
−0.166832 + 0.985985i \(0.553354\pi\)
\(270\) 0 0
\(271\) 11.1710 0.678589 0.339295 0.940680i \(-0.389812\pi\)
0.339295 + 0.940680i \(0.389812\pi\)
\(272\) 0 0
\(273\) 9.16135 0.554470
\(274\) 0 0
\(275\) 3.63795 0.219376
\(276\) 0 0
\(277\) −23.5462 −1.41475 −0.707377 0.706837i \(-0.750122\pi\)
−0.707377 + 0.706837i \(0.750122\pi\)
\(278\) 0 0
\(279\) −23.4695 −1.40508
\(280\) 0 0
\(281\) −5.88015 −0.350780 −0.175390 0.984499i \(-0.556119\pi\)
−0.175390 + 0.984499i \(0.556119\pi\)
\(282\) 0 0
\(283\) −17.4270 −1.03593 −0.517964 0.855403i \(-0.673310\pi\)
−0.517964 + 0.855403i \(0.673310\pi\)
\(284\) 0 0
\(285\) 1.30761 0.0774562
\(286\) 0 0
\(287\) 1.96378 0.115918
\(288\) 0 0
\(289\) −0.927879 −0.0545811
\(290\) 0 0
\(291\) −24.1201 −1.41395
\(292\) 0 0
\(293\) −25.5468 −1.49246 −0.746229 0.665689i \(-0.768138\pi\)
−0.746229 + 0.665689i \(0.768138\pi\)
\(294\) 0 0
\(295\) 5.83373 0.339653
\(296\) 0 0
\(297\) −6.92743 −0.401971
\(298\) 0 0
\(299\) 19.8751 1.14941
\(300\) 0 0
\(301\) 10.3072 0.594099
\(302\) 0 0
\(303\) −15.9681 −0.917345
\(304\) 0 0
\(305\) 9.44664 0.540913
\(306\) 0 0
\(307\) 0.0681924 0.00389194 0.00194597 0.999998i \(-0.499381\pi\)
0.00194597 + 0.999998i \(0.499381\pi\)
\(308\) 0 0
\(309\) 2.08912 0.118846
\(310\) 0 0
\(311\) −33.9157 −1.92318 −0.961592 0.274483i \(-0.911493\pi\)
−0.961592 + 0.274483i \(0.911493\pi\)
\(312\) 0 0
\(313\) 3.72134 0.210343 0.105171 0.994454i \(-0.466461\pi\)
0.105171 + 0.994454i \(0.466461\pi\)
\(314\) 0 0
\(315\) −5.31768 −0.299617
\(316\) 0 0
\(317\) 1.50585 0.0845769 0.0422885 0.999105i \(-0.486535\pi\)
0.0422885 + 0.999105i \(0.486535\pi\)
\(318\) 0 0
\(319\) −6.25503 −0.350214
\(320\) 0 0
\(321\) 26.9142 1.50221
\(322\) 0 0
\(323\) 2.02016 0.112404
\(324\) 0 0
\(325\) −2.47890 −0.137505
\(326\) 0 0
\(327\) −10.4405 −0.577360
\(328\) 0 0
\(329\) 10.6684 0.588165
\(330\) 0 0
\(331\) 2.61045 0.143483 0.0717417 0.997423i \(-0.477144\pi\)
0.0717417 + 0.997423i \(0.477144\pi\)
\(332\) 0 0
\(333\) 19.0130 1.04191
\(334\) 0 0
\(335\) −9.06165 −0.495091
\(336\) 0 0
\(337\) −27.0266 −1.47223 −0.736117 0.676855i \(-0.763342\pi\)
−0.736117 + 0.676855i \(0.763342\pi\)
\(338\) 0 0
\(339\) −32.6151 −1.77141
\(340\) 0 0
\(341\) −22.8669 −1.23831
\(342\) 0 0
\(343\) −17.0500 −0.920613
\(344\) 0 0
\(345\) −20.8056 −1.12014
\(346\) 0 0
\(347\) −7.73203 −0.415077 −0.207539 0.978227i \(-0.566545\pi\)
−0.207539 + 0.978227i \(0.566545\pi\)
\(348\) 0 0
\(349\) 4.20935 0.225322 0.112661 0.993634i \(-0.464063\pi\)
0.112661 + 0.993634i \(0.464063\pi\)
\(350\) 0 0
\(351\) 4.72036 0.251954
\(352\) 0 0
\(353\) −16.7101 −0.889391 −0.444696 0.895682i \(-0.646688\pi\)
−0.444696 + 0.895682i \(0.646688\pi\)
\(354\) 0 0
\(355\) 9.23923 0.490367
\(356\) 0 0
\(357\) −14.8162 −0.784157
\(358\) 0 0
\(359\) −35.9142 −1.89548 −0.947740 0.319042i \(-0.896639\pi\)
−0.947740 + 0.319042i \(0.896639\pi\)
\(360\) 0 0
\(361\) −18.7461 −0.986636
\(362\) 0 0
\(363\) −5.79882 −0.304359
\(364\) 0 0
\(365\) 7.53548 0.394425
\(366\) 0 0
\(367\) −18.6666 −0.974388 −0.487194 0.873294i \(-0.661980\pi\)
−0.487194 + 0.873294i \(0.661980\pi\)
\(368\) 0 0
\(369\) 5.14844 0.268017
\(370\) 0 0
\(371\) −11.0861 −0.575563
\(372\) 0 0
\(373\) 4.92470 0.254991 0.127496 0.991839i \(-0.459306\pi\)
0.127496 + 0.991839i \(0.459306\pi\)
\(374\) 0 0
\(375\) 2.59496 0.134003
\(376\) 0 0
\(377\) 4.26218 0.219514
\(378\) 0 0
\(379\) 25.0669 1.28760 0.643801 0.765193i \(-0.277356\pi\)
0.643801 + 0.765193i \(0.277356\pi\)
\(380\) 0 0
\(381\) −5.14959 −0.263822
\(382\) 0 0
\(383\) 3.05637 0.156173 0.0780867 0.996947i \(-0.475119\pi\)
0.0780867 + 0.996947i \(0.475119\pi\)
\(384\) 0 0
\(385\) −5.18115 −0.264056
\(386\) 0 0
\(387\) 27.0225 1.37363
\(388\) 0 0
\(389\) −2.17911 −0.110485 −0.0552426 0.998473i \(-0.517593\pi\)
−0.0552426 + 0.998473i \(0.517593\pi\)
\(390\) 0 0
\(391\) −32.1430 −1.62554
\(392\) 0 0
\(393\) 2.14868 0.108387
\(394\) 0 0
\(395\) 10.3976 0.523162
\(396\) 0 0
\(397\) 30.3900 1.52523 0.762616 0.646852i \(-0.223915\pi\)
0.762616 + 0.646852i \(0.223915\pi\)
\(398\) 0 0
\(399\) −1.86230 −0.0932314
\(400\) 0 0
\(401\) 1.00000 0.0499376
\(402\) 0 0
\(403\) 15.5815 0.776170
\(404\) 0 0
\(405\) 6.26008 0.311066
\(406\) 0 0
\(407\) 18.5248 0.918243
\(408\) 0 0
\(409\) 6.84265 0.338347 0.169174 0.985586i \(-0.445890\pi\)
0.169174 + 0.985586i \(0.445890\pi\)
\(410\) 0 0
\(411\) −31.7630 −1.56676
\(412\) 0 0
\(413\) −8.30838 −0.408828
\(414\) 0 0
\(415\) −6.25543 −0.307067
\(416\) 0 0
\(417\) −49.3254 −2.41547
\(418\) 0 0
\(419\) 27.9516 1.36553 0.682764 0.730639i \(-0.260778\pi\)
0.682764 + 0.730639i \(0.260778\pi\)
\(420\) 0 0
\(421\) 2.33475 0.113789 0.0568944 0.998380i \(-0.481880\pi\)
0.0568944 + 0.998380i \(0.481880\pi\)
\(422\) 0 0
\(423\) 27.9692 1.35991
\(424\) 0 0
\(425\) 4.00900 0.194465
\(426\) 0 0
\(427\) −13.4539 −0.651078
\(428\) 0 0
\(429\) 23.4016 1.12984
\(430\) 0 0
\(431\) −12.6286 −0.608298 −0.304149 0.952624i \(-0.598372\pi\)
−0.304149 + 0.952624i \(0.598372\pi\)
\(432\) 0 0
\(433\) −16.4901 −0.792465 −0.396233 0.918150i \(-0.629683\pi\)
−0.396233 + 0.918150i \(0.629683\pi\)
\(434\) 0 0
\(435\) −4.46173 −0.213924
\(436\) 0 0
\(437\) −4.04016 −0.193267
\(438\) 0 0
\(439\) −17.2439 −0.823006 −0.411503 0.911408i \(-0.634996\pi\)
−0.411503 + 0.911408i \(0.634996\pi\)
\(440\) 0 0
\(441\) −18.5633 −0.883965
\(442\) 0 0
\(443\) 17.1801 0.816252 0.408126 0.912926i \(-0.366182\pi\)
0.408126 + 0.912926i \(0.366182\pi\)
\(444\) 0 0
\(445\) −2.74123 −0.129947
\(446\) 0 0
\(447\) 54.9744 2.60020
\(448\) 0 0
\(449\) −37.3687 −1.76354 −0.881769 0.471682i \(-0.843647\pi\)
−0.881769 + 0.471682i \(0.843647\pi\)
\(450\) 0 0
\(451\) 5.01625 0.236206
\(452\) 0 0
\(453\) −42.7530 −2.00871
\(454\) 0 0
\(455\) 3.53044 0.165510
\(456\) 0 0
\(457\) −24.3362 −1.13840 −0.569200 0.822199i \(-0.692747\pi\)
−0.569200 + 0.822199i \(0.692747\pi\)
\(458\) 0 0
\(459\) −7.63401 −0.356325
\(460\) 0 0
\(461\) 17.0938 0.796137 0.398069 0.917356i \(-0.369681\pi\)
0.398069 + 0.917356i \(0.369681\pi\)
\(462\) 0 0
\(463\) −12.5515 −0.583316 −0.291658 0.956523i \(-0.594207\pi\)
−0.291658 + 0.956523i \(0.594207\pi\)
\(464\) 0 0
\(465\) −16.3110 −0.756405
\(466\) 0 0
\(467\) 32.5500 1.50624 0.753118 0.657886i \(-0.228549\pi\)
0.753118 + 0.657886i \(0.228549\pi\)
\(468\) 0 0
\(469\) 12.9056 0.595923
\(470\) 0 0
\(471\) 16.9682 0.781855
\(472\) 0 0
\(473\) 26.3286 1.21059
\(474\) 0 0
\(475\) 0.503905 0.0231207
\(476\) 0 0
\(477\) −29.0645 −1.33077
\(478\) 0 0
\(479\) 10.7692 0.492059 0.246030 0.969262i \(-0.420874\pi\)
0.246030 + 0.969262i \(0.420874\pi\)
\(480\) 0 0
\(481\) −12.6229 −0.575553
\(482\) 0 0
\(483\) 29.6313 1.34827
\(484\) 0 0
\(485\) −9.29500 −0.422064
\(486\) 0 0
\(487\) −19.3407 −0.876411 −0.438206 0.898875i \(-0.644386\pi\)
−0.438206 + 0.898875i \(0.644386\pi\)
\(488\) 0 0
\(489\) 13.5435 0.612456
\(490\) 0 0
\(491\) 26.9486 1.21617 0.608086 0.793871i \(-0.291938\pi\)
0.608086 + 0.793871i \(0.291938\pi\)
\(492\) 0 0
\(493\) −6.89302 −0.310446
\(494\) 0 0
\(495\) −13.5834 −0.610529
\(496\) 0 0
\(497\) −13.1585 −0.590238
\(498\) 0 0
\(499\) 6.53278 0.292447 0.146224 0.989252i \(-0.453288\pi\)
0.146224 + 0.989252i \(0.453288\pi\)
\(500\) 0 0
\(501\) −55.8202 −2.49386
\(502\) 0 0
\(503\) 13.6923 0.610508 0.305254 0.952271i \(-0.401259\pi\)
0.305254 + 0.952271i \(0.401259\pi\)
\(504\) 0 0
\(505\) −6.15352 −0.273828
\(506\) 0 0
\(507\) 17.7886 0.790019
\(508\) 0 0
\(509\) 6.57046 0.291230 0.145615 0.989341i \(-0.453484\pi\)
0.145615 + 0.989341i \(0.453484\pi\)
\(510\) 0 0
\(511\) −10.7320 −0.474756
\(512\) 0 0
\(513\) −0.959543 −0.0423649
\(514\) 0 0
\(515\) 0.805067 0.0354755
\(516\) 0 0
\(517\) 27.2511 1.19850
\(518\) 0 0
\(519\) −39.8508 −1.74926
\(520\) 0 0
\(521\) 12.0777 0.529135 0.264568 0.964367i \(-0.414771\pi\)
0.264568 + 0.964367i \(0.414771\pi\)
\(522\) 0 0
\(523\) 20.9073 0.914212 0.457106 0.889412i \(-0.348886\pi\)
0.457106 + 0.889412i \(0.348886\pi\)
\(524\) 0 0
\(525\) −3.69573 −0.161295
\(526\) 0 0
\(527\) −25.1992 −1.09769
\(528\) 0 0
\(529\) 41.2836 1.79494
\(530\) 0 0
\(531\) −21.7821 −0.945261
\(532\) 0 0
\(533\) −3.41808 −0.148053
\(534\) 0 0
\(535\) 10.3717 0.448409
\(536\) 0 0
\(537\) 2.29262 0.0989338
\(538\) 0 0
\(539\) −18.0866 −0.779047
\(540\) 0 0
\(541\) −20.2377 −0.870088 −0.435044 0.900409i \(-0.643267\pi\)
−0.435044 + 0.900409i \(0.643267\pi\)
\(542\) 0 0
\(543\) −1.77283 −0.0760794
\(544\) 0 0
\(545\) −4.02337 −0.172342
\(546\) 0 0
\(547\) 5.53845 0.236807 0.118404 0.992966i \(-0.462222\pi\)
0.118404 + 0.992966i \(0.462222\pi\)
\(548\) 0 0
\(549\) −35.2720 −1.50537
\(550\) 0 0
\(551\) −0.866406 −0.0369101
\(552\) 0 0
\(553\) −14.8083 −0.629711
\(554\) 0 0
\(555\) 13.2138 0.560896
\(556\) 0 0
\(557\) −11.7355 −0.497247 −0.248624 0.968600i \(-0.579978\pi\)
−0.248624 + 0.968600i \(0.579978\pi\)
\(558\) 0 0
\(559\) −17.9404 −0.758797
\(560\) 0 0
\(561\) −37.8463 −1.59787
\(562\) 0 0
\(563\) 24.3519 1.02631 0.513155 0.858296i \(-0.328477\pi\)
0.513155 + 0.858296i \(0.328477\pi\)
\(564\) 0 0
\(565\) −12.5686 −0.528766
\(566\) 0 0
\(567\) −8.91558 −0.374419
\(568\) 0 0
\(569\) −37.7052 −1.58069 −0.790343 0.612665i \(-0.790098\pi\)
−0.790343 + 0.612665i \(0.790098\pi\)
\(570\) 0 0
\(571\) 20.7929 0.870157 0.435078 0.900393i \(-0.356721\pi\)
0.435078 + 0.900393i \(0.356721\pi\)
\(572\) 0 0
\(573\) −42.2834 −1.76641
\(574\) 0 0
\(575\) −8.01771 −0.334362
\(576\) 0 0
\(577\) −35.9303 −1.49580 −0.747898 0.663813i \(-0.768937\pi\)
−0.747898 + 0.663813i \(0.768937\pi\)
\(578\) 0 0
\(579\) −44.4693 −1.84808
\(580\) 0 0
\(581\) 8.90895 0.369606
\(582\) 0 0
\(583\) −28.3183 −1.17282
\(584\) 0 0
\(585\) 9.25575 0.382678
\(586\) 0 0
\(587\) −45.9010 −1.89454 −0.947268 0.320443i \(-0.896168\pi\)
−0.947268 + 0.320443i \(0.896168\pi\)
\(588\) 0 0
\(589\) −3.16737 −0.130509
\(590\) 0 0
\(591\) −0.463474 −0.0190648
\(592\) 0 0
\(593\) −26.0219 −1.06859 −0.534295 0.845298i \(-0.679423\pi\)
−0.534295 + 0.845298i \(0.679423\pi\)
\(594\) 0 0
\(595\) −5.70961 −0.234071
\(596\) 0 0
\(597\) −18.3559 −0.751256
\(598\) 0 0
\(599\) −29.5387 −1.20692 −0.603460 0.797393i \(-0.706212\pi\)
−0.603460 + 0.797393i \(0.706212\pi\)
\(600\) 0 0
\(601\) 3.37231 0.137559 0.0687797 0.997632i \(-0.478089\pi\)
0.0687797 + 0.997632i \(0.478089\pi\)
\(602\) 0 0
\(603\) 33.8345 1.37785
\(604\) 0 0
\(605\) −2.23465 −0.0908513
\(606\) 0 0
\(607\) 13.9276 0.565302 0.282651 0.959223i \(-0.408786\pi\)
0.282651 + 0.959223i \(0.408786\pi\)
\(608\) 0 0
\(609\) 6.35438 0.257493
\(610\) 0 0
\(611\) −18.5689 −0.751218
\(612\) 0 0
\(613\) −28.3379 −1.14456 −0.572279 0.820059i \(-0.693941\pi\)
−0.572279 + 0.820059i \(0.693941\pi\)
\(614\) 0 0
\(615\) 3.57811 0.144283
\(616\) 0 0
\(617\) 8.43683 0.339654 0.169827 0.985474i \(-0.445679\pi\)
0.169827 + 0.985474i \(0.445679\pi\)
\(618\) 0 0
\(619\) 0.781251 0.0314011 0.0157006 0.999877i \(-0.495002\pi\)
0.0157006 + 0.999877i \(0.495002\pi\)
\(620\) 0 0
\(621\) 15.2674 0.612662
\(622\) 0 0
\(623\) 3.90405 0.156413
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −4.75702 −0.189977
\(628\) 0 0
\(629\) 20.4143 0.813972
\(630\) 0 0
\(631\) −3.47116 −0.138185 −0.0690923 0.997610i \(-0.522010\pi\)
−0.0690923 + 0.997610i \(0.522010\pi\)
\(632\) 0 0
\(633\) 18.6220 0.740156
\(634\) 0 0
\(635\) −1.98446 −0.0787509
\(636\) 0 0
\(637\) 12.3243 0.488305
\(638\) 0 0
\(639\) −34.4976 −1.36470
\(640\) 0 0
\(641\) −0.174923 −0.00690906 −0.00345453 0.999994i \(-0.501100\pi\)
−0.00345453 + 0.999994i \(0.501100\pi\)
\(642\) 0 0
\(643\) 23.1130 0.911489 0.455745 0.890111i \(-0.349373\pi\)
0.455745 + 0.890111i \(0.349373\pi\)
\(644\) 0 0
\(645\) 18.7803 0.739474
\(646\) 0 0
\(647\) 4.79588 0.188545 0.0942727 0.995546i \(-0.469947\pi\)
0.0942727 + 0.995546i \(0.469947\pi\)
\(648\) 0 0
\(649\) −21.2228 −0.833068
\(650\) 0 0
\(651\) 23.2301 0.910458
\(652\) 0 0
\(653\) −49.6716 −1.94380 −0.971900 0.235393i \(-0.924362\pi\)
−0.971900 + 0.235393i \(0.924362\pi\)
\(654\) 0 0
\(655\) 0.828022 0.0323535
\(656\) 0 0
\(657\) −28.1361 −1.09769
\(658\) 0 0
\(659\) −27.5862 −1.07461 −0.537303 0.843389i \(-0.680557\pi\)
−0.537303 + 0.843389i \(0.680557\pi\)
\(660\) 0 0
\(661\) −47.2481 −1.83774 −0.918869 0.394562i \(-0.870896\pi\)
−0.918869 + 0.394562i \(0.870896\pi\)
\(662\) 0 0
\(663\) 25.7885 1.00154
\(664\) 0 0
\(665\) −0.717659 −0.0278296
\(666\) 0 0
\(667\) 13.7855 0.533778
\(668\) 0 0
\(669\) 21.0673 0.814510
\(670\) 0 0
\(671\) −34.3664 −1.32670
\(672\) 0 0
\(673\) −16.9272 −0.652497 −0.326249 0.945284i \(-0.605785\pi\)
−0.326249 + 0.945284i \(0.605785\pi\)
\(674\) 0 0
\(675\) −1.90422 −0.0732933
\(676\) 0 0
\(677\) −33.8684 −1.30167 −0.650835 0.759219i \(-0.725581\pi\)
−0.650835 + 0.759219i \(0.725581\pi\)
\(678\) 0 0
\(679\) 13.2379 0.508024
\(680\) 0 0
\(681\) −22.9095 −0.877894
\(682\) 0 0
\(683\) 28.7464 1.09995 0.549975 0.835181i \(-0.314637\pi\)
0.549975 + 0.835181i \(0.314637\pi\)
\(684\) 0 0
\(685\) −12.2403 −0.467677
\(686\) 0 0
\(687\) 37.2248 1.42021
\(688\) 0 0
\(689\) 19.2961 0.735123
\(690\) 0 0
\(691\) 9.21658 0.350615 0.175308 0.984514i \(-0.443908\pi\)
0.175308 + 0.984514i \(0.443908\pi\)
\(692\) 0 0
\(693\) 19.3454 0.734872
\(694\) 0 0
\(695\) −19.0082 −0.721020
\(696\) 0 0
\(697\) 5.52789 0.209384
\(698\) 0 0
\(699\) 48.1961 1.82294
\(700\) 0 0
\(701\) −31.6359 −1.19487 −0.597435 0.801917i \(-0.703813\pi\)
−0.597435 + 0.801917i \(0.703813\pi\)
\(702\) 0 0
\(703\) 2.56594 0.0967763
\(704\) 0 0
\(705\) 19.4383 0.732088
\(706\) 0 0
\(707\) 8.76382 0.329597
\(708\) 0 0
\(709\) 35.0993 1.31818 0.659091 0.752063i \(-0.270941\pi\)
0.659091 + 0.752063i \(0.270941\pi\)
\(710\) 0 0
\(711\) −38.8228 −1.45597
\(712\) 0 0
\(713\) 50.3965 1.88736
\(714\) 0 0
\(715\) 9.01811 0.337258
\(716\) 0 0
\(717\) 73.6701 2.75126
\(718\) 0 0
\(719\) 16.6574 0.621215 0.310608 0.950538i \(-0.399467\pi\)
0.310608 + 0.950538i \(0.399467\pi\)
\(720\) 0 0
\(721\) −1.14657 −0.0427006
\(722\) 0 0
\(723\) 18.5843 0.691156
\(724\) 0 0
\(725\) −1.71938 −0.0638564
\(726\) 0 0
\(727\) −23.6433 −0.876881 −0.438441 0.898760i \(-0.644469\pi\)
−0.438441 + 0.898760i \(0.644469\pi\)
\(728\) 0 0
\(729\) −38.1981 −1.41474
\(730\) 0 0
\(731\) 29.0141 1.07312
\(732\) 0 0
\(733\) 21.0606 0.777890 0.388945 0.921261i \(-0.372840\pi\)
0.388945 + 0.921261i \(0.372840\pi\)
\(734\) 0 0
\(735\) −12.9013 −0.475871
\(736\) 0 0
\(737\) 32.9658 1.21431
\(738\) 0 0
\(739\) 34.1042 1.25454 0.627271 0.778801i \(-0.284172\pi\)
0.627271 + 0.778801i \(0.284172\pi\)
\(740\) 0 0
\(741\) 3.24144 0.119077
\(742\) 0 0
\(743\) −11.3882 −0.417794 −0.208897 0.977938i \(-0.566987\pi\)
−0.208897 + 0.977938i \(0.566987\pi\)
\(744\) 0 0
\(745\) 21.1851 0.776161
\(746\) 0 0
\(747\) 23.3566 0.854573
\(748\) 0 0
\(749\) −14.7714 −0.539735
\(750\) 0 0
\(751\) 38.6841 1.41160 0.705802 0.708409i \(-0.250587\pi\)
0.705802 + 0.708409i \(0.250587\pi\)
\(752\) 0 0
\(753\) −11.6214 −0.423507
\(754\) 0 0
\(755\) −16.4754 −0.599601
\(756\) 0 0
\(757\) −25.4459 −0.924848 −0.462424 0.886659i \(-0.653020\pi\)
−0.462424 + 0.886659i \(0.653020\pi\)
\(758\) 0 0
\(759\) 75.6897 2.74736
\(760\) 0 0
\(761\) −18.8715 −0.684093 −0.342046 0.939683i \(-0.611120\pi\)
−0.342046 + 0.939683i \(0.611120\pi\)
\(762\) 0 0
\(763\) 5.73007 0.207442
\(764\) 0 0
\(765\) −14.9689 −0.541201
\(766\) 0 0
\(767\) 14.4612 0.522165
\(768\) 0 0
\(769\) 3.80388 0.137171 0.0685857 0.997645i \(-0.478151\pi\)
0.0685857 + 0.997645i \(0.478151\pi\)
\(770\) 0 0
\(771\) 21.0038 0.756434
\(772\) 0 0
\(773\) −39.6538 −1.42625 −0.713123 0.701039i \(-0.752720\pi\)
−0.713123 + 0.701039i \(0.752720\pi\)
\(774\) 0 0
\(775\) −6.28565 −0.225787
\(776\) 0 0
\(777\) −18.8191 −0.675131
\(778\) 0 0
\(779\) 0.694818 0.0248944
\(780\) 0 0
\(781\) −33.6118 −1.20273
\(782\) 0 0
\(783\) 3.27408 0.117006
\(784\) 0 0
\(785\) 6.53892 0.233384
\(786\) 0 0
\(787\) 20.5552 0.732714 0.366357 0.930474i \(-0.380605\pi\)
0.366357 + 0.930474i \(0.380605\pi\)
\(788\) 0 0
\(789\) 48.2121 1.71640
\(790\) 0 0
\(791\) 17.9002 0.636457
\(792\) 0 0
\(793\) 23.4173 0.831572
\(794\) 0 0
\(795\) −20.1995 −0.716403
\(796\) 0 0
\(797\) −44.3768 −1.57191 −0.785953 0.618286i \(-0.787827\pi\)
−0.785953 + 0.618286i \(0.787827\pi\)
\(798\) 0 0
\(799\) 30.0306 1.06241
\(800\) 0 0
\(801\) 10.2353 0.361645
\(802\) 0 0
\(803\) −27.4137 −0.967407
\(804\) 0 0
\(805\) 11.4188 0.402459
\(806\) 0 0
\(807\) 14.2009 0.499895
\(808\) 0 0
\(809\) −15.9158 −0.559570 −0.279785 0.960063i \(-0.590263\pi\)
−0.279785 + 0.960063i \(0.590263\pi\)
\(810\) 0 0
\(811\) −16.4178 −0.576507 −0.288254 0.957554i \(-0.593075\pi\)
−0.288254 + 0.957554i \(0.593075\pi\)
\(812\) 0 0
\(813\) −28.9883 −1.01666
\(814\) 0 0
\(815\) 5.21914 0.182818
\(816\) 0 0
\(817\) 3.64687 0.127588
\(818\) 0 0
\(819\) −13.1820 −0.460617
\(820\) 0 0
\(821\) 5.85873 0.204471 0.102236 0.994760i \(-0.467400\pi\)
0.102236 + 0.994760i \(0.467400\pi\)
\(822\) 0 0
\(823\) −23.3572 −0.814182 −0.407091 0.913388i \(-0.633457\pi\)
−0.407091 + 0.913388i \(0.633457\pi\)
\(824\) 0 0
\(825\) −9.44032 −0.328670
\(826\) 0 0
\(827\) 45.9011 1.59614 0.798069 0.602566i \(-0.205855\pi\)
0.798069 + 0.602566i \(0.205855\pi\)
\(828\) 0 0
\(829\) 10.4465 0.362822 0.181411 0.983407i \(-0.441934\pi\)
0.181411 + 0.983407i \(0.441934\pi\)
\(830\) 0 0
\(831\) 61.1014 2.11958
\(832\) 0 0
\(833\) −19.9314 −0.690583
\(834\) 0 0
\(835\) −21.5110 −0.744420
\(836\) 0 0
\(837\) 11.9692 0.413717
\(838\) 0 0
\(839\) −21.0564 −0.726947 −0.363473 0.931605i \(-0.618409\pi\)
−0.363473 + 0.931605i \(0.618409\pi\)
\(840\) 0 0
\(841\) −26.0437 −0.898059
\(842\) 0 0
\(843\) 15.2588 0.525539
\(844\) 0 0
\(845\) 6.85505 0.235821
\(846\) 0 0
\(847\) 3.18258 0.109355
\(848\) 0 0
\(849\) 45.2224 1.55203
\(850\) 0 0
\(851\) −40.8271 −1.39954
\(852\) 0 0
\(853\) −2.24512 −0.0768713 −0.0384356 0.999261i \(-0.512237\pi\)
−0.0384356 + 0.999261i \(0.512237\pi\)
\(854\) 0 0
\(855\) −1.88149 −0.0643454
\(856\) 0 0
\(857\) −25.8802 −0.884052 −0.442026 0.897002i \(-0.645740\pi\)
−0.442026 + 0.897002i \(0.645740\pi\)
\(858\) 0 0
\(859\) −46.6926 −1.59313 −0.796565 0.604553i \(-0.793352\pi\)
−0.796565 + 0.604553i \(0.793352\pi\)
\(860\) 0 0
\(861\) −5.09593 −0.173669
\(862\) 0 0
\(863\) 23.2973 0.793050 0.396525 0.918024i \(-0.370216\pi\)
0.396525 + 0.918024i \(0.370216\pi\)
\(864\) 0 0
\(865\) −15.3570 −0.522154
\(866\) 0 0
\(867\) 2.40781 0.0817735
\(868\) 0 0
\(869\) −37.8260 −1.28316
\(870\) 0 0
\(871\) −22.4629 −0.761127
\(872\) 0 0
\(873\) 34.7058 1.17461
\(874\) 0 0
\(875\) −1.42420 −0.0481466
\(876\) 0 0
\(877\) 43.6745 1.47478 0.737391 0.675466i \(-0.236058\pi\)
0.737391 + 0.675466i \(0.236058\pi\)
\(878\) 0 0
\(879\) 66.2929 2.23600
\(880\) 0 0
\(881\) −54.8569 −1.84818 −0.924088 0.382179i \(-0.875174\pi\)
−0.924088 + 0.382179i \(0.875174\pi\)
\(882\) 0 0
\(883\) 33.9440 1.14231 0.571154 0.820843i \(-0.306496\pi\)
0.571154 + 0.820843i \(0.306496\pi\)
\(884\) 0 0
\(885\) −15.1383 −0.508868
\(886\) 0 0
\(887\) −16.9930 −0.570568 −0.285284 0.958443i \(-0.592088\pi\)
−0.285284 + 0.958443i \(0.592088\pi\)
\(888\) 0 0
\(889\) 2.82626 0.0947897
\(890\) 0 0
\(891\) −22.7738 −0.762952
\(892\) 0 0
\(893\) 3.77464 0.126314
\(894\) 0 0
\(895\) 0.883490 0.0295318
\(896\) 0 0
\(897\) −51.5751 −1.72204
\(898\) 0 0
\(899\) 10.8075 0.360449
\(900\) 0 0
\(901\) −31.2066 −1.03964
\(902\) 0 0
\(903\) −26.7469 −0.890080
\(904\) 0 0
\(905\) −0.683182 −0.0227097
\(906\) 0 0
\(907\) 18.8580 0.626169 0.313085 0.949725i \(-0.398638\pi\)
0.313085 + 0.949725i \(0.398638\pi\)
\(908\) 0 0
\(909\) 22.9761 0.762069
\(910\) 0 0
\(911\) 39.7194 1.31596 0.657982 0.753034i \(-0.271410\pi\)
0.657982 + 0.753034i \(0.271410\pi\)
\(912\) 0 0
\(913\) 22.7569 0.753143
\(914\) 0 0
\(915\) −24.5136 −0.810396
\(916\) 0 0
\(917\) −1.17927 −0.0389428
\(918\) 0 0
\(919\) −40.4926 −1.33573 −0.667864 0.744283i \(-0.732791\pi\)
−0.667864 + 0.744283i \(0.732791\pi\)
\(920\) 0 0
\(921\) −0.176956 −0.00583091
\(922\) 0 0
\(923\) 22.9031 0.753866
\(924\) 0 0
\(925\) 5.09212 0.167428
\(926\) 0 0
\(927\) −3.00597 −0.0987290
\(928\) 0 0
\(929\) −30.5170 −1.00123 −0.500616 0.865670i \(-0.666893\pi\)
−0.500616 + 0.865670i \(0.666893\pi\)
\(930\) 0 0
\(931\) −2.50524 −0.0821061
\(932\) 0 0
\(933\) 88.0099 2.88131
\(934\) 0 0
\(935\) −14.5845 −0.476966
\(936\) 0 0
\(937\) 0.327421 0.0106964 0.00534819 0.999986i \(-0.498298\pi\)
0.00534819 + 0.999986i \(0.498298\pi\)
\(938\) 0 0
\(939\) −9.65672 −0.315135
\(940\) 0 0
\(941\) −14.4811 −0.472069 −0.236035 0.971745i \(-0.575848\pi\)
−0.236035 + 0.971745i \(0.575848\pi\)
\(942\) 0 0
\(943\) −11.0554 −0.360012
\(944\) 0 0
\(945\) 2.71198 0.0882206
\(946\) 0 0
\(947\) 4.50133 0.146273 0.0731367 0.997322i \(-0.476699\pi\)
0.0731367 + 0.997322i \(0.476699\pi\)
\(948\) 0 0
\(949\) 18.6797 0.606369
\(950\) 0 0
\(951\) −3.90762 −0.126713
\(952\) 0 0
\(953\) −23.7032 −0.767822 −0.383911 0.923370i \(-0.625423\pi\)
−0.383911 + 0.923370i \(0.625423\pi\)
\(954\) 0 0
\(955\) −16.2944 −0.527276
\(956\) 0 0
\(957\) 16.2315 0.524691
\(958\) 0 0
\(959\) 17.4326 0.562927
\(960\) 0 0
\(961\) 8.50942 0.274497
\(962\) 0 0
\(963\) −38.7261 −1.24793
\(964\) 0 0
\(965\) −17.1368 −0.551653
\(966\) 0 0
\(967\) 36.7675 1.18236 0.591181 0.806539i \(-0.298662\pi\)
0.591181 + 0.806539i \(0.298662\pi\)
\(968\) 0 0
\(969\) −5.24222 −0.168404
\(970\) 0 0
\(971\) −28.8370 −0.925422 −0.462711 0.886509i \(-0.653123\pi\)
−0.462711 + 0.886509i \(0.653123\pi\)
\(972\) 0 0
\(973\) 27.0713 0.867867
\(974\) 0 0
\(975\) 6.43265 0.206010
\(976\) 0 0
\(977\) 26.2326 0.839256 0.419628 0.907696i \(-0.362160\pi\)
0.419628 + 0.907696i \(0.362160\pi\)
\(978\) 0 0
\(979\) 9.97245 0.318721
\(980\) 0 0
\(981\) 15.0225 0.479632
\(982\) 0 0
\(983\) −47.6140 −1.51865 −0.759325 0.650711i \(-0.774471\pi\)
−0.759325 + 0.650711i \(0.774471\pi\)
\(984\) 0 0
\(985\) −0.178606 −0.00569085
\(986\) 0 0
\(987\) −27.6839 −0.881189
\(988\) 0 0
\(989\) −58.0260 −1.84512
\(990\) 0 0
\(991\) 25.5023 0.810108 0.405054 0.914293i \(-0.367253\pi\)
0.405054 + 0.914293i \(0.367253\pi\)
\(992\) 0 0
\(993\) −6.77401 −0.214967
\(994\) 0 0
\(995\) −7.07367 −0.224250
\(996\) 0 0
\(997\) −20.3487 −0.644449 −0.322225 0.946663i \(-0.604431\pi\)
−0.322225 + 0.946663i \(0.604431\pi\)
\(998\) 0 0
\(999\) −9.69649 −0.306783
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 \(a_p\))