Properties

Label 8008.2.a.v.1.11
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 11
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(1\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{4} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Root \(-2.90994\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.90994 q^{3} -1.16917 q^{5} -1.00000 q^{7} +5.46776 q^{9} +O(q^{10})\) \(q+2.90994 q^{3} -1.16917 q^{5} -1.00000 q^{7} +5.46776 q^{9} +1.00000 q^{11} -1.00000 q^{13} -3.40221 q^{15} -5.91520 q^{17} -2.04963 q^{19} -2.90994 q^{21} +5.20762 q^{23} -3.63305 q^{25} +7.18104 q^{27} -4.12176 q^{29} +0.961296 q^{31} +2.90994 q^{33} +1.16917 q^{35} -7.61804 q^{37} -2.90994 q^{39} -7.64480 q^{41} -1.91716 q^{43} -6.39273 q^{45} +5.20762 q^{47} +1.00000 q^{49} -17.2129 q^{51} -3.94714 q^{53} -1.16917 q^{55} -5.96430 q^{57} +1.97452 q^{59} -7.98894 q^{61} -5.46776 q^{63} +1.16917 q^{65} -4.62609 q^{67} +15.1539 q^{69} +11.1079 q^{71} +3.77526 q^{73} -10.5720 q^{75} -1.00000 q^{77} +6.29845 q^{79} +4.49313 q^{81} -17.2308 q^{83} +6.91586 q^{85} -11.9941 q^{87} +1.13850 q^{89} +1.00000 q^{91} +2.79732 q^{93} +2.39636 q^{95} -13.5854 q^{97} +5.46776 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 2q^{3} + 2q^{5} - 11q^{7} + 9q^{9} + O(q^{10}) \) \( 11q - 2q^{3} + 2q^{5} - 11q^{7} + 9q^{9} + 11q^{11} - 11q^{13} - 7q^{15} - 4q^{17} - 16q^{19} + 2q^{21} - 3q^{23} + 11q^{25} - 11q^{27} + q^{29} + 14q^{31} - 2q^{33} - 2q^{35} - 8q^{37} + 2q^{39} + 4q^{41} - 30q^{43} + 13q^{45} - 3q^{47} + 11q^{49} - 14q^{51} - 5q^{53} + 2q^{55} - 22q^{57} + 11q^{59} + 15q^{61} - 9q^{63} - 2q^{65} - 41q^{67} + 12q^{69} + q^{71} - 8q^{73} - 24q^{75} - 11q^{77} - 26q^{79} + 19q^{81} - 31q^{83} - 27q^{85} - 25q^{87} + 2q^{89} + 11q^{91} - 37q^{93} - 6q^{97} + 9q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.90994 1.68006 0.840028 0.542543i \(-0.182539\pi\)
0.840028 + 0.542543i \(0.182539\pi\)
\(4\) 0 0
\(5\) −1.16917 −0.522868 −0.261434 0.965221i \(-0.584195\pi\)
−0.261434 + 0.965221i \(0.584195\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 5.46776 1.82259
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −3.40221 −0.878447
\(16\) 0 0
\(17\) −5.91520 −1.43465 −0.717323 0.696741i \(-0.754633\pi\)
−0.717323 + 0.696741i \(0.754633\pi\)
\(18\) 0 0
\(19\) −2.04963 −0.470217 −0.235109 0.971969i \(-0.575545\pi\)
−0.235109 + 0.971969i \(0.575545\pi\)
\(20\) 0 0
\(21\) −2.90994 −0.635001
\(22\) 0 0
\(23\) 5.20762 1.08586 0.542932 0.839777i \(-0.317314\pi\)
0.542932 + 0.839777i \(0.317314\pi\)
\(24\) 0 0
\(25\) −3.63305 −0.726609
\(26\) 0 0
\(27\) 7.18104 1.38199
\(28\) 0 0
\(29\) −4.12176 −0.765392 −0.382696 0.923874i \(-0.625004\pi\)
−0.382696 + 0.923874i \(0.625004\pi\)
\(30\) 0 0
\(31\) 0.961296 0.172654 0.0863269 0.996267i \(-0.472487\pi\)
0.0863269 + 0.996267i \(0.472487\pi\)
\(32\) 0 0
\(33\) 2.90994 0.506556
\(34\) 0 0
\(35\) 1.16917 0.197625
\(36\) 0 0
\(37\) −7.61804 −1.25240 −0.626199 0.779663i \(-0.715390\pi\)
−0.626199 + 0.779663i \(0.715390\pi\)
\(38\) 0 0
\(39\) −2.90994 −0.465964
\(40\) 0 0
\(41\) −7.64480 −1.19392 −0.596958 0.802272i \(-0.703624\pi\)
−0.596958 + 0.802272i \(0.703624\pi\)
\(42\) 0 0
\(43\) −1.91716 −0.292363 −0.146182 0.989258i \(-0.546698\pi\)
−0.146182 + 0.989258i \(0.546698\pi\)
\(44\) 0 0
\(45\) −6.39273 −0.952972
\(46\) 0 0
\(47\) 5.20762 0.759609 0.379804 0.925067i \(-0.375991\pi\)
0.379804 + 0.925067i \(0.375991\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −17.2129 −2.41028
\(52\) 0 0
\(53\) −3.94714 −0.542182 −0.271091 0.962554i \(-0.587384\pi\)
−0.271091 + 0.962554i \(0.587384\pi\)
\(54\) 0 0
\(55\) −1.16917 −0.157651
\(56\) 0 0
\(57\) −5.96430 −0.789991
\(58\) 0 0
\(59\) 1.97452 0.257061 0.128531 0.991706i \(-0.458974\pi\)
0.128531 + 0.991706i \(0.458974\pi\)
\(60\) 0 0
\(61\) −7.98894 −1.02288 −0.511439 0.859319i \(-0.670887\pi\)
−0.511439 + 0.859319i \(0.670887\pi\)
\(62\) 0 0
\(63\) −5.46776 −0.688873
\(64\) 0 0
\(65\) 1.16917 0.145017
\(66\) 0 0
\(67\) −4.62609 −0.565167 −0.282583 0.959243i \(-0.591191\pi\)
−0.282583 + 0.959243i \(0.591191\pi\)
\(68\) 0 0
\(69\) 15.1539 1.82431
\(70\) 0 0
\(71\) 11.1079 1.31826 0.659130 0.752029i \(-0.270925\pi\)
0.659130 + 0.752029i \(0.270925\pi\)
\(72\) 0 0
\(73\) 3.77526 0.441861 0.220930 0.975290i \(-0.429091\pi\)
0.220930 + 0.975290i \(0.429091\pi\)
\(74\) 0 0
\(75\) −10.5720 −1.22074
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 6.29845 0.708631 0.354315 0.935126i \(-0.384714\pi\)
0.354315 + 0.935126i \(0.384714\pi\)
\(80\) 0 0
\(81\) 4.49313 0.499236
\(82\) 0 0
\(83\) −17.2308 −1.89133 −0.945666 0.325141i \(-0.894588\pi\)
−0.945666 + 0.325141i \(0.894588\pi\)
\(84\) 0 0
\(85\) 6.91586 0.750130
\(86\) 0 0
\(87\) −11.9941 −1.28590
\(88\) 0 0
\(89\) 1.13850 0.120681 0.0603403 0.998178i \(-0.480781\pi\)
0.0603403 + 0.998178i \(0.480781\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) 2.79732 0.290068
\(94\) 0 0
\(95\) 2.39636 0.245861
\(96\) 0 0
\(97\) −13.5854 −1.37939 −0.689696 0.724099i \(-0.742256\pi\)
−0.689696 + 0.724099i \(0.742256\pi\)
\(98\) 0 0
\(99\) 5.46776 0.549531
\(100\) 0 0
\(101\) 18.3121 1.82212 0.911062 0.412268i \(-0.135263\pi\)
0.911062 + 0.412268i \(0.135263\pi\)
\(102\) 0 0
\(103\) −5.45742 −0.537735 −0.268868 0.963177i \(-0.586649\pi\)
−0.268868 + 0.963177i \(0.586649\pi\)
\(104\) 0 0
\(105\) 3.40221 0.332022
\(106\) 0 0
\(107\) −4.38564 −0.423976 −0.211988 0.977272i \(-0.567994\pi\)
−0.211988 + 0.977272i \(0.567994\pi\)
\(108\) 0 0
\(109\) −16.1408 −1.54601 −0.773005 0.634400i \(-0.781247\pi\)
−0.773005 + 0.634400i \(0.781247\pi\)
\(110\) 0 0
\(111\) −22.1680 −2.10410
\(112\) 0 0
\(113\) −3.48934 −0.328249 −0.164125 0.986440i \(-0.552480\pi\)
−0.164125 + 0.986440i \(0.552480\pi\)
\(114\) 0 0
\(115\) −6.08858 −0.567763
\(116\) 0 0
\(117\) −5.46776 −0.505495
\(118\) 0 0
\(119\) 5.91520 0.542245
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −22.2459 −2.00585
\(124\) 0 0
\(125\) 10.0935 0.902788
\(126\) 0 0
\(127\) 18.4815 1.63996 0.819982 0.572389i \(-0.193983\pi\)
0.819982 + 0.572389i \(0.193983\pi\)
\(128\) 0 0
\(129\) −5.57881 −0.491187
\(130\) 0 0
\(131\) −13.7542 −1.20171 −0.600856 0.799357i \(-0.705173\pi\)
−0.600856 + 0.799357i \(0.705173\pi\)
\(132\) 0 0
\(133\) 2.04963 0.177725
\(134\) 0 0
\(135\) −8.39584 −0.722599
\(136\) 0 0
\(137\) −9.28537 −0.793302 −0.396651 0.917969i \(-0.629828\pi\)
−0.396651 + 0.917969i \(0.629828\pi\)
\(138\) 0 0
\(139\) 9.48179 0.804235 0.402118 0.915588i \(-0.368274\pi\)
0.402118 + 0.915588i \(0.368274\pi\)
\(140\) 0 0
\(141\) 15.1539 1.27619
\(142\) 0 0
\(143\) −1.00000 −0.0836242
\(144\) 0 0
\(145\) 4.81903 0.400199
\(146\) 0 0
\(147\) 2.90994 0.240008
\(148\) 0 0
\(149\) −18.5929 −1.52319 −0.761594 0.648054i \(-0.775583\pi\)
−0.761594 + 0.648054i \(0.775583\pi\)
\(150\) 0 0
\(151\) −0.264310 −0.0215092 −0.0107546 0.999942i \(-0.503423\pi\)
−0.0107546 + 0.999942i \(0.503423\pi\)
\(152\) 0 0
\(153\) −32.3429 −2.61477
\(154\) 0 0
\(155\) −1.12392 −0.0902752
\(156\) 0 0
\(157\) 2.64728 0.211276 0.105638 0.994405i \(-0.466312\pi\)
0.105638 + 0.994405i \(0.466312\pi\)
\(158\) 0 0
\(159\) −11.4860 −0.910896
\(160\) 0 0
\(161\) −5.20762 −0.410418
\(162\) 0 0
\(163\) −15.2628 −1.19547 −0.597737 0.801692i \(-0.703933\pi\)
−0.597737 + 0.801692i \(0.703933\pi\)
\(164\) 0 0
\(165\) −3.40221 −0.264862
\(166\) 0 0
\(167\) 11.3724 0.880023 0.440012 0.897992i \(-0.354974\pi\)
0.440012 + 0.897992i \(0.354974\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −11.2069 −0.857012
\(172\) 0 0
\(173\) −6.81083 −0.517818 −0.258909 0.965902i \(-0.583363\pi\)
−0.258909 + 0.965902i \(0.583363\pi\)
\(174\) 0 0
\(175\) 3.63305 0.274632
\(176\) 0 0
\(177\) 5.74575 0.431877
\(178\) 0 0
\(179\) 5.92885 0.443143 0.221571 0.975144i \(-0.428881\pi\)
0.221571 + 0.975144i \(0.428881\pi\)
\(180\) 0 0
\(181\) 9.93972 0.738813 0.369407 0.929268i \(-0.379561\pi\)
0.369407 + 0.929268i \(0.379561\pi\)
\(182\) 0 0
\(183\) −23.2473 −1.71849
\(184\) 0 0
\(185\) 8.90677 0.654839
\(186\) 0 0
\(187\) −5.91520 −0.432562
\(188\) 0 0
\(189\) −7.18104 −0.522344
\(190\) 0 0
\(191\) 4.74438 0.343291 0.171646 0.985159i \(-0.445092\pi\)
0.171646 + 0.985159i \(0.445092\pi\)
\(192\) 0 0
\(193\) −18.7613 −1.35047 −0.675236 0.737602i \(-0.735958\pi\)
−0.675236 + 0.737602i \(0.735958\pi\)
\(194\) 0 0
\(195\) 3.40221 0.243637
\(196\) 0 0
\(197\) −23.8790 −1.70131 −0.850655 0.525725i \(-0.823794\pi\)
−0.850655 + 0.525725i \(0.823794\pi\)
\(198\) 0 0
\(199\) −2.28067 −0.161672 −0.0808362 0.996727i \(-0.525759\pi\)
−0.0808362 + 0.996727i \(0.525759\pi\)
\(200\) 0 0
\(201\) −13.4617 −0.949512
\(202\) 0 0
\(203\) 4.12176 0.289291
\(204\) 0 0
\(205\) 8.93805 0.624261
\(206\) 0 0
\(207\) 28.4740 1.97908
\(208\) 0 0
\(209\) −2.04963 −0.141776
\(210\) 0 0
\(211\) 3.20483 0.220630 0.110315 0.993897i \(-0.464814\pi\)
0.110315 + 0.993897i \(0.464814\pi\)
\(212\) 0 0
\(213\) 32.3232 2.21475
\(214\) 0 0
\(215\) 2.24148 0.152867
\(216\) 0 0
\(217\) −0.961296 −0.0652570
\(218\) 0 0
\(219\) 10.9858 0.742351
\(220\) 0 0
\(221\) 5.91520 0.397899
\(222\) 0 0
\(223\) 15.8970 1.06454 0.532271 0.846574i \(-0.321339\pi\)
0.532271 + 0.846574i \(0.321339\pi\)
\(224\) 0 0
\(225\) −19.8646 −1.32431
\(226\) 0 0
\(227\) 24.4701 1.62414 0.812068 0.583563i \(-0.198342\pi\)
0.812068 + 0.583563i \(0.198342\pi\)
\(228\) 0 0
\(229\) 28.3405 1.87279 0.936396 0.350944i \(-0.114139\pi\)
0.936396 + 0.350944i \(0.114139\pi\)
\(230\) 0 0
\(231\) −2.90994 −0.191460
\(232\) 0 0
\(233\) 0.824406 0.0540086 0.0270043 0.999635i \(-0.491403\pi\)
0.0270043 + 0.999635i \(0.491403\pi\)
\(234\) 0 0
\(235\) −6.08858 −0.397175
\(236\) 0 0
\(237\) 18.3281 1.19054
\(238\) 0 0
\(239\) 4.51005 0.291731 0.145865 0.989304i \(-0.453403\pi\)
0.145865 + 0.989304i \(0.453403\pi\)
\(240\) 0 0
\(241\) 10.9230 0.703614 0.351807 0.936073i \(-0.385567\pi\)
0.351807 + 0.936073i \(0.385567\pi\)
\(242\) 0 0
\(243\) −8.46839 −0.543247
\(244\) 0 0
\(245\) −1.16917 −0.0746954
\(246\) 0 0
\(247\) 2.04963 0.130415
\(248\) 0 0
\(249\) −50.1408 −3.17754
\(250\) 0 0
\(251\) 20.3185 1.28249 0.641246 0.767336i \(-0.278418\pi\)
0.641246 + 0.767336i \(0.278418\pi\)
\(252\) 0 0
\(253\) 5.20762 0.327400
\(254\) 0 0
\(255\) 20.1247 1.26026
\(256\) 0 0
\(257\) 10.7720 0.671941 0.335971 0.941872i \(-0.390936\pi\)
0.335971 + 0.941872i \(0.390936\pi\)
\(258\) 0 0
\(259\) 7.61804 0.473362
\(260\) 0 0
\(261\) −22.5368 −1.39499
\(262\) 0 0
\(263\) −15.6846 −0.967152 −0.483576 0.875302i \(-0.660662\pi\)
−0.483576 + 0.875302i \(0.660662\pi\)
\(264\) 0 0
\(265\) 4.61488 0.283490
\(266\) 0 0
\(267\) 3.31296 0.202750
\(268\) 0 0
\(269\) −21.6449 −1.31971 −0.659857 0.751391i \(-0.729383\pi\)
−0.659857 + 0.751391i \(0.729383\pi\)
\(270\) 0 0
\(271\) −19.0786 −1.15894 −0.579470 0.814994i \(-0.696740\pi\)
−0.579470 + 0.814994i \(0.696740\pi\)
\(272\) 0 0
\(273\) 2.90994 0.176118
\(274\) 0 0
\(275\) −3.63305 −0.219081
\(276\) 0 0
\(277\) 17.0330 1.02342 0.511708 0.859159i \(-0.329013\pi\)
0.511708 + 0.859159i \(0.329013\pi\)
\(278\) 0 0
\(279\) 5.25614 0.314677
\(280\) 0 0
\(281\) −15.6379 −0.932879 −0.466439 0.884553i \(-0.654463\pi\)
−0.466439 + 0.884553i \(0.654463\pi\)
\(282\) 0 0
\(283\) −29.4271 −1.74926 −0.874630 0.484790i \(-0.838896\pi\)
−0.874630 + 0.484790i \(0.838896\pi\)
\(284\) 0 0
\(285\) 6.97327 0.413061
\(286\) 0 0
\(287\) 7.64480 0.451258
\(288\) 0 0
\(289\) 17.9896 1.05821
\(290\) 0 0
\(291\) −39.5328 −2.31745
\(292\) 0 0
\(293\) −17.0330 −0.995078 −0.497539 0.867442i \(-0.665763\pi\)
−0.497539 + 0.867442i \(0.665763\pi\)
\(294\) 0 0
\(295\) −2.30855 −0.134409
\(296\) 0 0
\(297\) 7.18104 0.416686
\(298\) 0 0
\(299\) −5.20762 −0.301164
\(300\) 0 0
\(301\) 1.91716 0.110503
\(302\) 0 0
\(303\) 53.2872 3.06127
\(304\) 0 0
\(305\) 9.34041 0.534830
\(306\) 0 0
\(307\) 23.8369 1.36044 0.680221 0.733007i \(-0.261884\pi\)
0.680221 + 0.733007i \(0.261884\pi\)
\(308\) 0 0
\(309\) −15.8808 −0.903425
\(310\) 0 0
\(311\) 23.2215 1.31677 0.658385 0.752681i \(-0.271240\pi\)
0.658385 + 0.752681i \(0.271240\pi\)
\(312\) 0 0
\(313\) 12.4544 0.703965 0.351982 0.936007i \(-0.385508\pi\)
0.351982 + 0.936007i \(0.385508\pi\)
\(314\) 0 0
\(315\) 6.39273 0.360190
\(316\) 0 0
\(317\) −12.0519 −0.676902 −0.338451 0.940984i \(-0.609903\pi\)
−0.338451 + 0.940984i \(0.609903\pi\)
\(318\) 0 0
\(319\) −4.12176 −0.230774
\(320\) 0 0
\(321\) −12.7619 −0.712303
\(322\) 0 0
\(323\) 12.1240 0.674595
\(324\) 0 0
\(325\) 3.63305 0.201525
\(326\) 0 0
\(327\) −46.9689 −2.59738
\(328\) 0 0
\(329\) −5.20762 −0.287105
\(330\) 0 0
\(331\) −4.32592 −0.237774 −0.118887 0.992908i \(-0.537933\pi\)
−0.118887 + 0.992908i \(0.537933\pi\)
\(332\) 0 0
\(333\) −41.6536 −2.28260
\(334\) 0 0
\(335\) 5.40868 0.295508
\(336\) 0 0
\(337\) −21.2166 −1.15574 −0.577871 0.816128i \(-0.696116\pi\)
−0.577871 + 0.816128i \(0.696116\pi\)
\(338\) 0 0
\(339\) −10.1538 −0.551477
\(340\) 0 0
\(341\) 0.961296 0.0520571
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −17.7174 −0.953873
\(346\) 0 0
\(347\) 31.2424 1.67718 0.838589 0.544764i \(-0.183381\pi\)
0.838589 + 0.544764i \(0.183381\pi\)
\(348\) 0 0
\(349\) 31.6059 1.69182 0.845911 0.533324i \(-0.179057\pi\)
0.845911 + 0.533324i \(0.179057\pi\)
\(350\) 0 0
\(351\) −7.18104 −0.383296
\(352\) 0 0
\(353\) −15.1385 −0.805742 −0.402871 0.915257i \(-0.631988\pi\)
−0.402871 + 0.915257i \(0.631988\pi\)
\(354\) 0 0
\(355\) −12.9870 −0.689276
\(356\) 0 0
\(357\) 17.2129 0.911002
\(358\) 0 0
\(359\) −24.8290 −1.31042 −0.655212 0.755445i \(-0.727421\pi\)
−0.655212 + 0.755445i \(0.727421\pi\)
\(360\) 0 0
\(361\) −14.7990 −0.778896
\(362\) 0 0
\(363\) 2.90994 0.152732
\(364\) 0 0
\(365\) −4.41391 −0.231035
\(366\) 0 0
\(367\) 13.5980 0.709810 0.354905 0.934902i \(-0.384513\pi\)
0.354905 + 0.934902i \(0.384513\pi\)
\(368\) 0 0
\(369\) −41.7999 −2.17602
\(370\) 0 0
\(371\) 3.94714 0.204926
\(372\) 0 0
\(373\) −15.2937 −0.791879 −0.395940 0.918277i \(-0.629581\pi\)
−0.395940 + 0.918277i \(0.629581\pi\)
\(374\) 0 0
\(375\) 29.3714 1.51673
\(376\) 0 0
\(377\) 4.12176 0.212282
\(378\) 0 0
\(379\) −23.6586 −1.21526 −0.607631 0.794219i \(-0.707880\pi\)
−0.607631 + 0.794219i \(0.707880\pi\)
\(380\) 0 0
\(381\) 53.7800 2.75523
\(382\) 0 0
\(383\) −12.0507 −0.615763 −0.307882 0.951425i \(-0.599620\pi\)
−0.307882 + 0.951425i \(0.599620\pi\)
\(384\) 0 0
\(385\) 1.16917 0.0595863
\(386\) 0 0
\(387\) −10.4825 −0.532858
\(388\) 0 0
\(389\) −3.95795 −0.200676 −0.100338 0.994953i \(-0.531992\pi\)
−0.100338 + 0.994953i \(0.531992\pi\)
\(390\) 0 0
\(391\) −30.8041 −1.55783
\(392\) 0 0
\(393\) −40.0240 −2.01894
\(394\) 0 0
\(395\) −7.36394 −0.370520
\(396\) 0 0
\(397\) −17.8178 −0.894250 −0.447125 0.894471i \(-0.647552\pi\)
−0.447125 + 0.894471i \(0.647552\pi\)
\(398\) 0 0
\(399\) 5.96430 0.298589
\(400\) 0 0
\(401\) −24.5860 −1.22777 −0.613883 0.789397i \(-0.710393\pi\)
−0.613883 + 0.789397i \(0.710393\pi\)
\(402\) 0 0
\(403\) −0.961296 −0.0478856
\(404\) 0 0
\(405\) −5.25322 −0.261035
\(406\) 0 0
\(407\) −7.61804 −0.377612
\(408\) 0 0
\(409\) 13.3972 0.662451 0.331225 0.943552i \(-0.392538\pi\)
0.331225 + 0.943552i \(0.392538\pi\)
\(410\) 0 0
\(411\) −27.0199 −1.33279
\(412\) 0 0
\(413\) −1.97452 −0.0971600
\(414\) 0 0
\(415\) 20.1458 0.988916
\(416\) 0 0
\(417\) 27.5915 1.35116
\(418\) 0 0
\(419\) 4.94153 0.241410 0.120705 0.992688i \(-0.461485\pi\)
0.120705 + 0.992688i \(0.461485\pi\)
\(420\) 0 0
\(421\) −21.5301 −1.04931 −0.524656 0.851315i \(-0.675806\pi\)
−0.524656 + 0.851315i \(0.675806\pi\)
\(422\) 0 0
\(423\) 28.4740 1.38445
\(424\) 0 0
\(425\) 21.4902 1.04243
\(426\) 0 0
\(427\) 7.98894 0.386612
\(428\) 0 0
\(429\) −2.90994 −0.140493
\(430\) 0 0
\(431\) −20.0047 −0.963595 −0.481797 0.876283i \(-0.660016\pi\)
−0.481797 + 0.876283i \(0.660016\pi\)
\(432\) 0 0
\(433\) −29.4079 −1.41325 −0.706627 0.707587i \(-0.749784\pi\)
−0.706627 + 0.707587i \(0.749784\pi\)
\(434\) 0 0
\(435\) 14.0231 0.672357
\(436\) 0 0
\(437\) −10.6737 −0.510592
\(438\) 0 0
\(439\) 28.5440 1.36233 0.681165 0.732130i \(-0.261474\pi\)
0.681165 + 0.732130i \(0.261474\pi\)
\(440\) 0 0
\(441\) 5.46776 0.260370
\(442\) 0 0
\(443\) 7.84235 0.372601 0.186301 0.982493i \(-0.440350\pi\)
0.186301 + 0.982493i \(0.440350\pi\)
\(444\) 0 0
\(445\) −1.33110 −0.0631000
\(446\) 0 0
\(447\) −54.1042 −2.55904
\(448\) 0 0
\(449\) 21.0341 0.992661 0.496331 0.868134i \(-0.334680\pi\)
0.496331 + 0.868134i \(0.334680\pi\)
\(450\) 0 0
\(451\) −7.64480 −0.359979
\(452\) 0 0
\(453\) −0.769126 −0.0361367
\(454\) 0 0
\(455\) −1.16917 −0.0548114
\(456\) 0 0
\(457\) 32.2475 1.50847 0.754237 0.656602i \(-0.228007\pi\)
0.754237 + 0.656602i \(0.228007\pi\)
\(458\) 0 0
\(459\) −42.4773 −1.98267
\(460\) 0 0
\(461\) −38.2475 −1.78136 −0.890681 0.454629i \(-0.849772\pi\)
−0.890681 + 0.454629i \(0.849772\pi\)
\(462\) 0 0
\(463\) −9.55243 −0.443939 −0.221970 0.975054i \(-0.571249\pi\)
−0.221970 + 0.975054i \(0.571249\pi\)
\(464\) 0 0
\(465\) −3.27053 −0.151667
\(466\) 0 0
\(467\) −7.95322 −0.368031 −0.184016 0.982923i \(-0.558910\pi\)
−0.184016 + 0.982923i \(0.558910\pi\)
\(468\) 0 0
\(469\) 4.62609 0.213613
\(470\) 0 0
\(471\) 7.70343 0.354955
\(472\) 0 0
\(473\) −1.91716 −0.0881509
\(474\) 0 0
\(475\) 7.44640 0.341664
\(476\) 0 0
\(477\) −21.5820 −0.988174
\(478\) 0 0
\(479\) −16.7258 −0.764222 −0.382111 0.924116i \(-0.624803\pi\)
−0.382111 + 0.924116i \(0.624803\pi\)
\(480\) 0 0
\(481\) 7.61804 0.347353
\(482\) 0 0
\(483\) −15.1539 −0.689525
\(484\) 0 0
\(485\) 15.8837 0.721239
\(486\) 0 0
\(487\) 22.2426 1.00791 0.503954 0.863730i \(-0.331878\pi\)
0.503954 + 0.863730i \(0.331878\pi\)
\(488\) 0 0
\(489\) −44.4138 −2.00846
\(490\) 0 0
\(491\) 10.9920 0.496063 0.248031 0.968752i \(-0.420216\pi\)
0.248031 + 0.968752i \(0.420216\pi\)
\(492\) 0 0
\(493\) 24.3810 1.09807
\(494\) 0 0
\(495\) −6.39273 −0.287332
\(496\) 0 0
\(497\) −11.1079 −0.498255
\(498\) 0 0
\(499\) −38.0374 −1.70279 −0.851394 0.524526i \(-0.824243\pi\)
−0.851394 + 0.524526i \(0.824243\pi\)
\(500\) 0 0
\(501\) 33.0930 1.47849
\(502\) 0 0
\(503\) 26.4044 1.17732 0.588658 0.808383i \(-0.299657\pi\)
0.588658 + 0.808383i \(0.299657\pi\)
\(504\) 0 0
\(505\) −21.4100 −0.952730
\(506\) 0 0
\(507\) 2.90994 0.129235
\(508\) 0 0
\(509\) −8.62431 −0.382266 −0.191133 0.981564i \(-0.561216\pi\)
−0.191133 + 0.981564i \(0.561216\pi\)
\(510\) 0 0
\(511\) −3.77526 −0.167008
\(512\) 0 0
\(513\) −14.7185 −0.649836
\(514\) 0 0
\(515\) 6.38064 0.281165
\(516\) 0 0
\(517\) 5.20762 0.229031
\(518\) 0 0
\(519\) −19.8191 −0.869963
\(520\) 0 0
\(521\) −5.13203 −0.224838 −0.112419 0.993661i \(-0.535860\pi\)
−0.112419 + 0.993661i \(0.535860\pi\)
\(522\) 0 0
\(523\) 32.3238 1.41342 0.706711 0.707503i \(-0.250178\pi\)
0.706711 + 0.707503i \(0.250178\pi\)
\(524\) 0 0
\(525\) 10.5720 0.461398
\(526\) 0 0
\(527\) −5.68625 −0.247697
\(528\) 0 0
\(529\) 4.11927 0.179099
\(530\) 0 0
\(531\) 10.7962 0.468516
\(532\) 0 0
\(533\) 7.64480 0.331133
\(534\) 0 0
\(535\) 5.12755 0.221683
\(536\) 0 0
\(537\) 17.2526 0.744504
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) 25.6379 1.10226 0.551130 0.834419i \(-0.314197\pi\)
0.551130 + 0.834419i \(0.314197\pi\)
\(542\) 0 0
\(543\) 28.9240 1.24125
\(544\) 0 0
\(545\) 18.8713 0.808359
\(546\) 0 0
\(547\) −11.7038 −0.500417 −0.250208 0.968192i \(-0.580499\pi\)
−0.250208 + 0.968192i \(0.580499\pi\)
\(548\) 0 0
\(549\) −43.6816 −1.86428
\(550\) 0 0
\(551\) 8.44809 0.359901
\(552\) 0 0
\(553\) −6.29845 −0.267837
\(554\) 0 0
\(555\) 25.9182 1.10017
\(556\) 0 0
\(557\) 24.6149 1.04297 0.521484 0.853261i \(-0.325378\pi\)
0.521484 + 0.853261i \(0.325378\pi\)
\(558\) 0 0
\(559\) 1.91716 0.0810870
\(560\) 0 0
\(561\) −17.2129 −0.726728
\(562\) 0 0
\(563\) 13.7661 0.580171 0.290086 0.957001i \(-0.406316\pi\)
0.290086 + 0.957001i \(0.406316\pi\)
\(564\) 0 0
\(565\) 4.07962 0.171631
\(566\) 0 0
\(567\) −4.49313 −0.188694
\(568\) 0 0
\(569\) 45.6622 1.91426 0.957128 0.289664i \(-0.0935435\pi\)
0.957128 + 0.289664i \(0.0935435\pi\)
\(570\) 0 0
\(571\) −10.5471 −0.441381 −0.220690 0.975344i \(-0.570831\pi\)
−0.220690 + 0.975344i \(0.570831\pi\)
\(572\) 0 0
\(573\) 13.8059 0.576748
\(574\) 0 0
\(575\) −18.9195 −0.788998
\(576\) 0 0
\(577\) 31.1186 1.29548 0.647742 0.761860i \(-0.275713\pi\)
0.647742 + 0.761860i \(0.275713\pi\)
\(578\) 0 0
\(579\) −54.5944 −2.26887
\(580\) 0 0
\(581\) 17.2308 0.714856
\(582\) 0 0
\(583\) −3.94714 −0.163474
\(584\) 0 0
\(585\) 6.39273 0.264307
\(586\) 0 0
\(587\) −16.8660 −0.696136 −0.348068 0.937469i \(-0.613162\pi\)
−0.348068 + 0.937469i \(0.613162\pi\)
\(588\) 0 0
\(589\) −1.97030 −0.0811848
\(590\) 0 0
\(591\) −69.4865 −2.85829
\(592\) 0 0
\(593\) −34.8391 −1.43067 −0.715334 0.698782i \(-0.753726\pi\)
−0.715334 + 0.698782i \(0.753726\pi\)
\(594\) 0 0
\(595\) −6.91586 −0.283523
\(596\) 0 0
\(597\) −6.63662 −0.271619
\(598\) 0 0
\(599\) 23.0816 0.943088 0.471544 0.881843i \(-0.343697\pi\)
0.471544 + 0.881843i \(0.343697\pi\)
\(600\) 0 0
\(601\) 16.6140 0.677698 0.338849 0.940841i \(-0.389962\pi\)
0.338849 + 0.940841i \(0.389962\pi\)
\(602\) 0 0
\(603\) −25.2944 −1.03007
\(604\) 0 0
\(605\) −1.16917 −0.0475334
\(606\) 0 0
\(607\) 44.2153 1.79464 0.897322 0.441376i \(-0.145510\pi\)
0.897322 + 0.441376i \(0.145510\pi\)
\(608\) 0 0
\(609\) 11.9941 0.486025
\(610\) 0 0
\(611\) −5.20762 −0.210678
\(612\) 0 0
\(613\) −39.6930 −1.60319 −0.801593 0.597870i \(-0.796014\pi\)
−0.801593 + 0.597870i \(0.796014\pi\)
\(614\) 0 0
\(615\) 26.0092 1.04879
\(616\) 0 0
\(617\) −11.2609 −0.453348 −0.226674 0.973971i \(-0.572785\pi\)
−0.226674 + 0.973971i \(0.572785\pi\)
\(618\) 0 0
\(619\) −27.4814 −1.10457 −0.552285 0.833656i \(-0.686244\pi\)
−0.552285 + 0.833656i \(0.686244\pi\)
\(620\) 0 0
\(621\) 37.3961 1.50065
\(622\) 0 0
\(623\) −1.13850 −0.0456130
\(624\) 0 0
\(625\) 6.36425 0.254570
\(626\) 0 0
\(627\) −5.96430 −0.238191
\(628\) 0 0
\(629\) 45.0622 1.79675
\(630\) 0 0
\(631\) 9.55126 0.380230 0.190115 0.981762i \(-0.439114\pi\)
0.190115 + 0.981762i \(0.439114\pi\)
\(632\) 0 0
\(633\) 9.32588 0.370670
\(634\) 0 0
\(635\) −21.6079 −0.857485
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 60.7351 2.40264
\(640\) 0 0
\(641\) 27.4180 1.08295 0.541473 0.840718i \(-0.317867\pi\)
0.541473 + 0.840718i \(0.317867\pi\)
\(642\) 0 0
\(643\) −5.15156 −0.203158 −0.101579 0.994827i \(-0.532389\pi\)
−0.101579 + 0.994827i \(0.532389\pi\)
\(644\) 0 0
\(645\) 6.52257 0.256826
\(646\) 0 0
\(647\) −42.4286 −1.66804 −0.834021 0.551733i \(-0.813967\pi\)
−0.834021 + 0.551733i \(0.813967\pi\)
\(648\) 0 0
\(649\) 1.97452 0.0775069
\(650\) 0 0
\(651\) −2.79732 −0.109635
\(652\) 0 0
\(653\) 22.8485 0.894132 0.447066 0.894501i \(-0.352469\pi\)
0.447066 + 0.894501i \(0.352469\pi\)
\(654\) 0 0
\(655\) 16.0810 0.628336
\(656\) 0 0
\(657\) 20.6422 0.805330
\(658\) 0 0
\(659\) −20.2815 −0.790053 −0.395027 0.918670i \(-0.629265\pi\)
−0.395027 + 0.918670i \(0.629265\pi\)
\(660\) 0 0
\(661\) −6.70253 −0.260698 −0.130349 0.991468i \(-0.541610\pi\)
−0.130349 + 0.991468i \(0.541610\pi\)
\(662\) 0 0
\(663\) 17.2129 0.668493
\(664\) 0 0
\(665\) −2.39636 −0.0929269
\(666\) 0 0
\(667\) −21.4646 −0.831111
\(668\) 0 0
\(669\) 46.2594 1.78849
\(670\) 0 0
\(671\) −7.98894 −0.308409
\(672\) 0 0
\(673\) −16.2565 −0.626642 −0.313321 0.949647i \(-0.601442\pi\)
−0.313321 + 0.949647i \(0.601442\pi\)
\(674\) 0 0
\(675\) −26.0890 −1.00417
\(676\) 0 0
\(677\) −15.1073 −0.580620 −0.290310 0.956933i \(-0.593758\pi\)
−0.290310 + 0.956933i \(0.593758\pi\)
\(678\) 0 0
\(679\) 13.5854 0.521361
\(680\) 0 0
\(681\) 71.2065 2.72864
\(682\) 0 0
\(683\) 27.5615 1.05461 0.527306 0.849676i \(-0.323202\pi\)
0.527306 + 0.849676i \(0.323202\pi\)
\(684\) 0 0
\(685\) 10.8562 0.414792
\(686\) 0 0
\(687\) 82.4692 3.14640
\(688\) 0 0
\(689\) 3.94714 0.150374
\(690\) 0 0
\(691\) 19.5169 0.742459 0.371229 0.928541i \(-0.378936\pi\)
0.371229 + 0.928541i \(0.378936\pi\)
\(692\) 0 0
\(693\) −5.46776 −0.207703
\(694\) 0 0
\(695\) −11.0858 −0.420509
\(696\) 0 0
\(697\) 45.2205 1.71285
\(698\) 0 0
\(699\) 2.39897 0.0907375
\(700\) 0 0
\(701\) −7.28846 −0.275281 −0.137641 0.990482i \(-0.543952\pi\)
−0.137641 + 0.990482i \(0.543952\pi\)
\(702\) 0 0
\(703\) 15.6142 0.588899
\(704\) 0 0
\(705\) −17.7174 −0.667276
\(706\) 0 0
\(707\) −18.3121 −0.688698
\(708\) 0 0
\(709\) 39.3079 1.47624 0.738120 0.674670i \(-0.235714\pi\)
0.738120 + 0.674670i \(0.235714\pi\)
\(710\) 0 0
\(711\) 34.4384 1.29154
\(712\) 0 0
\(713\) 5.00606 0.187478
\(714\) 0 0
\(715\) 1.16917 0.0437244
\(716\) 0 0
\(717\) 13.1240 0.490124
\(718\) 0 0
\(719\) −2.88228 −0.107491 −0.0537454 0.998555i \(-0.517116\pi\)
−0.0537454 + 0.998555i \(0.517116\pi\)
\(720\) 0 0
\(721\) 5.45742 0.203245
\(722\) 0 0
\(723\) 31.7854 1.18211
\(724\) 0 0
\(725\) 14.9746 0.556141
\(726\) 0 0
\(727\) −19.4261 −0.720473 −0.360237 0.932861i \(-0.617304\pi\)
−0.360237 + 0.932861i \(0.617304\pi\)
\(728\) 0 0
\(729\) −38.1219 −1.41192
\(730\) 0 0
\(731\) 11.3403 0.419438
\(732\) 0 0
\(733\) 39.5041 1.45912 0.729558 0.683919i \(-0.239726\pi\)
0.729558 + 0.683919i \(0.239726\pi\)
\(734\) 0 0
\(735\) −3.40221 −0.125492
\(736\) 0 0
\(737\) −4.62609 −0.170404
\(738\) 0 0
\(739\) 21.1493 0.777991 0.388996 0.921240i \(-0.372822\pi\)
0.388996 + 0.921240i \(0.372822\pi\)
\(740\) 0 0
\(741\) 5.96430 0.219104
\(742\) 0 0
\(743\) −23.3505 −0.856647 −0.428324 0.903625i \(-0.640896\pi\)
−0.428324 + 0.903625i \(0.640896\pi\)
\(744\) 0 0
\(745\) 21.7382 0.796426
\(746\) 0 0
\(747\) −94.2141 −3.44712
\(748\) 0 0
\(749\) 4.38564 0.160248
\(750\) 0 0
\(751\) 28.6706 1.04620 0.523102 0.852270i \(-0.324775\pi\)
0.523102 + 0.852270i \(0.324775\pi\)
\(752\) 0 0
\(753\) 59.1256 2.15466
\(754\) 0 0
\(755\) 0.309023 0.0112465
\(756\) 0 0
\(757\) 6.43531 0.233895 0.116948 0.993138i \(-0.462689\pi\)
0.116948 + 0.993138i \(0.462689\pi\)
\(758\) 0 0
\(759\) 15.1539 0.550050
\(760\) 0 0
\(761\) −5.39718 −0.195648 −0.0978239 0.995204i \(-0.531188\pi\)
−0.0978239 + 0.995204i \(0.531188\pi\)
\(762\) 0 0
\(763\) 16.1408 0.584337
\(764\) 0 0
\(765\) 37.8143 1.36718
\(766\) 0 0
\(767\) −1.97452 −0.0712960
\(768\) 0 0
\(769\) 1.94472 0.0701283 0.0350642 0.999385i \(-0.488836\pi\)
0.0350642 + 0.999385i \(0.488836\pi\)
\(770\) 0 0
\(771\) 31.3460 1.12890
\(772\) 0 0
\(773\) 22.6995 0.816443 0.408221 0.912883i \(-0.366149\pi\)
0.408221 + 0.912883i \(0.366149\pi\)
\(774\) 0 0
\(775\) −3.49243 −0.125452
\(776\) 0 0
\(777\) 22.1680 0.795274
\(778\) 0 0
\(779\) 15.6690 0.561400
\(780\) 0 0
\(781\) 11.1079 0.397470
\(782\) 0 0
\(783\) −29.5986 −1.05777
\(784\) 0 0
\(785\) −3.09511 −0.110469
\(786\) 0 0
\(787\) 38.4305 1.36990 0.684950 0.728591i \(-0.259824\pi\)
0.684950 + 0.728591i \(0.259824\pi\)
\(788\) 0 0
\(789\) −45.6412 −1.62487
\(790\) 0 0
\(791\) 3.48934 0.124067
\(792\) 0 0
\(793\) 7.98894 0.283695
\(794\) 0 0
\(795\) 13.4290 0.476278
\(796\) 0 0
\(797\) −9.88069 −0.349992 −0.174996 0.984569i \(-0.555991\pi\)
−0.174996 + 0.984569i \(0.555991\pi\)
\(798\) 0 0
\(799\) −30.8041 −1.08977
\(800\) 0 0
\(801\) 6.22504 0.219951
\(802\) 0 0
\(803\) 3.77526 0.133226
\(804\) 0 0
\(805\) 6.08858 0.214594
\(806\) 0 0
\(807\) −62.9855 −2.21719
\(808\) 0 0
\(809\) 12.3960 0.435822 0.217911 0.975969i \(-0.430076\pi\)
0.217911 + 0.975969i \(0.430076\pi\)
\(810\) 0 0
\(811\) −43.1531 −1.51531 −0.757655 0.652655i \(-0.773655\pi\)
−0.757655 + 0.652655i \(0.773655\pi\)
\(812\) 0 0
\(813\) −55.5175 −1.94708
\(814\) 0 0
\(815\) 17.8448 0.625075
\(816\) 0 0
\(817\) 3.92946 0.137474
\(818\) 0 0
\(819\) 5.46776 0.191059
\(820\) 0 0
\(821\) 3.45499 0.120580 0.0602900 0.998181i \(-0.480797\pi\)
0.0602900 + 0.998181i \(0.480797\pi\)
\(822\) 0 0
\(823\) −18.5544 −0.646765 −0.323383 0.946268i \(-0.604820\pi\)
−0.323383 + 0.946268i \(0.604820\pi\)
\(824\) 0 0
\(825\) −10.5720 −0.368068
\(826\) 0 0
\(827\) −11.0690 −0.384906 −0.192453 0.981306i \(-0.561644\pi\)
−0.192453 + 0.981306i \(0.561644\pi\)
\(828\) 0 0
\(829\) 24.1043 0.837178 0.418589 0.908176i \(-0.362525\pi\)
0.418589 + 0.908176i \(0.362525\pi\)
\(830\) 0 0
\(831\) 49.5652 1.71940
\(832\) 0 0
\(833\) −5.91520 −0.204949
\(834\) 0 0
\(835\) −13.2963 −0.460136
\(836\) 0 0
\(837\) 6.90310 0.238606
\(838\) 0 0
\(839\) 28.4491 0.982173 0.491086 0.871111i \(-0.336600\pi\)
0.491086 + 0.871111i \(0.336600\pi\)
\(840\) 0 0
\(841\) −12.0111 −0.414175
\(842\) 0 0
\(843\) −45.5054 −1.56729
\(844\) 0 0
\(845\) −1.16917 −0.0402206
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) −85.6312 −2.93886
\(850\) 0 0
\(851\) −39.6718 −1.35993
\(852\) 0 0
\(853\) −9.45076 −0.323588 −0.161794 0.986825i \(-0.551728\pi\)
−0.161794 + 0.986825i \(0.551728\pi\)
\(854\) 0 0
\(855\) 13.1027 0.448104
\(856\) 0 0
\(857\) −30.3193 −1.03569 −0.517844 0.855475i \(-0.673265\pi\)
−0.517844 + 0.855475i \(0.673265\pi\)
\(858\) 0 0
\(859\) −19.8096 −0.675896 −0.337948 0.941165i \(-0.609733\pi\)
−0.337948 + 0.941165i \(0.609733\pi\)
\(860\) 0 0
\(861\) 22.2459 0.758139
\(862\) 0 0
\(863\) −49.4083 −1.68188 −0.840940 0.541129i \(-0.817997\pi\)
−0.840940 + 0.541129i \(0.817997\pi\)
\(864\) 0 0
\(865\) 7.96301 0.270750
\(866\) 0 0
\(867\) 52.3485 1.77785
\(868\) 0 0
\(869\) 6.29845 0.213660
\(870\) 0 0
\(871\) 4.62609 0.156749
\(872\) 0 0
\(873\) −74.2819 −2.51406
\(874\) 0 0
\(875\) −10.0935 −0.341222
\(876\) 0 0
\(877\) 50.9650 1.72097 0.860483 0.509480i \(-0.170162\pi\)
0.860483 + 0.509480i \(0.170162\pi\)
\(878\) 0 0
\(879\) −49.5650 −1.67179
\(880\) 0 0
\(881\) 23.3840 0.787829 0.393914 0.919147i \(-0.371121\pi\)
0.393914 + 0.919147i \(0.371121\pi\)
\(882\) 0 0
\(883\) 25.0697 0.843662 0.421831 0.906675i \(-0.361388\pi\)
0.421831 + 0.906675i \(0.361388\pi\)
\(884\) 0 0
\(885\) −6.71775 −0.225815
\(886\) 0 0
\(887\) −7.19577 −0.241610 −0.120805 0.992676i \(-0.538548\pi\)
−0.120805 + 0.992676i \(0.538548\pi\)
\(888\) 0 0
\(889\) −18.4815 −0.619848
\(890\) 0 0
\(891\) 4.49313 0.150525
\(892\) 0 0
\(893\) −10.6737 −0.357181
\(894\) 0 0
\(895\) −6.93182 −0.231705
\(896\) 0 0
\(897\) −15.1539 −0.505973
\(898\) 0 0
\(899\) −3.96224 −0.132148
\(900\) 0 0
\(901\) 23.3481 0.777839
\(902\) 0 0
\(903\) 5.57881 0.185651
\(904\) 0 0
\(905\) −11.6212 −0.386302
\(906\) 0 0
\(907\) −16.8870 −0.560724 −0.280362 0.959894i \(-0.590454\pi\)
−0.280362 + 0.959894i \(0.590454\pi\)
\(908\) 0 0
\(909\) 100.126 3.32098
\(910\) 0 0
\(911\) 18.0905 0.599366 0.299683 0.954039i \(-0.403119\pi\)
0.299683 + 0.954039i \(0.403119\pi\)
\(912\) 0 0
\(913\) −17.2308 −0.570258
\(914\) 0 0
\(915\) 27.1800 0.898544
\(916\) 0 0
\(917\) 13.7542 0.454204
\(918\) 0 0
\(919\) 38.7151 1.27709 0.638547 0.769583i \(-0.279536\pi\)
0.638547 + 0.769583i \(0.279536\pi\)
\(920\) 0 0
\(921\) 69.3639 2.28562
\(922\) 0 0
\(923\) −11.1079 −0.365620
\(924\) 0 0
\(925\) 27.6767 0.910004
\(926\) 0 0
\(927\) −29.8399 −0.980070
\(928\) 0 0
\(929\) 48.5134 1.59167 0.795837 0.605511i \(-0.207031\pi\)
0.795837 + 0.605511i \(0.207031\pi\)
\(930\) 0 0
\(931\) −2.04963 −0.0671739
\(932\) 0 0
\(933\) 67.5732 2.21225
\(934\) 0 0
\(935\) 6.91586 0.226173
\(936\) 0 0
\(937\) 28.2144 0.921725 0.460863 0.887471i \(-0.347540\pi\)
0.460863 + 0.887471i \(0.347540\pi\)
\(938\) 0 0
\(939\) 36.2416 1.18270
\(940\) 0 0
\(941\) 56.7604 1.85033 0.925167 0.379560i \(-0.123924\pi\)
0.925167 + 0.379560i \(0.123924\pi\)
\(942\) 0 0
\(943\) −39.8112 −1.29643
\(944\) 0 0
\(945\) 8.39584 0.273117
\(946\) 0 0
\(947\) 20.5131 0.666586 0.333293 0.942823i \(-0.391840\pi\)
0.333293 + 0.942823i \(0.391840\pi\)
\(948\) 0 0
\(949\) −3.77526 −0.122550
\(950\) 0 0
\(951\) −35.0703 −1.13723
\(952\) 0 0
\(953\) −41.1569 −1.33320 −0.666601 0.745415i \(-0.732252\pi\)
−0.666601 + 0.745415i \(0.732252\pi\)
\(954\) 0 0
\(955\) −5.54697 −0.179496
\(956\) 0 0
\(957\) −11.9941 −0.387714
\(958\) 0 0
\(959\) 9.28537 0.299840
\(960\) 0 0
\(961\) −30.0759 −0.970191
\(962\) 0 0
\(963\) −23.9796 −0.772732
\(964\) 0 0
\(965\) 21.9352 0.706118
\(966\) 0 0
\(967\) −46.8348 −1.50611 −0.753053 0.657960i \(-0.771420\pi\)
−0.753053 + 0.657960i \(0.771420\pi\)
\(968\) 0 0
\(969\) 35.2800 1.13336
\(970\) 0 0
\(971\) −27.0701 −0.868722 −0.434361 0.900739i \(-0.643026\pi\)
−0.434361 + 0.900739i \(0.643026\pi\)
\(972\) 0 0
\(973\) −9.48179 −0.303972
\(974\) 0 0
\(975\) 10.5720 0.338573
\(976\) 0 0
\(977\) 35.8623 1.14734 0.573668 0.819088i \(-0.305520\pi\)
0.573668 + 0.819088i \(0.305520\pi\)
\(978\) 0 0
\(979\) 1.13850 0.0363866
\(980\) 0 0
\(981\) −88.2542 −2.81774
\(982\) 0 0
\(983\) 21.0442 0.671207 0.335603 0.942003i \(-0.391060\pi\)
0.335603 + 0.942003i \(0.391060\pi\)
\(984\) 0 0
\(985\) 27.9186 0.889560
\(986\) 0 0
\(987\) −15.1539 −0.482353
\(988\) 0 0
\(989\) −9.98381 −0.317467
\(990\) 0 0
\(991\) −18.4345 −0.585591 −0.292796 0.956175i \(-0.594586\pi\)
−0.292796 + 0.956175i \(0.594586\pi\)
\(992\) 0 0
\(993\) −12.5882 −0.399474
\(994\) 0 0
\(995\) 2.66649 0.0845333
\(996\) 0 0
\(997\) 8.86721 0.280827 0.140414 0.990093i \(-0.455157\pi\)
0.140414 + 0.990093i \(0.455157\pi\)
\(998\) 0 0
\(999\) −54.7054 −1.73080
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 \(a_p\))