Properties

Label 4028.2.a.d.1.5
Level 4028
Weight 2
Character 4028.1
Self dual Yes
Analytic conductor 32.164
Analytic rank 1
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4028 = 2^{2} \cdot 19 \cdot 53 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4028.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1637419342\)
Analytic rank: \(1\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(2.05170\)
Character \(\chi\) = 4028.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.05170 q^{3} +2.67326 q^{5} +0.688434 q^{7} +1.20949 q^{9} +O(q^{10})\) \(q-2.05170 q^{3} +2.67326 q^{5} +0.688434 q^{7} +1.20949 q^{9} -5.36452 q^{11} +1.75191 q^{13} -5.48473 q^{15} +3.58294 q^{17} -1.00000 q^{19} -1.41246 q^{21} +1.71126 q^{23} +2.14631 q^{25} +3.67360 q^{27} -10.2791 q^{29} -1.27276 q^{31} +11.0064 q^{33} +1.84036 q^{35} +1.26348 q^{37} -3.59440 q^{39} +9.70817 q^{41} +2.83145 q^{43} +3.23327 q^{45} -7.30266 q^{47} -6.52606 q^{49} -7.35114 q^{51} +1.00000 q^{53} -14.3408 q^{55} +2.05170 q^{57} -7.26302 q^{59} -14.4852 q^{61} +0.832651 q^{63} +4.68331 q^{65} -4.38693 q^{67} -3.51100 q^{69} -0.131451 q^{71} +9.46729 q^{73} -4.40359 q^{75} -3.69312 q^{77} -7.19961 q^{79} -11.1656 q^{81} -6.22376 q^{83} +9.57814 q^{85} +21.0898 q^{87} +6.04098 q^{89} +1.20607 q^{91} +2.61132 q^{93} -2.67326 q^{95} +10.7584 q^{97} -6.48832 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} + O(q^{10}) \) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} - 11q^{11} + q^{13} - 20q^{15} - q^{17} - 19q^{19} - 10q^{21} - 16q^{23} + 21q^{25} - 4q^{27} - 9q^{31} + 7q^{33} - 25q^{37} - 25q^{39} + q^{41} - 41q^{43} - 27q^{45} - 29q^{47} + 14q^{49} - 24q^{51} + 19q^{53} - 28q^{55} + 4q^{57} - 42q^{59} + q^{61} - 41q^{63} + 2q^{65} - 41q^{67} - 25q^{69} - 20q^{73} + 11q^{75} - 19q^{77} - 38q^{79} + 23q^{81} - 36q^{83} - 58q^{85} - 30q^{87} - 25q^{89} - 55q^{91} - 38q^{93} + 2q^{95} - 13q^{97} + q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.05170 −1.18455 −0.592276 0.805735i \(-0.701770\pi\)
−0.592276 + 0.805735i \(0.701770\pi\)
\(4\) 0 0
\(5\) 2.67326 1.19552 0.597759 0.801676i \(-0.296058\pi\)
0.597759 + 0.801676i \(0.296058\pi\)
\(6\) 0 0
\(7\) 0.688434 0.260203 0.130102 0.991501i \(-0.458470\pi\)
0.130102 + 0.991501i \(0.458470\pi\)
\(8\) 0 0
\(9\) 1.20949 0.403162
\(10\) 0 0
\(11\) −5.36452 −1.61746 −0.808732 0.588177i \(-0.799846\pi\)
−0.808732 + 0.588177i \(0.799846\pi\)
\(12\) 0 0
\(13\) 1.75191 0.485892 0.242946 0.970040i \(-0.421886\pi\)
0.242946 + 0.970040i \(0.421886\pi\)
\(14\) 0 0
\(15\) −5.48473 −1.41615
\(16\) 0 0
\(17\) 3.58294 0.868992 0.434496 0.900674i \(-0.356927\pi\)
0.434496 + 0.900674i \(0.356927\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) −1.41246 −0.308224
\(22\) 0 0
\(23\) 1.71126 0.356823 0.178411 0.983956i \(-0.442904\pi\)
0.178411 + 0.983956i \(0.442904\pi\)
\(24\) 0 0
\(25\) 2.14631 0.429262
\(26\) 0 0
\(27\) 3.67360 0.706985
\(28\) 0 0
\(29\) −10.2791 −1.90879 −0.954395 0.298547i \(-0.903498\pi\)
−0.954395 + 0.298547i \(0.903498\pi\)
\(30\) 0 0
\(31\) −1.27276 −0.228594 −0.114297 0.993447i \(-0.536462\pi\)
−0.114297 + 0.993447i \(0.536462\pi\)
\(32\) 0 0
\(33\) 11.0064 1.91597
\(34\) 0 0
\(35\) 1.84036 0.311078
\(36\) 0 0
\(37\) 1.26348 0.207715 0.103857 0.994592i \(-0.466881\pi\)
0.103857 + 0.994592i \(0.466881\pi\)
\(38\) 0 0
\(39\) −3.59440 −0.575564
\(40\) 0 0
\(41\) 9.70817 1.51616 0.758081 0.652161i \(-0.226137\pi\)
0.758081 + 0.652161i \(0.226137\pi\)
\(42\) 0 0
\(43\) 2.83145 0.431793 0.215896 0.976416i \(-0.430733\pi\)
0.215896 + 0.976416i \(0.430733\pi\)
\(44\) 0 0
\(45\) 3.23327 0.481987
\(46\) 0 0
\(47\) −7.30266 −1.06520 −0.532601 0.846366i \(-0.678785\pi\)
−0.532601 + 0.846366i \(0.678785\pi\)
\(48\) 0 0
\(49\) −6.52606 −0.932294
\(50\) 0 0
\(51\) −7.35114 −1.02937
\(52\) 0 0
\(53\) 1.00000 0.137361
\(54\) 0 0
\(55\) −14.3408 −1.93371
\(56\) 0 0
\(57\) 2.05170 0.271755
\(58\) 0 0
\(59\) −7.26302 −0.945565 −0.472782 0.881179i \(-0.656750\pi\)
−0.472782 + 0.881179i \(0.656750\pi\)
\(60\) 0 0
\(61\) −14.4852 −1.85464 −0.927318 0.374274i \(-0.877892\pi\)
−0.927318 + 0.374274i \(0.877892\pi\)
\(62\) 0 0
\(63\) 0.832651 0.104904
\(64\) 0 0
\(65\) 4.68331 0.580893
\(66\) 0 0
\(67\) −4.38693 −0.535949 −0.267974 0.963426i \(-0.586354\pi\)
−0.267974 + 0.963426i \(0.586354\pi\)
\(68\) 0 0
\(69\) −3.51100 −0.422675
\(70\) 0 0
\(71\) −0.131451 −0.0156003 −0.00780015 0.999970i \(-0.502483\pi\)
−0.00780015 + 0.999970i \(0.502483\pi\)
\(72\) 0 0
\(73\) 9.46729 1.10806 0.554031 0.832496i \(-0.313089\pi\)
0.554031 + 0.832496i \(0.313089\pi\)
\(74\) 0 0
\(75\) −4.40359 −0.508483
\(76\) 0 0
\(77\) −3.69312 −0.420870
\(78\) 0 0
\(79\) −7.19961 −0.810020 −0.405010 0.914312i \(-0.632732\pi\)
−0.405010 + 0.914312i \(0.632732\pi\)
\(80\) 0 0
\(81\) −11.1656 −1.24062
\(82\) 0 0
\(83\) −6.22376 −0.683146 −0.341573 0.939855i \(-0.610960\pi\)
−0.341573 + 0.939855i \(0.610960\pi\)
\(84\) 0 0
\(85\) 9.57814 1.03889
\(86\) 0 0
\(87\) 21.0898 2.26106
\(88\) 0 0
\(89\) 6.04098 0.640343 0.320171 0.947360i \(-0.396260\pi\)
0.320171 + 0.947360i \(0.396260\pi\)
\(90\) 0 0
\(91\) 1.20607 0.126431
\(92\) 0 0
\(93\) 2.61132 0.270781
\(94\) 0 0
\(95\) −2.67326 −0.274271
\(96\) 0 0
\(97\) 10.7584 1.09235 0.546176 0.837670i \(-0.316083\pi\)
0.546176 + 0.837670i \(0.316083\pi\)
\(98\) 0 0
\(99\) −6.48832 −0.652100
\(100\) 0 0
\(101\) 1.43012 0.142302 0.0711512 0.997466i \(-0.477333\pi\)
0.0711512 + 0.997466i \(0.477333\pi\)
\(102\) 0 0
\(103\) −4.52410 −0.445773 −0.222886 0.974844i \(-0.571548\pi\)
−0.222886 + 0.974844i \(0.571548\pi\)
\(104\) 0 0
\(105\) −3.77588 −0.368488
\(106\) 0 0
\(107\) 9.61719 0.929728 0.464864 0.885382i \(-0.346103\pi\)
0.464864 + 0.885382i \(0.346103\pi\)
\(108\) 0 0
\(109\) 2.61052 0.250043 0.125021 0.992154i \(-0.460100\pi\)
0.125021 + 0.992154i \(0.460100\pi\)
\(110\) 0 0
\(111\) −2.59229 −0.246049
\(112\) 0 0
\(113\) 16.2523 1.52889 0.764444 0.644690i \(-0.223013\pi\)
0.764444 + 0.644690i \(0.223013\pi\)
\(114\) 0 0
\(115\) 4.57464 0.426588
\(116\) 0 0
\(117\) 2.11891 0.195893
\(118\) 0 0
\(119\) 2.46662 0.226115
\(120\) 0 0
\(121\) 17.7781 1.61619
\(122\) 0 0
\(123\) −19.9183 −1.79597
\(124\) 0 0
\(125\) −7.62865 −0.682327
\(126\) 0 0
\(127\) −22.3178 −1.98038 −0.990192 0.139711i \(-0.955383\pi\)
−0.990192 + 0.139711i \(0.955383\pi\)
\(128\) 0 0
\(129\) −5.80930 −0.511481
\(130\) 0 0
\(131\) −9.70655 −0.848065 −0.424033 0.905647i \(-0.639386\pi\)
−0.424033 + 0.905647i \(0.639386\pi\)
\(132\) 0 0
\(133\) −0.688434 −0.0596948
\(134\) 0 0
\(135\) 9.82049 0.845213
\(136\) 0 0
\(137\) 11.6636 0.996488 0.498244 0.867037i \(-0.333978\pi\)
0.498244 + 0.867037i \(0.333978\pi\)
\(138\) 0 0
\(139\) 3.49402 0.296359 0.148179 0.988961i \(-0.452659\pi\)
0.148179 + 0.988961i \(0.452659\pi\)
\(140\) 0 0
\(141\) 14.9829 1.26179
\(142\) 0 0
\(143\) −9.39816 −0.785913
\(144\) 0 0
\(145\) −27.4788 −2.28199
\(146\) 0 0
\(147\) 13.3895 1.10435
\(148\) 0 0
\(149\) 1.16712 0.0956141 0.0478070 0.998857i \(-0.484777\pi\)
0.0478070 + 0.998857i \(0.484777\pi\)
\(150\) 0 0
\(151\) −5.68464 −0.462610 −0.231305 0.972881i \(-0.574299\pi\)
−0.231305 + 0.972881i \(0.574299\pi\)
\(152\) 0 0
\(153\) 4.33352 0.350345
\(154\) 0 0
\(155\) −3.40241 −0.273288
\(156\) 0 0
\(157\) −10.7537 −0.858241 −0.429120 0.903247i \(-0.641176\pi\)
−0.429120 + 0.903247i \(0.641176\pi\)
\(158\) 0 0
\(159\) −2.05170 −0.162711
\(160\) 0 0
\(161\) 1.17809 0.0928465
\(162\) 0 0
\(163\) 3.77174 0.295426 0.147713 0.989030i \(-0.452809\pi\)
0.147713 + 0.989030i \(0.452809\pi\)
\(164\) 0 0
\(165\) 29.4230 2.29058
\(166\) 0 0
\(167\) −10.0827 −0.780221 −0.390110 0.920768i \(-0.627563\pi\)
−0.390110 + 0.920768i \(0.627563\pi\)
\(168\) 0 0
\(169\) −9.93081 −0.763909
\(170\) 0 0
\(171\) −1.20949 −0.0924917
\(172\) 0 0
\(173\) −13.8105 −1.05000 −0.524998 0.851104i \(-0.675934\pi\)
−0.524998 + 0.851104i \(0.675934\pi\)
\(174\) 0 0
\(175\) 1.47759 0.111696
\(176\) 0 0
\(177\) 14.9016 1.12007
\(178\) 0 0
\(179\) −1.58868 −0.118744 −0.0593718 0.998236i \(-0.518910\pi\)
−0.0593718 + 0.998236i \(0.518910\pi\)
\(180\) 0 0
\(181\) −19.3651 −1.43939 −0.719697 0.694289i \(-0.755719\pi\)
−0.719697 + 0.694289i \(0.755719\pi\)
\(182\) 0 0
\(183\) 29.7193 2.19691
\(184\) 0 0
\(185\) 3.37761 0.248327
\(186\) 0 0
\(187\) −19.2208 −1.40556
\(188\) 0 0
\(189\) 2.52903 0.183960
\(190\) 0 0
\(191\) −20.9567 −1.51637 −0.758187 0.652037i \(-0.773914\pi\)
−0.758187 + 0.652037i \(0.773914\pi\)
\(192\) 0 0
\(193\) −6.33053 −0.455682 −0.227841 0.973698i \(-0.573167\pi\)
−0.227841 + 0.973698i \(0.573167\pi\)
\(194\) 0 0
\(195\) −9.60876 −0.688097
\(196\) 0 0
\(197\) 14.9006 1.06163 0.530813 0.847489i \(-0.321887\pi\)
0.530813 + 0.847489i \(0.321887\pi\)
\(198\) 0 0
\(199\) −21.0567 −1.49267 −0.746335 0.665570i \(-0.768188\pi\)
−0.746335 + 0.665570i \(0.768188\pi\)
\(200\) 0 0
\(201\) 9.00068 0.634859
\(202\) 0 0
\(203\) −7.07651 −0.496674
\(204\) 0 0
\(205\) 25.9524 1.81260
\(206\) 0 0
\(207\) 2.06975 0.143857
\(208\) 0 0
\(209\) 5.36452 0.371072
\(210\) 0 0
\(211\) 3.83490 0.264006 0.132003 0.991249i \(-0.457859\pi\)
0.132003 + 0.991249i \(0.457859\pi\)
\(212\) 0 0
\(213\) 0.269698 0.0184794
\(214\) 0 0
\(215\) 7.56921 0.516216
\(216\) 0 0
\(217\) −0.876209 −0.0594809
\(218\) 0 0
\(219\) −19.4241 −1.31256
\(220\) 0 0
\(221\) 6.27699 0.422236
\(222\) 0 0
\(223\) 26.2227 1.75600 0.878001 0.478658i \(-0.158877\pi\)
0.878001 + 0.478658i \(0.158877\pi\)
\(224\) 0 0
\(225\) 2.59593 0.173062
\(226\) 0 0
\(227\) 6.75562 0.448386 0.224193 0.974545i \(-0.428025\pi\)
0.224193 + 0.974545i \(0.428025\pi\)
\(228\) 0 0
\(229\) −7.52706 −0.497402 −0.248701 0.968580i \(-0.580004\pi\)
−0.248701 + 0.968580i \(0.580004\pi\)
\(230\) 0 0
\(231\) 7.57718 0.498542
\(232\) 0 0
\(233\) −19.6746 −1.28893 −0.644464 0.764634i \(-0.722920\pi\)
−0.644464 + 0.764634i \(0.722920\pi\)
\(234\) 0 0
\(235\) −19.5219 −1.27347
\(236\) 0 0
\(237\) 14.7715 0.959510
\(238\) 0 0
\(239\) 2.86141 0.185089 0.0925445 0.995709i \(-0.470500\pi\)
0.0925445 + 0.995709i \(0.470500\pi\)
\(240\) 0 0
\(241\) −14.2261 −0.916386 −0.458193 0.888853i \(-0.651503\pi\)
−0.458193 + 0.888853i \(0.651503\pi\)
\(242\) 0 0
\(243\) 11.8877 0.762596
\(244\) 0 0
\(245\) −17.4458 −1.11457
\(246\) 0 0
\(247\) −1.75191 −0.111471
\(248\) 0 0
\(249\) 12.7693 0.809222
\(250\) 0 0
\(251\) −1.21246 −0.0765297 −0.0382648 0.999268i \(-0.512183\pi\)
−0.0382648 + 0.999268i \(0.512183\pi\)
\(252\) 0 0
\(253\) −9.18010 −0.577148
\(254\) 0 0
\(255\) −19.6515 −1.23062
\(256\) 0 0
\(257\) −15.9057 −0.992173 −0.496086 0.868273i \(-0.665230\pi\)
−0.496086 + 0.868273i \(0.665230\pi\)
\(258\) 0 0
\(259\) 0.869822 0.0540481
\(260\) 0 0
\(261\) −12.4325 −0.769552
\(262\) 0 0
\(263\) 21.2856 1.31253 0.656263 0.754532i \(-0.272136\pi\)
0.656263 + 0.754532i \(0.272136\pi\)
\(264\) 0 0
\(265\) 2.67326 0.164217
\(266\) 0 0
\(267\) −12.3943 −0.758519
\(268\) 0 0
\(269\) −22.0518 −1.34452 −0.672261 0.740315i \(-0.734677\pi\)
−0.672261 + 0.740315i \(0.734677\pi\)
\(270\) 0 0
\(271\) −27.2142 −1.65314 −0.826572 0.562831i \(-0.809712\pi\)
−0.826572 + 0.562831i \(0.809712\pi\)
\(272\) 0 0
\(273\) −2.47450 −0.149764
\(274\) 0 0
\(275\) −11.5139 −0.694316
\(276\) 0 0
\(277\) 0.665156 0.0399654 0.0199827 0.999800i \(-0.493639\pi\)
0.0199827 + 0.999800i \(0.493639\pi\)
\(278\) 0 0
\(279\) −1.53938 −0.0921604
\(280\) 0 0
\(281\) 13.9904 0.834600 0.417300 0.908769i \(-0.362976\pi\)
0.417300 + 0.908769i \(0.362976\pi\)
\(282\) 0 0
\(283\) 5.64144 0.335349 0.167674 0.985842i \(-0.446374\pi\)
0.167674 + 0.985842i \(0.446374\pi\)
\(284\) 0 0
\(285\) 5.48473 0.324888
\(286\) 0 0
\(287\) 6.68343 0.394510
\(288\) 0 0
\(289\) −4.16251 −0.244853
\(290\) 0 0
\(291\) −22.0731 −1.29395
\(292\) 0 0
\(293\) −30.8081 −1.79983 −0.899915 0.436065i \(-0.856372\pi\)
−0.899915 + 0.436065i \(0.856372\pi\)
\(294\) 0 0
\(295\) −19.4159 −1.13044
\(296\) 0 0
\(297\) −19.7071 −1.14352
\(298\) 0 0
\(299\) 2.99797 0.173377
\(300\) 0 0
\(301\) 1.94927 0.112354
\(302\) 0 0
\(303\) −2.93419 −0.168565
\(304\) 0 0
\(305\) −38.7226 −2.21725
\(306\) 0 0
\(307\) 20.1847 1.15200 0.576000 0.817450i \(-0.304613\pi\)
0.576000 + 0.817450i \(0.304613\pi\)
\(308\) 0 0
\(309\) 9.28211 0.528041
\(310\) 0 0
\(311\) −15.8353 −0.897936 −0.448968 0.893548i \(-0.648208\pi\)
−0.448968 + 0.893548i \(0.648208\pi\)
\(312\) 0 0
\(313\) −30.1257 −1.70280 −0.851402 0.524514i \(-0.824247\pi\)
−0.851402 + 0.524514i \(0.824247\pi\)
\(314\) 0 0
\(315\) 2.22589 0.125415
\(316\) 0 0
\(317\) −9.37205 −0.526387 −0.263193 0.964743i \(-0.584776\pi\)
−0.263193 + 0.964743i \(0.584776\pi\)
\(318\) 0 0
\(319\) 55.1427 3.08740
\(320\) 0 0
\(321\) −19.7316 −1.10131
\(322\) 0 0
\(323\) −3.58294 −0.199360
\(324\) 0 0
\(325\) 3.76014 0.208575
\(326\) 0 0
\(327\) −5.35602 −0.296189
\(328\) 0 0
\(329\) −5.02740 −0.277169
\(330\) 0 0
\(331\) 13.8940 0.763682 0.381841 0.924228i \(-0.375290\pi\)
0.381841 + 0.924228i \(0.375290\pi\)
\(332\) 0 0
\(333\) 1.52816 0.0837427
\(334\) 0 0
\(335\) −11.7274 −0.640736
\(336\) 0 0
\(337\) −16.7493 −0.912392 −0.456196 0.889879i \(-0.650788\pi\)
−0.456196 + 0.889879i \(0.650788\pi\)
\(338\) 0 0
\(339\) −33.3449 −1.81105
\(340\) 0 0
\(341\) 6.82774 0.369743
\(342\) 0 0
\(343\) −9.31179 −0.502790
\(344\) 0 0
\(345\) −9.38581 −0.505315
\(346\) 0 0
\(347\) −18.4496 −0.990427 −0.495214 0.868771i \(-0.664910\pi\)
−0.495214 + 0.868771i \(0.664910\pi\)
\(348\) 0 0
\(349\) −8.47158 −0.453473 −0.226737 0.973956i \(-0.572806\pi\)
−0.226737 + 0.973956i \(0.572806\pi\)
\(350\) 0 0
\(351\) 6.43582 0.343519
\(352\) 0 0
\(353\) 21.5749 1.14832 0.574158 0.818744i \(-0.305329\pi\)
0.574158 + 0.818744i \(0.305329\pi\)
\(354\) 0 0
\(355\) −0.351401 −0.0186504
\(356\) 0 0
\(357\) −5.06077 −0.267844
\(358\) 0 0
\(359\) 5.12932 0.270715 0.135358 0.990797i \(-0.456782\pi\)
0.135358 + 0.990797i \(0.456782\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −36.4754 −1.91446
\(364\) 0 0
\(365\) 25.3085 1.32471
\(366\) 0 0
\(367\) −1.04598 −0.0545998 −0.0272999 0.999627i \(-0.508691\pi\)
−0.0272999 + 0.999627i \(0.508691\pi\)
\(368\) 0 0
\(369\) 11.7419 0.611259
\(370\) 0 0
\(371\) 0.688434 0.0357417
\(372\) 0 0
\(373\) −4.18140 −0.216505 −0.108252 0.994123i \(-0.534525\pi\)
−0.108252 + 0.994123i \(0.534525\pi\)
\(374\) 0 0
\(375\) 15.6517 0.808252
\(376\) 0 0
\(377\) −18.0081 −0.927466
\(378\) 0 0
\(379\) 1.97671 0.101537 0.0507683 0.998710i \(-0.483833\pi\)
0.0507683 + 0.998710i \(0.483833\pi\)
\(380\) 0 0
\(381\) 45.7895 2.34587
\(382\) 0 0
\(383\) 38.6302 1.97391 0.986955 0.160999i \(-0.0514716\pi\)
0.986955 + 0.160999i \(0.0514716\pi\)
\(384\) 0 0
\(385\) −9.87266 −0.503157
\(386\) 0 0
\(387\) 3.42460 0.174082
\(388\) 0 0
\(389\) −7.88051 −0.399558 −0.199779 0.979841i \(-0.564022\pi\)
−0.199779 + 0.979841i \(0.564022\pi\)
\(390\) 0 0
\(391\) 6.13135 0.310076
\(392\) 0 0
\(393\) 19.9150 1.00458
\(394\) 0 0
\(395\) −19.2464 −0.968393
\(396\) 0 0
\(397\) −15.9614 −0.801080 −0.400540 0.916279i \(-0.631177\pi\)
−0.400540 + 0.916279i \(0.631177\pi\)
\(398\) 0 0
\(399\) 1.41246 0.0707115
\(400\) 0 0
\(401\) 6.22351 0.310787 0.155394 0.987853i \(-0.450335\pi\)
0.155394 + 0.987853i \(0.450335\pi\)
\(402\) 0 0
\(403\) −2.22976 −0.111072
\(404\) 0 0
\(405\) −29.8485 −1.48319
\(406\) 0 0
\(407\) −6.77796 −0.335971
\(408\) 0 0
\(409\) 20.9180 1.03433 0.517164 0.855886i \(-0.326988\pi\)
0.517164 + 0.855886i \(0.326988\pi\)
\(410\) 0 0
\(411\) −23.9302 −1.18039
\(412\) 0 0
\(413\) −5.00011 −0.246039
\(414\) 0 0
\(415\) −16.6377 −0.816714
\(416\) 0 0
\(417\) −7.16869 −0.351052
\(418\) 0 0
\(419\) −18.3679 −0.897331 −0.448665 0.893700i \(-0.648100\pi\)
−0.448665 + 0.893700i \(0.648100\pi\)
\(420\) 0 0
\(421\) 20.3859 0.993548 0.496774 0.867880i \(-0.334518\pi\)
0.496774 + 0.867880i \(0.334518\pi\)
\(422\) 0 0
\(423\) −8.83246 −0.429449
\(424\) 0 0
\(425\) 7.69011 0.373025
\(426\) 0 0
\(427\) −9.97208 −0.482583
\(428\) 0 0
\(429\) 19.2822 0.930955
\(430\) 0 0
\(431\) −10.6564 −0.513301 −0.256651 0.966504i \(-0.582619\pi\)
−0.256651 + 0.966504i \(0.582619\pi\)
\(432\) 0 0
\(433\) 23.6612 1.13708 0.568542 0.822654i \(-0.307508\pi\)
0.568542 + 0.822654i \(0.307508\pi\)
\(434\) 0 0
\(435\) 56.3784 2.70314
\(436\) 0 0
\(437\) −1.71126 −0.0818607
\(438\) 0 0
\(439\) 33.3773 1.59301 0.796506 0.604630i \(-0.206679\pi\)
0.796506 + 0.604630i \(0.206679\pi\)
\(440\) 0 0
\(441\) −7.89318 −0.375866
\(442\) 0 0
\(443\) −29.2843 −1.39134 −0.695670 0.718361i \(-0.744893\pi\)
−0.695670 + 0.718361i \(0.744893\pi\)
\(444\) 0 0
\(445\) 16.1491 0.765541
\(446\) 0 0
\(447\) −2.39458 −0.113260
\(448\) 0 0
\(449\) 24.9640 1.17812 0.589061 0.808089i \(-0.299498\pi\)
0.589061 + 0.808089i \(0.299498\pi\)
\(450\) 0 0
\(451\) −52.0797 −2.45234
\(452\) 0 0
\(453\) 11.6632 0.547985
\(454\) 0 0
\(455\) 3.22415 0.151150
\(456\) 0 0
\(457\) −19.0056 −0.889044 −0.444522 0.895768i \(-0.646626\pi\)
−0.444522 + 0.895768i \(0.646626\pi\)
\(458\) 0 0
\(459\) 13.1623 0.614364
\(460\) 0 0
\(461\) −20.4148 −0.950811 −0.475405 0.879767i \(-0.657699\pi\)
−0.475405 + 0.879767i \(0.657699\pi\)
\(462\) 0 0
\(463\) 24.6655 1.14630 0.573151 0.819450i \(-0.305721\pi\)
0.573151 + 0.819450i \(0.305721\pi\)
\(464\) 0 0
\(465\) 6.98073 0.323724
\(466\) 0 0
\(467\) −37.8873 −1.75322 −0.876608 0.481206i \(-0.840199\pi\)
−0.876608 + 0.481206i \(0.840199\pi\)
\(468\) 0 0
\(469\) −3.02011 −0.139456
\(470\) 0 0
\(471\) 22.0635 1.01663
\(472\) 0 0
\(473\) −15.1894 −0.698409
\(474\) 0 0
\(475\) −2.14631 −0.0984795
\(476\) 0 0
\(477\) 1.20949 0.0553786
\(478\) 0 0
\(479\) 9.44817 0.431698 0.215849 0.976427i \(-0.430748\pi\)
0.215849 + 0.976427i \(0.430748\pi\)
\(480\) 0 0
\(481\) 2.21350 0.100927
\(482\) 0 0
\(483\) −2.41709 −0.109981
\(484\) 0 0
\(485\) 28.7601 1.30593
\(486\) 0 0
\(487\) −37.7835 −1.71213 −0.856067 0.516865i \(-0.827099\pi\)
−0.856067 + 0.516865i \(0.827099\pi\)
\(488\) 0 0
\(489\) −7.73850 −0.349947
\(490\) 0 0
\(491\) −11.6092 −0.523914 −0.261957 0.965079i \(-0.584368\pi\)
−0.261957 + 0.965079i \(0.584368\pi\)
\(492\) 0 0
\(493\) −36.8296 −1.65872
\(494\) 0 0
\(495\) −17.3449 −0.779597
\(496\) 0 0
\(497\) −0.0904950 −0.00405925
\(498\) 0 0
\(499\) −7.23875 −0.324051 −0.162026 0.986787i \(-0.551803\pi\)
−0.162026 + 0.986787i \(0.551803\pi\)
\(500\) 0 0
\(501\) 20.6867 0.924212
\(502\) 0 0
\(503\) −11.7813 −0.525302 −0.262651 0.964891i \(-0.584597\pi\)
−0.262651 + 0.964891i \(0.584597\pi\)
\(504\) 0 0
\(505\) 3.82309 0.170125
\(506\) 0 0
\(507\) 20.3751 0.904889
\(508\) 0 0
\(509\) 40.8441 1.81038 0.905191 0.425005i \(-0.139728\pi\)
0.905191 + 0.425005i \(0.139728\pi\)
\(510\) 0 0
\(511\) 6.51760 0.288322
\(512\) 0 0
\(513\) −3.67360 −0.162194
\(514\) 0 0
\(515\) −12.0941 −0.532929
\(516\) 0 0
\(517\) 39.1753 1.72293
\(518\) 0 0
\(519\) 28.3351 1.24377
\(520\) 0 0
\(521\) −20.2565 −0.887453 −0.443726 0.896162i \(-0.646344\pi\)
−0.443726 + 0.896162i \(0.646344\pi\)
\(522\) 0 0
\(523\) 16.0528 0.701941 0.350970 0.936387i \(-0.385852\pi\)
0.350970 + 0.936387i \(0.385852\pi\)
\(524\) 0 0
\(525\) −3.03158 −0.132309
\(526\) 0 0
\(527\) −4.56022 −0.198646
\(528\) 0 0
\(529\) −20.0716 −0.872678
\(530\) 0 0
\(531\) −8.78452 −0.381216
\(532\) 0 0
\(533\) 17.0078 0.736691
\(534\) 0 0
\(535\) 25.7092 1.11151
\(536\) 0 0
\(537\) 3.25950 0.140658
\(538\) 0 0
\(539\) 35.0092 1.50795
\(540\) 0 0
\(541\) −33.1284 −1.42430 −0.712151 0.702026i \(-0.752279\pi\)
−0.712151 + 0.702026i \(0.752279\pi\)
\(542\) 0 0
\(543\) 39.7314 1.70504
\(544\) 0 0
\(545\) 6.97860 0.298931
\(546\) 0 0
\(547\) −9.67593 −0.413713 −0.206856 0.978371i \(-0.566323\pi\)
−0.206856 + 0.978371i \(0.566323\pi\)
\(548\) 0 0
\(549\) −17.5196 −0.747719
\(550\) 0 0
\(551\) 10.2791 0.437906
\(552\) 0 0
\(553\) −4.95646 −0.210770
\(554\) 0 0
\(555\) −6.92985 −0.294156
\(556\) 0 0
\(557\) 13.9545 0.591270 0.295635 0.955301i \(-0.404469\pi\)
0.295635 + 0.955301i \(0.404469\pi\)
\(558\) 0 0
\(559\) 4.96045 0.209805
\(560\) 0 0
\(561\) 39.4353 1.66496
\(562\) 0 0
\(563\) −12.5614 −0.529402 −0.264701 0.964331i \(-0.585273\pi\)
−0.264701 + 0.964331i \(0.585273\pi\)
\(564\) 0 0
\(565\) 43.4466 1.82781
\(566\) 0 0
\(567\) −7.68678 −0.322814
\(568\) 0 0
\(569\) 30.0275 1.25882 0.629410 0.777074i \(-0.283297\pi\)
0.629410 + 0.777074i \(0.283297\pi\)
\(570\) 0 0
\(571\) −29.6364 −1.24024 −0.620122 0.784505i \(-0.712917\pi\)
−0.620122 + 0.784505i \(0.712917\pi\)
\(572\) 0 0
\(573\) 42.9969 1.79622
\(574\) 0 0
\(575\) 3.67290 0.153170
\(576\) 0 0
\(577\) −14.4863 −0.603072 −0.301536 0.953455i \(-0.597499\pi\)
−0.301536 + 0.953455i \(0.597499\pi\)
\(578\) 0 0
\(579\) 12.9884 0.539779
\(580\) 0 0
\(581\) −4.28465 −0.177757
\(582\) 0 0
\(583\) −5.36452 −0.222176
\(584\) 0 0
\(585\) 5.66439 0.234194
\(586\) 0 0
\(587\) 22.2906 0.920030 0.460015 0.887911i \(-0.347844\pi\)
0.460015 + 0.887911i \(0.347844\pi\)
\(588\) 0 0
\(589\) 1.27276 0.0524431
\(590\) 0 0
\(591\) −30.5717 −1.25755
\(592\) 0 0
\(593\) 25.1368 1.03224 0.516121 0.856515i \(-0.327375\pi\)
0.516121 + 0.856515i \(0.327375\pi\)
\(594\) 0 0
\(595\) 6.59391 0.270324
\(596\) 0 0
\(597\) 43.2021 1.76814
\(598\) 0 0
\(599\) 1.40362 0.0573504 0.0286752 0.999589i \(-0.490871\pi\)
0.0286752 + 0.999589i \(0.490871\pi\)
\(600\) 0 0
\(601\) −12.1969 −0.497523 −0.248761 0.968565i \(-0.580023\pi\)
−0.248761 + 0.968565i \(0.580023\pi\)
\(602\) 0 0
\(603\) −5.30593 −0.216074
\(604\) 0 0
\(605\) 47.5254 1.93218
\(606\) 0 0
\(607\) −12.5491 −0.509352 −0.254676 0.967026i \(-0.581969\pi\)
−0.254676 + 0.967026i \(0.581969\pi\)
\(608\) 0 0
\(609\) 14.5189 0.588336
\(610\) 0 0
\(611\) −12.7936 −0.517573
\(612\) 0 0
\(613\) 13.9971 0.565337 0.282669 0.959218i \(-0.408780\pi\)
0.282669 + 0.959218i \(0.408780\pi\)
\(614\) 0 0
\(615\) −53.2467 −2.14711
\(616\) 0 0
\(617\) 18.9172 0.761576 0.380788 0.924662i \(-0.375653\pi\)
0.380788 + 0.924662i \(0.375653\pi\)
\(618\) 0 0
\(619\) 3.15793 0.126928 0.0634640 0.997984i \(-0.479785\pi\)
0.0634640 + 0.997984i \(0.479785\pi\)
\(620\) 0 0
\(621\) 6.28649 0.252268
\(622\) 0 0
\(623\) 4.15881 0.166619
\(624\) 0 0
\(625\) −31.1249 −1.24500
\(626\) 0 0
\(627\) −11.0064 −0.439554
\(628\) 0 0
\(629\) 4.52698 0.180502
\(630\) 0 0
\(631\) −22.4939 −0.895469 −0.447734 0.894167i \(-0.647769\pi\)
−0.447734 + 0.894167i \(0.647769\pi\)
\(632\) 0 0
\(633\) −7.86808 −0.312728
\(634\) 0 0
\(635\) −59.6613 −2.36758
\(636\) 0 0
\(637\) −11.4331 −0.452995
\(638\) 0 0
\(639\) −0.158988 −0.00628945
\(640\) 0 0
\(641\) −10.6681 −0.421366 −0.210683 0.977554i \(-0.567569\pi\)
−0.210683 + 0.977554i \(0.567569\pi\)
\(642\) 0 0
\(643\) 41.6557 1.64274 0.821370 0.570396i \(-0.193210\pi\)
0.821370 + 0.570396i \(0.193210\pi\)
\(644\) 0 0
\(645\) −15.5298 −0.611484
\(646\) 0 0
\(647\) 2.12688 0.0836162 0.0418081 0.999126i \(-0.486688\pi\)
0.0418081 + 0.999126i \(0.486688\pi\)
\(648\) 0 0
\(649\) 38.9626 1.52942
\(650\) 0 0
\(651\) 1.79772 0.0704582
\(652\) 0 0
\(653\) 7.11558 0.278454 0.139227 0.990260i \(-0.455538\pi\)
0.139227 + 0.990260i \(0.455538\pi\)
\(654\) 0 0
\(655\) −25.9481 −1.01388
\(656\) 0 0
\(657\) 11.4506 0.446729
\(658\) 0 0
\(659\) 34.9080 1.35982 0.679911 0.733295i \(-0.262018\pi\)
0.679911 + 0.733295i \(0.262018\pi\)
\(660\) 0 0
\(661\) 35.6020 1.38476 0.692379 0.721534i \(-0.256563\pi\)
0.692379 + 0.721534i \(0.256563\pi\)
\(662\) 0 0
\(663\) −12.8785 −0.500161
\(664\) 0 0
\(665\) −1.84036 −0.0713661
\(666\) 0 0
\(667\) −17.5903 −0.681099
\(668\) 0 0
\(669\) −53.8012 −2.08008
\(670\) 0 0
\(671\) 77.7060 2.99981
\(672\) 0 0
\(673\) 12.1762 0.469360 0.234680 0.972073i \(-0.424596\pi\)
0.234680 + 0.972073i \(0.424596\pi\)
\(674\) 0 0
\(675\) 7.88469 0.303482
\(676\) 0 0
\(677\) −7.14162 −0.274475 −0.137237 0.990538i \(-0.543822\pi\)
−0.137237 + 0.990538i \(0.543822\pi\)
\(678\) 0 0
\(679\) 7.40646 0.284234
\(680\) 0 0
\(681\) −13.8605 −0.531137
\(682\) 0 0
\(683\) 39.6862 1.51855 0.759276 0.650769i \(-0.225553\pi\)
0.759276 + 0.650769i \(0.225553\pi\)
\(684\) 0 0
\(685\) 31.1798 1.19132
\(686\) 0 0
\(687\) 15.4433 0.589199
\(688\) 0 0
\(689\) 1.75191 0.0667424
\(690\) 0 0
\(691\) 33.7169 1.28265 0.641325 0.767269i \(-0.278385\pi\)
0.641325 + 0.767269i \(0.278385\pi\)
\(692\) 0 0
\(693\) −4.46677 −0.169679
\(694\) 0 0
\(695\) 9.34041 0.354302
\(696\) 0 0
\(697\) 34.7838 1.31753
\(698\) 0 0
\(699\) 40.3665 1.52680
\(700\) 0 0
\(701\) 7.55443 0.285327 0.142664 0.989771i \(-0.454433\pi\)
0.142664 + 0.989771i \(0.454433\pi\)
\(702\) 0 0
\(703\) −1.26348 −0.0476530
\(704\) 0 0
\(705\) 40.0531 1.50849
\(706\) 0 0
\(707\) 0.984544 0.0370276
\(708\) 0 0
\(709\) 49.9410 1.87558 0.937788 0.347209i \(-0.112871\pi\)
0.937788 + 0.347209i \(0.112871\pi\)
\(710\) 0 0
\(711\) −8.70783 −0.326569
\(712\) 0 0
\(713\) −2.17802 −0.0815675
\(714\) 0 0
\(715\) −25.1237 −0.939573
\(716\) 0 0
\(717\) −5.87076 −0.219247
\(718\) 0 0
\(719\) −8.33614 −0.310885 −0.155443 0.987845i \(-0.549680\pi\)
−0.155443 + 0.987845i \(0.549680\pi\)
\(720\) 0 0
\(721\) −3.11454 −0.115992
\(722\) 0 0
\(723\) 29.1878 1.08551
\(724\) 0 0
\(725\) −22.0622 −0.819371
\(726\) 0 0
\(727\) 16.8955 0.626621 0.313311 0.949651i \(-0.398562\pi\)
0.313311 + 0.949651i \(0.398562\pi\)
\(728\) 0 0
\(729\) 9.10679 0.337288
\(730\) 0 0
\(731\) 10.1449 0.375224
\(732\) 0 0
\(733\) −30.5227 −1.12738 −0.563691 0.825986i \(-0.690619\pi\)
−0.563691 + 0.825986i \(0.690619\pi\)
\(734\) 0 0
\(735\) 35.7937 1.32027
\(736\) 0 0
\(737\) 23.5338 0.866878
\(738\) 0 0
\(739\) 26.5270 0.975812 0.487906 0.872896i \(-0.337761\pi\)
0.487906 + 0.872896i \(0.337761\pi\)
\(740\) 0 0
\(741\) 3.59440 0.132044
\(742\) 0 0
\(743\) −22.9543 −0.842113 −0.421057 0.907034i \(-0.638341\pi\)
−0.421057 + 0.907034i \(0.638341\pi\)
\(744\) 0 0
\(745\) 3.12001 0.114308
\(746\) 0 0
\(747\) −7.52755 −0.275419
\(748\) 0 0
\(749\) 6.62079 0.241919
\(750\) 0 0
\(751\) −21.0347 −0.767567 −0.383783 0.923423i \(-0.625379\pi\)
−0.383783 + 0.923423i \(0.625379\pi\)
\(752\) 0 0
\(753\) 2.48760 0.0906533
\(754\) 0 0
\(755\) −15.1965 −0.553058
\(756\) 0 0
\(757\) −36.2915 −1.31904 −0.659519 0.751688i \(-0.729240\pi\)
−0.659519 + 0.751688i \(0.729240\pi\)
\(758\) 0 0
\(759\) 18.8348 0.683661
\(760\) 0 0
\(761\) 4.90249 0.177715 0.0888575 0.996044i \(-0.471678\pi\)
0.0888575 + 0.996044i \(0.471678\pi\)
\(762\) 0 0
\(763\) 1.79717 0.0650620
\(764\) 0 0
\(765\) 11.5846 0.418843
\(766\) 0 0
\(767\) −12.7242 −0.459443
\(768\) 0 0
\(769\) −1.30765 −0.0471550 −0.0235775 0.999722i \(-0.507506\pi\)
−0.0235775 + 0.999722i \(0.507506\pi\)
\(770\) 0 0
\(771\) 32.6338 1.17528
\(772\) 0 0
\(773\) 16.3103 0.586641 0.293321 0.956014i \(-0.405240\pi\)
0.293321 + 0.956014i \(0.405240\pi\)
\(774\) 0 0
\(775\) −2.73173 −0.0981267
\(776\) 0 0
\(777\) −1.78462 −0.0640228
\(778\) 0 0
\(779\) −9.70817 −0.347831
\(780\) 0 0
\(781\) 0.705169 0.0252329
\(782\) 0 0
\(783\) −37.7615 −1.34949
\(784\) 0 0
\(785\) −28.7475 −1.02604
\(786\) 0 0
\(787\) 45.5598 1.62403 0.812015 0.583636i \(-0.198371\pi\)
0.812015 + 0.583636i \(0.198371\pi\)
\(788\) 0 0
\(789\) −43.6717 −1.55475
\(790\) 0 0
\(791\) 11.1886 0.397822
\(792\) 0 0
\(793\) −25.3767 −0.901154
\(794\) 0 0
\(795\) −5.48473 −0.194523
\(796\) 0 0
\(797\) −8.76534 −0.310484 −0.155242 0.987876i \(-0.549616\pi\)
−0.155242 + 0.987876i \(0.549616\pi\)
\(798\) 0 0
\(799\) −26.1650 −0.925652
\(800\) 0 0
\(801\) 7.30648 0.258162
\(802\) 0 0
\(803\) −50.7875 −1.79225
\(804\) 0 0
\(805\) 3.14934 0.111000
\(806\) 0 0
\(807\) 45.2437 1.59265
\(808\) 0 0
\(809\) 12.8952 0.453373 0.226686 0.973968i \(-0.427211\pi\)
0.226686 + 0.973968i \(0.427211\pi\)
\(810\) 0 0
\(811\) −27.8727 −0.978742 −0.489371 0.872076i \(-0.662774\pi\)
−0.489371 + 0.872076i \(0.662774\pi\)
\(812\) 0 0
\(813\) 55.8354 1.95823
\(814\) 0 0
\(815\) 10.0828 0.353187
\(816\) 0 0
\(817\) −2.83145 −0.0990600
\(818\) 0 0
\(819\) 1.45873 0.0509721
\(820\) 0 0
\(821\) −28.0674 −0.979559 −0.489780 0.871846i \(-0.662923\pi\)
−0.489780 + 0.871846i \(0.662923\pi\)
\(822\) 0 0
\(823\) 21.1117 0.735909 0.367954 0.929844i \(-0.380058\pi\)
0.367954 + 0.929844i \(0.380058\pi\)
\(824\) 0 0
\(825\) 23.6232 0.822453
\(826\) 0 0
\(827\) 20.9063 0.726983 0.363491 0.931598i \(-0.381585\pi\)
0.363491 + 0.931598i \(0.381585\pi\)
\(828\) 0 0
\(829\) −40.8405 −1.41845 −0.709225 0.704982i \(-0.750955\pi\)
−0.709225 + 0.704982i \(0.750955\pi\)
\(830\) 0 0
\(831\) −1.36470 −0.0473410
\(832\) 0 0
\(833\) −23.3825 −0.810156
\(834\) 0 0
\(835\) −26.9536 −0.932768
\(836\) 0 0
\(837\) −4.67561 −0.161613
\(838\) 0 0
\(839\) 22.1992 0.766401 0.383200 0.923665i \(-0.374822\pi\)
0.383200 + 0.923665i \(0.374822\pi\)
\(840\) 0 0
\(841\) 76.6609 2.64348
\(842\) 0 0
\(843\) −28.7042 −0.988627
\(844\) 0 0
\(845\) −26.5476 −0.913266
\(846\) 0 0
\(847\) 12.2390 0.420538
\(848\) 0 0
\(849\) −11.5746 −0.397238
\(850\) 0 0
\(851\) 2.16214 0.0741173
\(852\) 0 0
\(853\) 48.3086 1.65406 0.827028 0.562160i \(-0.190030\pi\)
0.827028 + 0.562160i \(0.190030\pi\)
\(854\) 0 0
\(855\) −3.23327 −0.110575
\(856\) 0 0
\(857\) 35.4816 1.21203 0.606014 0.795454i \(-0.292767\pi\)
0.606014 + 0.795454i \(0.292767\pi\)
\(858\) 0 0
\(859\) −31.8670 −1.08729 −0.543644 0.839316i \(-0.682956\pi\)
−0.543644 + 0.839316i \(0.682956\pi\)
\(860\) 0 0
\(861\) −13.7124 −0.467318
\(862\) 0 0
\(863\) 22.3988 0.762464 0.381232 0.924479i \(-0.375500\pi\)
0.381232 + 0.924479i \(0.375500\pi\)
\(864\) 0 0
\(865\) −36.9191 −1.25529
\(866\) 0 0
\(867\) 8.54023 0.290041
\(868\) 0 0
\(869\) 38.6225 1.31018
\(870\) 0 0
\(871\) −7.68550 −0.260413
\(872\) 0 0
\(873\) 13.0122 0.440395
\(874\) 0 0
\(875\) −5.25182 −0.177544
\(876\) 0 0
\(877\) −38.3390 −1.29462 −0.647308 0.762228i \(-0.724105\pi\)
−0.647308 + 0.762228i \(0.724105\pi\)
\(878\) 0 0
\(879\) 63.2091 2.13199
\(880\) 0 0
\(881\) 40.5900 1.36751 0.683755 0.729712i \(-0.260346\pi\)
0.683755 + 0.729712i \(0.260346\pi\)
\(882\) 0 0
\(883\) −16.0431 −0.539892 −0.269946 0.962875i \(-0.587006\pi\)
−0.269946 + 0.962875i \(0.587006\pi\)
\(884\) 0 0
\(885\) 39.8357 1.33906
\(886\) 0 0
\(887\) −3.37948 −0.113472 −0.0567359 0.998389i \(-0.518069\pi\)
−0.0567359 + 0.998389i \(0.518069\pi\)
\(888\) 0 0
\(889\) −15.3643 −0.515303
\(890\) 0 0
\(891\) 59.8981 2.00666
\(892\) 0 0
\(893\) 7.30266 0.244374
\(894\) 0 0
\(895\) −4.24695 −0.141960
\(896\) 0 0
\(897\) −6.15095 −0.205374
\(898\) 0 0
\(899\) 13.0829 0.436338
\(900\) 0 0
\(901\) 3.58294 0.119365
\(902\) 0 0
\(903\) −3.99932 −0.133089
\(904\) 0 0
\(905\) −51.7678 −1.72082
\(906\) 0 0
\(907\) −2.67056 −0.0886745 −0.0443372 0.999017i \(-0.514118\pi\)
−0.0443372 + 0.999017i \(0.514118\pi\)
\(908\) 0 0
\(909\) 1.72971 0.0573710
\(910\) 0 0
\(911\) 18.7800 0.622209 0.311105 0.950376i \(-0.399301\pi\)
0.311105 + 0.950376i \(0.399301\pi\)
\(912\) 0 0
\(913\) 33.3875 1.10496
\(914\) 0 0
\(915\) 79.4473 2.62645
\(916\) 0 0
\(917\) −6.68232 −0.220670
\(918\) 0 0
\(919\) 43.8555 1.44666 0.723330 0.690503i \(-0.242611\pi\)
0.723330 + 0.690503i \(0.242611\pi\)
\(920\) 0 0
\(921\) −41.4130 −1.36460
\(922\) 0 0
\(923\) −0.230289 −0.00758007
\(924\) 0 0
\(925\) 2.71182 0.0891641
\(926\) 0 0
\(927\) −5.47184 −0.179719
\(928\) 0 0
\(929\) −30.2236 −0.991604 −0.495802 0.868436i \(-0.665126\pi\)
−0.495802 + 0.868436i \(0.665126\pi\)
\(930\) 0 0
\(931\) 6.52606 0.213883
\(932\) 0 0
\(933\) 32.4893 1.06365
\(934\) 0 0
\(935\) −51.3821 −1.68038
\(936\) 0 0
\(937\) −5.88444 −0.192236 −0.0961182 0.995370i \(-0.530643\pi\)
−0.0961182 + 0.995370i \(0.530643\pi\)
\(938\) 0 0
\(939\) 61.8090 2.01706
\(940\) 0 0
\(941\) −35.4073 −1.15424 −0.577122 0.816658i \(-0.695824\pi\)
−0.577122 + 0.816658i \(0.695824\pi\)
\(942\) 0 0
\(943\) 16.6132 0.541001
\(944\) 0 0
\(945\) 6.76076 0.219927
\(946\) 0 0
\(947\) 23.6233 0.767653 0.383827 0.923405i \(-0.374606\pi\)
0.383827 + 0.923405i \(0.374606\pi\)
\(948\) 0 0
\(949\) 16.5858 0.538399
\(950\) 0 0
\(951\) 19.2287 0.623532
\(952\) 0 0
\(953\) 8.57550 0.277788 0.138894 0.990307i \(-0.455645\pi\)
0.138894 + 0.990307i \(0.455645\pi\)
\(954\) 0 0
\(955\) −56.0227 −1.81285
\(956\) 0 0
\(957\) −113.136 −3.65718
\(958\) 0 0
\(959\) 8.02961 0.259290
\(960\) 0 0
\(961\) −29.3801 −0.947745
\(962\) 0 0
\(963\) 11.6319 0.374831
\(964\) 0 0
\(965\) −16.9232 −0.544776
\(966\) 0 0
\(967\) 52.5010 1.68832 0.844160 0.536092i \(-0.180100\pi\)
0.844160 + 0.536092i \(0.180100\pi\)
\(968\) 0 0
\(969\) 7.35114 0.236153
\(970\) 0 0
\(971\) −17.5733 −0.563955 −0.281977 0.959421i \(-0.590990\pi\)
−0.281977 + 0.959421i \(0.590990\pi\)
\(972\) 0 0
\(973\) 2.40540 0.0771135
\(974\) 0 0
\(975\) −7.71470 −0.247068
\(976\) 0 0
\(977\) −22.1812 −0.709641 −0.354820 0.934935i \(-0.615458\pi\)
−0.354820 + 0.934935i \(0.615458\pi\)
\(978\) 0 0
\(979\) −32.4070 −1.03573
\(980\) 0 0
\(981\) 3.15739 0.100808
\(982\) 0 0
\(983\) −61.4344 −1.95945 −0.979727 0.200336i \(-0.935797\pi\)
−0.979727 + 0.200336i \(0.935797\pi\)
\(984\) 0 0
\(985\) 39.8333 1.26919
\(986\) 0 0
\(987\) 10.3147 0.328321
\(988\) 0 0
\(989\) 4.84536 0.154073
\(990\) 0 0
\(991\) 4.45220 0.141429 0.0707143 0.997497i \(-0.477472\pi\)
0.0707143 + 0.997497i \(0.477472\pi\)
\(992\) 0 0
\(993\) −28.5063 −0.904620
\(994\) 0 0
\(995\) −56.2900 −1.78451
\(996\) 0 0
\(997\) −35.1944 −1.11462 −0.557308 0.830306i \(-0.688166\pi\)
−0.557308 + 0.830306i \(0.688166\pi\)
\(998\) 0 0
\(999\) 4.64152 0.146851
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 \(a_p\))