Properties

Label 4028.2.a.d.1.11
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 1.11
Root \(-0.346400\)
Character \(\chi\) = 4028.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.346400 q^{3} +0.720634 q^{5} -2.22237 q^{7} -2.88001 q^{9} +O(q^{10})\) \(q+0.346400 q^{3} +0.720634 q^{5} -2.22237 q^{7} -2.88001 q^{9} +2.78340 q^{11} +3.24197 q^{13} +0.249627 q^{15} -0.710604 q^{17} -1.00000 q^{19} -0.769828 q^{21} +1.68771 q^{23} -4.48069 q^{25} -2.03683 q^{27} -7.75104 q^{29} +1.25896 q^{31} +0.964168 q^{33} -1.60151 q^{35} +2.09938 q^{37} +1.12302 q^{39} -2.36373 q^{41} -10.0964 q^{43} -2.07543 q^{45} +0.417239 q^{47} -2.06108 q^{49} -0.246153 q^{51} +1.00000 q^{53} +2.00581 q^{55} -0.346400 q^{57} +3.65806 q^{59} +13.5228 q^{61} +6.40044 q^{63} +2.33627 q^{65} +8.76347 q^{67} +0.584623 q^{69} -2.98537 q^{71} -6.93629 q^{73} -1.55211 q^{75} -6.18573 q^{77} -8.08026 q^{79} +7.93446 q^{81} -5.16898 q^{83} -0.512086 q^{85} -2.68496 q^{87} -11.0222 q^{89} -7.20485 q^{91} +0.436103 q^{93} -0.720634 q^{95} -7.60335 q^{97} -8.01620 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} + O(q^{10}) \) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} - 11q^{11} + q^{13} - 20q^{15} - q^{17} - 19q^{19} - 10q^{21} - 16q^{23} + 21q^{25} - 4q^{27} - 9q^{31} + 7q^{33} - 25q^{37} - 25q^{39} + q^{41} - 41q^{43} - 27q^{45} - 29q^{47} + 14q^{49} - 24q^{51} + 19q^{53} - 28q^{55} + 4q^{57} - 42q^{59} + q^{61} - 41q^{63} + 2q^{65} - 41q^{67} - 25q^{69} - 20q^{73} + 11q^{75} - 19q^{77} - 38q^{79} + 23q^{81} - 36q^{83} - 58q^{85} - 30q^{87} - 25q^{89} - 55q^{91} - 38q^{93} + 2q^{95} - 13q^{97} + q^{99} + O(q^{100}) \)

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
\(3\) 0.346400 0.199994 0.0999970 0.994988i \(-0.468117\pi\)
0.0999970 + 0.994988i \(0.468117\pi\)
\(4\) 0 0
\(5\) 0.720634 0.322277 0.161139 0.986932i \(-0.448483\pi\)
0.161139 + 0.986932i \(0.448483\pi\)
\(6\) 0 0
\(7\) −2.22237 −0.839976 −0.419988 0.907530i \(-0.637966\pi\)
−0.419988 + 0.907530i \(0.637966\pi\)
\(8\) 0 0
\(9\) −2.88001 −0.960002
\(10\) 0 0
\(11\) 2.78340 0.839226 0.419613 0.907703i \(-0.362166\pi\)
0.419613 + 0.907703i \(0.362166\pi\)
\(12\) 0 0
\(13\) 3.24197 0.899161 0.449580 0.893240i \(-0.351574\pi\)
0.449580 + 0.893240i \(0.351574\pi\)
\(14\) 0 0
\(15\) 0.249627 0.0644535
\(16\) 0 0
\(17\) −0.710604 −0.172347 −0.0861734 0.996280i \(-0.527464\pi\)
−0.0861734 + 0.996280i \(0.527464\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) −0.769828 −0.167990
\(22\) 0 0
\(23\) 1.68771 0.351912 0.175956 0.984398i \(-0.443698\pi\)
0.175956 + 0.984398i \(0.443698\pi\)
\(24\) 0 0
\(25\) −4.48069 −0.896137
\(26\) 0 0
\(27\) −2.03683 −0.391989
\(28\) 0 0
\(29\) −7.75104 −1.43933 −0.719666 0.694320i \(-0.755705\pi\)
−0.719666 + 0.694320i \(0.755705\pi\)
\(30\) 0 0
\(31\) 1.25896 0.226116 0.113058 0.993588i \(-0.463935\pi\)
0.113058 + 0.993588i \(0.463935\pi\)
\(32\) 0 0
\(33\) 0.964168 0.167840
\(34\) 0 0
\(35\) −1.60151 −0.270705
\(36\) 0 0
\(37\) 2.09938 0.345137 0.172568 0.984998i \(-0.444793\pi\)
0.172568 + 0.984998i \(0.444793\pi\)
\(38\) 0 0
\(39\) 1.12302 0.179827
\(40\) 0 0
\(41\) −2.36373 −0.369153 −0.184576 0.982818i \(-0.559091\pi\)
−0.184576 + 0.982818i \(0.559091\pi\)
\(42\) 0 0
\(43\) −10.0964 −1.53969 −0.769843 0.638234i \(-0.779665\pi\)
−0.769843 + 0.638234i \(0.779665\pi\)
\(44\) 0 0
\(45\) −2.07543 −0.309387
\(46\) 0 0
\(47\) 0.417239 0.0608606 0.0304303 0.999537i \(-0.490312\pi\)
0.0304303 + 0.999537i \(0.490312\pi\)
\(48\) 0 0
\(49\) −2.06108 −0.294440
\(50\) 0 0
\(51\) −0.246153 −0.0344683
\(52\) 0 0
\(53\) 1.00000 0.137361
\(54\) 0 0
\(55\) 2.00581 0.270463
\(56\) 0 0
\(57\) −0.346400 −0.0458818
\(58\) 0 0
\(59\) 3.65806 0.476239 0.238120 0.971236i \(-0.423469\pi\)
0.238120 + 0.971236i \(0.423469\pi\)
\(60\) 0 0
\(61\) 13.5228 1.73142 0.865710 0.500545i \(-0.166867\pi\)
0.865710 + 0.500545i \(0.166867\pi\)
\(62\) 0 0
\(63\) 6.40044 0.806379
\(64\) 0 0
\(65\) 2.33627 0.289779
\(66\) 0 0
\(67\) 8.76347 1.07063 0.535314 0.844653i \(-0.320193\pi\)
0.535314 + 0.844653i \(0.320193\pi\)
\(68\) 0 0
\(69\) 0.584623 0.0703803
\(70\) 0 0
\(71\) −2.98537 −0.354298 −0.177149 0.984184i \(-0.556688\pi\)
−0.177149 + 0.984184i \(0.556688\pi\)
\(72\) 0 0
\(73\) −6.93629 −0.811832 −0.405916 0.913910i \(-0.633047\pi\)
−0.405916 + 0.913910i \(0.633047\pi\)
\(74\) 0 0
\(75\) −1.55211 −0.179222
\(76\) 0 0
\(77\) −6.18573 −0.704930
\(78\) 0 0
\(79\) −8.08026 −0.909100 −0.454550 0.890721i \(-0.650200\pi\)
−0.454550 + 0.890721i \(0.650200\pi\)
\(80\) 0 0
\(81\) 7.93446 0.881607
\(82\) 0 0
\(83\) −5.16898 −0.567369 −0.283684 0.958918i \(-0.591557\pi\)
−0.283684 + 0.958918i \(0.591557\pi\)
\(84\) 0 0
\(85\) −0.512086 −0.0555435
\(86\) 0 0
\(87\) −2.68496 −0.287858
\(88\) 0 0
\(89\) −11.0222 −1.16835 −0.584174 0.811628i \(-0.698582\pi\)
−0.584174 + 0.811628i \(0.698582\pi\)
\(90\) 0 0
\(91\) −7.20485 −0.755274
\(92\) 0 0
\(93\) 0.436103 0.0452218
\(94\) 0 0
\(95\) −0.720634 −0.0739355
\(96\) 0 0
\(97\) −7.60335 −0.772004 −0.386002 0.922498i \(-0.626144\pi\)
−0.386002 + 0.922498i \(0.626144\pi\)
\(98\) 0 0
\(99\) −8.01620 −0.805659
\(100\) 0 0
\(101\) −2.30523 −0.229379 −0.114689 0.993401i \(-0.536587\pi\)
−0.114689 + 0.993401i \(0.536587\pi\)
\(102\) 0 0
\(103\) −19.0290 −1.87499 −0.937493 0.348005i \(-0.886859\pi\)
−0.937493 + 0.348005i \(0.886859\pi\)
\(104\) 0 0
\(105\) −0.554764 −0.0541394
\(106\) 0 0
\(107\) −13.2535 −1.28126 −0.640632 0.767848i \(-0.721327\pi\)
−0.640632 + 0.767848i \(0.721327\pi\)
\(108\) 0 0
\(109\) 13.0744 1.25230 0.626149 0.779704i \(-0.284630\pi\)
0.626149 + 0.779704i \(0.284630\pi\)
\(110\) 0 0
\(111\) 0.727226 0.0690252
\(112\) 0 0
\(113\) 13.3979 1.26037 0.630185 0.776445i \(-0.282979\pi\)
0.630185 + 0.776445i \(0.282979\pi\)
\(114\) 0 0
\(115\) 1.21622 0.113413
\(116\) 0 0
\(117\) −9.33690 −0.863197
\(118\) 0 0
\(119\) 1.57922 0.144767
\(120\) 0 0
\(121\) −3.25270 −0.295700
\(122\) 0 0
\(123\) −0.818795 −0.0738283
\(124\) 0 0
\(125\) −6.83211 −0.611082
\(126\) 0 0
\(127\) 0.173674 0.0154111 0.00770555 0.999970i \(-0.497547\pi\)
0.00770555 + 0.999970i \(0.497547\pi\)
\(128\) 0 0
\(129\) −3.49739 −0.307928
\(130\) 0 0
\(131\) 11.6921 1.02154 0.510772 0.859716i \(-0.329360\pi\)
0.510772 + 0.859716i \(0.329360\pi\)
\(132\) 0 0
\(133\) 2.22237 0.192704
\(134\) 0 0
\(135\) −1.46781 −0.126329
\(136\) 0 0
\(137\) −6.00319 −0.512887 −0.256444 0.966559i \(-0.582551\pi\)
−0.256444 + 0.966559i \(0.582551\pi\)
\(138\) 0 0
\(139\) −10.0859 −0.855475 −0.427737 0.903903i \(-0.640689\pi\)
−0.427737 + 0.903903i \(0.640689\pi\)
\(140\) 0 0
\(141\) 0.144532 0.0121718
\(142\) 0 0
\(143\) 9.02369 0.754599
\(144\) 0 0
\(145\) −5.58566 −0.463864
\(146\) 0 0
\(147\) −0.713958 −0.0588863
\(148\) 0 0
\(149\) −13.5191 −1.10753 −0.553765 0.832673i \(-0.686810\pi\)
−0.553765 + 0.832673i \(0.686810\pi\)
\(150\) 0 0
\(151\) −11.0696 −0.900833 −0.450417 0.892819i \(-0.648725\pi\)
−0.450417 + 0.892819i \(0.648725\pi\)
\(152\) 0 0
\(153\) 2.04655 0.165453
\(154\) 0 0
\(155\) 0.907249 0.0728720
\(156\) 0 0
\(157\) 23.3388 1.86264 0.931318 0.364206i \(-0.118660\pi\)
0.931318 + 0.364206i \(0.118660\pi\)
\(158\) 0 0
\(159\) 0.346400 0.0274713
\(160\) 0 0
\(161\) −3.75072 −0.295598
\(162\) 0 0
\(163\) −7.42979 −0.581946 −0.290973 0.956731i \(-0.593979\pi\)
−0.290973 + 0.956731i \(0.593979\pi\)
\(164\) 0 0
\(165\) 0.694812 0.0540911
\(166\) 0 0
\(167\) −21.8387 −1.68993 −0.844964 0.534823i \(-0.820378\pi\)
−0.844964 + 0.534823i \(0.820378\pi\)
\(168\) 0 0
\(169\) −2.48963 −0.191510
\(170\) 0 0
\(171\) 2.88001 0.220240
\(172\) 0 0
\(173\) −22.6928 −1.72530 −0.862652 0.505798i \(-0.831198\pi\)
−0.862652 + 0.505798i \(0.831198\pi\)
\(174\) 0 0
\(175\) 9.95773 0.752734
\(176\) 0 0
\(177\) 1.26715 0.0952449
\(178\) 0 0
\(179\) −23.5535 −1.76047 −0.880235 0.474539i \(-0.842615\pi\)
−0.880235 + 0.474539i \(0.842615\pi\)
\(180\) 0 0
\(181\) −4.56883 −0.339598 −0.169799 0.985479i \(-0.554312\pi\)
−0.169799 + 0.985479i \(0.554312\pi\)
\(182\) 0 0
\(183\) 4.68430 0.346274
\(184\) 0 0
\(185\) 1.51289 0.111230
\(186\) 0 0
\(187\) −1.97789 −0.144638
\(188\) 0 0
\(189\) 4.52659 0.329261
\(190\) 0 0
\(191\) −21.0357 −1.52209 −0.761044 0.648700i \(-0.775313\pi\)
−0.761044 + 0.648700i \(0.775313\pi\)
\(192\) 0 0
\(193\) −6.44441 −0.463879 −0.231939 0.972730i \(-0.574507\pi\)
−0.231939 + 0.972730i \(0.574507\pi\)
\(194\) 0 0
\(195\) 0.809285 0.0579541
\(196\) 0 0
\(197\) 12.5334 0.892967 0.446484 0.894792i \(-0.352676\pi\)
0.446484 + 0.894792i \(0.352676\pi\)
\(198\) 0 0
\(199\) −17.7391 −1.25749 −0.628744 0.777612i \(-0.716431\pi\)
−0.628744 + 0.777612i \(0.716431\pi\)
\(200\) 0 0
\(201\) 3.03566 0.214119
\(202\) 0 0
\(203\) 17.2257 1.20900
\(204\) 0 0
\(205\) −1.70338 −0.118970
\(206\) 0 0
\(207\) −4.86062 −0.337836
\(208\) 0 0
\(209\) −2.78340 −0.192532
\(210\) 0 0
\(211\) 16.9787 1.16886 0.584430 0.811444i \(-0.301318\pi\)
0.584430 + 0.811444i \(0.301318\pi\)
\(212\) 0 0
\(213\) −1.03413 −0.0708575
\(214\) 0 0
\(215\) −7.27580 −0.496206
\(216\) 0 0
\(217\) −2.79787 −0.189932
\(218\) 0 0
\(219\) −2.40273 −0.162361
\(220\) 0 0
\(221\) −2.30376 −0.154968
\(222\) 0 0
\(223\) −5.56648 −0.372759 −0.186379 0.982478i \(-0.559675\pi\)
−0.186379 + 0.982478i \(0.559675\pi\)
\(224\) 0 0
\(225\) 12.9044 0.860294
\(226\) 0 0
\(227\) 13.7367 0.911737 0.455868 0.890047i \(-0.349329\pi\)
0.455868 + 0.890047i \(0.349329\pi\)
\(228\) 0 0
\(229\) 11.5539 0.763500 0.381750 0.924266i \(-0.375322\pi\)
0.381750 + 0.924266i \(0.375322\pi\)
\(230\) 0 0
\(231\) −2.14274 −0.140982
\(232\) 0 0
\(233\) 10.8863 0.713188 0.356594 0.934259i \(-0.383938\pi\)
0.356594 + 0.934259i \(0.383938\pi\)
\(234\) 0 0
\(235\) 0.300677 0.0196140
\(236\) 0 0
\(237\) −2.79900 −0.181815
\(238\) 0 0
\(239\) 17.4246 1.12710 0.563550 0.826082i \(-0.309435\pi\)
0.563550 + 0.826082i \(0.309435\pi\)
\(240\) 0 0
\(241\) 3.99167 0.257126 0.128563 0.991701i \(-0.458964\pi\)
0.128563 + 0.991701i \(0.458964\pi\)
\(242\) 0 0
\(243\) 8.85899 0.568305
\(244\) 0 0
\(245\) −1.48529 −0.0948914
\(246\) 0 0
\(247\) −3.24197 −0.206282
\(248\) 0 0
\(249\) −1.79053 −0.113470
\(250\) 0 0
\(251\) −5.80686 −0.366526 −0.183263 0.983064i \(-0.558666\pi\)
−0.183263 + 0.983064i \(0.558666\pi\)
\(252\) 0 0
\(253\) 4.69757 0.295334
\(254\) 0 0
\(255\) −0.177386 −0.0111084
\(256\) 0 0
\(257\) 6.93977 0.432891 0.216446 0.976295i \(-0.430554\pi\)
0.216446 + 0.976295i \(0.430554\pi\)
\(258\) 0 0
\(259\) −4.66560 −0.289906
\(260\) 0 0
\(261\) 22.3231 1.38176
\(262\) 0 0
\(263\) 5.45091 0.336118 0.168059 0.985777i \(-0.446250\pi\)
0.168059 + 0.985777i \(0.446250\pi\)
\(264\) 0 0
\(265\) 0.720634 0.0442682
\(266\) 0 0
\(267\) −3.81808 −0.233663
\(268\) 0 0
\(269\) −8.39226 −0.511685 −0.255842 0.966718i \(-0.582353\pi\)
−0.255842 + 0.966718i \(0.582353\pi\)
\(270\) 0 0
\(271\) 6.92172 0.420465 0.210232 0.977651i \(-0.432578\pi\)
0.210232 + 0.977651i \(0.432578\pi\)
\(272\) 0 0
\(273\) −2.49576 −0.151050
\(274\) 0 0
\(275\) −12.4715 −0.752062
\(276\) 0 0
\(277\) 23.9822 1.44095 0.720475 0.693481i \(-0.243924\pi\)
0.720475 + 0.693481i \(0.243924\pi\)
\(278\) 0 0
\(279\) −3.62581 −0.217072
\(280\) 0 0
\(281\) 24.8257 1.48097 0.740487 0.672070i \(-0.234595\pi\)
0.740487 + 0.672070i \(0.234595\pi\)
\(282\) 0 0
\(283\) −13.0293 −0.774514 −0.387257 0.921972i \(-0.626577\pi\)
−0.387257 + 0.921972i \(0.626577\pi\)
\(284\) 0 0
\(285\) −0.249627 −0.0147867
\(286\) 0 0
\(287\) 5.25308 0.310079
\(288\) 0 0
\(289\) −16.4950 −0.970297
\(290\) 0 0
\(291\) −2.63380 −0.154396
\(292\) 0 0
\(293\) 2.98307 0.174273 0.0871363 0.996196i \(-0.472228\pi\)
0.0871363 + 0.996196i \(0.472228\pi\)
\(294\) 0 0
\(295\) 2.63612 0.153481
\(296\) 0 0
\(297\) −5.66932 −0.328967
\(298\) 0 0
\(299\) 5.47151 0.316426
\(300\) 0 0
\(301\) 22.4379 1.29330
\(302\) 0 0
\(303\) −0.798531 −0.0458744
\(304\) 0 0
\(305\) 9.74501 0.557998
\(306\) 0 0
\(307\) 27.7305 1.58266 0.791331 0.611388i \(-0.209388\pi\)
0.791331 + 0.611388i \(0.209388\pi\)
\(308\) 0 0
\(309\) −6.59165 −0.374986
\(310\) 0 0
\(311\) −17.2006 −0.975356 −0.487678 0.873023i \(-0.662156\pi\)
−0.487678 + 0.873023i \(0.662156\pi\)
\(312\) 0 0
\(313\) −24.6078 −1.39091 −0.695457 0.718568i \(-0.744798\pi\)
−0.695457 + 0.718568i \(0.744798\pi\)
\(314\) 0 0
\(315\) 4.61237 0.259878
\(316\) 0 0
\(317\) −11.6548 −0.654600 −0.327300 0.944920i \(-0.606139\pi\)
−0.327300 + 0.944920i \(0.606139\pi\)
\(318\) 0 0
\(319\) −21.5742 −1.20792
\(320\) 0 0
\(321\) −4.59101 −0.256245
\(322\) 0 0
\(323\) 0.710604 0.0395391
\(324\) 0 0
\(325\) −14.5263 −0.805772
\(326\) 0 0
\(327\) 4.52896 0.250452
\(328\) 0 0
\(329\) −0.927259 −0.0511215
\(330\) 0 0
\(331\) −9.23557 −0.507633 −0.253816 0.967252i \(-0.581686\pi\)
−0.253816 + 0.967252i \(0.581686\pi\)
\(332\) 0 0
\(333\) −6.04624 −0.331332
\(334\) 0 0
\(335\) 6.31525 0.345039
\(336\) 0 0
\(337\) −10.5639 −0.575451 −0.287725 0.957713i \(-0.592899\pi\)
−0.287725 + 0.957713i \(0.592899\pi\)
\(338\) 0 0
\(339\) 4.64104 0.252066
\(340\) 0 0
\(341\) 3.50418 0.189762
\(342\) 0 0
\(343\) 20.1371 1.08730
\(344\) 0 0
\(345\) 0.421299 0.0226820
\(346\) 0 0
\(347\) 22.2507 1.19448 0.597241 0.802062i \(-0.296264\pi\)
0.597241 + 0.802062i \(0.296264\pi\)
\(348\) 0 0
\(349\) −29.6577 −1.58754 −0.793771 0.608217i \(-0.791885\pi\)
−0.793771 + 0.608217i \(0.791885\pi\)
\(350\) 0 0
\(351\) −6.60335 −0.352461
\(352\) 0 0
\(353\) 1.59015 0.0846349 0.0423175 0.999104i \(-0.486526\pi\)
0.0423175 + 0.999104i \(0.486526\pi\)
\(354\) 0 0
\(355\) −2.15136 −0.114182
\(356\) 0 0
\(357\) 0.547043 0.0289526
\(358\) 0 0
\(359\) −10.0570 −0.530790 −0.265395 0.964140i \(-0.585502\pi\)
−0.265395 + 0.964140i \(0.585502\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −1.12673 −0.0591382
\(364\) 0 0
\(365\) −4.99853 −0.261635
\(366\) 0 0
\(367\) −14.6349 −0.763934 −0.381967 0.924176i \(-0.624753\pi\)
−0.381967 + 0.924176i \(0.624753\pi\)
\(368\) 0 0
\(369\) 6.80756 0.354387
\(370\) 0 0
\(371\) −2.22237 −0.115380
\(372\) 0 0
\(373\) −7.00123 −0.362510 −0.181255 0.983436i \(-0.558016\pi\)
−0.181255 + 0.983436i \(0.558016\pi\)
\(374\) 0 0
\(375\) −2.36664 −0.122213
\(376\) 0 0
\(377\) −25.1286 −1.29419
\(378\) 0 0
\(379\) 4.88858 0.251110 0.125555 0.992087i \(-0.459929\pi\)
0.125555 + 0.992087i \(0.459929\pi\)
\(380\) 0 0
\(381\) 0.0601607 0.00308213
\(382\) 0 0
\(383\) −11.8258 −0.604272 −0.302136 0.953265i \(-0.597700\pi\)
−0.302136 + 0.953265i \(0.597700\pi\)
\(384\) 0 0
\(385\) −4.45765 −0.227183
\(386\) 0 0
\(387\) 29.0777 1.47810
\(388\) 0 0
\(389\) 13.6778 0.693489 0.346745 0.937960i \(-0.387287\pi\)
0.346745 + 0.937960i \(0.387287\pi\)
\(390\) 0 0
\(391\) −1.19929 −0.0606509
\(392\) 0 0
\(393\) 4.05014 0.204303
\(394\) 0 0
\(395\) −5.82291 −0.292982
\(396\) 0 0
\(397\) 29.4367 1.47739 0.738694 0.674041i \(-0.235443\pi\)
0.738694 + 0.674041i \(0.235443\pi\)
\(398\) 0 0
\(399\) 0.769828 0.0385396
\(400\) 0 0
\(401\) −10.4277 −0.520736 −0.260368 0.965510i \(-0.583844\pi\)
−0.260368 + 0.965510i \(0.583844\pi\)
\(402\) 0 0
\(403\) 4.08151 0.203314
\(404\) 0 0
\(405\) 5.71784 0.284122
\(406\) 0 0
\(407\) 5.84342 0.289648
\(408\) 0 0
\(409\) 25.9306 1.28219 0.641093 0.767463i \(-0.278481\pi\)
0.641093 + 0.767463i \(0.278481\pi\)
\(410\) 0 0
\(411\) −2.07950 −0.102574
\(412\) 0 0
\(413\) −8.12956 −0.400029
\(414\) 0 0
\(415\) −3.72494 −0.182850
\(416\) 0 0
\(417\) −3.49375 −0.171090
\(418\) 0 0
\(419\) 26.2995 1.28482 0.642408 0.766363i \(-0.277935\pi\)
0.642408 + 0.766363i \(0.277935\pi\)
\(420\) 0 0
\(421\) 37.3871 1.82214 0.911068 0.412256i \(-0.135259\pi\)
0.911068 + 0.412256i \(0.135259\pi\)
\(422\) 0 0
\(423\) −1.20165 −0.0584263
\(424\) 0 0
\(425\) 3.18399 0.154446
\(426\) 0 0
\(427\) −30.0527 −1.45435
\(428\) 0 0
\(429\) 3.12580 0.150915
\(430\) 0 0
\(431\) 3.23482 0.155816 0.0779080 0.996961i \(-0.475176\pi\)
0.0779080 + 0.996961i \(0.475176\pi\)
\(432\) 0 0
\(433\) 5.62682 0.270408 0.135204 0.990818i \(-0.456831\pi\)
0.135204 + 0.990818i \(0.456831\pi\)
\(434\) 0 0
\(435\) −1.93487 −0.0927700
\(436\) 0 0
\(437\) −1.68771 −0.0807342
\(438\) 0 0
\(439\) −32.0845 −1.53131 −0.765654 0.643252i \(-0.777585\pi\)
−0.765654 + 0.643252i \(0.777585\pi\)
\(440\) 0 0
\(441\) 5.93593 0.282663
\(442\) 0 0
\(443\) −7.29854 −0.346764 −0.173382 0.984855i \(-0.555470\pi\)
−0.173382 + 0.984855i \(0.555470\pi\)
\(444\) 0 0
\(445\) −7.94296 −0.376532
\(446\) 0 0
\(447\) −4.68302 −0.221499
\(448\) 0 0
\(449\) −15.1789 −0.716336 −0.358168 0.933657i \(-0.616598\pi\)
−0.358168 + 0.933657i \(0.616598\pi\)
\(450\) 0 0
\(451\) −6.57920 −0.309802
\(452\) 0 0
\(453\) −3.83451 −0.180161
\(454\) 0 0
\(455\) −5.19206 −0.243408
\(456\) 0 0
\(457\) 28.3934 1.32819 0.664094 0.747649i \(-0.268818\pi\)
0.664094 + 0.747649i \(0.268818\pi\)
\(458\) 0 0
\(459\) 1.44738 0.0675580
\(460\) 0 0
\(461\) 19.3896 0.903061 0.451531 0.892256i \(-0.350878\pi\)
0.451531 + 0.892256i \(0.350878\pi\)
\(462\) 0 0
\(463\) −32.9603 −1.53180 −0.765898 0.642962i \(-0.777705\pi\)
−0.765898 + 0.642962i \(0.777705\pi\)
\(464\) 0 0
\(465\) 0.314271 0.0145740
\(466\) 0 0
\(467\) −4.22530 −0.195524 −0.0977618 0.995210i \(-0.531168\pi\)
−0.0977618 + 0.995210i \(0.531168\pi\)
\(468\) 0 0
\(469\) −19.4756 −0.899302
\(470\) 0 0
\(471\) 8.08454 0.372516
\(472\) 0 0
\(473\) −28.1023 −1.29214
\(474\) 0 0
\(475\) 4.48069 0.205588
\(476\) 0 0
\(477\) −2.88001 −0.131866
\(478\) 0 0
\(479\) −35.3560 −1.61546 −0.807728 0.589556i \(-0.799303\pi\)
−0.807728 + 0.589556i \(0.799303\pi\)
\(480\) 0 0
\(481\) 6.80614 0.310333
\(482\) 0 0
\(483\) −1.29925 −0.0591178
\(484\) 0 0
\(485\) −5.47924 −0.248799
\(486\) 0 0
\(487\) −8.79732 −0.398645 −0.199322 0.979934i \(-0.563874\pi\)
−0.199322 + 0.979934i \(0.563874\pi\)
\(488\) 0 0
\(489\) −2.57368 −0.116386
\(490\) 0 0
\(491\) 3.37429 0.152280 0.0761398 0.997097i \(-0.475740\pi\)
0.0761398 + 0.997097i \(0.475740\pi\)
\(492\) 0 0
\(493\) 5.50792 0.248064
\(494\) 0 0
\(495\) −5.77675 −0.259646
\(496\) 0 0
\(497\) 6.63459 0.297602
\(498\) 0 0
\(499\) 16.6930 0.747281 0.373640 0.927574i \(-0.378109\pi\)
0.373640 + 0.927574i \(0.378109\pi\)
\(500\) 0 0
\(501\) −7.56492 −0.337976
\(502\) 0 0
\(503\) −13.3813 −0.596641 −0.298321 0.954466i \(-0.596426\pi\)
−0.298321 + 0.954466i \(0.596426\pi\)
\(504\) 0 0
\(505\) −1.66123 −0.0739236
\(506\) 0 0
\(507\) −0.862406 −0.0383008
\(508\) 0 0
\(509\) 8.34006 0.369667 0.184833 0.982770i \(-0.440825\pi\)
0.184833 + 0.982770i \(0.440825\pi\)
\(510\) 0 0
\(511\) 15.4150 0.681919
\(512\) 0 0
\(513\) 2.03683 0.0899284
\(514\) 0 0
\(515\) −13.7130 −0.604265
\(516\) 0 0
\(517\) 1.16134 0.0510758
\(518\) 0 0
\(519\) −7.86079 −0.345050
\(520\) 0 0
\(521\) −10.6310 −0.465755 −0.232877 0.972506i \(-0.574814\pi\)
−0.232877 + 0.972506i \(0.574814\pi\)
\(522\) 0 0
\(523\) −24.3580 −1.06510 −0.532550 0.846399i \(-0.678766\pi\)
−0.532550 + 0.846399i \(0.678766\pi\)
\(524\) 0 0
\(525\) 3.44936 0.150542
\(526\) 0 0
\(527\) −0.894622 −0.0389703
\(528\) 0 0
\(529\) −20.1516 −0.876158
\(530\) 0 0
\(531\) −10.5352 −0.457191
\(532\) 0 0
\(533\) −7.66314 −0.331928
\(534\) 0 0
\(535\) −9.55092 −0.412922
\(536\) 0 0
\(537\) −8.15892 −0.352083
\(538\) 0 0
\(539\) −5.73681 −0.247102
\(540\) 0 0
\(541\) 44.0282 1.89292 0.946460 0.322820i \(-0.104631\pi\)
0.946460 + 0.322820i \(0.104631\pi\)
\(542\) 0 0
\(543\) −1.58264 −0.0679176
\(544\) 0 0
\(545\) 9.42184 0.403587
\(546\) 0 0
\(547\) 24.5917 1.05146 0.525732 0.850650i \(-0.323791\pi\)
0.525732 + 0.850650i \(0.323791\pi\)
\(548\) 0 0
\(549\) −38.9458 −1.66217
\(550\) 0 0
\(551\) 7.75104 0.330205
\(552\) 0 0
\(553\) 17.9573 0.763623
\(554\) 0 0
\(555\) 0.524064 0.0222453
\(556\) 0 0
\(557\) 15.4790 0.655866 0.327933 0.944701i \(-0.393648\pi\)
0.327933 + 0.944701i \(0.393648\pi\)
\(558\) 0 0
\(559\) −32.7322 −1.38442
\(560\) 0 0
\(561\) −0.685142 −0.0289267
\(562\) 0 0
\(563\) 43.6618 1.84013 0.920063 0.391771i \(-0.128137\pi\)
0.920063 + 0.391771i \(0.128137\pi\)
\(564\) 0 0
\(565\) 9.65500 0.406189
\(566\) 0 0
\(567\) −17.6333 −0.740529
\(568\) 0 0
\(569\) 29.6225 1.24184 0.620920 0.783874i \(-0.286759\pi\)
0.620920 + 0.783874i \(0.286759\pi\)
\(570\) 0 0
\(571\) −7.16244 −0.299739 −0.149869 0.988706i \(-0.547885\pi\)
−0.149869 + 0.988706i \(0.547885\pi\)
\(572\) 0 0
\(573\) −7.28676 −0.304409
\(574\) 0 0
\(575\) −7.56211 −0.315362
\(576\) 0 0
\(577\) −19.7602 −0.822629 −0.411314 0.911494i \(-0.634930\pi\)
−0.411314 + 0.911494i \(0.634930\pi\)
\(578\) 0 0
\(579\) −2.23234 −0.0927730
\(580\) 0 0
\(581\) 11.4874 0.476576
\(582\) 0 0
\(583\) 2.78340 0.115277
\(584\) 0 0
\(585\) −6.72849 −0.278189
\(586\) 0 0
\(587\) 19.4507 0.802817 0.401408 0.915899i \(-0.368521\pi\)
0.401408 + 0.915899i \(0.368521\pi\)
\(588\) 0 0
\(589\) −1.25896 −0.0518745
\(590\) 0 0
\(591\) 4.34156 0.178588
\(592\) 0 0
\(593\) −0.0325528 −0.00133678 −0.000668392 1.00000i \(-0.500213\pi\)
−0.000668392 1.00000i \(0.500213\pi\)
\(594\) 0 0
\(595\) 1.13804 0.0466552
\(596\) 0 0
\(597\) −6.14480 −0.251490
\(598\) 0 0
\(599\) 42.8235 1.74972 0.874861 0.484375i \(-0.160953\pi\)
0.874861 + 0.484375i \(0.160953\pi\)
\(600\) 0 0
\(601\) 19.4942 0.795183 0.397592 0.917562i \(-0.369846\pi\)
0.397592 + 0.917562i \(0.369846\pi\)
\(602\) 0 0
\(603\) −25.2388 −1.02781
\(604\) 0 0
\(605\) −2.34401 −0.0952974
\(606\) 0 0
\(607\) −44.3556 −1.80034 −0.900169 0.435540i \(-0.856557\pi\)
−0.900169 + 0.435540i \(0.856557\pi\)
\(608\) 0 0
\(609\) 5.96696 0.241794
\(610\) 0 0
\(611\) 1.35268 0.0547235
\(612\) 0 0
\(613\) −23.5469 −0.951050 −0.475525 0.879702i \(-0.657742\pi\)
−0.475525 + 0.879702i \(0.657742\pi\)
\(614\) 0 0
\(615\) −0.590052 −0.0237932
\(616\) 0 0
\(617\) −2.64021 −0.106291 −0.0531454 0.998587i \(-0.516925\pi\)
−0.0531454 + 0.998587i \(0.516925\pi\)
\(618\) 0 0
\(619\) 24.1575 0.970973 0.485486 0.874244i \(-0.338643\pi\)
0.485486 + 0.874244i \(0.338643\pi\)
\(620\) 0 0
\(621\) −3.43759 −0.137946
\(622\) 0 0
\(623\) 24.4953 0.981385
\(624\) 0 0
\(625\) 17.4800 0.699199
\(626\) 0 0
\(627\) −0.964168 −0.0385052
\(628\) 0 0
\(629\) −1.49183 −0.0594832
\(630\) 0 0
\(631\) 22.5486 0.897647 0.448823 0.893620i \(-0.351843\pi\)
0.448823 + 0.893620i \(0.351843\pi\)
\(632\) 0 0
\(633\) 5.88141 0.233765
\(634\) 0 0
\(635\) 0.125156 0.00496665
\(636\) 0 0
\(637\) −6.68197 −0.264749
\(638\) 0 0
\(639\) 8.59789 0.340127
\(640\) 0 0
\(641\) 14.0639 0.555490 0.277745 0.960655i \(-0.410413\pi\)
0.277745 + 0.960655i \(0.410413\pi\)
\(642\) 0 0
\(643\) −8.54719 −0.337068 −0.168534 0.985696i \(-0.553903\pi\)
−0.168534 + 0.985696i \(0.553903\pi\)
\(644\) 0 0
\(645\) −2.52034 −0.0992381
\(646\) 0 0
\(647\) −17.2190 −0.676948 −0.338474 0.940976i \(-0.609911\pi\)
−0.338474 + 0.940976i \(0.609911\pi\)
\(648\) 0 0
\(649\) 10.1818 0.399672
\(650\) 0 0
\(651\) −0.969181 −0.0379852
\(652\) 0 0
\(653\) 42.1998 1.65141 0.825704 0.564104i \(-0.190778\pi\)
0.825704 + 0.564104i \(0.190778\pi\)
\(654\) 0 0
\(655\) 8.42573 0.329220
\(656\) 0 0
\(657\) 19.9766 0.779360
\(658\) 0 0
\(659\) −32.4581 −1.26439 −0.632195 0.774809i \(-0.717846\pi\)
−0.632195 + 0.774809i \(0.717846\pi\)
\(660\) 0 0
\(661\) 14.3667 0.558801 0.279400 0.960175i \(-0.409864\pi\)
0.279400 + 0.960175i \(0.409864\pi\)
\(662\) 0 0
\(663\) −0.798021 −0.0309926
\(664\) 0 0
\(665\) 1.60151 0.0621040
\(666\) 0 0
\(667\) −13.0815 −0.506518
\(668\) 0 0
\(669\) −1.92823 −0.0745495
\(670\) 0 0
\(671\) 37.6394 1.45305
\(672\) 0 0
\(673\) −46.6634 −1.79874 −0.899371 0.437186i \(-0.855975\pi\)
−0.899371 + 0.437186i \(0.855975\pi\)
\(674\) 0 0
\(675\) 9.12641 0.351276
\(676\) 0 0
\(677\) 23.6579 0.909247 0.454624 0.890684i \(-0.349774\pi\)
0.454624 + 0.890684i \(0.349774\pi\)
\(678\) 0 0
\(679\) 16.8974 0.648465
\(680\) 0 0
\(681\) 4.75839 0.182342
\(682\) 0 0
\(683\) 32.4841 1.24297 0.621484 0.783427i \(-0.286530\pi\)
0.621484 + 0.783427i \(0.286530\pi\)
\(684\) 0 0
\(685\) −4.32610 −0.165292
\(686\) 0 0
\(687\) 4.00225 0.152695
\(688\) 0 0
\(689\) 3.24197 0.123509
\(690\) 0 0
\(691\) −42.1576 −1.60375 −0.801875 0.597491i \(-0.796164\pi\)
−0.801875 + 0.597491i \(0.796164\pi\)
\(692\) 0 0
\(693\) 17.8150 0.676734
\(694\) 0 0
\(695\) −7.26824 −0.275700
\(696\) 0 0
\(697\) 1.67968 0.0636223
\(698\) 0 0
\(699\) 3.77103 0.142633
\(700\) 0 0
\(701\) −14.1908 −0.535979 −0.267990 0.963422i \(-0.586359\pi\)
−0.267990 + 0.963422i \(0.586359\pi\)
\(702\) 0 0
\(703\) −2.09938 −0.0791798
\(704\) 0 0
\(705\) 0.104154 0.00392268
\(706\) 0 0
\(707\) 5.12307 0.192673
\(708\) 0 0
\(709\) 20.5555 0.771978 0.385989 0.922503i \(-0.373860\pi\)
0.385989 + 0.922503i \(0.373860\pi\)
\(710\) 0 0
\(711\) 23.2712 0.872739
\(712\) 0 0
\(713\) 2.12476 0.0795729
\(714\) 0 0
\(715\) 6.50278 0.243190
\(716\) 0 0
\(717\) 6.03586 0.225413
\(718\) 0 0
\(719\) 36.3223 1.35459 0.677296 0.735710i \(-0.263151\pi\)
0.677296 + 0.735710i \(0.263151\pi\)
\(720\) 0 0
\(721\) 42.2895 1.57494
\(722\) 0 0
\(723\) 1.38271 0.0514236
\(724\) 0 0
\(725\) 34.7300 1.28984
\(726\) 0 0
\(727\) 35.0925 1.30151 0.650755 0.759288i \(-0.274452\pi\)
0.650755 + 0.759288i \(0.274452\pi\)
\(728\) 0 0
\(729\) −20.7346 −0.767950
\(730\) 0 0
\(731\) 7.17454 0.265360
\(732\) 0 0
\(733\) 20.8515 0.770168 0.385084 0.922882i \(-0.374172\pi\)
0.385084 + 0.922882i \(0.374172\pi\)
\(734\) 0 0
\(735\) −0.514503 −0.0189777
\(736\) 0 0
\(737\) 24.3922 0.898499
\(738\) 0 0
\(739\) 31.3770 1.15422 0.577110 0.816666i \(-0.304180\pi\)
0.577110 + 0.816666i \(0.304180\pi\)
\(740\) 0 0
\(741\) −1.12302 −0.0412551
\(742\) 0 0
\(743\) 9.35265 0.343116 0.171558 0.985174i \(-0.445120\pi\)
0.171558 + 0.985174i \(0.445120\pi\)
\(744\) 0 0
\(745\) −9.74235 −0.356932
\(746\) 0 0
\(747\) 14.8867 0.544675
\(748\) 0 0
\(749\) 29.4541 1.07623
\(750\) 0 0
\(751\) 9.20700 0.335968 0.167984 0.985790i \(-0.446274\pi\)
0.167984 + 0.985790i \(0.446274\pi\)
\(752\) 0 0
\(753\) −2.01149 −0.0733029
\(754\) 0 0
\(755\) −7.97715 −0.290318
\(756\) 0 0
\(757\) −29.3581 −1.06704 −0.533519 0.845788i \(-0.679131\pi\)
−0.533519 + 0.845788i \(0.679131\pi\)
\(758\) 0 0
\(759\) 1.62724 0.0590650
\(760\) 0 0
\(761\) 54.0730 1.96015 0.980073 0.198639i \(-0.0636522\pi\)
0.980073 + 0.198639i \(0.0636522\pi\)
\(762\) 0 0
\(763\) −29.0561 −1.05190
\(764\) 0 0
\(765\) 1.47481 0.0533219
\(766\) 0 0
\(767\) 11.8593 0.428215
\(768\) 0 0
\(769\) −7.26019 −0.261809 −0.130905 0.991395i \(-0.541788\pi\)
−0.130905 + 0.991395i \(0.541788\pi\)
\(770\) 0 0
\(771\) 2.40394 0.0865756
\(772\) 0 0
\(773\) −11.8109 −0.424810 −0.212405 0.977182i \(-0.568130\pi\)
−0.212405 + 0.977182i \(0.568130\pi\)
\(774\) 0 0
\(775\) −5.64100 −0.202631
\(776\) 0 0
\(777\) −1.61616 −0.0579796
\(778\) 0 0
\(779\) 2.36373 0.0846894
\(780\) 0 0
\(781\) −8.30948 −0.297336
\(782\) 0 0
\(783\) 15.7876 0.564202
\(784\) 0 0
\(785\) 16.8187 0.600286
\(786\) 0 0
\(787\) 18.5851 0.662488 0.331244 0.943545i \(-0.392532\pi\)
0.331244 + 0.943545i \(0.392532\pi\)
\(788\) 0 0
\(789\) 1.88819 0.0672215
\(790\) 0 0
\(791\) −29.7751 −1.05868
\(792\) 0 0
\(793\) 43.8406 1.55683
\(794\) 0 0
\(795\) 0.249627 0.00885337
\(796\) 0 0
\(797\) −15.5975 −0.552493 −0.276246 0.961087i \(-0.589091\pi\)
−0.276246 + 0.961087i \(0.589091\pi\)
\(798\) 0 0
\(799\) −0.296492 −0.0104891
\(800\) 0 0
\(801\) 31.7440 1.12162
\(802\) 0 0
\(803\) −19.3065 −0.681310
\(804\) 0 0
\(805\) −2.70289 −0.0952645
\(806\) 0 0
\(807\) −2.90708 −0.102334
\(808\) 0 0
\(809\) −3.11526 −0.109527 −0.0547634 0.998499i \(-0.517440\pi\)
−0.0547634 + 0.998499i \(0.517440\pi\)
\(810\) 0 0
\(811\) −51.2793 −1.80066 −0.900330 0.435208i \(-0.856675\pi\)
−0.900330 + 0.435208i \(0.856675\pi\)
\(812\) 0 0
\(813\) 2.39768 0.0840904
\(814\) 0 0
\(815\) −5.35416 −0.187548
\(816\) 0 0
\(817\) 10.0964 0.353228
\(818\) 0 0
\(819\) 20.7500 0.725065
\(820\) 0 0
\(821\) −54.8738 −1.91511 −0.957555 0.288250i \(-0.906927\pi\)
−0.957555 + 0.288250i \(0.906927\pi\)
\(822\) 0 0
\(823\) −15.5407 −0.541714 −0.270857 0.962620i \(-0.587307\pi\)
−0.270857 + 0.962620i \(0.587307\pi\)
\(824\) 0 0
\(825\) −4.32014 −0.150408
\(826\) 0 0
\(827\) 39.2172 1.36372 0.681858 0.731485i \(-0.261172\pi\)
0.681858 + 0.731485i \(0.261172\pi\)
\(828\) 0 0
\(829\) −11.0077 −0.382312 −0.191156 0.981560i \(-0.561224\pi\)
−0.191156 + 0.981560i \(0.561224\pi\)
\(830\) 0 0
\(831\) 8.30742 0.288181
\(832\) 0 0
\(833\) 1.46461 0.0507458
\(834\) 0 0
\(835\) −15.7377 −0.544626
\(836\) 0 0
\(837\) −2.56429 −0.0886348
\(838\) 0 0
\(839\) −44.4047 −1.53302 −0.766510 0.642233i \(-0.778008\pi\)
−0.766510 + 0.642233i \(0.778008\pi\)
\(840\) 0 0
\(841\) 31.0786 1.07168
\(842\) 0 0
\(843\) 8.59960 0.296186
\(844\) 0 0
\(845\) −1.79411 −0.0617192
\(846\) 0 0
\(847\) 7.22869 0.248381
\(848\) 0 0
\(849\) −4.51336 −0.154898
\(850\) 0 0
\(851\) 3.54315 0.121458
\(852\) 0 0
\(853\) 7.69793 0.263572 0.131786 0.991278i \(-0.457929\pi\)
0.131786 + 0.991278i \(0.457929\pi\)
\(854\) 0 0
\(855\) 2.07543 0.0709783
\(856\) 0 0
\(857\) −42.0258 −1.43557 −0.717787 0.696263i \(-0.754845\pi\)
−0.717787 + 0.696263i \(0.754845\pi\)
\(858\) 0 0
\(859\) 36.0136 1.22877 0.614384 0.789007i \(-0.289404\pi\)
0.614384 + 0.789007i \(0.289404\pi\)
\(860\) 0 0
\(861\) 1.81966 0.0620140
\(862\) 0 0
\(863\) 44.2147 1.50509 0.752543 0.658544i \(-0.228827\pi\)
0.752543 + 0.658544i \(0.228827\pi\)
\(864\) 0 0
\(865\) −16.3532 −0.556026
\(866\) 0 0
\(867\) −5.71388 −0.194053
\(868\) 0 0
\(869\) −22.4906 −0.762941
\(870\) 0 0
\(871\) 28.4109 0.962667
\(872\) 0 0
\(873\) 21.8977 0.741125
\(874\) 0 0
\(875\) 15.1835 0.513294
\(876\) 0 0
\(877\) −39.2047 −1.32385 −0.661923 0.749571i \(-0.730260\pi\)
−0.661923 + 0.749571i \(0.730260\pi\)
\(878\) 0 0
\(879\) 1.03333 0.0348535
\(880\) 0 0
\(881\) −18.2309 −0.614215 −0.307108 0.951675i \(-0.599361\pi\)
−0.307108 + 0.951675i \(0.599361\pi\)
\(882\) 0 0
\(883\) −25.2739 −0.850536 −0.425268 0.905068i \(-0.639820\pi\)
−0.425268 + 0.905068i \(0.639820\pi\)
\(884\) 0 0
\(885\) 0.913152 0.0306953
\(886\) 0 0
\(887\) −14.0379 −0.471348 −0.235674 0.971832i \(-0.575730\pi\)
−0.235674 + 0.971832i \(0.575730\pi\)
\(888\) 0 0
\(889\) −0.385968 −0.0129450
\(890\) 0 0
\(891\) 22.0848 0.739867
\(892\) 0 0
\(893\) −0.417239 −0.0139624
\(894\) 0 0
\(895\) −16.9734 −0.567359
\(896\) 0 0
\(897\) 1.89533 0.0632832
\(898\) 0 0
\(899\) −9.75824 −0.325456
\(900\) 0 0
\(901\) −0.710604 −0.0236737
\(902\) 0 0
\(903\) 7.77248 0.258652
\(904\) 0 0
\(905\) −3.29245 −0.109445
\(906\) 0 0
\(907\) 11.7739 0.390947 0.195473 0.980709i \(-0.437376\pi\)
0.195473 + 0.980709i \(0.437376\pi\)
\(908\) 0 0
\(909\) 6.63908 0.220204
\(910\) 0 0
\(911\) −18.1967 −0.602884 −0.301442 0.953484i \(-0.597468\pi\)
−0.301442 + 0.953484i \(0.597468\pi\)
\(912\) 0 0
\(913\) −14.3873 −0.476151
\(914\) 0 0
\(915\) 3.37567 0.111596
\(916\) 0 0
\(917\) −25.9842 −0.858072
\(918\) 0 0
\(919\) −11.1207 −0.366837 −0.183418 0.983035i \(-0.558716\pi\)
−0.183418 + 0.983035i \(0.558716\pi\)
\(920\) 0 0
\(921\) 9.60583 0.316523
\(922\) 0 0
\(923\) −9.67849 −0.318571
\(924\) 0 0
\(925\) −9.40668 −0.309290
\(926\) 0 0
\(927\) 54.8037 1.79999
\(928\) 0 0
\(929\) 59.0155 1.93624 0.968119 0.250492i \(-0.0805924\pi\)
0.968119 + 0.250492i \(0.0805924\pi\)
\(930\) 0 0
\(931\) 2.06108 0.0675492
\(932\) 0 0
\(933\) −5.95828 −0.195065
\(934\) 0 0
\(935\) −1.42534 −0.0466135
\(936\) 0 0
\(937\) −29.7877 −0.973122 −0.486561 0.873647i \(-0.661749\pi\)
−0.486561 + 0.873647i \(0.661749\pi\)
\(938\) 0 0
\(939\) −8.52413 −0.278174
\(940\) 0 0
\(941\) 56.2456 1.83355 0.916777 0.399400i \(-0.130781\pi\)
0.916777 + 0.399400i \(0.130781\pi\)
\(942\) 0 0
\(943\) −3.98929 −0.129909
\(944\) 0 0
\(945\) 3.26202 0.106113
\(946\) 0 0
\(947\) 13.0743 0.424856 0.212428 0.977177i \(-0.431863\pi\)
0.212428 + 0.977177i \(0.431863\pi\)
\(948\) 0 0
\(949\) −22.4873 −0.729967
\(950\) 0 0
\(951\) −4.03723 −0.130916
\(952\) 0 0
\(953\) 17.1537 0.555661 0.277831 0.960630i \(-0.410385\pi\)
0.277831 + 0.960630i \(0.410385\pi\)
\(954\) 0 0
\(955\) −15.1590 −0.490535
\(956\) 0 0
\(957\) −7.47331 −0.241578
\(958\) 0 0
\(959\) 13.3413 0.430813
\(960\) 0 0
\(961\) −29.4150 −0.948872
\(962\) 0 0
\(963\) 38.1702 1.23002
\(964\) 0 0
\(965\) −4.64406 −0.149498
\(966\) 0 0
\(967\) −18.0857 −0.581596 −0.290798 0.956785i \(-0.593921\pi\)
−0.290798 + 0.956785i \(0.593921\pi\)
\(968\) 0 0
\(969\) 0.246153 0.00790758
\(970\) 0 0
\(971\) 52.5054 1.68498 0.842489 0.538713i \(-0.181089\pi\)
0.842489 + 0.538713i \(0.181089\pi\)
\(972\) 0 0
\(973\) 22.4146 0.718578
\(974\) 0 0
\(975\) −5.03189 −0.161149
\(976\) 0 0
\(977\) 37.1839 1.18962 0.594810 0.803866i \(-0.297227\pi\)
0.594810 + 0.803866i \(0.297227\pi\)
\(978\) 0 0
\(979\) −30.6791 −0.980508
\(980\) 0 0
\(981\) −37.6543 −1.20221
\(982\) 0 0
\(983\) 28.7298 0.916339 0.458170 0.888865i \(-0.348505\pi\)
0.458170 + 0.888865i \(0.348505\pi\)
\(984\) 0 0
\(985\) 9.03199 0.287783
\(986\) 0 0
\(987\) −0.321202 −0.0102240
\(988\) 0 0
\(989\) −17.0398 −0.541834
\(990\) 0 0
\(991\) −6.59860 −0.209611 −0.104806 0.994493i \(-0.533422\pi\)
−0.104806 + 0.994493i \(0.533422\pi\)
\(992\) 0 0
\(993\) −3.19920 −0.101524
\(994\) 0 0
\(995\) −12.7834 −0.405260
\(996\) 0 0
\(997\) −29.2232 −0.925507 −0.462754 0.886487i \(-0.653139\pi\)
−0.462754 + 0.886487i \(0.653139\pi\)
\(998\) 0 0
\(999\) −4.27609 −0.135290
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 \(a_p\))