Properties

Label 8036.2.a.t.1.10
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 20
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1677830643\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(-0.0954148\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.0954148 q^{3}\) \(-0.581124 q^{5}\) \(-2.99090 q^{9}\) \(+O(q^{10})\) \(q\)\(-0.0954148 q^{3}\) \(-0.581124 q^{5}\) \(-2.99090 q^{9}\) \(-4.59295 q^{11}\) \(-5.44659 q^{13}\) \(+0.0554478 q^{15}\) \(-0.983634 q^{17}\) \(+0.599838 q^{19}\) \(+5.72519 q^{23}\) \(-4.66230 q^{25}\) \(+0.571620 q^{27}\) \(+6.69584 q^{29}\) \(+1.57820 q^{31}\) \(+0.438235 q^{33}\) \(-8.89231 q^{37}\) \(+0.519685 q^{39}\) \(-1.00000 q^{41}\) \(-5.24063 q^{43}\) \(+1.73808 q^{45}\) \(-7.66590 q^{47}\) \(+0.0938533 q^{51}\) \(-11.3390 q^{53}\) \(+2.66907 q^{55}\) \(-0.0572334 q^{57}\) \(+7.53338 q^{59}\) \(+5.90355 q^{61}\) \(+3.16514 q^{65}\) \(+2.45712 q^{67}\) \(-0.546268 q^{69}\) \(-8.01542 q^{71}\) \(-15.2262 q^{73}\) \(+0.444852 q^{75}\) \(+13.2660 q^{79}\) \(+8.91815 q^{81}\) \(-15.3819 q^{83}\) \(+0.571613 q^{85}\) \(-0.638882 q^{87}\) \(+10.0913 q^{89}\) \(-0.150584 q^{93}\) \(-0.348580 q^{95}\) \(+1.44854 q^{97}\) \(+13.7370 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut -\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 24q^{19} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 20q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 12q^{29} \) \(\mathstrut +\mathstrut 44q^{33} \) \(\mathstrut +\mathstrut 12q^{37} \) \(\mathstrut +\mathstrut 12q^{39} \) \(\mathstrut -\mathstrut 20q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 40q^{45} \) \(\mathstrut +\mathstrut 4q^{47} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 28q^{57} \) \(\mathstrut +\mathstrut 16q^{59} \) \(\mathstrut +\mathstrut 68q^{61} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 32q^{69} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 48q^{73} \) \(\mathstrut +\mathstrut 60q^{75} \) \(\mathstrut -\mathstrut 20q^{79} \) \(\mathstrut +\mathstrut 32q^{81} \) \(\mathstrut -\mathstrut 8q^{83} \) \(\mathstrut -\mathstrut 28q^{85} \) \(\mathstrut +\mathstrut 60q^{89} \) \(\mathstrut -\mathstrut 16q^{93} \) \(\mathstrut +\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 40q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.0954148 −0.0550878 −0.0275439 0.999621i \(-0.508769\pi\)
−0.0275439 + 0.999621i \(0.508769\pi\)
\(4\) 0 0
\(5\) −0.581124 −0.259886 −0.129943 0.991521i \(-0.541479\pi\)
−0.129943 + 0.991521i \(0.541479\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −2.99090 −0.996965
\(10\) 0 0
\(11\) −4.59295 −1.38483 −0.692413 0.721501i \(-0.743452\pi\)
−0.692413 + 0.721501i \(0.743452\pi\)
\(12\) 0 0
\(13\) −5.44659 −1.51061 −0.755306 0.655373i \(-0.772512\pi\)
−0.755306 + 0.655373i \(0.772512\pi\)
\(14\) 0 0
\(15\) 0.0554478 0.0143166
\(16\) 0 0
\(17\) −0.983634 −0.238566 −0.119283 0.992860i \(-0.538060\pi\)
−0.119283 + 0.992860i \(0.538060\pi\)
\(18\) 0 0
\(19\) 0.599838 0.137612 0.0688061 0.997630i \(-0.478081\pi\)
0.0688061 + 0.997630i \(0.478081\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 5.72519 1.19379 0.596893 0.802321i \(-0.296402\pi\)
0.596893 + 0.802321i \(0.296402\pi\)
\(24\) 0 0
\(25\) −4.66230 −0.932459
\(26\) 0 0
\(27\) 0.571620 0.110008
\(28\) 0 0
\(29\) 6.69584 1.24339 0.621693 0.783261i \(-0.286445\pi\)
0.621693 + 0.783261i \(0.286445\pi\)
\(30\) 0 0
\(31\) 1.57820 0.283454 0.141727 0.989906i \(-0.454735\pi\)
0.141727 + 0.989906i \(0.454735\pi\)
\(32\) 0 0
\(33\) 0.438235 0.0762870
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −8.89231 −1.46189 −0.730944 0.682438i \(-0.760920\pi\)
−0.730944 + 0.682438i \(0.760920\pi\)
\(38\) 0 0
\(39\) 0.519685 0.0832162
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −5.24063 −0.799188 −0.399594 0.916692i \(-0.630849\pi\)
−0.399594 + 0.916692i \(0.630849\pi\)
\(44\) 0 0
\(45\) 1.73808 0.259098
\(46\) 0 0
\(47\) −7.66590 −1.11819 −0.559093 0.829105i \(-0.688851\pi\)
−0.559093 + 0.829105i \(0.688851\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 0.0938533 0.0131421
\(52\) 0 0
\(53\) −11.3390 −1.55753 −0.778767 0.627313i \(-0.784155\pi\)
−0.778767 + 0.627313i \(0.784155\pi\)
\(54\) 0 0
\(55\) 2.66907 0.359897
\(56\) 0 0
\(57\) −0.0572334 −0.00758075
\(58\) 0 0
\(59\) 7.53338 0.980763 0.490381 0.871508i \(-0.336858\pi\)
0.490381 + 0.871508i \(0.336858\pi\)
\(60\) 0 0
\(61\) 5.90355 0.755872 0.377936 0.925832i \(-0.376634\pi\)
0.377936 + 0.925832i \(0.376634\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 3.16514 0.392587
\(66\) 0 0
\(67\) 2.45712 0.300184 0.150092 0.988672i \(-0.452043\pi\)
0.150092 + 0.988672i \(0.452043\pi\)
\(68\) 0 0
\(69\) −0.546268 −0.0657630
\(70\) 0 0
\(71\) −8.01542 −0.951255 −0.475628 0.879647i \(-0.657779\pi\)
−0.475628 + 0.879647i \(0.657779\pi\)
\(72\) 0 0
\(73\) −15.2262 −1.78209 −0.891045 0.453915i \(-0.850027\pi\)
−0.891045 + 0.453915i \(0.850027\pi\)
\(74\) 0 0
\(75\) 0.444852 0.0513671
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 13.2660 1.49254 0.746269 0.665644i \(-0.231843\pi\)
0.746269 + 0.665644i \(0.231843\pi\)
\(80\) 0 0
\(81\) 8.91815 0.990905
\(82\) 0 0
\(83\) −15.3819 −1.68838 −0.844190 0.536044i \(-0.819918\pi\)
−0.844190 + 0.536044i \(0.819918\pi\)
\(84\) 0 0
\(85\) 0.571613 0.0620001
\(86\) 0 0
\(87\) −0.638882 −0.0684954
\(88\) 0 0
\(89\) 10.0913 1.06967 0.534835 0.844956i \(-0.320374\pi\)
0.534835 + 0.844956i \(0.320374\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −0.150584 −0.0156148
\(94\) 0 0
\(95\) −0.348580 −0.0357636
\(96\) 0 0
\(97\) 1.44854 0.147077 0.0735383 0.997292i \(-0.476571\pi\)
0.0735383 + 0.997292i \(0.476571\pi\)
\(98\) 0 0
\(99\) 13.7370 1.38062
\(100\) 0 0
\(101\) 6.29563 0.626438 0.313219 0.949681i \(-0.398593\pi\)
0.313219 + 0.949681i \(0.398593\pi\)
\(102\) 0 0
\(103\) −6.62534 −0.652814 −0.326407 0.945229i \(-0.605838\pi\)
−0.326407 + 0.945229i \(0.605838\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 7.55352 0.730226 0.365113 0.930963i \(-0.381030\pi\)
0.365113 + 0.930963i \(0.381030\pi\)
\(108\) 0 0
\(109\) −11.8097 −1.13116 −0.565581 0.824693i \(-0.691348\pi\)
−0.565581 + 0.824693i \(0.691348\pi\)
\(110\) 0 0
\(111\) 0.848458 0.0805321
\(112\) 0 0
\(113\) −14.8380 −1.39584 −0.697921 0.716175i \(-0.745891\pi\)
−0.697921 + 0.716175i \(0.745891\pi\)
\(114\) 0 0
\(115\) −3.32705 −0.310249
\(116\) 0 0
\(117\) 16.2902 1.50603
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 10.0952 0.917743
\(122\) 0 0
\(123\) 0.0954148 0.00860326
\(124\) 0 0
\(125\) 5.61499 0.502220
\(126\) 0 0
\(127\) 0.395980 0.0351375 0.0175688 0.999846i \(-0.494407\pi\)
0.0175688 + 0.999846i \(0.494407\pi\)
\(128\) 0 0
\(129\) 0.500033 0.0440255
\(130\) 0 0
\(131\) 20.4474 1.78650 0.893249 0.449562i \(-0.148420\pi\)
0.893249 + 0.449562i \(0.148420\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −0.332182 −0.0285897
\(136\) 0 0
\(137\) −16.0149 −1.36825 −0.684123 0.729367i \(-0.739815\pi\)
−0.684123 + 0.729367i \(0.739815\pi\)
\(138\) 0 0
\(139\) 19.5142 1.65517 0.827587 0.561338i \(-0.189713\pi\)
0.827587 + 0.561338i \(0.189713\pi\)
\(140\) 0 0
\(141\) 0.731440 0.0615984
\(142\) 0 0
\(143\) 25.0159 2.09193
\(144\) 0 0
\(145\) −3.89111 −0.323139
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 11.6265 0.952480 0.476240 0.879315i \(-0.341999\pi\)
0.476240 + 0.879315i \(0.341999\pi\)
\(150\) 0 0
\(151\) 13.2062 1.07470 0.537352 0.843358i \(-0.319425\pi\)
0.537352 + 0.843358i \(0.319425\pi\)
\(152\) 0 0
\(153\) 2.94195 0.237842
\(154\) 0 0
\(155\) −0.917131 −0.0736657
\(156\) 0 0
\(157\) 5.52975 0.441322 0.220661 0.975351i \(-0.429178\pi\)
0.220661 + 0.975351i \(0.429178\pi\)
\(158\) 0 0
\(159\) 1.08191 0.0858010
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −8.36982 −0.655575 −0.327787 0.944752i \(-0.606303\pi\)
−0.327787 + 0.944752i \(0.606303\pi\)
\(164\) 0 0
\(165\) −0.254669 −0.0198259
\(166\) 0 0
\(167\) 17.4012 1.34654 0.673272 0.739395i \(-0.264888\pi\)
0.673272 + 0.739395i \(0.264888\pi\)
\(168\) 0 0
\(169\) 16.6653 1.28195
\(170\) 0 0
\(171\) −1.79405 −0.137195
\(172\) 0 0
\(173\) 21.5364 1.63738 0.818691 0.574234i \(-0.194700\pi\)
0.818691 + 0.574234i \(0.194700\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −0.718796 −0.0540280
\(178\) 0 0
\(179\) 11.8043 0.882292 0.441146 0.897435i \(-0.354572\pi\)
0.441146 + 0.897435i \(0.354572\pi\)
\(180\) 0 0
\(181\) 20.4162 1.51753 0.758764 0.651366i \(-0.225804\pi\)
0.758764 + 0.651366i \(0.225804\pi\)
\(182\) 0 0
\(183\) −0.563286 −0.0416393
\(184\) 0 0
\(185\) 5.16753 0.379925
\(186\) 0 0
\(187\) 4.51778 0.330373
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −11.1007 −0.803221 −0.401610 0.915811i \(-0.631549\pi\)
−0.401610 + 0.915811i \(0.631549\pi\)
\(192\) 0 0
\(193\) −11.9320 −0.858887 −0.429443 0.903094i \(-0.641290\pi\)
−0.429443 + 0.903094i \(0.641290\pi\)
\(194\) 0 0
\(195\) −0.302001 −0.0216268
\(196\) 0 0
\(197\) 21.0210 1.49768 0.748841 0.662750i \(-0.230611\pi\)
0.748841 + 0.662750i \(0.230611\pi\)
\(198\) 0 0
\(199\) −15.4861 −1.09778 −0.548890 0.835895i \(-0.684949\pi\)
−0.548890 + 0.835895i \(0.684949\pi\)
\(200\) 0 0
\(201\) −0.234445 −0.0165365
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0.581124 0.0405874
\(206\) 0 0
\(207\) −17.1235 −1.19016
\(208\) 0 0
\(209\) −2.75503 −0.190569
\(210\) 0 0
\(211\) 1.51633 0.104389 0.0521943 0.998637i \(-0.483378\pi\)
0.0521943 + 0.998637i \(0.483378\pi\)
\(212\) 0 0
\(213\) 0.764789 0.0524025
\(214\) 0 0
\(215\) 3.04545 0.207698
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 1.45280 0.0981714
\(220\) 0 0
\(221\) 5.35745 0.360381
\(222\) 0 0
\(223\) 6.28641 0.420969 0.210485 0.977597i \(-0.432496\pi\)
0.210485 + 0.977597i \(0.432496\pi\)
\(224\) 0 0
\(225\) 13.9444 0.929629
\(226\) 0 0
\(227\) −0.493741 −0.0327707 −0.0163854 0.999866i \(-0.505216\pi\)
−0.0163854 + 0.999866i \(0.505216\pi\)
\(228\) 0 0
\(229\) 7.56972 0.500221 0.250111 0.968217i \(-0.419533\pi\)
0.250111 + 0.968217i \(0.419533\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 6.34824 0.415887 0.207943 0.978141i \(-0.433323\pi\)
0.207943 + 0.978141i \(0.433323\pi\)
\(234\) 0 0
\(235\) 4.45483 0.290601
\(236\) 0 0
\(237\) −1.26577 −0.0822206
\(238\) 0 0
\(239\) 6.25165 0.404385 0.202193 0.979346i \(-0.435193\pi\)
0.202193 + 0.979346i \(0.435193\pi\)
\(240\) 0 0
\(241\) 24.6273 1.58638 0.793192 0.608972i \(-0.208418\pi\)
0.793192 + 0.608972i \(0.208418\pi\)
\(242\) 0 0
\(243\) −2.56578 −0.164595
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −3.26707 −0.207879
\(248\) 0 0
\(249\) 1.46766 0.0930091
\(250\) 0 0
\(251\) −27.0165 −1.70527 −0.852634 0.522508i \(-0.824996\pi\)
−0.852634 + 0.522508i \(0.824996\pi\)
\(252\) 0 0
\(253\) −26.2955 −1.65319
\(254\) 0 0
\(255\) −0.0545403 −0.00341545
\(256\) 0 0
\(257\) 18.7011 1.16654 0.583272 0.812277i \(-0.301772\pi\)
0.583272 + 0.812277i \(0.301772\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −20.0266 −1.23961
\(262\) 0 0
\(263\) −13.8753 −0.855589 −0.427795 0.903876i \(-0.640709\pi\)
−0.427795 + 0.903876i \(0.640709\pi\)
\(264\) 0 0
\(265\) 6.58937 0.404782
\(266\) 0 0
\(267\) −0.962855 −0.0589257
\(268\) 0 0
\(269\) 3.83150 0.233610 0.116805 0.993155i \(-0.462735\pi\)
0.116805 + 0.993155i \(0.462735\pi\)
\(270\) 0 0
\(271\) 8.34801 0.507105 0.253553 0.967322i \(-0.418401\pi\)
0.253553 + 0.967322i \(0.418401\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 21.4137 1.29129
\(276\) 0 0
\(277\) −26.9207 −1.61751 −0.808755 0.588146i \(-0.799858\pi\)
−0.808755 + 0.588146i \(0.799858\pi\)
\(278\) 0 0
\(279\) −4.72024 −0.282593
\(280\) 0 0
\(281\) 0.388605 0.0231822 0.0115911 0.999933i \(-0.496310\pi\)
0.0115911 + 0.999933i \(0.496310\pi\)
\(282\) 0 0
\(283\) 24.3878 1.44970 0.724851 0.688906i \(-0.241909\pi\)
0.724851 + 0.688906i \(0.241909\pi\)
\(284\) 0 0
\(285\) 0.0332597 0.00197013
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −16.0325 −0.943086
\(290\) 0 0
\(291\) −0.138212 −0.00810213
\(292\) 0 0
\(293\) 5.78762 0.338116 0.169058 0.985606i \(-0.445927\pi\)
0.169058 + 0.985606i \(0.445927\pi\)
\(294\) 0 0
\(295\) −4.37782 −0.254887
\(296\) 0 0
\(297\) −2.62542 −0.152342
\(298\) 0 0
\(299\) −31.1828 −1.80335
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −0.600696 −0.0345091
\(304\) 0 0
\(305\) −3.43069 −0.196441
\(306\) 0 0
\(307\) −4.26739 −0.243553 −0.121776 0.992558i \(-0.538859\pi\)
−0.121776 + 0.992558i \(0.538859\pi\)
\(308\) 0 0
\(309\) 0.632155 0.0359621
\(310\) 0 0
\(311\) −16.1879 −0.917929 −0.458965 0.888455i \(-0.651780\pi\)
−0.458965 + 0.888455i \(0.651780\pi\)
\(312\) 0 0
\(313\) −27.0694 −1.53005 −0.765026 0.644000i \(-0.777274\pi\)
−0.765026 + 0.644000i \(0.777274\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 6.39340 0.359089 0.179545 0.983750i \(-0.442538\pi\)
0.179545 + 0.983750i \(0.442538\pi\)
\(318\) 0 0
\(319\) −30.7537 −1.72187
\(320\) 0 0
\(321\) −0.720717 −0.0402265
\(322\) 0 0
\(323\) −0.590021 −0.0328297
\(324\) 0 0
\(325\) 25.3936 1.40858
\(326\) 0 0
\(327\) 1.12682 0.0623132
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 28.0413 1.54129 0.770645 0.637265i \(-0.219934\pi\)
0.770645 + 0.637265i \(0.219934\pi\)
\(332\) 0 0
\(333\) 26.5960 1.45745
\(334\) 0 0
\(335\) −1.42789 −0.0780138
\(336\) 0 0
\(337\) −7.07825 −0.385577 −0.192788 0.981240i \(-0.561753\pi\)
−0.192788 + 0.981240i \(0.561753\pi\)
\(338\) 0 0
\(339\) 1.41576 0.0768938
\(340\) 0 0
\(341\) −7.24860 −0.392534
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0.317449 0.0170909
\(346\) 0 0
\(347\) −28.8184 −1.54705 −0.773527 0.633763i \(-0.781509\pi\)
−0.773527 + 0.633763i \(0.781509\pi\)
\(348\) 0 0
\(349\) 12.9849 0.695068 0.347534 0.937667i \(-0.387019\pi\)
0.347534 + 0.937667i \(0.387019\pi\)
\(350\) 0 0
\(351\) −3.11338 −0.166180
\(352\) 0 0
\(353\) −4.77530 −0.254163 −0.127082 0.991892i \(-0.540561\pi\)
−0.127082 + 0.991892i \(0.540561\pi\)
\(354\) 0 0
\(355\) 4.65795 0.247218
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −7.81936 −0.412690 −0.206345 0.978479i \(-0.566157\pi\)
−0.206345 + 0.978479i \(0.566157\pi\)
\(360\) 0 0
\(361\) −18.6402 −0.981063
\(362\) 0 0
\(363\) −0.963229 −0.0505564
\(364\) 0 0
\(365\) 8.84830 0.463141
\(366\) 0 0
\(367\) 20.6849 1.07974 0.539872 0.841747i \(-0.318473\pi\)
0.539872 + 0.841747i \(0.318473\pi\)
\(368\) 0 0
\(369\) 2.99090 0.155700
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 14.2162 0.736087 0.368043 0.929809i \(-0.380028\pi\)
0.368043 + 0.929809i \(0.380028\pi\)
\(374\) 0 0
\(375\) −0.535753 −0.0276662
\(376\) 0 0
\(377\) −36.4695 −1.87827
\(378\) 0 0
\(379\) 18.8430 0.967898 0.483949 0.875096i \(-0.339202\pi\)
0.483949 + 0.875096i \(0.339202\pi\)
\(380\) 0 0
\(381\) −0.0377823 −0.00193565
\(382\) 0 0
\(383\) 30.4597 1.55642 0.778209 0.628005i \(-0.216128\pi\)
0.778209 + 0.628005i \(0.216128\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 15.6742 0.796763
\(388\) 0 0
\(389\) −19.2411 −0.975562 −0.487781 0.872966i \(-0.662194\pi\)
−0.487781 + 0.872966i \(0.662194\pi\)
\(390\) 0 0
\(391\) −5.63150 −0.284797
\(392\) 0 0
\(393\) −1.95098 −0.0984142
\(394\) 0 0
\(395\) −7.70917 −0.387890
\(396\) 0 0
\(397\) 17.0342 0.854920 0.427460 0.904034i \(-0.359409\pi\)
0.427460 + 0.904034i \(0.359409\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 14.8576 0.741953 0.370976 0.928642i \(-0.379023\pi\)
0.370976 + 0.928642i \(0.379023\pi\)
\(402\) 0 0
\(403\) −8.59582 −0.428188
\(404\) 0 0
\(405\) −5.18255 −0.257523
\(406\) 0 0
\(407\) 40.8419 2.02446
\(408\) 0 0
\(409\) −24.0336 −1.18838 −0.594191 0.804324i \(-0.702528\pi\)
−0.594191 + 0.804324i \(0.702528\pi\)
\(410\) 0 0
\(411\) 1.52806 0.0753736
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 8.93877 0.438787
\(416\) 0 0
\(417\) −1.86194 −0.0911798
\(418\) 0 0
\(419\) −33.2915 −1.62640 −0.813199 0.581986i \(-0.802276\pi\)
−0.813199 + 0.581986i \(0.802276\pi\)
\(420\) 0 0
\(421\) 36.2319 1.76583 0.882917 0.469528i \(-0.155576\pi\)
0.882917 + 0.469528i \(0.155576\pi\)
\(422\) 0 0
\(423\) 22.9279 1.11479
\(424\) 0 0
\(425\) 4.58599 0.222453
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −2.38689 −0.115240
\(430\) 0 0
\(431\) −31.1137 −1.49869 −0.749347 0.662178i \(-0.769632\pi\)
−0.749347 + 0.662178i \(0.769632\pi\)
\(432\) 0 0
\(433\) −7.86622 −0.378026 −0.189013 0.981975i \(-0.560529\pi\)
−0.189013 + 0.981975i \(0.560529\pi\)
\(434\) 0 0
\(435\) 0.371270 0.0178010
\(436\) 0 0
\(437\) 3.43419 0.164280
\(438\) 0 0
\(439\) 18.6709 0.891115 0.445558 0.895253i \(-0.353005\pi\)
0.445558 + 0.895253i \(0.353005\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −10.4653 −0.497222 −0.248611 0.968603i \(-0.579974\pi\)
−0.248611 + 0.968603i \(0.579974\pi\)
\(444\) 0 0
\(445\) −5.86426 −0.277993
\(446\) 0 0
\(447\) −1.10934 −0.0524700
\(448\) 0 0
\(449\) 20.9301 0.987754 0.493877 0.869532i \(-0.335579\pi\)
0.493877 + 0.869532i \(0.335579\pi\)
\(450\) 0 0
\(451\) 4.59295 0.216274
\(452\) 0 0
\(453\) −1.26007 −0.0592030
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 22.8341 1.06813 0.534066 0.845443i \(-0.320663\pi\)
0.534066 + 0.845443i \(0.320663\pi\)
\(458\) 0 0
\(459\) −0.562265 −0.0262443
\(460\) 0 0
\(461\) 40.8607 1.90307 0.951535 0.307540i \(-0.0995057\pi\)
0.951535 + 0.307540i \(0.0995057\pi\)
\(462\) 0 0
\(463\) −17.7860 −0.826587 −0.413294 0.910598i \(-0.635622\pi\)
−0.413294 + 0.910598i \(0.635622\pi\)
\(464\) 0 0
\(465\) 0.0875078 0.00405808
\(466\) 0 0
\(467\) −20.9022 −0.967237 −0.483618 0.875279i \(-0.660678\pi\)
−0.483618 + 0.875279i \(0.660678\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −0.527620 −0.0243115
\(472\) 0 0
\(473\) 24.0699 1.10674
\(474\) 0 0
\(475\) −2.79662 −0.128318
\(476\) 0 0
\(477\) 33.9138 1.55281
\(478\) 0 0
\(479\) −12.7888 −0.584336 −0.292168 0.956367i \(-0.594377\pi\)
−0.292168 + 0.956367i \(0.594377\pi\)
\(480\) 0 0
\(481\) 48.4328 2.20834
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −0.841779 −0.0382232
\(486\) 0 0
\(487\) −23.5318 −1.06633 −0.533165 0.846011i \(-0.678997\pi\)
−0.533165 + 0.846011i \(0.678997\pi\)
\(488\) 0 0
\(489\) 0.798605 0.0361141
\(490\) 0 0
\(491\) −24.3633 −1.09950 −0.549749 0.835330i \(-0.685277\pi\)
−0.549749 + 0.835330i \(0.685277\pi\)
\(492\) 0 0
\(493\) −6.58626 −0.296630
\(494\) 0 0
\(495\) −7.98291 −0.358805
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −13.7231 −0.614331 −0.307166 0.951656i \(-0.599381\pi\)
−0.307166 + 0.951656i \(0.599381\pi\)
\(500\) 0 0
\(501\) −1.66033 −0.0741781
\(502\) 0 0
\(503\) 9.60601 0.428311 0.214155 0.976800i \(-0.431300\pi\)
0.214155 + 0.976800i \(0.431300\pi\)
\(504\) 0 0
\(505\) −3.65854 −0.162803
\(506\) 0 0
\(507\) −1.59012 −0.0706196
\(508\) 0 0
\(509\) −32.6017 −1.44505 −0.722523 0.691347i \(-0.757018\pi\)
−0.722523 + 0.691347i \(0.757018\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0.342880 0.0151385
\(514\) 0 0
\(515\) 3.85014 0.169657
\(516\) 0 0
\(517\) 35.2091 1.54849
\(518\) 0 0
\(519\) −2.05489 −0.0901997
\(520\) 0 0
\(521\) −4.97451 −0.217937 −0.108969 0.994045i \(-0.534755\pi\)
−0.108969 + 0.994045i \(0.534755\pi\)
\(522\) 0 0
\(523\) 31.7275 1.38735 0.693674 0.720289i \(-0.255991\pi\)
0.693674 + 0.720289i \(0.255991\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.55237 −0.0676225
\(528\) 0 0
\(529\) 9.77785 0.425124
\(530\) 0 0
\(531\) −22.5316 −0.977786
\(532\) 0 0
\(533\) 5.44659 0.235918
\(534\) 0 0
\(535\) −4.38953 −0.189776
\(536\) 0 0
\(537\) −1.12630 −0.0486035
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −41.1725 −1.77014 −0.885071 0.465456i \(-0.845890\pi\)
−0.885071 + 0.465456i \(0.845890\pi\)
\(542\) 0 0
\(543\) −1.94801 −0.0835972
\(544\) 0 0
\(545\) 6.86288 0.293974
\(546\) 0 0
\(547\) −41.3456 −1.76781 −0.883906 0.467665i \(-0.845096\pi\)
−0.883906 + 0.467665i \(0.845096\pi\)
\(548\) 0 0
\(549\) −17.6569 −0.753578
\(550\) 0 0
\(551\) 4.01642 0.171105
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −0.493059 −0.0209292
\(556\) 0 0
\(557\) 6.17315 0.261565 0.130782 0.991411i \(-0.458251\pi\)
0.130782 + 0.991411i \(0.458251\pi\)
\(558\) 0 0
\(559\) 28.5435 1.20726
\(560\) 0 0
\(561\) −0.431063 −0.0181995
\(562\) 0 0
\(563\) −26.7733 −1.12836 −0.564179 0.825652i \(-0.690807\pi\)
−0.564179 + 0.825652i \(0.690807\pi\)
\(564\) 0 0
\(565\) 8.62271 0.362760
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −8.05626 −0.337736 −0.168868 0.985639i \(-0.554011\pi\)
−0.168868 + 0.985639i \(0.554011\pi\)
\(570\) 0 0
\(571\) 18.7571 0.784961 0.392481 0.919760i \(-0.371617\pi\)
0.392481 + 0.919760i \(0.371617\pi\)
\(572\) 0 0
\(573\) 1.05917 0.0442476
\(574\) 0 0
\(575\) −26.6925 −1.11316
\(576\) 0 0
\(577\) 25.0101 1.04118 0.520591 0.853806i \(-0.325712\pi\)
0.520591 + 0.853806i \(0.325712\pi\)
\(578\) 0 0
\(579\) 1.13849 0.0473141
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 52.0795 2.15691
\(584\) 0 0
\(585\) −9.46661 −0.391396
\(586\) 0 0
\(587\) −36.6357 −1.51212 −0.756059 0.654503i \(-0.772878\pi\)
−0.756059 + 0.654503i \(0.772878\pi\)
\(588\) 0 0
\(589\) 0.946666 0.0390067
\(590\) 0 0
\(591\) −2.00571 −0.0825039
\(592\) 0 0
\(593\) −14.6459 −0.601435 −0.300717 0.953713i \(-0.597226\pi\)
−0.300717 + 0.953713i \(0.597226\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 1.47760 0.0604742
\(598\) 0 0
\(599\) −3.88764 −0.158845 −0.0794223 0.996841i \(-0.525308\pi\)
−0.0794223 + 0.996841i \(0.525308\pi\)
\(600\) 0 0
\(601\) −12.5556 −0.512154 −0.256077 0.966656i \(-0.582430\pi\)
−0.256077 + 0.966656i \(0.582430\pi\)
\(602\) 0 0
\(603\) −7.34898 −0.299273
\(604\) 0 0
\(605\) −5.86654 −0.238509
\(606\) 0 0
\(607\) 46.4201 1.88413 0.942066 0.335427i \(-0.108880\pi\)
0.942066 + 0.335427i \(0.108880\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 41.7530 1.68914
\(612\) 0 0
\(613\) 47.3316 1.91170 0.955852 0.293848i \(-0.0949361\pi\)
0.955852 + 0.293848i \(0.0949361\pi\)
\(614\) 0 0
\(615\) −0.0554478 −0.00223587
\(616\) 0 0
\(617\) −9.61953 −0.387268 −0.193634 0.981074i \(-0.562027\pi\)
−0.193634 + 0.981074i \(0.562027\pi\)
\(618\) 0 0
\(619\) 26.4825 1.06442 0.532211 0.846612i \(-0.321361\pi\)
0.532211 + 0.846612i \(0.321361\pi\)
\(620\) 0 0
\(621\) 3.27264 0.131326
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 20.0485 0.801939
\(626\) 0 0
\(627\) 0.262870 0.0104980
\(628\) 0 0
\(629\) 8.74679 0.348757
\(630\) 0 0
\(631\) 22.5890 0.899256 0.449628 0.893216i \(-0.351557\pi\)
0.449628 + 0.893216i \(0.351557\pi\)
\(632\) 0 0
\(633\) −0.144680 −0.00575053
\(634\) 0 0
\(635\) −0.230113 −0.00913177
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 23.9733 0.948368
\(640\) 0 0
\(641\) −9.40462 −0.371460 −0.185730 0.982601i \(-0.559465\pi\)
−0.185730 + 0.982601i \(0.559465\pi\)
\(642\) 0 0
\(643\) 27.6967 1.09225 0.546126 0.837703i \(-0.316102\pi\)
0.546126 + 0.837703i \(0.316102\pi\)
\(644\) 0 0
\(645\) −0.290581 −0.0114416
\(646\) 0 0
\(647\) 3.51502 0.138190 0.0690949 0.997610i \(-0.477989\pi\)
0.0690949 + 0.997610i \(0.477989\pi\)
\(648\) 0 0
\(649\) −34.6004 −1.35819
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 21.7146 0.849758 0.424879 0.905250i \(-0.360317\pi\)
0.424879 + 0.905250i \(0.360317\pi\)
\(654\) 0 0
\(655\) −11.8825 −0.464286
\(656\) 0 0
\(657\) 45.5399 1.77668
\(658\) 0 0
\(659\) 25.4011 0.989488 0.494744 0.869039i \(-0.335262\pi\)
0.494744 + 0.869039i \(0.335262\pi\)
\(660\) 0 0
\(661\) 14.1958 0.552154 0.276077 0.961135i \(-0.410965\pi\)
0.276077 + 0.961135i \(0.410965\pi\)
\(662\) 0 0
\(663\) −0.511180 −0.0198526
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 38.3350 1.48434
\(668\) 0 0
\(669\) −0.599816 −0.0231902
\(670\) 0 0
\(671\) −27.1147 −1.04675
\(672\) 0 0
\(673\) −22.0625 −0.850447 −0.425223 0.905088i \(-0.639804\pi\)
−0.425223 + 0.905088i \(0.639804\pi\)
\(674\) 0 0
\(675\) −2.66506 −0.102578
\(676\) 0 0
\(677\) −1.95203 −0.0750225 −0.0375113 0.999296i \(-0.511943\pi\)
−0.0375113 + 0.999296i \(0.511943\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0.0471102 0.00180526
\(682\) 0 0
\(683\) 34.2307 1.30980 0.654901 0.755715i \(-0.272710\pi\)
0.654901 + 0.755715i \(0.272710\pi\)
\(684\) 0 0
\(685\) 9.30664 0.355588
\(686\) 0 0
\(687\) −0.722263 −0.0275561
\(688\) 0 0
\(689\) 61.7590 2.35283
\(690\) 0 0
\(691\) −15.3176 −0.582708 −0.291354 0.956615i \(-0.594106\pi\)
−0.291354 + 0.956615i \(0.594106\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −11.3402 −0.430157
\(696\) 0 0
\(697\) 0.983634 0.0372578
\(698\) 0 0
\(699\) −0.605716 −0.0229103
\(700\) 0 0
\(701\) −0.218657 −0.00825856 −0.00412928 0.999991i \(-0.501314\pi\)
−0.00412928 + 0.999991i \(0.501314\pi\)
\(702\) 0 0
\(703\) −5.33395 −0.201174
\(704\) 0 0
\(705\) −0.425057 −0.0160086
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −47.6398 −1.78915 −0.894576 0.446916i \(-0.852522\pi\)
−0.894576 + 0.446916i \(0.852522\pi\)
\(710\) 0 0
\(711\) −39.6771 −1.48801
\(712\) 0 0
\(713\) 9.03552 0.338383
\(714\) 0 0
\(715\) −14.5373 −0.543665
\(716\) 0 0
\(717\) −0.596499 −0.0222767
\(718\) 0 0
\(719\) −44.2096 −1.64874 −0.824371 0.566050i \(-0.808471\pi\)
−0.824371 + 0.566050i \(0.808471\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −2.34981 −0.0873903
\(724\) 0 0
\(725\) −31.2180 −1.15941
\(726\) 0 0
\(727\) −40.9714 −1.51955 −0.759773 0.650189i \(-0.774690\pi\)
−0.759773 + 0.650189i \(0.774690\pi\)
\(728\) 0 0
\(729\) −26.5096 −0.981838
\(730\) 0 0
\(731\) 5.15486 0.190659
\(732\) 0 0
\(733\) 49.0440 1.81148 0.905741 0.423831i \(-0.139315\pi\)
0.905741 + 0.423831i \(0.139315\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −11.2854 −0.415703
\(738\) 0 0
\(739\) 45.0783 1.65823 0.829116 0.559077i \(-0.188844\pi\)
0.829116 + 0.559077i \(0.188844\pi\)
\(740\) 0 0
\(741\) 0.311727 0.0114516
\(742\) 0 0
\(743\) 0.752868 0.0276200 0.0138100 0.999905i \(-0.495604\pi\)
0.0138100 + 0.999905i \(0.495604\pi\)
\(744\) 0 0
\(745\) −6.75643 −0.247536
\(746\) 0 0
\(747\) 46.0056 1.68326
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 3.88864 0.141898 0.0709492 0.997480i \(-0.477397\pi\)
0.0709492 + 0.997480i \(0.477397\pi\)
\(752\) 0 0
\(753\) 2.57778 0.0939394
\(754\) 0 0
\(755\) −7.67442 −0.279301
\(756\) 0 0
\(757\) −1.51890 −0.0552054 −0.0276027 0.999619i \(-0.508787\pi\)
−0.0276027 + 0.999619i \(0.508787\pi\)
\(758\) 0 0
\(759\) 2.50898 0.0910703
\(760\) 0 0
\(761\) 4.91919 0.178321 0.0891603 0.996017i \(-0.471582\pi\)
0.0891603 + 0.996017i \(0.471582\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −1.70964 −0.0618120
\(766\) 0 0
\(767\) −41.0312 −1.48155
\(768\) 0 0
\(769\) 42.8410 1.54489 0.772443 0.635084i \(-0.219035\pi\)
0.772443 + 0.635084i \(0.219035\pi\)
\(770\) 0 0
\(771\) −1.78436 −0.0642622
\(772\) 0 0
\(773\) 14.7391 0.530128 0.265064 0.964231i \(-0.414607\pi\)
0.265064 + 0.964231i \(0.414607\pi\)
\(774\) 0 0
\(775\) −7.35805 −0.264309
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −0.599838 −0.0214914
\(780\) 0 0
\(781\) 36.8144 1.31732
\(782\) 0 0
\(783\) 3.82748 0.136783
\(784\) 0 0
\(785\) −3.21347 −0.114694
\(786\) 0 0
\(787\) −0.810739 −0.0288997 −0.0144499 0.999896i \(-0.504600\pi\)
−0.0144499 + 0.999896i \(0.504600\pi\)
\(788\) 0 0
\(789\) 1.32391 0.0471325
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −32.1542 −1.14183
\(794\) 0 0
\(795\) −0.628723 −0.0222985
\(796\) 0 0
\(797\) −24.7544 −0.876844 −0.438422 0.898769i \(-0.644463\pi\)
−0.438422 + 0.898769i \(0.644463\pi\)
\(798\) 0 0
\(799\) 7.54044 0.266762
\(800\) 0 0
\(801\) −30.1819 −1.06642
\(802\) 0 0
\(803\) 69.9331 2.46789
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −0.365581 −0.0128691
\(808\) 0 0
\(809\) 37.5304 1.31950 0.659750 0.751485i \(-0.270662\pi\)
0.659750 + 0.751485i \(0.270662\pi\)
\(810\) 0 0
\(811\) 43.5412 1.52894 0.764470 0.644660i \(-0.223001\pi\)
0.764470 + 0.644660i \(0.223001\pi\)
\(812\) 0 0
\(813\) −0.796523 −0.0279353
\(814\) 0 0
\(815\) 4.86390 0.170375
\(816\) 0 0
\(817\) −3.14353 −0.109978
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −15.9523 −0.556739 −0.278370 0.960474i \(-0.589794\pi\)
−0.278370 + 0.960474i \(0.589794\pi\)
\(822\) 0 0
\(823\) −53.2301 −1.85549 −0.927743 0.373220i \(-0.878254\pi\)
−0.927743 + 0.373220i \(0.878254\pi\)
\(824\) 0 0
\(825\) −2.04318 −0.0711345
\(826\) 0 0
\(827\) 31.9051 1.10945 0.554724 0.832034i \(-0.312824\pi\)
0.554724 + 0.832034i \(0.312824\pi\)
\(828\) 0 0
\(829\) 2.57219 0.0893357 0.0446679 0.999002i \(-0.485777\pi\)
0.0446679 + 0.999002i \(0.485777\pi\)
\(830\) 0 0
\(831\) 2.56864 0.0891050
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −10.1122 −0.349948
\(836\) 0 0
\(837\) 0.902132 0.0311823
\(838\) 0 0
\(839\) −10.5911 −0.365644 −0.182822 0.983146i \(-0.558523\pi\)
−0.182822 + 0.983146i \(0.558523\pi\)
\(840\) 0 0
\(841\) 15.8343 0.546010
\(842\) 0 0
\(843\) −0.0370787 −0.00127706
\(844\) 0 0
\(845\) −9.68461 −0.333161
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −2.32695 −0.0798608
\(850\) 0 0
\(851\) −50.9102 −1.74518
\(852\) 0 0
\(853\) −28.8643 −0.988296 −0.494148 0.869378i \(-0.664520\pi\)
−0.494148 + 0.869378i \(0.664520\pi\)
\(854\) 0 0
\(855\) 1.04257 0.0356550
\(856\) 0 0
\(857\) −21.0012 −0.717386 −0.358693 0.933456i \(-0.616778\pi\)
−0.358693 + 0.933456i \(0.616778\pi\)
\(858\) 0 0
\(859\) −20.3172 −0.693214 −0.346607 0.938010i \(-0.612666\pi\)
−0.346607 + 0.938010i \(0.612666\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 5.50558 0.187412 0.0937061 0.995600i \(-0.470129\pi\)
0.0937061 + 0.995600i \(0.470129\pi\)
\(864\) 0 0
\(865\) −12.5153 −0.425533
\(866\) 0 0
\(867\) 1.52973 0.0519525
\(868\) 0 0
\(869\) −60.9299 −2.06691
\(870\) 0 0
\(871\) −13.3829 −0.453462
\(872\) 0 0
\(873\) −4.33243 −0.146630
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 9.96003 0.336326 0.168163 0.985759i \(-0.446216\pi\)
0.168163 + 0.985759i \(0.446216\pi\)
\(878\) 0 0
\(879\) −0.552224 −0.0186261
\(880\) 0 0
\(881\) 30.1577 1.01604 0.508019 0.861346i \(-0.330378\pi\)
0.508019 + 0.861346i \(0.330378\pi\)
\(882\) 0 0
\(883\) −30.2088 −1.01661 −0.508304 0.861178i \(-0.669727\pi\)
−0.508304 + 0.861178i \(0.669727\pi\)
\(884\) 0 0
\(885\) 0.417709 0.0140411
\(886\) 0 0
\(887\) −12.4675 −0.418616 −0.209308 0.977850i \(-0.567121\pi\)
−0.209308 + 0.977850i \(0.567121\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −40.9606 −1.37223
\(892\) 0 0
\(893\) −4.59830 −0.153876
\(894\) 0 0
\(895\) −6.85974 −0.229296
\(896\) 0 0
\(897\) 2.97530 0.0993423
\(898\) 0 0
\(899\) 10.5674 0.352442
\(900\) 0 0
\(901\) 11.1534 0.371575
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −11.8644 −0.394385
\(906\) 0 0
\(907\) 28.5295 0.947306 0.473653 0.880712i \(-0.342935\pi\)
0.473653 + 0.880712i \(0.342935\pi\)
\(908\) 0 0
\(909\) −18.8296 −0.624537
\(910\) 0 0
\(911\) 28.1381 0.932258 0.466129 0.884717i \(-0.345648\pi\)
0.466129 + 0.884717i \(0.345648\pi\)
\(912\) 0 0
\(913\) 70.6482 2.33811
\(914\) 0 0
\(915\) 0.327339 0.0108215
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −19.4022 −0.640021 −0.320011 0.947414i \(-0.603686\pi\)
−0.320011 + 0.947414i \(0.603686\pi\)
\(920\) 0 0
\(921\) 0.407172 0.0134168
\(922\) 0 0
\(923\) 43.6567 1.43698
\(924\) 0 0
\(925\) 41.4586 1.36315
\(926\) 0 0
\(927\) 19.8157 0.650833
\(928\) 0 0
\(929\) −4.26837 −0.140041 −0.0700203 0.997546i \(-0.522306\pi\)
−0.0700203 + 0.997546i \(0.522306\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 1.54456 0.0505667
\(934\) 0 0
\(935\) −2.62539 −0.0858594
\(936\) 0 0
\(937\) −31.3745 −1.02496 −0.512481 0.858699i \(-0.671273\pi\)
−0.512481 + 0.858699i \(0.671273\pi\)
\(938\) 0 0
\(939\) 2.58282 0.0842871
\(940\) 0 0
\(941\) −34.2915 −1.11787 −0.558935 0.829212i \(-0.688790\pi\)
−0.558935 + 0.829212i \(0.688790\pi\)
\(942\) 0 0
\(943\) −5.72519 −0.186438
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −30.3857 −0.987403 −0.493701 0.869632i \(-0.664356\pi\)
−0.493701 + 0.869632i \(0.664356\pi\)
\(948\) 0 0
\(949\) 82.9308 2.69205
\(950\) 0 0
\(951\) −0.610025 −0.0197814
\(952\) 0 0
\(953\) −30.1336 −0.976124 −0.488062 0.872809i \(-0.662296\pi\)
−0.488062 + 0.872809i \(0.662296\pi\)
\(954\) 0 0
\(955\) 6.45090 0.208746
\(956\) 0 0
\(957\) 2.93435 0.0948542
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −28.5093 −0.919654
\(962\) 0 0
\(963\) −22.5918 −0.728010
\(964\) 0 0
\(965\) 6.93399 0.223213
\(966\) 0 0
\(967\) 6.17238 0.198490 0.0992451 0.995063i \(-0.468357\pi\)
0.0992451 + 0.995063i \(0.468357\pi\)
\(968\) 0 0
\(969\) 0.0562968 0.00180851
\(970\) 0 0
\(971\) −50.8413 −1.63157 −0.815787 0.578353i \(-0.803696\pi\)
−0.815787 + 0.578353i \(0.803696\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −2.42292 −0.0775957
\(976\) 0 0
\(977\) 31.6934 1.01396 0.506981 0.861957i \(-0.330761\pi\)
0.506981 + 0.861957i \(0.330761\pi\)
\(978\) 0 0
\(979\) −46.3486 −1.48131
\(980\) 0 0
\(981\) 35.3215 1.12773
\(982\) 0 0
\(983\) −0.0998845 −0.00318582 −0.00159291 0.999999i \(-0.500507\pi\)
−0.00159291 + 0.999999i \(0.500507\pi\)
\(984\) 0 0
\(985\) −12.2158 −0.389227
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −30.0036 −0.954059
\(990\) 0 0
\(991\) −7.29957 −0.231879 −0.115939 0.993256i \(-0.536988\pi\)
−0.115939 + 0.993256i \(0.536988\pi\)
\(992\) 0 0
\(993\) −2.67555 −0.0849062
\(994\) 0 0
\(995\) 8.99933 0.285298
\(996\) 0 0
\(997\) 16.3456 0.517669 0.258834 0.965922i \(-0.416662\pi\)
0.258834 + 0.965922i \(0.416662\pi\)
\(998\) 0 0
\(999\) −5.08303 −0.160820
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 \(a_p\))