Properties

Label 8020.2.a.c.1.15
Level 8020
Weight 2
Character 8020.1
Self dual Yes
Analytic conductor 64.040
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 8020.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.167528 q^{3}\) \(-1.00000 q^{5}\) \(-3.89143 q^{7}\) \(-2.97193 q^{9}\) \(+O(q^{10})\) \(q\)\(+0.167528 q^{3}\) \(-1.00000 q^{5}\) \(-3.89143 q^{7}\) \(-2.97193 q^{9}\) \(+3.80808 q^{11}\) \(+0.290451 q^{13}\) \(-0.167528 q^{15}\) \(-0.491694 q^{17}\) \(-4.25879 q^{19}\) \(-0.651922 q^{21}\) \(+8.71853 q^{23}\) \(+1.00000 q^{25}\) \(-1.00047 q^{27}\) \(+2.00707 q^{29}\) \(+2.46257 q^{31}\) \(+0.637959 q^{33}\) \(+3.89143 q^{35}\) \(+8.86566 q^{37}\) \(+0.0486587 q^{39}\) \(-6.82952 q^{41}\) \(-10.9057 q^{43}\) \(+2.97193 q^{45}\) \(+5.14522 q^{47}\) \(+8.14319 q^{49}\) \(-0.0823725 q^{51}\) \(+4.63701 q^{53}\) \(-3.80808 q^{55}\) \(-0.713466 q^{57}\) \(+11.0465 q^{59}\) \(-0.286775 q^{61}\) \(+11.5651 q^{63}\) \(-0.290451 q^{65}\) \(-3.22227 q^{67}\) \(+1.46060 q^{69}\) \(-2.53421 q^{71}\) \(-5.56543 q^{73}\) \(+0.167528 q^{75}\) \(-14.8188 q^{77}\) \(-10.6404 q^{79}\) \(+8.74820 q^{81}\) \(+1.47038 q^{83}\) \(+0.491694 q^{85}\) \(+0.336241 q^{87}\) \(+8.34625 q^{89}\) \(-1.13027 q^{91}\) \(+0.412550 q^{93}\) \(+4.25879 q^{95}\) \(-10.4387 q^{97}\) \(-11.3174 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 3q^{13} \) \(\mathstrut -\mathstrut 3q^{15} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut +\mathstrut 28q^{25} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut -\mathstrut 37q^{29} \) \(\mathstrut -\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 2q^{33} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut -\mathstrut 3q^{37} \) \(\mathstrut -\mathstrut 19q^{39} \) \(\mathstrut -\mathstrut 30q^{41} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut -\mathstrut 17q^{45} \) \(\mathstrut -\mathstrut 15q^{47} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 2q^{55} \) \(\mathstrut -\mathstrut 22q^{57} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut -\mathstrut 33q^{61} \) \(\mathstrut -\mathstrut 20q^{63} \) \(\mathstrut -\mathstrut 3q^{65} \) \(\mathstrut +\mathstrut 19q^{67} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut -\mathstrut 42q^{77} \) \(\mathstrut -\mathstrut 29q^{79} \) \(\mathstrut -\mathstrut 36q^{81} \) \(\mathstrut +\mathstrut 14q^{83} \) \(\mathstrut +\mathstrut 10q^{85} \) \(\mathstrut -\mathstrut 32q^{87} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 7q^{91} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 39q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.167528 0.0967223 0.0483611 0.998830i \(-0.484600\pi\)
0.0483611 + 0.998830i \(0.484600\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −3.89143 −1.47082 −0.735410 0.677622i \(-0.763011\pi\)
−0.735410 + 0.677622i \(0.763011\pi\)
\(8\) 0 0
\(9\) −2.97193 −0.990645
\(10\) 0 0
\(11\) 3.80808 1.14818 0.574089 0.818793i \(-0.305356\pi\)
0.574089 + 0.818793i \(0.305356\pi\)
\(12\) 0 0
\(13\) 0.290451 0.0805567 0.0402784 0.999188i \(-0.487176\pi\)
0.0402784 + 0.999188i \(0.487176\pi\)
\(14\) 0 0
\(15\) −0.167528 −0.0432555
\(16\) 0 0
\(17\) −0.491694 −0.119253 −0.0596267 0.998221i \(-0.518991\pi\)
−0.0596267 + 0.998221i \(0.518991\pi\)
\(18\) 0 0
\(19\) −4.25879 −0.977033 −0.488517 0.872555i \(-0.662462\pi\)
−0.488517 + 0.872555i \(0.662462\pi\)
\(20\) 0 0
\(21\) −0.651922 −0.142261
\(22\) 0 0
\(23\) 8.71853 1.81794 0.908970 0.416862i \(-0.136870\pi\)
0.908970 + 0.416862i \(0.136870\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −1.00047 −0.192540
\(28\) 0 0
\(29\) 2.00707 0.372704 0.186352 0.982483i \(-0.440334\pi\)
0.186352 + 0.982483i \(0.440334\pi\)
\(30\) 0 0
\(31\) 2.46257 0.442291 0.221146 0.975241i \(-0.429020\pi\)
0.221146 + 0.975241i \(0.429020\pi\)
\(32\) 0 0
\(33\) 0.637959 0.111054
\(34\) 0 0
\(35\) 3.89143 0.657771
\(36\) 0 0
\(37\) 8.86566 1.45751 0.728753 0.684776i \(-0.240100\pi\)
0.728753 + 0.684776i \(0.240100\pi\)
\(38\) 0 0
\(39\) 0.0486587 0.00779163
\(40\) 0 0
\(41\) −6.82952 −1.06659 −0.533296 0.845929i \(-0.679047\pi\)
−0.533296 + 0.845929i \(0.679047\pi\)
\(42\) 0 0
\(43\) −10.9057 −1.66310 −0.831549 0.555451i \(-0.812545\pi\)
−0.831549 + 0.555451i \(0.812545\pi\)
\(44\) 0 0
\(45\) 2.97193 0.443030
\(46\) 0 0
\(47\) 5.14522 0.750507 0.375253 0.926922i \(-0.377556\pi\)
0.375253 + 0.926922i \(0.377556\pi\)
\(48\) 0 0
\(49\) 8.14319 1.16331
\(50\) 0 0
\(51\) −0.0823725 −0.0115345
\(52\) 0 0
\(53\) 4.63701 0.636942 0.318471 0.947933i \(-0.396831\pi\)
0.318471 + 0.947933i \(0.396831\pi\)
\(54\) 0 0
\(55\) −3.80808 −0.513481
\(56\) 0 0
\(57\) −0.713466 −0.0945009
\(58\) 0 0
\(59\) 11.0465 1.43814 0.719069 0.694939i \(-0.244569\pi\)
0.719069 + 0.694939i \(0.244569\pi\)
\(60\) 0 0
\(61\) −0.286775 −0.0367177 −0.0183589 0.999831i \(-0.505844\pi\)
−0.0183589 + 0.999831i \(0.505844\pi\)
\(62\) 0 0
\(63\) 11.5651 1.45706
\(64\) 0 0
\(65\) −0.290451 −0.0360261
\(66\) 0 0
\(67\) −3.22227 −0.393664 −0.196832 0.980437i \(-0.563065\pi\)
−0.196832 + 0.980437i \(0.563065\pi\)
\(68\) 0 0
\(69\) 1.46060 0.175835
\(70\) 0 0
\(71\) −2.53421 −0.300755 −0.150378 0.988629i \(-0.548049\pi\)
−0.150378 + 0.988629i \(0.548049\pi\)
\(72\) 0 0
\(73\) −5.56543 −0.651384 −0.325692 0.945476i \(-0.605597\pi\)
−0.325692 + 0.945476i \(0.605597\pi\)
\(74\) 0 0
\(75\) 0.167528 0.0193445
\(76\) 0 0
\(77\) −14.8188 −1.68876
\(78\) 0 0
\(79\) −10.6404 −1.19713 −0.598567 0.801073i \(-0.704263\pi\)
−0.598567 + 0.801073i \(0.704263\pi\)
\(80\) 0 0
\(81\) 8.74820 0.972022
\(82\) 0 0
\(83\) 1.47038 0.161395 0.0806975 0.996739i \(-0.474285\pi\)
0.0806975 + 0.996739i \(0.474285\pi\)
\(84\) 0 0
\(85\) 0.491694 0.0533317
\(86\) 0 0
\(87\) 0.336241 0.0360488
\(88\) 0 0
\(89\) 8.34625 0.884701 0.442350 0.896842i \(-0.354145\pi\)
0.442350 + 0.896842i \(0.354145\pi\)
\(90\) 0 0
\(91\) −1.13027 −0.118484
\(92\) 0 0
\(93\) 0.412550 0.0427794
\(94\) 0 0
\(95\) 4.25879 0.436942
\(96\) 0 0
\(97\) −10.4387 −1.05989 −0.529943 0.848034i \(-0.677787\pi\)
−0.529943 + 0.848034i \(0.677787\pi\)
\(98\) 0 0
\(99\) −11.3174 −1.13744
\(100\) 0 0
\(101\) 10.7396 1.06863 0.534314 0.845286i \(-0.320570\pi\)
0.534314 + 0.845286i \(0.320570\pi\)
\(102\) 0 0
\(103\) −10.8116 −1.06530 −0.532649 0.846336i \(-0.678803\pi\)
−0.532649 + 0.846336i \(0.678803\pi\)
\(104\) 0 0
\(105\) 0.651922 0.0636211
\(106\) 0 0
\(107\) −5.52515 −0.534136 −0.267068 0.963678i \(-0.586055\pi\)
−0.267068 + 0.963678i \(0.586055\pi\)
\(108\) 0 0
\(109\) −11.2933 −1.08170 −0.540849 0.841120i \(-0.681897\pi\)
−0.540849 + 0.841120i \(0.681897\pi\)
\(110\) 0 0
\(111\) 1.48525 0.140973
\(112\) 0 0
\(113\) 11.8815 1.11772 0.558858 0.829264i \(-0.311240\pi\)
0.558858 + 0.829264i \(0.311240\pi\)
\(114\) 0 0
\(115\) −8.71853 −0.813007
\(116\) 0 0
\(117\) −0.863202 −0.0798031
\(118\) 0 0
\(119\) 1.91339 0.175400
\(120\) 0 0
\(121\) 3.50144 0.318313
\(122\) 0 0
\(123\) −1.14413 −0.103163
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 1.41226 0.125318 0.0626590 0.998035i \(-0.480042\pi\)
0.0626590 + 0.998035i \(0.480042\pi\)
\(128\) 0 0
\(129\) −1.82700 −0.160859
\(130\) 0 0
\(131\) 1.64353 0.143596 0.0717980 0.997419i \(-0.477126\pi\)
0.0717980 + 0.997419i \(0.477126\pi\)
\(132\) 0 0
\(133\) 16.5728 1.43704
\(134\) 0 0
\(135\) 1.00047 0.0861064
\(136\) 0 0
\(137\) −10.6338 −0.908508 −0.454254 0.890872i \(-0.650094\pi\)
−0.454254 + 0.890872i \(0.650094\pi\)
\(138\) 0 0
\(139\) 4.89433 0.415131 0.207566 0.978221i \(-0.433446\pi\)
0.207566 + 0.978221i \(0.433446\pi\)
\(140\) 0 0
\(141\) 0.861967 0.0725907
\(142\) 0 0
\(143\) 1.10606 0.0924935
\(144\) 0 0
\(145\) −2.00707 −0.166678
\(146\) 0 0
\(147\) 1.36421 0.112518
\(148\) 0 0
\(149\) −5.51254 −0.451605 −0.225802 0.974173i \(-0.572500\pi\)
−0.225802 + 0.974173i \(0.572500\pi\)
\(150\) 0 0
\(151\) −6.40935 −0.521586 −0.260793 0.965395i \(-0.583984\pi\)
−0.260793 + 0.965395i \(0.583984\pi\)
\(152\) 0 0
\(153\) 1.46128 0.118138
\(154\) 0 0
\(155\) −2.46257 −0.197799
\(156\) 0 0
\(157\) −20.5657 −1.64132 −0.820660 0.571417i \(-0.806394\pi\)
−0.820660 + 0.571417i \(0.806394\pi\)
\(158\) 0 0
\(159\) 0.776828 0.0616065
\(160\) 0 0
\(161\) −33.9275 −2.67386
\(162\) 0 0
\(163\) 12.7435 0.998145 0.499072 0.866560i \(-0.333674\pi\)
0.499072 + 0.866560i \(0.333674\pi\)
\(164\) 0 0
\(165\) −0.637959 −0.0496650
\(166\) 0 0
\(167\) −16.1650 −1.25088 −0.625442 0.780271i \(-0.715081\pi\)
−0.625442 + 0.780271i \(0.715081\pi\)
\(168\) 0 0
\(169\) −12.9156 −0.993511
\(170\) 0 0
\(171\) 12.6568 0.967893
\(172\) 0 0
\(173\) 13.5417 1.02955 0.514777 0.857324i \(-0.327875\pi\)
0.514777 + 0.857324i \(0.327875\pi\)
\(174\) 0 0
\(175\) −3.89143 −0.294164
\(176\) 0 0
\(177\) 1.85060 0.139100
\(178\) 0 0
\(179\) −2.44981 −0.183108 −0.0915538 0.995800i \(-0.529183\pi\)
−0.0915538 + 0.995800i \(0.529183\pi\)
\(180\) 0 0
\(181\) −0.0186908 −0.00138928 −0.000694640 1.00000i \(-0.500221\pi\)
−0.000694640 1.00000i \(0.500221\pi\)
\(182\) 0 0
\(183\) −0.0480427 −0.00355142
\(184\) 0 0
\(185\) −8.86566 −0.651817
\(186\) 0 0
\(187\) −1.87241 −0.136924
\(188\) 0 0
\(189\) 3.89324 0.283191
\(190\) 0 0
\(191\) −5.53162 −0.400254 −0.200127 0.979770i \(-0.564135\pi\)
−0.200127 + 0.979770i \(0.564135\pi\)
\(192\) 0 0
\(193\) 19.1560 1.37888 0.689438 0.724345i \(-0.257857\pi\)
0.689438 + 0.724345i \(0.257857\pi\)
\(194\) 0 0
\(195\) −0.0486587 −0.00348452
\(196\) 0 0
\(197\) −17.4071 −1.24020 −0.620102 0.784521i \(-0.712909\pi\)
−0.620102 + 0.784521i \(0.712909\pi\)
\(198\) 0 0
\(199\) −4.65465 −0.329959 −0.164980 0.986297i \(-0.552756\pi\)
−0.164980 + 0.986297i \(0.552756\pi\)
\(200\) 0 0
\(201\) −0.539821 −0.0380760
\(202\) 0 0
\(203\) −7.81038 −0.548181
\(204\) 0 0
\(205\) 6.82952 0.476994
\(206\) 0 0
\(207\) −25.9109 −1.80093
\(208\) 0 0
\(209\) −16.2178 −1.12181
\(210\) 0 0
\(211\) −25.7612 −1.77348 −0.886738 0.462273i \(-0.847034\pi\)
−0.886738 + 0.462273i \(0.847034\pi\)
\(212\) 0 0
\(213\) −0.424551 −0.0290897
\(214\) 0 0
\(215\) 10.9057 0.743760
\(216\) 0 0
\(217\) −9.58292 −0.650531
\(218\) 0 0
\(219\) −0.932364 −0.0630033
\(220\) 0 0
\(221\) −0.142813 −0.00960666
\(222\) 0 0
\(223\) 9.14177 0.612178 0.306089 0.952003i \(-0.400979\pi\)
0.306089 + 0.952003i \(0.400979\pi\)
\(224\) 0 0
\(225\) −2.97193 −0.198129
\(226\) 0 0
\(227\) 3.27798 0.217567 0.108784 0.994065i \(-0.465304\pi\)
0.108784 + 0.994065i \(0.465304\pi\)
\(228\) 0 0
\(229\) −18.4092 −1.21652 −0.608258 0.793740i \(-0.708131\pi\)
−0.608258 + 0.793740i \(0.708131\pi\)
\(230\) 0 0
\(231\) −2.48257 −0.163341
\(232\) 0 0
\(233\) −7.14449 −0.468051 −0.234025 0.972230i \(-0.575190\pi\)
−0.234025 + 0.972230i \(0.575190\pi\)
\(234\) 0 0
\(235\) −5.14522 −0.335637
\(236\) 0 0
\(237\) −1.78256 −0.115790
\(238\) 0 0
\(239\) 14.6506 0.947671 0.473836 0.880613i \(-0.342869\pi\)
0.473836 + 0.880613i \(0.342869\pi\)
\(240\) 0 0
\(241\) 7.98268 0.514210 0.257105 0.966383i \(-0.417231\pi\)
0.257105 + 0.966383i \(0.417231\pi\)
\(242\) 0 0
\(243\) 4.46696 0.286556
\(244\) 0 0
\(245\) −8.14319 −0.520250
\(246\) 0 0
\(247\) −1.23697 −0.0787066
\(248\) 0 0
\(249\) 0.246329 0.0156105
\(250\) 0 0
\(251\) −13.0627 −0.824510 −0.412255 0.911069i \(-0.635259\pi\)
−0.412255 + 0.911069i \(0.635259\pi\)
\(252\) 0 0
\(253\) 33.2008 2.08732
\(254\) 0 0
\(255\) 0.0823725 0.00515837
\(256\) 0 0
\(257\) 12.2393 0.763464 0.381732 0.924273i \(-0.375328\pi\)
0.381732 + 0.924273i \(0.375328\pi\)
\(258\) 0 0
\(259\) −34.5001 −2.14373
\(260\) 0 0
\(261\) −5.96489 −0.369217
\(262\) 0 0
\(263\) 26.1594 1.61306 0.806528 0.591196i \(-0.201344\pi\)
0.806528 + 0.591196i \(0.201344\pi\)
\(264\) 0 0
\(265\) −4.63701 −0.284849
\(266\) 0 0
\(267\) 1.39823 0.0855703
\(268\) 0 0
\(269\) 8.10981 0.494464 0.247232 0.968956i \(-0.420479\pi\)
0.247232 + 0.968956i \(0.420479\pi\)
\(270\) 0 0
\(271\) −0.350519 −0.0212925 −0.0106463 0.999943i \(-0.503389\pi\)
−0.0106463 + 0.999943i \(0.503389\pi\)
\(272\) 0 0
\(273\) −0.189352 −0.0114601
\(274\) 0 0
\(275\) 3.80808 0.229636
\(276\) 0 0
\(277\) −16.3250 −0.980871 −0.490436 0.871477i \(-0.663162\pi\)
−0.490436 + 0.871477i \(0.663162\pi\)
\(278\) 0 0
\(279\) −7.31861 −0.438154
\(280\) 0 0
\(281\) −22.2566 −1.32772 −0.663860 0.747857i \(-0.731083\pi\)
−0.663860 + 0.747857i \(0.731083\pi\)
\(282\) 0 0
\(283\) −19.5738 −1.16354 −0.581771 0.813353i \(-0.697640\pi\)
−0.581771 + 0.813353i \(0.697640\pi\)
\(284\) 0 0
\(285\) 0.713466 0.0422621
\(286\) 0 0
\(287\) 26.5766 1.56876
\(288\) 0 0
\(289\) −16.7582 −0.985779
\(290\) 0 0
\(291\) −1.74877 −0.102514
\(292\) 0 0
\(293\) −17.5087 −1.02287 −0.511435 0.859322i \(-0.670886\pi\)
−0.511435 + 0.859322i \(0.670886\pi\)
\(294\) 0 0
\(295\) −11.0465 −0.643154
\(296\) 0 0
\(297\) −3.80985 −0.221070
\(298\) 0 0
\(299\) 2.53231 0.146447
\(300\) 0 0
\(301\) 42.4386 2.44612
\(302\) 0 0
\(303\) 1.79918 0.103360
\(304\) 0 0
\(305\) 0.286775 0.0164207
\(306\) 0 0
\(307\) 6.18354 0.352913 0.176457 0.984308i \(-0.443536\pi\)
0.176457 + 0.984308i \(0.443536\pi\)
\(308\) 0 0
\(309\) −1.81124 −0.103038
\(310\) 0 0
\(311\) −15.7369 −0.892359 −0.446180 0.894943i \(-0.647216\pi\)
−0.446180 + 0.894943i \(0.647216\pi\)
\(312\) 0 0
\(313\) 17.0198 0.962018 0.481009 0.876716i \(-0.340270\pi\)
0.481009 + 0.876716i \(0.340270\pi\)
\(314\) 0 0
\(315\) −11.5651 −0.651617
\(316\) 0 0
\(317\) −8.64336 −0.485460 −0.242730 0.970094i \(-0.578043\pi\)
−0.242730 + 0.970094i \(0.578043\pi\)
\(318\) 0 0
\(319\) 7.64309 0.427931
\(320\) 0 0
\(321\) −0.925617 −0.0516629
\(322\) 0 0
\(323\) 2.09402 0.116514
\(324\) 0 0
\(325\) 0.290451 0.0161113
\(326\) 0 0
\(327\) −1.89194 −0.104624
\(328\) 0 0
\(329\) −20.0222 −1.10386
\(330\) 0 0
\(331\) −14.1262 −0.776447 −0.388223 0.921565i \(-0.626911\pi\)
−0.388223 + 0.921565i \(0.626911\pi\)
\(332\) 0 0
\(333\) −26.3482 −1.44387
\(334\) 0 0
\(335\) 3.22227 0.176052
\(336\) 0 0
\(337\) −12.7314 −0.693522 −0.346761 0.937954i \(-0.612718\pi\)
−0.346761 + 0.937954i \(0.612718\pi\)
\(338\) 0 0
\(339\) 1.99048 0.108108
\(340\) 0 0
\(341\) 9.37767 0.507829
\(342\) 0 0
\(343\) −4.44866 −0.240205
\(344\) 0 0
\(345\) −1.46060 −0.0786359
\(346\) 0 0
\(347\) 1.45968 0.0783595 0.0391798 0.999232i \(-0.487525\pi\)
0.0391798 + 0.999232i \(0.487525\pi\)
\(348\) 0 0
\(349\) −28.7787 −1.54049 −0.770244 0.637749i \(-0.779866\pi\)
−0.770244 + 0.637749i \(0.779866\pi\)
\(350\) 0 0
\(351\) −0.290587 −0.0155104
\(352\) 0 0
\(353\) 26.6016 1.41586 0.707930 0.706282i \(-0.249629\pi\)
0.707930 + 0.706282i \(0.249629\pi\)
\(354\) 0 0
\(355\) 2.53421 0.134502
\(356\) 0 0
\(357\) 0.320546 0.0169651
\(358\) 0 0
\(359\) −11.8903 −0.627549 −0.313774 0.949498i \(-0.601594\pi\)
−0.313774 + 0.949498i \(0.601594\pi\)
\(360\) 0 0
\(361\) −0.862722 −0.0454064
\(362\) 0 0
\(363\) 0.586590 0.0307880
\(364\) 0 0
\(365\) 5.56543 0.291308
\(366\) 0 0
\(367\) −11.7937 −0.615628 −0.307814 0.951447i \(-0.599597\pi\)
−0.307814 + 0.951447i \(0.599597\pi\)
\(368\) 0 0
\(369\) 20.2969 1.05661
\(370\) 0 0
\(371\) −18.0446 −0.936827
\(372\) 0 0
\(373\) −25.7122 −1.33133 −0.665665 0.746251i \(-0.731852\pi\)
−0.665665 + 0.746251i \(0.731852\pi\)
\(374\) 0 0
\(375\) −0.167528 −0.00865110
\(376\) 0 0
\(377\) 0.582957 0.0300238
\(378\) 0 0
\(379\) −15.9527 −0.819435 −0.409718 0.912212i \(-0.634373\pi\)
−0.409718 + 0.912212i \(0.634373\pi\)
\(380\) 0 0
\(381\) 0.236593 0.0121210
\(382\) 0 0
\(383\) 1.21784 0.0622287 0.0311143 0.999516i \(-0.490094\pi\)
0.0311143 + 0.999516i \(0.490094\pi\)
\(384\) 0 0
\(385\) 14.8188 0.755238
\(386\) 0 0
\(387\) 32.4109 1.64754
\(388\) 0 0
\(389\) −18.1756 −0.921540 −0.460770 0.887520i \(-0.652427\pi\)
−0.460770 + 0.887520i \(0.652427\pi\)
\(390\) 0 0
\(391\) −4.28685 −0.216795
\(392\) 0 0
\(393\) 0.275337 0.0138889
\(394\) 0 0
\(395\) 10.6404 0.535375
\(396\) 0 0
\(397\) 5.47535 0.274800 0.137400 0.990516i \(-0.456125\pi\)
0.137400 + 0.990516i \(0.456125\pi\)
\(398\) 0 0
\(399\) 2.77640 0.138994
\(400\) 0 0
\(401\) 1.00000 0.0499376
\(402\) 0 0
\(403\) 0.715258 0.0356295
\(404\) 0 0
\(405\) −8.74820 −0.434701
\(406\) 0 0
\(407\) 33.7611 1.67348
\(408\) 0 0
\(409\) −26.6852 −1.31950 −0.659749 0.751486i \(-0.729337\pi\)
−0.659749 + 0.751486i \(0.729337\pi\)
\(410\) 0 0
\(411\) −1.78146 −0.0878729
\(412\) 0 0
\(413\) −42.9868 −2.11524
\(414\) 0 0
\(415\) −1.47038 −0.0721781
\(416\) 0 0
\(417\) 0.819936 0.0401525
\(418\) 0 0
\(419\) 19.4873 0.952017 0.476008 0.879441i \(-0.342083\pi\)
0.476008 + 0.879441i \(0.342083\pi\)
\(420\) 0 0
\(421\) −33.4824 −1.63183 −0.815915 0.578172i \(-0.803766\pi\)
−0.815915 + 0.578172i \(0.803766\pi\)
\(422\) 0 0
\(423\) −15.2912 −0.743486
\(424\) 0 0
\(425\) −0.491694 −0.0238507
\(426\) 0 0
\(427\) 1.11596 0.0540052
\(428\) 0 0
\(429\) 0.185296 0.00894618
\(430\) 0 0
\(431\) 2.86253 0.137883 0.0689416 0.997621i \(-0.478038\pi\)
0.0689416 + 0.997621i \(0.478038\pi\)
\(432\) 0 0
\(433\) 0.577693 0.0277622 0.0138811 0.999904i \(-0.495581\pi\)
0.0138811 + 0.999904i \(0.495581\pi\)
\(434\) 0 0
\(435\) −0.336241 −0.0161215
\(436\) 0 0
\(437\) −37.1304 −1.77619
\(438\) 0 0
\(439\) −19.4584 −0.928698 −0.464349 0.885652i \(-0.653712\pi\)
−0.464349 + 0.885652i \(0.653712\pi\)
\(440\) 0 0
\(441\) −24.2010 −1.15243
\(442\) 0 0
\(443\) 17.6336 0.837796 0.418898 0.908033i \(-0.362417\pi\)
0.418898 + 0.908033i \(0.362417\pi\)
\(444\) 0 0
\(445\) −8.34625 −0.395650
\(446\) 0 0
\(447\) −0.923504 −0.0436803
\(448\) 0 0
\(449\) 4.39251 0.207296 0.103648 0.994614i \(-0.466949\pi\)
0.103648 + 0.994614i \(0.466949\pi\)
\(450\) 0 0
\(451\) −26.0073 −1.22464
\(452\) 0 0
\(453\) −1.07374 −0.0504489
\(454\) 0 0
\(455\) 1.13027 0.0529879
\(456\) 0 0
\(457\) −16.4326 −0.768683 −0.384342 0.923191i \(-0.625572\pi\)
−0.384342 + 0.923191i \(0.625572\pi\)
\(458\) 0 0
\(459\) 0.491923 0.0229610
\(460\) 0 0
\(461\) −13.9029 −0.647522 −0.323761 0.946139i \(-0.604947\pi\)
−0.323761 + 0.946139i \(0.604947\pi\)
\(462\) 0 0
\(463\) −21.6555 −1.00642 −0.503208 0.864165i \(-0.667847\pi\)
−0.503208 + 0.864165i \(0.667847\pi\)
\(464\) 0 0
\(465\) −0.412550 −0.0191315
\(466\) 0 0
\(467\) 11.6077 0.537142 0.268571 0.963260i \(-0.413449\pi\)
0.268571 + 0.963260i \(0.413449\pi\)
\(468\) 0 0
\(469\) 12.5392 0.579008
\(470\) 0 0
\(471\) −3.44532 −0.158752
\(472\) 0 0
\(473\) −41.5296 −1.90953
\(474\) 0 0
\(475\) −4.25879 −0.195407
\(476\) 0 0
\(477\) −13.7809 −0.630983
\(478\) 0 0
\(479\) 27.0285 1.23496 0.617482 0.786585i \(-0.288153\pi\)
0.617482 + 0.786585i \(0.288153\pi\)
\(480\) 0 0
\(481\) 2.57504 0.117412
\(482\) 0 0
\(483\) −5.68381 −0.258622
\(484\) 0 0
\(485\) 10.4387 0.473995
\(486\) 0 0
\(487\) 37.7965 1.71272 0.856361 0.516378i \(-0.172720\pi\)
0.856361 + 0.516378i \(0.172720\pi\)
\(488\) 0 0
\(489\) 2.13488 0.0965428
\(490\) 0 0
\(491\) 25.1387 1.13449 0.567247 0.823548i \(-0.308009\pi\)
0.567247 + 0.823548i \(0.308009\pi\)
\(492\) 0 0
\(493\) −0.986866 −0.0444462
\(494\) 0 0
\(495\) 11.3174 0.508677
\(496\) 0 0
\(497\) 9.86169 0.442357
\(498\) 0 0
\(499\) −5.85404 −0.262063 −0.131031 0.991378i \(-0.541829\pi\)
−0.131031 + 0.991378i \(0.541829\pi\)
\(500\) 0 0
\(501\) −2.70808 −0.120988
\(502\) 0 0
\(503\) 9.83758 0.438636 0.219318 0.975653i \(-0.429617\pi\)
0.219318 + 0.975653i \(0.429617\pi\)
\(504\) 0 0
\(505\) −10.7396 −0.477905
\(506\) 0 0
\(507\) −2.16373 −0.0960946
\(508\) 0 0
\(509\) 14.5931 0.646826 0.323413 0.946258i \(-0.395170\pi\)
0.323413 + 0.946258i \(0.395170\pi\)
\(510\) 0 0
\(511\) 21.6574 0.958069
\(512\) 0 0
\(513\) 4.26077 0.188118
\(514\) 0 0
\(515\) 10.8116 0.476416
\(516\) 0 0
\(517\) 19.5934 0.861715
\(518\) 0 0
\(519\) 2.26861 0.0995809
\(520\) 0 0
\(521\) 30.6354 1.34216 0.671081 0.741384i \(-0.265830\pi\)
0.671081 + 0.741384i \(0.265830\pi\)
\(522\) 0 0
\(523\) 11.4840 0.502162 0.251081 0.967966i \(-0.419214\pi\)
0.251081 + 0.967966i \(0.419214\pi\)
\(524\) 0 0
\(525\) −0.651922 −0.0284522
\(526\) 0 0
\(527\) −1.21083 −0.0527447
\(528\) 0 0
\(529\) 53.0128 2.30491
\(530\) 0 0
\(531\) −32.8296 −1.42468
\(532\) 0 0
\(533\) −1.98364 −0.0859211
\(534\) 0 0
\(535\) 5.52515 0.238873
\(536\) 0 0
\(537\) −0.410412 −0.0177106
\(538\) 0 0
\(539\) 31.0099 1.33569
\(540\) 0 0
\(541\) 24.0130 1.03240 0.516201 0.856468i \(-0.327346\pi\)
0.516201 + 0.856468i \(0.327346\pi\)
\(542\) 0 0
\(543\) −0.00313124 −0.000134374 0
\(544\) 0 0
\(545\) 11.2933 0.483750
\(546\) 0 0
\(547\) 32.9079 1.40704 0.703520 0.710676i \(-0.251611\pi\)
0.703520 + 0.710676i \(0.251611\pi\)
\(548\) 0 0
\(549\) 0.852275 0.0363742
\(550\) 0 0
\(551\) −8.54770 −0.364144
\(552\) 0 0
\(553\) 41.4062 1.76077
\(554\) 0 0
\(555\) −1.48525 −0.0630452
\(556\) 0 0
\(557\) −35.4795 −1.50331 −0.751657 0.659554i \(-0.770745\pi\)
−0.751657 + 0.659554i \(0.770745\pi\)
\(558\) 0 0
\(559\) −3.16756 −0.133974
\(560\) 0 0
\(561\) −0.313681 −0.0132436
\(562\) 0 0
\(563\) 36.6742 1.54564 0.772818 0.634628i \(-0.218847\pi\)
0.772818 + 0.634628i \(0.218847\pi\)
\(564\) 0 0
\(565\) −11.8815 −0.499857
\(566\) 0 0
\(567\) −34.0430 −1.42967
\(568\) 0 0
\(569\) −13.5530 −0.568172 −0.284086 0.958799i \(-0.591690\pi\)
−0.284086 + 0.958799i \(0.591690\pi\)
\(570\) 0 0
\(571\) −33.7913 −1.41412 −0.707060 0.707154i \(-0.749979\pi\)
−0.707060 + 0.707154i \(0.749979\pi\)
\(572\) 0 0
\(573\) −0.926700 −0.0387135
\(574\) 0 0
\(575\) 8.71853 0.363588
\(576\) 0 0
\(577\) 45.2813 1.88509 0.942543 0.334086i \(-0.108428\pi\)
0.942543 + 0.334086i \(0.108428\pi\)
\(578\) 0 0
\(579\) 3.20916 0.133368
\(580\) 0 0
\(581\) −5.72187 −0.237383
\(582\) 0 0
\(583\) 17.6581 0.731323
\(584\) 0 0
\(585\) 0.863202 0.0356890
\(586\) 0 0
\(587\) 32.5132 1.34196 0.670981 0.741474i \(-0.265873\pi\)
0.670981 + 0.741474i \(0.265873\pi\)
\(588\) 0 0
\(589\) −10.4876 −0.432133
\(590\) 0 0
\(591\) −2.91617 −0.119955
\(592\) 0 0
\(593\) −1.39687 −0.0573626 −0.0286813 0.999589i \(-0.509131\pi\)
−0.0286813 + 0.999589i \(0.509131\pi\)
\(594\) 0 0
\(595\) −1.91339 −0.0784414
\(596\) 0 0
\(597\) −0.779784 −0.0319144
\(598\) 0 0
\(599\) −23.4307 −0.957354 −0.478677 0.877991i \(-0.658883\pi\)
−0.478677 + 0.877991i \(0.658883\pi\)
\(600\) 0 0
\(601\) −8.40119 −0.342692 −0.171346 0.985211i \(-0.554812\pi\)
−0.171346 + 0.985211i \(0.554812\pi\)
\(602\) 0 0
\(603\) 9.57639 0.389981
\(604\) 0 0
\(605\) −3.50144 −0.142354
\(606\) 0 0
\(607\) −2.33107 −0.0946151 −0.0473075 0.998880i \(-0.515064\pi\)
−0.0473075 + 0.998880i \(0.515064\pi\)
\(608\) 0 0
\(609\) −1.30846 −0.0530213
\(610\) 0 0
\(611\) 1.49443 0.0604584
\(612\) 0 0
\(613\) 39.8865 1.61100 0.805500 0.592596i \(-0.201897\pi\)
0.805500 + 0.592596i \(0.201897\pi\)
\(614\) 0 0
\(615\) 1.14413 0.0461360
\(616\) 0 0
\(617\) 6.77020 0.272558 0.136279 0.990670i \(-0.456486\pi\)
0.136279 + 0.990670i \(0.456486\pi\)
\(618\) 0 0
\(619\) −6.15830 −0.247523 −0.123762 0.992312i \(-0.539496\pi\)
−0.123762 + 0.992312i \(0.539496\pi\)
\(620\) 0 0
\(621\) −8.72259 −0.350026
\(622\) 0 0
\(623\) −32.4788 −1.30124
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −2.71693 −0.108504
\(628\) 0 0
\(629\) −4.35920 −0.173813
\(630\) 0 0
\(631\) −35.5305 −1.41445 −0.707223 0.706991i \(-0.750052\pi\)
−0.707223 + 0.706991i \(0.750052\pi\)
\(632\) 0 0
\(633\) −4.31572 −0.171535
\(634\) 0 0
\(635\) −1.41226 −0.0560439
\(636\) 0 0
\(637\) 2.36520 0.0937127
\(638\) 0 0
\(639\) 7.53151 0.297942
\(640\) 0 0
\(641\) −28.4406 −1.12334 −0.561669 0.827362i \(-0.689841\pi\)
−0.561669 + 0.827362i \(0.689841\pi\)
\(642\) 0 0
\(643\) 32.2090 1.27020 0.635099 0.772431i \(-0.280959\pi\)
0.635099 + 0.772431i \(0.280959\pi\)
\(644\) 0 0
\(645\) 1.82700 0.0719382
\(646\) 0 0
\(647\) −10.6222 −0.417602 −0.208801 0.977958i \(-0.566956\pi\)
−0.208801 + 0.977958i \(0.566956\pi\)
\(648\) 0 0
\(649\) 42.0661 1.65124
\(650\) 0 0
\(651\) −1.60541 −0.0629209
\(652\) 0 0
\(653\) −0.188320 −0.00736951 −0.00368476 0.999993i \(-0.501173\pi\)
−0.00368476 + 0.999993i \(0.501173\pi\)
\(654\) 0 0
\(655\) −1.64353 −0.0642181
\(656\) 0 0
\(657\) 16.5401 0.645290
\(658\) 0 0
\(659\) −23.2043 −0.903910 −0.451955 0.892041i \(-0.649273\pi\)
−0.451955 + 0.892041i \(0.649273\pi\)
\(660\) 0 0
\(661\) 43.3302 1.68535 0.842676 0.538422i \(-0.180979\pi\)
0.842676 + 0.538422i \(0.180979\pi\)
\(662\) 0 0
\(663\) −0.0239252 −0.000929178 0
\(664\) 0 0
\(665\) −16.5728 −0.642664
\(666\) 0 0
\(667\) 17.4987 0.677554
\(668\) 0 0
\(669\) 1.53150 0.0592112
\(670\) 0 0
\(671\) −1.09206 −0.0421585
\(672\) 0 0
\(673\) −46.2392 −1.78239 −0.891196 0.453619i \(-0.850133\pi\)
−0.891196 + 0.453619i \(0.850133\pi\)
\(674\) 0 0
\(675\) −1.00047 −0.0385079
\(676\) 0 0
\(677\) −17.2254 −0.662024 −0.331012 0.943626i \(-0.607390\pi\)
−0.331012 + 0.943626i \(0.607390\pi\)
\(678\) 0 0
\(679\) 40.6213 1.55890
\(680\) 0 0
\(681\) 0.549153 0.0210436
\(682\) 0 0
\(683\) −10.8786 −0.416259 −0.208130 0.978101i \(-0.566738\pi\)
−0.208130 + 0.978101i \(0.566738\pi\)
\(684\) 0 0
\(685\) 10.6338 0.406297
\(686\) 0 0
\(687\) −3.08406 −0.117664
\(688\) 0 0
\(689\) 1.34682 0.0513099
\(690\) 0 0
\(691\) 31.8085 1.21005 0.605027 0.796205i \(-0.293162\pi\)
0.605027 + 0.796205i \(0.293162\pi\)
\(692\) 0 0
\(693\) 44.0406 1.67297
\(694\) 0 0
\(695\) −4.89433 −0.185652
\(696\) 0 0
\(697\) 3.35803 0.127195
\(698\) 0 0
\(699\) −1.19690 −0.0452710
\(700\) 0 0
\(701\) −29.9457 −1.13103 −0.565517 0.824737i \(-0.691323\pi\)
−0.565517 + 0.824737i \(0.691323\pi\)
\(702\) 0 0
\(703\) −37.7570 −1.42403
\(704\) 0 0
\(705\) −0.861967 −0.0324636
\(706\) 0 0
\(707\) −41.7923 −1.57176
\(708\) 0 0
\(709\) −27.1642 −1.02017 −0.510087 0.860123i \(-0.670387\pi\)
−0.510087 + 0.860123i \(0.670387\pi\)
\(710\) 0 0
\(711\) 31.6224 1.18593
\(712\) 0 0
\(713\) 21.4700 0.804059
\(714\) 0 0
\(715\) −1.10606 −0.0413643
\(716\) 0 0
\(717\) 2.45439 0.0916609
\(718\) 0 0
\(719\) 23.4084 0.872987 0.436493 0.899707i \(-0.356220\pi\)
0.436493 + 0.899707i \(0.356220\pi\)
\(720\) 0 0
\(721\) 42.0725 1.56686
\(722\) 0 0
\(723\) 1.33732 0.0497355
\(724\) 0 0
\(725\) 2.00707 0.0745408
\(726\) 0 0
\(727\) −27.6260 −1.02459 −0.512296 0.858809i \(-0.671205\pi\)
−0.512296 + 0.858809i \(0.671205\pi\)
\(728\) 0 0
\(729\) −25.4963 −0.944306
\(730\) 0 0
\(731\) 5.36225 0.198330
\(732\) 0 0
\(733\) −40.6431 −1.50119 −0.750593 0.660765i \(-0.770232\pi\)
−0.750593 + 0.660765i \(0.770232\pi\)
\(734\) 0 0
\(735\) −1.36421 −0.0503197
\(736\) 0 0
\(737\) −12.2707 −0.451996
\(738\) 0 0
\(739\) −29.2296 −1.07523 −0.537613 0.843192i \(-0.680674\pi\)
−0.537613 + 0.843192i \(0.680674\pi\)
\(740\) 0 0
\(741\) −0.207227 −0.00761268
\(742\) 0 0
\(743\) 32.6987 1.19960 0.599800 0.800150i \(-0.295247\pi\)
0.599800 + 0.800150i \(0.295247\pi\)
\(744\) 0 0
\(745\) 5.51254 0.201964
\(746\) 0 0
\(747\) −4.36987 −0.159885
\(748\) 0 0
\(749\) 21.5007 0.785619
\(750\) 0 0
\(751\) −2.97400 −0.108523 −0.0542613 0.998527i \(-0.517280\pi\)
−0.0542613 + 0.998527i \(0.517280\pi\)
\(752\) 0 0
\(753\) −2.18836 −0.0797484
\(754\) 0 0
\(755\) 6.40935 0.233260
\(756\) 0 0
\(757\) 32.8433 1.19371 0.596855 0.802349i \(-0.296417\pi\)
0.596855 + 0.802349i \(0.296417\pi\)
\(758\) 0 0
\(759\) 5.56207 0.201890
\(760\) 0 0
\(761\) 40.9171 1.48324 0.741622 0.670818i \(-0.234057\pi\)
0.741622 + 0.670818i \(0.234057\pi\)
\(762\) 0 0
\(763\) 43.9469 1.59098
\(764\) 0 0
\(765\) −1.46128 −0.0528328
\(766\) 0 0
\(767\) 3.20848 0.115852
\(768\) 0 0
\(769\) −12.5503 −0.452574 −0.226287 0.974061i \(-0.572659\pi\)
−0.226287 + 0.974061i \(0.572659\pi\)
\(770\) 0 0
\(771\) 2.05042 0.0738440
\(772\) 0 0
\(773\) −15.4109 −0.554291 −0.277145 0.960828i \(-0.589388\pi\)
−0.277145 + 0.960828i \(0.589388\pi\)
\(774\) 0 0
\(775\) 2.46257 0.0884583
\(776\) 0 0
\(777\) −5.77973 −0.207346
\(778\) 0 0
\(779\) 29.0855 1.04210
\(780\) 0 0
\(781\) −9.65047 −0.345321
\(782\) 0 0
\(783\) −2.00801 −0.0717603
\(784\) 0 0
\(785\) 20.5657 0.734020
\(786\) 0 0
\(787\) −4.87593 −0.173808 −0.0869040 0.996217i \(-0.527697\pi\)
−0.0869040 + 0.996217i \(0.527697\pi\)
\(788\) 0 0
\(789\) 4.38242 0.156018
\(790\) 0 0
\(791\) −46.2359 −1.64396
\(792\) 0 0
\(793\) −0.0832941 −0.00295786
\(794\) 0 0
\(795\) −0.776828 −0.0275512
\(796\) 0 0
\(797\) −40.3984 −1.43098 −0.715492 0.698621i \(-0.753797\pi\)
−0.715492 + 0.698621i \(0.753797\pi\)
\(798\) 0 0
\(799\) −2.52987 −0.0895005
\(800\) 0 0
\(801\) −24.8045 −0.876424
\(802\) 0 0
\(803\) −21.1936 −0.747905
\(804\) 0 0
\(805\) 33.9275 1.19579
\(806\) 0 0
\(807\) 1.35862 0.0478257
\(808\) 0 0
\(809\) −39.4863 −1.38827 −0.694133 0.719847i \(-0.744212\pi\)
−0.694133 + 0.719847i \(0.744212\pi\)
\(810\) 0 0
\(811\) 23.4821 0.824569 0.412284 0.911055i \(-0.364731\pi\)
0.412284 + 0.911055i \(0.364731\pi\)
\(812\) 0 0
\(813\) −0.0587218 −0.00205946
\(814\) 0 0
\(815\) −12.7435 −0.446384
\(816\) 0 0
\(817\) 46.4449 1.62490
\(818\) 0 0
\(819\) 3.35909 0.117376
\(820\) 0 0
\(821\) 24.3493 0.849795 0.424897 0.905242i \(-0.360310\pi\)
0.424897 + 0.905242i \(0.360310\pi\)
\(822\) 0 0
\(823\) 35.2922 1.23021 0.615104 0.788446i \(-0.289114\pi\)
0.615104 + 0.788446i \(0.289114\pi\)
\(824\) 0 0
\(825\) 0.637959 0.0222109
\(826\) 0 0
\(827\) −6.54431 −0.227568 −0.113784 0.993506i \(-0.536297\pi\)
−0.113784 + 0.993506i \(0.536297\pi\)
\(828\) 0 0
\(829\) 9.35532 0.324924 0.162462 0.986715i \(-0.448057\pi\)
0.162462 + 0.986715i \(0.448057\pi\)
\(830\) 0 0
\(831\) −2.73488 −0.0948721
\(832\) 0 0
\(833\) −4.00396 −0.138729
\(834\) 0 0
\(835\) 16.1650 0.559412
\(836\) 0 0
\(837\) −2.46372 −0.0851586
\(838\) 0 0
\(839\) −16.9419 −0.584899 −0.292450 0.956281i \(-0.594470\pi\)
−0.292450 + 0.956281i \(0.594470\pi\)
\(840\) 0 0
\(841\) −24.9717 −0.861092
\(842\) 0 0
\(843\) −3.72861 −0.128420
\(844\) 0 0
\(845\) 12.9156 0.444311
\(846\) 0 0
\(847\) −13.6256 −0.468182
\(848\) 0 0
\(849\) −3.27916 −0.112540
\(850\) 0 0
\(851\) 77.2956 2.64966
\(852\) 0 0
\(853\) −27.8745 −0.954405 −0.477203 0.878793i \(-0.658349\pi\)
−0.477203 + 0.878793i \(0.658349\pi\)
\(854\) 0 0
\(855\) −12.6568 −0.432855
\(856\) 0 0
\(857\) −3.66296 −0.125124 −0.0625621 0.998041i \(-0.519927\pi\)
−0.0625621 + 0.998041i \(0.519927\pi\)
\(858\) 0 0
\(859\) −0.603877 −0.0206040 −0.0103020 0.999947i \(-0.503279\pi\)
−0.0103020 + 0.999947i \(0.503279\pi\)
\(860\) 0 0
\(861\) 4.45232 0.151734
\(862\) 0 0
\(863\) 5.87184 0.199880 0.0999399 0.994993i \(-0.468135\pi\)
0.0999399 + 0.994993i \(0.468135\pi\)
\(864\) 0 0
\(865\) −13.5417 −0.460431
\(866\) 0 0
\(867\) −2.80747 −0.0953468
\(868\) 0 0
\(869\) −40.5193 −1.37452
\(870\) 0 0
\(871\) −0.935914 −0.0317122
\(872\) 0 0
\(873\) 31.0230 1.04997
\(874\) 0 0
\(875\) 3.89143 0.131554
\(876\) 0 0
\(877\) −45.2888 −1.52930 −0.764648 0.644448i \(-0.777087\pi\)
−0.764648 + 0.644448i \(0.777087\pi\)
\(878\) 0 0
\(879\) −2.93320 −0.0989343
\(880\) 0 0
\(881\) −12.5944 −0.424318 −0.212159 0.977235i \(-0.568049\pi\)
−0.212159 + 0.977235i \(0.568049\pi\)
\(882\) 0 0
\(883\) 17.7247 0.596483 0.298242 0.954490i \(-0.403600\pi\)
0.298242 + 0.954490i \(0.403600\pi\)
\(884\) 0 0
\(885\) −1.85060 −0.0622074
\(886\) 0 0
\(887\) 10.7875 0.362210 0.181105 0.983464i \(-0.442033\pi\)
0.181105 + 0.983464i \(0.442033\pi\)
\(888\) 0 0
\(889\) −5.49571 −0.184320
\(890\) 0 0
\(891\) 33.3138 1.11605
\(892\) 0 0
\(893\) −21.9124 −0.733270
\(894\) 0 0
\(895\) 2.44981 0.0818882
\(896\) 0 0
\(897\) 0.424233 0.0141647
\(898\) 0 0
\(899\) 4.94257 0.164844
\(900\) 0 0
\(901\) −2.27999 −0.0759575
\(902\) 0 0
\(903\) 7.10965 0.236594
\(904\) 0 0
\(905\) 0.0186908 0.000621305 0
\(906\) 0 0
\(907\) −30.9256 −1.02687 −0.513433 0.858129i \(-0.671627\pi\)
−0.513433 + 0.858129i \(0.671627\pi\)
\(908\) 0 0
\(909\) −31.9173 −1.05863
\(910\) 0 0
\(911\) 6.10261 0.202188 0.101094 0.994877i \(-0.467766\pi\)
0.101094 + 0.994877i \(0.467766\pi\)
\(912\) 0 0
\(913\) 5.59931 0.185310
\(914\) 0 0
\(915\) 0.0480427 0.00158824
\(916\) 0 0
\(917\) −6.39568 −0.211204
\(918\) 0 0
\(919\) −16.9989 −0.560741 −0.280371 0.959892i \(-0.590457\pi\)
−0.280371 + 0.959892i \(0.590457\pi\)
\(920\) 0 0
\(921\) 1.03592 0.0341346
\(922\) 0 0
\(923\) −0.736065 −0.0242279
\(924\) 0 0
\(925\) 8.86566 0.291501
\(926\) 0 0
\(927\) 32.1314 1.05533
\(928\) 0 0
\(929\) −19.3858 −0.636027 −0.318014 0.948086i \(-0.603016\pi\)
−0.318014 + 0.948086i \(0.603016\pi\)
\(930\) 0 0
\(931\) −34.6801 −1.13660
\(932\) 0 0
\(933\) −2.63637 −0.0863110
\(934\) 0 0
\(935\) 1.87241 0.0612343
\(936\) 0 0
\(937\) 50.3467 1.64475 0.822377 0.568943i \(-0.192648\pi\)
0.822377 + 0.568943i \(0.192648\pi\)
\(938\) 0 0
\(939\) 2.85130 0.0930485
\(940\) 0 0
\(941\) −5.47031 −0.178327 −0.0891634 0.996017i \(-0.528419\pi\)
−0.0891634 + 0.996017i \(0.528419\pi\)
\(942\) 0 0
\(943\) −59.5434 −1.93900
\(944\) 0 0
\(945\) −3.89324 −0.126647
\(946\) 0 0
\(947\) −26.3468 −0.856156 −0.428078 0.903742i \(-0.640809\pi\)
−0.428078 + 0.903742i \(0.640809\pi\)
\(948\) 0 0
\(949\) −1.61649 −0.0524733
\(950\) 0 0
\(951\) −1.44800 −0.0469548
\(952\) 0 0
\(953\) 12.5156 0.405419 0.202709 0.979239i \(-0.435025\pi\)
0.202709 + 0.979239i \(0.435025\pi\)
\(954\) 0 0
\(955\) 5.53162 0.178999
\(956\) 0 0
\(957\) 1.28043 0.0413904
\(958\) 0 0
\(959\) 41.3807 1.33625
\(960\) 0 0
\(961\) −24.9357 −0.804378
\(962\) 0 0
\(963\) 16.4204 0.529139
\(964\) 0 0
\(965\) −19.1560 −0.616652
\(966\) 0 0
\(967\) −30.4452 −0.979051 −0.489525 0.871989i \(-0.662830\pi\)
−0.489525 + 0.871989i \(0.662830\pi\)
\(968\) 0 0
\(969\) 0.350807 0.0112695
\(970\) 0 0
\(971\) 18.0458 0.579119 0.289559 0.957160i \(-0.406491\pi\)
0.289559 + 0.957160i \(0.406491\pi\)
\(972\) 0 0
\(973\) −19.0459 −0.610584
\(974\) 0 0
\(975\) 0.0486587 0.00155833
\(976\) 0 0
\(977\) 0.921257 0.0294736 0.0147368 0.999891i \(-0.495309\pi\)
0.0147368 + 0.999891i \(0.495309\pi\)
\(978\) 0 0
\(979\) 31.7832 1.01579
\(980\) 0 0
\(981\) 33.5628 1.07158
\(982\) 0 0
\(983\) −32.4193 −1.03402 −0.517008 0.855981i \(-0.672954\pi\)
−0.517008 + 0.855981i \(0.672954\pi\)
\(984\) 0 0
\(985\) 17.4071 0.554636
\(986\) 0 0
\(987\) −3.35428 −0.106768
\(988\) 0 0
\(989\) −95.0814 −3.02341
\(990\) 0 0
\(991\) −11.9063 −0.378215 −0.189108 0.981956i \(-0.560559\pi\)
−0.189108 + 0.981956i \(0.560559\pi\)
\(992\) 0 0
\(993\) −2.36653 −0.0750997
\(994\) 0 0
\(995\) 4.65465 0.147562
\(996\) 0 0
\(997\) −44.5748 −1.41170 −0.705849 0.708362i \(-0.749434\pi\)
−0.705849 + 0.708362i \(0.749434\pi\)
\(998\) 0 0
\(999\) −8.86979 −0.280628
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 \(a_p\))