Properties

Label 8016.2.a.bg.1.12
Level 8016
Weight 2
Character 8016.1
Self dual Yes
Analytic conductor 64.008
Analytic rank 0
Dimension 13
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8016 = 2^{4} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8016.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0080822603\)
Analytic rank: \(0\)
Dimension: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Root \(3.38131\)
Character \(\chi\) = 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(+3.38131 q^{5}\) \(-2.18014 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(+3.38131 q^{5}\) \(-2.18014 q^{7}\) \(+1.00000 q^{9}\) \(-1.42337 q^{11}\) \(+5.00143 q^{13}\) \(-3.38131 q^{15}\) \(+5.50797 q^{17}\) \(+7.82733 q^{19}\) \(+2.18014 q^{21}\) \(-7.75758 q^{23}\) \(+6.43326 q^{25}\) \(-1.00000 q^{27}\) \(+6.29374 q^{29}\) \(+9.08688 q^{31}\) \(+1.42337 q^{33}\) \(-7.37172 q^{35}\) \(+4.72415 q^{37}\) \(-5.00143 q^{39}\) \(-11.8364 q^{41}\) \(+7.11615 q^{43}\) \(+3.38131 q^{45}\) \(+8.21355 q^{47}\) \(-2.24700 q^{49}\) \(-5.50797 q^{51}\) \(-10.8063 q^{53}\) \(-4.81285 q^{55}\) \(-7.82733 q^{57}\) \(+6.83956 q^{59}\) \(-1.73720 q^{61}\) \(-2.18014 q^{63}\) \(+16.9114 q^{65}\) \(+1.61452 q^{67}\) \(+7.75758 q^{69}\) \(-16.0154 q^{71}\) \(+4.43455 q^{73}\) \(-6.43326 q^{75}\) \(+3.10314 q^{77}\) \(-4.26342 q^{79}\) \(+1.00000 q^{81}\) \(-4.41440 q^{83}\) \(+18.6241 q^{85}\) \(-6.29374 q^{87}\) \(-8.56376 q^{89}\) \(-10.9038 q^{91}\) \(-9.08688 q^{93}\) \(+26.4666 q^{95}\) \(-10.2977 q^{97}\) \(-1.42337 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(13q \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(13q \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 15q^{17} \) \(\mathstrut -\mathstrut 14q^{19} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut -\mathstrut 9q^{23} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 13q^{27} \) \(\mathstrut -\mathstrut 3q^{29} \) \(\mathstrut +\mathstrut 17q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 15q^{35} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut -\mathstrut 12q^{39} \) \(\mathstrut +\mathstrut 12q^{41} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut +\mathstrut 6q^{47} \) \(\mathstrut +\mathstrut 26q^{49} \) \(\mathstrut -\mathstrut 15q^{51} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 7q^{55} \) \(\mathstrut +\mathstrut 14q^{57} \) \(\mathstrut -\mathstrut 14q^{59} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut -\mathstrut q^{63} \) \(\mathstrut +\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 3q^{67} \) \(\mathstrut +\mathstrut 9q^{69} \) \(\mathstrut -\mathstrut 17q^{71} \) \(\mathstrut +\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 37q^{75} \) \(\mathstrut +\mathstrut 30q^{77} \) \(\mathstrut -\mathstrut 10q^{79} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 25q^{85} \) \(\mathstrut +\mathstrut 3q^{87} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 29q^{91} \) \(\mathstrut -\mathstrut 17q^{93} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 38q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 3.38131 1.51217 0.756084 0.654475i \(-0.227110\pi\)
0.756084 + 0.654475i \(0.227110\pi\)
\(6\) 0 0
\(7\) −2.18014 −0.824014 −0.412007 0.911181i \(-0.635172\pi\)
−0.412007 + 0.911181i \(0.635172\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −1.42337 −0.429162 −0.214581 0.976706i \(-0.568839\pi\)
−0.214581 + 0.976706i \(0.568839\pi\)
\(12\) 0 0
\(13\) 5.00143 1.38715 0.693574 0.720386i \(-0.256035\pi\)
0.693574 + 0.720386i \(0.256035\pi\)
\(14\) 0 0
\(15\) −3.38131 −0.873051
\(16\) 0 0
\(17\) 5.50797 1.33588 0.667939 0.744216i \(-0.267177\pi\)
0.667939 + 0.744216i \(0.267177\pi\)
\(18\) 0 0
\(19\) 7.82733 1.79571 0.897856 0.440289i \(-0.145124\pi\)
0.897856 + 0.440289i \(0.145124\pi\)
\(20\) 0 0
\(21\) 2.18014 0.475745
\(22\) 0 0
\(23\) −7.75758 −1.61757 −0.808784 0.588106i \(-0.799874\pi\)
−0.808784 + 0.588106i \(0.799874\pi\)
\(24\) 0 0
\(25\) 6.43326 1.28665
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 6.29374 1.16872 0.584359 0.811495i \(-0.301346\pi\)
0.584359 + 0.811495i \(0.301346\pi\)
\(30\) 0 0
\(31\) 9.08688 1.63205 0.816026 0.578015i \(-0.196172\pi\)
0.816026 + 0.578015i \(0.196172\pi\)
\(32\) 0 0
\(33\) 1.42337 0.247777
\(34\) 0 0
\(35\) −7.37172 −1.24605
\(36\) 0 0
\(37\) 4.72415 0.776646 0.388323 0.921523i \(-0.373055\pi\)
0.388323 + 0.921523i \(0.373055\pi\)
\(38\) 0 0
\(39\) −5.00143 −0.800870
\(40\) 0 0
\(41\) −11.8364 −1.84853 −0.924267 0.381748i \(-0.875322\pi\)
−0.924267 + 0.381748i \(0.875322\pi\)
\(42\) 0 0
\(43\) 7.11615 1.08520 0.542601 0.839991i \(-0.317440\pi\)
0.542601 + 0.839991i \(0.317440\pi\)
\(44\) 0 0
\(45\) 3.38131 0.504056
\(46\) 0 0
\(47\) 8.21355 1.19807 0.599035 0.800723i \(-0.295551\pi\)
0.599035 + 0.800723i \(0.295551\pi\)
\(48\) 0 0
\(49\) −2.24700 −0.321000
\(50\) 0 0
\(51\) −5.50797 −0.771270
\(52\) 0 0
\(53\) −10.8063 −1.48436 −0.742179 0.670201i \(-0.766208\pi\)
−0.742179 + 0.670201i \(0.766208\pi\)
\(54\) 0 0
\(55\) −4.81285 −0.648964
\(56\) 0 0
\(57\) −7.82733 −1.03676
\(58\) 0 0
\(59\) 6.83956 0.890435 0.445218 0.895422i \(-0.353126\pi\)
0.445218 + 0.895422i \(0.353126\pi\)
\(60\) 0 0
\(61\) −1.73720 −0.222426 −0.111213 0.993797i \(-0.535474\pi\)
−0.111213 + 0.993797i \(0.535474\pi\)
\(62\) 0 0
\(63\) −2.18014 −0.274671
\(64\) 0 0
\(65\) 16.9114 2.09760
\(66\) 0 0
\(67\) 1.61452 0.197245 0.0986225 0.995125i \(-0.468556\pi\)
0.0986225 + 0.995125i \(0.468556\pi\)
\(68\) 0 0
\(69\) 7.75758 0.933903
\(70\) 0 0
\(71\) −16.0154 −1.90068 −0.950340 0.311214i \(-0.899264\pi\)
−0.950340 + 0.311214i \(0.899264\pi\)
\(72\) 0 0
\(73\) 4.43455 0.519025 0.259513 0.965740i \(-0.416438\pi\)
0.259513 + 0.965740i \(0.416438\pi\)
\(74\) 0 0
\(75\) −6.43326 −0.742849
\(76\) 0 0
\(77\) 3.10314 0.353635
\(78\) 0 0
\(79\) −4.26342 −0.479673 −0.239836 0.970813i \(-0.577094\pi\)
−0.239836 + 0.970813i \(0.577094\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −4.41440 −0.484544 −0.242272 0.970208i \(-0.577893\pi\)
−0.242272 + 0.970208i \(0.577893\pi\)
\(84\) 0 0
\(85\) 18.6241 2.02007
\(86\) 0 0
\(87\) −6.29374 −0.674759
\(88\) 0 0
\(89\) −8.56376 −0.907757 −0.453879 0.891064i \(-0.649960\pi\)
−0.453879 + 0.891064i \(0.649960\pi\)
\(90\) 0 0
\(91\) −10.9038 −1.14303
\(92\) 0 0
\(93\) −9.08688 −0.942266
\(94\) 0 0
\(95\) 26.4666 2.71542
\(96\) 0 0
\(97\) −10.2977 −1.04557 −0.522786 0.852464i \(-0.675107\pi\)
−0.522786 + 0.852464i \(0.675107\pi\)
\(98\) 0 0
\(99\) −1.42337 −0.143054
\(100\) 0 0
\(101\) 5.31154 0.528518 0.264259 0.964452i \(-0.414873\pi\)
0.264259 + 0.964452i \(0.414873\pi\)
\(102\) 0 0
\(103\) 0.971769 0.0957513 0.0478756 0.998853i \(-0.484755\pi\)
0.0478756 + 0.998853i \(0.484755\pi\)
\(104\) 0 0
\(105\) 7.37172 0.719406
\(106\) 0 0
\(107\) 13.7609 1.33031 0.665156 0.746704i \(-0.268365\pi\)
0.665156 + 0.746704i \(0.268365\pi\)
\(108\) 0 0
\(109\) −5.15480 −0.493741 −0.246870 0.969049i \(-0.579402\pi\)
−0.246870 + 0.969049i \(0.579402\pi\)
\(110\) 0 0
\(111\) −4.72415 −0.448397
\(112\) 0 0
\(113\) −17.9885 −1.69221 −0.846106 0.533015i \(-0.821059\pi\)
−0.846106 + 0.533015i \(0.821059\pi\)
\(114\) 0 0
\(115\) −26.2308 −2.44603
\(116\) 0 0
\(117\) 5.00143 0.462383
\(118\) 0 0
\(119\) −12.0081 −1.10078
\(120\) 0 0
\(121\) −8.97402 −0.815820
\(122\) 0 0
\(123\) 11.8364 1.06725
\(124\) 0 0
\(125\) 4.84630 0.433466
\(126\) 0 0
\(127\) 16.3783 1.45334 0.726668 0.686989i \(-0.241068\pi\)
0.726668 + 0.686989i \(0.241068\pi\)
\(128\) 0 0
\(129\) −7.11615 −0.626542
\(130\) 0 0
\(131\) 12.0066 1.04902 0.524512 0.851403i \(-0.324248\pi\)
0.524512 + 0.851403i \(0.324248\pi\)
\(132\) 0 0
\(133\) −17.0647 −1.47969
\(134\) 0 0
\(135\) −3.38131 −0.291017
\(136\) 0 0
\(137\) 7.24650 0.619110 0.309555 0.950881i \(-0.399820\pi\)
0.309555 + 0.950881i \(0.399820\pi\)
\(138\) 0 0
\(139\) 7.39592 0.627314 0.313657 0.949536i \(-0.398446\pi\)
0.313657 + 0.949536i \(0.398446\pi\)
\(140\) 0 0
\(141\) −8.21355 −0.691706
\(142\) 0 0
\(143\) −7.11888 −0.595310
\(144\) 0 0
\(145\) 21.2811 1.76730
\(146\) 0 0
\(147\) 2.24700 0.185330
\(148\) 0 0
\(149\) 23.8445 1.95341 0.976707 0.214577i \(-0.0688373\pi\)
0.976707 + 0.214577i \(0.0688373\pi\)
\(150\) 0 0
\(151\) −1.42298 −0.115800 −0.0579002 0.998322i \(-0.518441\pi\)
−0.0579002 + 0.998322i \(0.518441\pi\)
\(152\) 0 0
\(153\) 5.50797 0.445293
\(154\) 0 0
\(155\) 30.7256 2.46794
\(156\) 0 0
\(157\) 19.8822 1.58677 0.793386 0.608718i \(-0.208316\pi\)
0.793386 + 0.608718i \(0.208316\pi\)
\(158\) 0 0
\(159\) 10.8063 0.856995
\(160\) 0 0
\(161\) 16.9126 1.33290
\(162\) 0 0
\(163\) −14.3419 −1.12335 −0.561674 0.827359i \(-0.689842\pi\)
−0.561674 + 0.827359i \(0.689842\pi\)
\(164\) 0 0
\(165\) 4.81285 0.374680
\(166\) 0 0
\(167\) 1.00000 0.0773823
\(168\) 0 0
\(169\) 12.0143 0.924179
\(170\) 0 0
\(171\) 7.82733 0.598571
\(172\) 0 0
\(173\) −4.94096 −0.375654 −0.187827 0.982202i \(-0.560144\pi\)
−0.187827 + 0.982202i \(0.560144\pi\)
\(174\) 0 0
\(175\) −14.0254 −1.06022
\(176\) 0 0
\(177\) −6.83956 −0.514093
\(178\) 0 0
\(179\) −1.94308 −0.145233 −0.0726163 0.997360i \(-0.523135\pi\)
−0.0726163 + 0.997360i \(0.523135\pi\)
\(180\) 0 0
\(181\) 11.2531 0.836439 0.418220 0.908346i \(-0.362654\pi\)
0.418220 + 0.908346i \(0.362654\pi\)
\(182\) 0 0
\(183\) 1.73720 0.128418
\(184\) 0 0
\(185\) 15.9738 1.17442
\(186\) 0 0
\(187\) −7.83986 −0.573308
\(188\) 0 0
\(189\) 2.18014 0.158582
\(190\) 0 0
\(191\) 8.97683 0.649541 0.324770 0.945793i \(-0.394713\pi\)
0.324770 + 0.945793i \(0.394713\pi\)
\(192\) 0 0
\(193\) −10.0704 −0.724884 −0.362442 0.932006i \(-0.618057\pi\)
−0.362442 + 0.932006i \(0.618057\pi\)
\(194\) 0 0
\(195\) −16.9114 −1.21105
\(196\) 0 0
\(197\) −19.4156 −1.38330 −0.691652 0.722231i \(-0.743117\pi\)
−0.691652 + 0.722231i \(0.743117\pi\)
\(198\) 0 0
\(199\) −5.98916 −0.424560 −0.212280 0.977209i \(-0.568089\pi\)
−0.212280 + 0.977209i \(0.568089\pi\)
\(200\) 0 0
\(201\) −1.61452 −0.113880
\(202\) 0 0
\(203\) −13.7212 −0.963040
\(204\) 0 0
\(205\) −40.0225 −2.79529
\(206\) 0 0
\(207\) −7.75758 −0.539189
\(208\) 0 0
\(209\) −11.1412 −0.770651
\(210\) 0 0
\(211\) 7.53399 0.518661 0.259331 0.965789i \(-0.416498\pi\)
0.259331 + 0.965789i \(0.416498\pi\)
\(212\) 0 0
\(213\) 16.0154 1.09736
\(214\) 0 0
\(215\) 24.0619 1.64101
\(216\) 0 0
\(217\) −19.8107 −1.34484
\(218\) 0 0
\(219\) −4.43455 −0.299659
\(220\) 0 0
\(221\) 27.5477 1.85306
\(222\) 0 0
\(223\) −1.15074 −0.0770591 −0.0385295 0.999257i \(-0.512267\pi\)
−0.0385295 + 0.999257i \(0.512267\pi\)
\(224\) 0 0
\(225\) 6.43326 0.428884
\(226\) 0 0
\(227\) 25.0325 1.66147 0.830733 0.556671i \(-0.187922\pi\)
0.830733 + 0.556671i \(0.187922\pi\)
\(228\) 0 0
\(229\) 7.40955 0.489637 0.244818 0.969569i \(-0.421272\pi\)
0.244818 + 0.969569i \(0.421272\pi\)
\(230\) 0 0
\(231\) −3.10314 −0.204171
\(232\) 0 0
\(233\) −2.93657 −0.192381 −0.0961906 0.995363i \(-0.530666\pi\)
−0.0961906 + 0.995363i \(0.530666\pi\)
\(234\) 0 0
\(235\) 27.7726 1.81168
\(236\) 0 0
\(237\) 4.26342 0.276939
\(238\) 0 0
\(239\) −26.6134 −1.72148 −0.860738 0.509048i \(-0.829998\pi\)
−0.860738 + 0.509048i \(0.829998\pi\)
\(240\) 0 0
\(241\) 16.8419 1.08488 0.542441 0.840094i \(-0.317500\pi\)
0.542441 + 0.840094i \(0.317500\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −7.59781 −0.485406
\(246\) 0 0
\(247\) 39.1479 2.49092
\(248\) 0 0
\(249\) 4.41440 0.279751
\(250\) 0 0
\(251\) −5.78068 −0.364873 −0.182437 0.983218i \(-0.558398\pi\)
−0.182437 + 0.983218i \(0.558398\pi\)
\(252\) 0 0
\(253\) 11.0419 0.694198
\(254\) 0 0
\(255\) −18.6241 −1.16629
\(256\) 0 0
\(257\) 28.5244 1.77930 0.889651 0.456641i \(-0.150948\pi\)
0.889651 + 0.456641i \(0.150948\pi\)
\(258\) 0 0
\(259\) −10.2993 −0.639967
\(260\) 0 0
\(261\) 6.29374 0.389573
\(262\) 0 0
\(263\) −4.27282 −0.263473 −0.131737 0.991285i \(-0.542055\pi\)
−0.131737 + 0.991285i \(0.542055\pi\)
\(264\) 0 0
\(265\) −36.5394 −2.24460
\(266\) 0 0
\(267\) 8.56376 0.524094
\(268\) 0 0
\(269\) 7.38718 0.450404 0.225202 0.974312i \(-0.427696\pi\)
0.225202 + 0.974312i \(0.427696\pi\)
\(270\) 0 0
\(271\) −14.7734 −0.897420 −0.448710 0.893677i \(-0.648116\pi\)
−0.448710 + 0.893677i \(0.648116\pi\)
\(272\) 0 0
\(273\) 10.9038 0.659929
\(274\) 0 0
\(275\) −9.15690 −0.552182
\(276\) 0 0
\(277\) −2.05325 −0.123368 −0.0616839 0.998096i \(-0.519647\pi\)
−0.0616839 + 0.998096i \(0.519647\pi\)
\(278\) 0 0
\(279\) 9.08688 0.544018
\(280\) 0 0
\(281\) 25.3998 1.51523 0.757613 0.652704i \(-0.226365\pi\)
0.757613 + 0.652704i \(0.226365\pi\)
\(282\) 0 0
\(283\) −2.37163 −0.140979 −0.0704894 0.997513i \(-0.522456\pi\)
−0.0704894 + 0.997513i \(0.522456\pi\)
\(284\) 0 0
\(285\) −26.4666 −1.56775
\(286\) 0 0
\(287\) 25.8050 1.52322
\(288\) 0 0
\(289\) 13.3377 0.784571
\(290\) 0 0
\(291\) 10.2977 0.603661
\(292\) 0 0
\(293\) 8.38097 0.489621 0.244811 0.969571i \(-0.421274\pi\)
0.244811 + 0.969571i \(0.421274\pi\)
\(294\) 0 0
\(295\) 23.1267 1.34649
\(296\) 0 0
\(297\) 1.42337 0.0825922
\(298\) 0 0
\(299\) −38.7990 −2.24381
\(300\) 0 0
\(301\) −15.5142 −0.894222
\(302\) 0 0
\(303\) −5.31154 −0.305140
\(304\) 0 0
\(305\) −5.87403 −0.336346
\(306\) 0 0
\(307\) −23.1839 −1.32318 −0.661588 0.749868i \(-0.730117\pi\)
−0.661588 + 0.749868i \(0.730117\pi\)
\(308\) 0 0
\(309\) −0.971769 −0.0552820
\(310\) 0 0
\(311\) −22.1324 −1.25501 −0.627506 0.778612i \(-0.715924\pi\)
−0.627506 + 0.778612i \(0.715924\pi\)
\(312\) 0 0
\(313\) −25.6297 −1.44868 −0.724338 0.689445i \(-0.757854\pi\)
−0.724338 + 0.689445i \(0.757854\pi\)
\(314\) 0 0
\(315\) −7.37172 −0.415349
\(316\) 0 0
\(317\) −34.5554 −1.94082 −0.970412 0.241454i \(-0.922376\pi\)
−0.970412 + 0.241454i \(0.922376\pi\)
\(318\) 0 0
\(319\) −8.95830 −0.501569
\(320\) 0 0
\(321\) −13.7609 −0.768056
\(322\) 0 0
\(323\) 43.1127 2.39885
\(324\) 0 0
\(325\) 32.1755 1.78478
\(326\) 0 0
\(327\) 5.15480 0.285061
\(328\) 0 0
\(329\) −17.9067 −0.987227
\(330\) 0 0
\(331\) 9.70159 0.533247 0.266624 0.963801i \(-0.414092\pi\)
0.266624 + 0.963801i \(0.414092\pi\)
\(332\) 0 0
\(333\) 4.72415 0.258882
\(334\) 0 0
\(335\) 5.45920 0.298268
\(336\) 0 0
\(337\) 7.56357 0.412014 0.206007 0.978551i \(-0.433953\pi\)
0.206007 + 0.978551i \(0.433953\pi\)
\(338\) 0 0
\(339\) 17.9885 0.976999
\(340\) 0 0
\(341\) −12.9340 −0.700414
\(342\) 0 0
\(343\) 20.1597 1.08852
\(344\) 0 0
\(345\) 26.2308 1.41222
\(346\) 0 0
\(347\) 7.21673 0.387415 0.193707 0.981059i \(-0.437949\pi\)
0.193707 + 0.981059i \(0.437949\pi\)
\(348\) 0 0
\(349\) 13.2805 0.710889 0.355444 0.934697i \(-0.384330\pi\)
0.355444 + 0.934697i \(0.384330\pi\)
\(350\) 0 0
\(351\) −5.00143 −0.266957
\(352\) 0 0
\(353\) −16.4226 −0.874087 −0.437043 0.899440i \(-0.643974\pi\)
−0.437043 + 0.899440i \(0.643974\pi\)
\(354\) 0 0
\(355\) −54.1531 −2.87415
\(356\) 0 0
\(357\) 12.0081 0.635537
\(358\) 0 0
\(359\) −0.150138 −0.00792397 −0.00396198 0.999992i \(-0.501261\pi\)
−0.00396198 + 0.999992i \(0.501261\pi\)
\(360\) 0 0
\(361\) 42.2671 2.22458
\(362\) 0 0
\(363\) 8.97402 0.471014
\(364\) 0 0
\(365\) 14.9946 0.784853
\(366\) 0 0
\(367\) −21.6880 −1.13211 −0.566053 0.824369i \(-0.691530\pi\)
−0.566053 + 0.824369i \(0.691530\pi\)
\(368\) 0 0
\(369\) −11.8364 −0.616178
\(370\) 0 0
\(371\) 23.5592 1.22313
\(372\) 0 0
\(373\) 17.2389 0.892595 0.446298 0.894885i \(-0.352742\pi\)
0.446298 + 0.894885i \(0.352742\pi\)
\(374\) 0 0
\(375\) −4.84630 −0.250262
\(376\) 0 0
\(377\) 31.4777 1.62118
\(378\) 0 0
\(379\) 5.48673 0.281834 0.140917 0.990021i \(-0.454995\pi\)
0.140917 + 0.990021i \(0.454995\pi\)
\(380\) 0 0
\(381\) −16.3783 −0.839084
\(382\) 0 0
\(383\) 15.0351 0.768256 0.384128 0.923280i \(-0.374502\pi\)
0.384128 + 0.923280i \(0.374502\pi\)
\(384\) 0 0
\(385\) 10.4927 0.534756
\(386\) 0 0
\(387\) 7.11615 0.361734
\(388\) 0 0
\(389\) −22.5552 −1.14359 −0.571797 0.820395i \(-0.693753\pi\)
−0.571797 + 0.820395i \(0.693753\pi\)
\(390\) 0 0
\(391\) −42.7285 −2.16087
\(392\) 0 0
\(393\) −12.0066 −0.605655
\(394\) 0 0
\(395\) −14.4160 −0.725346
\(396\) 0 0
\(397\) 14.6044 0.732975 0.366488 0.930423i \(-0.380560\pi\)
0.366488 + 0.930423i \(0.380560\pi\)
\(398\) 0 0
\(399\) 17.0647 0.854301
\(400\) 0 0
\(401\) −8.53046 −0.425991 −0.212995 0.977053i \(-0.568322\pi\)
−0.212995 + 0.977053i \(0.568322\pi\)
\(402\) 0 0
\(403\) 45.4474 2.26390
\(404\) 0 0
\(405\) 3.38131 0.168019
\(406\) 0 0
\(407\) −6.72421 −0.333307
\(408\) 0 0
\(409\) 32.9598 1.62976 0.814879 0.579631i \(-0.196803\pi\)
0.814879 + 0.579631i \(0.196803\pi\)
\(410\) 0 0
\(411\) −7.24650 −0.357444
\(412\) 0 0
\(413\) −14.9112 −0.733731
\(414\) 0 0
\(415\) −14.9265 −0.732711
\(416\) 0 0
\(417\) −7.39592 −0.362180
\(418\) 0 0
\(419\) −22.4830 −1.09837 −0.549183 0.835702i \(-0.685061\pi\)
−0.549183 + 0.835702i \(0.685061\pi\)
\(420\) 0 0
\(421\) −2.13889 −0.104243 −0.0521215 0.998641i \(-0.516598\pi\)
−0.0521215 + 0.998641i \(0.516598\pi\)
\(422\) 0 0
\(423\) 8.21355 0.399356
\(424\) 0 0
\(425\) 35.4342 1.71881
\(426\) 0 0
\(427\) 3.78734 0.183282
\(428\) 0 0
\(429\) 7.11888 0.343703
\(430\) 0 0
\(431\) 37.6297 1.81256 0.906278 0.422681i \(-0.138911\pi\)
0.906278 + 0.422681i \(0.138911\pi\)
\(432\) 0 0
\(433\) 4.34024 0.208579 0.104289 0.994547i \(-0.466743\pi\)
0.104289 + 0.994547i \(0.466743\pi\)
\(434\) 0 0
\(435\) −21.2811 −1.02035
\(436\) 0 0
\(437\) −60.7212 −2.90469
\(438\) 0 0
\(439\) 3.88893 0.185609 0.0928044 0.995684i \(-0.470417\pi\)
0.0928044 + 0.995684i \(0.470417\pi\)
\(440\) 0 0
\(441\) −2.24700 −0.107000
\(442\) 0 0
\(443\) 4.35696 0.207005 0.103503 0.994629i \(-0.466995\pi\)
0.103503 + 0.994629i \(0.466995\pi\)
\(444\) 0 0
\(445\) −28.9567 −1.37268
\(446\) 0 0
\(447\) −23.8445 −1.12780
\(448\) 0 0
\(449\) 18.8021 0.887328 0.443664 0.896193i \(-0.353678\pi\)
0.443664 + 0.896193i \(0.353678\pi\)
\(450\) 0 0
\(451\) 16.8475 0.793319
\(452\) 0 0
\(453\) 1.42298 0.0668573
\(454\) 0 0
\(455\) −36.8692 −1.72845
\(456\) 0 0
\(457\) 26.5750 1.24313 0.621563 0.783364i \(-0.286498\pi\)
0.621563 + 0.783364i \(0.286498\pi\)
\(458\) 0 0
\(459\) −5.50797 −0.257090
\(460\) 0 0
\(461\) 20.0895 0.935662 0.467831 0.883818i \(-0.345036\pi\)
0.467831 + 0.883818i \(0.345036\pi\)
\(462\) 0 0
\(463\) −29.0599 −1.35053 −0.675264 0.737576i \(-0.735970\pi\)
−0.675264 + 0.737576i \(0.735970\pi\)
\(464\) 0 0
\(465\) −30.7256 −1.42486
\(466\) 0 0
\(467\) −25.4129 −1.17597 −0.587984 0.808872i \(-0.700078\pi\)
−0.587984 + 0.808872i \(0.700078\pi\)
\(468\) 0 0
\(469\) −3.51988 −0.162533
\(470\) 0 0
\(471\) −19.8822 −0.916124
\(472\) 0 0
\(473\) −10.1289 −0.465727
\(474\) 0 0
\(475\) 50.3553 2.31046
\(476\) 0 0
\(477\) −10.8063 −0.494786
\(478\) 0 0
\(479\) −2.72548 −0.124530 −0.0622651 0.998060i \(-0.519832\pi\)
−0.0622651 + 0.998060i \(0.519832\pi\)
\(480\) 0 0
\(481\) 23.6275 1.07732
\(482\) 0 0
\(483\) −16.9126 −0.769550
\(484\) 0 0
\(485\) −34.8197 −1.58108
\(486\) 0 0
\(487\) −23.1754 −1.05018 −0.525089 0.851047i \(-0.675968\pi\)
−0.525089 + 0.851047i \(0.675968\pi\)
\(488\) 0 0
\(489\) 14.3419 0.648565
\(490\) 0 0
\(491\) 22.3994 1.01087 0.505434 0.862865i \(-0.331332\pi\)
0.505434 + 0.862865i \(0.331332\pi\)
\(492\) 0 0
\(493\) 34.6657 1.56126
\(494\) 0 0
\(495\) −4.81285 −0.216321
\(496\) 0 0
\(497\) 34.9158 1.56619
\(498\) 0 0
\(499\) 22.4678 1.00580 0.502898 0.864346i \(-0.332267\pi\)
0.502898 + 0.864346i \(0.332267\pi\)
\(500\) 0 0
\(501\) −1.00000 −0.0446767
\(502\) 0 0
\(503\) −34.4958 −1.53809 −0.769046 0.639193i \(-0.779269\pi\)
−0.769046 + 0.639193i \(0.779269\pi\)
\(504\) 0 0
\(505\) 17.9600 0.799208
\(506\) 0 0
\(507\) −12.0143 −0.533575
\(508\) 0 0
\(509\) 36.0445 1.59765 0.798823 0.601567i \(-0.205457\pi\)
0.798823 + 0.601567i \(0.205457\pi\)
\(510\) 0 0
\(511\) −9.66794 −0.427684
\(512\) 0 0
\(513\) −7.82733 −0.345585
\(514\) 0 0
\(515\) 3.28585 0.144792
\(516\) 0 0
\(517\) −11.6909 −0.514165
\(518\) 0 0
\(519\) 4.94096 0.216884
\(520\) 0 0
\(521\) −15.3650 −0.673154 −0.336577 0.941656i \(-0.609269\pi\)
−0.336577 + 0.941656i \(0.609269\pi\)
\(522\) 0 0
\(523\) −11.7306 −0.512941 −0.256471 0.966552i \(-0.582560\pi\)
−0.256471 + 0.966552i \(0.582560\pi\)
\(524\) 0 0
\(525\) 14.0254 0.612118
\(526\) 0 0
\(527\) 50.0503 2.18022
\(528\) 0 0
\(529\) 37.1801 1.61653
\(530\) 0 0
\(531\) 6.83956 0.296812
\(532\) 0 0
\(533\) −59.1989 −2.56419
\(534\) 0 0
\(535\) 46.5297 2.01166
\(536\) 0 0
\(537\) 1.94308 0.0838501
\(538\) 0 0
\(539\) 3.19831 0.137761
\(540\) 0 0
\(541\) −26.9718 −1.15961 −0.579804 0.814756i \(-0.696871\pi\)
−0.579804 + 0.814756i \(0.696871\pi\)
\(542\) 0 0
\(543\) −11.2531 −0.482919
\(544\) 0 0
\(545\) −17.4300 −0.746619
\(546\) 0 0
\(547\) −38.4592 −1.64440 −0.822198 0.569202i \(-0.807252\pi\)
−0.822198 + 0.569202i \(0.807252\pi\)
\(548\) 0 0
\(549\) −1.73720 −0.0741420
\(550\) 0 0
\(551\) 49.2632 2.09868
\(552\) 0 0
\(553\) 9.29485 0.395257
\(554\) 0 0
\(555\) −15.9738 −0.678051
\(556\) 0 0
\(557\) −15.1906 −0.643648 −0.321824 0.946800i \(-0.604296\pi\)
−0.321824 + 0.946800i \(0.604296\pi\)
\(558\) 0 0
\(559\) 35.5909 1.50534
\(560\) 0 0
\(561\) 7.83986 0.330999
\(562\) 0 0
\(563\) −13.3816 −0.563969 −0.281985 0.959419i \(-0.590993\pi\)
−0.281985 + 0.959419i \(0.590993\pi\)
\(564\) 0 0
\(565\) −60.8246 −2.55891
\(566\) 0 0
\(567\) −2.18014 −0.0915572
\(568\) 0 0
\(569\) −19.6459 −0.823600 −0.411800 0.911274i \(-0.635100\pi\)
−0.411800 + 0.911274i \(0.635100\pi\)
\(570\) 0 0
\(571\) 15.2035 0.636249 0.318124 0.948049i \(-0.396947\pi\)
0.318124 + 0.948049i \(0.396947\pi\)
\(572\) 0 0
\(573\) −8.97683 −0.375013
\(574\) 0 0
\(575\) −49.9066 −2.08125
\(576\) 0 0
\(577\) 0.699702 0.0291290 0.0145645 0.999894i \(-0.495364\pi\)
0.0145645 + 0.999894i \(0.495364\pi\)
\(578\) 0 0
\(579\) 10.0704 0.418512
\(580\) 0 0
\(581\) 9.62400 0.399271
\(582\) 0 0
\(583\) 15.3813 0.637030
\(584\) 0 0
\(585\) 16.9114 0.699200
\(586\) 0 0
\(587\) 12.4446 0.513645 0.256822 0.966459i \(-0.417324\pi\)
0.256822 + 0.966459i \(0.417324\pi\)
\(588\) 0 0
\(589\) 71.1260 2.93070
\(590\) 0 0
\(591\) 19.4156 0.798651
\(592\) 0 0
\(593\) 17.1187 0.702982 0.351491 0.936191i \(-0.385675\pi\)
0.351491 + 0.936191i \(0.385675\pi\)
\(594\) 0 0
\(595\) −40.6032 −1.66457
\(596\) 0 0
\(597\) 5.98916 0.245120
\(598\) 0 0
\(599\) 16.8211 0.687289 0.343645 0.939100i \(-0.388338\pi\)
0.343645 + 0.939100i \(0.388338\pi\)
\(600\) 0 0
\(601\) −22.5830 −0.921178 −0.460589 0.887614i \(-0.652362\pi\)
−0.460589 + 0.887614i \(0.652362\pi\)
\(602\) 0 0
\(603\) 1.61452 0.0657484
\(604\) 0 0
\(605\) −30.3440 −1.23366
\(606\) 0 0
\(607\) 9.60797 0.389976 0.194988 0.980806i \(-0.437533\pi\)
0.194988 + 0.980806i \(0.437533\pi\)
\(608\) 0 0
\(609\) 13.7212 0.556012
\(610\) 0 0
\(611\) 41.0795 1.66190
\(612\) 0 0
\(613\) 31.4590 1.27062 0.635308 0.772259i \(-0.280873\pi\)
0.635308 + 0.772259i \(0.280873\pi\)
\(614\) 0 0
\(615\) 40.0225 1.61386
\(616\) 0 0
\(617\) −15.2764 −0.615005 −0.307503 0.951547i \(-0.599493\pi\)
−0.307503 + 0.951547i \(0.599493\pi\)
\(618\) 0 0
\(619\) −34.1164 −1.37126 −0.685628 0.727952i \(-0.740472\pi\)
−0.685628 + 0.727952i \(0.740472\pi\)
\(620\) 0 0
\(621\) 7.75758 0.311301
\(622\) 0 0
\(623\) 18.6702 0.748005
\(624\) 0 0
\(625\) −15.7795 −0.631178
\(626\) 0 0
\(627\) 11.1412 0.444935
\(628\) 0 0
\(629\) 26.0205 1.03750
\(630\) 0 0
\(631\) 29.8395 1.18789 0.593946 0.804505i \(-0.297569\pi\)
0.593946 + 0.804505i \(0.297569\pi\)
\(632\) 0 0
\(633\) −7.53399 −0.299449
\(634\) 0 0
\(635\) 55.3800 2.19769
\(636\) 0 0
\(637\) −11.2382 −0.445275
\(638\) 0 0
\(639\) −16.0154 −0.633560
\(640\) 0 0
\(641\) 1.98414 0.0783690 0.0391845 0.999232i \(-0.487524\pi\)
0.0391845 + 0.999232i \(0.487524\pi\)
\(642\) 0 0
\(643\) −15.6832 −0.618484 −0.309242 0.950983i \(-0.600075\pi\)
−0.309242 + 0.950983i \(0.600075\pi\)
\(644\) 0 0
\(645\) −24.0619 −0.947436
\(646\) 0 0
\(647\) 9.16451 0.360294 0.180147 0.983640i \(-0.442343\pi\)
0.180147 + 0.983640i \(0.442343\pi\)
\(648\) 0 0
\(649\) −9.73521 −0.382141
\(650\) 0 0
\(651\) 19.8107 0.776441
\(652\) 0 0
\(653\) 12.0883 0.473050 0.236525 0.971625i \(-0.423991\pi\)
0.236525 + 0.971625i \(0.423991\pi\)
\(654\) 0 0
\(655\) 40.5982 1.58630
\(656\) 0 0
\(657\) 4.43455 0.173008
\(658\) 0 0
\(659\) 42.2128 1.64438 0.822188 0.569217i \(-0.192753\pi\)
0.822188 + 0.569217i \(0.192753\pi\)
\(660\) 0 0
\(661\) −10.0116 −0.389404 −0.194702 0.980862i \(-0.562374\pi\)
−0.194702 + 0.980862i \(0.562374\pi\)
\(662\) 0 0
\(663\) −27.5477 −1.06987
\(664\) 0 0
\(665\) −57.7009 −2.23754
\(666\) 0 0
\(667\) −48.8242 −1.89048
\(668\) 0 0
\(669\) 1.15074 0.0444901
\(670\) 0 0
\(671\) 2.47268 0.0954567
\(672\) 0 0
\(673\) 15.8885 0.612457 0.306229 0.951958i \(-0.400933\pi\)
0.306229 + 0.951958i \(0.400933\pi\)
\(674\) 0 0
\(675\) −6.43326 −0.247616
\(676\) 0 0
\(677\) 31.1756 1.19817 0.599087 0.800684i \(-0.295530\pi\)
0.599087 + 0.800684i \(0.295530\pi\)
\(678\) 0 0
\(679\) 22.4504 0.861566
\(680\) 0 0
\(681\) −25.0325 −0.959248
\(682\) 0 0
\(683\) −19.7517 −0.755780 −0.377890 0.925851i \(-0.623350\pi\)
−0.377890 + 0.925851i \(0.623350\pi\)
\(684\) 0 0
\(685\) 24.5027 0.936199
\(686\) 0 0
\(687\) −7.40955 −0.282692
\(688\) 0 0
\(689\) −54.0469 −2.05902
\(690\) 0 0
\(691\) 35.7668 1.36063 0.680316 0.732919i \(-0.261842\pi\)
0.680316 + 0.732919i \(0.261842\pi\)
\(692\) 0 0
\(693\) 3.10314 0.117878
\(694\) 0 0
\(695\) 25.0079 0.948604
\(696\) 0 0
\(697\) −65.1944 −2.46942
\(698\) 0 0
\(699\) 2.93657 0.111071
\(700\) 0 0
\(701\) −23.2240 −0.877160 −0.438580 0.898692i \(-0.644518\pi\)
−0.438580 + 0.898692i \(0.644518\pi\)
\(702\) 0 0
\(703\) 36.9775 1.39463
\(704\) 0 0
\(705\) −27.7726 −1.04598
\(706\) 0 0
\(707\) −11.5799 −0.435506
\(708\) 0 0
\(709\) 19.8679 0.746156 0.373078 0.927800i \(-0.378302\pi\)
0.373078 + 0.927800i \(0.378302\pi\)
\(710\) 0 0
\(711\) −4.26342 −0.159891
\(712\) 0 0
\(713\) −70.4923 −2.63996
\(714\) 0 0
\(715\) −24.0711 −0.900209
\(716\) 0 0
\(717\) 26.6134 0.993895
\(718\) 0 0
\(719\) −5.79193 −0.216003 −0.108001 0.994151i \(-0.534445\pi\)
−0.108001 + 0.994151i \(0.534445\pi\)
\(720\) 0 0
\(721\) −2.11859 −0.0789004
\(722\) 0 0
\(723\) −16.8419 −0.626357
\(724\) 0 0
\(725\) 40.4893 1.50373
\(726\) 0 0
\(727\) 22.2264 0.824331 0.412165 0.911109i \(-0.364773\pi\)
0.412165 + 0.911109i \(0.364773\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 39.1955 1.44970
\(732\) 0 0
\(733\) −2.28416 −0.0843672 −0.0421836 0.999110i \(-0.513431\pi\)
−0.0421836 + 0.999110i \(0.513431\pi\)
\(734\) 0 0
\(735\) 7.59781 0.280249
\(736\) 0 0
\(737\) −2.29806 −0.0846500
\(738\) 0 0
\(739\) −1.67059 −0.0614538 −0.0307269 0.999528i \(-0.509782\pi\)
−0.0307269 + 0.999528i \(0.509782\pi\)
\(740\) 0 0
\(741\) −39.1479 −1.43813
\(742\) 0 0
\(743\) 49.4665 1.81475 0.907375 0.420323i \(-0.138083\pi\)
0.907375 + 0.420323i \(0.138083\pi\)
\(744\) 0 0
\(745\) 80.6255 2.95389
\(746\) 0 0
\(747\) −4.41440 −0.161515
\(748\) 0 0
\(749\) −30.0006 −1.09620
\(750\) 0 0
\(751\) −38.2975 −1.39749 −0.698747 0.715369i \(-0.746259\pi\)
−0.698747 + 0.715369i \(0.746259\pi\)
\(752\) 0 0
\(753\) 5.78068 0.210660
\(754\) 0 0
\(755\) −4.81153 −0.175110
\(756\) 0 0
\(757\) 30.3444 1.10288 0.551442 0.834213i \(-0.314078\pi\)
0.551442 + 0.834213i \(0.314078\pi\)
\(758\) 0 0
\(759\) −11.0419 −0.400795
\(760\) 0 0
\(761\) 13.5231 0.490214 0.245107 0.969496i \(-0.421177\pi\)
0.245107 + 0.969496i \(0.421177\pi\)
\(762\) 0 0
\(763\) 11.2382 0.406849
\(764\) 0 0
\(765\) 18.6241 0.673358
\(766\) 0 0
\(767\) 34.2076 1.23517
\(768\) 0 0
\(769\) 12.8744 0.464261 0.232131 0.972685i \(-0.425430\pi\)
0.232131 + 0.972685i \(0.425430\pi\)
\(770\) 0 0
\(771\) −28.5244 −1.02728
\(772\) 0 0
\(773\) −5.91163 −0.212627 −0.106313 0.994333i \(-0.533905\pi\)
−0.106313 + 0.994333i \(0.533905\pi\)
\(774\) 0 0
\(775\) 58.4583 2.09988
\(776\) 0 0
\(777\) 10.2993 0.369485
\(778\) 0 0
\(779\) −92.6473 −3.31943
\(780\) 0 0
\(781\) 22.7958 0.815699
\(782\) 0 0
\(783\) −6.29374 −0.224920
\(784\) 0 0
\(785\) 67.2279 2.39947
\(786\) 0 0
\(787\) −26.3311 −0.938601 −0.469301 0.883039i \(-0.655494\pi\)
−0.469301 + 0.883039i \(0.655494\pi\)
\(788\) 0 0
\(789\) 4.27282 0.152116
\(790\) 0 0
\(791\) 39.2173 1.39441
\(792\) 0 0
\(793\) −8.68851 −0.308538
\(794\) 0 0
\(795\) 36.5394 1.29592
\(796\) 0 0
\(797\) −50.7848 −1.79889 −0.899445 0.437035i \(-0.856029\pi\)
−0.899445 + 0.437035i \(0.856029\pi\)
\(798\) 0 0
\(799\) 45.2400 1.60047
\(800\) 0 0
\(801\) −8.56376 −0.302586
\(802\) 0 0
\(803\) −6.31200 −0.222746
\(804\) 0 0
\(805\) 57.1867 2.01557
\(806\) 0 0
\(807\) −7.38718 −0.260041
\(808\) 0 0
\(809\) 22.0939 0.776781 0.388391 0.921495i \(-0.373031\pi\)
0.388391 + 0.921495i \(0.373031\pi\)
\(810\) 0 0
\(811\) 10.9802 0.385567 0.192783 0.981241i \(-0.438249\pi\)
0.192783 + 0.981241i \(0.438249\pi\)
\(812\) 0 0
\(813\) 14.7734 0.518126
\(814\) 0 0
\(815\) −48.4946 −1.69869
\(816\) 0 0
\(817\) 55.7004 1.94871
\(818\) 0 0
\(819\) −10.9038 −0.381010
\(820\) 0 0
\(821\) 22.8208 0.796451 0.398226 0.917287i \(-0.369626\pi\)
0.398226 + 0.917287i \(0.369626\pi\)
\(822\) 0 0
\(823\) −4.73811 −0.165160 −0.0825802 0.996584i \(-0.526316\pi\)
−0.0825802 + 0.996584i \(0.526316\pi\)
\(824\) 0 0
\(825\) 9.15690 0.318802
\(826\) 0 0
\(827\) −17.6761 −0.614658 −0.307329 0.951603i \(-0.599435\pi\)
−0.307329 + 0.951603i \(0.599435\pi\)
\(828\) 0 0
\(829\) −6.25537 −0.217258 −0.108629 0.994082i \(-0.534646\pi\)
−0.108629 + 0.994082i \(0.534646\pi\)
\(830\) 0 0
\(831\) 2.05325 0.0712264
\(832\) 0 0
\(833\) −12.3764 −0.428817
\(834\) 0 0
\(835\) 3.38131 0.117015
\(836\) 0 0
\(837\) −9.08688 −0.314089
\(838\) 0 0
\(839\) −31.0898 −1.07334 −0.536669 0.843793i \(-0.680318\pi\)
−0.536669 + 0.843793i \(0.680318\pi\)
\(840\) 0 0
\(841\) 10.6111 0.365901
\(842\) 0 0
\(843\) −25.3998 −0.874816
\(844\) 0 0
\(845\) 40.6242 1.39751
\(846\) 0 0
\(847\) 19.5646 0.672248
\(848\) 0 0
\(849\) 2.37163 0.0813941
\(850\) 0 0
\(851\) −36.6480 −1.25628
\(852\) 0 0
\(853\) −3.71143 −0.127077 −0.0635385 0.997979i \(-0.520239\pi\)
−0.0635385 + 0.997979i \(0.520239\pi\)
\(854\) 0 0
\(855\) 26.4666 0.905140
\(856\) 0 0
\(857\) −26.9041 −0.919026 −0.459513 0.888171i \(-0.651976\pi\)
−0.459513 + 0.888171i \(0.651976\pi\)
\(858\) 0 0
\(859\) 15.3548 0.523901 0.261950 0.965081i \(-0.415634\pi\)
0.261950 + 0.965081i \(0.415634\pi\)
\(860\) 0 0
\(861\) −25.8050 −0.879430
\(862\) 0 0
\(863\) 52.1838 1.77636 0.888179 0.459498i \(-0.151971\pi\)
0.888179 + 0.459498i \(0.151971\pi\)
\(864\) 0 0
\(865\) −16.7069 −0.568052
\(866\) 0 0
\(867\) −13.3377 −0.452972
\(868\) 0 0
\(869\) 6.06842 0.205857
\(870\) 0 0
\(871\) 8.07492 0.273608
\(872\) 0 0
\(873\) −10.2977 −0.348524
\(874\) 0 0
\(875\) −10.5656 −0.357183
\(876\) 0 0
\(877\) 48.6674 1.64338 0.821691 0.569934i \(-0.193031\pi\)
0.821691 + 0.569934i \(0.193031\pi\)
\(878\) 0 0
\(879\) −8.38097 −0.282683
\(880\) 0 0
\(881\) −0.713672 −0.0240442 −0.0120221 0.999928i \(-0.503827\pi\)
−0.0120221 + 0.999928i \(0.503827\pi\)
\(882\) 0 0
\(883\) 8.62220 0.290160 0.145080 0.989420i \(-0.453656\pi\)
0.145080 + 0.989420i \(0.453656\pi\)
\(884\) 0 0
\(885\) −23.1267 −0.777395
\(886\) 0 0
\(887\) −8.51090 −0.285768 −0.142884 0.989739i \(-0.545638\pi\)
−0.142884 + 0.989739i \(0.545638\pi\)
\(888\) 0 0
\(889\) −35.7069 −1.19757
\(890\) 0 0
\(891\) −1.42337 −0.0476846
\(892\) 0 0
\(893\) 64.2902 2.15139
\(894\) 0 0
\(895\) −6.57016 −0.219616
\(896\) 0 0
\(897\) 38.7990 1.29546
\(898\) 0 0
\(899\) 57.1905 1.90741
\(900\) 0 0
\(901\) −59.5207 −1.98292
\(902\) 0 0
\(903\) 15.5142 0.516279
\(904\) 0 0
\(905\) 38.0504 1.26484
\(906\) 0 0
\(907\) 29.3979 0.976143 0.488071 0.872804i \(-0.337701\pi\)
0.488071 + 0.872804i \(0.337701\pi\)
\(908\) 0 0
\(909\) 5.31154 0.176173
\(910\) 0 0
\(911\) −0.694625 −0.0230140 −0.0115070 0.999934i \(-0.503663\pi\)
−0.0115070 + 0.999934i \(0.503663\pi\)
\(912\) 0 0
\(913\) 6.28332 0.207947
\(914\) 0 0
\(915\) 5.87403 0.194189
\(916\) 0 0
\(917\) −26.1761 −0.864412
\(918\) 0 0
\(919\) 45.2759 1.49351 0.746757 0.665097i \(-0.231610\pi\)
0.746757 + 0.665097i \(0.231610\pi\)
\(920\) 0 0
\(921\) 23.1839 0.763936
\(922\) 0 0
\(923\) −80.1000 −2.63652
\(924\) 0 0
\(925\) 30.3917 0.999273
\(926\) 0 0
\(927\) 0.971769 0.0319171
\(928\) 0 0
\(929\) −50.0209 −1.64113 −0.820566 0.571551i \(-0.806342\pi\)
−0.820566 + 0.571551i \(0.806342\pi\)
\(930\) 0 0
\(931\) −17.5880 −0.576424
\(932\) 0 0
\(933\) 22.1324 0.724581
\(934\) 0 0
\(935\) −26.5090 −0.866938
\(936\) 0 0
\(937\) −52.3630 −1.71062 −0.855312 0.518114i \(-0.826634\pi\)
−0.855312 + 0.518114i \(0.826634\pi\)
\(938\) 0 0
\(939\) 25.6297 0.836393
\(940\) 0 0
\(941\) −49.6749 −1.61935 −0.809677 0.586875i \(-0.800358\pi\)
−0.809677 + 0.586875i \(0.800358\pi\)
\(942\) 0 0
\(943\) 91.8218 2.99013
\(944\) 0 0
\(945\) 7.37172 0.239802
\(946\) 0 0
\(947\) 31.6023 1.02694 0.513468 0.858109i \(-0.328360\pi\)
0.513468 + 0.858109i \(0.328360\pi\)
\(948\) 0 0
\(949\) 22.1791 0.719965
\(950\) 0 0
\(951\) 34.5554 1.12054
\(952\) 0 0
\(953\) −44.2157 −1.43229 −0.716143 0.697953i \(-0.754094\pi\)
−0.716143 + 0.697953i \(0.754094\pi\)
\(954\) 0 0
\(955\) 30.3535 0.982215
\(956\) 0 0
\(957\) 8.95830 0.289581
\(958\) 0 0
\(959\) −15.7984 −0.510156
\(960\) 0 0
\(961\) 51.5715 1.66360
\(962\) 0 0
\(963\) 13.7609 0.443437
\(964\) 0 0
\(965\) −34.0512 −1.09615
\(966\) 0 0
\(967\) 31.8623 1.02462 0.512311 0.858800i \(-0.328790\pi\)
0.512311 + 0.858800i \(0.328790\pi\)
\(968\) 0 0
\(969\) −43.1127 −1.38498
\(970\) 0 0
\(971\) −24.6768 −0.791917 −0.395958 0.918268i \(-0.629588\pi\)
−0.395958 + 0.918268i \(0.629588\pi\)
\(972\) 0 0
\(973\) −16.1241 −0.516916
\(974\) 0 0
\(975\) −32.1755 −1.03044
\(976\) 0 0
\(977\) −27.3621 −0.875392 −0.437696 0.899123i \(-0.644205\pi\)
−0.437696 + 0.899123i \(0.644205\pi\)
\(978\) 0 0
\(979\) 12.1894 0.389574
\(980\) 0 0
\(981\) −5.15480 −0.164580
\(982\) 0 0
\(983\) 10.2808 0.327906 0.163953 0.986468i \(-0.447575\pi\)
0.163953 + 0.986468i \(0.447575\pi\)
\(984\) 0 0
\(985\) −65.6502 −2.09179
\(986\) 0 0
\(987\) 17.9067 0.569975
\(988\) 0 0
\(989\) −55.2041 −1.75539
\(990\) 0 0
\(991\) −6.86212 −0.217982 −0.108991 0.994043i \(-0.534762\pi\)
−0.108991 + 0.994043i \(0.534762\pi\)
\(992\) 0 0
\(993\) −9.70159 −0.307871
\(994\) 0 0
\(995\) −20.2512 −0.642006
\(996\) 0 0
\(997\) 41.7713 1.32291 0.661456 0.749984i \(-0.269939\pi\)
0.661456 + 0.749984i \(0.269939\pi\)
\(998\) 0 0
\(999\) −4.72415 −0.149466
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 \(a_p\))