Properties

Label 8024.2.a.y.1.6
Level 8024
Weight 2
Character 8024.1
Self dual Yes
Analytic conductor 64.072
Analytic rank 1
Dimension 23
CM No

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Newspace parameters

Level: \( N \) = \( 8024 = 2^{3} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8024.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0719625819\)
Analytic rank: \(1\)
Dimension: \(23\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 8024.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.74430 q^{3}\) \(+1.05481 q^{5}\) \(+1.84260 q^{7}\) \(+0.0425790 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.74430 q^{3}\) \(+1.05481 q^{5}\) \(+1.84260 q^{7}\) \(+0.0425790 q^{9}\) \(+6.02375 q^{11}\) \(-0.598711 q^{13}\) \(-1.83991 q^{15}\) \(-1.00000 q^{17}\) \(+2.57381 q^{19}\) \(-3.21405 q^{21}\) \(-5.74361 q^{23}\) \(-3.88737 q^{25}\) \(+5.15863 q^{27}\) \(-2.33430 q^{29}\) \(-4.57189 q^{31}\) \(-10.5072 q^{33}\) \(+1.94360 q^{35}\) \(+8.60753 q^{37}\) \(+1.04433 q^{39}\) \(-10.8058 q^{41}\) \(-4.58088 q^{43}\) \(+0.0449129 q^{45}\) \(+2.41769 q^{47}\) \(-3.60481 q^{49}\) \(+1.74430 q^{51}\) \(-2.12083 q^{53}\) \(+6.35394 q^{55}\) \(-4.48949 q^{57}\) \(-1.00000 q^{59}\) \(-0.502075 q^{61}\) \(+0.0784562 q^{63}\) \(-0.631529 q^{65}\) \(-8.85713 q^{67}\) \(+10.0186 q^{69}\) \(-7.47697 q^{71}\) \(+2.03259 q^{73}\) \(+6.78073 q^{75}\) \(+11.0994 q^{77}\) \(-15.5536 q^{79}\) \(-9.12592 q^{81}\) \(-15.7037 q^{83}\) \(-1.05481 q^{85}\) \(+4.07171 q^{87}\) \(-2.18348 q^{89}\) \(-1.10319 q^{91}\) \(+7.97475 q^{93}\) \(+2.71489 q^{95}\) \(-11.0393 q^{97}\) \(+0.256485 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(23q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(23q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 23q^{17} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut -\mathstrut 29q^{23} \) \(\mathstrut +\mathstrut 31q^{25} \) \(\mathstrut -\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 22q^{35} \) \(\mathstrut +\mathstrut 5q^{37} \) \(\mathstrut +\mathstrut 16q^{39} \) \(\mathstrut +\mathstrut 11q^{41} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut -\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 39q^{47} \) \(\mathstrut +\mathstrut 16q^{49} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut -\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 35q^{55} \) \(\mathstrut +\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 23q^{59} \) \(\mathstrut -\mathstrut 37q^{61} \) \(\mathstrut +\mathstrut 33q^{65} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut -\mathstrut 66q^{69} \) \(\mathstrut -\mathstrut 13q^{71} \) \(\mathstrut -\mathstrut 14q^{73} \) \(\mathstrut -\mathstrut 81q^{75} \) \(\mathstrut -\mathstrut 4q^{77} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut q^{81} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut +\mathstrut 28q^{89} \) \(\mathstrut -\mathstrut 18q^{91} \) \(\mathstrut -\mathstrut 62q^{93} \) \(\mathstrut -\mathstrut 33q^{95} \) \(\mathstrut -\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.74430 −1.00707 −0.503536 0.863974i \(-0.667968\pi\)
−0.503536 + 0.863974i \(0.667968\pi\)
\(4\) 0 0
\(5\) 1.05481 0.471727 0.235864 0.971786i \(-0.424208\pi\)
0.235864 + 0.971786i \(0.424208\pi\)
\(6\) 0 0
\(7\) 1.84260 0.696439 0.348219 0.937413i \(-0.386786\pi\)
0.348219 + 0.937413i \(0.386786\pi\)
\(8\) 0 0
\(9\) 0.0425790 0.0141930
\(10\) 0 0
\(11\) 6.02375 1.81623 0.908115 0.418721i \(-0.137521\pi\)
0.908115 + 0.418721i \(0.137521\pi\)
\(12\) 0 0
\(13\) −0.598711 −0.166053 −0.0830263 0.996547i \(-0.526459\pi\)
−0.0830263 + 0.996547i \(0.526459\pi\)
\(14\) 0 0
\(15\) −1.83991 −0.475063
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) 2.57381 0.590472 0.295236 0.955424i \(-0.404602\pi\)
0.295236 + 0.955424i \(0.404602\pi\)
\(20\) 0 0
\(21\) −3.21405 −0.701364
\(22\) 0 0
\(23\) −5.74361 −1.19763 −0.598813 0.800889i \(-0.704361\pi\)
−0.598813 + 0.800889i \(0.704361\pi\)
\(24\) 0 0
\(25\) −3.88737 −0.777474
\(26\) 0 0
\(27\) 5.15863 0.992778
\(28\) 0 0
\(29\) −2.33430 −0.433468 −0.216734 0.976231i \(-0.569540\pi\)
−0.216734 + 0.976231i \(0.569540\pi\)
\(30\) 0 0
\(31\) −4.57189 −0.821136 −0.410568 0.911830i \(-0.634670\pi\)
−0.410568 + 0.911830i \(0.634670\pi\)
\(32\) 0 0
\(33\) −10.5072 −1.82907
\(34\) 0 0
\(35\) 1.94360 0.328529
\(36\) 0 0
\(37\) 8.60753 1.41507 0.707535 0.706678i \(-0.249807\pi\)
0.707535 + 0.706678i \(0.249807\pi\)
\(38\) 0 0
\(39\) 1.04433 0.167227
\(40\) 0 0
\(41\) −10.8058 −1.68758 −0.843789 0.536675i \(-0.819680\pi\)
−0.843789 + 0.536675i \(0.819680\pi\)
\(42\) 0 0
\(43\) −4.58088 −0.698577 −0.349289 0.937015i \(-0.613577\pi\)
−0.349289 + 0.937015i \(0.613577\pi\)
\(44\) 0 0
\(45\) 0.0449129 0.00669522
\(46\) 0 0
\(47\) 2.41769 0.352656 0.176328 0.984331i \(-0.443578\pi\)
0.176328 + 0.984331i \(0.443578\pi\)
\(48\) 0 0
\(49\) −3.60481 −0.514973
\(50\) 0 0
\(51\) 1.74430 0.244251
\(52\) 0 0
\(53\) −2.12083 −0.291319 −0.145659 0.989335i \(-0.546530\pi\)
−0.145659 + 0.989335i \(0.546530\pi\)
\(54\) 0 0
\(55\) 6.35394 0.856765
\(56\) 0 0
\(57\) −4.48949 −0.594647
\(58\) 0 0
\(59\) −1.00000 −0.130189
\(60\) 0 0
\(61\) −0.502075 −0.0642841 −0.0321421 0.999483i \(-0.510233\pi\)
−0.0321421 + 0.999483i \(0.510233\pi\)
\(62\) 0 0
\(63\) 0.0784562 0.00988455
\(64\) 0 0
\(65\) −0.631529 −0.0783315
\(66\) 0 0
\(67\) −8.85713 −1.08207 −0.541035 0.841000i \(-0.681967\pi\)
−0.541035 + 0.841000i \(0.681967\pi\)
\(68\) 0 0
\(69\) 10.0186 1.20609
\(70\) 0 0
\(71\) −7.47697 −0.887353 −0.443677 0.896187i \(-0.646326\pi\)
−0.443677 + 0.896187i \(0.646326\pi\)
\(72\) 0 0
\(73\) 2.03259 0.237897 0.118948 0.992900i \(-0.462048\pi\)
0.118948 + 0.992900i \(0.462048\pi\)
\(74\) 0 0
\(75\) 6.78073 0.782971
\(76\) 0 0
\(77\) 11.0994 1.26489
\(78\) 0 0
\(79\) −15.5536 −1.74991 −0.874957 0.484200i \(-0.839111\pi\)
−0.874957 + 0.484200i \(0.839111\pi\)
\(80\) 0 0
\(81\) −9.12592 −1.01399
\(82\) 0 0
\(83\) −15.7037 −1.72371 −0.861853 0.507159i \(-0.830696\pi\)
−0.861853 + 0.507159i \(0.830696\pi\)
\(84\) 0 0
\(85\) −1.05481 −0.114411
\(86\) 0 0
\(87\) 4.07171 0.436534
\(88\) 0 0
\(89\) −2.18348 −0.231448 −0.115724 0.993281i \(-0.536919\pi\)
−0.115724 + 0.993281i \(0.536919\pi\)
\(90\) 0 0
\(91\) −1.10319 −0.115645
\(92\) 0 0
\(93\) 7.97475 0.826943
\(94\) 0 0
\(95\) 2.71489 0.278541
\(96\) 0 0
\(97\) −11.0393 −1.12087 −0.560435 0.828198i \(-0.689366\pi\)
−0.560435 + 0.828198i \(0.689366\pi\)
\(98\) 0 0
\(99\) 0.256485 0.0257777
\(100\) 0 0
\(101\) 10.8829 1.08289 0.541443 0.840737i \(-0.317878\pi\)
0.541443 + 0.840737i \(0.317878\pi\)
\(102\) 0 0
\(103\) −13.1289 −1.29363 −0.646813 0.762649i \(-0.723898\pi\)
−0.646813 + 0.762649i \(0.723898\pi\)
\(104\) 0 0
\(105\) −3.39023 −0.330852
\(106\) 0 0
\(107\) −5.55060 −0.536596 −0.268298 0.963336i \(-0.586461\pi\)
−0.268298 + 0.963336i \(0.586461\pi\)
\(108\) 0 0
\(109\) −2.34236 −0.224357 −0.112179 0.993688i \(-0.535783\pi\)
−0.112179 + 0.993688i \(0.535783\pi\)
\(110\) 0 0
\(111\) −15.0141 −1.42508
\(112\) 0 0
\(113\) 14.4344 1.35787 0.678936 0.734197i \(-0.262441\pi\)
0.678936 + 0.734197i \(0.262441\pi\)
\(114\) 0 0
\(115\) −6.05844 −0.564953
\(116\) 0 0
\(117\) −0.0254925 −0.00235678
\(118\) 0 0
\(119\) −1.84260 −0.168911
\(120\) 0 0
\(121\) 25.2856 2.29869
\(122\) 0 0
\(123\) 18.8485 1.69951
\(124\) 0 0
\(125\) −9.37452 −0.838482
\(126\) 0 0
\(127\) 10.9128 0.968358 0.484179 0.874969i \(-0.339118\pi\)
0.484179 + 0.874969i \(0.339118\pi\)
\(128\) 0 0
\(129\) 7.99042 0.703517
\(130\) 0 0
\(131\) 5.98620 0.523017 0.261508 0.965201i \(-0.415780\pi\)
0.261508 + 0.965201i \(0.415780\pi\)
\(132\) 0 0
\(133\) 4.74251 0.411227
\(134\) 0 0
\(135\) 5.44139 0.468320
\(136\) 0 0
\(137\) 20.6815 1.76694 0.883469 0.468490i \(-0.155202\pi\)
0.883469 + 0.468490i \(0.155202\pi\)
\(138\) 0 0
\(139\) 18.0761 1.53319 0.766597 0.642128i \(-0.221948\pi\)
0.766597 + 0.642128i \(0.221948\pi\)
\(140\) 0 0
\(141\) −4.21717 −0.355150
\(142\) 0 0
\(143\) −3.60649 −0.301590
\(144\) 0 0
\(145\) −2.46225 −0.204479
\(146\) 0 0
\(147\) 6.28786 0.518614
\(148\) 0 0
\(149\) 19.8053 1.62252 0.811259 0.584687i \(-0.198783\pi\)
0.811259 + 0.584687i \(0.198783\pi\)
\(150\) 0 0
\(151\) −4.89709 −0.398519 −0.199260 0.979947i \(-0.563854\pi\)
−0.199260 + 0.979947i \(0.563854\pi\)
\(152\) 0 0
\(153\) −0.0425790 −0.00344231
\(154\) 0 0
\(155\) −4.82250 −0.387352
\(156\) 0 0
\(157\) −8.42032 −0.672014 −0.336007 0.941859i \(-0.609077\pi\)
−0.336007 + 0.941859i \(0.609077\pi\)
\(158\) 0 0
\(159\) 3.69937 0.293379
\(160\) 0 0
\(161\) −10.5832 −0.834073
\(162\) 0 0
\(163\) 14.1317 1.10688 0.553442 0.832888i \(-0.313314\pi\)
0.553442 + 0.832888i \(0.313314\pi\)
\(164\) 0 0
\(165\) −11.0832 −0.862824
\(166\) 0 0
\(167\) −15.2263 −1.17824 −0.589122 0.808044i \(-0.700526\pi\)
−0.589122 + 0.808044i \(0.700526\pi\)
\(168\) 0 0
\(169\) −12.6415 −0.972427
\(170\) 0 0
\(171\) 0.109590 0.00838056
\(172\) 0 0
\(173\) −6.45291 −0.490605 −0.245303 0.969447i \(-0.578887\pi\)
−0.245303 + 0.969447i \(0.578887\pi\)
\(174\) 0 0
\(175\) −7.16288 −0.541463
\(176\) 0 0
\(177\) 1.74430 0.131110
\(178\) 0 0
\(179\) −5.99581 −0.448148 −0.224074 0.974572i \(-0.571936\pi\)
−0.224074 + 0.974572i \(0.571936\pi\)
\(180\) 0 0
\(181\) −11.2116 −0.833352 −0.416676 0.909055i \(-0.636805\pi\)
−0.416676 + 0.909055i \(0.636805\pi\)
\(182\) 0 0
\(183\) 0.875769 0.0647387
\(184\) 0 0
\(185\) 9.07935 0.667527
\(186\) 0 0
\(187\) −6.02375 −0.440501
\(188\) 0 0
\(189\) 9.50531 0.691409
\(190\) 0 0
\(191\) 1.74364 0.126165 0.0630826 0.998008i \(-0.479907\pi\)
0.0630826 + 0.998008i \(0.479907\pi\)
\(192\) 0 0
\(193\) 1.07360 0.0772794 0.0386397 0.999253i \(-0.487698\pi\)
0.0386397 + 0.999253i \(0.487698\pi\)
\(194\) 0 0
\(195\) 1.10158 0.0788854
\(196\) 0 0
\(197\) −4.59941 −0.327695 −0.163847 0.986486i \(-0.552390\pi\)
−0.163847 + 0.986486i \(0.552390\pi\)
\(198\) 0 0
\(199\) 11.0181 0.781050 0.390525 0.920592i \(-0.372293\pi\)
0.390525 + 0.920592i \(0.372293\pi\)
\(200\) 0 0
\(201\) 15.4495 1.08972
\(202\) 0 0
\(203\) −4.30119 −0.301884
\(204\) 0 0
\(205\) −11.3981 −0.796076
\(206\) 0 0
\(207\) −0.244557 −0.0169979
\(208\) 0 0
\(209\) 15.5040 1.07243
\(210\) 0 0
\(211\) −23.5634 −1.62217 −0.811085 0.584928i \(-0.801123\pi\)
−0.811085 + 0.584928i \(0.801123\pi\)
\(212\) 0 0
\(213\) 13.0421 0.893628
\(214\) 0 0
\(215\) −4.83197 −0.329538
\(216\) 0 0
\(217\) −8.42419 −0.571871
\(218\) 0 0
\(219\) −3.54544 −0.239579
\(220\) 0 0
\(221\) 0.598711 0.0402737
\(222\) 0 0
\(223\) −0.620274 −0.0415366 −0.0207683 0.999784i \(-0.506611\pi\)
−0.0207683 + 0.999784i \(0.506611\pi\)
\(224\) 0 0
\(225\) −0.165520 −0.0110347
\(226\) 0 0
\(227\) 6.35233 0.421619 0.210810 0.977527i \(-0.432390\pi\)
0.210810 + 0.977527i \(0.432390\pi\)
\(228\) 0 0
\(229\) 28.4085 1.87729 0.938644 0.344887i \(-0.112083\pi\)
0.938644 + 0.344887i \(0.112083\pi\)
\(230\) 0 0
\(231\) −19.3607 −1.27384
\(232\) 0 0
\(233\) 9.88718 0.647730 0.323865 0.946103i \(-0.395018\pi\)
0.323865 + 0.946103i \(0.395018\pi\)
\(234\) 0 0
\(235\) 2.55021 0.166358
\(236\) 0 0
\(237\) 27.1301 1.76229
\(238\) 0 0
\(239\) 5.23987 0.338939 0.169469 0.985535i \(-0.445795\pi\)
0.169469 + 0.985535i \(0.445795\pi\)
\(240\) 0 0
\(241\) 20.5495 1.32371 0.661855 0.749632i \(-0.269769\pi\)
0.661855 + 0.749632i \(0.269769\pi\)
\(242\) 0 0
\(243\) 0.442460 0.0283838
\(244\) 0 0
\(245\) −3.80240 −0.242927
\(246\) 0 0
\(247\) −1.54097 −0.0980493
\(248\) 0 0
\(249\) 27.3920 1.73589
\(250\) 0 0
\(251\) −7.03512 −0.444053 −0.222026 0.975041i \(-0.571267\pi\)
−0.222026 + 0.975041i \(0.571267\pi\)
\(252\) 0 0
\(253\) −34.5981 −2.17516
\(254\) 0 0
\(255\) 1.83991 0.115220
\(256\) 0 0
\(257\) −7.69867 −0.480230 −0.240115 0.970744i \(-0.577185\pi\)
−0.240115 + 0.970744i \(0.577185\pi\)
\(258\) 0 0
\(259\) 15.8603 0.985510
\(260\) 0 0
\(261\) −0.0993921 −0.00615221
\(262\) 0 0
\(263\) −10.2284 −0.630708 −0.315354 0.948974i \(-0.602123\pi\)
−0.315354 + 0.948974i \(0.602123\pi\)
\(264\) 0 0
\(265\) −2.23709 −0.137423
\(266\) 0 0
\(267\) 3.80864 0.233085
\(268\) 0 0
\(269\) −23.3933 −1.42631 −0.713156 0.701006i \(-0.752735\pi\)
−0.713156 + 0.701006i \(0.752735\pi\)
\(270\) 0 0
\(271\) −9.34130 −0.567444 −0.283722 0.958907i \(-0.591569\pi\)
−0.283722 + 0.958907i \(0.591569\pi\)
\(272\) 0 0
\(273\) 1.92429 0.116463
\(274\) 0 0
\(275\) −23.4165 −1.41207
\(276\) 0 0
\(277\) −16.3186 −0.980492 −0.490246 0.871584i \(-0.663093\pi\)
−0.490246 + 0.871584i \(0.663093\pi\)
\(278\) 0 0
\(279\) −0.194667 −0.0116544
\(280\) 0 0
\(281\) −13.0799 −0.780279 −0.390140 0.920756i \(-0.627573\pi\)
−0.390140 + 0.920756i \(0.627573\pi\)
\(282\) 0 0
\(283\) −18.3941 −1.09342 −0.546708 0.837323i \(-0.684119\pi\)
−0.546708 + 0.837323i \(0.684119\pi\)
\(284\) 0 0
\(285\) −4.73557 −0.280511
\(286\) 0 0
\(287\) −19.9108 −1.17529
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 19.2558 1.12880
\(292\) 0 0
\(293\) −0.946606 −0.0553013 −0.0276507 0.999618i \(-0.508803\pi\)
−0.0276507 + 0.999618i \(0.508803\pi\)
\(294\) 0 0
\(295\) −1.05481 −0.0614136
\(296\) 0 0
\(297\) 31.0743 1.80311
\(298\) 0 0
\(299\) 3.43876 0.198869
\(300\) 0 0
\(301\) −8.44074 −0.486516
\(302\) 0 0
\(303\) −18.9830 −1.09054
\(304\) 0 0
\(305\) −0.529596 −0.0303246
\(306\) 0 0
\(307\) 30.6189 1.74751 0.873757 0.486364i \(-0.161677\pi\)
0.873757 + 0.486364i \(0.161677\pi\)
\(308\) 0 0
\(309\) 22.9007 1.30277
\(310\) 0 0
\(311\) −31.2056 −1.76951 −0.884754 0.466059i \(-0.845673\pi\)
−0.884754 + 0.466059i \(0.845673\pi\)
\(312\) 0 0
\(313\) −20.2398 −1.14402 −0.572011 0.820246i \(-0.693836\pi\)
−0.572011 + 0.820246i \(0.693836\pi\)
\(314\) 0 0
\(315\) 0.0827567 0.00466281
\(316\) 0 0
\(317\) −9.78770 −0.549732 −0.274866 0.961483i \(-0.588634\pi\)
−0.274866 + 0.961483i \(0.588634\pi\)
\(318\) 0 0
\(319\) −14.0612 −0.787278
\(320\) 0 0
\(321\) 9.68190 0.540391
\(322\) 0 0
\(323\) −2.57381 −0.143210
\(324\) 0 0
\(325\) 2.32741 0.129101
\(326\) 0 0
\(327\) 4.08577 0.225944
\(328\) 0 0
\(329\) 4.45485 0.245604
\(330\) 0 0
\(331\) −13.4945 −0.741726 −0.370863 0.928688i \(-0.620938\pi\)
−0.370863 + 0.928688i \(0.620938\pi\)
\(332\) 0 0
\(333\) 0.366500 0.0200841
\(334\) 0 0
\(335\) −9.34262 −0.510442
\(336\) 0 0
\(337\) 21.2821 1.15931 0.579656 0.814861i \(-0.303187\pi\)
0.579656 + 0.814861i \(0.303187\pi\)
\(338\) 0 0
\(339\) −25.1779 −1.36747
\(340\) 0 0
\(341\) −27.5400 −1.49137
\(342\) 0 0
\(343\) −19.5405 −1.05509
\(344\) 0 0
\(345\) 10.5677 0.568948
\(346\) 0 0
\(347\) 9.52748 0.511462 0.255731 0.966748i \(-0.417684\pi\)
0.255731 + 0.966748i \(0.417684\pi\)
\(348\) 0 0
\(349\) 5.71491 0.305912 0.152956 0.988233i \(-0.451121\pi\)
0.152956 + 0.988233i \(0.451121\pi\)
\(350\) 0 0
\(351\) −3.08853 −0.164853
\(352\) 0 0
\(353\) 15.7744 0.839585 0.419792 0.907620i \(-0.362103\pi\)
0.419792 + 0.907620i \(0.362103\pi\)
\(354\) 0 0
\(355\) −7.88681 −0.418589
\(356\) 0 0
\(357\) 3.21405 0.170106
\(358\) 0 0
\(359\) 2.42723 0.128104 0.0640521 0.997947i \(-0.479598\pi\)
0.0640521 + 0.997947i \(0.479598\pi\)
\(360\) 0 0
\(361\) −12.3755 −0.651343
\(362\) 0 0
\(363\) −44.1057 −2.31495
\(364\) 0 0
\(365\) 2.14400 0.112222
\(366\) 0 0
\(367\) −2.31877 −0.121039 −0.0605194 0.998167i \(-0.519276\pi\)
−0.0605194 + 0.998167i \(0.519276\pi\)
\(368\) 0 0
\(369\) −0.460099 −0.0239518
\(370\) 0 0
\(371\) −3.90786 −0.202886
\(372\) 0 0
\(373\) 15.4912 0.802102 0.401051 0.916056i \(-0.368645\pi\)
0.401051 + 0.916056i \(0.368645\pi\)
\(374\) 0 0
\(375\) 16.3520 0.844412
\(376\) 0 0
\(377\) 1.39757 0.0719785
\(378\) 0 0
\(379\) −10.6790 −0.548543 −0.274272 0.961652i \(-0.588437\pi\)
−0.274272 + 0.961652i \(0.588437\pi\)
\(380\) 0 0
\(381\) −19.0353 −0.975206
\(382\) 0 0
\(383\) 1.85770 0.0949243 0.0474621 0.998873i \(-0.484887\pi\)
0.0474621 + 0.998873i \(0.484887\pi\)
\(384\) 0 0
\(385\) 11.7078 0.596685
\(386\) 0 0
\(387\) −0.195049 −0.00991490
\(388\) 0 0
\(389\) 23.4064 1.18675 0.593375 0.804926i \(-0.297795\pi\)
0.593375 + 0.804926i \(0.297795\pi\)
\(390\) 0 0
\(391\) 5.74361 0.290467
\(392\) 0 0
\(393\) −10.4417 −0.526715
\(394\) 0 0
\(395\) −16.4061 −0.825482
\(396\) 0 0
\(397\) 26.5294 1.33147 0.665737 0.746187i \(-0.268117\pi\)
0.665737 + 0.746187i \(0.268117\pi\)
\(398\) 0 0
\(399\) −8.27235 −0.414135
\(400\) 0 0
\(401\) −9.33532 −0.466184 −0.233092 0.972455i \(-0.574884\pi\)
−0.233092 + 0.972455i \(0.574884\pi\)
\(402\) 0 0
\(403\) 2.73724 0.136352
\(404\) 0 0
\(405\) −9.62615 −0.478327
\(406\) 0 0
\(407\) 51.8497 2.57009
\(408\) 0 0
\(409\) −7.33101 −0.362495 −0.181248 0.983438i \(-0.558014\pi\)
−0.181248 + 0.983438i \(0.558014\pi\)
\(410\) 0 0
\(411\) −36.0747 −1.77943
\(412\) 0 0
\(413\) −1.84260 −0.0906686
\(414\) 0 0
\(415\) −16.5645 −0.813119
\(416\) 0 0
\(417\) −31.5301 −1.54404
\(418\) 0 0
\(419\) −14.1976 −0.693598 −0.346799 0.937939i \(-0.612731\pi\)
−0.346799 + 0.937939i \(0.612731\pi\)
\(420\) 0 0
\(421\) −19.6703 −0.958672 −0.479336 0.877632i \(-0.659122\pi\)
−0.479336 + 0.877632i \(0.659122\pi\)
\(422\) 0 0
\(423\) 0.102943 0.00500525
\(424\) 0 0
\(425\) 3.88737 0.188565
\(426\) 0 0
\(427\) −0.925126 −0.0447700
\(428\) 0 0
\(429\) 6.29079 0.303722
\(430\) 0 0
\(431\) −18.7827 −0.904731 −0.452366 0.891833i \(-0.649420\pi\)
−0.452366 + 0.891833i \(0.649420\pi\)
\(432\) 0 0
\(433\) 19.5745 0.940692 0.470346 0.882482i \(-0.344129\pi\)
0.470346 + 0.882482i \(0.344129\pi\)
\(434\) 0 0
\(435\) 4.29490 0.205925
\(436\) 0 0
\(437\) −14.7829 −0.707164
\(438\) 0 0
\(439\) 15.9031 0.759011 0.379506 0.925189i \(-0.376094\pi\)
0.379506 + 0.925189i \(0.376094\pi\)
\(440\) 0 0
\(441\) −0.153489 −0.00730900
\(442\) 0 0
\(443\) 9.65861 0.458894 0.229447 0.973321i \(-0.426308\pi\)
0.229447 + 0.973321i \(0.426308\pi\)
\(444\) 0 0
\(445\) −2.30316 −0.109180
\(446\) 0 0
\(447\) −34.5464 −1.63399
\(448\) 0 0
\(449\) −27.9027 −1.31681 −0.658406 0.752663i \(-0.728769\pi\)
−0.658406 + 0.752663i \(0.728769\pi\)
\(450\) 0 0
\(451\) −65.0913 −3.06503
\(452\) 0 0
\(453\) 8.54198 0.401337
\(454\) 0 0
\(455\) −1.16366 −0.0545531
\(456\) 0 0
\(457\) −11.7190 −0.548191 −0.274095 0.961703i \(-0.588378\pi\)
−0.274095 + 0.961703i \(0.588378\pi\)
\(458\) 0 0
\(459\) −5.15863 −0.240784
\(460\) 0 0
\(461\) −3.60889 −0.168083 −0.0840413 0.996462i \(-0.526783\pi\)
−0.0840413 + 0.996462i \(0.526783\pi\)
\(462\) 0 0
\(463\) 40.8473 1.89833 0.949167 0.314774i \(-0.101929\pi\)
0.949167 + 0.314774i \(0.101929\pi\)
\(464\) 0 0
\(465\) 8.41188 0.390091
\(466\) 0 0
\(467\) −24.6197 −1.13926 −0.569631 0.821901i \(-0.692914\pi\)
−0.569631 + 0.821901i \(0.692914\pi\)
\(468\) 0 0
\(469\) −16.3202 −0.753596
\(470\) 0 0
\(471\) 14.6875 0.676766
\(472\) 0 0
\(473\) −27.5941 −1.26878
\(474\) 0 0
\(475\) −10.0053 −0.459076
\(476\) 0 0
\(477\) −0.0903030 −0.00413469
\(478\) 0 0
\(479\) 32.9638 1.50616 0.753078 0.657932i \(-0.228568\pi\)
0.753078 + 0.657932i \(0.228568\pi\)
\(480\) 0 0
\(481\) −5.15343 −0.234976
\(482\) 0 0
\(483\) 18.4603 0.839971
\(484\) 0 0
\(485\) −11.6444 −0.528745
\(486\) 0 0
\(487\) 19.4456 0.881166 0.440583 0.897712i \(-0.354772\pi\)
0.440583 + 0.897712i \(0.354772\pi\)
\(488\) 0 0
\(489\) −24.6500 −1.11471
\(490\) 0 0
\(491\) −24.4257 −1.10231 −0.551157 0.834401i \(-0.685814\pi\)
−0.551157 + 0.834401i \(0.685814\pi\)
\(492\) 0 0
\(493\) 2.33430 0.105132
\(494\) 0 0
\(495\) 0.270544 0.0121601
\(496\) 0 0
\(497\) −13.7771 −0.617987
\(498\) 0 0
\(499\) −35.8808 −1.60624 −0.803122 0.595814i \(-0.796829\pi\)
−0.803122 + 0.595814i \(0.796829\pi\)
\(500\) 0 0
\(501\) 26.5592 1.18658
\(502\) 0 0
\(503\) −33.1367 −1.47749 −0.738746 0.673984i \(-0.764582\pi\)
−0.738746 + 0.673984i \(0.764582\pi\)
\(504\) 0 0
\(505\) 11.4794 0.510827
\(506\) 0 0
\(507\) 22.0506 0.979303
\(508\) 0 0
\(509\) −0.321190 −0.0142365 −0.00711825 0.999975i \(-0.502266\pi\)
−0.00711825 + 0.999975i \(0.502266\pi\)
\(510\) 0 0
\(511\) 3.74526 0.165680
\(512\) 0 0
\(513\) 13.2773 0.586207
\(514\) 0 0
\(515\) −13.8485 −0.610238
\(516\) 0 0
\(517\) 14.5636 0.640505
\(518\) 0 0
\(519\) 11.2558 0.494075
\(520\) 0 0
\(521\) 41.9003 1.83569 0.917843 0.396943i \(-0.129929\pi\)
0.917843 + 0.396943i \(0.129929\pi\)
\(522\) 0 0
\(523\) 28.7697 1.25801 0.629005 0.777402i \(-0.283463\pi\)
0.629005 + 0.777402i \(0.283463\pi\)
\(524\) 0 0
\(525\) 12.4942 0.545292
\(526\) 0 0
\(527\) 4.57189 0.199155
\(528\) 0 0
\(529\) 9.98907 0.434308
\(530\) 0 0
\(531\) −0.0425790 −0.00184777
\(532\) 0 0
\(533\) 6.46953 0.280227
\(534\) 0 0
\(535\) −5.85485 −0.253127
\(536\) 0 0
\(537\) 10.4585 0.451317
\(538\) 0 0
\(539\) −21.7145 −0.935309
\(540\) 0 0
\(541\) 11.0728 0.476055 0.238028 0.971258i \(-0.423499\pi\)
0.238028 + 0.971258i \(0.423499\pi\)
\(542\) 0 0
\(543\) 19.5564 0.839245
\(544\) 0 0
\(545\) −2.47075 −0.105835
\(546\) 0 0
\(547\) 25.8147 1.10376 0.551878 0.833925i \(-0.313911\pi\)
0.551878 + 0.833925i \(0.313911\pi\)
\(548\) 0 0
\(549\) −0.0213778 −0.000912384 0
\(550\) 0 0
\(551\) −6.00803 −0.255951
\(552\) 0 0
\(553\) −28.6591 −1.21871
\(554\) 0 0
\(555\) −15.8371 −0.672247
\(556\) 0 0
\(557\) −35.0864 −1.48666 −0.743330 0.668925i \(-0.766755\pi\)
−0.743330 + 0.668925i \(0.766755\pi\)
\(558\) 0 0
\(559\) 2.74262 0.116001
\(560\) 0 0
\(561\) 10.5072 0.443615
\(562\) 0 0
\(563\) −37.3591 −1.57450 −0.787250 0.616634i \(-0.788496\pi\)
−0.787250 + 0.616634i \(0.788496\pi\)
\(564\) 0 0
\(565\) 15.2256 0.640545
\(566\) 0 0
\(567\) −16.8155 −0.706183
\(568\) 0 0
\(569\) −31.4081 −1.31669 −0.658347 0.752715i \(-0.728744\pi\)
−0.658347 + 0.752715i \(0.728744\pi\)
\(570\) 0 0
\(571\) −15.3355 −0.641769 −0.320884 0.947118i \(-0.603980\pi\)
−0.320884 + 0.947118i \(0.603980\pi\)
\(572\) 0 0
\(573\) −3.04143 −0.127057
\(574\) 0 0
\(575\) 22.3275 0.931122
\(576\) 0 0
\(577\) 0.919402 0.0382752 0.0191376 0.999817i \(-0.493908\pi\)
0.0191376 + 0.999817i \(0.493908\pi\)
\(578\) 0 0
\(579\) −1.87268 −0.0778259
\(580\) 0 0
\(581\) −28.9357 −1.20046
\(582\) 0 0
\(583\) −12.7754 −0.529102
\(584\) 0 0
\(585\) −0.0268898 −0.00111176
\(586\) 0 0
\(587\) −5.59692 −0.231010 −0.115505 0.993307i \(-0.536849\pi\)
−0.115505 + 0.993307i \(0.536849\pi\)
\(588\) 0 0
\(589\) −11.7672 −0.484858
\(590\) 0 0
\(591\) 8.02275 0.330012
\(592\) 0 0
\(593\) −8.00852 −0.328871 −0.164435 0.986388i \(-0.552580\pi\)
−0.164435 + 0.986388i \(0.552580\pi\)
\(594\) 0 0
\(595\) −1.94360 −0.0796800
\(596\) 0 0
\(597\) −19.2188 −0.786574
\(598\) 0 0
\(599\) −1.85097 −0.0756284 −0.0378142 0.999285i \(-0.512040\pi\)
−0.0378142 + 0.999285i \(0.512040\pi\)
\(600\) 0 0
\(601\) −13.3221 −0.543420 −0.271710 0.962379i \(-0.587589\pi\)
−0.271710 + 0.962379i \(0.587589\pi\)
\(602\) 0 0
\(603\) −0.377127 −0.0153578
\(604\) 0 0
\(605\) 26.6716 1.08436
\(606\) 0 0
\(607\) −30.0742 −1.22067 −0.610336 0.792142i \(-0.708966\pi\)
−0.610336 + 0.792142i \(0.708966\pi\)
\(608\) 0 0
\(609\) 7.50256 0.304019
\(610\) 0 0
\(611\) −1.44750 −0.0585595
\(612\) 0 0
\(613\) −30.9975 −1.25198 −0.625989 0.779832i \(-0.715305\pi\)
−0.625989 + 0.779832i \(0.715305\pi\)
\(614\) 0 0
\(615\) 19.8817 0.801706
\(616\) 0 0
\(617\) 38.3757 1.54495 0.772473 0.635048i \(-0.219020\pi\)
0.772473 + 0.635048i \(0.219020\pi\)
\(618\) 0 0
\(619\) −42.0343 −1.68950 −0.844750 0.535160i \(-0.820251\pi\)
−0.844750 + 0.535160i \(0.820251\pi\)
\(620\) 0 0
\(621\) −29.6291 −1.18898
\(622\) 0 0
\(623\) −4.02329 −0.161190
\(624\) 0 0
\(625\) 9.54847 0.381939
\(626\) 0 0
\(627\) −27.0436 −1.08002
\(628\) 0 0
\(629\) −8.60753 −0.343205
\(630\) 0 0
\(631\) −14.5397 −0.578815 −0.289408 0.957206i \(-0.593458\pi\)
−0.289408 + 0.957206i \(0.593458\pi\)
\(632\) 0 0
\(633\) 41.1016 1.63364
\(634\) 0 0
\(635\) 11.5110 0.456801
\(636\) 0 0
\(637\) 2.15824 0.0855126
\(638\) 0 0
\(639\) −0.318362 −0.0125942
\(640\) 0 0
\(641\) −22.7997 −0.900533 −0.450267 0.892894i \(-0.648671\pi\)
−0.450267 + 0.892894i \(0.648671\pi\)
\(642\) 0 0
\(643\) 8.76457 0.345641 0.172820 0.984953i \(-0.444712\pi\)
0.172820 + 0.984953i \(0.444712\pi\)
\(644\) 0 0
\(645\) 8.42840 0.331868
\(646\) 0 0
\(647\) 22.2589 0.875086 0.437543 0.899197i \(-0.355849\pi\)
0.437543 + 0.899197i \(0.355849\pi\)
\(648\) 0 0
\(649\) −6.02375 −0.236453
\(650\) 0 0
\(651\) 14.6943 0.575915
\(652\) 0 0
\(653\) 22.8514 0.894246 0.447123 0.894472i \(-0.352449\pi\)
0.447123 + 0.894472i \(0.352449\pi\)
\(654\) 0 0
\(655\) 6.31433 0.246721
\(656\) 0 0
\(657\) 0.0865455 0.00337646
\(658\) 0 0
\(659\) 25.4683 0.992105 0.496052 0.868293i \(-0.334782\pi\)
0.496052 + 0.868293i \(0.334782\pi\)
\(660\) 0 0
\(661\) 10.4114 0.404956 0.202478 0.979287i \(-0.435100\pi\)
0.202478 + 0.979287i \(0.435100\pi\)
\(662\) 0 0
\(663\) −1.04433 −0.0405585
\(664\) 0 0
\(665\) 5.00246 0.193987
\(666\) 0 0
\(667\) 13.4073 0.519133
\(668\) 0 0
\(669\) 1.08194 0.0418303
\(670\) 0 0
\(671\) −3.02438 −0.116755
\(672\) 0 0
\(673\) −6.49351 −0.250306 −0.125153 0.992137i \(-0.539942\pi\)
−0.125153 + 0.992137i \(0.539942\pi\)
\(674\) 0 0
\(675\) −20.0535 −0.771859
\(676\) 0 0
\(677\) −23.7743 −0.913719 −0.456859 0.889539i \(-0.651026\pi\)
−0.456859 + 0.889539i \(0.651026\pi\)
\(678\) 0 0
\(679\) −20.3411 −0.780618
\(680\) 0 0
\(681\) −11.0804 −0.424600
\(682\) 0 0
\(683\) −22.8021 −0.872500 −0.436250 0.899826i \(-0.643694\pi\)
−0.436250 + 0.899826i \(0.643694\pi\)
\(684\) 0 0
\(685\) 21.8151 0.833513
\(686\) 0 0
\(687\) −49.5530 −1.89056
\(688\) 0 0
\(689\) 1.26977 0.0483743
\(690\) 0 0
\(691\) 8.45066 0.321478 0.160739 0.986997i \(-0.448612\pi\)
0.160739 + 0.986997i \(0.448612\pi\)
\(692\) 0 0
\(693\) 0.472601 0.0179526
\(694\) 0 0
\(695\) 19.0669 0.723250
\(696\) 0 0
\(697\) 10.8058 0.409298
\(698\) 0 0
\(699\) −17.2462 −0.652311
\(700\) 0 0
\(701\) 27.4604 1.03717 0.518583 0.855027i \(-0.326460\pi\)
0.518583 + 0.855027i \(0.326460\pi\)
\(702\) 0 0
\(703\) 22.1541 0.835559
\(704\) 0 0
\(705\) −4.44833 −0.167534
\(706\) 0 0
\(707\) 20.0528 0.754164
\(708\) 0 0
\(709\) 18.0106 0.676403 0.338201 0.941074i \(-0.390181\pi\)
0.338201 + 0.941074i \(0.390181\pi\)
\(710\) 0 0
\(711\) −0.662256 −0.0248365
\(712\) 0 0
\(713\) 26.2592 0.983414
\(714\) 0 0
\(715\) −3.80417 −0.142268
\(716\) 0 0
\(717\) −9.13990 −0.341336
\(718\) 0 0
\(719\) 3.79330 0.141466 0.0707332 0.997495i \(-0.477466\pi\)
0.0707332 + 0.997495i \(0.477466\pi\)
\(720\) 0 0
\(721\) −24.1913 −0.900931
\(722\) 0 0
\(723\) −35.8445 −1.33307
\(724\) 0 0
\(725\) 9.07428 0.337010
\(726\) 0 0
\(727\) −25.3067 −0.938575 −0.469288 0.883045i \(-0.655489\pi\)
−0.469288 + 0.883045i \(0.655489\pi\)
\(728\) 0 0
\(729\) 26.6060 0.985407
\(730\) 0 0
\(731\) 4.58088 0.169430
\(732\) 0 0
\(733\) −41.6292 −1.53761 −0.768804 0.639484i \(-0.779148\pi\)
−0.768804 + 0.639484i \(0.779148\pi\)
\(734\) 0 0
\(735\) 6.63253 0.244644
\(736\) 0 0
\(737\) −53.3532 −1.96529
\(738\) 0 0
\(739\) −23.5029 −0.864569 −0.432285 0.901737i \(-0.642292\pi\)
−0.432285 + 0.901737i \(0.642292\pi\)
\(740\) 0 0
\(741\) 2.68791 0.0987427
\(742\) 0 0
\(743\) 34.6695 1.27190 0.635951 0.771730i \(-0.280608\pi\)
0.635951 + 0.771730i \(0.280608\pi\)
\(744\) 0 0
\(745\) 20.8910 0.765385
\(746\) 0 0
\(747\) −0.668648 −0.0244645
\(748\) 0 0
\(749\) −10.2276 −0.373707
\(750\) 0 0
\(751\) −27.1286 −0.989936 −0.494968 0.868911i \(-0.664820\pi\)
−0.494968 + 0.868911i \(0.664820\pi\)
\(752\) 0 0
\(753\) 12.2713 0.447193
\(754\) 0 0
\(755\) −5.16552 −0.187992
\(756\) 0 0
\(757\) −24.7890 −0.900972 −0.450486 0.892784i \(-0.648749\pi\)
−0.450486 + 0.892784i \(0.648749\pi\)
\(758\) 0 0
\(759\) 60.3494 2.19055
\(760\) 0 0
\(761\) 41.7373 1.51298 0.756488 0.654008i \(-0.226914\pi\)
0.756488 + 0.654008i \(0.226914\pi\)
\(762\) 0 0
\(763\) −4.31604 −0.156251
\(764\) 0 0
\(765\) −0.0449129 −0.00162383
\(766\) 0 0
\(767\) 0.598711 0.0216182
\(768\) 0 0
\(769\) 13.2623 0.478251 0.239125 0.970989i \(-0.423139\pi\)
0.239125 + 0.970989i \(0.423139\pi\)
\(770\) 0 0
\(771\) 13.4288 0.483626
\(772\) 0 0
\(773\) 23.0304 0.828345 0.414173 0.910198i \(-0.364071\pi\)
0.414173 + 0.910198i \(0.364071\pi\)
\(774\) 0 0
\(775\) 17.7726 0.638412
\(776\) 0 0
\(777\) −27.6651 −0.992479
\(778\) 0 0
\(779\) −27.8119 −0.996467
\(780\) 0 0
\(781\) −45.0394 −1.61164
\(782\) 0 0
\(783\) −12.0418 −0.430338
\(784\) 0 0
\(785\) −8.88187 −0.317007
\(786\) 0 0
\(787\) 9.77237 0.348347 0.174174 0.984715i \(-0.444275\pi\)
0.174174 + 0.984715i \(0.444275\pi\)
\(788\) 0 0
\(789\) 17.8413 0.635168
\(790\) 0 0
\(791\) 26.5969 0.945675
\(792\) 0 0
\(793\) 0.300598 0.0106745
\(794\) 0 0
\(795\) 3.90215 0.138395
\(796\) 0 0
\(797\) −24.8939 −0.881787 −0.440894 0.897559i \(-0.645338\pi\)
−0.440894 + 0.897559i \(0.645338\pi\)
\(798\) 0 0
\(799\) −2.41769 −0.0855317
\(800\) 0 0
\(801\) −0.0929703 −0.00328494
\(802\) 0 0
\(803\) 12.2438 0.432075
\(804\) 0 0
\(805\) −11.1633 −0.393455
\(806\) 0 0
\(807\) 40.8048 1.43640
\(808\) 0 0
\(809\) −45.1403 −1.58705 −0.793525 0.608538i \(-0.791756\pi\)
−0.793525 + 0.608538i \(0.791756\pi\)
\(810\) 0 0
\(811\) −9.85589 −0.346087 −0.173043 0.984914i \(-0.555360\pi\)
−0.173043 + 0.984914i \(0.555360\pi\)
\(812\) 0 0
\(813\) 16.2940 0.571456
\(814\) 0 0
\(815\) 14.9064 0.522147
\(816\) 0 0
\(817\) −11.7903 −0.412490
\(818\) 0 0
\(819\) −0.0469726 −0.00164136
\(820\) 0 0
\(821\) 42.5113 1.48366 0.741828 0.670590i \(-0.233959\pi\)
0.741828 + 0.670590i \(0.233959\pi\)
\(822\) 0 0
\(823\) −53.6620 −1.87054 −0.935270 0.353934i \(-0.884844\pi\)
−0.935270 + 0.353934i \(0.884844\pi\)
\(824\) 0 0
\(825\) 40.8455 1.42206
\(826\) 0 0
\(827\) 11.3397 0.394320 0.197160 0.980371i \(-0.436828\pi\)
0.197160 + 0.980371i \(0.436828\pi\)
\(828\) 0 0
\(829\) −19.8919 −0.690874 −0.345437 0.938442i \(-0.612269\pi\)
−0.345437 + 0.938442i \(0.612269\pi\)
\(830\) 0 0
\(831\) 28.4646 0.987425
\(832\) 0 0
\(833\) 3.60481 0.124899
\(834\) 0 0
\(835\) −16.0609 −0.555810
\(836\) 0 0
\(837\) −23.5847 −0.815206
\(838\) 0 0
\(839\) 40.3093 1.39163 0.695816 0.718220i \(-0.255043\pi\)
0.695816 + 0.718220i \(0.255043\pi\)
\(840\) 0 0
\(841\) −23.5510 −0.812105
\(842\) 0 0
\(843\) 22.8152 0.785797
\(844\) 0 0
\(845\) −13.3345 −0.458720
\(846\) 0 0
\(847\) 46.5914 1.60090
\(848\) 0 0
\(849\) 32.0848 1.10115
\(850\) 0 0
\(851\) −49.4383 −1.69472
\(852\) 0 0
\(853\) 21.4704 0.735133 0.367566 0.929997i \(-0.380191\pi\)
0.367566 + 0.929997i \(0.380191\pi\)
\(854\) 0 0
\(855\) 0.115597 0.00395334
\(856\) 0 0
\(857\) −2.04572 −0.0698804 −0.0349402 0.999389i \(-0.511124\pi\)
−0.0349402 + 0.999389i \(0.511124\pi\)
\(858\) 0 0
\(859\) −8.24249 −0.281230 −0.140615 0.990064i \(-0.544908\pi\)
−0.140615 + 0.990064i \(0.544908\pi\)
\(860\) 0 0
\(861\) 34.7303 1.18361
\(862\) 0 0
\(863\) 43.8494 1.49265 0.746326 0.665581i \(-0.231816\pi\)
0.746326 + 0.665581i \(0.231816\pi\)
\(864\) 0 0
\(865\) −6.80662 −0.231432
\(866\) 0 0
\(867\) −1.74430 −0.0592395
\(868\) 0 0
\(869\) −93.6910 −3.17825
\(870\) 0 0
\(871\) 5.30286 0.179681
\(872\) 0 0
\(873\) −0.470042 −0.0159085
\(874\) 0 0
\(875\) −17.2735 −0.583952
\(876\) 0 0
\(877\) −22.6505 −0.764853 −0.382426 0.923986i \(-0.624911\pi\)
−0.382426 + 0.923986i \(0.624911\pi\)
\(878\) 0 0
\(879\) 1.65116 0.0556924
\(880\) 0 0
\(881\) −23.9661 −0.807437 −0.403718 0.914883i \(-0.632282\pi\)
−0.403718 + 0.914883i \(0.632282\pi\)
\(882\) 0 0
\(883\) 22.8823 0.770052 0.385026 0.922906i \(-0.374192\pi\)
0.385026 + 0.922906i \(0.374192\pi\)
\(884\) 0 0
\(885\) 1.83991 0.0618479
\(886\) 0 0
\(887\) −4.76460 −0.159980 −0.0799898 0.996796i \(-0.525489\pi\)
−0.0799898 + 0.996796i \(0.525489\pi\)
\(888\) 0 0
\(889\) 20.1080 0.674402
\(890\) 0 0
\(891\) −54.9723 −1.84164
\(892\) 0 0
\(893\) 6.22266 0.208233
\(894\) 0 0
\(895\) −6.32447 −0.211404
\(896\) 0 0
\(897\) −5.99823 −0.200275
\(898\) 0 0
\(899\) 10.6722 0.355937
\(900\) 0 0
\(901\) 2.12083 0.0706552
\(902\) 0 0
\(903\) 14.7232 0.489957
\(904\) 0 0
\(905\) −11.8262 −0.393115
\(906\) 0 0
\(907\) 53.7124 1.78349 0.891746 0.452536i \(-0.149481\pi\)
0.891746 + 0.452536i \(0.149481\pi\)
\(908\) 0 0
\(909\) 0.463382 0.0153694
\(910\) 0 0
\(911\) −19.9907 −0.662320 −0.331160 0.943575i \(-0.607440\pi\)
−0.331160 + 0.943575i \(0.607440\pi\)
\(912\) 0 0
\(913\) −94.5952 −3.13065
\(914\) 0 0
\(915\) 0.923774 0.0305390
\(916\) 0 0
\(917\) 11.0302 0.364249
\(918\) 0 0
\(919\) −13.8769 −0.457757 −0.228878 0.973455i \(-0.573506\pi\)
−0.228878 + 0.973455i \(0.573506\pi\)
\(920\) 0 0
\(921\) −53.4085 −1.75987
\(922\) 0 0
\(923\) 4.47655 0.147347
\(924\) 0 0
\(925\) −33.4607 −1.10018
\(926\) 0 0
\(927\) −0.559014 −0.0183604
\(928\) 0 0
\(929\) −24.9854 −0.819744 −0.409872 0.912143i \(-0.634427\pi\)
−0.409872 + 0.912143i \(0.634427\pi\)
\(930\) 0 0
\(931\) −9.27808 −0.304077
\(932\) 0 0
\(933\) 54.4319 1.78202
\(934\) 0 0
\(935\) −6.35394 −0.207796
\(936\) 0 0
\(937\) 10.8038 0.352944 0.176472 0.984306i \(-0.443532\pi\)
0.176472 + 0.984306i \(0.443532\pi\)
\(938\) 0 0
\(939\) 35.3043 1.15211
\(940\) 0 0
\(941\) −4.64358 −0.151376 −0.0756882 0.997132i \(-0.524115\pi\)
−0.0756882 + 0.997132i \(0.524115\pi\)
\(942\) 0 0
\(943\) 62.0641 2.02109
\(944\) 0 0
\(945\) 10.0263 0.326157
\(946\) 0 0
\(947\) 25.9173 0.842199 0.421099 0.907014i \(-0.361644\pi\)
0.421099 + 0.907014i \(0.361644\pi\)
\(948\) 0 0
\(949\) −1.21693 −0.0395033
\(950\) 0 0
\(951\) 17.0727 0.553619
\(952\) 0 0
\(953\) 9.22969 0.298979 0.149490 0.988763i \(-0.452237\pi\)
0.149490 + 0.988763i \(0.452237\pi\)
\(954\) 0 0
\(955\) 1.83921 0.0595156
\(956\) 0 0
\(957\) 24.5270 0.792846
\(958\) 0 0
\(959\) 38.1078 1.23056
\(960\) 0 0
\(961\) −10.0978 −0.325735
\(962\) 0 0
\(963\) −0.236339 −0.00761591
\(964\) 0 0
\(965\) 1.13245 0.0364548
\(966\) 0 0
\(967\) −54.1981 −1.74289 −0.871447 0.490490i \(-0.836818\pi\)
−0.871447 + 0.490490i \(0.836818\pi\)
\(968\) 0 0
\(969\) 4.48949 0.144223
\(970\) 0 0
\(971\) −29.0364 −0.931822 −0.465911 0.884832i \(-0.654273\pi\)
−0.465911 + 0.884832i \(0.654273\pi\)
\(972\) 0 0
\(973\) 33.3071 1.06778
\(974\) 0 0
\(975\) −4.05970 −0.130014
\(976\) 0 0
\(977\) 43.6200 1.39553 0.697763 0.716329i \(-0.254179\pi\)
0.697763 + 0.716329i \(0.254179\pi\)
\(978\) 0 0
\(979\) −13.1527 −0.420363
\(980\) 0 0
\(981\) −0.0997352 −0.00318430
\(982\) 0 0
\(983\) −16.4486 −0.524629 −0.262314 0.964983i \(-0.584486\pi\)
−0.262314 + 0.964983i \(0.584486\pi\)
\(984\) 0 0
\(985\) −4.85153 −0.154582
\(986\) 0 0
\(987\) −7.77058 −0.247340
\(988\) 0 0
\(989\) 26.3108 0.836634
\(990\) 0 0
\(991\) −20.1702 −0.640728 −0.320364 0.947295i \(-0.603805\pi\)
−0.320364 + 0.947295i \(0.603805\pi\)
\(992\) 0 0
\(993\) 23.5385 0.746971
\(994\) 0 0
\(995\) 11.6220 0.368443
\(996\) 0 0
\(997\) 42.1453 1.33476 0.667378 0.744719i \(-0.267417\pi\)
0.667378 + 0.744719i \(0.267417\pi\)
\(998\) 0 0
\(999\) 44.4031 1.40485
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 \(a_p\))