Properties

Label 4028.2.a.d.1.1
Level 4028
Weight 2
Character 4028.1
Self dual Yes
Analytic conductor 32.164
Analytic rank 1
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4028 = 2^{2} \cdot 19 \cdot 53 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4028.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1637419342\)
Analytic rank: \(1\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(3.25955\)
Character \(\chi\) = 4028.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.25955 q^{3} +3.01882 q^{5} +1.05463 q^{7} +7.62467 q^{9} +O(q^{10})\) \(q-3.25955 q^{3} +3.01882 q^{5} +1.05463 q^{7} +7.62467 q^{9} +0.331559 q^{11} +5.94995 q^{13} -9.83998 q^{15} -5.88242 q^{17} -1.00000 q^{19} -3.43761 q^{21} -7.02557 q^{23} +4.11325 q^{25} -15.0743 q^{27} -0.630623 q^{29} +1.75086 q^{31} -1.08073 q^{33} +3.18372 q^{35} -8.41283 q^{37} -19.3942 q^{39} -3.43168 q^{41} -12.5011 q^{43} +23.0175 q^{45} -11.6939 q^{47} -5.88776 q^{49} +19.1741 q^{51} +1.00000 q^{53} +1.00092 q^{55} +3.25955 q^{57} +5.04111 q^{59} +8.88242 q^{61} +8.04118 q^{63} +17.9618 q^{65} -9.48288 q^{67} +22.9002 q^{69} +3.45336 q^{71} -11.7327 q^{73} -13.4073 q^{75} +0.349671 q^{77} +1.29391 q^{79} +26.2616 q^{81} +14.1005 q^{83} -17.7579 q^{85} +2.05555 q^{87} +0.759900 q^{89} +6.27497 q^{91} -5.70701 q^{93} -3.01882 q^{95} -7.99724 q^{97} +2.52803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} + O(q^{10}) \) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} - 11q^{11} + q^{13} - 20q^{15} - q^{17} - 19q^{19} - 10q^{21} - 16q^{23} + 21q^{25} - 4q^{27} - 9q^{31} + 7q^{33} - 25q^{37} - 25q^{39} + q^{41} - 41q^{43} - 27q^{45} - 29q^{47} + 14q^{49} - 24q^{51} + 19q^{53} - 28q^{55} + 4q^{57} - 42q^{59} + q^{61} - 41q^{63} + 2q^{65} - 41q^{67} - 25q^{69} - 20q^{73} + 11q^{75} - 19q^{77} - 38q^{79} + 23q^{81} - 36q^{83} - 58q^{85} - 30q^{87} - 25q^{89} - 55q^{91} - 38q^{93} + 2q^{95} - 13q^{97} + q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −3.25955 −1.88190 −0.940951 0.338542i \(-0.890066\pi\)
−0.940951 + 0.338542i \(0.890066\pi\)
\(4\) 0 0
\(5\) 3.01882 1.35006 0.675028 0.737792i \(-0.264132\pi\)
0.675028 + 0.737792i \(0.264132\pi\)
\(6\) 0 0
\(7\) 1.05463 0.398611 0.199306 0.979937i \(-0.436131\pi\)
0.199306 + 0.979937i \(0.436131\pi\)
\(8\) 0 0
\(9\) 7.62467 2.54156
\(10\) 0 0
\(11\) 0.331559 0.0999688 0.0499844 0.998750i \(-0.484083\pi\)
0.0499844 + 0.998750i \(0.484083\pi\)
\(12\) 0 0
\(13\) 5.94995 1.65022 0.825110 0.564972i \(-0.191113\pi\)
0.825110 + 0.564972i \(0.191113\pi\)
\(14\) 0 0
\(15\) −9.83998 −2.54067
\(16\) 0 0
\(17\) −5.88242 −1.42670 −0.713349 0.700809i \(-0.752822\pi\)
−0.713349 + 0.700809i \(0.752822\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) −3.43761 −0.750147
\(22\) 0 0
\(23\) −7.02557 −1.46493 −0.732466 0.680804i \(-0.761631\pi\)
−0.732466 + 0.680804i \(0.761631\pi\)
\(24\) 0 0
\(25\) 4.11325 0.822649
\(26\) 0 0
\(27\) −15.0743 −2.90106
\(28\) 0 0
\(29\) −0.630623 −0.117104 −0.0585518 0.998284i \(-0.518648\pi\)
−0.0585518 + 0.998284i \(0.518648\pi\)
\(30\) 0 0
\(31\) 1.75086 0.314463 0.157232 0.987562i \(-0.449743\pi\)
0.157232 + 0.987562i \(0.449743\pi\)
\(32\) 0 0
\(33\) −1.08073 −0.188132
\(34\) 0 0
\(35\) 3.18372 0.538147
\(36\) 0 0
\(37\) −8.41283 −1.38306 −0.691531 0.722347i \(-0.743063\pi\)
−0.691531 + 0.722347i \(0.743063\pi\)
\(38\) 0 0
\(39\) −19.3942 −3.10555
\(40\) 0 0
\(41\) −3.43168 −0.535938 −0.267969 0.963427i \(-0.586353\pi\)
−0.267969 + 0.963427i \(0.586353\pi\)
\(42\) 0 0
\(43\) −12.5011 −1.90641 −0.953203 0.302333i \(-0.902235\pi\)
−0.953203 + 0.302333i \(0.902235\pi\)
\(44\) 0 0
\(45\) 23.0175 3.43124
\(46\) 0 0
\(47\) −11.6939 −1.70573 −0.852866 0.522130i \(-0.825137\pi\)
−0.852866 + 0.522130i \(0.825137\pi\)
\(48\) 0 0
\(49\) −5.88776 −0.841109
\(50\) 0 0
\(51\) 19.1741 2.68490
\(52\) 0 0
\(53\) 1.00000 0.137361
\(54\) 0 0
\(55\) 1.00092 0.134963
\(56\) 0 0
\(57\) 3.25955 0.431738
\(58\) 0 0
\(59\) 5.04111 0.656296 0.328148 0.944626i \(-0.393576\pi\)
0.328148 + 0.944626i \(0.393576\pi\)
\(60\) 0 0
\(61\) 8.88242 1.13728 0.568639 0.822587i \(-0.307470\pi\)
0.568639 + 0.822587i \(0.307470\pi\)
\(62\) 0 0
\(63\) 8.04118 1.01309
\(64\) 0 0
\(65\) 17.9618 2.22789
\(66\) 0 0
\(67\) −9.48288 −1.15852 −0.579259 0.815144i \(-0.696658\pi\)
−0.579259 + 0.815144i \(0.696658\pi\)
\(68\) 0 0
\(69\) 22.9002 2.75686
\(70\) 0 0
\(71\) 3.45336 0.409838 0.204919 0.978779i \(-0.434307\pi\)
0.204919 + 0.978779i \(0.434307\pi\)
\(72\) 0 0
\(73\) −11.7327 −1.37321 −0.686604 0.727032i \(-0.740899\pi\)
−0.686604 + 0.727032i \(0.740899\pi\)
\(74\) 0 0
\(75\) −13.4073 −1.54815
\(76\) 0 0
\(77\) 0.349671 0.0398487
\(78\) 0 0
\(79\) 1.29391 0.145576 0.0727882 0.997347i \(-0.476810\pi\)
0.0727882 + 0.997347i \(0.476810\pi\)
\(80\) 0 0
\(81\) 26.2616 2.91795
\(82\) 0 0
\(83\) 14.1005 1.54773 0.773866 0.633349i \(-0.218320\pi\)
0.773866 + 0.633349i \(0.218320\pi\)
\(84\) 0 0
\(85\) −17.7579 −1.92612
\(86\) 0 0
\(87\) 2.05555 0.220378
\(88\) 0 0
\(89\) 0.759900 0.0805492 0.0402746 0.999189i \(-0.487177\pi\)
0.0402746 + 0.999189i \(0.487177\pi\)
\(90\) 0 0
\(91\) 6.27497 0.657796
\(92\) 0 0
\(93\) −5.70701 −0.591789
\(94\) 0 0
\(95\) −3.01882 −0.309724
\(96\) 0 0
\(97\) −7.99724 −0.811996 −0.405998 0.913874i \(-0.633076\pi\)
−0.405998 + 0.913874i \(0.633076\pi\)
\(98\) 0 0
\(99\) 2.52803 0.254076
\(100\) 0 0
\(101\) −8.67774 −0.863467 −0.431734 0.902001i \(-0.642098\pi\)
−0.431734 + 0.902001i \(0.642098\pi\)
\(102\) 0 0
\(103\) −19.5852 −1.92978 −0.964891 0.262650i \(-0.915403\pi\)
−0.964891 + 0.262650i \(0.915403\pi\)
\(104\) 0 0
\(105\) −10.3775 −1.01274
\(106\) 0 0
\(107\) 17.7875 1.71958 0.859790 0.510648i \(-0.170595\pi\)
0.859790 + 0.510648i \(0.170595\pi\)
\(108\) 0 0
\(109\) −6.71722 −0.643393 −0.321697 0.946843i \(-0.604253\pi\)
−0.321697 + 0.946843i \(0.604253\pi\)
\(110\) 0 0
\(111\) 27.4221 2.60279
\(112\) 0 0
\(113\) 13.9055 1.30812 0.654060 0.756443i \(-0.273064\pi\)
0.654060 + 0.756443i \(0.273064\pi\)
\(114\) 0 0
\(115\) −21.2089 −1.97774
\(116\) 0 0
\(117\) 45.3664 4.19413
\(118\) 0 0
\(119\) −6.20376 −0.568697
\(120\) 0 0
\(121\) −10.8901 −0.990006
\(122\) 0 0
\(123\) 11.1857 1.00858
\(124\) 0 0
\(125\) −2.67695 −0.239434
\(126\) 0 0
\(127\) 17.9613 1.59380 0.796902 0.604108i \(-0.206471\pi\)
0.796902 + 0.604108i \(0.206471\pi\)
\(128\) 0 0
\(129\) 40.7481 3.58767
\(130\) 0 0
\(131\) −20.4071 −1.78297 −0.891487 0.453046i \(-0.850337\pi\)
−0.891487 + 0.453046i \(0.850337\pi\)
\(132\) 0 0
\(133\) −1.05463 −0.0914477
\(134\) 0 0
\(135\) −45.5067 −3.91659
\(136\) 0 0
\(137\) 20.2060 1.72631 0.863157 0.504936i \(-0.168484\pi\)
0.863157 + 0.504936i \(0.168484\pi\)
\(138\) 0 0
\(139\) −15.3310 −1.30036 −0.650178 0.759782i \(-0.725306\pi\)
−0.650178 + 0.759782i \(0.725306\pi\)
\(140\) 0 0
\(141\) 38.1169 3.21002
\(142\) 0 0
\(143\) 1.97276 0.164970
\(144\) 0 0
\(145\) −1.90373 −0.158096
\(146\) 0 0
\(147\) 19.1915 1.58289
\(148\) 0 0
\(149\) −10.8655 −0.890136 −0.445068 0.895497i \(-0.646820\pi\)
−0.445068 + 0.895497i \(0.646820\pi\)
\(150\) 0 0
\(151\) 14.9050 1.21295 0.606477 0.795101i \(-0.292582\pi\)
0.606477 + 0.795101i \(0.292582\pi\)
\(152\) 0 0
\(153\) −44.8515 −3.62603
\(154\) 0 0
\(155\) 5.28552 0.424543
\(156\) 0 0
\(157\) −7.90326 −0.630749 −0.315374 0.948967i \(-0.602130\pi\)
−0.315374 + 0.948967i \(0.602130\pi\)
\(158\) 0 0
\(159\) −3.25955 −0.258499
\(160\) 0 0
\(161\) −7.40935 −0.583938
\(162\) 0 0
\(163\) −9.78577 −0.766480 −0.383240 0.923649i \(-0.625192\pi\)
−0.383240 + 0.923649i \(0.625192\pi\)
\(164\) 0 0
\(165\) −3.26253 −0.253988
\(166\) 0 0
\(167\) 4.07577 0.315393 0.157696 0.987488i \(-0.449593\pi\)
0.157696 + 0.987488i \(0.449593\pi\)
\(168\) 0 0
\(169\) 22.4019 1.72322
\(170\) 0 0
\(171\) −7.62467 −0.583073
\(172\) 0 0
\(173\) 4.69793 0.357177 0.178588 0.983924i \(-0.442847\pi\)
0.178588 + 0.983924i \(0.442847\pi\)
\(174\) 0 0
\(175\) 4.33794 0.327917
\(176\) 0 0
\(177\) −16.4317 −1.23509
\(178\) 0 0
\(179\) −10.2545 −0.766454 −0.383227 0.923654i \(-0.625187\pi\)
−0.383227 + 0.923654i \(0.625187\pi\)
\(180\) 0 0
\(181\) 2.96755 0.220576 0.110288 0.993900i \(-0.464823\pi\)
0.110288 + 0.993900i \(0.464823\pi\)
\(182\) 0 0
\(183\) −28.9527 −2.14024
\(184\) 0 0
\(185\) −25.3968 −1.86721
\(186\) 0 0
\(187\) −1.95037 −0.142625
\(188\) 0 0
\(189\) −15.8978 −1.15639
\(190\) 0 0
\(191\) −2.27081 −0.164310 −0.0821550 0.996620i \(-0.526180\pi\)
−0.0821550 + 0.996620i \(0.526180\pi\)
\(192\) 0 0
\(193\) 8.42938 0.606760 0.303380 0.952870i \(-0.401885\pi\)
0.303380 + 0.952870i \(0.401885\pi\)
\(194\) 0 0
\(195\) −58.5474 −4.19267
\(196\) 0 0
\(197\) 6.00992 0.428189 0.214095 0.976813i \(-0.431320\pi\)
0.214095 + 0.976813i \(0.431320\pi\)
\(198\) 0 0
\(199\) 27.3567 1.93927 0.969633 0.244565i \(-0.0786452\pi\)
0.969633 + 0.244565i \(0.0786452\pi\)
\(200\) 0 0
\(201\) 30.9099 2.18022
\(202\) 0 0
\(203\) −0.665071 −0.0466788
\(204\) 0 0
\(205\) −10.3596 −0.723547
\(206\) 0 0
\(207\) −53.5676 −3.72321
\(208\) 0 0
\(209\) −0.331559 −0.0229344
\(210\) 0 0
\(211\) 4.78615 0.329492 0.164746 0.986336i \(-0.447320\pi\)
0.164746 + 0.986336i \(0.447320\pi\)
\(212\) 0 0
\(213\) −11.2564 −0.771275
\(214\) 0 0
\(215\) −37.7386 −2.57375
\(216\) 0 0
\(217\) 1.84650 0.125349
\(218\) 0 0
\(219\) 38.2433 2.58424
\(220\) 0 0
\(221\) −35.0001 −2.35436
\(222\) 0 0
\(223\) −15.0186 −1.00572 −0.502859 0.864369i \(-0.667718\pi\)
−0.502859 + 0.864369i \(0.667718\pi\)
\(224\) 0 0
\(225\) 31.3621 2.09081
\(226\) 0 0
\(227\) 0.347715 0.0230786 0.0115393 0.999933i \(-0.496327\pi\)
0.0115393 + 0.999933i \(0.496327\pi\)
\(228\) 0 0
\(229\) −7.34107 −0.485112 −0.242556 0.970137i \(-0.577986\pi\)
−0.242556 + 0.970137i \(0.577986\pi\)
\(230\) 0 0
\(231\) −1.13977 −0.0749913
\(232\) 0 0
\(233\) −16.8167 −1.10170 −0.550849 0.834605i \(-0.685696\pi\)
−0.550849 + 0.834605i \(0.685696\pi\)
\(234\) 0 0
\(235\) −35.3017 −2.30283
\(236\) 0 0
\(237\) −4.21757 −0.273961
\(238\) 0 0
\(239\) −7.82872 −0.506398 −0.253199 0.967414i \(-0.581483\pi\)
−0.253199 + 0.967414i \(0.581483\pi\)
\(240\) 0 0
\(241\) 1.61594 0.104092 0.0520458 0.998645i \(-0.483426\pi\)
0.0520458 + 0.998645i \(0.483426\pi\)
\(242\) 0 0
\(243\) −40.3779 −2.59025
\(244\) 0 0
\(245\) −17.7741 −1.13554
\(246\) 0 0
\(247\) −5.94995 −0.378586
\(248\) 0 0
\(249\) −45.9613 −2.91268
\(250\) 0 0
\(251\) 18.9517 1.19622 0.598111 0.801413i \(-0.295918\pi\)
0.598111 + 0.801413i \(0.295918\pi\)
\(252\) 0 0
\(253\) −2.32939 −0.146448
\(254\) 0 0
\(255\) 57.8829 3.62477
\(256\) 0 0
\(257\) −7.49487 −0.467517 −0.233759 0.972295i \(-0.575103\pi\)
−0.233759 + 0.972295i \(0.575103\pi\)
\(258\) 0 0
\(259\) −8.87239 −0.551304
\(260\) 0 0
\(261\) −4.80829 −0.297626
\(262\) 0 0
\(263\) 6.47807 0.399455 0.199727 0.979851i \(-0.435994\pi\)
0.199727 + 0.979851i \(0.435994\pi\)
\(264\) 0 0
\(265\) 3.01882 0.185444
\(266\) 0 0
\(267\) −2.47693 −0.151586
\(268\) 0 0
\(269\) 12.0852 0.736850 0.368425 0.929657i \(-0.379897\pi\)
0.368425 + 0.929657i \(0.379897\pi\)
\(270\) 0 0
\(271\) −19.0918 −1.15974 −0.579872 0.814708i \(-0.696897\pi\)
−0.579872 + 0.814708i \(0.696897\pi\)
\(272\) 0 0
\(273\) −20.4536 −1.23791
\(274\) 0 0
\(275\) 1.36378 0.0822393
\(276\) 0 0
\(277\) −22.9238 −1.37736 −0.688680 0.725065i \(-0.741809\pi\)
−0.688680 + 0.725065i \(0.741809\pi\)
\(278\) 0 0
\(279\) 13.3497 0.799226
\(280\) 0 0
\(281\) −15.4236 −0.920095 −0.460048 0.887894i \(-0.652168\pi\)
−0.460048 + 0.887894i \(0.652168\pi\)
\(282\) 0 0
\(283\) 1.62130 0.0963765 0.0481883 0.998838i \(-0.484655\pi\)
0.0481883 + 0.998838i \(0.484655\pi\)
\(284\) 0 0
\(285\) 9.83998 0.582870
\(286\) 0 0
\(287\) −3.61914 −0.213631
\(288\) 0 0
\(289\) 17.6029 1.03546
\(290\) 0 0
\(291\) 26.0674 1.52810
\(292\) 0 0
\(293\) 10.1597 0.593538 0.296769 0.954949i \(-0.404091\pi\)
0.296769 + 0.954949i \(0.404091\pi\)
\(294\) 0 0
\(295\) 15.2182 0.886036
\(296\) 0 0
\(297\) −4.99804 −0.290015
\(298\) 0 0
\(299\) −41.8018 −2.41746
\(300\) 0 0
\(301\) −13.1840 −0.759914
\(302\) 0 0
\(303\) 28.2855 1.62496
\(304\) 0 0
\(305\) 26.8144 1.53539
\(306\) 0 0
\(307\) −30.8456 −1.76045 −0.880227 0.474553i \(-0.842610\pi\)
−0.880227 + 0.474553i \(0.842610\pi\)
\(308\) 0 0
\(309\) 63.8388 3.63166
\(310\) 0 0
\(311\) 25.3115 1.43529 0.717643 0.696411i \(-0.245221\pi\)
0.717643 + 0.696411i \(0.245221\pi\)
\(312\) 0 0
\(313\) −16.4433 −0.929428 −0.464714 0.885461i \(-0.653843\pi\)
−0.464714 + 0.885461i \(0.653843\pi\)
\(314\) 0 0
\(315\) 24.2748 1.36773
\(316\) 0 0
\(317\) −22.4750 −1.26232 −0.631162 0.775651i \(-0.717422\pi\)
−0.631162 + 0.775651i \(0.717422\pi\)
\(318\) 0 0
\(319\) −0.209089 −0.0117067
\(320\) 0 0
\(321\) −57.9791 −3.23608
\(322\) 0 0
\(323\) 5.88242 0.327307
\(324\) 0 0
\(325\) 24.4736 1.35755
\(326\) 0 0
\(327\) 21.8951 1.21080
\(328\) 0 0
\(329\) −12.3327 −0.679924
\(330\) 0 0
\(331\) −26.3487 −1.44825 −0.724127 0.689667i \(-0.757757\pi\)
−0.724127 + 0.689667i \(0.757757\pi\)
\(332\) 0 0
\(333\) −64.1451 −3.51513
\(334\) 0 0
\(335\) −28.6271 −1.56406
\(336\) 0 0
\(337\) 27.0126 1.47147 0.735736 0.677268i \(-0.236836\pi\)
0.735736 + 0.677268i \(0.236836\pi\)
\(338\) 0 0
\(339\) −45.3257 −2.46175
\(340\) 0 0
\(341\) 0.580513 0.0314365
\(342\) 0 0
\(343\) −13.5918 −0.733887
\(344\) 0 0
\(345\) 69.1314 3.72191
\(346\) 0 0
\(347\) 9.44339 0.506947 0.253474 0.967342i \(-0.418427\pi\)
0.253474 + 0.967342i \(0.418427\pi\)
\(348\) 0 0
\(349\) 32.3767 1.73308 0.866542 0.499104i \(-0.166338\pi\)
0.866542 + 0.499104i \(0.166338\pi\)
\(350\) 0 0
\(351\) −89.6916 −4.78738
\(352\) 0 0
\(353\) 21.4662 1.14253 0.571265 0.820765i \(-0.306453\pi\)
0.571265 + 0.820765i \(0.306453\pi\)
\(354\) 0 0
\(355\) 10.4250 0.553304
\(356\) 0 0
\(357\) 20.2215 1.07023
\(358\) 0 0
\(359\) −8.48430 −0.447784 −0.223892 0.974614i \(-0.571876\pi\)
−0.223892 + 0.974614i \(0.571876\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 35.4967 1.86310
\(364\) 0 0
\(365\) −35.4188 −1.85391
\(366\) 0 0
\(367\) 2.51304 0.131179 0.0655897 0.997847i \(-0.479107\pi\)
0.0655897 + 0.997847i \(0.479107\pi\)
\(368\) 0 0
\(369\) −26.1654 −1.36212
\(370\) 0 0
\(371\) 1.05463 0.0547535
\(372\) 0 0
\(373\) −10.2941 −0.533010 −0.266505 0.963834i \(-0.585869\pi\)
−0.266505 + 0.963834i \(0.585869\pi\)
\(374\) 0 0
\(375\) 8.72565 0.450591
\(376\) 0 0
\(377\) −3.75217 −0.193247
\(378\) 0 0
\(379\) 9.99086 0.513196 0.256598 0.966518i \(-0.417398\pi\)
0.256598 + 0.966518i \(0.417398\pi\)
\(380\) 0 0
\(381\) −58.5457 −2.99938
\(382\) 0 0
\(383\) 26.6459 1.36154 0.680771 0.732496i \(-0.261645\pi\)
0.680771 + 0.732496i \(0.261645\pi\)
\(384\) 0 0
\(385\) 1.05559 0.0537979
\(386\) 0 0
\(387\) −95.3170 −4.84524
\(388\) 0 0
\(389\) −11.4540 −0.580740 −0.290370 0.956914i \(-0.593778\pi\)
−0.290370 + 0.956914i \(0.593778\pi\)
\(390\) 0 0
\(391\) 41.3274 2.09001
\(392\) 0 0
\(393\) 66.5179 3.35538
\(394\) 0 0
\(395\) 3.90608 0.196536
\(396\) 0 0
\(397\) 2.62351 0.131670 0.0658351 0.997831i \(-0.479029\pi\)
0.0658351 + 0.997831i \(0.479029\pi\)
\(398\) 0 0
\(399\) 3.43761 0.172096
\(400\) 0 0
\(401\) 17.0531 0.851591 0.425796 0.904819i \(-0.359994\pi\)
0.425796 + 0.904819i \(0.359994\pi\)
\(402\) 0 0
\(403\) 10.4175 0.518933
\(404\) 0 0
\(405\) 79.2789 3.93940
\(406\) 0 0
\(407\) −2.78935 −0.138263
\(408\) 0 0
\(409\) 18.6613 0.922744 0.461372 0.887207i \(-0.347357\pi\)
0.461372 + 0.887207i \(0.347357\pi\)
\(410\) 0 0
\(411\) −65.8624 −3.24875
\(412\) 0 0
\(413\) 5.31648 0.261607
\(414\) 0 0
\(415\) 42.5668 2.08952
\(416\) 0 0
\(417\) 49.9721 2.44714
\(418\) 0 0
\(419\) 3.26616 0.159563 0.0797813 0.996812i \(-0.474578\pi\)
0.0797813 + 0.996812i \(0.474578\pi\)
\(420\) 0 0
\(421\) 5.73520 0.279517 0.139758 0.990186i \(-0.455367\pi\)
0.139758 + 0.990186i \(0.455367\pi\)
\(422\) 0 0
\(423\) −89.1622 −4.33521
\(424\) 0 0
\(425\) −24.1958 −1.17367
\(426\) 0 0
\(427\) 9.36763 0.453331
\(428\) 0 0
\(429\) −6.43031 −0.310458
\(430\) 0 0
\(431\) −31.7553 −1.52960 −0.764801 0.644267i \(-0.777163\pi\)
−0.764801 + 0.644267i \(0.777163\pi\)
\(432\) 0 0
\(433\) 14.2356 0.684121 0.342060 0.939678i \(-0.388875\pi\)
0.342060 + 0.939678i \(0.388875\pi\)
\(434\) 0 0
\(435\) 6.20531 0.297522
\(436\) 0 0
\(437\) 7.02557 0.336078
\(438\) 0 0
\(439\) 5.29394 0.252666 0.126333 0.991988i \(-0.459679\pi\)
0.126333 + 0.991988i \(0.459679\pi\)
\(440\) 0 0
\(441\) −44.8923 −2.13773
\(442\) 0 0
\(443\) 39.0521 1.85542 0.927711 0.373298i \(-0.121773\pi\)
0.927711 + 0.373298i \(0.121773\pi\)
\(444\) 0 0
\(445\) 2.29400 0.108746
\(446\) 0 0
\(447\) 35.4166 1.67515
\(448\) 0 0
\(449\) −12.6599 −0.597456 −0.298728 0.954338i \(-0.596562\pi\)
−0.298728 + 0.954338i \(0.596562\pi\)
\(450\) 0 0
\(451\) −1.13780 −0.0535771
\(452\) 0 0
\(453\) −48.5837 −2.28266
\(454\) 0 0
\(455\) 18.9430 0.888061
\(456\) 0 0
\(457\) −39.5236 −1.84884 −0.924419 0.381379i \(-0.875449\pi\)
−0.924419 + 0.381379i \(0.875449\pi\)
\(458\) 0 0
\(459\) 88.6737 4.13893
\(460\) 0 0
\(461\) −1.81260 −0.0844213 −0.0422106 0.999109i \(-0.513440\pi\)
−0.0422106 + 0.999109i \(0.513440\pi\)
\(462\) 0 0
\(463\) 40.0534 1.86144 0.930719 0.365736i \(-0.119183\pi\)
0.930719 + 0.365736i \(0.119183\pi\)
\(464\) 0 0
\(465\) −17.2284 −0.798948
\(466\) 0 0
\(467\) −6.25240 −0.289327 −0.144663 0.989481i \(-0.546210\pi\)
−0.144663 + 0.989481i \(0.546210\pi\)
\(468\) 0 0
\(469\) −10.0009 −0.461798
\(470\) 0 0
\(471\) 25.7611 1.18701
\(472\) 0 0
\(473\) −4.14486 −0.190581
\(474\) 0 0
\(475\) −4.11325 −0.188729
\(476\) 0 0
\(477\) 7.62467 0.349110
\(478\) 0 0
\(479\) 7.77440 0.355221 0.177611 0.984101i \(-0.443163\pi\)
0.177611 + 0.984101i \(0.443163\pi\)
\(480\) 0 0
\(481\) −50.0560 −2.28236
\(482\) 0 0
\(483\) 24.1511 1.09891
\(484\) 0 0
\(485\) −24.1422 −1.09624
\(486\) 0 0
\(487\) 8.07103 0.365733 0.182867 0.983138i \(-0.441462\pi\)
0.182867 + 0.983138i \(0.441462\pi\)
\(488\) 0 0
\(489\) 31.8972 1.44244
\(490\) 0 0
\(491\) 28.5768 1.28965 0.644826 0.764329i \(-0.276930\pi\)
0.644826 + 0.764329i \(0.276930\pi\)
\(492\) 0 0
\(493\) 3.70959 0.167071
\(494\) 0 0
\(495\) 7.63165 0.343017
\(496\) 0 0
\(497\) 3.64200 0.163366
\(498\) 0 0
\(499\) −18.5531 −0.830551 −0.415275 0.909696i \(-0.636315\pi\)
−0.415275 + 0.909696i \(0.636315\pi\)
\(500\) 0 0
\(501\) −13.2852 −0.593538
\(502\) 0 0
\(503\) 34.4682 1.53686 0.768430 0.639934i \(-0.221038\pi\)
0.768430 + 0.639934i \(0.221038\pi\)
\(504\) 0 0
\(505\) −26.1965 −1.16573
\(506\) 0 0
\(507\) −73.0202 −3.24294
\(508\) 0 0
\(509\) 6.39583 0.283490 0.141745 0.989903i \(-0.454729\pi\)
0.141745 + 0.989903i \(0.454729\pi\)
\(510\) 0 0
\(511\) −12.3736 −0.547376
\(512\) 0 0
\(513\) 15.0743 0.665549
\(514\) 0 0
\(515\) −59.1240 −2.60531
\(516\) 0 0
\(517\) −3.87722 −0.170520
\(518\) 0 0
\(519\) −15.3131 −0.672172
\(520\) 0 0
\(521\) 30.1952 1.32288 0.661438 0.750000i \(-0.269947\pi\)
0.661438 + 0.750000i \(0.269947\pi\)
\(522\) 0 0
\(523\) −16.4307 −0.718463 −0.359231 0.933249i \(-0.616961\pi\)
−0.359231 + 0.933249i \(0.616961\pi\)
\(524\) 0 0
\(525\) −14.1397 −0.617108
\(526\) 0 0
\(527\) −10.2993 −0.448644
\(528\) 0 0
\(529\) 26.3586 1.14603
\(530\) 0 0
\(531\) 38.4368 1.66801
\(532\) 0 0
\(533\) −20.4183 −0.884416
\(534\) 0 0
\(535\) 53.6971 2.32153
\(536\) 0 0
\(537\) 33.4249 1.44239
\(538\) 0 0
\(539\) −1.95214 −0.0840847
\(540\) 0 0
\(541\) −0.619098 −0.0266171 −0.0133086 0.999911i \(-0.504236\pi\)
−0.0133086 + 0.999911i \(0.504236\pi\)
\(542\) 0 0
\(543\) −9.67287 −0.415103
\(544\) 0 0
\(545\) −20.2781 −0.868617
\(546\) 0 0
\(547\) 29.1904 1.24809 0.624046 0.781388i \(-0.285488\pi\)
0.624046 + 0.781388i \(0.285488\pi\)
\(548\) 0 0
\(549\) 67.7255 2.89045
\(550\) 0 0
\(551\) 0.630623 0.0268654
\(552\) 0 0
\(553\) 1.36459 0.0580284
\(554\) 0 0
\(555\) 82.7821 3.51391
\(556\) 0 0
\(557\) 0.976219 0.0413637 0.0206819 0.999786i \(-0.493416\pi\)
0.0206819 + 0.999786i \(0.493416\pi\)
\(558\) 0 0
\(559\) −74.3811 −3.14599
\(560\) 0 0
\(561\) 6.35733 0.268407
\(562\) 0 0
\(563\) −1.41097 −0.0594652 −0.0297326 0.999558i \(-0.509466\pi\)
−0.0297326 + 0.999558i \(0.509466\pi\)
\(564\) 0 0
\(565\) 41.9782 1.76603
\(566\) 0 0
\(567\) 27.6962 1.16313
\(568\) 0 0
\(569\) −28.5801 −1.19814 −0.599071 0.800696i \(-0.704463\pi\)
−0.599071 + 0.800696i \(0.704463\pi\)
\(570\) 0 0
\(571\) 4.38818 0.183640 0.0918198 0.995776i \(-0.470732\pi\)
0.0918198 + 0.995776i \(0.470732\pi\)
\(572\) 0 0
\(573\) 7.40182 0.309215
\(574\) 0 0
\(575\) −28.8979 −1.20512
\(576\) 0 0
\(577\) 13.0500 0.543277 0.271638 0.962399i \(-0.412435\pi\)
0.271638 + 0.962399i \(0.412435\pi\)
\(578\) 0 0
\(579\) −27.4760 −1.14186
\(580\) 0 0
\(581\) 14.8708 0.616943
\(582\) 0 0
\(583\) 0.331559 0.0137318
\(584\) 0 0
\(585\) 136.953 5.66230
\(586\) 0 0
\(587\) −11.0863 −0.457581 −0.228791 0.973476i \(-0.573477\pi\)
−0.228791 + 0.973476i \(0.573477\pi\)
\(588\) 0 0
\(589\) −1.75086 −0.0721428
\(590\) 0 0
\(591\) −19.5896 −0.805810
\(592\) 0 0
\(593\) −14.9559 −0.614164 −0.307082 0.951683i \(-0.599353\pi\)
−0.307082 + 0.951683i \(0.599353\pi\)
\(594\) 0 0
\(595\) −18.7280 −0.767773
\(596\) 0 0
\(597\) −89.1706 −3.64951
\(598\) 0 0
\(599\) 11.4107 0.466230 0.233115 0.972449i \(-0.425108\pi\)
0.233115 + 0.972449i \(0.425108\pi\)
\(600\) 0 0
\(601\) −23.4013 −0.954558 −0.477279 0.878752i \(-0.658377\pi\)
−0.477279 + 0.878752i \(0.658377\pi\)
\(602\) 0 0
\(603\) −72.3038 −2.94444
\(604\) 0 0
\(605\) −32.8751 −1.33656
\(606\) 0 0
\(607\) 0.210265 0.00853441 0.00426721 0.999991i \(-0.498642\pi\)
0.00426721 + 0.999991i \(0.498642\pi\)
\(608\) 0 0
\(609\) 2.16783 0.0878450
\(610\) 0 0
\(611\) −69.5782 −2.81483
\(612\) 0 0
\(613\) −12.6532 −0.511056 −0.255528 0.966802i \(-0.582249\pi\)
−0.255528 + 0.966802i \(0.582249\pi\)
\(614\) 0 0
\(615\) 33.7677 1.36164
\(616\) 0 0
\(617\) −10.2821 −0.413942 −0.206971 0.978347i \(-0.566361\pi\)
−0.206971 + 0.978347i \(0.566361\pi\)
\(618\) 0 0
\(619\) −4.31481 −0.173427 −0.0867134 0.996233i \(-0.527636\pi\)
−0.0867134 + 0.996233i \(0.527636\pi\)
\(620\) 0 0
\(621\) 105.906 4.24985
\(622\) 0 0
\(623\) 0.801410 0.0321078
\(624\) 0 0
\(625\) −28.6474 −1.14590
\(626\) 0 0
\(627\) 1.08073 0.0431603
\(628\) 0 0
\(629\) 49.4879 1.97321
\(630\) 0 0
\(631\) −16.5934 −0.660573 −0.330286 0.943881i \(-0.607145\pi\)
−0.330286 + 0.943881i \(0.607145\pi\)
\(632\) 0 0
\(633\) −15.6007 −0.620072
\(634\) 0 0
\(635\) 54.2217 2.15172
\(636\) 0 0
\(637\) −35.0319 −1.38801
\(638\) 0 0
\(639\) 26.3307 1.04163
\(640\) 0 0
\(641\) −21.2596 −0.839702 −0.419851 0.907593i \(-0.637918\pi\)
−0.419851 + 0.907593i \(0.637918\pi\)
\(642\) 0 0
\(643\) −35.0880 −1.38374 −0.691869 0.722023i \(-0.743212\pi\)
−0.691869 + 0.722023i \(0.743212\pi\)
\(644\) 0 0
\(645\) 123.011 4.84355
\(646\) 0 0
\(647\) −32.7770 −1.28860 −0.644298 0.764774i \(-0.722850\pi\)
−0.644298 + 0.764774i \(0.722850\pi\)
\(648\) 0 0
\(649\) 1.67142 0.0656091
\(650\) 0 0
\(651\) −6.01876 −0.235894
\(652\) 0 0
\(653\) −3.89507 −0.152426 −0.0762130 0.997092i \(-0.524283\pi\)
−0.0762130 + 0.997092i \(0.524283\pi\)
\(654\) 0 0
\(655\) −61.6052 −2.40711
\(656\) 0 0
\(657\) −89.4579 −3.49008
\(658\) 0 0
\(659\) −35.6021 −1.38686 −0.693430 0.720524i \(-0.743901\pi\)
−0.693430 + 0.720524i \(0.743901\pi\)
\(660\) 0 0
\(661\) 13.0640 0.508131 0.254065 0.967187i \(-0.418232\pi\)
0.254065 + 0.967187i \(0.418232\pi\)
\(662\) 0 0
\(663\) 114.085 4.43068
\(664\) 0 0
\(665\) −3.18372 −0.123459
\(666\) 0 0
\(667\) 4.43048 0.171549
\(668\) 0 0
\(669\) 48.9538 1.89266
\(670\) 0 0
\(671\) 2.94505 0.113692
\(672\) 0 0
\(673\) −49.3187 −1.90110 −0.950548 0.310578i \(-0.899477\pi\)
−0.950548 + 0.310578i \(0.899477\pi\)
\(674\) 0 0
\(675\) −62.0045 −2.38655
\(676\) 0 0
\(677\) 14.2902 0.549217 0.274609 0.961556i \(-0.411452\pi\)
0.274609 + 0.961556i \(0.411452\pi\)
\(678\) 0 0
\(679\) −8.43409 −0.323671
\(680\) 0 0
\(681\) −1.13339 −0.0434317
\(682\) 0 0
\(683\) −5.75039 −0.220033 −0.110016 0.993930i \(-0.535090\pi\)
−0.110016 + 0.993930i \(0.535090\pi\)
\(684\) 0 0
\(685\) 60.9981 2.33062
\(686\) 0 0
\(687\) 23.9286 0.912933
\(688\) 0 0
\(689\) 5.94995 0.226675
\(690\) 0 0
\(691\) 2.28460 0.0869104 0.0434552 0.999055i \(-0.486163\pi\)
0.0434552 + 0.999055i \(0.486163\pi\)
\(692\) 0 0
\(693\) 2.66612 0.101278
\(694\) 0 0
\(695\) −46.2814 −1.75555
\(696\) 0 0
\(697\) 20.1866 0.764622
\(698\) 0 0
\(699\) 54.8149 2.07329
\(700\) 0 0
\(701\) 19.0938 0.721161 0.360581 0.932728i \(-0.382579\pi\)
0.360581 + 0.932728i \(0.382579\pi\)
\(702\) 0 0
\(703\) 8.41283 0.317296
\(704\) 0 0
\(705\) 115.068 4.33370
\(706\) 0 0
\(707\) −9.15177 −0.344188
\(708\) 0 0
\(709\) 49.6459 1.86449 0.932245 0.361829i \(-0.117848\pi\)
0.932245 + 0.361829i \(0.117848\pi\)
\(710\) 0 0
\(711\) 9.86565 0.369991
\(712\) 0 0
\(713\) −12.3008 −0.460667
\(714\) 0 0
\(715\) 5.95540 0.222719
\(716\) 0 0
\(717\) 25.5181 0.952992
\(718\) 0 0
\(719\) 47.2805 1.76326 0.881632 0.471937i \(-0.156445\pi\)
0.881632 + 0.471937i \(0.156445\pi\)
\(720\) 0 0
\(721\) −20.6550 −0.769233
\(722\) 0 0
\(723\) −5.26723 −0.195890
\(724\) 0 0
\(725\) −2.59391 −0.0963352
\(726\) 0 0
\(727\) 29.5633 1.09644 0.548222 0.836333i \(-0.315305\pi\)
0.548222 + 0.836333i \(0.315305\pi\)
\(728\) 0 0
\(729\) 52.8292 1.95664
\(730\) 0 0
\(731\) 73.5370 2.71986
\(732\) 0 0
\(733\) −6.93156 −0.256023 −0.128012 0.991773i \(-0.540859\pi\)
−0.128012 + 0.991773i \(0.540859\pi\)
\(734\) 0 0
\(735\) 57.9355 2.13698
\(736\) 0 0
\(737\) −3.14413 −0.115816
\(738\) 0 0
\(739\) −5.43256 −0.199840 −0.0999199 0.994995i \(-0.531859\pi\)
−0.0999199 + 0.994995i \(0.531859\pi\)
\(740\) 0 0
\(741\) 19.3942 0.712463
\(742\) 0 0
\(743\) 13.6644 0.501297 0.250648 0.968078i \(-0.419356\pi\)
0.250648 + 0.968078i \(0.419356\pi\)
\(744\) 0 0
\(745\) −32.8009 −1.20173
\(746\) 0 0
\(747\) 107.512 3.93365
\(748\) 0 0
\(749\) 18.7591 0.685444
\(750\) 0 0
\(751\) 27.3953 0.999669 0.499834 0.866121i \(-0.333394\pi\)
0.499834 + 0.866121i \(0.333394\pi\)
\(752\) 0 0
\(753\) −61.7741 −2.25117
\(754\) 0 0
\(755\) 44.9955 1.63756
\(756\) 0 0
\(757\) 28.6977 1.04303 0.521517 0.853241i \(-0.325366\pi\)
0.521517 + 0.853241i \(0.325366\pi\)
\(758\) 0 0
\(759\) 7.59277 0.275600
\(760\) 0 0
\(761\) 23.6984 0.859067 0.429534 0.903051i \(-0.358678\pi\)
0.429534 + 0.903051i \(0.358678\pi\)
\(762\) 0 0
\(763\) −7.08416 −0.256464
\(764\) 0 0
\(765\) −135.399 −4.89534
\(766\) 0 0
\(767\) 29.9943 1.08303
\(768\) 0 0
\(769\) 27.4336 0.989281 0.494641 0.869098i \(-0.335300\pi\)
0.494641 + 0.869098i \(0.335300\pi\)
\(770\) 0 0
\(771\) 24.4299 0.879822
\(772\) 0 0
\(773\) −9.82676 −0.353444 −0.176722 0.984261i \(-0.556549\pi\)
−0.176722 + 0.984261i \(0.556549\pi\)
\(774\) 0 0
\(775\) 7.20171 0.258693
\(776\) 0 0
\(777\) 28.9200 1.03750
\(778\) 0 0
\(779\) 3.43168 0.122953
\(780\) 0 0
\(781\) 1.14499 0.0409710
\(782\) 0 0
\(783\) 9.50622 0.339725
\(784\) 0 0
\(785\) −23.8585 −0.851546
\(786\) 0 0
\(787\) −31.8143 −1.13406 −0.567029 0.823698i \(-0.691907\pi\)
−0.567029 + 0.823698i \(0.691907\pi\)
\(788\) 0 0
\(789\) −21.1156 −0.751735
\(790\) 0 0
\(791\) 14.6651 0.521431
\(792\) 0 0
\(793\) 52.8500 1.87676
\(794\) 0 0
\(795\) −9.83998 −0.348988
\(796\) 0 0
\(797\) −3.73650 −0.132354 −0.0661768 0.997808i \(-0.521080\pi\)
−0.0661768 + 0.997808i \(0.521080\pi\)
\(798\) 0 0
\(799\) 68.7885 2.43356
\(800\) 0 0
\(801\) 5.79399 0.204720
\(802\) 0 0
\(803\) −3.89008 −0.137278
\(804\) 0 0
\(805\) −22.3674 −0.788349
\(806\) 0 0
\(807\) −39.3925 −1.38668
\(808\) 0 0
\(809\) 27.3092 0.960141 0.480071 0.877230i \(-0.340611\pi\)
0.480071 + 0.877230i \(0.340611\pi\)
\(810\) 0 0
\(811\) −23.7177 −0.832841 −0.416421 0.909172i \(-0.636716\pi\)
−0.416421 + 0.909172i \(0.636716\pi\)
\(812\) 0 0
\(813\) 62.2306 2.18252
\(814\) 0 0
\(815\) −29.5414 −1.03479
\(816\) 0 0
\(817\) 12.5011 0.437359
\(818\) 0 0
\(819\) 47.8446 1.67183
\(820\) 0 0
\(821\) −0.421489 −0.0147101 −0.00735504 0.999973i \(-0.502341\pi\)
−0.00735504 + 0.999973i \(0.502341\pi\)
\(822\) 0 0
\(823\) 12.1082 0.422066 0.211033 0.977479i \(-0.432317\pi\)
0.211033 + 0.977479i \(0.432317\pi\)
\(824\) 0 0
\(825\) −4.44532 −0.154766
\(826\) 0 0
\(827\) −41.2512 −1.43444 −0.717222 0.696845i \(-0.754586\pi\)
−0.717222 + 0.696845i \(0.754586\pi\)
\(828\) 0 0
\(829\) −24.7971 −0.861239 −0.430619 0.902534i \(-0.641705\pi\)
−0.430619 + 0.902534i \(0.641705\pi\)
\(830\) 0 0
\(831\) 74.7214 2.59206
\(832\) 0 0
\(833\) 34.6343 1.20001
\(834\) 0 0
\(835\) 12.3040 0.425798
\(836\) 0 0
\(837\) −26.3930 −0.912277
\(838\) 0 0
\(839\) −16.6884 −0.576148 −0.288074 0.957608i \(-0.593015\pi\)
−0.288074 + 0.957608i \(0.593015\pi\)
\(840\) 0 0
\(841\) −28.6023 −0.986287
\(842\) 0 0
\(843\) 50.2740 1.73153
\(844\) 0 0
\(845\) 67.6272 2.32645
\(846\) 0 0
\(847\) −11.4849 −0.394628
\(848\) 0 0
\(849\) −5.28472 −0.181371
\(850\) 0 0
\(851\) 59.1049 2.02609
\(852\) 0 0
\(853\) −35.6352 −1.22013 −0.610063 0.792353i \(-0.708856\pi\)
−0.610063 + 0.792353i \(0.708856\pi\)
\(854\) 0 0
\(855\) −23.0175 −0.787181
\(856\) 0 0
\(857\) 14.4335 0.493039 0.246520 0.969138i \(-0.420713\pi\)
0.246520 + 0.969138i \(0.420713\pi\)
\(858\) 0 0
\(859\) −20.9505 −0.714823 −0.357412 0.933947i \(-0.616341\pi\)
−0.357412 + 0.933947i \(0.616341\pi\)
\(860\) 0 0
\(861\) 11.7968 0.402033
\(862\) 0 0
\(863\) −12.6525 −0.430697 −0.215349 0.976537i \(-0.569089\pi\)
−0.215349 + 0.976537i \(0.569089\pi\)
\(864\) 0 0
\(865\) 14.1822 0.482208
\(866\) 0 0
\(867\) −57.3776 −1.94864
\(868\) 0 0
\(869\) 0.429008 0.0145531
\(870\) 0 0
\(871\) −56.4227 −1.91181
\(872\) 0 0
\(873\) −60.9763 −2.06373
\(874\) 0 0
\(875\) −2.82318 −0.0954409
\(876\) 0 0
\(877\) 0.134343 0.00453646 0.00226823 0.999997i \(-0.499278\pi\)
0.00226823 + 0.999997i \(0.499278\pi\)
\(878\) 0 0
\(879\) −33.1162 −1.11698
\(880\) 0 0
\(881\) 28.1276 0.947644 0.473822 0.880621i \(-0.342874\pi\)
0.473822 + 0.880621i \(0.342874\pi\)
\(882\) 0 0
\(883\) 10.4037 0.350113 0.175057 0.984558i \(-0.443989\pi\)
0.175057 + 0.984558i \(0.443989\pi\)
\(884\) 0 0
\(885\) −49.6044 −1.66743
\(886\) 0 0
\(887\) 33.0479 1.10964 0.554819 0.831971i \(-0.312787\pi\)
0.554819 + 0.831971i \(0.312787\pi\)
\(888\) 0 0
\(889\) 18.9424 0.635308
\(890\) 0 0
\(891\) 8.70727 0.291704
\(892\) 0 0
\(893\) 11.6939 0.391322
\(894\) 0 0
\(895\) −30.9563 −1.03476
\(896\) 0 0
\(897\) 136.255 4.54942
\(898\) 0 0
\(899\) −1.10413 −0.0368248
\(900\) 0 0
\(901\) −5.88242 −0.195972
\(902\) 0 0
\(903\) 42.9740 1.43008
\(904\) 0 0
\(905\) 8.95847 0.297790
\(906\) 0 0
\(907\) −46.4475 −1.54226 −0.771132 0.636675i \(-0.780309\pi\)
−0.771132 + 0.636675i \(0.780309\pi\)
\(908\) 0 0
\(909\) −66.1649 −2.19455
\(910\) 0 0
\(911\) −9.67776 −0.320638 −0.160319 0.987065i \(-0.551252\pi\)
−0.160319 + 0.987065i \(0.551252\pi\)
\(912\) 0 0
\(913\) 4.67515 0.154725
\(914\) 0 0
\(915\) −87.4028 −2.88945
\(916\) 0 0
\(917\) −21.5218 −0.710713
\(918\) 0 0
\(919\) 1.82359 0.0601546 0.0300773 0.999548i \(-0.490425\pi\)
0.0300773 + 0.999548i \(0.490425\pi\)
\(920\) 0 0
\(921\) 100.543 3.31300
\(922\) 0 0
\(923\) 20.5473 0.676323
\(924\) 0 0
\(925\) −34.6041 −1.13777
\(926\) 0 0
\(927\) −149.330 −4.90465
\(928\) 0 0
\(929\) −23.8989 −0.784098 −0.392049 0.919944i \(-0.628234\pi\)
−0.392049 + 0.919944i \(0.628234\pi\)
\(930\) 0 0
\(931\) 5.88776 0.192964
\(932\) 0 0
\(933\) −82.5043 −2.70107
\(934\) 0 0
\(935\) −5.88781 −0.192552
\(936\) 0 0
\(937\) −7.10061 −0.231967 −0.115983 0.993251i \(-0.537002\pi\)
−0.115983 + 0.993251i \(0.537002\pi\)
\(938\) 0 0
\(939\) 53.5976 1.74909
\(940\) 0 0
\(941\) 34.6443 1.12937 0.564686 0.825306i \(-0.308997\pi\)
0.564686 + 0.825306i \(0.308997\pi\)
\(942\) 0 0
\(943\) 24.1095 0.785113
\(944\) 0 0
\(945\) −47.9925 −1.56120
\(946\) 0 0
\(947\) −58.1245 −1.88879 −0.944396 0.328810i \(-0.893353\pi\)
−0.944396 + 0.328810i \(0.893353\pi\)
\(948\) 0 0
\(949\) −69.8089 −2.26609
\(950\) 0 0
\(951\) 73.2585 2.37557
\(952\) 0 0
\(953\) −15.9422 −0.516419 −0.258209 0.966089i \(-0.583132\pi\)
−0.258209 + 0.966089i \(0.583132\pi\)
\(954\) 0 0
\(955\) −6.85515 −0.221828
\(956\) 0 0
\(957\) 0.681535 0.0220309
\(958\) 0 0
\(959\) 21.3098 0.688128
\(960\) 0 0
\(961\) −27.9345 −0.901113
\(962\) 0 0
\(963\) 135.624 4.37041
\(964\) 0 0
\(965\) 25.4468 0.819160
\(966\) 0 0
\(967\) 26.4373 0.850167 0.425083 0.905154i \(-0.360245\pi\)
0.425083 + 0.905154i \(0.360245\pi\)
\(968\) 0 0
\(969\) −19.1741 −0.615959
\(970\) 0 0
\(971\) −12.5015 −0.401192 −0.200596 0.979674i \(-0.564288\pi\)
−0.200596 + 0.979674i \(0.564288\pi\)
\(972\) 0 0
\(973\) −16.1684 −0.518337
\(974\) 0 0
\(975\) −79.7730 −2.55478
\(976\) 0 0
\(977\) −43.8965 −1.40437 −0.702187 0.711993i \(-0.747793\pi\)
−0.702187 + 0.711993i \(0.747793\pi\)
\(978\) 0 0
\(979\) 0.251952 0.00805241
\(980\) 0 0
\(981\) −51.2166 −1.63522
\(982\) 0 0
\(983\) 61.3680 1.95734 0.978668 0.205447i \(-0.0658648\pi\)
0.978668 + 0.205447i \(0.0658648\pi\)
\(984\) 0 0
\(985\) 18.1428 0.578079
\(986\) 0 0
\(987\) 40.1991 1.27955
\(988\) 0 0
\(989\) 87.8276 2.79275
\(990\) 0 0
\(991\) 11.7544 0.373392 0.186696 0.982418i \(-0.440222\pi\)
0.186696 + 0.982418i \(0.440222\pi\)
\(992\) 0 0
\(993\) 85.8848 2.72547
\(994\) 0 0
\(995\) 82.5848 2.61812
\(996\) 0 0
\(997\) −28.4239 −0.900193 −0.450097 0.892980i \(-0.648610\pi\)
−0.450097 + 0.892980i \(0.648610\pi\)
\(998\) 0 0
\(999\) 126.818 4.01234
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 \(a_p\))