Properties

Label 8020.2.a.c.1.2
Level 8020
Weight 2
Character 8020.1
Self dual Yes
Analytic conductor 64.040
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 8020.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.61261 q^{3}\) \(-1.00000 q^{5}\) \(-1.36796 q^{7}\) \(+3.82575 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.61261 q^{3}\) \(-1.00000 q^{5}\) \(-1.36796 q^{7}\) \(+3.82575 q^{9}\) \(-3.20956 q^{11}\) \(-0.991251 q^{13}\) \(+2.61261 q^{15}\) \(-6.53588 q^{17}\) \(+2.43792 q^{19}\) \(+3.57396 q^{21}\) \(+2.25201 q^{23}\) \(+1.00000 q^{25}\) \(-2.15737 q^{27}\) \(-4.41202 q^{29}\) \(+5.35748 q^{31}\) \(+8.38535 q^{33}\) \(+1.36796 q^{35}\) \(+11.4289 q^{37}\) \(+2.58976 q^{39}\) \(-4.67265 q^{41}\) \(-2.19240 q^{43}\) \(-3.82575 q^{45}\) \(-0.392606 q^{47}\) \(-5.12868 q^{49}\) \(+17.0757 q^{51}\) \(+9.29821 q^{53}\) \(+3.20956 q^{55}\) \(-6.36935 q^{57}\) \(-1.84032 q^{59}\) \(-5.30011 q^{61}\) \(-5.23349 q^{63}\) \(+0.991251 q^{65}\) \(+9.05832 q^{67}\) \(-5.88364 q^{69}\) \(+1.03723 q^{71}\) \(+15.0142 q^{73}\) \(-2.61261 q^{75}\) \(+4.39056 q^{77}\) \(-14.6718 q^{79}\) \(-5.84088 q^{81}\) \(+1.71945 q^{83}\) \(+6.53588 q^{85}\) \(+11.5269 q^{87}\) \(+13.6317 q^{89}\) \(+1.35600 q^{91}\) \(-13.9970 q^{93}\) \(-2.43792 q^{95}\) \(+3.23219 q^{97}\) \(-12.2790 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 3q^{13} \) \(\mathstrut -\mathstrut 3q^{15} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut +\mathstrut 28q^{25} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut -\mathstrut 37q^{29} \) \(\mathstrut -\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 2q^{33} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut -\mathstrut 3q^{37} \) \(\mathstrut -\mathstrut 19q^{39} \) \(\mathstrut -\mathstrut 30q^{41} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut -\mathstrut 17q^{45} \) \(\mathstrut -\mathstrut 15q^{47} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 2q^{55} \) \(\mathstrut -\mathstrut 22q^{57} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut -\mathstrut 33q^{61} \) \(\mathstrut -\mathstrut 20q^{63} \) \(\mathstrut -\mathstrut 3q^{65} \) \(\mathstrut +\mathstrut 19q^{67} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut -\mathstrut 42q^{77} \) \(\mathstrut -\mathstrut 29q^{79} \) \(\mathstrut -\mathstrut 36q^{81} \) \(\mathstrut +\mathstrut 14q^{83} \) \(\mathstrut +\mathstrut 10q^{85} \) \(\mathstrut -\mathstrut 32q^{87} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 7q^{91} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 39q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.61261 −1.50839 −0.754197 0.656649i \(-0.771974\pi\)
−0.754197 + 0.656649i \(0.771974\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −1.36796 −0.517041 −0.258521 0.966006i \(-0.583235\pi\)
−0.258521 + 0.966006i \(0.583235\pi\)
\(8\) 0 0
\(9\) 3.82575 1.27525
\(10\) 0 0
\(11\) −3.20956 −0.967720 −0.483860 0.875146i \(-0.660766\pi\)
−0.483860 + 0.875146i \(0.660766\pi\)
\(12\) 0 0
\(13\) −0.991251 −0.274924 −0.137462 0.990507i \(-0.543894\pi\)
−0.137462 + 0.990507i \(0.543894\pi\)
\(14\) 0 0
\(15\) 2.61261 0.674574
\(16\) 0 0
\(17\) −6.53588 −1.58518 −0.792592 0.609753i \(-0.791269\pi\)
−0.792592 + 0.609753i \(0.791269\pi\)
\(18\) 0 0
\(19\) 2.43792 0.559298 0.279649 0.960102i \(-0.409782\pi\)
0.279649 + 0.960102i \(0.409782\pi\)
\(20\) 0 0
\(21\) 3.57396 0.779902
\(22\) 0 0
\(23\) 2.25201 0.469577 0.234789 0.972046i \(-0.424560\pi\)
0.234789 + 0.972046i \(0.424560\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −2.15737 −0.415186
\(28\) 0 0
\(29\) −4.41202 −0.819291 −0.409646 0.912245i \(-0.634348\pi\)
−0.409646 + 0.912245i \(0.634348\pi\)
\(30\) 0 0
\(31\) 5.35748 0.962232 0.481116 0.876657i \(-0.340232\pi\)
0.481116 + 0.876657i \(0.340232\pi\)
\(32\) 0 0
\(33\) 8.38535 1.45970
\(34\) 0 0
\(35\) 1.36796 0.231228
\(36\) 0 0
\(37\) 11.4289 1.87890 0.939449 0.342690i \(-0.111338\pi\)
0.939449 + 0.342690i \(0.111338\pi\)
\(38\) 0 0
\(39\) 2.58976 0.414693
\(40\) 0 0
\(41\) −4.67265 −0.729745 −0.364873 0.931057i \(-0.618887\pi\)
−0.364873 + 0.931057i \(0.618887\pi\)
\(42\) 0 0
\(43\) −2.19240 −0.334338 −0.167169 0.985928i \(-0.553463\pi\)
−0.167169 + 0.985928i \(0.553463\pi\)
\(44\) 0 0
\(45\) −3.82575 −0.570309
\(46\) 0 0
\(47\) −0.392606 −0.0572674 −0.0286337 0.999590i \(-0.509116\pi\)
−0.0286337 + 0.999590i \(0.509116\pi\)
\(48\) 0 0
\(49\) −5.12868 −0.732668
\(50\) 0 0
\(51\) 17.0757 2.39108
\(52\) 0 0
\(53\) 9.29821 1.27721 0.638603 0.769536i \(-0.279512\pi\)
0.638603 + 0.769536i \(0.279512\pi\)
\(54\) 0 0
\(55\) 3.20956 0.432777
\(56\) 0 0
\(57\) −6.36935 −0.843641
\(58\) 0 0
\(59\) −1.84032 −0.239589 −0.119794 0.992799i \(-0.538224\pi\)
−0.119794 + 0.992799i \(0.538224\pi\)
\(60\) 0 0
\(61\) −5.30011 −0.678609 −0.339304 0.940677i \(-0.610192\pi\)
−0.339304 + 0.940677i \(0.610192\pi\)
\(62\) 0 0
\(63\) −5.23349 −0.659357
\(64\) 0 0
\(65\) 0.991251 0.122950
\(66\) 0 0
\(67\) 9.05832 1.10665 0.553325 0.832966i \(-0.313359\pi\)
0.553325 + 0.832966i \(0.313359\pi\)
\(68\) 0 0
\(69\) −5.88364 −0.708307
\(70\) 0 0
\(71\) 1.03723 0.123096 0.0615480 0.998104i \(-0.480396\pi\)
0.0615480 + 0.998104i \(0.480396\pi\)
\(72\) 0 0
\(73\) 15.0142 1.75728 0.878640 0.477484i \(-0.158451\pi\)
0.878640 + 0.477484i \(0.158451\pi\)
\(74\) 0 0
\(75\) −2.61261 −0.301679
\(76\) 0 0
\(77\) 4.39056 0.500351
\(78\) 0 0
\(79\) −14.6718 −1.65070 −0.825352 0.564619i \(-0.809023\pi\)
−0.825352 + 0.564619i \(0.809023\pi\)
\(80\) 0 0
\(81\) −5.84088 −0.648986
\(82\) 0 0
\(83\) 1.71945 0.188734 0.0943668 0.995537i \(-0.469917\pi\)
0.0943668 + 0.995537i \(0.469917\pi\)
\(84\) 0 0
\(85\) 6.53588 0.708916
\(86\) 0 0
\(87\) 11.5269 1.23581
\(88\) 0 0
\(89\) 13.6317 1.44496 0.722481 0.691391i \(-0.243002\pi\)
0.722481 + 0.691391i \(0.243002\pi\)
\(90\) 0 0
\(91\) 1.35600 0.142147
\(92\) 0 0
\(93\) −13.9970 −1.45142
\(94\) 0 0
\(95\) −2.43792 −0.250126
\(96\) 0 0
\(97\) 3.23219 0.328179 0.164090 0.986445i \(-0.447531\pi\)
0.164090 + 0.986445i \(0.447531\pi\)
\(98\) 0 0
\(99\) −12.2790 −1.23409
\(100\) 0 0
\(101\) −8.92963 −0.888531 −0.444266 0.895895i \(-0.646535\pi\)
−0.444266 + 0.895895i \(0.646535\pi\)
\(102\) 0 0
\(103\) 16.8692 1.66217 0.831087 0.556142i \(-0.187719\pi\)
0.831087 + 0.556142i \(0.187719\pi\)
\(104\) 0 0
\(105\) −3.57396 −0.348783
\(106\) 0 0
\(107\) 7.06973 0.683456 0.341728 0.939799i \(-0.388988\pi\)
0.341728 + 0.939799i \(0.388988\pi\)
\(108\) 0 0
\(109\) −2.95797 −0.283322 −0.141661 0.989915i \(-0.545244\pi\)
−0.141661 + 0.989915i \(0.545244\pi\)
\(110\) 0 0
\(111\) −29.8593 −2.83412
\(112\) 0 0
\(113\) 4.73283 0.445227 0.222614 0.974907i \(-0.428541\pi\)
0.222614 + 0.974907i \(0.428541\pi\)
\(114\) 0 0
\(115\) −2.25201 −0.210001
\(116\) 0 0
\(117\) −3.79228 −0.350597
\(118\) 0 0
\(119\) 8.94084 0.819606
\(120\) 0 0
\(121\) −0.698708 −0.0635189
\(122\) 0 0
\(123\) 12.2078 1.10074
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −2.56666 −0.227754 −0.113877 0.993495i \(-0.536327\pi\)
−0.113877 + 0.993495i \(0.536327\pi\)
\(128\) 0 0
\(129\) 5.72790 0.504314
\(130\) 0 0
\(131\) −5.32207 −0.464992 −0.232496 0.972597i \(-0.574689\pi\)
−0.232496 + 0.972597i \(0.574689\pi\)
\(132\) 0 0
\(133\) −3.33499 −0.289180
\(134\) 0 0
\(135\) 2.15737 0.185677
\(136\) 0 0
\(137\) −10.5973 −0.905386 −0.452693 0.891666i \(-0.649537\pi\)
−0.452693 + 0.891666i \(0.649537\pi\)
\(138\) 0 0
\(139\) 2.60640 0.221072 0.110536 0.993872i \(-0.464743\pi\)
0.110536 + 0.993872i \(0.464743\pi\)
\(140\) 0 0
\(141\) 1.02573 0.0863818
\(142\) 0 0
\(143\) 3.18148 0.266049
\(144\) 0 0
\(145\) 4.41202 0.366398
\(146\) 0 0
\(147\) 13.3993 1.10515
\(148\) 0 0
\(149\) −10.1387 −0.830597 −0.415298 0.909685i \(-0.636323\pi\)
−0.415298 + 0.909685i \(0.636323\pi\)
\(150\) 0 0
\(151\) 11.6728 0.949922 0.474961 0.880007i \(-0.342462\pi\)
0.474961 + 0.880007i \(0.342462\pi\)
\(152\) 0 0
\(153\) −25.0047 −2.02151
\(154\) 0 0
\(155\) −5.35748 −0.430323
\(156\) 0 0
\(157\) 17.1147 1.36590 0.682951 0.730465i \(-0.260696\pi\)
0.682951 + 0.730465i \(0.260696\pi\)
\(158\) 0 0
\(159\) −24.2926 −1.92653
\(160\) 0 0
\(161\) −3.08067 −0.242791
\(162\) 0 0
\(163\) 12.1992 0.955515 0.477757 0.878492i \(-0.341450\pi\)
0.477757 + 0.878492i \(0.341450\pi\)
\(164\) 0 0
\(165\) −8.38535 −0.652798
\(166\) 0 0
\(167\) 11.3965 0.881885 0.440942 0.897535i \(-0.354644\pi\)
0.440942 + 0.897535i \(0.354644\pi\)
\(168\) 0 0
\(169\) −12.0174 −0.924417
\(170\) 0 0
\(171\) 9.32689 0.713245
\(172\) 0 0
\(173\) −16.5170 −1.25577 −0.627883 0.778308i \(-0.716078\pi\)
−0.627883 + 0.778308i \(0.716078\pi\)
\(174\) 0 0
\(175\) −1.36796 −0.103408
\(176\) 0 0
\(177\) 4.80804 0.361394
\(178\) 0 0
\(179\) −21.1787 −1.58297 −0.791486 0.611188i \(-0.790692\pi\)
−0.791486 + 0.611188i \(0.790692\pi\)
\(180\) 0 0
\(181\) 17.7398 1.31859 0.659296 0.751883i \(-0.270854\pi\)
0.659296 + 0.751883i \(0.270854\pi\)
\(182\) 0 0
\(183\) 13.8471 1.02361
\(184\) 0 0
\(185\) −11.4289 −0.840268
\(186\) 0 0
\(187\) 20.9773 1.53401
\(188\) 0 0
\(189\) 2.95121 0.214669
\(190\) 0 0
\(191\) 8.75806 0.633711 0.316855 0.948474i \(-0.397373\pi\)
0.316855 + 0.948474i \(0.397373\pi\)
\(192\) 0 0
\(193\) −19.2440 −1.38521 −0.692606 0.721316i \(-0.743538\pi\)
−0.692606 + 0.721316i \(0.743538\pi\)
\(194\) 0 0
\(195\) −2.58976 −0.185456
\(196\) 0 0
\(197\) −10.4914 −0.747480 −0.373740 0.927533i \(-0.621925\pi\)
−0.373740 + 0.927533i \(0.621925\pi\)
\(198\) 0 0
\(199\) 21.6944 1.53787 0.768936 0.639325i \(-0.220786\pi\)
0.768936 + 0.639325i \(0.220786\pi\)
\(200\) 0 0
\(201\) −23.6659 −1.66926
\(202\) 0 0
\(203\) 6.03548 0.423607
\(204\) 0 0
\(205\) 4.67265 0.326352
\(206\) 0 0
\(207\) 8.61565 0.598829
\(208\) 0 0
\(209\) −7.82467 −0.541244
\(210\) 0 0
\(211\) 28.2075 1.94188 0.970942 0.239317i \(-0.0769234\pi\)
0.970942 + 0.239317i \(0.0769234\pi\)
\(212\) 0 0
\(213\) −2.70987 −0.185677
\(214\) 0 0
\(215\) 2.19240 0.149521
\(216\) 0 0
\(217\) −7.32884 −0.497514
\(218\) 0 0
\(219\) −39.2263 −2.65067
\(220\) 0 0
\(221\) 6.47870 0.435804
\(222\) 0 0
\(223\) −28.7403 −1.92459 −0.962297 0.272000i \(-0.912315\pi\)
−0.962297 + 0.272000i \(0.912315\pi\)
\(224\) 0 0
\(225\) 3.82575 0.255050
\(226\) 0 0
\(227\) 26.8221 1.78025 0.890123 0.455721i \(-0.150618\pi\)
0.890123 + 0.455721i \(0.150618\pi\)
\(228\) 0 0
\(229\) 25.8803 1.71022 0.855109 0.518449i \(-0.173490\pi\)
0.855109 + 0.518449i \(0.173490\pi\)
\(230\) 0 0
\(231\) −11.4708 −0.754726
\(232\) 0 0
\(233\) −17.8218 −1.16755 −0.583774 0.811916i \(-0.698425\pi\)
−0.583774 + 0.811916i \(0.698425\pi\)
\(234\) 0 0
\(235\) 0.392606 0.0256108
\(236\) 0 0
\(237\) 38.3317 2.48991
\(238\) 0 0
\(239\) 20.9133 1.35277 0.676385 0.736548i \(-0.263545\pi\)
0.676385 + 0.736548i \(0.263545\pi\)
\(240\) 0 0
\(241\) 2.51678 0.162120 0.0810600 0.996709i \(-0.474169\pi\)
0.0810600 + 0.996709i \(0.474169\pi\)
\(242\) 0 0
\(243\) 21.7321 1.39411
\(244\) 0 0
\(245\) 5.12868 0.327659
\(246\) 0 0
\(247\) −2.41659 −0.153764
\(248\) 0 0
\(249\) −4.49225 −0.284685
\(250\) 0 0
\(251\) −15.9940 −1.00953 −0.504767 0.863255i \(-0.668422\pi\)
−0.504767 + 0.863255i \(0.668422\pi\)
\(252\) 0 0
\(253\) −7.22798 −0.454419
\(254\) 0 0
\(255\) −17.0757 −1.06932
\(256\) 0 0
\(257\) 4.01518 0.250460 0.125230 0.992128i \(-0.460033\pi\)
0.125230 + 0.992128i \(0.460033\pi\)
\(258\) 0 0
\(259\) −15.6343 −0.971468
\(260\) 0 0
\(261\) −16.8793 −1.04480
\(262\) 0 0
\(263\) 7.13676 0.440071 0.220036 0.975492i \(-0.429383\pi\)
0.220036 + 0.975492i \(0.429383\pi\)
\(264\) 0 0
\(265\) −9.29821 −0.571184
\(266\) 0 0
\(267\) −35.6145 −2.17957
\(268\) 0 0
\(269\) 3.46899 0.211508 0.105754 0.994392i \(-0.466274\pi\)
0.105754 + 0.994392i \(0.466274\pi\)
\(270\) 0 0
\(271\) −4.79503 −0.291277 −0.145639 0.989338i \(-0.546524\pi\)
−0.145639 + 0.989338i \(0.546524\pi\)
\(272\) 0 0
\(273\) −3.54269 −0.214413
\(274\) 0 0
\(275\) −3.20956 −0.193544
\(276\) 0 0
\(277\) −12.9177 −0.776147 −0.388074 0.921628i \(-0.626859\pi\)
−0.388074 + 0.921628i \(0.626859\pi\)
\(278\) 0 0
\(279\) 20.4964 1.22709
\(280\) 0 0
\(281\) −28.6750 −1.71061 −0.855304 0.518127i \(-0.826630\pi\)
−0.855304 + 0.518127i \(0.826630\pi\)
\(282\) 0 0
\(283\) 5.74356 0.341419 0.170710 0.985321i \(-0.445394\pi\)
0.170710 + 0.985321i \(0.445394\pi\)
\(284\) 0 0
\(285\) 6.36935 0.377288
\(286\) 0 0
\(287\) 6.39201 0.377308
\(288\) 0 0
\(289\) 25.7177 1.51281
\(290\) 0 0
\(291\) −8.44447 −0.495024
\(292\) 0 0
\(293\) −11.6349 −0.679721 −0.339860 0.940476i \(-0.610380\pi\)
−0.339860 + 0.940476i \(0.610380\pi\)
\(294\) 0 0
\(295\) 1.84032 0.107147
\(296\) 0 0
\(297\) 6.92422 0.401784
\(298\) 0 0
\(299\) −2.23231 −0.129098
\(300\) 0 0
\(301\) 2.99913 0.172867
\(302\) 0 0
\(303\) 23.3297 1.34026
\(304\) 0 0
\(305\) 5.30011 0.303483
\(306\) 0 0
\(307\) 11.7444 0.670290 0.335145 0.942167i \(-0.391215\pi\)
0.335145 + 0.942167i \(0.391215\pi\)
\(308\) 0 0
\(309\) −44.0728 −2.50721
\(310\) 0 0
\(311\) −26.1365 −1.48206 −0.741031 0.671470i \(-0.765663\pi\)
−0.741031 + 0.671470i \(0.765663\pi\)
\(312\) 0 0
\(313\) −11.4762 −0.648675 −0.324337 0.945941i \(-0.605141\pi\)
−0.324337 + 0.945941i \(0.605141\pi\)
\(314\) 0 0
\(315\) 5.23349 0.294874
\(316\) 0 0
\(317\) −13.6955 −0.769213 −0.384607 0.923081i \(-0.625663\pi\)
−0.384607 + 0.923081i \(0.625663\pi\)
\(318\) 0 0
\(319\) 14.1606 0.792844
\(320\) 0 0
\(321\) −18.4705 −1.03092
\(322\) 0 0
\(323\) −15.9340 −0.886590
\(324\) 0 0
\(325\) −0.991251 −0.0549847
\(326\) 0 0
\(327\) 7.72802 0.427361
\(328\) 0 0
\(329\) 0.537070 0.0296096
\(330\) 0 0
\(331\) −29.3218 −1.61167 −0.805837 0.592138i \(-0.798284\pi\)
−0.805837 + 0.592138i \(0.798284\pi\)
\(332\) 0 0
\(333\) 43.7241 2.39606
\(334\) 0 0
\(335\) −9.05832 −0.494909
\(336\) 0 0
\(337\) −13.0685 −0.711887 −0.355943 0.934507i \(-0.615840\pi\)
−0.355943 + 0.934507i \(0.615840\pi\)
\(338\) 0 0
\(339\) −12.3651 −0.671578
\(340\) 0 0
\(341\) −17.1952 −0.931171
\(342\) 0 0
\(343\) 16.5916 0.895861
\(344\) 0 0
\(345\) 5.88364 0.316765
\(346\) 0 0
\(347\) −0.973751 −0.0522737 −0.0261368 0.999658i \(-0.508321\pi\)
−0.0261368 + 0.999658i \(0.508321\pi\)
\(348\) 0 0
\(349\) 5.23236 0.280082 0.140041 0.990146i \(-0.455277\pi\)
0.140041 + 0.990146i \(0.455277\pi\)
\(350\) 0 0
\(351\) 2.13850 0.114145
\(352\) 0 0
\(353\) 9.74109 0.518466 0.259233 0.965815i \(-0.416530\pi\)
0.259233 + 0.965815i \(0.416530\pi\)
\(354\) 0 0
\(355\) −1.03723 −0.0550502
\(356\) 0 0
\(357\) −23.3590 −1.23629
\(358\) 0 0
\(359\) 25.4789 1.34473 0.672363 0.740222i \(-0.265279\pi\)
0.672363 + 0.740222i \(0.265279\pi\)
\(360\) 0 0
\(361\) −13.0565 −0.687186
\(362\) 0 0
\(363\) 1.82545 0.0958115
\(364\) 0 0
\(365\) −15.0142 −0.785880
\(366\) 0 0
\(367\) 9.77869 0.510443 0.255222 0.966883i \(-0.417852\pi\)
0.255222 + 0.966883i \(0.417852\pi\)
\(368\) 0 0
\(369\) −17.8764 −0.930608
\(370\) 0 0
\(371\) −12.7196 −0.660369
\(372\) 0 0
\(373\) −25.0304 −1.29602 −0.648011 0.761631i \(-0.724399\pi\)
−0.648011 + 0.761631i \(0.724399\pi\)
\(374\) 0 0
\(375\) 2.61261 0.134915
\(376\) 0 0
\(377\) 4.37342 0.225242
\(378\) 0 0
\(379\) −16.3935 −0.842076 −0.421038 0.907043i \(-0.638334\pi\)
−0.421038 + 0.907043i \(0.638334\pi\)
\(380\) 0 0
\(381\) 6.70569 0.343543
\(382\) 0 0
\(383\) −15.1666 −0.774976 −0.387488 0.921875i \(-0.626657\pi\)
−0.387488 + 0.921875i \(0.626657\pi\)
\(384\) 0 0
\(385\) −4.39056 −0.223764
\(386\) 0 0
\(387\) −8.38759 −0.426365
\(388\) 0 0
\(389\) 34.9845 1.77378 0.886891 0.461978i \(-0.152860\pi\)
0.886891 + 0.461978i \(0.152860\pi\)
\(390\) 0 0
\(391\) −14.7189 −0.744366
\(392\) 0 0
\(393\) 13.9045 0.701391
\(394\) 0 0
\(395\) 14.6718 0.738217
\(396\) 0 0
\(397\) −11.8801 −0.596244 −0.298122 0.954528i \(-0.596360\pi\)
−0.298122 + 0.954528i \(0.596360\pi\)
\(398\) 0 0
\(399\) 8.71304 0.436197
\(400\) 0 0
\(401\) 1.00000 0.0499376
\(402\) 0 0
\(403\) −5.31061 −0.264540
\(404\) 0 0
\(405\) 5.84088 0.290235
\(406\) 0 0
\(407\) −36.6817 −1.81825
\(408\) 0 0
\(409\) −34.1894 −1.69056 −0.845278 0.534326i \(-0.820565\pi\)
−0.845278 + 0.534326i \(0.820565\pi\)
\(410\) 0 0
\(411\) 27.6866 1.36568
\(412\) 0 0
\(413\) 2.51749 0.123877
\(414\) 0 0
\(415\) −1.71945 −0.0844043
\(416\) 0 0
\(417\) −6.80952 −0.333464
\(418\) 0 0
\(419\) 39.2267 1.91635 0.958174 0.286185i \(-0.0923872\pi\)
0.958174 + 0.286185i \(0.0923872\pi\)
\(420\) 0 0
\(421\) −4.98906 −0.243152 −0.121576 0.992582i \(-0.538795\pi\)
−0.121576 + 0.992582i \(0.538795\pi\)
\(422\) 0 0
\(423\) −1.50201 −0.0730303
\(424\) 0 0
\(425\) −6.53588 −0.317037
\(426\) 0 0
\(427\) 7.25035 0.350869
\(428\) 0 0
\(429\) −8.31199 −0.401307
\(430\) 0 0
\(431\) −3.28749 −0.158353 −0.0791764 0.996861i \(-0.525229\pi\)
−0.0791764 + 0.996861i \(0.525229\pi\)
\(432\) 0 0
\(433\) −38.6793 −1.85881 −0.929404 0.369065i \(-0.879678\pi\)
−0.929404 + 0.369065i \(0.879678\pi\)
\(434\) 0 0
\(435\) −11.5269 −0.552672
\(436\) 0 0
\(437\) 5.49024 0.262634
\(438\) 0 0
\(439\) −1.64495 −0.0785091 −0.0392545 0.999229i \(-0.512498\pi\)
−0.0392545 + 0.999229i \(0.512498\pi\)
\(440\) 0 0
\(441\) −19.6210 −0.934336
\(442\) 0 0
\(443\) −2.62465 −0.124701 −0.0623504 0.998054i \(-0.519860\pi\)
−0.0623504 + 0.998054i \(0.519860\pi\)
\(444\) 0 0
\(445\) −13.6317 −0.646206
\(446\) 0 0
\(447\) 26.4886 1.25287
\(448\) 0 0
\(449\) −34.3438 −1.62079 −0.810393 0.585887i \(-0.800746\pi\)
−0.810393 + 0.585887i \(0.800746\pi\)
\(450\) 0 0
\(451\) 14.9972 0.706189
\(452\) 0 0
\(453\) −30.4966 −1.43286
\(454\) 0 0
\(455\) −1.35600 −0.0635700
\(456\) 0 0
\(457\) −28.4786 −1.33217 −0.666087 0.745874i \(-0.732032\pi\)
−0.666087 + 0.745874i \(0.732032\pi\)
\(458\) 0 0
\(459\) 14.1003 0.658147
\(460\) 0 0
\(461\) −35.0769 −1.63369 −0.816847 0.576855i \(-0.804280\pi\)
−0.816847 + 0.576855i \(0.804280\pi\)
\(462\) 0 0
\(463\) 4.28748 0.199256 0.0996281 0.995025i \(-0.468235\pi\)
0.0996281 + 0.995025i \(0.468235\pi\)
\(464\) 0 0
\(465\) 13.9970 0.649097
\(466\) 0 0
\(467\) 2.88913 0.133693 0.0668465 0.997763i \(-0.478706\pi\)
0.0668465 + 0.997763i \(0.478706\pi\)
\(468\) 0 0
\(469\) −12.3914 −0.572184
\(470\) 0 0
\(471\) −44.7141 −2.06032
\(472\) 0 0
\(473\) 7.03665 0.323546
\(474\) 0 0
\(475\) 2.43792 0.111860
\(476\) 0 0
\(477\) 35.5726 1.62876
\(478\) 0 0
\(479\) −33.5805 −1.53433 −0.767165 0.641450i \(-0.778333\pi\)
−0.767165 + 0.641450i \(0.778333\pi\)
\(480\) 0 0
\(481\) −11.3289 −0.516553
\(482\) 0 0
\(483\) 8.04861 0.366224
\(484\) 0 0
\(485\) −3.23219 −0.146766
\(486\) 0 0
\(487\) −10.1239 −0.458758 −0.229379 0.973337i \(-0.573670\pi\)
−0.229379 + 0.973337i \(0.573670\pi\)
\(488\) 0 0
\(489\) −31.8718 −1.44129
\(490\) 0 0
\(491\) −6.81466 −0.307541 −0.153771 0.988107i \(-0.549142\pi\)
−0.153771 + 0.988107i \(0.549142\pi\)
\(492\) 0 0
\(493\) 28.8364 1.29873
\(494\) 0 0
\(495\) 12.2790 0.551900
\(496\) 0 0
\(497\) −1.41889 −0.0636457
\(498\) 0 0
\(499\) −28.4108 −1.27184 −0.635921 0.771754i \(-0.719380\pi\)
−0.635921 + 0.771754i \(0.719380\pi\)
\(500\) 0 0
\(501\) −29.7746 −1.33023
\(502\) 0 0
\(503\) 21.4288 0.955464 0.477732 0.878506i \(-0.341459\pi\)
0.477732 + 0.878506i \(0.341459\pi\)
\(504\) 0 0
\(505\) 8.92963 0.397363
\(506\) 0 0
\(507\) 31.3969 1.39438
\(508\) 0 0
\(509\) 13.9952 0.620325 0.310163 0.950684i \(-0.399617\pi\)
0.310163 + 0.950684i \(0.399617\pi\)
\(510\) 0 0
\(511\) −20.5389 −0.908587
\(512\) 0 0
\(513\) −5.25951 −0.232213
\(514\) 0 0
\(515\) −16.8692 −0.743347
\(516\) 0 0
\(517\) 1.26009 0.0554188
\(518\) 0 0
\(519\) 43.1526 1.89419
\(520\) 0 0
\(521\) 15.4782 0.678113 0.339056 0.940766i \(-0.389892\pi\)
0.339056 + 0.940766i \(0.389892\pi\)
\(522\) 0 0
\(523\) −13.4262 −0.587085 −0.293542 0.955946i \(-0.594834\pi\)
−0.293542 + 0.955946i \(0.594834\pi\)
\(524\) 0 0
\(525\) 3.57396 0.155980
\(526\) 0 0
\(527\) −35.0158 −1.52531
\(528\) 0 0
\(529\) −17.9284 −0.779497
\(530\) 0 0
\(531\) −7.04060 −0.305536
\(532\) 0 0
\(533\) 4.63177 0.200624
\(534\) 0 0
\(535\) −7.06973 −0.305651
\(536\) 0 0
\(537\) 55.3318 2.38774
\(538\) 0 0
\(539\) 16.4608 0.709017
\(540\) 0 0
\(541\) 33.2993 1.43165 0.715824 0.698280i \(-0.246051\pi\)
0.715824 + 0.698280i \(0.246051\pi\)
\(542\) 0 0
\(543\) −46.3474 −1.98896
\(544\) 0 0
\(545\) 2.95797 0.126705
\(546\) 0 0
\(547\) −43.1252 −1.84390 −0.921950 0.387308i \(-0.873405\pi\)
−0.921950 + 0.387308i \(0.873405\pi\)
\(548\) 0 0
\(549\) −20.2769 −0.865397
\(550\) 0 0
\(551\) −10.7562 −0.458228
\(552\) 0 0
\(553\) 20.0704 0.853482
\(554\) 0 0
\(555\) 29.8593 1.26746
\(556\) 0 0
\(557\) 12.7461 0.540070 0.270035 0.962851i \(-0.412965\pi\)
0.270035 + 0.962851i \(0.412965\pi\)
\(558\) 0 0
\(559\) 2.17322 0.0919175
\(560\) 0 0
\(561\) −54.8056 −2.31390
\(562\) 0 0
\(563\) 7.69223 0.324189 0.162094 0.986775i \(-0.448175\pi\)
0.162094 + 0.986775i \(0.448175\pi\)
\(564\) 0 0
\(565\) −4.73283 −0.199112
\(566\) 0 0
\(567\) 7.99010 0.335553
\(568\) 0 0
\(569\) 14.7351 0.617726 0.308863 0.951107i \(-0.400052\pi\)
0.308863 + 0.951107i \(0.400052\pi\)
\(570\) 0 0
\(571\) 34.0058 1.42310 0.711549 0.702637i \(-0.247994\pi\)
0.711549 + 0.702637i \(0.247994\pi\)
\(572\) 0 0
\(573\) −22.8814 −0.955885
\(574\) 0 0
\(575\) 2.25201 0.0939155
\(576\) 0 0
\(577\) −0.842175 −0.0350602 −0.0175301 0.999846i \(-0.505580\pi\)
−0.0175301 + 0.999846i \(0.505580\pi\)
\(578\) 0 0
\(579\) 50.2771 2.08945
\(580\) 0 0
\(581\) −2.35214 −0.0975831
\(582\) 0 0
\(583\) −29.8432 −1.23598
\(584\) 0 0
\(585\) 3.79228 0.156792
\(586\) 0 0
\(587\) −17.1065 −0.706063 −0.353031 0.935611i \(-0.614849\pi\)
−0.353031 + 0.935611i \(0.614849\pi\)
\(588\) 0 0
\(589\) 13.0611 0.538174
\(590\) 0 0
\(591\) 27.4099 1.12749
\(592\) 0 0
\(593\) −33.8043 −1.38818 −0.694089 0.719890i \(-0.744192\pi\)
−0.694089 + 0.719890i \(0.744192\pi\)
\(594\) 0 0
\(595\) −8.94084 −0.366539
\(596\) 0 0
\(597\) −56.6790 −2.31972
\(598\) 0 0
\(599\) 40.3297 1.64783 0.823914 0.566715i \(-0.191786\pi\)
0.823914 + 0.566715i \(0.191786\pi\)
\(600\) 0 0
\(601\) −25.4728 −1.03906 −0.519529 0.854453i \(-0.673893\pi\)
−0.519529 + 0.854453i \(0.673893\pi\)
\(602\) 0 0
\(603\) 34.6549 1.41126
\(604\) 0 0
\(605\) 0.698708 0.0284065
\(606\) 0 0
\(607\) −34.7204 −1.40926 −0.704629 0.709576i \(-0.748887\pi\)
−0.704629 + 0.709576i \(0.748887\pi\)
\(608\) 0 0
\(609\) −15.7684 −0.638967
\(610\) 0 0
\(611\) 0.389171 0.0157442
\(612\) 0 0
\(613\) 19.2832 0.778840 0.389420 0.921060i \(-0.372675\pi\)
0.389420 + 0.921060i \(0.372675\pi\)
\(614\) 0 0
\(615\) −12.2078 −0.492267
\(616\) 0 0
\(617\) −33.5601 −1.35108 −0.675539 0.737325i \(-0.736089\pi\)
−0.675539 + 0.737325i \(0.736089\pi\)
\(618\) 0 0
\(619\) −6.70266 −0.269403 −0.134701 0.990886i \(-0.543007\pi\)
−0.134701 + 0.990886i \(0.543007\pi\)
\(620\) 0 0
\(621\) −4.85843 −0.194962
\(622\) 0 0
\(623\) −18.6477 −0.747105
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 20.4428 0.816408
\(628\) 0 0
\(629\) −74.6978 −2.97840
\(630\) 0 0
\(631\) −29.8511 −1.18835 −0.594177 0.804334i \(-0.702522\pi\)
−0.594177 + 0.804334i \(0.702522\pi\)
\(632\) 0 0
\(633\) −73.6953 −2.92912
\(634\) 0 0
\(635\) 2.56666 0.101855
\(636\) 0 0
\(637\) 5.08381 0.201428
\(638\) 0 0
\(639\) 3.96817 0.156978
\(640\) 0 0
\(641\) −27.7421 −1.09575 −0.547874 0.836561i \(-0.684563\pi\)
−0.547874 + 0.836561i \(0.684563\pi\)
\(642\) 0 0
\(643\) 48.0533 1.89504 0.947519 0.319699i \(-0.103582\pi\)
0.947519 + 0.319699i \(0.103582\pi\)
\(644\) 0 0
\(645\) −5.72790 −0.225536
\(646\) 0 0
\(647\) −18.5956 −0.731070 −0.365535 0.930798i \(-0.619114\pi\)
−0.365535 + 0.930798i \(0.619114\pi\)
\(648\) 0 0
\(649\) 5.90661 0.231855
\(650\) 0 0
\(651\) 19.1474 0.750447
\(652\) 0 0
\(653\) 3.53683 0.138407 0.0692034 0.997603i \(-0.477954\pi\)
0.0692034 + 0.997603i \(0.477954\pi\)
\(654\) 0 0
\(655\) 5.32207 0.207951
\(656\) 0 0
\(657\) 57.4407 2.24097
\(658\) 0 0
\(659\) 29.4430 1.14694 0.573469 0.819228i \(-0.305597\pi\)
0.573469 + 0.819228i \(0.305597\pi\)
\(660\) 0 0
\(661\) 3.94650 0.153501 0.0767506 0.997050i \(-0.475545\pi\)
0.0767506 + 0.997050i \(0.475545\pi\)
\(662\) 0 0
\(663\) −16.9263 −0.657365
\(664\) 0 0
\(665\) 3.33499 0.129325
\(666\) 0 0
\(667\) −9.93593 −0.384721
\(668\) 0 0
\(669\) 75.0874 2.90305
\(670\) 0 0
\(671\) 17.0110 0.656703
\(672\) 0 0
\(673\) 13.3389 0.514177 0.257088 0.966388i \(-0.417237\pi\)
0.257088 + 0.966388i \(0.417237\pi\)
\(674\) 0 0
\(675\) −2.15737 −0.0830373
\(676\) 0 0
\(677\) −3.07411 −0.118148 −0.0590739 0.998254i \(-0.518815\pi\)
−0.0590739 + 0.998254i \(0.518815\pi\)
\(678\) 0 0
\(679\) −4.42152 −0.169682
\(680\) 0 0
\(681\) −70.0758 −2.68531
\(682\) 0 0
\(683\) 19.5880 0.749516 0.374758 0.927123i \(-0.377726\pi\)
0.374758 + 0.927123i \(0.377726\pi\)
\(684\) 0 0
\(685\) 10.5973 0.404901
\(686\) 0 0
\(687\) −67.6152 −2.57968
\(688\) 0 0
\(689\) −9.21686 −0.351134
\(690\) 0 0
\(691\) −3.34403 −0.127213 −0.0636064 0.997975i \(-0.520260\pi\)
−0.0636064 + 0.997975i \(0.520260\pi\)
\(692\) 0 0
\(693\) 16.7972 0.638073
\(694\) 0 0
\(695\) −2.60640 −0.0988664
\(696\) 0 0
\(697\) 30.5399 1.15678
\(698\) 0 0
\(699\) 46.5616 1.76112
\(700\) 0 0
\(701\) −24.1053 −0.910447 −0.455223 0.890377i \(-0.650441\pi\)
−0.455223 + 0.890377i \(0.650441\pi\)
\(702\) 0 0
\(703\) 27.8627 1.05086
\(704\) 0 0
\(705\) −1.02573 −0.0386311
\(706\) 0 0
\(707\) 12.2154 0.459408
\(708\) 0 0
\(709\) 11.4991 0.431860 0.215930 0.976409i \(-0.430722\pi\)
0.215930 + 0.976409i \(0.430722\pi\)
\(710\) 0 0
\(711\) −56.1306 −2.10506
\(712\) 0 0
\(713\) 12.0651 0.451842
\(714\) 0 0
\(715\) −3.18148 −0.118981
\(716\) 0 0
\(717\) −54.6384 −2.04051
\(718\) 0 0
\(719\) 29.8653 1.11379 0.556894 0.830584i \(-0.311993\pi\)
0.556894 + 0.830584i \(0.311993\pi\)
\(720\) 0 0
\(721\) −23.0765 −0.859413
\(722\) 0 0
\(723\) −6.57538 −0.244541
\(724\) 0 0
\(725\) −4.41202 −0.163858
\(726\) 0 0
\(727\) −32.4968 −1.20524 −0.602620 0.798028i \(-0.705877\pi\)
−0.602620 + 0.798028i \(0.705877\pi\)
\(728\) 0 0
\(729\) −39.2549 −1.45388
\(730\) 0 0
\(731\) 14.3293 0.529988
\(732\) 0 0
\(733\) 47.4215 1.75155 0.875777 0.482716i \(-0.160350\pi\)
0.875777 + 0.482716i \(0.160350\pi\)
\(734\) 0 0
\(735\) −13.3993 −0.494239
\(736\) 0 0
\(737\) −29.0732 −1.07093
\(738\) 0 0
\(739\) −50.7770 −1.86786 −0.933932 0.357451i \(-0.883646\pi\)
−0.933932 + 0.357451i \(0.883646\pi\)
\(740\) 0 0
\(741\) 6.31363 0.231937
\(742\) 0 0
\(743\) −37.4366 −1.37342 −0.686709 0.726933i \(-0.740945\pi\)
−0.686709 + 0.726933i \(0.740945\pi\)
\(744\) 0 0
\(745\) 10.1387 0.371454
\(746\) 0 0
\(747\) 6.57817 0.240683
\(748\) 0 0
\(749\) −9.67113 −0.353375
\(750\) 0 0
\(751\) −35.4765 −1.29456 −0.647279 0.762254i \(-0.724093\pi\)
−0.647279 + 0.762254i \(0.724093\pi\)
\(752\) 0 0
\(753\) 41.7863 1.52278
\(754\) 0 0
\(755\) −11.6728 −0.424818
\(756\) 0 0
\(757\) 21.6604 0.787260 0.393630 0.919269i \(-0.371219\pi\)
0.393630 + 0.919269i \(0.371219\pi\)
\(758\) 0 0
\(759\) 18.8839 0.685443
\(760\) 0 0
\(761\) −33.0889 −1.19947 −0.599736 0.800198i \(-0.704728\pi\)
−0.599736 + 0.800198i \(0.704728\pi\)
\(762\) 0 0
\(763\) 4.04639 0.146489
\(764\) 0 0
\(765\) 25.0047 0.904045
\(766\) 0 0
\(767\) 1.82422 0.0658687
\(768\) 0 0
\(769\) 18.9234 0.682395 0.341197 0.939992i \(-0.389168\pi\)
0.341197 + 0.939992i \(0.389168\pi\)
\(770\) 0 0
\(771\) −10.4901 −0.377792
\(772\) 0 0
\(773\) −6.25909 −0.225124 −0.112562 0.993645i \(-0.535906\pi\)
−0.112562 + 0.993645i \(0.535906\pi\)
\(774\) 0 0
\(775\) 5.35748 0.192446
\(776\) 0 0
\(777\) 40.8464 1.46536
\(778\) 0 0
\(779\) −11.3916 −0.408145
\(780\) 0 0
\(781\) −3.32904 −0.119122
\(782\) 0 0
\(783\) 9.51836 0.340159
\(784\) 0 0
\(785\) −17.1147 −0.610850
\(786\) 0 0
\(787\) −27.4763 −0.979423 −0.489711 0.871885i \(-0.662898\pi\)
−0.489711 + 0.871885i \(0.662898\pi\)
\(788\) 0 0
\(789\) −18.6456 −0.663800
\(790\) 0 0
\(791\) −6.47434 −0.230201
\(792\) 0 0
\(793\) 5.25374 0.186566
\(794\) 0 0
\(795\) 24.2926 0.861571
\(796\) 0 0
\(797\) 33.4892 1.18625 0.593123 0.805112i \(-0.297895\pi\)
0.593123 + 0.805112i \(0.297895\pi\)
\(798\) 0 0
\(799\) 2.56602 0.0907794
\(800\) 0 0
\(801\) 52.1516 1.84269
\(802\) 0 0
\(803\) −48.1891 −1.70055
\(804\) 0 0
\(805\) 3.08067 0.108579
\(806\) 0 0
\(807\) −9.06314 −0.319038
\(808\) 0 0
\(809\) 45.0476 1.58379 0.791895 0.610657i \(-0.209095\pi\)
0.791895 + 0.610657i \(0.209095\pi\)
\(810\) 0 0
\(811\) −25.4986 −0.895378 −0.447689 0.894189i \(-0.647753\pi\)
−0.447689 + 0.894189i \(0.647753\pi\)
\(812\) 0 0
\(813\) 12.5276 0.439361
\(814\) 0 0
\(815\) −12.1992 −0.427319
\(816\) 0 0
\(817\) −5.34491 −0.186995
\(818\) 0 0
\(819\) 5.18770 0.181273
\(820\) 0 0
\(821\) 26.2944 0.917682 0.458841 0.888518i \(-0.348265\pi\)
0.458841 + 0.888518i \(0.348265\pi\)
\(822\) 0 0
\(823\) 23.8950 0.832927 0.416464 0.909152i \(-0.363269\pi\)
0.416464 + 0.909152i \(0.363269\pi\)
\(824\) 0 0
\(825\) 8.38535 0.291940
\(826\) 0 0
\(827\) 19.9050 0.692165 0.346083 0.938204i \(-0.387512\pi\)
0.346083 + 0.938204i \(0.387512\pi\)
\(828\) 0 0
\(829\) −3.63035 −0.126087 −0.0630436 0.998011i \(-0.520081\pi\)
−0.0630436 + 0.998011i \(0.520081\pi\)
\(830\) 0 0
\(831\) 33.7489 1.17074
\(832\) 0 0
\(833\) 33.5204 1.16141
\(834\) 0 0
\(835\) −11.3965 −0.394391
\(836\) 0 0
\(837\) −11.5581 −0.399506
\(838\) 0 0
\(839\) 36.3796 1.25596 0.627981 0.778229i \(-0.283882\pi\)
0.627981 + 0.778229i \(0.283882\pi\)
\(840\) 0 0
\(841\) −9.53410 −0.328762
\(842\) 0 0
\(843\) 74.9167 2.58027
\(844\) 0 0
\(845\) 12.0174 0.413412
\(846\) 0 0
\(847\) 0.955806 0.0328419
\(848\) 0 0
\(849\) −15.0057 −0.514995
\(850\) 0 0
\(851\) 25.7380 0.882288
\(852\) 0 0
\(853\) −1.90614 −0.0652649 −0.0326325 0.999467i \(-0.510389\pi\)
−0.0326325 + 0.999467i \(0.510389\pi\)
\(854\) 0 0
\(855\) −9.32689 −0.318973
\(856\) 0 0
\(857\) 15.5649 0.531687 0.265843 0.964016i \(-0.414350\pi\)
0.265843 + 0.964016i \(0.414350\pi\)
\(858\) 0 0
\(859\) 22.8591 0.779942 0.389971 0.920827i \(-0.372485\pi\)
0.389971 + 0.920827i \(0.372485\pi\)
\(860\) 0 0
\(861\) −16.6999 −0.569130
\(862\) 0 0
\(863\) 14.3912 0.489884 0.244942 0.969538i \(-0.421231\pi\)
0.244942 + 0.969538i \(0.421231\pi\)
\(864\) 0 0
\(865\) 16.5170 0.561596
\(866\) 0 0
\(867\) −67.1905 −2.28191
\(868\) 0 0
\(869\) 47.0900 1.59742
\(870\) 0 0
\(871\) −8.97907 −0.304244
\(872\) 0 0
\(873\) 12.3656 0.418511
\(874\) 0 0
\(875\) 1.36796 0.0462456
\(876\) 0 0
\(877\) −13.4726 −0.454938 −0.227469 0.973785i \(-0.573045\pi\)
−0.227469 + 0.973785i \(0.573045\pi\)
\(878\) 0 0
\(879\) 30.3976 1.02529
\(880\) 0 0
\(881\) 46.5168 1.56719 0.783595 0.621272i \(-0.213384\pi\)
0.783595 + 0.621272i \(0.213384\pi\)
\(882\) 0 0
\(883\) 19.8116 0.666714 0.333357 0.942801i \(-0.391818\pi\)
0.333357 + 0.942801i \(0.391818\pi\)
\(884\) 0 0
\(885\) −4.80804 −0.161620
\(886\) 0 0
\(887\) −14.2450 −0.478302 −0.239151 0.970982i \(-0.576869\pi\)
−0.239151 + 0.970982i \(0.576869\pi\)
\(888\) 0 0
\(889\) 3.51110 0.117758
\(890\) 0 0
\(891\) 18.7467 0.628037
\(892\) 0 0
\(893\) −0.957142 −0.0320295
\(894\) 0 0
\(895\) 21.1787 0.707926
\(896\) 0 0
\(897\) 5.83217 0.194730
\(898\) 0 0
\(899\) −23.6373 −0.788348
\(900\) 0 0
\(901\) −60.7720 −2.02461
\(902\) 0 0
\(903\) −7.83556 −0.260751
\(904\) 0 0
\(905\) −17.7398 −0.589692
\(906\) 0 0
\(907\) 13.6509 0.453270 0.226635 0.973980i \(-0.427227\pi\)
0.226635 + 0.973980i \(0.427227\pi\)
\(908\) 0 0
\(909\) −34.1626 −1.13310
\(910\) 0 0
\(911\) −36.0471 −1.19429 −0.597146 0.802132i \(-0.703699\pi\)
−0.597146 + 0.802132i \(0.703699\pi\)
\(912\) 0 0
\(913\) −5.51867 −0.182641
\(914\) 0 0
\(915\) −13.8471 −0.457772
\(916\) 0 0
\(917\) 7.28040 0.240420
\(918\) 0 0
\(919\) −39.4256 −1.30053 −0.650265 0.759708i \(-0.725342\pi\)
−0.650265 + 0.759708i \(0.725342\pi\)
\(920\) 0 0
\(921\) −30.6836 −1.01106
\(922\) 0 0
\(923\) −1.02815 −0.0338420
\(924\) 0 0
\(925\) 11.4289 0.375779
\(926\) 0 0
\(927\) 64.5375 2.11969
\(928\) 0 0
\(929\) 11.9514 0.392114 0.196057 0.980593i \(-0.437186\pi\)
0.196057 + 0.980593i \(0.437186\pi\)
\(930\) 0 0
\(931\) −12.5033 −0.409780
\(932\) 0 0
\(933\) 68.2845 2.23553
\(934\) 0 0
\(935\) −20.9773 −0.686031
\(936\) 0 0
\(937\) 28.1498 0.919614 0.459807 0.888019i \(-0.347919\pi\)
0.459807 + 0.888019i \(0.347919\pi\)
\(938\) 0 0
\(939\) 29.9830 0.978457
\(940\) 0 0
\(941\) 41.4984 1.35281 0.676405 0.736530i \(-0.263537\pi\)
0.676405 + 0.736530i \(0.263537\pi\)
\(942\) 0 0
\(943\) −10.5229 −0.342672
\(944\) 0 0
\(945\) −2.95121 −0.0960027
\(946\) 0 0
\(947\) −54.5087 −1.77129 −0.885647 0.464358i \(-0.846285\pi\)
−0.885647 + 0.464358i \(0.846285\pi\)
\(948\) 0 0
\(949\) −14.8829 −0.483118
\(950\) 0 0
\(951\) 35.7809 1.16028
\(952\) 0 0
\(953\) 52.2598 1.69286 0.846431 0.532499i \(-0.178747\pi\)
0.846431 + 0.532499i \(0.178747\pi\)
\(954\) 0 0
\(955\) −8.75806 −0.283404
\(956\) 0 0
\(957\) −36.9963 −1.19592
\(958\) 0 0
\(959\) 14.4967 0.468122
\(960\) 0 0
\(961\) −2.29740 −0.0741095
\(962\) 0 0
\(963\) 27.0470 0.871578
\(964\) 0 0
\(965\) 19.2440 0.619486
\(966\) 0 0
\(967\) 40.4831 1.30185 0.650924 0.759143i \(-0.274382\pi\)
0.650924 + 0.759143i \(0.274382\pi\)
\(968\) 0 0
\(969\) 41.6293 1.33733
\(970\) 0 0
\(971\) 26.6327 0.854683 0.427342 0.904090i \(-0.359450\pi\)
0.427342 + 0.904090i \(0.359450\pi\)
\(972\) 0 0
\(973\) −3.56546 −0.114303
\(974\) 0 0
\(975\) 2.58976 0.0829386
\(976\) 0 0
\(977\) 8.29124 0.265260 0.132630 0.991166i \(-0.457658\pi\)
0.132630 + 0.991166i \(0.457658\pi\)
\(978\) 0 0
\(979\) −43.7519 −1.39832
\(980\) 0 0
\(981\) −11.3164 −0.361306
\(982\) 0 0
\(983\) −15.5643 −0.496423 −0.248211 0.968706i \(-0.579843\pi\)
−0.248211 + 0.968706i \(0.579843\pi\)
\(984\) 0 0
\(985\) 10.4914 0.334283
\(986\) 0 0
\(987\) −1.40316 −0.0446630
\(988\) 0 0
\(989\) −4.93732 −0.156998
\(990\) 0 0
\(991\) 8.40509 0.266996 0.133498 0.991049i \(-0.457379\pi\)
0.133498 + 0.991049i \(0.457379\pi\)
\(992\) 0 0
\(993\) 76.6066 2.43104
\(994\) 0 0
\(995\) −21.6944 −0.687758
\(996\) 0 0
\(997\) 58.8897 1.86506 0.932528 0.361096i \(-0.117598\pi\)
0.932528 + 0.361096i \(0.117598\pi\)
\(998\) 0 0
\(999\) −24.6564 −0.780093
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 \(a_p\))