Properties

Label 8040.2.a.t.1.3
Level 8040
Weight 2
Character 8040.1
Self dual Yes
Analytic conductor 64.200
Analytic rank 0
Dimension 7
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8040 = 2^{3} \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8040.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1997232251\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(3.95767\)
Character \(\chi\) = 8040.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} -1.00000 q^{5} -0.212435 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} -1.00000 q^{5} -0.212435 q^{7} +1.00000 q^{9} -2.52948 q^{11} -3.33132 q^{13} -1.00000 q^{15} -7.70550 q^{17} +7.01222 q^{19} -0.212435 q^{21} -1.74388 q^{23} +1.00000 q^{25} +1.00000 q^{27} +1.69465 q^{29} -2.26698 q^{31} -2.52948 q^{33} +0.212435 q^{35} +9.86329 q^{37} -3.33132 q^{39} +4.26698 q^{41} -1.58745 q^{43} -1.00000 q^{45} -5.44041 q^{47} -6.95487 q^{49} -7.70550 q^{51} +6.91104 q^{53} +2.52948 q^{55} +7.01222 q^{57} -7.97332 q^{59} +8.27524 q^{61} -0.212435 q^{63} +3.33132 q^{65} +1.00000 q^{67} -1.74388 q^{69} +4.11298 q^{71} +10.0883 q^{73} +1.00000 q^{75} +0.537349 q^{77} -6.71856 q^{79} +1.00000 q^{81} +6.07709 q^{83} +7.70550 q^{85} +1.69465 q^{87} -15.7411 q^{89} +0.707688 q^{91} -2.26698 q^{93} -7.01222 q^{95} +7.28158 q^{97} -2.52948 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 7q^{3} - 7q^{5} + 10q^{7} + 7q^{9} + O(q^{10}) \) \( 7q + 7q^{3} - 7q^{5} + 10q^{7} + 7q^{9} - q^{13} - 7q^{15} - 2q^{17} + 9q^{19} + 10q^{21} + 2q^{23} + 7q^{25} + 7q^{27} - q^{29} + 9q^{31} - 10q^{35} + 23q^{37} - q^{39} + 5q^{41} - 3q^{43} - 7q^{45} + 11q^{47} + 13q^{49} - 2q^{51} + 13q^{53} + 9q^{57} + q^{59} + 4q^{61} + 10q^{63} + q^{65} + 7q^{67} + 2q^{69} + q^{71} + 14q^{73} + 7q^{75} + 18q^{77} + 25q^{79} + 7q^{81} - 29q^{83} + 2q^{85} - q^{87} + 7q^{89} + 27q^{91} + 9q^{93} - 9q^{95} + 38q^{97} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −0.212435 −0.0802927 −0.0401464 0.999194i \(-0.512782\pi\)
−0.0401464 + 0.999194i \(0.512782\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −2.52948 −0.762667 −0.381333 0.924438i \(-0.624535\pi\)
−0.381333 + 0.924438i \(0.624535\pi\)
\(12\) 0 0
\(13\) −3.33132 −0.923943 −0.461971 0.886895i \(-0.652858\pi\)
−0.461971 + 0.886895i \(0.652858\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 0 0
\(17\) −7.70550 −1.86886 −0.934429 0.356148i \(-0.884090\pi\)
−0.934429 + 0.356148i \(0.884090\pi\)
\(18\) 0 0
\(19\) 7.01222 1.60871 0.804356 0.594147i \(-0.202510\pi\)
0.804356 + 0.594147i \(0.202510\pi\)
\(20\) 0 0
\(21\) −0.212435 −0.0463570
\(22\) 0 0
\(23\) −1.74388 −0.363623 −0.181812 0.983333i \(-0.558196\pi\)
−0.181812 + 0.983333i \(0.558196\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 1.69465 0.314688 0.157344 0.987544i \(-0.449707\pi\)
0.157344 + 0.987544i \(0.449707\pi\)
\(30\) 0 0
\(31\) −2.26698 −0.407161 −0.203581 0.979058i \(-0.565258\pi\)
−0.203581 + 0.979058i \(0.565258\pi\)
\(32\) 0 0
\(33\) −2.52948 −0.440326
\(34\) 0 0
\(35\) 0.212435 0.0359080
\(36\) 0 0
\(37\) 9.86329 1.62151 0.810757 0.585383i \(-0.199056\pi\)
0.810757 + 0.585383i \(0.199056\pi\)
\(38\) 0 0
\(39\) −3.33132 −0.533439
\(40\) 0 0
\(41\) 4.26698 0.666390 0.333195 0.942858i \(-0.391873\pi\)
0.333195 + 0.942858i \(0.391873\pi\)
\(42\) 0 0
\(43\) −1.58745 −0.242083 −0.121042 0.992647i \(-0.538623\pi\)
−0.121042 + 0.992647i \(0.538623\pi\)
\(44\) 0 0
\(45\) −1.00000 −0.149071
\(46\) 0 0
\(47\) −5.44041 −0.793565 −0.396783 0.917913i \(-0.629873\pi\)
−0.396783 + 0.917913i \(0.629873\pi\)
\(48\) 0 0
\(49\) −6.95487 −0.993553
\(50\) 0 0
\(51\) −7.70550 −1.07899
\(52\) 0 0
\(53\) 6.91104 0.949304 0.474652 0.880174i \(-0.342574\pi\)
0.474652 + 0.880174i \(0.342574\pi\)
\(54\) 0 0
\(55\) 2.52948 0.341075
\(56\) 0 0
\(57\) 7.01222 0.928791
\(58\) 0 0
\(59\) −7.97332 −1.03804 −0.519019 0.854763i \(-0.673703\pi\)
−0.519019 + 0.854763i \(0.673703\pi\)
\(60\) 0 0
\(61\) 8.27524 1.05954 0.529768 0.848143i \(-0.322279\pi\)
0.529768 + 0.848143i \(0.322279\pi\)
\(62\) 0 0
\(63\) −0.212435 −0.0267642
\(64\) 0 0
\(65\) 3.33132 0.413200
\(66\) 0 0
\(67\) 1.00000 0.122169
\(68\) 0 0
\(69\) −1.74388 −0.209938
\(70\) 0 0
\(71\) 4.11298 0.488121 0.244060 0.969760i \(-0.421520\pi\)
0.244060 + 0.969760i \(0.421520\pi\)
\(72\) 0 0
\(73\) 10.0883 1.18074 0.590370 0.807132i \(-0.298982\pi\)
0.590370 + 0.807132i \(0.298982\pi\)
\(74\) 0 0
\(75\) 1.00000 0.115470
\(76\) 0 0
\(77\) 0.537349 0.0612366
\(78\) 0 0
\(79\) −6.71856 −0.755897 −0.377948 0.925827i \(-0.623370\pi\)
−0.377948 + 0.925827i \(0.623370\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 6.07709 0.667047 0.333524 0.942742i \(-0.391762\pi\)
0.333524 + 0.942742i \(0.391762\pi\)
\(84\) 0 0
\(85\) 7.70550 0.835779
\(86\) 0 0
\(87\) 1.69465 0.181685
\(88\) 0 0
\(89\) −15.7411 −1.66855 −0.834277 0.551346i \(-0.814114\pi\)
−0.834277 + 0.551346i \(0.814114\pi\)
\(90\) 0 0
\(91\) 0.707688 0.0741859
\(92\) 0 0
\(93\) −2.26698 −0.235075
\(94\) 0 0
\(95\) −7.01222 −0.719438
\(96\) 0 0
\(97\) 7.28158 0.739332 0.369666 0.929165i \(-0.379472\pi\)
0.369666 + 0.929165i \(0.379472\pi\)
\(98\) 0 0
\(99\) −2.52948 −0.254222
\(100\) 0 0
\(101\) −5.69269 −0.566444 −0.283222 0.959054i \(-0.591403\pi\)
−0.283222 + 0.959054i \(0.591403\pi\)
\(102\) 0 0
\(103\) 15.5449 1.53169 0.765843 0.643028i \(-0.222322\pi\)
0.765843 + 0.643028i \(0.222322\pi\)
\(104\) 0 0
\(105\) 0.212435 0.0207315
\(106\) 0 0
\(107\) 5.04456 0.487676 0.243838 0.969816i \(-0.421594\pi\)
0.243838 + 0.969816i \(0.421594\pi\)
\(108\) 0 0
\(109\) 12.4786 1.19523 0.597615 0.801783i \(-0.296115\pi\)
0.597615 + 0.801783i \(0.296115\pi\)
\(110\) 0 0
\(111\) 9.86329 0.936182
\(112\) 0 0
\(113\) 14.5800 1.37157 0.685784 0.727805i \(-0.259460\pi\)
0.685784 + 0.727805i \(0.259460\pi\)
\(114\) 0 0
\(115\) 1.74388 0.162617
\(116\) 0 0
\(117\) −3.33132 −0.307981
\(118\) 0 0
\(119\) 1.63691 0.150056
\(120\) 0 0
\(121\) −4.60173 −0.418339
\(122\) 0 0
\(123\) 4.26698 0.384740
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −12.9783 −1.15163 −0.575817 0.817578i \(-0.695316\pi\)
−0.575817 + 0.817578i \(0.695316\pi\)
\(128\) 0 0
\(129\) −1.58745 −0.139767
\(130\) 0 0
\(131\) 22.1129 1.93201 0.966007 0.258517i \(-0.0832339\pi\)
0.966007 + 0.258517i \(0.0832339\pi\)
\(132\) 0 0
\(133\) −1.48964 −0.129168
\(134\) 0 0
\(135\) −1.00000 −0.0860663
\(136\) 0 0
\(137\) 11.9140 1.01788 0.508940 0.860802i \(-0.330037\pi\)
0.508940 + 0.860802i \(0.330037\pi\)
\(138\) 0 0
\(139\) 9.97144 0.845766 0.422883 0.906184i \(-0.361018\pi\)
0.422883 + 0.906184i \(0.361018\pi\)
\(140\) 0 0
\(141\) −5.44041 −0.458165
\(142\) 0 0
\(143\) 8.42651 0.704660
\(144\) 0 0
\(145\) −1.69465 −0.140733
\(146\) 0 0
\(147\) −6.95487 −0.573628
\(148\) 0 0
\(149\) −19.1380 −1.56785 −0.783925 0.620856i \(-0.786785\pi\)
−0.783925 + 0.620856i \(0.786785\pi\)
\(150\) 0 0
\(151\) 6.08188 0.494936 0.247468 0.968896i \(-0.420401\pi\)
0.247468 + 0.968896i \(0.420401\pi\)
\(152\) 0 0
\(153\) −7.70550 −0.622953
\(154\) 0 0
\(155\) 2.26698 0.182088
\(156\) 0 0
\(157\) 24.5267 1.95744 0.978722 0.205191i \(-0.0657815\pi\)
0.978722 + 0.205191i \(0.0657815\pi\)
\(158\) 0 0
\(159\) 6.91104 0.548081
\(160\) 0 0
\(161\) 0.370459 0.0291963
\(162\) 0 0
\(163\) 17.6879 1.38543 0.692713 0.721213i \(-0.256415\pi\)
0.692713 + 0.721213i \(0.256415\pi\)
\(164\) 0 0
\(165\) 2.52948 0.196920
\(166\) 0 0
\(167\) 6.23694 0.482629 0.241314 0.970447i \(-0.422422\pi\)
0.241314 + 0.970447i \(0.422422\pi\)
\(168\) 0 0
\(169\) −1.90229 −0.146330
\(170\) 0 0
\(171\) 7.01222 0.536238
\(172\) 0 0
\(173\) 10.0057 0.760719 0.380360 0.924839i \(-0.375800\pi\)
0.380360 + 0.924839i \(0.375800\pi\)
\(174\) 0 0
\(175\) −0.212435 −0.0160585
\(176\) 0 0
\(177\) −7.97332 −0.599311
\(178\) 0 0
\(179\) −3.75325 −0.280531 −0.140265 0.990114i \(-0.544796\pi\)
−0.140265 + 0.990114i \(0.544796\pi\)
\(180\) 0 0
\(181\) −1.67917 −0.124812 −0.0624058 0.998051i \(-0.519877\pi\)
−0.0624058 + 0.998051i \(0.519877\pi\)
\(182\) 0 0
\(183\) 8.27524 0.611723
\(184\) 0 0
\(185\) −9.86329 −0.725163
\(186\) 0 0
\(187\) 19.4909 1.42532
\(188\) 0 0
\(189\) −0.212435 −0.0154523
\(190\) 0 0
\(191\) −12.2025 −0.882944 −0.441472 0.897275i \(-0.645543\pi\)
−0.441472 + 0.897275i \(0.645543\pi\)
\(192\) 0 0
\(193\) −3.73803 −0.269069 −0.134535 0.990909i \(-0.542954\pi\)
−0.134535 + 0.990909i \(0.542954\pi\)
\(194\) 0 0
\(195\) 3.33132 0.238561
\(196\) 0 0
\(197\) 14.8662 1.05918 0.529588 0.848255i \(-0.322347\pi\)
0.529588 + 0.848255i \(0.322347\pi\)
\(198\) 0 0
\(199\) 19.6990 1.39642 0.698212 0.715891i \(-0.253979\pi\)
0.698212 + 0.715891i \(0.253979\pi\)
\(200\) 0 0
\(201\) 1.00000 0.0705346
\(202\) 0 0
\(203\) −0.360002 −0.0252672
\(204\) 0 0
\(205\) −4.26698 −0.298019
\(206\) 0 0
\(207\) −1.74388 −0.121208
\(208\) 0 0
\(209\) −17.7373 −1.22691
\(210\) 0 0
\(211\) −12.1149 −0.834026 −0.417013 0.908901i \(-0.636923\pi\)
−0.417013 + 0.908901i \(0.636923\pi\)
\(212\) 0 0
\(213\) 4.11298 0.281817
\(214\) 0 0
\(215\) 1.58745 0.108263
\(216\) 0 0
\(217\) 0.481584 0.0326921
\(218\) 0 0
\(219\) 10.0883 0.681701
\(220\) 0 0
\(221\) 25.6695 1.72672
\(222\) 0 0
\(223\) 16.7125 1.11915 0.559576 0.828779i \(-0.310964\pi\)
0.559576 + 0.828779i \(0.310964\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) −12.8830 −0.855072 −0.427536 0.903998i \(-0.640618\pi\)
−0.427536 + 0.903998i \(0.640618\pi\)
\(228\) 0 0
\(229\) −19.3688 −1.27992 −0.639962 0.768406i \(-0.721050\pi\)
−0.639962 + 0.768406i \(0.721050\pi\)
\(230\) 0 0
\(231\) 0.537349 0.0353550
\(232\) 0 0
\(233\) 17.3340 1.13559 0.567793 0.823171i \(-0.307797\pi\)
0.567793 + 0.823171i \(0.307797\pi\)
\(234\) 0 0
\(235\) 5.44041 0.354893
\(236\) 0 0
\(237\) −6.71856 −0.436417
\(238\) 0 0
\(239\) 14.5029 0.938115 0.469058 0.883168i \(-0.344594\pi\)
0.469058 + 0.883168i \(0.344594\pi\)
\(240\) 0 0
\(241\) −29.9192 −1.92727 −0.963634 0.267227i \(-0.913893\pi\)
−0.963634 + 0.267227i \(0.913893\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 6.95487 0.444330
\(246\) 0 0
\(247\) −23.3600 −1.48636
\(248\) 0 0
\(249\) 6.07709 0.385120
\(250\) 0 0
\(251\) −19.3907 −1.22393 −0.611966 0.790884i \(-0.709621\pi\)
−0.611966 + 0.790884i \(0.709621\pi\)
\(252\) 0 0
\(253\) 4.41110 0.277323
\(254\) 0 0
\(255\) 7.70550 0.482537
\(256\) 0 0
\(257\) −20.2810 −1.26509 −0.632547 0.774522i \(-0.717991\pi\)
−0.632547 + 0.774522i \(0.717991\pi\)
\(258\) 0 0
\(259\) −2.09530 −0.130196
\(260\) 0 0
\(261\) 1.69465 0.104896
\(262\) 0 0
\(263\) 22.1346 1.36488 0.682440 0.730942i \(-0.260919\pi\)
0.682440 + 0.730942i \(0.260919\pi\)
\(264\) 0 0
\(265\) −6.91104 −0.424542
\(266\) 0 0
\(267\) −15.7411 −0.963340
\(268\) 0 0
\(269\) 18.6744 1.13860 0.569299 0.822131i \(-0.307215\pi\)
0.569299 + 0.822131i \(0.307215\pi\)
\(270\) 0 0
\(271\) 1.49646 0.0909035 0.0454518 0.998967i \(-0.485527\pi\)
0.0454518 + 0.998967i \(0.485527\pi\)
\(272\) 0 0
\(273\) 0.707688 0.0428312
\(274\) 0 0
\(275\) −2.52948 −0.152533
\(276\) 0 0
\(277\) −23.2529 −1.39713 −0.698565 0.715547i \(-0.746177\pi\)
−0.698565 + 0.715547i \(0.746177\pi\)
\(278\) 0 0
\(279\) −2.26698 −0.135720
\(280\) 0 0
\(281\) −7.66461 −0.457232 −0.228616 0.973517i \(-0.573420\pi\)
−0.228616 + 0.973517i \(0.573420\pi\)
\(282\) 0 0
\(283\) −23.6825 −1.40778 −0.703888 0.710311i \(-0.748554\pi\)
−0.703888 + 0.710311i \(0.748554\pi\)
\(284\) 0 0
\(285\) −7.01222 −0.415368
\(286\) 0 0
\(287\) −0.906454 −0.0535063
\(288\) 0 0
\(289\) 42.3748 2.49263
\(290\) 0 0
\(291\) 7.28158 0.426854
\(292\) 0 0
\(293\) −9.94969 −0.581267 −0.290634 0.956834i \(-0.593866\pi\)
−0.290634 + 0.956834i \(0.593866\pi\)
\(294\) 0 0
\(295\) 7.97332 0.464225
\(296\) 0 0
\(297\) −2.52948 −0.146775
\(298\) 0 0
\(299\) 5.80941 0.335967
\(300\) 0 0
\(301\) 0.337229 0.0194375
\(302\) 0 0
\(303\) −5.69269 −0.327037
\(304\) 0 0
\(305\) −8.27524 −0.473839
\(306\) 0 0
\(307\) 0.901961 0.0514776 0.0257388 0.999669i \(-0.491806\pi\)
0.0257388 + 0.999669i \(0.491806\pi\)
\(308\) 0 0
\(309\) 15.5449 0.884319
\(310\) 0 0
\(311\) 30.1842 1.71159 0.855795 0.517316i \(-0.173069\pi\)
0.855795 + 0.517316i \(0.173069\pi\)
\(312\) 0 0
\(313\) −30.1003 −1.70137 −0.850685 0.525676i \(-0.823812\pi\)
−0.850685 + 0.525676i \(0.823812\pi\)
\(314\) 0 0
\(315\) 0.212435 0.0119693
\(316\) 0 0
\(317\) 18.3980 1.03334 0.516669 0.856185i \(-0.327172\pi\)
0.516669 + 0.856185i \(0.327172\pi\)
\(318\) 0 0
\(319\) −4.28658 −0.240002
\(320\) 0 0
\(321\) 5.04456 0.281560
\(322\) 0 0
\(323\) −54.0327 −3.00646
\(324\) 0 0
\(325\) −3.33132 −0.184789
\(326\) 0 0
\(327\) 12.4786 0.690067
\(328\) 0 0
\(329\) 1.15573 0.0637175
\(330\) 0 0
\(331\) −21.1271 −1.16125 −0.580624 0.814171i \(-0.697192\pi\)
−0.580624 + 0.814171i \(0.697192\pi\)
\(332\) 0 0
\(333\) 9.86329 0.540505
\(334\) 0 0
\(335\) −1.00000 −0.0546358
\(336\) 0 0
\(337\) 29.0141 1.58050 0.790250 0.612784i \(-0.209950\pi\)
0.790250 + 0.612784i \(0.209950\pi\)
\(338\) 0 0
\(339\) 14.5800 0.791875
\(340\) 0 0
\(341\) 5.73428 0.310528
\(342\) 0 0
\(343\) 2.96450 0.160068
\(344\) 0 0
\(345\) 1.74388 0.0938871
\(346\) 0 0
\(347\) 27.8380 1.49442 0.747212 0.664586i \(-0.231392\pi\)
0.747212 + 0.664586i \(0.231392\pi\)
\(348\) 0 0
\(349\) −2.90755 −0.155638 −0.0778189 0.996968i \(-0.524796\pi\)
−0.0778189 + 0.996968i \(0.524796\pi\)
\(350\) 0 0
\(351\) −3.33132 −0.177813
\(352\) 0 0
\(353\) 21.0904 1.12253 0.561266 0.827636i \(-0.310315\pi\)
0.561266 + 0.827636i \(0.310315\pi\)
\(354\) 0 0
\(355\) −4.11298 −0.218294
\(356\) 0 0
\(357\) 1.63691 0.0866347
\(358\) 0 0
\(359\) 12.0546 0.636216 0.318108 0.948055i \(-0.396953\pi\)
0.318108 + 0.948055i \(0.396953\pi\)
\(360\) 0 0
\(361\) 30.1712 1.58796
\(362\) 0 0
\(363\) −4.60173 −0.241528
\(364\) 0 0
\(365\) −10.0883 −0.528043
\(366\) 0 0
\(367\) 31.2712 1.63234 0.816171 0.577811i \(-0.196093\pi\)
0.816171 + 0.577811i \(0.196093\pi\)
\(368\) 0 0
\(369\) 4.26698 0.222130
\(370\) 0 0
\(371\) −1.46814 −0.0762222
\(372\) 0 0
\(373\) −29.9857 −1.55260 −0.776301 0.630363i \(-0.782906\pi\)
−0.776301 + 0.630363i \(0.782906\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) −5.64542 −0.290754
\(378\) 0 0
\(379\) 25.0562 1.28705 0.643525 0.765426i \(-0.277471\pi\)
0.643525 + 0.765426i \(0.277471\pi\)
\(380\) 0 0
\(381\) −12.9783 −0.664897
\(382\) 0 0
\(383\) −7.30875 −0.373460 −0.186730 0.982411i \(-0.559789\pi\)
−0.186730 + 0.982411i \(0.559789\pi\)
\(384\) 0 0
\(385\) −0.537349 −0.0273858
\(386\) 0 0
\(387\) −1.58745 −0.0806945
\(388\) 0 0
\(389\) −8.12284 −0.411844 −0.205922 0.978568i \(-0.566019\pi\)
−0.205922 + 0.978568i \(0.566019\pi\)
\(390\) 0 0
\(391\) 13.4374 0.679561
\(392\) 0 0
\(393\) 22.1129 1.11545
\(394\) 0 0
\(395\) 6.71856 0.338047
\(396\) 0 0
\(397\) 21.1178 1.05987 0.529937 0.848037i \(-0.322215\pi\)
0.529937 + 0.848037i \(0.322215\pi\)
\(398\) 0 0
\(399\) −1.48964 −0.0745751
\(400\) 0 0
\(401\) −31.8005 −1.58804 −0.794020 0.607891i \(-0.792016\pi\)
−0.794020 + 0.607891i \(0.792016\pi\)
\(402\) 0 0
\(403\) 7.55204 0.376194
\(404\) 0 0
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) −24.9490 −1.23668
\(408\) 0 0
\(409\) 14.3081 0.707488 0.353744 0.935342i \(-0.384908\pi\)
0.353744 + 0.935342i \(0.384908\pi\)
\(410\) 0 0
\(411\) 11.9140 0.587674
\(412\) 0 0
\(413\) 1.69381 0.0833469
\(414\) 0 0
\(415\) −6.07709 −0.298313
\(416\) 0 0
\(417\) 9.97144 0.488303
\(418\) 0 0
\(419\) −1.46362 −0.0715026 −0.0357513 0.999361i \(-0.511382\pi\)
−0.0357513 + 0.999361i \(0.511382\pi\)
\(420\) 0 0
\(421\) −16.3850 −0.798557 −0.399278 0.916830i \(-0.630739\pi\)
−0.399278 + 0.916830i \(0.630739\pi\)
\(422\) 0 0
\(423\) −5.44041 −0.264522
\(424\) 0 0
\(425\) −7.70550 −0.373772
\(426\) 0 0
\(427\) −1.75795 −0.0850730
\(428\) 0 0
\(429\) 8.42651 0.406836
\(430\) 0 0
\(431\) −13.5448 −0.652431 −0.326216 0.945295i \(-0.605774\pi\)
−0.326216 + 0.945295i \(0.605774\pi\)
\(432\) 0 0
\(433\) 38.2212 1.83679 0.918397 0.395659i \(-0.129484\pi\)
0.918397 + 0.395659i \(0.129484\pi\)
\(434\) 0 0
\(435\) −1.69465 −0.0812522
\(436\) 0 0
\(437\) −12.2284 −0.584965
\(438\) 0 0
\(439\) −6.90056 −0.329346 −0.164673 0.986348i \(-0.552657\pi\)
−0.164673 + 0.986348i \(0.552657\pi\)
\(440\) 0 0
\(441\) −6.95487 −0.331184
\(442\) 0 0
\(443\) −29.2928 −1.39174 −0.695871 0.718167i \(-0.744981\pi\)
−0.695871 + 0.718167i \(0.744981\pi\)
\(444\) 0 0
\(445\) 15.7411 0.746200
\(446\) 0 0
\(447\) −19.1380 −0.905198
\(448\) 0 0
\(449\) −10.4498 −0.493156 −0.246578 0.969123i \(-0.579306\pi\)
−0.246578 + 0.969123i \(0.579306\pi\)
\(450\) 0 0
\(451\) −10.7932 −0.508234
\(452\) 0 0
\(453\) 6.08188 0.285752
\(454\) 0 0
\(455\) −0.707688 −0.0331769
\(456\) 0 0
\(457\) −19.0231 −0.889864 −0.444932 0.895564i \(-0.646772\pi\)
−0.444932 + 0.895564i \(0.646772\pi\)
\(458\) 0 0
\(459\) −7.70550 −0.359662
\(460\) 0 0
\(461\) 7.17635 0.334236 0.167118 0.985937i \(-0.446554\pi\)
0.167118 + 0.985937i \(0.446554\pi\)
\(462\) 0 0
\(463\) 1.71960 0.0799167 0.0399583 0.999201i \(-0.487277\pi\)
0.0399583 + 0.999201i \(0.487277\pi\)
\(464\) 0 0
\(465\) 2.26698 0.105129
\(466\) 0 0
\(467\) −19.9954 −0.925277 −0.462639 0.886547i \(-0.653097\pi\)
−0.462639 + 0.886547i \(0.653097\pi\)
\(468\) 0 0
\(469\) −0.212435 −0.00980932
\(470\) 0 0
\(471\) 24.5267 1.13013
\(472\) 0 0
\(473\) 4.01541 0.184629
\(474\) 0 0
\(475\) 7.01222 0.321743
\(476\) 0 0
\(477\) 6.91104 0.316435
\(478\) 0 0
\(479\) 34.5385 1.57811 0.789053 0.614325i \(-0.210572\pi\)
0.789053 + 0.614325i \(0.210572\pi\)
\(480\) 0 0
\(481\) −32.8578 −1.49819
\(482\) 0 0
\(483\) 0.370459 0.0168565
\(484\) 0 0
\(485\) −7.28158 −0.330640
\(486\) 0 0
\(487\) 0.00256256 0.000116121 0 5.80603e−5 1.00000i \(-0.499982\pi\)
5.80603e−5 1.00000i \(0.499982\pi\)
\(488\) 0 0
\(489\) 17.6879 0.799876
\(490\) 0 0
\(491\) −0.220395 −0.00994629 −0.00497315 0.999988i \(-0.501583\pi\)
−0.00497315 + 0.999988i \(0.501583\pi\)
\(492\) 0 0
\(493\) −13.0581 −0.588108
\(494\) 0 0
\(495\) 2.52948 0.113692
\(496\) 0 0
\(497\) −0.873739 −0.0391926
\(498\) 0 0
\(499\) −0.0784875 −0.00351358 −0.00175679 0.999998i \(-0.500559\pi\)
−0.00175679 + 0.999998i \(0.500559\pi\)
\(500\) 0 0
\(501\) 6.23694 0.278646
\(502\) 0 0
\(503\) 18.5231 0.825903 0.412951 0.910753i \(-0.364498\pi\)
0.412951 + 0.910753i \(0.364498\pi\)
\(504\) 0 0
\(505\) 5.69269 0.253322
\(506\) 0 0
\(507\) −1.90229 −0.0844836
\(508\) 0 0
\(509\) 30.7175 1.36153 0.680765 0.732502i \(-0.261648\pi\)
0.680765 + 0.732502i \(0.261648\pi\)
\(510\) 0 0
\(511\) −2.14309 −0.0948049
\(512\) 0 0
\(513\) 7.01222 0.309597
\(514\) 0 0
\(515\) −15.5449 −0.684991
\(516\) 0 0
\(517\) 13.7614 0.605226
\(518\) 0 0
\(519\) 10.0057 0.439201
\(520\) 0 0
\(521\) 14.9739 0.656017 0.328009 0.944675i \(-0.393622\pi\)
0.328009 + 0.944675i \(0.393622\pi\)
\(522\) 0 0
\(523\) 41.2942 1.80567 0.902834 0.429990i \(-0.141483\pi\)
0.902834 + 0.429990i \(0.141483\pi\)
\(524\) 0 0
\(525\) −0.212435 −0.00927140
\(526\) 0 0
\(527\) 17.4682 0.760927
\(528\) 0 0
\(529\) −19.9589 −0.867778
\(530\) 0 0
\(531\) −7.97332 −0.346013
\(532\) 0 0
\(533\) −14.2147 −0.615706
\(534\) 0 0
\(535\) −5.04456 −0.218095
\(536\) 0 0
\(537\) −3.75325 −0.161964
\(538\) 0 0
\(539\) 17.5922 0.757750
\(540\) 0 0
\(541\) −5.13542 −0.220789 −0.110394 0.993888i \(-0.535211\pi\)
−0.110394 + 0.993888i \(0.535211\pi\)
\(542\) 0 0
\(543\) −1.67917 −0.0720600
\(544\) 0 0
\(545\) −12.4786 −0.534523
\(546\) 0 0
\(547\) 12.1938 0.521371 0.260686 0.965424i \(-0.416051\pi\)
0.260686 + 0.965424i \(0.416051\pi\)
\(548\) 0 0
\(549\) 8.27524 0.353179
\(550\) 0 0
\(551\) 11.8832 0.506243
\(552\) 0 0
\(553\) 1.42725 0.0606930
\(554\) 0 0
\(555\) −9.86329 −0.418673
\(556\) 0 0
\(557\) 24.0906 1.02075 0.510375 0.859952i \(-0.329506\pi\)
0.510375 + 0.859952i \(0.329506\pi\)
\(558\) 0 0
\(559\) 5.28830 0.223671
\(560\) 0 0
\(561\) 19.4909 0.822907
\(562\) 0 0
\(563\) −44.4180 −1.87199 −0.935997 0.352007i \(-0.885499\pi\)
−0.935997 + 0.352007i \(0.885499\pi\)
\(564\) 0 0
\(565\) −14.5800 −0.613384
\(566\) 0 0
\(567\) −0.212435 −0.00892141
\(568\) 0 0
\(569\) 34.6946 1.45447 0.727236 0.686387i \(-0.240805\pi\)
0.727236 + 0.686387i \(0.240805\pi\)
\(570\) 0 0
\(571\) 7.84002 0.328095 0.164047 0.986452i \(-0.447545\pi\)
0.164047 + 0.986452i \(0.447545\pi\)
\(572\) 0 0
\(573\) −12.2025 −0.509768
\(574\) 0 0
\(575\) −1.74388 −0.0727247
\(576\) 0 0
\(577\) 26.7169 1.11224 0.556119 0.831103i \(-0.312290\pi\)
0.556119 + 0.831103i \(0.312290\pi\)
\(578\) 0 0
\(579\) −3.73803 −0.155347
\(580\) 0 0
\(581\) −1.29098 −0.0535590
\(582\) 0 0
\(583\) −17.4813 −0.724003
\(584\) 0 0
\(585\) 3.33132 0.137733
\(586\) 0 0
\(587\) −40.0388 −1.65258 −0.826289 0.563246i \(-0.809552\pi\)
−0.826289 + 0.563246i \(0.809552\pi\)
\(588\) 0 0
\(589\) −15.8965 −0.655006
\(590\) 0 0
\(591\) 14.8662 0.611515
\(592\) 0 0
\(593\) −13.1721 −0.540914 −0.270457 0.962732i \(-0.587175\pi\)
−0.270457 + 0.962732i \(0.587175\pi\)
\(594\) 0 0
\(595\) −1.63691 −0.0671070
\(596\) 0 0
\(597\) 19.6990 0.806226
\(598\) 0 0
\(599\) 13.3011 0.543467 0.271734 0.962373i \(-0.412403\pi\)
0.271734 + 0.962373i \(0.412403\pi\)
\(600\) 0 0
\(601\) 45.1751 1.84273 0.921366 0.388696i \(-0.127074\pi\)
0.921366 + 0.388696i \(0.127074\pi\)
\(602\) 0 0
\(603\) 1.00000 0.0407231
\(604\) 0 0
\(605\) 4.60173 0.187087
\(606\) 0 0
\(607\) 29.1545 1.18334 0.591672 0.806179i \(-0.298468\pi\)
0.591672 + 0.806179i \(0.298468\pi\)
\(608\) 0 0
\(609\) −0.360002 −0.0145880
\(610\) 0 0
\(611\) 18.1238 0.733209
\(612\) 0 0
\(613\) −22.2457 −0.898495 −0.449247 0.893407i \(-0.648308\pi\)
−0.449247 + 0.893407i \(0.648308\pi\)
\(614\) 0 0
\(615\) −4.26698 −0.172061
\(616\) 0 0
\(617\) −3.64339 −0.146677 −0.0733387 0.997307i \(-0.523365\pi\)
−0.0733387 + 0.997307i \(0.523365\pi\)
\(618\) 0 0
\(619\) 42.5751 1.71124 0.855619 0.517606i \(-0.173177\pi\)
0.855619 + 0.517606i \(0.173177\pi\)
\(620\) 0 0
\(621\) −1.74388 −0.0699793
\(622\) 0 0
\(623\) 3.34395 0.133973
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −17.7373 −0.708358
\(628\) 0 0
\(629\) −76.0016 −3.03038
\(630\) 0 0
\(631\) −0.367702 −0.0146380 −0.00731898 0.999973i \(-0.502330\pi\)
−0.00731898 + 0.999973i \(0.502330\pi\)
\(632\) 0 0
\(633\) −12.1149 −0.481525
\(634\) 0 0
\(635\) 12.9783 0.515027
\(636\) 0 0
\(637\) 23.1689 0.917986
\(638\) 0 0
\(639\) 4.11298 0.162707
\(640\) 0 0
\(641\) −25.6375 −1.01262 −0.506311 0.862351i \(-0.668991\pi\)
−0.506311 + 0.862351i \(0.668991\pi\)
\(642\) 0 0
\(643\) 32.7395 1.29112 0.645560 0.763710i \(-0.276624\pi\)
0.645560 + 0.763710i \(0.276624\pi\)
\(644\) 0 0
\(645\) 1.58745 0.0625057
\(646\) 0 0
\(647\) 29.6166 1.16435 0.582174 0.813064i \(-0.302202\pi\)
0.582174 + 0.813064i \(0.302202\pi\)
\(648\) 0 0
\(649\) 20.1684 0.791677
\(650\) 0 0
\(651\) 0.481584 0.0188748
\(652\) 0 0
\(653\) −31.9237 −1.24927 −0.624636 0.780916i \(-0.714752\pi\)
−0.624636 + 0.780916i \(0.714752\pi\)
\(654\) 0 0
\(655\) −22.1129 −0.864023
\(656\) 0 0
\(657\) 10.0883 0.393580
\(658\) 0 0
\(659\) 36.5538 1.42394 0.711968 0.702212i \(-0.247804\pi\)
0.711968 + 0.702212i \(0.247804\pi\)
\(660\) 0 0
\(661\) 8.58271 0.333829 0.166914 0.985971i \(-0.446620\pi\)
0.166914 + 0.985971i \(0.446620\pi\)
\(662\) 0 0
\(663\) 25.6695 0.996921
\(664\) 0 0
\(665\) 1.48964 0.0577656
\(666\) 0 0
\(667\) −2.95526 −0.114428
\(668\) 0 0
\(669\) 16.7125 0.646143
\(670\) 0 0
\(671\) −20.9321 −0.808073
\(672\) 0 0
\(673\) −24.7150 −0.952693 −0.476347 0.879258i \(-0.658039\pi\)
−0.476347 + 0.879258i \(0.658039\pi\)
\(674\) 0 0
\(675\) 1.00000 0.0384900
\(676\) 0 0
\(677\) 2.85042 0.109550 0.0547752 0.998499i \(-0.482556\pi\)
0.0547752 + 0.998499i \(0.482556\pi\)
\(678\) 0 0
\(679\) −1.54686 −0.0593630
\(680\) 0 0
\(681\) −12.8830 −0.493676
\(682\) 0 0
\(683\) −13.7574 −0.526411 −0.263206 0.964740i \(-0.584780\pi\)
−0.263206 + 0.964740i \(0.584780\pi\)
\(684\) 0 0
\(685\) −11.9140 −0.455210
\(686\) 0 0
\(687\) −19.3688 −0.738965
\(688\) 0 0
\(689\) −23.0229 −0.877102
\(690\) 0 0
\(691\) −23.1176 −0.879436 −0.439718 0.898136i \(-0.644922\pi\)
−0.439718 + 0.898136i \(0.644922\pi\)
\(692\) 0 0
\(693\) 0.537349 0.0204122
\(694\) 0 0
\(695\) −9.97144 −0.378238
\(696\) 0 0
\(697\) −32.8792 −1.24539
\(698\) 0 0
\(699\) 17.3340 0.655631
\(700\) 0 0
\(701\) −15.6124 −0.589671 −0.294836 0.955548i \(-0.595265\pi\)
−0.294836 + 0.955548i \(0.595265\pi\)
\(702\) 0 0
\(703\) 69.1635 2.60855
\(704\) 0 0
\(705\) 5.44041 0.204898
\(706\) 0 0
\(707\) 1.20933 0.0454813
\(708\) 0 0
\(709\) −21.6799 −0.814205 −0.407102 0.913383i \(-0.633461\pi\)
−0.407102 + 0.913383i \(0.633461\pi\)
\(710\) 0 0
\(711\) −6.71856 −0.251966
\(712\) 0 0
\(713\) 3.95333 0.148053
\(714\) 0 0
\(715\) −8.42651 −0.315134
\(716\) 0 0
\(717\) 14.5029 0.541621
\(718\) 0 0
\(719\) −33.9102 −1.26464 −0.632318 0.774709i \(-0.717897\pi\)
−0.632318 + 0.774709i \(0.717897\pi\)
\(720\) 0 0
\(721\) −3.30228 −0.122983
\(722\) 0 0
\(723\) −29.9192 −1.11271
\(724\) 0 0
\(725\) 1.69465 0.0629377
\(726\) 0 0
\(727\) 47.0138 1.74364 0.871822 0.489823i \(-0.162938\pi\)
0.871822 + 0.489823i \(0.162938\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 12.2321 0.452420
\(732\) 0 0
\(733\) 40.6811 1.50259 0.751295 0.659966i \(-0.229429\pi\)
0.751295 + 0.659966i \(0.229429\pi\)
\(734\) 0 0
\(735\) 6.95487 0.256534
\(736\) 0 0
\(737\) −2.52948 −0.0931746
\(738\) 0 0
\(739\) 18.7355 0.689198 0.344599 0.938750i \(-0.388015\pi\)
0.344599 + 0.938750i \(0.388015\pi\)
\(740\) 0 0
\(741\) −23.3600 −0.858149
\(742\) 0 0
\(743\) −39.8737 −1.46282 −0.731412 0.681936i \(-0.761138\pi\)
−0.731412 + 0.681936i \(0.761138\pi\)
\(744\) 0 0
\(745\) 19.1380 0.701164
\(746\) 0 0
\(747\) 6.07709 0.222349
\(748\) 0 0
\(749\) −1.07164 −0.0391568
\(750\) 0 0
\(751\) 45.3132 1.65350 0.826751 0.562567i \(-0.190186\pi\)
0.826751 + 0.562567i \(0.190186\pi\)
\(752\) 0 0
\(753\) −19.3907 −0.706638
\(754\) 0 0
\(755\) −6.08188 −0.221342
\(756\) 0 0
\(757\) −46.4498 −1.68825 −0.844123 0.536150i \(-0.819878\pi\)
−0.844123 + 0.536150i \(0.819878\pi\)
\(758\) 0 0
\(759\) 4.41110 0.160113
\(760\) 0 0
\(761\) −19.7862 −0.717248 −0.358624 0.933482i \(-0.616754\pi\)
−0.358624 + 0.933482i \(0.616754\pi\)
\(762\) 0 0
\(763\) −2.65088 −0.0959683
\(764\) 0 0
\(765\) 7.70550 0.278593
\(766\) 0 0
\(767\) 26.5617 0.959088
\(768\) 0 0
\(769\) −26.6491 −0.960990 −0.480495 0.876997i \(-0.659543\pi\)
−0.480495 + 0.876997i \(0.659543\pi\)
\(770\) 0 0
\(771\) −20.2810 −0.730403
\(772\) 0 0
\(773\) −9.66514 −0.347631 −0.173815 0.984778i \(-0.555610\pi\)
−0.173815 + 0.984778i \(0.555610\pi\)
\(774\) 0 0
\(775\) −2.26698 −0.0814323
\(776\) 0 0
\(777\) −2.09530 −0.0751686
\(778\) 0 0
\(779\) 29.9210 1.07203
\(780\) 0 0
\(781\) −10.4037 −0.372274
\(782\) 0 0
\(783\) 1.69465 0.0605618
\(784\) 0 0
\(785\) −24.5267 −0.875396
\(786\) 0 0
\(787\) −18.4042 −0.656038 −0.328019 0.944671i \(-0.606381\pi\)
−0.328019 + 0.944671i \(0.606381\pi\)
\(788\) 0 0
\(789\) 22.1346 0.788013
\(790\) 0 0
\(791\) −3.09729 −0.110127
\(792\) 0 0
\(793\) −27.5675 −0.978951
\(794\) 0 0
\(795\) −6.91104 −0.245109
\(796\) 0 0
\(797\) −27.2176 −0.964097 −0.482048 0.876145i \(-0.660107\pi\)
−0.482048 + 0.876145i \(0.660107\pi\)
\(798\) 0 0
\(799\) 41.9211 1.48306
\(800\) 0 0
\(801\) −15.7411 −0.556184
\(802\) 0 0
\(803\) −25.5180 −0.900512
\(804\) 0 0
\(805\) −0.370459 −0.0130570
\(806\) 0 0
\(807\) 18.6744 0.657370
\(808\) 0 0
\(809\) 6.61720 0.232649 0.116324 0.993211i \(-0.462889\pi\)
0.116324 + 0.993211i \(0.462889\pi\)
\(810\) 0 0
\(811\) −8.00432 −0.281070 −0.140535 0.990076i \(-0.544882\pi\)
−0.140535 + 0.990076i \(0.544882\pi\)
\(812\) 0 0
\(813\) 1.49646 0.0524832
\(814\) 0 0
\(815\) −17.6879 −0.619581
\(816\) 0 0
\(817\) −11.1315 −0.389443
\(818\) 0 0
\(819\) 0.707688 0.0247286
\(820\) 0 0
\(821\) 6.23807 0.217710 0.108855 0.994058i \(-0.465282\pi\)
0.108855 + 0.994058i \(0.465282\pi\)
\(822\) 0 0
\(823\) 52.7005 1.83702 0.918512 0.395394i \(-0.129392\pi\)
0.918512 + 0.395394i \(0.129392\pi\)
\(824\) 0 0
\(825\) −2.52948 −0.0880652
\(826\) 0 0
\(827\) −49.9701 −1.73763 −0.868816 0.495135i \(-0.835118\pi\)
−0.868816 + 0.495135i \(0.835118\pi\)
\(828\) 0 0
\(829\) −55.9098 −1.94183 −0.970914 0.239427i \(-0.923041\pi\)
−0.970914 + 0.239427i \(0.923041\pi\)
\(830\) 0 0
\(831\) −23.2529 −0.806633
\(832\) 0 0
\(833\) 53.5908 1.85681
\(834\) 0 0
\(835\) −6.23694 −0.215838
\(836\) 0 0
\(837\) −2.26698 −0.0783582
\(838\) 0 0
\(839\) −22.8083 −0.787428 −0.393714 0.919233i \(-0.628810\pi\)
−0.393714 + 0.919233i \(0.628810\pi\)
\(840\) 0 0
\(841\) −26.1282 −0.900971
\(842\) 0 0
\(843\) −7.66461 −0.263983
\(844\) 0 0
\(845\) 1.90229 0.0654407
\(846\) 0 0
\(847\) 0.977567 0.0335896
\(848\) 0 0
\(849\) −23.6825 −0.812780
\(850\) 0 0
\(851\) −17.2003 −0.589620
\(852\) 0 0
\(853\) 8.14727 0.278957 0.139479 0.990225i \(-0.455457\pi\)
0.139479 + 0.990225i \(0.455457\pi\)
\(854\) 0 0
\(855\) −7.01222 −0.239813
\(856\) 0 0
\(857\) −43.0389 −1.47018 −0.735091 0.677968i \(-0.762861\pi\)
−0.735091 + 0.677968i \(0.762861\pi\)
\(858\) 0 0
\(859\) 44.2750 1.51064 0.755322 0.655354i \(-0.227480\pi\)
0.755322 + 0.655354i \(0.227480\pi\)
\(860\) 0 0
\(861\) −0.906454 −0.0308919
\(862\) 0 0
\(863\) 3.63083 0.123595 0.0617974 0.998089i \(-0.480317\pi\)
0.0617974 + 0.998089i \(0.480317\pi\)
\(864\) 0 0
\(865\) −10.0057 −0.340204
\(866\) 0 0
\(867\) 42.3748 1.43912
\(868\) 0 0
\(869\) 16.9945 0.576498
\(870\) 0 0
\(871\) −3.33132 −0.112878
\(872\) 0 0
\(873\) 7.28158 0.246444
\(874\) 0 0
\(875\) 0.212435 0.00718160
\(876\) 0 0
\(877\) −50.7268 −1.71292 −0.856461 0.516212i \(-0.827341\pi\)
−0.856461 + 0.516212i \(0.827341\pi\)
\(878\) 0 0
\(879\) −9.94969 −0.335595
\(880\) 0 0
\(881\) −30.5139 −1.02804 −0.514019 0.857779i \(-0.671844\pi\)
−0.514019 + 0.857779i \(0.671844\pi\)
\(882\) 0 0
\(883\) −1.88298 −0.0633674 −0.0316837 0.999498i \(-0.510087\pi\)
−0.0316837 + 0.999498i \(0.510087\pi\)
\(884\) 0 0
\(885\) 7.97332 0.268020
\(886\) 0 0
\(887\) 41.0893 1.37964 0.689822 0.723979i \(-0.257689\pi\)
0.689822 + 0.723979i \(0.257689\pi\)
\(888\) 0 0
\(889\) 2.75703 0.0924679
\(890\) 0 0
\(891\) −2.52948 −0.0847408
\(892\) 0 0
\(893\) −38.1493 −1.27662
\(894\) 0 0
\(895\) 3.75325 0.125457
\(896\) 0 0
\(897\) 5.80941 0.193971
\(898\) 0 0
\(899\) −3.84173 −0.128129
\(900\) 0 0
\(901\) −53.2530 −1.77412
\(902\) 0 0
\(903\) 0.337229 0.0112223
\(904\) 0 0
\(905\) 1.67917 0.0558174
\(906\) 0 0
\(907\) 39.8574 1.32344 0.661721 0.749750i \(-0.269826\pi\)
0.661721 + 0.749750i \(0.269826\pi\)
\(908\) 0 0
\(909\) −5.69269 −0.188815
\(910\) 0 0
\(911\) −34.2419 −1.13449 −0.567243 0.823551i \(-0.691990\pi\)
−0.567243 + 0.823551i \(0.691990\pi\)
\(912\) 0 0
\(913\) −15.3719 −0.508735
\(914\) 0 0
\(915\) −8.27524 −0.273571
\(916\) 0 0
\(917\) −4.69754 −0.155127
\(918\) 0 0
\(919\) −20.0814 −0.662425 −0.331212 0.943556i \(-0.607458\pi\)
−0.331212 + 0.943556i \(0.607458\pi\)
\(920\) 0 0
\(921\) 0.901961 0.0297206
\(922\) 0 0
\(923\) −13.7017 −0.450996
\(924\) 0 0
\(925\) 9.86329 0.324303
\(926\) 0 0
\(927\) 15.5449 0.510562
\(928\) 0 0
\(929\) 5.81521 0.190791 0.0953955 0.995439i \(-0.469588\pi\)
0.0953955 + 0.995439i \(0.469588\pi\)
\(930\) 0 0
\(931\) −48.7691 −1.59834
\(932\) 0 0
\(933\) 30.1842 0.988187
\(934\) 0 0
\(935\) −19.4909 −0.637421
\(936\) 0 0
\(937\) 20.1697 0.658914 0.329457 0.944171i \(-0.393134\pi\)
0.329457 + 0.944171i \(0.393134\pi\)
\(938\) 0 0
\(939\) −30.1003 −0.982286
\(940\) 0 0
\(941\) 55.8940 1.82209 0.911046 0.412304i \(-0.135276\pi\)
0.911046 + 0.412304i \(0.135276\pi\)
\(942\) 0 0
\(943\) −7.44108 −0.242315
\(944\) 0 0
\(945\) 0.212435 0.00691050
\(946\) 0 0
\(947\) 48.9753 1.59148 0.795742 0.605636i \(-0.207081\pi\)
0.795742 + 0.605636i \(0.207081\pi\)
\(948\) 0 0
\(949\) −33.6072 −1.09094
\(950\) 0 0
\(951\) 18.3980 0.596598
\(952\) 0 0
\(953\) −7.58428 −0.245679 −0.122839 0.992427i \(-0.539200\pi\)
−0.122839 + 0.992427i \(0.539200\pi\)
\(954\) 0 0
\(955\) 12.2025 0.394864
\(956\) 0 0
\(957\) −4.28658 −0.138565
\(958\) 0 0
\(959\) −2.53094 −0.0817284
\(960\) 0 0
\(961\) −25.8608 −0.834220
\(962\) 0 0
\(963\) 5.04456 0.162559
\(964\) 0 0
\(965\) 3.73803 0.120331
\(966\) 0 0
\(967\) −42.5001 −1.36671 −0.683355 0.730086i \(-0.739480\pi\)
−0.683355 + 0.730086i \(0.739480\pi\)
\(968\) 0 0
\(969\) −54.0327 −1.73578
\(970\) 0 0
\(971\) −40.8770 −1.31180 −0.655902 0.754846i \(-0.727712\pi\)
−0.655902 + 0.754846i \(0.727712\pi\)
\(972\) 0 0
\(973\) −2.11828 −0.0679089
\(974\) 0 0
\(975\) −3.33132 −0.106688
\(976\) 0 0
\(977\) 27.5634 0.881830 0.440915 0.897549i \(-0.354654\pi\)
0.440915 + 0.897549i \(0.354654\pi\)
\(978\) 0 0
\(979\) 39.8168 1.27255
\(980\) 0 0
\(981\) 12.4786 0.398410
\(982\) 0 0
\(983\) 21.7873 0.694906 0.347453 0.937697i \(-0.387047\pi\)
0.347453 + 0.937697i \(0.387047\pi\)
\(984\) 0 0
\(985\) −14.8662 −0.473678
\(986\) 0 0
\(987\) 1.15573 0.0367873
\(988\) 0 0
\(989\) 2.76831 0.0880271
\(990\) 0 0
\(991\) −50.4050 −1.60117 −0.800583 0.599222i \(-0.795477\pi\)
−0.800583 + 0.599222i \(0.795477\pi\)
\(992\) 0 0
\(993\) −21.1271 −0.670447
\(994\) 0 0
\(995\) −19.6990 −0.624500
\(996\) 0 0
\(997\) 5.37551 0.170244 0.0851221 0.996371i \(-0.472872\pi\)
0.0851221 + 0.996371i \(0.472872\pi\)
\(998\) 0 0
\(999\) 9.86329 0.312061
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 \(a_p\))