Properties

Label 8024.2.a.y.1.18
Level 8024
Weight 2
Character 8024.1
Self dual Yes
Analytic conductor 64.072
Analytic rank 1
Dimension 23
CM No

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 8024.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.45598 q^{3} -0.727716 q^{5} +2.11595 q^{7} -0.880108 q^{9} +O(q^{10})\) \(q+1.45598 q^{3} -0.727716 q^{5} +2.11595 q^{7} -0.880108 q^{9} -2.82435 q^{11} +3.00198 q^{13} -1.05954 q^{15} -1.00000 q^{17} -1.63891 q^{19} +3.08079 q^{21} +6.69131 q^{23} -4.47043 q^{25} -5.64938 q^{27} -3.98396 q^{29} -6.44757 q^{31} -4.11222 q^{33} -1.53981 q^{35} +1.41132 q^{37} +4.37084 q^{39} -4.60384 q^{41} +4.91188 q^{43} +0.640469 q^{45} -1.35093 q^{47} -2.52275 q^{49} -1.45598 q^{51} +8.50181 q^{53} +2.05533 q^{55} -2.38623 q^{57} -1.00000 q^{59} +0.0785127 q^{61} -1.86227 q^{63} -2.18459 q^{65} -11.7866 q^{67} +9.74245 q^{69} +3.96861 q^{71} -9.33595 q^{73} -6.50888 q^{75} -5.97620 q^{77} -5.60545 q^{79} -5.58509 q^{81} -9.36973 q^{83} +0.727716 q^{85} -5.80059 q^{87} -14.7511 q^{89} +6.35205 q^{91} -9.38756 q^{93} +1.19266 q^{95} +1.70721 q^{97} +2.48574 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23q - 6q^{3} - q^{7} + 23q^{9} + O(q^{10}) \) \( 23q - 6q^{3} - q^{7} + 23q^{9} - 3q^{11} - 7q^{13} - 2q^{15} - 23q^{17} - 16q^{19} - 11q^{21} - 29q^{23} + 31q^{25} - 3q^{27} - 5q^{29} - 41q^{31} + 8q^{33} - 22q^{35} + 5q^{37} + 16q^{39} + 11q^{41} + 13q^{43} - 26q^{45} - 39q^{47} + 16q^{49} + 6q^{51} - 2q^{53} - 35q^{55} + 13q^{57} - 23q^{59} - 37q^{61} + 33q^{65} - 34q^{67} - 66q^{69} - 13q^{71} - 14q^{73} - 81q^{75} - 4q^{77} - 61q^{79} - q^{81} - 9q^{83} - 16q^{87} + 28q^{89} - 18q^{91} - 62q^{93} - 33q^{95} - 5q^{99} + O(q^{100}) \)

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
\(3\) 1.45598 0.840613 0.420307 0.907382i \(-0.361923\pi\)
0.420307 + 0.907382i \(0.361923\pi\)
\(4\) 0 0
\(5\) −0.727716 −0.325445 −0.162722 0.986672i \(-0.552027\pi\)
−0.162722 + 0.986672i \(0.552027\pi\)
\(6\) 0 0
\(7\) 2.11595 0.799755 0.399877 0.916569i \(-0.369053\pi\)
0.399877 + 0.916569i \(0.369053\pi\)
\(8\) 0 0
\(9\) −0.880108 −0.293369
\(10\) 0 0
\(11\) −2.82435 −0.851575 −0.425787 0.904823i \(-0.640003\pi\)
−0.425787 + 0.904823i \(0.640003\pi\)
\(12\) 0 0
\(13\) 3.00198 0.832600 0.416300 0.909227i \(-0.363327\pi\)
0.416300 + 0.909227i \(0.363327\pi\)
\(14\) 0 0
\(15\) −1.05954 −0.273573
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) −1.63891 −0.375992 −0.187996 0.982170i \(-0.560199\pi\)
−0.187996 + 0.982170i \(0.560199\pi\)
\(20\) 0 0
\(21\) 3.08079 0.672284
\(22\) 0 0
\(23\) 6.69131 1.39524 0.697618 0.716470i \(-0.254243\pi\)
0.697618 + 0.716470i \(0.254243\pi\)
\(24\) 0 0
\(25\) −4.47043 −0.894086
\(26\) 0 0
\(27\) −5.64938 −1.08722
\(28\) 0 0
\(29\) −3.98396 −0.739803 −0.369902 0.929071i \(-0.620609\pi\)
−0.369902 + 0.929071i \(0.620609\pi\)
\(30\) 0 0
\(31\) −6.44757 −1.15802 −0.579009 0.815321i \(-0.696560\pi\)
−0.579009 + 0.815321i \(0.696560\pi\)
\(32\) 0 0
\(33\) −4.11222 −0.715845
\(34\) 0 0
\(35\) −1.53981 −0.260276
\(36\) 0 0
\(37\) 1.41132 0.232019 0.116009 0.993248i \(-0.462990\pi\)
0.116009 + 0.993248i \(0.462990\pi\)
\(38\) 0 0
\(39\) 4.37084 0.699894
\(40\) 0 0
\(41\) −4.60384 −0.718998 −0.359499 0.933145i \(-0.617052\pi\)
−0.359499 + 0.933145i \(0.617052\pi\)
\(42\) 0 0
\(43\) 4.91188 0.749055 0.374527 0.927216i \(-0.377805\pi\)
0.374527 + 0.927216i \(0.377805\pi\)
\(44\) 0 0
\(45\) 0.640469 0.0954755
\(46\) 0 0
\(47\) −1.35093 −0.197053 −0.0985264 0.995134i \(-0.531413\pi\)
−0.0985264 + 0.995134i \(0.531413\pi\)
\(48\) 0 0
\(49\) −2.52275 −0.360393
\(50\) 0 0
\(51\) −1.45598 −0.203879
\(52\) 0 0
\(53\) 8.50181 1.16781 0.583907 0.811821i \(-0.301523\pi\)
0.583907 + 0.811821i \(0.301523\pi\)
\(54\) 0 0
\(55\) 2.05533 0.277140
\(56\) 0 0
\(57\) −2.38623 −0.316064
\(58\) 0 0
\(59\) −1.00000 −0.130189
\(60\) 0 0
\(61\) 0.0785127 0.0100525 0.00502626 0.999987i \(-0.498400\pi\)
0.00502626 + 0.999987i \(0.498400\pi\)
\(62\) 0 0
\(63\) −1.86227 −0.234623
\(64\) 0 0
\(65\) −2.18459 −0.270965
\(66\) 0 0
\(67\) −11.7866 −1.43996 −0.719982 0.693993i \(-0.755850\pi\)
−0.719982 + 0.693993i \(0.755850\pi\)
\(68\) 0 0
\(69\) 9.74245 1.17285
\(70\) 0 0
\(71\) 3.96861 0.470987 0.235494 0.971876i \(-0.424329\pi\)
0.235494 + 0.971876i \(0.424329\pi\)
\(72\) 0 0
\(73\) −9.33595 −1.09269 −0.546345 0.837560i \(-0.683981\pi\)
−0.546345 + 0.837560i \(0.683981\pi\)
\(74\) 0 0
\(75\) −6.50888 −0.751580
\(76\) 0 0
\(77\) −5.97620 −0.681051
\(78\) 0 0
\(79\) −5.60545 −0.630662 −0.315331 0.948982i \(-0.602116\pi\)
−0.315331 + 0.948982i \(0.602116\pi\)
\(80\) 0 0
\(81\) −5.58509 −0.620565
\(82\) 0 0
\(83\) −9.36973 −1.02846 −0.514231 0.857652i \(-0.671923\pi\)
−0.514231 + 0.857652i \(0.671923\pi\)
\(84\) 0 0
\(85\) 0.727716 0.0789319
\(86\) 0 0
\(87\) −5.80059 −0.621888
\(88\) 0 0
\(89\) −14.7511 −1.56361 −0.781804 0.623524i \(-0.785701\pi\)
−0.781804 + 0.623524i \(0.785701\pi\)
\(90\) 0 0
\(91\) 6.35205 0.665875
\(92\) 0 0
\(93\) −9.38756 −0.973445
\(94\) 0 0
\(95\) 1.19266 0.122364
\(96\) 0 0
\(97\) 1.70721 0.173341 0.0866705 0.996237i \(-0.472377\pi\)
0.0866705 + 0.996237i \(0.472377\pi\)
\(98\) 0 0
\(99\) 2.48574 0.249826
\(100\) 0 0
\(101\) 9.61708 0.956935 0.478468 0.878105i \(-0.341192\pi\)
0.478468 + 0.878105i \(0.341192\pi\)
\(102\) 0 0
\(103\) 3.67124 0.361738 0.180869 0.983507i \(-0.442109\pi\)
0.180869 + 0.983507i \(0.442109\pi\)
\(104\) 0 0
\(105\) −2.24194 −0.218791
\(106\) 0 0
\(107\) 9.64548 0.932464 0.466232 0.884662i \(-0.345611\pi\)
0.466232 + 0.884662i \(0.345611\pi\)
\(108\) 0 0
\(109\) −1.56056 −0.149475 −0.0747373 0.997203i \(-0.523812\pi\)
−0.0747373 + 0.997203i \(0.523812\pi\)
\(110\) 0 0
\(111\) 2.05485 0.195038
\(112\) 0 0
\(113\) −2.15275 −0.202514 −0.101257 0.994860i \(-0.532286\pi\)
−0.101257 + 0.994860i \(0.532286\pi\)
\(114\) 0 0
\(115\) −4.86938 −0.454072
\(116\) 0 0
\(117\) −2.64207 −0.244259
\(118\) 0 0
\(119\) −2.11595 −0.193969
\(120\) 0 0
\(121\) −3.02302 −0.274820
\(122\) 0 0
\(123\) −6.70312 −0.604400
\(124\) 0 0
\(125\) 6.89179 0.616420
\(126\) 0 0
\(127\) −5.62202 −0.498874 −0.249437 0.968391i \(-0.580245\pi\)
−0.249437 + 0.968391i \(0.580245\pi\)
\(128\) 0 0
\(129\) 7.15162 0.629665
\(130\) 0 0
\(131\) −8.61067 −0.752317 −0.376159 0.926555i \(-0.622755\pi\)
−0.376159 + 0.926555i \(0.622755\pi\)
\(132\) 0 0
\(133\) −3.46785 −0.300701
\(134\) 0 0
\(135\) 4.11115 0.353831
\(136\) 0 0
\(137\) 12.2448 1.04615 0.523073 0.852288i \(-0.324786\pi\)
0.523073 + 0.852288i \(0.324786\pi\)
\(138\) 0 0
\(139\) −8.12203 −0.688902 −0.344451 0.938804i \(-0.611935\pi\)
−0.344451 + 0.938804i \(0.611935\pi\)
\(140\) 0 0
\(141\) −1.96693 −0.165645
\(142\) 0 0
\(143\) −8.47866 −0.709021
\(144\) 0 0
\(145\) 2.89919 0.240765
\(146\) 0 0
\(147\) −3.67308 −0.302951
\(148\) 0 0
\(149\) −2.53604 −0.207761 −0.103880 0.994590i \(-0.533126\pi\)
−0.103880 + 0.994590i \(0.533126\pi\)
\(150\) 0 0
\(151\) 20.6674 1.68189 0.840946 0.541118i \(-0.181999\pi\)
0.840946 + 0.541118i \(0.181999\pi\)
\(152\) 0 0
\(153\) 0.880108 0.0711525
\(154\) 0 0
\(155\) 4.69200 0.376870
\(156\) 0 0
\(157\) −9.08435 −0.725010 −0.362505 0.931982i \(-0.618078\pi\)
−0.362505 + 0.931982i \(0.618078\pi\)
\(158\) 0 0
\(159\) 12.3785 0.981680
\(160\) 0 0
\(161\) 14.1585 1.11585
\(162\) 0 0
\(163\) 15.6995 1.22968 0.614840 0.788652i \(-0.289220\pi\)
0.614840 + 0.788652i \(0.289220\pi\)
\(164\) 0 0
\(165\) 2.99253 0.232968
\(166\) 0 0
\(167\) 0.0353012 0.00273169 0.00136584 0.999999i \(-0.499565\pi\)
0.00136584 + 0.999999i \(0.499565\pi\)
\(168\) 0 0
\(169\) −3.98811 −0.306778
\(170\) 0 0
\(171\) 1.44242 0.110304
\(172\) 0 0
\(173\) −21.0068 −1.59712 −0.798558 0.601917i \(-0.794404\pi\)
−0.798558 + 0.601917i \(0.794404\pi\)
\(174\) 0 0
\(175\) −9.45921 −0.715049
\(176\) 0 0
\(177\) −1.45598 −0.109439
\(178\) 0 0
\(179\) −11.4148 −0.853180 −0.426590 0.904445i \(-0.640285\pi\)
−0.426590 + 0.904445i \(0.640285\pi\)
\(180\) 0 0
\(181\) −13.3641 −0.993349 −0.496674 0.867937i \(-0.665446\pi\)
−0.496674 + 0.867937i \(0.665446\pi\)
\(182\) 0 0
\(183\) 0.114313 0.00845028
\(184\) 0 0
\(185\) −1.02704 −0.0755093
\(186\) 0 0
\(187\) 2.82435 0.206537
\(188\) 0 0
\(189\) −11.9538 −0.869512
\(190\) 0 0
\(191\) −5.59970 −0.405180 −0.202590 0.979264i \(-0.564936\pi\)
−0.202590 + 0.979264i \(0.564936\pi\)
\(192\) 0 0
\(193\) −12.6169 −0.908185 −0.454093 0.890955i \(-0.650036\pi\)
−0.454093 + 0.890955i \(0.650036\pi\)
\(194\) 0 0
\(195\) −3.18073 −0.227777
\(196\) 0 0
\(197\) 25.4130 1.81060 0.905302 0.424769i \(-0.139645\pi\)
0.905302 + 0.424769i \(0.139645\pi\)
\(198\) 0 0
\(199\) 0.631072 0.0447355 0.0223678 0.999750i \(-0.492880\pi\)
0.0223678 + 0.999750i \(0.492880\pi\)
\(200\) 0 0
\(201\) −17.1611 −1.21045
\(202\) 0 0
\(203\) −8.42987 −0.591661
\(204\) 0 0
\(205\) 3.35029 0.233994
\(206\) 0 0
\(207\) −5.88908 −0.409319
\(208\) 0 0
\(209\) 4.62886 0.320185
\(210\) 0 0
\(211\) −3.94770 −0.271771 −0.135885 0.990725i \(-0.543388\pi\)
−0.135885 + 0.990725i \(0.543388\pi\)
\(212\) 0 0
\(213\) 5.77824 0.395918
\(214\) 0 0
\(215\) −3.57446 −0.243776
\(216\) 0 0
\(217\) −13.6427 −0.926130
\(218\) 0 0
\(219\) −13.5930 −0.918530
\(220\) 0 0
\(221\) −3.00198 −0.201935
\(222\) 0 0
\(223\) 8.47780 0.567716 0.283858 0.958866i \(-0.408386\pi\)
0.283858 + 0.958866i \(0.408386\pi\)
\(224\) 0 0
\(225\) 3.93446 0.262297
\(226\) 0 0
\(227\) −0.522585 −0.0346852 −0.0173426 0.999850i \(-0.505521\pi\)
−0.0173426 + 0.999850i \(0.505521\pi\)
\(228\) 0 0
\(229\) −21.8923 −1.44668 −0.723341 0.690491i \(-0.757394\pi\)
−0.723341 + 0.690491i \(0.757394\pi\)
\(230\) 0 0
\(231\) −8.70125 −0.572500
\(232\) 0 0
\(233\) 8.68317 0.568853 0.284427 0.958698i \(-0.408197\pi\)
0.284427 + 0.958698i \(0.408197\pi\)
\(234\) 0 0
\(235\) 0.983090 0.0641298
\(236\) 0 0
\(237\) −8.16145 −0.530143
\(238\) 0 0
\(239\) −21.0339 −1.36057 −0.680286 0.732947i \(-0.738144\pi\)
−0.680286 + 0.732947i \(0.738144\pi\)
\(240\) 0 0
\(241\) −10.4530 −0.673339 −0.336670 0.941623i \(-0.609301\pi\)
−0.336670 + 0.941623i \(0.609301\pi\)
\(242\) 0 0
\(243\) 8.81633 0.565568
\(244\) 0 0
\(245\) 1.83585 0.117288
\(246\) 0 0
\(247\) −4.91997 −0.313050
\(248\) 0 0
\(249\) −13.6422 −0.864539
\(250\) 0 0
\(251\) 9.75276 0.615589 0.307794 0.951453i \(-0.400409\pi\)
0.307794 + 0.951453i \(0.400409\pi\)
\(252\) 0 0
\(253\) −18.8986 −1.18815
\(254\) 0 0
\(255\) 1.05954 0.0663512
\(256\) 0 0
\(257\) −26.1570 −1.63163 −0.815815 0.578312i \(-0.803711\pi\)
−0.815815 + 0.578312i \(0.803711\pi\)
\(258\) 0 0
\(259\) 2.98628 0.185558
\(260\) 0 0
\(261\) 3.50632 0.217036
\(262\) 0 0
\(263\) 19.0661 1.17567 0.587834 0.808981i \(-0.299981\pi\)
0.587834 + 0.808981i \(0.299981\pi\)
\(264\) 0 0
\(265\) −6.18691 −0.380059
\(266\) 0 0
\(267\) −21.4773 −1.31439
\(268\) 0 0
\(269\) −23.5799 −1.43769 −0.718846 0.695169i \(-0.755329\pi\)
−0.718846 + 0.695169i \(0.755329\pi\)
\(270\) 0 0
\(271\) 2.96411 0.180057 0.0900285 0.995939i \(-0.471304\pi\)
0.0900285 + 0.995939i \(0.471304\pi\)
\(272\) 0 0
\(273\) 9.24848 0.559744
\(274\) 0 0
\(275\) 12.6261 0.761381
\(276\) 0 0
\(277\) −25.0111 −1.50277 −0.751387 0.659862i \(-0.770615\pi\)
−0.751387 + 0.659862i \(0.770615\pi\)
\(278\) 0 0
\(279\) 5.67455 0.339727
\(280\) 0 0
\(281\) 26.0113 1.55170 0.775851 0.630917i \(-0.217321\pi\)
0.775851 + 0.630917i \(0.217321\pi\)
\(282\) 0 0
\(283\) −12.7923 −0.760423 −0.380212 0.924900i \(-0.624149\pi\)
−0.380212 + 0.924900i \(0.624149\pi\)
\(284\) 0 0
\(285\) 1.73650 0.102861
\(286\) 0 0
\(287\) −9.74149 −0.575022
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 2.48567 0.145713
\(292\) 0 0
\(293\) −16.7818 −0.980401 −0.490201 0.871610i \(-0.663077\pi\)
−0.490201 + 0.871610i \(0.663077\pi\)
\(294\) 0 0
\(295\) 0.727716 0.0423693
\(296\) 0 0
\(297\) 15.9558 0.925852
\(298\) 0 0
\(299\) 20.0872 1.16167
\(300\) 0 0
\(301\) 10.3933 0.599060
\(302\) 0 0
\(303\) 14.0023 0.804413
\(304\) 0 0
\(305\) −0.0571349 −0.00327154
\(306\) 0 0
\(307\) −15.7604 −0.899495 −0.449748 0.893156i \(-0.648486\pi\)
−0.449748 + 0.893156i \(0.648486\pi\)
\(308\) 0 0
\(309\) 5.34527 0.304082
\(310\) 0 0
\(311\) 27.7429 1.57316 0.786578 0.617491i \(-0.211851\pi\)
0.786578 + 0.617491i \(0.211851\pi\)
\(312\) 0 0
\(313\) 10.9822 0.620753 0.310376 0.950614i \(-0.399545\pi\)
0.310376 + 0.950614i \(0.399545\pi\)
\(314\) 0 0
\(315\) 1.35520 0.0763569
\(316\) 0 0
\(317\) 3.44135 0.193286 0.0966428 0.995319i \(-0.469190\pi\)
0.0966428 + 0.995319i \(0.469190\pi\)
\(318\) 0 0
\(319\) 11.2521 0.629998
\(320\) 0 0
\(321\) 14.0437 0.783842
\(322\) 0 0
\(323\) 1.63891 0.0911914
\(324\) 0 0
\(325\) −13.4201 −0.744416
\(326\) 0 0
\(327\) −2.27215 −0.125650
\(328\) 0 0
\(329\) −2.85849 −0.157594
\(330\) 0 0
\(331\) −14.0530 −0.772425 −0.386212 0.922410i \(-0.626217\pi\)
−0.386212 + 0.922410i \(0.626217\pi\)
\(332\) 0 0
\(333\) −1.24211 −0.0680672
\(334\) 0 0
\(335\) 8.57731 0.468629
\(336\) 0 0
\(337\) 35.8455 1.95263 0.976315 0.216354i \(-0.0694164\pi\)
0.976315 + 0.216354i \(0.0694164\pi\)
\(338\) 0 0
\(339\) −3.13437 −0.170236
\(340\) 0 0
\(341\) 18.2102 0.986138
\(342\) 0 0
\(343\) −20.1497 −1.08798
\(344\) 0 0
\(345\) −7.08974 −0.381699
\(346\) 0 0
\(347\) 0.990198 0.0531566 0.0265783 0.999647i \(-0.491539\pi\)
0.0265783 + 0.999647i \(0.491539\pi\)
\(348\) 0 0
\(349\) 21.3060 1.14049 0.570243 0.821476i \(-0.306849\pi\)
0.570243 + 0.821476i \(0.306849\pi\)
\(350\) 0 0
\(351\) −16.9593 −0.905222
\(352\) 0 0
\(353\) −1.94619 −0.103585 −0.0517926 0.998658i \(-0.516493\pi\)
−0.0517926 + 0.998658i \(0.516493\pi\)
\(354\) 0 0
\(355\) −2.88802 −0.153280
\(356\) 0 0
\(357\) −3.08079 −0.163053
\(358\) 0 0
\(359\) −28.6770 −1.51352 −0.756758 0.653695i \(-0.773218\pi\)
−0.756758 + 0.653695i \(0.773218\pi\)
\(360\) 0 0
\(361\) −16.3140 −0.858630
\(362\) 0 0
\(363\) −4.40147 −0.231017
\(364\) 0 0
\(365\) 6.79392 0.355610
\(366\) 0 0
\(367\) −3.41750 −0.178392 −0.0891961 0.996014i \(-0.528430\pi\)
−0.0891961 + 0.996014i \(0.528430\pi\)
\(368\) 0 0
\(369\) 4.05187 0.210932
\(370\) 0 0
\(371\) 17.9894 0.933964
\(372\) 0 0
\(373\) 18.8165 0.974282 0.487141 0.873323i \(-0.338040\pi\)
0.487141 + 0.873323i \(0.338040\pi\)
\(374\) 0 0
\(375\) 10.0343 0.518171
\(376\) 0 0
\(377\) −11.9598 −0.615960
\(378\) 0 0
\(379\) −24.4184 −1.25429 −0.627145 0.778902i \(-0.715777\pi\)
−0.627145 + 0.778902i \(0.715777\pi\)
\(380\) 0 0
\(381\) −8.18558 −0.419360
\(382\) 0 0
\(383\) −38.0485 −1.94419 −0.972095 0.234587i \(-0.924626\pi\)
−0.972095 + 0.234587i \(0.924626\pi\)
\(384\) 0 0
\(385\) 4.34898 0.221644
\(386\) 0 0
\(387\) −4.32298 −0.219750
\(388\) 0 0
\(389\) 11.5790 0.587081 0.293540 0.955947i \(-0.405167\pi\)
0.293540 + 0.955947i \(0.405167\pi\)
\(390\) 0 0
\(391\) −6.69131 −0.338394
\(392\) 0 0
\(393\) −12.5370 −0.632408
\(394\) 0 0
\(395\) 4.07918 0.205246
\(396\) 0 0
\(397\) 2.97890 0.149507 0.0747534 0.997202i \(-0.476183\pi\)
0.0747534 + 0.997202i \(0.476183\pi\)
\(398\) 0 0
\(399\) −5.04914 −0.252773
\(400\) 0 0
\(401\) 29.3861 1.46747 0.733735 0.679436i \(-0.237775\pi\)
0.733735 + 0.679436i \(0.237775\pi\)
\(402\) 0 0
\(403\) −19.3555 −0.964165
\(404\) 0 0
\(405\) 4.06436 0.201960
\(406\) 0 0
\(407\) −3.98606 −0.197581
\(408\) 0 0
\(409\) 15.7904 0.780787 0.390394 0.920648i \(-0.372339\pi\)
0.390394 + 0.920648i \(0.372339\pi\)
\(410\) 0 0
\(411\) 17.8283 0.879404
\(412\) 0 0
\(413\) −2.11595 −0.104119
\(414\) 0 0
\(415\) 6.81851 0.334707
\(416\) 0 0
\(417\) −11.8256 −0.579100
\(418\) 0 0
\(419\) −10.7003 −0.522745 −0.261372 0.965238i \(-0.584175\pi\)
−0.261372 + 0.965238i \(0.584175\pi\)
\(420\) 0 0
\(421\) 24.6110 1.19947 0.599734 0.800199i \(-0.295273\pi\)
0.599734 + 0.800199i \(0.295273\pi\)
\(422\) 0 0
\(423\) 1.18896 0.0578092
\(424\) 0 0
\(425\) 4.47043 0.216848
\(426\) 0 0
\(427\) 0.166129 0.00803955
\(428\) 0 0
\(429\) −12.3448 −0.596012
\(430\) 0 0
\(431\) 30.3348 1.46117 0.730587 0.682819i \(-0.239246\pi\)
0.730587 + 0.682819i \(0.239246\pi\)
\(432\) 0 0
\(433\) −20.2568 −0.973481 −0.486741 0.873547i \(-0.661814\pi\)
−0.486741 + 0.873547i \(0.661814\pi\)
\(434\) 0 0
\(435\) 4.22118 0.202390
\(436\) 0 0
\(437\) −10.9665 −0.524597
\(438\) 0 0
\(439\) −6.74120 −0.321740 −0.160870 0.986976i \(-0.551430\pi\)
−0.160870 + 0.986976i \(0.551430\pi\)
\(440\) 0 0
\(441\) 2.22029 0.105728
\(442\) 0 0
\(443\) 7.79905 0.370544 0.185272 0.982687i \(-0.440683\pi\)
0.185272 + 0.982687i \(0.440683\pi\)
\(444\) 0 0
\(445\) 10.7346 0.508868
\(446\) 0 0
\(447\) −3.69244 −0.174646
\(448\) 0 0
\(449\) 15.9787 0.754083 0.377041 0.926196i \(-0.376941\pi\)
0.377041 + 0.926196i \(0.376941\pi\)
\(450\) 0 0
\(451\) 13.0029 0.612281
\(452\) 0 0
\(453\) 30.0915 1.41382
\(454\) 0 0
\(455\) −4.62249 −0.216706
\(456\) 0 0
\(457\) −40.4234 −1.89093 −0.945464 0.325727i \(-0.894391\pi\)
−0.945464 + 0.325727i \(0.894391\pi\)
\(458\) 0 0
\(459\) 5.64938 0.263690
\(460\) 0 0
\(461\) 26.0949 1.21536 0.607679 0.794182i \(-0.292101\pi\)
0.607679 + 0.794182i \(0.292101\pi\)
\(462\) 0 0
\(463\) 16.6589 0.774202 0.387101 0.922037i \(-0.373476\pi\)
0.387101 + 0.922037i \(0.373476\pi\)
\(464\) 0 0
\(465\) 6.83148 0.316802
\(466\) 0 0
\(467\) −24.8414 −1.14952 −0.574761 0.818321i \(-0.694905\pi\)
−0.574761 + 0.818321i \(0.694905\pi\)
\(468\) 0 0
\(469\) −24.9399 −1.15162
\(470\) 0 0
\(471\) −13.2267 −0.609453
\(472\) 0 0
\(473\) −13.8729 −0.637876
\(474\) 0 0
\(475\) 7.32663 0.336169
\(476\) 0 0
\(477\) −7.48251 −0.342601
\(478\) 0 0
\(479\) 9.69969 0.443190 0.221595 0.975139i \(-0.428874\pi\)
0.221595 + 0.975139i \(0.428874\pi\)
\(480\) 0 0
\(481\) 4.23674 0.193179
\(482\) 0 0
\(483\) 20.6146 0.937995
\(484\) 0 0
\(485\) −1.24237 −0.0564129
\(486\) 0 0
\(487\) −5.75433 −0.260754 −0.130377 0.991465i \(-0.541619\pi\)
−0.130377 + 0.991465i \(0.541619\pi\)
\(488\) 0 0
\(489\) 22.8583 1.03369
\(490\) 0 0
\(491\) 38.7989 1.75097 0.875484 0.483247i \(-0.160543\pi\)
0.875484 + 0.483247i \(0.160543\pi\)
\(492\) 0 0
\(493\) 3.98396 0.179429
\(494\) 0 0
\(495\) −1.80891 −0.0813045
\(496\) 0 0
\(497\) 8.39739 0.376674
\(498\) 0 0
\(499\) 17.6385 0.789607 0.394804 0.918766i \(-0.370813\pi\)
0.394804 + 0.918766i \(0.370813\pi\)
\(500\) 0 0
\(501\) 0.0513980 0.00229629
\(502\) 0 0
\(503\) −3.37684 −0.150566 −0.0752830 0.997162i \(-0.523986\pi\)
−0.0752830 + 0.997162i \(0.523986\pi\)
\(504\) 0 0
\(505\) −6.99851 −0.311430
\(506\) 0 0
\(507\) −5.80663 −0.257882
\(508\) 0 0
\(509\) −2.97530 −0.131878 −0.0659390 0.997824i \(-0.521004\pi\)
−0.0659390 + 0.997824i \(0.521004\pi\)
\(510\) 0 0
\(511\) −19.7544 −0.873884
\(512\) 0 0
\(513\) 9.25882 0.408787
\(514\) 0 0
\(515\) −2.67162 −0.117726
\(516\) 0 0
\(517\) 3.81549 0.167805
\(518\) 0 0
\(519\) −30.5856 −1.34256
\(520\) 0 0
\(521\) −39.0247 −1.70970 −0.854851 0.518874i \(-0.826351\pi\)
−0.854851 + 0.518874i \(0.826351\pi\)
\(522\) 0 0
\(523\) −42.9153 −1.87655 −0.938277 0.345884i \(-0.887579\pi\)
−0.938277 + 0.345884i \(0.887579\pi\)
\(524\) 0 0
\(525\) −13.7725 −0.601080
\(526\) 0 0
\(527\) 6.44757 0.280860
\(528\) 0 0
\(529\) 21.7737 0.946681
\(530\) 0 0
\(531\) 0.880108 0.0381934
\(532\) 0 0
\(533\) −13.8206 −0.598638
\(534\) 0 0
\(535\) −7.01918 −0.303465
\(536\) 0 0
\(537\) −16.6197 −0.717195
\(538\) 0 0
\(539\) 7.12514 0.306901
\(540\) 0 0
\(541\) −24.2249 −1.04151 −0.520755 0.853706i \(-0.674349\pi\)
−0.520755 + 0.853706i \(0.674349\pi\)
\(542\) 0 0
\(543\) −19.4580 −0.835022
\(544\) 0 0
\(545\) 1.13565 0.0486457
\(546\) 0 0
\(547\) −41.7334 −1.78439 −0.892196 0.451648i \(-0.850836\pi\)
−0.892196 + 0.451648i \(0.850836\pi\)
\(548\) 0 0
\(549\) −0.0690996 −0.00294910
\(550\) 0 0
\(551\) 6.52935 0.278160
\(552\) 0 0
\(553\) −11.8609 −0.504375
\(554\) 0 0
\(555\) −1.49535 −0.0634741
\(556\) 0 0
\(557\) 43.4639 1.84163 0.920813 0.390005i \(-0.127527\pi\)
0.920813 + 0.390005i \(0.127527\pi\)
\(558\) 0 0
\(559\) 14.7454 0.623663
\(560\) 0 0
\(561\) 4.11222 0.173618
\(562\) 0 0
\(563\) −15.4297 −0.650285 −0.325143 0.945665i \(-0.605412\pi\)
−0.325143 + 0.945665i \(0.605412\pi\)
\(564\) 0 0
\(565\) 1.56659 0.0659070
\(566\) 0 0
\(567\) −11.8178 −0.496300
\(568\) 0 0
\(569\) 6.57229 0.275525 0.137762 0.990465i \(-0.456009\pi\)
0.137762 + 0.990465i \(0.456009\pi\)
\(570\) 0 0
\(571\) −35.7710 −1.49697 −0.748485 0.663152i \(-0.769218\pi\)
−0.748485 + 0.663152i \(0.769218\pi\)
\(572\) 0 0
\(573\) −8.15307 −0.340600
\(574\) 0 0
\(575\) −29.9130 −1.24746
\(576\) 0 0
\(577\) 23.4095 0.974550 0.487275 0.873249i \(-0.337991\pi\)
0.487275 + 0.873249i \(0.337991\pi\)
\(578\) 0 0
\(579\) −18.3700 −0.763433
\(580\) 0 0
\(581\) −19.8259 −0.822517
\(582\) 0 0
\(583\) −24.0121 −0.994481
\(584\) 0 0
\(585\) 1.92267 0.0794928
\(586\) 0 0
\(587\) −17.4407 −0.719856 −0.359928 0.932980i \(-0.617199\pi\)
−0.359928 + 0.932980i \(0.617199\pi\)
\(588\) 0 0
\(589\) 10.5670 0.435405
\(590\) 0 0
\(591\) 37.0010 1.52202
\(592\) 0 0
\(593\) 46.0152 1.88962 0.944808 0.327624i \(-0.106248\pi\)
0.944808 + 0.327624i \(0.106248\pi\)
\(594\) 0 0
\(595\) 1.53981 0.0631262
\(596\) 0 0
\(597\) 0.918832 0.0376053
\(598\) 0 0
\(599\) 7.78861 0.318234 0.159117 0.987260i \(-0.449135\pi\)
0.159117 + 0.987260i \(0.449135\pi\)
\(600\) 0 0
\(601\) 23.1313 0.943544 0.471772 0.881721i \(-0.343615\pi\)
0.471772 + 0.881721i \(0.343615\pi\)
\(602\) 0 0
\(603\) 10.3735 0.422441
\(604\) 0 0
\(605\) 2.19990 0.0894388
\(606\) 0 0
\(607\) −22.1994 −0.901045 −0.450522 0.892765i \(-0.648762\pi\)
−0.450522 + 0.892765i \(0.648762\pi\)
\(608\) 0 0
\(609\) −12.2738 −0.497358
\(610\) 0 0
\(611\) −4.05545 −0.164066
\(612\) 0 0
\(613\) −43.5233 −1.75789 −0.878944 0.476925i \(-0.841751\pi\)
−0.878944 + 0.476925i \(0.841751\pi\)
\(614\) 0 0
\(615\) 4.87797 0.196699
\(616\) 0 0
\(617\) 16.4335 0.661590 0.330795 0.943703i \(-0.392683\pi\)
0.330795 + 0.943703i \(0.392683\pi\)
\(618\) 0 0
\(619\) −13.7102 −0.551060 −0.275530 0.961292i \(-0.588853\pi\)
−0.275530 + 0.961292i \(0.588853\pi\)
\(620\) 0 0
\(621\) −37.8018 −1.51693
\(622\) 0 0
\(623\) −31.2125 −1.25050
\(624\) 0 0
\(625\) 17.3369 0.693475
\(626\) 0 0
\(627\) 6.73955 0.269152
\(628\) 0 0
\(629\) −1.41132 −0.0562728
\(630\) 0 0
\(631\) −5.13976 −0.204611 −0.102305 0.994753i \(-0.532622\pi\)
−0.102305 + 0.994753i \(0.532622\pi\)
\(632\) 0 0
\(633\) −5.74779 −0.228454
\(634\) 0 0
\(635\) 4.09124 0.162356
\(636\) 0 0
\(637\) −7.57324 −0.300063
\(638\) 0 0
\(639\) −3.49281 −0.138173
\(640\) 0 0
\(641\) 34.7310 1.37179 0.685896 0.727699i \(-0.259410\pi\)
0.685896 + 0.727699i \(0.259410\pi\)
\(642\) 0 0
\(643\) 13.3929 0.528163 0.264082 0.964500i \(-0.414931\pi\)
0.264082 + 0.964500i \(0.414931\pi\)
\(644\) 0 0
\(645\) −5.20435 −0.204921
\(646\) 0 0
\(647\) −6.53310 −0.256843 −0.128421 0.991720i \(-0.540991\pi\)
−0.128421 + 0.991720i \(0.540991\pi\)
\(648\) 0 0
\(649\) 2.82435 0.110866
\(650\) 0 0
\(651\) −19.8636 −0.778517
\(652\) 0 0
\(653\) 46.0149 1.80070 0.900351 0.435164i \(-0.143310\pi\)
0.900351 + 0.435164i \(0.143310\pi\)
\(654\) 0 0
\(655\) 6.26612 0.244838
\(656\) 0 0
\(657\) 8.21664 0.320562
\(658\) 0 0
\(659\) −21.2940 −0.829495 −0.414748 0.909936i \(-0.636130\pi\)
−0.414748 + 0.909936i \(0.636130\pi\)
\(660\) 0 0
\(661\) 12.4363 0.483715 0.241858 0.970312i \(-0.422243\pi\)
0.241858 + 0.970312i \(0.422243\pi\)
\(662\) 0 0
\(663\) −4.37084 −0.169749
\(664\) 0 0
\(665\) 2.52361 0.0978615
\(666\) 0 0
\(667\) −26.6579 −1.03220
\(668\) 0 0
\(669\) 12.3436 0.477229
\(670\) 0 0
\(671\) −0.221748 −0.00856047
\(672\) 0 0
\(673\) 16.8858 0.650901 0.325451 0.945559i \(-0.394484\pi\)
0.325451 + 0.945559i \(0.394484\pi\)
\(674\) 0 0
\(675\) 25.2551 0.972071
\(676\) 0 0
\(677\) −10.4061 −0.399940 −0.199970 0.979802i \(-0.564084\pi\)
−0.199970 + 0.979802i \(0.564084\pi\)
\(678\) 0 0
\(679\) 3.61238 0.138630
\(680\) 0 0
\(681\) −0.760876 −0.0291568
\(682\) 0 0
\(683\) −0.327480 −0.0125307 −0.00626533 0.999980i \(-0.501994\pi\)
−0.00626533 + 0.999980i \(0.501994\pi\)
\(684\) 0 0
\(685\) −8.91075 −0.340462
\(686\) 0 0
\(687\) −31.8748 −1.21610
\(688\) 0 0
\(689\) 25.5223 0.972321
\(690\) 0 0
\(691\) 26.2280 0.997760 0.498880 0.866671i \(-0.333745\pi\)
0.498880 + 0.866671i \(0.333745\pi\)
\(692\) 0 0
\(693\) 5.25970 0.199799
\(694\) 0 0
\(695\) 5.91053 0.224199
\(696\) 0 0
\(697\) 4.60384 0.174383
\(698\) 0 0
\(699\) 12.6426 0.478185
\(700\) 0 0
\(701\) 8.50739 0.321320 0.160660 0.987010i \(-0.448638\pi\)
0.160660 + 0.987010i \(0.448638\pi\)
\(702\) 0 0
\(703\) −2.31302 −0.0872371
\(704\) 0 0
\(705\) 1.43136 0.0539083
\(706\) 0 0
\(707\) 20.3493 0.765313
\(708\) 0 0
\(709\) −18.4949 −0.694590 −0.347295 0.937756i \(-0.612900\pi\)
−0.347295 + 0.937756i \(0.612900\pi\)
\(710\) 0 0
\(711\) 4.93340 0.185017
\(712\) 0 0
\(713\) −43.1427 −1.61571
\(714\) 0 0
\(715\) 6.17006 0.230747
\(716\) 0 0
\(717\) −30.6251 −1.14371
\(718\) 0 0
\(719\) −18.0974 −0.674919 −0.337459 0.941340i \(-0.609568\pi\)
−0.337459 + 0.941340i \(0.609568\pi\)
\(720\) 0 0
\(721\) 7.76817 0.289302
\(722\) 0 0
\(723\) −15.2195 −0.566018
\(724\) 0 0
\(725\) 17.8100 0.661448
\(726\) 0 0
\(727\) −16.1549 −0.599154 −0.299577 0.954072i \(-0.596846\pi\)
−0.299577 + 0.954072i \(0.596846\pi\)
\(728\) 0 0
\(729\) 29.5917 1.09599
\(730\) 0 0
\(731\) −4.91188 −0.181672
\(732\) 0 0
\(733\) −32.7603 −1.21003 −0.605014 0.796215i \(-0.706832\pi\)
−0.605014 + 0.796215i \(0.706832\pi\)
\(734\) 0 0
\(735\) 2.67296 0.0985937
\(736\) 0 0
\(737\) 33.2896 1.22624
\(738\) 0 0
\(739\) 31.8684 1.17230 0.586150 0.810203i \(-0.300643\pi\)
0.586150 + 0.810203i \(0.300643\pi\)
\(740\) 0 0
\(741\) −7.16341 −0.263154
\(742\) 0 0
\(743\) −18.2836 −0.670761 −0.335380 0.942083i \(-0.608865\pi\)
−0.335380 + 0.942083i \(0.608865\pi\)
\(744\) 0 0
\(745\) 1.84552 0.0676146
\(746\) 0 0
\(747\) 8.24637 0.301719
\(748\) 0 0
\(749\) 20.4094 0.745742
\(750\) 0 0
\(751\) 23.6181 0.861837 0.430918 0.902391i \(-0.358190\pi\)
0.430918 + 0.902391i \(0.358190\pi\)
\(752\) 0 0
\(753\) 14.1999 0.517472
\(754\) 0 0
\(755\) −15.0400 −0.547363
\(756\) 0 0
\(757\) 32.6453 1.18652 0.593258 0.805013i \(-0.297842\pi\)
0.593258 + 0.805013i \(0.297842\pi\)
\(758\) 0 0
\(759\) −27.5161 −0.998772
\(760\) 0 0
\(761\) 44.4111 1.60990 0.804951 0.593342i \(-0.202192\pi\)
0.804951 + 0.593342i \(0.202192\pi\)
\(762\) 0 0
\(763\) −3.30207 −0.119543
\(764\) 0 0
\(765\) −0.640469 −0.0231562
\(766\) 0 0
\(767\) −3.00198 −0.108395
\(768\) 0 0
\(769\) −18.3467 −0.661599 −0.330800 0.943701i \(-0.607318\pi\)
−0.330800 + 0.943701i \(0.607318\pi\)
\(770\) 0 0
\(771\) −38.0842 −1.37157
\(772\) 0 0
\(773\) 14.0536 0.505474 0.252737 0.967535i \(-0.418669\pi\)
0.252737 + 0.967535i \(0.418669\pi\)
\(774\) 0 0
\(775\) 28.8234 1.03537
\(776\) 0 0
\(777\) 4.34797 0.155983
\(778\) 0 0
\(779\) 7.54527 0.270337
\(780\) 0 0
\(781\) −11.2088 −0.401081
\(782\) 0 0
\(783\) 22.5069 0.804331
\(784\) 0 0
\(785\) 6.61083 0.235951
\(786\) 0 0
\(787\) 36.2651 1.29271 0.646355 0.763037i \(-0.276292\pi\)
0.646355 + 0.763037i \(0.276292\pi\)
\(788\) 0 0
\(789\) 27.7600 0.988283
\(790\) 0 0
\(791\) −4.55512 −0.161961
\(792\) 0 0
\(793\) 0.235693 0.00836972
\(794\) 0 0
\(795\) −9.00805 −0.319482
\(796\) 0 0
\(797\) 21.8314 0.773309 0.386655 0.922225i \(-0.373631\pi\)
0.386655 + 0.922225i \(0.373631\pi\)
\(798\) 0 0
\(799\) 1.35093 0.0477923
\(800\) 0 0
\(801\) 12.9825 0.458715
\(802\) 0 0
\(803\) 26.3680 0.930507
\(804\) 0 0
\(805\) −10.3034 −0.363146
\(806\) 0 0
\(807\) −34.3320 −1.20854
\(808\) 0 0
\(809\) 51.1904 1.79976 0.899879 0.436140i \(-0.143655\pi\)
0.899879 + 0.436140i \(0.143655\pi\)
\(810\) 0 0
\(811\) 1.36518 0.0479381 0.0239690 0.999713i \(-0.492370\pi\)
0.0239690 + 0.999713i \(0.492370\pi\)
\(812\) 0 0
\(813\) 4.31570 0.151358
\(814\) 0 0
\(815\) −11.4248 −0.400193
\(816\) 0 0
\(817\) −8.05013 −0.281638
\(818\) 0 0
\(819\) −5.59048 −0.195347
\(820\) 0 0
\(821\) −55.0183 −1.92015 −0.960076 0.279738i \(-0.909752\pi\)
−0.960076 + 0.279738i \(0.909752\pi\)
\(822\) 0 0
\(823\) −11.1630 −0.389117 −0.194559 0.980891i \(-0.562327\pi\)
−0.194559 + 0.980891i \(0.562327\pi\)
\(824\) 0 0
\(825\) 18.3834 0.640027
\(826\) 0 0
\(827\) −18.6522 −0.648600 −0.324300 0.945954i \(-0.605129\pi\)
−0.324300 + 0.945954i \(0.605129\pi\)
\(828\) 0 0
\(829\) 19.2597 0.668918 0.334459 0.942410i \(-0.391446\pi\)
0.334459 + 0.942410i \(0.391446\pi\)
\(830\) 0 0
\(831\) −36.4158 −1.26325
\(832\) 0 0
\(833\) 2.52275 0.0874081
\(834\) 0 0
\(835\) −0.0256892 −0.000889013 0
\(836\) 0 0
\(837\) 36.4247 1.25902
\(838\) 0 0
\(839\) 33.8697 1.16931 0.584656 0.811282i \(-0.301230\pi\)
0.584656 + 0.811282i \(0.301230\pi\)
\(840\) 0 0
\(841\) −13.1280 −0.452691
\(842\) 0 0
\(843\) 37.8720 1.30438
\(844\) 0 0
\(845\) 2.90221 0.0998392
\(846\) 0 0
\(847\) −6.39657 −0.219789
\(848\) 0 0
\(849\) −18.6254 −0.639222
\(850\) 0 0
\(851\) 9.44355 0.323721
\(852\) 0 0
\(853\) 4.58890 0.157121 0.0785604 0.996909i \(-0.474968\pi\)
0.0785604 + 0.996909i \(0.474968\pi\)
\(854\) 0 0
\(855\) −1.04967 −0.0358980
\(856\) 0 0
\(857\) −39.4641 −1.34807 −0.674034 0.738700i \(-0.735440\pi\)
−0.674034 + 0.738700i \(0.735440\pi\)
\(858\) 0 0
\(859\) −39.4009 −1.34434 −0.672170 0.740397i \(-0.734638\pi\)
−0.672170 + 0.740397i \(0.734638\pi\)
\(860\) 0 0
\(861\) −14.1835 −0.483371
\(862\) 0 0
\(863\) 36.6708 1.24829 0.624144 0.781309i \(-0.285448\pi\)
0.624144 + 0.781309i \(0.285448\pi\)
\(864\) 0 0
\(865\) 15.2870 0.519773
\(866\) 0 0
\(867\) 1.45598 0.0494478
\(868\) 0 0
\(869\) 15.8318 0.537056
\(870\) 0 0
\(871\) −35.3832 −1.19891
\(872\) 0 0
\(873\) −1.50253 −0.0508529
\(874\) 0 0
\(875\) 14.5827 0.492985
\(876\) 0 0
\(877\) 39.2168 1.32426 0.662128 0.749391i \(-0.269654\pi\)
0.662128 + 0.749391i \(0.269654\pi\)
\(878\) 0 0
\(879\) −24.4340 −0.824138
\(880\) 0 0
\(881\) −57.0746 −1.92289 −0.961445 0.274996i \(-0.911324\pi\)
−0.961445 + 0.274996i \(0.911324\pi\)
\(882\) 0 0
\(883\) 11.7791 0.396398 0.198199 0.980162i \(-0.436491\pi\)
0.198199 + 0.980162i \(0.436491\pi\)
\(884\) 0 0
\(885\) 1.05954 0.0356162
\(886\) 0 0
\(887\) −26.4333 −0.887544 −0.443772 0.896140i \(-0.646360\pi\)
−0.443772 + 0.896140i \(0.646360\pi\)
\(888\) 0 0
\(889\) −11.8959 −0.398976
\(890\) 0 0
\(891\) 15.7743 0.528458
\(892\) 0 0
\(893\) 2.21404 0.0740902
\(894\) 0 0
\(895\) 8.30672 0.277663
\(896\) 0 0
\(897\) 29.2467 0.976517
\(898\) 0 0
\(899\) 25.6869 0.856705
\(900\) 0 0
\(901\) −8.50181 −0.283236
\(902\) 0 0
\(903\) 15.1325 0.503578
\(904\) 0 0
\(905\) 9.72531 0.323280
\(906\) 0 0
\(907\) −23.1224 −0.767768 −0.383884 0.923381i \(-0.625414\pi\)
−0.383884 + 0.923381i \(0.625414\pi\)
\(908\) 0 0
\(909\) −8.46407 −0.280735
\(910\) 0 0
\(911\) −43.5964 −1.44441 −0.722207 0.691677i \(-0.756872\pi\)
−0.722207 + 0.691677i \(0.756872\pi\)
\(912\) 0 0
\(913\) 26.4634 0.875812
\(914\) 0 0
\(915\) −0.0831876 −0.00275010
\(916\) 0 0
\(917\) −18.2198 −0.601669
\(918\) 0 0
\(919\) −3.34727 −0.110416 −0.0552080 0.998475i \(-0.517582\pi\)
−0.0552080 + 0.998475i \(0.517582\pi\)
\(920\) 0 0
\(921\) −22.9469 −0.756128
\(922\) 0 0
\(923\) 11.9137 0.392144
\(924\) 0 0
\(925\) −6.30919 −0.207445
\(926\) 0 0
\(927\) −3.23109 −0.106123
\(928\) 0 0
\(929\) 47.4915 1.55814 0.779072 0.626934i \(-0.215690\pi\)
0.779072 + 0.626934i \(0.215690\pi\)
\(930\) 0 0
\(931\) 4.13456 0.135505
\(932\) 0 0
\(933\) 40.3933 1.32242
\(934\) 0 0
\(935\) −2.05533 −0.0672164
\(936\) 0 0
\(937\) 32.5218 1.06244 0.531220 0.847234i \(-0.321734\pi\)
0.531220 + 0.847234i \(0.321734\pi\)
\(938\) 0 0
\(939\) 15.9900 0.521813
\(940\) 0 0
\(941\) −18.7638 −0.611682 −0.305841 0.952083i \(-0.598938\pi\)
−0.305841 + 0.952083i \(0.598938\pi\)
\(942\) 0 0
\(943\) −30.8057 −1.00317
\(944\) 0 0
\(945\) 8.69898 0.282978
\(946\) 0 0
\(947\) −20.8462 −0.677409 −0.338705 0.940893i \(-0.609989\pi\)
−0.338705 + 0.940893i \(0.609989\pi\)
\(948\) 0 0
\(949\) −28.0263 −0.909773
\(950\) 0 0
\(951\) 5.01056 0.162479
\(952\) 0 0
\(953\) −5.96476 −0.193217 −0.0966087 0.995322i \(-0.530800\pi\)
−0.0966087 + 0.995322i \(0.530800\pi\)
\(954\) 0 0
\(955\) 4.07499 0.131864
\(956\) 0 0
\(957\) 16.3829 0.529585
\(958\) 0 0
\(959\) 25.9094 0.836659
\(960\) 0 0
\(961\) 10.5711 0.341004
\(962\) 0 0
\(963\) −8.48906 −0.273556
\(964\) 0 0
\(965\) 9.18153 0.295564
\(966\) 0 0
\(967\) −4.74397 −0.152556 −0.0762780 0.997087i \(-0.524304\pi\)
−0.0762780 + 0.997087i \(0.524304\pi\)
\(968\) 0 0
\(969\) 2.38623 0.0766567
\(970\) 0 0
\(971\) 58.3277 1.87183 0.935913 0.352232i \(-0.114577\pi\)
0.935913 + 0.352232i \(0.114577\pi\)
\(972\) 0 0
\(973\) −17.1858 −0.550952
\(974\) 0 0
\(975\) −19.5395 −0.625766
\(976\) 0 0
\(977\) −17.0264 −0.544722 −0.272361 0.962195i \(-0.587805\pi\)
−0.272361 + 0.962195i \(0.587805\pi\)
\(978\) 0 0
\(979\) 41.6622 1.33153
\(980\) 0 0
\(981\) 1.37346 0.0438513
\(982\) 0 0
\(983\) −14.8076 −0.472290 −0.236145 0.971718i \(-0.575884\pi\)
−0.236145 + 0.971718i \(0.575884\pi\)
\(984\) 0 0
\(985\) −18.4935 −0.589251
\(986\) 0 0
\(987\) −4.16192 −0.132475
\(988\) 0 0
\(989\) 32.8669 1.04511
\(990\) 0 0
\(991\) −23.5340 −0.747583 −0.373791 0.927513i \(-0.621942\pi\)
−0.373791 + 0.927513i \(0.621942\pi\)
\(992\) 0 0
\(993\) −20.4610 −0.649310
\(994\) 0 0
\(995\) −0.459242 −0.0145589
\(996\) 0 0
\(997\) −0.754010 −0.0238797 −0.0119399 0.999929i \(-0.503801\pi\)
−0.0119399 + 0.999929i \(0.503801\pi\)
\(998\) 0 0
\(999\) −7.97306 −0.252256
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 \(a_p\))