Properties

Label 8020.2.a.c.1.6
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 1.6
Character \(\chi\) = 8020.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.62538 q^{3}\) \(-1.00000 q^{5}\) \(+4.42157 q^{7}\) \(-0.358130 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.62538 q^{3}\) \(-1.00000 q^{5}\) \(+4.42157 q^{7}\) \(-0.358130 q^{9}\) \(-1.81850 q^{11}\) \(-1.06376 q^{13}\) \(+1.62538 q^{15}\) \(-1.23283 q^{17}\) \(+4.12363 q^{19}\) \(-7.18675 q^{21}\) \(-4.61525 q^{23}\) \(+1.00000 q^{25}\) \(+5.45825 q^{27}\) \(+0.847315 q^{29}\) \(-0.697606 q^{31}\) \(+2.95575 q^{33}\) \(-4.42157 q^{35}\) \(+3.45352 q^{37}\) \(+1.72901 q^{39}\) \(-3.20797 q^{41}\) \(-10.5027 q^{43}\) \(+0.358130 q^{45}\) \(+4.77104 q^{47}\) \(+12.5503 q^{49}\) \(+2.00381 q^{51}\) \(+3.05860 q^{53}\) \(+1.81850 q^{55}\) \(-6.70247 q^{57}\) \(-10.5261 q^{59}\) \(+9.43455 q^{61}\) \(-1.58350 q^{63}\) \(+1.06376 q^{65}\) \(+4.76942 q^{67}\) \(+7.50154 q^{69}\) \(+0.533751 q^{71}\) \(-7.64125 q^{73}\) \(-1.62538 q^{75}\) \(-8.04062 q^{77}\) \(-9.62077 q^{79}\) \(-7.79735 q^{81}\) \(-6.01040 q^{83}\) \(+1.23283 q^{85}\) \(-1.37721 q^{87}\) \(-6.21176 q^{89}\) \(-4.70348 q^{91}\) \(+1.13388 q^{93}\) \(-4.12363 q^{95}\) \(+12.6850 q^{97}\) \(+0.651259 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 3q^{13} \) \(\mathstrut -\mathstrut 3q^{15} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut +\mathstrut 28q^{25} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut -\mathstrut 37q^{29} \) \(\mathstrut -\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 2q^{33} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut -\mathstrut 3q^{37} \) \(\mathstrut -\mathstrut 19q^{39} \) \(\mathstrut -\mathstrut 30q^{41} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut -\mathstrut 17q^{45} \) \(\mathstrut -\mathstrut 15q^{47} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 2q^{55} \) \(\mathstrut -\mathstrut 22q^{57} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut -\mathstrut 33q^{61} \) \(\mathstrut -\mathstrut 20q^{63} \) \(\mathstrut -\mathstrut 3q^{65} \) \(\mathstrut +\mathstrut 19q^{67} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut -\mathstrut 42q^{77} \) \(\mathstrut -\mathstrut 29q^{79} \) \(\mathstrut -\mathstrut 36q^{81} \) \(\mathstrut +\mathstrut 14q^{83} \) \(\mathstrut +\mathstrut 10q^{85} \) \(\mathstrut -\mathstrut 32q^{87} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 7q^{91} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 39q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.62538 −0.938415 −0.469208 0.883088i \(-0.655460\pi\)
−0.469208 + 0.883088i \(0.655460\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 4.42157 1.67120 0.835599 0.549340i \(-0.185121\pi\)
0.835599 + 0.549340i \(0.185121\pi\)
\(8\) 0 0
\(9\) −0.358130 −0.119377
\(10\) 0 0
\(11\) −1.81850 −0.548297 −0.274149 0.961687i \(-0.588396\pi\)
−0.274149 + 0.961687i \(0.588396\pi\)
\(12\) 0 0
\(13\) −1.06376 −0.295033 −0.147517 0.989060i \(-0.547128\pi\)
−0.147517 + 0.989060i \(0.547128\pi\)
\(14\) 0 0
\(15\) 1.62538 0.419672
\(16\) 0 0
\(17\) −1.23283 −0.299004 −0.149502 0.988761i \(-0.547767\pi\)
−0.149502 + 0.988761i \(0.547767\pi\)
\(18\) 0 0
\(19\) 4.12363 0.946024 0.473012 0.881056i \(-0.343167\pi\)
0.473012 + 0.881056i \(0.343167\pi\)
\(20\) 0 0
\(21\) −7.18675 −1.56828
\(22\) 0 0
\(23\) −4.61525 −0.962345 −0.481173 0.876626i \(-0.659789\pi\)
−0.481173 + 0.876626i \(0.659789\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 5.45825 1.05044
\(28\) 0 0
\(29\) 0.847315 0.157342 0.0786712 0.996901i \(-0.474932\pi\)
0.0786712 + 0.996901i \(0.474932\pi\)
\(30\) 0 0
\(31\) −0.697606 −0.125294 −0.0626469 0.998036i \(-0.519954\pi\)
−0.0626469 + 0.998036i \(0.519954\pi\)
\(32\) 0 0
\(33\) 2.95575 0.514531
\(34\) 0 0
\(35\) −4.42157 −0.747382
\(36\) 0 0
\(37\) 3.45352 0.567755 0.283877 0.958861i \(-0.408379\pi\)
0.283877 + 0.958861i \(0.408379\pi\)
\(38\) 0 0
\(39\) 1.72901 0.276864
\(40\) 0 0
\(41\) −3.20797 −0.501001 −0.250500 0.968116i \(-0.580595\pi\)
−0.250500 + 0.968116i \(0.580595\pi\)
\(42\) 0 0
\(43\) −10.5027 −1.60164 −0.800820 0.598905i \(-0.795603\pi\)
−0.800820 + 0.598905i \(0.795603\pi\)
\(44\) 0 0
\(45\) 0.358130 0.0533869
\(46\) 0 0
\(47\) 4.77104 0.695928 0.347964 0.937508i \(-0.386873\pi\)
0.347964 + 0.937508i \(0.386873\pi\)
\(48\) 0 0
\(49\) 12.5503 1.79290
\(50\) 0 0
\(51\) 2.00381 0.280590
\(52\) 0 0
\(53\) 3.05860 0.420131 0.210066 0.977687i \(-0.432632\pi\)
0.210066 + 0.977687i \(0.432632\pi\)
\(54\) 0 0
\(55\) 1.81850 0.245206
\(56\) 0 0
\(57\) −6.70247 −0.887764
\(58\) 0 0
\(59\) −10.5261 −1.37038 −0.685191 0.728364i \(-0.740281\pi\)
−0.685191 + 0.728364i \(0.740281\pi\)
\(60\) 0 0
\(61\) 9.43455 1.20797 0.603985 0.796996i \(-0.293579\pi\)
0.603985 + 0.796996i \(0.293579\pi\)
\(62\) 0 0
\(63\) −1.58350 −0.199502
\(64\) 0 0
\(65\) 1.06376 0.131943
\(66\) 0 0
\(67\) 4.76942 0.582677 0.291339 0.956620i \(-0.405899\pi\)
0.291339 + 0.956620i \(0.405899\pi\)
\(68\) 0 0
\(69\) 7.50154 0.903080
\(70\) 0 0
\(71\) 0.533751 0.0633446 0.0316723 0.999498i \(-0.489917\pi\)
0.0316723 + 0.999498i \(0.489917\pi\)
\(72\) 0 0
\(73\) −7.64125 −0.894341 −0.447171 0.894449i \(-0.647568\pi\)
−0.447171 + 0.894449i \(0.647568\pi\)
\(74\) 0 0
\(75\) −1.62538 −0.187683
\(76\) 0 0
\(77\) −8.04062 −0.916313
\(78\) 0 0
\(79\) −9.62077 −1.08242 −0.541210 0.840887i \(-0.682034\pi\)
−0.541210 + 0.840887i \(0.682034\pi\)
\(80\) 0 0
\(81\) −7.79735 −0.866372
\(82\) 0 0
\(83\) −6.01040 −0.659727 −0.329864 0.944029i \(-0.607003\pi\)
−0.329864 + 0.944029i \(0.607003\pi\)
\(84\) 0 0
\(85\) 1.23283 0.133719
\(86\) 0 0
\(87\) −1.37721 −0.147653
\(88\) 0 0
\(89\) −6.21176 −0.658445 −0.329222 0.944252i \(-0.606787\pi\)
−0.329222 + 0.944252i \(0.606787\pi\)
\(90\) 0 0
\(91\) −4.70348 −0.493059
\(92\) 0 0
\(93\) 1.13388 0.117578
\(94\) 0 0
\(95\) −4.12363 −0.423075
\(96\) 0 0
\(97\) 12.6850 1.28797 0.643984 0.765039i \(-0.277280\pi\)
0.643984 + 0.765039i \(0.277280\pi\)
\(98\) 0 0
\(99\) 0.651259 0.0654540
\(100\) 0 0
\(101\) −9.56613 −0.951865 −0.475933 0.879482i \(-0.657889\pi\)
−0.475933 + 0.879482i \(0.657889\pi\)
\(102\) 0 0
\(103\) −9.56470 −0.942438 −0.471219 0.882016i \(-0.656186\pi\)
−0.471219 + 0.882016i \(0.656186\pi\)
\(104\) 0 0
\(105\) 7.18675 0.701355
\(106\) 0 0
\(107\) 6.77911 0.655361 0.327681 0.944789i \(-0.393733\pi\)
0.327681 + 0.944789i \(0.393733\pi\)
\(108\) 0 0
\(109\) 5.53790 0.530435 0.265217 0.964189i \(-0.414556\pi\)
0.265217 + 0.964189i \(0.414556\pi\)
\(110\) 0 0
\(111\) −5.61329 −0.532790
\(112\) 0 0
\(113\) −16.2741 −1.53094 −0.765471 0.643470i \(-0.777494\pi\)
−0.765471 + 0.643470i \(0.777494\pi\)
\(114\) 0 0
\(115\) 4.61525 0.430374
\(116\) 0 0
\(117\) 0.380964 0.0352201
\(118\) 0 0
\(119\) −5.45103 −0.499695
\(120\) 0 0
\(121\) −7.69307 −0.699370
\(122\) 0 0
\(123\) 5.21418 0.470147
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −1.53521 −0.136228 −0.0681140 0.997678i \(-0.521698\pi\)
−0.0681140 + 0.997678i \(0.521698\pi\)
\(128\) 0 0
\(129\) 17.0708 1.50300
\(130\) 0 0
\(131\) 17.1128 1.49515 0.747576 0.664176i \(-0.231218\pi\)
0.747576 + 0.664176i \(0.231218\pi\)
\(132\) 0 0
\(133\) 18.2329 1.58099
\(134\) 0 0
\(135\) −5.45825 −0.469771
\(136\) 0 0
\(137\) 20.8091 1.77784 0.888920 0.458062i \(-0.151456\pi\)
0.888920 + 0.458062i \(0.151456\pi\)
\(138\) 0 0
\(139\) 1.51691 0.128662 0.0643312 0.997929i \(-0.479509\pi\)
0.0643312 + 0.997929i \(0.479509\pi\)
\(140\) 0 0
\(141\) −7.75477 −0.653069
\(142\) 0 0
\(143\) 1.93444 0.161766
\(144\) 0 0
\(145\) −0.847315 −0.0703657
\(146\) 0 0
\(147\) −20.3991 −1.68249
\(148\) 0 0
\(149\) 22.4601 1.84000 0.920000 0.391919i \(-0.128189\pi\)
0.920000 + 0.391919i \(0.128189\pi\)
\(150\) 0 0
\(151\) 19.6913 1.60245 0.801227 0.598360i \(-0.204181\pi\)
0.801227 + 0.598360i \(0.204181\pi\)
\(152\) 0 0
\(153\) 0.441512 0.0356942
\(154\) 0 0
\(155\) 0.697606 0.0560331
\(156\) 0 0
\(157\) 2.04837 0.163478 0.0817388 0.996654i \(-0.473953\pi\)
0.0817388 + 0.996654i \(0.473953\pi\)
\(158\) 0 0
\(159\) −4.97140 −0.394258
\(160\) 0 0
\(161\) −20.4067 −1.60827
\(162\) 0 0
\(163\) −3.99410 −0.312842 −0.156421 0.987690i \(-0.549996\pi\)
−0.156421 + 0.987690i \(0.549996\pi\)
\(164\) 0 0
\(165\) −2.95575 −0.230105
\(166\) 0 0
\(167\) −15.3495 −1.18778 −0.593889 0.804547i \(-0.702408\pi\)
−0.593889 + 0.804547i \(0.702408\pi\)
\(168\) 0 0
\(169\) −11.8684 −0.912955
\(170\) 0 0
\(171\) −1.47680 −0.112933
\(172\) 0 0
\(173\) −24.3080 −1.84810 −0.924051 0.382270i \(-0.875143\pi\)
−0.924051 + 0.382270i \(0.875143\pi\)
\(174\) 0 0
\(175\) 4.42157 0.334240
\(176\) 0 0
\(177\) 17.1089 1.28599
\(178\) 0 0
\(179\) 5.21931 0.390110 0.195055 0.980792i \(-0.437512\pi\)
0.195055 + 0.980792i \(0.437512\pi\)
\(180\) 0 0
\(181\) 7.44881 0.553666 0.276833 0.960918i \(-0.410715\pi\)
0.276833 + 0.960918i \(0.410715\pi\)
\(182\) 0 0
\(183\) −15.3347 −1.13358
\(184\) 0 0
\(185\) −3.45352 −0.253908
\(186\) 0 0
\(187\) 2.24189 0.163943
\(188\) 0 0
\(189\) 24.1340 1.75549
\(190\) 0 0
\(191\) −10.4691 −0.757515 −0.378757 0.925496i \(-0.623649\pi\)
−0.378757 + 0.925496i \(0.623649\pi\)
\(192\) 0 0
\(193\) 2.75123 0.198038 0.0990189 0.995086i \(-0.468430\pi\)
0.0990189 + 0.995086i \(0.468430\pi\)
\(194\) 0 0
\(195\) −1.72901 −0.123817
\(196\) 0 0
\(197\) 1.62752 0.115956 0.0579781 0.998318i \(-0.481535\pi\)
0.0579781 + 0.998318i \(0.481535\pi\)
\(198\) 0 0
\(199\) −17.7008 −1.25477 −0.627387 0.778707i \(-0.715876\pi\)
−0.627387 + 0.778707i \(0.715876\pi\)
\(200\) 0 0
\(201\) −7.75213 −0.546793
\(202\) 0 0
\(203\) 3.74647 0.262950
\(204\) 0 0
\(205\) 3.20797 0.224054
\(206\) 0 0
\(207\) 1.65286 0.114882
\(208\) 0 0
\(209\) −7.49880 −0.518703
\(210\) 0 0
\(211\) 8.62214 0.593573 0.296786 0.954944i \(-0.404085\pi\)
0.296786 + 0.954944i \(0.404085\pi\)
\(212\) 0 0
\(213\) −0.867550 −0.0594435
\(214\) 0 0
\(215\) 10.5027 0.716276
\(216\) 0 0
\(217\) −3.08452 −0.209391
\(218\) 0 0
\(219\) 12.4200 0.839263
\(220\) 0 0
\(221\) 1.31143 0.0882162
\(222\) 0 0
\(223\) 12.0986 0.810185 0.405092 0.914276i \(-0.367239\pi\)
0.405092 + 0.914276i \(0.367239\pi\)
\(224\) 0 0
\(225\) −0.358130 −0.0238754
\(226\) 0 0
\(227\) −26.8451 −1.78177 −0.890887 0.454226i \(-0.849916\pi\)
−0.890887 + 0.454226i \(0.849916\pi\)
\(228\) 0 0
\(229\) −7.38780 −0.488200 −0.244100 0.969750i \(-0.578492\pi\)
−0.244100 + 0.969750i \(0.578492\pi\)
\(230\) 0 0
\(231\) 13.0691 0.859882
\(232\) 0 0
\(233\) −21.1908 −1.38825 −0.694127 0.719853i \(-0.744209\pi\)
−0.694127 + 0.719853i \(0.744209\pi\)
\(234\) 0 0
\(235\) −4.77104 −0.311228
\(236\) 0 0
\(237\) 15.6374 1.01576
\(238\) 0 0
\(239\) 5.29768 0.342678 0.171339 0.985212i \(-0.445191\pi\)
0.171339 + 0.985212i \(0.445191\pi\)
\(240\) 0 0
\(241\) 5.28096 0.340177 0.170088 0.985429i \(-0.445595\pi\)
0.170088 + 0.985429i \(0.445595\pi\)
\(242\) 0 0
\(243\) −3.70106 −0.237423
\(244\) 0 0
\(245\) −12.5503 −0.801810
\(246\) 0 0
\(247\) −4.38654 −0.279109
\(248\) 0 0
\(249\) 9.76920 0.619098
\(250\) 0 0
\(251\) 5.21532 0.329188 0.164594 0.986361i \(-0.447369\pi\)
0.164594 + 0.986361i \(0.447369\pi\)
\(252\) 0 0
\(253\) 8.39281 0.527651
\(254\) 0 0
\(255\) −2.00381 −0.125484
\(256\) 0 0
\(257\) −8.33349 −0.519829 −0.259914 0.965632i \(-0.583694\pi\)
−0.259914 + 0.965632i \(0.583694\pi\)
\(258\) 0 0
\(259\) 15.2700 0.948831
\(260\) 0 0
\(261\) −0.303449 −0.0187830
\(262\) 0 0
\(263\) 15.9773 0.985203 0.492601 0.870255i \(-0.336046\pi\)
0.492601 + 0.870255i \(0.336046\pi\)
\(264\) 0 0
\(265\) −3.05860 −0.187888
\(266\) 0 0
\(267\) 10.0965 0.617895
\(268\) 0 0
\(269\) 3.74626 0.228413 0.114207 0.993457i \(-0.463567\pi\)
0.114207 + 0.993457i \(0.463567\pi\)
\(270\) 0 0
\(271\) −13.8456 −0.841060 −0.420530 0.907279i \(-0.638156\pi\)
−0.420530 + 0.907279i \(0.638156\pi\)
\(272\) 0 0
\(273\) 7.64496 0.462694
\(274\) 0 0
\(275\) −1.81850 −0.109659
\(276\) 0 0
\(277\) 1.46676 0.0881289 0.0440645 0.999029i \(-0.485969\pi\)
0.0440645 + 0.999029i \(0.485969\pi\)
\(278\) 0 0
\(279\) 0.249834 0.0149572
\(280\) 0 0
\(281\) −29.0767 −1.73457 −0.867284 0.497813i \(-0.834136\pi\)
−0.867284 + 0.497813i \(0.834136\pi\)
\(282\) 0 0
\(283\) 25.6843 1.52678 0.763388 0.645941i \(-0.223535\pi\)
0.763388 + 0.645941i \(0.223535\pi\)
\(284\) 0 0
\(285\) 6.70247 0.397020
\(286\) 0 0
\(287\) −14.1843 −0.837272
\(288\) 0 0
\(289\) −15.4801 −0.910597
\(290\) 0 0
\(291\) −20.6180 −1.20865
\(292\) 0 0
\(293\) 5.96190 0.348298 0.174149 0.984719i \(-0.444283\pi\)
0.174149 + 0.984719i \(0.444283\pi\)
\(294\) 0 0
\(295\) 10.5261 0.612853
\(296\) 0 0
\(297\) −9.92581 −0.575954
\(298\) 0 0
\(299\) 4.90950 0.283924
\(300\) 0 0
\(301\) −46.4383 −2.67666
\(302\) 0 0
\(303\) 15.5486 0.893245
\(304\) 0 0
\(305\) −9.43455 −0.540220
\(306\) 0 0
\(307\) −5.14528 −0.293656 −0.146828 0.989162i \(-0.546906\pi\)
−0.146828 + 0.989162i \(0.546906\pi\)
\(308\) 0 0
\(309\) 15.5463 0.884399
\(310\) 0 0
\(311\) 1.26295 0.0716154 0.0358077 0.999359i \(-0.488600\pi\)
0.0358077 + 0.999359i \(0.488600\pi\)
\(312\) 0 0
\(313\) 13.8392 0.782239 0.391120 0.920340i \(-0.372088\pi\)
0.391120 + 0.920340i \(0.372088\pi\)
\(314\) 0 0
\(315\) 1.58350 0.0892201
\(316\) 0 0
\(317\) 4.93169 0.276991 0.138496 0.990363i \(-0.455773\pi\)
0.138496 + 0.990363i \(0.455773\pi\)
\(318\) 0 0
\(319\) −1.54084 −0.0862704
\(320\) 0 0
\(321\) −11.0186 −0.615001
\(322\) 0 0
\(323\) −5.08371 −0.282865
\(324\) 0 0
\(325\) −1.06376 −0.0590067
\(326\) 0 0
\(327\) −9.00121 −0.497768
\(328\) 0 0
\(329\) 21.0955 1.16303
\(330\) 0 0
\(331\) −10.4049 −0.571908 −0.285954 0.958243i \(-0.592310\pi\)
−0.285954 + 0.958243i \(0.592310\pi\)
\(332\) 0 0
\(333\) −1.23681 −0.0677768
\(334\) 0 0
\(335\) −4.76942 −0.260581
\(336\) 0 0
\(337\) −25.0621 −1.36522 −0.682610 0.730783i \(-0.739155\pi\)
−0.682610 + 0.730783i \(0.739155\pi\)
\(338\) 0 0
\(339\) 26.4517 1.43666
\(340\) 0 0
\(341\) 1.26859 0.0686983
\(342\) 0 0
\(343\) 24.5411 1.32510
\(344\) 0 0
\(345\) −7.50154 −0.403870
\(346\) 0 0
\(347\) 13.8943 0.745887 0.372943 0.927854i \(-0.378349\pi\)
0.372943 + 0.927854i \(0.378349\pi\)
\(348\) 0 0
\(349\) −11.8128 −0.632327 −0.316163 0.948705i \(-0.602395\pi\)
−0.316163 + 0.948705i \(0.602395\pi\)
\(350\) 0 0
\(351\) −5.80625 −0.309915
\(352\) 0 0
\(353\) −18.2525 −0.971485 −0.485743 0.874102i \(-0.661451\pi\)
−0.485743 + 0.874102i \(0.661451\pi\)
\(354\) 0 0
\(355\) −0.533751 −0.0283286
\(356\) 0 0
\(357\) 8.86001 0.468921
\(358\) 0 0
\(359\) −28.0793 −1.48197 −0.740986 0.671521i \(-0.765641\pi\)
−0.740986 + 0.671521i \(0.765641\pi\)
\(360\) 0 0
\(361\) −1.99572 −0.105038
\(362\) 0 0
\(363\) 12.5042 0.656299
\(364\) 0 0
\(365\) 7.64125 0.399961
\(366\) 0 0
\(367\) 0.686369 0.0358282 0.0179141 0.999840i \(-0.494297\pi\)
0.0179141 + 0.999840i \(0.494297\pi\)
\(368\) 0 0
\(369\) 1.14887 0.0598079
\(370\) 0 0
\(371\) 13.5238 0.702123
\(372\) 0 0
\(373\) −5.58581 −0.289222 −0.144611 0.989489i \(-0.546193\pi\)
−0.144611 + 0.989489i \(0.546193\pi\)
\(374\) 0 0
\(375\) 1.62538 0.0839344
\(376\) 0 0
\(377\) −0.901338 −0.0464213
\(378\) 0 0
\(379\) −9.47553 −0.486726 −0.243363 0.969935i \(-0.578251\pi\)
−0.243363 + 0.969935i \(0.578251\pi\)
\(380\) 0 0
\(381\) 2.49531 0.127838
\(382\) 0 0
\(383\) 3.02327 0.154482 0.0772409 0.997012i \(-0.475389\pi\)
0.0772409 + 0.997012i \(0.475389\pi\)
\(384\) 0 0
\(385\) 8.04062 0.409788
\(386\) 0 0
\(387\) 3.76132 0.191199
\(388\) 0 0
\(389\) −19.8063 −1.00422 −0.502109 0.864804i \(-0.667442\pi\)
−0.502109 + 0.864804i \(0.667442\pi\)
\(390\) 0 0
\(391\) 5.68979 0.287745
\(392\) 0 0
\(393\) −27.8148 −1.40307
\(394\) 0 0
\(395\) 9.62077 0.484073
\(396\) 0 0
\(397\) −23.0475 −1.15672 −0.578362 0.815781i \(-0.696308\pi\)
−0.578362 + 0.815781i \(0.696308\pi\)
\(398\) 0 0
\(399\) −29.6355 −1.48363
\(400\) 0 0
\(401\) 1.00000 0.0499376
\(402\) 0 0
\(403\) 0.742084 0.0369658
\(404\) 0 0
\(405\) 7.79735 0.387454
\(406\) 0 0
\(407\) −6.28021 −0.311299
\(408\) 0 0
\(409\) −29.1460 −1.44118 −0.720588 0.693363i \(-0.756128\pi\)
−0.720588 + 0.693363i \(0.756128\pi\)
\(410\) 0 0
\(411\) −33.8227 −1.66835
\(412\) 0 0
\(413\) −46.5419 −2.29018
\(414\) 0 0
\(415\) 6.01040 0.295039
\(416\) 0 0
\(417\) −2.46556 −0.120739
\(418\) 0 0
\(419\) −10.2572 −0.501096 −0.250548 0.968104i \(-0.580611\pi\)
−0.250548 + 0.968104i \(0.580611\pi\)
\(420\) 0 0
\(421\) −1.67406 −0.0815889 −0.0407945 0.999168i \(-0.512989\pi\)
−0.0407945 + 0.999168i \(0.512989\pi\)
\(422\) 0 0
\(423\) −1.70865 −0.0830776
\(424\) 0 0
\(425\) −1.23283 −0.0598008
\(426\) 0 0
\(427\) 41.7155 2.01876
\(428\) 0 0
\(429\) −3.14421 −0.151804
\(430\) 0 0
\(431\) −24.7069 −1.19009 −0.595045 0.803692i \(-0.702866\pi\)
−0.595045 + 0.803692i \(0.702866\pi\)
\(432\) 0 0
\(433\) 31.4314 1.51049 0.755247 0.655440i \(-0.227517\pi\)
0.755247 + 0.655440i \(0.227517\pi\)
\(434\) 0 0
\(435\) 1.37721 0.0660322
\(436\) 0 0
\(437\) −19.0315 −0.910402
\(438\) 0 0
\(439\) −14.9372 −0.712914 −0.356457 0.934312i \(-0.616015\pi\)
−0.356457 + 0.934312i \(0.616015\pi\)
\(440\) 0 0
\(441\) −4.49465 −0.214031
\(442\) 0 0
\(443\) 0.673491 0.0319985 0.0159993 0.999872i \(-0.494907\pi\)
0.0159993 + 0.999872i \(0.494907\pi\)
\(444\) 0 0
\(445\) 6.21176 0.294466
\(446\) 0 0
\(447\) −36.5062 −1.72668
\(448\) 0 0
\(449\) −8.62968 −0.407260 −0.203630 0.979048i \(-0.565274\pi\)
−0.203630 + 0.979048i \(0.565274\pi\)
\(450\) 0 0
\(451\) 5.83368 0.274697
\(452\) 0 0
\(453\) −32.0059 −1.50377
\(454\) 0 0
\(455\) 4.70348 0.220503
\(456\) 0 0
\(457\) −30.5412 −1.42866 −0.714329 0.699810i \(-0.753268\pi\)
−0.714329 + 0.699810i \(0.753268\pi\)
\(458\) 0 0
\(459\) −6.72907 −0.314086
\(460\) 0 0
\(461\) −20.8363 −0.970444 −0.485222 0.874391i \(-0.661261\pi\)
−0.485222 + 0.874391i \(0.661261\pi\)
\(462\) 0 0
\(463\) 11.9447 0.555118 0.277559 0.960709i \(-0.410475\pi\)
0.277559 + 0.960709i \(0.410475\pi\)
\(464\) 0 0
\(465\) −1.13388 −0.0525823
\(466\) 0 0
\(467\) −20.9025 −0.967253 −0.483627 0.875274i \(-0.660681\pi\)
−0.483627 + 0.875274i \(0.660681\pi\)
\(468\) 0 0
\(469\) 21.0883 0.973769
\(470\) 0 0
\(471\) −3.32938 −0.153410
\(472\) 0 0
\(473\) 19.0991 0.878175
\(474\) 0 0
\(475\) 4.12363 0.189205
\(476\) 0 0
\(477\) −1.09538 −0.0501539
\(478\) 0 0
\(479\) 28.5391 1.30398 0.651992 0.758226i \(-0.273934\pi\)
0.651992 + 0.758226i \(0.273934\pi\)
\(480\) 0 0
\(481\) −3.67371 −0.167507
\(482\) 0 0
\(483\) 33.1686 1.50922
\(484\) 0 0
\(485\) −12.6850 −0.575997
\(486\) 0 0
\(487\) 25.1344 1.13895 0.569473 0.822010i \(-0.307147\pi\)
0.569473 + 0.822010i \(0.307147\pi\)
\(488\) 0 0
\(489\) 6.49194 0.293576
\(490\) 0 0
\(491\) −43.2133 −1.95019 −0.975093 0.221794i \(-0.928809\pi\)
−0.975093 + 0.221794i \(0.928809\pi\)
\(492\) 0 0
\(493\) −1.04459 −0.0470460
\(494\) 0 0
\(495\) −0.651259 −0.0292719
\(496\) 0 0
\(497\) 2.36002 0.105861
\(498\) 0 0
\(499\) 30.2184 1.35276 0.676381 0.736552i \(-0.263547\pi\)
0.676381 + 0.736552i \(0.263547\pi\)
\(500\) 0 0
\(501\) 24.9488 1.11463
\(502\) 0 0
\(503\) −24.5662 −1.09535 −0.547676 0.836690i \(-0.684488\pi\)
−0.547676 + 0.836690i \(0.684488\pi\)
\(504\) 0 0
\(505\) 9.56613 0.425687
\(506\) 0 0
\(507\) 19.2907 0.856731
\(508\) 0 0
\(509\) −14.2824 −0.633057 −0.316529 0.948583i \(-0.602517\pi\)
−0.316529 + 0.948583i \(0.602517\pi\)
\(510\) 0 0
\(511\) −33.7864 −1.49462
\(512\) 0 0
\(513\) 22.5078 0.993742
\(514\) 0 0
\(515\) 9.56470 0.421471
\(516\) 0 0
\(517\) −8.67612 −0.381575
\(518\) 0 0
\(519\) 39.5098 1.73429
\(520\) 0 0
\(521\) −28.8306 −1.26309 −0.631545 0.775339i \(-0.717579\pi\)
−0.631545 + 0.775339i \(0.717579\pi\)
\(522\) 0 0
\(523\) 25.7614 1.12647 0.563234 0.826297i \(-0.309557\pi\)
0.563234 + 0.826297i \(0.309557\pi\)
\(524\) 0 0
\(525\) −7.18675 −0.313656
\(526\) 0 0
\(527\) 0.860027 0.0374634
\(528\) 0 0
\(529\) −1.69950 −0.0738912
\(530\) 0 0
\(531\) 3.76972 0.163592
\(532\) 0 0
\(533\) 3.41250 0.147812
\(534\) 0 0
\(535\) −6.77911 −0.293086
\(536\) 0 0
\(537\) −8.48338 −0.366085
\(538\) 0 0
\(539\) −22.8227 −0.983044
\(540\) 0 0
\(541\) −29.2832 −1.25898 −0.629492 0.777007i \(-0.716737\pi\)
−0.629492 + 0.777007i \(0.716737\pi\)
\(542\) 0 0
\(543\) −12.1072 −0.519568
\(544\) 0 0
\(545\) −5.53790 −0.237218
\(546\) 0 0
\(547\) −19.2524 −0.823175 −0.411587 0.911370i \(-0.635025\pi\)
−0.411587 + 0.911370i \(0.635025\pi\)
\(548\) 0 0
\(549\) −3.37880 −0.144204
\(550\) 0 0
\(551\) 3.49401 0.148850
\(552\) 0 0
\(553\) −42.5389 −1.80894
\(554\) 0 0
\(555\) 5.61329 0.238271
\(556\) 0 0
\(557\) 14.8252 0.628162 0.314081 0.949396i \(-0.398304\pi\)
0.314081 + 0.949396i \(0.398304\pi\)
\(558\) 0 0
\(559\) 11.1723 0.472537
\(560\) 0 0
\(561\) −3.64393 −0.153847
\(562\) 0 0
\(563\) −13.0922 −0.551770 −0.275885 0.961191i \(-0.588971\pi\)
−0.275885 + 0.961191i \(0.588971\pi\)
\(564\) 0 0
\(565\) 16.2741 0.684658
\(566\) 0 0
\(567\) −34.4766 −1.44788
\(568\) 0 0
\(569\) 21.4256 0.898207 0.449104 0.893480i \(-0.351743\pi\)
0.449104 + 0.893480i \(0.351743\pi\)
\(570\) 0 0
\(571\) 14.6522 0.613175 0.306587 0.951843i \(-0.400813\pi\)
0.306587 + 0.951843i \(0.400813\pi\)
\(572\) 0 0
\(573\) 17.0162 0.710863
\(574\) 0 0
\(575\) −4.61525 −0.192469
\(576\) 0 0
\(577\) −5.21697 −0.217185 −0.108593 0.994086i \(-0.534634\pi\)
−0.108593 + 0.994086i \(0.534634\pi\)
\(578\) 0 0
\(579\) −4.47180 −0.185842
\(580\) 0 0
\(581\) −26.5754 −1.10253
\(582\) 0 0
\(583\) −5.56206 −0.230357
\(584\) 0 0
\(585\) −0.380964 −0.0157509
\(586\) 0 0
\(587\) 36.5655 1.50922 0.754611 0.656173i \(-0.227826\pi\)
0.754611 + 0.656173i \(0.227826\pi\)
\(588\) 0 0
\(589\) −2.87667 −0.118531
\(590\) 0 0
\(591\) −2.64535 −0.108815
\(592\) 0 0
\(593\) −33.1765 −1.36239 −0.681197 0.732100i \(-0.738540\pi\)
−0.681197 + 0.732100i \(0.738540\pi\)
\(594\) 0 0
\(595\) 5.45103 0.223470
\(596\) 0 0
\(597\) 28.7705 1.17750
\(598\) 0 0
\(599\) −9.54284 −0.389910 −0.194955 0.980812i \(-0.562456\pi\)
−0.194955 + 0.980812i \(0.562456\pi\)
\(600\) 0 0
\(601\) −36.3137 −1.48127 −0.740634 0.671909i \(-0.765475\pi\)
−0.740634 + 0.671909i \(0.765475\pi\)
\(602\) 0 0
\(603\) −1.70807 −0.0695581
\(604\) 0 0
\(605\) 7.69307 0.312768
\(606\) 0 0
\(607\) −22.7975 −0.925321 −0.462660 0.886536i \(-0.653105\pi\)
−0.462660 + 0.886536i \(0.653105\pi\)
\(608\) 0 0
\(609\) −6.08944 −0.246757
\(610\) 0 0
\(611\) −5.07523 −0.205322
\(612\) 0 0
\(613\) −14.7378 −0.595254 −0.297627 0.954682i \(-0.596195\pi\)
−0.297627 + 0.954682i \(0.596195\pi\)
\(614\) 0 0
\(615\) −5.21418 −0.210256
\(616\) 0 0
\(617\) 10.0465 0.404456 0.202228 0.979338i \(-0.435182\pi\)
0.202228 + 0.979338i \(0.435182\pi\)
\(618\) 0 0
\(619\) −41.3237 −1.66094 −0.830469 0.557065i \(-0.811928\pi\)
−0.830469 + 0.557065i \(0.811928\pi\)
\(620\) 0 0
\(621\) −25.1912 −1.01089
\(622\) 0 0
\(623\) −27.4657 −1.10039
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 12.1884 0.486759
\(628\) 0 0
\(629\) −4.25759 −0.169761
\(630\) 0 0
\(631\) 32.4599 1.29221 0.646105 0.763249i \(-0.276397\pi\)
0.646105 + 0.763249i \(0.276397\pi\)
\(632\) 0 0
\(633\) −14.0143 −0.557018
\(634\) 0 0
\(635\) 1.53521 0.0609230
\(636\) 0 0
\(637\) −13.3505 −0.528966
\(638\) 0 0
\(639\) −0.191152 −0.00756187
\(640\) 0 0
\(641\) −3.29789 −0.130259 −0.0651293 0.997877i \(-0.520746\pi\)
−0.0651293 + 0.997877i \(0.520746\pi\)
\(642\) 0 0
\(643\) −6.89098 −0.271754 −0.135877 0.990726i \(-0.543385\pi\)
−0.135877 + 0.990726i \(0.543385\pi\)
\(644\) 0 0
\(645\) −17.0708 −0.672164
\(646\) 0 0
\(647\) −8.35604 −0.328510 −0.164255 0.986418i \(-0.552522\pi\)
−0.164255 + 0.986418i \(0.552522\pi\)
\(648\) 0 0
\(649\) 19.1417 0.751376
\(650\) 0 0
\(651\) 5.01352 0.196495
\(652\) 0 0
\(653\) 34.1612 1.33683 0.668416 0.743788i \(-0.266973\pi\)
0.668416 + 0.743788i \(0.266973\pi\)
\(654\) 0 0
\(655\) −17.1128 −0.668652
\(656\) 0 0
\(657\) 2.73656 0.106764
\(658\) 0 0
\(659\) 19.9226 0.776074 0.388037 0.921644i \(-0.373153\pi\)
0.388037 + 0.921644i \(0.373153\pi\)
\(660\) 0 0
\(661\) 41.8320 1.62708 0.813539 0.581511i \(-0.197538\pi\)
0.813539 + 0.581511i \(0.197538\pi\)
\(662\) 0 0
\(663\) −2.13157 −0.0827834
\(664\) 0 0
\(665\) −18.2329 −0.707042
\(666\) 0 0
\(667\) −3.91057 −0.151418
\(668\) 0 0
\(669\) −19.6649 −0.760290
\(670\) 0 0
\(671\) −17.1567 −0.662327
\(672\) 0 0
\(673\) −5.82606 −0.224578 −0.112289 0.993676i \(-0.535818\pi\)
−0.112289 + 0.993676i \(0.535818\pi\)
\(674\) 0 0
\(675\) 5.45825 0.210088
\(676\) 0 0
\(677\) −13.8212 −0.531193 −0.265596 0.964084i \(-0.585569\pi\)
−0.265596 + 0.964084i \(0.585569\pi\)
\(678\) 0 0
\(679\) 56.0877 2.15245
\(680\) 0 0
\(681\) 43.6336 1.67204
\(682\) 0 0
\(683\) −5.57951 −0.213494 −0.106747 0.994286i \(-0.534043\pi\)
−0.106747 + 0.994286i \(0.534043\pi\)
\(684\) 0 0
\(685\) −20.8091 −0.795075
\(686\) 0 0
\(687\) 12.0080 0.458134
\(688\) 0 0
\(689\) −3.25361 −0.123953
\(690\) 0 0
\(691\) −40.4727 −1.53965 −0.769826 0.638254i \(-0.779657\pi\)
−0.769826 + 0.638254i \(0.779657\pi\)
\(692\) 0 0
\(693\) 2.87959 0.109387
\(694\) 0 0
\(695\) −1.51691 −0.0575396
\(696\) 0 0
\(697\) 3.95487 0.149801
\(698\) 0 0
\(699\) 34.4431 1.30276
\(700\) 0 0
\(701\) −19.7507 −0.745975 −0.372987 0.927836i \(-0.621666\pi\)
−0.372987 + 0.927836i \(0.621666\pi\)
\(702\) 0 0
\(703\) 14.2410 0.537110
\(704\) 0 0
\(705\) 7.75477 0.292061
\(706\) 0 0
\(707\) −42.2973 −1.59076
\(708\) 0 0
\(709\) −25.3283 −0.951222 −0.475611 0.879656i \(-0.657773\pi\)
−0.475611 + 0.879656i \(0.657773\pi\)
\(710\) 0 0
\(711\) 3.44549 0.129216
\(712\) 0 0
\(713\) 3.21963 0.120576
\(714\) 0 0
\(715\) −1.93444 −0.0723440
\(716\) 0 0
\(717\) −8.61075 −0.321574
\(718\) 0 0
\(719\) −7.17722 −0.267665 −0.133833 0.991004i \(-0.542728\pi\)
−0.133833 + 0.991004i \(0.542728\pi\)
\(720\) 0 0
\(721\) −42.2910 −1.57500
\(722\) 0 0
\(723\) −8.58359 −0.319227
\(724\) 0 0
\(725\) 0.847315 0.0314685
\(726\) 0 0
\(727\) 27.7846 1.03047 0.515237 0.857048i \(-0.327704\pi\)
0.515237 + 0.857048i \(0.327704\pi\)
\(728\) 0 0
\(729\) 29.4077 1.08917
\(730\) 0 0
\(731\) 12.9479 0.478897
\(732\) 0 0
\(733\) −23.5720 −0.870653 −0.435327 0.900273i \(-0.643367\pi\)
−0.435327 + 0.900273i \(0.643367\pi\)
\(734\) 0 0
\(735\) 20.3991 0.752431
\(736\) 0 0
\(737\) −8.67317 −0.319480
\(738\) 0 0
\(739\) −48.1819 −1.77240 −0.886200 0.463303i \(-0.846664\pi\)
−0.886200 + 0.463303i \(0.846664\pi\)
\(740\) 0 0
\(741\) 7.12980 0.261920
\(742\) 0 0
\(743\) 24.9637 0.915830 0.457915 0.888996i \(-0.348596\pi\)
0.457915 + 0.888996i \(0.348596\pi\)
\(744\) 0 0
\(745\) −22.4601 −0.822873
\(746\) 0 0
\(747\) 2.15251 0.0787561
\(748\) 0 0
\(749\) 29.9743 1.09524
\(750\) 0 0
\(751\) −3.31934 −0.121125 −0.0605623 0.998164i \(-0.519289\pi\)
−0.0605623 + 0.998164i \(0.519289\pi\)
\(752\) 0 0
\(753\) −8.47690 −0.308915
\(754\) 0 0
\(755\) −19.6913 −0.716640
\(756\) 0 0
\(757\) 29.4811 1.07151 0.535754 0.844374i \(-0.320028\pi\)
0.535754 + 0.844374i \(0.320028\pi\)
\(758\) 0 0
\(759\) −13.6415 −0.495156
\(760\) 0 0
\(761\) −17.4559 −0.632777 −0.316388 0.948630i \(-0.602470\pi\)
−0.316388 + 0.948630i \(0.602470\pi\)
\(762\) 0 0
\(763\) 24.4863 0.886462
\(764\) 0 0
\(765\) −0.441512 −0.0159629
\(766\) 0 0
\(767\) 11.1972 0.404308
\(768\) 0 0
\(769\) 18.1727 0.655325 0.327662 0.944795i \(-0.393739\pi\)
0.327662 + 0.944795i \(0.393739\pi\)
\(770\) 0 0
\(771\) 13.5451 0.487815
\(772\) 0 0
\(773\) 33.8354 1.21697 0.608487 0.793564i \(-0.291777\pi\)
0.608487 + 0.793564i \(0.291777\pi\)
\(774\) 0 0
\(775\) −0.697606 −0.0250588
\(776\) 0 0
\(777\) −24.8196 −0.890397
\(778\) 0 0
\(779\) −13.2285 −0.473959
\(780\) 0 0
\(781\) −0.970624 −0.0347317
\(782\) 0 0
\(783\) 4.62485 0.165279
\(784\) 0 0
\(785\) −2.04837 −0.0731094
\(786\) 0 0
\(787\) 9.92229 0.353692 0.176846 0.984239i \(-0.443411\pi\)
0.176846 + 0.984239i \(0.443411\pi\)
\(788\) 0 0
\(789\) −25.9692 −0.924529
\(790\) 0 0
\(791\) −71.9573 −2.55851
\(792\) 0 0
\(793\) −10.0361 −0.356391
\(794\) 0 0
\(795\) 4.97140 0.176317
\(796\) 0 0
\(797\) −28.2666 −1.00126 −0.500628 0.865663i \(-0.666897\pi\)
−0.500628 + 0.865663i \(0.666897\pi\)
\(798\) 0 0
\(799\) −5.88186 −0.208085
\(800\) 0 0
\(801\) 2.22462 0.0786030
\(802\) 0 0
\(803\) 13.8956 0.490365
\(804\) 0 0
\(805\) 20.4067 0.719240
\(806\) 0 0
\(807\) −6.08910 −0.214346
\(808\) 0 0
\(809\) −39.7494 −1.39752 −0.698758 0.715358i \(-0.746264\pi\)
−0.698758 + 0.715358i \(0.746264\pi\)
\(810\) 0 0
\(811\) 5.60060 0.196664 0.0983319 0.995154i \(-0.468649\pi\)
0.0983319 + 0.995154i \(0.468649\pi\)
\(812\) 0 0
\(813\) 22.5044 0.789264
\(814\) 0 0
\(815\) 3.99410 0.139907
\(816\) 0 0
\(817\) −43.3090 −1.51519
\(818\) 0 0
\(819\) 1.68446 0.0588598
\(820\) 0 0
\(821\) −29.6542 −1.03494 −0.517469 0.855702i \(-0.673126\pi\)
−0.517469 + 0.855702i \(0.673126\pi\)
\(822\) 0 0
\(823\) −12.4945 −0.435531 −0.217765 0.976001i \(-0.569877\pi\)
−0.217765 + 0.976001i \(0.569877\pi\)
\(824\) 0 0
\(825\) 2.95575 0.102906
\(826\) 0 0
\(827\) −33.2840 −1.15740 −0.578700 0.815541i \(-0.696440\pi\)
−0.578700 + 0.815541i \(0.696440\pi\)
\(828\) 0 0
\(829\) −33.0337 −1.14731 −0.573654 0.819098i \(-0.694474\pi\)
−0.573654 + 0.819098i \(0.694474\pi\)
\(830\) 0 0
\(831\) −2.38404 −0.0827015
\(832\) 0 0
\(833\) −15.4723 −0.536085
\(834\) 0 0
\(835\) 15.3495 0.531191
\(836\) 0 0
\(837\) −3.80771 −0.131614
\(838\) 0 0
\(839\) −23.3786 −0.807120 −0.403560 0.914953i \(-0.632227\pi\)
−0.403560 + 0.914953i \(0.632227\pi\)
\(840\) 0 0
\(841\) −28.2821 −0.975243
\(842\) 0 0
\(843\) 47.2607 1.62775
\(844\) 0 0
\(845\) 11.8684 0.408286
\(846\) 0 0
\(847\) −34.0155 −1.16879
\(848\) 0 0
\(849\) −41.7469 −1.43275
\(850\) 0 0
\(851\) −15.9388 −0.546376
\(852\) 0 0
\(853\) 32.9431 1.12795 0.563975 0.825792i \(-0.309271\pi\)
0.563975 + 0.825792i \(0.309271\pi\)
\(854\) 0 0
\(855\) 1.47680 0.0505053
\(856\) 0 0
\(857\) 7.72706 0.263951 0.131976 0.991253i \(-0.457868\pi\)
0.131976 + 0.991253i \(0.457868\pi\)
\(858\) 0 0
\(859\) −21.8310 −0.744863 −0.372431 0.928060i \(-0.621476\pi\)
−0.372431 + 0.928060i \(0.621476\pi\)
\(860\) 0 0
\(861\) 23.0549 0.785709
\(862\) 0 0
\(863\) −24.3905 −0.830263 −0.415131 0.909761i \(-0.636264\pi\)
−0.415131 + 0.909761i \(0.636264\pi\)
\(864\) 0 0
\(865\) 24.3080 0.826496
\(866\) 0 0
\(867\) 25.1612 0.854518
\(868\) 0 0
\(869\) 17.4953 0.593489
\(870\) 0 0
\(871\) −5.07350 −0.171909
\(872\) 0 0
\(873\) −4.54289 −0.153753
\(874\) 0 0
\(875\) −4.42157 −0.149476
\(876\) 0 0
\(877\) −5.89927 −0.199204 −0.0996021 0.995027i \(-0.531757\pi\)
−0.0996021 + 0.995027i \(0.531757\pi\)
\(878\) 0 0
\(879\) −9.69038 −0.326848
\(880\) 0 0
\(881\) 16.9087 0.569668 0.284834 0.958577i \(-0.408061\pi\)
0.284834 + 0.958577i \(0.408061\pi\)
\(882\) 0 0
\(883\) 26.9248 0.906091 0.453046 0.891487i \(-0.350337\pi\)
0.453046 + 0.891487i \(0.350337\pi\)
\(884\) 0 0
\(885\) −17.1089 −0.575111
\(886\) 0 0
\(887\) 35.5378 1.19324 0.596621 0.802523i \(-0.296510\pi\)
0.596621 + 0.802523i \(0.296510\pi\)
\(888\) 0 0
\(889\) −6.78805 −0.227664
\(890\) 0 0
\(891\) 14.1795 0.475030
\(892\) 0 0
\(893\) 19.6740 0.658365
\(894\) 0 0
\(895\) −5.21931 −0.174462
\(896\) 0 0
\(897\) −7.97982 −0.266439
\(898\) 0 0
\(899\) −0.591092 −0.0197140
\(900\) 0 0
\(901\) −3.77072 −0.125621
\(902\) 0 0
\(903\) 75.4800 2.51182
\(904\) 0 0
\(905\) −7.44881 −0.247607
\(906\) 0 0
\(907\) 1.02937 0.0341796 0.0170898 0.999854i \(-0.494560\pi\)
0.0170898 + 0.999854i \(0.494560\pi\)
\(908\) 0 0
\(909\) 3.42592 0.113631
\(910\) 0 0
\(911\) 14.9038 0.493785 0.246893 0.969043i \(-0.420591\pi\)
0.246893 + 0.969043i \(0.420591\pi\)
\(912\) 0 0
\(913\) 10.9299 0.361727
\(914\) 0 0
\(915\) 15.3347 0.506951
\(916\) 0 0
\(917\) 75.6655 2.49869
\(918\) 0 0
\(919\) −8.36916 −0.276073 −0.138037 0.990427i \(-0.544079\pi\)
−0.138037 + 0.990427i \(0.544079\pi\)
\(920\) 0 0
\(921\) 8.36305 0.275572
\(922\) 0 0
\(923\) −0.567782 −0.0186888
\(924\) 0 0
\(925\) 3.45352 0.113551
\(926\) 0 0
\(927\) 3.42541 0.112505
\(928\) 0 0
\(929\) −43.9155 −1.44082 −0.720410 0.693548i \(-0.756046\pi\)
−0.720410 + 0.693548i \(0.756046\pi\)
\(930\) 0 0
\(931\) 51.7528 1.69613
\(932\) 0 0
\(933\) −2.05278 −0.0672049
\(934\) 0 0
\(935\) −2.24189 −0.0733176
\(936\) 0 0
\(937\) 42.5033 1.38852 0.694261 0.719724i \(-0.255731\pi\)
0.694261 + 0.719724i \(0.255731\pi\)
\(938\) 0 0
\(939\) −22.4940 −0.734065
\(940\) 0 0
\(941\) −19.9326 −0.649783 −0.324891 0.945751i \(-0.605328\pi\)
−0.324891 + 0.945751i \(0.605328\pi\)
\(942\) 0 0
\(943\) 14.8056 0.482136
\(944\) 0 0
\(945\) −24.1340 −0.785081
\(946\) 0 0
\(947\) −39.7373 −1.29129 −0.645644 0.763639i \(-0.723411\pi\)
−0.645644 + 0.763639i \(0.723411\pi\)
\(948\) 0 0
\(949\) 8.12844 0.263860
\(950\) 0 0
\(951\) −8.01589 −0.259933
\(952\) 0 0
\(953\) 6.10032 0.197609 0.0988044 0.995107i \(-0.468498\pi\)
0.0988044 + 0.995107i \(0.468498\pi\)
\(954\) 0 0
\(955\) 10.4691 0.338771
\(956\) 0 0
\(957\) 2.50445 0.0809575
\(958\) 0 0
\(959\) 92.0089 2.97112
\(960\) 0 0
\(961\) −30.5133 −0.984301
\(962\) 0 0
\(963\) −2.42781 −0.0782349
\(964\) 0 0
\(965\) −2.75123 −0.0885652
\(966\) 0 0
\(967\) −21.4093 −0.688478 −0.344239 0.938882i \(-0.611863\pi\)
−0.344239 + 0.938882i \(0.611863\pi\)
\(968\) 0 0
\(969\) 8.26298 0.265445
\(970\) 0 0
\(971\) 19.5770 0.628256 0.314128 0.949381i \(-0.398288\pi\)
0.314128 + 0.949381i \(0.398288\pi\)
\(972\) 0 0
\(973\) 6.70712 0.215020
\(974\) 0 0
\(975\) 1.72901 0.0553728
\(976\) 0 0
\(977\) 21.0987 0.675009 0.337504 0.941324i \(-0.390417\pi\)
0.337504 + 0.941324i \(0.390417\pi\)
\(978\) 0 0
\(979\) 11.2961 0.361024
\(980\) 0 0
\(981\) −1.98329 −0.0633216
\(982\) 0 0
\(983\) 22.5009 0.717667 0.358834 0.933402i \(-0.383175\pi\)
0.358834 + 0.933402i \(0.383175\pi\)
\(984\) 0 0
\(985\) −1.62752 −0.0518572
\(986\) 0 0
\(987\) −34.2883 −1.09141
\(988\) 0 0
\(989\) 48.4724 1.54133
\(990\) 0 0
\(991\) 25.6980 0.816322 0.408161 0.912910i \(-0.366170\pi\)
0.408161 + 0.912910i \(0.366170\pi\)
\(992\) 0 0
\(993\) 16.9120 0.536687
\(994\) 0 0
\(995\) 17.7008 0.561152
\(996\) 0 0
\(997\) 50.6604 1.60443 0.802216 0.597034i \(-0.203654\pi\)
0.802216 + 0.597034i \(0.203654\pi\)
\(998\) 0 0
\(999\) 18.8502 0.596393
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 \(a_p\))