Properties

Label 8020.2.a.c.1.20
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 1.20
Character \(\chi\) = 8020.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.67955 q^{3}\) \(-1.00000 q^{5}\) \(-2.58133 q^{7}\) \(-0.179108 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.67955 q^{3}\) \(-1.00000 q^{5}\) \(-2.58133 q^{7}\) \(-0.179108 q^{9}\) \(+4.59416 q^{11}\) \(+6.44343 q^{13}\) \(-1.67955 q^{15}\) \(+3.22423 q^{17}\) \(-7.28131 q^{19}\) \(-4.33547 q^{21}\) \(-7.91521 q^{23}\) \(+1.00000 q^{25}\) \(-5.33947 q^{27}\) \(-9.25560 q^{29}\) \(-3.08945 q^{31}\) \(+7.71613 q^{33}\) \(+2.58133 q^{35}\) \(+2.24163 q^{37}\) \(+10.8221 q^{39}\) \(+2.13339 q^{41}\) \(+7.12005 q^{43}\) \(+0.179108 q^{45}\) \(-1.12364 q^{47}\) \(-0.336745 q^{49}\) \(+5.41526 q^{51}\) \(-13.2332 q^{53}\) \(-4.59416 q^{55}\) \(-12.2293 q^{57}\) \(+3.97345 q^{59}\) \(+8.25721 q^{61}\) \(+0.462336 q^{63}\) \(-6.44343 q^{65}\) \(+0.637996 q^{67}\) \(-13.2940 q^{69}\) \(-3.08049 q^{71}\) \(-5.63615 q^{73}\) \(+1.67955 q^{75}\) \(-11.8590 q^{77}\) \(+8.87088 q^{79}\) \(-8.43060 q^{81}\) \(+12.7834 q^{83}\) \(-3.22423 q^{85}\) \(-15.5453 q^{87}\) \(+5.95597 q^{89}\) \(-16.6326 q^{91}\) \(-5.18889 q^{93}\) \(+7.28131 q^{95}\) \(-15.2444 q^{97}\) \(-0.822850 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 3q^{13} \) \(\mathstrut -\mathstrut 3q^{15} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut +\mathstrut 28q^{25} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut -\mathstrut 37q^{29} \) \(\mathstrut -\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 2q^{33} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut -\mathstrut 3q^{37} \) \(\mathstrut -\mathstrut 19q^{39} \) \(\mathstrut -\mathstrut 30q^{41} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut -\mathstrut 17q^{45} \) \(\mathstrut -\mathstrut 15q^{47} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 2q^{55} \) \(\mathstrut -\mathstrut 22q^{57} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut -\mathstrut 33q^{61} \) \(\mathstrut -\mathstrut 20q^{63} \) \(\mathstrut -\mathstrut 3q^{65} \) \(\mathstrut +\mathstrut 19q^{67} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut -\mathstrut 42q^{77} \) \(\mathstrut -\mathstrut 29q^{79} \) \(\mathstrut -\mathstrut 36q^{81} \) \(\mathstrut +\mathstrut 14q^{83} \) \(\mathstrut +\mathstrut 10q^{85} \) \(\mathstrut -\mathstrut 32q^{87} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 7q^{91} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 39q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.67955 0.969689 0.484845 0.874600i \(-0.338876\pi\)
0.484845 + 0.874600i \(0.338876\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −2.58133 −0.975650 −0.487825 0.872941i \(-0.662210\pi\)
−0.487825 + 0.872941i \(0.662210\pi\)
\(8\) 0 0
\(9\) −0.179108 −0.0597026
\(10\) 0 0
\(11\) 4.59416 1.38519 0.692596 0.721326i \(-0.256467\pi\)
0.692596 + 0.721326i \(0.256467\pi\)
\(12\) 0 0
\(13\) 6.44343 1.78709 0.893543 0.448978i \(-0.148212\pi\)
0.893543 + 0.448978i \(0.148212\pi\)
\(14\) 0 0
\(15\) −1.67955 −0.433658
\(16\) 0 0
\(17\) 3.22423 0.781990 0.390995 0.920393i \(-0.372131\pi\)
0.390995 + 0.920393i \(0.372131\pi\)
\(18\) 0 0
\(19\) −7.28131 −1.67045 −0.835224 0.549910i \(-0.814662\pi\)
−0.835224 + 0.549910i \(0.814662\pi\)
\(20\) 0 0
\(21\) −4.33547 −0.946078
\(22\) 0 0
\(23\) −7.91521 −1.65044 −0.825218 0.564815i \(-0.808948\pi\)
−0.825218 + 0.564815i \(0.808948\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −5.33947 −1.02758
\(28\) 0 0
\(29\) −9.25560 −1.71872 −0.859361 0.511369i \(-0.829139\pi\)
−0.859361 + 0.511369i \(0.829139\pi\)
\(30\) 0 0
\(31\) −3.08945 −0.554882 −0.277441 0.960743i \(-0.589486\pi\)
−0.277441 + 0.960743i \(0.589486\pi\)
\(32\) 0 0
\(33\) 7.71613 1.34321
\(34\) 0 0
\(35\) 2.58133 0.436324
\(36\) 0 0
\(37\) 2.24163 0.368521 0.184260 0.982877i \(-0.441011\pi\)
0.184260 + 0.982877i \(0.441011\pi\)
\(38\) 0 0
\(39\) 10.8221 1.73292
\(40\) 0 0
\(41\) 2.13339 0.333179 0.166589 0.986026i \(-0.446725\pi\)
0.166589 + 0.986026i \(0.446725\pi\)
\(42\) 0 0
\(43\) 7.12005 1.08580 0.542898 0.839798i \(-0.317327\pi\)
0.542898 + 0.839798i \(0.317327\pi\)
\(44\) 0 0
\(45\) 0.179108 0.0266998
\(46\) 0 0
\(47\) −1.12364 −0.163899 −0.0819497 0.996636i \(-0.526115\pi\)
−0.0819497 + 0.996636i \(0.526115\pi\)
\(48\) 0 0
\(49\) −0.336745 −0.0481064
\(50\) 0 0
\(51\) 5.41526 0.758288
\(52\) 0 0
\(53\) −13.2332 −1.81772 −0.908858 0.417106i \(-0.863044\pi\)
−0.908858 + 0.417106i \(0.863044\pi\)
\(54\) 0 0
\(55\) −4.59416 −0.619476
\(56\) 0 0
\(57\) −12.2293 −1.61982
\(58\) 0 0
\(59\) 3.97345 0.517299 0.258650 0.965971i \(-0.416723\pi\)
0.258650 + 0.965971i \(0.416723\pi\)
\(60\) 0 0
\(61\) 8.25721 1.05723 0.528614 0.848862i \(-0.322712\pi\)
0.528614 + 0.848862i \(0.322712\pi\)
\(62\) 0 0
\(63\) 0.462336 0.0582489
\(64\) 0 0
\(65\) −6.44343 −0.799209
\(66\) 0 0
\(67\) 0.637996 0.0779436 0.0389718 0.999240i \(-0.487592\pi\)
0.0389718 + 0.999240i \(0.487592\pi\)
\(68\) 0 0
\(69\) −13.2940 −1.60041
\(70\) 0 0
\(71\) −3.08049 −0.365587 −0.182794 0.983151i \(-0.558514\pi\)
−0.182794 + 0.983151i \(0.558514\pi\)
\(72\) 0 0
\(73\) −5.63615 −0.659661 −0.329831 0.944040i \(-0.606992\pi\)
−0.329831 + 0.944040i \(0.606992\pi\)
\(74\) 0 0
\(75\) 1.67955 0.193938
\(76\) 0 0
\(77\) −11.8590 −1.35146
\(78\) 0 0
\(79\) 8.87088 0.998052 0.499026 0.866587i \(-0.333691\pi\)
0.499026 + 0.866587i \(0.333691\pi\)
\(80\) 0 0
\(81\) −8.43060 −0.936733
\(82\) 0 0
\(83\) 12.7834 1.40316 0.701578 0.712593i \(-0.252479\pi\)
0.701578 + 0.712593i \(0.252479\pi\)
\(84\) 0 0
\(85\) −3.22423 −0.349717
\(86\) 0 0
\(87\) −15.5453 −1.66663
\(88\) 0 0
\(89\) 5.95597 0.631332 0.315666 0.948870i \(-0.397772\pi\)
0.315666 + 0.948870i \(0.397772\pi\)
\(90\) 0 0
\(91\) −16.6326 −1.74357
\(92\) 0 0
\(93\) −5.18889 −0.538063
\(94\) 0 0
\(95\) 7.28131 0.747047
\(96\) 0 0
\(97\) −15.2444 −1.54784 −0.773918 0.633286i \(-0.781706\pi\)
−0.773918 + 0.633286i \(0.781706\pi\)
\(98\) 0 0
\(99\) −0.822850 −0.0826996
\(100\) 0 0
\(101\) −9.63749 −0.958966 −0.479483 0.877551i \(-0.659176\pi\)
−0.479483 + 0.877551i \(0.659176\pi\)
\(102\) 0 0
\(103\) −7.20489 −0.709919 −0.354960 0.934882i \(-0.615505\pi\)
−0.354960 + 0.934882i \(0.615505\pi\)
\(104\) 0 0
\(105\) 4.33547 0.423099
\(106\) 0 0
\(107\) 7.91334 0.765011 0.382506 0.923953i \(-0.375061\pi\)
0.382506 + 0.923953i \(0.375061\pi\)
\(108\) 0 0
\(109\) −5.89407 −0.564550 −0.282275 0.959334i \(-0.591089\pi\)
−0.282275 + 0.959334i \(0.591089\pi\)
\(110\) 0 0
\(111\) 3.76492 0.357351
\(112\) 0 0
\(113\) −16.3182 −1.53508 −0.767542 0.640999i \(-0.778520\pi\)
−0.767542 + 0.640999i \(0.778520\pi\)
\(114\) 0 0
\(115\) 7.91521 0.738097
\(116\) 0 0
\(117\) −1.15407 −0.106694
\(118\) 0 0
\(119\) −8.32279 −0.762949
\(120\) 0 0
\(121\) 10.1063 0.918755
\(122\) 0 0
\(123\) 3.58313 0.323080
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −4.59767 −0.407977 −0.203988 0.978973i \(-0.565390\pi\)
−0.203988 + 0.978973i \(0.565390\pi\)
\(128\) 0 0
\(129\) 11.9585 1.05289
\(130\) 0 0
\(131\) 3.86247 0.337466 0.168733 0.985662i \(-0.446032\pi\)
0.168733 + 0.985662i \(0.446032\pi\)
\(132\) 0 0
\(133\) 18.7955 1.62977
\(134\) 0 0
\(135\) 5.33947 0.459549
\(136\) 0 0
\(137\) −20.5234 −1.75343 −0.876714 0.481012i \(-0.840269\pi\)
−0.876714 + 0.481012i \(0.840269\pi\)
\(138\) 0 0
\(139\) −0.583586 −0.0494991 −0.0247496 0.999694i \(-0.507879\pi\)
−0.0247496 + 0.999694i \(0.507879\pi\)
\(140\) 0 0
\(141\) −1.88721 −0.158931
\(142\) 0 0
\(143\) 29.6021 2.47546
\(144\) 0 0
\(145\) 9.25560 0.768636
\(146\) 0 0
\(147\) −0.565580 −0.0466483
\(148\) 0 0
\(149\) −3.08589 −0.252806 −0.126403 0.991979i \(-0.540343\pi\)
−0.126403 + 0.991979i \(0.540343\pi\)
\(150\) 0 0
\(151\) 15.0643 1.22592 0.612958 0.790116i \(-0.289980\pi\)
0.612958 + 0.790116i \(0.289980\pi\)
\(152\) 0 0
\(153\) −0.577485 −0.0466869
\(154\) 0 0
\(155\) 3.08945 0.248151
\(156\) 0 0
\(157\) −13.7025 −1.09358 −0.546788 0.837271i \(-0.684150\pi\)
−0.546788 + 0.837271i \(0.684150\pi\)
\(158\) 0 0
\(159\) −22.2258 −1.76262
\(160\) 0 0
\(161\) 20.4318 1.61025
\(162\) 0 0
\(163\) −12.0417 −0.943181 −0.471591 0.881818i \(-0.656320\pi\)
−0.471591 + 0.881818i \(0.656320\pi\)
\(164\) 0 0
\(165\) −7.71613 −0.600700
\(166\) 0 0
\(167\) −7.41046 −0.573439 −0.286719 0.958015i \(-0.592565\pi\)
−0.286719 + 0.958015i \(0.592565\pi\)
\(168\) 0 0
\(169\) 28.5178 2.19368
\(170\) 0 0
\(171\) 1.30414 0.0997302
\(172\) 0 0
\(173\) −4.53388 −0.344704 −0.172352 0.985035i \(-0.555137\pi\)
−0.172352 + 0.985035i \(0.555137\pi\)
\(174\) 0 0
\(175\) −2.58133 −0.195130
\(176\) 0 0
\(177\) 6.67361 0.501619
\(178\) 0 0
\(179\) −3.99188 −0.298367 −0.149184 0.988810i \(-0.547665\pi\)
−0.149184 + 0.988810i \(0.547665\pi\)
\(180\) 0 0
\(181\) −2.55190 −0.189681 −0.0948407 0.995492i \(-0.530234\pi\)
−0.0948407 + 0.995492i \(0.530234\pi\)
\(182\) 0 0
\(183\) 13.8684 1.02518
\(184\) 0 0
\(185\) −2.24163 −0.164808
\(186\) 0 0
\(187\) 14.8126 1.08321
\(188\) 0 0
\(189\) 13.7829 1.00256
\(190\) 0 0
\(191\) 6.34859 0.459368 0.229684 0.973265i \(-0.426231\pi\)
0.229684 + 0.973265i \(0.426231\pi\)
\(192\) 0 0
\(193\) 1.62059 0.116653 0.0583263 0.998298i \(-0.481424\pi\)
0.0583263 + 0.998298i \(0.481424\pi\)
\(194\) 0 0
\(195\) −10.8221 −0.774985
\(196\) 0 0
\(197\) 7.14222 0.508862 0.254431 0.967091i \(-0.418112\pi\)
0.254431 + 0.967091i \(0.418112\pi\)
\(198\) 0 0
\(199\) 2.55292 0.180972 0.0904858 0.995898i \(-0.471158\pi\)
0.0904858 + 0.995898i \(0.471158\pi\)
\(200\) 0 0
\(201\) 1.07155 0.0755811
\(202\) 0 0
\(203\) 23.8918 1.67687
\(204\) 0 0
\(205\) −2.13339 −0.149002
\(206\) 0 0
\(207\) 1.41768 0.0985354
\(208\) 0 0
\(209\) −33.4515 −2.31389
\(210\) 0 0
\(211\) −8.33625 −0.573891 −0.286946 0.957947i \(-0.592640\pi\)
−0.286946 + 0.957947i \(0.592640\pi\)
\(212\) 0 0
\(213\) −5.17385 −0.354506
\(214\) 0 0
\(215\) −7.12005 −0.485583
\(216\) 0 0
\(217\) 7.97489 0.541371
\(218\) 0 0
\(219\) −9.46620 −0.639667
\(220\) 0 0
\(221\) 20.7751 1.39748
\(222\) 0 0
\(223\) −7.57485 −0.507249 −0.253625 0.967303i \(-0.581623\pi\)
−0.253625 + 0.967303i \(0.581623\pi\)
\(224\) 0 0
\(225\) −0.179108 −0.0119405
\(226\) 0 0
\(227\) −10.2642 −0.681261 −0.340631 0.940197i \(-0.610641\pi\)
−0.340631 + 0.940197i \(0.610641\pi\)
\(228\) 0 0
\(229\) −6.42972 −0.424888 −0.212444 0.977173i \(-0.568142\pi\)
−0.212444 + 0.977173i \(0.568142\pi\)
\(230\) 0 0
\(231\) −19.9179 −1.31050
\(232\) 0 0
\(233\) 16.4905 1.08033 0.540165 0.841559i \(-0.318362\pi\)
0.540165 + 0.841559i \(0.318362\pi\)
\(234\) 0 0
\(235\) 1.12364 0.0732980
\(236\) 0 0
\(237\) 14.8991 0.967800
\(238\) 0 0
\(239\) 1.59350 0.103075 0.0515374 0.998671i \(-0.483588\pi\)
0.0515374 + 0.998671i \(0.483588\pi\)
\(240\) 0 0
\(241\) −2.70370 −0.174161 −0.0870804 0.996201i \(-0.527754\pi\)
−0.0870804 + 0.996201i \(0.527754\pi\)
\(242\) 0 0
\(243\) 1.85881 0.119242
\(244\) 0 0
\(245\) 0.336745 0.0215138
\(246\) 0 0
\(247\) −46.9166 −2.98523
\(248\) 0 0
\(249\) 21.4703 1.36063
\(250\) 0 0
\(251\) −0.787430 −0.0497021 −0.0248511 0.999691i \(-0.507911\pi\)
−0.0248511 + 0.999691i \(0.507911\pi\)
\(252\) 0 0
\(253\) −36.3637 −2.28617
\(254\) 0 0
\(255\) −5.41526 −0.339116
\(256\) 0 0
\(257\) 8.52813 0.531970 0.265985 0.963977i \(-0.414303\pi\)
0.265985 + 0.963977i \(0.414303\pi\)
\(258\) 0 0
\(259\) −5.78637 −0.359548
\(260\) 0 0
\(261\) 1.65775 0.102612
\(262\) 0 0
\(263\) −13.0631 −0.805506 −0.402753 0.915309i \(-0.631947\pi\)
−0.402753 + 0.915309i \(0.631947\pi\)
\(264\) 0 0
\(265\) 13.2332 0.812907
\(266\) 0 0
\(267\) 10.0034 0.612196
\(268\) 0 0
\(269\) −28.0367 −1.70943 −0.854715 0.519097i \(-0.826268\pi\)
−0.854715 + 0.519097i \(0.826268\pi\)
\(270\) 0 0
\(271\) −14.1917 −0.862087 −0.431043 0.902331i \(-0.641854\pi\)
−0.431043 + 0.902331i \(0.641854\pi\)
\(272\) 0 0
\(273\) −27.9353 −1.69072
\(274\) 0 0
\(275\) 4.59416 0.277038
\(276\) 0 0
\(277\) −8.46869 −0.508834 −0.254417 0.967095i \(-0.581884\pi\)
−0.254417 + 0.967095i \(0.581884\pi\)
\(278\) 0 0
\(279\) 0.553346 0.0331279
\(280\) 0 0
\(281\) −10.3898 −0.619804 −0.309902 0.950768i \(-0.600296\pi\)
−0.309902 + 0.950768i \(0.600296\pi\)
\(282\) 0 0
\(283\) 4.49892 0.267433 0.133717 0.991020i \(-0.457309\pi\)
0.133717 + 0.991020i \(0.457309\pi\)
\(284\) 0 0
\(285\) 12.2293 0.724403
\(286\) 0 0
\(287\) −5.50697 −0.325066
\(288\) 0 0
\(289\) −6.60435 −0.388491
\(290\) 0 0
\(291\) −25.6038 −1.50092
\(292\) 0 0
\(293\) 12.2358 0.714822 0.357411 0.933947i \(-0.383659\pi\)
0.357411 + 0.933947i \(0.383659\pi\)
\(294\) 0 0
\(295\) −3.97345 −0.231343
\(296\) 0 0
\(297\) −24.5304 −1.42340
\(298\) 0 0
\(299\) −51.0011 −2.94947
\(300\) 0 0
\(301\) −18.3792 −1.05936
\(302\) 0 0
\(303\) −16.1867 −0.929899
\(304\) 0 0
\(305\) −8.25721 −0.472807
\(306\) 0 0
\(307\) −6.04890 −0.345229 −0.172614 0.984989i \(-0.555221\pi\)
−0.172614 + 0.984989i \(0.555221\pi\)
\(308\) 0 0
\(309\) −12.1010 −0.688401
\(310\) 0 0
\(311\) −24.9972 −1.41746 −0.708730 0.705479i \(-0.750732\pi\)
−0.708730 + 0.705479i \(0.750732\pi\)
\(312\) 0 0
\(313\) 4.23082 0.239140 0.119570 0.992826i \(-0.461848\pi\)
0.119570 + 0.992826i \(0.461848\pi\)
\(314\) 0 0
\(315\) −0.462336 −0.0260497
\(316\) 0 0
\(317\) −32.3166 −1.81508 −0.907539 0.419967i \(-0.862042\pi\)
−0.907539 + 0.419967i \(0.862042\pi\)
\(318\) 0 0
\(319\) −42.5217 −2.38076
\(320\) 0 0
\(321\) 13.2909 0.741823
\(322\) 0 0
\(323\) −23.4766 −1.30627
\(324\) 0 0
\(325\) 6.44343 0.357417
\(326\) 0 0
\(327\) −9.89940 −0.547438
\(328\) 0 0
\(329\) 2.90048 0.159908
\(330\) 0 0
\(331\) −9.99656 −0.549461 −0.274730 0.961521i \(-0.588589\pi\)
−0.274730 + 0.961521i \(0.588589\pi\)
\(332\) 0 0
\(333\) −0.401493 −0.0220017
\(334\) 0 0
\(335\) −0.637996 −0.0348574
\(336\) 0 0
\(337\) −10.8754 −0.592421 −0.296211 0.955123i \(-0.595723\pi\)
−0.296211 + 0.955123i \(0.595723\pi\)
\(338\) 0 0
\(339\) −27.4072 −1.48855
\(340\) 0 0
\(341\) −14.1934 −0.768618
\(342\) 0 0
\(343\) 18.9385 1.02259
\(344\) 0 0
\(345\) 13.2940 0.715725
\(346\) 0 0
\(347\) 33.7763 1.81321 0.906603 0.421986i \(-0.138667\pi\)
0.906603 + 0.421986i \(0.138667\pi\)
\(348\) 0 0
\(349\) −22.7292 −1.21667 −0.608333 0.793682i \(-0.708162\pi\)
−0.608333 + 0.793682i \(0.708162\pi\)
\(350\) 0 0
\(351\) −34.4045 −1.83638
\(352\) 0 0
\(353\) 11.3547 0.604352 0.302176 0.953252i \(-0.402287\pi\)
0.302176 + 0.953252i \(0.402287\pi\)
\(354\) 0 0
\(355\) 3.08049 0.163496
\(356\) 0 0
\(357\) −13.9786 −0.739823
\(358\) 0 0
\(359\) −14.4162 −0.760858 −0.380429 0.924810i \(-0.624224\pi\)
−0.380429 + 0.924810i \(0.624224\pi\)
\(360\) 0 0
\(361\) 34.0175 1.79040
\(362\) 0 0
\(363\) 16.9741 0.890907
\(364\) 0 0
\(365\) 5.63615 0.295010
\(366\) 0 0
\(367\) 20.7212 1.08164 0.540819 0.841139i \(-0.318114\pi\)
0.540819 + 0.841139i \(0.318114\pi\)
\(368\) 0 0
\(369\) −0.382106 −0.0198917
\(370\) 0 0
\(371\) 34.1592 1.77346
\(372\) 0 0
\(373\) 31.5493 1.63356 0.816780 0.576949i \(-0.195757\pi\)
0.816780 + 0.576949i \(0.195757\pi\)
\(374\) 0 0
\(375\) −1.67955 −0.0867316
\(376\) 0 0
\(377\) −59.6378 −3.07151
\(378\) 0 0
\(379\) −21.3142 −1.09484 −0.547419 0.836859i \(-0.684389\pi\)
−0.547419 + 0.836859i \(0.684389\pi\)
\(380\) 0 0
\(381\) −7.72201 −0.395611
\(382\) 0 0
\(383\) 25.3013 1.29283 0.646417 0.762984i \(-0.276267\pi\)
0.646417 + 0.762984i \(0.276267\pi\)
\(384\) 0 0
\(385\) 11.8590 0.604392
\(386\) 0 0
\(387\) −1.27526 −0.0648250
\(388\) 0 0
\(389\) 16.4409 0.833586 0.416793 0.909001i \(-0.363154\pi\)
0.416793 + 0.909001i \(0.363154\pi\)
\(390\) 0 0
\(391\) −25.5204 −1.29062
\(392\) 0 0
\(393\) 6.48722 0.327237
\(394\) 0 0
\(395\) −8.87088 −0.446342
\(396\) 0 0
\(397\) −22.6377 −1.13615 −0.568076 0.822976i \(-0.692312\pi\)
−0.568076 + 0.822976i \(0.692312\pi\)
\(398\) 0 0
\(399\) 31.5679 1.58037
\(400\) 0 0
\(401\) 1.00000 0.0499376
\(402\) 0 0
\(403\) −19.9067 −0.991622
\(404\) 0 0
\(405\) 8.43060 0.418920
\(406\) 0 0
\(407\) 10.2984 0.510472
\(408\) 0 0
\(409\) −10.5807 −0.523180 −0.261590 0.965179i \(-0.584247\pi\)
−0.261590 + 0.965179i \(0.584247\pi\)
\(410\) 0 0
\(411\) −34.4700 −1.70028
\(412\) 0 0
\(413\) −10.2568 −0.504703
\(414\) 0 0
\(415\) −12.7834 −0.627510
\(416\) 0 0
\(417\) −0.980163 −0.0479988
\(418\) 0 0
\(419\) −1.55883 −0.0761537 −0.0380769 0.999275i \(-0.512123\pi\)
−0.0380769 + 0.999275i \(0.512123\pi\)
\(420\) 0 0
\(421\) 1.07986 0.0526291 0.0263146 0.999654i \(-0.491623\pi\)
0.0263146 + 0.999654i \(0.491623\pi\)
\(422\) 0 0
\(423\) 0.201252 0.00978522
\(424\) 0 0
\(425\) 3.22423 0.156398
\(426\) 0 0
\(427\) −21.3146 −1.03148
\(428\) 0 0
\(429\) 49.7183 2.40042
\(430\) 0 0
\(431\) 31.1168 1.49884 0.749421 0.662094i \(-0.230332\pi\)
0.749421 + 0.662094i \(0.230332\pi\)
\(432\) 0 0
\(433\) −21.3006 −1.02364 −0.511820 0.859092i \(-0.671029\pi\)
−0.511820 + 0.859092i \(0.671029\pi\)
\(434\) 0 0
\(435\) 15.5453 0.745338
\(436\) 0 0
\(437\) 57.6331 2.75697
\(438\) 0 0
\(439\) 8.57119 0.409080 0.204540 0.978858i \(-0.434430\pi\)
0.204540 + 0.978858i \(0.434430\pi\)
\(440\) 0 0
\(441\) 0.0603137 0.00287208
\(442\) 0 0
\(443\) 33.2640 1.58042 0.790210 0.612836i \(-0.209971\pi\)
0.790210 + 0.612836i \(0.209971\pi\)
\(444\) 0 0
\(445\) −5.95597 −0.282340
\(446\) 0 0
\(447\) −5.18291 −0.245143
\(448\) 0 0
\(449\) −22.4485 −1.05941 −0.529704 0.848182i \(-0.677697\pi\)
−0.529704 + 0.848182i \(0.677697\pi\)
\(450\) 0 0
\(451\) 9.80111 0.461516
\(452\) 0 0
\(453\) 25.3013 1.18876
\(454\) 0 0
\(455\) 16.6326 0.779749
\(456\) 0 0
\(457\) 16.0366 0.750162 0.375081 0.926992i \(-0.377615\pi\)
0.375081 + 0.926992i \(0.377615\pi\)
\(458\) 0 0
\(459\) −17.2157 −0.803559
\(460\) 0 0
\(461\) 2.43704 0.113504 0.0567521 0.998388i \(-0.481926\pi\)
0.0567521 + 0.998388i \(0.481926\pi\)
\(462\) 0 0
\(463\) −37.5880 −1.74686 −0.873432 0.486946i \(-0.838111\pi\)
−0.873432 + 0.486946i \(0.838111\pi\)
\(464\) 0 0
\(465\) 5.18889 0.240629
\(466\) 0 0
\(467\) 10.5098 0.486335 0.243168 0.969984i \(-0.421813\pi\)
0.243168 + 0.969984i \(0.421813\pi\)
\(468\) 0 0
\(469\) −1.64688 −0.0760457
\(470\) 0 0
\(471\) −23.0140 −1.06043
\(472\) 0 0
\(473\) 32.7106 1.50404
\(474\) 0 0
\(475\) −7.28131 −0.334090
\(476\) 0 0
\(477\) 2.37017 0.108522
\(478\) 0 0
\(479\) −33.2100 −1.51740 −0.758701 0.651439i \(-0.774166\pi\)
−0.758701 + 0.651439i \(0.774166\pi\)
\(480\) 0 0
\(481\) 14.4438 0.658579
\(482\) 0 0
\(483\) 34.3162 1.56144
\(484\) 0 0
\(485\) 15.2444 0.692213
\(486\) 0 0
\(487\) 30.1639 1.36686 0.683428 0.730018i \(-0.260488\pi\)
0.683428 + 0.730018i \(0.260488\pi\)
\(488\) 0 0
\(489\) −20.2247 −0.914593
\(490\) 0 0
\(491\) −0.422756 −0.0190787 −0.00953936 0.999954i \(-0.503037\pi\)
−0.00953936 + 0.999954i \(0.503037\pi\)
\(492\) 0 0
\(493\) −29.8422 −1.34402
\(494\) 0 0
\(495\) 0.822850 0.0369844
\(496\) 0 0
\(497\) 7.95177 0.356685
\(498\) 0 0
\(499\) −6.46635 −0.289474 −0.144737 0.989470i \(-0.546234\pi\)
−0.144737 + 0.989470i \(0.546234\pi\)
\(500\) 0 0
\(501\) −12.4463 −0.556058
\(502\) 0 0
\(503\) 38.2733 1.70652 0.853261 0.521485i \(-0.174622\pi\)
0.853261 + 0.521485i \(0.174622\pi\)
\(504\) 0 0
\(505\) 9.63749 0.428863
\(506\) 0 0
\(507\) 47.8971 2.12718
\(508\) 0 0
\(509\) −31.3957 −1.39159 −0.695794 0.718241i \(-0.744947\pi\)
−0.695794 + 0.718241i \(0.744947\pi\)
\(510\) 0 0
\(511\) 14.5488 0.643599
\(512\) 0 0
\(513\) 38.8784 1.71652
\(514\) 0 0
\(515\) 7.20489 0.317485
\(516\) 0 0
\(517\) −5.16217 −0.227032
\(518\) 0 0
\(519\) −7.61488 −0.334256
\(520\) 0 0
\(521\) −17.5577 −0.769219 −0.384609 0.923079i \(-0.625664\pi\)
−0.384609 + 0.923079i \(0.625664\pi\)
\(522\) 0 0
\(523\) 1.58125 0.0691432 0.0345716 0.999402i \(-0.488993\pi\)
0.0345716 + 0.999402i \(0.488993\pi\)
\(524\) 0 0
\(525\) −4.33547 −0.189216
\(526\) 0 0
\(527\) −9.96110 −0.433912
\(528\) 0 0
\(529\) 39.6506 1.72394
\(530\) 0 0
\(531\) −0.711676 −0.0308841
\(532\) 0 0
\(533\) 13.7463 0.595419
\(534\) 0 0
\(535\) −7.91334 −0.342123
\(536\) 0 0
\(537\) −6.70457 −0.289323
\(538\) 0 0
\(539\) −1.54706 −0.0666366
\(540\) 0 0
\(541\) 6.50947 0.279864 0.139932 0.990161i \(-0.455312\pi\)
0.139932 + 0.990161i \(0.455312\pi\)
\(542\) 0 0
\(543\) −4.28605 −0.183932
\(544\) 0 0
\(545\) 5.89407 0.252474
\(546\) 0 0
\(547\) 34.4477 1.47288 0.736439 0.676504i \(-0.236506\pi\)
0.736439 + 0.676504i \(0.236506\pi\)
\(548\) 0 0
\(549\) −1.47893 −0.0631193
\(550\) 0 0
\(551\) 67.3930 2.87104
\(552\) 0 0
\(553\) −22.8987 −0.973750
\(554\) 0 0
\(555\) −3.76492 −0.159812
\(556\) 0 0
\(557\) −43.3036 −1.83483 −0.917416 0.397929i \(-0.869729\pi\)
−0.917416 + 0.397929i \(0.869729\pi\)
\(558\) 0 0
\(559\) 45.8775 1.94041
\(560\) 0 0
\(561\) 24.8786 1.05037
\(562\) 0 0
\(563\) −42.4344 −1.78840 −0.894198 0.447671i \(-0.852254\pi\)
−0.894198 + 0.447671i \(0.852254\pi\)
\(564\) 0 0
\(565\) 16.3182 0.686510
\(566\) 0 0
\(567\) 21.7621 0.913924
\(568\) 0 0
\(569\) 20.3579 0.853448 0.426724 0.904382i \(-0.359668\pi\)
0.426724 + 0.904382i \(0.359668\pi\)
\(570\) 0 0
\(571\) 24.1569 1.01094 0.505468 0.862845i \(-0.331320\pi\)
0.505468 + 0.862845i \(0.331320\pi\)
\(572\) 0 0
\(573\) 10.6628 0.445444
\(574\) 0 0
\(575\) −7.91521 −0.330087
\(576\) 0 0
\(577\) −38.9382 −1.62102 −0.810510 0.585725i \(-0.800810\pi\)
−0.810510 + 0.585725i \(0.800810\pi\)
\(578\) 0 0
\(579\) 2.72186 0.113117
\(580\) 0 0
\(581\) −32.9980 −1.36899
\(582\) 0 0
\(583\) −60.7953 −2.51788
\(584\) 0 0
\(585\) 1.15407 0.0477149
\(586\) 0 0
\(587\) −16.3066 −0.673047 −0.336524 0.941675i \(-0.609251\pi\)
−0.336524 + 0.941675i \(0.609251\pi\)
\(588\) 0 0
\(589\) 22.4953 0.926902
\(590\) 0 0
\(591\) 11.9957 0.493438
\(592\) 0 0
\(593\) 30.5859 1.25601 0.628006 0.778209i \(-0.283871\pi\)
0.628006 + 0.778209i \(0.283871\pi\)
\(594\) 0 0
\(595\) 8.32279 0.341201
\(596\) 0 0
\(597\) 4.28776 0.175486
\(598\) 0 0
\(599\) −15.5538 −0.635511 −0.317755 0.948173i \(-0.602929\pi\)
−0.317755 + 0.948173i \(0.602929\pi\)
\(600\) 0 0
\(601\) −28.9614 −1.18136 −0.590680 0.806906i \(-0.701140\pi\)
−0.590680 + 0.806906i \(0.701140\pi\)
\(602\) 0 0
\(603\) −0.114270 −0.00465344
\(604\) 0 0
\(605\) −10.1063 −0.410880
\(606\) 0 0
\(607\) 6.12304 0.248527 0.124263 0.992249i \(-0.460343\pi\)
0.124263 + 0.992249i \(0.460343\pi\)
\(608\) 0 0
\(609\) 40.1274 1.62605
\(610\) 0 0
\(611\) −7.24008 −0.292902
\(612\) 0 0
\(613\) −33.8842 −1.36857 −0.684286 0.729214i \(-0.739886\pi\)
−0.684286 + 0.729214i \(0.739886\pi\)
\(614\) 0 0
\(615\) −3.58313 −0.144486
\(616\) 0 0
\(617\) −5.52236 −0.222322 −0.111161 0.993802i \(-0.535457\pi\)
−0.111161 + 0.993802i \(0.535457\pi\)
\(618\) 0 0
\(619\) 6.63594 0.266721 0.133360 0.991068i \(-0.457423\pi\)
0.133360 + 0.991068i \(0.457423\pi\)
\(620\) 0 0
\(621\) 42.2631 1.69596
\(622\) 0 0
\(623\) −15.3743 −0.615959
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −56.1835 −2.24375
\(628\) 0 0
\(629\) 7.22751 0.288180
\(630\) 0 0
\(631\) −7.23719 −0.288108 −0.144054 0.989570i \(-0.546014\pi\)
−0.144054 + 0.989570i \(0.546014\pi\)
\(632\) 0 0
\(633\) −14.0012 −0.556496
\(634\) 0 0
\(635\) 4.59767 0.182453
\(636\) 0 0
\(637\) −2.16979 −0.0859703
\(638\) 0 0
\(639\) 0.551741 0.0218265
\(640\) 0 0
\(641\) 24.8354 0.980940 0.490470 0.871458i \(-0.336825\pi\)
0.490470 + 0.871458i \(0.336825\pi\)
\(642\) 0 0
\(643\) 28.7654 1.13440 0.567198 0.823582i \(-0.308028\pi\)
0.567198 + 0.823582i \(0.308028\pi\)
\(644\) 0 0
\(645\) −11.9585 −0.470865
\(646\) 0 0
\(647\) 12.7061 0.499530 0.249765 0.968307i \(-0.419647\pi\)
0.249765 + 0.968307i \(0.419647\pi\)
\(648\) 0 0
\(649\) 18.2547 0.716558
\(650\) 0 0
\(651\) 13.3942 0.524962
\(652\) 0 0
\(653\) −12.4665 −0.487851 −0.243926 0.969794i \(-0.578435\pi\)
−0.243926 + 0.969794i \(0.578435\pi\)
\(654\) 0 0
\(655\) −3.86247 −0.150919
\(656\) 0 0
\(657\) 1.00948 0.0393835
\(658\) 0 0
\(659\) −33.1425 −1.29105 −0.645525 0.763739i \(-0.723361\pi\)
−0.645525 + 0.763739i \(0.723361\pi\)
\(660\) 0 0
\(661\) −4.30159 −0.167313 −0.0836563 0.996495i \(-0.526660\pi\)
−0.0836563 + 0.996495i \(0.526660\pi\)
\(662\) 0 0
\(663\) 34.8928 1.35513
\(664\) 0 0
\(665\) −18.7955 −0.728857
\(666\) 0 0
\(667\) 73.2601 2.83664
\(668\) 0 0
\(669\) −12.7223 −0.491874
\(670\) 0 0
\(671\) 37.9349 1.46446
\(672\) 0 0
\(673\) 40.4514 1.55929 0.779643 0.626224i \(-0.215400\pi\)
0.779643 + 0.626224i \(0.215400\pi\)
\(674\) 0 0
\(675\) −5.33947 −0.205516
\(676\) 0 0
\(677\) 47.6791 1.83246 0.916229 0.400655i \(-0.131217\pi\)
0.916229 + 0.400655i \(0.131217\pi\)
\(678\) 0 0
\(679\) 39.3508 1.51015
\(680\) 0 0
\(681\) −17.2393 −0.660612
\(682\) 0 0
\(683\) −47.4403 −1.81525 −0.907626 0.419780i \(-0.862107\pi\)
−0.907626 + 0.419780i \(0.862107\pi\)
\(684\) 0 0
\(685\) 20.5234 0.784157
\(686\) 0 0
\(687\) −10.7991 −0.412009
\(688\) 0 0
\(689\) −85.2670 −3.24841
\(690\) 0 0
\(691\) 31.8319 1.21094 0.605470 0.795868i \(-0.292985\pi\)
0.605470 + 0.795868i \(0.292985\pi\)
\(692\) 0 0
\(693\) 2.12405 0.0806859
\(694\) 0 0
\(695\) 0.583586 0.0221367
\(696\) 0 0
\(697\) 6.87852 0.260543
\(698\) 0 0
\(699\) 27.6967 1.04758
\(700\) 0 0
\(701\) −39.7995 −1.50321 −0.751603 0.659616i \(-0.770719\pi\)
−0.751603 + 0.659616i \(0.770719\pi\)
\(702\) 0 0
\(703\) −16.3220 −0.615595
\(704\) 0 0
\(705\) 1.88721 0.0710763
\(706\) 0 0
\(707\) 24.8775 0.935615
\(708\) 0 0
\(709\) 9.17219 0.344469 0.172234 0.985056i \(-0.444901\pi\)
0.172234 + 0.985056i \(0.444901\pi\)
\(710\) 0 0
\(711\) −1.58884 −0.0595863
\(712\) 0 0
\(713\) 24.4537 0.915797
\(714\) 0 0
\(715\) −29.6021 −1.10706
\(716\) 0 0
\(717\) 2.67636 0.0999506
\(718\) 0 0
\(719\) −30.8573 −1.15078 −0.575392 0.817878i \(-0.695151\pi\)
−0.575392 + 0.817878i \(0.695151\pi\)
\(720\) 0 0
\(721\) 18.5982 0.692633
\(722\) 0 0
\(723\) −4.54101 −0.168882
\(724\) 0 0
\(725\) −9.25560 −0.343745
\(726\) 0 0
\(727\) 31.8367 1.18076 0.590378 0.807127i \(-0.298979\pi\)
0.590378 + 0.807127i \(0.298979\pi\)
\(728\) 0 0
\(729\) 28.4137 1.05236
\(730\) 0 0
\(731\) 22.9567 0.849083
\(732\) 0 0
\(733\) −24.1615 −0.892424 −0.446212 0.894927i \(-0.647227\pi\)
−0.446212 + 0.894927i \(0.647227\pi\)
\(734\) 0 0
\(735\) 0.565580 0.0208617
\(736\) 0 0
\(737\) 2.93105 0.107967
\(738\) 0 0
\(739\) 39.2435 1.44360 0.721798 0.692103i \(-0.243316\pi\)
0.721798 + 0.692103i \(0.243316\pi\)
\(740\) 0 0
\(741\) −78.7989 −2.89475
\(742\) 0 0
\(743\) 13.5190 0.495963 0.247982 0.968765i \(-0.420233\pi\)
0.247982 + 0.968765i \(0.420233\pi\)
\(744\) 0 0
\(745\) 3.08589 0.113058
\(746\) 0 0
\(747\) −2.28960 −0.0837721
\(748\) 0 0
\(749\) −20.4269 −0.746383
\(750\) 0 0
\(751\) −2.36282 −0.0862204 −0.0431102 0.999070i \(-0.513727\pi\)
−0.0431102 + 0.999070i \(0.513727\pi\)
\(752\) 0 0
\(753\) −1.32253 −0.0481956
\(754\) 0 0
\(755\) −15.0643 −0.548246
\(756\) 0 0
\(757\) 19.4097 0.705459 0.352729 0.935725i \(-0.385254\pi\)
0.352729 + 0.935725i \(0.385254\pi\)
\(758\) 0 0
\(759\) −61.0748 −2.21687
\(760\) 0 0
\(761\) 27.4865 0.996383 0.498192 0.867067i \(-0.333998\pi\)
0.498192 + 0.867067i \(0.333998\pi\)
\(762\) 0 0
\(763\) 15.2145 0.550803
\(764\) 0 0
\(765\) 0.577485 0.0208790
\(766\) 0 0
\(767\) 25.6026 0.924458
\(768\) 0 0
\(769\) 29.6475 1.06912 0.534558 0.845132i \(-0.320478\pi\)
0.534558 + 0.845132i \(0.320478\pi\)
\(770\) 0 0
\(771\) 14.3234 0.515846
\(772\) 0 0
\(773\) −33.7025 −1.21219 −0.606096 0.795391i \(-0.707265\pi\)
−0.606096 + 0.795391i \(0.707265\pi\)
\(774\) 0 0
\(775\) −3.08945 −0.110976
\(776\) 0 0
\(777\) −9.71851 −0.348649
\(778\) 0 0
\(779\) −15.5338 −0.556558
\(780\) 0 0
\(781\) −14.1523 −0.506408
\(782\) 0 0
\(783\) 49.4201 1.76613
\(784\) 0 0
\(785\) 13.7025 0.489062
\(786\) 0 0
\(787\) −41.8199 −1.49072 −0.745358 0.666664i \(-0.767722\pi\)
−0.745358 + 0.666664i \(0.767722\pi\)
\(788\) 0 0
\(789\) −21.9402 −0.781090
\(790\) 0 0
\(791\) 42.1225 1.49770
\(792\) 0 0
\(793\) 53.2048 1.88936
\(794\) 0 0
\(795\) 22.2258 0.788267
\(796\) 0 0
\(797\) 8.16193 0.289110 0.144555 0.989497i \(-0.453825\pi\)
0.144555 + 0.989497i \(0.453825\pi\)
\(798\) 0 0
\(799\) −3.62286 −0.128168
\(800\) 0 0
\(801\) −1.06676 −0.0376922
\(802\) 0 0
\(803\) −25.8934 −0.913757
\(804\) 0 0
\(805\) −20.4318 −0.720125
\(806\) 0 0
\(807\) −47.0891 −1.65762
\(808\) 0 0
\(809\) 26.9762 0.948433 0.474216 0.880408i \(-0.342731\pi\)
0.474216 + 0.880408i \(0.342731\pi\)
\(810\) 0 0
\(811\) 5.65551 0.198592 0.0992960 0.995058i \(-0.468341\pi\)
0.0992960 + 0.995058i \(0.468341\pi\)
\(812\) 0 0
\(813\) −23.8357 −0.835956
\(814\) 0 0
\(815\) 12.0417 0.421803
\(816\) 0 0
\(817\) −51.8433 −1.81377
\(818\) 0 0
\(819\) 2.97903 0.104096
\(820\) 0 0
\(821\) 21.5188 0.751010 0.375505 0.926820i \(-0.377469\pi\)
0.375505 + 0.926820i \(0.377469\pi\)
\(822\) 0 0
\(823\) 21.0631 0.734214 0.367107 0.930179i \(-0.380348\pi\)
0.367107 + 0.930179i \(0.380348\pi\)
\(824\) 0 0
\(825\) 7.71613 0.268641
\(826\) 0 0
\(827\) −7.17097 −0.249359 −0.124679 0.992197i \(-0.539790\pi\)
−0.124679 + 0.992197i \(0.539790\pi\)
\(828\) 0 0
\(829\) −11.9526 −0.415132 −0.207566 0.978221i \(-0.566554\pi\)
−0.207566 + 0.978221i \(0.566554\pi\)
\(830\) 0 0
\(831\) −14.2236 −0.493411
\(832\) 0 0
\(833\) −1.08574 −0.0376187
\(834\) 0 0
\(835\) 7.41046 0.256450
\(836\) 0 0
\(837\) 16.4961 0.570187
\(838\) 0 0
\(839\) 37.0510 1.27914 0.639572 0.768731i \(-0.279112\pi\)
0.639572 + 0.768731i \(0.279112\pi\)
\(840\) 0 0
\(841\) 56.6662 1.95401
\(842\) 0 0
\(843\) −17.4502 −0.601018
\(844\) 0 0
\(845\) −28.5178 −0.981042
\(846\) 0 0
\(847\) −26.0877 −0.896383
\(848\) 0 0
\(849\) 7.55617 0.259327
\(850\) 0 0
\(851\) −17.7429 −0.608220
\(852\) 0 0
\(853\) 32.1374 1.10037 0.550183 0.835044i \(-0.314558\pi\)
0.550183 + 0.835044i \(0.314558\pi\)
\(854\) 0 0
\(855\) −1.30414 −0.0446007
\(856\) 0 0
\(857\) −32.0607 −1.09517 −0.547587 0.836749i \(-0.684454\pi\)
−0.547587 + 0.836749i \(0.684454\pi\)
\(858\) 0 0
\(859\) −15.5109 −0.529224 −0.264612 0.964355i \(-0.585244\pi\)
−0.264612 + 0.964355i \(0.585244\pi\)
\(860\) 0 0
\(861\) −9.24923 −0.315213
\(862\) 0 0
\(863\) 51.8139 1.76376 0.881882 0.471470i \(-0.156276\pi\)
0.881882 + 0.471470i \(0.156276\pi\)
\(864\) 0 0
\(865\) 4.53388 0.154156
\(866\) 0 0
\(867\) −11.0923 −0.376716
\(868\) 0 0
\(869\) 40.7542 1.38249
\(870\) 0 0
\(871\) 4.11088 0.139292
\(872\) 0 0
\(873\) 2.73039 0.0924099
\(874\) 0 0
\(875\) 2.58133 0.0872648
\(876\) 0 0
\(877\) 31.2657 1.05577 0.527884 0.849317i \(-0.322986\pi\)
0.527884 + 0.849317i \(0.322986\pi\)
\(878\) 0 0
\(879\) 20.5506 0.693156
\(880\) 0 0
\(881\) 18.7450 0.631536 0.315768 0.948836i \(-0.397738\pi\)
0.315768 + 0.948836i \(0.397738\pi\)
\(882\) 0 0
\(883\) 8.62047 0.290102 0.145051 0.989424i \(-0.453665\pi\)
0.145051 + 0.989424i \(0.453665\pi\)
\(884\) 0 0
\(885\) −6.67361 −0.224331
\(886\) 0 0
\(887\) 7.43060 0.249495 0.124748 0.992189i \(-0.460188\pi\)
0.124748 + 0.992189i \(0.460188\pi\)
\(888\) 0 0
\(889\) 11.8681 0.398043
\(890\) 0 0
\(891\) −38.7315 −1.29755
\(892\) 0 0
\(893\) 8.18155 0.273785
\(894\) 0 0
\(895\) 3.99188 0.133434
\(896\) 0 0
\(897\) −85.6590 −2.86007
\(898\) 0 0
\(899\) 28.5948 0.953688
\(900\) 0 0
\(901\) −42.6668 −1.42144
\(902\) 0 0
\(903\) −30.8688 −1.02725
\(904\) 0 0
\(905\) 2.55190 0.0848281
\(906\) 0 0
\(907\) −39.5834 −1.31435 −0.657173 0.753740i \(-0.728248\pi\)
−0.657173 + 0.753740i \(0.728248\pi\)
\(908\) 0 0
\(909\) 1.72615 0.0572528
\(910\) 0 0
\(911\) 24.8966 0.824862 0.412431 0.910989i \(-0.364680\pi\)
0.412431 + 0.910989i \(0.364680\pi\)
\(912\) 0 0
\(913\) 58.7288 1.94364
\(914\) 0 0
\(915\) −13.8684 −0.458475
\(916\) 0 0
\(917\) −9.97031 −0.329249
\(918\) 0 0
\(919\) 34.0156 1.12207 0.561035 0.827792i \(-0.310403\pi\)
0.561035 + 0.827792i \(0.310403\pi\)
\(920\) 0 0
\(921\) −10.1594 −0.334765
\(922\) 0 0
\(923\) −19.8490 −0.653336
\(924\) 0 0
\(925\) 2.24163 0.0737042
\(926\) 0 0
\(927\) 1.29045 0.0423840
\(928\) 0 0
\(929\) 7.65125 0.251029 0.125515 0.992092i \(-0.459942\pi\)
0.125515 + 0.992092i \(0.459942\pi\)
\(930\) 0 0
\(931\) 2.45194 0.0803592
\(932\) 0 0
\(933\) −41.9841 −1.37450
\(934\) 0 0
\(935\) −14.8126 −0.484424
\(936\) 0 0
\(937\) −1.89496 −0.0619056 −0.0309528 0.999521i \(-0.509854\pi\)
−0.0309528 + 0.999521i \(0.509854\pi\)
\(938\) 0 0
\(939\) 7.10588 0.231892
\(940\) 0 0
\(941\) −13.5652 −0.442213 −0.221107 0.975250i \(-0.570967\pi\)
−0.221107 + 0.975250i \(0.570967\pi\)
\(942\) 0 0
\(943\) −16.8862 −0.549890
\(944\) 0 0
\(945\) −13.7829 −0.448359
\(946\) 0 0
\(947\) −0.317586 −0.0103202 −0.00516008 0.999987i \(-0.501643\pi\)
−0.00516008 + 0.999987i \(0.501643\pi\)
\(948\) 0 0
\(949\) −36.3161 −1.17887
\(950\) 0 0
\(951\) −54.2773 −1.76006
\(952\) 0 0
\(953\) −28.1040 −0.910377 −0.455188 0.890395i \(-0.650428\pi\)
−0.455188 + 0.890395i \(0.650428\pi\)
\(954\) 0 0
\(955\) −6.34859 −0.205435
\(956\) 0 0
\(957\) −71.4174 −2.30860
\(958\) 0 0
\(959\) 52.9775 1.71073
\(960\) 0 0
\(961\) −21.4553 −0.692106
\(962\) 0 0
\(963\) −1.41734 −0.0456732
\(964\) 0 0
\(965\) −1.62059 −0.0521686
\(966\) 0 0
\(967\) 17.0331 0.547747 0.273873 0.961766i \(-0.411695\pi\)
0.273873 + 0.961766i \(0.411695\pi\)
\(968\) 0 0
\(969\) −39.4302 −1.26668
\(970\) 0 0
\(971\) −7.21690 −0.231601 −0.115801 0.993272i \(-0.536943\pi\)
−0.115801 + 0.993272i \(0.536943\pi\)
\(972\) 0 0
\(973\) 1.50643 0.0482938
\(974\) 0 0
\(975\) 10.8221 0.346584
\(976\) 0 0
\(977\) −32.0798 −1.02633 −0.513163 0.858291i \(-0.671526\pi\)
−0.513163 + 0.858291i \(0.671526\pi\)
\(978\) 0 0
\(979\) 27.3627 0.874515
\(980\) 0 0
\(981\) 1.05568 0.0337051
\(982\) 0 0
\(983\) 20.3622 0.649453 0.324726 0.945808i \(-0.394728\pi\)
0.324726 + 0.945808i \(0.394728\pi\)
\(984\) 0 0
\(985\) −7.14222 −0.227570
\(986\) 0 0
\(987\) 4.87150 0.155061
\(988\) 0 0
\(989\) −56.3567 −1.79204
\(990\) 0 0
\(991\) −46.1409 −1.46571 −0.732857 0.680383i \(-0.761813\pi\)
−0.732857 + 0.680383i \(0.761813\pi\)
\(992\) 0 0
\(993\) −16.7897 −0.532806
\(994\) 0 0
\(995\) −2.55292 −0.0809330
\(996\) 0 0
\(997\) 37.3831 1.18393 0.591967 0.805962i \(-0.298351\pi\)
0.591967 + 0.805962i \(0.298351\pi\)
\(998\) 0 0
\(999\) −11.9691 −0.378686
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 \(a_p\))