Properties

Label 8020.2.a.c.1.5
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 1.5
Character \(\chi\) = 8020.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.26002 q^{3}\) \(-1.00000 q^{5}\) \(-3.39221 q^{7}\) \(+2.10771 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.26002 q^{3}\) \(-1.00000 q^{5}\) \(-3.39221 q^{7}\) \(+2.10771 q^{9}\) \(-3.74534 q^{11}\) \(-4.09762 q^{13}\) \(+2.26002 q^{15}\) \(+1.81997 q^{17}\) \(-0.507197 q^{19}\) \(+7.66648 q^{21}\) \(+2.07431 q^{23}\) \(+1.00000 q^{25}\) \(+2.01660 q^{27}\) \(-2.08288 q^{29}\) \(-3.75361 q^{31}\) \(+8.46457 q^{33}\) \(+3.39221 q^{35}\) \(+5.62876 q^{37}\) \(+9.26071 q^{39}\) \(-1.53690 q^{41}\) \(+6.39486 q^{43}\) \(-2.10771 q^{45}\) \(+11.8482 q^{47}\) \(+4.50709 q^{49}\) \(-4.11318 q^{51}\) \(-11.1822 q^{53}\) \(+3.74534 q^{55}\) \(+1.14628 q^{57}\) \(+13.8248 q^{59}\) \(-3.22244 q^{61}\) \(-7.14979 q^{63}\) \(+4.09762 q^{65}\) \(+2.15862 q^{67}\) \(-4.68799 q^{69}\) \(+9.69871 q^{71}\) \(-5.04323 q^{73}\) \(-2.26002 q^{75}\) \(+12.7050 q^{77}\) \(+0.358510 q^{79}\) \(-10.8807 q^{81}\) \(+15.6083 q^{83}\) \(-1.81997 q^{85}\) \(+4.70736 q^{87}\) \(-15.3504 q^{89}\) \(+13.9000 q^{91}\) \(+8.48325 q^{93}\) \(+0.507197 q^{95}\) \(-6.27268 q^{97}\) \(-7.89409 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 3q^{13} \) \(\mathstrut -\mathstrut 3q^{15} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut +\mathstrut 28q^{25} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut -\mathstrut 37q^{29} \) \(\mathstrut -\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 2q^{33} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut -\mathstrut 3q^{37} \) \(\mathstrut -\mathstrut 19q^{39} \) \(\mathstrut -\mathstrut 30q^{41} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut -\mathstrut 17q^{45} \) \(\mathstrut -\mathstrut 15q^{47} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 2q^{55} \) \(\mathstrut -\mathstrut 22q^{57} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut -\mathstrut 33q^{61} \) \(\mathstrut -\mathstrut 20q^{63} \) \(\mathstrut -\mathstrut 3q^{65} \) \(\mathstrut +\mathstrut 19q^{67} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut -\mathstrut 42q^{77} \) \(\mathstrut -\mathstrut 29q^{79} \) \(\mathstrut -\mathstrut 36q^{81} \) \(\mathstrut +\mathstrut 14q^{83} \) \(\mathstrut +\mathstrut 10q^{85} \) \(\mathstrut -\mathstrut 32q^{87} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 7q^{91} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 39q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.26002 −1.30483 −0.652413 0.757864i \(-0.726243\pi\)
−0.652413 + 0.757864i \(0.726243\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −3.39221 −1.28214 −0.641068 0.767484i \(-0.721508\pi\)
−0.641068 + 0.767484i \(0.721508\pi\)
\(8\) 0 0
\(9\) 2.10771 0.702570
\(10\) 0 0
\(11\) −3.74534 −1.12926 −0.564632 0.825343i \(-0.690982\pi\)
−0.564632 + 0.825343i \(0.690982\pi\)
\(12\) 0 0
\(13\) −4.09762 −1.13647 −0.568237 0.822865i \(-0.692374\pi\)
−0.568237 + 0.822865i \(0.692374\pi\)
\(14\) 0 0
\(15\) 2.26002 0.583536
\(16\) 0 0
\(17\) 1.81997 0.441408 0.220704 0.975341i \(-0.429165\pi\)
0.220704 + 0.975341i \(0.429165\pi\)
\(18\) 0 0
\(19\) −0.507197 −0.116359 −0.0581795 0.998306i \(-0.518530\pi\)
−0.0581795 + 0.998306i \(0.518530\pi\)
\(20\) 0 0
\(21\) 7.66648 1.67296
\(22\) 0 0
\(23\) 2.07431 0.432524 0.216262 0.976335i \(-0.430614\pi\)
0.216262 + 0.976335i \(0.430614\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 2.01660 0.388095
\(28\) 0 0
\(29\) −2.08288 −0.386781 −0.193391 0.981122i \(-0.561948\pi\)
−0.193391 + 0.981122i \(0.561948\pi\)
\(30\) 0 0
\(31\) −3.75361 −0.674168 −0.337084 0.941474i \(-0.609441\pi\)
−0.337084 + 0.941474i \(0.609441\pi\)
\(32\) 0 0
\(33\) 8.46457 1.47349
\(34\) 0 0
\(35\) 3.39221 0.573388
\(36\) 0 0
\(37\) 5.62876 0.925363 0.462681 0.886525i \(-0.346887\pi\)
0.462681 + 0.886525i \(0.346887\pi\)
\(38\) 0 0
\(39\) 9.26071 1.48290
\(40\) 0 0
\(41\) −1.53690 −0.240024 −0.120012 0.992772i \(-0.538293\pi\)
−0.120012 + 0.992772i \(0.538293\pi\)
\(42\) 0 0
\(43\) 6.39486 0.975207 0.487603 0.873065i \(-0.337871\pi\)
0.487603 + 0.873065i \(0.337871\pi\)
\(44\) 0 0
\(45\) −2.10771 −0.314199
\(46\) 0 0
\(47\) 11.8482 1.72824 0.864118 0.503289i \(-0.167877\pi\)
0.864118 + 0.503289i \(0.167877\pi\)
\(48\) 0 0
\(49\) 4.50709 0.643870
\(50\) 0 0
\(51\) −4.11318 −0.575960
\(52\) 0 0
\(53\) −11.1822 −1.53599 −0.767995 0.640456i \(-0.778746\pi\)
−0.767995 + 0.640456i \(0.778746\pi\)
\(54\) 0 0
\(55\) 3.74534 0.505022
\(56\) 0 0
\(57\) 1.14628 0.151828
\(58\) 0 0
\(59\) 13.8248 1.79983 0.899917 0.436061i \(-0.143627\pi\)
0.899917 + 0.436061i \(0.143627\pi\)
\(60\) 0 0
\(61\) −3.22244 −0.412592 −0.206296 0.978490i \(-0.566141\pi\)
−0.206296 + 0.978490i \(0.566141\pi\)
\(62\) 0 0
\(63\) −7.14979 −0.900789
\(64\) 0 0
\(65\) 4.09762 0.508247
\(66\) 0 0
\(67\) 2.15862 0.263717 0.131859 0.991269i \(-0.457905\pi\)
0.131859 + 0.991269i \(0.457905\pi\)
\(68\) 0 0
\(69\) −4.68799 −0.564368
\(70\) 0 0
\(71\) 9.69871 1.15103 0.575513 0.817793i \(-0.304803\pi\)
0.575513 + 0.817793i \(0.304803\pi\)
\(72\) 0 0
\(73\) −5.04323 −0.590265 −0.295132 0.955456i \(-0.595364\pi\)
−0.295132 + 0.955456i \(0.595364\pi\)
\(74\) 0 0
\(75\) −2.26002 −0.260965
\(76\) 0 0
\(77\) 12.7050 1.44787
\(78\) 0 0
\(79\) 0.358510 0.0403356 0.0201678 0.999797i \(-0.493580\pi\)
0.0201678 + 0.999797i \(0.493580\pi\)
\(80\) 0 0
\(81\) −10.8807 −1.20897
\(82\) 0 0
\(83\) 15.6083 1.71323 0.856617 0.515952i \(-0.172562\pi\)
0.856617 + 0.515952i \(0.172562\pi\)
\(84\) 0 0
\(85\) −1.81997 −0.197403
\(86\) 0 0
\(87\) 4.70736 0.504682
\(88\) 0 0
\(89\) −15.3504 −1.62714 −0.813568 0.581470i \(-0.802478\pi\)
−0.813568 + 0.581470i \(0.802478\pi\)
\(90\) 0 0
\(91\) 13.9000 1.45711
\(92\) 0 0
\(93\) 8.48325 0.879672
\(94\) 0 0
\(95\) 0.507197 0.0520373
\(96\) 0 0
\(97\) −6.27268 −0.636894 −0.318447 0.947941i \(-0.603161\pi\)
−0.318447 + 0.947941i \(0.603161\pi\)
\(98\) 0 0
\(99\) −7.89409 −0.793386
\(100\) 0 0
\(101\) 12.9627 1.28984 0.644919 0.764251i \(-0.276891\pi\)
0.644919 + 0.764251i \(0.276891\pi\)
\(102\) 0 0
\(103\) −2.95389 −0.291055 −0.145528 0.989354i \(-0.546488\pi\)
−0.145528 + 0.989354i \(0.546488\pi\)
\(104\) 0 0
\(105\) −7.66648 −0.748172
\(106\) 0 0
\(107\) 4.40788 0.426126 0.213063 0.977039i \(-0.431656\pi\)
0.213063 + 0.977039i \(0.431656\pi\)
\(108\) 0 0
\(109\) 0.488243 0.0467652 0.0233826 0.999727i \(-0.492556\pi\)
0.0233826 + 0.999727i \(0.492556\pi\)
\(110\) 0 0
\(111\) −12.7211 −1.20744
\(112\) 0 0
\(113\) −9.31385 −0.876173 −0.438087 0.898933i \(-0.644344\pi\)
−0.438087 + 0.898933i \(0.644344\pi\)
\(114\) 0 0
\(115\) −2.07431 −0.193430
\(116\) 0 0
\(117\) −8.63658 −0.798453
\(118\) 0 0
\(119\) −6.17372 −0.565944
\(120\) 0 0
\(121\) 3.02760 0.275236
\(122\) 0 0
\(123\) 3.47343 0.313189
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 11.0353 0.979227 0.489614 0.871940i \(-0.337138\pi\)
0.489614 + 0.871940i \(0.337138\pi\)
\(128\) 0 0
\(129\) −14.4525 −1.27247
\(130\) 0 0
\(131\) 17.7826 1.55368 0.776838 0.629701i \(-0.216822\pi\)
0.776838 + 0.629701i \(0.216822\pi\)
\(132\) 0 0
\(133\) 1.72052 0.149188
\(134\) 0 0
\(135\) −2.01660 −0.173561
\(136\) 0 0
\(137\) 0.381459 0.0325902 0.0162951 0.999867i \(-0.494813\pi\)
0.0162951 + 0.999867i \(0.494813\pi\)
\(138\) 0 0
\(139\) −18.2364 −1.54679 −0.773396 0.633923i \(-0.781444\pi\)
−0.773396 + 0.633923i \(0.781444\pi\)
\(140\) 0 0
\(141\) −26.7772 −2.25505
\(142\) 0 0
\(143\) 15.3470 1.28338
\(144\) 0 0
\(145\) 2.08288 0.172974
\(146\) 0 0
\(147\) −10.1861 −0.840139
\(148\) 0 0
\(149\) −10.2845 −0.842542 −0.421271 0.906935i \(-0.638416\pi\)
−0.421271 + 0.906935i \(0.638416\pi\)
\(150\) 0 0
\(151\) −12.9619 −1.05482 −0.527412 0.849610i \(-0.676837\pi\)
−0.527412 + 0.849610i \(0.676837\pi\)
\(152\) 0 0
\(153\) 3.83597 0.310120
\(154\) 0 0
\(155\) 3.75361 0.301497
\(156\) 0 0
\(157\) 22.3779 1.78595 0.892977 0.450102i \(-0.148612\pi\)
0.892977 + 0.450102i \(0.148612\pi\)
\(158\) 0 0
\(159\) 25.2720 2.00420
\(160\) 0 0
\(161\) −7.03650 −0.554554
\(162\) 0 0
\(163\) 5.83282 0.456862 0.228431 0.973560i \(-0.426641\pi\)
0.228431 + 0.973560i \(0.426641\pi\)
\(164\) 0 0
\(165\) −8.46457 −0.658966
\(166\) 0 0
\(167\) −16.3904 −1.26833 −0.634165 0.773198i \(-0.718656\pi\)
−0.634165 + 0.773198i \(0.718656\pi\)
\(168\) 0 0
\(169\) 3.79046 0.291574
\(170\) 0 0
\(171\) −1.06902 −0.0817503
\(172\) 0 0
\(173\) −14.8047 −1.12558 −0.562792 0.826599i \(-0.690273\pi\)
−0.562792 + 0.826599i \(0.690273\pi\)
\(174\) 0 0
\(175\) −3.39221 −0.256427
\(176\) 0 0
\(177\) −31.2444 −2.34847
\(178\) 0 0
\(179\) 14.7287 1.10087 0.550436 0.834878i \(-0.314462\pi\)
0.550436 + 0.834878i \(0.314462\pi\)
\(180\) 0 0
\(181\) 2.65539 0.197373 0.0986867 0.995119i \(-0.468536\pi\)
0.0986867 + 0.995119i \(0.468536\pi\)
\(182\) 0 0
\(183\) 7.28280 0.538360
\(184\) 0 0
\(185\) −5.62876 −0.413835
\(186\) 0 0
\(187\) −6.81641 −0.498466
\(188\) 0 0
\(189\) −6.84073 −0.497590
\(190\) 0 0
\(191\) −21.3629 −1.54576 −0.772881 0.634551i \(-0.781185\pi\)
−0.772881 + 0.634551i \(0.781185\pi\)
\(192\) 0 0
\(193\) 21.7573 1.56613 0.783064 0.621941i \(-0.213656\pi\)
0.783064 + 0.621941i \(0.213656\pi\)
\(194\) 0 0
\(195\) −9.26071 −0.663173
\(196\) 0 0
\(197\) −1.53627 −0.109454 −0.0547272 0.998501i \(-0.517429\pi\)
−0.0547272 + 0.998501i \(0.517429\pi\)
\(198\) 0 0
\(199\) 8.79522 0.623477 0.311738 0.950168i \(-0.399089\pi\)
0.311738 + 0.950168i \(0.399089\pi\)
\(200\) 0 0
\(201\) −4.87853 −0.344105
\(202\) 0 0
\(203\) 7.06557 0.495906
\(204\) 0 0
\(205\) 1.53690 0.107342
\(206\) 0 0
\(207\) 4.37204 0.303878
\(208\) 0 0
\(209\) 1.89963 0.131400
\(210\) 0 0
\(211\) 19.1073 1.31540 0.657700 0.753280i \(-0.271530\pi\)
0.657700 + 0.753280i \(0.271530\pi\)
\(212\) 0 0
\(213\) −21.9193 −1.50189
\(214\) 0 0
\(215\) −6.39486 −0.436126
\(216\) 0 0
\(217\) 12.7330 0.864375
\(218\) 0 0
\(219\) 11.3978 0.770193
\(220\) 0 0
\(221\) −7.45754 −0.501648
\(222\) 0 0
\(223\) 13.2852 0.889642 0.444821 0.895620i \(-0.353267\pi\)
0.444821 + 0.895620i \(0.353267\pi\)
\(224\) 0 0
\(225\) 2.10771 0.140514
\(226\) 0 0
\(227\) −7.04735 −0.467749 −0.233874 0.972267i \(-0.575140\pi\)
−0.233874 + 0.972267i \(0.575140\pi\)
\(228\) 0 0
\(229\) −3.56354 −0.235486 −0.117743 0.993044i \(-0.537566\pi\)
−0.117743 + 0.993044i \(0.537566\pi\)
\(230\) 0 0
\(231\) −28.7136 −1.88922
\(232\) 0 0
\(233\) 29.6161 1.94022 0.970109 0.242671i \(-0.0780234\pi\)
0.970109 + 0.242671i \(0.0780234\pi\)
\(234\) 0 0
\(235\) −11.8482 −0.772891
\(236\) 0 0
\(237\) −0.810242 −0.0526309
\(238\) 0 0
\(239\) −10.3630 −0.670328 −0.335164 0.942160i \(-0.608792\pi\)
−0.335164 + 0.942160i \(0.608792\pi\)
\(240\) 0 0
\(241\) 6.38911 0.411559 0.205780 0.978598i \(-0.434027\pi\)
0.205780 + 0.978598i \(0.434027\pi\)
\(242\) 0 0
\(243\) 18.5408 1.18939
\(244\) 0 0
\(245\) −4.50709 −0.287948
\(246\) 0 0
\(247\) 2.07830 0.132239
\(248\) 0 0
\(249\) −35.2752 −2.23547
\(250\) 0 0
\(251\) −18.5430 −1.17042 −0.585212 0.810880i \(-0.698989\pi\)
−0.585212 + 0.810880i \(0.698989\pi\)
\(252\) 0 0
\(253\) −7.76900 −0.488433
\(254\) 0 0
\(255\) 4.11318 0.257577
\(256\) 0 0
\(257\) −20.4171 −1.27359 −0.636793 0.771035i \(-0.719739\pi\)
−0.636793 + 0.771035i \(0.719739\pi\)
\(258\) 0 0
\(259\) −19.0939 −1.18644
\(260\) 0 0
\(261\) −4.39011 −0.271741
\(262\) 0 0
\(263\) −20.4290 −1.25971 −0.629853 0.776714i \(-0.716885\pi\)
−0.629853 + 0.776714i \(0.716885\pi\)
\(264\) 0 0
\(265\) 11.1822 0.686916
\(266\) 0 0
\(267\) 34.6922 2.12313
\(268\) 0 0
\(269\) 20.8410 1.27070 0.635348 0.772226i \(-0.280856\pi\)
0.635348 + 0.772226i \(0.280856\pi\)
\(270\) 0 0
\(271\) −31.8020 −1.93184 −0.965918 0.258847i \(-0.916657\pi\)
−0.965918 + 0.258847i \(0.916657\pi\)
\(272\) 0 0
\(273\) −31.4143 −1.90128
\(274\) 0 0
\(275\) −3.74534 −0.225853
\(276\) 0 0
\(277\) 12.2380 0.735312 0.367656 0.929962i \(-0.380160\pi\)
0.367656 + 0.929962i \(0.380160\pi\)
\(278\) 0 0
\(279\) −7.91152 −0.473650
\(280\) 0 0
\(281\) −9.90590 −0.590936 −0.295468 0.955353i \(-0.595476\pi\)
−0.295468 + 0.955353i \(0.595476\pi\)
\(282\) 0 0
\(283\) 9.95462 0.591741 0.295870 0.955228i \(-0.404390\pi\)
0.295870 + 0.955228i \(0.404390\pi\)
\(284\) 0 0
\(285\) −1.14628 −0.0678996
\(286\) 0 0
\(287\) 5.21349 0.307743
\(288\) 0 0
\(289\) −13.6877 −0.805159
\(290\) 0 0
\(291\) 14.1764 0.831036
\(292\) 0 0
\(293\) 16.7691 0.979663 0.489831 0.871817i \(-0.337058\pi\)
0.489831 + 0.871817i \(0.337058\pi\)
\(294\) 0 0
\(295\) −13.8248 −0.804910
\(296\) 0 0
\(297\) −7.55286 −0.438261
\(298\) 0 0
\(299\) −8.49973 −0.491552
\(300\) 0 0
\(301\) −21.6927 −1.25035
\(302\) 0 0
\(303\) −29.2960 −1.68301
\(304\) 0 0
\(305\) 3.22244 0.184517
\(306\) 0 0
\(307\) −10.7919 −0.615928 −0.307964 0.951398i \(-0.599648\pi\)
−0.307964 + 0.951398i \(0.599648\pi\)
\(308\) 0 0
\(309\) 6.67585 0.379776
\(310\) 0 0
\(311\) 20.9120 1.18581 0.592906 0.805272i \(-0.297981\pi\)
0.592906 + 0.805272i \(0.297981\pi\)
\(312\) 0 0
\(313\) −17.6297 −0.996490 −0.498245 0.867036i \(-0.666022\pi\)
−0.498245 + 0.867036i \(0.666022\pi\)
\(314\) 0 0
\(315\) 7.14979 0.402845
\(316\) 0 0
\(317\) 30.3357 1.70382 0.851910 0.523688i \(-0.175444\pi\)
0.851910 + 0.523688i \(0.175444\pi\)
\(318\) 0 0
\(319\) 7.80111 0.436778
\(320\) 0 0
\(321\) −9.96191 −0.556020
\(322\) 0 0
\(323\) −0.923083 −0.0513617
\(324\) 0 0
\(325\) −4.09762 −0.227295
\(326\) 0 0
\(327\) −1.10344 −0.0610204
\(328\) 0 0
\(329\) −40.1916 −2.21583
\(330\) 0 0
\(331\) −27.5661 −1.51517 −0.757586 0.652736i \(-0.773621\pi\)
−0.757586 + 0.652736i \(0.773621\pi\)
\(332\) 0 0
\(333\) 11.8638 0.650132
\(334\) 0 0
\(335\) −2.15862 −0.117938
\(336\) 0 0
\(337\) 22.0074 1.19882 0.599408 0.800443i \(-0.295403\pi\)
0.599408 + 0.800443i \(0.295403\pi\)
\(338\) 0 0
\(339\) 21.0495 1.14325
\(340\) 0 0
\(341\) 14.0586 0.761314
\(342\) 0 0
\(343\) 8.45647 0.456606
\(344\) 0 0
\(345\) 4.68799 0.252393
\(346\) 0 0
\(347\) 27.4502 1.47361 0.736803 0.676107i \(-0.236334\pi\)
0.736803 + 0.676107i \(0.236334\pi\)
\(348\) 0 0
\(349\) −18.8851 −1.01090 −0.505449 0.862857i \(-0.668673\pi\)
−0.505449 + 0.862857i \(0.668673\pi\)
\(350\) 0 0
\(351\) −8.26325 −0.441060
\(352\) 0 0
\(353\) 20.3719 1.08429 0.542143 0.840286i \(-0.317613\pi\)
0.542143 + 0.840286i \(0.317613\pi\)
\(354\) 0 0
\(355\) −9.69871 −0.514754
\(356\) 0 0
\(357\) 13.9528 0.738458
\(358\) 0 0
\(359\) −12.4579 −0.657504 −0.328752 0.944416i \(-0.606628\pi\)
−0.328752 + 0.944416i \(0.606628\pi\)
\(360\) 0 0
\(361\) −18.7428 −0.986461
\(362\) 0 0
\(363\) −6.84244 −0.359135
\(364\) 0 0
\(365\) 5.04323 0.263974
\(366\) 0 0
\(367\) −26.0304 −1.35877 −0.679387 0.733780i \(-0.737754\pi\)
−0.679387 + 0.733780i \(0.737754\pi\)
\(368\) 0 0
\(369\) −3.23934 −0.168633
\(370\) 0 0
\(371\) 37.9323 1.96935
\(372\) 0 0
\(373\) −7.60542 −0.393794 −0.196897 0.980424i \(-0.563086\pi\)
−0.196897 + 0.980424i \(0.563086\pi\)
\(374\) 0 0
\(375\) 2.26002 0.116707
\(376\) 0 0
\(377\) 8.53485 0.439567
\(378\) 0 0
\(379\) 1.62179 0.0833058 0.0416529 0.999132i \(-0.486738\pi\)
0.0416529 + 0.999132i \(0.486738\pi\)
\(380\) 0 0
\(381\) −24.9401 −1.27772
\(382\) 0 0
\(383\) 7.38142 0.377173 0.188586 0.982057i \(-0.439609\pi\)
0.188586 + 0.982057i \(0.439609\pi\)
\(384\) 0 0
\(385\) −12.7050 −0.647506
\(386\) 0 0
\(387\) 13.4785 0.685151
\(388\) 0 0
\(389\) −8.03121 −0.407199 −0.203599 0.979054i \(-0.565264\pi\)
−0.203599 + 0.979054i \(0.565264\pi\)
\(390\) 0 0
\(391\) 3.77518 0.190919
\(392\) 0 0
\(393\) −40.1892 −2.02728
\(394\) 0 0
\(395\) −0.358510 −0.0180386
\(396\) 0 0
\(397\) 29.5537 1.48326 0.741630 0.670809i \(-0.234053\pi\)
0.741630 + 0.670809i \(0.234053\pi\)
\(398\) 0 0
\(399\) −3.88841 −0.194664
\(400\) 0 0
\(401\) 1.00000 0.0499376
\(402\) 0 0
\(403\) 15.3809 0.766175
\(404\) 0 0
\(405\) 10.8807 0.540666
\(406\) 0 0
\(407\) −21.0816 −1.04498
\(408\) 0 0
\(409\) 9.87886 0.488478 0.244239 0.969715i \(-0.421462\pi\)
0.244239 + 0.969715i \(0.421462\pi\)
\(410\) 0 0
\(411\) −0.862106 −0.0425246
\(412\) 0 0
\(413\) −46.8966 −2.30763
\(414\) 0 0
\(415\) −15.6083 −0.766182
\(416\) 0 0
\(417\) 41.2147 2.01829
\(418\) 0 0
\(419\) 9.54485 0.466297 0.233148 0.972441i \(-0.425097\pi\)
0.233148 + 0.972441i \(0.425097\pi\)
\(420\) 0 0
\(421\) −37.6977 −1.83727 −0.918636 0.395105i \(-0.870708\pi\)
−0.918636 + 0.395105i \(0.870708\pi\)
\(422\) 0 0
\(423\) 24.9725 1.21421
\(424\) 0 0
\(425\) 1.81997 0.0882815
\(426\) 0 0
\(427\) 10.9312 0.528998
\(428\) 0 0
\(429\) −34.6845 −1.67459
\(430\) 0 0
\(431\) −6.48138 −0.312197 −0.156098 0.987742i \(-0.549892\pi\)
−0.156098 + 0.987742i \(0.549892\pi\)
\(432\) 0 0
\(433\) −6.09537 −0.292925 −0.146462 0.989216i \(-0.546789\pi\)
−0.146462 + 0.989216i \(0.546789\pi\)
\(434\) 0 0
\(435\) −4.70736 −0.225701
\(436\) 0 0
\(437\) −1.05208 −0.0503280
\(438\) 0 0
\(439\) 29.4219 1.40423 0.702114 0.712064i \(-0.252239\pi\)
0.702114 + 0.712064i \(0.252239\pi\)
\(440\) 0 0
\(441\) 9.49964 0.452364
\(442\) 0 0
\(443\) −13.8208 −0.656648 −0.328324 0.944565i \(-0.606484\pi\)
−0.328324 + 0.944565i \(0.606484\pi\)
\(444\) 0 0
\(445\) 15.3504 0.727677
\(446\) 0 0
\(447\) 23.2433 1.09937
\(448\) 0 0
\(449\) 13.8881 0.655420 0.327710 0.944778i \(-0.393723\pi\)
0.327710 + 0.944778i \(0.393723\pi\)
\(450\) 0 0
\(451\) 5.75622 0.271050
\(452\) 0 0
\(453\) 29.2942 1.37636
\(454\) 0 0
\(455\) −13.9000 −0.651641
\(456\) 0 0
\(457\) 22.2624 1.04139 0.520695 0.853743i \(-0.325673\pi\)
0.520695 + 0.853743i \(0.325673\pi\)
\(458\) 0 0
\(459\) 3.67015 0.171308
\(460\) 0 0
\(461\) 18.8057 0.875867 0.437933 0.899007i \(-0.355711\pi\)
0.437933 + 0.899007i \(0.355711\pi\)
\(462\) 0 0
\(463\) 5.73689 0.266616 0.133308 0.991075i \(-0.457440\pi\)
0.133308 + 0.991075i \(0.457440\pi\)
\(464\) 0 0
\(465\) −8.48325 −0.393401
\(466\) 0 0
\(467\) −25.6640 −1.18759 −0.593793 0.804618i \(-0.702370\pi\)
−0.593793 + 0.804618i \(0.702370\pi\)
\(468\) 0 0
\(469\) −7.32249 −0.338121
\(470\) 0 0
\(471\) −50.5747 −2.33036
\(472\) 0 0
\(473\) −23.9509 −1.10127
\(474\) 0 0
\(475\) −0.507197 −0.0232718
\(476\) 0 0
\(477\) −23.5688 −1.07914
\(478\) 0 0
\(479\) 2.81042 0.128411 0.0642056 0.997937i \(-0.479549\pi\)
0.0642056 + 0.997937i \(0.479549\pi\)
\(480\) 0 0
\(481\) −23.0645 −1.05165
\(482\) 0 0
\(483\) 15.9027 0.723596
\(484\) 0 0
\(485\) 6.27268 0.284828
\(486\) 0 0
\(487\) −13.2505 −0.600437 −0.300218 0.953870i \(-0.597060\pi\)
−0.300218 + 0.953870i \(0.597060\pi\)
\(488\) 0 0
\(489\) −13.1823 −0.596125
\(490\) 0 0
\(491\) 6.99717 0.315778 0.157889 0.987457i \(-0.449531\pi\)
0.157889 + 0.987457i \(0.449531\pi\)
\(492\) 0 0
\(493\) −3.79078 −0.170728
\(494\) 0 0
\(495\) 7.89409 0.354813
\(496\) 0 0
\(497\) −32.9001 −1.47577
\(498\) 0 0
\(499\) 34.3136 1.53609 0.768044 0.640397i \(-0.221230\pi\)
0.768044 + 0.640397i \(0.221230\pi\)
\(500\) 0 0
\(501\) 37.0428 1.65495
\(502\) 0 0
\(503\) −26.0040 −1.15946 −0.579731 0.814808i \(-0.696842\pi\)
−0.579731 + 0.814808i \(0.696842\pi\)
\(504\) 0 0
\(505\) −12.9627 −0.576833
\(506\) 0 0
\(507\) −8.56654 −0.380453
\(508\) 0 0
\(509\) −12.7628 −0.565701 −0.282850 0.959164i \(-0.591280\pi\)
−0.282850 + 0.959164i \(0.591280\pi\)
\(510\) 0 0
\(511\) 17.1077 0.756799
\(512\) 0 0
\(513\) −1.02281 −0.0451583
\(514\) 0 0
\(515\) 2.95389 0.130164
\(516\) 0 0
\(517\) −44.3756 −1.95163
\(518\) 0 0
\(519\) 33.4591 1.46869
\(520\) 0 0
\(521\) −40.0435 −1.75434 −0.877168 0.480183i \(-0.840570\pi\)
−0.877168 + 0.480183i \(0.840570\pi\)
\(522\) 0 0
\(523\) −31.4358 −1.37459 −0.687296 0.726377i \(-0.741203\pi\)
−0.687296 + 0.726377i \(0.741203\pi\)
\(524\) 0 0
\(525\) 7.66648 0.334593
\(526\) 0 0
\(527\) −6.83146 −0.297583
\(528\) 0 0
\(529\) −18.6972 −0.812923
\(530\) 0 0
\(531\) 29.1386 1.26451
\(532\) 0 0
\(533\) 6.29763 0.272781
\(534\) 0 0
\(535\) −4.40788 −0.190569
\(536\) 0 0
\(537\) −33.2871 −1.43645
\(538\) 0 0
\(539\) −16.8806 −0.727099
\(540\) 0 0
\(541\) −6.01018 −0.258398 −0.129199 0.991619i \(-0.541241\pi\)
−0.129199 + 0.991619i \(0.541241\pi\)
\(542\) 0 0
\(543\) −6.00124 −0.257538
\(544\) 0 0
\(545\) −0.488243 −0.0209140
\(546\) 0 0
\(547\) −12.0973 −0.517242 −0.258621 0.965979i \(-0.583268\pi\)
−0.258621 + 0.965979i \(0.583268\pi\)
\(548\) 0 0
\(549\) −6.79197 −0.289874
\(550\) 0 0
\(551\) 1.05643 0.0450055
\(552\) 0 0
\(553\) −1.21614 −0.0517156
\(554\) 0 0
\(555\) 12.7211 0.539982
\(556\) 0 0
\(557\) −3.38716 −0.143519 −0.0717594 0.997422i \(-0.522861\pi\)
−0.0717594 + 0.997422i \(0.522861\pi\)
\(558\) 0 0
\(559\) −26.2037 −1.10830
\(560\) 0 0
\(561\) 15.4053 0.650411
\(562\) 0 0
\(563\) −16.3650 −0.689703 −0.344852 0.938657i \(-0.612071\pi\)
−0.344852 + 0.938657i \(0.612071\pi\)
\(564\) 0 0
\(565\) 9.31385 0.391837
\(566\) 0 0
\(567\) 36.9096 1.55006
\(568\) 0 0
\(569\) −2.67962 −0.112335 −0.0561677 0.998421i \(-0.517888\pi\)
−0.0561677 + 0.998421i \(0.517888\pi\)
\(570\) 0 0
\(571\) −29.9569 −1.25366 −0.626830 0.779156i \(-0.715648\pi\)
−0.626830 + 0.779156i \(0.715648\pi\)
\(572\) 0 0
\(573\) 48.2806 2.01695
\(574\) 0 0
\(575\) 2.07431 0.0865047
\(576\) 0 0
\(577\) −11.7316 −0.488393 −0.244197 0.969726i \(-0.578524\pi\)
−0.244197 + 0.969726i \(0.578524\pi\)
\(578\) 0 0
\(579\) −49.1721 −2.04352
\(580\) 0 0
\(581\) −52.9467 −2.19660
\(582\) 0 0
\(583\) 41.8811 1.73454
\(584\) 0 0
\(585\) 8.63658 0.357079
\(586\) 0 0
\(587\) 30.6515 1.26512 0.632561 0.774511i \(-0.282004\pi\)
0.632561 + 0.774511i \(0.282004\pi\)
\(588\) 0 0
\(589\) 1.90382 0.0784455
\(590\) 0 0
\(591\) 3.47200 0.142819
\(592\) 0 0
\(593\) 34.6617 1.42338 0.711692 0.702491i \(-0.247929\pi\)
0.711692 + 0.702491i \(0.247929\pi\)
\(594\) 0 0
\(595\) 6.17372 0.253098
\(596\) 0 0
\(597\) −19.8774 −0.813528
\(598\) 0 0
\(599\) −36.1452 −1.47685 −0.738426 0.674334i \(-0.764431\pi\)
−0.738426 + 0.674334i \(0.764431\pi\)
\(600\) 0 0
\(601\) 12.8712 0.525027 0.262513 0.964928i \(-0.415449\pi\)
0.262513 + 0.964928i \(0.415449\pi\)
\(602\) 0 0
\(603\) 4.54974 0.185280
\(604\) 0 0
\(605\) −3.02760 −0.123089
\(606\) 0 0
\(607\) −31.3330 −1.27177 −0.635883 0.771786i \(-0.719364\pi\)
−0.635883 + 0.771786i \(0.719364\pi\)
\(608\) 0 0
\(609\) −15.9684 −0.647071
\(610\) 0 0
\(611\) −48.5494 −1.96410
\(612\) 0 0
\(613\) −12.0796 −0.487889 −0.243944 0.969789i \(-0.578441\pi\)
−0.243944 + 0.969789i \(0.578441\pi\)
\(614\) 0 0
\(615\) −3.47343 −0.140062
\(616\) 0 0
\(617\) −43.2988 −1.74314 −0.871572 0.490267i \(-0.836899\pi\)
−0.871572 + 0.490267i \(0.836899\pi\)
\(618\) 0 0
\(619\) 16.7755 0.674266 0.337133 0.941457i \(-0.390543\pi\)
0.337133 + 0.941457i \(0.390543\pi\)
\(620\) 0 0
\(621\) 4.18305 0.167860
\(622\) 0 0
\(623\) 52.0717 2.08621
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −4.29320 −0.171454
\(628\) 0 0
\(629\) 10.2442 0.408462
\(630\) 0 0
\(631\) −41.2859 −1.64357 −0.821783 0.569801i \(-0.807020\pi\)
−0.821783 + 0.569801i \(0.807020\pi\)
\(632\) 0 0
\(633\) −43.1829 −1.71637
\(634\) 0 0
\(635\) −11.0353 −0.437924
\(636\) 0 0
\(637\) −18.4683 −0.731742
\(638\) 0 0
\(639\) 20.4421 0.808676
\(640\) 0 0
\(641\) 36.9689 1.46018 0.730092 0.683349i \(-0.239477\pi\)
0.730092 + 0.683349i \(0.239477\pi\)
\(642\) 0 0
\(643\) −6.65748 −0.262545 −0.131273 0.991346i \(-0.541906\pi\)
−0.131273 + 0.991346i \(0.541906\pi\)
\(644\) 0 0
\(645\) 14.4525 0.569068
\(646\) 0 0
\(647\) 16.6223 0.653491 0.326745 0.945112i \(-0.394048\pi\)
0.326745 + 0.945112i \(0.394048\pi\)
\(648\) 0 0
\(649\) −51.7786 −2.03249
\(650\) 0 0
\(651\) −28.7770 −1.12786
\(652\) 0 0
\(653\) −38.0685 −1.48974 −0.744869 0.667211i \(-0.767488\pi\)
−0.744869 + 0.667211i \(0.767488\pi\)
\(654\) 0 0
\(655\) −17.7826 −0.694825
\(656\) 0 0
\(657\) −10.6297 −0.414702
\(658\) 0 0
\(659\) 23.6347 0.920678 0.460339 0.887743i \(-0.347728\pi\)
0.460339 + 0.887743i \(0.347728\pi\)
\(660\) 0 0
\(661\) 27.6608 1.07588 0.537940 0.842983i \(-0.319203\pi\)
0.537940 + 0.842983i \(0.319203\pi\)
\(662\) 0 0
\(663\) 16.8542 0.654564
\(664\) 0 0
\(665\) −1.72052 −0.0667189
\(666\) 0 0
\(667\) −4.32054 −0.167292
\(668\) 0 0
\(669\) −30.0248 −1.16083
\(670\) 0 0
\(671\) 12.0692 0.465925
\(672\) 0 0
\(673\) −3.49481 −0.134715 −0.0673575 0.997729i \(-0.521457\pi\)
−0.0673575 + 0.997729i \(0.521457\pi\)
\(674\) 0 0
\(675\) 2.01660 0.0776189
\(676\) 0 0
\(677\) −37.6498 −1.44700 −0.723500 0.690325i \(-0.757468\pi\)
−0.723500 + 0.690325i \(0.757468\pi\)
\(678\) 0 0
\(679\) 21.2783 0.816585
\(680\) 0 0
\(681\) 15.9272 0.610331
\(682\) 0 0
\(683\) −26.4630 −1.01258 −0.506288 0.862364i \(-0.668983\pi\)
−0.506288 + 0.862364i \(0.668983\pi\)
\(684\) 0 0
\(685\) −0.381459 −0.0145748
\(686\) 0 0
\(687\) 8.05369 0.307268
\(688\) 0 0
\(689\) 45.8203 1.74561
\(690\) 0 0
\(691\) 0.435246 0.0165575 0.00827877 0.999966i \(-0.497365\pi\)
0.00827877 + 0.999966i \(0.497365\pi\)
\(692\) 0 0
\(693\) 26.7784 1.01723
\(694\) 0 0
\(695\) 18.2364 0.691747
\(696\) 0 0
\(697\) −2.79711 −0.105948
\(698\) 0 0
\(699\) −66.9332 −2.53165
\(700\) 0 0
\(701\) −49.6967 −1.87702 −0.938509 0.345254i \(-0.887793\pi\)
−0.938509 + 0.345254i \(0.887793\pi\)
\(702\) 0 0
\(703\) −2.85489 −0.107674
\(704\) 0 0
\(705\) 26.7772 1.00849
\(706\) 0 0
\(707\) −43.9722 −1.65375
\(708\) 0 0
\(709\) −26.3514 −0.989646 −0.494823 0.868994i \(-0.664767\pi\)
−0.494823 + 0.868994i \(0.664767\pi\)
\(710\) 0 0
\(711\) 0.755636 0.0283386
\(712\) 0 0
\(713\) −7.78615 −0.291594
\(714\) 0 0
\(715\) −15.3470 −0.573945
\(716\) 0 0
\(717\) 23.4207 0.874661
\(718\) 0 0
\(719\) 44.6579 1.66546 0.832730 0.553679i \(-0.186777\pi\)
0.832730 + 0.553679i \(0.186777\pi\)
\(720\) 0 0
\(721\) 10.0202 0.373172
\(722\) 0 0
\(723\) −14.4396 −0.537013
\(724\) 0 0
\(725\) −2.08288 −0.0773563
\(726\) 0 0
\(727\) 8.39329 0.311290 0.155645 0.987813i \(-0.450254\pi\)
0.155645 + 0.987813i \(0.450254\pi\)
\(728\) 0 0
\(729\) −9.26064 −0.342987
\(730\) 0 0
\(731\) 11.6385 0.430464
\(732\) 0 0
\(733\) 10.7144 0.395746 0.197873 0.980228i \(-0.436597\pi\)
0.197873 + 0.980228i \(0.436597\pi\)
\(734\) 0 0
\(735\) 10.1861 0.375721
\(736\) 0 0
\(737\) −8.08477 −0.297806
\(738\) 0 0
\(739\) 31.6523 1.16435 0.582173 0.813065i \(-0.302202\pi\)
0.582173 + 0.813065i \(0.302202\pi\)
\(740\) 0 0
\(741\) −4.69700 −0.172549
\(742\) 0 0
\(743\) 37.7808 1.38604 0.693021 0.720918i \(-0.256279\pi\)
0.693021 + 0.720918i \(0.256279\pi\)
\(744\) 0 0
\(745\) 10.2845 0.376796
\(746\) 0 0
\(747\) 32.8978 1.20367
\(748\) 0 0
\(749\) −14.9524 −0.546351
\(750\) 0 0
\(751\) 40.0582 1.46174 0.730871 0.682515i \(-0.239114\pi\)
0.730871 + 0.682515i \(0.239114\pi\)
\(752\) 0 0
\(753\) 41.9076 1.52720
\(754\) 0 0
\(755\) 12.9619 0.471731
\(756\) 0 0
\(757\) −20.9954 −0.763092 −0.381546 0.924350i \(-0.624608\pi\)
−0.381546 + 0.924350i \(0.624608\pi\)
\(758\) 0 0
\(759\) 17.5581 0.637320
\(760\) 0 0
\(761\) −47.3283 −1.71565 −0.857825 0.513942i \(-0.828185\pi\)
−0.857825 + 0.513942i \(0.828185\pi\)
\(762\) 0 0
\(763\) −1.65622 −0.0599593
\(764\) 0 0
\(765\) −3.83597 −0.138690
\(766\) 0 0
\(767\) −56.6487 −2.04547
\(768\) 0 0
\(769\) 21.0421 0.758797 0.379399 0.925233i \(-0.376131\pi\)
0.379399 + 0.925233i \(0.376131\pi\)
\(770\) 0 0
\(771\) 46.1432 1.66181
\(772\) 0 0
\(773\) 6.72545 0.241898 0.120949 0.992659i \(-0.461406\pi\)
0.120949 + 0.992659i \(0.461406\pi\)
\(774\) 0 0
\(775\) −3.75361 −0.134834
\(776\) 0 0
\(777\) 43.1528 1.54810
\(778\) 0 0
\(779\) 0.779511 0.0279289
\(780\) 0 0
\(781\) −36.3250 −1.29981
\(782\) 0 0
\(783\) −4.20034 −0.150108
\(784\) 0 0
\(785\) −22.3779 −0.798703
\(786\) 0 0
\(787\) 33.0061 1.17654 0.588270 0.808665i \(-0.299809\pi\)
0.588270 + 0.808665i \(0.299809\pi\)
\(788\) 0 0
\(789\) 46.1701 1.64370
\(790\) 0 0
\(791\) 31.5945 1.12337
\(792\) 0 0
\(793\) 13.2043 0.468900
\(794\) 0 0
\(795\) −25.2720 −0.896305
\(796\) 0 0
\(797\) −26.2697 −0.930522 −0.465261 0.885173i \(-0.654040\pi\)
−0.465261 + 0.885173i \(0.654040\pi\)
\(798\) 0 0
\(799\) 21.5634 0.762857
\(800\) 0 0
\(801\) −32.3541 −1.14318
\(802\) 0 0
\(803\) 18.8886 0.666565
\(804\) 0 0
\(805\) 7.03650 0.248004
\(806\) 0 0
\(807\) −47.1011 −1.65804
\(808\) 0 0
\(809\) 50.6705 1.78148 0.890740 0.454513i \(-0.150187\pi\)
0.890740 + 0.454513i \(0.150187\pi\)
\(810\) 0 0
\(811\) 16.6755 0.585554 0.292777 0.956181i \(-0.405421\pi\)
0.292777 + 0.956181i \(0.405421\pi\)
\(812\) 0 0
\(813\) 71.8734 2.52071
\(814\) 0 0
\(815\) −5.83282 −0.204315
\(816\) 0 0
\(817\) −3.24345 −0.113474
\(818\) 0 0
\(819\) 29.2971 1.02372
\(820\) 0 0
\(821\) −20.5920 −0.718667 −0.359334 0.933209i \(-0.616996\pi\)
−0.359334 + 0.933209i \(0.616996\pi\)
\(822\) 0 0
\(823\) −13.3359 −0.464859 −0.232430 0.972613i \(-0.574668\pi\)
−0.232430 + 0.972613i \(0.574668\pi\)
\(824\) 0 0
\(825\) 8.46457 0.294698
\(826\) 0 0
\(827\) −51.7704 −1.80023 −0.900116 0.435650i \(-0.856518\pi\)
−0.900116 + 0.435650i \(0.856518\pi\)
\(828\) 0 0
\(829\) 40.9639 1.42273 0.711367 0.702821i \(-0.248076\pi\)
0.711367 + 0.702821i \(0.248076\pi\)
\(830\) 0 0
\(831\) −27.6583 −0.959454
\(832\) 0 0
\(833\) 8.20277 0.284209
\(834\) 0 0
\(835\) 16.3904 0.567214
\(836\) 0 0
\(837\) −7.56953 −0.261641
\(838\) 0 0
\(839\) −4.44499 −0.153458 −0.0767291 0.997052i \(-0.524448\pi\)
−0.0767291 + 0.997052i \(0.524448\pi\)
\(840\) 0 0
\(841\) −24.6616 −0.850400
\(842\) 0 0
\(843\) 22.3876 0.771069
\(844\) 0 0
\(845\) −3.79046 −0.130396
\(846\) 0 0
\(847\) −10.2702 −0.352890
\(848\) 0 0
\(849\) −22.4977 −0.772118
\(850\) 0 0
\(851\) 11.6758 0.400241
\(852\) 0 0
\(853\) 17.0743 0.584613 0.292307 0.956325i \(-0.405577\pi\)
0.292307 + 0.956325i \(0.405577\pi\)
\(854\) 0 0
\(855\) 1.06902 0.0365598
\(856\) 0 0
\(857\) 4.15338 0.141877 0.0709384 0.997481i \(-0.477401\pi\)
0.0709384 + 0.997481i \(0.477401\pi\)
\(858\) 0 0
\(859\) −15.0953 −0.515046 −0.257523 0.966272i \(-0.582906\pi\)
−0.257523 + 0.966272i \(0.582906\pi\)
\(860\) 0 0
\(861\) −11.7826 −0.401550
\(862\) 0 0
\(863\) 10.9329 0.372159 0.186080 0.982535i \(-0.440422\pi\)
0.186080 + 0.982535i \(0.440422\pi\)
\(864\) 0 0
\(865\) 14.8047 0.503376
\(866\) 0 0
\(867\) 30.9346 1.05059
\(868\) 0 0
\(869\) −1.34274 −0.0455495
\(870\) 0 0
\(871\) −8.84520 −0.299708
\(872\) 0 0
\(873\) −13.2210 −0.447463
\(874\) 0 0
\(875\) 3.39221 0.114678
\(876\) 0 0
\(877\) 37.9563 1.28169 0.640847 0.767669i \(-0.278583\pi\)
0.640847 + 0.767669i \(0.278583\pi\)
\(878\) 0 0
\(879\) −37.8986 −1.27829
\(880\) 0 0
\(881\) 29.4011 0.990549 0.495274 0.868737i \(-0.335068\pi\)
0.495274 + 0.868737i \(0.335068\pi\)
\(882\) 0 0
\(883\) 29.5819 0.995509 0.497754 0.867318i \(-0.334158\pi\)
0.497754 + 0.867318i \(0.334158\pi\)
\(884\) 0 0
\(885\) 31.2444 1.05027
\(886\) 0 0
\(887\) −15.7308 −0.528189 −0.264095 0.964497i \(-0.585073\pi\)
−0.264095 + 0.964497i \(0.585073\pi\)
\(888\) 0 0
\(889\) −37.4342 −1.25550
\(890\) 0 0
\(891\) 40.7519 1.36524
\(892\) 0 0
\(893\) −6.00937 −0.201096
\(894\) 0 0
\(895\) −14.7287 −0.492325
\(896\) 0 0
\(897\) 19.2096 0.641390
\(898\) 0 0
\(899\) 7.81833 0.260756
\(900\) 0 0
\(901\) −20.3512 −0.677998
\(902\) 0 0
\(903\) 49.0260 1.63148
\(904\) 0 0
\(905\) −2.65539 −0.0882681
\(906\) 0 0
\(907\) 21.8268 0.724746 0.362373 0.932033i \(-0.381967\pi\)
0.362373 + 0.932033i \(0.381967\pi\)
\(908\) 0 0
\(909\) 27.3216 0.906201
\(910\) 0 0
\(911\) −30.3478 −1.00547 −0.502734 0.864441i \(-0.667673\pi\)
−0.502734 + 0.864441i \(0.667673\pi\)
\(912\) 0 0
\(913\) −58.4585 −1.93469
\(914\) 0 0
\(915\) −7.28280 −0.240762
\(916\) 0 0
\(917\) −60.3224 −1.99202
\(918\) 0 0
\(919\) −37.7901 −1.24658 −0.623290 0.781991i \(-0.714204\pi\)
−0.623290 + 0.781991i \(0.714204\pi\)
\(920\) 0 0
\(921\) 24.3900 0.803679
\(922\) 0 0
\(923\) −39.7416 −1.30811
\(924\) 0 0
\(925\) 5.62876 0.185073
\(926\) 0 0
\(927\) −6.22593 −0.204486
\(928\) 0 0
\(929\) 45.8919 1.50567 0.752833 0.658212i \(-0.228687\pi\)
0.752833 + 0.658212i \(0.228687\pi\)
\(930\) 0 0
\(931\) −2.28598 −0.0749201
\(932\) 0 0
\(933\) −47.2617 −1.54728
\(934\) 0 0
\(935\) 6.81641 0.222921
\(936\) 0 0
\(937\) 6.88964 0.225075 0.112537 0.993647i \(-0.464102\pi\)
0.112537 + 0.993647i \(0.464102\pi\)
\(938\) 0 0
\(939\) 39.8436 1.30025
\(940\) 0 0
\(941\) −27.3078 −0.890210 −0.445105 0.895478i \(-0.646834\pi\)
−0.445105 + 0.895478i \(0.646834\pi\)
\(942\) 0 0
\(943\) −3.18801 −0.103816
\(944\) 0 0
\(945\) 6.84073 0.222529
\(946\) 0 0
\(947\) −39.4271 −1.28121 −0.640604 0.767872i \(-0.721316\pi\)
−0.640604 + 0.767872i \(0.721316\pi\)
\(948\) 0 0
\(949\) 20.6652 0.670821
\(950\) 0 0
\(951\) −68.5593 −2.22319
\(952\) 0 0
\(953\) 38.0324 1.23199 0.615995 0.787750i \(-0.288754\pi\)
0.615995 + 0.787750i \(0.288754\pi\)
\(954\) 0 0
\(955\) 21.3629 0.691286
\(956\) 0 0
\(957\) −17.6307 −0.569919
\(958\) 0 0
\(959\) −1.29399 −0.0417851
\(960\) 0 0
\(961\) −16.9104 −0.545497
\(962\) 0 0
\(963\) 9.29052 0.299383
\(964\) 0 0
\(965\) −21.7573 −0.700394
\(966\) 0 0
\(967\) 25.7662 0.828587 0.414293 0.910143i \(-0.364029\pi\)
0.414293 + 0.910143i \(0.364029\pi\)
\(968\) 0 0
\(969\) 2.08619 0.0670181
\(970\) 0 0
\(971\) 5.29562 0.169944 0.0849722 0.996383i \(-0.472920\pi\)
0.0849722 + 0.996383i \(0.472920\pi\)
\(972\) 0 0
\(973\) 61.8618 1.98320
\(974\) 0 0
\(975\) 9.26071 0.296580
\(976\) 0 0
\(977\) −35.1477 −1.12447 −0.562237 0.826976i \(-0.690059\pi\)
−0.562237 + 0.826976i \(0.690059\pi\)
\(978\) 0 0
\(979\) 57.4924 1.83747
\(980\) 0 0
\(981\) 1.02907 0.0328558
\(982\) 0 0
\(983\) 13.7793 0.439492 0.219746 0.975557i \(-0.429477\pi\)
0.219746 + 0.975557i \(0.429477\pi\)
\(984\) 0 0
\(985\) 1.53627 0.0489495
\(986\) 0 0
\(987\) 90.8339 2.89128
\(988\) 0 0
\(989\) 13.2649 0.421800
\(990\) 0 0
\(991\) −4.03898 −0.128302 −0.0641512 0.997940i \(-0.520434\pi\)
−0.0641512 + 0.997940i \(0.520434\pi\)
\(992\) 0 0
\(993\) 62.3001 1.97703
\(994\) 0 0
\(995\) −8.79522 −0.278827
\(996\) 0 0
\(997\) 52.7065 1.66923 0.834616 0.550833i \(-0.185690\pi\)
0.834616 + 0.550833i \(0.185690\pi\)
\(998\) 0 0
\(999\) 11.3510 0.359128
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 \(a_p\))