Properties

Label 8018.2.a.d.1.16
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 30
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(30\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -0.219326 q^{3} +1.00000 q^{4} +2.27443 q^{5} -0.219326 q^{6} -3.32577 q^{7} +1.00000 q^{8} -2.95190 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -0.219326 q^{3} +1.00000 q^{4} +2.27443 q^{5} -0.219326 q^{6} -3.32577 q^{7} +1.00000 q^{8} -2.95190 q^{9} +2.27443 q^{10} +3.87014 q^{11} -0.219326 q^{12} -1.48964 q^{13} -3.32577 q^{14} -0.498840 q^{15} +1.00000 q^{16} +0.776211 q^{17} -2.95190 q^{18} +1.00000 q^{19} +2.27443 q^{20} +0.729426 q^{21} +3.87014 q^{22} -8.89752 q^{23} -0.219326 q^{24} +0.173023 q^{25} -1.48964 q^{26} +1.30540 q^{27} -3.32577 q^{28} +4.85906 q^{29} -0.498840 q^{30} +2.88048 q^{31} +1.00000 q^{32} -0.848822 q^{33} +0.776211 q^{34} -7.56422 q^{35} -2.95190 q^{36} -7.10422 q^{37} +1.00000 q^{38} +0.326715 q^{39} +2.27443 q^{40} -7.81788 q^{41} +0.729426 q^{42} +0.180535 q^{43} +3.87014 q^{44} -6.71388 q^{45} -8.89752 q^{46} +3.93186 q^{47} -0.219326 q^{48} +4.06072 q^{49} +0.173023 q^{50} -0.170243 q^{51} -1.48964 q^{52} +2.43017 q^{53} +1.30540 q^{54} +8.80236 q^{55} -3.32577 q^{56} -0.219326 q^{57} +4.85906 q^{58} -9.44317 q^{59} -0.498840 q^{60} -5.88140 q^{61} +2.88048 q^{62} +9.81732 q^{63} +1.00000 q^{64} -3.38807 q^{65} -0.848822 q^{66} -0.157168 q^{67} +0.776211 q^{68} +1.95145 q^{69} -7.56422 q^{70} +4.50788 q^{71} -2.95190 q^{72} -8.65662 q^{73} -7.10422 q^{74} -0.0379485 q^{75} +1.00000 q^{76} -12.8712 q^{77} +0.326715 q^{78} -7.31318 q^{79} +2.27443 q^{80} +8.56938 q^{81} -7.81788 q^{82} -11.8891 q^{83} +0.729426 q^{84} +1.76544 q^{85} +0.180535 q^{86} -1.06572 q^{87} +3.87014 q^{88} +6.08863 q^{89} -6.71388 q^{90} +4.95418 q^{91} -8.89752 q^{92} -0.631762 q^{93} +3.93186 q^{94} +2.27443 q^{95} -0.219326 q^{96} -0.915773 q^{97} +4.06072 q^{98} -11.4243 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 30q^{2} - 10q^{3} + 30q^{4} - 12q^{5} - 10q^{6} - 15q^{7} + 30q^{8} + 10q^{9} + O(q^{10}) \) \( 30q + 30q^{2} - 10q^{3} + 30q^{4} - 12q^{5} - 10q^{6} - 15q^{7} + 30q^{8} + 10q^{9} - 12q^{10} - 17q^{11} - 10q^{12} - 19q^{13} - 15q^{14} - 8q^{15} + 30q^{16} - 18q^{17} + 10q^{18} + 30q^{19} - 12q^{20} - 14q^{21} - 17q^{22} - 15q^{23} - 10q^{24} - 4q^{25} - 19q^{26} - 37q^{27} - 15q^{28} - 37q^{29} - 8q^{30} - 11q^{31} + 30q^{32} + 6q^{33} - 18q^{34} - 4q^{35} + 10q^{36} - 46q^{37} + 30q^{38} - 12q^{40} - 28q^{41} - 14q^{42} - 61q^{43} - 17q^{44} - 14q^{45} - 15q^{46} - 4q^{47} - 10q^{48} - q^{49} - 4q^{50} - 8q^{51} - 19q^{52} - 19q^{53} - 37q^{54} - 17q^{55} - 15q^{56} - 10q^{57} - 37q^{58} - 6q^{59} - 8q^{60} - 32q^{61} - 11q^{62} - 24q^{63} + 30q^{64} - 24q^{65} + 6q^{66} - 44q^{67} - 18q^{68} - 2q^{69} - 4q^{70} + 10q^{71} + 10q^{72} - 58q^{73} - 46q^{74} - 42q^{75} + 30q^{76} - 32q^{77} - 42q^{79} - 12q^{80} - 38q^{81} - 28q^{82} - 25q^{83} - 14q^{84} - 48q^{85} - 61q^{86} - 15q^{87} - 17q^{88} - 39q^{89} - 14q^{90} - 21q^{91} - 15q^{92} - 45q^{93} - 4q^{94} - 12q^{95} - 10q^{96} - 33q^{97} - q^{98} - 38q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −0.219326 −0.126628 −0.0633139 0.997994i \(-0.520167\pi\)
−0.0633139 + 0.997994i \(0.520167\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.27443 1.01716 0.508578 0.861016i \(-0.330171\pi\)
0.508578 + 0.861016i \(0.330171\pi\)
\(6\) −0.219326 −0.0895393
\(7\) −3.32577 −1.25702 −0.628511 0.777801i \(-0.716335\pi\)
−0.628511 + 0.777801i \(0.716335\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.95190 −0.983965
\(10\) 2.27443 0.719237
\(11\) 3.87014 1.16689 0.583446 0.812152i \(-0.301704\pi\)
0.583446 + 0.812152i \(0.301704\pi\)
\(12\) −0.219326 −0.0633139
\(13\) −1.48964 −0.413150 −0.206575 0.978431i \(-0.566232\pi\)
−0.206575 + 0.978431i \(0.566232\pi\)
\(14\) −3.32577 −0.888849
\(15\) −0.498840 −0.128800
\(16\) 1.00000 0.250000
\(17\) 0.776211 0.188259 0.0941294 0.995560i \(-0.469993\pi\)
0.0941294 + 0.995560i \(0.469993\pi\)
\(18\) −2.95190 −0.695769
\(19\) 1.00000 0.229416
\(20\) 2.27443 0.508578
\(21\) 0.729426 0.159174
\(22\) 3.87014 0.825117
\(23\) −8.89752 −1.85526 −0.927631 0.373498i \(-0.878158\pi\)
−0.927631 + 0.373498i \(0.878158\pi\)
\(24\) −0.219326 −0.0447697
\(25\) 0.173023 0.0346047
\(26\) −1.48964 −0.292141
\(27\) 1.30540 0.251225
\(28\) −3.32577 −0.628511
\(29\) 4.85906 0.902305 0.451153 0.892447i \(-0.351013\pi\)
0.451153 + 0.892447i \(0.351013\pi\)
\(30\) −0.498840 −0.0910754
\(31\) 2.88048 0.517349 0.258674 0.965965i \(-0.416714\pi\)
0.258674 + 0.965965i \(0.416714\pi\)
\(32\) 1.00000 0.176777
\(33\) −0.848822 −0.147761
\(34\) 0.776211 0.133119
\(35\) −7.56422 −1.27859
\(36\) −2.95190 −0.491983
\(37\) −7.10422 −1.16793 −0.583964 0.811780i \(-0.698499\pi\)
−0.583964 + 0.811780i \(0.698499\pi\)
\(38\) 1.00000 0.162221
\(39\) 0.326715 0.0523163
\(40\) 2.27443 0.359619
\(41\) −7.81788 −1.22095 −0.610474 0.792036i \(-0.709021\pi\)
−0.610474 + 0.792036i \(0.709021\pi\)
\(42\) 0.729426 0.112553
\(43\) 0.180535 0.0275314 0.0137657 0.999905i \(-0.495618\pi\)
0.0137657 + 0.999905i \(0.495618\pi\)
\(44\) 3.87014 0.583446
\(45\) −6.71388 −1.00085
\(46\) −8.89752 −1.31187
\(47\) 3.93186 0.573521 0.286761 0.958002i \(-0.407422\pi\)
0.286761 + 0.958002i \(0.407422\pi\)
\(48\) −0.219326 −0.0316569
\(49\) 4.06072 0.580103
\(50\) 0.173023 0.0244692
\(51\) −0.170243 −0.0238388
\(52\) −1.48964 −0.206575
\(53\) 2.43017 0.333809 0.166905 0.985973i \(-0.446623\pi\)
0.166905 + 0.985973i \(0.446623\pi\)
\(54\) 1.30540 0.177643
\(55\) 8.80236 1.18691
\(56\) −3.32577 −0.444424
\(57\) −0.219326 −0.0290504
\(58\) 4.85906 0.638026
\(59\) −9.44317 −1.22940 −0.614698 0.788763i \(-0.710722\pi\)
−0.614698 + 0.788763i \(0.710722\pi\)
\(60\) −0.498840 −0.0644000
\(61\) −5.88140 −0.753036 −0.376518 0.926409i \(-0.622879\pi\)
−0.376518 + 0.926409i \(0.622879\pi\)
\(62\) 2.88048 0.365821
\(63\) 9.81732 1.23687
\(64\) 1.00000 0.125000
\(65\) −3.38807 −0.420238
\(66\) −0.848822 −0.104483
\(67\) −0.157168 −0.0192011 −0.00960056 0.999954i \(-0.503056\pi\)
−0.00960056 + 0.999954i \(0.503056\pi\)
\(68\) 0.776211 0.0941294
\(69\) 1.95145 0.234928
\(70\) −7.56422 −0.904097
\(71\) 4.50788 0.534987 0.267494 0.963560i \(-0.413805\pi\)
0.267494 + 0.963560i \(0.413805\pi\)
\(72\) −2.95190 −0.347884
\(73\) −8.65662 −1.01318 −0.506590 0.862187i \(-0.669094\pi\)
−0.506590 + 0.862187i \(0.669094\pi\)
\(74\) −7.10422 −0.825849
\(75\) −0.0379485 −0.00438191
\(76\) 1.00000 0.114708
\(77\) −12.8712 −1.46681
\(78\) 0.326715 0.0369932
\(79\) −7.31318 −0.822797 −0.411399 0.911455i \(-0.634960\pi\)
−0.411399 + 0.911455i \(0.634960\pi\)
\(80\) 2.27443 0.254289
\(81\) 8.56938 0.952153
\(82\) −7.81788 −0.863341
\(83\) −11.8891 −1.30500 −0.652498 0.757790i \(-0.726279\pi\)
−0.652498 + 0.757790i \(0.726279\pi\)
\(84\) 0.729426 0.0795869
\(85\) 1.76544 0.191488
\(86\) 0.180535 0.0194676
\(87\) −1.06572 −0.114257
\(88\) 3.87014 0.412559
\(89\) 6.08863 0.645393 0.322697 0.946502i \(-0.395411\pi\)
0.322697 + 0.946502i \(0.395411\pi\)
\(90\) −6.71388 −0.707705
\(91\) 4.95418 0.519339
\(92\) −8.89752 −0.927631
\(93\) −0.631762 −0.0655107
\(94\) 3.93186 0.405541
\(95\) 2.27443 0.233351
\(96\) −0.219326 −0.0223848
\(97\) −0.915773 −0.0929826 −0.0464913 0.998919i \(-0.514804\pi\)
−0.0464913 + 0.998919i \(0.514804\pi\)
\(98\) 4.06072 0.410195
\(99\) −11.4243 −1.14818
\(100\) 0.173023 0.0173023
\(101\) 13.9362 1.38670 0.693352 0.720599i \(-0.256133\pi\)
0.693352 + 0.720599i \(0.256133\pi\)
\(102\) −0.170243 −0.0168566
\(103\) 0.216189 0.0213018 0.0106509 0.999943i \(-0.496610\pi\)
0.0106509 + 0.999943i \(0.496610\pi\)
\(104\) −1.48964 −0.146071
\(105\) 1.65903 0.161904
\(106\) 2.43017 0.236039
\(107\) −8.87146 −0.857636 −0.428818 0.903391i \(-0.641070\pi\)
−0.428818 + 0.903391i \(0.641070\pi\)
\(108\) 1.30540 0.125613
\(109\) −14.8224 −1.41973 −0.709866 0.704336i \(-0.751245\pi\)
−0.709866 + 0.704336i \(0.751245\pi\)
\(110\) 8.80236 0.839272
\(111\) 1.55814 0.147892
\(112\) −3.32577 −0.314255
\(113\) 8.48491 0.798193 0.399096 0.916909i \(-0.369324\pi\)
0.399096 + 0.916909i \(0.369324\pi\)
\(114\) −0.219326 −0.0205417
\(115\) −20.2368 −1.88709
\(116\) 4.85906 0.451153
\(117\) 4.39725 0.406526
\(118\) −9.44317 −0.869314
\(119\) −2.58150 −0.236645
\(120\) −0.498840 −0.0455377
\(121\) 3.97800 0.361637
\(122\) −5.88140 −0.532477
\(123\) 1.71466 0.154606
\(124\) 2.88048 0.258674
\(125\) −10.9786 −0.981957
\(126\) 9.81732 0.874596
\(127\) −5.31550 −0.471675 −0.235837 0.971793i \(-0.575783\pi\)
−0.235837 + 0.971793i \(0.575783\pi\)
\(128\) 1.00000 0.0883883
\(129\) −0.0395960 −0.00348623
\(130\) −3.38807 −0.297153
\(131\) 2.03558 0.177849 0.0889245 0.996038i \(-0.471657\pi\)
0.0889245 + 0.996038i \(0.471657\pi\)
\(132\) −0.848822 −0.0738804
\(133\) −3.32577 −0.288381
\(134\) −0.157168 −0.0135772
\(135\) 2.96905 0.255535
\(136\) 0.776211 0.0665595
\(137\) 0.269241 0.0230028 0.0115014 0.999934i \(-0.496339\pi\)
0.0115014 + 0.999934i \(0.496339\pi\)
\(138\) 1.95145 0.166119
\(139\) 13.5163 1.14644 0.573221 0.819401i \(-0.305694\pi\)
0.573221 + 0.819401i \(0.305694\pi\)
\(140\) −7.56422 −0.639293
\(141\) −0.862358 −0.0726237
\(142\) 4.50788 0.378293
\(143\) −5.76510 −0.482102
\(144\) −2.95190 −0.245991
\(145\) 11.0516 0.917784
\(146\) −8.65662 −0.716427
\(147\) −0.890621 −0.0734572
\(148\) −7.10422 −0.583964
\(149\) 16.1543 1.32342 0.661708 0.749762i \(-0.269832\pi\)
0.661708 + 0.749762i \(0.269832\pi\)
\(150\) −0.0379485 −0.00309848
\(151\) −2.60227 −0.211770 −0.105885 0.994378i \(-0.533768\pi\)
−0.105885 + 0.994378i \(0.533768\pi\)
\(152\) 1.00000 0.0811107
\(153\) −2.29129 −0.185240
\(154\) −12.8712 −1.03719
\(155\) 6.55143 0.526224
\(156\) 0.326715 0.0261581
\(157\) −22.9956 −1.83525 −0.917623 0.397452i \(-0.869895\pi\)
−0.917623 + 0.397452i \(0.869895\pi\)
\(158\) −7.31318 −0.581806
\(159\) −0.532998 −0.0422695
\(160\) 2.27443 0.179809
\(161\) 29.5911 2.33210
\(162\) 8.56938 0.673274
\(163\) −0.813102 −0.0636870 −0.0318435 0.999493i \(-0.510138\pi\)
−0.0318435 + 0.999493i \(0.510138\pi\)
\(164\) −7.81788 −0.610474
\(165\) −1.93058 −0.150296
\(166\) −11.8891 −0.922772
\(167\) −0.224287 −0.0173558 −0.00867791 0.999962i \(-0.502762\pi\)
−0.00867791 + 0.999962i \(0.502762\pi\)
\(168\) 0.729426 0.0562764
\(169\) −10.7810 −0.829307
\(170\) 1.76544 0.135403
\(171\) −2.95190 −0.225737
\(172\) 0.180535 0.0137657
\(173\) −3.97111 −0.301918 −0.150959 0.988540i \(-0.548236\pi\)
−0.150959 + 0.988540i \(0.548236\pi\)
\(174\) −1.06572 −0.0807918
\(175\) −0.575435 −0.0434988
\(176\) 3.87014 0.291723
\(177\) 2.07113 0.155676
\(178\) 6.08863 0.456362
\(179\) −1.17036 −0.0874768 −0.0437384 0.999043i \(-0.513927\pi\)
−0.0437384 + 0.999043i \(0.513927\pi\)
\(180\) −6.71388 −0.500423
\(181\) −8.51244 −0.632725 −0.316362 0.948638i \(-0.602462\pi\)
−0.316362 + 0.948638i \(0.602462\pi\)
\(182\) 4.95418 0.367228
\(183\) 1.28994 0.0953553
\(184\) −8.89752 −0.655934
\(185\) −16.1580 −1.18796
\(186\) −0.631762 −0.0463230
\(187\) 3.00405 0.219678
\(188\) 3.93186 0.286761
\(189\) −4.34147 −0.315795
\(190\) 2.27443 0.165004
\(191\) −26.5812 −1.92335 −0.961674 0.274196i \(-0.911588\pi\)
−0.961674 + 0.274196i \(0.911588\pi\)
\(192\) −0.219326 −0.0158285
\(193\) 2.02726 0.145925 0.0729627 0.997335i \(-0.476755\pi\)
0.0729627 + 0.997335i \(0.476755\pi\)
\(194\) −0.915773 −0.0657486
\(195\) 0.743090 0.0532138
\(196\) 4.06072 0.290052
\(197\) −23.4024 −1.66735 −0.833676 0.552254i \(-0.813768\pi\)
−0.833676 + 0.552254i \(0.813768\pi\)
\(198\) −11.4243 −0.811887
\(199\) 12.2850 0.870860 0.435430 0.900223i \(-0.356596\pi\)
0.435430 + 0.900223i \(0.356596\pi\)
\(200\) 0.173023 0.0122346
\(201\) 0.0344710 0.00243139
\(202\) 13.9362 0.980547
\(203\) −16.1601 −1.13422
\(204\) −0.170243 −0.0119194
\(205\) −17.7812 −1.24189
\(206\) 0.216189 0.0150626
\(207\) 26.2646 1.82551
\(208\) −1.48964 −0.103288
\(209\) 3.87014 0.267703
\(210\) 1.65903 0.114484
\(211\) −1.00000 −0.0688428
\(212\) 2.43017 0.166905
\(213\) −0.988694 −0.0677442
\(214\) −8.87146 −0.606440
\(215\) 0.410614 0.0280037
\(216\) 1.30540 0.0888215
\(217\) −9.57979 −0.650318
\(218\) −14.8224 −1.00390
\(219\) 1.89862 0.128297
\(220\) 8.80236 0.593455
\(221\) −1.15627 −0.0777792
\(222\) 1.55814 0.104575
\(223\) 9.42269 0.630990 0.315495 0.948927i \(-0.397829\pi\)
0.315495 + 0.948927i \(0.397829\pi\)
\(224\) −3.32577 −0.222212
\(225\) −0.510747 −0.0340498
\(226\) 8.48491 0.564408
\(227\) −23.2406 −1.54254 −0.771268 0.636511i \(-0.780377\pi\)
−0.771268 + 0.636511i \(0.780377\pi\)
\(228\) −0.219326 −0.0145252
\(229\) 5.04393 0.333312 0.166656 0.986015i \(-0.446703\pi\)
0.166656 + 0.986015i \(0.446703\pi\)
\(230\) −20.2368 −1.33437
\(231\) 2.82298 0.185739
\(232\) 4.85906 0.319013
\(233\) 0.0399453 0.00261690 0.00130845 0.999999i \(-0.499584\pi\)
0.00130845 + 0.999999i \(0.499584\pi\)
\(234\) 4.39725 0.287457
\(235\) 8.94274 0.583360
\(236\) −9.44317 −0.614698
\(237\) 1.60397 0.104189
\(238\) −2.58150 −0.167334
\(239\) 18.8370 1.21847 0.609233 0.792992i \(-0.291478\pi\)
0.609233 + 0.792992i \(0.291478\pi\)
\(240\) −0.498840 −0.0322000
\(241\) −17.3048 −1.11470 −0.557352 0.830277i \(-0.688182\pi\)
−0.557352 + 0.830277i \(0.688182\pi\)
\(242\) 3.97800 0.255716
\(243\) −5.79570 −0.371794
\(244\) −5.88140 −0.376518
\(245\) 9.23582 0.590055
\(246\) 1.71466 0.109323
\(247\) −1.48964 −0.0947832
\(248\) 2.88048 0.182910
\(249\) 2.60758 0.165249
\(250\) −10.9786 −0.694348
\(251\) 0.183589 0.0115880 0.00579402 0.999983i \(-0.498156\pi\)
0.00579402 + 0.999983i \(0.498156\pi\)
\(252\) 9.81732 0.618433
\(253\) −34.4347 −2.16489
\(254\) −5.31550 −0.333524
\(255\) −0.387205 −0.0242477
\(256\) 1.00000 0.0625000
\(257\) −28.6461 −1.78690 −0.893448 0.449166i \(-0.851721\pi\)
−0.893448 + 0.449166i \(0.851721\pi\)
\(258\) −0.0395960 −0.00246514
\(259\) 23.6270 1.46811
\(260\) −3.38807 −0.210119
\(261\) −14.3434 −0.887837
\(262\) 2.03558 0.125758
\(263\) −13.6178 −0.839710 −0.419855 0.907591i \(-0.637919\pi\)
−0.419855 + 0.907591i \(0.637919\pi\)
\(264\) −0.848822 −0.0522414
\(265\) 5.52724 0.339536
\(266\) −3.32577 −0.203916
\(267\) −1.33539 −0.0817247
\(268\) −0.157168 −0.00960056
\(269\) −3.95941 −0.241410 −0.120705 0.992688i \(-0.538515\pi\)
−0.120705 + 0.992688i \(0.538515\pi\)
\(270\) 2.96905 0.180690
\(271\) −4.17077 −0.253356 −0.126678 0.991944i \(-0.540432\pi\)
−0.126678 + 0.991944i \(0.540432\pi\)
\(272\) 0.776211 0.0470647
\(273\) −1.08658 −0.0657627
\(274\) 0.269241 0.0162655
\(275\) 0.669625 0.0403799
\(276\) 1.95145 0.117464
\(277\) 17.6128 1.05825 0.529126 0.848543i \(-0.322520\pi\)
0.529126 + 0.848543i \(0.322520\pi\)
\(278\) 13.5163 0.810656
\(279\) −8.50286 −0.509053
\(280\) −7.56422 −0.452048
\(281\) −15.1516 −0.903866 −0.451933 0.892052i \(-0.649265\pi\)
−0.451933 + 0.892052i \(0.649265\pi\)
\(282\) −0.862358 −0.0513527
\(283\) 32.2846 1.91912 0.959559 0.281506i \(-0.0908339\pi\)
0.959559 + 0.281506i \(0.0908339\pi\)
\(284\) 4.50788 0.267494
\(285\) −0.498840 −0.0295488
\(286\) −5.76510 −0.340898
\(287\) 26.0005 1.53476
\(288\) −2.95190 −0.173942
\(289\) −16.3975 −0.964559
\(290\) 11.0516 0.648972
\(291\) 0.200852 0.0117742
\(292\) −8.65662 −0.506590
\(293\) 26.6325 1.55589 0.777945 0.628332i \(-0.216262\pi\)
0.777945 + 0.628332i \(0.216262\pi\)
\(294\) −0.890621 −0.0519421
\(295\) −21.4778 −1.25049
\(296\) −7.10422 −0.412925
\(297\) 5.05210 0.293152
\(298\) 16.1543 0.935796
\(299\) 13.2541 0.766502
\(300\) −0.0379485 −0.00219096
\(301\) −0.600418 −0.0346075
\(302\) −2.60227 −0.149744
\(303\) −3.05657 −0.175595
\(304\) 1.00000 0.0573539
\(305\) −13.3768 −0.765955
\(306\) −2.29129 −0.130985
\(307\) 17.8341 1.01784 0.508922 0.860813i \(-0.330044\pi\)
0.508922 + 0.860813i \(0.330044\pi\)
\(308\) −12.8712 −0.733404
\(309\) −0.0474159 −0.00269739
\(310\) 6.55143 0.372096
\(311\) −23.3430 −1.32366 −0.661830 0.749654i \(-0.730220\pi\)
−0.661830 + 0.749654i \(0.730220\pi\)
\(312\) 0.326715 0.0184966
\(313\) 0.540099 0.0305282 0.0152641 0.999883i \(-0.495141\pi\)
0.0152641 + 0.999883i \(0.495141\pi\)
\(314\) −22.9956 −1.29771
\(315\) 22.3288 1.25808
\(316\) −7.31318 −0.411399
\(317\) 17.0554 0.957925 0.478963 0.877835i \(-0.341013\pi\)
0.478963 + 0.877835i \(0.341013\pi\)
\(318\) −0.532998 −0.0298890
\(319\) 18.8053 1.05289
\(320\) 2.27443 0.127144
\(321\) 1.94574 0.108600
\(322\) 29.5911 1.64905
\(323\) 0.776211 0.0431895
\(324\) 8.56938 0.476077
\(325\) −0.257742 −0.0142969
\(326\) −0.813102 −0.0450335
\(327\) 3.25094 0.179777
\(328\) −7.81788 −0.431670
\(329\) −13.0765 −0.720929
\(330\) −1.93058 −0.106275
\(331\) 34.0474 1.87142 0.935708 0.352776i \(-0.114762\pi\)
0.935708 + 0.352776i \(0.114762\pi\)
\(332\) −11.8891 −0.652498
\(333\) 20.9709 1.14920
\(334\) −0.224287 −0.0122724
\(335\) −0.357467 −0.0195305
\(336\) 0.729426 0.0397934
\(337\) −9.48533 −0.516699 −0.258350 0.966052i \(-0.583179\pi\)
−0.258350 + 0.966052i \(0.583179\pi\)
\(338\) −10.7810 −0.586408
\(339\) −1.86096 −0.101073
\(340\) 1.76544 0.0957442
\(341\) 11.1478 0.603690
\(342\) −2.95190 −0.159620
\(343\) 9.77535 0.527819
\(344\) 0.180535 0.00973381
\(345\) 4.43844 0.238958
\(346\) −3.97111 −0.213488
\(347\) −36.5159 −1.96028 −0.980139 0.198313i \(-0.936454\pi\)
−0.980139 + 0.198313i \(0.936454\pi\)
\(348\) −1.06572 −0.0571284
\(349\) 5.10461 0.273243 0.136622 0.990623i \(-0.456376\pi\)
0.136622 + 0.990623i \(0.456376\pi\)
\(350\) −0.575435 −0.0307583
\(351\) −1.94457 −0.103794
\(352\) 3.87014 0.206279
\(353\) −9.06775 −0.482628 −0.241314 0.970447i \(-0.577578\pi\)
−0.241314 + 0.970447i \(0.577578\pi\)
\(354\) 2.07113 0.110079
\(355\) 10.2529 0.544165
\(356\) 6.08863 0.322697
\(357\) 0.566188 0.0299659
\(358\) −1.17036 −0.0618554
\(359\) 15.4124 0.813434 0.406717 0.913554i \(-0.366673\pi\)
0.406717 + 0.913554i \(0.366673\pi\)
\(360\) −6.71388 −0.353852
\(361\) 1.00000 0.0526316
\(362\) −8.51244 −0.447404
\(363\) −0.872478 −0.0457932
\(364\) 4.95418 0.259670
\(365\) −19.6889 −1.03056
\(366\) 1.28994 0.0674264
\(367\) −23.5461 −1.22910 −0.614548 0.788880i \(-0.710661\pi\)
−0.614548 + 0.788880i \(0.710661\pi\)
\(368\) −8.89752 −0.463815
\(369\) 23.0776 1.20137
\(370\) −16.1580 −0.840017
\(371\) −8.08217 −0.419605
\(372\) −0.631762 −0.0327553
\(373\) 18.0439 0.934280 0.467140 0.884183i \(-0.345284\pi\)
0.467140 + 0.884183i \(0.345284\pi\)
\(374\) 3.00405 0.155336
\(375\) 2.40789 0.124343
\(376\) 3.93186 0.202770
\(377\) −7.23823 −0.372788
\(378\) −4.34147 −0.223301
\(379\) 25.5307 1.31143 0.655713 0.755010i \(-0.272368\pi\)
0.655713 + 0.755010i \(0.272368\pi\)
\(380\) 2.27443 0.116676
\(381\) 1.16583 0.0597271
\(382\) −26.5812 −1.36001
\(383\) 10.9443 0.559226 0.279613 0.960113i \(-0.409794\pi\)
0.279613 + 0.960113i \(0.409794\pi\)
\(384\) −0.219326 −0.0111924
\(385\) −29.2746 −1.49197
\(386\) 2.02726 0.103185
\(387\) −0.532921 −0.0270899
\(388\) −0.915773 −0.0464913
\(389\) 11.8152 0.599054 0.299527 0.954088i \(-0.403171\pi\)
0.299527 + 0.954088i \(0.403171\pi\)
\(390\) 0.743090 0.0376278
\(391\) −6.90635 −0.349269
\(392\) 4.06072 0.205098
\(393\) −0.446454 −0.0225206
\(394\) −23.4024 −1.17900
\(395\) −16.6333 −0.836913
\(396\) −11.4243 −0.574091
\(397\) −25.4826 −1.27893 −0.639467 0.768819i \(-0.720845\pi\)
−0.639467 + 0.768819i \(0.720845\pi\)
\(398\) 12.2850 0.615791
\(399\) 0.729426 0.0365170
\(400\) 0.173023 0.00865117
\(401\) −26.9100 −1.34382 −0.671911 0.740632i \(-0.734526\pi\)
−0.671911 + 0.740632i \(0.734526\pi\)
\(402\) 0.0344710 0.00171926
\(403\) −4.29086 −0.213743
\(404\) 13.9362 0.693352
\(405\) 19.4904 0.968488
\(406\) −16.1601 −0.802013
\(407\) −27.4944 −1.36284
\(408\) −0.170243 −0.00842828
\(409\) −17.8779 −0.884007 −0.442003 0.897013i \(-0.645732\pi\)
−0.442003 + 0.897013i \(0.645732\pi\)
\(410\) −17.7812 −0.878152
\(411\) −0.0590515 −0.00291280
\(412\) 0.216189 0.0106509
\(413\) 31.4058 1.54538
\(414\) 26.2646 1.29083
\(415\) −27.0409 −1.32738
\(416\) −1.48964 −0.0730354
\(417\) −2.96448 −0.145171
\(418\) 3.87014 0.189295
\(419\) 1.95105 0.0953150 0.0476575 0.998864i \(-0.484824\pi\)
0.0476575 + 0.998864i \(0.484824\pi\)
\(420\) 1.65903 0.0809522
\(421\) 7.76004 0.378201 0.189101 0.981958i \(-0.439443\pi\)
0.189101 + 0.981958i \(0.439443\pi\)
\(422\) −1.00000 −0.0486792
\(423\) −11.6065 −0.564325
\(424\) 2.43017 0.118019
\(425\) 0.134303 0.00651464
\(426\) −0.988694 −0.0479024
\(427\) 19.5602 0.946583
\(428\) −8.87146 −0.428818
\(429\) 1.26443 0.0610475
\(430\) 0.410614 0.0198016
\(431\) −12.2312 −0.589156 −0.294578 0.955627i \(-0.595179\pi\)
−0.294578 + 0.955627i \(0.595179\pi\)
\(432\) 1.30540 0.0628063
\(433\) 18.6933 0.898342 0.449171 0.893446i \(-0.351719\pi\)
0.449171 + 0.893446i \(0.351719\pi\)
\(434\) −9.57979 −0.459845
\(435\) −2.42390 −0.116217
\(436\) −14.8224 −0.709866
\(437\) −8.89752 −0.425626
\(438\) 1.89862 0.0907195
\(439\) −10.4972 −0.501005 −0.250502 0.968116i \(-0.580596\pi\)
−0.250502 + 0.968116i \(0.580596\pi\)
\(440\) 8.80236 0.419636
\(441\) −11.9868 −0.570802
\(442\) −1.15627 −0.0549982
\(443\) 38.5842 1.83319 0.916596 0.399814i \(-0.130925\pi\)
0.916596 + 0.399814i \(0.130925\pi\)
\(444\) 1.55814 0.0739460
\(445\) 13.8481 0.656465
\(446\) 9.42269 0.446178
\(447\) −3.54306 −0.167581
\(448\) −3.32577 −0.157128
\(449\) −30.0086 −1.41619 −0.708096 0.706116i \(-0.750446\pi\)
−0.708096 + 0.706116i \(0.750446\pi\)
\(450\) −0.510747 −0.0240769
\(451\) −30.2563 −1.42471
\(452\) 8.48491 0.399096
\(453\) 0.570745 0.0268159
\(454\) −23.2406 −1.09074
\(455\) 11.2679 0.528248
\(456\) −0.219326 −0.0102709
\(457\) 34.4348 1.61079 0.805397 0.592736i \(-0.201952\pi\)
0.805397 + 0.592736i \(0.201952\pi\)
\(458\) 5.04393 0.235687
\(459\) 1.01327 0.0472953
\(460\) −20.2368 −0.943545
\(461\) −8.96726 −0.417647 −0.208823 0.977953i \(-0.566963\pi\)
−0.208823 + 0.977953i \(0.566963\pi\)
\(462\) 2.82298 0.131337
\(463\) −12.2753 −0.570480 −0.285240 0.958456i \(-0.592073\pi\)
−0.285240 + 0.958456i \(0.592073\pi\)
\(464\) 4.85906 0.225576
\(465\) −1.43690 −0.0666345
\(466\) 0.0399453 0.00185043
\(467\) 37.4755 1.73416 0.867079 0.498171i \(-0.165995\pi\)
0.867079 + 0.498171i \(0.165995\pi\)
\(468\) 4.39725 0.203263
\(469\) 0.522704 0.0241362
\(470\) 8.94274 0.412498
\(471\) 5.04352 0.232393
\(472\) −9.44317 −0.434657
\(473\) 0.698697 0.0321261
\(474\) 1.60397 0.0736727
\(475\) 0.173023 0.00793886
\(476\) −2.58150 −0.118323
\(477\) −7.17360 −0.328457
\(478\) 18.8370 0.861585
\(479\) −0.888395 −0.0405918 −0.0202959 0.999794i \(-0.506461\pi\)
−0.0202959 + 0.999794i \(0.506461\pi\)
\(480\) −0.498840 −0.0227688
\(481\) 10.5827 0.482530
\(482\) −17.3048 −0.788214
\(483\) −6.49008 −0.295309
\(484\) 3.97800 0.180818
\(485\) −2.08286 −0.0945777
\(486\) −5.79570 −0.262898
\(487\) −22.8576 −1.03578 −0.517888 0.855448i \(-0.673282\pi\)
−0.517888 + 0.855448i \(0.673282\pi\)
\(488\) −5.88140 −0.266239
\(489\) 0.178334 0.00806454
\(490\) 9.23582 0.417232
\(491\) 12.6592 0.571303 0.285652 0.958334i \(-0.407790\pi\)
0.285652 + 0.958334i \(0.407790\pi\)
\(492\) 1.71466 0.0773030
\(493\) 3.77166 0.169867
\(494\) −1.48964 −0.0670218
\(495\) −25.9837 −1.16788
\(496\) 2.88048 0.129337
\(497\) −14.9922 −0.672490
\(498\) 2.60758 0.116849
\(499\) 43.5023 1.94743 0.973715 0.227768i \(-0.0731427\pi\)
0.973715 + 0.227768i \(0.0731427\pi\)
\(500\) −10.9786 −0.490978
\(501\) 0.0491918 0.00219773
\(502\) 0.183589 0.00819398
\(503\) 3.62671 0.161707 0.0808534 0.996726i \(-0.474235\pi\)
0.0808534 + 0.996726i \(0.474235\pi\)
\(504\) 9.81732 0.437298
\(505\) 31.6969 1.41049
\(506\) −34.4347 −1.53081
\(507\) 2.36455 0.105013
\(508\) −5.31550 −0.235837
\(509\) −24.9347 −1.10521 −0.552606 0.833443i \(-0.686366\pi\)
−0.552606 + 0.833443i \(0.686366\pi\)
\(510\) −0.387205 −0.0171457
\(511\) 28.7899 1.27359
\(512\) 1.00000 0.0441942
\(513\) 1.30540 0.0576350
\(514\) −28.6461 −1.26353
\(515\) 0.491707 0.0216672
\(516\) −0.0395960 −0.00174312
\(517\) 15.2169 0.669237
\(518\) 23.6270 1.03811
\(519\) 0.870965 0.0382311
\(520\) −3.38807 −0.148577
\(521\) 3.44440 0.150902 0.0754510 0.997150i \(-0.475960\pi\)
0.0754510 + 0.997150i \(0.475960\pi\)
\(522\) −14.3434 −0.627796
\(523\) 18.8977 0.826341 0.413170 0.910654i \(-0.364421\pi\)
0.413170 + 0.910654i \(0.364421\pi\)
\(524\) 2.03558 0.0889245
\(525\) 0.126208 0.00550816
\(526\) −13.6178 −0.593765
\(527\) 2.23586 0.0973954
\(528\) −0.848822 −0.0369402
\(529\) 56.1659 2.44200
\(530\) 5.52724 0.240088
\(531\) 27.8753 1.20968
\(532\) −3.32577 −0.144190
\(533\) 11.6458 0.504435
\(534\) −1.33539 −0.0577881
\(535\) −20.1775 −0.872349
\(536\) −0.157168 −0.00678862
\(537\) 0.256690 0.0110770
\(538\) −3.95941 −0.170702
\(539\) 15.7156 0.676918
\(540\) 2.96905 0.127767
\(541\) 16.7703 0.721011 0.360505 0.932757i \(-0.382604\pi\)
0.360505 + 0.932757i \(0.382604\pi\)
\(542\) −4.17077 −0.179150
\(543\) 1.86700 0.0801205
\(544\) 0.776211 0.0332798
\(545\) −33.7126 −1.44409
\(546\) −1.08658 −0.0465013
\(547\) −25.6690 −1.09753 −0.548764 0.835977i \(-0.684902\pi\)
−0.548764 + 0.835977i \(0.684902\pi\)
\(548\) 0.269241 0.0115014
\(549\) 17.3613 0.740962
\(550\) 0.669625 0.0285529
\(551\) 4.85906 0.207003
\(552\) 1.95145 0.0830594
\(553\) 24.3219 1.03427
\(554\) 17.6128 0.748297
\(555\) 3.54387 0.150429
\(556\) 13.5163 0.573221
\(557\) −30.3522 −1.28607 −0.643033 0.765838i \(-0.722324\pi\)
−0.643033 + 0.765838i \(0.722324\pi\)
\(558\) −8.50286 −0.359955
\(559\) −0.268932 −0.0113746
\(560\) −7.56422 −0.319647
\(561\) −0.658865 −0.0278173
\(562\) −15.1516 −0.639130
\(563\) −15.3643 −0.647528 −0.323764 0.946138i \(-0.604948\pi\)
−0.323764 + 0.946138i \(0.604948\pi\)
\(564\) −0.862358 −0.0363118
\(565\) 19.2983 0.811886
\(566\) 32.2846 1.35702
\(567\) −28.4998 −1.19688
\(568\) 4.50788 0.189147
\(569\) 2.41097 0.101073 0.0505366 0.998722i \(-0.483907\pi\)
0.0505366 + 0.998722i \(0.483907\pi\)
\(570\) −0.498840 −0.0208941
\(571\) 13.9963 0.585725 0.292863 0.956155i \(-0.405392\pi\)
0.292863 + 0.956155i \(0.405392\pi\)
\(572\) −5.76510 −0.241051
\(573\) 5.82994 0.243549
\(574\) 26.0005 1.08524
\(575\) −1.53948 −0.0642007
\(576\) −2.95190 −0.122996
\(577\) 6.63098 0.276051 0.138026 0.990429i \(-0.455924\pi\)
0.138026 + 0.990429i \(0.455924\pi\)
\(578\) −16.3975 −0.682046
\(579\) −0.444630 −0.0184782
\(580\) 11.0516 0.458892
\(581\) 39.5403 1.64041
\(582\) 0.200852 0.00832560
\(583\) 9.40509 0.389519
\(584\) −8.65662 −0.358213
\(585\) 10.0012 0.413500
\(586\) 26.6325 1.10018
\(587\) −37.7032 −1.55618 −0.778088 0.628155i \(-0.783810\pi\)
−0.778088 + 0.628155i \(0.783810\pi\)
\(588\) −0.890621 −0.0367286
\(589\) 2.88048 0.118688
\(590\) −21.4778 −0.884227
\(591\) 5.13275 0.211133
\(592\) −7.10422 −0.291982
\(593\) −2.24240 −0.0920845 −0.0460422 0.998939i \(-0.514661\pi\)
−0.0460422 + 0.998939i \(0.514661\pi\)
\(594\) 5.05210 0.207290
\(595\) −5.87143 −0.240705
\(596\) 16.1543 0.661708
\(597\) −2.69441 −0.110275
\(598\) 13.2541 0.541999
\(599\) 37.6138 1.53686 0.768430 0.639934i \(-0.221038\pi\)
0.768430 + 0.639934i \(0.221038\pi\)
\(600\) −0.0379485 −0.00154924
\(601\) −21.9816 −0.896650 −0.448325 0.893871i \(-0.647979\pi\)
−0.448325 + 0.893871i \(0.647979\pi\)
\(602\) −0.600418 −0.0244712
\(603\) 0.463943 0.0188932
\(604\) −2.60227 −0.105885
\(605\) 9.04768 0.367841
\(606\) −3.05657 −0.124164
\(607\) 18.8259 0.764118 0.382059 0.924138i \(-0.375215\pi\)
0.382059 + 0.924138i \(0.375215\pi\)
\(608\) 1.00000 0.0405554
\(609\) 3.54433 0.143623
\(610\) −13.3768 −0.541612
\(611\) −5.85704 −0.236951
\(612\) −2.29129 −0.0926201
\(613\) −34.1263 −1.37835 −0.689174 0.724596i \(-0.742027\pi\)
−0.689174 + 0.724596i \(0.742027\pi\)
\(614\) 17.8341 0.719725
\(615\) 3.89988 0.157258
\(616\) −12.8712 −0.518595
\(617\) −8.79088 −0.353907 −0.176954 0.984219i \(-0.556624\pi\)
−0.176954 + 0.984219i \(0.556624\pi\)
\(618\) −0.0474159 −0.00190735
\(619\) −13.6216 −0.547500 −0.273750 0.961801i \(-0.588264\pi\)
−0.273750 + 0.961801i \(0.588264\pi\)
\(620\) 6.55143 0.263112
\(621\) −11.6149 −0.466088
\(622\) −23.3430 −0.935969
\(623\) −20.2494 −0.811273
\(624\) 0.326715 0.0130791
\(625\) −25.8352 −1.03341
\(626\) 0.540099 0.0215867
\(627\) −0.848822 −0.0338987
\(628\) −22.9956 −0.917623
\(629\) −5.51438 −0.219873
\(630\) 22.3288 0.889600
\(631\) 16.0179 0.637664 0.318832 0.947811i \(-0.396709\pi\)
0.318832 + 0.947811i \(0.396709\pi\)
\(632\) −7.31318 −0.290903
\(633\) 0.219326 0.00871741
\(634\) 17.0554 0.677356
\(635\) −12.0897 −0.479766
\(636\) −0.532998 −0.0211347
\(637\) −6.04900 −0.239670
\(638\) 18.8053 0.744507
\(639\) −13.3068 −0.526409
\(640\) 2.27443 0.0899047
\(641\) −7.21015 −0.284784 −0.142392 0.989810i \(-0.545479\pi\)
−0.142392 + 0.989810i \(0.545479\pi\)
\(642\) 1.94574 0.0767921
\(643\) 4.15506 0.163860 0.0819298 0.996638i \(-0.473892\pi\)
0.0819298 + 0.996638i \(0.473892\pi\)
\(644\) 29.5911 1.16605
\(645\) −0.0900583 −0.00354604
\(646\) 0.776211 0.0305396
\(647\) 40.2218 1.58128 0.790642 0.612279i \(-0.209747\pi\)
0.790642 + 0.612279i \(0.209747\pi\)
\(648\) 8.56938 0.336637
\(649\) −36.5464 −1.43457
\(650\) −0.257742 −0.0101095
\(651\) 2.10109 0.0823483
\(652\) −0.813102 −0.0318435
\(653\) −16.0758 −0.629096 −0.314548 0.949242i \(-0.601853\pi\)
−0.314548 + 0.949242i \(0.601853\pi\)
\(654\) 3.25094 0.127122
\(655\) 4.62977 0.180900
\(656\) −7.81788 −0.305237
\(657\) 25.5534 0.996934
\(658\) −13.0765 −0.509773
\(659\) −32.3698 −1.26095 −0.630473 0.776211i \(-0.717139\pi\)
−0.630473 + 0.776211i \(0.717139\pi\)
\(660\) −1.93058 −0.0751479
\(661\) 28.3297 1.10190 0.550948 0.834539i \(-0.314266\pi\)
0.550948 + 0.834539i \(0.314266\pi\)
\(662\) 34.0474 1.32329
\(663\) 0.253600 0.00984900
\(664\) −11.8891 −0.461386
\(665\) −7.56422 −0.293328
\(666\) 20.9709 0.812607
\(667\) −43.2336 −1.67401
\(668\) −0.224287 −0.00867791
\(669\) −2.06664 −0.0799009
\(670\) −0.357467 −0.0138102
\(671\) −22.7619 −0.878712
\(672\) 0.729426 0.0281382
\(673\) 5.58056 0.215115 0.107557 0.994199i \(-0.465697\pi\)
0.107557 + 0.994199i \(0.465697\pi\)
\(674\) −9.48533 −0.365361
\(675\) 0.225865 0.00869356
\(676\) −10.7810 −0.414653
\(677\) 36.5549 1.40492 0.702459 0.711724i \(-0.252085\pi\)
0.702459 + 0.711724i \(0.252085\pi\)
\(678\) −1.86096 −0.0714696
\(679\) 3.04565 0.116881
\(680\) 1.76544 0.0677014
\(681\) 5.09727 0.195328
\(682\) 11.1478 0.426873
\(683\) −5.59207 −0.213975 −0.106987 0.994260i \(-0.534120\pi\)
−0.106987 + 0.994260i \(0.534120\pi\)
\(684\) −2.95190 −0.112869
\(685\) 0.612370 0.0233975
\(686\) 9.77535 0.373224
\(687\) −1.10626 −0.0422066
\(688\) 0.180535 0.00688284
\(689\) −3.62006 −0.137913
\(690\) 4.43844 0.168969
\(691\) 7.35685 0.279868 0.139934 0.990161i \(-0.455311\pi\)
0.139934 + 0.990161i \(0.455311\pi\)
\(692\) −3.97111 −0.150959
\(693\) 37.9944 1.44329
\(694\) −36.5159 −1.38613
\(695\) 30.7420 1.16611
\(696\) −1.06572 −0.0403959
\(697\) −6.06833 −0.229854
\(698\) 5.10461 0.193212
\(699\) −0.00876102 −0.000331372 0
\(700\) −0.575435 −0.0217494
\(701\) 42.9081 1.62062 0.810308 0.586004i \(-0.199300\pi\)
0.810308 + 0.586004i \(0.199300\pi\)
\(702\) −1.94457 −0.0733932
\(703\) −7.10422 −0.267941
\(704\) 3.87014 0.145861
\(705\) −1.96137 −0.0738696
\(706\) −9.06775 −0.341269
\(707\) −46.3485 −1.74312
\(708\) 2.07113 0.0778378
\(709\) 1.97574 0.0742004 0.0371002 0.999312i \(-0.488188\pi\)
0.0371002 + 0.999312i \(0.488188\pi\)
\(710\) 10.2529 0.384783
\(711\) 21.5878 0.809604
\(712\) 6.08863 0.228181
\(713\) −25.6291 −0.959817
\(714\) 0.566188 0.0211891
\(715\) −13.1123 −0.490372
\(716\) −1.17036 −0.0437384
\(717\) −4.13144 −0.154291
\(718\) 15.4124 0.575185
\(719\) 8.80075 0.328213 0.164106 0.986443i \(-0.447526\pi\)
0.164106 + 0.986443i \(0.447526\pi\)
\(720\) −6.71388 −0.250211
\(721\) −0.718995 −0.0267768
\(722\) 1.00000 0.0372161
\(723\) 3.79540 0.141152
\(724\) −8.51244 −0.316362
\(725\) 0.840731 0.0312240
\(726\) −0.872478 −0.0323807
\(727\) −2.66065 −0.0986782 −0.0493391 0.998782i \(-0.515711\pi\)
−0.0493391 + 0.998782i \(0.515711\pi\)
\(728\) 4.95418 0.183614
\(729\) −24.4370 −0.905074
\(730\) −19.6889 −0.728717
\(731\) 0.140133 0.00518302
\(732\) 1.28994 0.0476776
\(733\) −29.0243 −1.07204 −0.536018 0.844207i \(-0.680072\pi\)
−0.536018 + 0.844207i \(0.680072\pi\)
\(734\) −23.5461 −0.869102
\(735\) −2.02565 −0.0747173
\(736\) −8.89752 −0.327967
\(737\) −0.608262 −0.0224056
\(738\) 23.0776 0.849498
\(739\) 33.7327 1.24088 0.620440 0.784254i \(-0.286954\pi\)
0.620440 + 0.784254i \(0.286954\pi\)
\(740\) −16.1580 −0.593982
\(741\) 0.326715 0.0120022
\(742\) −8.08217 −0.296706
\(743\) −33.7006 −1.23636 −0.618178 0.786038i \(-0.712129\pi\)
−0.618178 + 0.786038i \(0.712129\pi\)
\(744\) −0.631762 −0.0231615
\(745\) 36.7419 1.34612
\(746\) 18.0439 0.660635
\(747\) 35.0954 1.28407
\(748\) 3.00405 0.109839
\(749\) 29.5044 1.07807
\(750\) 2.40789 0.0879237
\(751\) 46.4367 1.69450 0.847250 0.531194i \(-0.178256\pi\)
0.847250 + 0.531194i \(0.178256\pi\)
\(752\) 3.93186 0.143380
\(753\) −0.0402658 −0.00146737
\(754\) −7.23823 −0.263601
\(755\) −5.91868 −0.215403
\(756\) −4.34147 −0.157898
\(757\) 14.3009 0.519775 0.259887 0.965639i \(-0.416315\pi\)
0.259887 + 0.965639i \(0.416315\pi\)
\(758\) 25.5307 0.927318
\(759\) 7.55241 0.274135
\(760\) 2.27443 0.0825022
\(761\) −16.1913 −0.586936 −0.293468 0.955969i \(-0.594809\pi\)
−0.293468 + 0.955969i \(0.594809\pi\)
\(762\) 1.16583 0.0422334
\(763\) 49.2960 1.78463
\(764\) −26.5812 −0.961674
\(765\) −5.21138 −0.188418
\(766\) 10.9443 0.395433
\(767\) 14.0669 0.507925
\(768\) −0.219326 −0.00791423
\(769\) −35.2375 −1.27070 −0.635349 0.772225i \(-0.719144\pi\)
−0.635349 + 0.772225i \(0.719144\pi\)
\(770\) −29.2746 −1.05498
\(771\) 6.28283 0.226271
\(772\) 2.02726 0.0729627
\(773\) −16.6163 −0.597646 −0.298823 0.954308i \(-0.596594\pi\)
−0.298823 + 0.954308i \(0.596594\pi\)
\(774\) −0.532921 −0.0191555
\(775\) 0.498390 0.0179027
\(776\) −0.915773 −0.0328743
\(777\) −5.18200 −0.185903
\(778\) 11.8152 0.423595
\(779\) −7.81788 −0.280105
\(780\) 0.743090 0.0266069
\(781\) 17.4461 0.624272
\(782\) −6.90635 −0.246971
\(783\) 6.34304 0.226682
\(784\) 4.06072 0.145026
\(785\) −52.3018 −1.86673
\(786\) −0.446454 −0.0159245
\(787\) 55.4813 1.97769 0.988847 0.148932i \(-0.0475835\pi\)
0.988847 + 0.148932i \(0.0475835\pi\)
\(788\) −23.4024 −0.833676
\(789\) 2.98674 0.106331
\(790\) −16.6333 −0.591787
\(791\) −28.2188 −1.00335
\(792\) −11.4243 −0.405943
\(793\) 8.76114 0.311117
\(794\) −25.4826 −0.904343
\(795\) −1.21227 −0.0429946
\(796\) 12.2850 0.435430
\(797\) −22.0708 −0.781786 −0.390893 0.920436i \(-0.627834\pi\)
−0.390893 + 0.920436i \(0.627834\pi\)
\(798\) 0.729426 0.0258214
\(799\) 3.05196 0.107970
\(800\) 0.173023 0.00611730
\(801\) −17.9730 −0.635045
\(802\) −26.9100 −0.950226
\(803\) −33.5023 −1.18227
\(804\) 0.0344710 0.00121570
\(805\) 67.3028 2.37211
\(806\) −4.29086 −0.151139
\(807\) 0.868401 0.0305692
\(808\) 13.9362 0.490274
\(809\) −25.6910 −0.903248 −0.451624 0.892208i \(-0.649155\pi\)
−0.451624 + 0.892208i \(0.649155\pi\)
\(810\) 19.4904 0.684824
\(811\) 11.5579 0.405854 0.202927 0.979194i \(-0.434955\pi\)
0.202927 + 0.979194i \(0.434955\pi\)
\(812\) −16.1601 −0.567109
\(813\) 0.914757 0.0320819
\(814\) −27.4944 −0.963677
\(815\) −1.84934 −0.0647796
\(816\) −0.170243 −0.00595970
\(817\) 0.180535 0.00631613
\(818\) −17.8779 −0.625087
\(819\) −14.6242 −0.511012
\(820\) −17.7812 −0.620947
\(821\) 9.87345 0.344586 0.172293 0.985046i \(-0.444882\pi\)
0.172293 + 0.985046i \(0.444882\pi\)
\(822\) −0.0590515 −0.00205966
\(823\) 39.6575 1.38237 0.691186 0.722677i \(-0.257088\pi\)
0.691186 + 0.722677i \(0.257088\pi\)
\(824\) 0.216189 0.00753131
\(825\) −0.146866 −0.00511322
\(826\) 31.4058 1.09275
\(827\) −28.3694 −0.986501 −0.493250 0.869887i \(-0.664191\pi\)
−0.493250 + 0.869887i \(0.664191\pi\)
\(828\) 26.2646 0.912757
\(829\) −4.82781 −0.167677 −0.0838383 0.996479i \(-0.526718\pi\)
−0.0838383 + 0.996479i \(0.526718\pi\)
\(830\) −27.0409 −0.938603
\(831\) −3.86294 −0.134004
\(832\) −1.48964 −0.0516438
\(833\) 3.15198 0.109210
\(834\) −2.96448 −0.102652
\(835\) −0.510124 −0.0176536
\(836\) 3.87014 0.133852
\(837\) 3.76018 0.129971
\(838\) 1.95105 0.0673979
\(839\) −5.59719 −0.193237 −0.0966183 0.995322i \(-0.530803\pi\)
−0.0966183 + 0.995322i \(0.530803\pi\)
\(840\) 1.65903 0.0572419
\(841\) −5.38952 −0.185845
\(842\) 7.76004 0.267429
\(843\) 3.32313 0.114455
\(844\) −1.00000 −0.0344214
\(845\) −24.5206 −0.843534
\(846\) −11.6065 −0.399038
\(847\) −13.2299 −0.454585
\(848\) 2.43017 0.0834523
\(849\) −7.08084 −0.243014
\(850\) 0.134303 0.00460654
\(851\) 63.2100 2.16681
\(852\) −0.988694 −0.0338721
\(853\) 44.5474 1.52527 0.762637 0.646827i \(-0.223904\pi\)
0.762637 + 0.646827i \(0.223904\pi\)
\(854\) 19.5602 0.669335
\(855\) −6.71388 −0.229610
\(856\) −8.87146 −0.303220
\(857\) −17.4083 −0.594656 −0.297328 0.954775i \(-0.596096\pi\)
−0.297328 + 0.954775i \(0.596096\pi\)
\(858\) 1.26443 0.0431671
\(859\) −32.1652 −1.09746 −0.548731 0.835999i \(-0.684889\pi\)
−0.548731 + 0.835999i \(0.684889\pi\)
\(860\) 0.410614 0.0140018
\(861\) −5.70257 −0.194343
\(862\) −12.2312 −0.416596
\(863\) 44.8554 1.52689 0.763447 0.645870i \(-0.223505\pi\)
0.763447 + 0.645870i \(0.223505\pi\)
\(864\) 1.30540 0.0444107
\(865\) −9.03200 −0.307097
\(866\) 18.6933 0.635224
\(867\) 3.59639 0.122140
\(868\) −9.57979 −0.325159
\(869\) −28.3031 −0.960116
\(870\) −2.42390 −0.0821778
\(871\) 0.234123 0.00793295
\(872\) −14.8224 −0.501951
\(873\) 2.70327 0.0914917
\(874\) −8.89752 −0.300963
\(875\) 36.5123 1.23434
\(876\) 1.89862 0.0641484
\(877\) 32.1443 1.08544 0.542718 0.839915i \(-0.317395\pi\)
0.542718 + 0.839915i \(0.317395\pi\)
\(878\) −10.4972 −0.354264
\(879\) −5.84120 −0.197019
\(880\) 8.80236 0.296728
\(881\) 14.7435 0.496721 0.248361 0.968668i \(-0.420108\pi\)
0.248361 + 0.968668i \(0.420108\pi\)
\(882\) −11.9868 −0.403618
\(883\) −53.3082 −1.79396 −0.896981 0.442068i \(-0.854245\pi\)
−0.896981 + 0.442068i \(0.854245\pi\)
\(884\) −1.15627 −0.0388896
\(885\) 4.71063 0.158346
\(886\) 38.5842 1.29626
\(887\) −15.3308 −0.514757 −0.257379 0.966311i \(-0.582859\pi\)
−0.257379 + 0.966311i \(0.582859\pi\)
\(888\) 1.55814 0.0522877
\(889\) 17.6781 0.592905
\(890\) 13.8481 0.464191
\(891\) 33.1647 1.11106
\(892\) 9.42269 0.315495
\(893\) 3.93186 0.131575
\(894\) −3.54306 −0.118498
\(895\) −2.66190 −0.0889775
\(896\) −3.32577 −0.111106
\(897\) −2.90696 −0.0970604
\(898\) −30.0086 −1.00140
\(899\) 13.9964 0.466806
\(900\) −0.510747 −0.0170249
\(901\) 1.88632 0.0628425
\(902\) −30.2563 −1.00743
\(903\) 0.131687 0.00438227
\(904\) 8.48491 0.282204
\(905\) −19.3609 −0.643579
\(906\) 0.570745 0.0189617
\(907\) −55.8503 −1.85448 −0.927240 0.374467i \(-0.877826\pi\)
−0.927240 + 0.374467i \(0.877826\pi\)
\(908\) −23.2406 −0.771268
\(909\) −41.1382 −1.36447
\(910\) 11.2679 0.373528
\(911\) 8.85277 0.293305 0.146653 0.989188i \(-0.453150\pi\)
0.146653 + 0.989188i \(0.453150\pi\)
\(912\) −0.219326 −0.00726260
\(913\) −46.0125 −1.52279
\(914\) 34.4348 1.13900
\(915\) 2.93388 0.0969911
\(916\) 5.04393 0.166656
\(917\) −6.76985 −0.223560
\(918\) 1.01327 0.0334428
\(919\) 42.5615 1.40397 0.701987 0.712190i \(-0.252297\pi\)
0.701987 + 0.712190i \(0.252297\pi\)
\(920\) −20.2368 −0.667187
\(921\) −3.91147 −0.128887
\(922\) −8.96726 −0.295321
\(923\) −6.71510 −0.221030
\(924\) 2.82298 0.0928693
\(925\) −1.22920 −0.0404157
\(926\) −12.2753 −0.403391
\(927\) −0.638168 −0.0209602
\(928\) 4.85906 0.159507
\(929\) −2.58457 −0.0847969 −0.0423984 0.999101i \(-0.513500\pi\)
−0.0423984 + 0.999101i \(0.513500\pi\)
\(930\) −1.43690 −0.0471177
\(931\) 4.06072 0.133085
\(932\) 0.0399453 0.00130845
\(933\) 5.11972 0.167612
\(934\) 37.4755 1.22623
\(935\) 6.83249 0.223446
\(936\) 4.39725 0.143729
\(937\) −41.7399 −1.36358 −0.681792 0.731546i \(-0.738799\pi\)
−0.681792 + 0.731546i \(0.738799\pi\)
\(938\) 0.522704 0.0170669
\(939\) −0.118457 −0.00386571
\(940\) 8.94274 0.291680
\(941\) 47.6551 1.55351 0.776756 0.629801i \(-0.216864\pi\)
0.776756 + 0.629801i \(0.216864\pi\)
\(942\) 5.04352 0.164327
\(943\) 69.5598 2.26518
\(944\) −9.44317 −0.307349
\(945\) −9.87436 −0.321213
\(946\) 0.698697 0.0227166
\(947\) 19.9334 0.647747 0.323874 0.946100i \(-0.395015\pi\)
0.323874 + 0.946100i \(0.395015\pi\)
\(948\) 1.60397 0.0520945
\(949\) 12.8952 0.418596
\(950\) 0.173023 0.00561362
\(951\) −3.74068 −0.121300
\(952\) −2.58150 −0.0836668
\(953\) −8.20450 −0.265770 −0.132885 0.991131i \(-0.542424\pi\)
−0.132885 + 0.991131i \(0.542424\pi\)
\(954\) −7.17360 −0.232254
\(955\) −60.4570 −1.95634
\(956\) 18.8370 0.609233
\(957\) −4.12448 −0.133325
\(958\) −0.888395 −0.0287027
\(959\) −0.895434 −0.0289151
\(960\) −0.498840 −0.0161000
\(961\) −22.7029 −0.732350
\(962\) 10.5827 0.341200
\(963\) 26.1876 0.843884
\(964\) −17.3048 −0.557352
\(965\) 4.61086 0.148429
\(966\) −6.49008 −0.208815
\(967\) −3.43780 −0.110552 −0.0552762 0.998471i \(-0.517604\pi\)
−0.0552762 + 0.998471i \(0.517604\pi\)
\(968\) 3.97800 0.127858
\(969\) −0.170243 −0.00546899
\(970\) −2.08286 −0.0668766
\(971\) 28.9208 0.928112 0.464056 0.885806i \(-0.346394\pi\)
0.464056 + 0.885806i \(0.346394\pi\)
\(972\) −5.79570 −0.185897
\(973\) −44.9522 −1.44110
\(974\) −22.8576 −0.732404
\(975\) 0.0565294 0.00181039
\(976\) −5.88140 −0.188259
\(977\) 8.58772 0.274746 0.137373 0.990519i \(-0.456134\pi\)
0.137373 + 0.990519i \(0.456134\pi\)
\(978\) 0.178334 0.00570249
\(979\) 23.5639 0.753104
\(980\) 9.23582 0.295028
\(981\) 43.7543 1.39697
\(982\) 12.6592 0.403972
\(983\) −19.0744 −0.608378 −0.304189 0.952612i \(-0.598385\pi\)
−0.304189 + 0.952612i \(0.598385\pi\)
\(984\) 1.71466 0.0546614
\(985\) −53.2271 −1.69596
\(986\) 3.77166 0.120114
\(987\) 2.86800 0.0912895
\(988\) −1.48964 −0.0473916
\(989\) −1.60632 −0.0510779
\(990\) −25.9837 −0.825815
\(991\) 54.0756 1.71777 0.858884 0.512170i \(-0.171158\pi\)
0.858884 + 0.512170i \(0.171158\pi\)
\(992\) 2.88048 0.0914552
\(993\) −7.46747 −0.236973
\(994\) −14.9922 −0.475523
\(995\) 27.9413 0.885799
\(996\) 2.60758 0.0826244
\(997\) −29.1666 −0.923714 −0.461857 0.886954i \(-0.652817\pi\)
−0.461857 + 0.886954i \(0.652817\pi\)
\(998\) 43.5023 1.37704
\(999\) −9.27388 −0.293412
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 \(a_p\))