Properties

Label 4005.2.a.l.1.3
Level 4005
Weight 2
Character 4005.1
Self dual Yes
Analytic conductor 31.980
Analytic rank 0
Dimension 4
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4005 = 3^{2} \cdot 5 \cdot 89 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4005.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9800860095\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.4.725.1
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.35567\)
Character \(\chi\) = 4005.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.162147 q^{2} -1.97371 q^{4} +1.00000 q^{5} -0.475281 q^{7} +0.644326 q^{8} +O(q^{10})\) \(q-0.162147 q^{2} -1.97371 q^{4} +1.00000 q^{5} -0.475281 q^{7} +0.644326 q^{8} -0.162147 q^{10} +5.19353 q^{11} -1.30490 q^{13} +0.0770654 q^{14} +3.84294 q^{16} +7.40330 q^{17} +6.83604 q^{19} -1.97371 q^{20} -0.842116 q^{22} -2.69195 q^{23} +1.00000 q^{25} +0.211586 q^{26} +0.938065 q^{28} +0.00689789 q^{29} -8.54230 q^{31} -1.91177 q^{32} -1.20042 q^{34} -0.475281 q^{35} -4.56119 q^{37} -1.10845 q^{38} +0.644326 q^{40} -3.41020 q^{41} +9.87858 q^{43} -10.2505 q^{44} +0.436493 q^{46} +4.62493 q^{47} -6.77411 q^{49} -0.162147 q^{50} +2.57549 q^{52} -2.86526 q^{53} +5.19353 q^{55} -0.306236 q^{56} -0.00111847 q^{58} +1.13767 q^{59} +7.30684 q^{61} +1.38511 q^{62} -7.37589 q^{64} -1.30490 q^{65} -1.79531 q^{67} -14.6120 q^{68} +0.0770654 q^{70} -2.91492 q^{71} -2.26369 q^{73} +0.739584 q^{74} -13.4924 q^{76} -2.46838 q^{77} -10.5104 q^{79} +3.84294 q^{80} +0.552955 q^{82} -6.35650 q^{83} +7.40330 q^{85} -1.60178 q^{86} +3.34632 q^{88} +1.00000 q^{89} +0.620194 q^{91} +5.31313 q^{92} -0.749920 q^{94} +6.83604 q^{95} +18.3113 q^{97} +1.09840 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - q^{2} + 3q^{4} + 4q^{5} + 2q^{7} + 9q^{8} + O(q^{10}) \) \( 4q - q^{2} + 3q^{4} + 4q^{5} + 2q^{7} + 9q^{8} - q^{10} + 14q^{11} - 5q^{13} + 5q^{14} - 3q^{16} + 3q^{17} - q^{19} + 3q^{20} + 2q^{22} + 3q^{23} + 4q^{25} + 9q^{26} + 5q^{28} + 10q^{29} - 11q^{31} + 2q^{32} - 8q^{34} + 2q^{35} + 3q^{37} - 2q^{38} + 9q^{40} + 3q^{41} + 9q^{43} + 9q^{44} - 4q^{46} + 24q^{47} - q^{50} + 8q^{52} - 3q^{53} + 14q^{55} + 13q^{56} + 19q^{58} + 22q^{59} - 3q^{61} + 24q^{62} - 11q^{64} - 5q^{65} - 9q^{67} - 31q^{68} + 5q^{70} - 16q^{71} + 3q^{73} - 31q^{74} - 24q^{76} + 4q^{77} - 27q^{79} - 3q^{80} - 15q^{82} - 6q^{83} + 3q^{85} - 15q^{86} + 30q^{88} + 4q^{89} - 29q^{91} + 17q^{92} + 13q^{94} - q^{95} + 41q^{97} - 22q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.162147 −0.114655 −0.0573277 0.998355i \(-0.518258\pi\)
−0.0573277 + 0.998355i \(0.518258\pi\)
\(3\) 0 0
\(4\) −1.97371 −0.986854
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −0.475281 −0.179639 −0.0898196 0.995958i \(-0.528629\pi\)
−0.0898196 + 0.995958i \(0.528629\pi\)
\(8\) 0.644326 0.227804
\(9\) 0 0
\(10\) −0.162147 −0.0512754
\(11\) 5.19353 1.56591 0.782954 0.622080i \(-0.213712\pi\)
0.782954 + 0.622080i \(0.213712\pi\)
\(12\) 0 0
\(13\) −1.30490 −0.361914 −0.180957 0.983491i \(-0.557920\pi\)
−0.180957 + 0.983491i \(0.557920\pi\)
\(14\) 0.0770654 0.0205966
\(15\) 0 0
\(16\) 3.84294 0.960735
\(17\) 7.40330 1.79556 0.897782 0.440439i \(-0.145177\pi\)
0.897782 + 0.440439i \(0.145177\pi\)
\(18\) 0 0
\(19\) 6.83604 1.56830 0.784148 0.620574i \(-0.213100\pi\)
0.784148 + 0.620574i \(0.213100\pi\)
\(20\) −1.97371 −0.441335
\(21\) 0 0
\(22\) −0.842116 −0.179540
\(23\) −2.69195 −0.561311 −0.280656 0.959809i \(-0.590552\pi\)
−0.280656 + 0.959809i \(0.590552\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0.211586 0.0414954
\(27\) 0 0
\(28\) 0.938065 0.177278
\(29\) 0.00689789 0.00128091 0.000640453 1.00000i \(-0.499796\pi\)
0.000640453 1.00000i \(0.499796\pi\)
\(30\) 0 0
\(31\) −8.54230 −1.53424 −0.767121 0.641502i \(-0.778312\pi\)
−0.767121 + 0.641502i \(0.778312\pi\)
\(32\) −1.91177 −0.337957
\(33\) 0 0
\(34\) −1.20042 −0.205871
\(35\) −0.475281 −0.0803371
\(36\) 0 0
\(37\) −4.56119 −0.749855 −0.374927 0.927054i \(-0.622332\pi\)
−0.374927 + 0.927054i \(0.622332\pi\)
\(38\) −1.10845 −0.179814
\(39\) 0 0
\(40\) 0.644326 0.101877
\(41\) −3.41020 −0.532584 −0.266292 0.963892i \(-0.585799\pi\)
−0.266292 + 0.963892i \(0.585799\pi\)
\(42\) 0 0
\(43\) 9.87858 1.50647 0.753235 0.657752i \(-0.228492\pi\)
0.753235 + 0.657752i \(0.228492\pi\)
\(44\) −10.2505 −1.54532
\(45\) 0 0
\(46\) 0.436493 0.0643574
\(47\) 4.62493 0.674616 0.337308 0.941394i \(-0.390484\pi\)
0.337308 + 0.941394i \(0.390484\pi\)
\(48\) 0 0
\(49\) −6.77411 −0.967730
\(50\) −0.162147 −0.0229311
\(51\) 0 0
\(52\) 2.57549 0.357157
\(53\) −2.86526 −0.393574 −0.196787 0.980446i \(-0.563051\pi\)
−0.196787 + 0.980446i \(0.563051\pi\)
\(54\) 0 0
\(55\) 5.19353 0.700295
\(56\) −0.306236 −0.0409224
\(57\) 0 0
\(58\) −0.00111847 −0.000146863 0
\(59\) 1.13767 0.148111 0.0740557 0.997254i \(-0.476406\pi\)
0.0740557 + 0.997254i \(0.476406\pi\)
\(60\) 0 0
\(61\) 7.30684 0.935546 0.467773 0.883849i \(-0.345057\pi\)
0.467773 + 0.883849i \(0.345057\pi\)
\(62\) 1.38511 0.175909
\(63\) 0 0
\(64\) −7.37589 −0.921987
\(65\) −1.30490 −0.161853
\(66\) 0 0
\(67\) −1.79531 −0.219332 −0.109666 0.993968i \(-0.534978\pi\)
−0.109666 + 0.993968i \(0.534978\pi\)
\(68\) −14.6120 −1.77196
\(69\) 0 0
\(70\) 0.0770654 0.00921108
\(71\) −2.91492 −0.345937 −0.172969 0.984927i \(-0.555336\pi\)
−0.172969 + 0.984927i \(0.555336\pi\)
\(72\) 0 0
\(73\) −2.26369 −0.264945 −0.132473 0.991187i \(-0.542292\pi\)
−0.132473 + 0.991187i \(0.542292\pi\)
\(74\) 0.739584 0.0859749
\(75\) 0 0
\(76\) −13.4924 −1.54768
\(77\) −2.46838 −0.281298
\(78\) 0 0
\(79\) −10.5104 −1.18251 −0.591257 0.806483i \(-0.701368\pi\)
−0.591257 + 0.806483i \(0.701368\pi\)
\(80\) 3.84294 0.429654
\(81\) 0 0
\(82\) 0.552955 0.0610636
\(83\) −6.35650 −0.697716 −0.348858 0.937176i \(-0.613431\pi\)
−0.348858 + 0.937176i \(0.613431\pi\)
\(84\) 0 0
\(85\) 7.40330 0.803001
\(86\) −1.60178 −0.172725
\(87\) 0 0
\(88\) 3.34632 0.356719
\(89\) 1.00000 0.106000
\(90\) 0 0
\(91\) 0.620194 0.0650140
\(92\) 5.31313 0.553932
\(93\) 0 0
\(94\) −0.749920 −0.0773483
\(95\) 6.83604 0.701363
\(96\) 0 0
\(97\) 18.3113 1.85923 0.929617 0.368528i \(-0.120138\pi\)
0.929617 + 0.368528i \(0.120138\pi\)
\(98\) 1.09840 0.110955
\(99\) 0 0
\(100\) −1.97371 −0.197371
\(101\) 14.3545 1.42832 0.714162 0.699981i \(-0.246808\pi\)
0.714162 + 0.699981i \(0.246808\pi\)
\(102\) 0 0
\(103\) 5.43964 0.535983 0.267992 0.963421i \(-0.413640\pi\)
0.267992 + 0.963421i \(0.413640\pi\)
\(104\) −0.840781 −0.0824454
\(105\) 0 0
\(106\) 0.464594 0.0451254
\(107\) 7.27486 0.703287 0.351643 0.936134i \(-0.385623\pi\)
0.351643 + 0.936134i \(0.385623\pi\)
\(108\) 0 0
\(109\) 3.92293 0.375749 0.187874 0.982193i \(-0.439840\pi\)
0.187874 + 0.982193i \(0.439840\pi\)
\(110\) −0.842116 −0.0802926
\(111\) 0 0
\(112\) −1.82648 −0.172586
\(113\) 15.2119 1.43102 0.715509 0.698603i \(-0.246195\pi\)
0.715509 + 0.698603i \(0.246195\pi\)
\(114\) 0 0
\(115\) −2.69195 −0.251026
\(116\) −0.0136144 −0.00126407
\(117\) 0 0
\(118\) −0.184469 −0.0169818
\(119\) −3.51865 −0.322554
\(120\) 0 0
\(121\) 15.9727 1.45207
\(122\) −1.18478 −0.107265
\(123\) 0 0
\(124\) 16.8600 1.51407
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 14.3082 1.26965 0.634823 0.772658i \(-0.281073\pi\)
0.634823 + 0.772658i \(0.281073\pi\)
\(128\) 5.01953 0.443668
\(129\) 0 0
\(130\) 0.211586 0.0185573
\(131\) 5.16529 0.451294 0.225647 0.974209i \(-0.427550\pi\)
0.225647 + 0.974209i \(0.427550\pi\)
\(132\) 0 0
\(133\) −3.24904 −0.281727
\(134\) 0.291105 0.0251476
\(135\) 0 0
\(136\) 4.77014 0.409036
\(137\) 10.1033 0.863181 0.431590 0.902070i \(-0.357953\pi\)
0.431590 + 0.902070i \(0.357953\pi\)
\(138\) 0 0
\(139\) −21.0062 −1.78172 −0.890862 0.454275i \(-0.849898\pi\)
−0.890862 + 0.454275i \(0.849898\pi\)
\(140\) 0.938065 0.0792810
\(141\) 0 0
\(142\) 0.472646 0.0396636
\(143\) −6.77704 −0.566724
\(144\) 0 0
\(145\) 0.00689789 0.000572838 0
\(146\) 0.367052 0.0303774
\(147\) 0 0
\(148\) 9.00245 0.739997
\(149\) 4.55954 0.373532 0.186766 0.982404i \(-0.440199\pi\)
0.186766 + 0.982404i \(0.440199\pi\)
\(150\) 0 0
\(151\) 3.64071 0.296276 0.148138 0.988967i \(-0.452672\pi\)
0.148138 + 0.988967i \(0.452672\pi\)
\(152\) 4.40464 0.357263
\(153\) 0 0
\(154\) 0.400241 0.0322524
\(155\) −8.54230 −0.686134
\(156\) 0 0
\(157\) 17.3667 1.38601 0.693006 0.720932i \(-0.256286\pi\)
0.693006 + 0.720932i \(0.256286\pi\)
\(158\) 1.70423 0.135582
\(159\) 0 0
\(160\) −1.91177 −0.151139
\(161\) 1.27943 0.100834
\(162\) 0 0
\(163\) −9.06918 −0.710353 −0.355177 0.934799i \(-0.615579\pi\)
−0.355177 + 0.934799i \(0.615579\pi\)
\(164\) 6.73074 0.525583
\(165\) 0 0
\(166\) 1.03069 0.0799970
\(167\) −4.29059 −0.332016 −0.166008 0.986124i \(-0.553088\pi\)
−0.166008 + 0.986124i \(0.553088\pi\)
\(168\) 0 0
\(169\) −11.2972 −0.869018
\(170\) −1.20042 −0.0920684
\(171\) 0 0
\(172\) −19.4974 −1.48667
\(173\) −21.1969 −1.61157 −0.805787 0.592206i \(-0.798257\pi\)
−0.805787 + 0.592206i \(0.798257\pi\)
\(174\) 0 0
\(175\) −0.475281 −0.0359278
\(176\) 19.9584 1.50442
\(177\) 0 0
\(178\) −0.162147 −0.0121534
\(179\) −0.468991 −0.0350541 −0.0175270 0.999846i \(-0.505579\pi\)
−0.0175270 + 0.999846i \(0.505579\pi\)
\(180\) 0 0
\(181\) −22.2732 −1.65555 −0.827776 0.561058i \(-0.810394\pi\)
−0.827776 + 0.561058i \(0.810394\pi\)
\(182\) −0.100563 −0.00745420
\(183\) 0 0
\(184\) −1.73450 −0.127869
\(185\) −4.56119 −0.335345
\(186\) 0 0
\(187\) 38.4493 2.81169
\(188\) −9.12827 −0.665747
\(189\) 0 0
\(190\) −1.10845 −0.0804151
\(191\) 21.3072 1.54173 0.770867 0.636996i \(-0.219823\pi\)
0.770867 + 0.636996i \(0.219823\pi\)
\(192\) 0 0
\(193\) −1.33822 −0.0963275 −0.0481637 0.998839i \(-0.515337\pi\)
−0.0481637 + 0.998839i \(0.515337\pi\)
\(194\) −2.96913 −0.213171
\(195\) 0 0
\(196\) 13.3701 0.955008
\(197\) 9.65959 0.688217 0.344109 0.938930i \(-0.388181\pi\)
0.344109 + 0.938930i \(0.388181\pi\)
\(198\) 0 0
\(199\) 9.85738 0.698771 0.349386 0.936979i \(-0.386390\pi\)
0.349386 + 0.936979i \(0.386390\pi\)
\(200\) 0.644326 0.0455607
\(201\) 0 0
\(202\) −2.32754 −0.163765
\(203\) −0.00327843 −0.000230101 0
\(204\) 0 0
\(205\) −3.41020 −0.238179
\(206\) −0.882022 −0.0614534
\(207\) 0 0
\(208\) −5.01466 −0.347704
\(209\) 35.5032 2.45581
\(210\) 0 0
\(211\) −12.2510 −0.843396 −0.421698 0.906736i \(-0.638566\pi\)
−0.421698 + 0.906736i \(0.638566\pi\)
\(212\) 5.65519 0.388400
\(213\) 0 0
\(214\) −1.17960 −0.0806356
\(215\) 9.87858 0.673714
\(216\) 0 0
\(217\) 4.05999 0.275610
\(218\) −0.636093 −0.0430816
\(219\) 0 0
\(220\) −10.2505 −0.691089
\(221\) −9.66057 −0.649841
\(222\) 0 0
\(223\) −22.4242 −1.50163 −0.750817 0.660511i \(-0.770340\pi\)
−0.750817 + 0.660511i \(0.770340\pi\)
\(224\) 0.908629 0.0607103
\(225\) 0 0
\(226\) −2.46657 −0.164074
\(227\) 23.1665 1.53762 0.768809 0.639479i \(-0.220850\pi\)
0.768809 + 0.639479i \(0.220850\pi\)
\(228\) 0 0
\(229\) 4.15788 0.274761 0.137380 0.990518i \(-0.456132\pi\)
0.137380 + 0.990518i \(0.456132\pi\)
\(230\) 0.436493 0.0287815
\(231\) 0 0
\(232\) 0.00444449 0.000291795 0
\(233\) 11.7721 0.771215 0.385607 0.922663i \(-0.373992\pi\)
0.385607 + 0.922663i \(0.373992\pi\)
\(234\) 0 0
\(235\) 4.62493 0.301697
\(236\) −2.24542 −0.146164
\(237\) 0 0
\(238\) 0.570539 0.0369825
\(239\) 20.3834 1.31849 0.659246 0.751927i \(-0.270875\pi\)
0.659246 + 0.751927i \(0.270875\pi\)
\(240\) 0 0
\(241\) −11.3468 −0.730908 −0.365454 0.930829i \(-0.619086\pi\)
−0.365454 + 0.930829i \(0.619086\pi\)
\(242\) −2.58993 −0.166487
\(243\) 0 0
\(244\) −14.4216 −0.923247
\(245\) −6.77411 −0.432782
\(246\) 0 0
\(247\) −8.92036 −0.567589
\(248\) −5.50403 −0.349506
\(249\) 0 0
\(250\) −0.162147 −0.0102551
\(251\) 16.0015 1.01000 0.505002 0.863118i \(-0.331492\pi\)
0.505002 + 0.863118i \(0.331492\pi\)
\(252\) 0 0
\(253\) −13.9807 −0.878962
\(254\) −2.32003 −0.145572
\(255\) 0 0
\(256\) 13.9379 0.871118
\(257\) −9.71532 −0.606025 −0.303012 0.952987i \(-0.597992\pi\)
−0.303012 + 0.952987i \(0.597992\pi\)
\(258\) 0 0
\(259\) 2.16784 0.134703
\(260\) 2.57549 0.159725
\(261\) 0 0
\(262\) −0.837538 −0.0517432
\(263\) −23.1738 −1.42896 −0.714479 0.699657i \(-0.753336\pi\)
−0.714479 + 0.699657i \(0.753336\pi\)
\(264\) 0 0
\(265\) −2.86526 −0.176012
\(266\) 0.526823 0.0323016
\(267\) 0 0
\(268\) 3.54342 0.216449
\(269\) 4.92771 0.300448 0.150224 0.988652i \(-0.452001\pi\)
0.150224 + 0.988652i \(0.452001\pi\)
\(270\) 0 0
\(271\) 16.5952 1.00809 0.504044 0.863678i \(-0.331845\pi\)
0.504044 + 0.863678i \(0.331845\pi\)
\(272\) 28.4505 1.72506
\(273\) 0 0
\(274\) −1.63822 −0.0989684
\(275\) 5.19353 0.313181
\(276\) 0 0
\(277\) −12.9860 −0.780256 −0.390128 0.920761i \(-0.627569\pi\)
−0.390128 + 0.920761i \(0.627569\pi\)
\(278\) 3.40610 0.204284
\(279\) 0 0
\(280\) −0.306236 −0.0183011
\(281\) −29.4497 −1.75682 −0.878412 0.477904i \(-0.841397\pi\)
−0.878412 + 0.477904i \(0.841397\pi\)
\(282\) 0 0
\(283\) −14.8999 −0.885708 −0.442854 0.896594i \(-0.646034\pi\)
−0.442854 + 0.896594i \(0.646034\pi\)
\(284\) 5.75320 0.341390
\(285\) 0 0
\(286\) 1.09888 0.0649780
\(287\) 1.62080 0.0956729
\(288\) 0 0
\(289\) 37.8089 2.22405
\(290\) −0.00111847 −6.56790e−5 0
\(291\) 0 0
\(292\) 4.46787 0.261462
\(293\) 2.70575 0.158072 0.0790358 0.996872i \(-0.474816\pi\)
0.0790358 + 0.996872i \(0.474816\pi\)
\(294\) 0 0
\(295\) 1.13767 0.0662374
\(296\) −2.93889 −0.170820
\(297\) 0 0
\(298\) −0.739316 −0.0428274
\(299\) 3.51273 0.203147
\(300\) 0 0
\(301\) −4.69510 −0.270621
\(302\) −0.590330 −0.0339697
\(303\) 0 0
\(304\) 26.2705 1.50672
\(305\) 7.30684 0.418389
\(306\) 0 0
\(307\) −15.4273 −0.880481 −0.440241 0.897880i \(-0.645107\pi\)
−0.440241 + 0.897880i \(0.645107\pi\)
\(308\) 4.87187 0.277600
\(309\) 0 0
\(310\) 1.38511 0.0786690
\(311\) 9.28894 0.526728 0.263364 0.964697i \(-0.415168\pi\)
0.263364 + 0.964697i \(0.415168\pi\)
\(312\) 0 0
\(313\) −5.56675 −0.314651 −0.157326 0.987547i \(-0.550287\pi\)
−0.157326 + 0.987547i \(0.550287\pi\)
\(314\) −2.81596 −0.158914
\(315\) 0 0
\(316\) 20.7445 1.16697
\(317\) −30.9404 −1.73778 −0.868892 0.495002i \(-0.835167\pi\)
−0.868892 + 0.495002i \(0.835167\pi\)
\(318\) 0 0
\(319\) 0.0358244 0.00200578
\(320\) −7.37589 −0.412325
\(321\) 0 0
\(322\) −0.207457 −0.0115611
\(323\) 50.6093 2.81598
\(324\) 0 0
\(325\) −1.30490 −0.0723829
\(326\) 1.47054 0.0814458
\(327\) 0 0
\(328\) −2.19728 −0.121325
\(329\) −2.19814 −0.121187
\(330\) 0 0
\(331\) 0.0734460 0.00403696 0.00201848 0.999998i \(-0.499357\pi\)
0.00201848 + 0.999998i \(0.499357\pi\)
\(332\) 12.5459 0.688544
\(333\) 0 0
\(334\) 0.695708 0.0380674
\(335\) −1.79531 −0.0980884
\(336\) 0 0
\(337\) 16.9619 0.923971 0.461986 0.886887i \(-0.347137\pi\)
0.461986 + 0.886887i \(0.347137\pi\)
\(338\) 1.83182 0.0996376
\(339\) 0 0
\(340\) −14.6120 −0.792445
\(341\) −44.3647 −2.40248
\(342\) 0 0
\(343\) 6.54657 0.353481
\(344\) 6.36503 0.343179
\(345\) 0 0
\(346\) 3.43702 0.184776
\(347\) 21.2221 1.13926 0.569630 0.821901i \(-0.307087\pi\)
0.569630 + 0.821901i \(0.307087\pi\)
\(348\) 0 0
\(349\) 7.48298 0.400555 0.200277 0.979739i \(-0.435816\pi\)
0.200277 + 0.979739i \(0.435816\pi\)
\(350\) 0.0770654 0.00411932
\(351\) 0 0
\(352\) −9.92885 −0.529209
\(353\) −2.09475 −0.111492 −0.0557461 0.998445i \(-0.517754\pi\)
−0.0557461 + 0.998445i \(0.517754\pi\)
\(354\) 0 0
\(355\) −2.91492 −0.154708
\(356\) −1.97371 −0.104606
\(357\) 0 0
\(358\) 0.0760456 0.00401914
\(359\) 1.57842 0.0833059 0.0416529 0.999132i \(-0.486738\pi\)
0.0416529 + 0.999132i \(0.486738\pi\)
\(360\) 0 0
\(361\) 27.7315 1.45955
\(362\) 3.61153 0.189818
\(363\) 0 0
\(364\) −1.22408 −0.0641593
\(365\) −2.26369 −0.118487
\(366\) 0 0
\(367\) 34.6898 1.81079 0.905397 0.424567i \(-0.139574\pi\)
0.905397 + 0.424567i \(0.139574\pi\)
\(368\) −10.3450 −0.539272
\(369\) 0 0
\(370\) 0.739584 0.0384491
\(371\) 1.36180 0.0707013
\(372\) 0 0
\(373\) 28.3861 1.46977 0.734887 0.678189i \(-0.237235\pi\)
0.734887 + 0.678189i \(0.237235\pi\)
\(374\) −6.23444 −0.322375
\(375\) 0 0
\(376\) 2.97996 0.153680
\(377\) −0.00900106 −0.000463578 0
\(378\) 0 0
\(379\) −15.3669 −0.789344 −0.394672 0.918822i \(-0.629142\pi\)
−0.394672 + 0.918822i \(0.629142\pi\)
\(380\) −13.4924 −0.692143
\(381\) 0 0
\(382\) −3.45490 −0.176768
\(383\) 23.8489 1.21862 0.609311 0.792932i \(-0.291446\pi\)
0.609311 + 0.792932i \(0.291446\pi\)
\(384\) 0 0
\(385\) −2.46838 −0.125800
\(386\) 0.216989 0.0110445
\(387\) 0 0
\(388\) −36.1412 −1.83479
\(389\) −11.7669 −0.596603 −0.298302 0.954472i \(-0.596420\pi\)
−0.298302 + 0.954472i \(0.596420\pi\)
\(390\) 0 0
\(391\) −19.9294 −1.00787
\(392\) −4.36473 −0.220452
\(393\) 0 0
\(394\) −1.56628 −0.0789078
\(395\) −10.5104 −0.528836
\(396\) 0 0
\(397\) −11.2778 −0.566019 −0.283009 0.959117i \(-0.591333\pi\)
−0.283009 + 0.959117i \(0.591333\pi\)
\(398\) −1.59835 −0.0801179
\(399\) 0 0
\(400\) 3.84294 0.192147
\(401\) −12.9916 −0.648770 −0.324385 0.945925i \(-0.605157\pi\)
−0.324385 + 0.945925i \(0.605157\pi\)
\(402\) 0 0
\(403\) 11.1469 0.555264
\(404\) −28.3315 −1.40955
\(405\) 0 0
\(406\) 0.000531589 0 2.63823e−5 0
\(407\) −23.6887 −1.17420
\(408\) 0 0
\(409\) −14.2198 −0.703124 −0.351562 0.936165i \(-0.614349\pi\)
−0.351562 + 0.936165i \(0.614349\pi\)
\(410\) 0.552955 0.0273085
\(411\) 0 0
\(412\) −10.7363 −0.528937
\(413\) −0.540710 −0.0266066
\(414\) 0 0
\(415\) −6.35650 −0.312028
\(416\) 2.49467 0.122311
\(417\) 0 0
\(418\) −5.75674 −0.281571
\(419\) 32.8278 1.60374 0.801871 0.597497i \(-0.203838\pi\)
0.801871 + 0.597497i \(0.203838\pi\)
\(420\) 0 0
\(421\) 35.9329 1.75126 0.875630 0.482982i \(-0.160447\pi\)
0.875630 + 0.482982i \(0.160447\pi\)
\(422\) 1.98647 0.0966999
\(423\) 0 0
\(424\) −1.84616 −0.0896576
\(425\) 7.40330 0.359113
\(426\) 0 0
\(427\) −3.47280 −0.168061
\(428\) −14.3584 −0.694042
\(429\) 0 0
\(430\) −1.60178 −0.0772449
\(431\) 24.7729 1.19327 0.596634 0.802513i \(-0.296504\pi\)
0.596634 + 0.802513i \(0.296504\pi\)
\(432\) 0 0
\(433\) 28.1739 1.35395 0.676976 0.736005i \(-0.263290\pi\)
0.676976 + 0.736005i \(0.263290\pi\)
\(434\) −0.658316 −0.0316002
\(435\) 0 0
\(436\) −7.74273 −0.370809
\(437\) −18.4023 −0.880302
\(438\) 0 0
\(439\) −0.128231 −0.00612014 −0.00306007 0.999995i \(-0.500974\pi\)
−0.00306007 + 0.999995i \(0.500974\pi\)
\(440\) 3.34632 0.159530
\(441\) 0 0
\(442\) 1.56644 0.0745077
\(443\) −3.96327 −0.188301 −0.0941504 0.995558i \(-0.530013\pi\)
−0.0941504 + 0.995558i \(0.530013\pi\)
\(444\) 0 0
\(445\) 1.00000 0.0474045
\(446\) 3.63602 0.172170
\(447\) 0 0
\(448\) 3.50562 0.165625
\(449\) 5.39593 0.254650 0.127325 0.991861i \(-0.459361\pi\)
0.127325 + 0.991861i \(0.459361\pi\)
\(450\) 0 0
\(451\) −17.7110 −0.833977
\(452\) −30.0239 −1.41221
\(453\) 0 0
\(454\) −3.75639 −0.176296
\(455\) 0.620194 0.0290751
\(456\) 0 0
\(457\) 0.665823 0.0311459 0.0155729 0.999879i \(-0.495043\pi\)
0.0155729 + 0.999879i \(0.495043\pi\)
\(458\) −0.674189 −0.0315028
\(459\) 0 0
\(460\) 5.31313 0.247726
\(461\) −42.6998 −1.98873 −0.994365 0.106010i \(-0.966192\pi\)
−0.994365 + 0.106010i \(0.966192\pi\)
\(462\) 0 0
\(463\) 7.05789 0.328008 0.164004 0.986460i \(-0.447559\pi\)
0.164004 + 0.986460i \(0.447559\pi\)
\(464\) 0.0265082 0.00123061
\(465\) 0 0
\(466\) −1.90881 −0.0884239
\(467\) 30.6233 1.41708 0.708540 0.705671i \(-0.249354\pi\)
0.708540 + 0.705671i \(0.249354\pi\)
\(468\) 0 0
\(469\) 0.853277 0.0394007
\(470\) −0.749920 −0.0345912
\(471\) 0 0
\(472\) 0.733027 0.0337403
\(473\) 51.3047 2.35899
\(474\) 0 0
\(475\) 6.83604 0.313659
\(476\) 6.94478 0.318314
\(477\) 0 0
\(478\) −3.30511 −0.151172
\(479\) −24.7778 −1.13213 −0.566063 0.824362i \(-0.691534\pi\)
−0.566063 + 0.824362i \(0.691534\pi\)
\(480\) 0 0
\(481\) 5.95190 0.271383
\(482\) 1.83984 0.0838026
\(483\) 0 0
\(484\) −31.5255 −1.43298
\(485\) 18.3113 0.831474
\(486\) 0 0
\(487\) 41.0479 1.86006 0.930029 0.367486i \(-0.119782\pi\)
0.930029 + 0.367486i \(0.119782\pi\)
\(488\) 4.70799 0.213121
\(489\) 0 0
\(490\) 1.09840 0.0496208
\(491\) −32.1154 −1.44935 −0.724674 0.689092i \(-0.758010\pi\)
−0.724674 + 0.689092i \(0.758010\pi\)
\(492\) 0 0
\(493\) 0.0510671 0.00229995
\(494\) 1.44641 0.0650771
\(495\) 0 0
\(496\) −32.8276 −1.47400
\(497\) 1.38540 0.0621439
\(498\) 0 0
\(499\) −29.5346 −1.32215 −0.661074 0.750321i \(-0.729899\pi\)
−0.661074 + 0.750321i \(0.729899\pi\)
\(500\) −1.97371 −0.0882669
\(501\) 0 0
\(502\) −2.59459 −0.115802
\(503\) −17.9883 −0.802058 −0.401029 0.916065i \(-0.631347\pi\)
−0.401029 + 0.916065i \(0.631347\pi\)
\(504\) 0 0
\(505\) 14.3545 0.638766
\(506\) 2.26694 0.100778
\(507\) 0 0
\(508\) −28.2402 −1.25295
\(509\) −28.2936 −1.25409 −0.627045 0.778983i \(-0.715736\pi\)
−0.627045 + 0.778983i \(0.715736\pi\)
\(510\) 0 0
\(511\) 1.07589 0.0475946
\(512\) −12.2990 −0.543546
\(513\) 0 0
\(514\) 1.57531 0.0694840
\(515\) 5.43964 0.239699
\(516\) 0 0
\(517\) 24.0197 1.05639
\(518\) −0.351510 −0.0154445
\(519\) 0 0
\(520\) −0.840781 −0.0368707
\(521\) 13.2784 0.581739 0.290870 0.956763i \(-0.406055\pi\)
0.290870 + 0.956763i \(0.406055\pi\)
\(522\) 0 0
\(523\) −23.7559 −1.03877 −0.519386 0.854540i \(-0.673839\pi\)
−0.519386 + 0.854540i \(0.673839\pi\)
\(524\) −10.1948 −0.445361
\(525\) 0 0
\(526\) 3.75757 0.163838
\(527\) −63.2413 −2.75483
\(528\) 0 0
\(529\) −15.7534 −0.684930
\(530\) 0.464594 0.0201807
\(531\) 0 0
\(532\) 6.41265 0.278024
\(533\) 4.44997 0.192750
\(534\) 0 0
\(535\) 7.27486 0.314519
\(536\) −1.15677 −0.0499647
\(537\) 0 0
\(538\) −0.799014 −0.0344479
\(539\) −35.1815 −1.51538
\(540\) 0 0
\(541\) −12.9184 −0.555404 −0.277702 0.960667i \(-0.589573\pi\)
−0.277702 + 0.960667i \(0.589573\pi\)
\(542\) −2.69087 −0.115583
\(543\) 0 0
\(544\) −14.1534 −0.606824
\(545\) 3.92293 0.168040
\(546\) 0 0
\(547\) 39.0481 1.66958 0.834788 0.550571i \(-0.185590\pi\)
0.834788 + 0.550571i \(0.185590\pi\)
\(548\) −19.9409 −0.851834
\(549\) 0 0
\(550\) −0.842116 −0.0359079
\(551\) 0.0471543 0.00200884
\(552\) 0 0
\(553\) 4.99540 0.212426
\(554\) 2.10565 0.0894605
\(555\) 0 0
\(556\) 41.4601 1.75830
\(557\) −5.51252 −0.233573 −0.116786 0.993157i \(-0.537259\pi\)
−0.116786 + 0.993157i \(0.537259\pi\)
\(558\) 0 0
\(559\) −12.8906 −0.545213
\(560\) −1.82648 −0.0771827
\(561\) 0 0
\(562\) 4.77519 0.201429
\(563\) 37.2064 1.56806 0.784031 0.620722i \(-0.213160\pi\)
0.784031 + 0.620722i \(0.213160\pi\)
\(564\) 0 0
\(565\) 15.2119 0.639971
\(566\) 2.41598 0.101551
\(567\) 0 0
\(568\) −1.87816 −0.0788057
\(569\) 27.0351 1.13337 0.566685 0.823935i \(-0.308226\pi\)
0.566685 + 0.823935i \(0.308226\pi\)
\(570\) 0 0
\(571\) 32.8494 1.37471 0.687353 0.726324i \(-0.258773\pi\)
0.687353 + 0.726324i \(0.258773\pi\)
\(572\) 13.3759 0.559274
\(573\) 0 0
\(574\) −0.262809 −0.0109694
\(575\) −2.69195 −0.112262
\(576\) 0 0
\(577\) 35.2109 1.46585 0.732925 0.680309i \(-0.238155\pi\)
0.732925 + 0.680309i \(0.238155\pi\)
\(578\) −6.13061 −0.255000
\(579\) 0 0
\(580\) −0.0136144 −0.000565308 0
\(581\) 3.02112 0.125337
\(582\) 0 0
\(583\) −14.8808 −0.616301
\(584\) −1.45856 −0.0603555
\(585\) 0 0
\(586\) −0.438730 −0.0181238
\(587\) −40.2094 −1.65962 −0.829811 0.558045i \(-0.811552\pi\)
−0.829811 + 0.558045i \(0.811552\pi\)
\(588\) 0 0
\(589\) −58.3956 −2.40615
\(590\) −0.184469 −0.00759448
\(591\) 0 0
\(592\) −17.5284 −0.720412
\(593\) −29.5937 −1.21527 −0.607633 0.794218i \(-0.707881\pi\)
−0.607633 + 0.794218i \(0.707881\pi\)
\(594\) 0 0
\(595\) −3.51865 −0.144250
\(596\) −8.99920 −0.368621
\(597\) 0 0
\(598\) −0.569580 −0.0232919
\(599\) 8.74518 0.357318 0.178659 0.983911i \(-0.442824\pi\)
0.178659 + 0.983911i \(0.442824\pi\)
\(600\) 0 0
\(601\) 3.42482 0.139701 0.0698507 0.997557i \(-0.477748\pi\)
0.0698507 + 0.997557i \(0.477748\pi\)
\(602\) 0.761297 0.0310282
\(603\) 0 0
\(604\) −7.18569 −0.292382
\(605\) 15.9727 0.649384
\(606\) 0 0
\(607\) −20.5908 −0.835756 −0.417878 0.908503i \(-0.637226\pi\)
−0.417878 + 0.908503i \(0.637226\pi\)
\(608\) −13.0690 −0.530017
\(609\) 0 0
\(610\) −1.18478 −0.0479705
\(611\) −6.03508 −0.244153
\(612\) 0 0
\(613\) −26.4547 −1.06850 −0.534248 0.845328i \(-0.679405\pi\)
−0.534248 + 0.845328i \(0.679405\pi\)
\(614\) 2.50149 0.100952
\(615\) 0 0
\(616\) −1.59044 −0.0640808
\(617\) 43.8302 1.76454 0.882268 0.470747i \(-0.156015\pi\)
0.882268 + 0.470747i \(0.156015\pi\)
\(618\) 0 0
\(619\) −0.0432321 −0.00173765 −0.000868823 1.00000i \(-0.500277\pi\)
−0.000868823 1.00000i \(0.500277\pi\)
\(620\) 16.8600 0.677115
\(621\) 0 0
\(622\) −1.50618 −0.0603922
\(623\) −0.475281 −0.0190417
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0.902633 0.0360765
\(627\) 0 0
\(628\) −34.2768 −1.36779
\(629\) −33.7679 −1.34641
\(630\) 0 0
\(631\) −29.9042 −1.19047 −0.595233 0.803553i \(-0.702940\pi\)
−0.595233 + 0.803553i \(0.702940\pi\)
\(632\) −6.77213 −0.269381
\(633\) 0 0
\(634\) 5.01689 0.199246
\(635\) 14.3082 0.567803
\(636\) 0 0
\(637\) 8.83954 0.350235
\(638\) −0.00580882 −0.000229973 0
\(639\) 0 0
\(640\) 5.01953 0.198414
\(641\) 16.3131 0.644330 0.322165 0.946684i \(-0.395589\pi\)
0.322165 + 0.946684i \(0.395589\pi\)
\(642\) 0 0
\(643\) 17.2134 0.678832 0.339416 0.940636i \(-0.389771\pi\)
0.339416 + 0.940636i \(0.389771\pi\)
\(644\) −2.52523 −0.0995080
\(645\) 0 0
\(646\) −8.20616 −0.322867
\(647\) −28.3178 −1.11329 −0.556645 0.830751i \(-0.687912\pi\)
−0.556645 + 0.830751i \(0.687912\pi\)
\(648\) 0 0
\(649\) 5.90850 0.231929
\(650\) 0.211586 0.00829909
\(651\) 0 0
\(652\) 17.8999 0.701015
\(653\) −27.2771 −1.06743 −0.533717 0.845663i \(-0.679205\pi\)
−0.533717 + 0.845663i \(0.679205\pi\)
\(654\) 0 0
\(655\) 5.16529 0.201825
\(656\) −13.1052 −0.511672
\(657\) 0 0
\(658\) 0.356422 0.0138948
\(659\) 36.6207 1.42654 0.713270 0.700889i \(-0.247213\pi\)
0.713270 + 0.700889i \(0.247213\pi\)
\(660\) 0 0
\(661\) −39.6430 −1.54193 −0.770967 0.636875i \(-0.780227\pi\)
−0.770967 + 0.636875i \(0.780227\pi\)
\(662\) −0.0119091 −0.000462859 0
\(663\) 0 0
\(664\) −4.09566 −0.158942
\(665\) −3.24904 −0.125992
\(666\) 0 0
\(667\) −0.0185688 −0.000718987 0
\(668\) 8.46838 0.327652
\(669\) 0 0
\(670\) 0.291105 0.0112464
\(671\) 37.9483 1.46498
\(672\) 0 0
\(673\) 7.70607 0.297047 0.148524 0.988909i \(-0.452548\pi\)
0.148524 + 0.988909i \(0.452548\pi\)
\(674\) −2.75032 −0.105938
\(675\) 0 0
\(676\) 22.2974 0.857594
\(677\) 16.9048 0.649706 0.324853 0.945765i \(-0.394685\pi\)
0.324853 + 0.945765i \(0.394685\pi\)
\(678\) 0 0
\(679\) −8.70302 −0.333991
\(680\) 4.77014 0.182926
\(681\) 0 0
\(682\) 7.19361 0.275458
\(683\) 7.11167 0.272120 0.136060 0.990701i \(-0.456556\pi\)
0.136060 + 0.990701i \(0.456556\pi\)
\(684\) 0 0
\(685\) 10.1033 0.386026
\(686\) −1.06151 −0.0405285
\(687\) 0 0
\(688\) 37.9628 1.44732
\(689\) 3.73888 0.142440
\(690\) 0 0
\(691\) 18.0632 0.687156 0.343578 0.939124i \(-0.388361\pi\)
0.343578 + 0.939124i \(0.388361\pi\)
\(692\) 41.8366 1.59039
\(693\) 0 0
\(694\) −3.44110 −0.130622
\(695\) −21.0062 −0.796811
\(696\) 0 0
\(697\) −25.2468 −0.956289
\(698\) −1.21334 −0.0459258
\(699\) 0 0
\(700\) 0.938065 0.0354555
\(701\) −14.5894 −0.551034 −0.275517 0.961296i \(-0.588849\pi\)
−0.275517 + 0.961296i \(0.588849\pi\)
\(702\) 0 0
\(703\) −31.1805 −1.17599
\(704\) −38.3069 −1.44375
\(705\) 0 0
\(706\) 0.339658 0.0127832
\(707\) −6.82240 −0.256583
\(708\) 0 0
\(709\) 19.9577 0.749527 0.374763 0.927120i \(-0.377724\pi\)
0.374763 + 0.927120i \(0.377724\pi\)
\(710\) 0.472646 0.0177381
\(711\) 0 0
\(712\) 0.644326 0.0241471
\(713\) 22.9955 0.861188
\(714\) 0 0
\(715\) −6.77704 −0.253447
\(716\) 0.925652 0.0345932
\(717\) 0 0
\(718\) −0.255937 −0.00955147
\(719\) 1.62038 0.0604298 0.0302149 0.999543i \(-0.490381\pi\)
0.0302149 + 0.999543i \(0.490381\pi\)
\(720\) 0 0
\(721\) −2.58535 −0.0962836
\(722\) −4.49658 −0.167345
\(723\) 0 0
\(724\) 43.9608 1.63379
\(725\) 0.00689789 0.000256181 0
\(726\) 0 0
\(727\) 5.61596 0.208284 0.104142 0.994562i \(-0.466790\pi\)
0.104142 + 0.994562i \(0.466790\pi\)
\(728\) 0.399607 0.0148104
\(729\) 0 0
\(730\) 0.367052 0.0135852
\(731\) 73.1342 2.70496
\(732\) 0 0
\(733\) 48.1350 1.77791 0.888953 0.457998i \(-0.151433\pi\)
0.888953 + 0.457998i \(0.151433\pi\)
\(734\) −5.62485 −0.207617
\(735\) 0 0
\(736\) 5.14641 0.189699
\(737\) −9.32400 −0.343454
\(738\) 0 0
\(739\) −8.98910 −0.330669 −0.165335 0.986238i \(-0.552870\pi\)
−0.165335 + 0.986238i \(0.552870\pi\)
\(740\) 9.00245 0.330937
\(741\) 0 0
\(742\) −0.220813 −0.00810629
\(743\) −2.20072 −0.0807365 −0.0403683 0.999185i \(-0.512853\pi\)
−0.0403683 + 0.999185i \(0.512853\pi\)
\(744\) 0 0
\(745\) 4.55954 0.167049
\(746\) −4.60272 −0.168518
\(747\) 0 0
\(748\) −75.8876 −2.77473
\(749\) −3.45760 −0.126338
\(750\) 0 0
\(751\) −22.7671 −0.830781 −0.415391 0.909643i \(-0.636355\pi\)
−0.415391 + 0.909643i \(0.636355\pi\)
\(752\) 17.7733 0.648127
\(753\) 0 0
\(754\) 0.00145950 5.31517e−5 0
\(755\) 3.64071 0.132499
\(756\) 0 0
\(757\) −30.2022 −1.09772 −0.548859 0.835915i \(-0.684937\pi\)
−0.548859 + 0.835915i \(0.684937\pi\)
\(758\) 2.49170 0.0905026
\(759\) 0 0
\(760\) 4.40464 0.159773
\(761\) −17.4802 −0.633656 −0.316828 0.948483i \(-0.602618\pi\)
−0.316828 + 0.948483i \(0.602618\pi\)
\(762\) 0 0
\(763\) −1.86449 −0.0674992
\(764\) −42.0542 −1.52147
\(765\) 0 0
\(766\) −3.86703 −0.139722
\(767\) −1.48454 −0.0536036
\(768\) 0 0
\(769\) −28.0588 −1.01183 −0.505913 0.862585i \(-0.668844\pi\)
−0.505913 + 0.862585i \(0.668844\pi\)
\(770\) 0.400241 0.0144237
\(771\) 0 0
\(772\) 2.64126 0.0950612
\(773\) 2.19223 0.0788489 0.0394245 0.999223i \(-0.487448\pi\)
0.0394245 + 0.999223i \(0.487448\pi\)
\(774\) 0 0
\(775\) −8.54230 −0.306849
\(776\) 11.7985 0.423540
\(777\) 0 0
\(778\) 1.90796 0.0684038
\(779\) −23.3123 −0.835249
\(780\) 0 0
\(781\) −15.1387 −0.541706
\(782\) 3.23149 0.115558
\(783\) 0 0
\(784\) −26.0325 −0.929732
\(785\) 17.3667 0.619843
\(786\) 0 0
\(787\) −36.7899 −1.31142 −0.655709 0.755013i \(-0.727630\pi\)
−0.655709 + 0.755013i \(0.727630\pi\)
\(788\) −19.0652 −0.679170
\(789\) 0 0
\(790\) 1.70423 0.0606339
\(791\) −7.22994 −0.257067
\(792\) 0 0
\(793\) −9.53471 −0.338587
\(794\) 1.82867 0.0648971
\(795\) 0 0
\(796\) −19.4556 −0.689585
\(797\) 42.4563 1.50388 0.751941 0.659231i \(-0.229118\pi\)
0.751941 + 0.659231i \(0.229118\pi\)
\(798\) 0 0
\(799\) 34.2398 1.21132
\(800\) −1.91177 −0.0675914
\(801\) 0 0
\(802\) 2.10655 0.0743850
\(803\) −11.7566 −0.414880
\(804\) 0 0
\(805\) 1.27943 0.0450941
\(806\) −1.80743 −0.0636641
\(807\) 0 0
\(808\) 9.24896 0.325377
\(809\) −28.4853 −1.00149 −0.500744 0.865595i \(-0.666940\pi\)
−0.500744 + 0.865595i \(0.666940\pi\)
\(810\) 0 0
\(811\) −17.7783 −0.624282 −0.312141 0.950036i \(-0.601046\pi\)
−0.312141 + 0.950036i \(0.601046\pi\)
\(812\) 0.00647067 0.000227076 0
\(813\) 0 0
\(814\) 3.84105 0.134629
\(815\) −9.06918 −0.317680
\(816\) 0 0
\(817\) 67.5304 2.36259
\(818\) 2.30570 0.0806169
\(819\) 0 0
\(820\) 6.73074 0.235048
\(821\) −31.1566 −1.08737 −0.543687 0.839288i \(-0.682972\pi\)
−0.543687 + 0.839288i \(0.682972\pi\)
\(822\) 0 0
\(823\) 20.4644 0.713346 0.356673 0.934229i \(-0.383911\pi\)
0.356673 + 0.934229i \(0.383911\pi\)
\(824\) 3.50490 0.122099
\(825\) 0 0
\(826\) 0.0876747 0.00305059
\(827\) 16.0701 0.558812 0.279406 0.960173i \(-0.409862\pi\)
0.279406 + 0.960173i \(0.409862\pi\)
\(828\) 0 0
\(829\) −34.1508 −1.18611 −0.593053 0.805163i \(-0.702078\pi\)
−0.593053 + 0.805163i \(0.702078\pi\)
\(830\) 1.03069 0.0357757
\(831\) 0 0
\(832\) 9.62481 0.333680
\(833\) −50.1508 −1.73762
\(834\) 0 0
\(835\) −4.29059 −0.148482
\(836\) −70.0729 −2.42352
\(837\) 0 0
\(838\) −5.32293 −0.183878
\(839\) 2.87004 0.0990846 0.0495423 0.998772i \(-0.484224\pi\)
0.0495423 + 0.998772i \(0.484224\pi\)
\(840\) 0 0
\(841\) −29.0000 −0.999998
\(842\) −5.82641 −0.200791
\(843\) 0 0
\(844\) 24.1800 0.832309
\(845\) −11.2972 −0.388637
\(846\) 0 0
\(847\) −7.59153 −0.260848
\(848\) −11.0110 −0.378121
\(849\) 0 0
\(850\) −1.20042 −0.0411742
\(851\) 12.2785 0.420902
\(852\) 0 0
\(853\) 22.6448 0.775344 0.387672 0.921797i \(-0.373279\pi\)
0.387672 + 0.921797i \(0.373279\pi\)
\(854\) 0.563105 0.0192691
\(855\) 0 0
\(856\) 4.68738 0.160211
\(857\) −22.5002 −0.768594 −0.384297 0.923210i \(-0.625556\pi\)
−0.384297 + 0.923210i \(0.625556\pi\)
\(858\) 0 0
\(859\) −38.7537 −1.32226 −0.661129 0.750272i \(-0.729923\pi\)
−0.661129 + 0.750272i \(0.729923\pi\)
\(860\) −19.4974 −0.664857
\(861\) 0 0
\(862\) −4.01686 −0.136815
\(863\) −29.5580 −1.00617 −0.503083 0.864238i \(-0.667801\pi\)
−0.503083 + 0.864238i \(0.667801\pi\)
\(864\) 0 0
\(865\) −21.1969 −0.720718
\(866\) −4.56832 −0.155238
\(867\) 0 0
\(868\) −8.01324 −0.271987
\(869\) −54.5861 −1.85171
\(870\) 0 0
\(871\) 2.34270 0.0793795
\(872\) 2.52765 0.0855969
\(873\) 0 0
\(874\) 2.98388 0.100931
\(875\) −0.475281 −0.0160674
\(876\) 0 0
\(877\) −0.306586 −0.0103527 −0.00517633 0.999987i \(-0.501648\pi\)
−0.00517633 + 0.999987i \(0.501648\pi\)
\(878\) 0.0207923 0.000701707 0
\(879\) 0 0
\(880\) 19.9584 0.672798
\(881\) −4.86851 −0.164024 −0.0820121 0.996631i \(-0.526135\pi\)
−0.0820121 + 0.996631i \(0.526135\pi\)
\(882\) 0 0
\(883\) 54.1155 1.82113 0.910565 0.413366i \(-0.135647\pi\)
0.910565 + 0.413366i \(0.135647\pi\)
\(884\) 19.0672 0.641298
\(885\) 0 0
\(886\) 0.642634 0.0215897
\(887\) 42.0954 1.41343 0.706713 0.707500i \(-0.250177\pi\)
0.706713 + 0.707500i \(0.250177\pi\)
\(888\) 0 0
\(889\) −6.80040 −0.228078
\(890\) −0.162147 −0.00543519
\(891\) 0 0
\(892\) 44.2588 1.48189
\(893\) 31.6162 1.05800
\(894\) 0 0
\(895\) −0.468991 −0.0156767
\(896\) −2.38568 −0.0797001
\(897\) 0 0
\(898\) −0.874935 −0.0291970
\(899\) −0.0589238 −0.00196522
\(900\) 0 0
\(901\) −21.2124 −0.706688
\(902\) 2.87178 0.0956200
\(903\) 0 0
\(904\) 9.80144 0.325991
\(905\) −22.2732 −0.740386
\(906\) 0 0
\(907\) −3.59534 −0.119381 −0.0596907 0.998217i \(-0.519011\pi\)
−0.0596907 + 0.998217i \(0.519011\pi\)
\(908\) −45.7240 −1.51740
\(909\) 0 0
\(910\) −0.100563 −0.00333362
\(911\) −51.3001 −1.69965 −0.849823 0.527068i \(-0.823291\pi\)
−0.849823 + 0.527068i \(0.823291\pi\)
\(912\) 0 0
\(913\) −33.0127 −1.09256
\(914\) −0.107961 −0.00357104
\(915\) 0 0
\(916\) −8.20645 −0.271149
\(917\) −2.45496 −0.0810700
\(918\) 0 0
\(919\) −24.6752 −0.813959 −0.406979 0.913437i \(-0.633418\pi\)
−0.406979 + 0.913437i \(0.633418\pi\)
\(920\) −1.73450 −0.0571846
\(921\) 0 0
\(922\) 6.92366 0.228019
\(923\) 3.80368 0.125200
\(924\) 0 0
\(925\) −4.56119 −0.149971
\(926\) −1.14442 −0.0376079
\(927\) 0 0
\(928\) −0.0131872 −0.000432891 0
\(929\) 6.23375 0.204523 0.102261 0.994758i \(-0.467392\pi\)
0.102261 + 0.994758i \(0.467392\pi\)
\(930\) 0 0
\(931\) −46.3081 −1.51769
\(932\) −23.2347 −0.761076
\(933\) 0 0
\(934\) −4.96549 −0.162476
\(935\) 38.4493 1.25743
\(936\) 0 0
\(937\) −10.7283 −0.350479 −0.175240 0.984526i \(-0.556070\pi\)
−0.175240 + 0.984526i \(0.556070\pi\)
\(938\) −0.138356 −0.00451750
\(939\) 0 0
\(940\) −9.12827 −0.297731
\(941\) −11.6152 −0.378644 −0.189322 0.981915i \(-0.560629\pi\)
−0.189322 + 0.981915i \(0.560629\pi\)
\(942\) 0 0
\(943\) 9.18011 0.298945
\(944\) 4.37198 0.142296
\(945\) 0 0
\(946\) −8.31891 −0.270471
\(947\) −9.67739 −0.314473 −0.157236 0.987561i \(-0.550258\pi\)
−0.157236 + 0.987561i \(0.550258\pi\)
\(948\) 0 0
\(949\) 2.95390 0.0958875
\(950\) −1.10845 −0.0359627
\(951\) 0 0
\(952\) −2.26715 −0.0734789
\(953\) −18.4382 −0.597273 −0.298636 0.954367i \(-0.596532\pi\)
−0.298636 + 0.954367i \(0.596532\pi\)
\(954\) 0 0
\(955\) 21.3072 0.689485
\(956\) −40.2309 −1.30116
\(957\) 0 0
\(958\) 4.01765 0.129804
\(959\) −4.80189 −0.155061
\(960\) 0 0
\(961\) 41.9709 1.35390
\(962\) −0.965083 −0.0311155
\(963\) 0 0
\(964\) 22.3952 0.721300
\(965\) −1.33822 −0.0430790
\(966\) 0 0
\(967\) −45.7382 −1.47084 −0.735420 0.677611i \(-0.763015\pi\)
−0.735420 + 0.677611i \(0.763015\pi\)
\(968\) 10.2916 0.330786
\(969\) 0 0
\(970\) −2.96913 −0.0953330
\(971\) 18.8604 0.605259 0.302629 0.953108i \(-0.402136\pi\)
0.302629 + 0.953108i \(0.402136\pi\)
\(972\) 0 0
\(973\) 9.98384 0.320067
\(974\) −6.65580 −0.213266
\(975\) 0 0
\(976\) 28.0798 0.898812
\(977\) 5.89342 0.188547 0.0942736 0.995546i \(-0.469947\pi\)
0.0942736 + 0.995546i \(0.469947\pi\)
\(978\) 0 0
\(979\) 5.19353 0.165986
\(980\) 13.3701 0.427093
\(981\) 0 0
\(982\) 5.20742 0.166175
\(983\) −2.88660 −0.0920683 −0.0460341 0.998940i \(-0.514658\pi\)
−0.0460341 + 0.998940i \(0.514658\pi\)
\(984\) 0 0
\(985\) 9.65959 0.307780
\(986\) −0.00828040 −0.000263702 0
\(987\) 0 0
\(988\) 17.6062 0.560127
\(989\) −26.5927 −0.845599
\(990\) 0 0
\(991\) 15.8725 0.504206 0.252103 0.967700i \(-0.418878\pi\)
0.252103 + 0.967700i \(0.418878\pi\)
\(992\) 16.3309 0.518508
\(993\) 0 0
\(994\) −0.224639 −0.00712513
\(995\) 9.85738 0.312500
\(996\) 0 0
\(997\) −28.4316 −0.900437 −0.450218 0.892918i \(-0.648654\pi\)
−0.450218 + 0.892918i \(0.648654\pi\)
\(998\) 4.78895 0.151591
\(999\) 0 0
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 \(a_p\))