Properties

Label 5077.2.a.c.1.10
Level 5077
Weight 2
Character 5077.1
Self dual Yes
Analytic conductor 40.540
Analytic rank 0
Dimension 216
CM No

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Newspace parameters

Level: \( N \) = \( 5077 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 5077.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(40.5400491062\)
Analytic rank: \(0\)
Dimension: \(216\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 5077.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.52071 q^{2} -0.980647 q^{3} +4.35400 q^{4} -1.18681 q^{5} +2.47193 q^{6} -1.94632 q^{7} -5.93376 q^{8} -2.03833 q^{9} +O(q^{10})\) \(q-2.52071 q^{2} -0.980647 q^{3} +4.35400 q^{4} -1.18681 q^{5} +2.47193 q^{6} -1.94632 q^{7} -5.93376 q^{8} -2.03833 q^{9} +2.99161 q^{10} +2.89822 q^{11} -4.26974 q^{12} +3.30163 q^{13} +4.90612 q^{14} +1.16384 q^{15} +6.24932 q^{16} -0.746810 q^{17} +5.13805 q^{18} -7.97907 q^{19} -5.16737 q^{20} +1.90865 q^{21} -7.30558 q^{22} -8.84993 q^{23} +5.81892 q^{24} -3.59148 q^{25} -8.32245 q^{26} +4.94082 q^{27} -8.47428 q^{28} +4.82931 q^{29} -2.93371 q^{30} -0.935875 q^{31} -3.88523 q^{32} -2.84213 q^{33} +1.88250 q^{34} +2.30991 q^{35} -8.87490 q^{36} +2.66344 q^{37} +20.1130 q^{38} -3.23773 q^{39} +7.04225 q^{40} -8.17591 q^{41} -4.81117 q^{42} -0.493311 q^{43} +12.6188 q^{44} +2.41911 q^{45} +22.3081 q^{46} +11.4708 q^{47} -6.12838 q^{48} -3.21184 q^{49} +9.05310 q^{50} +0.732357 q^{51} +14.3753 q^{52} -4.28000 q^{53} -12.4544 q^{54} -3.43963 q^{55} +11.5490 q^{56} +7.82465 q^{57} -12.1733 q^{58} -11.2567 q^{59} +5.06736 q^{60} +7.24474 q^{61} +2.35907 q^{62} +3.96725 q^{63} -2.70510 q^{64} -3.91840 q^{65} +7.16419 q^{66} -14.6611 q^{67} -3.25161 q^{68} +8.67865 q^{69} -5.82263 q^{70} +12.9179 q^{71} +12.0950 q^{72} -11.1221 q^{73} -6.71376 q^{74} +3.52198 q^{75} -34.7409 q^{76} -5.64086 q^{77} +8.16139 q^{78} +1.03085 q^{79} -7.41675 q^{80} +1.26980 q^{81} +20.6091 q^{82} +8.53295 q^{83} +8.31028 q^{84} +0.886322 q^{85} +1.24350 q^{86} -4.73584 q^{87} -17.1973 q^{88} -12.4235 q^{89} -6.09789 q^{90} -6.42602 q^{91} -38.5326 q^{92} +0.917762 q^{93} -28.9147 q^{94} +9.46963 q^{95} +3.81003 q^{96} +7.46487 q^{97} +8.09612 q^{98} -5.90753 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + O(q^{10}) \) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + 24q^{10} + 89q^{11} + 114q^{12} + 34q^{13} + 53q^{14} + 61q^{15} + 229q^{16} + 76q^{17} + 57q^{18} + 54q^{19} + 118q^{20} + 25q^{21} + 26q^{22} + 109q^{23} + 65q^{24} + 232q^{25} + 58q^{26} + 236q^{27} + 57q^{28} + 54q^{29} + 6q^{30} + 77q^{31} + 155q^{32} + 80q^{33} + 28q^{34} + 137q^{35} + 257q^{36} + 42q^{37} + 104q^{38} + 46q^{39} + 47q^{40} + 109q^{41} + 27q^{42} + 68q^{43} + 145q^{44} + 109q^{45} - 7q^{46} + 264q^{47} + 198q^{48} + 222q^{49} + 86q^{50} + 57q^{51} + 68q^{52} + 95q^{53} + 79q^{54} + 50q^{55} + 108q^{56} + 55q^{57} + 38q^{58} + 292q^{59} + 91q^{60} + 16q^{61} + 91q^{62} + 113q^{63} + 231q^{64} + 68q^{65} - 15q^{66} + 152q^{67} + 199q^{68} + 83q^{69} + 24q^{70} + 131q^{71} + 162q^{72} + 71q^{73} + 10q^{74} + 232q^{75} + 60q^{76} + 131q^{77} + 102q^{78} + 10q^{79} + 236q^{80} + 268q^{81} + 54q^{82} + 299q^{83} - 9q^{85} + 35q^{86} + 103q^{87} + 45q^{88} + 134q^{89} + 8q^{90} + 79q^{91} + 206q^{92} + 95q^{93} + 18q^{94} + 119q^{95} + 77q^{96} + 129q^{97} + 150q^{98} + 221q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.52071 −1.78241 −0.891207 0.453597i \(-0.850141\pi\)
−0.891207 + 0.453597i \(0.850141\pi\)
\(3\) −0.980647 −0.566177 −0.283088 0.959094i \(-0.591359\pi\)
−0.283088 + 0.959094i \(0.591359\pi\)
\(4\) 4.35400 2.17700
\(5\) −1.18681 −0.530757 −0.265379 0.964144i \(-0.585497\pi\)
−0.265379 + 0.964144i \(0.585497\pi\)
\(6\) 2.47193 1.00916
\(7\) −1.94632 −0.735640 −0.367820 0.929897i \(-0.619896\pi\)
−0.367820 + 0.929897i \(0.619896\pi\)
\(8\) −5.93376 −2.09790
\(9\) −2.03833 −0.679444
\(10\) 2.99161 0.946029
\(11\) 2.89822 0.873845 0.436923 0.899499i \(-0.356068\pi\)
0.436923 + 0.899499i \(0.356068\pi\)
\(12\) −4.26974 −1.23257
\(13\) 3.30163 0.915706 0.457853 0.889028i \(-0.348619\pi\)
0.457853 + 0.889028i \(0.348619\pi\)
\(14\) 4.90612 1.31122
\(15\) 1.16384 0.300502
\(16\) 6.24932 1.56233
\(17\) −0.746810 −0.181128 −0.0905640 0.995891i \(-0.528867\pi\)
−0.0905640 + 0.995891i \(0.528867\pi\)
\(18\) 5.13805 1.21105
\(19\) −7.97907 −1.83052 −0.915262 0.402859i \(-0.868016\pi\)
−0.915262 + 0.402859i \(0.868016\pi\)
\(20\) −5.16737 −1.15546
\(21\) 1.90865 0.416502
\(22\) −7.30558 −1.55755
\(23\) −8.84993 −1.84534 −0.922669 0.385594i \(-0.873997\pi\)
−0.922669 + 0.385594i \(0.873997\pi\)
\(24\) 5.81892 1.18778
\(25\) −3.59148 −0.718297
\(26\) −8.32245 −1.63217
\(27\) 4.94082 0.950862
\(28\) −8.47428 −1.60149
\(29\) 4.82931 0.896780 0.448390 0.893838i \(-0.351998\pi\)
0.448390 + 0.893838i \(0.351998\pi\)
\(30\) −2.93371 −0.535620
\(31\) −0.935875 −0.168088 −0.0840440 0.996462i \(-0.526784\pi\)
−0.0840440 + 0.996462i \(0.526784\pi\)
\(32\) −3.88523 −0.686818
\(33\) −2.84213 −0.494751
\(34\) 1.88250 0.322845
\(35\) 2.30991 0.390446
\(36\) −8.87490 −1.47915
\(37\) 2.66344 0.437866 0.218933 0.975740i \(-0.429742\pi\)
0.218933 + 0.975740i \(0.429742\pi\)
\(38\) 20.1130 3.26275
\(39\) −3.23773 −0.518451
\(40\) 7.04225 1.11348
\(41\) −8.17591 −1.27686 −0.638432 0.769679i \(-0.720416\pi\)
−0.638432 + 0.769679i \(0.720416\pi\)
\(42\) −4.81117 −0.742379
\(43\) −0.493311 −0.0752292 −0.0376146 0.999292i \(-0.511976\pi\)
−0.0376146 + 0.999292i \(0.511976\pi\)
\(44\) 12.6188 1.90236
\(45\) 2.41911 0.360620
\(46\) 22.3081 3.28916
\(47\) 11.4708 1.67319 0.836596 0.547820i \(-0.184542\pi\)
0.836596 + 0.547820i \(0.184542\pi\)
\(48\) −6.12838 −0.884555
\(49\) −3.21184 −0.458834
\(50\) 9.05310 1.28030
\(51\) 0.732357 0.102550
\(52\) 14.3753 1.99349
\(53\) −4.28000 −0.587904 −0.293952 0.955820i \(-0.594971\pi\)
−0.293952 + 0.955820i \(0.594971\pi\)
\(54\) −12.4544 −1.69483
\(55\) −3.43963 −0.463800
\(56\) 11.5490 1.54330
\(57\) 7.82465 1.03640
\(58\) −12.1733 −1.59843
\(59\) −11.2567 −1.46550 −0.732749 0.680499i \(-0.761763\pi\)
−0.732749 + 0.680499i \(0.761763\pi\)
\(60\) 5.06736 0.654194
\(61\) 7.24474 0.927594 0.463797 0.885942i \(-0.346487\pi\)
0.463797 + 0.885942i \(0.346487\pi\)
\(62\) 2.35907 0.299603
\(63\) 3.96725 0.499826
\(64\) −2.70510 −0.338137
\(65\) −3.91840 −0.486018
\(66\) 7.16419 0.881851
\(67\) −14.6611 −1.79114 −0.895572 0.444916i \(-0.853234\pi\)
−0.895572 + 0.444916i \(0.853234\pi\)
\(68\) −3.25161 −0.394316
\(69\) 8.67865 1.04479
\(70\) −5.82263 −0.695937
\(71\) 12.9179 1.53307 0.766536 0.642201i \(-0.221979\pi\)
0.766536 + 0.642201i \(0.221979\pi\)
\(72\) 12.0950 1.42541
\(73\) −11.1221 −1.30174 −0.650870 0.759189i \(-0.725596\pi\)
−0.650870 + 0.759189i \(0.725596\pi\)
\(74\) −6.71376 −0.780459
\(75\) 3.52198 0.406683
\(76\) −34.7409 −3.98505
\(77\) −5.64086 −0.642836
\(78\) 8.16139 0.924095
\(79\) 1.03085 0.115979 0.0579896 0.998317i \(-0.481531\pi\)
0.0579896 + 0.998317i \(0.481531\pi\)
\(80\) −7.41675 −0.829218
\(81\) 1.26980 0.141088
\(82\) 20.6091 2.27590
\(83\) 8.53295 0.936612 0.468306 0.883566i \(-0.344864\pi\)
0.468306 + 0.883566i \(0.344864\pi\)
\(84\) 8.31028 0.906725
\(85\) 0.886322 0.0961351
\(86\) 1.24350 0.134090
\(87\) −4.73584 −0.507736
\(88\) −17.1973 −1.83324
\(89\) −12.4235 −1.31688 −0.658442 0.752631i \(-0.728784\pi\)
−0.658442 + 0.752631i \(0.728784\pi\)
\(90\) −6.09789 −0.642774
\(91\) −6.42602 −0.673630
\(92\) −38.5326 −4.01730
\(93\) 0.917762 0.0951675
\(94\) −28.9147 −2.98232
\(95\) 9.46963 0.971564
\(96\) 3.81003 0.388860
\(97\) 7.46487 0.757943 0.378971 0.925408i \(-0.376278\pi\)
0.378971 + 0.925408i \(0.376278\pi\)
\(98\) 8.09612 0.817832
\(99\) −5.90753 −0.593729
\(100\) −15.6373 −1.56373
\(101\) −12.0375 −1.19778 −0.598888 0.800833i \(-0.704391\pi\)
−0.598888 + 0.800833i \(0.704391\pi\)
\(102\) −1.84606 −0.182787
\(103\) 2.60602 0.256779 0.128390 0.991724i \(-0.459019\pi\)
0.128390 + 0.991724i \(0.459019\pi\)
\(104\) −19.5911 −1.92106
\(105\) −2.26521 −0.221062
\(106\) 10.7887 1.04789
\(107\) 14.2814 1.38063 0.690317 0.723507i \(-0.257471\pi\)
0.690317 + 0.723507i \(0.257471\pi\)
\(108\) 21.5123 2.07003
\(109\) −17.3463 −1.66148 −0.830739 0.556663i \(-0.812082\pi\)
−0.830739 + 0.556663i \(0.812082\pi\)
\(110\) 8.67033 0.826683
\(111\) −2.61189 −0.247910
\(112\) −12.1632 −1.14931
\(113\) −6.37208 −0.599435 −0.299718 0.954028i \(-0.596892\pi\)
−0.299718 + 0.954028i \(0.596892\pi\)
\(114\) −19.7237 −1.84729
\(115\) 10.5032 0.979426
\(116\) 21.0268 1.95229
\(117\) −6.72981 −0.622171
\(118\) 28.3749 2.61212
\(119\) 1.45353 0.133245
\(120\) −6.90596 −0.630425
\(121\) −2.60034 −0.236394
\(122\) −18.2619 −1.65336
\(123\) 8.01768 0.722930
\(124\) −4.07480 −0.365928
\(125\) 10.1965 0.911999
\(126\) −10.0003 −0.890898
\(127\) 13.2112 1.17231 0.586154 0.810200i \(-0.300641\pi\)
0.586154 + 0.810200i \(0.300641\pi\)
\(128\) 14.5892 1.28952
\(129\) 0.483764 0.0425930
\(130\) 9.87717 0.866285
\(131\) −19.9805 −1.74571 −0.872854 0.487981i \(-0.837734\pi\)
−0.872854 + 0.487981i \(0.837734\pi\)
\(132\) −12.3746 −1.07707
\(133\) 15.5298 1.34661
\(134\) 36.9566 3.19256
\(135\) −5.86382 −0.504677
\(136\) 4.43140 0.379989
\(137\) 11.1315 0.951027 0.475513 0.879708i \(-0.342262\pi\)
0.475513 + 0.879708i \(0.342262\pi\)
\(138\) −21.8764 −1.86224
\(139\) −6.29602 −0.534021 −0.267011 0.963694i \(-0.586036\pi\)
−0.267011 + 0.963694i \(0.586036\pi\)
\(140\) 10.0574 0.850002
\(141\) −11.2488 −0.947322
\(142\) −32.5623 −2.73257
\(143\) 9.56883 0.800185
\(144\) −12.7382 −1.06152
\(145\) −5.73147 −0.475972
\(146\) 28.0356 2.32024
\(147\) 3.14968 0.259781
\(148\) 11.5966 0.953235
\(149\) 15.5345 1.27263 0.636317 0.771428i \(-0.280457\pi\)
0.636317 + 0.771428i \(0.280457\pi\)
\(150\) −8.87789 −0.724877
\(151\) −11.4959 −0.935525 −0.467763 0.883854i \(-0.654940\pi\)
−0.467763 + 0.883854i \(0.654940\pi\)
\(152\) 47.3459 3.84026
\(153\) 1.52225 0.123066
\(154\) 14.2190 1.14580
\(155\) 1.11071 0.0892140
\(156\) −14.0971 −1.12867
\(157\) −6.99236 −0.558051 −0.279026 0.960284i \(-0.590011\pi\)
−0.279026 + 0.960284i \(0.590011\pi\)
\(158\) −2.59847 −0.206723
\(159\) 4.19717 0.332857
\(160\) 4.61102 0.364533
\(161\) 17.2248 1.35750
\(162\) −3.20079 −0.251478
\(163\) −12.4171 −0.972581 −0.486290 0.873797i \(-0.661650\pi\)
−0.486290 + 0.873797i \(0.661650\pi\)
\(164\) −35.5979 −2.77973
\(165\) 3.37306 0.262593
\(166\) −21.5091 −1.66943
\(167\) −11.6423 −0.900910 −0.450455 0.892799i \(-0.648738\pi\)
−0.450455 + 0.892799i \(0.648738\pi\)
\(168\) −11.3255 −0.873781
\(169\) −2.09927 −0.161482
\(170\) −2.23416 −0.171353
\(171\) 16.2640 1.24374
\(172\) −2.14788 −0.163774
\(173\) 16.2664 1.23671 0.618355 0.785899i \(-0.287799\pi\)
0.618355 + 0.785899i \(0.287799\pi\)
\(174\) 11.9377 0.904995
\(175\) 6.99018 0.528408
\(176\) 18.1119 1.36524
\(177\) 11.0388 0.829730
\(178\) 31.3160 2.34723
\(179\) 4.90086 0.366308 0.183154 0.983084i \(-0.441369\pi\)
0.183154 + 0.983084i \(0.441369\pi\)
\(180\) 10.5328 0.785070
\(181\) −15.0566 −1.11915 −0.559573 0.828781i \(-0.689035\pi\)
−0.559573 + 0.828781i \(0.689035\pi\)
\(182\) 16.1982 1.20069
\(183\) −7.10453 −0.525182
\(184\) 52.5134 3.87134
\(185\) −3.16099 −0.232401
\(186\) −2.31342 −0.169628
\(187\) −2.16442 −0.158278
\(188\) 49.9440 3.64254
\(189\) −9.61643 −0.699492
\(190\) −23.8702 −1.73173
\(191\) −18.3458 −1.32746 −0.663729 0.747973i \(-0.731027\pi\)
−0.663729 + 0.747973i \(0.731027\pi\)
\(192\) 2.65274 0.191445
\(193\) −13.1686 −0.947900 −0.473950 0.880552i \(-0.657172\pi\)
−0.473950 + 0.880552i \(0.657172\pi\)
\(194\) −18.8168 −1.35097
\(195\) 3.84257 0.275172
\(196\) −13.9843 −0.998881
\(197\) −3.20713 −0.228499 −0.114249 0.993452i \(-0.536446\pi\)
−0.114249 + 0.993452i \(0.536446\pi\)
\(198\) 14.8912 1.05827
\(199\) 19.3244 1.36987 0.684935 0.728604i \(-0.259831\pi\)
0.684935 + 0.728604i \(0.259831\pi\)
\(200\) 21.3110 1.50692
\(201\) 14.3774 1.01410
\(202\) 30.3431 2.13493
\(203\) −9.39938 −0.659707
\(204\) 3.18868 0.223252
\(205\) 9.70325 0.677704
\(206\) −6.56904 −0.457687
\(207\) 18.0391 1.25380
\(208\) 20.6329 1.43064
\(209\) −23.1251 −1.59959
\(210\) 5.70994 0.394023
\(211\) −3.40274 −0.234255 −0.117127 0.993117i \(-0.537369\pi\)
−0.117127 + 0.993117i \(0.537369\pi\)
\(212\) −18.6351 −1.27987
\(213\) −12.6679 −0.867990
\(214\) −35.9993 −2.46086
\(215\) 0.585466 0.0399285
\(216\) −29.3177 −1.99482
\(217\) 1.82151 0.123652
\(218\) 43.7251 2.96144
\(219\) 10.9068 0.737015
\(220\) −14.9762 −1.00969
\(221\) −2.46569 −0.165860
\(222\) 6.58383 0.441878
\(223\) −0.644659 −0.0431696 −0.0215848 0.999767i \(-0.506871\pi\)
−0.0215848 + 0.999767i \(0.506871\pi\)
\(224\) 7.56190 0.505251
\(225\) 7.32064 0.488042
\(226\) 16.0622 1.06844
\(227\) 13.8964 0.922333 0.461167 0.887314i \(-0.347431\pi\)
0.461167 + 0.887314i \(0.347431\pi\)
\(228\) 34.0685 2.25624
\(229\) −6.20855 −0.410272 −0.205136 0.978733i \(-0.565764\pi\)
−0.205136 + 0.978733i \(0.565764\pi\)
\(230\) −26.4755 −1.74574
\(231\) 5.53169 0.363958
\(232\) −28.6560 −1.88136
\(233\) −17.3558 −1.13701 −0.568507 0.822678i \(-0.692479\pi\)
−0.568507 + 0.822678i \(0.692479\pi\)
\(234\) 16.9639 1.10897
\(235\) −13.6137 −0.888059
\(236\) −49.0117 −3.19039
\(237\) −1.01090 −0.0656647
\(238\) −3.66394 −0.237498
\(239\) 19.7102 1.27495 0.637473 0.770473i \(-0.279980\pi\)
0.637473 + 0.770473i \(0.279980\pi\)
\(240\) 7.27321 0.469484
\(241\) 2.40000 0.154597 0.0772987 0.997008i \(-0.475370\pi\)
0.0772987 + 0.997008i \(0.475370\pi\)
\(242\) 6.55471 0.421353
\(243\) −16.0677 −1.03074
\(244\) 31.5436 2.01937
\(245\) 3.81184 0.243529
\(246\) −20.2103 −1.28856
\(247\) −26.3439 −1.67622
\(248\) 5.55326 0.352632
\(249\) −8.36780 −0.530288
\(250\) −25.7023 −1.62556
\(251\) 2.29749 0.145017 0.0725083 0.997368i \(-0.476900\pi\)
0.0725083 + 0.997368i \(0.476900\pi\)
\(252\) 17.2734 1.08812
\(253\) −25.6490 −1.61254
\(254\) −33.3018 −2.08954
\(255\) −0.869168 −0.0544294
\(256\) −31.3651 −1.96032
\(257\) −1.70038 −0.106067 −0.0530333 0.998593i \(-0.516889\pi\)
−0.0530333 + 0.998593i \(0.516889\pi\)
\(258\) −1.21943 −0.0759184
\(259\) −5.18390 −0.322112
\(260\) −17.0607 −1.05806
\(261\) −9.84373 −0.609312
\(262\) 50.3653 3.11158
\(263\) 7.70098 0.474863 0.237432 0.971404i \(-0.423694\pi\)
0.237432 + 0.971404i \(0.423694\pi\)
\(264\) 16.8645 1.03794
\(265\) 5.07955 0.312034
\(266\) −39.1463 −2.40021
\(267\) 12.1830 0.745589
\(268\) −63.8347 −3.89932
\(269\) −13.8858 −0.846635 −0.423317 0.905981i \(-0.639134\pi\)
−0.423317 + 0.905981i \(0.639134\pi\)
\(270\) 14.7810 0.899543
\(271\) 15.1567 0.920704 0.460352 0.887736i \(-0.347723\pi\)
0.460352 + 0.887736i \(0.347723\pi\)
\(272\) −4.66706 −0.282982
\(273\) 6.30166 0.381394
\(274\) −28.0593 −1.69512
\(275\) −10.4089 −0.627680
\(276\) 37.7868 2.27450
\(277\) −19.5814 −1.17653 −0.588267 0.808667i \(-0.700190\pi\)
−0.588267 + 0.808667i \(0.700190\pi\)
\(278\) 15.8705 0.951847
\(279\) 1.90762 0.114206
\(280\) −13.7065 −0.819118
\(281\) −2.01246 −0.120053 −0.0600267 0.998197i \(-0.519119\pi\)
−0.0600267 + 0.998197i \(0.519119\pi\)
\(282\) 28.3551 1.68852
\(283\) 3.84501 0.228562 0.114281 0.993448i \(-0.463544\pi\)
0.114281 + 0.993448i \(0.463544\pi\)
\(284\) 56.2445 3.33750
\(285\) −9.28636 −0.550077
\(286\) −24.1203 −1.42626
\(287\) 15.9129 0.939312
\(288\) 7.91938 0.466654
\(289\) −16.4423 −0.967193
\(290\) 14.4474 0.848380
\(291\) −7.32040 −0.429129
\(292\) −48.4255 −2.83389
\(293\) 10.1194 0.591182 0.295591 0.955315i \(-0.404483\pi\)
0.295591 + 0.955315i \(0.404483\pi\)
\(294\) −7.93943 −0.463037
\(295\) 13.3596 0.777823
\(296\) −15.8042 −0.918601
\(297\) 14.3196 0.830906
\(298\) −39.1580 −2.26836
\(299\) −29.2191 −1.68979
\(300\) 15.3347 0.885348
\(301\) 0.960142 0.0553416
\(302\) 28.9779 1.66749
\(303\) 11.8045 0.678153
\(304\) −49.8638 −2.85988
\(305\) −8.59812 −0.492327
\(306\) −3.83715 −0.219355
\(307\) −19.5475 −1.11563 −0.557817 0.829964i \(-0.688361\pi\)
−0.557817 + 0.829964i \(0.688361\pi\)
\(308\) −24.5603 −1.39945
\(309\) −2.55559 −0.145382
\(310\) −2.79977 −0.159016
\(311\) 15.1788 0.860713 0.430357 0.902659i \(-0.358388\pi\)
0.430357 + 0.902659i \(0.358388\pi\)
\(312\) 19.2119 1.08766
\(313\) −5.69413 −0.321851 −0.160926 0.986967i \(-0.551448\pi\)
−0.160926 + 0.986967i \(0.551448\pi\)
\(314\) 17.6258 0.994679
\(315\) −4.70837 −0.265287
\(316\) 4.48830 0.252487
\(317\) 12.7153 0.714165 0.357083 0.934073i \(-0.383771\pi\)
0.357083 + 0.934073i \(0.383771\pi\)
\(318\) −10.5799 −0.593289
\(319\) 13.9964 0.783647
\(320\) 3.21043 0.179469
\(321\) −14.0050 −0.781682
\(322\) −43.4188 −2.41963
\(323\) 5.95885 0.331559
\(324\) 5.52869 0.307149
\(325\) −11.8577 −0.657749
\(326\) 31.2999 1.73354
\(327\) 17.0106 0.940689
\(328\) 48.5139 2.67873
\(329\) −22.3259 −1.23087
\(330\) −8.50253 −0.468049
\(331\) −21.8814 −1.20271 −0.601354 0.798983i \(-0.705372\pi\)
−0.601354 + 0.798983i \(0.705372\pi\)
\(332\) 37.1525 2.03901
\(333\) −5.42897 −0.297506
\(334\) 29.3470 1.60579
\(335\) 17.4000 0.950663
\(336\) 11.9278 0.650714
\(337\) 11.3326 0.617327 0.308664 0.951171i \(-0.400118\pi\)
0.308664 + 0.951171i \(0.400118\pi\)
\(338\) 5.29166 0.287828
\(339\) 6.24876 0.339386
\(340\) 3.85904 0.209286
\(341\) −2.71237 −0.146883
\(342\) −40.9969 −2.21686
\(343\) 19.8755 1.07318
\(344\) 2.92719 0.157824
\(345\) −10.2999 −0.554528
\(346\) −41.0029 −2.20433
\(347\) 22.3723 1.20101 0.600505 0.799621i \(-0.294966\pi\)
0.600505 + 0.799621i \(0.294966\pi\)
\(348\) −20.6199 −1.10534
\(349\) 29.6033 1.58463 0.792315 0.610113i \(-0.208876\pi\)
0.792315 + 0.610113i \(0.208876\pi\)
\(350\) −17.6202 −0.941842
\(351\) 16.3127 0.870710
\(352\) −11.2602 −0.600172
\(353\) −3.03000 −0.161271 −0.0806353 0.996744i \(-0.525695\pi\)
−0.0806353 + 0.996744i \(0.525695\pi\)
\(354\) −27.8258 −1.47892
\(355\) −15.3311 −0.813690
\(356\) −54.0918 −2.86686
\(357\) −1.42540 −0.0754402
\(358\) −12.3537 −0.652912
\(359\) −22.4504 −1.18489 −0.592443 0.805613i \(-0.701836\pi\)
−0.592443 + 0.805613i \(0.701836\pi\)
\(360\) −14.3544 −0.756545
\(361\) 44.6655 2.35082
\(362\) 37.9533 1.99478
\(363\) 2.55001 0.133841
\(364\) −27.9789 −1.46649
\(365\) 13.1998 0.690909
\(366\) 17.9085 0.936091
\(367\) 12.0000 0.626396 0.313198 0.949688i \(-0.398600\pi\)
0.313198 + 0.949688i \(0.398600\pi\)
\(368\) −55.3060 −2.88303
\(369\) 16.6652 0.867557
\(370\) 7.96796 0.414234
\(371\) 8.33026 0.432485
\(372\) 3.99594 0.207180
\(373\) −26.0230 −1.34742 −0.673711 0.738995i \(-0.735301\pi\)
−0.673711 + 0.738995i \(0.735301\pi\)
\(374\) 5.45588 0.282117
\(375\) −9.99912 −0.516352
\(376\) −68.0652 −3.51019
\(377\) 15.9446 0.821187
\(378\) 24.2403 1.24678
\(379\) −5.26003 −0.270190 −0.135095 0.990833i \(-0.543134\pi\)
−0.135095 + 0.990833i \(0.543134\pi\)
\(380\) 41.2308 2.11510
\(381\) −12.9556 −0.663733
\(382\) 46.2446 2.36608
\(383\) 1.86422 0.0952574 0.0476287 0.998865i \(-0.484834\pi\)
0.0476287 + 0.998865i \(0.484834\pi\)
\(384\) −14.3069 −0.730095
\(385\) 6.69463 0.341190
\(386\) 33.1944 1.68955
\(387\) 1.00553 0.0511141
\(388\) 32.5020 1.65004
\(389\) 22.3463 1.13300 0.566501 0.824061i \(-0.308297\pi\)
0.566501 + 0.824061i \(0.308297\pi\)
\(390\) −9.68601 −0.490470
\(391\) 6.60922 0.334242
\(392\) 19.0583 0.962588
\(393\) 19.5939 0.988379
\(394\) 8.08426 0.407279
\(395\) −1.22342 −0.0615568
\(396\) −25.7214 −1.29255
\(397\) −12.7692 −0.640866 −0.320433 0.947271i \(-0.603828\pi\)
−0.320433 + 0.947271i \(0.603828\pi\)
\(398\) −48.7113 −2.44168
\(399\) −15.2293 −0.762417
\(400\) −22.4443 −1.12222
\(401\) −1.25016 −0.0624300 −0.0312150 0.999513i \(-0.509938\pi\)
−0.0312150 + 0.999513i \(0.509938\pi\)
\(402\) −36.2413 −1.80755
\(403\) −3.08991 −0.153919
\(404\) −52.4113 −2.60756
\(405\) −1.50701 −0.0748837
\(406\) 23.6932 1.17587
\(407\) 7.71922 0.382627
\(408\) −4.34563 −0.215141
\(409\) 30.0533 1.48604 0.743021 0.669268i \(-0.233392\pi\)
0.743021 + 0.669268i \(0.233392\pi\)
\(410\) −24.4591 −1.20795
\(411\) −10.9161 −0.538449
\(412\) 11.3466 0.559008
\(413\) 21.9091 1.07808
\(414\) −45.4714 −2.23480
\(415\) −10.1270 −0.497114
\(416\) −12.8276 −0.628923
\(417\) 6.17417 0.302350
\(418\) 58.2917 2.85114
\(419\) −0.807249 −0.0394367 −0.0197183 0.999806i \(-0.506277\pi\)
−0.0197183 + 0.999806i \(0.506277\pi\)
\(420\) −9.86271 −0.481251
\(421\) 29.5261 1.43901 0.719506 0.694486i \(-0.244368\pi\)
0.719506 + 0.694486i \(0.244368\pi\)
\(422\) 8.57735 0.417539
\(423\) −23.3814 −1.13684
\(424\) 25.3965 1.23336
\(425\) 2.68216 0.130104
\(426\) 31.9321 1.54712
\(427\) −14.1006 −0.682375
\(428\) 62.1812 3.00564
\(429\) −9.38364 −0.453046
\(430\) −1.47579 −0.0711691
\(431\) 7.30632 0.351933 0.175967 0.984396i \(-0.443695\pi\)
0.175967 + 0.984396i \(0.443695\pi\)
\(432\) 30.8768 1.48556
\(433\) 1.15833 0.0556658 0.0278329 0.999613i \(-0.491139\pi\)
0.0278329 + 0.999613i \(0.491139\pi\)
\(434\) −4.59151 −0.220400
\(435\) 5.62054 0.269484
\(436\) −75.5259 −3.61704
\(437\) 70.6142 3.37793
\(438\) −27.4930 −1.31367
\(439\) 12.5178 0.597444 0.298722 0.954340i \(-0.403440\pi\)
0.298722 + 0.954340i \(0.403440\pi\)
\(440\) 20.4100 0.973007
\(441\) 6.54679 0.311752
\(442\) 6.21529 0.295631
\(443\) −4.65330 −0.221085 −0.110542 0.993871i \(-0.535259\pi\)
−0.110542 + 0.993871i \(0.535259\pi\)
\(444\) −11.3722 −0.539699
\(445\) 14.7443 0.698946
\(446\) 1.62500 0.0769461
\(447\) −15.2338 −0.720535
\(448\) 5.26498 0.248747
\(449\) −28.8236 −1.36027 −0.680136 0.733086i \(-0.738079\pi\)
−0.680136 + 0.733086i \(0.738079\pi\)
\(450\) −18.4532 −0.869894
\(451\) −23.6956 −1.11578
\(452\) −27.7441 −1.30497
\(453\) 11.2734 0.529672
\(454\) −35.0287 −1.64398
\(455\) 7.62646 0.357534
\(456\) −46.4296 −2.17427
\(457\) −22.9727 −1.07462 −0.537309 0.843386i \(-0.680559\pi\)
−0.537309 + 0.843386i \(0.680559\pi\)
\(458\) 15.6500 0.731275
\(459\) −3.68986 −0.172228
\(460\) 45.7308 2.13221
\(461\) 18.0613 0.841201 0.420600 0.907246i \(-0.361819\pi\)
0.420600 + 0.907246i \(0.361819\pi\)
\(462\) −13.9438 −0.648725
\(463\) 35.7934 1.66346 0.831731 0.555179i \(-0.187350\pi\)
0.831731 + 0.555179i \(0.187350\pi\)
\(464\) 30.1799 1.40107
\(465\) −1.08921 −0.0505109
\(466\) 43.7489 2.02663
\(467\) 34.8526 1.61279 0.806393 0.591379i \(-0.201416\pi\)
0.806393 + 0.591379i \(0.201416\pi\)
\(468\) −29.3016 −1.35447
\(469\) 28.5353 1.31764
\(470\) 34.3162 1.58289
\(471\) 6.85704 0.315956
\(472\) 66.7946 3.07447
\(473\) −1.42972 −0.0657387
\(474\) 2.54818 0.117042
\(475\) 28.6567 1.31486
\(476\) 6.32868 0.290075
\(477\) 8.72407 0.399448
\(478\) −49.6838 −2.27248
\(479\) 5.37162 0.245436 0.122718 0.992442i \(-0.460839\pi\)
0.122718 + 0.992442i \(0.460839\pi\)
\(480\) −4.52179 −0.206390
\(481\) 8.79367 0.400957
\(482\) −6.04971 −0.275557
\(483\) −16.8914 −0.768587
\(484\) −11.3219 −0.514631
\(485\) −8.85938 −0.402284
\(486\) 40.5021 1.83721
\(487\) 31.8012 1.44105 0.720525 0.693429i \(-0.243901\pi\)
0.720525 + 0.693429i \(0.243901\pi\)
\(488\) −42.9886 −1.94600
\(489\) 12.1768 0.550652
\(490\) −9.60855 −0.434070
\(491\) 21.9378 0.990039 0.495019 0.868882i \(-0.335161\pi\)
0.495019 + 0.868882i \(0.335161\pi\)
\(492\) 34.9090 1.57382
\(493\) −3.60658 −0.162432
\(494\) 66.4054 2.98772
\(495\) 7.01111 0.315126
\(496\) −5.84858 −0.262609
\(497\) −25.1424 −1.12779
\(498\) 21.0928 0.945193
\(499\) −14.2616 −0.638438 −0.319219 0.947681i \(-0.603421\pi\)
−0.319219 + 0.947681i \(0.603421\pi\)
\(500\) 44.3954 1.98542
\(501\) 11.4170 0.510074
\(502\) −5.79132 −0.258479
\(503\) 6.16467 0.274869 0.137435 0.990511i \(-0.456114\pi\)
0.137435 + 0.990511i \(0.456114\pi\)
\(504\) −23.5407 −1.04859
\(505\) 14.2862 0.635728
\(506\) 64.6538 2.87421
\(507\) 2.05864 0.0914275
\(508\) 57.5218 2.55212
\(509\) 31.3900 1.39134 0.695669 0.718363i \(-0.255108\pi\)
0.695669 + 0.718363i \(0.255108\pi\)
\(510\) 2.19092 0.0970158
\(511\) 21.6471 0.957613
\(512\) 49.8840 2.20458
\(513\) −39.4232 −1.74058
\(514\) 4.28616 0.189054
\(515\) −3.09285 −0.136287
\(516\) 2.10631 0.0927250
\(517\) 33.2450 1.46211
\(518\) 13.0671 0.574137
\(519\) −15.9516 −0.700196
\(520\) 23.2509 1.01962
\(521\) −22.2625 −0.975338 −0.487669 0.873029i \(-0.662153\pi\)
−0.487669 + 0.873029i \(0.662153\pi\)
\(522\) 24.8132 1.08605
\(523\) −37.8191 −1.65372 −0.826858 0.562411i \(-0.809874\pi\)
−0.826858 + 0.562411i \(0.809874\pi\)
\(524\) −86.9953 −3.80041
\(525\) −6.85489 −0.299172
\(526\) −19.4120 −0.846403
\(527\) 0.698921 0.0304455
\(528\) −17.7614 −0.772964
\(529\) 55.3212 2.40527
\(530\) −12.8041 −0.556174
\(531\) 22.9449 0.995723
\(532\) 67.6169 2.93156
\(533\) −26.9938 −1.16923
\(534\) −30.7099 −1.32895
\(535\) −16.9493 −0.732781
\(536\) 86.9958 3.75765
\(537\) −4.80601 −0.207395
\(538\) 35.0022 1.50905
\(539\) −9.30860 −0.400950
\(540\) −25.5311 −1.09868
\(541\) −8.12177 −0.349182 −0.174591 0.984641i \(-0.555860\pi\)
−0.174591 + 0.984641i \(0.555860\pi\)
\(542\) −38.2057 −1.64108
\(543\) 14.7652 0.633635
\(544\) 2.90153 0.124402
\(545\) 20.5868 0.881841
\(546\) −15.8847 −0.679801
\(547\) −10.0550 −0.429920 −0.214960 0.976623i \(-0.568962\pi\)
−0.214960 + 0.976623i \(0.568962\pi\)
\(548\) 48.4665 2.07039
\(549\) −14.7672 −0.630248
\(550\) 26.2379 1.11879
\(551\) −38.5334 −1.64158
\(552\) −51.4971 −2.19186
\(553\) −2.00636 −0.0853190
\(554\) 49.3592 2.09707
\(555\) 3.09982 0.131580
\(556\) −27.4129 −1.16256
\(557\) 7.20499 0.305285 0.152643 0.988281i \(-0.451222\pi\)
0.152643 + 0.988281i \(0.451222\pi\)
\(558\) −4.80858 −0.203563
\(559\) −1.62873 −0.0688879
\(560\) 14.4354 0.610006
\(561\) 2.12253 0.0896133
\(562\) 5.07284 0.213985
\(563\) 25.6059 1.07916 0.539579 0.841935i \(-0.318583\pi\)
0.539579 + 0.841935i \(0.318583\pi\)
\(564\) −48.9774 −2.06232
\(565\) 7.56245 0.318155
\(566\) −9.69218 −0.407393
\(567\) −2.47143 −0.103790
\(568\) −76.6518 −3.21624
\(569\) −41.7589 −1.75062 −0.875311 0.483560i \(-0.839343\pi\)
−0.875311 + 0.483560i \(0.839343\pi\)
\(570\) 23.4083 0.980465
\(571\) 4.86181 0.203460 0.101730 0.994812i \(-0.467562\pi\)
0.101730 + 0.994812i \(0.467562\pi\)
\(572\) 41.6627 1.74200
\(573\) 17.9908 0.751576
\(574\) −40.1120 −1.67424
\(575\) 31.7844 1.32550
\(576\) 5.51388 0.229745
\(577\) 14.3774 0.598538 0.299269 0.954169i \(-0.403257\pi\)
0.299269 + 0.954169i \(0.403257\pi\)
\(578\) 41.4463 1.72394
\(579\) 12.9138 0.536679
\(580\) −24.9548 −1.03619
\(581\) −16.6078 −0.689010
\(582\) 18.4526 0.764886
\(583\) −12.4044 −0.513737
\(584\) 65.9958 2.73093
\(585\) 7.98700 0.330222
\(586\) −25.5081 −1.05373
\(587\) 25.0645 1.03452 0.517261 0.855828i \(-0.326952\pi\)
0.517261 + 0.855828i \(0.326952\pi\)
\(588\) 13.7137 0.565543
\(589\) 7.46741 0.307689
\(590\) −33.6756 −1.38640
\(591\) 3.14506 0.129371
\(592\) 16.6447 0.684092
\(593\) 39.3259 1.61492 0.807461 0.589922i \(-0.200841\pi\)
0.807461 + 0.589922i \(0.200841\pi\)
\(594\) −36.0956 −1.48102
\(595\) −1.72507 −0.0707208
\(596\) 67.6371 2.77052
\(597\) −18.9504 −0.775588
\(598\) 73.6531 3.01190
\(599\) 13.8883 0.567459 0.283730 0.958904i \(-0.408428\pi\)
0.283730 + 0.958904i \(0.408428\pi\)
\(600\) −20.8986 −0.853181
\(601\) 32.2808 1.31676 0.658381 0.752685i \(-0.271241\pi\)
0.658381 + 0.752685i \(0.271241\pi\)
\(602\) −2.42024 −0.0986417
\(603\) 29.8843 1.21698
\(604\) −50.0533 −2.03664
\(605\) 3.08611 0.125468
\(606\) −29.7559 −1.20875
\(607\) 48.0296 1.94946 0.974731 0.223383i \(-0.0717102\pi\)
0.974731 + 0.223383i \(0.0717102\pi\)
\(608\) 31.0005 1.25724
\(609\) 9.21747 0.373511
\(610\) 21.6734 0.877531
\(611\) 37.8724 1.53215
\(612\) 6.62787 0.267916
\(613\) 4.69920 0.189799 0.0948995 0.995487i \(-0.469747\pi\)
0.0948995 + 0.995487i \(0.469747\pi\)
\(614\) 49.2736 1.98852
\(615\) −9.51546 −0.383700
\(616\) 33.4715 1.34861
\(617\) 28.8626 1.16197 0.580983 0.813916i \(-0.302668\pi\)
0.580983 + 0.813916i \(0.302668\pi\)
\(618\) 6.44191 0.259131
\(619\) −23.1985 −0.932427 −0.466213 0.884672i \(-0.654382\pi\)
−0.466213 + 0.884672i \(0.654382\pi\)
\(620\) 4.83601 0.194219
\(621\) −43.7259 −1.75466
\(622\) −38.2615 −1.53415
\(623\) 24.1800 0.968753
\(624\) −20.2336 −0.809992
\(625\) 5.85617 0.234247
\(626\) 14.3533 0.573672
\(627\) 22.6775 0.905653
\(628\) −30.4448 −1.21488
\(629\) −1.98908 −0.0793099
\(630\) 11.8685 0.472850
\(631\) 11.4096 0.454210 0.227105 0.973870i \(-0.427074\pi\)
0.227105 + 0.973870i \(0.427074\pi\)
\(632\) −6.11680 −0.243313
\(633\) 3.33689 0.132629
\(634\) −32.0518 −1.27294
\(635\) −15.6792 −0.622211
\(636\) 18.2745 0.724630
\(637\) −10.6043 −0.420157
\(638\) −35.2809 −1.39678
\(639\) −26.3310 −1.04164
\(640\) −17.3146 −0.684421
\(641\) 8.54498 0.337506 0.168753 0.985658i \(-0.446026\pi\)
0.168753 + 0.985658i \(0.446026\pi\)
\(642\) 35.3026 1.39328
\(643\) −34.4380 −1.35810 −0.679051 0.734091i \(-0.737609\pi\)
−0.679051 + 0.734091i \(0.737609\pi\)
\(644\) 74.9968 2.95529
\(645\) −0.574135 −0.0226066
\(646\) −15.0206 −0.590976
\(647\) 10.0859 0.396517 0.198259 0.980150i \(-0.436471\pi\)
0.198259 + 0.980150i \(0.436471\pi\)
\(648\) −7.53467 −0.295990
\(649\) −32.6244 −1.28062
\(650\) 29.8900 1.17238
\(651\) −1.78626 −0.0700091
\(652\) −54.0640 −2.11731
\(653\) 20.0347 0.784019 0.392009 0.919961i \(-0.371780\pi\)
0.392009 + 0.919961i \(0.371780\pi\)
\(654\) −42.8789 −1.67670
\(655\) 23.7131 0.926548
\(656\) −51.0939 −1.99488
\(657\) 22.6705 0.884460
\(658\) 56.2773 2.19392
\(659\) 12.6426 0.492485 0.246243 0.969208i \(-0.420804\pi\)
0.246243 + 0.969208i \(0.420804\pi\)
\(660\) 14.6863 0.571664
\(661\) 13.6107 0.529397 0.264698 0.964331i \(-0.414728\pi\)
0.264698 + 0.964331i \(0.414728\pi\)
\(662\) 55.1566 2.14372
\(663\) 2.41797 0.0939061
\(664\) −50.6325 −1.96492
\(665\) −18.4309 −0.714721
\(666\) 13.6849 0.530278
\(667\) −42.7390 −1.65486
\(668\) −50.6907 −1.96128
\(669\) 0.632183 0.0244416
\(670\) −43.8604 −1.69448
\(671\) 20.9968 0.810573
\(672\) −7.41555 −0.286061
\(673\) 8.64200 0.333125 0.166562 0.986031i \(-0.446733\pi\)
0.166562 + 0.986031i \(0.446733\pi\)
\(674\) −28.5663 −1.10033
\(675\) −17.7449 −0.683001
\(676\) −9.14023 −0.351547
\(677\) −29.3805 −1.12918 −0.564591 0.825371i \(-0.690966\pi\)
−0.564591 + 0.825371i \(0.690966\pi\)
\(678\) −15.7513 −0.604927
\(679\) −14.5290 −0.557573
\(680\) −5.25922 −0.201682
\(681\) −13.6274 −0.522204
\(682\) 6.83711 0.261806
\(683\) 14.6705 0.561352 0.280676 0.959803i \(-0.409441\pi\)
0.280676 + 0.959803i \(0.409441\pi\)
\(684\) 70.8134 2.70762
\(685\) −13.2110 −0.504764
\(686\) −50.1005 −1.91285
\(687\) 6.08839 0.232287
\(688\) −3.08286 −0.117533
\(689\) −14.1310 −0.538347
\(690\) 25.9631 0.988399
\(691\) 14.6780 0.558376 0.279188 0.960236i \(-0.409935\pi\)
0.279188 + 0.960236i \(0.409935\pi\)
\(692\) 70.8239 2.69232
\(693\) 11.4979 0.436771
\(694\) −56.3943 −2.14070
\(695\) 7.47218 0.283436
\(696\) 28.1014 1.06518
\(697\) 6.10586 0.231276
\(698\) −74.6215 −2.82447
\(699\) 17.0199 0.643751
\(700\) 30.4352 1.15034
\(701\) −30.7007 −1.15955 −0.579775 0.814777i \(-0.696859\pi\)
−0.579775 + 0.814777i \(0.696859\pi\)
\(702\) −41.1198 −1.55197
\(703\) −21.2517 −0.801524
\(704\) −7.83995 −0.295479
\(705\) 13.3502 0.502798
\(706\) 7.63776 0.287451
\(707\) 23.4288 0.881132
\(708\) 48.0631 1.80632
\(709\) 4.84441 0.181936 0.0909678 0.995854i \(-0.471004\pi\)
0.0909678 + 0.995854i \(0.471004\pi\)
\(710\) 38.6453 1.45033
\(711\) −2.10121 −0.0788014
\(712\) 73.7179 2.76270
\(713\) 8.28242 0.310179
\(714\) 3.59303 0.134466
\(715\) −11.3564 −0.424704
\(716\) 21.3384 0.797452
\(717\) −19.3287 −0.721845
\(718\) 56.5910 2.11196
\(719\) 19.0759 0.711411 0.355705 0.934598i \(-0.384241\pi\)
0.355705 + 0.934598i \(0.384241\pi\)
\(720\) 15.1178 0.563408
\(721\) −5.07216 −0.188897
\(722\) −112.589 −4.19013
\(723\) −2.35355 −0.0875294
\(724\) −65.5564 −2.43638
\(725\) −17.3444 −0.644154
\(726\) −6.42785 −0.238560
\(727\) −26.7547 −0.992275 −0.496138 0.868244i \(-0.665249\pi\)
−0.496138 + 0.868244i \(0.665249\pi\)
\(728\) 38.1305 1.41321
\(729\) 11.9473 0.442494
\(730\) −33.2729 −1.23149
\(731\) 0.368410 0.0136261
\(732\) −30.9331 −1.14332
\(733\) −27.6326 −1.02063 −0.510317 0.859987i \(-0.670472\pi\)
−0.510317 + 0.859987i \(0.670472\pi\)
\(734\) −30.2486 −1.11650
\(735\) −3.73806 −0.137881
\(736\) 34.3840 1.26741
\(737\) −42.4912 −1.56518
\(738\) −42.0083 −1.54635
\(739\) 14.4939 0.533167 0.266583 0.963812i \(-0.414105\pi\)
0.266583 + 0.963812i \(0.414105\pi\)
\(740\) −13.7630 −0.505936
\(741\) 25.8340 0.949037
\(742\) −20.9982 −0.770868
\(743\) −13.6275 −0.499946 −0.249973 0.968253i \(-0.580422\pi\)
−0.249973 + 0.968253i \(0.580422\pi\)
\(744\) −5.44579 −0.199652
\(745\) −18.4365 −0.675459
\(746\) 65.5966 2.40166
\(747\) −17.3930 −0.636376
\(748\) −9.42388 −0.344571
\(749\) −27.7962 −1.01565
\(750\) 25.2049 0.920354
\(751\) −21.6108 −0.788588 −0.394294 0.918984i \(-0.629011\pi\)
−0.394294 + 0.918984i \(0.629011\pi\)
\(752\) 71.6849 2.61408
\(753\) −2.25303 −0.0821049
\(754\) −40.1917 −1.46369
\(755\) 13.6435 0.496537
\(756\) −41.8699 −1.52279
\(757\) 39.1116 1.42153 0.710767 0.703428i \(-0.248348\pi\)
0.710767 + 0.703428i \(0.248348\pi\)
\(758\) 13.2590 0.481590
\(759\) 25.1526 0.912982
\(760\) −56.1906 −2.03825
\(761\) −48.8752 −1.77173 −0.885863 0.463947i \(-0.846433\pi\)
−0.885863 + 0.463947i \(0.846433\pi\)
\(762\) 32.6573 1.18305
\(763\) 33.7615 1.22225
\(764\) −79.8778 −2.88988
\(765\) −1.80662 −0.0653184
\(766\) −4.69918 −0.169788
\(767\) −37.1654 −1.34196
\(768\) 30.7581 1.10989
\(769\) 49.6948 1.79204 0.896019 0.444015i \(-0.146446\pi\)
0.896019 + 0.444015i \(0.146446\pi\)
\(770\) −16.8752 −0.608141
\(771\) 1.66747 0.0600524
\(772\) −57.3363 −2.06358
\(773\) −34.5505 −1.24270 −0.621348 0.783535i \(-0.713414\pi\)
−0.621348 + 0.783535i \(0.713414\pi\)
\(774\) −2.53466 −0.0911064
\(775\) 3.36118 0.120737
\(776\) −44.2948 −1.59009
\(777\) 5.08357 0.182372
\(778\) −56.3286 −2.01948
\(779\) 65.2362 2.33733
\(780\) 16.7305 0.599049
\(781\) 37.4389 1.33967
\(782\) −16.6599 −0.595758
\(783\) 23.8608 0.852714
\(784\) −20.0718 −0.716850
\(785\) 8.29860 0.296190
\(786\) −49.3905 −1.76170
\(787\) −5.98510 −0.213346 −0.106673 0.994294i \(-0.534020\pi\)
−0.106673 + 0.994294i \(0.534020\pi\)
\(788\) −13.9638 −0.497441
\(789\) −7.55194 −0.268856
\(790\) 3.08389 0.109720
\(791\) 12.4021 0.440969
\(792\) 35.0539 1.24559
\(793\) 23.9194 0.849403
\(794\) 32.1874 1.14229
\(795\) −4.98124 −0.176666
\(796\) 84.1384 2.98221
\(797\) −7.45225 −0.263972 −0.131986 0.991252i \(-0.542135\pi\)
−0.131986 + 0.991252i \(0.542135\pi\)
\(798\) 38.3886 1.35894
\(799\) −8.56653 −0.303062
\(800\) 13.9537 0.493339
\(801\) 25.3232 0.894750
\(802\) 3.15129 0.111276
\(803\) −32.2342 −1.13752
\(804\) 62.5992 2.20770
\(805\) −20.4426 −0.720505
\(806\) 7.78878 0.274348
\(807\) 13.6171 0.479345
\(808\) 71.4277 2.51282
\(809\) 7.58456 0.266659 0.133329 0.991072i \(-0.457433\pi\)
0.133329 + 0.991072i \(0.457433\pi\)
\(810\) 3.79873 0.133474
\(811\) −44.9980 −1.58009 −0.790047 0.613047i \(-0.789944\pi\)
−0.790047 + 0.613047i \(0.789944\pi\)
\(812\) −40.9249 −1.43618
\(813\) −14.8634 −0.521281
\(814\) −19.4579 −0.682000
\(815\) 14.7367 0.516204
\(816\) 4.57673 0.160218
\(817\) 3.93616 0.137709
\(818\) −75.7559 −2.64874
\(819\) 13.0984 0.457694
\(820\) 42.2480 1.47536
\(821\) 13.7994 0.481603 0.240801 0.970574i \(-0.422590\pi\)
0.240801 + 0.970574i \(0.422590\pi\)
\(822\) 27.5162 0.959739
\(823\) −19.6550 −0.685131 −0.342565 0.939494i \(-0.611296\pi\)
−0.342565 + 0.939494i \(0.611296\pi\)
\(824\) −15.4635 −0.538697
\(825\) 10.2074 0.355378
\(826\) −55.2267 −1.92158
\(827\) −3.23932 −0.112642 −0.0563211 0.998413i \(-0.517937\pi\)
−0.0563211 + 0.998413i \(0.517937\pi\)
\(828\) 78.5422 2.72953
\(829\) −33.0203 −1.14684 −0.573422 0.819260i \(-0.694384\pi\)
−0.573422 + 0.819260i \(0.694384\pi\)
\(830\) 25.5272 0.886063
\(831\) 19.2025 0.666126
\(832\) −8.93121 −0.309634
\(833\) 2.39863 0.0831077
\(834\) −15.5633 −0.538914
\(835\) 13.8172 0.478165
\(836\) −100.687 −3.48232
\(837\) −4.62399 −0.159829
\(838\) 2.03484 0.0702925
\(839\) −29.8195 −1.02948 −0.514741 0.857345i \(-0.672112\pi\)
−0.514741 + 0.857345i \(0.672112\pi\)
\(840\) 13.4412 0.463766
\(841\) −5.67780 −0.195786
\(842\) −74.4267 −2.56491
\(843\) 1.97351 0.0679714
\(844\) −14.8156 −0.509972
\(845\) 2.49143 0.0857080
\(846\) 58.9377 2.02632
\(847\) 5.06109 0.173901
\(848\) −26.7471 −0.918500
\(849\) −3.77060 −0.129407
\(850\) −6.76095 −0.231899
\(851\) −23.5712 −0.808011
\(852\) −55.1560 −1.88961
\(853\) 55.7160 1.90768 0.953840 0.300316i \(-0.0970920\pi\)
0.953840 + 0.300316i \(0.0970920\pi\)
\(854\) 35.5435 1.21628
\(855\) −19.3023 −0.660123
\(856\) −84.7424 −2.89643
\(857\) 57.0817 1.94987 0.974936 0.222485i \(-0.0714168\pi\)
0.974936 + 0.222485i \(0.0714168\pi\)
\(858\) 23.6535 0.807516
\(859\) 27.2485 0.929708 0.464854 0.885387i \(-0.346107\pi\)
0.464854 + 0.885387i \(0.346107\pi\)
\(860\) 2.54912 0.0869243
\(861\) −15.6050 −0.531816
\(862\) −18.4172 −0.627291
\(863\) 10.5011 0.357462 0.178731 0.983898i \(-0.442801\pi\)
0.178731 + 0.983898i \(0.442801\pi\)
\(864\) −19.1962 −0.653069
\(865\) −19.3051 −0.656393
\(866\) −2.91982 −0.0992196
\(867\) 16.1241 0.547602
\(868\) 7.93087 0.269191
\(869\) 2.98762 0.101348
\(870\) −14.1678 −0.480333
\(871\) −48.4056 −1.64016
\(872\) 102.929 3.48562
\(873\) −15.2159 −0.514980
\(874\) −177.998 −6.02088
\(875\) −19.8456 −0.670903
\(876\) 47.4883 1.60448
\(877\) 55.5439 1.87559 0.937793 0.347196i \(-0.112866\pi\)
0.937793 + 0.347196i \(0.112866\pi\)
\(878\) −31.5539 −1.06489
\(879\) −9.92356 −0.334713
\(880\) −21.4954 −0.724609
\(881\) −15.8831 −0.535115 −0.267557 0.963542i \(-0.586217\pi\)
−0.267557 + 0.963542i \(0.586217\pi\)
\(882\) −16.5026 −0.555671
\(883\) 0.898097 0.0302234 0.0151117 0.999886i \(-0.495190\pi\)
0.0151117 + 0.999886i \(0.495190\pi\)
\(884\) −10.7356 −0.361077
\(885\) −13.1010 −0.440385
\(886\) 11.7296 0.394065
\(887\) 50.8490 1.70734 0.853671 0.520812i \(-0.174371\pi\)
0.853671 + 0.520812i \(0.174371\pi\)
\(888\) 15.4983 0.520090
\(889\) −25.7133 −0.862397
\(890\) −37.1661 −1.24581
\(891\) 3.68014 0.123289
\(892\) −2.80685 −0.0939802
\(893\) −91.5265 −3.06282
\(894\) 38.4001 1.28429
\(895\) −5.81639 −0.194420
\(896\) −28.3953 −0.948621
\(897\) 28.6536 0.956718
\(898\) 72.6562 2.42457
\(899\) −4.51963 −0.150738
\(900\) 31.8741 1.06247
\(901\) 3.19635 0.106486
\(902\) 59.7298 1.98878
\(903\) −0.941560 −0.0313331
\(904\) 37.8104 1.25756
\(905\) 17.8693 0.593995
\(906\) −28.4171 −0.944096
\(907\) 26.2902 0.872951 0.436476 0.899716i \(-0.356227\pi\)
0.436476 + 0.899716i \(0.356227\pi\)
\(908\) 60.5047 2.00792
\(909\) 24.5364 0.813822
\(910\) −19.2241 −0.637274
\(911\) −9.31596 −0.308652 −0.154326 0.988020i \(-0.549321\pi\)
−0.154326 + 0.988020i \(0.549321\pi\)
\(912\) 48.8987 1.61920
\(913\) 24.7303 0.818454
\(914\) 57.9076 1.91541
\(915\) 8.43172 0.278744
\(916\) −27.0320 −0.893163
\(917\) 38.8886 1.28421
\(918\) 9.30108 0.306981
\(919\) 40.3167 1.32993 0.664963 0.746876i \(-0.268447\pi\)
0.664963 + 0.746876i \(0.268447\pi\)
\(920\) −62.3234 −2.05474
\(921\) 19.1692 0.631645
\(922\) −45.5275 −1.49937
\(923\) 42.6501 1.40384
\(924\) 24.0850 0.792338
\(925\) −9.56569 −0.314518
\(926\) −90.2250 −2.96498
\(927\) −5.31194 −0.174467
\(928\) −18.7630 −0.615924
\(929\) 45.1884 1.48258 0.741292 0.671183i \(-0.234213\pi\)
0.741292 + 0.671183i \(0.234213\pi\)
\(930\) 2.74559 0.0900313
\(931\) 25.6275 0.839906
\(932\) −75.5670 −2.47528
\(933\) −14.8851 −0.487316
\(934\) −87.8535 −2.87465
\(935\) 2.56875 0.0840072
\(936\) 39.9331 1.30525
\(937\) −34.4862 −1.12662 −0.563308 0.826247i \(-0.690472\pi\)
−0.563308 + 0.826247i \(0.690472\pi\)
\(938\) −71.9293 −2.34858
\(939\) 5.58393 0.182225
\(940\) −59.2740 −1.93331
\(941\) 9.95083 0.324388 0.162194 0.986759i \(-0.448143\pi\)
0.162194 + 0.986759i \(0.448143\pi\)
\(942\) −17.2846 −0.563164
\(943\) 72.3562 2.35624
\(944\) −70.3467 −2.28959
\(945\) 11.4129 0.371261
\(946\) 3.60392 0.117174
\(947\) −8.71000 −0.283037 −0.141518 0.989936i \(-0.545198\pi\)
−0.141518 + 0.989936i \(0.545198\pi\)
\(948\) −4.40144 −0.142952
\(949\) −36.7209 −1.19201
\(950\) −72.2353 −2.34362
\(951\) −12.4693 −0.404344
\(952\) −8.62492 −0.279535
\(953\) −20.6225 −0.668028 −0.334014 0.942568i \(-0.608403\pi\)
−0.334014 + 0.942568i \(0.608403\pi\)
\(954\) −21.9909 −0.711981
\(955\) 21.7730 0.704558
\(956\) 85.8182 2.77556
\(957\) −13.7255 −0.443682
\(958\) −13.5403 −0.437468
\(959\) −21.6654 −0.699613
\(960\) −3.14830 −0.101611
\(961\) −30.1241 −0.971746
\(962\) −22.1663 −0.714671
\(963\) −29.1102 −0.938063
\(964\) 10.4496 0.336559
\(965\) 15.6287 0.503105
\(966\) 42.5785 1.36994
\(967\) −36.0017 −1.15774 −0.578869 0.815421i \(-0.696506\pi\)
−0.578869 + 0.815421i \(0.696506\pi\)
\(968\) 15.4298 0.495932
\(969\) −5.84353 −0.187721
\(970\) 22.3320 0.717036
\(971\) −31.8310 −1.02151 −0.510753 0.859728i \(-0.670633\pi\)
−0.510753 + 0.859728i \(0.670633\pi\)
\(972\) −69.9587 −2.24393
\(973\) 12.2541 0.392847
\(974\) −80.1618 −2.56855
\(975\) 11.6282 0.372402
\(976\) 45.2747 1.44921
\(977\) 4.39252 0.140529 0.0702646 0.997528i \(-0.477616\pi\)
0.0702646 + 0.997528i \(0.477616\pi\)
\(978\) −30.6942 −0.981491
\(979\) −36.0059 −1.15075
\(980\) 16.5967 0.530163
\(981\) 35.3576 1.12888
\(982\) −55.2989 −1.76466
\(983\) 0.225862 0.00720389 0.00360194 0.999994i \(-0.498853\pi\)
0.00360194 + 0.999994i \(0.498853\pi\)
\(984\) −47.5750 −1.51664
\(985\) 3.80625 0.121277
\(986\) 9.09115 0.289521
\(987\) 21.8938 0.696888
\(988\) −114.701 −3.64914
\(989\) 4.36577 0.138823
\(990\) −17.6730 −0.561685
\(991\) 45.5591 1.44723 0.723616 0.690203i \(-0.242479\pi\)
0.723616 + 0.690203i \(0.242479\pi\)
\(992\) 3.63609 0.115446
\(993\) 21.4579 0.680945
\(994\) 63.3767 2.01019
\(995\) −22.9344 −0.727069
\(996\) −36.4334 −1.15444
\(997\) −37.1478 −1.17648 −0.588242 0.808685i \(-0.700180\pi\)
−0.588242 + 0.808685i \(0.700180\pi\)
\(998\) 35.9495 1.13796
\(999\) 13.1596 0.416350
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 \(a_p\))