Properties

Label 5077.2.a.c.1.8
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 1.8
Character \(\chi\) = 5077.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.60586 q^{2} -2.49081 q^{3} +4.79053 q^{4} -1.82309 q^{5} +6.49071 q^{6} +1.00898 q^{7} -7.27175 q^{8} +3.20413 q^{9} +O(q^{10})\) \(q-2.60586 q^{2} -2.49081 q^{3} +4.79053 q^{4} -1.82309 q^{5} +6.49071 q^{6} +1.00898 q^{7} -7.27175 q^{8} +3.20413 q^{9} +4.75073 q^{10} +0.511549 q^{11} -11.9323 q^{12} -1.90222 q^{13} -2.62927 q^{14} +4.54097 q^{15} +9.36813 q^{16} +2.82608 q^{17} -8.34952 q^{18} -6.99053 q^{19} -8.73357 q^{20} -2.51318 q^{21} -1.33303 q^{22} +0.587350 q^{23} +18.1125 q^{24} -1.67634 q^{25} +4.95693 q^{26} -0.508441 q^{27} +4.83355 q^{28} -2.47910 q^{29} -11.8331 q^{30} -6.46857 q^{31} -9.86858 q^{32} -1.27417 q^{33} -7.36439 q^{34} -1.83946 q^{35} +15.3495 q^{36} -4.94263 q^{37} +18.2164 q^{38} +4.73806 q^{39} +13.2570 q^{40} +6.23684 q^{41} +6.54900 q^{42} +6.10118 q^{43} +2.45059 q^{44} -5.84141 q^{45} -1.53056 q^{46} -7.83478 q^{47} -23.3342 q^{48} -5.98196 q^{49} +4.36833 q^{50} -7.03923 q^{51} -9.11264 q^{52} +8.97211 q^{53} +1.32493 q^{54} -0.932600 q^{55} -7.33705 q^{56} +17.4121 q^{57} +6.46019 q^{58} +8.10985 q^{59} +21.7536 q^{60} -7.44405 q^{61} +16.8562 q^{62} +3.23290 q^{63} +6.97993 q^{64} +3.46792 q^{65} +3.32032 q^{66} +3.14046 q^{67} +13.5384 q^{68} -1.46298 q^{69} +4.79339 q^{70} -9.63889 q^{71} -23.2996 q^{72} -1.31652 q^{73} +12.8798 q^{74} +4.17545 q^{75} -33.4884 q^{76} +0.516143 q^{77} -12.3468 q^{78} -3.25687 q^{79} -17.0789 q^{80} -8.34595 q^{81} -16.2524 q^{82} +11.2454 q^{83} -12.0394 q^{84} -5.15220 q^{85} -15.8989 q^{86} +6.17496 q^{87} -3.71986 q^{88} -4.85320 q^{89} +15.2219 q^{90} -1.91930 q^{91} +2.81372 q^{92} +16.1120 q^{93} +20.4164 q^{94} +12.7444 q^{95} +24.5807 q^{96} +9.47521 q^{97} +15.5882 q^{98} +1.63907 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + O(q^{10}) \) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + 24q^{10} + 89q^{11} + 114q^{12} + 34q^{13} + 53q^{14} + 61q^{15} + 229q^{16} + 76q^{17} + 57q^{18} + 54q^{19} + 118q^{20} + 25q^{21} + 26q^{22} + 109q^{23} + 65q^{24} + 232q^{25} + 58q^{26} + 236q^{27} + 57q^{28} + 54q^{29} + 6q^{30} + 77q^{31} + 155q^{32} + 80q^{33} + 28q^{34} + 137q^{35} + 257q^{36} + 42q^{37} + 104q^{38} + 46q^{39} + 47q^{40} + 109q^{41} + 27q^{42} + 68q^{43} + 145q^{44} + 109q^{45} - 7q^{46} + 264q^{47} + 198q^{48} + 222q^{49} + 86q^{50} + 57q^{51} + 68q^{52} + 95q^{53} + 79q^{54} + 50q^{55} + 108q^{56} + 55q^{57} + 38q^{58} + 292q^{59} + 91q^{60} + 16q^{61} + 91q^{62} + 113q^{63} + 231q^{64} + 68q^{65} - 15q^{66} + 152q^{67} + 199q^{68} + 83q^{69} + 24q^{70} + 131q^{71} + 162q^{72} + 71q^{73} + 10q^{74} + 232q^{75} + 60q^{76} + 131q^{77} + 102q^{78} + 10q^{79} + 236q^{80} + 268q^{81} + 54q^{82} + 299q^{83} - 9q^{85} + 35q^{86} + 103q^{87} + 45q^{88} + 134q^{89} + 8q^{90} + 79q^{91} + 206q^{92} + 95q^{93} + 18q^{94} + 119q^{95} + 77q^{96} + 129q^{97} + 150q^{98} + 221q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.60586 −1.84262 −0.921312 0.388823i \(-0.872882\pi\)
−0.921312 + 0.388823i \(0.872882\pi\)
\(3\) −2.49081 −1.43807 −0.719034 0.694974i \(-0.755416\pi\)
−0.719034 + 0.694974i \(0.755416\pi\)
\(4\) 4.79053 2.39527
\(5\) −1.82309 −0.815311 −0.407655 0.913136i \(-0.633653\pi\)
−0.407655 + 0.913136i \(0.633653\pi\)
\(6\) 6.49071 2.64982
\(7\) 1.00898 0.381359 0.190679 0.981652i \(-0.438931\pi\)
0.190679 + 0.981652i \(0.438931\pi\)
\(8\) −7.27175 −2.57095
\(9\) 3.20413 1.06804
\(10\) 4.75073 1.50231
\(11\) 0.511549 0.154238 0.0771189 0.997022i \(-0.475428\pi\)
0.0771189 + 0.997022i \(0.475428\pi\)
\(12\) −11.9323 −3.44456
\(13\) −1.90222 −0.527581 −0.263790 0.964580i \(-0.584973\pi\)
−0.263790 + 0.964580i \(0.584973\pi\)
\(14\) −2.62927 −0.702701
\(15\) 4.54097 1.17247
\(16\) 9.36813 2.34203
\(17\) 2.82608 0.685426 0.342713 0.939440i \(-0.388654\pi\)
0.342713 + 0.939440i \(0.388654\pi\)
\(18\) −8.34952 −1.96800
\(19\) −6.99053 −1.60374 −0.801869 0.597500i \(-0.796161\pi\)
−0.801869 + 0.597500i \(0.796161\pi\)
\(20\) −8.73357 −1.95289
\(21\) −2.51318 −0.548420
\(22\) −1.33303 −0.284203
\(23\) 0.587350 0.122471 0.0612355 0.998123i \(-0.480496\pi\)
0.0612355 + 0.998123i \(0.480496\pi\)
\(24\) 18.1125 3.69721
\(25\) −1.67634 −0.335269
\(26\) 4.95693 0.972133
\(27\) −0.508441 −0.0978495
\(28\) 4.83355 0.913455
\(29\) −2.47910 −0.460357 −0.230178 0.973148i \(-0.573931\pi\)
−0.230178 + 0.973148i \(0.573931\pi\)
\(30\) −11.8331 −2.16043
\(31\) −6.46857 −1.16179 −0.580894 0.813979i \(-0.697297\pi\)
−0.580894 + 0.813979i \(0.697297\pi\)
\(32\) −9.86858 −1.74454
\(33\) −1.27417 −0.221805
\(34\) −7.36439 −1.26298
\(35\) −1.83946 −0.310926
\(36\) 15.3495 2.55825
\(37\) −4.94263 −0.812564 −0.406282 0.913748i \(-0.633175\pi\)
−0.406282 + 0.913748i \(0.633175\pi\)
\(38\) 18.2164 2.95509
\(39\) 4.73806 0.758697
\(40\) 13.2570 2.09612
\(41\) 6.23684 0.974031 0.487015 0.873393i \(-0.338086\pi\)
0.487015 + 0.873393i \(0.338086\pi\)
\(42\) 6.54900 1.01053
\(43\) 6.10118 0.930422 0.465211 0.885200i \(-0.345978\pi\)
0.465211 + 0.885200i \(0.345978\pi\)
\(44\) 2.45059 0.369441
\(45\) −5.84141 −0.870786
\(46\) −1.53056 −0.225668
\(47\) −7.83478 −1.14282 −0.571410 0.820665i \(-0.693603\pi\)
−0.571410 + 0.820665i \(0.693603\pi\)
\(48\) −23.3342 −3.36800
\(49\) −5.98196 −0.854566
\(50\) 4.36833 0.617774
\(51\) −7.03923 −0.985690
\(52\) −9.11264 −1.26370
\(53\) 8.97211 1.23241 0.616207 0.787584i \(-0.288668\pi\)
0.616207 + 0.787584i \(0.288668\pi\)
\(54\) 1.32493 0.180300
\(55\) −0.932600 −0.125752
\(56\) −7.33705 −0.980454
\(57\) 17.4121 2.30629
\(58\) 6.46019 0.848265
\(59\) 8.10985 1.05581 0.527906 0.849303i \(-0.322977\pi\)
0.527906 + 0.849303i \(0.322977\pi\)
\(60\) 21.7536 2.80838
\(61\) −7.44405 −0.953113 −0.476556 0.879144i \(-0.658115\pi\)
−0.476556 + 0.879144i \(0.658115\pi\)
\(62\) 16.8562 2.14074
\(63\) 3.23290 0.407307
\(64\) 6.97993 0.872492
\(65\) 3.46792 0.430142
\(66\) 3.32032 0.408703
\(67\) 3.14046 0.383668 0.191834 0.981427i \(-0.438557\pi\)
0.191834 + 0.981427i \(0.438557\pi\)
\(68\) 13.5384 1.64178
\(69\) −1.46298 −0.176122
\(70\) 4.79339 0.572919
\(71\) −9.63889 −1.14393 −0.571963 0.820279i \(-0.693818\pi\)
−0.571963 + 0.820279i \(0.693818\pi\)
\(72\) −23.2996 −2.74588
\(73\) −1.31652 −0.154087 −0.0770435 0.997028i \(-0.524548\pi\)
−0.0770435 + 0.997028i \(0.524548\pi\)
\(74\) 12.8798 1.49725
\(75\) 4.17545 0.482140
\(76\) −33.4884 −3.84138
\(77\) 0.516143 0.0588199
\(78\) −12.3468 −1.39799
\(79\) −3.25687 −0.366426 −0.183213 0.983073i \(-0.558650\pi\)
−0.183213 + 0.983073i \(0.558650\pi\)
\(80\) −17.0789 −1.90948
\(81\) −8.34595 −0.927328
\(82\) −16.2524 −1.79477
\(83\) 11.2454 1.23434 0.617171 0.786829i \(-0.288279\pi\)
0.617171 + 0.786829i \(0.288279\pi\)
\(84\) −12.0394 −1.31361
\(85\) −5.15220 −0.558835
\(86\) −15.8989 −1.71442
\(87\) 6.17496 0.662025
\(88\) −3.71986 −0.396538
\(89\) −4.85320 −0.514438 −0.257219 0.966353i \(-0.582806\pi\)
−0.257219 + 0.966353i \(0.582806\pi\)
\(90\) 15.2219 1.60453
\(91\) −1.91930 −0.201197
\(92\) 2.81372 0.293351
\(93\) 16.1120 1.67073
\(94\) 20.4164 2.10579
\(95\) 12.7444 1.30754
\(96\) 24.5807 2.50876
\(97\) 9.47521 0.962062 0.481031 0.876704i \(-0.340262\pi\)
0.481031 + 0.876704i \(0.340262\pi\)
\(98\) 15.5882 1.57464
\(99\) 1.63907 0.164733
\(100\) −8.03058 −0.803058
\(101\) −0.234664 −0.0233499 −0.0116750 0.999932i \(-0.503716\pi\)
−0.0116750 + 0.999932i \(0.503716\pi\)
\(102\) 18.3433 1.81626
\(103\) −13.9259 −1.37216 −0.686082 0.727524i \(-0.740671\pi\)
−0.686082 + 0.727524i \(0.740671\pi\)
\(104\) 13.8325 1.35638
\(105\) 4.58175 0.447133
\(106\) −23.3801 −2.27088
\(107\) 4.84502 0.468386 0.234193 0.972190i \(-0.424755\pi\)
0.234193 + 0.972190i \(0.424755\pi\)
\(108\) −2.43570 −0.234376
\(109\) 2.65863 0.254651 0.127325 0.991861i \(-0.459361\pi\)
0.127325 + 0.991861i \(0.459361\pi\)
\(110\) 2.43023 0.231713
\(111\) 12.3111 1.16852
\(112\) 9.45225 0.893154
\(113\) −8.68881 −0.817375 −0.408687 0.912674i \(-0.634013\pi\)
−0.408687 + 0.912674i \(0.634013\pi\)
\(114\) −45.3735 −4.24962
\(115\) −1.07079 −0.0998519
\(116\) −11.8762 −1.10268
\(117\) −6.09495 −0.563478
\(118\) −21.1332 −1.94547
\(119\) 2.85146 0.261393
\(120\) −33.0208 −3.01437
\(121\) −10.7383 −0.976211
\(122\) 19.3982 1.75623
\(123\) −15.5348 −1.40072
\(124\) −30.9879 −2.78279
\(125\) 12.1716 1.08866
\(126\) −8.42450 −0.750514
\(127\) 20.3895 1.80928 0.904640 0.426177i \(-0.140140\pi\)
0.904640 + 0.426177i \(0.140140\pi\)
\(128\) 1.54840 0.136861
\(129\) −15.1969 −1.33801
\(130\) −9.03692 −0.792590
\(131\) 7.87096 0.687689 0.343845 0.939027i \(-0.388271\pi\)
0.343845 + 0.939027i \(0.388271\pi\)
\(132\) −6.10396 −0.531281
\(133\) −7.05331 −0.611599
\(134\) −8.18360 −0.706956
\(135\) 0.926934 0.0797778
\(136\) −20.5506 −1.76220
\(137\) −10.1279 −0.865287 −0.432644 0.901565i \(-0.642419\pi\)
−0.432644 + 0.901565i \(0.642419\pi\)
\(138\) 3.81232 0.324526
\(139\) −1.08895 −0.0923635 −0.0461818 0.998933i \(-0.514705\pi\)
−0.0461818 + 0.998933i \(0.514705\pi\)
\(140\) −8.81200 −0.744750
\(141\) 19.5149 1.64345
\(142\) 25.1177 2.10783
\(143\) −0.973079 −0.0813729
\(144\) 30.0167 2.50139
\(145\) 4.51962 0.375334
\(146\) 3.43067 0.283925
\(147\) 14.8999 1.22892
\(148\) −23.6778 −1.94631
\(149\) −5.14799 −0.421740 −0.210870 0.977514i \(-0.567630\pi\)
−0.210870 + 0.977514i \(0.567630\pi\)
\(150\) −10.8807 −0.888402
\(151\) −15.3967 −1.25296 −0.626482 0.779436i \(-0.715506\pi\)
−0.626482 + 0.779436i \(0.715506\pi\)
\(152\) 50.8334 4.12313
\(153\) 9.05513 0.732064
\(154\) −1.34500 −0.108383
\(155\) 11.7928 0.947219
\(156\) 22.6978 1.81728
\(157\) −5.04819 −0.402889 −0.201445 0.979500i \(-0.564564\pi\)
−0.201445 + 0.979500i \(0.564564\pi\)
\(158\) 8.48696 0.675186
\(159\) −22.3478 −1.77230
\(160\) 17.9913 1.42234
\(161\) 0.592625 0.0467054
\(162\) 21.7484 1.70872
\(163\) −6.10587 −0.478248 −0.239124 0.970989i \(-0.576860\pi\)
−0.239124 + 0.970989i \(0.576860\pi\)
\(164\) 29.8778 2.33306
\(165\) 2.32293 0.180840
\(166\) −29.3040 −2.27443
\(167\) 5.15193 0.398668 0.199334 0.979932i \(-0.436122\pi\)
0.199334 + 0.979932i \(0.436122\pi\)
\(168\) 18.2752 1.40996
\(169\) −9.38156 −0.721659
\(170\) 13.4259 1.02972
\(171\) −22.3985 −1.71286
\(172\) 29.2279 2.22861
\(173\) 0.917417 0.0697499 0.0348750 0.999392i \(-0.488897\pi\)
0.0348750 + 0.999392i \(0.488897\pi\)
\(174\) −16.0911 −1.21986
\(175\) −1.69140 −0.127858
\(176\) 4.79226 0.361230
\(177\) −20.2001 −1.51833
\(178\) 12.6468 0.947917
\(179\) −21.3926 −1.59896 −0.799481 0.600692i \(-0.794892\pi\)
−0.799481 + 0.600692i \(0.794892\pi\)
\(180\) −27.9835 −2.08576
\(181\) −8.36271 −0.621596 −0.310798 0.950476i \(-0.600596\pi\)
−0.310798 + 0.950476i \(0.600596\pi\)
\(182\) 5.00144 0.370731
\(183\) 18.5417 1.37064
\(184\) −4.27106 −0.314867
\(185\) 9.01086 0.662492
\(186\) −41.9856 −3.07853
\(187\) 1.44568 0.105719
\(188\) −37.5328 −2.73736
\(189\) −0.513007 −0.0373158
\(190\) −33.2101 −2.40931
\(191\) −18.2098 −1.31762 −0.658809 0.752310i \(-0.728940\pi\)
−0.658809 + 0.752310i \(0.728940\pi\)
\(192\) −17.3857 −1.25470
\(193\) −9.56005 −0.688147 −0.344074 0.938943i \(-0.611807\pi\)
−0.344074 + 0.938943i \(0.611807\pi\)
\(194\) −24.6911 −1.77272
\(195\) −8.63792 −0.618574
\(196\) −28.6568 −2.04691
\(197\) −26.9883 −1.92284 −0.961418 0.275091i \(-0.911292\pi\)
−0.961418 + 0.275091i \(0.911292\pi\)
\(198\) −4.27119 −0.303540
\(199\) −9.79020 −0.694009 −0.347004 0.937863i \(-0.612801\pi\)
−0.347004 + 0.937863i \(0.612801\pi\)
\(200\) 12.1899 0.861960
\(201\) −7.82227 −0.551741
\(202\) 0.611503 0.0430252
\(203\) −2.50136 −0.175561
\(204\) −33.7217 −2.36099
\(205\) −11.3703 −0.794137
\(206\) 36.2891 2.52838
\(207\) 1.88194 0.130804
\(208\) −17.8202 −1.23561
\(209\) −3.57600 −0.247357
\(210\) −11.9394 −0.823897
\(211\) 12.0283 0.828062 0.414031 0.910263i \(-0.364121\pi\)
0.414031 + 0.910263i \(0.364121\pi\)
\(212\) 42.9812 2.95196
\(213\) 24.0086 1.64504
\(214\) −12.6255 −0.863059
\(215\) −11.1230 −0.758583
\(216\) 3.69726 0.251566
\(217\) −6.52665 −0.443058
\(218\) −6.92803 −0.469226
\(219\) 3.27920 0.221588
\(220\) −4.46765 −0.301209
\(221\) −5.37583 −0.361617
\(222\) −32.0812 −2.15315
\(223\) 0.646705 0.0433065 0.0216533 0.999766i \(-0.493107\pi\)
0.0216533 + 0.999766i \(0.493107\pi\)
\(224\) −9.95720 −0.665294
\(225\) −5.37122 −0.358081
\(226\) 22.6419 1.50611
\(227\) −6.67837 −0.443259 −0.221629 0.975131i \(-0.571138\pi\)
−0.221629 + 0.975131i \(0.571138\pi\)
\(228\) 83.4131 5.52417
\(229\) 15.9744 1.05562 0.527810 0.849362i \(-0.323013\pi\)
0.527810 + 0.849362i \(0.323013\pi\)
\(230\) 2.79034 0.183990
\(231\) −1.28561 −0.0845871
\(232\) 18.0274 1.18355
\(233\) 2.38839 0.156468 0.0782342 0.996935i \(-0.475072\pi\)
0.0782342 + 0.996935i \(0.475072\pi\)
\(234\) 15.8826 1.03828
\(235\) 14.2835 0.931754
\(236\) 38.8505 2.52895
\(237\) 8.11224 0.526947
\(238\) −7.43052 −0.481649
\(239\) −13.7632 −0.890269 −0.445134 0.895464i \(-0.646844\pi\)
−0.445134 + 0.895464i \(0.646844\pi\)
\(240\) 42.5404 2.74597
\(241\) 23.5847 1.51922 0.759612 0.650377i \(-0.225389\pi\)
0.759612 + 0.650377i \(0.225389\pi\)
\(242\) 27.9826 1.79879
\(243\) 22.3135 1.43141
\(244\) −35.6610 −2.28296
\(245\) 10.9056 0.696736
\(246\) 40.4815 2.58101
\(247\) 13.2975 0.846101
\(248\) 47.0378 2.98690
\(249\) −28.0101 −1.77507
\(250\) −31.7175 −2.00599
\(251\) 2.30491 0.145484 0.0727422 0.997351i \(-0.476825\pi\)
0.0727422 + 0.997351i \(0.476825\pi\)
\(252\) 15.4873 0.975609
\(253\) 0.300459 0.0188897
\(254\) −53.1324 −3.33382
\(255\) 12.8332 0.803643
\(256\) −17.9948 −1.12467
\(257\) −20.6002 −1.28501 −0.642503 0.766283i \(-0.722104\pi\)
−0.642503 + 0.766283i \(0.722104\pi\)
\(258\) 39.6010 2.46545
\(259\) −4.98702 −0.309878
\(260\) 16.6132 1.03030
\(261\) −7.94334 −0.491681
\(262\) −20.5107 −1.26715
\(263\) −17.3874 −1.07216 −0.536078 0.844169i \(-0.680095\pi\)
−0.536078 + 0.844169i \(0.680095\pi\)
\(264\) 9.26545 0.570249
\(265\) −16.3570 −1.00480
\(266\) 18.3800 1.12695
\(267\) 12.0884 0.739798
\(268\) 15.0445 0.918986
\(269\) −9.39296 −0.572699 −0.286350 0.958125i \(-0.592442\pi\)
−0.286350 + 0.958125i \(0.592442\pi\)
\(270\) −2.41546 −0.147000
\(271\) −2.74135 −0.166525 −0.0832627 0.996528i \(-0.526534\pi\)
−0.0832627 + 0.996528i \(0.526534\pi\)
\(272\) 26.4751 1.60529
\(273\) 4.78061 0.289336
\(274\) 26.3920 1.59440
\(275\) −0.857532 −0.0517111
\(276\) −7.00844 −0.421858
\(277\) −27.9439 −1.67898 −0.839492 0.543372i \(-0.817147\pi\)
−0.839492 + 0.543372i \(0.817147\pi\)
\(278\) 2.83766 0.170191
\(279\) −20.7261 −1.24084
\(280\) 13.3761 0.799375
\(281\) 31.7298 1.89284 0.946420 0.322938i \(-0.104671\pi\)
0.946420 + 0.322938i \(0.104671\pi\)
\(282\) −50.8533 −3.02827
\(283\) 4.56782 0.271529 0.135764 0.990741i \(-0.456651\pi\)
0.135764 + 0.990741i \(0.456651\pi\)
\(284\) −46.1754 −2.74001
\(285\) −31.7438 −1.88034
\(286\) 2.53571 0.149940
\(287\) 6.29285 0.371455
\(288\) −31.6202 −1.86324
\(289\) −9.01325 −0.530191
\(290\) −11.7775 −0.691599
\(291\) −23.6009 −1.38351
\(292\) −6.30683 −0.369079
\(293\) 9.06200 0.529408 0.264704 0.964330i \(-0.414726\pi\)
0.264704 + 0.964330i \(0.414726\pi\)
\(294\) −38.8272 −2.26445
\(295\) −14.7850 −0.860815
\(296\) 35.9416 2.08906
\(297\) −0.260093 −0.0150921
\(298\) 13.4150 0.777109
\(299\) −1.11727 −0.0646133
\(300\) 20.0026 1.15485
\(301\) 6.15597 0.354824
\(302\) 40.1217 2.30874
\(303\) 0.584503 0.0335788
\(304\) −65.4882 −3.75601
\(305\) 13.5712 0.777083
\(306\) −23.5964 −1.34892
\(307\) 12.5727 0.717562 0.358781 0.933422i \(-0.383193\pi\)
0.358781 + 0.933422i \(0.383193\pi\)
\(308\) 2.47260 0.140889
\(309\) 34.6869 1.97327
\(310\) −30.7304 −1.74537
\(311\) 7.52906 0.426934 0.213467 0.976950i \(-0.431524\pi\)
0.213467 + 0.976950i \(0.431524\pi\)
\(312\) −34.4540 −1.95057
\(313\) −31.8445 −1.79996 −0.899979 0.435933i \(-0.856418\pi\)
−0.899979 + 0.435933i \(0.856418\pi\)
\(314\) 13.1549 0.742374
\(315\) −5.89387 −0.332082
\(316\) −15.6021 −0.877689
\(317\) 0.582959 0.0327423 0.0163711 0.999866i \(-0.494789\pi\)
0.0163711 + 0.999866i \(0.494789\pi\)
\(318\) 58.2354 3.26568
\(319\) −1.26818 −0.0710045
\(320\) −12.7250 −0.711352
\(321\) −12.0680 −0.673571
\(322\) −1.54430 −0.0860604
\(323\) −19.7558 −1.09924
\(324\) −39.9815 −2.22120
\(325\) 3.18877 0.176881
\(326\) 15.9111 0.881232
\(327\) −6.62214 −0.366205
\(328\) −45.3527 −2.50418
\(329\) −7.90514 −0.435824
\(330\) −6.05324 −0.333220
\(331\) −1.13949 −0.0626320 −0.0313160 0.999510i \(-0.509970\pi\)
−0.0313160 + 0.999510i \(0.509970\pi\)
\(332\) 53.8714 2.95658
\(333\) −15.8368 −0.867852
\(334\) −13.4252 −0.734596
\(335\) −5.72533 −0.312808
\(336\) −23.5438 −1.28442
\(337\) −0.152131 −0.00828712 −0.00414356 0.999991i \(-0.501319\pi\)
−0.00414356 + 0.999991i \(0.501319\pi\)
\(338\) 24.4471 1.32975
\(339\) 21.6422 1.17544
\(340\) −24.6818 −1.33856
\(341\) −3.30899 −0.179192
\(342\) 58.3676 3.15616
\(343\) −13.0985 −0.707255
\(344\) −44.3663 −2.39207
\(345\) 2.66714 0.143594
\(346\) −2.39066 −0.128523
\(347\) 0.120036 0.00644387 0.00322194 0.999995i \(-0.498974\pi\)
0.00322194 + 0.999995i \(0.498974\pi\)
\(348\) 29.5813 1.58573
\(349\) 13.1587 0.704368 0.352184 0.935931i \(-0.385439\pi\)
0.352184 + 0.935931i \(0.385439\pi\)
\(350\) 4.40755 0.235594
\(351\) 0.967166 0.0516235
\(352\) −5.04827 −0.269073
\(353\) 34.2251 1.82162 0.910808 0.412830i \(-0.135459\pi\)
0.910808 + 0.412830i \(0.135459\pi\)
\(354\) 52.6387 2.79772
\(355\) 17.5726 0.932655
\(356\) −23.2494 −1.23222
\(357\) −7.10244 −0.375901
\(358\) 55.7463 2.94629
\(359\) −12.1287 −0.640126 −0.320063 0.947396i \(-0.603704\pi\)
−0.320063 + 0.947396i \(0.603704\pi\)
\(360\) 42.4773 2.23875
\(361\) 29.8675 1.57198
\(362\) 21.7921 1.14537
\(363\) 26.7471 1.40386
\(364\) −9.19447 −0.481921
\(365\) 2.40013 0.125629
\(366\) −48.3172 −2.52558
\(367\) −17.8610 −0.932334 −0.466167 0.884697i \(-0.654365\pi\)
−0.466167 + 0.884697i \(0.654365\pi\)
\(368\) 5.50237 0.286831
\(369\) 19.9836 1.04031
\(370\) −23.4811 −1.22072
\(371\) 9.05268 0.469992
\(372\) 77.1848 4.00185
\(373\) −11.5526 −0.598168 −0.299084 0.954227i \(-0.596681\pi\)
−0.299084 + 0.954227i \(0.596681\pi\)
\(374\) −3.76725 −0.194800
\(375\) −30.3171 −1.56557
\(376\) 56.9726 2.93814
\(377\) 4.71579 0.242875
\(378\) 1.33683 0.0687589
\(379\) 11.2799 0.579412 0.289706 0.957116i \(-0.406442\pi\)
0.289706 + 0.957116i \(0.406442\pi\)
\(380\) 61.0523 3.13192
\(381\) −50.7865 −2.60187
\(382\) 47.4524 2.42788
\(383\) 35.8703 1.83289 0.916444 0.400162i \(-0.131046\pi\)
0.916444 + 0.400162i \(0.131046\pi\)
\(384\) −3.85677 −0.196815
\(385\) −0.940975 −0.0479565
\(386\) 24.9122 1.26800
\(387\) 19.5490 0.993730
\(388\) 45.3913 2.30439
\(389\) −0.603763 −0.0306120 −0.0153060 0.999883i \(-0.504872\pi\)
−0.0153060 + 0.999883i \(0.504872\pi\)
\(390\) 22.5092 1.13980
\(391\) 1.65990 0.0839448
\(392\) 43.4993 2.19705
\(393\) −19.6051 −0.988944
\(394\) 70.3278 3.54307
\(395\) 5.93757 0.298751
\(396\) 7.85201 0.394578
\(397\) 14.8741 0.746509 0.373255 0.927729i \(-0.378242\pi\)
0.373255 + 0.927729i \(0.378242\pi\)
\(398\) 25.5119 1.27880
\(399\) 17.5684 0.879522
\(400\) −15.7042 −0.785210
\(401\) −4.22916 −0.211194 −0.105597 0.994409i \(-0.533675\pi\)
−0.105597 + 0.994409i \(0.533675\pi\)
\(402\) 20.3838 1.01665
\(403\) 12.3046 0.612937
\(404\) −1.12417 −0.0559293
\(405\) 15.2154 0.756060
\(406\) 6.51821 0.323493
\(407\) −2.52840 −0.125328
\(408\) 51.1875 2.53416
\(409\) 29.6035 1.46380 0.731900 0.681412i \(-0.238634\pi\)
0.731900 + 0.681412i \(0.238634\pi\)
\(410\) 29.6295 1.46330
\(411\) 25.2267 1.24434
\(412\) −66.7127 −3.28670
\(413\) 8.18268 0.402643
\(414\) −4.90409 −0.241023
\(415\) −20.5014 −1.00637
\(416\) 18.7722 0.920383
\(417\) 2.71237 0.132825
\(418\) 9.31857 0.455786
\(419\) −13.5660 −0.662744 −0.331372 0.943500i \(-0.607512\pi\)
−0.331372 + 0.943500i \(0.607512\pi\)
\(420\) 21.9490 1.07100
\(421\) 28.3994 1.38410 0.692051 0.721848i \(-0.256707\pi\)
0.692051 + 0.721848i \(0.256707\pi\)
\(422\) −31.3441 −1.52581
\(423\) −25.1036 −1.22058
\(424\) −65.2429 −3.16848
\(425\) −4.73749 −0.229802
\(426\) −62.5633 −3.03120
\(427\) −7.51090 −0.363478
\(428\) 23.2102 1.12191
\(429\) 2.42375 0.117020
\(430\) 28.9851 1.39778
\(431\) 5.22646 0.251750 0.125875 0.992046i \(-0.459826\pi\)
0.125875 + 0.992046i \(0.459826\pi\)
\(432\) −4.76314 −0.229167
\(433\) −16.5974 −0.797621 −0.398810 0.917033i \(-0.630577\pi\)
−0.398810 + 0.917033i \(0.630577\pi\)
\(434\) 17.0076 0.816390
\(435\) −11.2575 −0.539756
\(436\) 12.7363 0.609956
\(437\) −4.10589 −0.196411
\(438\) −8.54515 −0.408303
\(439\) −19.2735 −0.919873 −0.459937 0.887952i \(-0.652128\pi\)
−0.459937 + 0.887952i \(0.652128\pi\)
\(440\) 6.78163 0.323302
\(441\) −19.1670 −0.912712
\(442\) 14.0087 0.666325
\(443\) 21.4715 1.02014 0.510070 0.860133i \(-0.329619\pi\)
0.510070 + 0.860133i \(0.329619\pi\)
\(444\) 58.9769 2.79892
\(445\) 8.84782 0.419427
\(446\) −1.68522 −0.0797977
\(447\) 12.8227 0.606491
\(448\) 7.04261 0.332732
\(449\) 31.4800 1.48564 0.742818 0.669494i \(-0.233489\pi\)
0.742818 + 0.669494i \(0.233489\pi\)
\(450\) 13.9967 0.659809
\(451\) 3.19045 0.150232
\(452\) −41.6240 −1.95783
\(453\) 38.3502 1.80185
\(454\) 17.4029 0.816760
\(455\) 3.49906 0.164038
\(456\) −126.616 −5.92935
\(457\) 5.20215 0.243347 0.121673 0.992570i \(-0.461174\pi\)
0.121673 + 0.992570i \(0.461174\pi\)
\(458\) −41.6272 −1.94511
\(459\) −1.43690 −0.0670686
\(460\) −5.12966 −0.239172
\(461\) −1.77185 −0.0825232 −0.0412616 0.999148i \(-0.513138\pi\)
−0.0412616 + 0.999148i \(0.513138\pi\)
\(462\) 3.35013 0.155862
\(463\) −24.0150 −1.11607 −0.558035 0.829817i \(-0.688445\pi\)
−0.558035 + 0.829817i \(0.688445\pi\)
\(464\) −23.2245 −1.07817
\(465\) −29.3735 −1.36217
\(466\) −6.22381 −0.288312
\(467\) 24.9213 1.15322 0.576610 0.817019i \(-0.304375\pi\)
0.576610 + 0.817019i \(0.304375\pi\)
\(468\) −29.1981 −1.34968
\(469\) 3.16866 0.146315
\(470\) −37.2209 −1.71687
\(471\) 12.5741 0.579383
\(472\) −58.9728 −2.71444
\(473\) 3.12106 0.143506
\(474\) −21.1394 −0.970965
\(475\) 11.7185 0.537683
\(476\) 13.6600 0.626106
\(477\) 28.7478 1.31627
\(478\) 35.8651 1.64043
\(479\) 5.10932 0.233451 0.116725 0.993164i \(-0.462760\pi\)
0.116725 + 0.993164i \(0.462760\pi\)
\(480\) −44.8129 −2.04542
\(481\) 9.40197 0.428693
\(482\) −61.4585 −2.79936
\(483\) −1.47611 −0.0671655
\(484\) −51.4422 −2.33828
\(485\) −17.2742 −0.784379
\(486\) −58.1459 −2.63755
\(487\) −12.6127 −0.571537 −0.285768 0.958299i \(-0.592249\pi\)
−0.285768 + 0.958299i \(0.592249\pi\)
\(488\) 54.1313 2.45041
\(489\) 15.2085 0.687754
\(490\) −28.4186 −1.28382
\(491\) −24.3935 −1.10087 −0.550433 0.834880i \(-0.685537\pi\)
−0.550433 + 0.834880i \(0.685537\pi\)
\(492\) −74.4198 −3.35510
\(493\) −7.00614 −0.315540
\(494\) −34.6515 −1.55905
\(495\) −2.98817 −0.134308
\(496\) −60.5984 −2.72095
\(497\) −9.72545 −0.436246
\(498\) 72.9906 3.27079
\(499\) 3.22212 0.144242 0.0721210 0.997396i \(-0.477023\pi\)
0.0721210 + 0.997396i \(0.477023\pi\)
\(500\) 58.3083 2.60763
\(501\) −12.8325 −0.573312
\(502\) −6.00628 −0.268073
\(503\) 5.29761 0.236209 0.118104 0.993001i \(-0.462318\pi\)
0.118104 + 0.993001i \(0.462318\pi\)
\(504\) −23.5088 −1.04717
\(505\) 0.427814 0.0190375
\(506\) −0.782954 −0.0348066
\(507\) 23.3677 1.03779
\(508\) 97.6768 4.33371
\(509\) 3.76173 0.166736 0.0833679 0.996519i \(-0.473432\pi\)
0.0833679 + 0.996519i \(0.473432\pi\)
\(510\) −33.4415 −1.48081
\(511\) −1.32834 −0.0587624
\(512\) 43.7952 1.93549
\(513\) 3.55427 0.156925
\(514\) 53.6814 2.36779
\(515\) 25.3882 1.11874
\(516\) −72.8011 −3.20489
\(517\) −4.00788 −0.176266
\(518\) 12.9955 0.570989
\(519\) −2.28511 −0.100305
\(520\) −25.2178 −1.10587
\(521\) 32.2817 1.41429 0.707144 0.707070i \(-0.249983\pi\)
0.707144 + 0.707070i \(0.249983\pi\)
\(522\) 20.6993 0.905983
\(523\) 24.6596 1.07829 0.539144 0.842213i \(-0.318748\pi\)
0.539144 + 0.842213i \(0.318748\pi\)
\(524\) 37.7061 1.64720
\(525\) 4.21295 0.183868
\(526\) 45.3093 1.97558
\(527\) −18.2807 −0.796320
\(528\) −11.9366 −0.519474
\(529\) −22.6550 −0.985001
\(530\) 42.6240 1.85147
\(531\) 25.9850 1.12765
\(532\) −33.7891 −1.46494
\(533\) −11.8638 −0.513880
\(534\) −31.5007 −1.36317
\(535\) −8.83290 −0.381880
\(536\) −22.8366 −0.986391
\(537\) 53.2850 2.29942
\(538\) 24.4768 1.05527
\(539\) −3.06007 −0.131806
\(540\) 4.44051 0.191089
\(541\) 6.42711 0.276323 0.138162 0.990410i \(-0.455881\pi\)
0.138162 + 0.990410i \(0.455881\pi\)
\(542\) 7.14359 0.306844
\(543\) 20.8299 0.893897
\(544\) −27.8894 −1.19575
\(545\) −4.84692 −0.207619
\(546\) −12.4576 −0.533137
\(547\) 30.3950 1.29960 0.649798 0.760107i \(-0.274854\pi\)
0.649798 + 0.760107i \(0.274854\pi\)
\(548\) −48.5181 −2.07259
\(549\) −23.8517 −1.01796
\(550\) 2.23461 0.0952842
\(551\) 17.3302 0.738292
\(552\) 10.6384 0.452800
\(553\) −3.28612 −0.139740
\(554\) 72.8179 3.09374
\(555\) −22.4443 −0.952709
\(556\) −5.21665 −0.221235
\(557\) −46.0868 −1.95276 −0.976381 0.216058i \(-0.930680\pi\)
−0.976381 + 0.216058i \(0.930680\pi\)
\(558\) 54.0094 2.28640
\(559\) −11.6058 −0.490873
\(560\) −17.2323 −0.728198
\(561\) −3.60091 −0.152031
\(562\) −82.6835 −3.48779
\(563\) 14.9732 0.631044 0.315522 0.948918i \(-0.397820\pi\)
0.315522 + 0.948918i \(0.397820\pi\)
\(564\) 93.4870 3.93651
\(565\) 15.8405 0.666414
\(566\) −11.9031 −0.500326
\(567\) −8.42090 −0.353644
\(568\) 70.0916 2.94098
\(569\) 0.144784 0.00606967 0.00303483 0.999995i \(-0.499034\pi\)
0.00303483 + 0.999995i \(0.499034\pi\)
\(570\) 82.7200 3.46476
\(571\) 16.7381 0.700469 0.350234 0.936662i \(-0.386102\pi\)
0.350234 + 0.936662i \(0.386102\pi\)
\(572\) −4.66156 −0.194910
\(573\) 45.3572 1.89483
\(574\) −16.3983 −0.684452
\(575\) −0.984601 −0.0410607
\(576\) 22.3646 0.931858
\(577\) 18.2490 0.759717 0.379858 0.925045i \(-0.375973\pi\)
0.379858 + 0.925045i \(0.375973\pi\)
\(578\) 23.4873 0.976944
\(579\) 23.8122 0.989603
\(580\) 21.6514 0.899024
\(581\) 11.3464 0.470727
\(582\) 61.5008 2.54929
\(583\) 4.58968 0.190085
\(584\) 9.57340 0.396150
\(585\) 11.1116 0.459410
\(586\) −23.6144 −0.975500
\(587\) 23.0261 0.950390 0.475195 0.879881i \(-0.342378\pi\)
0.475195 + 0.879881i \(0.342378\pi\)
\(588\) 71.3785 2.94360
\(589\) 45.2187 1.86320
\(590\) 38.5277 1.58616
\(591\) 67.2227 2.76517
\(592\) −46.3032 −1.90305
\(593\) −2.49751 −0.102560 −0.0512801 0.998684i \(-0.516330\pi\)
−0.0512801 + 0.998684i \(0.516330\pi\)
\(594\) 0.677766 0.0278091
\(595\) −5.19847 −0.213117
\(596\) −24.6616 −1.01018
\(597\) 24.3855 0.998033
\(598\) 2.91145 0.119058
\(599\) −25.7810 −1.05338 −0.526692 0.850056i \(-0.676568\pi\)
−0.526692 + 0.850056i \(0.676568\pi\)
\(600\) −30.3628 −1.23956
\(601\) −1.21827 −0.0496943 −0.0248471 0.999691i \(-0.507910\pi\)
−0.0248471 + 0.999691i \(0.507910\pi\)
\(602\) −16.0416 −0.653808
\(603\) 10.0624 0.409773
\(604\) −73.7583 −3.00118
\(605\) 19.5769 0.795915
\(606\) −1.52314 −0.0618732
\(607\) 17.0989 0.694023 0.347011 0.937861i \(-0.387197\pi\)
0.347011 + 0.937861i \(0.387197\pi\)
\(608\) 68.9866 2.79778
\(609\) 6.23041 0.252469
\(610\) −35.3646 −1.43187
\(611\) 14.9035 0.602930
\(612\) 43.3789 1.75349
\(613\) 5.42080 0.218944 0.109472 0.993990i \(-0.465084\pi\)
0.109472 + 0.993990i \(0.465084\pi\)
\(614\) −32.7628 −1.32220
\(615\) 28.3213 1.14202
\(616\) −3.75326 −0.151223
\(617\) −30.3190 −1.22060 −0.610298 0.792172i \(-0.708950\pi\)
−0.610298 + 0.792172i \(0.708950\pi\)
\(618\) −90.3893 −3.63599
\(619\) 33.8769 1.36163 0.680814 0.732457i \(-0.261626\pi\)
0.680814 + 0.732457i \(0.261626\pi\)
\(620\) 56.4937 2.26884
\(621\) −0.298633 −0.0119837
\(622\) −19.6197 −0.786679
\(623\) −4.89678 −0.196186
\(624\) 44.3868 1.77689
\(625\) −13.8082 −0.552326
\(626\) 82.9825 3.31665
\(627\) 8.90713 0.355717
\(628\) −24.1835 −0.965027
\(629\) −13.9683 −0.556952
\(630\) 15.3586 0.611902
\(631\) 12.6245 0.502574 0.251287 0.967913i \(-0.419146\pi\)
0.251287 + 0.967913i \(0.419146\pi\)
\(632\) 23.6831 0.942065
\(633\) −29.9602 −1.19081
\(634\) −1.51911 −0.0603317
\(635\) −37.1720 −1.47512
\(636\) −107.058 −4.24512
\(637\) 11.3790 0.450852
\(638\) 3.30471 0.130835
\(639\) −30.8842 −1.22176
\(640\) −2.82287 −0.111584
\(641\) −19.9617 −0.788441 −0.394220 0.919016i \(-0.628985\pi\)
−0.394220 + 0.919016i \(0.628985\pi\)
\(642\) 31.4476 1.24114
\(643\) 33.2942 1.31299 0.656497 0.754328i \(-0.272037\pi\)
0.656497 + 0.754328i \(0.272037\pi\)
\(644\) 2.83899 0.111872
\(645\) 27.7053 1.09089
\(646\) 51.4810 2.02549
\(647\) 20.2749 0.797089 0.398544 0.917149i \(-0.369516\pi\)
0.398544 + 0.917149i \(0.369516\pi\)
\(648\) 60.6897 2.38411
\(649\) 4.14859 0.162846
\(650\) −8.30951 −0.325926
\(651\) 16.2566 0.637148
\(652\) −29.2503 −1.14553
\(653\) −9.38264 −0.367171 −0.183585 0.983004i \(-0.558770\pi\)
−0.183585 + 0.983004i \(0.558770\pi\)
\(654\) 17.2564 0.674779
\(655\) −14.3495 −0.560680
\(656\) 58.4275 2.28121
\(657\) −4.21830 −0.164571
\(658\) 20.5997 0.803061
\(659\) 20.3747 0.793684 0.396842 0.917887i \(-0.370106\pi\)
0.396842 + 0.917887i \(0.370106\pi\)
\(660\) 11.1281 0.433159
\(661\) −26.1158 −1.01579 −0.507893 0.861420i \(-0.669576\pi\)
−0.507893 + 0.861420i \(0.669576\pi\)
\(662\) 2.96936 0.115407
\(663\) 13.3902 0.520031
\(664\) −81.7736 −3.17343
\(665\) 12.8588 0.498643
\(666\) 41.2686 1.59913
\(667\) −1.45610 −0.0563803
\(668\) 24.6805 0.954916
\(669\) −1.61082 −0.0622778
\(670\) 14.9194 0.576388
\(671\) −3.80800 −0.147006
\(672\) 24.8015 0.956738
\(673\) −11.0833 −0.427229 −0.213614 0.976918i \(-0.568524\pi\)
−0.213614 + 0.976918i \(0.568524\pi\)
\(674\) 0.396433 0.0152700
\(675\) 0.852322 0.0328059
\(676\) −44.9427 −1.72856
\(677\) 30.0550 1.15511 0.577554 0.816353i \(-0.304007\pi\)
0.577554 + 0.816353i \(0.304007\pi\)
\(678\) −56.3966 −2.16590
\(679\) 9.56030 0.366891
\(680\) 37.4655 1.43674
\(681\) 16.6345 0.637437
\(682\) 8.62278 0.330183
\(683\) 12.2145 0.467375 0.233688 0.972312i \(-0.424921\pi\)
0.233688 + 0.972312i \(0.424921\pi\)
\(684\) −107.301 −4.10275
\(685\) 18.4641 0.705478
\(686\) 34.1330 1.30320
\(687\) −39.7893 −1.51806
\(688\) 57.1567 2.17908
\(689\) −17.0669 −0.650198
\(690\) −6.95020 −0.264590
\(691\) 34.3195 1.30558 0.652788 0.757541i \(-0.273599\pi\)
0.652788 + 0.757541i \(0.273599\pi\)
\(692\) 4.39491 0.167070
\(693\) 1.65379 0.0628222
\(694\) −0.312798 −0.0118736
\(695\) 1.98525 0.0753050
\(696\) −44.9027 −1.70203
\(697\) 17.6258 0.667626
\(698\) −34.2897 −1.29789
\(699\) −5.94901 −0.225012
\(700\) −8.10269 −0.306253
\(701\) 18.2364 0.688778 0.344389 0.938827i \(-0.388086\pi\)
0.344389 + 0.938827i \(0.388086\pi\)
\(702\) −2.52031 −0.0951228
\(703\) 34.5516 1.30314
\(704\) 3.57058 0.134571
\(705\) −35.5775 −1.33993
\(706\) −89.1859 −3.35656
\(707\) −0.236771 −0.00890470
\(708\) −96.7692 −3.63681
\(709\) 11.0432 0.414737 0.207369 0.978263i \(-0.433510\pi\)
0.207369 + 0.978263i \(0.433510\pi\)
\(710\) −45.7917 −1.71853
\(711\) −10.4354 −0.391359
\(712\) 35.2913 1.32260
\(713\) −3.79931 −0.142285
\(714\) 18.5080 0.692645
\(715\) 1.77401 0.0663442
\(716\) −102.482 −3.82994
\(717\) 34.2815 1.28027
\(718\) 31.6056 1.17951
\(719\) −20.7963 −0.775573 −0.387786 0.921749i \(-0.626760\pi\)
−0.387786 + 0.921749i \(0.626760\pi\)
\(720\) −54.7231 −2.03941
\(721\) −14.0510 −0.523287
\(722\) −77.8307 −2.89656
\(723\) −58.7449 −2.18475
\(724\) −40.0618 −1.48889
\(725\) 4.15582 0.154343
\(726\) −69.6993 −2.58678
\(727\) 34.2227 1.26925 0.634626 0.772820i \(-0.281154\pi\)
0.634626 + 0.772820i \(0.281154\pi\)
\(728\) 13.9567 0.517269
\(729\) −30.5408 −1.13114
\(730\) −6.25443 −0.231487
\(731\) 17.2425 0.637735
\(732\) 88.8246 3.28305
\(733\) 19.0539 0.703770 0.351885 0.936043i \(-0.385541\pi\)
0.351885 + 0.936043i \(0.385541\pi\)
\(734\) 46.5432 1.71794
\(735\) −27.1639 −1.00195
\(736\) −5.79631 −0.213655
\(737\) 1.60650 0.0591761
\(738\) −52.0746 −1.91689
\(739\) −19.3324 −0.711154 −0.355577 0.934647i \(-0.615716\pi\)
−0.355577 + 0.934647i \(0.615716\pi\)
\(740\) 43.1668 1.58684
\(741\) −33.1216 −1.21675
\(742\) −23.5901 −0.866018
\(743\) −3.84534 −0.141072 −0.0705360 0.997509i \(-0.522471\pi\)
−0.0705360 + 0.997509i \(0.522471\pi\)
\(744\) −117.162 −4.29537
\(745\) 9.38525 0.343849
\(746\) 30.1044 1.10220
\(747\) 36.0317 1.31833
\(748\) 6.92558 0.253224
\(749\) 4.88853 0.178623
\(750\) 79.0022 2.88475
\(751\) 30.3013 1.10571 0.552856 0.833277i \(-0.313538\pi\)
0.552856 + 0.833277i \(0.313538\pi\)
\(752\) −73.3973 −2.67652
\(753\) −5.74108 −0.209217
\(754\) −12.2887 −0.447528
\(755\) 28.0695 1.02156
\(756\) −2.45758 −0.0893812
\(757\) 4.48076 0.162856 0.0814280 0.996679i \(-0.474052\pi\)
0.0814280 + 0.996679i \(0.474052\pi\)
\(758\) −29.3940 −1.06764
\(759\) −0.748385 −0.0271646
\(760\) −92.6738 −3.36163
\(761\) 12.5828 0.456126 0.228063 0.973646i \(-0.426761\pi\)
0.228063 + 0.973646i \(0.426761\pi\)
\(762\) 132.343 4.79427
\(763\) 2.68251 0.0971132
\(764\) −87.2348 −3.15605
\(765\) −16.5083 −0.596859
\(766\) −93.4733 −3.37733
\(767\) −15.4267 −0.557026
\(768\) 44.8216 1.61736
\(769\) 6.77960 0.244478 0.122239 0.992501i \(-0.460992\pi\)
0.122239 + 0.992501i \(0.460992\pi\)
\(770\) 2.45205 0.0883659
\(771\) 51.3112 1.84793
\(772\) −45.7977 −1.64830
\(773\) −29.6637 −1.06693 −0.533465 0.845822i \(-0.679110\pi\)
−0.533465 + 0.845822i \(0.679110\pi\)
\(774\) −50.9420 −1.83107
\(775\) 10.8435 0.389511
\(776\) −68.9013 −2.47341
\(777\) 12.4217 0.445626
\(778\) 1.57332 0.0564064
\(779\) −43.5988 −1.56209
\(780\) −41.3802 −1.48165
\(781\) −4.93077 −0.176437
\(782\) −4.32548 −0.154679
\(783\) 1.26048 0.0450457
\(784\) −56.0398 −2.00142
\(785\) 9.20330 0.328480
\(786\) 51.0881 1.82225
\(787\) 12.6089 0.449458 0.224729 0.974421i \(-0.427850\pi\)
0.224729 + 0.974421i \(0.427850\pi\)
\(788\) −129.288 −4.60570
\(789\) 43.3088 1.54183
\(790\) −15.4725 −0.550487
\(791\) −8.76684 −0.311713
\(792\) −11.9189 −0.423519
\(793\) 14.1602 0.502844
\(794\) −38.7599 −1.37554
\(795\) 40.7421 1.44497
\(796\) −46.9003 −1.66234
\(797\) −11.4369 −0.405115 −0.202558 0.979270i \(-0.564925\pi\)
−0.202558 + 0.979270i \(0.564925\pi\)
\(798\) −45.7810 −1.62063
\(799\) −22.1418 −0.783319
\(800\) 16.5431 0.584888
\(801\) −15.5503 −0.549442
\(802\) 11.0206 0.389151
\(803\) −0.673465 −0.0237661
\(804\) −37.4728 −1.32157
\(805\) −1.08041 −0.0380794
\(806\) −32.0642 −1.12941
\(807\) 23.3961 0.823581
\(808\) 1.70642 0.0600316
\(809\) 12.1518 0.427235 0.213617 0.976917i \(-0.431475\pi\)
0.213617 + 0.976917i \(0.431475\pi\)
\(810\) −39.6493 −1.39314
\(811\) −51.7254 −1.81632 −0.908162 0.418618i \(-0.862515\pi\)
−0.908162 + 0.418618i \(0.862515\pi\)
\(812\) −11.9828 −0.420515
\(813\) 6.82818 0.239475
\(814\) 6.58867 0.230933
\(815\) 11.1315 0.389921
\(816\) −65.9444 −2.30852
\(817\) −42.6505 −1.49215
\(818\) −77.1428 −2.69724
\(819\) −6.14968 −0.214887
\(820\) −54.4699 −1.90217
\(821\) −18.1746 −0.634296 −0.317148 0.948376i \(-0.602725\pi\)
−0.317148 + 0.948376i \(0.602725\pi\)
\(822\) −65.7374 −2.29286
\(823\) 38.8847 1.35544 0.677718 0.735322i \(-0.262969\pi\)
0.677718 + 0.735322i \(0.262969\pi\)
\(824\) 101.266 3.52777
\(825\) 2.13595 0.0743642
\(826\) −21.3230 −0.741920
\(827\) 51.0148 1.77396 0.886980 0.461808i \(-0.152799\pi\)
0.886980 + 0.461808i \(0.152799\pi\)
\(828\) 9.01551 0.313311
\(829\) −16.7616 −0.582154 −0.291077 0.956700i \(-0.594014\pi\)
−0.291077 + 0.956700i \(0.594014\pi\)
\(830\) 53.4238 1.85437
\(831\) 69.6028 2.41449
\(832\) −13.2774 −0.460310
\(833\) −16.9055 −0.585741
\(834\) −7.06806 −0.244747
\(835\) −9.39242 −0.325038
\(836\) −17.1309 −0.592486
\(837\) 3.28888 0.113680
\(838\) 35.3512 1.22119
\(839\) 36.1741 1.24887 0.624434 0.781078i \(-0.285330\pi\)
0.624434 + 0.781078i \(0.285330\pi\)
\(840\) −33.3173 −1.14956
\(841\) −22.8541 −0.788072
\(842\) −74.0050 −2.55038
\(843\) −79.0328 −2.72203
\(844\) 57.6219 1.98343
\(845\) 17.1034 0.588376
\(846\) 65.4167 2.24907
\(847\) −10.8347 −0.372286
\(848\) 84.0519 2.88635
\(849\) −11.3776 −0.390477
\(850\) 12.3453 0.423439
\(851\) −2.90306 −0.0995155
\(852\) 115.014 3.94032
\(853\) −13.6631 −0.467817 −0.233909 0.972259i \(-0.575152\pi\)
−0.233909 + 0.972259i \(0.575152\pi\)
\(854\) 19.5724 0.669753
\(855\) 40.8346 1.39651
\(856\) −35.2318 −1.20420
\(857\) −56.4956 −1.92985 −0.964927 0.262517i \(-0.915447\pi\)
−0.964927 + 0.262517i \(0.915447\pi\)
\(858\) −6.31597 −0.215624
\(859\) −51.2510 −1.74866 −0.874331 0.485330i \(-0.838699\pi\)
−0.874331 + 0.485330i \(0.838699\pi\)
\(860\) −53.2851 −1.81701
\(861\) −15.6743 −0.534178
\(862\) −13.6194 −0.463880
\(863\) 31.5105 1.07263 0.536315 0.844018i \(-0.319816\pi\)
0.536315 + 0.844018i \(0.319816\pi\)
\(864\) 5.01759 0.170702
\(865\) −1.67253 −0.0568678
\(866\) 43.2506 1.46972
\(867\) 22.4503 0.762452
\(868\) −31.2661 −1.06124
\(869\) −1.66605 −0.0565168
\(870\) 29.3355 0.994567
\(871\) −5.97383 −0.202416
\(872\) −19.3329 −0.654694
\(873\) 30.3598 1.02752
\(874\) 10.6994 0.361912
\(875\) 12.2809 0.415169
\(876\) 15.7091 0.530762
\(877\) −37.4596 −1.26492 −0.632461 0.774592i \(-0.717955\pi\)
−0.632461 + 0.774592i \(0.717955\pi\)
\(878\) 50.2241 1.69498
\(879\) −22.5717 −0.761325
\(880\) −8.73672 −0.294515
\(881\) 10.6576 0.359063 0.179532 0.983752i \(-0.442542\pi\)
0.179532 + 0.983752i \(0.442542\pi\)
\(882\) 49.9465 1.68179
\(883\) 18.6573 0.627868 0.313934 0.949445i \(-0.398353\pi\)
0.313934 + 0.949445i \(0.398353\pi\)
\(884\) −25.7531 −0.866170
\(885\) 36.8266 1.23791
\(886\) −55.9518 −1.87974
\(887\) −54.8453 −1.84152 −0.920762 0.390125i \(-0.872432\pi\)
−0.920762 + 0.390125i \(0.872432\pi\)
\(888\) −89.5236 −3.00421
\(889\) 20.5726 0.689984
\(890\) −23.0562 −0.772847
\(891\) −4.26936 −0.143029
\(892\) 3.09806 0.103731
\(893\) 54.7693 1.83278
\(894\) −33.4141 −1.11754
\(895\) 39.0007 1.30365
\(896\) 1.56231 0.0521930
\(897\) 2.78290 0.0929184
\(898\) −82.0327 −2.73747
\(899\) 16.0362 0.534837
\(900\) −25.7310 −0.857700
\(901\) 25.3559 0.844729
\(902\) −8.31388 −0.276822
\(903\) −15.3334 −0.510262
\(904\) 63.1829 2.10143
\(905\) 15.2460 0.506793
\(906\) −99.9355 −3.32013
\(907\) 5.91976 0.196562 0.0982812 0.995159i \(-0.468666\pi\)
0.0982812 + 0.995159i \(0.468666\pi\)
\(908\) −31.9929 −1.06172
\(909\) −0.751893 −0.0249387
\(910\) −9.11807 −0.302261
\(911\) 18.5577 0.614844 0.307422 0.951573i \(-0.400534\pi\)
0.307422 + 0.951573i \(0.400534\pi\)
\(912\) 163.119 5.40140
\(913\) 5.75257 0.190382
\(914\) −13.5561 −0.448396
\(915\) −33.8032 −1.11750
\(916\) 76.5261 2.52849
\(917\) 7.94164 0.262256
\(918\) 3.74436 0.123582
\(919\) −15.6685 −0.516856 −0.258428 0.966031i \(-0.583205\pi\)
−0.258428 + 0.966031i \(0.583205\pi\)
\(920\) 7.78653 0.256714
\(921\) −31.3162 −1.03190
\(922\) 4.61720 0.152059
\(923\) 18.3353 0.603513
\(924\) −6.15877 −0.202609
\(925\) 8.28555 0.272427
\(926\) 62.5798 2.05650
\(927\) −44.6205 −1.46553
\(928\) 24.4652 0.803109
\(929\) −17.9017 −0.587337 −0.293669 0.955907i \(-0.594876\pi\)
−0.293669 + 0.955907i \(0.594876\pi\)
\(930\) 76.5435 2.50996
\(931\) 41.8171 1.37050
\(932\) 11.4416 0.374783
\(933\) −18.7535 −0.613960
\(934\) −64.9415 −2.12495
\(935\) −2.63561 −0.0861935
\(936\) 44.3210 1.44868
\(937\) 13.3190 0.435114 0.217557 0.976048i \(-0.430191\pi\)
0.217557 + 0.976048i \(0.430191\pi\)
\(938\) −8.25709 −0.269604
\(939\) 79.3186 2.58846
\(940\) 68.4256 2.23180
\(941\) 24.9670 0.813901 0.406950 0.913450i \(-0.366592\pi\)
0.406950 + 0.913450i \(0.366592\pi\)
\(942\) −32.7663 −1.06758
\(943\) 3.66321 0.119290
\(944\) 75.9741 2.47275
\(945\) 0.935258 0.0304239
\(946\) −8.13305 −0.264428
\(947\) 55.4434 1.80167 0.900835 0.434162i \(-0.142955\pi\)
0.900835 + 0.434162i \(0.142955\pi\)
\(948\) 38.8619 1.26218
\(949\) 2.50431 0.0812933
\(950\) −30.5369 −0.990748
\(951\) −1.45204 −0.0470856
\(952\) −20.7351 −0.672029
\(953\) −14.5306 −0.470692 −0.235346 0.971912i \(-0.575622\pi\)
−0.235346 + 0.971912i \(0.575622\pi\)
\(954\) −74.9128 −2.42539
\(955\) 33.1982 1.07427
\(956\) −65.9331 −2.13243
\(957\) 3.15879 0.102109
\(958\) −13.3142 −0.430162
\(959\) −10.2189 −0.329985
\(960\) 31.6957 1.02297
\(961\) 10.8423 0.349753
\(962\) −24.5003 −0.789920
\(963\) 15.5241 0.500256
\(964\) 112.983 3.63894
\(965\) 17.4288 0.561054
\(966\) 3.84655 0.123761
\(967\) −8.27100 −0.265977 −0.132989 0.991118i \(-0.542457\pi\)
−0.132989 + 0.991118i \(0.542457\pi\)
\(968\) 78.0863 2.50979
\(969\) 49.2080 1.58079
\(970\) 45.0141 1.44532
\(971\) −47.7019 −1.53083 −0.765414 0.643538i \(-0.777466\pi\)
−0.765414 + 0.643538i \(0.777466\pi\)
\(972\) 106.893 3.42861
\(973\) −1.09873 −0.0352236
\(974\) 32.8670 1.05313
\(975\) −7.94262 −0.254368
\(976\) −69.7368 −2.23222
\(977\) −14.1422 −0.452448 −0.226224 0.974075i \(-0.572638\pi\)
−0.226224 + 0.974075i \(0.572638\pi\)
\(978\) −39.6314 −1.26727
\(979\) −2.48265 −0.0793459
\(980\) 52.2439 1.66887
\(981\) 8.51859 0.271978
\(982\) 63.5663 2.02848
\(983\) −14.6631 −0.467681 −0.233841 0.972275i \(-0.575129\pi\)
−0.233841 + 0.972275i \(0.575129\pi\)
\(984\) 112.965 3.60119
\(985\) 49.2021 1.56771
\(986\) 18.2570 0.581423
\(987\) 19.6902 0.626746
\(988\) 63.7022 2.02664
\(989\) 3.58353 0.113950
\(990\) 7.78677 0.247480
\(991\) −14.1814 −0.450487 −0.225244 0.974302i \(-0.572318\pi\)
−0.225244 + 0.974302i \(0.572318\pi\)
\(992\) 63.8356 2.02678
\(993\) 2.83825 0.0900691
\(994\) 25.3432 0.803838
\(995\) 17.8484 0.565833
\(996\) −134.183 −4.25176
\(997\) −2.72541 −0.0863145 −0.0431573 0.999068i \(-0.513742\pi\)
−0.0431573 + 0.999068i \(0.513742\pi\)
\(998\) −8.39642 −0.265784
\(999\) 2.51304 0.0795090
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 \(a_p\))