Properties

Label 619.2.a.b.1.16
Level 619
Weight 2
Character 619.1
Self dual Yes
Analytic conductor 4.943
Analytic rank 0
Dimension 30
CM No

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Newspace parameters

Level: \( N \) = \( 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 619.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(4.94273988512\)
Analytic rank: \(0\)
Dimension: \(30\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 619.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.271769 q^{2} -1.01788 q^{3} -1.92614 q^{4} +4.11968 q^{5} -0.276629 q^{6} +2.70884 q^{7} -1.06700 q^{8} -1.96391 q^{9} +O(q^{10})\) \(q+0.271769 q^{2} -1.01788 q^{3} -1.92614 q^{4} +4.11968 q^{5} -0.276629 q^{6} +2.70884 q^{7} -1.06700 q^{8} -1.96391 q^{9} +1.11960 q^{10} +2.02726 q^{11} +1.96059 q^{12} +1.50165 q^{13} +0.736178 q^{14} -4.19335 q^{15} +3.56230 q^{16} -3.18512 q^{17} -0.533731 q^{18} -6.45131 q^{19} -7.93509 q^{20} -2.75728 q^{21} +0.550946 q^{22} +8.15881 q^{23} +1.08608 q^{24} +11.9718 q^{25} +0.408102 q^{26} +5.05268 q^{27} -5.21761 q^{28} +2.94582 q^{29} -1.13962 q^{30} -0.223792 q^{31} +3.10213 q^{32} -2.06351 q^{33} -0.865616 q^{34} +11.1596 q^{35} +3.78278 q^{36} +11.8677 q^{37} -1.75326 q^{38} -1.52851 q^{39} -4.39571 q^{40} -0.427260 q^{41} -0.749343 q^{42} +2.47041 q^{43} -3.90479 q^{44} -8.09070 q^{45} +2.21731 q^{46} -4.43123 q^{47} -3.62601 q^{48} +0.337810 q^{49} +3.25355 q^{50} +3.24208 q^{51} -2.89239 q^{52} +1.65769 q^{53} +1.37316 q^{54} +8.35166 q^{55} -2.89034 q^{56} +6.56667 q^{57} +0.800584 q^{58} -8.46187 q^{59} +8.07699 q^{60} +5.39744 q^{61} -0.0608198 q^{62} -5.31993 q^{63} -6.28155 q^{64} +6.18633 q^{65} -0.560799 q^{66} -5.24914 q^{67} +6.13499 q^{68} -8.30471 q^{69} +3.03282 q^{70} -3.81688 q^{71} +2.09550 q^{72} +13.1620 q^{73} +3.22527 q^{74} -12.1858 q^{75} +12.4261 q^{76} +5.49152 q^{77} -0.415400 q^{78} +3.12269 q^{79} +14.6756 q^{80} +0.748706 q^{81} -0.116116 q^{82} -17.6721 q^{83} +5.31091 q^{84} -13.1217 q^{85} +0.671381 q^{86} -2.99850 q^{87} -2.16309 q^{88} +4.40165 q^{89} -2.19880 q^{90} +4.06773 q^{91} -15.7150 q^{92} +0.227794 q^{93} -1.20427 q^{94} -26.5773 q^{95} -3.15761 q^{96} -8.58956 q^{97} +0.0918062 q^{98} -3.98136 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + O(q^{10}) \) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + 5q^{10} + 23q^{11} - 6q^{12} + 9q^{13} + 7q^{14} - 2q^{15} + 35q^{16} + 4q^{17} + 10q^{18} - q^{19} + 29q^{20} + 30q^{21} + 4q^{23} + 4q^{24} + 35q^{25} + q^{26} - 5q^{27} - 13q^{28} + 90q^{29} - 31q^{30} + 2q^{31} + 43q^{32} - 6q^{33} - 9q^{34} + 9q^{35} + 33q^{36} + 19q^{37} + 5q^{38} + 32q^{39} - 12q^{40} + 59q^{41} - 25q^{42} - 4q^{43} + 52q^{44} + 30q^{45} - q^{46} + 4q^{47} - 44q^{48} + 30q^{49} + 31q^{50} - 12q^{52} + 34q^{53} - 28q^{54} - 17q^{55} + 2q^{56} - 8q^{57} + 6q^{58} + 13q^{59} - 64q^{60} + 16q^{61} + 28q^{62} - 40q^{63} + 37q^{64} + 31q^{65} - 59q^{66} - 11q^{67} - 52q^{68} + 6q^{69} - 40q^{70} + 42q^{71} + 6q^{72} - 4q^{73} + 16q^{74} - 52q^{75} - 42q^{76} + 29q^{77} - 56q^{78} + 3q^{79} + 21q^{80} + 30q^{81} - 43q^{82} - 11q^{83} - 36q^{84} + 19q^{85} - 11q^{86} - 20q^{87} - 47q^{88} + 58q^{89} - 33q^{90} - 39q^{91} - 7q^{92} - 15q^{93} - 46q^{94} + 23q^{95} - 70q^{96} - 9q^{97} - 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.271769 0.192170 0.0960848 0.995373i \(-0.469368\pi\)
0.0960848 + 0.995373i \(0.469368\pi\)
\(3\) −1.01788 −0.587675 −0.293837 0.955855i \(-0.594932\pi\)
−0.293837 + 0.955855i \(0.594932\pi\)
\(4\) −1.92614 −0.963071
\(5\) 4.11968 1.84238 0.921188 0.389117i \(-0.127220\pi\)
0.921188 + 0.389117i \(0.127220\pi\)
\(6\) −0.276629 −0.112933
\(7\) 2.70884 1.02384 0.511922 0.859032i \(-0.328933\pi\)
0.511922 + 0.859032i \(0.328933\pi\)
\(8\) −1.06700 −0.377243
\(9\) −1.96391 −0.654638
\(10\) 1.11960 0.354049
\(11\) 2.02726 0.611242 0.305621 0.952153i \(-0.401136\pi\)
0.305621 + 0.952153i \(0.401136\pi\)
\(12\) 1.96059 0.565972
\(13\) 1.50165 0.416483 0.208242 0.978077i \(-0.433226\pi\)
0.208242 + 0.978077i \(0.433226\pi\)
\(14\) 0.736178 0.196752
\(15\) −4.19335 −1.08272
\(16\) 3.56230 0.890576
\(17\) −3.18512 −0.772504 −0.386252 0.922393i \(-0.626231\pi\)
−0.386252 + 0.922393i \(0.626231\pi\)
\(18\) −0.533731 −0.125802
\(19\) −6.45131 −1.48003 −0.740015 0.672590i \(-0.765182\pi\)
−0.740015 + 0.672590i \(0.765182\pi\)
\(20\) −7.93509 −1.77434
\(21\) −2.75728 −0.601688
\(22\) 0.550946 0.117462
\(23\) 8.15881 1.70123 0.850614 0.525790i \(-0.176230\pi\)
0.850614 + 0.525790i \(0.176230\pi\)
\(24\) 1.08608 0.221696
\(25\) 11.9718 2.39435
\(26\) 0.408102 0.0800355
\(27\) 5.05268 0.972389
\(28\) −5.21761 −0.986035
\(29\) 2.94582 0.547026 0.273513 0.961868i \(-0.411814\pi\)
0.273513 + 0.961868i \(0.411814\pi\)
\(30\) −1.13962 −0.208066
\(31\) −0.223792 −0.0401943 −0.0200971 0.999798i \(-0.506398\pi\)
−0.0200971 + 0.999798i \(0.506398\pi\)
\(32\) 3.10213 0.548384
\(33\) −2.06351 −0.359211
\(34\) −0.865616 −0.148452
\(35\) 11.1596 1.88631
\(36\) 3.78278 0.630463
\(37\) 11.8677 1.95103 0.975517 0.219924i \(-0.0705810\pi\)
0.975517 + 0.219924i \(0.0705810\pi\)
\(38\) −1.75326 −0.284417
\(39\) −1.52851 −0.244757
\(40\) −4.39571 −0.695023
\(41\) −0.427260 −0.0667267 −0.0333634 0.999443i \(-0.510622\pi\)
−0.0333634 + 0.999443i \(0.510622\pi\)
\(42\) −0.749343 −0.115626
\(43\) 2.47041 0.376734 0.188367 0.982099i \(-0.439681\pi\)
0.188367 + 0.982099i \(0.439681\pi\)
\(44\) −3.90479 −0.588669
\(45\) −8.09070 −1.20609
\(46\) 2.21731 0.326925
\(47\) −4.43123 −0.646361 −0.323181 0.946337i \(-0.604752\pi\)
−0.323181 + 0.946337i \(0.604752\pi\)
\(48\) −3.62601 −0.523369
\(49\) 0.337810 0.0482585
\(50\) 3.25355 0.460122
\(51\) 3.24208 0.453981
\(52\) −2.89239 −0.401103
\(53\) 1.65769 0.227701 0.113851 0.993498i \(-0.463681\pi\)
0.113851 + 0.993498i \(0.463681\pi\)
\(54\) 1.37316 0.186864
\(55\) 8.35166 1.12614
\(56\) −2.89034 −0.386238
\(57\) 6.56667 0.869777
\(58\) 0.800584 0.105122
\(59\) −8.46187 −1.10164 −0.550821 0.834623i \(-0.685685\pi\)
−0.550821 + 0.834623i \(0.685685\pi\)
\(60\) 8.07699 1.04273
\(61\) 5.39744 0.691071 0.345535 0.938406i \(-0.387697\pi\)
0.345535 + 0.938406i \(0.387697\pi\)
\(62\) −0.0608198 −0.00772412
\(63\) −5.31993 −0.670248
\(64\) −6.28155 −0.785193
\(65\) 6.18633 0.767319
\(66\) −0.560799 −0.0690295
\(67\) −5.24914 −0.641285 −0.320642 0.947200i \(-0.603899\pi\)
−0.320642 + 0.947200i \(0.603899\pi\)
\(68\) 6.13499 0.743976
\(69\) −8.30471 −0.999769
\(70\) 3.03282 0.362491
\(71\) −3.81688 −0.452980 −0.226490 0.974013i \(-0.572725\pi\)
−0.226490 + 0.974013i \(0.572725\pi\)
\(72\) 2.09550 0.246958
\(73\) 13.1620 1.54049 0.770247 0.637746i \(-0.220133\pi\)
0.770247 + 0.637746i \(0.220133\pi\)
\(74\) 3.22527 0.374930
\(75\) −12.1858 −1.40710
\(76\) 12.4261 1.42537
\(77\) 5.49152 0.625817
\(78\) −0.415400 −0.0470348
\(79\) 3.12269 0.351330 0.175665 0.984450i \(-0.443792\pi\)
0.175665 + 0.984450i \(0.443792\pi\)
\(80\) 14.6756 1.64078
\(81\) 0.748706 0.0831895
\(82\) −0.116116 −0.0128229
\(83\) −17.6721 −1.93976 −0.969881 0.243581i \(-0.921678\pi\)
−0.969881 + 0.243581i \(0.921678\pi\)
\(84\) 5.31091 0.579468
\(85\) −13.1217 −1.42324
\(86\) 0.671381 0.0723969
\(87\) −2.99850 −0.321473
\(88\) −2.16309 −0.230586
\(89\) 4.40165 0.466574 0.233287 0.972408i \(-0.425052\pi\)
0.233287 + 0.972408i \(0.425052\pi\)
\(90\) −2.19880 −0.231774
\(91\) 4.06773 0.426414
\(92\) −15.7150 −1.63840
\(93\) 0.227794 0.0236212
\(94\) −1.20427 −0.124211
\(95\) −26.5773 −2.72677
\(96\) −3.15761 −0.322272
\(97\) −8.58956 −0.872137 −0.436069 0.899913i \(-0.643630\pi\)
−0.436069 + 0.899913i \(0.643630\pi\)
\(98\) 0.0918062 0.00927383
\(99\) −3.98136 −0.400142
\(100\) −23.0593 −2.30593
\(101\) −12.8755 −1.28116 −0.640582 0.767890i \(-0.721307\pi\)
−0.640582 + 0.767890i \(0.721307\pi\)
\(102\) 0.881096 0.0872415
\(103\) −8.44379 −0.831992 −0.415996 0.909367i \(-0.636567\pi\)
−0.415996 + 0.909367i \(0.636567\pi\)
\(104\) −1.60227 −0.157115
\(105\) −11.3591 −1.10854
\(106\) 0.450509 0.0437573
\(107\) 3.71446 0.359091 0.179545 0.983750i \(-0.442537\pi\)
0.179545 + 0.983750i \(0.442537\pi\)
\(108\) −9.73218 −0.936480
\(109\) −5.27166 −0.504933 −0.252467 0.967606i \(-0.581242\pi\)
−0.252467 + 0.967606i \(0.581242\pi\)
\(110\) 2.26972 0.216409
\(111\) −12.0799 −1.14657
\(112\) 9.64971 0.911812
\(113\) −1.63271 −0.153593 −0.0767963 0.997047i \(-0.524469\pi\)
−0.0767963 + 0.997047i \(0.524469\pi\)
\(114\) 1.78462 0.167145
\(115\) 33.6117 3.13430
\(116\) −5.67407 −0.526825
\(117\) −2.94912 −0.272646
\(118\) −2.29967 −0.211702
\(119\) −8.62797 −0.790925
\(120\) 4.47432 0.408448
\(121\) −6.89022 −0.626384
\(122\) 1.46686 0.132803
\(123\) 0.434900 0.0392136
\(124\) 0.431055 0.0387099
\(125\) 28.7214 2.56892
\(126\) −1.44579 −0.128801
\(127\) 12.2944 1.09095 0.545477 0.838126i \(-0.316348\pi\)
0.545477 + 0.838126i \(0.316348\pi\)
\(128\) −7.91139 −0.699275
\(129\) −2.51459 −0.221397
\(130\) 1.68125 0.147455
\(131\) 10.1547 0.887220 0.443610 0.896220i \(-0.353697\pi\)
0.443610 + 0.896220i \(0.353697\pi\)
\(132\) 3.97462 0.345946
\(133\) −17.4755 −1.51532
\(134\) −1.42655 −0.123235
\(135\) 20.8154 1.79151
\(136\) 3.39853 0.291422
\(137\) 10.5856 0.904388 0.452194 0.891920i \(-0.350642\pi\)
0.452194 + 0.891920i \(0.350642\pi\)
\(138\) −2.25696 −0.192125
\(139\) −22.5766 −1.91493 −0.957463 0.288557i \(-0.906824\pi\)
−0.957463 + 0.288557i \(0.906824\pi\)
\(140\) −21.4949 −1.81665
\(141\) 4.51047 0.379850
\(142\) −1.03731 −0.0870490
\(143\) 3.04424 0.254572
\(144\) −6.99606 −0.583005
\(145\) 12.1359 1.00783
\(146\) 3.57702 0.296036
\(147\) −0.343851 −0.0283603
\(148\) −22.8588 −1.87898
\(149\) 5.66725 0.464279 0.232140 0.972682i \(-0.425427\pi\)
0.232140 + 0.972682i \(0.425427\pi\)
\(150\) −3.31174 −0.270402
\(151\) −0.732899 −0.0596425 −0.0298212 0.999555i \(-0.509494\pi\)
−0.0298212 + 0.999555i \(0.509494\pi\)
\(152\) 6.88357 0.558331
\(153\) 6.25530 0.505711
\(154\) 1.49242 0.120263
\(155\) −0.921952 −0.0740530
\(156\) 2.94412 0.235718
\(157\) −21.3274 −1.70211 −0.851056 0.525075i \(-0.824037\pi\)
−0.851056 + 0.525075i \(0.824037\pi\)
\(158\) 0.848649 0.0675149
\(159\) −1.68733 −0.133814
\(160\) 12.7798 1.01033
\(161\) 22.1009 1.74179
\(162\) 0.203475 0.0159865
\(163\) −11.6678 −0.913894 −0.456947 0.889494i \(-0.651057\pi\)
−0.456947 + 0.889494i \(0.651057\pi\)
\(164\) 0.822963 0.0642626
\(165\) −8.50101 −0.661803
\(166\) −4.80272 −0.372763
\(167\) −21.8480 −1.69065 −0.845326 0.534251i \(-0.820594\pi\)
−0.845326 + 0.534251i \(0.820594\pi\)
\(168\) 2.94203 0.226982
\(169\) −10.7450 −0.826542
\(170\) −3.56606 −0.273504
\(171\) 12.6698 0.968885
\(172\) −4.75836 −0.362822
\(173\) 25.1286 1.91049 0.955246 0.295814i \(-0.0955908\pi\)
0.955246 + 0.295814i \(0.0955908\pi\)
\(174\) −0.814900 −0.0617774
\(175\) 32.4296 2.45145
\(176\) 7.22171 0.544357
\(177\) 8.61319 0.647407
\(178\) 1.19623 0.0896614
\(179\) −13.0245 −0.973497 −0.486749 0.873542i \(-0.661817\pi\)
−0.486749 + 0.873542i \(0.661817\pi\)
\(180\) 15.5838 1.16155
\(181\) 6.85902 0.509827 0.254913 0.966964i \(-0.417953\pi\)
0.254913 + 0.966964i \(0.417953\pi\)
\(182\) 1.10548 0.0819439
\(183\) −5.49396 −0.406125
\(184\) −8.70548 −0.641776
\(185\) 48.8910 3.59454
\(186\) 0.0619074 0.00453927
\(187\) −6.45706 −0.472187
\(188\) 8.53517 0.622492
\(189\) 13.6869 0.995576
\(190\) −7.22289 −0.524003
\(191\) −15.7242 −1.13776 −0.568881 0.822420i \(-0.692624\pi\)
−0.568881 + 0.822420i \(0.692624\pi\)
\(192\) 6.39388 0.461438
\(193\) 6.86553 0.494192 0.247096 0.968991i \(-0.420524\pi\)
0.247096 + 0.968991i \(0.420524\pi\)
\(194\) −2.33438 −0.167598
\(195\) −6.29695 −0.450934
\(196\) −0.650669 −0.0464764
\(197\) −3.53952 −0.252180 −0.126090 0.992019i \(-0.540243\pi\)
−0.126090 + 0.992019i \(0.540243\pi\)
\(198\) −1.08201 −0.0768952
\(199\) −9.80106 −0.694779 −0.347389 0.937721i \(-0.612932\pi\)
−0.347389 + 0.937721i \(0.612932\pi\)
\(200\) −12.7739 −0.903252
\(201\) 5.34301 0.376867
\(202\) −3.49917 −0.246201
\(203\) 7.97976 0.560070
\(204\) −6.24470 −0.437216
\(205\) −1.76017 −0.122936
\(206\) −2.29476 −0.159884
\(207\) −16.0232 −1.11369
\(208\) 5.34934 0.370910
\(209\) −13.0785 −0.904656
\(210\) −3.08705 −0.213027
\(211\) 6.58763 0.453511 0.226756 0.973952i \(-0.427188\pi\)
0.226756 + 0.973952i \(0.427188\pi\)
\(212\) −3.19295 −0.219292
\(213\) 3.88513 0.266205
\(214\) 1.00948 0.0690064
\(215\) 10.1773 0.694086
\(216\) −5.39123 −0.366827
\(217\) −0.606217 −0.0411527
\(218\) −1.43267 −0.0970328
\(219\) −13.3974 −0.905310
\(220\) −16.0865 −1.08455
\(221\) −4.78294 −0.321735
\(222\) −3.28294 −0.220337
\(223\) −2.96678 −0.198670 −0.0993352 0.995054i \(-0.531672\pi\)
−0.0993352 + 0.995054i \(0.531672\pi\)
\(224\) 8.40317 0.561461
\(225\) −23.5115 −1.56743
\(226\) −0.443720 −0.0295158
\(227\) 26.1735 1.73719 0.868597 0.495520i \(-0.165022\pi\)
0.868597 + 0.495520i \(0.165022\pi\)
\(228\) −12.6483 −0.837657
\(229\) −20.7596 −1.37183 −0.685915 0.727681i \(-0.740598\pi\)
−0.685915 + 0.727681i \(0.740598\pi\)
\(230\) 9.13461 0.602318
\(231\) −5.58972 −0.367777
\(232\) −3.14320 −0.206361
\(233\) 15.6978 1.02840 0.514198 0.857672i \(-0.328090\pi\)
0.514198 + 0.857672i \(0.328090\pi\)
\(234\) −0.801478 −0.0523943
\(235\) −18.2552 −1.19084
\(236\) 16.2988 1.06096
\(237\) −3.17853 −0.206468
\(238\) −2.34481 −0.151992
\(239\) −0.453376 −0.0293265 −0.0146632 0.999892i \(-0.504668\pi\)
−0.0146632 + 0.999892i \(0.504668\pi\)
\(240\) −14.9380 −0.964243
\(241\) 20.6853 1.33246 0.666228 0.745748i \(-0.267908\pi\)
0.666228 + 0.745748i \(0.267908\pi\)
\(242\) −1.87255 −0.120372
\(243\) −15.9201 −1.02128
\(244\) −10.3962 −0.665550
\(245\) 1.39167 0.0889104
\(246\) 0.118192 0.00753567
\(247\) −9.68761 −0.616408
\(248\) 0.238787 0.0151630
\(249\) 17.9881 1.13995
\(250\) 7.80559 0.493669
\(251\) −12.1881 −0.769305 −0.384652 0.923062i \(-0.625679\pi\)
−0.384652 + 0.923062i \(0.625679\pi\)
\(252\) 10.2469 0.645496
\(253\) 16.5400 1.03986
\(254\) 3.34125 0.209648
\(255\) 13.3563 0.836405
\(256\) 10.4130 0.650814
\(257\) −12.6889 −0.791509 −0.395754 0.918356i \(-0.629517\pi\)
−0.395754 + 0.918356i \(0.629517\pi\)
\(258\) −0.683387 −0.0425458
\(259\) 32.1476 1.99756
\(260\) −11.9157 −0.738983
\(261\) −5.78535 −0.358104
\(262\) 2.75973 0.170497
\(263\) −9.68316 −0.597089 −0.298545 0.954396i \(-0.596501\pi\)
−0.298545 + 0.954396i \(0.596501\pi\)
\(264\) 2.20177 0.135510
\(265\) 6.82915 0.419512
\(266\) −4.74931 −0.291199
\(267\) −4.48036 −0.274194
\(268\) 10.1106 0.617602
\(269\) 27.2152 1.65934 0.829670 0.558255i \(-0.188529\pi\)
0.829670 + 0.558255i \(0.188529\pi\)
\(270\) 5.65699 0.344273
\(271\) −11.7172 −0.711768 −0.355884 0.934530i \(-0.615820\pi\)
−0.355884 + 0.934530i \(0.615820\pi\)
\(272\) −11.3464 −0.687974
\(273\) −4.14048 −0.250593
\(274\) 2.87683 0.173796
\(275\) 24.2699 1.46353
\(276\) 15.9960 0.962849
\(277\) −9.47889 −0.569531 −0.284766 0.958597i \(-0.591916\pi\)
−0.284766 + 0.958597i \(0.591916\pi\)
\(278\) −6.13563 −0.367991
\(279\) 0.439509 0.0263127
\(280\) −11.9073 −0.711596
\(281\) 3.31339 0.197660 0.0988302 0.995104i \(-0.468490\pi\)
0.0988302 + 0.995104i \(0.468490\pi\)
\(282\) 1.22581 0.0729957
\(283\) −9.04286 −0.537542 −0.268771 0.963204i \(-0.586618\pi\)
−0.268771 + 0.963204i \(0.586618\pi\)
\(284\) 7.35185 0.436252
\(285\) 27.0526 1.60246
\(286\) 0.827329 0.0489210
\(287\) −1.15738 −0.0683178
\(288\) −6.09232 −0.358993
\(289\) −6.85503 −0.403237
\(290\) 3.29815 0.193674
\(291\) 8.74316 0.512533
\(292\) −25.3519 −1.48361
\(293\) −2.54060 −0.148423 −0.0742116 0.997243i \(-0.523644\pi\)
−0.0742116 + 0.997243i \(0.523644\pi\)
\(294\) −0.0934480 −0.00545000
\(295\) −34.8602 −2.02964
\(296\) −12.6629 −0.736013
\(297\) 10.2431 0.594365
\(298\) 1.54018 0.0892204
\(299\) 12.2517 0.708533
\(300\) 23.4717 1.35514
\(301\) 6.69195 0.385717
\(302\) −0.199179 −0.0114615
\(303\) 13.1058 0.752908
\(304\) −22.9815 −1.31808
\(305\) 22.2357 1.27321
\(306\) 1.70000 0.0971823
\(307\) 13.9556 0.796489 0.398245 0.917279i \(-0.369619\pi\)
0.398245 + 0.917279i \(0.369619\pi\)
\(308\) −10.5774 −0.602706
\(309\) 8.59479 0.488941
\(310\) −0.250558 −0.0142307
\(311\) 19.0445 1.07991 0.539957 0.841693i \(-0.318441\pi\)
0.539957 + 0.841693i \(0.318441\pi\)
\(312\) 1.63092 0.0923327
\(313\) −29.7123 −1.67944 −0.839720 0.543019i \(-0.817281\pi\)
−0.839720 + 0.543019i \(0.817281\pi\)
\(314\) −5.79613 −0.327094
\(315\) −21.9164 −1.23485
\(316\) −6.01474 −0.338355
\(317\) −3.87438 −0.217607 −0.108804 0.994063i \(-0.534702\pi\)
−0.108804 + 0.994063i \(0.534702\pi\)
\(318\) −0.458565 −0.0257151
\(319\) 5.97195 0.334365
\(320\) −25.8780 −1.44662
\(321\) −3.78089 −0.211029
\(322\) 6.00634 0.334720
\(323\) 20.5482 1.14333
\(324\) −1.44211 −0.0801174
\(325\) 17.9774 0.997208
\(326\) −3.17095 −0.175623
\(327\) 5.36593 0.296736
\(328\) 0.455888 0.0251722
\(329\) −12.0035 −0.661774
\(330\) −2.31031 −0.127178
\(331\) 12.8804 0.707973 0.353987 0.935250i \(-0.384826\pi\)
0.353987 + 0.935250i \(0.384826\pi\)
\(332\) 34.0389 1.86813
\(333\) −23.3071 −1.27722
\(334\) −5.93762 −0.324892
\(335\) −21.6248 −1.18149
\(336\) −9.82227 −0.535849
\(337\) 12.0646 0.657203 0.328601 0.944469i \(-0.393423\pi\)
0.328601 + 0.944469i \(0.393423\pi\)
\(338\) −2.92017 −0.158836
\(339\) 1.66191 0.0902625
\(340\) 25.2742 1.37068
\(341\) −0.453685 −0.0245684
\(342\) 3.44326 0.186190
\(343\) −18.0468 −0.974436
\(344\) −2.63594 −0.142120
\(345\) −34.2127 −1.84195
\(346\) 6.82917 0.367138
\(347\) 18.5048 0.993392 0.496696 0.867925i \(-0.334546\pi\)
0.496696 + 0.867925i \(0.334546\pi\)
\(348\) 5.77554 0.309602
\(349\) −25.0414 −1.34044 −0.670218 0.742165i \(-0.733799\pi\)
−0.670218 + 0.742165i \(0.733799\pi\)
\(350\) 8.81335 0.471094
\(351\) 7.58737 0.404984
\(352\) 6.28882 0.335195
\(353\) 27.1954 1.44747 0.723733 0.690080i \(-0.242424\pi\)
0.723733 + 0.690080i \(0.242424\pi\)
\(354\) 2.34080 0.124412
\(355\) −15.7243 −0.834560
\(356\) −8.47820 −0.449344
\(357\) 8.78226 0.464807
\(358\) −3.53966 −0.187077
\(359\) 9.97496 0.526458 0.263229 0.964733i \(-0.415212\pi\)
0.263229 + 0.964733i \(0.415212\pi\)
\(360\) 8.63281 0.454989
\(361\) 22.6193 1.19049
\(362\) 1.86407 0.0979733
\(363\) 7.01344 0.368110
\(364\) −7.83503 −0.410667
\(365\) 54.2232 2.83817
\(366\) −1.49309 −0.0780449
\(367\) −5.85006 −0.305371 −0.152685 0.988275i \(-0.548792\pi\)
−0.152685 + 0.988275i \(0.548792\pi\)
\(368\) 29.0642 1.51507
\(369\) 0.839102 0.0436819
\(370\) 13.2871 0.690762
\(371\) 4.49042 0.233131
\(372\) −0.438764 −0.0227488
\(373\) −1.88111 −0.0974002 −0.0487001 0.998813i \(-0.515508\pi\)
−0.0487001 + 0.998813i \(0.515508\pi\)
\(374\) −1.75483 −0.0907400
\(375\) −29.2350 −1.50969
\(376\) 4.72814 0.243835
\(377\) 4.42360 0.227827
\(378\) 3.71968 0.191320
\(379\) −7.65780 −0.393355 −0.196677 0.980468i \(-0.563015\pi\)
−0.196677 + 0.980468i \(0.563015\pi\)
\(380\) 51.1917 2.62608
\(381\) −12.5143 −0.641127
\(382\) −4.27335 −0.218644
\(383\) −6.17114 −0.315331 −0.157665 0.987493i \(-0.550397\pi\)
−0.157665 + 0.987493i \(0.550397\pi\)
\(384\) 8.05287 0.410946
\(385\) 22.6233 1.15299
\(386\) 1.86584 0.0949687
\(387\) −4.85168 −0.246625
\(388\) 16.5447 0.839930
\(389\) −7.08595 −0.359272 −0.179636 0.983733i \(-0.557492\pi\)
−0.179636 + 0.983733i \(0.557492\pi\)
\(390\) −1.71132 −0.0866559
\(391\) −25.9868 −1.31421
\(392\) −0.360444 −0.0182052
\(393\) −10.3363 −0.521397
\(394\) −0.961932 −0.0484614
\(395\) 12.8645 0.647282
\(396\) 7.66867 0.385365
\(397\) −26.6389 −1.33697 −0.668485 0.743726i \(-0.733057\pi\)
−0.668485 + 0.743726i \(0.733057\pi\)
\(398\) −2.66362 −0.133515
\(399\) 17.7881 0.890517
\(400\) 42.6471 2.13235
\(401\) −28.6353 −1.42998 −0.714990 0.699135i \(-0.753569\pi\)
−0.714990 + 0.699135i \(0.753569\pi\)
\(402\) 1.45206 0.0724224
\(403\) −0.336058 −0.0167402
\(404\) 24.8001 1.23385
\(405\) 3.08443 0.153266
\(406\) 2.16865 0.107628
\(407\) 24.0589 1.19255
\(408\) −3.45931 −0.171261
\(409\) 38.0898 1.88342 0.941708 0.336430i \(-0.109220\pi\)
0.941708 + 0.336430i \(0.109220\pi\)
\(410\) −0.478360 −0.0236245
\(411\) −10.7749 −0.531486
\(412\) 16.2639 0.801267
\(413\) −22.9219 −1.12791
\(414\) −4.35461 −0.214017
\(415\) −72.8033 −3.57377
\(416\) 4.65832 0.228393
\(417\) 22.9804 1.12535
\(418\) −3.55432 −0.173848
\(419\) 0.271523 0.0132648 0.00663239 0.999978i \(-0.497889\pi\)
0.00663239 + 0.999978i \(0.497889\pi\)
\(420\) 21.8793 1.06760
\(421\) −21.7211 −1.05862 −0.529312 0.848427i \(-0.677550\pi\)
−0.529312 + 0.848427i \(0.677550\pi\)
\(422\) 1.79031 0.0871511
\(423\) 8.70256 0.423133
\(424\) −1.76876 −0.0858986
\(425\) −38.1315 −1.84965
\(426\) 1.05586 0.0511565
\(427\) 14.6208 0.707550
\(428\) −7.15458 −0.345830
\(429\) −3.09868 −0.149606
\(430\) 2.76588 0.133382
\(431\) −22.9382 −1.10489 −0.552446 0.833549i \(-0.686306\pi\)
−0.552446 + 0.833549i \(0.686306\pi\)
\(432\) 17.9992 0.865987
\(433\) −36.0147 −1.73075 −0.865377 0.501121i \(-0.832921\pi\)
−0.865377 + 0.501121i \(0.832921\pi\)
\(434\) −0.164751 −0.00790830
\(435\) −12.3529 −0.592275
\(436\) 10.1540 0.486286
\(437\) −52.6350 −2.51787
\(438\) −3.64099 −0.173973
\(439\) 37.1522 1.77318 0.886588 0.462559i \(-0.153069\pi\)
0.886588 + 0.462559i \(0.153069\pi\)
\(440\) −8.91125 −0.424827
\(441\) −0.663430 −0.0315919
\(442\) −1.29985 −0.0618277
\(443\) −23.2317 −1.10377 −0.551885 0.833920i \(-0.686091\pi\)
−0.551885 + 0.833920i \(0.686091\pi\)
\(444\) 23.2676 1.10423
\(445\) 18.1334 0.859605
\(446\) −0.806279 −0.0381784
\(447\) −5.76860 −0.272845
\(448\) −17.0157 −0.803916
\(449\) 17.8162 0.840797 0.420398 0.907340i \(-0.361890\pi\)
0.420398 + 0.907340i \(0.361890\pi\)
\(450\) −6.38970 −0.301213
\(451\) −0.866166 −0.0407862
\(452\) 3.14483 0.147920
\(453\) 0.746005 0.0350504
\(454\) 7.11313 0.333836
\(455\) 16.7578 0.785616
\(456\) −7.00666 −0.328117
\(457\) 9.23617 0.432050 0.216025 0.976388i \(-0.430691\pi\)
0.216025 + 0.976388i \(0.430691\pi\)
\(458\) −5.64181 −0.263624
\(459\) −16.0934 −0.751175
\(460\) −64.7408 −3.01856
\(461\) 20.7990 0.968704 0.484352 0.874873i \(-0.339055\pi\)
0.484352 + 0.874873i \(0.339055\pi\)
\(462\) −1.51911 −0.0706755
\(463\) 39.7758 1.84854 0.924268 0.381743i \(-0.124676\pi\)
0.924268 + 0.381743i \(0.124676\pi\)
\(464\) 10.4939 0.487168
\(465\) 0.938439 0.0435191
\(466\) 4.26617 0.197626
\(467\) 32.1310 1.48685 0.743423 0.668821i \(-0.233201\pi\)
0.743423 + 0.668821i \(0.233201\pi\)
\(468\) 5.68042 0.262577
\(469\) −14.2191 −0.656576
\(470\) −4.96121 −0.228844
\(471\) 21.7088 1.00029
\(472\) 9.02885 0.415586
\(473\) 5.00816 0.230276
\(474\) −0.863826 −0.0396768
\(475\) −77.2335 −3.54372
\(476\) 16.6187 0.761717
\(477\) −3.25556 −0.149062
\(478\) −0.123214 −0.00563566
\(479\) 27.9025 1.27490 0.637448 0.770494i \(-0.279990\pi\)
0.637448 + 0.770494i \(0.279990\pi\)
\(480\) −13.0083 −0.593746
\(481\) 17.8211 0.812573
\(482\) 5.62162 0.256058
\(483\) −22.4961 −1.02361
\(484\) 13.2715 0.603252
\(485\) −35.3862 −1.60681
\(486\) −4.32660 −0.196259
\(487\) −22.9609 −1.04046 −0.520229 0.854027i \(-0.674153\pi\)
−0.520229 + 0.854027i \(0.674153\pi\)
\(488\) −5.75908 −0.260701
\(489\) 11.8765 0.537072
\(490\) 0.378212 0.0170859
\(491\) 5.67595 0.256152 0.128076 0.991764i \(-0.459120\pi\)
0.128076 + 0.991764i \(0.459120\pi\)
\(492\) −0.837679 −0.0377655
\(493\) −9.38279 −0.422580
\(494\) −2.63279 −0.118455
\(495\) −16.4019 −0.737213
\(496\) −0.797216 −0.0357961
\(497\) −10.3393 −0.463781
\(498\) 4.88861 0.219064
\(499\) 27.4858 1.23043 0.615216 0.788358i \(-0.289069\pi\)
0.615216 + 0.788358i \(0.289069\pi\)
\(500\) −55.3215 −2.47405
\(501\) 22.2387 0.993553
\(502\) −3.31234 −0.147837
\(503\) −26.0771 −1.16272 −0.581360 0.813647i \(-0.697479\pi\)
−0.581360 + 0.813647i \(0.697479\pi\)
\(504\) 5.67638 0.252846
\(505\) −53.0431 −2.36039
\(506\) 4.49506 0.199830
\(507\) 10.9372 0.485738
\(508\) −23.6808 −1.05067
\(509\) 11.7249 0.519696 0.259848 0.965649i \(-0.416327\pi\)
0.259848 + 0.965649i \(0.416327\pi\)
\(510\) 3.62983 0.160732
\(511\) 35.6537 1.57723
\(512\) 18.6527 0.824342
\(513\) −32.5964 −1.43917
\(514\) −3.44844 −0.152104
\(515\) −34.7857 −1.53284
\(516\) 4.84345 0.213221
\(517\) −8.98325 −0.395083
\(518\) 8.73673 0.383870
\(519\) −25.5780 −1.12275
\(520\) −6.60083 −0.289466
\(521\) −28.3655 −1.24272 −0.621358 0.783526i \(-0.713419\pi\)
−0.621358 + 0.783526i \(0.713419\pi\)
\(522\) −1.57228 −0.0688167
\(523\) 22.9618 1.00405 0.502025 0.864853i \(-0.332589\pi\)
0.502025 + 0.864853i \(0.332589\pi\)
\(524\) −19.5594 −0.854456
\(525\) −33.0095 −1.44065
\(526\) −2.63158 −0.114742
\(527\) 0.712804 0.0310502
\(528\) −7.35086 −0.319905
\(529\) 43.5661 1.89418
\(530\) 1.85595 0.0806174
\(531\) 16.6184 0.721177
\(532\) 33.6604 1.45936
\(533\) −0.641595 −0.0277906
\(534\) −1.21762 −0.0526917
\(535\) 15.3024 0.661580
\(536\) 5.60085 0.241920
\(537\) 13.2574 0.572100
\(538\) 7.39624 0.318875
\(539\) 0.684828 0.0294976
\(540\) −40.0935 −1.72535
\(541\) 7.88327 0.338928 0.169464 0.985536i \(-0.445796\pi\)
0.169464 + 0.985536i \(0.445796\pi\)
\(542\) −3.18437 −0.136780
\(543\) −6.98168 −0.299612
\(544\) −9.88065 −0.423629
\(545\) −21.7175 −0.930277
\(546\) −1.12525 −0.0481564
\(547\) −41.4286 −1.77136 −0.885681 0.464295i \(-0.846308\pi\)
−0.885681 + 0.464295i \(0.846308\pi\)
\(548\) −20.3893 −0.870989
\(549\) −10.6001 −0.452401
\(550\) 6.59580 0.281246
\(551\) −19.0044 −0.809615
\(552\) 8.86115 0.377156
\(553\) 8.45886 0.359707
\(554\) −2.57607 −0.109447
\(555\) −49.7653 −2.11242
\(556\) 43.4858 1.84421
\(557\) −17.2729 −0.731875 −0.365938 0.930639i \(-0.619252\pi\)
−0.365938 + 0.930639i \(0.619252\pi\)
\(558\) 0.119445 0.00505650
\(559\) 3.70970 0.156903
\(560\) 39.7537 1.67990
\(561\) 6.57253 0.277492
\(562\) 0.900477 0.0379843
\(563\) −27.7854 −1.17102 −0.585508 0.810667i \(-0.699105\pi\)
−0.585508 + 0.810667i \(0.699105\pi\)
\(564\) −8.68781 −0.365823
\(565\) −6.72625 −0.282975
\(566\) −2.45757 −0.103299
\(567\) 2.02812 0.0851732
\(568\) 4.07262 0.170883
\(569\) 45.4195 1.90409 0.952043 0.305965i \(-0.0989790\pi\)
0.952043 + 0.305965i \(0.0989790\pi\)
\(570\) 7.35205 0.307944
\(571\) 21.8927 0.916181 0.458090 0.888906i \(-0.348534\pi\)
0.458090 + 0.888906i \(0.348534\pi\)
\(572\) −5.86363 −0.245171
\(573\) 16.0054 0.668635
\(574\) −0.314539 −0.0131286
\(575\) 97.6753 4.07334
\(576\) 12.3364 0.514018
\(577\) −20.0580 −0.835025 −0.417513 0.908671i \(-0.637098\pi\)
−0.417513 + 0.908671i \(0.637098\pi\)
\(578\) −1.86298 −0.0774899
\(579\) −6.98830 −0.290424
\(580\) −23.3754 −0.970609
\(581\) −47.8708 −1.98601
\(582\) 2.37612 0.0984933
\(583\) 3.36057 0.139180
\(584\) −14.0439 −0.581140
\(585\) −12.1494 −0.502317
\(586\) −0.690455 −0.0285224
\(587\) −3.71110 −0.153173 −0.0765867 0.997063i \(-0.524402\pi\)
−0.0765867 + 0.997063i \(0.524402\pi\)
\(588\) 0.662305 0.0273130
\(589\) 1.44375 0.0594888
\(590\) −9.47392 −0.390035
\(591\) 3.60282 0.148200
\(592\) 42.2763 1.73754
\(593\) −37.2399 −1.52926 −0.764630 0.644469i \(-0.777078\pi\)
−0.764630 + 0.644469i \(0.777078\pi\)
\(594\) 2.78376 0.114219
\(595\) −35.5445 −1.45718
\(596\) −10.9159 −0.447134
\(597\) 9.97633 0.408304
\(598\) 3.32963 0.136159
\(599\) 24.9077 1.01770 0.508851 0.860855i \(-0.330070\pi\)
0.508851 + 0.860855i \(0.330070\pi\)
\(600\) 13.0023 0.530818
\(601\) 16.4362 0.670446 0.335223 0.942139i \(-0.391188\pi\)
0.335223 + 0.942139i \(0.391188\pi\)
\(602\) 1.81866 0.0741232
\(603\) 10.3089 0.419809
\(604\) 1.41167 0.0574399
\(605\) −28.3855 −1.15403
\(606\) 3.56175 0.144686
\(607\) −20.9172 −0.849002 −0.424501 0.905428i \(-0.639550\pi\)
−0.424501 + 0.905428i \(0.639550\pi\)
\(608\) −20.0128 −0.811626
\(609\) −8.12246 −0.329139
\(610\) 6.04298 0.244673
\(611\) −6.65416 −0.269199
\(612\) −12.0486 −0.487035
\(613\) −27.9735 −1.12984 −0.564920 0.825146i \(-0.691093\pi\)
−0.564920 + 0.825146i \(0.691093\pi\)
\(614\) 3.79271 0.153061
\(615\) 1.79165 0.0722463
\(616\) −5.85947 −0.236085
\(617\) 3.87299 0.155921 0.0779603 0.996956i \(-0.475159\pi\)
0.0779603 + 0.996956i \(0.475159\pi\)
\(618\) 2.33580 0.0939595
\(619\) 1.00000 0.0401934
\(620\) 1.77581 0.0713183
\(621\) 41.2239 1.65426
\(622\) 5.17570 0.207527
\(623\) 11.9234 0.477699
\(624\) −5.44500 −0.217975
\(625\) 58.4643 2.33857
\(626\) −8.07489 −0.322738
\(627\) 13.3123 0.531644
\(628\) 41.0796 1.63925
\(629\) −37.7999 −1.50718
\(630\) −5.95620 −0.237301
\(631\) 7.23501 0.288021 0.144011 0.989576i \(-0.454000\pi\)
0.144011 + 0.989576i \(0.454000\pi\)
\(632\) −3.33192 −0.132537
\(633\) −6.70544 −0.266517
\(634\) −1.05294 −0.0418175
\(635\) 50.6491 2.00995
\(636\) 3.25004 0.128873
\(637\) 0.507273 0.0200989
\(638\) 1.62299 0.0642548
\(639\) 7.49602 0.296538
\(640\) −32.5924 −1.28833
\(641\) 4.09219 0.161632 0.0808159 0.996729i \(-0.474247\pi\)
0.0808159 + 0.996729i \(0.474247\pi\)
\(642\) −1.02753 −0.0405533
\(643\) −8.79425 −0.346812 −0.173406 0.984850i \(-0.555477\pi\)
−0.173406 + 0.984850i \(0.555477\pi\)
\(644\) −42.5695 −1.67747
\(645\) −10.3593 −0.407897
\(646\) 5.58435 0.219713
\(647\) −6.06021 −0.238252 −0.119126 0.992879i \(-0.538009\pi\)
−0.119126 + 0.992879i \(0.538009\pi\)
\(648\) −0.798872 −0.0313826
\(649\) −17.1544 −0.673369
\(650\) 4.88570 0.191633
\(651\) 0.617058 0.0241844
\(652\) 22.4739 0.880144
\(653\) 39.0372 1.52764 0.763821 0.645428i \(-0.223321\pi\)
0.763821 + 0.645428i \(0.223321\pi\)
\(654\) 1.45829 0.0570238
\(655\) 41.8341 1.63459
\(656\) −1.52203 −0.0594252
\(657\) −25.8490 −1.00847
\(658\) −3.26218 −0.127173
\(659\) 10.4561 0.407312 0.203656 0.979043i \(-0.434718\pi\)
0.203656 + 0.979043i \(0.434718\pi\)
\(660\) 16.3741 0.637363
\(661\) 20.5425 0.799011 0.399505 0.916731i \(-0.369182\pi\)
0.399505 + 0.916731i \(0.369182\pi\)
\(662\) 3.50051 0.136051
\(663\) 4.86847 0.189076
\(664\) 18.8562 0.731761
\(665\) −71.9937 −2.79179
\(666\) −6.33415 −0.245443
\(667\) 24.0344 0.930616
\(668\) 42.0824 1.62822
\(669\) 3.01983 0.116754
\(670\) −5.87694 −0.227046
\(671\) 10.9420 0.422411
\(672\) −8.55345 −0.329956
\(673\) −27.3398 −1.05387 −0.526935 0.849905i \(-0.676659\pi\)
−0.526935 + 0.849905i \(0.676659\pi\)
\(674\) 3.27880 0.126294
\(675\) 60.4895 2.32824
\(676\) 20.6965 0.796018
\(677\) 5.84160 0.224511 0.112256 0.993679i \(-0.464192\pi\)
0.112256 + 0.993679i \(0.464192\pi\)
\(678\) 0.451655 0.0173457
\(679\) −23.2677 −0.892933
\(680\) 14.0009 0.536908
\(681\) −26.6415 −1.02090
\(682\) −0.123297 −0.00472130
\(683\) 37.7715 1.44529 0.722643 0.691222i \(-0.242927\pi\)
0.722643 + 0.691222i \(0.242927\pi\)
\(684\) −24.4039 −0.933105
\(685\) 43.6092 1.66622
\(686\) −4.90456 −0.187257
\(687\) 21.1308 0.806191
\(688\) 8.80036 0.335511
\(689\) 2.48927 0.0948338
\(690\) −9.29796 −0.353967
\(691\) −24.6219 −0.936662 −0.468331 0.883553i \(-0.655145\pi\)
−0.468331 + 0.883553i \(0.655145\pi\)
\(692\) −48.4012 −1.83994
\(693\) −10.7849 −0.409684
\(694\) 5.02904 0.190900
\(695\) −93.0085 −3.52801
\(696\) 3.19941 0.121273
\(697\) 1.36087 0.0515467
\(698\) −6.80547 −0.257591
\(699\) −15.9785 −0.604362
\(700\) −62.4640 −2.36092
\(701\) 27.2724 1.03006 0.515032 0.857171i \(-0.327780\pi\)
0.515032 + 0.857171i \(0.327780\pi\)
\(702\) 2.06201 0.0778256
\(703\) −76.5620 −2.88759
\(704\) −12.7343 −0.479943
\(705\) 18.5817 0.699827
\(706\) 7.39088 0.278159
\(707\) −34.8778 −1.31171
\(708\) −16.5902 −0.623499
\(709\) 24.5199 0.920863 0.460432 0.887695i \(-0.347695\pi\)
0.460432 + 0.887695i \(0.347695\pi\)
\(710\) −4.27338 −0.160377
\(711\) −6.13269 −0.229994
\(712\) −4.69658 −0.176012
\(713\) −1.82588 −0.0683797
\(714\) 2.38675 0.0893217
\(715\) 12.5413 0.469017
\(716\) 25.0870 0.937547
\(717\) 0.461484 0.0172344
\(718\) 2.71088 0.101169
\(719\) −16.1409 −0.601953 −0.300976 0.953632i \(-0.597313\pi\)
−0.300976 + 0.953632i \(0.597313\pi\)
\(720\) −28.8215 −1.07412
\(721\) −22.8729 −0.851830
\(722\) 6.14724 0.228776
\(723\) −21.0552 −0.783051
\(724\) −13.2114 −0.490999
\(725\) 35.2667 1.30977
\(726\) 1.90603 0.0707396
\(727\) 17.1187 0.634898 0.317449 0.948275i \(-0.397174\pi\)
0.317449 + 0.948275i \(0.397174\pi\)
\(728\) −4.34029 −0.160862
\(729\) 13.9587 0.516990
\(730\) 14.7362 0.545410
\(731\) −7.86855 −0.291029
\(732\) 10.5821 0.391127
\(733\) −32.1015 −1.18570 −0.592849 0.805314i \(-0.701997\pi\)
−0.592849 + 0.805314i \(0.701997\pi\)
\(734\) −1.58987 −0.0586830
\(735\) −1.41655 −0.0522504
\(736\) 25.3097 0.932928
\(737\) −10.6414 −0.391980
\(738\) 0.228042 0.00839433
\(739\) −19.1899 −0.705912 −0.352956 0.935640i \(-0.614823\pi\)
−0.352956 + 0.935640i \(0.614823\pi\)
\(740\) −94.1710 −3.46180
\(741\) 9.86086 0.362248
\(742\) 1.22036 0.0448007
\(743\) 22.2557 0.816481 0.408240 0.912874i \(-0.366143\pi\)
0.408240 + 0.912874i \(0.366143\pi\)
\(744\) −0.243057 −0.00891091
\(745\) 23.3473 0.855378
\(746\) −0.511227 −0.0187174
\(747\) 34.7064 1.26984
\(748\) 12.4372 0.454749
\(749\) 10.0619 0.367653
\(750\) −7.94518 −0.290117
\(751\) −40.1503 −1.46511 −0.732553 0.680710i \(-0.761671\pi\)
−0.732553 + 0.680710i \(0.761671\pi\)
\(752\) −15.7854 −0.575634
\(753\) 12.4060 0.452101
\(754\) 1.20220 0.0437815
\(755\) −3.01931 −0.109884
\(756\) −26.3629 −0.958810
\(757\) −6.80057 −0.247171 −0.123586 0.992334i \(-0.539439\pi\)
−0.123586 + 0.992334i \(0.539439\pi\)
\(758\) −2.08115 −0.0755909
\(759\) −16.8358 −0.611101
\(760\) 28.3581 1.02866
\(761\) −10.1297 −0.367202 −0.183601 0.983001i \(-0.558776\pi\)
−0.183601 + 0.983001i \(0.558776\pi\)
\(762\) −3.40100 −0.123205
\(763\) −14.2801 −0.516973
\(764\) 30.2870 1.09575
\(765\) 25.7698 0.931710
\(766\) −1.67713 −0.0605970
\(767\) −12.7068 −0.458815
\(768\) −10.5992 −0.382467
\(769\) 21.5844 0.778355 0.389177 0.921163i \(-0.372759\pi\)
0.389177 + 0.921163i \(0.372759\pi\)
\(770\) 6.14831 0.221570
\(771\) 12.9158 0.465150
\(772\) −13.2240 −0.475942
\(773\) −26.5785 −0.955961 −0.477981 0.878370i \(-0.658631\pi\)
−0.477981 + 0.878370i \(0.658631\pi\)
\(774\) −1.31854 −0.0473938
\(775\) −2.67919 −0.0962392
\(776\) 9.16509 0.329007
\(777\) −32.7225 −1.17391
\(778\) −1.92574 −0.0690412
\(779\) 2.75638 0.0987576
\(780\) 12.1288 0.434282
\(781\) −7.73780 −0.276880
\(782\) −7.06239 −0.252551
\(783\) 14.8843 0.531922
\(784\) 1.20338 0.0429779
\(785\) −87.8621 −3.13593
\(786\) −2.80908 −0.100197
\(787\) 50.0507 1.78412 0.892058 0.451920i \(-0.149261\pi\)
0.892058 + 0.451920i \(0.149261\pi\)
\(788\) 6.81762 0.242868
\(789\) 9.85632 0.350894
\(790\) 3.49616 0.124388
\(791\) −4.42275 −0.157255
\(792\) 4.24813 0.150951
\(793\) 8.10507 0.287820
\(794\) −7.23963 −0.256925
\(795\) −6.95128 −0.246536
\(796\) 18.8782 0.669121
\(797\) −3.05525 −0.108222 −0.0541112 0.998535i \(-0.517233\pi\)
−0.0541112 + 0.998535i \(0.517233\pi\)
\(798\) 4.83424 0.171130
\(799\) 14.1140 0.499317
\(800\) 37.1380 1.31303
\(801\) −8.64447 −0.305437
\(802\) −7.78219 −0.274799
\(803\) 26.6828 0.941614
\(804\) −10.2914 −0.362949
\(805\) 91.0486 3.20904
\(806\) −0.0913301 −0.00321697
\(807\) −27.7019 −0.975152
\(808\) 13.7382 0.483310
\(809\) −47.5999 −1.67352 −0.836762 0.547567i \(-0.815554\pi\)
−0.836762 + 0.547567i \(0.815554\pi\)
\(810\) 0.838252 0.0294532
\(811\) 30.2343 1.06167 0.530834 0.847476i \(-0.321879\pi\)
0.530834 + 0.847476i \(0.321879\pi\)
\(812\) −15.3702 −0.539387
\(813\) 11.9267 0.418288
\(814\) 6.53845 0.229173
\(815\) −48.0677 −1.68374
\(816\) 11.5493 0.404305
\(817\) −15.9374 −0.557578
\(818\) 10.3516 0.361936
\(819\) −7.98868 −0.279147
\(820\) 3.39034 0.118396
\(821\) 41.0622 1.43308 0.716541 0.697545i \(-0.245724\pi\)
0.716541 + 0.697545i \(0.245724\pi\)
\(822\) −2.92828 −0.102135
\(823\) −17.2687 −0.601949 −0.300975 0.953632i \(-0.597312\pi\)
−0.300975 + 0.953632i \(0.597312\pi\)
\(824\) 9.00956 0.313863
\(825\) −24.7039 −0.860079
\(826\) −6.22945 −0.216750
\(827\) 14.1870 0.493329 0.246665 0.969101i \(-0.420665\pi\)
0.246665 + 0.969101i \(0.420665\pi\)
\(828\) 30.8630 1.07256
\(829\) 54.6423 1.89780 0.948902 0.315570i \(-0.102196\pi\)
0.948902 + 0.315570i \(0.102196\pi\)
\(830\) −19.7857 −0.686771
\(831\) 9.64839 0.334699
\(832\) −9.43270 −0.327020
\(833\) −1.07596 −0.0372799
\(834\) 6.24535 0.216259
\(835\) −90.0069 −3.11482
\(836\) 25.1910 0.871248
\(837\) −1.13075 −0.0390845
\(838\) 0.0737916 0.00254909
\(839\) −37.6067 −1.29833 −0.649164 0.760648i \(-0.724881\pi\)
−0.649164 + 0.760648i \(0.724881\pi\)
\(840\) 12.1202 0.418187
\(841\) −20.3221 −0.700763
\(842\) −5.90313 −0.203435
\(843\) −3.37264 −0.116160
\(844\) −12.6887 −0.436764
\(845\) −44.2661 −1.52280
\(846\) 2.36508 0.0813133
\(847\) −18.6645 −0.641320
\(848\) 5.90520 0.202785
\(849\) 9.20457 0.315900
\(850\) −10.3629 −0.355446
\(851\) 96.8261 3.31916
\(852\) −7.48332 −0.256374
\(853\) −35.9729 −1.23169 −0.615844 0.787868i \(-0.711185\pi\)
−0.615844 + 0.787868i \(0.711185\pi\)
\(854\) 3.97348 0.135970
\(855\) 52.1956 1.78505
\(856\) −3.96335 −0.135464
\(857\) 14.8445 0.507078 0.253539 0.967325i \(-0.418405\pi\)
0.253539 + 0.967325i \(0.418405\pi\)
\(858\) −0.842124 −0.0287496
\(859\) 34.1604 1.16554 0.582769 0.812638i \(-0.301969\pi\)
0.582769 + 0.812638i \(0.301969\pi\)
\(860\) −19.6029 −0.668454
\(861\) 1.17807 0.0401487
\(862\) −6.23388 −0.212327
\(863\) 27.9265 0.950630 0.475315 0.879816i \(-0.342334\pi\)
0.475315 + 0.879816i \(0.342334\pi\)
\(864\) 15.6741 0.533243
\(865\) 103.522 3.51984
\(866\) −9.78767 −0.332599
\(867\) 6.97762 0.236972
\(868\) 1.16766 0.0396330
\(869\) 6.33049 0.214747
\(870\) −3.35713 −0.113817
\(871\) −7.88238 −0.267084
\(872\) 5.62488 0.190482
\(873\) 16.8692 0.570935
\(874\) −14.3045 −0.483859
\(875\) 77.8017 2.63018
\(876\) 25.8052 0.871877
\(877\) −11.3007 −0.381598 −0.190799 0.981629i \(-0.561108\pi\)
−0.190799 + 0.981629i \(0.561108\pi\)
\(878\) 10.0968 0.340751
\(879\) 2.58603 0.0872246
\(880\) 29.7512 1.00291
\(881\) −9.82922 −0.331155 −0.165577 0.986197i \(-0.552949\pi\)
−0.165577 + 0.986197i \(0.552949\pi\)
\(882\) −0.180300 −0.00607100
\(883\) 21.7118 0.730660 0.365330 0.930878i \(-0.380956\pi\)
0.365330 + 0.930878i \(0.380956\pi\)
\(884\) 9.21261 0.309854
\(885\) 35.4836 1.19277
\(886\) −6.31365 −0.212111
\(887\) 10.5742 0.355047 0.177523 0.984117i \(-0.443191\pi\)
0.177523 + 0.984117i \(0.443191\pi\)
\(888\) 12.8893 0.432536
\(889\) 33.3036 1.11697
\(890\) 4.92809 0.165190
\(891\) 1.51782 0.0508489
\(892\) 5.71444 0.191334
\(893\) 28.5872 0.956635
\(894\) −1.56773 −0.0524326
\(895\) −53.6568 −1.79355
\(896\) −21.4307 −0.715949
\(897\) −12.4708 −0.416387
\(898\) 4.84188 0.161576
\(899\) −0.659252 −0.0219873
\(900\) 45.2865 1.50955
\(901\) −5.27994 −0.175900
\(902\) −0.235397 −0.00783786
\(903\) −6.81162 −0.226676
\(904\) 1.74211 0.0579417
\(905\) 28.2570 0.939293
\(906\) 0.202741 0.00673562
\(907\) 19.1504 0.635878 0.317939 0.948111i \(-0.397009\pi\)
0.317939 + 0.948111i \(0.397009\pi\)
\(908\) −50.4138 −1.67304
\(909\) 25.2865 0.838699
\(910\) 4.55424 0.150972
\(911\) −54.1932 −1.79550 −0.897750 0.440506i \(-0.854799\pi\)
−0.897750 + 0.440506i \(0.854799\pi\)
\(912\) 23.3925 0.774603
\(913\) −35.8259 −1.18566
\(914\) 2.51010 0.0830269
\(915\) −22.6333 −0.748235
\(916\) 39.9859 1.32117
\(917\) 27.5075 0.908376
\(918\) −4.37368 −0.144353
\(919\) −23.0702 −0.761015 −0.380508 0.924778i \(-0.624251\pi\)
−0.380508 + 0.924778i \(0.624251\pi\)
\(920\) −35.8638 −1.18239
\(921\) −14.2052 −0.468077
\(922\) 5.65251 0.186156
\(923\) −5.73162 −0.188659
\(924\) 10.7666 0.354195
\(925\) 142.077 4.67146
\(926\) 10.8098 0.355233
\(927\) 16.5829 0.544654
\(928\) 9.13833 0.299980
\(929\) −8.64908 −0.283767 −0.141884 0.989883i \(-0.545316\pi\)
−0.141884 + 0.989883i \(0.545316\pi\)
\(930\) 0.255039 0.00836305
\(931\) −2.17931 −0.0714241
\(932\) −30.2361 −0.990418
\(933\) −19.3850 −0.634638
\(934\) 8.73221 0.285727
\(935\) −26.6010 −0.869946
\(936\) 3.14672 0.102854
\(937\) 14.5679 0.475912 0.237956 0.971276i \(-0.423523\pi\)
0.237956 + 0.971276i \(0.423523\pi\)
\(938\) −3.86430 −0.126174
\(939\) 30.2437 0.986965
\(940\) 35.1622 1.14686
\(941\) 11.0975 0.361767 0.180883 0.983505i \(-0.442104\pi\)
0.180883 + 0.983505i \(0.442104\pi\)
\(942\) 5.89978 0.192225
\(943\) −3.48593 −0.113517
\(944\) −30.1438 −0.981096
\(945\) 56.3857 1.83423
\(946\) 1.36106 0.0442520
\(947\) 38.9764 1.26656 0.633281 0.773922i \(-0.281708\pi\)
0.633281 + 0.773922i \(0.281708\pi\)
\(948\) 6.12230 0.198843
\(949\) 19.7647 0.641590
\(950\) −20.9897 −0.680995
\(951\) 3.94367 0.127882
\(952\) 9.20607 0.298371
\(953\) 34.5149 1.11805 0.559024 0.829151i \(-0.311176\pi\)
0.559024 + 0.829151i \(0.311176\pi\)
\(954\) −0.884761 −0.0286452
\(955\) −64.7786 −2.09619
\(956\) 0.873266 0.0282435
\(957\) −6.07874 −0.196498
\(958\) 7.58302 0.244996
\(959\) 28.6747 0.925953
\(960\) 26.3407 0.850143
\(961\) −30.9499 −0.998384
\(962\) 4.84323 0.156152
\(963\) −7.29489 −0.235075
\(964\) −39.8428 −1.28325
\(965\) 28.2838 0.910487
\(966\) −6.11375 −0.196707
\(967\) −37.1460 −1.19454 −0.597268 0.802042i \(-0.703747\pi\)
−0.597268 + 0.802042i \(0.703747\pi\)
\(968\) 7.35189 0.236299
\(969\) −20.9156 −0.671907
\(970\) −9.61688 −0.308779
\(971\) 35.7713 1.14796 0.573978 0.818871i \(-0.305399\pi\)
0.573978 + 0.818871i \(0.305399\pi\)
\(972\) 30.6645 0.983563
\(973\) −61.1565 −1.96059
\(974\) −6.24006 −0.199944
\(975\) −18.2989 −0.586034
\(976\) 19.2273 0.615451
\(977\) −38.8879 −1.24414 −0.622068 0.782964i \(-0.713707\pi\)
−0.622068 + 0.782964i \(0.713707\pi\)
\(978\) 3.22765 0.103209
\(979\) 8.92329 0.285189
\(980\) −2.68055 −0.0856270
\(981\) 10.3531 0.330549
\(982\) 1.54255 0.0492246
\(983\) 30.9773 0.988023 0.494012 0.869455i \(-0.335530\pi\)
0.494012 + 0.869455i \(0.335530\pi\)
\(984\) −0.464040 −0.0147931
\(985\) −14.5817 −0.464611
\(986\) −2.54995 −0.0812070
\(987\) 12.2181 0.388908
\(988\) 18.6597 0.593645
\(989\) 20.1556 0.640911
\(990\) −4.45754 −0.141670
\(991\) 32.2781 1.02535 0.512674 0.858583i \(-0.328655\pi\)
0.512674 + 0.858583i \(0.328655\pi\)
\(992\) −0.694233 −0.0220419
\(993\) −13.1108 −0.416058
\(994\) −2.80990 −0.0891247
\(995\) −40.3772 −1.28004
\(996\) −34.6476 −1.09785
\(997\) 9.50712 0.301094 0.150547 0.988603i \(-0.451897\pi\)
0.150547 + 0.988603i \(0.451897\pi\)
\(998\) 7.46978 0.236452
\(999\) 59.9636 1.89716
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 \(a_p\))