Properties

Label 8018.2.a.f.1.18
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 34
CM No

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Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(34\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -0.358038 q^{3} +1.00000 q^{4} +3.12453 q^{5} +0.358038 q^{6} -3.38298 q^{7} -1.00000 q^{8} -2.87181 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -0.358038 q^{3} +1.00000 q^{4} +3.12453 q^{5} +0.358038 q^{6} -3.38298 q^{7} -1.00000 q^{8} -2.87181 q^{9} -3.12453 q^{10} -3.00081 q^{11} -0.358038 q^{12} +5.58343 q^{13} +3.38298 q^{14} -1.11870 q^{15} +1.00000 q^{16} +0.615120 q^{17} +2.87181 q^{18} -1.00000 q^{19} +3.12453 q^{20} +1.21123 q^{21} +3.00081 q^{22} +7.17487 q^{23} +0.358038 q^{24} +4.76266 q^{25} -5.58343 q^{26} +2.10233 q^{27} -3.38298 q^{28} -1.35524 q^{29} +1.11870 q^{30} -6.18047 q^{31} -1.00000 q^{32} +1.07440 q^{33} -0.615120 q^{34} -10.5702 q^{35} -2.87181 q^{36} +4.34611 q^{37} +1.00000 q^{38} -1.99908 q^{39} -3.12453 q^{40} -4.36696 q^{41} -1.21123 q^{42} -1.24575 q^{43} -3.00081 q^{44} -8.97304 q^{45} -7.17487 q^{46} -6.56595 q^{47} -0.358038 q^{48} +4.44452 q^{49} -4.76266 q^{50} -0.220236 q^{51} +5.58343 q^{52} +2.38333 q^{53} -2.10233 q^{54} -9.37610 q^{55} +3.38298 q^{56} +0.358038 q^{57} +1.35524 q^{58} -0.0783359 q^{59} -1.11870 q^{60} -11.8770 q^{61} +6.18047 q^{62} +9.71526 q^{63} +1.00000 q^{64} +17.4456 q^{65} -1.07440 q^{66} +1.93235 q^{67} +0.615120 q^{68} -2.56887 q^{69} +10.5702 q^{70} -8.93518 q^{71} +2.87181 q^{72} +2.99156 q^{73} -4.34611 q^{74} -1.70521 q^{75} -1.00000 q^{76} +10.1517 q^{77} +1.99908 q^{78} +4.20610 q^{79} +3.12453 q^{80} +7.86271 q^{81} +4.36696 q^{82} +7.46260 q^{83} +1.21123 q^{84} +1.92196 q^{85} +1.24575 q^{86} +0.485227 q^{87} +3.00081 q^{88} +4.41557 q^{89} +8.97304 q^{90} -18.8886 q^{91} +7.17487 q^{92} +2.21284 q^{93} +6.56595 q^{94} -3.12453 q^{95} +0.358038 q^{96} +13.5539 q^{97} -4.44452 q^{98} +8.61775 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 34q^{2} - 10q^{3} + 34q^{4} + 7q^{5} + 10q^{6} - 6q^{7} - 34q^{8} + 38q^{9} + O(q^{10}) \) \( 34q - 34q^{2} - 10q^{3} + 34q^{4} + 7q^{5} + 10q^{6} - 6q^{7} - 34q^{8} + 38q^{9} - 7q^{10} + 4q^{11} - 10q^{12} - 5q^{13} + 6q^{14} - 17q^{15} + 34q^{16} + 8q^{17} - 38q^{18} - 34q^{19} + 7q^{20} - 4q^{22} - 24q^{23} + 10q^{24} + 5q^{25} + 5q^{26} - 31q^{27} - 6q^{28} + 24q^{29} + 17q^{30} - 28q^{31} - 34q^{32} - 16q^{33} - 8q^{34} + 2q^{35} + 38q^{36} - 36q^{37} + 34q^{38} - 9q^{39} - 7q^{40} + 9q^{41} - 24q^{43} + 4q^{44} + 22q^{45} + 24q^{46} - 29q^{47} - 10q^{48} + 22q^{49} - 5q^{50} - 21q^{51} - 5q^{52} - 9q^{53} + 31q^{54} - 28q^{55} + 6q^{56} + 10q^{57} - 24q^{58} - 28q^{59} - 17q^{60} + 23q^{61} + 28q^{62} - 27q^{63} + 34q^{64} - 6q^{65} + 16q^{66} - 51q^{67} + 8q^{68} - 17q^{69} - 2q^{70} - 31q^{71} - 38q^{72} - 26q^{73} + 36q^{74} - 109q^{75} - 34q^{76} - 28q^{77} + 9q^{78} - 36q^{79} + 7q^{80} + 6q^{81} - 9q^{82} - 10q^{83} - 32q^{85} + 24q^{86} - 8q^{87} - 4q^{88} - 34q^{89} - 22q^{90} - 41q^{91} - 24q^{92} - 33q^{93} + 29q^{94} - 7q^{95} + 10q^{96} - 56q^{97} - 22q^{98} - 28q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −0.358038 −0.206713 −0.103357 0.994644i \(-0.532958\pi\)
−0.103357 + 0.994644i \(0.532958\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.12453 1.39733 0.698665 0.715449i \(-0.253778\pi\)
0.698665 + 0.715449i \(0.253778\pi\)
\(6\) 0.358038 0.146168
\(7\) −3.38298 −1.27864 −0.639322 0.768939i \(-0.720785\pi\)
−0.639322 + 0.768939i \(0.720785\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.87181 −0.957270
\(10\) −3.12453 −0.988062
\(11\) −3.00081 −0.904778 −0.452389 0.891821i \(-0.649428\pi\)
−0.452389 + 0.891821i \(0.649428\pi\)
\(12\) −0.358038 −0.103357
\(13\) 5.58343 1.54856 0.774282 0.632841i \(-0.218111\pi\)
0.774282 + 0.632841i \(0.218111\pi\)
\(14\) 3.38298 0.904138
\(15\) −1.11870 −0.288847
\(16\) 1.00000 0.250000
\(17\) 0.615120 0.149188 0.0745942 0.997214i \(-0.476234\pi\)
0.0745942 + 0.997214i \(0.476234\pi\)
\(18\) 2.87181 0.676892
\(19\) −1.00000 −0.229416
\(20\) 3.12453 0.698665
\(21\) 1.21123 0.264313
\(22\) 3.00081 0.639774
\(23\) 7.17487 1.49606 0.748032 0.663663i \(-0.230999\pi\)
0.748032 + 0.663663i \(0.230999\pi\)
\(24\) 0.358038 0.0730841
\(25\) 4.76266 0.952532
\(26\) −5.58343 −1.09500
\(27\) 2.10233 0.404593
\(28\) −3.38298 −0.639322
\(29\) −1.35524 −0.251662 −0.125831 0.992052i \(-0.540160\pi\)
−0.125831 + 0.992052i \(0.540160\pi\)
\(30\) 1.11870 0.204245
\(31\) −6.18047 −1.11004 −0.555022 0.831835i \(-0.687290\pi\)
−0.555022 + 0.831835i \(0.687290\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.07440 0.187029
\(34\) −0.615120 −0.105492
\(35\) −10.5702 −1.78669
\(36\) −2.87181 −0.478635
\(37\) 4.34611 0.714497 0.357248 0.934009i \(-0.383715\pi\)
0.357248 + 0.934009i \(0.383715\pi\)
\(38\) 1.00000 0.162221
\(39\) −1.99908 −0.320109
\(40\) −3.12453 −0.494031
\(41\) −4.36696 −0.682005 −0.341002 0.940062i \(-0.610766\pi\)
−0.341002 + 0.940062i \(0.610766\pi\)
\(42\) −1.21123 −0.186897
\(43\) −1.24575 −0.189975 −0.0949876 0.995478i \(-0.530281\pi\)
−0.0949876 + 0.995478i \(0.530281\pi\)
\(44\) −3.00081 −0.452389
\(45\) −8.97304 −1.33762
\(46\) −7.17487 −1.05788
\(47\) −6.56595 −0.957742 −0.478871 0.877885i \(-0.658954\pi\)
−0.478871 + 0.877885i \(0.658954\pi\)
\(48\) −0.358038 −0.0516783
\(49\) 4.44452 0.634932
\(50\) −4.76266 −0.673542
\(51\) −0.220236 −0.0308392
\(52\) 5.58343 0.774282
\(53\) 2.38333 0.327376 0.163688 0.986512i \(-0.447661\pi\)
0.163688 + 0.986512i \(0.447661\pi\)
\(54\) −2.10233 −0.286091
\(55\) −9.37610 −1.26427
\(56\) 3.38298 0.452069
\(57\) 0.358038 0.0474233
\(58\) 1.35524 0.177952
\(59\) −0.0783359 −0.0101985 −0.00509923 0.999987i \(-0.501623\pi\)
−0.00509923 + 0.999987i \(0.501623\pi\)
\(60\) −1.11870 −0.144423
\(61\) −11.8770 −1.52069 −0.760346 0.649519i \(-0.774970\pi\)
−0.760346 + 0.649519i \(0.774970\pi\)
\(62\) 6.18047 0.784920
\(63\) 9.71526 1.22401
\(64\) 1.00000 0.125000
\(65\) 17.4456 2.16386
\(66\) −1.07440 −0.132250
\(67\) 1.93235 0.236074 0.118037 0.993009i \(-0.462340\pi\)
0.118037 + 0.993009i \(0.462340\pi\)
\(68\) 0.615120 0.0745942
\(69\) −2.56887 −0.309256
\(70\) 10.5702 1.26338
\(71\) −8.93518 −1.06041 −0.530205 0.847869i \(-0.677885\pi\)
−0.530205 + 0.847869i \(0.677885\pi\)
\(72\) 2.87181 0.338446
\(73\) 2.99156 0.350136 0.175068 0.984556i \(-0.443986\pi\)
0.175068 + 0.984556i \(0.443986\pi\)
\(74\) −4.34611 −0.505225
\(75\) −1.70521 −0.196901
\(76\) −1.00000 −0.114708
\(77\) 10.1517 1.15689
\(78\) 1.99908 0.226351
\(79\) 4.20610 0.473223 0.236611 0.971604i \(-0.423963\pi\)
0.236611 + 0.971604i \(0.423963\pi\)
\(80\) 3.12453 0.349333
\(81\) 7.86271 0.873635
\(82\) 4.36696 0.482250
\(83\) 7.46260 0.819127 0.409564 0.912282i \(-0.365681\pi\)
0.409564 + 0.912282i \(0.365681\pi\)
\(84\) 1.21123 0.132156
\(85\) 1.92196 0.208465
\(86\) 1.24575 0.134333
\(87\) 0.485227 0.0520218
\(88\) 3.00081 0.319887
\(89\) 4.41557 0.468050 0.234025 0.972231i \(-0.424810\pi\)
0.234025 + 0.972231i \(0.424810\pi\)
\(90\) 8.97304 0.945841
\(91\) −18.8886 −1.98006
\(92\) 7.17487 0.748032
\(93\) 2.21284 0.229461
\(94\) 6.56595 0.677226
\(95\) −3.12453 −0.320570
\(96\) 0.358038 0.0365421
\(97\) 13.5539 1.37619 0.688096 0.725620i \(-0.258447\pi\)
0.688096 + 0.725620i \(0.258447\pi\)
\(98\) −4.44452 −0.448965
\(99\) 8.61775 0.866116
\(100\) 4.76266 0.476266
\(101\) 2.45726 0.244506 0.122253 0.992499i \(-0.460988\pi\)
0.122253 + 0.992499i \(0.460988\pi\)
\(102\) 0.220236 0.0218066
\(103\) −7.74280 −0.762921 −0.381461 0.924385i \(-0.624579\pi\)
−0.381461 + 0.924385i \(0.624579\pi\)
\(104\) −5.58343 −0.547500
\(105\) 3.78453 0.369332
\(106\) −2.38333 −0.231490
\(107\) 9.74932 0.942502 0.471251 0.881999i \(-0.343803\pi\)
0.471251 + 0.881999i \(0.343803\pi\)
\(108\) 2.10233 0.202297
\(109\) −1.84992 −0.177191 −0.0885953 0.996068i \(-0.528238\pi\)
−0.0885953 + 0.996068i \(0.528238\pi\)
\(110\) 9.37610 0.893976
\(111\) −1.55607 −0.147696
\(112\) −3.38298 −0.319661
\(113\) −10.8551 −1.02117 −0.510583 0.859828i \(-0.670570\pi\)
−0.510583 + 0.859828i \(0.670570\pi\)
\(114\) −0.358038 −0.0335333
\(115\) 22.4181 2.09049
\(116\) −1.35524 −0.125831
\(117\) −16.0345 −1.48239
\(118\) 0.0783359 0.00721140
\(119\) −2.08093 −0.190759
\(120\) 1.11870 0.102123
\(121\) −1.99515 −0.181377
\(122\) 11.8770 1.07529
\(123\) 1.56354 0.140979
\(124\) −6.18047 −0.555022
\(125\) −0.741577 −0.0663287
\(126\) −9.71526 −0.865504
\(127\) 3.98375 0.353500 0.176750 0.984256i \(-0.443442\pi\)
0.176750 + 0.984256i \(0.443442\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0.446026 0.0392704
\(130\) −17.4456 −1.53008
\(131\) −3.90039 −0.340779 −0.170389 0.985377i \(-0.554503\pi\)
−0.170389 + 0.985377i \(0.554503\pi\)
\(132\) 1.07440 0.0935147
\(133\) 3.38298 0.293341
\(134\) −1.93235 −0.166929
\(135\) 6.56878 0.565351
\(136\) −0.615120 −0.0527461
\(137\) −4.07235 −0.347925 −0.173962 0.984752i \(-0.555657\pi\)
−0.173962 + 0.984752i \(0.555657\pi\)
\(138\) 2.56887 0.218677
\(139\) −5.65075 −0.479290 −0.239645 0.970861i \(-0.577031\pi\)
−0.239645 + 0.970861i \(0.577031\pi\)
\(140\) −10.5702 −0.893344
\(141\) 2.35086 0.197978
\(142\) 8.93518 0.749823
\(143\) −16.7548 −1.40111
\(144\) −2.87181 −0.239317
\(145\) −4.23448 −0.351655
\(146\) −2.99156 −0.247583
\(147\) −1.59131 −0.131249
\(148\) 4.34611 0.357248
\(149\) 4.46885 0.366103 0.183051 0.983103i \(-0.441403\pi\)
0.183051 + 0.983103i \(0.441403\pi\)
\(150\) 1.70521 0.139230
\(151\) −3.01879 −0.245665 −0.122833 0.992427i \(-0.539198\pi\)
−0.122833 + 0.992427i \(0.539198\pi\)
\(152\) 1.00000 0.0811107
\(153\) −1.76651 −0.142814
\(154\) −10.1517 −0.818044
\(155\) −19.3110 −1.55110
\(156\) −1.99908 −0.160054
\(157\) 14.3364 1.14417 0.572084 0.820195i \(-0.306135\pi\)
0.572084 + 0.820195i \(0.306135\pi\)
\(158\) −4.20610 −0.334619
\(159\) −0.853324 −0.0676730
\(160\) −3.12453 −0.247015
\(161\) −24.2724 −1.91293
\(162\) −7.86271 −0.617753
\(163\) −16.1862 −1.26780 −0.633902 0.773413i \(-0.718548\pi\)
−0.633902 + 0.773413i \(0.718548\pi\)
\(164\) −4.36696 −0.341002
\(165\) 3.35700 0.261342
\(166\) −7.46260 −0.579210
\(167\) −16.2282 −1.25578 −0.627888 0.778304i \(-0.716080\pi\)
−0.627888 + 0.778304i \(0.716080\pi\)
\(168\) −1.21123 −0.0934486
\(169\) 18.1747 1.39805
\(170\) −1.92196 −0.147407
\(171\) 2.87181 0.219613
\(172\) −1.24575 −0.0949876
\(173\) 12.7558 0.969804 0.484902 0.874568i \(-0.338855\pi\)
0.484902 + 0.874568i \(0.338855\pi\)
\(174\) −0.485227 −0.0367850
\(175\) −16.1120 −1.21795
\(176\) −3.00081 −0.226194
\(177\) 0.0280472 0.00210816
\(178\) −4.41557 −0.330961
\(179\) −4.28228 −0.320073 −0.160036 0.987111i \(-0.551161\pi\)
−0.160036 + 0.987111i \(0.551161\pi\)
\(180\) −8.97304 −0.668811
\(181\) −0.0191058 −0.00142012 −0.000710061 1.00000i \(-0.500226\pi\)
−0.000710061 1.00000i \(0.500226\pi\)
\(182\) 18.8886 1.40012
\(183\) 4.25241 0.314347
\(184\) −7.17487 −0.528938
\(185\) 13.5795 0.998388
\(186\) −2.21284 −0.162253
\(187\) −1.84586 −0.134982
\(188\) −6.56595 −0.478871
\(189\) −7.11213 −0.517331
\(190\) 3.12453 0.226677
\(191\) −27.2759 −1.97361 −0.986807 0.161903i \(-0.948237\pi\)
−0.986807 + 0.161903i \(0.948237\pi\)
\(192\) −0.358038 −0.0258391
\(193\) −17.1033 −1.23113 −0.615563 0.788088i \(-0.711071\pi\)
−0.615563 + 0.788088i \(0.711071\pi\)
\(194\) −13.5539 −0.973115
\(195\) −6.24617 −0.447297
\(196\) 4.44452 0.317466
\(197\) −6.67123 −0.475305 −0.237653 0.971350i \(-0.576378\pi\)
−0.237653 + 0.971350i \(0.576378\pi\)
\(198\) −8.61775 −0.612437
\(199\) −11.7554 −0.833321 −0.416661 0.909062i \(-0.636800\pi\)
−0.416661 + 0.909062i \(0.636800\pi\)
\(200\) −4.76266 −0.336771
\(201\) −0.691853 −0.0487996
\(202\) −2.45726 −0.172892
\(203\) 4.58475 0.321786
\(204\) −0.220236 −0.0154196
\(205\) −13.6447 −0.952986
\(206\) 7.74280 0.539467
\(207\) −20.6048 −1.43214
\(208\) 5.58343 0.387141
\(209\) 3.00081 0.207570
\(210\) −3.78453 −0.261157
\(211\) −1.00000 −0.0688428
\(212\) 2.38333 0.163688
\(213\) 3.19913 0.219201
\(214\) −9.74932 −0.666450
\(215\) −3.89238 −0.265458
\(216\) −2.10233 −0.143045
\(217\) 20.9084 1.41935
\(218\) 1.84992 0.125293
\(219\) −1.07109 −0.0723776
\(220\) −9.37610 −0.632137
\(221\) 3.43448 0.231028
\(222\) 1.55607 0.104437
\(223\) 4.71137 0.315497 0.157748 0.987479i \(-0.449577\pi\)
0.157748 + 0.987479i \(0.449577\pi\)
\(224\) 3.38298 0.226035
\(225\) −13.6774 −0.911830
\(226\) 10.8551 0.722074
\(227\) 23.1619 1.53731 0.768655 0.639663i \(-0.220926\pi\)
0.768655 + 0.639663i \(0.220926\pi\)
\(228\) 0.358038 0.0237116
\(229\) −12.7547 −0.842854 −0.421427 0.906862i \(-0.638471\pi\)
−0.421427 + 0.906862i \(0.638471\pi\)
\(230\) −22.4181 −1.47820
\(231\) −3.63468 −0.239144
\(232\) 1.35524 0.0889759
\(233\) 14.8648 0.973827 0.486914 0.873450i \(-0.338123\pi\)
0.486914 + 0.873450i \(0.338123\pi\)
\(234\) 16.0345 1.04821
\(235\) −20.5155 −1.33828
\(236\) −0.0783359 −0.00509923
\(237\) −1.50594 −0.0978214
\(238\) 2.08093 0.134887
\(239\) 4.70178 0.304133 0.152066 0.988370i \(-0.451407\pi\)
0.152066 + 0.988370i \(0.451407\pi\)
\(240\) −1.11870 −0.0722116
\(241\) 1.84635 0.118934 0.0594671 0.998230i \(-0.481060\pi\)
0.0594671 + 0.998230i \(0.481060\pi\)
\(242\) 1.99515 0.128253
\(243\) −9.12214 −0.585185
\(244\) −11.8770 −0.760346
\(245\) 13.8870 0.887209
\(246\) −1.56354 −0.0996875
\(247\) −5.58343 −0.355265
\(248\) 6.18047 0.392460
\(249\) −2.67189 −0.169324
\(250\) 0.741577 0.0469015
\(251\) −10.7902 −0.681069 −0.340534 0.940232i \(-0.610608\pi\)
−0.340534 + 0.940232i \(0.610608\pi\)
\(252\) 9.71526 0.612004
\(253\) −21.5304 −1.35360
\(254\) −3.98375 −0.249963
\(255\) −0.688133 −0.0430926
\(256\) 1.00000 0.0625000
\(257\) −8.57704 −0.535021 −0.267510 0.963555i \(-0.586201\pi\)
−0.267510 + 0.963555i \(0.586201\pi\)
\(258\) −0.446026 −0.0277684
\(259\) −14.7028 −0.913587
\(260\) 17.4456 1.08193
\(261\) 3.89199 0.240908
\(262\) 3.90039 0.240967
\(263\) 6.01493 0.370896 0.185448 0.982654i \(-0.440626\pi\)
0.185448 + 0.982654i \(0.440626\pi\)
\(264\) −1.07440 −0.0661249
\(265\) 7.44679 0.457453
\(266\) −3.38298 −0.207424
\(267\) −1.58094 −0.0967521
\(268\) 1.93235 0.118037
\(269\) −8.11925 −0.495039 −0.247520 0.968883i \(-0.579615\pi\)
−0.247520 + 0.968883i \(0.579615\pi\)
\(270\) −6.56878 −0.399763
\(271\) 4.06018 0.246638 0.123319 0.992367i \(-0.460646\pi\)
0.123319 + 0.992367i \(0.460646\pi\)
\(272\) 0.615120 0.0372971
\(273\) 6.76283 0.409305
\(274\) 4.07235 0.246020
\(275\) −14.2918 −0.861829
\(276\) −2.56887 −0.154628
\(277\) −8.51449 −0.511586 −0.255793 0.966732i \(-0.582337\pi\)
−0.255793 + 0.966732i \(0.582337\pi\)
\(278\) 5.65075 0.338909
\(279\) 17.7491 1.06261
\(280\) 10.5702 0.631690
\(281\) 3.50678 0.209197 0.104599 0.994515i \(-0.466644\pi\)
0.104599 + 0.994515i \(0.466644\pi\)
\(282\) −2.35086 −0.139992
\(283\) −16.1688 −0.961137 −0.480568 0.876957i \(-0.659570\pi\)
−0.480568 + 0.876957i \(0.659570\pi\)
\(284\) −8.93518 −0.530205
\(285\) 1.11870 0.0662659
\(286\) 16.7548 0.990732
\(287\) 14.7733 0.872042
\(288\) 2.87181 0.169223
\(289\) −16.6216 −0.977743
\(290\) 4.23448 0.248657
\(291\) −4.85281 −0.284477
\(292\) 2.99156 0.175068
\(293\) −10.2467 −0.598617 −0.299308 0.954156i \(-0.596756\pi\)
−0.299308 + 0.954156i \(0.596756\pi\)
\(294\) 1.59131 0.0928069
\(295\) −0.244763 −0.0142506
\(296\) −4.34611 −0.252613
\(297\) −6.30869 −0.366067
\(298\) −4.46885 −0.258874
\(299\) 40.0604 2.31675
\(300\) −1.70521 −0.0984504
\(301\) 4.21434 0.242911
\(302\) 3.01879 0.173712
\(303\) −0.879791 −0.0505426
\(304\) −1.00000 −0.0573539
\(305\) −37.1099 −2.12491
\(306\) 1.76651 0.100984
\(307\) 3.54653 0.202411 0.101206 0.994866i \(-0.467730\pi\)
0.101206 + 0.994866i \(0.467730\pi\)
\(308\) 10.1517 0.578444
\(309\) 2.77222 0.157706
\(310\) 19.3110 1.09679
\(311\) −10.8457 −0.615003 −0.307501 0.951548i \(-0.599493\pi\)
−0.307501 + 0.951548i \(0.599493\pi\)
\(312\) 1.99908 0.113175
\(313\) −4.14525 −0.234303 −0.117152 0.993114i \(-0.537376\pi\)
−0.117152 + 0.993114i \(0.537376\pi\)
\(314\) −14.3364 −0.809050
\(315\) 30.3556 1.71034
\(316\) 4.20610 0.236611
\(317\) 20.3736 1.14430 0.572148 0.820150i \(-0.306110\pi\)
0.572148 + 0.820150i \(0.306110\pi\)
\(318\) 0.853324 0.0478520
\(319\) 4.06682 0.227698
\(320\) 3.12453 0.174666
\(321\) −3.49062 −0.194828
\(322\) 24.2724 1.35265
\(323\) −0.615120 −0.0342262
\(324\) 7.86271 0.436817
\(325\) 26.5920 1.47506
\(326\) 16.1862 0.896473
\(327\) 0.662343 0.0366276
\(328\) 4.36696 0.241125
\(329\) 22.2124 1.22461
\(330\) −3.35700 −0.184797
\(331\) −15.1441 −0.832394 −0.416197 0.909274i \(-0.636637\pi\)
−0.416197 + 0.909274i \(0.636637\pi\)
\(332\) 7.46260 0.409564
\(333\) −12.4812 −0.683966
\(334\) 16.2282 0.887968
\(335\) 6.03767 0.329873
\(336\) 1.21123 0.0660782
\(337\) −13.4583 −0.733122 −0.366561 0.930394i \(-0.619465\pi\)
−0.366561 + 0.930394i \(0.619465\pi\)
\(338\) −18.1747 −0.988572
\(339\) 3.88655 0.211089
\(340\) 1.92196 0.104233
\(341\) 18.5464 1.00434
\(342\) −2.87181 −0.155290
\(343\) 8.64512 0.466793
\(344\) 1.24575 0.0671664
\(345\) −8.02651 −0.432133
\(346\) −12.7558 −0.685755
\(347\) −32.6416 −1.75229 −0.876147 0.482043i \(-0.839895\pi\)
−0.876147 + 0.482043i \(0.839895\pi\)
\(348\) 0.485227 0.0260109
\(349\) −18.0042 −0.963742 −0.481871 0.876242i \(-0.660043\pi\)
−0.481871 + 0.876242i \(0.660043\pi\)
\(350\) 16.1120 0.861220
\(351\) 11.7382 0.626539
\(352\) 3.00081 0.159944
\(353\) −29.7728 −1.58465 −0.792323 0.610102i \(-0.791128\pi\)
−0.792323 + 0.610102i \(0.791128\pi\)
\(354\) −0.0280472 −0.00149069
\(355\) −27.9182 −1.48174
\(356\) 4.41557 0.234025
\(357\) 0.745053 0.0394324
\(358\) 4.28228 0.226325
\(359\) −32.1488 −1.69675 −0.848373 0.529398i \(-0.822418\pi\)
−0.848373 + 0.529398i \(0.822418\pi\)
\(360\) 8.97304 0.472921
\(361\) 1.00000 0.0526316
\(362\) 0.0191058 0.00100418
\(363\) 0.714340 0.0374931
\(364\) −18.8886 −0.990032
\(365\) 9.34721 0.489255
\(366\) −4.25241 −0.222277
\(367\) 24.4044 1.27390 0.636951 0.770905i \(-0.280196\pi\)
0.636951 + 0.770905i \(0.280196\pi\)
\(368\) 7.17487 0.374016
\(369\) 12.5411 0.652863
\(370\) −13.5795 −0.705967
\(371\) −8.06276 −0.418598
\(372\) 2.21284 0.114730
\(373\) −24.2893 −1.25765 −0.628826 0.777546i \(-0.716464\pi\)
−0.628826 + 0.777546i \(0.716464\pi\)
\(374\) 1.84586 0.0954469
\(375\) 0.265513 0.0137110
\(376\) 6.56595 0.338613
\(377\) −7.56689 −0.389715
\(378\) 7.11213 0.365808
\(379\) 10.7478 0.552077 0.276038 0.961147i \(-0.410978\pi\)
0.276038 + 0.961147i \(0.410978\pi\)
\(380\) −3.12453 −0.160285
\(381\) −1.42633 −0.0730732
\(382\) 27.2759 1.39556
\(383\) −21.1458 −1.08050 −0.540249 0.841505i \(-0.681670\pi\)
−0.540249 + 0.841505i \(0.681670\pi\)
\(384\) 0.358038 0.0182710
\(385\) 31.7191 1.61656
\(386\) 17.1033 0.870537
\(387\) 3.57756 0.181858
\(388\) 13.5539 0.688096
\(389\) 10.0628 0.510206 0.255103 0.966914i \(-0.417891\pi\)
0.255103 + 0.966914i \(0.417891\pi\)
\(390\) 6.24617 0.316287
\(391\) 4.41340 0.223195
\(392\) −4.44452 −0.224482
\(393\) 1.39649 0.0704434
\(394\) 6.67123 0.336091
\(395\) 13.1421 0.661248
\(396\) 8.61775 0.433058
\(397\) 16.9112 0.848748 0.424374 0.905487i \(-0.360494\pi\)
0.424374 + 0.905487i \(0.360494\pi\)
\(398\) 11.7554 0.589247
\(399\) −1.21123 −0.0606375
\(400\) 4.76266 0.238133
\(401\) 26.5788 1.32728 0.663641 0.748051i \(-0.269010\pi\)
0.663641 + 0.748051i \(0.269010\pi\)
\(402\) 0.691853 0.0345065
\(403\) −34.5082 −1.71898
\(404\) 2.45726 0.122253
\(405\) 24.5672 1.22076
\(406\) −4.58475 −0.227537
\(407\) −13.0419 −0.646461
\(408\) 0.220236 0.0109033
\(409\) −8.32028 −0.411412 −0.205706 0.978614i \(-0.565949\pi\)
−0.205706 + 0.978614i \(0.565949\pi\)
\(410\) 13.6447 0.673863
\(411\) 1.45806 0.0719206
\(412\) −7.74280 −0.381461
\(413\) 0.265008 0.0130402
\(414\) 20.6048 1.01267
\(415\) 23.3171 1.14459
\(416\) −5.58343 −0.273750
\(417\) 2.02318 0.0990756
\(418\) −3.00081 −0.146774
\(419\) −32.8304 −1.60387 −0.801935 0.597411i \(-0.796196\pi\)
−0.801935 + 0.597411i \(0.796196\pi\)
\(420\) 3.78453 0.184666
\(421\) 2.12978 0.103799 0.0518994 0.998652i \(-0.483472\pi\)
0.0518994 + 0.998652i \(0.483472\pi\)
\(422\) 1.00000 0.0486792
\(423\) 18.8562 0.916817
\(424\) −2.38333 −0.115745
\(425\) 2.92960 0.142107
\(426\) −3.19913 −0.154998
\(427\) 40.1795 1.94442
\(428\) 9.74932 0.471251
\(429\) 5.99885 0.289627
\(430\) 3.89238 0.187707
\(431\) −33.8992 −1.63286 −0.816432 0.577441i \(-0.804051\pi\)
−0.816432 + 0.577441i \(0.804051\pi\)
\(432\) 2.10233 0.101148
\(433\) 0.554211 0.0266337 0.0133168 0.999911i \(-0.495761\pi\)
0.0133168 + 0.999911i \(0.495761\pi\)
\(434\) −20.9084 −1.00363
\(435\) 1.51610 0.0726917
\(436\) −1.84992 −0.0885953
\(437\) −7.17487 −0.343220
\(438\) 1.07109 0.0511787
\(439\) 21.5358 1.02785 0.513923 0.857837i \(-0.328192\pi\)
0.513923 + 0.857837i \(0.328192\pi\)
\(440\) 9.37610 0.446988
\(441\) −12.7638 −0.607801
\(442\) −3.43448 −0.163361
\(443\) −19.3598 −0.919812 −0.459906 0.887968i \(-0.652117\pi\)
−0.459906 + 0.887968i \(0.652117\pi\)
\(444\) −1.55607 −0.0738479
\(445\) 13.7966 0.654020
\(446\) −4.71137 −0.223090
\(447\) −1.60002 −0.0756783
\(448\) −3.38298 −0.159831
\(449\) −28.3635 −1.33855 −0.669277 0.743013i \(-0.733396\pi\)
−0.669277 + 0.743013i \(0.733396\pi\)
\(450\) 13.6774 0.644761
\(451\) 13.1044 0.617063
\(452\) −10.8551 −0.510583
\(453\) 1.08084 0.0507823
\(454\) −23.1619 −1.08704
\(455\) −59.0179 −2.76680
\(456\) −0.358038 −0.0167667
\(457\) −1.65460 −0.0773989 −0.0386994 0.999251i \(-0.512321\pi\)
−0.0386994 + 0.999251i \(0.512321\pi\)
\(458\) 12.7547 0.595988
\(459\) 1.29318 0.0603606
\(460\) 22.4181 1.04525
\(461\) 39.2786 1.82939 0.914693 0.404149i \(-0.132432\pi\)
0.914693 + 0.404149i \(0.132432\pi\)
\(462\) 3.63468 0.169100
\(463\) 15.0384 0.698892 0.349446 0.936957i \(-0.386370\pi\)
0.349446 + 0.936957i \(0.386370\pi\)
\(464\) −1.35524 −0.0629155
\(465\) 6.91408 0.320633
\(466\) −14.8648 −0.688600
\(467\) −13.5231 −0.625773 −0.312886 0.949791i \(-0.601296\pi\)
−0.312886 + 0.949791i \(0.601296\pi\)
\(468\) −16.0345 −0.741197
\(469\) −6.53709 −0.301855
\(470\) 20.5155 0.946308
\(471\) −5.13297 −0.236515
\(472\) 0.0783359 0.00360570
\(473\) 3.73826 0.171885
\(474\) 1.50594 0.0691702
\(475\) −4.76266 −0.218526
\(476\) −2.08093 −0.0953795
\(477\) −6.84448 −0.313387
\(478\) −4.70178 −0.215054
\(479\) −16.7659 −0.766055 −0.383027 0.923737i \(-0.625118\pi\)
−0.383027 + 0.923737i \(0.625118\pi\)
\(480\) 1.11870 0.0510613
\(481\) 24.2662 1.10644
\(482\) −1.84635 −0.0840992
\(483\) 8.69043 0.395428
\(484\) −1.99515 −0.0906887
\(485\) 42.3496 1.92299
\(486\) 9.12214 0.413788
\(487\) −21.8167 −0.988611 −0.494305 0.869288i \(-0.664578\pi\)
−0.494305 + 0.869288i \(0.664578\pi\)
\(488\) 11.8770 0.537646
\(489\) 5.79529 0.262072
\(490\) −13.8870 −0.627352
\(491\) 18.8936 0.852657 0.426329 0.904568i \(-0.359807\pi\)
0.426329 + 0.904568i \(0.359807\pi\)
\(492\) 1.56354 0.0704897
\(493\) −0.833635 −0.0375450
\(494\) 5.58343 0.251210
\(495\) 26.9264 1.21025
\(496\) −6.18047 −0.277511
\(497\) 30.2275 1.35589
\(498\) 2.67189 0.119730
\(499\) −19.8282 −0.887634 −0.443817 0.896117i \(-0.646376\pi\)
−0.443817 + 0.896117i \(0.646376\pi\)
\(500\) −0.741577 −0.0331643
\(501\) 5.81031 0.259586
\(502\) 10.7902 0.481588
\(503\) −8.98579 −0.400657 −0.200328 0.979729i \(-0.564201\pi\)
−0.200328 + 0.979729i \(0.564201\pi\)
\(504\) −9.71526 −0.432752
\(505\) 7.67776 0.341656
\(506\) 21.5304 0.957143
\(507\) −6.50722 −0.288996
\(508\) 3.98375 0.176750
\(509\) −12.9747 −0.575093 −0.287546 0.957767i \(-0.592840\pi\)
−0.287546 + 0.957767i \(0.592840\pi\)
\(510\) 0.688133 0.0304710
\(511\) −10.1204 −0.447699
\(512\) −1.00000 −0.0441942
\(513\) −2.10233 −0.0928201
\(514\) 8.57704 0.378317
\(515\) −24.1926 −1.06605
\(516\) 0.446026 0.0196352
\(517\) 19.7032 0.866544
\(518\) 14.7028 0.646004
\(519\) −4.56705 −0.200471
\(520\) −17.4456 −0.765039
\(521\) −29.2714 −1.28240 −0.641201 0.767373i \(-0.721563\pi\)
−0.641201 + 0.767373i \(0.721563\pi\)
\(522\) −3.89199 −0.170348
\(523\) −3.09694 −0.135420 −0.0677099 0.997705i \(-0.521569\pi\)
−0.0677099 + 0.997705i \(0.521569\pi\)
\(524\) −3.90039 −0.170389
\(525\) 5.76869 0.251766
\(526\) −6.01493 −0.262263
\(527\) −3.80173 −0.165606
\(528\) 1.07440 0.0467574
\(529\) 28.4787 1.23821
\(530\) −7.44679 −0.323468
\(531\) 0.224966 0.00976268
\(532\) 3.38298 0.146671
\(533\) −24.3826 −1.05613
\(534\) 1.58094 0.0684141
\(535\) 30.4620 1.31699
\(536\) −1.93235 −0.0834647
\(537\) 1.53322 0.0661632
\(538\) 8.11925 0.350046
\(539\) −13.3372 −0.574472
\(540\) 6.56878 0.282675
\(541\) 28.7730 1.23705 0.618524 0.785766i \(-0.287731\pi\)
0.618524 + 0.785766i \(0.287731\pi\)
\(542\) −4.06018 −0.174400
\(543\) 0.00684059 0.000293558 0
\(544\) −0.615120 −0.0263730
\(545\) −5.78014 −0.247594
\(546\) −6.76283 −0.289422
\(547\) −36.6068 −1.56519 −0.782597 0.622529i \(-0.786105\pi\)
−0.782597 + 0.622529i \(0.786105\pi\)
\(548\) −4.07235 −0.173962
\(549\) 34.1084 1.45571
\(550\) 14.2918 0.609405
\(551\) 1.35524 0.0577352
\(552\) 2.56887 0.109338
\(553\) −14.2291 −0.605084
\(554\) 8.51449 0.361746
\(555\) −4.86199 −0.206380
\(556\) −5.65075 −0.239645
\(557\) −0.621524 −0.0263348 −0.0131674 0.999913i \(-0.504191\pi\)
−0.0131674 + 0.999913i \(0.504191\pi\)
\(558\) −17.7491 −0.751380
\(559\) −6.95556 −0.294189
\(560\) −10.5702 −0.446672
\(561\) 0.660886 0.0279026
\(562\) −3.50678 −0.147925
\(563\) −27.1266 −1.14325 −0.571625 0.820515i \(-0.693687\pi\)
−0.571625 + 0.820515i \(0.693687\pi\)
\(564\) 2.35086 0.0989890
\(565\) −33.9172 −1.42691
\(566\) 16.1688 0.679626
\(567\) −26.5994 −1.11707
\(568\) 8.93518 0.374912
\(569\) 12.7725 0.535451 0.267726 0.963495i \(-0.413728\pi\)
0.267726 + 0.963495i \(0.413728\pi\)
\(570\) −1.11870 −0.0468571
\(571\) 16.4930 0.690209 0.345104 0.938564i \(-0.387844\pi\)
0.345104 + 0.938564i \(0.387844\pi\)
\(572\) −16.7548 −0.700553
\(573\) 9.76579 0.407972
\(574\) −14.7733 −0.616627
\(575\) 34.1714 1.42505
\(576\) −2.87181 −0.119659
\(577\) 16.2653 0.677132 0.338566 0.940943i \(-0.390058\pi\)
0.338566 + 0.940943i \(0.390058\pi\)
\(578\) 16.6216 0.691369
\(579\) 6.12364 0.254490
\(580\) −4.23448 −0.175827
\(581\) −25.2458 −1.04737
\(582\) 4.85281 0.201156
\(583\) −7.15193 −0.296203
\(584\) −2.99156 −0.123792
\(585\) −50.1003 −2.07139
\(586\) 10.2467 0.423286
\(587\) 47.0653 1.94259 0.971296 0.237873i \(-0.0764501\pi\)
0.971296 + 0.237873i \(0.0764501\pi\)
\(588\) −1.59131 −0.0656244
\(589\) 6.18047 0.254662
\(590\) 0.244763 0.0100767
\(591\) 2.38855 0.0982518
\(592\) 4.34611 0.178624
\(593\) 16.7663 0.688508 0.344254 0.938876i \(-0.388132\pi\)
0.344254 + 0.938876i \(0.388132\pi\)
\(594\) 6.30869 0.258849
\(595\) −6.50193 −0.266553
\(596\) 4.46885 0.183051
\(597\) 4.20889 0.172258
\(598\) −40.0604 −1.63819
\(599\) −7.65934 −0.312952 −0.156476 0.987682i \(-0.550013\pi\)
−0.156476 + 0.987682i \(0.550013\pi\)
\(600\) 1.70521 0.0696150
\(601\) −1.79716 −0.0733078 −0.0366539 0.999328i \(-0.511670\pi\)
−0.0366539 + 0.999328i \(0.511670\pi\)
\(602\) −4.21434 −0.171764
\(603\) −5.54933 −0.225986
\(604\) −3.01879 −0.122833
\(605\) −6.23390 −0.253444
\(606\) 0.879791 0.0357390
\(607\) 3.69879 0.150129 0.0750647 0.997179i \(-0.476084\pi\)
0.0750647 + 0.997179i \(0.476084\pi\)
\(608\) 1.00000 0.0405554
\(609\) −1.64151 −0.0665174
\(610\) 37.1099 1.50254
\(611\) −36.6605 −1.48313
\(612\) −1.76651 −0.0714068
\(613\) 12.5828 0.508216 0.254108 0.967176i \(-0.418218\pi\)
0.254108 + 0.967176i \(0.418218\pi\)
\(614\) −3.54653 −0.143126
\(615\) 4.88531 0.196995
\(616\) −10.1517 −0.409022
\(617\) 25.3603 1.02097 0.510484 0.859887i \(-0.329466\pi\)
0.510484 + 0.859887i \(0.329466\pi\)
\(618\) −2.77222 −0.111515
\(619\) −27.6129 −1.10986 −0.554928 0.831899i \(-0.687254\pi\)
−0.554928 + 0.831899i \(0.687254\pi\)
\(620\) −19.3110 −0.775550
\(621\) 15.0839 0.605297
\(622\) 10.8457 0.434873
\(623\) −14.9378 −0.598470
\(624\) −1.99908 −0.0800272
\(625\) −26.1304 −1.04521
\(626\) 4.14525 0.165678
\(627\) −1.07440 −0.0429075
\(628\) 14.3364 0.572084
\(629\) 2.67338 0.106595
\(630\) −30.3556 −1.20939
\(631\) 13.8660 0.551995 0.275998 0.961158i \(-0.410992\pi\)
0.275998 + 0.961158i \(0.410992\pi\)
\(632\) −4.20610 −0.167310
\(633\) 0.358038 0.0142307
\(634\) −20.3736 −0.809139
\(635\) 12.4473 0.493957
\(636\) −0.853324 −0.0338365
\(637\) 24.8157 0.983233
\(638\) −4.06682 −0.161007
\(639\) 25.6601 1.01510
\(640\) −3.12453 −0.123508
\(641\) −32.3492 −1.27772 −0.638858 0.769325i \(-0.720593\pi\)
−0.638858 + 0.769325i \(0.720593\pi\)
\(642\) 3.49062 0.137764
\(643\) −39.6253 −1.56267 −0.781334 0.624113i \(-0.785461\pi\)
−0.781334 + 0.624113i \(0.785461\pi\)
\(644\) −24.2724 −0.956466
\(645\) 1.39362 0.0548737
\(646\) 0.615120 0.0242016
\(647\) 22.3852 0.880052 0.440026 0.897985i \(-0.354969\pi\)
0.440026 + 0.897985i \(0.354969\pi\)
\(648\) −7.86271 −0.308877
\(649\) 0.235071 0.00922734
\(650\) −26.5920 −1.04302
\(651\) −7.48599 −0.293399
\(652\) −16.1862 −0.633902
\(653\) −25.3919 −0.993662 −0.496831 0.867847i \(-0.665503\pi\)
−0.496831 + 0.867847i \(0.665503\pi\)
\(654\) −0.662343 −0.0258997
\(655\) −12.1869 −0.476180
\(656\) −4.36696 −0.170501
\(657\) −8.59119 −0.335174
\(658\) −22.2124 −0.865931
\(659\) 0.0400543 0.00156030 0.000780148 1.00000i \(-0.499752\pi\)
0.000780148 1.00000i \(0.499752\pi\)
\(660\) 3.35700 0.130671
\(661\) −43.2027 −1.68039 −0.840195 0.542284i \(-0.817560\pi\)
−0.840195 + 0.542284i \(0.817560\pi\)
\(662\) 15.1441 0.588592
\(663\) −1.22967 −0.0477565
\(664\) −7.46260 −0.289605
\(665\) 10.5702 0.409894
\(666\) 12.4812 0.483637
\(667\) −9.72367 −0.376502
\(668\) −16.2282 −0.627888
\(669\) −1.68685 −0.0652173
\(670\) −6.03767 −0.233256
\(671\) 35.6405 1.37589
\(672\) −1.21123 −0.0467243
\(673\) 12.7442 0.491252 0.245626 0.969365i \(-0.421006\pi\)
0.245626 + 0.969365i \(0.421006\pi\)
\(674\) 13.4583 0.518396
\(675\) 10.0127 0.385388
\(676\) 18.1747 0.699026
\(677\) −14.3958 −0.553274 −0.276637 0.960974i \(-0.589220\pi\)
−0.276637 + 0.960974i \(0.589220\pi\)
\(678\) −3.88655 −0.149262
\(679\) −45.8526 −1.75966
\(680\) −1.92196 −0.0737037
\(681\) −8.29284 −0.317782
\(682\) −18.5464 −0.710178
\(683\) −13.0006 −0.497455 −0.248727 0.968574i \(-0.580012\pi\)
−0.248727 + 0.968574i \(0.580012\pi\)
\(684\) 2.87181 0.109806
\(685\) −12.7242 −0.486166
\(686\) −8.64512 −0.330072
\(687\) 4.56666 0.174229
\(688\) −1.24575 −0.0474938
\(689\) 13.3072 0.506963
\(690\) 8.02651 0.305564
\(691\) 0.218049 0.00829499 0.00414749 0.999991i \(-0.498680\pi\)
0.00414749 + 0.999991i \(0.498680\pi\)
\(692\) 12.7558 0.484902
\(693\) −29.1536 −1.10745
\(694\) 32.6416 1.23906
\(695\) −17.6559 −0.669726
\(696\) −0.485227 −0.0183925
\(697\) −2.68620 −0.101747
\(698\) 18.0042 0.681468
\(699\) −5.32217 −0.201303
\(700\) −16.1120 −0.608975
\(701\) 25.2798 0.954806 0.477403 0.878684i \(-0.341578\pi\)
0.477403 + 0.878684i \(0.341578\pi\)
\(702\) −11.7382 −0.443030
\(703\) −4.34611 −0.163917
\(704\) −3.00081 −0.113097
\(705\) 7.34531 0.276641
\(706\) 29.7728 1.12051
\(707\) −8.31284 −0.312636
\(708\) 0.0280472 0.00105408
\(709\) 9.79497 0.367858 0.183929 0.982940i \(-0.441118\pi\)
0.183929 + 0.982940i \(0.441118\pi\)
\(710\) 27.9182 1.04775
\(711\) −12.0791 −0.453002
\(712\) −4.41557 −0.165481
\(713\) −44.3440 −1.66070
\(714\) −0.745053 −0.0278829
\(715\) −52.3508 −1.95781
\(716\) −4.28228 −0.160036
\(717\) −1.68341 −0.0628682
\(718\) 32.1488 1.19978
\(719\) 38.7960 1.44685 0.723424 0.690404i \(-0.242567\pi\)
0.723424 + 0.690404i \(0.242567\pi\)
\(720\) −8.97304 −0.334405
\(721\) 26.1937 0.975505
\(722\) −1.00000 −0.0372161
\(723\) −0.661065 −0.0245853
\(724\) −0.0191058 −0.000710061 0
\(725\) −6.45455 −0.239716
\(726\) −0.714340 −0.0265116
\(727\) −1.53700 −0.0570043 −0.0285021 0.999594i \(-0.509074\pi\)
−0.0285021 + 0.999594i \(0.509074\pi\)
\(728\) 18.8886 0.700058
\(729\) −20.3221 −0.752669
\(730\) −9.34721 −0.345956
\(731\) −0.766286 −0.0283421
\(732\) 4.25241 0.157173
\(733\) 50.8935 1.87980 0.939898 0.341455i \(-0.110920\pi\)
0.939898 + 0.341455i \(0.110920\pi\)
\(734\) −24.4044 −0.900784
\(735\) −4.97208 −0.183398
\(736\) −7.17487 −0.264469
\(737\) −5.79860 −0.213594
\(738\) −12.5411 −0.461644
\(739\) −5.83827 −0.214764 −0.107382 0.994218i \(-0.534247\pi\)
−0.107382 + 0.994218i \(0.534247\pi\)
\(740\) 13.5795 0.499194
\(741\) 1.99908 0.0734380
\(742\) 8.06276 0.295993
\(743\) 45.9366 1.68525 0.842625 0.538501i \(-0.181009\pi\)
0.842625 + 0.538501i \(0.181009\pi\)
\(744\) −2.21284 −0.0811267
\(745\) 13.9630 0.511567
\(746\) 24.2893 0.889294
\(747\) −21.4312 −0.784126
\(748\) −1.84586 −0.0674912
\(749\) −32.9817 −1.20513
\(750\) −0.265513 −0.00969515
\(751\) 16.1899 0.590779 0.295390 0.955377i \(-0.404551\pi\)
0.295390 + 0.955377i \(0.404551\pi\)
\(752\) −6.56595 −0.239436
\(753\) 3.86328 0.140786
\(754\) 7.56689 0.275570
\(755\) −9.43228 −0.343276
\(756\) −7.11213 −0.258666
\(757\) −36.3310 −1.32047 −0.660236 0.751059i \(-0.729544\pi\)
−0.660236 + 0.751059i \(0.729544\pi\)
\(758\) −10.7478 −0.390377
\(759\) 7.70869 0.279808
\(760\) 3.12453 0.113338
\(761\) −6.83122 −0.247632 −0.123816 0.992305i \(-0.539513\pi\)
−0.123816 + 0.992305i \(0.539513\pi\)
\(762\) 1.42633 0.0516706
\(763\) 6.25825 0.226564
\(764\) −27.2759 −0.986807
\(765\) −5.51949 −0.199558
\(766\) 21.1458 0.764028
\(767\) −0.437383 −0.0157930
\(768\) −0.358038 −0.0129196
\(769\) −10.3997 −0.375024 −0.187512 0.982262i \(-0.560042\pi\)
−0.187512 + 0.982262i \(0.560042\pi\)
\(770\) −31.7191 −1.14308
\(771\) 3.07090 0.110596
\(772\) −17.1033 −0.615563
\(773\) −5.54935 −0.199596 −0.0997981 0.995008i \(-0.531820\pi\)
−0.0997981 + 0.995008i \(0.531820\pi\)
\(774\) −3.57756 −0.128593
\(775\) −29.4355 −1.05735
\(776\) −13.5539 −0.486557
\(777\) 5.26415 0.188850
\(778\) −10.0628 −0.360770
\(779\) 4.36696 0.156463
\(780\) −6.24617 −0.223649
\(781\) 26.8127 0.959435
\(782\) −4.41340 −0.157823
\(783\) −2.84916 −0.101821
\(784\) 4.44452 0.158733
\(785\) 44.7944 1.59878
\(786\) −1.39649 −0.0498110
\(787\) −3.95969 −0.141148 −0.0705738 0.997507i \(-0.522483\pi\)
−0.0705738 + 0.997507i \(0.522483\pi\)
\(788\) −6.67123 −0.237653
\(789\) −2.15357 −0.0766692
\(790\) −13.1421 −0.467573
\(791\) 36.7227 1.30571
\(792\) −8.61775 −0.306218
\(793\) −66.3143 −2.35489
\(794\) −16.9112 −0.600155
\(795\) −2.66623 −0.0945615
\(796\) −11.7554 −0.416661
\(797\) −0.820786 −0.0290737 −0.0145369 0.999894i \(-0.504627\pi\)
−0.0145369 + 0.999894i \(0.504627\pi\)
\(798\) 1.21123 0.0428772
\(799\) −4.03884 −0.142884
\(800\) −4.76266 −0.168385
\(801\) −12.6807 −0.448050
\(802\) −26.5788 −0.938530
\(803\) −8.97710 −0.316795
\(804\) −0.691853 −0.0243998
\(805\) −75.8397 −2.67300
\(806\) 34.5082 1.21550
\(807\) 2.90700 0.102331
\(808\) −2.45726 −0.0864460
\(809\) 11.5408 0.405753 0.202876 0.979204i \(-0.434971\pi\)
0.202876 + 0.979204i \(0.434971\pi\)
\(810\) −24.5672 −0.863205
\(811\) −15.8151 −0.555342 −0.277671 0.960676i \(-0.589563\pi\)
−0.277671 + 0.960676i \(0.589563\pi\)
\(812\) 4.58475 0.160893
\(813\) −1.45370 −0.0509834
\(814\) 13.0419 0.457117
\(815\) −50.5743 −1.77154
\(816\) −0.220236 −0.00770980
\(817\) 1.24575 0.0435833
\(818\) 8.32028 0.290912
\(819\) 54.2445 1.89545
\(820\) −13.6447 −0.476493
\(821\) 7.13775 0.249109 0.124555 0.992213i \(-0.460250\pi\)
0.124555 + 0.992213i \(0.460250\pi\)
\(822\) −1.45806 −0.0508555
\(823\) 22.3234 0.778145 0.389073 0.921207i \(-0.372796\pi\)
0.389073 + 0.921207i \(0.372796\pi\)
\(824\) 7.74280 0.269733
\(825\) 5.11701 0.178152
\(826\) −0.265008 −0.00922082
\(827\) −41.7018 −1.45011 −0.725057 0.688688i \(-0.758187\pi\)
−0.725057 + 0.688688i \(0.758187\pi\)
\(828\) −20.6048 −0.716068
\(829\) −49.0713 −1.70432 −0.852158 0.523285i \(-0.824706\pi\)
−0.852158 + 0.523285i \(0.824706\pi\)
\(830\) −23.3171 −0.809348
\(831\) 3.04851 0.105752
\(832\) 5.58343 0.193571
\(833\) 2.73391 0.0947244
\(834\) −2.02318 −0.0700570
\(835\) −50.7054 −1.75473
\(836\) 3.00081 0.103785
\(837\) −12.9934 −0.449117
\(838\) 32.8304 1.13411
\(839\) 19.1731 0.661928 0.330964 0.943643i \(-0.392626\pi\)
0.330964 + 0.943643i \(0.392626\pi\)
\(840\) −3.78453 −0.130579
\(841\) −27.1633 −0.936666
\(842\) −2.12978 −0.0733969
\(843\) −1.25556 −0.0432438
\(844\) −1.00000 −0.0344214
\(845\) 56.7872 1.95354
\(846\) −18.8562 −0.648288
\(847\) 6.74955 0.231917
\(848\) 2.38333 0.0818440
\(849\) 5.78905 0.198680
\(850\) −2.92960 −0.100485
\(851\) 31.1828 1.06893
\(852\) 3.19913 0.109600
\(853\) −20.3042 −0.695201 −0.347601 0.937643i \(-0.613003\pi\)
−0.347601 + 0.937643i \(0.613003\pi\)
\(854\) −40.1795 −1.37491
\(855\) 8.97304 0.306872
\(856\) −9.74932 −0.333225
\(857\) 8.86837 0.302938 0.151469 0.988462i \(-0.451600\pi\)
0.151469 + 0.988462i \(0.451600\pi\)
\(858\) −5.99885 −0.204797
\(859\) 36.6955 1.25203 0.626017 0.779809i \(-0.284684\pi\)
0.626017 + 0.779809i \(0.284684\pi\)
\(860\) −3.89238 −0.132729
\(861\) −5.28941 −0.180263
\(862\) 33.8992 1.15461
\(863\) 28.8863 0.983302 0.491651 0.870792i \(-0.336394\pi\)
0.491651 + 0.870792i \(0.336394\pi\)
\(864\) −2.10233 −0.0715227
\(865\) 39.8558 1.35514
\(866\) −0.554211 −0.0188328
\(867\) 5.95117 0.202112
\(868\) 20.9084 0.709676
\(869\) −12.6217 −0.428161
\(870\) −1.51610 −0.0514008
\(871\) 10.7891 0.365576
\(872\) 1.84992 0.0626463
\(873\) −38.9243 −1.31739
\(874\) 7.17487 0.242694
\(875\) 2.50874 0.0848108
\(876\) −1.07109 −0.0361888
\(877\) 19.2468 0.649917 0.324958 0.945728i \(-0.394650\pi\)
0.324958 + 0.945728i \(0.394650\pi\)
\(878\) −21.5358 −0.726796
\(879\) 3.66869 0.123742
\(880\) −9.37610 −0.316068
\(881\) 32.7640 1.10385 0.551924 0.833895i \(-0.313894\pi\)
0.551924 + 0.833895i \(0.313894\pi\)
\(882\) 12.7638 0.429780
\(883\) −39.0126 −1.31288 −0.656439 0.754379i \(-0.727938\pi\)
−0.656439 + 0.754379i \(0.727938\pi\)
\(884\) 3.43448 0.115514
\(885\) 0.0876342 0.00294579
\(886\) 19.3598 0.650405
\(887\) −40.4343 −1.35765 −0.678825 0.734300i \(-0.737511\pi\)
−0.678825 + 0.734300i \(0.737511\pi\)
\(888\) 1.55607 0.0522184
\(889\) −13.4769 −0.452001
\(890\) −13.7966 −0.462462
\(891\) −23.5945 −0.790445
\(892\) 4.71137 0.157748
\(893\) 6.56595 0.219721
\(894\) 1.60002 0.0535126
\(895\) −13.3801 −0.447247
\(896\) 3.38298 0.113017
\(897\) −14.3431 −0.478903
\(898\) 28.3635 0.946501
\(899\) 8.37602 0.279356
\(900\) −13.6774 −0.455915
\(901\) 1.46604 0.0488407
\(902\) −13.1044 −0.436329
\(903\) −1.50889 −0.0502129
\(904\) 10.8551 0.361037
\(905\) −0.0596965 −0.00198438
\(906\) −1.08084 −0.0359085
\(907\) −25.5757 −0.849229 −0.424614 0.905374i \(-0.639590\pi\)
−0.424614 + 0.905374i \(0.639590\pi\)
\(908\) 23.1619 0.768655
\(909\) −7.05677 −0.234058
\(910\) 59.0179 1.95642
\(911\) −45.4379 −1.50542 −0.752712 0.658350i \(-0.771255\pi\)
−0.752712 + 0.658350i \(0.771255\pi\)
\(912\) 0.358038 0.0118558
\(913\) −22.3938 −0.741128
\(914\) 1.65460 0.0547293
\(915\) 13.2868 0.439246
\(916\) −12.7547 −0.421427
\(917\) 13.1949 0.435735
\(918\) −1.29318 −0.0426814
\(919\) 34.4806 1.13741 0.568706 0.822541i \(-0.307444\pi\)
0.568706 + 0.822541i \(0.307444\pi\)
\(920\) −22.4181 −0.739101
\(921\) −1.26979 −0.0418410
\(922\) −39.2786 −1.29357
\(923\) −49.8889 −1.64211
\(924\) −3.63468 −0.119572
\(925\) 20.6991 0.680581
\(926\) −15.0384 −0.494191
\(927\) 22.2358 0.730321
\(928\) 1.35524 0.0444880
\(929\) 58.4115 1.91642 0.958210 0.286065i \(-0.0923472\pi\)
0.958210 + 0.286065i \(0.0923472\pi\)
\(930\) −6.91408 −0.226722
\(931\) −4.44452 −0.145663
\(932\) 14.8648 0.486914
\(933\) 3.88317 0.127129
\(934\) 13.5231 0.442488
\(935\) −5.76742 −0.188615
\(936\) 16.0345 0.524105
\(937\) 2.99786 0.0979357 0.0489678 0.998800i \(-0.484407\pi\)
0.0489678 + 0.998800i \(0.484407\pi\)
\(938\) 6.53709 0.213443
\(939\) 1.48416 0.0484336
\(940\) −20.5155 −0.669141
\(941\) −48.7190 −1.58819 −0.794097 0.607791i \(-0.792056\pi\)
−0.794097 + 0.607791i \(0.792056\pi\)
\(942\) 5.13297 0.167241
\(943\) −31.3324 −1.02032
\(944\) −0.0783359 −0.00254962
\(945\) −22.2220 −0.722882
\(946\) −3.73826 −0.121541
\(947\) 30.5376 0.992338 0.496169 0.868226i \(-0.334740\pi\)
0.496169 + 0.868226i \(0.334740\pi\)
\(948\) −1.50594 −0.0489107
\(949\) 16.7032 0.542208
\(950\) 4.76266 0.154521
\(951\) −7.29452 −0.236541
\(952\) 2.08093 0.0674435
\(953\) −18.2301 −0.590532 −0.295266 0.955415i \(-0.595408\pi\)
−0.295266 + 0.955415i \(0.595408\pi\)
\(954\) 6.84448 0.221598
\(955\) −85.2242 −2.75779
\(956\) 4.70178 0.152066
\(957\) −1.45607 −0.0470682
\(958\) 16.7659 0.541682
\(959\) 13.7767 0.444872
\(960\) −1.11870 −0.0361058
\(961\) 7.19819 0.232200
\(962\) −24.2662 −0.782374
\(963\) −27.9982 −0.902229
\(964\) 1.84635 0.0594671
\(965\) −53.4398 −1.72029
\(966\) −8.69043 −0.279610
\(967\) −48.3574 −1.55507 −0.777535 0.628840i \(-0.783530\pi\)
−0.777535 + 0.628840i \(0.783530\pi\)
\(968\) 1.99515 0.0641266
\(969\) 0.220236 0.00707500
\(970\) −42.3496 −1.35976
\(971\) −30.5748 −0.981191 −0.490595 0.871388i \(-0.663221\pi\)
−0.490595 + 0.871388i \(0.663221\pi\)
\(972\) −9.12214 −0.292593
\(973\) 19.1163 0.612841
\(974\) 21.8167 0.699053
\(975\) −9.52093 −0.304914
\(976\) −11.8770 −0.380173
\(977\) −24.8139 −0.793867 −0.396933 0.917847i \(-0.629926\pi\)
−0.396933 + 0.917847i \(0.629926\pi\)
\(978\) −5.79529 −0.185313
\(979\) −13.2503 −0.423481
\(980\) 13.8870 0.443605
\(981\) 5.31263 0.169619
\(982\) −18.8936 −0.602920
\(983\) 22.4403 0.715734 0.357867 0.933773i \(-0.383504\pi\)
0.357867 + 0.933773i \(0.383504\pi\)
\(984\) −1.56354 −0.0498437
\(985\) −20.8444 −0.664158
\(986\) 0.833635 0.0265483
\(987\) −7.95289 −0.253143
\(988\) −5.58343 −0.177633
\(989\) −8.93810 −0.284215
\(990\) −26.9264 −0.855776
\(991\) 17.9030 0.568708 0.284354 0.958719i \(-0.408221\pi\)
0.284354 + 0.958719i \(0.408221\pi\)
\(992\) 6.18047 0.196230
\(993\) 5.42215 0.172067
\(994\) −30.2275 −0.958757
\(995\) −36.7302 −1.16442
\(996\) −2.67189 −0.0846622
\(997\) −37.7752 −1.19635 −0.598177 0.801364i \(-0.704108\pi\)
−0.598177 + 0.801364i \(0.704108\pi\)
\(998\) 19.8282 0.627652
\(999\) 9.13696 0.289081
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 \(a_p\))