Properties

Label 619.2.a.b.1.15
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 1.15
Character \(\chi\) = 619.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.262115 q^{2} -0.800074 q^{3} -1.93130 q^{4} -2.40890 q^{5} -0.209711 q^{6} +1.00913 q^{7} -1.03045 q^{8} -2.35988 q^{9} +O(q^{10})\) \(q+0.262115 q^{2} -0.800074 q^{3} -1.93130 q^{4} -2.40890 q^{5} -0.209711 q^{6} +1.00913 q^{7} -1.03045 q^{8} -2.35988 q^{9} -0.631409 q^{10} +2.12041 q^{11} +1.54518 q^{12} -0.383666 q^{13} +0.264508 q^{14} +1.92730 q^{15} +3.59249 q^{16} +3.95666 q^{17} -0.618560 q^{18} +3.69738 q^{19} +4.65230 q^{20} -0.807379 q^{21} +0.555792 q^{22} +4.85826 q^{23} +0.824438 q^{24} +0.802803 q^{25} -0.100565 q^{26} +4.28830 q^{27} -1.94893 q^{28} -3.08630 q^{29} +0.505174 q^{30} +0.275136 q^{31} +3.00255 q^{32} -1.69649 q^{33} +1.03710 q^{34} -2.43089 q^{35} +4.55763 q^{36} -3.06862 q^{37} +0.969139 q^{38} +0.306961 q^{39} +2.48226 q^{40} +2.32888 q^{41} -0.211626 q^{42} +8.80051 q^{43} -4.09514 q^{44} +5.68472 q^{45} +1.27342 q^{46} +1.90425 q^{47} -2.87426 q^{48} -5.98166 q^{49} +0.210427 q^{50} -3.16563 q^{51} +0.740973 q^{52} +8.51466 q^{53} +1.12403 q^{54} -5.10786 q^{55} -1.03986 q^{56} -2.95818 q^{57} -0.808965 q^{58} +0.748989 q^{59} -3.72218 q^{60} +8.47450 q^{61} +0.0721173 q^{62} -2.38143 q^{63} -6.39798 q^{64} +0.924214 q^{65} -0.444674 q^{66} -7.23066 q^{67} -7.64149 q^{68} -3.88697 q^{69} -0.637174 q^{70} +13.5055 q^{71} +2.43174 q^{72} -3.23037 q^{73} -0.804330 q^{74} -0.642302 q^{75} -7.14074 q^{76} +2.13977 q^{77} +0.0804592 q^{78} -5.96598 q^{79} -8.65396 q^{80} +3.64868 q^{81} +0.610433 q^{82} +2.05758 q^{83} +1.55929 q^{84} -9.53121 q^{85} +2.30674 q^{86} +2.46927 q^{87} -2.18498 q^{88} -6.75369 q^{89} +1.49005 q^{90} -0.387169 q^{91} -9.38273 q^{92} -0.220129 q^{93} +0.499131 q^{94} -8.90663 q^{95} -2.40226 q^{96} +1.61662 q^{97} -1.56788 q^{98} -5.00392 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + O(q^{10}) \) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + 5q^{10} + 23q^{11} - 6q^{12} + 9q^{13} + 7q^{14} - 2q^{15} + 35q^{16} + 4q^{17} + 10q^{18} - q^{19} + 29q^{20} + 30q^{21} + 4q^{23} + 4q^{24} + 35q^{25} + q^{26} - 5q^{27} - 13q^{28} + 90q^{29} - 31q^{30} + 2q^{31} + 43q^{32} - 6q^{33} - 9q^{34} + 9q^{35} + 33q^{36} + 19q^{37} + 5q^{38} + 32q^{39} - 12q^{40} + 59q^{41} - 25q^{42} - 4q^{43} + 52q^{44} + 30q^{45} - q^{46} + 4q^{47} - 44q^{48} + 30q^{49} + 31q^{50} - 12q^{52} + 34q^{53} - 28q^{54} - 17q^{55} + 2q^{56} - 8q^{57} + 6q^{58} + 13q^{59} - 64q^{60} + 16q^{61} + 28q^{62} - 40q^{63} + 37q^{64} + 31q^{65} - 59q^{66} - 11q^{67} - 52q^{68} + 6q^{69} - 40q^{70} + 42q^{71} + 6q^{72} - 4q^{73} + 16q^{74} - 52q^{75} - 42q^{76} + 29q^{77} - 56q^{78} + 3q^{79} + 21q^{80} + 30q^{81} - 43q^{82} - 11q^{83} - 36q^{84} + 19q^{85} - 11q^{86} - 20q^{87} - 47q^{88} + 58q^{89} - 33q^{90} - 39q^{91} - 7q^{92} - 15q^{93} - 46q^{94} + 23q^{95} - 70q^{96} - 9q^{97} - 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.262115 0.185343 0.0926717 0.995697i \(-0.470459\pi\)
0.0926717 + 0.995697i \(0.470459\pi\)
\(3\) −0.800074 −0.461923 −0.230962 0.972963i \(-0.574187\pi\)
−0.230962 + 0.972963i \(0.574187\pi\)
\(4\) −1.93130 −0.965648
\(5\) −2.40890 −1.07729 −0.538647 0.842532i \(-0.681064\pi\)
−0.538647 + 0.842532i \(0.681064\pi\)
\(6\) −0.209711 −0.0856143
\(7\) 1.00913 0.381415 0.190708 0.981647i \(-0.438922\pi\)
0.190708 + 0.981647i \(0.438922\pi\)
\(8\) −1.03045 −0.364320
\(9\) −2.35988 −0.786627
\(10\) −0.631409 −0.199669
\(11\) 2.12041 0.639328 0.319664 0.947531i \(-0.396430\pi\)
0.319664 + 0.947531i \(0.396430\pi\)
\(12\) 1.54518 0.446055
\(13\) −0.383666 −0.106410 −0.0532049 0.998584i \(-0.516944\pi\)
−0.0532049 + 0.998584i \(0.516944\pi\)
\(14\) 0.264508 0.0706928
\(15\) 1.92730 0.497627
\(16\) 3.59249 0.898124
\(17\) 3.95666 0.959632 0.479816 0.877369i \(-0.340703\pi\)
0.479816 + 0.877369i \(0.340703\pi\)
\(18\) −0.618560 −0.145796
\(19\) 3.69738 0.848238 0.424119 0.905607i \(-0.360584\pi\)
0.424119 + 0.905607i \(0.360584\pi\)
\(20\) 4.65230 1.04029
\(21\) −0.807379 −0.176185
\(22\) 0.555792 0.118495
\(23\) 4.85826 1.01302 0.506508 0.862235i \(-0.330936\pi\)
0.506508 + 0.862235i \(0.330936\pi\)
\(24\) 0.824438 0.168288
\(25\) 0.802803 0.160561
\(26\) −0.100565 −0.0197224
\(27\) 4.28830 0.825284
\(28\) −1.94893 −0.368313
\(29\) −3.08630 −0.573111 −0.286555 0.958064i \(-0.592510\pi\)
−0.286555 + 0.958064i \(0.592510\pi\)
\(30\) 0.505174 0.0922317
\(31\) 0.275136 0.0494159 0.0247079 0.999695i \(-0.492134\pi\)
0.0247079 + 0.999695i \(0.492134\pi\)
\(32\) 3.00255 0.530781
\(33\) −1.69649 −0.295320
\(34\) 1.03710 0.177861
\(35\) −2.43089 −0.410896
\(36\) 4.55763 0.759605
\(37\) −3.06862 −0.504477 −0.252239 0.967665i \(-0.581167\pi\)
−0.252239 + 0.967665i \(0.581167\pi\)
\(38\) 0.969139 0.157215
\(39\) 0.306961 0.0491532
\(40\) 2.48226 0.392479
\(41\) 2.32888 0.363709 0.181855 0.983325i \(-0.441790\pi\)
0.181855 + 0.983325i \(0.441790\pi\)
\(42\) −0.211626 −0.0326546
\(43\) 8.80051 1.34206 0.671032 0.741428i \(-0.265851\pi\)
0.671032 + 0.741428i \(0.265851\pi\)
\(44\) −4.09514 −0.617366
\(45\) 5.68472 0.847428
\(46\) 1.27342 0.187756
\(47\) 1.90425 0.277763 0.138881 0.990309i \(-0.455649\pi\)
0.138881 + 0.990309i \(0.455649\pi\)
\(48\) −2.87426 −0.414864
\(49\) −5.98166 −0.854522
\(50\) 0.210427 0.0297589
\(51\) −3.16563 −0.443276
\(52\) 0.740973 0.102754
\(53\) 8.51466 1.16958 0.584789 0.811185i \(-0.301177\pi\)
0.584789 + 0.811185i \(0.301177\pi\)
\(54\) 1.12403 0.152961
\(55\) −5.10786 −0.688744
\(56\) −1.03986 −0.138957
\(57\) −2.95818 −0.391820
\(58\) −0.808965 −0.106222
\(59\) 0.748989 0.0975101 0.0487550 0.998811i \(-0.484475\pi\)
0.0487550 + 0.998811i \(0.484475\pi\)
\(60\) −3.72218 −0.480532
\(61\) 8.47450 1.08505 0.542524 0.840040i \(-0.317469\pi\)
0.542524 + 0.840040i \(0.317469\pi\)
\(62\) 0.0721173 0.00915890
\(63\) −2.38143 −0.300032
\(64\) −6.39798 −0.799747
\(65\) 0.924214 0.114635
\(66\) −0.444674 −0.0547356
\(67\) −7.23066 −0.883366 −0.441683 0.897171i \(-0.645618\pi\)
−0.441683 + 0.897171i \(0.645618\pi\)
\(68\) −7.64149 −0.926667
\(69\) −3.88697 −0.467936
\(70\) −0.637174 −0.0761569
\(71\) 13.5055 1.60281 0.801404 0.598123i \(-0.204087\pi\)
0.801404 + 0.598123i \(0.204087\pi\)
\(72\) 2.43174 0.286584
\(73\) −3.23037 −0.378087 −0.189043 0.981969i \(-0.560539\pi\)
−0.189043 + 0.981969i \(0.560539\pi\)
\(74\) −0.804330 −0.0935015
\(75\) −0.642302 −0.0741667
\(76\) −7.14074 −0.819099
\(77\) 2.13977 0.243849
\(78\) 0.0804592 0.00911021
\(79\) −5.96598 −0.671226 −0.335613 0.942000i \(-0.608943\pi\)
−0.335613 + 0.942000i \(0.608943\pi\)
\(80\) −8.65396 −0.967543
\(81\) 3.64868 0.405409
\(82\) 0.610433 0.0674111
\(83\) 2.05758 0.225849 0.112924 0.993604i \(-0.463978\pi\)
0.112924 + 0.993604i \(0.463978\pi\)
\(84\) 1.55929 0.170132
\(85\) −9.53121 −1.03381
\(86\) 2.30674 0.248743
\(87\) 2.46927 0.264733
\(88\) −2.18498 −0.232920
\(89\) −6.75369 −0.715890 −0.357945 0.933743i \(-0.616522\pi\)
−0.357945 + 0.933743i \(0.616522\pi\)
\(90\) 1.49005 0.157065
\(91\) −0.387169 −0.0405863
\(92\) −9.38273 −0.978217
\(93\) −0.220129 −0.0228263
\(94\) 0.499131 0.0514815
\(95\) −8.90663 −0.913801
\(96\) −2.40226 −0.245180
\(97\) 1.61662 0.164143 0.0820717 0.996626i \(-0.473846\pi\)
0.0820717 + 0.996626i \(0.473846\pi\)
\(98\) −1.56788 −0.158380
\(99\) −5.00392 −0.502913
\(100\) −1.55045 −0.155045
\(101\) 10.1205 1.00703 0.503514 0.863987i \(-0.332040\pi\)
0.503514 + 0.863987i \(0.332040\pi\)
\(102\) −0.829758 −0.0821583
\(103\) −6.95922 −0.685712 −0.342856 0.939388i \(-0.611394\pi\)
−0.342856 + 0.939388i \(0.611394\pi\)
\(104\) 0.395349 0.0387672
\(105\) 1.94490 0.189802
\(106\) 2.23182 0.216774
\(107\) 0.297802 0.0287896 0.0143948 0.999896i \(-0.495418\pi\)
0.0143948 + 0.999896i \(0.495418\pi\)
\(108\) −8.28198 −0.796934
\(109\) 14.4679 1.38577 0.692885 0.721049i \(-0.256340\pi\)
0.692885 + 0.721049i \(0.256340\pi\)
\(110\) −1.33885 −0.127654
\(111\) 2.45512 0.233030
\(112\) 3.62529 0.342558
\(113\) −9.51734 −0.895316 −0.447658 0.894205i \(-0.647742\pi\)
−0.447658 + 0.894205i \(0.647742\pi\)
\(114\) −0.775383 −0.0726213
\(115\) −11.7031 −1.09132
\(116\) 5.96055 0.553423
\(117\) 0.905407 0.0837049
\(118\) 0.196321 0.0180728
\(119\) 3.99279 0.366018
\(120\) −1.98599 −0.181295
\(121\) −6.50386 −0.591260
\(122\) 2.22129 0.201106
\(123\) −1.86327 −0.168006
\(124\) −0.531369 −0.0477183
\(125\) 10.1106 0.904322
\(126\) −0.624208 −0.0556089
\(127\) 9.24816 0.820642 0.410321 0.911941i \(-0.365417\pi\)
0.410321 + 0.911941i \(0.365417\pi\)
\(128\) −7.68211 −0.679009
\(129\) −7.04106 −0.619930
\(130\) 0.242250 0.0212468
\(131\) −5.64071 −0.492831 −0.246416 0.969164i \(-0.579253\pi\)
−0.246416 + 0.969164i \(0.579253\pi\)
\(132\) 3.27642 0.285175
\(133\) 3.73114 0.323531
\(134\) −1.89526 −0.163726
\(135\) −10.3301 −0.889073
\(136\) −4.07715 −0.349613
\(137\) 12.1718 1.03991 0.519955 0.854194i \(-0.325949\pi\)
0.519955 + 0.854194i \(0.325949\pi\)
\(138\) −1.01883 −0.0867288
\(139\) 3.67807 0.311970 0.155985 0.987759i \(-0.450145\pi\)
0.155985 + 0.987759i \(0.450145\pi\)
\(140\) 4.69478 0.396781
\(141\) −1.52354 −0.128305
\(142\) 3.54000 0.297070
\(143\) −0.813530 −0.0680308
\(144\) −8.47786 −0.706488
\(145\) 7.43458 0.617408
\(146\) −0.846730 −0.0700758
\(147\) 4.78577 0.394724
\(148\) 5.92640 0.487147
\(149\) −3.21754 −0.263591 −0.131796 0.991277i \(-0.542074\pi\)
−0.131796 + 0.991277i \(0.542074\pi\)
\(150\) −0.168357 −0.0137463
\(151\) 8.66435 0.705094 0.352547 0.935794i \(-0.385316\pi\)
0.352547 + 0.935794i \(0.385316\pi\)
\(152\) −3.80997 −0.309030
\(153\) −9.33726 −0.754873
\(154\) 0.560866 0.0451959
\(155\) −0.662775 −0.0532354
\(156\) −0.592833 −0.0474646
\(157\) 18.5287 1.47875 0.739375 0.673294i \(-0.235121\pi\)
0.739375 + 0.673294i \(0.235121\pi\)
\(158\) −1.56377 −0.124407
\(159\) −6.81236 −0.540255
\(160\) −7.23285 −0.571807
\(161\) 4.90261 0.386380
\(162\) 0.956375 0.0751399
\(163\) 9.98299 0.781928 0.390964 0.920406i \(-0.372142\pi\)
0.390964 + 0.920406i \(0.372142\pi\)
\(164\) −4.49775 −0.351215
\(165\) 4.08667 0.318147
\(166\) 0.539322 0.0418595
\(167\) 2.79958 0.216638 0.108319 0.994116i \(-0.465453\pi\)
0.108319 + 0.994116i \(0.465453\pi\)
\(168\) 0.831965 0.0641875
\(169\) −12.8528 −0.988677
\(170\) −2.49827 −0.191609
\(171\) −8.72538 −0.667247
\(172\) −16.9964 −1.29596
\(173\) 8.63473 0.656486 0.328243 0.944593i \(-0.393544\pi\)
0.328243 + 0.944593i \(0.393544\pi\)
\(174\) 0.647232 0.0490665
\(175\) 0.810133 0.0612403
\(176\) 7.61756 0.574196
\(177\) −0.599247 −0.0450421
\(178\) −1.77024 −0.132685
\(179\) 16.2997 1.21830 0.609150 0.793055i \(-0.291511\pi\)
0.609150 + 0.793055i \(0.291511\pi\)
\(180\) −10.9789 −0.818317
\(181\) −21.9972 −1.63504 −0.817518 0.575903i \(-0.804651\pi\)
−0.817518 + 0.575903i \(0.804651\pi\)
\(182\) −0.101483 −0.00752241
\(183\) −6.78023 −0.501209
\(184\) −5.00620 −0.369062
\(185\) 7.39199 0.543470
\(186\) −0.0576992 −0.00423071
\(187\) 8.38976 0.613520
\(188\) −3.67766 −0.268221
\(189\) 4.32746 0.314776
\(190\) −2.33456 −0.169367
\(191\) 8.79300 0.636239 0.318120 0.948051i \(-0.396949\pi\)
0.318120 + 0.948051i \(0.396949\pi\)
\(192\) 5.11885 0.369422
\(193\) 1.50460 0.108304 0.0541518 0.998533i \(-0.482755\pi\)
0.0541518 + 0.998533i \(0.482755\pi\)
\(194\) 0.423742 0.0304229
\(195\) −0.739439 −0.0529524
\(196\) 11.5523 0.825168
\(197\) −3.97952 −0.283529 −0.141765 0.989900i \(-0.545278\pi\)
−0.141765 + 0.989900i \(0.545278\pi\)
\(198\) −1.31160 −0.0932115
\(199\) −22.6337 −1.60446 −0.802230 0.597016i \(-0.796353\pi\)
−0.802230 + 0.597016i \(0.796353\pi\)
\(200\) −0.827250 −0.0584954
\(201\) 5.78506 0.408047
\(202\) 2.65274 0.186646
\(203\) −3.11447 −0.218593
\(204\) 6.11376 0.428049
\(205\) −5.61003 −0.391822
\(206\) −1.82412 −0.127092
\(207\) −11.4649 −0.796866
\(208\) −1.37832 −0.0955692
\(209\) 7.83997 0.542302
\(210\) 0.509786 0.0351786
\(211\) 2.96100 0.203844 0.101922 0.994792i \(-0.467501\pi\)
0.101922 + 0.994792i \(0.467501\pi\)
\(212\) −16.4443 −1.12940
\(213\) −10.8054 −0.740374
\(214\) 0.0780583 0.00533595
\(215\) −21.1995 −1.44580
\(216\) −4.41889 −0.300667
\(217\) 0.277648 0.0188480
\(218\) 3.79224 0.256843
\(219\) 2.58454 0.174647
\(220\) 9.86479 0.665084
\(221\) −1.51804 −0.102114
\(222\) 0.643524 0.0431905
\(223\) −12.0183 −0.804806 −0.402403 0.915463i \(-0.631825\pi\)
−0.402403 + 0.915463i \(0.631825\pi\)
\(224\) 3.02996 0.202448
\(225\) −1.89452 −0.126301
\(226\) −2.49464 −0.165941
\(227\) −4.40039 −0.292064 −0.146032 0.989280i \(-0.546650\pi\)
−0.146032 + 0.989280i \(0.546650\pi\)
\(228\) 5.71312 0.378361
\(229\) 15.6483 1.03407 0.517034 0.855965i \(-0.327036\pi\)
0.517034 + 0.855965i \(0.327036\pi\)
\(230\) −3.06755 −0.202268
\(231\) −1.71198 −0.112640
\(232\) 3.18028 0.208796
\(233\) −9.00072 −0.589657 −0.294828 0.955550i \(-0.595262\pi\)
−0.294828 + 0.955550i \(0.595262\pi\)
\(234\) 0.237321 0.0155141
\(235\) −4.58714 −0.299232
\(236\) −1.44652 −0.0941604
\(237\) 4.77323 0.310055
\(238\) 1.04657 0.0678391
\(239\) 12.6679 0.819422 0.409711 0.912215i \(-0.365630\pi\)
0.409711 + 0.912215i \(0.365630\pi\)
\(240\) 6.92381 0.446930
\(241\) 14.8688 0.957781 0.478891 0.877875i \(-0.341039\pi\)
0.478891 + 0.877875i \(0.341039\pi\)
\(242\) −1.70476 −0.109586
\(243\) −15.7841 −1.01255
\(244\) −16.3668 −1.04777
\(245\) 14.4092 0.920571
\(246\) −0.488392 −0.0311387
\(247\) −1.41856 −0.0902608
\(248\) −0.283514 −0.0180032
\(249\) −1.64621 −0.104325
\(250\) 2.65015 0.167610
\(251\) −3.77537 −0.238299 −0.119150 0.992876i \(-0.538017\pi\)
−0.119150 + 0.992876i \(0.538017\pi\)
\(252\) 4.59924 0.289725
\(253\) 10.3015 0.647650
\(254\) 2.42408 0.152100
\(255\) 7.62568 0.477538
\(256\) 10.7824 0.673897
\(257\) 14.4687 0.902532 0.451266 0.892389i \(-0.350973\pi\)
0.451266 + 0.892389i \(0.350973\pi\)
\(258\) −1.84557 −0.114900
\(259\) −3.09663 −0.192415
\(260\) −1.78493 −0.110697
\(261\) 7.28329 0.450825
\(262\) −1.47851 −0.0913429
\(263\) 24.7739 1.52763 0.763813 0.645438i \(-0.223325\pi\)
0.763813 + 0.645438i \(0.223325\pi\)
\(264\) 1.74815 0.107591
\(265\) −20.5110 −1.25998
\(266\) 0.977988 0.0599643
\(267\) 5.40345 0.330686
\(268\) 13.9645 0.853020
\(269\) 19.4958 1.18868 0.594339 0.804215i \(-0.297414\pi\)
0.594339 + 0.804215i \(0.297414\pi\)
\(270\) −2.70767 −0.164784
\(271\) −21.4412 −1.30246 −0.651229 0.758881i \(-0.725746\pi\)
−0.651229 + 0.758881i \(0.725746\pi\)
\(272\) 14.2143 0.861868
\(273\) 0.309764 0.0187478
\(274\) 3.19042 0.192740
\(275\) 1.70227 0.102651
\(276\) 7.50688 0.451861
\(277\) 15.9152 0.956250 0.478125 0.878292i \(-0.341317\pi\)
0.478125 + 0.878292i \(0.341317\pi\)
\(278\) 0.964077 0.0578215
\(279\) −0.649288 −0.0388719
\(280\) 2.50492 0.149698
\(281\) 29.9031 1.78387 0.891934 0.452166i \(-0.149349\pi\)
0.891934 + 0.452166i \(0.149349\pi\)
\(282\) −0.399342 −0.0237805
\(283\) −3.34136 −0.198623 −0.0993116 0.995056i \(-0.531664\pi\)
−0.0993116 + 0.995056i \(0.531664\pi\)
\(284\) −26.0831 −1.54775
\(285\) 7.12596 0.422106
\(286\) −0.213238 −0.0126091
\(287\) 2.35014 0.138724
\(288\) −7.08566 −0.417527
\(289\) −1.34480 −0.0791060
\(290\) 1.94872 0.114433
\(291\) −1.29342 −0.0758216
\(292\) 6.23881 0.365099
\(293\) 4.26459 0.249140 0.124570 0.992211i \(-0.460245\pi\)
0.124570 + 0.992211i \(0.460245\pi\)
\(294\) 1.25442 0.0731594
\(295\) −1.80424 −0.105047
\(296\) 3.16206 0.183791
\(297\) 9.09296 0.527627
\(298\) −0.843366 −0.0488549
\(299\) −1.86395 −0.107795
\(300\) 1.24048 0.0716189
\(301\) 8.88086 0.511884
\(302\) 2.27106 0.130685
\(303\) −8.09716 −0.465169
\(304\) 13.2828 0.761822
\(305\) −20.4142 −1.16892
\(306\) −2.44744 −0.139911
\(307\) −14.3903 −0.821298 −0.410649 0.911793i \(-0.634698\pi\)
−0.410649 + 0.911793i \(0.634698\pi\)
\(308\) −4.13253 −0.235473
\(309\) 5.56789 0.316746
\(310\) −0.173723 −0.00986682
\(311\) −10.1113 −0.573358 −0.286679 0.958027i \(-0.592551\pi\)
−0.286679 + 0.958027i \(0.592551\pi\)
\(312\) −0.316309 −0.0179075
\(313\) 1.93265 0.109240 0.0546199 0.998507i \(-0.482605\pi\)
0.0546199 + 0.998507i \(0.482605\pi\)
\(314\) 4.85664 0.274076
\(315\) 5.73662 0.323222
\(316\) 11.5221 0.648168
\(317\) −3.41079 −0.191569 −0.0957845 0.995402i \(-0.530536\pi\)
−0.0957845 + 0.995402i \(0.530536\pi\)
\(318\) −1.78562 −0.100133
\(319\) −6.54422 −0.366406
\(320\) 15.4121 0.861562
\(321\) −0.238263 −0.0132986
\(322\) 1.28505 0.0716130
\(323\) 14.6293 0.813996
\(324\) −7.04669 −0.391483
\(325\) −0.308009 −0.0170852
\(326\) 2.61669 0.144925
\(327\) −11.5754 −0.640119
\(328\) −2.39979 −0.132506
\(329\) 1.92163 0.105943
\(330\) 1.07118 0.0589663
\(331\) −5.01276 −0.275526 −0.137763 0.990465i \(-0.543991\pi\)
−0.137763 + 0.990465i \(0.543991\pi\)
\(332\) −3.97379 −0.218090
\(333\) 7.24157 0.396835
\(334\) 0.733813 0.0401525
\(335\) 17.4179 0.951644
\(336\) −2.90050 −0.158235
\(337\) 10.5267 0.573423 0.286712 0.958017i \(-0.407438\pi\)
0.286712 + 0.958017i \(0.407438\pi\)
\(338\) −3.36891 −0.183245
\(339\) 7.61457 0.413567
\(340\) 18.4076 0.998292
\(341\) 0.583401 0.0315930
\(342\) −2.28705 −0.123670
\(343\) −13.1002 −0.707343
\(344\) −9.06850 −0.488941
\(345\) 9.36332 0.504104
\(346\) 2.26329 0.121675
\(347\) −33.0916 −1.77645 −0.888226 0.459407i \(-0.848062\pi\)
−0.888226 + 0.459407i \(0.848062\pi\)
\(348\) −4.76888 −0.255639
\(349\) −16.5572 −0.886285 −0.443142 0.896451i \(-0.646136\pi\)
−0.443142 + 0.896451i \(0.646136\pi\)
\(350\) 0.212348 0.0113505
\(351\) −1.64528 −0.0878184
\(352\) 6.36664 0.339343
\(353\) −6.01295 −0.320037 −0.160019 0.987114i \(-0.551155\pi\)
−0.160019 + 0.987114i \(0.551155\pi\)
\(354\) −0.157072 −0.00834826
\(355\) −32.5334 −1.72669
\(356\) 13.0434 0.691297
\(357\) −3.19453 −0.169072
\(358\) 4.27241 0.225804
\(359\) −8.74423 −0.461503 −0.230751 0.973013i \(-0.574118\pi\)
−0.230751 + 0.973013i \(0.574118\pi\)
\(360\) −5.85783 −0.308735
\(361\) −5.32937 −0.280493
\(362\) −5.76579 −0.303043
\(363\) 5.20357 0.273117
\(364\) 0.747738 0.0391921
\(365\) 7.78165 0.407310
\(366\) −1.77720 −0.0928957
\(367\) 6.83596 0.356834 0.178417 0.983955i \(-0.442902\pi\)
0.178417 + 0.983955i \(0.442902\pi\)
\(368\) 17.4533 0.909814
\(369\) −5.49587 −0.286104
\(370\) 1.93755 0.100729
\(371\) 8.59240 0.446095
\(372\) 0.425135 0.0220422
\(373\) −22.7402 −1.17744 −0.588721 0.808336i \(-0.700368\pi\)
−0.588721 + 0.808336i \(0.700368\pi\)
\(374\) 2.19908 0.113712
\(375\) −8.08925 −0.417727
\(376\) −1.96223 −0.101194
\(377\) 1.18411 0.0609846
\(378\) 1.13429 0.0583416
\(379\) 30.0357 1.54283 0.771415 0.636333i \(-0.219549\pi\)
0.771415 + 0.636333i \(0.219549\pi\)
\(380\) 17.2013 0.882410
\(381\) −7.39921 −0.379073
\(382\) 2.30478 0.117923
\(383\) 1.26648 0.0647139 0.0323569 0.999476i \(-0.489699\pi\)
0.0323569 + 0.999476i \(0.489699\pi\)
\(384\) 6.14625 0.313650
\(385\) −5.15450 −0.262697
\(386\) 0.394379 0.0200734
\(387\) −20.7681 −1.05570
\(388\) −3.12218 −0.158505
\(389\) 36.1037 1.83053 0.915265 0.402852i \(-0.131981\pi\)
0.915265 + 0.402852i \(0.131981\pi\)
\(390\) −0.193818 −0.00981437
\(391\) 19.2225 0.972123
\(392\) 6.16381 0.311319
\(393\) 4.51299 0.227650
\(394\) −1.04309 −0.0525503
\(395\) 14.3715 0.723107
\(396\) 9.66405 0.485637
\(397\) −23.5430 −1.18159 −0.590796 0.806821i \(-0.701186\pi\)
−0.590796 + 0.806821i \(0.701186\pi\)
\(398\) −5.93263 −0.297376
\(399\) −2.98519 −0.149446
\(400\) 2.88407 0.144203
\(401\) 28.8556 1.44098 0.720490 0.693466i \(-0.243917\pi\)
0.720490 + 0.693466i \(0.243917\pi\)
\(402\) 1.51635 0.0756288
\(403\) −0.105560 −0.00525834
\(404\) −19.5457 −0.972435
\(405\) −8.78932 −0.436745
\(406\) −0.816351 −0.0405148
\(407\) −6.50673 −0.322526
\(408\) 3.26202 0.161494
\(409\) −4.19880 −0.207617 −0.103809 0.994597i \(-0.533103\pi\)
−0.103809 + 0.994597i \(0.533103\pi\)
\(410\) −1.47047 −0.0726215
\(411\) −9.73837 −0.480358
\(412\) 13.4403 0.662156
\(413\) 0.755827 0.0371918
\(414\) −3.00513 −0.147694
\(415\) −4.95650 −0.243305
\(416\) −1.15198 −0.0564803
\(417\) −2.94273 −0.144106
\(418\) 2.05497 0.100512
\(419\) 20.9705 1.02448 0.512239 0.858843i \(-0.328816\pi\)
0.512239 + 0.858843i \(0.328816\pi\)
\(420\) −3.75617 −0.183282
\(421\) 12.9690 0.632072 0.316036 0.948747i \(-0.397648\pi\)
0.316036 + 0.948747i \(0.397648\pi\)
\(422\) 0.776122 0.0377810
\(423\) −4.49379 −0.218496
\(424\) −8.77395 −0.426101
\(425\) 3.17642 0.154079
\(426\) −2.83226 −0.137223
\(427\) 8.55187 0.413854
\(428\) −0.575143 −0.0278006
\(429\) 0.650884 0.0314250
\(430\) −5.55672 −0.267969
\(431\) −9.27696 −0.446855 −0.223428 0.974721i \(-0.571725\pi\)
−0.223428 + 0.974721i \(0.571725\pi\)
\(432\) 15.4057 0.741207
\(433\) −6.06108 −0.291277 −0.145638 0.989338i \(-0.546524\pi\)
−0.145638 + 0.989338i \(0.546524\pi\)
\(434\) 0.0727757 0.00349335
\(435\) −5.94822 −0.285195
\(436\) −27.9417 −1.33816
\(437\) 17.9628 0.859279
\(438\) 0.677446 0.0323696
\(439\) 8.23653 0.393108 0.196554 0.980493i \(-0.437025\pi\)
0.196554 + 0.980493i \(0.437025\pi\)
\(440\) 5.26340 0.250923
\(441\) 14.1160 0.672190
\(442\) −0.397901 −0.0189262
\(443\) 10.7693 0.511664 0.255832 0.966721i \(-0.417651\pi\)
0.255832 + 0.966721i \(0.417651\pi\)
\(444\) −4.74156 −0.225025
\(445\) 16.2690 0.771223
\(446\) −3.15018 −0.149165
\(447\) 2.57427 0.121759
\(448\) −6.45639 −0.305036
\(449\) 22.1975 1.04757 0.523783 0.851852i \(-0.324520\pi\)
0.523783 + 0.851852i \(0.324520\pi\)
\(450\) −0.496582 −0.0234091
\(451\) 4.93817 0.232530
\(452\) 18.3808 0.864560
\(453\) −6.93212 −0.325699
\(454\) −1.15341 −0.0541321
\(455\) 0.932652 0.0437234
\(456\) 3.04826 0.142748
\(457\) −14.2708 −0.667558 −0.333779 0.942651i \(-0.608324\pi\)
−0.333779 + 0.942651i \(0.608324\pi\)
\(458\) 4.10165 0.191657
\(459\) 16.9674 0.791969
\(460\) 22.6021 1.05383
\(461\) −7.11632 −0.331440 −0.165720 0.986173i \(-0.552995\pi\)
−0.165720 + 0.986173i \(0.552995\pi\)
\(462\) −0.448734 −0.0208770
\(463\) −34.0230 −1.58118 −0.790592 0.612343i \(-0.790227\pi\)
−0.790592 + 0.612343i \(0.790227\pi\)
\(464\) −11.0875 −0.514724
\(465\) 0.530269 0.0245907
\(466\) −2.35922 −0.109289
\(467\) −34.8259 −1.61155 −0.805776 0.592220i \(-0.798252\pi\)
−0.805776 + 0.592220i \(0.798252\pi\)
\(468\) −1.74861 −0.0808294
\(469\) −7.29668 −0.336929
\(470\) −1.20236 −0.0554607
\(471\) −14.8243 −0.683068
\(472\) −0.771797 −0.0355248
\(473\) 18.6607 0.858019
\(474\) 1.25114 0.0574665
\(475\) 2.96827 0.136194
\(476\) −7.71126 −0.353445
\(477\) −20.0936 −0.920023
\(478\) 3.32046 0.151874
\(479\) 4.37495 0.199896 0.0999482 0.994993i \(-0.468132\pi\)
0.0999482 + 0.994993i \(0.468132\pi\)
\(480\) 5.78681 0.264131
\(481\) 1.17732 0.0536813
\(482\) 3.89733 0.177518
\(483\) −3.92245 −0.178478
\(484\) 12.5609 0.570949
\(485\) −3.89429 −0.176831
\(486\) −4.13726 −0.187670
\(487\) −17.8840 −0.810403 −0.405201 0.914228i \(-0.632799\pi\)
−0.405201 + 0.914228i \(0.632799\pi\)
\(488\) −8.73256 −0.395304
\(489\) −7.98713 −0.361191
\(490\) 3.77687 0.170622
\(491\) −20.4968 −0.925009 −0.462504 0.886617i \(-0.653049\pi\)
−0.462504 + 0.886617i \(0.653049\pi\)
\(492\) 3.59853 0.162234
\(493\) −12.2114 −0.549976
\(494\) −0.371826 −0.0167292
\(495\) 12.0539 0.541784
\(496\) 0.988425 0.0443816
\(497\) 13.6288 0.611336
\(498\) −0.431498 −0.0193359
\(499\) −36.1253 −1.61719 −0.808596 0.588364i \(-0.799772\pi\)
−0.808596 + 0.588364i \(0.799772\pi\)
\(500\) −19.5266 −0.873257
\(501\) −2.23987 −0.100070
\(502\) −0.989582 −0.0441672
\(503\) −35.1350 −1.56659 −0.783297 0.621648i \(-0.786464\pi\)
−0.783297 + 0.621648i \(0.786464\pi\)
\(504\) 2.45395 0.109307
\(505\) −24.3793 −1.08486
\(506\) 2.70018 0.120038
\(507\) 10.2832 0.456693
\(508\) −17.8609 −0.792451
\(509\) 11.1424 0.493876 0.246938 0.969031i \(-0.420576\pi\)
0.246938 + 0.969031i \(0.420576\pi\)
\(510\) 1.99880 0.0885086
\(511\) −3.25987 −0.144208
\(512\) 18.1904 0.803911
\(513\) 15.8555 0.700037
\(514\) 3.79246 0.167278
\(515\) 16.7641 0.738713
\(516\) 13.5984 0.598635
\(517\) 4.03778 0.177582
\(518\) −0.811674 −0.0356629
\(519\) −6.90842 −0.303246
\(520\) −0.952358 −0.0417636
\(521\) 20.1245 0.881671 0.440836 0.897588i \(-0.354682\pi\)
0.440836 + 0.897588i \(0.354682\pi\)
\(522\) 1.90906 0.0835573
\(523\) 6.00331 0.262506 0.131253 0.991349i \(-0.458100\pi\)
0.131253 + 0.991349i \(0.458100\pi\)
\(524\) 10.8939 0.475901
\(525\) −0.648167 −0.0282883
\(526\) 6.49362 0.283135
\(527\) 1.08862 0.0474211
\(528\) −6.09462 −0.265234
\(529\) 0.602666 0.0262029
\(530\) −5.37624 −0.233529
\(531\) −1.76753 −0.0767041
\(532\) −7.20593 −0.312417
\(533\) −0.893511 −0.0387023
\(534\) 1.41633 0.0612904
\(535\) −0.717375 −0.0310148
\(536\) 7.45085 0.321828
\(537\) −13.0410 −0.562761
\(538\) 5.11013 0.220314
\(539\) −12.6836 −0.546320
\(540\) 19.9505 0.858531
\(541\) −15.8329 −0.680709 −0.340354 0.940297i \(-0.610547\pi\)
−0.340354 + 0.940297i \(0.610547\pi\)
\(542\) −5.62005 −0.241402
\(543\) 17.5994 0.755261
\(544\) 11.8801 0.509354
\(545\) −34.8516 −1.49288
\(546\) 0.0811938 0.00347477
\(547\) 7.50332 0.320819 0.160409 0.987051i \(-0.448719\pi\)
0.160409 + 0.987051i \(0.448719\pi\)
\(548\) −23.5074 −1.00419
\(549\) −19.9988 −0.853529
\(550\) 0.446191 0.0190257
\(551\) −11.4112 −0.486134
\(552\) 4.00533 0.170478
\(553\) −6.02045 −0.256016
\(554\) 4.17161 0.177235
\(555\) −5.91414 −0.251041
\(556\) −7.10343 −0.301253
\(557\) 24.0444 1.01879 0.509397 0.860531i \(-0.329868\pi\)
0.509397 + 0.860531i \(0.329868\pi\)
\(558\) −0.170188 −0.00720464
\(559\) −3.37646 −0.142809
\(560\) −8.73298 −0.369036
\(561\) −6.71243 −0.283399
\(562\) 7.83804 0.330628
\(563\) −31.5911 −1.33141 −0.665703 0.746217i \(-0.731868\pi\)
−0.665703 + 0.746217i \(0.731868\pi\)
\(564\) 2.94240 0.123897
\(565\) 22.9263 0.964517
\(566\) −0.875820 −0.0368135
\(567\) 3.68200 0.154629
\(568\) −13.9168 −0.583935
\(569\) −21.5037 −0.901484 −0.450742 0.892654i \(-0.648840\pi\)
−0.450742 + 0.892654i \(0.648840\pi\)
\(570\) 1.86782 0.0782344
\(571\) 41.1731 1.72304 0.861519 0.507725i \(-0.169513\pi\)
0.861519 + 0.507725i \(0.169513\pi\)
\(572\) 1.57117 0.0656938
\(573\) −7.03505 −0.293894
\(574\) 0.616007 0.0257116
\(575\) 3.90023 0.162651
\(576\) 15.0985 0.629103
\(577\) −38.3133 −1.59500 −0.797501 0.603317i \(-0.793845\pi\)
−0.797501 + 0.603317i \(0.793845\pi\)
\(578\) −0.352493 −0.0146618
\(579\) −1.20379 −0.0500279
\(580\) −14.3584 −0.596199
\(581\) 2.07636 0.0861421
\(582\) −0.339025 −0.0140530
\(583\) 18.0546 0.747744
\(584\) 3.32874 0.137744
\(585\) −2.18103 −0.0901747
\(586\) 1.11781 0.0461764
\(587\) −22.0197 −0.908849 −0.454425 0.890785i \(-0.650155\pi\)
−0.454425 + 0.890785i \(0.650155\pi\)
\(588\) −9.24273 −0.381164
\(589\) 1.01728 0.0419164
\(590\) −0.472918 −0.0194697
\(591\) 3.18391 0.130969
\(592\) −11.0240 −0.453083
\(593\) −22.4640 −0.922487 −0.461244 0.887274i \(-0.652597\pi\)
−0.461244 + 0.887274i \(0.652597\pi\)
\(594\) 2.38340 0.0977922
\(595\) −9.61824 −0.394309
\(596\) 6.21403 0.254536
\(597\) 18.1086 0.741137
\(598\) −0.488569 −0.0199791
\(599\) 20.1519 0.823385 0.411692 0.911323i \(-0.364938\pi\)
0.411692 + 0.911323i \(0.364938\pi\)
\(600\) 0.661861 0.0270204
\(601\) −38.0446 −1.55187 −0.775936 0.630812i \(-0.782722\pi\)
−0.775936 + 0.630812i \(0.782722\pi\)
\(602\) 2.32781 0.0948743
\(603\) 17.0635 0.694879
\(604\) −16.7334 −0.680873
\(605\) 15.6671 0.636960
\(606\) −2.12239 −0.0862160
\(607\) −2.91732 −0.118410 −0.0592051 0.998246i \(-0.518857\pi\)
−0.0592051 + 0.998246i \(0.518857\pi\)
\(608\) 11.1016 0.450228
\(609\) 2.49181 0.100973
\(610\) −5.35088 −0.216651
\(611\) −0.730595 −0.0295567
\(612\) 18.0330 0.728941
\(613\) 2.06332 0.0833368 0.0416684 0.999131i \(-0.486733\pi\)
0.0416684 + 0.999131i \(0.486733\pi\)
\(614\) −3.77192 −0.152222
\(615\) 4.48844 0.180991
\(616\) −2.20493 −0.0888392
\(617\) −17.5993 −0.708519 −0.354260 0.935147i \(-0.615267\pi\)
−0.354260 + 0.935147i \(0.615267\pi\)
\(618\) 1.45943 0.0587068
\(619\) 1.00000 0.0401934
\(620\) 1.28002 0.0514066
\(621\) 20.8337 0.836027
\(622\) −2.65032 −0.106268
\(623\) −6.81535 −0.273051
\(624\) 1.10276 0.0441456
\(625\) −28.3695 −1.13478
\(626\) 0.506577 0.0202469
\(627\) −6.27256 −0.250502
\(628\) −35.7844 −1.42795
\(629\) −12.1415 −0.484113
\(630\) 1.50366 0.0599071
\(631\) −10.2646 −0.408627 −0.204314 0.978906i \(-0.565496\pi\)
−0.204314 + 0.978906i \(0.565496\pi\)
\(632\) 6.14766 0.244541
\(633\) −2.36902 −0.0941600
\(634\) −0.894019 −0.0355060
\(635\) −22.2779 −0.884072
\(636\) 13.1567 0.521696
\(637\) 2.29496 0.0909296
\(638\) −1.71534 −0.0679109
\(639\) −31.8714 −1.26081
\(640\) 18.5054 0.731491
\(641\) −0.596268 −0.0235512 −0.0117756 0.999931i \(-0.503748\pi\)
−0.0117756 + 0.999931i \(0.503748\pi\)
\(642\) −0.0624524 −0.00246480
\(643\) −11.2477 −0.443564 −0.221782 0.975096i \(-0.571187\pi\)
−0.221782 + 0.975096i \(0.571187\pi\)
\(644\) −9.46840 −0.373107
\(645\) 16.9612 0.667847
\(646\) 3.83456 0.150869
\(647\) 21.3388 0.838915 0.419458 0.907775i \(-0.362220\pi\)
0.419458 + 0.907775i \(0.362220\pi\)
\(648\) −3.75979 −0.147699
\(649\) 1.58816 0.0623409
\(650\) −0.0807337 −0.00316663
\(651\) −0.222139 −0.00870631
\(652\) −19.2801 −0.755068
\(653\) −28.2196 −1.10432 −0.552159 0.833739i \(-0.686196\pi\)
−0.552159 + 0.833739i \(0.686196\pi\)
\(654\) −3.03407 −0.118642
\(655\) 13.5879 0.530924
\(656\) 8.36647 0.326656
\(657\) 7.62330 0.297413
\(658\) 0.503689 0.0196358
\(659\) 4.65272 0.181244 0.0906221 0.995885i \(-0.471114\pi\)
0.0906221 + 0.995885i \(0.471114\pi\)
\(660\) −7.89256 −0.307218
\(661\) 12.1011 0.470677 0.235339 0.971913i \(-0.424380\pi\)
0.235339 + 0.971913i \(0.424380\pi\)
\(662\) −1.31392 −0.0510670
\(663\) 1.21454 0.0471689
\(664\) −2.12023 −0.0822811
\(665\) −8.98795 −0.348538
\(666\) 1.89812 0.0735508
\(667\) −14.9940 −0.580571
\(668\) −5.40682 −0.209196
\(669\) 9.61554 0.371758
\(670\) 4.56550 0.176381
\(671\) 17.9694 0.693702
\(672\) −2.42420 −0.0935154
\(673\) −26.9341 −1.03823 −0.519116 0.854704i \(-0.673739\pi\)
−0.519116 + 0.854704i \(0.673739\pi\)
\(674\) 2.75919 0.106280
\(675\) 3.44266 0.132508
\(676\) 24.8226 0.954714
\(677\) −34.9794 −1.34437 −0.672183 0.740385i \(-0.734643\pi\)
−0.672183 + 0.740385i \(0.734643\pi\)
\(678\) 1.99589 0.0766519
\(679\) 1.63138 0.0626068
\(680\) 9.82145 0.376636
\(681\) 3.52064 0.134911
\(682\) 0.152918 0.00585554
\(683\) −19.9925 −0.764993 −0.382496 0.923957i \(-0.624936\pi\)
−0.382496 + 0.923957i \(0.624936\pi\)
\(684\) 16.8513 0.644325
\(685\) −29.3207 −1.12029
\(686\) −3.43375 −0.131101
\(687\) −12.5198 −0.477660
\(688\) 31.6158 1.20534
\(689\) −3.26679 −0.124455
\(690\) 2.45427 0.0934323
\(691\) 17.5169 0.666375 0.333187 0.942861i \(-0.391876\pi\)
0.333187 + 0.942861i \(0.391876\pi\)
\(692\) −16.6762 −0.633934
\(693\) −5.04960 −0.191819
\(694\) −8.67381 −0.329253
\(695\) −8.86010 −0.336083
\(696\) −2.54446 −0.0964475
\(697\) 9.21458 0.349027
\(698\) −4.33988 −0.164267
\(699\) 7.20124 0.272376
\(700\) −1.56461 −0.0591366
\(701\) 38.9945 1.47280 0.736401 0.676545i \(-0.236523\pi\)
0.736401 + 0.676545i \(0.236523\pi\)
\(702\) −0.431252 −0.0162765
\(703\) −11.3458 −0.427917
\(704\) −13.5663 −0.511301
\(705\) 3.67005 0.138222
\(706\) −1.57609 −0.0593168
\(707\) 10.2129 0.384096
\(708\) 1.15732 0.0434948
\(709\) 37.2995 1.40081 0.700406 0.713745i \(-0.253002\pi\)
0.700406 + 0.713745i \(0.253002\pi\)
\(710\) −8.52750 −0.320031
\(711\) 14.0790 0.528004
\(712\) 6.95935 0.260813
\(713\) 1.33668 0.0500591
\(714\) −0.837334 −0.0313364
\(715\) 1.95971 0.0732891
\(716\) −31.4796 −1.17645
\(717\) −10.1353 −0.378510
\(718\) −2.29199 −0.0855365
\(719\) 1.18695 0.0442658 0.0221329 0.999755i \(-0.492954\pi\)
0.0221329 + 0.999755i \(0.492954\pi\)
\(720\) 20.4223 0.761095
\(721\) −7.02276 −0.261541
\(722\) −1.39691 −0.0519875
\(723\) −11.8961 −0.442421
\(724\) 42.4830 1.57887
\(725\) −2.47769 −0.0920191
\(726\) 1.36393 0.0506203
\(727\) −15.7890 −0.585583 −0.292792 0.956176i \(-0.594584\pi\)
−0.292792 + 0.956176i \(0.594584\pi\)
\(728\) 0.398959 0.0147864
\(729\) 1.68242 0.0623117
\(730\) 2.03969 0.0754922
\(731\) 34.8207 1.28789
\(732\) 13.0946 0.483991
\(733\) −20.1850 −0.745549 −0.372775 0.927922i \(-0.621594\pi\)
−0.372775 + 0.927922i \(0.621594\pi\)
\(734\) 1.79181 0.0661368
\(735\) −11.5284 −0.425233
\(736\) 14.5872 0.537690
\(737\) −15.3320 −0.564760
\(738\) −1.44055 −0.0530274
\(739\) 20.5447 0.755749 0.377874 0.925857i \(-0.376655\pi\)
0.377874 + 0.925857i \(0.376655\pi\)
\(740\) −14.2761 −0.524801
\(741\) 1.13495 0.0416936
\(742\) 2.25220 0.0826808
\(743\) −50.2502 −1.84350 −0.921750 0.387784i \(-0.873241\pi\)
−0.921750 + 0.387784i \(0.873241\pi\)
\(744\) 0.226832 0.00831608
\(745\) 7.75074 0.283965
\(746\) −5.96055 −0.218231
\(747\) −4.85564 −0.177659
\(748\) −16.2031 −0.592444
\(749\) 0.300521 0.0109808
\(750\) −2.12031 −0.0774230
\(751\) 41.5373 1.51572 0.757859 0.652418i \(-0.226245\pi\)
0.757859 + 0.652418i \(0.226245\pi\)
\(752\) 6.84099 0.249465
\(753\) 3.02058 0.110076
\(754\) 0.310372 0.0113031
\(755\) −20.8715 −0.759593
\(756\) −8.35760 −0.303963
\(757\) 31.5365 1.14621 0.573107 0.819481i \(-0.305738\pi\)
0.573107 + 0.819481i \(0.305738\pi\)
\(758\) 7.87280 0.285953
\(759\) −8.24196 −0.299164
\(760\) 9.17785 0.332916
\(761\) −11.6535 −0.422439 −0.211220 0.977439i \(-0.567743\pi\)
−0.211220 + 0.977439i \(0.567743\pi\)
\(762\) −1.93945 −0.0702587
\(763\) 14.5999 0.528554
\(764\) −16.9819 −0.614383
\(765\) 22.4925 0.813219
\(766\) 0.331962 0.0119943
\(767\) −0.287362 −0.0103760
\(768\) −8.62668 −0.311289
\(769\) −12.1474 −0.438045 −0.219022 0.975720i \(-0.570287\pi\)
−0.219022 + 0.975720i \(0.570287\pi\)
\(770\) −1.35107 −0.0486892
\(771\) −11.5760 −0.416900
\(772\) −2.90583 −0.104583
\(773\) 40.7959 1.46733 0.733664 0.679513i \(-0.237809\pi\)
0.733664 + 0.679513i \(0.237809\pi\)
\(774\) −5.44364 −0.195668
\(775\) 0.220880 0.00793425
\(776\) −1.66585 −0.0598007
\(777\) 2.47754 0.0888811
\(778\) 9.46332 0.339277
\(779\) 8.61074 0.308512
\(780\) 1.42808 0.0511333
\(781\) 28.6372 1.02472
\(782\) 5.03851 0.180177
\(783\) −13.2350 −0.472979
\(784\) −21.4891 −0.767467
\(785\) −44.6337 −1.59305
\(786\) 1.18292 0.0421934
\(787\) 19.2173 0.685024 0.342512 0.939513i \(-0.388722\pi\)
0.342512 + 0.939513i \(0.388722\pi\)
\(788\) 7.68564 0.273789
\(789\) −19.8210 −0.705645
\(790\) 3.76698 0.134023
\(791\) −9.60423 −0.341487
\(792\) 5.15630 0.183221
\(793\) −3.25138 −0.115460
\(794\) −6.17098 −0.219000
\(795\) 16.4103 0.582013
\(796\) 43.7123 1.54934
\(797\) 24.5973 0.871281 0.435641 0.900121i \(-0.356522\pi\)
0.435641 + 0.900121i \(0.356522\pi\)
\(798\) −0.782463 −0.0276989
\(799\) 7.53446 0.266550
\(800\) 2.41046 0.0852225
\(801\) 15.9379 0.563138
\(802\) 7.56348 0.267076
\(803\) −6.84972 −0.241721
\(804\) −11.1727 −0.394030
\(805\) −11.8099 −0.416245
\(806\) −0.0276690 −0.000974597 0
\(807\) −15.5981 −0.549078
\(808\) −10.4287 −0.366880
\(809\) −7.85945 −0.276323 −0.138162 0.990410i \(-0.544119\pi\)
−0.138162 + 0.990410i \(0.544119\pi\)
\(810\) −2.30381 −0.0809477
\(811\) −3.90177 −0.137010 −0.0685048 0.997651i \(-0.521823\pi\)
−0.0685048 + 0.997651i \(0.521823\pi\)
\(812\) 6.01497 0.211084
\(813\) 17.1545 0.601636
\(814\) −1.70551 −0.0597781
\(815\) −24.0480 −0.842366
\(816\) −11.3725 −0.398117
\(817\) 32.5388 1.13839
\(818\) −1.10057 −0.0384805
\(819\) 0.913673 0.0319263
\(820\) 10.8346 0.378362
\(821\) −35.8129 −1.24988 −0.624940 0.780673i \(-0.714877\pi\)
−0.624940 + 0.780673i \(0.714877\pi\)
\(822\) −2.55257 −0.0890312
\(823\) 17.2606 0.601666 0.300833 0.953677i \(-0.402735\pi\)
0.300833 + 0.953677i \(0.402735\pi\)
\(824\) 7.17114 0.249818
\(825\) −1.36194 −0.0474168
\(826\) 0.198114 0.00689326
\(827\) 21.7249 0.755450 0.377725 0.925918i \(-0.376706\pi\)
0.377725 + 0.925918i \(0.376706\pi\)
\(828\) 22.1421 0.769492
\(829\) 19.5563 0.679218 0.339609 0.940567i \(-0.389705\pi\)
0.339609 + 0.940567i \(0.389705\pi\)
\(830\) −1.29917 −0.0450950
\(831\) −12.7333 −0.441714
\(832\) 2.45469 0.0851009
\(833\) −23.6674 −0.820027
\(834\) −0.771333 −0.0267091
\(835\) −6.74392 −0.233383
\(836\) −15.1413 −0.523673
\(837\) 1.17987 0.0407821
\(838\) 5.49669 0.189880
\(839\) −4.74068 −0.163667 −0.0818333 0.996646i \(-0.526078\pi\)
−0.0818333 + 0.996646i \(0.526078\pi\)
\(840\) −2.00412 −0.0691487
\(841\) −19.4748 −0.671544
\(842\) 3.39938 0.117150
\(843\) −23.9247 −0.824009
\(844\) −5.71856 −0.196841
\(845\) 30.9611 1.06509
\(846\) −1.17789 −0.0404967
\(847\) −6.56324 −0.225516
\(848\) 30.5889 1.05043
\(849\) 2.67333 0.0917486
\(850\) 0.832589 0.0285576
\(851\) −14.9081 −0.511044
\(852\) 20.8684 0.714941
\(853\) 20.3318 0.696147 0.348073 0.937467i \(-0.386836\pi\)
0.348073 + 0.937467i \(0.386836\pi\)
\(854\) 2.24157 0.0767051
\(855\) 21.0186 0.718820
\(856\) −0.306870 −0.0104886
\(857\) −36.5460 −1.24839 −0.624194 0.781269i \(-0.714573\pi\)
−0.624194 + 0.781269i \(0.714573\pi\)
\(858\) 0.170607 0.00582441
\(859\) 49.2965 1.68197 0.840987 0.541056i \(-0.181975\pi\)
0.840987 + 0.541056i \(0.181975\pi\)
\(860\) 40.9426 1.39613
\(861\) −1.88029 −0.0640800
\(862\) −2.43163 −0.0828217
\(863\) 23.9058 0.813763 0.406881 0.913481i \(-0.366616\pi\)
0.406881 + 0.913481i \(0.366616\pi\)
\(864\) 12.8758 0.438045
\(865\) −20.8002 −0.707228
\(866\) −1.58870 −0.0539862
\(867\) 1.07594 0.0365409
\(868\) −0.536220 −0.0182005
\(869\) −12.6503 −0.429133
\(870\) −1.55912 −0.0528590
\(871\) 2.77416 0.0939988
\(872\) −14.9084 −0.504863
\(873\) −3.81504 −0.129120
\(874\) 4.70833 0.159262
\(875\) 10.2029 0.344922
\(876\) −4.99151 −0.168647
\(877\) 43.0857 1.45490 0.727451 0.686160i \(-0.240705\pi\)
0.727451 + 0.686160i \(0.240705\pi\)
\(878\) 2.15892 0.0728600
\(879\) −3.41199 −0.115083
\(880\) −18.3500 −0.618577
\(881\) 11.7673 0.396451 0.198225 0.980156i \(-0.436482\pi\)
0.198225 + 0.980156i \(0.436482\pi\)
\(882\) 3.70002 0.124586
\(883\) 24.4742 0.823623 0.411811 0.911269i \(-0.364896\pi\)
0.411811 + 0.911269i \(0.364896\pi\)
\(884\) 2.93178 0.0986065
\(885\) 1.44353 0.0485236
\(886\) 2.82279 0.0948334
\(887\) −13.6220 −0.457381 −0.228691 0.973499i \(-0.573444\pi\)
−0.228691 + 0.973499i \(0.573444\pi\)
\(888\) −2.52988 −0.0848973
\(889\) 9.33260 0.313005
\(890\) 4.26434 0.142941
\(891\) 7.73671 0.259190
\(892\) 23.2109 0.777159
\(893\) 7.04073 0.235609
\(894\) 0.674756 0.0225672
\(895\) −39.2645 −1.31247
\(896\) −7.75224 −0.258984
\(897\) 1.49130 0.0497930
\(898\) 5.81831 0.194159
\(899\) −0.849151 −0.0283208
\(900\) 3.65888 0.121963
\(901\) 33.6897 1.12237
\(902\) 1.29437 0.0430978
\(903\) −7.10534 −0.236451
\(904\) 9.80715 0.326181
\(905\) 52.9890 1.76141
\(906\) −1.81701 −0.0603662
\(907\) 41.7337 1.38574 0.692872 0.721061i \(-0.256345\pi\)
0.692872 + 0.721061i \(0.256345\pi\)
\(908\) 8.49846 0.282031
\(909\) −23.8832 −0.792156
\(910\) 0.244462 0.00810384
\(911\) 7.64253 0.253208 0.126604 0.991953i \(-0.459592\pi\)
0.126604 + 0.991953i \(0.459592\pi\)
\(912\) −10.6272 −0.351903
\(913\) 4.36291 0.144391
\(914\) −3.74058 −0.123727
\(915\) 16.3329 0.539949
\(916\) −30.2215 −0.998545
\(917\) −5.69221 −0.187973
\(918\) 4.44740 0.146786
\(919\) 4.45650 0.147006 0.0735032 0.997295i \(-0.476582\pi\)
0.0735032 + 0.997295i \(0.476582\pi\)
\(920\) 12.0594 0.397588
\(921\) 11.5133 0.379377
\(922\) −1.86529 −0.0614302
\(923\) −5.18160 −0.170555
\(924\) 3.30633 0.108770
\(925\) −2.46350 −0.0809992
\(926\) −8.91795 −0.293062
\(927\) 16.4229 0.539400
\(928\) −9.26676 −0.304196
\(929\) 29.8968 0.980881 0.490440 0.871475i \(-0.336836\pi\)
0.490440 + 0.871475i \(0.336836\pi\)
\(930\) 0.138992 0.00455771
\(931\) −22.1165 −0.724838
\(932\) 17.3830 0.569401
\(933\) 8.08978 0.264847
\(934\) −9.12840 −0.298690
\(935\) −20.2101 −0.660941
\(936\) −0.932978 −0.0304953
\(937\) −39.2012 −1.28065 −0.640323 0.768106i \(-0.721200\pi\)
−0.640323 + 0.768106i \(0.721200\pi\)
\(938\) −1.91257 −0.0624476
\(939\) −1.54626 −0.0504604
\(940\) 8.85912 0.288953
\(941\) −20.1105 −0.655584 −0.327792 0.944750i \(-0.606305\pi\)
−0.327792 + 0.944750i \(0.606305\pi\)
\(942\) −3.88568 −0.126602
\(943\) 11.3143 0.368444
\(944\) 2.69074 0.0875761
\(945\) −10.4244 −0.339106
\(946\) 4.89125 0.159028
\(947\) −56.7523 −1.84420 −0.922102 0.386948i \(-0.873529\pi\)
−0.922102 + 0.386948i \(0.873529\pi\)
\(948\) −9.21852 −0.299404
\(949\) 1.23939 0.0402321
\(950\) 0.778028 0.0252426
\(951\) 2.72888 0.0884902
\(952\) −4.11438 −0.133348
\(953\) 49.6844 1.60943 0.804717 0.593658i \(-0.202317\pi\)
0.804717 + 0.593658i \(0.202317\pi\)
\(954\) −5.26683 −0.170520
\(955\) −21.1815 −0.685416
\(956\) −24.4656 −0.791273
\(957\) 5.23586 0.169251
\(958\) 1.14674 0.0370495
\(959\) 12.2830 0.396637
\(960\) −12.3308 −0.397975
\(961\) −30.9243 −0.997558
\(962\) 0.308594 0.00994948
\(963\) −0.702777 −0.0226467
\(964\) −28.7160 −0.924880
\(965\) −3.62444 −0.116675
\(966\) −1.02813 −0.0330797
\(967\) −0.945457 −0.0304039 −0.0152019 0.999884i \(-0.504839\pi\)
−0.0152019 + 0.999884i \(0.504839\pi\)
\(968\) 6.70191 0.215408
\(969\) −11.7045 −0.376004
\(970\) −1.02075 −0.0327744
\(971\) 6.60315 0.211905 0.105953 0.994371i \(-0.466211\pi\)
0.105953 + 0.994371i \(0.466211\pi\)
\(972\) 30.4838 0.977769
\(973\) 3.71165 0.118990
\(974\) −4.68767 −0.150203
\(975\) 0.246430 0.00789206
\(976\) 30.4446 0.974508
\(977\) −1.77714 −0.0568558 −0.0284279 0.999596i \(-0.509050\pi\)
−0.0284279 + 0.999596i \(0.509050\pi\)
\(978\) −2.09355 −0.0669443
\(979\) −14.3206 −0.457688
\(980\) −27.8285 −0.888948
\(981\) −34.1424 −1.09008
\(982\) −5.37253 −0.171444
\(983\) 50.3861 1.60707 0.803534 0.595259i \(-0.202950\pi\)
0.803534 + 0.595259i \(0.202950\pi\)
\(984\) 1.92001 0.0612078
\(985\) 9.58628 0.305444
\(986\) −3.20080 −0.101934
\(987\) −1.53745 −0.0489375
\(988\) 2.73966 0.0871602
\(989\) 42.7551 1.35953
\(990\) 3.15952 0.100416
\(991\) 38.9186 1.23629 0.618144 0.786065i \(-0.287885\pi\)
0.618144 + 0.786065i \(0.287885\pi\)
\(992\) 0.826110 0.0262290
\(993\) 4.01058 0.127272
\(994\) 3.57232 0.113307
\(995\) 54.5223 1.72847
\(996\) 3.17933 0.100741
\(997\) 59.0463 1.87002 0.935008 0.354627i \(-0.115392\pi\)
0.935008 + 0.354627i \(0.115392\pi\)
\(998\) −9.46899 −0.299736
\(999\) −13.1592 −0.416337
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 \(a_p\))