Properties

Label 4003.2.a.b.1.11
Level 4003
Weight 2
Character 4003.1
Self dual Yes
Analytic conductor 31.964
Analytic rank 1
Dimension 152
CM No

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Newspace parameters

Level: \( N \) = \( 4003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9641159291\)
Analytic rank: \(1\)
Dimension: \(152\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.57418 q^{2} +1.68195 q^{3} +4.62641 q^{4} -3.90988 q^{5} -4.32965 q^{6} +1.64141 q^{7} -6.76085 q^{8} -0.171031 q^{9} +O(q^{10})\) \(q-2.57418 q^{2} +1.68195 q^{3} +4.62641 q^{4} -3.90988 q^{5} -4.32965 q^{6} +1.64141 q^{7} -6.76085 q^{8} -0.171031 q^{9} +10.0647 q^{10} -2.81413 q^{11} +7.78141 q^{12} -1.31278 q^{13} -4.22528 q^{14} -6.57624 q^{15} +8.15084 q^{16} +6.25005 q^{17} +0.440264 q^{18} +2.24150 q^{19} -18.0887 q^{20} +2.76077 q^{21} +7.24408 q^{22} -6.83949 q^{23} -11.3714 q^{24} +10.2872 q^{25} +3.37934 q^{26} -5.33353 q^{27} +7.59382 q^{28} +2.21320 q^{29} +16.9284 q^{30} +2.29852 q^{31} -7.46004 q^{32} -4.73324 q^{33} -16.0888 q^{34} -6.41770 q^{35} -0.791257 q^{36} +10.0689 q^{37} -5.77003 q^{38} -2.20804 q^{39} +26.4341 q^{40} +5.39843 q^{41} -7.10672 q^{42} -6.85484 q^{43} -13.0193 q^{44} +0.668709 q^{45} +17.6061 q^{46} +2.35069 q^{47} +13.7093 q^{48} -4.30579 q^{49} -26.4810 q^{50} +10.5123 q^{51} -6.07346 q^{52} -0.921929 q^{53} +13.7295 q^{54} +11.0029 q^{55} -11.0973 q^{56} +3.77010 q^{57} -5.69717 q^{58} -5.04597 q^{59} -30.4244 q^{60} -5.37742 q^{61} -5.91680 q^{62} -0.280731 q^{63} +2.90180 q^{64} +5.13282 q^{65} +12.1842 q^{66} +12.8008 q^{67} +28.9153 q^{68} -11.5037 q^{69} +16.5203 q^{70} +3.30042 q^{71} +1.15631 q^{72} -3.61155 q^{73} -25.9192 q^{74} +17.3025 q^{75} +10.3701 q^{76} -4.61913 q^{77} +5.68389 q^{78} +12.8611 q^{79} -31.8688 q^{80} -8.45766 q^{81} -13.8965 q^{82} -0.794973 q^{83} +12.7724 q^{84} -24.4370 q^{85} +17.6456 q^{86} +3.72249 q^{87} +19.0259 q^{88} +4.96940 q^{89} -1.72138 q^{90} -2.15481 q^{91} -31.6423 q^{92} +3.86600 q^{93} -6.05111 q^{94} -8.76400 q^{95} -12.5474 q^{96} +5.63651 q^{97} +11.0839 q^{98} +0.481302 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} + O(q^{10}) \) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} - 15q^{10} - 40q^{11} - 53q^{12} - 59q^{13} - 36q^{14} - 40q^{15} + 118q^{16} - 93q^{17} - 59q^{18} - 16q^{19} - 108q^{20} - 62q^{21} - 37q^{22} - 107q^{23} - 31q^{24} + 101q^{25} - 64q^{26} - 63q^{27} - 53q^{28} - 124q^{29} - 68q^{30} - 15q^{31} - 129q^{32} - 49q^{33} - 76q^{35} + 45q^{36} - 98q^{37} - 125q^{38} - 47q^{39} - 7q^{40} - 56q^{41} - 84q^{42} - 62q^{43} - 114q^{44} - 142q^{45} - 3q^{46} - 111q^{47} - 92q^{48} + 117q^{49} - 64q^{50} - 21q^{51} - 85q^{52} - 347q^{53} + 3q^{54} - 16q^{55} - 73q^{56} - 115q^{57} - 29q^{58} - 50q^{59} - 54q^{60} - 62q^{61} - 55q^{62} - 70q^{63} + 64q^{64} - 147q^{65} + 34q^{66} - 86q^{67} - 174q^{68} - 104q^{69} - 7q^{70} - 86q^{71} - 139q^{72} - 27q^{73} - 52q^{74} - 49q^{75} - 11q^{76} - 346q^{77} - 59q^{78} - 17q^{79} - 149q^{80} - 8q^{81} - 31q^{82} - 106q^{83} - 51q^{84} - 69q^{85} - 85q^{86} - 32q^{87} - 113q^{88} - 59q^{89} + 10q^{90} - 9q^{91} - 314q^{92} - 230q^{93} + 7q^{94} - 74q^{95} - 54q^{96} - 60q^{97} - 77q^{98} - 96q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.57418 −1.82022 −0.910110 0.414366i \(-0.864003\pi\)
−0.910110 + 0.414366i \(0.864003\pi\)
\(3\) 1.68195 0.971077 0.485538 0.874215i \(-0.338624\pi\)
0.485538 + 0.874215i \(0.338624\pi\)
\(4\) 4.62641 2.31320
\(5\) −3.90988 −1.74855 −0.874275 0.485430i \(-0.838663\pi\)
−0.874275 + 0.485430i \(0.838663\pi\)
\(6\) −4.32965 −1.76757
\(7\) 1.64141 0.620393 0.310197 0.950672i \(-0.399605\pi\)
0.310197 + 0.950672i \(0.399605\pi\)
\(8\) −6.76085 −2.39032
\(9\) −0.171031 −0.0570102
\(10\) 10.0647 3.18275
\(11\) −2.81413 −0.848492 −0.424246 0.905547i \(-0.639461\pi\)
−0.424246 + 0.905547i \(0.639461\pi\)
\(12\) 7.78141 2.24630
\(13\) −1.31278 −0.364100 −0.182050 0.983289i \(-0.558273\pi\)
−0.182050 + 0.983289i \(0.558273\pi\)
\(14\) −4.22528 −1.12925
\(15\) −6.57624 −1.69798
\(16\) 8.15084 2.03771
\(17\) 6.25005 1.51586 0.757930 0.652335i \(-0.226211\pi\)
0.757930 + 0.652335i \(0.226211\pi\)
\(18\) 0.440264 0.103771
\(19\) 2.24150 0.514236 0.257118 0.966380i \(-0.417227\pi\)
0.257118 + 0.966380i \(0.417227\pi\)
\(20\) −18.0887 −4.04476
\(21\) 2.76077 0.602449
\(22\) 7.24408 1.54444
\(23\) −6.83949 −1.42613 −0.713066 0.701097i \(-0.752694\pi\)
−0.713066 + 0.701097i \(0.752694\pi\)
\(24\) −11.3714 −2.32119
\(25\) 10.2872 2.05743
\(26\) 3.37934 0.662743
\(27\) −5.33353 −1.02644
\(28\) 7.59382 1.43510
\(29\) 2.21320 0.410980 0.205490 0.978659i \(-0.434121\pi\)
0.205490 + 0.978659i \(0.434121\pi\)
\(30\) 16.9284 3.09069
\(31\) 2.29852 0.412826 0.206413 0.978465i \(-0.433821\pi\)
0.206413 + 0.978465i \(0.433821\pi\)
\(32\) −7.46004 −1.31876
\(33\) −4.73324 −0.823951
\(34\) −16.0888 −2.75920
\(35\) −6.41770 −1.08479
\(36\) −0.791257 −0.131876
\(37\) 10.0689 1.65532 0.827659 0.561231i \(-0.189672\pi\)
0.827659 + 0.561231i \(0.189672\pi\)
\(38\) −5.77003 −0.936023
\(39\) −2.20804 −0.353569
\(40\) 26.4341 4.17960
\(41\) 5.39843 0.843093 0.421547 0.906807i \(-0.361487\pi\)
0.421547 + 0.906807i \(0.361487\pi\)
\(42\) −7.10672 −1.09659
\(43\) −6.85484 −1.04535 −0.522677 0.852531i \(-0.675067\pi\)
−0.522677 + 0.852531i \(0.675067\pi\)
\(44\) −13.0193 −1.96274
\(45\) 0.668709 0.0996852
\(46\) 17.6061 2.59588
\(47\) 2.35069 0.342884 0.171442 0.985194i \(-0.445157\pi\)
0.171442 + 0.985194i \(0.445157\pi\)
\(48\) 13.7093 1.97877
\(49\) −4.30579 −0.615112
\(50\) −26.4810 −3.74498
\(51\) 10.5123 1.47202
\(52\) −6.07346 −0.842238
\(53\) −0.921929 −0.126637 −0.0633184 0.997993i \(-0.520168\pi\)
−0.0633184 + 0.997993i \(0.520168\pi\)
\(54\) 13.7295 1.86834
\(55\) 11.0029 1.48363
\(56\) −11.0973 −1.48294
\(57\) 3.77010 0.499362
\(58\) −5.69717 −0.748075
\(59\) −5.04597 −0.656929 −0.328465 0.944516i \(-0.606531\pi\)
−0.328465 + 0.944516i \(0.606531\pi\)
\(60\) −30.4244 −3.92777
\(61\) −5.37742 −0.688508 −0.344254 0.938877i \(-0.611868\pi\)
−0.344254 + 0.938877i \(0.611868\pi\)
\(62\) −5.91680 −0.751435
\(63\) −0.280731 −0.0353687
\(64\) 2.90180 0.362725
\(65\) 5.13282 0.636648
\(66\) 12.1842 1.49977
\(67\) 12.8008 1.56387 0.781936 0.623359i \(-0.214232\pi\)
0.781936 + 0.623359i \(0.214232\pi\)
\(68\) 28.9153 3.50650
\(69\) −11.5037 −1.38488
\(70\) 16.5203 1.97456
\(71\) 3.30042 0.391688 0.195844 0.980635i \(-0.437255\pi\)
0.195844 + 0.980635i \(0.437255\pi\)
\(72\) 1.15631 0.136273
\(73\) −3.61155 −0.422700 −0.211350 0.977410i \(-0.567786\pi\)
−0.211350 + 0.977410i \(0.567786\pi\)
\(74\) −25.9192 −3.01304
\(75\) 17.3025 1.99792
\(76\) 10.3701 1.18953
\(77\) −4.61913 −0.526399
\(78\) 5.68389 0.643574
\(79\) 12.8611 1.44699 0.723495 0.690330i \(-0.242535\pi\)
0.723495 + 0.690330i \(0.242535\pi\)
\(80\) −31.8688 −3.56304
\(81\) −8.45766 −0.939740
\(82\) −13.8965 −1.53462
\(83\) −0.794973 −0.0872596 −0.0436298 0.999048i \(-0.513892\pi\)
−0.0436298 + 0.999048i \(0.513892\pi\)
\(84\) 12.7724 1.39359
\(85\) −24.4370 −2.65056
\(86\) 17.6456 1.90277
\(87\) 3.72249 0.399093
\(88\) 19.0259 2.02817
\(89\) 4.96940 0.526755 0.263378 0.964693i \(-0.415163\pi\)
0.263378 + 0.964693i \(0.415163\pi\)
\(90\) −1.72138 −0.181449
\(91\) −2.15481 −0.225885
\(92\) −31.6423 −3.29894
\(93\) 3.86600 0.400886
\(94\) −6.05111 −0.624124
\(95\) −8.76400 −0.899168
\(96\) −12.5474 −1.28062
\(97\) 5.63651 0.572301 0.286150 0.958185i \(-0.407624\pi\)
0.286150 + 0.958185i \(0.407624\pi\)
\(98\) 11.0839 1.11964
\(99\) 0.481302 0.0483727
\(100\) 47.5926 4.75926
\(101\) −7.93993 −0.790052 −0.395026 0.918670i \(-0.629264\pi\)
−0.395026 + 0.918670i \(0.629264\pi\)
\(102\) −27.0606 −2.67940
\(103\) 4.72876 0.465938 0.232969 0.972484i \(-0.425156\pi\)
0.232969 + 0.972484i \(0.425156\pi\)
\(104\) 8.87552 0.870317
\(105\) −10.7943 −1.05341
\(106\) 2.37321 0.230507
\(107\) −16.5157 −1.59663 −0.798317 0.602237i \(-0.794276\pi\)
−0.798317 + 0.602237i \(0.794276\pi\)
\(108\) −24.6751 −2.37436
\(109\) −18.9129 −1.81153 −0.905764 0.423782i \(-0.860702\pi\)
−0.905764 + 0.423782i \(0.860702\pi\)
\(110\) −28.3235 −2.70054
\(111\) 16.9354 1.60744
\(112\) 13.3788 1.26418
\(113\) −7.47603 −0.703286 −0.351643 0.936134i \(-0.614377\pi\)
−0.351643 + 0.936134i \(0.614377\pi\)
\(114\) −9.70493 −0.908950
\(115\) 26.7416 2.49367
\(116\) 10.2392 0.950681
\(117\) 0.224526 0.0207574
\(118\) 12.9892 1.19576
\(119\) 10.2589 0.940430
\(120\) 44.4610 4.05871
\(121\) −3.08067 −0.280061
\(122\) 13.8424 1.25324
\(123\) 9.07991 0.818708
\(124\) 10.6339 0.954951
\(125\) −20.6721 −1.84897
\(126\) 0.722652 0.0643789
\(127\) −5.22643 −0.463770 −0.231885 0.972743i \(-0.574489\pi\)
−0.231885 + 0.972743i \(0.574489\pi\)
\(128\) 7.45031 0.658520
\(129\) −11.5295 −1.01512
\(130\) −13.2128 −1.15884
\(131\) 13.2445 1.15718 0.578590 0.815619i \(-0.303603\pi\)
0.578590 + 0.815619i \(0.303603\pi\)
\(132\) −21.8979 −1.90597
\(133\) 3.67922 0.319028
\(134\) −32.9517 −2.84659
\(135\) 20.8534 1.79478
\(136\) −42.2557 −3.62340
\(137\) 18.4405 1.57548 0.787741 0.616007i \(-0.211251\pi\)
0.787741 + 0.616007i \(0.211251\pi\)
\(138\) 29.6126 2.52079
\(139\) −15.7244 −1.33372 −0.666861 0.745182i \(-0.732363\pi\)
−0.666861 + 0.745182i \(0.732363\pi\)
\(140\) −29.6909 −2.50934
\(141\) 3.95376 0.332966
\(142\) −8.49587 −0.712958
\(143\) 3.69434 0.308936
\(144\) −1.39404 −0.116170
\(145\) −8.65333 −0.718620
\(146\) 9.29679 0.769408
\(147\) −7.24213 −0.597321
\(148\) 46.5829 3.82909
\(149\) −13.7306 −1.12485 −0.562426 0.826848i \(-0.690132\pi\)
−0.562426 + 0.826848i \(0.690132\pi\)
\(150\) −44.5398 −3.63666
\(151\) 0.503504 0.0409746 0.0204873 0.999790i \(-0.493478\pi\)
0.0204873 + 0.999790i \(0.493478\pi\)
\(152\) −15.1545 −1.22919
\(153\) −1.06895 −0.0864195
\(154\) 11.8905 0.958162
\(155\) −8.98693 −0.721848
\(156\) −10.2153 −0.817878
\(157\) −11.4268 −0.911961 −0.455981 0.889990i \(-0.650711\pi\)
−0.455981 + 0.889990i \(0.650711\pi\)
\(158\) −33.1069 −2.63384
\(159\) −1.55064 −0.122974
\(160\) 29.1678 2.30592
\(161\) −11.2264 −0.884763
\(162\) 21.7715 1.71053
\(163\) −12.5192 −0.980578 −0.490289 0.871560i \(-0.663109\pi\)
−0.490289 + 0.871560i \(0.663109\pi\)
\(164\) 24.9753 1.95025
\(165\) 18.5064 1.44072
\(166\) 2.04640 0.158832
\(167\) −24.2451 −1.87614 −0.938070 0.346446i \(-0.887388\pi\)
−0.938070 + 0.346446i \(0.887388\pi\)
\(168\) −18.6652 −1.44005
\(169\) −11.2766 −0.867431
\(170\) 62.9051 4.82460
\(171\) −0.383365 −0.0293167
\(172\) −31.7133 −2.41812
\(173\) 2.60144 0.197784 0.0988920 0.995098i \(-0.468470\pi\)
0.0988920 + 0.995098i \(0.468470\pi\)
\(174\) −9.58238 −0.726438
\(175\) 16.8854 1.27642
\(176\) −22.9375 −1.72898
\(177\) −8.48709 −0.637929
\(178\) −12.7921 −0.958811
\(179\) −16.3474 −1.22187 −0.610933 0.791682i \(-0.709205\pi\)
−0.610933 + 0.791682i \(0.709205\pi\)
\(180\) 3.09372 0.230592
\(181\) −11.2401 −0.835467 −0.417734 0.908570i \(-0.637175\pi\)
−0.417734 + 0.908570i \(0.637175\pi\)
\(182\) 5.54687 0.411161
\(183\) −9.04457 −0.668594
\(184\) 46.2408 3.40892
\(185\) −39.3682 −2.89441
\(186\) −9.95179 −0.729701
\(187\) −17.5885 −1.28620
\(188\) 10.8753 0.793160
\(189\) −8.75448 −0.636795
\(190\) 22.5601 1.63668
\(191\) 7.65034 0.553559 0.276780 0.960933i \(-0.410733\pi\)
0.276780 + 0.960933i \(0.410733\pi\)
\(192\) 4.88070 0.352234
\(193\) −18.8090 −1.35390 −0.676952 0.736027i \(-0.736700\pi\)
−0.676952 + 0.736027i \(0.736700\pi\)
\(194\) −14.5094 −1.04171
\(195\) 8.63316 0.618234
\(196\) −19.9203 −1.42288
\(197\) −1.69956 −0.121089 −0.0605444 0.998166i \(-0.519284\pi\)
−0.0605444 + 0.998166i \(0.519284\pi\)
\(198\) −1.23896 −0.0880490
\(199\) 9.35245 0.662978 0.331489 0.943459i \(-0.392449\pi\)
0.331489 + 0.943459i \(0.392449\pi\)
\(200\) −69.5499 −4.91792
\(201\) 21.5304 1.51864
\(202\) 20.4388 1.43807
\(203\) 3.63275 0.254969
\(204\) 48.6342 3.40508
\(205\) −21.1072 −1.47419
\(206\) −12.1727 −0.848110
\(207\) 1.16976 0.0813041
\(208\) −10.7003 −0.741930
\(209\) −6.30788 −0.436325
\(210\) 27.7864 1.91745
\(211\) 16.3239 1.12378 0.561890 0.827212i \(-0.310074\pi\)
0.561890 + 0.827212i \(0.310074\pi\)
\(212\) −4.26522 −0.292937
\(213\) 5.55115 0.380359
\(214\) 42.5145 2.90623
\(215\) 26.8016 1.82785
\(216\) 36.0592 2.45352
\(217\) 3.77280 0.256115
\(218\) 48.6853 3.29738
\(219\) −6.07447 −0.410474
\(220\) 50.9039 3.43194
\(221\) −8.20496 −0.551925
\(222\) −43.5949 −2.92590
\(223\) −11.9494 −0.800192 −0.400096 0.916473i \(-0.631023\pi\)
−0.400096 + 0.916473i \(0.631023\pi\)
\(224\) −12.2449 −0.818150
\(225\) −1.75942 −0.117295
\(226\) 19.2447 1.28014
\(227\) 8.50040 0.564192 0.282096 0.959386i \(-0.408970\pi\)
0.282096 + 0.959386i \(0.408970\pi\)
\(228\) 17.4420 1.15513
\(229\) 3.78194 0.249918 0.124959 0.992162i \(-0.460120\pi\)
0.124959 + 0.992162i \(0.460120\pi\)
\(230\) −68.8377 −4.53902
\(231\) −7.76916 −0.511173
\(232\) −14.9631 −0.982375
\(233\) 12.7680 0.836457 0.418228 0.908342i \(-0.362651\pi\)
0.418228 + 0.908342i \(0.362651\pi\)
\(234\) −0.577970 −0.0377831
\(235\) −9.19093 −0.599550
\(236\) −23.3447 −1.51961
\(237\) 21.6318 1.40514
\(238\) −26.4082 −1.71179
\(239\) 8.46041 0.547258 0.273629 0.961835i \(-0.411776\pi\)
0.273629 + 0.961835i \(0.411776\pi\)
\(240\) −53.6019 −3.45998
\(241\) 25.3492 1.63288 0.816442 0.577427i \(-0.195943\pi\)
0.816442 + 0.577427i \(0.195943\pi\)
\(242\) 7.93021 0.509773
\(243\) 1.77519 0.113879
\(244\) −24.8781 −1.59266
\(245\) 16.8351 1.07556
\(246\) −23.3733 −1.49023
\(247\) −2.94260 −0.187233
\(248\) −15.5399 −0.986788
\(249\) −1.33711 −0.0847357
\(250\) 53.2138 3.36554
\(251\) −16.1833 −1.02148 −0.510740 0.859735i \(-0.670629\pi\)
−0.510740 + 0.859735i \(0.670629\pi\)
\(252\) −1.29877 −0.0818151
\(253\) 19.2472 1.21006
\(254\) 13.4538 0.844165
\(255\) −41.1018 −2.57390
\(256\) −24.9820 −1.56138
\(257\) −7.52711 −0.469528 −0.234764 0.972052i \(-0.575432\pi\)
−0.234764 + 0.972052i \(0.575432\pi\)
\(258\) 29.6791 1.84774
\(259\) 16.5272 1.02695
\(260\) 23.7465 1.47270
\(261\) −0.378524 −0.0234301
\(262\) −34.0938 −2.10632
\(263\) 1.37815 0.0849805 0.0424902 0.999097i \(-0.486471\pi\)
0.0424902 + 0.999097i \(0.486471\pi\)
\(264\) 32.0007 1.96951
\(265\) 3.60463 0.221431
\(266\) −9.47097 −0.580702
\(267\) 8.35830 0.511520
\(268\) 59.2219 3.61755
\(269\) −22.4390 −1.36813 −0.684064 0.729422i \(-0.739789\pi\)
−0.684064 + 0.729422i \(0.739789\pi\)
\(270\) −53.6806 −3.26689
\(271\) −1.74848 −0.106213 −0.0531063 0.998589i \(-0.516912\pi\)
−0.0531063 + 0.998589i \(0.516912\pi\)
\(272\) 50.9432 3.08888
\(273\) −3.62429 −0.219352
\(274\) −47.4693 −2.86772
\(275\) −28.9494 −1.74571
\(276\) −53.2209 −3.20352
\(277\) −1.62754 −0.0977894 −0.0488947 0.998804i \(-0.515570\pi\)
−0.0488947 + 0.998804i \(0.515570\pi\)
\(278\) 40.4773 2.42767
\(279\) −0.393117 −0.0235353
\(280\) 43.3891 2.59300
\(281\) 10.5531 0.629546 0.314773 0.949167i \(-0.398072\pi\)
0.314773 + 0.949167i \(0.398072\pi\)
\(282\) −10.1777 −0.606073
\(283\) −11.1400 −0.662203 −0.331101 0.943595i \(-0.607420\pi\)
−0.331101 + 0.943595i \(0.607420\pi\)
\(284\) 15.2691 0.906053
\(285\) −14.7407 −0.873161
\(286\) −9.50990 −0.562332
\(287\) 8.86101 0.523049
\(288\) 1.27589 0.0751828
\(289\) 22.0632 1.29783
\(290\) 22.2752 1.30805
\(291\) 9.48035 0.555748
\(292\) −16.7085 −0.977792
\(293\) 2.72502 0.159197 0.0795986 0.996827i \(-0.474636\pi\)
0.0795986 + 0.996827i \(0.474636\pi\)
\(294\) 18.6426 1.08726
\(295\) 19.7291 1.14867
\(296\) −68.0744 −3.95674
\(297\) 15.0092 0.870924
\(298\) 35.3450 2.04748
\(299\) 8.97876 0.519255
\(300\) 80.0485 4.62160
\(301\) −11.2516 −0.648530
\(302\) −1.29611 −0.0745828
\(303\) −13.3546 −0.767201
\(304\) 18.2701 1.04786
\(305\) 21.0251 1.20389
\(306\) 2.75167 0.157303
\(307\) −3.92758 −0.224159 −0.112080 0.993699i \(-0.535751\pi\)
−0.112080 + 0.993699i \(0.535751\pi\)
\(308\) −21.3700 −1.21767
\(309\) 7.95355 0.452462
\(310\) 23.1340 1.31392
\(311\) 11.5196 0.653217 0.326609 0.945160i \(-0.394094\pi\)
0.326609 + 0.945160i \(0.394094\pi\)
\(312\) 14.9282 0.845144
\(313\) 26.4712 1.49624 0.748121 0.663562i \(-0.230956\pi\)
0.748121 + 0.663562i \(0.230956\pi\)
\(314\) 29.4148 1.65997
\(315\) 1.09762 0.0618440
\(316\) 59.5008 3.34718
\(317\) −33.7517 −1.89569 −0.947844 0.318736i \(-0.896742\pi\)
−0.947844 + 0.318736i \(0.896742\pi\)
\(318\) 3.99164 0.223840
\(319\) −6.22822 −0.348713
\(320\) −11.3457 −0.634244
\(321\) −27.7787 −1.55045
\(322\) 28.8987 1.61046
\(323\) 14.0095 0.779510
\(324\) −39.1286 −2.17381
\(325\) −13.5048 −0.749111
\(326\) 32.2266 1.78487
\(327\) −31.8106 −1.75913
\(328\) −36.4980 −2.01526
\(329\) 3.85844 0.212723
\(330\) −47.6388 −2.62243
\(331\) 35.5910 1.95626 0.978128 0.208005i \(-0.0666970\pi\)
0.978128 + 0.208005i \(0.0666970\pi\)
\(332\) −3.67787 −0.201849
\(333\) −1.72209 −0.0943700
\(334\) 62.4112 3.41499
\(335\) −50.0497 −2.73451
\(336\) 22.5026 1.22762
\(337\) −7.41648 −0.404002 −0.202001 0.979385i \(-0.564744\pi\)
−0.202001 + 0.979385i \(0.564744\pi\)
\(338\) 29.0280 1.57892
\(339\) −12.5743 −0.682945
\(340\) −113.055 −6.13129
\(341\) −6.46833 −0.350280
\(342\) 0.986852 0.0533629
\(343\) −18.5574 −1.00200
\(344\) 46.3446 2.49873
\(345\) 44.9781 2.42154
\(346\) −6.69658 −0.360011
\(347\) 6.04385 0.324451 0.162225 0.986754i \(-0.448133\pi\)
0.162225 + 0.986754i \(0.448133\pi\)
\(348\) 17.2218 0.923184
\(349\) −20.4992 −1.09730 −0.548649 0.836053i \(-0.684858\pi\)
−0.548649 + 0.836053i \(0.684858\pi\)
\(350\) −43.4661 −2.32336
\(351\) 7.00176 0.373726
\(352\) 20.9935 1.11896
\(353\) 32.7765 1.74452 0.872259 0.489044i \(-0.162654\pi\)
0.872259 + 0.489044i \(0.162654\pi\)
\(354\) 21.8473 1.16117
\(355\) −12.9042 −0.684886
\(356\) 22.9905 1.21849
\(357\) 17.2550 0.913229
\(358\) 42.0813 2.22407
\(359\) −19.5331 −1.03092 −0.515458 0.856915i \(-0.672378\pi\)
−0.515458 + 0.856915i \(0.672378\pi\)
\(360\) −4.52104 −0.238280
\(361\) −13.9757 −0.735561
\(362\) 28.9340 1.52073
\(363\) −5.18155 −0.271961
\(364\) −9.96902 −0.522519
\(365\) 14.1207 0.739113
\(366\) 23.2824 1.21699
\(367\) −15.1994 −0.793401 −0.396701 0.917948i \(-0.629845\pi\)
−0.396701 + 0.917948i \(0.629845\pi\)
\(368\) −55.7476 −2.90604
\(369\) −0.923297 −0.0480649
\(370\) 101.341 5.26846
\(371\) −1.51326 −0.0785646
\(372\) 17.8857 0.927331
\(373\) −15.9565 −0.826195 −0.413097 0.910687i \(-0.635553\pi\)
−0.413097 + 0.910687i \(0.635553\pi\)
\(374\) 45.2759 2.34116
\(375\) −34.7696 −1.79549
\(376\) −15.8927 −0.819603
\(377\) −2.90544 −0.149638
\(378\) 22.5356 1.15911
\(379\) 3.62806 0.186361 0.0931805 0.995649i \(-0.470297\pi\)
0.0931805 + 0.995649i \(0.470297\pi\)
\(380\) −40.5459 −2.07996
\(381\) −8.79061 −0.450357
\(382\) −19.6934 −1.00760
\(383\) −33.0296 −1.68773 −0.843866 0.536554i \(-0.819726\pi\)
−0.843866 + 0.536554i \(0.819726\pi\)
\(384\) 12.5311 0.639474
\(385\) 18.0602 0.920435
\(386\) 48.4179 2.46440
\(387\) 1.17239 0.0595958
\(388\) 26.0768 1.32385
\(389\) 33.2699 1.68685 0.843425 0.537248i \(-0.180536\pi\)
0.843425 + 0.537248i \(0.180536\pi\)
\(390\) −22.2233 −1.12532
\(391\) −42.7472 −2.16182
\(392\) 29.1108 1.47032
\(393\) 22.2767 1.12371
\(394\) 4.37498 0.220408
\(395\) −50.2854 −2.53013
\(396\) 2.22670 0.111896
\(397\) 6.25079 0.313718 0.156859 0.987621i \(-0.449863\pi\)
0.156859 + 0.987621i \(0.449863\pi\)
\(398\) −24.0749 −1.20677
\(399\) 6.18827 0.309801
\(400\) 83.8489 4.19245
\(401\) 9.72971 0.485878 0.242939 0.970042i \(-0.421888\pi\)
0.242939 + 0.970042i \(0.421888\pi\)
\(402\) −55.4232 −2.76426
\(403\) −3.01745 −0.150310
\(404\) −36.7333 −1.82755
\(405\) 33.0684 1.64318
\(406\) −9.35137 −0.464101
\(407\) −28.3352 −1.40452
\(408\) −71.0721 −3.51859
\(409\) −38.9591 −1.92640 −0.963202 0.268777i \(-0.913381\pi\)
−0.963202 + 0.268777i \(0.913381\pi\)
\(410\) 54.3338 2.68335
\(411\) 31.0161 1.52991
\(412\) 21.8772 1.07781
\(413\) −8.28249 −0.407555
\(414\) −3.01118 −0.147991
\(415\) 3.10825 0.152578
\(416\) 9.79340 0.480161
\(417\) −26.4476 −1.29515
\(418\) 16.2376 0.794208
\(419\) 8.35650 0.408242 0.204121 0.978946i \(-0.434566\pi\)
0.204121 + 0.978946i \(0.434566\pi\)
\(420\) −49.9387 −2.43676
\(421\) −25.5645 −1.24594 −0.622968 0.782248i \(-0.714073\pi\)
−0.622968 + 0.782248i \(0.714073\pi\)
\(422\) −42.0206 −2.04553
\(423\) −0.402040 −0.0195479
\(424\) 6.23303 0.302703
\(425\) 64.2953 3.11878
\(426\) −14.2897 −0.692337
\(427\) −8.82653 −0.427146
\(428\) −76.4085 −3.69334
\(429\) 6.21371 0.300001
\(430\) −68.9922 −3.32710
\(431\) −14.5800 −0.702295 −0.351147 0.936320i \(-0.614208\pi\)
−0.351147 + 0.936320i \(0.614208\pi\)
\(432\) −43.4727 −2.09158
\(433\) −21.9601 −1.05533 −0.527667 0.849451i \(-0.676933\pi\)
−0.527667 + 0.849451i \(0.676933\pi\)
\(434\) −9.71188 −0.466185
\(435\) −14.5545 −0.697835
\(436\) −87.4989 −4.19044
\(437\) −15.3307 −0.733369
\(438\) 15.6368 0.747154
\(439\) −34.2330 −1.63385 −0.816927 0.576741i \(-0.804324\pi\)
−0.816927 + 0.576741i \(0.804324\pi\)
\(440\) −74.3890 −3.54636
\(441\) 0.736421 0.0350677
\(442\) 21.1210 1.00463
\(443\) −24.1910 −1.14935 −0.574675 0.818381i \(-0.694872\pi\)
−0.574675 + 0.818381i \(0.694872\pi\)
\(444\) 78.3503 3.71834
\(445\) −19.4298 −0.921059
\(446\) 30.7600 1.45653
\(447\) −23.0942 −1.09232
\(448\) 4.76304 0.225032
\(449\) −32.6112 −1.53902 −0.769509 0.638636i \(-0.779499\pi\)
−0.769509 + 0.638636i \(0.779499\pi\)
\(450\) 4.52906 0.213502
\(451\) −15.1919 −0.715358
\(452\) −34.5872 −1.62684
\(453\) 0.846871 0.0397895
\(454\) −21.8816 −1.02695
\(455\) 8.42504 0.394972
\(456\) −25.4891 −1.19364
\(457\) 23.0892 1.08007 0.540034 0.841643i \(-0.318411\pi\)
0.540034 + 0.841643i \(0.318411\pi\)
\(458\) −9.73540 −0.454905
\(459\) −33.3348 −1.55594
\(460\) 123.717 5.76836
\(461\) 12.9303 0.602223 0.301112 0.953589i \(-0.402642\pi\)
0.301112 + 0.953589i \(0.402642\pi\)
\(462\) 19.9992 0.930449
\(463\) 3.75957 0.174722 0.0873610 0.996177i \(-0.472157\pi\)
0.0873610 + 0.996177i \(0.472157\pi\)
\(464\) 18.0394 0.837459
\(465\) −15.1156 −0.700969
\(466\) −32.8670 −1.52254
\(467\) −9.98448 −0.462026 −0.231013 0.972951i \(-0.574204\pi\)
−0.231013 + 0.972951i \(0.574204\pi\)
\(468\) 1.03875 0.0480162
\(469\) 21.0114 0.970215
\(470\) 23.6591 1.09131
\(471\) −19.2194 −0.885584
\(472\) 34.1151 1.57027
\(473\) 19.2904 0.886974
\(474\) −55.6842 −2.55766
\(475\) 23.0587 1.05800
\(476\) 47.4618 2.17541
\(477\) 0.157678 0.00721959
\(478\) −21.7786 −0.996131
\(479\) −17.3875 −0.794455 −0.397228 0.917720i \(-0.630028\pi\)
−0.397228 + 0.917720i \(0.630028\pi\)
\(480\) 49.0590 2.23922
\(481\) −13.2183 −0.602702
\(482\) −65.2534 −2.97221
\(483\) −18.8823 −0.859172
\(484\) −14.2525 −0.647839
\(485\) −22.0381 −1.00070
\(486\) −4.56967 −0.207284
\(487\) 24.3573 1.10374 0.551868 0.833931i \(-0.313915\pi\)
0.551868 + 0.833931i \(0.313915\pi\)
\(488\) 36.3559 1.64576
\(489\) −21.0567 −0.952216
\(490\) −43.3366 −1.95775
\(491\) 21.9248 0.989451 0.494725 0.869049i \(-0.335269\pi\)
0.494725 + 0.869049i \(0.335269\pi\)
\(492\) 42.0074 1.89384
\(493\) 13.8326 0.622989
\(494\) 7.57479 0.340806
\(495\) −1.88183 −0.0845821
\(496\) 18.7349 0.841220
\(497\) 5.41733 0.243000
\(498\) 3.44196 0.154238
\(499\) 1.44106 0.0645107 0.0322554 0.999480i \(-0.489731\pi\)
0.0322554 + 0.999480i \(0.489731\pi\)
\(500\) −95.6377 −4.27705
\(501\) −40.7791 −1.82188
\(502\) 41.6587 1.85932
\(503\) −24.1921 −1.07867 −0.539337 0.842090i \(-0.681325\pi\)
−0.539337 + 0.842090i \(0.681325\pi\)
\(504\) 1.89798 0.0845427
\(505\) 31.0441 1.38145
\(506\) −49.5458 −2.20258
\(507\) −18.9667 −0.842342
\(508\) −24.1796 −1.07280
\(509\) −18.4215 −0.816518 −0.408259 0.912866i \(-0.633864\pi\)
−0.408259 + 0.912866i \(0.633864\pi\)
\(510\) 105.804 4.68506
\(511\) −5.92803 −0.262240
\(512\) 49.4077 2.18353
\(513\) −11.9551 −0.527831
\(514\) 19.3762 0.854646
\(515\) −18.4889 −0.814717
\(516\) −53.3403 −2.34818
\(517\) −6.61516 −0.290934
\(518\) −42.5439 −1.86927
\(519\) 4.37551 0.192063
\(520\) −34.7022 −1.52179
\(521\) 8.66130 0.379459 0.189729 0.981836i \(-0.439239\pi\)
0.189729 + 0.981836i \(0.439239\pi\)
\(522\) 0.974390 0.0426479
\(523\) −24.7933 −1.08414 −0.542068 0.840335i \(-0.682358\pi\)
−0.542068 + 0.840335i \(0.682358\pi\)
\(524\) 61.2746 2.67679
\(525\) 28.4005 1.23950
\(526\) −3.54761 −0.154683
\(527\) 14.3659 0.625787
\(528\) −38.5799 −1.67897
\(529\) 23.7786 1.03385
\(530\) −9.27898 −0.403053
\(531\) 0.863015 0.0374517
\(532\) 17.0216 0.737978
\(533\) −7.08696 −0.306970
\(534\) −21.5158 −0.931079
\(535\) 64.5745 2.79180
\(536\) −86.5446 −3.73816
\(537\) −27.4957 −1.18653
\(538\) 57.7619 2.49029
\(539\) 12.1170 0.521918
\(540\) 96.4766 4.15169
\(541\) −18.0975 −0.778074 −0.389037 0.921222i \(-0.627192\pi\)
−0.389037 + 0.921222i \(0.627192\pi\)
\(542\) 4.50091 0.193330
\(543\) −18.9053 −0.811303
\(544\) −46.6256 −1.99906
\(545\) 73.9472 3.16755
\(546\) 9.32957 0.399269
\(547\) 12.7052 0.543235 0.271618 0.962405i \(-0.412441\pi\)
0.271618 + 0.962405i \(0.412441\pi\)
\(548\) 85.3135 3.64441
\(549\) 0.919703 0.0392520
\(550\) 74.5210 3.17758
\(551\) 4.96089 0.211341
\(552\) 77.7749 3.31032
\(553\) 21.1103 0.897702
\(554\) 4.18958 0.177998
\(555\) −66.2155 −2.81069
\(556\) −72.7473 −3.08517
\(557\) 7.53352 0.319205 0.159603 0.987181i \(-0.448979\pi\)
0.159603 + 0.987181i \(0.448979\pi\)
\(558\) 1.01195 0.0428395
\(559\) 8.99891 0.380613
\(560\) −52.3096 −2.21049
\(561\) −29.5830 −1.24899
\(562\) −27.1656 −1.14591
\(563\) −14.0284 −0.591226 −0.295613 0.955308i \(-0.595524\pi\)
−0.295613 + 0.955308i \(0.595524\pi\)
\(564\) 18.2917 0.770219
\(565\) 29.2304 1.22973
\(566\) 28.6763 1.20536
\(567\) −13.8824 −0.583008
\(568\) −22.3136 −0.936259
\(569\) −33.5442 −1.40624 −0.703122 0.711069i \(-0.748211\pi\)
−0.703122 + 0.711069i \(0.748211\pi\)
\(570\) 37.9451 1.58935
\(571\) 8.51441 0.356317 0.178158 0.984002i \(-0.442986\pi\)
0.178158 + 0.984002i \(0.442986\pi\)
\(572\) 17.0915 0.714632
\(573\) 12.8675 0.537549
\(574\) −22.8099 −0.952065
\(575\) −70.3589 −2.93417
\(576\) −0.496297 −0.0206790
\(577\) −33.8241 −1.40812 −0.704058 0.710142i \(-0.748631\pi\)
−0.704058 + 0.710142i \(0.748631\pi\)
\(578\) −56.7946 −2.36234
\(579\) −31.6359 −1.31474
\(580\) −40.0338 −1.66231
\(581\) −1.30487 −0.0541353
\(582\) −24.4041 −1.01158
\(583\) 2.59443 0.107450
\(584\) 24.4172 1.01039
\(585\) −0.877869 −0.0362954
\(586\) −7.01469 −0.289774
\(587\) 27.3114 1.12726 0.563631 0.826027i \(-0.309404\pi\)
0.563631 + 0.826027i \(0.309404\pi\)
\(588\) −33.5051 −1.38173
\(589\) 5.15214 0.212290
\(590\) −50.7864 −2.09084
\(591\) −2.85858 −0.117586
\(592\) 82.0701 3.37306
\(593\) 5.31376 0.218210 0.109105 0.994030i \(-0.465202\pi\)
0.109105 + 0.994030i \(0.465202\pi\)
\(594\) −38.6365 −1.58527
\(595\) −40.1110 −1.64439
\(596\) −63.5232 −2.60201
\(597\) 15.7304 0.643802
\(598\) −23.1129 −0.945159
\(599\) −30.7507 −1.25644 −0.628220 0.778036i \(-0.716216\pi\)
−0.628220 + 0.778036i \(0.716216\pi\)
\(600\) −116.980 −4.77568
\(601\) −32.0551 −1.30756 −0.653778 0.756686i \(-0.726817\pi\)
−0.653778 + 0.756686i \(0.726817\pi\)
\(602\) 28.9636 1.18047
\(603\) −2.18934 −0.0891566
\(604\) 2.32942 0.0947826
\(605\) 12.0451 0.489701
\(606\) 34.3771 1.39648
\(607\) 3.40148 0.138062 0.0690308 0.997615i \(-0.478009\pi\)
0.0690308 + 0.997615i \(0.478009\pi\)
\(608\) −16.7217 −0.678154
\(609\) 6.11013 0.247595
\(610\) −54.1223 −2.19135
\(611\) −3.08595 −0.124844
\(612\) −4.94540 −0.199906
\(613\) −3.89362 −0.157262 −0.0786309 0.996904i \(-0.525055\pi\)
−0.0786309 + 0.996904i \(0.525055\pi\)
\(614\) 10.1103 0.408019
\(615\) −35.5013 −1.43155
\(616\) 31.2293 1.25826
\(617\) −12.4463 −0.501068 −0.250534 0.968108i \(-0.580606\pi\)
−0.250534 + 0.968108i \(0.580606\pi\)
\(618\) −20.4739 −0.823580
\(619\) −3.98933 −0.160345 −0.0801724 0.996781i \(-0.525547\pi\)
−0.0801724 + 0.996781i \(0.525547\pi\)
\(620\) −41.5772 −1.66978
\(621\) 36.4786 1.46384
\(622\) −29.6536 −1.18900
\(623\) 8.15680 0.326795
\(624\) −17.9974 −0.720471
\(625\) 29.3897 1.17559
\(626\) −68.1418 −2.72349
\(627\) −10.6096 −0.423705
\(628\) −52.8652 −2.10955
\(629\) 62.9312 2.50923
\(630\) −2.82548 −0.112570
\(631\) 39.4303 1.56970 0.784849 0.619687i \(-0.212741\pi\)
0.784849 + 0.619687i \(0.212741\pi\)
\(632\) −86.9522 −3.45877
\(633\) 27.4560 1.09128
\(634\) 86.8831 3.45057
\(635\) 20.4347 0.810926
\(636\) −7.17391 −0.284464
\(637\) 5.65256 0.223962
\(638\) 16.0326 0.634736
\(639\) −0.564472 −0.0223302
\(640\) −29.1298 −1.15146
\(641\) −19.0244 −0.751417 −0.375709 0.926738i \(-0.622601\pi\)
−0.375709 + 0.926738i \(0.622601\pi\)
\(642\) 71.5074 2.82217
\(643\) −21.0604 −0.830541 −0.415270 0.909698i \(-0.636313\pi\)
−0.415270 + 0.909698i \(0.636313\pi\)
\(644\) −51.9378 −2.04664
\(645\) 45.0791 1.77499
\(646\) −36.0630 −1.41888
\(647\) 15.9164 0.625739 0.312870 0.949796i \(-0.398710\pi\)
0.312870 + 0.949796i \(0.398710\pi\)
\(648\) 57.1810 2.24628
\(649\) 14.2000 0.557399
\(650\) 34.7638 1.36355
\(651\) 6.34568 0.248707
\(652\) −57.9189 −2.26828
\(653\) −33.5859 −1.31432 −0.657159 0.753752i \(-0.728242\pi\)
−0.657159 + 0.753752i \(0.728242\pi\)
\(654\) 81.8864 3.20201
\(655\) −51.7845 −2.02339
\(656\) 44.0017 1.71798
\(657\) 0.617686 0.0240982
\(658\) −9.93233 −0.387202
\(659\) 34.1333 1.32965 0.664823 0.747001i \(-0.268507\pi\)
0.664823 + 0.747001i \(0.268507\pi\)
\(660\) 85.6181 3.33268
\(661\) 23.2609 0.904742 0.452371 0.891830i \(-0.350578\pi\)
0.452371 + 0.891830i \(0.350578\pi\)
\(662\) −91.6176 −3.56082
\(663\) −13.8004 −0.535962
\(664\) 5.37469 0.208579
\(665\) −14.3853 −0.557838
\(666\) 4.43297 0.171774
\(667\) −15.1371 −0.586112
\(668\) −112.168 −4.33990
\(669\) −20.0984 −0.777048
\(670\) 128.837 4.97741
\(671\) 15.1328 0.584193
\(672\) −20.5954 −0.794486
\(673\) −31.3343 −1.20785 −0.603925 0.797041i \(-0.706397\pi\)
−0.603925 + 0.797041i \(0.706397\pi\)
\(674\) 19.0914 0.735372
\(675\) −54.8668 −2.11182
\(676\) −52.1702 −2.00655
\(677\) 10.7206 0.412027 0.206013 0.978549i \(-0.433951\pi\)
0.206013 + 0.978549i \(0.433951\pi\)
\(678\) 32.3686 1.24311
\(679\) 9.25180 0.355052
\(680\) 165.215 6.33569
\(681\) 14.2973 0.547873
\(682\) 16.6507 0.637587
\(683\) −29.1085 −1.11380 −0.556902 0.830578i \(-0.688010\pi\)
−0.556902 + 0.830578i \(0.688010\pi\)
\(684\) −1.77361 −0.0678155
\(685\) −72.1003 −2.75481
\(686\) 47.7701 1.82387
\(687\) 6.36105 0.242689
\(688\) −55.8727 −2.13013
\(689\) 1.21029 0.0461085
\(690\) −115.782 −4.40774
\(691\) 16.2246 0.617214 0.308607 0.951190i \(-0.400137\pi\)
0.308607 + 0.951190i \(0.400137\pi\)
\(692\) 12.0353 0.457515
\(693\) 0.790012 0.0300101
\(694\) −15.5580 −0.590572
\(695\) 61.4803 2.33208
\(696\) −25.1672 −0.953962
\(697\) 33.7405 1.27801
\(698\) 52.7687 1.99732
\(699\) 21.4751 0.812263
\(700\) 78.1187 2.95261
\(701\) 36.6427 1.38398 0.691988 0.721909i \(-0.256735\pi\)
0.691988 + 0.721909i \(0.256735\pi\)
\(702\) −18.0238 −0.680264
\(703\) 22.5695 0.851224
\(704\) −8.16605 −0.307770
\(705\) −15.4587 −0.582209
\(706\) −84.3727 −3.17541
\(707\) −13.0326 −0.490143
\(708\) −39.2647 −1.47566
\(709\) −18.0859 −0.679230 −0.339615 0.940564i \(-0.610297\pi\)
−0.339615 + 0.940564i \(0.610297\pi\)
\(710\) 33.2178 1.24664
\(711\) −2.19965 −0.0824932
\(712\) −33.5974 −1.25911
\(713\) −15.7207 −0.588745
\(714\) −44.4174 −1.66228
\(715\) −14.4444 −0.540190
\(716\) −75.6300 −2.82642
\(717\) 14.2300 0.531430
\(718\) 50.2817 1.87650
\(719\) 38.4342 1.43335 0.716676 0.697406i \(-0.245662\pi\)
0.716676 + 0.697406i \(0.245662\pi\)
\(720\) 5.45054 0.203130
\(721\) 7.76181 0.289065
\(722\) 35.9759 1.33888
\(723\) 42.6362 1.58566
\(724\) −52.0011 −1.93261
\(725\) 22.7675 0.845563
\(726\) 13.3383 0.495029
\(727\) −35.6788 −1.32326 −0.661628 0.749833i \(-0.730134\pi\)
−0.661628 + 0.749833i \(0.730134\pi\)
\(728\) 14.5683 0.539938
\(729\) 28.3588 1.05032
\(730\) −36.3493 −1.34535
\(731\) −42.8431 −1.58461
\(732\) −41.8439 −1.54659
\(733\) −40.9054 −1.51088 −0.755438 0.655220i \(-0.772576\pi\)
−0.755438 + 0.655220i \(0.772576\pi\)
\(734\) 39.1260 1.44417
\(735\) 28.3159 1.04445
\(736\) 51.0228 1.88073
\(737\) −36.0232 −1.32693
\(738\) 2.37673 0.0874887
\(739\) 18.0475 0.663887 0.331943 0.943299i \(-0.392296\pi\)
0.331943 + 0.943299i \(0.392296\pi\)
\(740\) −182.133 −6.69536
\(741\) −4.94932 −0.181818
\(742\) 3.89541 0.143005
\(743\) −27.9337 −1.02479 −0.512394 0.858750i \(-0.671241\pi\)
−0.512394 + 0.858750i \(0.671241\pi\)
\(744\) −26.1375 −0.958246
\(745\) 53.6849 1.96686
\(746\) 41.0749 1.50386
\(747\) 0.135965 0.00497469
\(748\) −81.3714 −2.97523
\(749\) −27.1090 −0.990541
\(750\) 89.5032 3.26819
\(751\) −1.70135 −0.0620830 −0.0310415 0.999518i \(-0.509882\pi\)
−0.0310415 + 0.999518i \(0.509882\pi\)
\(752\) 19.1601 0.698698
\(753\) −27.2196 −0.991936
\(754\) 7.47914 0.272374
\(755\) −1.96864 −0.0716461
\(756\) −40.5018 −1.47304
\(757\) −22.2521 −0.808766 −0.404383 0.914590i \(-0.632514\pi\)
−0.404383 + 0.914590i \(0.632514\pi\)
\(758\) −9.33929 −0.339218
\(759\) 32.3729 1.17506
\(760\) 59.2521 2.14930
\(761\) 20.3333 0.737080 0.368540 0.929612i \(-0.379858\pi\)
0.368540 + 0.929612i \(0.379858\pi\)
\(762\) 22.6286 0.819749
\(763\) −31.0438 −1.12386
\(764\) 35.3936 1.28050
\(765\) 4.17947 0.151109
\(766\) 85.0241 3.07205
\(767\) 6.62426 0.239188
\(768\) −42.0186 −1.51622
\(769\) 14.6082 0.526784 0.263392 0.964689i \(-0.415159\pi\)
0.263392 + 0.964689i \(0.415159\pi\)
\(770\) −46.4903 −1.67539
\(771\) −12.6603 −0.455948
\(772\) −87.0183 −3.13186
\(773\) −4.03237 −0.145034 −0.0725171 0.997367i \(-0.523103\pi\)
−0.0725171 + 0.997367i \(0.523103\pi\)
\(774\) −3.01794 −0.108478
\(775\) 23.6452 0.849361
\(776\) −38.1076 −1.36798
\(777\) 27.7979 0.997245
\(778\) −85.6427 −3.07044
\(779\) 12.1006 0.433549
\(780\) 39.9405 1.43010
\(781\) −9.28780 −0.332344
\(782\) 110.039 3.93499
\(783\) −11.8041 −0.421846
\(784\) −35.0958 −1.25342
\(785\) 44.6776 1.59461
\(786\) −57.3442 −2.04540
\(787\) −4.46744 −0.159247 −0.0796235 0.996825i \(-0.525372\pi\)
−0.0796235 + 0.996825i \(0.525372\pi\)
\(788\) −7.86287 −0.280103
\(789\) 2.31799 0.0825226
\(790\) 129.444 4.60540
\(791\) −12.2712 −0.436314
\(792\) −3.25401 −0.115626
\(793\) 7.05938 0.250686
\(794\) −16.0907 −0.571037
\(795\) 6.06283 0.215026
\(796\) 43.2683 1.53360
\(797\) 28.1389 0.996732 0.498366 0.866967i \(-0.333934\pi\)
0.498366 + 0.866967i \(0.333934\pi\)
\(798\) −15.9297 −0.563906
\(799\) 14.6920 0.519764
\(800\) −76.7425 −2.71326
\(801\) −0.849919 −0.0300304
\(802\) −25.0460 −0.884406
\(803\) 10.1634 0.358658
\(804\) 99.6085 3.51292
\(805\) 43.8938 1.54705
\(806\) 7.76747 0.273598
\(807\) −37.7413 −1.32856
\(808\) 53.6807 1.88848
\(809\) 16.2523 0.571400 0.285700 0.958319i \(-0.407774\pi\)
0.285700 + 0.958319i \(0.407774\pi\)
\(810\) −85.1241 −2.99096
\(811\) 43.6465 1.53264 0.766318 0.642461i \(-0.222087\pi\)
0.766318 + 0.642461i \(0.222087\pi\)
\(812\) 16.8066 0.589796
\(813\) −2.94086 −0.103141
\(814\) 72.9400 2.55654
\(815\) 48.9485 1.71459
\(816\) 85.6841 2.99954
\(817\) −15.3651 −0.537558
\(818\) 100.288 3.50648
\(819\) 0.368538 0.0128778
\(820\) −97.6506 −3.41011
\(821\) −0.500515 −0.0174681 −0.00873404 0.999962i \(-0.502780\pi\)
−0.00873404 + 0.999962i \(0.502780\pi\)
\(822\) −79.8412 −2.78478
\(823\) 16.6432 0.580146 0.290073 0.957004i \(-0.406320\pi\)
0.290073 + 0.957004i \(0.406320\pi\)
\(824\) −31.9704 −1.11374
\(825\) −48.6915 −1.69522
\(826\) 21.3206 0.741839
\(827\) 28.2338 0.981785 0.490892 0.871220i \(-0.336671\pi\)
0.490892 + 0.871220i \(0.336671\pi\)
\(828\) 5.41180 0.188073
\(829\) 26.1145 0.906994 0.453497 0.891258i \(-0.350176\pi\)
0.453497 + 0.891258i \(0.350176\pi\)
\(830\) −8.00119 −0.277725
\(831\) −2.73745 −0.0949610
\(832\) −3.80943 −0.132068
\(833\) −26.9114 −0.932425
\(834\) 68.0810 2.35745
\(835\) 94.7953 3.28053
\(836\) −29.1828 −1.00931
\(837\) −12.2592 −0.423740
\(838\) −21.5112 −0.743090
\(839\) −0.0732583 −0.00252916 −0.00126458 0.999999i \(-0.500403\pi\)
−0.00126458 + 0.999999i \(0.500403\pi\)
\(840\) 72.9785 2.51800
\(841\) −24.1018 −0.831095
\(842\) 65.8075 2.26788
\(843\) 17.7498 0.611337
\(844\) 75.5208 2.59953
\(845\) 44.0902 1.51675
\(846\) 1.03492 0.0355815
\(847\) −5.05664 −0.173748
\(848\) −7.51450 −0.258049
\(849\) −18.7369 −0.643050
\(850\) −165.508 −5.67687
\(851\) −68.8662 −2.36070
\(852\) 25.6819 0.879847
\(853\) 32.5591 1.11480 0.557401 0.830243i \(-0.311798\pi\)
0.557401 + 0.830243i \(0.311798\pi\)
\(854\) 22.7211 0.777499
\(855\) 1.49891 0.0512617
\(856\) 111.660 3.81647
\(857\) −21.6975 −0.741172 −0.370586 0.928798i \(-0.620843\pi\)
−0.370586 + 0.928798i \(0.620843\pi\)
\(858\) −15.9952 −0.546067
\(859\) 9.29798 0.317243 0.158621 0.987339i \(-0.449295\pi\)
0.158621 + 0.987339i \(0.449295\pi\)
\(860\) 123.995 4.22820
\(861\) 14.9038 0.507921
\(862\) 37.5316 1.27833
\(863\) −41.6038 −1.41621 −0.708105 0.706108i \(-0.750449\pi\)
−0.708105 + 0.706108i \(0.750449\pi\)
\(864\) 39.7883 1.35363
\(865\) −10.1713 −0.345835
\(866\) 56.5292 1.92094
\(867\) 37.1093 1.26030
\(868\) 17.4545 0.592445
\(869\) −36.1929 −1.22776
\(870\) 37.4659 1.27021
\(871\) −16.8047 −0.569406
\(872\) 127.867 4.33014
\(873\) −0.964016 −0.0326270
\(874\) 39.4641 1.33489
\(875\) −33.9314 −1.14709
\(876\) −28.1030 −0.949511
\(877\) −42.0490 −1.41989 −0.709947 0.704256i \(-0.751281\pi\)
−0.709947 + 0.704256i \(0.751281\pi\)
\(878\) 88.1220 2.97398
\(879\) 4.58336 0.154593
\(880\) 89.6829 3.02321
\(881\) 40.7302 1.37223 0.686117 0.727491i \(-0.259314\pi\)
0.686117 + 0.727491i \(0.259314\pi\)
\(882\) −1.89568 −0.0638309
\(883\) −12.3268 −0.414829 −0.207414 0.978253i \(-0.566505\pi\)
−0.207414 + 0.978253i \(0.566505\pi\)
\(884\) −37.9595 −1.27672
\(885\) 33.1835 1.11545
\(886\) 62.2721 2.09207
\(887\) 26.3564 0.884962 0.442481 0.896778i \(-0.354098\pi\)
0.442481 + 0.896778i \(0.354098\pi\)
\(888\) −114.498 −3.84230
\(889\) −8.57869 −0.287720
\(890\) 50.0157 1.67653
\(891\) 23.8009 0.797362
\(892\) −55.2829 −1.85101
\(893\) 5.26908 0.176323
\(894\) 59.4486 1.98826
\(895\) 63.9165 2.13649
\(896\) 12.2290 0.408541
\(897\) 15.1019 0.504236
\(898\) 83.9472 2.80135
\(899\) 5.08707 0.169663
\(900\) −8.13979 −0.271326
\(901\) −5.76211 −0.191964
\(902\) 39.1067 1.30211
\(903\) −18.9246 −0.629773
\(904\) 50.5444 1.68108
\(905\) 43.9473 1.46086
\(906\) −2.18000 −0.0724256
\(907\) 5.15926 0.171310 0.0856552 0.996325i \(-0.472702\pi\)
0.0856552 + 0.996325i \(0.472702\pi\)
\(908\) 39.3263 1.30509
\(909\) 1.35797 0.0450410
\(910\) −21.6876 −0.718936
\(911\) −53.0668 −1.75818 −0.879090 0.476655i \(-0.841849\pi\)
−0.879090 + 0.476655i \(0.841849\pi\)
\(912\) 30.7295 1.01756
\(913\) 2.23716 0.0740391
\(914\) −59.4358 −1.96596
\(915\) 35.3632 1.16907
\(916\) 17.4968 0.578111
\(917\) 21.7396 0.717906
\(918\) 85.8099 2.83215
\(919\) 23.8029 0.785187 0.392593 0.919712i \(-0.371578\pi\)
0.392593 + 0.919712i \(0.371578\pi\)
\(920\) −180.796 −5.96066
\(921\) −6.60602 −0.217676
\(922\) −33.2849 −1.09618
\(923\) −4.33273 −0.142613
\(924\) −35.9433 −1.18245
\(925\) 103.580 3.40570
\(926\) −9.67781 −0.318033
\(927\) −0.808762 −0.0265632
\(928\) −16.5105 −0.541985
\(929\) 3.70963 0.121709 0.0608544 0.998147i \(-0.480617\pi\)
0.0608544 + 0.998147i \(0.480617\pi\)
\(930\) 38.9103 1.27592
\(931\) −9.65143 −0.316313
\(932\) 59.0698 1.93489
\(933\) 19.3755 0.634324
\(934\) 25.7019 0.840990
\(935\) 68.7688 2.24898
\(936\) −1.51799 −0.0496169
\(937\) −2.80367 −0.0915918 −0.0457959 0.998951i \(-0.514582\pi\)
−0.0457959 + 0.998951i \(0.514582\pi\)
\(938\) −54.0871 −1.76601
\(939\) 44.5234 1.45297
\(940\) −42.5210 −1.38688
\(941\) −28.9946 −0.945198 −0.472599 0.881278i \(-0.656684\pi\)
−0.472599 + 0.881278i \(0.656684\pi\)
\(942\) 49.4743 1.61196
\(943\) −36.9225 −1.20236
\(944\) −41.1289 −1.33863
\(945\) 34.2290 1.11347
\(946\) −49.6570 −1.61449
\(947\) 32.6491 1.06095 0.530477 0.847699i \(-0.322013\pi\)
0.530477 + 0.847699i \(0.322013\pi\)
\(948\) 100.078 3.25037
\(949\) 4.74118 0.153905
\(950\) −59.3572 −1.92580
\(951\) −56.7689 −1.84086
\(952\) −69.3587 −2.24793
\(953\) 33.8079 1.09515 0.547573 0.836758i \(-0.315552\pi\)
0.547573 + 0.836758i \(0.315552\pi\)
\(954\) −0.405892 −0.0131412
\(955\) −29.9119 −0.967927
\(956\) 39.1413 1.26592
\(957\) −10.4756 −0.338628
\(958\) 44.7586 1.44608
\(959\) 30.2684 0.977418
\(960\) −19.0829 −0.615899
\(961\) −25.7168 −0.829575
\(962\) 34.0262 1.09705
\(963\) 2.82469 0.0910245
\(964\) 117.276 3.77720
\(965\) 73.5410 2.36737
\(966\) 48.6064 1.56388
\(967\) 50.2856 1.61708 0.808538 0.588445i \(-0.200259\pi\)
0.808538 + 0.588445i \(0.200259\pi\)
\(968\) 20.8280 0.669437
\(969\) 23.5634 0.756964
\(970\) 56.7300 1.82149
\(971\) −18.1070 −0.581082 −0.290541 0.956863i \(-0.593835\pi\)
−0.290541 + 0.956863i \(0.593835\pi\)
\(972\) 8.21277 0.263425
\(973\) −25.8101 −0.827432
\(974\) −62.7002 −2.00904
\(975\) −22.7144 −0.727444
\(976\) −43.8305 −1.40298
\(977\) −4.15102 −0.132803 −0.0664015 0.997793i \(-0.521152\pi\)
−0.0664015 + 0.997793i \(0.521152\pi\)
\(978\) 54.2037 1.73324
\(979\) −13.9845 −0.446948
\(980\) 77.8861 2.48798
\(981\) 3.23469 0.103276
\(982\) −56.4383 −1.80102
\(983\) 33.6068 1.07189 0.535945 0.844253i \(-0.319955\pi\)
0.535945 + 0.844253i \(0.319955\pi\)
\(984\) −61.3879 −1.95698
\(985\) 6.64508 0.211730
\(986\) −35.6076 −1.13398
\(987\) 6.48972 0.206570
\(988\) −13.6137 −0.433109
\(989\) 46.8836 1.49081
\(990\) 4.84418 0.153958
\(991\) −43.3944 −1.37847 −0.689234 0.724538i \(-0.742053\pi\)
−0.689234 + 0.724538i \(0.742053\pi\)
\(992\) −17.1470 −0.544419
\(993\) 59.8623 1.89967
\(994\) −13.9452 −0.442314
\(995\) −36.5669 −1.15925
\(996\) −6.18601 −0.196011
\(997\) −43.0154 −1.36231 −0.681155 0.732139i \(-0.738522\pi\)
−0.681155 + 0.732139i \(0.738522\pi\)
\(998\) −3.70955 −0.117424
\(999\) −53.7028 −1.69908
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 \(a_p\))