Properties

Label 4017.2.a.j.1.19
Level 4017
Weight 2
Character 4017.1
Self dual Yes
Analytic conductor 32.076
Analytic rank 0
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0759064919\)
Analytic rank: \(0\)
Dimension: \(25\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 4017.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.86177 q^{2} -1.00000 q^{3} +1.46619 q^{4} -1.56946 q^{5} -1.86177 q^{6} +2.25881 q^{7} -0.993826 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.86177 q^{2} -1.00000 q^{3} +1.46619 q^{4} -1.56946 q^{5} -1.86177 q^{6} +2.25881 q^{7} -0.993826 q^{8} +1.00000 q^{9} -2.92198 q^{10} +6.29697 q^{11} -1.46619 q^{12} +1.00000 q^{13} +4.20539 q^{14} +1.56946 q^{15} -4.78266 q^{16} -4.10223 q^{17} +1.86177 q^{18} +8.25707 q^{19} -2.30113 q^{20} -2.25881 q^{21} +11.7235 q^{22} -2.99206 q^{23} +0.993826 q^{24} -2.53680 q^{25} +1.86177 q^{26} -1.00000 q^{27} +3.31186 q^{28} -0.0882376 q^{29} +2.92198 q^{30} -7.72751 q^{31} -6.91658 q^{32} -6.29697 q^{33} -7.63742 q^{34} -3.54512 q^{35} +1.46619 q^{36} +7.34373 q^{37} +15.3728 q^{38} -1.00000 q^{39} +1.55977 q^{40} +5.08697 q^{41} -4.20539 q^{42} -1.50267 q^{43} +9.23258 q^{44} -1.56946 q^{45} -5.57053 q^{46} +11.9728 q^{47} +4.78266 q^{48} -1.89776 q^{49} -4.72293 q^{50} +4.10223 q^{51} +1.46619 q^{52} +10.8404 q^{53} -1.86177 q^{54} -9.88285 q^{55} -2.24487 q^{56} -8.25707 q^{57} -0.164278 q^{58} +6.81304 q^{59} +2.30113 q^{60} +6.84133 q^{61} -14.3869 q^{62} +2.25881 q^{63} -3.31176 q^{64} -1.56946 q^{65} -11.7235 q^{66} +4.62221 q^{67} -6.01466 q^{68} +2.99206 q^{69} -6.60020 q^{70} +4.74962 q^{71} -0.993826 q^{72} -0.130293 q^{73} +13.6723 q^{74} +2.53680 q^{75} +12.1065 q^{76} +14.2237 q^{77} -1.86177 q^{78} -10.1097 q^{79} +7.50620 q^{80} +1.00000 q^{81} +9.47078 q^{82} -17.1480 q^{83} -3.31186 q^{84} +6.43829 q^{85} -2.79763 q^{86} +0.0882376 q^{87} -6.25809 q^{88} -6.49793 q^{89} -2.92198 q^{90} +2.25881 q^{91} -4.38694 q^{92} +7.72751 q^{93} +22.2906 q^{94} -12.9591 q^{95} +6.91658 q^{96} -10.0318 q^{97} -3.53320 q^{98} +6.29697 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} + O(q^{10}) \) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} - 6q^{10} + 21q^{11} - 28q^{12} + 25q^{13} + 10q^{14} - 7q^{15} + 30q^{16} + 14q^{17} + 6q^{18} + 12q^{19} + 24q^{20} - 17q^{21} + 3q^{22} + 41q^{23} - 21q^{24} + 30q^{25} + 6q^{26} - 25q^{27} + 14q^{28} + 22q^{29} + 6q^{30} + 14q^{31} + 28q^{32} - 21q^{33} - 11q^{34} + 14q^{35} + 28q^{36} - 6q^{37} + 16q^{38} - 25q^{39} - 34q^{40} + 33q^{41} - 10q^{42} + 35q^{43} + 45q^{44} + 7q^{45} + 3q^{46} + 48q^{47} - 30q^{48} - 4q^{49} + 7q^{50} - 14q^{51} + 28q^{52} + 18q^{53} - 6q^{54} + 10q^{55} + 32q^{56} - 12q^{57} + 33q^{58} + 46q^{59} - 24q^{60} - 19q^{61} + 5q^{62} + 17q^{63} + 29q^{64} + 7q^{65} - 3q^{66} + 16q^{67} + 20q^{68} - 41q^{69} - 43q^{70} + 60q^{71} + 21q^{72} - 14q^{73} - 50q^{74} - 30q^{75} + 59q^{77} - 6q^{78} + 7q^{79} + 32q^{80} + 25q^{81} + 18q^{82} + 23q^{83} - 14q^{84} - 9q^{85} - 9q^{86} - 22q^{87} + 23q^{88} + 10q^{89} - 6q^{90} + 17q^{91} + 69q^{92} - 14q^{93} - 30q^{94} + 81q^{95} - 28q^{96} - 10q^{97} + 55q^{98} + 21q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.86177 1.31647 0.658236 0.752812i \(-0.271303\pi\)
0.658236 + 0.752812i \(0.271303\pi\)
\(3\) −1.00000 −0.577350
\(4\) 1.46619 0.733097
\(5\) −1.56946 −0.701884 −0.350942 0.936397i \(-0.614139\pi\)
−0.350942 + 0.936397i \(0.614139\pi\)
\(6\) −1.86177 −0.760065
\(7\) 2.25881 0.853751 0.426876 0.904310i \(-0.359614\pi\)
0.426876 + 0.904310i \(0.359614\pi\)
\(8\) −0.993826 −0.351370
\(9\) 1.00000 0.333333
\(10\) −2.92198 −0.924010
\(11\) 6.29697 1.89861 0.949304 0.314358i \(-0.101789\pi\)
0.949304 + 0.314358i \(0.101789\pi\)
\(12\) −1.46619 −0.423254
\(13\) 1.00000 0.277350
\(14\) 4.20539 1.12394
\(15\) 1.56946 0.405233
\(16\) −4.78266 −1.19567
\(17\) −4.10223 −0.994937 −0.497468 0.867482i \(-0.665737\pi\)
−0.497468 + 0.867482i \(0.665737\pi\)
\(18\) 1.86177 0.438824
\(19\) 8.25707 1.89430 0.947151 0.320787i \(-0.103948\pi\)
0.947151 + 0.320787i \(0.103948\pi\)
\(20\) −2.30113 −0.514549
\(21\) −2.25881 −0.492913
\(22\) 11.7235 2.49946
\(23\) −2.99206 −0.623887 −0.311944 0.950101i \(-0.600980\pi\)
−0.311944 + 0.950101i \(0.600980\pi\)
\(24\) 0.993826 0.202864
\(25\) −2.53680 −0.507359
\(26\) 1.86177 0.365123
\(27\) −1.00000 −0.192450
\(28\) 3.31186 0.625882
\(29\) −0.0882376 −0.0163853 −0.00819265 0.999966i \(-0.502608\pi\)
−0.00819265 + 0.999966i \(0.502608\pi\)
\(30\) 2.92198 0.533477
\(31\) −7.72751 −1.38790 −0.693951 0.720022i \(-0.744132\pi\)
−0.693951 + 0.720022i \(0.744132\pi\)
\(32\) −6.91658 −1.22269
\(33\) −6.29697 −1.09616
\(34\) −7.63742 −1.30981
\(35\) −3.54512 −0.599234
\(36\) 1.46619 0.244366
\(37\) 7.34373 1.20730 0.603651 0.797249i \(-0.293712\pi\)
0.603651 + 0.797249i \(0.293712\pi\)
\(38\) 15.3728 2.49379
\(39\) −1.00000 −0.160128
\(40\) 1.55977 0.246621
\(41\) 5.08697 0.794451 0.397226 0.917721i \(-0.369973\pi\)
0.397226 + 0.917721i \(0.369973\pi\)
\(42\) −4.20539 −0.648906
\(43\) −1.50267 −0.229155 −0.114578 0.993414i \(-0.536551\pi\)
−0.114578 + 0.993414i \(0.536551\pi\)
\(44\) 9.23258 1.39186
\(45\) −1.56946 −0.233961
\(46\) −5.57053 −0.821330
\(47\) 11.9728 1.74641 0.873205 0.487353i \(-0.162037\pi\)
0.873205 + 0.487353i \(0.162037\pi\)
\(48\) 4.78266 0.690318
\(49\) −1.89776 −0.271109
\(50\) −4.72293 −0.667924
\(51\) 4.10223 0.574427
\(52\) 1.46619 0.203324
\(53\) 10.8404 1.48905 0.744523 0.667597i \(-0.232677\pi\)
0.744523 + 0.667597i \(0.232677\pi\)
\(54\) −1.86177 −0.253355
\(55\) −9.88285 −1.33260
\(56\) −2.24487 −0.299983
\(57\) −8.25707 −1.09368
\(58\) −0.164278 −0.0215708
\(59\) 6.81304 0.886982 0.443491 0.896279i \(-0.353740\pi\)
0.443491 + 0.896279i \(0.353740\pi\)
\(60\) 2.30113 0.297075
\(61\) 6.84133 0.875942 0.437971 0.898989i \(-0.355697\pi\)
0.437971 + 0.898989i \(0.355697\pi\)
\(62\) −14.3869 −1.82713
\(63\) 2.25881 0.284584
\(64\) −3.31176 −0.413970
\(65\) −1.56946 −0.194668
\(66\) −11.7235 −1.44307
\(67\) 4.62221 0.564693 0.282346 0.959313i \(-0.408887\pi\)
0.282346 + 0.959313i \(0.408887\pi\)
\(68\) −6.01466 −0.729385
\(69\) 2.99206 0.360201
\(70\) −6.60020 −0.788875
\(71\) 4.74962 0.563677 0.281838 0.959462i \(-0.409056\pi\)
0.281838 + 0.959462i \(0.409056\pi\)
\(72\) −0.993826 −0.117123
\(73\) −0.130293 −0.0152497 −0.00762483 0.999971i \(-0.502427\pi\)
−0.00762483 + 0.999971i \(0.502427\pi\)
\(74\) 13.6723 1.58938
\(75\) 2.53680 0.292924
\(76\) 12.1065 1.38871
\(77\) 14.2237 1.62094
\(78\) −1.86177 −0.210804
\(79\) −10.1097 −1.13743 −0.568715 0.822535i \(-0.692559\pi\)
−0.568715 + 0.822535i \(0.692559\pi\)
\(80\) 7.50620 0.839219
\(81\) 1.00000 0.111111
\(82\) 9.47078 1.04587
\(83\) −17.1480 −1.88224 −0.941118 0.338079i \(-0.890223\pi\)
−0.941118 + 0.338079i \(0.890223\pi\)
\(84\) −3.31186 −0.361353
\(85\) 6.43829 0.698330
\(86\) −2.79763 −0.301676
\(87\) 0.0882376 0.00946006
\(88\) −6.25809 −0.667115
\(89\) −6.49793 −0.688780 −0.344390 0.938827i \(-0.611914\pi\)
−0.344390 + 0.938827i \(0.611914\pi\)
\(90\) −2.92198 −0.308003
\(91\) 2.25881 0.236788
\(92\) −4.38694 −0.457370
\(93\) 7.72751 0.801305
\(94\) 22.2906 2.29910
\(95\) −12.9591 −1.32958
\(96\) 6.91658 0.705920
\(97\) −10.0318 −1.01858 −0.509288 0.860596i \(-0.670091\pi\)
−0.509288 + 0.860596i \(0.670091\pi\)
\(98\) −3.53320 −0.356907
\(99\) 6.29697 0.632870
\(100\) −3.71943 −0.371943
\(101\) 14.3062 1.42352 0.711762 0.702421i \(-0.247897\pi\)
0.711762 + 0.702421i \(0.247897\pi\)
\(102\) 7.63742 0.756217
\(103\) −1.00000 −0.0985329
\(104\) −0.993826 −0.0974526
\(105\) 3.54512 0.345968
\(106\) 20.1824 1.96029
\(107\) 14.1867 1.37148 0.685739 0.727848i \(-0.259479\pi\)
0.685739 + 0.727848i \(0.259479\pi\)
\(108\) −1.46619 −0.141085
\(109\) 0.400719 0.0383819 0.0191909 0.999816i \(-0.493891\pi\)
0.0191909 + 0.999816i \(0.493891\pi\)
\(110\) −18.3996 −1.75433
\(111\) −7.34373 −0.697036
\(112\) −10.8031 −1.02080
\(113\) 10.7347 1.00984 0.504918 0.863167i \(-0.331523\pi\)
0.504918 + 0.863167i \(0.331523\pi\)
\(114\) −15.3728 −1.43979
\(115\) 4.69591 0.437896
\(116\) −0.129373 −0.0120120
\(117\) 1.00000 0.0924500
\(118\) 12.6843 1.16769
\(119\) −9.26617 −0.849428
\(120\) −1.55977 −0.142387
\(121\) 28.6519 2.60472
\(122\) 12.7370 1.15315
\(123\) −5.08697 −0.458677
\(124\) −11.3300 −1.01747
\(125\) 11.8287 1.05799
\(126\) 4.20539 0.374646
\(127\) 2.42583 0.215258 0.107629 0.994191i \(-0.465674\pi\)
0.107629 + 0.994191i \(0.465674\pi\)
\(128\) 7.66741 0.677710
\(129\) 1.50267 0.132303
\(130\) −2.92198 −0.256274
\(131\) −6.31062 −0.551361 −0.275681 0.961249i \(-0.588903\pi\)
−0.275681 + 0.961249i \(0.588903\pi\)
\(132\) −9.23258 −0.803593
\(133\) 18.6512 1.61726
\(134\) 8.60550 0.743402
\(135\) 1.56946 0.135078
\(136\) 4.07690 0.349591
\(137\) 21.7361 1.85704 0.928521 0.371279i \(-0.121081\pi\)
0.928521 + 0.371279i \(0.121081\pi\)
\(138\) 5.57053 0.474195
\(139\) 17.1967 1.45861 0.729304 0.684190i \(-0.239844\pi\)
0.729304 + 0.684190i \(0.239844\pi\)
\(140\) −5.19783 −0.439297
\(141\) −11.9728 −1.00829
\(142\) 8.84272 0.742064
\(143\) 6.29697 0.526579
\(144\) −4.78266 −0.398555
\(145\) 0.138485 0.0115006
\(146\) −0.242576 −0.0200757
\(147\) 1.89776 0.156525
\(148\) 10.7673 0.885069
\(149\) 2.90495 0.237983 0.118992 0.992895i \(-0.462034\pi\)
0.118992 + 0.992895i \(0.462034\pi\)
\(150\) 4.72293 0.385626
\(151\) −12.0229 −0.978411 −0.489205 0.872169i \(-0.662713\pi\)
−0.489205 + 0.872169i \(0.662713\pi\)
\(152\) −8.20609 −0.665602
\(153\) −4.10223 −0.331646
\(154\) 26.4813 2.13392
\(155\) 12.1280 0.974146
\(156\) −1.46619 −0.117389
\(157\) 3.12910 0.249730 0.124865 0.992174i \(-0.460150\pi\)
0.124865 + 0.992174i \(0.460150\pi\)
\(158\) −18.8219 −1.49739
\(159\) −10.8404 −0.859701
\(160\) 10.8553 0.858186
\(161\) −6.75850 −0.532644
\(162\) 1.86177 0.146275
\(163\) 18.7831 1.47120 0.735602 0.677414i \(-0.236899\pi\)
0.735602 + 0.677414i \(0.236899\pi\)
\(164\) 7.45848 0.582410
\(165\) 9.88285 0.769379
\(166\) −31.9256 −2.47791
\(167\) 9.35561 0.723959 0.361979 0.932186i \(-0.382101\pi\)
0.361979 + 0.932186i \(0.382101\pi\)
\(168\) 2.24487 0.173195
\(169\) 1.00000 0.0769231
\(170\) 11.9866 0.919332
\(171\) 8.25707 0.631434
\(172\) −2.20321 −0.167993
\(173\) 9.69810 0.737333 0.368666 0.929562i \(-0.379814\pi\)
0.368666 + 0.929562i \(0.379814\pi\)
\(174\) 0.164278 0.0124539
\(175\) −5.73015 −0.433158
\(176\) −30.1163 −2.27010
\(177\) −6.81304 −0.512099
\(178\) −12.0977 −0.906759
\(179\) 2.84544 0.212678 0.106339 0.994330i \(-0.466087\pi\)
0.106339 + 0.994330i \(0.466087\pi\)
\(180\) −2.30113 −0.171516
\(181\) −4.83800 −0.359606 −0.179803 0.983703i \(-0.557546\pi\)
−0.179803 + 0.983703i \(0.557546\pi\)
\(182\) 4.20539 0.311725
\(183\) −6.84133 −0.505725
\(184\) 2.97358 0.219215
\(185\) −11.5257 −0.847385
\(186\) 14.3869 1.05490
\(187\) −25.8316 −1.88900
\(188\) 17.5544 1.28029
\(189\) −2.25881 −0.164304
\(190\) −24.1270 −1.75035
\(191\) −13.8101 −0.999261 −0.499631 0.866239i \(-0.666531\pi\)
−0.499631 + 0.866239i \(0.666531\pi\)
\(192\) 3.31176 0.239006
\(193\) −7.34299 −0.528560 −0.264280 0.964446i \(-0.585134\pi\)
−0.264280 + 0.964446i \(0.585134\pi\)
\(194\) −18.6769 −1.34093
\(195\) 1.56946 0.112391
\(196\) −2.78249 −0.198749
\(197\) 7.11104 0.506641 0.253320 0.967382i \(-0.418477\pi\)
0.253320 + 0.967382i \(0.418477\pi\)
\(198\) 11.7235 0.833155
\(199\) 2.75212 0.195093 0.0975463 0.995231i \(-0.468901\pi\)
0.0975463 + 0.995231i \(0.468901\pi\)
\(200\) 2.52113 0.178271
\(201\) −4.62221 −0.326026
\(202\) 26.6349 1.87403
\(203\) −0.199312 −0.0139890
\(204\) 6.01466 0.421111
\(205\) −7.98380 −0.557613
\(206\) −1.86177 −0.129716
\(207\) −2.99206 −0.207962
\(208\) −4.78266 −0.331618
\(209\) 51.9946 3.59654
\(210\) 6.60020 0.455457
\(211\) −7.77779 −0.535445 −0.267723 0.963496i \(-0.586271\pi\)
−0.267723 + 0.963496i \(0.586271\pi\)
\(212\) 15.8941 1.09161
\(213\) −4.74962 −0.325439
\(214\) 26.4123 1.80551
\(215\) 2.35838 0.160840
\(216\) 0.993826 0.0676213
\(217\) −17.4550 −1.18492
\(218\) 0.746047 0.0505286
\(219\) 0.130293 0.00880439
\(220\) −14.4902 −0.976927
\(221\) −4.10223 −0.275946
\(222\) −13.6723 −0.917627
\(223\) −14.4522 −0.967791 −0.483896 0.875126i \(-0.660779\pi\)
−0.483896 + 0.875126i \(0.660779\pi\)
\(224\) −15.6233 −1.04387
\(225\) −2.53680 −0.169120
\(226\) 19.9856 1.32942
\(227\) −3.65605 −0.242661 −0.121330 0.992612i \(-0.538716\pi\)
−0.121330 + 0.992612i \(0.538716\pi\)
\(228\) −12.1065 −0.801770
\(229\) −7.00073 −0.462621 −0.231311 0.972880i \(-0.574301\pi\)
−0.231311 + 0.972880i \(0.574301\pi\)
\(230\) 8.74272 0.576478
\(231\) −14.2237 −0.935850
\(232\) 0.0876928 0.00575731
\(233\) −0.911437 −0.0597102 −0.0298551 0.999554i \(-0.509505\pi\)
−0.0298551 + 0.999554i \(0.509505\pi\)
\(234\) 1.86177 0.121708
\(235\) −18.7908 −1.22578
\(236\) 9.98923 0.650244
\(237\) 10.1097 0.656695
\(238\) −17.2515 −1.11825
\(239\) −5.55401 −0.359259 −0.179630 0.983734i \(-0.557490\pi\)
−0.179630 + 0.983734i \(0.557490\pi\)
\(240\) −7.50620 −0.484523
\(241\) −11.5522 −0.744141 −0.372071 0.928204i \(-0.621352\pi\)
−0.372071 + 0.928204i \(0.621352\pi\)
\(242\) 53.3432 3.42903
\(243\) −1.00000 −0.0641500
\(244\) 10.0307 0.642150
\(245\) 2.97846 0.190287
\(246\) −9.47078 −0.603835
\(247\) 8.25707 0.525385
\(248\) 7.67980 0.487668
\(249\) 17.1480 1.08671
\(250\) 22.0223 1.39281
\(251\) −17.2837 −1.09094 −0.545468 0.838132i \(-0.683648\pi\)
−0.545468 + 0.838132i \(0.683648\pi\)
\(252\) 3.31186 0.208627
\(253\) −18.8409 −1.18452
\(254\) 4.51635 0.283381
\(255\) −6.43829 −0.403181
\(256\) 20.8985 1.30616
\(257\) −9.43669 −0.588645 −0.294322 0.955706i \(-0.595094\pi\)
−0.294322 + 0.955706i \(0.595094\pi\)
\(258\) 2.79763 0.174173
\(259\) 16.5881 1.03073
\(260\) −2.30113 −0.142710
\(261\) −0.0882376 −0.00546177
\(262\) −11.7489 −0.725851
\(263\) 25.6603 1.58228 0.791142 0.611632i \(-0.209487\pi\)
0.791142 + 0.611632i \(0.209487\pi\)
\(264\) 6.25809 0.385159
\(265\) −17.0136 −1.04514
\(266\) 34.7242 2.12908
\(267\) 6.49793 0.397667
\(268\) 6.77706 0.413975
\(269\) 30.8547 1.88124 0.940621 0.339458i \(-0.110244\pi\)
0.940621 + 0.339458i \(0.110244\pi\)
\(270\) 2.92198 0.177826
\(271\) −27.8837 −1.69381 −0.846906 0.531743i \(-0.821537\pi\)
−0.846906 + 0.531743i \(0.821537\pi\)
\(272\) 19.6196 1.18961
\(273\) −2.25881 −0.136710
\(274\) 40.4677 2.44474
\(275\) −15.9741 −0.963276
\(276\) 4.38694 0.264063
\(277\) 1.10800 0.0665733 0.0332866 0.999446i \(-0.489403\pi\)
0.0332866 + 0.999446i \(0.489403\pi\)
\(278\) 32.0164 1.92022
\(279\) −7.72751 −0.462634
\(280\) 3.52323 0.210553
\(281\) −24.6142 −1.46836 −0.734181 0.678954i \(-0.762433\pi\)
−0.734181 + 0.678954i \(0.762433\pi\)
\(282\) −22.2906 −1.32739
\(283\) −13.9248 −0.827746 −0.413873 0.910335i \(-0.635824\pi\)
−0.413873 + 0.910335i \(0.635824\pi\)
\(284\) 6.96387 0.413230
\(285\) 12.9591 0.767634
\(286\) 11.7235 0.693227
\(287\) 11.4905 0.678264
\(288\) −6.91658 −0.407563
\(289\) −0.171710 −0.0101006
\(290\) 0.257828 0.0151402
\(291\) 10.0318 0.588075
\(292\) −0.191035 −0.0111795
\(293\) 2.79845 0.163487 0.0817435 0.996653i \(-0.473951\pi\)
0.0817435 + 0.996653i \(0.473951\pi\)
\(294\) 3.53320 0.206060
\(295\) −10.6928 −0.622558
\(296\) −7.29838 −0.424210
\(297\) −6.29697 −0.365387
\(298\) 5.40836 0.313298
\(299\) −2.99206 −0.173035
\(300\) 3.71943 0.214742
\(301\) −3.39425 −0.195641
\(302\) −22.3839 −1.28805
\(303\) −14.3062 −0.821872
\(304\) −39.4908 −2.26495
\(305\) −10.7372 −0.614810
\(306\) −7.63742 −0.436602
\(307\) 8.30771 0.474146 0.237073 0.971492i \(-0.423812\pi\)
0.237073 + 0.971492i \(0.423812\pi\)
\(308\) 20.8547 1.18831
\(309\) 1.00000 0.0568880
\(310\) 22.5796 1.28244
\(311\) −21.6061 −1.22517 −0.612586 0.790404i \(-0.709871\pi\)
−0.612586 + 0.790404i \(0.709871\pi\)
\(312\) 0.993826 0.0562643
\(313\) 5.64234 0.318924 0.159462 0.987204i \(-0.449024\pi\)
0.159462 + 0.987204i \(0.449024\pi\)
\(314\) 5.82567 0.328762
\(315\) −3.54512 −0.199745
\(316\) −14.8228 −0.833846
\(317\) −12.4310 −0.698193 −0.349097 0.937087i \(-0.613511\pi\)
−0.349097 + 0.937087i \(0.613511\pi\)
\(318\) −20.1824 −1.13177
\(319\) −0.555630 −0.0311093
\(320\) 5.19767 0.290559
\(321\) −14.1867 −0.791823
\(322\) −12.5828 −0.701211
\(323\) −33.8724 −1.88471
\(324\) 1.46619 0.0814552
\(325\) −2.53680 −0.140716
\(326\) 34.9698 1.93680
\(327\) −0.400719 −0.0221598
\(328\) −5.05556 −0.279147
\(329\) 27.0443 1.49100
\(330\) 18.3996 1.01286
\(331\) 18.9862 1.04357 0.521787 0.853076i \(-0.325266\pi\)
0.521787 + 0.853076i \(0.325266\pi\)
\(332\) −25.1423 −1.37986
\(333\) 7.34373 0.402434
\(334\) 17.4180 0.953071
\(335\) −7.25437 −0.396349
\(336\) 10.8031 0.589360
\(337\) −33.6146 −1.83110 −0.915551 0.402201i \(-0.868245\pi\)
−0.915551 + 0.402201i \(0.868245\pi\)
\(338\) 1.86177 0.101267
\(339\) −10.7347 −0.583029
\(340\) 9.43977 0.511944
\(341\) −48.6599 −2.63508
\(342\) 15.3728 0.831265
\(343\) −20.0984 −1.08521
\(344\) 1.49339 0.0805183
\(345\) −4.69591 −0.252820
\(346\) 18.0556 0.970677
\(347\) 25.5823 1.37333 0.686664 0.726975i \(-0.259074\pi\)
0.686664 + 0.726975i \(0.259074\pi\)
\(348\) 0.129373 0.00693514
\(349\) −30.0749 −1.60987 −0.804936 0.593361i \(-0.797801\pi\)
−0.804936 + 0.593361i \(0.797801\pi\)
\(350\) −10.6682 −0.570241
\(351\) −1.00000 −0.0533761
\(352\) −43.5535 −2.32141
\(353\) −16.6497 −0.886174 −0.443087 0.896479i \(-0.646117\pi\)
−0.443087 + 0.896479i \(0.646117\pi\)
\(354\) −12.6843 −0.674164
\(355\) −7.45435 −0.395636
\(356\) −9.52723 −0.504942
\(357\) 9.26617 0.490418
\(358\) 5.29755 0.279984
\(359\) −14.6032 −0.770727 −0.385363 0.922765i \(-0.625924\pi\)
−0.385363 + 0.922765i \(0.625924\pi\)
\(360\) 1.55977 0.0822071
\(361\) 49.1793 2.58838
\(362\) −9.00725 −0.473410
\(363\) −28.6519 −1.50383
\(364\) 3.31186 0.173589
\(365\) 0.204490 0.0107035
\(366\) −12.7370 −0.665773
\(367\) 26.8928 1.40379 0.701896 0.712279i \(-0.252337\pi\)
0.701896 + 0.712279i \(0.252337\pi\)
\(368\) 14.3100 0.745961
\(369\) 5.08697 0.264817
\(370\) −21.4582 −1.11556
\(371\) 24.4865 1.27127
\(372\) 11.3300 0.587434
\(373\) −16.4048 −0.849408 −0.424704 0.905332i \(-0.639622\pi\)
−0.424704 + 0.905332i \(0.639622\pi\)
\(374\) −48.0926 −2.48681
\(375\) −11.8287 −0.610831
\(376\) −11.8989 −0.613637
\(377\) −0.0882376 −0.00454447
\(378\) −4.20539 −0.216302
\(379\) 21.9502 1.12751 0.563753 0.825944i \(-0.309357\pi\)
0.563753 + 0.825944i \(0.309357\pi\)
\(380\) −19.0006 −0.974711
\(381\) −2.42583 −0.124279
\(382\) −25.7112 −1.31550
\(383\) −13.3214 −0.680691 −0.340345 0.940300i \(-0.610544\pi\)
−0.340345 + 0.940300i \(0.610544\pi\)
\(384\) −7.66741 −0.391276
\(385\) −22.3235 −1.13771
\(386\) −13.6710 −0.695834
\(387\) −1.50267 −0.0763851
\(388\) −14.7086 −0.746715
\(389\) 8.48281 0.430096 0.215048 0.976604i \(-0.431009\pi\)
0.215048 + 0.976604i \(0.431009\pi\)
\(390\) 2.92198 0.147960
\(391\) 12.2741 0.620728
\(392\) 1.88605 0.0952597
\(393\) 6.31062 0.318328
\(394\) 13.2391 0.666978
\(395\) 15.8668 0.798343
\(396\) 9.23258 0.463955
\(397\) −26.8086 −1.34549 −0.672743 0.739876i \(-0.734884\pi\)
−0.672743 + 0.739876i \(0.734884\pi\)
\(398\) 5.12382 0.256834
\(399\) −18.6512 −0.933727
\(400\) 12.1326 0.606632
\(401\) −35.4638 −1.77098 −0.885489 0.464661i \(-0.846176\pi\)
−0.885489 + 0.464661i \(0.846176\pi\)
\(402\) −8.60550 −0.429203
\(403\) −7.72751 −0.384935
\(404\) 20.9757 1.04358
\(405\) −1.56946 −0.0779871
\(406\) −0.371074 −0.0184161
\(407\) 46.2432 2.29219
\(408\) −4.07690 −0.201837
\(409\) −10.7234 −0.530237 −0.265118 0.964216i \(-0.585411\pi\)
−0.265118 + 0.964216i \(0.585411\pi\)
\(410\) −14.8640 −0.734081
\(411\) −21.7361 −1.07216
\(412\) −1.46619 −0.0722342
\(413\) 15.3894 0.757262
\(414\) −5.57053 −0.273777
\(415\) 26.9131 1.32111
\(416\) −6.91658 −0.339113
\(417\) −17.1967 −0.842128
\(418\) 96.8020 4.73474
\(419\) −14.3837 −0.702689 −0.351344 0.936246i \(-0.614275\pi\)
−0.351344 + 0.936246i \(0.614275\pi\)
\(420\) 5.19783 0.253628
\(421\) 2.64706 0.129010 0.0645048 0.997917i \(-0.479453\pi\)
0.0645048 + 0.997917i \(0.479453\pi\)
\(422\) −14.4805 −0.704899
\(423\) 11.9728 0.582137
\(424\) −10.7735 −0.523207
\(425\) 10.4065 0.504790
\(426\) −8.84272 −0.428431
\(427\) 15.4533 0.747836
\(428\) 20.8004 1.00543
\(429\) −6.29697 −0.304021
\(430\) 4.39077 0.211742
\(431\) 1.86512 0.0898397 0.0449199 0.998991i \(-0.485697\pi\)
0.0449199 + 0.998991i \(0.485697\pi\)
\(432\) 4.78266 0.230106
\(433\) 40.8079 1.96110 0.980550 0.196267i \(-0.0628820\pi\)
0.980550 + 0.196267i \(0.0628820\pi\)
\(434\) −32.4972 −1.55992
\(435\) −0.138485 −0.00663986
\(436\) 0.587531 0.0281376
\(437\) −24.7056 −1.18183
\(438\) 0.242576 0.0115907
\(439\) −21.3173 −1.01742 −0.508710 0.860938i \(-0.669877\pi\)
−0.508710 + 0.860938i \(0.669877\pi\)
\(440\) 9.82183 0.468237
\(441\) −1.89776 −0.0903697
\(442\) −7.63742 −0.363275
\(443\) −19.0780 −0.906425 −0.453212 0.891403i \(-0.649722\pi\)
−0.453212 + 0.891403i \(0.649722\pi\)
\(444\) −10.7673 −0.510995
\(445\) 10.1982 0.483443
\(446\) −26.9067 −1.27407
\(447\) −2.90495 −0.137400
\(448\) −7.48064 −0.353427
\(449\) 17.6287 0.831949 0.415974 0.909376i \(-0.363441\pi\)
0.415974 + 0.909376i \(0.363441\pi\)
\(450\) −4.72293 −0.222641
\(451\) 32.0325 1.50835
\(452\) 15.7391 0.740307
\(453\) 12.0229 0.564886
\(454\) −6.80674 −0.319456
\(455\) −3.54512 −0.166198
\(456\) 8.20609 0.384285
\(457\) 30.3878 1.42148 0.710742 0.703453i \(-0.248359\pi\)
0.710742 + 0.703453i \(0.248359\pi\)
\(458\) −13.0338 −0.609028
\(459\) 4.10223 0.191476
\(460\) 6.88512 0.321020
\(461\) −18.4832 −0.860850 −0.430425 0.902626i \(-0.641636\pi\)
−0.430425 + 0.902626i \(0.641636\pi\)
\(462\) −26.4813 −1.23202
\(463\) −1.43876 −0.0668649 −0.0334325 0.999441i \(-0.510644\pi\)
−0.0334325 + 0.999441i \(0.510644\pi\)
\(464\) 0.422011 0.0195914
\(465\) −12.1280 −0.562423
\(466\) −1.69689 −0.0786068
\(467\) 4.30295 0.199117 0.0995585 0.995032i \(-0.468257\pi\)
0.0995585 + 0.995032i \(0.468257\pi\)
\(468\) 1.46619 0.0677748
\(469\) 10.4407 0.482107
\(470\) −34.9842 −1.61370
\(471\) −3.12910 −0.144181
\(472\) −6.77097 −0.311659
\(473\) −9.46228 −0.435076
\(474\) 18.8219 0.864520
\(475\) −20.9465 −0.961091
\(476\) −13.5860 −0.622713
\(477\) 10.8404 0.496348
\(478\) −10.3403 −0.472955
\(479\) −37.4876 −1.71285 −0.856427 0.516269i \(-0.827321\pi\)
−0.856427 + 0.516269i \(0.827321\pi\)
\(480\) −10.8553 −0.495474
\(481\) 7.34373 0.334845
\(482\) −21.5075 −0.979640
\(483\) 6.75850 0.307522
\(484\) 42.0092 1.90951
\(485\) 15.7445 0.714922
\(486\) −1.86177 −0.0844517
\(487\) −11.7948 −0.534476 −0.267238 0.963631i \(-0.586111\pi\)
−0.267238 + 0.963631i \(0.586111\pi\)
\(488\) −6.79908 −0.307780
\(489\) −18.7831 −0.849400
\(490\) 5.54522 0.250507
\(491\) −23.3888 −1.05552 −0.527761 0.849393i \(-0.676968\pi\)
−0.527761 + 0.849393i \(0.676968\pi\)
\(492\) −7.45848 −0.336254
\(493\) 0.361971 0.0163023
\(494\) 15.3728 0.691654
\(495\) −9.88285 −0.444201
\(496\) 36.9581 1.65947
\(497\) 10.7285 0.481240
\(498\) 31.9256 1.43062
\(499\) −16.9072 −0.756871 −0.378435 0.925628i \(-0.623538\pi\)
−0.378435 + 0.925628i \(0.623538\pi\)
\(500\) 17.3432 0.775610
\(501\) −9.35561 −0.417978
\(502\) −32.1782 −1.43618
\(503\) −7.62989 −0.340200 −0.170100 0.985427i \(-0.554409\pi\)
−0.170100 + 0.985427i \(0.554409\pi\)
\(504\) −2.24487 −0.0999943
\(505\) −22.4531 −0.999148
\(506\) −35.0775 −1.55938
\(507\) −1.00000 −0.0444116
\(508\) 3.55674 0.157805
\(509\) 22.1165 0.980295 0.490148 0.871639i \(-0.336943\pi\)
0.490148 + 0.871639i \(0.336943\pi\)
\(510\) −11.9866 −0.530776
\(511\) −0.294308 −0.0130194
\(512\) 23.5734 1.04181
\(513\) −8.25707 −0.364559
\(514\) −17.5690 −0.774934
\(515\) 1.56946 0.0691587
\(516\) 2.20321 0.0969908
\(517\) 75.3923 3.31575
\(518\) 30.8833 1.35693
\(519\) −9.69810 −0.425699
\(520\) 1.55977 0.0684004
\(521\) −11.3798 −0.498557 −0.249278 0.968432i \(-0.580193\pi\)
−0.249278 + 0.968432i \(0.580193\pi\)
\(522\) −0.164278 −0.00719026
\(523\) 27.0292 1.18190 0.590951 0.806707i \(-0.298753\pi\)
0.590951 + 0.806707i \(0.298753\pi\)
\(524\) −9.25258 −0.404201
\(525\) 5.73015 0.250084
\(526\) 47.7737 2.08303
\(527\) 31.7000 1.38087
\(528\) 30.1163 1.31064
\(529\) −14.0476 −0.610765
\(530\) −31.6754 −1.37589
\(531\) 6.81304 0.295661
\(532\) 27.3462 1.18561
\(533\) 5.08697 0.220341
\(534\) 12.0977 0.523517
\(535\) −22.2654 −0.962618
\(536\) −4.59367 −0.198416
\(537\) −2.84544 −0.122790
\(538\) 57.4444 2.47660
\(539\) −11.9502 −0.514730
\(540\) 2.30113 0.0990250
\(541\) 25.5420 1.09814 0.549069 0.835777i \(-0.314982\pi\)
0.549069 + 0.835777i \(0.314982\pi\)
\(542\) −51.9130 −2.22985
\(543\) 4.83800 0.207618
\(544\) 28.3734 1.21650
\(545\) −0.628912 −0.0269396
\(546\) −4.20539 −0.179974
\(547\) −4.95564 −0.211888 −0.105944 0.994372i \(-0.533786\pi\)
−0.105944 + 0.994372i \(0.533786\pi\)
\(548\) 31.8694 1.36139
\(549\) 6.84133 0.291981
\(550\) −29.7402 −1.26813
\(551\) −0.728584 −0.0310387
\(552\) −2.97358 −0.126564
\(553\) −22.8359 −0.971081
\(554\) 2.06284 0.0876418
\(555\) 11.5257 0.489238
\(556\) 25.2137 1.06930
\(557\) 24.0526 1.01914 0.509571 0.860429i \(-0.329804\pi\)
0.509571 + 0.860429i \(0.329804\pi\)
\(558\) −14.3869 −0.609044
\(559\) −1.50267 −0.0635562
\(560\) 16.9551 0.716484
\(561\) 25.8316 1.09061
\(562\) −45.8261 −1.93306
\(563\) −6.38648 −0.269158 −0.134579 0.990903i \(-0.542968\pi\)
−0.134579 + 0.990903i \(0.542968\pi\)
\(564\) −17.5544 −0.739174
\(565\) −16.8477 −0.708787
\(566\) −25.9249 −1.08970
\(567\) 2.25881 0.0948612
\(568\) −4.72030 −0.198059
\(569\) 14.4713 0.606668 0.303334 0.952884i \(-0.401900\pi\)
0.303334 + 0.952884i \(0.401900\pi\)
\(570\) 24.1270 1.01057
\(571\) −43.1996 −1.80785 −0.903924 0.427693i \(-0.859326\pi\)
−0.903924 + 0.427693i \(0.859326\pi\)
\(572\) 9.23258 0.386034
\(573\) 13.8101 0.576924
\(574\) 21.3927 0.892915
\(575\) 7.59024 0.316535
\(576\) −3.31176 −0.137990
\(577\) 1.30090 0.0541572 0.0270786 0.999633i \(-0.491380\pi\)
0.0270786 + 0.999633i \(0.491380\pi\)
\(578\) −0.319686 −0.0132972
\(579\) 7.34299 0.305164
\(580\) 0.203046 0.00843104
\(581\) −38.7341 −1.60696
\(582\) 18.6769 0.774184
\(583\) 68.2618 2.82711
\(584\) 0.129489 0.00535828
\(585\) −1.56946 −0.0648892
\(586\) 5.21007 0.215226
\(587\) −17.4285 −0.719352 −0.359676 0.933077i \(-0.617113\pi\)
−0.359676 + 0.933077i \(0.617113\pi\)
\(588\) 2.78249 0.114748
\(589\) −63.8066 −2.62911
\(590\) −19.9075 −0.819580
\(591\) −7.11104 −0.292509
\(592\) −35.1226 −1.44353
\(593\) 16.3440 0.671166 0.335583 0.942011i \(-0.391067\pi\)
0.335583 + 0.942011i \(0.391067\pi\)
\(594\) −11.7235 −0.481022
\(595\) 14.5429 0.596200
\(596\) 4.25922 0.174465
\(597\) −2.75212 −0.112637
\(598\) −5.57053 −0.227796
\(599\) 6.85876 0.280242 0.140121 0.990134i \(-0.455251\pi\)
0.140121 + 0.990134i \(0.455251\pi\)
\(600\) −2.52113 −0.102925
\(601\) −25.9055 −1.05671 −0.528354 0.849024i \(-0.677191\pi\)
−0.528354 + 0.849024i \(0.677191\pi\)
\(602\) −6.31932 −0.257556
\(603\) 4.62221 0.188231
\(604\) −17.6279 −0.717270
\(605\) −44.9680 −1.82821
\(606\) −26.6349 −1.08197
\(607\) −29.5102 −1.19778 −0.598892 0.800830i \(-0.704392\pi\)
−0.598892 + 0.800830i \(0.704392\pi\)
\(608\) −57.1107 −2.31614
\(609\) 0.199312 0.00807654
\(610\) −19.9902 −0.809379
\(611\) 11.9728 0.484367
\(612\) −6.01466 −0.243128
\(613\) 21.8619 0.882996 0.441498 0.897262i \(-0.354447\pi\)
0.441498 + 0.897262i \(0.354447\pi\)
\(614\) 15.4671 0.624200
\(615\) 7.98380 0.321938
\(616\) −14.1359 −0.569550
\(617\) 36.7047 1.47767 0.738837 0.673884i \(-0.235375\pi\)
0.738837 + 0.673884i \(0.235375\pi\)
\(618\) 1.86177 0.0748914
\(619\) −15.4592 −0.621357 −0.310679 0.950515i \(-0.600556\pi\)
−0.310679 + 0.950515i \(0.600556\pi\)
\(620\) 17.7820 0.714143
\(621\) 2.99206 0.120067
\(622\) −40.2257 −1.61290
\(623\) −14.6776 −0.588046
\(624\) 4.78266 0.191460
\(625\) −5.88069 −0.235228
\(626\) 10.5047 0.419854
\(627\) −51.9946 −2.07646
\(628\) 4.58787 0.183076
\(629\) −30.1257 −1.20119
\(630\) −6.60020 −0.262958
\(631\) 28.8182 1.14724 0.573618 0.819123i \(-0.305539\pi\)
0.573618 + 0.819123i \(0.305539\pi\)
\(632\) 10.0473 0.399659
\(633\) 7.77779 0.309140
\(634\) −23.1436 −0.919151
\(635\) −3.80725 −0.151086
\(636\) −15.8941 −0.630244
\(637\) −1.89776 −0.0751921
\(638\) −1.03446 −0.0409545
\(639\) 4.74962 0.187892
\(640\) −12.0337 −0.475674
\(641\) 13.6517 0.539212 0.269606 0.962971i \(-0.413107\pi\)
0.269606 + 0.962971i \(0.413107\pi\)
\(642\) −26.4123 −1.04241
\(643\) 42.1100 1.66066 0.830329 0.557274i \(-0.188153\pi\)
0.830329 + 0.557274i \(0.188153\pi\)
\(644\) −9.90927 −0.390480
\(645\) −2.35838 −0.0928612
\(646\) −63.0627 −2.48117
\(647\) 38.2621 1.50424 0.752120 0.659026i \(-0.229031\pi\)
0.752120 + 0.659026i \(0.229031\pi\)
\(648\) −0.993826 −0.0390412
\(649\) 42.9015 1.68403
\(650\) −4.72293 −0.185249
\(651\) 17.4550 0.684115
\(652\) 27.5396 1.07853
\(653\) −13.9046 −0.544130 −0.272065 0.962279i \(-0.587707\pi\)
−0.272065 + 0.962279i \(0.587707\pi\)
\(654\) −0.746047 −0.0291727
\(655\) 9.90426 0.386991
\(656\) −24.3293 −0.949898
\(657\) −0.130293 −0.00508322
\(658\) 50.3503 1.96286
\(659\) −44.7137 −1.74180 −0.870899 0.491462i \(-0.836463\pi\)
−0.870899 + 0.491462i \(0.836463\pi\)
\(660\) 14.4902 0.564029
\(661\) −48.5856 −1.88976 −0.944880 0.327417i \(-0.893822\pi\)
−0.944880 + 0.327417i \(0.893822\pi\)
\(662\) 35.3479 1.37384
\(663\) 4.10223 0.159317
\(664\) 17.0421 0.661362
\(665\) −29.2723 −1.13513
\(666\) 13.6723 0.529792
\(667\) 0.264012 0.0102226
\(668\) 13.7171 0.530732
\(669\) 14.4522 0.558755
\(670\) −13.5060 −0.521782
\(671\) 43.0796 1.66307
\(672\) 15.6233 0.602680
\(673\) −31.2441 −1.20437 −0.602187 0.798355i \(-0.705704\pi\)
−0.602187 + 0.798355i \(0.705704\pi\)
\(674\) −62.5827 −2.41059
\(675\) 2.53680 0.0976413
\(676\) 1.46619 0.0563921
\(677\) −5.43786 −0.208994 −0.104497 0.994525i \(-0.533323\pi\)
−0.104497 + 0.994525i \(0.533323\pi\)
\(678\) −19.9856 −0.767541
\(679\) −22.6600 −0.869610
\(680\) −6.39853 −0.245373
\(681\) 3.65605 0.140100
\(682\) −90.5937 −3.46901
\(683\) −15.9902 −0.611848 −0.305924 0.952056i \(-0.598965\pi\)
−0.305924 + 0.952056i \(0.598965\pi\)
\(684\) 12.1065 0.462902
\(685\) −34.1140 −1.30343
\(686\) −37.4186 −1.42865
\(687\) 7.00073 0.267095
\(688\) 7.18677 0.273993
\(689\) 10.8404 0.412987
\(690\) −8.74272 −0.332830
\(691\) 1.91968 0.0730280 0.0365140 0.999333i \(-0.488375\pi\)
0.0365140 + 0.999333i \(0.488375\pi\)
\(692\) 14.2193 0.540536
\(693\) 14.2237 0.540313
\(694\) 47.6283 1.80795
\(695\) −26.9896 −1.02377
\(696\) −0.0876928 −0.00332399
\(697\) −20.8679 −0.790429
\(698\) −55.9926 −2.11935
\(699\) 0.911437 0.0344737
\(700\) −8.40150 −0.317547
\(701\) 7.69884 0.290781 0.145391 0.989374i \(-0.453556\pi\)
0.145391 + 0.989374i \(0.453556\pi\)
\(702\) −1.86177 −0.0702680
\(703\) 60.6377 2.28699
\(704\) −20.8541 −0.785967
\(705\) 18.7908 0.707703
\(706\) −30.9979 −1.16662
\(707\) 32.3151 1.21534
\(708\) −9.98923 −0.375418
\(709\) 41.3316 1.55224 0.776120 0.630586i \(-0.217185\pi\)
0.776120 + 0.630586i \(0.217185\pi\)
\(710\) −13.8783 −0.520843
\(711\) −10.1097 −0.379143
\(712\) 6.45781 0.242017
\(713\) 23.1212 0.865894
\(714\) 17.2515 0.645621
\(715\) −9.88285 −0.369598
\(716\) 4.17196 0.155913
\(717\) 5.55401 0.207418
\(718\) −27.1878 −1.01464
\(719\) 16.2299 0.605272 0.302636 0.953106i \(-0.402133\pi\)
0.302636 + 0.953106i \(0.402133\pi\)
\(720\) 7.50620 0.279740
\(721\) −2.25881 −0.0841226
\(722\) 91.5605 3.40753
\(723\) 11.5522 0.429630
\(724\) −7.09344 −0.263626
\(725\) 0.223841 0.00831323
\(726\) −53.3432 −1.97975
\(727\) −14.9840 −0.555728 −0.277864 0.960620i \(-0.589626\pi\)
−0.277864 + 0.960620i \(0.589626\pi\)
\(728\) −2.24487 −0.0832003
\(729\) 1.00000 0.0370370
\(730\) 0.380713 0.0140908
\(731\) 6.16430 0.227995
\(732\) −10.0307 −0.370746
\(733\) 4.13745 0.152820 0.0764101 0.997076i \(-0.475654\pi\)
0.0764101 + 0.997076i \(0.475654\pi\)
\(734\) 50.0682 1.84805
\(735\) −2.97846 −0.109862
\(736\) 20.6948 0.762820
\(737\) 29.1059 1.07213
\(738\) 9.47078 0.348624
\(739\) 41.1580 1.51402 0.757011 0.653402i \(-0.226659\pi\)
0.757011 + 0.653402i \(0.226659\pi\)
\(740\) −16.8989 −0.621215
\(741\) −8.25707 −0.303331
\(742\) 45.5882 1.67360
\(743\) 49.6684 1.82216 0.911079 0.412232i \(-0.135251\pi\)
0.911079 + 0.412232i \(0.135251\pi\)
\(744\) −7.67980 −0.281555
\(745\) −4.55921 −0.167036
\(746\) −30.5420 −1.11822
\(747\) −17.1480 −0.627412
\(748\) −37.8742 −1.38482
\(749\) 32.0450 1.17090
\(750\) −22.0223 −0.804142
\(751\) 27.8496 1.01625 0.508123 0.861284i \(-0.330339\pi\)
0.508123 + 0.861284i \(0.330339\pi\)
\(752\) −57.2618 −2.08812
\(753\) 17.2837 0.629852
\(754\) −0.164278 −0.00598266
\(755\) 18.8695 0.686731
\(756\) −3.31186 −0.120451
\(757\) 14.8108 0.538307 0.269154 0.963097i \(-0.413256\pi\)
0.269154 + 0.963097i \(0.413256\pi\)
\(758\) 40.8662 1.48433
\(759\) 18.8409 0.683882
\(760\) 12.8791 0.467175
\(761\) −31.3382 −1.13601 −0.568004 0.823026i \(-0.692284\pi\)
−0.568004 + 0.823026i \(0.692284\pi\)
\(762\) −4.51635 −0.163610
\(763\) 0.905149 0.0327686
\(764\) −20.2482 −0.732555
\(765\) 6.43829 0.232777
\(766\) −24.8014 −0.896110
\(767\) 6.81304 0.246005
\(768\) −20.8985 −0.754109
\(769\) −32.7375 −1.18055 −0.590273 0.807204i \(-0.700980\pi\)
−0.590273 + 0.807204i \(0.700980\pi\)
\(770\) −41.5613 −1.49776
\(771\) 9.43669 0.339854
\(772\) −10.7662 −0.387486
\(773\) 31.6059 1.13679 0.568393 0.822757i \(-0.307565\pi\)
0.568393 + 0.822757i \(0.307565\pi\)
\(774\) −2.79763 −0.100559
\(775\) 19.6031 0.704164
\(776\) 9.96987 0.357897
\(777\) −16.5881 −0.595095
\(778\) 15.7931 0.566209
\(779\) 42.0035 1.50493
\(780\) 2.30113 0.0823938
\(781\) 29.9083 1.07020
\(782\) 22.8516 0.817171
\(783\) 0.0882376 0.00315335
\(784\) 9.07636 0.324156
\(785\) −4.91100 −0.175281
\(786\) 11.7489 0.419070
\(787\) −16.4804 −0.587463 −0.293732 0.955888i \(-0.594897\pi\)
−0.293732 + 0.955888i \(0.594897\pi\)
\(788\) 10.4262 0.371417
\(789\) −25.6603 −0.913533
\(790\) 29.5403 1.05100
\(791\) 24.2477 0.862148
\(792\) −6.25809 −0.222372
\(793\) 6.84133 0.242943
\(794\) −49.9115 −1.77129
\(795\) 17.0136 0.603410
\(796\) 4.03514 0.143022
\(797\) −17.5556 −0.621851 −0.310925 0.950434i \(-0.600639\pi\)
−0.310925 + 0.950434i \(0.600639\pi\)
\(798\) −34.7242 −1.22923
\(799\) −49.1151 −1.73757
\(800\) 17.5459 0.620343
\(801\) −6.49793 −0.229593
\(802\) −66.0255 −2.33144
\(803\) −0.820452 −0.0289531
\(804\) −6.77706 −0.239008
\(805\) 10.6072 0.373854
\(806\) −14.3869 −0.506755
\(807\) −30.8547 −1.08614
\(808\) −14.2179 −0.500184
\(809\) −26.0745 −0.916732 −0.458366 0.888764i \(-0.651565\pi\)
−0.458366 + 0.888764i \(0.651565\pi\)
\(810\) −2.92198 −0.102668
\(811\) −43.6580 −1.53304 −0.766521 0.642220i \(-0.778014\pi\)
−0.766521 + 0.642220i \(0.778014\pi\)
\(812\) −0.292230 −0.0102553
\(813\) 27.8837 0.977922
\(814\) 86.0944 3.01761
\(815\) −29.4793 −1.03261
\(816\) −19.6196 −0.686823
\(817\) −12.4077 −0.434089
\(818\) −19.9645 −0.698041
\(819\) 2.25881 0.0789293
\(820\) −11.7058 −0.408784
\(821\) 35.9072 1.25317 0.626585 0.779353i \(-0.284452\pi\)
0.626585 + 0.779353i \(0.284452\pi\)
\(822\) −40.4677 −1.41147
\(823\) −21.9078 −0.763657 −0.381828 0.924233i \(-0.624705\pi\)
−0.381828 + 0.924233i \(0.624705\pi\)
\(824\) 0.993826 0.0346216
\(825\) 15.9741 0.556148
\(826\) 28.6515 0.996914
\(827\) −8.38794 −0.291677 −0.145839 0.989308i \(-0.546588\pi\)
−0.145839 + 0.989308i \(0.546588\pi\)
\(828\) −4.38694 −0.152457
\(829\) −43.2560 −1.50234 −0.751171 0.660108i \(-0.770510\pi\)
−0.751171 + 0.660108i \(0.770510\pi\)
\(830\) 50.1060 1.73920
\(831\) −1.10800 −0.0384361
\(832\) −3.31176 −0.114815
\(833\) 7.78506 0.269736
\(834\) −32.0164 −1.10864
\(835\) −14.6833 −0.508135
\(836\) 76.2341 2.63661
\(837\) 7.72751 0.267102
\(838\) −26.7791 −0.925070
\(839\) 53.5221 1.84779 0.923894 0.382648i \(-0.124988\pi\)
0.923894 + 0.382648i \(0.124988\pi\)
\(840\) −3.52323 −0.121563
\(841\) −28.9922 −0.999732
\(842\) 4.92821 0.169837
\(843\) 24.6142 0.847759
\(844\) −11.4038 −0.392533
\(845\) −1.56946 −0.0539911
\(846\) 22.2906 0.766366
\(847\) 64.7192 2.22378
\(848\) −51.8461 −1.78040
\(849\) 13.9248 0.477900
\(850\) 19.3746 0.664542
\(851\) −21.9729 −0.753220
\(852\) −6.96387 −0.238578
\(853\) −24.2736 −0.831113 −0.415557 0.909567i \(-0.636413\pi\)
−0.415557 + 0.909567i \(0.636413\pi\)
\(854\) 28.7705 0.984505
\(855\) −12.9591 −0.443193
\(856\) −14.0991 −0.481897
\(857\) −50.6639 −1.73065 −0.865323 0.501214i \(-0.832887\pi\)
−0.865323 + 0.501214i \(0.832887\pi\)
\(858\) −11.7235 −0.400235
\(859\) −11.3242 −0.386377 −0.193188 0.981162i \(-0.561883\pi\)
−0.193188 + 0.981162i \(0.561883\pi\)
\(860\) 3.45784 0.117912
\(861\) −11.4905 −0.391596
\(862\) 3.47243 0.118271
\(863\) 34.7110 1.18158 0.590788 0.806827i \(-0.298817\pi\)
0.590788 + 0.806827i \(0.298817\pi\)
\(864\) 6.91658 0.235307
\(865\) −15.2208 −0.517522
\(866\) 75.9749 2.58173
\(867\) 0.171710 0.00583159
\(868\) −25.5924 −0.868663
\(869\) −63.6605 −2.15953
\(870\) −0.257828 −0.00874119
\(871\) 4.62221 0.156618
\(872\) −0.398244 −0.0134863
\(873\) −10.0318 −0.339525
\(874\) −45.9963 −1.55585
\(875\) 26.7188 0.903261
\(876\) 0.191035 0.00645447
\(877\) −11.2275 −0.379127 −0.189564 0.981868i \(-0.560707\pi\)
−0.189564 + 0.981868i \(0.560707\pi\)
\(878\) −39.6880 −1.33940
\(879\) −2.79845 −0.0943892
\(880\) 47.2663 1.59335
\(881\) −48.5663 −1.63624 −0.818120 0.575047i \(-0.804984\pi\)
−0.818120 + 0.575047i \(0.804984\pi\)
\(882\) −3.53320 −0.118969
\(883\) 10.5796 0.356033 0.178016 0.984028i \(-0.443032\pi\)
0.178016 + 0.984028i \(0.443032\pi\)
\(884\) −6.01466 −0.202295
\(885\) 10.6928 0.359434
\(886\) −35.5189 −1.19328
\(887\) 9.40046 0.315637 0.157818 0.987468i \(-0.449554\pi\)
0.157818 + 0.987468i \(0.449554\pi\)
\(888\) 7.29838 0.244918
\(889\) 5.47950 0.183777
\(890\) 18.9868 0.636439
\(891\) 6.29697 0.210957
\(892\) −21.1897 −0.709485
\(893\) 98.8602 3.30823
\(894\) −5.40836 −0.180883
\(895\) −4.46580 −0.149275
\(896\) 17.3193 0.578596
\(897\) 2.99206 0.0999019
\(898\) 32.8206 1.09524
\(899\) 0.681857 0.0227412
\(900\) −3.71943 −0.123981
\(901\) −44.4699 −1.48151
\(902\) 59.6372 1.98570
\(903\) 3.39425 0.112954
\(904\) −10.6684 −0.354826
\(905\) 7.59304 0.252401
\(906\) 22.3839 0.743656
\(907\) 48.2415 1.60183 0.800917 0.598775i \(-0.204346\pi\)
0.800917 + 0.598775i \(0.204346\pi\)
\(908\) −5.36048 −0.177894
\(909\) 14.3062 0.474508
\(910\) −6.60020 −0.218794
\(911\) −5.40615 −0.179114 −0.0895569 0.995982i \(-0.528545\pi\)
−0.0895569 + 0.995982i \(0.528545\pi\)
\(912\) 39.4908 1.30767
\(913\) −107.980 −3.57363
\(914\) 56.5752 1.87134
\(915\) 10.7372 0.354960
\(916\) −10.2644 −0.339146
\(917\) −14.2545 −0.470725
\(918\) 7.63742 0.252072
\(919\) 5.22341 0.172304 0.0861522 0.996282i \(-0.472543\pi\)
0.0861522 + 0.996282i \(0.472543\pi\)
\(920\) −4.66692 −0.153864
\(921\) −8.30771 −0.273748
\(922\) −34.4115 −1.13328
\(923\) 4.74962 0.156336
\(924\) −20.8547 −0.686068
\(925\) −18.6295 −0.612535
\(926\) −2.67865 −0.0880258
\(927\) −1.00000 −0.0328443
\(928\) 0.610302 0.0200341
\(929\) −26.5938 −0.872515 −0.436258 0.899822i \(-0.643696\pi\)
−0.436258 + 0.899822i \(0.643696\pi\)
\(930\) −22.5796 −0.740414
\(931\) −15.6700 −0.513562
\(932\) −1.33634 −0.0437734
\(933\) 21.6061 0.707353
\(934\) 8.01112 0.262132
\(935\) 40.5417 1.32586
\(936\) −0.993826 −0.0324842
\(937\) 35.2974 1.15311 0.576557 0.817057i \(-0.304396\pi\)
0.576557 + 0.817057i \(0.304396\pi\)
\(938\) 19.4382 0.634680
\(939\) −5.64234 −0.184131
\(940\) −27.5510 −0.898613
\(941\) −14.9835 −0.488449 −0.244224 0.969719i \(-0.578533\pi\)
−0.244224 + 0.969719i \(0.578533\pi\)
\(942\) −5.82567 −0.189811
\(943\) −15.2205 −0.495648
\(944\) −32.5845 −1.06053
\(945\) 3.54512 0.115323
\(946\) −17.6166 −0.572765
\(947\) 39.0354 1.26848 0.634240 0.773137i \(-0.281313\pi\)
0.634240 + 0.773137i \(0.281313\pi\)
\(948\) 14.8228 0.481421
\(949\) −0.130293 −0.00422949
\(950\) −38.9976 −1.26525
\(951\) 12.4310 0.403102
\(952\) 9.20896 0.298464
\(953\) −17.0114 −0.551053 −0.275527 0.961293i \(-0.588852\pi\)
−0.275527 + 0.961293i \(0.588852\pi\)
\(954\) 20.1824 0.653429
\(955\) 21.6743 0.701365
\(956\) −8.14326 −0.263372
\(957\) 0.555630 0.0179610
\(958\) −69.7934 −2.25492
\(959\) 49.0978 1.58545
\(960\) −5.19767 −0.167754
\(961\) 28.7144 0.926271
\(962\) 13.6723 0.440814
\(963\) 14.1867 0.457159
\(964\) −16.9377 −0.545527
\(965\) 11.5245 0.370988
\(966\) 12.5828 0.404844
\(967\) −1.49089 −0.0479439 −0.0239720 0.999713i \(-0.507631\pi\)
−0.0239720 + 0.999713i \(0.507631\pi\)
\(968\) −28.4750 −0.915220
\(969\) 33.8724 1.08814
\(970\) 29.3127 0.941174
\(971\) 26.5605 0.852366 0.426183 0.904637i \(-0.359858\pi\)
0.426183 + 0.904637i \(0.359858\pi\)
\(972\) −1.46619 −0.0470282
\(973\) 38.8442 1.24529
\(974\) −21.9593 −0.703622
\(975\) 2.53680 0.0812425
\(976\) −32.7198 −1.04733
\(977\) 4.51459 0.144434 0.0722172 0.997389i \(-0.476993\pi\)
0.0722172 + 0.997389i \(0.476993\pi\)
\(978\) −34.9698 −1.11821
\(979\) −40.9173 −1.30772
\(980\) 4.36700 0.139499
\(981\) 0.400719 0.0127940
\(982\) −43.5446 −1.38956
\(983\) 28.9362 0.922922 0.461461 0.887160i \(-0.347325\pi\)
0.461461 + 0.887160i \(0.347325\pi\)
\(984\) 5.05556 0.161165
\(985\) −11.1605 −0.355603
\(986\) 0.673907 0.0214616
\(987\) −27.0443 −0.860829
\(988\) 12.1065 0.385158
\(989\) 4.49608 0.142967
\(990\) −18.3996 −0.584778
\(991\) 2.53040 0.0803808 0.0401904 0.999192i \(-0.487204\pi\)
0.0401904 + 0.999192i \(0.487204\pi\)
\(992\) 53.4479 1.69697
\(993\) −18.9862 −0.602508
\(994\) 19.9740 0.633538
\(995\) −4.31934 −0.136932
\(996\) 25.1423 0.796663
\(997\) −11.3967 −0.360936 −0.180468 0.983581i \(-0.557761\pi\)
−0.180468 + 0.983581i \(0.557761\pi\)
\(998\) −31.4774 −0.996399
\(999\) −7.34373 −0.232345
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 \(a_p\))