Properties

Label 8041.2.a.i.1.9
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 78
CM No

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Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(0\)
Dimension: \(78\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.30463 q^{2} -0.694087 q^{3} +3.31131 q^{4} +3.08057 q^{5} +1.59961 q^{6} +3.70671 q^{7} -3.02207 q^{8} -2.51824 q^{9} +O(q^{10})\) \(q-2.30463 q^{2} -0.694087 q^{3} +3.31131 q^{4} +3.08057 q^{5} +1.59961 q^{6} +3.70671 q^{7} -3.02207 q^{8} -2.51824 q^{9} -7.09957 q^{10} +1.00000 q^{11} -2.29834 q^{12} -2.20765 q^{13} -8.54258 q^{14} -2.13819 q^{15} +0.342136 q^{16} -1.00000 q^{17} +5.80361 q^{18} +1.82863 q^{19} +10.2007 q^{20} -2.57278 q^{21} -2.30463 q^{22} +8.54581 q^{23} +2.09758 q^{24} +4.48993 q^{25} +5.08781 q^{26} +3.83014 q^{27} +12.2740 q^{28} -4.48487 q^{29} +4.92772 q^{30} -3.62000 q^{31} +5.25565 q^{32} -0.694087 q^{33} +2.30463 q^{34} +11.4188 q^{35} -8.33867 q^{36} +10.9777 q^{37} -4.21431 q^{38} +1.53230 q^{39} -9.30971 q^{40} +2.53773 q^{41} +5.92930 q^{42} -1.00000 q^{43} +3.31131 q^{44} -7.75763 q^{45} -19.6949 q^{46} -3.78518 q^{47} -0.237472 q^{48} +6.73968 q^{49} -10.3476 q^{50} +0.694087 q^{51} -7.31021 q^{52} -4.35173 q^{53} -8.82705 q^{54} +3.08057 q^{55} -11.2019 q^{56} -1.26923 q^{57} +10.3360 q^{58} -2.26513 q^{59} -7.08019 q^{60} -5.57300 q^{61} +8.34275 q^{62} -9.33439 q^{63} -12.7966 q^{64} -6.80083 q^{65} +1.59961 q^{66} -4.49231 q^{67} -3.31131 q^{68} -5.93154 q^{69} -26.3160 q^{70} -11.2044 q^{71} +7.61031 q^{72} +6.97097 q^{73} -25.2995 q^{74} -3.11640 q^{75} +6.05515 q^{76} +3.70671 q^{77} -3.53139 q^{78} +7.85595 q^{79} +1.05397 q^{80} +4.89627 q^{81} -5.84851 q^{82} +0.718572 q^{83} -8.51926 q^{84} -3.08057 q^{85} +2.30463 q^{86} +3.11289 q^{87} -3.02207 q^{88} +16.6904 q^{89} +17.8784 q^{90} -8.18312 q^{91} +28.2978 q^{92} +2.51260 q^{93} +8.72342 q^{94} +5.63323 q^{95} -3.64788 q^{96} +5.92488 q^{97} -15.5324 q^{98} -2.51824 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + O(q^{10}) \) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + 3q^{10} + 78q^{11} + 31q^{12} - 16q^{13} + 31q^{14} + 38q^{15} + 121q^{16} - 78q^{17} + 11q^{18} + 51q^{20} + 6q^{21} + 7q^{22} + 48q^{23} + 11q^{24} + 101q^{25} + 18q^{26} + 46q^{27} + 27q^{28} + 22q^{29} + 14q^{30} + 56q^{31} + 83q^{32} + 10q^{33} - 7q^{34} + 24q^{35} + 139q^{36} + 53q^{37} + 10q^{38} + 79q^{39} - q^{40} + 23q^{41} + 17q^{42} - 78q^{43} + 91q^{44} + 76q^{45} + 21q^{46} + 57q^{47} + 78q^{48} + 115q^{49} + 58q^{50} - 10q^{51} - 63q^{52} + 22q^{53} - 18q^{54} + 17q^{55} + 111q^{56} - 11q^{57} + 36q^{58} + 71q^{59} + 36q^{60} + 4q^{61} - 5q^{62} + 71q^{63} + 183q^{64} + 47q^{65} + 12q^{66} + 11q^{67} - 91q^{68} + 31q^{69} + 33q^{70} + 159q^{71} + 59q^{72} + 2q^{73} - 4q^{74} + 83q^{75} - 44q^{76} + 11q^{77} + 101q^{78} + 35q^{79} + 85q^{80} + 170q^{81} + 98q^{82} - 32q^{83} + 44q^{84} - 17q^{85} - 7q^{86} - 6q^{87} + 33q^{88} + 50q^{89} - 5q^{90} + 86q^{91} + 106q^{92} + 68q^{93} - q^{94} + 109q^{95} - 50q^{96} + 40q^{97} + 106q^{98} + 102q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.30463 −1.62962 −0.814809 0.579730i \(-0.803158\pi\)
−0.814809 + 0.579730i \(0.803158\pi\)
\(3\) −0.694087 −0.400732 −0.200366 0.979721i \(-0.564213\pi\)
−0.200366 + 0.979721i \(0.564213\pi\)
\(4\) 3.31131 1.65565
\(5\) 3.08057 1.37767 0.688837 0.724916i \(-0.258122\pi\)
0.688837 + 0.724916i \(0.258122\pi\)
\(6\) 1.59961 0.653039
\(7\) 3.70671 1.40100 0.700502 0.713651i \(-0.252960\pi\)
0.700502 + 0.713651i \(0.252960\pi\)
\(8\) −3.02207 −1.06846
\(9\) −2.51824 −0.839414
\(10\) −7.09957 −2.24508
\(11\) 1.00000 0.301511
\(12\) −2.29834 −0.663472
\(13\) −2.20765 −0.612292 −0.306146 0.951985i \(-0.599040\pi\)
−0.306146 + 0.951985i \(0.599040\pi\)
\(14\) −8.54258 −2.28310
\(15\) −2.13819 −0.552077
\(16\) 0.342136 0.0855340
\(17\) −1.00000 −0.242536
\(18\) 5.80361 1.36792
\(19\) 1.82863 0.419517 0.209758 0.977753i \(-0.432732\pi\)
0.209758 + 0.977753i \(0.432732\pi\)
\(20\) 10.2007 2.28095
\(21\) −2.57278 −0.561426
\(22\) −2.30463 −0.491348
\(23\) 8.54581 1.78193 0.890963 0.454076i \(-0.150031\pi\)
0.890963 + 0.454076i \(0.150031\pi\)
\(24\) 2.09758 0.428167
\(25\) 4.48993 0.897985
\(26\) 5.08781 0.997802
\(27\) 3.83014 0.737111
\(28\) 12.2740 2.31958
\(29\) −4.48487 −0.832819 −0.416410 0.909177i \(-0.636712\pi\)
−0.416410 + 0.909177i \(0.636712\pi\)
\(30\) 4.92772 0.899675
\(31\) −3.62000 −0.650171 −0.325086 0.945685i \(-0.605393\pi\)
−0.325086 + 0.945685i \(0.605393\pi\)
\(32\) 5.25565 0.929076
\(33\) −0.694087 −0.120825
\(34\) 2.30463 0.395240
\(35\) 11.4188 1.93013
\(36\) −8.33867 −1.38978
\(37\) 10.9777 1.80472 0.902361 0.430980i \(-0.141832\pi\)
0.902361 + 0.430980i \(0.141832\pi\)
\(38\) −4.21431 −0.683652
\(39\) 1.53230 0.245365
\(40\) −9.30971 −1.47199
\(41\) 2.53773 0.396326 0.198163 0.980169i \(-0.436502\pi\)
0.198163 + 0.980169i \(0.436502\pi\)
\(42\) 5.92930 0.914910
\(43\) −1.00000 −0.152499
\(44\) 3.31131 0.499198
\(45\) −7.75763 −1.15644
\(46\) −19.6949 −2.90386
\(47\) −3.78518 −0.552125 −0.276062 0.961140i \(-0.589030\pi\)
−0.276062 + 0.961140i \(0.589030\pi\)
\(48\) −0.237472 −0.0342762
\(49\) 6.73968 0.962811
\(50\) −10.3476 −1.46337
\(51\) 0.694087 0.0971917
\(52\) −7.31021 −1.01374
\(53\) −4.35173 −0.597756 −0.298878 0.954291i \(-0.596612\pi\)
−0.298878 + 0.954291i \(0.596612\pi\)
\(54\) −8.82705 −1.20121
\(55\) 3.08057 0.415384
\(56\) −11.2019 −1.49692
\(57\) −1.26923 −0.168114
\(58\) 10.3360 1.35718
\(59\) −2.26513 −0.294895 −0.147448 0.989070i \(-0.547106\pi\)
−0.147448 + 0.989070i \(0.547106\pi\)
\(60\) −7.08019 −0.914049
\(61\) −5.57300 −0.713549 −0.356775 0.934190i \(-0.616124\pi\)
−0.356775 + 0.934190i \(0.616124\pi\)
\(62\) 8.34275 1.05953
\(63\) −9.33439 −1.17602
\(64\) −12.7966 −1.59957
\(65\) −6.80083 −0.843539
\(66\) 1.59961 0.196899
\(67\) −4.49231 −0.548823 −0.274412 0.961612i \(-0.588483\pi\)
−0.274412 + 0.961612i \(0.588483\pi\)
\(68\) −3.31131 −0.401555
\(69\) −5.93154 −0.714074
\(70\) −26.3160 −3.14537
\(71\) −11.2044 −1.32972 −0.664860 0.746968i \(-0.731509\pi\)
−0.664860 + 0.746968i \(0.731509\pi\)
\(72\) 7.61031 0.896884
\(73\) 6.97097 0.815891 0.407945 0.913006i \(-0.366245\pi\)
0.407945 + 0.913006i \(0.366245\pi\)
\(74\) −25.2995 −2.94101
\(75\) −3.11640 −0.359851
\(76\) 6.05515 0.694574
\(77\) 3.70671 0.422418
\(78\) −3.53139 −0.399851
\(79\) 7.85595 0.883864 0.441932 0.897049i \(-0.354293\pi\)
0.441932 + 0.897049i \(0.354293\pi\)
\(80\) 1.05397 0.117838
\(81\) 4.89627 0.544030
\(82\) −5.84851 −0.645860
\(83\) 0.718572 0.0788735 0.0394368 0.999222i \(-0.487444\pi\)
0.0394368 + 0.999222i \(0.487444\pi\)
\(84\) −8.51926 −0.929527
\(85\) −3.08057 −0.334135
\(86\) 2.30463 0.248514
\(87\) 3.11289 0.333737
\(88\) −3.02207 −0.322154
\(89\) 16.6904 1.76918 0.884589 0.466372i \(-0.154439\pi\)
0.884589 + 0.466372i \(0.154439\pi\)
\(90\) 17.8784 1.88455
\(91\) −8.18312 −0.857824
\(92\) 28.2978 2.95025
\(93\) 2.51260 0.260544
\(94\) 8.72342 0.899753
\(95\) 5.63323 0.577957
\(96\) −3.64788 −0.372310
\(97\) 5.92488 0.601580 0.300790 0.953690i \(-0.402750\pi\)
0.300790 + 0.953690i \(0.402750\pi\)
\(98\) −15.5324 −1.56901
\(99\) −2.51824 −0.253093
\(100\) 14.8675 1.48675
\(101\) −7.86191 −0.782289 −0.391145 0.920329i \(-0.627921\pi\)
−0.391145 + 0.920329i \(0.627921\pi\)
\(102\) −1.59961 −0.158385
\(103\) 12.0119 1.18357 0.591785 0.806096i \(-0.298424\pi\)
0.591785 + 0.806096i \(0.298424\pi\)
\(104\) 6.67168 0.654212
\(105\) −7.92563 −0.773462
\(106\) 10.0291 0.974113
\(107\) 3.10129 0.299813 0.149907 0.988700i \(-0.452103\pi\)
0.149907 + 0.988700i \(0.452103\pi\)
\(108\) 12.6828 1.22040
\(109\) 10.8009 1.03454 0.517268 0.855823i \(-0.326949\pi\)
0.517268 + 0.855823i \(0.326949\pi\)
\(110\) −7.09957 −0.676917
\(111\) −7.61948 −0.723209
\(112\) 1.26820 0.119833
\(113\) 12.9869 1.22171 0.610855 0.791743i \(-0.290826\pi\)
0.610855 + 0.791743i \(0.290826\pi\)
\(114\) 2.92510 0.273961
\(115\) 26.3260 2.45491
\(116\) −14.8508 −1.37886
\(117\) 5.55940 0.513967
\(118\) 5.22029 0.480567
\(119\) −3.70671 −0.339793
\(120\) 6.46175 0.589875
\(121\) 1.00000 0.0909091
\(122\) 12.8437 1.16281
\(123\) −1.76140 −0.158820
\(124\) −11.9869 −1.07646
\(125\) −1.57132 −0.140543
\(126\) 21.5123 1.91647
\(127\) −16.6906 −1.48106 −0.740528 0.672026i \(-0.765424\pi\)
−0.740528 + 0.672026i \(0.765424\pi\)
\(128\) 18.9800 1.67762
\(129\) 0.694087 0.0611110
\(130\) 15.6734 1.37465
\(131\) 2.67425 0.233650 0.116825 0.993152i \(-0.462728\pi\)
0.116825 + 0.993152i \(0.462728\pi\)
\(132\) −2.29834 −0.200044
\(133\) 6.77820 0.587744
\(134\) 10.3531 0.894372
\(135\) 11.7990 1.01550
\(136\) 3.02207 0.259141
\(137\) 15.2558 1.30339 0.651694 0.758482i \(-0.274059\pi\)
0.651694 + 0.758482i \(0.274059\pi\)
\(138\) 13.6700 1.16367
\(139\) −6.67475 −0.566145 −0.283072 0.959099i \(-0.591354\pi\)
−0.283072 + 0.959099i \(0.591354\pi\)
\(140\) 37.8111 3.19562
\(141\) 2.62724 0.221254
\(142\) 25.8220 2.16694
\(143\) −2.20765 −0.184613
\(144\) −0.861581 −0.0717984
\(145\) −13.8160 −1.14735
\(146\) −16.0655 −1.32959
\(147\) −4.67793 −0.385829
\(148\) 36.3505 2.98799
\(149\) −8.50984 −0.697153 −0.348577 0.937280i \(-0.613335\pi\)
−0.348577 + 0.937280i \(0.613335\pi\)
\(150\) 7.18214 0.586419
\(151\) 12.2971 1.00073 0.500363 0.865816i \(-0.333200\pi\)
0.500363 + 0.865816i \(0.333200\pi\)
\(152\) −5.52625 −0.448238
\(153\) 2.51824 0.203588
\(154\) −8.54258 −0.688381
\(155\) −11.1517 −0.895724
\(156\) 5.07392 0.406239
\(157\) −21.7672 −1.73721 −0.868606 0.495504i \(-0.834983\pi\)
−0.868606 + 0.495504i \(0.834983\pi\)
\(158\) −18.1050 −1.44036
\(159\) 3.02048 0.239540
\(160\) 16.1904 1.27996
\(161\) 31.6768 2.49648
\(162\) −11.2841 −0.886561
\(163\) −7.99913 −0.626540 −0.313270 0.949664i \(-0.601425\pi\)
−0.313270 + 0.949664i \(0.601425\pi\)
\(164\) 8.40319 0.656179
\(165\) −2.13819 −0.166458
\(166\) −1.65604 −0.128534
\(167\) 18.3801 1.42229 0.711147 0.703043i \(-0.248176\pi\)
0.711147 + 0.703043i \(0.248176\pi\)
\(168\) 7.77512 0.599864
\(169\) −8.12628 −0.625098
\(170\) 7.09957 0.544512
\(171\) −4.60493 −0.352148
\(172\) −3.31131 −0.252485
\(173\) 21.3999 1.62701 0.813503 0.581561i \(-0.197558\pi\)
0.813503 + 0.581561i \(0.197558\pi\)
\(174\) −7.17406 −0.543864
\(175\) 16.6428 1.25808
\(176\) 0.342136 0.0257895
\(177\) 1.57220 0.118174
\(178\) −38.4651 −2.88308
\(179\) −15.7639 −1.17825 −0.589124 0.808043i \(-0.700527\pi\)
−0.589124 + 0.808043i \(0.700527\pi\)
\(180\) −25.6879 −1.91466
\(181\) 24.9670 1.85578 0.927890 0.372854i \(-0.121621\pi\)
0.927890 + 0.372854i \(0.121621\pi\)
\(182\) 18.8590 1.39792
\(183\) 3.86815 0.285942
\(184\) −25.8261 −1.90392
\(185\) 33.8176 2.48632
\(186\) −5.79060 −0.424587
\(187\) −1.00000 −0.0731272
\(188\) −12.5339 −0.914127
\(189\) 14.1972 1.03270
\(190\) −12.9825 −0.941849
\(191\) −11.6340 −0.841807 −0.420903 0.907106i \(-0.638287\pi\)
−0.420903 + 0.907106i \(0.638287\pi\)
\(192\) 8.88195 0.640999
\(193\) −13.0433 −0.938879 −0.469439 0.882965i \(-0.655544\pi\)
−0.469439 + 0.882965i \(0.655544\pi\)
\(194\) −13.6546 −0.980346
\(195\) 4.72037 0.338033
\(196\) 22.3171 1.59408
\(197\) 26.7822 1.90815 0.954077 0.299560i \(-0.0968399\pi\)
0.954077 + 0.299560i \(0.0968399\pi\)
\(198\) 5.80361 0.412445
\(199\) 25.7217 1.82336 0.911682 0.410896i \(-0.134784\pi\)
0.911682 + 0.410896i \(0.134784\pi\)
\(200\) −13.5689 −0.959464
\(201\) 3.11806 0.219931
\(202\) 18.1188 1.27483
\(203\) −16.6241 −1.16678
\(204\) 2.29834 0.160916
\(205\) 7.81765 0.546008
\(206\) −27.6830 −1.92877
\(207\) −21.5204 −1.49577
\(208\) −0.755317 −0.0523718
\(209\) 1.82863 0.126489
\(210\) 18.2656 1.26045
\(211\) −15.8034 −1.08795 −0.543975 0.839101i \(-0.683081\pi\)
−0.543975 + 0.839101i \(0.683081\pi\)
\(212\) −14.4099 −0.989676
\(213\) 7.77685 0.532861
\(214\) −7.14732 −0.488581
\(215\) −3.08057 −0.210093
\(216\) −11.5750 −0.787577
\(217\) −13.4183 −0.910892
\(218\) −24.8920 −1.68590
\(219\) −4.83847 −0.326953
\(220\) 10.2007 0.687732
\(221\) 2.20765 0.148503
\(222\) 17.5601 1.17855
\(223\) 22.3927 1.49953 0.749764 0.661705i \(-0.230167\pi\)
0.749764 + 0.661705i \(0.230167\pi\)
\(224\) 19.4811 1.30164
\(225\) −11.3067 −0.753781
\(226\) −29.9301 −1.99092
\(227\) 23.9347 1.58860 0.794299 0.607527i \(-0.207838\pi\)
0.794299 + 0.607527i \(0.207838\pi\)
\(228\) −4.20281 −0.278338
\(229\) −2.34414 −0.154905 −0.0774524 0.996996i \(-0.524679\pi\)
−0.0774524 + 0.996996i \(0.524679\pi\)
\(230\) −60.6716 −4.00057
\(231\) −2.57278 −0.169276
\(232\) 13.5536 0.889837
\(233\) 8.78772 0.575702 0.287851 0.957675i \(-0.407059\pi\)
0.287851 + 0.957675i \(0.407059\pi\)
\(234\) −12.8123 −0.837569
\(235\) −11.6605 −0.760648
\(236\) −7.50055 −0.488244
\(237\) −5.45272 −0.354192
\(238\) 8.54258 0.553733
\(239\) −15.8447 −1.02491 −0.512454 0.858715i \(-0.671263\pi\)
−0.512454 + 0.858715i \(0.671263\pi\)
\(240\) −0.731550 −0.0472214
\(241\) −15.6352 −1.00715 −0.503574 0.863952i \(-0.667982\pi\)
−0.503574 + 0.863952i \(0.667982\pi\)
\(242\) −2.30463 −0.148147
\(243\) −14.8889 −0.955122
\(244\) −18.4539 −1.18139
\(245\) 20.7621 1.32644
\(246\) 4.05938 0.258817
\(247\) −4.03698 −0.256867
\(248\) 10.9399 0.694684
\(249\) −0.498752 −0.0316071
\(250\) 3.62131 0.229032
\(251\) 13.4314 0.847784 0.423892 0.905713i \(-0.360664\pi\)
0.423892 + 0.905713i \(0.360664\pi\)
\(252\) −30.9090 −1.94708
\(253\) 8.54581 0.537271
\(254\) 38.4657 2.41355
\(255\) 2.13819 0.133898
\(256\) −18.1488 −1.13430
\(257\) 11.6332 0.725657 0.362829 0.931856i \(-0.381811\pi\)
0.362829 + 0.931856i \(0.381811\pi\)
\(258\) −1.59961 −0.0995875
\(259\) 40.6911 2.52842
\(260\) −22.5196 −1.39661
\(261\) 11.2940 0.699080
\(262\) −6.16315 −0.380761
\(263\) −21.2984 −1.31332 −0.656659 0.754187i \(-0.728031\pi\)
−0.656659 + 0.754187i \(0.728031\pi\)
\(264\) 2.09758 0.129097
\(265\) −13.4058 −0.823512
\(266\) −15.6212 −0.957798
\(267\) −11.5846 −0.708965
\(268\) −14.8754 −0.908661
\(269\) 23.7164 1.44601 0.723007 0.690840i \(-0.242759\pi\)
0.723007 + 0.690840i \(0.242759\pi\)
\(270\) −27.1924 −1.65487
\(271\) 18.7128 1.13672 0.568361 0.822779i \(-0.307578\pi\)
0.568361 + 0.822779i \(0.307578\pi\)
\(272\) −0.342136 −0.0207450
\(273\) 5.67980 0.343757
\(274\) −35.1589 −2.12402
\(275\) 4.48993 0.270753
\(276\) −19.6412 −1.18226
\(277\) −14.7870 −0.888464 −0.444232 0.895912i \(-0.646523\pi\)
−0.444232 + 0.895912i \(0.646523\pi\)
\(278\) 15.3828 0.922600
\(279\) 9.11604 0.545763
\(280\) −34.5084 −2.06227
\(281\) 0.848238 0.0506016 0.0253008 0.999680i \(-0.491946\pi\)
0.0253008 + 0.999680i \(0.491946\pi\)
\(282\) −6.05482 −0.360559
\(283\) 4.82669 0.286917 0.143458 0.989656i \(-0.454178\pi\)
0.143458 + 0.989656i \(0.454178\pi\)
\(284\) −37.1013 −2.20156
\(285\) −3.90995 −0.231606
\(286\) 5.08781 0.300849
\(287\) 9.40661 0.555254
\(288\) −13.2350 −0.779880
\(289\) 1.00000 0.0588235
\(290\) 31.8406 1.86975
\(291\) −4.11238 −0.241072
\(292\) 23.0830 1.35083
\(293\) −32.7621 −1.91398 −0.956990 0.290122i \(-0.906304\pi\)
−0.956990 + 0.290122i \(0.906304\pi\)
\(294\) 10.7809 0.628753
\(295\) −6.97791 −0.406270
\(296\) −33.1754 −1.92828
\(297\) 3.83014 0.222247
\(298\) 19.6120 1.13609
\(299\) −18.8662 −1.09106
\(300\) −10.3194 −0.595788
\(301\) −3.70671 −0.213651
\(302\) −28.3403 −1.63080
\(303\) 5.45685 0.313488
\(304\) 0.625640 0.0358829
\(305\) −17.1680 −0.983038
\(306\) −5.80361 −0.331770
\(307\) −4.30262 −0.245563 −0.122782 0.992434i \(-0.539182\pi\)
−0.122782 + 0.992434i \(0.539182\pi\)
\(308\) 12.2740 0.699378
\(309\) −8.33732 −0.474294
\(310\) 25.7004 1.45969
\(311\) −12.4691 −0.707055 −0.353528 0.935424i \(-0.615018\pi\)
−0.353528 + 0.935424i \(0.615018\pi\)
\(312\) −4.63073 −0.262163
\(313\) 21.5567 1.21846 0.609229 0.792994i \(-0.291479\pi\)
0.609229 + 0.792994i \(0.291479\pi\)
\(314\) 50.1653 2.83099
\(315\) −28.7553 −1.62018
\(316\) 26.0135 1.46337
\(317\) 13.4095 0.753152 0.376576 0.926386i \(-0.377101\pi\)
0.376576 + 0.926386i \(0.377101\pi\)
\(318\) −6.96108 −0.390358
\(319\) −4.48487 −0.251105
\(320\) −39.4208 −2.20369
\(321\) −2.15257 −0.120145
\(322\) −73.0033 −4.06831
\(323\) −1.82863 −0.101748
\(324\) 16.2131 0.900726
\(325\) −9.91219 −0.549829
\(326\) 18.4350 1.02102
\(327\) −7.49676 −0.414572
\(328\) −7.66919 −0.423460
\(329\) −14.0305 −0.773529
\(330\) 4.92772 0.271262
\(331\) 23.4848 1.29084 0.645421 0.763827i \(-0.276682\pi\)
0.645421 + 0.763827i \(0.276682\pi\)
\(332\) 2.37941 0.130587
\(333\) −27.6445 −1.51491
\(334\) −42.3593 −2.31780
\(335\) −13.8389 −0.756099
\(336\) −0.880240 −0.0480210
\(337\) −8.79842 −0.479280 −0.239640 0.970862i \(-0.577029\pi\)
−0.239640 + 0.970862i \(0.577029\pi\)
\(338\) 18.7280 1.01867
\(339\) −9.01408 −0.489578
\(340\) −10.2007 −0.553212
\(341\) −3.62000 −0.196034
\(342\) 10.6127 0.573867
\(343\) −0.964942 −0.0521020
\(344\) 3.02207 0.162939
\(345\) −18.2725 −0.983761
\(346\) −49.3188 −2.65140
\(347\) −16.2572 −0.872733 −0.436366 0.899769i \(-0.643735\pi\)
−0.436366 + 0.899769i \(0.643735\pi\)
\(348\) 10.3077 0.552553
\(349\) −30.7187 −1.64434 −0.822168 0.569244i \(-0.807236\pi\)
−0.822168 + 0.569244i \(0.807236\pi\)
\(350\) −38.3555 −2.05019
\(351\) −8.45562 −0.451328
\(352\) 5.25565 0.280127
\(353\) −9.43362 −0.502101 −0.251050 0.967974i \(-0.580776\pi\)
−0.251050 + 0.967974i \(0.580776\pi\)
\(354\) −3.62334 −0.192578
\(355\) −34.5160 −1.83192
\(356\) 55.2670 2.92914
\(357\) 2.57278 0.136166
\(358\) 36.3299 1.92009
\(359\) 21.1969 1.11873 0.559366 0.828921i \(-0.311045\pi\)
0.559366 + 0.828921i \(0.311045\pi\)
\(360\) 23.4441 1.23561
\(361\) −15.6561 −0.824006
\(362\) −57.5395 −3.02421
\(363\) −0.694087 −0.0364301
\(364\) −27.0968 −1.42026
\(365\) 21.4746 1.12403
\(366\) −8.91464 −0.465976
\(367\) 5.42407 0.283134 0.141567 0.989929i \(-0.454786\pi\)
0.141567 + 0.989929i \(0.454786\pi\)
\(368\) 2.92383 0.152415
\(369\) −6.39061 −0.332682
\(370\) −77.9369 −4.05175
\(371\) −16.1306 −0.837458
\(372\) 8.31997 0.431371
\(373\) 2.21586 0.114733 0.0573664 0.998353i \(-0.481730\pi\)
0.0573664 + 0.998353i \(0.481730\pi\)
\(374\) 2.30463 0.119169
\(375\) 1.09064 0.0563202
\(376\) 11.4391 0.589925
\(377\) 9.90103 0.509929
\(378\) −32.7193 −1.68290
\(379\) −17.4205 −0.894833 −0.447417 0.894326i \(-0.647656\pi\)
−0.447417 + 0.894326i \(0.647656\pi\)
\(380\) 18.6533 0.956896
\(381\) 11.5848 0.593506
\(382\) 26.8120 1.37182
\(383\) 32.1577 1.64318 0.821591 0.570078i \(-0.193087\pi\)
0.821591 + 0.570078i \(0.193087\pi\)
\(384\) −13.1738 −0.672273
\(385\) 11.4188 0.581955
\(386\) 30.0600 1.53001
\(387\) 2.51824 0.128009
\(388\) 19.6191 0.996008
\(389\) 21.7253 1.10151 0.550757 0.834666i \(-0.314339\pi\)
0.550757 + 0.834666i \(0.314339\pi\)
\(390\) −10.8787 −0.550864
\(391\) −8.54581 −0.432180
\(392\) −20.3678 −1.02873
\(393\) −1.85616 −0.0936311
\(394\) −61.7231 −3.10956
\(395\) 24.2008 1.21768
\(396\) −8.33867 −0.419034
\(397\) −5.45373 −0.273715 −0.136857 0.990591i \(-0.543700\pi\)
−0.136857 + 0.990591i \(0.543700\pi\)
\(398\) −59.2790 −2.97139
\(399\) −4.70466 −0.235528
\(400\) 1.53616 0.0768082
\(401\) 38.3657 1.91589 0.957945 0.286952i \(-0.0926421\pi\)
0.957945 + 0.286952i \(0.0926421\pi\)
\(402\) −7.18596 −0.358403
\(403\) 7.99170 0.398095
\(404\) −26.0332 −1.29520
\(405\) 15.0833 0.749496
\(406\) 38.3123 1.90141
\(407\) 10.9777 0.544144
\(408\) −2.09758 −0.103846
\(409\) −19.4340 −0.960948 −0.480474 0.877009i \(-0.659535\pi\)
−0.480474 + 0.877009i \(0.659535\pi\)
\(410\) −18.0168 −0.889785
\(411\) −10.5888 −0.522309
\(412\) 39.7751 1.95958
\(413\) −8.39619 −0.413149
\(414\) 49.5966 2.43754
\(415\) 2.21361 0.108662
\(416\) −11.6026 −0.568866
\(417\) 4.63286 0.226872
\(418\) −4.21431 −0.206129
\(419\) −25.1553 −1.22892 −0.614458 0.788950i \(-0.710625\pi\)
−0.614458 + 0.788950i \(0.710625\pi\)
\(420\) −26.2442 −1.28059
\(421\) −13.0378 −0.635423 −0.317712 0.948187i \(-0.602914\pi\)
−0.317712 + 0.948187i \(0.602914\pi\)
\(422\) 36.4209 1.77294
\(423\) 9.53200 0.463462
\(424\) 13.1512 0.638680
\(425\) −4.48993 −0.217793
\(426\) −17.9227 −0.868359
\(427\) −20.6575 −0.999685
\(428\) 10.2693 0.496387
\(429\) 1.53230 0.0739803
\(430\) 7.09957 0.342372
\(431\) 23.3378 1.12414 0.562072 0.827088i \(-0.310004\pi\)
0.562072 + 0.827088i \(0.310004\pi\)
\(432\) 1.31043 0.0630481
\(433\) −3.35230 −0.161101 −0.0805506 0.996751i \(-0.525668\pi\)
−0.0805506 + 0.996751i \(0.525668\pi\)
\(434\) 30.9241 1.48441
\(435\) 9.58949 0.459781
\(436\) 35.7650 1.71283
\(437\) 15.6271 0.747547
\(438\) 11.1509 0.532809
\(439\) 2.66791 0.127333 0.0636663 0.997971i \(-0.479721\pi\)
0.0636663 + 0.997971i \(0.479721\pi\)
\(440\) −9.30971 −0.443823
\(441\) −16.9721 −0.808197
\(442\) −5.08781 −0.242003
\(443\) 10.6111 0.504148 0.252074 0.967708i \(-0.418887\pi\)
0.252074 + 0.967708i \(0.418887\pi\)
\(444\) −25.2304 −1.19738
\(445\) 51.4159 2.43735
\(446\) −51.6069 −2.44366
\(447\) 5.90657 0.279371
\(448\) −47.4332 −2.24101
\(449\) 19.8559 0.937057 0.468528 0.883449i \(-0.344784\pi\)
0.468528 + 0.883449i \(0.344784\pi\)
\(450\) 26.0578 1.22838
\(451\) 2.53773 0.119497
\(452\) 43.0038 2.02273
\(453\) −8.53529 −0.401023
\(454\) −55.1604 −2.58881
\(455\) −25.2087 −1.18180
\(456\) 3.83570 0.179623
\(457\) −25.5907 −1.19708 −0.598541 0.801092i \(-0.704253\pi\)
−0.598541 + 0.801092i \(0.704253\pi\)
\(458\) 5.40236 0.252436
\(459\) −3.83014 −0.178776
\(460\) 87.1734 4.06448
\(461\) 38.4897 1.79264 0.896322 0.443403i \(-0.146229\pi\)
0.896322 + 0.443403i \(0.146229\pi\)
\(462\) 5.92930 0.275856
\(463\) 13.7876 0.640765 0.320383 0.947288i \(-0.396188\pi\)
0.320383 + 0.947288i \(0.396188\pi\)
\(464\) −1.53444 −0.0712344
\(465\) 7.74023 0.358945
\(466\) −20.2524 −0.938175
\(467\) 1.70939 0.0791010 0.0395505 0.999218i \(-0.487407\pi\)
0.0395505 + 0.999218i \(0.487407\pi\)
\(468\) 18.4089 0.850951
\(469\) −16.6517 −0.768903
\(470\) 26.8731 1.23957
\(471\) 15.1083 0.696155
\(472\) 6.84540 0.315085
\(473\) −1.00000 −0.0459800
\(474\) 12.5665 0.577198
\(475\) 8.21041 0.376720
\(476\) −12.2740 −0.562580
\(477\) 10.9587 0.501765
\(478\) 36.5161 1.67021
\(479\) 30.7191 1.40359 0.701797 0.712377i \(-0.252381\pi\)
0.701797 + 0.712377i \(0.252381\pi\)
\(480\) −11.2376 −0.512922
\(481\) −24.2349 −1.10502
\(482\) 36.0332 1.64127
\(483\) −21.9865 −1.00042
\(484\) 3.31131 0.150514
\(485\) 18.2520 0.828781
\(486\) 34.3133 1.55648
\(487\) −35.1720 −1.59379 −0.796897 0.604115i \(-0.793527\pi\)
−0.796897 + 0.604115i \(0.793527\pi\)
\(488\) 16.8420 0.762402
\(489\) 5.55210 0.251075
\(490\) −47.8488 −2.16159
\(491\) 23.7828 1.07330 0.536652 0.843803i \(-0.319689\pi\)
0.536652 + 0.843803i \(0.319689\pi\)
\(492\) −5.83255 −0.262952
\(493\) 4.48487 0.201988
\(494\) 9.30373 0.418595
\(495\) −7.75763 −0.348679
\(496\) −1.23853 −0.0556117
\(497\) −41.5315 −1.86294
\(498\) 1.14944 0.0515075
\(499\) 6.70034 0.299948 0.149974 0.988690i \(-0.452081\pi\)
0.149974 + 0.988690i \(0.452081\pi\)
\(500\) −5.20313 −0.232691
\(501\) −12.7574 −0.569958
\(502\) −30.9544 −1.38156
\(503\) −37.2696 −1.66177 −0.830885 0.556443i \(-0.812166\pi\)
−0.830885 + 0.556443i \(0.812166\pi\)
\(504\) 28.2092 1.25654
\(505\) −24.2192 −1.07774
\(506\) −19.6949 −0.875546
\(507\) 5.64035 0.250497
\(508\) −55.2678 −2.45211
\(509\) −27.1425 −1.20307 −0.601536 0.798846i \(-0.705444\pi\)
−0.601536 + 0.798846i \(0.705444\pi\)
\(510\) −4.92772 −0.218203
\(511\) 25.8394 1.14307
\(512\) 3.86606 0.170858
\(513\) 7.00392 0.309230
\(514\) −26.8101 −1.18254
\(515\) 37.0036 1.63057
\(516\) 2.29834 0.101179
\(517\) −3.78518 −0.166472
\(518\) −93.7778 −4.12036
\(519\) −14.8534 −0.651993
\(520\) 20.5526 0.901291
\(521\) −24.4008 −1.06902 −0.534509 0.845163i \(-0.679503\pi\)
−0.534509 + 0.845163i \(0.679503\pi\)
\(522\) −26.0284 −1.13923
\(523\) −17.7438 −0.775880 −0.387940 0.921685i \(-0.626813\pi\)
−0.387940 + 0.921685i \(0.626813\pi\)
\(524\) 8.85526 0.386844
\(525\) −11.5516 −0.504152
\(526\) 49.0850 2.14021
\(527\) 3.62000 0.157690
\(528\) −0.237472 −0.0103347
\(529\) 50.0309 2.17526
\(530\) 30.8954 1.34201
\(531\) 5.70416 0.247539
\(532\) 22.4447 0.973100
\(533\) −5.60241 −0.242667
\(534\) 26.6982 1.15534
\(535\) 9.55375 0.413045
\(536\) 13.5761 0.586398
\(537\) 10.9415 0.472161
\(538\) −54.6575 −2.35645
\(539\) 6.73968 0.290298
\(540\) 39.0702 1.68131
\(541\) 3.09173 0.132924 0.0664620 0.997789i \(-0.478829\pi\)
0.0664620 + 0.997789i \(0.478829\pi\)
\(542\) −43.1260 −1.85242
\(543\) −17.3293 −0.743670
\(544\) −5.25565 −0.225334
\(545\) 33.2729 1.42525
\(546\) −13.0898 −0.560192
\(547\) −16.5702 −0.708489 −0.354245 0.935153i \(-0.615262\pi\)
−0.354245 + 0.935153i \(0.615262\pi\)
\(548\) 50.5165 2.15796
\(549\) 14.0342 0.598963
\(550\) −10.3476 −0.441223
\(551\) −8.20117 −0.349382
\(552\) 17.9255 0.762962
\(553\) 29.1197 1.23830
\(554\) 34.0785 1.44786
\(555\) −23.4724 −0.996346
\(556\) −22.1021 −0.937339
\(557\) −7.34964 −0.311414 −0.155707 0.987803i \(-0.549766\pi\)
−0.155707 + 0.987803i \(0.549766\pi\)
\(558\) −21.0091 −0.889385
\(559\) 2.20765 0.0933737
\(560\) 3.90677 0.165091
\(561\) 0.694087 0.0293044
\(562\) −1.95487 −0.0824613
\(563\) 27.6376 1.16479 0.582393 0.812907i \(-0.302116\pi\)
0.582393 + 0.812907i \(0.302116\pi\)
\(564\) 8.69961 0.366320
\(565\) 40.0072 1.68312
\(566\) −11.1237 −0.467564
\(567\) 18.1491 0.762189
\(568\) 33.8606 1.42076
\(569\) 31.9126 1.33785 0.668924 0.743331i \(-0.266755\pi\)
0.668924 + 0.743331i \(0.266755\pi\)
\(570\) 9.01098 0.377429
\(571\) −37.3063 −1.56122 −0.780611 0.625017i \(-0.785092\pi\)
−0.780611 + 0.625017i \(0.785092\pi\)
\(572\) −7.31021 −0.305655
\(573\) 8.07501 0.337338
\(574\) −21.6787 −0.904852
\(575\) 38.3701 1.60014
\(576\) 32.2249 1.34270
\(577\) −7.05552 −0.293725 −0.146863 0.989157i \(-0.546918\pi\)
−0.146863 + 0.989157i \(0.546918\pi\)
\(578\) −2.30463 −0.0958599
\(579\) 9.05321 0.376238
\(580\) −45.7489 −1.89962
\(581\) 2.66354 0.110502
\(582\) 9.47751 0.392855
\(583\) −4.35173 −0.180230
\(584\) −21.0668 −0.871750
\(585\) 17.1261 0.708079
\(586\) 75.5043 3.11905
\(587\) 2.03167 0.0838560 0.0419280 0.999121i \(-0.486650\pi\)
0.0419280 + 0.999121i \(0.486650\pi\)
\(588\) −15.4900 −0.638799
\(589\) −6.61964 −0.272758
\(590\) 16.0815 0.662064
\(591\) −18.5892 −0.764658
\(592\) 3.75586 0.154365
\(593\) 27.4258 1.12624 0.563122 0.826374i \(-0.309600\pi\)
0.563122 + 0.826374i \(0.309600\pi\)
\(594\) −8.82705 −0.362178
\(595\) −11.4188 −0.468124
\(596\) −28.1787 −1.15424
\(597\) −17.8531 −0.730680
\(598\) 43.4795 1.77801
\(599\) 31.0388 1.26821 0.634106 0.773246i \(-0.281368\pi\)
0.634106 + 0.773246i \(0.281368\pi\)
\(600\) 9.41799 0.384488
\(601\) 10.6181 0.433123 0.216561 0.976269i \(-0.430516\pi\)
0.216561 + 0.976269i \(0.430516\pi\)
\(602\) 8.54258 0.348169
\(603\) 11.3127 0.460690
\(604\) 40.7196 1.65686
\(605\) 3.08057 0.125243
\(606\) −12.5760 −0.510865
\(607\) −8.82037 −0.358008 −0.179004 0.983848i \(-0.557287\pi\)
−0.179004 + 0.983848i \(0.557287\pi\)
\(608\) 9.61064 0.389763
\(609\) 11.5386 0.467567
\(610\) 39.5659 1.60198
\(611\) 8.35635 0.338062
\(612\) 8.33867 0.337071
\(613\) −21.0897 −0.851805 −0.425903 0.904769i \(-0.640043\pi\)
−0.425903 + 0.904769i \(0.640043\pi\)
\(614\) 9.91593 0.400175
\(615\) −5.42613 −0.218803
\(616\) −11.2019 −0.451339
\(617\) −13.5453 −0.545314 −0.272657 0.962111i \(-0.587902\pi\)
−0.272657 + 0.962111i \(0.587902\pi\)
\(618\) 19.2144 0.772917
\(619\) 10.1383 0.407492 0.203746 0.979024i \(-0.434688\pi\)
0.203746 + 0.979024i \(0.434688\pi\)
\(620\) −36.9266 −1.48301
\(621\) 32.7317 1.31348
\(622\) 28.7365 1.15223
\(623\) 61.8664 2.47862
\(624\) 0.524256 0.0209870
\(625\) −27.2902 −1.09161
\(626\) −49.6802 −1.98562
\(627\) −1.26923 −0.0506881
\(628\) −72.0778 −2.87622
\(629\) −10.9777 −0.437710
\(630\) 66.2701 2.64027
\(631\) −5.70047 −0.226932 −0.113466 0.993542i \(-0.536195\pi\)
−0.113466 + 0.993542i \(0.536195\pi\)
\(632\) −23.7413 −0.944376
\(633\) 10.9689 0.435976
\(634\) −30.9039 −1.22735
\(635\) −51.4167 −2.04041
\(636\) 10.0017 0.396594
\(637\) −14.8789 −0.589522
\(638\) 10.3360 0.409204
\(639\) 28.2155 1.11619
\(640\) 58.4694 2.31121
\(641\) −19.1348 −0.755779 −0.377889 0.925851i \(-0.623350\pi\)
−0.377889 + 0.925851i \(0.623350\pi\)
\(642\) 4.96087 0.195790
\(643\) 27.0018 1.06485 0.532424 0.846478i \(-0.321281\pi\)
0.532424 + 0.846478i \(0.321281\pi\)
\(644\) 104.892 4.13331
\(645\) 2.13819 0.0841910
\(646\) 4.21431 0.165810
\(647\) 7.42279 0.291820 0.145910 0.989298i \(-0.453389\pi\)
0.145910 + 0.989298i \(0.453389\pi\)
\(648\) −14.7969 −0.581277
\(649\) −2.26513 −0.0889143
\(650\) 22.8439 0.896011
\(651\) 9.31346 0.365023
\(652\) −26.4876 −1.03733
\(653\) −9.70158 −0.379652 −0.189826 0.981818i \(-0.560792\pi\)
−0.189826 + 0.981818i \(0.560792\pi\)
\(654\) 17.2772 0.675593
\(655\) 8.23822 0.321894
\(656\) 0.868247 0.0338994
\(657\) −17.5546 −0.684870
\(658\) 32.3352 1.26056
\(659\) 13.1684 0.512966 0.256483 0.966549i \(-0.417436\pi\)
0.256483 + 0.966549i \(0.417436\pi\)
\(660\) −7.08019 −0.275596
\(661\) 34.4073 1.33829 0.669144 0.743133i \(-0.266661\pi\)
0.669144 + 0.743133i \(0.266661\pi\)
\(662\) −54.1237 −2.10358
\(663\) −1.53230 −0.0595097
\(664\) −2.17158 −0.0842735
\(665\) 20.8807 0.809720
\(666\) 63.7103 2.46872
\(667\) −38.3269 −1.48402
\(668\) 60.8621 2.35483
\(669\) −15.5425 −0.600908
\(670\) 31.8935 1.23215
\(671\) −5.57300 −0.215143
\(672\) −13.5216 −0.521608
\(673\) 24.1977 0.932753 0.466377 0.884586i \(-0.345559\pi\)
0.466377 + 0.884586i \(0.345559\pi\)
\(674\) 20.2771 0.781044
\(675\) 17.1971 0.661915
\(676\) −26.9086 −1.03495
\(677\) −23.6630 −0.909444 −0.454722 0.890633i \(-0.650261\pi\)
−0.454722 + 0.890633i \(0.650261\pi\)
\(678\) 20.7741 0.797824
\(679\) 21.9618 0.842816
\(680\) 9.30971 0.357011
\(681\) −16.6127 −0.636602
\(682\) 8.34275 0.319460
\(683\) −22.1462 −0.847400 −0.423700 0.905803i \(-0.639269\pi\)
−0.423700 + 0.905803i \(0.639269\pi\)
\(684\) −15.2483 −0.583035
\(685\) 46.9965 1.79564
\(686\) 2.22383 0.0849063
\(687\) 1.62703 0.0620753
\(688\) −0.342136 −0.0130438
\(689\) 9.60710 0.366001
\(690\) 42.1114 1.60315
\(691\) −21.5348 −0.819221 −0.409610 0.912261i \(-0.634335\pi\)
−0.409610 + 0.912261i \(0.634335\pi\)
\(692\) 70.8617 2.69376
\(693\) −9.33439 −0.354584
\(694\) 37.4668 1.42222
\(695\) −20.5620 −0.779963
\(696\) −9.40738 −0.356586
\(697\) −2.53773 −0.0961232
\(698\) 70.7953 2.67964
\(699\) −6.09944 −0.230702
\(700\) 55.1095 2.08294
\(701\) −5.28937 −0.199777 −0.0998885 0.994999i \(-0.531849\pi\)
−0.0998885 + 0.994999i \(0.531849\pi\)
\(702\) 19.4871 0.735491
\(703\) 20.0742 0.757111
\(704\) −12.7966 −0.482289
\(705\) 8.09342 0.304816
\(706\) 21.7410 0.818232
\(707\) −29.1418 −1.09599
\(708\) 5.20604 0.195655
\(709\) −20.2639 −0.761028 −0.380514 0.924775i \(-0.624253\pi\)
−0.380514 + 0.924775i \(0.624253\pi\)
\(710\) 79.5466 2.98533
\(711\) −19.7832 −0.741928
\(712\) −50.4395 −1.89030
\(713\) −30.9358 −1.15856
\(714\) −5.92930 −0.221898
\(715\) −6.80083 −0.254337
\(716\) −52.1990 −1.95077
\(717\) 10.9976 0.410713
\(718\) −48.8510 −1.82310
\(719\) −41.7053 −1.55534 −0.777672 0.628670i \(-0.783600\pi\)
−0.777672 + 0.628670i \(0.783600\pi\)
\(720\) −2.65416 −0.0989148
\(721\) 44.5247 1.65818
\(722\) 36.0815 1.34281
\(723\) 10.8522 0.403596
\(724\) 82.6733 3.07253
\(725\) −20.1367 −0.747859
\(726\) 1.59961 0.0593672
\(727\) −25.8932 −0.960326 −0.480163 0.877179i \(-0.659423\pi\)
−0.480163 + 0.877179i \(0.659423\pi\)
\(728\) 24.7300 0.916553
\(729\) −4.35464 −0.161283
\(730\) −49.4909 −1.83174
\(731\) 1.00000 0.0369863
\(732\) 12.8086 0.473420
\(733\) −36.8943 −1.36272 −0.681362 0.731947i \(-0.738612\pi\)
−0.681362 + 0.731947i \(0.738612\pi\)
\(734\) −12.5005 −0.461401
\(735\) −14.4107 −0.531546
\(736\) 44.9138 1.65554
\(737\) −4.49231 −0.165476
\(738\) 14.7280 0.542144
\(739\) −14.4893 −0.532999 −0.266499 0.963835i \(-0.585867\pi\)
−0.266499 + 0.963835i \(0.585867\pi\)
\(740\) 111.980 4.11648
\(741\) 2.80202 0.102935
\(742\) 37.1750 1.36474
\(743\) 37.5194 1.37645 0.688226 0.725496i \(-0.258390\pi\)
0.688226 + 0.725496i \(0.258390\pi\)
\(744\) −7.59325 −0.278382
\(745\) −26.2152 −0.960449
\(746\) −5.10673 −0.186971
\(747\) −1.80954 −0.0662076
\(748\) −3.31131 −0.121073
\(749\) 11.4956 0.420039
\(750\) −2.51351 −0.0917803
\(751\) −32.2504 −1.17683 −0.588416 0.808558i \(-0.700248\pi\)
−0.588416 + 0.808558i \(0.700248\pi\)
\(752\) −1.29505 −0.0472254
\(753\) −9.32259 −0.339734
\(754\) −22.8182 −0.830989
\(755\) 37.8822 1.37867
\(756\) 47.0113 1.70979
\(757\) 44.3654 1.61249 0.806244 0.591583i \(-0.201497\pi\)
0.806244 + 0.591583i \(0.201497\pi\)
\(758\) 40.1479 1.45824
\(759\) −5.93154 −0.215301
\(760\) −17.0240 −0.617526
\(761\) 16.6548 0.603735 0.301867 0.953350i \(-0.402390\pi\)
0.301867 + 0.953350i \(0.402390\pi\)
\(762\) −26.6986 −0.967187
\(763\) 40.0357 1.44939
\(764\) −38.5237 −1.39374
\(765\) 7.75763 0.280478
\(766\) −74.1115 −2.67776
\(767\) 5.00063 0.180562
\(768\) 12.5968 0.454549
\(769\) 24.9015 0.897971 0.448985 0.893539i \(-0.351786\pi\)
0.448985 + 0.893539i \(0.351786\pi\)
\(770\) −26.3160 −0.948364
\(771\) −8.07444 −0.290794
\(772\) −43.1904 −1.55446
\(773\) 33.8813 1.21863 0.609313 0.792930i \(-0.291445\pi\)
0.609313 + 0.792930i \(0.291445\pi\)
\(774\) −5.80361 −0.208606
\(775\) −16.2535 −0.583844
\(776\) −17.9054 −0.642767
\(777\) −28.2432 −1.01322
\(778\) −50.0686 −1.79505
\(779\) 4.64056 0.166265
\(780\) 15.6306 0.559665
\(781\) −11.2044 −0.400926
\(782\) 19.6949 0.704289
\(783\) −17.1777 −0.613881
\(784\) 2.30589 0.0823531
\(785\) −67.0554 −2.39331
\(786\) 4.27777 0.152583
\(787\) 0.105538 0.00376202 0.00188101 0.999998i \(-0.499401\pi\)
0.00188101 + 0.999998i \(0.499401\pi\)
\(788\) 88.6842 3.15924
\(789\) 14.7830 0.526288
\(790\) −55.7739 −1.98435
\(791\) 48.1388 1.71162
\(792\) 7.61031 0.270421
\(793\) 12.3032 0.436901
\(794\) 12.5688 0.446050
\(795\) 9.30480 0.330007
\(796\) 85.1725 3.01886
\(797\) 10.7265 0.379952 0.189976 0.981789i \(-0.439159\pi\)
0.189976 + 0.981789i \(0.439159\pi\)
\(798\) 10.8425 0.383820
\(799\) 3.78518 0.133910
\(800\) 23.5975 0.834296
\(801\) −42.0304 −1.48507
\(802\) −88.4185 −3.12217
\(803\) 6.97097 0.246000
\(804\) 10.3248 0.364129
\(805\) 97.5828 3.43934
\(806\) −18.4179 −0.648742
\(807\) −16.4613 −0.579464
\(808\) 23.7592 0.835847
\(809\) −28.6097 −1.00586 −0.502932 0.864326i \(-0.667745\pi\)
−0.502932 + 0.864326i \(0.667745\pi\)
\(810\) −34.7614 −1.22139
\(811\) −32.5642 −1.14348 −0.571742 0.820433i \(-0.693732\pi\)
−0.571742 + 0.820433i \(0.693732\pi\)
\(812\) −55.0475 −1.93179
\(813\) −12.9883 −0.455520
\(814\) −25.2995 −0.886747
\(815\) −24.6419 −0.863168
\(816\) 0.237472 0.00831319
\(817\) −1.82863 −0.0639757
\(818\) 44.7881 1.56598
\(819\) 20.6071 0.720069
\(820\) 25.8866 0.904000
\(821\) −24.9277 −0.869984 −0.434992 0.900434i \(-0.643249\pi\)
−0.434992 + 0.900434i \(0.643249\pi\)
\(822\) 24.4033 0.851164
\(823\) 44.7510 1.55992 0.779961 0.625828i \(-0.215239\pi\)
0.779961 + 0.625828i \(0.215239\pi\)
\(824\) −36.3009 −1.26460
\(825\) −3.11640 −0.108499
\(826\) 19.3501 0.673275
\(827\) −13.3013 −0.462532 −0.231266 0.972891i \(-0.574287\pi\)
−0.231266 + 0.972891i \(0.574287\pi\)
\(828\) −71.2607 −2.47648
\(829\) −35.1222 −1.21985 −0.609923 0.792461i \(-0.708800\pi\)
−0.609923 + 0.792461i \(0.708800\pi\)
\(830\) −5.10155 −0.177077
\(831\) 10.2635 0.356036
\(832\) 28.2504 0.979406
\(833\) −6.73968 −0.233516
\(834\) −10.6770 −0.369715
\(835\) 56.6212 1.95946
\(836\) 6.05515 0.209422
\(837\) −13.8651 −0.479248
\(838\) 57.9735 2.00266
\(839\) 25.7797 0.890013 0.445007 0.895527i \(-0.353201\pi\)
0.445007 + 0.895527i \(0.353201\pi\)
\(840\) 23.9518 0.826416
\(841\) −8.88594 −0.306412
\(842\) 30.0473 1.03550
\(843\) −0.588751 −0.0202777
\(844\) −52.3298 −1.80127
\(845\) −25.0336 −0.861181
\(846\) −21.9677 −0.755265
\(847\) 3.70671 0.127364
\(848\) −1.48888 −0.0511284
\(849\) −3.35014 −0.114977
\(850\) 10.3476 0.354920
\(851\) 93.8134 3.21588
\(852\) 25.7515 0.882233
\(853\) 7.06395 0.241865 0.120932 0.992661i \(-0.461412\pi\)
0.120932 + 0.992661i \(0.461412\pi\)
\(854\) 47.6078 1.62910
\(855\) −14.1858 −0.485145
\(856\) −9.37232 −0.320339
\(857\) −26.3846 −0.901281 −0.450640 0.892706i \(-0.648804\pi\)
−0.450640 + 0.892706i \(0.648804\pi\)
\(858\) −3.53139 −0.120560
\(859\) 43.2579 1.47594 0.737970 0.674833i \(-0.235785\pi\)
0.737970 + 0.674833i \(0.235785\pi\)
\(860\) −10.2007 −0.347842
\(861\) −6.52901 −0.222508
\(862\) −53.7850 −1.83193
\(863\) −27.6360 −0.940739 −0.470370 0.882470i \(-0.655879\pi\)
−0.470370 + 0.882470i \(0.655879\pi\)
\(864\) 20.1299 0.684832
\(865\) 65.9240 2.24148
\(866\) 7.72580 0.262533
\(867\) −0.694087 −0.0235724
\(868\) −44.4320 −1.50812
\(869\) 7.85595 0.266495
\(870\) −22.1002 −0.749267
\(871\) 9.91746 0.336040
\(872\) −32.6410 −1.10537
\(873\) −14.9203 −0.504975
\(874\) −36.0147 −1.21822
\(875\) −5.82443 −0.196902
\(876\) −16.0216 −0.541321
\(877\) 21.9636 0.741657 0.370829 0.928701i \(-0.379074\pi\)
0.370829 + 0.928701i \(0.379074\pi\)
\(878\) −6.14855 −0.207503
\(879\) 22.7397 0.766992
\(880\) 1.05397 0.0355295
\(881\) 18.5236 0.624077 0.312039 0.950069i \(-0.398988\pi\)
0.312039 + 0.950069i \(0.398988\pi\)
\(882\) 39.1145 1.31705
\(883\) 41.9748 1.41257 0.706283 0.707930i \(-0.250371\pi\)
0.706283 + 0.707930i \(0.250371\pi\)
\(884\) 7.31021 0.245869
\(885\) 4.84328 0.162805
\(886\) −24.4546 −0.821568
\(887\) −14.8914 −0.500004 −0.250002 0.968245i \(-0.580431\pi\)
−0.250002 + 0.968245i \(0.580431\pi\)
\(888\) 23.0266 0.772723
\(889\) −61.8673 −2.07496
\(890\) −118.495 −3.97195
\(891\) 4.89627 0.164031
\(892\) 74.1492 2.48270
\(893\) −6.92169 −0.231626
\(894\) −13.6124 −0.455268
\(895\) −48.5618 −1.62324
\(896\) 70.3535 2.35034
\(897\) 13.0948 0.437222
\(898\) −45.7604 −1.52704
\(899\) 16.2352 0.541475
\(900\) −37.4400 −1.24800
\(901\) 4.35173 0.144977
\(902\) −5.84851 −0.194734
\(903\) 2.57278 0.0856167
\(904\) −39.2475 −1.30535
\(905\) 76.9125 2.55666
\(906\) 19.6707 0.653514
\(907\) 5.27828 0.175262 0.0876312 0.996153i \(-0.472070\pi\)
0.0876312 + 0.996153i \(0.472070\pi\)
\(908\) 79.2550 2.63017
\(909\) 19.7982 0.656665
\(910\) 58.0966 1.92588
\(911\) 41.5392 1.37625 0.688127 0.725590i \(-0.258433\pi\)
0.688127 + 0.725590i \(0.258433\pi\)
\(912\) −0.434249 −0.0143794
\(913\) 0.718572 0.0237813
\(914\) 58.9770 1.95079
\(915\) 11.9161 0.393934
\(916\) −7.76215 −0.256469
\(917\) 9.91266 0.327345
\(918\) 8.82705 0.291336
\(919\) −15.6250 −0.515422 −0.257711 0.966222i \(-0.582968\pi\)
−0.257711 + 0.966222i \(0.582968\pi\)
\(920\) −79.5590 −2.62298
\(921\) 2.98639 0.0984050
\(922\) −88.7044 −2.92133
\(923\) 24.7355 0.814177
\(924\) −8.51926 −0.280263
\(925\) 49.2890 1.62061
\(926\) −31.7753 −1.04420
\(927\) −30.2489 −0.993505
\(928\) −23.5709 −0.773753
\(929\) −17.8744 −0.586442 −0.293221 0.956045i \(-0.594727\pi\)
−0.293221 + 0.956045i \(0.594727\pi\)
\(930\) −17.8384 −0.584943
\(931\) 12.3244 0.403915
\(932\) 29.0988 0.953163
\(933\) 8.65461 0.283339
\(934\) −3.93950 −0.128904
\(935\) −3.08057 −0.100745
\(936\) −16.8009 −0.549155
\(937\) −22.5454 −0.736525 −0.368263 0.929722i \(-0.620047\pi\)
−0.368263 + 0.929722i \(0.620047\pi\)
\(938\) 38.3759 1.25302
\(939\) −14.9623 −0.488275
\(940\) −38.6115 −1.25937
\(941\) −1.22495 −0.0399323 −0.0199662 0.999801i \(-0.506356\pi\)
−0.0199662 + 0.999801i \(0.506356\pi\)
\(942\) −34.8191 −1.13447
\(943\) 21.6869 0.706224
\(944\) −0.774984 −0.0252236
\(945\) 43.7356 1.42272
\(946\) 2.30463 0.0749299
\(947\) 22.6657 0.736537 0.368269 0.929719i \(-0.379951\pi\)
0.368269 + 0.929719i \(0.379951\pi\)
\(948\) −18.0556 −0.586419
\(949\) −15.3895 −0.499564
\(950\) −18.9219 −0.613909
\(951\) −9.30736 −0.301812
\(952\) 11.2019 0.363057
\(953\) 0.756122 0.0244932 0.0122466 0.999925i \(-0.496102\pi\)
0.0122466 + 0.999925i \(0.496102\pi\)
\(954\) −25.2557 −0.817684
\(955\) −35.8394 −1.15973
\(956\) −52.4666 −1.69689
\(957\) 3.11289 0.100626
\(958\) −70.7962 −2.28732
\(959\) 56.5487 1.82605
\(960\) 27.3615 0.883088
\(961\) −17.8956 −0.577278
\(962\) 55.8525 1.80076
\(963\) −7.80980 −0.251667
\(964\) −51.7728 −1.66749
\(965\) −40.1809 −1.29347
\(966\) 50.6707 1.63030
\(967\) −15.7627 −0.506893 −0.253447 0.967349i \(-0.581564\pi\)
−0.253447 + 0.967349i \(0.581564\pi\)
\(968\) −3.02207 −0.0971331
\(969\) 1.26923 0.0407735
\(970\) −42.0641 −1.35060
\(971\) 51.9825 1.66820 0.834099 0.551615i \(-0.185988\pi\)
0.834099 + 0.551615i \(0.185988\pi\)
\(972\) −49.3016 −1.58135
\(973\) −24.7413 −0.793171
\(974\) 81.0582 2.59727
\(975\) 6.87993 0.220334
\(976\) −1.90672 −0.0610327
\(977\) −57.8715 −1.85147 −0.925737 0.378167i \(-0.876555\pi\)
−0.925737 + 0.378167i \(0.876555\pi\)
\(978\) −12.7955 −0.409155
\(979\) 16.6904 0.533427
\(980\) 68.7495 2.19612
\(981\) −27.1992 −0.868405
\(982\) −54.8106 −1.74908
\(983\) −5.69178 −0.181540 −0.0907698 0.995872i \(-0.528933\pi\)
−0.0907698 + 0.995872i \(0.528933\pi\)
\(984\) 5.32309 0.169694
\(985\) 82.5046 2.62881
\(986\) −10.3360 −0.329164
\(987\) 9.73843 0.309978
\(988\) −13.3677 −0.425282
\(989\) −8.54581 −0.271741
\(990\) 17.8784 0.568214
\(991\) 58.7428 1.86603 0.933013 0.359844i \(-0.117170\pi\)
0.933013 + 0.359844i \(0.117170\pi\)
\(992\) −19.0254 −0.604058
\(993\) −16.3005 −0.517281
\(994\) 95.7146 3.03588
\(995\) 79.2376 2.51200
\(996\) −1.65152 −0.0523304
\(997\) −4.85531 −0.153769 −0.0768846 0.997040i \(-0.524497\pi\)
−0.0768846 + 0.997040i \(0.524497\pi\)
\(998\) −15.4418 −0.488801
\(999\) 42.0462 1.33028
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 \(a_p\))