Properties

Label 8042.2.a.c.1.11
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 0
Dimension 86
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(0\)
Dimension: \(86\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.49912 q^{3} +1.00000 q^{4} -3.77840 q^{5} +2.49912 q^{6} -0.508744 q^{7} -1.00000 q^{8} +3.24558 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.49912 q^{3} +1.00000 q^{4} -3.77840 q^{5} +2.49912 q^{6} -0.508744 q^{7} -1.00000 q^{8} +3.24558 q^{9} +3.77840 q^{10} +4.72877 q^{11} -2.49912 q^{12} -1.56616 q^{13} +0.508744 q^{14} +9.44266 q^{15} +1.00000 q^{16} -1.70941 q^{17} -3.24558 q^{18} -7.33030 q^{19} -3.77840 q^{20} +1.27141 q^{21} -4.72877 q^{22} +6.82278 q^{23} +2.49912 q^{24} +9.27631 q^{25} +1.56616 q^{26} -0.613729 q^{27} -0.508744 q^{28} +6.46138 q^{29} -9.44266 q^{30} -0.0712862 q^{31} -1.00000 q^{32} -11.8177 q^{33} +1.70941 q^{34} +1.92224 q^{35} +3.24558 q^{36} +9.42635 q^{37} +7.33030 q^{38} +3.91402 q^{39} +3.77840 q^{40} -5.14690 q^{41} -1.27141 q^{42} +1.98166 q^{43} +4.72877 q^{44} -12.2631 q^{45} -6.82278 q^{46} +5.36150 q^{47} -2.49912 q^{48} -6.74118 q^{49} -9.27631 q^{50} +4.27200 q^{51} -1.56616 q^{52} +0.630655 q^{53} +0.613729 q^{54} -17.8672 q^{55} +0.508744 q^{56} +18.3193 q^{57} -6.46138 q^{58} -3.96183 q^{59} +9.44266 q^{60} +10.9418 q^{61} +0.0712862 q^{62} -1.65117 q^{63} +1.00000 q^{64} +5.91758 q^{65} +11.8177 q^{66} -0.192213 q^{67} -1.70941 q^{68} -17.0509 q^{69} -1.92224 q^{70} +4.53092 q^{71} -3.24558 q^{72} +0.588797 q^{73} -9.42635 q^{74} -23.1826 q^{75} -7.33030 q^{76} -2.40573 q^{77} -3.91402 q^{78} -16.1449 q^{79} -3.77840 q^{80} -8.20296 q^{81} +5.14690 q^{82} +6.65631 q^{83} +1.27141 q^{84} +6.45882 q^{85} -1.98166 q^{86} -16.1477 q^{87} -4.72877 q^{88} -0.667289 q^{89} +12.2631 q^{90} +0.796775 q^{91} +6.82278 q^{92} +0.178152 q^{93} -5.36150 q^{94} +27.6968 q^{95} +2.49912 q^{96} +2.10060 q^{97} +6.74118 q^{98} +15.3476 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 86q - 86q^{2} + 12q^{3} + 86q^{4} - 4q^{5} - 12q^{6} + 35q^{7} - 86q^{8} + 72q^{9} + O(q^{10}) \) \( 86q - 86q^{2} + 12q^{3} + 86q^{4} - 4q^{5} - 12q^{6} + 35q^{7} - 86q^{8} + 72q^{9} + 4q^{10} + 13q^{11} + 12q^{12} + 45q^{13} - 35q^{14} + 17q^{15} + 86q^{16} + 5q^{17} - 72q^{18} + 47q^{19} - 4q^{20} + 15q^{21} - 13q^{22} + 6q^{23} - 12q^{24} + 112q^{25} - 45q^{26} + 51q^{27} + 35q^{28} - 14q^{29} - 17q^{30} + 24q^{31} - 86q^{32} + 43q^{33} - 5q^{34} + 42q^{35} + 72q^{36} + 61q^{37} - 47q^{38} + 20q^{39} + 4q^{40} - 16q^{41} - 15q^{42} + 72q^{43} + 13q^{44} + 6q^{45} - 6q^{46} + 11q^{47} + 12q^{48} + 89q^{49} - 112q^{50} + 56q^{51} + 45q^{52} - 7q^{53} - 51q^{54} + 48q^{55} - 35q^{56} + 65q^{57} + 14q^{58} + 24q^{59} + 17q^{60} + 31q^{61} - 24q^{62} + 98q^{63} + 86q^{64} - 9q^{65} - 43q^{66} + 157q^{67} + 5q^{68} + q^{69} - 42q^{70} - 11q^{71} - 72q^{72} + 74q^{73} - 61q^{74} + 76q^{75} + 47q^{76} - 13q^{77} - 20q^{78} + 57q^{79} - 4q^{80} + 34q^{81} + 16q^{82} + 65q^{83} + 15q^{84} + 102q^{85} - 72q^{86} + 49q^{87} - 13q^{88} - 34q^{89} - 6q^{90} + 91q^{91} + 6q^{92} + 57q^{93} - 11q^{94} - 13q^{95} - 12q^{96} + 64q^{97} - 89q^{98} + 56q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.49912 −1.44287 −0.721433 0.692485i \(-0.756516\pi\)
−0.721433 + 0.692485i \(0.756516\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.77840 −1.68975 −0.844876 0.534962i \(-0.820326\pi\)
−0.844876 + 0.534962i \(0.820326\pi\)
\(6\) 2.49912 1.02026
\(7\) −0.508744 −0.192287 −0.0961436 0.995367i \(-0.530651\pi\)
−0.0961436 + 0.995367i \(0.530651\pi\)
\(8\) −1.00000 −0.353553
\(9\) 3.24558 1.08186
\(10\) 3.77840 1.19483
\(11\) 4.72877 1.42578 0.712889 0.701277i \(-0.247386\pi\)
0.712889 + 0.701277i \(0.247386\pi\)
\(12\) −2.49912 −0.721433
\(13\) −1.56616 −0.434375 −0.217187 0.976130i \(-0.569688\pi\)
−0.217187 + 0.976130i \(0.569688\pi\)
\(14\) 0.508744 0.135968
\(15\) 9.44266 2.43808
\(16\) 1.00000 0.250000
\(17\) −1.70941 −0.414592 −0.207296 0.978278i \(-0.566466\pi\)
−0.207296 + 0.978278i \(0.566466\pi\)
\(18\) −3.24558 −0.764990
\(19\) −7.33030 −1.68169 −0.840843 0.541278i \(-0.817941\pi\)
−0.840843 + 0.541278i \(0.817941\pi\)
\(20\) −3.77840 −0.844876
\(21\) 1.27141 0.277444
\(22\) −4.72877 −1.00818
\(23\) 6.82278 1.42265 0.711324 0.702865i \(-0.248096\pi\)
0.711324 + 0.702865i \(0.248096\pi\)
\(24\) 2.49912 0.510130
\(25\) 9.27631 1.85526
\(26\) 1.56616 0.307149
\(27\) −0.613729 −0.118112
\(28\) −0.508744 −0.0961436
\(29\) 6.46138 1.19985 0.599924 0.800057i \(-0.295197\pi\)
0.599924 + 0.800057i \(0.295197\pi\)
\(30\) −9.44266 −1.72399
\(31\) −0.0712862 −0.0128034 −0.00640169 0.999980i \(-0.502038\pi\)
−0.00640169 + 0.999980i \(0.502038\pi\)
\(32\) −1.00000 −0.176777
\(33\) −11.8177 −2.05720
\(34\) 1.70941 0.293161
\(35\) 1.92224 0.324917
\(36\) 3.24558 0.540930
\(37\) 9.42635 1.54968 0.774841 0.632156i \(-0.217830\pi\)
0.774841 + 0.632156i \(0.217830\pi\)
\(38\) 7.33030 1.18913
\(39\) 3.91402 0.626744
\(40\) 3.77840 0.597417
\(41\) −5.14690 −0.803810 −0.401905 0.915681i \(-0.631652\pi\)
−0.401905 + 0.915681i \(0.631652\pi\)
\(42\) −1.27141 −0.196183
\(43\) 1.98166 0.302200 0.151100 0.988518i \(-0.451718\pi\)
0.151100 + 0.988518i \(0.451718\pi\)
\(44\) 4.72877 0.712889
\(45\) −12.2631 −1.82807
\(46\) −6.82278 −1.00596
\(47\) 5.36150 0.782055 0.391028 0.920379i \(-0.372120\pi\)
0.391028 + 0.920379i \(0.372120\pi\)
\(48\) −2.49912 −0.360716
\(49\) −6.74118 −0.963026
\(50\) −9.27631 −1.31187
\(51\) 4.27200 0.598200
\(52\) −1.56616 −0.217187
\(53\) 0.630655 0.0866271 0.0433136 0.999062i \(-0.486209\pi\)
0.0433136 + 0.999062i \(0.486209\pi\)
\(54\) 0.613729 0.0835179
\(55\) −17.8672 −2.40921
\(56\) 0.508744 0.0679838
\(57\) 18.3193 2.42645
\(58\) −6.46138 −0.848421
\(59\) −3.96183 −0.515787 −0.257893 0.966173i \(-0.583028\pi\)
−0.257893 + 0.966173i \(0.583028\pi\)
\(60\) 9.44266 1.21904
\(61\) 10.9418 1.40095 0.700477 0.713675i \(-0.252971\pi\)
0.700477 + 0.713675i \(0.252971\pi\)
\(62\) 0.0712862 0.00905335
\(63\) −1.65117 −0.208028
\(64\) 1.00000 0.125000
\(65\) 5.91758 0.733986
\(66\) 11.8177 1.45466
\(67\) −0.192213 −0.0234825 −0.0117412 0.999931i \(-0.503737\pi\)
−0.0117412 + 0.999931i \(0.503737\pi\)
\(68\) −1.70941 −0.207296
\(69\) −17.0509 −2.05269
\(70\) −1.92224 −0.229751
\(71\) 4.53092 0.537721 0.268861 0.963179i \(-0.413353\pi\)
0.268861 + 0.963179i \(0.413353\pi\)
\(72\) −3.24558 −0.382495
\(73\) 0.588797 0.0689134 0.0344567 0.999406i \(-0.489030\pi\)
0.0344567 + 0.999406i \(0.489030\pi\)
\(74\) −9.42635 −1.09579
\(75\) −23.1826 −2.67689
\(76\) −7.33030 −0.840843
\(77\) −2.40573 −0.274159
\(78\) −3.91402 −0.443175
\(79\) −16.1449 −1.81644 −0.908221 0.418492i \(-0.862559\pi\)
−0.908221 + 0.418492i \(0.862559\pi\)
\(80\) −3.77840 −0.422438
\(81\) −8.20296 −0.911440
\(82\) 5.14690 0.568380
\(83\) 6.65631 0.730625 0.365312 0.930885i \(-0.380962\pi\)
0.365312 + 0.930885i \(0.380962\pi\)
\(84\) 1.27141 0.138722
\(85\) 6.45882 0.700558
\(86\) −1.98166 −0.213688
\(87\) −16.1477 −1.73122
\(88\) −4.72877 −0.504089
\(89\) −0.667289 −0.0707325 −0.0353662 0.999374i \(-0.511260\pi\)
−0.0353662 + 0.999374i \(0.511260\pi\)
\(90\) 12.2631 1.29264
\(91\) 0.796775 0.0835247
\(92\) 6.82278 0.711324
\(93\) 0.178152 0.0184735
\(94\) −5.36150 −0.552997
\(95\) 27.6968 2.84163
\(96\) 2.49912 0.255065
\(97\) 2.10060 0.213284 0.106642 0.994297i \(-0.465990\pi\)
0.106642 + 0.994297i \(0.465990\pi\)
\(98\) 6.74118 0.680962
\(99\) 15.3476 1.54249
\(100\) 9.27631 0.927631
\(101\) 2.07226 0.206198 0.103099 0.994671i \(-0.467124\pi\)
0.103099 + 0.994671i \(0.467124\pi\)
\(102\) −4.27200 −0.422992
\(103\) 14.2849 1.40753 0.703764 0.710434i \(-0.251501\pi\)
0.703764 + 0.710434i \(0.251501\pi\)
\(104\) 1.56616 0.153575
\(105\) −4.80389 −0.468812
\(106\) −0.630655 −0.0612546
\(107\) −10.1314 −0.979437 −0.489718 0.871881i \(-0.662900\pi\)
−0.489718 + 0.871881i \(0.662900\pi\)
\(108\) −0.613729 −0.0590561
\(109\) 13.6923 1.31148 0.655742 0.754985i \(-0.272356\pi\)
0.655742 + 0.754985i \(0.272356\pi\)
\(110\) 17.8672 1.70357
\(111\) −23.5575 −2.23598
\(112\) −0.508744 −0.0480718
\(113\) −8.47807 −0.797550 −0.398775 0.917049i \(-0.630565\pi\)
−0.398775 + 0.917049i \(0.630565\pi\)
\(114\) −18.3193 −1.71576
\(115\) −25.7792 −2.40392
\(116\) 6.46138 0.599924
\(117\) −5.08310 −0.469933
\(118\) 3.96183 0.364716
\(119\) 0.869650 0.0797207
\(120\) −9.44266 −0.861993
\(121\) 11.3613 1.03284
\(122\) −10.9418 −0.990624
\(123\) 12.8627 1.15979
\(124\) −0.0712862 −0.00640169
\(125\) −16.1576 −1.44518
\(126\) 1.65117 0.147098
\(127\) −14.9791 −1.32918 −0.664590 0.747208i \(-0.731394\pi\)
−0.664590 + 0.747208i \(0.731394\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −4.95240 −0.436034
\(130\) −5.91758 −0.519006
\(131\) −10.5654 −0.923106 −0.461553 0.887113i \(-0.652708\pi\)
−0.461553 + 0.887113i \(0.652708\pi\)
\(132\) −11.8177 −1.02860
\(133\) 3.72925 0.323367
\(134\) 0.192213 0.0166046
\(135\) 2.31891 0.199580
\(136\) 1.70941 0.146580
\(137\) −11.8114 −1.00912 −0.504559 0.863377i \(-0.668345\pi\)
−0.504559 + 0.863377i \(0.668345\pi\)
\(138\) 17.0509 1.45147
\(139\) −2.76617 −0.234624 −0.117312 0.993095i \(-0.537428\pi\)
−0.117312 + 0.993095i \(0.537428\pi\)
\(140\) 1.92224 0.162459
\(141\) −13.3990 −1.12840
\(142\) −4.53092 −0.380226
\(143\) −7.40602 −0.619322
\(144\) 3.24558 0.270465
\(145\) −24.4137 −2.02745
\(146\) −0.588797 −0.0487291
\(147\) 16.8470 1.38952
\(148\) 9.42635 0.774841
\(149\) 0.0224216 0.00183685 0.000918426 1.00000i \(-0.499708\pi\)
0.000918426 1.00000i \(0.499708\pi\)
\(150\) 23.1826 1.89285
\(151\) 15.8603 1.29070 0.645348 0.763888i \(-0.276712\pi\)
0.645348 + 0.763888i \(0.276712\pi\)
\(152\) 7.33030 0.594566
\(153\) −5.54801 −0.448530
\(154\) 2.40573 0.193859
\(155\) 0.269348 0.0216345
\(156\) 3.91402 0.313372
\(157\) 5.68936 0.454061 0.227030 0.973888i \(-0.427098\pi\)
0.227030 + 0.973888i \(0.427098\pi\)
\(158\) 16.1449 1.28442
\(159\) −1.57608 −0.124991
\(160\) 3.77840 0.298709
\(161\) −3.47105 −0.273557
\(162\) 8.20296 0.644485
\(163\) 4.12095 0.322777 0.161389 0.986891i \(-0.448403\pi\)
0.161389 + 0.986891i \(0.448403\pi\)
\(164\) −5.14690 −0.401905
\(165\) 44.6522 3.47617
\(166\) −6.65631 −0.516630
\(167\) 2.34577 0.181521 0.0907607 0.995873i \(-0.471070\pi\)
0.0907607 + 0.995873i \(0.471070\pi\)
\(168\) −1.27141 −0.0980914
\(169\) −10.5471 −0.811318
\(170\) −6.45882 −0.495369
\(171\) −23.7911 −1.81935
\(172\) 1.98166 0.151100
\(173\) −16.9073 −1.28544 −0.642718 0.766103i \(-0.722193\pi\)
−0.642718 + 0.766103i \(0.722193\pi\)
\(174\) 16.1477 1.22416
\(175\) −4.71926 −0.356743
\(176\) 4.72877 0.356444
\(177\) 9.90108 0.744211
\(178\) 0.667289 0.0500154
\(179\) −25.4604 −1.90300 −0.951498 0.307654i \(-0.900456\pi\)
−0.951498 + 0.307654i \(0.900456\pi\)
\(180\) −12.2631 −0.914037
\(181\) −1.99371 −0.148191 −0.0740957 0.997251i \(-0.523607\pi\)
−0.0740957 + 0.997251i \(0.523607\pi\)
\(182\) −0.796775 −0.0590609
\(183\) −27.3448 −2.02139
\(184\) −6.82278 −0.502982
\(185\) −35.6165 −2.61858
\(186\) −0.178152 −0.0130628
\(187\) −8.08339 −0.591116
\(188\) 5.36150 0.391028
\(189\) 0.312231 0.0227114
\(190\) −27.6968 −2.00934
\(191\) −14.4859 −1.04816 −0.524081 0.851669i \(-0.675591\pi\)
−0.524081 + 0.851669i \(0.675591\pi\)
\(192\) −2.49912 −0.180358
\(193\) 21.0958 1.51851 0.759254 0.650794i \(-0.225564\pi\)
0.759254 + 0.650794i \(0.225564\pi\)
\(194\) −2.10060 −0.150815
\(195\) −14.7887 −1.05904
\(196\) −6.74118 −0.481513
\(197\) −24.1967 −1.72394 −0.861970 0.506959i \(-0.830770\pi\)
−0.861970 + 0.506959i \(0.830770\pi\)
\(198\) −15.3476 −1.09071
\(199\) 16.5051 1.17002 0.585008 0.811028i \(-0.301091\pi\)
0.585008 + 0.811028i \(0.301091\pi\)
\(200\) −9.27631 −0.655934
\(201\) 0.480361 0.0338821
\(202\) −2.07226 −0.145804
\(203\) −3.28719 −0.230715
\(204\) 4.27200 0.299100
\(205\) 19.4470 1.35824
\(206\) −14.2849 −0.995273
\(207\) 22.1439 1.53910
\(208\) −1.56616 −0.108594
\(209\) −34.6633 −2.39771
\(210\) 4.80389 0.331500
\(211\) 12.4250 0.855375 0.427688 0.903927i \(-0.359328\pi\)
0.427688 + 0.903927i \(0.359328\pi\)
\(212\) 0.630655 0.0433136
\(213\) −11.3233 −0.775859
\(214\) 10.1314 0.692566
\(215\) −7.48751 −0.510644
\(216\) 0.613729 0.0417589
\(217\) 0.0362664 0.00246192
\(218\) −13.6923 −0.927360
\(219\) −1.47147 −0.0994328
\(220\) −17.8672 −1.20461
\(221\) 2.67721 0.180088
\(222\) 23.5575 1.58108
\(223\) −13.1348 −0.879569 −0.439784 0.898103i \(-0.644945\pi\)
−0.439784 + 0.898103i \(0.644945\pi\)
\(224\) 0.508744 0.0339919
\(225\) 30.1070 2.00713
\(226\) 8.47807 0.563953
\(227\) −8.32519 −0.552562 −0.276281 0.961077i \(-0.589102\pi\)
−0.276281 + 0.961077i \(0.589102\pi\)
\(228\) 18.3193 1.21322
\(229\) −10.2884 −0.679875 −0.339937 0.940448i \(-0.610406\pi\)
−0.339937 + 0.940448i \(0.610406\pi\)
\(230\) 25.7792 1.69983
\(231\) 6.01220 0.395574
\(232\) −6.46138 −0.424210
\(233\) 29.6620 1.94322 0.971611 0.236582i \(-0.0760273\pi\)
0.971611 + 0.236582i \(0.0760273\pi\)
\(234\) 5.08310 0.332293
\(235\) −20.2579 −1.32148
\(236\) −3.96183 −0.257893
\(237\) 40.3479 2.62088
\(238\) −0.869650 −0.0563710
\(239\) −27.9429 −1.80748 −0.903738 0.428086i \(-0.859188\pi\)
−0.903738 + 0.428086i \(0.859188\pi\)
\(240\) 9.44266 0.609521
\(241\) 8.10538 0.522113 0.261057 0.965323i \(-0.415929\pi\)
0.261057 + 0.965323i \(0.415929\pi\)
\(242\) −11.3613 −0.730330
\(243\) 22.3413 1.43320
\(244\) 10.9418 0.700477
\(245\) 25.4709 1.62727
\(246\) −12.8627 −0.820095
\(247\) 11.4804 0.730483
\(248\) 0.0712862 0.00452668
\(249\) −16.6349 −1.05419
\(250\) 16.1576 1.02190
\(251\) 22.2154 1.40223 0.701113 0.713050i \(-0.252687\pi\)
0.701113 + 0.713050i \(0.252687\pi\)
\(252\) −1.65117 −0.104014
\(253\) 32.2633 2.02838
\(254\) 14.9791 0.939873
\(255\) −16.1413 −1.01081
\(256\) 1.00000 0.0625000
\(257\) −11.3368 −0.707168 −0.353584 0.935403i \(-0.615037\pi\)
−0.353584 + 0.935403i \(0.615037\pi\)
\(258\) 4.95240 0.308323
\(259\) −4.79560 −0.297984
\(260\) 5.91758 0.366993
\(261\) 20.9709 1.29807
\(262\) 10.5654 0.652735
\(263\) −14.7510 −0.909589 −0.454794 0.890596i \(-0.650287\pi\)
−0.454794 + 0.890596i \(0.650287\pi\)
\(264\) 11.8177 0.727332
\(265\) −2.38287 −0.146378
\(266\) −3.72925 −0.228655
\(267\) 1.66763 0.102057
\(268\) −0.192213 −0.0117412
\(269\) 20.7231 1.26351 0.631753 0.775169i \(-0.282336\pi\)
0.631753 + 0.775169i \(0.282336\pi\)
\(270\) −2.31891 −0.141124
\(271\) −28.7047 −1.74369 −0.871844 0.489784i \(-0.837076\pi\)
−0.871844 + 0.489784i \(0.837076\pi\)
\(272\) −1.70941 −0.103648
\(273\) −1.99123 −0.120515
\(274\) 11.8114 0.713554
\(275\) 43.8655 2.64519
\(276\) −17.0509 −1.02634
\(277\) −18.6874 −1.12282 −0.561409 0.827539i \(-0.689740\pi\)
−0.561409 + 0.827539i \(0.689740\pi\)
\(278\) 2.76617 0.165904
\(279\) −0.231365 −0.0138515
\(280\) −1.92224 −0.114876
\(281\) −21.3536 −1.27385 −0.636924 0.770926i \(-0.719794\pi\)
−0.636924 + 0.770926i \(0.719794\pi\)
\(282\) 13.3990 0.797899
\(283\) 22.4804 1.33632 0.668160 0.744018i \(-0.267082\pi\)
0.668160 + 0.744018i \(0.267082\pi\)
\(284\) 4.53092 0.268861
\(285\) −69.2175 −4.10009
\(286\) 7.40602 0.437927
\(287\) 2.61845 0.154562
\(288\) −3.24558 −0.191248
\(289\) −14.0779 −0.828113
\(290\) 24.4137 1.43362
\(291\) −5.24965 −0.307740
\(292\) 0.588797 0.0344567
\(293\) 14.4598 0.844752 0.422376 0.906421i \(-0.361196\pi\)
0.422376 + 0.906421i \(0.361196\pi\)
\(294\) −16.8470 −0.982536
\(295\) 14.9694 0.871552
\(296\) −9.42635 −0.547896
\(297\) −2.90218 −0.168402
\(298\) −0.0224216 −0.00129885
\(299\) −10.6856 −0.617962
\(300\) −23.1826 −1.33845
\(301\) −1.00816 −0.0581093
\(302\) −15.8603 −0.912660
\(303\) −5.17882 −0.297516
\(304\) −7.33030 −0.420422
\(305\) −41.3425 −2.36726
\(306\) 5.54801 0.317159
\(307\) −8.08162 −0.461242 −0.230621 0.973044i \(-0.574076\pi\)
−0.230621 + 0.973044i \(0.574076\pi\)
\(308\) −2.40573 −0.137079
\(309\) −35.6995 −2.03087
\(310\) −0.269348 −0.0152979
\(311\) −21.1984 −1.20205 −0.601027 0.799229i \(-0.705242\pi\)
−0.601027 + 0.799229i \(0.705242\pi\)
\(312\) −3.91402 −0.221588
\(313\) 16.5817 0.937252 0.468626 0.883397i \(-0.344749\pi\)
0.468626 + 0.883397i \(0.344749\pi\)
\(314\) −5.68936 −0.321069
\(315\) 6.23877 0.351515
\(316\) −16.1449 −0.908221
\(317\) 20.8454 1.17079 0.585397 0.810747i \(-0.300939\pi\)
0.585397 + 0.810747i \(0.300939\pi\)
\(318\) 1.57608 0.0883822
\(319\) 30.5544 1.71072
\(320\) −3.77840 −0.211219
\(321\) 25.3195 1.41320
\(322\) 3.47105 0.193434
\(323\) 12.5305 0.697214
\(324\) −8.20296 −0.455720
\(325\) −14.5282 −0.805879
\(326\) −4.12095 −0.228238
\(327\) −34.2186 −1.89229
\(328\) 5.14690 0.284190
\(329\) −2.72763 −0.150379
\(330\) −44.6522 −2.45802
\(331\) −3.40899 −0.187375 −0.0936875 0.995602i \(-0.529865\pi\)
−0.0936875 + 0.995602i \(0.529865\pi\)
\(332\) 6.65631 0.365312
\(333\) 30.5940 1.67654
\(334\) −2.34577 −0.128355
\(335\) 0.726256 0.0396796
\(336\) 1.27141 0.0693611
\(337\) 13.2438 0.721434 0.360717 0.932675i \(-0.382532\pi\)
0.360717 + 0.932675i \(0.382532\pi\)
\(338\) 10.5471 0.573689
\(339\) 21.1877 1.15076
\(340\) 6.45882 0.350279
\(341\) −0.337096 −0.0182548
\(342\) 23.7911 1.28647
\(343\) 6.99074 0.377465
\(344\) −1.98166 −0.106844
\(345\) 64.4252 3.46853
\(346\) 16.9073 0.908940
\(347\) 16.4422 0.882664 0.441332 0.897344i \(-0.354506\pi\)
0.441332 + 0.897344i \(0.354506\pi\)
\(348\) −16.1477 −0.865610
\(349\) 4.96654 0.265853 0.132926 0.991126i \(-0.457563\pi\)
0.132926 + 0.991126i \(0.457563\pi\)
\(350\) 4.71926 0.252255
\(351\) 0.961198 0.0513049
\(352\) −4.72877 −0.252044
\(353\) −12.8929 −0.686217 −0.343109 0.939296i \(-0.611480\pi\)
−0.343109 + 0.939296i \(0.611480\pi\)
\(354\) −9.90108 −0.526236
\(355\) −17.1196 −0.908616
\(356\) −0.667289 −0.0353662
\(357\) −2.17336 −0.115026
\(358\) 25.4604 1.34562
\(359\) −0.764622 −0.0403552 −0.0201776 0.999796i \(-0.506423\pi\)
−0.0201776 + 0.999796i \(0.506423\pi\)
\(360\) 12.2631 0.646322
\(361\) 34.7333 1.82807
\(362\) 1.99371 0.104787
\(363\) −28.3931 −1.49025
\(364\) 0.796775 0.0417623
\(365\) −2.22471 −0.116447
\(366\) 27.3448 1.42934
\(367\) −20.4308 −1.06648 −0.533239 0.845964i \(-0.679025\pi\)
−0.533239 + 0.845964i \(0.679025\pi\)
\(368\) 6.82278 0.355662
\(369\) −16.7047 −0.869610
\(370\) 35.6165 1.85162
\(371\) −0.320842 −0.0166573
\(372\) 0.178152 0.00923677
\(373\) 12.5231 0.648422 0.324211 0.945985i \(-0.394901\pi\)
0.324211 + 0.945985i \(0.394901\pi\)
\(374\) 8.08339 0.417982
\(375\) 40.3797 2.08520
\(376\) −5.36150 −0.276498
\(377\) −10.1196 −0.521184
\(378\) −0.312231 −0.0160594
\(379\) 32.1780 1.65287 0.826436 0.563031i \(-0.190365\pi\)
0.826436 + 0.563031i \(0.190365\pi\)
\(380\) 27.6968 1.42082
\(381\) 37.4345 1.91783
\(382\) 14.4859 0.741162
\(383\) 37.0698 1.89418 0.947089 0.320971i \(-0.104009\pi\)
0.947089 + 0.320971i \(0.104009\pi\)
\(384\) 2.49912 0.127532
\(385\) 9.08982 0.463260
\(386\) −21.0958 −1.07375
\(387\) 6.43164 0.326938
\(388\) 2.10060 0.106642
\(389\) −10.0922 −0.511697 −0.255849 0.966717i \(-0.582355\pi\)
−0.255849 + 0.966717i \(0.582355\pi\)
\(390\) 14.7887 0.748856
\(391\) −11.6629 −0.589818
\(392\) 6.74118 0.340481
\(393\) 26.4042 1.33192
\(394\) 24.1967 1.21901
\(395\) 61.0018 3.06933
\(396\) 15.3476 0.771246
\(397\) 19.5206 0.979713 0.489856 0.871803i \(-0.337049\pi\)
0.489856 + 0.871803i \(0.337049\pi\)
\(398\) −16.5051 −0.827326
\(399\) −9.31982 −0.466575
\(400\) 9.27631 0.463815
\(401\) 23.5426 1.17566 0.587829 0.808985i \(-0.299983\pi\)
0.587829 + 0.808985i \(0.299983\pi\)
\(402\) −0.480361 −0.0239582
\(403\) 0.111646 0.00556147
\(404\) 2.07226 0.103099
\(405\) 30.9940 1.54011
\(406\) 3.28719 0.163140
\(407\) 44.5751 2.20950
\(408\) −4.27200 −0.211496
\(409\) −36.4807 −1.80385 −0.901927 0.431889i \(-0.857847\pi\)
−0.901927 + 0.431889i \(0.857847\pi\)
\(410\) −19.4470 −0.960421
\(411\) 29.5181 1.45602
\(412\) 14.2849 0.703764
\(413\) 2.01556 0.0991792
\(414\) −22.1439 −1.08831
\(415\) −25.1502 −1.23457
\(416\) 1.56616 0.0767874
\(417\) 6.91299 0.338531
\(418\) 34.6633 1.69544
\(419\) 5.85624 0.286096 0.143048 0.989716i \(-0.454310\pi\)
0.143048 + 0.989716i \(0.454310\pi\)
\(420\) −4.80389 −0.234406
\(421\) 14.3591 0.699819 0.349909 0.936784i \(-0.386212\pi\)
0.349909 + 0.936784i \(0.386212\pi\)
\(422\) −12.4250 −0.604842
\(423\) 17.4012 0.846074
\(424\) −0.630655 −0.0306273
\(425\) −15.8570 −0.769177
\(426\) 11.3233 0.548615
\(427\) −5.56657 −0.269385
\(428\) −10.1314 −0.489718
\(429\) 18.5085 0.893598
\(430\) 7.48751 0.361080
\(431\) −10.4899 −0.505280 −0.252640 0.967560i \(-0.581299\pi\)
−0.252640 + 0.967560i \(0.581299\pi\)
\(432\) −0.613729 −0.0295280
\(433\) −36.7641 −1.76677 −0.883384 0.468650i \(-0.844741\pi\)
−0.883384 + 0.468650i \(0.844741\pi\)
\(434\) −0.0362664 −0.00174084
\(435\) 61.0126 2.92533
\(436\) 13.6923 0.655742
\(437\) −50.0130 −2.39245
\(438\) 1.47147 0.0703096
\(439\) 38.0471 1.81589 0.907943 0.419093i \(-0.137652\pi\)
0.907943 + 0.419093i \(0.137652\pi\)
\(440\) 17.8672 0.851785
\(441\) −21.8790 −1.04186
\(442\) −2.67721 −0.127342
\(443\) 38.1362 1.81190 0.905952 0.423381i \(-0.139157\pi\)
0.905952 + 0.423381i \(0.139157\pi\)
\(444\) −23.5575 −1.11799
\(445\) 2.52128 0.119520
\(446\) 13.1348 0.621949
\(447\) −0.0560342 −0.00265033
\(448\) −0.508744 −0.0240359
\(449\) 9.26607 0.437293 0.218646 0.975804i \(-0.429836\pi\)
0.218646 + 0.975804i \(0.429836\pi\)
\(450\) −30.1070 −1.41926
\(451\) −24.3385 −1.14605
\(452\) −8.47807 −0.398775
\(453\) −39.6368 −1.86230
\(454\) 8.32519 0.390720
\(455\) −3.01053 −0.141136
\(456\) −18.3193 −0.857879
\(457\) 40.9023 1.91333 0.956665 0.291189i \(-0.0940509\pi\)
0.956665 + 0.291189i \(0.0940509\pi\)
\(458\) 10.2884 0.480744
\(459\) 1.04911 0.0489683
\(460\) −25.7792 −1.20196
\(461\) 4.97150 0.231546 0.115773 0.993276i \(-0.463065\pi\)
0.115773 + 0.993276i \(0.463065\pi\)
\(462\) −6.01220 −0.279713
\(463\) 26.8750 1.24899 0.624494 0.781030i \(-0.285305\pi\)
0.624494 + 0.781030i \(0.285305\pi\)
\(464\) 6.46138 0.299962
\(465\) −0.673131 −0.0312157
\(466\) −29.6620 −1.37407
\(467\) 3.24381 0.150105 0.0750527 0.997180i \(-0.476087\pi\)
0.0750527 + 0.997180i \(0.476087\pi\)
\(468\) −5.08310 −0.234966
\(469\) 0.0977869 0.00451538
\(470\) 20.2579 0.934427
\(471\) −14.2184 −0.655148
\(472\) 3.96183 0.182358
\(473\) 9.37082 0.430871
\(474\) −40.3479 −1.85324
\(475\) −67.9981 −3.11997
\(476\) 0.869650 0.0398604
\(477\) 2.04684 0.0937184
\(478\) 27.9429 1.27808
\(479\) 28.9709 1.32371 0.661856 0.749631i \(-0.269769\pi\)
0.661856 + 0.749631i \(0.269769\pi\)
\(480\) −9.44266 −0.430996
\(481\) −14.7632 −0.673143
\(482\) −8.10538 −0.369190
\(483\) 8.67455 0.394705
\(484\) 11.3613 0.516421
\(485\) −7.93692 −0.360397
\(486\) −22.3413 −1.01342
\(487\) −5.33853 −0.241912 −0.120956 0.992658i \(-0.538596\pi\)
−0.120956 + 0.992658i \(0.538596\pi\)
\(488\) −10.9418 −0.495312
\(489\) −10.2987 −0.465724
\(490\) −25.4709 −1.15066
\(491\) 26.8776 1.21297 0.606484 0.795096i \(-0.292580\pi\)
0.606484 + 0.795096i \(0.292580\pi\)
\(492\) 12.8627 0.579895
\(493\) −11.0451 −0.497448
\(494\) −11.4804 −0.516529
\(495\) −57.9893 −2.60643
\(496\) −0.0712862 −0.00320084
\(497\) −2.30508 −0.103397
\(498\) 16.6349 0.745427
\(499\) 25.8270 1.15618 0.578088 0.815975i \(-0.303799\pi\)
0.578088 + 0.815975i \(0.303799\pi\)
\(500\) −16.1576 −0.722590
\(501\) −5.86236 −0.261911
\(502\) −22.2154 −0.991524
\(503\) 27.8491 1.24173 0.620866 0.783917i \(-0.286781\pi\)
0.620866 + 0.783917i \(0.286781\pi\)
\(504\) 1.65117 0.0735489
\(505\) −7.82983 −0.348423
\(506\) −32.2633 −1.43428
\(507\) 26.3585 1.17062
\(508\) −14.9791 −0.664590
\(509\) 7.29862 0.323505 0.161753 0.986831i \(-0.448285\pi\)
0.161753 + 0.986831i \(0.448285\pi\)
\(510\) 16.1413 0.714751
\(511\) −0.299547 −0.0132512
\(512\) −1.00000 −0.0441942
\(513\) 4.49882 0.198628
\(514\) 11.3368 0.500043
\(515\) −53.9739 −2.37837
\(516\) −4.95240 −0.218017
\(517\) 25.3533 1.11504
\(518\) 4.79560 0.210707
\(519\) 42.2532 1.85471
\(520\) −5.91758 −0.259503
\(521\) −29.9555 −1.31237 −0.656187 0.754598i \(-0.727832\pi\)
−0.656187 + 0.754598i \(0.727832\pi\)
\(522\) −20.9709 −0.917872
\(523\) 29.8986 1.30737 0.653686 0.756766i \(-0.273222\pi\)
0.653686 + 0.756766i \(0.273222\pi\)
\(524\) −10.5654 −0.461553
\(525\) 11.7940 0.514732
\(526\) 14.7510 0.643176
\(527\) 0.121857 0.00530818
\(528\) −11.8177 −0.514301
\(529\) 23.5503 1.02393
\(530\) 2.38287 0.103505
\(531\) −12.8584 −0.558009
\(532\) 3.72925 0.161683
\(533\) 8.06087 0.349155
\(534\) −1.66763 −0.0721655
\(535\) 38.2804 1.65501
\(536\) 0.192213 0.00830232
\(537\) 63.6284 2.74577
\(538\) −20.7231 −0.893434
\(539\) −31.8775 −1.37306
\(540\) 2.31891 0.0997901
\(541\) −11.9125 −0.512158 −0.256079 0.966656i \(-0.582431\pi\)
−0.256079 + 0.966656i \(0.582431\pi\)
\(542\) 28.7047 1.23297
\(543\) 4.98251 0.213820
\(544\) 1.70941 0.0732902
\(545\) −51.7350 −2.21608
\(546\) 1.99123 0.0852169
\(547\) −20.9557 −0.896001 −0.448001 0.894033i \(-0.647864\pi\)
−0.448001 + 0.894033i \(0.647864\pi\)
\(548\) −11.8114 −0.504559
\(549\) 35.5125 1.51563
\(550\) −43.8655 −1.87043
\(551\) −47.3639 −2.01777
\(552\) 17.0509 0.725735
\(553\) 8.21361 0.349278
\(554\) 18.6874 0.793952
\(555\) 89.0098 3.77826
\(556\) −2.76617 −0.117312
\(557\) −40.3513 −1.70974 −0.854869 0.518843i \(-0.826363\pi\)
−0.854869 + 0.518843i \(0.826363\pi\)
\(558\) 0.231365 0.00979446
\(559\) −3.10360 −0.131268
\(560\) 1.92224 0.0812294
\(561\) 20.2013 0.852901
\(562\) 21.3536 0.900747
\(563\) −30.5264 −1.28653 −0.643266 0.765643i \(-0.722421\pi\)
−0.643266 + 0.765643i \(0.722421\pi\)
\(564\) −13.3990 −0.564200
\(565\) 32.0335 1.34766
\(566\) −22.4804 −0.944920
\(567\) 4.17320 0.175258
\(568\) −4.53092 −0.190113
\(569\) −5.77079 −0.241924 −0.120962 0.992657i \(-0.538598\pi\)
−0.120962 + 0.992657i \(0.538598\pi\)
\(570\) 69.2175 2.89920
\(571\) 1.36888 0.0572859 0.0286429 0.999590i \(-0.490881\pi\)
0.0286429 + 0.999590i \(0.490881\pi\)
\(572\) −7.40602 −0.309661
\(573\) 36.2019 1.51235
\(574\) −2.61845 −0.109292
\(575\) 63.2902 2.63938
\(576\) 3.24558 0.135232
\(577\) 8.91467 0.371123 0.185561 0.982633i \(-0.440590\pi\)
0.185561 + 0.982633i \(0.440590\pi\)
\(578\) 14.0779 0.585565
\(579\) −52.7208 −2.19100
\(580\) −24.4137 −1.01372
\(581\) −3.38636 −0.140490
\(582\) 5.24965 0.217605
\(583\) 2.98222 0.123511
\(584\) −0.588797 −0.0243646
\(585\) 19.2060 0.794069
\(586\) −14.4598 −0.597330
\(587\) −40.2858 −1.66277 −0.831386 0.555695i \(-0.812452\pi\)
−0.831386 + 0.555695i \(0.812452\pi\)
\(588\) 16.8470 0.694758
\(589\) 0.522549 0.0215313
\(590\) −14.9694 −0.616280
\(591\) 60.4702 2.48741
\(592\) 9.42635 0.387421
\(593\) −11.7372 −0.481990 −0.240995 0.970526i \(-0.577474\pi\)
−0.240995 + 0.970526i \(0.577474\pi\)
\(594\) 2.90218 0.119078
\(595\) −3.28589 −0.134708
\(596\) 0.0224216 0.000918426 0
\(597\) −41.2482 −1.68817
\(598\) 10.6856 0.436965
\(599\) −24.5752 −1.00411 −0.502057 0.864835i \(-0.667423\pi\)
−0.502057 + 0.864835i \(0.667423\pi\)
\(600\) 23.1826 0.946424
\(601\) −1.53950 −0.0627973 −0.0313987 0.999507i \(-0.509996\pi\)
−0.0313987 + 0.999507i \(0.509996\pi\)
\(602\) 1.00816 0.0410894
\(603\) −0.623841 −0.0254048
\(604\) 15.8603 0.645348
\(605\) −42.9274 −1.74525
\(606\) 5.17882 0.210375
\(607\) 16.9070 0.686232 0.343116 0.939293i \(-0.388518\pi\)
0.343116 + 0.939293i \(0.388518\pi\)
\(608\) 7.33030 0.297283
\(609\) 8.21506 0.332891
\(610\) 41.3425 1.67391
\(611\) −8.39697 −0.339705
\(612\) −5.54801 −0.224265
\(613\) 29.9590 1.21003 0.605017 0.796212i \(-0.293166\pi\)
0.605017 + 0.796212i \(0.293166\pi\)
\(614\) 8.08162 0.326148
\(615\) −48.6004 −1.95976
\(616\) 2.40573 0.0969297
\(617\) −23.8586 −0.960510 −0.480255 0.877129i \(-0.659456\pi\)
−0.480255 + 0.877129i \(0.659456\pi\)
\(618\) 35.6995 1.43604
\(619\) −22.9469 −0.922316 −0.461158 0.887318i \(-0.652566\pi\)
−0.461158 + 0.887318i \(0.652566\pi\)
\(620\) 0.269348 0.0108173
\(621\) −4.18733 −0.168032
\(622\) 21.1984 0.849980
\(623\) 0.339479 0.0136009
\(624\) 3.91402 0.156686
\(625\) 14.6683 0.586733
\(626\) −16.5817 −0.662737
\(627\) 86.6276 3.45957
\(628\) 5.68936 0.227030
\(629\) −16.1135 −0.642486
\(630\) −6.23877 −0.248559
\(631\) −30.4685 −1.21293 −0.606467 0.795109i \(-0.707414\pi\)
−0.606467 + 0.795109i \(0.707414\pi\)
\(632\) 16.1449 0.642209
\(633\) −31.0516 −1.23419
\(634\) −20.8454 −0.827876
\(635\) 56.5971 2.24599
\(636\) −1.57608 −0.0624956
\(637\) 10.5578 0.418314
\(638\) −30.5544 −1.20966
\(639\) 14.7055 0.581739
\(640\) 3.77840 0.149354
\(641\) −26.6974 −1.05448 −0.527241 0.849716i \(-0.676774\pi\)
−0.527241 + 0.849716i \(0.676774\pi\)
\(642\) −25.3195 −0.999280
\(643\) 22.7392 0.896748 0.448374 0.893846i \(-0.352003\pi\)
0.448374 + 0.893846i \(0.352003\pi\)
\(644\) −3.47105 −0.136778
\(645\) 18.7121 0.736790
\(646\) −12.5305 −0.493005
\(647\) 7.31694 0.287659 0.143829 0.989603i \(-0.454058\pi\)
0.143829 + 0.989603i \(0.454058\pi\)
\(648\) 8.20296 0.322243
\(649\) −18.7346 −0.735397
\(650\) 14.5282 0.569842
\(651\) −0.0906339 −0.00355222
\(652\) 4.12095 0.161389
\(653\) −17.8937 −0.700236 −0.350118 0.936706i \(-0.613858\pi\)
−0.350118 + 0.936706i \(0.613858\pi\)
\(654\) 34.2186 1.33805
\(655\) 39.9204 1.55982
\(656\) −5.14690 −0.200953
\(657\) 1.91099 0.0745546
\(658\) 2.72763 0.106334
\(659\) 23.3582 0.909905 0.454952 0.890516i \(-0.349656\pi\)
0.454952 + 0.890516i \(0.349656\pi\)
\(660\) 44.6522 1.73808
\(661\) 22.6576 0.881280 0.440640 0.897684i \(-0.354752\pi\)
0.440640 + 0.897684i \(0.354752\pi\)
\(662\) 3.40899 0.132494
\(663\) −6.69065 −0.259843
\(664\) −6.65631 −0.258315
\(665\) −14.0906 −0.546409
\(666\) −30.5940 −1.18549
\(667\) 44.0846 1.70696
\(668\) 2.34577 0.0907607
\(669\) 32.8253 1.26910
\(670\) −0.726256 −0.0280577
\(671\) 51.7412 1.99745
\(672\) −1.27141 −0.0490457
\(673\) −7.86813 −0.303294 −0.151647 0.988435i \(-0.548458\pi\)
−0.151647 + 0.988435i \(0.548458\pi\)
\(674\) −13.2438 −0.510131
\(675\) −5.69313 −0.219129
\(676\) −10.5471 −0.405659
\(677\) 36.0153 1.38418 0.692090 0.721811i \(-0.256690\pi\)
0.692090 + 0.721811i \(0.256690\pi\)
\(678\) −21.1877 −0.813708
\(679\) −1.06867 −0.0410118
\(680\) −6.45882 −0.247685
\(681\) 20.8056 0.797273
\(682\) 0.337096 0.0129081
\(683\) −26.3791 −1.00937 −0.504685 0.863304i \(-0.668391\pi\)
−0.504685 + 0.863304i \(0.668391\pi\)
\(684\) −23.7911 −0.909674
\(685\) 44.6283 1.70516
\(686\) −6.99074 −0.266908
\(687\) 25.7118 0.980968
\(688\) 1.98166 0.0755501
\(689\) −0.987707 −0.0376287
\(690\) −64.4252 −2.45262
\(691\) −1.26320 −0.0480543 −0.0240271 0.999711i \(-0.507649\pi\)
−0.0240271 + 0.999711i \(0.507649\pi\)
\(692\) −16.9073 −0.642718
\(693\) −7.80799 −0.296601
\(694\) −16.4422 −0.624138
\(695\) 10.4517 0.396456
\(696\) 16.1477 0.612078
\(697\) 8.79814 0.333253
\(698\) −4.96654 −0.187986
\(699\) −74.1288 −2.80381
\(700\) −4.71926 −0.178371
\(701\) −21.1907 −0.800362 −0.400181 0.916436i \(-0.631053\pi\)
−0.400181 + 0.916436i \(0.631053\pi\)
\(702\) −0.961198 −0.0362781
\(703\) −69.0980 −2.60608
\(704\) 4.72877 0.178222
\(705\) 50.6268 1.90672
\(706\) 12.8929 0.485229
\(707\) −1.05425 −0.0396492
\(708\) 9.90108 0.372105
\(709\) −35.9556 −1.35034 −0.675171 0.737661i \(-0.735930\pi\)
−0.675171 + 0.737661i \(0.735930\pi\)
\(710\) 17.1196 0.642488
\(711\) −52.3995 −1.96513
\(712\) 0.667289 0.0250077
\(713\) −0.486370 −0.0182147
\(714\) 2.17336 0.0813358
\(715\) 27.9829 1.04650
\(716\) −25.4604 −0.951498
\(717\) 69.8325 2.60794
\(718\) 0.764622 0.0285354
\(719\) −24.7782 −0.924070 −0.462035 0.886862i \(-0.652881\pi\)
−0.462035 + 0.886862i \(0.652881\pi\)
\(720\) −12.2631 −0.457018
\(721\) −7.26733 −0.270650
\(722\) −34.7333 −1.29264
\(723\) −20.2563 −0.753339
\(724\) −1.99371 −0.0740957
\(725\) 59.9378 2.22603
\(726\) 28.3931 1.05377
\(727\) 10.8869 0.403775 0.201887 0.979409i \(-0.435293\pi\)
0.201887 + 0.979409i \(0.435293\pi\)
\(728\) −0.796775 −0.0295304
\(729\) −31.2247 −1.15647
\(730\) 2.22471 0.0823402
\(731\) −3.38746 −0.125290
\(732\) −27.3448 −1.01069
\(733\) 32.3175 1.19368 0.596838 0.802362i \(-0.296424\pi\)
0.596838 + 0.802362i \(0.296424\pi\)
\(734\) 20.4308 0.754114
\(735\) −63.6547 −2.34794
\(736\) −6.82278 −0.251491
\(737\) −0.908929 −0.0334808
\(738\) 16.7047 0.614907
\(739\) −20.6425 −0.759346 −0.379673 0.925121i \(-0.623963\pi\)
−0.379673 + 0.925121i \(0.623963\pi\)
\(740\) −35.6165 −1.30929
\(741\) −28.6909 −1.05399
\(742\) 0.320842 0.0117785
\(743\) 32.4736 1.19134 0.595670 0.803230i \(-0.296887\pi\)
0.595670 + 0.803230i \(0.296887\pi\)
\(744\) −0.178152 −0.00653138
\(745\) −0.0847179 −0.00310382
\(746\) −12.5231 −0.458503
\(747\) 21.6036 0.790434
\(748\) −8.08339 −0.295558
\(749\) 5.15427 0.188333
\(750\) −40.3797 −1.47446
\(751\) 1.17709 0.0429525 0.0214763 0.999769i \(-0.493163\pi\)
0.0214763 + 0.999769i \(0.493163\pi\)
\(752\) 5.36150 0.195514
\(753\) −55.5189 −2.02322
\(754\) 10.1196 0.368533
\(755\) −59.9267 −2.18096
\(756\) 0.312231 0.0113557
\(757\) −6.43499 −0.233884 −0.116942 0.993139i \(-0.537309\pi\)
−0.116942 + 0.993139i \(0.537309\pi\)
\(758\) −32.1780 −1.16876
\(759\) −80.6298 −2.92668
\(760\) −27.6968 −1.00467
\(761\) 21.5453 0.781015 0.390508 0.920600i \(-0.372300\pi\)
0.390508 + 0.920600i \(0.372300\pi\)
\(762\) −37.4345 −1.35611
\(763\) −6.96587 −0.252182
\(764\) −14.4859 −0.524081
\(765\) 20.9626 0.757905
\(766\) −37.0698 −1.33939
\(767\) 6.20487 0.224045
\(768\) −2.49912 −0.0901791
\(769\) −23.3646 −0.842550 −0.421275 0.906933i \(-0.638417\pi\)
−0.421275 + 0.906933i \(0.638417\pi\)
\(770\) −9.08982 −0.327574
\(771\) 28.3319 1.02035
\(772\) 21.0958 0.759254
\(773\) 12.0401 0.433052 0.216526 0.976277i \(-0.430527\pi\)
0.216526 + 0.976277i \(0.430527\pi\)
\(774\) −6.43164 −0.231180
\(775\) −0.661272 −0.0237536
\(776\) −2.10060 −0.0754073
\(777\) 11.9848 0.429951
\(778\) 10.0922 0.361825
\(779\) 37.7283 1.35176
\(780\) −14.7887 −0.529521
\(781\) 21.4257 0.766671
\(782\) 11.6629 0.417065
\(783\) −3.96553 −0.141717
\(784\) −6.74118 −0.240756
\(785\) −21.4967 −0.767250
\(786\) −26.4042 −0.941808
\(787\) 23.8812 0.851272 0.425636 0.904894i \(-0.360050\pi\)
0.425636 + 0.904894i \(0.360050\pi\)
\(788\) −24.1967 −0.861970
\(789\) 36.8646 1.31241
\(790\) −61.0018 −2.17035
\(791\) 4.31317 0.153359
\(792\) −15.3476 −0.545353
\(793\) −17.1366 −0.608539
\(794\) −19.5206 −0.692761
\(795\) 5.95506 0.211204
\(796\) 16.5051 0.585008
\(797\) 22.4521 0.795295 0.397648 0.917538i \(-0.369827\pi\)
0.397648 + 0.917538i \(0.369827\pi\)
\(798\) 9.31982 0.329918
\(799\) −9.16498 −0.324234
\(800\) −9.27631 −0.327967
\(801\) −2.16574 −0.0765226
\(802\) −23.5426 −0.831316
\(803\) 2.78428 0.0982552
\(804\) 0.480361 0.0169410
\(805\) 13.1150 0.462243
\(806\) −0.111646 −0.00393255
\(807\) −51.7893 −1.82307
\(808\) −2.07226 −0.0729019
\(809\) −19.8751 −0.698772 −0.349386 0.936979i \(-0.613610\pi\)
−0.349386 + 0.936979i \(0.613610\pi\)
\(810\) −30.9940 −1.08902
\(811\) 6.78435 0.238231 0.119115 0.992880i \(-0.461994\pi\)
0.119115 + 0.992880i \(0.461994\pi\)
\(812\) −3.28719 −0.115358
\(813\) 71.7364 2.51591
\(814\) −44.5751 −1.56235
\(815\) −15.5706 −0.545414
\(816\) 4.27200 0.149550
\(817\) −14.5262 −0.508207
\(818\) 36.4807 1.27552
\(819\) 2.58600 0.0903620
\(820\) 19.4470 0.679120
\(821\) −31.2628 −1.09108 −0.545540 0.838085i \(-0.683675\pi\)
−0.545540 + 0.838085i \(0.683675\pi\)
\(822\) −29.5181 −1.02956
\(823\) 42.3528 1.47632 0.738162 0.674623i \(-0.235694\pi\)
0.738162 + 0.674623i \(0.235694\pi\)
\(824\) −14.2849 −0.497636
\(825\) −109.625 −3.81665
\(826\) −2.01556 −0.0701303
\(827\) 35.5451 1.23602 0.618011 0.786169i \(-0.287939\pi\)
0.618011 + 0.786169i \(0.287939\pi\)
\(828\) 22.1439 0.769552
\(829\) 4.59014 0.159422 0.0797111 0.996818i \(-0.474600\pi\)
0.0797111 + 0.996818i \(0.474600\pi\)
\(830\) 25.1502 0.872976
\(831\) 46.7020 1.62007
\(832\) −1.56616 −0.0542969
\(833\) 11.5234 0.399263
\(834\) −6.91299 −0.239377
\(835\) −8.86327 −0.306726
\(836\) −34.6633 −1.19886
\(837\) 0.0437504 0.00151223
\(838\) −5.85624 −0.202300
\(839\) −1.67928 −0.0579753 −0.0289877 0.999580i \(-0.509228\pi\)
−0.0289877 + 0.999580i \(0.509228\pi\)
\(840\) 4.80389 0.165750
\(841\) 12.7495 0.439636
\(842\) −14.3591 −0.494847
\(843\) 53.3651 1.83799
\(844\) 12.4250 0.427688
\(845\) 39.8513 1.37093
\(846\) −17.4012 −0.598265
\(847\) −5.77997 −0.198602
\(848\) 0.630655 0.0216568
\(849\) −56.1810 −1.92813
\(850\) 15.8570 0.543890
\(851\) 64.3139 2.20465
\(852\) −11.3233 −0.387930
\(853\) −20.2165 −0.692201 −0.346101 0.938197i \(-0.612494\pi\)
−0.346101 + 0.938197i \(0.612494\pi\)
\(854\) 5.56657 0.190484
\(855\) 89.8922 3.07425
\(856\) 10.1314 0.346283
\(857\) −7.18968 −0.245595 −0.122797 0.992432i \(-0.539187\pi\)
−0.122797 + 0.992432i \(0.539187\pi\)
\(858\) −18.5085 −0.631869
\(859\) −31.0062 −1.05792 −0.528959 0.848647i \(-0.677417\pi\)
−0.528959 + 0.848647i \(0.677417\pi\)
\(860\) −7.48751 −0.255322
\(861\) −6.54381 −0.223013
\(862\) 10.4899 0.357287
\(863\) 19.8583 0.675986 0.337993 0.941149i \(-0.390252\pi\)
0.337993 + 0.941149i \(0.390252\pi\)
\(864\) 0.613729 0.0208795
\(865\) 63.8824 2.17207
\(866\) 36.7641 1.24929
\(867\) 35.1824 1.19486
\(868\) 0.0362664 0.00123096
\(869\) −76.3454 −2.58984
\(870\) −61.0126 −2.06852
\(871\) 0.301036 0.0102002
\(872\) −13.6923 −0.463680
\(873\) 6.81767 0.230743
\(874\) 50.0130 1.69172
\(875\) 8.22008 0.277889
\(876\) −1.47147 −0.0497164
\(877\) 23.8428 0.805114 0.402557 0.915395i \(-0.368122\pi\)
0.402557 + 0.915395i \(0.368122\pi\)
\(878\) −38.0471 −1.28403
\(879\) −36.1368 −1.21886
\(880\) −17.8672 −0.602303
\(881\) −21.4631 −0.723110 −0.361555 0.932351i \(-0.617754\pi\)
−0.361555 + 0.932351i \(0.617754\pi\)
\(882\) 21.8790 0.736705
\(883\) −9.49777 −0.319626 −0.159813 0.987147i \(-0.551089\pi\)
−0.159813 + 0.987147i \(0.551089\pi\)
\(884\) 2.67721 0.0900442
\(885\) −37.4102 −1.25753
\(886\) −38.1362 −1.28121
\(887\) 16.9315 0.568504 0.284252 0.958750i \(-0.408255\pi\)
0.284252 + 0.958750i \(0.408255\pi\)
\(888\) 23.5575 0.790539
\(889\) 7.62053 0.255584
\(890\) −2.52128 −0.0845136
\(891\) −38.7899 −1.29951
\(892\) −13.1348 −0.439784
\(893\) −39.3014 −1.31517
\(894\) 0.0560342 0.00187407
\(895\) 96.1994 3.21559
\(896\) 0.508744 0.0169959
\(897\) 26.7045 0.891636
\(898\) −9.26607 −0.309213
\(899\) −0.460607 −0.0153621
\(900\) 30.1070 1.00357
\(901\) −1.07805 −0.0359149
\(902\) 24.3385 0.810383
\(903\) 2.51950 0.0838438
\(904\) 8.47807 0.281976
\(905\) 7.53304 0.250407
\(906\) 39.6368 1.31685
\(907\) 45.8683 1.52303 0.761516 0.648146i \(-0.224456\pi\)
0.761516 + 0.648146i \(0.224456\pi\)
\(908\) −8.32519 −0.276281
\(909\) 6.72569 0.223077
\(910\) 3.01053 0.0997982
\(911\) 49.6128 1.64375 0.821873 0.569671i \(-0.192929\pi\)
0.821873 + 0.569671i \(0.192929\pi\)
\(912\) 18.3193 0.606612
\(913\) 31.4762 1.04171
\(914\) −40.9023 −1.35293
\(915\) 103.320 3.41564
\(916\) −10.2884 −0.339937
\(917\) 5.37510 0.177501
\(918\) −1.04911 −0.0346258
\(919\) 44.4103 1.46496 0.732481 0.680787i \(-0.238362\pi\)
0.732481 + 0.680787i \(0.238362\pi\)
\(920\) 25.7792 0.849914
\(921\) 20.1969 0.665510
\(922\) −4.97150 −0.163728
\(923\) −7.09615 −0.233573
\(924\) 6.01220 0.197787
\(925\) 87.4417 2.87507
\(926\) −26.8750 −0.883167
\(927\) 46.3626 1.52275
\(928\) −6.46138 −0.212105
\(929\) 11.7818 0.386549 0.193274 0.981145i \(-0.438089\pi\)
0.193274 + 0.981145i \(0.438089\pi\)
\(930\) 0.673131 0.0220728
\(931\) 49.4149 1.61951
\(932\) 29.6620 0.971611
\(933\) 52.9774 1.73440
\(934\) −3.24381 −0.106141
\(935\) 30.5423 0.998840
\(936\) 5.08310 0.166146
\(937\) 1.07946 0.0352644 0.0176322 0.999845i \(-0.494387\pi\)
0.0176322 + 0.999845i \(0.494387\pi\)
\(938\) −0.0977869 −0.00319286
\(939\) −41.4395 −1.35233
\(940\) −20.2579 −0.660740
\(941\) 42.9535 1.40024 0.700121 0.714024i \(-0.253129\pi\)
0.700121 + 0.714024i \(0.253129\pi\)
\(942\) 14.2184 0.463260
\(943\) −35.1161 −1.14354
\(944\) −3.96183 −0.128947
\(945\) −1.17973 −0.0383767
\(946\) −9.37082 −0.304672
\(947\) 9.97975 0.324298 0.162149 0.986766i \(-0.448157\pi\)
0.162149 + 0.986766i \(0.448157\pi\)
\(948\) 40.3479 1.31044
\(949\) −0.922150 −0.0299343
\(950\) 67.9981 2.20615
\(951\) −52.0950 −1.68930
\(952\) −0.869650 −0.0281855
\(953\) −17.2418 −0.558516 −0.279258 0.960216i \(-0.590089\pi\)
−0.279258 + 0.960216i \(0.590089\pi\)
\(954\) −2.04684 −0.0662689
\(955\) 54.7334 1.77113
\(956\) −27.9429 −0.903738
\(957\) −76.3589 −2.46833
\(958\) −28.9709 −0.936006
\(959\) 6.00899 0.194040
\(960\) 9.44266 0.304760
\(961\) −30.9949 −0.999836
\(962\) 14.7632 0.475984
\(963\) −32.8822 −1.05961
\(964\) 8.10538 0.261057
\(965\) −79.7083 −2.56590
\(966\) −8.67455 −0.279099
\(967\) −2.59124 −0.0833286 −0.0416643 0.999132i \(-0.513266\pi\)
−0.0416643 + 0.999132i \(0.513266\pi\)
\(968\) −11.3613 −0.365165
\(969\) −31.3151 −1.00599
\(970\) 7.93692 0.254839
\(971\) −56.9588 −1.82790 −0.913948 0.405832i \(-0.866982\pi\)
−0.913948 + 0.405832i \(0.866982\pi\)
\(972\) 22.3413 0.716598
\(973\) 1.40727 0.0451151
\(974\) 5.33853 0.171058
\(975\) 36.3076 1.16277
\(976\) 10.9418 0.350238
\(977\) 14.5138 0.464338 0.232169 0.972676i \(-0.425418\pi\)
0.232169 + 0.972676i \(0.425418\pi\)
\(978\) 10.2987 0.329317
\(979\) −3.15546 −0.100849
\(980\) 25.4709 0.813637
\(981\) 44.4394 1.41884
\(982\) −26.8776 −0.857697
\(983\) −28.6998 −0.915381 −0.457691 0.889112i \(-0.651323\pi\)
−0.457691 + 0.889112i \(0.651323\pi\)
\(984\) −12.8627 −0.410048
\(985\) 91.4246 2.91303
\(986\) 11.0451 0.351749
\(987\) 6.81666 0.216977
\(988\) 11.4804 0.365241
\(989\) 13.5204 0.429925
\(990\) 57.9893 1.84302
\(991\) −32.0748 −1.01889 −0.509444 0.860504i \(-0.670149\pi\)
−0.509444 + 0.860504i \(0.670149\pi\)
\(992\) 0.0712862 0.00226334
\(993\) 8.51946 0.270357
\(994\) 2.30508 0.0731126
\(995\) −62.3629 −1.97704
\(996\) −16.6349 −0.527097
\(997\) 17.8809 0.566295 0.283147 0.959076i \(-0.408621\pi\)
0.283147 + 0.959076i \(0.408621\pi\)
\(998\) −25.8270 −0.817539
\(999\) −5.78522 −0.183036
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 \(a_p\))