Properties

Label 8007.2.a.f.1.5
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 1
Dimension 48
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(48\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.39228 q^{2} -1.00000 q^{3} +3.72299 q^{4} +0.325110 q^{5} +2.39228 q^{6} -0.363079 q^{7} -4.12187 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.39228 q^{2} -1.00000 q^{3} +3.72299 q^{4} +0.325110 q^{5} +2.39228 q^{6} -0.363079 q^{7} -4.12187 q^{8} +1.00000 q^{9} -0.777753 q^{10} -0.861044 q^{11} -3.72299 q^{12} -0.164103 q^{13} +0.868585 q^{14} -0.325110 q^{15} +2.41467 q^{16} -1.00000 q^{17} -2.39228 q^{18} -8.07048 q^{19} +1.21038 q^{20} +0.363079 q^{21} +2.05986 q^{22} +3.99691 q^{23} +4.12187 q^{24} -4.89430 q^{25} +0.392579 q^{26} -1.00000 q^{27} -1.35174 q^{28} -3.43052 q^{29} +0.777753 q^{30} +5.64736 q^{31} +2.46717 q^{32} +0.861044 q^{33} +2.39228 q^{34} -0.118041 q^{35} +3.72299 q^{36} +5.74569 q^{37} +19.3068 q^{38} +0.164103 q^{39} -1.34006 q^{40} -3.17263 q^{41} -0.868585 q^{42} +8.78267 q^{43} -3.20566 q^{44} +0.325110 q^{45} -9.56171 q^{46} +4.83327 q^{47} -2.41467 q^{48} -6.86817 q^{49} +11.7085 q^{50} +1.00000 q^{51} -0.610953 q^{52} -4.72827 q^{53} +2.39228 q^{54} -0.279934 q^{55} +1.49656 q^{56} +8.07048 q^{57} +8.20675 q^{58} +5.82740 q^{59} -1.21038 q^{60} +11.6859 q^{61} -13.5100 q^{62} -0.363079 q^{63} -10.7315 q^{64} -0.0533514 q^{65} -2.05986 q^{66} -12.1330 q^{67} -3.72299 q^{68} -3.99691 q^{69} +0.282386 q^{70} +12.9376 q^{71} -4.12187 q^{72} +14.9024 q^{73} -13.7453 q^{74} +4.89430 q^{75} -30.0463 q^{76} +0.312627 q^{77} -0.392579 q^{78} +5.13168 q^{79} +0.785034 q^{80} +1.00000 q^{81} +7.58980 q^{82} -16.2792 q^{83} +1.35174 q^{84} -0.325110 q^{85} -21.0106 q^{86} +3.43052 q^{87} +3.54911 q^{88} +17.9831 q^{89} -0.777753 q^{90} +0.0595822 q^{91} +14.8804 q^{92} -5.64736 q^{93} -11.5625 q^{94} -2.62379 q^{95} -2.46717 q^{96} -11.0881 q^{97} +16.4306 q^{98} -0.861044 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.39228 −1.69160 −0.845798 0.533504i \(-0.820875\pi\)
−0.845798 + 0.533504i \(0.820875\pi\)
\(3\) −1.00000 −0.577350
\(4\) 3.72299 1.86149
\(5\) 0.325110 0.145394 0.0726968 0.997354i \(-0.476839\pi\)
0.0726968 + 0.997354i \(0.476839\pi\)
\(6\) 2.39228 0.976643
\(7\) −0.363079 −0.137231 −0.0686155 0.997643i \(-0.521858\pi\)
−0.0686155 + 0.997643i \(0.521858\pi\)
\(8\) −4.12187 −1.45730
\(9\) 1.00000 0.333333
\(10\) −0.777753 −0.245947
\(11\) −0.861044 −0.259614 −0.129807 0.991539i \(-0.541436\pi\)
−0.129807 + 0.991539i \(0.541436\pi\)
\(12\) −3.72299 −1.07473
\(13\) −0.164103 −0.0455139 −0.0227570 0.999741i \(-0.507244\pi\)
−0.0227570 + 0.999741i \(0.507244\pi\)
\(14\) 0.868585 0.232139
\(15\) −0.325110 −0.0839430
\(16\) 2.41467 0.603668
\(17\) −1.00000 −0.242536
\(18\) −2.39228 −0.563865
\(19\) −8.07048 −1.85149 −0.925747 0.378143i \(-0.876563\pi\)
−0.925747 + 0.378143i \(0.876563\pi\)
\(20\) 1.21038 0.270649
\(21\) 0.363079 0.0792303
\(22\) 2.05986 0.439163
\(23\) 3.99691 0.833413 0.416706 0.909041i \(-0.363184\pi\)
0.416706 + 0.909041i \(0.363184\pi\)
\(24\) 4.12187 0.841373
\(25\) −4.89430 −0.978861
\(26\) 0.392579 0.0769911
\(27\) −1.00000 −0.192450
\(28\) −1.35174 −0.255455
\(29\) −3.43052 −0.637031 −0.318516 0.947918i \(-0.603184\pi\)
−0.318516 + 0.947918i \(0.603184\pi\)
\(30\) 0.777753 0.141998
\(31\) 5.64736 1.01430 0.507148 0.861859i \(-0.330700\pi\)
0.507148 + 0.861859i \(0.330700\pi\)
\(32\) 2.46717 0.436138
\(33\) 0.861044 0.149888
\(34\) 2.39228 0.410272
\(35\) −0.118041 −0.0199525
\(36\) 3.72299 0.620498
\(37\) 5.74569 0.944585 0.472293 0.881442i \(-0.343427\pi\)
0.472293 + 0.881442i \(0.343427\pi\)
\(38\) 19.3068 3.13198
\(39\) 0.164103 0.0262775
\(40\) −1.34006 −0.211882
\(41\) −3.17263 −0.495481 −0.247741 0.968826i \(-0.579688\pi\)
−0.247741 + 0.968826i \(0.579688\pi\)
\(42\) −0.868585 −0.134026
\(43\) 8.78267 1.33934 0.669672 0.742657i \(-0.266435\pi\)
0.669672 + 0.742657i \(0.266435\pi\)
\(44\) −3.20566 −0.483271
\(45\) 0.325110 0.0484645
\(46\) −9.56171 −1.40980
\(47\) 4.83327 0.705005 0.352503 0.935811i \(-0.385331\pi\)
0.352503 + 0.935811i \(0.385331\pi\)
\(48\) −2.41467 −0.348528
\(49\) −6.86817 −0.981168
\(50\) 11.7085 1.65584
\(51\) 1.00000 0.140028
\(52\) −0.610953 −0.0847239
\(53\) −4.72827 −0.649478 −0.324739 0.945804i \(-0.605276\pi\)
−0.324739 + 0.945804i \(0.605276\pi\)
\(54\) 2.39228 0.325548
\(55\) −0.279934 −0.0377463
\(56\) 1.49656 0.199987
\(57\) 8.07048 1.06896
\(58\) 8.20675 1.07760
\(59\) 5.82740 0.758663 0.379331 0.925261i \(-0.376154\pi\)
0.379331 + 0.925261i \(0.376154\pi\)
\(60\) −1.21038 −0.156260
\(61\) 11.6859 1.49622 0.748112 0.663573i \(-0.230961\pi\)
0.748112 + 0.663573i \(0.230961\pi\)
\(62\) −13.5100 −1.71578
\(63\) −0.363079 −0.0457436
\(64\) −10.7315 −1.34144
\(65\) −0.0533514 −0.00661743
\(66\) −2.05986 −0.253551
\(67\) −12.1330 −1.48229 −0.741143 0.671347i \(-0.765716\pi\)
−0.741143 + 0.671347i \(0.765716\pi\)
\(68\) −3.72299 −0.451479
\(69\) −3.99691 −0.481171
\(70\) 0.282386 0.0337516
\(71\) 12.9376 1.53541 0.767703 0.640806i \(-0.221400\pi\)
0.767703 + 0.640806i \(0.221400\pi\)
\(72\) −4.12187 −0.485767
\(73\) 14.9024 1.74419 0.872094 0.489338i \(-0.162762\pi\)
0.872094 + 0.489338i \(0.162762\pi\)
\(74\) −13.7453 −1.59786
\(75\) 4.89430 0.565145
\(76\) −30.0463 −3.44655
\(77\) 0.312627 0.0356271
\(78\) −0.392579 −0.0444509
\(79\) 5.13168 0.577359 0.288679 0.957426i \(-0.406784\pi\)
0.288679 + 0.957426i \(0.406784\pi\)
\(80\) 0.785034 0.0877695
\(81\) 1.00000 0.111111
\(82\) 7.58980 0.838154
\(83\) −16.2792 −1.78688 −0.893439 0.449185i \(-0.851714\pi\)
−0.893439 + 0.449185i \(0.851714\pi\)
\(84\) 1.35174 0.147487
\(85\) −0.325110 −0.0352631
\(86\) −21.0106 −2.26563
\(87\) 3.43052 0.367790
\(88\) 3.54911 0.378336
\(89\) 17.9831 1.90621 0.953105 0.302640i \(-0.0978681\pi\)
0.953105 + 0.302640i \(0.0978681\pi\)
\(90\) −0.777753 −0.0819824
\(91\) 0.0595822 0.00624592
\(92\) 14.8804 1.55139
\(93\) −5.64736 −0.585604
\(94\) −11.5625 −1.19258
\(95\) −2.62379 −0.269195
\(96\) −2.46717 −0.251805
\(97\) −11.0881 −1.12583 −0.562914 0.826516i \(-0.690320\pi\)
−0.562914 + 0.826516i \(0.690320\pi\)
\(98\) 16.4306 1.65974
\(99\) −0.861044 −0.0865382
\(100\) −18.2214 −1.82214
\(101\) 5.04213 0.501711 0.250856 0.968025i \(-0.419288\pi\)
0.250856 + 0.968025i \(0.419288\pi\)
\(102\) −2.39228 −0.236871
\(103\) −13.3677 −1.31716 −0.658578 0.752513i \(-0.728842\pi\)
−0.658578 + 0.752513i \(0.728842\pi\)
\(104\) 0.676410 0.0663275
\(105\) 0.118041 0.0115196
\(106\) 11.3113 1.09865
\(107\) 11.7694 1.13780 0.568898 0.822408i \(-0.307370\pi\)
0.568898 + 0.822408i \(0.307370\pi\)
\(108\) −3.72299 −0.358245
\(109\) −8.52725 −0.816763 −0.408381 0.912811i \(-0.633907\pi\)
−0.408381 + 0.912811i \(0.633907\pi\)
\(110\) 0.669680 0.0638514
\(111\) −5.74569 −0.545356
\(112\) −0.876717 −0.0828419
\(113\) 10.9586 1.03090 0.515450 0.856919i \(-0.327625\pi\)
0.515450 + 0.856919i \(0.327625\pi\)
\(114\) −19.3068 −1.80825
\(115\) 1.29943 0.121173
\(116\) −12.7718 −1.18583
\(117\) −0.164103 −0.0151713
\(118\) −13.9408 −1.28335
\(119\) 0.363079 0.0332834
\(120\) 1.34006 0.122330
\(121\) −10.2586 −0.932600
\(122\) −27.9559 −2.53100
\(123\) 3.17263 0.286066
\(124\) 21.0250 1.88810
\(125\) −3.21674 −0.287714
\(126\) 0.868585 0.0773797
\(127\) −17.2632 −1.53186 −0.765929 0.642926i \(-0.777720\pi\)
−0.765929 + 0.642926i \(0.777720\pi\)
\(128\) 20.7384 1.83303
\(129\) −8.78267 −0.773271
\(130\) 0.127631 0.0111940
\(131\) 2.60700 0.227775 0.113887 0.993494i \(-0.463670\pi\)
0.113887 + 0.993494i \(0.463670\pi\)
\(132\) 3.20566 0.279017
\(133\) 2.93022 0.254082
\(134\) 29.0256 2.50743
\(135\) −0.325110 −0.0279810
\(136\) 4.12187 0.353447
\(137\) −7.69283 −0.657243 −0.328621 0.944462i \(-0.606584\pi\)
−0.328621 + 0.944462i \(0.606584\pi\)
\(138\) 9.56171 0.813947
\(139\) −2.53629 −0.215125 −0.107562 0.994198i \(-0.534305\pi\)
−0.107562 + 0.994198i \(0.534305\pi\)
\(140\) −0.439464 −0.0371415
\(141\) −4.83327 −0.407035
\(142\) −30.9502 −2.59729
\(143\) 0.141300 0.0118161
\(144\) 2.41467 0.201223
\(145\) −1.11530 −0.0926203
\(146\) −35.6506 −2.95046
\(147\) 6.86817 0.566477
\(148\) 21.3911 1.75834
\(149\) 5.69535 0.466582 0.233291 0.972407i \(-0.425051\pi\)
0.233291 + 0.972407i \(0.425051\pi\)
\(150\) −11.7085 −0.955997
\(151\) 1.51584 0.123358 0.0616788 0.998096i \(-0.480355\pi\)
0.0616788 + 0.998096i \(0.480355\pi\)
\(152\) 33.2654 2.69818
\(153\) −1.00000 −0.0808452
\(154\) −0.747890 −0.0602667
\(155\) 1.83601 0.147472
\(156\) 0.610953 0.0489154
\(157\) −1.00000 −0.0798087
\(158\) −12.2764 −0.976657
\(159\) 4.72827 0.374976
\(160\) 0.802102 0.0634117
\(161\) −1.45119 −0.114370
\(162\) −2.39228 −0.187955
\(163\) −3.71552 −0.291022 −0.145511 0.989357i \(-0.546483\pi\)
−0.145511 + 0.989357i \(0.546483\pi\)
\(164\) −11.8117 −0.922336
\(165\) 0.279934 0.0217928
\(166\) 38.9444 3.02267
\(167\) 0.109122 0.00844409 0.00422204 0.999991i \(-0.498656\pi\)
0.00422204 + 0.999991i \(0.498656\pi\)
\(168\) −1.49656 −0.115462
\(169\) −12.9731 −0.997928
\(170\) 0.777753 0.0596509
\(171\) −8.07048 −0.617165
\(172\) 32.6978 2.49318
\(173\) 9.41645 0.715919 0.357960 0.933737i \(-0.383473\pi\)
0.357960 + 0.933737i \(0.383473\pi\)
\(174\) −8.20675 −0.622152
\(175\) 1.77702 0.134330
\(176\) −2.07914 −0.156721
\(177\) −5.82740 −0.438014
\(178\) −43.0207 −3.22454
\(179\) 19.5434 1.46074 0.730371 0.683050i \(-0.239347\pi\)
0.730371 + 0.683050i \(0.239347\pi\)
\(180\) 1.21038 0.0902165
\(181\) −0.0568237 −0.00422367 −0.00211184 0.999998i \(-0.500672\pi\)
−0.00211184 + 0.999998i \(0.500672\pi\)
\(182\) −0.142537 −0.0105656
\(183\) −11.6859 −0.863845
\(184\) −16.4747 −1.21453
\(185\) 1.86798 0.137337
\(186\) 13.5100 0.990604
\(187\) 0.861044 0.0629658
\(188\) 17.9942 1.31236
\(189\) 0.363079 0.0264101
\(190\) 6.27684 0.455370
\(191\) −19.3049 −1.39686 −0.698428 0.715680i \(-0.746117\pi\)
−0.698428 + 0.715680i \(0.746117\pi\)
\(192\) 10.7315 0.774479
\(193\) 3.06885 0.220901 0.110450 0.993882i \(-0.464771\pi\)
0.110450 + 0.993882i \(0.464771\pi\)
\(194\) 26.5258 1.90444
\(195\) 0.0533514 0.00382058
\(196\) −25.5701 −1.82644
\(197\) 13.5643 0.966413 0.483207 0.875506i \(-0.339472\pi\)
0.483207 + 0.875506i \(0.339472\pi\)
\(198\) 2.05986 0.146388
\(199\) 16.1080 1.14187 0.570933 0.820997i \(-0.306582\pi\)
0.570933 + 0.820997i \(0.306582\pi\)
\(200\) 20.1737 1.42649
\(201\) 12.1330 0.855799
\(202\) −12.0622 −0.848692
\(203\) 1.24555 0.0874204
\(204\) 3.72299 0.260661
\(205\) −1.03145 −0.0720398
\(206\) 31.9792 2.22809
\(207\) 3.99691 0.277804
\(208\) −0.396255 −0.0274753
\(209\) 6.94903 0.480675
\(210\) −0.282386 −0.0194865
\(211\) −7.51372 −0.517266 −0.258633 0.965976i \(-0.583272\pi\)
−0.258633 + 0.965976i \(0.583272\pi\)
\(212\) −17.6033 −1.20900
\(213\) −12.9376 −0.886467
\(214\) −28.1558 −1.92469
\(215\) 2.85533 0.194732
\(216\) 4.12187 0.280458
\(217\) −2.05044 −0.139193
\(218\) 20.3996 1.38163
\(219\) −14.9024 −1.00701
\(220\) −1.04219 −0.0702645
\(221\) 0.164103 0.0110387
\(222\) 13.7453 0.922522
\(223\) −28.4921 −1.90797 −0.953985 0.299854i \(-0.903062\pi\)
−0.953985 + 0.299854i \(0.903062\pi\)
\(224\) −0.895778 −0.0598517
\(225\) −4.89430 −0.326287
\(226\) −26.2161 −1.74387
\(227\) 0.333603 0.0221420 0.0110710 0.999939i \(-0.496476\pi\)
0.0110710 + 0.999939i \(0.496476\pi\)
\(228\) 30.0463 1.98986
\(229\) −1.04440 −0.0690159 −0.0345080 0.999404i \(-0.510986\pi\)
−0.0345080 + 0.999404i \(0.510986\pi\)
\(230\) −3.10861 −0.204975
\(231\) −0.312627 −0.0205693
\(232\) 14.1401 0.928346
\(233\) 13.1069 0.858663 0.429331 0.903147i \(-0.358749\pi\)
0.429331 + 0.903147i \(0.358749\pi\)
\(234\) 0.392579 0.0256637
\(235\) 1.57135 0.102503
\(236\) 21.6953 1.41225
\(237\) −5.13168 −0.333338
\(238\) −0.868585 −0.0563020
\(239\) −1.16543 −0.0753857 −0.0376928 0.999289i \(-0.512001\pi\)
−0.0376928 + 0.999289i \(0.512001\pi\)
\(240\) −0.785034 −0.0506738
\(241\) −14.3270 −0.922881 −0.461441 0.887171i \(-0.652667\pi\)
−0.461441 + 0.887171i \(0.652667\pi\)
\(242\) 24.5414 1.57758
\(243\) −1.00000 −0.0641500
\(244\) 43.5064 2.78521
\(245\) −2.23291 −0.142656
\(246\) −7.58980 −0.483908
\(247\) 1.32439 0.0842687
\(248\) −23.2777 −1.47813
\(249\) 16.2792 1.03165
\(250\) 7.69533 0.486695
\(251\) −4.08839 −0.258057 −0.129028 0.991641i \(-0.541186\pi\)
−0.129028 + 0.991641i \(0.541186\pi\)
\(252\) −1.35174 −0.0851515
\(253\) −3.44151 −0.216366
\(254\) 41.2982 2.59128
\(255\) 0.325110 0.0203592
\(256\) −28.1490 −1.75931
\(257\) −26.0711 −1.62627 −0.813135 0.582075i \(-0.802241\pi\)
−0.813135 + 0.582075i \(0.802241\pi\)
\(258\) 21.0106 1.30806
\(259\) −2.08614 −0.129626
\(260\) −0.198627 −0.0123183
\(261\) −3.43052 −0.212344
\(262\) −6.23667 −0.385303
\(263\) −6.78628 −0.418460 −0.209230 0.977866i \(-0.567096\pi\)
−0.209230 + 0.977866i \(0.567096\pi\)
\(264\) −3.54911 −0.218433
\(265\) −1.53721 −0.0944300
\(266\) −7.00990 −0.429804
\(267\) −17.9831 −1.10055
\(268\) −45.1712 −2.75927
\(269\) 0.198615 0.0121098 0.00605489 0.999982i \(-0.498073\pi\)
0.00605489 + 0.999982i \(0.498073\pi\)
\(270\) 0.777753 0.0473326
\(271\) −22.4067 −1.36111 −0.680556 0.732697i \(-0.738261\pi\)
−0.680556 + 0.732697i \(0.738261\pi\)
\(272\) −2.41467 −0.146411
\(273\) −0.0595822 −0.00360608
\(274\) 18.4034 1.11179
\(275\) 4.21421 0.254126
\(276\) −14.8804 −0.895697
\(277\) −14.8527 −0.892414 −0.446207 0.894930i \(-0.647226\pi\)
−0.446207 + 0.894930i \(0.647226\pi\)
\(278\) 6.06750 0.363904
\(279\) 5.64736 0.338098
\(280\) 0.486548 0.0290768
\(281\) −1.14199 −0.0681253 −0.0340626 0.999420i \(-0.510845\pi\)
−0.0340626 + 0.999420i \(0.510845\pi\)
\(282\) 11.5625 0.688539
\(283\) 11.8706 0.705633 0.352817 0.935692i \(-0.385224\pi\)
0.352817 + 0.935692i \(0.385224\pi\)
\(284\) 48.1664 2.85815
\(285\) 2.62379 0.155420
\(286\) −0.338028 −0.0199880
\(287\) 1.15191 0.0679953
\(288\) 2.46717 0.145379
\(289\) 1.00000 0.0588235
\(290\) 2.66810 0.156676
\(291\) 11.0881 0.649997
\(292\) 55.4813 3.24680
\(293\) −3.33015 −0.194550 −0.0972748 0.995258i \(-0.531013\pi\)
−0.0972748 + 0.995258i \(0.531013\pi\)
\(294\) −16.4306 −0.958251
\(295\) 1.89455 0.110305
\(296\) −23.6830 −1.37654
\(297\) 0.861044 0.0499628
\(298\) −13.6249 −0.789267
\(299\) −0.655903 −0.0379319
\(300\) 18.2214 1.05202
\(301\) −3.18880 −0.183799
\(302\) −3.62632 −0.208671
\(303\) −5.04213 −0.289663
\(304\) −19.4876 −1.11769
\(305\) 3.79920 0.217541
\(306\) 2.39228 0.136757
\(307\) 11.4073 0.651049 0.325524 0.945534i \(-0.394459\pi\)
0.325524 + 0.945534i \(0.394459\pi\)
\(308\) 1.16391 0.0663197
\(309\) 13.3677 0.760460
\(310\) −4.39225 −0.249463
\(311\) 16.2862 0.923504 0.461752 0.887009i \(-0.347221\pi\)
0.461752 + 0.887009i \(0.347221\pi\)
\(312\) −0.676410 −0.0382942
\(313\) −5.08060 −0.287172 −0.143586 0.989638i \(-0.545863\pi\)
−0.143586 + 0.989638i \(0.545863\pi\)
\(314\) 2.39228 0.135004
\(315\) −0.118041 −0.00665083
\(316\) 19.1052 1.07475
\(317\) −28.8502 −1.62039 −0.810195 0.586161i \(-0.800639\pi\)
−0.810195 + 0.586161i \(0.800639\pi\)
\(318\) −11.3113 −0.634308
\(319\) 2.95383 0.165383
\(320\) −3.48892 −0.195036
\(321\) −11.7694 −0.656907
\(322\) 3.47165 0.193468
\(323\) 8.07048 0.449053
\(324\) 3.72299 0.206833
\(325\) 0.803169 0.0445518
\(326\) 8.88856 0.492292
\(327\) 8.52725 0.471558
\(328\) 13.0772 0.722065
\(329\) −1.75486 −0.0967485
\(330\) −0.669680 −0.0368646
\(331\) 12.0989 0.665014 0.332507 0.943101i \(-0.392106\pi\)
0.332507 + 0.943101i \(0.392106\pi\)
\(332\) −60.6074 −3.32626
\(333\) 5.74569 0.314862
\(334\) −0.261049 −0.0142840
\(335\) −3.94457 −0.215515
\(336\) 0.876717 0.0478288
\(337\) −17.5789 −0.957581 −0.478791 0.877929i \(-0.658925\pi\)
−0.478791 + 0.877929i \(0.658925\pi\)
\(338\) 31.0352 1.68809
\(339\) −10.9586 −0.595191
\(340\) −1.21038 −0.0656421
\(341\) −4.86262 −0.263326
\(342\) 19.3068 1.04399
\(343\) 5.03524 0.271877
\(344\) −36.2010 −1.95183
\(345\) −1.29943 −0.0699592
\(346\) −22.5268 −1.21105
\(347\) 11.8556 0.636441 0.318220 0.948017i \(-0.396915\pi\)
0.318220 + 0.948017i \(0.396915\pi\)
\(348\) 12.7718 0.684640
\(349\) 18.1376 0.970883 0.485442 0.874269i \(-0.338659\pi\)
0.485442 + 0.874269i \(0.338659\pi\)
\(350\) −4.25112 −0.227232
\(351\) 0.164103 0.00875916
\(352\) −2.12434 −0.113228
\(353\) 7.93436 0.422303 0.211152 0.977453i \(-0.432279\pi\)
0.211152 + 0.977453i \(0.432279\pi\)
\(354\) 13.9408 0.740943
\(355\) 4.20613 0.223238
\(356\) 66.9511 3.54840
\(357\) −0.363079 −0.0192162
\(358\) −46.7532 −2.47099
\(359\) −6.05604 −0.319626 −0.159813 0.987147i \(-0.551089\pi\)
−0.159813 + 0.987147i \(0.551089\pi\)
\(360\) −1.34006 −0.0706274
\(361\) 46.1326 2.42803
\(362\) 0.135938 0.00714474
\(363\) 10.2586 0.538437
\(364\) 0.221824 0.0116267
\(365\) 4.84490 0.253594
\(366\) 27.9559 1.46128
\(367\) −22.5163 −1.17534 −0.587671 0.809100i \(-0.699955\pi\)
−0.587671 + 0.809100i \(0.699955\pi\)
\(368\) 9.65122 0.503105
\(369\) −3.17263 −0.165160
\(370\) −4.46873 −0.232318
\(371\) 1.71674 0.0891285
\(372\) −21.0250 −1.09010
\(373\) 35.5761 1.84206 0.921031 0.389489i \(-0.127348\pi\)
0.921031 + 0.389489i \(0.127348\pi\)
\(374\) −2.05986 −0.106513
\(375\) 3.21674 0.166112
\(376\) −19.9221 −1.02740
\(377\) 0.562958 0.0289938
\(378\) −0.868585 −0.0446752
\(379\) 18.7211 0.961637 0.480818 0.876820i \(-0.340340\pi\)
0.480818 + 0.876820i \(0.340340\pi\)
\(380\) −9.76835 −0.501106
\(381\) 17.2632 0.884418
\(382\) 46.1828 2.36292
\(383\) 4.43044 0.226385 0.113192 0.993573i \(-0.463892\pi\)
0.113192 + 0.993573i \(0.463892\pi\)
\(384\) −20.7384 −1.05830
\(385\) 0.101638 0.00517996
\(386\) −7.34154 −0.373675
\(387\) 8.78267 0.446448
\(388\) −41.2809 −2.09572
\(389\) −11.1334 −0.564487 −0.282244 0.959343i \(-0.591079\pi\)
−0.282244 + 0.959343i \(0.591079\pi\)
\(390\) −0.127631 −0.00646287
\(391\) −3.99691 −0.202132
\(392\) 28.3097 1.42986
\(393\) −2.60700 −0.131506
\(394\) −32.4495 −1.63478
\(395\) 1.66836 0.0839443
\(396\) −3.20566 −0.161090
\(397\) −28.5223 −1.43149 −0.715746 0.698361i \(-0.753913\pi\)
−0.715746 + 0.698361i \(0.753913\pi\)
\(398\) −38.5348 −1.93157
\(399\) −2.93022 −0.146694
\(400\) −11.8181 −0.590907
\(401\) −36.6755 −1.83149 −0.915744 0.401762i \(-0.868398\pi\)
−0.915744 + 0.401762i \(0.868398\pi\)
\(402\) −29.0256 −1.44766
\(403\) −0.926747 −0.0461645
\(404\) 18.7718 0.933933
\(405\) 0.325110 0.0161548
\(406\) −2.97970 −0.147880
\(407\) −4.94729 −0.245228
\(408\) −4.12187 −0.204063
\(409\) 14.5550 0.719697 0.359849 0.933011i \(-0.382828\pi\)
0.359849 + 0.933011i \(0.382828\pi\)
\(410\) 2.46752 0.121862
\(411\) 7.69283 0.379459
\(412\) −49.7677 −2.45188
\(413\) −2.11581 −0.104112
\(414\) −9.56171 −0.469932
\(415\) −5.29254 −0.259801
\(416\) −0.404870 −0.0198504
\(417\) 2.53629 0.124202
\(418\) −16.6240 −0.813107
\(419\) 28.5433 1.39443 0.697215 0.716862i \(-0.254422\pi\)
0.697215 + 0.716862i \(0.254422\pi\)
\(420\) 0.439464 0.0214436
\(421\) 22.6795 1.10533 0.552666 0.833403i \(-0.313611\pi\)
0.552666 + 0.833403i \(0.313611\pi\)
\(422\) 17.9749 0.875005
\(423\) 4.83327 0.235002
\(424\) 19.4893 0.946485
\(425\) 4.89430 0.237409
\(426\) 30.9502 1.49954
\(427\) −4.24290 −0.205328
\(428\) 43.8175 2.11800
\(429\) −0.141300 −0.00682201
\(430\) −6.83075 −0.329408
\(431\) 12.5283 0.603466 0.301733 0.953392i \(-0.402435\pi\)
0.301733 + 0.953392i \(0.402435\pi\)
\(432\) −2.41467 −0.116176
\(433\) 4.52180 0.217304 0.108652 0.994080i \(-0.465347\pi\)
0.108652 + 0.994080i \(0.465347\pi\)
\(434\) 4.90521 0.235458
\(435\) 1.11530 0.0534744
\(436\) −31.7469 −1.52040
\(437\) −32.2569 −1.54306
\(438\) 35.6506 1.70345
\(439\) −12.6756 −0.604971 −0.302486 0.953154i \(-0.597816\pi\)
−0.302486 + 0.953154i \(0.597816\pi\)
\(440\) 1.15385 0.0550077
\(441\) −6.86817 −0.327056
\(442\) −0.392579 −0.0186731
\(443\) −22.1413 −1.05196 −0.525982 0.850496i \(-0.676302\pi\)
−0.525982 + 0.850496i \(0.676302\pi\)
\(444\) −21.3911 −1.01518
\(445\) 5.84650 0.277151
\(446\) 68.1609 3.22751
\(447\) −5.69535 −0.269381
\(448\) 3.89638 0.184087
\(449\) −1.54679 −0.0729974 −0.0364987 0.999334i \(-0.511620\pi\)
−0.0364987 + 0.999334i \(0.511620\pi\)
\(450\) 11.7085 0.551945
\(451\) 2.73177 0.128634
\(452\) 40.7989 1.91902
\(453\) −1.51584 −0.0712206
\(454\) −0.798070 −0.0374553
\(455\) 0.0193708 0.000908116 0
\(456\) −33.2654 −1.55780
\(457\) 29.5396 1.38180 0.690902 0.722948i \(-0.257214\pi\)
0.690902 + 0.722948i \(0.257214\pi\)
\(458\) 2.49850 0.116747
\(459\) 1.00000 0.0466760
\(460\) 4.83778 0.225563
\(461\) 0.703831 0.0327807 0.0163903 0.999866i \(-0.494783\pi\)
0.0163903 + 0.999866i \(0.494783\pi\)
\(462\) 0.747890 0.0347950
\(463\) −24.4734 −1.13738 −0.568688 0.822554i \(-0.692549\pi\)
−0.568688 + 0.822554i \(0.692549\pi\)
\(464\) −8.28358 −0.384556
\(465\) −1.83601 −0.0851430
\(466\) −31.3554 −1.45251
\(467\) −28.9602 −1.34012 −0.670059 0.742308i \(-0.733731\pi\)
−0.670059 + 0.742308i \(0.733731\pi\)
\(468\) −0.610953 −0.0282413
\(469\) 4.40525 0.203416
\(470\) −3.75909 −0.173394
\(471\) 1.00000 0.0460776
\(472\) −24.0198 −1.10560
\(473\) −7.56226 −0.347713
\(474\) 12.2764 0.563873
\(475\) 39.4994 1.81235
\(476\) 1.35174 0.0619569
\(477\) −4.72827 −0.216493
\(478\) 2.78804 0.127522
\(479\) 17.0037 0.776918 0.388459 0.921466i \(-0.373007\pi\)
0.388459 + 0.921466i \(0.373007\pi\)
\(480\) −0.802102 −0.0366108
\(481\) −0.942883 −0.0429918
\(482\) 34.2741 1.56114
\(483\) 1.45119 0.0660315
\(484\) −38.1927 −1.73603
\(485\) −3.60486 −0.163688
\(486\) 2.39228 0.108516
\(487\) −20.5710 −0.932159 −0.466080 0.884743i \(-0.654334\pi\)
−0.466080 + 0.884743i \(0.654334\pi\)
\(488\) −48.1677 −2.18045
\(489\) 3.71552 0.168022
\(490\) 5.34174 0.241315
\(491\) 31.8835 1.43888 0.719441 0.694553i \(-0.244398\pi\)
0.719441 + 0.694553i \(0.244398\pi\)
\(492\) 11.8117 0.532511
\(493\) 3.43052 0.154503
\(494\) −3.16830 −0.142549
\(495\) −0.279934 −0.0125821
\(496\) 13.6365 0.612298
\(497\) −4.69736 −0.210705
\(498\) −38.9444 −1.74514
\(499\) −23.8861 −1.06929 −0.534645 0.845077i \(-0.679555\pi\)
−0.534645 + 0.845077i \(0.679555\pi\)
\(500\) −11.9759 −0.535578
\(501\) −0.109122 −0.00487520
\(502\) 9.78056 0.436528
\(503\) 42.4906 1.89456 0.947282 0.320402i \(-0.103818\pi\)
0.947282 + 0.320402i \(0.103818\pi\)
\(504\) 1.49656 0.0666622
\(505\) 1.63925 0.0729456
\(506\) 8.23305 0.366004
\(507\) 12.9731 0.576154
\(508\) −64.2705 −2.85154
\(509\) 17.6220 0.781081 0.390541 0.920586i \(-0.372288\pi\)
0.390541 + 0.920586i \(0.372288\pi\)
\(510\) −0.777753 −0.0344395
\(511\) −5.41073 −0.239357
\(512\) 25.8633 1.14301
\(513\) 8.07048 0.356320
\(514\) 62.3693 2.75099
\(515\) −4.34596 −0.191506
\(516\) −32.6978 −1.43944
\(517\) −4.16166 −0.183030
\(518\) 4.99062 0.219275
\(519\) −9.41645 −0.413336
\(520\) 0.219908 0.00964359
\(521\) −16.9983 −0.744707 −0.372353 0.928091i \(-0.621449\pi\)
−0.372353 + 0.928091i \(0.621449\pi\)
\(522\) 8.20675 0.359200
\(523\) 11.7351 0.513142 0.256571 0.966525i \(-0.417407\pi\)
0.256571 + 0.966525i \(0.417407\pi\)
\(524\) 9.70584 0.424001
\(525\) −1.77702 −0.0775554
\(526\) 16.2347 0.707865
\(527\) −5.64736 −0.246003
\(528\) 2.07914 0.0904829
\(529\) −7.02474 −0.305423
\(530\) 3.67743 0.159737
\(531\) 5.82740 0.252888
\(532\) 10.9092 0.472973
\(533\) 0.520637 0.0225513
\(534\) 43.0207 1.86169
\(535\) 3.82637 0.165428
\(536\) 50.0108 2.16014
\(537\) −19.5434 −0.843360
\(538\) −0.475143 −0.0204848
\(539\) 5.91380 0.254725
\(540\) −1.21038 −0.0520865
\(541\) 10.2845 0.442166 0.221083 0.975255i \(-0.429041\pi\)
0.221083 + 0.975255i \(0.429041\pi\)
\(542\) 53.6031 2.30245
\(543\) 0.0568237 0.00243854
\(544\) −2.46717 −0.105779
\(545\) −2.77230 −0.118752
\(546\) 0.142537 0.00610003
\(547\) 16.9824 0.726116 0.363058 0.931767i \(-0.381733\pi\)
0.363058 + 0.931767i \(0.381733\pi\)
\(548\) −28.6403 −1.22345
\(549\) 11.6859 0.498741
\(550\) −10.0816 −0.429879
\(551\) 27.6859 1.17946
\(552\) 16.4747 0.701211
\(553\) −1.86320 −0.0792315
\(554\) 35.5318 1.50960
\(555\) −1.86798 −0.0792913
\(556\) −9.44256 −0.400454
\(557\) −12.2317 −0.518276 −0.259138 0.965840i \(-0.583438\pi\)
−0.259138 + 0.965840i \(0.583438\pi\)
\(558\) −13.5100 −0.571926
\(559\) −1.44126 −0.0609588
\(560\) −0.285029 −0.0120447
\(561\) −0.861044 −0.0363533
\(562\) 2.73195 0.115240
\(563\) 12.3117 0.518877 0.259439 0.965760i \(-0.416462\pi\)
0.259439 + 0.965760i \(0.416462\pi\)
\(564\) −17.9942 −0.757694
\(565\) 3.56276 0.149886
\(566\) −28.3977 −1.19365
\(567\) −0.363079 −0.0152479
\(568\) −53.3269 −2.23755
\(569\) −39.3746 −1.65067 −0.825335 0.564643i \(-0.809014\pi\)
−0.825335 + 0.564643i \(0.809014\pi\)
\(570\) −6.27684 −0.262908
\(571\) 40.7039 1.70341 0.851703 0.524024i \(-0.175570\pi\)
0.851703 + 0.524024i \(0.175570\pi\)
\(572\) 0.526057 0.0219956
\(573\) 19.3049 0.806475
\(574\) −2.75570 −0.115021
\(575\) −19.5621 −0.815795
\(576\) −10.7315 −0.447146
\(577\) −2.88372 −0.120051 −0.0600254 0.998197i \(-0.519118\pi\)
−0.0600254 + 0.998197i \(0.519118\pi\)
\(578\) −2.39228 −0.0995056
\(579\) −3.06885 −0.127537
\(580\) −4.15224 −0.172412
\(581\) 5.91064 0.245215
\(582\) −26.5258 −1.09953
\(583\) 4.07125 0.168614
\(584\) −61.4255 −2.54181
\(585\) −0.0533514 −0.00220581
\(586\) 7.96665 0.329099
\(587\) −8.26843 −0.341275 −0.170637 0.985334i \(-0.554583\pi\)
−0.170637 + 0.985334i \(0.554583\pi\)
\(588\) 25.5701 1.05449
\(589\) −45.5768 −1.87796
\(590\) −4.53228 −0.186591
\(591\) −13.5643 −0.557959
\(592\) 13.8740 0.570216
\(593\) −36.8666 −1.51393 −0.756964 0.653456i \(-0.773318\pi\)
−0.756964 + 0.653456i \(0.773318\pi\)
\(594\) −2.05986 −0.0845169
\(595\) 0.118041 0.00483919
\(596\) 21.2037 0.868539
\(597\) −16.1080 −0.659256
\(598\) 1.56910 0.0641654
\(599\) −34.5880 −1.41323 −0.706614 0.707599i \(-0.749778\pi\)
−0.706614 + 0.707599i \(0.749778\pi\)
\(600\) −20.1737 −0.823587
\(601\) −13.0419 −0.531990 −0.265995 0.963974i \(-0.585700\pi\)
−0.265995 + 0.963974i \(0.585700\pi\)
\(602\) 7.62850 0.310914
\(603\) −12.1330 −0.494096
\(604\) 5.64347 0.229630
\(605\) −3.33517 −0.135594
\(606\) 12.0622 0.489993
\(607\) −42.7696 −1.73597 −0.867983 0.496594i \(-0.834584\pi\)
−0.867983 + 0.496594i \(0.834584\pi\)
\(608\) −19.9112 −0.807507
\(609\) −1.24555 −0.0504722
\(610\) −9.08873 −0.367992
\(611\) −0.793154 −0.0320876
\(612\) −3.72299 −0.150493
\(613\) −24.8469 −1.00356 −0.501778 0.864996i \(-0.667321\pi\)
−0.501778 + 0.864996i \(0.667321\pi\)
\(614\) −27.2894 −1.10131
\(615\) 1.03145 0.0415922
\(616\) −1.28861 −0.0519194
\(617\) 16.6363 0.669754 0.334877 0.942262i \(-0.391305\pi\)
0.334877 + 0.942262i \(0.391305\pi\)
\(618\) −31.9792 −1.28639
\(619\) 16.9519 0.681355 0.340678 0.940180i \(-0.389344\pi\)
0.340678 + 0.940180i \(0.389344\pi\)
\(620\) 6.83545 0.274518
\(621\) −3.99691 −0.160390
\(622\) −38.9610 −1.56219
\(623\) −6.52930 −0.261591
\(624\) 0.396255 0.0158629
\(625\) 23.4257 0.937029
\(626\) 12.1542 0.485779
\(627\) −6.94903 −0.277518
\(628\) −3.72299 −0.148563
\(629\) −5.74569 −0.229096
\(630\) 0.282386 0.0112505
\(631\) 7.47510 0.297579 0.148789 0.988869i \(-0.452462\pi\)
0.148789 + 0.988869i \(0.452462\pi\)
\(632\) −21.1521 −0.841385
\(633\) 7.51372 0.298644
\(634\) 69.0177 2.74104
\(635\) −5.61242 −0.222722
\(636\) 17.6033 0.698016
\(637\) 1.12709 0.0446568
\(638\) −7.06637 −0.279760
\(639\) 12.9376 0.511802
\(640\) 6.74226 0.266511
\(641\) −26.3900 −1.04234 −0.521171 0.853452i \(-0.674505\pi\)
−0.521171 + 0.853452i \(0.674505\pi\)
\(642\) 28.1558 1.11122
\(643\) 5.36126 0.211427 0.105714 0.994397i \(-0.466287\pi\)
0.105714 + 0.994397i \(0.466287\pi\)
\(644\) −5.40277 −0.212899
\(645\) −2.85533 −0.112429
\(646\) −19.3068 −0.759616
\(647\) 3.32466 0.130706 0.0653530 0.997862i \(-0.479183\pi\)
0.0653530 + 0.997862i \(0.479183\pi\)
\(648\) −4.12187 −0.161922
\(649\) −5.01765 −0.196960
\(650\) −1.92140 −0.0753636
\(651\) 2.05044 0.0803629
\(652\) −13.8329 −0.541736
\(653\) −29.9595 −1.17240 −0.586202 0.810165i \(-0.699378\pi\)
−0.586202 + 0.810165i \(0.699378\pi\)
\(654\) −20.3996 −0.797686
\(655\) 0.847562 0.0331170
\(656\) −7.66086 −0.299106
\(657\) 14.9024 0.581396
\(658\) 4.19811 0.163659
\(659\) 8.72952 0.340054 0.170027 0.985439i \(-0.445615\pi\)
0.170027 + 0.985439i \(0.445615\pi\)
\(660\) 1.04219 0.0405672
\(661\) −23.9398 −0.931151 −0.465575 0.885008i \(-0.654153\pi\)
−0.465575 + 0.885008i \(0.654153\pi\)
\(662\) −28.9438 −1.12493
\(663\) −0.164103 −0.00637322
\(664\) 67.1008 2.60402
\(665\) 0.952644 0.0369419
\(666\) −13.7453 −0.532619
\(667\) −13.7115 −0.530910
\(668\) 0.406259 0.0157186
\(669\) 28.4921 1.10157
\(670\) 9.43651 0.364564
\(671\) −10.0621 −0.388441
\(672\) 0.895778 0.0345554
\(673\) −24.1134 −0.929502 −0.464751 0.885441i \(-0.653856\pi\)
−0.464751 + 0.885441i \(0.653856\pi\)
\(674\) 42.0535 1.61984
\(675\) 4.89430 0.188382
\(676\) −48.2986 −1.85764
\(677\) −35.6750 −1.37110 −0.685550 0.728026i \(-0.740438\pi\)
−0.685550 + 0.728026i \(0.740438\pi\)
\(678\) 26.2161 1.00682
\(679\) 4.02586 0.154498
\(680\) 1.34006 0.0513890
\(681\) −0.333603 −0.0127837
\(682\) 11.6327 0.445440
\(683\) −35.9133 −1.37418 −0.687091 0.726571i \(-0.741113\pi\)
−0.687091 + 0.726571i \(0.741113\pi\)
\(684\) −30.0463 −1.14885
\(685\) −2.50102 −0.0955589
\(686\) −12.0457 −0.459907
\(687\) 1.04440 0.0398464
\(688\) 21.2073 0.808520
\(689\) 0.775922 0.0295603
\(690\) 3.10861 0.118343
\(691\) −33.5700 −1.27706 −0.638531 0.769596i \(-0.720458\pi\)
−0.638531 + 0.769596i \(0.720458\pi\)
\(692\) 35.0573 1.33268
\(693\) 0.312627 0.0118757
\(694\) −28.3618 −1.07660
\(695\) −0.824572 −0.0312778
\(696\) −14.1401 −0.535981
\(697\) 3.17263 0.120172
\(698\) −43.3902 −1.64234
\(699\) −13.1069 −0.495749
\(700\) 6.61582 0.250055
\(701\) −8.13135 −0.307117 −0.153558 0.988140i \(-0.549073\pi\)
−0.153558 + 0.988140i \(0.549073\pi\)
\(702\) −0.392579 −0.0148170
\(703\) −46.3704 −1.74889
\(704\) 9.24029 0.348257
\(705\) −1.57135 −0.0591803
\(706\) −18.9812 −0.714366
\(707\) −1.83069 −0.0688503
\(708\) −21.6953 −0.815361
\(709\) −6.19866 −0.232795 −0.116398 0.993203i \(-0.537135\pi\)
−0.116398 + 0.993203i \(0.537135\pi\)
\(710\) −10.0622 −0.377629
\(711\) 5.13168 0.192453
\(712\) −74.1242 −2.77792
\(713\) 22.5720 0.845326
\(714\) 0.868585 0.0325060
\(715\) 0.0459379 0.00171798
\(716\) 72.7599 2.71917
\(717\) 1.16543 0.0435239
\(718\) 14.4877 0.540677
\(719\) 11.2195 0.418415 0.209208 0.977871i \(-0.432912\pi\)
0.209208 + 0.977871i \(0.432912\pi\)
\(720\) 0.785034 0.0292565
\(721\) 4.85352 0.180754
\(722\) −110.362 −4.10724
\(723\) 14.3270 0.532826
\(724\) −0.211554 −0.00786234
\(725\) 16.7900 0.623565
\(726\) −24.5414 −0.910818
\(727\) 9.23540 0.342522 0.171261 0.985226i \(-0.445216\pi\)
0.171261 + 0.985226i \(0.445216\pi\)
\(728\) −0.245590 −0.00910218
\(729\) 1.00000 0.0370370
\(730\) −11.5904 −0.428978
\(731\) −8.78267 −0.324839
\(732\) −43.5064 −1.60804
\(733\) −50.1110 −1.85089 −0.925445 0.378882i \(-0.876309\pi\)
−0.925445 + 0.378882i \(0.876309\pi\)
\(734\) 53.8653 1.98820
\(735\) 2.23291 0.0823622
\(736\) 9.86105 0.363483
\(737\) 10.4471 0.384823
\(738\) 7.58980 0.279385
\(739\) −20.1733 −0.742087 −0.371044 0.928615i \(-0.621000\pi\)
−0.371044 + 0.928615i \(0.621000\pi\)
\(740\) 6.95447 0.255651
\(741\) −1.32439 −0.0486526
\(742\) −4.10691 −0.150769
\(743\) −5.84990 −0.214612 −0.107306 0.994226i \(-0.534222\pi\)
−0.107306 + 0.994226i \(0.534222\pi\)
\(744\) 23.2777 0.853400
\(745\) 1.85162 0.0678380
\(746\) −85.1080 −3.11602
\(747\) −16.2792 −0.595626
\(748\) 3.20566 0.117210
\(749\) −4.27324 −0.156141
\(750\) −7.69533 −0.280994
\(751\) 34.7838 1.26928 0.634639 0.772809i \(-0.281149\pi\)
0.634639 + 0.772809i \(0.281149\pi\)
\(752\) 11.6708 0.425589
\(753\) 4.08839 0.148989
\(754\) −1.34675 −0.0490458
\(755\) 0.492816 0.0179354
\(756\) 1.35174 0.0491623
\(757\) −14.6112 −0.531052 −0.265526 0.964104i \(-0.585546\pi\)
−0.265526 + 0.964104i \(0.585546\pi\)
\(758\) −44.7860 −1.62670
\(759\) 3.44151 0.124919
\(760\) 10.8149 0.392299
\(761\) −32.7708 −1.18794 −0.593970 0.804487i \(-0.702440\pi\)
−0.593970 + 0.804487i \(0.702440\pi\)
\(762\) −41.2982 −1.49608
\(763\) 3.09607 0.112085
\(764\) −71.8721 −2.60024
\(765\) −0.325110 −0.0117544
\(766\) −10.5988 −0.382951
\(767\) −0.956292 −0.0345297
\(768\) 28.1490 1.01574
\(769\) −6.40981 −0.231144 −0.115572 0.993299i \(-0.536870\pi\)
−0.115572 + 0.993299i \(0.536870\pi\)
\(770\) −0.243146 −0.00876239
\(771\) 26.0711 0.938928
\(772\) 11.4253 0.411206
\(773\) −30.8208 −1.10855 −0.554273 0.832335i \(-0.687004\pi\)
−0.554273 + 0.832335i \(0.687004\pi\)
\(774\) −21.0106 −0.755209
\(775\) −27.6399 −0.992854
\(776\) 45.7038 1.64067
\(777\) 2.08614 0.0748398
\(778\) 26.6343 0.954884
\(779\) 25.6046 0.917380
\(780\) 0.198627 0.00711198
\(781\) −11.1398 −0.398614
\(782\) 9.56171 0.341926
\(783\) 3.43052 0.122597
\(784\) −16.5844 −0.592300
\(785\) −0.325110 −0.0116037
\(786\) 6.23667 0.222455
\(787\) −8.77816 −0.312908 −0.156454 0.987685i \(-0.550006\pi\)
−0.156454 + 0.987685i \(0.550006\pi\)
\(788\) 50.4996 1.79897
\(789\) 6.78628 0.241598
\(790\) −3.99118 −0.142000
\(791\) −3.97885 −0.141471
\(792\) 3.54911 0.126112
\(793\) −1.91768 −0.0680990
\(794\) 68.2331 2.42150
\(795\) 1.53721 0.0545192
\(796\) 59.9699 2.12558
\(797\) −6.89139 −0.244106 −0.122053 0.992524i \(-0.538948\pi\)
−0.122053 + 0.992524i \(0.538948\pi\)
\(798\) 7.00990 0.248148
\(799\) −4.83327 −0.170989
\(800\) −12.0751 −0.426919
\(801\) 17.9831 0.635403
\(802\) 87.7380 3.09814
\(803\) −12.8316 −0.452817
\(804\) 45.1712 1.59306
\(805\) −0.471797 −0.0166287
\(806\) 2.21703 0.0780917
\(807\) −0.198615 −0.00699159
\(808\) −20.7830 −0.731144
\(809\) −6.76958 −0.238006 −0.119003 0.992894i \(-0.537970\pi\)
−0.119003 + 0.992894i \(0.537970\pi\)
\(810\) −0.777753 −0.0273275
\(811\) 49.3825 1.73405 0.867027 0.498261i \(-0.166028\pi\)
0.867027 + 0.498261i \(0.166028\pi\)
\(812\) 4.63717 0.162733
\(813\) 22.4067 0.785838
\(814\) 11.8353 0.414826
\(815\) −1.20795 −0.0423128
\(816\) 2.41467 0.0845305
\(817\) −70.8803 −2.47979
\(818\) −34.8195 −1.21744
\(819\) 0.0595822 0.00208197
\(820\) −3.84009 −0.134102
\(821\) −35.1327 −1.22614 −0.613070 0.790028i \(-0.710066\pi\)
−0.613070 + 0.790028i \(0.710066\pi\)
\(822\) −18.4034 −0.641891
\(823\) 25.5098 0.889215 0.444607 0.895726i \(-0.353343\pi\)
0.444607 + 0.895726i \(0.353343\pi\)
\(824\) 55.0998 1.91949
\(825\) −4.21421 −0.146720
\(826\) 5.06159 0.176115
\(827\) 16.4263 0.571198 0.285599 0.958349i \(-0.407808\pi\)
0.285599 + 0.958349i \(0.407808\pi\)
\(828\) 14.8804 0.517131
\(829\) −6.12019 −0.212563 −0.106282 0.994336i \(-0.533894\pi\)
−0.106282 + 0.994336i \(0.533894\pi\)
\(830\) 12.6612 0.439477
\(831\) 14.8527 0.515236
\(832\) 1.76107 0.0610541
\(833\) 6.86817 0.237968
\(834\) −6.06750 −0.210100
\(835\) 0.0354765 0.00122772
\(836\) 25.8712 0.894773
\(837\) −5.64736 −0.195201
\(838\) −68.2834 −2.35881
\(839\) −34.1188 −1.17791 −0.588956 0.808165i \(-0.700461\pi\)
−0.588956 + 0.808165i \(0.700461\pi\)
\(840\) −0.486548 −0.0167875
\(841\) −17.2315 −0.594191
\(842\) −54.2557 −1.86977
\(843\) 1.14199 0.0393322
\(844\) −27.9735 −0.962888
\(845\) −4.21767 −0.145092
\(846\) −11.5625 −0.397528
\(847\) 3.72468 0.127982
\(848\) −11.4172 −0.392069
\(849\) −11.8706 −0.407398
\(850\) −11.7085 −0.401599
\(851\) 22.9650 0.787229
\(852\) −48.1664 −1.65015
\(853\) 0.186385 0.00638169 0.00319085 0.999995i \(-0.498984\pi\)
0.00319085 + 0.999995i \(0.498984\pi\)
\(854\) 10.1502 0.347332
\(855\) −2.62379 −0.0897318
\(856\) −48.5121 −1.65811
\(857\) −19.6326 −0.670635 −0.335318 0.942105i \(-0.608844\pi\)
−0.335318 + 0.942105i \(0.608844\pi\)
\(858\) 0.338028 0.0115401
\(859\) 9.55139 0.325889 0.162945 0.986635i \(-0.447901\pi\)
0.162945 + 0.986635i \(0.447901\pi\)
\(860\) 10.6304 0.362493
\(861\) −1.15191 −0.0392571
\(862\) −29.9711 −1.02082
\(863\) 31.8855 1.08540 0.542698 0.839928i \(-0.317403\pi\)
0.542698 + 0.839928i \(0.317403\pi\)
\(864\) −2.46717 −0.0839348
\(865\) 3.06138 0.104090
\(866\) −10.8174 −0.367590
\(867\) −1.00000 −0.0339618
\(868\) −7.63375 −0.259106
\(869\) −4.41860 −0.149891
\(870\) −2.66810 −0.0904570
\(871\) 1.99107 0.0674647
\(872\) 35.1482 1.19027
\(873\) −11.0881 −0.375276
\(874\) 77.1675 2.61023
\(875\) 1.16793 0.0394832
\(876\) −55.4813 −1.87454
\(877\) −40.7107 −1.37470 −0.687351 0.726325i \(-0.741227\pi\)
−0.687351 + 0.726325i \(0.741227\pi\)
\(878\) 30.3234 1.02337
\(879\) 3.33015 0.112323
\(880\) −0.675949 −0.0227862
\(881\) −29.9144 −1.00784 −0.503921 0.863750i \(-0.668110\pi\)
−0.503921 + 0.863750i \(0.668110\pi\)
\(882\) 16.4306 0.553246
\(883\) 23.6433 0.795662 0.397831 0.917459i \(-0.369763\pi\)
0.397831 + 0.917459i \(0.369763\pi\)
\(884\) 0.610953 0.0205486
\(885\) −1.89455 −0.0636845
\(886\) 52.9681 1.77950
\(887\) 15.2931 0.513492 0.256746 0.966479i \(-0.417350\pi\)
0.256746 + 0.966479i \(0.417350\pi\)
\(888\) 23.6830 0.794748
\(889\) 6.26789 0.210218
\(890\) −13.9864 −0.468827
\(891\) −0.861044 −0.0288461
\(892\) −106.076 −3.55168
\(893\) −39.0068 −1.30531
\(894\) 13.6249 0.455684
\(895\) 6.35376 0.212383
\(896\) −7.52967 −0.251549
\(897\) 0.655903 0.0219000
\(898\) 3.70035 0.123482
\(899\) −19.3734 −0.646138
\(900\) −18.2214 −0.607381
\(901\) 4.72827 0.157522
\(902\) −6.53515 −0.217597
\(903\) 3.18880 0.106117
\(904\) −45.1700 −1.50233
\(905\) −0.0184739 −0.000614095 0
\(906\) 3.62632 0.120476
\(907\) 16.6982 0.554456 0.277228 0.960804i \(-0.410584\pi\)
0.277228 + 0.960804i \(0.410584\pi\)
\(908\) 1.24200 0.0412172
\(909\) 5.04213 0.167237
\(910\) −0.0463403 −0.00153617
\(911\) −26.7876 −0.887513 −0.443757 0.896147i \(-0.646355\pi\)
−0.443757 + 0.896147i \(0.646355\pi\)
\(912\) 19.4876 0.645298
\(913\) 14.0171 0.463899
\(914\) −70.6669 −2.33745
\(915\) −3.79920 −0.125598
\(916\) −3.88829 −0.128473
\(917\) −0.946547 −0.0312577
\(918\) −2.39228 −0.0789569
\(919\) 0.941694 0.0310636 0.0155318 0.999879i \(-0.495056\pi\)
0.0155318 + 0.999879i \(0.495056\pi\)
\(920\) −5.35610 −0.176585
\(921\) −11.4073 −0.375883
\(922\) −1.68376 −0.0554517
\(923\) −2.12309 −0.0698824
\(924\) −1.16391 −0.0382897
\(925\) −28.1211 −0.924617
\(926\) 58.5471 1.92398
\(927\) −13.3677 −0.439052
\(928\) −8.46368 −0.277834
\(929\) −45.4060 −1.48972 −0.744862 0.667219i \(-0.767485\pi\)
−0.744862 + 0.667219i \(0.767485\pi\)
\(930\) 4.39225 0.144028
\(931\) 55.4294 1.81663
\(932\) 48.7969 1.59840
\(933\) −16.2862 −0.533185
\(934\) 69.2808 2.26694
\(935\) 0.279934 0.00915482
\(936\) 0.676410 0.0221092
\(937\) −46.8806 −1.53152 −0.765762 0.643125i \(-0.777638\pi\)
−0.765762 + 0.643125i \(0.777638\pi\)
\(938\) −10.5386 −0.344097
\(939\) 5.08060 0.165799
\(940\) 5.85010 0.190809
\(941\) 41.5888 1.35575 0.677877 0.735175i \(-0.262900\pi\)
0.677877 + 0.735175i \(0.262900\pi\)
\(942\) −2.39228 −0.0779446
\(943\) −12.6807 −0.412940
\(944\) 14.0713 0.457981
\(945\) 0.118041 0.00383986
\(946\) 18.0910 0.588190
\(947\) −17.3673 −0.564362 −0.282181 0.959361i \(-0.591058\pi\)
−0.282181 + 0.959361i \(0.591058\pi\)
\(948\) −19.1052 −0.620507
\(949\) −2.44552 −0.0793848
\(950\) −94.4934 −3.06577
\(951\) 28.8502 0.935532
\(952\) −1.49656 −0.0485039
\(953\) −17.2033 −0.557269 −0.278635 0.960397i \(-0.589882\pi\)
−0.278635 + 0.960397i \(0.589882\pi\)
\(954\) 11.3113 0.366218
\(955\) −6.27623 −0.203094
\(956\) −4.33890 −0.140330
\(957\) −2.95383 −0.0954837
\(958\) −40.6775 −1.31423
\(959\) 2.79310 0.0901940
\(960\) 3.48892 0.112604
\(961\) 0.892626 0.0287944
\(962\) 2.25564 0.0727247
\(963\) 11.7694 0.379265
\(964\) −53.3392 −1.71794
\(965\) 0.997714 0.0321176
\(966\) −3.47165 −0.111699
\(967\) 19.4776 0.626358 0.313179 0.949694i \(-0.398606\pi\)
0.313179 + 0.949694i \(0.398606\pi\)
\(968\) 42.2846 1.35908
\(969\) −8.07048 −0.259261
\(970\) 8.62382 0.276894
\(971\) 11.1417 0.357555 0.178777 0.983890i \(-0.442786\pi\)
0.178777 + 0.983890i \(0.442786\pi\)
\(972\) −3.72299 −0.119415
\(973\) 0.920872 0.0295218
\(974\) 49.2114 1.57684
\(975\) −0.803169 −0.0257220
\(976\) 28.2176 0.903223
\(977\) 4.24510 0.135813 0.0679064 0.997692i \(-0.478368\pi\)
0.0679064 + 0.997692i \(0.478368\pi\)
\(978\) −8.88856 −0.284225
\(979\) −15.4843 −0.494880
\(980\) −8.31311 −0.265553
\(981\) −8.52725 −0.272254
\(982\) −76.2742 −2.43401
\(983\) −24.8723 −0.793304 −0.396652 0.917969i \(-0.629828\pi\)
−0.396652 + 0.917969i \(0.629828\pi\)
\(984\) −13.0772 −0.416884
\(985\) 4.40987 0.140510
\(986\) −8.20675 −0.261356
\(987\) 1.75486 0.0558578
\(988\) 4.93068 0.156866
\(989\) 35.1035 1.11623
\(990\) 0.669680 0.0212838
\(991\) −11.1540 −0.354318 −0.177159 0.984182i \(-0.556691\pi\)
−0.177159 + 0.984182i \(0.556691\pi\)
\(992\) 13.9330 0.442373
\(993\) −12.0989 −0.383946
\(994\) 11.2374 0.356428
\(995\) 5.23687 0.166020
\(996\) 60.6074 1.92042
\(997\) −48.7606 −1.54427 −0.772133 0.635461i \(-0.780810\pi\)
−0.772133 + 0.635461i \(0.780810\pi\)
\(998\) 57.1422 1.80880
\(999\) −5.74569 −0.181785
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 \(a_p\))