Properties

Label 4010.2.a.k.1.5
Level 4010
Weight 2
Character 4010.1
Self dual Yes
Analytic conductor 32.020
Analytic rank 1
Dimension 15
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4010 = 2 \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4010.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0200112105\)
Analytic rank: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-2.62108\)
Character \(\chi\) = 4010.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.88769 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.88769 q^{6} +1.11871 q^{7} -1.00000 q^{8} +0.563364 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.88769 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.88769 q^{6} +1.11871 q^{7} -1.00000 q^{8} +0.563364 q^{9} +1.00000 q^{10} -6.32315 q^{11} -1.88769 q^{12} -2.82666 q^{13} -1.11871 q^{14} +1.88769 q^{15} +1.00000 q^{16} +3.93054 q^{17} -0.563364 q^{18} -1.08531 q^{19} -1.00000 q^{20} -2.11177 q^{21} +6.32315 q^{22} +5.37635 q^{23} +1.88769 q^{24} +1.00000 q^{25} +2.82666 q^{26} +4.59961 q^{27} +1.11871 q^{28} +3.07398 q^{29} -1.88769 q^{30} +3.88716 q^{31} -1.00000 q^{32} +11.9361 q^{33} -3.93054 q^{34} -1.11871 q^{35} +0.563364 q^{36} -0.283699 q^{37} +1.08531 q^{38} +5.33585 q^{39} +1.00000 q^{40} +11.9618 q^{41} +2.11177 q^{42} -10.1723 q^{43} -6.32315 q^{44} -0.563364 q^{45} -5.37635 q^{46} -6.23186 q^{47} -1.88769 q^{48} -5.74849 q^{49} -1.00000 q^{50} -7.41963 q^{51} -2.82666 q^{52} -0.293135 q^{53} -4.59961 q^{54} +6.32315 q^{55} -1.11871 q^{56} +2.04874 q^{57} -3.07398 q^{58} +6.60549 q^{59} +1.88769 q^{60} +11.7860 q^{61} -3.88716 q^{62} +0.630239 q^{63} +1.00000 q^{64} +2.82666 q^{65} -11.9361 q^{66} +14.2743 q^{67} +3.93054 q^{68} -10.1489 q^{69} +1.11871 q^{70} +4.56770 q^{71} -0.563364 q^{72} -16.1342 q^{73} +0.283699 q^{74} -1.88769 q^{75} -1.08531 q^{76} -7.07375 q^{77} -5.33585 q^{78} -11.2037 q^{79} -1.00000 q^{80} -10.3727 q^{81} -11.9618 q^{82} -6.28436 q^{83} -2.11177 q^{84} -3.93054 q^{85} +10.1723 q^{86} -5.80270 q^{87} +6.32315 q^{88} +7.99086 q^{89} +0.563364 q^{90} -3.16220 q^{91} +5.37635 q^{92} -7.33775 q^{93} +6.23186 q^{94} +1.08531 q^{95} +1.88769 q^{96} -8.56664 q^{97} +5.74849 q^{98} -3.56223 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - 15q^{2} - 6q^{3} + 15q^{4} - 15q^{5} + 6q^{6} - 5q^{7} - 15q^{8} + 19q^{9} + O(q^{10}) \) \( 15q - 15q^{2} - 6q^{3} + 15q^{4} - 15q^{5} + 6q^{6} - 5q^{7} - 15q^{8} + 19q^{9} + 15q^{10} - 2q^{11} - 6q^{12} - 13q^{13} + 5q^{14} + 6q^{15} + 15q^{16} + 11q^{17} - 19q^{18} - 15q^{19} - 15q^{20} - 2q^{21} + 2q^{22} - 3q^{23} + 6q^{24} + 15q^{25} + 13q^{26} - 12q^{27} - 5q^{28} + 28q^{29} - 6q^{30} - 12q^{31} - 15q^{32} - 22q^{33} - 11q^{34} + 5q^{35} + 19q^{36} - 23q^{37} + 15q^{38} - 2q^{39} + 15q^{40} + 24q^{41} + 2q^{42} - 24q^{43} - 2q^{44} - 19q^{45} + 3q^{46} - 3q^{47} - 6q^{48} + 20q^{49} - 15q^{50} - 5q^{51} - 13q^{52} + 10q^{53} + 12q^{54} + 2q^{55} + 5q^{56} - 11q^{57} - 28q^{58} + 2q^{59} + 6q^{60} + 15q^{61} + 12q^{62} - 2q^{63} + 15q^{64} + 13q^{65} + 22q^{66} - 48q^{67} + 11q^{68} + 21q^{69} - 5q^{70} + 15q^{71} - 19q^{72} - 47q^{73} + 23q^{74} - 6q^{75} - 15q^{76} + 7q^{77} + 2q^{78} - 34q^{79} - 15q^{80} + 43q^{81} - 24q^{82} - 32q^{83} - 2q^{84} - 11q^{85} + 24q^{86} + 14q^{87} + 2q^{88} + 25q^{89} + 19q^{90} - 32q^{91} - 3q^{92} - 42q^{93} + 3q^{94} + 15q^{95} + 6q^{96} - 34q^{97} - 20q^{98} + 4q^{99} + O(q^{100}) \)

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
\(3\) −1.88769 −1.08986 −0.544928 0.838483i \(-0.683443\pi\)
−0.544928 + 0.838483i \(0.683443\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 1.88769 0.770645
\(7\) 1.11871 0.422832 0.211416 0.977396i \(-0.432193\pi\)
0.211416 + 0.977396i \(0.432193\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.563364 0.187788
\(10\) 1.00000 0.316228
\(11\) −6.32315 −1.90650 −0.953250 0.302182i \(-0.902285\pi\)
−0.953250 + 0.302182i \(0.902285\pi\)
\(12\) −1.88769 −0.544928
\(13\) −2.82666 −0.783974 −0.391987 0.919971i \(-0.628212\pi\)
−0.391987 + 0.919971i \(0.628212\pi\)
\(14\) −1.11871 −0.298987
\(15\) 1.88769 0.487399
\(16\) 1.00000 0.250000
\(17\) 3.93054 0.953296 0.476648 0.879094i \(-0.341852\pi\)
0.476648 + 0.879094i \(0.341852\pi\)
\(18\) −0.563364 −0.132786
\(19\) −1.08531 −0.248988 −0.124494 0.992220i \(-0.539731\pi\)
−0.124494 + 0.992220i \(0.539731\pi\)
\(20\) −1.00000 −0.223607
\(21\) −2.11177 −0.460826
\(22\) 6.32315 1.34810
\(23\) 5.37635 1.12105 0.560523 0.828139i \(-0.310600\pi\)
0.560523 + 0.828139i \(0.310600\pi\)
\(24\) 1.88769 0.385323
\(25\) 1.00000 0.200000
\(26\) 2.82666 0.554353
\(27\) 4.59961 0.885195
\(28\) 1.11871 0.211416
\(29\) 3.07398 0.570823 0.285411 0.958405i \(-0.407870\pi\)
0.285411 + 0.958405i \(0.407870\pi\)
\(30\) −1.88769 −0.344643
\(31\) 3.88716 0.698155 0.349078 0.937094i \(-0.386495\pi\)
0.349078 + 0.937094i \(0.386495\pi\)
\(32\) −1.00000 −0.176777
\(33\) 11.9361 2.07781
\(34\) −3.93054 −0.674082
\(35\) −1.11871 −0.189096
\(36\) 0.563364 0.0938939
\(37\) −0.283699 −0.0466398 −0.0233199 0.999728i \(-0.507424\pi\)
−0.0233199 + 0.999728i \(0.507424\pi\)
\(38\) 1.08531 0.176061
\(39\) 5.33585 0.854419
\(40\) 1.00000 0.158114
\(41\) 11.9618 1.86812 0.934061 0.357113i \(-0.116239\pi\)
0.934061 + 0.357113i \(0.116239\pi\)
\(42\) 2.11177 0.325853
\(43\) −10.1723 −1.55126 −0.775632 0.631185i \(-0.782569\pi\)
−0.775632 + 0.631185i \(0.782569\pi\)
\(44\) −6.32315 −0.953250
\(45\) −0.563364 −0.0839813
\(46\) −5.37635 −0.792699
\(47\) −6.23186 −0.909010 −0.454505 0.890744i \(-0.650184\pi\)
−0.454505 + 0.890744i \(0.650184\pi\)
\(48\) −1.88769 −0.272464
\(49\) −5.74849 −0.821214
\(50\) −1.00000 −0.141421
\(51\) −7.41963 −1.03896
\(52\) −2.82666 −0.391987
\(53\) −0.293135 −0.0402651 −0.0201326 0.999797i \(-0.506409\pi\)
−0.0201326 + 0.999797i \(0.506409\pi\)
\(54\) −4.59961 −0.625927
\(55\) 6.32315 0.852613
\(56\) −1.11871 −0.149494
\(57\) 2.04874 0.271362
\(58\) −3.07398 −0.403633
\(59\) 6.60549 0.859962 0.429981 0.902838i \(-0.358520\pi\)
0.429981 + 0.902838i \(0.358520\pi\)
\(60\) 1.88769 0.243699
\(61\) 11.7860 1.50904 0.754520 0.656277i \(-0.227870\pi\)
0.754520 + 0.656277i \(0.227870\pi\)
\(62\) −3.88716 −0.493670
\(63\) 0.630239 0.0794026
\(64\) 1.00000 0.125000
\(65\) 2.82666 0.350604
\(66\) −11.9361 −1.46924
\(67\) 14.2743 1.74389 0.871944 0.489606i \(-0.162860\pi\)
0.871944 + 0.489606i \(0.162860\pi\)
\(68\) 3.93054 0.476648
\(69\) −10.1489 −1.22178
\(70\) 1.11871 0.133711
\(71\) 4.56770 0.542086 0.271043 0.962567i \(-0.412631\pi\)
0.271043 + 0.962567i \(0.412631\pi\)
\(72\) −0.563364 −0.0663930
\(73\) −16.1342 −1.88836 −0.944181 0.329428i \(-0.893144\pi\)
−0.944181 + 0.329428i \(0.893144\pi\)
\(74\) 0.283699 0.0329793
\(75\) −1.88769 −0.217971
\(76\) −1.08531 −0.124494
\(77\) −7.07375 −0.806128
\(78\) −5.33585 −0.604166
\(79\) −11.2037 −1.26051 −0.630255 0.776388i \(-0.717050\pi\)
−0.630255 + 0.776388i \(0.717050\pi\)
\(80\) −1.00000 −0.111803
\(81\) −10.3727 −1.15252
\(82\) −11.9618 −1.32096
\(83\) −6.28436 −0.689798 −0.344899 0.938640i \(-0.612087\pi\)
−0.344899 + 0.938640i \(0.612087\pi\)
\(84\) −2.11177 −0.230413
\(85\) −3.93054 −0.426327
\(86\) 10.1723 1.09691
\(87\) −5.80270 −0.622115
\(88\) 6.32315 0.674050
\(89\) 7.99086 0.847029 0.423515 0.905889i \(-0.360796\pi\)
0.423515 + 0.905889i \(0.360796\pi\)
\(90\) 0.563364 0.0593837
\(91\) −3.16220 −0.331489
\(92\) 5.37635 0.560523
\(93\) −7.33775 −0.760889
\(94\) 6.23186 0.642767
\(95\) 1.08531 0.111351
\(96\) 1.88769 0.192661
\(97\) −8.56664 −0.869810 −0.434905 0.900476i \(-0.643218\pi\)
−0.434905 + 0.900476i \(0.643218\pi\)
\(98\) 5.74849 0.580686
\(99\) −3.56223 −0.358018
\(100\) 1.00000 0.100000
\(101\) −1.14404 −0.113836 −0.0569180 0.998379i \(-0.518127\pi\)
−0.0569180 + 0.998379i \(0.518127\pi\)
\(102\) 7.41963 0.734653
\(103\) −16.5367 −1.62941 −0.814704 0.579877i \(-0.803101\pi\)
−0.814704 + 0.579877i \(0.803101\pi\)
\(104\) 2.82666 0.277177
\(105\) 2.11177 0.206088
\(106\) 0.293135 0.0284717
\(107\) −0.551506 −0.0533161 −0.0266580 0.999645i \(-0.508487\pi\)
−0.0266580 + 0.999645i \(0.508487\pi\)
\(108\) 4.59961 0.442597
\(109\) 6.39040 0.612089 0.306045 0.952017i \(-0.400994\pi\)
0.306045 + 0.952017i \(0.400994\pi\)
\(110\) −6.32315 −0.602888
\(111\) 0.535534 0.0508307
\(112\) 1.11871 0.105708
\(113\) 17.6089 1.65651 0.828254 0.560352i \(-0.189334\pi\)
0.828254 + 0.560352i \(0.189334\pi\)
\(114\) −2.04874 −0.191882
\(115\) −5.37635 −0.501347
\(116\) 3.07398 0.285411
\(117\) −1.59244 −0.147221
\(118\) −6.60549 −0.608085
\(119\) 4.39712 0.403083
\(120\) −1.88769 −0.172321
\(121\) 28.9822 2.63474
\(122\) −11.7860 −1.06705
\(123\) −22.5802 −2.03599
\(124\) 3.88716 0.349078
\(125\) −1.00000 −0.0894427
\(126\) −0.630239 −0.0561461
\(127\) 16.8182 1.49238 0.746188 0.665736i \(-0.231882\pi\)
0.746188 + 0.665736i \(0.231882\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 19.2022 1.69066
\(130\) −2.82666 −0.247914
\(131\) 9.34216 0.816229 0.408114 0.912931i \(-0.366186\pi\)
0.408114 + 0.912931i \(0.366186\pi\)
\(132\) 11.9361 1.03891
\(133\) −1.21415 −0.105280
\(134\) −14.2743 −1.23311
\(135\) −4.59961 −0.395871
\(136\) −3.93054 −0.337041
\(137\) −10.1181 −0.864444 −0.432222 0.901767i \(-0.642270\pi\)
−0.432222 + 0.901767i \(0.642270\pi\)
\(138\) 10.1489 0.863929
\(139\) −18.4350 −1.56364 −0.781818 0.623507i \(-0.785707\pi\)
−0.781818 + 0.623507i \(0.785707\pi\)
\(140\) −1.11871 −0.0945480
\(141\) 11.7638 0.990691
\(142\) −4.56770 −0.383313
\(143\) 17.8734 1.49465
\(144\) 0.563364 0.0469470
\(145\) −3.07398 −0.255280
\(146\) 16.1342 1.33527
\(147\) 10.8514 0.895005
\(148\) −0.283699 −0.0233199
\(149\) 5.02014 0.411266 0.205633 0.978629i \(-0.434075\pi\)
0.205633 + 0.978629i \(0.434075\pi\)
\(150\) 1.88769 0.154129
\(151\) 10.6556 0.867144 0.433572 0.901119i \(-0.357253\pi\)
0.433572 + 0.901119i \(0.357253\pi\)
\(152\) 1.08531 0.0880307
\(153\) 2.21432 0.179017
\(154\) 7.07375 0.570019
\(155\) −3.88716 −0.312225
\(156\) 5.33585 0.427210
\(157\) 11.3236 0.903724 0.451862 0.892088i \(-0.350760\pi\)
0.451862 + 0.892088i \(0.350760\pi\)
\(158\) 11.2037 0.891315
\(159\) 0.553346 0.0438832
\(160\) 1.00000 0.0790569
\(161\) 6.01456 0.474014
\(162\) 10.3727 0.814957
\(163\) −20.0968 −1.57411 −0.787053 0.616886i \(-0.788394\pi\)
−0.787053 + 0.616886i \(0.788394\pi\)
\(164\) 11.9618 0.934061
\(165\) −11.9361 −0.929226
\(166\) 6.28436 0.487761
\(167\) −4.63853 −0.358940 −0.179470 0.983763i \(-0.557438\pi\)
−0.179470 + 0.983763i \(0.557438\pi\)
\(168\) 2.11177 0.162927
\(169\) −5.01001 −0.385385
\(170\) 3.93054 0.301459
\(171\) −0.611427 −0.0467570
\(172\) −10.1723 −0.775632
\(173\) −11.5342 −0.876928 −0.438464 0.898749i \(-0.644477\pi\)
−0.438464 + 0.898749i \(0.644477\pi\)
\(174\) 5.80270 0.439902
\(175\) 1.11871 0.0845663
\(176\) −6.32315 −0.476625
\(177\) −12.4691 −0.937235
\(178\) −7.99086 −0.598940
\(179\) 15.8541 1.18499 0.592494 0.805575i \(-0.298143\pi\)
0.592494 + 0.805575i \(0.298143\pi\)
\(180\) −0.563364 −0.0419906
\(181\) −23.0672 −1.71457 −0.857284 0.514844i \(-0.827850\pi\)
−0.857284 + 0.514844i \(0.827850\pi\)
\(182\) 3.16220 0.234398
\(183\) −22.2483 −1.64464
\(184\) −5.37635 −0.396350
\(185\) 0.283699 0.0208579
\(186\) 7.33775 0.538030
\(187\) −24.8534 −1.81746
\(188\) −6.23186 −0.454505
\(189\) 5.14561 0.374288
\(190\) −1.08531 −0.0787370
\(191\) −0.0467554 −0.00338310 −0.00169155 0.999999i \(-0.500538\pi\)
−0.00169155 + 0.999999i \(0.500538\pi\)
\(192\) −1.88769 −0.136232
\(193\) 6.39884 0.460599 0.230299 0.973120i \(-0.426029\pi\)
0.230299 + 0.973120i \(0.426029\pi\)
\(194\) 8.56664 0.615049
\(195\) −5.33585 −0.382108
\(196\) −5.74849 −0.410607
\(197\) −12.5182 −0.891882 −0.445941 0.895062i \(-0.647131\pi\)
−0.445941 + 0.895062i \(0.647131\pi\)
\(198\) 3.56223 0.253157
\(199\) −5.08884 −0.360738 −0.180369 0.983599i \(-0.557729\pi\)
−0.180369 + 0.983599i \(0.557729\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −26.9455 −1.90059
\(202\) 1.14404 0.0804942
\(203\) 3.43888 0.241362
\(204\) −7.41963 −0.519478
\(205\) −11.9618 −0.835450
\(206\) 16.5367 1.15217
\(207\) 3.02884 0.210519
\(208\) −2.82666 −0.195993
\(209\) 6.86261 0.474696
\(210\) −2.11177 −0.145726
\(211\) −15.9524 −1.09821 −0.549103 0.835754i \(-0.685031\pi\)
−0.549103 + 0.835754i \(0.685031\pi\)
\(212\) −0.293135 −0.0201326
\(213\) −8.62239 −0.590796
\(214\) 0.551506 0.0377002
\(215\) 10.1723 0.693746
\(216\) −4.59961 −0.312964
\(217\) 4.34860 0.295202
\(218\) −6.39040 −0.432813
\(219\) 30.4563 2.05804
\(220\) 6.32315 0.426306
\(221\) −11.1103 −0.747359
\(222\) −0.535534 −0.0359427
\(223\) −5.88038 −0.393780 −0.196890 0.980426i \(-0.563084\pi\)
−0.196890 + 0.980426i \(0.563084\pi\)
\(224\) −1.11871 −0.0747468
\(225\) 0.563364 0.0375576
\(226\) −17.6089 −1.17133
\(227\) 2.83467 0.188143 0.0940717 0.995565i \(-0.470012\pi\)
0.0940717 + 0.995565i \(0.470012\pi\)
\(228\) 2.04874 0.135681
\(229\) 0.844296 0.0557926 0.0278963 0.999611i \(-0.491119\pi\)
0.0278963 + 0.999611i \(0.491119\pi\)
\(230\) 5.37635 0.354506
\(231\) 13.3530 0.878565
\(232\) −3.07398 −0.201816
\(233\) −10.7431 −0.703802 −0.351901 0.936037i \(-0.614465\pi\)
−0.351901 + 0.936037i \(0.614465\pi\)
\(234\) 1.59244 0.104101
\(235\) 6.23186 0.406522
\(236\) 6.60549 0.429981
\(237\) 21.1490 1.37378
\(238\) −4.39712 −0.285023
\(239\) 19.0311 1.23102 0.615509 0.788130i \(-0.288951\pi\)
0.615509 + 0.788130i \(0.288951\pi\)
\(240\) 1.88769 0.121850
\(241\) 11.7762 0.758569 0.379285 0.925280i \(-0.376170\pi\)
0.379285 + 0.925280i \(0.376170\pi\)
\(242\) −28.9822 −1.86305
\(243\) 5.78161 0.370891
\(244\) 11.7860 0.754520
\(245\) 5.74849 0.367258
\(246\) 22.5802 1.43966
\(247\) 3.06781 0.195200
\(248\) −3.88716 −0.246835
\(249\) 11.8629 0.751781
\(250\) 1.00000 0.0632456
\(251\) −19.1035 −1.20580 −0.602900 0.797817i \(-0.705988\pi\)
−0.602900 + 0.797817i \(0.705988\pi\)
\(252\) 0.630239 0.0397013
\(253\) −33.9954 −2.13727
\(254\) −16.8182 −1.05527
\(255\) 7.41963 0.464635
\(256\) 1.00000 0.0625000
\(257\) 6.77930 0.422881 0.211441 0.977391i \(-0.432185\pi\)
0.211441 + 0.977391i \(0.432185\pi\)
\(258\) −19.2022 −1.19547
\(259\) −0.317376 −0.0197208
\(260\) 2.82666 0.175302
\(261\) 1.73177 0.107194
\(262\) −9.34216 −0.577161
\(263\) −23.3670 −1.44087 −0.720437 0.693521i \(-0.756059\pi\)
−0.720437 + 0.693521i \(0.756059\pi\)
\(264\) −11.9361 −0.734618
\(265\) 0.293135 0.0180071
\(266\) 1.21415 0.0744443
\(267\) −15.0842 −0.923141
\(268\) 14.2743 0.871944
\(269\) 6.81642 0.415604 0.207802 0.978171i \(-0.433369\pi\)
0.207802 + 0.978171i \(0.433369\pi\)
\(270\) 4.59961 0.279923
\(271\) 2.58394 0.156963 0.0784815 0.996916i \(-0.474993\pi\)
0.0784815 + 0.996916i \(0.474993\pi\)
\(272\) 3.93054 0.238324
\(273\) 5.96925 0.361275
\(274\) 10.1181 0.611254
\(275\) −6.32315 −0.381300
\(276\) −10.1489 −0.610890
\(277\) −26.6772 −1.60288 −0.801439 0.598076i \(-0.795932\pi\)
−0.801439 + 0.598076i \(0.795932\pi\)
\(278\) 18.4350 1.10566
\(279\) 2.18989 0.131105
\(280\) 1.11871 0.0668555
\(281\) 14.4915 0.864492 0.432246 0.901756i \(-0.357721\pi\)
0.432246 + 0.901756i \(0.357721\pi\)
\(282\) −11.7638 −0.700524
\(283\) 1.14439 0.0680271 0.0340136 0.999421i \(-0.489171\pi\)
0.0340136 + 0.999421i \(0.489171\pi\)
\(284\) 4.56770 0.271043
\(285\) −2.04874 −0.121357
\(286\) −17.8734 −1.05687
\(287\) 13.3818 0.789901
\(288\) −0.563364 −0.0331965
\(289\) −1.55086 −0.0912272
\(290\) 3.07398 0.180510
\(291\) 16.1711 0.947969
\(292\) −16.1342 −0.944181
\(293\) −27.9405 −1.63230 −0.816151 0.577838i \(-0.803896\pi\)
−0.816151 + 0.577838i \(0.803896\pi\)
\(294\) −10.8514 −0.632864
\(295\) −6.60549 −0.384587
\(296\) 0.283699 0.0164896
\(297\) −29.0840 −1.68762
\(298\) −5.02014 −0.290809
\(299\) −15.1971 −0.878871
\(300\) −1.88769 −0.108986
\(301\) −11.3798 −0.655923
\(302\) −10.6556 −0.613163
\(303\) 2.15959 0.124065
\(304\) −1.08531 −0.0622471
\(305\) −11.7860 −0.674864
\(306\) −2.21432 −0.126584
\(307\) −16.9869 −0.969492 −0.484746 0.874655i \(-0.661088\pi\)
−0.484746 + 0.874655i \(0.661088\pi\)
\(308\) −7.07375 −0.403064
\(309\) 31.2161 1.77582
\(310\) 3.88716 0.220776
\(311\) −31.2663 −1.77295 −0.886476 0.462775i \(-0.846854\pi\)
−0.886476 + 0.462775i \(0.846854\pi\)
\(312\) −5.33585 −0.302083
\(313\) 24.6006 1.39051 0.695254 0.718764i \(-0.255292\pi\)
0.695254 + 0.718764i \(0.255292\pi\)
\(314\) −11.3236 −0.639029
\(315\) −0.630239 −0.0355099
\(316\) −11.2037 −0.630255
\(317\) −12.4915 −0.701592 −0.350796 0.936452i \(-0.614089\pi\)
−0.350796 + 0.936452i \(0.614089\pi\)
\(318\) −0.553346 −0.0310301
\(319\) −19.4372 −1.08827
\(320\) −1.00000 −0.0559017
\(321\) 1.04107 0.0581069
\(322\) −6.01456 −0.335178
\(323\) −4.26587 −0.237360
\(324\) −10.3727 −0.576262
\(325\) −2.82666 −0.156795
\(326\) 20.0968 1.11306
\(327\) −12.0631 −0.667090
\(328\) −11.9618 −0.660481
\(329\) −6.97163 −0.384358
\(330\) 11.9361 0.657062
\(331\) −33.8103 −1.85838 −0.929191 0.369600i \(-0.879495\pi\)
−0.929191 + 0.369600i \(0.879495\pi\)
\(332\) −6.28436 −0.344899
\(333\) −0.159825 −0.00875838
\(334\) 4.63853 0.253809
\(335\) −14.2743 −0.779890
\(336\) −2.11177 −0.115206
\(337\) 5.49671 0.299425 0.149712 0.988730i \(-0.452165\pi\)
0.149712 + 0.988730i \(0.452165\pi\)
\(338\) 5.01001 0.272508
\(339\) −33.2402 −1.80536
\(340\) −3.93054 −0.213163
\(341\) −24.5791 −1.33103
\(342\) 0.611427 0.0330622
\(343\) −14.2618 −0.770066
\(344\) 10.1723 0.548455
\(345\) 10.1489 0.546396
\(346\) 11.5342 0.620082
\(347\) −4.26340 −0.228871 −0.114436 0.993431i \(-0.536506\pi\)
−0.114436 + 0.993431i \(0.536506\pi\)
\(348\) −5.80270 −0.311058
\(349\) 20.0459 1.07303 0.536515 0.843891i \(-0.319740\pi\)
0.536515 + 0.843891i \(0.319740\pi\)
\(350\) −1.11871 −0.0597974
\(351\) −13.0015 −0.693970
\(352\) 6.32315 0.337025
\(353\) 16.6467 0.886013 0.443007 0.896518i \(-0.353912\pi\)
0.443007 + 0.896518i \(0.353912\pi\)
\(354\) 12.4691 0.662725
\(355\) −4.56770 −0.242428
\(356\) 7.99086 0.423515
\(357\) −8.30039 −0.439303
\(358\) −15.8541 −0.837913
\(359\) 21.7678 1.14886 0.574430 0.818554i \(-0.305224\pi\)
0.574430 + 0.818554i \(0.305224\pi\)
\(360\) 0.563364 0.0296919
\(361\) −17.8221 −0.938005
\(362\) 23.0672 1.21238
\(363\) −54.7093 −2.87149
\(364\) −3.16220 −0.165744
\(365\) 16.1342 0.844501
\(366\) 22.2483 1.16294
\(367\) −25.6853 −1.34076 −0.670382 0.742017i \(-0.733870\pi\)
−0.670382 + 0.742017i \(0.733870\pi\)
\(368\) 5.37635 0.280261
\(369\) 6.73885 0.350811
\(370\) −0.283699 −0.0147488
\(371\) −0.327932 −0.0170254
\(372\) −7.33775 −0.380445
\(373\) 0.356374 0.0184524 0.00922618 0.999957i \(-0.497063\pi\)
0.00922618 + 0.999957i \(0.497063\pi\)
\(374\) 24.8534 1.28514
\(375\) 1.88769 0.0974798
\(376\) 6.23186 0.321384
\(377\) −8.68908 −0.447510
\(378\) −5.14561 −0.264662
\(379\) −21.9006 −1.12496 −0.562480 0.826811i \(-0.690153\pi\)
−0.562480 + 0.826811i \(0.690153\pi\)
\(380\) 1.08531 0.0556755
\(381\) −31.7475 −1.62648
\(382\) 0.0467554 0.00239222
\(383\) 21.5332 1.10029 0.550146 0.835068i \(-0.314572\pi\)
0.550146 + 0.835068i \(0.314572\pi\)
\(384\) 1.88769 0.0963306
\(385\) 7.07375 0.360512
\(386\) −6.39884 −0.325692
\(387\) −5.73071 −0.291309
\(388\) −8.56664 −0.434905
\(389\) 32.5057 1.64810 0.824052 0.566514i \(-0.191708\pi\)
0.824052 + 0.566514i \(0.191708\pi\)
\(390\) 5.33585 0.270191
\(391\) 21.1319 1.06869
\(392\) 5.74849 0.290343
\(393\) −17.6351 −0.889572
\(394\) 12.5182 0.630656
\(395\) 11.2037 0.563717
\(396\) −3.56223 −0.179009
\(397\) 2.06463 0.103621 0.0518104 0.998657i \(-0.483501\pi\)
0.0518104 + 0.998657i \(0.483501\pi\)
\(398\) 5.08884 0.255080
\(399\) 2.29193 0.114740
\(400\) 1.00000 0.0500000
\(401\) −1.00000 −0.0499376
\(402\) 26.9455 1.34392
\(403\) −10.9877 −0.547335
\(404\) −1.14404 −0.0569180
\(405\) 10.3727 0.515424
\(406\) −3.43888 −0.170669
\(407\) 1.79387 0.0889187
\(408\) 7.41963 0.367326
\(409\) 19.7765 0.977883 0.488942 0.872317i \(-0.337383\pi\)
0.488942 + 0.872317i \(0.337383\pi\)
\(410\) 11.9618 0.590752
\(411\) 19.0997 0.942120
\(412\) −16.5367 −0.814704
\(413\) 7.38961 0.363619
\(414\) −3.02884 −0.148859
\(415\) 6.28436 0.308487
\(416\) 2.82666 0.138588
\(417\) 34.7995 1.70414
\(418\) −6.86261 −0.335661
\(419\) −12.3716 −0.604390 −0.302195 0.953246i \(-0.597719\pi\)
−0.302195 + 0.953246i \(0.597719\pi\)
\(420\) 2.11177 0.103044
\(421\) −12.3321 −0.601031 −0.300515 0.953777i \(-0.597159\pi\)
−0.300515 + 0.953777i \(0.597159\pi\)
\(422\) 15.9524 0.776549
\(423\) −3.51080 −0.170701
\(424\) 0.293135 0.0142359
\(425\) 3.93054 0.190659
\(426\) 8.62239 0.417756
\(427\) 13.1851 0.638070
\(428\) −0.551506 −0.0266580
\(429\) −33.7393 −1.62895
\(430\) −10.1723 −0.490553
\(431\) 8.60836 0.414650 0.207325 0.978272i \(-0.433524\pi\)
0.207325 + 0.978272i \(0.433524\pi\)
\(432\) 4.59961 0.221299
\(433\) 38.3308 1.84206 0.921029 0.389493i \(-0.127350\pi\)
0.921029 + 0.389493i \(0.127350\pi\)
\(434\) −4.34860 −0.208739
\(435\) 5.80270 0.278218
\(436\) 6.39040 0.306045
\(437\) −5.83503 −0.279127
\(438\) −30.4563 −1.45526
\(439\) −11.4306 −0.545553 −0.272777 0.962077i \(-0.587942\pi\)
−0.272777 + 0.962077i \(0.587942\pi\)
\(440\) −6.32315 −0.301444
\(441\) −3.23849 −0.154214
\(442\) 11.1103 0.528463
\(443\) −10.0730 −0.478581 −0.239290 0.970948i \(-0.576915\pi\)
−0.239290 + 0.970948i \(0.576915\pi\)
\(444\) 0.535534 0.0254153
\(445\) −7.99086 −0.378803
\(446\) 5.88038 0.278444
\(447\) −9.47646 −0.448221
\(448\) 1.11871 0.0528539
\(449\) −2.76964 −0.130707 −0.0653537 0.997862i \(-0.520818\pi\)
−0.0653537 + 0.997862i \(0.520818\pi\)
\(450\) −0.563364 −0.0265572
\(451\) −75.6363 −3.56158
\(452\) 17.6089 0.828254
\(453\) −20.1145 −0.945063
\(454\) −2.83467 −0.133037
\(455\) 3.16220 0.148246
\(456\) −2.04874 −0.0959408
\(457\) 11.5039 0.538131 0.269066 0.963122i \(-0.413285\pi\)
0.269066 + 0.963122i \(0.413285\pi\)
\(458\) −0.844296 −0.0394513
\(459\) 18.0789 0.843853
\(460\) −5.37635 −0.250673
\(461\) −27.0428 −1.25951 −0.629753 0.776795i \(-0.716844\pi\)
−0.629753 + 0.776795i \(0.716844\pi\)
\(462\) −13.3530 −0.621239
\(463\) −6.63967 −0.308571 −0.154286 0.988026i \(-0.549308\pi\)
−0.154286 + 0.988026i \(0.549308\pi\)
\(464\) 3.07398 0.142706
\(465\) 7.33775 0.340280
\(466\) 10.7431 0.497663
\(467\) −29.1236 −1.34768 −0.673840 0.738878i \(-0.735356\pi\)
−0.673840 + 0.738878i \(0.735356\pi\)
\(468\) −1.59244 −0.0736104
\(469\) 15.9688 0.737370
\(470\) −6.23186 −0.287454
\(471\) −21.3755 −0.984930
\(472\) −6.60549 −0.304042
\(473\) 64.3211 2.95749
\(474\) −21.1490 −0.971406
\(475\) −1.08531 −0.0497977
\(476\) 4.39712 0.201542
\(477\) −0.165141 −0.00756130
\(478\) −19.0311 −0.870460
\(479\) −24.4284 −1.11616 −0.558082 0.829786i \(-0.688463\pi\)
−0.558082 + 0.829786i \(0.688463\pi\)
\(480\) −1.88769 −0.0861607
\(481\) 0.801919 0.0365644
\(482\) −11.7762 −0.536389
\(483\) −11.3536 −0.516607
\(484\) 28.9822 1.31737
\(485\) 8.56664 0.388991
\(486\) −5.78161 −0.262259
\(487\) 13.9875 0.633832 0.316916 0.948454i \(-0.397353\pi\)
0.316916 + 0.948454i \(0.397353\pi\)
\(488\) −11.7860 −0.533527
\(489\) 37.9365 1.71555
\(490\) −5.74849 −0.259691
\(491\) 14.0743 0.635164 0.317582 0.948231i \(-0.397129\pi\)
0.317582 + 0.948231i \(0.397129\pi\)
\(492\) −22.5802 −1.01799
\(493\) 12.0824 0.544163
\(494\) −3.06781 −0.138027
\(495\) 3.56223 0.160110
\(496\) 3.88716 0.174539
\(497\) 5.10992 0.229211
\(498\) −11.8629 −0.531589
\(499\) −31.8753 −1.42693 −0.713466 0.700690i \(-0.752876\pi\)
−0.713466 + 0.700690i \(0.752876\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 8.75609 0.391193
\(502\) 19.1035 0.852629
\(503\) −20.0354 −0.893336 −0.446668 0.894700i \(-0.647389\pi\)
−0.446668 + 0.894700i \(0.647389\pi\)
\(504\) −0.630239 −0.0280731
\(505\) 1.14404 0.0509090
\(506\) 33.9954 1.51128
\(507\) 9.45733 0.420015
\(508\) 16.8182 0.746188
\(509\) −43.8582 −1.94398 −0.971990 0.235020i \(-0.924484\pi\)
−0.971990 + 0.235020i \(0.924484\pi\)
\(510\) −7.41963 −0.328547
\(511\) −18.0494 −0.798459
\(512\) −1.00000 −0.0441942
\(513\) −4.99202 −0.220403
\(514\) −6.77930 −0.299022
\(515\) 16.5367 0.728693
\(516\) 19.2022 0.845328
\(517\) 39.4050 1.73303
\(518\) 0.317376 0.0139447
\(519\) 21.7729 0.955726
\(520\) −2.82666 −0.123957
\(521\) 13.3044 0.582878 0.291439 0.956589i \(-0.405866\pi\)
0.291439 + 0.956589i \(0.405866\pi\)
\(522\) −1.73177 −0.0757973
\(523\) 42.5883 1.86226 0.931128 0.364693i \(-0.118826\pi\)
0.931128 + 0.364693i \(0.118826\pi\)
\(524\) 9.34216 0.408114
\(525\) −2.11177 −0.0921652
\(526\) 23.3670 1.01885
\(527\) 15.2787 0.665549
\(528\) 11.9361 0.519453
\(529\) 5.90511 0.256744
\(530\) −0.293135 −0.0127330
\(531\) 3.72129 0.161490
\(532\) −1.21415 −0.0526401
\(533\) −33.8120 −1.46456
\(534\) 15.0842 0.652759
\(535\) 0.551506 0.0238437
\(536\) −14.2743 −0.616557
\(537\) −29.9275 −1.29147
\(538\) −6.81642 −0.293877
\(539\) 36.3486 1.56564
\(540\) −4.59961 −0.197936
\(541\) 17.1178 0.735954 0.367977 0.929835i \(-0.380051\pi\)
0.367977 + 0.929835i \(0.380051\pi\)
\(542\) −2.58394 −0.110990
\(543\) 43.5436 1.86863
\(544\) −3.93054 −0.168520
\(545\) −6.39040 −0.273735
\(546\) −5.96925 −0.255460
\(547\) −21.8392 −0.933776 −0.466888 0.884316i \(-0.654625\pi\)
−0.466888 + 0.884316i \(0.654625\pi\)
\(548\) −10.1181 −0.432222
\(549\) 6.63979 0.283380
\(550\) 6.32315 0.269620
\(551\) −3.33623 −0.142128
\(552\) 10.1489 0.431964
\(553\) −12.5336 −0.532984
\(554\) 26.6772 1.13341
\(555\) −0.535534 −0.0227322
\(556\) −18.4350 −0.781818
\(557\) 22.3679 0.947760 0.473880 0.880589i \(-0.342853\pi\)
0.473880 + 0.880589i \(0.342853\pi\)
\(558\) −2.18989 −0.0927053
\(559\) 28.7537 1.21615
\(560\) −1.11871 −0.0472740
\(561\) 46.9154 1.98077
\(562\) −14.4915 −0.611288
\(563\) 3.39487 0.143077 0.0715383 0.997438i \(-0.477209\pi\)
0.0715383 + 0.997438i \(0.477209\pi\)
\(564\) 11.7638 0.495346
\(565\) −17.6089 −0.740813
\(566\) −1.14439 −0.0481025
\(567\) −11.6040 −0.487323
\(568\) −4.56770 −0.191656
\(569\) −40.4114 −1.69414 −0.847068 0.531484i \(-0.821634\pi\)
−0.847068 + 0.531484i \(0.821634\pi\)
\(570\) 2.04874 0.0858121
\(571\) 5.23106 0.218913 0.109457 0.993992i \(-0.465089\pi\)
0.109457 + 0.993992i \(0.465089\pi\)
\(572\) 17.8734 0.747323
\(573\) 0.0882596 0.00368710
\(574\) −13.3818 −0.558544
\(575\) 5.37635 0.224209
\(576\) 0.563364 0.0234735
\(577\) 6.48134 0.269822 0.134911 0.990858i \(-0.456925\pi\)
0.134911 + 0.990858i \(0.456925\pi\)
\(578\) 1.55086 0.0645074
\(579\) −12.0790 −0.501987
\(580\) −3.07398 −0.127640
\(581\) −7.03035 −0.291668
\(582\) −16.1711 −0.670315
\(583\) 1.85353 0.0767655
\(584\) 16.1342 0.667637
\(585\) 1.59244 0.0658391
\(586\) 27.9405 1.15421
\(587\) 9.53819 0.393683 0.196842 0.980435i \(-0.436931\pi\)
0.196842 + 0.980435i \(0.436931\pi\)
\(588\) 10.8514 0.447503
\(589\) −4.21880 −0.173833
\(590\) 6.60549 0.271944
\(591\) 23.6304 0.972023
\(592\) −0.283699 −0.0116599
\(593\) −36.0759 −1.48146 −0.740730 0.671803i \(-0.765520\pi\)
−0.740730 + 0.671803i \(0.765520\pi\)
\(594\) 29.0840 1.19333
\(595\) −4.39712 −0.180264
\(596\) 5.02014 0.205633
\(597\) 9.60614 0.393153
\(598\) 15.1971 0.621455
\(599\) −7.81205 −0.319192 −0.159596 0.987182i \(-0.551019\pi\)
−0.159596 + 0.987182i \(0.551019\pi\)
\(600\) 1.88769 0.0770645
\(601\) 26.5910 1.08467 0.542335 0.840162i \(-0.317540\pi\)
0.542335 + 0.840162i \(0.317540\pi\)
\(602\) 11.3798 0.463808
\(603\) 8.04164 0.327481
\(604\) 10.6556 0.433572
\(605\) −28.9822 −1.17829
\(606\) −2.15959 −0.0877272
\(607\) 28.9721 1.17594 0.587971 0.808882i \(-0.299927\pi\)
0.587971 + 0.808882i \(0.299927\pi\)
\(608\) 1.08531 0.0440153
\(609\) −6.49153 −0.263050
\(610\) 11.7860 0.477201
\(611\) 17.6153 0.712640
\(612\) 2.21432 0.0895087
\(613\) −41.4118 −1.67261 −0.836304 0.548266i \(-0.815288\pi\)
−0.836304 + 0.548266i \(0.815288\pi\)
\(614\) 16.9869 0.685535
\(615\) 22.5802 0.910521
\(616\) 7.07375 0.285009
\(617\) −17.3638 −0.699040 −0.349520 0.936929i \(-0.613655\pi\)
−0.349520 + 0.936929i \(0.613655\pi\)
\(618\) −31.2161 −1.25570
\(619\) 24.6645 0.991351 0.495676 0.868508i \(-0.334921\pi\)
0.495676 + 0.868508i \(0.334921\pi\)
\(620\) −3.88716 −0.156112
\(621\) 24.7291 0.992344
\(622\) 31.2663 1.25367
\(623\) 8.93943 0.358151
\(624\) 5.33585 0.213605
\(625\) 1.00000 0.0400000
\(626\) −24.6006 −0.983238
\(627\) −12.9545 −0.517351
\(628\) 11.3236 0.451862
\(629\) −1.11509 −0.0444615
\(630\) 0.630239 0.0251093
\(631\) −4.10085 −0.163252 −0.0816261 0.996663i \(-0.526011\pi\)
−0.0816261 + 0.996663i \(0.526011\pi\)
\(632\) 11.2037 0.445658
\(633\) 30.1131 1.19689
\(634\) 12.4915 0.496100
\(635\) −16.8182 −0.667410
\(636\) 0.553346 0.0219416
\(637\) 16.2490 0.643810
\(638\) 19.4372 0.769526
\(639\) 2.57328 0.101797
\(640\) 1.00000 0.0395285
\(641\) 3.53153 0.139487 0.0697434 0.997565i \(-0.477782\pi\)
0.0697434 + 0.997565i \(0.477782\pi\)
\(642\) −1.04107 −0.0410878
\(643\) −1.61958 −0.0638698 −0.0319349 0.999490i \(-0.510167\pi\)
−0.0319349 + 0.999490i \(0.510167\pi\)
\(644\) 6.01456 0.237007
\(645\) −19.2022 −0.756084
\(646\) 4.26587 0.167839
\(647\) −19.8361 −0.779838 −0.389919 0.920849i \(-0.627497\pi\)
−0.389919 + 0.920849i \(0.627497\pi\)
\(648\) 10.3727 0.407479
\(649\) −41.7675 −1.63952
\(650\) 2.82666 0.110871
\(651\) −8.20879 −0.321728
\(652\) −20.0968 −0.787053
\(653\) 5.88330 0.230231 0.115116 0.993352i \(-0.463276\pi\)
0.115116 + 0.993352i \(0.463276\pi\)
\(654\) 12.0631 0.471704
\(655\) −9.34216 −0.365029
\(656\) 11.9618 0.467031
\(657\) −9.08940 −0.354611
\(658\) 6.97163 0.271782
\(659\) 13.9830 0.544700 0.272350 0.962198i \(-0.412199\pi\)
0.272350 + 0.962198i \(0.412199\pi\)
\(660\) −11.9361 −0.464613
\(661\) −26.3791 −1.02603 −0.513015 0.858380i \(-0.671471\pi\)
−0.513015 + 0.858380i \(0.671471\pi\)
\(662\) 33.8103 1.31407
\(663\) 20.9728 0.814514
\(664\) 6.28436 0.243880
\(665\) 1.21415 0.0470827
\(666\) 0.159825 0.00619311
\(667\) 16.5268 0.639919
\(668\) −4.63853 −0.179470
\(669\) 11.1003 0.429163
\(670\) 14.2743 0.551466
\(671\) −74.5245 −2.87699
\(672\) 2.11177 0.0814633
\(673\) −15.1399 −0.583600 −0.291800 0.956479i \(-0.594254\pi\)
−0.291800 + 0.956479i \(0.594254\pi\)
\(674\) −5.49671 −0.211725
\(675\) 4.59961 0.177039
\(676\) −5.01001 −0.192693
\(677\) −30.4463 −1.17015 −0.585073 0.810981i \(-0.698934\pi\)
−0.585073 + 0.810981i \(0.698934\pi\)
\(678\) 33.2402 1.27658
\(679\) −9.58356 −0.367783
\(680\) 3.93054 0.150729
\(681\) −5.35096 −0.205049
\(682\) 24.5791 0.941183
\(683\) 28.6511 1.09630 0.548151 0.836379i \(-0.315332\pi\)
0.548151 + 0.836379i \(0.315332\pi\)
\(684\) −0.611427 −0.0233785
\(685\) 10.1181 0.386591
\(686\) 14.2618 0.544519
\(687\) −1.59377 −0.0608060
\(688\) −10.1723 −0.387816
\(689\) 0.828591 0.0315668
\(690\) −10.1489 −0.386361
\(691\) −19.6343 −0.746922 −0.373461 0.927646i \(-0.621829\pi\)
−0.373461 + 0.927646i \(0.621829\pi\)
\(692\) −11.5342 −0.438464
\(693\) −3.98509 −0.151381
\(694\) 4.26340 0.161836
\(695\) 18.4350 0.699279
\(696\) 5.80270 0.219951
\(697\) 47.0164 1.78087
\(698\) −20.0459 −0.758747
\(699\) 20.2796 0.767043
\(700\) 1.11871 0.0422832
\(701\) 26.9110 1.01641 0.508207 0.861235i \(-0.330309\pi\)
0.508207 + 0.861235i \(0.330309\pi\)
\(702\) 13.0015 0.490711
\(703\) 0.307902 0.0116128
\(704\) −6.32315 −0.238313
\(705\) −11.7638 −0.443051
\(706\) −16.6467 −0.626506
\(707\) −1.27984 −0.0481335
\(708\) −12.4691 −0.468618
\(709\) 43.8293 1.64604 0.823022 0.568009i \(-0.192286\pi\)
0.823022 + 0.568009i \(0.192286\pi\)
\(710\) 4.56770 0.171423
\(711\) −6.31173 −0.236709
\(712\) −7.99086 −0.299470
\(713\) 20.8987 0.782664
\(714\) 8.30039 0.310634
\(715\) −17.8734 −0.668426
\(716\) 15.8541 0.592494
\(717\) −35.9247 −1.34163
\(718\) −21.7678 −0.812367
\(719\) 12.7580 0.475792 0.237896 0.971291i \(-0.423542\pi\)
0.237896 + 0.971291i \(0.423542\pi\)
\(720\) −0.563364 −0.0209953
\(721\) −18.4997 −0.688965
\(722\) 17.8221 0.663270
\(723\) −22.2297 −0.826732
\(724\) −23.0672 −0.857284
\(725\) 3.07398 0.114165
\(726\) 54.7093 2.03045
\(727\) 17.8320 0.661352 0.330676 0.943744i \(-0.392723\pi\)
0.330676 + 0.943744i \(0.392723\pi\)
\(728\) 3.16220 0.117199
\(729\) 20.2043 0.748306
\(730\) −16.1342 −0.597152
\(731\) −39.9827 −1.47881
\(732\) −22.2483 −0.822319
\(733\) 19.6882 0.727201 0.363601 0.931555i \(-0.381547\pi\)
0.363601 + 0.931555i \(0.381547\pi\)
\(734\) 25.6853 0.948063
\(735\) −10.8514 −0.400258
\(736\) −5.37635 −0.198175
\(737\) −90.2587 −3.32472
\(738\) −6.73885 −0.248061
\(739\) −28.9558 −1.06516 −0.532579 0.846380i \(-0.678777\pi\)
−0.532579 + 0.846380i \(0.678777\pi\)
\(740\) 0.283699 0.0104290
\(741\) −5.79107 −0.212740
\(742\) 0.327932 0.0120388
\(743\) −17.2562 −0.633070 −0.316535 0.948581i \(-0.602519\pi\)
−0.316535 + 0.948581i \(0.602519\pi\)
\(744\) 7.33775 0.269015
\(745\) −5.02014 −0.183924
\(746\) −0.356374 −0.0130478
\(747\) −3.54038 −0.129536
\(748\) −24.8534 −0.908729
\(749\) −0.616974 −0.0225437
\(750\) −1.88769 −0.0689286
\(751\) 9.47577 0.345776 0.172888 0.984942i \(-0.444690\pi\)
0.172888 + 0.984942i \(0.444690\pi\)
\(752\) −6.23186 −0.227253
\(753\) 36.0614 1.31415
\(754\) 8.68908 0.316437
\(755\) −10.6556 −0.387799
\(756\) 5.14561 0.187144
\(757\) −33.2134 −1.20716 −0.603581 0.797302i \(-0.706260\pi\)
−0.603581 + 0.797302i \(0.706260\pi\)
\(758\) 21.9006 0.795467
\(759\) 64.1727 2.32932
\(760\) −1.08531 −0.0393685
\(761\) 25.4815 0.923703 0.461852 0.886957i \(-0.347185\pi\)
0.461852 + 0.886957i \(0.347185\pi\)
\(762\) 31.7475 1.15009
\(763\) 7.14899 0.258811
\(764\) −0.0467554 −0.00169155
\(765\) −2.21432 −0.0800590
\(766\) −21.5332 −0.778025
\(767\) −18.6715 −0.674187
\(768\) −1.88769 −0.0681161
\(769\) −38.3795 −1.38400 −0.691999 0.721898i \(-0.743270\pi\)
−0.691999 + 0.721898i \(0.743270\pi\)
\(770\) −7.07375 −0.254920
\(771\) −12.7972 −0.460880
\(772\) 6.39884 0.230299
\(773\) −47.4193 −1.70555 −0.852777 0.522275i \(-0.825083\pi\)
−0.852777 + 0.522275i \(0.825083\pi\)
\(774\) 5.73071 0.205986
\(775\) 3.88716 0.139631
\(776\) 8.56664 0.307524
\(777\) 0.599106 0.0214928
\(778\) −32.5057 −1.16539
\(779\) −12.9823 −0.465141
\(780\) −5.33585 −0.191054
\(781\) −28.8822 −1.03349
\(782\) −21.1319 −0.755677
\(783\) 14.1391 0.505289
\(784\) −5.74849 −0.205303
\(785\) −11.3236 −0.404158
\(786\) 17.6351 0.629023
\(787\) 29.2019 1.04093 0.520467 0.853882i \(-0.325758\pi\)
0.520467 + 0.853882i \(0.325758\pi\)
\(788\) −12.5182 −0.445941
\(789\) 44.1097 1.57035
\(790\) −11.2037 −0.398608
\(791\) 19.6992 0.700424
\(792\) 3.56223 0.126578
\(793\) −33.3149 −1.18305
\(794\) −2.06463 −0.0732709
\(795\) −0.553346 −0.0196252
\(796\) −5.08884 −0.180369
\(797\) 30.7905 1.09065 0.545327 0.838223i \(-0.316405\pi\)
0.545327 + 0.838223i \(0.316405\pi\)
\(798\) −2.29193 −0.0811336
\(799\) −24.4946 −0.866556
\(800\) −1.00000 −0.0353553
\(801\) 4.50176 0.159062
\(802\) 1.00000 0.0353112
\(803\) 102.019 3.60016
\(804\) −26.9455 −0.950294
\(805\) −6.01456 −0.211985
\(806\) 10.9877 0.387025
\(807\) −12.8673 −0.452949
\(808\) 1.14404 0.0402471
\(809\) 40.3267 1.41781 0.708906 0.705303i \(-0.249189\pi\)
0.708906 + 0.705303i \(0.249189\pi\)
\(810\) −10.3727 −0.364460
\(811\) −47.0840 −1.65334 −0.826672 0.562684i \(-0.809769\pi\)
−0.826672 + 0.562684i \(0.809769\pi\)
\(812\) 3.43888 0.120681
\(813\) −4.87766 −0.171067
\(814\) −1.79387 −0.0628750
\(815\) 20.0968 0.703961
\(816\) −7.41963 −0.259739
\(817\) 11.0402 0.386247
\(818\) −19.7765 −0.691468
\(819\) −1.78147 −0.0622496
\(820\) −11.9618 −0.417725
\(821\) 47.0778 1.64303 0.821514 0.570188i \(-0.193130\pi\)
0.821514 + 0.570188i \(0.193130\pi\)
\(822\) −19.0997 −0.666179
\(823\) −0.172122 −0.00599978 −0.00299989 0.999996i \(-0.500955\pi\)
−0.00299989 + 0.999996i \(0.500955\pi\)
\(824\) 16.5367 0.576083
\(825\) 11.9361 0.415563
\(826\) −7.38961 −0.257117
\(827\) 17.9045 0.622602 0.311301 0.950311i \(-0.399235\pi\)
0.311301 + 0.950311i \(0.399235\pi\)
\(828\) 3.02884 0.105259
\(829\) 56.5520 1.96413 0.982066 0.188535i \(-0.0603739\pi\)
0.982066 + 0.188535i \(0.0603739\pi\)
\(830\) −6.28436 −0.218133
\(831\) 50.3582 1.74691
\(832\) −2.82666 −0.0979967
\(833\) −22.5947 −0.782859
\(834\) −34.7995 −1.20501
\(835\) 4.63853 0.160523
\(836\) 6.86261 0.237348
\(837\) 17.8794 0.618004
\(838\) 12.3716 0.427368
\(839\) −33.5857 −1.15951 −0.579753 0.814792i \(-0.696851\pi\)
−0.579753 + 0.814792i \(0.696851\pi\)
\(840\) −2.11177 −0.0728630
\(841\) −19.5507 −0.674161
\(842\) 12.3321 0.424993
\(843\) −27.3555 −0.942173
\(844\) −15.9524 −0.549103
\(845\) 5.01001 0.172349
\(846\) 3.51080 0.120704
\(847\) 32.4226 1.11405
\(848\) −0.293135 −0.0100663
\(849\) −2.16026 −0.0741398
\(850\) −3.93054 −0.134816
\(851\) −1.52526 −0.0522853
\(852\) −8.62239 −0.295398
\(853\) 12.4194 0.425234 0.212617 0.977136i \(-0.431801\pi\)
0.212617 + 0.977136i \(0.431801\pi\)
\(854\) −13.1851 −0.451184
\(855\) 0.611427 0.0209104
\(856\) 0.551506 0.0188501
\(857\) −19.8772 −0.678993 −0.339496 0.940607i \(-0.610257\pi\)
−0.339496 + 0.940607i \(0.610257\pi\)
\(858\) 33.7393 1.15184
\(859\) 7.25545 0.247553 0.123776 0.992310i \(-0.460499\pi\)
0.123776 + 0.992310i \(0.460499\pi\)
\(860\) 10.1723 0.346873
\(861\) −25.2606 −0.860879
\(862\) −8.60836 −0.293202
\(863\) −54.1785 −1.84426 −0.922129 0.386883i \(-0.873552\pi\)
−0.922129 + 0.386883i \(0.873552\pi\)
\(864\) −4.59961 −0.156482
\(865\) 11.5342 0.392174
\(866\) −38.3308 −1.30253
\(867\) 2.92754 0.0994246
\(868\) 4.34860 0.147601
\(869\) 70.8424 2.40316
\(870\) −5.80270 −0.196730
\(871\) −40.3486 −1.36716
\(872\) −6.39040 −0.216406
\(873\) −4.82613 −0.163340
\(874\) 5.83503 0.197373
\(875\) −1.11871 −0.0378192
\(876\) 30.4563 1.02902
\(877\) −48.4468 −1.63593 −0.817967 0.575265i \(-0.804899\pi\)
−0.817967 + 0.575265i \(0.804899\pi\)
\(878\) 11.4306 0.385764
\(879\) 52.7430 1.77898
\(880\) 6.32315 0.213153
\(881\) 21.8562 0.736354 0.368177 0.929756i \(-0.379982\pi\)
0.368177 + 0.929756i \(0.379982\pi\)
\(882\) 3.23849 0.109046
\(883\) −1.11929 −0.0376670 −0.0188335 0.999823i \(-0.505995\pi\)
−0.0188335 + 0.999823i \(0.505995\pi\)
\(884\) −11.1103 −0.373679
\(885\) 12.4691 0.419144
\(886\) 10.0730 0.338408
\(887\) −20.8129 −0.698827 −0.349414 0.936969i \(-0.613619\pi\)
−0.349414 + 0.936969i \(0.613619\pi\)
\(888\) −0.535534 −0.0179714
\(889\) 18.8147 0.631023
\(890\) 7.99086 0.267854
\(891\) 65.5882 2.19729
\(892\) −5.88038 −0.196890
\(893\) 6.76353 0.226333
\(894\) 9.47646 0.316940
\(895\) −15.8541 −0.529943
\(896\) −1.11871 −0.0373734
\(897\) 28.6874 0.957843
\(898\) 2.76964 0.0924241
\(899\) 11.9490 0.398523
\(900\) 0.563364 0.0187788
\(901\) −1.15218 −0.0383846
\(902\) 75.6363 2.51841
\(903\) 21.4816 0.714862
\(904\) −17.6089 −0.585664
\(905\) 23.0672 0.766778
\(906\) 20.1145 0.668260
\(907\) 11.6928 0.388252 0.194126 0.980977i \(-0.437813\pi\)
0.194126 + 0.980977i \(0.437813\pi\)
\(908\) 2.83467 0.0940717
\(909\) −0.644509 −0.0213770
\(910\) −3.16220 −0.104826
\(911\) −20.6054 −0.682686 −0.341343 0.939939i \(-0.610882\pi\)
−0.341343 + 0.939939i \(0.610882\pi\)
\(912\) 2.04874 0.0678404
\(913\) 39.7369 1.31510
\(914\) −11.5039 −0.380516
\(915\) 22.2483 0.735505
\(916\) 0.844296 0.0278963
\(917\) 10.4511 0.345127
\(918\) −18.0789 −0.596694
\(919\) −33.4146 −1.10224 −0.551122 0.834424i \(-0.685800\pi\)
−0.551122 + 0.834424i \(0.685800\pi\)
\(920\) 5.37635 0.177253
\(921\) 32.0659 1.05661
\(922\) 27.0428 0.890606
\(923\) −12.9113 −0.424981
\(924\) 13.3530 0.439282
\(925\) −0.283699 −0.00932795
\(926\) 6.63967 0.218193
\(927\) −9.31616 −0.305983
\(928\) −3.07398 −0.100908
\(929\) 22.2841 0.731118 0.365559 0.930788i \(-0.380878\pi\)
0.365559 + 0.930788i \(0.380878\pi\)
\(930\) −7.33775 −0.240614
\(931\) 6.23893 0.204473
\(932\) −10.7431 −0.351901
\(933\) 59.0211 1.93226
\(934\) 29.1236 0.952953
\(935\) 24.8534 0.812792
\(936\) 1.59244 0.0520504
\(937\) −36.2633 −1.18467 −0.592335 0.805691i \(-0.701794\pi\)
−0.592335 + 0.805691i \(0.701794\pi\)
\(938\) −15.9688 −0.521400
\(939\) −46.4382 −1.51545
\(940\) 6.23186 0.203261
\(941\) 20.1434 0.656655 0.328328 0.944564i \(-0.393515\pi\)
0.328328 + 0.944564i \(0.393515\pi\)
\(942\) 21.3755 0.696450
\(943\) 64.3109 2.09425
\(944\) 6.60549 0.214990
\(945\) −5.14561 −0.167387
\(946\) −64.3211 −2.09126
\(947\) −35.3544 −1.14886 −0.574432 0.818552i \(-0.694777\pi\)
−0.574432 + 0.818552i \(0.694777\pi\)
\(948\) 21.1490 0.686888
\(949\) 45.6058 1.48043
\(950\) 1.08531 0.0352123
\(951\) 23.5800 0.764634
\(952\) −4.39712 −0.142512
\(953\) 32.9513 1.06740 0.533699 0.845675i \(-0.320802\pi\)
0.533699 + 0.845675i \(0.320802\pi\)
\(954\) 0.165141 0.00534665
\(955\) 0.0467554 0.00151297
\(956\) 19.0311 0.615509
\(957\) 36.6913 1.18606
\(958\) 24.4284 0.789247
\(959\) −11.3191 −0.365514
\(960\) 1.88769 0.0609248
\(961\) −15.8900 −0.512579
\(962\) −0.801919 −0.0258549
\(963\) −0.310698 −0.0100121
\(964\) 11.7762 0.379285
\(965\) −6.39884 −0.205986
\(966\) 11.3536 0.365296
\(967\) −57.1028 −1.83630 −0.918152 0.396229i \(-0.870319\pi\)
−0.918152 + 0.396229i \(0.870319\pi\)
\(968\) −28.9822 −0.931523
\(969\) 8.05263 0.258688
\(970\) −8.56664 −0.275058
\(971\) −24.8459 −0.797344 −0.398672 0.917094i \(-0.630529\pi\)
−0.398672 + 0.917094i \(0.630529\pi\)
\(972\) 5.78161 0.185445
\(973\) −20.6234 −0.661154
\(974\) −13.9875 −0.448187
\(975\) 5.33585 0.170884
\(976\) 11.7860 0.377260
\(977\) −19.4149 −0.621139 −0.310570 0.950551i \(-0.600520\pi\)
−0.310570 + 0.950551i \(0.600520\pi\)
\(978\) −37.9365 −1.21308
\(979\) −50.5274 −1.61486
\(980\) 5.74849 0.183629
\(981\) 3.60012 0.114943
\(982\) −14.0743 −0.449128
\(983\) −25.1465 −0.802050 −0.401025 0.916067i \(-0.631346\pi\)
−0.401025 + 0.916067i \(0.631346\pi\)
\(984\) 22.5802 0.719830
\(985\) 12.5182 0.398862
\(986\) −12.0824 −0.384781
\(987\) 13.1603 0.418895
\(988\) 3.06781 0.0976002
\(989\) −54.6899 −1.73904
\(990\) −3.56223 −0.113215
\(991\) −54.4483 −1.72961 −0.864804 0.502109i \(-0.832558\pi\)
−0.864804 + 0.502109i \(0.832558\pi\)
\(992\) −3.88716 −0.123418
\(993\) 63.8233 2.02537
\(994\) −5.10992 −0.162077
\(995\) 5.08884 0.161327
\(996\) 11.8629 0.375890
\(997\) 15.8069 0.500608 0.250304 0.968167i \(-0.419469\pi\)
0.250304 + 0.968167i \(0.419469\pi\)
\(998\) 31.8753 1.00899
\(999\) −1.30490 −0.0412853
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 \(a_p\))