Properties

Label 8047.2.a.b.1.5
Level 8047
Weight 2
Character 8047.1
Self dual Yes
Analytic conductor 64.256
Analytic rank 1
Dimension 142
CM No

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Newspace parameters

Level: \( N \) = \( 8047 = 13 \cdot 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2556185065\)
Analytic rank: \(1\)
Dimension: \(142\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 8047.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.66381 q^{2} +1.33027 q^{3} +5.09589 q^{4} -0.440221 q^{5} -3.54360 q^{6} +2.49453 q^{7} -8.24687 q^{8} -1.23037 q^{9} +O(q^{10})\) \(q-2.66381 q^{2} +1.33027 q^{3} +5.09589 q^{4} -0.440221 q^{5} -3.54360 q^{6} +2.49453 q^{7} -8.24687 q^{8} -1.23037 q^{9} +1.17267 q^{10} -5.46776 q^{11} +6.77893 q^{12} +1.00000 q^{13} -6.64496 q^{14} -0.585614 q^{15} +11.7763 q^{16} +0.152671 q^{17} +3.27748 q^{18} +4.10836 q^{19} -2.24332 q^{20} +3.31841 q^{21} +14.5651 q^{22} -2.16586 q^{23} -10.9706 q^{24} -4.80621 q^{25} -2.66381 q^{26} -5.62755 q^{27} +12.7119 q^{28} +4.88879 q^{29} +1.55997 q^{30} +4.13458 q^{31} -14.8762 q^{32} -7.27361 q^{33} -0.406688 q^{34} -1.09815 q^{35} -6.26985 q^{36} +10.1206 q^{37} -10.9439 q^{38} +1.33027 q^{39} +3.63044 q^{40} -6.15833 q^{41} -8.83962 q^{42} -4.89590 q^{43} -27.8631 q^{44} +0.541636 q^{45} +5.76944 q^{46} +1.00342 q^{47} +15.6657 q^{48} -0.777305 q^{49} +12.8028 q^{50} +0.203095 q^{51} +5.09589 q^{52} +6.20913 q^{53} +14.9907 q^{54} +2.40702 q^{55} -20.5721 q^{56} +5.46524 q^{57} -13.0228 q^{58} +6.32041 q^{59} -2.98423 q^{60} -7.00282 q^{61} -11.0137 q^{62} -3.06921 q^{63} +16.0746 q^{64} -0.440221 q^{65} +19.3755 q^{66} -8.29660 q^{67} +0.777997 q^{68} -2.88118 q^{69} +2.92525 q^{70} -9.42526 q^{71} +10.1467 q^{72} +0.293707 q^{73} -26.9593 q^{74} -6.39357 q^{75} +20.9358 q^{76} -13.6395 q^{77} -3.54360 q^{78} +5.56071 q^{79} -5.18418 q^{80} -3.79506 q^{81} +16.4046 q^{82} +13.8116 q^{83} +16.9103 q^{84} -0.0672091 q^{85} +13.0418 q^{86} +6.50343 q^{87} +45.0919 q^{88} +4.02581 q^{89} -1.44282 q^{90} +2.49453 q^{91} -11.0370 q^{92} +5.50012 q^{93} -2.67292 q^{94} -1.80859 q^{95} -19.7894 q^{96} +11.3966 q^{97} +2.07060 q^{98} +6.72738 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} + O(q^{10}) \) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} - 25q^{10} - 25q^{11} - 62q^{12} + 142q^{13} - 57q^{14} - 14q^{15} + 111q^{16} - 141q^{17} - 29q^{18} - 3q^{19} - 87q^{20} - 19q^{21} - 24q^{22} - 69q^{23} - 40q^{24} + 87q^{25} - 13q^{26} - 95q^{27} - 34q^{28} - 147q^{29} - 2q^{30} - 21q^{31} - 66q^{32} - 62q^{33} - 6q^{34} - 59q^{35} + 74q^{36} - 37q^{37} - 76q^{38} - 26q^{39} - 61q^{40} - 97q^{41} - 29q^{42} - 33q^{43} - 57q^{44} - 86q^{45} - q^{46} - 102q^{47} - 141q^{48} + 70q^{49} - 28q^{50} - 13q^{51} + 129q^{52} - 137q^{53} - 29q^{54} - 24q^{55} - 130q^{56} - 65q^{57} - 15q^{58} - 56q^{59} + 11q^{60} - 77q^{61} - 150q^{62} - 32q^{63} + 73q^{64} - 37q^{65} - 32q^{66} - 9q^{67} - 226q^{68} - 113q^{69} + 6q^{70} - 18q^{71} - 82q^{72} - 117q^{73} - 70q^{74} - 83q^{75} + 40q^{76} - 214q^{77} - 15q^{78} - 52q^{79} - 161q^{80} - 10q^{81} - 36q^{82} - 74q^{83} + 53q^{84} + 2q^{85} + 17q^{86} - 49q^{87} - 29q^{88} - 171q^{89} - 57q^{90} - 14q^{91} - 187q^{92} - 39q^{93} + 13q^{94} - 150q^{95} - 47q^{96} - 126q^{97} - 85q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.66381 −1.88360 −0.941800 0.336175i \(-0.890867\pi\)
−0.941800 + 0.336175i \(0.890867\pi\)
\(3\) 1.33027 0.768034 0.384017 0.923326i \(-0.374540\pi\)
0.384017 + 0.923326i \(0.374540\pi\)
\(4\) 5.09589 2.54795
\(5\) −0.440221 −0.196873 −0.0984364 0.995143i \(-0.531384\pi\)
−0.0984364 + 0.995143i \(0.531384\pi\)
\(6\) −3.54360 −1.44667
\(7\) 2.49453 0.942845 0.471422 0.881908i \(-0.343741\pi\)
0.471422 + 0.881908i \(0.343741\pi\)
\(8\) −8.24687 −2.91571
\(9\) −1.23037 −0.410124
\(10\) 1.17267 0.370829
\(11\) −5.46776 −1.64859 −0.824295 0.566160i \(-0.808428\pi\)
−0.824295 + 0.566160i \(0.808428\pi\)
\(12\) 6.77893 1.95691
\(13\) 1.00000 0.277350
\(14\) −6.64496 −1.77594
\(15\) −0.585614 −0.151205
\(16\) 11.7763 2.94408
\(17\) 0.152671 0.0370282 0.0185141 0.999829i \(-0.494106\pi\)
0.0185141 + 0.999829i \(0.494106\pi\)
\(18\) 3.27748 0.772510
\(19\) 4.10836 0.942523 0.471261 0.881994i \(-0.343799\pi\)
0.471261 + 0.881994i \(0.343799\pi\)
\(20\) −2.24332 −0.501621
\(21\) 3.31841 0.724136
\(22\) 14.5651 3.10528
\(23\) −2.16586 −0.451613 −0.225806 0.974172i \(-0.572502\pi\)
−0.225806 + 0.974172i \(0.572502\pi\)
\(24\) −10.9706 −2.23936
\(25\) −4.80621 −0.961241
\(26\) −2.66381 −0.522416
\(27\) −5.62755 −1.08302
\(28\) 12.7119 2.40232
\(29\) 4.88879 0.907826 0.453913 0.891046i \(-0.350028\pi\)
0.453913 + 0.891046i \(0.350028\pi\)
\(30\) 1.55997 0.284809
\(31\) 4.13458 0.742592 0.371296 0.928515i \(-0.378914\pi\)
0.371296 + 0.928515i \(0.378914\pi\)
\(32\) −14.8762 −2.62976
\(33\) −7.27361 −1.26617
\(34\) −0.406688 −0.0697464
\(35\) −1.09815 −0.185621
\(36\) −6.26985 −1.04497
\(37\) 10.1206 1.66381 0.831907 0.554915i \(-0.187249\pi\)
0.831907 + 0.554915i \(0.187249\pi\)
\(38\) −10.9439 −1.77533
\(39\) 1.33027 0.213014
\(40\) 3.63044 0.574024
\(41\) −6.15833 −0.961770 −0.480885 0.876784i \(-0.659685\pi\)
−0.480885 + 0.876784i \(0.659685\pi\)
\(42\) −8.83962 −1.36398
\(43\) −4.89590 −0.746618 −0.373309 0.927707i \(-0.621777\pi\)
−0.373309 + 0.927707i \(0.621777\pi\)
\(44\) −27.8631 −4.20052
\(45\) 0.541636 0.0807424
\(46\) 5.76944 0.850658
\(47\) 1.00342 0.146364 0.0731819 0.997319i \(-0.476685\pi\)
0.0731819 + 0.997319i \(0.476685\pi\)
\(48\) 15.6657 2.26115
\(49\) −0.777305 −0.111044
\(50\) 12.8028 1.81059
\(51\) 0.203095 0.0284389
\(52\) 5.09589 0.706673
\(53\) 6.20913 0.852889 0.426445 0.904514i \(-0.359766\pi\)
0.426445 + 0.904514i \(0.359766\pi\)
\(54\) 14.9907 2.03998
\(55\) 2.40702 0.324563
\(56\) −20.5721 −2.74906
\(57\) 5.46524 0.723889
\(58\) −13.0228 −1.70998
\(59\) 6.32041 0.822847 0.411423 0.911444i \(-0.365032\pi\)
0.411423 + 0.911444i \(0.365032\pi\)
\(60\) −2.98423 −0.385262
\(61\) −7.00282 −0.896620 −0.448310 0.893878i \(-0.647974\pi\)
−0.448310 + 0.893878i \(0.647974\pi\)
\(62\) −11.0137 −1.39875
\(63\) −3.06921 −0.386684
\(64\) 16.0746 2.00933
\(65\) −0.440221 −0.0546027
\(66\) 19.3755 2.38496
\(67\) −8.29660 −1.01359 −0.506796 0.862066i \(-0.669170\pi\)
−0.506796 + 0.862066i \(0.669170\pi\)
\(68\) 0.777997 0.0943459
\(69\) −2.88118 −0.346854
\(70\) 2.92525 0.349635
\(71\) −9.42526 −1.11857 −0.559286 0.828975i \(-0.688925\pi\)
−0.559286 + 0.828975i \(0.688925\pi\)
\(72\) 10.1467 1.19580
\(73\) 0.293707 0.0343759 0.0171879 0.999852i \(-0.494529\pi\)
0.0171879 + 0.999852i \(0.494529\pi\)
\(74\) −26.9593 −3.13396
\(75\) −6.39357 −0.738265
\(76\) 20.9358 2.40150
\(77\) −13.6395 −1.55437
\(78\) −3.54360 −0.401233
\(79\) 5.56071 0.625629 0.312814 0.949814i \(-0.398728\pi\)
0.312814 + 0.949814i \(0.398728\pi\)
\(80\) −5.18418 −0.579609
\(81\) −3.79506 −0.421673
\(82\) 16.4046 1.81159
\(83\) 13.8116 1.51602 0.758010 0.652243i \(-0.226172\pi\)
0.758010 + 0.652243i \(0.226172\pi\)
\(84\) 16.9103 1.84506
\(85\) −0.0672091 −0.00728986
\(86\) 13.0418 1.40633
\(87\) 6.50343 0.697240
\(88\) 45.0919 4.80681
\(89\) 4.02581 0.426735 0.213368 0.976972i \(-0.431557\pi\)
0.213368 + 0.976972i \(0.431557\pi\)
\(90\) −1.44282 −0.152086
\(91\) 2.49453 0.261498
\(92\) −11.0370 −1.15068
\(93\) 5.50012 0.570335
\(94\) −2.67292 −0.275691
\(95\) −1.80859 −0.185557
\(96\) −19.7894 −2.01974
\(97\) 11.3966 1.15715 0.578577 0.815628i \(-0.303608\pi\)
0.578577 + 0.815628i \(0.303608\pi\)
\(98\) 2.07060 0.209162
\(99\) 6.72738 0.676127
\(100\) −24.4919 −2.44919
\(101\) −9.66762 −0.961964 −0.480982 0.876730i \(-0.659720\pi\)
−0.480982 + 0.876730i \(0.659720\pi\)
\(102\) −0.541006 −0.0535675
\(103\) 2.09117 0.206049 0.103024 0.994679i \(-0.467148\pi\)
0.103024 + 0.994679i \(0.467148\pi\)
\(104\) −8.24687 −0.808672
\(105\) −1.46083 −0.142563
\(106\) −16.5399 −1.60650
\(107\) −3.00777 −0.290772 −0.145386 0.989375i \(-0.546442\pi\)
−0.145386 + 0.989375i \(0.546442\pi\)
\(108\) −28.6774 −2.75948
\(109\) 6.49584 0.622189 0.311094 0.950379i \(-0.399304\pi\)
0.311094 + 0.950379i \(0.399304\pi\)
\(110\) −6.41185 −0.611346
\(111\) 13.4631 1.27786
\(112\) 29.3764 2.77581
\(113\) −14.8774 −1.39955 −0.699775 0.714364i \(-0.746716\pi\)
−0.699775 + 0.714364i \(0.746716\pi\)
\(114\) −14.5584 −1.36352
\(115\) 0.953457 0.0889103
\(116\) 24.9127 2.31309
\(117\) −1.23037 −0.113748
\(118\) −16.8364 −1.54991
\(119\) 0.380844 0.0349119
\(120\) 4.82948 0.440869
\(121\) 18.8964 1.71785
\(122\) 18.6542 1.68887
\(123\) −8.19226 −0.738672
\(124\) 21.0693 1.89208
\(125\) 4.31690 0.386115
\(126\) 8.17579 0.728357
\(127\) −9.08826 −0.806452 −0.403226 0.915100i \(-0.632111\pi\)
−0.403226 + 0.915100i \(0.632111\pi\)
\(128\) −13.0675 −1.15501
\(129\) −6.51289 −0.573428
\(130\) 1.17267 0.102850
\(131\) 13.2120 1.15433 0.577167 0.816626i \(-0.304158\pi\)
0.577167 + 0.816626i \(0.304158\pi\)
\(132\) −37.0655 −3.22614
\(133\) 10.2484 0.888653
\(134\) 22.1006 1.90920
\(135\) 2.47737 0.213218
\(136\) −1.25906 −0.107964
\(137\) 4.20245 0.359039 0.179520 0.983754i \(-0.442546\pi\)
0.179520 + 0.983754i \(0.442546\pi\)
\(138\) 7.67493 0.653334
\(139\) −2.66839 −0.226330 −0.113165 0.993576i \(-0.536099\pi\)
−0.113165 + 0.993576i \(0.536099\pi\)
\(140\) −5.59603 −0.472951
\(141\) 1.33482 0.112412
\(142\) 25.1071 2.10694
\(143\) −5.46776 −0.457237
\(144\) −14.4893 −1.20744
\(145\) −2.15215 −0.178726
\(146\) −0.782381 −0.0647503
\(147\) −1.03403 −0.0852852
\(148\) 51.5734 4.23931
\(149\) −17.9190 −1.46799 −0.733993 0.679157i \(-0.762345\pi\)
−0.733993 + 0.679157i \(0.762345\pi\)
\(150\) 17.0313 1.39060
\(151\) −5.57176 −0.453423 −0.226712 0.973962i \(-0.572798\pi\)
−0.226712 + 0.973962i \(0.572798\pi\)
\(152\) −33.8811 −2.74812
\(153\) −0.187843 −0.0151862
\(154\) 36.3331 2.92780
\(155\) −1.82013 −0.146196
\(156\) 6.77893 0.542748
\(157\) 4.61888 0.368627 0.184313 0.982868i \(-0.440994\pi\)
0.184313 + 0.982868i \(0.440994\pi\)
\(158\) −14.8127 −1.17843
\(159\) 8.25983 0.655047
\(160\) 6.54880 0.517728
\(161\) −5.40281 −0.425801
\(162\) 10.1093 0.794264
\(163\) −7.45500 −0.583921 −0.291961 0.956430i \(-0.594308\pi\)
−0.291961 + 0.956430i \(0.594308\pi\)
\(164\) −31.3822 −2.45054
\(165\) 3.20200 0.249275
\(166\) −36.7915 −2.85557
\(167\) −17.3687 −1.34403 −0.672014 0.740539i \(-0.734570\pi\)
−0.672014 + 0.740539i \(0.734570\pi\)
\(168\) −27.3665 −2.11137
\(169\) 1.00000 0.0769231
\(170\) 0.179032 0.0137312
\(171\) −5.05482 −0.386552
\(172\) −24.9490 −1.90234
\(173\) −12.3626 −0.939914 −0.469957 0.882689i \(-0.655731\pi\)
−0.469957 + 0.882689i \(0.655731\pi\)
\(174\) −17.3239 −1.31332
\(175\) −11.9892 −0.906301
\(176\) −64.3900 −4.85358
\(177\) 8.40787 0.631974
\(178\) −10.7240 −0.803798
\(179\) −12.6922 −0.948663 −0.474331 0.880346i \(-0.657310\pi\)
−0.474331 + 0.880346i \(0.657310\pi\)
\(180\) 2.76012 0.205727
\(181\) −16.3797 −1.21749 −0.608746 0.793365i \(-0.708327\pi\)
−0.608746 + 0.793365i \(0.708327\pi\)
\(182\) −6.64496 −0.492558
\(183\) −9.31567 −0.688634
\(184\) 17.8616 1.31677
\(185\) −4.45529 −0.327560
\(186\) −14.6513 −1.07428
\(187\) −0.834770 −0.0610444
\(188\) 5.11332 0.372927
\(189\) −14.0381 −1.02112
\(190\) 4.81773 0.349515
\(191\) −3.97075 −0.287314 −0.143657 0.989628i \(-0.545886\pi\)
−0.143657 + 0.989628i \(0.545886\pi\)
\(192\) 21.3837 1.54323
\(193\) −5.66275 −0.407614 −0.203807 0.979011i \(-0.565331\pi\)
−0.203807 + 0.979011i \(0.565331\pi\)
\(194\) −30.3585 −2.17961
\(195\) −0.585614 −0.0419367
\(196\) −3.96106 −0.282933
\(197\) 11.5263 0.821213 0.410607 0.911813i \(-0.365317\pi\)
0.410607 + 0.911813i \(0.365317\pi\)
\(198\) −17.9205 −1.27355
\(199\) 24.0615 1.70568 0.852838 0.522175i \(-0.174879\pi\)
0.852838 + 0.522175i \(0.174879\pi\)
\(200\) 39.6361 2.80270
\(201\) −11.0367 −0.778472
\(202\) 25.7527 1.81196
\(203\) 12.1952 0.855939
\(204\) 1.03495 0.0724608
\(205\) 2.71103 0.189346
\(206\) −5.57047 −0.388113
\(207\) 2.66482 0.185218
\(208\) 11.7763 0.816541
\(209\) −22.4635 −1.55383
\(210\) 3.89139 0.268531
\(211\) −27.9188 −1.92201 −0.961005 0.276532i \(-0.910815\pi\)
−0.961005 + 0.276532i \(0.910815\pi\)
\(212\) 31.6410 2.17311
\(213\) −12.5382 −0.859101
\(214\) 8.01212 0.547697
\(215\) 2.15528 0.146989
\(216\) 46.4097 3.15778
\(217\) 10.3138 0.700149
\(218\) −17.3037 −1.17195
\(219\) 0.390711 0.0264018
\(220\) 12.2659 0.826968
\(221\) 0.152671 0.0102698
\(222\) −35.8633 −2.40698
\(223\) 9.09228 0.608864 0.304432 0.952534i \(-0.401533\pi\)
0.304432 + 0.952534i \(0.401533\pi\)
\(224\) −37.1091 −2.47945
\(225\) 5.91343 0.394229
\(226\) 39.6306 2.63619
\(227\) −5.91878 −0.392843 −0.196422 0.980520i \(-0.562932\pi\)
−0.196422 + 0.980520i \(0.562932\pi\)
\(228\) 27.8503 1.84443
\(229\) −23.7366 −1.56856 −0.784279 0.620408i \(-0.786967\pi\)
−0.784279 + 0.620408i \(0.786967\pi\)
\(230\) −2.53983 −0.167471
\(231\) −18.1443 −1.19380
\(232\) −40.3172 −2.64695
\(233\) −4.06035 −0.266002 −0.133001 0.991116i \(-0.542461\pi\)
−0.133001 + 0.991116i \(0.542461\pi\)
\(234\) 3.27748 0.214256
\(235\) −0.441726 −0.0288151
\(236\) 32.2081 2.09657
\(237\) 7.39726 0.480504
\(238\) −1.01450 −0.0657600
\(239\) 15.2285 0.985048 0.492524 0.870299i \(-0.336074\pi\)
0.492524 + 0.870299i \(0.336074\pi\)
\(240\) −6.89638 −0.445159
\(241\) −15.3926 −0.991524 −0.495762 0.868458i \(-0.665111\pi\)
−0.495762 + 0.868458i \(0.665111\pi\)
\(242\) −50.3363 −3.23574
\(243\) 11.8342 0.759164
\(244\) −35.6856 −2.28454
\(245\) 0.342186 0.0218615
\(246\) 21.8226 1.39136
\(247\) 4.10836 0.261409
\(248\) −34.0973 −2.16518
\(249\) 18.3732 1.16435
\(250\) −11.4994 −0.727286
\(251\) −18.5682 −1.17201 −0.586007 0.810306i \(-0.699301\pi\)
−0.586007 + 0.810306i \(0.699301\pi\)
\(252\) −15.6403 −0.985249
\(253\) 11.8424 0.744525
\(254\) 24.2094 1.51903
\(255\) −0.0894065 −0.00559885
\(256\) 2.66003 0.166252
\(257\) −12.3395 −0.769720 −0.384860 0.922975i \(-0.625750\pi\)
−0.384860 + 0.922975i \(0.625750\pi\)
\(258\) 17.3491 1.08011
\(259\) 25.2461 1.56872
\(260\) −2.24332 −0.139125
\(261\) −6.01504 −0.372321
\(262\) −35.1942 −2.17430
\(263\) −25.1615 −1.55153 −0.775763 0.631025i \(-0.782635\pi\)
−0.775763 + 0.631025i \(0.782635\pi\)
\(264\) 59.9845 3.69179
\(265\) −2.73339 −0.167911
\(266\) −27.2999 −1.67387
\(267\) 5.35543 0.327747
\(268\) −42.2786 −2.58258
\(269\) 2.93704 0.179074 0.0895371 0.995983i \(-0.471461\pi\)
0.0895371 + 0.995983i \(0.471461\pi\)
\(270\) −6.59924 −0.401617
\(271\) 5.75609 0.349658 0.174829 0.984599i \(-0.444063\pi\)
0.174829 + 0.984599i \(0.444063\pi\)
\(272\) 1.79791 0.109014
\(273\) 3.31841 0.200839
\(274\) −11.1945 −0.676286
\(275\) 26.2792 1.58469
\(276\) −14.6822 −0.883765
\(277\) 1.30910 0.0786563 0.0393282 0.999226i \(-0.487478\pi\)
0.0393282 + 0.999226i \(0.487478\pi\)
\(278\) 7.10810 0.426316
\(279\) −5.08707 −0.304555
\(280\) 9.05626 0.541215
\(281\) −5.58080 −0.332922 −0.166461 0.986048i \(-0.553234\pi\)
−0.166461 + 0.986048i \(0.553234\pi\)
\(282\) −3.55571 −0.211740
\(283\) −14.5275 −0.863569 −0.431784 0.901977i \(-0.642116\pi\)
−0.431784 + 0.901977i \(0.642116\pi\)
\(284\) −48.0301 −2.85006
\(285\) −2.40591 −0.142514
\(286\) 14.5651 0.861251
\(287\) −15.3622 −0.906800
\(288\) 18.3032 1.07853
\(289\) −16.9767 −0.998629
\(290\) 5.73292 0.336648
\(291\) 15.1606 0.888732
\(292\) 1.49670 0.0875878
\(293\) −16.4954 −0.963672 −0.481836 0.876261i \(-0.660030\pi\)
−0.481836 + 0.876261i \(0.660030\pi\)
\(294\) 2.75446 0.160643
\(295\) −2.78238 −0.161996
\(296\) −83.4631 −4.85119
\(297\) 30.7701 1.78546
\(298\) 47.7330 2.76510
\(299\) −2.16586 −0.125255
\(300\) −32.5809 −1.88106
\(301\) −12.2130 −0.703945
\(302\) 14.8421 0.854068
\(303\) −12.8606 −0.738821
\(304\) 48.3814 2.77486
\(305\) 3.08279 0.176520
\(306\) 0.500378 0.0286047
\(307\) −2.81088 −0.160425 −0.0802127 0.996778i \(-0.525560\pi\)
−0.0802127 + 0.996778i \(0.525560\pi\)
\(308\) −69.5054 −3.96044
\(309\) 2.78182 0.158252
\(310\) 4.84848 0.275375
\(311\) −9.08501 −0.515163 −0.257582 0.966257i \(-0.582926\pi\)
−0.257582 + 0.966257i \(0.582926\pi\)
\(312\) −10.9706 −0.621087
\(313\) 5.66049 0.319950 0.159975 0.987121i \(-0.448859\pi\)
0.159975 + 0.987121i \(0.448859\pi\)
\(314\) −12.3038 −0.694345
\(315\) 1.35113 0.0761275
\(316\) 28.3368 1.59407
\(317\) 17.0508 0.957667 0.478834 0.877906i \(-0.341060\pi\)
0.478834 + 0.877906i \(0.341060\pi\)
\(318\) −22.0026 −1.23385
\(319\) −26.7307 −1.49663
\(320\) −7.07639 −0.395582
\(321\) −4.00115 −0.223322
\(322\) 14.3921 0.802038
\(323\) 0.627229 0.0349000
\(324\) −19.3392 −1.07440
\(325\) −4.80621 −0.266600
\(326\) 19.8587 1.09987
\(327\) 8.64124 0.477862
\(328\) 50.7870 2.80424
\(329\) 2.50306 0.137998
\(330\) −8.52951 −0.469534
\(331\) 15.9122 0.874613 0.437307 0.899312i \(-0.355932\pi\)
0.437307 + 0.899312i \(0.355932\pi\)
\(332\) 70.3824 3.86274
\(333\) −12.4521 −0.682371
\(334\) 46.2668 2.53161
\(335\) 3.65234 0.199549
\(336\) 39.0787 2.13192
\(337\) 20.4550 1.11426 0.557129 0.830426i \(-0.311903\pi\)
0.557129 + 0.830426i \(0.311903\pi\)
\(338\) −2.66381 −0.144892
\(339\) −19.7910 −1.07490
\(340\) −0.342490 −0.0185742
\(341\) −22.6069 −1.22423
\(342\) 13.4651 0.728108
\(343\) −19.4007 −1.04754
\(344\) 40.3759 2.17692
\(345\) 1.26836 0.0682861
\(346\) 32.9317 1.77042
\(347\) 16.6060 0.891454 0.445727 0.895169i \(-0.352945\pi\)
0.445727 + 0.895169i \(0.352945\pi\)
\(348\) 33.1407 1.77653
\(349\) −30.0478 −1.60842 −0.804212 0.594343i \(-0.797412\pi\)
−0.804212 + 0.594343i \(0.797412\pi\)
\(350\) 31.9371 1.70711
\(351\) −5.62755 −0.300377
\(352\) 81.3392 4.33539
\(353\) 25.2855 1.34581 0.672905 0.739728i \(-0.265046\pi\)
0.672905 + 0.739728i \(0.265046\pi\)
\(354\) −22.3970 −1.19039
\(355\) 4.14920 0.220216
\(356\) 20.5151 1.08730
\(357\) 0.506626 0.0268135
\(358\) 33.8097 1.78690
\(359\) 20.3577 1.07444 0.537219 0.843443i \(-0.319475\pi\)
0.537219 + 0.843443i \(0.319475\pi\)
\(360\) −4.46680 −0.235421
\(361\) −2.12137 −0.111651
\(362\) 43.6324 2.29327
\(363\) 25.1373 1.31937
\(364\) 12.7119 0.666283
\(365\) −0.129296 −0.00676767
\(366\) 24.8152 1.29711
\(367\) −32.8217 −1.71328 −0.856640 0.515915i \(-0.827452\pi\)
−0.856640 + 0.515915i \(0.827452\pi\)
\(368\) −25.5059 −1.32958
\(369\) 7.57705 0.394445
\(370\) 11.8681 0.616991
\(371\) 15.4889 0.804142
\(372\) 28.0280 1.45318
\(373\) −26.0814 −1.35044 −0.675221 0.737615i \(-0.735952\pi\)
−0.675221 + 0.737615i \(0.735952\pi\)
\(374\) 2.22367 0.114983
\(375\) 5.74265 0.296549
\(376\) −8.27507 −0.426754
\(377\) 4.88879 0.251786
\(378\) 37.3949 1.92339
\(379\) −12.5468 −0.644487 −0.322243 0.946657i \(-0.604437\pi\)
−0.322243 + 0.946657i \(0.604437\pi\)
\(380\) −9.21636 −0.472789
\(381\) −12.0899 −0.619382
\(382\) 10.5773 0.541184
\(383\) −20.3825 −1.04150 −0.520750 0.853709i \(-0.674348\pi\)
−0.520750 + 0.853709i \(0.674348\pi\)
\(384\) −17.3833 −0.887089
\(385\) 6.00439 0.306012
\(386\) 15.0845 0.767781
\(387\) 6.02379 0.306206
\(388\) 58.0760 2.94836
\(389\) −13.6265 −0.690891 −0.345445 0.938439i \(-0.612272\pi\)
−0.345445 + 0.938439i \(0.612272\pi\)
\(390\) 1.55997 0.0789919
\(391\) −0.330665 −0.0167224
\(392\) 6.41034 0.323771
\(393\) 17.5755 0.886568
\(394\) −30.7038 −1.54684
\(395\) −2.44794 −0.123169
\(396\) 34.2820 1.72274
\(397\) −5.21873 −0.261921 −0.130960 0.991388i \(-0.541806\pi\)
−0.130960 + 0.991388i \(0.541806\pi\)
\(398\) −64.0954 −3.21281
\(399\) 13.6332 0.682515
\(400\) −56.5994 −2.82997
\(401\) −12.2240 −0.610438 −0.305219 0.952282i \(-0.598730\pi\)
−0.305219 + 0.952282i \(0.598730\pi\)
\(402\) 29.3998 1.46633
\(403\) 4.13458 0.205958
\(404\) −49.2651 −2.45103
\(405\) 1.67067 0.0830160
\(406\) −32.4858 −1.61225
\(407\) −55.3369 −2.74295
\(408\) −1.67489 −0.0829196
\(409\) 1.65730 0.0819481 0.0409741 0.999160i \(-0.486954\pi\)
0.0409741 + 0.999160i \(0.486954\pi\)
\(410\) −7.22167 −0.356653
\(411\) 5.59041 0.275754
\(412\) 10.6564 0.525001
\(413\) 15.7665 0.775817
\(414\) −7.09857 −0.348876
\(415\) −6.08016 −0.298463
\(416\) −14.8762 −0.729364
\(417\) −3.54969 −0.173829
\(418\) 59.8386 2.92680
\(419\) 11.7516 0.574104 0.287052 0.957915i \(-0.407325\pi\)
0.287052 + 0.957915i \(0.407325\pi\)
\(420\) −7.44425 −0.363242
\(421\) −29.9855 −1.46140 −0.730702 0.682696i \(-0.760807\pi\)
−0.730702 + 0.682696i \(0.760807\pi\)
\(422\) 74.3704 3.62030
\(423\) −1.23458 −0.0600274
\(424\) −51.2058 −2.48678
\(425\) −0.733770 −0.0355931
\(426\) 33.3993 1.61820
\(427\) −17.4688 −0.845373
\(428\) −15.3272 −0.740870
\(429\) −7.27361 −0.351173
\(430\) −5.74126 −0.276868
\(431\) −7.89639 −0.380356 −0.190178 0.981750i \(-0.560906\pi\)
−0.190178 + 0.981750i \(0.560906\pi\)
\(432\) −66.2719 −3.18851
\(433\) 12.9655 0.623083 0.311541 0.950233i \(-0.399155\pi\)
0.311541 + 0.950233i \(0.399155\pi\)
\(434\) −27.4741 −1.31880
\(435\) −2.86295 −0.137268
\(436\) 33.1021 1.58530
\(437\) −8.89813 −0.425655
\(438\) −1.04078 −0.0497304
\(439\) 13.3872 0.638934 0.319467 0.947597i \(-0.396496\pi\)
0.319467 + 0.947597i \(0.396496\pi\)
\(440\) −19.8504 −0.946330
\(441\) 0.956376 0.0455417
\(442\) −0.406688 −0.0193442
\(443\) −0.0946884 −0.00449878 −0.00224939 0.999997i \(-0.500716\pi\)
−0.00224939 + 0.999997i \(0.500716\pi\)
\(444\) 68.6067 3.25593
\(445\) −1.77225 −0.0840126
\(446\) −24.2201 −1.14686
\(447\) −23.8372 −1.12746
\(448\) 40.0987 1.89449
\(449\) 15.3328 0.723601 0.361801 0.932256i \(-0.382162\pi\)
0.361801 + 0.932256i \(0.382162\pi\)
\(450\) −15.7523 −0.742568
\(451\) 33.6723 1.58557
\(452\) −75.8137 −3.56597
\(453\) −7.41196 −0.348244
\(454\) 15.7665 0.739959
\(455\) −1.09815 −0.0514819
\(456\) −45.0711 −2.11065
\(457\) −1.68978 −0.0790444 −0.0395222 0.999219i \(-0.512584\pi\)
−0.0395222 + 0.999219i \(0.512584\pi\)
\(458\) 63.2298 2.95454
\(459\) −0.859166 −0.0401024
\(460\) 4.85871 0.226539
\(461\) −19.5620 −0.911094 −0.455547 0.890212i \(-0.650556\pi\)
−0.455547 + 0.890212i \(0.650556\pi\)
\(462\) 48.3329 2.24865
\(463\) −0.815748 −0.0379110 −0.0189555 0.999820i \(-0.506034\pi\)
−0.0189555 + 0.999820i \(0.506034\pi\)
\(464\) 57.5720 2.67271
\(465\) −2.42127 −0.112284
\(466\) 10.8160 0.501042
\(467\) 22.1348 1.02428 0.512138 0.858903i \(-0.328853\pi\)
0.512138 + 0.858903i \(0.328853\pi\)
\(468\) −6.26985 −0.289824
\(469\) −20.6962 −0.955659
\(470\) 1.17668 0.0542760
\(471\) 6.14437 0.283118
\(472\) −52.1236 −2.39918
\(473\) 26.7696 1.23087
\(474\) −19.7049 −0.905077
\(475\) −19.7456 −0.905991
\(476\) 1.94074 0.0889536
\(477\) −7.63954 −0.349791
\(478\) −40.5658 −1.85544
\(479\) 27.0578 1.23630 0.618151 0.786060i \(-0.287882\pi\)
0.618151 + 0.786060i \(0.287882\pi\)
\(480\) 8.71169 0.397632
\(481\) 10.1206 0.461459
\(482\) 41.0030 1.86763
\(483\) −7.18721 −0.327029
\(484\) 96.2938 4.37699
\(485\) −5.01704 −0.227812
\(486\) −31.5240 −1.42996
\(487\) −18.4923 −0.837965 −0.418982 0.907994i \(-0.637613\pi\)
−0.418982 + 0.907994i \(0.637613\pi\)
\(488\) 57.7514 2.61428
\(489\) −9.91719 −0.448471
\(490\) −0.911520 −0.0411783
\(491\) −15.2272 −0.687193 −0.343597 0.939117i \(-0.611645\pi\)
−0.343597 + 0.939117i \(0.611645\pi\)
\(492\) −41.7469 −1.88209
\(493\) 0.746378 0.0336152
\(494\) −10.9439 −0.492389
\(495\) −2.96154 −0.133111
\(496\) 48.6901 2.18625
\(497\) −23.5116 −1.05464
\(498\) −48.9428 −2.19318
\(499\) 21.2734 0.952328 0.476164 0.879357i \(-0.342027\pi\)
0.476164 + 0.879357i \(0.342027\pi\)
\(500\) 21.9984 0.983800
\(501\) −23.1051 −1.03226
\(502\) 49.4622 2.20761
\(503\) 27.4256 1.22285 0.611423 0.791304i \(-0.290598\pi\)
0.611423 + 0.791304i \(0.290598\pi\)
\(504\) 25.3113 1.12746
\(505\) 4.25589 0.189385
\(506\) −31.5459 −1.40239
\(507\) 1.33027 0.0590795
\(508\) −46.3128 −2.05480
\(509\) 21.7366 0.963458 0.481729 0.876320i \(-0.340009\pi\)
0.481729 + 0.876320i \(0.340009\pi\)
\(510\) 0.238162 0.0105460
\(511\) 0.732663 0.0324111
\(512\) 19.0491 0.841861
\(513\) −23.1200 −1.02077
\(514\) 32.8702 1.44984
\(515\) −0.920576 −0.0405654
\(516\) −33.1890 −1.46106
\(517\) −5.48645 −0.241294
\(518\) −67.2509 −2.95484
\(519\) −16.4457 −0.721886
\(520\) 3.63044 0.159206
\(521\) 4.09195 0.179271 0.0896357 0.995975i \(-0.471430\pi\)
0.0896357 + 0.995975i \(0.471430\pi\)
\(522\) 16.0229 0.701304
\(523\) −43.5497 −1.90430 −0.952148 0.305636i \(-0.901131\pi\)
−0.952148 + 0.305636i \(0.901131\pi\)
\(524\) 67.3267 2.94118
\(525\) −15.9490 −0.696070
\(526\) 67.0255 2.92245
\(527\) 0.631231 0.0274969
\(528\) −85.6564 −3.72771
\(529\) −18.3091 −0.796046
\(530\) 7.28123 0.316276
\(531\) −7.77646 −0.337470
\(532\) 52.2249 2.26424
\(533\) −6.15833 −0.266747
\(534\) −14.2659 −0.617344
\(535\) 1.32408 0.0572450
\(536\) 68.4210 2.95534
\(537\) −16.8842 −0.728605
\(538\) −7.82371 −0.337304
\(539\) 4.25012 0.183066
\(540\) 12.6244 0.543267
\(541\) −15.0144 −0.645518 −0.322759 0.946481i \(-0.604610\pi\)
−0.322759 + 0.946481i \(0.604610\pi\)
\(542\) −15.3331 −0.658615
\(543\) −21.7895 −0.935075
\(544\) −2.27116 −0.0973753
\(545\) −2.85961 −0.122492
\(546\) −8.83962 −0.378301
\(547\) 21.3879 0.914479 0.457239 0.889344i \(-0.348838\pi\)
0.457239 + 0.889344i \(0.348838\pi\)
\(548\) 21.4152 0.914813
\(549\) 8.61609 0.367726
\(550\) −70.0027 −2.98493
\(551\) 20.0849 0.855646
\(552\) 23.7607 1.01132
\(553\) 13.8714 0.589871
\(554\) −3.48720 −0.148157
\(555\) −5.92676 −0.251577
\(556\) −13.5978 −0.576677
\(557\) 35.7561 1.51503 0.757517 0.652816i \(-0.226412\pi\)
0.757517 + 0.652816i \(0.226412\pi\)
\(558\) 13.5510 0.573660
\(559\) −4.89590 −0.207075
\(560\) −12.9321 −0.546482
\(561\) −1.11047 −0.0468842
\(562\) 14.8662 0.627092
\(563\) −18.7101 −0.788535 −0.394267 0.918996i \(-0.629002\pi\)
−0.394267 + 0.918996i \(0.629002\pi\)
\(564\) 6.80211 0.286420
\(565\) 6.54935 0.275533
\(566\) 38.6985 1.62662
\(567\) −9.46690 −0.397573
\(568\) 77.7288 3.26143
\(569\) 4.44828 0.186482 0.0932408 0.995644i \(-0.470277\pi\)
0.0932408 + 0.995644i \(0.470277\pi\)
\(570\) 6.40890 0.268439
\(571\) 4.99950 0.209222 0.104611 0.994513i \(-0.466640\pi\)
0.104611 + 0.994513i \(0.466640\pi\)
\(572\) −27.8631 −1.16501
\(573\) −5.28219 −0.220666
\(574\) 40.9219 1.70805
\(575\) 10.4096 0.434109
\(576\) −19.7778 −0.824075
\(577\) 21.1564 0.880753 0.440377 0.897813i \(-0.354845\pi\)
0.440377 + 0.897813i \(0.354845\pi\)
\(578\) 45.2227 1.88102
\(579\) −7.53301 −0.313061
\(580\) −10.9671 −0.455385
\(581\) 34.4535 1.42937
\(582\) −40.3851 −1.67402
\(583\) −33.9500 −1.40606
\(584\) −2.42217 −0.100230
\(585\) 0.541636 0.0223939
\(586\) 43.9407 1.81517
\(587\) −5.09867 −0.210445 −0.105222 0.994449i \(-0.533555\pi\)
−0.105222 + 0.994449i \(0.533555\pi\)
\(588\) −5.26930 −0.217302
\(589\) 16.9863 0.699910
\(590\) 7.41172 0.305136
\(591\) 15.3331 0.630719
\(592\) 119.183 4.89840
\(593\) −28.7552 −1.18083 −0.590417 0.807098i \(-0.701037\pi\)
−0.590417 + 0.807098i \(0.701037\pi\)
\(594\) −81.9657 −3.36309
\(595\) −0.167655 −0.00687320
\(596\) −91.3135 −3.74035
\(597\) 32.0084 1.31002
\(598\) 5.76944 0.235930
\(599\) −14.9768 −0.611935 −0.305968 0.952042i \(-0.598980\pi\)
−0.305968 + 0.952042i \(0.598980\pi\)
\(600\) 52.7269 2.15257
\(601\) 29.7869 1.21503 0.607516 0.794308i \(-0.292166\pi\)
0.607516 + 0.794308i \(0.292166\pi\)
\(602\) 32.5331 1.32595
\(603\) 10.2079 0.415699
\(604\) −28.3931 −1.15530
\(605\) −8.31858 −0.338198
\(606\) 34.2582 1.39164
\(607\) 23.2853 0.945121 0.472561 0.881298i \(-0.343330\pi\)
0.472561 + 0.881298i \(0.343330\pi\)
\(608\) −61.1166 −2.47861
\(609\) 16.2230 0.657390
\(610\) −8.21197 −0.332493
\(611\) 1.00342 0.0405940
\(612\) −0.957226 −0.0386936
\(613\) −1.07230 −0.0433098 −0.0216549 0.999766i \(-0.506894\pi\)
−0.0216549 + 0.999766i \(0.506894\pi\)
\(614\) 7.48765 0.302177
\(615\) 3.60641 0.145424
\(616\) 112.483 4.53208
\(617\) −9.79726 −0.394423 −0.197211 0.980361i \(-0.563189\pi\)
−0.197211 + 0.980361i \(0.563189\pi\)
\(618\) −7.41025 −0.298084
\(619\) 1.00000 0.0401934
\(620\) −9.27517 −0.372500
\(621\) 12.1885 0.489107
\(622\) 24.2007 0.970361
\(623\) 10.0425 0.402345
\(624\) 15.6657 0.627131
\(625\) 22.1306 0.885226
\(626\) −15.0785 −0.602657
\(627\) −29.8826 −1.19340
\(628\) 23.5373 0.939241
\(629\) 1.54512 0.0616081
\(630\) −3.59915 −0.143394
\(631\) 31.8051 1.26614 0.633071 0.774093i \(-0.281794\pi\)
0.633071 + 0.774093i \(0.281794\pi\)
\(632\) −45.8584 −1.82415
\(633\) −37.1396 −1.47617
\(634\) −45.4201 −1.80386
\(635\) 4.00084 0.158769
\(636\) 42.0912 1.66902
\(637\) −0.777305 −0.0307980
\(638\) 71.2056 2.81906
\(639\) 11.5966 0.458754
\(640\) 5.75258 0.227391
\(641\) −16.9932 −0.671190 −0.335595 0.942006i \(-0.608937\pi\)
−0.335595 + 0.942006i \(0.608937\pi\)
\(642\) 10.6583 0.420650
\(643\) −2.42827 −0.0957618 −0.0478809 0.998853i \(-0.515247\pi\)
−0.0478809 + 0.998853i \(0.515247\pi\)
\(644\) −27.5321 −1.08492
\(645\) 2.86711 0.112892
\(646\) −1.67082 −0.0657375
\(647\) 11.4411 0.449797 0.224898 0.974382i \(-0.427795\pi\)
0.224898 + 0.974382i \(0.427795\pi\)
\(648\) 31.2974 1.22948
\(649\) −34.5584 −1.35654
\(650\) 12.8028 0.502168
\(651\) 13.7202 0.537738
\(652\) −37.9899 −1.48780
\(653\) −38.3571 −1.50103 −0.750515 0.660854i \(-0.770194\pi\)
−0.750515 + 0.660854i \(0.770194\pi\)
\(654\) −23.0186 −0.900100
\(655\) −5.81618 −0.227257
\(656\) −72.5225 −2.83153
\(657\) −0.361370 −0.0140984
\(658\) −6.66769 −0.259934
\(659\) 36.9986 1.44126 0.720631 0.693319i \(-0.243852\pi\)
0.720631 + 0.693319i \(0.243852\pi\)
\(660\) 16.3170 0.635139
\(661\) 29.3919 1.14321 0.571606 0.820528i \(-0.306321\pi\)
0.571606 + 0.820528i \(0.306321\pi\)
\(662\) −42.3871 −1.64742
\(663\) 0.203095 0.00788754
\(664\) −113.902 −4.42027
\(665\) −4.51158 −0.174952
\(666\) 33.1700 1.28531
\(667\) −10.5884 −0.409986
\(668\) −88.5088 −3.42451
\(669\) 12.0952 0.467628
\(670\) −9.72914 −0.375870
\(671\) 38.2897 1.47816
\(672\) −49.3652 −1.90430
\(673\) 11.2057 0.431948 0.215974 0.976399i \(-0.430707\pi\)
0.215974 + 0.976399i \(0.430707\pi\)
\(674\) −54.4884 −2.09881
\(675\) 27.0472 1.04105
\(676\) 5.09589 0.195996
\(677\) 10.0514 0.386307 0.193153 0.981169i \(-0.438129\pi\)
0.193153 + 0.981169i \(0.438129\pi\)
\(678\) 52.7195 2.02468
\(679\) 28.4293 1.09102
\(680\) 0.554265 0.0212551
\(681\) −7.87359 −0.301717
\(682\) 60.2204 2.30596
\(683\) −36.0856 −1.38078 −0.690389 0.723438i \(-0.742561\pi\)
−0.690389 + 0.723438i \(0.742561\pi\)
\(684\) −25.7588 −0.984912
\(685\) −1.85001 −0.0706851
\(686\) 51.6799 1.97315
\(687\) −31.5762 −1.20471
\(688\) −57.6557 −2.19810
\(689\) 6.20913 0.236549
\(690\) −3.37867 −0.128624
\(691\) −7.18320 −0.273262 −0.136631 0.990622i \(-0.543627\pi\)
−0.136631 + 0.990622i \(0.543627\pi\)
\(692\) −62.9987 −2.39485
\(693\) 16.7817 0.637483
\(694\) −44.2351 −1.67914
\(695\) 1.17468 0.0445583
\(696\) −53.6329 −2.03295
\(697\) −0.940201 −0.0356127
\(698\) 80.0418 3.02963
\(699\) −5.40137 −0.204299
\(700\) −61.0958 −2.30921
\(701\) −4.11665 −0.155484 −0.0777418 0.996974i \(-0.524771\pi\)
−0.0777418 + 0.996974i \(0.524771\pi\)
\(702\) 14.9907 0.565789
\(703\) 41.5790 1.56818
\(704\) −87.8922 −3.31256
\(705\) −0.587617 −0.0221309
\(706\) −67.3558 −2.53497
\(707\) −24.1162 −0.906983
\(708\) 42.8456 1.61023
\(709\) 9.32269 0.350121 0.175061 0.984558i \(-0.443988\pi\)
0.175061 + 0.984558i \(0.443988\pi\)
\(710\) −11.0527 −0.414799
\(711\) −6.84175 −0.256586
\(712\) −33.2003 −1.24424
\(713\) −8.95491 −0.335364
\(714\) −1.34956 −0.0505059
\(715\) 2.40702 0.0900175
\(716\) −64.6783 −2.41714
\(717\) 20.2580 0.756550
\(718\) −54.2290 −2.02381
\(719\) 15.7596 0.587732 0.293866 0.955847i \(-0.405058\pi\)
0.293866 + 0.955847i \(0.405058\pi\)
\(720\) 6.37848 0.237712
\(721\) 5.21648 0.194272
\(722\) 5.65093 0.210306
\(723\) −20.4763 −0.761524
\(724\) −83.4691 −3.10210
\(725\) −23.4965 −0.872639
\(726\) −66.9611 −2.48516
\(727\) −21.1571 −0.784674 −0.392337 0.919821i \(-0.628333\pi\)
−0.392337 + 0.919821i \(0.628333\pi\)
\(728\) −20.5721 −0.762452
\(729\) 27.1279 1.00474
\(730\) 0.344421 0.0127476
\(731\) −0.747464 −0.0276460
\(732\) −47.4716 −1.75460
\(733\) −20.5972 −0.760774 −0.380387 0.924827i \(-0.624209\pi\)
−0.380387 + 0.924827i \(0.624209\pi\)
\(734\) 87.4309 3.22713
\(735\) 0.455201 0.0167903
\(736\) 32.2197 1.18763
\(737\) 45.3638 1.67100
\(738\) −20.1838 −0.742977
\(739\) −33.9463 −1.24874 −0.624368 0.781130i \(-0.714643\pi\)
−0.624368 + 0.781130i \(0.714643\pi\)
\(740\) −22.7037 −0.834604
\(741\) 5.46524 0.200771
\(742\) −41.2594 −1.51468
\(743\) −17.3969 −0.638230 −0.319115 0.947716i \(-0.603386\pi\)
−0.319115 + 0.947716i \(0.603386\pi\)
\(744\) −45.3587 −1.66293
\(745\) 7.88834 0.289006
\(746\) 69.4759 2.54369
\(747\) −16.9934 −0.621757
\(748\) −4.25390 −0.155538
\(749\) −7.50297 −0.274153
\(750\) −15.2973 −0.558580
\(751\) −2.94008 −0.107285 −0.0536425 0.998560i \(-0.517083\pi\)
−0.0536425 + 0.998560i \(0.517083\pi\)
\(752\) 11.8166 0.430907
\(753\) −24.7008 −0.900147
\(754\) −13.0228 −0.474263
\(755\) 2.45281 0.0892667
\(756\) −71.5367 −2.60176
\(757\) −6.17434 −0.224410 −0.112205 0.993685i \(-0.535791\pi\)
−0.112205 + 0.993685i \(0.535791\pi\)
\(758\) 33.4224 1.21395
\(759\) 15.7536 0.571820
\(760\) 14.9152 0.541030
\(761\) −31.6628 −1.14777 −0.573887 0.818934i \(-0.694565\pi\)
−0.573887 + 0.818934i \(0.694565\pi\)
\(762\) 32.2051 1.16667
\(763\) 16.2041 0.586627
\(764\) −20.2345 −0.732059
\(765\) 0.0826923 0.00298975
\(766\) 54.2953 1.96177
\(767\) 6.32041 0.228217
\(768\) 3.53857 0.127687
\(769\) 36.7166 1.32404 0.662018 0.749488i \(-0.269700\pi\)
0.662018 + 0.749488i \(0.269700\pi\)
\(770\) −15.9946 −0.576404
\(771\) −16.4150 −0.591171
\(772\) −28.8568 −1.03858
\(773\) −41.3165 −1.48605 −0.743026 0.669263i \(-0.766610\pi\)
−0.743026 + 0.669263i \(0.766610\pi\)
\(774\) −16.0462 −0.576770
\(775\) −19.8716 −0.713810
\(776\) −93.9866 −3.37392
\(777\) 33.5842 1.20483
\(778\) 36.2984 1.30136
\(779\) −25.3007 −0.906490
\(780\) −2.98423 −0.106852
\(781\) 51.5350 1.84407
\(782\) 0.880828 0.0314984
\(783\) −27.5119 −0.983196
\(784\) −9.15380 −0.326921
\(785\) −2.03333 −0.0725726
\(786\) −46.8179 −1.66994
\(787\) −39.6024 −1.41167 −0.705837 0.708375i \(-0.749429\pi\)
−0.705837 + 0.708375i \(0.749429\pi\)
\(788\) 58.7366 2.09241
\(789\) −33.4717 −1.19162
\(790\) 6.52085 0.232002
\(791\) −37.1122 −1.31956
\(792\) −55.4798 −1.97139
\(793\) −7.00282 −0.248678
\(794\) 13.9017 0.493354
\(795\) −3.63615 −0.128961
\(796\) 122.615 4.34597
\(797\) 34.3800 1.21780 0.608900 0.793247i \(-0.291611\pi\)
0.608900 + 0.793247i \(0.291611\pi\)
\(798\) −36.3163 −1.28558
\(799\) 0.153193 0.00541959
\(800\) 71.4979 2.52783
\(801\) −4.95325 −0.175015
\(802\) 32.5624 1.14982
\(803\) −1.60592 −0.0566717
\(804\) −56.2421 −1.98350
\(805\) 2.37843 0.0838286
\(806\) −11.0137 −0.387942
\(807\) 3.90706 0.137535
\(808\) 79.7276 2.80481
\(809\) 49.6364 1.74512 0.872562 0.488503i \(-0.162457\pi\)
0.872562 + 0.488503i \(0.162457\pi\)
\(810\) −4.45034 −0.156369
\(811\) −9.66203 −0.339280 −0.169640 0.985506i \(-0.554260\pi\)
−0.169640 + 0.985506i \(0.554260\pi\)
\(812\) 62.1456 2.18088
\(813\) 7.65717 0.268549
\(814\) 147.407 5.16661
\(815\) 3.28185 0.114958
\(816\) 2.39171 0.0837265
\(817\) −20.1141 −0.703705
\(818\) −4.41473 −0.154357
\(819\) −3.06921 −0.107247
\(820\) 13.8151 0.482444
\(821\) −33.3848 −1.16514 −0.582569 0.812782i \(-0.697952\pi\)
−0.582569 + 0.812782i \(0.697952\pi\)
\(822\) −14.8918 −0.519411
\(823\) −32.3402 −1.12731 −0.563654 0.826011i \(-0.690605\pi\)
−0.563654 + 0.826011i \(0.690605\pi\)
\(824\) −17.2456 −0.600778
\(825\) 34.9585 1.21710
\(826\) −41.9989 −1.46133
\(827\) 57.0332 1.98324 0.991620 0.129189i \(-0.0412373\pi\)
0.991620 + 0.129189i \(0.0412373\pi\)
\(828\) 13.5796 0.471924
\(829\) −28.3739 −0.985467 −0.492734 0.870180i \(-0.664002\pi\)
−0.492734 + 0.870180i \(0.664002\pi\)
\(830\) 16.1964 0.562185
\(831\) 1.74146 0.0604107
\(832\) 16.0746 0.557288
\(833\) −0.118672 −0.00411175
\(834\) 9.45571 0.327425
\(835\) 7.64605 0.264602
\(836\) −114.472 −3.95908
\(837\) −23.2675 −0.804244
\(838\) −31.3041 −1.08138
\(839\) −17.9181 −0.618602 −0.309301 0.950964i \(-0.600095\pi\)
−0.309301 + 0.950964i \(0.600095\pi\)
\(840\) 12.0473 0.415672
\(841\) −5.09973 −0.175853
\(842\) 79.8758 2.75270
\(843\) −7.42398 −0.255696
\(844\) −142.271 −4.89718
\(845\) −0.440221 −0.0151441
\(846\) 3.28869 0.113067
\(847\) 47.1376 1.61967
\(848\) 73.1206 2.51097
\(849\) −19.3255 −0.663250
\(850\) 1.95462 0.0670431
\(851\) −21.9198 −0.751400
\(852\) −63.8931 −2.18894
\(853\) 34.5309 1.18232 0.591158 0.806556i \(-0.298671\pi\)
0.591158 + 0.806556i \(0.298671\pi\)
\(854\) 46.5335 1.59234
\(855\) 2.22524 0.0761015
\(856\) 24.8046 0.847805
\(857\) 27.7764 0.948822 0.474411 0.880303i \(-0.342661\pi\)
0.474411 + 0.880303i \(0.342661\pi\)
\(858\) 19.3755 0.661469
\(859\) −18.6297 −0.635636 −0.317818 0.948152i \(-0.602950\pi\)
−0.317818 + 0.948152i \(0.602950\pi\)
\(860\) 10.9831 0.374520
\(861\) −20.4359 −0.696453
\(862\) 21.0345 0.716438
\(863\) −8.49846 −0.289291 −0.144646 0.989484i \(-0.546204\pi\)
−0.144646 + 0.989484i \(0.546204\pi\)
\(864\) 83.7163 2.84809
\(865\) 5.44229 0.185044
\(866\) −34.5377 −1.17364
\(867\) −22.5836 −0.766980
\(868\) 52.5582 1.78394
\(869\) −30.4046 −1.03141
\(870\) 7.62635 0.258557
\(871\) −8.29660 −0.281120
\(872\) −53.5703 −1.81412
\(873\) −14.0221 −0.474577
\(874\) 23.7029 0.801764
\(875\) 10.7686 0.364047
\(876\) 1.99102 0.0672704
\(877\) −35.8100 −1.20922 −0.604609 0.796522i \(-0.706671\pi\)
−0.604609 + 0.796522i \(0.706671\pi\)
\(878\) −35.6609 −1.20350
\(879\) −21.9434 −0.740133
\(880\) 28.3459 0.955539
\(881\) −15.3589 −0.517454 −0.258727 0.965951i \(-0.583303\pi\)
−0.258727 + 0.965951i \(0.583303\pi\)
\(882\) −2.54761 −0.0857823
\(883\) −51.8512 −1.74493 −0.872466 0.488675i \(-0.837481\pi\)
−0.872466 + 0.488675i \(0.837481\pi\)
\(884\) 0.777997 0.0261669
\(885\) −3.70132 −0.124418
\(886\) 0.252232 0.00847390
\(887\) −7.80562 −0.262087 −0.131043 0.991377i \(-0.541833\pi\)
−0.131043 + 0.991377i \(0.541833\pi\)
\(888\) −111.029 −3.72588
\(889\) −22.6710 −0.760359
\(890\) 4.72093 0.158246
\(891\) 20.7505 0.695167
\(892\) 46.3333 1.55135
\(893\) 4.12241 0.137951
\(894\) 63.4979 2.12369
\(895\) 5.58739 0.186766
\(896\) −32.5973 −1.08900
\(897\) −2.88118 −0.0962000
\(898\) −40.8438 −1.36297
\(899\) 20.2131 0.674144
\(900\) 30.1342 1.00447
\(901\) 0.947956 0.0315810
\(902\) −89.6966 −2.98657
\(903\) −16.2466 −0.540654
\(904\) 122.692 4.08068
\(905\) 7.21068 0.239691
\(906\) 19.7441 0.655953
\(907\) −37.4616 −1.24389 −0.621945 0.783061i \(-0.713657\pi\)
−0.621945 + 0.783061i \(0.713657\pi\)
\(908\) −30.1614 −1.00094
\(909\) 11.8948 0.394525
\(910\) 2.92525 0.0969712
\(911\) −49.6740 −1.64577 −0.822886 0.568207i \(-0.807637\pi\)
−0.822886 + 0.568207i \(0.807637\pi\)
\(912\) 64.3604 2.13119
\(913\) −75.5185 −2.49930
\(914\) 4.50125 0.148888
\(915\) 4.10095 0.135573
\(916\) −120.959 −3.99660
\(917\) 32.9577 1.08836
\(918\) 2.28866 0.0755369
\(919\) −34.3881 −1.13436 −0.567180 0.823594i \(-0.691965\pi\)
−0.567180 + 0.823594i \(0.691965\pi\)
\(920\) −7.86303 −0.259237
\(921\) −3.73924 −0.123212
\(922\) 52.1095 1.71614
\(923\) −9.42526 −0.310236
\(924\) −92.4612 −3.04175
\(925\) −48.6416 −1.59933
\(926\) 2.17300 0.0714091
\(927\) −2.57292 −0.0845057
\(928\) −72.7264 −2.38736
\(929\) 10.5335 0.345592 0.172796 0.984958i \(-0.444720\pi\)
0.172796 + 0.984958i \(0.444720\pi\)
\(930\) 6.44980 0.211497
\(931\) −3.19345 −0.104661
\(932\) −20.6911 −0.677759
\(933\) −12.0855 −0.395663
\(934\) −58.9630 −1.92933
\(935\) 0.367483 0.0120180
\(936\) 10.1467 0.331656
\(937\) 41.9340 1.36992 0.684962 0.728579i \(-0.259819\pi\)
0.684962 + 0.728579i \(0.259819\pi\)
\(938\) 55.1306 1.80008
\(939\) 7.53000 0.245732
\(940\) −2.25099 −0.0734192
\(941\) −0.235916 −0.00769066 −0.00384533 0.999993i \(-0.501224\pi\)
−0.00384533 + 0.999993i \(0.501224\pi\)
\(942\) −16.3674 −0.533280
\(943\) 13.3381 0.434348
\(944\) 74.4311 2.42253
\(945\) 6.17987 0.201031
\(946\) −71.3092 −2.31846
\(947\) 23.1991 0.753869 0.376935 0.926240i \(-0.376978\pi\)
0.376935 + 0.926240i \(0.376978\pi\)
\(948\) 37.6956 1.22430
\(949\) 0.293707 0.00953415
\(950\) 52.5986 1.70652
\(951\) 22.6822 0.735521
\(952\) −3.14077 −0.101793
\(953\) −54.1582 −1.75435 −0.877177 0.480167i \(-0.840576\pi\)
−0.877177 + 0.480167i \(0.840576\pi\)
\(954\) 20.3503 0.658865
\(955\) 1.74801 0.0565642
\(956\) 77.6026 2.50985
\(957\) −35.5592 −1.14946
\(958\) −72.0768 −2.32870
\(959\) 10.4831 0.338519
\(960\) −9.41353 −0.303821
\(961\) −13.9053 −0.448558
\(962\) −26.9593 −0.869203
\(963\) 3.70067 0.119253
\(964\) −78.4390 −2.52635
\(965\) 2.49286 0.0802481
\(966\) 19.1454 0.615992
\(967\) −53.2182 −1.71138 −0.855692 0.517486i \(-0.826868\pi\)
−0.855692 + 0.517486i \(0.826868\pi\)
\(968\) −155.836 −5.00875
\(969\) 0.834386 0.0268043
\(970\) 13.3644 0.429107
\(971\) −29.7906 −0.956025 −0.478012 0.878353i \(-0.658643\pi\)
−0.478012 + 0.878353i \(0.658643\pi\)
\(972\) 60.3057 1.93431
\(973\) −6.65640 −0.213394
\(974\) 49.2599 1.57839
\(975\) −6.39357 −0.204758
\(976\) −82.4675 −2.63972
\(977\) −9.51647 −0.304459 −0.152229 0.988345i \(-0.548645\pi\)
−0.152229 + 0.988345i \(0.548645\pi\)
\(978\) 26.4175 0.844739
\(979\) −22.0122 −0.703512
\(980\) 1.74374 0.0557018
\(981\) −7.99231 −0.255175
\(982\) 40.5624 1.29440
\(983\) −16.4464 −0.524557 −0.262279 0.964992i \(-0.584474\pi\)
−0.262279 + 0.964992i \(0.584474\pi\)
\(984\) 67.5605 2.15375
\(985\) −5.07411 −0.161675
\(986\) −1.98821 −0.0633175
\(987\) 3.32976 0.105987
\(988\) 20.9358 0.666055
\(989\) 10.6038 0.337182
\(990\) 7.88897 0.250728
\(991\) −6.92862 −0.220095 −0.110047 0.993926i \(-0.535100\pi\)
−0.110047 + 0.993926i \(0.535100\pi\)
\(992\) −61.5066 −1.95284
\(993\) 21.1676 0.671732
\(994\) 62.6305 1.98652
\(995\) −10.5924 −0.335801
\(996\) 93.6278 2.96671
\(997\) 35.6378 1.12866 0.564330 0.825549i \(-0.309135\pi\)
0.564330 + 0.825549i \(0.309135\pi\)
\(998\) −56.6683 −1.79380
\(999\) −56.9541 −1.80195
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 \(a_p\))