Properties

Label 8013.2.a.d.1.6
Level 8013
Weight 2
Character 8013.1
Self dual Yes
Analytic conductor 63.984
Analytic rank 0
Dimension 129
CM No

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Newspace parameters

Level: \( N \) = \( 8013 = 3 \cdot 2671 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8013.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9841271397\)
Analytic rank: \(0\)
Dimension: \(129\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 8013.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.59970 q^{2} +1.00000 q^{3} +4.75846 q^{4} +1.02648 q^{5} -2.59970 q^{6} -4.07018 q^{7} -7.17119 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.59970 q^{2} +1.00000 q^{3} +4.75846 q^{4} +1.02648 q^{5} -2.59970 q^{6} -4.07018 q^{7} -7.17119 q^{8} +1.00000 q^{9} -2.66854 q^{10} -2.37383 q^{11} +4.75846 q^{12} +4.83564 q^{13} +10.5813 q^{14} +1.02648 q^{15} +9.12606 q^{16} +1.25033 q^{17} -2.59970 q^{18} +6.30041 q^{19} +4.88446 q^{20} -4.07018 q^{21} +6.17125 q^{22} -2.91520 q^{23} -7.17119 q^{24} -3.94634 q^{25} -12.5712 q^{26} +1.00000 q^{27} -19.3678 q^{28} -7.88097 q^{29} -2.66854 q^{30} -1.97118 q^{31} -9.38267 q^{32} -2.37383 q^{33} -3.25050 q^{34} -4.17796 q^{35} +4.75846 q^{36} -0.814054 q^{37} -16.3792 q^{38} +4.83564 q^{39} -7.36107 q^{40} -2.01068 q^{41} +10.5813 q^{42} -3.25216 q^{43} -11.2958 q^{44} +1.02648 q^{45} +7.57865 q^{46} +6.79314 q^{47} +9.12606 q^{48} +9.56640 q^{49} +10.2593 q^{50} +1.25033 q^{51} +23.0102 q^{52} +2.75569 q^{53} -2.59970 q^{54} -2.43668 q^{55} +29.1881 q^{56} +6.30041 q^{57} +20.4882 q^{58} +6.56759 q^{59} +4.88446 q^{60} -0.0575094 q^{61} +5.12447 q^{62} -4.07018 q^{63} +6.14005 q^{64} +4.96367 q^{65} +6.17125 q^{66} +1.04040 q^{67} +5.94967 q^{68} -2.91520 q^{69} +10.8615 q^{70} -3.04806 q^{71} -7.17119 q^{72} +0.895688 q^{73} +2.11630 q^{74} -3.94634 q^{75} +29.9803 q^{76} +9.66192 q^{77} -12.5712 q^{78} +15.4614 q^{79} +9.36770 q^{80} +1.00000 q^{81} +5.22717 q^{82} +2.31992 q^{83} -19.3678 q^{84} +1.28344 q^{85} +8.45467 q^{86} -7.88097 q^{87} +17.0232 q^{88} -7.16653 q^{89} -2.66854 q^{90} -19.6819 q^{91} -13.8719 q^{92} -1.97118 q^{93} -17.6602 q^{94} +6.46723 q^{95} -9.38267 q^{96} -10.0203 q^{97} -24.8698 q^{98} -2.37383 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 129q + 15q^{2} + 129q^{3} + 151q^{4} + 16q^{5} + 15q^{6} + 61q^{7} + 42q^{8} + 129q^{9} + O(q^{10}) \) \( 129q + 15q^{2} + 129q^{3} + 151q^{4} + 16q^{5} + 15q^{6} + 61q^{7} + 42q^{8} + 129q^{9} + 41q^{10} + 51q^{11} + 151q^{12} + 56q^{13} + 5q^{14} + 16q^{15} + 195q^{16} + 18q^{17} + 15q^{18} + 93q^{19} + 44q^{20} + 61q^{21} + 46q^{22} + 50q^{23} + 42q^{24} + 193q^{25} + q^{26} + 129q^{27} + 145q^{28} + 24q^{29} + 41q^{30} + 67q^{31} + 89q^{32} + 51q^{33} + 73q^{34} + 56q^{35} + 151q^{36} + 95q^{37} + 9q^{38} + 56q^{39} + 103q^{40} + 7q^{41} + 5q^{42} + 150q^{43} + 69q^{44} + 16q^{45} + 72q^{46} + 53q^{47} + 195q^{48} + 240q^{49} + 17q^{50} + 18q^{51} + 124q^{52} + 34q^{53} + 15q^{54} + 66q^{55} - 17q^{56} + 93q^{57} + 57q^{58} + 49q^{59} + 44q^{60} + 113q^{61} + 27q^{62} + 61q^{63} + 262q^{64} + 22q^{65} + 46q^{66} + 185q^{67} + 2q^{68} + 50q^{69} + 25q^{70} + 41q^{71} + 42q^{72} + 153q^{73} - q^{74} + 193q^{75} + 190q^{76} + 39q^{77} + q^{78} + 101q^{79} + 48q^{80} + 129q^{81} + 15q^{82} + 162q^{83} + 145q^{84} + 99q^{85} + 13q^{86} + 24q^{87} + 86q^{88} - 4q^{89} + 41q^{90} + 117q^{91} + 56q^{92} + 67q^{93} + 49q^{94} + 71q^{95} + 89q^{96} + 159q^{97} + 40q^{98} + 51q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.59970 −1.83827 −0.919134 0.393944i \(-0.871110\pi\)
−0.919134 + 0.393944i \(0.871110\pi\)
\(3\) 1.00000 0.577350
\(4\) 4.75846 2.37923
\(5\) 1.02648 0.459055 0.229528 0.973302i \(-0.426282\pi\)
0.229528 + 0.973302i \(0.426282\pi\)
\(6\) −2.59970 −1.06133
\(7\) −4.07018 −1.53838 −0.769192 0.639017i \(-0.779341\pi\)
−0.769192 + 0.639017i \(0.779341\pi\)
\(8\) −7.17119 −2.53540
\(9\) 1.00000 0.333333
\(10\) −2.66854 −0.843867
\(11\) −2.37383 −0.715736 −0.357868 0.933772i \(-0.616496\pi\)
−0.357868 + 0.933772i \(0.616496\pi\)
\(12\) 4.75846 1.37365
\(13\) 4.83564 1.34116 0.670582 0.741835i \(-0.266044\pi\)
0.670582 + 0.741835i \(0.266044\pi\)
\(14\) 10.5813 2.82797
\(15\) 1.02648 0.265036
\(16\) 9.12606 2.28151
\(17\) 1.25033 0.303250 0.151625 0.988438i \(-0.451549\pi\)
0.151625 + 0.988438i \(0.451549\pi\)
\(18\) −2.59970 −0.612756
\(19\) 6.30041 1.44541 0.722707 0.691155i \(-0.242898\pi\)
0.722707 + 0.691155i \(0.242898\pi\)
\(20\) 4.88446 1.09220
\(21\) −4.07018 −0.888187
\(22\) 6.17125 1.31572
\(23\) −2.91520 −0.607861 −0.303930 0.952694i \(-0.598299\pi\)
−0.303930 + 0.952694i \(0.598299\pi\)
\(24\) −7.17119 −1.46381
\(25\) −3.94634 −0.789268
\(26\) −12.5712 −2.46542
\(27\) 1.00000 0.192450
\(28\) −19.3678 −3.66018
\(29\) −7.88097 −1.46346 −0.731730 0.681595i \(-0.761287\pi\)
−0.731730 + 0.681595i \(0.761287\pi\)
\(30\) −2.66854 −0.487207
\(31\) −1.97118 −0.354034 −0.177017 0.984208i \(-0.556645\pi\)
−0.177017 + 0.984208i \(0.556645\pi\)
\(32\) −9.38267 −1.65864
\(33\) −2.37383 −0.413231
\(34\) −3.25050 −0.557456
\(35\) −4.17796 −0.706203
\(36\) 4.75846 0.793077
\(37\) −0.814054 −0.133830 −0.0669148 0.997759i \(-0.521316\pi\)
−0.0669148 + 0.997759i \(0.521316\pi\)
\(38\) −16.3792 −2.65706
\(39\) 4.83564 0.774321
\(40\) −7.36107 −1.16389
\(41\) −2.01068 −0.314015 −0.157008 0.987597i \(-0.550185\pi\)
−0.157008 + 0.987597i \(0.550185\pi\)
\(42\) 10.5813 1.63273
\(43\) −3.25216 −0.495950 −0.247975 0.968766i \(-0.579765\pi\)
−0.247975 + 0.968766i \(0.579765\pi\)
\(44\) −11.2958 −1.70290
\(45\) 1.02648 0.153018
\(46\) 7.57865 1.11741
\(47\) 6.79314 0.990881 0.495441 0.868642i \(-0.335007\pi\)
0.495441 + 0.868642i \(0.335007\pi\)
\(48\) 9.12606 1.31723
\(49\) 9.56640 1.36663
\(50\) 10.2593 1.45089
\(51\) 1.25033 0.175082
\(52\) 23.0102 3.19094
\(53\) 2.75569 0.378523 0.189261 0.981927i \(-0.439391\pi\)
0.189261 + 0.981927i \(0.439391\pi\)
\(54\) −2.59970 −0.353775
\(55\) −2.43668 −0.328562
\(56\) 29.1881 3.90042
\(57\) 6.30041 0.834510
\(58\) 20.4882 2.69023
\(59\) 6.56759 0.855027 0.427514 0.904009i \(-0.359390\pi\)
0.427514 + 0.904009i \(0.359390\pi\)
\(60\) 4.88446 0.630581
\(61\) −0.0575094 −0.00736332 −0.00368166 0.999993i \(-0.501172\pi\)
−0.00368166 + 0.999993i \(0.501172\pi\)
\(62\) 5.12447 0.650809
\(63\) −4.07018 −0.512795
\(64\) 6.14005 0.767506
\(65\) 4.96367 0.615668
\(66\) 6.17125 0.759629
\(67\) 1.04040 0.127105 0.0635523 0.997979i \(-0.479757\pi\)
0.0635523 + 0.997979i \(0.479757\pi\)
\(68\) 5.94967 0.721503
\(69\) −2.91520 −0.350948
\(70\) 10.8615 1.29819
\(71\) −3.04806 −0.361738 −0.180869 0.983507i \(-0.557891\pi\)
−0.180869 + 0.983507i \(0.557891\pi\)
\(72\) −7.17119 −0.845133
\(73\) 0.895688 0.104832 0.0524161 0.998625i \(-0.483308\pi\)
0.0524161 + 0.998625i \(0.483308\pi\)
\(74\) 2.11630 0.246015
\(75\) −3.94634 −0.455684
\(76\) 29.9803 3.43897
\(77\) 9.66192 1.10108
\(78\) −12.5712 −1.42341
\(79\) 15.4614 1.73954 0.869771 0.493455i \(-0.164266\pi\)
0.869771 + 0.493455i \(0.164266\pi\)
\(80\) 9.36770 1.04734
\(81\) 1.00000 0.111111
\(82\) 5.22717 0.577245
\(83\) 2.31992 0.254644 0.127322 0.991861i \(-0.459362\pi\)
0.127322 + 0.991861i \(0.459362\pi\)
\(84\) −19.3678 −2.11320
\(85\) 1.28344 0.139209
\(86\) 8.45467 0.911690
\(87\) −7.88097 −0.844929
\(88\) 17.0232 1.81468
\(89\) −7.16653 −0.759650 −0.379825 0.925058i \(-0.624016\pi\)
−0.379825 + 0.925058i \(0.624016\pi\)
\(90\) −2.66854 −0.281289
\(91\) −19.6819 −2.06323
\(92\) −13.8719 −1.44624
\(93\) −1.97118 −0.204401
\(94\) −17.6602 −1.82151
\(95\) 6.46723 0.663524
\(96\) −9.38267 −0.957615
\(97\) −10.0203 −1.01741 −0.508706 0.860941i \(-0.669876\pi\)
−0.508706 + 0.860941i \(0.669876\pi\)
\(98\) −24.8698 −2.51223
\(99\) −2.37383 −0.238579
\(100\) −18.7785 −1.87785
\(101\) −17.6323 −1.75448 −0.877239 0.480053i \(-0.840617\pi\)
−0.877239 + 0.480053i \(0.840617\pi\)
\(102\) −3.25050 −0.321847
\(103\) 7.03561 0.693239 0.346620 0.938006i \(-0.387330\pi\)
0.346620 + 0.938006i \(0.387330\pi\)
\(104\) −34.6773 −3.40039
\(105\) −4.17796 −0.407727
\(106\) −7.16397 −0.695826
\(107\) 7.73840 0.748100 0.374050 0.927409i \(-0.377969\pi\)
0.374050 + 0.927409i \(0.377969\pi\)
\(108\) 4.75846 0.457883
\(109\) 17.0334 1.63151 0.815753 0.578400i \(-0.196323\pi\)
0.815753 + 0.578400i \(0.196323\pi\)
\(110\) 6.33466 0.603986
\(111\) −0.814054 −0.0772666
\(112\) −37.1447 −3.50985
\(113\) 8.90159 0.837391 0.418696 0.908127i \(-0.362487\pi\)
0.418696 + 0.908127i \(0.362487\pi\)
\(114\) −16.3792 −1.53405
\(115\) −2.99239 −0.279041
\(116\) −37.5013 −3.48191
\(117\) 4.83564 0.447055
\(118\) −17.0738 −1.57177
\(119\) −5.08909 −0.466516
\(120\) −7.36107 −0.671971
\(121\) −5.36494 −0.487722
\(122\) 0.149507 0.0135358
\(123\) −2.01068 −0.181297
\(124\) −9.37977 −0.842328
\(125\) −9.18323 −0.821373
\(126\) 10.5813 0.942655
\(127\) 16.9662 1.50551 0.752756 0.658300i \(-0.228724\pi\)
0.752756 + 0.658300i \(0.228724\pi\)
\(128\) 2.80302 0.247754
\(129\) −3.25216 −0.286337
\(130\) −12.9041 −1.13176
\(131\) −7.94817 −0.694435 −0.347218 0.937785i \(-0.612873\pi\)
−0.347218 + 0.937785i \(0.612873\pi\)
\(132\) −11.2958 −0.983172
\(133\) −25.6438 −2.22360
\(134\) −2.70472 −0.233653
\(135\) 1.02648 0.0883452
\(136\) −8.96638 −0.768861
\(137\) −3.80116 −0.324755 −0.162378 0.986729i \(-0.551916\pi\)
−0.162378 + 0.986729i \(0.551916\pi\)
\(138\) 7.57865 0.645138
\(139\) 9.84042 0.834654 0.417327 0.908756i \(-0.362967\pi\)
0.417327 + 0.908756i \(0.362967\pi\)
\(140\) −19.8807 −1.68022
\(141\) 6.79314 0.572086
\(142\) 7.92406 0.664972
\(143\) −11.4790 −0.959920
\(144\) 9.12606 0.760505
\(145\) −8.08964 −0.671808
\(146\) −2.32852 −0.192710
\(147\) 9.56640 0.789023
\(148\) −3.87365 −0.318412
\(149\) 11.7342 0.961306 0.480653 0.876911i \(-0.340400\pi\)
0.480653 + 0.876911i \(0.340400\pi\)
\(150\) 10.2593 0.837670
\(151\) −10.1801 −0.828446 −0.414223 0.910175i \(-0.635947\pi\)
−0.414223 + 0.910175i \(0.635947\pi\)
\(152\) −45.1815 −3.66470
\(153\) 1.25033 0.101083
\(154\) −25.1181 −2.02408
\(155\) −2.02337 −0.162521
\(156\) 23.0102 1.84229
\(157\) 20.9789 1.67430 0.837151 0.546972i \(-0.184220\pi\)
0.837151 + 0.546972i \(0.184220\pi\)
\(158\) −40.1950 −3.19775
\(159\) 2.75569 0.218540
\(160\) −9.63110 −0.761406
\(161\) 11.8654 0.935124
\(162\) −2.59970 −0.204252
\(163\) −4.64229 −0.363613 −0.181806 0.983334i \(-0.558194\pi\)
−0.181806 + 0.983334i \(0.558194\pi\)
\(164\) −9.56774 −0.747115
\(165\) −2.43668 −0.189696
\(166\) −6.03110 −0.468104
\(167\) −1.28107 −0.0991319 −0.0495659 0.998771i \(-0.515784\pi\)
−0.0495659 + 0.998771i \(0.515784\pi\)
\(168\) 29.1881 2.25191
\(169\) 10.3834 0.798721
\(170\) −3.33657 −0.255903
\(171\) 6.30041 0.481804
\(172\) −15.4753 −1.17998
\(173\) 3.18117 0.241860 0.120930 0.992661i \(-0.461412\pi\)
0.120930 + 0.992661i \(0.461412\pi\)
\(174\) 20.4882 1.55321
\(175\) 16.0623 1.21420
\(176\) −21.6637 −1.63296
\(177\) 6.56759 0.493650
\(178\) 18.6309 1.39644
\(179\) 5.58298 0.417292 0.208646 0.977991i \(-0.433094\pi\)
0.208646 + 0.977991i \(0.433094\pi\)
\(180\) 4.88446 0.364066
\(181\) −2.59246 −0.192696 −0.0963481 0.995348i \(-0.530716\pi\)
−0.0963481 + 0.995348i \(0.530716\pi\)
\(182\) 51.1672 3.79277
\(183\) −0.0575094 −0.00425122
\(184\) 20.9054 1.54117
\(185\) −0.835609 −0.0614352
\(186\) 5.12447 0.375745
\(187\) −2.96808 −0.217047
\(188\) 32.3249 2.35754
\(189\) −4.07018 −0.296062
\(190\) −16.8129 −1.21974
\(191\) −20.7352 −1.50035 −0.750173 0.661242i \(-0.770030\pi\)
−0.750173 + 0.661242i \(0.770030\pi\)
\(192\) 6.14005 0.443120
\(193\) 6.42548 0.462516 0.231258 0.972892i \(-0.425716\pi\)
0.231258 + 0.972892i \(0.425716\pi\)
\(194\) 26.0499 1.87028
\(195\) 4.96367 0.355456
\(196\) 45.5214 3.25153
\(197\) −10.8247 −0.771229 −0.385614 0.922660i \(-0.626011\pi\)
−0.385614 + 0.922660i \(0.626011\pi\)
\(198\) 6.17125 0.438572
\(199\) 9.39737 0.666162 0.333081 0.942898i \(-0.391912\pi\)
0.333081 + 0.942898i \(0.391912\pi\)
\(200\) 28.3000 2.00111
\(201\) 1.04040 0.0733839
\(202\) 45.8387 3.22520
\(203\) 32.0770 2.25136
\(204\) 5.94967 0.416560
\(205\) −2.06392 −0.144150
\(206\) −18.2905 −1.27436
\(207\) −2.91520 −0.202620
\(208\) 44.1303 3.05989
\(209\) −14.9561 −1.03453
\(210\) 10.8615 0.749511
\(211\) −0.579477 −0.0398929 −0.0199464 0.999801i \(-0.506350\pi\)
−0.0199464 + 0.999801i \(0.506350\pi\)
\(212\) 13.1128 0.900593
\(213\) −3.04806 −0.208850
\(214\) −20.1176 −1.37521
\(215\) −3.33828 −0.227668
\(216\) −7.17119 −0.487938
\(217\) 8.02305 0.544640
\(218\) −44.2819 −2.99915
\(219\) 0.895688 0.0605250
\(220\) −11.5949 −0.781726
\(221\) 6.04616 0.406709
\(222\) 2.11630 0.142037
\(223\) −5.76932 −0.386342 −0.193171 0.981165i \(-0.561877\pi\)
−0.193171 + 0.981165i \(0.561877\pi\)
\(224\) 38.1892 2.55162
\(225\) −3.94634 −0.263089
\(226\) −23.1415 −1.53935
\(227\) 20.6353 1.36961 0.684807 0.728725i \(-0.259887\pi\)
0.684807 + 0.728725i \(0.259887\pi\)
\(228\) 29.9803 1.98549
\(229\) −9.06771 −0.599211 −0.299606 0.954063i \(-0.596855\pi\)
−0.299606 + 0.954063i \(0.596855\pi\)
\(230\) 7.77932 0.512953
\(231\) 9.66192 0.635708
\(232\) 56.5160 3.71045
\(233\) −4.05467 −0.265630 −0.132815 0.991141i \(-0.542402\pi\)
−0.132815 + 0.991141i \(0.542402\pi\)
\(234\) −12.5712 −0.821807
\(235\) 6.97301 0.454869
\(236\) 31.2516 2.03431
\(237\) 15.4614 1.00433
\(238\) 13.2301 0.857582
\(239\) −13.1040 −0.847627 −0.423813 0.905750i \(-0.639309\pi\)
−0.423813 + 0.905750i \(0.639309\pi\)
\(240\) 9.36770 0.604682
\(241\) 24.8821 1.60279 0.801397 0.598133i \(-0.204090\pi\)
0.801397 + 0.598133i \(0.204090\pi\)
\(242\) 13.9473 0.896563
\(243\) 1.00000 0.0641500
\(244\) −0.273656 −0.0175191
\(245\) 9.81970 0.627358
\(246\) 5.22717 0.333272
\(247\) 30.4665 1.93854
\(248\) 14.1357 0.897617
\(249\) 2.31992 0.147019
\(250\) 23.8737 1.50990
\(251\) −21.8411 −1.37860 −0.689299 0.724477i \(-0.742081\pi\)
−0.689299 + 0.724477i \(0.742081\pi\)
\(252\) −19.3678 −1.22006
\(253\) 6.92018 0.435068
\(254\) −44.1072 −2.76753
\(255\) 1.28344 0.0803721
\(256\) −19.5671 −1.22294
\(257\) −6.78537 −0.423260 −0.211630 0.977350i \(-0.567877\pi\)
−0.211630 + 0.977350i \(0.567877\pi\)
\(258\) 8.45467 0.526364
\(259\) 3.31335 0.205882
\(260\) 23.6195 1.46482
\(261\) −7.88097 −0.487820
\(262\) 20.6629 1.27656
\(263\) −2.57516 −0.158791 −0.0793956 0.996843i \(-0.525299\pi\)
−0.0793956 + 0.996843i \(0.525299\pi\)
\(264\) 17.0232 1.04770
\(265\) 2.82865 0.173763
\(266\) 66.6664 4.08758
\(267\) −7.16653 −0.438584
\(268\) 4.95069 0.302412
\(269\) 9.47293 0.577575 0.288787 0.957393i \(-0.406748\pi\)
0.288787 + 0.957393i \(0.406748\pi\)
\(270\) −2.66854 −0.162402
\(271\) 5.88575 0.357534 0.178767 0.983891i \(-0.442789\pi\)
0.178767 + 0.983891i \(0.442789\pi\)
\(272\) 11.4106 0.691870
\(273\) −19.6819 −1.19120
\(274\) 9.88190 0.596988
\(275\) 9.36794 0.564908
\(276\) −13.8719 −0.834988
\(277\) 7.51482 0.451522 0.225761 0.974183i \(-0.427513\pi\)
0.225761 + 0.974183i \(0.427513\pi\)
\(278\) −25.5822 −1.53432
\(279\) −1.97118 −0.118011
\(280\) 29.9609 1.79051
\(281\) 3.51751 0.209837 0.104918 0.994481i \(-0.466542\pi\)
0.104918 + 0.994481i \(0.466542\pi\)
\(282\) −17.6602 −1.05165
\(283\) −7.39641 −0.439671 −0.219835 0.975537i \(-0.570552\pi\)
−0.219835 + 0.975537i \(0.570552\pi\)
\(284\) −14.5041 −0.860660
\(285\) 6.46723 0.383086
\(286\) 29.8419 1.76459
\(287\) 8.18383 0.483076
\(288\) −9.38267 −0.552879
\(289\) −15.4367 −0.908039
\(290\) 21.0307 1.23496
\(291\) −10.0203 −0.587403
\(292\) 4.26210 0.249420
\(293\) −6.89255 −0.402667 −0.201334 0.979523i \(-0.564528\pi\)
−0.201334 + 0.979523i \(0.564528\pi\)
\(294\) −24.8698 −1.45044
\(295\) 6.74149 0.392505
\(296\) 5.83774 0.339312
\(297\) −2.37383 −0.137744
\(298\) −30.5055 −1.76714
\(299\) −14.0968 −0.815241
\(300\) −18.7785 −1.08418
\(301\) 13.2369 0.762963
\(302\) 26.4653 1.52291
\(303\) −17.6323 −1.01295
\(304\) 57.4979 3.29773
\(305\) −0.0590321 −0.00338017
\(306\) −3.25050 −0.185819
\(307\) 9.83725 0.561442 0.280721 0.959789i \(-0.409427\pi\)
0.280721 + 0.959789i \(0.409427\pi\)
\(308\) 45.9759 2.61972
\(309\) 7.03561 0.400242
\(310\) 5.26016 0.298757
\(311\) 4.49528 0.254904 0.127452 0.991845i \(-0.459320\pi\)
0.127452 + 0.991845i \(0.459320\pi\)
\(312\) −34.6773 −1.96321
\(313\) −4.03795 −0.228238 −0.114119 0.993467i \(-0.536405\pi\)
−0.114119 + 0.993467i \(0.536405\pi\)
\(314\) −54.5391 −3.07782
\(315\) −4.17796 −0.235401
\(316\) 73.5725 4.13878
\(317\) 33.1515 1.86197 0.930986 0.365055i \(-0.118950\pi\)
0.930986 + 0.365055i \(0.118950\pi\)
\(318\) −7.16397 −0.401736
\(319\) 18.7081 1.04745
\(320\) 6.30263 0.352328
\(321\) 7.73840 0.431916
\(322\) −30.8465 −1.71901
\(323\) 7.87761 0.438322
\(324\) 4.75846 0.264359
\(325\) −19.0831 −1.05854
\(326\) 12.0686 0.668418
\(327\) 17.0334 0.941951
\(328\) 14.4190 0.796154
\(329\) −27.6493 −1.52436
\(330\) 6.33466 0.348711
\(331\) 13.0377 0.716618 0.358309 0.933603i \(-0.383354\pi\)
0.358309 + 0.933603i \(0.383354\pi\)
\(332\) 11.0393 0.605858
\(333\) −0.814054 −0.0446099
\(334\) 3.33039 0.182231
\(335\) 1.06794 0.0583480
\(336\) −37.1447 −2.02641
\(337\) 5.81223 0.316613 0.158306 0.987390i \(-0.449397\pi\)
0.158306 + 0.987390i \(0.449397\pi\)
\(338\) −26.9937 −1.46826
\(339\) 8.90159 0.483468
\(340\) 6.10721 0.331210
\(341\) 4.67923 0.253395
\(342\) −16.3792 −0.885686
\(343\) −10.4457 −0.564016
\(344\) 23.3219 1.25743
\(345\) −2.99239 −0.161105
\(346\) −8.27009 −0.444603
\(347\) 35.6214 1.91226 0.956128 0.292951i \(-0.0946372\pi\)
0.956128 + 0.292951i \(0.0946372\pi\)
\(348\) −37.5013 −2.01028
\(349\) 9.83278 0.526337 0.263168 0.964750i \(-0.415233\pi\)
0.263168 + 0.964750i \(0.415233\pi\)
\(350\) −41.7573 −2.23202
\(351\) 4.83564 0.258107
\(352\) 22.2728 1.18715
\(353\) −17.2384 −0.917508 −0.458754 0.888563i \(-0.651704\pi\)
−0.458754 + 0.888563i \(0.651704\pi\)
\(354\) −17.0738 −0.907462
\(355\) −3.12877 −0.166058
\(356\) −34.1017 −1.80738
\(357\) −5.08909 −0.269343
\(358\) −14.5141 −0.767095
\(359\) 6.84798 0.361423 0.180711 0.983536i \(-0.442160\pi\)
0.180711 + 0.983536i \(0.442160\pi\)
\(360\) −7.36107 −0.387963
\(361\) 20.6952 1.08922
\(362\) 6.73964 0.354228
\(363\) −5.36494 −0.281586
\(364\) −93.6558 −4.90890
\(365\) 0.919404 0.0481238
\(366\) 0.149507 0.00781488
\(367\) −10.6940 −0.558225 −0.279112 0.960258i \(-0.590040\pi\)
−0.279112 + 0.960258i \(0.590040\pi\)
\(368\) −26.6043 −1.38684
\(369\) −2.01068 −0.104672
\(370\) 2.17234 0.112934
\(371\) −11.2162 −0.582314
\(372\) −9.37977 −0.486318
\(373\) −10.0366 −0.519674 −0.259837 0.965652i \(-0.583669\pi\)
−0.259837 + 0.965652i \(0.583669\pi\)
\(374\) 7.71613 0.398991
\(375\) −9.18323 −0.474220
\(376\) −48.7149 −2.51228
\(377\) −38.1095 −1.96274
\(378\) 10.5813 0.544242
\(379\) −2.48673 −0.127735 −0.0638673 0.997958i \(-0.520343\pi\)
−0.0638673 + 0.997958i \(0.520343\pi\)
\(380\) 30.7741 1.57868
\(381\) 16.9662 0.869207
\(382\) 53.9054 2.75804
\(383\) −17.4184 −0.890041 −0.445021 0.895520i \(-0.646804\pi\)
−0.445021 + 0.895520i \(0.646804\pi\)
\(384\) 2.80302 0.143041
\(385\) 9.91775 0.505455
\(386\) −16.7043 −0.850229
\(387\) −3.25216 −0.165317
\(388\) −47.6814 −2.42066
\(389\) −28.8224 −1.46135 −0.730677 0.682723i \(-0.760796\pi\)
−0.730677 + 0.682723i \(0.760796\pi\)
\(390\) −12.9041 −0.653424
\(391\) −3.64497 −0.184334
\(392\) −68.6025 −3.46495
\(393\) −7.94817 −0.400932
\(394\) 28.1411 1.41773
\(395\) 15.8708 0.798546
\(396\) −11.2958 −0.567634
\(397\) 37.2030 1.86716 0.933582 0.358363i \(-0.116665\pi\)
0.933582 + 0.358363i \(0.116665\pi\)
\(398\) −24.4304 −1.22458
\(399\) −25.6438 −1.28380
\(400\) −36.0145 −1.80073
\(401\) 11.9679 0.597650 0.298825 0.954308i \(-0.403405\pi\)
0.298825 + 0.954308i \(0.403405\pi\)
\(402\) −2.70472 −0.134899
\(403\) −9.53189 −0.474817
\(404\) −83.9026 −4.17431
\(405\) 1.02648 0.0510061
\(406\) −83.3907 −4.13861
\(407\) 1.93243 0.0957868
\(408\) −8.96638 −0.443902
\(409\) 14.4765 0.715816 0.357908 0.933757i \(-0.383490\pi\)
0.357908 + 0.933757i \(0.383490\pi\)
\(410\) 5.36558 0.264987
\(411\) −3.80116 −0.187498
\(412\) 33.4787 1.64938
\(413\) −26.7313 −1.31536
\(414\) 7.57865 0.372470
\(415\) 2.38135 0.116896
\(416\) −45.3712 −2.22450
\(417\) 9.84042 0.481887
\(418\) 38.8814 1.90175
\(419\) 0.843042 0.0411853 0.0205926 0.999788i \(-0.493445\pi\)
0.0205926 + 0.999788i \(0.493445\pi\)
\(420\) −19.8807 −0.970077
\(421\) −8.52732 −0.415596 −0.207798 0.978172i \(-0.566630\pi\)
−0.207798 + 0.978172i \(0.566630\pi\)
\(422\) 1.50647 0.0733338
\(423\) 6.79314 0.330294
\(424\) −19.7616 −0.959706
\(425\) −4.93424 −0.239346
\(426\) 7.92406 0.383922
\(427\) 0.234074 0.0113276
\(428\) 36.8229 1.77990
\(429\) −11.4790 −0.554210
\(430\) 8.67853 0.418516
\(431\) −15.9995 −0.770670 −0.385335 0.922777i \(-0.625914\pi\)
−0.385335 + 0.922777i \(0.625914\pi\)
\(432\) 9.12606 0.439078
\(433\) 38.0094 1.82662 0.913309 0.407268i \(-0.133518\pi\)
0.913309 + 0.407268i \(0.133518\pi\)
\(434\) −20.8576 −1.00119
\(435\) −8.08964 −0.387869
\(436\) 81.0530 3.88173
\(437\) −18.3669 −0.878610
\(438\) −2.32852 −0.111261
\(439\) −6.54202 −0.312233 −0.156117 0.987739i \(-0.549898\pi\)
−0.156117 + 0.987739i \(0.549898\pi\)
\(440\) 17.4739 0.833037
\(441\) 9.56640 0.455543
\(442\) −15.7182 −0.747640
\(443\) 21.5203 1.02246 0.511229 0.859445i \(-0.329190\pi\)
0.511229 + 0.859445i \(0.329190\pi\)
\(444\) −3.87365 −0.183835
\(445\) −7.35628 −0.348721
\(446\) 14.9985 0.710200
\(447\) 11.7342 0.555010
\(448\) −24.9911 −1.18072
\(449\) 24.3737 1.15027 0.575134 0.818059i \(-0.304950\pi\)
0.575134 + 0.818059i \(0.304950\pi\)
\(450\) 10.2593 0.483629
\(451\) 4.77301 0.224752
\(452\) 42.3579 1.99235
\(453\) −10.1801 −0.478304
\(454\) −53.6457 −2.51772
\(455\) −20.2031 −0.947135
\(456\) −45.1815 −2.11582
\(457\) 14.7107 0.688138 0.344069 0.938944i \(-0.388195\pi\)
0.344069 + 0.938944i \(0.388195\pi\)
\(458\) 23.5734 1.10151
\(459\) 1.25033 0.0583606
\(460\) −14.2392 −0.663904
\(461\) 11.1049 0.517208 0.258604 0.965983i \(-0.416738\pi\)
0.258604 + 0.965983i \(0.416738\pi\)
\(462\) −25.1181 −1.16860
\(463\) 31.5632 1.46686 0.733432 0.679763i \(-0.237917\pi\)
0.733432 + 0.679763i \(0.237917\pi\)
\(464\) −71.9222 −3.33890
\(465\) −2.02337 −0.0938315
\(466\) 10.5409 0.488300
\(467\) 0.242139 0.0112049 0.00560243 0.999984i \(-0.498217\pi\)
0.00560243 + 0.999984i \(0.498217\pi\)
\(468\) 23.0102 1.06365
\(469\) −4.23461 −0.195536
\(470\) −18.1278 −0.836172
\(471\) 20.9789 0.966659
\(472\) −47.0975 −2.16784
\(473\) 7.72008 0.354970
\(474\) −40.1950 −1.84622
\(475\) −24.8636 −1.14082
\(476\) −24.2162 −1.10995
\(477\) 2.75569 0.126174
\(478\) 34.0665 1.55817
\(479\) 32.3970 1.48026 0.740129 0.672465i \(-0.234765\pi\)
0.740129 + 0.672465i \(0.234765\pi\)
\(480\) −9.63110 −0.439598
\(481\) −3.93647 −0.179488
\(482\) −64.6860 −2.94637
\(483\) 11.8654 0.539894
\(484\) −25.5289 −1.16040
\(485\) −10.2857 −0.467048
\(486\) −2.59970 −0.117925
\(487\) 16.7196 0.757636 0.378818 0.925471i \(-0.376331\pi\)
0.378818 + 0.925471i \(0.376331\pi\)
\(488\) 0.412411 0.0186690
\(489\) −4.64229 −0.209932
\(490\) −25.5283 −1.15325
\(491\) 9.07243 0.409433 0.204716 0.978821i \(-0.434373\pi\)
0.204716 + 0.978821i \(0.434373\pi\)
\(492\) −9.56774 −0.431347
\(493\) −9.85384 −0.443795
\(494\) −79.2039 −3.56355
\(495\) −2.43668 −0.109521
\(496\) −17.9891 −0.807733
\(497\) 12.4062 0.556493
\(498\) −6.03110 −0.270260
\(499\) 41.4678 1.85635 0.928177 0.372138i \(-0.121375\pi\)
0.928177 + 0.372138i \(0.121375\pi\)
\(500\) −43.6981 −1.95424
\(501\) −1.28107 −0.0572338
\(502\) 56.7804 2.53423
\(503\) 7.89599 0.352065 0.176032 0.984384i \(-0.443674\pi\)
0.176032 + 0.984384i \(0.443674\pi\)
\(504\) 29.1881 1.30014
\(505\) −18.0992 −0.805402
\(506\) −17.9904 −0.799772
\(507\) 10.3834 0.461142
\(508\) 80.7333 3.58196
\(509\) −6.09805 −0.270291 −0.135146 0.990826i \(-0.543150\pi\)
−0.135146 + 0.990826i \(0.543150\pi\)
\(510\) −3.33657 −0.147746
\(511\) −3.64561 −0.161272
\(512\) 45.2627 2.00035
\(513\) 6.30041 0.278170
\(514\) 17.6400 0.778066
\(515\) 7.22190 0.318235
\(516\) −15.4753 −0.681262
\(517\) −16.1258 −0.709210
\(518\) −8.61373 −0.378466
\(519\) 3.18117 0.139638
\(520\) −35.5955 −1.56096
\(521\) −6.33909 −0.277721 −0.138860 0.990312i \(-0.544344\pi\)
−0.138860 + 0.990312i \(0.544344\pi\)
\(522\) 20.4882 0.896744
\(523\) −22.7979 −0.996883 −0.498442 0.866923i \(-0.666094\pi\)
−0.498442 + 0.866923i \(0.666094\pi\)
\(524\) −37.8211 −1.65222
\(525\) 16.0623 0.701018
\(526\) 6.69466 0.291901
\(527\) −2.46463 −0.107361
\(528\) −21.6637 −0.942792
\(529\) −14.5016 −0.630506
\(530\) −7.35366 −0.319423
\(531\) 6.56759 0.285009
\(532\) −122.025 −5.29047
\(533\) −9.72291 −0.421146
\(534\) 18.6309 0.806236
\(535\) 7.94330 0.343419
\(536\) −7.46089 −0.322261
\(537\) 5.58298 0.240924
\(538\) −24.6268 −1.06174
\(539\) −22.7090 −0.978146
\(540\) 4.88446 0.210194
\(541\) 19.9653 0.858376 0.429188 0.903215i \(-0.358800\pi\)
0.429188 + 0.903215i \(0.358800\pi\)
\(542\) −15.3012 −0.657244
\(543\) −2.59246 −0.111253
\(544\) −11.7315 −0.502982
\(545\) 17.4844 0.748951
\(546\) 51.1672 2.18975
\(547\) −5.36865 −0.229547 −0.114773 0.993392i \(-0.536614\pi\)
−0.114773 + 0.993392i \(0.536614\pi\)
\(548\) −18.0877 −0.772668
\(549\) −0.0575094 −0.00245444
\(550\) −24.3539 −1.03845
\(551\) −49.6533 −2.11530
\(552\) 20.9054 0.889795
\(553\) −62.9307 −2.67609
\(554\) −19.5363 −0.830018
\(555\) −0.835609 −0.0354696
\(556\) 46.8253 1.98583
\(557\) −15.8883 −0.673208 −0.336604 0.941646i \(-0.609278\pi\)
−0.336604 + 0.941646i \(0.609278\pi\)
\(558\) 5.12447 0.216936
\(559\) −15.7263 −0.665151
\(560\) −38.1283 −1.61121
\(561\) −2.96808 −0.125312
\(562\) −9.14448 −0.385736
\(563\) 7.67544 0.323481 0.161741 0.986833i \(-0.448289\pi\)
0.161741 + 0.986833i \(0.448289\pi\)
\(564\) 32.3249 1.36112
\(565\) 9.13729 0.384409
\(566\) 19.2285 0.808233
\(567\) −4.07018 −0.170932
\(568\) 21.8582 0.917152
\(569\) 13.8353 0.580006 0.290003 0.957026i \(-0.406344\pi\)
0.290003 + 0.957026i \(0.406344\pi\)
\(570\) −16.8129 −0.704215
\(571\) 9.21485 0.385630 0.192815 0.981235i \(-0.438238\pi\)
0.192815 + 0.981235i \(0.438238\pi\)
\(572\) −54.6223 −2.28387
\(573\) −20.7352 −0.866225
\(574\) −21.2755 −0.888024
\(575\) 11.5044 0.479765
\(576\) 6.14005 0.255835
\(577\) −17.4636 −0.727018 −0.363509 0.931591i \(-0.618421\pi\)
−0.363509 + 0.931591i \(0.618421\pi\)
\(578\) 40.1308 1.66922
\(579\) 6.42548 0.267034
\(580\) −38.4943 −1.59839
\(581\) −9.44250 −0.391741
\(582\) 26.0499 1.07980
\(583\) −6.54153 −0.270922
\(584\) −6.42315 −0.265792
\(585\) 4.96367 0.205223
\(586\) 17.9186 0.740211
\(587\) 29.2954 1.20915 0.604576 0.796548i \(-0.293343\pi\)
0.604576 + 0.796548i \(0.293343\pi\)
\(588\) 45.5214 1.87727
\(589\) −12.4192 −0.511725
\(590\) −17.5259 −0.721529
\(591\) −10.8247 −0.445269
\(592\) −7.42911 −0.305334
\(593\) 25.5900 1.05086 0.525429 0.850838i \(-0.323905\pi\)
0.525429 + 0.850838i \(0.323905\pi\)
\(594\) 6.17125 0.253210
\(595\) −5.22384 −0.214156
\(596\) 55.8369 2.28717
\(597\) 9.39737 0.384609
\(598\) 36.6476 1.49863
\(599\) 12.8508 0.525070 0.262535 0.964923i \(-0.415442\pi\)
0.262535 + 0.964923i \(0.415442\pi\)
\(600\) 28.3000 1.15534
\(601\) −6.57908 −0.268366 −0.134183 0.990957i \(-0.542841\pi\)
−0.134183 + 0.990957i \(0.542841\pi\)
\(602\) −34.4120 −1.40253
\(603\) 1.04040 0.0423682
\(604\) −48.4417 −1.97107
\(605\) −5.50699 −0.223891
\(606\) 45.8387 1.86207
\(607\) −3.67511 −0.149168 −0.0745841 0.997215i \(-0.523763\pi\)
−0.0745841 + 0.997215i \(0.523763\pi\)
\(608\) −59.1147 −2.39742
\(609\) 32.0770 1.29983
\(610\) 0.153466 0.00621366
\(611\) 32.8492 1.32893
\(612\) 5.94967 0.240501
\(613\) −9.58731 −0.387228 −0.193614 0.981078i \(-0.562021\pi\)
−0.193614 + 0.981078i \(0.562021\pi\)
\(614\) −25.5739 −1.03208
\(615\) −2.06392 −0.0832252
\(616\) −69.2875 −2.79167
\(617\) −48.5144 −1.95312 −0.976558 0.215254i \(-0.930942\pi\)
−0.976558 + 0.215254i \(0.930942\pi\)
\(618\) −18.2905 −0.735752
\(619\) 32.7471 1.31622 0.658109 0.752923i \(-0.271357\pi\)
0.658109 + 0.752923i \(0.271357\pi\)
\(620\) −9.62813 −0.386675
\(621\) −2.91520 −0.116983
\(622\) −11.6864 −0.468582
\(623\) 29.1691 1.16863
\(624\) 44.1303 1.76663
\(625\) 10.3053 0.412213
\(626\) 10.4975 0.419563
\(627\) −14.9561 −0.597289
\(628\) 99.8276 3.98355
\(629\) −1.01784 −0.0405839
\(630\) 10.8615 0.432731
\(631\) −29.9006 −1.19032 −0.595161 0.803606i \(-0.702912\pi\)
−0.595161 + 0.803606i \(0.702912\pi\)
\(632\) −110.877 −4.41044
\(633\) −0.579477 −0.0230322
\(634\) −86.1840 −3.42280
\(635\) 17.4155 0.691112
\(636\) 13.1128 0.519958
\(637\) 46.2596 1.83287
\(638\) −48.6355 −1.92550
\(639\) −3.04806 −0.120579
\(640\) 2.87724 0.113733
\(641\) 7.08309 0.279765 0.139883 0.990168i \(-0.455327\pi\)
0.139883 + 0.990168i \(0.455327\pi\)
\(642\) −20.1176 −0.793977
\(643\) 2.45035 0.0966322 0.0483161 0.998832i \(-0.484615\pi\)
0.0483161 + 0.998832i \(0.484615\pi\)
\(644\) 56.4610 2.22488
\(645\) −3.33828 −0.131444
\(646\) −20.4795 −0.805754
\(647\) −10.9253 −0.429516 −0.214758 0.976667i \(-0.568896\pi\)
−0.214758 + 0.976667i \(0.568896\pi\)
\(648\) −7.17119 −0.281711
\(649\) −15.5903 −0.611974
\(650\) 49.6104 1.94588
\(651\) 8.02305 0.314448
\(652\) −22.0902 −0.865119
\(653\) 23.1792 0.907073 0.453536 0.891238i \(-0.350162\pi\)
0.453536 + 0.891238i \(0.350162\pi\)
\(654\) −44.2819 −1.73156
\(655\) −8.15863 −0.318784
\(656\) −18.3496 −0.716430
\(657\) 0.895688 0.0349441
\(658\) 71.8801 2.80218
\(659\) −45.1554 −1.75900 −0.879502 0.475895i \(-0.842124\pi\)
−0.879502 + 0.475895i \(0.842124\pi\)
\(660\) −11.5949 −0.451330
\(661\) −0.573851 −0.0223202 −0.0111601 0.999938i \(-0.503552\pi\)
−0.0111601 + 0.999938i \(0.503552\pi\)
\(662\) −33.8942 −1.31734
\(663\) 6.04616 0.234813
\(664\) −16.6366 −0.645625
\(665\) −26.3228 −1.02076
\(666\) 2.11630 0.0820050
\(667\) 22.9746 0.889579
\(668\) −6.09591 −0.235858
\(669\) −5.76932 −0.223055
\(670\) −2.77634 −0.107259
\(671\) 0.136517 0.00527020
\(672\) 38.1892 1.47318
\(673\) 32.1480 1.23921 0.619607 0.784912i \(-0.287292\pi\)
0.619607 + 0.784912i \(0.287292\pi\)
\(674\) −15.1101 −0.582019
\(675\) −3.94634 −0.151895
\(676\) 49.4089 1.90034
\(677\) 35.7059 1.37229 0.686145 0.727465i \(-0.259301\pi\)
0.686145 + 0.727465i \(0.259301\pi\)
\(678\) −23.1415 −0.888744
\(679\) 40.7846 1.56517
\(680\) −9.20380 −0.352950
\(681\) 20.6353 0.790747
\(682\) −12.1646 −0.465808
\(683\) 10.9963 0.420761 0.210380 0.977620i \(-0.432530\pi\)
0.210380 + 0.977620i \(0.432530\pi\)
\(684\) 29.9803 1.14632
\(685\) −3.90181 −0.149081
\(686\) 27.1558 1.03681
\(687\) −9.06771 −0.345955
\(688\) −29.6794 −1.13152
\(689\) 13.3255 0.507661
\(690\) 7.77932 0.296154
\(691\) 27.2872 1.03806 0.519028 0.854758i \(-0.326294\pi\)
0.519028 + 0.854758i \(0.326294\pi\)
\(692\) 15.1375 0.575440
\(693\) 9.66192 0.367026
\(694\) −92.6050 −3.51524
\(695\) 10.1010 0.383152
\(696\) 56.5160 2.14223
\(697\) −2.51402 −0.0952253
\(698\) −25.5623 −0.967548
\(699\) −4.05467 −0.153362
\(700\) 76.4321 2.88886
\(701\) −23.3289 −0.881120 −0.440560 0.897723i \(-0.645220\pi\)
−0.440560 + 0.897723i \(0.645220\pi\)
\(702\) −12.5712 −0.474470
\(703\) −5.12888 −0.193439
\(704\) −14.5754 −0.549332
\(705\) 6.97301 0.262619
\(706\) 44.8148 1.68663
\(707\) 71.7667 2.69906
\(708\) 31.2516 1.17451
\(709\) 16.6842 0.626588 0.313294 0.949656i \(-0.398567\pi\)
0.313294 + 0.949656i \(0.398567\pi\)
\(710\) 8.13388 0.305259
\(711\) 15.4614 0.579847
\(712\) 51.3926 1.92602
\(713\) 5.74636 0.215203
\(714\) 13.2301 0.495125
\(715\) −11.7829 −0.440656
\(716\) 26.5664 0.992834
\(717\) −13.1040 −0.489378
\(718\) −17.8027 −0.664392
\(719\) 20.1339 0.750866 0.375433 0.926849i \(-0.377494\pi\)
0.375433 + 0.926849i \(0.377494\pi\)
\(720\) 9.36770 0.349114
\(721\) −28.6362 −1.06647
\(722\) −53.8013 −2.00228
\(723\) 24.8821 0.925374
\(724\) −12.3361 −0.458469
\(725\) 31.1010 1.15506
\(726\) 13.9473 0.517631
\(727\) 15.7036 0.582414 0.291207 0.956660i \(-0.405943\pi\)
0.291207 + 0.956660i \(0.405943\pi\)
\(728\) 141.143 5.23110
\(729\) 1.00000 0.0370370
\(730\) −2.39018 −0.0884645
\(731\) −4.06629 −0.150397
\(732\) −0.273656 −0.0101146
\(733\) 44.7785 1.65393 0.826965 0.562253i \(-0.190065\pi\)
0.826965 + 0.562253i \(0.190065\pi\)
\(734\) 27.8014 1.02617
\(735\) 9.81970 0.362205
\(736\) 27.3523 1.00822
\(737\) −2.46972 −0.0909734
\(738\) 5.22717 0.192415
\(739\) 16.7201 0.615058 0.307529 0.951539i \(-0.400498\pi\)
0.307529 + 0.951539i \(0.400498\pi\)
\(740\) −3.97622 −0.146169
\(741\) 30.4665 1.11921
\(742\) 29.1587 1.07045
\(743\) 23.2226 0.851956 0.425978 0.904734i \(-0.359930\pi\)
0.425978 + 0.904734i \(0.359930\pi\)
\(744\) 14.1357 0.518239
\(745\) 12.0449 0.441292
\(746\) 26.0921 0.955301
\(747\) 2.31992 0.0848814
\(748\) −14.1235 −0.516406
\(749\) −31.4967 −1.15087
\(750\) 23.8737 0.871743
\(751\) −37.9132 −1.38347 −0.691735 0.722151i \(-0.743154\pi\)
−0.691735 + 0.722151i \(0.743154\pi\)
\(752\) 61.9946 2.26071
\(753\) −21.8411 −0.795934
\(754\) 99.0734 3.60804
\(755\) −10.4497 −0.380302
\(756\) −19.3678 −0.704401
\(757\) −50.1984 −1.82449 −0.912245 0.409645i \(-0.865653\pi\)
−0.912245 + 0.409645i \(0.865653\pi\)
\(758\) 6.46476 0.234811
\(759\) 6.92018 0.251187
\(760\) −46.3778 −1.68230
\(761\) 23.5439 0.853466 0.426733 0.904378i \(-0.359664\pi\)
0.426733 + 0.904378i \(0.359664\pi\)
\(762\) −44.1072 −1.59784
\(763\) −69.3292 −2.50989
\(764\) −98.6677 −3.56967
\(765\) 1.28344 0.0464029
\(766\) 45.2828 1.63613
\(767\) 31.7585 1.14673
\(768\) −19.5671 −0.706068
\(769\) 5.44001 0.196172 0.0980859 0.995178i \(-0.468728\pi\)
0.0980859 + 0.995178i \(0.468728\pi\)
\(770\) −25.7832 −0.929163
\(771\) −6.78537 −0.244369
\(772\) 30.5754 1.10043
\(773\) −7.70465 −0.277117 −0.138559 0.990354i \(-0.544247\pi\)
−0.138559 + 0.990354i \(0.544247\pi\)
\(774\) 8.45467 0.303897
\(775\) 7.77893 0.279428
\(776\) 71.8578 2.57954
\(777\) 3.31335 0.118866
\(778\) 74.9298 2.68636
\(779\) −12.6681 −0.453882
\(780\) 23.6195 0.845713
\(781\) 7.23558 0.258909
\(782\) 9.47584 0.338855
\(783\) −7.88097 −0.281643
\(784\) 87.3035 3.11798
\(785\) 21.5344 0.768597
\(786\) 20.6629 0.737021
\(787\) 11.1301 0.396744 0.198372 0.980127i \(-0.436435\pi\)
0.198372 + 0.980127i \(0.436435\pi\)
\(788\) −51.5090 −1.83493
\(789\) −2.57516 −0.0916782
\(790\) −41.2593 −1.46794
\(791\) −36.2311 −1.28823
\(792\) 17.0232 0.604893
\(793\) −0.278095 −0.00987543
\(794\) −96.7168 −3.43235
\(795\) 2.82865 0.100322
\(796\) 44.7170 1.58495
\(797\) −22.6263 −0.801465 −0.400733 0.916195i \(-0.631244\pi\)
−0.400733 + 0.916195i \(0.631244\pi\)
\(798\) 66.6664 2.35996
\(799\) 8.49369 0.300485
\(800\) 37.0272 1.30911
\(801\) −7.16653 −0.253217
\(802\) −31.1131 −1.09864
\(803\) −2.12621 −0.0750323
\(804\) 4.95069 0.174597
\(805\) 12.1796 0.429273
\(806\) 24.7801 0.872841
\(807\) 9.47293 0.333463
\(808\) 126.445 4.44830
\(809\) −7.66768 −0.269581 −0.134791 0.990874i \(-0.543036\pi\)
−0.134791 + 0.990874i \(0.543036\pi\)
\(810\) −2.66854 −0.0937629
\(811\) 38.3699 1.34735 0.673674 0.739028i \(-0.264715\pi\)
0.673674 + 0.739028i \(0.264715\pi\)
\(812\) 152.637 5.35652
\(813\) 5.88575 0.206422
\(814\) −5.02374 −0.176082
\(815\) −4.76521 −0.166918
\(816\) 11.4106 0.399451
\(817\) −20.4900 −0.716853
\(818\) −37.6346 −1.31586
\(819\) −19.6819 −0.687742
\(820\) −9.82108 −0.342967
\(821\) −46.7528 −1.63168 −0.815842 0.578275i \(-0.803726\pi\)
−0.815842 + 0.578275i \(0.803726\pi\)
\(822\) 9.88190 0.344671
\(823\) −47.1983 −1.64523 −0.822614 0.568600i \(-0.807485\pi\)
−0.822614 + 0.568600i \(0.807485\pi\)
\(824\) −50.4537 −1.75764
\(825\) 9.36794 0.326150
\(826\) 69.4935 2.41799
\(827\) 31.2545 1.08683 0.543413 0.839465i \(-0.317132\pi\)
0.543413 + 0.839465i \(0.317132\pi\)
\(828\) −13.8719 −0.482081
\(829\) −4.85338 −0.168565 −0.0842825 0.996442i \(-0.526860\pi\)
−0.0842825 + 0.996442i \(0.526860\pi\)
\(830\) −6.19080 −0.214886
\(831\) 7.51482 0.260686
\(832\) 29.6910 1.02935
\(833\) 11.9612 0.414431
\(834\) −25.5822 −0.885839
\(835\) −1.31499 −0.0455070
\(836\) −71.1681 −2.46140
\(837\) −1.97118 −0.0681338
\(838\) −2.19166 −0.0757096
\(839\) 28.1752 0.972716 0.486358 0.873760i \(-0.338325\pi\)
0.486358 + 0.873760i \(0.338325\pi\)
\(840\) 29.9609 1.03375
\(841\) 33.1097 1.14171
\(842\) 22.1685 0.763978
\(843\) 3.51751 0.121149
\(844\) −2.75742 −0.0949144
\(845\) 10.6583 0.366657
\(846\) −17.6602 −0.607169
\(847\) 21.8363 0.750303
\(848\) 25.1486 0.863605
\(849\) −7.39641 −0.253844
\(850\) 12.8276 0.439982
\(851\) 2.37313 0.0813498
\(852\) −14.5041 −0.496902
\(853\) −3.61354 −0.123725 −0.0618626 0.998085i \(-0.519704\pi\)
−0.0618626 + 0.998085i \(0.519704\pi\)
\(854\) −0.608523 −0.0208232
\(855\) 6.46723 0.221175
\(856\) −55.4936 −1.89673
\(857\) −28.1944 −0.963103 −0.481551 0.876418i \(-0.659927\pi\)
−0.481551 + 0.876418i \(0.659927\pi\)
\(858\) 29.8419 1.01879
\(859\) −31.4098 −1.07169 −0.535843 0.844317i \(-0.680006\pi\)
−0.535843 + 0.844317i \(0.680006\pi\)
\(860\) −15.8851 −0.541676
\(861\) 8.18383 0.278904
\(862\) 41.5940 1.41670
\(863\) 33.4840 1.13981 0.569904 0.821711i \(-0.306980\pi\)
0.569904 + 0.821711i \(0.306980\pi\)
\(864\) −9.38267 −0.319205
\(865\) 3.26540 0.111027
\(866\) −98.8133 −3.35781
\(867\) −15.4367 −0.524257
\(868\) 38.1774 1.29582
\(869\) −36.7027 −1.24505
\(870\) 21.0307 0.713007
\(871\) 5.03098 0.170468
\(872\) −122.150 −4.13652
\(873\) −10.0203 −0.339137
\(874\) 47.7486 1.61512
\(875\) 37.3774 1.26359
\(876\) 4.26210 0.144003
\(877\) −48.3169 −1.63155 −0.815773 0.578372i \(-0.803688\pi\)
−0.815773 + 0.578372i \(0.803688\pi\)
\(878\) 17.0073 0.573969
\(879\) −6.89255 −0.232480
\(880\) −22.2373 −0.749620
\(881\) −53.5836 −1.80528 −0.902639 0.430399i \(-0.858373\pi\)
−0.902639 + 0.430399i \(0.858373\pi\)
\(882\) −24.8698 −0.837410
\(883\) 3.09441 0.104135 0.0520676 0.998644i \(-0.483419\pi\)
0.0520676 + 0.998644i \(0.483419\pi\)
\(884\) 28.7704 0.967654
\(885\) 6.74149 0.226613
\(886\) −55.9463 −1.87955
\(887\) 37.5967 1.26237 0.631187 0.775631i \(-0.282568\pi\)
0.631187 + 0.775631i \(0.282568\pi\)
\(888\) 5.83774 0.195902
\(889\) −69.0558 −2.31606
\(890\) 19.1242 0.641043
\(891\) −2.37383 −0.0795263
\(892\) −27.4531 −0.919197
\(893\) 42.7996 1.43223
\(894\) −30.5055 −1.02026
\(895\) 5.73081 0.191560
\(896\) −11.4088 −0.381141
\(897\) −14.0968 −0.470679
\(898\) −63.3645 −2.11450
\(899\) 15.5348 0.518114
\(900\) −18.7785 −0.625951
\(901\) 3.44553 0.114787
\(902\) −12.4084 −0.413155
\(903\) 13.2369 0.440497
\(904\) −63.8350 −2.12312
\(905\) −2.66111 −0.0884582
\(906\) 26.4653 0.879251
\(907\) 34.2699 1.13791 0.568956 0.822368i \(-0.307347\pi\)
0.568956 + 0.822368i \(0.307347\pi\)
\(908\) 98.1924 3.25863
\(909\) −17.6323 −0.584826
\(910\) 52.5220 1.74109
\(911\) 35.6531 1.18124 0.590620 0.806950i \(-0.298883\pi\)
0.590620 + 0.806950i \(0.298883\pi\)
\(912\) 57.4979 1.90395
\(913\) −5.50709 −0.182258
\(914\) −38.2435 −1.26498
\(915\) −0.0590321 −0.00195154
\(916\) −43.1484 −1.42566
\(917\) 32.3505 1.06831
\(918\) −3.25050 −0.107282
\(919\) 12.2073 0.402682 0.201341 0.979521i \(-0.435470\pi\)
0.201341 + 0.979521i \(0.435470\pi\)
\(920\) 21.4590 0.707482
\(921\) 9.83725 0.324148
\(922\) −28.8695 −0.950767
\(923\) −14.7393 −0.485151
\(924\) 45.9759 1.51250
\(925\) 3.21254 0.105628
\(926\) −82.0549 −2.69649
\(927\) 7.03561 0.231080
\(928\) 73.9445 2.42735
\(929\) 3.15561 0.103532 0.0517662 0.998659i \(-0.483515\pi\)
0.0517662 + 0.998659i \(0.483515\pi\)
\(930\) 5.26016 0.172487
\(931\) 60.2722 1.97534
\(932\) −19.2940 −0.631996
\(933\) 4.49528 0.147169
\(934\) −0.629490 −0.0205976
\(935\) −3.04667 −0.0996367
\(936\) −34.6773 −1.13346
\(937\) 22.8448 0.746305 0.373153 0.927770i \(-0.378277\pi\)
0.373153 + 0.927770i \(0.378277\pi\)
\(938\) 11.0087 0.359448
\(939\) −4.03795 −0.131773
\(940\) 33.1808 1.08224
\(941\) 1.51666 0.0494418 0.0247209 0.999694i \(-0.492130\pi\)
0.0247209 + 0.999694i \(0.492130\pi\)
\(942\) −54.5391 −1.77698
\(943\) 5.86152 0.190878
\(944\) 59.9362 1.95076
\(945\) −4.17796 −0.135909
\(946\) −20.0699 −0.652530
\(947\) 20.7148 0.673141 0.336570 0.941658i \(-0.390733\pi\)
0.336570 + 0.941658i \(0.390733\pi\)
\(948\) 73.5725 2.38952
\(949\) 4.33122 0.140597
\(950\) 64.6380 2.09713
\(951\) 33.1515 1.07501
\(952\) 36.4948 1.18280
\(953\) 59.7534 1.93560 0.967800 0.251719i \(-0.0809958\pi\)
0.967800 + 0.251719i \(0.0809958\pi\)
\(954\) −7.16397 −0.231942
\(955\) −21.2842 −0.688741
\(956\) −62.3549 −2.01670
\(957\) 18.7081 0.604746
\(958\) −84.2227 −2.72111
\(959\) 15.4714 0.499599
\(960\) 6.30263 0.203416
\(961\) −27.1145 −0.874660
\(962\) 10.2337 0.329946
\(963\) 7.73840 0.249367
\(964\) 118.400 3.81342
\(965\) 6.59561 0.212320
\(966\) −30.8465 −0.992470
\(967\) 14.3287 0.460780 0.230390 0.973098i \(-0.426000\pi\)
0.230390 + 0.973098i \(0.426000\pi\)
\(968\) 38.4730 1.23657
\(969\) 7.87761 0.253065
\(970\) 26.7397 0.858559
\(971\) −34.0186 −1.09171 −0.545855 0.837880i \(-0.683795\pi\)
−0.545855 + 0.837880i \(0.683795\pi\)
\(972\) 4.75846 0.152628
\(973\) −40.0523 −1.28402
\(974\) −43.4660 −1.39274
\(975\) −19.0831 −0.611147
\(976\) −0.524834 −0.0167995
\(977\) 22.5677 0.722004 0.361002 0.932565i \(-0.382435\pi\)
0.361002 + 0.932565i \(0.382435\pi\)
\(978\) 12.0686 0.385911
\(979\) 17.0121 0.543709
\(980\) 46.7267 1.49263
\(981\) 17.0334 0.543836
\(982\) −23.5856 −0.752648
\(983\) 15.6439 0.498961 0.249481 0.968380i \(-0.419740\pi\)
0.249481 + 0.968380i \(0.419740\pi\)
\(984\) 14.4190 0.459660
\(985\) −11.1113 −0.354037
\(986\) 25.6171 0.815814
\(987\) −27.6493 −0.880088
\(988\) 144.974 4.61223
\(989\) 9.48070 0.301469
\(990\) 6.33466 0.201329
\(991\) −8.79260 −0.279306 −0.139653 0.990200i \(-0.544599\pi\)
−0.139653 + 0.990200i \(0.544599\pi\)
\(992\) 18.4949 0.587213
\(993\) 13.0377 0.413739
\(994\) −32.2524 −1.02298
\(995\) 9.64619 0.305805
\(996\) 11.0393 0.349792
\(997\) −45.2410 −1.43280 −0.716399 0.697691i \(-0.754211\pi\)
−0.716399 + 0.697691i \(0.754211\pi\)
\(998\) −107.804 −3.41248
\(999\) −0.814054 −0.0257555
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 \(a_p\))