Properties

Label 8013.2.a.d.1.20
Level 8013
Weight 2
Character 8013.1
Self dual Yes
Analytic conductor 63.984
Analytic rank 0
Dimension 129
CM No

Related objects

Downloads

Learn more about

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 1.20
Character \(\chi\) = 8013.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.06267 q^{2} +1.00000 q^{3} +2.25459 q^{4} -1.75345 q^{5} -2.06267 q^{6} -2.34820 q^{7} -0.525142 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.06267 q^{2} +1.00000 q^{3} +2.25459 q^{4} -1.75345 q^{5} -2.06267 q^{6} -2.34820 q^{7} -0.525142 q^{8} +1.00000 q^{9} +3.61679 q^{10} -5.74292 q^{11} +2.25459 q^{12} +5.83807 q^{13} +4.84355 q^{14} -1.75345 q^{15} -3.42599 q^{16} -2.97113 q^{17} -2.06267 q^{18} -6.07952 q^{19} -3.95332 q^{20} -2.34820 q^{21} +11.8457 q^{22} -2.78663 q^{23} -0.525142 q^{24} -1.92540 q^{25} -12.0420 q^{26} +1.00000 q^{27} -5.29423 q^{28} -5.89421 q^{29} +3.61679 q^{30} +9.09188 q^{31} +8.11697 q^{32} -5.74292 q^{33} +6.12844 q^{34} +4.11745 q^{35} +2.25459 q^{36} -6.61608 q^{37} +12.5400 q^{38} +5.83807 q^{39} +0.920811 q^{40} -5.29461 q^{41} +4.84355 q^{42} -1.19262 q^{43} -12.9480 q^{44} -1.75345 q^{45} +5.74789 q^{46} -2.71820 q^{47} -3.42599 q^{48} -1.48597 q^{49} +3.97146 q^{50} -2.97113 q^{51} +13.1625 q^{52} -4.93841 q^{53} -2.06267 q^{54} +10.0699 q^{55} +1.23314 q^{56} -6.07952 q^{57} +12.1578 q^{58} -8.99053 q^{59} -3.95332 q^{60} -3.13818 q^{61} -18.7535 q^{62} -2.34820 q^{63} -9.89061 q^{64} -10.2368 q^{65} +11.8457 q^{66} +10.6438 q^{67} -6.69868 q^{68} -2.78663 q^{69} -8.49293 q^{70} +8.04529 q^{71} -0.525142 q^{72} -15.1625 q^{73} +13.6468 q^{74} -1.92540 q^{75} -13.7068 q^{76} +13.4855 q^{77} -12.0420 q^{78} +9.80770 q^{79} +6.00732 q^{80} +1.00000 q^{81} +10.9210 q^{82} +7.39844 q^{83} -5.29423 q^{84} +5.20973 q^{85} +2.45998 q^{86} -5.89421 q^{87} +3.01585 q^{88} -6.33713 q^{89} +3.61679 q^{90} -13.7089 q^{91} -6.28272 q^{92} +9.09188 q^{93} +5.60674 q^{94} +10.6602 q^{95} +8.11697 q^{96} +11.9290 q^{97} +3.06507 q^{98} -5.74292 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 129q + 15q^{2} + 129q^{3} + 151q^{4} + 16q^{5} + 15q^{6} + 61q^{7} + 42q^{8} + 129q^{9} + O(q^{10}) \) \( 129q + 15q^{2} + 129q^{3} + 151q^{4} + 16q^{5} + 15q^{6} + 61q^{7} + 42q^{8} + 129q^{9} + 41q^{10} + 51q^{11} + 151q^{12} + 56q^{13} + 5q^{14} + 16q^{15} + 195q^{16} + 18q^{17} + 15q^{18} + 93q^{19} + 44q^{20} + 61q^{21} + 46q^{22} + 50q^{23} + 42q^{24} + 193q^{25} + q^{26} + 129q^{27} + 145q^{28} + 24q^{29} + 41q^{30} + 67q^{31} + 89q^{32} + 51q^{33} + 73q^{34} + 56q^{35} + 151q^{36} + 95q^{37} + 9q^{38} + 56q^{39} + 103q^{40} + 7q^{41} + 5q^{42} + 150q^{43} + 69q^{44} + 16q^{45} + 72q^{46} + 53q^{47} + 195q^{48} + 240q^{49} + 17q^{50} + 18q^{51} + 124q^{52} + 34q^{53} + 15q^{54} + 66q^{55} - 17q^{56} + 93q^{57} + 57q^{58} + 49q^{59} + 44q^{60} + 113q^{61} + 27q^{62} + 61q^{63} + 262q^{64} + 22q^{65} + 46q^{66} + 185q^{67} + 2q^{68} + 50q^{69} + 25q^{70} + 41q^{71} + 42q^{72} + 153q^{73} - q^{74} + 193q^{75} + 190q^{76} + 39q^{77} + q^{78} + 101q^{79} + 48q^{80} + 129q^{81} + 15q^{82} + 162q^{83} + 145q^{84} + 99q^{85} + 13q^{86} + 24q^{87} + 86q^{88} - 4q^{89} + 41q^{90} + 117q^{91} + 56q^{92} + 67q^{93} + 49q^{94} + 71q^{95} + 89q^{96} + 159q^{97} + 40q^{98} + 51q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.06267 −1.45853 −0.729263 0.684234i \(-0.760137\pi\)
−0.729263 + 0.684234i \(0.760137\pi\)
\(3\) 1.00000 0.577350
\(4\) 2.25459 1.12730
\(5\) −1.75345 −0.784168 −0.392084 0.919929i \(-0.628246\pi\)
−0.392084 + 0.919929i \(0.628246\pi\)
\(6\) −2.06267 −0.842080
\(7\) −2.34820 −0.887535 −0.443767 0.896142i \(-0.646358\pi\)
−0.443767 + 0.896142i \(0.646358\pi\)
\(8\) −0.525142 −0.185666
\(9\) 1.00000 0.333333
\(10\) 3.61679 1.14373
\(11\) −5.74292 −1.73156 −0.865778 0.500429i \(-0.833176\pi\)
−0.865778 + 0.500429i \(0.833176\pi\)
\(12\) 2.25459 0.650845
\(13\) 5.83807 1.61919 0.809594 0.586990i \(-0.199687\pi\)
0.809594 + 0.586990i \(0.199687\pi\)
\(14\) 4.84355 1.29449
\(15\) −1.75345 −0.452740
\(16\) −3.42599 −0.856499
\(17\) −2.97113 −0.720604 −0.360302 0.932836i \(-0.617326\pi\)
−0.360302 + 0.932836i \(0.617326\pi\)
\(18\) −2.06267 −0.486175
\(19\) −6.07952 −1.39474 −0.697369 0.716713i \(-0.745646\pi\)
−0.697369 + 0.716713i \(0.745646\pi\)
\(20\) −3.95332 −0.883990
\(21\) −2.34820 −0.512419
\(22\) 11.8457 2.52552
\(23\) −2.78663 −0.581053 −0.290527 0.956867i \(-0.593830\pi\)
−0.290527 + 0.956867i \(0.593830\pi\)
\(24\) −0.525142 −0.107194
\(25\) −1.92540 −0.385081
\(26\) −12.0420 −2.36163
\(27\) 1.00000 0.192450
\(28\) −5.29423 −1.00052
\(29\) −5.89421 −1.09453 −0.547264 0.836960i \(-0.684330\pi\)
−0.547264 + 0.836960i \(0.684330\pi\)
\(30\) 3.61679 0.660332
\(31\) 9.09188 1.63295 0.816475 0.577381i \(-0.195925\pi\)
0.816475 + 0.577381i \(0.195925\pi\)
\(32\) 8.11697 1.43489
\(33\) −5.74292 −0.999714
\(34\) 6.12844 1.05102
\(35\) 4.11745 0.695976
\(36\) 2.25459 0.375766
\(37\) −6.61608 −1.08768 −0.543838 0.839190i \(-0.683030\pi\)
−0.543838 + 0.839190i \(0.683030\pi\)
\(38\) 12.5400 2.03426
\(39\) 5.83807 0.934839
\(40\) 0.920811 0.145593
\(41\) −5.29461 −0.826880 −0.413440 0.910531i \(-0.635673\pi\)
−0.413440 + 0.910531i \(0.635673\pi\)
\(42\) 4.84355 0.747376
\(43\) −1.19262 −0.181873 −0.0909367 0.995857i \(-0.528986\pi\)
−0.0909367 + 0.995857i \(0.528986\pi\)
\(44\) −12.9480 −1.95198
\(45\) −1.75345 −0.261389
\(46\) 5.74789 0.847481
\(47\) −2.71820 −0.396490 −0.198245 0.980152i \(-0.563524\pi\)
−0.198245 + 0.980152i \(0.563524\pi\)
\(48\) −3.42599 −0.494500
\(49\) −1.48597 −0.212282
\(50\) 3.97146 0.561650
\(51\) −2.97113 −0.416041
\(52\) 13.1625 1.82531
\(53\) −4.93841 −0.678342 −0.339171 0.940725i \(-0.610147\pi\)
−0.339171 + 0.940725i \(0.610147\pi\)
\(54\) −2.06267 −0.280693
\(55\) 10.0699 1.35783
\(56\) 1.23314 0.164785
\(57\) −6.07952 −0.805252
\(58\) 12.1578 1.59640
\(59\) −8.99053 −1.17047 −0.585234 0.810865i \(-0.698997\pi\)
−0.585234 + 0.810865i \(0.698997\pi\)
\(60\) −3.95332 −0.510372
\(61\) −3.13818 −0.401802 −0.200901 0.979612i \(-0.564387\pi\)
−0.200901 + 0.979612i \(0.564387\pi\)
\(62\) −18.7535 −2.38170
\(63\) −2.34820 −0.295845
\(64\) −9.89061 −1.23633
\(65\) −10.2368 −1.26972
\(66\) 11.8457 1.45811
\(67\) 10.6438 1.30035 0.650173 0.759787i \(-0.274697\pi\)
0.650173 + 0.759787i \(0.274697\pi\)
\(68\) −6.69868 −0.812334
\(69\) −2.78663 −0.335471
\(70\) −8.49293 −1.01510
\(71\) 8.04529 0.954800 0.477400 0.878686i \(-0.341579\pi\)
0.477400 + 0.878686i \(0.341579\pi\)
\(72\) −0.525142 −0.0618886
\(73\) −15.1625 −1.77463 −0.887317 0.461160i \(-0.847433\pi\)
−0.887317 + 0.461160i \(0.847433\pi\)
\(74\) 13.6468 1.58640
\(75\) −1.92540 −0.222326
\(76\) −13.7068 −1.57228
\(77\) 13.4855 1.53682
\(78\) −12.0420 −1.36349
\(79\) 9.80770 1.10345 0.551726 0.834025i \(-0.313969\pi\)
0.551726 + 0.834025i \(0.313969\pi\)
\(80\) 6.00732 0.671639
\(81\) 1.00000 0.111111
\(82\) 10.9210 1.20602
\(83\) 7.39844 0.812084 0.406042 0.913854i \(-0.366909\pi\)
0.406042 + 0.913854i \(0.366909\pi\)
\(84\) −5.29423 −0.577648
\(85\) 5.20973 0.565074
\(86\) 2.45998 0.265267
\(87\) −5.89421 −0.631926
\(88\) 3.01585 0.321490
\(89\) −6.33713 −0.671735 −0.335867 0.941909i \(-0.609029\pi\)
−0.335867 + 0.941909i \(0.609029\pi\)
\(90\) 3.61679 0.381243
\(91\) −13.7089 −1.43709
\(92\) −6.28272 −0.655019
\(93\) 9.09188 0.942784
\(94\) 5.60674 0.578291
\(95\) 10.6602 1.09371
\(96\) 8.11697 0.828435
\(97\) 11.9290 1.21121 0.605603 0.795767i \(-0.292932\pi\)
0.605603 + 0.795767i \(0.292932\pi\)
\(98\) 3.06507 0.309618
\(99\) −5.74292 −0.577185
\(100\) −4.34100 −0.434100
\(101\) 6.45468 0.642264 0.321132 0.947034i \(-0.395937\pi\)
0.321132 + 0.947034i \(0.395937\pi\)
\(102\) 6.12844 0.606806
\(103\) −17.1113 −1.68603 −0.843013 0.537893i \(-0.819221\pi\)
−0.843013 + 0.537893i \(0.819221\pi\)
\(104\) −3.06581 −0.300628
\(105\) 4.11745 0.401822
\(106\) 10.1863 0.989379
\(107\) −5.91023 −0.571364 −0.285682 0.958325i \(-0.592220\pi\)
−0.285682 + 0.958325i \(0.592220\pi\)
\(108\) 2.25459 0.216948
\(109\) 7.56804 0.724887 0.362443 0.932006i \(-0.381943\pi\)
0.362443 + 0.932006i \(0.381943\pi\)
\(110\) −20.7709 −1.98043
\(111\) −6.61608 −0.627970
\(112\) 8.04491 0.760173
\(113\) −4.78968 −0.450575 −0.225288 0.974292i \(-0.572332\pi\)
−0.225288 + 0.974292i \(0.572332\pi\)
\(114\) 12.5400 1.17448
\(115\) 4.88623 0.455643
\(116\) −13.2890 −1.23386
\(117\) 5.83807 0.539729
\(118\) 18.5445 1.70716
\(119\) 6.97679 0.639561
\(120\) 0.920811 0.0840582
\(121\) 21.9811 1.99829
\(122\) 6.47301 0.586039
\(123\) −5.29461 −0.477399
\(124\) 20.4985 1.84082
\(125\) 12.1434 1.08614
\(126\) 4.84355 0.431497
\(127\) 0.269947 0.0239539 0.0119770 0.999928i \(-0.496188\pi\)
0.0119770 + 0.999928i \(0.496188\pi\)
\(128\) 4.16710 0.368323
\(129\) −1.19262 −0.105005
\(130\) 21.1150 1.85191
\(131\) −11.2691 −0.984582 −0.492291 0.870431i \(-0.663840\pi\)
−0.492291 + 0.870431i \(0.663840\pi\)
\(132\) −12.9480 −1.12697
\(133\) 14.2759 1.23788
\(134\) −21.9546 −1.89659
\(135\) −1.75345 −0.150913
\(136\) 1.56026 0.133791
\(137\) −9.18249 −0.784513 −0.392257 0.919856i \(-0.628305\pi\)
−0.392257 + 0.919856i \(0.628305\pi\)
\(138\) 5.74789 0.489293
\(139\) −10.4519 −0.886517 −0.443258 0.896394i \(-0.646178\pi\)
−0.443258 + 0.896394i \(0.646178\pi\)
\(140\) 9.28318 0.784572
\(141\) −2.71820 −0.228914
\(142\) −16.5947 −1.39260
\(143\) −33.5275 −2.80371
\(144\) −3.42599 −0.285500
\(145\) 10.3352 0.858293
\(146\) 31.2751 2.58835
\(147\) −1.48597 −0.122561
\(148\) −14.9166 −1.22613
\(149\) 14.7891 1.21157 0.605786 0.795627i \(-0.292859\pi\)
0.605786 + 0.795627i \(0.292859\pi\)
\(150\) 3.97146 0.324269
\(151\) −7.03452 −0.572461 −0.286231 0.958161i \(-0.592402\pi\)
−0.286231 + 0.958161i \(0.592402\pi\)
\(152\) 3.19261 0.258955
\(153\) −2.97113 −0.240201
\(154\) −27.8161 −2.24149
\(155\) −15.9422 −1.28051
\(156\) 13.1625 1.05384
\(157\) −22.7939 −1.81915 −0.909577 0.415536i \(-0.863594\pi\)
−0.909577 + 0.415536i \(0.863594\pi\)
\(158\) −20.2300 −1.60941
\(159\) −4.93841 −0.391641
\(160\) −14.2327 −1.12520
\(161\) 6.54356 0.515705
\(162\) −2.06267 −0.162058
\(163\) −18.5965 −1.45659 −0.728295 0.685264i \(-0.759687\pi\)
−0.728295 + 0.685264i \(0.759687\pi\)
\(164\) −11.9372 −0.932139
\(165\) 10.0699 0.783944
\(166\) −15.2605 −1.18445
\(167\) −11.5593 −0.894488 −0.447244 0.894412i \(-0.647594\pi\)
−0.447244 + 0.894412i \(0.647594\pi\)
\(168\) 1.23314 0.0951385
\(169\) 21.0830 1.62177
\(170\) −10.7459 −0.824175
\(171\) −6.07952 −0.464912
\(172\) −2.68888 −0.205025
\(173\) −15.8244 −1.20311 −0.601555 0.798831i \(-0.705452\pi\)
−0.601555 + 0.798831i \(0.705452\pi\)
\(174\) 12.1578 0.921680
\(175\) 4.52123 0.341773
\(176\) 19.6752 1.48308
\(177\) −8.99053 −0.675770
\(178\) 13.0714 0.979742
\(179\) −10.1264 −0.756881 −0.378441 0.925626i \(-0.623540\pi\)
−0.378441 + 0.925626i \(0.623540\pi\)
\(180\) −3.95332 −0.294663
\(181\) 12.5748 0.934680 0.467340 0.884078i \(-0.345212\pi\)
0.467340 + 0.884078i \(0.345212\pi\)
\(182\) 28.2769 2.09603
\(183\) −3.13818 −0.231981
\(184\) 1.46338 0.107882
\(185\) 11.6010 0.852921
\(186\) −18.7535 −1.37507
\(187\) 17.0629 1.24777
\(188\) −6.12844 −0.446962
\(189\) −2.34820 −0.170806
\(190\) −21.9883 −1.59520
\(191\) 14.6363 1.05905 0.529523 0.848296i \(-0.322371\pi\)
0.529523 + 0.848296i \(0.322371\pi\)
\(192\) −9.89061 −0.713793
\(193\) −9.66327 −0.695577 −0.347789 0.937573i \(-0.613067\pi\)
−0.347789 + 0.937573i \(0.613067\pi\)
\(194\) −24.6055 −1.76658
\(195\) −10.2368 −0.733070
\(196\) −3.35026 −0.239305
\(197\) 17.2104 1.22619 0.613097 0.790008i \(-0.289924\pi\)
0.613097 + 0.790008i \(0.289924\pi\)
\(198\) 11.8457 0.841839
\(199\) 7.80333 0.553164 0.276582 0.960990i \(-0.410798\pi\)
0.276582 + 0.960990i \(0.410798\pi\)
\(200\) 1.01111 0.0714962
\(201\) 10.6438 0.750755
\(202\) −13.3138 −0.936759
\(203\) 13.8408 0.971431
\(204\) −6.69868 −0.469001
\(205\) 9.28385 0.648412
\(206\) 35.2949 2.45911
\(207\) −2.78663 −0.193684
\(208\) −20.0012 −1.38683
\(209\) 34.9142 2.41507
\(210\) −8.49293 −0.586068
\(211\) 3.59317 0.247364 0.123682 0.992322i \(-0.460530\pi\)
0.123682 + 0.992322i \(0.460530\pi\)
\(212\) −11.1341 −0.764693
\(213\) 8.04529 0.551254
\(214\) 12.1908 0.833348
\(215\) 2.09121 0.142619
\(216\) −0.525142 −0.0357314
\(217\) −21.3495 −1.44930
\(218\) −15.6103 −1.05727
\(219\) −15.1625 −1.02459
\(220\) 22.7036 1.53068
\(221\) −17.3456 −1.16679
\(222\) 13.6468 0.915911
\(223\) 10.5070 0.703600 0.351800 0.936075i \(-0.385570\pi\)
0.351800 + 0.936075i \(0.385570\pi\)
\(224\) −19.0602 −1.27352
\(225\) −1.92540 −0.128360
\(226\) 9.87951 0.657175
\(227\) 15.5628 1.03294 0.516469 0.856306i \(-0.327246\pi\)
0.516469 + 0.856306i \(0.327246\pi\)
\(228\) −13.7068 −0.907758
\(229\) 23.7411 1.56885 0.784427 0.620221i \(-0.212957\pi\)
0.784427 + 0.620221i \(0.212957\pi\)
\(230\) −10.0787 −0.664567
\(231\) 13.4855 0.887281
\(232\) 3.09530 0.203216
\(233\) −15.2471 −0.998870 −0.499435 0.866351i \(-0.666459\pi\)
−0.499435 + 0.866351i \(0.666459\pi\)
\(234\) −12.0420 −0.787209
\(235\) 4.76624 0.310915
\(236\) −20.2700 −1.31946
\(237\) 9.80770 0.637079
\(238\) −14.3908 −0.932816
\(239\) −8.59060 −0.555680 −0.277840 0.960627i \(-0.589618\pi\)
−0.277840 + 0.960627i \(0.589618\pi\)
\(240\) 6.00732 0.387771
\(241\) 8.98556 0.578811 0.289405 0.957207i \(-0.406542\pi\)
0.289405 + 0.957207i \(0.406542\pi\)
\(242\) −45.3398 −2.91455
\(243\) 1.00000 0.0641500
\(244\) −7.07531 −0.452950
\(245\) 2.60558 0.166465
\(246\) 10.9210 0.696299
\(247\) −35.4926 −2.25834
\(248\) −4.77453 −0.303183
\(249\) 7.39844 0.468857
\(250\) −25.0477 −1.58416
\(251\) −12.8348 −0.810127 −0.405064 0.914288i \(-0.632751\pi\)
−0.405064 + 0.914288i \(0.632751\pi\)
\(252\) −5.29423 −0.333505
\(253\) 16.0034 1.00613
\(254\) −0.556811 −0.0349374
\(255\) 5.20973 0.326246
\(256\) 11.1859 0.699118
\(257\) 3.09995 0.193369 0.0966847 0.995315i \(-0.469176\pi\)
0.0966847 + 0.995315i \(0.469176\pi\)
\(258\) 2.45998 0.153152
\(259\) 15.5359 0.965351
\(260\) −23.0798 −1.43135
\(261\) −5.89421 −0.364842
\(262\) 23.2443 1.43604
\(263\) 3.24562 0.200133 0.100067 0.994981i \(-0.468094\pi\)
0.100067 + 0.994981i \(0.468094\pi\)
\(264\) 3.01585 0.185613
\(265\) 8.65926 0.531934
\(266\) −29.4464 −1.80548
\(267\) −6.33713 −0.387826
\(268\) 23.9974 1.46588
\(269\) −4.15844 −0.253545 −0.126772 0.991932i \(-0.540462\pi\)
−0.126772 + 0.991932i \(0.540462\pi\)
\(270\) 3.61679 0.220111
\(271\) 14.1637 0.860381 0.430190 0.902738i \(-0.358446\pi\)
0.430190 + 0.902738i \(0.358446\pi\)
\(272\) 10.1791 0.617196
\(273\) −13.7089 −0.829702
\(274\) 18.9404 1.14423
\(275\) 11.0574 0.666789
\(276\) −6.28272 −0.378176
\(277\) 26.6355 1.60037 0.800187 0.599750i \(-0.204733\pi\)
0.800187 + 0.599750i \(0.204733\pi\)
\(278\) 21.5587 1.29301
\(279\) 9.09188 0.544317
\(280\) −2.16225 −0.129219
\(281\) −15.8670 −0.946548 −0.473274 0.880915i \(-0.656928\pi\)
−0.473274 + 0.880915i \(0.656928\pi\)
\(282\) 5.60674 0.333877
\(283\) 12.8776 0.765496 0.382748 0.923853i \(-0.374978\pi\)
0.382748 + 0.923853i \(0.374978\pi\)
\(284\) 18.1389 1.07634
\(285\) 10.6602 0.631453
\(286\) 69.1561 4.08929
\(287\) 12.4328 0.733884
\(288\) 8.11697 0.478297
\(289\) −8.17241 −0.480730
\(290\) −21.3181 −1.25184
\(291\) 11.9290 0.699290
\(292\) −34.1852 −2.00054
\(293\) −2.17925 −0.127313 −0.0636566 0.997972i \(-0.520276\pi\)
−0.0636566 + 0.997972i \(0.520276\pi\)
\(294\) 3.06507 0.178758
\(295\) 15.7645 0.917843
\(296\) 3.47438 0.201944
\(297\) −5.74292 −0.333238
\(298\) −30.5050 −1.76711
\(299\) −16.2685 −0.940834
\(300\) −4.34100 −0.250628
\(301\) 2.80051 0.161419
\(302\) 14.5099 0.834949
\(303\) 6.45468 0.370811
\(304\) 20.8284 1.19459
\(305\) 5.50264 0.315080
\(306\) 6.12844 0.350340
\(307\) −6.21056 −0.354456 −0.177228 0.984170i \(-0.556713\pi\)
−0.177228 + 0.984170i \(0.556713\pi\)
\(308\) 30.4043 1.73245
\(309\) −17.1113 −0.973428
\(310\) 32.8834 1.86765
\(311\) −21.1652 −1.20017 −0.600083 0.799938i \(-0.704866\pi\)
−0.600083 + 0.799938i \(0.704866\pi\)
\(312\) −3.06581 −0.173567
\(313\) 16.1280 0.911610 0.455805 0.890080i \(-0.349351\pi\)
0.455805 + 0.890080i \(0.349351\pi\)
\(314\) 47.0163 2.65328
\(315\) 4.11745 0.231992
\(316\) 22.1124 1.24392
\(317\) −22.2477 −1.24956 −0.624779 0.780802i \(-0.714811\pi\)
−0.624779 + 0.780802i \(0.714811\pi\)
\(318\) 10.1863 0.571218
\(319\) 33.8500 1.89523
\(320\) 17.3427 0.969488
\(321\) −5.91023 −0.329877
\(322\) −13.4972 −0.752169
\(323\) 18.0630 1.00505
\(324\) 2.25459 0.125255
\(325\) −11.2406 −0.623518
\(326\) 38.3584 2.12447
\(327\) 7.56804 0.418514
\(328\) 2.78042 0.153523
\(329\) 6.38287 0.351899
\(330\) −20.7709 −1.14340
\(331\) −18.5760 −1.02103 −0.510515 0.859869i \(-0.670545\pi\)
−0.510515 + 0.859869i \(0.670545\pi\)
\(332\) 16.6805 0.915460
\(333\) −6.61608 −0.362559
\(334\) 23.8431 1.30463
\(335\) −18.6634 −1.01969
\(336\) 8.04491 0.438886
\(337\) −1.96414 −0.106994 −0.0534968 0.998568i \(-0.517037\pi\)
−0.0534968 + 0.998568i \(0.517037\pi\)
\(338\) −43.4872 −2.36539
\(339\) −4.78968 −0.260140
\(340\) 11.7458 0.637007
\(341\) −52.2139 −2.82754
\(342\) 12.5400 0.678087
\(343\) 19.9267 1.07594
\(344\) 0.626296 0.0337676
\(345\) 4.88623 0.263066
\(346\) 32.6406 1.75477
\(347\) 33.9997 1.82520 0.912599 0.408856i \(-0.134072\pi\)
0.912599 + 0.408856i \(0.134072\pi\)
\(348\) −13.2890 −0.712368
\(349\) −30.7446 −1.64572 −0.822861 0.568243i \(-0.807623\pi\)
−0.822861 + 0.568243i \(0.807623\pi\)
\(350\) −9.32578 −0.498484
\(351\) 5.83807 0.311613
\(352\) −46.6151 −2.48459
\(353\) −6.19576 −0.329767 −0.164884 0.986313i \(-0.552725\pi\)
−0.164884 + 0.986313i \(0.552725\pi\)
\(354\) 18.5445 0.985627
\(355\) −14.1070 −0.748723
\(356\) −14.2877 −0.757244
\(357\) 6.97679 0.369251
\(358\) 20.8873 1.10393
\(359\) −0.607933 −0.0320855 −0.0160427 0.999871i \(-0.505107\pi\)
−0.0160427 + 0.999871i \(0.505107\pi\)
\(360\) 0.920811 0.0485310
\(361\) 17.9606 0.945292
\(362\) −25.9377 −1.36325
\(363\) 21.9811 1.15371
\(364\) −30.9081 −1.62002
\(365\) 26.5867 1.39161
\(366\) 6.47301 0.338350
\(367\) 31.7741 1.65860 0.829298 0.558807i \(-0.188741\pi\)
0.829298 + 0.558807i \(0.188741\pi\)
\(368\) 9.54699 0.497671
\(369\) −5.29461 −0.275627
\(370\) −23.9290 −1.24401
\(371\) 11.5963 0.602052
\(372\) 20.4985 1.06280
\(373\) 27.4055 1.41900 0.709501 0.704705i \(-0.248921\pi\)
0.709501 + 0.704705i \(0.248921\pi\)
\(374\) −35.1952 −1.81990
\(375\) 12.1434 0.627081
\(376\) 1.42744 0.0736146
\(377\) −34.4108 −1.77225
\(378\) 4.84355 0.249125
\(379\) −27.8233 −1.42919 −0.714593 0.699541i \(-0.753388\pi\)
−0.714593 + 0.699541i \(0.753388\pi\)
\(380\) 24.0343 1.23293
\(381\) 0.269947 0.0138298
\(382\) −30.1898 −1.54465
\(383\) −3.85887 −0.197179 −0.0985895 0.995128i \(-0.531433\pi\)
−0.0985895 + 0.995128i \(0.531433\pi\)
\(384\) 4.16710 0.212651
\(385\) −23.6462 −1.20512
\(386\) 19.9321 1.01452
\(387\) −1.19262 −0.0606245
\(388\) 26.8950 1.36539
\(389\) 15.3786 0.779724 0.389862 0.920873i \(-0.372523\pi\)
0.389862 + 0.920873i \(0.372523\pi\)
\(390\) 21.1150 1.06920
\(391\) 8.27943 0.418709
\(392\) 0.780346 0.0394134
\(393\) −11.2691 −0.568448
\(394\) −35.4994 −1.78843
\(395\) −17.1973 −0.865292
\(396\) −12.9480 −0.650659
\(397\) −26.2945 −1.31968 −0.659842 0.751405i \(-0.729377\pi\)
−0.659842 + 0.751405i \(0.729377\pi\)
\(398\) −16.0957 −0.806803
\(399\) 14.2759 0.714689
\(400\) 6.59642 0.329821
\(401\) 22.0082 1.09904 0.549518 0.835482i \(-0.314811\pi\)
0.549518 + 0.835482i \(0.314811\pi\)
\(402\) −21.9546 −1.09499
\(403\) 53.0790 2.64405
\(404\) 14.5527 0.724022
\(405\) −1.75345 −0.0871298
\(406\) −28.5489 −1.41686
\(407\) 37.9956 1.88337
\(408\) 1.56026 0.0772445
\(409\) −12.5874 −0.622409 −0.311204 0.950343i \(-0.600732\pi\)
−0.311204 + 0.950343i \(0.600732\pi\)
\(410\) −19.1495 −0.945726
\(411\) −9.18249 −0.452939
\(412\) −38.5790 −1.90065
\(413\) 21.1115 1.03883
\(414\) 5.74789 0.282494
\(415\) −12.9728 −0.636810
\(416\) 47.3874 2.32336
\(417\) −10.4519 −0.511831
\(418\) −72.0163 −3.52243
\(419\) 20.8928 1.02068 0.510340 0.859973i \(-0.329519\pi\)
0.510340 + 0.859973i \(0.329519\pi\)
\(420\) 9.28318 0.452973
\(421\) 30.5896 1.49085 0.745424 0.666591i \(-0.232247\pi\)
0.745424 + 0.666591i \(0.232247\pi\)
\(422\) −7.41151 −0.360787
\(423\) −2.71820 −0.132163
\(424\) 2.59336 0.125945
\(425\) 5.72061 0.277491
\(426\) −16.5947 −0.804018
\(427\) 7.36905 0.356614
\(428\) −13.3252 −0.644096
\(429\) −33.5275 −1.61873
\(430\) −4.31347 −0.208014
\(431\) 33.6344 1.62011 0.810055 0.586354i \(-0.199437\pi\)
0.810055 + 0.586354i \(0.199437\pi\)
\(432\) −3.42599 −0.164833
\(433\) −19.2716 −0.926135 −0.463068 0.886323i \(-0.653251\pi\)
−0.463068 + 0.886323i \(0.653251\pi\)
\(434\) 44.0369 2.11384
\(435\) 10.3352 0.495536
\(436\) 17.0629 0.817163
\(437\) 16.9414 0.810416
\(438\) 31.2751 1.49438
\(439\) −15.5932 −0.744223 −0.372112 0.928188i \(-0.621366\pi\)
−0.372112 + 0.928188i \(0.621366\pi\)
\(440\) −5.28815 −0.252102
\(441\) −1.48597 −0.0707606
\(442\) 35.7782 1.70180
\(443\) −7.80685 −0.370915 −0.185457 0.982652i \(-0.559377\pi\)
−0.185457 + 0.982652i \(0.559377\pi\)
\(444\) −14.9166 −0.707909
\(445\) 11.1119 0.526753
\(446\) −21.6724 −1.02622
\(447\) 14.7891 0.699502
\(448\) 23.2251 1.09728
\(449\) −35.5066 −1.67566 −0.837831 0.545930i \(-0.816176\pi\)
−0.837831 + 0.545930i \(0.816176\pi\)
\(450\) 3.97146 0.187217
\(451\) 30.4065 1.43179
\(452\) −10.7988 −0.507932
\(453\) −7.03452 −0.330511
\(454\) −32.1009 −1.50657
\(455\) 24.0380 1.12692
\(456\) 3.19261 0.149508
\(457\) 11.0396 0.516412 0.258206 0.966090i \(-0.416869\pi\)
0.258206 + 0.966090i \(0.416869\pi\)
\(458\) −48.9699 −2.28821
\(459\) −2.97113 −0.138680
\(460\) 11.0165 0.513645
\(461\) 14.8216 0.690311 0.345155 0.938546i \(-0.387826\pi\)
0.345155 + 0.938546i \(0.387826\pi\)
\(462\) −27.8161 −1.29412
\(463\) −2.52769 −0.117472 −0.0587360 0.998274i \(-0.518707\pi\)
−0.0587360 + 0.998274i \(0.518707\pi\)
\(464\) 20.1935 0.937461
\(465\) −15.9422 −0.739301
\(466\) 31.4497 1.45688
\(467\) 6.69876 0.309982 0.154991 0.987916i \(-0.450465\pi\)
0.154991 + 0.987916i \(0.450465\pi\)
\(468\) 13.1625 0.608435
\(469\) −24.9937 −1.15410
\(470\) −9.83116 −0.453477
\(471\) −22.7939 −1.05029
\(472\) 4.72130 0.217316
\(473\) 6.84914 0.314924
\(474\) −20.2300 −0.929195
\(475\) 11.7055 0.537086
\(476\) 15.7298 0.720975
\(477\) −4.93841 −0.226114
\(478\) 17.7195 0.810473
\(479\) −0.230724 −0.0105421 −0.00527104 0.999986i \(-0.501678\pi\)
−0.00527104 + 0.999986i \(0.501678\pi\)
\(480\) −14.2327 −0.649632
\(481\) −38.6251 −1.76115
\(482\) −18.5342 −0.844210
\(483\) 6.54356 0.297742
\(484\) 49.5585 2.25266
\(485\) −20.9169 −0.949789
\(486\) −2.06267 −0.0935645
\(487\) 7.98851 0.361994 0.180997 0.983484i \(-0.442068\pi\)
0.180997 + 0.983484i \(0.442068\pi\)
\(488\) 1.64799 0.0746009
\(489\) −18.5965 −0.840963
\(490\) −5.37445 −0.242793
\(491\) −24.1943 −1.09187 −0.545936 0.837827i \(-0.683826\pi\)
−0.545936 + 0.837827i \(0.683826\pi\)
\(492\) −11.9372 −0.538171
\(493\) 17.5124 0.788720
\(494\) 73.2095 3.29385
\(495\) 10.0699 0.452610
\(496\) −31.1487 −1.39862
\(497\) −18.8919 −0.847418
\(498\) −15.2605 −0.683840
\(499\) 15.1278 0.677214 0.338607 0.940928i \(-0.390044\pi\)
0.338607 + 0.940928i \(0.390044\pi\)
\(500\) 27.3784 1.22440
\(501\) −11.5593 −0.516433
\(502\) 26.4740 1.18159
\(503\) 9.93484 0.442972 0.221486 0.975164i \(-0.428909\pi\)
0.221486 + 0.975164i \(0.428909\pi\)
\(504\) 1.23314 0.0549283
\(505\) −11.3180 −0.503643
\(506\) −33.0097 −1.46746
\(507\) 21.0830 0.936329
\(508\) 0.608621 0.0270032
\(509\) 19.4853 0.863670 0.431835 0.901953i \(-0.357866\pi\)
0.431835 + 0.901953i \(0.357866\pi\)
\(510\) −10.7459 −0.475838
\(511\) 35.6045 1.57505
\(512\) −31.4070 −1.38800
\(513\) −6.07952 −0.268417
\(514\) −6.39416 −0.282034
\(515\) 30.0039 1.32213
\(516\) −2.68888 −0.118371
\(517\) 15.6104 0.686545
\(518\) −32.0453 −1.40799
\(519\) −15.8244 −0.694616
\(520\) 5.37576 0.235743
\(521\) 4.55599 0.199601 0.0998007 0.995007i \(-0.468179\pi\)
0.0998007 + 0.995007i \(0.468179\pi\)
\(522\) 12.1578 0.532132
\(523\) −10.0869 −0.441071 −0.220535 0.975379i \(-0.570780\pi\)
−0.220535 + 0.975379i \(0.570780\pi\)
\(524\) −25.4071 −1.10992
\(525\) 4.52123 0.197322
\(526\) −6.69462 −0.291900
\(527\) −27.0131 −1.17671
\(528\) 19.6752 0.856254
\(529\) −15.2347 −0.662377
\(530\) −17.8612 −0.775840
\(531\) −8.99053 −0.390156
\(532\) 32.1864 1.39546
\(533\) −30.9103 −1.33887
\(534\) 13.0714 0.565654
\(535\) 10.3633 0.448045
\(536\) −5.58950 −0.241429
\(537\) −10.1264 −0.436986
\(538\) 8.57748 0.369801
\(539\) 8.53382 0.367578
\(540\) −3.95332 −0.170124
\(541\) −13.3524 −0.574066 −0.287033 0.957921i \(-0.592669\pi\)
−0.287033 + 0.957921i \(0.592669\pi\)
\(542\) −29.2149 −1.25489
\(543\) 12.5748 0.539638
\(544\) −24.1165 −1.03399
\(545\) −13.2702 −0.568433
\(546\) 28.2769 1.21014
\(547\) −19.6539 −0.840340 −0.420170 0.907445i \(-0.638030\pi\)
−0.420170 + 0.907445i \(0.638030\pi\)
\(548\) −20.7028 −0.884379
\(549\) −3.13818 −0.133934
\(550\) −22.8078 −0.972528
\(551\) 35.8340 1.52658
\(552\) 1.46338 0.0622855
\(553\) −23.0304 −0.979353
\(554\) −54.9402 −2.33419
\(555\) 11.6010 0.492434
\(556\) −23.5647 −0.999368
\(557\) 6.55433 0.277716 0.138858 0.990312i \(-0.455657\pi\)
0.138858 + 0.990312i \(0.455657\pi\)
\(558\) −18.7535 −0.793900
\(559\) −6.96261 −0.294487
\(560\) −14.1064 −0.596103
\(561\) 17.0629 0.720398
\(562\) 32.7284 1.38056
\(563\) 22.2577 0.938051 0.469025 0.883185i \(-0.344605\pi\)
0.469025 + 0.883185i \(0.344605\pi\)
\(564\) −6.12844 −0.258054
\(565\) 8.39848 0.353327
\(566\) −26.5623 −1.11649
\(567\) −2.34820 −0.0986150
\(568\) −4.22492 −0.177274
\(569\) −31.1963 −1.30782 −0.653909 0.756573i \(-0.726872\pi\)
−0.653909 + 0.756573i \(0.726872\pi\)
\(570\) −21.9883 −0.920990
\(571\) 2.54348 0.106441 0.0532206 0.998583i \(-0.483051\pi\)
0.0532206 + 0.998583i \(0.483051\pi\)
\(572\) −75.5910 −3.16062
\(573\) 14.6363 0.611440
\(574\) −25.6447 −1.07039
\(575\) 5.36539 0.223752
\(576\) −9.89061 −0.412109
\(577\) −21.2119 −0.883061 −0.441530 0.897246i \(-0.645564\pi\)
−0.441530 + 0.897246i \(0.645564\pi\)
\(578\) 16.8570 0.701157
\(579\) −9.66327 −0.401592
\(580\) 23.3017 0.967551
\(581\) −17.3730 −0.720753
\(582\) −24.6055 −1.01993
\(583\) 28.3609 1.17459
\(584\) 7.96245 0.329489
\(585\) −10.2368 −0.423238
\(586\) 4.49507 0.185689
\(587\) −16.2897 −0.672348 −0.336174 0.941800i \(-0.609133\pi\)
−0.336174 + 0.941800i \(0.609133\pi\)
\(588\) −3.35026 −0.138163
\(589\) −55.2743 −2.27754
\(590\) −32.5168 −1.33870
\(591\) 17.2104 0.707943
\(592\) 22.6667 0.931594
\(593\) −5.00956 −0.205718 −0.102859 0.994696i \(-0.532799\pi\)
−0.102859 + 0.994696i \(0.532799\pi\)
\(594\) 11.8457 0.486036
\(595\) −12.2335 −0.501523
\(596\) 33.3435 1.36580
\(597\) 7.80333 0.319369
\(598\) 33.5566 1.37223
\(599\) 2.44227 0.0997883 0.0498942 0.998755i \(-0.484112\pi\)
0.0498942 + 0.998755i \(0.484112\pi\)
\(600\) 1.01111 0.0412784
\(601\) 31.6885 1.29260 0.646301 0.763082i \(-0.276315\pi\)
0.646301 + 0.763082i \(0.276315\pi\)
\(602\) −5.77653 −0.235434
\(603\) 10.6438 0.433448
\(604\) −15.8600 −0.645334
\(605\) −38.5429 −1.56699
\(606\) −13.3138 −0.540838
\(607\) 20.1771 0.818962 0.409481 0.912319i \(-0.365710\pi\)
0.409481 + 0.912319i \(0.365710\pi\)
\(608\) −49.3473 −2.00130
\(609\) 13.8408 0.560856
\(610\) −11.3501 −0.459553
\(611\) −15.8690 −0.641992
\(612\) −6.69868 −0.270778
\(613\) 10.6343 0.429517 0.214758 0.976667i \(-0.431104\pi\)
0.214758 + 0.976667i \(0.431104\pi\)
\(614\) 12.8103 0.516983
\(615\) 9.28385 0.374361
\(616\) −7.08180 −0.285334
\(617\) 45.9155 1.84849 0.924244 0.381802i \(-0.124696\pi\)
0.924244 + 0.381802i \(0.124696\pi\)
\(618\) 35.2949 1.41977
\(619\) 12.6650 0.509051 0.254526 0.967066i \(-0.418081\pi\)
0.254526 + 0.967066i \(0.418081\pi\)
\(620\) −35.9431 −1.44351
\(621\) −2.78663 −0.111824
\(622\) 43.6567 1.75047
\(623\) 14.8808 0.596188
\(624\) −20.0012 −0.800688
\(625\) −11.6658 −0.466632
\(626\) −33.2667 −1.32961
\(627\) 34.9142 1.39434
\(628\) −51.3911 −2.05073
\(629\) 19.6572 0.783784
\(630\) −8.49293 −0.338366
\(631\) 43.5251 1.73271 0.866354 0.499430i \(-0.166457\pi\)
0.866354 + 0.499430i \(0.166457\pi\)
\(632\) −5.15043 −0.204873
\(633\) 3.59317 0.142816
\(634\) 45.8897 1.82251
\(635\) −0.473340 −0.0187839
\(636\) −11.1341 −0.441496
\(637\) −8.67520 −0.343724
\(638\) −69.8212 −2.76425
\(639\) 8.04529 0.318267
\(640\) −7.30681 −0.288827
\(641\) −21.4752 −0.848221 −0.424111 0.905610i \(-0.639413\pi\)
−0.424111 + 0.905610i \(0.639413\pi\)
\(642\) 12.1908 0.481134
\(643\) 4.46377 0.176034 0.0880169 0.996119i \(-0.471947\pi\)
0.0880169 + 0.996119i \(0.471947\pi\)
\(644\) 14.7531 0.581352
\(645\) 2.09121 0.0823413
\(646\) −37.2580 −1.46590
\(647\) 17.6308 0.693140 0.346570 0.938024i \(-0.387346\pi\)
0.346570 + 0.938024i \(0.387346\pi\)
\(648\) −0.525142 −0.0206295
\(649\) 51.6319 2.02673
\(650\) 23.1857 0.909417
\(651\) −21.3495 −0.836754
\(652\) −41.9276 −1.64201
\(653\) −3.75621 −0.146992 −0.0734960 0.997296i \(-0.523416\pi\)
−0.0734960 + 0.997296i \(0.523416\pi\)
\(654\) −15.6103 −0.610413
\(655\) 19.7597 0.772077
\(656\) 18.1393 0.708221
\(657\) −15.1625 −0.591545
\(658\) −13.1657 −0.513254
\(659\) −29.9039 −1.16489 −0.582445 0.812870i \(-0.697904\pi\)
−0.582445 + 0.812870i \(0.697904\pi\)
\(660\) 22.7036 0.883737
\(661\) −10.4154 −0.405111 −0.202556 0.979271i \(-0.564925\pi\)
−0.202556 + 0.979271i \(0.564925\pi\)
\(662\) 38.3161 1.48920
\(663\) −17.3456 −0.673648
\(664\) −3.88523 −0.150776
\(665\) −25.0321 −0.970704
\(666\) 13.6468 0.528801
\(667\) 16.4250 0.635978
\(668\) −26.0616 −1.00835
\(669\) 10.5070 0.406224
\(670\) 38.4963 1.48724
\(671\) 18.0223 0.695743
\(672\) −19.0602 −0.735265
\(673\) 11.0022 0.424103 0.212051 0.977259i \(-0.431986\pi\)
0.212051 + 0.977259i \(0.431986\pi\)
\(674\) 4.05137 0.156053
\(675\) −1.92540 −0.0741088
\(676\) 47.5336 1.82822
\(677\) −17.7667 −0.682831 −0.341415 0.939913i \(-0.610906\pi\)
−0.341415 + 0.939913i \(0.610906\pi\)
\(678\) 9.87951 0.379420
\(679\) −28.0116 −1.07499
\(680\) −2.73585 −0.104915
\(681\) 15.5628 0.596368
\(682\) 107.700 4.12404
\(683\) 41.3786 1.58331 0.791653 0.610971i \(-0.209221\pi\)
0.791653 + 0.610971i \(0.209221\pi\)
\(684\) −13.7068 −0.524094
\(685\) 16.1011 0.615190
\(686\) −41.1022 −1.56929
\(687\) 23.7411 0.905778
\(688\) 4.08592 0.155774
\(689\) −28.8307 −1.09836
\(690\) −10.0787 −0.383688
\(691\) 22.8807 0.870424 0.435212 0.900328i \(-0.356673\pi\)
0.435212 + 0.900328i \(0.356673\pi\)
\(692\) −35.6777 −1.35626
\(693\) 13.4855 0.512272
\(694\) −70.1300 −2.66210
\(695\) 18.3269 0.695178
\(696\) 3.09530 0.117327
\(697\) 15.7310 0.595853
\(698\) 63.4159 2.40033
\(699\) −15.2471 −0.576698
\(700\) 10.1935 0.385279
\(701\) 36.3433 1.37267 0.686333 0.727287i \(-0.259219\pi\)
0.686333 + 0.727287i \(0.259219\pi\)
\(702\) −12.0420 −0.454495
\(703\) 40.2226 1.51702
\(704\) 56.8010 2.14077
\(705\) 4.76624 0.179507
\(706\) 12.7798 0.480974
\(707\) −15.1568 −0.570032
\(708\) −20.2700 −0.761793
\(709\) 18.4936 0.694542 0.347271 0.937765i \(-0.387108\pi\)
0.347271 + 0.937765i \(0.387108\pi\)
\(710\) 29.0981 1.09203
\(711\) 9.80770 0.367817
\(712\) 3.32789 0.124718
\(713\) −25.3357 −0.948830
\(714\) −14.3908 −0.538562
\(715\) 58.7890 2.19858
\(716\) −22.8309 −0.853230
\(717\) −8.59060 −0.320822
\(718\) 1.25396 0.0467975
\(719\) −14.1463 −0.527567 −0.263784 0.964582i \(-0.584971\pi\)
−0.263784 + 0.964582i \(0.584971\pi\)
\(720\) 6.00732 0.223880
\(721\) 40.1807 1.49641
\(722\) −37.0466 −1.37873
\(723\) 8.98556 0.334177
\(724\) 28.3511 1.05366
\(725\) 11.3487 0.421481
\(726\) −45.3398 −1.68272
\(727\) −43.1277 −1.59952 −0.799759 0.600321i \(-0.795039\pi\)
−0.799759 + 0.600321i \(0.795039\pi\)
\(728\) 7.19913 0.266818
\(729\) 1.00000 0.0370370
\(730\) −54.8395 −2.02970
\(731\) 3.54343 0.131059
\(732\) −7.07531 −0.261511
\(733\) 28.2638 1.04395 0.521973 0.852962i \(-0.325196\pi\)
0.521973 + 0.852962i \(0.325196\pi\)
\(734\) −65.5394 −2.41910
\(735\) 2.60558 0.0961084
\(736\) −22.6190 −0.833748
\(737\) −61.1264 −2.25162
\(738\) 10.9210 0.402008
\(739\) −11.4938 −0.422808 −0.211404 0.977399i \(-0.567804\pi\)
−0.211404 + 0.977399i \(0.567804\pi\)
\(740\) 26.1555 0.961495
\(741\) −35.4926 −1.30385
\(742\) −23.9194 −0.878109
\(743\) −45.7776 −1.67942 −0.839709 0.543037i \(-0.817274\pi\)
−0.839709 + 0.543037i \(0.817274\pi\)
\(744\) −4.77453 −0.175043
\(745\) −25.9320 −0.950076
\(746\) −56.5283 −2.06965
\(747\) 7.39844 0.270695
\(748\) 38.4700 1.40660
\(749\) 13.8784 0.507105
\(750\) −25.0477 −0.914613
\(751\) −8.56790 −0.312647 −0.156324 0.987706i \(-0.549964\pi\)
−0.156324 + 0.987706i \(0.549964\pi\)
\(752\) 9.31254 0.339593
\(753\) −12.8348 −0.467727
\(754\) 70.9780 2.58487
\(755\) 12.3347 0.448906
\(756\) −5.29423 −0.192549
\(757\) 34.3507 1.24850 0.624249 0.781225i \(-0.285405\pi\)
0.624249 + 0.781225i \(0.285405\pi\)
\(758\) 57.3901 2.08450
\(759\) 16.0034 0.580887
\(760\) −5.59809 −0.203064
\(761\) 17.4524 0.632651 0.316325 0.948651i \(-0.397551\pi\)
0.316325 + 0.948651i \(0.397551\pi\)
\(762\) −0.556811 −0.0201711
\(763\) −17.7712 −0.643362
\(764\) 32.9989 1.19386
\(765\) 5.20973 0.188358
\(766\) 7.95956 0.287591
\(767\) −52.4873 −1.89521
\(768\) 11.1859 0.403636
\(769\) 27.2706 0.983401 0.491701 0.870764i \(-0.336375\pi\)
0.491701 + 0.870764i \(0.336375\pi\)
\(770\) 48.7742 1.75770
\(771\) 3.09995 0.111642
\(772\) −21.7867 −0.784122
\(773\) −3.98214 −0.143228 −0.0716138 0.997432i \(-0.522815\pi\)
−0.0716138 + 0.997432i \(0.522815\pi\)
\(774\) 2.45998 0.0884223
\(775\) −17.5055 −0.628817
\(776\) −6.26441 −0.224879
\(777\) 15.5359 0.557346
\(778\) −31.7208 −1.13725
\(779\) 32.1887 1.15328
\(780\) −23.0798 −0.826388
\(781\) −46.2034 −1.65329
\(782\) −17.0777 −0.610698
\(783\) −5.89421 −0.210642
\(784\) 5.09093 0.181819
\(785\) 39.9681 1.42652
\(786\) 23.2443 0.829097
\(787\) −42.5511 −1.51678 −0.758391 0.651800i \(-0.774014\pi\)
−0.758391 + 0.651800i \(0.774014\pi\)
\(788\) 38.8025 1.38228
\(789\) 3.24562 0.115547
\(790\) 35.4724 1.26205
\(791\) 11.2471 0.399901
\(792\) 3.01585 0.107163
\(793\) −18.3209 −0.650593
\(794\) 54.2368 1.92479
\(795\) 8.65926 0.307112
\(796\) 17.5933 0.623580
\(797\) 32.9982 1.16886 0.584428 0.811445i \(-0.301319\pi\)
0.584428 + 0.811445i \(0.301319\pi\)
\(798\) −29.4464 −1.04239
\(799\) 8.07611 0.285712
\(800\) −15.6284 −0.552549
\(801\) −6.33713 −0.223912
\(802\) −45.3955 −1.60297
\(803\) 87.0769 3.07288
\(804\) 23.9974 0.846323
\(805\) −11.4738 −0.404399
\(806\) −109.484 −3.85642
\(807\) −4.15844 −0.146384
\(808\) −3.38962 −0.119246
\(809\) −14.8147 −0.520857 −0.260428 0.965493i \(-0.583864\pi\)
−0.260428 + 0.965493i \(0.583864\pi\)
\(810\) 3.61679 0.127081
\(811\) 29.4365 1.03365 0.516827 0.856090i \(-0.327113\pi\)
0.516827 + 0.856090i \(0.327113\pi\)
\(812\) 31.2053 1.09509
\(813\) 14.1637 0.496741
\(814\) −78.3723 −2.74695
\(815\) 32.6081 1.14221
\(816\) 10.1791 0.356338
\(817\) 7.25058 0.253666
\(818\) 25.9637 0.907799
\(819\) −13.7089 −0.479029
\(820\) 20.9313 0.730953
\(821\) 12.4308 0.433840 0.216920 0.976189i \(-0.430399\pi\)
0.216920 + 0.976189i \(0.430399\pi\)
\(822\) 18.9404 0.660623
\(823\) 0.940208 0.0327736 0.0163868 0.999866i \(-0.494784\pi\)
0.0163868 + 0.999866i \(0.494784\pi\)
\(824\) 8.98586 0.313037
\(825\) 11.0574 0.384971
\(826\) −43.5461 −1.51516
\(827\) 10.7058 0.372278 0.186139 0.982523i \(-0.440403\pi\)
0.186139 + 0.982523i \(0.440403\pi\)
\(828\) −6.28272 −0.218340
\(829\) −24.0501 −0.835294 −0.417647 0.908609i \(-0.637145\pi\)
−0.417647 + 0.908609i \(0.637145\pi\)
\(830\) 26.7586 0.928804
\(831\) 26.6355 0.923977
\(832\) −57.7420 −2.00184
\(833\) 4.41501 0.152971
\(834\) 21.5587 0.746518
\(835\) 20.2688 0.701429
\(836\) 78.7173 2.72250
\(837\) 9.09188 0.314261
\(838\) −43.0949 −1.48869
\(839\) 46.3803 1.60123 0.800613 0.599181i \(-0.204507\pi\)
0.800613 + 0.599181i \(0.204507\pi\)
\(840\) −2.16225 −0.0746046
\(841\) 5.74170 0.197990
\(842\) −63.0962 −2.17444
\(843\) −15.8670 −0.546490
\(844\) 8.10114 0.278853
\(845\) −36.9681 −1.27174
\(846\) 5.60674 0.192764
\(847\) −51.6160 −1.77355
\(848\) 16.9190 0.580999
\(849\) 12.8776 0.441959
\(850\) −11.7997 −0.404727
\(851\) 18.4366 0.631998
\(852\) 18.1389 0.621427
\(853\) 21.6466 0.741167 0.370583 0.928799i \(-0.379158\pi\)
0.370583 + 0.928799i \(0.379158\pi\)
\(854\) −15.1999 −0.520130
\(855\) 10.6602 0.364569
\(856\) 3.10371 0.106083
\(857\) −27.5031 −0.939487 −0.469743 0.882803i \(-0.655654\pi\)
−0.469743 + 0.882803i \(0.655654\pi\)
\(858\) 69.1561 2.36095
\(859\) −53.8884 −1.83865 −0.919324 0.393500i \(-0.871264\pi\)
−0.919324 + 0.393500i \(0.871264\pi\)
\(860\) 4.71483 0.160774
\(861\) 12.4328 0.423708
\(862\) −69.3765 −2.36297
\(863\) 37.5483 1.27816 0.639079 0.769141i \(-0.279316\pi\)
0.639079 + 0.769141i \(0.279316\pi\)
\(864\) 8.11697 0.276145
\(865\) 27.7474 0.943441
\(866\) 39.7509 1.35079
\(867\) −8.17241 −0.277550
\(868\) −48.1345 −1.63379
\(869\) −56.3248 −1.91069
\(870\) −21.3181 −0.722752
\(871\) 62.1391 2.10550
\(872\) −3.97429 −0.134587
\(873\) 11.9290 0.403735
\(874\) −34.9444 −1.18201
\(875\) −28.5150 −0.963983
\(876\) −34.1852 −1.15501
\(877\) 15.5272 0.524315 0.262157 0.965025i \(-0.415566\pi\)
0.262157 + 0.965025i \(0.415566\pi\)
\(878\) 32.1636 1.08547
\(879\) −2.17925 −0.0735043
\(880\) −34.4996 −1.16298
\(881\) −15.7766 −0.531526 −0.265763 0.964038i \(-0.585624\pi\)
−0.265763 + 0.964038i \(0.585624\pi\)
\(882\) 3.06507 0.103206
\(883\) 34.1536 1.14936 0.574679 0.818379i \(-0.305127\pi\)
0.574679 + 0.818379i \(0.305127\pi\)
\(884\) −39.1073 −1.31532
\(885\) 15.7645 0.529917
\(886\) 16.1029 0.540989
\(887\) 10.7691 0.361591 0.180796 0.983521i \(-0.442133\pi\)
0.180796 + 0.983521i \(0.442133\pi\)
\(888\) 3.47438 0.116593
\(889\) −0.633889 −0.0212600
\(890\) −22.9201 −0.768282
\(891\) −5.74292 −0.192395
\(892\) 23.6890 0.793166
\(893\) 16.5254 0.553000
\(894\) −30.5050 −1.02024
\(895\) 17.7561 0.593522
\(896\) −9.78516 −0.326899
\(897\) −16.2685 −0.543191
\(898\) 73.2383 2.44400
\(899\) −53.5894 −1.78731
\(900\) −4.34100 −0.144700
\(901\) 14.6726 0.488816
\(902\) −62.7186 −2.08830
\(903\) 2.80051 0.0931953
\(904\) 2.51526 0.0836563
\(905\) −22.0494 −0.732946
\(906\) 14.5099 0.482058
\(907\) 5.13784 0.170599 0.0852996 0.996355i \(-0.472815\pi\)
0.0852996 + 0.996355i \(0.472815\pi\)
\(908\) 35.0878 1.16443
\(909\) 6.45468 0.214088
\(910\) −49.5823 −1.64364
\(911\) −43.5976 −1.44445 −0.722227 0.691656i \(-0.756881\pi\)
−0.722227 + 0.691656i \(0.756881\pi\)
\(912\) 20.8284 0.689697
\(913\) −42.4886 −1.40617
\(914\) −22.7711 −0.753200
\(915\) 5.50264 0.181912
\(916\) 53.5265 1.76856
\(917\) 26.4619 0.873850
\(918\) 6.12844 0.202269
\(919\) −55.9314 −1.84501 −0.922503 0.385989i \(-0.873860\pi\)
−0.922503 + 0.385989i \(0.873860\pi\)
\(920\) −2.56596 −0.0845973
\(921\) −6.21056 −0.204645
\(922\) −30.5720 −1.00684
\(923\) 46.9689 1.54600
\(924\) 30.4043 1.00023
\(925\) 12.7386 0.418843
\(926\) 5.21379 0.171336
\(927\) −17.1113 −0.562009
\(928\) −47.8431 −1.57053
\(929\) −30.7456 −1.00873 −0.504365 0.863491i \(-0.668273\pi\)
−0.504365 + 0.863491i \(0.668273\pi\)
\(930\) 32.8834 1.07829
\(931\) 9.03400 0.296077
\(932\) −34.3760 −1.12602
\(933\) −21.1652 −0.692916
\(934\) −13.8173 −0.452116
\(935\) −29.9191 −0.978458
\(936\) −3.06581 −0.100209
\(937\) 56.9278 1.85975 0.929875 0.367876i \(-0.119915\pi\)
0.929875 + 0.367876i \(0.119915\pi\)
\(938\) 51.5537 1.68329
\(939\) 16.1280 0.526318
\(940\) 10.7459 0.350493
\(941\) 6.52231 0.212621 0.106311 0.994333i \(-0.466096\pi\)
0.106311 + 0.994333i \(0.466096\pi\)
\(942\) 47.0163 1.53187
\(943\) 14.7541 0.480461
\(944\) 30.8015 1.00250
\(945\) 4.11745 0.133941
\(946\) −14.1275 −0.459325
\(947\) −14.5284 −0.472111 −0.236056 0.971740i \(-0.575855\pi\)
−0.236056 + 0.971740i \(0.575855\pi\)
\(948\) 22.1124 0.718177
\(949\) −88.5195 −2.87347
\(950\) −24.1446 −0.783354
\(951\) −22.2477 −0.721432
\(952\) −3.66380 −0.118745
\(953\) −4.28788 −0.138898 −0.0694490 0.997586i \(-0.522124\pi\)
−0.0694490 + 0.997586i \(0.522124\pi\)
\(954\) 10.1863 0.329793
\(955\) −25.6641 −0.830470
\(956\) −19.3683 −0.626416
\(957\) 33.8500 1.09421
\(958\) 0.475908 0.0153759
\(959\) 21.5623 0.696283
\(960\) 17.3427 0.559734
\(961\) 51.6623 1.66652
\(962\) 79.6707 2.56869
\(963\) −5.91023 −0.190455
\(964\) 20.2588 0.652492
\(965\) 16.9441 0.545449
\(966\) −13.4972 −0.434265
\(967\) −22.9901 −0.739312 −0.369656 0.929169i \(-0.620525\pi\)
−0.369656 + 0.929169i \(0.620525\pi\)
\(968\) −11.5432 −0.371013
\(969\) 18.0630 0.580268
\(970\) 43.1447 1.38529
\(971\) 41.2096 1.32248 0.661240 0.750175i \(-0.270031\pi\)
0.661240 + 0.750175i \(0.270031\pi\)
\(972\) 2.25459 0.0723161
\(973\) 24.5431 0.786815
\(974\) −16.4776 −0.527977
\(975\) −11.2406 −0.359988
\(976\) 10.7514 0.344143
\(977\) 41.6660 1.33301 0.666507 0.745499i \(-0.267789\pi\)
0.666507 + 0.745499i \(0.267789\pi\)
\(978\) 38.3584 1.22657
\(979\) 36.3936 1.16315
\(980\) 5.87453 0.187655
\(981\) 7.56804 0.241629
\(982\) 49.9047 1.59252
\(983\) −8.68142 −0.276894 −0.138447 0.990370i \(-0.544211\pi\)
−0.138447 + 0.990370i \(0.544211\pi\)
\(984\) 2.78042 0.0886366
\(985\) −30.1777 −0.961541
\(986\) −36.1223 −1.15037
\(987\) 6.38287 0.203169
\(988\) −80.0215 −2.54582
\(989\) 3.32340 0.105678
\(990\) −20.7709 −0.660143
\(991\) 30.2222 0.960039 0.480020 0.877258i \(-0.340630\pi\)
0.480020 + 0.877258i \(0.340630\pi\)
\(992\) 73.7985 2.34310
\(993\) −18.5760 −0.589492
\(994\) 38.9677 1.23598
\(995\) −13.6828 −0.433773
\(996\) 16.6805 0.528541
\(997\) −20.2230 −0.640468 −0.320234 0.947338i \(-0.603762\pi\)
−0.320234 + 0.947338i \(0.603762\pi\)
\(998\) −31.2036 −0.987734
\(999\) −6.61608 −0.209323
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 \(a_p\))