Properties

Label 8041.2.a.g.1.3
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 1
Dimension 69
CM No

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Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.75592 q^{2} +2.83072 q^{3} +5.59510 q^{4} -1.76173 q^{5} -7.80125 q^{6} +2.47832 q^{7} -9.90779 q^{8} +5.01300 q^{9} +O(q^{10})\) \(q-2.75592 q^{2} +2.83072 q^{3} +5.59510 q^{4} -1.76173 q^{5} -7.80125 q^{6} +2.47832 q^{7} -9.90779 q^{8} +5.01300 q^{9} +4.85519 q^{10} -1.00000 q^{11} +15.8382 q^{12} -0.921197 q^{13} -6.83004 q^{14} -4.98697 q^{15} +16.1149 q^{16} +1.00000 q^{17} -13.8154 q^{18} +1.06613 q^{19} -9.85705 q^{20} +7.01543 q^{21} +2.75592 q^{22} -6.87843 q^{23} -28.0462 q^{24} -1.89631 q^{25} +2.53874 q^{26} +5.69825 q^{27} +13.8664 q^{28} -1.83349 q^{29} +13.7437 q^{30} +3.24055 q^{31} -24.5958 q^{32} -2.83072 q^{33} -2.75592 q^{34} -4.36613 q^{35} +28.0482 q^{36} +4.84851 q^{37} -2.93817 q^{38} -2.60765 q^{39} +17.4549 q^{40} -9.01731 q^{41} -19.3340 q^{42} +1.00000 q^{43} -5.59510 q^{44} -8.83155 q^{45} +18.9564 q^{46} -10.9088 q^{47} +45.6168 q^{48} -0.857947 q^{49} +5.22607 q^{50} +2.83072 q^{51} -5.15418 q^{52} +12.6434 q^{53} -15.7039 q^{54} +1.76173 q^{55} -24.5547 q^{56} +3.01792 q^{57} +5.05295 q^{58} +9.80491 q^{59} -27.9026 q^{60} -13.8630 q^{61} -8.93069 q^{62} +12.4238 q^{63} +35.5542 q^{64} +1.62290 q^{65} +7.80125 q^{66} -8.65927 q^{67} +5.59510 q^{68} -19.4709 q^{69} +12.0327 q^{70} +2.10228 q^{71} -49.6678 q^{72} -14.5623 q^{73} -13.3621 q^{74} -5.36792 q^{75} +5.96510 q^{76} -2.47832 q^{77} +7.18648 q^{78} +9.90070 q^{79} -28.3901 q^{80} +1.09117 q^{81} +24.8510 q^{82} -12.1513 q^{83} +39.2520 q^{84} -1.76173 q^{85} -2.75592 q^{86} -5.19010 q^{87} +9.90779 q^{88} +1.88208 q^{89} +24.3391 q^{90} -2.28302 q^{91} -38.4854 q^{92} +9.17309 q^{93} +30.0638 q^{94} -1.87823 q^{95} -69.6239 q^{96} +4.30806 q^{97} +2.36443 q^{98} -5.01300 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} + O(q^{10}) \) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} - q^{10} - 69q^{11} - 3q^{12} - 28q^{13} - 15q^{14} - 45q^{15} + 53q^{16} + 69q^{17} - 17q^{18} - 32q^{19} - 21q^{20} - 38q^{21} + 11q^{22} - 41q^{23} - 11q^{24} + 67q^{25} - 6q^{26} - 3q^{27} - 21q^{28} - 22q^{29} - 22q^{30} - 27q^{31} - 87q^{32} + 3q^{33} - 11q^{34} - 44q^{35} + 59q^{36} + 24q^{37} - 22q^{38} - 59q^{39} + q^{40} - 43q^{41} - 15q^{42} + 69q^{43} - 65q^{44} - 12q^{45} - 21q^{46} - 99q^{47} + 2q^{48} + 64q^{49} - 78q^{50} - 3q^{51} - 57q^{52} - 50q^{53} + 20q^{54} + 6q^{55} - 59q^{56} - 15q^{57} + 22q^{58} - 82q^{59} - 86q^{60} - 24q^{61} + 15q^{62} - 63q^{63} + 63q^{64} - 23q^{65} + 10q^{66} - 54q^{67} + 65q^{68} + 36q^{69} + 9q^{70} - 128q^{71} - 69q^{72} + 2q^{73} - 58q^{74} - 31q^{75} - 76q^{76} + 11q^{77} - 19q^{78} - 43q^{79} - 19q^{80} + 49q^{81} - 2q^{82} - 62q^{83} - 82q^{84} - 6q^{85} - 11q^{86} - 62q^{87} + 33q^{88} - 49q^{89} - 37q^{90} - 2q^{91} - 96q^{92} - 29q^{93} - 75q^{94} - 133q^{95} - 86q^{96} + 5q^{97} - 72q^{98} - 56q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.75592 −1.94873 −0.974365 0.224974i \(-0.927770\pi\)
−0.974365 + 0.224974i \(0.927770\pi\)
\(3\) 2.83072 1.63432 0.817160 0.576411i \(-0.195547\pi\)
0.817160 + 0.576411i \(0.195547\pi\)
\(4\) 5.59510 2.79755
\(5\) −1.76173 −0.787870 −0.393935 0.919138i \(-0.628886\pi\)
−0.393935 + 0.919138i \(0.628886\pi\)
\(6\) −7.80125 −3.18485
\(7\) 2.47832 0.936716 0.468358 0.883539i \(-0.344846\pi\)
0.468358 + 0.883539i \(0.344846\pi\)
\(8\) −9.90779 −3.50293
\(9\) 5.01300 1.67100
\(10\) 4.85519 1.53535
\(11\) −1.00000 −0.301511
\(12\) 15.8382 4.57209
\(13\) −0.921197 −0.255494 −0.127747 0.991807i \(-0.540775\pi\)
−0.127747 + 0.991807i \(0.540775\pi\)
\(14\) −6.83004 −1.82541
\(15\) −4.98697 −1.28763
\(16\) 16.1149 4.02873
\(17\) 1.00000 0.242536
\(18\) −13.8154 −3.25633
\(19\) 1.06613 0.244587 0.122294 0.992494i \(-0.460975\pi\)
0.122294 + 0.992494i \(0.460975\pi\)
\(20\) −9.85705 −2.20410
\(21\) 7.01543 1.53089
\(22\) 2.75592 0.587564
\(23\) −6.87843 −1.43425 −0.717125 0.696944i \(-0.754543\pi\)
−0.717125 + 0.696944i \(0.754543\pi\)
\(24\) −28.0462 −5.72491
\(25\) −1.89631 −0.379261
\(26\) 2.53874 0.497889
\(27\) 5.69825 1.09663
\(28\) 13.8664 2.62051
\(29\) −1.83349 −0.340470 −0.170235 0.985403i \(-0.554453\pi\)
−0.170235 + 0.985403i \(0.554453\pi\)
\(30\) 13.7437 2.50924
\(31\) 3.24055 0.582019 0.291010 0.956720i \(-0.406009\pi\)
0.291010 + 0.956720i \(0.406009\pi\)
\(32\) −24.5958 −4.34796
\(33\) −2.83072 −0.492766
\(34\) −2.75592 −0.472636
\(35\) −4.36613 −0.738010
\(36\) 28.0482 4.67470
\(37\) 4.84851 0.797090 0.398545 0.917149i \(-0.369515\pi\)
0.398545 + 0.917149i \(0.369515\pi\)
\(38\) −2.93817 −0.476634
\(39\) −2.60765 −0.417559
\(40\) 17.4549 2.75986
\(41\) −9.01731 −1.40827 −0.704134 0.710067i \(-0.748664\pi\)
−0.704134 + 0.710067i \(0.748664\pi\)
\(42\) −19.3340 −2.98330
\(43\) 1.00000 0.152499
\(44\) −5.59510 −0.843492
\(45\) −8.83155 −1.31653
\(46\) 18.9564 2.79497
\(47\) −10.9088 −1.59121 −0.795607 0.605814i \(-0.792848\pi\)
−0.795607 + 0.605814i \(0.792848\pi\)
\(48\) 45.6168 6.58422
\(49\) −0.857947 −0.122564
\(50\) 5.22607 0.739077
\(51\) 2.83072 0.396381
\(52\) −5.15418 −0.714757
\(53\) 12.6434 1.73671 0.868354 0.495945i \(-0.165178\pi\)
0.868354 + 0.495945i \(0.165178\pi\)
\(54\) −15.7039 −2.13703
\(55\) 1.76173 0.237552
\(56\) −24.5547 −3.28125
\(57\) 3.01792 0.399734
\(58\) 5.05295 0.663484
\(59\) 9.80491 1.27649 0.638245 0.769833i \(-0.279661\pi\)
0.638245 + 0.769833i \(0.279661\pi\)
\(60\) −27.9026 −3.60221
\(61\) −13.8630 −1.77497 −0.887485 0.460837i \(-0.847549\pi\)
−0.887485 + 0.460837i \(0.847549\pi\)
\(62\) −8.93069 −1.13420
\(63\) 12.4238 1.56525
\(64\) 35.5542 4.44428
\(65\) 1.62290 0.201296
\(66\) 7.80125 0.960267
\(67\) −8.65927 −1.05790 −0.528949 0.848654i \(-0.677414\pi\)
−0.528949 + 0.848654i \(0.677414\pi\)
\(68\) 5.59510 0.678505
\(69\) −19.4709 −2.34402
\(70\) 12.0327 1.43818
\(71\) 2.10228 0.249494 0.124747 0.992189i \(-0.460188\pi\)
0.124747 + 0.992189i \(0.460188\pi\)
\(72\) −49.6678 −5.85340
\(73\) −14.5623 −1.70439 −0.852194 0.523226i \(-0.824728\pi\)
−0.852194 + 0.523226i \(0.824728\pi\)
\(74\) −13.3621 −1.55331
\(75\) −5.36792 −0.619834
\(76\) 5.96510 0.684244
\(77\) −2.47832 −0.282430
\(78\) 7.18648 0.813709
\(79\) 9.90070 1.11392 0.556958 0.830541i \(-0.311968\pi\)
0.556958 + 0.830541i \(0.311968\pi\)
\(80\) −28.3901 −3.17411
\(81\) 1.09117 0.121241
\(82\) 24.8510 2.74433
\(83\) −12.1513 −1.33378 −0.666889 0.745157i \(-0.732374\pi\)
−0.666889 + 0.745157i \(0.732374\pi\)
\(84\) 39.2520 4.28274
\(85\) −1.76173 −0.191087
\(86\) −2.75592 −0.297179
\(87\) −5.19010 −0.556437
\(88\) 9.90779 1.05617
\(89\) 1.88208 0.199500 0.0997502 0.995013i \(-0.468196\pi\)
0.0997502 + 0.995013i \(0.468196\pi\)
\(90\) 24.3391 2.56556
\(91\) −2.28302 −0.239325
\(92\) −38.4854 −4.01239
\(93\) 9.17309 0.951205
\(94\) 30.0638 3.10084
\(95\) −1.87823 −0.192703
\(96\) −69.6239 −7.10596
\(97\) 4.30806 0.437417 0.218709 0.975790i \(-0.429816\pi\)
0.218709 + 0.975790i \(0.429816\pi\)
\(98\) 2.36443 0.238844
\(99\) −5.01300 −0.503825
\(100\) −10.6100 −1.06100
\(101\) −10.4147 −1.03630 −0.518149 0.855290i \(-0.673379\pi\)
−0.518149 + 0.855290i \(0.673379\pi\)
\(102\) −7.80125 −0.772439
\(103\) −0.613022 −0.0604028 −0.0302014 0.999544i \(-0.509615\pi\)
−0.0302014 + 0.999544i \(0.509615\pi\)
\(104\) 9.12703 0.894979
\(105\) −12.3593 −1.20614
\(106\) −34.8443 −3.38437
\(107\) −3.93219 −0.380139 −0.190070 0.981771i \(-0.560871\pi\)
−0.190070 + 0.981771i \(0.560871\pi\)
\(108\) 31.8822 3.06787
\(109\) −18.5754 −1.77920 −0.889600 0.456740i \(-0.849017\pi\)
−0.889600 + 0.456740i \(0.849017\pi\)
\(110\) −4.85519 −0.462924
\(111\) 13.7248 1.30270
\(112\) 39.9378 3.77377
\(113\) 7.98301 0.750978 0.375489 0.926827i \(-0.377475\pi\)
0.375489 + 0.926827i \(0.377475\pi\)
\(114\) −8.31715 −0.778973
\(115\) 12.1179 1.13000
\(116\) −10.2585 −0.952481
\(117\) −4.61796 −0.426930
\(118\) −27.0216 −2.48754
\(119\) 2.47832 0.227187
\(120\) 49.4099 4.51049
\(121\) 1.00000 0.0909091
\(122\) 38.2052 3.45894
\(123\) −25.5255 −2.30156
\(124\) 18.1312 1.62823
\(125\) 12.1494 1.08668
\(126\) −34.2390 −3.05025
\(127\) 18.7012 1.65946 0.829730 0.558165i \(-0.188494\pi\)
0.829730 + 0.558165i \(0.188494\pi\)
\(128\) −48.7930 −4.31273
\(129\) 2.83072 0.249231
\(130\) −4.47258 −0.392271
\(131\) −16.4833 −1.44015 −0.720075 0.693897i \(-0.755892\pi\)
−0.720075 + 0.693897i \(0.755892\pi\)
\(132\) −15.8382 −1.37854
\(133\) 2.64221 0.229109
\(134\) 23.8643 2.06156
\(135\) −10.0388 −0.864000
\(136\) −9.90779 −0.849586
\(137\) −9.01685 −0.770362 −0.385181 0.922841i \(-0.625861\pi\)
−0.385181 + 0.922841i \(0.625861\pi\)
\(138\) 53.6603 4.56787
\(139\) 1.87254 0.158827 0.0794133 0.996842i \(-0.474695\pi\)
0.0794133 + 0.996842i \(0.474695\pi\)
\(140\) −24.4289 −2.06462
\(141\) −30.8798 −2.60055
\(142\) −5.79371 −0.486197
\(143\) 0.921197 0.0770343
\(144\) 80.7840 6.73200
\(145\) 3.23011 0.268246
\(146\) 40.1325 3.32139
\(147\) −2.42861 −0.200308
\(148\) 27.1279 2.22990
\(149\) −17.1622 −1.40598 −0.702991 0.711199i \(-0.748153\pi\)
−0.702991 + 0.711199i \(0.748153\pi\)
\(150\) 14.7936 1.20789
\(151\) −4.39570 −0.357717 −0.178858 0.983875i \(-0.557240\pi\)
−0.178858 + 0.983875i \(0.557240\pi\)
\(152\) −10.5630 −0.856773
\(153\) 5.01300 0.405277
\(154\) 6.83004 0.550381
\(155\) −5.70897 −0.458555
\(156\) −14.5901 −1.16814
\(157\) 19.2593 1.53706 0.768528 0.639816i \(-0.220989\pi\)
0.768528 + 0.639816i \(0.220989\pi\)
\(158\) −27.2855 −2.17072
\(159\) 35.7900 2.83834
\(160\) 43.3311 3.42563
\(161\) −17.0469 −1.34349
\(162\) −3.00717 −0.236266
\(163\) −7.82558 −0.612947 −0.306473 0.951879i \(-0.599149\pi\)
−0.306473 + 0.951879i \(0.599149\pi\)
\(164\) −50.4527 −3.93970
\(165\) 4.98697 0.388235
\(166\) 33.4880 2.59917
\(167\) 19.7179 1.52581 0.762907 0.646508i \(-0.223771\pi\)
0.762907 + 0.646508i \(0.223771\pi\)
\(168\) −69.5075 −5.36262
\(169\) −12.1514 −0.934723
\(170\) 4.85519 0.372376
\(171\) 5.34451 0.408705
\(172\) 5.59510 0.426622
\(173\) 0.737860 0.0560985 0.0280492 0.999607i \(-0.491070\pi\)
0.0280492 + 0.999607i \(0.491070\pi\)
\(174\) 14.3035 1.08435
\(175\) −4.69965 −0.355260
\(176\) −16.1149 −1.21471
\(177\) 27.7550 2.08619
\(178\) −5.18687 −0.388772
\(179\) 5.29334 0.395643 0.197821 0.980238i \(-0.436613\pi\)
0.197821 + 0.980238i \(0.436613\pi\)
\(180\) −49.4134 −3.68306
\(181\) −2.09291 −0.155564 −0.0777822 0.996970i \(-0.524784\pi\)
−0.0777822 + 0.996970i \(0.524784\pi\)
\(182\) 6.29181 0.466380
\(183\) −39.2422 −2.90087
\(184\) 68.1500 5.02409
\(185\) −8.54176 −0.628003
\(186\) −25.2803 −1.85364
\(187\) −1.00000 −0.0731272
\(188\) −61.0358 −4.45149
\(189\) 14.1221 1.02723
\(190\) 5.17627 0.375526
\(191\) 16.0745 1.16311 0.581554 0.813508i \(-0.302445\pi\)
0.581554 + 0.813508i \(0.302445\pi\)
\(192\) 100.644 7.26337
\(193\) 19.4948 1.40326 0.701631 0.712540i \(-0.252455\pi\)
0.701631 + 0.712540i \(0.252455\pi\)
\(194\) −11.8727 −0.852408
\(195\) 4.59398 0.328982
\(196\) −4.80029 −0.342878
\(197\) 14.7496 1.05087 0.525434 0.850835i \(-0.323903\pi\)
0.525434 + 0.850835i \(0.323903\pi\)
\(198\) 13.8154 0.981820
\(199\) −22.6232 −1.60372 −0.801858 0.597515i \(-0.796155\pi\)
−0.801858 + 0.597515i \(0.796155\pi\)
\(200\) 18.7882 1.32853
\(201\) −24.5120 −1.72894
\(202\) 28.7020 2.01947
\(203\) −4.54396 −0.318924
\(204\) 15.8382 1.10889
\(205\) 15.8861 1.10953
\(206\) 1.68944 0.117709
\(207\) −34.4815 −2.39663
\(208\) −14.8450 −1.02931
\(209\) −1.06613 −0.0737458
\(210\) 34.0612 2.35045
\(211\) −4.91662 −0.338474 −0.169237 0.985575i \(-0.554130\pi\)
−0.169237 + 0.985575i \(0.554130\pi\)
\(212\) 70.7412 4.85852
\(213\) 5.95097 0.407754
\(214\) 10.8368 0.740789
\(215\) −1.76173 −0.120149
\(216\) −56.4571 −3.84142
\(217\) 8.03110 0.545187
\(218\) 51.1923 3.46718
\(219\) −41.2218 −2.78551
\(220\) 9.85705 0.664562
\(221\) −0.921197 −0.0619664
\(222\) −37.8244 −2.53861
\(223\) −7.17471 −0.480454 −0.240227 0.970717i \(-0.577222\pi\)
−0.240227 + 0.970717i \(0.577222\pi\)
\(224\) −60.9561 −4.07280
\(225\) −9.50618 −0.633745
\(226\) −22.0005 −1.46345
\(227\) −4.96024 −0.329223 −0.164611 0.986358i \(-0.552637\pi\)
−0.164611 + 0.986358i \(0.552637\pi\)
\(228\) 16.8856 1.11827
\(229\) 0.879426 0.0581141 0.0290570 0.999578i \(-0.490750\pi\)
0.0290570 + 0.999578i \(0.490750\pi\)
\(230\) −33.3961 −2.20207
\(231\) −7.01543 −0.461581
\(232\) 18.1658 1.19264
\(233\) −9.96700 −0.652960 −0.326480 0.945204i \(-0.605863\pi\)
−0.326480 + 0.945204i \(0.605863\pi\)
\(234\) 12.7267 0.831972
\(235\) 19.2184 1.25367
\(236\) 54.8594 3.57104
\(237\) 28.0262 1.82049
\(238\) −6.83004 −0.442726
\(239\) 2.35828 0.152544 0.0762721 0.997087i \(-0.475698\pi\)
0.0762721 + 0.997087i \(0.475698\pi\)
\(240\) −80.3646 −5.18751
\(241\) −7.25887 −0.467585 −0.233793 0.972286i \(-0.575114\pi\)
−0.233793 + 0.972286i \(0.575114\pi\)
\(242\) −2.75592 −0.177157
\(243\) −14.0059 −0.898482
\(244\) −77.5646 −4.96556
\(245\) 1.51147 0.0965643
\(246\) 70.3463 4.48512
\(247\) −0.982116 −0.0624905
\(248\) −32.1067 −2.03878
\(249\) −34.3970 −2.17982
\(250\) −33.4829 −2.11764
\(251\) 16.3341 1.03100 0.515500 0.856890i \(-0.327606\pi\)
0.515500 + 0.856890i \(0.327606\pi\)
\(252\) 69.5123 4.37887
\(253\) 6.87843 0.432443
\(254\) −51.5389 −3.23384
\(255\) −4.98697 −0.312296
\(256\) 63.3612 3.96008
\(257\) 3.55239 0.221592 0.110796 0.993843i \(-0.464660\pi\)
0.110796 + 0.993843i \(0.464660\pi\)
\(258\) −7.80125 −0.485685
\(259\) 12.0161 0.746646
\(260\) 9.08028 0.563135
\(261\) −9.19127 −0.568926
\(262\) 45.4266 2.80646
\(263\) −28.6084 −1.76407 −0.882035 0.471185i \(-0.843827\pi\)
−0.882035 + 0.471185i \(0.843827\pi\)
\(264\) 28.0462 1.72613
\(265\) −22.2743 −1.36830
\(266\) −7.28172 −0.446471
\(267\) 5.32766 0.326047
\(268\) −48.4494 −2.95952
\(269\) −3.41441 −0.208180 −0.104090 0.994568i \(-0.533193\pi\)
−0.104090 + 0.994568i \(0.533193\pi\)
\(270\) 27.6661 1.68370
\(271\) −20.1976 −1.22692 −0.613459 0.789727i \(-0.710222\pi\)
−0.613459 + 0.789727i \(0.710222\pi\)
\(272\) 16.1149 0.977109
\(273\) −6.46259 −0.391134
\(274\) 24.8497 1.50123
\(275\) 1.89631 0.114352
\(276\) −108.942 −6.55752
\(277\) −1.64326 −0.0987338 −0.0493669 0.998781i \(-0.515720\pi\)
−0.0493669 + 0.998781i \(0.515720\pi\)
\(278\) −5.16056 −0.309510
\(279\) 16.2449 0.972554
\(280\) 43.2587 2.58520
\(281\) 4.58914 0.273765 0.136883 0.990587i \(-0.456292\pi\)
0.136883 + 0.990587i \(0.456292\pi\)
\(282\) 85.1023 5.06777
\(283\) 14.4492 0.858918 0.429459 0.903086i \(-0.358704\pi\)
0.429459 + 0.903086i \(0.358704\pi\)
\(284\) 11.7624 0.697973
\(285\) −5.31676 −0.314938
\(286\) −2.53874 −0.150119
\(287\) −22.3478 −1.31915
\(288\) −123.299 −7.26544
\(289\) 1.00000 0.0588235
\(290\) −8.90193 −0.522739
\(291\) 12.1949 0.714880
\(292\) −81.4774 −4.76811
\(293\) −29.4566 −1.72087 −0.860436 0.509559i \(-0.829809\pi\)
−0.860436 + 0.509559i \(0.829809\pi\)
\(294\) 6.69306 0.390347
\(295\) −17.2736 −1.00571
\(296\) −48.0380 −2.79215
\(297\) −5.69825 −0.330646
\(298\) 47.2976 2.73988
\(299\) 6.33638 0.366442
\(300\) −30.0340 −1.73401
\(301\) 2.47832 0.142848
\(302\) 12.1142 0.697093
\(303\) −29.4811 −1.69364
\(304\) 17.1806 0.985374
\(305\) 24.4228 1.39845
\(306\) −13.8154 −0.789775
\(307\) −19.3455 −1.10411 −0.552053 0.833809i \(-0.686155\pi\)
−0.552053 + 0.833809i \(0.686155\pi\)
\(308\) −13.8664 −0.790112
\(309\) −1.73530 −0.0987175
\(310\) 15.7335 0.893601
\(311\) 10.9241 0.619451 0.309725 0.950826i \(-0.399763\pi\)
0.309725 + 0.950826i \(0.399763\pi\)
\(312\) 25.8361 1.46268
\(313\) −34.9660 −1.97639 −0.988197 0.153189i \(-0.951046\pi\)
−0.988197 + 0.153189i \(0.951046\pi\)
\(314\) −53.0770 −2.99531
\(315\) −21.8874 −1.23321
\(316\) 55.3954 3.11623
\(317\) −27.5945 −1.54986 −0.774930 0.632048i \(-0.782215\pi\)
−0.774930 + 0.632048i \(0.782215\pi\)
\(318\) −98.6345 −5.53115
\(319\) 1.83349 0.102656
\(320\) −62.6370 −3.50151
\(321\) −11.1309 −0.621269
\(322\) 46.9799 2.61809
\(323\) 1.06613 0.0593211
\(324\) 6.10519 0.339177
\(325\) 1.74687 0.0968989
\(326\) 21.5667 1.19447
\(327\) −52.5818 −2.90778
\(328\) 89.3417 4.93307
\(329\) −27.0355 −1.49051
\(330\) −13.7437 −0.756566
\(331\) −15.8221 −0.869659 −0.434830 0.900513i \(-0.643191\pi\)
−0.434830 + 0.900513i \(0.643191\pi\)
\(332\) −67.9876 −3.73131
\(333\) 24.3056 1.33194
\(334\) −54.3409 −2.97340
\(335\) 15.2553 0.833486
\(336\) 113.053 6.16755
\(337\) 26.1285 1.42331 0.711654 0.702530i \(-0.247946\pi\)
0.711654 + 0.702530i \(0.247946\pi\)
\(338\) 33.4883 1.82152
\(339\) 22.5977 1.22734
\(340\) −9.85705 −0.534574
\(341\) −3.24055 −0.175485
\(342\) −14.7290 −0.796456
\(343\) −19.4745 −1.05152
\(344\) −9.90779 −0.534193
\(345\) 34.3025 1.84679
\(346\) −2.03348 −0.109321
\(347\) 29.3008 1.57295 0.786474 0.617624i \(-0.211905\pi\)
0.786474 + 0.617624i \(0.211905\pi\)
\(348\) −29.0391 −1.55666
\(349\) 25.1926 1.34853 0.674263 0.738491i \(-0.264461\pi\)
0.674263 + 0.738491i \(0.264461\pi\)
\(350\) 12.9518 0.692305
\(351\) −5.24921 −0.280182
\(352\) 24.5958 1.31096
\(353\) 16.6865 0.888131 0.444066 0.895994i \(-0.353536\pi\)
0.444066 + 0.895994i \(0.353536\pi\)
\(354\) −76.4906 −4.06543
\(355\) −3.70365 −0.196569
\(356\) 10.5304 0.558112
\(357\) 7.01543 0.371296
\(358\) −14.5880 −0.771001
\(359\) −16.4783 −0.869691 −0.434846 0.900505i \(-0.643197\pi\)
−0.434846 + 0.900505i \(0.643197\pi\)
\(360\) 87.5012 4.61172
\(361\) −17.8634 −0.940177
\(362\) 5.76788 0.303153
\(363\) 2.83072 0.148574
\(364\) −12.7737 −0.669524
\(365\) 25.6548 1.34284
\(366\) 108.148 5.65301
\(367\) −19.1797 −1.00117 −0.500587 0.865686i \(-0.666882\pi\)
−0.500587 + 0.865686i \(0.666882\pi\)
\(368\) −110.845 −5.77820
\(369\) −45.2038 −2.35321
\(370\) 23.5404 1.22381
\(371\) 31.3344 1.62680
\(372\) 51.3243 2.66104
\(373\) 3.58225 0.185482 0.0927410 0.995690i \(-0.470437\pi\)
0.0927410 + 0.995690i \(0.470437\pi\)
\(374\) 2.75592 0.142505
\(375\) 34.3917 1.77598
\(376\) 108.082 5.57392
\(377\) 1.68900 0.0869881
\(378\) −38.9193 −2.00179
\(379\) 7.29998 0.374975 0.187487 0.982267i \(-0.439966\pi\)
0.187487 + 0.982267i \(0.439966\pi\)
\(380\) −10.5089 −0.539095
\(381\) 52.9379 2.71209
\(382\) −44.3000 −2.26658
\(383\) 7.91922 0.404653 0.202327 0.979318i \(-0.435150\pi\)
0.202327 + 0.979318i \(0.435150\pi\)
\(384\) −138.120 −7.04838
\(385\) 4.36613 0.222518
\(386\) −53.7260 −2.73458
\(387\) 5.01300 0.254825
\(388\) 24.1040 1.22370
\(389\) 5.96354 0.302364 0.151182 0.988506i \(-0.451692\pi\)
0.151182 + 0.988506i \(0.451692\pi\)
\(390\) −12.6606 −0.641097
\(391\) −6.87843 −0.347857
\(392\) 8.50036 0.429333
\(393\) −46.6596 −2.35366
\(394\) −40.6488 −2.04786
\(395\) −17.4424 −0.877621
\(396\) −28.0482 −1.40948
\(397\) −21.4910 −1.07860 −0.539302 0.842112i \(-0.681312\pi\)
−0.539302 + 0.842112i \(0.681312\pi\)
\(398\) 62.3477 3.12521
\(399\) 7.47937 0.374437
\(400\) −30.5588 −1.52794
\(401\) 9.86409 0.492589 0.246295 0.969195i \(-0.420787\pi\)
0.246295 + 0.969195i \(0.420787\pi\)
\(402\) 67.5531 3.36924
\(403\) −2.98518 −0.148702
\(404\) −58.2711 −2.89910
\(405\) −1.92234 −0.0955220
\(406\) 12.5228 0.621496
\(407\) −4.84851 −0.240332
\(408\) −28.0462 −1.38850
\(409\) 6.52919 0.322848 0.161424 0.986885i \(-0.448391\pi\)
0.161424 + 0.986885i \(0.448391\pi\)
\(410\) −43.7807 −2.16218
\(411\) −25.5242 −1.25902
\(412\) −3.42991 −0.168980
\(413\) 24.2997 1.19571
\(414\) 95.0284 4.67039
\(415\) 21.4073 1.05084
\(416\) 22.6576 1.11088
\(417\) 5.30064 0.259573
\(418\) 2.93817 0.143711
\(419\) 14.8248 0.724239 0.362120 0.932132i \(-0.382053\pi\)
0.362120 + 0.932132i \(0.382053\pi\)
\(420\) −69.1515 −3.37425
\(421\) −11.5694 −0.563856 −0.281928 0.959436i \(-0.590974\pi\)
−0.281928 + 0.959436i \(0.590974\pi\)
\(422\) 13.5498 0.659595
\(423\) −54.6858 −2.65892
\(424\) −125.268 −6.08357
\(425\) −1.89631 −0.0919843
\(426\) −16.4004 −0.794602
\(427\) −34.3568 −1.66264
\(428\) −22.0010 −1.06346
\(429\) 2.60765 0.125899
\(430\) 4.85519 0.234138
\(431\) −27.3899 −1.31932 −0.659662 0.751563i \(-0.729300\pi\)
−0.659662 + 0.751563i \(0.729300\pi\)
\(432\) 91.8267 4.41801
\(433\) 36.4841 1.75332 0.876658 0.481114i \(-0.159768\pi\)
0.876658 + 0.481114i \(0.159768\pi\)
\(434\) −22.1331 −1.06242
\(435\) 9.14355 0.438400
\(436\) −103.931 −4.97740
\(437\) −7.33330 −0.350799
\(438\) 113.604 5.42821
\(439\) −18.0335 −0.860692 −0.430346 0.902664i \(-0.641608\pi\)
−0.430346 + 0.902664i \(0.641608\pi\)
\(440\) −17.4549 −0.832128
\(441\) −4.30089 −0.204804
\(442\) 2.53874 0.120756
\(443\) −7.71254 −0.366434 −0.183217 0.983073i \(-0.558651\pi\)
−0.183217 + 0.983073i \(0.558651\pi\)
\(444\) 76.7915 3.64436
\(445\) −3.31572 −0.157180
\(446\) 19.7729 0.936276
\(447\) −48.5815 −2.29782
\(448\) 88.1146 4.16302
\(449\) 11.6899 0.551681 0.275841 0.961203i \(-0.411044\pi\)
0.275841 + 0.961203i \(0.411044\pi\)
\(450\) 26.1983 1.23500
\(451\) 9.01731 0.424609
\(452\) 44.6657 2.10090
\(453\) −12.4430 −0.584623
\(454\) 13.6700 0.641566
\(455\) 4.02206 0.188557
\(456\) −29.9010 −1.40024
\(457\) 4.54533 0.212621 0.106311 0.994333i \(-0.466096\pi\)
0.106311 + 0.994333i \(0.466096\pi\)
\(458\) −2.42363 −0.113249
\(459\) 5.69825 0.265971
\(460\) 67.8010 3.16124
\(461\) −4.53893 −0.211399 −0.105700 0.994398i \(-0.533708\pi\)
−0.105700 + 0.994398i \(0.533708\pi\)
\(462\) 19.3340 0.899498
\(463\) −5.08023 −0.236098 −0.118049 0.993008i \(-0.537664\pi\)
−0.118049 + 0.993008i \(0.537664\pi\)
\(464\) −29.5465 −1.37166
\(465\) −16.1605 −0.749426
\(466\) 27.4683 1.27244
\(467\) 21.1311 0.977832 0.488916 0.872331i \(-0.337393\pi\)
0.488916 + 0.872331i \(0.337393\pi\)
\(468\) −25.8379 −1.19436
\(469\) −21.4604 −0.990950
\(470\) −52.9643 −2.44306
\(471\) 54.5177 2.51204
\(472\) −97.1451 −4.47146
\(473\) −1.00000 −0.0459800
\(474\) −77.2378 −3.54765
\(475\) −2.02171 −0.0927624
\(476\) 13.8664 0.635566
\(477\) 63.3815 2.90204
\(478\) −6.49922 −0.297267
\(479\) 38.4202 1.75546 0.877732 0.479152i \(-0.159056\pi\)
0.877732 + 0.479152i \(0.159056\pi\)
\(480\) 122.659 5.59857
\(481\) −4.46643 −0.203652
\(482\) 20.0049 0.911197
\(483\) −48.2551 −2.19568
\(484\) 5.59510 0.254323
\(485\) −7.58965 −0.344628
\(486\) 38.5993 1.75090
\(487\) 14.5613 0.659835 0.329917 0.944010i \(-0.392979\pi\)
0.329917 + 0.944010i \(0.392979\pi\)
\(488\) 137.351 6.21760
\(489\) −22.1521 −1.00175
\(490\) −4.16549 −0.188178
\(491\) 10.5346 0.475420 0.237710 0.971336i \(-0.423603\pi\)
0.237710 + 0.971336i \(0.423603\pi\)
\(492\) −142.818 −6.43872
\(493\) −1.83349 −0.0825761
\(494\) 2.70663 0.121777
\(495\) 8.83155 0.396949
\(496\) 52.2211 2.34480
\(497\) 5.21011 0.233705
\(498\) 94.7953 4.24788
\(499\) −2.83366 −0.126852 −0.0634260 0.997987i \(-0.520203\pi\)
−0.0634260 + 0.997987i \(0.520203\pi\)
\(500\) 67.9772 3.04003
\(501\) 55.8158 2.49367
\(502\) −45.0155 −2.00914
\(503\) −31.6956 −1.41324 −0.706619 0.707594i \(-0.749781\pi\)
−0.706619 + 0.707594i \(0.749781\pi\)
\(504\) −123.092 −5.48297
\(505\) 18.3478 0.816469
\(506\) −18.9564 −0.842714
\(507\) −34.3973 −1.52764
\(508\) 104.635 4.64242
\(509\) −13.4644 −0.596800 −0.298400 0.954441i \(-0.596453\pi\)
−0.298400 + 0.954441i \(0.596453\pi\)
\(510\) 13.7437 0.608581
\(511\) −36.0900 −1.59653
\(512\) −77.0324 −3.40438
\(513\) 6.07508 0.268221
\(514\) −9.79009 −0.431822
\(515\) 1.07998 0.0475896
\(516\) 15.8382 0.697237
\(517\) 10.9088 0.479769
\(518\) −33.1155 −1.45501
\(519\) 2.08868 0.0916829
\(520\) −16.0794 −0.705127
\(521\) 22.9484 1.00539 0.502694 0.864464i \(-0.332342\pi\)
0.502694 + 0.864464i \(0.332342\pi\)
\(522\) 25.3304 1.10868
\(523\) 3.71790 0.162573 0.0812863 0.996691i \(-0.474097\pi\)
0.0812863 + 0.996691i \(0.474097\pi\)
\(524\) −92.2254 −4.02889
\(525\) −13.3034 −0.580608
\(526\) 78.8425 3.43769
\(527\) 3.24055 0.141160
\(528\) −45.6168 −1.98522
\(529\) 24.3127 1.05708
\(530\) 61.3862 2.66645
\(531\) 49.1520 2.13302
\(532\) 14.7834 0.640942
\(533\) 8.30672 0.359804
\(534\) −14.6826 −0.635378
\(535\) 6.92746 0.299500
\(536\) 85.7943 3.70575
\(537\) 14.9840 0.646607
\(538\) 9.40984 0.405687
\(539\) 0.857947 0.0369544
\(540\) −56.1679 −2.41708
\(541\) −30.7807 −1.32337 −0.661683 0.749783i \(-0.730158\pi\)
−0.661683 + 0.749783i \(0.730158\pi\)
\(542\) 55.6630 2.39093
\(543\) −5.92444 −0.254242
\(544\) −24.5958 −1.05454
\(545\) 32.7248 1.40178
\(546\) 17.8104 0.762214
\(547\) 15.8214 0.676475 0.338237 0.941061i \(-0.390169\pi\)
0.338237 + 0.941061i \(0.390169\pi\)
\(548\) −50.4502 −2.15512
\(549\) −69.4950 −2.96597
\(550\) −5.22607 −0.222840
\(551\) −1.95474 −0.0832746
\(552\) 192.914 8.21096
\(553\) 24.5371 1.04342
\(554\) 4.52869 0.192406
\(555\) −24.1794 −1.02636
\(556\) 10.4770 0.444325
\(557\) −36.5420 −1.54833 −0.774167 0.632982i \(-0.781831\pi\)
−0.774167 + 0.632982i \(0.781831\pi\)
\(558\) −44.7695 −1.89525
\(559\) −0.921197 −0.0389625
\(560\) −70.3597 −2.97324
\(561\) −2.83072 −0.119513
\(562\) −12.6473 −0.533495
\(563\) −0.692623 −0.0291906 −0.0145953 0.999893i \(-0.504646\pi\)
−0.0145953 + 0.999893i \(0.504646\pi\)
\(564\) −172.776 −7.27516
\(565\) −14.0639 −0.591673
\(566\) −39.8209 −1.67380
\(567\) 2.70426 0.113568
\(568\) −20.8289 −0.873963
\(569\) 7.22464 0.302873 0.151436 0.988467i \(-0.451610\pi\)
0.151436 + 0.988467i \(0.451610\pi\)
\(570\) 14.6526 0.613729
\(571\) 25.9170 1.08459 0.542297 0.840187i \(-0.317555\pi\)
0.542297 + 0.840187i \(0.317555\pi\)
\(572\) 5.15418 0.215507
\(573\) 45.5024 1.90089
\(574\) 61.5886 2.57066
\(575\) 13.0436 0.543956
\(576\) 178.233 7.42639
\(577\) 25.9861 1.08181 0.540907 0.841082i \(-0.318081\pi\)
0.540907 + 0.841082i \(0.318081\pi\)
\(578\) −2.75592 −0.114631
\(579\) 55.1843 2.29338
\(580\) 18.0728 0.750431
\(581\) −30.1148 −1.24937
\(582\) −33.6083 −1.39311
\(583\) −12.6434 −0.523637
\(584\) 144.280 5.97036
\(585\) 8.13560 0.336366
\(586\) 81.1800 3.35351
\(587\) 10.7970 0.445638 0.222819 0.974860i \(-0.428474\pi\)
0.222819 + 0.974860i \(0.428474\pi\)
\(588\) −13.5883 −0.560372
\(589\) 3.45485 0.142354
\(590\) 47.6047 1.95985
\(591\) 41.7521 1.71745
\(592\) 78.1332 3.21126
\(593\) −7.78692 −0.319771 −0.159885 0.987136i \(-0.551112\pi\)
−0.159885 + 0.987136i \(0.551112\pi\)
\(594\) 15.7039 0.644339
\(595\) −4.36613 −0.178994
\(596\) −96.0241 −3.93330
\(597\) −64.0400 −2.62098
\(598\) −17.4626 −0.714097
\(599\) −9.17818 −0.375010 −0.187505 0.982264i \(-0.560040\pi\)
−0.187505 + 0.982264i \(0.560040\pi\)
\(600\) 53.1842 2.17124
\(601\) 39.3717 1.60601 0.803003 0.595976i \(-0.203234\pi\)
0.803003 + 0.595976i \(0.203234\pi\)
\(602\) −6.83004 −0.278372
\(603\) −43.4089 −1.76775
\(604\) −24.5943 −1.00073
\(605\) −1.76173 −0.0716245
\(606\) 81.2475 3.30045
\(607\) 30.4587 1.23628 0.618140 0.786068i \(-0.287886\pi\)
0.618140 + 0.786068i \(0.287886\pi\)
\(608\) −26.2223 −1.06346
\(609\) −12.8627 −0.521223
\(610\) −67.3073 −2.72519
\(611\) 10.0492 0.406545
\(612\) 28.0482 1.13378
\(613\) −9.14982 −0.369558 −0.184779 0.982780i \(-0.559157\pi\)
−0.184779 + 0.982780i \(0.559157\pi\)
\(614\) 53.3146 2.15160
\(615\) 44.9691 1.81333
\(616\) 24.5547 0.989335
\(617\) −16.7057 −0.672545 −0.336273 0.941765i \(-0.609166\pi\)
−0.336273 + 0.941765i \(0.609166\pi\)
\(618\) 4.78234 0.192374
\(619\) 28.6779 1.15266 0.576332 0.817216i \(-0.304484\pi\)
0.576332 + 0.817216i \(0.304484\pi\)
\(620\) −31.9422 −1.28283
\(621\) −39.1950 −1.57284
\(622\) −30.1060 −1.20714
\(623\) 4.66440 0.186875
\(624\) −42.0221 −1.68223
\(625\) −11.9225 −0.476900
\(626\) 96.3634 3.85146
\(627\) −3.01792 −0.120524
\(628\) 107.757 4.29999
\(629\) 4.84851 0.193323
\(630\) 60.3199 2.40320
\(631\) −18.6284 −0.741587 −0.370793 0.928715i \(-0.620914\pi\)
−0.370793 + 0.928715i \(0.620914\pi\)
\(632\) −98.0941 −3.90197
\(633\) −13.9176 −0.553175
\(634\) 76.0481 3.02026
\(635\) −32.9464 −1.30744
\(636\) 200.249 7.94038
\(637\) 0.790338 0.0313143
\(638\) −5.05295 −0.200048
\(639\) 10.5387 0.416905
\(640\) 85.9601 3.39787
\(641\) 14.6407 0.578275 0.289137 0.957288i \(-0.406632\pi\)
0.289137 + 0.957288i \(0.406632\pi\)
\(642\) 30.6760 1.21069
\(643\) 44.5045 1.75509 0.877543 0.479499i \(-0.159182\pi\)
0.877543 + 0.479499i \(0.159182\pi\)
\(644\) −95.3791 −3.75846
\(645\) −4.98697 −0.196362
\(646\) −2.93817 −0.115601
\(647\) 12.2137 0.480172 0.240086 0.970752i \(-0.422824\pi\)
0.240086 + 0.970752i \(0.422824\pi\)
\(648\) −10.8111 −0.424699
\(649\) −9.80491 −0.384876
\(650\) −4.81423 −0.188830
\(651\) 22.7338 0.891009
\(652\) −43.7849 −1.71475
\(653\) 20.9830 0.821127 0.410563 0.911832i \(-0.365332\pi\)
0.410563 + 0.911832i \(0.365332\pi\)
\(654\) 144.911 5.66648
\(655\) 29.0391 1.13465
\(656\) −145.313 −5.67352
\(657\) −73.0008 −2.84803
\(658\) 74.5076 2.90461
\(659\) 0.330303 0.0128668 0.00643338 0.999979i \(-0.497952\pi\)
0.00643338 + 0.999979i \(0.497952\pi\)
\(660\) 27.9026 1.08611
\(661\) −20.7386 −0.806637 −0.403319 0.915060i \(-0.632143\pi\)
−0.403319 + 0.915060i \(0.632143\pi\)
\(662\) 43.6043 1.69473
\(663\) −2.60765 −0.101273
\(664\) 120.393 4.67214
\(665\) −4.65486 −0.180508
\(666\) −66.9842 −2.59559
\(667\) 12.6115 0.488320
\(668\) 110.323 4.26854
\(669\) −20.3096 −0.785216
\(670\) −42.0424 −1.62424
\(671\) 13.8630 0.535174
\(672\) −172.550 −6.65626
\(673\) 2.11347 0.0814682 0.0407341 0.999170i \(-0.487030\pi\)
0.0407341 + 0.999170i \(0.487030\pi\)
\(674\) −72.0080 −2.77364
\(675\) −10.8056 −0.415908
\(676\) −67.9882 −2.61493
\(677\) 23.5772 0.906144 0.453072 0.891474i \(-0.350328\pi\)
0.453072 + 0.891474i \(0.350328\pi\)
\(678\) −62.2774 −2.39175
\(679\) 10.6767 0.409736
\(680\) 17.4549 0.669364
\(681\) −14.0411 −0.538055
\(682\) 8.93069 0.341974
\(683\) 39.3453 1.50551 0.752754 0.658302i \(-0.228725\pi\)
0.752754 + 0.658302i \(0.228725\pi\)
\(684\) 29.9031 1.14337
\(685\) 15.8853 0.606945
\(686\) 53.6701 2.04913
\(687\) 2.48941 0.0949770
\(688\) 16.1149 0.614375
\(689\) −11.6471 −0.443718
\(690\) −94.5350 −3.59889
\(691\) −39.4293 −1.49996 −0.749981 0.661460i \(-0.769937\pi\)
−0.749981 + 0.661460i \(0.769937\pi\)
\(692\) 4.12840 0.156938
\(693\) −12.4238 −0.471941
\(694\) −80.7506 −3.06525
\(695\) −3.29891 −0.125135
\(696\) 51.4224 1.94916
\(697\) −9.01731 −0.341555
\(698\) −69.4287 −2.62791
\(699\) −28.2138 −1.06715
\(700\) −26.2950 −0.993856
\(701\) −32.9071 −1.24288 −0.621441 0.783461i \(-0.713453\pi\)
−0.621441 + 0.783461i \(0.713453\pi\)
\(702\) 14.4664 0.545999
\(703\) 5.16914 0.194958
\(704\) −35.5542 −1.34000
\(705\) 54.4019 2.04890
\(706\) −45.9866 −1.73073
\(707\) −25.8109 −0.970717
\(708\) 155.292 5.83623
\(709\) 18.2810 0.686557 0.343279 0.939234i \(-0.388463\pi\)
0.343279 + 0.939234i \(0.388463\pi\)
\(710\) 10.2070 0.383060
\(711\) 49.6322 1.86135
\(712\) −18.6473 −0.698837
\(713\) −22.2899 −0.834762
\(714\) −19.3340 −0.723556
\(715\) −1.62290 −0.0606930
\(716\) 29.6167 1.10683
\(717\) 6.67563 0.249306
\(718\) 45.4129 1.69479
\(719\) −11.2974 −0.421322 −0.210661 0.977559i \(-0.567562\pi\)
−0.210661 + 0.977559i \(0.567562\pi\)
\(720\) −142.320 −5.30394
\(721\) −1.51926 −0.0565803
\(722\) 49.2300 1.83215
\(723\) −20.5479 −0.764183
\(724\) −11.7100 −0.435199
\(725\) 3.47685 0.129127
\(726\) −7.80125 −0.289532
\(727\) −36.4839 −1.35311 −0.676556 0.736391i \(-0.736529\pi\)
−0.676556 + 0.736391i \(0.736529\pi\)
\(728\) 22.6197 0.838340
\(729\) −42.9205 −1.58965
\(730\) −70.7027 −2.61682
\(731\) 1.00000 0.0369863
\(732\) −219.564 −8.11532
\(733\) 22.7033 0.838567 0.419283 0.907855i \(-0.362281\pi\)
0.419283 + 0.907855i \(0.362281\pi\)
\(734\) 52.8578 1.95102
\(735\) 4.27856 0.157817
\(736\) 169.180 6.23607
\(737\) 8.65927 0.318968
\(738\) 124.578 4.58578
\(739\) −24.4395 −0.899020 −0.449510 0.893275i \(-0.648401\pi\)
−0.449510 + 0.893275i \(0.648401\pi\)
\(740\) −47.7920 −1.75687
\(741\) −2.78010 −0.102129
\(742\) −86.3551 −3.17020
\(743\) −11.1211 −0.407992 −0.203996 0.978972i \(-0.565393\pi\)
−0.203996 + 0.978972i \(0.565393\pi\)
\(744\) −90.8851 −3.33201
\(745\) 30.2352 1.10773
\(746\) −9.87240 −0.361454
\(747\) −60.9144 −2.22874
\(748\) −5.59510 −0.204577
\(749\) −9.74521 −0.356082
\(750\) −94.7808 −3.46090
\(751\) −20.5367 −0.749397 −0.374698 0.927147i \(-0.622254\pi\)
−0.374698 + 0.927147i \(0.622254\pi\)
\(752\) −175.794 −6.41056
\(753\) 46.2373 1.68498
\(754\) −4.65476 −0.169516
\(755\) 7.74403 0.281834
\(756\) 79.0143 2.87372
\(757\) −1.18717 −0.0431485 −0.0215742 0.999767i \(-0.506868\pi\)
−0.0215742 + 0.999767i \(0.506868\pi\)
\(758\) −20.1182 −0.730724
\(759\) 19.4709 0.706750
\(760\) 18.6092 0.675025
\(761\) 12.3912 0.449180 0.224590 0.974453i \(-0.427896\pi\)
0.224590 + 0.974453i \(0.427896\pi\)
\(762\) −145.892 −5.28513
\(763\) −46.0357 −1.66660
\(764\) 89.9382 3.25385
\(765\) −8.83155 −0.319306
\(766\) −21.8247 −0.788560
\(767\) −9.03225 −0.326136
\(768\) 179.358 6.47203
\(769\) 24.6363 0.888408 0.444204 0.895926i \(-0.353487\pi\)
0.444204 + 0.895926i \(0.353487\pi\)
\(770\) −12.0327 −0.433628
\(771\) 10.0558 0.362152
\(772\) 109.075 3.92569
\(773\) −33.1192 −1.19122 −0.595608 0.803275i \(-0.703089\pi\)
−0.595608 + 0.803275i \(0.703089\pi\)
\(774\) −13.8154 −0.496585
\(775\) −6.14507 −0.220737
\(776\) −42.6834 −1.53224
\(777\) 34.0144 1.22026
\(778\) −16.4350 −0.589225
\(779\) −9.61363 −0.344444
\(780\) 25.7038 0.920343
\(781\) −2.10228 −0.0752254
\(782\) 18.9564 0.677879
\(783\) −10.4477 −0.373369
\(784\) −13.8257 −0.493776
\(785\) −33.9296 −1.21100
\(786\) 128.590 4.58666
\(787\) 40.5431 1.44520 0.722602 0.691264i \(-0.242946\pi\)
0.722602 + 0.691264i \(0.242946\pi\)
\(788\) 82.5255 2.93985
\(789\) −80.9825 −2.88305
\(790\) 48.0698 1.71025
\(791\) 19.7844 0.703453
\(792\) 49.6678 1.76487
\(793\) 12.7705 0.453494
\(794\) 59.2276 2.10191
\(795\) −63.0524 −2.23624
\(796\) −126.579 −4.48647
\(797\) −29.8682 −1.05799 −0.528993 0.848626i \(-0.677430\pi\)
−0.528993 + 0.848626i \(0.677430\pi\)
\(798\) −20.6125 −0.729676
\(799\) −10.9088 −0.385926
\(800\) 46.6411 1.64901
\(801\) 9.43488 0.333365
\(802\) −27.1846 −0.959923
\(803\) 14.5623 0.513892
\(804\) −137.147 −4.83680
\(805\) 30.0321 1.05849
\(806\) 8.22692 0.289781
\(807\) −9.66525 −0.340233
\(808\) 103.186 3.63009
\(809\) 7.52998 0.264740 0.132370 0.991200i \(-0.457741\pi\)
0.132370 + 0.991200i \(0.457741\pi\)
\(810\) 5.29782 0.186147
\(811\) 0.326093 0.0114507 0.00572533 0.999984i \(-0.498178\pi\)
0.00572533 + 0.999984i \(0.498178\pi\)
\(812\) −25.4239 −0.892204
\(813\) −57.1739 −2.00518
\(814\) 13.3621 0.468341
\(815\) 13.7866 0.482922
\(816\) 45.6168 1.59691
\(817\) 1.06613 0.0372992
\(818\) −17.9939 −0.629143
\(819\) −11.4448 −0.399912
\(820\) 88.8841 3.10397
\(821\) 15.3574 0.535978 0.267989 0.963422i \(-0.413641\pi\)
0.267989 + 0.963422i \(0.413641\pi\)
\(822\) 70.3427 2.45348
\(823\) −26.6683 −0.929598 −0.464799 0.885416i \(-0.653873\pi\)
−0.464799 + 0.885416i \(0.653873\pi\)
\(824\) 6.07369 0.211587
\(825\) 5.36792 0.186887
\(826\) −66.9680 −2.33011
\(827\) 3.81560 0.132681 0.0663406 0.997797i \(-0.478868\pi\)
0.0663406 + 0.997797i \(0.478868\pi\)
\(828\) −192.928 −6.70470
\(829\) −23.2155 −0.806307 −0.403154 0.915132i \(-0.632086\pi\)
−0.403154 + 0.915132i \(0.632086\pi\)
\(830\) −58.9968 −2.04781
\(831\) −4.65161 −0.161363
\(832\) −32.7524 −1.13549
\(833\) −0.857947 −0.0297261
\(834\) −14.6081 −0.505838
\(835\) −34.7376 −1.20214
\(836\) −5.96510 −0.206307
\(837\) 18.4654 0.638259
\(838\) −40.8560 −1.41135
\(839\) −55.2486 −1.90739 −0.953697 0.300769i \(-0.902757\pi\)
−0.953697 + 0.300769i \(0.902757\pi\)
\(840\) 122.453 4.22504
\(841\) −25.6383 −0.884080
\(842\) 31.8842 1.09880
\(843\) 12.9906 0.447420
\(844\) −27.5090 −0.946898
\(845\) 21.4075 0.736440
\(846\) 150.710 5.18151
\(847\) 2.47832 0.0851560
\(848\) 203.748 6.99672
\(849\) 40.9018 1.40375
\(850\) 5.22607 0.179253
\(851\) −33.3501 −1.14323
\(852\) 33.2962 1.14071
\(853\) −31.5328 −1.07966 −0.539831 0.841774i \(-0.681512\pi\)
−0.539831 + 0.841774i \(0.681512\pi\)
\(854\) 94.6846 3.24004
\(855\) −9.41559 −0.322006
\(856\) 38.9593 1.33160
\(857\) 32.5709 1.11260 0.556300 0.830981i \(-0.312220\pi\)
0.556300 + 0.830981i \(0.312220\pi\)
\(858\) −7.18648 −0.245343
\(859\) −20.9748 −0.715652 −0.357826 0.933788i \(-0.616482\pi\)
−0.357826 + 0.933788i \(0.616482\pi\)
\(860\) −9.85705 −0.336123
\(861\) −63.2603 −2.15591
\(862\) 75.4843 2.57100
\(863\) −18.0096 −0.613055 −0.306527 0.951862i \(-0.599167\pi\)
−0.306527 + 0.951862i \(0.599167\pi\)
\(864\) −140.153 −4.76810
\(865\) −1.29991 −0.0441983
\(866\) −100.547 −3.41674
\(867\) 2.83072 0.0961364
\(868\) 44.9348 1.52519
\(869\) −9.90070 −0.335858
\(870\) −25.1989 −0.854323
\(871\) 7.97689 0.270287
\(872\) 184.041 6.23242
\(873\) 21.5963 0.730925
\(874\) 20.2100 0.683613
\(875\) 30.1101 1.01791
\(876\) −230.640 −7.79261
\(877\) −29.9665 −1.01190 −0.505949 0.862563i \(-0.668858\pi\)
−0.505949 + 0.862563i \(0.668858\pi\)
\(878\) 49.6989 1.67726
\(879\) −83.3835 −2.81245
\(880\) 28.3901 0.957030
\(881\) −24.2676 −0.817597 −0.408799 0.912625i \(-0.634052\pi\)
−0.408799 + 0.912625i \(0.634052\pi\)
\(882\) 11.8529 0.399108
\(883\) −18.3773 −0.618447 −0.309223 0.950989i \(-0.600069\pi\)
−0.309223 + 0.950989i \(0.600069\pi\)
\(884\) −5.15418 −0.173354
\(885\) −48.8968 −1.64365
\(886\) 21.2551 0.714080
\(887\) 47.2937 1.58797 0.793984 0.607939i \(-0.208004\pi\)
0.793984 + 0.607939i \(0.208004\pi\)
\(888\) −135.982 −4.56327
\(889\) 46.3474 1.55444
\(890\) 9.13786 0.306302
\(891\) −1.09117 −0.0365555
\(892\) −40.1432 −1.34409
\(893\) −11.6302 −0.389190
\(894\) 133.887 4.47784
\(895\) −9.32544 −0.311715
\(896\) −120.925 −4.03981
\(897\) 17.9366 0.598884
\(898\) −32.2165 −1.07508
\(899\) −5.94150 −0.198160
\(900\) −53.1880 −1.77293
\(901\) 12.6434 0.421214
\(902\) −24.8510 −0.827447
\(903\) 7.01543 0.233459
\(904\) −79.0940 −2.63063
\(905\) 3.68714 0.122565
\(906\) 34.2919 1.13927
\(907\) −43.0248 −1.42862 −0.714308 0.699831i \(-0.753259\pi\)
−0.714308 + 0.699831i \(0.753259\pi\)
\(908\) −27.7530 −0.921017
\(909\) −52.2088 −1.73166
\(910\) −11.0845 −0.367447
\(911\) −45.2369 −1.49877 −0.749383 0.662137i \(-0.769650\pi\)
−0.749383 + 0.662137i \(0.769650\pi\)
\(912\) 48.6335 1.61042
\(913\) 12.1513 0.402149
\(914\) −12.5266 −0.414342
\(915\) 69.1342 2.28551
\(916\) 4.92047 0.162577
\(917\) −40.8507 −1.34901
\(918\) −15.7039 −0.518306
\(919\) −39.9984 −1.31943 −0.659713 0.751517i \(-0.729322\pi\)
−0.659713 + 0.751517i \(0.729322\pi\)
\(920\) −120.062 −3.95833
\(921\) −54.7617 −1.80446
\(922\) 12.5089 0.411960
\(923\) −1.93661 −0.0637443
\(924\) −39.2520 −1.29130
\(925\) −9.19425 −0.302305
\(926\) 14.0007 0.460091
\(927\) −3.07308 −0.100933
\(928\) 45.0961 1.48035
\(929\) −9.65282 −0.316699 −0.158349 0.987383i \(-0.550617\pi\)
−0.158349 + 0.987383i \(0.550617\pi\)
\(930\) 44.5371 1.46043
\(931\) −0.914683 −0.0299775
\(932\) −55.7663 −1.82669
\(933\) 30.9232 1.01238
\(934\) −58.2357 −1.90553
\(935\) 1.76173 0.0576147
\(936\) 45.7538 1.49551
\(937\) 42.0166 1.37262 0.686312 0.727308i \(-0.259229\pi\)
0.686312 + 0.727308i \(0.259229\pi\)
\(938\) 59.1432 1.93109
\(939\) −98.9790 −3.23006
\(940\) 107.529 3.50720
\(941\) −52.7524 −1.71968 −0.859840 0.510564i \(-0.829436\pi\)
−0.859840 + 0.510564i \(0.829436\pi\)
\(942\) −150.246 −4.89529
\(943\) 62.0249 2.01981
\(944\) 158.005 5.14263
\(945\) −24.8793 −0.809323
\(946\) 2.75592 0.0896027
\(947\) −21.2503 −0.690542 −0.345271 0.938503i \(-0.612213\pi\)
−0.345271 + 0.938503i \(0.612213\pi\)
\(948\) 156.809 5.09292
\(949\) 13.4147 0.435461
\(950\) 5.57167 0.180769
\(951\) −78.1123 −2.53296
\(952\) −24.5547 −0.795821
\(953\) 11.8297 0.383202 0.191601 0.981473i \(-0.438632\pi\)
0.191601 + 0.981473i \(0.438632\pi\)
\(954\) −174.674 −5.65529
\(955\) −28.3189 −0.916378
\(956\) 13.1948 0.426750
\(957\) 5.19010 0.167772
\(958\) −105.883 −3.42093
\(959\) −22.3466 −0.721610
\(960\) −177.308 −5.72259
\(961\) −20.4989 −0.661254
\(962\) 12.3091 0.396862
\(963\) −19.7121 −0.635213
\(964\) −40.6141 −1.30809
\(965\) −34.3445 −1.10559
\(966\) 132.987 4.27879
\(967\) −11.4167 −0.367136 −0.183568 0.983007i \(-0.558765\pi\)
−0.183568 + 0.983007i \(0.558765\pi\)
\(968\) −9.90779 −0.318449
\(969\) 3.01792 0.0969496
\(970\) 20.9165 0.671587
\(971\) 51.9125 1.66595 0.832975 0.553310i \(-0.186636\pi\)
0.832975 + 0.553310i \(0.186636\pi\)
\(972\) −78.3646 −2.51355
\(973\) 4.64074 0.148775
\(974\) −40.1297 −1.28584
\(975\) 4.94491 0.158364
\(976\) −223.400 −7.15087
\(977\) −43.5467 −1.39318 −0.696592 0.717468i \(-0.745301\pi\)
−0.696592 + 0.717468i \(0.745301\pi\)
\(978\) 61.0493 1.95214
\(979\) −1.88208 −0.0601516
\(980\) 8.45682 0.270143
\(981\) −93.1185 −2.97304
\(982\) −29.0325 −0.926465
\(983\) 50.1447 1.59937 0.799684 0.600422i \(-0.205001\pi\)
0.799684 + 0.600422i \(0.205001\pi\)
\(984\) 252.902 8.06221
\(985\) −25.9849 −0.827947
\(986\) 5.05295 0.160919
\(987\) −76.5300 −2.43598
\(988\) −5.49503 −0.174820
\(989\) −6.87843 −0.218721
\(990\) −24.3391 −0.773546
\(991\) −24.4273 −0.775960 −0.387980 0.921668i \(-0.626827\pi\)
−0.387980 + 0.921668i \(0.626827\pi\)
\(992\) −79.7038 −2.53060
\(993\) −44.7879 −1.42130
\(994\) −14.3586 −0.455429
\(995\) 39.8560 1.26352
\(996\) −192.454 −6.09815
\(997\) −55.0435 −1.74325 −0.871623 0.490176i \(-0.836932\pi\)
−0.871623 + 0.490176i \(0.836932\pi\)
\(998\) 7.80934 0.247200
\(999\) 27.6280 0.874111
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 \(a_p\))