Properties

Label 8015.2.a.l.1.4
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.48664 q^{2} +3.28438 q^{3} +4.18340 q^{4} -1.00000 q^{5} -8.16709 q^{6} -1.00000 q^{7} -5.42933 q^{8} +7.78717 q^{9} +O(q^{10})\) \(q-2.48664 q^{2} +3.28438 q^{3} +4.18340 q^{4} -1.00000 q^{5} -8.16709 q^{6} -1.00000 q^{7} -5.42933 q^{8} +7.78717 q^{9} +2.48664 q^{10} -3.56103 q^{11} +13.7399 q^{12} +1.97454 q^{13} +2.48664 q^{14} -3.28438 q^{15} +5.13402 q^{16} -7.88010 q^{17} -19.3639 q^{18} -2.56746 q^{19} -4.18340 q^{20} -3.28438 q^{21} +8.85502 q^{22} +1.14897 q^{23} -17.8320 q^{24} +1.00000 q^{25} -4.90997 q^{26} +15.7229 q^{27} -4.18340 q^{28} +1.72372 q^{29} +8.16709 q^{30} +6.82699 q^{31} -1.90781 q^{32} -11.6958 q^{33} +19.5950 q^{34} +1.00000 q^{35} +32.5768 q^{36} +7.16654 q^{37} +6.38435 q^{38} +6.48514 q^{39} +5.42933 q^{40} -3.32254 q^{41} +8.16709 q^{42} -4.87597 q^{43} -14.8972 q^{44} -7.78717 q^{45} -2.85707 q^{46} +3.93309 q^{47} +16.8621 q^{48} +1.00000 q^{49} -2.48664 q^{50} -25.8813 q^{51} +8.26027 q^{52} -3.77441 q^{53} -39.0973 q^{54} +3.56103 q^{55} +5.42933 q^{56} -8.43251 q^{57} -4.28627 q^{58} +6.42701 q^{59} -13.7399 q^{60} -14.5197 q^{61} -16.9763 q^{62} -7.78717 q^{63} -5.52400 q^{64} -1.97454 q^{65} +29.0833 q^{66} +9.79842 q^{67} -32.9656 q^{68} +3.77364 q^{69} -2.48664 q^{70} +10.8647 q^{71} -42.2791 q^{72} +10.4860 q^{73} -17.8206 q^{74} +3.28438 q^{75} -10.7407 q^{76} +3.56103 q^{77} -16.1262 q^{78} +9.78565 q^{79} -5.13402 q^{80} +28.2785 q^{81} +8.26198 q^{82} -2.98903 q^{83} -13.7399 q^{84} +7.88010 q^{85} +12.1248 q^{86} +5.66135 q^{87} +19.3340 q^{88} -1.05934 q^{89} +19.3639 q^{90} -1.97454 q^{91} +4.80658 q^{92} +22.4224 q^{93} -9.78019 q^{94} +2.56746 q^{95} -6.26597 q^{96} +8.30149 q^{97} -2.48664 q^{98} -27.7304 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.48664 −1.75832 −0.879161 0.476524i \(-0.841896\pi\)
−0.879161 + 0.476524i \(0.841896\pi\)
\(3\) 3.28438 1.89624 0.948120 0.317914i \(-0.102982\pi\)
0.948120 + 0.317914i \(0.102982\pi\)
\(4\) 4.18340 2.09170
\(5\) −1.00000 −0.447214
\(6\) −8.16709 −3.33420
\(7\) −1.00000 −0.377964
\(8\) −5.42933 −1.91956
\(9\) 7.78717 2.59572
\(10\) 2.48664 0.786346
\(11\) −3.56103 −1.07369 −0.536846 0.843680i \(-0.680384\pi\)
−0.536846 + 0.843680i \(0.680384\pi\)
\(12\) 13.7399 3.96636
\(13\) 1.97454 0.547638 0.273819 0.961781i \(-0.411713\pi\)
0.273819 + 0.961781i \(0.411713\pi\)
\(14\) 2.48664 0.664583
\(15\) −3.28438 −0.848024
\(16\) 5.13402 1.28350
\(17\) −7.88010 −1.91121 −0.955603 0.294657i \(-0.904795\pi\)
−0.955603 + 0.294657i \(0.904795\pi\)
\(18\) −19.3639 −4.56412
\(19\) −2.56746 −0.589015 −0.294507 0.955649i \(-0.595156\pi\)
−0.294507 + 0.955649i \(0.595156\pi\)
\(20\) −4.18340 −0.935436
\(21\) −3.28438 −0.716711
\(22\) 8.85502 1.88790
\(23\) 1.14897 0.239576 0.119788 0.992799i \(-0.461779\pi\)
0.119788 + 0.992799i \(0.461779\pi\)
\(24\) −17.8320 −3.63994
\(25\) 1.00000 0.200000
\(26\) −4.90997 −0.962924
\(27\) 15.7229 3.02587
\(28\) −4.18340 −0.790588
\(29\) 1.72372 0.320086 0.160043 0.987110i \(-0.448837\pi\)
0.160043 + 0.987110i \(0.448837\pi\)
\(30\) 8.16709 1.49110
\(31\) 6.82699 1.22616 0.613082 0.790019i \(-0.289930\pi\)
0.613082 + 0.790019i \(0.289930\pi\)
\(32\) −1.90781 −0.337256
\(33\) −11.6958 −2.03598
\(34\) 19.5950 3.36052
\(35\) 1.00000 0.169031
\(36\) 32.5768 5.42947
\(37\) 7.16654 1.17817 0.589086 0.808070i \(-0.299488\pi\)
0.589086 + 0.808070i \(0.299488\pi\)
\(38\) 6.38435 1.03568
\(39\) 6.48514 1.03845
\(40\) 5.42933 0.858452
\(41\) −3.32254 −0.518894 −0.259447 0.965757i \(-0.583540\pi\)
−0.259447 + 0.965757i \(0.583540\pi\)
\(42\) 8.16709 1.26021
\(43\) −4.87597 −0.743578 −0.371789 0.928317i \(-0.621256\pi\)
−0.371789 + 0.928317i \(0.621256\pi\)
\(44\) −14.8972 −2.24584
\(45\) −7.78717 −1.16084
\(46\) −2.85707 −0.421252
\(47\) 3.93309 0.573700 0.286850 0.957976i \(-0.407392\pi\)
0.286850 + 0.957976i \(0.407392\pi\)
\(48\) 16.8621 2.43383
\(49\) 1.00000 0.142857
\(50\) −2.48664 −0.351665
\(51\) −25.8813 −3.62410
\(52\) 8.26027 1.14549
\(53\) −3.77441 −0.518456 −0.259228 0.965816i \(-0.583468\pi\)
−0.259228 + 0.965816i \(0.583468\pi\)
\(54\) −39.0973 −5.32046
\(55\) 3.56103 0.480170
\(56\) 5.42933 0.725525
\(57\) −8.43251 −1.11691
\(58\) −4.28627 −0.562815
\(59\) 6.42701 0.836725 0.418363 0.908280i \(-0.362604\pi\)
0.418363 + 0.908280i \(0.362604\pi\)
\(60\) −13.7399 −1.77381
\(61\) −14.5197 −1.85905 −0.929526 0.368756i \(-0.879784\pi\)
−0.929526 + 0.368756i \(0.879784\pi\)
\(62\) −16.9763 −2.15599
\(63\) −7.78717 −0.981091
\(64\) −5.52400 −0.690499
\(65\) −1.97454 −0.244911
\(66\) 29.0833 3.57990
\(67\) 9.79842 1.19707 0.598534 0.801097i \(-0.295750\pi\)
0.598534 + 0.801097i \(0.295750\pi\)
\(68\) −32.9656 −3.99767
\(69\) 3.77364 0.454293
\(70\) −2.48664 −0.297211
\(71\) 10.8647 1.28940 0.644702 0.764434i \(-0.276982\pi\)
0.644702 + 0.764434i \(0.276982\pi\)
\(72\) −42.2791 −4.98264
\(73\) 10.4860 1.22729 0.613644 0.789583i \(-0.289703\pi\)
0.613644 + 0.789583i \(0.289703\pi\)
\(74\) −17.8206 −2.07161
\(75\) 3.28438 0.379248
\(76\) −10.7407 −1.23204
\(77\) 3.56103 0.405817
\(78\) −16.1262 −1.82594
\(79\) 9.78565 1.10097 0.550486 0.834844i \(-0.314442\pi\)
0.550486 + 0.834844i \(0.314442\pi\)
\(80\) −5.13402 −0.574000
\(81\) 28.2785 3.14206
\(82\) 8.26198 0.912383
\(83\) −2.98903 −0.328088 −0.164044 0.986453i \(-0.552454\pi\)
−0.164044 + 0.986453i \(0.552454\pi\)
\(84\) −13.7399 −1.49914
\(85\) 7.88010 0.854717
\(86\) 12.1248 1.30745
\(87\) 5.66135 0.606960
\(88\) 19.3340 2.06101
\(89\) −1.05934 −0.112289 −0.0561447 0.998423i \(-0.517881\pi\)
−0.0561447 + 0.998423i \(0.517881\pi\)
\(90\) 19.3639 2.04114
\(91\) −1.97454 −0.206988
\(92\) 4.80658 0.501121
\(93\) 22.4224 2.32510
\(94\) −9.78019 −1.00875
\(95\) 2.56746 0.263415
\(96\) −6.26597 −0.639518
\(97\) 8.30149 0.842889 0.421444 0.906854i \(-0.361523\pi\)
0.421444 + 0.906854i \(0.361523\pi\)
\(98\) −2.48664 −0.251189
\(99\) −27.7304 −2.78701
\(100\) 4.18340 0.418340
\(101\) −13.1811 −1.31157 −0.655785 0.754948i \(-0.727662\pi\)
−0.655785 + 0.754948i \(0.727662\pi\)
\(102\) 64.3575 6.37234
\(103\) 10.3389 1.01872 0.509359 0.860554i \(-0.329883\pi\)
0.509359 + 0.860554i \(0.329883\pi\)
\(104\) −10.7204 −1.05122
\(105\) 3.28438 0.320523
\(106\) 9.38562 0.911612
\(107\) −1.21505 −0.117463 −0.0587316 0.998274i \(-0.518706\pi\)
−0.0587316 + 0.998274i \(0.518706\pi\)
\(108\) 65.7751 6.32922
\(109\) 2.28859 0.219207 0.109603 0.993975i \(-0.465042\pi\)
0.109603 + 0.993975i \(0.465042\pi\)
\(110\) −8.85502 −0.844293
\(111\) 23.5377 2.23410
\(112\) −5.13402 −0.485119
\(113\) −14.4375 −1.35817 −0.679084 0.734060i \(-0.737623\pi\)
−0.679084 + 0.734060i \(0.737623\pi\)
\(114\) 20.9686 1.96389
\(115\) −1.14897 −0.107142
\(116\) 7.21100 0.669524
\(117\) 15.3761 1.42152
\(118\) −15.9817 −1.47123
\(119\) 7.88010 0.722368
\(120\) 17.8320 1.62783
\(121\) 1.68096 0.152815
\(122\) 36.1052 3.26881
\(123\) −10.9125 −0.983947
\(124\) 28.5600 2.56476
\(125\) −1.00000 −0.0894427
\(126\) 19.3639 1.72508
\(127\) 1.31794 0.116949 0.0584743 0.998289i \(-0.481376\pi\)
0.0584743 + 0.998289i \(0.481376\pi\)
\(128\) 17.5518 1.55138
\(129\) −16.0145 −1.41000
\(130\) 4.90997 0.430633
\(131\) 18.2716 1.59640 0.798198 0.602395i \(-0.205787\pi\)
0.798198 + 0.602395i \(0.205787\pi\)
\(132\) −48.9282 −4.25865
\(133\) 2.56746 0.222627
\(134\) −24.3652 −2.10483
\(135\) −15.7229 −1.35321
\(136\) 42.7837 3.66867
\(137\) −2.10301 −0.179673 −0.0898363 0.995957i \(-0.528634\pi\)
−0.0898363 + 0.995957i \(0.528634\pi\)
\(138\) −9.38371 −0.798794
\(139\) −6.87366 −0.583016 −0.291508 0.956568i \(-0.594157\pi\)
−0.291508 + 0.956568i \(0.594157\pi\)
\(140\) 4.18340 0.353562
\(141\) 12.9178 1.08787
\(142\) −27.0167 −2.26719
\(143\) −7.03139 −0.587995
\(144\) 39.9795 3.33162
\(145\) −1.72372 −0.143147
\(146\) −26.0748 −2.15797
\(147\) 3.28438 0.270891
\(148\) 29.9805 2.46438
\(149\) −3.86043 −0.316258 −0.158129 0.987418i \(-0.550546\pi\)
−0.158129 + 0.987418i \(0.550546\pi\)
\(150\) −8.16709 −0.666840
\(151\) 14.0677 1.14481 0.572406 0.819971i \(-0.306010\pi\)
0.572406 + 0.819971i \(0.306010\pi\)
\(152\) 13.9396 1.13065
\(153\) −61.3637 −4.96096
\(154\) −8.85502 −0.713558
\(155\) −6.82699 −0.548357
\(156\) 27.1299 2.17213
\(157\) −0.799106 −0.0637756 −0.0318878 0.999491i \(-0.510152\pi\)
−0.0318878 + 0.999491i \(0.510152\pi\)
\(158\) −24.3334 −1.93586
\(159\) −12.3966 −0.983116
\(160\) 1.90781 0.150825
\(161\) −1.14897 −0.0905512
\(162\) −70.3186 −5.52475
\(163\) 7.01804 0.549695 0.274848 0.961488i \(-0.411373\pi\)
0.274848 + 0.961488i \(0.411373\pi\)
\(164\) −13.8995 −1.08537
\(165\) 11.6958 0.910517
\(166\) 7.43264 0.576885
\(167\) 14.5887 1.12891 0.564454 0.825464i \(-0.309087\pi\)
0.564454 + 0.825464i \(0.309087\pi\)
\(168\) 17.8320 1.37577
\(169\) −9.10120 −0.700093
\(170\) −19.5950 −1.50287
\(171\) −19.9932 −1.52892
\(172\) −20.3981 −1.55534
\(173\) 18.1670 1.38121 0.690606 0.723232i \(-0.257344\pi\)
0.690606 + 0.723232i \(0.257344\pi\)
\(174\) −14.0778 −1.06723
\(175\) −1.00000 −0.0755929
\(176\) −18.2824 −1.37809
\(177\) 21.1088 1.58663
\(178\) 2.63419 0.197441
\(179\) 11.1634 0.834391 0.417196 0.908817i \(-0.363013\pi\)
0.417196 + 0.908817i \(0.363013\pi\)
\(180\) −32.5768 −2.42813
\(181\) 0.368337 0.0273783 0.0136891 0.999906i \(-0.495642\pi\)
0.0136891 + 0.999906i \(0.495642\pi\)
\(182\) 4.90997 0.363951
\(183\) −47.6881 −3.52521
\(184\) −6.23811 −0.459880
\(185\) −7.16654 −0.526895
\(186\) −55.7566 −4.08828
\(187\) 28.0613 2.05205
\(188\) 16.4537 1.20001
\(189\) −15.7229 −1.14367
\(190\) −6.38435 −0.463169
\(191\) 13.0207 0.942144 0.471072 0.882095i \(-0.343867\pi\)
0.471072 + 0.882095i \(0.343867\pi\)
\(192\) −18.1429 −1.30935
\(193\) 7.13123 0.513317 0.256659 0.966502i \(-0.417378\pi\)
0.256659 + 0.966502i \(0.417378\pi\)
\(194\) −20.6428 −1.48207
\(195\) −6.48514 −0.464410
\(196\) 4.18340 0.298814
\(197\) −6.90082 −0.491663 −0.245832 0.969313i \(-0.579061\pi\)
−0.245832 + 0.969313i \(0.579061\pi\)
\(198\) 68.9556 4.90046
\(199\) −12.6513 −0.896830 −0.448415 0.893825i \(-0.648011\pi\)
−0.448415 + 0.893825i \(0.648011\pi\)
\(200\) −5.42933 −0.383912
\(201\) 32.1818 2.26993
\(202\) 32.7767 2.30616
\(203\) −1.72372 −0.120981
\(204\) −108.272 −7.58053
\(205\) 3.32254 0.232056
\(206\) −25.7091 −1.79123
\(207\) 8.94719 0.621873
\(208\) 10.1373 0.702895
\(209\) 9.14280 0.632421
\(210\) −8.16709 −0.563583
\(211\) 2.92960 0.201682 0.100841 0.994903i \(-0.467847\pi\)
0.100841 + 0.994903i \(0.467847\pi\)
\(212\) −15.7899 −1.08445
\(213\) 35.6839 2.44502
\(214\) 3.02139 0.206538
\(215\) 4.87597 0.332538
\(216\) −85.3648 −5.80834
\(217\) −6.82699 −0.463446
\(218\) −5.69090 −0.385436
\(219\) 34.4399 2.32723
\(220\) 14.8972 1.00437
\(221\) −15.5596 −1.04665
\(222\) −58.5298 −3.92826
\(223\) 13.4568 0.901131 0.450565 0.892743i \(-0.351222\pi\)
0.450565 + 0.892743i \(0.351222\pi\)
\(224\) 1.90781 0.127471
\(225\) 7.78717 0.519145
\(226\) 35.9010 2.38810
\(227\) 17.3492 1.15151 0.575753 0.817624i \(-0.304709\pi\)
0.575753 + 0.817624i \(0.304709\pi\)
\(228\) −35.2765 −2.33625
\(229\) 1.00000 0.0660819
\(230\) 2.85707 0.188390
\(231\) 11.6958 0.769527
\(232\) −9.35863 −0.614424
\(233\) −21.6011 −1.41513 −0.707567 0.706646i \(-0.750207\pi\)
−0.707567 + 0.706646i \(0.750207\pi\)
\(234\) −38.2348 −2.49949
\(235\) −3.93309 −0.256566
\(236\) 26.8867 1.75018
\(237\) 32.1398 2.08771
\(238\) −19.5950 −1.27016
\(239\) 24.5242 1.58634 0.793170 0.609000i \(-0.208429\pi\)
0.793170 + 0.609000i \(0.208429\pi\)
\(240\) −16.8621 −1.08844
\(241\) 6.34370 0.408634 0.204317 0.978905i \(-0.434503\pi\)
0.204317 + 0.978905i \(0.434503\pi\)
\(242\) −4.17995 −0.268697
\(243\) 45.7088 2.93222
\(244\) −60.7415 −3.88858
\(245\) −1.00000 −0.0638877
\(246\) 27.1355 1.73010
\(247\) −5.06954 −0.322567
\(248\) −37.0660 −2.35369
\(249\) −9.81711 −0.622134
\(250\) 2.48664 0.157269
\(251\) 1.35108 0.0852791 0.0426396 0.999091i \(-0.486423\pi\)
0.0426396 + 0.999091i \(0.486423\pi\)
\(252\) −32.5768 −2.05215
\(253\) −4.09151 −0.257231
\(254\) −3.27726 −0.205633
\(255\) 25.8813 1.62075
\(256\) −32.5971 −2.03732
\(257\) 3.56974 0.222674 0.111337 0.993783i \(-0.464487\pi\)
0.111337 + 0.993783i \(0.464487\pi\)
\(258\) 39.8225 2.47924
\(259\) −7.16654 −0.445307
\(260\) −8.26027 −0.512280
\(261\) 13.4229 0.830856
\(262\) −45.4349 −2.80698
\(263\) 17.2626 1.06446 0.532230 0.846600i \(-0.321354\pi\)
0.532230 + 0.846600i \(0.321354\pi\)
\(264\) 63.5003 3.90818
\(265\) 3.77441 0.231860
\(266\) −6.38435 −0.391450
\(267\) −3.47926 −0.212928
\(268\) 40.9907 2.50391
\(269\) −15.6063 −0.951535 −0.475768 0.879571i \(-0.657830\pi\)
−0.475768 + 0.879571i \(0.657830\pi\)
\(270\) 39.0973 2.37938
\(271\) 28.5180 1.73235 0.866174 0.499743i \(-0.166572\pi\)
0.866174 + 0.499743i \(0.166572\pi\)
\(272\) −40.4566 −2.45304
\(273\) −6.48514 −0.392498
\(274\) 5.22945 0.315922
\(275\) −3.56103 −0.214738
\(276\) 15.7866 0.950245
\(277\) 2.42119 0.145475 0.0727377 0.997351i \(-0.476826\pi\)
0.0727377 + 0.997351i \(0.476826\pi\)
\(278\) 17.0923 1.02513
\(279\) 53.1629 3.18278
\(280\) −5.42933 −0.324465
\(281\) −13.5128 −0.806107 −0.403054 0.915176i \(-0.632051\pi\)
−0.403054 + 0.915176i \(0.632051\pi\)
\(282\) −32.1219 −1.91283
\(283\) −2.24471 −0.133434 −0.0667171 0.997772i \(-0.521253\pi\)
−0.0667171 + 0.997772i \(0.521253\pi\)
\(284\) 45.4514 2.69704
\(285\) 8.43251 0.499499
\(286\) 17.4846 1.03388
\(287\) 3.32254 0.196124
\(288\) −14.8564 −0.875423
\(289\) 45.0960 2.65271
\(290\) 4.28627 0.251699
\(291\) 27.2653 1.59832
\(292\) 43.8669 2.56712
\(293\) −12.3215 −0.719830 −0.359915 0.932985i \(-0.617194\pi\)
−0.359915 + 0.932985i \(0.617194\pi\)
\(294\) −8.16709 −0.476314
\(295\) −6.42701 −0.374195
\(296\) −38.9095 −2.26157
\(297\) −55.9898 −3.24886
\(298\) 9.59951 0.556084
\(299\) 2.26868 0.131201
\(300\) 13.7399 0.793272
\(301\) 4.87597 0.281046
\(302\) −34.9813 −2.01295
\(303\) −43.2918 −2.48705
\(304\) −13.1814 −0.756003
\(305\) 14.5197 0.831394
\(306\) 152.590 8.72297
\(307\) 4.74010 0.270532 0.135266 0.990809i \(-0.456811\pi\)
0.135266 + 0.990809i \(0.456811\pi\)
\(308\) 14.8972 0.848848
\(309\) 33.9568 1.93173
\(310\) 16.9763 0.964189
\(311\) 5.08306 0.288234 0.144117 0.989561i \(-0.453966\pi\)
0.144117 + 0.989561i \(0.453966\pi\)
\(312\) −35.2099 −1.99337
\(313\) 18.6127 1.05205 0.526027 0.850468i \(-0.323681\pi\)
0.526027 + 0.850468i \(0.323681\pi\)
\(314\) 1.98709 0.112138
\(315\) 7.78717 0.438757
\(316\) 40.9373 2.30290
\(317\) −14.6893 −0.825031 −0.412516 0.910950i \(-0.635350\pi\)
−0.412516 + 0.910950i \(0.635350\pi\)
\(318\) 30.8260 1.72864
\(319\) −6.13822 −0.343674
\(320\) 5.52400 0.308801
\(321\) −3.99068 −0.222738
\(322\) 2.85707 0.159218
\(323\) 20.2318 1.12573
\(324\) 118.300 6.57224
\(325\) 1.97454 0.109528
\(326\) −17.4514 −0.966541
\(327\) 7.51659 0.415668
\(328\) 18.0392 0.996047
\(329\) −3.93309 −0.216838
\(330\) −29.0833 −1.60098
\(331\) −6.90169 −0.379351 −0.189676 0.981847i \(-0.560744\pi\)
−0.189676 + 0.981847i \(0.560744\pi\)
\(332\) −12.5043 −0.686262
\(333\) 55.8071 3.05821
\(334\) −36.2769 −1.98499
\(335\) −9.79842 −0.535345
\(336\) −16.8621 −0.919901
\(337\) 29.8381 1.62538 0.812691 0.582695i \(-0.198002\pi\)
0.812691 + 0.582695i \(0.198002\pi\)
\(338\) 22.6315 1.23099
\(339\) −47.4184 −2.57541
\(340\) 32.9656 1.78781
\(341\) −24.3111 −1.31652
\(342\) 49.7160 2.68833
\(343\) −1.00000 −0.0539949
\(344\) 26.4732 1.42734
\(345\) −3.77364 −0.203166
\(346\) −45.1748 −2.42861
\(347\) 16.2530 0.872506 0.436253 0.899824i \(-0.356305\pi\)
0.436253 + 0.899824i \(0.356305\pi\)
\(348\) 23.6837 1.26958
\(349\) −32.7580 −1.75350 −0.876748 0.480950i \(-0.840292\pi\)
−0.876748 + 0.480950i \(0.840292\pi\)
\(350\) 2.48664 0.132917
\(351\) 31.0455 1.65708
\(352\) 6.79376 0.362109
\(353\) 3.94008 0.209709 0.104855 0.994488i \(-0.466562\pi\)
0.104855 + 0.994488i \(0.466562\pi\)
\(354\) −52.4900 −2.78981
\(355\) −10.8647 −0.576639
\(356\) −4.43162 −0.234876
\(357\) 25.8813 1.36978
\(358\) −27.7594 −1.46713
\(359\) 0.694703 0.0366650 0.0183325 0.999832i \(-0.494164\pi\)
0.0183325 + 0.999832i \(0.494164\pi\)
\(360\) 42.2791 2.22831
\(361\) −12.4082 −0.653061
\(362\) −0.915923 −0.0481399
\(363\) 5.52092 0.289773
\(364\) −8.26027 −0.432956
\(365\) −10.4860 −0.548860
\(366\) 118.583 6.19845
\(367\) 23.0002 1.20060 0.600300 0.799775i \(-0.295048\pi\)
0.600300 + 0.799775i \(0.295048\pi\)
\(368\) 5.89881 0.307497
\(369\) −25.8732 −1.34691
\(370\) 17.8206 0.926451
\(371\) 3.77441 0.195958
\(372\) 93.8020 4.86341
\(373\) 33.5364 1.73645 0.868225 0.496171i \(-0.165261\pi\)
0.868225 + 0.496171i \(0.165261\pi\)
\(374\) −69.7785 −3.60816
\(375\) −3.28438 −0.169605
\(376\) −21.3540 −1.10125
\(377\) 3.40354 0.175291
\(378\) 39.0973 2.01095
\(379\) −19.6980 −1.01182 −0.505909 0.862587i \(-0.668843\pi\)
−0.505909 + 0.862587i \(0.668843\pi\)
\(380\) 10.7407 0.550986
\(381\) 4.32863 0.221763
\(382\) −32.3778 −1.65659
\(383\) 15.4538 0.789653 0.394826 0.918756i \(-0.370805\pi\)
0.394826 + 0.918756i \(0.370805\pi\)
\(384\) 57.6469 2.94178
\(385\) −3.56103 −0.181487
\(386\) −17.7328 −0.902577
\(387\) −37.9700 −1.93012
\(388\) 34.7284 1.76307
\(389\) 9.61295 0.487396 0.243698 0.969851i \(-0.421639\pi\)
0.243698 + 0.969851i \(0.421639\pi\)
\(390\) 16.1262 0.816583
\(391\) −9.05397 −0.457879
\(392\) −5.42933 −0.274223
\(393\) 60.0109 3.02715
\(394\) 17.1599 0.864503
\(395\) −9.78565 −0.492370
\(396\) −116.007 −5.82958
\(397\) −32.2987 −1.62103 −0.810513 0.585720i \(-0.800812\pi\)
−0.810513 + 0.585720i \(0.800812\pi\)
\(398\) 31.4594 1.57692
\(399\) 8.43251 0.422154
\(400\) 5.13402 0.256701
\(401\) 1.02512 0.0511922 0.0255961 0.999672i \(-0.491852\pi\)
0.0255961 + 0.999672i \(0.491852\pi\)
\(402\) −80.0246 −3.99126
\(403\) 13.4801 0.671494
\(404\) −55.1418 −2.74341
\(405\) −28.2785 −1.40517
\(406\) 4.28627 0.212724
\(407\) −25.5203 −1.26499
\(408\) 140.518 6.95668
\(409\) 17.9055 0.885372 0.442686 0.896677i \(-0.354026\pi\)
0.442686 + 0.896677i \(0.354026\pi\)
\(410\) −8.26198 −0.408030
\(411\) −6.90710 −0.340702
\(412\) 43.2515 2.13085
\(413\) −6.42701 −0.316252
\(414\) −22.2485 −1.09345
\(415\) 2.98903 0.146726
\(416\) −3.76703 −0.184694
\(417\) −22.5757 −1.10554
\(418\) −22.7349 −1.11200
\(419\) 32.0126 1.56392 0.781959 0.623330i \(-0.214221\pi\)
0.781959 + 0.623330i \(0.214221\pi\)
\(420\) 13.7399 0.670437
\(421\) −17.1113 −0.833956 −0.416978 0.908917i \(-0.636911\pi\)
−0.416978 + 0.908917i \(0.636911\pi\)
\(422\) −7.28487 −0.354622
\(423\) 30.6276 1.48917
\(424\) 20.4925 0.995206
\(425\) −7.88010 −0.382241
\(426\) −88.7330 −4.29913
\(427\) 14.5197 0.702656
\(428\) −5.08303 −0.245697
\(429\) −23.0938 −1.11498
\(430\) −12.1248 −0.584710
\(431\) 23.4068 1.12747 0.563734 0.825956i \(-0.309364\pi\)
0.563734 + 0.825956i \(0.309364\pi\)
\(432\) 80.7216 3.88372
\(433\) 20.4289 0.981748 0.490874 0.871231i \(-0.336678\pi\)
0.490874 + 0.871231i \(0.336678\pi\)
\(434\) 16.9763 0.814888
\(435\) −5.66135 −0.271441
\(436\) 9.57406 0.458514
\(437\) −2.94992 −0.141114
\(438\) −85.6397 −4.09202
\(439\) −11.1468 −0.532007 −0.266004 0.963972i \(-0.585703\pi\)
−0.266004 + 0.963972i \(0.585703\pi\)
\(440\) −19.3340 −0.921714
\(441\) 7.78717 0.370818
\(442\) 38.6911 1.84035
\(443\) −18.0499 −0.857578 −0.428789 0.903405i \(-0.641060\pi\)
−0.428789 + 0.903405i \(0.641060\pi\)
\(444\) 98.4674 4.67306
\(445\) 1.05934 0.0502173
\(446\) −33.4621 −1.58448
\(447\) −12.6791 −0.599702
\(448\) 5.52400 0.260984
\(449\) −7.74944 −0.365719 −0.182859 0.983139i \(-0.558535\pi\)
−0.182859 + 0.983139i \(0.558535\pi\)
\(450\) −19.3639 −0.912824
\(451\) 11.8317 0.557132
\(452\) −60.3979 −2.84088
\(453\) 46.2036 2.17084
\(454\) −43.1412 −2.02472
\(455\) 1.97454 0.0925677
\(456\) 45.7829 2.14398
\(457\) 38.1423 1.78422 0.892111 0.451817i \(-0.149224\pi\)
0.892111 + 0.451817i \(0.149224\pi\)
\(458\) −2.48664 −0.116193
\(459\) −123.898 −5.78307
\(460\) −4.80658 −0.224108
\(461\) −4.91934 −0.229116 −0.114558 0.993417i \(-0.536545\pi\)
−0.114558 + 0.993417i \(0.536545\pi\)
\(462\) −29.0833 −1.35308
\(463\) −38.7665 −1.80163 −0.900815 0.434203i \(-0.857030\pi\)
−0.900815 + 0.434203i \(0.857030\pi\)
\(464\) 8.84959 0.410832
\(465\) −22.4224 −1.03982
\(466\) 53.7142 2.48826
\(467\) −5.59374 −0.258847 −0.129424 0.991589i \(-0.541313\pi\)
−0.129424 + 0.991589i \(0.541313\pi\)
\(468\) 64.3241 2.97338
\(469\) −9.79842 −0.452449
\(470\) 9.78019 0.451126
\(471\) −2.62457 −0.120934
\(472\) −34.8944 −1.60614
\(473\) 17.3635 0.798374
\(474\) −79.9203 −3.67086
\(475\) −2.56746 −0.117803
\(476\) 32.9656 1.51098
\(477\) −29.3920 −1.34577
\(478\) −60.9830 −2.78930
\(479\) −27.6797 −1.26472 −0.632360 0.774675i \(-0.717913\pi\)
−0.632360 + 0.774675i \(0.717913\pi\)
\(480\) 6.26597 0.286001
\(481\) 14.1506 0.645212
\(482\) −15.7745 −0.718510
\(483\) −3.77364 −0.171707
\(484\) 7.03213 0.319642
\(485\) −8.30149 −0.376951
\(486\) −113.661 −5.15579
\(487\) −39.0276 −1.76851 −0.884254 0.467007i \(-0.845332\pi\)
−0.884254 + 0.467007i \(0.845332\pi\)
\(488\) 78.8321 3.56856
\(489\) 23.0499 1.04235
\(490\) 2.48664 0.112335
\(491\) −33.5268 −1.51304 −0.756522 0.653968i \(-0.773103\pi\)
−0.756522 + 0.653968i \(0.773103\pi\)
\(492\) −45.6513 −2.05812
\(493\) −13.5831 −0.611751
\(494\) 12.6061 0.567177
\(495\) 27.7304 1.24639
\(496\) 35.0499 1.57379
\(497\) −10.8647 −0.487349
\(498\) 24.4117 1.09391
\(499\) −24.6300 −1.10259 −0.551294 0.834311i \(-0.685866\pi\)
−0.551294 + 0.834311i \(0.685866\pi\)
\(500\) −4.18340 −0.187087
\(501\) 47.9149 2.14068
\(502\) −3.35964 −0.149948
\(503\) −4.35206 −0.194049 −0.0970244 0.995282i \(-0.530932\pi\)
−0.0970244 + 0.995282i \(0.530932\pi\)
\(504\) 42.2791 1.88326
\(505\) 13.1811 0.586552
\(506\) 10.1741 0.452295
\(507\) −29.8918 −1.32754
\(508\) 5.51348 0.244621
\(509\) 13.5231 0.599400 0.299700 0.954033i \(-0.403113\pi\)
0.299700 + 0.954033i \(0.403113\pi\)
\(510\) −64.3575 −2.84980
\(511\) −10.4860 −0.463871
\(512\) 45.9538 2.03089
\(513\) −40.3679 −1.78228
\(514\) −8.87666 −0.391533
\(515\) −10.3389 −0.455584
\(516\) −66.9952 −2.94930
\(517\) −14.0059 −0.615977
\(518\) 17.8206 0.782994
\(519\) 59.6674 2.61911
\(520\) 10.7204 0.470121
\(521\) 20.8328 0.912702 0.456351 0.889800i \(-0.349156\pi\)
0.456351 + 0.889800i \(0.349156\pi\)
\(522\) −33.3779 −1.46091
\(523\) −4.14453 −0.181228 −0.0906138 0.995886i \(-0.528883\pi\)
−0.0906138 + 0.995886i \(0.528883\pi\)
\(524\) 76.4373 3.33918
\(525\) −3.28438 −0.143342
\(526\) −42.9260 −1.87166
\(527\) −53.7974 −2.34345
\(528\) −60.0464 −2.61318
\(529\) −21.6799 −0.942603
\(530\) −9.38562 −0.407685
\(531\) 50.0482 2.17191
\(532\) 10.7407 0.465668
\(533\) −6.56048 −0.284166
\(534\) 8.65169 0.374395
\(535\) 1.21505 0.0525311
\(536\) −53.1989 −2.29784
\(537\) 36.6648 1.58221
\(538\) 38.8074 1.67311
\(539\) −3.56103 −0.153385
\(540\) −65.7751 −2.83051
\(541\) 34.2434 1.47224 0.736120 0.676851i \(-0.236656\pi\)
0.736120 + 0.676851i \(0.236656\pi\)
\(542\) −70.9142 −3.04603
\(543\) 1.20976 0.0519158
\(544\) 15.0337 0.644565
\(545\) −2.28859 −0.0980322
\(546\) 16.1262 0.690139
\(547\) 18.1159 0.774581 0.387291 0.921958i \(-0.373411\pi\)
0.387291 + 0.921958i \(0.373411\pi\)
\(548\) −8.79774 −0.375821
\(549\) −113.067 −4.82559
\(550\) 8.85502 0.377579
\(551\) −4.42557 −0.188536
\(552\) −20.4884 −0.872042
\(553\) −9.78565 −0.416128
\(554\) −6.02064 −0.255793
\(555\) −23.5377 −0.999118
\(556\) −28.7552 −1.21949
\(557\) 24.4835 1.03740 0.518700 0.854957i \(-0.326416\pi\)
0.518700 + 0.854957i \(0.326416\pi\)
\(558\) −132.197 −5.59636
\(559\) −9.62778 −0.407212
\(560\) 5.13402 0.216952
\(561\) 92.1641 3.89117
\(562\) 33.6016 1.41740
\(563\) −14.5774 −0.614366 −0.307183 0.951650i \(-0.599386\pi\)
−0.307183 + 0.951650i \(0.599386\pi\)
\(564\) 54.0401 2.27550
\(565\) 14.4375 0.607391
\(566\) 5.58180 0.234620
\(567\) −28.2785 −1.18759
\(568\) −58.9881 −2.47508
\(569\) 31.7672 1.33175 0.665875 0.746064i \(-0.268059\pi\)
0.665875 + 0.746064i \(0.268059\pi\)
\(570\) −20.9686 −0.878280
\(571\) −2.50021 −0.104631 −0.0523154 0.998631i \(-0.516660\pi\)
−0.0523154 + 0.998631i \(0.516660\pi\)
\(572\) −29.4151 −1.22991
\(573\) 42.7649 1.78653
\(574\) −8.26198 −0.344848
\(575\) 1.14897 0.0479152
\(576\) −43.0163 −1.79235
\(577\) −13.6979 −0.570253 −0.285126 0.958490i \(-0.592036\pi\)
−0.285126 + 0.958490i \(0.592036\pi\)
\(578\) −112.138 −4.66432
\(579\) 23.4217 0.973372
\(580\) −7.21100 −0.299420
\(581\) 2.98903 0.124006
\(582\) −67.7990 −2.81036
\(583\) 13.4408 0.556662
\(584\) −56.9317 −2.35585
\(585\) −15.3761 −0.635722
\(586\) 30.6392 1.26569
\(587\) −17.2091 −0.710294 −0.355147 0.934810i \(-0.615569\pi\)
−0.355147 + 0.934810i \(0.615569\pi\)
\(588\) 13.7399 0.566623
\(589\) −17.5280 −0.722229
\(590\) 15.9817 0.657955
\(591\) −22.6649 −0.932311
\(592\) 36.7931 1.51219
\(593\) −2.29597 −0.0942843 −0.0471422 0.998888i \(-0.515011\pi\)
−0.0471422 + 0.998888i \(0.515011\pi\)
\(594\) 139.227 5.71254
\(595\) −7.88010 −0.323053
\(596\) −16.1497 −0.661517
\(597\) −41.5519 −1.70060
\(598\) −5.64139 −0.230694
\(599\) 30.5006 1.24622 0.623109 0.782135i \(-0.285869\pi\)
0.623109 + 0.782135i \(0.285869\pi\)
\(600\) −17.8320 −0.727988
\(601\) 13.6138 0.555319 0.277659 0.960680i \(-0.410441\pi\)
0.277659 + 0.960680i \(0.410441\pi\)
\(602\) −12.1248 −0.494170
\(603\) 76.3020 3.10726
\(604\) 58.8507 2.39460
\(605\) −1.68096 −0.0683408
\(606\) 107.651 4.37304
\(607\) 35.7065 1.44928 0.724641 0.689127i \(-0.242006\pi\)
0.724641 + 0.689127i \(0.242006\pi\)
\(608\) 4.89821 0.198649
\(609\) −5.66135 −0.229409
\(610\) −36.1052 −1.46186
\(611\) 7.76603 0.314180
\(612\) −256.709 −10.3768
\(613\) −28.0691 −1.13370 −0.566849 0.823822i \(-0.691838\pi\)
−0.566849 + 0.823822i \(0.691838\pi\)
\(614\) −11.7870 −0.475683
\(615\) 10.9125 0.440035
\(616\) −19.3340 −0.778990
\(617\) 38.2188 1.53863 0.769316 0.638869i \(-0.220597\pi\)
0.769316 + 0.638869i \(0.220597\pi\)
\(618\) −84.4384 −3.39661
\(619\) 15.1355 0.608349 0.304174 0.952616i \(-0.401619\pi\)
0.304174 + 0.952616i \(0.401619\pi\)
\(620\) −28.5600 −1.14700
\(621\) 18.0651 0.724927
\(622\) −12.6397 −0.506808
\(623\) 1.05934 0.0424414
\(624\) 33.2948 1.33286
\(625\) 1.00000 0.0400000
\(626\) −46.2832 −1.84985
\(627\) 30.0285 1.19922
\(628\) −3.34298 −0.133399
\(629\) −56.4731 −2.25173
\(630\) −19.3639 −0.771477
\(631\) 25.6019 1.01919 0.509597 0.860413i \(-0.329794\pi\)
0.509597 + 0.860413i \(0.329794\pi\)
\(632\) −53.1295 −2.11338
\(633\) 9.62193 0.382437
\(634\) 36.5270 1.45067
\(635\) −1.31794 −0.0523010
\(636\) −51.8600 −2.05638
\(637\) 1.97454 0.0782340
\(638\) 15.2636 0.604290
\(639\) 84.6053 3.34693
\(640\) −17.5518 −0.693797
\(641\) −33.4308 −1.32044 −0.660219 0.751073i \(-0.729536\pi\)
−0.660219 + 0.751073i \(0.729536\pi\)
\(642\) 9.92341 0.391646
\(643\) 40.1619 1.58383 0.791915 0.610632i \(-0.209084\pi\)
0.791915 + 0.610632i \(0.209084\pi\)
\(644\) −4.80658 −0.189406
\(645\) 16.0145 0.630572
\(646\) −50.3093 −1.97939
\(647\) −41.1155 −1.61642 −0.808209 0.588895i \(-0.799563\pi\)
−0.808209 + 0.588895i \(0.799563\pi\)
\(648\) −153.533 −6.03136
\(649\) −22.8868 −0.898385
\(650\) −4.90997 −0.192585
\(651\) −22.4224 −0.878805
\(652\) 29.3592 1.14980
\(653\) 17.9715 0.703280 0.351640 0.936135i \(-0.385624\pi\)
0.351640 + 0.936135i \(0.385624\pi\)
\(654\) −18.6911 −0.730879
\(655\) −18.2716 −0.713930
\(656\) −17.0580 −0.666002
\(657\) 81.6559 3.18570
\(658\) 9.78019 0.381271
\(659\) −19.0812 −0.743296 −0.371648 0.928374i \(-0.621207\pi\)
−0.371648 + 0.928374i \(0.621207\pi\)
\(660\) 48.9282 1.90453
\(661\) −33.3225 −1.29609 −0.648047 0.761600i \(-0.724414\pi\)
−0.648047 + 0.761600i \(0.724414\pi\)
\(662\) 17.1620 0.667021
\(663\) −51.1035 −1.98470
\(664\) 16.2284 0.629785
\(665\) −2.56746 −0.0995617
\(666\) −138.772 −5.37732
\(667\) 1.98049 0.0766850
\(668\) 61.0304 2.36134
\(669\) 44.1971 1.70876
\(670\) 24.3652 0.941309
\(671\) 51.7050 1.99605
\(672\) 6.26597 0.241715
\(673\) −9.94512 −0.383356 −0.191678 0.981458i \(-0.561393\pi\)
−0.191678 + 0.981458i \(0.561393\pi\)
\(674\) −74.1966 −2.85795
\(675\) 15.7229 0.605175
\(676\) −38.0739 −1.46438
\(677\) 21.5207 0.827107 0.413554 0.910480i \(-0.364287\pi\)
0.413554 + 0.910480i \(0.364287\pi\)
\(678\) 117.913 4.52841
\(679\) −8.30149 −0.318582
\(680\) −42.7837 −1.64068
\(681\) 56.9814 2.18353
\(682\) 60.4531 2.31487
\(683\) 8.63902 0.330563 0.165281 0.986246i \(-0.447147\pi\)
0.165281 + 0.986246i \(0.447147\pi\)
\(684\) −83.6396 −3.19804
\(685\) 2.10301 0.0803520
\(686\) 2.48664 0.0949405
\(687\) 3.28438 0.125307
\(688\) −25.0333 −0.954385
\(689\) −7.45272 −0.283926
\(690\) 9.38371 0.357232
\(691\) −17.9794 −0.683969 −0.341984 0.939706i \(-0.611099\pi\)
−0.341984 + 0.939706i \(0.611099\pi\)
\(692\) 75.9997 2.88908
\(693\) 27.7304 1.05339
\(694\) −40.4154 −1.53415
\(695\) 6.87366 0.260733
\(696\) −30.7373 −1.16510
\(697\) 26.1820 0.991713
\(698\) 81.4575 3.08321
\(699\) −70.9462 −2.68343
\(700\) −4.18340 −0.158118
\(701\) −13.8650 −0.523675 −0.261837 0.965112i \(-0.584328\pi\)
−0.261837 + 0.965112i \(0.584328\pi\)
\(702\) −77.1990 −2.91369
\(703\) −18.3998 −0.693961
\(704\) 19.6711 0.741384
\(705\) −12.9178 −0.486511
\(706\) −9.79756 −0.368736
\(707\) 13.1811 0.495727
\(708\) 88.3063 3.31875
\(709\) −9.54439 −0.358447 −0.179224 0.983808i \(-0.557359\pi\)
−0.179224 + 0.983808i \(0.557359\pi\)
\(710\) 27.0167 1.01392
\(711\) 76.2025 2.85782
\(712\) 5.75148 0.215546
\(713\) 7.84398 0.293759
\(714\) −64.3575 −2.40852
\(715\) 7.03139 0.262959
\(716\) 46.7009 1.74529
\(717\) 80.5469 3.00808
\(718\) −1.72748 −0.0644690
\(719\) 0.192431 0.00717647 0.00358823 0.999994i \(-0.498858\pi\)
0.00358823 + 0.999994i \(0.498858\pi\)
\(720\) −39.9795 −1.48995
\(721\) −10.3389 −0.385039
\(722\) 30.8547 1.14829
\(723\) 20.8351 0.774867
\(724\) 1.54090 0.0572671
\(725\) 1.72372 0.0640173
\(726\) −13.7286 −0.509515
\(727\) 50.2974 1.86543 0.932714 0.360618i \(-0.117434\pi\)
0.932714 + 0.360618i \(0.117434\pi\)
\(728\) 10.7204 0.397325
\(729\) 65.2896 2.41813
\(730\) 26.0748 0.965073
\(731\) 38.4231 1.42113
\(732\) −199.498 −7.37367
\(733\) 37.8290 1.39724 0.698622 0.715491i \(-0.253797\pi\)
0.698622 + 0.715491i \(0.253797\pi\)
\(734\) −57.1933 −2.11104
\(735\) −3.28438 −0.121146
\(736\) −2.19200 −0.0807984
\(737\) −34.8925 −1.28528
\(738\) 64.3375 2.36829
\(739\) −37.0416 −1.36260 −0.681299 0.732005i \(-0.738585\pi\)
−0.681299 + 0.732005i \(0.738585\pi\)
\(740\) −29.9805 −1.10210
\(741\) −16.6503 −0.611664
\(742\) −9.38562 −0.344557
\(743\) −46.8626 −1.71922 −0.859611 0.510949i \(-0.829294\pi\)
−0.859611 + 0.510949i \(0.829294\pi\)
\(744\) −121.739 −4.46316
\(745\) 3.86043 0.141435
\(746\) −83.3931 −3.05324
\(747\) −23.2761 −0.851627
\(748\) 117.392 4.29226
\(749\) 1.21505 0.0443969
\(750\) 8.16709 0.298220
\(751\) −43.9175 −1.60257 −0.801286 0.598282i \(-0.795850\pi\)
−0.801286 + 0.598282i \(0.795850\pi\)
\(752\) 20.1925 0.736346
\(753\) 4.43745 0.161710
\(754\) −8.46340 −0.308219
\(755\) −14.0677 −0.511975
\(756\) −65.7751 −2.39222
\(757\) −19.7190 −0.716698 −0.358349 0.933588i \(-0.616660\pi\)
−0.358349 + 0.933588i \(0.616660\pi\)
\(758\) 48.9819 1.77910
\(759\) −13.4381 −0.487771
\(760\) −13.9396 −0.505641
\(761\) −0.374516 −0.0135762 −0.00678809 0.999977i \(-0.502161\pi\)
−0.00678809 + 0.999977i \(0.502161\pi\)
\(762\) −10.7638 −0.389930
\(763\) −2.28859 −0.0828524
\(764\) 54.4707 1.97068
\(765\) 61.3637 2.21861
\(766\) −38.4281 −1.38846
\(767\) 12.6904 0.458223
\(768\) −107.061 −3.86325
\(769\) 33.6633 1.21393 0.606965 0.794729i \(-0.292387\pi\)
0.606965 + 0.794729i \(0.292387\pi\)
\(770\) 8.85502 0.319113
\(771\) 11.7244 0.422243
\(772\) 29.8328 1.07370
\(773\) −0.0785286 −0.00282448 −0.00141224 0.999999i \(-0.500450\pi\)
−0.00141224 + 0.999999i \(0.500450\pi\)
\(774\) 94.4179 3.39378
\(775\) 6.82699 0.245233
\(776\) −45.0715 −1.61797
\(777\) −23.5377 −0.844409
\(778\) −23.9040 −0.857000
\(779\) 8.53048 0.305636
\(780\) −27.1299 −0.971406
\(781\) −38.6896 −1.38442
\(782\) 22.5140 0.805099
\(783\) 27.1018 0.968541
\(784\) 5.13402 0.183358
\(785\) 0.799106 0.0285213
\(786\) −149.226 −5.32270
\(787\) −45.9656 −1.63850 −0.819249 0.573438i \(-0.805609\pi\)
−0.819249 + 0.573438i \(0.805609\pi\)
\(788\) −28.8689 −1.02841
\(789\) 56.6971 2.01847
\(790\) 24.3334 0.865744
\(791\) 14.4375 0.513339
\(792\) 150.557 5.34982
\(793\) −28.6696 −1.01809
\(794\) 80.3154 2.85029
\(795\) 12.3966 0.439663
\(796\) −52.9256 −1.87590
\(797\) −17.8234 −0.631338 −0.315669 0.948869i \(-0.602229\pi\)
−0.315669 + 0.948869i \(0.602229\pi\)
\(798\) −20.9686 −0.742282
\(799\) −30.9931 −1.09646
\(800\) −1.90781 −0.0674511
\(801\) −8.24923 −0.291472
\(802\) −2.54912 −0.0900125
\(803\) −37.3408 −1.31773
\(804\) 134.629 4.74800
\(805\) 1.14897 0.0404957
\(806\) −33.5203 −1.18070
\(807\) −51.2572 −1.80434
\(808\) 71.5646 2.51763
\(809\) 36.6016 1.28685 0.643423 0.765511i \(-0.277514\pi\)
0.643423 + 0.765511i \(0.277514\pi\)
\(810\) 70.3186 2.47074
\(811\) 11.6237 0.408164 0.204082 0.978954i \(-0.434579\pi\)
0.204082 + 0.978954i \(0.434579\pi\)
\(812\) −7.21100 −0.253056
\(813\) 93.6642 3.28495
\(814\) 63.4599 2.22427
\(815\) −7.01804 −0.245831
\(816\) −132.875 −4.65155
\(817\) 12.5188 0.437979
\(818\) −44.5247 −1.55677
\(819\) −15.3761 −0.537283
\(820\) 13.8995 0.485392
\(821\) −24.2189 −0.845246 −0.422623 0.906306i \(-0.638890\pi\)
−0.422623 + 0.906306i \(0.638890\pi\)
\(822\) 17.1755 0.599064
\(823\) −51.3024 −1.78829 −0.894144 0.447779i \(-0.852215\pi\)
−0.894144 + 0.447779i \(0.852215\pi\)
\(824\) −56.1331 −1.95549
\(825\) −11.6958 −0.407195
\(826\) 15.9817 0.556074
\(827\) −27.1158 −0.942909 −0.471455 0.881890i \(-0.656271\pi\)
−0.471455 + 0.881890i \(0.656271\pi\)
\(828\) 37.4297 1.30077
\(829\) −36.3908 −1.26391 −0.631953 0.775007i \(-0.717746\pi\)
−0.631953 + 0.775007i \(0.717746\pi\)
\(830\) −7.43264 −0.257991
\(831\) 7.95213 0.275856
\(832\) −10.9073 −0.378144
\(833\) −7.88010 −0.273029
\(834\) 56.1378 1.94389
\(835\) −14.5887 −0.504863
\(836\) 38.2480 1.32283
\(837\) 107.340 3.71022
\(838\) −79.6039 −2.74987
\(839\) −55.0079 −1.89908 −0.949541 0.313643i \(-0.898451\pi\)
−0.949541 + 0.313643i \(0.898451\pi\)
\(840\) −17.8320 −0.615262
\(841\) −26.0288 −0.897545
\(842\) 42.5498 1.46636
\(843\) −44.3813 −1.52857
\(844\) 12.2557 0.421858
\(845\) 9.10120 0.313091
\(846\) −76.1600 −2.61843
\(847\) −1.68096 −0.0577585
\(848\) −19.3779 −0.665440
\(849\) −7.37249 −0.253023
\(850\) 19.5950 0.672103
\(851\) 8.23411 0.282262
\(852\) 149.280 5.11424
\(853\) 22.3079 0.763808 0.381904 0.924202i \(-0.375269\pi\)
0.381904 + 0.924202i \(0.375269\pi\)
\(854\) −36.1052 −1.23550
\(855\) 19.9932 0.683754
\(856\) 6.59690 0.225477
\(857\) −6.49791 −0.221964 −0.110982 0.993822i \(-0.535400\pi\)
−0.110982 + 0.993822i \(0.535400\pi\)
\(858\) 57.4260 1.96049
\(859\) 30.9448 1.05582 0.527911 0.849300i \(-0.322976\pi\)
0.527911 + 0.849300i \(0.322976\pi\)
\(860\) 20.3981 0.695570
\(861\) 10.9125 0.371897
\(862\) −58.2045 −1.98245
\(863\) −42.5620 −1.44883 −0.724413 0.689366i \(-0.757889\pi\)
−0.724413 + 0.689366i \(0.757889\pi\)
\(864\) −29.9963 −1.02049
\(865\) −18.1670 −0.617696
\(866\) −50.7993 −1.72623
\(867\) 148.113 5.03017
\(868\) −28.5600 −0.969390
\(869\) −34.8470 −1.18210
\(870\) 14.0778 0.477281
\(871\) 19.3473 0.655560
\(872\) −12.4255 −0.420780
\(873\) 64.6451 2.18791
\(874\) 7.33540 0.248124
\(875\) 1.00000 0.0338062
\(876\) 144.076 4.86787
\(877\) −26.1764 −0.883914 −0.441957 0.897036i \(-0.645716\pi\)
−0.441957 + 0.897036i \(0.645716\pi\)
\(878\) 27.7181 0.935440
\(879\) −40.4686 −1.36497
\(880\) 18.2824 0.616300
\(881\) −27.9158 −0.940506 −0.470253 0.882532i \(-0.655837\pi\)
−0.470253 + 0.882532i \(0.655837\pi\)
\(882\) −19.3639 −0.652017
\(883\) −57.3263 −1.92918 −0.964591 0.263750i \(-0.915041\pi\)
−0.964591 + 0.263750i \(0.915041\pi\)
\(884\) −65.0918 −2.18927
\(885\) −21.1088 −0.709563
\(886\) 44.8838 1.50790
\(887\) 41.1089 1.38030 0.690152 0.723665i \(-0.257544\pi\)
0.690152 + 0.723665i \(0.257544\pi\)
\(888\) −127.794 −4.28848
\(889\) −1.31794 −0.0442024
\(890\) −2.63419 −0.0882983
\(891\) −100.701 −3.37360
\(892\) 56.2949 1.88489
\(893\) −10.0980 −0.337918
\(894\) 31.5285 1.05447
\(895\) −11.1634 −0.373151
\(896\) −17.5518 −0.586365
\(897\) 7.45120 0.248788
\(898\) 19.2701 0.643051
\(899\) 11.7678 0.392478
\(900\) 32.5768 1.08589
\(901\) 29.7428 0.990876
\(902\) −29.4212 −0.979618
\(903\) 16.0145 0.532931
\(904\) 78.3861 2.60708
\(905\) −0.368337 −0.0122439
\(906\) −114.892 −3.81703
\(907\) 43.6513 1.44942 0.724709 0.689055i \(-0.241974\pi\)
0.724709 + 0.689055i \(0.241974\pi\)
\(908\) 72.5785 2.40860
\(909\) −102.644 −3.40447
\(910\) −4.90997 −0.162764
\(911\) −57.6015 −1.90842 −0.954211 0.299135i \(-0.903302\pi\)
−0.954211 + 0.299135i \(0.903302\pi\)
\(912\) −43.2926 −1.43356
\(913\) 10.6440 0.352266
\(914\) −94.8463 −3.13724
\(915\) 47.6881 1.57652
\(916\) 4.18340 0.138223
\(917\) −18.2716 −0.603381
\(918\) 308.090 10.1685
\(919\) −49.8054 −1.64293 −0.821464 0.570261i \(-0.806842\pi\)
−0.821464 + 0.570261i \(0.806842\pi\)
\(920\) 6.23811 0.205665
\(921\) 15.5683 0.512994
\(922\) 12.2326 0.402860
\(923\) 21.4528 0.706126
\(924\) 48.9282 1.60962
\(925\) 7.16654 0.235634
\(926\) 96.3984 3.16785
\(927\) 80.5105 2.64431
\(928\) −3.28852 −0.107951
\(929\) 14.1498 0.464239 0.232120 0.972687i \(-0.425434\pi\)
0.232120 + 0.972687i \(0.425434\pi\)
\(930\) 55.7566 1.82833
\(931\) −2.56746 −0.0841450
\(932\) −90.3659 −2.96003
\(933\) 16.6947 0.546560
\(934\) 13.9096 0.455137
\(935\) −28.0613 −0.917703
\(936\) −83.4817 −2.72868
\(937\) 24.7070 0.807141 0.403571 0.914949i \(-0.367769\pi\)
0.403571 + 0.914949i \(0.367769\pi\)
\(938\) 24.3652 0.795552
\(939\) 61.1313 1.99494
\(940\) −16.4537 −0.536659
\(941\) 12.9427 0.421920 0.210960 0.977495i \(-0.432341\pi\)
0.210960 + 0.977495i \(0.432341\pi\)
\(942\) 6.52637 0.212641
\(943\) −3.81749 −0.124315
\(944\) 32.9964 1.07394
\(945\) 15.7229 0.511466
\(946\) −43.1768 −1.40380
\(947\) 5.70726 0.185461 0.0927304 0.995691i \(-0.470441\pi\)
0.0927304 + 0.995691i \(0.470441\pi\)
\(948\) 134.454 4.36685
\(949\) 20.7049 0.672110
\(950\) 6.38435 0.207136
\(951\) −48.2452 −1.56446
\(952\) −42.7837 −1.38663
\(953\) −19.1077 −0.618960 −0.309480 0.950906i \(-0.600155\pi\)
−0.309480 + 0.950906i \(0.600155\pi\)
\(954\) 73.0875 2.36629
\(955\) −13.0207 −0.421339
\(956\) 102.595 3.31815
\(957\) −20.1603 −0.651689
\(958\) 68.8296 2.22378
\(959\) 2.10301 0.0679099
\(960\) 18.1429 0.585560
\(961\) 15.6078 0.503477
\(962\) −35.1875 −1.13449
\(963\) −9.46179 −0.304902
\(964\) 26.5382 0.854738
\(965\) −7.13123 −0.229562
\(966\) 9.38371 0.301916
\(967\) 27.5502 0.885953 0.442977 0.896533i \(-0.353922\pi\)
0.442977 + 0.896533i \(0.353922\pi\)
\(968\) −9.12649 −0.293336
\(969\) 66.4491 2.13465
\(970\) 20.6428 0.662802
\(971\) 40.5061 1.29990 0.649952 0.759975i \(-0.274789\pi\)
0.649952 + 0.759975i \(0.274789\pi\)
\(972\) 191.218 6.13332
\(973\) 6.87366 0.220359
\(974\) 97.0476 3.10961
\(975\) 6.48514 0.207691
\(976\) −74.5442 −2.38610
\(977\) 55.3291 1.77014 0.885068 0.465462i \(-0.154112\pi\)
0.885068 + 0.465462i \(0.154112\pi\)
\(978\) −57.3169 −1.83279
\(979\) 3.77233 0.120564
\(980\) −4.18340 −0.133634
\(981\) 17.8216 0.569000
\(982\) 83.3693 2.66042
\(983\) 58.4717 1.86496 0.932478 0.361226i \(-0.117642\pi\)
0.932478 + 0.361226i \(0.117642\pi\)
\(984\) 59.2476 1.88874
\(985\) 6.90082 0.219878
\(986\) 33.7763 1.07566
\(987\) −12.9178 −0.411177
\(988\) −21.2079 −0.674713
\(989\) −5.60232 −0.178143
\(990\) −68.9556 −2.19155
\(991\) −43.8189 −1.39195 −0.695976 0.718065i \(-0.745028\pi\)
−0.695976 + 0.718065i \(0.745028\pi\)
\(992\) −13.0246 −0.413531
\(993\) −22.6678 −0.719340
\(994\) 27.0167 0.856916
\(995\) 12.6513 0.401075
\(996\) −41.0689 −1.30132
\(997\) 7.19453 0.227853 0.113926 0.993489i \(-0.463657\pi\)
0.113926 + 0.993489i \(0.463657\pi\)
\(998\) 61.2460 1.93871
\(999\) 112.679 3.56500
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 \(a_p\))