Properties

Label 8018.2.a.d.1.14
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 30
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(30\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -0.851234 q^{3} +1.00000 q^{4} -2.73591 q^{5} -0.851234 q^{6} +0.590237 q^{7} +1.00000 q^{8} -2.27540 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -0.851234 q^{3} +1.00000 q^{4} -2.73591 q^{5} -0.851234 q^{6} +0.590237 q^{7} +1.00000 q^{8} -2.27540 q^{9} -2.73591 q^{10} -1.85097 q^{11} -0.851234 q^{12} +1.88529 q^{13} +0.590237 q^{14} +2.32890 q^{15} +1.00000 q^{16} -4.96288 q^{17} -2.27540 q^{18} +1.00000 q^{19} -2.73591 q^{20} -0.502429 q^{21} -1.85097 q^{22} +9.18427 q^{23} -0.851234 q^{24} +2.48522 q^{25} +1.88529 q^{26} +4.49060 q^{27} +0.590237 q^{28} +5.21129 q^{29} +2.32890 q^{30} +2.14709 q^{31} +1.00000 q^{32} +1.57561 q^{33} -4.96288 q^{34} -1.61484 q^{35} -2.27540 q^{36} +4.56743 q^{37} +1.00000 q^{38} -1.60482 q^{39} -2.73591 q^{40} +2.66253 q^{41} -0.502429 q^{42} -2.82781 q^{43} -1.85097 q^{44} +6.22530 q^{45} +9.18427 q^{46} -5.33483 q^{47} -0.851234 q^{48} -6.65162 q^{49} +2.48522 q^{50} +4.22457 q^{51} +1.88529 q^{52} -4.12591 q^{53} +4.49060 q^{54} +5.06408 q^{55} +0.590237 q^{56} -0.851234 q^{57} +5.21129 q^{58} -1.38390 q^{59} +2.32890 q^{60} +2.88432 q^{61} +2.14709 q^{62} -1.34302 q^{63} +1.00000 q^{64} -5.15798 q^{65} +1.57561 q^{66} -5.02573 q^{67} -4.96288 q^{68} -7.81796 q^{69} -1.61484 q^{70} +3.68758 q^{71} -2.27540 q^{72} -2.34064 q^{73} +4.56743 q^{74} -2.11550 q^{75} +1.00000 q^{76} -1.09251 q^{77} -1.60482 q^{78} -5.28066 q^{79} -2.73591 q^{80} +3.00365 q^{81} +2.66253 q^{82} +4.69968 q^{83} -0.502429 q^{84} +13.5780 q^{85} -2.82781 q^{86} -4.43603 q^{87} -1.85097 q^{88} +11.7557 q^{89} +6.22530 q^{90} +1.11276 q^{91} +9.18427 q^{92} -1.82768 q^{93} -5.33483 q^{94} -2.73591 q^{95} -0.851234 q^{96} +14.6135 q^{97} -6.65162 q^{98} +4.21169 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 30q^{2} - 10q^{3} + 30q^{4} - 12q^{5} - 10q^{6} - 15q^{7} + 30q^{8} + 10q^{9} + O(q^{10}) \) \( 30q + 30q^{2} - 10q^{3} + 30q^{4} - 12q^{5} - 10q^{6} - 15q^{7} + 30q^{8} + 10q^{9} - 12q^{10} - 17q^{11} - 10q^{12} - 19q^{13} - 15q^{14} - 8q^{15} + 30q^{16} - 18q^{17} + 10q^{18} + 30q^{19} - 12q^{20} - 14q^{21} - 17q^{22} - 15q^{23} - 10q^{24} - 4q^{25} - 19q^{26} - 37q^{27} - 15q^{28} - 37q^{29} - 8q^{30} - 11q^{31} + 30q^{32} + 6q^{33} - 18q^{34} - 4q^{35} + 10q^{36} - 46q^{37} + 30q^{38} - 12q^{40} - 28q^{41} - 14q^{42} - 61q^{43} - 17q^{44} - 14q^{45} - 15q^{46} - 4q^{47} - 10q^{48} - q^{49} - 4q^{50} - 8q^{51} - 19q^{52} - 19q^{53} - 37q^{54} - 17q^{55} - 15q^{56} - 10q^{57} - 37q^{58} - 6q^{59} - 8q^{60} - 32q^{61} - 11q^{62} - 24q^{63} + 30q^{64} - 24q^{65} + 6q^{66} - 44q^{67} - 18q^{68} - 2q^{69} - 4q^{70} + 10q^{71} + 10q^{72} - 58q^{73} - 46q^{74} - 42q^{75} + 30q^{76} - 32q^{77} - 42q^{79} - 12q^{80} - 38q^{81} - 28q^{82} - 25q^{83} - 14q^{84} - 48q^{85} - 61q^{86} - 15q^{87} - 17q^{88} - 39q^{89} - 14q^{90} - 21q^{91} - 15q^{92} - 45q^{93} - 4q^{94} - 12q^{95} - 10q^{96} - 33q^{97} - q^{98} - 38q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −0.851234 −0.491460 −0.245730 0.969338i \(-0.579028\pi\)
−0.245730 + 0.969338i \(0.579028\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.73591 −1.22354 −0.611769 0.791037i \(-0.709542\pi\)
−0.611769 + 0.791037i \(0.709542\pi\)
\(6\) −0.851234 −0.347515
\(7\) 0.590237 0.223088 0.111544 0.993759i \(-0.464420\pi\)
0.111544 + 0.993759i \(0.464420\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.27540 −0.758467
\(10\) −2.73591 −0.865171
\(11\) −1.85097 −0.558087 −0.279044 0.960278i \(-0.590017\pi\)
−0.279044 + 0.960278i \(0.590017\pi\)
\(12\) −0.851234 −0.245730
\(13\) 1.88529 0.522884 0.261442 0.965219i \(-0.415802\pi\)
0.261442 + 0.965219i \(0.415802\pi\)
\(14\) 0.590237 0.157747
\(15\) 2.32890 0.601320
\(16\) 1.00000 0.250000
\(17\) −4.96288 −1.20367 −0.601837 0.798619i \(-0.705564\pi\)
−0.601837 + 0.798619i \(0.705564\pi\)
\(18\) −2.27540 −0.536317
\(19\) 1.00000 0.229416
\(20\) −2.73591 −0.611769
\(21\) −0.502429 −0.109639
\(22\) −1.85097 −0.394627
\(23\) 9.18427 1.91505 0.957526 0.288346i \(-0.0931053\pi\)
0.957526 + 0.288346i \(0.0931053\pi\)
\(24\) −0.851234 −0.173757
\(25\) 2.48522 0.497043
\(26\) 1.88529 0.369735
\(27\) 4.49060 0.864217
\(28\) 0.590237 0.111544
\(29\) 5.21129 0.967712 0.483856 0.875148i \(-0.339236\pi\)
0.483856 + 0.875148i \(0.339236\pi\)
\(30\) 2.32890 0.425197
\(31\) 2.14709 0.385629 0.192814 0.981235i \(-0.438238\pi\)
0.192814 + 0.981235i \(0.438238\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.57561 0.274278
\(34\) −4.96288 −0.851126
\(35\) −1.61484 −0.272957
\(36\) −2.27540 −0.379233
\(37\) 4.56743 0.750881 0.375440 0.926847i \(-0.377491\pi\)
0.375440 + 0.926847i \(0.377491\pi\)
\(38\) 1.00000 0.162221
\(39\) −1.60482 −0.256977
\(40\) −2.73591 −0.432586
\(41\) 2.66253 0.415817 0.207909 0.978148i \(-0.433334\pi\)
0.207909 + 0.978148i \(0.433334\pi\)
\(42\) −0.502429 −0.0775266
\(43\) −2.82781 −0.431238 −0.215619 0.976478i \(-0.569177\pi\)
−0.215619 + 0.976478i \(0.569177\pi\)
\(44\) −1.85097 −0.279044
\(45\) 6.22530 0.928012
\(46\) 9.18427 1.35415
\(47\) −5.33483 −0.778165 −0.389083 0.921203i \(-0.627208\pi\)
−0.389083 + 0.921203i \(0.627208\pi\)
\(48\) −0.851234 −0.122865
\(49\) −6.65162 −0.950232
\(50\) 2.48522 0.351463
\(51\) 4.22457 0.591558
\(52\) 1.88529 0.261442
\(53\) −4.12591 −0.566737 −0.283368 0.959011i \(-0.591452\pi\)
−0.283368 + 0.959011i \(0.591452\pi\)
\(54\) 4.49060 0.611093
\(55\) 5.06408 0.682841
\(56\) 0.590237 0.0788737
\(57\) −0.851234 −0.112749
\(58\) 5.21129 0.684276
\(59\) −1.38390 −0.180168 −0.0900842 0.995934i \(-0.528714\pi\)
−0.0900842 + 0.995934i \(0.528714\pi\)
\(60\) 2.32890 0.300660
\(61\) 2.88432 0.369299 0.184650 0.982804i \(-0.440885\pi\)
0.184650 + 0.982804i \(0.440885\pi\)
\(62\) 2.14709 0.272681
\(63\) −1.34302 −0.169205
\(64\) 1.00000 0.125000
\(65\) −5.15798 −0.639768
\(66\) 1.57561 0.193944
\(67\) −5.02573 −0.613991 −0.306995 0.951711i \(-0.599324\pi\)
−0.306995 + 0.951711i \(0.599324\pi\)
\(68\) −4.96288 −0.601837
\(69\) −7.81796 −0.941172
\(70\) −1.61484 −0.193010
\(71\) 3.68758 0.437635 0.218817 0.975766i \(-0.429780\pi\)
0.218817 + 0.975766i \(0.429780\pi\)
\(72\) −2.27540 −0.268159
\(73\) −2.34064 −0.273951 −0.136975 0.990574i \(-0.543738\pi\)
−0.136975 + 0.990574i \(0.543738\pi\)
\(74\) 4.56743 0.530953
\(75\) −2.11550 −0.244277
\(76\) 1.00000 0.114708
\(77\) −1.09251 −0.124503
\(78\) −1.60482 −0.181710
\(79\) −5.28066 −0.594121 −0.297060 0.954859i \(-0.596006\pi\)
−0.297060 + 0.954859i \(0.596006\pi\)
\(80\) −2.73591 −0.305884
\(81\) 3.00365 0.333739
\(82\) 2.66253 0.294027
\(83\) 4.69968 0.515857 0.257929 0.966164i \(-0.416960\pi\)
0.257929 + 0.966164i \(0.416960\pi\)
\(84\) −0.502429 −0.0548195
\(85\) 13.5780 1.47274
\(86\) −2.82781 −0.304931
\(87\) −4.43603 −0.475592
\(88\) −1.85097 −0.197314
\(89\) 11.7557 1.24610 0.623051 0.782181i \(-0.285893\pi\)
0.623051 + 0.782181i \(0.285893\pi\)
\(90\) 6.22530 0.656204
\(91\) 1.11276 0.116649
\(92\) 9.18427 0.957526
\(93\) −1.82768 −0.189521
\(94\) −5.33483 −0.550246
\(95\) −2.73591 −0.280699
\(96\) −0.851234 −0.0868787
\(97\) 14.6135 1.48377 0.741887 0.670525i \(-0.233931\pi\)
0.741887 + 0.670525i \(0.233931\pi\)
\(98\) −6.65162 −0.671915
\(99\) 4.21169 0.423291
\(100\) 2.48522 0.248522
\(101\) −12.8472 −1.27835 −0.639173 0.769063i \(-0.720723\pi\)
−0.639173 + 0.769063i \(0.720723\pi\)
\(102\) 4.22457 0.418295
\(103\) −16.3116 −1.60723 −0.803613 0.595152i \(-0.797092\pi\)
−0.803613 + 0.595152i \(0.797092\pi\)
\(104\) 1.88529 0.184867
\(105\) 1.37460 0.134148
\(106\) −4.12591 −0.400743
\(107\) −14.6131 −1.41270 −0.706350 0.707862i \(-0.749660\pi\)
−0.706350 + 0.707862i \(0.749660\pi\)
\(108\) 4.49060 0.432108
\(109\) −13.7129 −1.31345 −0.656727 0.754128i \(-0.728060\pi\)
−0.656727 + 0.754128i \(0.728060\pi\)
\(110\) 5.06408 0.482841
\(111\) −3.88795 −0.369028
\(112\) 0.590237 0.0557721
\(113\) 9.58561 0.901738 0.450869 0.892590i \(-0.351114\pi\)
0.450869 + 0.892590i \(0.351114\pi\)
\(114\) −0.851234 −0.0797254
\(115\) −25.1274 −2.34314
\(116\) 5.21129 0.483856
\(117\) −4.28978 −0.396590
\(118\) −1.38390 −0.127398
\(119\) −2.92927 −0.268526
\(120\) 2.32890 0.212599
\(121\) −7.57392 −0.688538
\(122\) 2.88432 0.261134
\(123\) −2.26643 −0.204358
\(124\) 2.14709 0.192814
\(125\) 6.88023 0.615387
\(126\) −1.34302 −0.119646
\(127\) −11.2005 −0.993886 −0.496943 0.867783i \(-0.665544\pi\)
−0.496943 + 0.867783i \(0.665544\pi\)
\(128\) 1.00000 0.0883883
\(129\) 2.40713 0.211936
\(130\) −5.15798 −0.452384
\(131\) 22.0343 1.92515 0.962573 0.271023i \(-0.0873619\pi\)
0.962573 + 0.271023i \(0.0873619\pi\)
\(132\) 1.57561 0.137139
\(133\) 0.590237 0.0511800
\(134\) −5.02573 −0.434157
\(135\) −12.2859 −1.05740
\(136\) −4.96288 −0.425563
\(137\) −12.8366 −1.09670 −0.548351 0.836248i \(-0.684744\pi\)
−0.548351 + 0.836248i \(0.684744\pi\)
\(138\) −7.81796 −0.665509
\(139\) −13.2901 −1.12725 −0.563625 0.826031i \(-0.690594\pi\)
−0.563625 + 0.826031i \(0.690594\pi\)
\(140\) −1.61484 −0.136478
\(141\) 4.54119 0.382437
\(142\) 3.68758 0.309454
\(143\) −3.48960 −0.291815
\(144\) −2.27540 −0.189617
\(145\) −14.2576 −1.18403
\(146\) −2.34064 −0.193713
\(147\) 5.66209 0.467001
\(148\) 4.56743 0.375440
\(149\) −9.18506 −0.752469 −0.376235 0.926524i \(-0.622781\pi\)
−0.376235 + 0.926524i \(0.622781\pi\)
\(150\) −2.11550 −0.172730
\(151\) −18.1659 −1.47832 −0.739161 0.673529i \(-0.764778\pi\)
−0.739161 + 0.673529i \(0.764778\pi\)
\(152\) 1.00000 0.0811107
\(153\) 11.2925 0.912947
\(154\) −1.09251 −0.0880368
\(155\) −5.87425 −0.471831
\(156\) −1.60482 −0.128488
\(157\) −6.86544 −0.547921 −0.273961 0.961741i \(-0.588334\pi\)
−0.273961 + 0.961741i \(0.588334\pi\)
\(158\) −5.28066 −0.420107
\(159\) 3.51211 0.278529
\(160\) −2.73591 −0.216293
\(161\) 5.42089 0.427226
\(162\) 3.00365 0.235989
\(163\) −7.85359 −0.615141 −0.307570 0.951525i \(-0.599516\pi\)
−0.307570 + 0.951525i \(0.599516\pi\)
\(164\) 2.66253 0.207909
\(165\) −4.31072 −0.335589
\(166\) 4.69968 0.364766
\(167\) −3.06987 −0.237554 −0.118777 0.992921i \(-0.537897\pi\)
−0.118777 + 0.992921i \(0.537897\pi\)
\(168\) −0.502429 −0.0387633
\(169\) −9.44570 −0.726592
\(170\) 13.5780 1.04138
\(171\) −2.27540 −0.174004
\(172\) −2.82781 −0.215619
\(173\) 8.70636 0.661932 0.330966 0.943643i \(-0.392625\pi\)
0.330966 + 0.943643i \(0.392625\pi\)
\(174\) −4.43603 −0.336294
\(175\) 1.46686 0.110885
\(176\) −1.85097 −0.139522
\(177\) 1.17802 0.0885456
\(178\) 11.7557 0.881128
\(179\) −18.7136 −1.39872 −0.699360 0.714769i \(-0.746532\pi\)
−0.699360 + 0.714769i \(0.746532\pi\)
\(180\) 6.22530 0.464006
\(181\) −12.8415 −0.954498 −0.477249 0.878768i \(-0.658366\pi\)
−0.477249 + 0.878768i \(0.658366\pi\)
\(182\) 1.11276 0.0824836
\(183\) −2.45523 −0.181496
\(184\) 9.18427 0.677073
\(185\) −12.4961 −0.918731
\(186\) −1.82768 −0.134012
\(187\) 9.18612 0.671755
\(188\) −5.33483 −0.389083
\(189\) 2.65052 0.192797
\(190\) −2.73591 −0.198484
\(191\) 18.4358 1.33396 0.666982 0.745074i \(-0.267586\pi\)
0.666982 + 0.745074i \(0.267586\pi\)
\(192\) −0.851234 −0.0614325
\(193\) 1.16570 0.0839086 0.0419543 0.999120i \(-0.486642\pi\)
0.0419543 + 0.999120i \(0.486642\pi\)
\(194\) 14.6135 1.04919
\(195\) 4.39064 0.314421
\(196\) −6.65162 −0.475116
\(197\) −0.461268 −0.0328640 −0.0164320 0.999865i \(-0.505231\pi\)
−0.0164320 + 0.999865i \(0.505231\pi\)
\(198\) 4.21169 0.299312
\(199\) −24.2470 −1.71883 −0.859413 0.511282i \(-0.829171\pi\)
−0.859413 + 0.511282i \(0.829171\pi\)
\(200\) 2.48522 0.175731
\(201\) 4.27807 0.301752
\(202\) −12.8472 −0.903927
\(203\) 3.07589 0.215885
\(204\) 4.22457 0.295779
\(205\) −7.28444 −0.508768
\(206\) −16.3116 −1.13648
\(207\) −20.8979 −1.45250
\(208\) 1.88529 0.130721
\(209\) −1.85097 −0.128034
\(210\) 1.37460 0.0948566
\(211\) −1.00000 −0.0688428
\(212\) −4.12591 −0.283368
\(213\) −3.13899 −0.215080
\(214\) −14.6131 −0.998930
\(215\) 7.73665 0.527635
\(216\) 4.49060 0.305547
\(217\) 1.26729 0.0860293
\(218\) −13.7129 −0.928752
\(219\) 1.99243 0.134636
\(220\) 5.06408 0.341420
\(221\) −9.35644 −0.629382
\(222\) −3.88795 −0.260942
\(223\) 23.5388 1.57628 0.788138 0.615499i \(-0.211045\pi\)
0.788138 + 0.615499i \(0.211045\pi\)
\(224\) 0.590237 0.0394368
\(225\) −5.65486 −0.376991
\(226\) 9.58561 0.637625
\(227\) −22.4844 −1.49234 −0.746172 0.665754i \(-0.768110\pi\)
−0.746172 + 0.665754i \(0.768110\pi\)
\(228\) −0.851234 −0.0563744
\(229\) 14.6615 0.968857 0.484428 0.874831i \(-0.339028\pi\)
0.484428 + 0.874831i \(0.339028\pi\)
\(230\) −25.1274 −1.65685
\(231\) 0.929980 0.0611882
\(232\) 5.21129 0.342138
\(233\) 6.87666 0.450505 0.225252 0.974300i \(-0.427679\pi\)
0.225252 + 0.974300i \(0.427679\pi\)
\(234\) −4.28978 −0.280432
\(235\) 14.5956 0.952114
\(236\) −1.38390 −0.0900842
\(237\) 4.49508 0.291987
\(238\) −2.92927 −0.189876
\(239\) −13.6353 −0.881997 −0.440998 0.897508i \(-0.645376\pi\)
−0.440998 + 0.897508i \(0.645376\pi\)
\(240\) 2.32890 0.150330
\(241\) 9.32981 0.600986 0.300493 0.953784i \(-0.402849\pi\)
0.300493 + 0.953784i \(0.402849\pi\)
\(242\) −7.57392 −0.486870
\(243\) −16.0286 −1.02824
\(244\) 2.88432 0.184650
\(245\) 18.1983 1.16264
\(246\) −2.26643 −0.144503
\(247\) 1.88529 0.119958
\(248\) 2.14709 0.136340
\(249\) −4.00053 −0.253523
\(250\) 6.88023 0.435144
\(251\) 4.53768 0.286416 0.143208 0.989693i \(-0.454258\pi\)
0.143208 + 0.989693i \(0.454258\pi\)
\(252\) −1.34302 −0.0846026
\(253\) −16.9998 −1.06877
\(254\) −11.2005 −0.702784
\(255\) −11.5580 −0.723793
\(256\) 1.00000 0.0625000
\(257\) −19.6876 −1.22808 −0.614039 0.789276i \(-0.710456\pi\)
−0.614039 + 0.789276i \(0.710456\pi\)
\(258\) 2.40713 0.149862
\(259\) 2.69586 0.167513
\(260\) −5.15798 −0.319884
\(261\) −11.8578 −0.733977
\(262\) 22.0343 1.36128
\(263\) 7.31531 0.451081 0.225541 0.974234i \(-0.427585\pi\)
0.225541 + 0.974234i \(0.427585\pi\)
\(264\) 1.57561 0.0969719
\(265\) 11.2881 0.693424
\(266\) 0.590237 0.0361897
\(267\) −10.0069 −0.612410
\(268\) −5.02573 −0.306995
\(269\) 22.7402 1.38650 0.693248 0.720699i \(-0.256179\pi\)
0.693248 + 0.720699i \(0.256179\pi\)
\(270\) −12.2859 −0.747695
\(271\) −0.653391 −0.0396907 −0.0198453 0.999803i \(-0.506317\pi\)
−0.0198453 + 0.999803i \(0.506317\pi\)
\(272\) −4.96288 −0.300919
\(273\) −0.947223 −0.0573285
\(274\) −12.8366 −0.775486
\(275\) −4.60005 −0.277394
\(276\) −7.81796 −0.470586
\(277\) 3.66730 0.220347 0.110173 0.993912i \(-0.464859\pi\)
0.110173 + 0.993912i \(0.464859\pi\)
\(278\) −13.2901 −0.797086
\(279\) −4.88549 −0.292487
\(280\) −1.61484 −0.0965049
\(281\) 14.2063 0.847478 0.423739 0.905784i \(-0.360717\pi\)
0.423739 + 0.905784i \(0.360717\pi\)
\(282\) 4.54119 0.270424
\(283\) 14.2527 0.847236 0.423618 0.905841i \(-0.360760\pi\)
0.423618 + 0.905841i \(0.360760\pi\)
\(284\) 3.68758 0.218817
\(285\) 2.32890 0.137952
\(286\) −3.48960 −0.206344
\(287\) 1.57152 0.0927640
\(288\) −2.27540 −0.134079
\(289\) 7.63013 0.448831
\(290\) −14.2576 −0.837237
\(291\) −12.4395 −0.729216
\(292\) −2.34064 −0.136975
\(293\) −13.3014 −0.777073 −0.388537 0.921433i \(-0.627019\pi\)
−0.388537 + 0.921433i \(0.627019\pi\)
\(294\) 5.66209 0.330220
\(295\) 3.78623 0.220443
\(296\) 4.56743 0.265476
\(297\) −8.31195 −0.482308
\(298\) −9.18506 −0.532076
\(299\) 17.3150 1.00135
\(300\) −2.11550 −0.122138
\(301\) −1.66908 −0.0962041
\(302\) −18.1659 −1.04533
\(303\) 10.9360 0.628256
\(304\) 1.00000 0.0573539
\(305\) −7.89124 −0.451851
\(306\) 11.2925 0.645551
\(307\) 27.9110 1.59297 0.796483 0.604661i \(-0.206691\pi\)
0.796483 + 0.604661i \(0.206691\pi\)
\(308\) −1.09251 −0.0622514
\(309\) 13.8850 0.789888
\(310\) −5.87425 −0.333635
\(311\) 12.2226 0.693078 0.346539 0.938036i \(-0.387357\pi\)
0.346539 + 0.938036i \(0.387357\pi\)
\(312\) −1.60482 −0.0908550
\(313\) 23.3705 1.32098 0.660490 0.750835i \(-0.270349\pi\)
0.660490 + 0.750835i \(0.270349\pi\)
\(314\) −6.86544 −0.387439
\(315\) 3.67440 0.207029
\(316\) −5.28066 −0.297060
\(317\) −5.04135 −0.283151 −0.141575 0.989927i \(-0.545217\pi\)
−0.141575 + 0.989927i \(0.545217\pi\)
\(318\) 3.51211 0.196949
\(319\) −9.64592 −0.540068
\(320\) −2.73591 −0.152942
\(321\) 12.4392 0.694286
\(322\) 5.42089 0.302094
\(323\) −4.96288 −0.276142
\(324\) 3.00365 0.166869
\(325\) 4.68534 0.259896
\(326\) −7.85359 −0.434970
\(327\) 11.6729 0.645511
\(328\) 2.66253 0.147014
\(329\) −3.14881 −0.173600
\(330\) −4.31072 −0.237297
\(331\) −27.5631 −1.51500 −0.757502 0.652833i \(-0.773580\pi\)
−0.757502 + 0.652833i \(0.773580\pi\)
\(332\) 4.69968 0.257929
\(333\) −10.3927 −0.569518
\(334\) −3.06987 −0.167976
\(335\) 13.7500 0.751241
\(336\) −0.502429 −0.0274098
\(337\) −10.5707 −0.575822 −0.287911 0.957657i \(-0.592961\pi\)
−0.287911 + 0.957657i \(0.592961\pi\)
\(338\) −9.44570 −0.513778
\(339\) −8.15960 −0.443168
\(340\) 13.5780 0.736370
\(341\) −3.97419 −0.215215
\(342\) −2.27540 −0.123040
\(343\) −8.05769 −0.435074
\(344\) −2.82781 −0.152466
\(345\) 21.3893 1.15156
\(346\) 8.70636 0.468057
\(347\) 12.6630 0.679787 0.339894 0.940464i \(-0.389609\pi\)
0.339894 + 0.940464i \(0.389609\pi\)
\(348\) −4.43603 −0.237796
\(349\) −28.4933 −1.52521 −0.762606 0.646863i \(-0.776081\pi\)
−0.762606 + 0.646863i \(0.776081\pi\)
\(350\) 1.46686 0.0784072
\(351\) 8.46606 0.451885
\(352\) −1.85097 −0.0986569
\(353\) −21.5746 −1.14830 −0.574150 0.818750i \(-0.694667\pi\)
−0.574150 + 0.818750i \(0.694667\pi\)
\(354\) 1.17802 0.0626112
\(355\) −10.0889 −0.535462
\(356\) 11.7557 0.623051
\(357\) 2.49349 0.131970
\(358\) −18.7136 −0.989045
\(359\) 23.0994 1.21914 0.609571 0.792731i \(-0.291342\pi\)
0.609571 + 0.792731i \(0.291342\pi\)
\(360\) 6.22530 0.328102
\(361\) 1.00000 0.0526316
\(362\) −12.8415 −0.674932
\(363\) 6.44718 0.338389
\(364\) 1.11276 0.0583247
\(365\) 6.40378 0.335189
\(366\) −2.45523 −0.128337
\(367\) −13.3317 −0.695910 −0.347955 0.937511i \(-0.613124\pi\)
−0.347955 + 0.937511i \(0.613124\pi\)
\(368\) 9.18427 0.478763
\(369\) −6.05832 −0.315383
\(370\) −12.4961 −0.649641
\(371\) −2.43526 −0.126432
\(372\) −1.82768 −0.0947606
\(373\) −22.7148 −1.17613 −0.588063 0.808815i \(-0.700109\pi\)
−0.588063 + 0.808815i \(0.700109\pi\)
\(374\) 9.18612 0.475003
\(375\) −5.85669 −0.302438
\(376\) −5.33483 −0.275123
\(377\) 9.82476 0.506001
\(378\) 2.65052 0.136328
\(379\) 27.9622 1.43632 0.718162 0.695876i \(-0.244984\pi\)
0.718162 + 0.695876i \(0.244984\pi\)
\(380\) −2.73591 −0.140349
\(381\) 9.53427 0.488456
\(382\) 18.4358 0.943255
\(383\) −4.12225 −0.210637 −0.105319 0.994439i \(-0.533586\pi\)
−0.105319 + 0.994439i \(0.533586\pi\)
\(384\) −0.851234 −0.0434394
\(385\) 2.98901 0.152334
\(386\) 1.16570 0.0593324
\(387\) 6.43441 0.327079
\(388\) 14.6135 0.741887
\(389\) 13.2545 0.672028 0.336014 0.941857i \(-0.390921\pi\)
0.336014 + 0.941857i \(0.390921\pi\)
\(390\) 4.39064 0.222329
\(391\) −45.5804 −2.30510
\(392\) −6.65162 −0.335958
\(393\) −18.7563 −0.946133
\(394\) −0.461268 −0.0232383
\(395\) 14.4474 0.726929
\(396\) 4.21169 0.211645
\(397\) 9.35973 0.469751 0.234876 0.972025i \(-0.424532\pi\)
0.234876 + 0.972025i \(0.424532\pi\)
\(398\) −24.2470 −1.21539
\(399\) −0.502429 −0.0251529
\(400\) 2.48522 0.124261
\(401\) 23.9174 1.19438 0.597188 0.802101i \(-0.296285\pi\)
0.597188 + 0.802101i \(0.296285\pi\)
\(402\) 4.27807 0.213371
\(403\) 4.04788 0.201639
\(404\) −12.8472 −0.639173
\(405\) −8.21772 −0.408342
\(406\) 3.07589 0.152654
\(407\) −8.45416 −0.419057
\(408\) 4.22457 0.209147
\(409\) −24.4329 −1.20813 −0.604065 0.796935i \(-0.706453\pi\)
−0.604065 + 0.796935i \(0.706453\pi\)
\(410\) −7.28444 −0.359753
\(411\) 10.9269 0.538986
\(412\) −16.3116 −0.803613
\(413\) −0.816828 −0.0401935
\(414\) −20.8979 −1.02708
\(415\) −12.8579 −0.631170
\(416\) 1.88529 0.0924337
\(417\) 11.3130 0.553998
\(418\) −1.85097 −0.0905337
\(419\) 7.08550 0.346149 0.173075 0.984909i \(-0.444630\pi\)
0.173075 + 0.984909i \(0.444630\pi\)
\(420\) 1.37460 0.0670738
\(421\) −25.9286 −1.26368 −0.631841 0.775098i \(-0.717701\pi\)
−0.631841 + 0.775098i \(0.717701\pi\)
\(422\) −1.00000 −0.0486792
\(423\) 12.1389 0.590213
\(424\) −4.12591 −0.200372
\(425\) −12.3338 −0.598278
\(426\) −3.13899 −0.152085
\(427\) 1.70243 0.0823864
\(428\) −14.6131 −0.706350
\(429\) 2.97047 0.143416
\(430\) 7.73665 0.373095
\(431\) −22.2780 −1.07309 −0.536546 0.843871i \(-0.680271\pi\)
−0.536546 + 0.843871i \(0.680271\pi\)
\(432\) 4.49060 0.216054
\(433\) −8.14495 −0.391422 −0.195711 0.980662i \(-0.562701\pi\)
−0.195711 + 0.980662i \(0.562701\pi\)
\(434\) 1.26729 0.0608319
\(435\) 12.1366 0.581904
\(436\) −13.7129 −0.656727
\(437\) 9.18427 0.439343
\(438\) 1.99243 0.0952020
\(439\) −23.9146 −1.14138 −0.570692 0.821164i \(-0.693325\pi\)
−0.570692 + 0.821164i \(0.693325\pi\)
\(440\) 5.06408 0.241421
\(441\) 15.1351 0.720719
\(442\) −9.35644 −0.445040
\(443\) −18.2748 −0.868262 −0.434131 0.900850i \(-0.642944\pi\)
−0.434131 + 0.900850i \(0.642944\pi\)
\(444\) −3.88795 −0.184514
\(445\) −32.1626 −1.52465
\(446\) 23.5388 1.11460
\(447\) 7.81864 0.369809
\(448\) 0.590237 0.0278861
\(449\) −32.7585 −1.54597 −0.772984 0.634426i \(-0.781237\pi\)
−0.772984 + 0.634426i \(0.781237\pi\)
\(450\) −5.65486 −0.266573
\(451\) −4.92825 −0.232062
\(452\) 9.58561 0.450869
\(453\) 15.4635 0.726537
\(454\) −22.4844 −1.05525
\(455\) −3.04443 −0.142725
\(456\) −0.851234 −0.0398627
\(457\) −3.45841 −0.161777 −0.0808887 0.996723i \(-0.525776\pi\)
−0.0808887 + 0.996723i \(0.525776\pi\)
\(458\) 14.6615 0.685085
\(459\) −22.2863 −1.04024
\(460\) −25.1274 −1.17157
\(461\) −30.8497 −1.43681 −0.718406 0.695624i \(-0.755128\pi\)
−0.718406 + 0.695624i \(0.755128\pi\)
\(462\) 0.929980 0.0432666
\(463\) −39.7861 −1.84902 −0.924508 0.381163i \(-0.875524\pi\)
−0.924508 + 0.381163i \(0.875524\pi\)
\(464\) 5.21129 0.241928
\(465\) 5.00036 0.231886
\(466\) 6.87666 0.318555
\(467\) −4.95261 −0.229180 −0.114590 0.993413i \(-0.536555\pi\)
−0.114590 + 0.993413i \(0.536555\pi\)
\(468\) −4.28978 −0.198295
\(469\) −2.96637 −0.136974
\(470\) 14.5956 0.673247
\(471\) 5.84409 0.269282
\(472\) −1.38390 −0.0636991
\(473\) 5.23419 0.240668
\(474\) 4.49508 0.206466
\(475\) 2.48522 0.114029
\(476\) −2.92927 −0.134263
\(477\) 9.38809 0.429851
\(478\) −13.6353 −0.623666
\(479\) 1.34533 0.0614699 0.0307349 0.999528i \(-0.490215\pi\)
0.0307349 + 0.999528i \(0.490215\pi\)
\(480\) 2.32890 0.106299
\(481\) 8.61091 0.392624
\(482\) 9.32981 0.424961
\(483\) −4.61445 −0.209965
\(484\) −7.57392 −0.344269
\(485\) −39.9812 −1.81545
\(486\) −16.0286 −0.727073
\(487\) −32.4030 −1.46832 −0.734160 0.678977i \(-0.762424\pi\)
−0.734160 + 0.678977i \(0.762424\pi\)
\(488\) 2.88432 0.130567
\(489\) 6.68524 0.302317
\(490\) 18.1983 0.822113
\(491\) 3.96106 0.178760 0.0893800 0.995998i \(-0.471511\pi\)
0.0893800 + 0.995998i \(0.471511\pi\)
\(492\) −2.26643 −0.102179
\(493\) −25.8630 −1.16481
\(494\) 1.88529 0.0848230
\(495\) −11.5228 −0.517912
\(496\) 2.14709 0.0964072
\(497\) 2.17654 0.0976312
\(498\) −4.00053 −0.179268
\(499\) −14.9638 −0.669871 −0.334935 0.942241i \(-0.608715\pi\)
−0.334935 + 0.942241i \(0.608715\pi\)
\(500\) 6.88023 0.307693
\(501\) 2.61318 0.116748
\(502\) 4.53768 0.202526
\(503\) 2.73170 0.121801 0.0609003 0.998144i \(-0.480603\pi\)
0.0609003 + 0.998144i \(0.480603\pi\)
\(504\) −1.34302 −0.0598231
\(505\) 35.1488 1.56410
\(506\) −16.9998 −0.755732
\(507\) 8.04050 0.357091
\(508\) −11.2005 −0.496943
\(509\) 8.11268 0.359588 0.179794 0.983704i \(-0.442457\pi\)
0.179794 + 0.983704i \(0.442457\pi\)
\(510\) −11.5580 −0.511799
\(511\) −1.38153 −0.0611153
\(512\) 1.00000 0.0441942
\(513\) 4.49060 0.198265
\(514\) −19.6876 −0.868383
\(515\) 44.6270 1.96650
\(516\) 2.40713 0.105968
\(517\) 9.87460 0.434284
\(518\) 2.69586 0.118449
\(519\) −7.41115 −0.325313
\(520\) −5.15798 −0.226192
\(521\) 25.4442 1.11473 0.557366 0.830267i \(-0.311812\pi\)
0.557366 + 0.830267i \(0.311812\pi\)
\(522\) −11.8578 −0.519000
\(523\) −18.5770 −0.812315 −0.406157 0.913803i \(-0.633132\pi\)
−0.406157 + 0.913803i \(0.633132\pi\)
\(524\) 22.0343 0.962573
\(525\) −1.24865 −0.0544954
\(526\) 7.31531 0.318962
\(527\) −10.6557 −0.464171
\(528\) 1.57561 0.0685695
\(529\) 61.3508 2.66743
\(530\) 11.2881 0.490325
\(531\) 3.14893 0.136652
\(532\) 0.590237 0.0255900
\(533\) 5.01963 0.217424
\(534\) −10.0069 −0.433039
\(535\) 39.9801 1.72849
\(536\) −5.02573 −0.217079
\(537\) 15.9297 0.687415
\(538\) 22.7402 0.980400
\(539\) 12.3119 0.530312
\(540\) −12.2859 −0.528701
\(541\) 9.21356 0.396122 0.198061 0.980190i \(-0.436536\pi\)
0.198061 + 0.980190i \(0.436536\pi\)
\(542\) −0.653391 −0.0280656
\(543\) 10.9311 0.469098
\(544\) −4.96288 −0.212782
\(545\) 37.5172 1.60706
\(546\) −0.947223 −0.0405374
\(547\) 32.4664 1.38816 0.694082 0.719896i \(-0.255810\pi\)
0.694082 + 0.719896i \(0.255810\pi\)
\(548\) −12.8366 −0.548351
\(549\) −6.56298 −0.280101
\(550\) −4.60005 −0.196147
\(551\) 5.21129 0.222008
\(552\) −7.81796 −0.332755
\(553\) −3.11684 −0.132541
\(554\) 3.66730 0.155809
\(555\) 10.6371 0.451520
\(556\) −13.2901 −0.563625
\(557\) 22.9713 0.973325 0.486662 0.873590i \(-0.338214\pi\)
0.486662 + 0.873590i \(0.338214\pi\)
\(558\) −4.88549 −0.206819
\(559\) −5.33124 −0.225487
\(560\) −1.61484 −0.0682392
\(561\) −7.81954 −0.330141
\(562\) 14.2063 0.599258
\(563\) 46.2540 1.94937 0.974686 0.223577i \(-0.0717734\pi\)
0.974686 + 0.223577i \(0.0717734\pi\)
\(564\) 4.54119 0.191219
\(565\) −26.2254 −1.10331
\(566\) 14.2527 0.599086
\(567\) 1.77286 0.0744533
\(568\) 3.68758 0.154727
\(569\) −44.3647 −1.85987 −0.929933 0.367730i \(-0.880135\pi\)
−0.929933 + 0.367730i \(0.880135\pi\)
\(570\) 2.32890 0.0975470
\(571\) −30.1679 −1.26249 −0.631244 0.775584i \(-0.717455\pi\)
−0.631244 + 0.775584i \(0.717455\pi\)
\(572\) −3.48960 −0.145908
\(573\) −15.6931 −0.655590
\(574\) 1.57152 0.0655940
\(575\) 22.8249 0.951864
\(576\) −2.27540 −0.0948084
\(577\) 41.1781 1.71427 0.857133 0.515095i \(-0.172243\pi\)
0.857133 + 0.515095i \(0.172243\pi\)
\(578\) 7.63013 0.317372
\(579\) −0.992280 −0.0412377
\(580\) −14.2576 −0.592016
\(581\) 2.77392 0.115082
\(582\) −12.4395 −0.515634
\(583\) 7.63692 0.316289
\(584\) −2.34064 −0.0968563
\(585\) 11.7365 0.485243
\(586\) −13.3014 −0.549474
\(587\) −23.0521 −0.951462 −0.475731 0.879591i \(-0.657816\pi\)
−0.475731 + 0.879591i \(0.657816\pi\)
\(588\) 5.66209 0.233501
\(589\) 2.14709 0.0884693
\(590\) 3.78623 0.155877
\(591\) 0.392647 0.0161513
\(592\) 4.56743 0.187720
\(593\) −10.5408 −0.432861 −0.216430 0.976298i \(-0.569441\pi\)
−0.216430 + 0.976298i \(0.569441\pi\)
\(594\) −8.31195 −0.341044
\(595\) 8.01423 0.328551
\(596\) −9.18506 −0.376235
\(597\) 20.6399 0.844735
\(598\) 17.3150 0.708062
\(599\) −27.4181 −1.12027 −0.560136 0.828400i \(-0.689251\pi\)
−0.560136 + 0.828400i \(0.689251\pi\)
\(600\) −2.11550 −0.0863649
\(601\) 46.3625 1.89117 0.945583 0.325382i \(-0.105493\pi\)
0.945583 + 0.325382i \(0.105493\pi\)
\(602\) −1.66908 −0.0680266
\(603\) 11.4356 0.465692
\(604\) −18.1659 −0.739161
\(605\) 20.7216 0.842452
\(606\) 10.9360 0.444244
\(607\) −3.71754 −0.150890 −0.0754452 0.997150i \(-0.524038\pi\)
−0.0754452 + 0.997150i \(0.524038\pi\)
\(608\) 1.00000 0.0405554
\(609\) −2.61830 −0.106099
\(610\) −7.89124 −0.319507
\(611\) −10.0577 −0.406890
\(612\) 11.2925 0.456473
\(613\) −19.0907 −0.771067 −0.385534 0.922694i \(-0.625983\pi\)
−0.385534 + 0.922694i \(0.625983\pi\)
\(614\) 27.9110 1.12640
\(615\) 6.20077 0.250039
\(616\) −1.09251 −0.0440184
\(617\) −3.08331 −0.124130 −0.0620648 0.998072i \(-0.519769\pi\)
−0.0620648 + 0.998072i \(0.519769\pi\)
\(618\) 13.8850 0.558535
\(619\) −20.1500 −0.809898 −0.404949 0.914339i \(-0.632711\pi\)
−0.404949 + 0.914339i \(0.632711\pi\)
\(620\) −5.87425 −0.235915
\(621\) 41.2429 1.65502
\(622\) 12.2226 0.490080
\(623\) 6.93865 0.277991
\(624\) −1.60482 −0.0642442
\(625\) −31.2498 −1.24999
\(626\) 23.3705 0.934073
\(627\) 1.57561 0.0629236
\(628\) −6.86544 −0.273961
\(629\) −22.6676 −0.903816
\(630\) 3.67440 0.146391
\(631\) 22.4966 0.895576 0.447788 0.894140i \(-0.352212\pi\)
0.447788 + 0.894140i \(0.352212\pi\)
\(632\) −5.28066 −0.210053
\(633\) 0.851234 0.0338335
\(634\) −5.04135 −0.200218
\(635\) 30.6437 1.21606
\(636\) 3.51211 0.139264
\(637\) −12.5402 −0.496861
\(638\) −9.64592 −0.381886
\(639\) −8.39071 −0.331931
\(640\) −2.73591 −0.108146
\(641\) −33.6952 −1.33088 −0.665440 0.746452i \(-0.731756\pi\)
−0.665440 + 0.746452i \(0.731756\pi\)
\(642\) 12.4392 0.490935
\(643\) −0.279610 −0.0110267 −0.00551337 0.999985i \(-0.501755\pi\)
−0.00551337 + 0.999985i \(0.501755\pi\)
\(644\) 5.42089 0.213613
\(645\) −6.58570 −0.259312
\(646\) −4.96288 −0.195262
\(647\) 35.1454 1.38171 0.690855 0.722994i \(-0.257234\pi\)
0.690855 + 0.722994i \(0.257234\pi\)
\(648\) 3.00365 0.117994
\(649\) 2.56155 0.100550
\(650\) 4.68534 0.183774
\(651\) −1.07876 −0.0422800
\(652\) −7.85359 −0.307570
\(653\) 43.4375 1.69984 0.849921 0.526910i \(-0.176650\pi\)
0.849921 + 0.526910i \(0.176650\pi\)
\(654\) 11.6729 0.456445
\(655\) −60.2839 −2.35549
\(656\) 2.66253 0.103954
\(657\) 5.32589 0.207783
\(658\) −3.14881 −0.122754
\(659\) 16.2510 0.633051 0.316525 0.948584i \(-0.397484\pi\)
0.316525 + 0.948584i \(0.397484\pi\)
\(660\) −4.31072 −0.167795
\(661\) −37.3742 −1.45369 −0.726843 0.686803i \(-0.759013\pi\)
−0.726843 + 0.686803i \(0.759013\pi\)
\(662\) −27.5631 −1.07127
\(663\) 7.96452 0.309316
\(664\) 4.69968 0.182383
\(665\) −1.61484 −0.0626206
\(666\) −10.3927 −0.402710
\(667\) 47.8619 1.85322
\(668\) −3.06987 −0.118777
\(669\) −20.0370 −0.774677
\(670\) 13.7500 0.531207
\(671\) −5.33878 −0.206101
\(672\) −0.502429 −0.0193816
\(673\) −21.8313 −0.841534 −0.420767 0.907169i \(-0.638239\pi\)
−0.420767 + 0.907169i \(0.638239\pi\)
\(674\) −10.5707 −0.407168
\(675\) 11.1601 0.429553
\(676\) −9.44570 −0.363296
\(677\) −30.7230 −1.18078 −0.590390 0.807118i \(-0.701026\pi\)
−0.590390 + 0.807118i \(0.701026\pi\)
\(678\) −8.15960 −0.313367
\(679\) 8.62541 0.331013
\(680\) 13.5780 0.520692
\(681\) 19.1395 0.733427
\(682\) −3.97419 −0.152180
\(683\) −50.1126 −1.91750 −0.958752 0.284245i \(-0.908257\pi\)
−0.958752 + 0.284245i \(0.908257\pi\)
\(684\) −2.27540 −0.0870021
\(685\) 35.1197 1.34186
\(686\) −8.05769 −0.307644
\(687\) −12.4803 −0.476154
\(688\) −2.82781 −0.107809
\(689\) −7.77851 −0.296338
\(690\) 21.3893 0.814275
\(691\) −33.4120 −1.27105 −0.635526 0.772079i \(-0.719217\pi\)
−0.635526 + 0.772079i \(0.719217\pi\)
\(692\) 8.70636 0.330966
\(693\) 2.48589 0.0944313
\(694\) 12.6630 0.480682
\(695\) 36.3605 1.37923
\(696\) −4.43603 −0.168147
\(697\) −13.2138 −0.500508
\(698\) −28.4933 −1.07849
\(699\) −5.85364 −0.221405
\(700\) 1.46686 0.0554423
\(701\) −22.1771 −0.837619 −0.418809 0.908074i \(-0.637552\pi\)
−0.418809 + 0.908074i \(0.637552\pi\)
\(702\) 8.46606 0.319531
\(703\) 4.56743 0.172264
\(704\) −1.85097 −0.0697609
\(705\) −12.4243 −0.467926
\(706\) −21.5746 −0.811970
\(707\) −7.58289 −0.285184
\(708\) 1.17802 0.0442728
\(709\) 11.9572 0.449061 0.224531 0.974467i \(-0.427915\pi\)
0.224531 + 0.974467i \(0.427915\pi\)
\(710\) −10.0889 −0.378629
\(711\) 12.0156 0.450621
\(712\) 11.7557 0.440564
\(713\) 19.7194 0.738499
\(714\) 2.49349 0.0933167
\(715\) 9.54724 0.357047
\(716\) −18.7136 −0.699360
\(717\) 11.6069 0.433466
\(718\) 23.0994 0.862064
\(719\) 29.3090 1.09304 0.546521 0.837445i \(-0.315952\pi\)
0.546521 + 0.837445i \(0.315952\pi\)
\(720\) 6.22530 0.232003
\(721\) −9.62768 −0.358554
\(722\) 1.00000 0.0372161
\(723\) −7.94186 −0.295361
\(724\) −12.8415 −0.477249
\(725\) 12.9512 0.480994
\(726\) 6.44718 0.239277
\(727\) 11.9179 0.442010 0.221005 0.975273i \(-0.429066\pi\)
0.221005 + 0.975273i \(0.429066\pi\)
\(728\) 1.11276 0.0412418
\(729\) 4.63315 0.171598
\(730\) 6.40378 0.237014
\(731\) 14.0341 0.519070
\(732\) −2.45523 −0.0907480
\(733\) −15.5131 −0.572991 −0.286496 0.958082i \(-0.592490\pi\)
−0.286496 + 0.958082i \(0.592490\pi\)
\(734\) −13.3317 −0.492083
\(735\) −15.4910 −0.571393
\(736\) 9.18427 0.338537
\(737\) 9.30246 0.342661
\(738\) −6.05832 −0.223010
\(739\) 11.6483 0.428490 0.214245 0.976780i \(-0.431271\pi\)
0.214245 + 0.976780i \(0.431271\pi\)
\(740\) −12.4961 −0.459365
\(741\) −1.60482 −0.0589545
\(742\) −2.43526 −0.0894012
\(743\) 0.558624 0.0204939 0.0102470 0.999947i \(-0.496738\pi\)
0.0102470 + 0.999947i \(0.496738\pi\)
\(744\) −1.82768 −0.0670059
\(745\) 25.1295 0.920674
\(746\) −22.7148 −0.831647
\(747\) −10.6937 −0.391261
\(748\) 9.18612 0.335878
\(749\) −8.62518 −0.315157
\(750\) −5.85669 −0.213856
\(751\) −14.6166 −0.533368 −0.266684 0.963784i \(-0.585928\pi\)
−0.266684 + 0.963784i \(0.585928\pi\)
\(752\) −5.33483 −0.194541
\(753\) −3.86262 −0.140762
\(754\) 9.82476 0.357797
\(755\) 49.7004 1.80878
\(756\) 2.65052 0.0963984
\(757\) −38.1142 −1.38528 −0.692642 0.721281i \(-0.743554\pi\)
−0.692642 + 0.721281i \(0.743554\pi\)
\(758\) 27.9622 1.01563
\(759\) 14.4708 0.525256
\(760\) −2.73591 −0.0992420
\(761\) 11.4364 0.414568 0.207284 0.978281i \(-0.433538\pi\)
0.207284 + 0.978281i \(0.433538\pi\)
\(762\) 9.53427 0.345390
\(763\) −8.09383 −0.293016
\(764\) 18.4358 0.666982
\(765\) −30.8954 −1.11702
\(766\) −4.12225 −0.148943
\(767\) −2.60905 −0.0942072
\(768\) −0.851234 −0.0307163
\(769\) −1.30181 −0.0469444 −0.0234722 0.999724i \(-0.507472\pi\)
−0.0234722 + 0.999724i \(0.507472\pi\)
\(770\) 2.98901 0.107716
\(771\) 16.7588 0.603552
\(772\) 1.16570 0.0419543
\(773\) −14.9282 −0.536930 −0.268465 0.963289i \(-0.586516\pi\)
−0.268465 + 0.963289i \(0.586516\pi\)
\(774\) 6.43441 0.231280
\(775\) 5.33598 0.191674
\(776\) 14.6135 0.524593
\(777\) −2.29481 −0.0823259
\(778\) 13.2545 0.475196
\(779\) 2.66253 0.0953950
\(780\) 4.39064 0.157210
\(781\) −6.82558 −0.244238
\(782\) −45.5804 −1.62995
\(783\) 23.4018 0.836313
\(784\) −6.65162 −0.237558
\(785\) 18.7832 0.670402
\(786\) −18.7563 −0.669017
\(787\) 15.7775 0.562407 0.281203 0.959648i \(-0.409266\pi\)
0.281203 + 0.959648i \(0.409266\pi\)
\(788\) −0.461268 −0.0164320
\(789\) −6.22704 −0.221688
\(790\) 14.4474 0.514016
\(791\) 5.65778 0.201167
\(792\) 4.21169 0.149656
\(793\) 5.43777 0.193101
\(794\) 9.35973 0.332164
\(795\) −9.60883 −0.340790
\(796\) −24.2470 −0.859413
\(797\) 4.18880 0.148375 0.0741875 0.997244i \(-0.476364\pi\)
0.0741875 + 0.997244i \(0.476364\pi\)
\(798\) −0.502429 −0.0177858
\(799\) 26.4761 0.936658
\(800\) 2.48522 0.0878656
\(801\) −26.7489 −0.945127
\(802\) 23.9174 0.844551
\(803\) 4.33244 0.152889
\(804\) 4.27807 0.150876
\(805\) −14.8311 −0.522727
\(806\) 4.04788 0.142580
\(807\) −19.3572 −0.681407
\(808\) −12.8472 −0.451963
\(809\) −32.8100 −1.15354 −0.576769 0.816907i \(-0.695687\pi\)
−0.576769 + 0.816907i \(0.695687\pi\)
\(810\) −8.21772 −0.288741
\(811\) −23.5911 −0.828394 −0.414197 0.910187i \(-0.635938\pi\)
−0.414197 + 0.910187i \(0.635938\pi\)
\(812\) 3.07589 0.107943
\(813\) 0.556189 0.0195064
\(814\) −8.45416 −0.296318
\(815\) 21.4867 0.752647
\(816\) 4.22457 0.147889
\(817\) −2.82781 −0.0989327
\(818\) −24.4329 −0.854277
\(819\) −2.53198 −0.0884747
\(820\) −7.28444 −0.254384
\(821\) 20.2176 0.705598 0.352799 0.935699i \(-0.385230\pi\)
0.352799 + 0.935699i \(0.385230\pi\)
\(822\) 10.9269 0.381120
\(823\) 33.7231 1.17551 0.587757 0.809038i \(-0.300011\pi\)
0.587757 + 0.809038i \(0.300011\pi\)
\(824\) −16.3116 −0.568240
\(825\) 3.91572 0.136328
\(826\) −0.816828 −0.0284211
\(827\) 44.8266 1.55877 0.779387 0.626542i \(-0.215531\pi\)
0.779387 + 0.626542i \(0.215531\pi\)
\(828\) −20.8979 −0.726252
\(829\) 49.8577 1.73163 0.865816 0.500363i \(-0.166800\pi\)
0.865816 + 0.500363i \(0.166800\pi\)
\(830\) −12.8579 −0.446305
\(831\) −3.12174 −0.108292
\(832\) 1.88529 0.0653605
\(833\) 33.0112 1.14377
\(834\) 11.3130 0.391736
\(835\) 8.39890 0.290656
\(836\) −1.85097 −0.0640170
\(837\) 9.64172 0.333267
\(838\) 7.08550 0.244765
\(839\) −50.0326 −1.72732 −0.863658 0.504078i \(-0.831832\pi\)
−0.863658 + 0.504078i \(0.831832\pi\)
\(840\) 1.37460 0.0474283
\(841\) −1.84248 −0.0635340
\(842\) −25.9286 −0.893558
\(843\) −12.0929 −0.416502
\(844\) −1.00000 −0.0344214
\(845\) 25.8426 0.889013
\(846\) 12.1389 0.417343
\(847\) −4.47041 −0.153605
\(848\) −4.12591 −0.141684
\(849\) −12.1324 −0.416383
\(850\) −12.3338 −0.423046
\(851\) 41.9485 1.43798
\(852\) −3.13899 −0.107540
\(853\) −43.1050 −1.47589 −0.737944 0.674862i \(-0.764203\pi\)
−0.737944 + 0.674862i \(0.764203\pi\)
\(854\) 1.70243 0.0582560
\(855\) 6.22530 0.212901
\(856\) −14.6131 −0.499465
\(857\) 8.23730 0.281381 0.140690 0.990054i \(-0.455068\pi\)
0.140690 + 0.990054i \(0.455068\pi\)
\(858\) 2.97047 0.101410
\(859\) 5.09199 0.173737 0.0868683 0.996220i \(-0.472314\pi\)
0.0868683 + 0.996220i \(0.472314\pi\)
\(860\) 7.73665 0.263818
\(861\) −1.33773 −0.0455898
\(862\) −22.2780 −0.758791
\(863\) 44.4564 1.51331 0.756657 0.653812i \(-0.226831\pi\)
0.756657 + 0.653812i \(0.226831\pi\)
\(864\) 4.49060 0.152773
\(865\) −23.8198 −0.809899
\(866\) −8.14495 −0.276777
\(867\) −6.49503 −0.220583
\(868\) 1.26729 0.0430146
\(869\) 9.77433 0.331571
\(870\) 12.1366 0.411468
\(871\) −9.47494 −0.321046
\(872\) −13.7129 −0.464376
\(873\) −33.2515 −1.12539
\(874\) 9.18427 0.310663
\(875\) 4.06096 0.137286
\(876\) 1.99243 0.0673180
\(877\) −20.3998 −0.688853 −0.344427 0.938813i \(-0.611927\pi\)
−0.344427 + 0.938813i \(0.611927\pi\)
\(878\) −23.9146 −0.807080
\(879\) 11.3226 0.381901
\(880\) 5.06408 0.170710
\(881\) −18.0011 −0.606473 −0.303237 0.952915i \(-0.598067\pi\)
−0.303237 + 0.952915i \(0.598067\pi\)
\(882\) 15.1351 0.509625
\(883\) 18.3131 0.616283 0.308142 0.951340i \(-0.400293\pi\)
0.308142 + 0.951340i \(0.400293\pi\)
\(884\) −9.35644 −0.314691
\(885\) −3.22297 −0.108339
\(886\) −18.2748 −0.613954
\(887\) −32.1648 −1.07999 −0.539994 0.841669i \(-0.681574\pi\)
−0.539994 + 0.841669i \(0.681574\pi\)
\(888\) −3.88795 −0.130471
\(889\) −6.61096 −0.221725
\(890\) −32.1626 −1.07809
\(891\) −5.55965 −0.186255
\(892\) 23.5388 0.788138
\(893\) −5.33483 −0.178523
\(894\) 7.81864 0.261494
\(895\) 51.1988 1.71139
\(896\) 0.590237 0.0197184
\(897\) −14.7391 −0.492124
\(898\) −32.7585 −1.09316
\(899\) 11.1891 0.373177
\(900\) −5.65486 −0.188495
\(901\) 20.4764 0.682166
\(902\) −4.92825 −0.164093
\(903\) 1.42078 0.0472805
\(904\) 9.58561 0.318813
\(905\) 35.1331 1.16786
\(906\) 15.4635 0.513739
\(907\) −20.0049 −0.664251 −0.332125 0.943235i \(-0.607766\pi\)
−0.332125 + 0.943235i \(0.607766\pi\)
\(908\) −22.4844 −0.746172
\(909\) 29.2326 0.969583
\(910\) −3.04443 −0.100922
\(911\) −18.5493 −0.614565 −0.307283 0.951618i \(-0.599420\pi\)
−0.307283 + 0.951618i \(0.599420\pi\)
\(912\) −0.851234 −0.0281872
\(913\) −8.69896 −0.287893
\(914\) −3.45841 −0.114394
\(915\) 6.71730 0.222067
\(916\) 14.6615 0.484428
\(917\) 13.0054 0.429478
\(918\) −22.2863 −0.735557
\(919\) 23.9314 0.789423 0.394711 0.918805i \(-0.370845\pi\)
0.394711 + 0.918805i \(0.370845\pi\)
\(920\) −25.1274 −0.828424
\(921\) −23.7588 −0.782879
\(922\) −30.8497 −1.01598
\(923\) 6.95213 0.228832
\(924\) 0.929980 0.0305941
\(925\) 11.3510 0.373220
\(926\) −39.7861 −1.30745
\(927\) 37.1153 1.21903
\(928\) 5.21129 0.171069
\(929\) −27.6684 −0.907770 −0.453885 0.891060i \(-0.649962\pi\)
−0.453885 + 0.891060i \(0.649962\pi\)
\(930\) 5.00036 0.163968
\(931\) −6.65162 −0.217998
\(932\) 6.87666 0.225252
\(933\) −10.4043 −0.340620
\(934\) −4.95261 −0.162054
\(935\) −25.1324 −0.821918
\(936\) −4.28978 −0.140216
\(937\) −30.6488 −1.00125 −0.500626 0.865664i \(-0.666897\pi\)
−0.500626 + 0.865664i \(0.666897\pi\)
\(938\) −2.96637 −0.0968554
\(939\) −19.8938 −0.649209
\(940\) 14.5956 0.476057
\(941\) −25.0236 −0.815745 −0.407873 0.913039i \(-0.633729\pi\)
−0.407873 + 0.913039i \(0.633729\pi\)
\(942\) 5.84409 0.190411
\(943\) 24.4534 0.796311
\(944\) −1.38390 −0.0450421
\(945\) −7.25158 −0.235894
\(946\) 5.23419 0.170178
\(947\) 35.9832 1.16930 0.584648 0.811287i \(-0.301233\pi\)
0.584648 + 0.811287i \(0.301233\pi\)
\(948\) 4.49508 0.145993
\(949\) −4.41277 −0.143245
\(950\) 2.48522 0.0806310
\(951\) 4.29137 0.139157
\(952\) −2.92927 −0.0949382
\(953\) 49.1700 1.59277 0.796386 0.604789i \(-0.206743\pi\)
0.796386 + 0.604789i \(0.206743\pi\)
\(954\) 9.38809 0.303951
\(955\) −50.4386 −1.63215
\(956\) −13.6353 −0.440998
\(957\) 8.21094 0.265422
\(958\) 1.34533 0.0434658
\(959\) −7.57661 −0.244662
\(960\) 2.32890 0.0751650
\(961\) −26.3900 −0.851291
\(962\) 8.61091 0.277627
\(963\) 33.2506 1.07149
\(964\) 9.32981 0.300493
\(965\) −3.18924 −0.102665
\(966\) −4.61445 −0.148467
\(967\) 27.1270 0.872345 0.436172 0.899863i \(-0.356334\pi\)
0.436172 + 0.899863i \(0.356334\pi\)
\(968\) −7.57392 −0.243435
\(969\) 4.22457 0.135713
\(970\) −39.9812 −1.28372
\(971\) 14.3827 0.461564 0.230782 0.973006i \(-0.425872\pi\)
0.230782 + 0.973006i \(0.425872\pi\)
\(972\) −16.0286 −0.514118
\(973\) −7.84429 −0.251476
\(974\) −32.4030 −1.03826
\(975\) −3.98832 −0.127729
\(976\) 2.88432 0.0923248
\(977\) 17.1218 0.547774 0.273887 0.961762i \(-0.411691\pi\)
0.273887 + 0.961762i \(0.411691\pi\)
\(978\) 6.68524 0.213770
\(979\) −21.7594 −0.695434
\(980\) 18.1983 0.581322
\(981\) 31.2023 0.996211
\(982\) 3.96106 0.126402
\(983\) −14.0672 −0.448675 −0.224338 0.974512i \(-0.572022\pi\)
−0.224338 + 0.974512i \(0.572022\pi\)
\(984\) −2.26643 −0.0722513
\(985\) 1.26199 0.0402103
\(986\) −25.8630 −0.823645
\(987\) 2.68038 0.0853174
\(988\) 1.88529 0.0599789
\(989\) −25.9714 −0.825843
\(990\) −11.5228 −0.366219
\(991\) −2.44087 −0.0775367 −0.0387683 0.999248i \(-0.512343\pi\)
−0.0387683 + 0.999248i \(0.512343\pi\)
\(992\) 2.14709 0.0681702
\(993\) 23.4626 0.744564
\(994\) 2.17654 0.0690357
\(995\) 66.3377 2.10305
\(996\) −4.00053 −0.126762
\(997\) 20.7114 0.655936 0.327968 0.944689i \(-0.393636\pi\)
0.327968 + 0.944689i \(0.393636\pi\)
\(998\) −14.9638 −0.473670
\(999\) 20.5105 0.648924
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 \(a_p\))