Properties

Label 8043.2.a.t.1.18
Level 8043
Weight 2
Character 8043.1
Self dual Yes
Analytic conductor 64.224
Analytic rank 0
Dimension 52
CM No

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Newspace parameters

Level: \( N \) = \( 8043 = 3 \cdot 7 \cdot 383 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8043.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2236783457\)
Analytic rank: \(0\)
Dimension: \(52\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 8043.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.890431 q^{2} -1.00000 q^{3} -1.20713 q^{4} -2.94587 q^{5} +0.890431 q^{6} +1.00000 q^{7} +2.85573 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.890431 q^{2} -1.00000 q^{3} -1.20713 q^{4} -2.94587 q^{5} +0.890431 q^{6} +1.00000 q^{7} +2.85573 q^{8} +1.00000 q^{9} +2.62309 q^{10} +0.179614 q^{11} +1.20713 q^{12} -1.10516 q^{13} -0.890431 q^{14} +2.94587 q^{15} -0.128564 q^{16} +5.29902 q^{17} -0.890431 q^{18} +7.81335 q^{19} +3.55606 q^{20} -1.00000 q^{21} -0.159933 q^{22} -0.108668 q^{23} -2.85573 q^{24} +3.67816 q^{25} +0.984070 q^{26} -1.00000 q^{27} -1.20713 q^{28} +8.19715 q^{29} -2.62309 q^{30} +7.92895 q^{31} -5.59698 q^{32} -0.179614 q^{33} -4.71841 q^{34} -2.94587 q^{35} -1.20713 q^{36} +6.33542 q^{37} -6.95724 q^{38} +1.10516 q^{39} -8.41261 q^{40} +9.17700 q^{41} +0.890431 q^{42} -3.90929 q^{43} -0.216817 q^{44} -2.94587 q^{45} +0.0967615 q^{46} +5.06383 q^{47} +0.128564 q^{48} +1.00000 q^{49} -3.27514 q^{50} -5.29902 q^{51} +1.33408 q^{52} +3.78868 q^{53} +0.890431 q^{54} -0.529118 q^{55} +2.85573 q^{56} -7.81335 q^{57} -7.29899 q^{58} -2.54639 q^{59} -3.55606 q^{60} -3.05804 q^{61} -7.06018 q^{62} +1.00000 q^{63} +5.24085 q^{64} +3.25566 q^{65} +0.159933 q^{66} +12.8695 q^{67} -6.39663 q^{68} +0.108668 q^{69} +2.62309 q^{70} +4.82286 q^{71} +2.85573 q^{72} +11.1792 q^{73} -5.64125 q^{74} -3.67816 q^{75} -9.43175 q^{76} +0.179614 q^{77} -0.984070 q^{78} +8.14904 q^{79} +0.378732 q^{80} +1.00000 q^{81} -8.17148 q^{82} -2.18994 q^{83} +1.20713 q^{84} -15.6102 q^{85} +3.48095 q^{86} -8.19715 q^{87} +0.512928 q^{88} -18.0733 q^{89} +2.62309 q^{90} -1.10516 q^{91} +0.131177 q^{92} -7.92895 q^{93} -4.50899 q^{94} -23.0171 q^{95} +5.59698 q^{96} +3.58909 q^{97} -0.890431 q^{98} +0.179614 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q + 3q^{2} - 52q^{3} + 61q^{4} - 7q^{5} - 3q^{6} + 52q^{7} + 24q^{8} + 52q^{9} + O(q^{10}) \) \( 52q + 3q^{2} - 52q^{3} + 61q^{4} - 7q^{5} - 3q^{6} + 52q^{7} + 24q^{8} + 52q^{9} - 2q^{10} + 9q^{11} - 61q^{12} + 44q^{13} + 3q^{14} + 7q^{15} + 95q^{16} - 6q^{17} + 3q^{18} + 7q^{19} - 21q^{20} - 52q^{21} + 19q^{22} - 4q^{23} - 24q^{24} + 83q^{25} - 5q^{26} - 52q^{27} + 61q^{28} + 31q^{29} + 2q^{30} + 11q^{31} + 71q^{32} - 9q^{33} + 17q^{34} - 7q^{35} + 61q^{36} + 71q^{37} - 8q^{38} - 44q^{39} + 20q^{40} - 25q^{41} - 3q^{42} + 75q^{43} + 14q^{44} - 7q^{45} + 36q^{46} - 20q^{47} - 95q^{48} + 52q^{49} + 26q^{50} + 6q^{51} + 88q^{52} + 70q^{53} - 3q^{54} + 12q^{55} + 24q^{56} - 7q^{57} + 48q^{58} - 27q^{59} + 21q^{60} + 59q^{61} - 23q^{62} + 52q^{63} + 138q^{64} + 44q^{65} - 19q^{66} + 65q^{67} - 8q^{68} + 4q^{69} - 2q^{70} - 11q^{71} + 24q^{72} + 34q^{73} + 38q^{74} - 83q^{75} + 31q^{76} + 9q^{77} + 5q^{78} + 74q^{79} - 5q^{80} + 52q^{81} + 51q^{82} - 30q^{83} - 61q^{84} + 70q^{85} + 29q^{86} - 31q^{87} + 90q^{88} - q^{89} - 2q^{90} + 44q^{91} + 34q^{92} - 11q^{93} + 27q^{94} + 9q^{95} - 71q^{96} + 73q^{97} + 3q^{98} + 9q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.890431 −0.629630 −0.314815 0.949153i \(-0.601942\pi\)
−0.314815 + 0.949153i \(0.601942\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.20713 −0.603567
\(5\) −2.94587 −1.31743 −0.658717 0.752391i \(-0.728900\pi\)
−0.658717 + 0.752391i \(0.728900\pi\)
\(6\) 0.890431 0.363517
\(7\) 1.00000 0.377964
\(8\) 2.85573 1.00965
\(9\) 1.00000 0.333333
\(10\) 2.62309 0.829495
\(11\) 0.179614 0.0541555 0.0270778 0.999633i \(-0.491380\pi\)
0.0270778 + 0.999633i \(0.491380\pi\)
\(12\) 1.20713 0.348469
\(13\) −1.10516 −0.306517 −0.153258 0.988186i \(-0.548977\pi\)
−0.153258 + 0.988186i \(0.548977\pi\)
\(14\) −0.890431 −0.237978
\(15\) 2.94587 0.760621
\(16\) −0.128564 −0.0321409
\(17\) 5.29902 1.28520 0.642601 0.766201i \(-0.277855\pi\)
0.642601 + 0.766201i \(0.277855\pi\)
\(18\) −0.890431 −0.209877
\(19\) 7.81335 1.79250 0.896252 0.443545i \(-0.146279\pi\)
0.896252 + 0.443545i \(0.146279\pi\)
\(20\) 3.55606 0.795159
\(21\) −1.00000 −0.218218
\(22\) −0.159933 −0.0340979
\(23\) −0.108668 −0.0226589 −0.0113294 0.999936i \(-0.503606\pi\)
−0.0113294 + 0.999936i \(0.503606\pi\)
\(24\) −2.85573 −0.582923
\(25\) 3.67816 0.735632
\(26\) 0.984070 0.192992
\(27\) −1.00000 −0.192450
\(28\) −1.20713 −0.228127
\(29\) 8.19715 1.52217 0.761086 0.648651i \(-0.224667\pi\)
0.761086 + 0.648651i \(0.224667\pi\)
\(30\) −2.62309 −0.478909
\(31\) 7.92895 1.42408 0.712040 0.702139i \(-0.247771\pi\)
0.712040 + 0.702139i \(0.247771\pi\)
\(32\) −5.59698 −0.989416
\(33\) −0.179614 −0.0312667
\(34\) −4.71841 −0.809201
\(35\) −2.94587 −0.497943
\(36\) −1.20713 −0.201189
\(37\) 6.33542 1.04154 0.520768 0.853698i \(-0.325646\pi\)
0.520768 + 0.853698i \(0.325646\pi\)
\(38\) −6.95724 −1.12861
\(39\) 1.10516 0.176968
\(40\) −8.41261 −1.33015
\(41\) 9.17700 1.43321 0.716603 0.697481i \(-0.245696\pi\)
0.716603 + 0.697481i \(0.245696\pi\)
\(42\) 0.890431 0.137396
\(43\) −3.90929 −0.596161 −0.298081 0.954541i \(-0.596346\pi\)
−0.298081 + 0.954541i \(0.596346\pi\)
\(44\) −0.216817 −0.0326865
\(45\) −2.94587 −0.439145
\(46\) 0.0967615 0.0142667
\(47\) 5.06383 0.738636 0.369318 0.929303i \(-0.379591\pi\)
0.369318 + 0.929303i \(0.379591\pi\)
\(48\) 0.128564 0.0185565
\(49\) 1.00000 0.142857
\(50\) −3.27514 −0.463175
\(51\) −5.29902 −0.742012
\(52\) 1.33408 0.185003
\(53\) 3.78868 0.520415 0.260207 0.965553i \(-0.416209\pi\)
0.260207 + 0.965553i \(0.416209\pi\)
\(54\) 0.890431 0.121172
\(55\) −0.529118 −0.0713463
\(56\) 2.85573 0.381613
\(57\) −7.81335 −1.03490
\(58\) −7.29899 −0.958405
\(59\) −2.54639 −0.331512 −0.165756 0.986167i \(-0.553006\pi\)
−0.165756 + 0.986167i \(0.553006\pi\)
\(60\) −3.55606 −0.459085
\(61\) −3.05804 −0.391542 −0.195771 0.980650i \(-0.562721\pi\)
−0.195771 + 0.980650i \(0.562721\pi\)
\(62\) −7.06018 −0.896643
\(63\) 1.00000 0.125988
\(64\) 5.24085 0.655107
\(65\) 3.25566 0.403815
\(66\) 0.159933 0.0196864
\(67\) 12.8695 1.57226 0.786130 0.618061i \(-0.212081\pi\)
0.786130 + 0.618061i \(0.212081\pi\)
\(68\) −6.39663 −0.775705
\(69\) 0.108668 0.0130821
\(70\) 2.62309 0.313520
\(71\) 4.82286 0.572368 0.286184 0.958175i \(-0.407613\pi\)
0.286184 + 0.958175i \(0.407613\pi\)
\(72\) 2.85573 0.336551
\(73\) 11.1792 1.30843 0.654215 0.756308i \(-0.272999\pi\)
0.654215 + 0.756308i \(0.272999\pi\)
\(74\) −5.64125 −0.655782
\(75\) −3.67816 −0.424717
\(76\) −9.43175 −1.08190
\(77\) 0.179614 0.0204689
\(78\) −0.984070 −0.111424
\(79\) 8.14904 0.916838 0.458419 0.888736i \(-0.348416\pi\)
0.458419 + 0.888736i \(0.348416\pi\)
\(80\) 0.378732 0.0423435
\(81\) 1.00000 0.111111
\(82\) −8.17148 −0.902389
\(83\) −2.18994 −0.240377 −0.120189 0.992751i \(-0.538350\pi\)
−0.120189 + 0.992751i \(0.538350\pi\)
\(84\) 1.20713 0.131709
\(85\) −15.6102 −1.69317
\(86\) 3.48095 0.375361
\(87\) −8.19715 −0.878826
\(88\) 0.512928 0.0546783
\(89\) −18.0733 −1.91576 −0.957882 0.287161i \(-0.907289\pi\)
−0.957882 + 0.287161i \(0.907289\pi\)
\(90\) 2.62309 0.276498
\(91\) −1.10516 −0.115852
\(92\) 0.131177 0.0136761
\(93\) −7.92895 −0.822193
\(94\) −4.50899 −0.465067
\(95\) −23.0171 −2.36151
\(96\) 5.59698 0.571240
\(97\) 3.58909 0.364416 0.182208 0.983260i \(-0.441675\pi\)
0.182208 + 0.983260i \(0.441675\pi\)
\(98\) −0.890431 −0.0899471
\(99\) 0.179614 0.0180518
\(100\) −4.44003 −0.444003
\(101\) −6.96029 −0.692575 −0.346287 0.938128i \(-0.612558\pi\)
−0.346287 + 0.938128i \(0.612558\pi\)
\(102\) 4.71841 0.467192
\(103\) −8.75017 −0.862180 −0.431090 0.902309i \(-0.641871\pi\)
−0.431090 + 0.902309i \(0.641871\pi\)
\(104\) −3.15604 −0.309476
\(105\) 2.94587 0.287488
\(106\) −3.37355 −0.327668
\(107\) 17.6296 1.70432 0.852158 0.523285i \(-0.175294\pi\)
0.852158 + 0.523285i \(0.175294\pi\)
\(108\) 1.20713 0.116156
\(109\) 18.1317 1.73670 0.868349 0.495954i \(-0.165182\pi\)
0.868349 + 0.495954i \(0.165182\pi\)
\(110\) 0.471143 0.0449217
\(111\) −6.33542 −0.601331
\(112\) −0.128564 −0.0121481
\(113\) −18.2232 −1.71430 −0.857149 0.515069i \(-0.827766\pi\)
−0.857149 + 0.515069i \(0.827766\pi\)
\(114\) 6.95724 0.651605
\(115\) 0.320123 0.0298516
\(116\) −9.89505 −0.918732
\(117\) −1.10516 −0.102172
\(118\) 2.26738 0.208730
\(119\) 5.29902 0.485761
\(120\) 8.41261 0.767963
\(121\) −10.9677 −0.997067
\(122\) 2.72297 0.246527
\(123\) −9.17700 −0.827462
\(124\) −9.57129 −0.859527
\(125\) 3.89398 0.348288
\(126\) −0.890431 −0.0793259
\(127\) −17.4437 −1.54788 −0.773941 0.633258i \(-0.781717\pi\)
−0.773941 + 0.633258i \(0.781717\pi\)
\(128\) 6.52735 0.576942
\(129\) 3.90929 0.344194
\(130\) −2.89894 −0.254254
\(131\) 0.203233 0.0177566 0.00887829 0.999961i \(-0.497174\pi\)
0.00887829 + 0.999961i \(0.497174\pi\)
\(132\) 0.216817 0.0188715
\(133\) 7.81335 0.677503
\(134\) −11.4594 −0.989942
\(135\) 2.94587 0.253540
\(136\) 15.1326 1.29761
\(137\) 17.0426 1.45604 0.728022 0.685554i \(-0.240440\pi\)
0.728022 + 0.685554i \(0.240440\pi\)
\(138\) −0.0967615 −0.00823689
\(139\) −10.6387 −0.902359 −0.451179 0.892433i \(-0.648997\pi\)
−0.451179 + 0.892433i \(0.648997\pi\)
\(140\) 3.55606 0.300542
\(141\) −5.06383 −0.426452
\(142\) −4.29442 −0.360380
\(143\) −0.198502 −0.0165996
\(144\) −0.128564 −0.0107136
\(145\) −24.1477 −2.00536
\(146\) −9.95433 −0.823827
\(147\) −1.00000 −0.0824786
\(148\) −7.64769 −0.628637
\(149\) −23.8580 −1.95453 −0.977264 0.212027i \(-0.931993\pi\)
−0.977264 + 0.212027i \(0.931993\pi\)
\(150\) 3.27514 0.267414
\(151\) −2.24687 −0.182848 −0.0914238 0.995812i \(-0.529142\pi\)
−0.0914238 + 0.995812i \(0.529142\pi\)
\(152\) 22.3128 1.80981
\(153\) 5.29902 0.428401
\(154\) −0.159933 −0.0128878
\(155\) −23.3577 −1.87613
\(156\) −1.33408 −0.106812
\(157\) 17.3498 1.38467 0.692333 0.721578i \(-0.256583\pi\)
0.692333 + 0.721578i \(0.256583\pi\)
\(158\) −7.25615 −0.577269
\(159\) −3.78868 −0.300462
\(160\) 16.4880 1.30349
\(161\) −0.108668 −0.00856425
\(162\) −0.890431 −0.0699588
\(163\) −1.99087 −0.155937 −0.0779685 0.996956i \(-0.524843\pi\)
−0.0779685 + 0.996956i \(0.524843\pi\)
\(164\) −11.0779 −0.865035
\(165\) 0.529118 0.0411918
\(166\) 1.94999 0.151349
\(167\) 6.68332 0.517171 0.258586 0.965988i \(-0.416744\pi\)
0.258586 + 0.965988i \(0.416744\pi\)
\(168\) −2.85573 −0.220324
\(169\) −11.7786 −0.906047
\(170\) 13.8998 1.06607
\(171\) 7.81335 0.597501
\(172\) 4.71904 0.359823
\(173\) −4.49817 −0.341989 −0.170995 0.985272i \(-0.554698\pi\)
−0.170995 + 0.985272i \(0.554698\pi\)
\(174\) 7.29899 0.553335
\(175\) 3.67816 0.278043
\(176\) −0.0230918 −0.00174061
\(177\) 2.54639 0.191398
\(178\) 16.0930 1.20622
\(179\) −19.2849 −1.44142 −0.720710 0.693237i \(-0.756184\pi\)
−0.720710 + 0.693237i \(0.756184\pi\)
\(180\) 3.55606 0.265053
\(181\) 22.3462 1.66098 0.830490 0.557034i \(-0.188061\pi\)
0.830490 + 0.557034i \(0.188061\pi\)
\(182\) 0.984070 0.0729441
\(183\) 3.05804 0.226057
\(184\) −0.310327 −0.0228776
\(185\) −18.6633 −1.37216
\(186\) 7.06018 0.517677
\(187\) 0.951776 0.0696008
\(188\) −6.11272 −0.445816
\(189\) −1.00000 −0.0727393
\(190\) 20.4951 1.48687
\(191\) 3.26969 0.236586 0.118293 0.992979i \(-0.462258\pi\)
0.118293 + 0.992979i \(0.462258\pi\)
\(192\) −5.24085 −0.378226
\(193\) 23.0322 1.65790 0.828948 0.559325i \(-0.188940\pi\)
0.828948 + 0.559325i \(0.188940\pi\)
\(194\) −3.19583 −0.229447
\(195\) −3.25566 −0.233143
\(196\) −1.20713 −0.0862238
\(197\) 1.86990 0.133225 0.0666123 0.997779i \(-0.478781\pi\)
0.0666123 + 0.997779i \(0.478781\pi\)
\(198\) −0.159933 −0.0113660
\(199\) 5.49704 0.389675 0.194837 0.980836i \(-0.437582\pi\)
0.194837 + 0.980836i \(0.437582\pi\)
\(200\) 10.5038 0.742733
\(201\) −12.8695 −0.907745
\(202\) 6.19766 0.436066
\(203\) 8.19715 0.575327
\(204\) 6.39663 0.447853
\(205\) −27.0342 −1.88815
\(206\) 7.79142 0.542854
\(207\) −0.108668 −0.00755296
\(208\) 0.142084 0.00985172
\(209\) 1.40338 0.0970740
\(210\) −2.62309 −0.181011
\(211\) 21.6086 1.48759 0.743797 0.668405i \(-0.233023\pi\)
0.743797 + 0.668405i \(0.233023\pi\)
\(212\) −4.57344 −0.314105
\(213\) −4.82286 −0.330457
\(214\) −15.6979 −1.07309
\(215\) 11.5163 0.785403
\(216\) −2.85573 −0.194308
\(217\) 7.92895 0.538252
\(218\) −16.1450 −1.09348
\(219\) −11.1792 −0.755423
\(220\) 0.638716 0.0430622
\(221\) −5.85628 −0.393936
\(222\) 5.64125 0.378616
\(223\) −9.50590 −0.636562 −0.318281 0.947996i \(-0.603106\pi\)
−0.318281 + 0.947996i \(0.603106\pi\)
\(224\) −5.59698 −0.373964
\(225\) 3.67816 0.245211
\(226\) 16.2265 1.07937
\(227\) 8.04296 0.533830 0.266915 0.963720i \(-0.413996\pi\)
0.266915 + 0.963720i \(0.413996\pi\)
\(228\) 9.43175 0.624633
\(229\) 25.4483 1.68167 0.840834 0.541293i \(-0.182065\pi\)
0.840834 + 0.541293i \(0.182065\pi\)
\(230\) −0.285047 −0.0187954
\(231\) −0.179614 −0.0118177
\(232\) 23.4088 1.53687
\(233\) 6.54227 0.428598 0.214299 0.976768i \(-0.431253\pi\)
0.214299 + 0.976768i \(0.431253\pi\)
\(234\) 0.984070 0.0643307
\(235\) −14.9174 −0.973104
\(236\) 3.07383 0.200089
\(237\) −8.14904 −0.529337
\(238\) −4.71841 −0.305849
\(239\) −4.76519 −0.308235 −0.154117 0.988053i \(-0.549253\pi\)
−0.154117 + 0.988053i \(0.549253\pi\)
\(240\) −0.378732 −0.0244470
\(241\) −23.1446 −1.49087 −0.745437 0.666576i \(-0.767759\pi\)
−0.745437 + 0.666576i \(0.767759\pi\)
\(242\) 9.76601 0.627783
\(243\) −1.00000 −0.0641500
\(244\) 3.69146 0.236322
\(245\) −2.94587 −0.188205
\(246\) 8.17148 0.520994
\(247\) −8.63501 −0.549433
\(248\) 22.6429 1.43783
\(249\) 2.18994 0.138782
\(250\) −3.46732 −0.219292
\(251\) −17.9686 −1.13417 −0.567084 0.823660i \(-0.691928\pi\)
−0.567084 + 0.823660i \(0.691928\pi\)
\(252\) −1.20713 −0.0760422
\(253\) −0.0195183 −0.00122710
\(254\) 15.5324 0.974592
\(255\) 15.6102 0.977551
\(256\) −16.2939 −1.01837
\(257\) −20.7887 −1.29676 −0.648381 0.761316i \(-0.724554\pi\)
−0.648381 + 0.761316i \(0.724554\pi\)
\(258\) −3.48095 −0.216715
\(259\) 6.33542 0.393664
\(260\) −3.93002 −0.243730
\(261\) 8.19715 0.507391
\(262\) −0.180965 −0.0111801
\(263\) −1.97070 −0.121519 −0.0607593 0.998152i \(-0.519352\pi\)
−0.0607593 + 0.998152i \(0.519352\pi\)
\(264\) −0.512928 −0.0315685
\(265\) −11.1610 −0.685612
\(266\) −6.95724 −0.426576
\(267\) 18.0733 1.10607
\(268\) −15.5352 −0.948964
\(269\) −0.0240334 −0.00146534 −0.000732670 1.00000i \(-0.500233\pi\)
−0.000732670 1.00000i \(0.500233\pi\)
\(270\) −2.62309 −0.159636
\(271\) −31.5550 −1.91683 −0.958416 0.285374i \(-0.907882\pi\)
−0.958416 + 0.285374i \(0.907882\pi\)
\(272\) −0.681261 −0.0413075
\(273\) 1.10516 0.0668874
\(274\) −15.1752 −0.916768
\(275\) 0.660647 0.0398385
\(276\) −0.131177 −0.00789593
\(277\) −21.0207 −1.26301 −0.631506 0.775371i \(-0.717563\pi\)
−0.631506 + 0.775371i \(0.717563\pi\)
\(278\) 9.47299 0.568152
\(279\) 7.92895 0.474694
\(280\) −8.41261 −0.502750
\(281\) −2.03809 −0.121582 −0.0607910 0.998151i \(-0.519362\pi\)
−0.0607910 + 0.998151i \(0.519362\pi\)
\(282\) 4.50899 0.268507
\(283\) 2.37671 0.141281 0.0706404 0.997502i \(-0.477496\pi\)
0.0706404 + 0.997502i \(0.477496\pi\)
\(284\) −5.82183 −0.345462
\(285\) 23.0171 1.36342
\(286\) 0.176752 0.0104516
\(287\) 9.17700 0.541701
\(288\) −5.59698 −0.329805
\(289\) 11.0796 0.651744
\(290\) 21.5019 1.26263
\(291\) −3.58909 −0.210396
\(292\) −13.4948 −0.789725
\(293\) −1.11171 −0.0649466 −0.0324733 0.999473i \(-0.510338\pi\)
−0.0324733 + 0.999473i \(0.510338\pi\)
\(294\) 0.890431 0.0519310
\(295\) 7.50133 0.436745
\(296\) 18.0922 1.05159
\(297\) −0.179614 −0.0104222
\(298\) 21.2439 1.23063
\(299\) 0.120096 0.00694533
\(300\) 4.44003 0.256345
\(301\) −3.90929 −0.225328
\(302\) 2.00068 0.115126
\(303\) 6.96029 0.399858
\(304\) −1.00451 −0.0576127
\(305\) 9.00860 0.515831
\(306\) −4.71841 −0.269734
\(307\) 9.80791 0.559767 0.279883 0.960034i \(-0.409704\pi\)
0.279883 + 0.960034i \(0.409704\pi\)
\(308\) −0.216817 −0.0123543
\(309\) 8.75017 0.497780
\(310\) 20.7984 1.18127
\(311\) −2.01734 −0.114393 −0.0571965 0.998363i \(-0.518216\pi\)
−0.0571965 + 0.998363i \(0.518216\pi\)
\(312\) 3.15604 0.178676
\(313\) 5.85414 0.330896 0.165448 0.986219i \(-0.447093\pi\)
0.165448 + 0.986219i \(0.447093\pi\)
\(314\) −15.4488 −0.871827
\(315\) −2.94587 −0.165981
\(316\) −9.83697 −0.553373
\(317\) −4.04197 −0.227020 −0.113510 0.993537i \(-0.536209\pi\)
−0.113510 + 0.993537i \(0.536209\pi\)
\(318\) 3.37355 0.189179
\(319\) 1.47232 0.0824340
\(320\) −15.4389 −0.863059
\(321\) −17.6296 −0.983987
\(322\) 0.0967615 0.00539231
\(323\) 41.4031 2.30373
\(324\) −1.20713 −0.0670629
\(325\) −4.06496 −0.225483
\(326\) 1.77273 0.0981826
\(327\) −18.1317 −1.00268
\(328\) 26.2070 1.44704
\(329\) 5.06383 0.279178
\(330\) −0.471143 −0.0259356
\(331\) 32.8278 1.80438 0.902189 0.431341i \(-0.141959\pi\)
0.902189 + 0.431341i \(0.141959\pi\)
\(332\) 2.64355 0.145084
\(333\) 6.33542 0.347179
\(334\) −5.95104 −0.325626
\(335\) −37.9119 −2.07135
\(336\) 0.128564 0.00701372
\(337\) −3.12536 −0.170249 −0.0851246 0.996370i \(-0.527129\pi\)
−0.0851246 + 0.996370i \(0.527129\pi\)
\(338\) 10.4880 0.570474
\(339\) 18.2232 0.989750
\(340\) 18.8436 1.02194
\(341\) 1.42415 0.0771218
\(342\) −6.95724 −0.376205
\(343\) 1.00000 0.0539949
\(344\) −11.1639 −0.601916
\(345\) −0.320123 −0.0172348
\(346\) 4.00530 0.215327
\(347\) −5.18110 −0.278136 −0.139068 0.990283i \(-0.544411\pi\)
−0.139068 + 0.990283i \(0.544411\pi\)
\(348\) 9.89505 0.530430
\(349\) 6.95601 0.372347 0.186173 0.982517i \(-0.440391\pi\)
0.186173 + 0.982517i \(0.440391\pi\)
\(350\) −3.27514 −0.175064
\(351\) 1.10516 0.0589892
\(352\) −1.00529 −0.0535823
\(353\) 23.4941 1.25047 0.625233 0.780438i \(-0.285004\pi\)
0.625233 + 0.780438i \(0.285004\pi\)
\(354\) −2.26738 −0.120510
\(355\) −14.2075 −0.754056
\(356\) 21.8169 1.15629
\(357\) −5.29902 −0.280454
\(358\) 17.1719 0.907561
\(359\) −2.70150 −0.142580 −0.0712898 0.997456i \(-0.522712\pi\)
−0.0712898 + 0.997456i \(0.522712\pi\)
\(360\) −8.41261 −0.443384
\(361\) 42.0484 2.21307
\(362\) −19.8977 −1.04580
\(363\) 10.9677 0.575657
\(364\) 1.33408 0.0699247
\(365\) −32.9326 −1.72377
\(366\) −2.72297 −0.142332
\(367\) 22.5269 1.17590 0.587948 0.808899i \(-0.299936\pi\)
0.587948 + 0.808899i \(0.299936\pi\)
\(368\) 0.0139708 0.000728277 0
\(369\) 9.17700 0.477735
\(370\) 16.6184 0.863950
\(371\) 3.78868 0.196698
\(372\) 9.57129 0.496248
\(373\) 18.5352 0.959714 0.479857 0.877347i \(-0.340689\pi\)
0.479857 + 0.877347i \(0.340689\pi\)
\(374\) −0.847491 −0.0438227
\(375\) −3.89398 −0.201084
\(376\) 14.4609 0.745766
\(377\) −9.05917 −0.466571
\(378\) 0.890431 0.0457988
\(379\) 29.6595 1.52351 0.761754 0.647866i \(-0.224339\pi\)
0.761754 + 0.647866i \(0.224339\pi\)
\(380\) 27.7847 1.42533
\(381\) 17.4437 0.893670
\(382\) −2.91143 −0.148962
\(383\) −1.00000 −0.0510976
\(384\) −6.52735 −0.333097
\(385\) −0.529118 −0.0269664
\(386\) −20.5086 −1.04386
\(387\) −3.90929 −0.198720
\(388\) −4.33250 −0.219950
\(389\) 15.9439 0.808389 0.404194 0.914673i \(-0.367552\pi\)
0.404194 + 0.914673i \(0.367552\pi\)
\(390\) 2.89894 0.146794
\(391\) −0.575835 −0.0291212
\(392\) 2.85573 0.144236
\(393\) −0.203233 −0.0102518
\(394\) −1.66501 −0.0838821
\(395\) −24.0060 −1.20787
\(396\) −0.216817 −0.0108955
\(397\) −23.5523 −1.18206 −0.591028 0.806651i \(-0.701278\pi\)
−0.591028 + 0.806651i \(0.701278\pi\)
\(398\) −4.89473 −0.245351
\(399\) −7.81335 −0.391157
\(400\) −0.472877 −0.0236438
\(401\) −23.9425 −1.19563 −0.597815 0.801634i \(-0.703964\pi\)
−0.597815 + 0.801634i \(0.703964\pi\)
\(402\) 11.4594 0.571543
\(403\) −8.76277 −0.436505
\(404\) 8.40200 0.418015
\(405\) −2.94587 −0.146382
\(406\) −7.29899 −0.362243
\(407\) 1.13793 0.0564050
\(408\) −15.1326 −0.749174
\(409\) −27.8489 −1.37704 −0.688521 0.725217i \(-0.741740\pi\)
−0.688521 + 0.725217i \(0.741740\pi\)
\(410\) 24.0721 1.18884
\(411\) −17.0426 −0.840647
\(412\) 10.5626 0.520383
\(413\) −2.54639 −0.125300
\(414\) 0.0967615 0.00475557
\(415\) 6.45129 0.316681
\(416\) 6.18557 0.303273
\(417\) 10.6387 0.520977
\(418\) −1.24961 −0.0611207
\(419\) −14.5369 −0.710176 −0.355088 0.934833i \(-0.615549\pi\)
−0.355088 + 0.934833i \(0.615549\pi\)
\(420\) −3.55606 −0.173518
\(421\) 2.89161 0.140928 0.0704641 0.997514i \(-0.477552\pi\)
0.0704641 + 0.997514i \(0.477552\pi\)
\(422\) −19.2409 −0.936634
\(423\) 5.06383 0.246212
\(424\) 10.8194 0.525438
\(425\) 19.4906 0.945435
\(426\) 4.29442 0.208065
\(427\) −3.05804 −0.147989
\(428\) −21.2813 −1.02867
\(429\) 0.198502 0.00958377
\(430\) −10.2544 −0.494513
\(431\) −20.4085 −0.983043 −0.491521 0.870865i \(-0.663559\pi\)
−0.491521 + 0.870865i \(0.663559\pi\)
\(432\) 0.128564 0.00618552
\(433\) −13.3664 −0.642350 −0.321175 0.947020i \(-0.604078\pi\)
−0.321175 + 0.947020i \(0.604078\pi\)
\(434\) −7.06018 −0.338899
\(435\) 24.1477 1.15780
\(436\) −21.8873 −1.04821
\(437\) −0.849062 −0.0406162
\(438\) 9.95433 0.475636
\(439\) −3.69398 −0.176304 −0.0881520 0.996107i \(-0.528096\pi\)
−0.0881520 + 0.996107i \(0.528096\pi\)
\(440\) −1.51102 −0.0720350
\(441\) 1.00000 0.0476190
\(442\) 5.21461 0.248034
\(443\) 1.01285 0.0481222 0.0240611 0.999710i \(-0.492340\pi\)
0.0240611 + 0.999710i \(0.492340\pi\)
\(444\) 7.64769 0.362944
\(445\) 53.2416 2.52389
\(446\) 8.46435 0.400798
\(447\) 23.8580 1.12845
\(448\) 5.24085 0.247607
\(449\) 10.7969 0.509537 0.254769 0.967002i \(-0.418001\pi\)
0.254769 + 0.967002i \(0.418001\pi\)
\(450\) −3.27514 −0.154392
\(451\) 1.64831 0.0776160
\(452\) 21.9979 1.03469
\(453\) 2.24687 0.105567
\(454\) −7.16170 −0.336115
\(455\) 3.25566 0.152628
\(456\) −22.3128 −1.04489
\(457\) 14.5257 0.679482 0.339741 0.940519i \(-0.389661\pi\)
0.339741 + 0.940519i \(0.389661\pi\)
\(458\) −22.6599 −1.05883
\(459\) −5.29902 −0.247337
\(460\) −0.386430 −0.0180174
\(461\) −5.73860 −0.267273 −0.133637 0.991030i \(-0.542666\pi\)
−0.133637 + 0.991030i \(0.542666\pi\)
\(462\) 0.159933 0.00744078
\(463\) −12.6109 −0.586080 −0.293040 0.956100i \(-0.594667\pi\)
−0.293040 + 0.956100i \(0.594667\pi\)
\(464\) −1.05385 −0.0489240
\(465\) 23.3577 1.08319
\(466\) −5.82544 −0.269858
\(467\) −24.1168 −1.11599 −0.557997 0.829843i \(-0.688430\pi\)
−0.557997 + 0.829843i \(0.688430\pi\)
\(468\) 1.33408 0.0616677
\(469\) 12.8695 0.594259
\(470\) 13.2829 0.612695
\(471\) −17.3498 −0.799438
\(472\) −7.27180 −0.334712
\(473\) −0.702162 −0.0322854
\(474\) 7.25615 0.333286
\(475\) 28.7387 1.31862
\(476\) −6.39663 −0.293189
\(477\) 3.78868 0.173472
\(478\) 4.24307 0.194074
\(479\) 27.9106 1.27527 0.637635 0.770339i \(-0.279913\pi\)
0.637635 + 0.770339i \(0.279913\pi\)
\(480\) −16.4880 −0.752570
\(481\) −7.00166 −0.319248
\(482\) 20.6087 0.938698
\(483\) 0.108668 0.00494457
\(484\) 13.2395 0.601796
\(485\) −10.5730 −0.480095
\(486\) 0.890431 0.0403908
\(487\) 21.1250 0.957263 0.478632 0.878016i \(-0.341133\pi\)
0.478632 + 0.878016i \(0.341133\pi\)
\(488\) −8.73294 −0.395322
\(489\) 1.99087 0.0900303
\(490\) 2.62309 0.118499
\(491\) 24.7918 1.11884 0.559420 0.828885i \(-0.311024\pi\)
0.559420 + 0.828885i \(0.311024\pi\)
\(492\) 11.0779 0.499428
\(493\) 43.4369 1.95630
\(494\) 7.68888 0.345939
\(495\) −0.529118 −0.0237821
\(496\) −1.01937 −0.0457712
\(497\) 4.82286 0.216335
\(498\) −1.94999 −0.0873812
\(499\) 5.84699 0.261747 0.130874 0.991399i \(-0.458222\pi\)
0.130874 + 0.991399i \(0.458222\pi\)
\(500\) −4.70055 −0.210215
\(501\) −6.68332 −0.298589
\(502\) 15.9998 0.714106
\(503\) 2.96347 0.132134 0.0660672 0.997815i \(-0.478955\pi\)
0.0660672 + 0.997815i \(0.478955\pi\)
\(504\) 2.85573 0.127204
\(505\) 20.5041 0.912422
\(506\) 0.0173797 0.000772621 0
\(507\) 11.7786 0.523107
\(508\) 21.0569 0.934249
\(509\) −15.6701 −0.694566 −0.347283 0.937760i \(-0.612896\pi\)
−0.347283 + 0.937760i \(0.612896\pi\)
\(510\) −13.8998 −0.615495
\(511\) 11.1792 0.494540
\(512\) 1.45385 0.0642519
\(513\) −7.81335 −0.344968
\(514\) 18.5109 0.816480
\(515\) 25.7769 1.13586
\(516\) −4.71904 −0.207744
\(517\) 0.909533 0.0400012
\(518\) −5.64125 −0.247862
\(519\) 4.49817 0.197448
\(520\) 9.29730 0.407713
\(521\) 16.4535 0.720842 0.360421 0.932790i \(-0.382633\pi\)
0.360421 + 0.932790i \(0.382633\pi\)
\(522\) −7.29899 −0.319468
\(523\) −2.50744 −0.109643 −0.0548213 0.998496i \(-0.517459\pi\)
−0.0548213 + 0.998496i \(0.517459\pi\)
\(524\) −0.245330 −0.0107173
\(525\) −3.67816 −0.160528
\(526\) 1.75477 0.0765118
\(527\) 42.0157 1.83023
\(528\) 0.0230918 0.00100494
\(529\) −22.9882 −0.999487
\(530\) 9.93805 0.431681
\(531\) −2.54639 −0.110504
\(532\) −9.43175 −0.408918
\(533\) −10.1421 −0.439302
\(534\) −16.0930 −0.696413
\(535\) −51.9345 −2.24532
\(536\) 36.7518 1.58744
\(537\) 19.2849 0.832204
\(538\) 0.0214000 0.000922621 0
\(539\) 0.179614 0.00773650
\(540\) −3.55606 −0.153028
\(541\) 30.3724 1.30581 0.652905 0.757439i \(-0.273550\pi\)
0.652905 + 0.757439i \(0.273550\pi\)
\(542\) 28.0976 1.20689
\(543\) −22.3462 −0.958967
\(544\) −29.6585 −1.27160
\(545\) −53.4135 −2.28798
\(546\) −0.984070 −0.0421143
\(547\) 1.19088 0.0509183 0.0254591 0.999676i \(-0.491895\pi\)
0.0254591 + 0.999676i \(0.491895\pi\)
\(548\) −20.5726 −0.878819
\(549\) −3.05804 −0.130514
\(550\) −0.588260 −0.0250835
\(551\) 64.0471 2.72850
\(552\) 0.310327 0.0132084
\(553\) 8.14904 0.346532
\(554\) 18.7175 0.795230
\(555\) 18.6633 0.792214
\(556\) 12.8423 0.544634
\(557\) −27.8643 −1.18065 −0.590324 0.807166i \(-0.701000\pi\)
−0.590324 + 0.807166i \(0.701000\pi\)
\(558\) −7.06018 −0.298881
\(559\) 4.32040 0.182733
\(560\) 0.378732 0.0160043
\(561\) −0.951776 −0.0401840
\(562\) 1.81477 0.0765516
\(563\) −16.8300 −0.709299 −0.354649 0.934999i \(-0.615400\pi\)
−0.354649 + 0.934999i \(0.615400\pi\)
\(564\) 6.11272 0.257392
\(565\) 53.6833 2.25847
\(566\) −2.11630 −0.0889546
\(567\) 1.00000 0.0419961
\(568\) 13.7728 0.577893
\(569\) −33.8841 −1.42050 −0.710248 0.703952i \(-0.751417\pi\)
−0.710248 + 0.703952i \(0.751417\pi\)
\(570\) −20.4951 −0.858447
\(571\) 4.55793 0.190743 0.0953717 0.995442i \(-0.469596\pi\)
0.0953717 + 0.995442i \(0.469596\pi\)
\(572\) 0.239618 0.0100189
\(573\) −3.26969 −0.136593
\(574\) −8.17148 −0.341071
\(575\) −0.399699 −0.0166686
\(576\) 5.24085 0.218369
\(577\) 44.1403 1.83758 0.918792 0.394742i \(-0.129166\pi\)
0.918792 + 0.394742i \(0.129166\pi\)
\(578\) −9.86566 −0.410357
\(579\) −23.0322 −0.957187
\(580\) 29.1495 1.21037
\(581\) −2.18994 −0.0908541
\(582\) 3.19583 0.132472
\(583\) 0.680497 0.0281833
\(584\) 31.9249 1.32106
\(585\) 3.25566 0.134605
\(586\) 0.989898 0.0408923
\(587\) 41.3913 1.70840 0.854201 0.519943i \(-0.174047\pi\)
0.854201 + 0.519943i \(0.174047\pi\)
\(588\) 1.20713 0.0497813
\(589\) 61.9516 2.55267
\(590\) −6.67942 −0.274987
\(591\) −1.86990 −0.0769172
\(592\) −0.814504 −0.0334759
\(593\) −16.9202 −0.694831 −0.347416 0.937711i \(-0.612941\pi\)
−0.347416 + 0.937711i \(0.612941\pi\)
\(594\) 0.159933 0.00656215
\(595\) −15.6102 −0.639957
\(596\) 28.7998 1.17969
\(597\) −5.49704 −0.224979
\(598\) −0.106937 −0.00437298
\(599\) 30.7165 1.25504 0.627522 0.778599i \(-0.284069\pi\)
0.627522 + 0.778599i \(0.284069\pi\)
\(600\) −10.5038 −0.428817
\(601\) 9.87946 0.402991 0.201496 0.979489i \(-0.435420\pi\)
0.201496 + 0.979489i \(0.435420\pi\)
\(602\) 3.48095 0.141873
\(603\) 12.8695 0.524087
\(604\) 2.71227 0.110361
\(605\) 32.3095 1.31357
\(606\) −6.19766 −0.251763
\(607\) 11.3103 0.459072 0.229536 0.973300i \(-0.426279\pi\)
0.229536 + 0.973300i \(0.426279\pi\)
\(608\) −43.7312 −1.77353
\(609\) −8.19715 −0.332165
\(610\) −8.02153 −0.324782
\(611\) −5.59635 −0.226404
\(612\) −6.39663 −0.258568
\(613\) 17.9127 0.723489 0.361744 0.932277i \(-0.382181\pi\)
0.361744 + 0.932277i \(0.382181\pi\)
\(614\) −8.73326 −0.352446
\(615\) 27.0342 1.09013
\(616\) 0.512928 0.0206664
\(617\) 35.7533 1.43938 0.719688 0.694298i \(-0.244285\pi\)
0.719688 + 0.694298i \(0.244285\pi\)
\(618\) −7.79142 −0.313417
\(619\) −4.52029 −0.181686 −0.0908429 0.995865i \(-0.528956\pi\)
−0.0908429 + 0.995865i \(0.528956\pi\)
\(620\) 28.1958 1.13237
\(621\) 0.108668 0.00436070
\(622\) 1.79630 0.0720252
\(623\) −18.0733 −0.724091
\(624\) −0.142084 −0.00568789
\(625\) −29.8619 −1.19448
\(626\) −5.21271 −0.208342
\(627\) −1.40338 −0.0560457
\(628\) −20.9435 −0.835739
\(629\) 33.5715 1.33858
\(630\) 2.62309 0.104507
\(631\) −20.4559 −0.814337 −0.407168 0.913353i \(-0.633484\pi\)
−0.407168 + 0.913353i \(0.633484\pi\)
\(632\) 23.2715 0.925689
\(633\) −21.6086 −0.858863
\(634\) 3.59910 0.142938
\(635\) 51.3870 2.03923
\(636\) 4.57344 0.181349
\(637\) −1.10516 −0.0437881
\(638\) −1.31100 −0.0519029
\(639\) 4.82286 0.190789
\(640\) −19.2287 −0.760082
\(641\) −34.5673 −1.36532 −0.682662 0.730734i \(-0.739178\pi\)
−0.682662 + 0.730734i \(0.739178\pi\)
\(642\) 15.6979 0.619548
\(643\) 4.81828 0.190014 0.0950071 0.995477i \(-0.469713\pi\)
0.0950071 + 0.995477i \(0.469713\pi\)
\(644\) 0.131177 0.00516910
\(645\) −11.5163 −0.453453
\(646\) −36.8666 −1.45050
\(647\) −24.1169 −0.948132 −0.474066 0.880489i \(-0.657214\pi\)
−0.474066 + 0.880489i \(0.657214\pi\)
\(648\) 2.85573 0.112184
\(649\) −0.457366 −0.0179532
\(650\) 3.61956 0.141971
\(651\) −7.92895 −0.310760
\(652\) 2.40325 0.0941184
\(653\) −33.1468 −1.29714 −0.648568 0.761157i \(-0.724632\pi\)
−0.648568 + 0.761157i \(0.724632\pi\)
\(654\) 16.1450 0.631319
\(655\) −0.598699 −0.0233931
\(656\) −1.17983 −0.0460645
\(657\) 11.1792 0.436143
\(658\) −4.50899 −0.175779
\(659\) −12.3931 −0.482768 −0.241384 0.970430i \(-0.577601\pi\)
−0.241384 + 0.970430i \(0.577601\pi\)
\(660\) −0.638716 −0.0248620
\(661\) 10.8871 0.423460 0.211730 0.977328i \(-0.432090\pi\)
0.211730 + 0.977328i \(0.432090\pi\)
\(662\) −29.2309 −1.13609
\(663\) 5.85628 0.227439
\(664\) −6.25388 −0.242698
\(665\) −23.0171 −0.892565
\(666\) −5.64125 −0.218594
\(667\) −0.890769 −0.0344907
\(668\) −8.06766 −0.312147
\(669\) 9.50590 0.367519
\(670\) 33.7579 1.30418
\(671\) −0.549266 −0.0212042
\(672\) 5.59698 0.215908
\(673\) −42.7063 −1.64621 −0.823104 0.567891i \(-0.807759\pi\)
−0.823104 + 0.567891i \(0.807759\pi\)
\(674\) 2.78292 0.107194
\(675\) −3.67816 −0.141572
\(676\) 14.2184 0.546860
\(677\) −50.2974 −1.93309 −0.966544 0.256501i \(-0.917430\pi\)
−0.966544 + 0.256501i \(0.917430\pi\)
\(678\) −16.2265 −0.623176
\(679\) 3.58909 0.137736
\(680\) −44.5786 −1.70951
\(681\) −8.04296 −0.308207
\(682\) −1.26810 −0.0485582
\(683\) 11.5889 0.443437 0.221718 0.975111i \(-0.428833\pi\)
0.221718 + 0.975111i \(0.428833\pi\)
\(684\) −9.43175 −0.360632
\(685\) −50.2052 −1.91824
\(686\) −0.890431 −0.0339968
\(687\) −25.4483 −0.970912
\(688\) 0.502592 0.0191612
\(689\) −4.18710 −0.159516
\(690\) 0.285047 0.0108516
\(691\) 22.0525 0.838918 0.419459 0.907774i \(-0.362220\pi\)
0.419459 + 0.907774i \(0.362220\pi\)
\(692\) 5.42988 0.206413
\(693\) 0.179614 0.00682295
\(694\) 4.61341 0.175123
\(695\) 31.3401 1.18880
\(696\) −23.4088 −0.887310
\(697\) 48.6291 1.84196
\(698\) −6.19384 −0.234440
\(699\) −6.54227 −0.247451
\(700\) −4.44003 −0.167817
\(701\) 11.4967 0.434225 0.217113 0.976147i \(-0.430336\pi\)
0.217113 + 0.976147i \(0.430336\pi\)
\(702\) −0.984070 −0.0371413
\(703\) 49.5008 1.86696
\(704\) 0.941328 0.0354776
\(705\) 14.9174 0.561822
\(706\) −20.9199 −0.787330
\(707\) −6.96029 −0.261769
\(708\) −3.07383 −0.115522
\(709\) 25.9943 0.976237 0.488119 0.872777i \(-0.337683\pi\)
0.488119 + 0.872777i \(0.337683\pi\)
\(710\) 12.6508 0.474776
\(711\) 8.14904 0.305613
\(712\) −51.6124 −1.93426
\(713\) −0.861624 −0.0322681
\(714\) 4.71841 0.176582
\(715\) 0.584761 0.0218688
\(716\) 23.2794 0.869993
\(717\) 4.76519 0.177959
\(718\) 2.40550 0.0897723
\(719\) −15.1295 −0.564234 −0.282117 0.959380i \(-0.591037\pi\)
−0.282117 + 0.959380i \(0.591037\pi\)
\(720\) 0.378732 0.0141145
\(721\) −8.75017 −0.325873
\(722\) −37.4412 −1.39342
\(723\) 23.1446 0.860756
\(724\) −26.9748 −1.00251
\(725\) 30.1504 1.11976
\(726\) −9.76601 −0.362451
\(727\) 0.394234 0.0146213 0.00731067 0.999973i \(-0.497673\pi\)
0.00731067 + 0.999973i \(0.497673\pi\)
\(728\) −3.15604 −0.116971
\(729\) 1.00000 0.0370370
\(730\) 29.3242 1.08534
\(731\) −20.7154 −0.766188
\(732\) −3.69146 −0.136440
\(733\) −30.2905 −1.11881 −0.559403 0.828896i \(-0.688970\pi\)
−0.559403 + 0.828896i \(0.688970\pi\)
\(734\) −20.0587 −0.740379
\(735\) 2.94587 0.108660
\(736\) 0.608214 0.0224191
\(737\) 2.31154 0.0851466
\(738\) −8.17148 −0.300796
\(739\) 50.5886 1.86093 0.930466 0.366378i \(-0.119402\pi\)
0.930466 + 0.366378i \(0.119402\pi\)
\(740\) 22.5291 0.828187
\(741\) 8.63501 0.317215
\(742\) −3.37355 −0.123847
\(743\) −5.07292 −0.186107 −0.0930536 0.995661i \(-0.529663\pi\)
−0.0930536 + 0.995661i \(0.529663\pi\)
\(744\) −22.6429 −0.830130
\(745\) 70.2827 2.57496
\(746\) −16.5043 −0.604264
\(747\) −2.18994 −0.0801258
\(748\) −1.14892 −0.0420087
\(749\) 17.6296 0.644171
\(750\) 3.46732 0.126609
\(751\) −5.11461 −0.186635 −0.0933174 0.995636i \(-0.529747\pi\)
−0.0933174 + 0.995636i \(0.529747\pi\)
\(752\) −0.651024 −0.0237404
\(753\) 17.9686 0.654812
\(754\) 8.06657 0.293767
\(755\) 6.61899 0.240890
\(756\) 1.20713 0.0439030
\(757\) 19.7492 0.717797 0.358898 0.933377i \(-0.383152\pi\)
0.358898 + 0.933377i \(0.383152\pi\)
\(758\) −26.4098 −0.959246
\(759\) 0.0195183 0.000708469 0
\(760\) −65.7306 −2.38430
\(761\) −25.1720 −0.912485 −0.456242 0.889856i \(-0.650805\pi\)
−0.456242 + 0.889856i \(0.650805\pi\)
\(762\) −15.5324 −0.562681
\(763\) 18.1317 0.656410
\(764\) −3.94695 −0.142796
\(765\) −15.6102 −0.564389
\(766\) 0.890431 0.0321726
\(767\) 2.81417 0.101614
\(768\) 16.2939 0.587954
\(769\) −38.0079 −1.37060 −0.685300 0.728261i \(-0.740329\pi\)
−0.685300 + 0.728261i \(0.740329\pi\)
\(770\) 0.471143 0.0169788
\(771\) 20.7887 0.748686
\(772\) −27.8030 −1.00065
\(773\) 50.9564 1.83278 0.916388 0.400292i \(-0.131091\pi\)
0.916388 + 0.400292i \(0.131091\pi\)
\(774\) 3.48095 0.125120
\(775\) 29.1639 1.04760
\(776\) 10.2495 0.367934
\(777\) −6.33542 −0.227282
\(778\) −14.1970 −0.508986
\(779\) 71.7030 2.56903
\(780\) 3.93002 0.140717
\(781\) 0.866250 0.0309969
\(782\) 0.512741 0.0183356
\(783\) −8.19715 −0.292942
\(784\) −0.128564 −0.00459156
\(785\) −51.1104 −1.82421
\(786\) 0.180965 0.00645482
\(787\) −43.2607 −1.54208 −0.771039 0.636787i \(-0.780263\pi\)
−0.771039 + 0.636787i \(0.780263\pi\)
\(788\) −2.25721 −0.0804099
\(789\) 1.97070 0.0701589
\(790\) 21.3757 0.760513
\(791\) −18.2232 −0.647943
\(792\) 0.512928 0.0182261
\(793\) 3.37963 0.120014
\(794\) 20.9717 0.744257
\(795\) 11.1610 0.395838
\(796\) −6.63566 −0.235195
\(797\) −37.5932 −1.33162 −0.665810 0.746121i \(-0.731914\pi\)
−0.665810 + 0.746121i \(0.731914\pi\)
\(798\) 6.95724 0.246284
\(799\) 26.8334 0.949296
\(800\) −20.5866 −0.727846
\(801\) −18.0733 −0.638588
\(802\) 21.3191 0.752804
\(803\) 2.00794 0.0708587
\(804\) 15.5352 0.547885
\(805\) 0.320123 0.0112828
\(806\) 7.80264 0.274836
\(807\) 0.0240334 0.000846014 0
\(808\) −19.8767 −0.699260
\(809\) 23.0303 0.809702 0.404851 0.914383i \(-0.367323\pi\)
0.404851 + 0.914383i \(0.367323\pi\)
\(810\) 2.62309 0.0921661
\(811\) −39.7311 −1.39515 −0.697573 0.716513i \(-0.745737\pi\)
−0.697573 + 0.716513i \(0.745737\pi\)
\(812\) −9.89505 −0.347248
\(813\) 31.5550 1.10668
\(814\) −1.01325 −0.0355142
\(815\) 5.86485 0.205437
\(816\) 0.681261 0.0238489
\(817\) −30.5446 −1.06862
\(818\) 24.7976 0.867026
\(819\) −1.10516 −0.0386175
\(820\) 32.6339 1.13963
\(821\) 33.8058 1.17983 0.589914 0.807466i \(-0.299161\pi\)
0.589914 + 0.807466i \(0.299161\pi\)
\(822\) 15.1752 0.529296
\(823\) 22.3721 0.779841 0.389921 0.920848i \(-0.372502\pi\)
0.389921 + 0.920848i \(0.372502\pi\)
\(824\) −24.9881 −0.870502
\(825\) −0.660647 −0.0230008
\(826\) 2.26738 0.0788924
\(827\) 37.8507 1.31620 0.658099 0.752931i \(-0.271361\pi\)
0.658099 + 0.752931i \(0.271361\pi\)
\(828\) 0.131177 0.00455872
\(829\) −33.4541 −1.16191 −0.580955 0.813936i \(-0.697321\pi\)
−0.580955 + 0.813936i \(0.697321\pi\)
\(830\) −5.74442 −0.199392
\(831\) 21.0207 0.729200
\(832\) −5.79199 −0.200801
\(833\) 5.29902 0.183600
\(834\) −9.47299 −0.328023
\(835\) −19.6882 −0.681339
\(836\) −1.69407 −0.0585906
\(837\) −7.92895 −0.274064
\(838\) 12.9441 0.447148
\(839\) −17.3285 −0.598247 −0.299123 0.954214i \(-0.596694\pi\)
−0.299123 + 0.954214i \(0.596694\pi\)
\(840\) 8.41261 0.290263
\(841\) 38.1932 1.31701
\(842\) −2.57477 −0.0887326
\(843\) 2.03809 0.0701954
\(844\) −26.0844 −0.897862
\(845\) 34.6983 1.19366
\(846\) −4.50899 −0.155022
\(847\) −10.9677 −0.376856
\(848\) −0.487086 −0.0167266
\(849\) −2.37671 −0.0815685
\(850\) −17.3551 −0.595274
\(851\) −0.688459 −0.0236001
\(852\) 5.82183 0.199453
\(853\) −4.52297 −0.154864 −0.0774318 0.996998i \(-0.524672\pi\)
−0.0774318 + 0.996998i \(0.524672\pi\)
\(854\) 2.72297 0.0931783
\(855\) −23.0171 −0.787169
\(856\) 50.3453 1.72077
\(857\) −6.56825 −0.224367 −0.112184 0.993688i \(-0.535784\pi\)
−0.112184 + 0.993688i \(0.535784\pi\)
\(858\) −0.176752 −0.00603422
\(859\) −41.9273 −1.43054 −0.715270 0.698849i \(-0.753696\pi\)
−0.715270 + 0.698849i \(0.753696\pi\)
\(860\) −13.9017 −0.474043
\(861\) −9.17700 −0.312751
\(862\) 18.1724 0.618953
\(863\) 48.3610 1.64623 0.823114 0.567876i \(-0.192235\pi\)
0.823114 + 0.567876i \(0.192235\pi\)
\(864\) 5.59698 0.190413
\(865\) 13.2510 0.450548
\(866\) 11.9019 0.404443
\(867\) −11.0796 −0.376284
\(868\) −9.57129 −0.324871
\(869\) 1.46368 0.0496519
\(870\) −21.5019 −0.728982
\(871\) −14.2229 −0.481924
\(872\) 51.7791 1.75346
\(873\) 3.58909 0.121472
\(874\) 0.756031 0.0255731
\(875\) 3.89398 0.131640
\(876\) 13.4948 0.455948
\(877\) −54.0861 −1.82636 −0.913179 0.407559i \(-0.866380\pi\)
−0.913179 + 0.407559i \(0.866380\pi\)
\(878\) 3.28923 0.111006
\(879\) 1.11171 0.0374970
\(880\) 0.0680253 0.00229313
\(881\) −49.8600 −1.67983 −0.839913 0.542721i \(-0.817394\pi\)
−0.839913 + 0.542721i \(0.817394\pi\)
\(882\) −0.890431 −0.0299824
\(883\) −36.6056 −1.23188 −0.615938 0.787795i \(-0.711223\pi\)
−0.615938 + 0.787795i \(0.711223\pi\)
\(884\) 7.06931 0.237767
\(885\) −7.50133 −0.252155
\(886\) −0.901877 −0.0302991
\(887\) −51.4721 −1.72827 −0.864133 0.503264i \(-0.832132\pi\)
−0.864133 + 0.503264i \(0.832132\pi\)
\(888\) −18.0922 −0.607136
\(889\) −17.4437 −0.585044
\(890\) −47.4079 −1.58912
\(891\) 0.179614 0.00601728
\(892\) 11.4749 0.384208
\(893\) 39.5655 1.32401
\(894\) −21.2439 −0.710504
\(895\) 56.8108 1.89898
\(896\) 6.52735 0.218063
\(897\) −0.120096 −0.00400989
\(898\) −9.61390 −0.320820
\(899\) 64.9947 2.16770
\(900\) −4.44003 −0.148001
\(901\) 20.0763 0.668838
\(902\) −1.46771 −0.0488693
\(903\) 3.90929 0.130093
\(904\) −52.0406 −1.73085
\(905\) −65.8290 −2.18823
\(906\) −2.00068 −0.0664682
\(907\) 50.7450 1.68496 0.842481 0.538726i \(-0.181094\pi\)
0.842481 + 0.538726i \(0.181094\pi\)
\(908\) −9.70893 −0.322202
\(909\) −6.96029 −0.230858
\(910\) −2.89894 −0.0960990
\(911\) −50.7678 −1.68201 −0.841006 0.541025i \(-0.818036\pi\)
−0.841006 + 0.541025i \(0.818036\pi\)
\(912\) 1.00451 0.0332627
\(913\) −0.393343 −0.0130178
\(914\) −12.9341 −0.427822
\(915\) −9.00860 −0.297815
\(916\) −30.7194 −1.01500
\(917\) 0.203233 0.00671136
\(918\) 4.71841 0.155731
\(919\) −37.7250 −1.24443 −0.622217 0.782845i \(-0.713768\pi\)
−0.622217 + 0.782845i \(0.713768\pi\)
\(920\) 0.914183 0.0301397
\(921\) −9.80791 −0.323182
\(922\) 5.10983 0.168283
\(923\) −5.33004 −0.175440
\(924\) 0.216817 0.00713277
\(925\) 23.3027 0.766187
\(926\) 11.2292 0.369013
\(927\) −8.75017 −0.287393
\(928\) −45.8793 −1.50606
\(929\) 19.1943 0.629744 0.314872 0.949134i \(-0.398038\pi\)
0.314872 + 0.949134i \(0.398038\pi\)
\(930\) −20.7984 −0.682006
\(931\) 7.81335 0.256072
\(932\) −7.89739 −0.258688
\(933\) 2.01734 0.0660448
\(934\) 21.4744 0.702662
\(935\) −2.80381 −0.0916944
\(936\) −3.15604 −0.103159
\(937\) −45.7399 −1.49426 −0.747128 0.664680i \(-0.768568\pi\)
−0.747128 + 0.664680i \(0.768568\pi\)
\(938\) −11.4594 −0.374163
\(939\) −5.85414 −0.191043
\(940\) 18.0073 0.587333
\(941\) 26.7344 0.871516 0.435758 0.900064i \(-0.356480\pi\)
0.435758 + 0.900064i \(0.356480\pi\)
\(942\) 15.4488 0.503350
\(943\) −0.997248 −0.0324748
\(944\) 0.327373 0.0106551
\(945\) 2.94587 0.0958292
\(946\) 0.625226 0.0203279
\(947\) −11.0398 −0.358745 −0.179372 0.983781i \(-0.557407\pi\)
−0.179372 + 0.983781i \(0.557407\pi\)
\(948\) 9.83697 0.319490
\(949\) −12.3549 −0.401056
\(950\) −25.5898 −0.830244
\(951\) 4.04197 0.131070
\(952\) 15.1326 0.490450
\(953\) −47.0511 −1.52413 −0.762067 0.647498i \(-0.775816\pi\)
−0.762067 + 0.647498i \(0.775816\pi\)
\(954\) −3.37355 −0.109223
\(955\) −9.63208 −0.311687
\(956\) 5.75222 0.186040
\(957\) −1.47232 −0.0475933
\(958\) −24.8525 −0.802948
\(959\) 17.0426 0.550333
\(960\) 15.4389 0.498288
\(961\) 31.8682 1.02801
\(962\) 6.23450 0.201008
\(963\) 17.6296 0.568105
\(964\) 27.9386 0.899842
\(965\) −67.8500 −2.18417
\(966\) −0.0967615 −0.00311325
\(967\) −4.99050 −0.160484 −0.0802418 0.996775i \(-0.525569\pi\)
−0.0802418 + 0.996775i \(0.525569\pi\)
\(968\) −31.3209 −1.00669
\(969\) −41.4031 −1.33006
\(970\) 9.41451 0.302282
\(971\) −39.9038 −1.28057 −0.640286 0.768136i \(-0.721184\pi\)
−0.640286 + 0.768136i \(0.721184\pi\)
\(972\) 1.20713 0.0387188
\(973\) −10.6387 −0.341060
\(974\) −18.8103 −0.602721
\(975\) 4.06496 0.130183
\(976\) 0.393153 0.0125845
\(977\) 19.6317 0.628074 0.314037 0.949411i \(-0.398318\pi\)
0.314037 + 0.949411i \(0.398318\pi\)
\(978\) −1.77273 −0.0566857
\(979\) −3.24621 −0.103749
\(980\) 3.55606 0.113594
\(981\) 18.1317 0.578899
\(982\) −22.0754 −0.704454
\(983\) −8.59545 −0.274152 −0.137076 0.990561i \(-0.543771\pi\)
−0.137076 + 0.990561i \(0.543771\pi\)
\(984\) −26.2070 −0.835449
\(985\) −5.50847 −0.175514
\(986\) −38.6775 −1.23174
\(987\) −5.06383 −0.161184
\(988\) 10.4236 0.331619
\(989\) 0.424816 0.0135084
\(990\) 0.471143 0.0149739
\(991\) 39.1777 1.24452 0.622261 0.782810i \(-0.286214\pi\)
0.622261 + 0.782810i \(0.286214\pi\)
\(992\) −44.3782 −1.40901
\(993\) −32.8278 −1.04176
\(994\) −4.29442 −0.136211
\(995\) −16.1936 −0.513370
\(996\) −2.64355 −0.0837641
\(997\) −51.4864 −1.63059 −0.815296 0.579044i \(-0.803426\pi\)
−0.815296 + 0.579044i \(0.803426\pi\)
\(998\) −5.20634 −0.164804
\(999\) −6.33542 −0.200444
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 \(a_p\))