Properties

Label 4030.2.a.n.1.7
Level 4030
Weight 2
Character 4030.1
Self dual Yes
Analytic conductor 32.180
Analytic rank 0
Dimension 8
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4030.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1797120146\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-2.63528\)
Character \(\chi\) = 4030.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +2.63528 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.63528 q^{6} +0.203142 q^{7} +1.00000 q^{8} +3.94469 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +2.63528 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.63528 q^{6} +0.203142 q^{7} +1.00000 q^{8} +3.94469 q^{9} -1.00000 q^{10} +4.83652 q^{11} +2.63528 q^{12} -1.00000 q^{13} +0.203142 q^{14} -2.63528 q^{15} +1.00000 q^{16} -0.0683421 q^{17} +3.94469 q^{18} +3.00496 q^{19} -1.00000 q^{20} +0.535335 q^{21} +4.83652 q^{22} +4.98419 q^{23} +2.63528 q^{24} +1.00000 q^{25} -1.00000 q^{26} +2.48951 q^{27} +0.203142 q^{28} -4.67817 q^{29} -2.63528 q^{30} -1.00000 q^{31} +1.00000 q^{32} +12.7456 q^{33} -0.0683421 q^{34} -0.203142 q^{35} +3.94469 q^{36} +6.73026 q^{37} +3.00496 q^{38} -2.63528 q^{39} -1.00000 q^{40} -11.8907 q^{41} +0.535335 q^{42} -0.517514 q^{43} +4.83652 q^{44} -3.94469 q^{45} +4.98419 q^{46} +2.49431 q^{47} +2.63528 q^{48} -6.95873 q^{49} +1.00000 q^{50} -0.180100 q^{51} -1.00000 q^{52} +7.40140 q^{53} +2.48951 q^{54} -4.83652 q^{55} +0.203142 q^{56} +7.91891 q^{57} -4.67817 q^{58} -9.25770 q^{59} -2.63528 q^{60} +8.56694 q^{61} -1.00000 q^{62} +0.801330 q^{63} +1.00000 q^{64} +1.00000 q^{65} +12.7456 q^{66} -5.12785 q^{67} -0.0683421 q^{68} +13.1347 q^{69} -0.203142 q^{70} +1.20157 q^{71} +3.94469 q^{72} -2.64613 q^{73} +6.73026 q^{74} +2.63528 q^{75} +3.00496 q^{76} +0.982499 q^{77} -2.63528 q^{78} +7.88727 q^{79} -1.00000 q^{80} -5.27351 q^{81} -11.8907 q^{82} +14.3936 q^{83} +0.535335 q^{84} +0.0683421 q^{85} -0.517514 q^{86} -12.3283 q^{87} +4.83652 q^{88} +13.1568 q^{89} -3.94469 q^{90} -0.203142 q^{91} +4.98419 q^{92} -2.63528 q^{93} +2.49431 q^{94} -3.00496 q^{95} +2.63528 q^{96} -1.83994 q^{97} -6.95873 q^{98} +19.0786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{2} - q^{3} + 8q^{4} - 8q^{5} - q^{6} + q^{7} + 8q^{8} + 9q^{9} + O(q^{10}) \) \( 8q + 8q^{2} - q^{3} + 8q^{4} - 8q^{5} - q^{6} + q^{7} + 8q^{8} + 9q^{9} - 8q^{10} + 4q^{11} - q^{12} - 8q^{13} + q^{14} + q^{15} + 8q^{16} - 5q^{17} + 9q^{18} + 2q^{19} - 8q^{20} + 17q^{21} + 4q^{22} + 4q^{23} - q^{24} + 8q^{25} - 8q^{26} + 11q^{27} + q^{28} + 11q^{29} + q^{30} - 8q^{31} + 8q^{32} + 10q^{33} - 5q^{34} - q^{35} + 9q^{36} + 19q^{37} + 2q^{38} + q^{39} - 8q^{40} + 10q^{41} + 17q^{42} + 19q^{43} + 4q^{44} - 9q^{45} + 4q^{46} + 11q^{47} - q^{48} + 11q^{49} + 8q^{50} + 7q^{51} - 8q^{52} + 8q^{53} + 11q^{54} - 4q^{55} + q^{56} - 11q^{57} + 11q^{58} + 28q^{59} + q^{60} - 12q^{61} - 8q^{62} + 20q^{63} + 8q^{64} + 8q^{65} + 10q^{66} + 24q^{67} - 5q^{68} + 30q^{69} - q^{70} + 18q^{71} + 9q^{72} - 3q^{73} + 19q^{74} - q^{75} + 2q^{76} - 7q^{77} + q^{78} + 22q^{79} - 8q^{80} + 24q^{81} + 10q^{82} + 17q^{83} + 17q^{84} + 5q^{85} + 19q^{86} + 11q^{87} + 4q^{88} + 17q^{89} - 9q^{90} - q^{91} + 4q^{92} + q^{93} + 11q^{94} - 2q^{95} - q^{96} - 24q^{97} + 11q^{98} + 23q^{99} + O(q^{100}) \)

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
\(3\) 2.63528 1.52148 0.760739 0.649058i \(-0.224837\pi\)
0.760739 + 0.649058i \(0.224837\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 2.63528 1.07585
\(7\) 0.203142 0.0767803 0.0383902 0.999263i \(-0.487777\pi\)
0.0383902 + 0.999263i \(0.487777\pi\)
\(8\) 1.00000 0.353553
\(9\) 3.94469 1.31490
\(10\) −1.00000 −0.316228
\(11\) 4.83652 1.45827 0.729133 0.684372i \(-0.239923\pi\)
0.729133 + 0.684372i \(0.239923\pi\)
\(12\) 2.63528 0.760739
\(13\) −1.00000 −0.277350
\(14\) 0.203142 0.0542919
\(15\) −2.63528 −0.680426
\(16\) 1.00000 0.250000
\(17\) −0.0683421 −0.0165754 −0.00828770 0.999966i \(-0.502638\pi\)
−0.00828770 + 0.999966i \(0.502638\pi\)
\(18\) 3.94469 0.929771
\(19\) 3.00496 0.689386 0.344693 0.938715i \(-0.387983\pi\)
0.344693 + 0.938715i \(0.387983\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0.535335 0.116820
\(22\) 4.83652 1.03115
\(23\) 4.98419 1.03927 0.519637 0.854387i \(-0.326067\pi\)
0.519637 + 0.854387i \(0.326067\pi\)
\(24\) 2.63528 0.537924
\(25\) 1.00000 0.200000
\(26\) −1.00000 −0.196116
\(27\) 2.48951 0.479106
\(28\) 0.203142 0.0383902
\(29\) −4.67817 −0.868714 −0.434357 0.900741i \(-0.643024\pi\)
−0.434357 + 0.900741i \(0.643024\pi\)
\(30\) −2.63528 −0.481134
\(31\) −1.00000 −0.179605
\(32\) 1.00000 0.176777
\(33\) 12.7456 2.21872
\(34\) −0.0683421 −0.0117206
\(35\) −0.203142 −0.0343372
\(36\) 3.94469 0.657448
\(37\) 6.73026 1.10645 0.553224 0.833033i \(-0.313398\pi\)
0.553224 + 0.833033i \(0.313398\pi\)
\(38\) 3.00496 0.487470
\(39\) −2.63528 −0.421982
\(40\) −1.00000 −0.158114
\(41\) −11.8907 −1.85701 −0.928505 0.371320i \(-0.878905\pi\)
−0.928505 + 0.371320i \(0.878905\pi\)
\(42\) 0.535335 0.0826039
\(43\) −0.517514 −0.0789202 −0.0394601 0.999221i \(-0.512564\pi\)
−0.0394601 + 0.999221i \(0.512564\pi\)
\(44\) 4.83652 0.729133
\(45\) −3.94469 −0.588039
\(46\) 4.98419 0.734878
\(47\) 2.49431 0.363832 0.181916 0.983314i \(-0.441770\pi\)
0.181916 + 0.983314i \(0.441770\pi\)
\(48\) 2.63528 0.380369
\(49\) −6.95873 −0.994105
\(50\) 1.00000 0.141421
\(51\) −0.180100 −0.0252191
\(52\) −1.00000 −0.138675
\(53\) 7.40140 1.01666 0.508330 0.861162i \(-0.330263\pi\)
0.508330 + 0.861162i \(0.330263\pi\)
\(54\) 2.48951 0.338779
\(55\) −4.83652 −0.652157
\(56\) 0.203142 0.0271459
\(57\) 7.91891 1.04889
\(58\) −4.67817 −0.614273
\(59\) −9.25770 −1.20525 −0.602625 0.798025i \(-0.705878\pi\)
−0.602625 + 0.798025i \(0.705878\pi\)
\(60\) −2.63528 −0.340213
\(61\) 8.56694 1.09688 0.548442 0.836188i \(-0.315221\pi\)
0.548442 + 0.836188i \(0.315221\pi\)
\(62\) −1.00000 −0.127000
\(63\) 0.801330 0.100958
\(64\) 1.00000 0.125000
\(65\) 1.00000 0.124035
\(66\) 12.7456 1.56887
\(67\) −5.12785 −0.626467 −0.313234 0.949676i \(-0.601412\pi\)
−0.313234 + 0.949676i \(0.601412\pi\)
\(68\) −0.0683421 −0.00828770
\(69\) 13.1347 1.58123
\(70\) −0.203142 −0.0242801
\(71\) 1.20157 0.142600 0.0712998 0.997455i \(-0.477285\pi\)
0.0712998 + 0.997455i \(0.477285\pi\)
\(72\) 3.94469 0.464886
\(73\) −2.64613 −0.309707 −0.154853 0.987937i \(-0.549490\pi\)
−0.154853 + 0.987937i \(0.549490\pi\)
\(74\) 6.73026 0.782376
\(75\) 2.63528 0.304296
\(76\) 3.00496 0.344693
\(77\) 0.982499 0.111966
\(78\) −2.63528 −0.298386
\(79\) 7.88727 0.887387 0.443694 0.896178i \(-0.353668\pi\)
0.443694 + 0.896178i \(0.353668\pi\)
\(80\) −1.00000 −0.111803
\(81\) −5.27351 −0.585946
\(82\) −11.8907 −1.31310
\(83\) 14.3936 1.57990 0.789952 0.613169i \(-0.210105\pi\)
0.789952 + 0.613169i \(0.210105\pi\)
\(84\) 0.535335 0.0584098
\(85\) 0.0683421 0.00741275
\(86\) −0.517514 −0.0558050
\(87\) −12.3283 −1.32173
\(88\) 4.83652 0.515575
\(89\) 13.1568 1.39461 0.697307 0.716773i \(-0.254382\pi\)
0.697307 + 0.716773i \(0.254382\pi\)
\(90\) −3.94469 −0.415806
\(91\) −0.203142 −0.0212950
\(92\) 4.98419 0.519637
\(93\) −2.63528 −0.273266
\(94\) 2.49431 0.257268
\(95\) −3.00496 −0.308303
\(96\) 2.63528 0.268962
\(97\) −1.83994 −0.186817 −0.0934086 0.995628i \(-0.529776\pi\)
−0.0934086 + 0.995628i \(0.529776\pi\)
\(98\) −6.95873 −0.702938
\(99\) 19.0786 1.91747
\(100\) 1.00000 0.100000
\(101\) 2.38178 0.236996 0.118498 0.992954i \(-0.462192\pi\)
0.118498 + 0.992954i \(0.462192\pi\)
\(102\) −0.180100 −0.0178326
\(103\) −6.44296 −0.634844 −0.317422 0.948284i \(-0.602817\pi\)
−0.317422 + 0.948284i \(0.602817\pi\)
\(104\) −1.00000 −0.0980581
\(105\) −0.535335 −0.0522433
\(106\) 7.40140 0.718887
\(107\) −4.19546 −0.405591 −0.202795 0.979221i \(-0.565003\pi\)
−0.202795 + 0.979221i \(0.565003\pi\)
\(108\) 2.48951 0.239553
\(109\) −7.15776 −0.685589 −0.342794 0.939410i \(-0.611373\pi\)
−0.342794 + 0.939410i \(0.611373\pi\)
\(110\) −4.83652 −0.461144
\(111\) 17.7361 1.68344
\(112\) 0.203142 0.0191951
\(113\) 0.127104 0.0119569 0.00597845 0.999982i \(-0.498097\pi\)
0.00597845 + 0.999982i \(0.498097\pi\)
\(114\) 7.91891 0.741674
\(115\) −4.98419 −0.464778
\(116\) −4.67817 −0.434357
\(117\) −3.94469 −0.364686
\(118\) −9.25770 −0.852240
\(119\) −0.0138831 −0.00127267
\(120\) −2.63528 −0.240567
\(121\) 12.3920 1.12654
\(122\) 8.56694 0.775615
\(123\) −31.3352 −2.82540
\(124\) −1.00000 −0.0898027
\(125\) −1.00000 −0.0894427
\(126\) 0.801330 0.0713882
\(127\) 6.91730 0.613811 0.306905 0.951740i \(-0.400706\pi\)
0.306905 + 0.951740i \(0.400706\pi\)
\(128\) 1.00000 0.0883883
\(129\) −1.36379 −0.120075
\(130\) 1.00000 0.0877058
\(131\) −12.1974 −1.06569 −0.532844 0.846213i \(-0.678877\pi\)
−0.532844 + 0.846213i \(0.678877\pi\)
\(132\) 12.7456 1.10936
\(133\) 0.610433 0.0529313
\(134\) −5.12785 −0.442979
\(135\) −2.48951 −0.214263
\(136\) −0.0683421 −0.00586029
\(137\) 4.52125 0.386277 0.193138 0.981172i \(-0.438133\pi\)
0.193138 + 0.981172i \(0.438133\pi\)
\(138\) 13.1347 1.11810
\(139\) −10.2832 −0.872206 −0.436103 0.899897i \(-0.643642\pi\)
−0.436103 + 0.899897i \(0.643642\pi\)
\(140\) −0.203142 −0.0171686
\(141\) 6.57320 0.553563
\(142\) 1.20157 0.100833
\(143\) −4.83652 −0.404450
\(144\) 3.94469 0.328724
\(145\) 4.67817 0.388501
\(146\) −2.64613 −0.218996
\(147\) −18.3382 −1.51251
\(148\) 6.73026 0.553224
\(149\) 19.4531 1.59366 0.796829 0.604204i \(-0.206509\pi\)
0.796829 + 0.604204i \(0.206509\pi\)
\(150\) 2.63528 0.215169
\(151\) 12.0592 0.981364 0.490682 0.871339i \(-0.336748\pi\)
0.490682 + 0.871339i \(0.336748\pi\)
\(152\) 3.00496 0.243735
\(153\) −0.269588 −0.0217949
\(154\) 0.982499 0.0791721
\(155\) 1.00000 0.0803219
\(156\) −2.63528 −0.210991
\(157\) −19.6491 −1.56817 −0.784084 0.620655i \(-0.786867\pi\)
−0.784084 + 0.620655i \(0.786867\pi\)
\(158\) 7.88727 0.627478
\(159\) 19.5047 1.54683
\(160\) −1.00000 −0.0790569
\(161\) 1.01250 0.0797959
\(162\) −5.27351 −0.414326
\(163\) −8.98152 −0.703487 −0.351743 0.936096i \(-0.614411\pi\)
−0.351743 + 0.936096i \(0.614411\pi\)
\(164\) −11.8907 −0.928505
\(165\) −12.7456 −0.992242
\(166\) 14.3936 1.11716
\(167\) −13.4277 −1.03906 −0.519532 0.854451i \(-0.673894\pi\)
−0.519532 + 0.854451i \(0.673894\pi\)
\(168\) 0.535335 0.0413020
\(169\) 1.00000 0.0769231
\(170\) 0.0683421 0.00524160
\(171\) 11.8536 0.906470
\(172\) −0.517514 −0.0394601
\(173\) 15.0496 1.14420 0.572100 0.820184i \(-0.306129\pi\)
0.572100 + 0.820184i \(0.306129\pi\)
\(174\) −12.3283 −0.934603
\(175\) 0.203142 0.0153561
\(176\) 4.83652 0.364567
\(177\) −24.3966 −1.83376
\(178\) 13.1568 0.986140
\(179\) −10.0195 −0.748891 −0.374445 0.927249i \(-0.622167\pi\)
−0.374445 + 0.927249i \(0.622167\pi\)
\(180\) −3.94469 −0.294020
\(181\) 8.45118 0.628171 0.314086 0.949395i \(-0.398302\pi\)
0.314086 + 0.949395i \(0.398302\pi\)
\(182\) −0.203142 −0.0150579
\(183\) 22.5763 1.66889
\(184\) 4.98419 0.367439
\(185\) −6.73026 −0.494818
\(186\) −2.63528 −0.193228
\(187\) −0.330538 −0.0241714
\(188\) 2.49431 0.181916
\(189\) 0.505723 0.0367859
\(190\) −3.00496 −0.218003
\(191\) 0.282464 0.0204384 0.0102192 0.999948i \(-0.496747\pi\)
0.0102192 + 0.999948i \(0.496747\pi\)
\(192\) 2.63528 0.190185
\(193\) 3.11170 0.223985 0.111992 0.993709i \(-0.464277\pi\)
0.111992 + 0.993709i \(0.464277\pi\)
\(194\) −1.83994 −0.132100
\(195\) 2.63528 0.188716
\(196\) −6.95873 −0.497052
\(197\) −0.893060 −0.0636279 −0.0318140 0.999494i \(-0.510128\pi\)
−0.0318140 + 0.999494i \(0.510128\pi\)
\(198\) 19.0786 1.35585
\(199\) 5.49310 0.389396 0.194698 0.980863i \(-0.437627\pi\)
0.194698 + 0.980863i \(0.437627\pi\)
\(200\) 1.00000 0.0707107
\(201\) −13.5133 −0.953156
\(202\) 2.38178 0.167581
\(203\) −0.950330 −0.0667001
\(204\) −0.180100 −0.0126096
\(205\) 11.8907 0.830480
\(206\) −6.44296 −0.448902
\(207\) 19.6611 1.36654
\(208\) −1.00000 −0.0693375
\(209\) 14.5336 1.00531
\(210\) −0.535335 −0.0369416
\(211\) −12.1262 −0.834805 −0.417403 0.908722i \(-0.637059\pi\)
−0.417403 + 0.908722i \(0.637059\pi\)
\(212\) 7.40140 0.508330
\(213\) 3.16646 0.216962
\(214\) −4.19546 −0.286796
\(215\) 0.517514 0.0352942
\(216\) 2.48951 0.169390
\(217\) −0.203142 −0.0137902
\(218\) −7.15776 −0.484784
\(219\) −6.97330 −0.471212
\(220\) −4.83652 −0.326078
\(221\) 0.0683421 0.00459719
\(222\) 17.7361 1.19037
\(223\) 4.43362 0.296897 0.148449 0.988920i \(-0.452572\pi\)
0.148449 + 0.988920i \(0.452572\pi\)
\(224\) 0.203142 0.0135730
\(225\) 3.94469 0.262979
\(226\) 0.127104 0.00845481
\(227\) −25.4808 −1.69122 −0.845610 0.533802i \(-0.820763\pi\)
−0.845610 + 0.533802i \(0.820763\pi\)
\(228\) 7.91891 0.524443
\(229\) −7.75619 −0.512543 −0.256272 0.966605i \(-0.582494\pi\)
−0.256272 + 0.966605i \(0.582494\pi\)
\(230\) −4.98419 −0.328648
\(231\) 2.58916 0.170354
\(232\) −4.67817 −0.307137
\(233\) −16.0043 −1.04848 −0.524239 0.851571i \(-0.675650\pi\)
−0.524239 + 0.851571i \(0.675650\pi\)
\(234\) −3.94469 −0.257872
\(235\) −2.49431 −0.162711
\(236\) −9.25770 −0.602625
\(237\) 20.7851 1.35014
\(238\) −0.0138831 −0.000899910 0
\(239\) −10.1862 −0.658891 −0.329446 0.944175i \(-0.606862\pi\)
−0.329446 + 0.944175i \(0.606862\pi\)
\(240\) −2.63528 −0.170106
\(241\) −11.5154 −0.741770 −0.370885 0.928679i \(-0.620946\pi\)
−0.370885 + 0.928679i \(0.620946\pi\)
\(242\) 12.3920 0.796585
\(243\) −21.3657 −1.37061
\(244\) 8.56694 0.548442
\(245\) 6.95873 0.444577
\(246\) −31.3352 −1.99786
\(247\) −3.00496 −0.191201
\(248\) −1.00000 −0.0635001
\(249\) 37.9311 2.40379
\(250\) −1.00000 −0.0632456
\(251\) −6.50524 −0.410607 −0.205303 0.978698i \(-0.565818\pi\)
−0.205303 + 0.978698i \(0.565818\pi\)
\(252\) 0.801330 0.0504791
\(253\) 24.1061 1.51554
\(254\) 6.91730 0.434030
\(255\) 0.180100 0.0112783
\(256\) 1.00000 0.0625000
\(257\) −10.5507 −0.658134 −0.329067 0.944307i \(-0.606734\pi\)
−0.329067 + 0.944307i \(0.606734\pi\)
\(258\) −1.36379 −0.0849061
\(259\) 1.36720 0.0849534
\(260\) 1.00000 0.0620174
\(261\) −18.4539 −1.14227
\(262\) −12.1974 −0.753556
\(263\) 1.12009 0.0690677 0.0345339 0.999404i \(-0.489005\pi\)
0.0345339 + 0.999404i \(0.489005\pi\)
\(264\) 12.7456 0.784436
\(265\) −7.40140 −0.454664
\(266\) 0.610433 0.0374281
\(267\) 34.6717 2.12187
\(268\) −5.12785 −0.313234
\(269\) −20.5157 −1.25087 −0.625433 0.780278i \(-0.715078\pi\)
−0.625433 + 0.780278i \(0.715078\pi\)
\(270\) −2.48951 −0.151507
\(271\) 15.3800 0.934269 0.467134 0.884186i \(-0.345286\pi\)
0.467134 + 0.884186i \(0.345286\pi\)
\(272\) −0.0683421 −0.00414385
\(273\) −0.535335 −0.0323999
\(274\) 4.52125 0.273139
\(275\) 4.83652 0.291653
\(276\) 13.1347 0.790617
\(277\) −4.93138 −0.296298 −0.148149 0.988965i \(-0.547331\pi\)
−0.148149 + 0.988965i \(0.547331\pi\)
\(278\) −10.2832 −0.616742
\(279\) −3.94469 −0.236162
\(280\) −0.203142 −0.0121400
\(281\) 16.0892 0.959800 0.479900 0.877323i \(-0.340673\pi\)
0.479900 + 0.877323i \(0.340673\pi\)
\(282\) 6.57320 0.391428
\(283\) 27.9171 1.65950 0.829749 0.558137i \(-0.188484\pi\)
0.829749 + 0.558137i \(0.188484\pi\)
\(284\) 1.20157 0.0712998
\(285\) −7.91891 −0.469076
\(286\) −4.83652 −0.285990
\(287\) −2.41549 −0.142582
\(288\) 3.94469 0.232443
\(289\) −16.9953 −0.999725
\(290\) 4.67817 0.274711
\(291\) −4.84874 −0.284238
\(292\) −2.64613 −0.154853
\(293\) 1.98261 0.115825 0.0579127 0.998322i \(-0.481556\pi\)
0.0579127 + 0.998322i \(0.481556\pi\)
\(294\) −18.3382 −1.06951
\(295\) 9.25770 0.539004
\(296\) 6.73026 0.391188
\(297\) 12.0406 0.698665
\(298\) 19.4531 1.12689
\(299\) −4.98419 −0.288243
\(300\) 2.63528 0.152148
\(301\) −0.105129 −0.00605952
\(302\) 12.0592 0.693929
\(303\) 6.27664 0.360584
\(304\) 3.00496 0.172346
\(305\) −8.56694 −0.490542
\(306\) −0.269588 −0.0154113
\(307\) −2.21971 −0.126685 −0.0633426 0.997992i \(-0.520176\pi\)
−0.0633426 + 0.997992i \(0.520176\pi\)
\(308\) 0.982499 0.0559831
\(309\) −16.9790 −0.965901
\(310\) 1.00000 0.0567962
\(311\) 0.631295 0.0357975 0.0178987 0.999840i \(-0.494302\pi\)
0.0178987 + 0.999840i \(0.494302\pi\)
\(312\) −2.63528 −0.149193
\(313\) −2.04157 −0.115396 −0.0576981 0.998334i \(-0.518376\pi\)
−0.0576981 + 0.998334i \(0.518376\pi\)
\(314\) −19.6491 −1.10886
\(315\) −0.801330 −0.0451498
\(316\) 7.88727 0.443694
\(317\) 3.86021 0.216811 0.108406 0.994107i \(-0.465426\pi\)
0.108406 + 0.994107i \(0.465426\pi\)
\(318\) 19.5047 1.09377
\(319\) −22.6261 −1.26682
\(320\) −1.00000 −0.0559017
\(321\) −11.0562 −0.617097
\(322\) 1.01250 0.0564242
\(323\) −0.205366 −0.0114269
\(324\) −5.27351 −0.292973
\(325\) −1.00000 −0.0554700
\(326\) −8.98152 −0.497440
\(327\) −18.8627 −1.04311
\(328\) −11.8907 −0.656552
\(329\) 0.506698 0.0279352
\(330\) −12.7456 −0.701621
\(331\) 5.36697 0.294995 0.147498 0.989062i \(-0.452878\pi\)
0.147498 + 0.989062i \(0.452878\pi\)
\(332\) 14.3936 0.789952
\(333\) 26.5487 1.45486
\(334\) −13.4277 −0.734729
\(335\) 5.12785 0.280165
\(336\) 0.535335 0.0292049
\(337\) −14.5518 −0.792685 −0.396342 0.918103i \(-0.629721\pi\)
−0.396342 + 0.918103i \(0.629721\pi\)
\(338\) 1.00000 0.0543928
\(339\) 0.334953 0.0181922
\(340\) 0.0683421 0.00370637
\(341\) −4.83652 −0.261912
\(342\) 11.8536 0.640971
\(343\) −2.83560 −0.153108
\(344\) −0.517514 −0.0279025
\(345\) −13.1347 −0.707149
\(346\) 15.0496 0.809071
\(347\) −34.5256 −1.85343 −0.926716 0.375763i \(-0.877381\pi\)
−0.926716 + 0.375763i \(0.877381\pi\)
\(348\) −12.3283 −0.660864
\(349\) 12.4174 0.664687 0.332343 0.943158i \(-0.392161\pi\)
0.332343 + 0.943158i \(0.392161\pi\)
\(350\) 0.203142 0.0108584
\(351\) −2.48951 −0.132880
\(352\) 4.83652 0.257788
\(353\) −4.79438 −0.255179 −0.127590 0.991827i \(-0.540724\pi\)
−0.127590 + 0.991827i \(0.540724\pi\)
\(354\) −24.3966 −1.29666
\(355\) −1.20157 −0.0637725
\(356\) 13.1568 0.697307
\(357\) −0.0365859 −0.00193633
\(358\) −10.0195 −0.529546
\(359\) −11.3590 −0.599504 −0.299752 0.954017i \(-0.596904\pi\)
−0.299752 + 0.954017i \(0.596904\pi\)
\(360\) −3.94469 −0.207903
\(361\) −9.97019 −0.524747
\(362\) 8.45118 0.444184
\(363\) 32.6562 1.71401
\(364\) −0.203142 −0.0106475
\(365\) 2.64613 0.138505
\(366\) 22.5763 1.18008
\(367\) −14.6997 −0.767316 −0.383658 0.923475i \(-0.625336\pi\)
−0.383658 + 0.923475i \(0.625336\pi\)
\(368\) 4.98419 0.259819
\(369\) −46.9049 −2.44177
\(370\) −6.73026 −0.349889
\(371\) 1.50353 0.0780595
\(372\) −2.63528 −0.136633
\(373\) −20.0256 −1.03689 −0.518443 0.855112i \(-0.673488\pi\)
−0.518443 + 0.855112i \(0.673488\pi\)
\(374\) −0.330538 −0.0170917
\(375\) −2.63528 −0.136085
\(376\) 2.49431 0.128634
\(377\) 4.67817 0.240938
\(378\) 0.505723 0.0260116
\(379\) 10.5500 0.541915 0.270957 0.962591i \(-0.412660\pi\)
0.270957 + 0.962591i \(0.412660\pi\)
\(380\) −3.00496 −0.154151
\(381\) 18.2290 0.933900
\(382\) 0.282464 0.0144521
\(383\) −22.0178 −1.12506 −0.562529 0.826778i \(-0.690171\pi\)
−0.562529 + 0.826778i \(0.690171\pi\)
\(384\) 2.63528 0.134481
\(385\) −0.982499 −0.0500728
\(386\) 3.11170 0.158381
\(387\) −2.04143 −0.103772
\(388\) −1.83994 −0.0934086
\(389\) 9.92601 0.503269 0.251634 0.967822i \(-0.419032\pi\)
0.251634 + 0.967822i \(0.419032\pi\)
\(390\) 2.63528 0.133442
\(391\) −0.340630 −0.0172264
\(392\) −6.95873 −0.351469
\(393\) −32.1434 −1.62142
\(394\) −0.893060 −0.0449917
\(395\) −7.88727 −0.396852
\(396\) 19.0786 0.958734
\(397\) −30.3617 −1.52381 −0.761905 0.647689i \(-0.775736\pi\)
−0.761905 + 0.647689i \(0.775736\pi\)
\(398\) 5.49310 0.275344
\(399\) 1.60866 0.0805338
\(400\) 1.00000 0.0500000
\(401\) −21.9321 −1.09524 −0.547619 0.836728i \(-0.684465\pi\)
−0.547619 + 0.836728i \(0.684465\pi\)
\(402\) −13.5133 −0.673983
\(403\) 1.00000 0.0498135
\(404\) 2.38178 0.118498
\(405\) 5.27351 0.262043
\(406\) −0.950330 −0.0471641
\(407\) 32.5510 1.61350
\(408\) −0.180100 −0.00891630
\(409\) −2.08788 −0.103239 −0.0516194 0.998667i \(-0.516438\pi\)
−0.0516194 + 0.998667i \(0.516438\pi\)
\(410\) 11.8907 0.587238
\(411\) 11.9148 0.587712
\(412\) −6.44296 −0.317422
\(413\) −1.88062 −0.0925395
\(414\) 19.6611 0.966288
\(415\) −14.3936 −0.706554
\(416\) −1.00000 −0.0490290
\(417\) −27.0990 −1.32704
\(418\) 14.5336 0.710860
\(419\) −34.6798 −1.69422 −0.847110 0.531418i \(-0.821659\pi\)
−0.847110 + 0.531418i \(0.821659\pi\)
\(420\) −0.535335 −0.0261217
\(421\) −0.223194 −0.0108778 −0.00543889 0.999985i \(-0.501731\pi\)
−0.00543889 + 0.999985i \(0.501731\pi\)
\(422\) −12.1262 −0.590296
\(423\) 9.83927 0.478402
\(424\) 7.40140 0.359444
\(425\) −0.0683421 −0.00331508
\(426\) 3.16646 0.153415
\(427\) 1.74030 0.0842192
\(428\) −4.19546 −0.202795
\(429\) −12.7456 −0.615362
\(430\) 0.517514 0.0249568
\(431\) −20.9742 −1.01029 −0.505145 0.863035i \(-0.668561\pi\)
−0.505145 + 0.863035i \(0.668561\pi\)
\(432\) 2.48951 0.119777
\(433\) −14.6915 −0.706028 −0.353014 0.935618i \(-0.614843\pi\)
−0.353014 + 0.935618i \(0.614843\pi\)
\(434\) −0.203142 −0.00975111
\(435\) 12.3283 0.591095
\(436\) −7.15776 −0.342794
\(437\) 14.9773 0.716461
\(438\) −6.97330 −0.333197
\(439\) −38.7604 −1.84993 −0.924966 0.380049i \(-0.875907\pi\)
−0.924966 + 0.380049i \(0.875907\pi\)
\(440\) −4.83652 −0.230572
\(441\) −27.4500 −1.30714
\(442\) 0.0683421 0.00325070
\(443\) −28.2306 −1.34128 −0.670639 0.741784i \(-0.733980\pi\)
−0.670639 + 0.741784i \(0.733980\pi\)
\(444\) 17.7361 0.841718
\(445\) −13.1568 −0.623690
\(446\) 4.43362 0.209938
\(447\) 51.2643 2.42472
\(448\) 0.203142 0.00959754
\(449\) 36.3549 1.71570 0.857848 0.513904i \(-0.171801\pi\)
0.857848 + 0.513904i \(0.171801\pi\)
\(450\) 3.94469 0.185954
\(451\) −57.5095 −2.70802
\(452\) 0.127104 0.00597845
\(453\) 31.7793 1.49312
\(454\) −25.4808 −1.19587
\(455\) 0.203142 0.00952343
\(456\) 7.91891 0.370837
\(457\) 31.8140 1.48820 0.744099 0.668069i \(-0.232879\pi\)
0.744099 + 0.668069i \(0.232879\pi\)
\(458\) −7.75619 −0.362423
\(459\) −0.170138 −0.00794138
\(460\) −4.98419 −0.232389
\(461\) −15.5327 −0.723431 −0.361716 0.932288i \(-0.617809\pi\)
−0.361716 + 0.932288i \(0.617809\pi\)
\(462\) 2.58916 0.120459
\(463\) 27.7525 1.28977 0.644885 0.764279i \(-0.276905\pi\)
0.644885 + 0.764279i \(0.276905\pi\)
\(464\) −4.67817 −0.217178
\(465\) 2.63528 0.122208
\(466\) −16.0043 −0.741386
\(467\) −20.6674 −0.956375 −0.478188 0.878258i \(-0.658706\pi\)
−0.478188 + 0.878258i \(0.658706\pi\)
\(468\) −3.94469 −0.182343
\(469\) −1.04168 −0.0481004
\(470\) −2.49431 −0.115054
\(471\) −51.7808 −2.38593
\(472\) −9.25770 −0.426120
\(473\) −2.50297 −0.115087
\(474\) 20.7851 0.954693
\(475\) 3.00496 0.137877
\(476\) −0.0138831 −0.000636333 0
\(477\) 29.1962 1.33680
\(478\) −10.1862 −0.465906
\(479\) 15.9286 0.727798 0.363899 0.931438i \(-0.381445\pi\)
0.363899 + 0.931438i \(0.381445\pi\)
\(480\) −2.63528 −0.120283
\(481\) −6.73026 −0.306873
\(482\) −11.5154 −0.524511
\(483\) 2.66821 0.121408
\(484\) 12.3920 0.563271
\(485\) 1.83994 0.0835472
\(486\) −21.3657 −0.969167
\(487\) −20.3387 −0.921633 −0.460817 0.887495i \(-0.652443\pi\)
−0.460817 + 0.887495i \(0.652443\pi\)
\(488\) 8.56694 0.387807
\(489\) −23.6688 −1.07034
\(490\) 6.95873 0.314364
\(491\) 29.8096 1.34529 0.672645 0.739965i \(-0.265158\pi\)
0.672645 + 0.739965i \(0.265158\pi\)
\(492\) −31.3352 −1.41270
\(493\) 0.319716 0.0143993
\(494\) −3.00496 −0.135200
\(495\) −19.0786 −0.857518
\(496\) −1.00000 −0.0449013
\(497\) 0.244088 0.0109488
\(498\) 37.9311 1.69974
\(499\) 2.18894 0.0979904 0.0489952 0.998799i \(-0.484398\pi\)
0.0489952 + 0.998799i \(0.484398\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −35.3856 −1.58091
\(502\) −6.50524 −0.290343
\(503\) −15.7771 −0.703465 −0.351732 0.936101i \(-0.614407\pi\)
−0.351732 + 0.936101i \(0.614407\pi\)
\(504\) 0.801330 0.0356941
\(505\) −2.38178 −0.105988
\(506\) 24.1061 1.07165
\(507\) 2.63528 0.117037
\(508\) 6.91730 0.306905
\(509\) 27.9587 1.23925 0.619623 0.784899i \(-0.287285\pi\)
0.619623 + 0.784899i \(0.287285\pi\)
\(510\) 0.180100 0.00797498
\(511\) −0.537540 −0.0237794
\(512\) 1.00000 0.0441942
\(513\) 7.48089 0.330289
\(514\) −10.5507 −0.465371
\(515\) 6.44296 0.283911
\(516\) −1.36379 −0.0600377
\(517\) 12.0638 0.530565
\(518\) 1.36720 0.0600711
\(519\) 39.6598 1.74087
\(520\) 1.00000 0.0438529
\(521\) 36.2792 1.58942 0.794709 0.606990i \(-0.207623\pi\)
0.794709 + 0.606990i \(0.207623\pi\)
\(522\) −18.4539 −0.807705
\(523\) 22.8142 0.997595 0.498798 0.866718i \(-0.333775\pi\)
0.498798 + 0.866718i \(0.333775\pi\)
\(524\) −12.1974 −0.532844
\(525\) 0.535335 0.0233639
\(526\) 1.12009 0.0488382
\(527\) 0.0683421 0.00297703
\(528\) 12.7456 0.554680
\(529\) 1.84212 0.0800921
\(530\) −7.40140 −0.321496
\(531\) −36.5187 −1.58478
\(532\) 0.610433 0.0264656
\(533\) 11.8907 0.515042
\(534\) 34.6717 1.50039
\(535\) 4.19546 0.181386
\(536\) −5.12785 −0.221490
\(537\) −26.4041 −1.13942
\(538\) −20.5157 −0.884496
\(539\) −33.6561 −1.44967
\(540\) −2.48951 −0.107131
\(541\) 38.4605 1.65355 0.826773 0.562536i \(-0.190174\pi\)
0.826773 + 0.562536i \(0.190174\pi\)
\(542\) 15.3800 0.660628
\(543\) 22.2712 0.955749
\(544\) −0.0683421 −0.00293015
\(545\) 7.15776 0.306605
\(546\) −0.535335 −0.0229102
\(547\) −31.3197 −1.33913 −0.669567 0.742752i \(-0.733520\pi\)
−0.669567 + 0.742752i \(0.733520\pi\)
\(548\) 4.52125 0.193138
\(549\) 33.7939 1.44229
\(550\) 4.83652 0.206230
\(551\) −14.0577 −0.598879
\(552\) 13.1347 0.559051
\(553\) 1.60223 0.0681339
\(554\) −4.93138 −0.209514
\(555\) −17.7361 −0.752855
\(556\) −10.2832 −0.436103
\(557\) 10.9919 0.465742 0.232871 0.972508i \(-0.425188\pi\)
0.232871 + 0.972508i \(0.425188\pi\)
\(558\) −3.94469 −0.166992
\(559\) 0.517514 0.0218885
\(560\) −0.203142 −0.00858430
\(561\) −0.871060 −0.0367762
\(562\) 16.0892 0.678681
\(563\) 11.7230 0.494064 0.247032 0.969007i \(-0.420545\pi\)
0.247032 + 0.969007i \(0.420545\pi\)
\(564\) 6.57320 0.276782
\(565\) −0.127104 −0.00534729
\(566\) 27.9171 1.17344
\(567\) −1.07127 −0.0449891
\(568\) 1.20157 0.0504166
\(569\) 43.2745 1.81416 0.907081 0.420957i \(-0.138306\pi\)
0.907081 + 0.420957i \(0.138306\pi\)
\(570\) −7.91891 −0.331687
\(571\) 10.7786 0.451070 0.225535 0.974235i \(-0.427587\pi\)
0.225535 + 0.974235i \(0.427587\pi\)
\(572\) −4.83652 −0.202225
\(573\) 0.744372 0.0310966
\(574\) −2.41549 −0.100821
\(575\) 4.98419 0.207855
\(576\) 3.94469 0.164362
\(577\) −41.9527 −1.74651 −0.873256 0.487262i \(-0.837996\pi\)
−0.873256 + 0.487262i \(0.837996\pi\)
\(578\) −16.9953 −0.706913
\(579\) 8.20018 0.340788
\(580\) 4.67817 0.194250
\(581\) 2.92394 0.121306
\(582\) −4.84874 −0.200987
\(583\) 35.7970 1.48256
\(584\) −2.64613 −0.109498
\(585\) 3.94469 0.163093
\(586\) 1.98261 0.0819009
\(587\) −0.719381 −0.0296920 −0.0148460 0.999890i \(-0.504726\pi\)
−0.0148460 + 0.999890i \(0.504726\pi\)
\(588\) −18.3382 −0.756254
\(589\) −3.00496 −0.123817
\(590\) 9.25770 0.381133
\(591\) −2.35346 −0.0968085
\(592\) 6.73026 0.276612
\(593\) 32.1995 1.32227 0.661137 0.750266i \(-0.270074\pi\)
0.661137 + 0.750266i \(0.270074\pi\)
\(594\) 12.0406 0.494030
\(595\) 0.0138831 0.000569153 0
\(596\) 19.4531 0.796829
\(597\) 14.4758 0.592457
\(598\) −4.98419 −0.203819
\(599\) −6.63600 −0.271140 −0.135570 0.990768i \(-0.543286\pi\)
−0.135570 + 0.990768i \(0.543286\pi\)
\(600\) 2.63528 0.107585
\(601\) 41.9368 1.71064 0.855318 0.518103i \(-0.173362\pi\)
0.855318 + 0.518103i \(0.173362\pi\)
\(602\) −0.105129 −0.00428473
\(603\) −20.2278 −0.823739
\(604\) 12.0592 0.490682
\(605\) −12.3920 −0.503805
\(606\) 6.27664 0.254971
\(607\) 17.1288 0.695235 0.347617 0.937636i \(-0.386991\pi\)
0.347617 + 0.937636i \(0.386991\pi\)
\(608\) 3.00496 0.121867
\(609\) −2.50438 −0.101483
\(610\) −8.56694 −0.346865
\(611\) −2.49431 −0.100909
\(612\) −0.269588 −0.0108975
\(613\) 31.0071 1.25236 0.626182 0.779677i \(-0.284617\pi\)
0.626182 + 0.779677i \(0.284617\pi\)
\(614\) −2.21971 −0.0895800
\(615\) 31.3352 1.26356
\(616\) 0.982499 0.0395860
\(617\) 19.1720 0.771837 0.385918 0.922533i \(-0.373885\pi\)
0.385918 + 0.922533i \(0.373885\pi\)
\(618\) −16.9790 −0.682995
\(619\) −10.9693 −0.440894 −0.220447 0.975399i \(-0.570752\pi\)
−0.220447 + 0.975399i \(0.570752\pi\)
\(620\) 1.00000 0.0401610
\(621\) 12.4082 0.497923
\(622\) 0.631295 0.0253126
\(623\) 2.67269 0.107079
\(624\) −2.63528 −0.105496
\(625\) 1.00000 0.0400000
\(626\) −2.04157 −0.0815975
\(627\) 38.3000 1.52955
\(628\) −19.6491 −0.784084
\(629\) −0.459960 −0.0183398
\(630\) −0.801330 −0.0319258
\(631\) −11.8054 −0.469965 −0.234982 0.972000i \(-0.575503\pi\)
−0.234982 + 0.972000i \(0.575503\pi\)
\(632\) 7.88727 0.313739
\(633\) −31.9560 −1.27014
\(634\) 3.86021 0.153309
\(635\) −6.91730 −0.274505
\(636\) 19.5047 0.773413
\(637\) 6.95873 0.275715
\(638\) −22.6261 −0.895774
\(639\) 4.73980 0.187504
\(640\) −1.00000 −0.0395285
\(641\) −14.2924 −0.564514 −0.282257 0.959339i \(-0.591083\pi\)
−0.282257 + 0.959339i \(0.591083\pi\)
\(642\) −11.0562 −0.436354
\(643\) 9.11564 0.359486 0.179743 0.983714i \(-0.442473\pi\)
0.179743 + 0.983714i \(0.442473\pi\)
\(644\) 1.01250 0.0398979
\(645\) 1.36379 0.0536993
\(646\) −0.205366 −0.00808000
\(647\) 3.54098 0.139210 0.0696051 0.997575i \(-0.477826\pi\)
0.0696051 + 0.997575i \(0.477826\pi\)
\(648\) −5.27351 −0.207163
\(649\) −44.7751 −1.75758
\(650\) −1.00000 −0.0392232
\(651\) −0.535335 −0.0209814
\(652\) −8.98152 −0.351743
\(653\) 45.8053 1.79250 0.896250 0.443550i \(-0.146281\pi\)
0.896250 + 0.443550i \(0.146281\pi\)
\(654\) −18.8627 −0.737589
\(655\) 12.1974 0.476591
\(656\) −11.8907 −0.464253
\(657\) −10.4382 −0.407232
\(658\) 0.506698 0.0197532
\(659\) 10.2160 0.397958 0.198979 0.980004i \(-0.436237\pi\)
0.198979 + 0.980004i \(0.436237\pi\)
\(660\) −12.7456 −0.496121
\(661\) −20.3176 −0.790264 −0.395132 0.918624i \(-0.629301\pi\)
−0.395132 + 0.918624i \(0.629301\pi\)
\(662\) 5.36697 0.208593
\(663\) 0.180100 0.00699452
\(664\) 14.3936 0.558580
\(665\) −0.610433 −0.0236716
\(666\) 26.5487 1.02874
\(667\) −23.3169 −0.902832
\(668\) −13.4277 −0.519532
\(669\) 11.6838 0.451722
\(670\) 5.12785 0.198106
\(671\) 41.4342 1.59955
\(672\) 0.535335 0.0206510
\(673\) −37.3963 −1.44152 −0.720761 0.693184i \(-0.756207\pi\)
−0.720761 + 0.693184i \(0.756207\pi\)
\(674\) −14.5518 −0.560513
\(675\) 2.48951 0.0958213
\(676\) 1.00000 0.0384615
\(677\) −1.79070 −0.0688224 −0.0344112 0.999408i \(-0.510956\pi\)
−0.0344112 + 0.999408i \(0.510956\pi\)
\(678\) 0.334953 0.0128638
\(679\) −0.373768 −0.0143439
\(680\) 0.0683421 0.00262080
\(681\) −67.1489 −2.57315
\(682\) −4.83652 −0.185200
\(683\) 18.4293 0.705177 0.352588 0.935779i \(-0.385302\pi\)
0.352588 + 0.935779i \(0.385302\pi\)
\(684\) 11.8536 0.453235
\(685\) −4.52125 −0.172748
\(686\) −2.83560 −0.108264
\(687\) −20.4397 −0.779823
\(688\) −0.517514 −0.0197300
\(689\) −7.40140 −0.281971
\(690\) −13.1347 −0.500030
\(691\) −27.3619 −1.04090 −0.520448 0.853893i \(-0.674235\pi\)
−0.520448 + 0.853893i \(0.674235\pi\)
\(692\) 15.0496 0.572100
\(693\) 3.87565 0.147224
\(694\) −34.5256 −1.31057
\(695\) 10.2832 0.390062
\(696\) −12.3283 −0.467302
\(697\) 0.812634 0.0307807
\(698\) 12.4174 0.470005
\(699\) −42.1758 −1.59524
\(700\) 0.203142 0.00767803
\(701\) −12.3238 −0.465462 −0.232731 0.972541i \(-0.574766\pi\)
−0.232731 + 0.972541i \(0.574766\pi\)
\(702\) −2.48951 −0.0939605
\(703\) 20.2242 0.762769
\(704\) 4.83652 0.182283
\(705\) −6.57320 −0.247561
\(706\) −4.79438 −0.180439
\(707\) 0.483838 0.0181966
\(708\) −24.3966 −0.916880
\(709\) −7.38825 −0.277471 −0.138736 0.990329i \(-0.544304\pi\)
−0.138736 + 0.990329i \(0.544304\pi\)
\(710\) −1.20157 −0.0450940
\(711\) 31.1128 1.16682
\(712\) 13.1568 0.493070
\(713\) −4.98419 −0.186659
\(714\) −0.0365859 −0.00136919
\(715\) 4.83652 0.180876
\(716\) −10.0195 −0.374445
\(717\) −26.8435 −1.00249
\(718\) −11.3590 −0.423914
\(719\) 35.9631 1.34120 0.670600 0.741820i \(-0.266037\pi\)
0.670600 + 0.741820i \(0.266037\pi\)
\(720\) −3.94469 −0.147010
\(721\) −1.30883 −0.0487435
\(722\) −9.97019 −0.371052
\(723\) −30.3462 −1.12859
\(724\) 8.45118 0.314086
\(725\) −4.67817 −0.173743
\(726\) 32.6562 1.21199
\(727\) 13.2386 0.490994 0.245497 0.969397i \(-0.421049\pi\)
0.245497 + 0.969397i \(0.421049\pi\)
\(728\) −0.203142 −0.00752893
\(729\) −40.4840 −1.49941
\(730\) 2.64613 0.0979378
\(731\) 0.0353680 0.00130813
\(732\) 22.5763 0.834443
\(733\) 15.1478 0.559497 0.279749 0.960073i \(-0.409749\pi\)
0.279749 + 0.960073i \(0.409749\pi\)
\(734\) −14.6997 −0.542574
\(735\) 18.3382 0.676414
\(736\) 4.98419 0.183720
\(737\) −24.8010 −0.913556
\(738\) −46.9049 −1.72659
\(739\) 12.4022 0.456223 0.228111 0.973635i \(-0.426745\pi\)
0.228111 + 0.973635i \(0.426745\pi\)
\(740\) −6.73026 −0.247409
\(741\) −7.91891 −0.290909
\(742\) 1.50353 0.0551964
\(743\) 9.69652 0.355731 0.177865 0.984055i \(-0.443081\pi\)
0.177865 + 0.984055i \(0.443081\pi\)
\(744\) −2.63528 −0.0966139
\(745\) −19.4531 −0.712706
\(746\) −20.0256 −0.733190
\(747\) 56.7783 2.07741
\(748\) −0.330538 −0.0120857
\(749\) −0.852274 −0.0311414
\(750\) −2.63528 −0.0962267
\(751\) 9.26706 0.338160 0.169080 0.985602i \(-0.445920\pi\)
0.169080 + 0.985602i \(0.445920\pi\)
\(752\) 2.49431 0.0909581
\(753\) −17.1431 −0.624729
\(754\) 4.67817 0.170369
\(755\) −12.0592 −0.438879
\(756\) 0.505723 0.0183930
\(757\) −40.4386 −1.46977 −0.734883 0.678194i \(-0.762763\pi\)
−0.734883 + 0.678194i \(0.762763\pi\)
\(758\) 10.5500 0.383191
\(759\) 63.5263 2.30586
\(760\) −3.00496 −0.109001
\(761\) −52.0192 −1.88569 −0.942847 0.333227i \(-0.891862\pi\)
−0.942847 + 0.333227i \(0.891862\pi\)
\(762\) 18.2290 0.660367
\(763\) −1.45404 −0.0526397
\(764\) 0.282464 0.0102192
\(765\) 0.269588 0.00974698
\(766\) −22.0178 −0.795536
\(767\) 9.25770 0.334276
\(768\) 2.63528 0.0950924
\(769\) 33.4408 1.20591 0.602953 0.797777i \(-0.293991\pi\)
0.602953 + 0.797777i \(0.293991\pi\)
\(770\) −0.982499 −0.0354068
\(771\) −27.8040 −1.00134
\(772\) 3.11170 0.111992
\(773\) 40.3103 1.44986 0.724930 0.688823i \(-0.241872\pi\)
0.724930 + 0.688823i \(0.241872\pi\)
\(774\) −2.04143 −0.0733777
\(775\) −1.00000 −0.0359211
\(776\) −1.83994 −0.0660498
\(777\) 3.60294 0.129255
\(778\) 9.92601 0.355865
\(779\) −35.7310 −1.28020
\(780\) 2.63528 0.0943581
\(781\) 5.81140 0.207948
\(782\) −0.340630 −0.0121809
\(783\) −11.6463 −0.416206
\(784\) −6.95873 −0.248526
\(785\) 19.6491 0.701306
\(786\) −32.1434 −1.14652
\(787\) −4.16425 −0.148440 −0.0742198 0.997242i \(-0.523647\pi\)
−0.0742198 + 0.997242i \(0.523647\pi\)
\(788\) −0.893060 −0.0318140
\(789\) 2.95175 0.105085
\(790\) −7.88727 −0.280617
\(791\) 0.0258201 0.000918055 0
\(792\) 19.0786 0.677927
\(793\) −8.56694 −0.304221
\(794\) −30.3617 −1.07750
\(795\) −19.5047 −0.691762
\(796\) 5.49310 0.194698
\(797\) 4.73708 0.167796 0.0838981 0.996474i \(-0.473263\pi\)
0.0838981 + 0.996474i \(0.473263\pi\)
\(798\) 1.60866 0.0569460
\(799\) −0.170466 −0.00603067
\(800\) 1.00000 0.0353553
\(801\) 51.8993 1.83377
\(802\) −21.9321 −0.774450
\(803\) −12.7981 −0.451635
\(804\) −13.5133 −0.476578
\(805\) −1.01250 −0.0356858
\(806\) 1.00000 0.0352235
\(807\) −54.0647 −1.90317
\(808\) 2.38178 0.0837906
\(809\) 29.6006 1.04070 0.520351 0.853952i \(-0.325801\pi\)
0.520351 + 0.853952i \(0.325801\pi\)
\(810\) 5.27351 0.185292
\(811\) −1.15683 −0.0406219 −0.0203110 0.999794i \(-0.506466\pi\)
−0.0203110 + 0.999794i \(0.506466\pi\)
\(812\) −0.950330 −0.0333501
\(813\) 40.5306 1.42147
\(814\) 32.5510 1.14091
\(815\) 8.98152 0.314609
\(816\) −0.180100 −0.00630478
\(817\) −1.55511 −0.0544065
\(818\) −2.08788 −0.0730009
\(819\) −0.801330 −0.0280007
\(820\) 11.8907 0.415240
\(821\) 4.74940 0.165755 0.0828776 0.996560i \(-0.473589\pi\)
0.0828776 + 0.996560i \(0.473589\pi\)
\(822\) 11.9148 0.415575
\(823\) −21.9283 −0.764373 −0.382186 0.924085i \(-0.624829\pi\)
−0.382186 + 0.924085i \(0.624829\pi\)
\(824\) −6.44296 −0.224451
\(825\) 12.7456 0.443744
\(826\) −1.88062 −0.0654353
\(827\) 51.0416 1.77489 0.887445 0.460914i \(-0.152478\pi\)
0.887445 + 0.460914i \(0.152478\pi\)
\(828\) 19.6611 0.683269
\(829\) 34.7117 1.20559 0.602793 0.797897i \(-0.294054\pi\)
0.602793 + 0.797897i \(0.294054\pi\)
\(830\) −14.3936 −0.499609
\(831\) −12.9955 −0.450811
\(832\) −1.00000 −0.0346688
\(833\) 0.475575 0.0164777
\(834\) −27.0990 −0.938360
\(835\) 13.4277 0.464683
\(836\) 14.5336 0.502654
\(837\) −2.48951 −0.0860500
\(838\) −34.6798 −1.19799
\(839\) 15.5885 0.538175 0.269088 0.963116i \(-0.413278\pi\)
0.269088 + 0.963116i \(0.413278\pi\)
\(840\) −0.535335 −0.0184708
\(841\) −7.11476 −0.245337
\(842\) −0.223194 −0.00769176
\(843\) 42.3994 1.46031
\(844\) −12.1262 −0.417403
\(845\) −1.00000 −0.0344010
\(846\) 9.83927 0.338281
\(847\) 2.51732 0.0864962
\(848\) 7.40140 0.254165
\(849\) 73.5692 2.52489
\(850\) −0.0683421 −0.00234412
\(851\) 33.5449 1.14990
\(852\) 3.16646 0.108481
\(853\) −39.7065 −1.35952 −0.679762 0.733432i \(-0.737917\pi\)
−0.679762 + 0.733432i \(0.737917\pi\)
\(854\) 1.74030 0.0595519
\(855\) −11.8536 −0.405386
\(856\) −4.19546 −0.143398
\(857\) 10.1410 0.346408 0.173204 0.984886i \(-0.444588\pi\)
0.173204 + 0.984886i \(0.444588\pi\)
\(858\) −12.7456 −0.435127
\(859\) −24.3423 −0.830550 −0.415275 0.909696i \(-0.636315\pi\)
−0.415275 + 0.909696i \(0.636315\pi\)
\(860\) 0.517514 0.0176471
\(861\) −6.36549 −0.216935
\(862\) −20.9742 −0.714383
\(863\) 46.1396 1.57061 0.785306 0.619108i \(-0.212506\pi\)
0.785306 + 0.619108i \(0.212506\pi\)
\(864\) 2.48951 0.0846948
\(865\) −15.0496 −0.511701
\(866\) −14.6915 −0.499237
\(867\) −44.7874 −1.52106
\(868\) −0.203142 −0.00689508
\(869\) 38.1470 1.29405
\(870\) 12.3283 0.417967
\(871\) 5.12785 0.173751
\(872\) −7.15776 −0.242392
\(873\) −7.25797 −0.245645
\(874\) 14.9773 0.506615
\(875\) −0.203142 −0.00686744
\(876\) −6.97330 −0.235606
\(877\) −25.3312 −0.855373 −0.427687 0.903927i \(-0.640671\pi\)
−0.427687 + 0.903927i \(0.640671\pi\)
\(878\) −38.7604 −1.30810
\(879\) 5.22473 0.176226
\(880\) −4.83652 −0.163039
\(881\) 53.1604 1.79102 0.895510 0.445041i \(-0.146811\pi\)
0.895510 + 0.445041i \(0.146811\pi\)
\(882\) −27.4500 −0.924290
\(883\) −10.0176 −0.337119 −0.168560 0.985691i \(-0.553912\pi\)
−0.168560 + 0.985691i \(0.553912\pi\)
\(884\) 0.0683421 0.00229859
\(885\) 24.3966 0.820083
\(886\) −28.2306 −0.948427
\(887\) −4.54847 −0.152723 −0.0763613 0.997080i \(-0.524330\pi\)
−0.0763613 + 0.997080i \(0.524330\pi\)
\(888\) 17.7361 0.595184
\(889\) 1.40519 0.0471286
\(890\) −13.1568 −0.441015
\(891\) −25.5055 −0.854465
\(892\) 4.43362 0.148449
\(893\) 7.49531 0.250821
\(894\) 51.2643 1.71453
\(895\) 10.0195 0.334914
\(896\) 0.203142 0.00678649
\(897\) −13.1347 −0.438555
\(898\) 36.3549 1.21318
\(899\) 4.67817 0.156026
\(900\) 3.94469 0.131490
\(901\) −0.505827 −0.0168516
\(902\) −57.5095 −1.91486
\(903\) −0.277043 −0.00921942
\(904\) 0.127104 0.00422741
\(905\) −8.45118 −0.280927
\(906\) 31.7793 1.05580
\(907\) 27.3180 0.907078 0.453539 0.891236i \(-0.350161\pi\)
0.453539 + 0.891236i \(0.350161\pi\)
\(908\) −25.4808 −0.845610
\(909\) 9.39536 0.311625
\(910\) 0.203142 0.00673408
\(911\) −50.0911 −1.65959 −0.829797 0.558066i \(-0.811544\pi\)
−0.829797 + 0.558066i \(0.811544\pi\)
\(912\) 7.91891 0.262221
\(913\) 69.6150 2.30392
\(914\) 31.8140 1.05232
\(915\) −22.5763 −0.746348
\(916\) −7.75619 −0.256272
\(917\) −2.47779 −0.0818240
\(918\) −0.170138 −0.00561540
\(919\) 21.5037 0.709342 0.354671 0.934991i \(-0.384593\pi\)
0.354671 + 0.934991i \(0.384593\pi\)
\(920\) −4.98419 −0.164324
\(921\) −5.84954 −0.192749
\(922\) −15.5327 −0.511543
\(923\) −1.20157 −0.0395500
\(924\) 2.58916 0.0851771
\(925\) 6.73026 0.221289
\(926\) 27.7525 0.912005
\(927\) −25.4154 −0.834753
\(928\) −4.67817 −0.153568
\(929\) 43.3836 1.42337 0.711686 0.702498i \(-0.247932\pi\)
0.711686 + 0.702498i \(0.247932\pi\)
\(930\) 2.63528 0.0864141
\(931\) −20.9107 −0.685322
\(932\) −16.0043 −0.524239
\(933\) 1.66364 0.0544650
\(934\) −20.6674 −0.676259
\(935\) 0.330538 0.0108098
\(936\) −3.94469 −0.128936
\(937\) −43.1554 −1.40983 −0.704913 0.709294i \(-0.749014\pi\)
−0.704913 + 0.709294i \(0.749014\pi\)
\(938\) −1.04168 −0.0340121
\(939\) −5.38010 −0.175573
\(940\) −2.49431 −0.0813554
\(941\) 11.4513 0.373303 0.186652 0.982426i \(-0.440236\pi\)
0.186652 + 0.982426i \(0.440236\pi\)
\(942\) −51.7808 −1.68711
\(943\) −59.2653 −1.92994
\(944\) −9.25770 −0.301312
\(945\) −0.505723 −0.0164512
\(946\) −2.50297 −0.0813786
\(947\) 22.5810 0.733785 0.366893 0.930263i \(-0.380422\pi\)
0.366893 + 0.930263i \(0.380422\pi\)
\(948\) 20.7851 0.675070
\(949\) 2.64613 0.0858972
\(950\) 3.00496 0.0974939
\(951\) 10.1727 0.329873
\(952\) −0.0138831 −0.000449955 0
\(953\) −32.2718 −1.04539 −0.522693 0.852521i \(-0.675073\pi\)
−0.522693 + 0.852521i \(0.675073\pi\)
\(954\) 29.1962 0.945262
\(955\) −0.282464 −0.00914033
\(956\) −10.1862 −0.329446
\(957\) −59.6259 −1.92743
\(958\) 15.9286 0.514631
\(959\) 0.918455 0.0296585
\(960\) −2.63528 −0.0850532
\(961\) 1.00000 0.0322581
\(962\) −6.73026 −0.216992
\(963\) −16.5498 −0.533309
\(964\) −11.5154 −0.370885
\(965\) −3.11170 −0.100169
\(966\) 2.66821 0.0858482
\(967\) 47.0898 1.51431 0.757154 0.653237i \(-0.226589\pi\)
0.757154 + 0.653237i \(0.226589\pi\)
\(968\) 12.3920 0.398292
\(969\) −0.541195 −0.0173857
\(970\) 1.83994 0.0590768
\(971\) 1.02586 0.0329215 0.0164607 0.999865i \(-0.494760\pi\)
0.0164607 + 0.999865i \(0.494760\pi\)
\(972\) −21.3657 −0.685305
\(973\) −2.08894 −0.0669682
\(974\) −20.3387 −0.651693
\(975\) −2.63528 −0.0843964
\(976\) 8.56694 0.274221
\(977\) 18.3514 0.587113 0.293556 0.955942i \(-0.405161\pi\)
0.293556 + 0.955942i \(0.405161\pi\)
\(978\) −23.6688 −0.756844
\(979\) 63.6329 2.03372
\(980\) 6.95873 0.222289
\(981\) −28.2351 −0.901477
\(982\) 29.8096 0.951264
\(983\) 26.5509 0.846844 0.423422 0.905933i \(-0.360829\pi\)
0.423422 + 0.905933i \(0.360829\pi\)
\(984\) −31.3352 −0.998930
\(985\) 0.893060 0.0284553
\(986\) 0.319716 0.0101818
\(987\) 1.33529 0.0425028
\(988\) −3.00496 −0.0956006
\(989\) −2.57939 −0.0820198
\(990\) −19.0786 −0.606357
\(991\) −39.3894 −1.25125 −0.625623 0.780125i \(-0.715155\pi\)
−0.625623 + 0.780125i \(0.715155\pi\)
\(992\) −1.00000 −0.0317500
\(993\) 14.1434 0.448829
\(994\) 0.244088 0.00774200
\(995\) −5.49310 −0.174143
\(996\) 37.9311 1.20189
\(997\) −50.6245 −1.60330 −0.801648 0.597797i \(-0.796043\pi\)
−0.801648 + 0.597797i \(0.796043\pi\)
\(998\) 2.18894 0.0692897
\(999\) 16.7550 0.530106
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 \(a_p\))