Properties

Label 4030.2.a.n.1.4
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 1.4
Root \(0.635022\)
Character \(\chi\) = 4030.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -0.635022 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.635022 q^{6} +1.23180 q^{7} +1.00000 q^{8} -2.59675 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -0.635022 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.635022 q^{6} +1.23180 q^{7} +1.00000 q^{8} -2.59675 q^{9} -1.00000 q^{10} +0.272596 q^{11} -0.635022 q^{12} -1.00000 q^{13} +1.23180 q^{14} +0.635022 q^{15} +1.00000 q^{16} +7.11122 q^{17} -2.59675 q^{18} -1.95394 q^{19} -1.00000 q^{20} -0.782218 q^{21} +0.272596 q^{22} -1.59230 q^{23} -0.635022 q^{24} +1.00000 q^{25} -1.00000 q^{26} +3.55406 q^{27} +1.23180 q^{28} +0.671264 q^{29} +0.635022 q^{30} -1.00000 q^{31} +1.00000 q^{32} -0.173104 q^{33} +7.11122 q^{34} -1.23180 q^{35} -2.59675 q^{36} +6.46612 q^{37} -1.95394 q^{38} +0.635022 q^{39} -1.00000 q^{40} -11.0790 q^{41} -0.782218 q^{42} +6.68387 q^{43} +0.272596 q^{44} +2.59675 q^{45} -1.59230 q^{46} +2.10016 q^{47} -0.635022 q^{48} -5.48268 q^{49} +1.00000 q^{50} -4.51578 q^{51} -1.00000 q^{52} +7.92467 q^{53} +3.55406 q^{54} -0.272596 q^{55} +1.23180 q^{56} +1.24080 q^{57} +0.671264 q^{58} +8.12564 q^{59} +0.635022 q^{60} -8.58732 q^{61} -1.00000 q^{62} -3.19866 q^{63} +1.00000 q^{64} +1.00000 q^{65} -0.173104 q^{66} +4.35909 q^{67} +7.11122 q^{68} +1.01115 q^{69} -1.23180 q^{70} +5.14505 q^{71} -2.59675 q^{72} +10.1523 q^{73} +6.46612 q^{74} -0.635022 q^{75} -1.95394 q^{76} +0.335782 q^{77} +0.635022 q^{78} +13.5679 q^{79} -1.00000 q^{80} +5.53334 q^{81} -11.0790 q^{82} -9.00122 q^{83} -0.782218 q^{84} -7.11122 q^{85} +6.68387 q^{86} -0.426267 q^{87} +0.272596 q^{88} +8.93093 q^{89} +2.59675 q^{90} -1.23180 q^{91} -1.59230 q^{92} +0.635022 q^{93} +2.10016 q^{94} +1.95394 q^{95} -0.635022 q^{96} +15.7222 q^{97} -5.48268 q^{98} -0.707862 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{2} - q^{3} + 8q^{4} - 8q^{5} - q^{6} + q^{7} + 8q^{8} + 9q^{9} + O(q^{10}) \) \( 8q + 8q^{2} - q^{3} + 8q^{4} - 8q^{5} - q^{6} + q^{7} + 8q^{8} + 9q^{9} - 8q^{10} + 4q^{11} - q^{12} - 8q^{13} + q^{14} + q^{15} + 8q^{16} - 5q^{17} + 9q^{18} + 2q^{19} - 8q^{20} + 17q^{21} + 4q^{22} + 4q^{23} - q^{24} + 8q^{25} - 8q^{26} + 11q^{27} + q^{28} + 11q^{29} + q^{30} - 8q^{31} + 8q^{32} + 10q^{33} - 5q^{34} - q^{35} + 9q^{36} + 19q^{37} + 2q^{38} + q^{39} - 8q^{40} + 10q^{41} + 17q^{42} + 19q^{43} + 4q^{44} - 9q^{45} + 4q^{46} + 11q^{47} - q^{48} + 11q^{49} + 8q^{50} + 7q^{51} - 8q^{52} + 8q^{53} + 11q^{54} - 4q^{55} + q^{56} - 11q^{57} + 11q^{58} + 28q^{59} + q^{60} - 12q^{61} - 8q^{62} + 20q^{63} + 8q^{64} + 8q^{65} + 10q^{66} + 24q^{67} - 5q^{68} + 30q^{69} - q^{70} + 18q^{71} + 9q^{72} - 3q^{73} + 19q^{74} - q^{75} + 2q^{76} - 7q^{77} + q^{78} + 22q^{79} - 8q^{80} + 24q^{81} + 10q^{82} + 17q^{83} + 17q^{84} + 5q^{85} + 19q^{86} + 11q^{87} + 4q^{88} + 17q^{89} - 9q^{90} - q^{91} + 4q^{92} + q^{93} + 11q^{94} - 2q^{95} - q^{96} - 24q^{97} + 11q^{98} + 23q^{99} + O(q^{100}) \)

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
\(3\) −0.635022 −0.366630 −0.183315 0.983054i \(-0.558683\pi\)
−0.183315 + 0.983054i \(0.558683\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −0.635022 −0.259247
\(7\) 1.23180 0.465575 0.232788 0.972528i \(-0.425215\pi\)
0.232788 + 0.972528i \(0.425215\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.59675 −0.865582
\(10\) −1.00000 −0.316228
\(11\) 0.272596 0.0821907 0.0410953 0.999155i \(-0.486915\pi\)
0.0410953 + 0.999155i \(0.486915\pi\)
\(12\) −0.635022 −0.183315
\(13\) −1.00000 −0.277350
\(14\) 1.23180 0.329211
\(15\) 0.635022 0.163962
\(16\) 1.00000 0.250000
\(17\) 7.11122 1.72473 0.862363 0.506291i \(-0.168984\pi\)
0.862363 + 0.506291i \(0.168984\pi\)
\(18\) −2.59675 −0.612059
\(19\) −1.95394 −0.448265 −0.224133 0.974559i \(-0.571955\pi\)
−0.224133 + 0.974559i \(0.571955\pi\)
\(20\) −1.00000 −0.223607
\(21\) −0.782218 −0.170694
\(22\) 0.272596 0.0581176
\(23\) −1.59230 −0.332018 −0.166009 0.986124i \(-0.553088\pi\)
−0.166009 + 0.986124i \(0.553088\pi\)
\(24\) −0.635022 −0.129623
\(25\) 1.00000 0.200000
\(26\) −1.00000 −0.196116
\(27\) 3.55406 0.683979
\(28\) 1.23180 0.232788
\(29\) 0.671264 0.124651 0.0623253 0.998056i \(-0.480148\pi\)
0.0623253 + 0.998056i \(0.480148\pi\)
\(30\) 0.635022 0.115939
\(31\) −1.00000 −0.179605
\(32\) 1.00000 0.176777
\(33\) −0.173104 −0.0301336
\(34\) 7.11122 1.21956
\(35\) −1.23180 −0.208212
\(36\) −2.59675 −0.432791
\(37\) 6.46612 1.06302 0.531512 0.847051i \(-0.321624\pi\)
0.531512 + 0.847051i \(0.321624\pi\)
\(38\) −1.95394 −0.316972
\(39\) 0.635022 0.101685
\(40\) −1.00000 −0.158114
\(41\) −11.0790 −1.73025 −0.865126 0.501554i \(-0.832762\pi\)
−0.865126 + 0.501554i \(0.832762\pi\)
\(42\) −0.782218 −0.120699
\(43\) 6.68387 1.01928 0.509640 0.860387i \(-0.329778\pi\)
0.509640 + 0.860387i \(0.329778\pi\)
\(44\) 0.272596 0.0410953
\(45\) 2.59675 0.387100
\(46\) −1.59230 −0.234772
\(47\) 2.10016 0.306340 0.153170 0.988200i \(-0.451052\pi\)
0.153170 + 0.988200i \(0.451052\pi\)
\(48\) −0.635022 −0.0916575
\(49\) −5.48268 −0.783240
\(50\) 1.00000 0.141421
\(51\) −4.51578 −0.632336
\(52\) −1.00000 −0.138675
\(53\) 7.92467 1.08854 0.544269 0.838911i \(-0.316807\pi\)
0.544269 + 0.838911i \(0.316807\pi\)
\(54\) 3.55406 0.483646
\(55\) −0.272596 −0.0367568
\(56\) 1.23180 0.164606
\(57\) 1.24080 0.164348
\(58\) 0.671264 0.0881413
\(59\) 8.12564 1.05787 0.528934 0.848663i \(-0.322592\pi\)
0.528934 + 0.848663i \(0.322592\pi\)
\(60\) 0.635022 0.0819810
\(61\) −8.58732 −1.09949 −0.549747 0.835331i \(-0.685276\pi\)
−0.549747 + 0.835331i \(0.685276\pi\)
\(62\) −1.00000 −0.127000
\(63\) −3.19866 −0.402994
\(64\) 1.00000 0.125000
\(65\) 1.00000 0.124035
\(66\) −0.173104 −0.0213077
\(67\) 4.35909 0.532547 0.266274 0.963897i \(-0.414208\pi\)
0.266274 + 0.963897i \(0.414208\pi\)
\(68\) 7.11122 0.862363
\(69\) 1.01115 0.121728
\(70\) −1.23180 −0.147228
\(71\) 5.14505 0.610606 0.305303 0.952255i \(-0.401242\pi\)
0.305303 + 0.952255i \(0.401242\pi\)
\(72\) −2.59675 −0.306030
\(73\) 10.1523 1.18824 0.594118 0.804378i \(-0.297501\pi\)
0.594118 + 0.804378i \(0.297501\pi\)
\(74\) 6.46612 0.751671
\(75\) −0.635022 −0.0733260
\(76\) −1.95394 −0.224133
\(77\) 0.335782 0.0382660
\(78\) 0.635022 0.0719021
\(79\) 13.5679 1.52650 0.763252 0.646101i \(-0.223602\pi\)
0.763252 + 0.646101i \(0.223602\pi\)
\(80\) −1.00000 −0.111803
\(81\) 5.53334 0.614815
\(82\) −11.0790 −1.22347
\(83\) −9.00122 −0.988012 −0.494006 0.869459i \(-0.664468\pi\)
−0.494006 + 0.869459i \(0.664468\pi\)
\(84\) −0.782218 −0.0853469
\(85\) −7.11122 −0.771320
\(86\) 6.68387 0.720741
\(87\) −0.426267 −0.0457007
\(88\) 0.272596 0.0290588
\(89\) 8.93093 0.946677 0.473338 0.880881i \(-0.343049\pi\)
0.473338 + 0.880881i \(0.343049\pi\)
\(90\) 2.59675 0.273721
\(91\) −1.23180 −0.129127
\(92\) −1.59230 −0.166009
\(93\) 0.635022 0.0658487
\(94\) 2.10016 0.216615
\(95\) 1.95394 0.200470
\(96\) −0.635022 −0.0648116
\(97\) 15.7222 1.59634 0.798172 0.602430i \(-0.205801\pi\)
0.798172 + 0.602430i \(0.205801\pi\)
\(98\) −5.48268 −0.553834
\(99\) −0.707862 −0.0711428
\(100\) 1.00000 0.100000
\(101\) 7.64601 0.760806 0.380403 0.924821i \(-0.375785\pi\)
0.380403 + 0.924821i \(0.375785\pi\)
\(102\) −4.51578 −0.447129
\(103\) −5.75324 −0.566884 −0.283442 0.958989i \(-0.591476\pi\)
−0.283442 + 0.958989i \(0.591476\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0.782218 0.0763366
\(106\) 7.92467 0.769712
\(107\) −4.45612 −0.430789 −0.215394 0.976527i \(-0.569104\pi\)
−0.215394 + 0.976527i \(0.569104\pi\)
\(108\) 3.55406 0.341989
\(109\) 8.27284 0.792394 0.396197 0.918165i \(-0.370330\pi\)
0.396197 + 0.918165i \(0.370330\pi\)
\(110\) −0.272596 −0.0259910
\(111\) −4.10613 −0.389736
\(112\) 1.23180 0.116394
\(113\) 9.85052 0.926659 0.463330 0.886186i \(-0.346655\pi\)
0.463330 + 0.886186i \(0.346655\pi\)
\(114\) 1.24080 0.116211
\(115\) 1.59230 0.148483
\(116\) 0.671264 0.0623253
\(117\) 2.59675 0.240069
\(118\) 8.12564 0.748026
\(119\) 8.75958 0.802989
\(120\) 0.635022 0.0579693
\(121\) −10.9257 −0.993245
\(122\) −8.58732 −0.777459
\(123\) 7.03542 0.634363
\(124\) −1.00000 −0.0898027
\(125\) −1.00000 −0.0894427
\(126\) −3.19866 −0.284960
\(127\) −17.2692 −1.53239 −0.766195 0.642608i \(-0.777852\pi\)
−0.766195 + 0.642608i \(0.777852\pi\)
\(128\) 1.00000 0.0883883
\(129\) −4.24441 −0.373699
\(130\) 1.00000 0.0877058
\(131\) 6.28322 0.548968 0.274484 0.961592i \(-0.411493\pi\)
0.274484 + 0.961592i \(0.411493\pi\)
\(132\) −0.173104 −0.0150668
\(133\) −2.40686 −0.208701
\(134\) 4.35909 0.376568
\(135\) −3.55406 −0.305885
\(136\) 7.11122 0.609782
\(137\) −5.33968 −0.456200 −0.228100 0.973638i \(-0.573251\pi\)
−0.228100 + 0.973638i \(0.573251\pi\)
\(138\) 1.01115 0.0860746
\(139\) 12.2006 1.03484 0.517422 0.855731i \(-0.326892\pi\)
0.517422 + 0.855731i \(0.326892\pi\)
\(140\) −1.23180 −0.104106
\(141\) −1.33365 −0.112314
\(142\) 5.14505 0.431763
\(143\) −0.272596 −0.0227956
\(144\) −2.59675 −0.216396
\(145\) −0.671264 −0.0557454
\(146\) 10.1523 0.840210
\(147\) 3.48162 0.287159
\(148\) 6.46612 0.531512
\(149\) −7.79203 −0.638348 −0.319174 0.947696i \(-0.603405\pi\)
−0.319174 + 0.947696i \(0.603405\pi\)
\(150\) −0.635022 −0.0518493
\(151\) 18.9468 1.54187 0.770935 0.636914i \(-0.219789\pi\)
0.770935 + 0.636914i \(0.219789\pi\)
\(152\) −1.95394 −0.158486
\(153\) −18.4660 −1.49289
\(154\) 0.335782 0.0270581
\(155\) 1.00000 0.0803219
\(156\) 0.635022 0.0508424
\(157\) 7.62496 0.608538 0.304269 0.952586i \(-0.401588\pi\)
0.304269 + 0.952586i \(0.401588\pi\)
\(158\) 13.5679 1.07940
\(159\) −5.03234 −0.399090
\(160\) −1.00000 −0.0790569
\(161\) −1.96139 −0.154580
\(162\) 5.53334 0.434740
\(163\) −8.43039 −0.660319 −0.330159 0.943925i \(-0.607103\pi\)
−0.330159 + 0.943925i \(0.607103\pi\)
\(164\) −11.0790 −0.865126
\(165\) 0.173104 0.0134761
\(166\) −9.00122 −0.698630
\(167\) 24.1193 1.86641 0.933203 0.359351i \(-0.117002\pi\)
0.933203 + 0.359351i \(0.117002\pi\)
\(168\) −0.782218 −0.0603494
\(169\) 1.00000 0.0769231
\(170\) −7.11122 −0.545406
\(171\) 5.07390 0.388011
\(172\) 6.68387 0.509640
\(173\) 1.59651 0.121380 0.0606900 0.998157i \(-0.480670\pi\)
0.0606900 + 0.998157i \(0.480670\pi\)
\(174\) −0.426267 −0.0323152
\(175\) 1.23180 0.0931151
\(176\) 0.272596 0.0205477
\(177\) −5.15996 −0.387846
\(178\) 8.93093 0.669401
\(179\) 10.8435 0.810483 0.405242 0.914210i \(-0.367187\pi\)
0.405242 + 0.914210i \(0.367187\pi\)
\(180\) 2.59675 0.193550
\(181\) −0.0526882 −0.00391628 −0.00195814 0.999998i \(-0.500623\pi\)
−0.00195814 + 0.999998i \(0.500623\pi\)
\(182\) −1.23180 −0.0913068
\(183\) 5.45313 0.403107
\(184\) −1.59230 −0.117386
\(185\) −6.46612 −0.475398
\(186\) 0.635022 0.0465621
\(187\) 1.93849 0.141756
\(188\) 2.10016 0.153170
\(189\) 4.37787 0.318444
\(190\) 1.95394 0.141754
\(191\) −1.31127 −0.0948801 −0.0474401 0.998874i \(-0.515106\pi\)
−0.0474401 + 0.998874i \(0.515106\pi\)
\(192\) −0.635022 −0.0458288
\(193\) 5.15787 0.371272 0.185636 0.982619i \(-0.440566\pi\)
0.185636 + 0.982619i \(0.440566\pi\)
\(194\) 15.7222 1.12879
\(195\) −0.635022 −0.0454749
\(196\) −5.48268 −0.391620
\(197\) −0.571208 −0.0406969 −0.0203485 0.999793i \(-0.506478\pi\)
−0.0203485 + 0.999793i \(0.506478\pi\)
\(198\) −0.707862 −0.0503056
\(199\) 0.766897 0.0543639 0.0271820 0.999631i \(-0.491347\pi\)
0.0271820 + 0.999631i \(0.491347\pi\)
\(200\) 1.00000 0.0707107
\(201\) −2.76812 −0.195248
\(202\) 7.64601 0.537971
\(203\) 0.826861 0.0580342
\(204\) −4.51578 −0.316168
\(205\) 11.0790 0.773792
\(206\) −5.75324 −0.400847
\(207\) 4.13481 0.287389
\(208\) −1.00000 −0.0693375
\(209\) −0.532637 −0.0368432
\(210\) 0.782218 0.0539781
\(211\) −9.86552 −0.679170 −0.339585 0.940575i \(-0.610287\pi\)
−0.339585 + 0.940575i \(0.610287\pi\)
\(212\) 7.92467 0.544269
\(213\) −3.26722 −0.223866
\(214\) −4.45612 −0.304614
\(215\) −6.68387 −0.455836
\(216\) 3.55406 0.241823
\(217\) −1.23180 −0.0836198
\(218\) 8.27284 0.560307
\(219\) −6.44693 −0.435643
\(220\) −0.272596 −0.0183784
\(221\) −7.11122 −0.478353
\(222\) −4.10613 −0.275585
\(223\) −2.04843 −0.137173 −0.0685865 0.997645i \(-0.521849\pi\)
−0.0685865 + 0.997645i \(0.521849\pi\)
\(224\) 1.23180 0.0823029
\(225\) −2.59675 −0.173116
\(226\) 9.85052 0.655247
\(227\) −10.9084 −0.724019 −0.362010 0.932174i \(-0.617909\pi\)
−0.362010 + 0.932174i \(0.617909\pi\)
\(228\) 1.24080 0.0821738
\(229\) −3.97344 −0.262572 −0.131286 0.991345i \(-0.541911\pi\)
−0.131286 + 0.991345i \(0.541911\pi\)
\(230\) 1.59230 0.104993
\(231\) −0.213229 −0.0140294
\(232\) 0.671264 0.0440706
\(233\) −0.177298 −0.0116152 −0.00580759 0.999983i \(-0.501849\pi\)
−0.00580759 + 0.999983i \(0.501849\pi\)
\(234\) 2.59675 0.169755
\(235\) −2.10016 −0.137000
\(236\) 8.12564 0.528934
\(237\) −8.61589 −0.559662
\(238\) 8.75958 0.567799
\(239\) −18.7030 −1.20980 −0.604898 0.796303i \(-0.706786\pi\)
−0.604898 + 0.796303i \(0.706786\pi\)
\(240\) 0.635022 0.0409905
\(241\) 14.8399 0.955920 0.477960 0.878382i \(-0.341376\pi\)
0.477960 + 0.878382i \(0.341376\pi\)
\(242\) −10.9257 −0.702330
\(243\) −14.1760 −0.909388
\(244\) −8.58732 −0.549747
\(245\) 5.48268 0.350275
\(246\) 7.03542 0.448562
\(247\) 1.95394 0.124326
\(248\) −1.00000 −0.0635001
\(249\) 5.71597 0.362235
\(250\) −1.00000 −0.0632456
\(251\) 6.18551 0.390426 0.195213 0.980761i \(-0.437460\pi\)
0.195213 + 0.980761i \(0.437460\pi\)
\(252\) −3.19866 −0.201497
\(253\) −0.434055 −0.0272888
\(254\) −17.2692 −1.08356
\(255\) 4.51578 0.282789
\(256\) 1.00000 0.0625000
\(257\) −5.66129 −0.353141 −0.176571 0.984288i \(-0.556500\pi\)
−0.176571 + 0.984288i \(0.556500\pi\)
\(258\) −4.24441 −0.264245
\(259\) 7.96494 0.494917
\(260\) 1.00000 0.0620174
\(261\) −1.74310 −0.107895
\(262\) 6.28322 0.388179
\(263\) 9.59564 0.591692 0.295846 0.955236i \(-0.404398\pi\)
0.295846 + 0.955236i \(0.404398\pi\)
\(264\) −0.173104 −0.0106538
\(265\) −7.92467 −0.486809
\(266\) −2.40686 −0.147574
\(267\) −5.67134 −0.347080
\(268\) 4.35909 0.266274
\(269\) −20.4741 −1.24833 −0.624165 0.781292i \(-0.714561\pi\)
−0.624165 + 0.781292i \(0.714561\pi\)
\(270\) −3.55406 −0.216293
\(271\) −5.75652 −0.349683 −0.174842 0.984597i \(-0.555941\pi\)
−0.174842 + 0.984597i \(0.555941\pi\)
\(272\) 7.11122 0.431181
\(273\) 0.782218 0.0473420
\(274\) −5.33968 −0.322582
\(275\) 0.272596 0.0164381
\(276\) 1.01115 0.0608639
\(277\) 10.7117 0.643603 0.321802 0.946807i \(-0.395712\pi\)
0.321802 + 0.946807i \(0.395712\pi\)
\(278\) 12.2006 0.731745
\(279\) 2.59675 0.155463
\(280\) −1.23180 −0.0736139
\(281\) 5.43868 0.324444 0.162222 0.986754i \(-0.448134\pi\)
0.162222 + 0.986754i \(0.448134\pi\)
\(282\) −1.33365 −0.0794177
\(283\) −17.9430 −1.06660 −0.533301 0.845926i \(-0.679049\pi\)
−0.533301 + 0.845926i \(0.679049\pi\)
\(284\) 5.14505 0.305303
\(285\) −1.24080 −0.0734985
\(286\) −0.272596 −0.0161189
\(287\) −13.6471 −0.805563
\(288\) −2.59675 −0.153015
\(289\) 33.5695 1.97468
\(290\) −0.671264 −0.0394180
\(291\) −9.98392 −0.585268
\(292\) 10.1523 0.594118
\(293\) 6.11034 0.356970 0.178485 0.983943i \(-0.442880\pi\)
0.178485 + 0.983943i \(0.442880\pi\)
\(294\) 3.48162 0.203052
\(295\) −8.12564 −0.473093
\(296\) 6.46612 0.375835
\(297\) 0.968820 0.0562167
\(298\) −7.79203 −0.451380
\(299\) 1.59230 0.0920853
\(300\) −0.635022 −0.0366630
\(301\) 8.23317 0.474552
\(302\) 18.9468 1.09027
\(303\) −4.85538 −0.278934
\(304\) −1.95394 −0.112066
\(305\) 8.58732 0.491708
\(306\) −18.4660 −1.05563
\(307\) 9.38551 0.535659 0.267830 0.963466i \(-0.413694\pi\)
0.267830 + 0.963466i \(0.413694\pi\)
\(308\) 0.335782 0.0191330
\(309\) 3.65343 0.207837
\(310\) 1.00000 0.0567962
\(311\) −33.2713 −1.88664 −0.943322 0.331880i \(-0.892317\pi\)
−0.943322 + 0.331880i \(0.892317\pi\)
\(312\) 0.635022 0.0359510
\(313\) −15.2607 −0.862585 −0.431293 0.902212i \(-0.641942\pi\)
−0.431293 + 0.902212i \(0.641942\pi\)
\(314\) 7.62496 0.430301
\(315\) 3.19866 0.180224
\(316\) 13.5679 0.763252
\(317\) 19.3544 1.08705 0.543525 0.839393i \(-0.317089\pi\)
0.543525 + 0.839393i \(0.317089\pi\)
\(318\) −5.03234 −0.282200
\(319\) 0.182984 0.0102451
\(320\) −1.00000 −0.0559017
\(321\) 2.82973 0.157940
\(322\) −1.96139 −0.109304
\(323\) −13.8949 −0.773135
\(324\) 5.53334 0.307408
\(325\) −1.00000 −0.0554700
\(326\) −8.43039 −0.466916
\(327\) −5.25343 −0.290515
\(328\) −11.0790 −0.611737
\(329\) 2.58698 0.142625
\(330\) 0.173104 0.00952907
\(331\) 10.1890 0.560038 0.280019 0.959994i \(-0.409659\pi\)
0.280019 + 0.959994i \(0.409659\pi\)
\(332\) −9.00122 −0.494006
\(333\) −16.7909 −0.920134
\(334\) 24.1193 1.31975
\(335\) −4.35909 −0.238162
\(336\) −0.782218 −0.0426735
\(337\) −13.0282 −0.709690 −0.354845 0.934925i \(-0.615466\pi\)
−0.354845 + 0.934925i \(0.615466\pi\)
\(338\) 1.00000 0.0543928
\(339\) −6.25530 −0.339741
\(340\) −7.11122 −0.385660
\(341\) −0.272596 −0.0147619
\(342\) 5.07390 0.274365
\(343\) −15.3761 −0.830232
\(344\) 6.68387 0.360370
\(345\) −1.01115 −0.0544384
\(346\) 1.59651 0.0858286
\(347\) 16.6741 0.895110 0.447555 0.894256i \(-0.352295\pi\)
0.447555 + 0.894256i \(0.352295\pi\)
\(348\) −0.426267 −0.0228503
\(349\) 7.19094 0.384922 0.192461 0.981305i \(-0.438353\pi\)
0.192461 + 0.981305i \(0.438353\pi\)
\(350\) 1.23180 0.0658423
\(351\) −3.55406 −0.189702
\(352\) 0.272596 0.0145294
\(353\) 3.90993 0.208105 0.104052 0.994572i \(-0.466819\pi\)
0.104052 + 0.994572i \(0.466819\pi\)
\(354\) −5.15996 −0.274249
\(355\) −5.14505 −0.273071
\(356\) 8.93093 0.473338
\(357\) −5.56252 −0.294400
\(358\) 10.8435 0.573098
\(359\) 11.1264 0.587231 0.293616 0.955924i \(-0.405141\pi\)
0.293616 + 0.955924i \(0.405141\pi\)
\(360\) 2.59675 0.136861
\(361\) −15.1821 −0.799058
\(362\) −0.0526882 −0.00276923
\(363\) 6.93805 0.364153
\(364\) −1.23180 −0.0645637
\(365\) −10.1523 −0.531395
\(366\) 5.45313 0.285040
\(367\) 6.59930 0.344481 0.172240 0.985055i \(-0.444899\pi\)
0.172240 + 0.985055i \(0.444899\pi\)
\(368\) −1.59230 −0.0830046
\(369\) 28.7694 1.49768
\(370\) −6.46612 −0.336157
\(371\) 9.76158 0.506796
\(372\) 0.635022 0.0329243
\(373\) 24.2258 1.25436 0.627181 0.778874i \(-0.284209\pi\)
0.627181 + 0.778874i \(0.284209\pi\)
\(374\) 1.93849 0.100237
\(375\) 0.635022 0.0327924
\(376\) 2.10016 0.108308
\(377\) −0.671264 −0.0345719
\(378\) 4.37787 0.225174
\(379\) 0.870831 0.0447316 0.0223658 0.999750i \(-0.492880\pi\)
0.0223658 + 0.999750i \(0.492880\pi\)
\(380\) 1.95394 0.100235
\(381\) 10.9663 0.561820
\(382\) −1.31127 −0.0670904
\(383\) 18.4271 0.941581 0.470791 0.882245i \(-0.343969\pi\)
0.470791 + 0.882245i \(0.343969\pi\)
\(384\) −0.635022 −0.0324058
\(385\) −0.335782 −0.0171131
\(386\) 5.15787 0.262529
\(387\) −17.3563 −0.882272
\(388\) 15.7222 0.798172
\(389\) 21.8910 1.10992 0.554959 0.831878i \(-0.312734\pi\)
0.554959 + 0.831878i \(0.312734\pi\)
\(390\) −0.635022 −0.0321556
\(391\) −11.3232 −0.572640
\(392\) −5.48268 −0.276917
\(393\) −3.98998 −0.201268
\(394\) −0.571208 −0.0287771
\(395\) −13.5679 −0.682673
\(396\) −0.707862 −0.0355714
\(397\) −20.1091 −1.00925 −0.504624 0.863339i \(-0.668369\pi\)
−0.504624 + 0.863339i \(0.668369\pi\)
\(398\) 0.766897 0.0384411
\(399\) 1.52841 0.0765162
\(400\) 1.00000 0.0500000
\(401\) 1.96722 0.0982385 0.0491193 0.998793i \(-0.484359\pi\)
0.0491193 + 0.998793i \(0.484359\pi\)
\(402\) −2.76812 −0.138061
\(403\) 1.00000 0.0498135
\(404\) 7.64601 0.380403
\(405\) −5.53334 −0.274954
\(406\) 0.826861 0.0410364
\(407\) 1.76264 0.0873706
\(408\) −4.51578 −0.223565
\(409\) 8.94583 0.442343 0.221171 0.975235i \(-0.429012\pi\)
0.221171 + 0.975235i \(0.429012\pi\)
\(410\) 11.0790 0.547154
\(411\) 3.39081 0.167257
\(412\) −5.75324 −0.283442
\(413\) 10.0091 0.492517
\(414\) 4.13481 0.203215
\(415\) 9.00122 0.441852
\(416\) −1.00000 −0.0490290
\(417\) −7.74766 −0.379405
\(418\) −0.532637 −0.0260521
\(419\) 26.9093 1.31461 0.657303 0.753626i \(-0.271697\pi\)
0.657303 + 0.753626i \(0.271697\pi\)
\(420\) 0.782218 0.0381683
\(421\) −7.55904 −0.368405 −0.184203 0.982888i \(-0.558970\pi\)
−0.184203 + 0.982888i \(0.558970\pi\)
\(422\) −9.86552 −0.480246
\(423\) −5.45360 −0.265163
\(424\) 7.92467 0.384856
\(425\) 7.11122 0.344945
\(426\) −3.26722 −0.158297
\(427\) −10.5778 −0.511897
\(428\) −4.45612 −0.215394
\(429\) 0.173104 0.00835755
\(430\) −6.68387 −0.322325
\(431\) 6.12573 0.295066 0.147533 0.989057i \(-0.452867\pi\)
0.147533 + 0.989057i \(0.452867\pi\)
\(432\) 3.55406 0.170995
\(433\) −32.8758 −1.57991 −0.789955 0.613165i \(-0.789896\pi\)
−0.789955 + 0.613165i \(0.789896\pi\)
\(434\) −1.23180 −0.0591281
\(435\) 0.426267 0.0204380
\(436\) 8.27284 0.396197
\(437\) 3.11127 0.148832
\(438\) −6.44693 −0.308046
\(439\) −0.617160 −0.0294554 −0.0147277 0.999892i \(-0.504688\pi\)
−0.0147277 + 0.999892i \(0.504688\pi\)
\(440\) −0.272596 −0.0129955
\(441\) 14.2371 0.677958
\(442\) −7.11122 −0.338246
\(443\) 25.0624 1.19075 0.595375 0.803448i \(-0.297003\pi\)
0.595375 + 0.803448i \(0.297003\pi\)
\(444\) −4.10613 −0.194868
\(445\) −8.93093 −0.423367
\(446\) −2.04843 −0.0969960
\(447\) 4.94811 0.234037
\(448\) 1.23180 0.0581969
\(449\) −27.1106 −1.27943 −0.639715 0.768612i \(-0.720948\pi\)
−0.639715 + 0.768612i \(0.720948\pi\)
\(450\) −2.59675 −0.122412
\(451\) −3.02009 −0.142211
\(452\) 9.85052 0.463330
\(453\) −12.0316 −0.565296
\(454\) −10.9084 −0.511959
\(455\) 1.23180 0.0577475
\(456\) 1.24080 0.0581056
\(457\) −31.6368 −1.47991 −0.739954 0.672657i \(-0.765153\pi\)
−0.739954 + 0.672657i \(0.765153\pi\)
\(458\) −3.97344 −0.185667
\(459\) 25.2737 1.17967
\(460\) 1.59230 0.0742416
\(461\) −24.8568 −1.15770 −0.578848 0.815436i \(-0.696497\pi\)
−0.578848 + 0.815436i \(0.696497\pi\)
\(462\) −0.213229 −0.00992032
\(463\) −12.7600 −0.593007 −0.296503 0.955032i \(-0.595821\pi\)
−0.296503 + 0.955032i \(0.595821\pi\)
\(464\) 0.671264 0.0311626
\(465\) −0.635022 −0.0294484
\(466\) −0.177298 −0.00821318
\(467\) −0.528860 −0.0244727 −0.0122364 0.999925i \(-0.503895\pi\)
−0.0122364 + 0.999925i \(0.503895\pi\)
\(468\) 2.59675 0.120035
\(469\) 5.36951 0.247941
\(470\) −2.10016 −0.0968734
\(471\) −4.84201 −0.223108
\(472\) 8.12564 0.374013
\(473\) 1.82199 0.0837754
\(474\) −8.61589 −0.395741
\(475\) −1.95394 −0.0896531
\(476\) 8.75958 0.401495
\(477\) −20.5784 −0.942219
\(478\) −18.7030 −0.855455
\(479\) 3.07938 0.140701 0.0703503 0.997522i \(-0.477588\pi\)
0.0703503 + 0.997522i \(0.477588\pi\)
\(480\) 0.635022 0.0289846
\(481\) −6.46612 −0.294830
\(482\) 14.8399 0.675938
\(483\) 1.24553 0.0566735
\(484\) −10.9257 −0.496622
\(485\) −15.7222 −0.713907
\(486\) −14.1760 −0.643035
\(487\) −8.04516 −0.364561 −0.182280 0.983247i \(-0.558348\pi\)
−0.182280 + 0.983247i \(0.558348\pi\)
\(488\) −8.58732 −0.388730
\(489\) 5.35348 0.242093
\(490\) 5.48268 0.247682
\(491\) 18.0102 0.812789 0.406395 0.913698i \(-0.366786\pi\)
0.406395 + 0.913698i \(0.366786\pi\)
\(492\) 7.03542 0.317181
\(493\) 4.77351 0.214988
\(494\) 1.95394 0.0879121
\(495\) 0.707862 0.0318160
\(496\) −1.00000 −0.0449013
\(497\) 6.33766 0.284283
\(498\) 5.71597 0.256139
\(499\) −27.2005 −1.21766 −0.608830 0.793300i \(-0.708361\pi\)
−0.608830 + 0.793300i \(0.708361\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −15.3163 −0.684280
\(502\) 6.18551 0.276073
\(503\) 16.0727 0.716646 0.358323 0.933598i \(-0.383349\pi\)
0.358323 + 0.933598i \(0.383349\pi\)
\(504\) −3.19866 −0.142480
\(505\) −7.64601 −0.340243
\(506\) −0.434055 −0.0192961
\(507\) −0.635022 −0.0282023
\(508\) −17.2692 −0.766195
\(509\) −7.86530 −0.348623 −0.174312 0.984691i \(-0.555770\pi\)
−0.174312 + 0.984691i \(0.555770\pi\)
\(510\) 4.51578 0.199962
\(511\) 12.5056 0.553213
\(512\) 1.00000 0.0441942
\(513\) −6.94443 −0.306604
\(514\) −5.66129 −0.249709
\(515\) 5.75324 0.253518
\(516\) −4.24441 −0.186850
\(517\) 0.572496 0.0251783
\(518\) 7.96494 0.349959
\(519\) −1.01382 −0.0445016
\(520\) 1.00000 0.0438529
\(521\) −4.09836 −0.179553 −0.0897763 0.995962i \(-0.528615\pi\)
−0.0897763 + 0.995962i \(0.528615\pi\)
\(522\) −1.74310 −0.0762935
\(523\) −42.2018 −1.84536 −0.922678 0.385573i \(-0.874004\pi\)
−0.922678 + 0.385573i \(0.874004\pi\)
\(524\) 6.28322 0.274484
\(525\) −0.782218 −0.0341388
\(526\) 9.59564 0.418390
\(527\) −7.11122 −0.309770
\(528\) −0.173104 −0.00753339
\(529\) −20.4646 −0.889764
\(530\) −7.92467 −0.344226
\(531\) −21.1002 −0.915672
\(532\) −2.40686 −0.104351
\(533\) 11.0790 0.479886
\(534\) −5.67134 −0.245423
\(535\) 4.45612 0.192655
\(536\) 4.35909 0.188284
\(537\) −6.88588 −0.297147
\(538\) −20.4741 −0.882703
\(539\) −1.49455 −0.0643750
\(540\) −3.55406 −0.152942
\(541\) −33.2862 −1.43108 −0.715542 0.698570i \(-0.753820\pi\)
−0.715542 + 0.698570i \(0.753820\pi\)
\(542\) −5.75652 −0.247264
\(543\) 0.0334582 0.00143583
\(544\) 7.11122 0.304891
\(545\) −8.27284 −0.354369
\(546\) 0.782218 0.0334758
\(547\) 1.75889 0.0752045 0.0376023 0.999293i \(-0.488028\pi\)
0.0376023 + 0.999293i \(0.488028\pi\)
\(548\) −5.33968 −0.228100
\(549\) 22.2991 0.951702
\(550\) 0.272596 0.0116235
\(551\) −1.31161 −0.0558765
\(552\) 1.01115 0.0430373
\(553\) 16.7128 0.710702
\(554\) 10.7117 0.455096
\(555\) 4.10613 0.174295
\(556\) 12.2006 0.517422
\(557\) 4.03845 0.171115 0.0855573 0.996333i \(-0.472733\pi\)
0.0855573 + 0.996333i \(0.472733\pi\)
\(558\) 2.59675 0.109929
\(559\) −6.68387 −0.282698
\(560\) −1.23180 −0.0520529
\(561\) −1.23098 −0.0519721
\(562\) 5.43868 0.229417
\(563\) 22.4793 0.947388 0.473694 0.880690i \(-0.342920\pi\)
0.473694 + 0.880690i \(0.342920\pi\)
\(564\) −1.33365 −0.0561568
\(565\) −9.85052 −0.414415
\(566\) −17.9430 −0.754201
\(567\) 6.81595 0.286243
\(568\) 5.14505 0.215882
\(569\) −20.2194 −0.847640 −0.423820 0.905746i \(-0.639311\pi\)
−0.423820 + 0.905746i \(0.639311\pi\)
\(570\) −1.24080 −0.0519713
\(571\) −23.2457 −0.972803 −0.486401 0.873736i \(-0.661691\pi\)
−0.486401 + 0.873736i \(0.661691\pi\)
\(572\) −0.272596 −0.0113978
\(573\) 0.832685 0.0347859
\(574\) −13.6471 −0.569619
\(575\) −1.59230 −0.0664037
\(576\) −2.59675 −0.108198
\(577\) −38.4366 −1.60014 −0.800069 0.599909i \(-0.795204\pi\)
−0.800069 + 0.599909i \(0.795204\pi\)
\(578\) 33.5695 1.39631
\(579\) −3.27536 −0.136119
\(580\) −0.671264 −0.0278727
\(581\) −11.0877 −0.459994
\(582\) −9.98392 −0.413847
\(583\) 2.16023 0.0894676
\(584\) 10.1523 0.420105
\(585\) −2.59675 −0.107362
\(586\) 6.11034 0.252416
\(587\) −12.2666 −0.506296 −0.253148 0.967428i \(-0.581466\pi\)
−0.253148 + 0.967428i \(0.581466\pi\)
\(588\) 3.48162 0.143580
\(589\) 1.95394 0.0805108
\(590\) −8.12564 −0.334527
\(591\) 0.362730 0.0149207
\(592\) 6.46612 0.265756
\(593\) −10.8058 −0.443741 −0.221870 0.975076i \(-0.571216\pi\)
−0.221870 + 0.975076i \(0.571216\pi\)
\(594\) 0.968820 0.0397512
\(595\) −8.75958 −0.359108
\(596\) −7.79203 −0.319174
\(597\) −0.486997 −0.0199314
\(598\) 1.59230 0.0651141
\(599\) 21.8357 0.892184 0.446092 0.894987i \(-0.352815\pi\)
0.446092 + 0.894987i \(0.352815\pi\)
\(600\) −0.635022 −0.0259247
\(601\) −32.6514 −1.33188 −0.665938 0.746007i \(-0.731969\pi\)
−0.665938 + 0.746007i \(0.731969\pi\)
\(602\) 8.23317 0.335559
\(603\) −11.3194 −0.460964
\(604\) 18.9468 0.770935
\(605\) 10.9257 0.444193
\(606\) −4.85538 −0.197236
\(607\) 18.8305 0.764307 0.382154 0.924099i \(-0.375183\pi\)
0.382154 + 0.924099i \(0.375183\pi\)
\(608\) −1.95394 −0.0792429
\(609\) −0.525075 −0.0212771
\(610\) 8.58732 0.347690
\(611\) −2.10016 −0.0849636
\(612\) −18.4660 −0.746446
\(613\) 12.1312 0.489975 0.244987 0.969526i \(-0.421216\pi\)
0.244987 + 0.969526i \(0.421216\pi\)
\(614\) 9.38551 0.378768
\(615\) −7.03542 −0.283696
\(616\) 0.335782 0.0135291
\(617\) −22.3515 −0.899838 −0.449919 0.893069i \(-0.648547\pi\)
−0.449919 + 0.893069i \(0.648547\pi\)
\(618\) 3.65343 0.146963
\(619\) 30.6469 1.23180 0.615901 0.787823i \(-0.288792\pi\)
0.615901 + 0.787823i \(0.288792\pi\)
\(620\) 1.00000 0.0401610
\(621\) −5.65914 −0.227093
\(622\) −33.2713 −1.33406
\(623\) 11.0011 0.440749
\(624\) 0.635022 0.0254212
\(625\) 1.00000 0.0400000
\(626\) −15.2607 −0.609940
\(627\) 0.338236 0.0135078
\(628\) 7.62496 0.304269
\(629\) 45.9820 1.83342
\(630\) 3.19866 0.127438
\(631\) −29.7798 −1.18552 −0.592758 0.805381i \(-0.701961\pi\)
−0.592758 + 0.805381i \(0.701961\pi\)
\(632\) 13.5679 0.539700
\(633\) 6.26482 0.249004
\(634\) 19.3544 0.768661
\(635\) 17.2692 0.685306
\(636\) −5.03234 −0.199545
\(637\) 5.48268 0.217232
\(638\) 0.182984 0.00724439
\(639\) −13.3604 −0.528530
\(640\) −1.00000 −0.0395285
\(641\) 19.5760 0.773206 0.386603 0.922246i \(-0.373648\pi\)
0.386603 + 0.922246i \(0.373648\pi\)
\(642\) 2.82973 0.111681
\(643\) −33.8021 −1.33302 −0.666512 0.745495i \(-0.732213\pi\)
−0.666512 + 0.745495i \(0.732213\pi\)
\(644\) −1.96139 −0.0772898
\(645\) 4.24441 0.167123
\(646\) −13.8949 −0.546689
\(647\) −31.5700 −1.24114 −0.620572 0.784149i \(-0.713100\pi\)
−0.620572 + 0.784149i \(0.713100\pi\)
\(648\) 5.53334 0.217370
\(649\) 2.21501 0.0869469
\(650\) −1.00000 −0.0392232
\(651\) 0.782218 0.0306575
\(652\) −8.43039 −0.330159
\(653\) −35.7069 −1.39732 −0.698659 0.715455i \(-0.746220\pi\)
−0.698659 + 0.715455i \(0.746220\pi\)
\(654\) −5.25343 −0.205425
\(655\) −6.28322 −0.245506
\(656\) −11.0790 −0.432563
\(657\) −26.3629 −1.02852
\(658\) 2.58698 0.100851
\(659\) 24.3706 0.949343 0.474671 0.880163i \(-0.342567\pi\)
0.474671 + 0.880163i \(0.342567\pi\)
\(660\) 0.173104 0.00673807
\(661\) 8.64646 0.336308 0.168154 0.985761i \(-0.446219\pi\)
0.168154 + 0.985761i \(0.446219\pi\)
\(662\) 10.1890 0.396006
\(663\) 4.51578 0.175378
\(664\) −9.00122 −0.349315
\(665\) 2.40686 0.0933341
\(666\) −16.7909 −0.650633
\(667\) −1.06886 −0.0413863
\(668\) 24.1193 0.933203
\(669\) 1.30080 0.0502918
\(670\) −4.35909 −0.168406
\(671\) −2.34087 −0.0903681
\(672\) −0.782218 −0.0301747
\(673\) −39.9771 −1.54101 −0.770503 0.637437i \(-0.779995\pi\)
−0.770503 + 0.637437i \(0.779995\pi\)
\(674\) −13.0282 −0.501826
\(675\) 3.55406 0.136796
\(676\) 1.00000 0.0384615
\(677\) 27.0593 1.03997 0.519987 0.854174i \(-0.325937\pi\)
0.519987 + 0.854174i \(0.325937\pi\)
\(678\) −6.25530 −0.240233
\(679\) 19.3665 0.743218
\(680\) −7.11122 −0.272703
\(681\) 6.92710 0.265447
\(682\) −0.272596 −0.0104382
\(683\) 5.93046 0.226923 0.113461 0.993542i \(-0.463806\pi\)
0.113461 + 0.993542i \(0.463806\pi\)
\(684\) 5.07390 0.194005
\(685\) 5.33968 0.204019
\(686\) −15.3761 −0.587063
\(687\) 2.52322 0.0962669
\(688\) 6.68387 0.254820
\(689\) −7.92467 −0.301906
\(690\) −1.01115 −0.0384937
\(691\) 5.13122 0.195201 0.0976005 0.995226i \(-0.468883\pi\)
0.0976005 + 0.995226i \(0.468883\pi\)
\(692\) 1.59651 0.0606900
\(693\) −0.871942 −0.0331223
\(694\) 16.6741 0.632938
\(695\) −12.2006 −0.462796
\(696\) −0.426267 −0.0161576
\(697\) −78.7854 −2.98421
\(698\) 7.19094 0.272181
\(699\) 0.112588 0.00425848
\(700\) 1.23180 0.0465575
\(701\) 0.838202 0.0316584 0.0158292 0.999875i \(-0.494961\pi\)
0.0158292 + 0.999875i \(0.494961\pi\)
\(702\) −3.55406 −0.134139
\(703\) −12.6344 −0.476517
\(704\) 0.272596 0.0102738
\(705\) 1.33365 0.0502282
\(706\) 3.90993 0.147152
\(707\) 9.41833 0.354213
\(708\) −5.15996 −0.193923
\(709\) 19.1224 0.718158 0.359079 0.933307i \(-0.383091\pi\)
0.359079 + 0.933307i \(0.383091\pi\)
\(710\) −5.14505 −0.193090
\(711\) −35.2323 −1.32131
\(712\) 8.93093 0.334701
\(713\) 1.59230 0.0596323
\(714\) −5.56252 −0.208172
\(715\) 0.272596 0.0101945
\(716\) 10.8435 0.405242
\(717\) 11.8768 0.443548
\(718\) 11.1264 0.415235
\(719\) −35.2362 −1.31409 −0.657044 0.753853i \(-0.728193\pi\)
−0.657044 + 0.753853i \(0.728193\pi\)
\(720\) 2.59675 0.0967751
\(721\) −7.08682 −0.263927
\(722\) −15.1821 −0.565019
\(723\) −9.42364 −0.350469
\(724\) −0.0526882 −0.00195814
\(725\) 0.671264 0.0249301
\(726\) 6.93805 0.257495
\(727\) 12.4556 0.461952 0.230976 0.972959i \(-0.425808\pi\)
0.230976 + 0.972959i \(0.425808\pi\)
\(728\) −1.23180 −0.0456534
\(729\) −7.59797 −0.281406
\(730\) −10.1523 −0.375753
\(731\) 47.5305 1.75798
\(732\) 5.45313 0.201554
\(733\) −12.7415 −0.470620 −0.235310 0.971920i \(-0.575610\pi\)
−0.235310 + 0.971920i \(0.575610\pi\)
\(734\) 6.59930 0.243585
\(735\) −3.48162 −0.128421
\(736\) −1.59230 −0.0586931
\(737\) 1.18827 0.0437704
\(738\) 28.7694 1.05902
\(739\) 32.9455 1.21192 0.605960 0.795495i \(-0.292789\pi\)
0.605960 + 0.795495i \(0.292789\pi\)
\(740\) −6.46612 −0.237699
\(741\) −1.24080 −0.0455818
\(742\) 9.76158 0.358359
\(743\) −6.67402 −0.244846 −0.122423 0.992478i \(-0.539066\pi\)
−0.122423 + 0.992478i \(0.539066\pi\)
\(744\) 0.635022 0.0232810
\(745\) 7.79203 0.285478
\(746\) 24.2258 0.886968
\(747\) 23.3739 0.855206
\(748\) 1.93849 0.0708782
\(749\) −5.48903 −0.200565
\(750\) 0.635022 0.0231877
\(751\) 20.6764 0.754492 0.377246 0.926113i \(-0.376871\pi\)
0.377246 + 0.926113i \(0.376871\pi\)
\(752\) 2.10016 0.0765851
\(753\) −3.92793 −0.143142
\(754\) −0.671264 −0.0244460
\(755\) −18.9468 −0.689545
\(756\) 4.37787 0.159222
\(757\) −11.1005 −0.403456 −0.201728 0.979442i \(-0.564656\pi\)
−0.201728 + 0.979442i \(0.564656\pi\)
\(758\) 0.870831 0.0316300
\(759\) 0.275634 0.0100049
\(760\) 1.95394 0.0708770
\(761\) 19.0219 0.689542 0.344771 0.938687i \(-0.387957\pi\)
0.344771 + 0.938687i \(0.387957\pi\)
\(762\) 10.9663 0.397267
\(763\) 10.1905 0.368919
\(764\) −1.31127 −0.0474401
\(765\) 18.4660 0.667641
\(766\) 18.4271 0.665798
\(767\) −8.12564 −0.293400
\(768\) −0.635022 −0.0229144
\(769\) −14.3658 −0.518042 −0.259021 0.965872i \(-0.583400\pi\)
−0.259021 + 0.965872i \(0.583400\pi\)
\(770\) −0.335782 −0.0121008
\(771\) 3.59504 0.129472
\(772\) 5.15787 0.185636
\(773\) −2.02694 −0.0729038 −0.0364519 0.999335i \(-0.511606\pi\)
−0.0364519 + 0.999335i \(0.511606\pi\)
\(774\) −17.3563 −0.623860
\(775\) −1.00000 −0.0359211
\(776\) 15.7222 0.564393
\(777\) −5.05791 −0.181452
\(778\) 21.8910 0.784830
\(779\) 21.6478 0.775612
\(780\) −0.635022 −0.0227374
\(781\) 1.40252 0.0501861
\(782\) −11.3232 −0.404918
\(783\) 2.38571 0.0852583
\(784\) −5.48268 −0.195810
\(785\) −7.62496 −0.272146
\(786\) −3.98998 −0.142318
\(787\) −1.92174 −0.0685027 −0.0342514 0.999413i \(-0.510905\pi\)
−0.0342514 + 0.999413i \(0.510905\pi\)
\(788\) −0.571208 −0.0203485
\(789\) −6.09344 −0.216932
\(790\) −13.5679 −0.482723
\(791\) 12.1338 0.431430
\(792\) −0.707862 −0.0251528
\(793\) 8.58732 0.304945
\(794\) −20.1091 −0.713646
\(795\) 5.03234 0.178479
\(796\) 0.766897 0.0271820
\(797\) 16.2020 0.573904 0.286952 0.957945i \(-0.407358\pi\)
0.286952 + 0.957945i \(0.407358\pi\)
\(798\) 1.52841 0.0541051
\(799\) 14.9347 0.528353
\(800\) 1.00000 0.0353553
\(801\) −23.1914 −0.819427
\(802\) 1.96722 0.0694651
\(803\) 2.76747 0.0976619
\(804\) −2.76812 −0.0976239
\(805\) 1.96139 0.0691301
\(806\) 1.00000 0.0352235
\(807\) 13.0015 0.457675
\(808\) 7.64601 0.268986
\(809\) −21.9073 −0.770221 −0.385111 0.922870i \(-0.625837\pi\)
−0.385111 + 0.922870i \(0.625837\pi\)
\(810\) −5.53334 −0.194422
\(811\) 52.5171 1.84412 0.922062 0.387043i \(-0.126503\pi\)
0.922062 + 0.387043i \(0.126503\pi\)
\(812\) 0.826861 0.0290171
\(813\) 3.65551 0.128204
\(814\) 1.76264 0.0617803
\(815\) 8.43039 0.295304
\(816\) −4.51578 −0.158084
\(817\) −13.0599 −0.456908
\(818\) 8.94583 0.312784
\(819\) 3.19866 0.111770
\(820\) 11.0790 0.386896
\(821\) 13.9807 0.487930 0.243965 0.969784i \(-0.421552\pi\)
0.243965 + 0.969784i \(0.421552\pi\)
\(822\) 3.39081 0.118268
\(823\) −6.90815 −0.240803 −0.120402 0.992725i \(-0.538418\pi\)
−0.120402 + 0.992725i \(0.538418\pi\)
\(824\) −5.75324 −0.200424
\(825\) −0.173104 −0.00602671
\(826\) 10.0091 0.348262
\(827\) −13.4592 −0.468022 −0.234011 0.972234i \(-0.575185\pi\)
−0.234011 + 0.972234i \(0.575185\pi\)
\(828\) 4.13481 0.143695
\(829\) −27.2579 −0.946707 −0.473353 0.880873i \(-0.656957\pi\)
−0.473353 + 0.880873i \(0.656957\pi\)
\(830\) 9.00122 0.312437
\(831\) −6.80216 −0.235964
\(832\) −1.00000 −0.0346688
\(833\) −38.9885 −1.35087
\(834\) −7.74766 −0.268280
\(835\) −24.1193 −0.834682
\(836\) −0.532637 −0.0184216
\(837\) −3.55406 −0.122846
\(838\) 26.9093 0.929567
\(839\) 50.0451 1.72775 0.863874 0.503708i \(-0.168031\pi\)
0.863874 + 0.503708i \(0.168031\pi\)
\(840\) 0.782218 0.0269891
\(841\) −28.5494 −0.984462
\(842\) −7.55904 −0.260502
\(843\) −3.45368 −0.118951
\(844\) −9.86552 −0.339585
\(845\) −1.00000 −0.0344010
\(846\) −5.45360 −0.187498
\(847\) −13.4582 −0.462430
\(848\) 7.92467 0.272134
\(849\) 11.3942 0.391048
\(850\) 7.11122 0.243913
\(851\) −10.2960 −0.352943
\(852\) −3.26722 −0.111933
\(853\) −11.2662 −0.385747 −0.192873 0.981224i \(-0.561781\pi\)
−0.192873 + 0.981224i \(0.561781\pi\)
\(854\) −10.5778 −0.361966
\(855\) −5.07390 −0.173524
\(856\) −4.45612 −0.152307
\(857\) −53.1205 −1.81456 −0.907280 0.420526i \(-0.861845\pi\)
−0.907280 + 0.420526i \(0.861845\pi\)
\(858\) 0.173104 0.00590968
\(859\) 24.0616 0.820970 0.410485 0.911867i \(-0.365359\pi\)
0.410485 + 0.911867i \(0.365359\pi\)
\(860\) −6.68387 −0.227918
\(861\) 8.66621 0.295344
\(862\) 6.12573 0.208643
\(863\) −8.86015 −0.301603 −0.150801 0.988564i \(-0.548185\pi\)
−0.150801 + 0.988564i \(0.548185\pi\)
\(864\) 3.55406 0.120911
\(865\) −1.59651 −0.0542828
\(866\) −32.8758 −1.11717
\(867\) −21.3174 −0.723976
\(868\) −1.23180 −0.0418099
\(869\) 3.69854 0.125464
\(870\) 0.426267 0.0144518
\(871\) −4.35909 −0.147702
\(872\) 8.27284 0.280154
\(873\) −40.8265 −1.38177
\(874\) 3.11127 0.105240
\(875\) −1.23180 −0.0416423
\(876\) −6.44693 −0.217821
\(877\) −28.1897 −0.951900 −0.475950 0.879472i \(-0.657896\pi\)
−0.475950 + 0.879472i \(0.657896\pi\)
\(878\) −0.617160 −0.0208281
\(879\) −3.88020 −0.130876
\(880\) −0.272596 −0.00918920
\(881\) −31.8962 −1.07461 −0.537305 0.843388i \(-0.680558\pi\)
−0.537305 + 0.843388i \(0.680558\pi\)
\(882\) 14.2371 0.479389
\(883\) 39.0760 1.31501 0.657506 0.753449i \(-0.271611\pi\)
0.657506 + 0.753449i \(0.271611\pi\)
\(884\) −7.11122 −0.239176
\(885\) 5.15996 0.173450
\(886\) 25.0624 0.841988
\(887\) 2.94756 0.0989693 0.0494846 0.998775i \(-0.484242\pi\)
0.0494846 + 0.998775i \(0.484242\pi\)
\(888\) −4.10613 −0.137793
\(889\) −21.2721 −0.713443
\(890\) −8.93093 −0.299365
\(891\) 1.50836 0.0505321
\(892\) −2.04843 −0.0685865
\(893\) −4.10360 −0.137322
\(894\) 4.94811 0.165489
\(895\) −10.8435 −0.362459
\(896\) 1.23180 0.0411514
\(897\) −1.01115 −0.0337612
\(898\) −27.1106 −0.904694
\(899\) −0.671264 −0.0223879
\(900\) −2.59675 −0.0865582
\(901\) 56.3541 1.87743
\(902\) −3.02009 −0.100558
\(903\) −5.22824 −0.173985
\(904\) 9.85052 0.327623
\(905\) 0.0526882 0.00175142
\(906\) −12.0316 −0.399725
\(907\) 40.3728 1.34056 0.670278 0.742110i \(-0.266175\pi\)
0.670278 + 0.742110i \(0.266175\pi\)
\(908\) −10.9084 −0.362010
\(909\) −19.8548 −0.658541
\(910\) 1.23180 0.0408337
\(911\) −14.5546 −0.482214 −0.241107 0.970499i \(-0.577511\pi\)
−0.241107 + 0.970499i \(0.577511\pi\)
\(912\) 1.24080 0.0410869
\(913\) −2.45369 −0.0812054
\(914\) −31.6368 −1.04645
\(915\) −5.45313 −0.180275
\(916\) −3.97344 −0.131286
\(917\) 7.73965 0.255586
\(918\) 25.2737 0.834156
\(919\) 46.0433 1.51883 0.759414 0.650607i \(-0.225486\pi\)
0.759414 + 0.650607i \(0.225486\pi\)
\(920\) 1.59230 0.0524967
\(921\) −5.96000 −0.196389
\(922\) −24.8568 −0.818614
\(923\) −5.14505 −0.169352
\(924\) −0.213229 −0.00701472
\(925\) 6.46612 0.212605
\(926\) −12.7600 −0.419319
\(927\) 14.9397 0.490685
\(928\) 0.671264 0.0220353
\(929\) −12.2841 −0.403029 −0.201514 0.979486i \(-0.564586\pi\)
−0.201514 + 0.979486i \(0.564586\pi\)
\(930\) −0.635022 −0.0208232
\(931\) 10.7128 0.351099
\(932\) −0.177298 −0.00580759
\(933\) 21.1280 0.691700
\(934\) −0.528860 −0.0173048
\(935\) −1.93849 −0.0633954
\(936\) 2.59675 0.0848773
\(937\) −13.8708 −0.453139 −0.226570 0.973995i \(-0.572751\pi\)
−0.226570 + 0.973995i \(0.572751\pi\)
\(938\) 5.36951 0.175321
\(939\) 9.69087 0.316250
\(940\) −2.10016 −0.0684998
\(941\) −0.552739 −0.0180188 −0.00900939 0.999959i \(-0.502868\pi\)
−0.00900939 + 0.999959i \(0.502868\pi\)
\(942\) −4.84201 −0.157761
\(943\) 17.6412 0.574476
\(944\) 8.12564 0.264467
\(945\) −4.37787 −0.142412
\(946\) 1.82199 0.0592382
\(947\) 1.18091 0.0383743 0.0191872 0.999816i \(-0.493892\pi\)
0.0191872 + 0.999816i \(0.493892\pi\)
\(948\) −8.61589 −0.279831
\(949\) −10.1523 −0.329557
\(950\) −1.95394 −0.0633943
\(951\) −12.2905 −0.398546
\(952\) 8.75958 0.283900
\(953\) 60.8222 1.97023 0.985113 0.171908i \(-0.0549933\pi\)
0.985113 + 0.171908i \(0.0549933\pi\)
\(954\) −20.5784 −0.666249
\(955\) 1.31127 0.0424317
\(956\) −18.7030 −0.604898
\(957\) −0.116199 −0.00375617
\(958\) 3.07938 0.0994904
\(959\) −6.57740 −0.212395
\(960\) 0.635022 0.0204952
\(961\) 1.00000 0.0322581
\(962\) −6.46612 −0.208476
\(963\) 11.5714 0.372883
\(964\) 14.8399 0.477960
\(965\) −5.15787 −0.166038
\(966\) 1.24553 0.0400742
\(967\) −29.5228 −0.949391 −0.474695 0.880150i \(-0.657442\pi\)
−0.474695 + 0.880150i \(0.657442\pi\)
\(968\) −10.9257 −0.351165
\(969\) 8.82358 0.283454
\(970\) −15.7222 −0.504808
\(971\) −19.2480 −0.617699 −0.308849 0.951111i \(-0.599944\pi\)
−0.308849 + 0.951111i \(0.599944\pi\)
\(972\) −14.1760 −0.454694
\(973\) 15.0287 0.481798
\(974\) −8.04516 −0.257783
\(975\) 0.635022 0.0203370
\(976\) −8.58732 −0.274873
\(977\) 39.7794 1.27265 0.636327 0.771419i \(-0.280453\pi\)
0.636327 + 0.771419i \(0.280453\pi\)
\(978\) 5.35348 0.171185
\(979\) 2.43453 0.0778080
\(980\) 5.48268 0.175138
\(981\) −21.4825 −0.685882
\(982\) 18.0102 0.574729
\(983\) −1.07234 −0.0342024 −0.0171012 0.999854i \(-0.505444\pi\)
−0.0171012 + 0.999854i \(0.505444\pi\)
\(984\) 7.03542 0.224281
\(985\) 0.571208 0.0182002
\(986\) 4.77351 0.152019
\(987\) −1.64279 −0.0522904
\(988\) 1.95394 0.0621632
\(989\) −10.6428 −0.338420
\(990\) 0.707862 0.0224973
\(991\) −19.4967 −0.619334 −0.309667 0.950845i \(-0.600218\pi\)
−0.309667 + 0.950845i \(0.600218\pi\)
\(992\) −1.00000 −0.0317500
\(993\) −6.47023 −0.205327
\(994\) 6.33766 0.201018
\(995\) −0.766897 −0.0243123
\(996\) 5.71597 0.181117
\(997\) −5.97916 −0.189362 −0.0946810 0.995508i \(-0.530183\pi\)
−0.0946810 + 0.995508i \(0.530183\pi\)
\(998\) −27.2005 −0.861016
\(999\) 22.9809 0.727085
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 \(a_p\))