Properties

Label 8015.2.a.l.1.43
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.43
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.24614 q^{2} +2.46236 q^{3} -0.447139 q^{4} -1.00000 q^{5} +3.06845 q^{6} -1.00000 q^{7} -3.04947 q^{8} +3.06324 q^{9} +O(q^{10})\) \(q+1.24614 q^{2} +2.46236 q^{3} -0.447139 q^{4} -1.00000 q^{5} +3.06845 q^{6} -1.00000 q^{7} -3.04947 q^{8} +3.06324 q^{9} -1.24614 q^{10} +1.46291 q^{11} -1.10102 q^{12} -4.42027 q^{13} -1.24614 q^{14} -2.46236 q^{15} -2.90579 q^{16} -0.0499232 q^{17} +3.81722 q^{18} -0.658238 q^{19} +0.447139 q^{20} -2.46236 q^{21} +1.82298 q^{22} +4.57297 q^{23} -7.50891 q^{24} +1.00000 q^{25} -5.50827 q^{26} +0.155708 q^{27} +0.447139 q^{28} +4.16152 q^{29} -3.06845 q^{30} -5.17544 q^{31} +2.47793 q^{32} +3.60220 q^{33} -0.0622113 q^{34} +1.00000 q^{35} -1.36969 q^{36} +2.60005 q^{37} -0.820255 q^{38} -10.8843 q^{39} +3.04947 q^{40} +6.25946 q^{41} -3.06845 q^{42} +5.47750 q^{43} -0.654122 q^{44} -3.06324 q^{45} +5.69855 q^{46} +10.4755 q^{47} -7.15511 q^{48} +1.00000 q^{49} +1.24614 q^{50} -0.122929 q^{51} +1.97647 q^{52} +8.42397 q^{53} +0.194034 q^{54} -1.46291 q^{55} +3.04947 q^{56} -1.62082 q^{57} +5.18582 q^{58} +8.86491 q^{59} +1.10102 q^{60} +9.68144 q^{61} -6.44931 q^{62} -3.06324 q^{63} +8.89942 q^{64} +4.42027 q^{65} +4.48885 q^{66} -1.18665 q^{67} +0.0223226 q^{68} +11.2603 q^{69} +1.24614 q^{70} -4.70654 q^{71} -9.34126 q^{72} +8.22538 q^{73} +3.24002 q^{74} +2.46236 q^{75} +0.294324 q^{76} -1.46291 q^{77} -13.5634 q^{78} +15.8964 q^{79} +2.90579 q^{80} -8.80630 q^{81} +7.80015 q^{82} -8.75408 q^{83} +1.10102 q^{84} +0.0499232 q^{85} +6.82572 q^{86} +10.2472 q^{87} -4.46109 q^{88} +13.3176 q^{89} -3.81722 q^{90} +4.42027 q^{91} -2.04475 q^{92} -12.7438 q^{93} +13.0539 q^{94} +0.658238 q^{95} +6.10157 q^{96} +5.42424 q^{97} +1.24614 q^{98} +4.48122 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.24614 0.881153 0.440576 0.897715i \(-0.354774\pi\)
0.440576 + 0.897715i \(0.354774\pi\)
\(3\) 2.46236 1.42165 0.710823 0.703371i \(-0.248323\pi\)
0.710823 + 0.703371i \(0.248323\pi\)
\(4\) −0.447139 −0.223569
\(5\) −1.00000 −0.447214
\(6\) 3.06845 1.25269
\(7\) −1.00000 −0.377964
\(8\) −3.04947 −1.07815
\(9\) 3.06324 1.02108
\(10\) −1.24614 −0.394064
\(11\) 1.46291 0.441082 0.220541 0.975378i \(-0.429218\pi\)
0.220541 + 0.975378i \(0.429218\pi\)
\(12\) −1.10102 −0.317837
\(13\) −4.42027 −1.22596 −0.612981 0.790098i \(-0.710030\pi\)
−0.612981 + 0.790098i \(0.710030\pi\)
\(14\) −1.24614 −0.333045
\(15\) −2.46236 −0.635780
\(16\) −2.90579 −0.726447
\(17\) −0.0499232 −0.0121082 −0.00605408 0.999982i \(-0.501927\pi\)
−0.00605408 + 0.999982i \(0.501927\pi\)
\(18\) 3.81722 0.899726
\(19\) −0.658238 −0.151010 −0.0755050 0.997145i \(-0.524057\pi\)
−0.0755050 + 0.997145i \(0.524057\pi\)
\(20\) 0.447139 0.0999833
\(21\) −2.46236 −0.537332
\(22\) 1.82298 0.388661
\(23\) 4.57297 0.953529 0.476765 0.879031i \(-0.341809\pi\)
0.476765 + 0.879031i \(0.341809\pi\)
\(24\) −7.50891 −1.53275
\(25\) 1.00000 0.200000
\(26\) −5.50827 −1.08026
\(27\) 0.155708 0.0299660
\(28\) 0.447139 0.0845013
\(29\) 4.16152 0.772774 0.386387 0.922337i \(-0.373723\pi\)
0.386387 + 0.922337i \(0.373723\pi\)
\(30\) −3.06845 −0.560219
\(31\) −5.17544 −0.929536 −0.464768 0.885432i \(-0.653862\pi\)
−0.464768 + 0.885432i \(0.653862\pi\)
\(32\) 2.47793 0.438041
\(33\) 3.60220 0.627063
\(34\) −0.0622113 −0.0106691
\(35\) 1.00000 0.169031
\(36\) −1.36969 −0.228282
\(37\) 2.60005 0.427445 0.213722 0.976894i \(-0.431441\pi\)
0.213722 + 0.976894i \(0.431441\pi\)
\(38\) −0.820255 −0.133063
\(39\) −10.8843 −1.74288
\(40\) 3.04947 0.482164
\(41\) 6.25946 0.977563 0.488782 0.872406i \(-0.337441\pi\)
0.488782 + 0.872406i \(0.337441\pi\)
\(42\) −3.06845 −0.473472
\(43\) 5.47750 0.835310 0.417655 0.908606i \(-0.362852\pi\)
0.417655 + 0.908606i \(0.362852\pi\)
\(44\) −0.654122 −0.0986126
\(45\) −3.06324 −0.456640
\(46\) 5.69855 0.840205
\(47\) 10.4755 1.52801 0.764003 0.645212i \(-0.223231\pi\)
0.764003 + 0.645212i \(0.223231\pi\)
\(48\) −7.15511 −1.03275
\(49\) 1.00000 0.142857
\(50\) 1.24614 0.176231
\(51\) −0.122929 −0.0172135
\(52\) 1.97647 0.274088
\(53\) 8.42397 1.15712 0.578561 0.815639i \(-0.303615\pi\)
0.578561 + 0.815639i \(0.303615\pi\)
\(54\) 0.194034 0.0264046
\(55\) −1.46291 −0.197258
\(56\) 3.04947 0.407503
\(57\) −1.62082 −0.214683
\(58\) 5.18582 0.680932
\(59\) 8.86491 1.15411 0.577056 0.816704i \(-0.304201\pi\)
0.577056 + 0.816704i \(0.304201\pi\)
\(60\) 1.10102 0.142141
\(61\) 9.68144 1.23958 0.619790 0.784767i \(-0.287218\pi\)
0.619790 + 0.784767i \(0.287218\pi\)
\(62\) −6.44931 −0.819064
\(63\) −3.06324 −0.385931
\(64\) 8.89942 1.11243
\(65\) 4.42027 0.548267
\(66\) 4.48885 0.552539
\(67\) −1.18665 −0.144972 −0.0724859 0.997369i \(-0.523093\pi\)
−0.0724859 + 0.997369i \(0.523093\pi\)
\(68\) 0.0223226 0.00270702
\(69\) 11.2603 1.35558
\(70\) 1.24614 0.148942
\(71\) −4.70654 −0.558563 −0.279282 0.960209i \(-0.590096\pi\)
−0.279282 + 0.960209i \(0.590096\pi\)
\(72\) −9.34126 −1.10088
\(73\) 8.22538 0.962708 0.481354 0.876526i \(-0.340145\pi\)
0.481354 + 0.876526i \(0.340145\pi\)
\(74\) 3.24002 0.376644
\(75\) 2.46236 0.284329
\(76\) 0.294324 0.0337612
\(77\) −1.46291 −0.166714
\(78\) −13.5634 −1.53575
\(79\) 15.8964 1.78849 0.894243 0.447583i \(-0.147715\pi\)
0.894243 + 0.447583i \(0.147715\pi\)
\(80\) 2.90579 0.324877
\(81\) −8.80630 −0.978477
\(82\) 7.80015 0.861383
\(83\) −8.75408 −0.960885 −0.480442 0.877026i \(-0.659524\pi\)
−0.480442 + 0.877026i \(0.659524\pi\)
\(84\) 1.10102 0.120131
\(85\) 0.0499232 0.00541493
\(86\) 6.82572 0.736036
\(87\) 10.2472 1.09861
\(88\) −4.46109 −0.475554
\(89\) 13.3176 1.41167 0.705834 0.708377i \(-0.250573\pi\)
0.705834 + 0.708377i \(0.250573\pi\)
\(90\) −3.81722 −0.402370
\(91\) 4.42027 0.463370
\(92\) −2.04475 −0.213180
\(93\) −12.7438 −1.32147
\(94\) 13.0539 1.34641
\(95\) 0.658238 0.0675337
\(96\) 6.10157 0.622739
\(97\) 5.42424 0.550748 0.275374 0.961337i \(-0.411198\pi\)
0.275374 + 0.961337i \(0.411198\pi\)
\(98\) 1.24614 0.125879
\(99\) 4.48122 0.450380
\(100\) −0.447139 −0.0447139
\(101\) 17.7053 1.76175 0.880873 0.473353i \(-0.156956\pi\)
0.880873 + 0.473353i \(0.156956\pi\)
\(102\) −0.153187 −0.0151677
\(103\) 1.42123 0.140038 0.0700189 0.997546i \(-0.477694\pi\)
0.0700189 + 0.997546i \(0.477694\pi\)
\(104\) 13.4795 1.32177
\(105\) 2.46236 0.240302
\(106\) 10.4974 1.01960
\(107\) −6.61729 −0.639718 −0.319859 0.947465i \(-0.603635\pi\)
−0.319859 + 0.947465i \(0.603635\pi\)
\(108\) −0.0696231 −0.00669948
\(109\) −17.9093 −1.71540 −0.857698 0.514154i \(-0.828106\pi\)
−0.857698 + 0.514154i \(0.828106\pi\)
\(110\) −1.82298 −0.173815
\(111\) 6.40226 0.607676
\(112\) 2.90579 0.274571
\(113\) −17.5204 −1.64818 −0.824092 0.566457i \(-0.808314\pi\)
−0.824092 + 0.566457i \(0.808314\pi\)
\(114\) −2.01977 −0.189168
\(115\) −4.57297 −0.426431
\(116\) −1.86078 −0.172769
\(117\) −13.5403 −1.25180
\(118\) 11.0469 1.01695
\(119\) 0.0499232 0.00457645
\(120\) 7.50891 0.685467
\(121\) −8.85991 −0.805446
\(122\) 12.0644 1.09226
\(123\) 15.4131 1.38975
\(124\) 2.31414 0.207816
\(125\) −1.00000 −0.0894427
\(126\) −3.81722 −0.340065
\(127\) −4.97063 −0.441072 −0.220536 0.975379i \(-0.570781\pi\)
−0.220536 + 0.975379i \(0.570781\pi\)
\(128\) 6.13405 0.542179
\(129\) 13.4876 1.18752
\(130\) 5.50827 0.483107
\(131\) −4.51695 −0.394648 −0.197324 0.980338i \(-0.563225\pi\)
−0.197324 + 0.980338i \(0.563225\pi\)
\(132\) −1.61069 −0.140192
\(133\) 0.658238 0.0570764
\(134\) −1.47873 −0.127742
\(135\) −0.155708 −0.0134012
\(136\) 0.152240 0.0130544
\(137\) 11.0480 0.943895 0.471947 0.881627i \(-0.343551\pi\)
0.471947 + 0.881627i \(0.343551\pi\)
\(138\) 14.0319 1.19447
\(139\) −0.473739 −0.0401820 −0.0200910 0.999798i \(-0.506396\pi\)
−0.0200910 + 0.999798i \(0.506396\pi\)
\(140\) −0.447139 −0.0377901
\(141\) 25.7945 2.17229
\(142\) −5.86500 −0.492180
\(143\) −6.46643 −0.540750
\(144\) −8.90111 −0.741760
\(145\) −4.16152 −0.345595
\(146\) 10.2500 0.848293
\(147\) 2.46236 0.203092
\(148\) −1.16258 −0.0955636
\(149\) −8.81604 −0.722238 −0.361119 0.932520i \(-0.617605\pi\)
−0.361119 + 0.932520i \(0.617605\pi\)
\(150\) 3.06845 0.250538
\(151\) −11.0369 −0.898171 −0.449086 0.893489i \(-0.648250\pi\)
−0.449086 + 0.893489i \(0.648250\pi\)
\(152\) 2.00728 0.162812
\(153\) −0.152927 −0.0123634
\(154\) −1.82298 −0.146900
\(155\) 5.17544 0.415701
\(156\) 4.86680 0.389656
\(157\) −4.94050 −0.394295 −0.197147 0.980374i \(-0.563168\pi\)
−0.197147 + 0.980374i \(0.563168\pi\)
\(158\) 19.8091 1.57593
\(159\) 20.7429 1.64502
\(160\) −2.47793 −0.195898
\(161\) −4.57297 −0.360400
\(162\) −10.9739 −0.862188
\(163\) −20.6345 −1.61622 −0.808109 0.589033i \(-0.799509\pi\)
−0.808109 + 0.589033i \(0.799509\pi\)
\(164\) −2.79885 −0.218553
\(165\) −3.60220 −0.280431
\(166\) −10.9088 −0.846686
\(167\) −8.98507 −0.695286 −0.347643 0.937627i \(-0.613018\pi\)
−0.347643 + 0.937627i \(0.613018\pi\)
\(168\) 7.50891 0.579325
\(169\) 6.53876 0.502982
\(170\) 0.0622113 0.00477139
\(171\) −2.01634 −0.154193
\(172\) −2.44920 −0.186750
\(173\) 10.5897 0.805118 0.402559 0.915394i \(-0.368121\pi\)
0.402559 + 0.915394i \(0.368121\pi\)
\(174\) 12.7694 0.968045
\(175\) −1.00000 −0.0755929
\(176\) −4.25089 −0.320423
\(177\) 21.8286 1.64074
\(178\) 16.5956 1.24390
\(179\) −0.907167 −0.0678048 −0.0339024 0.999425i \(-0.510794\pi\)
−0.0339024 + 0.999425i \(0.510794\pi\)
\(180\) 1.36969 0.102091
\(181\) −25.6659 −1.90773 −0.953866 0.300234i \(-0.902935\pi\)
−0.953866 + 0.300234i \(0.902935\pi\)
\(182\) 5.50827 0.408300
\(183\) 23.8392 1.76225
\(184\) −13.9451 −1.02805
\(185\) −2.60005 −0.191159
\(186\) −15.8806 −1.16442
\(187\) −0.0730329 −0.00534070
\(188\) −4.68400 −0.341616
\(189\) −0.155708 −0.0113261
\(190\) 0.820255 0.0595076
\(191\) 2.53195 0.183206 0.0916028 0.995796i \(-0.470801\pi\)
0.0916028 + 0.995796i \(0.470801\pi\)
\(192\) 21.9136 1.58148
\(193\) 15.2175 1.09538 0.547689 0.836682i \(-0.315508\pi\)
0.547689 + 0.836682i \(0.315508\pi\)
\(194\) 6.75935 0.485293
\(195\) 10.8843 0.779441
\(196\) −0.447139 −0.0319385
\(197\) 23.6872 1.68764 0.843821 0.536625i \(-0.180301\pi\)
0.843821 + 0.536625i \(0.180301\pi\)
\(198\) 5.58422 0.396853
\(199\) −19.3994 −1.37519 −0.687593 0.726096i \(-0.741333\pi\)
−0.687593 + 0.726096i \(0.741333\pi\)
\(200\) −3.04947 −0.215630
\(201\) −2.92195 −0.206099
\(202\) 22.0633 1.55237
\(203\) −4.16152 −0.292081
\(204\) 0.0549664 0.00384842
\(205\) −6.25946 −0.437180
\(206\) 1.77105 0.123395
\(207\) 14.0081 0.973628
\(208\) 12.8444 0.890596
\(209\) −0.962939 −0.0666079
\(210\) 3.06845 0.211743
\(211\) 10.3328 0.711340 0.355670 0.934612i \(-0.384253\pi\)
0.355670 + 0.934612i \(0.384253\pi\)
\(212\) −3.76669 −0.258697
\(213\) −11.5892 −0.794079
\(214\) −8.24606 −0.563689
\(215\) −5.47750 −0.373562
\(216\) −0.474827 −0.0323079
\(217\) 5.17544 0.351332
\(218\) −22.3174 −1.51153
\(219\) 20.2539 1.36863
\(220\) 0.654122 0.0441009
\(221\) 0.220674 0.0148441
\(222\) 7.97810 0.535455
\(223\) −11.0550 −0.740294 −0.370147 0.928973i \(-0.620693\pi\)
−0.370147 + 0.928973i \(0.620693\pi\)
\(224\) −2.47793 −0.165564
\(225\) 3.06324 0.204216
\(226\) −21.8329 −1.45230
\(227\) 28.3039 1.87859 0.939297 0.343106i \(-0.111479\pi\)
0.939297 + 0.343106i \(0.111479\pi\)
\(228\) 0.724732 0.0479965
\(229\) 1.00000 0.0660819
\(230\) −5.69855 −0.375751
\(231\) −3.60220 −0.237008
\(232\) −12.6904 −0.833168
\(233\) 28.0706 1.83896 0.919482 0.393133i \(-0.128609\pi\)
0.919482 + 0.393133i \(0.128609\pi\)
\(234\) −16.8731 −1.10303
\(235\) −10.4755 −0.683345
\(236\) −3.96385 −0.258024
\(237\) 39.1427 2.54259
\(238\) 0.0622113 0.00403256
\(239\) 2.82887 0.182985 0.0914923 0.995806i \(-0.470836\pi\)
0.0914923 + 0.995806i \(0.470836\pi\)
\(240\) 7.15511 0.461860
\(241\) 5.22088 0.336307 0.168153 0.985761i \(-0.446220\pi\)
0.168153 + 0.985761i \(0.446220\pi\)
\(242\) −11.0407 −0.709721
\(243\) −22.1514 −1.42101
\(244\) −4.32895 −0.277132
\(245\) −1.00000 −0.0638877
\(246\) 19.2068 1.22458
\(247\) 2.90959 0.185133
\(248\) 15.7824 1.00218
\(249\) −21.5557 −1.36604
\(250\) −1.24614 −0.0788127
\(251\) 7.51392 0.474275 0.237137 0.971476i \(-0.423791\pi\)
0.237137 + 0.971476i \(0.423791\pi\)
\(252\) 1.36969 0.0862825
\(253\) 6.68982 0.420585
\(254\) −6.19409 −0.388652
\(255\) 0.122929 0.00769812
\(256\) −10.1550 −0.634686
\(257\) −8.34268 −0.520402 −0.260201 0.965554i \(-0.583789\pi\)
−0.260201 + 0.965554i \(0.583789\pi\)
\(258\) 16.8074 1.04638
\(259\) −2.60005 −0.161559
\(260\) −1.97647 −0.122576
\(261\) 12.7477 0.789063
\(262\) −5.62875 −0.347745
\(263\) −20.8310 −1.28450 −0.642249 0.766496i \(-0.721998\pi\)
−0.642249 + 0.766496i \(0.721998\pi\)
\(264\) −10.9848 −0.676069
\(265\) −8.42397 −0.517480
\(266\) 0.820255 0.0502931
\(267\) 32.7929 2.00689
\(268\) 0.530596 0.0324113
\(269\) 16.6297 1.01393 0.506964 0.861967i \(-0.330768\pi\)
0.506964 + 0.861967i \(0.330768\pi\)
\(270\) −0.194034 −0.0118085
\(271\) 14.0574 0.853924 0.426962 0.904270i \(-0.359584\pi\)
0.426962 + 0.904270i \(0.359584\pi\)
\(272\) 0.145066 0.00879594
\(273\) 10.8843 0.658748
\(274\) 13.7673 0.831716
\(275\) 1.46291 0.0882165
\(276\) −5.03492 −0.303067
\(277\) −20.9685 −1.25987 −0.629937 0.776647i \(-0.716919\pi\)
−0.629937 + 0.776647i \(0.716919\pi\)
\(278\) −0.590344 −0.0354065
\(279\) −15.8536 −0.949130
\(280\) −3.04947 −0.182241
\(281\) −1.21515 −0.0724900 −0.0362450 0.999343i \(-0.511540\pi\)
−0.0362450 + 0.999343i \(0.511540\pi\)
\(282\) 32.1435 1.91412
\(283\) −14.6614 −0.871528 −0.435764 0.900061i \(-0.643522\pi\)
−0.435764 + 0.900061i \(0.643522\pi\)
\(284\) 2.10448 0.124878
\(285\) 1.62082 0.0960091
\(286\) −8.05807 −0.476484
\(287\) −6.25946 −0.369484
\(288\) 7.59049 0.447274
\(289\) −16.9975 −0.999853
\(290\) −5.18582 −0.304522
\(291\) 13.3564 0.782969
\(292\) −3.67789 −0.215232
\(293\) 1.81819 0.106220 0.0531099 0.998589i \(-0.483087\pi\)
0.0531099 + 0.998589i \(0.483087\pi\)
\(294\) 3.06845 0.178955
\(295\) −8.86491 −0.516135
\(296\) −7.92877 −0.460851
\(297\) 0.227786 0.0132175
\(298\) −10.9860 −0.636402
\(299\) −20.2137 −1.16899
\(300\) −1.10102 −0.0635674
\(301\) −5.47750 −0.315718
\(302\) −13.7535 −0.791426
\(303\) 43.5970 2.50458
\(304\) 1.91270 0.109701
\(305\) −9.68144 −0.554357
\(306\) −0.190568 −0.0108940
\(307\) 6.47220 0.369388 0.184694 0.982796i \(-0.440871\pi\)
0.184694 + 0.982796i \(0.440871\pi\)
\(308\) 0.654122 0.0372721
\(309\) 3.49958 0.199084
\(310\) 6.44931 0.366296
\(311\) −3.98045 −0.225711 −0.112855 0.993611i \(-0.536000\pi\)
−0.112855 + 0.993611i \(0.536000\pi\)
\(312\) 33.1914 1.87909
\(313\) 15.3360 0.866840 0.433420 0.901192i \(-0.357307\pi\)
0.433420 + 0.901192i \(0.357307\pi\)
\(314\) −6.15655 −0.347434
\(315\) 3.06324 0.172594
\(316\) −7.10790 −0.399851
\(317\) 29.3652 1.64931 0.824656 0.565635i \(-0.191369\pi\)
0.824656 + 0.565635i \(0.191369\pi\)
\(318\) 25.8485 1.44951
\(319\) 6.08790 0.340857
\(320\) −8.89942 −0.497493
\(321\) −16.2942 −0.909452
\(322\) −5.69855 −0.317568
\(323\) 0.0328613 0.00182845
\(324\) 3.93764 0.218758
\(325\) −4.42027 −0.245192
\(326\) −25.7134 −1.42414
\(327\) −44.0991 −2.43869
\(328\) −19.0881 −1.05396
\(329\) −10.4755 −0.577532
\(330\) −4.48885 −0.247103
\(331\) 9.56626 0.525809 0.262905 0.964822i \(-0.415320\pi\)
0.262905 + 0.964822i \(0.415320\pi\)
\(332\) 3.91429 0.214825
\(333\) 7.96455 0.436455
\(334\) −11.1966 −0.612653
\(335\) 1.18665 0.0648334
\(336\) 7.15511 0.390343
\(337\) 26.0666 1.41994 0.709970 0.704232i \(-0.248709\pi\)
0.709970 + 0.704232i \(0.248709\pi\)
\(338\) 8.14821 0.443204
\(339\) −43.1417 −2.34313
\(340\) −0.0223226 −0.00121061
\(341\) −7.57118 −0.410002
\(342\) −2.51263 −0.135868
\(343\) −1.00000 −0.0539949
\(344\) −16.7035 −0.900591
\(345\) −11.2603 −0.606235
\(346\) 13.1962 0.709432
\(347\) −22.3314 −1.19881 −0.599407 0.800444i \(-0.704597\pi\)
−0.599407 + 0.800444i \(0.704597\pi\)
\(348\) −4.58191 −0.245616
\(349\) 21.8905 1.17177 0.585886 0.810393i \(-0.300746\pi\)
0.585886 + 0.810393i \(0.300746\pi\)
\(350\) −1.24614 −0.0666089
\(351\) −0.688271 −0.0367372
\(352\) 3.62498 0.193212
\(353\) 11.3822 0.605812 0.302906 0.953020i \(-0.402043\pi\)
0.302906 + 0.953020i \(0.402043\pi\)
\(354\) 27.2015 1.44574
\(355\) 4.70654 0.249797
\(356\) −5.95484 −0.315606
\(357\) 0.122929 0.00650610
\(358\) −1.13046 −0.0597464
\(359\) 14.6229 0.771769 0.385885 0.922547i \(-0.373896\pi\)
0.385885 + 0.922547i \(0.373896\pi\)
\(360\) 9.34126 0.492327
\(361\) −18.5667 −0.977196
\(362\) −31.9833 −1.68100
\(363\) −21.8163 −1.14506
\(364\) −1.97647 −0.103595
\(365\) −8.22538 −0.430536
\(366\) 29.7070 1.55281
\(367\) 9.42730 0.492101 0.246051 0.969257i \(-0.420867\pi\)
0.246051 + 0.969257i \(0.420867\pi\)
\(368\) −13.2881 −0.692689
\(369\) 19.1742 0.998169
\(370\) −3.24002 −0.168440
\(371\) −8.42397 −0.437351
\(372\) 5.69826 0.295441
\(373\) −32.6395 −1.69001 −0.845005 0.534759i \(-0.820402\pi\)
−0.845005 + 0.534759i \(0.820402\pi\)
\(374\) −0.0910092 −0.00470597
\(375\) −2.46236 −0.127156
\(376\) −31.9447 −1.64742
\(377\) −18.3950 −0.947391
\(378\) −0.194034 −0.00998001
\(379\) 6.14818 0.315811 0.157905 0.987454i \(-0.449526\pi\)
0.157905 + 0.987454i \(0.449526\pi\)
\(380\) −0.294324 −0.0150985
\(381\) −12.2395 −0.627049
\(382\) 3.15516 0.161432
\(383\) 36.8177 1.88130 0.940648 0.339382i \(-0.110218\pi\)
0.940648 + 0.339382i \(0.110218\pi\)
\(384\) 15.1043 0.770786
\(385\) 1.46291 0.0745565
\(386\) 18.9631 0.965196
\(387\) 16.7789 0.852917
\(388\) −2.42539 −0.123130
\(389\) 14.6758 0.744093 0.372046 0.928214i \(-0.378656\pi\)
0.372046 + 0.928214i \(0.378656\pi\)
\(390\) 13.5634 0.686807
\(391\) −0.228297 −0.0115455
\(392\) −3.04947 −0.154022
\(393\) −11.1224 −0.561050
\(394\) 29.5175 1.48707
\(395\) −15.8964 −0.799835
\(396\) −2.00373 −0.100691
\(397\) −12.6910 −0.636943 −0.318472 0.947932i \(-0.603170\pi\)
−0.318472 + 0.947932i \(0.603170\pi\)
\(398\) −24.1743 −1.21175
\(399\) 1.62082 0.0811425
\(400\) −2.90579 −0.145289
\(401\) 12.6280 0.630610 0.315305 0.948990i \(-0.397893\pi\)
0.315305 + 0.948990i \(0.397893\pi\)
\(402\) −3.64116 −0.181605
\(403\) 22.8768 1.13958
\(404\) −7.91674 −0.393873
\(405\) 8.80630 0.437588
\(406\) −5.18582 −0.257368
\(407\) 3.80362 0.188538
\(408\) 0.374869 0.0185588
\(409\) 9.17000 0.453427 0.226714 0.973961i \(-0.427202\pi\)
0.226714 + 0.973961i \(0.427202\pi\)
\(410\) −7.80015 −0.385222
\(411\) 27.2042 1.34188
\(412\) −0.635486 −0.0313082
\(413\) −8.86491 −0.436214
\(414\) 17.4560 0.857915
\(415\) 8.75408 0.429721
\(416\) −10.9531 −0.537021
\(417\) −1.16652 −0.0571246
\(418\) −1.19996 −0.0586917
\(419\) 37.5140 1.83268 0.916340 0.400400i \(-0.131129\pi\)
0.916340 + 0.400400i \(0.131129\pi\)
\(420\) −1.10102 −0.0537242
\(421\) −40.2654 −1.96242 −0.981209 0.192949i \(-0.938195\pi\)
−0.981209 + 0.192949i \(0.938195\pi\)
\(422\) 12.8761 0.626799
\(423\) 32.0889 1.56021
\(424\) −25.6887 −1.24755
\(425\) −0.0499232 −0.00242163
\(426\) −14.4418 −0.699705
\(427\) −9.68144 −0.468518
\(428\) 2.95885 0.143021
\(429\) −15.9227 −0.768756
\(430\) −6.82572 −0.329165
\(431\) −20.7022 −0.997189 −0.498594 0.866835i \(-0.666150\pi\)
−0.498594 + 0.866835i \(0.666150\pi\)
\(432\) −0.452454 −0.0217687
\(433\) 30.1961 1.45113 0.725565 0.688153i \(-0.241578\pi\)
0.725565 + 0.688153i \(0.241578\pi\)
\(434\) 6.44931 0.309577
\(435\) −10.2472 −0.491314
\(436\) 8.00793 0.383510
\(437\) −3.01010 −0.143993
\(438\) 25.2391 1.20597
\(439\) 38.9141 1.85727 0.928635 0.370996i \(-0.120984\pi\)
0.928635 + 0.370996i \(0.120984\pi\)
\(440\) 4.46109 0.212674
\(441\) 3.06324 0.145868
\(442\) 0.274990 0.0130800
\(443\) 9.72130 0.461873 0.230936 0.972969i \(-0.425821\pi\)
0.230936 + 0.972969i \(0.425821\pi\)
\(444\) −2.86270 −0.135858
\(445\) −13.3176 −0.631317
\(446\) −13.7760 −0.652312
\(447\) −21.7083 −1.02677
\(448\) −8.89942 −0.420458
\(449\) 23.3906 1.10387 0.551935 0.833887i \(-0.313890\pi\)
0.551935 + 0.833887i \(0.313890\pi\)
\(450\) 3.81722 0.179945
\(451\) 9.15699 0.431186
\(452\) 7.83407 0.368483
\(453\) −27.1769 −1.27688
\(454\) 35.2705 1.65533
\(455\) −4.42027 −0.207225
\(456\) 4.94265 0.231461
\(457\) 40.7818 1.90769 0.953846 0.300297i \(-0.0970859\pi\)
0.953846 + 0.300297i \(0.0970859\pi\)
\(458\) 1.24614 0.0582282
\(459\) −0.00777344 −0.000362833 0
\(460\) 2.04475 0.0953370
\(461\) −38.7404 −1.80432 −0.902161 0.431399i \(-0.858020\pi\)
−0.902161 + 0.431399i \(0.858020\pi\)
\(462\) −4.48885 −0.208840
\(463\) −10.0870 −0.468783 −0.234391 0.972142i \(-0.575310\pi\)
−0.234391 + 0.972142i \(0.575310\pi\)
\(464\) −12.0925 −0.561379
\(465\) 12.7438 0.590980
\(466\) 34.9798 1.62041
\(467\) 27.1624 1.25693 0.628464 0.777839i \(-0.283684\pi\)
0.628464 + 0.777839i \(0.283684\pi\)
\(468\) 6.05440 0.279865
\(469\) 1.18665 0.0547942
\(470\) −13.0539 −0.602132
\(471\) −12.1653 −0.560548
\(472\) −27.0333 −1.24431
\(473\) 8.01306 0.368441
\(474\) 48.7773 2.24041
\(475\) −0.658238 −0.0302020
\(476\) −0.0223226 −0.00102316
\(477\) 25.8046 1.18151
\(478\) 3.52517 0.161237
\(479\) −21.8972 −1.00051 −0.500255 0.865878i \(-0.666760\pi\)
−0.500255 + 0.865878i \(0.666760\pi\)
\(480\) −6.10157 −0.278497
\(481\) −11.4929 −0.524031
\(482\) 6.50594 0.296338
\(483\) −11.2603 −0.512362
\(484\) 3.96161 0.180073
\(485\) −5.42424 −0.246302
\(486\) −27.6037 −1.25213
\(487\) −31.8642 −1.44390 −0.721952 0.691943i \(-0.756755\pi\)
−0.721952 + 0.691943i \(0.756755\pi\)
\(488\) −29.5233 −1.33646
\(489\) −50.8096 −2.29769
\(490\) −1.24614 −0.0562948
\(491\) −3.89185 −0.175637 −0.0878183 0.996137i \(-0.527989\pi\)
−0.0878183 + 0.996137i \(0.527989\pi\)
\(492\) −6.89178 −0.310706
\(493\) −0.207756 −0.00935687
\(494\) 3.62575 0.163130
\(495\) −4.48122 −0.201416
\(496\) 15.0387 0.675259
\(497\) 4.70654 0.211117
\(498\) −26.8614 −1.20369
\(499\) 9.56614 0.428239 0.214120 0.976807i \(-0.431312\pi\)
0.214120 + 0.976807i \(0.431312\pi\)
\(500\) 0.447139 0.0199967
\(501\) −22.1245 −0.988450
\(502\) 9.36339 0.417908
\(503\) 24.2825 1.08271 0.541353 0.840796i \(-0.317912\pi\)
0.541353 + 0.840796i \(0.317912\pi\)
\(504\) 9.34126 0.416093
\(505\) −17.7053 −0.787877
\(506\) 8.33644 0.370600
\(507\) 16.1008 0.715062
\(508\) 2.22256 0.0986103
\(509\) 14.8541 0.658396 0.329198 0.944261i \(-0.393222\pi\)
0.329198 + 0.944261i \(0.393222\pi\)
\(510\) 0.153187 0.00678322
\(511\) −8.22538 −0.363869
\(512\) −24.9226 −1.10143
\(513\) −0.102493 −0.00452517
\(514\) −10.3961 −0.458554
\(515\) −1.42123 −0.0626268
\(516\) −6.03083 −0.265492
\(517\) 15.3246 0.673977
\(518\) −3.24002 −0.142358
\(519\) 26.0756 1.14459
\(520\) −13.4795 −0.591115
\(521\) −41.5556 −1.82058 −0.910292 0.413966i \(-0.864143\pi\)
−0.910292 + 0.413966i \(0.864143\pi\)
\(522\) 15.8854 0.695285
\(523\) −34.0040 −1.48689 −0.743446 0.668796i \(-0.766810\pi\)
−0.743446 + 0.668796i \(0.766810\pi\)
\(524\) 2.01971 0.0882313
\(525\) −2.46236 −0.107466
\(526\) −25.9584 −1.13184
\(527\) 0.258375 0.0112550
\(528\) −10.4672 −0.455528
\(529\) −2.08798 −0.0907816
\(530\) −10.4974 −0.455979
\(531\) 27.1553 1.17844
\(532\) −0.294324 −0.0127605
\(533\) −27.6685 −1.19845
\(534\) 40.8645 1.76838
\(535\) 6.61729 0.286090
\(536\) 3.61865 0.156302
\(537\) −2.23377 −0.0963945
\(538\) 20.7229 0.893426
\(539\) 1.46291 0.0630118
\(540\) 0.0696231 0.00299610
\(541\) −8.88257 −0.381891 −0.190946 0.981601i \(-0.561155\pi\)
−0.190946 + 0.981601i \(0.561155\pi\)
\(542\) 17.5174 0.752437
\(543\) −63.1988 −2.71212
\(544\) −0.123706 −0.00530387
\(545\) 17.9093 0.767149
\(546\) 13.5634 0.580458
\(547\) 26.0102 1.11212 0.556058 0.831143i \(-0.312313\pi\)
0.556058 + 0.831143i \(0.312313\pi\)
\(548\) −4.93999 −0.211026
\(549\) 29.6565 1.26571
\(550\) 1.82298 0.0777322
\(551\) −2.73927 −0.116697
\(552\) −34.3380 −1.46152
\(553\) −15.8964 −0.675984
\(554\) −26.1296 −1.11014
\(555\) −6.40226 −0.271761
\(556\) 0.211827 0.00898347
\(557\) 17.6210 0.746627 0.373313 0.927705i \(-0.378222\pi\)
0.373313 + 0.927705i \(0.378222\pi\)
\(558\) −19.7558 −0.836328
\(559\) −24.2120 −1.02406
\(560\) −2.90579 −0.122792
\(561\) −0.179834 −0.00759258
\(562\) −1.51425 −0.0638748
\(563\) 18.1411 0.764556 0.382278 0.924047i \(-0.375140\pi\)
0.382278 + 0.924047i \(0.375140\pi\)
\(564\) −11.5337 −0.485657
\(565\) 17.5204 0.737090
\(566\) −18.2701 −0.767949
\(567\) 8.80630 0.369830
\(568\) 14.3525 0.602216
\(569\) 12.3029 0.515764 0.257882 0.966176i \(-0.416975\pi\)
0.257882 + 0.966176i \(0.416975\pi\)
\(570\) 2.01977 0.0845987
\(571\) 26.7895 1.12111 0.560553 0.828118i \(-0.310588\pi\)
0.560553 + 0.828118i \(0.310588\pi\)
\(572\) 2.89139 0.120895
\(573\) 6.23458 0.260454
\(574\) −7.80015 −0.325572
\(575\) 4.57297 0.190706
\(576\) 27.2610 1.13588
\(577\) 28.2833 1.17745 0.588724 0.808334i \(-0.299631\pi\)
0.588724 + 0.808334i \(0.299631\pi\)
\(578\) −21.1812 −0.881024
\(579\) 37.4710 1.55724
\(580\) 1.86078 0.0772645
\(581\) 8.75408 0.363180
\(582\) 16.6440 0.689915
\(583\) 12.3235 0.510386
\(584\) −25.0831 −1.03794
\(585\) 13.5403 0.559823
\(586\) 2.26572 0.0935960
\(587\) 25.3798 1.04754 0.523768 0.851861i \(-0.324526\pi\)
0.523768 + 0.851861i \(0.324526\pi\)
\(588\) −1.10102 −0.0454053
\(589\) 3.40667 0.140369
\(590\) −11.0469 −0.454794
\(591\) 58.3264 2.39923
\(592\) −7.55518 −0.310516
\(593\) −5.13745 −0.210970 −0.105485 0.994421i \(-0.533639\pi\)
−0.105485 + 0.994421i \(0.533639\pi\)
\(594\) 0.283853 0.0116466
\(595\) −0.0499232 −0.00204665
\(596\) 3.94200 0.161470
\(597\) −47.7683 −1.95503
\(598\) −25.1891 −1.03006
\(599\) 12.1205 0.495228 0.247614 0.968859i \(-0.420353\pi\)
0.247614 + 0.968859i \(0.420353\pi\)
\(600\) −7.50891 −0.306550
\(601\) 25.5231 1.04111 0.520555 0.853828i \(-0.325725\pi\)
0.520555 + 0.853828i \(0.325725\pi\)
\(602\) −6.82572 −0.278196
\(603\) −3.63498 −0.148028
\(604\) 4.93503 0.200804
\(605\) 8.85991 0.360207
\(606\) 54.3278 2.20692
\(607\) −37.9248 −1.53932 −0.769661 0.638453i \(-0.779575\pi\)
−0.769661 + 0.638453i \(0.779575\pi\)
\(608\) −1.63107 −0.0661486
\(609\) −10.2472 −0.415236
\(610\) −12.0644 −0.488474
\(611\) −46.3045 −1.87328
\(612\) 0.0683794 0.00276407
\(613\) −17.5547 −0.709026 −0.354513 0.935051i \(-0.615353\pi\)
−0.354513 + 0.935051i \(0.615353\pi\)
\(614\) 8.06526 0.325487
\(615\) −15.4131 −0.621515
\(616\) 4.46109 0.179742
\(617\) −5.89116 −0.237169 −0.118585 0.992944i \(-0.537836\pi\)
−0.118585 + 0.992944i \(0.537836\pi\)
\(618\) 4.36096 0.175424
\(619\) 42.3799 1.70339 0.851695 0.524038i \(-0.175575\pi\)
0.851695 + 0.524038i \(0.175575\pi\)
\(620\) −2.31414 −0.0929381
\(621\) 0.712047 0.0285735
\(622\) −4.96019 −0.198886
\(623\) −13.3176 −0.533560
\(624\) 31.6275 1.26611
\(625\) 1.00000 0.0400000
\(626\) 19.1107 0.763819
\(627\) −2.37111 −0.0946929
\(628\) 2.20909 0.0881523
\(629\) −0.129803 −0.00517557
\(630\) 3.81722 0.152081
\(631\) −6.13013 −0.244037 −0.122018 0.992528i \(-0.538937\pi\)
−0.122018 + 0.992528i \(0.538937\pi\)
\(632\) −48.4757 −1.92826
\(633\) 25.4431 1.01127
\(634\) 36.5930 1.45330
\(635\) 4.97063 0.197253
\(636\) −9.27495 −0.367776
\(637\) −4.42027 −0.175137
\(638\) 7.58637 0.300347
\(639\) −14.4172 −0.570337
\(640\) −6.13405 −0.242470
\(641\) −0.919866 −0.0363325 −0.0181663 0.999835i \(-0.505783\pi\)
−0.0181663 + 0.999835i \(0.505783\pi\)
\(642\) −20.3048 −0.801366
\(643\) −21.8237 −0.860642 −0.430321 0.902676i \(-0.641600\pi\)
−0.430321 + 0.902676i \(0.641600\pi\)
\(644\) 2.04475 0.0805745
\(645\) −13.4876 −0.531073
\(646\) 0.0409498 0.00161115
\(647\) 24.0684 0.946227 0.473114 0.881001i \(-0.343130\pi\)
0.473114 + 0.881001i \(0.343130\pi\)
\(648\) 26.8546 1.05495
\(649\) 12.9685 0.509059
\(650\) −5.50827 −0.216052
\(651\) 12.7438 0.499470
\(652\) 9.22648 0.361337
\(653\) 23.3108 0.912221 0.456111 0.889923i \(-0.349242\pi\)
0.456111 + 0.889923i \(0.349242\pi\)
\(654\) −54.9536 −2.14886
\(655\) 4.51695 0.176492
\(656\) −18.1887 −0.710148
\(657\) 25.1963 0.983000
\(658\) −13.0539 −0.508894
\(659\) 15.3521 0.598033 0.299016 0.954248i \(-0.403341\pi\)
0.299016 + 0.954248i \(0.403341\pi\)
\(660\) 1.61069 0.0626959
\(661\) −22.8289 −0.887941 −0.443970 0.896041i \(-0.646430\pi\)
−0.443970 + 0.896041i \(0.646430\pi\)
\(662\) 11.9209 0.463318
\(663\) 0.543380 0.0211031
\(664\) 26.6953 1.03598
\(665\) −0.658238 −0.0255254
\(666\) 9.92493 0.384583
\(667\) 19.0305 0.736863
\(668\) 4.01758 0.155445
\(669\) −27.2213 −1.05244
\(670\) 1.47873 0.0571281
\(671\) 14.1630 0.546757
\(672\) −6.10157 −0.235373
\(673\) 6.58459 0.253817 0.126909 0.991914i \(-0.459494\pi\)
0.126909 + 0.991914i \(0.459494\pi\)
\(674\) 32.4826 1.25118
\(675\) 0.155708 0.00599320
\(676\) −2.92374 −0.112451
\(677\) −37.6023 −1.44517 −0.722587 0.691280i \(-0.757047\pi\)
−0.722587 + 0.691280i \(0.757047\pi\)
\(678\) −53.7605 −2.06466
\(679\) −5.42424 −0.208163
\(680\) −0.152240 −0.00583812
\(681\) 69.6944 2.67070
\(682\) −9.43474 −0.361275
\(683\) −8.83601 −0.338101 −0.169050 0.985607i \(-0.554070\pi\)
−0.169050 + 0.985607i \(0.554070\pi\)
\(684\) 0.901583 0.0344729
\(685\) −11.0480 −0.422123
\(686\) −1.24614 −0.0475778
\(687\) 2.46236 0.0939450
\(688\) −15.9164 −0.606809
\(689\) −37.2362 −1.41859
\(690\) −14.0319 −0.534185
\(691\) −30.8214 −1.17250 −0.586250 0.810130i \(-0.699396\pi\)
−0.586250 + 0.810130i \(0.699396\pi\)
\(692\) −4.73506 −0.180000
\(693\) −4.48122 −0.170228
\(694\) −27.8281 −1.05634
\(695\) 0.473739 0.0179699
\(696\) −31.2485 −1.18447
\(697\) −0.312492 −0.0118365
\(698\) 27.2786 1.03251
\(699\) 69.1199 2.61436
\(700\) 0.447139 0.0169003
\(701\) 29.2705 1.10553 0.552766 0.833336i \(-0.313572\pi\)
0.552766 + 0.833336i \(0.313572\pi\)
\(702\) −0.857680 −0.0323711
\(703\) −1.71145 −0.0645485
\(704\) 13.0190 0.490673
\(705\) −25.7945 −0.971476
\(706\) 14.1838 0.533813
\(707\) −17.7053 −0.665877
\(708\) −9.76043 −0.366819
\(709\) −52.2672 −1.96293 −0.981467 0.191630i \(-0.938623\pi\)
−0.981467 + 0.191630i \(0.938623\pi\)
\(710\) 5.86500 0.220109
\(711\) 48.6944 1.82618
\(712\) −40.6118 −1.52199
\(713\) −23.6671 −0.886340
\(714\) 0.153187 0.00573287
\(715\) 6.46643 0.241831
\(716\) 0.405630 0.0151591
\(717\) 6.96571 0.260139
\(718\) 18.2222 0.680047
\(719\) −23.7345 −0.885148 −0.442574 0.896732i \(-0.645935\pi\)
−0.442574 + 0.896732i \(0.645935\pi\)
\(720\) 8.90111 0.331725
\(721\) −1.42123 −0.0529293
\(722\) −23.1367 −0.861059
\(723\) 12.8557 0.478109
\(724\) 11.4762 0.426510
\(725\) 4.16152 0.154555
\(726\) −27.1862 −1.00897
\(727\) 14.3640 0.532730 0.266365 0.963872i \(-0.414177\pi\)
0.266365 + 0.963872i \(0.414177\pi\)
\(728\) −13.4795 −0.499583
\(729\) −28.1260 −1.04170
\(730\) −10.2500 −0.379368
\(731\) −0.273454 −0.0101141
\(732\) −10.6594 −0.393984
\(733\) 28.0463 1.03591 0.517957 0.855407i \(-0.326693\pi\)
0.517957 + 0.855407i \(0.326693\pi\)
\(734\) 11.7477 0.433616
\(735\) −2.46236 −0.0908257
\(736\) 11.3315 0.417685
\(737\) −1.73595 −0.0639446
\(738\) 23.8937 0.879539
\(739\) −23.4194 −0.861496 −0.430748 0.902472i \(-0.641750\pi\)
−0.430748 + 0.902472i \(0.641750\pi\)
\(740\) 1.16258 0.0427374
\(741\) 7.16446 0.263193
\(742\) −10.4974 −0.385373
\(743\) −7.55917 −0.277319 −0.138660 0.990340i \(-0.544279\pi\)
−0.138660 + 0.990340i \(0.544279\pi\)
\(744\) 38.8619 1.42475
\(745\) 8.81604 0.322995
\(746\) −40.6733 −1.48916
\(747\) −26.8158 −0.981139
\(748\) 0.0326559 0.00119402
\(749\) 6.61729 0.241790
\(750\) −3.06845 −0.112044
\(751\) −43.5914 −1.59067 −0.795336 0.606169i \(-0.792706\pi\)
−0.795336 + 0.606169i \(0.792706\pi\)
\(752\) −30.4396 −1.11002
\(753\) 18.5020 0.674251
\(754\) −22.9227 −0.834797
\(755\) 11.0369 0.401674
\(756\) 0.0696231 0.00253217
\(757\) 33.2588 1.20881 0.604405 0.796677i \(-0.293411\pi\)
0.604405 + 0.796677i \(0.293411\pi\)
\(758\) 7.66149 0.278278
\(759\) 16.4728 0.597923
\(760\) −2.00728 −0.0728116
\(761\) −45.9238 −1.66474 −0.832369 0.554222i \(-0.813016\pi\)
−0.832369 + 0.554222i \(0.813016\pi\)
\(762\) −15.2521 −0.552526
\(763\) 17.9093 0.648359
\(764\) −1.13213 −0.0409592
\(765\) 0.152927 0.00552907
\(766\) 45.8800 1.65771
\(767\) −39.1853 −1.41490
\(768\) −25.0052 −0.902299
\(769\) −36.3144 −1.30953 −0.654765 0.755833i \(-0.727232\pi\)
−0.654765 + 0.755833i \(0.727232\pi\)
\(770\) 1.82298 0.0656957
\(771\) −20.5427 −0.739828
\(772\) −6.80433 −0.244893
\(773\) −3.29503 −0.118514 −0.0592570 0.998243i \(-0.518873\pi\)
−0.0592570 + 0.998243i \(0.518873\pi\)
\(774\) 20.9088 0.751551
\(775\) −5.17544 −0.185907
\(776\) −16.5411 −0.593790
\(777\) −6.40226 −0.229680
\(778\) 18.2881 0.655660
\(779\) −4.12021 −0.147622
\(780\) −4.86680 −0.174259
\(781\) −6.88522 −0.246372
\(782\) −0.284490 −0.0101733
\(783\) 0.647981 0.0231569
\(784\) −2.90579 −0.103778
\(785\) 4.94050 0.176334
\(786\) −13.8600 −0.494371
\(787\) 16.6352 0.592982 0.296491 0.955036i \(-0.404183\pi\)
0.296491 + 0.955036i \(0.404183\pi\)
\(788\) −10.5915 −0.377305
\(789\) −51.2936 −1.82610
\(790\) −19.8091 −0.704777
\(791\) 17.5204 0.622955
\(792\) −13.6654 −0.485578
\(793\) −42.7945 −1.51968
\(794\) −15.8147 −0.561244
\(795\) −20.7429 −0.735674
\(796\) 8.67422 0.307450
\(797\) 23.1724 0.820809 0.410404 0.911904i \(-0.365388\pi\)
0.410404 + 0.911904i \(0.365388\pi\)
\(798\) 2.01977 0.0714990
\(799\) −0.522970 −0.0185014
\(800\) 2.47793 0.0876082
\(801\) 40.7951 1.44142
\(802\) 15.7362 0.555664
\(803\) 12.0329 0.424633
\(804\) 1.30652 0.0460774
\(805\) 4.57297 0.161176
\(806\) 28.5077 1.00414
\(807\) 40.9483 1.44145
\(808\) −53.9919 −1.89943
\(809\) −4.99812 −0.175725 −0.0878623 0.996133i \(-0.528004\pi\)
−0.0878623 + 0.996133i \(0.528004\pi\)
\(810\) 10.9739 0.385582
\(811\) −35.4858 −1.24607 −0.623037 0.782193i \(-0.714101\pi\)
−0.623037 + 0.782193i \(0.714101\pi\)
\(812\) 1.86078 0.0653004
\(813\) 34.6143 1.21398
\(814\) 4.73984 0.166131
\(815\) 20.6345 0.722795
\(816\) 0.357206 0.0125047
\(817\) −3.60549 −0.126140
\(818\) 11.4271 0.399539
\(819\) 13.5403 0.473137
\(820\) 2.79885 0.0977400
\(821\) 30.5028 1.06456 0.532278 0.846569i \(-0.321336\pi\)
0.532278 + 0.846569i \(0.321336\pi\)
\(822\) 33.9002 1.18241
\(823\) −6.09578 −0.212486 −0.106243 0.994340i \(-0.533882\pi\)
−0.106243 + 0.994340i \(0.533882\pi\)
\(824\) −4.33400 −0.150982
\(825\) 3.60220 0.125413
\(826\) −11.0469 −0.384371
\(827\) −18.3520 −0.638160 −0.319080 0.947728i \(-0.603374\pi\)
−0.319080 + 0.947728i \(0.603374\pi\)
\(828\) −6.26356 −0.217674
\(829\) 11.0345 0.383243 0.191622 0.981469i \(-0.438625\pi\)
0.191622 + 0.981469i \(0.438625\pi\)
\(830\) 10.9088 0.378650
\(831\) −51.6320 −1.79109
\(832\) −39.3378 −1.36379
\(833\) −0.0499232 −0.00172974
\(834\) −1.45364 −0.0503355
\(835\) 8.98507 0.310941
\(836\) 0.430568 0.0148915
\(837\) −0.805857 −0.0278545
\(838\) 46.7477 1.61487
\(839\) 22.3307 0.770940 0.385470 0.922720i \(-0.374039\pi\)
0.385470 + 0.922720i \(0.374039\pi\)
\(840\) −7.50891 −0.259082
\(841\) −11.6818 −0.402820
\(842\) −50.1763 −1.72919
\(843\) −2.99215 −0.103055
\(844\) −4.62020 −0.159034
\(845\) −6.53876 −0.224940
\(846\) 39.9872 1.37479
\(847\) 8.85991 0.304430
\(848\) −24.4783 −0.840588
\(849\) −36.1016 −1.23900
\(850\) −0.0622113 −0.00213383
\(851\) 11.8899 0.407581
\(852\) 5.18198 0.177532
\(853\) −23.9554 −0.820219 −0.410109 0.912036i \(-0.634509\pi\)
−0.410109 + 0.912036i \(0.634509\pi\)
\(854\) −12.0644 −0.412836
\(855\) 2.01634 0.0689572
\(856\) 20.1793 0.689713
\(857\) 2.84743 0.0972664 0.0486332 0.998817i \(-0.484513\pi\)
0.0486332 + 0.998817i \(0.484513\pi\)
\(858\) −19.8419 −0.677391
\(859\) 18.6463 0.636203 0.318101 0.948057i \(-0.396955\pi\)
0.318101 + 0.948057i \(0.396955\pi\)
\(860\) 2.44920 0.0835171
\(861\) −15.4131 −0.525276
\(862\) −25.7978 −0.878676
\(863\) 10.6560 0.362734 0.181367 0.983416i \(-0.441948\pi\)
0.181367 + 0.983416i \(0.441948\pi\)
\(864\) 0.385834 0.0131263
\(865\) −10.5897 −0.360060
\(866\) 37.6285 1.27867
\(867\) −41.8540 −1.42144
\(868\) −2.31414 −0.0785471
\(869\) 23.2549 0.788869
\(870\) −12.7694 −0.432923
\(871\) 5.24529 0.177730
\(872\) 54.6138 1.84946
\(873\) 16.6157 0.562357
\(874\) −3.75100 −0.126879
\(875\) 1.00000 0.0338062
\(876\) −9.05629 −0.305984
\(877\) −48.3368 −1.63222 −0.816109 0.577899i \(-0.803873\pi\)
−0.816109 + 0.577899i \(0.803873\pi\)
\(878\) 48.4924 1.63654
\(879\) 4.47705 0.151007
\(880\) 4.25089 0.143298
\(881\) 3.76075 0.126703 0.0633514 0.997991i \(-0.479821\pi\)
0.0633514 + 0.997991i \(0.479821\pi\)
\(882\) 3.81722 0.128532
\(883\) −24.2839 −0.817219 −0.408609 0.912709i \(-0.633986\pi\)
−0.408609 + 0.912709i \(0.633986\pi\)
\(884\) −0.0986720 −0.00331870
\(885\) −21.8286 −0.733761
\(886\) 12.1141 0.406981
\(887\) −40.4748 −1.35901 −0.679505 0.733671i \(-0.737805\pi\)
−0.679505 + 0.733671i \(0.737805\pi\)
\(888\) −19.5235 −0.655166
\(889\) 4.97063 0.166710
\(890\) −16.5956 −0.556287
\(891\) −12.8828 −0.431589
\(892\) 4.94310 0.165507
\(893\) −6.89536 −0.230744
\(894\) −27.0515 −0.904739
\(895\) 0.907167 0.0303232
\(896\) −6.13405 −0.204924
\(897\) −49.7736 −1.66189
\(898\) 29.1479 0.972679
\(899\) −21.5377 −0.718322
\(900\) −1.36969 −0.0456564
\(901\) −0.420552 −0.0140106
\(902\) 11.4109 0.379941
\(903\) −13.4876 −0.448839
\(904\) 53.4281 1.77699
\(905\) 25.6659 0.853163
\(906\) −33.8662 −1.12513
\(907\) −10.2924 −0.341754 −0.170877 0.985292i \(-0.554660\pi\)
−0.170877 + 0.985292i \(0.554660\pi\)
\(908\) −12.6558 −0.419996
\(909\) 54.2356 1.79888
\(910\) −5.50827 −0.182597
\(911\) −41.4665 −1.37385 −0.686923 0.726731i \(-0.741039\pi\)
−0.686923 + 0.726731i \(0.741039\pi\)
\(912\) 4.70976 0.155956
\(913\) −12.8064 −0.423829
\(914\) 50.8197 1.68097
\(915\) −23.8392 −0.788100
\(916\) −0.447139 −0.0147739
\(917\) 4.51695 0.149163
\(918\) −0.00968678 −0.000319712 0
\(919\) 36.2294 1.19510 0.597549 0.801832i \(-0.296141\pi\)
0.597549 + 0.801832i \(0.296141\pi\)
\(920\) 13.9451 0.459758
\(921\) 15.9369 0.525139
\(922\) −48.2760 −1.58988
\(923\) 20.8041 0.684777
\(924\) 1.61069 0.0529877
\(925\) 2.60005 0.0854890
\(926\) −12.5698 −0.413069
\(927\) 4.35356 0.142990
\(928\) 10.3120 0.338507
\(929\) −26.2810 −0.862253 −0.431126 0.902292i \(-0.641884\pi\)
−0.431126 + 0.902292i \(0.641884\pi\)
\(930\) 15.8806 0.520744
\(931\) −0.658238 −0.0215729
\(932\) −12.5514 −0.411136
\(933\) −9.80132 −0.320881
\(934\) 33.8482 1.10755
\(935\) 0.0730329 0.00238843
\(936\) 41.2908 1.34963
\(937\) −45.2152 −1.47712 −0.738558 0.674190i \(-0.764493\pi\)
−0.738558 + 0.674190i \(0.764493\pi\)
\(938\) 1.47873 0.0482821
\(939\) 37.7627 1.23234
\(940\) 4.68400 0.152775
\(941\) −41.9913 −1.36888 −0.684438 0.729071i \(-0.739953\pi\)
−0.684438 + 0.729071i \(0.739953\pi\)
\(942\) −15.1597 −0.493928
\(943\) 28.6243 0.932135
\(944\) −25.7596 −0.838402
\(945\) 0.155708 0.00506518
\(946\) 9.98538 0.324653
\(947\) −16.3529 −0.531396 −0.265698 0.964056i \(-0.585602\pi\)
−0.265698 + 0.964056i \(0.585602\pi\)
\(948\) −17.5022 −0.568446
\(949\) −36.3584 −1.18024
\(950\) −0.820255 −0.0266126
\(951\) 72.3077 2.34474
\(952\) −0.152240 −0.00493411
\(953\) −56.4313 −1.82799 −0.913995 0.405725i \(-0.867019\pi\)
−0.913995 + 0.405725i \(0.867019\pi\)
\(954\) 32.1561 1.04109
\(955\) −2.53195 −0.0819320
\(956\) −1.26490 −0.0409098
\(957\) 14.9906 0.484578
\(958\) −27.2870 −0.881602
\(959\) −11.0480 −0.356759
\(960\) −21.9136 −0.707259
\(961\) −4.21482 −0.135962
\(962\) −14.3217 −0.461752
\(963\) −20.2703 −0.653202
\(964\) −2.33446 −0.0751879
\(965\) −15.2175 −0.489868
\(966\) −14.0319 −0.451469
\(967\) −9.96427 −0.320429 −0.160215 0.987082i \(-0.551219\pi\)
−0.160215 + 0.987082i \(0.551219\pi\)
\(968\) 27.0181 0.868393
\(969\) 0.0809166 0.00259941
\(970\) −6.75935 −0.217030
\(971\) 50.6361 1.62499 0.812495 0.582969i \(-0.198109\pi\)
0.812495 + 0.582969i \(0.198109\pi\)
\(972\) 9.90477 0.317696
\(973\) 0.473739 0.0151874
\(974\) −39.7072 −1.27230
\(975\) −10.8843 −0.348577
\(976\) −28.1322 −0.900490
\(977\) 36.0245 1.15252 0.576262 0.817265i \(-0.304511\pi\)
0.576262 + 0.817265i \(0.304511\pi\)
\(978\) −63.3158 −2.02462
\(979\) 19.4825 0.622662
\(980\) 0.447139 0.0142833
\(981\) −54.8603 −1.75155
\(982\) −4.84978 −0.154763
\(983\) −51.3856 −1.63895 −0.819473 0.573118i \(-0.805734\pi\)
−0.819473 + 0.573118i \(0.805734\pi\)
\(984\) −47.0017 −1.49836
\(985\) −23.6872 −0.754736
\(986\) −0.258893 −0.00824484
\(987\) −25.7945 −0.821047
\(988\) −1.30099 −0.0413900
\(989\) 25.0484 0.796493
\(990\) −5.58422 −0.177478
\(991\) −31.4982 −1.00057 −0.500287 0.865859i \(-0.666772\pi\)
−0.500287 + 0.865859i \(0.666772\pi\)
\(992\) −12.8244 −0.407175
\(993\) 23.5556 0.747515
\(994\) 5.86500 0.186026
\(995\) 19.3994 0.615002
\(996\) 9.63840 0.305405
\(997\) 27.4756 0.870163 0.435081 0.900391i \(-0.356720\pi\)
0.435081 + 0.900391i \(0.356720\pi\)
\(998\) 11.9207 0.377344
\(999\) 0.404848 0.0128088
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 \(a_p\))