Properties

Label 8013.2.a.d.1.19
Level 8013
Weight 2
Character 8013.1
Self dual Yes
Analytic conductor 63.984
Analytic rank 0
Dimension 129
CM No

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Newspace parameters

Level: \( N \) = \( 8013 = 3 \cdot 2671 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8013.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9841271397\)
Analytic rank: \(0\)
Dimension: \(129\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 8013.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.08790 q^{2} +1.00000 q^{3} +2.35934 q^{4} +0.999516 q^{5} -2.08790 q^{6} -2.01365 q^{7} -0.750272 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.08790 q^{2} +1.00000 q^{3} +2.35934 q^{4} +0.999516 q^{5} -2.08790 q^{6} -2.01365 q^{7} -0.750272 q^{8} +1.00000 q^{9} -2.08689 q^{10} -2.08706 q^{11} +2.35934 q^{12} -3.80897 q^{13} +4.20430 q^{14} +0.999516 q^{15} -3.15219 q^{16} -1.14562 q^{17} -2.08790 q^{18} -7.01905 q^{19} +2.35820 q^{20} -2.01365 q^{21} +4.35759 q^{22} +5.35009 q^{23} -0.750272 q^{24} -4.00097 q^{25} +7.95276 q^{26} +1.00000 q^{27} -4.75089 q^{28} +1.71873 q^{29} -2.08689 q^{30} +2.60484 q^{31} +8.08201 q^{32} -2.08706 q^{33} +2.39194 q^{34} -2.01267 q^{35} +2.35934 q^{36} -0.899584 q^{37} +14.6551 q^{38} -3.80897 q^{39} -0.749909 q^{40} +11.4481 q^{41} +4.20430 q^{42} -3.59734 q^{43} -4.92410 q^{44} +0.999516 q^{45} -11.1705 q^{46} -5.79377 q^{47} -3.15219 q^{48} -2.94522 q^{49} +8.35364 q^{50} -1.14562 q^{51} -8.98666 q^{52} -13.1743 q^{53} -2.08790 q^{54} -2.08605 q^{55} +1.51078 q^{56} -7.01905 q^{57} -3.58854 q^{58} -6.79416 q^{59} +2.35820 q^{60} +11.5720 q^{61} -5.43867 q^{62} -2.01365 q^{63} -10.5701 q^{64} -3.80712 q^{65} +4.35759 q^{66} +14.2860 q^{67} -2.70291 q^{68} +5.35009 q^{69} +4.20227 q^{70} -15.1350 q^{71} -0.750272 q^{72} -1.41883 q^{73} +1.87824 q^{74} -4.00097 q^{75} -16.5603 q^{76} +4.20261 q^{77} +7.95276 q^{78} +0.661519 q^{79} -3.15066 q^{80} +1.00000 q^{81} -23.9025 q^{82} -5.04774 q^{83} -4.75089 q^{84} -1.14506 q^{85} +7.51089 q^{86} +1.71873 q^{87} +1.56587 q^{88} +17.6190 q^{89} -2.08689 q^{90} +7.66992 q^{91} +12.6227 q^{92} +2.60484 q^{93} +12.0968 q^{94} -7.01565 q^{95} +8.08201 q^{96} -12.5482 q^{97} +6.14934 q^{98} -2.08706 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 129q + 15q^{2} + 129q^{3} + 151q^{4} + 16q^{5} + 15q^{6} + 61q^{7} + 42q^{8} + 129q^{9} + O(q^{10}) \) \( 129q + 15q^{2} + 129q^{3} + 151q^{4} + 16q^{5} + 15q^{6} + 61q^{7} + 42q^{8} + 129q^{9} + 41q^{10} + 51q^{11} + 151q^{12} + 56q^{13} + 5q^{14} + 16q^{15} + 195q^{16} + 18q^{17} + 15q^{18} + 93q^{19} + 44q^{20} + 61q^{21} + 46q^{22} + 50q^{23} + 42q^{24} + 193q^{25} + q^{26} + 129q^{27} + 145q^{28} + 24q^{29} + 41q^{30} + 67q^{31} + 89q^{32} + 51q^{33} + 73q^{34} + 56q^{35} + 151q^{36} + 95q^{37} + 9q^{38} + 56q^{39} + 103q^{40} + 7q^{41} + 5q^{42} + 150q^{43} + 69q^{44} + 16q^{45} + 72q^{46} + 53q^{47} + 195q^{48} + 240q^{49} + 17q^{50} + 18q^{51} + 124q^{52} + 34q^{53} + 15q^{54} + 66q^{55} - 17q^{56} + 93q^{57} + 57q^{58} + 49q^{59} + 44q^{60} + 113q^{61} + 27q^{62} + 61q^{63} + 262q^{64} + 22q^{65} + 46q^{66} + 185q^{67} + 2q^{68} + 50q^{69} + 25q^{70} + 41q^{71} + 42q^{72} + 153q^{73} - q^{74} + 193q^{75} + 190q^{76} + 39q^{77} + q^{78} + 101q^{79} + 48q^{80} + 129q^{81} + 15q^{82} + 162q^{83} + 145q^{84} + 99q^{85} + 13q^{86} + 24q^{87} + 86q^{88} - 4q^{89} + 41q^{90} + 117q^{91} + 56q^{92} + 67q^{93} + 49q^{94} + 71q^{95} + 89q^{96} + 159q^{97} + 40q^{98} + 51q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.08790 −1.47637 −0.738185 0.674598i \(-0.764317\pi\)
−0.738185 + 0.674598i \(0.764317\pi\)
\(3\) 1.00000 0.577350
\(4\) 2.35934 1.17967
\(5\) 0.999516 0.446997 0.223498 0.974704i \(-0.428252\pi\)
0.223498 + 0.974704i \(0.428252\pi\)
\(6\) −2.08790 −0.852383
\(7\) −2.01365 −0.761087 −0.380544 0.924763i \(-0.624263\pi\)
−0.380544 + 0.924763i \(0.624263\pi\)
\(8\) −0.750272 −0.265261
\(9\) 1.00000 0.333333
\(10\) −2.08689 −0.659933
\(11\) −2.08706 −0.629273 −0.314637 0.949212i \(-0.601883\pi\)
−0.314637 + 0.949212i \(0.601883\pi\)
\(12\) 2.35934 0.681083
\(13\) −3.80897 −1.05642 −0.528209 0.849115i \(-0.677136\pi\)
−0.528209 + 0.849115i \(0.677136\pi\)
\(14\) 4.20430 1.12365
\(15\) 0.999516 0.258074
\(16\) −3.15219 −0.788047
\(17\) −1.14562 −0.277854 −0.138927 0.990303i \(-0.544365\pi\)
−0.138927 + 0.990303i \(0.544365\pi\)
\(18\) −2.08790 −0.492124
\(19\) −7.01905 −1.61028 −0.805141 0.593084i \(-0.797910\pi\)
−0.805141 + 0.593084i \(0.797910\pi\)
\(20\) 2.35820 0.527309
\(21\) −2.01365 −0.439414
\(22\) 4.35759 0.929041
\(23\) 5.35009 1.11557 0.557785 0.829985i \(-0.311651\pi\)
0.557785 + 0.829985i \(0.311651\pi\)
\(24\) −0.750272 −0.153149
\(25\) −4.00097 −0.800194
\(26\) 7.95276 1.55966
\(27\) 1.00000 0.192450
\(28\) −4.75089 −0.897833
\(29\) 1.71873 0.319160 0.159580 0.987185i \(-0.448986\pi\)
0.159580 + 0.987185i \(0.448986\pi\)
\(30\) −2.08689 −0.381013
\(31\) 2.60484 0.467844 0.233922 0.972255i \(-0.424844\pi\)
0.233922 + 0.972255i \(0.424844\pi\)
\(32\) 8.08201 1.42871
\(33\) −2.08706 −0.363311
\(34\) 2.39194 0.410215
\(35\) −2.01267 −0.340204
\(36\) 2.35934 0.393224
\(37\) −0.899584 −0.147891 −0.0739453 0.997262i \(-0.523559\pi\)
−0.0739453 + 0.997262i \(0.523559\pi\)
\(38\) 14.6551 2.37737
\(39\) −3.80897 −0.609923
\(40\) −0.749909 −0.118571
\(41\) 11.4481 1.78789 0.893945 0.448177i \(-0.147926\pi\)
0.893945 + 0.448177i \(0.147926\pi\)
\(42\) 4.20430 0.648738
\(43\) −3.59734 −0.548589 −0.274294 0.961646i \(-0.588444\pi\)
−0.274294 + 0.961646i \(0.588444\pi\)
\(44\) −4.92410 −0.742336
\(45\) 0.999516 0.148999
\(46\) −11.1705 −1.64700
\(47\) −5.79377 −0.845108 −0.422554 0.906338i \(-0.638866\pi\)
−0.422554 + 0.906338i \(0.638866\pi\)
\(48\) −3.15219 −0.454979
\(49\) −2.94522 −0.420746
\(50\) 8.35364 1.18138
\(51\) −1.14562 −0.160419
\(52\) −8.98666 −1.24623
\(53\) −13.1743 −1.80963 −0.904815 0.425804i \(-0.859991\pi\)
−0.904815 + 0.425804i \(0.859991\pi\)
\(54\) −2.08790 −0.284128
\(55\) −2.08605 −0.281283
\(56\) 1.51078 0.201887
\(57\) −7.01905 −0.929696
\(58\) −3.58854 −0.471198
\(59\) −6.79416 −0.884524 −0.442262 0.896886i \(-0.645824\pi\)
−0.442262 + 0.896886i \(0.645824\pi\)
\(60\) 2.35820 0.304442
\(61\) 11.5720 1.48164 0.740822 0.671701i \(-0.234436\pi\)
0.740822 + 0.671701i \(0.234436\pi\)
\(62\) −5.43867 −0.690711
\(63\) −2.01365 −0.253696
\(64\) −10.5701 −1.32126
\(65\) −3.80712 −0.472215
\(66\) 4.35759 0.536382
\(67\) 14.2860 1.74531 0.872657 0.488334i \(-0.162395\pi\)
0.872657 + 0.488334i \(0.162395\pi\)
\(68\) −2.70291 −0.327776
\(69\) 5.35009 0.644075
\(70\) 4.20227 0.502267
\(71\) −15.1350 −1.79620 −0.898098 0.439796i \(-0.855051\pi\)
−0.898098 + 0.439796i \(0.855051\pi\)
\(72\) −0.750272 −0.0884204
\(73\) −1.41883 −0.166062 −0.0830309 0.996547i \(-0.526460\pi\)
−0.0830309 + 0.996547i \(0.526460\pi\)
\(74\) 1.87824 0.218341
\(75\) −4.00097 −0.461992
\(76\) −16.5603 −1.89960
\(77\) 4.20261 0.478932
\(78\) 7.95276 0.900472
\(79\) 0.661519 0.0744267 0.0372133 0.999307i \(-0.488152\pi\)
0.0372133 + 0.999307i \(0.488152\pi\)
\(80\) −3.15066 −0.352255
\(81\) 1.00000 0.111111
\(82\) −23.9025 −2.63959
\(83\) −5.04774 −0.554062 −0.277031 0.960861i \(-0.589350\pi\)
−0.277031 + 0.960861i \(0.589350\pi\)
\(84\) −4.75089 −0.518364
\(85\) −1.14506 −0.124200
\(86\) 7.51089 0.809920
\(87\) 1.71873 0.184267
\(88\) 1.56587 0.166922
\(89\) 17.6190 1.86761 0.933805 0.357782i \(-0.116467\pi\)
0.933805 + 0.357782i \(0.116467\pi\)
\(90\) −2.08689 −0.219978
\(91\) 7.66992 0.804026
\(92\) 12.6227 1.31601
\(93\) 2.60484 0.270110
\(94\) 12.0968 1.24769
\(95\) −7.01565 −0.719791
\(96\) 8.08201 0.824867
\(97\) −12.5482 −1.27408 −0.637041 0.770830i \(-0.719842\pi\)
−0.637041 + 0.770830i \(0.719842\pi\)
\(98\) 6.14934 0.621177
\(99\) −2.08706 −0.209758
\(100\) −9.43965 −0.943965
\(101\) −15.9567 −1.58776 −0.793878 0.608077i \(-0.791941\pi\)
−0.793878 + 0.608077i \(0.791941\pi\)
\(102\) 2.39194 0.236838
\(103\) 15.4800 1.52529 0.762643 0.646820i \(-0.223902\pi\)
0.762643 + 0.646820i \(0.223902\pi\)
\(104\) 2.85776 0.280227
\(105\) −2.01267 −0.196417
\(106\) 27.5067 2.67169
\(107\) 10.2250 0.988491 0.494246 0.869322i \(-0.335444\pi\)
0.494246 + 0.869322i \(0.335444\pi\)
\(108\) 2.35934 0.227028
\(109\) 11.2361 1.07622 0.538111 0.842874i \(-0.319138\pi\)
0.538111 + 0.842874i \(0.319138\pi\)
\(110\) 4.35548 0.415278
\(111\) −0.899584 −0.0853847
\(112\) 6.34740 0.599773
\(113\) 3.75603 0.353337 0.176669 0.984270i \(-0.443468\pi\)
0.176669 + 0.984270i \(0.443468\pi\)
\(114\) 14.6551 1.37258
\(115\) 5.34750 0.498657
\(116\) 4.05507 0.376503
\(117\) −3.80897 −0.352139
\(118\) 14.1855 1.30589
\(119\) 2.30688 0.211471
\(120\) −0.749909 −0.0684570
\(121\) −6.64416 −0.604015
\(122\) −24.1613 −2.18746
\(123\) 11.4481 1.03224
\(124\) 6.14572 0.551902
\(125\) −8.99661 −0.804681
\(126\) 4.20430 0.374549
\(127\) 12.1830 1.08107 0.540533 0.841323i \(-0.318223\pi\)
0.540533 + 0.841323i \(0.318223\pi\)
\(128\) 5.90530 0.521959
\(129\) −3.59734 −0.316728
\(130\) 7.94890 0.697165
\(131\) −0.278300 −0.0243152 −0.0121576 0.999926i \(-0.503870\pi\)
−0.0121576 + 0.999926i \(0.503870\pi\)
\(132\) −4.92410 −0.428588
\(133\) 14.1339 1.22556
\(134\) −29.8278 −2.57673
\(135\) 0.999516 0.0860246
\(136\) 0.859527 0.0737038
\(137\) 6.98356 0.596645 0.298323 0.954465i \(-0.403573\pi\)
0.298323 + 0.954465i \(0.403573\pi\)
\(138\) −11.1705 −0.950894
\(139\) 20.5088 1.73953 0.869767 0.493463i \(-0.164269\pi\)
0.869767 + 0.493463i \(0.164269\pi\)
\(140\) −4.74858 −0.401329
\(141\) −5.79377 −0.487923
\(142\) 31.6004 2.65185
\(143\) 7.94956 0.664775
\(144\) −3.15219 −0.262682
\(145\) 1.71789 0.142663
\(146\) 2.96239 0.245169
\(147\) −2.94522 −0.242918
\(148\) −2.12243 −0.174462
\(149\) −13.9341 −1.14153 −0.570764 0.821114i \(-0.693353\pi\)
−0.570764 + 0.821114i \(0.693353\pi\)
\(150\) 8.35364 0.682072
\(151\) 3.09314 0.251716 0.125858 0.992048i \(-0.459832\pi\)
0.125858 + 0.992048i \(0.459832\pi\)
\(152\) 5.26620 0.427145
\(153\) −1.14562 −0.0926179
\(154\) −8.77465 −0.707081
\(155\) 2.60358 0.209125
\(156\) −8.98666 −0.719508
\(157\) 5.43945 0.434115 0.217058 0.976159i \(-0.430354\pi\)
0.217058 + 0.976159i \(0.430354\pi\)
\(158\) −1.38119 −0.109881
\(159\) −13.1743 −1.04479
\(160\) 8.07810 0.638629
\(161\) −10.7732 −0.849047
\(162\) −2.08790 −0.164041
\(163\) −5.02474 −0.393568 −0.196784 0.980447i \(-0.563050\pi\)
−0.196784 + 0.980447i \(0.563050\pi\)
\(164\) 27.0099 2.10912
\(165\) −2.08605 −0.162399
\(166\) 10.5392 0.818001
\(167\) 0.462761 0.0358096 0.0179048 0.999840i \(-0.494300\pi\)
0.0179048 + 0.999840i \(0.494300\pi\)
\(168\) 1.51078 0.116560
\(169\) 1.50823 0.116018
\(170\) 2.39079 0.183365
\(171\) −7.01905 −0.536760
\(172\) −8.48735 −0.647154
\(173\) 14.9951 1.14005 0.570027 0.821626i \(-0.306933\pi\)
0.570027 + 0.821626i \(0.306933\pi\)
\(174\) −3.58854 −0.272046
\(175\) 8.05654 0.609017
\(176\) 6.57882 0.495897
\(177\) −6.79416 −0.510680
\(178\) −36.7868 −2.75729
\(179\) 2.25917 0.168858 0.0844290 0.996429i \(-0.473093\pi\)
0.0844290 + 0.996429i \(0.473093\pi\)
\(180\) 2.35820 0.175770
\(181\) −15.1992 −1.12975 −0.564876 0.825176i \(-0.691076\pi\)
−0.564876 + 0.825176i \(0.691076\pi\)
\(182\) −16.0141 −1.18704
\(183\) 11.5720 0.855428
\(184\) −4.01402 −0.295918
\(185\) −0.899148 −0.0661067
\(186\) −5.43867 −0.398782
\(187\) 2.39098 0.174846
\(188\) −13.6695 −0.996949
\(189\) −2.01365 −0.146471
\(190\) 14.6480 1.06268
\(191\) 7.02323 0.508183 0.254092 0.967180i \(-0.418223\pi\)
0.254092 + 0.967180i \(0.418223\pi\)
\(192\) −10.5701 −0.762830
\(193\) 3.31169 0.238380 0.119190 0.992871i \(-0.461970\pi\)
0.119190 + 0.992871i \(0.461970\pi\)
\(194\) 26.1995 1.88102
\(195\) −3.80712 −0.272634
\(196\) −6.94879 −0.496342
\(197\) 16.4857 1.17455 0.587277 0.809386i \(-0.300200\pi\)
0.587277 + 0.809386i \(0.300200\pi\)
\(198\) 4.35759 0.309680
\(199\) −6.61629 −0.469016 −0.234508 0.972114i \(-0.575348\pi\)
−0.234508 + 0.972114i \(0.575348\pi\)
\(200\) 3.00182 0.212260
\(201\) 14.2860 1.00766
\(202\) 33.3161 2.34412
\(203\) −3.46091 −0.242908
\(204\) −2.70291 −0.189242
\(205\) 11.4425 0.799181
\(206\) −32.3207 −2.25189
\(207\) 5.35009 0.371857
\(208\) 12.0066 0.832507
\(209\) 14.6492 1.01331
\(210\) 4.20227 0.289984
\(211\) −15.1031 −1.03974 −0.519869 0.854246i \(-0.674019\pi\)
−0.519869 + 0.854246i \(0.674019\pi\)
\(212\) −31.0827 −2.13477
\(213\) −15.1350 −1.03703
\(214\) −21.3489 −1.45938
\(215\) −3.59559 −0.245217
\(216\) −0.750272 −0.0510496
\(217\) −5.24524 −0.356070
\(218\) −23.4599 −1.58890
\(219\) −1.41883 −0.0958759
\(220\) −4.92171 −0.331822
\(221\) 4.36363 0.293529
\(222\) 1.87824 0.126059
\(223\) 18.0409 1.20811 0.604054 0.796944i \(-0.293551\pi\)
0.604054 + 0.796944i \(0.293551\pi\)
\(224\) −16.2743 −1.08737
\(225\) −4.00097 −0.266731
\(226\) −7.84222 −0.521657
\(227\) 18.9997 1.26106 0.630528 0.776167i \(-0.282838\pi\)
0.630528 + 0.776167i \(0.282838\pi\)
\(228\) −16.5603 −1.09674
\(229\) 15.8562 1.04781 0.523903 0.851778i \(-0.324475\pi\)
0.523903 + 0.851778i \(0.324475\pi\)
\(230\) −11.1651 −0.736202
\(231\) 4.20261 0.276512
\(232\) −1.28951 −0.0846607
\(233\) −7.80994 −0.511646 −0.255823 0.966724i \(-0.582346\pi\)
−0.255823 + 0.966724i \(0.582346\pi\)
\(234\) 7.95276 0.519888
\(235\) −5.79096 −0.377761
\(236\) −16.0297 −1.04345
\(237\) 0.661519 0.0429703
\(238\) −4.81653 −0.312210
\(239\) 27.7193 1.79301 0.896505 0.443033i \(-0.146097\pi\)
0.896505 + 0.443033i \(0.146097\pi\)
\(240\) −3.15066 −0.203374
\(241\) 24.9905 1.60978 0.804890 0.593424i \(-0.202224\pi\)
0.804890 + 0.593424i \(0.202224\pi\)
\(242\) 13.8724 0.891750
\(243\) 1.00000 0.0641500
\(244\) 27.3023 1.74785
\(245\) −2.94379 −0.188072
\(246\) −23.9025 −1.52397
\(247\) 26.7353 1.70113
\(248\) −1.95434 −0.124101
\(249\) −5.04774 −0.319888
\(250\) 18.7841 1.18801
\(251\) −13.9240 −0.878874 −0.439437 0.898273i \(-0.644822\pi\)
−0.439437 + 0.898273i \(0.644822\pi\)
\(252\) −4.75089 −0.299278
\(253\) −11.1660 −0.701999
\(254\) −25.4369 −1.59605
\(255\) −1.14506 −0.0717068
\(256\) 8.81048 0.550655
\(257\) −5.18862 −0.323657 −0.161829 0.986819i \(-0.551739\pi\)
−0.161829 + 0.986819i \(0.551739\pi\)
\(258\) 7.51089 0.467608
\(259\) 1.81144 0.112558
\(260\) −8.98230 −0.557059
\(261\) 1.71873 0.106387
\(262\) 0.581064 0.0358982
\(263\) −12.1369 −0.748394 −0.374197 0.927349i \(-0.622082\pi\)
−0.374197 + 0.927349i \(0.622082\pi\)
\(264\) 1.56587 0.0963724
\(265\) −13.1679 −0.808899
\(266\) −29.5102 −1.80939
\(267\) 17.6190 1.07827
\(268\) 33.7056 2.05890
\(269\) 6.67485 0.406973 0.203486 0.979078i \(-0.434773\pi\)
0.203486 + 0.979078i \(0.434773\pi\)
\(270\) −2.08689 −0.127004
\(271\) 4.79175 0.291078 0.145539 0.989353i \(-0.453508\pi\)
0.145539 + 0.989353i \(0.453508\pi\)
\(272\) 3.61121 0.218962
\(273\) 7.66992 0.464205
\(274\) −14.5810 −0.880870
\(275\) 8.35028 0.503541
\(276\) 12.6227 0.759797
\(277\) 6.84461 0.411253 0.205626 0.978631i \(-0.434077\pi\)
0.205626 + 0.978631i \(0.434077\pi\)
\(278\) −42.8204 −2.56820
\(279\) 2.60484 0.155948
\(280\) 1.51005 0.0902429
\(281\) −6.53725 −0.389980 −0.194990 0.980805i \(-0.562467\pi\)
−0.194990 + 0.980805i \(0.562467\pi\)
\(282\) 12.0968 0.720356
\(283\) 28.2024 1.67646 0.838230 0.545317i \(-0.183591\pi\)
0.838230 + 0.545317i \(0.183591\pi\)
\(284\) −35.7087 −2.11892
\(285\) −7.01565 −0.415571
\(286\) −16.5979 −0.981455
\(287\) −23.0524 −1.36074
\(288\) 8.08201 0.476237
\(289\) −15.6876 −0.922797
\(290\) −3.58680 −0.210624
\(291\) −12.5482 −0.735591
\(292\) −3.34751 −0.195898
\(293\) −5.75477 −0.336198 −0.168099 0.985770i \(-0.553763\pi\)
−0.168099 + 0.985770i \(0.553763\pi\)
\(294\) 6.14934 0.358637
\(295\) −6.79086 −0.395379
\(296\) 0.674933 0.0392297
\(297\) −2.08706 −0.121104
\(298\) 29.0931 1.68532
\(299\) −20.3783 −1.17851
\(300\) −9.43965 −0.544999
\(301\) 7.24377 0.417524
\(302\) −6.45817 −0.371626
\(303\) −15.9567 −0.916691
\(304\) 22.1254 1.26898
\(305\) 11.5664 0.662291
\(306\) 2.39194 0.136738
\(307\) −8.30892 −0.474215 −0.237108 0.971483i \(-0.576199\pi\)
−0.237108 + 0.971483i \(0.576199\pi\)
\(308\) 9.91540 0.564982
\(309\) 15.4800 0.880624
\(310\) −5.43603 −0.308746
\(311\) 7.60851 0.431439 0.215720 0.976455i \(-0.430790\pi\)
0.215720 + 0.976455i \(0.430790\pi\)
\(312\) 2.85776 0.161789
\(313\) −31.5023 −1.78062 −0.890308 0.455359i \(-0.849511\pi\)
−0.890308 + 0.455359i \(0.849511\pi\)
\(314\) −11.3570 −0.640915
\(315\) −2.01267 −0.113401
\(316\) 1.56075 0.0877990
\(317\) 9.66632 0.542915 0.271457 0.962450i \(-0.412494\pi\)
0.271457 + 0.962450i \(0.412494\pi\)
\(318\) 27.5067 1.54250
\(319\) −3.58709 −0.200839
\(320\) −10.5650 −0.590599
\(321\) 10.2250 0.570706
\(322\) 22.4934 1.25351
\(323\) 8.04117 0.447423
\(324\) 2.35934 0.131075
\(325\) 15.2396 0.845339
\(326\) 10.4912 0.581052
\(327\) 11.2361 0.621357
\(328\) −8.58918 −0.474258
\(329\) 11.6666 0.643201
\(330\) 4.35548 0.239761
\(331\) 22.2653 1.22381 0.611906 0.790930i \(-0.290403\pi\)
0.611906 + 0.790930i \(0.290403\pi\)
\(332\) −11.9094 −0.653611
\(333\) −0.899584 −0.0492969
\(334\) −0.966201 −0.0528682
\(335\) 14.2791 0.780150
\(336\) 6.34740 0.346279
\(337\) −1.70613 −0.0929387 −0.0464694 0.998920i \(-0.514797\pi\)
−0.0464694 + 0.998920i \(0.514797\pi\)
\(338\) −3.14903 −0.171285
\(339\) 3.75603 0.203999
\(340\) −2.70160 −0.146515
\(341\) −5.43648 −0.294402
\(342\) 14.6551 0.792457
\(343\) 20.0262 1.08131
\(344\) 2.69898 0.145519
\(345\) 5.34750 0.287900
\(346\) −31.3083 −1.68314
\(347\) 19.4312 1.04312 0.521559 0.853215i \(-0.325350\pi\)
0.521559 + 0.853215i \(0.325350\pi\)
\(348\) 4.05507 0.217374
\(349\) −23.1312 −1.23819 −0.619093 0.785318i \(-0.712500\pi\)
−0.619093 + 0.785318i \(0.712500\pi\)
\(350\) −16.8213 −0.899136
\(351\) −3.80897 −0.203308
\(352\) −16.8677 −0.899050
\(353\) 15.7988 0.840884 0.420442 0.907319i \(-0.361875\pi\)
0.420442 + 0.907319i \(0.361875\pi\)
\(354\) 14.1855 0.753953
\(355\) −15.1277 −0.802894
\(356\) 41.5693 2.20317
\(357\) 2.30688 0.122093
\(358\) −4.71692 −0.249297
\(359\) −16.8896 −0.891398 −0.445699 0.895183i \(-0.647045\pi\)
−0.445699 + 0.895183i \(0.647045\pi\)
\(360\) −0.749909 −0.0395237
\(361\) 30.2671 1.59301
\(362\) 31.7346 1.66793
\(363\) −6.64416 −0.348728
\(364\) 18.0960 0.948486
\(365\) −1.41815 −0.0742291
\(366\) −24.1613 −1.26293
\(367\) −22.0324 −1.15008 −0.575042 0.818124i \(-0.695014\pi\)
−0.575042 + 0.818124i \(0.695014\pi\)
\(368\) −16.8645 −0.879122
\(369\) 11.4481 0.595963
\(370\) 1.87733 0.0975980
\(371\) 26.5284 1.37729
\(372\) 6.14572 0.318641
\(373\) −13.3789 −0.692735 −0.346368 0.938099i \(-0.612585\pi\)
−0.346368 + 0.938099i \(0.612585\pi\)
\(374\) −4.99214 −0.258137
\(375\) −8.99661 −0.464583
\(376\) 4.34690 0.224174
\(377\) −6.54657 −0.337166
\(378\) 4.20430 0.216246
\(379\) 10.0797 0.517758 0.258879 0.965910i \(-0.416647\pi\)
0.258879 + 0.965910i \(0.416647\pi\)
\(380\) −16.5523 −0.849116
\(381\) 12.1830 0.624154
\(382\) −14.6638 −0.750267
\(383\) −8.12285 −0.415058 −0.207529 0.978229i \(-0.566542\pi\)
−0.207529 + 0.978229i \(0.566542\pi\)
\(384\) 5.90530 0.301353
\(385\) 4.20058 0.214081
\(386\) −6.91448 −0.351938
\(387\) −3.59734 −0.182863
\(388\) −29.6056 −1.50300
\(389\) 36.1450 1.83263 0.916313 0.400463i \(-0.131151\pi\)
0.916313 + 0.400463i \(0.131151\pi\)
\(390\) 7.94890 0.402508
\(391\) −6.12917 −0.309965
\(392\) 2.20972 0.111608
\(393\) −0.278300 −0.0140384
\(394\) −34.4205 −1.73408
\(395\) 0.661198 0.0332685
\(396\) −4.92410 −0.247445
\(397\) 14.6817 0.736854 0.368427 0.929657i \(-0.379897\pi\)
0.368427 + 0.929657i \(0.379897\pi\)
\(398\) 13.8142 0.692442
\(399\) 14.1339 0.707580
\(400\) 12.6118 0.630590
\(401\) 9.20173 0.459512 0.229756 0.973248i \(-0.426207\pi\)
0.229756 + 0.973248i \(0.426207\pi\)
\(402\) −29.8278 −1.48768
\(403\) −9.92177 −0.494238
\(404\) −37.6474 −1.87303
\(405\) 0.999516 0.0496663
\(406\) 7.22605 0.358623
\(407\) 1.87749 0.0930636
\(408\) 0.859527 0.0425529
\(409\) −11.2093 −0.554265 −0.277132 0.960832i \(-0.589384\pi\)
−0.277132 + 0.960832i \(0.589384\pi\)
\(410\) −23.8909 −1.17989
\(411\) 6.98356 0.344473
\(412\) 36.5225 1.79934
\(413\) 13.6810 0.673200
\(414\) −11.1705 −0.548999
\(415\) −5.04530 −0.247664
\(416\) −30.7841 −1.50932
\(417\) 20.5088 1.00432
\(418\) −30.5861 −1.49602
\(419\) −7.33142 −0.358163 −0.179082 0.983834i \(-0.557313\pi\)
−0.179082 + 0.983834i \(0.557313\pi\)
\(420\) −4.74858 −0.231707
\(421\) 16.6015 0.809107 0.404553 0.914514i \(-0.367427\pi\)
0.404553 + 0.914514i \(0.367427\pi\)
\(422\) 31.5337 1.53504
\(423\) −5.79377 −0.281703
\(424\) 9.88432 0.480025
\(425\) 4.58359 0.222337
\(426\) 31.6004 1.53105
\(427\) −23.3020 −1.12766
\(428\) 24.1243 1.16609
\(429\) 7.94956 0.383808
\(430\) 7.50725 0.362032
\(431\) 37.3416 1.79868 0.899341 0.437247i \(-0.144047\pi\)
0.899341 + 0.437247i \(0.144047\pi\)
\(432\) −3.15219 −0.151660
\(433\) 6.82529 0.328003 0.164001 0.986460i \(-0.447560\pi\)
0.164001 + 0.986460i \(0.447560\pi\)
\(434\) 10.9516 0.525692
\(435\) 1.71789 0.0823667
\(436\) 26.5098 1.26959
\(437\) −37.5526 −1.79638
\(438\) 2.96239 0.141548
\(439\) 30.2157 1.44212 0.721059 0.692874i \(-0.243656\pi\)
0.721059 + 0.692874i \(0.243656\pi\)
\(440\) 1.56511 0.0746136
\(441\) −2.94522 −0.140249
\(442\) −9.11084 −0.433358
\(443\) −19.7631 −0.938972 −0.469486 0.882940i \(-0.655561\pi\)
−0.469486 + 0.882940i \(0.655561\pi\)
\(444\) −2.12243 −0.100726
\(445\) 17.6105 0.834816
\(446\) −37.6676 −1.78361
\(447\) −13.9341 −0.659061
\(448\) 21.2844 1.00559
\(449\) 4.49889 0.212316 0.106158 0.994349i \(-0.466145\pi\)
0.106158 + 0.994349i \(0.466145\pi\)
\(450\) 8.35364 0.393794
\(451\) −23.8929 −1.12507
\(452\) 8.86175 0.416822
\(453\) 3.09314 0.145328
\(454\) −39.6696 −1.86179
\(455\) 7.66620 0.359397
\(456\) 5.26620 0.246612
\(457\) −31.4088 −1.46924 −0.734622 0.678477i \(-0.762640\pi\)
−0.734622 + 0.678477i \(0.762640\pi\)
\(458\) −33.1062 −1.54695
\(459\) −1.14562 −0.0534730
\(460\) 12.6166 0.588251
\(461\) −13.4092 −0.624527 −0.312264 0.949996i \(-0.601087\pi\)
−0.312264 + 0.949996i \(0.601087\pi\)
\(462\) −8.77465 −0.408234
\(463\) −32.4070 −1.50608 −0.753042 0.657973i \(-0.771414\pi\)
−0.753042 + 0.657973i \(0.771414\pi\)
\(464\) −5.41775 −0.251513
\(465\) 2.60358 0.120738
\(466\) 16.3064 0.755379
\(467\) −13.7165 −0.634725 −0.317363 0.948304i \(-0.602797\pi\)
−0.317363 + 0.948304i \(0.602797\pi\)
\(468\) −8.98666 −0.415408
\(469\) −28.7670 −1.32834
\(470\) 12.0910 0.557715
\(471\) 5.43945 0.250636
\(472\) 5.09747 0.234630
\(473\) 7.50787 0.345212
\(474\) −1.38119 −0.0634400
\(475\) 28.0830 1.28854
\(476\) 5.44271 0.249466
\(477\) −13.1743 −0.603210
\(478\) −57.8752 −2.64715
\(479\) −14.9543 −0.683281 −0.341641 0.939831i \(-0.610983\pi\)
−0.341641 + 0.939831i \(0.610983\pi\)
\(480\) 8.07810 0.368713
\(481\) 3.42648 0.156234
\(482\) −52.1778 −2.37663
\(483\) −10.7732 −0.490197
\(484\) −15.6759 −0.712539
\(485\) −12.5422 −0.569510
\(486\) −2.08790 −0.0947092
\(487\) −27.7656 −1.25818 −0.629090 0.777332i \(-0.716572\pi\)
−0.629090 + 0.777332i \(0.716572\pi\)
\(488\) −8.68216 −0.393023
\(489\) −5.02474 −0.227227
\(490\) 6.14636 0.277664
\(491\) −11.1613 −0.503702 −0.251851 0.967766i \(-0.581039\pi\)
−0.251851 + 0.967766i \(0.581039\pi\)
\(492\) 27.0099 1.21770
\(493\) −1.96901 −0.0886797
\(494\) −55.8208 −2.51150
\(495\) −2.08605 −0.0937611
\(496\) −8.21096 −0.368683
\(497\) 30.4766 1.36706
\(498\) 10.5392 0.472273
\(499\) 42.2277 1.89037 0.945186 0.326532i \(-0.105880\pi\)
0.945186 + 0.326532i \(0.105880\pi\)
\(500\) −21.2261 −0.949259
\(501\) 0.462761 0.0206747
\(502\) 29.0719 1.29754
\(503\) −12.3933 −0.552592 −0.276296 0.961073i \(-0.589107\pi\)
−0.276296 + 0.961073i \(0.589107\pi\)
\(504\) 1.51078 0.0672957
\(505\) −15.9490 −0.709722
\(506\) 23.3135 1.03641
\(507\) 1.50823 0.0669827
\(508\) 28.7439 1.27530
\(509\) −35.6903 −1.58194 −0.790971 0.611853i \(-0.790424\pi\)
−0.790971 + 0.611853i \(0.790424\pi\)
\(510\) 2.39079 0.105866
\(511\) 2.85703 0.126388
\(512\) −30.2060 −1.33493
\(513\) −7.01905 −0.309899
\(514\) 10.8333 0.477838
\(515\) 15.4725 0.681798
\(516\) −8.48735 −0.373635
\(517\) 12.0920 0.531804
\(518\) −3.78212 −0.166177
\(519\) 14.9951 0.658211
\(520\) 2.85638 0.125260
\(521\) 8.36612 0.366526 0.183263 0.983064i \(-0.441334\pi\)
0.183263 + 0.983064i \(0.441334\pi\)
\(522\) −3.58854 −0.157066
\(523\) 37.4987 1.63970 0.819851 0.572577i \(-0.194056\pi\)
0.819851 + 0.572577i \(0.194056\pi\)
\(524\) −0.656605 −0.0286839
\(525\) 8.05654 0.351616
\(526\) 25.3407 1.10491
\(527\) −2.98416 −0.129992
\(528\) 6.57882 0.286306
\(529\) 5.62345 0.244498
\(530\) 27.4934 1.19424
\(531\) −6.79416 −0.294841
\(532\) 33.3467 1.44576
\(533\) −43.6054 −1.88876
\(534\) −36.7868 −1.59192
\(535\) 10.2201 0.441852
\(536\) −10.7184 −0.462964
\(537\) 2.25917 0.0974902
\(538\) −13.9364 −0.600843
\(539\) 6.14686 0.264764
\(540\) 2.35820 0.101481
\(541\) 17.9603 0.772175 0.386088 0.922462i \(-0.373826\pi\)
0.386088 + 0.922462i \(0.373826\pi\)
\(542\) −10.0047 −0.429739
\(543\) −15.1992 −0.652262
\(544\) −9.25891 −0.396973
\(545\) 11.2306 0.481068
\(546\) −16.0141 −0.685338
\(547\) −24.3729 −1.04211 −0.521056 0.853523i \(-0.674462\pi\)
−0.521056 + 0.853523i \(0.674462\pi\)
\(548\) 16.4766 0.703845
\(549\) 11.5720 0.493882
\(550\) −17.4346 −0.743413
\(551\) −12.0638 −0.513937
\(552\) −4.01402 −0.170848
\(553\) −1.33207 −0.0566452
\(554\) −14.2909 −0.607161
\(555\) −0.899148 −0.0381667
\(556\) 48.3873 2.05208
\(557\) −5.51859 −0.233830 −0.116915 0.993142i \(-0.537301\pi\)
−0.116915 + 0.993142i \(0.537301\pi\)
\(558\) −5.43867 −0.230237
\(559\) 13.7021 0.579539
\(560\) 6.34432 0.268097
\(561\) 2.39098 0.100947
\(562\) 13.6491 0.575754
\(563\) 2.76655 0.116596 0.0582982 0.998299i \(-0.481433\pi\)
0.0582982 + 0.998299i \(0.481433\pi\)
\(564\) −13.6695 −0.575589
\(565\) 3.75421 0.157941
\(566\) −58.8839 −2.47508
\(567\) −2.01365 −0.0845653
\(568\) 11.3554 0.476461
\(569\) 9.85186 0.413012 0.206506 0.978445i \(-0.433791\pi\)
0.206506 + 0.978445i \(0.433791\pi\)
\(570\) 14.6480 0.613537
\(571\) −26.2457 −1.09835 −0.549175 0.835707i \(-0.685058\pi\)
−0.549175 + 0.835707i \(0.685058\pi\)
\(572\) 18.7557 0.784216
\(573\) 7.02323 0.293400
\(574\) 48.1312 2.00896
\(575\) −21.4055 −0.892673
\(576\) −10.5701 −0.440420
\(577\) 2.14883 0.0894570 0.0447285 0.998999i \(-0.485758\pi\)
0.0447285 + 0.998999i \(0.485758\pi\)
\(578\) 32.7541 1.36239
\(579\) 3.31169 0.137629
\(580\) 4.05310 0.168296
\(581\) 10.1644 0.421689
\(582\) 26.1995 1.08601
\(583\) 27.4956 1.13875
\(584\) 1.06451 0.0440498
\(585\) −3.80712 −0.157405
\(586\) 12.0154 0.496352
\(587\) 35.9289 1.48294 0.741471 0.670985i \(-0.234128\pi\)
0.741471 + 0.670985i \(0.234128\pi\)
\(588\) −6.94879 −0.286563
\(589\) −18.2835 −0.753360
\(590\) 14.1787 0.583727
\(591\) 16.4857 0.678129
\(592\) 2.83566 0.116545
\(593\) 0.855164 0.0351174 0.0175587 0.999846i \(-0.494411\pi\)
0.0175587 + 0.999846i \(0.494411\pi\)
\(594\) 4.35759 0.178794
\(595\) 2.30576 0.0945269
\(596\) −32.8754 −1.34663
\(597\) −6.61629 −0.270787
\(598\) 42.5479 1.73992
\(599\) −19.3012 −0.788627 −0.394314 0.918976i \(-0.629018\pi\)
−0.394314 + 0.918976i \(0.629018\pi\)
\(600\) 3.00182 0.122549
\(601\) 40.7292 1.66138 0.830690 0.556736i \(-0.187946\pi\)
0.830690 + 0.556736i \(0.187946\pi\)
\(602\) −15.1243 −0.616420
\(603\) 14.2860 0.581771
\(604\) 7.29777 0.296942
\(605\) −6.64095 −0.269993
\(606\) 33.3161 1.35338
\(607\) 6.75833 0.274312 0.137156 0.990549i \(-0.456204\pi\)
0.137156 + 0.990549i \(0.456204\pi\)
\(608\) −56.7281 −2.30063
\(609\) −3.46091 −0.140243
\(610\) −24.1495 −0.977787
\(611\) 22.0683 0.892787
\(612\) −2.70291 −0.109259
\(613\) 42.8050 1.72888 0.864439 0.502738i \(-0.167674\pi\)
0.864439 + 0.502738i \(0.167674\pi\)
\(614\) 17.3482 0.700117
\(615\) 11.4425 0.461408
\(616\) −3.15310 −0.127042
\(617\) −13.6177 −0.548228 −0.274114 0.961697i \(-0.588385\pi\)
−0.274114 + 0.961697i \(0.588385\pi\)
\(618\) −32.3207 −1.30013
\(619\) −18.0650 −0.726093 −0.363046 0.931771i \(-0.618263\pi\)
−0.363046 + 0.931771i \(0.618263\pi\)
\(620\) 6.14274 0.246699
\(621\) 5.35009 0.214692
\(622\) −15.8858 −0.636964
\(623\) −35.4785 −1.42141
\(624\) 12.0066 0.480648
\(625\) 11.0126 0.440504
\(626\) 65.7738 2.62885
\(627\) 14.6492 0.585033
\(628\) 12.8335 0.512113
\(629\) 1.03058 0.0410920
\(630\) 4.20227 0.167422
\(631\) −19.2493 −0.766302 −0.383151 0.923686i \(-0.625161\pi\)
−0.383151 + 0.923686i \(0.625161\pi\)
\(632\) −0.496319 −0.0197425
\(633\) −15.1031 −0.600292
\(634\) −20.1823 −0.801543
\(635\) 12.1771 0.483233
\(636\) −31.0827 −1.23251
\(637\) 11.2182 0.444483
\(638\) 7.48951 0.296512
\(639\) −15.1350 −0.598732
\(640\) 5.90244 0.233314
\(641\) −18.5854 −0.734078 −0.367039 0.930206i \(-0.619628\pi\)
−0.367039 + 0.930206i \(0.619628\pi\)
\(642\) −21.3489 −0.842573
\(643\) 22.8451 0.900923 0.450462 0.892796i \(-0.351259\pi\)
0.450462 + 0.892796i \(0.351259\pi\)
\(644\) −25.4177 −1.00160
\(645\) −3.59559 −0.141576
\(646\) −16.7892 −0.660562
\(647\) 20.1908 0.793784 0.396892 0.917865i \(-0.370089\pi\)
0.396892 + 0.917865i \(0.370089\pi\)
\(648\) −0.750272 −0.0294735
\(649\) 14.1798 0.556607
\(650\) −31.8187 −1.24803
\(651\) −5.24524 −0.205577
\(652\) −11.8551 −0.464281
\(653\) 15.6444 0.612213 0.306107 0.951997i \(-0.400974\pi\)
0.306107 + 0.951997i \(0.400974\pi\)
\(654\) −23.4599 −0.917353
\(655\) −0.278165 −0.0108688
\(656\) −36.0865 −1.40894
\(657\) −1.41883 −0.0553539
\(658\) −24.3588 −0.949603
\(659\) −22.0939 −0.860655 −0.430328 0.902673i \(-0.641602\pi\)
−0.430328 + 0.902673i \(0.641602\pi\)
\(660\) −4.92171 −0.191577
\(661\) 29.8830 1.16231 0.581157 0.813791i \(-0.302600\pi\)
0.581157 + 0.813791i \(0.302600\pi\)
\(662\) −46.4878 −1.80680
\(663\) 4.36363 0.169469
\(664\) 3.78718 0.146971
\(665\) 14.1271 0.547824
\(666\) 1.87824 0.0727805
\(667\) 9.19534 0.356045
\(668\) 1.09181 0.0422435
\(669\) 18.0409 0.697501
\(670\) −29.8134 −1.15179
\(671\) −24.1515 −0.932360
\(672\) −16.2743 −0.627796
\(673\) 43.2201 1.66601 0.833007 0.553263i \(-0.186618\pi\)
0.833007 + 0.553263i \(0.186618\pi\)
\(674\) 3.56223 0.137212
\(675\) −4.00097 −0.153997
\(676\) 3.55843 0.136863
\(677\) 13.4132 0.515510 0.257755 0.966210i \(-0.417017\pi\)
0.257755 + 0.966210i \(0.417017\pi\)
\(678\) −7.84222 −0.301179
\(679\) 25.2678 0.969687
\(680\) 0.859110 0.0329454
\(681\) 18.9997 0.728071
\(682\) 11.3508 0.434646
\(683\) 0.183155 0.00700825 0.00350412 0.999994i \(-0.498885\pi\)
0.00350412 + 0.999994i \(0.498885\pi\)
\(684\) −16.5603 −0.633201
\(685\) 6.98017 0.266699
\(686\) −41.8127 −1.59642
\(687\) 15.8562 0.604951
\(688\) 11.3395 0.432314
\(689\) 50.1805 1.91173
\(690\) −11.1651 −0.425047
\(691\) −6.13113 −0.233239 −0.116620 0.993177i \(-0.537206\pi\)
−0.116620 + 0.993177i \(0.537206\pi\)
\(692\) 35.3785 1.34489
\(693\) 4.20261 0.159644
\(694\) −40.5704 −1.54003
\(695\) 20.4989 0.777566
\(696\) −1.28951 −0.0488789
\(697\) −13.1152 −0.496772
\(698\) 48.2958 1.82802
\(699\) −7.80994 −0.295399
\(700\) 19.0081 0.718440
\(701\) 14.4799 0.546897 0.273448 0.961887i \(-0.411836\pi\)
0.273448 + 0.961887i \(0.411836\pi\)
\(702\) 7.95276 0.300157
\(703\) 6.31423 0.238146
\(704\) 22.0604 0.831434
\(705\) −5.79096 −0.218100
\(706\) −32.9863 −1.24146
\(707\) 32.1313 1.20842
\(708\) −16.0297 −0.602434
\(709\) −24.1894 −0.908453 −0.454227 0.890886i \(-0.650084\pi\)
−0.454227 + 0.890886i \(0.650084\pi\)
\(710\) 31.5851 1.18537
\(711\) 0.661519 0.0248089
\(712\) −13.2190 −0.495405
\(713\) 13.9362 0.521913
\(714\) −4.81653 −0.180254
\(715\) 7.94570 0.297153
\(716\) 5.33015 0.199197
\(717\) 27.7193 1.03520
\(718\) 35.2638 1.31603
\(719\) 2.85437 0.106450 0.0532251 0.998583i \(-0.483050\pi\)
0.0532251 + 0.998583i \(0.483050\pi\)
\(720\) −3.15066 −0.117418
\(721\) −31.1712 −1.16088
\(722\) −63.1948 −2.35187
\(723\) 24.9905 0.929407
\(724\) −35.8602 −1.33273
\(725\) −6.87657 −0.255390
\(726\) 13.8724 0.514852
\(727\) −24.6037 −0.912500 −0.456250 0.889852i \(-0.650808\pi\)
−0.456250 + 0.889852i \(0.650808\pi\)
\(728\) −5.75453 −0.213277
\(729\) 1.00000 0.0370370
\(730\) 2.96095 0.109590
\(731\) 4.12118 0.152427
\(732\) 27.3023 1.00912
\(733\) −6.47028 −0.238985 −0.119493 0.992835i \(-0.538127\pi\)
−0.119493 + 0.992835i \(0.538127\pi\)
\(734\) 46.0016 1.69795
\(735\) −2.94379 −0.108583
\(736\) 43.2395 1.59383
\(737\) −29.8158 −1.09828
\(738\) −23.9025 −0.879863
\(739\) 12.0154 0.441994 0.220997 0.975275i \(-0.429069\pi\)
0.220997 + 0.975275i \(0.429069\pi\)
\(740\) −2.12140 −0.0779841
\(741\) 26.7353 0.982147
\(742\) −55.3888 −2.03339
\(743\) 12.3768 0.454062 0.227031 0.973888i \(-0.427098\pi\)
0.227031 + 0.973888i \(0.427098\pi\)
\(744\) −1.95434 −0.0716497
\(745\) −13.9274 −0.510259
\(746\) 27.9339 1.02273
\(747\) −5.04774 −0.184687
\(748\) 5.64115 0.206261
\(749\) −20.5896 −0.752328
\(750\) 18.7841 0.685897
\(751\) 9.76033 0.356159 0.178080 0.984016i \(-0.443012\pi\)
0.178080 + 0.984016i \(0.443012\pi\)
\(752\) 18.2630 0.665985
\(753\) −13.9240 −0.507418
\(754\) 13.6686 0.497782
\(755\) 3.09164 0.112516
\(756\) −4.75089 −0.172788
\(757\) −23.0769 −0.838743 −0.419371 0.907815i \(-0.637750\pi\)
−0.419371 + 0.907815i \(0.637750\pi\)
\(758\) −21.0454 −0.764403
\(759\) −11.1660 −0.405299
\(760\) 5.26365 0.190933
\(761\) −35.8092 −1.29808 −0.649042 0.760753i \(-0.724830\pi\)
−0.649042 + 0.760753i \(0.724830\pi\)
\(762\) −25.4369 −0.921483
\(763\) −22.6255 −0.819099
\(764\) 16.5702 0.599489
\(765\) −1.14506 −0.0413999
\(766\) 16.9597 0.612780
\(767\) 25.8787 0.934426
\(768\) 8.81048 0.317921
\(769\) −18.0824 −0.652069 −0.326034 0.945358i \(-0.605713\pi\)
−0.326034 + 0.945358i \(0.605713\pi\)
\(770\) −8.77040 −0.316063
\(771\) −5.18862 −0.186864
\(772\) 7.81340 0.281210
\(773\) 36.2646 1.30435 0.652174 0.758069i \(-0.273857\pi\)
0.652174 + 0.758069i \(0.273857\pi\)
\(774\) 7.51089 0.269973
\(775\) −10.4219 −0.374366
\(776\) 9.41460 0.337964
\(777\) 1.81144 0.0649852
\(778\) −75.4673 −2.70564
\(779\) −80.3547 −2.87901
\(780\) −8.98230 −0.321618
\(781\) 31.5877 1.13030
\(782\) 12.7971 0.457624
\(783\) 1.71873 0.0614223
\(784\) 9.28389 0.331568
\(785\) 5.43681 0.194048
\(786\) 0.581064 0.0207259
\(787\) 31.0695 1.10751 0.553754 0.832680i \(-0.313195\pi\)
0.553754 + 0.832680i \(0.313195\pi\)
\(788\) 38.8953 1.38559
\(789\) −12.1369 −0.432086
\(790\) −1.38052 −0.0491166
\(791\) −7.56331 −0.268921
\(792\) 1.56587 0.0556406
\(793\) −44.0774 −1.56524
\(794\) −30.6540 −1.08787
\(795\) −13.1679 −0.467018
\(796\) −15.6101 −0.553285
\(797\) 0.639795 0.0226627 0.0113314 0.999936i \(-0.496393\pi\)
0.0113314 + 0.999936i \(0.496393\pi\)
\(798\) −29.5102 −1.04465
\(799\) 6.63746 0.234816
\(800\) −32.3359 −1.14325
\(801\) 17.6190 0.622537
\(802\) −19.2123 −0.678411
\(803\) 2.96119 0.104498
\(804\) 33.7056 1.18870
\(805\) −10.7680 −0.379521
\(806\) 20.7157 0.729679
\(807\) 6.67485 0.234966
\(808\) 11.9719 0.421170
\(809\) −12.5367 −0.440769 −0.220384 0.975413i \(-0.570731\pi\)
−0.220384 + 0.975413i \(0.570731\pi\)
\(810\) −2.08689 −0.0733259
\(811\) 28.8175 1.01192 0.505959 0.862557i \(-0.331139\pi\)
0.505959 + 0.862557i \(0.331139\pi\)
\(812\) −8.16548 −0.286552
\(813\) 4.79175 0.168054
\(814\) −3.92002 −0.137396
\(815\) −5.02231 −0.175924
\(816\) 3.61121 0.126418
\(817\) 25.2499 0.883382
\(818\) 23.4040 0.818300
\(819\) 7.66992 0.268009
\(820\) 26.9969 0.942771
\(821\) −44.0308 −1.53668 −0.768342 0.640039i \(-0.778918\pi\)
−0.768342 + 0.640039i \(0.778918\pi\)
\(822\) −14.5810 −0.508571
\(823\) 37.0674 1.29209 0.646044 0.763300i \(-0.276422\pi\)
0.646044 + 0.763300i \(0.276422\pi\)
\(824\) −11.6142 −0.404599
\(825\) 8.35028 0.290719
\(826\) −28.5647 −0.993893
\(827\) 23.7913 0.827305 0.413653 0.910435i \(-0.364253\pi\)
0.413653 + 0.910435i \(0.364253\pi\)
\(828\) 12.6227 0.438669
\(829\) 11.7372 0.407650 0.203825 0.979007i \(-0.434663\pi\)
0.203825 + 0.979007i \(0.434663\pi\)
\(830\) 10.5341 0.365644
\(831\) 6.84461 0.237437
\(832\) 40.2611 1.39580
\(833\) 3.37410 0.116906
\(834\) −42.8204 −1.48275
\(835\) 0.462537 0.0160068
\(836\) 34.5625 1.19537
\(837\) 2.60484 0.0900366
\(838\) 15.3073 0.528782
\(839\) 15.6897 0.541670 0.270835 0.962626i \(-0.412700\pi\)
0.270835 + 0.962626i \(0.412700\pi\)
\(840\) 1.51005 0.0521018
\(841\) −26.0460 −0.898137
\(842\) −34.6623 −1.19454
\(843\) −6.53725 −0.225155
\(844\) −35.6333 −1.22655
\(845\) 1.50750 0.0518595
\(846\) 12.0968 0.415898
\(847\) 13.3790 0.459708
\(848\) 41.5279 1.42607
\(849\) 28.2024 0.967905
\(850\) −9.57009 −0.328252
\(851\) −4.81285 −0.164982
\(852\) −35.7087 −1.22336
\(853\) 46.1827 1.58126 0.790632 0.612292i \(-0.209752\pi\)
0.790632 + 0.612292i \(0.209752\pi\)
\(854\) 48.6523 1.66485
\(855\) −7.01565 −0.239930
\(856\) −7.67156 −0.262208
\(857\) 8.44028 0.288315 0.144157 0.989555i \(-0.453953\pi\)
0.144157 + 0.989555i \(0.453953\pi\)
\(858\) −16.5979 −0.566643
\(859\) 41.5744 1.41850 0.709251 0.704956i \(-0.249033\pi\)
0.709251 + 0.704956i \(0.249033\pi\)
\(860\) −8.48324 −0.289276
\(861\) −23.0524 −0.785624
\(862\) −77.9657 −2.65552
\(863\) 3.92882 0.133739 0.0668693 0.997762i \(-0.478699\pi\)
0.0668693 + 0.997762i \(0.478699\pi\)
\(864\) 8.08201 0.274956
\(865\) 14.9878 0.509601
\(866\) −14.2506 −0.484254
\(867\) −15.6876 −0.532777
\(868\) −12.3753 −0.420046
\(869\) −1.38063 −0.0468347
\(870\) −3.58680 −0.121604
\(871\) −54.4149 −1.84378
\(872\) −8.43012 −0.285480
\(873\) −12.5482 −0.424694
\(874\) 78.4061 2.65213
\(875\) 18.1160 0.612433
\(876\) −3.34751 −0.113102
\(877\) 32.0100 1.08090 0.540450 0.841376i \(-0.318254\pi\)
0.540450 + 0.841376i \(0.318254\pi\)
\(878\) −63.0875 −2.12910
\(879\) −5.75477 −0.194104
\(880\) 6.57563 0.221664
\(881\) −7.60441 −0.256199 −0.128099 0.991761i \(-0.540888\pi\)
−0.128099 + 0.991761i \(0.540888\pi\)
\(882\) 6.14934 0.207059
\(883\) 52.5015 1.76682 0.883408 0.468604i \(-0.155243\pi\)
0.883408 + 0.468604i \(0.155243\pi\)
\(884\) 10.2953 0.346268
\(885\) −6.79086 −0.228272
\(886\) 41.2634 1.38627
\(887\) 25.0388 0.840719 0.420360 0.907358i \(-0.361904\pi\)
0.420360 + 0.907358i \(0.361904\pi\)
\(888\) 0.674933 0.0226493
\(889\) −24.5323 −0.822786
\(890\) −36.7690 −1.23250
\(891\) −2.08706 −0.0699193
\(892\) 42.5646 1.42517
\(893\) 40.6668 1.36086
\(894\) 29.0931 0.973019
\(895\) 2.25807 0.0754790
\(896\) −11.8912 −0.397257
\(897\) −20.3783 −0.680412
\(898\) −9.39325 −0.313457
\(899\) 4.47702 0.149317
\(900\) −9.43965 −0.314655
\(901\) 15.0928 0.502813
\(902\) 49.8860 1.66102
\(903\) 7.24377 0.241058
\(904\) −2.81804 −0.0937267
\(905\) −15.1919 −0.504995
\(906\) −6.45817 −0.214558
\(907\) −41.1145 −1.36518 −0.682592 0.730800i \(-0.739147\pi\)
−0.682592 + 0.730800i \(0.739147\pi\)
\(908\) 44.8269 1.48763
\(909\) −15.9567 −0.529252
\(910\) −16.0063 −0.530603
\(911\) 29.2966 0.970641 0.485320 0.874336i \(-0.338703\pi\)
0.485320 + 0.874336i \(0.338703\pi\)
\(912\) 22.1254 0.732644
\(913\) 10.5350 0.348656
\(914\) 65.5786 2.16915
\(915\) 11.5664 0.382374
\(916\) 37.4102 1.23607
\(917\) 0.560398 0.0185060
\(918\) 2.39194 0.0789459
\(919\) 0.611800 0.0201814 0.0100907 0.999949i \(-0.496788\pi\)
0.0100907 + 0.999949i \(0.496788\pi\)
\(920\) −4.01208 −0.132274
\(921\) −8.30892 −0.273788
\(922\) 27.9970 0.922034
\(923\) 57.6487 1.89753
\(924\) 9.91540 0.326193
\(925\) 3.59921 0.118341
\(926\) 67.6628 2.22354
\(927\) 15.4800 0.508428
\(928\) 13.8908 0.455987
\(929\) −27.8253 −0.912919 −0.456460 0.889744i \(-0.650883\pi\)
−0.456460 + 0.889744i \(0.650883\pi\)
\(930\) −5.43603 −0.178254
\(931\) 20.6727 0.677519
\(932\) −18.4263 −0.603574
\(933\) 7.60851 0.249091
\(934\) 28.6388 0.937090
\(935\) 2.38982 0.0781556
\(936\) 2.85776 0.0934089
\(937\) −12.8123 −0.418558 −0.209279 0.977856i \(-0.567112\pi\)
−0.209279 + 0.977856i \(0.567112\pi\)
\(938\) 60.0627 1.96112
\(939\) −31.5023 −1.02804
\(940\) −13.6629 −0.445633
\(941\) −15.0918 −0.491978 −0.245989 0.969273i \(-0.579113\pi\)
−0.245989 + 0.969273i \(0.579113\pi\)
\(942\) −11.3570 −0.370032
\(943\) 61.2482 1.99452
\(944\) 21.4165 0.697046
\(945\) −2.01267 −0.0654722
\(946\) −15.6757 −0.509661
\(947\) −56.0711 −1.82207 −0.911033 0.412333i \(-0.864714\pi\)
−0.911033 + 0.412333i \(0.864714\pi\)
\(948\) 1.56075 0.0506908
\(949\) 5.40429 0.175431
\(950\) −58.6346 −1.90236
\(951\) 9.66632 0.313452
\(952\) −1.73078 −0.0560951
\(953\) −31.3330 −1.01497 −0.507487 0.861659i \(-0.669426\pi\)
−0.507487 + 0.861659i \(0.669426\pi\)
\(954\) 27.5067 0.890562
\(955\) 7.01983 0.227156
\(956\) 65.3993 2.11516
\(957\) −3.58709 −0.115954
\(958\) 31.2232 1.00878
\(959\) −14.0624 −0.454099
\(960\) −10.5650 −0.340983
\(961\) −24.2148 −0.781122
\(962\) −7.15417 −0.230660
\(963\) 10.2250 0.329497
\(964\) 58.9611 1.89901
\(965\) 3.31008 0.106555
\(966\) 22.4934 0.723713
\(967\) 21.8772 0.703523 0.351762 0.936090i \(-0.385583\pi\)
0.351762 + 0.936090i \(0.385583\pi\)
\(968\) 4.98493 0.160222
\(969\) 8.04117 0.258320
\(970\) 26.1868 0.840809
\(971\) 32.0158 1.02743 0.513717 0.857959i \(-0.328268\pi\)
0.513717 + 0.857959i \(0.328268\pi\)
\(972\) 2.35934 0.0756759
\(973\) −41.2975 −1.32394
\(974\) 57.9719 1.85754
\(975\) 15.2396 0.488056
\(976\) −36.4772 −1.16761
\(977\) −38.0026 −1.21581 −0.607906 0.794009i \(-0.707990\pi\)
−0.607906 + 0.794009i \(0.707990\pi\)
\(978\) 10.4912 0.335471
\(979\) −36.7720 −1.17524
\(980\) −6.94542 −0.221863
\(981\) 11.2361 0.358740
\(982\) 23.3037 0.743651
\(983\) 50.6805 1.61646 0.808228 0.588869i \(-0.200427\pi\)
0.808228 + 0.588869i \(0.200427\pi\)
\(984\) −8.58918 −0.273813
\(985\) 16.4777 0.525022
\(986\) 4.11110 0.130924
\(987\) 11.6666 0.371352
\(988\) 63.0778 2.00677
\(989\) −19.2461 −0.611989
\(990\) 4.35548 0.138426
\(991\) −6.53080 −0.207458 −0.103729 0.994606i \(-0.533077\pi\)
−0.103729 + 0.994606i \(0.533077\pi\)
\(992\) 21.0524 0.668414
\(993\) 22.2653 0.706569
\(994\) −63.6322 −2.01829
\(995\) −6.61308 −0.209649
\(996\) −11.9094 −0.377362
\(997\) −21.1550 −0.669986 −0.334993 0.942221i \(-0.608734\pi\)
−0.334993 + 0.942221i \(0.608734\pi\)
\(998\) −88.1674 −2.79089
\(999\) −0.899584 −0.0284616
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 \(a_p\))