Properties

Label 8023.2.a.c.1.1
Level 8023
Weight 2
Character 8023.1
Self dual Yes
Analytic conductor 64.064
Analytic rank 1
Dimension 158
CM No

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Newspace parameters

Level: \( N \) = \( 8023 = 71 \cdot 113 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0639775417\)
Analytic rank: \(1\)
Dimension: \(158\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 8023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.79904 q^{2}\) \(-0.951830 q^{3}\) \(+5.83462 q^{4}\) \(+2.72456 q^{5}\) \(+2.66421 q^{6}\) \(+1.55879 q^{7}\) \(-10.7333 q^{8}\) \(-2.09402 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.79904 q^{2}\) \(-0.951830 q^{3}\) \(+5.83462 q^{4}\) \(+2.72456 q^{5}\) \(+2.66421 q^{6}\) \(+1.55879 q^{7}\) \(-10.7333 q^{8}\) \(-2.09402 q^{9}\) \(-7.62616 q^{10}\) \(+4.52022 q^{11}\) \(-5.55357 q^{12}\) \(-4.81472 q^{13}\) \(-4.36313 q^{14}\) \(-2.59332 q^{15}\) \(+18.3736 q^{16}\) \(+4.93209 q^{17}\) \(+5.86124 q^{18}\) \(-6.45811 q^{19}\) \(+15.8968 q^{20}\) \(-1.48371 q^{21}\) \(-12.6523 q^{22}\) \(-0.588724 q^{23}\) \(+10.2162 q^{24}\) \(+2.42324 q^{25}\) \(+13.4766 q^{26}\) \(+4.84864 q^{27}\) \(+9.09497 q^{28}\) \(-7.40239 q^{29}\) \(+7.25881 q^{30}\) \(+4.71218 q^{31}\) \(-29.9618 q^{32}\) \(-4.30249 q^{33}\) \(-13.8051 q^{34}\) \(+4.24703 q^{35}\) \(-12.2178 q^{36}\) \(-9.59806 q^{37}\) \(+18.0765 q^{38}\) \(+4.58280 q^{39}\) \(-29.2434 q^{40}\) \(+3.80683 q^{41}\) \(+4.15296 q^{42}\) \(-3.38931 q^{43}\) \(+26.3738 q^{44}\) \(-5.70528 q^{45}\) \(+1.64786 q^{46}\) \(-2.11515 q^{47}\) \(-17.4885 q^{48}\) \(-4.57016 q^{49}\) \(-6.78273 q^{50}\) \(-4.69451 q^{51}\) \(-28.0921 q^{52}\) \(+7.56236 q^{53}\) \(-13.5715 q^{54}\) \(+12.3156 q^{55}\) \(-16.7309 q^{56}\) \(+6.14702 q^{57}\) \(+20.7196 q^{58}\) \(-0.485115 q^{59}\) \(-15.1310 q^{60}\) \(+11.8614 q^{61}\) \(-13.1896 q^{62}\) \(-3.26414 q^{63}\) \(+47.1172 q^{64}\) \(-13.1180 q^{65}\) \(+12.0428 q^{66}\) \(-1.53815 q^{67}\) \(+28.7769 q^{68}\) \(+0.560365 q^{69}\) \(-11.8876 q^{70}\) \(-1.00000 q^{71}\) \(+22.4756 q^{72}\) \(+9.26795 q^{73}\) \(+26.8653 q^{74}\) \(-2.30651 q^{75}\) \(-37.6806 q^{76}\) \(+7.04610 q^{77}\) \(-12.8274 q^{78}\) \(+1.69346 q^{79}\) \(+50.0599 q^{80}\) \(+1.66697 q^{81}\) \(-10.6555 q^{82}\) \(-14.2688 q^{83}\) \(-8.65687 q^{84}\) \(+13.4378 q^{85}\) \(+9.48681 q^{86}\) \(+7.04582 q^{87}\) \(-48.5167 q^{88}\) \(-4.19505 q^{89}\) \(+15.9693 q^{90}\) \(-7.50516 q^{91}\) \(-3.43498 q^{92}\) \(-4.48519 q^{93}\) \(+5.92038 q^{94}\) \(-17.5955 q^{95}\) \(+28.5186 q^{96}\) \(+16.9329 q^{97}\) \(+12.7921 q^{98}\) \(-9.46544 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut 46q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 27q^{14} \) \(\mathstrut -\mathstrut 41q^{15} \) \(\mathstrut +\mathstrut 150q^{16} \) \(\mathstrut -\mathstrut 137q^{17} \) \(\mathstrut -\mathstrut 67q^{18} \) \(\mathstrut -\mathstrut 42q^{19} \) \(\mathstrut -\mathstrut 66q^{20} \) \(\mathstrut -\mathstrut 46q^{21} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 48q^{24} \) \(\mathstrut +\mathstrut 129q^{25} \) \(\mathstrut -\mathstrut 67q^{26} \) \(\mathstrut -\mathstrut 89q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 79q^{29} \) \(\mathstrut -\mathstrut 11q^{30} \) \(\mathstrut +\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 147q^{32} \) \(\mathstrut -\mathstrut 112q^{33} \) \(\mathstrut -\mathstrut 28q^{34} \) \(\mathstrut -\mathstrut 53q^{35} \) \(\mathstrut +\mathstrut 141q^{36} \) \(\mathstrut -\mathstrut 60q^{37} \) \(\mathstrut -\mathstrut 53q^{38} \) \(\mathstrut -\mathstrut 3q^{39} \) \(\mathstrut -\mathstrut 48q^{40} \) \(\mathstrut -\mathstrut 128q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 63q^{43} \) \(\mathstrut -\mathstrut 88q^{45} \) \(\mathstrut -\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 92q^{47} \) \(\mathstrut -\mathstrut 131q^{48} \) \(\mathstrut +\mathstrut 122q^{49} \) \(\mathstrut -\mathstrut 116q^{50} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 89q^{52} \) \(\mathstrut -\mathstrut 94q^{53} \) \(\mathstrut -\mathstrut 71q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 104q^{56} \) \(\mathstrut -\mathstrut 93q^{57} \) \(\mathstrut -\mathstrut 65q^{58} \) \(\mathstrut -\mathstrut 54q^{59} \) \(\mathstrut -\mathstrut 12q^{60} \) \(\mathstrut +\mathstrut 17q^{61} \) \(\mathstrut -\mathstrut 97q^{62} \) \(\mathstrut -\mathstrut 28q^{63} \) \(\mathstrut +\mathstrut 163q^{64} \) \(\mathstrut -\mathstrut 163q^{65} \) \(\mathstrut -\mathstrut 65q^{66} \) \(\mathstrut -\mathstrut 35q^{67} \) \(\mathstrut -\mathstrut 217q^{68} \) \(\mathstrut -\mathstrut 46q^{69} \) \(\mathstrut -\mathstrut 79q^{70} \) \(\mathstrut -\mathstrut 158q^{71} \) \(\mathstrut -\mathstrut 99q^{72} \) \(\mathstrut -\mathstrut 165q^{73} \) \(\mathstrut -\mathstrut 94q^{75} \) \(\mathstrut -\mathstrut 93q^{76} \) \(\mathstrut -\mathstrut 140q^{77} \) \(\mathstrut +\mathstrut 25q^{78} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut 134q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 158q^{83} \) \(\mathstrut -\mathstrut 160q^{84} \) \(\mathstrut +\mathstrut 23q^{85} \) \(\mathstrut -\mathstrut 122q^{86} \) \(\mathstrut -\mathstrut 71q^{87} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 251q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut -\mathstrut 57q^{91} \) \(\mathstrut -\mathstrut 58q^{92} \) \(\mathstrut -\mathstrut 52q^{93} \) \(\mathstrut -\mathstrut 64q^{94} \) \(\mathstrut -\mathstrut 84q^{95} \) \(\mathstrut -\mathstrut 98q^{96} \) \(\mathstrut -\mathstrut 48q^{97} \) \(\mathstrut -\mathstrut 84q^{98} \) \(\mathstrut +\mathstrut 85q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.79904 −1.97922 −0.989610 0.143779i \(-0.954075\pi\)
−0.989610 + 0.143779i \(0.954075\pi\)
\(3\) −0.951830 −0.549540 −0.274770 0.961510i \(-0.588602\pi\)
−0.274770 + 0.961510i \(0.588602\pi\)
\(4\) 5.83462 2.91731
\(5\) 2.72456 1.21846 0.609231 0.792993i \(-0.291478\pi\)
0.609231 + 0.792993i \(0.291478\pi\)
\(6\) 2.66421 1.08766
\(7\) 1.55879 0.589169 0.294584 0.955625i \(-0.404819\pi\)
0.294584 + 0.955625i \(0.404819\pi\)
\(8\) −10.7333 −3.79478
\(9\) −2.09402 −0.698006
\(10\) −7.62616 −2.41160
\(11\) 4.52022 1.36290 0.681450 0.731865i \(-0.261350\pi\)
0.681450 + 0.731865i \(0.261350\pi\)
\(12\) −5.55357 −1.60318
\(13\) −4.81472 −1.33536 −0.667682 0.744447i \(-0.732713\pi\)
−0.667682 + 0.744447i \(0.732713\pi\)
\(14\) −4.36313 −1.16609
\(15\) −2.59332 −0.669593
\(16\) 18.3736 4.59339
\(17\) 4.93209 1.19621 0.598104 0.801419i \(-0.295921\pi\)
0.598104 + 0.801419i \(0.295921\pi\)
\(18\) 5.86124 1.38151
\(19\) −6.45811 −1.48159 −0.740796 0.671730i \(-0.765551\pi\)
−0.740796 + 0.671730i \(0.765551\pi\)
\(20\) 15.8968 3.55463
\(21\) −1.48371 −0.323772
\(22\) −12.6523 −2.69748
\(23\) −0.588724 −0.122757 −0.0613787 0.998115i \(-0.519550\pi\)
−0.0613787 + 0.998115i \(0.519550\pi\)
\(24\) 10.2162 2.08538
\(25\) 2.42324 0.484647
\(26\) 13.4766 2.64298
\(27\) 4.84864 0.933122
\(28\) 9.09497 1.71879
\(29\) −7.40239 −1.37459 −0.687295 0.726379i \(-0.741202\pi\)
−0.687295 + 0.726379i \(0.741202\pi\)
\(30\) 7.25881 1.32527
\(31\) 4.71218 0.846332 0.423166 0.906052i \(-0.360919\pi\)
0.423166 + 0.906052i \(0.360919\pi\)
\(32\) −29.9618 −5.29655
\(33\) −4.30249 −0.748967
\(34\) −13.8051 −2.36756
\(35\) 4.24703 0.717879
\(36\) −12.2178 −2.03630
\(37\) −9.59806 −1.57791 −0.788955 0.614451i \(-0.789378\pi\)
−0.788955 + 0.614451i \(0.789378\pi\)
\(38\) 18.0765 2.93239
\(39\) 4.58280 0.733835
\(40\) −29.2434 −4.62379
\(41\) 3.80683 0.594527 0.297264 0.954795i \(-0.403926\pi\)
0.297264 + 0.954795i \(0.403926\pi\)
\(42\) 4.15296 0.640815
\(43\) −3.38931 −0.516865 −0.258432 0.966029i \(-0.583206\pi\)
−0.258432 + 0.966029i \(0.583206\pi\)
\(44\) 26.3738 3.97600
\(45\) −5.70528 −0.850493
\(46\) 1.64786 0.242964
\(47\) −2.11515 −0.308526 −0.154263 0.988030i \(-0.549300\pi\)
−0.154263 + 0.988030i \(0.549300\pi\)
\(48\) −17.4885 −2.52425
\(49\) −4.57016 −0.652880
\(50\) −6.78273 −0.959224
\(51\) −4.69451 −0.657363
\(52\) −28.0921 −3.89567
\(53\) 7.56236 1.03877 0.519385 0.854540i \(-0.326161\pi\)
0.519385 + 0.854540i \(0.326161\pi\)
\(54\) −13.5715 −1.84685
\(55\) 12.3156 1.66064
\(56\) −16.7309 −2.23577
\(57\) 6.14702 0.814193
\(58\) 20.7196 2.72061
\(59\) −0.485115 −0.0631566 −0.0315783 0.999501i \(-0.510053\pi\)
−0.0315783 + 0.999501i \(0.510053\pi\)
\(60\) −15.1310 −1.95341
\(61\) 11.8614 1.51869 0.759345 0.650688i \(-0.225519\pi\)
0.759345 + 0.650688i \(0.225519\pi\)
\(62\) −13.1896 −1.67508
\(63\) −3.26414 −0.411244
\(64\) 47.1172 5.88965
\(65\) −13.1180 −1.62709
\(66\) 12.0428 1.48237
\(67\) −1.53815 −0.187915 −0.0939575 0.995576i \(-0.529952\pi\)
−0.0939575 + 0.995576i \(0.529952\pi\)
\(68\) 28.7769 3.48971
\(69\) 0.560365 0.0674601
\(70\) −11.8876 −1.42084
\(71\) −1.00000 −0.118678
\(72\) 22.4756 2.64878
\(73\) 9.26795 1.08473 0.542366 0.840143i \(-0.317529\pi\)
0.542366 + 0.840143i \(0.317529\pi\)
\(74\) 26.8653 3.12303
\(75\) −2.30651 −0.266333
\(76\) −37.6806 −4.32226
\(77\) 7.04610 0.802978
\(78\) −12.8274 −1.45242
\(79\) 1.69346 0.190529 0.0952647 0.995452i \(-0.469630\pi\)
0.0952647 + 0.995452i \(0.469630\pi\)
\(80\) 50.0599 5.59687
\(81\) 1.66697 0.185219
\(82\) −10.6555 −1.17670
\(83\) −14.2688 −1.56621 −0.783104 0.621891i \(-0.786365\pi\)
−0.783104 + 0.621891i \(0.786365\pi\)
\(84\) −8.65687 −0.944542
\(85\) 13.4378 1.45753
\(86\) 9.48681 1.02299
\(87\) 7.04582 0.755391
\(88\) −48.5167 −5.17190
\(89\) −4.19505 −0.444675 −0.222337 0.974970i \(-0.571369\pi\)
−0.222337 + 0.974970i \(0.571369\pi\)
\(90\) 15.9693 1.68331
\(91\) −7.50516 −0.786754
\(92\) −3.43498 −0.358122
\(93\) −4.48519 −0.465093
\(94\) 5.92038 0.610640
\(95\) −17.5955 −1.80526
\(96\) 28.5186 2.91066
\(97\) 16.9329 1.71927 0.859636 0.510908i \(-0.170691\pi\)
0.859636 + 0.510908i \(0.170691\pi\)
\(98\) 12.7921 1.29219
\(99\) −9.46544 −0.951312
\(100\) 14.1387 1.41387
\(101\) 3.60427 0.358638 0.179319 0.983791i \(-0.442611\pi\)
0.179319 + 0.983791i \(0.442611\pi\)
\(102\) 13.1401 1.30107
\(103\) 7.52131 0.741097 0.370548 0.928813i \(-0.379170\pi\)
0.370548 + 0.928813i \(0.379170\pi\)
\(104\) 51.6776 5.06741
\(105\) −4.04245 −0.394503
\(106\) −21.1674 −2.05595
\(107\) 7.78789 0.752884 0.376442 0.926440i \(-0.377147\pi\)
0.376442 + 0.926440i \(0.377147\pi\)
\(108\) 28.2900 2.72221
\(109\) −6.68192 −0.640012 −0.320006 0.947416i \(-0.603685\pi\)
−0.320006 + 0.947416i \(0.603685\pi\)
\(110\) −34.4719 −3.28677
\(111\) 9.13572 0.867124
\(112\) 28.6406 2.70628
\(113\) −1.00000 −0.0940721
\(114\) −17.2058 −1.61147
\(115\) −1.60401 −0.149575
\(116\) −43.1901 −4.01010
\(117\) 10.0821 0.932092
\(118\) 1.35786 0.125001
\(119\) 7.68811 0.704768
\(120\) 27.8348 2.54096
\(121\) 9.43243 0.857494
\(122\) −33.2004 −3.00582
\(123\) −3.62346 −0.326716
\(124\) 27.4938 2.46901
\(125\) −7.02055 −0.627937
\(126\) 9.13647 0.813941
\(127\) −10.6704 −0.946848 −0.473424 0.880835i \(-0.656982\pi\)
−0.473424 + 0.880835i \(0.656982\pi\)
\(128\) −71.9592 −6.36035
\(129\) 3.22605 0.284038
\(130\) 36.7178 3.22037
\(131\) −17.7640 −1.55205 −0.776026 0.630701i \(-0.782767\pi\)
−0.776026 + 0.630701i \(0.782767\pi\)
\(132\) −25.1034 −2.18497
\(133\) −10.0669 −0.872907
\(134\) 4.30534 0.371925
\(135\) 13.2104 1.13697
\(136\) −52.9374 −4.53934
\(137\) −13.2043 −1.12812 −0.564061 0.825733i \(-0.690762\pi\)
−0.564061 + 0.825733i \(0.690762\pi\)
\(138\) −1.56848 −0.133518
\(139\) 14.0241 1.18951 0.594754 0.803908i \(-0.297249\pi\)
0.594754 + 0.803908i \(0.297249\pi\)
\(140\) 24.7798 2.09428
\(141\) 2.01326 0.169547
\(142\) 2.79904 0.234890
\(143\) −21.7636 −1.81997
\(144\) −38.4746 −3.20622
\(145\) −20.1683 −1.67488
\(146\) −25.9414 −2.14692
\(147\) 4.35002 0.358783
\(148\) −56.0010 −4.60326
\(149\) 18.7475 1.53586 0.767928 0.640537i \(-0.221288\pi\)
0.767928 + 0.640537i \(0.221288\pi\)
\(150\) 6.45601 0.527131
\(151\) −10.2197 −0.831671 −0.415836 0.909440i \(-0.636511\pi\)
−0.415836 + 0.909440i \(0.636511\pi\)
\(152\) 69.3165 5.62231
\(153\) −10.3279 −0.834960
\(154\) −19.7223 −1.58927
\(155\) 12.8386 1.03122
\(156\) 26.7389 2.14082
\(157\) 2.27234 0.181352 0.0906761 0.995880i \(-0.471097\pi\)
0.0906761 + 0.995880i \(0.471097\pi\)
\(158\) −4.74007 −0.377099
\(159\) −7.19809 −0.570845
\(160\) −81.6328 −6.45364
\(161\) −0.917699 −0.0723248
\(162\) −4.66592 −0.366589
\(163\) −18.6264 −1.45893 −0.729465 0.684019i \(-0.760231\pi\)
−0.729465 + 0.684019i \(0.760231\pi\)
\(164\) 22.2114 1.73442
\(165\) −11.7224 −0.912587
\(166\) 39.9390 3.09987
\(167\) −23.1945 −1.79484 −0.897422 0.441173i \(-0.854563\pi\)
−0.897422 + 0.441173i \(0.854563\pi\)
\(168\) 15.9250 1.22864
\(169\) 10.1815 0.783195
\(170\) −37.6129 −2.88478
\(171\) 13.5234 1.03416
\(172\) −19.7753 −1.50785
\(173\) −18.9370 −1.43975 −0.719876 0.694103i \(-0.755801\pi\)
−0.719876 + 0.694103i \(0.755801\pi\)
\(174\) −19.7215 −1.49509
\(175\) 3.77733 0.285539
\(176\) 83.0526 6.26033
\(177\) 0.461747 0.0347070
\(178\) 11.7421 0.880109
\(179\) −10.2103 −0.763153 −0.381577 0.924337i \(-0.624619\pi\)
−0.381577 + 0.924337i \(0.624619\pi\)
\(180\) −33.2882 −2.48115
\(181\) 3.78721 0.281501 0.140751 0.990045i \(-0.455048\pi\)
0.140751 + 0.990045i \(0.455048\pi\)
\(182\) 21.0072 1.55716
\(183\) −11.2900 −0.834580
\(184\) 6.31892 0.465837
\(185\) −26.1505 −1.92262
\(186\) 12.5542 0.920521
\(187\) 22.2942 1.63031
\(188\) −12.3411 −0.900065
\(189\) 7.55804 0.549766
\(190\) 49.2505 3.57301
\(191\) 17.7306 1.28294 0.641471 0.767147i \(-0.278324\pi\)
0.641471 + 0.767147i \(0.278324\pi\)
\(192\) −44.8476 −3.23659
\(193\) −6.63178 −0.477366 −0.238683 0.971098i \(-0.576716\pi\)
−0.238683 + 0.971098i \(0.576716\pi\)
\(194\) −47.3957 −3.40282
\(195\) 12.4861 0.894149
\(196\) −26.6652 −1.90465
\(197\) −26.1932 −1.86619 −0.933094 0.359633i \(-0.882902\pi\)
−0.933094 + 0.359633i \(0.882902\pi\)
\(198\) 26.4941 1.88286
\(199\) −5.79633 −0.410891 −0.205445 0.978669i \(-0.565864\pi\)
−0.205445 + 0.978669i \(0.565864\pi\)
\(200\) −26.0092 −1.83913
\(201\) 1.46406 0.103267
\(202\) −10.0885 −0.709824
\(203\) −11.5388 −0.809865
\(204\) −27.3907 −1.91773
\(205\) 10.3719 0.724408
\(206\) −21.0524 −1.46679
\(207\) 1.23280 0.0856854
\(208\) −88.4636 −6.13385
\(209\) −29.1921 −2.01926
\(210\) 11.3150 0.780808
\(211\) 21.4352 1.47566 0.737830 0.674987i \(-0.235851\pi\)
0.737830 + 0.674987i \(0.235851\pi\)
\(212\) 44.1235 3.03042
\(213\) 0.951830 0.0652183
\(214\) −21.7986 −1.49012
\(215\) −9.23438 −0.629779
\(216\) −52.0417 −3.54099
\(217\) 7.34531 0.498632
\(218\) 18.7029 1.26672
\(219\) −8.82152 −0.596103
\(220\) 71.8570 4.84460
\(221\) −23.7466 −1.59737
\(222\) −25.5712 −1.71623
\(223\) −7.28428 −0.487791 −0.243896 0.969801i \(-0.578425\pi\)
−0.243896 + 0.969801i \(0.578425\pi\)
\(224\) −46.7043 −3.12056
\(225\) −5.07430 −0.338287
\(226\) 2.79904 0.186189
\(227\) −0.774392 −0.0513982 −0.0256991 0.999670i \(-0.508181\pi\)
−0.0256991 + 0.999670i \(0.508181\pi\)
\(228\) 35.8655 2.37525
\(229\) 3.83151 0.253193 0.126597 0.991954i \(-0.459595\pi\)
0.126597 + 0.991954i \(0.459595\pi\)
\(230\) 4.48970 0.296042
\(231\) −6.70669 −0.441268
\(232\) 79.4518 5.21626
\(233\) −22.4638 −1.47165 −0.735825 0.677171i \(-0.763206\pi\)
−0.735825 + 0.677171i \(0.763206\pi\)
\(234\) −28.2202 −1.84481
\(235\) −5.76285 −0.375927
\(236\) −2.83046 −0.184247
\(237\) −1.61189 −0.104703
\(238\) −21.5193 −1.39489
\(239\) −8.61463 −0.557234 −0.278617 0.960402i \(-0.589876\pi\)
−0.278617 + 0.960402i \(0.589876\pi\)
\(240\) −47.6485 −3.07570
\(241\) 13.2008 0.850341 0.425171 0.905113i \(-0.360214\pi\)
0.425171 + 0.905113i \(0.360214\pi\)
\(242\) −26.4017 −1.69717
\(243\) −16.1326 −1.03491
\(244\) 69.2065 4.43049
\(245\) −12.4517 −0.795509
\(246\) 10.1422 0.646643
\(247\) 31.0940 1.97846
\(248\) −50.5770 −3.21164
\(249\) 13.5815 0.860693
\(250\) 19.6508 1.24283
\(251\) 19.2217 1.21327 0.606633 0.794982i \(-0.292520\pi\)
0.606633 + 0.794982i \(0.292520\pi\)
\(252\) −19.0450 −1.19973
\(253\) −2.66116 −0.167306
\(254\) 29.8670 1.87402
\(255\) −12.7905 −0.800972
\(256\) 107.182 6.69889
\(257\) −28.6703 −1.78840 −0.894202 0.447663i \(-0.852257\pi\)
−0.894202 + 0.447663i \(0.852257\pi\)
\(258\) −9.02983 −0.562173
\(259\) −14.9614 −0.929656
\(260\) −76.5386 −4.74672
\(261\) 15.5007 0.959472
\(262\) 49.7223 3.07185
\(263\) −4.38944 −0.270665 −0.135332 0.990800i \(-0.543210\pi\)
−0.135332 + 0.990800i \(0.543210\pi\)
\(264\) 46.1797 2.84216
\(265\) 20.6041 1.26570
\(266\) 28.1775 1.72768
\(267\) 3.99298 0.244366
\(268\) −8.97452 −0.548206
\(269\) 2.28116 0.139085 0.0695423 0.997579i \(-0.477846\pi\)
0.0695423 + 0.997579i \(0.477846\pi\)
\(270\) −36.9765 −2.25032
\(271\) −28.3719 −1.72347 −0.861736 0.507357i \(-0.830622\pi\)
−0.861736 + 0.507357i \(0.830622\pi\)
\(272\) 90.6201 5.49465
\(273\) 7.14364 0.432353
\(274\) 36.9594 2.23280
\(275\) 10.9536 0.660525
\(276\) 3.26952 0.196802
\(277\) −9.90508 −0.595139 −0.297569 0.954700i \(-0.596176\pi\)
−0.297569 + 0.954700i \(0.596176\pi\)
\(278\) −39.2540 −2.35430
\(279\) −9.86738 −0.590745
\(280\) −45.5845 −2.72419
\(281\) 22.5145 1.34310 0.671550 0.740959i \(-0.265629\pi\)
0.671550 + 0.740959i \(0.265629\pi\)
\(282\) −5.63519 −0.335571
\(283\) −12.9633 −0.770588 −0.385294 0.922794i \(-0.625900\pi\)
−0.385294 + 0.922794i \(0.625900\pi\)
\(284\) −5.83462 −0.346221
\(285\) 16.7479 0.992062
\(286\) 60.9172 3.60211
\(287\) 5.93406 0.350277
\(288\) 62.7406 3.69703
\(289\) 7.32551 0.430912
\(290\) 56.4518 3.31496
\(291\) −16.1172 −0.944807
\(292\) 54.0750 3.16450
\(293\) −5.78203 −0.337790 −0.168895 0.985634i \(-0.554020\pi\)
−0.168895 + 0.985634i \(0.554020\pi\)
\(294\) −12.1759 −0.710111
\(295\) −1.32173 −0.0769538
\(296\) 103.018 5.98782
\(297\) 21.9170 1.27175
\(298\) −52.4750 −3.03980
\(299\) 2.83454 0.163926
\(300\) −13.4576 −0.776976
\(301\) −5.28323 −0.304521
\(302\) 28.6055 1.64606
\(303\) −3.43065 −0.197086
\(304\) −118.658 −6.80553
\(305\) 32.3170 1.85046
\(306\) 28.9082 1.65257
\(307\) 9.45478 0.539613 0.269806 0.962915i \(-0.413040\pi\)
0.269806 + 0.962915i \(0.413040\pi\)
\(308\) 41.1113 2.34253
\(309\) −7.15901 −0.407262
\(310\) −35.9358 −2.04102
\(311\) −0.299660 −0.0169922 −0.00849609 0.999964i \(-0.502704\pi\)
−0.00849609 + 0.999964i \(0.502704\pi\)
\(312\) −49.1883 −2.78474
\(313\) 21.1267 1.19415 0.597077 0.802184i \(-0.296329\pi\)
0.597077 + 0.802184i \(0.296329\pi\)
\(314\) −6.36036 −0.358936
\(315\) −8.89336 −0.501084
\(316\) 9.88071 0.555833
\(317\) 17.0324 0.956635 0.478318 0.878187i \(-0.341247\pi\)
0.478318 + 0.878187i \(0.341247\pi\)
\(318\) 20.1477 1.12983
\(319\) −33.4605 −1.87343
\(320\) 128.374 7.17630
\(321\) −7.41275 −0.413740
\(322\) 2.56868 0.143147
\(323\) −31.8520 −1.77229
\(324\) 9.72614 0.540341
\(325\) −11.6672 −0.647180
\(326\) 52.1359 2.88754
\(327\) 6.36005 0.351712
\(328\) −40.8597 −2.25610
\(329\) −3.29708 −0.181774
\(330\) 32.8114 1.80621
\(331\) −18.6341 −1.02422 −0.512112 0.858918i \(-0.671137\pi\)
−0.512112 + 0.858918i \(0.671137\pi\)
\(332\) −83.2532 −4.56911
\(333\) 20.0985 1.10139
\(334\) 64.9223 3.55239
\(335\) −4.19078 −0.228967
\(336\) −27.2610 −1.48721
\(337\) −0.878329 −0.0478456 −0.0239228 0.999714i \(-0.507616\pi\)
−0.0239228 + 0.999714i \(0.507616\pi\)
\(338\) −28.4985 −1.55012
\(339\) 0.951830 0.0516963
\(340\) 78.4044 4.25207
\(341\) 21.3001 1.15346
\(342\) −37.8525 −2.04683
\(343\) −18.0355 −0.973825
\(344\) 36.3783 1.96139
\(345\) 1.52675 0.0821975
\(346\) 53.0053 2.84958
\(347\) 1.55446 0.0834477 0.0417239 0.999129i \(-0.486715\pi\)
0.0417239 + 0.999129i \(0.486715\pi\)
\(348\) 41.1097 2.20371
\(349\) −10.4934 −0.561700 −0.280850 0.959752i \(-0.590616\pi\)
−0.280850 + 0.959752i \(0.590616\pi\)
\(350\) −10.5729 −0.565145
\(351\) −23.3449 −1.24606
\(352\) −135.434 −7.21866
\(353\) −19.9786 −1.06335 −0.531677 0.846947i \(-0.678438\pi\)
−0.531677 + 0.846947i \(0.678438\pi\)
\(354\) −1.29245 −0.0686929
\(355\) −2.72456 −0.144605
\(356\) −24.4765 −1.29725
\(357\) −7.31778 −0.387298
\(358\) 28.5790 1.51045
\(359\) −14.7281 −0.777318 −0.388659 0.921382i \(-0.627062\pi\)
−0.388659 + 0.921382i \(0.627062\pi\)
\(360\) 61.2363 3.22743
\(361\) 22.7071 1.19511
\(362\) −10.6006 −0.557153
\(363\) −8.97808 −0.471227
\(364\) −43.7898 −2.29521
\(365\) 25.2511 1.32170
\(366\) 31.6011 1.65182
\(367\) −21.7557 −1.13564 −0.567820 0.823153i \(-0.692213\pi\)
−0.567820 + 0.823153i \(0.692213\pi\)
\(368\) −10.8170 −0.563873
\(369\) −7.97157 −0.414984
\(370\) 73.1963 3.80529
\(371\) 11.7882 0.612011
\(372\) −26.1694 −1.35682
\(373\) 12.0515 0.624004 0.312002 0.950081i \(-0.399000\pi\)
0.312002 + 0.950081i \(0.399000\pi\)
\(374\) −62.4022 −3.22674
\(375\) 6.68237 0.345076
\(376\) 22.7024 1.17079
\(377\) 35.6404 1.83558
\(378\) −21.1552 −1.08811
\(379\) 24.9294 1.28054 0.640268 0.768151i \(-0.278823\pi\)
0.640268 + 0.768151i \(0.278823\pi\)
\(380\) −102.663 −5.26651
\(381\) 10.1564 0.520330
\(382\) −49.6287 −2.53922
\(383\) −18.3164 −0.935925 −0.467963 0.883748i \(-0.655012\pi\)
−0.467963 + 0.883748i \(0.655012\pi\)
\(384\) 68.4929 3.49527
\(385\) 19.1975 0.978397
\(386\) 18.5626 0.944812
\(387\) 7.09728 0.360775
\(388\) 98.7968 5.01565
\(389\) −1.38101 −0.0700199 −0.0350099 0.999387i \(-0.511146\pi\)
−0.0350099 + 0.999387i \(0.511146\pi\)
\(390\) −34.9491 −1.76972
\(391\) −2.90364 −0.146843
\(392\) 49.0527 2.47754
\(393\) 16.9084 0.852914
\(394\) 73.3158 3.69359
\(395\) 4.61394 0.232153
\(396\) −55.2272 −2.77527
\(397\) 21.9907 1.10368 0.551841 0.833950i \(-0.313926\pi\)
0.551841 + 0.833950i \(0.313926\pi\)
\(398\) 16.2241 0.813243
\(399\) 9.58194 0.479697
\(400\) 44.5235 2.22617
\(401\) −32.5599 −1.62597 −0.812983 0.582288i \(-0.802158\pi\)
−0.812983 + 0.582288i \(0.802158\pi\)
\(402\) −4.09796 −0.204387
\(403\) −22.6878 −1.13016
\(404\) 21.0295 1.04626
\(405\) 4.54177 0.225682
\(406\) 32.2976 1.60290
\(407\) −43.3854 −2.15053
\(408\) 50.3874 2.49455
\(409\) −32.5465 −1.60932 −0.804660 0.593736i \(-0.797652\pi\)
−0.804660 + 0.593736i \(0.797652\pi\)
\(410\) −29.0315 −1.43376
\(411\) 12.5683 0.619948
\(412\) 43.8840 2.16201
\(413\) −0.756194 −0.0372099
\(414\) −3.45065 −0.169590
\(415\) −38.8763 −1.90836
\(416\) 144.258 7.07282
\(417\) −13.3486 −0.653682
\(418\) 81.7098 3.99656
\(419\) 34.5682 1.68877 0.844384 0.535738i \(-0.179966\pi\)
0.844384 + 0.535738i \(0.179966\pi\)
\(420\) −23.5862 −1.15089
\(421\) −0.364949 −0.0177865 −0.00889325 0.999960i \(-0.502831\pi\)
−0.00889325 + 0.999960i \(0.502831\pi\)
\(422\) −59.9979 −2.92065
\(423\) 4.42916 0.215353
\(424\) −81.1688 −3.94190
\(425\) 11.9516 0.579739
\(426\) −2.66421 −0.129081
\(427\) 18.4894 0.894765
\(428\) 45.4394 2.19640
\(429\) 20.7153 1.00014
\(430\) 25.8474 1.24647
\(431\) −17.8486 −0.859736 −0.429868 0.902892i \(-0.641440\pi\)
−0.429868 + 0.902892i \(0.641440\pi\)
\(432\) 89.0868 4.28619
\(433\) −30.9228 −1.48605 −0.743027 0.669262i \(-0.766610\pi\)
−0.743027 + 0.669262i \(0.766610\pi\)
\(434\) −20.5598 −0.986903
\(435\) 19.1968 0.920415
\(436\) −38.9865 −1.86711
\(437\) 3.80204 0.181876
\(438\) 24.6918 1.17982
\(439\) 35.1753 1.67882 0.839412 0.543495i \(-0.182899\pi\)
0.839412 + 0.543495i \(0.182899\pi\)
\(440\) −132.187 −6.30176
\(441\) 9.57000 0.455714
\(442\) 66.4678 3.16155
\(443\) 8.21427 0.390272 0.195136 0.980776i \(-0.437485\pi\)
0.195136 + 0.980776i \(0.437485\pi\)
\(444\) 53.3035 2.52967
\(445\) −11.4297 −0.541819
\(446\) 20.3890 0.965446
\(447\) −17.8444 −0.844013
\(448\) 73.4460 3.47000
\(449\) −5.35415 −0.252678 −0.126339 0.991987i \(-0.540323\pi\)
−0.126339 + 0.991987i \(0.540323\pi\)
\(450\) 14.2032 0.669544
\(451\) 17.2077 0.810280
\(452\) −5.83462 −0.274437
\(453\) 9.72746 0.457036
\(454\) 2.16755 0.101728
\(455\) −20.4483 −0.958630
\(456\) −65.9776 −3.08968
\(457\) 5.39398 0.252320 0.126160 0.992010i \(-0.459735\pi\)
0.126160 + 0.992010i \(0.459735\pi\)
\(458\) −10.7245 −0.501125
\(459\) 23.9139 1.11621
\(460\) −9.35882 −0.436357
\(461\) −14.9094 −0.694401 −0.347200 0.937791i \(-0.612868\pi\)
−0.347200 + 0.937791i \(0.612868\pi\)
\(462\) 18.7723 0.873366
\(463\) 30.7873 1.43081 0.715405 0.698710i \(-0.246242\pi\)
0.715405 + 0.698710i \(0.246242\pi\)
\(464\) −136.008 −6.31403
\(465\) −12.2202 −0.566697
\(466\) 62.8770 2.91272
\(467\) 15.3885 0.712096 0.356048 0.934468i \(-0.384124\pi\)
0.356048 + 0.934468i \(0.384124\pi\)
\(468\) 58.8253 2.71920
\(469\) −2.39766 −0.110714
\(470\) 16.1304 0.744041
\(471\) −2.16288 −0.0996603
\(472\) 5.20686 0.239665
\(473\) −15.3204 −0.704434
\(474\) 4.51174 0.207231
\(475\) −15.6495 −0.718049
\(476\) 44.8572 2.05603
\(477\) −15.8357 −0.725068
\(478\) 24.1127 1.10289
\(479\) 31.2711 1.42881 0.714407 0.699731i \(-0.246697\pi\)
0.714407 + 0.699731i \(0.246697\pi\)
\(480\) 77.7006 3.54653
\(481\) 46.2120 2.10708
\(482\) −36.9497 −1.68301
\(483\) 0.873494 0.0397454
\(484\) 55.0347 2.50158
\(485\) 46.1346 2.09486
\(486\) 45.1558 2.04831
\(487\) −28.2574 −1.28047 −0.640233 0.768181i \(-0.721162\pi\)
−0.640233 + 0.768181i \(0.721162\pi\)
\(488\) −127.311 −5.76309
\(489\) 17.7291 0.801739
\(490\) 34.8528 1.57449
\(491\) −24.1233 −1.08867 −0.544335 0.838868i \(-0.683218\pi\)
−0.544335 + 0.838868i \(0.683218\pi\)
\(492\) −21.1415 −0.953132
\(493\) −36.5093 −1.64429
\(494\) −87.0333 −3.91581
\(495\) −25.7892 −1.15914
\(496\) 86.5795 3.88753
\(497\) −1.55879 −0.0699215
\(498\) −38.0152 −1.70350
\(499\) 24.8489 1.11239 0.556195 0.831052i \(-0.312261\pi\)
0.556195 + 0.831052i \(0.312261\pi\)
\(500\) −40.9623 −1.83189
\(501\) 22.0772 0.986338
\(502\) −53.8024 −2.40132
\(503\) 16.9000 0.753532 0.376766 0.926308i \(-0.377036\pi\)
0.376766 + 0.926308i \(0.377036\pi\)
\(504\) 35.0349 1.56058
\(505\) 9.82005 0.436987
\(506\) 7.44870 0.331135
\(507\) −9.69110 −0.430397
\(508\) −62.2579 −2.76225
\(509\) 6.06807 0.268962 0.134481 0.990916i \(-0.457063\pi\)
0.134481 + 0.990916i \(0.457063\pi\)
\(510\) 35.8011 1.58530
\(511\) 14.4468 0.639090
\(512\) −156.089 −6.89822
\(513\) −31.3130 −1.38250
\(514\) 80.2493 3.53965
\(515\) 20.4923 0.902997
\(516\) 18.8228 0.828626
\(517\) −9.56093 −0.420489
\(518\) 41.8775 1.83999
\(519\) 18.0248 0.791200
\(520\) 140.799 6.17444
\(521\) −1.40716 −0.0616487 −0.0308243 0.999525i \(-0.509813\pi\)
−0.0308243 + 0.999525i \(0.509813\pi\)
\(522\) −43.3872 −1.89901
\(523\) 12.8262 0.560851 0.280425 0.959876i \(-0.409524\pi\)
0.280425 + 0.959876i \(0.409524\pi\)
\(524\) −103.646 −4.52782
\(525\) −3.59537 −0.156915
\(526\) 12.2862 0.535705
\(527\) 23.2409 1.01239
\(528\) −79.0520 −3.44030
\(529\) −22.6534 −0.984931
\(530\) −57.6718 −2.50510
\(531\) 1.01584 0.0440837
\(532\) −58.7363 −2.54654
\(533\) −18.3288 −0.793910
\(534\) −11.1765 −0.483655
\(535\) 21.2186 0.917360
\(536\) 16.5094 0.713096
\(537\) 9.71847 0.419383
\(538\) −6.38505 −0.275279
\(539\) −20.6582 −0.889810
\(540\) 77.0778 3.31690
\(541\) −7.38366 −0.317448 −0.158724 0.987323i \(-0.550738\pi\)
−0.158724 + 0.987323i \(0.550738\pi\)
\(542\) 79.4141 3.41113
\(543\) −3.60478 −0.154696
\(544\) −147.774 −6.33577
\(545\) −18.2053 −0.779829
\(546\) −19.9953 −0.855721
\(547\) 20.7782 0.888412 0.444206 0.895925i \(-0.353486\pi\)
0.444206 + 0.895925i \(0.353486\pi\)
\(548\) −77.0423 −3.29108
\(549\) −24.8379 −1.06006
\(550\) −30.6595 −1.30732
\(551\) 47.8054 2.03658
\(552\) −6.01454 −0.255996
\(553\) 2.63976 0.112254
\(554\) 27.7247 1.17791
\(555\) 24.8908 1.05656
\(556\) 81.8253 3.47017
\(557\) 38.4553 1.62941 0.814703 0.579879i \(-0.196900\pi\)
0.814703 + 0.579879i \(0.196900\pi\)
\(558\) 27.6192 1.16921
\(559\) 16.3186 0.690202
\(560\) 78.0331 3.29750
\(561\) −21.2203 −0.895920
\(562\) −63.0189 −2.65829
\(563\) −16.6860 −0.703229 −0.351615 0.936145i \(-0.614367\pi\)
−0.351615 + 0.936145i \(0.614367\pi\)
\(564\) 11.7466 0.494622
\(565\) −2.72456 −0.114623
\(566\) 36.2848 1.52516
\(567\) 2.59846 0.109125
\(568\) 10.7333 0.450357
\(569\) −41.0491 −1.72087 −0.860433 0.509563i \(-0.829807\pi\)
−0.860433 + 0.509563i \(0.829807\pi\)
\(570\) −46.8781 −1.96351
\(571\) −31.3959 −1.31388 −0.656938 0.753945i \(-0.728149\pi\)
−0.656938 + 0.753945i \(0.728149\pi\)
\(572\) −126.982 −5.30940
\(573\) −16.8765 −0.705027
\(574\) −16.6097 −0.693275
\(575\) −1.42662 −0.0594941
\(576\) −98.6642 −4.11101
\(577\) −35.2447 −1.46726 −0.733629 0.679550i \(-0.762175\pi\)
−0.733629 + 0.679550i \(0.762175\pi\)
\(578\) −20.5044 −0.852870
\(579\) 6.31233 0.262331
\(580\) −117.674 −4.88616
\(581\) −22.2422 −0.922761
\(582\) 45.1127 1.86998
\(583\) 34.1836 1.41574
\(584\) −99.4753 −4.11632
\(585\) 27.4693 1.13572
\(586\) 16.1841 0.668561
\(587\) 7.02358 0.289894 0.144947 0.989439i \(-0.453699\pi\)
0.144947 + 0.989439i \(0.453699\pi\)
\(588\) 25.3807 1.04668
\(589\) −30.4317 −1.25392
\(590\) 3.69956 0.152309
\(591\) 24.9315 1.02554
\(592\) −176.350 −7.24796
\(593\) 0.588708 0.0241754 0.0120877 0.999927i \(-0.496152\pi\)
0.0120877 + 0.999927i \(0.496152\pi\)
\(594\) −61.3464 −2.51707
\(595\) 20.9467 0.858732
\(596\) 109.385 4.48057
\(597\) 5.51712 0.225801
\(598\) −7.93399 −0.324445
\(599\) −25.6346 −1.04740 −0.523702 0.851902i \(-0.675449\pi\)
−0.523702 + 0.851902i \(0.675449\pi\)
\(600\) 24.7564 1.01067
\(601\) 15.1624 0.618486 0.309243 0.950983i \(-0.399924\pi\)
0.309243 + 0.950983i \(0.399924\pi\)
\(602\) 14.7880 0.602713
\(603\) 3.22091 0.131166
\(604\) −59.6283 −2.42624
\(605\) 25.6992 1.04482
\(606\) 9.60253 0.390076
\(607\) 2.47771 0.100567 0.0502835 0.998735i \(-0.483987\pi\)
0.0502835 + 0.998735i \(0.483987\pi\)
\(608\) 193.497 7.84732
\(609\) 10.9830 0.445053
\(610\) −90.4565 −3.66248
\(611\) 10.1838 0.411994
\(612\) −60.2593 −2.43584
\(613\) −30.1231 −1.21666 −0.608330 0.793684i \(-0.708160\pi\)
−0.608330 + 0.793684i \(0.708160\pi\)
\(614\) −26.4643 −1.06801
\(615\) −9.87233 −0.398091
\(616\) −75.6276 −3.04712
\(617\) 3.17681 0.127894 0.0639468 0.997953i \(-0.479631\pi\)
0.0639468 + 0.997953i \(0.479631\pi\)
\(618\) 20.0384 0.806061
\(619\) 44.6994 1.79662 0.898311 0.439360i \(-0.144795\pi\)
0.898311 + 0.439360i \(0.144795\pi\)
\(620\) 74.9084 3.00840
\(621\) −2.85451 −0.114548
\(622\) 0.838761 0.0336312
\(623\) −6.53922 −0.261988
\(624\) 84.2023 3.37079
\(625\) −31.2441 −1.24976
\(626\) −59.1346 −2.36349
\(627\) 27.7859 1.10966
\(628\) 13.2582 0.529061
\(629\) −47.3385 −1.88751
\(630\) 24.8929 0.991756
\(631\) −22.7524 −0.905758 −0.452879 0.891572i \(-0.649603\pi\)
−0.452879 + 0.891572i \(0.649603\pi\)
\(632\) −18.1764 −0.723017
\(633\) −20.4027 −0.810933
\(634\) −47.6744 −1.89339
\(635\) −29.0722 −1.15370
\(636\) −41.9981 −1.66533
\(637\) 22.0041 0.871832
\(638\) 93.6572 3.70792
\(639\) 2.09402 0.0828381
\(640\) −196.057 −7.74984
\(641\) −20.3231 −0.802714 −0.401357 0.915922i \(-0.631461\pi\)
−0.401357 + 0.915922i \(0.631461\pi\)
\(642\) 20.7486 0.818882
\(643\) 6.90125 0.272159 0.136079 0.990698i \(-0.456550\pi\)
0.136079 + 0.990698i \(0.456550\pi\)
\(644\) −5.35443 −0.210994
\(645\) 8.78956 0.346089
\(646\) 89.1549 3.50775
\(647\) −2.92065 −0.114822 −0.0574112 0.998351i \(-0.518285\pi\)
−0.0574112 + 0.998351i \(0.518285\pi\)
\(648\) −17.8920 −0.702865
\(649\) −2.19283 −0.0860760
\(650\) 32.6570 1.28091
\(651\) −6.99149 −0.274018
\(652\) −108.678 −4.25615
\(653\) 2.59117 0.101400 0.0507002 0.998714i \(-0.483855\pi\)
0.0507002 + 0.998714i \(0.483855\pi\)
\(654\) −17.8020 −0.696115
\(655\) −48.3992 −1.89111
\(656\) 69.9450 2.73089
\(657\) −19.4073 −0.757149
\(658\) 9.22865 0.359770
\(659\) −35.4851 −1.38230 −0.691152 0.722710i \(-0.742896\pi\)
−0.691152 + 0.722710i \(0.742896\pi\)
\(660\) −68.3957 −2.66230
\(661\) 16.9763 0.660303 0.330152 0.943928i \(-0.392900\pi\)
0.330152 + 0.943928i \(0.392900\pi\)
\(662\) 52.1577 2.02717
\(663\) 22.6028 0.877819
\(664\) 153.151 5.94341
\(665\) −27.4278 −1.06360
\(666\) −56.2565 −2.17990
\(667\) 4.35796 0.168741
\(668\) −135.331 −5.23612
\(669\) 6.93340 0.268061
\(670\) 11.7302 0.453176
\(671\) 53.6160 2.06982
\(672\) 44.4546 1.71487
\(673\) 3.46985 0.133753 0.0668765 0.997761i \(-0.478697\pi\)
0.0668765 + 0.997761i \(0.478697\pi\)
\(674\) 2.45848 0.0946970
\(675\) 11.7494 0.452235
\(676\) 59.4054 2.28482
\(677\) 47.3242 1.81882 0.909409 0.415903i \(-0.136534\pi\)
0.909409 + 0.415903i \(0.136534\pi\)
\(678\) −2.66421 −0.102318
\(679\) 26.3948 1.01294
\(680\) −144.231 −5.53101
\(681\) 0.737090 0.0282453
\(682\) −59.6198 −2.28296
\(683\) −13.9532 −0.533904 −0.266952 0.963710i \(-0.586017\pi\)
−0.266952 + 0.963710i \(0.586017\pi\)
\(684\) 78.9039 3.01697
\(685\) −35.9760 −1.37457
\(686\) 50.4821 1.92741
\(687\) −3.64695 −0.139140
\(688\) −62.2737 −2.37416
\(689\) −36.4107 −1.38714
\(690\) −4.27343 −0.162687
\(691\) 44.1286 1.67873 0.839365 0.543568i \(-0.182927\pi\)
0.839365 + 0.543568i \(0.182927\pi\)
\(692\) −110.490 −4.20020
\(693\) −14.7547 −0.560483
\(694\) −4.35099 −0.165161
\(695\) 38.2095 1.44937
\(696\) −75.6246 −2.86654
\(697\) 18.7756 0.711178
\(698\) 29.3715 1.11173
\(699\) 21.3817 0.808730
\(700\) 22.0393 0.833006
\(701\) 10.7832 0.407276 0.203638 0.979046i \(-0.434723\pi\)
0.203638 + 0.979046i \(0.434723\pi\)
\(702\) 65.3432 2.46622
\(703\) 61.9853 2.33782
\(704\) 212.980 8.02699
\(705\) 5.48525 0.206587
\(706\) 55.9210 2.10461
\(707\) 5.61831 0.211298
\(708\) 2.69412 0.101251
\(709\) 30.7319 1.15416 0.577080 0.816687i \(-0.304192\pi\)
0.577080 + 0.816687i \(0.304192\pi\)
\(710\) 7.62616 0.286205
\(711\) −3.54614 −0.132991
\(712\) 45.0266 1.68744
\(713\) −2.77417 −0.103894
\(714\) 20.4828 0.766548
\(715\) −59.2963 −2.21756
\(716\) −59.5732 −2.22636
\(717\) 8.19967 0.306222
\(718\) 41.2245 1.53848
\(719\) 32.1913 1.20053 0.600267 0.799800i \(-0.295061\pi\)
0.600267 + 0.799800i \(0.295061\pi\)
\(720\) −104.826 −3.90665
\(721\) 11.7242 0.436631
\(722\) −63.5582 −2.36539
\(723\) −12.5650 −0.467296
\(724\) 22.0969 0.821227
\(725\) −17.9377 −0.666191
\(726\) 25.1300 0.932661
\(727\) −21.6385 −0.802529 −0.401265 0.915962i \(-0.631429\pi\)
−0.401265 + 0.915962i \(0.631429\pi\)
\(728\) 80.5548 2.98556
\(729\) 10.3546 0.383503
\(730\) −70.6788 −2.61594
\(731\) −16.7164 −0.618277
\(732\) −65.8728 −2.43473
\(733\) 28.6036 1.05650 0.528248 0.849090i \(-0.322849\pi\)
0.528248 + 0.849090i \(0.322849\pi\)
\(734\) 60.8951 2.24768
\(735\) 11.8519 0.437164
\(736\) 17.6392 0.650191
\(737\) −6.95278 −0.256109
\(738\) 22.3127 0.821344
\(739\) −29.2269 −1.07513 −0.537564 0.843223i \(-0.680655\pi\)
−0.537564 + 0.843223i \(0.680655\pi\)
\(740\) −152.578 −5.60889
\(741\) −29.5962 −1.08724
\(742\) −32.9955 −1.21130
\(743\) −3.07880 −0.112950 −0.0564751 0.998404i \(-0.517986\pi\)
−0.0564751 + 0.998404i \(0.517986\pi\)
\(744\) 48.1407 1.76492
\(745\) 51.0787 1.87138
\(746\) −33.7327 −1.23504
\(747\) 29.8792 1.09322
\(748\) 130.078 4.75612
\(749\) 12.1397 0.443576
\(750\) −18.7042 −0.682982
\(751\) −28.3789 −1.03556 −0.517780 0.855514i \(-0.673241\pi\)
−0.517780 + 0.855514i \(0.673241\pi\)
\(752\) −38.8628 −1.41718
\(753\) −18.2958 −0.666738
\(754\) −99.7590 −3.63301
\(755\) −27.8443 −1.01336
\(756\) 44.0983 1.60384
\(757\) 5.51550 0.200464 0.100232 0.994964i \(-0.468041\pi\)
0.100232 + 0.994964i \(0.468041\pi\)
\(758\) −69.7783 −2.53446
\(759\) 2.53298 0.0919413
\(760\) 188.857 6.85057
\(761\) −42.0455 −1.52415 −0.762074 0.647490i \(-0.775819\pi\)
−0.762074 + 0.647490i \(0.775819\pi\)
\(762\) −28.4283 −1.02985
\(763\) −10.4157 −0.377075
\(764\) 103.451 3.74274
\(765\) −28.1390 −1.01737
\(766\) 51.2684 1.85240
\(767\) 2.33569 0.0843370
\(768\) −102.019 −3.68130
\(769\) −51.2803 −1.84921 −0.924607 0.380923i \(-0.875606\pi\)
−0.924607 + 0.380923i \(0.875606\pi\)
\(770\) −53.7347 −1.93646
\(771\) 27.2893 0.982799
\(772\) −38.6939 −1.39262
\(773\) −19.7305 −0.709656 −0.354828 0.934932i \(-0.615461\pi\)
−0.354828 + 0.934932i \(0.615461\pi\)
\(774\) −19.8656 −0.714053
\(775\) 11.4187 0.410172
\(776\) −181.745 −6.52425
\(777\) 14.2407 0.510883
\(778\) 3.86550 0.138585
\(779\) −24.5849 −0.880846
\(780\) 72.8518 2.60851
\(781\) −4.52022 −0.161746
\(782\) 8.12740 0.290635
\(783\) −35.8915 −1.28266
\(784\) −83.9701 −2.99893
\(785\) 6.19112 0.220971
\(786\) −47.3272 −1.68810
\(787\) −1.76911 −0.0630620 −0.0315310 0.999503i \(-0.510038\pi\)
−0.0315310 + 0.999503i \(0.510038\pi\)
\(788\) −152.827 −5.44425
\(789\) 4.17801 0.148741
\(790\) −12.9146 −0.459481
\(791\) −1.55879 −0.0554243
\(792\) 101.595 3.61002
\(793\) −57.1091 −2.02800
\(794\) −61.5528 −2.18443
\(795\) −19.6116 −0.695553
\(796\) −33.8194 −1.19870
\(797\) −37.9826 −1.34541 −0.672707 0.739909i \(-0.734869\pi\)
−0.672707 + 0.739909i \(0.734869\pi\)
\(798\) −26.8202 −0.949426
\(799\) −10.4321 −0.369061
\(800\) −72.6046 −2.56696
\(801\) 8.78452 0.310386
\(802\) 91.1365 3.21814
\(803\) 41.8932 1.47838
\(804\) 8.54222 0.301261
\(805\) −2.50033 −0.0881250
\(806\) 63.5041 2.23684
\(807\) −2.17127 −0.0764325
\(808\) −38.6855 −1.36095
\(809\) −25.7544 −0.905475 −0.452738 0.891644i \(-0.649553\pi\)
−0.452738 + 0.891644i \(0.649553\pi\)
\(810\) −12.7126 −0.446674
\(811\) 16.1452 0.566935 0.283468 0.958982i \(-0.408515\pi\)
0.283468 + 0.958982i \(0.408515\pi\)
\(812\) −67.3245 −2.36263
\(813\) 27.0053 0.947116
\(814\) 121.437 4.25638
\(815\) −50.7487 −1.77765
\(816\) −86.2549 −3.01953
\(817\) 21.8885 0.765782
\(818\) 91.0989 3.18520
\(819\) 15.7159 0.549160
\(820\) 60.5164 2.11332
\(821\) 29.6913 1.03623 0.518117 0.855310i \(-0.326633\pi\)
0.518117 + 0.855310i \(0.326633\pi\)
\(822\) −35.1791 −1.22701
\(823\) −6.58582 −0.229567 −0.114784 0.993391i \(-0.536617\pi\)
−0.114784 + 0.993391i \(0.536617\pi\)
\(824\) −80.7281 −2.81230
\(825\) −10.4259 −0.362985
\(826\) 2.11662 0.0736465
\(827\) −7.11821 −0.247525 −0.123762 0.992312i \(-0.539496\pi\)
−0.123762 + 0.992312i \(0.539496\pi\)
\(828\) 7.19291 0.249971
\(829\) −16.4817 −0.572433 −0.286217 0.958165i \(-0.592398\pi\)
−0.286217 + 0.958165i \(0.592398\pi\)
\(830\) 108.816 3.77707
\(831\) 9.42796 0.327052
\(832\) −226.856 −7.86482
\(833\) −22.5404 −0.780980
\(834\) 37.3632 1.29378
\(835\) −63.1949 −2.18695
\(836\) −170.325 −5.89081
\(837\) 22.8477 0.789730
\(838\) −96.7579 −3.34244
\(839\) −29.1410 −1.00606 −0.503029 0.864269i \(-0.667781\pi\)
−0.503029 + 0.864269i \(0.667781\pi\)
\(840\) 43.3887 1.49705
\(841\) 25.7954 0.889496
\(842\) 1.02151 0.0352034
\(843\) −21.4299 −0.738087
\(844\) 125.066 4.30496
\(845\) 27.7402 0.954293
\(846\) −12.3974 −0.426231
\(847\) 14.7032 0.505209
\(848\) 138.948 4.77148
\(849\) 12.3389 0.423469
\(850\) −33.4531 −1.14743
\(851\) 5.65060 0.193700
\(852\) 5.55357 0.190262
\(853\) −57.0947 −1.95489 −0.977443 0.211199i \(-0.932263\pi\)
−0.977443 + 0.211199i \(0.932263\pi\)
\(854\) −51.7526 −1.77094
\(855\) 36.8453 1.26008
\(856\) −83.5894 −2.85703
\(857\) 6.64210 0.226890 0.113445 0.993544i \(-0.463811\pi\)
0.113445 + 0.993544i \(0.463811\pi\)
\(858\) −57.9829 −1.97950
\(859\) −5.22720 −0.178350 −0.0891748 0.996016i \(-0.528423\pi\)
−0.0891748 + 0.996016i \(0.528423\pi\)
\(860\) −53.8791 −1.83726
\(861\) −5.64822 −0.192491
\(862\) 49.9589 1.70161
\(863\) 29.1300 0.991595 0.495798 0.868438i \(-0.334876\pi\)
0.495798 + 0.868438i \(0.334876\pi\)
\(864\) −145.274 −4.94233
\(865\) −51.5950 −1.75428
\(866\) 86.5540 2.94123
\(867\) −6.97264 −0.236803
\(868\) 42.8571 1.45467
\(869\) 7.65483 0.259672
\(870\) −53.7325 −1.82170
\(871\) 7.40576 0.250935
\(872\) 71.7187 2.42870
\(873\) −35.4577 −1.20006
\(874\) −10.6421 −0.359973
\(875\) −10.9436 −0.369961
\(876\) −51.4702 −1.73902
\(877\) −46.0981 −1.55662 −0.778311 0.627879i \(-0.783923\pi\)
−0.778311 + 0.627879i \(0.783923\pi\)
\(878\) −98.4570 −3.32276
\(879\) 5.50352 0.185629
\(880\) 226.282 7.62797
\(881\) −35.3559 −1.19117 −0.595585 0.803292i \(-0.703080\pi\)
−0.595585 + 0.803292i \(0.703080\pi\)
\(882\) −26.7868 −0.901959
\(883\) 2.32888 0.0783730 0.0391865 0.999232i \(-0.487523\pi\)
0.0391865 + 0.999232i \(0.487523\pi\)
\(884\) −138.553 −4.66003
\(885\) 1.25806 0.0422892
\(886\) −22.9921 −0.772433
\(887\) −22.8493 −0.767205 −0.383602 0.923498i \(-0.625317\pi\)
−0.383602 + 0.923498i \(0.625317\pi\)
\(888\) −98.0560 −3.29055
\(889\) −16.6330 −0.557853
\(890\) 31.9921 1.07238
\(891\) 7.53508 0.252435
\(892\) −42.5010 −1.42304
\(893\) 13.6598 0.457109
\(894\) 49.9473 1.67049
\(895\) −27.8186 −0.929873
\(896\) −112.170 −3.74732
\(897\) −2.69800 −0.0900837
\(898\) 14.9865 0.500105
\(899\) −34.8814 −1.16336
\(900\) −29.6066 −0.986888
\(901\) 37.2983 1.24258
\(902\) −48.1651 −1.60372
\(903\) 5.02874 0.167346
\(904\) 10.7333 0.356983
\(905\) 10.3185 0.342998
\(906\) −27.2276 −0.904575
\(907\) 40.7286 1.35237 0.676186 0.736731i \(-0.263632\pi\)
0.676186 + 0.736731i \(0.263632\pi\)
\(908\) −4.51828 −0.149944
\(909\) −7.54741 −0.250332
\(910\) 57.2355 1.89734
\(911\) 5.42463 0.179726 0.0898629 0.995954i \(-0.471357\pi\)
0.0898629 + 0.995954i \(0.471357\pi\)
\(912\) 112.943 3.73991
\(913\) −64.4983 −2.13458
\(914\) −15.0979 −0.499396
\(915\) −30.7603 −1.01690
\(916\) 22.3554 0.738643
\(917\) −27.6905 −0.914421
\(918\) −66.9361 −2.20922
\(919\) 18.1092 0.597366 0.298683 0.954352i \(-0.403453\pi\)
0.298683 + 0.954352i \(0.403453\pi\)
\(920\) 17.2163 0.567605
\(921\) −8.99935 −0.296539
\(922\) 41.7320 1.37437
\(923\) 4.81472 0.158478
\(924\) −39.1310 −1.28732
\(925\) −23.2584 −0.764730
\(926\) −86.1750 −2.83189
\(927\) −15.7498 −0.517290
\(928\) 221.789 7.28058
\(929\) 21.8749 0.717692 0.358846 0.933397i \(-0.383170\pi\)
0.358846 + 0.933397i \(0.383170\pi\)
\(930\) 34.2048 1.12162
\(931\) 29.5146 0.967301
\(932\) −131.068 −4.29326
\(933\) 0.285226 0.00933787
\(934\) −43.0731 −1.40939
\(935\) 60.7418 1.98647
\(936\) −108.214 −3.53708
\(937\) −3.82510 −0.124961 −0.0624803 0.998046i \(-0.519901\pi\)
−0.0624803 + 0.998046i \(0.519901\pi\)
\(938\) 6.71114 0.219127
\(939\) −20.1091 −0.656235
\(940\) −33.6240 −1.09669
\(941\) 36.1146 1.17730 0.588652 0.808387i \(-0.299659\pi\)
0.588652 + 0.808387i \(0.299659\pi\)
\(942\) 6.05399 0.197250
\(943\) −2.24117 −0.0729826
\(944\) −8.91329 −0.290103
\(945\) 20.5923 0.669869
\(946\) 42.8825 1.39423
\(947\) 4.53975 0.147522 0.0737610 0.997276i \(-0.476500\pi\)
0.0737610 + 0.997276i \(0.476500\pi\)
\(948\) −9.40476 −0.305452
\(949\) −44.6226 −1.44851
\(950\) 43.8036 1.42118
\(951\) −16.2120 −0.525709
\(952\) −82.5185 −2.67444
\(953\) 3.20087 0.103686 0.0518432 0.998655i \(-0.483490\pi\)
0.0518432 + 0.998655i \(0.483490\pi\)
\(954\) 44.3248 1.43507
\(955\) 48.3081 1.56322
\(956\) −50.2631 −1.62563
\(957\) 31.8487 1.02952
\(958\) −87.5291 −2.82794
\(959\) −20.5828 −0.664654
\(960\) −122.190 −3.94366
\(961\) −8.79540 −0.283723
\(962\) −129.349 −4.17038
\(963\) −16.3080 −0.525518
\(964\) 77.0219 2.48071
\(965\) −18.0687 −0.581652
\(966\) −2.44494 −0.0786648
\(967\) −19.5764 −0.629535 −0.314768 0.949169i \(-0.601927\pi\)
−0.314768 + 0.949169i \(0.601927\pi\)
\(968\) −101.241 −3.25400
\(969\) 30.3177 0.973944
\(970\) −129.133 −4.14620
\(971\) 31.7144 1.01776 0.508881 0.860837i \(-0.330059\pi\)
0.508881 + 0.860837i \(0.330059\pi\)
\(972\) −94.1276 −3.01914
\(973\) 21.8607 0.700821
\(974\) 79.0936 2.53432
\(975\) 11.1052 0.355651
\(976\) 217.935 6.97594
\(977\) −18.4518 −0.590326 −0.295163 0.955447i \(-0.595374\pi\)
−0.295163 + 0.955447i \(0.595374\pi\)
\(978\) −49.6246 −1.58682
\(979\) −18.9626 −0.606047
\(980\) −72.6509 −2.32075
\(981\) 13.9921 0.446732
\(982\) 67.5221 2.15472
\(983\) 16.7406 0.533941 0.266970 0.963705i \(-0.413977\pi\)
0.266970 + 0.963705i \(0.413977\pi\)
\(984\) 38.8915 1.23982
\(985\) −71.3650 −2.27388
\(986\) 102.191 3.25442
\(987\) 3.13826 0.0998919
\(988\) 181.422 5.77179
\(989\) 1.99537 0.0634490
\(990\) 72.1849 2.29419
\(991\) 5.27862 0.167681 0.0838405 0.996479i \(-0.473281\pi\)
0.0838405 + 0.996479i \(0.473281\pi\)
\(992\) −141.185 −4.48264
\(993\) 17.7365 0.562852
\(994\) 4.36313 0.138390
\(995\) −15.7925 −0.500654
\(996\) 79.2430 2.51091
\(997\) 4.99832 0.158298 0.0791491 0.996863i \(-0.474780\pi\)
0.0791491 + 0.996863i \(0.474780\pi\)
\(998\) −69.5531 −2.20166
\(999\) −46.5375 −1.47238
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 \(a_p\))