Properties

Label 8003.2.a.c.1.18
Level 8003
Weight 2
Character 8003.1
Self dual Yes
Analytic conductor 63.904
Analytic rank 0
Dimension 172
CM No

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Newspace parameters

Level: \( N \) = \( 8003 = 53 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9042767376\)
Analytic rank: \(0\)
Dimension: \(172\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.31012 q^{2}\) \(+2.93351 q^{3}\) \(+3.33667 q^{4}\) \(+2.06855 q^{5}\) \(-6.77677 q^{6}\) \(-0.615068 q^{7}\) \(-3.08788 q^{8}\) \(+5.60546 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.31012 q^{2}\) \(+2.93351 q^{3}\) \(+3.33667 q^{4}\) \(+2.06855 q^{5}\) \(-6.77677 q^{6}\) \(-0.615068 q^{7}\) \(-3.08788 q^{8}\) \(+5.60546 q^{9}\) \(-4.77860 q^{10}\) \(+4.10916 q^{11}\) \(+9.78815 q^{12}\) \(+2.91368 q^{13}\) \(+1.42088 q^{14}\) \(+6.06810 q^{15}\) \(+0.460042 q^{16}\) \(+7.15612 q^{17}\) \(-12.9493 q^{18}\) \(-4.02873 q^{19}\) \(+6.90207 q^{20}\) \(-1.80431 q^{21}\) \(-9.49267 q^{22}\) \(+2.67161 q^{23}\) \(-9.05832 q^{24}\) \(-0.721111 q^{25}\) \(-6.73095 q^{26}\) \(+7.64314 q^{27}\) \(-2.05228 q^{28}\) \(-2.92220 q^{29}\) \(-14.0181 q^{30}\) \(+4.57851 q^{31}\) \(+5.11301 q^{32}\) \(+12.0542 q^{33}\) \(-16.5315 q^{34}\) \(-1.27230 q^{35}\) \(+18.7036 q^{36}\) \(-7.07231 q^{37}\) \(+9.30687 q^{38}\) \(+8.54729 q^{39}\) \(-6.38743 q^{40}\) \(-5.98653 q^{41}\) \(+4.16817 q^{42}\) \(-8.52662 q^{43}\) \(+13.7109 q^{44}\) \(+11.5952 q^{45}\) \(-6.17175 q^{46}\) \(+3.52029 q^{47}\) \(+1.34954 q^{48}\) \(-6.62169 q^{49}\) \(+1.66586 q^{50}\) \(+20.9925 q^{51}\) \(+9.72199 q^{52}\) \(-1.00000 q^{53}\) \(-17.6566 q^{54}\) \(+8.49999 q^{55}\) \(+1.89926 q^{56}\) \(-11.8183 q^{57}\) \(+6.75065 q^{58}\) \(+8.19027 q^{59}\) \(+20.2473 q^{60}\) \(+10.0556 q^{61}\) \(-10.5769 q^{62}\) \(-3.44774 q^{63}\) \(-12.7318 q^{64}\) \(+6.02708 q^{65}\) \(-27.8468 q^{66}\) \(+3.56133 q^{67}\) \(+23.8776 q^{68}\) \(+7.83719 q^{69}\) \(+2.93916 q^{70}\) \(-3.32597 q^{71}\) \(-17.3090 q^{72}\) \(-3.68176 q^{73}\) \(+16.3379 q^{74}\) \(-2.11539 q^{75}\) \(-13.4426 q^{76}\) \(-2.52741 q^{77}\) \(-19.7453 q^{78}\) \(+15.0849 q^{79}\) \(+0.951618 q^{80}\) \(+5.60483 q^{81}\) \(+13.8296 q^{82}\) \(+13.1922 q^{83}\) \(-6.02038 q^{84}\) \(+14.8028 q^{85}\) \(+19.6975 q^{86}\) \(-8.57230 q^{87}\) \(-12.6886 q^{88}\) \(+18.6749 q^{89}\) \(-26.7863 q^{90}\) \(-1.79211 q^{91}\) \(+8.91429 q^{92}\) \(+13.4311 q^{93}\) \(-8.13230 q^{94}\) \(-8.33362 q^{95}\) \(+14.9990 q^{96}\) \(+10.9040 q^{97}\) \(+15.2969 q^{98}\) \(+23.0337 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 66q^{12} \) \(\mathstrut +\mathstrut 121q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 212q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 40q^{18} \) \(\mathstrut +\mathstrut 41q^{19} \) \(\mathstrut +\mathstrut 64q^{20} \) \(\mathstrut +\mathstrut 56q^{21} \) \(\mathstrut +\mathstrut 50q^{22} \) \(\mathstrut +\mathstrut 28q^{23} \) \(\mathstrut +\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 231q^{25} \) \(\mathstrut +\mathstrut 38q^{26} \) \(\mathstrut +\mathstrut 100q^{27} \) \(\mathstrut +\mathstrut 80q^{28} \) \(\mathstrut +\mathstrut 26q^{29} \) \(\mathstrut +\mathstrut 55q^{30} \) \(\mathstrut +\mathstrut 66q^{31} \) \(\mathstrut +\mathstrut 65q^{32} \) \(\mathstrut +\mathstrut 99q^{33} \) \(\mathstrut +\mathstrut 81q^{34} \) \(\mathstrut +\mathstrut 36q^{35} \) \(\mathstrut +\mathstrut 212q^{36} \) \(\mathstrut +\mathstrut 153q^{37} \) \(\mathstrut +\mathstrut q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 59q^{40} \) \(\mathstrut +\mathstrut 40q^{41} \) \(\mathstrut +\mathstrut 50q^{42} \) \(\mathstrut +\mathstrut 39q^{43} \) \(\mathstrut -\mathstrut 51q^{44} \) \(\mathstrut +\mathstrut 123q^{45} \) \(\mathstrut +\mathstrut 59q^{46} \) \(\mathstrut +\mathstrut 29q^{47} \) \(\mathstrut +\mathstrut 128q^{48} \) \(\mathstrut +\mathstrut 245q^{49} \) \(\mathstrut +\mathstrut 19q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 215q^{52} \) \(\mathstrut -\mathstrut 172q^{53} \) \(\mathstrut +\mathstrut 40q^{54} \) \(\mathstrut +\mathstrut 40q^{55} \) \(\mathstrut +\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 54q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 54q^{60} \) \(\mathstrut +\mathstrut 100q^{61} \) \(\mathstrut -\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 92q^{63} \) \(\mathstrut +\mathstrut 253q^{64} \) \(\mathstrut +\mathstrut 77q^{65} \) \(\mathstrut +\mathstrut 14q^{66} \) \(\mathstrut +\mathstrut 126q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut +\mathstrut 47q^{69} \) \(\mathstrut +\mathstrut 72q^{70} \) \(\mathstrut +\mathstrut 38q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 185q^{73} \) \(\mathstrut +\mathstrut 48q^{74} \) \(\mathstrut +\mathstrut 75q^{75} \) \(\mathstrut +\mathstrut 38q^{76} \) \(\mathstrut +\mathstrut 120q^{77} \) \(\mathstrut +\mathstrut 75q^{78} \) \(\mathstrut +\mathstrut 79q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 232q^{81} \) \(\mathstrut +\mathstrut 110q^{82} \) \(\mathstrut +\mathstrut 90q^{83} \) \(\mathstrut +\mathstrut 158q^{84} \) \(\mathstrut +\mathstrut 115q^{85} \) \(\mathstrut +\mathstrut 68q^{86} \) \(\mathstrut +\mathstrut 61q^{87} \) \(\mathstrut +\mathstrut 15q^{88} \) \(\mathstrut -\mathstrut 36q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 33q^{91} \) \(\mathstrut +\mathstrut 139q^{92} \) \(\mathstrut +\mathstrut 103q^{93} \) \(\mathstrut -\mathstrut 24q^{94} \) \(\mathstrut -\mathstrut 45q^{95} \) \(\mathstrut +\mathstrut 34q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut -\mathstrut 36q^{98} \) \(\mathstrut +\mathstrut 27q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.31012 −1.63350 −0.816752 0.576989i \(-0.804228\pi\)
−0.816752 + 0.576989i \(0.804228\pi\)
\(3\) 2.93351 1.69366 0.846831 0.531863i \(-0.178508\pi\)
0.846831 + 0.531863i \(0.178508\pi\)
\(4\) 3.33667 1.66834
\(5\) 2.06855 0.925083 0.462541 0.886598i \(-0.346938\pi\)
0.462541 + 0.886598i \(0.346938\pi\)
\(6\) −6.77677 −2.76660
\(7\) −0.615068 −0.232474 −0.116237 0.993222i \(-0.537083\pi\)
−0.116237 + 0.993222i \(0.537083\pi\)
\(8\) −3.08788 −1.09173
\(9\) 5.60546 1.86849
\(10\) −4.77860 −1.51113
\(11\) 4.10916 1.23896 0.619479 0.785013i \(-0.287344\pi\)
0.619479 + 0.785013i \(0.287344\pi\)
\(12\) 9.78815 2.82560
\(13\) 2.91368 0.808109 0.404054 0.914735i \(-0.367601\pi\)
0.404054 + 0.914735i \(0.367601\pi\)
\(14\) 1.42088 0.379747
\(15\) 6.06810 1.56678
\(16\) 0.460042 0.115010
\(17\) 7.15612 1.73561 0.867807 0.496901i \(-0.165529\pi\)
0.867807 + 0.496901i \(0.165529\pi\)
\(18\) −12.9493 −3.05218
\(19\) −4.02873 −0.924254 −0.462127 0.886814i \(-0.652914\pi\)
−0.462127 + 0.886814i \(0.652914\pi\)
\(20\) 6.90207 1.54335
\(21\) −1.80431 −0.393732
\(22\) −9.49267 −2.02384
\(23\) 2.67161 0.557069 0.278535 0.960426i \(-0.410151\pi\)
0.278535 + 0.960426i \(0.410151\pi\)
\(24\) −9.05832 −1.84902
\(25\) −0.721111 −0.144222
\(26\) −6.73095 −1.32005
\(27\) 7.64314 1.47092
\(28\) −2.05228 −0.387844
\(29\) −2.92220 −0.542639 −0.271320 0.962489i \(-0.587460\pi\)
−0.271320 + 0.962489i \(0.587460\pi\)
\(30\) −14.0181 −2.55934
\(31\) 4.57851 0.822324 0.411162 0.911562i \(-0.365123\pi\)
0.411162 + 0.911562i \(0.365123\pi\)
\(32\) 5.11301 0.903861
\(33\) 12.0542 2.09838
\(34\) −16.5315 −2.83513
\(35\) −1.27230 −0.215057
\(36\) 18.7036 3.11727
\(37\) −7.07231 −1.16268 −0.581340 0.813660i \(-0.697472\pi\)
−0.581340 + 0.813660i \(0.697472\pi\)
\(38\) 9.30687 1.50977
\(39\) 8.54729 1.36866
\(40\) −6.38743 −1.00994
\(41\) −5.98653 −0.934940 −0.467470 0.884009i \(-0.654834\pi\)
−0.467470 + 0.884009i \(0.654834\pi\)
\(42\) 4.16817 0.643162
\(43\) −8.52662 −1.30030 −0.650148 0.759807i \(-0.725293\pi\)
−0.650148 + 0.759807i \(0.725293\pi\)
\(44\) 13.7109 2.06700
\(45\) 11.5952 1.72851
\(46\) −6.17175 −0.909975
\(47\) 3.52029 0.513486 0.256743 0.966480i \(-0.417351\pi\)
0.256743 + 0.966480i \(0.417351\pi\)
\(48\) 1.34954 0.194789
\(49\) −6.62169 −0.945956
\(50\) 1.66586 0.235588
\(51\) 20.9925 2.93954
\(52\) 9.72199 1.34820
\(53\) −1.00000 −0.137361
\(54\) −17.6566 −2.40276
\(55\) 8.49999 1.14614
\(56\) 1.89926 0.253799
\(57\) −11.8183 −1.56537
\(58\) 6.75065 0.886403
\(59\) 8.19027 1.06628 0.533141 0.846026i \(-0.321011\pi\)
0.533141 + 0.846026i \(0.321011\pi\)
\(60\) 20.2473 2.61391
\(61\) 10.0556 1.28749 0.643744 0.765241i \(-0.277380\pi\)
0.643744 + 0.765241i \(0.277380\pi\)
\(62\) −10.5769 −1.34327
\(63\) −3.44774 −0.434374
\(64\) −12.7318 −1.59147
\(65\) 6.02708 0.747567
\(66\) −27.8468 −3.42771
\(67\) 3.56133 0.435086 0.217543 0.976051i \(-0.430196\pi\)
0.217543 + 0.976051i \(0.430196\pi\)
\(68\) 23.8776 2.89559
\(69\) 7.83719 0.943487
\(70\) 2.93916 0.351297
\(71\) −3.32597 −0.394721 −0.197360 0.980331i \(-0.563237\pi\)
−0.197360 + 0.980331i \(0.563237\pi\)
\(72\) −17.3090 −2.03989
\(73\) −3.68176 −0.430917 −0.215459 0.976513i \(-0.569125\pi\)
−0.215459 + 0.976513i \(0.569125\pi\)
\(74\) 16.3379 1.89924
\(75\) −2.11539 −0.244264
\(76\) −13.4426 −1.54197
\(77\) −2.52741 −0.288025
\(78\) −19.7453 −2.23572
\(79\) 15.0849 1.69718 0.848592 0.529048i \(-0.177451\pi\)
0.848592 + 0.529048i \(0.177451\pi\)
\(80\) 0.951618 0.106394
\(81\) 5.60483 0.622759
\(82\) 13.8296 1.52723
\(83\) 13.1922 1.44803 0.724015 0.689784i \(-0.242295\pi\)
0.724015 + 0.689784i \(0.242295\pi\)
\(84\) −6.02038 −0.656877
\(85\) 14.8028 1.60559
\(86\) 19.6975 2.12404
\(87\) −8.57230 −0.919047
\(88\) −12.6886 −1.35261
\(89\) 18.6749 1.97954 0.989770 0.142670i \(-0.0455688\pi\)
0.989770 + 0.142670i \(0.0455688\pi\)
\(90\) −26.7863 −2.82352
\(91\) −1.79211 −0.187864
\(92\) 8.91429 0.929379
\(93\) 13.4311 1.39274
\(94\) −8.13230 −0.838782
\(95\) −8.33362 −0.855012
\(96\) 14.9990 1.53083
\(97\) 10.9040 1.10713 0.553565 0.832806i \(-0.313267\pi\)
0.553565 + 0.832806i \(0.313267\pi\)
\(98\) 15.2969 1.54522
\(99\) 23.0337 2.31498
\(100\) −2.40611 −0.240611
\(101\) 5.04347 0.501844 0.250922 0.968007i \(-0.419266\pi\)
0.250922 + 0.968007i \(0.419266\pi\)
\(102\) −48.4954 −4.80176
\(103\) 3.10516 0.305961 0.152980 0.988229i \(-0.451113\pi\)
0.152980 + 0.988229i \(0.451113\pi\)
\(104\) −8.99709 −0.882237
\(105\) −3.73229 −0.364234
\(106\) 2.31012 0.224379
\(107\) 0.0193923 0.00187473 0.000937364 1.00000i \(-0.499702\pi\)
0.000937364 1.00000i \(0.499702\pi\)
\(108\) 25.5027 2.45400
\(109\) −12.1829 −1.16691 −0.583456 0.812145i \(-0.698300\pi\)
−0.583456 + 0.812145i \(0.698300\pi\)
\(110\) −19.6360 −1.87222
\(111\) −20.7467 −1.96919
\(112\) −0.282957 −0.0267369
\(113\) −2.54245 −0.239173 −0.119587 0.992824i \(-0.538157\pi\)
−0.119587 + 0.992824i \(0.538157\pi\)
\(114\) 27.3018 2.55704
\(115\) 5.52635 0.515335
\(116\) −9.75043 −0.905305
\(117\) 16.3325 1.50994
\(118\) −18.9205 −1.74178
\(119\) −4.40150 −0.403485
\(120\) −18.7376 −1.71050
\(121\) 5.88520 0.535018
\(122\) −23.2297 −2.10312
\(123\) −17.5615 −1.58347
\(124\) 15.2770 1.37191
\(125\) −11.8344 −1.05850
\(126\) 7.96470 0.709552
\(127\) −4.19943 −0.372640 −0.186320 0.982489i \(-0.559656\pi\)
−0.186320 + 0.982489i \(0.559656\pi\)
\(128\) 19.1859 1.69581
\(129\) −25.0129 −2.20226
\(130\) −13.9233 −1.22115
\(131\) 3.33030 0.290970 0.145485 0.989360i \(-0.453526\pi\)
0.145485 + 0.989360i \(0.453526\pi\)
\(132\) 40.2211 3.50080
\(133\) 2.47794 0.214865
\(134\) −8.22711 −0.710714
\(135\) 15.8102 1.36073
\(136\) −22.0972 −1.89482
\(137\) 5.36031 0.457962 0.228981 0.973431i \(-0.426461\pi\)
0.228981 + 0.973431i \(0.426461\pi\)
\(138\) −18.1049 −1.54119
\(139\) −11.6173 −0.985366 −0.492683 0.870209i \(-0.663984\pi\)
−0.492683 + 0.870209i \(0.663984\pi\)
\(140\) −4.24524 −0.358788
\(141\) 10.3268 0.869672
\(142\) 7.68341 0.644778
\(143\) 11.9728 1.00121
\(144\) 2.57875 0.214896
\(145\) −6.04471 −0.501986
\(146\) 8.50532 0.703905
\(147\) −19.4248 −1.60213
\(148\) −23.5980 −1.93974
\(149\) −11.8722 −0.972611 −0.486305 0.873789i \(-0.661656\pi\)
−0.486305 + 0.873789i \(0.661656\pi\)
\(150\) 4.88680 0.399006
\(151\) 1.00000 0.0813788
\(152\) 12.4402 1.00904
\(153\) 40.1134 3.24297
\(154\) 5.83863 0.470490
\(155\) 9.47086 0.760718
\(156\) 28.5195 2.28339
\(157\) −9.68481 −0.772932 −0.386466 0.922304i \(-0.626304\pi\)
−0.386466 + 0.922304i \(0.626304\pi\)
\(158\) −34.8480 −2.77236
\(159\) −2.93351 −0.232642
\(160\) 10.5765 0.836146
\(161\) −1.64322 −0.129504
\(162\) −12.9478 −1.01728
\(163\) −3.15098 −0.246804 −0.123402 0.992357i \(-0.539380\pi\)
−0.123402 + 0.992357i \(0.539380\pi\)
\(164\) −19.9751 −1.55979
\(165\) 24.9348 1.94117
\(166\) −30.4756 −2.36536
\(167\) 1.47239 0.113937 0.0569683 0.998376i \(-0.481857\pi\)
0.0569683 + 0.998376i \(0.481857\pi\)
\(168\) 5.57148 0.429849
\(169\) −4.51049 −0.346961
\(170\) −34.1962 −2.62273
\(171\) −22.5829 −1.72696
\(172\) −28.4505 −2.16933
\(173\) −1.00523 −0.0764261 −0.0382131 0.999270i \(-0.512167\pi\)
−0.0382131 + 0.999270i \(0.512167\pi\)
\(174\) 19.8031 1.50127
\(175\) 0.443532 0.0335279
\(176\) 1.89038 0.142493
\(177\) 24.0262 1.80592
\(178\) −43.1414 −3.23359
\(179\) 3.84594 0.287459 0.143729 0.989617i \(-0.454090\pi\)
0.143729 + 0.989617i \(0.454090\pi\)
\(180\) 38.6893 2.88373
\(181\) −13.4044 −0.996341 −0.498171 0.867079i \(-0.665995\pi\)
−0.498171 + 0.867079i \(0.665995\pi\)
\(182\) 4.13999 0.306877
\(183\) 29.4982 2.18057
\(184\) −8.24962 −0.608170
\(185\) −14.6294 −1.07558
\(186\) −31.0275 −2.27504
\(187\) 29.4056 2.15035
\(188\) 11.7460 0.856668
\(189\) −4.70105 −0.341951
\(190\) 19.2517 1.39667
\(191\) 13.3195 0.963763 0.481881 0.876237i \(-0.339954\pi\)
0.481881 + 0.876237i \(0.339954\pi\)
\(192\) −37.3487 −2.69541
\(193\) −20.7301 −1.49219 −0.746094 0.665840i \(-0.768073\pi\)
−0.746094 + 0.665840i \(0.768073\pi\)
\(194\) −25.1895 −1.80850
\(195\) 17.6805 1.26613
\(196\) −22.0944 −1.57817
\(197\) −17.8772 −1.27370 −0.636850 0.770988i \(-0.719763\pi\)
−0.636850 + 0.770988i \(0.719763\pi\)
\(198\) −53.2108 −3.78153
\(199\) 24.2161 1.71663 0.858317 0.513120i \(-0.171511\pi\)
0.858317 + 0.513120i \(0.171511\pi\)
\(200\) 2.22671 0.157452
\(201\) 10.4472 0.736887
\(202\) −11.6510 −0.819765
\(203\) 1.79735 0.126149
\(204\) 70.0452 4.90415
\(205\) −12.3834 −0.864896
\(206\) −7.17331 −0.499788
\(207\) 14.9756 1.04088
\(208\) 1.34041 0.0929409
\(209\) −16.5547 −1.14511
\(210\) 8.62205 0.594978
\(211\) 4.63521 0.319101 0.159550 0.987190i \(-0.448996\pi\)
0.159550 + 0.987190i \(0.448996\pi\)
\(212\) −3.33667 −0.229164
\(213\) −9.75677 −0.668523
\(214\) −0.0447987 −0.00306238
\(215\) −17.6377 −1.20288
\(216\) −23.6011 −1.60585
\(217\) −2.81609 −0.191169
\(218\) 28.1441 1.90616
\(219\) −10.8005 −0.729828
\(220\) 28.3617 1.91215
\(221\) 20.8506 1.40256
\(222\) 47.9274 3.21668
\(223\) 0.906853 0.0607273 0.0303637 0.999539i \(-0.490333\pi\)
0.0303637 + 0.999539i \(0.490333\pi\)
\(224\) −3.14485 −0.210124
\(225\) −4.04216 −0.269478
\(226\) 5.87337 0.390691
\(227\) −8.79310 −0.583619 −0.291809 0.956477i \(-0.594257\pi\)
−0.291809 + 0.956477i \(0.594257\pi\)
\(228\) −39.4338 −2.61157
\(229\) 7.88158 0.520830 0.260415 0.965497i \(-0.416141\pi\)
0.260415 + 0.965497i \(0.416141\pi\)
\(230\) −12.7666 −0.841802
\(231\) −7.41418 −0.487817
\(232\) 9.02341 0.592416
\(233\) −21.9517 −1.43810 −0.719052 0.694956i \(-0.755424\pi\)
−0.719052 + 0.694956i \(0.755424\pi\)
\(234\) −37.7301 −2.46650
\(235\) 7.28188 0.475017
\(236\) 27.3283 1.77892
\(237\) 44.2517 2.87446
\(238\) 10.1680 0.659094
\(239\) 6.20409 0.401309 0.200655 0.979662i \(-0.435693\pi\)
0.200655 + 0.979662i \(0.435693\pi\)
\(240\) 2.79158 0.180196
\(241\) −11.8291 −0.761976 −0.380988 0.924580i \(-0.624416\pi\)
−0.380988 + 0.924580i \(0.624416\pi\)
\(242\) −13.5955 −0.873954
\(243\) −6.48763 −0.416182
\(244\) 33.5523 2.14796
\(245\) −13.6973 −0.875087
\(246\) 40.5693 2.58661
\(247\) −11.7384 −0.746898
\(248\) −14.1379 −0.897756
\(249\) 38.6993 2.45247
\(250\) 27.3389 1.72906
\(251\) 6.70205 0.423030 0.211515 0.977375i \(-0.432160\pi\)
0.211515 + 0.977375i \(0.432160\pi\)
\(252\) −11.5040 −0.724682
\(253\) 10.9781 0.690186
\(254\) 9.70121 0.608708
\(255\) 43.4240 2.71932
\(256\) −18.8584 −1.17865
\(257\) 3.23677 0.201904 0.100952 0.994891i \(-0.467811\pi\)
0.100952 + 0.994891i \(0.467811\pi\)
\(258\) 57.7829 3.59740
\(259\) 4.34995 0.270293
\(260\) 20.1104 1.24719
\(261\) −16.3803 −1.01391
\(262\) −7.69341 −0.475301
\(263\) −15.4367 −0.951870 −0.475935 0.879481i \(-0.657890\pi\)
−0.475935 + 0.879481i \(0.657890\pi\)
\(264\) −37.2221 −2.29086
\(265\) −2.06855 −0.127070
\(266\) −5.72435 −0.350983
\(267\) 54.7831 3.35267
\(268\) 11.8830 0.725869
\(269\) 26.5820 1.62073 0.810367 0.585923i \(-0.199268\pi\)
0.810367 + 0.585923i \(0.199268\pi\)
\(270\) −36.5235 −2.22275
\(271\) 5.97893 0.363194 0.181597 0.983373i \(-0.441873\pi\)
0.181597 + 0.983373i \(0.441873\pi\)
\(272\) 3.29211 0.199614
\(273\) −5.25716 −0.318178
\(274\) −12.3830 −0.748083
\(275\) −2.96316 −0.178685
\(276\) 26.1501 1.57405
\(277\) 4.62414 0.277837 0.138919 0.990304i \(-0.455637\pi\)
0.138919 + 0.990304i \(0.455637\pi\)
\(278\) 26.8374 1.60960
\(279\) 25.6646 1.53650
\(280\) 3.92870 0.234785
\(281\) −8.45292 −0.504259 −0.252130 0.967694i \(-0.581131\pi\)
−0.252130 + 0.967694i \(0.581131\pi\)
\(282\) −23.8561 −1.42061
\(283\) 12.2533 0.728384 0.364192 0.931324i \(-0.381345\pi\)
0.364192 + 0.931324i \(0.381345\pi\)
\(284\) −11.0977 −0.658527
\(285\) −24.4467 −1.44810
\(286\) −27.6586 −1.63549
\(287\) 3.68212 0.217349
\(288\) 28.6608 1.68885
\(289\) 34.2101 2.01236
\(290\) 13.9640 0.819996
\(291\) 31.9868 1.87510
\(292\) −12.2848 −0.718915
\(293\) 2.68201 0.156684 0.0783422 0.996927i \(-0.475037\pi\)
0.0783422 + 0.996927i \(0.475037\pi\)
\(294\) 44.8736 2.61708
\(295\) 16.9420 0.986400
\(296\) 21.8385 1.26933
\(297\) 31.4069 1.82241
\(298\) 27.4263 1.58876
\(299\) 7.78421 0.450173
\(300\) −7.05835 −0.407514
\(301\) 5.24444 0.302285
\(302\) −2.31012 −0.132933
\(303\) 14.7951 0.849954
\(304\) −1.85338 −0.106299
\(305\) 20.8005 1.19103
\(306\) −92.6669 −5.29741
\(307\) −20.8631 −1.19072 −0.595361 0.803458i \(-0.702991\pi\)
−0.595361 + 0.803458i \(0.702991\pi\)
\(308\) −8.43315 −0.480523
\(309\) 9.10902 0.518194
\(310\) −21.8789 −1.24264
\(311\) −12.2628 −0.695359 −0.347680 0.937613i \(-0.613030\pi\)
−0.347680 + 0.937613i \(0.613030\pi\)
\(312\) −26.3930 −1.49421
\(313\) 12.0039 0.678499 0.339250 0.940696i \(-0.389827\pi\)
0.339250 + 0.940696i \(0.389827\pi\)
\(314\) 22.3731 1.26259
\(315\) −7.13181 −0.401832
\(316\) 50.3334 2.83147
\(317\) −7.40905 −0.416134 −0.208067 0.978115i \(-0.566717\pi\)
−0.208067 + 0.978115i \(0.566717\pi\)
\(318\) 6.77677 0.380022
\(319\) −12.0078 −0.672307
\(320\) −26.3363 −1.47224
\(321\) 0.0568876 0.00317515
\(322\) 3.79605 0.211545
\(323\) −28.8301 −1.60415
\(324\) 18.7015 1.03897
\(325\) −2.10109 −0.116547
\(326\) 7.27915 0.403155
\(327\) −35.7387 −1.97635
\(328\) 18.4857 1.02070
\(329\) −2.16521 −0.119372
\(330\) −57.6025 −3.17091
\(331\) −8.27138 −0.454636 −0.227318 0.973821i \(-0.572996\pi\)
−0.227318 + 0.973821i \(0.572996\pi\)
\(332\) 44.0180 2.41580
\(333\) −39.6436 −2.17246
\(334\) −3.40139 −0.186116
\(335\) 7.36678 0.402490
\(336\) −0.830055 −0.0452832
\(337\) 11.9036 0.648429 0.324215 0.945984i \(-0.394900\pi\)
0.324215 + 0.945984i \(0.394900\pi\)
\(338\) 10.4198 0.566762
\(339\) −7.45829 −0.405079
\(340\) 49.3920 2.67866
\(341\) 18.8138 1.01883
\(342\) 52.1693 2.82099
\(343\) 8.37826 0.452384
\(344\) 26.3292 1.41957
\(345\) 16.2116 0.872803
\(346\) 2.32220 0.124842
\(347\) 4.21986 0.226534 0.113267 0.993565i \(-0.463868\pi\)
0.113267 + 0.993565i \(0.463868\pi\)
\(348\) −28.6030 −1.53328
\(349\) −5.15735 −0.276067 −0.138033 0.990428i \(-0.544078\pi\)
−0.138033 + 0.990428i \(0.544078\pi\)
\(350\) −1.02461 −0.0547680
\(351\) 22.2697 1.18867
\(352\) 21.0102 1.11985
\(353\) −12.6771 −0.674734 −0.337367 0.941373i \(-0.609536\pi\)
−0.337367 + 0.941373i \(0.609536\pi\)
\(354\) −55.5036 −2.94998
\(355\) −6.87994 −0.365149
\(356\) 62.3122 3.30254
\(357\) −12.9118 −0.683366
\(358\) −8.88459 −0.469565
\(359\) −21.9341 −1.15764 −0.578818 0.815457i \(-0.696486\pi\)
−0.578818 + 0.815457i \(0.696486\pi\)
\(360\) −35.8045 −1.88706
\(361\) −2.76933 −0.145754
\(362\) 30.9658 1.62753
\(363\) 17.2643 0.906139
\(364\) −5.97968 −0.313420
\(365\) −7.61589 −0.398634
\(366\) −68.1445 −3.56197
\(367\) 15.1586 0.791275 0.395637 0.918407i \(-0.370524\pi\)
0.395637 + 0.918407i \(0.370524\pi\)
\(368\) 1.22905 0.0640688
\(369\) −33.5573 −1.74692
\(370\) 33.7958 1.75696
\(371\) 0.615068 0.0319327
\(372\) 44.8151 2.32356
\(373\) −30.7246 −1.59086 −0.795430 0.606046i \(-0.792755\pi\)
−0.795430 + 0.606046i \(0.792755\pi\)
\(374\) −67.9307 −3.51261
\(375\) −34.7163 −1.79274
\(376\) −10.8702 −0.560589
\(377\) −8.51435 −0.438511
\(378\) 10.8600 0.558579
\(379\) −11.6797 −0.599947 −0.299973 0.953948i \(-0.596978\pi\)
−0.299973 + 0.953948i \(0.596978\pi\)
\(380\) −27.8066 −1.42645
\(381\) −12.3191 −0.631125
\(382\) −30.7696 −1.57431
\(383\) 11.1127 0.567833 0.283916 0.958849i \(-0.408366\pi\)
0.283916 + 0.958849i \(0.408366\pi\)
\(384\) 56.2821 2.87213
\(385\) −5.22807 −0.266447
\(386\) 47.8892 2.43750
\(387\) −47.7956 −2.42959
\(388\) 36.3829 1.84706
\(389\) −13.7518 −0.697243 −0.348621 0.937264i \(-0.613350\pi\)
−0.348621 + 0.937264i \(0.613350\pi\)
\(390\) −40.8441 −2.06822
\(391\) 19.1184 0.966858
\(392\) 20.4470 1.03273
\(393\) 9.76947 0.492804
\(394\) 41.2986 2.08059
\(395\) 31.2038 1.57004
\(396\) 76.8561 3.86216
\(397\) 3.62482 0.181924 0.0909622 0.995854i \(-0.471006\pi\)
0.0909622 + 0.995854i \(0.471006\pi\)
\(398\) −55.9422 −2.80413
\(399\) 7.26906 0.363908
\(400\) −0.331741 −0.0165871
\(401\) 32.7071 1.63331 0.816657 0.577124i \(-0.195825\pi\)
0.816657 + 0.577124i \(0.195825\pi\)
\(402\) −24.1343 −1.20371
\(403\) 13.3403 0.664527
\(404\) 16.8284 0.837245
\(405\) 11.5939 0.576103
\(406\) −4.15210 −0.206065
\(407\) −29.0613 −1.44051
\(408\) −64.8224 −3.20919
\(409\) 33.2077 1.64202 0.821008 0.570916i \(-0.193412\pi\)
0.821008 + 0.570916i \(0.193412\pi\)
\(410\) 28.6073 1.41281
\(411\) 15.7245 0.775632
\(412\) 10.3609 0.510446
\(413\) −5.03757 −0.247883
\(414\) −34.5955 −1.70028
\(415\) 27.2886 1.33955
\(416\) 14.8977 0.730418
\(417\) −34.0794 −1.66888
\(418\) 38.2434 1.87055
\(419\) −36.5674 −1.78644 −0.893218 0.449624i \(-0.851558\pi\)
−0.893218 + 0.449624i \(0.851558\pi\)
\(420\) −12.4534 −0.607665
\(421\) 33.9220 1.65326 0.826628 0.562748i \(-0.190256\pi\)
0.826628 + 0.562748i \(0.190256\pi\)
\(422\) −10.7079 −0.521252
\(423\) 19.7328 0.959443
\(424\) 3.08788 0.149961
\(425\) −5.16036 −0.250314
\(426\) 22.5393 1.09203
\(427\) −6.18488 −0.299307
\(428\) 0.0647059 0.00312768
\(429\) 35.1222 1.69572
\(430\) 40.7453 1.96491
\(431\) −8.86244 −0.426889 −0.213444 0.976955i \(-0.568468\pi\)
−0.213444 + 0.976955i \(0.568468\pi\)
\(432\) 3.51616 0.169172
\(433\) −2.22454 −0.106905 −0.0534523 0.998570i \(-0.517023\pi\)
−0.0534523 + 0.998570i \(0.517023\pi\)
\(434\) 6.50552 0.312275
\(435\) −17.7322 −0.850194
\(436\) −40.6504 −1.94680
\(437\) −10.7632 −0.514874
\(438\) 24.9504 1.19218
\(439\) −39.3239 −1.87683 −0.938413 0.345516i \(-0.887704\pi\)
−0.938413 + 0.345516i \(0.887704\pi\)
\(440\) −26.2470 −1.25127
\(441\) −37.1176 −1.76751
\(442\) −48.1675 −2.29110
\(443\) −6.63160 −0.315077 −0.157538 0.987513i \(-0.550356\pi\)
−0.157538 + 0.987513i \(0.550356\pi\)
\(444\) −69.2249 −3.28527
\(445\) 38.6300 1.83124
\(446\) −2.09494 −0.0991984
\(447\) −34.8273 −1.64727
\(448\) 7.83090 0.369975
\(449\) −9.95113 −0.469623 −0.234812 0.972041i \(-0.575447\pi\)
−0.234812 + 0.972041i \(0.575447\pi\)
\(450\) 9.33790 0.440193
\(451\) −24.5996 −1.15835
\(452\) −8.48332 −0.399022
\(453\) 2.93351 0.137828
\(454\) 20.3132 0.953344
\(455\) −3.70706 −0.173790
\(456\) 36.4935 1.70897
\(457\) 15.6359 0.731417 0.365708 0.930730i \(-0.380827\pi\)
0.365708 + 0.930730i \(0.380827\pi\)
\(458\) −18.2074 −0.850778
\(459\) 54.6953 2.55296
\(460\) 18.4396 0.859753
\(461\) −18.6211 −0.867272 −0.433636 0.901088i \(-0.642770\pi\)
−0.433636 + 0.901088i \(0.642770\pi\)
\(462\) 17.1277 0.796851
\(463\) −40.5799 −1.88591 −0.942954 0.332922i \(-0.891965\pi\)
−0.942954 + 0.332922i \(0.891965\pi\)
\(464\) −1.34433 −0.0624091
\(465\) 27.7828 1.28840
\(466\) 50.7111 2.34915
\(467\) −2.85374 −0.132055 −0.0660276 0.997818i \(-0.521033\pi\)
−0.0660276 + 0.997818i \(0.521033\pi\)
\(468\) 54.4962 2.51909
\(469\) −2.19046 −0.101146
\(470\) −16.8220 −0.775943
\(471\) −28.4104 −1.30908
\(472\) −25.2906 −1.16409
\(473\) −35.0372 −1.61101
\(474\) −102.227 −4.69544
\(475\) 2.90516 0.133298
\(476\) −14.6864 −0.673148
\(477\) −5.60546 −0.256657
\(478\) −14.3322 −0.655540
\(479\) −15.8004 −0.721938 −0.360969 0.932578i \(-0.617554\pi\)
−0.360969 + 0.932578i \(0.617554\pi\)
\(480\) 31.0262 1.41615
\(481\) −20.6064 −0.939572
\(482\) 27.3266 1.24469
\(483\) −4.82040 −0.219336
\(484\) 19.6370 0.892590
\(485\) 22.5554 1.02419
\(486\) 14.9872 0.679835
\(487\) 18.5775 0.841825 0.420912 0.907101i \(-0.361710\pi\)
0.420912 + 0.907101i \(0.361710\pi\)
\(488\) −31.0505 −1.40559
\(489\) −9.24341 −0.418002
\(490\) 31.6424 1.42946
\(491\) −26.9268 −1.21519 −0.607595 0.794247i \(-0.707866\pi\)
−0.607595 + 0.794247i \(0.707866\pi\)
\(492\) −58.5971 −2.64176
\(493\) −20.9116 −0.941812
\(494\) 27.1172 1.22006
\(495\) 47.6464 2.14155
\(496\) 2.10630 0.0945758
\(497\) 2.04570 0.0917621
\(498\) −89.4003 −4.00612
\(499\) 17.2411 0.771817 0.385909 0.922537i \(-0.373888\pi\)
0.385909 + 0.922537i \(0.373888\pi\)
\(500\) −39.4875 −1.76593
\(501\) 4.31925 0.192970
\(502\) −15.4826 −0.691021
\(503\) 12.2494 0.546175 0.273087 0.961989i \(-0.411955\pi\)
0.273087 + 0.961989i \(0.411955\pi\)
\(504\) 10.6462 0.474220
\(505\) 10.4327 0.464247
\(506\) −25.3607 −1.12742
\(507\) −13.2315 −0.587634
\(508\) −14.0121 −0.621688
\(509\) −13.9608 −0.618801 −0.309401 0.950932i \(-0.600128\pi\)
−0.309401 + 0.950932i \(0.600128\pi\)
\(510\) −100.315 −4.44202
\(511\) 2.26453 0.100177
\(512\) 5.19330 0.229514
\(513\) −30.7922 −1.35951
\(514\) −7.47733 −0.329811
\(515\) 6.42318 0.283039
\(516\) −83.4598 −3.67411
\(517\) 14.4654 0.636188
\(518\) −10.0489 −0.441524
\(519\) −2.94885 −0.129440
\(520\) −18.6109 −0.816142
\(521\) −0.304817 −0.0133543 −0.00667714 0.999978i \(-0.502125\pi\)
−0.00667714 + 0.999978i \(0.502125\pi\)
\(522\) 37.8405 1.65623
\(523\) −8.56720 −0.374617 −0.187309 0.982301i \(-0.559976\pi\)
−0.187309 + 0.982301i \(0.559976\pi\)
\(524\) 11.1121 0.485436
\(525\) 1.30111 0.0567849
\(526\) 35.6608 1.55488
\(527\) 32.7643 1.42724
\(528\) 5.54546 0.241335
\(529\) −15.8625 −0.689674
\(530\) 4.77860 0.207569
\(531\) 45.9103 1.99234
\(532\) 8.26808 0.358467
\(533\) −17.4428 −0.755533
\(534\) −126.556 −5.47660
\(535\) 0.0401140 0.00173428
\(536\) −10.9970 −0.474996
\(537\) 11.2821 0.486858
\(538\) −61.4077 −2.64748
\(539\) −27.2096 −1.17200
\(540\) 52.7535 2.27015
\(541\) 36.5428 1.57110 0.785550 0.618799i \(-0.212380\pi\)
0.785550 + 0.618799i \(0.212380\pi\)
\(542\) −13.8121 −0.593279
\(543\) −39.3219 −1.68746
\(544\) 36.5893 1.56875
\(545\) −25.2010 −1.07949
\(546\) 12.1447 0.519745
\(547\) 23.6817 1.01255 0.506277 0.862371i \(-0.331021\pi\)
0.506277 + 0.862371i \(0.331021\pi\)
\(548\) 17.8856 0.764035
\(549\) 56.3663 2.40566
\(550\) 6.84527 0.291883
\(551\) 11.7728 0.501536
\(552\) −24.2003 −1.03003
\(553\) −9.27824 −0.394551
\(554\) −10.6823 −0.453849
\(555\) −42.9155 −1.82166
\(556\) −38.7631 −1.64392
\(557\) 5.28996 0.224143 0.112071 0.993700i \(-0.464251\pi\)
0.112071 + 0.993700i \(0.464251\pi\)
\(558\) −59.2885 −2.50988
\(559\) −24.8438 −1.05078
\(560\) −0.585309 −0.0247338
\(561\) 86.2617 3.64197
\(562\) 19.5273 0.823709
\(563\) −32.6367 −1.37547 −0.687737 0.725960i \(-0.741396\pi\)
−0.687737 + 0.725960i \(0.741396\pi\)
\(564\) 34.4571 1.45091
\(565\) −5.25918 −0.221255
\(566\) −28.3067 −1.18982
\(567\) −3.44735 −0.144775
\(568\) 10.2702 0.430929
\(569\) 11.3929 0.477614 0.238807 0.971067i \(-0.423244\pi\)
0.238807 + 0.971067i \(0.423244\pi\)
\(570\) 56.4750 2.36548
\(571\) 10.0116 0.418973 0.209486 0.977812i \(-0.432821\pi\)
0.209486 + 0.977812i \(0.432821\pi\)
\(572\) 39.9492 1.67036
\(573\) 39.0727 1.63229
\(574\) −8.50616 −0.355040
\(575\) −1.92653 −0.0803418
\(576\) −71.3675 −2.97364
\(577\) 27.8487 1.15936 0.579678 0.814845i \(-0.303178\pi\)
0.579678 + 0.814845i \(0.303178\pi\)
\(578\) −79.0295 −3.28719
\(579\) −60.8120 −2.52726
\(580\) −20.1692 −0.837482
\(581\) −8.11408 −0.336629
\(582\) −73.8936 −3.06299
\(583\) −4.10916 −0.170184
\(584\) 11.3688 0.470446
\(585\) 33.7846 1.39682
\(586\) −6.19577 −0.255945
\(587\) 39.2875 1.62157 0.810784 0.585346i \(-0.199041\pi\)
0.810784 + 0.585346i \(0.199041\pi\)
\(588\) −64.8141 −2.67289
\(589\) −18.4456 −0.760036
\(590\) −39.1381 −1.61129
\(591\) −52.4430 −2.15722
\(592\) −3.25356 −0.133720
\(593\) 11.4661 0.470857 0.235429 0.971892i \(-0.424351\pi\)
0.235429 + 0.971892i \(0.424351\pi\)
\(594\) −72.5538 −2.97692
\(595\) −9.10471 −0.373257
\(596\) −39.6137 −1.62264
\(597\) 71.0381 2.90739
\(598\) −17.9825 −0.735359
\(599\) 18.8914 0.771883 0.385942 0.922523i \(-0.373877\pi\)
0.385942 + 0.922523i \(0.373877\pi\)
\(600\) 6.53206 0.266670
\(601\) 19.0131 0.775560 0.387780 0.921752i \(-0.373242\pi\)
0.387780 + 0.921752i \(0.373242\pi\)
\(602\) −12.1153 −0.493783
\(603\) 19.9629 0.812952
\(604\) 3.33667 0.135767
\(605\) 12.1738 0.494936
\(606\) −34.1784 −1.38840
\(607\) −2.96450 −0.120326 −0.0601628 0.998189i \(-0.519162\pi\)
−0.0601628 + 0.998189i \(0.519162\pi\)
\(608\) −20.5989 −0.835397
\(609\) 5.27254 0.213654
\(610\) −48.0517 −1.94556
\(611\) 10.2570 0.414953
\(612\) 133.845 5.41037
\(613\) −3.82138 −0.154344 −0.0771720 0.997018i \(-0.524589\pi\)
−0.0771720 + 0.997018i \(0.524589\pi\)
\(614\) 48.1965 1.94505
\(615\) −36.3269 −1.46484
\(616\) 7.80434 0.314446
\(617\) 44.0056 1.77160 0.885799 0.464069i \(-0.153611\pi\)
0.885799 + 0.464069i \(0.153611\pi\)
\(618\) −21.0430 −0.846472
\(619\) −12.8987 −0.518442 −0.259221 0.965818i \(-0.583466\pi\)
−0.259221 + 0.965818i \(0.583466\pi\)
\(620\) 31.6012 1.26913
\(621\) 20.4195 0.819407
\(622\) 28.3286 1.13587
\(623\) −11.4864 −0.460191
\(624\) 3.93211 0.157410
\(625\) −20.8744 −0.834978
\(626\) −27.7304 −1.10833
\(627\) −48.5633 −1.93943
\(628\) −32.3150 −1.28951
\(629\) −50.6103 −2.01797
\(630\) 16.4754 0.656394
\(631\) −36.1067 −1.43739 −0.718693 0.695328i \(-0.755259\pi\)
−0.718693 + 0.695328i \(0.755259\pi\)
\(632\) −46.5804 −1.85287
\(633\) 13.5974 0.540448
\(634\) 17.1158 0.679756
\(635\) −8.68673 −0.344722
\(636\) −9.78815 −0.388126
\(637\) −19.2935 −0.764435
\(638\) 27.7395 1.09822
\(639\) −18.6436 −0.737530
\(640\) 39.6870 1.56877
\(641\) 34.6124 1.36711 0.683554 0.729900i \(-0.260433\pi\)
0.683554 + 0.729900i \(0.260433\pi\)
\(642\) −0.131417 −0.00518663
\(643\) 37.1047 1.46327 0.731633 0.681699i \(-0.238758\pi\)
0.731633 + 0.681699i \(0.238758\pi\)
\(644\) −5.48289 −0.216056
\(645\) −51.7403 −2.03727
\(646\) 66.6011 2.62038
\(647\) −7.51341 −0.295383 −0.147691 0.989033i \(-0.547184\pi\)
−0.147691 + 0.989033i \(0.547184\pi\)
\(648\) −17.3070 −0.679885
\(649\) 33.6551 1.32108
\(650\) 4.85377 0.190380
\(651\) −8.26102 −0.323775
\(652\) −10.5138 −0.411751
\(653\) 7.22899 0.282892 0.141446 0.989946i \(-0.454825\pi\)
0.141446 + 0.989946i \(0.454825\pi\)
\(654\) 82.5608 3.22838
\(655\) 6.88889 0.269171
\(656\) −2.75405 −0.107528
\(657\) −20.6380 −0.805163
\(658\) 5.00191 0.194995
\(659\) −38.2219 −1.48891 −0.744457 0.667671i \(-0.767291\pi\)
−0.744457 + 0.667671i \(0.767291\pi\)
\(660\) 83.1992 3.23853
\(661\) 19.4878 0.757987 0.378993 0.925399i \(-0.376270\pi\)
0.378993 + 0.925399i \(0.376270\pi\)
\(662\) 19.1079 0.742650
\(663\) 61.1654 2.37547
\(664\) −40.7359 −1.58086
\(665\) 5.12574 0.198768
\(666\) 91.5816 3.54871
\(667\) −7.80698 −0.302288
\(668\) 4.91287 0.190085
\(669\) 2.66026 0.102852
\(670\) −17.0182 −0.657469
\(671\) 41.3201 1.59514
\(672\) −9.22543 −0.355879
\(673\) −33.7697 −1.30173 −0.650864 0.759194i \(-0.725593\pi\)
−0.650864 + 0.759194i \(0.725593\pi\)
\(674\) −27.4987 −1.05921
\(675\) −5.51156 −0.212140
\(676\) −15.0500 −0.578847
\(677\) 10.1674 0.390765 0.195383 0.980727i \(-0.437405\pi\)
0.195383 + 0.980727i \(0.437405\pi\)
\(678\) 17.2296 0.661698
\(679\) −6.70667 −0.257378
\(680\) −45.7092 −1.75287
\(681\) −25.7946 −0.988452
\(682\) −43.4622 −1.66426
\(683\) −45.0819 −1.72501 −0.862506 0.506046i \(-0.831107\pi\)
−0.862506 + 0.506046i \(0.831107\pi\)
\(684\) −75.3518 −2.88115
\(685\) 11.0881 0.423653
\(686\) −19.3548 −0.738971
\(687\) 23.1207 0.882109
\(688\) −3.92260 −0.149548
\(689\) −2.91368 −0.111002
\(690\) −37.4508 −1.42573
\(691\) 18.1268 0.689577 0.344789 0.938680i \(-0.387951\pi\)
0.344789 + 0.938680i \(0.387951\pi\)
\(692\) −3.35412 −0.127505
\(693\) −14.1673 −0.538172
\(694\) −9.74840 −0.370044
\(695\) −24.0309 −0.911545
\(696\) 26.4702 1.00335
\(697\) −42.8404 −1.62269
\(698\) 11.9141 0.450956
\(699\) −64.3955 −2.43566
\(700\) 1.47992 0.0559358
\(701\) 5.44040 0.205481 0.102741 0.994708i \(-0.467239\pi\)
0.102741 + 0.994708i \(0.467239\pi\)
\(702\) −51.4457 −1.94169
\(703\) 28.4924 1.07461
\(704\) −52.3169 −1.97177
\(705\) 21.3614 0.804518
\(706\) 29.2857 1.10218
\(707\) −3.10208 −0.116666
\(708\) 80.1677 3.01289
\(709\) 40.0145 1.50278 0.751388 0.659860i \(-0.229384\pi\)
0.751388 + 0.659860i \(0.229384\pi\)
\(710\) 15.8935 0.596473
\(711\) 84.5579 3.17117
\(712\) −57.6660 −2.16113
\(713\) 12.2320 0.458092
\(714\) 29.8279 1.11628
\(715\) 24.7662 0.926205
\(716\) 12.8326 0.479578
\(717\) 18.1997 0.679682
\(718\) 50.6704 1.89100
\(719\) −31.7326 −1.18343 −0.591713 0.806149i \(-0.701548\pi\)
−0.591713 + 0.806149i \(0.701548\pi\)
\(720\) 5.33426 0.198796
\(721\) −1.90989 −0.0711278
\(722\) 6.39749 0.238090
\(723\) −34.7006 −1.29053
\(724\) −44.7261 −1.66223
\(725\) 2.10723 0.0782606
\(726\) −39.8826 −1.48018
\(727\) −46.3433 −1.71878 −0.859388 0.511323i \(-0.829155\pi\)
−0.859388 + 0.511323i \(0.829155\pi\)
\(728\) 5.53382 0.205097
\(729\) −35.8460 −1.32763
\(730\) 17.5937 0.651170
\(731\) −61.0175 −2.25681
\(732\) 98.4258 3.63792
\(733\) 5.21998 0.192804 0.0964021 0.995342i \(-0.469267\pi\)
0.0964021 + 0.995342i \(0.469267\pi\)
\(734\) −35.0183 −1.29255
\(735\) −40.1811 −1.48210
\(736\) 13.6600 0.503513
\(737\) 14.6341 0.539053
\(738\) 77.5215 2.85361
\(739\) 40.8166 1.50146 0.750731 0.660608i \(-0.229701\pi\)
0.750731 + 0.660608i \(0.229701\pi\)
\(740\) −48.8136 −1.79442
\(741\) −34.4347 −1.26499
\(742\) −1.42088 −0.0521622
\(743\) 6.96765 0.255618 0.127809 0.991799i \(-0.459206\pi\)
0.127809 + 0.991799i \(0.459206\pi\)
\(744\) −41.4736 −1.52050
\(745\) −24.5583 −0.899745
\(746\) 70.9776 2.59868
\(747\) 73.9483 2.70563
\(748\) 98.1170 3.58751
\(749\) −0.0119276 −0.000435825 0
\(750\) 80.1989 2.92845
\(751\) −18.8514 −0.687896 −0.343948 0.938989i \(-0.611764\pi\)
−0.343948 + 0.938989i \(0.611764\pi\)
\(752\) 1.61948 0.0590563
\(753\) 19.6605 0.716469
\(754\) 19.6692 0.716310
\(755\) 2.06855 0.0752821
\(756\) −15.6859 −0.570490
\(757\) −36.7389 −1.33530 −0.667650 0.744475i \(-0.732700\pi\)
−0.667650 + 0.744475i \(0.732700\pi\)
\(758\) 26.9816 0.980016
\(759\) 32.2043 1.16894
\(760\) 25.7332 0.933442
\(761\) −30.6593 −1.11140 −0.555699 0.831384i \(-0.687549\pi\)
−0.555699 + 0.831384i \(0.687549\pi\)
\(762\) 28.4586 1.03095
\(763\) 7.49332 0.271276
\(764\) 44.4427 1.60788
\(765\) 82.9764 3.00002
\(766\) −25.6717 −0.927557
\(767\) 23.8638 0.861672
\(768\) −55.3212 −1.99623
\(769\) −21.1643 −0.763203 −0.381601 0.924327i \(-0.624627\pi\)
−0.381601 + 0.924327i \(0.624627\pi\)
\(770\) 12.0775 0.435243
\(771\) 9.49508 0.341957
\(772\) −69.1697 −2.48947
\(773\) 35.3700 1.27217 0.636085 0.771619i \(-0.280553\pi\)
0.636085 + 0.771619i \(0.280553\pi\)
\(774\) 110.414 3.96874
\(775\) −3.30161 −0.118597
\(776\) −33.6701 −1.20869
\(777\) 12.7606 0.457784
\(778\) 31.7683 1.13895
\(779\) 24.1181 0.864122
\(780\) 58.9940 2.11232
\(781\) −13.6670 −0.489042
\(782\) −44.1658 −1.57937
\(783\) −22.3348 −0.798181
\(784\) −3.04625 −0.108795
\(785\) −20.0335 −0.715026
\(786\) −22.5687 −0.804998
\(787\) −16.7221 −0.596078 −0.298039 0.954554i \(-0.596333\pi\)
−0.298039 + 0.954554i \(0.596333\pi\)
\(788\) −59.6505 −2.12496
\(789\) −45.2838 −1.61214
\(790\) −72.0847 −2.56466
\(791\) 1.56378 0.0556015
\(792\) −71.1255 −2.52733
\(793\) 29.2988 1.04043
\(794\) −8.37378 −0.297174
\(795\) −6.06810 −0.215213
\(796\) 80.8012 2.86392
\(797\) 24.1425 0.855172 0.427586 0.903975i \(-0.359364\pi\)
0.427586 + 0.903975i \(0.359364\pi\)
\(798\) −16.7924 −0.594446
\(799\) 25.1916 0.891214
\(800\) −3.68705 −0.130357
\(801\) 104.682 3.69875
\(802\) −75.5574 −2.66802
\(803\) −15.1289 −0.533888
\(804\) 34.8588 1.22938
\(805\) −3.39908 −0.119802
\(806\) −30.8177 −1.08551
\(807\) 77.9785 2.74497
\(808\) −15.5736 −0.547879
\(809\) −28.8227 −1.01335 −0.506677 0.862136i \(-0.669126\pi\)
−0.506677 + 0.862136i \(0.669126\pi\)
\(810\) −26.7832 −0.941067
\(811\) −27.7049 −0.972850 −0.486425 0.873722i \(-0.661699\pi\)
−0.486425 + 0.873722i \(0.661699\pi\)
\(812\) 5.99717 0.210460
\(813\) 17.5392 0.615128
\(814\) 67.1351 2.35308
\(815\) −6.51795 −0.228314
\(816\) 9.65744 0.338078
\(817\) 34.3514 1.20180
\(818\) −76.7140 −2.68224
\(819\) −10.0456 −0.351022
\(820\) −41.3195 −1.44294
\(821\) 27.8358 0.971476 0.485738 0.874104i \(-0.338551\pi\)
0.485738 + 0.874104i \(0.338551\pi\)
\(822\) −36.3255 −1.26700
\(823\) 36.2378 1.26317 0.631585 0.775307i \(-0.282405\pi\)
0.631585 + 0.775307i \(0.282405\pi\)
\(824\) −9.58837 −0.334027
\(825\) −8.69246 −0.302633
\(826\) 11.6374 0.404918
\(827\) 6.28777 0.218647 0.109324 0.994006i \(-0.465132\pi\)
0.109324 + 0.994006i \(0.465132\pi\)
\(828\) 49.9687 1.73653
\(829\) −9.43320 −0.327629 −0.163814 0.986491i \(-0.552380\pi\)
−0.163814 + 0.986491i \(0.552380\pi\)
\(830\) −63.0402 −2.18816
\(831\) 13.5649 0.470562
\(832\) −37.0963 −1.28608
\(833\) −47.3856 −1.64181
\(834\) 78.7277 2.72612
\(835\) 3.04570 0.105401
\(836\) −55.2376 −1.91043
\(837\) 34.9942 1.20958
\(838\) 84.4753 2.91815
\(839\) 45.5282 1.57181 0.785904 0.618348i \(-0.212198\pi\)
0.785904 + 0.618348i \(0.212198\pi\)
\(840\) 11.5249 0.397646
\(841\) −20.4607 −0.705543
\(842\) −78.3640 −2.70060
\(843\) −24.7967 −0.854044
\(844\) 15.4662 0.532367
\(845\) −9.33016 −0.320967
\(846\) −45.5853 −1.56725
\(847\) −3.61979 −0.124378
\(848\) −0.460042 −0.0157979
\(849\) 35.9452 1.23363
\(850\) 11.9211 0.408889
\(851\) −18.8945 −0.647694
\(852\) −32.5551 −1.11532
\(853\) 19.0193 0.651209 0.325604 0.945506i \(-0.394432\pi\)
0.325604 + 0.945506i \(0.394432\pi\)
\(854\) 14.2878 0.488920
\(855\) −46.7138 −1.59758
\(856\) −0.0598812 −0.00204670
\(857\) −51.0851 −1.74504 −0.872518 0.488583i \(-0.837514\pi\)
−0.872518 + 0.488583i \(0.837514\pi\)
\(858\) −81.1366 −2.76996
\(859\) −43.5228 −1.48498 −0.742490 0.669857i \(-0.766355\pi\)
−0.742490 + 0.669857i \(0.766355\pi\)
\(860\) −58.8513 −2.00681
\(861\) 10.8015 0.368115
\(862\) 20.4733 0.697325
\(863\) 3.83588 0.130575 0.0652875 0.997866i \(-0.479204\pi\)
0.0652875 + 0.997866i \(0.479204\pi\)
\(864\) 39.0795 1.32951
\(865\) −2.07936 −0.0707005
\(866\) 5.13896 0.174629
\(867\) 100.355 3.40825
\(868\) −9.39637 −0.318934
\(869\) 61.9863 2.10274
\(870\) 40.9636 1.38880
\(871\) 10.3766 0.351596
\(872\) 37.6194 1.27395
\(873\) 61.1217 2.06866
\(874\) 24.8643 0.841049
\(875\) 7.27895 0.246073
\(876\) −36.0376 −1.21760
\(877\) 12.2481 0.413588 0.206794 0.978385i \(-0.433697\pi\)
0.206794 + 0.978385i \(0.433697\pi\)
\(878\) 90.8430 3.06580
\(879\) 7.86768 0.265370
\(880\) 3.91035 0.131818
\(881\) 5.48627 0.184837 0.0924186 0.995720i \(-0.470540\pi\)
0.0924186 + 0.995720i \(0.470540\pi\)
\(882\) 85.7464 2.88723
\(883\) 0.928178 0.0312357 0.0156178 0.999878i \(-0.495028\pi\)
0.0156178 + 0.999878i \(0.495028\pi\)
\(884\) 69.5717 2.33995
\(885\) 49.6994 1.67063
\(886\) 15.3198 0.514679
\(887\) −31.1138 −1.04470 −0.522349 0.852732i \(-0.674944\pi\)
−0.522349 + 0.852732i \(0.674944\pi\)
\(888\) 64.0633 2.14982
\(889\) 2.58294 0.0866289
\(890\) −89.2401 −2.99134
\(891\) 23.0311 0.771572
\(892\) 3.02587 0.101314
\(893\) −14.1823 −0.474592
\(894\) 80.4553 2.69083
\(895\) 7.95550 0.265923
\(896\) −11.8007 −0.394232
\(897\) 22.8350 0.762440
\(898\) 22.9884 0.767131
\(899\) −13.3793 −0.446225
\(900\) −13.4874 −0.449579
\(901\) −7.15612 −0.238405
\(902\) 56.8282 1.89217
\(903\) 15.3846 0.511968
\(904\) 7.85078 0.261113
\(905\) −27.7276 −0.921698
\(906\) −6.77677 −0.225143
\(907\) −54.0049 −1.79320 −0.896601 0.442838i \(-0.853972\pi\)
−0.896601 + 0.442838i \(0.853972\pi\)
\(908\) −29.3397 −0.973672
\(909\) 28.2710 0.937690
\(910\) 8.56377 0.283886
\(911\) 28.0961 0.930866 0.465433 0.885083i \(-0.345899\pi\)
0.465433 + 0.885083i \(0.345899\pi\)
\(912\) −5.43691 −0.180034
\(913\) 54.2088 1.79405
\(914\) −36.1209 −1.19477
\(915\) 61.0184 2.01721
\(916\) 26.2983 0.868919
\(917\) −2.04836 −0.0676429
\(918\) −126.353 −4.17027
\(919\) 16.3313 0.538719 0.269359 0.963040i \(-0.413188\pi\)
0.269359 + 0.963040i \(0.413188\pi\)
\(920\) −17.0647 −0.562607
\(921\) −61.2022 −2.01668
\(922\) 43.0171 1.41669
\(923\) −9.69081 −0.318977
\(924\) −24.7387 −0.813843
\(925\) 5.09993 0.167685
\(926\) 93.7446 3.08064
\(927\) 17.4059 0.571684
\(928\) −14.9412 −0.490470
\(929\) −57.9122 −1.90004 −0.950019 0.312192i \(-0.898937\pi\)
−0.950019 + 0.312192i \(0.898937\pi\)
\(930\) −64.1818 −2.10460
\(931\) 26.6770 0.874304
\(932\) −73.2456 −2.39924
\(933\) −35.9730 −1.17770
\(934\) 6.59249 0.215713
\(935\) 60.8270 1.98925
\(936\) −50.4328 −1.64845
\(937\) 27.5565 0.900231 0.450116 0.892970i \(-0.351383\pi\)
0.450116 + 0.892970i \(0.351383\pi\)
\(938\) 5.06023 0.165222
\(939\) 35.2135 1.14915
\(940\) 24.2972 0.792489
\(941\) 41.3882 1.34922 0.674608 0.738176i \(-0.264313\pi\)
0.674608 + 0.738176i \(0.264313\pi\)
\(942\) 65.6317 2.13839
\(943\) −15.9937 −0.520826
\(944\) 3.76787 0.122634
\(945\) −9.72435 −0.316333
\(946\) 80.9403 2.63160
\(947\) 36.9495 1.20070 0.600348 0.799739i \(-0.295029\pi\)
0.600348 + 0.799739i \(0.295029\pi\)
\(948\) 147.653 4.79556
\(949\) −10.7275 −0.348228
\(950\) −6.71129 −0.217743
\(951\) −21.7345 −0.704789
\(952\) 13.5913 0.440497
\(953\) 25.1874 0.815899 0.407949 0.913005i \(-0.366244\pi\)
0.407949 + 0.913005i \(0.366244\pi\)
\(954\) 12.9493 0.419250
\(955\) 27.5519 0.891560
\(956\) 20.7010 0.669519
\(957\) −35.2249 −1.13866
\(958\) 36.5009 1.17929
\(959\) −3.29695 −0.106464
\(960\) −77.2576 −2.49348
\(961\) −10.0373 −0.323783
\(962\) 47.6034 1.53480
\(963\) 0.108703 0.00350291
\(964\) −39.4697 −1.27123
\(965\) −42.8813 −1.38040
\(966\) 11.1357 0.358286
\(967\) −48.2200 −1.55065 −0.775326 0.631562i \(-0.782414\pi\)
−0.775326 + 0.631562i \(0.782414\pi\)
\(968\) −18.1728 −0.584095
\(969\) −84.5733 −2.71688
\(970\) −52.1057 −1.67301
\(971\) −7.70263 −0.247189 −0.123595 0.992333i \(-0.539442\pi\)
−0.123595 + 0.992333i \(0.539442\pi\)
\(972\) −21.6471 −0.694331
\(973\) 7.14542 0.229072
\(974\) −42.9162 −1.37512
\(975\) −6.16355 −0.197392
\(976\) 4.62600 0.148075
\(977\) 43.6045 1.39503 0.697516 0.716569i \(-0.254289\pi\)
0.697516 + 0.716569i \(0.254289\pi\)
\(978\) 21.3534 0.682808
\(979\) 76.7384 2.45257
\(980\) −45.7034 −1.45994
\(981\) −68.2909 −2.18036
\(982\) 62.2043 1.98502
\(983\) −31.0113 −0.989106 −0.494553 0.869147i \(-0.664668\pi\)
−0.494553 + 0.869147i \(0.664668\pi\)
\(984\) 54.2279 1.72872
\(985\) −36.9799 −1.17828
\(986\) 48.3084 1.53845
\(987\) −6.35167 −0.202176
\(988\) −39.1673 −1.24608
\(989\) −22.7798 −0.724356
\(990\) −110.069 −3.49823
\(991\) −46.7686 −1.48565 −0.742827 0.669483i \(-0.766516\pi\)
−0.742827 + 0.669483i \(0.766516\pi\)
\(992\) 23.4099 0.743266
\(993\) −24.2641 −0.769999
\(994\) −4.72582 −0.149894
\(995\) 50.0921 1.58803
\(996\) 129.127 4.09155
\(997\) 49.3844 1.56402 0.782009 0.623267i \(-0.214195\pi\)
0.782009 + 0.623267i \(0.214195\pi\)
\(998\) −39.8291 −1.26077
\(999\) −54.0547 −1.71022
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 \(a_p\))