Properties

Label 4019.2.a.b.1.4
Level 4019
Weight 2
Character 4019.1
Self dual Yes
Analytic conductor 32.092
Analytic rank 0
Dimension 186
CM No

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Newspace parameters

Level: \( N \) = \( 4019 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4019.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0918765724\)
Analytic rank: \(0\)
Dimension: \(186\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 4019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.77200 q^{2}\) \(-0.494167 q^{3}\) \(+5.68400 q^{4}\) \(+0.905775 q^{5}\) \(+1.36983 q^{6}\) \(+1.77801 q^{7}\) \(-10.2121 q^{8}\) \(-2.75580 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.77200 q^{2}\) \(-0.494167 q^{3}\) \(+5.68400 q^{4}\) \(+0.905775 q^{5}\) \(+1.36983 q^{6}\) \(+1.77801 q^{7}\) \(-10.2121 q^{8}\) \(-2.75580 q^{9}\) \(-2.51081 q^{10}\) \(-5.29890 q^{11}\) \(-2.80885 q^{12}\) \(+3.37709 q^{13}\) \(-4.92866 q^{14}\) \(-0.447605 q^{15}\) \(+16.9399 q^{16}\) \(+5.30058 q^{17}\) \(+7.63908 q^{18}\) \(+8.13474 q^{19}\) \(+5.14843 q^{20}\) \(-0.878636 q^{21}\) \(+14.6886 q^{22}\) \(+8.87716 q^{23}\) \(+5.04647 q^{24}\) \(-4.17957 q^{25}\) \(-9.36130 q^{26}\) \(+2.84433 q^{27}\) \(+10.1062 q^{28}\) \(+0.398274 q^{29}\) \(+1.24076 q^{30}\) \(+3.20183 q^{31}\) \(-26.5332 q^{32}\) \(+2.61854 q^{33}\) \(-14.6932 q^{34}\) \(+1.61048 q^{35}\) \(-15.6640 q^{36}\) \(+5.93696 q^{37}\) \(-22.5495 q^{38}\) \(-1.66885 q^{39}\) \(-9.24983 q^{40}\) \(-2.74138 q^{41}\) \(+2.43558 q^{42}\) \(-0.418221 q^{43}\) \(-30.1190 q^{44}\) \(-2.49613 q^{45}\) \(-24.6075 q^{46}\) \(+5.75059 q^{47}\) \(-8.37112 q^{48}\) \(-3.83867 q^{49}\) \(+11.5858 q^{50}\) \(-2.61937 q^{51}\) \(+19.1954 q^{52}\) \(-13.7207 q^{53}\) \(-7.88449 q^{54}\) \(-4.79961 q^{55}\) \(-18.1572 q^{56}\) \(-4.01992 q^{57}\) \(-1.10402 q^{58}\) \(+2.65182 q^{59}\) \(-2.54418 q^{60}\) \(+7.32357 q^{61}\) \(-8.87549 q^{62}\) \(-4.89985 q^{63}\) \(+39.6704 q^{64}\) \(+3.05888 q^{65}\) \(-7.25861 q^{66}\) \(-3.87411 q^{67}\) \(+30.1285 q^{68}\) \(-4.38680 q^{69}\) \(-4.46426 q^{70}\) \(+5.26003 q^{71}\) \(+28.1424 q^{72}\) \(-12.4796 q^{73}\) \(-16.4573 q^{74}\) \(+2.06541 q^{75}\) \(+46.2379 q^{76}\) \(-9.42152 q^{77}\) \(+4.62605 q^{78}\) \(-1.56647 q^{79}\) \(+15.3437 q^{80}\) \(+6.86182 q^{81}\) \(+7.59910 q^{82}\) \(+4.76727 q^{83}\) \(-4.99417 q^{84}\) \(+4.80113 q^{85}\) \(+1.15931 q^{86}\) \(-0.196814 q^{87}\) \(+54.1127 q^{88}\) \(-2.12567 q^{89}\) \(+6.91929 q^{90}\) \(+6.00451 q^{91}\) \(+50.4578 q^{92}\) \(-1.58224 q^{93}\) \(-15.9407 q^{94}\) \(+7.36825 q^{95}\) \(+13.1118 q^{96}\) \(+5.23499 q^{97}\) \(+10.6408 q^{98}\) \(+14.6027 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut 50q^{10} \) \(\mathstrut +\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 17q^{12} \) \(\mathstrut +\mathstrut 113q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 252q^{16} \) \(\mathstrut +\mathstrut 35q^{17} \) \(\mathstrut +\mathstrut 13q^{18} \) \(\mathstrut +\mathstrut 97q^{19} \) \(\mathstrut +\mathstrut 55q^{20} \) \(\mathstrut +\mathstrut 115q^{21} \) \(\mathstrut +\mathstrut 14q^{22} \) \(\mathstrut +\mathstrut 27q^{23} \) \(\mathstrut +\mathstrut 122q^{24} \) \(\mathstrut +\mathstrut 244q^{25} \) \(\mathstrut +\mathstrut 39q^{26} \) \(\mathstrut +\mathstrut 34q^{27} \) \(\mathstrut +\mathstrut 66q^{28} \) \(\mathstrut +\mathstrut 91q^{29} \) \(\mathstrut +\mathstrut 4q^{30} \) \(\mathstrut +\mathstrut 135q^{31} \) \(\mathstrut +\mathstrut 21q^{32} \) \(\mathstrut +\mathstrut 32q^{33} \) \(\mathstrut +\mathstrut 58q^{34} \) \(\mathstrut +\mathstrut 17q^{35} \) \(\mathstrut +\mathstrut 273q^{36} \) \(\mathstrut +\mathstrut 133q^{37} \) \(\mathstrut -\mathstrut 3q^{38} \) \(\mathstrut +\mathstrut 55q^{39} \) \(\mathstrut +\mathstrut 142q^{40} \) \(\mathstrut +\mathstrut 97q^{41} \) \(\mathstrut -\mathstrut 8q^{42} \) \(\mathstrut +\mathstrut 67q^{43} \) \(\mathstrut +\mathstrut 44q^{44} \) \(\mathstrut +\mathstrut 154q^{45} \) \(\mathstrut +\mathstrut 101q^{46} \) \(\mathstrut +\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 312q^{49} \) \(\mathstrut +\mathstrut 21q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut +\mathstrut 193q^{52} \) \(\mathstrut +\mathstrut 22q^{53} \) \(\mathstrut +\mathstrut 141q^{54} \) \(\mathstrut +\mathstrut 88q^{55} \) \(\mathstrut +\mathstrut 28q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 62q^{58} \) \(\mathstrut +\mathstrut 41q^{59} \) \(\mathstrut +\mathstrut q^{60} \) \(\mathstrut +\mathstrut 377q^{61} \) \(\mathstrut +\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 39q^{63} \) \(\mathstrut +\mathstrut 311q^{64} \) \(\mathstrut +\mathstrut 21q^{65} \) \(\mathstrut +\mathstrut 35q^{66} \) \(\mathstrut +\mathstrut 42q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut +\mathstrut 137q^{69} \) \(\mathstrut +\mathstrut 35q^{70} \) \(\mathstrut +\mathstrut 17q^{71} \) \(\mathstrut -\mathstrut 8q^{72} \) \(\mathstrut +\mathstrut 213q^{73} \) \(\mathstrut -\mathstrut 9q^{74} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut +\mathstrut 242q^{76} \) \(\mathstrut +\mathstrut 60q^{77} \) \(\mathstrut +\mathstrut 103q^{79} \) \(\mathstrut +\mathstrut 80q^{80} \) \(\mathstrut +\mathstrut 270q^{81} \) \(\mathstrut +\mathstrut 84q^{82} \) \(\mathstrut +\mathstrut 42q^{83} \) \(\mathstrut +\mathstrut 137q^{84} \) \(\mathstrut +\mathstrut 294q^{85} \) \(\mathstrut -\mathstrut 9q^{86} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut +\mathstrut 78q^{89} \) \(\mathstrut +\mathstrut 69q^{90} \) \(\mathstrut +\mathstrut 118q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 51q^{93} \) \(\mathstrut +\mathstrut 93q^{94} \) \(\mathstrut +\mathstrut 10q^{95} \) \(\mathstrut +\mathstrut 260q^{96} \) \(\mathstrut +\mathstrut 142q^{97} \) \(\mathstrut -\mathstrut 31q^{98} \) \(\mathstrut +\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.77200 −1.96010 −0.980051 0.198746i \(-0.936313\pi\)
−0.980051 + 0.198746i \(0.936313\pi\)
\(3\) −0.494167 −0.285308 −0.142654 0.989773i \(-0.545564\pi\)
−0.142654 + 0.989773i \(0.545564\pi\)
\(4\) 5.68400 2.84200
\(5\) 0.905775 0.405075 0.202537 0.979275i \(-0.435081\pi\)
0.202537 + 0.979275i \(0.435081\pi\)
\(6\) 1.36983 0.559232
\(7\) 1.77801 0.672026 0.336013 0.941857i \(-0.390921\pi\)
0.336013 + 0.941857i \(0.390921\pi\)
\(8\) −10.2121 −3.61051
\(9\) −2.75580 −0.918600
\(10\) −2.51081 −0.793988
\(11\) −5.29890 −1.59768 −0.798839 0.601544i \(-0.794552\pi\)
−0.798839 + 0.601544i \(0.794552\pi\)
\(12\) −2.80885 −0.810844
\(13\) 3.37709 0.936636 0.468318 0.883560i \(-0.344860\pi\)
0.468318 + 0.883560i \(0.344860\pi\)
\(14\) −4.92866 −1.31724
\(15\) −0.447605 −0.115571
\(16\) 16.9399 4.23496
\(17\) 5.30058 1.28558 0.642790 0.766043i \(-0.277777\pi\)
0.642790 + 0.766043i \(0.277777\pi\)
\(18\) 7.63908 1.80055
\(19\) 8.13474 1.86624 0.933119 0.359568i \(-0.117076\pi\)
0.933119 + 0.359568i \(0.117076\pi\)
\(20\) 5.14843 1.15122
\(21\) −0.878636 −0.191734
\(22\) 14.6886 3.13161
\(23\) 8.87716 1.85102 0.925508 0.378728i \(-0.123638\pi\)
0.925508 + 0.378728i \(0.123638\pi\)
\(24\) 5.04647 1.03011
\(25\) −4.17957 −0.835914
\(26\) −9.36130 −1.83590
\(27\) 2.84433 0.547391
\(28\) 10.1062 1.90990
\(29\) 0.398274 0.0739577 0.0369788 0.999316i \(-0.488227\pi\)
0.0369788 + 0.999316i \(0.488227\pi\)
\(30\) 1.24076 0.226531
\(31\) 3.20183 0.575066 0.287533 0.957771i \(-0.407165\pi\)
0.287533 + 0.957771i \(0.407165\pi\)
\(32\) −26.5332 −4.69045
\(33\) 2.61854 0.455830
\(34\) −14.6932 −2.51987
\(35\) 1.61048 0.272221
\(36\) −15.6640 −2.61066
\(37\) 5.93696 0.976030 0.488015 0.872835i \(-0.337721\pi\)
0.488015 + 0.872835i \(0.337721\pi\)
\(38\) −22.5495 −3.65802
\(39\) −1.66885 −0.267229
\(40\) −9.24983 −1.46253
\(41\) −2.74138 −0.428131 −0.214065 0.976819i \(-0.568671\pi\)
−0.214065 + 0.976819i \(0.568671\pi\)
\(42\) 2.43558 0.375819
\(43\) −0.418221 −0.0637781 −0.0318891 0.999491i \(-0.510152\pi\)
−0.0318891 + 0.999491i \(0.510152\pi\)
\(44\) −30.1190 −4.54060
\(45\) −2.49613 −0.372102
\(46\) −24.6075 −3.62818
\(47\) 5.75059 0.838810 0.419405 0.907799i \(-0.362239\pi\)
0.419405 + 0.907799i \(0.362239\pi\)
\(48\) −8.37112 −1.20827
\(49\) −3.83867 −0.548381
\(50\) 11.5858 1.63848
\(51\) −2.61937 −0.366786
\(52\) 19.1954 2.66192
\(53\) −13.7207 −1.88468 −0.942340 0.334657i \(-0.891380\pi\)
−0.942340 + 0.334657i \(0.891380\pi\)
\(54\) −7.88449 −1.07294
\(55\) −4.79961 −0.647180
\(56\) −18.1572 −2.42635
\(57\) −4.01992 −0.532452
\(58\) −1.10402 −0.144965
\(59\) 2.65182 0.345238 0.172619 0.984989i \(-0.444777\pi\)
0.172619 + 0.984989i \(0.444777\pi\)
\(60\) −2.54418 −0.328453
\(61\) 7.32357 0.937687 0.468844 0.883281i \(-0.344671\pi\)
0.468844 + 0.883281i \(0.344671\pi\)
\(62\) −8.87549 −1.12719
\(63\) −4.89985 −0.617323
\(64\) 39.6704 4.95880
\(65\) 3.05888 0.379408
\(66\) −7.25861 −0.893474
\(67\) −3.87411 −0.473298 −0.236649 0.971595i \(-0.576049\pi\)
−0.236649 + 0.971595i \(0.576049\pi\)
\(68\) 30.1285 3.65362
\(69\) −4.38680 −0.528109
\(70\) −4.46426 −0.533581
\(71\) 5.26003 0.624251 0.312126 0.950041i \(-0.398959\pi\)
0.312126 + 0.950041i \(0.398959\pi\)
\(72\) 28.1424 3.31661
\(73\) −12.4796 −1.46063 −0.730313 0.683112i \(-0.760626\pi\)
−0.730313 + 0.683112i \(0.760626\pi\)
\(74\) −16.4573 −1.91312
\(75\) 2.06541 0.238493
\(76\) 46.2379 5.30385
\(77\) −9.42152 −1.07368
\(78\) 4.62605 0.523797
\(79\) −1.56647 −0.176241 −0.0881206 0.996110i \(-0.528086\pi\)
−0.0881206 + 0.996110i \(0.528086\pi\)
\(80\) 15.3437 1.71548
\(81\) 6.86182 0.762425
\(82\) 7.59910 0.839180
\(83\) 4.76727 0.523276 0.261638 0.965166i \(-0.415737\pi\)
0.261638 + 0.965166i \(0.415737\pi\)
\(84\) −4.99417 −0.544908
\(85\) 4.80113 0.520756
\(86\) 1.15931 0.125012
\(87\) −0.196814 −0.0211007
\(88\) 54.1127 5.76843
\(89\) −2.12567 −0.225321 −0.112660 0.993634i \(-0.535937\pi\)
−0.112660 + 0.993634i \(0.535937\pi\)
\(90\) 6.91929 0.729357
\(91\) 6.00451 0.629444
\(92\) 50.4578 5.26059
\(93\) −1.58224 −0.164071
\(94\) −15.9407 −1.64415
\(95\) 7.36825 0.755966
\(96\) 13.1118 1.33822
\(97\) 5.23499 0.531533 0.265766 0.964037i \(-0.414375\pi\)
0.265766 + 0.964037i \(0.414375\pi\)
\(98\) 10.6408 1.07488
\(99\) 14.6027 1.46763
\(100\) −23.7567 −2.37567
\(101\) −14.6479 −1.45752 −0.728762 0.684768i \(-0.759904\pi\)
−0.728762 + 0.684768i \(0.759904\pi\)
\(102\) 7.26091 0.718937
\(103\) 2.70600 0.266631 0.133315 0.991074i \(-0.457438\pi\)
0.133315 + 0.991074i \(0.457438\pi\)
\(104\) −34.4870 −3.38173
\(105\) −0.795847 −0.0776667
\(106\) 38.0338 3.69417
\(107\) −18.0866 −1.74850 −0.874250 0.485477i \(-0.838646\pi\)
−0.874250 + 0.485477i \(0.838646\pi\)
\(108\) 16.1672 1.55569
\(109\) −3.20456 −0.306941 −0.153471 0.988153i \(-0.549045\pi\)
−0.153471 + 0.988153i \(0.549045\pi\)
\(110\) 13.3045 1.26854
\(111\) −2.93385 −0.278469
\(112\) 30.1193 2.84600
\(113\) −5.42530 −0.510369 −0.255184 0.966892i \(-0.582136\pi\)
−0.255184 + 0.966892i \(0.582136\pi\)
\(114\) 11.1432 1.04366
\(115\) 8.04071 0.749800
\(116\) 2.26379 0.210188
\(117\) −9.30658 −0.860393
\(118\) −7.35085 −0.676701
\(119\) 9.42450 0.863943
\(120\) 4.57096 0.417270
\(121\) 17.0784 1.55258
\(122\) −20.3010 −1.83796
\(123\) 1.35470 0.122149
\(124\) 18.1992 1.63434
\(125\) −8.31463 −0.743683
\(126\) 13.5824 1.21002
\(127\) −7.95904 −0.706251 −0.353125 0.935576i \(-0.614881\pi\)
−0.353125 + 0.935576i \(0.614881\pi\)
\(128\) −56.9001 −5.02930
\(129\) 0.206671 0.0181964
\(130\) −8.47923 −0.743678
\(131\) 3.73817 0.326605 0.163303 0.986576i \(-0.447785\pi\)
0.163303 + 0.986576i \(0.447785\pi\)
\(132\) 14.8838 1.29547
\(133\) 14.4637 1.25416
\(134\) 10.7390 0.927713
\(135\) 2.57632 0.221734
\(136\) −54.1298 −4.64159
\(137\) 1.79875 0.153677 0.0768387 0.997044i \(-0.475517\pi\)
0.0768387 + 0.997044i \(0.475517\pi\)
\(138\) 12.1602 1.03515
\(139\) 15.5309 1.31731 0.658656 0.752444i \(-0.271125\pi\)
0.658656 + 0.752444i \(0.271125\pi\)
\(140\) 9.15397 0.773652
\(141\) −2.84175 −0.239319
\(142\) −14.5808 −1.22360
\(143\) −17.8949 −1.49644
\(144\) −46.6828 −3.89024
\(145\) 0.360747 0.0299584
\(146\) 34.5935 2.86298
\(147\) 1.89695 0.156457
\(148\) 33.7457 2.77388
\(149\) 12.4228 1.01771 0.508857 0.860851i \(-0.330068\pi\)
0.508857 + 0.860851i \(0.330068\pi\)
\(150\) −5.72532 −0.467470
\(151\) −18.9938 −1.54569 −0.772847 0.634592i \(-0.781168\pi\)
−0.772847 + 0.634592i \(0.781168\pi\)
\(152\) −83.0724 −6.73806
\(153\) −14.6073 −1.18093
\(154\) 26.1165 2.10453
\(155\) 2.90014 0.232945
\(156\) −9.48573 −0.759466
\(157\) 17.4382 1.39172 0.695860 0.718177i \(-0.255023\pi\)
0.695860 + 0.718177i \(0.255023\pi\)
\(158\) 4.34225 0.345451
\(159\) 6.78031 0.537714
\(160\) −24.0331 −1.89998
\(161\) 15.7837 1.24393
\(162\) −19.0210 −1.49443
\(163\) −10.8274 −0.848069 −0.424034 0.905646i \(-0.639386\pi\)
−0.424034 + 0.905646i \(0.639386\pi\)
\(164\) −15.5820 −1.21675
\(165\) 2.37181 0.184645
\(166\) −13.2149 −1.02567
\(167\) 5.27574 0.408249 0.204124 0.978945i \(-0.434565\pi\)
0.204124 + 0.978945i \(0.434565\pi\)
\(168\) 8.97268 0.692258
\(169\) −1.59527 −0.122713
\(170\) −13.3088 −1.02073
\(171\) −22.4177 −1.71432
\(172\) −2.37717 −0.181257
\(173\) 9.85507 0.749267 0.374634 0.927173i \(-0.377769\pi\)
0.374634 + 0.927173i \(0.377769\pi\)
\(174\) 0.545569 0.0413595
\(175\) −7.43133 −0.561756
\(176\) −89.7626 −6.76611
\(177\) −1.31044 −0.0984990
\(178\) 5.89237 0.441652
\(179\) −0.597622 −0.0446683 −0.0223342 0.999751i \(-0.507110\pi\)
−0.0223342 + 0.999751i \(0.507110\pi\)
\(180\) −14.1880 −1.05751
\(181\) 23.5648 1.75156 0.875780 0.482711i \(-0.160348\pi\)
0.875780 + 0.482711i \(0.160348\pi\)
\(182\) −16.6445 −1.23377
\(183\) −3.61907 −0.267529
\(184\) −90.6541 −6.68311
\(185\) 5.37755 0.395365
\(186\) 4.38598 0.321595
\(187\) −28.0872 −2.05394
\(188\) 32.6864 2.38390
\(189\) 5.05725 0.367861
\(190\) −20.4248 −1.48177
\(191\) 20.3784 1.47453 0.737266 0.675603i \(-0.236117\pi\)
0.737266 + 0.675603i \(0.236117\pi\)
\(192\) −19.6038 −1.41478
\(193\) 19.6162 1.41200 0.706001 0.708211i \(-0.250497\pi\)
0.706001 + 0.708211i \(0.250497\pi\)
\(194\) −14.5114 −1.04186
\(195\) −1.51160 −0.108248
\(196\) −21.8190 −1.55850
\(197\) 11.4474 0.815594 0.407797 0.913073i \(-0.366297\pi\)
0.407797 + 0.913073i \(0.366297\pi\)
\(198\) −40.4787 −2.87670
\(199\) 15.7246 1.11469 0.557343 0.830282i \(-0.311821\pi\)
0.557343 + 0.830282i \(0.311821\pi\)
\(200\) 42.6820 3.01807
\(201\) 1.91446 0.135036
\(202\) 40.6041 2.85689
\(203\) 0.708137 0.0497015
\(204\) −14.8885 −1.04240
\(205\) −2.48307 −0.173425
\(206\) −7.50105 −0.522623
\(207\) −24.4637 −1.70034
\(208\) 57.2074 3.96662
\(209\) −43.1052 −2.98165
\(210\) 2.20609 0.152235
\(211\) −14.5328 −1.00048 −0.500241 0.865886i \(-0.666755\pi\)
−0.500241 + 0.865886i \(0.666755\pi\)
\(212\) −77.9883 −5.35626
\(213\) −2.59934 −0.178104
\(214\) 50.1362 3.42724
\(215\) −0.378814 −0.0258349
\(216\) −29.0464 −1.97636
\(217\) 5.69290 0.386459
\(218\) 8.88305 0.601636
\(219\) 6.16701 0.416728
\(220\) −27.2810 −1.83928
\(221\) 17.9005 1.20412
\(222\) 8.13265 0.545828
\(223\) −21.9740 −1.47149 −0.735745 0.677258i \(-0.763168\pi\)
−0.735745 + 0.677258i \(0.763168\pi\)
\(224\) −47.1764 −3.15211
\(225\) 11.5181 0.767870
\(226\) 15.0389 1.00038
\(227\) 12.7181 0.844133 0.422066 0.906565i \(-0.361305\pi\)
0.422066 + 0.906565i \(0.361305\pi\)
\(228\) −22.8492 −1.51323
\(229\) −0.297530 −0.0196613 −0.00983066 0.999952i \(-0.503129\pi\)
−0.00983066 + 0.999952i \(0.503129\pi\)
\(230\) −22.2889 −1.46968
\(231\) 4.65581 0.306330
\(232\) −4.06720 −0.267025
\(233\) 9.75073 0.638791 0.319396 0.947621i \(-0.396520\pi\)
0.319396 + 0.947621i \(0.396520\pi\)
\(234\) 25.7979 1.68646
\(235\) 5.20874 0.339781
\(236\) 15.0729 0.981165
\(237\) 0.774097 0.0502830
\(238\) −26.1247 −1.69342
\(239\) −24.2581 −1.56913 −0.784564 0.620048i \(-0.787113\pi\)
−0.784564 + 0.620048i \(0.787113\pi\)
\(240\) −7.58236 −0.489439
\(241\) 21.7791 1.40292 0.701458 0.712711i \(-0.252533\pi\)
0.701458 + 0.712711i \(0.252533\pi\)
\(242\) −47.3413 −3.04321
\(243\) −11.9239 −0.764917
\(244\) 41.6272 2.66491
\(245\) −3.47697 −0.222135
\(246\) −3.75523 −0.239425
\(247\) 27.4717 1.74799
\(248\) −32.6973 −2.07628
\(249\) −2.35583 −0.149295
\(250\) 23.0482 1.45769
\(251\) 9.46114 0.597182 0.298591 0.954381i \(-0.403483\pi\)
0.298591 + 0.954381i \(0.403483\pi\)
\(252\) −27.8507 −1.75443
\(253\) −47.0392 −2.95733
\(254\) 22.0625 1.38432
\(255\) −2.37256 −0.148576
\(256\) 78.3864 4.89915
\(257\) 27.3534 1.70626 0.853128 0.521702i \(-0.174703\pi\)
0.853128 + 0.521702i \(0.174703\pi\)
\(258\) −0.572893 −0.0356668
\(259\) 10.5560 0.655918
\(260\) 17.3867 1.07828
\(261\) −1.09756 −0.0679375
\(262\) −10.3622 −0.640180
\(263\) 17.3414 1.06932 0.534659 0.845068i \(-0.320440\pi\)
0.534659 + 0.845068i \(0.320440\pi\)
\(264\) −26.7407 −1.64578
\(265\) −12.4278 −0.763437
\(266\) −40.0934 −2.45828
\(267\) 1.05044 0.0642858
\(268\) −22.0205 −1.34511
\(269\) 28.7379 1.75218 0.876090 0.482148i \(-0.160143\pi\)
0.876090 + 0.482148i \(0.160143\pi\)
\(270\) −7.14157 −0.434622
\(271\) 19.5675 1.18864 0.594321 0.804228i \(-0.297421\pi\)
0.594321 + 0.804228i \(0.297421\pi\)
\(272\) 89.7910 5.44438
\(273\) −2.96723 −0.179585
\(274\) −4.98613 −0.301223
\(275\) 22.1471 1.33552
\(276\) −24.9346 −1.50089
\(277\) 12.3450 0.741741 0.370870 0.928685i \(-0.379059\pi\)
0.370870 + 0.928685i \(0.379059\pi\)
\(278\) −43.0516 −2.58206
\(279\) −8.82361 −0.528255
\(280\) −16.4463 −0.982855
\(281\) −7.15227 −0.426669 −0.213334 0.976979i \(-0.568432\pi\)
−0.213334 + 0.976979i \(0.568432\pi\)
\(282\) 7.87735 0.469089
\(283\) −23.9976 −1.42651 −0.713255 0.700905i \(-0.752780\pi\)
−0.713255 + 0.700905i \(0.752780\pi\)
\(284\) 29.8980 1.77412
\(285\) −3.64115 −0.215683
\(286\) 49.6046 2.93318
\(287\) −4.87420 −0.287715
\(288\) 73.1202 4.30865
\(289\) 11.0961 0.652714
\(290\) −0.999991 −0.0587215
\(291\) −2.58696 −0.151650
\(292\) −70.9340 −4.15110
\(293\) 14.4396 0.843571 0.421786 0.906696i \(-0.361403\pi\)
0.421786 + 0.906696i \(0.361403\pi\)
\(294\) −5.25834 −0.306672
\(295\) 2.40195 0.139847
\(296\) −60.6286 −3.52397
\(297\) −15.0718 −0.874555
\(298\) −34.4360 −1.99482
\(299\) 29.9790 1.73373
\(300\) 11.7398 0.677796
\(301\) −0.743603 −0.0428605
\(302\) 52.6509 3.02972
\(303\) 7.23853 0.415843
\(304\) 137.801 7.90345
\(305\) 6.63351 0.379834
\(306\) 40.4916 2.31475
\(307\) 0.871616 0.0497457 0.0248729 0.999691i \(-0.492082\pi\)
0.0248729 + 0.999691i \(0.492082\pi\)
\(308\) −53.5519 −3.05140
\(309\) −1.33722 −0.0760717
\(310\) −8.03920 −0.456596
\(311\) −15.0620 −0.854086 −0.427043 0.904231i \(-0.640445\pi\)
−0.427043 + 0.904231i \(0.640445\pi\)
\(312\) 17.0424 0.964834
\(313\) −17.9331 −1.01364 −0.506818 0.862053i \(-0.669179\pi\)
−0.506818 + 0.862053i \(0.669179\pi\)
\(314\) −48.3388 −2.72791
\(315\) −4.43816 −0.250062
\(316\) −8.90379 −0.500878
\(317\) −6.72890 −0.377933 −0.188966 0.981984i \(-0.560514\pi\)
−0.188966 + 0.981984i \(0.560514\pi\)
\(318\) −18.7950 −1.05397
\(319\) −2.11042 −0.118161
\(320\) 35.9325 2.00869
\(321\) 8.93782 0.498860
\(322\) −43.7525 −2.43823
\(323\) 43.1188 2.39920
\(324\) 39.0026 2.16681
\(325\) −14.1148 −0.782947
\(326\) 30.0136 1.66230
\(327\) 1.58359 0.0875727
\(328\) 27.9951 1.54577
\(329\) 10.2246 0.563702
\(330\) −6.57467 −0.361924
\(331\) 11.0243 0.605951 0.302975 0.952998i \(-0.402020\pi\)
0.302975 + 0.952998i \(0.402020\pi\)
\(332\) 27.0971 1.48715
\(333\) −16.3611 −0.896581
\(334\) −14.6244 −0.800209
\(335\) −3.50907 −0.191721
\(336\) −14.8840 −0.811987
\(337\) −14.2438 −0.775911 −0.387956 0.921678i \(-0.626819\pi\)
−0.387956 + 0.921678i \(0.626819\pi\)
\(338\) 4.42210 0.240531
\(339\) 2.68100 0.145612
\(340\) 27.2896 1.47999
\(341\) −16.9662 −0.918771
\(342\) 62.1419 3.36025
\(343\) −19.2713 −1.04055
\(344\) 4.27090 0.230271
\(345\) −3.97346 −0.213924
\(346\) −27.3183 −1.46864
\(347\) −13.7382 −0.737508 −0.368754 0.929527i \(-0.620216\pi\)
−0.368754 + 0.929527i \(0.620216\pi\)
\(348\) −1.11869 −0.0599682
\(349\) 12.9120 0.691166 0.345583 0.938388i \(-0.387681\pi\)
0.345583 + 0.938388i \(0.387681\pi\)
\(350\) 20.5997 1.10110
\(351\) 9.60555 0.512706
\(352\) 140.597 7.49384
\(353\) 8.85962 0.471550 0.235775 0.971808i \(-0.424237\pi\)
0.235775 + 0.971808i \(0.424237\pi\)
\(354\) 3.63255 0.193068
\(355\) 4.76441 0.252869
\(356\) −12.0823 −0.640362
\(357\) −4.65728 −0.246489
\(358\) 1.65661 0.0875545
\(359\) 13.1790 0.695562 0.347781 0.937576i \(-0.386935\pi\)
0.347781 + 0.937576i \(0.386935\pi\)
\(360\) 25.4907 1.34348
\(361\) 47.1740 2.48284
\(362\) −65.3218 −3.43324
\(363\) −8.43957 −0.442962
\(364\) 34.1296 1.78888
\(365\) −11.3037 −0.591663
\(366\) 10.0321 0.524385
\(367\) −17.8337 −0.930910 −0.465455 0.885072i \(-0.654109\pi\)
−0.465455 + 0.885072i \(0.654109\pi\)
\(368\) 150.378 7.83898
\(369\) 7.55468 0.393281
\(370\) −14.9066 −0.774957
\(371\) −24.3956 −1.26655
\(372\) −8.99346 −0.466289
\(373\) −8.98193 −0.465067 −0.232533 0.972588i \(-0.574701\pi\)
−0.232533 + 0.972588i \(0.574701\pi\)
\(374\) 77.8579 4.02594
\(375\) 4.10882 0.212178
\(376\) −58.7254 −3.02853
\(377\) 1.34501 0.0692714
\(378\) −14.0187 −0.721045
\(379\) −8.05620 −0.413819 −0.206910 0.978360i \(-0.566341\pi\)
−0.206910 + 0.978360i \(0.566341\pi\)
\(380\) 41.8811 2.14846
\(381\) 3.93310 0.201499
\(382\) −56.4890 −2.89023
\(383\) 25.5260 1.30432 0.652160 0.758081i \(-0.273863\pi\)
0.652160 + 0.758081i \(0.273863\pi\)
\(384\) 28.1182 1.43490
\(385\) −8.53378 −0.434922
\(386\) −54.3760 −2.76767
\(387\) 1.15253 0.0585865
\(388\) 29.7557 1.51062
\(389\) −34.5148 −1.74997 −0.874984 0.484151i \(-0.839129\pi\)
−0.874984 + 0.484151i \(0.839129\pi\)
\(390\) 4.19016 0.212177
\(391\) 47.0541 2.37963
\(392\) 39.2007 1.97993
\(393\) −1.84728 −0.0931830
\(394\) −31.7322 −1.59865
\(395\) −1.41887 −0.0713909
\(396\) 83.0018 4.17100
\(397\) −4.78082 −0.239943 −0.119971 0.992777i \(-0.538280\pi\)
−0.119971 + 0.992777i \(0.538280\pi\)
\(398\) −43.5886 −2.18490
\(399\) −7.14748 −0.357822
\(400\) −70.8013 −3.54007
\(401\) −8.95405 −0.447144 −0.223572 0.974687i \(-0.571772\pi\)
−0.223572 + 0.974687i \(0.571772\pi\)
\(402\) −5.30689 −0.264684
\(403\) 10.8129 0.538628
\(404\) −83.2588 −4.14228
\(405\) 6.21527 0.308839
\(406\) −1.96296 −0.0974199
\(407\) −31.4594 −1.55938
\(408\) 26.7492 1.32428
\(409\) −11.3249 −0.559979 −0.279990 0.960003i \(-0.590331\pi\)
−0.279990 + 0.960003i \(0.590331\pi\)
\(410\) 6.88308 0.339931
\(411\) −0.888882 −0.0438453
\(412\) 15.3809 0.757764
\(413\) 4.71497 0.232009
\(414\) 67.8134 3.33284
\(415\) 4.31807 0.211966
\(416\) −89.6050 −4.39325
\(417\) −7.67485 −0.375839
\(418\) 119.488 5.84434
\(419\) −8.84951 −0.432327 −0.216163 0.976357i \(-0.569354\pi\)
−0.216163 + 0.976357i \(0.569354\pi\)
\(420\) −4.52359 −0.220729
\(421\) 25.8641 1.26054 0.630269 0.776377i \(-0.282945\pi\)
0.630269 + 0.776377i \(0.282945\pi\)
\(422\) 40.2851 1.96105
\(423\) −15.8475 −0.770530
\(424\) 140.116 6.80465
\(425\) −22.1542 −1.07463
\(426\) 7.20537 0.349101
\(427\) 13.0214 0.630150
\(428\) −102.804 −4.96923
\(429\) 8.84306 0.426947
\(430\) 1.05007 0.0506391
\(431\) 12.9324 0.622930 0.311465 0.950258i \(-0.399180\pi\)
0.311465 + 0.950258i \(0.399180\pi\)
\(432\) 48.1825 2.31818
\(433\) −20.0216 −0.962175 −0.481088 0.876673i \(-0.659758\pi\)
−0.481088 + 0.876673i \(0.659758\pi\)
\(434\) −15.7807 −0.757500
\(435\) −0.178269 −0.00854736
\(436\) −18.2147 −0.872327
\(437\) 72.2134 3.45444
\(438\) −17.0950 −0.816830
\(439\) −16.7646 −0.800131 −0.400065 0.916487i \(-0.631013\pi\)
−0.400065 + 0.916487i \(0.631013\pi\)
\(440\) 49.0139 2.33665
\(441\) 10.5786 0.503743
\(442\) −49.6203 −2.36020
\(443\) −3.07696 −0.146191 −0.0730954 0.997325i \(-0.523288\pi\)
−0.0730954 + 0.997325i \(0.523288\pi\)
\(444\) −16.6760 −0.791409
\(445\) −1.92538 −0.0912718
\(446\) 60.9121 2.88427
\(447\) −6.13894 −0.290362
\(448\) 70.5345 3.33244
\(449\) 35.6048 1.68030 0.840148 0.542357i \(-0.182468\pi\)
0.840148 + 0.542357i \(0.182468\pi\)
\(450\) −31.9281 −1.50510
\(451\) 14.5263 0.684016
\(452\) −30.8374 −1.45047
\(453\) 9.38612 0.440999
\(454\) −35.2547 −1.65459
\(455\) 5.43873 0.254972
\(456\) 41.0517 1.92242
\(457\) 24.0634 1.12564 0.562819 0.826580i \(-0.309717\pi\)
0.562819 + 0.826580i \(0.309717\pi\)
\(458\) 0.824753 0.0385382
\(459\) 15.0766 0.703715
\(460\) 45.7034 2.13093
\(461\) 25.2591 1.17643 0.588216 0.808704i \(-0.299830\pi\)
0.588216 + 0.808704i \(0.299830\pi\)
\(462\) −12.9059 −0.600437
\(463\) −22.3282 −1.03768 −0.518841 0.854871i \(-0.673636\pi\)
−0.518841 + 0.854871i \(0.673636\pi\)
\(464\) 6.74671 0.313208
\(465\) −1.43315 −0.0664610
\(466\) −27.0290 −1.25210
\(467\) −26.7657 −1.23857 −0.619285 0.785167i \(-0.712577\pi\)
−0.619285 + 0.785167i \(0.712577\pi\)
\(468\) −52.8986 −2.44524
\(469\) −6.88822 −0.318069
\(470\) −14.4386 −0.666005
\(471\) −8.61740 −0.397069
\(472\) −27.0805 −1.24648
\(473\) 2.21611 0.101897
\(474\) −2.14580 −0.0985598
\(475\) −33.9997 −1.56001
\(476\) 53.5689 2.45532
\(477\) 37.8114 1.73127
\(478\) 67.2436 3.07565
\(479\) 0.590336 0.0269731 0.0134866 0.999909i \(-0.495707\pi\)
0.0134866 + 0.999909i \(0.495707\pi\)
\(480\) 11.8764 0.542080
\(481\) 20.0496 0.914185
\(482\) −60.3718 −2.74986
\(483\) −7.79980 −0.354903
\(484\) 97.0734 4.41243
\(485\) 4.74172 0.215311
\(486\) 33.0530 1.49932
\(487\) −20.7981 −0.942454 −0.471227 0.882012i \(-0.656189\pi\)
−0.471227 + 0.882012i \(0.656189\pi\)
\(488\) −74.7887 −3.38553
\(489\) 5.35056 0.241961
\(490\) 9.63817 0.435408
\(491\) 35.1037 1.58421 0.792105 0.610385i \(-0.208985\pi\)
0.792105 + 0.610385i \(0.208985\pi\)
\(492\) 7.70011 0.347148
\(493\) 2.11108 0.0950784
\(494\) −76.1517 −3.42623
\(495\) 13.2268 0.594499
\(496\) 54.2386 2.43538
\(497\) 9.35241 0.419513
\(498\) 6.53036 0.292633
\(499\) 28.0130 1.25403 0.627017 0.779005i \(-0.284276\pi\)
0.627017 + 0.779005i \(0.284276\pi\)
\(500\) −47.2603 −2.11355
\(501\) −2.60710 −0.116477
\(502\) −26.2263 −1.17054
\(503\) −25.8842 −1.15412 −0.577060 0.816702i \(-0.695800\pi\)
−0.577060 + 0.816702i \(0.695800\pi\)
\(504\) 50.0375 2.22885
\(505\) −13.2677 −0.590406
\(506\) 130.393 5.79667
\(507\) 0.788332 0.0350111
\(508\) −45.2392 −2.00716
\(509\) −9.41588 −0.417352 −0.208676 0.977985i \(-0.566915\pi\)
−0.208676 + 0.977985i \(0.566915\pi\)
\(510\) 6.57675 0.291224
\(511\) −22.1889 −0.981579
\(512\) −103.487 −4.57353
\(513\) 23.1379 1.02156
\(514\) −75.8236 −3.34444
\(515\) 2.45103 0.108005
\(516\) 1.17472 0.0517141
\(517\) −30.4718 −1.34015
\(518\) −29.2613 −1.28567
\(519\) −4.87005 −0.213772
\(520\) −31.2375 −1.36985
\(521\) −31.5161 −1.38074 −0.690372 0.723455i \(-0.742553\pi\)
−0.690372 + 0.723455i \(0.742553\pi\)
\(522\) 3.04245 0.133164
\(523\) −13.1551 −0.575231 −0.287615 0.957746i \(-0.592862\pi\)
−0.287615 + 0.957746i \(0.592862\pi\)
\(524\) 21.2477 0.928212
\(525\) 3.67232 0.160273
\(526\) −48.0705 −2.09597
\(527\) 16.9716 0.739293
\(528\) 44.3578 1.93042
\(529\) 55.8040 2.42626
\(530\) 34.4500 1.49641
\(531\) −7.30788 −0.317135
\(532\) 82.2115 3.56432
\(533\) −9.25787 −0.401003
\(534\) −2.91182 −0.126007
\(535\) −16.3824 −0.708273
\(536\) 39.5627 1.70885
\(537\) 0.295325 0.0127442
\(538\) −79.6615 −3.43445
\(539\) 20.3407 0.876137
\(540\) 14.6438 0.630169
\(541\) 27.6618 1.18927 0.594637 0.803994i \(-0.297296\pi\)
0.594637 + 0.803994i \(0.297296\pi\)
\(542\) −54.2412 −2.32986
\(543\) −11.6450 −0.499733
\(544\) −140.641 −6.02995
\(545\) −2.90261 −0.124334
\(546\) 8.22518 0.352005
\(547\) −7.08314 −0.302853 −0.151427 0.988469i \(-0.548387\pi\)
−0.151427 + 0.988469i \(0.548387\pi\)
\(548\) 10.2241 0.436751
\(549\) −20.1823 −0.861359
\(550\) −61.3919 −2.61776
\(551\) 3.23986 0.138023
\(552\) 44.7983 1.90674
\(553\) −2.78520 −0.118439
\(554\) −34.2204 −1.45389
\(555\) −2.65741 −0.112801
\(556\) 88.2775 3.74380
\(557\) −28.6732 −1.21492 −0.607462 0.794349i \(-0.707812\pi\)
−0.607462 + 0.794349i \(0.707812\pi\)
\(558\) 24.4591 1.03543
\(559\) −1.41237 −0.0597369
\(560\) 27.2813 1.15285
\(561\) 13.8798 0.586006
\(562\) 19.8261 0.836314
\(563\) 22.1551 0.933724 0.466862 0.884330i \(-0.345384\pi\)
0.466862 + 0.884330i \(0.345384\pi\)
\(564\) −16.1525 −0.680144
\(565\) −4.91410 −0.206738
\(566\) 66.5214 2.79610
\(567\) 12.2004 0.512369
\(568\) −53.7158 −2.25386
\(569\) −7.28316 −0.305326 −0.152663 0.988278i \(-0.548785\pi\)
−0.152663 + 0.988278i \(0.548785\pi\)
\(570\) 10.0933 0.422761
\(571\) 18.1044 0.757646 0.378823 0.925469i \(-0.376329\pi\)
0.378823 + 0.925469i \(0.376329\pi\)
\(572\) −101.714 −4.25289
\(573\) −10.0704 −0.420695
\(574\) 13.5113 0.563951
\(575\) −37.1027 −1.54729
\(576\) −109.324 −4.55515
\(577\) 22.2828 0.927645 0.463823 0.885928i \(-0.346477\pi\)
0.463823 + 0.885928i \(0.346477\pi\)
\(578\) −30.7585 −1.27939
\(579\) −9.69366 −0.402855
\(580\) 2.05048 0.0851417
\(581\) 8.47626 0.351655
\(582\) 7.17106 0.297250
\(583\) 72.7045 3.01111
\(584\) 127.442 5.27360
\(585\) −8.42966 −0.348524
\(586\) −40.0267 −1.65349
\(587\) 6.95991 0.287266 0.143633 0.989631i \(-0.454121\pi\)
0.143633 + 0.989631i \(0.454121\pi\)
\(588\) 10.7822 0.444652
\(589\) 26.0461 1.07321
\(590\) −6.65822 −0.274115
\(591\) −5.65693 −0.232695
\(592\) 100.571 4.13345
\(593\) −26.5140 −1.08880 −0.544401 0.838825i \(-0.683243\pi\)
−0.544401 + 0.838825i \(0.683243\pi\)
\(594\) 41.7791 1.71422
\(595\) 8.53648 0.349961
\(596\) 70.6111 2.89234
\(597\) −7.77058 −0.318029
\(598\) −83.1018 −3.39828
\(599\) −0.881356 −0.0360112 −0.0180056 0.999838i \(-0.505732\pi\)
−0.0180056 + 0.999838i \(0.505732\pi\)
\(600\) −21.0921 −0.861080
\(601\) 48.1482 1.96401 0.982003 0.188863i \(-0.0604802\pi\)
0.982003 + 0.188863i \(0.0604802\pi\)
\(602\) 2.06127 0.0840110
\(603\) 10.6763 0.434771
\(604\) −107.961 −4.39286
\(605\) 15.4692 0.628910
\(606\) −20.0652 −0.815094
\(607\) −9.21965 −0.374214 −0.187107 0.982340i \(-0.559911\pi\)
−0.187107 + 0.982340i \(0.559911\pi\)
\(608\) −215.841 −8.75350
\(609\) −0.349938 −0.0141802
\(610\) −18.3881 −0.744513
\(611\) 19.4203 0.785659
\(612\) −83.0281 −3.35621
\(613\) 11.2593 0.454761 0.227380 0.973806i \(-0.426984\pi\)
0.227380 + 0.973806i \(0.426984\pi\)
\(614\) −2.41612 −0.0975067
\(615\) 1.22705 0.0494795
\(616\) 96.2131 3.87654
\(617\) 38.7240 1.55897 0.779485 0.626420i \(-0.215481\pi\)
0.779485 + 0.626420i \(0.215481\pi\)
\(618\) 3.70678 0.149108
\(619\) 16.8749 0.678259 0.339129 0.940740i \(-0.389868\pi\)
0.339129 + 0.940740i \(0.389868\pi\)
\(620\) 16.4844 0.662029
\(621\) 25.2496 1.01323
\(622\) 41.7518 1.67410
\(623\) −3.77947 −0.151421
\(624\) −28.2700 −1.13171
\(625\) 13.3667 0.534667
\(626\) 49.7105 1.98683
\(627\) 21.3012 0.850687
\(628\) 99.1188 3.95527
\(629\) 31.4693 1.25476
\(630\) 12.3026 0.490147
\(631\) −20.9239 −0.832966 −0.416483 0.909144i \(-0.636737\pi\)
−0.416483 + 0.909144i \(0.636737\pi\)
\(632\) 15.9968 0.636320
\(633\) 7.18165 0.285445
\(634\) 18.6525 0.740786
\(635\) −7.20910 −0.286085
\(636\) 38.5393 1.52818
\(637\) −12.9635 −0.513633
\(638\) 5.85008 0.231607
\(639\) −14.4956 −0.573437
\(640\) −51.5387 −2.03725
\(641\) 40.1451 1.58564 0.792818 0.609459i \(-0.208613\pi\)
0.792818 + 0.609459i \(0.208613\pi\)
\(642\) −24.7757 −0.977817
\(643\) 1.73197 0.0683024 0.0341512 0.999417i \(-0.489127\pi\)
0.0341512 + 0.999417i \(0.489127\pi\)
\(644\) 89.7146 3.53525
\(645\) 0.187198 0.00737090
\(646\) −119.526 −4.70267
\(647\) −7.53992 −0.296425 −0.148213 0.988956i \(-0.547352\pi\)
−0.148213 + 0.988956i \(0.547352\pi\)
\(648\) −70.0733 −2.75274
\(649\) −14.0517 −0.551579
\(650\) 39.1262 1.53466
\(651\) −2.81325 −0.110260
\(652\) −61.5430 −2.41021
\(653\) 12.0153 0.470195 0.235097 0.971972i \(-0.424459\pi\)
0.235097 + 0.971972i \(0.424459\pi\)
\(654\) −4.38971 −0.171651
\(655\) 3.38594 0.132300
\(656\) −46.4385 −1.81312
\(657\) 34.3913 1.34173
\(658\) −28.3427 −1.10491
\(659\) 31.1457 1.21326 0.606632 0.794983i \(-0.292520\pi\)
0.606632 + 0.794983i \(0.292520\pi\)
\(660\) 13.4814 0.524762
\(661\) 20.8901 0.812532 0.406266 0.913755i \(-0.366831\pi\)
0.406266 + 0.913755i \(0.366831\pi\)
\(662\) −30.5594 −1.18773
\(663\) −8.84586 −0.343545
\(664\) −48.6836 −1.88929
\(665\) 13.1008 0.508029
\(666\) 45.3529 1.75739
\(667\) 3.53554 0.136897
\(668\) 29.9873 1.16024
\(669\) 10.8589 0.419828
\(670\) 9.72716 0.375793
\(671\) −38.8069 −1.49812
\(672\) 23.3130 0.899320
\(673\) 41.1665 1.58685 0.793427 0.608666i \(-0.208295\pi\)
0.793427 + 0.608666i \(0.208295\pi\)
\(674\) 39.4840 1.52087
\(675\) −11.8881 −0.457572
\(676\) −9.06753 −0.348751
\(677\) −25.3315 −0.973569 −0.486784 0.873522i \(-0.661830\pi\)
−0.486784 + 0.873522i \(0.661830\pi\)
\(678\) −7.43175 −0.285415
\(679\) 9.30788 0.357204
\(680\) −49.0294 −1.88019
\(681\) −6.28489 −0.240838
\(682\) 47.0303 1.80088
\(683\) −5.94916 −0.227638 −0.113819 0.993501i \(-0.536308\pi\)
−0.113819 + 0.993501i \(0.536308\pi\)
\(684\) −127.422 −4.87211
\(685\) 1.62926 0.0622509
\(686\) 53.4201 2.03959
\(687\) 0.147029 0.00560953
\(688\) −7.08460 −0.270098
\(689\) −46.3359 −1.76526
\(690\) 11.0144 0.419312
\(691\) −15.1326 −0.575673 −0.287837 0.957680i \(-0.592936\pi\)
−0.287837 + 0.957680i \(0.592936\pi\)
\(692\) 56.0162 2.12942
\(693\) 25.9638 0.986283
\(694\) 38.0825 1.44559
\(695\) 14.0675 0.533610
\(696\) 2.00988 0.0761842
\(697\) −14.5309 −0.550396
\(698\) −35.7922 −1.35476
\(699\) −4.81849 −0.182252
\(700\) −42.2397 −1.59651
\(701\) −5.05249 −0.190830 −0.0954149 0.995438i \(-0.530418\pi\)
−0.0954149 + 0.995438i \(0.530418\pi\)
\(702\) −26.6266 −1.00496
\(703\) 48.2956 1.82150
\(704\) −210.210 −7.92257
\(705\) −2.57399 −0.0969421
\(706\) −24.5589 −0.924286
\(707\) −26.0442 −0.979493
\(708\) −7.44856 −0.279934
\(709\) −29.6144 −1.11219 −0.556096 0.831118i \(-0.687701\pi\)
−0.556096 + 0.831118i \(0.687701\pi\)
\(710\) −13.2070 −0.495648
\(711\) 4.31687 0.161895
\(712\) 21.7075 0.813522
\(713\) 28.4232 1.06446
\(714\) 12.9100 0.483145
\(715\) −16.2087 −0.606172
\(716\) −3.39688 −0.126947
\(717\) 11.9876 0.447684
\(718\) −36.5323 −1.36337
\(719\) −17.3756 −0.648001 −0.324001 0.946057i \(-0.605028\pi\)
−0.324001 + 0.946057i \(0.605028\pi\)
\(720\) −42.2841 −1.57584
\(721\) 4.81131 0.179183
\(722\) −130.766 −4.86662
\(723\) −10.7625 −0.400263
\(724\) 133.942 4.97793
\(725\) −1.66462 −0.0618223
\(726\) 23.3945 0.868252
\(727\) 5.11045 0.189536 0.0947681 0.995499i \(-0.469789\pi\)
0.0947681 + 0.995499i \(0.469789\pi\)
\(728\) −61.3184 −2.27261
\(729\) −14.6931 −0.544188
\(730\) 31.3339 1.15972
\(731\) −2.21681 −0.0819918
\(732\) −20.5708 −0.760319
\(733\) 29.7387 1.09842 0.549212 0.835683i \(-0.314928\pi\)
0.549212 + 0.835683i \(0.314928\pi\)
\(734\) 49.4350 1.82468
\(735\) 1.71821 0.0633770
\(736\) −235.540 −8.68210
\(737\) 20.5285 0.756178
\(738\) −20.9416 −0.770871
\(739\) 16.3207 0.600368 0.300184 0.953881i \(-0.402952\pi\)
0.300184 + 0.953881i \(0.402952\pi\)
\(740\) 30.5660 1.12363
\(741\) −13.5756 −0.498714
\(742\) 67.6245 2.48257
\(743\) 4.09779 0.150333 0.0751667 0.997171i \(-0.476051\pi\)
0.0751667 + 0.997171i \(0.476051\pi\)
\(744\) 16.1579 0.592379
\(745\) 11.2522 0.412251
\(746\) 24.8979 0.911578
\(747\) −13.1376 −0.480681
\(748\) −159.648 −5.83731
\(749\) −32.1582 −1.17504
\(750\) −11.3897 −0.415891
\(751\) 23.6170 0.861798 0.430899 0.902400i \(-0.358197\pi\)
0.430899 + 0.902400i \(0.358197\pi\)
\(752\) 97.4142 3.55233
\(753\) −4.67539 −0.170381
\(754\) −3.72836 −0.135779
\(755\) −17.2041 −0.626122
\(756\) 28.7454 1.04546
\(757\) −23.2659 −0.845614 −0.422807 0.906220i \(-0.638955\pi\)
−0.422807 + 0.906220i \(0.638955\pi\)
\(758\) 22.3318 0.811128
\(759\) 23.2452 0.843749
\(760\) −75.2449 −2.72942
\(761\) 11.6645 0.422838 0.211419 0.977396i \(-0.432192\pi\)
0.211419 + 0.977396i \(0.432192\pi\)
\(762\) −10.9026 −0.394958
\(763\) −5.69775 −0.206272
\(764\) 115.831 4.19062
\(765\) −13.2310 −0.478366
\(766\) −70.7583 −2.55660
\(767\) 8.95543 0.323362
\(768\) −38.7360 −1.39776
\(769\) 15.5231 0.559778 0.279889 0.960032i \(-0.409702\pi\)
0.279889 + 0.960032i \(0.409702\pi\)
\(770\) 23.6557 0.852491
\(771\) −13.5171 −0.486808
\(772\) 111.498 4.01291
\(773\) 1.75053 0.0629622 0.0314811 0.999504i \(-0.489978\pi\)
0.0314811 + 0.999504i \(0.489978\pi\)
\(774\) −3.19482 −0.114836
\(775\) −13.3823 −0.480706
\(776\) −53.4600 −1.91910
\(777\) −5.21643 −0.187138
\(778\) 95.6751 3.43012
\(779\) −22.3004 −0.798994
\(780\) −8.59194 −0.307641
\(781\) −27.8724 −0.997353
\(782\) −130.434 −4.66431
\(783\) 1.13282 0.0404838
\(784\) −65.0265 −2.32237
\(785\) 15.7951 0.563751
\(786\) 5.12067 0.182648
\(787\) 32.0438 1.14224 0.571119 0.820867i \(-0.306510\pi\)
0.571119 + 0.820867i \(0.306510\pi\)
\(788\) 65.0670 2.31792
\(789\) −8.56957 −0.305085
\(790\) 3.93310 0.139933
\(791\) −9.64625 −0.342981
\(792\) −149.124 −5.29888
\(793\) 24.7324 0.878272
\(794\) 13.2525 0.470312
\(795\) 6.14144 0.217814
\(796\) 89.3785 3.16794
\(797\) −27.8422 −0.986222 −0.493111 0.869966i \(-0.664140\pi\)
−0.493111 + 0.869966i \(0.664140\pi\)
\(798\) 19.8128 0.701367
\(799\) 30.4815 1.07836
\(800\) 110.897 3.92082
\(801\) 5.85792 0.206980
\(802\) 24.8206 0.876447
\(803\) 66.1282 2.33361
\(804\) 10.8818 0.383771
\(805\) 14.2965 0.503885
\(806\) −29.9733 −1.05576
\(807\) −14.2013 −0.499910
\(808\) 149.585 5.26240
\(809\) 28.9516 1.01788 0.508942 0.860801i \(-0.330037\pi\)
0.508942 + 0.860801i \(0.330037\pi\)
\(810\) −17.2287 −0.605356
\(811\) 9.99310 0.350905 0.175453 0.984488i \(-0.443861\pi\)
0.175453 + 0.984488i \(0.443861\pi\)
\(812\) 4.02505 0.141252
\(813\) −9.66962 −0.339128
\(814\) 87.2055 3.05655
\(815\) −9.80720 −0.343531
\(816\) −44.3718 −1.55332
\(817\) −3.40212 −0.119025
\(818\) 31.3926 1.09762
\(819\) −16.5472 −0.578207
\(820\) −14.1138 −0.492874
\(821\) −11.3050 −0.394548 −0.197274 0.980348i \(-0.563209\pi\)
−0.197274 + 0.980348i \(0.563209\pi\)
\(822\) 2.46398 0.0859413
\(823\) −38.8116 −1.35289 −0.676443 0.736495i \(-0.736479\pi\)
−0.676443 + 0.736495i \(0.736479\pi\)
\(824\) −27.6339 −0.962672
\(825\) −10.9444 −0.381035
\(826\) −13.0699 −0.454761
\(827\) −47.3049 −1.64495 −0.822477 0.568798i \(-0.807408\pi\)
−0.822477 + 0.568798i \(0.807408\pi\)
\(828\) −139.051 −4.83237
\(829\) −51.1436 −1.77629 −0.888145 0.459564i \(-0.848006\pi\)
−0.888145 + 0.459564i \(0.848006\pi\)
\(830\) −11.9697 −0.415475
\(831\) −6.10051 −0.211624
\(832\) 133.970 4.64459
\(833\) −20.3472 −0.704988
\(834\) 21.2747 0.736683
\(835\) 4.77863 0.165371
\(836\) −245.010 −8.47384
\(837\) 9.10706 0.314786
\(838\) 24.5309 0.847404
\(839\) −0.995926 −0.0343832 −0.0171916 0.999852i \(-0.505473\pi\)
−0.0171916 + 0.999852i \(0.505473\pi\)
\(840\) 8.12723 0.280416
\(841\) −28.8414 −0.994530
\(842\) −71.6953 −2.47078
\(843\) 3.53442 0.121732
\(844\) −82.6046 −2.84337
\(845\) −1.44496 −0.0497081
\(846\) 43.9292 1.51032
\(847\) 30.3655 1.04337
\(848\) −232.426 −7.98155
\(849\) 11.8588 0.406994
\(850\) 61.4114 2.10639
\(851\) 52.7034 1.80665
\(852\) −14.7746 −0.506171
\(853\) −4.11526 −0.140904 −0.0704519 0.997515i \(-0.522444\pi\)
−0.0704519 + 0.997515i \(0.522444\pi\)
\(854\) −36.0954 −1.23516
\(855\) −20.3054 −0.694430
\(856\) 184.702 6.31297
\(857\) −4.98187 −0.170178 −0.0850888 0.996373i \(-0.527117\pi\)
−0.0850888 + 0.996373i \(0.527117\pi\)
\(858\) −24.5130 −0.836859
\(859\) 20.6496 0.704554 0.352277 0.935896i \(-0.385407\pi\)
0.352277 + 0.935896i \(0.385407\pi\)
\(860\) −2.15318 −0.0734228
\(861\) 2.40867 0.0820873
\(862\) −35.8485 −1.22101
\(863\) 3.36601 0.114580 0.0572902 0.998358i \(-0.481754\pi\)
0.0572902 + 0.998358i \(0.481754\pi\)
\(864\) −75.4691 −2.56751
\(865\) 8.92648 0.303509
\(866\) 55.4998 1.88596
\(867\) −5.48335 −0.186224
\(868\) 32.3584 1.09832
\(869\) 8.30055 0.281577
\(870\) 0.494163 0.0167537
\(871\) −13.0832 −0.443308
\(872\) 32.7251 1.10821
\(873\) −14.4266 −0.488266
\(874\) −200.176 −6.77105
\(875\) −14.7835 −0.499774
\(876\) 35.0533 1.18434
\(877\) −43.8942 −1.48220 −0.741101 0.671393i \(-0.765696\pi\)
−0.741101 + 0.671393i \(0.765696\pi\)
\(878\) 46.4715 1.56834
\(879\) −7.13559 −0.240677
\(880\) −81.3047 −2.74078
\(881\) −32.5655 −1.09716 −0.548580 0.836098i \(-0.684832\pi\)
−0.548580 + 0.836098i \(0.684832\pi\)
\(882\) −29.3239 −0.987387
\(883\) 56.7195 1.90876 0.954381 0.298591i \(-0.0965168\pi\)
0.954381 + 0.298591i \(0.0965168\pi\)
\(884\) 101.747 3.42211
\(885\) −1.18697 −0.0398995
\(886\) 8.52935 0.286549
\(887\) 15.7744 0.529653 0.264827 0.964296i \(-0.414685\pi\)
0.264827 + 0.964296i \(0.414685\pi\)
\(888\) 29.9607 1.00541
\(889\) −14.1513 −0.474619
\(890\) 5.33716 0.178902
\(891\) −36.3601 −1.21811
\(892\) −124.900 −4.18198
\(893\) 46.7796 1.56542
\(894\) 17.0171 0.569139
\(895\) −0.541311 −0.0180940
\(896\) −101.169 −3.37982
\(897\) −14.8146 −0.494646
\(898\) −98.6967 −3.29355
\(899\) 1.27521 0.0425305
\(900\) 65.4686 2.18229
\(901\) −72.7276 −2.42291
\(902\) −40.2669 −1.34074
\(903\) 0.367464 0.0122284
\(904\) 55.4034 1.84269
\(905\) 21.3444 0.709513
\(906\) −26.0184 −0.864402
\(907\) −32.3929 −1.07559 −0.537794 0.843076i \(-0.680742\pi\)
−0.537794 + 0.843076i \(0.680742\pi\)
\(908\) 72.2899 2.39902
\(909\) 40.3667 1.33888
\(910\) −15.0762 −0.499771
\(911\) 20.2327 0.670341 0.335170 0.942158i \(-0.391206\pi\)
0.335170 + 0.942158i \(0.391206\pi\)
\(912\) −68.0969 −2.25491
\(913\) −25.2613 −0.836026
\(914\) −66.7037 −2.20636
\(915\) −3.27806 −0.108369
\(916\) −1.69116 −0.0558775
\(917\) 6.64651 0.219487
\(918\) −41.7923 −1.37935
\(919\) −18.0644 −0.595890 −0.297945 0.954583i \(-0.596301\pi\)
−0.297945 + 0.954583i \(0.596301\pi\)
\(920\) −82.1122 −2.70716
\(921\) −0.430724 −0.0141928
\(922\) −70.0182 −2.30593
\(923\) 17.7636 0.584696
\(924\) 26.4636 0.870589
\(925\) −24.8140 −0.815878
\(926\) 61.8939 2.03396
\(927\) −7.45720 −0.244927
\(928\) −10.5675 −0.346895
\(929\) 7.05864 0.231586 0.115793 0.993273i \(-0.463059\pi\)
0.115793 + 0.993273i \(0.463059\pi\)
\(930\) 3.97271 0.130270
\(931\) −31.2266 −1.02341
\(932\) 55.4231 1.81545
\(933\) 7.44314 0.243677
\(934\) 74.1946 2.42772
\(935\) −25.4407 −0.832001
\(936\) 95.0393 3.10646
\(937\) 38.4453 1.25595 0.627976 0.778233i \(-0.283883\pi\)
0.627976 + 0.778233i \(0.283883\pi\)
\(938\) 19.0942 0.623447
\(939\) 8.86194 0.289198
\(940\) 29.6065 0.965657
\(941\) 12.8741 0.419684 0.209842 0.977735i \(-0.432705\pi\)
0.209842 + 0.977735i \(0.432705\pi\)
\(942\) 23.8874 0.778295
\(943\) −24.3356 −0.792477
\(944\) 44.9214 1.46207
\(945\) 4.58073 0.149011
\(946\) −6.14307 −0.199728
\(947\) 16.8370 0.547130 0.273565 0.961854i \(-0.411797\pi\)
0.273565 + 0.961854i \(0.411797\pi\)
\(948\) 4.39997 0.142904
\(949\) −42.1447 −1.36808
\(950\) 94.2474 3.05779
\(951\) 3.32520 0.107827
\(952\) −96.2435 −3.11927
\(953\) 30.6399 0.992523 0.496262 0.868173i \(-0.334706\pi\)
0.496262 + 0.868173i \(0.334706\pi\)
\(954\) −104.813 −3.39346
\(955\) 18.4583 0.597296
\(956\) −137.883 −4.45946
\(957\) 1.04290 0.0337121
\(958\) −1.63641 −0.0528701
\(959\) 3.19820 0.103275
\(960\) −17.7567 −0.573094
\(961\) −20.7483 −0.669299
\(962\) −55.5777 −1.79190
\(963\) 49.8431 1.60617
\(964\) 123.793 3.98709
\(965\) 17.7678 0.571966
\(966\) 21.6211 0.695646
\(967\) 19.4591 0.625763 0.312882 0.949792i \(-0.398706\pi\)
0.312882 + 0.949792i \(0.398706\pi\)
\(968\) −174.405 −5.60559
\(969\) −21.3079 −0.684509
\(970\) −13.1441 −0.422031
\(971\) −56.7863 −1.82236 −0.911180 0.412010i \(-0.864827\pi\)
−0.911180 + 0.412010i \(0.864827\pi\)
\(972\) −67.7753 −2.17389
\(973\) 27.6141 0.885267
\(974\) 57.6525 1.84731
\(975\) 6.97507 0.223381
\(976\) 124.060 3.97107
\(977\) 14.8072 0.473724 0.236862 0.971543i \(-0.423881\pi\)
0.236862 + 0.971543i \(0.423881\pi\)
\(978\) −14.8318 −0.474267
\(979\) 11.2637 0.359990
\(980\) −19.7631 −0.631309
\(981\) 8.83112 0.281956
\(982\) −97.3077 −3.10521
\(983\) −41.2239 −1.31484 −0.657420 0.753525i \(-0.728352\pi\)
−0.657420 + 0.753525i \(0.728352\pi\)
\(984\) −13.8343 −0.441020
\(985\) 10.3688 0.330377
\(986\) −5.85193 −0.186363
\(987\) −5.05268 −0.160829
\(988\) 156.149 4.96777
\(989\) −3.71262 −0.118054
\(990\) −36.6646 −1.16528
\(991\) −6.09459 −0.193601 −0.0968006 0.995304i \(-0.530861\pi\)
−0.0968006 + 0.995304i \(0.530861\pi\)
\(992\) −84.9549 −2.69732
\(993\) −5.44785 −0.172882
\(994\) −25.9249 −0.822288
\(995\) 14.2429 0.451531
\(996\) −13.3905 −0.424295
\(997\) 9.78096 0.309766 0.154883 0.987933i \(-0.450500\pi\)
0.154883 + 0.987933i \(0.450500\pi\)
\(998\) −77.6522 −2.45804
\(999\) 16.8867 0.534270
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 \(a_p\))