Properties

Label 8011.2.a.b.1.6
Level 8011
Weight 2
Character 8011.1
Self dual Yes
Analytic conductor 63.968
Analytic rank 0
Dimension 358
CM No

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Newspace parameters

Level: \( N \) = \( 8011 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8011.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9681570592\)
Analytic rank: \(0\)
Dimension: \(358\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 8011.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.70372 q^{2}\) \(-2.07244 q^{3}\) \(+5.31009 q^{4}\) \(+4.20593 q^{5}\) \(+5.60330 q^{6}\) \(+4.19315 q^{7}\) \(-8.94956 q^{8}\) \(+1.29501 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.70372 q^{2}\) \(-2.07244 q^{3}\) \(+5.31009 q^{4}\) \(+4.20593 q^{5}\) \(+5.60330 q^{6}\) \(+4.19315 q^{7}\) \(-8.94956 q^{8}\) \(+1.29501 q^{9}\) \(-11.3717 q^{10}\) \(-2.23649 q^{11}\) \(-11.0049 q^{12}\) \(+3.24584 q^{13}\) \(-11.3371 q^{14}\) \(-8.71655 q^{15}\) \(+13.5769 q^{16}\) \(+4.00059 q^{17}\) \(-3.50135 q^{18}\) \(-6.56274 q^{19}\) \(+22.3339 q^{20}\) \(-8.69006 q^{21}\) \(+6.04685 q^{22}\) \(+9.45662 q^{23}\) \(+18.5474 q^{24}\) \(+12.6899 q^{25}\) \(-8.77583 q^{26}\) \(+3.53349 q^{27}\) \(+22.2660 q^{28}\) \(+6.38044 q^{29}\) \(+23.5671 q^{30}\) \(+1.32287 q^{31}\) \(-18.8090 q^{32}\) \(+4.63500 q^{33}\) \(-10.8165 q^{34}\) \(+17.6361 q^{35}\) \(+6.87664 q^{36}\) \(-4.38564 q^{37}\) \(+17.7438 q^{38}\) \(-6.72681 q^{39}\) \(-37.6412 q^{40}\) \(+4.17632 q^{41}\) \(+23.4955 q^{42}\) \(+2.81123 q^{43}\) \(-11.8760 q^{44}\) \(+5.44674 q^{45}\) \(-25.5680 q^{46}\) \(-6.29850 q^{47}\) \(-28.1373 q^{48}\) \(+10.5825 q^{49}\) \(-34.3098 q^{50}\) \(-8.29099 q^{51}\) \(+17.2357 q^{52}\) \(+0.928598 q^{53}\) \(-9.55355 q^{54}\) \(-9.40654 q^{55}\) \(-37.5268 q^{56}\) \(+13.6009 q^{57}\) \(-17.2509 q^{58}\) \(+13.5817 q^{59}\) \(-46.2857 q^{60}\) \(+14.0085 q^{61}\) \(-3.57666 q^{62}\) \(+5.43018 q^{63}\) \(+23.7004 q^{64}\) \(+13.6518 q^{65}\) \(-12.5317 q^{66}\) \(-11.2403 q^{67}\) \(+21.2435 q^{68}\) \(-19.5983 q^{69}\) \(-47.6831 q^{70}\) \(-7.99596 q^{71}\) \(-11.5898 q^{72}\) \(+6.78034 q^{73}\) \(+11.8575 q^{74}\) \(-26.2990 q^{75}\) \(-34.8487 q^{76}\) \(-9.37796 q^{77}\) \(+18.1874 q^{78}\) \(-3.59777 q^{79}\) \(+57.1035 q^{80}\) \(-11.2080 q^{81}\) \(-11.2916 q^{82}\) \(+0.862536 q^{83}\) \(-46.1450 q^{84}\) \(+16.8262 q^{85}\) \(-7.60078 q^{86}\) \(-13.2231 q^{87}\) \(+20.0156 q^{88}\) \(-10.6574 q^{89}\) \(-14.7264 q^{90}\) \(+13.6103 q^{91}\) \(+50.2155 q^{92}\) \(-2.74156 q^{93}\) \(+17.0294 q^{94}\) \(-27.6024 q^{95}\) \(+38.9805 q^{96}\) \(+16.8653 q^{97}\) \(-28.6122 q^{98}\) \(-2.89629 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut 21q^{10} \) \(\mathstrut +\mathstrut 70q^{11} \) \(\mathstrut +\mathstrut 20q^{12} \) \(\mathstrut +\mathstrut 53q^{13} \) \(\mathstrut +\mathstrut 69q^{14} \) \(\mathstrut +\mathstrut 28q^{15} \) \(\mathstrut +\mathstrut 449q^{16} \) \(\mathstrut +\mathstrut 88q^{17} \) \(\mathstrut +\mathstrut 86q^{18} \) \(\mathstrut +\mathstrut 44q^{19} \) \(\mathstrut +\mathstrut 136q^{20} \) \(\mathstrut +\mathstrut 125q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 104q^{23} \) \(\mathstrut +\mathstrut 84q^{24} \) \(\mathstrut +\mathstrut 444q^{25} \) \(\mathstrut +\mathstrut 100q^{26} \) \(\mathstrut +\mathstrut 32q^{27} \) \(\mathstrut +\mathstrut 46q^{28} \) \(\mathstrut +\mathstrut 373q^{29} \) \(\mathstrut +\mathstrut 99q^{30} \) \(\mathstrut +\mathstrut 30q^{31} \) \(\mathstrut +\mathstrut 221q^{32} \) \(\mathstrut +\mathstrut 56q^{33} \) \(\mathstrut +\mathstrut 26q^{34} \) \(\mathstrut +\mathstrut 164q^{35} \) \(\mathstrut +\mathstrut 599q^{36} \) \(\mathstrut +\mathstrut 81q^{37} \) \(\mathstrut +\mathstrut 66q^{38} \) \(\mathstrut +\mathstrut 143q^{39} \) \(\mathstrut +\mathstrut 42q^{40} \) \(\mathstrut +\mathstrut 182q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut +\mathstrut 40q^{43} \) \(\mathstrut +\mathstrut 184q^{44} \) \(\mathstrut +\mathstrut 198q^{45} \) \(\mathstrut +\mathstrut 54q^{46} \) \(\mathstrut +\mathstrut 66q^{47} \) \(\mathstrut +\mathstrut 5q^{48} \) \(\mathstrut +\mathstrut 479q^{49} \) \(\mathstrut +\mathstrut 184q^{50} \) \(\mathstrut +\mathstrut 123q^{51} \) \(\mathstrut +\mathstrut 64q^{52} \) \(\mathstrut +\mathstrut 221q^{53} \) \(\mathstrut +\mathstrut 67q^{54} \) \(\mathstrut +\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 174q^{56} \) \(\mathstrut +\mathstrut 84q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut +\mathstrut 127q^{59} \) \(\mathstrut +\mathstrut 29q^{60} \) \(\mathstrut +\mathstrut 174q^{61} \) \(\mathstrut +\mathstrut 86q^{62} \) \(\mathstrut +\mathstrut 48q^{63} \) \(\mathstrut +\mathstrut 549q^{64} \) \(\mathstrut +\mathstrut 202q^{65} \) \(\mathstrut +\mathstrut 32q^{66} \) \(\mathstrut +\mathstrut 29q^{67} \) \(\mathstrut +\mathstrut 172q^{68} \) \(\mathstrut +\mathstrut 249q^{69} \) \(\mathstrut +\mathstrut 12q^{70} \) \(\mathstrut +\mathstrut 185q^{71} \) \(\mathstrut +\mathstrut 218q^{72} \) \(\mathstrut +\mathstrut 57q^{73} \) \(\mathstrut +\mathstrut 272q^{74} \) \(\mathstrut +\mathstrut 24q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 384q^{77} \) \(\mathstrut +\mathstrut 12q^{78} \) \(\mathstrut +\mathstrut 93q^{79} \) \(\mathstrut +\mathstrut 215q^{80} \) \(\mathstrut +\mathstrut 702q^{81} \) \(\mathstrut +\mathstrut 48q^{82} \) \(\mathstrut +\mathstrut 121q^{83} \) \(\mathstrut +\mathstrut 179q^{84} \) \(\mathstrut +\mathstrut 177q^{85} \) \(\mathstrut +\mathstrut 209q^{86} \) \(\mathstrut +\mathstrut 91q^{87} \) \(\mathstrut +\mathstrut 36q^{88} \) \(\mathstrut +\mathstrut 186q^{89} \) \(\mathstrut +\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 32q^{91} \) \(\mathstrut +\mathstrut 272q^{92} \) \(\mathstrut +\mathstrut 220q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 170q^{95} \) \(\mathstrut +\mathstrut 162q^{96} \) \(\mathstrut +\mathstrut 22q^{97} \) \(\mathstrut +\mathstrut 196q^{98} \) \(\mathstrut +\mathstrut 152q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.70372 −1.91182 −0.955909 0.293664i \(-0.905125\pi\)
−0.955909 + 0.293664i \(0.905125\pi\)
\(3\) −2.07244 −1.19652 −0.598262 0.801300i \(-0.704142\pi\)
−0.598262 + 0.801300i \(0.704142\pi\)
\(4\) 5.31009 2.65505
\(5\) 4.20593 1.88095 0.940475 0.339862i \(-0.110380\pi\)
0.940475 + 0.339862i \(0.110380\pi\)
\(6\) 5.60330 2.28754
\(7\) 4.19315 1.58486 0.792431 0.609961i \(-0.208815\pi\)
0.792431 + 0.609961i \(0.208815\pi\)
\(8\) −8.94956 −3.16415
\(9\) 1.29501 0.431671
\(10\) −11.3717 −3.59603
\(11\) −2.23649 −0.674328 −0.337164 0.941446i \(-0.609468\pi\)
−0.337164 + 0.941446i \(0.609468\pi\)
\(12\) −11.0049 −3.17683
\(13\) 3.24584 0.900233 0.450117 0.892970i \(-0.351382\pi\)
0.450117 + 0.892970i \(0.351382\pi\)
\(14\) −11.3371 −3.02997
\(15\) −8.71655 −2.25060
\(16\) 13.5769 3.39422
\(17\) 4.00059 0.970286 0.485143 0.874435i \(-0.338768\pi\)
0.485143 + 0.874435i \(0.338768\pi\)
\(18\) −3.50135 −0.825276
\(19\) −6.56274 −1.50560 −0.752798 0.658252i \(-0.771296\pi\)
−0.752798 + 0.658252i \(0.771296\pi\)
\(20\) 22.3339 4.99401
\(21\) −8.69006 −1.89633
\(22\) 6.04685 1.28919
\(23\) 9.45662 1.97184 0.985921 0.167214i \(-0.0534770\pi\)
0.985921 + 0.167214i \(0.0534770\pi\)
\(24\) 18.5474 3.78598
\(25\) 12.6899 2.53797
\(26\) −8.77583 −1.72108
\(27\) 3.53349 0.680020
\(28\) 22.2660 4.20788
\(29\) 6.38044 1.18482 0.592409 0.805638i \(-0.298177\pi\)
0.592409 + 0.805638i \(0.298177\pi\)
\(30\) 23.5671 4.30274
\(31\) 1.32287 0.237594 0.118797 0.992919i \(-0.462096\pi\)
0.118797 + 0.992919i \(0.462096\pi\)
\(32\) −18.8090 −3.32499
\(33\) 4.63500 0.806850
\(34\) −10.8165 −1.85501
\(35\) 17.6361 2.98105
\(36\) 6.87664 1.14611
\(37\) −4.38564 −0.720995 −0.360497 0.932760i \(-0.617393\pi\)
−0.360497 + 0.932760i \(0.617393\pi\)
\(38\) 17.7438 2.87842
\(39\) −6.72681 −1.07715
\(40\) −37.6412 −5.95160
\(41\) 4.17632 0.652231 0.326116 0.945330i \(-0.394260\pi\)
0.326116 + 0.945330i \(0.394260\pi\)
\(42\) 23.4955 3.62543
\(43\) 2.81123 0.428709 0.214354 0.976756i \(-0.431235\pi\)
0.214354 + 0.976756i \(0.431235\pi\)
\(44\) −11.8760 −1.79037
\(45\) 5.44674 0.811952
\(46\) −25.5680 −3.76980
\(47\) −6.29850 −0.918731 −0.459365 0.888247i \(-0.651923\pi\)
−0.459365 + 0.888247i \(0.651923\pi\)
\(48\) −28.1373 −4.06127
\(49\) 10.5825 1.51179
\(50\) −34.3098 −4.85214
\(51\) −8.29099 −1.16097
\(52\) 17.2357 2.39016
\(53\) 0.928598 0.127553 0.0637764 0.997964i \(-0.479686\pi\)
0.0637764 + 0.997964i \(0.479686\pi\)
\(54\) −9.55355 −1.30007
\(55\) −9.40654 −1.26838
\(56\) −37.5268 −5.01474
\(57\) 13.6009 1.80148
\(58\) −17.2509 −2.26515
\(59\) 13.5817 1.76819 0.884096 0.467306i \(-0.154775\pi\)
0.884096 + 0.467306i \(0.154775\pi\)
\(60\) −46.2857 −5.97545
\(61\) 14.0085 1.79361 0.896804 0.442428i \(-0.145883\pi\)
0.896804 + 0.442428i \(0.145883\pi\)
\(62\) −3.57666 −0.454236
\(63\) 5.43018 0.684139
\(64\) 23.7004 2.96255
\(65\) 13.6518 1.69329
\(66\) −12.5317 −1.54255
\(67\) −11.2403 −1.37323 −0.686614 0.727023i \(-0.740904\pi\)
−0.686614 + 0.727023i \(0.740904\pi\)
\(68\) 21.2435 2.57615
\(69\) −19.5983 −2.35936
\(70\) −47.6831 −5.69922
\(71\) −7.99596 −0.948946 −0.474473 0.880270i \(-0.657361\pi\)
−0.474473 + 0.880270i \(0.657361\pi\)
\(72\) −11.5898 −1.36587
\(73\) 6.78034 0.793579 0.396790 0.917910i \(-0.370124\pi\)
0.396790 + 0.917910i \(0.370124\pi\)
\(74\) 11.8575 1.37841
\(75\) −26.2990 −3.03675
\(76\) −34.8487 −3.99742
\(77\) −9.37796 −1.06872
\(78\) 18.1874 2.05932
\(79\) −3.59777 −0.404781 −0.202391 0.979305i \(-0.564871\pi\)
−0.202391 + 0.979305i \(0.564871\pi\)
\(80\) 57.1035 6.38436
\(81\) −11.2080 −1.24533
\(82\) −11.2916 −1.24695
\(83\) 0.862536 0.0946757 0.0473378 0.998879i \(-0.484926\pi\)
0.0473378 + 0.998879i \(0.484926\pi\)
\(84\) −46.1450 −5.03483
\(85\) 16.8262 1.82506
\(86\) −7.60078 −0.819613
\(87\) −13.2231 −1.41766
\(88\) 20.0156 2.13367
\(89\) −10.6574 −1.12968 −0.564839 0.825201i \(-0.691062\pi\)
−0.564839 + 0.825201i \(0.691062\pi\)
\(90\) −14.7264 −1.55230
\(91\) 13.6103 1.42675
\(92\) 50.2155 5.23533
\(93\) −2.74156 −0.284287
\(94\) 17.0294 1.75645
\(95\) −27.6024 −2.83195
\(96\) 38.9805 3.97843
\(97\) 16.8653 1.71241 0.856206 0.516634i \(-0.172815\pi\)
0.856206 + 0.516634i \(0.172815\pi\)
\(98\) −28.6122 −2.89026
\(99\) −2.89629 −0.291088
\(100\) 67.3844 6.73844
\(101\) −5.47287 −0.544571 −0.272285 0.962217i \(-0.587779\pi\)
−0.272285 + 0.962217i \(0.587779\pi\)
\(102\) 22.4165 2.21956
\(103\) −7.03762 −0.693437 −0.346718 0.937969i \(-0.612704\pi\)
−0.346718 + 0.937969i \(0.612704\pi\)
\(104\) −29.0488 −2.84847
\(105\) −36.5498 −3.56690
\(106\) −2.51067 −0.243858
\(107\) 4.26824 0.412626 0.206313 0.978486i \(-0.433853\pi\)
0.206313 + 0.978486i \(0.433853\pi\)
\(108\) 18.7631 1.80548
\(109\) −14.7631 −1.41405 −0.707026 0.707188i \(-0.749964\pi\)
−0.707026 + 0.707188i \(0.749964\pi\)
\(110\) 25.4326 2.42491
\(111\) 9.08898 0.862688
\(112\) 56.9300 5.37938
\(113\) 2.62783 0.247206 0.123603 0.992332i \(-0.460555\pi\)
0.123603 + 0.992332i \(0.460555\pi\)
\(114\) −36.7730 −3.44410
\(115\) 39.7739 3.70894
\(116\) 33.8807 3.14575
\(117\) 4.20340 0.388605
\(118\) −36.7212 −3.38046
\(119\) 16.7751 1.53777
\(120\) 78.0092 7.12124
\(121\) −5.99809 −0.545281
\(122\) −37.8751 −3.42905
\(123\) −8.65517 −0.780411
\(124\) 7.02454 0.630822
\(125\) 32.3431 2.89285
\(126\) −14.6817 −1.30795
\(127\) 2.50030 0.221866 0.110933 0.993828i \(-0.464616\pi\)
0.110933 + 0.993828i \(0.464616\pi\)
\(128\) −26.4612 −2.33886
\(129\) −5.82611 −0.512960
\(130\) −36.9106 −3.23727
\(131\) 9.96624 0.870754 0.435377 0.900248i \(-0.356615\pi\)
0.435377 + 0.900248i \(0.356615\pi\)
\(132\) 24.6123 2.14222
\(133\) −27.5185 −2.38616
\(134\) 30.3907 2.62536
\(135\) 14.8616 1.27908
\(136\) −35.8035 −3.07013
\(137\) 6.00872 0.513359 0.256680 0.966497i \(-0.417371\pi\)
0.256680 + 0.966497i \(0.417371\pi\)
\(138\) 52.9882 4.51066
\(139\) −8.07660 −0.685048 −0.342524 0.939509i \(-0.611282\pi\)
−0.342524 + 0.939509i \(0.611282\pi\)
\(140\) 93.6494 7.91482
\(141\) 13.0533 1.09928
\(142\) 21.6188 1.81421
\(143\) −7.25930 −0.607053
\(144\) 17.5822 1.46519
\(145\) 26.8357 2.22858
\(146\) −18.3321 −1.51718
\(147\) −21.9317 −1.80889
\(148\) −23.2881 −1.91427
\(149\) 18.7596 1.53684 0.768421 0.639944i \(-0.221043\pi\)
0.768421 + 0.639944i \(0.221043\pi\)
\(150\) 71.1051 5.80571
\(151\) −7.10135 −0.577899 −0.288950 0.957344i \(-0.593306\pi\)
−0.288950 + 0.957344i \(0.593306\pi\)
\(152\) 58.7336 4.76392
\(153\) 5.18082 0.418844
\(154\) 25.3554 2.04319
\(155\) 5.56389 0.446902
\(156\) −35.7200 −2.85989
\(157\) −1.71418 −0.136806 −0.0684032 0.997658i \(-0.521790\pi\)
−0.0684032 + 0.997658i \(0.521790\pi\)
\(158\) 9.72737 0.773868
\(159\) −1.92447 −0.152620
\(160\) −79.1093 −6.25414
\(161\) 39.6530 3.12510
\(162\) 30.3032 2.38085
\(163\) −15.7235 −1.23156 −0.615780 0.787918i \(-0.711159\pi\)
−0.615780 + 0.787918i \(0.711159\pi\)
\(164\) 22.1766 1.73170
\(165\) 19.4945 1.51765
\(166\) −2.33206 −0.181003
\(167\) 15.8853 1.22924 0.614621 0.788822i \(-0.289309\pi\)
0.614621 + 0.788822i \(0.289309\pi\)
\(168\) 77.7722 6.00025
\(169\) −2.46454 −0.189580
\(170\) −45.4933 −3.48918
\(171\) −8.49883 −0.649922
\(172\) 14.9279 1.13824
\(173\) 7.98341 0.606967 0.303484 0.952837i \(-0.401850\pi\)
0.303484 + 0.952837i \(0.401850\pi\)
\(174\) 35.7515 2.71031
\(175\) 53.2106 4.02234
\(176\) −30.3646 −2.28882
\(177\) −28.1474 −2.11568
\(178\) 28.8145 2.15974
\(179\) 18.0828 1.35158 0.675788 0.737096i \(-0.263804\pi\)
0.675788 + 0.737096i \(0.263804\pi\)
\(180\) 28.9227 2.15577
\(181\) 13.2551 0.985245 0.492623 0.870243i \(-0.336038\pi\)
0.492623 + 0.870243i \(0.336038\pi\)
\(182\) −36.7984 −2.72768
\(183\) −29.0318 −2.14610
\(184\) −84.6325 −6.23919
\(185\) −18.4457 −1.35616
\(186\) 7.41241 0.543504
\(187\) −8.94730 −0.654291
\(188\) −33.4456 −2.43927
\(189\) 14.8164 1.07774
\(190\) 74.6292 5.41417
\(191\) −5.07535 −0.367240 −0.183620 0.982997i \(-0.558782\pi\)
−0.183620 + 0.982997i \(0.558782\pi\)
\(192\) −49.1177 −3.54476
\(193\) −15.5604 −1.12006 −0.560032 0.828471i \(-0.689211\pi\)
−0.560032 + 0.828471i \(0.689211\pi\)
\(194\) −45.5990 −3.27382
\(195\) −28.2925 −2.02607
\(196\) 56.1942 4.01387
\(197\) −22.2303 −1.58385 −0.791923 0.610621i \(-0.790920\pi\)
−0.791923 + 0.610621i \(0.790920\pi\)
\(198\) 7.83075 0.556507
\(199\) 4.28616 0.303838 0.151919 0.988393i \(-0.451455\pi\)
0.151919 + 0.988393i \(0.451455\pi\)
\(200\) −113.569 −8.03052
\(201\) 23.2950 1.64310
\(202\) 14.7971 1.04112
\(203\) 26.7541 1.87777
\(204\) −44.0259 −3.08243
\(205\) 17.5653 1.22681
\(206\) 19.0277 1.32572
\(207\) 12.2464 0.851186
\(208\) 44.0684 3.05559
\(209\) 14.6775 1.01527
\(210\) 98.8204 6.81925
\(211\) −21.7826 −1.49958 −0.749789 0.661676i \(-0.769845\pi\)
−0.749789 + 0.661676i \(0.769845\pi\)
\(212\) 4.93094 0.338659
\(213\) 16.5712 1.13544
\(214\) −11.5401 −0.788866
\(215\) 11.8238 0.806380
\(216\) −31.6231 −2.15168
\(217\) 5.54698 0.376553
\(218\) 39.9154 2.70341
\(219\) −14.0519 −0.949537
\(220\) −49.9496 −3.36760
\(221\) 12.9853 0.873484
\(222\) −24.5740 −1.64930
\(223\) −15.4526 −1.03478 −0.517391 0.855749i \(-0.673097\pi\)
−0.517391 + 0.855749i \(0.673097\pi\)
\(224\) −78.8689 −5.26965
\(225\) 16.4335 1.09557
\(226\) −7.10492 −0.472613
\(227\) −6.80450 −0.451631 −0.225815 0.974170i \(-0.572505\pi\)
−0.225815 + 0.974170i \(0.572505\pi\)
\(228\) 72.2220 4.78302
\(229\) 8.88117 0.586884 0.293442 0.955977i \(-0.405199\pi\)
0.293442 + 0.955977i \(0.405199\pi\)
\(230\) −107.537 −7.09081
\(231\) 19.4353 1.27875
\(232\) −57.1021 −3.74894
\(233\) −22.5769 −1.47906 −0.739532 0.673121i \(-0.764953\pi\)
−0.739532 + 0.673121i \(0.764953\pi\)
\(234\) −11.3648 −0.742941
\(235\) −26.4911 −1.72809
\(236\) 72.1203 4.69463
\(237\) 7.45618 0.484331
\(238\) −45.3551 −2.93993
\(239\) −6.13566 −0.396883 −0.198441 0.980113i \(-0.563588\pi\)
−0.198441 + 0.980113i \(0.563588\pi\)
\(240\) −118.344 −7.63905
\(241\) 5.30845 0.341947 0.170974 0.985276i \(-0.445309\pi\)
0.170974 + 0.985276i \(0.445309\pi\)
\(242\) 16.2172 1.04248
\(243\) 12.6274 0.810049
\(244\) 74.3865 4.76211
\(245\) 44.5094 2.84360
\(246\) 23.4012 1.49200
\(247\) −21.3016 −1.35539
\(248\) −11.8391 −0.751781
\(249\) −1.78756 −0.113282
\(250\) −87.4466 −5.53061
\(251\) 29.7565 1.87821 0.939106 0.343627i \(-0.111656\pi\)
0.939106 + 0.343627i \(0.111656\pi\)
\(252\) 28.8348 1.81642
\(253\) −21.1497 −1.32967
\(254\) −6.76010 −0.424167
\(255\) −34.8713 −2.18373
\(256\) 24.1429 1.50893
\(257\) 17.7093 1.10468 0.552338 0.833620i \(-0.313736\pi\)
0.552338 + 0.833620i \(0.313736\pi\)
\(258\) 15.7522 0.980687
\(259\) −18.3896 −1.14268
\(260\) 72.4922 4.49577
\(261\) 8.26275 0.511451
\(262\) −26.9459 −1.66472
\(263\) −18.5231 −1.14218 −0.571091 0.820887i \(-0.693480\pi\)
−0.571091 + 0.820887i \(0.693480\pi\)
\(264\) −41.4812 −2.55299
\(265\) 3.90562 0.239920
\(266\) 74.4024 4.56190
\(267\) 22.0868 1.35169
\(268\) −59.6873 −3.64598
\(269\) −5.50627 −0.335723 −0.167861 0.985811i \(-0.553686\pi\)
−0.167861 + 0.985811i \(0.553686\pi\)
\(270\) −40.1816 −2.44537
\(271\) 21.4439 1.30262 0.651311 0.758811i \(-0.274219\pi\)
0.651311 + 0.758811i \(0.274219\pi\)
\(272\) 54.3156 3.29337
\(273\) −28.2065 −1.70714
\(274\) −16.2459 −0.981449
\(275\) −28.3808 −1.71143
\(276\) −104.069 −6.26420
\(277\) −17.8265 −1.07109 −0.535545 0.844507i \(-0.679894\pi\)
−0.535545 + 0.844507i \(0.679894\pi\)
\(278\) 21.8368 1.30969
\(279\) 1.71313 0.102562
\(280\) −157.835 −9.43247
\(281\) −6.55693 −0.391153 −0.195577 0.980688i \(-0.562658\pi\)
−0.195577 + 0.980688i \(0.562658\pi\)
\(282\) −35.2924 −2.10163
\(283\) −12.0206 −0.714550 −0.357275 0.933999i \(-0.616294\pi\)
−0.357275 + 0.933999i \(0.616294\pi\)
\(284\) −42.4593 −2.51949
\(285\) 57.2044 3.38850
\(286\) 19.6271 1.16057
\(287\) 17.5119 1.03370
\(288\) −24.3579 −1.43530
\(289\) −0.995277 −0.0585457
\(290\) −72.5562 −4.26064
\(291\) −34.9524 −2.04894
\(292\) 36.0042 2.10699
\(293\) −12.6267 −0.737659 −0.368830 0.929497i \(-0.620241\pi\)
−0.368830 + 0.929497i \(0.620241\pi\)
\(294\) 59.2970 3.45827
\(295\) 57.1239 3.32588
\(296\) 39.2495 2.28133
\(297\) −7.90262 −0.458557
\(298\) −50.7205 −2.93816
\(299\) 30.6947 1.77512
\(300\) −139.650 −8.06271
\(301\) 11.7879 0.679444
\(302\) 19.2000 1.10484
\(303\) 11.3422 0.651592
\(304\) −89.1016 −5.11033
\(305\) 58.9189 3.37369
\(306\) −14.0075 −0.800753
\(307\) −18.3145 −1.04526 −0.522631 0.852559i \(-0.675050\pi\)
−0.522631 + 0.852559i \(0.675050\pi\)
\(308\) −49.7978 −2.83749
\(309\) 14.5850 0.829714
\(310\) −15.0432 −0.854395
\(311\) −31.1654 −1.76723 −0.883615 0.468214i \(-0.844898\pi\)
−0.883615 + 0.468214i \(0.844898\pi\)
\(312\) 60.2019 3.40826
\(313\) −22.3881 −1.26545 −0.632725 0.774376i \(-0.718064\pi\)
−0.632725 + 0.774376i \(0.718064\pi\)
\(314\) 4.63465 0.261549
\(315\) 22.8390 1.28683
\(316\) −19.1045 −1.07471
\(317\) −9.62279 −0.540470 −0.270235 0.962794i \(-0.587101\pi\)
−0.270235 + 0.962794i \(0.587101\pi\)
\(318\) 5.20321 0.291782
\(319\) −14.2698 −0.798956
\(320\) 99.6823 5.57241
\(321\) −8.84567 −0.493717
\(322\) −107.211 −5.97462
\(323\) −26.2548 −1.46086
\(324\) −59.5154 −3.30641
\(325\) 41.1893 2.28477
\(326\) 42.5119 2.35452
\(327\) 30.5957 1.69195
\(328\) −37.3762 −2.06375
\(329\) −26.4106 −1.45606
\(330\) −52.7077 −2.90146
\(331\) 12.7961 0.703336 0.351668 0.936125i \(-0.385615\pi\)
0.351668 + 0.936125i \(0.385615\pi\)
\(332\) 4.58015 0.251368
\(333\) −5.67946 −0.311232
\(334\) −42.9494 −2.35009
\(335\) −47.2762 −2.58297
\(336\) −117.984 −6.43656
\(337\) 8.37278 0.456095 0.228047 0.973650i \(-0.426766\pi\)
0.228047 + 0.973650i \(0.426766\pi\)
\(338\) 6.66341 0.362442
\(339\) −5.44603 −0.295788
\(340\) 89.3487 4.84562
\(341\) −2.95858 −0.160216
\(342\) 22.9784 1.24253
\(343\) 15.0221 0.811115
\(344\) −25.1593 −1.35650
\(345\) −82.4291 −4.43783
\(346\) −21.5849 −1.16041
\(347\) 7.94098 0.426294 0.213147 0.977020i \(-0.431629\pi\)
0.213147 + 0.977020i \(0.431629\pi\)
\(348\) −70.2158 −3.76396
\(349\) 35.0210 1.87463 0.937316 0.348482i \(-0.113303\pi\)
0.937316 + 0.348482i \(0.113303\pi\)
\(350\) −143.866 −7.68998
\(351\) 11.4691 0.612177
\(352\) 42.0662 2.24213
\(353\) 16.9614 0.902762 0.451381 0.892331i \(-0.350932\pi\)
0.451381 + 0.892331i \(0.350932\pi\)
\(354\) 76.1025 4.04480
\(355\) −33.6305 −1.78492
\(356\) −56.5916 −2.99935
\(357\) −34.7654 −1.83998
\(358\) −48.8909 −2.58397
\(359\) 1.56656 0.0826799 0.0413400 0.999145i \(-0.486837\pi\)
0.0413400 + 0.999145i \(0.486837\pi\)
\(360\) −48.7459 −2.56913
\(361\) 24.0695 1.26682
\(362\) −35.8381 −1.88361
\(363\) 12.4307 0.652442
\(364\) 72.2719 3.78808
\(365\) 28.5177 1.49268
\(366\) 78.4939 4.10294
\(367\) 31.3881 1.63845 0.819223 0.573475i \(-0.194405\pi\)
0.819223 + 0.573475i \(0.194405\pi\)
\(368\) 128.391 6.69287
\(369\) 5.40839 0.281549
\(370\) 49.8720 2.59272
\(371\) 3.89375 0.202154
\(372\) −14.5579 −0.754794
\(373\) 2.08447 0.107930 0.0539649 0.998543i \(-0.482814\pi\)
0.0539649 + 0.998543i \(0.482814\pi\)
\(374\) 24.1910 1.25089
\(375\) −67.0291 −3.46137
\(376\) 56.3688 2.90700
\(377\) 20.7099 1.06661
\(378\) −40.0595 −2.06044
\(379\) −16.4732 −0.846171 −0.423085 0.906090i \(-0.639053\pi\)
−0.423085 + 0.906090i \(0.639053\pi\)
\(380\) −146.571 −7.51896
\(381\) −5.18172 −0.265468
\(382\) 13.7223 0.702095
\(383\) 22.0010 1.12420 0.562100 0.827069i \(-0.309993\pi\)
0.562100 + 0.827069i \(0.309993\pi\)
\(384\) 54.8393 2.79851
\(385\) −39.4431 −2.01020
\(386\) 42.0710 2.14136
\(387\) 3.64058 0.185061
\(388\) 89.5563 4.54653
\(389\) 26.9195 1.36487 0.682437 0.730944i \(-0.260920\pi\)
0.682437 + 0.730944i \(0.260920\pi\)
\(390\) 76.4950 3.87347
\(391\) 37.8321 1.91325
\(392\) −94.7089 −4.78352
\(393\) −20.6544 −1.04188
\(394\) 60.1045 3.02802
\(395\) −15.1320 −0.761373
\(396\) −15.3796 −0.772852
\(397\) 1.31921 0.0662094 0.0331047 0.999452i \(-0.489461\pi\)
0.0331047 + 0.999452i \(0.489461\pi\)
\(398\) −11.5886 −0.580883
\(399\) 57.0306 2.85510
\(400\) 172.289 8.61445
\(401\) −23.8196 −1.18950 −0.594748 0.803913i \(-0.702748\pi\)
−0.594748 + 0.803913i \(0.702748\pi\)
\(402\) −62.9830 −3.14131
\(403\) 4.29381 0.213890
\(404\) −29.0614 −1.44586
\(405\) −47.1400 −2.34241
\(406\) −72.3357 −3.58996
\(407\) 9.80846 0.486187
\(408\) 74.2007 3.67348
\(409\) 6.30258 0.311643 0.155821 0.987785i \(-0.450198\pi\)
0.155821 + 0.987785i \(0.450198\pi\)
\(410\) −47.4917 −2.34545
\(411\) −12.4527 −0.614247
\(412\) −37.3704 −1.84111
\(413\) 56.9503 2.80234
\(414\) −33.1109 −1.62731
\(415\) 3.62777 0.178080
\(416\) −61.0509 −2.99327
\(417\) 16.7383 0.819677
\(418\) −39.6839 −1.94100
\(419\) 6.07346 0.296708 0.148354 0.988934i \(-0.452602\pi\)
0.148354 + 0.988934i \(0.452602\pi\)
\(420\) −194.083 −9.47027
\(421\) 14.8931 0.725846 0.362923 0.931819i \(-0.381779\pi\)
0.362923 + 0.931819i \(0.381779\pi\)
\(422\) 58.8941 2.86692
\(423\) −8.15664 −0.396589
\(424\) −8.31054 −0.403596
\(425\) 50.7670 2.46256
\(426\) −44.8037 −2.17075
\(427\) 58.7399 2.84262
\(428\) 22.6647 1.09554
\(429\) 15.0445 0.726354
\(430\) −31.9684 −1.54165
\(431\) −20.0255 −0.964593 −0.482296 0.876008i \(-0.660197\pi\)
−0.482296 + 0.876008i \(0.660197\pi\)
\(432\) 47.9738 2.30814
\(433\) −24.8438 −1.19392 −0.596958 0.802273i \(-0.703624\pi\)
−0.596958 + 0.802273i \(0.703624\pi\)
\(434\) −14.9975 −0.719901
\(435\) −55.6154 −2.66655
\(436\) −78.3936 −3.75437
\(437\) −62.0613 −2.96879
\(438\) 37.9923 1.81534
\(439\) −19.8237 −0.946134 −0.473067 0.881027i \(-0.656853\pi\)
−0.473067 + 0.881027i \(0.656853\pi\)
\(440\) 84.1844 4.01333
\(441\) 13.7045 0.652595
\(442\) −35.1085 −1.66994
\(443\) −0.964313 −0.0458159 −0.0229080 0.999738i \(-0.507292\pi\)
−0.0229080 + 0.999738i \(0.507292\pi\)
\(444\) 48.2633 2.29048
\(445\) −44.8241 −2.12487
\(446\) 41.7795 1.97832
\(447\) −38.8781 −1.83887
\(448\) 99.3793 4.69523
\(449\) −17.3620 −0.819362 −0.409681 0.912229i \(-0.634360\pi\)
−0.409681 + 0.912229i \(0.634360\pi\)
\(450\) −44.4317 −2.09453
\(451\) −9.34031 −0.439818
\(452\) 13.9540 0.656343
\(453\) 14.7171 0.691471
\(454\) 18.3975 0.863435
\(455\) 57.2440 2.68364
\(456\) −121.722 −5.70015
\(457\) −17.4764 −0.817512 −0.408756 0.912644i \(-0.634037\pi\)
−0.408756 + 0.912644i \(0.634037\pi\)
\(458\) −24.0122 −1.12202
\(459\) 14.1360 0.659813
\(460\) 211.203 9.84739
\(461\) 26.9364 1.25455 0.627277 0.778797i \(-0.284170\pi\)
0.627277 + 0.778797i \(0.284170\pi\)
\(462\) −52.5475 −2.44473
\(463\) −18.4736 −0.858541 −0.429270 0.903176i \(-0.641229\pi\)
−0.429270 + 0.903176i \(0.641229\pi\)
\(464\) 86.6265 4.02153
\(465\) −11.5308 −0.534729
\(466\) 61.0417 2.82770
\(467\) −35.4717 −1.64143 −0.820716 0.571336i \(-0.806425\pi\)
−0.820716 + 0.571336i \(0.806425\pi\)
\(468\) 22.3204 1.03176
\(469\) −47.1325 −2.17638
\(470\) 71.6244 3.30379
\(471\) 3.55253 0.163692
\(472\) −121.551 −5.59482
\(473\) −6.28730 −0.289090
\(474\) −20.1594 −0.925952
\(475\) −83.2803 −3.82116
\(476\) 89.0772 4.08285
\(477\) 1.20255 0.0550608
\(478\) 16.5891 0.758768
\(479\) −10.1495 −0.463742 −0.231871 0.972747i \(-0.574485\pi\)
−0.231871 + 0.972747i \(0.574485\pi\)
\(480\) 163.949 7.48323
\(481\) −14.2351 −0.649063
\(482\) −14.3526 −0.653741
\(483\) −82.1786 −3.73926
\(484\) −31.8504 −1.44775
\(485\) 70.9344 3.22096
\(486\) −34.1410 −1.54867
\(487\) −33.7172 −1.52787 −0.763936 0.645292i \(-0.776736\pi\)
−0.763936 + 0.645292i \(0.776736\pi\)
\(488\) −125.370 −5.67524
\(489\) 32.5860 1.47359
\(490\) −120.341 −5.43644
\(491\) 34.1363 1.54055 0.770274 0.637713i \(-0.220119\pi\)
0.770274 + 0.637713i \(0.220119\pi\)
\(492\) −45.9598 −2.07203
\(493\) 25.5255 1.14961
\(494\) 57.5935 2.59125
\(495\) −12.1816 −0.547522
\(496\) 17.9604 0.806446
\(497\) −33.5283 −1.50395
\(498\) 4.83305 0.216574
\(499\) −25.1260 −1.12479 −0.562396 0.826868i \(-0.690120\pi\)
−0.562396 + 0.826868i \(0.690120\pi\)
\(500\) 171.745 7.68066
\(501\) −32.9214 −1.47082
\(502\) −80.4531 −3.59080
\(503\) 15.6115 0.696083 0.348041 0.937479i \(-0.386847\pi\)
0.348041 + 0.937479i \(0.386847\pi\)
\(504\) −48.5977 −2.16472
\(505\) −23.0185 −1.02431
\(506\) 57.1827 2.54208
\(507\) 5.10761 0.226837
\(508\) 13.2768 0.589063
\(509\) 15.1050 0.669516 0.334758 0.942304i \(-0.391345\pi\)
0.334758 + 0.942304i \(0.391345\pi\)
\(510\) 94.2823 4.17489
\(511\) 28.4310 1.25771
\(512\) −12.3532 −0.545938
\(513\) −23.1893 −1.02383
\(514\) −47.8810 −2.11194
\(515\) −29.5997 −1.30432
\(516\) −30.9372 −1.36193
\(517\) 14.0866 0.619526
\(518\) 49.7204 2.18459
\(519\) −16.5451 −0.726251
\(520\) −122.177 −5.35783
\(521\) −1.83477 −0.0803826 −0.0401913 0.999192i \(-0.512797\pi\)
−0.0401913 + 0.999192i \(0.512797\pi\)
\(522\) −22.3401 −0.977801
\(523\) 41.7506 1.82563 0.912813 0.408378i \(-0.133905\pi\)
0.912813 + 0.408378i \(0.133905\pi\)
\(524\) 52.9217 2.31189
\(525\) −110.276 −4.81283
\(526\) 50.0812 2.18364
\(527\) 5.29225 0.230534
\(528\) 62.9289 2.73863
\(529\) 66.4276 2.88816
\(530\) −10.5597 −0.458684
\(531\) 17.5885 0.763277
\(532\) −146.126 −6.33537
\(533\) 13.5557 0.587160
\(534\) −59.7164 −2.58418
\(535\) 17.9519 0.776129
\(536\) 100.596 4.34509
\(537\) −37.4756 −1.61719
\(538\) 14.8874 0.641841
\(539\) −23.6677 −1.01944
\(540\) 78.9165 3.39603
\(541\) −4.92370 −0.211686 −0.105843 0.994383i \(-0.533754\pi\)
−0.105843 + 0.994383i \(0.533754\pi\)
\(542\) −57.9782 −2.49038
\(543\) −27.4705 −1.17887
\(544\) −75.2470 −3.22619
\(545\) −62.0927 −2.65976
\(546\) 76.2625 3.26373
\(547\) 21.8369 0.933679 0.466839 0.884342i \(-0.345393\pi\)
0.466839 + 0.884342i \(0.345393\pi\)
\(548\) 31.9068 1.36299
\(549\) 18.1412 0.774248
\(550\) 76.7337 3.27194
\(551\) −41.8731 −1.78386
\(552\) 175.396 7.46535
\(553\) −15.0860 −0.641523
\(554\) 48.1978 2.04773
\(555\) 38.2276 1.62267
\(556\) −42.8875 −1.81883
\(557\) 10.4009 0.440700 0.220350 0.975421i \(-0.429280\pi\)
0.220350 + 0.975421i \(0.429280\pi\)
\(558\) −4.63182 −0.196080
\(559\) 9.12480 0.385938
\(560\) 239.444 10.1183
\(561\) 18.5427 0.782875
\(562\) 17.7281 0.747814
\(563\) 1.15178 0.0485418 0.0242709 0.999705i \(-0.492274\pi\)
0.0242709 + 0.999705i \(0.492274\pi\)
\(564\) 69.3141 2.91865
\(565\) 11.0525 0.464982
\(566\) 32.5003 1.36609
\(567\) −46.9968 −1.97368
\(568\) 71.5603 3.00260
\(569\) 24.9936 1.04779 0.523894 0.851784i \(-0.324479\pi\)
0.523894 + 0.851784i \(0.324479\pi\)
\(570\) −154.665 −6.47819
\(571\) 16.4086 0.686680 0.343340 0.939211i \(-0.388442\pi\)
0.343340 + 0.939211i \(0.388442\pi\)
\(572\) −38.5475 −1.61175
\(573\) 10.5184 0.439411
\(574\) −47.3473 −1.97624
\(575\) 120.003 5.00448
\(576\) 30.6923 1.27885
\(577\) −38.4905 −1.60238 −0.801190 0.598410i \(-0.795800\pi\)
−0.801190 + 0.598410i \(0.795800\pi\)
\(578\) 2.69095 0.111929
\(579\) 32.2481 1.34018
\(580\) 142.500 5.91699
\(581\) 3.61675 0.150048
\(582\) 94.5013 3.91721
\(583\) −2.07680 −0.0860125
\(584\) −60.6811 −2.51100
\(585\) 17.6792 0.730946
\(586\) 34.1390 1.41027
\(587\) −17.5738 −0.725350 −0.362675 0.931916i \(-0.618136\pi\)
−0.362675 + 0.931916i \(0.618136\pi\)
\(588\) −116.459 −4.80269
\(589\) −8.68162 −0.357720
\(590\) −154.447 −6.35848
\(591\) 46.0711 1.89511
\(592\) −59.5433 −2.44722
\(593\) −11.0646 −0.454368 −0.227184 0.973852i \(-0.572952\pi\)
−0.227184 + 0.973852i \(0.572952\pi\)
\(594\) 21.3665 0.876676
\(595\) 70.5549 2.89247
\(596\) 99.6150 4.08039
\(597\) −8.88282 −0.363550
\(598\) −82.9897 −3.39370
\(599\) −4.60773 −0.188267 −0.0941334 0.995560i \(-0.530008\pi\)
−0.0941334 + 0.995560i \(0.530008\pi\)
\(600\) 235.364 9.60871
\(601\) −43.6369 −1.77998 −0.889992 0.455976i \(-0.849290\pi\)
−0.889992 + 0.455976i \(0.849290\pi\)
\(602\) −31.8712 −1.29897
\(603\) −14.5564 −0.592782
\(604\) −37.7088 −1.53435
\(605\) −25.2276 −1.02565
\(606\) −30.6661 −1.24573
\(607\) −20.0007 −0.811803 −0.405902 0.913917i \(-0.633042\pi\)
−0.405902 + 0.913917i \(0.633042\pi\)
\(608\) 123.438 5.00609
\(609\) −55.4464 −2.24680
\(610\) −159.300 −6.44987
\(611\) −20.4439 −0.827072
\(612\) 27.5106 1.11205
\(613\) −12.0532 −0.486826 −0.243413 0.969923i \(-0.578267\pi\)
−0.243413 + 0.969923i \(0.578267\pi\)
\(614\) 49.5172 1.99835
\(615\) −36.4031 −1.46791
\(616\) 83.9286 3.38158
\(617\) −35.7421 −1.43892 −0.719462 0.694532i \(-0.755611\pi\)
−0.719462 + 0.694532i \(0.755611\pi\)
\(618\) −39.4339 −1.58626
\(619\) −28.4540 −1.14366 −0.571831 0.820372i \(-0.693767\pi\)
−0.571831 + 0.820372i \(0.693767\pi\)
\(620\) 29.5447 1.18655
\(621\) 33.4148 1.34089
\(622\) 84.2626 3.37862
\(623\) −44.6879 −1.79038
\(624\) −91.3291 −3.65609
\(625\) 72.5835 2.90334
\(626\) 60.5311 2.41931
\(627\) −30.4183 −1.21479
\(628\) −9.10244 −0.363227
\(629\) −17.5451 −0.699571
\(630\) −61.7502 −2.46019
\(631\) −5.90065 −0.234901 −0.117451 0.993079i \(-0.537472\pi\)
−0.117451 + 0.993079i \(0.537472\pi\)
\(632\) 32.1985 1.28079
\(633\) 45.1432 1.79428
\(634\) 26.0173 1.03328
\(635\) 10.5161 0.417318
\(636\) −10.2191 −0.405213
\(637\) 34.3491 1.36096
\(638\) 38.5815 1.52746
\(639\) −10.3549 −0.409632
\(640\) −111.294 −4.39929
\(641\) −16.8792 −0.666688 −0.333344 0.942805i \(-0.608177\pi\)
−0.333344 + 0.942805i \(0.608177\pi\)
\(642\) 23.9162 0.943897
\(643\) −22.8347 −0.900512 −0.450256 0.892899i \(-0.648667\pi\)
−0.450256 + 0.892899i \(0.648667\pi\)
\(644\) 210.561 8.29728
\(645\) −24.5042 −0.964853
\(646\) 70.9856 2.79289
\(647\) 3.65170 0.143563 0.0717816 0.997420i \(-0.477132\pi\)
0.0717816 + 0.997420i \(0.477132\pi\)
\(648\) 100.306 3.94041
\(649\) −30.3755 −1.19234
\(650\) −111.364 −4.36806
\(651\) −11.4958 −0.450555
\(652\) −83.4932 −3.26985
\(653\) −3.81715 −0.149376 −0.0746882 0.997207i \(-0.523796\pi\)
−0.0746882 + 0.997207i \(0.523796\pi\)
\(654\) −82.7222 −3.23469
\(655\) 41.9173 1.63785
\(656\) 56.7014 2.21382
\(657\) 8.78063 0.342565
\(658\) 71.4067 2.78372
\(659\) 7.76420 0.302450 0.151225 0.988499i \(-0.451678\pi\)
0.151225 + 0.988499i \(0.451678\pi\)
\(660\) 103.518 4.02942
\(661\) −39.8626 −1.55048 −0.775238 0.631669i \(-0.782370\pi\)
−0.775238 + 0.631669i \(0.782370\pi\)
\(662\) −34.5970 −1.34465
\(663\) −26.9112 −1.04514
\(664\) −7.71932 −0.299568
\(665\) −115.741 −4.48825
\(666\) 15.3557 0.595019
\(667\) 60.3374 2.33627
\(668\) 84.3525 3.26370
\(669\) 32.0246 1.23814
\(670\) 127.821 4.93817
\(671\) −31.3300 −1.20948
\(672\) 163.451 6.30527
\(673\) −32.2046 −1.24140 −0.620699 0.784049i \(-0.713151\pi\)
−0.620699 + 0.784049i \(0.713151\pi\)
\(674\) −22.6376 −0.871970
\(675\) 44.8395 1.72587
\(676\) −13.0869 −0.503343
\(677\) −33.1029 −1.27225 −0.636123 0.771588i \(-0.719463\pi\)
−0.636123 + 0.771588i \(0.719463\pi\)
\(678\) 14.7245 0.565492
\(679\) 70.7188 2.71394
\(680\) −150.587 −5.77475
\(681\) 14.1019 0.540387
\(682\) 7.99917 0.306304
\(683\) −8.19140 −0.313435 −0.156718 0.987643i \(-0.550091\pi\)
−0.156718 + 0.987643i \(0.550091\pi\)
\(684\) −45.1296 −1.72557
\(685\) 25.2723 0.965603
\(686\) −40.6154 −1.55070
\(687\) −18.4057 −0.702221
\(688\) 38.1678 1.45513
\(689\) 3.01408 0.114827
\(690\) 222.865 8.48433
\(691\) 16.4476 0.625698 0.312849 0.949803i \(-0.398717\pi\)
0.312849 + 0.949803i \(0.398717\pi\)
\(692\) 42.3926 1.61153
\(693\) −12.1446 −0.461334
\(694\) −21.4702 −0.814996
\(695\) −33.9696 −1.28854
\(696\) 118.341 4.48569
\(697\) 16.7077 0.632851
\(698\) −94.6869 −3.58395
\(699\) 46.7894 1.76974
\(700\) 282.553 10.6795
\(701\) 48.0109 1.81335 0.906674 0.421832i \(-0.138613\pi\)
0.906674 + 0.421832i \(0.138613\pi\)
\(702\) −31.0093 −1.17037
\(703\) 28.7818 1.08553
\(704\) −53.0058 −1.99773
\(705\) 54.9012 2.06770
\(706\) −45.8587 −1.72592
\(707\) −22.9486 −0.863070
\(708\) −149.465 −5.61724
\(709\) 5.09854 0.191480 0.0957398 0.995406i \(-0.469478\pi\)
0.0957398 + 0.995406i \(0.469478\pi\)
\(710\) 90.9273 3.41244
\(711\) −4.65916 −0.174732
\(712\) 95.3786 3.57447
\(713\) 12.5098 0.468497
\(714\) 93.9958 3.51770
\(715\) −30.5321 −1.14184
\(716\) 96.0216 3.58850
\(717\) 12.7158 0.474880
\(718\) −4.23554 −0.158069
\(719\) −0.437459 −0.0163145 −0.00815723 0.999967i \(-0.502597\pi\)
−0.00815723 + 0.999967i \(0.502597\pi\)
\(720\) 73.9497 2.75594
\(721\) −29.5098 −1.09900
\(722\) −65.0772 −2.42192
\(723\) −11.0014 −0.409148
\(724\) 70.3859 2.61587
\(725\) 80.9669 3.00704
\(726\) −33.6091 −1.24735
\(727\) 17.0533 0.632472 0.316236 0.948681i \(-0.397581\pi\)
0.316236 + 0.948681i \(0.397581\pi\)
\(728\) −121.806 −4.51443
\(729\) 7.45435 0.276087
\(730\) −77.1037 −2.85374
\(731\) 11.2466 0.415970
\(732\) −154.162 −5.69798
\(733\) 0.697825 0.0257748 0.0128874 0.999917i \(-0.495898\pi\)
0.0128874 + 0.999917i \(0.495898\pi\)
\(734\) −84.8646 −3.13241
\(735\) −92.2431 −3.40244
\(736\) −177.869 −6.55635
\(737\) 25.1390 0.926006
\(738\) −14.6227 −0.538271
\(739\) 52.3149 1.92444 0.962218 0.272281i \(-0.0877779\pi\)
0.962218 + 0.272281i \(0.0877779\pi\)
\(740\) −97.9484 −3.60065
\(741\) 44.1463 1.62175
\(742\) −10.5276 −0.386481
\(743\) 25.0747 0.919900 0.459950 0.887945i \(-0.347867\pi\)
0.459950 + 0.887945i \(0.347867\pi\)
\(744\) 24.5358 0.899525
\(745\) 78.9014 2.89072
\(746\) −5.63583 −0.206342
\(747\) 1.11700 0.0408687
\(748\) −47.5110 −1.73717
\(749\) 17.8974 0.653956
\(750\) 181.228 6.61751
\(751\) −53.1511 −1.93951 −0.969756 0.244077i \(-0.921515\pi\)
−0.969756 + 0.244077i \(0.921515\pi\)
\(752\) −85.5141 −3.11838
\(753\) −61.6686 −2.24733
\(754\) −55.9936 −2.03917
\(755\) −29.8678 −1.08700
\(756\) 78.6767 2.86144
\(757\) 49.0570 1.78301 0.891503 0.453015i \(-0.149652\pi\)
0.891503 + 0.453015i \(0.149652\pi\)
\(758\) 44.5389 1.61772
\(759\) 43.8314 1.59098
\(760\) 247.029 8.96070
\(761\) −16.6382 −0.603135 −0.301567 0.953445i \(-0.597510\pi\)
−0.301567 + 0.953445i \(0.597510\pi\)
\(762\) 14.0099 0.507526
\(763\) −61.9041 −2.24108
\(764\) −26.9506 −0.975038
\(765\) 21.7902 0.787825
\(766\) −59.4846 −2.14927
\(767\) 44.0841 1.59179
\(768\) −50.0348 −1.80547
\(769\) −13.5559 −0.488838 −0.244419 0.969670i \(-0.578597\pi\)
−0.244419 + 0.969670i \(0.578597\pi\)
\(770\) 106.643 3.84314
\(771\) −36.7015 −1.32177
\(772\) −82.6273 −2.97382
\(773\) 26.6687 0.959208 0.479604 0.877485i \(-0.340780\pi\)
0.479604 + 0.877485i \(0.340780\pi\)
\(774\) −9.84310 −0.353803
\(775\) 16.7870 0.603007
\(776\) −150.937 −5.41832
\(777\) 38.1115 1.36724
\(778\) −72.7828 −2.60939
\(779\) −27.4081 −0.981996
\(780\) −150.236 −5.37930
\(781\) 17.8829 0.639901
\(782\) −102.287 −3.65778
\(783\) 22.5452 0.805699
\(784\) 143.678 5.13135
\(785\) −7.20972 −0.257326
\(786\) 55.8438 1.99188
\(787\) 34.6806 1.23623 0.618115 0.786088i \(-0.287897\pi\)
0.618115 + 0.786088i \(0.287897\pi\)
\(788\) −118.045 −4.20518
\(789\) 38.3880 1.36665
\(790\) 40.9127 1.45561
\(791\) 11.0189 0.391787
\(792\) 25.9205 0.921044
\(793\) 45.4694 1.61467
\(794\) −3.56678 −0.126580
\(795\) −8.09417 −0.287071
\(796\) 22.7599 0.806704
\(797\) −45.1848 −1.60053 −0.800264 0.599649i \(-0.795307\pi\)
−0.800264 + 0.599649i \(0.795307\pi\)
\(798\) −154.195 −5.45843
\(799\) −25.1977 −0.891431
\(800\) −238.684 −8.43874
\(801\) −13.8014 −0.487649
\(802\) 64.4015 2.27410
\(803\) −15.1642 −0.535133
\(804\) 123.698 4.36251
\(805\) 166.778 5.87815
\(806\) −11.6092 −0.408918
\(807\) 11.4114 0.401701
\(808\) 48.9797 1.72310
\(809\) −33.5532 −1.17967 −0.589835 0.807524i \(-0.700807\pi\)
−0.589835 + 0.807524i \(0.700807\pi\)
\(810\) 127.453 4.47825
\(811\) 10.5482 0.370397 0.185199 0.982701i \(-0.440707\pi\)
0.185199 + 0.982701i \(0.440707\pi\)
\(812\) 142.067 4.98557
\(813\) −44.4412 −1.55862
\(814\) −26.5193 −0.929501
\(815\) −66.1320 −2.31650
\(816\) −112.566 −3.94059
\(817\) −18.4494 −0.645462
\(818\) −17.0404 −0.595804
\(819\) 17.6255 0.615885
\(820\) 93.2734 3.25725
\(821\) −13.7331 −0.479290 −0.239645 0.970861i \(-0.577031\pi\)
−0.239645 + 0.970861i \(0.577031\pi\)
\(822\) 33.6686 1.17433
\(823\) 43.3243 1.51019 0.755096 0.655615i \(-0.227590\pi\)
0.755096 + 0.655615i \(0.227590\pi\)
\(824\) 62.9835 2.19414
\(825\) 58.8176 2.04777
\(826\) −153.978 −5.35756
\(827\) 9.81621 0.341343 0.170672 0.985328i \(-0.445406\pi\)
0.170672 + 0.985328i \(0.445406\pi\)
\(828\) 65.0297 2.25994
\(829\) 18.4025 0.639144 0.319572 0.947562i \(-0.396461\pi\)
0.319572 + 0.947562i \(0.396461\pi\)
\(830\) −9.80847 −0.340457
\(831\) 36.9444 1.28159
\(832\) 76.9276 2.66699
\(833\) 42.3363 1.46687
\(834\) −45.2556 −1.56707
\(835\) 66.8126 2.31214
\(836\) 77.9390 2.69558
\(837\) 4.67433 0.161568
\(838\) −16.4209 −0.567252
\(839\) −38.0868 −1.31490 −0.657452 0.753497i \(-0.728366\pi\)
−0.657452 + 0.753497i \(0.728366\pi\)
\(840\) 327.105 11.2862
\(841\) 11.7100 0.403793
\(842\) −40.2668 −1.38769
\(843\) 13.5888 0.468025
\(844\) −115.668 −3.98145
\(845\) −10.3657 −0.356590
\(846\) 22.0533 0.758206
\(847\) −25.1509 −0.864196
\(848\) 12.6075 0.432943
\(849\) 24.9120 0.854977
\(850\) −137.260 −4.70797
\(851\) −41.4733 −1.42169
\(852\) 87.9944 3.01464
\(853\) 26.7963 0.917489 0.458744 0.888568i \(-0.348299\pi\)
0.458744 + 0.888568i \(0.348299\pi\)
\(854\) −158.816 −5.43457
\(855\) −35.7455 −1.22247
\(856\) −38.1988 −1.30561
\(857\) 27.0375 0.923582 0.461791 0.886989i \(-0.347207\pi\)
0.461791 + 0.886989i \(0.347207\pi\)
\(858\) −40.6760 −1.38866
\(859\) −39.0542 −1.33251 −0.666256 0.745723i \(-0.732104\pi\)
−0.666256 + 0.745723i \(0.732104\pi\)
\(860\) 62.7857 2.14098
\(861\) −36.2925 −1.23684
\(862\) 54.1432 1.84413
\(863\) 5.92785 0.201786 0.100893 0.994897i \(-0.467830\pi\)
0.100893 + 0.994897i \(0.467830\pi\)
\(864\) −66.4613 −2.26106
\(865\) 33.5777 1.14168
\(866\) 67.1705 2.28255
\(867\) 2.06265 0.0700514
\(868\) 29.4550 0.999767
\(869\) 8.04640 0.272955
\(870\) 150.368 5.09796
\(871\) −36.4844 −1.23623
\(872\) 132.123 4.47427
\(873\) 21.8408 0.739199
\(874\) 167.796 5.67579
\(875\) 135.619 4.58477
\(876\) −74.6167 −2.52106
\(877\) −47.3873 −1.60016 −0.800078 0.599896i \(-0.795209\pi\)
−0.800078 + 0.599896i \(0.795209\pi\)
\(878\) 53.5977 1.80883
\(879\) 26.1681 0.882627
\(880\) −127.712 −4.30516
\(881\) 55.3439 1.86458 0.932292 0.361708i \(-0.117806\pi\)
0.932292 + 0.361708i \(0.117806\pi\)
\(882\) −37.0531 −1.24764
\(883\) −31.8664 −1.07239 −0.536194 0.844094i \(-0.680139\pi\)
−0.536194 + 0.844094i \(0.680139\pi\)
\(884\) 68.9530 2.31914
\(885\) −118.386 −3.97950
\(886\) 2.60723 0.0875917
\(887\) −54.2931 −1.82298 −0.911492 0.411317i \(-0.865069\pi\)
−0.911492 + 0.411317i \(0.865069\pi\)
\(888\) −81.3423 −2.72967
\(889\) 10.4841 0.351627
\(890\) 121.192 4.06236
\(891\) 25.0666 0.839762
\(892\) −82.0547 −2.74740
\(893\) 41.3354 1.38324
\(894\) 105.115 3.51558
\(895\) 76.0553 2.54225
\(896\) −110.956 −3.70678
\(897\) −63.6129 −2.12397
\(898\) 46.9418 1.56647
\(899\) 8.44047 0.281505
\(900\) 87.2636 2.90879
\(901\) 3.71494 0.123763
\(902\) 25.2536 0.840852
\(903\) −24.4298 −0.812972
\(904\) −23.5180 −0.782195
\(905\) 55.7501 1.85320
\(906\) −39.7910 −1.32197
\(907\) −29.2243 −0.970376 −0.485188 0.874410i \(-0.661249\pi\)
−0.485188 + 0.874410i \(0.661249\pi\)
\(908\) −36.1325 −1.19910
\(909\) −7.08743 −0.235075
\(910\) −154.772 −5.13063
\(911\) −30.5507 −1.01219 −0.506095 0.862478i \(-0.668912\pi\)
−0.506095 + 0.862478i \(0.668912\pi\)
\(912\) 184.658 6.11463
\(913\) −1.92906 −0.0638425
\(914\) 47.2513 1.56293
\(915\) −122.106 −4.03670
\(916\) 47.1598 1.55820
\(917\) 41.7900 1.38003
\(918\) −38.2198 −1.26144
\(919\) −16.1576 −0.532989 −0.266495 0.963836i \(-0.585865\pi\)
−0.266495 + 0.963836i \(0.585865\pi\)
\(920\) −355.959 −11.7356
\(921\) 37.9557 1.25068
\(922\) −72.8284 −2.39848
\(923\) −25.9536 −0.854273
\(924\) 103.203 3.39513
\(925\) −55.6532 −1.82987
\(926\) 49.9474 1.64137
\(927\) −9.11380 −0.299337
\(928\) −120.010 −3.93951
\(929\) 4.16253 0.136568 0.0682841 0.997666i \(-0.478248\pi\)
0.0682841 + 0.997666i \(0.478248\pi\)
\(930\) 31.1761 1.02230
\(931\) −69.4503 −2.27614
\(932\) −119.886 −3.92698
\(933\) 64.5886 2.11453
\(934\) 95.9054 3.13812
\(935\) −37.6317 −1.23069
\(936\) −37.6186 −1.22960
\(937\) 28.8632 0.942918 0.471459 0.881888i \(-0.343728\pi\)
0.471459 + 0.881888i \(0.343728\pi\)
\(938\) 127.433 4.16083
\(939\) 46.3980 1.51414
\(940\) −140.670 −4.58815
\(941\) 36.9903 1.20585 0.602924 0.797799i \(-0.294002\pi\)
0.602924 + 0.797799i \(0.294002\pi\)
\(942\) −9.60505 −0.312949
\(943\) 39.4939 1.28610
\(944\) 184.398 6.00164
\(945\) 62.3170 2.02717
\(946\) 16.9991 0.552688
\(947\) −27.2588 −0.885791 −0.442896 0.896573i \(-0.646049\pi\)
−0.442896 + 0.896573i \(0.646049\pi\)
\(948\) 39.5930 1.28592
\(949\) 22.0079 0.714406
\(950\) 225.166 7.30536
\(951\) 19.9427 0.646685
\(952\) −150.130 −4.86573
\(953\) −42.8709 −1.38873 −0.694363 0.719625i \(-0.744314\pi\)
−0.694363 + 0.719625i \(0.744314\pi\)
\(954\) −3.25135 −0.105266
\(955\) −21.3466 −0.690760
\(956\) −32.5809 −1.05374
\(957\) 29.5733 0.955970
\(958\) 27.4414 0.886590
\(959\) 25.1955 0.813604
\(960\) −206.586 −6.66752
\(961\) −29.2500 −0.943549
\(962\) 38.4876 1.24089
\(963\) 5.52742 0.178119
\(964\) 28.1884 0.907886
\(965\) −65.4461 −2.10679
\(966\) 222.188 7.14877
\(967\) 12.2448 0.393765 0.196882 0.980427i \(-0.436918\pi\)
0.196882 + 0.980427i \(0.436918\pi\)
\(968\) 53.6803 1.72535
\(969\) 54.4116 1.74795
\(970\) −191.787 −6.15789
\(971\) 6.36973 0.204414 0.102207 0.994763i \(-0.467410\pi\)
0.102207 + 0.994763i \(0.467410\pi\)
\(972\) 67.0528 2.15072
\(973\) −33.8664 −1.08571
\(974\) 91.1618 2.92101
\(975\) −85.3623 −2.73378
\(976\) 190.192 6.08790
\(977\) −16.8318 −0.538498 −0.269249 0.963071i \(-0.586776\pi\)
−0.269249 + 0.963071i \(0.586776\pi\)
\(978\) −88.1034 −2.81724
\(979\) 23.8351 0.761774
\(980\) 236.349 7.54989
\(981\) −19.1184 −0.610405
\(982\) −92.2949 −2.94525
\(983\) 12.8157 0.408758 0.204379 0.978892i \(-0.434483\pi\)
0.204379 + 0.978892i \(0.434483\pi\)
\(984\) 77.4600 2.46933
\(985\) −93.4993 −2.97913
\(986\) −69.0138 −2.19785
\(987\) 54.7344 1.74221
\(988\) −113.113 −3.59861
\(989\) 26.5847 0.845346
\(990\) 32.9356 1.04676
\(991\) −24.8709 −0.790050 −0.395025 0.918670i \(-0.629264\pi\)
−0.395025 + 0.918670i \(0.629264\pi\)
\(992\) −24.8818 −0.789997
\(993\) −26.5191 −0.841558
\(994\) 90.6510 2.87528
\(995\) 18.0273 0.571504
\(996\) −9.49209 −0.300768
\(997\) 21.4452 0.679177 0.339588 0.940574i \(-0.389712\pi\)
0.339588 + 0.940574i \(0.389712\pi\)
\(998\) 67.9335 2.15040
\(999\) −15.4966 −0.490291
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 \(a_p\))