Properties

Label 5.8.a.b.1.2
Level 5
Weight 8
Character 5.1
Self dual Yes
Analytic conductor 1.562
Analytic rank 0
Dimension 2
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 5.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(1.56192512742\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{19}) \)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(4.35890\)
Character \(\chi\) = 5.1

$q$-expansion

\(f(q)\) \(=\) \(q+18.7178 q^{2} -59.7424 q^{3} +222.356 q^{4} -125.000 q^{5} -1118.25 q^{6} +438.197 q^{7} +1766.14 q^{8} +1382.15 q^{9} +O(q^{10})\) \(q+18.7178 q^{2} -59.7424 q^{3} +222.356 q^{4} -125.000 q^{5} -1118.25 q^{6} +438.197 q^{7} +1766.14 q^{8} +1382.15 q^{9} -2339.72 q^{10} +5759.12 q^{11} -13284.1 q^{12} -3530.42 q^{13} +8202.08 q^{14} +7467.80 q^{15} +4596.61 q^{16} -23991.9 q^{17} +25870.8 q^{18} +16590.3 q^{19} -27794.5 q^{20} -26178.9 q^{21} +107798. q^{22} -65626.9 q^{23} -105513. q^{24} +15625.0 q^{25} -66081.7 q^{26} +48083.5 q^{27} +97435.6 q^{28} +134041. q^{29} +139781. q^{30} +129002. q^{31} -140027. q^{32} -344064. q^{33} -449075. q^{34} -54774.6 q^{35} +307330. q^{36} +161108. q^{37} +310534. q^{38} +210916. q^{39} -220767. q^{40} -362989. q^{41} -490012. q^{42} +588189. q^{43} +1.28057e6 q^{44} -172769. q^{45} -1.22839e6 q^{46} +343895. q^{47} -274612. q^{48} -631527. q^{49} +292466. q^{50} +1.43333e6 q^{51} -785010. q^{52} -1.66139e6 q^{53} +900018. q^{54} -719890. q^{55} +773915. q^{56} -991144. q^{57} +2.50896e6 q^{58} -2.54214e6 q^{59} +1.66051e6 q^{60} +2.52337e6 q^{61} +2.41464e6 q^{62} +605655. q^{63} -3.20936e6 q^{64} +441303. q^{65} -6.44011e6 q^{66} +1.56618e6 q^{67} -5.33474e6 q^{68} +3.92071e6 q^{69} -1.02526e6 q^{70} -299354. q^{71} +2.44107e6 q^{72} +312494. q^{73} +3.01558e6 q^{74} -933475. q^{75} +3.68895e6 q^{76} +2.52363e6 q^{77} +3.94788e6 q^{78} -1.95247e6 q^{79} -574576. q^{80} -5.89539e6 q^{81} -6.79435e6 q^{82} -621372. q^{83} -5.82104e6 q^{84} +2.99898e6 q^{85} +1.10096e7 q^{86} -8.00795e6 q^{87} +1.01714e7 q^{88} +5.78298e6 q^{89} -3.23386e6 q^{90} -1.54702e6 q^{91} -1.45925e7 q^{92} -7.70690e6 q^{93} +6.43696e6 q^{94} -2.07379e6 q^{95} +8.36554e6 q^{96} +7.20152e6 q^{97} -1.18208e7 q^{98} +7.95998e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 20q^{2} + 20q^{3} + 96q^{4} - 250q^{5} - 1016q^{6} - 100q^{7} + 1440q^{8} + 5554q^{9} + O(q^{10}) \) \( 2q + 20q^{2} + 20q^{3} + 96q^{4} - 250q^{5} - 1016q^{6} - 100q^{7} + 1440q^{8} + 5554q^{9} - 2500q^{10} + 4544q^{11} - 23360q^{12} + 3540q^{13} + 7512q^{14} - 2500q^{15} + 20352q^{16} - 27340q^{17} + 31220q^{18} + 38760q^{19} - 12000q^{20} - 69096q^{21} + 106240q^{22} - 124140q^{23} - 131520q^{24} + 31250q^{25} - 57016q^{26} + 206360q^{27} + 165440q^{28} - 72260q^{29} + 127000q^{30} + 306824q^{31} - 78080q^{32} - 440960q^{33} - 453368q^{34} + 12500q^{35} - 219808q^{36} - 123020q^{37} + 338960q^{38} + 774728q^{39} - 180000q^{40} + 264364q^{41} - 545040q^{42} + 423300q^{43} + 1434112q^{44} - 694250q^{45} - 1303416q^{46} - 105460q^{47} + 981760q^{48} - 1165414q^{49} + 312500q^{50} + 1166344q^{51} - 1678400q^{52} - 2391580q^{53} + 1102960q^{54} - 568000q^{55} + 949440q^{56} + 776720q^{57} + 2244440q^{58} - 1120120q^{59} + 2920000q^{60} + 2257044q^{61} + 2642640q^{62} - 1639620q^{63} - 5146624q^{64} - 442500q^{65} - 6564352q^{66} + 4516460q^{67} - 4911680q^{68} - 745272q^{69} - 939000q^{70} + 621784q^{71} + 1080480q^{72} + 4569060q^{73} + 2651272q^{74} + 312500q^{75} + 887680q^{76} + 3177600q^{77} + 4670800q^{78} + 4333040q^{79} - 2544000q^{80} - 2397878q^{81} - 5989960q^{82} - 9793020q^{83} - 398208q^{84} + 3417500q^{85} + 10798184q^{86} - 24458920q^{87} + 10567680q^{88} + 6025620q^{89} - 3902500q^{90} - 5352296q^{91} - 7199040q^{92} + 6473040q^{93} + 5860792q^{94} - 4845000q^{95} + 13305344q^{96} + 4609540q^{97} - 12505340q^{98} + 2890688q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 18.7178 1.65444 0.827218 0.561882i \(-0.189922\pi\)
0.827218 + 0.561882i \(0.189922\pi\)
\(3\) −59.7424 −1.27749 −0.638746 0.769418i \(-0.720547\pi\)
−0.638746 + 0.769418i \(0.720547\pi\)
\(4\) 222.356 1.73716
\(5\) −125.000 −0.447214
\(6\) −1118.25 −2.11353
\(7\) 438.197 0.482865 0.241433 0.970418i \(-0.422383\pi\)
0.241433 + 0.970418i \(0.422383\pi\)
\(8\) 1766.14 1.21958
\(9\) 1382.15 0.631986
\(10\) −2339.72 −0.739886
\(11\) 5759.12 1.30461 0.652306 0.757955i \(-0.273802\pi\)
0.652306 + 0.757955i \(0.273802\pi\)
\(12\) −13284.1 −2.21920
\(13\) −3530.42 −0.445682 −0.222841 0.974855i \(-0.571533\pi\)
−0.222841 + 0.974855i \(0.571533\pi\)
\(14\) 8202.08 0.798869
\(15\) 7467.80 0.571312
\(16\) 4596.61 0.280555
\(17\) −23991.9 −1.18439 −0.592193 0.805797i \(-0.701738\pi\)
−0.592193 + 0.805797i \(0.701738\pi\)
\(18\) 25870.8 1.04558
\(19\) 16590.3 0.554903 0.277451 0.960740i \(-0.410510\pi\)
0.277451 + 0.960740i \(0.410510\pi\)
\(20\) −27794.5 −0.776880
\(21\) −26178.9 −0.616856
\(22\) 107798. 2.15840
\(23\) −65626.9 −1.12469 −0.562347 0.826902i \(-0.690101\pi\)
−0.562347 + 0.826902i \(0.690101\pi\)
\(24\) −105513. −1.55800
\(25\) 15625.0 0.200000
\(26\) −66081.7 −0.737351
\(27\) 48083.5 0.470136
\(28\) 97435.6 0.838812
\(29\) 134041. 1.02058 0.510289 0.860003i \(-0.329539\pi\)
0.510289 + 0.860003i \(0.329539\pi\)
\(30\) 139781. 0.945198
\(31\) 129002. 0.777734 0.388867 0.921294i \(-0.372867\pi\)
0.388867 + 0.921294i \(0.372867\pi\)
\(32\) −140027. −0.755417
\(33\) −344064. −1.66663
\(34\) −449075. −1.95949
\(35\) −54774.6 −0.215944
\(36\) 307330. 1.09786
\(37\) 161108. 0.522890 0.261445 0.965218i \(-0.415801\pi\)
0.261445 + 0.965218i \(0.415801\pi\)
\(38\) 310534. 0.918050
\(39\) 210916. 0.569355
\(40\) −220767. −0.545411
\(41\) −362989. −0.822526 −0.411263 0.911517i \(-0.634912\pi\)
−0.411263 + 0.911517i \(0.634912\pi\)
\(42\) −490012. −1.02055
\(43\) 588189. 1.12818 0.564089 0.825714i \(-0.309228\pi\)
0.564089 + 0.825714i \(0.309228\pi\)
\(44\) 1.28057e6 2.26632
\(45\) −172769. −0.282633
\(46\) −1.22839e6 −1.86073
\(47\) 343895. 0.483151 0.241576 0.970382i \(-0.422336\pi\)
0.241576 + 0.970382i \(0.422336\pi\)
\(48\) −274612. −0.358406
\(49\) −631527. −0.766841
\(50\) 292466. 0.330887
\(51\) 1.43333e6 1.51304
\(52\) −785010. −0.774219
\(53\) −1.66139e6 −1.53287 −0.766436 0.642320i \(-0.777972\pi\)
−0.766436 + 0.642320i \(0.777972\pi\)
\(54\) 900018. 0.777809
\(55\) −719890. −0.583441
\(56\) 773915. 0.588891
\(57\) −991144. −0.708884
\(58\) 2.50896e6 1.68848
\(59\) −2.54214e6 −1.61145 −0.805726 0.592289i \(-0.798224\pi\)
−0.805726 + 0.592289i \(0.798224\pi\)
\(60\) 1.66051e6 0.992458
\(61\) 2.52337e6 1.42340 0.711699 0.702484i \(-0.247926\pi\)
0.711699 + 0.702484i \(0.247926\pi\)
\(62\) 2.41464e6 1.28671
\(63\) 605655. 0.305164
\(64\) −3.20936e6 −1.53034
\(65\) 441303. 0.199315
\(66\) −6.44011e6 −2.75734
\(67\) 1.56618e6 0.636178 0.318089 0.948061i \(-0.396959\pi\)
0.318089 + 0.948061i \(0.396959\pi\)
\(68\) −5.33474e6 −2.05746
\(69\) 3.92071e6 1.43679
\(70\) −1.02526e6 −0.357265
\(71\) −299354. −0.0992615 −0.0496307 0.998768i \(-0.515804\pi\)
−0.0496307 + 0.998768i \(0.515804\pi\)
\(72\) 2.44107e6 0.770755
\(73\) 312494. 0.0940183 0.0470091 0.998894i \(-0.485031\pi\)
0.0470091 + 0.998894i \(0.485031\pi\)
\(74\) 3.01558e6 0.865087
\(75\) −933475. −0.255498
\(76\) 3.68895e6 0.963952
\(77\) 2.52363e6 0.629952
\(78\) 3.94788e6 0.941961
\(79\) −1.95247e6 −0.445542 −0.222771 0.974871i \(-0.571510\pi\)
−0.222771 + 0.974871i \(0.571510\pi\)
\(80\) −574576. −0.125468
\(81\) −5.89539e6 −1.23258
\(82\) −6.79435e6 −1.36082
\(83\) −621372. −0.119283 −0.0596414 0.998220i \(-0.518996\pi\)
−0.0596414 + 0.998220i \(0.518996\pi\)
\(84\) −5.82104e6 −1.07158
\(85\) 2.99898e6 0.529673
\(86\) 1.10096e7 1.86650
\(87\) −8.00795e6 −1.30378
\(88\) 1.01714e7 1.59108
\(89\) 5.78298e6 0.869534 0.434767 0.900543i \(-0.356831\pi\)
0.434767 + 0.900543i \(0.356831\pi\)
\(90\) −3.23386e6 −0.467597
\(91\) −1.54702e6 −0.215204
\(92\) −1.45925e7 −1.95377
\(93\) −7.70690e6 −0.993549
\(94\) 6.43696e6 0.799343
\(95\) −2.07379e6 −0.248160
\(96\) 8.36554e6 0.965039
\(97\) 7.20152e6 0.801167 0.400584 0.916260i \(-0.368807\pi\)
0.400584 + 0.916260i \(0.368807\pi\)
\(98\) −1.18208e7 −1.26869
\(99\) 7.95998e6 0.824496
\(100\) 3.47431e6 0.347431
\(101\) −2.91989e6 −0.281995 −0.140997 0.990010i \(-0.545031\pi\)
−0.140997 + 0.990010i \(0.545031\pi\)
\(102\) 2.68288e7 2.50323
\(103\) 3.94639e6 0.355852 0.177926 0.984044i \(-0.443061\pi\)
0.177926 + 0.984044i \(0.443061\pi\)
\(104\) −6.23520e6 −0.543543
\(105\) 3.27236e6 0.275867
\(106\) −3.10976e7 −2.53604
\(107\) −3.81991e6 −0.301446 −0.150723 0.988576i \(-0.548160\pi\)
−0.150723 + 0.988576i \(0.548160\pi\)
\(108\) 1.06917e7 0.816699
\(109\) −8.82259e6 −0.652534 −0.326267 0.945278i \(-0.605791\pi\)
−0.326267 + 0.945278i \(0.605791\pi\)
\(110\) −1.34748e7 −0.965265
\(111\) −9.62496e6 −0.667988
\(112\) 2.01422e6 0.135470
\(113\) 2.12074e7 1.38265 0.691324 0.722545i \(-0.257028\pi\)
0.691324 + 0.722545i \(0.257028\pi\)
\(114\) −1.85520e7 −1.17280
\(115\) 8.20336e6 0.502978
\(116\) 2.98049e7 1.77290
\(117\) −4.87958e6 −0.281664
\(118\) −4.75832e7 −2.66604
\(119\) −1.05132e7 −0.571898
\(120\) 1.31891e7 0.696758
\(121\) 1.36803e7 0.702015
\(122\) 4.72319e7 2.35492
\(123\) 2.16858e7 1.05077
\(124\) 2.86844e7 1.35105
\(125\) −1.95313e6 −0.0894427
\(126\) 1.13365e7 0.504874
\(127\) −2.55822e7 −1.10822 −0.554108 0.832445i \(-0.686941\pi\)
−0.554108 + 0.832445i \(0.686941\pi\)
\(128\) −4.21487e7 −1.77644
\(129\) −3.51398e7 −1.44124
\(130\) 8.26021e6 0.329754
\(131\) 1.30640e7 0.507722 0.253861 0.967241i \(-0.418299\pi\)
0.253861 + 0.967241i \(0.418299\pi\)
\(132\) −7.65046e7 −2.89520
\(133\) 7.26982e6 0.267943
\(134\) 2.93154e7 1.05252
\(135\) −6.01044e6 −0.210251
\(136\) −4.23729e7 −1.44445
\(137\) 2.14021e7 0.711106 0.355553 0.934656i \(-0.384293\pi\)
0.355553 + 0.934656i \(0.384293\pi\)
\(138\) 7.33870e7 2.37707
\(139\) 4.00656e7 1.26538 0.632688 0.774406i \(-0.281951\pi\)
0.632688 + 0.774406i \(0.281951\pi\)
\(140\) −1.21795e7 −0.375128
\(141\) −2.05451e7 −0.617222
\(142\) −5.60324e6 −0.164222
\(143\) −2.03321e7 −0.581442
\(144\) 6.35321e6 0.177307
\(145\) −1.67552e7 −0.456416
\(146\) 5.84921e6 0.155547
\(147\) 3.77289e7 0.979633
\(148\) 3.58233e7 0.908341
\(149\) −5.96142e7 −1.47638 −0.738190 0.674593i \(-0.764319\pi\)
−0.738190 + 0.674593i \(0.764319\pi\)
\(150\) −1.74726e7 −0.422706
\(151\) −5.21166e6 −0.123185 −0.0615924 0.998101i \(-0.519618\pi\)
−0.0615924 + 0.998101i \(0.519618\pi\)
\(152\) 2.93007e7 0.676746
\(153\) −3.31604e7 −0.748514
\(154\) 4.72367e7 1.04222
\(155\) −1.61253e7 −0.347813
\(156\) 4.68984e7 0.989058
\(157\) −1.10197e7 −0.227259 −0.113630 0.993523i \(-0.536248\pi\)
−0.113630 + 0.993523i \(0.536248\pi\)
\(158\) −3.65458e7 −0.737120
\(159\) 9.92554e7 1.95823
\(160\) 1.75034e7 0.337833
\(161\) −2.87575e7 −0.543075
\(162\) −1.10349e8 −2.03922
\(163\) 2.32415e7 0.420346 0.210173 0.977664i \(-0.432597\pi\)
0.210173 + 0.977664i \(0.432597\pi\)
\(164\) −8.07127e7 −1.42886
\(165\) 4.30079e7 0.745341
\(166\) −1.16307e7 −0.197346
\(167\) −5.84152e7 −0.970550 −0.485275 0.874361i \(-0.661281\pi\)
−0.485275 + 0.874361i \(0.661281\pi\)
\(168\) −4.62355e7 −0.752304
\(169\) −5.02846e7 −0.801368
\(170\) 5.61344e7 0.876310
\(171\) 2.29303e7 0.350690
\(172\) 1.30787e8 1.95982
\(173\) 1.18828e6 0.0174485 0.00872427 0.999962i \(-0.497223\pi\)
0.00872427 + 0.999962i \(0.497223\pi\)
\(174\) −1.49891e8 −2.15702
\(175\) 6.84682e6 0.0965730
\(176\) 2.64724e7 0.366015
\(177\) 1.51873e8 2.05862
\(178\) 1.08245e8 1.43859
\(179\) 1.28635e8 1.67638 0.838191 0.545377i \(-0.183613\pi\)
0.838191 + 0.545377i \(0.183613\pi\)
\(180\) −3.84162e7 −0.490977
\(181\) 1.40320e8 1.75892 0.879458 0.475976i \(-0.157905\pi\)
0.879458 + 0.475976i \(0.157905\pi\)
\(182\) −2.89568e7 −0.356041
\(183\) −1.50752e8 −1.81838
\(184\) −1.15906e8 −1.37165
\(185\) −2.01385e7 −0.233843
\(186\) −1.44256e8 −1.64376
\(187\) −1.38172e8 −1.54516
\(188\) 7.64671e7 0.839309
\(189\) 2.10700e7 0.227012
\(190\) −3.88167e7 −0.410565
\(191\) −3.81784e7 −0.396461 −0.198231 0.980155i \(-0.563519\pi\)
−0.198231 + 0.980155i \(0.563519\pi\)
\(192\) 1.91735e8 1.95500
\(193\) −1.35915e8 −1.36087 −0.680436 0.732807i \(-0.738210\pi\)
−0.680436 + 0.732807i \(0.738210\pi\)
\(194\) 1.34797e8 1.32548
\(195\) −2.63645e7 −0.254623
\(196\) −1.40424e8 −1.33212
\(197\) 6.16154e7 0.574193 0.287096 0.957902i \(-0.407310\pi\)
0.287096 + 0.957902i \(0.407310\pi\)
\(198\) 1.48993e8 1.36408
\(199\) −1.84377e8 −1.65852 −0.829261 0.558862i \(-0.811238\pi\)
−0.829261 + 0.558862i \(0.811238\pi\)
\(200\) 2.75959e7 0.243915
\(201\) −9.35671e7 −0.812713
\(202\) −5.46539e7 −0.466542
\(203\) 5.87365e7 0.492801
\(204\) 3.18710e8 2.62839
\(205\) 4.53736e7 0.367845
\(206\) 7.38677e7 0.588734
\(207\) −9.07063e7 −0.710790
\(208\) −1.62280e7 −0.125038
\(209\) 9.55455e7 0.723933
\(210\) 6.12515e7 0.456403
\(211\) 1.71174e8 1.25444 0.627218 0.778844i \(-0.284194\pi\)
0.627218 + 0.778844i \(0.284194\pi\)
\(212\) −3.69420e8 −2.66284
\(213\) 1.78841e7 0.126806
\(214\) −7.15003e7 −0.498723
\(215\) −7.35236e7 −0.504536
\(216\) 8.49220e7 0.573366
\(217\) 5.65283e7 0.375541
\(218\) −1.65139e8 −1.07958
\(219\) −1.86692e7 −0.120108
\(220\) −1.60072e8 −1.01353
\(221\) 8.47014e7 0.527859
\(222\) −1.80158e8 −1.10514
\(223\) 2.67014e8 1.61238 0.806190 0.591657i \(-0.201526\pi\)
0.806190 + 0.591657i \(0.201526\pi\)
\(224\) −6.13594e7 −0.364765
\(225\) 2.15961e7 0.126397
\(226\) 3.96955e8 2.28750
\(227\) 378641. 0.00214851 0.00107425 0.999999i \(-0.499658\pi\)
0.00107425 + 0.999999i \(0.499658\pi\)
\(228\) −2.20387e8 −1.23144
\(229\) −2.24429e8 −1.23497 −0.617483 0.786584i \(-0.711848\pi\)
−0.617483 + 0.786584i \(0.711848\pi\)
\(230\) 1.53549e8 0.832145
\(231\) −1.50767e8 −0.804759
\(232\) 2.36735e8 1.24467
\(233\) 1.55173e8 0.803656 0.401828 0.915715i \(-0.368375\pi\)
0.401828 + 0.915715i \(0.368375\pi\)
\(234\) −9.13350e7 −0.465995
\(235\) −4.29869e7 −0.216072
\(236\) −5.65260e8 −2.79934
\(237\) 1.16645e8 0.569176
\(238\) −1.96783e8 −0.946169
\(239\) 4.07160e7 0.192918 0.0964588 0.995337i \(-0.469248\pi\)
0.0964588 + 0.995337i \(0.469248\pi\)
\(240\) 3.43265e7 0.160284
\(241\) −3.06501e8 −1.41050 −0.705249 0.708960i \(-0.749165\pi\)
−0.705249 + 0.708960i \(0.749165\pi\)
\(242\) 2.56065e8 1.16144
\(243\) 2.47046e8 1.10448
\(244\) 5.61086e8 2.47266
\(245\) 7.89408e7 0.342942
\(246\) 4.05911e8 1.73843
\(247\) −5.85708e7 −0.247310
\(248\) 2.27835e8 0.948506
\(249\) 3.71222e7 0.152383
\(250\) −3.65582e7 −0.147977
\(251\) −1.30381e8 −0.520421 −0.260211 0.965552i \(-0.583792\pi\)
−0.260211 + 0.965552i \(0.583792\pi\)
\(252\) 1.34671e8 0.530117
\(253\) −3.77953e8 −1.46729
\(254\) −4.78842e8 −1.83347
\(255\) −1.79166e8 −0.676653
\(256\) −3.78133e8 −1.40866
\(257\) 3.23514e8 1.18885 0.594426 0.804151i \(-0.297380\pi\)
0.594426 + 0.804151i \(0.297380\pi\)
\(258\) −6.57740e8 −2.38443
\(259\) 7.05969e7 0.252485
\(260\) 9.81263e7 0.346241
\(261\) 1.85266e8 0.644990
\(262\) 2.44529e8 0.839994
\(263\) 2.39895e7 0.0813159 0.0406579 0.999173i \(-0.487055\pi\)
0.0406579 + 0.999173i \(0.487055\pi\)
\(264\) −6.07663e8 −2.03259
\(265\) 2.07674e8 0.685522
\(266\) 1.36075e8 0.443295
\(267\) −3.45489e8 −1.11082
\(268\) 3.48249e8 1.10514
\(269\) −1.73612e8 −0.543809 −0.271905 0.962324i \(-0.587654\pi\)
−0.271905 + 0.962324i \(0.587654\pi\)
\(270\) −1.12502e8 −0.347847
\(271\) 5.08478e8 1.55196 0.775978 0.630760i \(-0.217257\pi\)
0.775978 + 0.630760i \(0.217257\pi\)
\(272\) −1.10281e8 −0.332285
\(273\) 9.24226e7 0.274922
\(274\) 4.00600e8 1.17648
\(275\) 8.99862e7 0.260923
\(276\) 8.71792e8 2.49592
\(277\) −6.01050e8 −1.69915 −0.849575 0.527468i \(-0.823141\pi\)
−0.849575 + 0.527468i \(0.823141\pi\)
\(278\) 7.49940e8 2.09348
\(279\) 1.78301e8 0.491517
\(280\) −9.67394e7 −0.263360
\(281\) −6.36212e8 −1.71053 −0.855264 0.518193i \(-0.826605\pi\)
−0.855264 + 0.518193i \(0.826605\pi\)
\(282\) −3.84559e8 −1.02115
\(283\) 5.46181e7 0.143247 0.0716233 0.997432i \(-0.477182\pi\)
0.0716233 + 0.997432i \(0.477182\pi\)
\(284\) −6.65631e7 −0.172433
\(285\) 1.23893e8 0.317022
\(286\) −3.80572e8 −0.961958
\(287\) −1.59061e8 −0.397169
\(288\) −1.93539e8 −0.477413
\(289\) 1.65271e8 0.402768
\(290\) −3.13620e8 −0.755111
\(291\) −4.30236e8 −1.02348
\(292\) 6.94850e7 0.163324
\(293\) −1.22481e8 −0.284467 −0.142234 0.989833i \(-0.545428\pi\)
−0.142234 + 0.989833i \(0.545428\pi\)
\(294\) 7.06202e8 1.62074
\(295\) 3.17767e8 0.720663
\(296\) 2.84538e8 0.637704
\(297\) 2.76919e8 0.613345
\(298\) −1.11585e9 −2.44257
\(299\) 2.31690e8 0.501255
\(300\) −2.07564e8 −0.443841
\(301\) 2.57743e8 0.544758
\(302\) −9.75509e7 −0.203801
\(303\) 1.74441e8 0.360246
\(304\) 7.62591e7 0.155681
\(305\) −3.15421e8 −0.636563
\(306\) −6.20690e8 −1.23837
\(307\) 5.58187e8 1.10102 0.550510 0.834829i \(-0.314433\pi\)
0.550510 + 0.834829i \(0.314433\pi\)
\(308\) 5.61143e8 1.09433
\(309\) −2.35767e8 −0.454598
\(310\) −3.01830e8 −0.575434
\(311\) 8.94564e7 0.168636 0.0843180 0.996439i \(-0.473129\pi\)
0.0843180 + 0.996439i \(0.473129\pi\)
\(312\) 3.72506e8 0.694372
\(313\) −2.75895e8 −0.508556 −0.254278 0.967131i \(-0.581838\pi\)
−0.254278 + 0.967131i \(0.581838\pi\)
\(314\) −2.06265e8 −0.375986
\(315\) −7.57068e7 −0.136473
\(316\) −4.34142e8 −0.773976
\(317\) −4.40449e8 −0.776584 −0.388292 0.921536i \(-0.626935\pi\)
−0.388292 + 0.921536i \(0.626935\pi\)
\(318\) 1.85784e9 3.23977
\(319\) 7.71960e8 1.33146
\(320\) 4.01170e8 0.684390
\(321\) 2.28211e8 0.385095
\(322\) −5.38277e8 −0.898483
\(323\) −3.98032e8 −0.657218
\(324\) −1.31088e9 −2.14118
\(325\) −5.51628e7 −0.0891363
\(326\) 4.35030e8 0.695436
\(327\) 5.27082e8 0.833607
\(328\) −6.41088e8 −1.00313
\(329\) 1.50694e8 0.233297
\(330\) 8.05014e8 1.23312
\(331\) 1.68079e8 0.254751 0.127376 0.991855i \(-0.459345\pi\)
0.127376 + 0.991855i \(0.459345\pi\)
\(332\) −1.38166e8 −0.207213
\(333\) 2.22675e8 0.330459
\(334\) −1.09340e9 −1.60571
\(335\) −1.95772e8 −0.284508
\(336\) −1.20334e8 −0.173062
\(337\) 8.38651e8 1.19365 0.596824 0.802372i \(-0.296429\pi\)
0.596824 + 0.802372i \(0.296429\pi\)
\(338\) −9.41218e8 −1.32581
\(339\) −1.26698e9 −1.76632
\(340\) 6.66842e8 0.920125
\(341\) 7.42939e8 1.01464
\(342\) 4.29205e8 0.580195
\(343\) −6.37607e8 −0.853146
\(344\) 1.03882e9 1.37590
\(345\) −4.90088e8 −0.642551
\(346\) 2.22421e7 0.0288675
\(347\) −1.16128e9 −1.49205 −0.746023 0.665921i \(-0.768039\pi\)
−0.746023 + 0.665921i \(0.768039\pi\)
\(348\) −1.78062e9 −2.26487
\(349\) −8.37482e8 −1.05460 −0.527298 0.849680i \(-0.676795\pi\)
−0.527298 + 0.849680i \(0.676795\pi\)
\(350\) 1.28157e8 0.159774
\(351\) −1.69755e8 −0.209531
\(352\) −8.06432e8 −0.985527
\(353\) 7.61561e8 0.921496 0.460748 0.887531i \(-0.347581\pi\)
0.460748 + 0.887531i \(0.347581\pi\)
\(354\) 2.84274e9 3.40585
\(355\) 3.74192e7 0.0443911
\(356\) 1.28588e9 1.51052
\(357\) 6.28081e8 0.730596
\(358\) 2.40776e9 2.77347
\(359\) 3.19728e8 0.364712 0.182356 0.983233i \(-0.441628\pi\)
0.182356 + 0.983233i \(0.441628\pi\)
\(360\) −3.05134e8 −0.344692
\(361\) −6.18634e8 −0.692083
\(362\) 2.62649e9 2.91001
\(363\) −8.17293e8 −0.896818
\(364\) −3.43989e8 −0.373843
\(365\) −3.90618e7 −0.0420462
\(366\) −2.82175e9 −3.00839
\(367\) 1.25415e8 0.132440 0.0662199 0.997805i \(-0.478906\pi\)
0.0662199 + 0.997805i \(0.478906\pi\)
\(368\) −3.01661e8 −0.315538
\(369\) −5.01706e8 −0.519825
\(370\) −3.76948e8 −0.386879
\(371\) −7.28016e8 −0.740171
\(372\) −1.71367e9 −1.72595
\(373\) 1.71505e9 1.71118 0.855588 0.517657i \(-0.173196\pi\)
0.855588 + 0.517657i \(0.173196\pi\)
\(374\) −2.58628e9 −2.55637
\(375\) 1.16684e8 0.114262
\(376\) 6.07365e8 0.589240
\(377\) −4.73223e8 −0.454853
\(378\) 3.94385e8 0.375577
\(379\) −1.07297e8 −0.101239 −0.0506196 0.998718i \(-0.516120\pi\)
−0.0506196 + 0.998718i \(0.516120\pi\)
\(380\) −4.61119e8 −0.431093
\(381\) 1.52834e9 1.41574
\(382\) −7.14615e8 −0.655919
\(383\) −6.77468e8 −0.616160 −0.308080 0.951361i \(-0.599686\pi\)
−0.308080 + 0.951361i \(0.599686\pi\)
\(384\) 2.51807e9 2.26938
\(385\) −3.15453e8 −0.281723
\(386\) −2.54403e9 −2.25148
\(387\) 8.12967e8 0.712992
\(388\) 1.60130e9 1.39175
\(389\) 1.94836e9 1.67821 0.839104 0.543971i \(-0.183080\pi\)
0.839104 + 0.543971i \(0.183080\pi\)
\(390\) −4.93485e8 −0.421258
\(391\) 1.57451e9 1.33207
\(392\) −1.11536e9 −0.935222
\(393\) −7.80474e8 −0.648611
\(394\) 1.15331e9 0.949965
\(395\) 2.44058e8 0.199252
\(396\) 1.76995e9 1.43228
\(397\) −1.11752e9 −0.896369 −0.448185 0.893941i \(-0.647929\pi\)
−0.448185 + 0.893941i \(0.647929\pi\)
\(398\) −3.45113e9 −2.74392
\(399\) −4.34316e8 −0.342295
\(400\) 7.18220e7 0.0561110
\(401\) 1.61315e9 1.24931 0.624655 0.780901i \(-0.285240\pi\)
0.624655 + 0.780901i \(0.285240\pi\)
\(402\) −1.75137e9 −1.34458
\(403\) −4.55432e8 −0.346622
\(404\) −6.49254e8 −0.489869
\(405\) 7.36924e8 0.551226
\(406\) 1.09942e9 0.815308
\(407\) 9.27838e8 0.682169
\(408\) 2.53146e9 1.84527
\(409\) 1.32866e7 0.00960248 0.00480124 0.999988i \(-0.498472\pi\)
0.00480124 + 0.999988i \(0.498472\pi\)
\(410\) 8.49294e8 0.608576
\(411\) −1.27861e9 −0.908432
\(412\) 8.77503e8 0.618170
\(413\) −1.11396e9 −0.778114
\(414\) −1.69782e9 −1.17596
\(415\) 7.76715e7 0.0533449
\(416\) 4.94354e8 0.336676
\(417\) −2.39361e9 −1.61651
\(418\) 1.78840e9 1.19770
\(419\) −5.93249e7 −0.0393992 −0.0196996 0.999806i \(-0.506271\pi\)
−0.0196996 + 0.999806i \(0.506271\pi\)
\(420\) 7.27630e8 0.479223
\(421\) −2.93348e9 −1.91600 −0.958000 0.286769i \(-0.907419\pi\)
−0.958000 + 0.286769i \(0.907419\pi\)
\(422\) 3.20399e9 2.07538
\(423\) 4.75315e8 0.305345
\(424\) −2.93424e9 −1.86946
\(425\) −3.74873e8 −0.236877
\(426\) 3.34751e8 0.209792
\(427\) 1.10573e9 0.687310
\(428\) −8.49380e8 −0.523659
\(429\) 1.21469e9 0.742788
\(430\) −1.37620e9 −0.834723
\(431\) −1.96307e8 −0.118104 −0.0590520 0.998255i \(-0.518808\pi\)
−0.0590520 + 0.998255i \(0.518808\pi\)
\(432\) 2.21021e8 0.131899
\(433\) −7.68256e8 −0.454777 −0.227389 0.973804i \(-0.573019\pi\)
−0.227389 + 0.973804i \(0.573019\pi\)
\(434\) 1.05809e9 0.621308
\(435\) 1.00099e9 0.583068
\(436\) −1.96175e9 −1.13355
\(437\) −1.08877e9 −0.624095
\(438\) −3.49446e8 −0.198710
\(439\) −1.35112e9 −0.762197 −0.381099 0.924534i \(-0.624454\pi\)
−0.381099 + 0.924534i \(0.624454\pi\)
\(440\) −1.27142e9 −0.711551
\(441\) −8.72866e8 −0.484633
\(442\) 1.58542e9 0.873308
\(443\) 2.20956e9 1.20752 0.603759 0.797167i \(-0.293669\pi\)
0.603759 + 0.797167i \(0.293669\pi\)
\(444\) −2.14017e9 −1.16040
\(445\) −7.22872e8 −0.388867
\(446\) 4.99792e9 2.66758
\(447\) 3.56150e9 1.88606
\(448\) −1.40633e9 −0.738950
\(449\) 3.16264e9 1.64887 0.824436 0.565955i \(-0.191493\pi\)
0.824436 + 0.565955i \(0.191493\pi\)
\(450\) 4.04232e8 0.209116
\(451\) −2.09050e9 −1.07308
\(452\) 4.71558e9 2.40188
\(453\) 3.11357e8 0.157368
\(454\) 7.08732e6 0.00355457
\(455\) 1.93377e8 0.0962422
\(456\) −1.75050e9 −0.864538
\(457\) 5.97325e8 0.292755 0.146377 0.989229i \(-0.453239\pi\)
0.146377 + 0.989229i \(0.453239\pi\)
\(458\) −4.20082e9 −2.04317
\(459\) −1.15361e9 −0.556821
\(460\) 1.82407e9 0.873752
\(461\) −2.01803e9 −0.959346 −0.479673 0.877447i \(-0.659245\pi\)
−0.479673 + 0.877447i \(0.659245\pi\)
\(462\) −2.82204e9 −1.33142
\(463\) 1.32264e8 0.0619310 0.0309655 0.999520i \(-0.490142\pi\)
0.0309655 + 0.999520i \(0.490142\pi\)
\(464\) 6.16136e8 0.286328
\(465\) 9.63362e8 0.444329
\(466\) 2.90449e9 1.32960
\(467\) −3.62018e9 −1.64483 −0.822416 0.568887i \(-0.807374\pi\)
−0.822416 + 0.568887i \(0.807374\pi\)
\(468\) −1.08500e9 −0.489295
\(469\) 6.86293e8 0.307188
\(470\) −8.04619e8 −0.357477
\(471\) 6.58344e8 0.290322
\(472\) −4.48976e9 −1.96529
\(473\) 3.38745e9 1.47183
\(474\) 2.18334e9 0.941665
\(475\) 2.59224e8 0.110981
\(476\) −2.33766e9 −0.993477
\(477\) −2.29629e9 −0.968753
\(478\) 7.62113e8 0.319170
\(479\) −2.77900e9 −1.15535 −0.577675 0.816267i \(-0.696040\pi\)
−0.577675 + 0.816267i \(0.696040\pi\)
\(480\) −1.04569e9 −0.431579
\(481\) −5.68778e8 −0.233042
\(482\) −5.73703e9 −2.33358
\(483\) 1.71804e9 0.693774
\(484\) 3.04189e9 1.21951
\(485\) −9.00190e8 −0.358293
\(486\) 4.62416e9 1.82728
\(487\) 1.86684e9 0.732414 0.366207 0.930533i \(-0.380656\pi\)
0.366207 + 0.930533i \(0.380656\pi\)
\(488\) 4.45661e9 1.73594
\(489\) −1.38850e9 −0.536989
\(490\) 1.47760e9 0.567375
\(491\) 5.06515e9 1.93111 0.965555 0.260198i \(-0.0837879\pi\)
0.965555 + 0.260198i \(0.0837879\pi\)
\(492\) 4.82197e9 1.82535
\(493\) −3.21590e9 −1.20876
\(494\) −1.09632e9 −0.409158
\(495\) −9.94998e8 −0.368726
\(496\) 5.92973e8 0.218197
\(497\) −1.31176e8 −0.0479299
\(498\) 6.94846e8 0.252108
\(499\) −5.56606e8 −0.200538 −0.100269 0.994960i \(-0.531970\pi\)
−0.100269 + 0.994960i \(0.531970\pi\)
\(500\) −4.34289e8 −0.155376
\(501\) 3.48986e9 1.23987
\(502\) −2.44044e9 −0.861004
\(503\) −7.79533e8 −0.273116 −0.136558 0.990632i \(-0.543604\pi\)
−0.136558 + 0.990632i \(0.543604\pi\)
\(504\) 1.06967e9 0.372171
\(505\) 3.64986e8 0.126112
\(506\) −7.07445e9 −2.42754
\(507\) 3.00412e9 1.02374
\(508\) −5.68835e9 −1.92515
\(509\) −1.12351e9 −0.377629 −0.188814 0.982013i \(-0.560464\pi\)
−0.188814 + 0.982013i \(0.560464\pi\)
\(510\) −3.35360e9 −1.11948
\(511\) 1.36934e8 0.0453981
\(512\) −1.68278e9 −0.554094
\(513\) 7.97720e8 0.260879
\(514\) 6.05547e9 1.96688
\(515\) −4.93298e8 −0.159142
\(516\) −7.81355e9 −2.50365
\(517\) 1.98053e9 0.630326
\(518\) 1.32142e9 0.417721
\(519\) −7.09909e7 −0.0222904
\(520\) 7.79400e8 0.243080
\(521\) −6.43550e8 −0.199366 −0.0996828 0.995019i \(-0.531783\pi\)
−0.0996828 + 0.995019i \(0.531783\pi\)
\(522\) 3.46777e9 1.06709
\(523\) 6.30863e9 1.92832 0.964159 0.265324i \(-0.0854788\pi\)
0.964159 + 0.265324i \(0.0854788\pi\)
\(524\) 2.90486e9 0.881993
\(525\) −4.09046e8 −0.123371
\(526\) 4.49030e8 0.134532
\(527\) −3.09500e9 −0.921137
\(528\) −1.58153e9 −0.467582
\(529\) 9.02060e8 0.264936
\(530\) 3.88720e9 1.13415
\(531\) −3.51362e9 −1.01841
\(532\) 1.61649e9 0.465459
\(533\) 1.28150e9 0.366585
\(534\) −6.46679e9 −1.83778
\(535\) 4.77489e8 0.134811
\(536\) 2.76608e9 0.775868
\(537\) −7.68495e9 −2.14156
\(538\) −3.24963e9 −0.899697
\(539\) −3.63704e9 −1.00043
\(540\) −1.33646e9 −0.365239
\(541\) −3.71277e9 −1.00811 −0.504055 0.863672i \(-0.668159\pi\)
−0.504055 + 0.863672i \(0.668159\pi\)
\(542\) 9.51758e9 2.56761
\(543\) −8.38306e9 −2.24700
\(544\) 3.35951e9 0.894705
\(545\) 1.10282e9 0.291822
\(546\) 1.72995e9 0.454840
\(547\) 4.19241e9 1.09524 0.547619 0.836728i \(-0.315534\pi\)
0.547619 + 0.836728i \(0.315534\pi\)
\(548\) 4.75888e9 1.23530
\(549\) 3.48768e9 0.899567
\(550\) 1.68434e9 0.431680
\(551\) 2.22379e9 0.566321
\(552\) 6.92450e9 1.75227
\(553\) −8.55564e8 −0.215137
\(554\) −1.12503e10 −2.81113
\(555\) 1.20312e9 0.298733
\(556\) 8.90883e9 2.19816
\(557\) 2.52750e9 0.619723 0.309861 0.950782i \(-0.399717\pi\)
0.309861 + 0.950782i \(0.399717\pi\)
\(558\) 3.33740e9 0.813182
\(559\) −2.07656e9 −0.502808
\(560\) −2.51777e8 −0.0605841
\(561\) 8.25473e9 1.97393
\(562\) −1.19085e10 −2.82996
\(563\) −4.12649e9 −0.974543 −0.487272 0.873250i \(-0.662008\pi\)
−0.487272 + 0.873250i \(0.662008\pi\)
\(564\) −4.56833e9 −1.07221
\(565\) −2.65092e9 −0.618339
\(566\) 1.02233e9 0.236992
\(567\) −2.58334e9 −0.595170
\(568\) −5.28700e8 −0.121057
\(569\) 5.27044e8 0.119937 0.0599686 0.998200i \(-0.480900\pi\)
0.0599686 + 0.998200i \(0.480900\pi\)
\(570\) 2.31900e9 0.524493
\(571\) −3.18083e9 −0.715014 −0.357507 0.933911i \(-0.616373\pi\)
−0.357507 + 0.933911i \(0.616373\pi\)
\(572\) −4.52097e9 −1.01006
\(573\) 2.28087e9 0.506476
\(574\) −2.97726e9 −0.657091
\(575\) −1.02542e9 −0.224939
\(576\) −4.43583e9 −0.967155
\(577\) 4.88332e9 1.05828 0.529139 0.848535i \(-0.322515\pi\)
0.529139 + 0.848535i \(0.322515\pi\)
\(578\) 3.09351e9 0.666354
\(579\) 8.11990e9 1.73850
\(580\) −3.72561e9 −0.792866
\(581\) −2.72283e8 −0.0575976
\(582\) −8.05307e9 −1.69329
\(583\) −9.56814e9 −1.99981
\(584\) 5.51907e8 0.114662
\(585\) 6.09947e8 0.125964
\(586\) −2.29257e9 −0.470632
\(587\) 8.66750e8 0.176873 0.0884363 0.996082i \(-0.471813\pi\)
0.0884363 + 0.996082i \(0.471813\pi\)
\(588\) 8.38925e9 1.70178
\(589\) 2.14019e9 0.431567
\(590\) 5.94790e9 1.19229
\(591\) −3.68105e9 −0.733527
\(592\) 7.40549e8 0.146699
\(593\) −1.43710e9 −0.283007 −0.141503 0.989938i \(-0.545194\pi\)
−0.141503 + 0.989938i \(0.545194\pi\)
\(594\) 5.18331e9 1.01474
\(595\) 1.31414e9 0.255761
\(596\) −1.32556e10 −2.56470
\(597\) 1.10151e10 2.11875
\(598\) 4.33674e9 0.829294
\(599\) 7.50069e9 1.42596 0.712980 0.701185i \(-0.247345\pi\)
0.712980 + 0.701185i \(0.247345\pi\)
\(600\) −1.64864e9 −0.311600
\(601\) 5.05436e9 0.949741 0.474870 0.880056i \(-0.342495\pi\)
0.474870 + 0.880056i \(0.342495\pi\)
\(602\) 4.82437e9 0.901266
\(603\) 2.16469e9 0.402055
\(604\) −1.15884e9 −0.213991
\(605\) −1.71004e9 −0.313951
\(606\) 3.26515e9 0.596004
\(607\) −9.94598e8 −0.180504 −0.0902521 0.995919i \(-0.528767\pi\)
−0.0902521 + 0.995919i \(0.528767\pi\)
\(608\) −2.32309e9 −0.419183
\(609\) −3.50906e9 −0.629550
\(610\) −5.90399e9 −1.05315
\(611\) −1.21409e9 −0.215332
\(612\) −7.37342e9 −1.30029
\(613\) 1.58283e9 0.277539 0.138769 0.990325i \(-0.455685\pi\)
0.138769 + 0.990325i \(0.455685\pi\)
\(614\) 1.04480e10 1.82157
\(615\) −2.71073e9 −0.469919
\(616\) 4.45707e9 0.768275
\(617\) −8.35079e9 −1.43130 −0.715648 0.698461i \(-0.753868\pi\)
−0.715648 + 0.698461i \(0.753868\pi\)
\(618\) −4.41303e9 −0.752103
\(619\) 1.12049e9 0.189886 0.0949428 0.995483i \(-0.469733\pi\)
0.0949428 + 0.995483i \(0.469733\pi\)
\(620\) −3.58555e9 −0.604206
\(621\) −3.15557e9 −0.528758
\(622\) 1.67443e9 0.278997
\(623\) 2.53408e9 0.419868
\(624\) 9.69497e8 0.159735
\(625\) 2.44141e8 0.0400000
\(626\) −5.16415e9 −0.841372
\(627\) −5.70812e9 −0.924819
\(628\) −2.45030e9 −0.394785
\(629\) −3.86528e9 −0.619303
\(630\) −1.41706e9 −0.225786
\(631\) 3.72303e9 0.589921 0.294961 0.955509i \(-0.404693\pi\)
0.294961 + 0.955509i \(0.404693\pi\)
\(632\) −3.44832e9 −0.543372
\(633\) −1.02263e10 −1.60253
\(634\) −8.24424e9 −1.28481
\(635\) 3.19777e9 0.495610
\(636\) 2.20700e10 3.40176
\(637\) 2.22956e9 0.341767
\(638\) 1.44494e10 2.20281
\(639\) −4.13753e8 −0.0627318
\(640\) 5.26859e9 0.794447
\(641\) −1.08733e9 −0.163065 −0.0815323 0.996671i \(-0.525981\pi\)
−0.0815323 + 0.996671i \(0.525981\pi\)
\(642\) 4.27160e9 0.637115
\(643\) 9.30287e9 1.38000 0.689999 0.723810i \(-0.257611\pi\)
0.689999 + 0.723810i \(0.257611\pi\)
\(644\) −6.39440e9 −0.943407
\(645\) 4.39248e9 0.644541
\(646\) −7.45029e9 −1.08733
\(647\) −3.75633e9 −0.545254 −0.272627 0.962120i \(-0.587892\pi\)
−0.272627 + 0.962120i \(0.587892\pi\)
\(648\) −1.04121e10 −1.50323
\(649\) −1.46405e10 −2.10232
\(650\) −1.03253e9 −0.147470
\(651\) −3.37714e9 −0.479750
\(652\) 5.16788e9 0.730207
\(653\) 6.47262e9 0.909671 0.454835 0.890576i \(-0.349698\pi\)
0.454835 + 0.890576i \(0.349698\pi\)
\(654\) 9.86582e9 1.37915
\(655\) −1.63300e9 −0.227060
\(656\) −1.66852e9 −0.230764
\(657\) 4.31915e8 0.0594182
\(658\) 2.82065e9 0.385975
\(659\) 8.31257e9 1.13145 0.565726 0.824593i \(-0.308596\pi\)
0.565726 + 0.824593i \(0.308596\pi\)
\(660\) 9.56307e9 1.29477
\(661\) −1.42966e9 −0.192543 −0.0962714 0.995355i \(-0.530692\pi\)
−0.0962714 + 0.995355i \(0.530692\pi\)
\(662\) 3.14608e9 0.421470
\(663\) −5.06026e9 −0.674335
\(664\) −1.09743e9 −0.145475
\(665\) −9.08727e8 −0.119828
\(666\) 4.16799e9 0.546723
\(667\) −8.79672e9 −1.14784
\(668\) −1.29890e10 −1.68600
\(669\) −1.59521e10 −2.05980
\(670\) −3.66442e9 −0.470699
\(671\) 1.45324e10 1.85698
\(672\) 3.66575e9 0.465984
\(673\) 7.03224e9 0.889285 0.444642 0.895708i \(-0.353331\pi\)
0.444642 + 0.895708i \(0.353331\pi\)
\(674\) 1.56977e10 1.97481
\(675\) 7.51305e8 0.0940271
\(676\) −1.11811e10 −1.39210
\(677\) −5.75322e8 −0.0712608 −0.0356304 0.999365i \(-0.511344\pi\)
−0.0356304 + 0.999365i \(0.511344\pi\)
\(678\) −2.37150e10 −2.92227
\(679\) 3.15568e9 0.386856
\(680\) 5.29661e9 0.645977
\(681\) −2.26209e7 −0.00274470
\(682\) 1.39062e10 1.67866
\(683\) 7.67069e9 0.921217 0.460609 0.887603i \(-0.347631\pi\)
0.460609 + 0.887603i \(0.347631\pi\)
\(684\) 5.09870e9 0.609204
\(685\) −2.67526e9 −0.318016
\(686\) −1.19346e10 −1.41148
\(687\) 1.34079e10 1.57766
\(688\) 2.70368e9 0.316516
\(689\) 5.86541e9 0.683173
\(690\) −9.17337e9 −1.06306
\(691\) 3.62855e9 0.418369 0.209185 0.977876i \(-0.432919\pi\)
0.209185 + 0.977876i \(0.432919\pi\)
\(692\) 2.64222e8 0.0303108
\(693\) 3.48804e9 0.398121
\(694\) −2.17365e10 −2.46849
\(695\) −5.00820e9 −0.565894
\(696\) −1.41431e10 −1.59006
\(697\) 8.70878e9 0.974188
\(698\) −1.56758e10 −1.74476
\(699\) −9.27040e9 −1.02666
\(700\) 1.52243e9 0.167762
\(701\) −1.71375e10 −1.87904 −0.939518 0.342499i \(-0.888727\pi\)
−0.939518 + 0.342499i \(0.888727\pi\)
\(702\) −3.17744e9 −0.346655
\(703\) 2.67283e9 0.290153
\(704\) −1.84831e10 −1.99651
\(705\) 2.56814e9 0.276030
\(706\) 1.42547e10 1.52456
\(707\) −1.27948e9 −0.136166
\(708\) 3.37700e10 3.57614
\(709\) 1.34055e10 1.41260 0.706302 0.707911i \(-0.250362\pi\)
0.706302 + 0.707911i \(0.250362\pi\)
\(710\) 7.00406e8 0.0734422
\(711\) −2.69860e9 −0.281576
\(712\) 1.02135e10 1.06046
\(713\) −8.46601e9 −0.874712
\(714\) 1.17563e10 1.20872
\(715\) 2.54151e9 0.260029
\(716\) 2.86027e10 2.91214
\(717\) −2.43247e9 −0.246451
\(718\) 5.98460e9 0.603392
\(719\) −5.99982e9 −0.601987 −0.300994 0.953626i \(-0.597318\pi\)
−0.300994 + 0.953626i \(0.597318\pi\)
\(720\) −7.94152e8 −0.0792939
\(721\) 1.72929e9 0.171829
\(722\) −1.15795e10 −1.14501
\(723\) 1.83111e10 1.80190
\(724\) 3.12010e10 3.05551
\(725\) 2.09440e9 0.204116
\(726\) −1.52979e10 −1.48373
\(727\) −1.84312e10 −1.77903 −0.889513 0.456909i \(-0.848956\pi\)
−0.889513 + 0.456909i \(0.848956\pi\)
\(728\) −2.73225e9 −0.262458
\(729\) −1.86590e9 −0.178378
\(730\) −7.31151e8 −0.0695628
\(731\) −1.41118e10 −1.33620
\(732\) −3.35206e10 −3.15881
\(733\) −7.01069e9 −0.657502 −0.328751 0.944417i \(-0.606628\pi\)
−0.328751 + 0.944417i \(0.606628\pi\)
\(734\) 2.34749e9 0.219113
\(735\) −4.71611e9 −0.438105
\(736\) 9.18953e9 0.849613
\(737\) 9.01980e9 0.829966
\(738\) −9.39083e9 −0.860016
\(739\) 3.58081e9 0.326382 0.163191 0.986595i \(-0.447821\pi\)
0.163191 + 0.986595i \(0.447821\pi\)
\(740\) −4.47791e9 −0.406223
\(741\) 3.49916e9 0.315936
\(742\) −1.36268e10 −1.22456
\(743\) −4.23347e9 −0.378648 −0.189324 0.981915i \(-0.560630\pi\)
−0.189324 + 0.981915i \(0.560630\pi\)
\(744\) −1.36114e10 −1.21171
\(745\) 7.45178e9 0.660257
\(746\) 3.21019e10 2.83103
\(747\) −8.58830e8 −0.0753851
\(748\) −3.07234e10 −2.68419
\(749\) −1.67387e9 −0.145558
\(750\) 2.18407e9 0.189040
\(751\) 3.94072e9 0.339497 0.169749 0.985487i \(-0.445704\pi\)
0.169749 + 0.985487i \(0.445704\pi\)
\(752\) 1.58075e9 0.135550
\(753\) 7.78925e9 0.664834
\(754\) −8.85769e9 −0.752524
\(755\) 6.51458e8 0.0550899
\(756\) 4.68505e9 0.394355
\(757\) −8.01225e8 −0.0671303 −0.0335652 0.999437i \(-0.510686\pi\)
−0.0335652 + 0.999437i \(0.510686\pi\)
\(758\) −2.00836e9 −0.167494
\(759\) 2.25798e10 1.87445
\(760\) −3.66259e9 −0.302650
\(761\) −3.84688e9 −0.316419 −0.158209 0.987406i \(-0.550572\pi\)
−0.158209 + 0.987406i \(0.550572\pi\)
\(762\) 2.86072e10 2.34225
\(763\) −3.86603e9 −0.315086
\(764\) −8.48919e9 −0.688715
\(765\) 4.14505e9 0.334746
\(766\) −1.26807e10 −1.01940
\(767\) 8.97482e9 0.718194
\(768\) 2.25906e10 1.79955
\(769\) 4.40578e9 0.349366 0.174683 0.984625i \(-0.444110\pi\)
0.174683 + 0.984625i \(0.444110\pi\)
\(770\) −5.90459e9 −0.466093
\(771\) −1.93275e10 −1.51875
\(772\) −3.02216e10 −2.36405
\(773\) −1.54451e10 −1.20272 −0.601359 0.798979i \(-0.705374\pi\)
−0.601359 + 0.798979i \(0.705374\pi\)
\(774\) 1.52170e10 1.17960
\(775\) 2.01566e9 0.155547
\(776\) 1.27189e10 0.977085
\(777\) −4.21762e9 −0.322548
\(778\) 3.64690e10 2.77649
\(779\) −6.02210e9 −0.456422
\(780\) −5.86230e9 −0.442320
\(781\) −1.72401e9 −0.129498
\(782\) 2.94714e10 2.20382
\(783\) 6.44518e9 0.479810
\(784\) −2.90288e9 −0.215141
\(785\) 1.37746e9 0.101633
\(786\) −1.46088e10 −1.07309
\(787\) −2.40331e10 −1.75751 −0.878755 0.477274i \(-0.841625\pi\)
−0.878755 + 0.477274i \(0.841625\pi\)
\(788\) 1.37006e10 0.997463
\(789\) −1.43319e9 −0.103880
\(790\) 4.56823e9 0.329650
\(791\) 9.29299e9 0.667633
\(792\) 1.40584e10 1.00554
\(793\) −8.90856e9 −0.634383
\(794\) −2.09174e10 −1.48299
\(795\) −1.24069e10 −0.875748
\(796\) −4.09973e10 −2.88111
\(797\) 1.37624e10 0.962918 0.481459 0.876469i \(-0.340107\pi\)
0.481459 + 0.876469i \(0.340107\pi\)
\(798\) −8.12944e9 −0.566305
\(799\) −8.25068e9 −0.572237
\(800\) −2.18792e9 −0.151083
\(801\) 7.99296e9 0.549533
\(802\) 3.01947e10 2.06690
\(803\) 1.79969e9 0.122657
\(804\) −2.08052e10 −1.41181
\(805\) 3.59468e9 0.242871
\(806\) −8.52468e9 −0.573463
\(807\) 1.03720e10 0.694712
\(808\) −5.15692e9 −0.343914
\(809\) 5.00163e9 0.332118 0.166059 0.986116i \(-0.446896\pi\)
0.166059 + 0.986116i \(0.446896\pi\)
\(810\) 1.37936e10 0.911968
\(811\) 8.14966e9 0.536496 0.268248 0.963350i \(-0.413555\pi\)
0.268248 + 0.963350i \(0.413555\pi\)
\(812\) 1.30604e10 0.856073
\(813\) −3.03777e10 −1.98261
\(814\) 1.73671e10 1.12860
\(815\) −2.90519e9 −0.187985
\(816\) 6.58847e9 0.424491
\(817\) 9.75824e9 0.626029
\(818\) 2.48697e8 0.0158867
\(819\) −2.13822e9 −0.136006
\(820\) 1.00891e10 0.639004
\(821\) 1.30820e10 0.825035 0.412518 0.910950i \(-0.364650\pi\)
0.412518 + 0.910950i \(0.364650\pi\)
\(822\) −2.39328e10 −1.50294
\(823\) −3.12969e10 −1.95705 −0.978524 0.206133i \(-0.933912\pi\)
−0.978524 + 0.206133i \(0.933912\pi\)
\(824\) 6.96985e9 0.433989
\(825\) −5.37599e9 −0.333326
\(826\) −2.08508e10 −1.28734
\(827\) −1.98645e10 −1.22126 −0.610630 0.791916i \(-0.709084\pi\)
−0.610630 + 0.791916i \(0.709084\pi\)
\(828\) −2.01691e10 −1.23475
\(829\) 1.06183e10 0.647310 0.323655 0.946175i \(-0.395088\pi\)
0.323655 + 0.946175i \(0.395088\pi\)
\(830\) 1.45384e9 0.0882557
\(831\) 3.59082e10 2.17065
\(832\) 1.13304e10 0.682046
\(833\) 1.51515e10 0.908235
\(834\) −4.48032e10 −2.67441
\(835\) 7.30190e9 0.434043
\(836\) 2.12451e10 1.25758
\(837\) 6.20288e9 0.365640
\(838\) −1.11043e9 −0.0651834
\(839\) 4.19640e9 0.245307 0.122654 0.992450i \(-0.460860\pi\)
0.122654 + 0.992450i \(0.460860\pi\)
\(840\) 5.77944e9 0.336440
\(841\) 7.17225e8 0.0415785
\(842\) −5.49082e10 −3.16990
\(843\) 3.80088e10 2.18518
\(844\) 3.80615e10 2.17915
\(845\) 6.28558e9 0.358383
\(846\) 8.89685e9 0.505173
\(847\) 5.99465e9 0.338979
\(848\) −7.63676e9 −0.430055
\(849\) −3.26302e9 −0.182996
\(850\) −7.01680e9 −0.391898
\(851\) −1.05730e10 −0.588091
\(852\) 3.97664e9 0.220281
\(853\) 2.52606e10 1.39355 0.696775 0.717289i \(-0.254617\pi\)
0.696775 + 0.717289i \(0.254617\pi\)
\(854\) 2.06969e10 1.13711
\(855\) −2.86629e9 −0.156834
\(856\) −6.74648e9 −0.367637
\(857\) 1.07248e10 0.582046 0.291023 0.956716i \(-0.406004\pi\)
0.291023 + 0.956716i \(0.406004\pi\)
\(858\) 2.27363e10 1.22889
\(859\) −3.02643e10 −1.62913 −0.814563 0.580075i \(-0.803023\pi\)
−0.814563 + 0.580075i \(0.803023\pi\)
\(860\) −1.63484e10 −0.876458
\(861\) 9.50266e9 0.507381
\(862\) −3.67443e9 −0.195396
\(863\) −1.39177e10 −0.737106 −0.368553 0.929607i \(-0.620147\pi\)
−0.368553 + 0.929607i \(0.620147\pi\)
\(864\) −6.73299e9 −0.355148
\(865\) −1.48536e8 −0.00780322
\(866\) −1.43801e10 −0.752399
\(867\) −9.87370e9 −0.514533
\(868\) 1.25694e10 0.652373
\(869\) −1.12445e10 −0.581260
\(870\) 1.87364e10 0.964648
\(871\) −5.52926e9 −0.283533
\(872\) −1.55819e10 −0.795815
\(873\) 9.95360e9 0.506326
\(874\) −2.03794e10 −1.03253
\(875\) −8.55853e8 −0.0431888
\(876\) −4.15120e9 −0.208646
\(877\) −1.81702e10 −0.909622 −0.454811 0.890588i \(-0.650293\pi\)
−0.454811 + 0.890588i \(0.650293\pi\)
\(878\) −2.52900e10 −1.26101
\(879\) 7.31731e9 0.363404
\(880\) −3.30905e9 −0.163687
\(881\) −3.14352e10 −1.54882 −0.774409 0.632685i \(-0.781953\pi\)
−0.774409 + 0.632685i \(0.781953\pi\)
\(882\) −1.63381e10 −0.801793
\(883\) −2.11722e10 −1.03491 −0.517457 0.855709i \(-0.673121\pi\)
−0.517457 + 0.855709i \(0.673121\pi\)
\(884\) 1.88339e10 0.916973
\(885\) −1.89842e10 −0.920641
\(886\) 4.13582e10 1.99776
\(887\) 3.72771e10 1.79353 0.896766 0.442505i \(-0.145910\pi\)
0.896766 + 0.442505i \(0.145910\pi\)
\(888\) −1.69990e10 −0.814662
\(889\) −1.12100e10 −0.535119
\(890\) −1.35306e10 −0.643356
\(891\) −3.39523e10 −1.60804
\(892\) 5.93722e10 2.80095
\(893\) 5.70532e9 0.268102
\(894\) 6.66634e10 3.12037
\(895\) −1.60794e10 −0.749701
\(896\) −1.84694e10 −0.857780
\(897\) −1.38417e10 −0.640350
\(898\) 5.91976e10 2.72795
\(899\) 1.72916e10 0.793738
\(900\) 4.80203e9 0.219571
\(901\) 3.98599e10 1.81551
\(902\) −3.91295e10 −1.77534
\(903\) −1.53982e10 −0.695923
\(904\) 3.74551e10 1.68625
\(905\) −1.75400e10 −0.786611
\(906\) 5.82792e9 0.260354
\(907\) 1.00189e10 0.445854 0.222927 0.974835i \(-0.428439\pi\)
0.222927 + 0.974835i \(0.428439\pi\)
\(908\) 8.41930e7 0.00373229
\(909\) −4.03573e9 −0.178217
\(910\) 3.61960e9 0.159227
\(911\) 3.16088e10 1.38514 0.692571 0.721350i \(-0.256478\pi\)
0.692571 + 0.721350i \(0.256478\pi\)
\(912\) −4.55590e9 −0.198881
\(913\) −3.57855e9 −0.155618
\(914\) 1.11806e10 0.484344
\(915\) 1.88440e10 0.813204
\(916\) −4.99032e10 −2.14533
\(917\) 5.72460e9 0.245161
\(918\) −2.15931e10 −0.921225
\(919\) 7.18397e8 0.0305324 0.0152662 0.999883i \(-0.495140\pi\)
0.0152662 + 0.999883i \(0.495140\pi\)
\(920\) 1.44882e10 0.613421
\(921\) −3.33474e10 −1.40654
\(922\) −3.77732e10 −1.58718
\(923\) 1.05685e9 0.0442390
\(924\) −3.35240e10 −1.39799
\(925\) 2.51731e9 0.104578
\(926\) 2.47569e9 0.102461
\(927\) 5.45451e9 0.224893
\(928\) −1.87694e10 −0.770962
\(929\) −1.63954e10 −0.670915 −0.335458 0.942055i \(-0.608891\pi\)
−0.335458 + 0.942055i \(0.608891\pi\)
\(930\) 1.80320e10 0.735113
\(931\) −1.04772e10 −0.425522
\(932\) 3.45036e10 1.39608
\(933\) −5.34434e9 −0.215431
\(934\) −6.77618e10 −2.72127
\(935\) 1.72715e10 0.691018
\(936\) −8.61800e9 −0.343511
\(937\) −9.79890e9 −0.389125 −0.194562 0.980890i \(-0.562329\pi\)
−0.194562 + 0.980890i \(0.562329\pi\)
\(938\) 1.28459e10 0.508223
\(939\) 1.64826e10 0.649676
\(940\) −9.55839e9 −0.375351
\(941\) 1.68542e10 0.659394 0.329697 0.944087i \(-0.393053\pi\)
0.329697 + 0.944087i \(0.393053\pi\)
\(942\) 1.23227e10 0.480319
\(943\) 2.38218e10 0.925090
\(944\) −1.16852e10 −0.452100
\(945\) −2.63375e9 −0.101523
\(946\) 6.34056e10 2.43506
\(947\) 2.47225e10 0.945948 0.472974 0.881076i \(-0.343180\pi\)
0.472974 + 0.881076i \(0.343180\pi\)
\(948\) 2.59367e10 0.988748
\(949\) −1.10324e9 −0.0419022
\(950\) 4.85209e9 0.183610
\(951\) 2.63135e10 0.992080
\(952\) −1.85677e10 −0.697474
\(953\) −4.36738e9 −0.163454 −0.0817271 0.996655i \(-0.526044\pi\)
−0.0817271 + 0.996655i \(0.526044\pi\)
\(954\) −4.29816e10 −1.60274
\(955\) 4.77230e9 0.177303
\(956\) 9.05343e9 0.335128
\(957\) −4.61188e10 −1.70093
\(958\) −5.20167e10 −1.91145
\(959\) 9.37832e9 0.343368
\(960\) −2.39669e10 −0.874303
\(961\) −1.08711e10 −0.395130
\(962\) −1.06463e10 −0.385554
\(963\) −5.27970e9 −0.190510
\(964\) −6.81523e10 −2.45025
\(965\) 1.69894e10 0.608601
\(966\) 3.21579e10 1.14780
\(967\) −1.00818e10 −0.358547 −0.179274 0.983799i \(-0.557375\pi\)
−0.179274 + 0.983799i \(0.557375\pi\)
\(968\) 2.41612e10 0.856161
\(969\) 2.37794e10 0.839591
\(970\) −1.68496e10 −0.592772
\(971\) −1.19066e10 −0.417369 −0.208685 0.977983i \(-0.566918\pi\)
−0.208685 + 0.977983i \(0.566918\pi\)
\(972\) 5.49322e10 1.91865
\(973\) 1.75566e10 0.611006
\(974\) 3.49432e10 1.21173
\(975\) 3.29556e9 0.113871
\(976\) 1.15989e10 0.399341
\(977\) 1.99598e10 0.684741 0.342370 0.939565i \(-0.388770\pi\)
0.342370 + 0.939565i \(0.388770\pi\)
\(978\) −2.59897e10 −0.888414
\(979\) 3.33049e10 1.13441
\(980\) 1.75530e10 0.595743
\(981\) −1.21942e10 −0.412392
\(982\) 9.48085e10 3.19490
\(983\) −3.22193e10 −1.08188 −0.540940 0.841061i \(-0.681931\pi\)
−0.540940 + 0.841061i \(0.681931\pi\)
\(984\) 3.83001e10 1.28150
\(985\) −7.70193e9 −0.256787
\(986\) −6.01947e10 −1.99981
\(987\) −9.00280e9 −0.298035
\(988\) −1.30236e10 −0.429616
\(989\) −3.86010e10 −1.26885
\(990\) −1.86242e10 −0.610033
\(991\) −1.42552e10 −0.465281 −0.232640 0.972563i \(-0.574737\pi\)
−0.232640 + 0.972563i \(0.574737\pi\)
\(992\) −1.80638e10 −0.587513
\(993\) −1.00415e10 −0.325443
\(994\) −2.45532e9 −0.0792969
\(995\) 2.30471e10 0.741713
\(996\) 8.25435e9 0.264713
\(997\) −2.73327e10 −0.873475 −0.436737 0.899589i \(-0.643866\pi\)
−0.436737 + 0.899589i \(0.643866\pi\)
\(998\) −1.04184e10 −0.331776
\(999\) 7.74662e9 0.245829
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 \(a_p\))