Properties

Label 15.8.a.c.1.2
Level 15
Weight 8
Character 15.1
Self dual Yes
Analytic conductor 4.686
Analytic rank 0
Dimension 2
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 15 = 3 \cdot 5 \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 15.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(4.68577538226\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{601}) \)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-11.7577\)
Character \(\chi\) = 15.1

$q$-expansion

\(f(q)\) \(=\) \(q+15.7577 q^{2} +27.0000 q^{3} +120.304 q^{4} +125.000 q^{5} +425.457 q^{6} -34.4284 q^{7} -121.278 q^{8} +729.000 q^{9} +O(q^{10})\) \(q+15.7577 q^{2} +27.0000 q^{3} +120.304 q^{4} +125.000 q^{5} +425.457 q^{6} -34.4284 q^{7} -121.278 q^{8} +729.000 q^{9} +1969.71 q^{10} -3963.55 q^{11} +3248.20 q^{12} +5606.30 q^{13} -542.511 q^{14} +3375.00 q^{15} -17309.9 q^{16} -19906.7 q^{17} +11487.3 q^{18} -49993.7 q^{19} +15037.9 q^{20} -929.568 q^{21} -62456.2 q^{22} +109762. q^{23} -3274.50 q^{24} +15625.0 q^{25} +88342.2 q^{26} +19683.0 q^{27} -4141.86 q^{28} +192477. q^{29} +53182.1 q^{30} +125541. q^{31} -257240. q^{32} -107016. q^{33} -313683. q^{34} -4303.55 q^{35} +87701.3 q^{36} -74353.6 q^{37} -787784. q^{38} +151370. q^{39} -15159.7 q^{40} +577802. q^{41} -14647.8 q^{42} +264291. q^{43} -476829. q^{44} +91125.0 q^{45} +1.72959e6 q^{46} -306207. q^{47} -467368. q^{48} -822358. q^{49} +246213. q^{50} -537481. q^{51} +674458. q^{52} -446219. q^{53} +310158. q^{54} -495444. q^{55} +4175.41 q^{56} -1.34983e6 q^{57} +3.03299e6 q^{58} +1.97951e6 q^{59} +406024. q^{60} -1.27494e6 q^{61} +1.97824e6 q^{62} -25098.3 q^{63} -1.83783e6 q^{64} +700788. q^{65} -1.68632e6 q^{66} -4.12943e6 q^{67} -2.39485e6 q^{68} +2.96357e6 q^{69} -67813.9 q^{70} -2.81187e6 q^{71} -88411.6 q^{72} +4.01991e6 q^{73} -1.17164e6 q^{74} +421875. q^{75} -6.01442e6 q^{76} +136459. q^{77} +2.38524e6 q^{78} -1.32785e6 q^{79} -2.16374e6 q^{80} +531441. q^{81} +9.10480e6 q^{82} -1.91033e6 q^{83} -111830. q^{84} -2.48834e6 q^{85} +4.16460e6 q^{86} +5.19689e6 q^{87} +480691. q^{88} +8.00695e6 q^{89} +1.43592e6 q^{90} -193016. q^{91} +1.32047e7 q^{92} +3.38962e6 q^{93} -4.82511e6 q^{94} -6.24922e6 q^{95} -6.94548e6 q^{96} -3.89241e6 q^{97} -1.29584e7 q^{98} -2.88943e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 7q^{2} + 54q^{3} + 69q^{4} + 250q^{5} + 189q^{6} + 1304q^{7} + 1449q^{8} + 1458q^{9} + O(q^{10}) \) \( 2q + 7q^{2} + 54q^{3} + 69q^{4} + 250q^{5} + 189q^{6} + 1304q^{7} + 1449q^{8} + 1458q^{9} + 875q^{10} + 3448q^{11} + 1863q^{12} - 8988q^{13} - 12264q^{14} + 6750q^{15} - 24495q^{16} - 5492q^{17} + 5103q^{18} - 49584q^{19} + 8625q^{20} + 35208q^{21} - 127364q^{22} + 91848q^{23} + 39123q^{24} + 31250q^{25} + 216154q^{26} + 39366q^{27} - 72808q^{28} + 181772q^{29} + 23625q^{30} + 304232q^{31} - 395311q^{32} + 93096q^{33} - 439922q^{34} + 163000q^{35} + 50301q^{36} - 502316q^{37} - 791372q^{38} - 242676q^{39} + 181125q^{40} + 631172q^{41} - 331128q^{42} + 353640q^{43} - 857068q^{44} + 182250q^{45} + 1886472q^{46} - 467480q^{47} - 661365q^{48} + 145490q^{49} + 109375q^{50} - 148284q^{51} + 1423198q^{52} - 568052q^{53} + 137781q^{54} + 431000q^{55} + 2105880q^{56} - 1338768q^{57} + 3126746q^{58} + 287224q^{59} + 232875q^{60} - 2514180q^{61} + 413328q^{62} + 950616q^{63} + 291041q^{64} - 1123500q^{65} - 3438828q^{66} - 5073832q^{67} - 3134374q^{68} + 2479896q^{69} - 1533000q^{70} - 3748816q^{71} + 1056321q^{72} - 1477212q^{73} + 2576306q^{74} + 843750q^{75} - 6035444q^{76} + 10056288q^{77} + 5836158q^{78} - 4627720q^{79} - 3061875q^{80} + 1062882q^{81} + 8637398q^{82} - 6072936q^{83} - 1965816q^{84} - 686500q^{85} + 3382108q^{86} + 4907844q^{87} + 12118884q^{88} + 16516356q^{89} + 637875q^{90} - 19726448q^{91} + 14123784q^{92} + 8214264q^{93} - 3412736q^{94} - 6198000q^{95} - 10673397q^{96} + 2723428q^{97} - 21434497q^{98} + 2513592q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 15.7577 1.39279 0.696396 0.717657i \(-0.254786\pi\)
0.696396 + 0.717657i \(0.254786\pi\)
\(3\) 27.0000 0.577350
\(4\) 120.304 0.939872
\(5\) 125.000 0.447214
\(6\) 425.457 0.804129
\(7\) −34.4284 −0.0379380 −0.0189690 0.999820i \(-0.506038\pi\)
−0.0189690 + 0.999820i \(0.506038\pi\)
\(8\) −121.278 −0.0837465
\(9\) 729.000 0.333333
\(10\) 1969.71 0.622876
\(11\) −3963.55 −0.897863 −0.448931 0.893566i \(-0.648195\pi\)
−0.448931 + 0.893566i \(0.648195\pi\)
\(12\) 3248.20 0.542635
\(13\) 5606.30 0.707742 0.353871 0.935294i \(-0.384865\pi\)
0.353871 + 0.935294i \(0.384865\pi\)
\(14\) −542.511 −0.0528397
\(15\) 3375.00 0.258199
\(16\) −17309.9 −1.05651
\(17\) −19906.7 −0.982717 −0.491358 0.870958i \(-0.663499\pi\)
−0.491358 + 0.870958i \(0.663499\pi\)
\(18\) 11487.3 0.464264
\(19\) −49993.7 −1.67216 −0.836080 0.548607i \(-0.815158\pi\)
−0.836080 + 0.548607i \(0.815158\pi\)
\(20\) 15037.9 0.420323
\(21\) −929.568 −0.0219035
\(22\) −62456.2 −1.25054
\(23\) 109762. 1.88107 0.940533 0.339703i \(-0.110326\pi\)
0.940533 + 0.339703i \(0.110326\pi\)
\(24\) −3274.50 −0.0483511
\(25\) 15625.0 0.200000
\(26\) 88342.2 0.985738
\(27\) 19683.0 0.192450
\(28\) −4141.86 −0.0356568
\(29\) 192477. 1.46550 0.732752 0.680496i \(-0.238236\pi\)
0.732752 + 0.680496i \(0.238236\pi\)
\(30\) 53182.1 0.359618
\(31\) 125541. 0.756870 0.378435 0.925628i \(-0.376462\pi\)
0.378435 + 0.925628i \(0.376462\pi\)
\(32\) −257240. −1.38776
\(33\) −107016. −0.518381
\(34\) −313683. −1.36872
\(35\) −4303.55 −0.0169664
\(36\) 87701.3 0.313291
\(37\) −74353.6 −0.241322 −0.120661 0.992694i \(-0.538501\pi\)
−0.120661 + 0.992694i \(0.538501\pi\)
\(38\) −787784. −2.32897
\(39\) 151370. 0.408615
\(40\) −15159.7 −0.0374526
\(41\) 577802. 1.30929 0.654644 0.755937i \(-0.272818\pi\)
0.654644 + 0.755937i \(0.272818\pi\)
\(42\) −14647.8 −0.0305070
\(43\) 264291. 0.506923 0.253462 0.967345i \(-0.418431\pi\)
0.253462 + 0.967345i \(0.418431\pi\)
\(44\) −476829. −0.843876
\(45\) 91125.0 0.149071
\(46\) 1.72959e6 2.61993
\(47\) −306207. −0.430203 −0.215101 0.976592i \(-0.569008\pi\)
−0.215101 + 0.976592i \(0.569008\pi\)
\(48\) −467368. −0.609978
\(49\) −822358. −0.998561
\(50\) 246213. 0.278559
\(51\) −537481. −0.567372
\(52\) 674458. 0.665186
\(53\) −446219. −0.411702 −0.205851 0.978583i \(-0.565996\pi\)
−0.205851 + 0.978583i \(0.565996\pi\)
\(54\) 310158. 0.268043
\(55\) −495444. −0.401536
\(56\) 4175.41 0.00317717
\(57\) −1.34983e6 −0.965422
\(58\) 3.03299e6 2.04114
\(59\) 1.97951e6 1.25481 0.627403 0.778695i \(-0.284118\pi\)
0.627403 + 0.778695i \(0.284118\pi\)
\(60\) 406024. 0.242674
\(61\) −1.27494e6 −0.719175 −0.359587 0.933111i \(-0.617083\pi\)
−0.359587 + 0.933111i \(0.617083\pi\)
\(62\) 1.97824e6 1.05416
\(63\) −25098.3 −0.0126460
\(64\) −1.83783e6 −0.876345
\(65\) 700788. 0.316512
\(66\) −1.68632e6 −0.721998
\(67\) −4.12943e6 −1.67737 −0.838684 0.544619i \(-0.816674\pi\)
−0.838684 + 0.544619i \(0.816674\pi\)
\(68\) −2.39485e6 −0.923627
\(69\) 2.96357e6 1.08603
\(70\) −67813.9 −0.0236306
\(71\) −2.81187e6 −0.932377 −0.466188 0.884685i \(-0.654373\pi\)
−0.466188 + 0.884685i \(0.654373\pi\)
\(72\) −88411.6 −0.0279155
\(73\) 4.01991e6 1.20945 0.604723 0.796436i \(-0.293284\pi\)
0.604723 + 0.796436i \(0.293284\pi\)
\(74\) −1.17164e6 −0.336111
\(75\) 421875. 0.115470
\(76\) −6.01442e6 −1.57162
\(77\) 136459. 0.0340631
\(78\) 2.38524e6 0.569116
\(79\) −1.32785e6 −0.303009 −0.151505 0.988457i \(-0.548412\pi\)
−0.151505 + 0.988457i \(0.548412\pi\)
\(80\) −2.16374e6 −0.472487
\(81\) 531441. 0.111111
\(82\) 9.10480e6 1.82357
\(83\) −1.91033e6 −0.366721 −0.183361 0.983046i \(-0.558698\pi\)
−0.183361 + 0.983046i \(0.558698\pi\)
\(84\) −111830. −0.0205865
\(85\) −2.48834e6 −0.439484
\(86\) 4.16460e6 0.706039
\(87\) 5.19689e6 0.846109
\(88\) 480691. 0.0751929
\(89\) 8.00695e6 1.20393 0.601966 0.798522i \(-0.294384\pi\)
0.601966 + 0.798522i \(0.294384\pi\)
\(90\) 1.43592e6 0.207625
\(91\) −193016. −0.0268503
\(92\) 1.32047e7 1.76796
\(93\) 3.38962e6 0.436979
\(94\) −4.82511e6 −0.599183
\(95\) −6.24922e6 −0.747813
\(96\) −6.94548e6 −0.801222
\(97\) −3.89241e6 −0.433029 −0.216515 0.976279i \(-0.569469\pi\)
−0.216515 + 0.976279i \(0.569469\pi\)
\(98\) −1.29584e7 −1.39079
\(99\) −2.88943e6 −0.299288
\(100\) 1.87974e6 0.187974
\(101\) 1.07779e7 1.04090 0.520450 0.853892i \(-0.325764\pi\)
0.520450 + 0.853892i \(0.325764\pi\)
\(102\) −8.46944e6 −0.790231
\(103\) −1.93103e7 −1.74124 −0.870622 0.491952i \(-0.836283\pi\)
−0.870622 + 0.491952i \(0.836283\pi\)
\(104\) −679921. −0.0592709
\(105\) −116196. −0.00979554
\(106\) −7.03137e6 −0.573415
\(107\) −6.90473e6 −0.544883 −0.272442 0.962172i \(-0.587831\pi\)
−0.272442 + 0.962172i \(0.587831\pi\)
\(108\) 2.36793e6 0.180878
\(109\) 2.39533e7 1.77163 0.885814 0.464040i \(-0.153601\pi\)
0.885814 + 0.464040i \(0.153601\pi\)
\(110\) −7.80703e6 −0.559257
\(111\) −2.00755e6 −0.139327
\(112\) 595953. 0.0400820
\(113\) −9.56587e6 −0.623663 −0.311831 0.950137i \(-0.600942\pi\)
−0.311831 + 0.950137i \(0.600942\pi\)
\(114\) −2.12702e7 −1.34463
\(115\) 1.37202e7 0.841238
\(116\) 2.31557e7 1.37738
\(117\) 4.08700e6 0.235914
\(118\) 3.11925e7 1.74768
\(119\) 685357. 0.0372823
\(120\) −409313. −0.0216233
\(121\) −3.77744e6 −0.193843
\(122\) −2.00900e7 −1.00166
\(123\) 1.56006e7 0.755918
\(124\) 1.51031e7 0.711360
\(125\) 1.95313e6 0.0894427
\(126\) −395491. −0.0176132
\(127\) −1.19412e7 −0.517290 −0.258645 0.965972i \(-0.583276\pi\)
−0.258645 + 0.965972i \(0.583276\pi\)
\(128\) 3.96685e6 0.167190
\(129\) 7.13585e6 0.292672
\(130\) 1.10428e7 0.440835
\(131\) −1.60064e6 −0.0622077 −0.0311039 0.999516i \(-0.509902\pi\)
−0.0311039 + 0.999516i \(0.509902\pi\)
\(132\) −1.28744e7 −0.487212
\(133\) 1.72121e6 0.0634384
\(134\) −6.50701e7 −2.33623
\(135\) 2.46037e6 0.0860663
\(136\) 2.41424e6 0.0822991
\(137\) 2.88030e7 0.957008 0.478504 0.878085i \(-0.341179\pi\)
0.478504 + 0.878085i \(0.341179\pi\)
\(138\) 4.66989e7 1.51262
\(139\) −2.14740e6 −0.0678204 −0.0339102 0.999425i \(-0.510796\pi\)
−0.0339102 + 0.999425i \(0.510796\pi\)
\(140\) −517733. −0.0159462
\(141\) −8.26760e6 −0.248378
\(142\) −4.43085e7 −1.29861
\(143\) −2.22209e7 −0.635455
\(144\) −1.26189e7 −0.352171
\(145\) 2.40597e7 0.655393
\(146\) 6.33444e7 1.68451
\(147\) −2.22037e7 −0.576519
\(148\) −8.94501e6 −0.226811
\(149\) 4.96813e6 0.123038 0.0615192 0.998106i \(-0.480405\pi\)
0.0615192 + 0.998106i \(0.480405\pi\)
\(150\) 6.64776e6 0.160826
\(151\) −2.10485e7 −0.497511 −0.248756 0.968566i \(-0.580022\pi\)
−0.248756 + 0.968566i \(0.580022\pi\)
\(152\) 6.06313e6 0.140038
\(153\) −1.45120e7 −0.327572
\(154\) 2.15027e6 0.0474428
\(155\) 1.56927e7 0.338482
\(156\) 1.82104e7 0.384046
\(157\) −2.61392e7 −0.539069 −0.269534 0.962991i \(-0.586870\pi\)
−0.269534 + 0.962991i \(0.586870\pi\)
\(158\) −2.09239e7 −0.422029
\(159\) −1.20479e7 −0.237696
\(160\) −3.21550e7 −0.620624
\(161\) −3.77893e6 −0.0713638
\(162\) 8.37426e6 0.154755
\(163\) −1.01817e8 −1.84147 −0.920733 0.390194i \(-0.872408\pi\)
−0.920733 + 0.390194i \(0.872408\pi\)
\(164\) 6.95116e7 1.23056
\(165\) −1.33770e7 −0.231827
\(166\) −3.01024e7 −0.510766
\(167\) 6.14576e7 1.02110 0.510550 0.859848i \(-0.329442\pi\)
0.510550 + 0.859848i \(0.329442\pi\)
\(168\) 112736. 0.00183434
\(169\) −3.13179e7 −0.499101
\(170\) −3.92104e7 −0.612110
\(171\) −3.64454e7 −0.557387
\(172\) 3.17951e7 0.476443
\(173\) −2.74394e7 −0.402914 −0.201457 0.979497i \(-0.564568\pi\)
−0.201457 + 0.979497i \(0.564568\pi\)
\(174\) 8.18908e7 1.17845
\(175\) −537944. −0.00758760
\(176\) 6.86087e7 0.948604
\(177\) 5.34469e7 0.724462
\(178\) 1.26171e8 1.67683
\(179\) 4.05126e7 0.527964 0.263982 0.964528i \(-0.414964\pi\)
0.263982 + 0.964528i \(0.414964\pi\)
\(180\) 1.09627e7 0.140108
\(181\) 9.66189e7 1.21112 0.605560 0.795800i \(-0.292949\pi\)
0.605560 + 0.795800i \(0.292949\pi\)
\(182\) −3.04148e6 −0.0373969
\(183\) −3.44233e7 −0.415216
\(184\) −1.33117e7 −0.157533
\(185\) −9.29421e6 −0.107922
\(186\) 5.34124e7 0.608621
\(187\) 7.89012e7 0.882345
\(188\) −3.68378e7 −0.404335
\(189\) −677655. −0.00730117
\(190\) −9.84730e7 −1.04155
\(191\) −1.42378e8 −1.47852 −0.739260 0.673420i \(-0.764825\pi\)
−0.739260 + 0.673420i \(0.764825\pi\)
\(192\) −4.96214e7 −0.505958
\(193\) 1.27527e8 1.27688 0.638441 0.769671i \(-0.279580\pi\)
0.638441 + 0.769671i \(0.279580\pi\)
\(194\) −6.13352e7 −0.603120
\(195\) 1.89213e7 0.182738
\(196\) −9.89326e7 −0.938519
\(197\) −1.23507e8 −1.15096 −0.575479 0.817816i \(-0.695184\pi\)
−0.575479 + 0.817816i \(0.695184\pi\)
\(198\) −4.55306e7 −0.416846
\(199\) −7.46881e7 −0.671839 −0.335920 0.941891i \(-0.609047\pi\)
−0.335920 + 0.941891i \(0.609047\pi\)
\(200\) −1.89497e6 −0.0167493
\(201\) −1.11495e8 −0.968429
\(202\) 1.69834e8 1.44976
\(203\) −6.62670e6 −0.0555982
\(204\) −6.46609e7 −0.533256
\(205\) 7.22252e7 0.585532
\(206\) −3.04286e8 −2.42519
\(207\) 8.00164e7 0.627022
\(208\) −9.70446e7 −0.747739
\(209\) 1.98153e8 1.50137
\(210\) −1.83098e6 −0.0136432
\(211\) 1.24482e8 0.912257 0.456128 0.889914i \(-0.349236\pi\)
0.456128 + 0.889914i \(0.349236\pi\)
\(212\) −5.36818e7 −0.386947
\(213\) −7.59206e7 −0.538308
\(214\) −1.08802e8 −0.758910
\(215\) 3.30363e7 0.226703
\(216\) −2.38711e6 −0.0161170
\(217\) −4.32219e6 −0.0287141
\(218\) 3.77448e8 2.46751
\(219\) 1.08538e8 0.698274
\(220\) −5.96036e7 −0.377393
\(221\) −1.11603e8 −0.695510
\(222\) −3.16342e7 −0.194054
\(223\) 2.17519e8 1.31350 0.656749 0.754109i \(-0.271931\pi\)
0.656749 + 0.754109i \(0.271931\pi\)
\(224\) 8.85637e6 0.0526487
\(225\) 1.13906e7 0.0666667
\(226\) −1.50736e8 −0.868633
\(227\) 1.39021e8 0.788840 0.394420 0.918930i \(-0.370946\pi\)
0.394420 + 0.918930i \(0.370946\pi\)
\(228\) −1.62389e8 −0.907373
\(229\) 1.06507e8 0.586076 0.293038 0.956101i \(-0.405334\pi\)
0.293038 + 0.956101i \(0.405334\pi\)
\(230\) 2.16199e8 1.17167
\(231\) 3.68439e6 0.0196663
\(232\) −2.33433e7 −0.122731
\(233\) −3.55655e7 −0.184197 −0.0920986 0.995750i \(-0.529358\pi\)
−0.0920986 + 0.995750i \(0.529358\pi\)
\(234\) 6.44015e7 0.328579
\(235\) −3.82759e7 −0.192392
\(236\) 2.38143e8 1.17936
\(237\) −3.58521e7 −0.174942
\(238\) 1.07996e7 0.0519265
\(239\) −8.12794e7 −0.385113 −0.192556 0.981286i \(-0.561678\pi\)
−0.192556 + 0.981286i \(0.561678\pi\)
\(240\) −5.84209e7 −0.272790
\(241\) 1.78776e8 0.822717 0.411359 0.911474i \(-0.365054\pi\)
0.411359 + 0.911474i \(0.365054\pi\)
\(242\) −5.95236e7 −0.269983
\(243\) 1.43489e7 0.0641500
\(244\) −1.53379e8 −0.675932
\(245\) −1.02795e8 −0.446570
\(246\) 2.45830e8 1.05284
\(247\) −2.80280e8 −1.18346
\(248\) −1.52254e7 −0.0633852
\(249\) −5.15790e7 −0.211726
\(250\) 3.07767e7 0.124575
\(251\) −3.53343e7 −0.141039 −0.0705195 0.997510i \(-0.522466\pi\)
−0.0705195 + 0.997510i \(0.522466\pi\)
\(252\) −3.01942e6 −0.0118856
\(253\) −4.35047e8 −1.68894
\(254\) −1.88165e8 −0.720477
\(255\) −6.71851e7 −0.253736
\(256\) 2.97750e8 1.10921
\(257\) −4.18029e8 −1.53617 −0.768087 0.640345i \(-0.778791\pi\)
−0.768087 + 0.640345i \(0.778791\pi\)
\(258\) 1.12444e8 0.407632
\(259\) 2.55988e6 0.00915525
\(260\) 8.43073e7 0.297480
\(261\) 1.40316e8 0.488501
\(262\) −2.52223e7 −0.0866425
\(263\) 2.02813e8 0.687466 0.343733 0.939067i \(-0.388308\pi\)
0.343733 + 0.939067i \(0.388308\pi\)
\(264\) 1.29787e7 0.0434126
\(265\) −5.57774e7 −0.184119
\(266\) 2.71222e7 0.0883565
\(267\) 2.16188e8 0.695090
\(268\) −4.96785e8 −1.57651
\(269\) −2.88920e8 −0.904993 −0.452496 0.891766i \(-0.649466\pi\)
−0.452496 + 0.891766i \(0.649466\pi\)
\(270\) 3.87697e7 0.119873
\(271\) 3.61648e8 1.10381 0.551904 0.833908i \(-0.313902\pi\)
0.551904 + 0.833908i \(0.313902\pi\)
\(272\) 3.44583e8 1.03825
\(273\) −5.21144e6 −0.0155020
\(274\) 4.53867e8 1.33291
\(275\) −6.19305e7 −0.179573
\(276\) 3.56528e8 1.02073
\(277\) −3.16424e8 −0.894522 −0.447261 0.894404i \(-0.647600\pi\)
−0.447261 + 0.894404i \(0.647600\pi\)
\(278\) −3.38379e7 −0.0944597
\(279\) 9.15197e7 0.252290
\(280\) 521926. 0.00142088
\(281\) −3.81619e7 −0.102603 −0.0513013 0.998683i \(-0.516337\pi\)
−0.0513013 + 0.998683i \(0.516337\pi\)
\(282\) −1.30278e8 −0.345938
\(283\) −5.36394e8 −1.40680 −0.703398 0.710796i \(-0.748335\pi\)
−0.703398 + 0.710796i \(0.748335\pi\)
\(284\) −3.38278e8 −0.876314
\(285\) −1.68729e8 −0.431750
\(286\) −3.50149e8 −0.885057
\(287\) −1.98928e7 −0.0496718
\(288\) −1.87528e8 −0.462586
\(289\) −1.40615e7 −0.0342681
\(290\) 3.79124e8 0.912827
\(291\) −1.05095e8 −0.250009
\(292\) 4.83610e8 1.13672
\(293\) 5.38585e8 1.25088 0.625442 0.780270i \(-0.284919\pi\)
0.625442 + 0.780270i \(0.284919\pi\)
\(294\) −3.49877e8 −0.802972
\(295\) 2.47439e8 0.561166
\(296\) 9.01745e6 0.0202098
\(297\) −7.80146e7 −0.172794
\(298\) 7.82860e7 0.171367
\(299\) 6.15358e8 1.33131
\(300\) 5.07531e7 0.108527
\(301\) −9.09911e6 −0.0192316
\(302\) −3.31676e8 −0.692930
\(303\) 2.91003e8 0.600964
\(304\) 8.65387e8 1.76666
\(305\) −1.59367e8 −0.321625
\(306\) −2.28675e8 −0.456240
\(307\) 6.10303e7 0.120382 0.0601910 0.998187i \(-0.480829\pi\)
0.0601910 + 0.998187i \(0.480829\pi\)
\(308\) 1.64165e7 0.0320149
\(309\) −5.21379e8 −1.00531
\(310\) 2.47280e8 0.471436
\(311\) 5.75355e8 1.08461 0.542306 0.840181i \(-0.317551\pi\)
0.542306 + 0.840181i \(0.317551\pi\)
\(312\) −1.83579e7 −0.0342201
\(313\) 7.32396e8 1.35002 0.675011 0.737807i \(-0.264139\pi\)
0.675011 + 0.737807i \(0.264139\pi\)
\(314\) −4.11893e8 −0.750811
\(315\) −3.13729e6 −0.00565546
\(316\) −1.59746e8 −0.284790
\(317\) −1.67850e7 −0.0295947 −0.0147973 0.999891i \(-0.504710\pi\)
−0.0147973 + 0.999891i \(0.504710\pi\)
\(318\) −1.89847e8 −0.331061
\(319\) −7.62894e8 −1.31582
\(320\) −2.29729e8 −0.391913
\(321\) −1.86428e8 −0.314589
\(322\) −5.95470e7 −0.0993950
\(323\) 9.95211e8 1.64326
\(324\) 6.39342e7 0.104430
\(325\) 8.75985e7 0.141548
\(326\) −1.60440e9 −2.56478
\(327\) 6.46739e8 1.02285
\(328\) −7.00746e7 −0.109648
\(329\) 1.05422e7 0.0163210
\(330\) −2.10790e8 −0.322887
\(331\) −1.08406e9 −1.64306 −0.821532 0.570163i \(-0.806880\pi\)
−0.821532 + 0.570163i \(0.806880\pi\)
\(332\) −2.29820e8 −0.344671
\(333\) −5.42038e7 −0.0804405
\(334\) 9.68427e8 1.42218
\(335\) −5.16179e8 −0.750142
\(336\) 1.60907e7 0.0231413
\(337\) 7.36350e7 0.104804 0.0524022 0.998626i \(-0.483312\pi\)
0.0524022 + 0.998626i \(0.483312\pi\)
\(338\) −4.93496e8 −0.695145
\(339\) −2.58278e8 −0.360072
\(340\) −2.99356e8 −0.413059
\(341\) −4.97590e8 −0.679565
\(342\) −5.74294e8 −0.776324
\(343\) 5.66658e7 0.0758214
\(344\) −3.20526e7 −0.0424530
\(345\) 3.70446e8 0.485689
\(346\) −4.32380e8 −0.561176
\(347\) −2.99713e8 −0.385082 −0.192541 0.981289i \(-0.561673\pi\)
−0.192541 + 0.981289i \(0.561673\pi\)
\(348\) 6.25204e8 0.795233
\(349\) −4.00569e8 −0.504415 −0.252208 0.967673i \(-0.581157\pi\)
−0.252208 + 0.967673i \(0.581157\pi\)
\(350\) −8.47674e6 −0.0105679
\(351\) 1.10349e8 0.136205
\(352\) 1.01958e9 1.24602
\(353\) −5.93100e8 −0.717657 −0.358828 0.933404i \(-0.616824\pi\)
−0.358828 + 0.933404i \(0.616824\pi\)
\(354\) 8.42197e8 1.00903
\(355\) −3.51484e8 −0.416972
\(356\) 9.63264e8 1.13154
\(357\) 1.85046e7 0.0215249
\(358\) 6.38383e8 0.735344
\(359\) 8.77947e8 1.00147 0.500735 0.865601i \(-0.333063\pi\)
0.500735 + 0.865601i \(0.333063\pi\)
\(360\) −1.10514e7 −0.0124842
\(361\) 1.60550e9 1.79612
\(362\) 1.52249e9 1.68684
\(363\) −1.01991e8 −0.111915
\(364\) −2.32205e7 −0.0252358
\(365\) 5.02489e8 0.540881
\(366\) −5.42430e8 −0.578309
\(367\) 4.65347e8 0.491412 0.245706 0.969344i \(-0.420980\pi\)
0.245706 + 0.969344i \(0.420980\pi\)
\(368\) −1.89997e9 −1.98737
\(369\) 4.21217e8 0.436429
\(370\) −1.46455e8 −0.150313
\(371\) 1.53626e7 0.0156191
\(372\) 4.07783e8 0.410704
\(373\) −2.88096e8 −0.287446 −0.143723 0.989618i \(-0.545907\pi\)
−0.143723 + 0.989618i \(0.545907\pi\)
\(374\) 1.24330e9 1.22892
\(375\) 5.27344e7 0.0516398
\(376\) 3.71362e7 0.0360280
\(377\) 1.07909e9 1.03720
\(378\) −1.06782e7 −0.0101690
\(379\) −8.21572e8 −0.775190 −0.387595 0.921830i \(-0.626694\pi\)
−0.387595 + 0.921830i \(0.626694\pi\)
\(380\) −7.51803e8 −0.702848
\(381\) −3.22412e8 −0.298657
\(382\) −2.24355e9 −2.05927
\(383\) −6.41573e8 −0.583513 −0.291757 0.956493i \(-0.594240\pi\)
−0.291757 + 0.956493i \(0.594240\pi\)
\(384\) 1.07105e8 0.0965273
\(385\) 1.70574e7 0.0152335
\(386\) 2.00952e9 1.77843
\(387\) 1.92668e8 0.168974
\(388\) −4.68270e8 −0.406992
\(389\) −1.25481e9 −1.08082 −0.540411 0.841401i \(-0.681731\pi\)
−0.540411 + 0.841401i \(0.681731\pi\)
\(390\) 2.98155e8 0.254516
\(391\) −2.18500e9 −1.84855
\(392\) 9.97338e7 0.0836260
\(393\) −4.32173e7 −0.0359157
\(394\) −1.94618e9 −1.60305
\(395\) −1.65982e8 −0.135510
\(396\) −3.47608e8 −0.281292
\(397\) 1.29837e9 1.04144 0.520718 0.853729i \(-0.325664\pi\)
0.520718 + 0.853729i \(0.325664\pi\)
\(398\) −1.17691e9 −0.935733
\(399\) 4.64726e7 0.0366262
\(400\) −2.70467e8 −0.211303
\(401\) 2.16310e9 1.67522 0.837610 0.546268i \(-0.183952\pi\)
0.837610 + 0.546268i \(0.183952\pi\)
\(402\) −1.75689e9 −1.34882
\(403\) 7.03823e8 0.535668
\(404\) 1.29662e9 0.978313
\(405\) 6.64301e7 0.0496904
\(406\) −1.04421e8 −0.0774368
\(407\) 2.94704e8 0.216674
\(408\) 6.51846e7 0.0475154
\(409\) −1.26448e9 −0.913864 −0.456932 0.889502i \(-0.651052\pi\)
−0.456932 + 0.889502i \(0.651052\pi\)
\(410\) 1.13810e9 0.815524
\(411\) 7.77680e8 0.552529
\(412\) −2.32310e9 −1.63655
\(413\) −6.81516e7 −0.0476048
\(414\) 1.26087e9 0.873312
\(415\) −2.38792e8 −0.164003
\(416\) −1.44217e9 −0.982174
\(417\) −5.79797e7 −0.0391561
\(418\) 3.12242e9 2.09110
\(419\) −1.84627e9 −1.22616 −0.613080 0.790021i \(-0.710070\pi\)
−0.613080 + 0.790021i \(0.710070\pi\)
\(420\) −1.39788e7 −0.00920655
\(421\) 2.24531e9 1.46652 0.733262 0.679947i \(-0.237997\pi\)
0.733262 + 0.679947i \(0.237997\pi\)
\(422\) 1.96154e9 1.27058
\(423\) −2.23225e8 −0.143401
\(424\) 5.41165e7 0.0344786
\(425\) −3.11042e8 −0.196543
\(426\) −1.19633e9 −0.749752
\(427\) 4.38941e7 0.0272840
\(428\) −8.30664e8 −0.512120
\(429\) −5.99963e8 −0.366880
\(430\) 5.20575e8 0.315750
\(431\) −1.63983e9 −0.986568 −0.493284 0.869868i \(-0.664204\pi\)
−0.493284 + 0.869868i \(0.664204\pi\)
\(432\) −3.40711e8 −0.203326
\(433\) 2.53503e9 1.50063 0.750317 0.661078i \(-0.229901\pi\)
0.750317 + 0.661078i \(0.229901\pi\)
\(434\) −6.81076e7 −0.0399928
\(435\) 6.49611e8 0.378391
\(436\) 2.88167e9 1.66510
\(437\) −5.48740e9 −3.14544
\(438\) 1.71030e9 0.972551
\(439\) 1.74546e8 0.0984655 0.0492327 0.998787i \(-0.484322\pi\)
0.0492327 + 0.998787i \(0.484322\pi\)
\(440\) 6.00864e7 0.0336273
\(441\) −5.99499e8 −0.332854
\(442\) −1.75860e9 −0.968701
\(443\) −1.13523e9 −0.620400 −0.310200 0.950671i \(-0.600396\pi\)
−0.310200 + 0.950671i \(0.600396\pi\)
\(444\) −2.41515e8 −0.130950
\(445\) 1.00087e9 0.538415
\(446\) 3.42758e9 1.82943
\(447\) 1.34139e8 0.0710363
\(448\) 6.32736e7 0.0332468
\(449\) 2.28121e9 1.18933 0.594665 0.803973i \(-0.297285\pi\)
0.594665 + 0.803973i \(0.297285\pi\)
\(450\) 1.79489e8 0.0928528
\(451\) −2.29015e9 −1.17556
\(452\) −1.15081e9 −0.586163
\(453\) −5.68311e8 −0.287238
\(454\) 2.19064e9 1.09869
\(455\) −2.41270e7 −0.0120078
\(456\) 1.63705e8 0.0808507
\(457\) 2.93541e9 1.43867 0.719335 0.694663i \(-0.244447\pi\)
0.719335 + 0.694663i \(0.244447\pi\)
\(458\) 1.67830e9 0.816282
\(459\) −3.91824e8 −0.189124
\(460\) 1.65059e9 0.790656
\(461\) −6.32918e8 −0.300881 −0.150440 0.988619i \(-0.548069\pi\)
−0.150440 + 0.988619i \(0.548069\pi\)
\(462\) 5.80573e7 0.0273911
\(463\) −1.41260e9 −0.661431 −0.330716 0.943730i \(-0.607290\pi\)
−0.330716 + 0.943730i \(0.607290\pi\)
\(464\) −3.33177e9 −1.54832
\(465\) 4.23702e8 0.195423
\(466\) −5.60429e8 −0.256549
\(467\) −3.77542e8 −0.171536 −0.0857682 0.996315i \(-0.527334\pi\)
−0.0857682 + 0.996315i \(0.527334\pi\)
\(468\) 4.91680e8 0.221729
\(469\) 1.42170e8 0.0636359
\(470\) −6.03138e8 −0.267963
\(471\) −7.05760e8 −0.311232
\(472\) −2.40071e8 −0.105086
\(473\) −1.04753e9 −0.455147
\(474\) −5.64944e8 −0.243658
\(475\) −7.81152e8 −0.334432
\(476\) 8.24509e7 0.0350406
\(477\) −3.25294e8 −0.137234
\(478\) −1.28077e9 −0.536382
\(479\) 4.30550e9 1.78999 0.894993 0.446080i \(-0.147180\pi\)
0.894993 + 0.446080i \(0.147180\pi\)
\(480\) −8.68185e8 −0.358317
\(481\) −4.16849e8 −0.170793
\(482\) 2.81710e9 1.14587
\(483\) −1.02031e8 −0.0412019
\(484\) −4.54440e8 −0.182187
\(485\) −4.86551e8 −0.193656
\(486\) 2.26105e8 0.0893477
\(487\) 8.36858e8 0.328322 0.164161 0.986434i \(-0.447508\pi\)
0.164161 + 0.986434i \(0.447508\pi\)
\(488\) 1.54622e8 0.0602284
\(489\) −2.74906e9 −1.06317
\(490\) −1.61980e9 −0.621979
\(491\) 3.30420e9 1.25974 0.629870 0.776700i \(-0.283108\pi\)
0.629870 + 0.776700i \(0.283108\pi\)
\(492\) 1.87681e9 0.710466
\(493\) −3.83159e9 −1.44017
\(494\) −4.41656e9 −1.64831
\(495\) −3.61178e8 −0.133845
\(496\) −2.17311e9 −0.799643
\(497\) 9.68084e7 0.0353725
\(498\) −8.12764e8 −0.294891
\(499\) 3.42619e9 1.23441 0.617205 0.786802i \(-0.288265\pi\)
0.617205 + 0.786802i \(0.288265\pi\)
\(500\) 2.34968e8 0.0840647
\(501\) 1.65935e9 0.589532
\(502\) −5.56786e8 −0.196438
\(503\) 2.20556e9 0.772734 0.386367 0.922345i \(-0.373730\pi\)
0.386367 + 0.922345i \(0.373730\pi\)
\(504\) 3.04387e6 0.00105906
\(505\) 1.34724e9 0.465505
\(506\) −6.85531e9 −2.35234
\(507\) −8.45583e8 −0.288156
\(508\) −1.43656e9 −0.486186
\(509\) 1.55340e9 0.522122 0.261061 0.965322i \(-0.415928\pi\)
0.261061 + 0.965322i \(0.415928\pi\)
\(510\) −1.05868e9 −0.353402
\(511\) −1.38399e8 −0.0458839
\(512\) 4.18409e9 1.37770
\(513\) −9.84027e8 −0.321807
\(514\) −6.58715e9 −2.13957
\(515\) −2.41379e9 −0.778708
\(516\) 8.58468e8 0.275074
\(517\) 1.21367e9 0.386263
\(518\) 4.03377e7 0.0127514
\(519\) −7.40863e8 −0.232623
\(520\) −8.49901e7 −0.0265068
\(521\) 5.82978e9 1.80601 0.903005 0.429629i \(-0.141356\pi\)
0.903005 + 0.429629i \(0.141356\pi\)
\(522\) 2.21105e9 0.680381
\(523\) −1.98399e9 −0.606433 −0.303216 0.952922i \(-0.598060\pi\)
−0.303216 + 0.952922i \(0.598060\pi\)
\(524\) −1.92563e8 −0.0584673
\(525\) −1.45245e7 −0.00438070
\(526\) 3.19586e9 0.957498
\(527\) −2.49912e9 −0.743788
\(528\) 1.85243e9 0.547677
\(529\) 8.64284e9 2.53841
\(530\) −8.78921e8 −0.256439
\(531\) 1.44307e9 0.418269
\(532\) 2.07067e8 0.0596239
\(533\) 3.23933e9 0.926638
\(534\) 3.40661e9 0.968117
\(535\) −8.63091e8 −0.243679
\(536\) 5.00809e8 0.140474
\(537\) 1.09384e9 0.304820
\(538\) −4.55271e9 −1.26047
\(539\) 3.25946e9 0.896570
\(540\) 2.95992e8 0.0808913
\(541\) −7.16394e9 −1.94519 −0.972594 0.232511i \(-0.925306\pi\)
−0.972594 + 0.232511i \(0.925306\pi\)
\(542\) 5.69872e9 1.53737
\(543\) 2.60871e9 0.699240
\(544\) 5.12080e9 1.36377
\(545\) 2.99416e9 0.792296
\(546\) −8.21200e7 −0.0215911
\(547\) 1.97289e9 0.515403 0.257702 0.966225i \(-0.417035\pi\)
0.257702 + 0.966225i \(0.417035\pi\)
\(548\) 3.46510e9 0.899464
\(549\) −9.29429e8 −0.239725
\(550\) −9.75879e8 −0.250107
\(551\) −9.62266e9 −2.45056
\(552\) −3.59416e8 −0.0909515
\(553\) 4.57160e7 0.0114956
\(554\) −4.98611e9 −1.24588
\(555\) −2.50944e8 −0.0623090
\(556\) −2.58339e8 −0.0637424
\(557\) −6.01464e9 −1.47474 −0.737372 0.675487i \(-0.763933\pi\)
−0.737372 + 0.675487i \(0.763933\pi\)
\(558\) 1.44214e9 0.351388
\(559\) 1.48169e9 0.358771
\(560\) 7.44941e7 0.0179252
\(561\) 2.13033e9 0.509422
\(562\) −6.01342e8 −0.142904
\(563\) 1.43964e9 0.339996 0.169998 0.985444i \(-0.445624\pi\)
0.169998 + 0.985444i \(0.445624\pi\)
\(564\) −9.94621e8 −0.233443
\(565\) −1.19573e9 −0.278910
\(566\) −8.45231e9 −1.95938
\(567\) −1.82967e7 −0.00421533
\(568\) 3.41018e8 0.0780833
\(569\) −4.34990e9 −0.989889 −0.494944 0.868925i \(-0.664812\pi\)
−0.494944 + 0.868925i \(0.664812\pi\)
\(570\) −2.65877e9 −0.601338
\(571\) −3.91778e9 −0.880671 −0.440336 0.897833i \(-0.645141\pi\)
−0.440336 + 0.897833i \(0.645141\pi\)
\(572\) −2.67325e9 −0.597246
\(573\) −3.84422e9 −0.853624
\(574\) −3.13464e8 −0.0691825
\(575\) 1.71503e9 0.376213
\(576\) −1.33978e9 −0.292115
\(577\) −5.57477e9 −1.20812 −0.604062 0.796938i \(-0.706452\pi\)
−0.604062 + 0.796938i \(0.706452\pi\)
\(578\) −2.21577e8 −0.0477284
\(579\) 3.44322e9 0.737209
\(580\) 2.89446e9 0.615985
\(581\) 6.57698e7 0.0139127
\(582\) −1.65605e9 −0.348211
\(583\) 1.76861e9 0.369652
\(584\) −4.87526e8 −0.101287
\(585\) 5.10874e8 0.105504
\(586\) 8.48683e9 1.74222
\(587\) 3.96579e9 0.809275 0.404638 0.914477i \(-0.367398\pi\)
0.404638 + 0.914477i \(0.367398\pi\)
\(588\) −2.67118e9 −0.541854
\(589\) −6.27628e9 −1.26561
\(590\) 3.89906e9 0.781588
\(591\) −3.33469e9 −0.664506
\(592\) 1.28705e9 0.254959
\(593\) 1.59443e9 0.313988 0.156994 0.987600i \(-0.449820\pi\)
0.156994 + 0.987600i \(0.449820\pi\)
\(594\) −1.22933e9 −0.240666
\(595\) 8.56696e7 0.0166731
\(596\) 5.97683e8 0.115640
\(597\) −2.01658e9 −0.387887
\(598\) 9.69660e9 1.85424
\(599\) 1.99503e9 0.379276 0.189638 0.981854i \(-0.439269\pi\)
0.189638 + 0.981854i \(0.439269\pi\)
\(600\) −5.11641e7 −0.00967021
\(601\) 5.69444e9 1.07002 0.535008 0.844847i \(-0.320308\pi\)
0.535008 + 0.844847i \(0.320308\pi\)
\(602\) −1.43381e8 −0.0267857
\(603\) −3.01035e9 −0.559123
\(604\) −2.53221e9 −0.467597
\(605\) −4.72180e8 −0.0866890
\(606\) 4.58553e9 0.837019
\(607\) 1.61948e9 0.293910 0.146955 0.989143i \(-0.453053\pi\)
0.146955 + 0.989143i \(0.453053\pi\)
\(608\) 1.28604e10 2.32055
\(609\) −1.78921e8 −0.0320997
\(610\) −2.51125e9 −0.447956
\(611\) −1.71669e9 −0.304472
\(612\) −1.74584e9 −0.307876
\(613\) −8.66201e8 −0.151882 −0.0759412 0.997112i \(-0.524196\pi\)
−0.0759412 + 0.997112i \(0.524196\pi\)
\(614\) 9.61694e8 0.167667
\(615\) 1.95008e9 0.338057
\(616\) −1.65494e7 −0.00285267
\(617\) −8.93265e9 −1.53102 −0.765512 0.643421i \(-0.777514\pi\)
−0.765512 + 0.643421i \(0.777514\pi\)
\(618\) −8.21571e9 −1.40019
\(619\) −3.70947e9 −0.628630 −0.314315 0.949319i \(-0.601775\pi\)
−0.314315 + 0.949319i \(0.601775\pi\)
\(620\) 1.88788e9 0.318130
\(621\) 2.16044e9 0.362011
\(622\) 9.06625e9 1.51064
\(623\) −2.75667e8 −0.0456747
\(624\) −2.62020e9 −0.431707
\(625\) 2.44141e8 0.0400000
\(626\) 1.15408e10 1.88030
\(627\) 5.35012e9 0.866817
\(628\) −3.14464e9 −0.506656
\(629\) 1.48014e9 0.237151
\(630\) −4.94363e7 −0.00787688
\(631\) 1.11559e9 0.176767 0.0883834 0.996087i \(-0.471830\pi\)
0.0883834 + 0.996087i \(0.471830\pi\)
\(632\) 1.61039e8 0.0253760
\(633\) 3.36101e9 0.526692
\(634\) −2.64492e8 −0.0412192
\(635\) −1.49265e9 −0.231339
\(636\) −1.44941e9 −0.223404
\(637\) −4.61039e9 −0.706723
\(638\) −1.20214e10 −1.83267
\(639\) −2.04986e9 −0.310792
\(640\) 4.95856e8 0.0747697
\(641\) 4.96276e8 0.0744252 0.0372126 0.999307i \(-0.488152\pi\)
0.0372126 + 0.999307i \(0.488152\pi\)
\(642\) −2.93766e9 −0.438157
\(643\) −8.93408e8 −0.132529 −0.0662646 0.997802i \(-0.521108\pi\)
−0.0662646 + 0.997802i \(0.521108\pi\)
\(644\) −4.54619e8 −0.0670728
\(645\) 8.91981e8 0.130887
\(646\) 1.56822e10 2.28872
\(647\) 3.05033e9 0.442774 0.221387 0.975186i \(-0.428942\pi\)
0.221387 + 0.975186i \(0.428942\pi\)
\(648\) −6.44520e7 −0.00930517
\(649\) −7.84590e9 −1.12664
\(650\) 1.38035e9 0.197148
\(651\) −1.16699e8 −0.0165781
\(652\) −1.22489e10 −1.73074
\(653\) −1.29545e10 −1.82064 −0.910319 0.413908i \(-0.864164\pi\)
−0.910319 + 0.413908i \(0.864164\pi\)
\(654\) 1.01911e10 1.42462
\(655\) −2.00080e8 −0.0278201
\(656\) −1.00017e10 −1.38328
\(657\) 2.93052e9 0.403149
\(658\) 1.66121e8 0.0227318
\(659\) 8.43740e9 1.14844 0.574222 0.818700i \(-0.305305\pi\)
0.574222 + 0.818700i \(0.305305\pi\)
\(660\) −1.60930e9 −0.217888
\(661\) 7.97949e9 1.07466 0.537328 0.843373i \(-0.319434\pi\)
0.537328 + 0.843373i \(0.319434\pi\)
\(662\) −1.70822e10 −2.28845
\(663\) −3.01328e9 −0.401553
\(664\) 2.31681e8 0.0307116
\(665\) 2.15151e8 0.0283705
\(666\) −8.54125e8 −0.112037
\(667\) 2.11267e10 2.75671
\(668\) 7.39357e9 0.959702
\(669\) 5.87301e9 0.758349
\(670\) −8.13376e9 −1.04479
\(671\) 5.05328e9 0.645720
\(672\) 2.39122e8 0.0303967
\(673\) −4.53364e9 −0.573317 −0.286658 0.958033i \(-0.592544\pi\)
−0.286658 + 0.958033i \(0.592544\pi\)
\(674\) 1.16032e9 0.145971
\(675\) 3.07547e8 0.0384900
\(676\) −3.76765e9 −0.469091
\(677\) 1.06085e9 0.131400 0.0656998 0.997839i \(-0.479072\pi\)
0.0656998 + 0.997839i \(0.479072\pi\)
\(678\) −4.06986e9 −0.501505
\(679\) 1.34009e8 0.0164282
\(680\) 3.01781e8 0.0368053
\(681\) 3.75356e9 0.455437
\(682\) −7.84084e9 −0.946493
\(683\) 1.53865e9 0.184785 0.0923924 0.995723i \(-0.470549\pi\)
0.0923924 + 0.995723i \(0.470549\pi\)
\(684\) −4.38451e9 −0.523872
\(685\) 3.60037e9 0.427987
\(686\) 8.92920e8 0.105603
\(687\) 2.87569e9 0.338371
\(688\) −4.57485e9 −0.535571
\(689\) −2.50164e9 −0.291379
\(690\) 5.83736e9 0.676464
\(691\) −5.67788e9 −0.654656 −0.327328 0.944911i \(-0.606148\pi\)
−0.327328 + 0.944911i \(0.606148\pi\)
\(692\) −3.30105e9 −0.378688
\(693\) 9.94785e7 0.0113544
\(694\) −4.72278e9 −0.536339
\(695\) −2.68424e8 −0.0303302
\(696\) −6.30268e8 −0.0708586
\(697\) −1.15021e10 −1.28666
\(698\) −6.31202e9 −0.702546
\(699\) −9.60269e8 −0.106346
\(700\) −6.47166e7 −0.00713136
\(701\) 3.43469e9 0.376595 0.188298 0.982112i \(-0.439703\pi\)
0.188298 + 0.982112i \(0.439703\pi\)
\(702\) 1.73884e9 0.189705
\(703\) 3.71722e9 0.403528
\(704\) 7.28433e9 0.786837
\(705\) −1.03345e9 −0.111078
\(706\) −9.34587e9 −0.999547
\(707\) −3.71066e8 −0.0394897
\(708\) 6.42985e9 0.680902
\(709\) −1.79411e10 −1.89055 −0.945273 0.326281i \(-0.894204\pi\)
−0.945273 + 0.326281i \(0.894204\pi\)
\(710\) −5.53856e9 −0.580755
\(711\) −9.68006e8 −0.101003
\(712\) −9.71065e8 −0.100825
\(713\) 1.37797e10 1.42372
\(714\) 2.91590e8 0.0299798
\(715\) −2.77761e9 −0.284184
\(716\) 4.87381e9 0.496218
\(717\) −2.19455e9 −0.222345
\(718\) 1.38344e10 1.39484
\(719\) −5.25757e9 −0.527514 −0.263757 0.964589i \(-0.584962\pi\)
−0.263757 + 0.964589i \(0.584962\pi\)
\(720\) −1.57737e9 −0.157496
\(721\) 6.64825e8 0.0660593
\(722\) 2.52989e10 2.50162
\(723\) 4.82696e9 0.474996
\(724\) 1.16236e10 1.13830
\(725\) 3.00746e9 0.293101
\(726\) −1.60714e9 −0.155874
\(727\) 7.82419e9 0.755212 0.377606 0.925966i \(-0.376747\pi\)
0.377606 + 0.925966i \(0.376747\pi\)
\(728\) 2.34086e7 0.00224862
\(729\) 3.87420e8 0.0370370
\(730\) 7.91805e9 0.753335
\(731\) −5.26116e9 −0.498162
\(732\) −4.14125e9 −0.390249
\(733\) 4.35449e9 0.408388 0.204194 0.978930i \(-0.434543\pi\)
0.204194 + 0.978930i \(0.434543\pi\)
\(734\) 7.33278e9 0.684435
\(735\) −2.77546e9 −0.257827
\(736\) −2.82351e10 −2.61046
\(737\) 1.63672e10 1.50605
\(738\) 6.63740e9 0.607856
\(739\) 4.46423e9 0.406903 0.203452 0.979085i \(-0.434784\pi\)
0.203452 + 0.979085i \(0.434784\pi\)
\(740\) −1.11813e9 −0.101433
\(741\) −7.56756e9 −0.683270
\(742\) 2.42079e8 0.0217542
\(743\) 1.19060e9 0.106489 0.0532447 0.998581i \(-0.483044\pi\)
0.0532447 + 0.998581i \(0.483044\pi\)
\(744\) −4.11086e8 −0.0365955
\(745\) 6.21016e8 0.0550245
\(746\) −4.53971e9 −0.400352
\(747\) −1.39263e9 −0.122240
\(748\) 9.49210e9 0.829291
\(749\) 2.37719e8 0.0206718
\(750\) 8.30970e8 0.0719235
\(751\) −1.78291e9 −0.153599 −0.0767997 0.997047i \(-0.524470\pi\)
−0.0767997 + 0.997047i \(0.524470\pi\)
\(752\) 5.30042e9 0.454515
\(753\) −9.54027e8 −0.0814289
\(754\) 1.70039e10 1.44460
\(755\) −2.63107e9 −0.222494
\(756\) −8.15243e7 −0.00686216
\(757\) −5.28551e9 −0.442844 −0.221422 0.975178i \(-0.571070\pi\)
−0.221422 + 0.975178i \(0.571070\pi\)
\(758\) −1.29460e10 −1.07968
\(759\) −1.17463e10 −0.975109
\(760\) 7.57892e8 0.0626267
\(761\) −6.71171e9 −0.552061 −0.276030 0.961149i \(-0.589019\pi\)
−0.276030 + 0.961149i \(0.589019\pi\)
\(762\) −5.08045e9 −0.415968
\(763\) −8.24675e8 −0.0672120
\(764\) −1.71286e10 −1.38962
\(765\) −1.81400e9 −0.146495
\(766\) −1.01097e10 −0.812713
\(767\) 1.10978e10 0.888079
\(768\) 8.03926e9 0.640401
\(769\) 1.25190e10 0.992725 0.496363 0.868115i \(-0.334669\pi\)
0.496363 + 0.868115i \(0.334669\pi\)
\(770\) 2.68784e8 0.0212171
\(771\) −1.12868e10 −0.886911
\(772\) 1.53419e10 1.20011
\(773\) 1.89490e9 0.147556 0.0737781 0.997275i \(-0.476494\pi\)
0.0737781 + 0.997275i \(0.476494\pi\)
\(774\) 3.03599e9 0.235346
\(775\) 1.96158e9 0.151374
\(776\) 4.72063e8 0.0362647
\(777\) 6.91168e7 0.00528579
\(778\) −1.97729e10 −1.50536
\(779\) −2.88865e10 −2.18934
\(780\) 2.27630e9 0.171750
\(781\) 1.11450e10 0.837146
\(782\) −3.44304e10 −2.57465
\(783\) 3.78853e9 0.282036
\(784\) 1.42349e10 1.05499
\(785\) −3.26741e9 −0.241079
\(786\) −6.81003e8 −0.0500231
\(787\) −2.12095e10 −1.55103 −0.775513 0.631331i \(-0.782509\pi\)
−0.775513 + 0.631331i \(0.782509\pi\)
\(788\) −1.48583e10 −1.08175
\(789\) 5.47596e9 0.396909
\(790\) −2.61548e9 −0.188737
\(791\) 3.29338e8 0.0236605
\(792\) 3.50424e8 0.0250643
\(793\) −7.14769e9 −0.508990
\(794\) 2.04593e10 1.45050
\(795\) −1.50599e9 −0.106301
\(796\) −8.98524e9 −0.631443
\(797\) 5.56395e9 0.389295 0.194647 0.980873i \(-0.437644\pi\)
0.194647 + 0.980873i \(0.437644\pi\)
\(798\) 7.32298e8 0.0510127
\(799\) 6.09558e9 0.422767
\(800\) −4.01937e9 −0.277551
\(801\) 5.83706e9 0.401311
\(802\) 3.40854e10 2.33323
\(803\) −1.59331e10 −1.08592
\(804\) −1.34132e10 −0.910199
\(805\) −4.72366e8 −0.0319149
\(806\) 1.10906e10 0.746075
\(807\) −7.80085e9 −0.522498
\(808\) −1.30712e9 −0.0871718
\(809\) 6.34040e9 0.421014 0.210507 0.977592i \(-0.432488\pi\)
0.210507 + 0.977592i \(0.432488\pi\)
\(810\) 1.04678e9 0.0692084
\(811\) 1.06272e10 0.699597 0.349798 0.936825i \(-0.386250\pi\)
0.349798 + 0.936825i \(0.386250\pi\)
\(812\) −7.97215e8 −0.0522552
\(813\) 9.76449e9 0.637283
\(814\) 4.64385e9 0.301782
\(815\) −1.27271e10 −0.823528
\(816\) 9.30375e9 0.599436
\(817\) −1.32129e10 −0.847657
\(818\) −1.99253e10 −1.27282
\(819\) −1.40709e8 −0.00895010
\(820\) 8.68895e9 0.550324
\(821\) 2.17793e10 1.37355 0.686773 0.726872i \(-0.259027\pi\)
0.686773 + 0.726872i \(0.259027\pi\)
\(822\) 1.22544e10 0.769558
\(823\) 2.93033e10 1.83239 0.916194 0.400734i \(-0.131245\pi\)
0.916194 + 0.400734i \(0.131245\pi\)
\(824\) 2.34192e9 0.145823
\(825\) −1.67212e9 −0.103676
\(826\) −1.07391e9 −0.0663036
\(827\) 1.35378e10 0.832301 0.416150 0.909296i \(-0.363379\pi\)
0.416150 + 0.909296i \(0.363379\pi\)
\(828\) 9.62626e9 0.589320
\(829\) −5.06434e9 −0.308732 −0.154366 0.988014i \(-0.549334\pi\)
−0.154366 + 0.988014i \(0.549334\pi\)
\(830\) −3.76280e9 −0.228422
\(831\) −8.54346e9 −0.516452
\(832\) −1.03034e10 −0.620226
\(833\) 1.63704e10 0.981302
\(834\) −9.13624e8 −0.0545364
\(835\) 7.68220e9 0.456649
\(836\) 2.38385e10 1.41110
\(837\) 2.47103e9 0.145660
\(838\) −2.90929e10 −1.70779
\(839\) −7.42054e9 −0.433779 −0.216890 0.976196i \(-0.569591\pi\)
−0.216890 + 0.976196i \(0.569591\pi\)
\(840\) 1.40920e7 0.000820343 0
\(841\) 1.97977e10 1.14770
\(842\) 3.53808e10 2.04256
\(843\) −1.03037e9 −0.0592376
\(844\) 1.49756e10 0.857404
\(845\) −3.91473e9 −0.223205
\(846\) −3.51750e9 −0.199728
\(847\) 1.30051e8 0.00735399
\(848\) 7.72401e9 0.434968
\(849\) −1.44826e10 −0.812214
\(850\) −4.90130e9 −0.273744
\(851\) −8.16119e9 −0.453942
\(852\) −9.13351e9 −0.505940
\(853\) −5.19233e9 −0.286444 −0.143222 0.989691i \(-0.545746\pi\)
−0.143222 + 0.989691i \(0.545746\pi\)
\(854\) 6.91668e8 0.0380010
\(855\) −4.55568e9 −0.249271
\(856\) 8.37391e8 0.0456321
\(857\) −3.38094e10 −1.83486 −0.917432 0.397892i \(-0.869742\pi\)
−0.917432 + 0.397892i \(0.869742\pi\)
\(858\) −9.45401e9 −0.510988
\(859\) 1.19130e10 0.641277 0.320639 0.947202i \(-0.396103\pi\)
0.320639 + 0.947202i \(0.396103\pi\)
\(860\) 3.97439e9 0.213072
\(861\) −5.37106e8 −0.0286780
\(862\) −2.58398e10 −1.37408
\(863\) −1.42156e10 −0.752882 −0.376441 0.926441i \(-0.622852\pi\)
−0.376441 + 0.926441i \(0.622852\pi\)
\(864\) −5.06325e9 −0.267074
\(865\) −3.42992e9 −0.180189
\(866\) 3.99461e10 2.09007
\(867\) −3.79661e8 −0.0197847
\(868\) −5.19975e8 −0.0269876
\(869\) 5.26302e9 0.272061
\(870\) 1.02363e10 0.527021
\(871\) −2.31508e10 −1.18714
\(872\) −2.90501e9 −0.148368
\(873\) −2.83756e9 −0.144343
\(874\) −8.64686e10 −4.38095
\(875\) −6.72430e7 −0.00339328
\(876\) 1.30575e10 0.656288
\(877\) −2.34323e9 −0.117305 −0.0586525 0.998278i \(-0.518680\pi\)
−0.0586525 + 0.998278i \(0.518680\pi\)
\(878\) 2.75043e9 0.137142
\(879\) 1.45418e10 0.722198
\(880\) 8.57609e9 0.424228
\(881\) 1.08237e9 0.0533288 0.0266644 0.999644i \(-0.491511\pi\)
0.0266644 + 0.999644i \(0.491511\pi\)
\(882\) −9.44669e9 −0.463596
\(883\) −1.55829e10 −0.761705 −0.380852 0.924636i \(-0.624369\pi\)
−0.380852 + 0.924636i \(0.624369\pi\)
\(884\) −1.34262e10 −0.653690
\(885\) 6.68086e9 0.323989
\(886\) −1.78886e10 −0.864088
\(887\) −1.48785e10 −0.715858 −0.357929 0.933749i \(-0.616517\pi\)
−0.357929 + 0.933749i \(0.616517\pi\)
\(888\) 2.43471e8 0.0116682
\(889\) 4.11116e8 0.0196249
\(890\) 1.57713e10 0.749900
\(891\) −2.10639e9 −0.0997625
\(892\) 2.61683e10 1.23452
\(893\) 1.53084e10 0.719368
\(894\) 2.11372e9 0.0989388
\(895\) 5.06407e9 0.236113
\(896\) −1.36572e8 −0.00634286
\(897\) 1.66147e10 0.768632
\(898\) 3.59465e10 1.65649
\(899\) 2.41639e10 1.10919
\(900\) 1.37033e9 0.0626581
\(901\) 8.88276e9 0.404586
\(902\) −3.60873e10 −1.63731
\(903\) −2.45676e8 −0.0111034
\(904\) 1.16013e9 0.0522296
\(905\) 1.20774e10 0.541629
\(906\) −8.95524e9 −0.400063
\(907\) −3.01866e10 −1.34335 −0.671673 0.740848i \(-0.734424\pi\)
−0.671673 + 0.740848i \(0.734424\pi\)
\(908\) 1.67247e10 0.741408
\(909\) 7.85709e9 0.346967
\(910\) −3.80185e8 −0.0167244
\(911\) −3.12329e10 −1.36867 −0.684334 0.729168i \(-0.739907\pi\)
−0.684334 + 0.729168i \(0.739907\pi\)
\(912\) 2.33654e10 1.01998
\(913\) 7.57170e9 0.329265
\(914\) 4.62551e10 2.00377
\(915\) −4.30291e9 −0.185690
\(916\) 1.28132e10 0.550836
\(917\) 5.51076e7 0.00236004
\(918\) −6.17422e9 −0.263410
\(919\) −1.27737e10 −0.542891 −0.271446 0.962454i \(-0.587502\pi\)
−0.271446 + 0.962454i \(0.587502\pi\)
\(920\) −1.66396e9 −0.0704508
\(921\) 1.64782e9 0.0695025
\(922\) −9.97330e9 −0.419064
\(923\) −1.57642e10 −0.659882
\(924\) 4.43245e8 0.0184838
\(925\) −1.16178e9 −0.0482643
\(926\) −2.22592e10 −0.921237
\(927\) −1.40772e10 −0.580415
\(928\) −4.95129e10 −2.03376
\(929\) −3.36628e10 −1.37751 −0.688755 0.724994i \(-0.741843\pi\)
−0.688755 + 0.724994i \(0.741843\pi\)
\(930\) 6.67655e9 0.272184
\(931\) 4.11127e10 1.66975
\(932\) −4.27866e9 −0.173122
\(933\) 1.55346e10 0.626201
\(934\) −5.94917e9 −0.238915
\(935\) 9.86266e9 0.394596
\(936\) −4.95662e8 −0.0197570
\(937\) 3.94639e9 0.156715 0.0783577 0.996925i \(-0.475032\pi\)
0.0783577 + 0.996925i \(0.475032\pi\)
\(938\) 2.24026e9 0.0886317
\(939\) 1.97747e10 0.779436
\(940\) −4.60473e9 −0.180824
\(941\) −1.71604e10 −0.671373 −0.335686 0.941974i \(-0.608968\pi\)
−0.335686 + 0.941974i \(0.608968\pi\)
\(942\) −1.11211e10 −0.433481
\(943\) 6.34206e10 2.46286
\(944\) −3.42652e10 −1.32572
\(945\) −8.47069e7 −0.00326518
\(946\) −1.65066e10 −0.633926
\(947\) 2.96234e10 1.13347 0.566735 0.823900i \(-0.308206\pi\)
0.566735 + 0.823900i \(0.308206\pi\)
\(948\) −4.31313e9 −0.164423
\(949\) 2.25368e10 0.855976
\(950\) −1.23091e10 −0.465795
\(951\) −4.53194e8 −0.0170865
\(952\) −8.31186e7 −0.00312226
\(953\) −2.70351e9 −0.101182 −0.0505910 0.998719i \(-0.516111\pi\)
−0.0505910 + 0.998719i \(0.516111\pi\)
\(954\) −5.12587e9 −0.191138
\(955\) −1.77973e10 −0.661215
\(956\) −9.77821e9 −0.361957
\(957\) −2.05981e10 −0.759689
\(958\) 6.78446e10 2.49308
\(959\) −9.91642e8 −0.0363069
\(960\) −6.20267e9 −0.226271
\(961\) −1.17520e10 −0.427148
\(962\) −6.56856e9 −0.237880
\(963\) −5.03355e9 −0.181628
\(964\) 2.15074e10 0.773248
\(965\) 1.59409e10 0.571039
\(966\) −1.60777e9 −0.0573857
\(967\) 3.15584e10 1.12233 0.561167 0.827703i \(-0.310353\pi\)
0.561167 + 0.827703i \(0.310353\pi\)
\(968\) 4.58120e8 0.0162336
\(969\) 2.68707e10 0.948736
\(970\) −7.66690e9 −0.269723
\(971\) 2.06410e10 0.723540 0.361770 0.932267i \(-0.382173\pi\)
0.361770 + 0.932267i \(0.382173\pi\)
\(972\) 1.72622e9 0.0602928
\(973\) 7.39315e7 0.00257297
\(974\) 1.31869e10 0.457285
\(975\) 2.36516e9 0.0817230
\(976\) 2.20690e10 0.759817
\(977\) 3.75871e10 1.28946 0.644731 0.764410i \(-0.276970\pi\)
0.644731 + 0.764410i \(0.276970\pi\)
\(978\) −4.33187e10 −1.48078
\(979\) −3.17359e10 −1.08097
\(980\) −1.23666e10 −0.419718
\(981\) 1.74620e10 0.590543
\(982\) 5.20664e10 1.75456
\(983\) −6.64465e9 −0.223118 −0.111559 0.993758i \(-0.535584\pi\)
−0.111559 + 0.993758i \(0.535584\pi\)
\(984\) −1.89201e9 −0.0633055
\(985\) −1.54384e10 −0.514724
\(986\) −6.03769e10 −2.00586
\(987\) 2.84640e8 0.00942294
\(988\) −3.37187e10 −1.11230
\(989\) 2.90090e10 0.953556
\(990\) −5.69132e9 −0.186419
\(991\) 1.79433e10 0.585657 0.292829 0.956165i \(-0.405403\pi\)
0.292829 + 0.956165i \(0.405403\pi\)
\(992\) −3.22943e10 −1.05035
\(993\) −2.92696e10 −0.948623
\(994\) 1.52547e9 0.0492666
\(995\) −9.33601e9 −0.300456
\(996\) −6.20514e9 −0.198996
\(997\) −9.85820e8 −0.0315039 −0.0157520 0.999876i \(-0.505014\pi\)
−0.0157520 + 0.999876i \(0.505014\pi\)
\(998\) 5.39887e10 1.71928
\(999\) −1.46350e9 −0.0464424
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 \(a_p\))