Properties

Label 6.10.a.a.1.1
Level 6
Weight 10
Character 6.1
Self dual Yes
Analytic conductor 3.090
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6 = 2 \cdot 3 \)
Weight: \( k \) = \( 10 \)
Character orbit: \([\chi]\) = 6.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(3.09021501698\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0\)
Character \(\chi\) = 6.1

$q$-expansion

\(f(q)\) \(=\) \(q-16.0000 q^{2} +81.0000 q^{3} +256.000 q^{4} +2694.00 q^{5} -1296.00 q^{6} -3544.00 q^{7} -4096.00 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-16.0000 q^{2} +81.0000 q^{3} +256.000 q^{4} +2694.00 q^{5} -1296.00 q^{6} -3544.00 q^{7} -4096.00 q^{8} +6561.00 q^{9} -43104.0 q^{10} +29580.0 q^{11} +20736.0 q^{12} -44818.0 q^{13} +56704.0 q^{14} +218214. q^{15} +65536.0 q^{16} -101934. q^{17} -104976. q^{18} -895084. q^{19} +689664. q^{20} -287064. q^{21} -473280. q^{22} -1.11300e6 q^{23} -331776. q^{24} +5.30451e6 q^{25} +717088. q^{26} +531441. q^{27} -907264. q^{28} -2.35735e6 q^{29} -3.49142e6 q^{30} +175808. q^{31} -1.04858e6 q^{32} +2.39598e6 q^{33} +1.63094e6 q^{34} -9.54754e6 q^{35} +1.67962e6 q^{36} -2.91942e6 q^{37} +1.43213e7 q^{38} -3.63026e6 q^{39} -1.10346e7 q^{40} +2.62188e7 q^{41} +4.59302e6 q^{42} -1.87630e7 q^{43} +7.57248e6 q^{44} +1.76753e7 q^{45} +1.78080e7 q^{46} -2.09662e7 q^{47} +5.30842e6 q^{48} -2.77937e7 q^{49} -8.48722e7 q^{50} -8.25665e6 q^{51} -1.14734e7 q^{52} +5.72516e7 q^{53} -8.50306e6 q^{54} +7.96885e7 q^{55} +1.45162e7 q^{56} -7.25018e7 q^{57} +3.77175e7 q^{58} +3.35876e7 q^{59} +5.58628e7 q^{60} +8.22608e7 q^{61} -2.81293e6 q^{62} -2.32522e7 q^{63} +1.67772e7 q^{64} -1.20740e8 q^{65} -3.83357e7 q^{66} -1.88456e8 q^{67} -2.60951e7 q^{68} -9.01530e7 q^{69} +1.52761e8 q^{70} +8.09240e7 q^{71} -2.68739e7 q^{72} -2.36141e8 q^{73} +4.67107e7 q^{74} +4.29665e8 q^{75} -2.29142e8 q^{76} -1.04832e8 q^{77} +5.80841e7 q^{78} +5.26910e8 q^{79} +1.76554e8 q^{80} +4.30467e7 q^{81} -4.19501e8 q^{82} +1.83465e7 q^{83} -7.34884e7 q^{84} -2.74610e8 q^{85} +3.00207e8 q^{86} -1.90945e8 q^{87} -1.21160e8 q^{88} +6.90643e8 q^{89} -2.82805e8 q^{90} +1.58835e8 q^{91} -2.84928e8 q^{92} +1.42404e7 q^{93} +3.35459e8 q^{94} -2.41136e9 q^{95} -8.49347e7 q^{96} -4.38251e8 q^{97} +4.44699e8 q^{98} +1.94074e8 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −16.0000 −0.707107
\(3\) 81.0000 0.577350
\(4\) 256.000 0.500000
\(5\) 2694.00 1.92767 0.963835 0.266501i \(-0.0858674\pi\)
0.963835 + 0.266501i \(0.0858674\pi\)
\(6\) −1296.00 −0.408248
\(7\) −3544.00 −0.557895 −0.278948 0.960306i \(-0.589986\pi\)
−0.278948 + 0.960306i \(0.589986\pi\)
\(8\) −4096.00 −0.353553
\(9\) 6561.00 0.333333
\(10\) −43104.0 −1.36307
\(11\) 29580.0 0.609160 0.304580 0.952487i \(-0.401484\pi\)
0.304580 + 0.952487i \(0.401484\pi\)
\(12\) 20736.0 0.288675
\(13\) −44818.0 −0.435219 −0.217609 0.976036i \(-0.569826\pi\)
−0.217609 + 0.976036i \(0.569826\pi\)
\(14\) 56704.0 0.394491
\(15\) 218214. 1.11294
\(16\) 65536.0 0.250000
\(17\) −101934. −0.296005 −0.148002 0.988987i \(-0.547284\pi\)
−0.148002 + 0.988987i \(0.547284\pi\)
\(18\) −104976. −0.235702
\(19\) −895084. −1.57570 −0.787848 0.615869i \(-0.788805\pi\)
−0.787848 + 0.615869i \(0.788805\pi\)
\(20\) 689664. 0.963835
\(21\) −287064. −0.322101
\(22\) −473280. −0.430741
\(23\) −1.11300e6 −0.829316 −0.414658 0.909977i \(-0.636099\pi\)
−0.414658 + 0.909977i \(0.636099\pi\)
\(24\) −331776. −0.204124
\(25\) 5.30451e6 2.71591
\(26\) 717088. 0.307746
\(27\) 531441. 0.192450
\(28\) −907264. −0.278948
\(29\) −2.35735e6 −0.618917 −0.309458 0.950913i \(-0.600148\pi\)
−0.309458 + 0.950913i \(0.600148\pi\)
\(30\) −3.49142e6 −0.786968
\(31\) 175808. 0.0341909 0.0170955 0.999854i \(-0.494558\pi\)
0.0170955 + 0.999854i \(0.494558\pi\)
\(32\) −1.04858e6 −0.176777
\(33\) 2.39598e6 0.351698
\(34\) 1.63094e6 0.209307
\(35\) −9.54754e6 −1.07544
\(36\) 1.67962e6 0.166667
\(37\) −2.91942e6 −0.256088 −0.128044 0.991769i \(-0.540870\pi\)
−0.128044 + 0.991769i \(0.540870\pi\)
\(38\) 1.43213e7 1.11419
\(39\) −3.63026e6 −0.251274
\(40\) −1.10346e7 −0.681534
\(41\) 2.62188e7 1.44906 0.724528 0.689245i \(-0.242058\pi\)
0.724528 + 0.689245i \(0.242058\pi\)
\(42\) 4.59302e6 0.227760
\(43\) −1.87630e7 −0.836938 −0.418469 0.908231i \(-0.637433\pi\)
−0.418469 + 0.908231i \(0.637433\pi\)
\(44\) 7.57248e6 0.304580
\(45\) 1.76753e7 0.642556
\(46\) 1.78080e7 0.586415
\(47\) −2.09662e7 −0.626727 −0.313364 0.949633i \(-0.601456\pi\)
−0.313364 + 0.949633i \(0.601456\pi\)
\(48\) 5.30842e6 0.144338
\(49\) −2.77937e7 −0.688753
\(50\) −8.48722e7 −1.92044
\(51\) −8.25665e6 −0.170899
\(52\) −1.14734e7 −0.217609
\(53\) 5.72516e7 0.996658 0.498329 0.866988i \(-0.333947\pi\)
0.498329 + 0.866988i \(0.333947\pi\)
\(54\) −8.50306e6 −0.136083
\(55\) 7.96885e7 1.17426
\(56\) 1.45162e7 0.197246
\(57\) −7.25018e7 −0.909729
\(58\) 3.77175e7 0.437640
\(59\) 3.35876e7 0.360865 0.180432 0.983587i \(-0.442250\pi\)
0.180432 + 0.983587i \(0.442250\pi\)
\(60\) 5.58628e7 0.556470
\(61\) 8.22608e7 0.760692 0.380346 0.924844i \(-0.375805\pi\)
0.380346 + 0.924844i \(0.375805\pi\)
\(62\) −2.81293e6 −0.0241766
\(63\) −2.32522e7 −0.185965
\(64\) 1.67772e7 0.125000
\(65\) −1.20740e8 −0.838957
\(66\) −3.83357e7 −0.248688
\(67\) −1.88456e8 −1.14254 −0.571272 0.820761i \(-0.693550\pi\)
−0.571272 + 0.820761i \(0.693550\pi\)
\(68\) −2.60951e7 −0.148002
\(69\) −9.01530e7 −0.478806
\(70\) 1.52761e8 0.760449
\(71\) 8.09240e7 0.377933 0.188967 0.981984i \(-0.439486\pi\)
0.188967 + 0.981984i \(0.439486\pi\)
\(72\) −2.68739e7 −0.117851
\(73\) −2.36141e8 −0.973236 −0.486618 0.873615i \(-0.661770\pi\)
−0.486618 + 0.873615i \(0.661770\pi\)
\(74\) 4.67107e7 0.181081
\(75\) 4.29665e8 1.56803
\(76\) −2.29142e8 −0.787848
\(77\) −1.04832e8 −0.339847
\(78\) 5.80841e7 0.177677
\(79\) 5.26910e8 1.52200 0.761000 0.648752i \(-0.224709\pi\)
0.761000 + 0.648752i \(0.224709\pi\)
\(80\) 1.76554e8 0.481917
\(81\) 4.30467e7 0.111111
\(82\) −4.19501e8 −1.02464
\(83\) 1.83465e7 0.0424327 0.0212164 0.999775i \(-0.493246\pi\)
0.0212164 + 0.999775i \(0.493246\pi\)
\(84\) −7.34884e7 −0.161050
\(85\) −2.74610e8 −0.570600
\(86\) 3.00207e8 0.591805
\(87\) −1.90945e8 −0.357332
\(88\) −1.21160e8 −0.215370
\(89\) 6.90643e8 1.16681 0.583403 0.812183i \(-0.301721\pi\)
0.583403 + 0.812183i \(0.301721\pi\)
\(90\) −2.82805e8 −0.454356
\(91\) 1.58835e8 0.242806
\(92\) −2.84928e8 −0.414658
\(93\) 1.42404e7 0.0197401
\(94\) 3.35459e8 0.443163
\(95\) −2.41136e9 −3.03742
\(96\) −8.49347e7 −0.102062
\(97\) −4.38251e8 −0.502632 −0.251316 0.967905i \(-0.580863\pi\)
−0.251316 + 0.967905i \(0.580863\pi\)
\(98\) 4.44699e8 0.487022
\(99\) 1.94074e8 0.203053
\(100\) 1.35795e9 1.35795
\(101\) 9.80602e8 0.937663 0.468831 0.883288i \(-0.344675\pi\)
0.468831 + 0.883288i \(0.344675\pi\)
\(102\) 1.32106e8 0.120844
\(103\) 1.71909e9 1.50498 0.752489 0.658604i \(-0.228853\pi\)
0.752489 + 0.658604i \(0.228853\pi\)
\(104\) 1.83575e8 0.153873
\(105\) −7.73350e8 −0.620904
\(106\) −9.16025e8 −0.704743
\(107\) 4.25005e8 0.313449 0.156724 0.987642i \(-0.449907\pi\)
0.156724 + 0.987642i \(0.449907\pi\)
\(108\) 1.36049e8 0.0962250
\(109\) 8.74701e8 0.593527 0.296763 0.954951i \(-0.404093\pi\)
0.296763 + 0.954951i \(0.404093\pi\)
\(110\) −1.27502e9 −0.830326
\(111\) −2.36473e8 −0.147852
\(112\) −2.32260e8 −0.139474
\(113\) −4.42974e7 −0.0255579 −0.0127789 0.999918i \(-0.504068\pi\)
−0.0127789 + 0.999918i \(0.504068\pi\)
\(114\) 1.16003e9 0.643275
\(115\) −2.99842e9 −1.59865
\(116\) −6.03481e8 −0.309458
\(117\) −2.94051e8 −0.145073
\(118\) −5.37401e8 −0.255170
\(119\) 3.61254e8 0.165140
\(120\) −8.93805e8 −0.393484
\(121\) −1.48297e9 −0.628925
\(122\) −1.31617e9 −0.537890
\(123\) 2.12372e9 0.836613
\(124\) 4.50068e7 0.0170955
\(125\) 9.02863e9 3.30771
\(126\) 3.72035e8 0.131497
\(127\) −3.14845e9 −1.07394 −0.536970 0.843601i \(-0.680431\pi\)
−0.536970 + 0.843601i \(0.680431\pi\)
\(128\) −2.68435e8 −0.0883883
\(129\) −1.51980e9 −0.483207
\(130\) 1.93184e9 0.593233
\(131\) −4.16328e9 −1.23514 −0.617568 0.786517i \(-0.711882\pi\)
−0.617568 + 0.786517i \(0.711882\pi\)
\(132\) 6.13371e8 0.175849
\(133\) 3.17218e9 0.879073
\(134\) 3.01529e9 0.807901
\(135\) 1.43170e9 0.370980
\(136\) 4.17522e8 0.104654
\(137\) −7.36501e9 −1.78620 −0.893101 0.449856i \(-0.851475\pi\)
−0.893101 + 0.449856i \(0.851475\pi\)
\(138\) 1.44245e9 0.338567
\(139\) 4.51143e9 1.02506 0.512528 0.858670i \(-0.328709\pi\)
0.512528 + 0.858670i \(0.328709\pi\)
\(140\) −2.44417e9 −0.537719
\(141\) −1.69826e9 −0.361841
\(142\) −1.29478e9 −0.267239
\(143\) −1.32572e9 −0.265118
\(144\) 4.29982e8 0.0833333
\(145\) −6.35069e9 −1.19307
\(146\) 3.77825e9 0.688182
\(147\) −2.25129e9 −0.397652
\(148\) −7.47371e8 −0.128044
\(149\) −1.10533e9 −0.183718 −0.0918591 0.995772i \(-0.529281\pi\)
−0.0918591 + 0.995772i \(0.529281\pi\)
\(150\) −6.87465e9 −1.10877
\(151\) 1.03005e10 1.61236 0.806181 0.591668i \(-0.201531\pi\)
0.806181 + 0.591668i \(0.201531\pi\)
\(152\) 3.66626e9 0.557093
\(153\) −6.68789e8 −0.0986683
\(154\) 1.67730e9 0.240308
\(155\) 4.73627e8 0.0659088
\(156\) −9.29346e8 −0.125637
\(157\) −7.03726e8 −0.0924390 −0.0462195 0.998931i \(-0.514717\pi\)
−0.0462195 + 0.998931i \(0.514717\pi\)
\(158\) −8.43056e9 −1.07622
\(159\) 4.63738e9 0.575421
\(160\) −2.82486e9 −0.340767
\(161\) 3.94447e9 0.462671
\(162\) −6.88748e8 −0.0785674
\(163\) 1.10181e10 1.22253 0.611267 0.791424i \(-0.290660\pi\)
0.611267 + 0.791424i \(0.290660\pi\)
\(164\) 6.71201e9 0.724528
\(165\) 6.45477e9 0.677958
\(166\) −2.93543e8 −0.0300045
\(167\) 1.80357e9 0.179436 0.0897179 0.995967i \(-0.471403\pi\)
0.0897179 + 0.995967i \(0.471403\pi\)
\(168\) 1.17581e9 0.113880
\(169\) −8.59585e9 −0.810585
\(170\) 4.39376e9 0.403475
\(171\) −5.87265e9 −0.525232
\(172\) −4.80332e9 −0.418469
\(173\) −8.93250e9 −0.758168 −0.379084 0.925362i \(-0.623761\pi\)
−0.379084 + 0.925362i \(0.623761\pi\)
\(174\) 3.05512e9 0.252672
\(175\) −1.87992e10 −1.51519
\(176\) 1.93855e9 0.152290
\(177\) 2.72059e9 0.208345
\(178\) −1.10503e10 −0.825056
\(179\) −4.28652e9 −0.312080 −0.156040 0.987751i \(-0.549873\pi\)
−0.156040 + 0.987751i \(0.549873\pi\)
\(180\) 4.52489e9 0.321278
\(181\) 8.70114e8 0.0602591 0.0301295 0.999546i \(-0.490408\pi\)
0.0301295 + 0.999546i \(0.490408\pi\)
\(182\) −2.54136e9 −0.171690
\(183\) 6.66313e9 0.439186
\(184\) 4.55885e9 0.293207
\(185\) −7.86491e9 −0.493652
\(186\) −2.27847e8 −0.0139584
\(187\) −3.01521e9 −0.180314
\(188\) −5.36734e9 −0.313364
\(189\) −1.88343e9 −0.107367
\(190\) 3.85817e10 2.14778
\(191\) 3.19445e10 1.73678 0.868392 0.495879i \(-0.165154\pi\)
0.868392 + 0.495879i \(0.165154\pi\)
\(192\) 1.35895e9 0.0721688
\(193\) 4.89841e9 0.254125 0.127063 0.991895i \(-0.459445\pi\)
0.127063 + 0.991895i \(0.459445\pi\)
\(194\) 7.01202e9 0.355415
\(195\) −9.77992e9 −0.484372
\(196\) −7.11518e9 −0.344377
\(197\) 2.17836e10 1.03046 0.515230 0.857052i \(-0.327707\pi\)
0.515230 + 0.857052i \(0.327707\pi\)
\(198\) −3.10519e9 −0.143580
\(199\) −3.74165e10 −1.69131 −0.845657 0.533727i \(-0.820791\pi\)
−0.845657 + 0.533727i \(0.820791\pi\)
\(200\) −2.17273e10 −0.960219
\(201\) −1.52649e10 −0.659648
\(202\) −1.56896e10 −0.663028
\(203\) 8.35443e9 0.345291
\(204\) −2.11370e9 −0.0854493
\(205\) 7.06334e10 2.79330
\(206\) −2.75054e10 −1.06418
\(207\) −7.30239e9 −0.276439
\(208\) −2.93719e9 −0.108805
\(209\) −2.64766e10 −0.959851
\(210\) 1.23736e10 0.439045
\(211\) 5.74096e9 0.199395 0.0996973 0.995018i \(-0.468213\pi\)
0.0996973 + 0.995018i \(0.468213\pi\)
\(212\) 1.46564e10 0.498329
\(213\) 6.55485e9 0.218200
\(214\) −6.80007e9 −0.221642
\(215\) −5.05474e10 −1.61334
\(216\) −2.17678e9 −0.0680414
\(217\) −6.23064e8 −0.0190750
\(218\) −1.39952e10 −0.419687
\(219\) −1.91274e10 −0.561898
\(220\) 2.04003e10 0.587129
\(221\) 4.56848e9 0.128827
\(222\) 3.78357e9 0.104547
\(223\) 2.21571e10 0.599987 0.299993 0.953941i \(-0.403016\pi\)
0.299993 + 0.953941i \(0.403016\pi\)
\(224\) 3.71615e9 0.0986228
\(225\) 3.48029e10 0.905303
\(226\) 7.08758e8 0.0180722
\(227\) 7.46127e10 1.86508 0.932538 0.361073i \(-0.117589\pi\)
0.932538 + 0.361073i \(0.117589\pi\)
\(228\) −1.85605e10 −0.454864
\(229\) −6.44305e10 −1.54822 −0.774108 0.633054i \(-0.781801\pi\)
−0.774108 + 0.633054i \(0.781801\pi\)
\(230\) 4.79748e10 1.13041
\(231\) −8.49135e9 −0.196211
\(232\) 9.65569e9 0.218820
\(233\) −1.75635e10 −0.390400 −0.195200 0.980763i \(-0.562536\pi\)
−0.195200 + 0.980763i \(0.562536\pi\)
\(234\) 4.70481e9 0.102582
\(235\) −5.64828e10 −1.20812
\(236\) 8.59842e9 0.180432
\(237\) 4.26797e10 0.878727
\(238\) −5.78007e9 −0.116771
\(239\) 7.79759e9 0.154586 0.0772929 0.997008i \(-0.475372\pi\)
0.0772929 + 0.997008i \(0.475372\pi\)
\(240\) 1.43009e10 0.278235
\(241\) 4.74343e9 0.0905765 0.0452882 0.998974i \(-0.485579\pi\)
0.0452882 + 0.998974i \(0.485579\pi\)
\(242\) 2.37275e10 0.444717
\(243\) 3.48678e9 0.0641500
\(244\) 2.10588e10 0.380346
\(245\) −7.48761e10 −1.32769
\(246\) −3.39796e10 −0.591575
\(247\) 4.01159e10 0.685772
\(248\) −7.20110e8 −0.0120883
\(249\) 1.48606e9 0.0244985
\(250\) −1.44458e11 −2.33890
\(251\) −4.72379e10 −0.751205 −0.375603 0.926781i \(-0.622564\pi\)
−0.375603 + 0.926781i \(0.622564\pi\)
\(252\) −5.95256e9 −0.0929825
\(253\) −3.29225e10 −0.505186
\(254\) 5.03752e10 0.759390
\(255\) −2.22434e10 −0.329436
\(256\) 4.29497e9 0.0625000
\(257\) 7.47016e10 1.06815 0.534074 0.845438i \(-0.320661\pi\)
0.534074 + 0.845438i \(0.320661\pi\)
\(258\) 2.43168e10 0.341679
\(259\) 1.03464e10 0.142870
\(260\) −3.09094e10 −0.419479
\(261\) −1.54665e10 −0.206306
\(262\) 6.66125e10 0.873373
\(263\) 3.07988e10 0.396947 0.198474 0.980106i \(-0.436402\pi\)
0.198474 + 0.980106i \(0.436402\pi\)
\(264\) −9.81393e9 −0.124344
\(265\) 1.54236e11 1.92123
\(266\) −5.07548e10 −0.621599
\(267\) 5.59421e10 0.673656
\(268\) −4.82447e10 −0.571272
\(269\) −1.49384e11 −1.73948 −0.869738 0.493513i \(-0.835712\pi\)
−0.869738 + 0.493513i \(0.835712\pi\)
\(270\) −2.29072e10 −0.262323
\(271\) 1.32111e11 1.48791 0.743957 0.668228i \(-0.232947\pi\)
0.743957 + 0.668228i \(0.232947\pi\)
\(272\) −6.68035e9 −0.0740012
\(273\) 1.28656e10 0.140184
\(274\) 1.17840e11 1.26304
\(275\) 1.56907e11 1.65442
\(276\) −2.30792e10 −0.239403
\(277\) −9.19219e10 −0.938123 −0.469062 0.883165i \(-0.655408\pi\)
−0.469062 + 0.883165i \(0.655408\pi\)
\(278\) −7.21829e10 −0.724824
\(279\) 1.15348e9 0.0113970
\(280\) 3.91067e10 0.380225
\(281\) −6.21245e10 −0.594408 −0.297204 0.954814i \(-0.596054\pi\)
−0.297204 + 0.954814i \(0.596054\pi\)
\(282\) 2.71721e10 0.255860
\(283\) −1.46305e11 −1.35588 −0.677938 0.735119i \(-0.737126\pi\)
−0.677938 + 0.735119i \(0.737126\pi\)
\(284\) 2.07166e10 0.188967
\(285\) −1.95320e11 −1.75366
\(286\) 2.12115e10 0.187466
\(287\) −9.29194e10 −0.808422
\(288\) −6.87971e9 −0.0589256
\(289\) −1.08197e11 −0.912381
\(290\) 1.01611e11 0.843626
\(291\) −3.54983e10 −0.290195
\(292\) −6.04521e10 −0.486618
\(293\) 9.65207e10 0.765096 0.382548 0.923936i \(-0.375047\pi\)
0.382548 + 0.923936i \(0.375047\pi\)
\(294\) 3.60206e10 0.281182
\(295\) 9.04849e10 0.695628
\(296\) 1.19579e10 0.0905406
\(297\) 1.57200e10 0.117233
\(298\) 1.76852e10 0.129908
\(299\) 4.98824e10 0.360934
\(300\) 1.09994e11 0.784016
\(301\) 6.64959e10 0.466924
\(302\) −1.64808e11 −1.14011
\(303\) 7.94288e10 0.541360
\(304\) −5.86602e10 −0.393924
\(305\) 2.21611e11 1.46636
\(306\) 1.07006e10 0.0697690
\(307\) −2.74874e11 −1.76608 −0.883042 0.469294i \(-0.844509\pi\)
−0.883042 + 0.469294i \(0.844509\pi\)
\(308\) −2.68369e10 −0.169924
\(309\) 1.39246e11 0.868900
\(310\) −7.57803e9 −0.0466046
\(311\) −1.81295e11 −1.09891 −0.549457 0.835522i \(-0.685165\pi\)
−0.549457 + 0.835522i \(0.685165\pi\)
\(312\) 1.48695e10 0.0888386
\(313\) 1.59020e11 0.936489 0.468245 0.883599i \(-0.344887\pi\)
0.468245 + 0.883599i \(0.344887\pi\)
\(314\) 1.12596e10 0.0653642
\(315\) −6.26414e10 −0.358479
\(316\) 1.34889e11 0.761000
\(317\) 1.95485e11 1.08730 0.543648 0.839313i \(-0.317043\pi\)
0.543648 + 0.839313i \(0.317043\pi\)
\(318\) −7.41980e10 −0.406884
\(319\) −6.97303e10 −0.377019
\(320\) 4.51978e10 0.240959
\(321\) 3.44254e10 0.180970
\(322\) −6.31116e10 −0.327158
\(323\) 9.12395e10 0.466414
\(324\) 1.10200e10 0.0555556
\(325\) −2.37738e11 −1.18201
\(326\) −1.76289e11 −0.864463
\(327\) 7.08508e10 0.342673
\(328\) −1.07392e11 −0.512319
\(329\) 7.43041e10 0.349648
\(330\) −1.03276e11 −0.479389
\(331\) 3.97198e11 1.81878 0.909391 0.415942i \(-0.136548\pi\)
0.909391 + 0.415942i \(0.136548\pi\)
\(332\) 4.69669e9 0.0212164
\(333\) −1.91543e10 −0.0853625
\(334\) −2.88571e10 −0.126880
\(335\) −5.07700e11 −2.20245
\(336\) −1.88130e10 −0.0805252
\(337\) −2.59813e11 −1.09730 −0.548650 0.836052i \(-0.684858\pi\)
−0.548650 + 0.836052i \(0.684858\pi\)
\(338\) 1.37534e11 0.573170
\(339\) −3.58809e9 −0.0147558
\(340\) −7.03002e10 −0.285300
\(341\) 5.20040e9 0.0208277
\(342\) 9.39623e10 0.371395
\(343\) 2.41514e11 0.942147
\(344\) 7.68531e10 0.295902
\(345\) −2.42872e11 −0.922979
\(346\) 1.42920e11 0.536106
\(347\) −3.26152e11 −1.20764 −0.603820 0.797121i \(-0.706356\pi\)
−0.603820 + 0.797121i \(0.706356\pi\)
\(348\) −4.88819e10 −0.178666
\(349\) 1.54936e11 0.559032 0.279516 0.960141i \(-0.409826\pi\)
0.279516 + 0.960141i \(0.409826\pi\)
\(350\) 3.00787e11 1.07140
\(351\) −2.38181e10 −0.0837578
\(352\) −3.10169e10 −0.107685
\(353\) 3.48972e11 1.19620 0.598100 0.801421i \(-0.295922\pi\)
0.598100 + 0.801421i \(0.295922\pi\)
\(354\) −4.35295e10 −0.147322
\(355\) 2.18009e11 0.728530
\(356\) 1.76805e11 0.583403
\(357\) 2.92616e10 0.0953434
\(358\) 6.85843e10 0.220674
\(359\) 1.21868e11 0.387227 0.193613 0.981078i \(-0.437979\pi\)
0.193613 + 0.981078i \(0.437979\pi\)
\(360\) −7.23982e10 −0.227178
\(361\) 4.78488e11 1.48282
\(362\) −1.39218e10 −0.0426096
\(363\) −1.20121e11 −0.363110
\(364\) 4.06618e10 0.121403
\(365\) −6.36164e11 −1.87608
\(366\) −1.06610e11 −0.310551
\(367\) −5.08451e11 −1.46303 −0.731513 0.681828i \(-0.761185\pi\)
−0.731513 + 0.681828i \(0.761185\pi\)
\(368\) −7.29416e10 −0.207329
\(369\) 1.72022e11 0.483019
\(370\) 1.25839e11 0.349065
\(371\) −2.02900e11 −0.556030
\(372\) 3.64555e9 0.00987007
\(373\) −2.56076e11 −0.684983 −0.342492 0.939521i \(-0.611271\pi\)
−0.342492 + 0.939521i \(0.611271\pi\)
\(374\) 4.82433e10 0.127501
\(375\) 7.31319e11 1.90971
\(376\) 8.58774e10 0.221582
\(377\) 1.05652e11 0.269364
\(378\) 3.01348e10 0.0759199
\(379\) −5.53250e10 −0.137735 −0.0688676 0.997626i \(-0.521939\pi\)
−0.0688676 + 0.997626i \(0.521939\pi\)
\(380\) −6.17307e11 −1.51871
\(381\) −2.55025e11 −0.620040
\(382\) −5.11112e11 −1.22809
\(383\) −8.14772e10 −0.193482 −0.0967412 0.995310i \(-0.530842\pi\)
−0.0967412 + 0.995310i \(0.530842\pi\)
\(384\) −2.17433e10 −0.0510310
\(385\) −2.82416e11 −0.655113
\(386\) −7.83746e10 −0.179694
\(387\) −1.23104e11 −0.278979
\(388\) −1.12192e11 −0.251316
\(389\) 6.01212e11 1.33123 0.665617 0.746293i \(-0.268168\pi\)
0.665617 + 0.746293i \(0.268168\pi\)
\(390\) 1.56479e11 0.342503
\(391\) 1.13453e11 0.245482
\(392\) 1.13843e11 0.243511
\(393\) −3.37226e11 −0.713106
\(394\) −3.48537e11 −0.728645
\(395\) 1.41950e12 2.93391
\(396\) 4.96830e10 0.101527
\(397\) 1.31066e10 0.0264808 0.0132404 0.999912i \(-0.495785\pi\)
0.0132404 + 0.999912i \(0.495785\pi\)
\(398\) 5.98664e11 1.19594
\(399\) 2.56946e11 0.507533
\(400\) 3.47636e11 0.678977
\(401\) −5.98151e11 −1.15521 −0.577605 0.816316i \(-0.696013\pi\)
−0.577605 + 0.816316i \(0.696013\pi\)
\(402\) 2.44239e11 0.466442
\(403\) −7.87936e9 −0.0148805
\(404\) 2.51034e11 0.468831
\(405\) 1.15968e11 0.214185
\(406\) −1.33671e11 −0.244157
\(407\) −8.63564e10 −0.155998
\(408\) 3.38193e10 0.0604218
\(409\) −1.97716e11 −0.349371 −0.174686 0.984624i \(-0.555891\pi\)
−0.174686 + 0.984624i \(0.555891\pi\)
\(410\) −1.13013e12 −1.97516
\(411\) −5.96565e11 −1.03126
\(412\) 4.40086e11 0.752489
\(413\) −1.19034e11 −0.201325
\(414\) 1.16838e11 0.195472
\(415\) 4.94253e10 0.0817962
\(416\) 4.69951e10 0.0769365
\(417\) 3.65426e11 0.591817
\(418\) 4.23625e11 0.678717
\(419\) 3.37678e11 0.535229 0.267615 0.963526i \(-0.413765\pi\)
0.267615 + 0.963526i \(0.413765\pi\)
\(420\) −1.97978e11 −0.310452
\(421\) −1.07358e11 −0.166559 −0.0832793 0.996526i \(-0.526539\pi\)
−0.0832793 + 0.996526i \(0.526539\pi\)
\(422\) −9.18553e10 −0.140993
\(423\) −1.37559e11 −0.208909
\(424\) −2.34502e11 −0.352372
\(425\) −5.40710e11 −0.803923
\(426\) −1.04878e11 −0.154291
\(427\) −2.91532e11 −0.424386
\(428\) 1.08801e11 0.156724
\(429\) −1.07383e11 −0.153066
\(430\) 8.08759e11 1.14080
\(431\) −6.92353e11 −0.966452 −0.483226 0.875496i \(-0.660535\pi\)
−0.483226 + 0.875496i \(0.660535\pi\)
\(432\) 3.48285e10 0.0481125
\(433\) −1.03885e12 −1.42022 −0.710110 0.704091i \(-0.751355\pi\)
−0.710110 + 0.704091i \(0.751355\pi\)
\(434\) 9.96902e9 0.0134880
\(435\) −5.14406e11 −0.688818
\(436\) 2.23923e11 0.296763
\(437\) 9.96228e11 1.30675
\(438\) 3.06039e11 0.397322
\(439\) 9.11781e11 1.17166 0.585828 0.810435i \(-0.300769\pi\)
0.585828 + 0.810435i \(0.300769\pi\)
\(440\) −3.26404e11 −0.415163
\(441\) −1.82354e11 −0.229584
\(442\) −7.30956e10 −0.0910943
\(443\) −7.88303e11 −0.972470 −0.486235 0.873828i \(-0.661630\pi\)
−0.486235 + 0.873828i \(0.661630\pi\)
\(444\) −6.05371e10 −0.0739261
\(445\) 1.86059e12 2.24922
\(446\) −3.54514e11 −0.424255
\(447\) −8.95314e10 −0.106070
\(448\) −5.94585e10 −0.0697369
\(449\) −7.28687e11 −0.846121 −0.423060 0.906102i \(-0.639044\pi\)
−0.423060 + 0.906102i \(0.639044\pi\)
\(450\) −5.56846e11 −0.640146
\(451\) 7.75552e11 0.882707
\(452\) −1.13401e10 −0.0127789
\(453\) 8.34342e11 0.930898
\(454\) −1.19380e12 −1.31881
\(455\) 4.27901e11 0.468050
\(456\) 2.96967e11 0.321638
\(457\) −1.55747e11 −0.167031 −0.0835155 0.996506i \(-0.526615\pi\)
−0.0835155 + 0.996506i \(0.526615\pi\)
\(458\) 1.03089e12 1.09475
\(459\) −5.41719e10 −0.0569662
\(460\) −7.67596e11 −0.799323
\(461\) 5.84721e11 0.602969 0.301484 0.953471i \(-0.402518\pi\)
0.301484 + 0.953471i \(0.402518\pi\)
\(462\) 1.35862e11 0.138742
\(463\) 1.98254e11 0.200497 0.100249 0.994962i \(-0.468036\pi\)
0.100249 + 0.994962i \(0.468036\pi\)
\(464\) −1.54491e11 −0.154729
\(465\) 3.83638e10 0.0380525
\(466\) 2.81016e11 0.276054
\(467\) 1.90984e12 1.85810 0.929052 0.369949i \(-0.120625\pi\)
0.929052 + 0.369949i \(0.120625\pi\)
\(468\) −7.52770e10 −0.0725364
\(469\) 6.67887e11 0.637420
\(470\) 9.03725e11 0.854272
\(471\) −5.70018e10 −0.0533697
\(472\) −1.37575e11 −0.127585
\(473\) −5.55008e11 −0.509829
\(474\) −6.82875e11 −0.621353
\(475\) −4.74798e12 −4.27945
\(476\) 9.24810e10 0.0825698
\(477\) 3.75628e11 0.332219
\(478\) −1.24761e11 −0.109309
\(479\) −1.49603e12 −1.29846 −0.649232 0.760590i \(-0.724910\pi\)
−0.649232 + 0.760590i \(0.724910\pi\)
\(480\) −2.28814e11 −0.196742
\(481\) 1.30842e11 0.111454
\(482\) −7.58948e10 −0.0640472
\(483\) 3.19502e11 0.267123
\(484\) −3.79641e11 −0.314462
\(485\) −1.18065e12 −0.968908
\(486\) −5.57886e10 −0.0453609
\(487\) 3.57916e11 0.288337 0.144169 0.989553i \(-0.453949\pi\)
0.144169 + 0.989553i \(0.453949\pi\)
\(488\) −3.36940e11 −0.268945
\(489\) 8.92464e11 0.705831
\(490\) 1.19802e12 0.938817
\(491\) 7.23262e11 0.561603 0.280801 0.959766i \(-0.409400\pi\)
0.280801 + 0.959766i \(0.409400\pi\)
\(492\) 5.43673e11 0.418307
\(493\) 2.40294e11 0.183202
\(494\) −6.41854e11 −0.484914
\(495\) 5.22836e11 0.391419
\(496\) 1.15218e10 0.00854773
\(497\) −2.86795e11 −0.210847
\(498\) −2.37770e10 −0.0173231
\(499\) −6.16113e11 −0.444844 −0.222422 0.974950i \(-0.571396\pi\)
−0.222422 + 0.974950i \(0.571396\pi\)
\(500\) 2.31133e12 1.65385
\(501\) 1.46089e11 0.103597
\(502\) 7.55806e11 0.531182
\(503\) −2.17749e12 −1.51670 −0.758352 0.651845i \(-0.773995\pi\)
−0.758352 + 0.651845i \(0.773995\pi\)
\(504\) 9.52409e10 0.0657486
\(505\) 2.64174e12 1.80750
\(506\) 5.26761e11 0.357220
\(507\) −6.96264e11 −0.467991
\(508\) −8.06003e11 −0.536970
\(509\) −2.65267e11 −0.175167 −0.0875836 0.996157i \(-0.527914\pi\)
−0.0875836 + 0.996157i \(0.527914\pi\)
\(510\) 3.55895e11 0.232946
\(511\) 8.36883e11 0.542964
\(512\) −6.87195e10 −0.0441942
\(513\) −4.75684e11 −0.303243
\(514\) −1.19523e12 −0.755294
\(515\) 4.63122e12 2.90110
\(516\) −3.89069e11 −0.241603
\(517\) −6.20179e11 −0.381777
\(518\) −1.65543e11 −0.101024
\(519\) −7.23533e11 −0.437729
\(520\) 4.94550e11 0.296616
\(521\) −1.52002e12 −0.903814 −0.451907 0.892065i \(-0.649256\pi\)
−0.451907 + 0.892065i \(0.649256\pi\)
\(522\) 2.47465e11 0.145880
\(523\) 7.54029e11 0.440687 0.220344 0.975422i \(-0.429282\pi\)
0.220344 + 0.975422i \(0.429282\pi\)
\(524\) −1.06580e12 −0.617568
\(525\) −1.52273e12 −0.874797
\(526\) −4.92781e11 −0.280684
\(527\) −1.79208e10 −0.0101207
\(528\) 1.57023e11 0.0879246
\(529\) −5.62384e11 −0.312235
\(530\) −2.46777e12 −1.35851
\(531\) 2.20368e11 0.120288
\(532\) 8.12077e11 0.439537
\(533\) −1.17507e12 −0.630656
\(534\) −8.95073e11 −0.476347
\(535\) 1.14496e12 0.604226
\(536\) 7.71915e11 0.403950
\(537\) −3.47208e11 −0.180179
\(538\) 2.39014e12 1.23000
\(539\) −8.22137e11 −0.419561
\(540\) 3.66516e11 0.185490
\(541\) −2.05580e12 −1.03179 −0.515896 0.856651i \(-0.672541\pi\)
−0.515896 + 0.856651i \(0.672541\pi\)
\(542\) −2.11378e12 −1.05211
\(543\) 7.04792e10 0.0347906
\(544\) 1.06886e11 0.0523268
\(545\) 2.35644e12 1.14412
\(546\) −2.05850e11 −0.0991252
\(547\) 2.09022e12 0.998274 0.499137 0.866523i \(-0.333650\pi\)
0.499137 + 0.866523i \(0.333650\pi\)
\(548\) −1.88544e12 −0.893101
\(549\) 5.39713e11 0.253564
\(550\) −2.51052e12 −1.16985
\(551\) 2.11002e12 0.975225
\(552\) 3.69267e11 0.169283
\(553\) −1.86737e12 −0.849116
\(554\) 1.47075e12 0.663353
\(555\) −6.37058e11 −0.285010
\(556\) 1.15493e12 0.512528
\(557\) 2.24244e12 0.987126 0.493563 0.869710i \(-0.335694\pi\)
0.493563 + 0.869710i \(0.335694\pi\)
\(558\) −1.84556e10 −0.00805888
\(559\) 8.40919e11 0.364251
\(560\) −6.25707e11 −0.268859
\(561\) −2.44232e11 −0.104104
\(562\) 9.93992e11 0.420310
\(563\) −9.48976e10 −0.0398077 −0.0199039 0.999802i \(-0.506336\pi\)
−0.0199039 + 0.999802i \(0.506336\pi\)
\(564\) −4.34754e11 −0.180921
\(565\) −1.19337e11 −0.0492671
\(566\) 2.34088e12 0.958750
\(567\) −1.52558e11 −0.0619883
\(568\) −3.31465e11 −0.133620
\(569\) 8.02282e10 0.0320865 0.0160432 0.999871i \(-0.494893\pi\)
0.0160432 + 0.999871i \(0.494893\pi\)
\(570\) 3.12512e12 1.24002
\(571\) −2.64009e12 −1.03934 −0.519668 0.854368i \(-0.673944\pi\)
−0.519668 + 0.854368i \(0.673944\pi\)
\(572\) −3.39383e11 −0.132559
\(573\) 2.58750e12 1.00273
\(574\) 1.48671e12 0.571640
\(575\) −5.90392e12 −2.25235
\(576\) 1.10075e11 0.0416667
\(577\) −2.16306e12 −0.812414 −0.406207 0.913781i \(-0.633149\pi\)
−0.406207 + 0.913781i \(0.633149\pi\)
\(578\) 1.73116e12 0.645151
\(579\) 3.96772e11 0.146719
\(580\) −1.62578e12 −0.596534
\(581\) −6.50198e10 −0.0236730
\(582\) 5.67973e11 0.205199
\(583\) 1.69350e12 0.607124
\(584\) 9.67233e11 0.344091
\(585\) −7.92173e11 −0.279652
\(586\) −1.54433e12 −0.541005
\(587\) 5.67861e11 0.197411 0.0987053 0.995117i \(-0.468530\pi\)
0.0987053 + 0.995117i \(0.468530\pi\)
\(588\) −5.76330e11 −0.198826
\(589\) −1.57363e11 −0.0538745
\(590\) −1.44776e12 −0.491883
\(591\) 1.76447e12 0.594936
\(592\) −1.91327e11 −0.0640219
\(593\) 2.17049e12 0.720796 0.360398 0.932799i \(-0.382641\pi\)
0.360398 + 0.932799i \(0.382641\pi\)
\(594\) −2.51520e11 −0.0828961
\(595\) 9.73219e11 0.318335
\(596\) −2.82964e11 −0.0918591
\(597\) −3.03074e12 −0.976480
\(598\) −7.98119e11 −0.255219
\(599\) 2.65417e12 0.842379 0.421189 0.906973i \(-0.361613\pi\)
0.421189 + 0.906973i \(0.361613\pi\)
\(600\) −1.75991e12 −0.554383
\(601\) −4.55145e12 −1.42303 −0.711515 0.702670i \(-0.751991\pi\)
−0.711515 + 0.702670i \(0.751991\pi\)
\(602\) −1.06394e12 −0.330165
\(603\) −1.23646e12 −0.380848
\(604\) 2.63693e12 0.806181
\(605\) −3.99512e12 −1.21236
\(606\) −1.27086e12 −0.382799
\(607\) −3.34553e12 −1.00027 −0.500133 0.865949i \(-0.666716\pi\)
−0.500133 + 0.865949i \(0.666716\pi\)
\(608\) 9.38564e11 0.278546
\(609\) 6.76709e11 0.199354
\(610\) −3.54577e12 −1.03688
\(611\) 9.39661e11 0.272763
\(612\) −1.71210e11 −0.0493342
\(613\) 1.75508e12 0.502025 0.251012 0.967984i \(-0.419236\pi\)
0.251012 + 0.967984i \(0.419236\pi\)
\(614\) 4.39799e12 1.24881
\(615\) 5.72131e12 1.61271
\(616\) 4.29390e11 0.120154
\(617\) 3.30409e12 0.917843 0.458922 0.888477i \(-0.348236\pi\)
0.458922 + 0.888477i \(0.348236\pi\)
\(618\) −2.22794e12 −0.614405
\(619\) 1.58035e12 0.432658 0.216329 0.976321i \(-0.430592\pi\)
0.216329 + 0.976321i \(0.430592\pi\)
\(620\) 1.21248e11 0.0329544
\(621\) −5.91494e11 −0.159602
\(622\) 2.90072e12 0.777050
\(623\) −2.44764e12 −0.650955
\(624\) −2.37913e11 −0.0628184
\(625\) 1.39628e13 3.66026
\(626\) −2.54432e12 −0.662198
\(627\) −2.14460e12 −0.554170
\(628\) −1.80154e11 −0.0462195
\(629\) 2.97588e11 0.0758032
\(630\) 1.00226e12 0.253483
\(631\) 3.14102e12 0.788748 0.394374 0.918950i \(-0.370962\pi\)
0.394374 + 0.918950i \(0.370962\pi\)
\(632\) −2.15822e12 −0.538108
\(633\) 4.65018e11 0.115120
\(634\) −3.12777e12 −0.768834
\(635\) −8.48193e12 −2.07020
\(636\) 1.18717e12 0.287710
\(637\) 1.24566e12 0.299758
\(638\) 1.11568e12 0.266593
\(639\) 5.30943e11 0.125978
\(640\) −7.23165e11 −0.170384
\(641\) 3.77817e11 0.0883934 0.0441967 0.999023i \(-0.485927\pi\)
0.0441967 + 0.999023i \(0.485927\pi\)
\(642\) −5.50806e11 −0.127965
\(643\) 9.78208e11 0.225674 0.112837 0.993614i \(-0.464006\pi\)
0.112837 + 0.993614i \(0.464006\pi\)
\(644\) 1.00978e12 0.231336
\(645\) −4.09434e12 −0.931462
\(646\) −1.45983e12 −0.329804
\(647\) −3.41548e12 −0.766271 −0.383136 0.923692i \(-0.625156\pi\)
−0.383136 + 0.923692i \(0.625156\pi\)
\(648\) −1.76319e11 −0.0392837
\(649\) 9.93521e11 0.219824
\(650\) 3.80380e12 0.835810
\(651\) −5.04681e10 −0.0110129
\(652\) 2.82063e12 0.611267
\(653\) 1.27409e12 0.274215 0.137108 0.990556i \(-0.456219\pi\)
0.137108 + 0.990556i \(0.456219\pi\)
\(654\) −1.13361e12 −0.242306
\(655\) −1.12159e13 −2.38094
\(656\) 1.71827e12 0.362264
\(657\) −1.54932e12 −0.324412
\(658\) −1.18887e12 −0.247238
\(659\) −6.72931e12 −1.38991 −0.694954 0.719054i \(-0.744575\pi\)
−0.694954 + 0.719054i \(0.744575\pi\)
\(660\) 1.65242e12 0.338979
\(661\) −6.58592e12 −1.34187 −0.670934 0.741517i \(-0.734107\pi\)
−0.670934 + 0.741517i \(0.734107\pi\)
\(662\) −6.35516e12 −1.28607
\(663\) 3.70047e11 0.0743782
\(664\) −7.51471e10 −0.0150022
\(665\) 8.54585e12 1.69456
\(666\) 3.06469e11 0.0603604
\(667\) 2.62373e12 0.513278
\(668\) 4.61714e11 0.0897179
\(669\) 1.79473e12 0.346403
\(670\) 8.12320e12 1.55737
\(671\) 2.43328e12 0.463383
\(672\) 3.01008e11 0.0569399
\(673\) 2.28085e12 0.428577 0.214288 0.976770i \(-0.431257\pi\)
0.214288 + 0.976770i \(0.431257\pi\)
\(674\) 4.15700e12 0.775909
\(675\) 2.81903e12 0.522677
\(676\) −2.20054e12 −0.405292
\(677\) −1.66591e11 −0.0304791 −0.0152396 0.999884i \(-0.504851\pi\)
−0.0152396 + 0.999884i \(0.504851\pi\)
\(678\) 5.74094e10 0.0104340
\(679\) 1.55316e12 0.280416
\(680\) 1.12480e12 0.201737
\(681\) 6.04363e12 1.07680
\(682\) −8.32064e10 −0.0147274
\(683\) 6.38933e12 1.12347 0.561736 0.827317i \(-0.310134\pi\)
0.561736 + 0.827317i \(0.310134\pi\)
\(684\) −1.50340e12 −0.262616
\(685\) −1.98413e13 −3.44321
\(686\) −3.86422e12 −0.666199
\(687\) −5.21887e12 −0.893863
\(688\) −1.22965e12 −0.209235
\(689\) −2.56590e12 −0.433764
\(690\) 3.88595e12 0.652645
\(691\) 7.32350e12 1.22199 0.610995 0.791635i \(-0.290770\pi\)
0.610995 + 0.791635i \(0.290770\pi\)
\(692\) −2.28672e12 −0.379084
\(693\) −6.87800e11 −0.113282
\(694\) 5.21844e12 0.853931
\(695\) 1.21538e13 1.97597
\(696\) 7.82111e11 0.126336
\(697\) −2.67259e12 −0.428928
\(698\) −2.47897e12 −0.395295
\(699\) −1.42264e12 −0.225397
\(700\) −4.81259e12 −0.757596
\(701\) 8.91596e12 1.39456 0.697280 0.716799i \(-0.254393\pi\)
0.697280 + 0.716799i \(0.254393\pi\)
\(702\) 3.81090e11 0.0592257
\(703\) 2.61312e12 0.403516
\(704\) 4.96270e11 0.0761449
\(705\) −4.57511e12 −0.697510
\(706\) −5.58355e12 −0.845842
\(707\) −3.47525e12 −0.523118
\(708\) 6.96472e11 0.104173
\(709\) 1.02284e13 1.52020 0.760099 0.649808i \(-0.225151\pi\)
0.760099 + 0.649808i \(0.225151\pi\)
\(710\) −3.48815e12 −0.515149
\(711\) 3.45706e12 0.507333
\(712\) −2.82887e12 −0.412528
\(713\) −1.95674e11 −0.0283551
\(714\) −4.68185e11 −0.0674180
\(715\) −3.57148e12 −0.511059
\(716\) −1.09735e12 −0.156040
\(717\) 6.31605e11 0.0892502
\(718\) −1.94989e12 −0.273811
\(719\) −8.58812e12 −1.19845 −0.599223 0.800582i \(-0.704524\pi\)
−0.599223 + 0.800582i \(0.704524\pi\)
\(720\) 1.15837e12 0.160639
\(721\) −6.09244e12 −0.839620
\(722\) −7.65580e12 −1.04851
\(723\) 3.84217e11 0.0522943
\(724\) 2.22749e11 0.0301295
\(725\) −1.25046e13 −1.68092
\(726\) 1.92193e12 0.256757
\(727\) 6.40806e12 0.850789 0.425395 0.905008i \(-0.360135\pi\)
0.425395 + 0.905008i \(0.360135\pi\)
\(728\) −6.50588e11 −0.0858450
\(729\) 2.82430e11 0.0370370
\(730\) 1.01786e13 1.32659
\(731\) 1.91258e12 0.247738
\(732\) 1.70576e12 0.219593
\(733\) 7.38425e12 0.944797 0.472398 0.881385i \(-0.343388\pi\)
0.472398 + 0.881385i \(0.343388\pi\)
\(734\) 8.13522e12 1.03452
\(735\) −6.06497e12 −0.766541
\(736\) 1.16707e12 0.146604
\(737\) −5.57452e12 −0.695992
\(738\) −2.75234e12 −0.341546
\(739\) −1.13169e12 −0.139581 −0.0697907 0.997562i \(-0.522233\pi\)
−0.0697907 + 0.997562i \(0.522233\pi\)
\(740\) −2.01342e12 −0.246826
\(741\) 3.24939e12 0.395931
\(742\) 3.24639e12 0.393173
\(743\) 4.62444e12 0.556685 0.278343 0.960482i \(-0.410215\pi\)
0.278343 + 0.960482i \(0.410215\pi\)
\(744\) −5.83289e10 −0.00697920
\(745\) −2.97775e12 −0.354148
\(746\) 4.09722e12 0.484356
\(747\) 1.20371e11 0.0141442
\(748\) −7.71893e11 −0.0901571
\(749\) −1.50622e12 −0.174872
\(750\) −1.17011e13 −1.35037
\(751\) −3.04009e12 −0.348744 −0.174372 0.984680i \(-0.555790\pi\)
−0.174372 + 0.984680i \(0.555790\pi\)
\(752\) −1.37404e12 −0.156682
\(753\) −3.82627e12 −0.433709
\(754\) −1.69042e12 −0.190469
\(755\) 2.77496e13 3.10810
\(756\) −4.82157e11 −0.0536835
\(757\) 1.21727e13 1.34727 0.673636 0.739063i \(-0.264731\pi\)
0.673636 + 0.739063i \(0.264731\pi\)
\(758\) 8.85200e11 0.0973934
\(759\) −2.66673e12 −0.291669
\(760\) 9.87692e12 1.07389
\(761\) −1.48757e13 −1.60786 −0.803928 0.594727i \(-0.797260\pi\)
−0.803928 + 0.594727i \(0.797260\pi\)
\(762\) 4.08039e12 0.438434
\(763\) −3.09994e12 −0.331126
\(764\) 8.17779e12 0.868392
\(765\) −1.80172e12 −0.190200
\(766\) 1.30363e12 0.136813
\(767\) −1.50533e12 −0.157055
\(768\) 3.47892e11 0.0360844
\(769\) −4.34675e10 −0.00448225 −0.00224112 0.999997i \(-0.500713\pi\)
−0.00224112 + 0.999997i \(0.500713\pi\)
\(770\) 4.51866e12 0.463235
\(771\) 6.05083e12 0.616695
\(772\) 1.25399e12 0.127063
\(773\) −6.97640e12 −0.702787 −0.351393 0.936228i \(-0.614292\pi\)
−0.351393 + 0.936228i \(0.614292\pi\)
\(774\) 1.96966e12 0.197268
\(775\) 9.32575e11 0.0928595
\(776\) 1.79508e12 0.177707
\(777\) 8.38060e11 0.0824860
\(778\) −9.61940e12 −0.941325
\(779\) −2.34680e13 −2.28327
\(780\) −2.50366e12 −0.242186
\(781\) 2.39373e12 0.230222
\(782\) −1.81524e12 −0.173582
\(783\) −1.25279e12 −0.119111
\(784\) −1.82149e12 −0.172188
\(785\) −1.89584e12 −0.178192
\(786\) 5.39561e12 0.504242
\(787\) −1.28564e13 −1.19463 −0.597315 0.802007i \(-0.703766\pi\)
−0.597315 + 0.802007i \(0.703766\pi\)
\(788\) 5.57659e12 0.515230
\(789\) 2.49470e12 0.229178
\(790\) −2.27119e13 −2.07459
\(791\) 1.56990e11 0.0142586
\(792\) −7.94929e11 −0.0717901
\(793\) −3.68677e12 −0.331067
\(794\) −2.09705e11 −0.0187248
\(795\) 1.24931e13 1.10922
\(796\) −9.57862e12 −0.845657
\(797\) 1.84132e13 1.61647 0.808233 0.588862i \(-0.200424\pi\)
0.808233 + 0.588862i \(0.200424\pi\)
\(798\) −4.11114e12 −0.358880
\(799\) 2.13716e12 0.185514
\(800\) −5.56218e12 −0.480110
\(801\) 4.53131e12 0.388935
\(802\) 9.57041e12 0.816857
\(803\) −6.98505e12 −0.592856
\(804\) −3.90782e12 −0.329824
\(805\) 1.06264e13 0.891877
\(806\) 1.26070e11 0.0105221
\(807\) −1.21001e13 −1.00429
\(808\) −4.01655e12 −0.331514
\(809\) −5.67875e12 −0.466106 −0.233053 0.972464i \(-0.574872\pi\)
−0.233053 + 0.972464i \(0.574872\pi\)
\(810\) −1.85549e12 −0.151452
\(811\) −5.49523e12 −0.446058 −0.223029 0.974812i \(-0.571595\pi\)
−0.223029 + 0.974812i \(0.571595\pi\)
\(812\) 2.13874e12 0.172645
\(813\) 1.07010e13 0.859047
\(814\) 1.38170e12 0.110307
\(815\) 2.96827e13 2.35664
\(816\) −5.41108e11 −0.0427246
\(817\) 1.67944e13 1.31876
\(818\) 3.16346e12 0.247043
\(819\) 1.04212e12 0.0809354
\(820\) 1.80822e13 1.39665
\(821\) 1.56831e12 0.120473 0.0602363 0.998184i \(-0.480815\pi\)
0.0602363 + 0.998184i \(0.480815\pi\)
\(822\) 9.54505e12 0.729214
\(823\) −1.46315e13 −1.11171 −0.555853 0.831281i \(-0.687608\pi\)
−0.555853 + 0.831281i \(0.687608\pi\)
\(824\) −7.04138e12 −0.532090
\(825\) 1.27095e13 0.955181
\(826\) 1.90455e12 0.142358
\(827\) −3.06631e11 −0.0227951 −0.0113975 0.999935i \(-0.503628\pi\)
−0.0113975 + 0.999935i \(0.503628\pi\)
\(828\) −1.86941e12 −0.138219
\(829\) −1.41184e13 −1.03822 −0.519112 0.854706i \(-0.673737\pi\)
−0.519112 + 0.854706i \(0.673737\pi\)
\(830\) −7.90805e11 −0.0578387
\(831\) −7.44567e12 −0.541626
\(832\) −7.51921e11 −0.0544023
\(833\) 2.83312e12 0.203874
\(834\) −5.84682e12 −0.418478
\(835\) 4.85882e12 0.345893
\(836\) −6.77801e12 −0.479925
\(837\) 9.34316e10 0.00658005
\(838\) −5.40285e12 −0.378464
\(839\) −6.59420e12 −0.459445 −0.229722 0.973256i \(-0.573782\pi\)
−0.229722 + 0.973256i \(0.573782\pi\)
\(840\) 3.16764e12 0.219523
\(841\) −8.95007e12 −0.616942
\(842\) 1.71774e12 0.117775
\(843\) −5.03208e12 −0.343181
\(844\) 1.46969e12 0.0996973
\(845\) −2.31572e13 −1.56254
\(846\) 2.20094e12 0.147721
\(847\) 5.25565e12 0.350874
\(848\) 3.75204e12 0.249164
\(849\) −1.18507e13 −0.782816
\(850\) 8.65136e12 0.568459
\(851\) 3.24931e12 0.212377
\(852\) 1.67804e12 0.109100
\(853\) 7.39373e12 0.478182 0.239091 0.970997i \(-0.423151\pi\)
0.239091 + 0.970997i \(0.423151\pi\)
\(854\) 4.66452e12 0.300086
\(855\) −1.58209e13 −1.01247
\(856\) −1.74082e12 −0.110821
\(857\) 2.16563e13 1.37142 0.685710 0.727875i \(-0.259492\pi\)
0.685710 + 0.727875i \(0.259492\pi\)
\(858\) 1.71813e12 0.108234
\(859\) 1.80961e12 0.113401 0.0567004 0.998391i \(-0.481942\pi\)
0.0567004 + 0.998391i \(0.481942\pi\)
\(860\) −1.29401e13 −0.806670
\(861\) −7.52647e12 −0.466742
\(862\) 1.10777e13 0.683384
\(863\) −5.09775e12 −0.312846 −0.156423 0.987690i \(-0.549996\pi\)
−0.156423 + 0.987690i \(0.549996\pi\)
\(864\) −5.57256e11 −0.0340207
\(865\) −2.40642e13 −1.46150
\(866\) 1.66215e13 1.00425
\(867\) −8.76398e12 −0.526763
\(868\) −1.59504e11 −0.00953748
\(869\) 1.55860e13 0.927140
\(870\) 8.23049e12 0.487068
\(871\) 8.44621e12 0.497256
\(872\) −3.58277e12 −0.209843
\(873\) −2.87537e12 −0.167544
\(874\) −1.59397e13 −0.924012
\(875\) −3.19975e13 −1.84535
\(876\) −4.89662e12 −0.280949
\(877\) 2.30219e13 1.31415 0.657073 0.753827i \(-0.271794\pi\)
0.657073 + 0.753827i \(0.271794\pi\)
\(878\) −1.45885e13 −0.828486
\(879\) 7.81818e12 0.441729
\(880\) 5.22247e12 0.293565
\(881\) −2.78088e13 −1.55522 −0.777608 0.628749i \(-0.783567\pi\)
−0.777608 + 0.628749i \(0.783567\pi\)
\(882\) 2.91767e12 0.162341
\(883\) 2.53234e13 1.40184 0.700922 0.713238i \(-0.252772\pi\)
0.700922 + 0.713238i \(0.252772\pi\)
\(884\) 1.16953e12 0.0644134
\(885\) 7.32928e12 0.401621
\(886\) 1.26128e13 0.687640
\(887\) 2.70530e13 1.46744 0.733718 0.679454i \(-0.237784\pi\)
0.733718 + 0.679454i \(0.237784\pi\)
\(888\) 9.68593e11 0.0522737
\(889\) 1.11581e13 0.599146
\(890\) −2.97695e13 −1.59044
\(891\) 1.27332e12 0.0676844
\(892\) 5.67223e12 0.299993
\(893\) 1.87665e13 0.987532
\(894\) 1.43250e12 0.0750027
\(895\) −1.15479e13 −0.601587
\(896\) 9.51335e11 0.0493114
\(897\) 4.04048e12 0.208385
\(898\) 1.16590e13 0.598298
\(899\) −4.14440e11 −0.0211613
\(900\) 8.90954e12 0.452652
\(901\) −5.83588e12 −0.295016
\(902\) −1.24088e13 −0.624168
\(903\) 5.38617e12 0.269579
\(904\) 1.81442e11 0.00903608
\(905\) 2.34409e12 0.116160
\(906\) −1.33495e13 −0.658244
\(907\) −3.10370e13 −1.52282 −0.761408 0.648273i \(-0.775492\pi\)
−0.761408 + 0.648273i \(0.775492\pi\)
\(908\) 1.91009e13 0.932538
\(909\) 6.43373e12 0.312554
\(910\) −6.84642e12 −0.330962
\(911\) 3.06827e13 1.47591 0.737956 0.674849i \(-0.235791\pi\)
0.737956 + 0.674849i \(0.235791\pi\)
\(912\) −4.75148e12 −0.227432
\(913\) 5.42688e11 0.0258483
\(914\) 2.49195e12 0.118109
\(915\) 1.79505e13 0.846605
\(916\) −1.64942e13 −0.774108
\(917\) 1.47547e13 0.689077
\(918\) 8.66751e11 0.0402812
\(919\) −1.40349e13 −0.649067 −0.324534 0.945874i \(-0.605207\pi\)
−0.324534 + 0.945874i \(0.605207\pi\)
\(920\) 1.22815e13 0.565207
\(921\) −2.22648e13 −1.01965
\(922\) −9.35554e12 −0.426363
\(923\) −3.62685e12 −0.164484
\(924\) −2.17379e12 −0.0981054
\(925\) −1.54861e13 −0.695511
\(926\) −3.17207e12 −0.141773
\(927\) 1.12789e13 0.501660
\(928\) 2.47186e12 0.109410
\(929\) −5.44440e12 −0.239816 −0.119908 0.992785i \(-0.538260\pi\)
−0.119908 + 0.992785i \(0.538260\pi\)
\(930\) −6.13820e11 −0.0269072
\(931\) 2.48777e13 1.08527
\(932\) −4.49626e12 −0.195200
\(933\) −1.46849e13 −0.634458
\(934\) −3.05574e13 −1.31388
\(935\) −8.12297e12 −0.347586
\(936\) 1.20443e12 0.0512910
\(937\) −2.11139e13 −0.894828 −0.447414 0.894327i \(-0.647655\pi\)
−0.447414 + 0.894327i \(0.647655\pi\)
\(938\) −1.06862e13 −0.450724
\(939\) 1.28806e13 0.540682
\(940\) −1.44596e13 −0.604061
\(941\) −1.76055e13 −0.731975 −0.365987 0.930620i \(-0.619269\pi\)
−0.365987 + 0.930620i \(0.619269\pi\)
\(942\) 9.12029e11 0.0377381
\(943\) −2.91815e13 −1.20173
\(944\) 2.20120e12 0.0902162
\(945\) −5.07395e12 −0.206968
\(946\) 8.88014e12 0.360503
\(947\) −2.81821e13 −1.13867 −0.569336 0.822105i \(-0.692800\pi\)
−0.569336 + 0.822105i \(0.692800\pi\)
\(948\) 1.09260e13 0.439363
\(949\) 1.05834e13 0.423571
\(950\) 7.59677e13 3.02603
\(951\) 1.58343e13 0.627751
\(952\) −1.47970e12 −0.0583857
\(953\) −4.80527e13 −1.88712 −0.943561 0.331198i \(-0.892547\pi\)
−0.943561 + 0.331198i \(0.892547\pi\)
\(954\) −6.01004e12 −0.234914
\(955\) 8.60584e13 3.34795
\(956\) 1.99618e12 0.0772929
\(957\) −5.64815e12 −0.217672
\(958\) 2.39365e13 0.918153
\(959\) 2.61016e13 0.996513
\(960\) 3.66102e12 0.139118
\(961\) −2.64087e13 −0.998831
\(962\) −2.09348e12 −0.0788099
\(963\) 2.78846e12 0.104483
\(964\) 1.21432e12 0.0452882
\(965\) 1.31963e13 0.489869
\(966\) −5.11204e12 −0.188885
\(967\) −4.11360e13 −1.51287 −0.756437 0.654066i \(-0.773062\pi\)
−0.756437 + 0.654066i \(0.773062\pi\)
\(968\) 6.07425e12 0.222358
\(969\) 7.39040e12 0.269284
\(970\) 1.88904e13 0.685122
\(971\) 1.02331e13 0.369419 0.184709 0.982793i \(-0.440866\pi\)
0.184709 + 0.982793i \(0.440866\pi\)
\(972\) 8.92617e11 0.0320750
\(973\) −1.59885e13 −0.571874
\(974\) −5.72666e12 −0.203885
\(975\) −1.92567e13 −0.682436
\(976\) 5.39105e12 0.190173
\(977\) 3.01369e13 1.05821 0.529107 0.848555i \(-0.322527\pi\)
0.529107 + 0.848555i \(0.322527\pi\)
\(978\) −1.42794e13 −0.499098
\(979\) 2.04292e13 0.710771
\(980\) −1.91683e13 −0.663844
\(981\) 5.73891e12 0.197842
\(982\) −1.15722e13 −0.397113
\(983\) −1.71235e13 −0.584926 −0.292463 0.956277i \(-0.594475\pi\)
−0.292463 + 0.956277i \(0.594475\pi\)
\(984\) −8.69877e12 −0.295787
\(985\) 5.86849e13 1.98638
\(986\) −3.84470e12 −0.129544
\(987\) 6.01863e12 0.201869
\(988\) 1.02697e13 0.342886
\(989\) 2.08832e13 0.694086
\(990\) −8.36538e12 −0.276775
\(991\) 3.26099e13 1.07403 0.537016 0.843572i \(-0.319551\pi\)
0.537016 + 0.843572i \(0.319551\pi\)
\(992\) −1.84348e11 −0.00604416
\(993\) 3.21730e13 1.05007
\(994\) 4.58872e12 0.149091
\(995\) −1.00800e14 −3.26029
\(996\) 3.80432e11 0.0122493
\(997\) −3.52071e13 −1.12850 −0.564251 0.825603i \(-0.690835\pi\)
−0.564251 + 0.825603i \(0.690835\pi\)
\(998\) 9.85781e12 0.314552
\(999\) −1.55150e12 −0.0492841
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 \(a_p\))