Properties

Label 3.20.a.a.1.1
Level 3
Weight 20
Character 3.1
Self dual Yes
Analytic conductor 6.865
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 20 \)
Character orbit: \([\chi]\) = 3.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(6.86450089669\)
Analytic rank: \(1\)
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 \(\chi\) = 3.1

$q$-expansion

\(f(q)\) \(=\) \(q-1104.00 q^{2} +19683.0 q^{3} +694528. q^{4} +3.51627e6 q^{5} -2.17300e7 q^{6} -1.95591e8 q^{7} -1.87945e8 q^{8} +3.87420e8 q^{9} +O(q^{10})\) \(q-1104.00 q^{2} +19683.0 q^{3} +694528. q^{4} +3.51627e6 q^{5} -2.17300e7 q^{6} -1.95591e8 q^{7} -1.87945e8 q^{8} +3.87420e8 q^{9} -3.88196e9 q^{10} -2.74686e9 q^{11} +1.36704e10 q^{12} -4.44004e10 q^{13} +2.15932e11 q^{14} +6.92107e10 q^{15} -1.56641e11 q^{16} -7.85983e11 q^{17} -4.27712e11 q^{18} +3.15410e11 q^{19} +2.44215e12 q^{20} -3.84981e12 q^{21} +3.03253e12 q^{22} +4.90056e12 q^{23} -3.69932e12 q^{24} -6.70933e12 q^{25} +4.90181e13 q^{26} +7.62560e12 q^{27} -1.35843e14 q^{28} +1.21885e13 q^{29} -7.64087e13 q^{30} -4.27137e13 q^{31} +2.71469e14 q^{32} -5.40664e13 q^{33} +8.67725e14 q^{34} -6.87749e14 q^{35} +2.69074e14 q^{36} -4.23452e14 q^{37} -3.48213e14 q^{38} -8.73934e14 q^{39} -6.60865e14 q^{40} -1.11392e15 q^{41} +4.25019e15 q^{42} +1.13610e15 q^{43} -1.90777e15 q^{44} +1.36228e15 q^{45} -5.41022e15 q^{46} +1.53137e15 q^{47} -3.08317e15 q^{48} +2.68568e16 q^{49} +7.40710e15 q^{50} -1.54705e16 q^{51} -3.08374e16 q^{52} -1.80593e16 q^{53} -8.41866e15 q^{54} -9.65869e15 q^{55} +3.67603e16 q^{56} +6.20822e15 q^{57} -1.34561e16 q^{58} +9.27004e16 q^{59} +4.80688e16 q^{60} +2.13530e16 q^{61} +4.71559e16 q^{62} -7.57758e16 q^{63} -2.17577e17 q^{64} -1.56124e17 q^{65} +5.96893e16 q^{66} +2.68065e17 q^{67} -5.45887e17 q^{68} +9.64577e16 q^{69} +7.59275e17 q^{70} -1.13274e17 q^{71} -7.28137e16 q^{72} -5.45956e17 q^{73} +4.67491e17 q^{74} -1.32060e17 q^{75} +2.19061e17 q^{76} +5.37260e17 q^{77} +9.64823e17 q^{78} -1.80761e18 q^{79} -5.50794e17 q^{80} +1.50095e17 q^{81} +1.22977e18 q^{82} +1.46996e18 q^{83} -2.67380e18 q^{84} -2.76373e18 q^{85} -1.25425e18 q^{86} +2.39907e17 q^{87} +5.16258e17 q^{88} +2.97404e18 q^{89} -1.50395e18 q^{90} +8.68431e18 q^{91} +3.40358e18 q^{92} -8.40733e17 q^{93} -1.69063e18 q^{94} +1.10907e18 q^{95} +5.34333e18 q^{96} -6.92569e18 q^{97} -2.96499e19 q^{98} -1.06419e18 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1104.00 −1.52470 −0.762349 0.647166i \(-0.775954\pi\)
−0.762349 + 0.647166i \(0.775954\pi\)
\(3\) 19683.0 0.577350
\(4\) 694528. 1.32471
\(5\) 3.51627e6 0.805132 0.402566 0.915391i \(-0.368118\pi\)
0.402566 + 0.915391i \(0.368118\pi\)
\(6\) −2.17300e7 −0.880285
\(7\) −1.95591e8 −1.83196 −0.915981 0.401221i \(-0.868586\pi\)
−0.915981 + 0.401221i \(0.868586\pi\)
\(8\) −1.87945e8 −0.495080
\(9\) 3.87420e8 0.333333
\(10\) −3.88196e9 −1.22758
\(11\) −2.74686e9 −0.351241 −0.175621 0.984458i \(-0.556193\pi\)
−0.175621 + 0.984458i \(0.556193\pi\)
\(12\) 1.36704e10 0.764820
\(13\) −4.44004e10 −1.16125 −0.580625 0.814171i \(-0.697192\pi\)
−0.580625 + 0.814171i \(0.697192\pi\)
\(14\) 2.15932e11 2.79319
\(15\) 6.92107e10 0.464843
\(16\) −1.56641e11 −0.569858
\(17\) −7.85983e11 −1.60749 −0.803745 0.594974i \(-0.797162\pi\)
−0.803745 + 0.594974i \(0.797162\pi\)
\(18\) −4.27712e11 −0.508233
\(19\) 3.15410e11 0.224242 0.112121 0.993695i \(-0.464236\pi\)
0.112121 + 0.993695i \(0.464236\pi\)
\(20\) 2.44215e12 1.06656
\(21\) −3.84981e12 −1.05768
\(22\) 3.03253e12 0.535537
\(23\) 4.90056e12 0.567324 0.283662 0.958924i \(-0.408451\pi\)
0.283662 + 0.958924i \(0.408451\pi\)
\(24\) −3.69932e12 −0.285835
\(25\) −6.70933e12 −0.351762
\(26\) 4.90181e13 1.77056
\(27\) 7.62560e12 0.192450
\(28\) −1.35843e14 −2.42681
\(29\) 1.21885e13 0.156016 0.0780082 0.996953i \(-0.475144\pi\)
0.0780082 + 0.996953i \(0.475144\pi\)
\(30\) −7.64087e13 −0.708746
\(31\) −4.27137e13 −0.290155 −0.145078 0.989420i \(-0.546343\pi\)
−0.145078 + 0.989420i \(0.546343\pi\)
\(32\) 2.71469e14 1.36394
\(33\) −5.40664e13 −0.202789
\(34\) 8.67725e14 2.45094
\(35\) −6.87749e14 −1.47497
\(36\) 2.69074e14 0.441569
\(37\) −4.23452e14 −0.535659 −0.267829 0.963466i \(-0.586306\pi\)
−0.267829 + 0.963466i \(0.586306\pi\)
\(38\) −3.48213e14 −0.341901
\(39\) −8.73934e14 −0.670448
\(40\) −6.60865e14 −0.398605
\(41\) −1.11392e15 −0.531383 −0.265691 0.964058i \(-0.585600\pi\)
−0.265691 + 0.964058i \(0.585600\pi\)
\(42\) 4.25019e15 1.61265
\(43\) 1.13610e15 0.344720 0.172360 0.985034i \(-0.444861\pi\)
0.172360 + 0.985034i \(0.444861\pi\)
\(44\) −1.90777e15 −0.465292
\(45\) 1.36228e15 0.268377
\(46\) −5.41022e15 −0.864999
\(47\) 1.53137e15 0.199596 0.0997978 0.995008i \(-0.468180\pi\)
0.0997978 + 0.995008i \(0.468180\pi\)
\(48\) −3.08317e15 −0.329008
\(49\) 2.68568e16 2.35609
\(50\) 7.40710e15 0.536331
\(51\) −1.54705e16 −0.928084
\(52\) −3.08374e16 −1.53832
\(53\) −1.80593e16 −0.751762 −0.375881 0.926668i \(-0.622660\pi\)
−0.375881 + 0.926668i \(0.622660\pi\)
\(54\) −8.41866e15 −0.293428
\(55\) −9.65869e15 −0.282796
\(56\) 3.67603e16 0.906969
\(57\) 6.20822e15 0.129466
\(58\) −1.34561e16 −0.237878
\(59\) 9.27004e16 1.39312 0.696559 0.717500i \(-0.254714\pi\)
0.696559 + 0.717500i \(0.254714\pi\)
\(60\) 4.80688e16 0.615781
\(61\) 2.13530e16 0.233789 0.116895 0.993144i \(-0.462706\pi\)
0.116895 + 0.993144i \(0.462706\pi\)
\(62\) 4.71559e16 0.442400
\(63\) −7.57758e16 −0.610654
\(64\) −2.17577e17 −1.50974
\(65\) −1.56124e17 −0.934959
\(66\) 5.96893e16 0.309193
\(67\) 2.68065e17 1.20373 0.601866 0.798597i \(-0.294424\pi\)
0.601866 + 0.798597i \(0.294424\pi\)
\(68\) −5.45887e17 −2.12945
\(69\) 9.64577e16 0.327545
\(70\) 7.59275e17 2.24889
\(71\) −1.13274e17 −0.293207 −0.146603 0.989195i \(-0.546834\pi\)
−0.146603 + 0.989195i \(0.546834\pi\)
\(72\) −7.28137e16 −0.165027
\(73\) −5.45956e17 −1.08540 −0.542701 0.839926i \(-0.682598\pi\)
−0.542701 + 0.839926i \(0.682598\pi\)
\(74\) 4.67491e17 0.816718
\(75\) −1.32060e17 −0.203090
\(76\) 2.19061e17 0.297055
\(77\) 5.37260e17 0.643461
\(78\) 9.64823e17 1.02223
\(79\) −1.80761e18 −1.69687 −0.848433 0.529303i \(-0.822453\pi\)
−0.848433 + 0.529303i \(0.822453\pi\)
\(80\) −5.50794e17 −0.458811
\(81\) 1.50095e17 0.111111
\(82\) 1.22977e18 0.810199
\(83\) 1.46996e18 0.863104 0.431552 0.902088i \(-0.357966\pi\)
0.431552 + 0.902088i \(0.357966\pi\)
\(84\) −2.67380e18 −1.40112
\(85\) −2.76373e18 −1.29424
\(86\) −1.25425e18 −0.525594
\(87\) 2.39907e17 0.0900761
\(88\) 5.16258e17 0.173893
\(89\) 2.97404e18 0.899791 0.449896 0.893081i \(-0.351461\pi\)
0.449896 + 0.893081i \(0.351461\pi\)
\(90\) −1.50395e18 −0.409195
\(91\) 8.68431e18 2.12737
\(92\) 3.40358e18 0.751538
\(93\) −8.40733e17 −0.167521
\(94\) −1.69063e18 −0.304323
\(95\) 1.10907e18 0.180544
\(96\) 5.34333e18 0.787473
\(97\) −6.92569e18 −0.924978 −0.462489 0.886625i \(-0.653043\pi\)
−0.462489 + 0.886625i \(0.653043\pi\)
\(98\) −2.96499e19 −3.59232
\(99\) −1.06419e18 −0.117080
\(100\) −4.65982e18 −0.465982
\(101\) 1.78746e19 1.62623 0.813117 0.582100i \(-0.197769\pi\)
0.813117 + 0.582100i \(0.197769\pi\)
\(102\) 1.70794e19 1.41505
\(103\) −7.05681e18 −0.532911 −0.266456 0.963847i \(-0.585853\pi\)
−0.266456 + 0.963847i \(0.585853\pi\)
\(104\) 8.34484e18 0.574912
\(105\) −1.35370e19 −0.851575
\(106\) 1.99375e19 1.14621
\(107\) −1.77197e19 −0.931772 −0.465886 0.884845i \(-0.654264\pi\)
−0.465886 + 0.884845i \(0.654264\pi\)
\(108\) 5.29619e18 0.254940
\(109\) 8.11766e18 0.357997 0.178998 0.983849i \(-0.442714\pi\)
0.178998 + 0.983849i \(0.442714\pi\)
\(110\) 1.06632e19 0.431178
\(111\) −8.33481e18 −0.309263
\(112\) 3.06376e19 1.04396
\(113\) −4.38285e19 −1.37250 −0.686249 0.727367i \(-0.740744\pi\)
−0.686249 + 0.727367i \(0.740744\pi\)
\(114\) −6.85388e18 −0.197397
\(115\) 1.72317e19 0.456771
\(116\) 8.46527e18 0.206676
\(117\) −1.72016e19 −0.387083
\(118\) −1.02341e20 −2.12408
\(119\) 1.53731e20 2.94486
\(120\) −1.30078e19 −0.230135
\(121\) −5.36139e19 −0.876629
\(122\) −2.35737e19 −0.356458
\(123\) −2.19253e19 −0.306794
\(124\) −2.96658e19 −0.384371
\(125\) −9.06593e19 −1.08835
\(126\) 8.36565e19 0.931064
\(127\) 2.94833e19 0.304398 0.152199 0.988350i \(-0.451365\pi\)
0.152199 + 0.988350i \(0.451365\pi\)
\(128\) 9.78769e19 0.937962
\(129\) 2.23619e19 0.199024
\(130\) 1.72361e20 1.42553
\(131\) 1.29096e20 0.992738 0.496369 0.868112i \(-0.334666\pi\)
0.496369 + 0.868112i \(0.334666\pi\)
\(132\) −3.75506e19 −0.268636
\(133\) −6.16913e19 −0.410803
\(134\) −2.95944e20 −1.83533
\(135\) 2.68137e19 0.154948
\(136\) 1.47721e20 0.795837
\(137\) −1.15732e20 −0.581576 −0.290788 0.956788i \(-0.593917\pi\)
−0.290788 + 0.956788i \(0.593917\pi\)
\(138\) −1.06489e20 −0.499407
\(139\) −5.77640e19 −0.252939 −0.126470 0.991970i \(-0.540365\pi\)
−0.126470 + 0.991970i \(0.540365\pi\)
\(140\) −4.77661e20 −1.95391
\(141\) 3.01420e19 0.115237
\(142\) 1.25054e20 0.447052
\(143\) 1.21962e20 0.407879
\(144\) −6.06861e19 −0.189953
\(145\) 4.28581e19 0.125614
\(146\) 6.02736e20 1.65491
\(147\) 5.28622e20 1.36029
\(148\) −2.94100e20 −0.709591
\(149\) 9.58388e19 0.216906 0.108453 0.994102i \(-0.465410\pi\)
0.108453 + 0.994102i \(0.465410\pi\)
\(150\) 1.45794e20 0.309651
\(151\) 1.32704e20 0.264608 0.132304 0.991209i \(-0.457763\pi\)
0.132304 + 0.991209i \(0.457763\pi\)
\(152\) −5.92798e19 −0.111018
\(153\) −3.04506e20 −0.535830
\(154\) −5.93135e20 −0.981084
\(155\) −1.50193e20 −0.233613
\(156\) −6.06972e20 −0.888147
\(157\) −9.90999e20 −1.36467 −0.682333 0.731041i \(-0.739035\pi\)
−0.682333 + 0.731041i \(0.739035\pi\)
\(158\) 1.99560e21 2.58721
\(159\) −3.55462e20 −0.434030
\(160\) 9.54560e20 1.09815
\(161\) −9.58503e20 −1.03932
\(162\) −1.65704e20 −0.169411
\(163\) 1.74144e21 1.67929 0.839647 0.543133i \(-0.182762\pi\)
0.839647 + 0.543133i \(0.182762\pi\)
\(164\) −7.73649e20 −0.703927
\(165\) −1.90112e20 −0.163272
\(166\) −1.62283e21 −1.31597
\(167\) −2.34167e21 −1.79357 −0.896785 0.442466i \(-0.854104\pi\)
−0.896785 + 0.442466i \(0.854104\pi\)
\(168\) 7.23552e20 0.523639
\(169\) 5.09479e20 0.348500
\(170\) 3.05115e21 1.97333
\(171\) 1.22196e20 0.0747473
\(172\) 7.89053e20 0.456653
\(173\) −5.36374e20 −0.293785 −0.146892 0.989152i \(-0.546927\pi\)
−0.146892 + 0.989152i \(0.546927\pi\)
\(174\) −2.64857e20 −0.137339
\(175\) 1.31228e21 0.644415
\(176\) 4.30272e20 0.200158
\(177\) 1.82462e21 0.804317
\(178\) −3.28334e21 −1.37191
\(179\) 3.33179e21 1.32000 0.660000 0.751266i \(-0.270556\pi\)
0.660000 + 0.751266i \(0.270556\pi\)
\(180\) 9.46138e20 0.355521
\(181\) −3.97005e20 −0.141530 −0.0707652 0.997493i \(-0.522544\pi\)
−0.0707652 + 0.997493i \(0.522544\pi\)
\(182\) −9.58748e21 −3.24359
\(183\) 4.20290e20 0.134978
\(184\) −9.21036e20 −0.280871
\(185\) −1.48897e21 −0.431276
\(186\) 9.28169e20 0.255420
\(187\) 2.15898e21 0.564617
\(188\) 1.06358e21 0.264406
\(189\) −1.49150e21 −0.352561
\(190\) −1.22441e21 −0.275276
\(191\) 1.18297e20 0.0253022 0.0126511 0.999920i \(-0.495973\pi\)
0.0126511 + 0.999920i \(0.495973\pi\)
\(192\) −4.28257e21 −0.871651
\(193\) 3.76434e21 0.729281 0.364640 0.931148i \(-0.381192\pi\)
0.364640 + 0.931148i \(0.381192\pi\)
\(194\) 7.64596e21 1.41031
\(195\) −3.07299e21 −0.539799
\(196\) 1.86528e22 3.12112
\(197\) 4.37987e21 0.698283 0.349142 0.937070i \(-0.386473\pi\)
0.349142 + 0.937070i \(0.386473\pi\)
\(198\) 1.17486e21 0.178512
\(199\) −1.32104e22 −1.91343 −0.956715 0.291025i \(-0.906004\pi\)
−0.956715 + 0.291025i \(0.906004\pi\)
\(200\) 1.26099e21 0.174151
\(201\) 5.27632e21 0.694975
\(202\) −1.97335e22 −2.47952
\(203\) −2.38396e21 −0.285816
\(204\) −1.07447e22 −1.22944
\(205\) −3.91685e21 −0.427834
\(206\) 7.79072e21 0.812530
\(207\) 1.89858e21 0.189108
\(208\) 6.95495e21 0.661748
\(209\) −8.66388e20 −0.0787631
\(210\) 1.49448e22 1.29840
\(211\) −1.55480e22 −1.29120 −0.645598 0.763678i \(-0.723392\pi\)
−0.645598 + 0.763678i \(0.723392\pi\)
\(212\) −1.25427e22 −0.995865
\(213\) −2.22956e21 −0.169283
\(214\) 1.95625e22 1.42067
\(215\) 3.99484e21 0.277545
\(216\) −1.43319e21 −0.0952783
\(217\) 8.35439e21 0.531554
\(218\) −8.96190e21 −0.545837
\(219\) −1.07461e22 −0.626657
\(220\) −6.70823e21 −0.374622
\(221\) 3.48980e22 1.86670
\(222\) 9.20163e21 0.471533
\(223\) −1.04802e21 −0.0514602 −0.0257301 0.999669i \(-0.508191\pi\)
−0.0257301 + 0.999669i \(0.508191\pi\)
\(224\) −5.30969e22 −2.49869
\(225\) −2.59933e21 −0.117254
\(226\) 4.83867e22 2.09265
\(227\) −4.90340e21 −0.203354 −0.101677 0.994817i \(-0.532421\pi\)
−0.101677 + 0.994817i \(0.532421\pi\)
\(228\) 4.31179e21 0.171505
\(229\) 1.69013e22 0.644885 0.322443 0.946589i \(-0.395496\pi\)
0.322443 + 0.946589i \(0.395496\pi\)
\(230\) −1.90238e22 −0.696438
\(231\) 1.05749e22 0.371502
\(232\) −2.29077e21 −0.0772406
\(233\) −2.94863e22 −0.954418 −0.477209 0.878790i \(-0.658352\pi\)
−0.477209 + 0.878790i \(0.658352\pi\)
\(234\) 1.89906e22 0.590185
\(235\) 5.38472e21 0.160701
\(236\) 6.43831e22 1.84547
\(237\) −3.55792e22 −0.979686
\(238\) −1.69719e23 −4.49003
\(239\) −3.48672e22 −0.886415 −0.443208 0.896419i \(-0.646160\pi\)
−0.443208 + 0.896419i \(0.646160\pi\)
\(240\) −1.08413e22 −0.264895
\(241\) 3.10412e22 0.729083 0.364542 0.931187i \(-0.381226\pi\)
0.364542 + 0.931187i \(0.381226\pi\)
\(242\) 5.91897e22 1.33660
\(243\) 2.95431e21 0.0641500
\(244\) 1.48302e22 0.309702
\(245\) 9.44357e22 1.89696
\(246\) 2.42055e22 0.467769
\(247\) −1.40044e22 −0.260401
\(248\) 8.02782e21 0.143650
\(249\) 2.89332e22 0.498313
\(250\) 1.00088e23 1.65940
\(251\) 2.43352e21 0.0388449 0.0194224 0.999811i \(-0.493817\pi\)
0.0194224 + 0.999811i \(0.493817\pi\)
\(252\) −5.26284e22 −0.808938
\(253\) −1.34611e22 −0.199268
\(254\) −3.25496e22 −0.464115
\(255\) −5.43984e22 −0.747231
\(256\) 6.01696e21 0.0796338
\(257\) −7.09300e22 −0.904618 −0.452309 0.891861i \(-0.649400\pi\)
−0.452309 + 0.891861i \(0.649400\pi\)
\(258\) −2.46875e22 −0.303452
\(259\) 8.28233e22 0.981307
\(260\) −1.08432e23 −1.23855
\(261\) 4.72208e21 0.0520054
\(262\) −1.42522e23 −1.51363
\(263\) 8.10179e22 0.829854 0.414927 0.909855i \(-0.363807\pi\)
0.414927 + 0.909855i \(0.363807\pi\)
\(264\) 1.01615e22 0.100397
\(265\) −6.35014e22 −0.605268
\(266\) 6.81072e22 0.626351
\(267\) 5.85380e22 0.519495
\(268\) 1.86179e23 1.59459
\(269\) −2.10267e23 −1.73830 −0.869150 0.494549i \(-0.835333\pi\)
−0.869150 + 0.494549i \(0.835333\pi\)
\(270\) −2.96023e22 −0.236249
\(271\) −9.67500e22 −0.745491 −0.372746 0.927934i \(-0.621584\pi\)
−0.372746 + 0.927934i \(0.621584\pi\)
\(272\) 1.23117e23 0.916041
\(273\) 1.70933e23 1.22823
\(274\) 1.27768e23 0.886728
\(275\) 1.84296e22 0.123553
\(276\) 6.69926e22 0.433901
\(277\) −1.50223e23 −0.940112 −0.470056 0.882637i \(-0.655766\pi\)
−0.470056 + 0.882637i \(0.655766\pi\)
\(278\) 6.37714e22 0.385656
\(279\) −1.65481e22 −0.0967185
\(280\) 1.29259e23 0.730230
\(281\) −2.78843e23 −1.52282 −0.761412 0.648268i \(-0.775494\pi\)
−0.761412 + 0.648268i \(0.775494\pi\)
\(282\) −3.32768e22 −0.175701
\(283\) −9.74687e22 −0.497615 −0.248808 0.968553i \(-0.580039\pi\)
−0.248808 + 0.968553i \(0.580039\pi\)
\(284\) −7.86716e22 −0.388413
\(285\) 2.18298e22 0.104237
\(286\) −1.34646e23 −0.621892
\(287\) 2.17872e23 0.973474
\(288\) 1.05173e23 0.454648
\(289\) 3.78696e23 1.58402
\(290\) −4.73154e22 −0.191523
\(291\) −1.36318e23 −0.534036
\(292\) −3.79182e23 −1.43784
\(293\) 2.78548e23 1.02249 0.511243 0.859436i \(-0.329185\pi\)
0.511243 + 0.859436i \(0.329185\pi\)
\(294\) −5.83599e23 −2.07403
\(295\) 3.25960e23 1.12164
\(296\) 7.95857e22 0.265194
\(297\) −2.09464e22 −0.0675964
\(298\) −1.05806e23 −0.330716
\(299\) −2.17587e23 −0.658805
\(300\) −9.17192e22 −0.269035
\(301\) −2.22211e23 −0.631514
\(302\) −1.46505e23 −0.403447
\(303\) 3.51826e23 0.938907
\(304\) −4.94064e22 −0.127786
\(305\) 7.50828e22 0.188231
\(306\) 3.36174e23 0.816979
\(307\) 4.84526e23 1.14157 0.570785 0.821099i \(-0.306639\pi\)
0.570785 + 0.821099i \(0.306639\pi\)
\(308\) 3.73142e23 0.852397
\(309\) −1.38899e23 −0.307677
\(310\) 1.65813e23 0.356190
\(311\) 5.63561e23 1.17413 0.587067 0.809539i \(-0.300283\pi\)
0.587067 + 0.809539i \(0.300283\pi\)
\(312\) 1.64251e23 0.331926
\(313\) −5.79355e23 −1.13573 −0.567863 0.823123i \(-0.692230\pi\)
−0.567863 + 0.823123i \(0.692230\pi\)
\(314\) 1.09406e24 2.08071
\(315\) −2.66448e23 −0.491657
\(316\) −1.25544e24 −2.24785
\(317\) −1.07037e24 −1.85982 −0.929909 0.367791i \(-0.880114\pi\)
−0.929909 + 0.367791i \(0.880114\pi\)
\(318\) 3.92430e23 0.661766
\(319\) −3.34801e22 −0.0547994
\(320\) −7.65060e23 −1.21554
\(321\) −3.48776e23 −0.537959
\(322\) 1.05819e24 1.58465
\(323\) −2.47907e23 −0.360467
\(324\) 1.04245e23 0.147190
\(325\) 2.97897e23 0.408484
\(326\) −1.92255e24 −2.56042
\(327\) 1.59780e23 0.206690
\(328\) 2.09356e23 0.263077
\(329\) −2.99522e23 −0.365652
\(330\) 2.09884e23 0.248941
\(331\) −3.07182e23 −0.354022 −0.177011 0.984209i \(-0.556643\pi\)
−0.177011 + 0.984209i \(0.556643\pi\)
\(332\) 1.02093e24 1.14336
\(333\) −1.64054e23 −0.178553
\(334\) 2.58520e24 2.73465
\(335\) 9.42589e23 0.969163
\(336\) 6.03040e23 0.602730
\(337\) 1.59649e24 1.55125 0.775625 0.631194i \(-0.217435\pi\)
0.775625 + 0.631194i \(0.217435\pi\)
\(338\) −5.62465e23 −0.531358
\(339\) −8.62677e23 −0.792412
\(340\) −1.91949e24 −1.71449
\(341\) 1.17328e23 0.101915
\(342\) −1.34905e23 −0.113967
\(343\) −3.02342e24 −2.48430
\(344\) −2.13524e23 −0.170664
\(345\) 3.39171e23 0.263717
\(346\) 5.92157e23 0.447934
\(347\) 1.89344e24 1.39354 0.696772 0.717292i \(-0.254619\pi\)
0.696772 + 0.717292i \(0.254619\pi\)
\(348\) 1.66622e23 0.119324
\(349\) 3.19249e23 0.222478 0.111239 0.993794i \(-0.464518\pi\)
0.111239 + 0.993794i \(0.464518\pi\)
\(350\) −1.44876e24 −0.982539
\(351\) −3.38580e23 −0.223483
\(352\) −7.45688e23 −0.479073
\(353\) 2.10677e24 1.31752 0.658761 0.752352i \(-0.271081\pi\)
0.658761 + 0.752352i \(0.271081\pi\)
\(354\) −2.01438e24 −1.22634
\(355\) −3.98300e23 −0.236070
\(356\) 2.06555e24 1.19196
\(357\) 3.02588e24 1.70022
\(358\) −3.67830e24 −2.01260
\(359\) −1.45227e24 −0.773836 −0.386918 0.922114i \(-0.626460\pi\)
−0.386918 + 0.922114i \(0.626460\pi\)
\(360\) −2.56033e23 −0.132868
\(361\) −1.87894e24 −0.949716
\(362\) 4.38294e23 0.215791
\(363\) −1.05528e24 −0.506122
\(364\) 6.03150e24 2.81814
\(365\) −1.91973e24 −0.873892
\(366\) −4.64001e23 −0.205801
\(367\) −3.52842e23 −0.152494 −0.0762470 0.997089i \(-0.524294\pi\)
−0.0762470 + 0.997089i \(0.524294\pi\)
\(368\) −7.67631e23 −0.323294
\(369\) −4.31556e23 −0.177128
\(370\) 1.64383e24 0.657566
\(371\) 3.53223e24 1.37720
\(372\) −5.83913e23 −0.221917
\(373\) 3.12604e24 1.15814 0.579069 0.815278i \(-0.303416\pi\)
0.579069 + 0.815278i \(0.303416\pi\)
\(374\) −2.38352e24 −0.860871
\(375\) −1.78445e24 −0.628358
\(376\) −2.87814e23 −0.0988159
\(377\) −5.41176e23 −0.181174
\(378\) 1.64661e24 0.537550
\(379\) 5.18388e23 0.165037 0.0825187 0.996590i \(-0.473704\pi\)
0.0825187 + 0.996590i \(0.473704\pi\)
\(380\) 7.70279e23 0.239168
\(381\) 5.80321e23 0.175744
\(382\) −1.30600e23 −0.0385782
\(383\) 2.12429e23 0.0612106 0.0306053 0.999532i \(-0.490257\pi\)
0.0306053 + 0.999532i \(0.490257\pi\)
\(384\) 1.92651e24 0.541533
\(385\) 1.88915e24 0.518071
\(386\) −4.15583e24 −1.11193
\(387\) 4.40149e23 0.114907
\(388\) −4.81008e24 −1.22532
\(389\) −4.43856e24 −1.10337 −0.551685 0.834053i \(-0.686015\pi\)
−0.551685 + 0.834053i \(0.686015\pi\)
\(390\) 3.39258e24 0.823031
\(391\) −3.85175e24 −0.911968
\(392\) −5.04760e24 −1.16645
\(393\) 2.54099e24 0.573158
\(394\) −4.83537e24 −1.06467
\(395\) −6.35604e24 −1.36620
\(396\) −7.39109e23 −0.155097
\(397\) 4.22183e24 0.864951 0.432475 0.901646i \(-0.357640\pi\)
0.432475 + 0.901646i \(0.357640\pi\)
\(398\) 1.45843e25 2.91741
\(399\) −1.21427e24 −0.237177
\(400\) 1.05096e24 0.200455
\(401\) 3.29680e24 0.614075 0.307037 0.951697i \(-0.400662\pi\)
0.307037 + 0.951697i \(0.400662\pi\)
\(402\) −5.82506e24 −1.05963
\(403\) 1.89651e24 0.336943
\(404\) 1.24144e25 2.15428
\(405\) 5.27773e23 0.0894591
\(406\) 2.63189e24 0.435783
\(407\) 1.16316e24 0.188146
\(408\) 2.90760e24 0.459477
\(409\) 3.40224e24 0.525284 0.262642 0.964893i \(-0.415406\pi\)
0.262642 + 0.964893i \(0.415406\pi\)
\(410\) 4.32420e24 0.652317
\(411\) −2.27794e24 −0.335773
\(412\) −4.90116e24 −0.705952
\(413\) −1.81313e25 −2.55214
\(414\) −2.09603e24 −0.288333
\(415\) 5.16877e24 0.694913
\(416\) −1.20534e25 −1.58388
\(417\) −1.13697e24 −0.146035
\(418\) 9.56492e23 0.120090
\(419\) 2.53386e24 0.310992 0.155496 0.987837i \(-0.450302\pi\)
0.155496 + 0.987837i \(0.450302\pi\)
\(420\) −9.40180e24 −1.12809
\(421\) −1.07229e25 −1.25786 −0.628930 0.777462i \(-0.716507\pi\)
−0.628930 + 0.777462i \(0.716507\pi\)
\(422\) 1.71650e25 1.96868
\(423\) 5.93285e23 0.0665319
\(424\) 3.39416e24 0.372183
\(425\) 5.27342e24 0.565454
\(426\) 2.46144e24 0.258106
\(427\) −4.17644e24 −0.428293
\(428\) −1.23068e25 −1.23433
\(429\) 2.40057e24 0.235489
\(430\) −4.41030e24 −0.423173
\(431\) 1.57678e25 1.47992 0.739960 0.672651i \(-0.234845\pi\)
0.739960 + 0.672651i \(0.234845\pi\)
\(432\) −1.19448e24 −0.109669
\(433\) 7.64728e24 0.686866 0.343433 0.939177i \(-0.388410\pi\)
0.343433 + 0.939177i \(0.388410\pi\)
\(434\) −9.22325e24 −0.810460
\(435\) 8.43577e23 0.0725231
\(436\) 5.63794e24 0.474241
\(437\) 1.54569e24 0.127218
\(438\) 1.18636e25 0.955464
\(439\) −6.56625e24 −0.517493 −0.258747 0.965945i \(-0.583309\pi\)
−0.258747 + 0.965945i \(0.583309\pi\)
\(440\) 1.81530e24 0.140007
\(441\) 1.04049e25 0.785362
\(442\) −3.85274e25 −2.84615
\(443\) 7.45718e24 0.539187 0.269594 0.962974i \(-0.413111\pi\)
0.269594 + 0.962974i \(0.413111\pi\)
\(444\) −5.78876e24 −0.409683
\(445\) 1.04575e25 0.724451
\(446\) 1.15701e24 0.0784614
\(447\) 1.88639e24 0.125231
\(448\) 4.25560e25 2.76579
\(449\) −2.64059e25 −1.68020 −0.840101 0.542430i \(-0.817504\pi\)
−0.840101 + 0.542430i \(0.817504\pi\)
\(450\) 2.86966e24 0.178777
\(451\) 3.05978e24 0.186644
\(452\) −3.04401e25 −1.81816
\(453\) 2.61201e24 0.152771
\(454\) 5.41336e24 0.310053
\(455\) 3.05364e25 1.71281
\(456\) −1.16680e24 −0.0640962
\(457\) 1.31845e25 0.709347 0.354674 0.934990i \(-0.384592\pi\)
0.354674 + 0.934990i \(0.384592\pi\)
\(458\) −1.86590e25 −0.983256
\(459\) −5.99359e24 −0.309361
\(460\) 1.19679e25 0.605088
\(461\) −3.04421e25 −1.50770 −0.753851 0.657046i \(-0.771806\pi\)
−0.753851 + 0.657046i \(0.771806\pi\)
\(462\) −1.16747e25 −0.566429
\(463\) −3.64943e25 −1.73463 −0.867313 0.497764i \(-0.834155\pi\)
−0.867313 + 0.497764i \(0.834155\pi\)
\(464\) −1.90923e24 −0.0889072
\(465\) −2.95624e24 −0.134877
\(466\) 3.25529e25 1.45520
\(467\) 3.33264e25 1.45975 0.729875 0.683581i \(-0.239578\pi\)
0.729875 + 0.683581i \(0.239578\pi\)
\(468\) −1.19470e25 −0.512772
\(469\) −5.24310e25 −2.20519
\(470\) −5.94473e24 −0.245020
\(471\) −1.95058e25 −0.787890
\(472\) −1.74226e25 −0.689705
\(473\) −3.12071e24 −0.121080
\(474\) 3.92794e25 1.49373
\(475\) −2.11619e24 −0.0788798
\(476\) 1.06770e26 3.90108
\(477\) −6.99655e24 −0.250587
\(478\) 3.84934e25 1.35152
\(479\) 8.10234e24 0.278884 0.139442 0.990230i \(-0.455469\pi\)
0.139442 + 0.990230i \(0.455469\pi\)
\(480\) 1.87886e25 0.634020
\(481\) 1.88015e25 0.622033
\(482\) −3.42695e25 −1.11163
\(483\) −1.88662e25 −0.600050
\(484\) −3.72363e25 −1.16128
\(485\) −2.43526e25 −0.744729
\(486\) −3.26156e24 −0.0978095
\(487\) 4.90469e25 1.44240 0.721202 0.692725i \(-0.243590\pi\)
0.721202 + 0.692725i \(0.243590\pi\)
\(488\) −4.01318e24 −0.115745
\(489\) 3.42768e25 0.969541
\(490\) −1.04257e26 −2.89229
\(491\) 4.15501e25 1.13057 0.565285 0.824895i \(-0.308766\pi\)
0.565285 + 0.824895i \(0.308766\pi\)
\(492\) −1.52277e25 −0.406412
\(493\) −9.57996e24 −0.250795
\(494\) 1.54608e25 0.397033
\(495\) −3.74198e24 −0.0942652
\(496\) 6.69073e24 0.165347
\(497\) 2.21552e25 0.537144
\(498\) −3.19423e25 −0.759778
\(499\) −2.09237e25 −0.488297 −0.244148 0.969738i \(-0.578508\pi\)
−0.244148 + 0.969738i \(0.578508\pi\)
\(500\) −6.29655e25 −1.44174
\(501\) −4.60910e25 −1.03552
\(502\) −2.68660e24 −0.0592267
\(503\) −8.92504e25 −1.93070 −0.965349 0.260963i \(-0.915960\pi\)
−0.965349 + 0.260963i \(0.915960\pi\)
\(504\) 1.42417e25 0.302323
\(505\) 6.28519e25 1.30933
\(506\) 1.48611e25 0.303823
\(507\) 1.00281e25 0.201207
\(508\) 2.04770e25 0.403238
\(509\) 7.25766e25 1.40274 0.701371 0.712797i \(-0.252572\pi\)
0.701371 + 0.712797i \(0.252572\pi\)
\(510\) 6.00559e25 1.13930
\(511\) 1.06784e26 1.98842
\(512\) −5.79584e25 −1.05938
\(513\) 2.40519e24 0.0431554
\(514\) 7.83067e25 1.37927
\(515\) −2.48137e25 −0.429064
\(516\) 1.55309e25 0.263649
\(517\) −4.20646e24 −0.0701063
\(518\) −9.14369e25 −1.49620
\(519\) −1.05574e25 −0.169617
\(520\) 2.93427e25 0.462880
\(521\) −4.13657e25 −0.640741 −0.320370 0.947292i \(-0.603807\pi\)
−0.320370 + 0.947292i \(0.603807\pi\)
\(522\) −5.21318e24 −0.0792926
\(523\) −1.17484e26 −1.75475 −0.877373 0.479810i \(-0.840706\pi\)
−0.877373 + 0.479810i \(0.840706\pi\)
\(524\) 8.96607e25 1.31509
\(525\) 2.58296e25 0.372053
\(526\) −8.94438e25 −1.26528
\(527\) 3.35722e25 0.466422
\(528\) 8.46904e24 0.115561
\(529\) −5.06000e25 −0.678143
\(530\) 7.01056e25 0.922852
\(531\) 3.59140e25 0.464372
\(532\) −4.28463e25 −0.544193
\(533\) 4.94586e25 0.617068
\(534\) −6.46260e25 −0.792073
\(535\) −6.23071e25 −0.750200
\(536\) −5.03815e25 −0.595944
\(537\) 6.55796e25 0.762102
\(538\) 2.32135e26 2.65038
\(539\) −7.37718e25 −0.827555
\(540\) 1.86228e25 0.205260
\(541\) −4.86212e25 −0.526565 −0.263282 0.964719i \(-0.584805\pi\)
−0.263282 + 0.964719i \(0.584805\pi\)
\(542\) 1.06812e26 1.13665
\(543\) −7.81425e24 −0.0817126
\(544\) −2.13370e26 −2.19252
\(545\) 2.85439e25 0.288235
\(546\) −1.88710e26 −1.87269
\(547\) −3.16162e25 −0.308340 −0.154170 0.988044i \(-0.549270\pi\)
−0.154170 + 0.988044i \(0.549270\pi\)
\(548\) −8.03788e25 −0.770417
\(549\) 8.27258e24 0.0779298
\(550\) −2.03463e25 −0.188382
\(551\) 3.84439e24 0.0349854
\(552\) −1.81287e25 −0.162161
\(553\) 3.53551e26 3.10859
\(554\) 1.65847e26 1.43339
\(555\) −2.93075e25 −0.248997
\(556\) −4.01187e25 −0.335071
\(557\) −1.82242e26 −1.49632 −0.748158 0.663520i \(-0.769062\pi\)
−0.748158 + 0.663520i \(0.769062\pi\)
\(558\) 1.82692e25 0.147467
\(559\) −5.04434e25 −0.400306
\(560\) 1.07730e26 0.840525
\(561\) 4.24952e25 0.325982
\(562\) 3.07843e26 2.32185
\(563\) −3.15854e25 −0.234237 −0.117119 0.993118i \(-0.537366\pi\)
−0.117119 + 0.993118i \(0.537366\pi\)
\(564\) 2.09345e25 0.152655
\(565\) −1.54113e26 −1.10504
\(566\) 1.07605e26 0.758714
\(567\) −2.93571e25 −0.203551
\(568\) 2.12892e25 0.145161
\(569\) 1.47589e26 0.989666 0.494833 0.868988i \(-0.335229\pi\)
0.494833 + 0.868988i \(0.335229\pi\)
\(570\) −2.41001e25 −0.158931
\(571\) −1.69593e26 −1.09993 −0.549966 0.835187i \(-0.685359\pi\)
−0.549966 + 0.835187i \(0.685359\pi\)
\(572\) 8.47058e25 0.540320
\(573\) 2.32844e24 0.0146082
\(574\) −2.40531e26 −1.48425
\(575\) −3.28795e25 −0.199563
\(576\) −8.42938e25 −0.503248
\(577\) 7.03834e25 0.413333 0.206667 0.978411i \(-0.433738\pi\)
0.206667 + 0.978411i \(0.433738\pi\)
\(578\) −4.18080e26 −2.41516
\(579\) 7.40936e25 0.421050
\(580\) 2.97662e25 0.166401
\(581\) −2.87510e26 −1.58117
\(582\) 1.50495e26 0.814244
\(583\) 4.96064e25 0.264050
\(584\) 1.02610e26 0.537361
\(585\) −6.04856e25 −0.311653
\(586\) −3.07517e26 −1.55898
\(587\) 3.43137e25 0.171162 0.0855808 0.996331i \(-0.472725\pi\)
0.0855808 + 0.996331i \(0.472725\pi\)
\(588\) 3.67143e26 1.80198
\(589\) −1.34723e25 −0.0650650
\(590\) −3.59860e26 −1.71017
\(591\) 8.62089e25 0.403154
\(592\) 6.63302e25 0.305250
\(593\) 3.21922e26 1.45791 0.728955 0.684562i \(-0.240007\pi\)
0.728955 + 0.684562i \(0.240007\pi\)
\(594\) 2.31249e25 0.103064
\(595\) 5.40559e26 2.37100
\(596\) 6.65627e25 0.287337
\(597\) −2.60021e26 −1.10472
\(598\) 2.40216e26 1.00448
\(599\) 6.71773e25 0.276483 0.138241 0.990399i \(-0.455855\pi\)
0.138241 + 0.990399i \(0.455855\pi\)
\(600\) 2.48200e25 0.100546
\(601\) −1.65737e26 −0.660863 −0.330432 0.943830i \(-0.607194\pi\)
−0.330432 + 0.943830i \(0.607194\pi\)
\(602\) 2.45320e26 0.962869
\(603\) 1.03854e26 0.401244
\(604\) 9.21666e25 0.350528
\(605\) −1.88521e26 −0.705803
\(606\) −3.88415e26 −1.43155
\(607\) −1.07010e26 −0.388267 −0.194133 0.980975i \(-0.562189\pi\)
−0.194133 + 0.980975i \(0.562189\pi\)
\(608\) 8.56243e25 0.305853
\(609\) −4.69235e25 −0.165016
\(610\) −8.28914e25 −0.286996
\(611\) −6.79936e25 −0.231780
\(612\) −2.11488e26 −0.709818
\(613\) 1.05520e26 0.348708 0.174354 0.984683i \(-0.444216\pi\)
0.174354 + 0.984683i \(0.444216\pi\)
\(614\) −5.34917e26 −1.74055
\(615\) −7.70953e25 −0.247010
\(616\) −1.00975e26 −0.318565
\(617\) 5.70260e26 1.77159 0.885796 0.464074i \(-0.153613\pi\)
0.885796 + 0.464074i \(0.153613\pi\)
\(618\) 1.53345e26 0.469114
\(619\) 5.68518e26 1.71271 0.856353 0.516390i \(-0.172725\pi\)
0.856353 + 0.516390i \(0.172725\pi\)
\(620\) −1.04313e26 −0.309469
\(621\) 3.73697e25 0.109182
\(622\) −6.22172e26 −1.79020
\(623\) −5.81694e26 −1.64838
\(624\) 1.36894e26 0.382060
\(625\) −1.90812e26 −0.524501
\(626\) 6.39608e26 1.73164
\(627\) −1.70531e25 −0.0454739
\(628\) −6.88276e26 −1.80778
\(629\) 3.32826e26 0.861066
\(630\) 2.94159e26 0.749629
\(631\) −2.31534e26 −0.581214 −0.290607 0.956842i \(-0.593857\pi\)
−0.290607 + 0.956842i \(0.593857\pi\)
\(632\) 3.39731e26 0.840085
\(633\) −3.06032e26 −0.745472
\(634\) 1.18169e27 2.83566
\(635\) 1.03671e26 0.245080
\(636\) −2.46878e26 −0.574963
\(637\) −1.19245e27 −2.73600
\(638\) 3.69621e25 0.0835526
\(639\) −4.38845e25 −0.0977356
\(640\) 3.44162e26 0.755184
\(641\) 6.84136e26 1.47908 0.739539 0.673114i \(-0.235044\pi\)
0.739539 + 0.673114i \(0.235044\pi\)
\(642\) 3.85049e26 0.820225
\(643\) −4.41658e26 −0.927004 −0.463502 0.886096i \(-0.653407\pi\)
−0.463502 + 0.886096i \(0.653407\pi\)
\(644\) −6.65708e26 −1.37679
\(645\) 7.86303e25 0.160241
\(646\) 2.73689e26 0.549603
\(647\) 2.91842e26 0.577507 0.288754 0.957403i \(-0.406759\pi\)
0.288754 + 0.957403i \(0.406759\pi\)
\(648\) −2.82095e25 −0.0550089
\(649\) −2.54635e26 −0.489320
\(650\) −3.28879e26 −0.622815
\(651\) 1.64439e26 0.306893
\(652\) 1.20948e27 2.22457
\(653\) −9.04573e26 −1.63972 −0.819858 0.572567i \(-0.805948\pi\)
−0.819858 + 0.572567i \(0.805948\pi\)
\(654\) −1.76397e26 −0.315139
\(655\) 4.53936e26 0.799286
\(656\) 1.74486e26 0.302813
\(657\) −2.11515e26 −0.361801
\(658\) 3.30672e26 0.557509
\(659\) −2.65595e26 −0.441375 −0.220688 0.975345i \(-0.570830\pi\)
−0.220688 + 0.975345i \(0.570830\pi\)
\(660\) −1.32038e26 −0.216288
\(661\) 3.55026e26 0.573253 0.286627 0.958042i \(-0.407466\pi\)
0.286627 + 0.958042i \(0.407466\pi\)
\(662\) 3.39129e26 0.539777
\(663\) 6.86897e26 1.07774
\(664\) −2.76271e26 −0.427306
\(665\) −2.16923e26 −0.330751
\(666\) 1.81116e26 0.272239
\(667\) 5.97306e25 0.0885118
\(668\) −1.62635e27 −2.37595
\(669\) −2.06281e25 −0.0297106
\(670\) −1.04062e27 −1.47768
\(671\) −5.86536e25 −0.0821165
\(672\) −1.04511e27 −1.44262
\(673\) −3.58165e26 −0.487461 −0.243731 0.969843i \(-0.578371\pi\)
−0.243731 + 0.969843i \(0.578371\pi\)
\(674\) −1.76252e27 −2.36519
\(675\) −5.11627e25 −0.0676967
\(676\) 3.53848e26 0.461660
\(677\) 4.80665e26 0.618373 0.309186 0.951001i \(-0.399943\pi\)
0.309186 + 0.951001i \(0.399943\pi\)
\(678\) 9.52395e26 1.20819
\(679\) 1.35460e27 1.69452
\(680\) 5.19429e26 0.640754
\(681\) −9.65137e25 −0.117406
\(682\) −1.29531e26 −0.155389
\(683\) 9.71565e26 1.14941 0.574705 0.818360i \(-0.305117\pi\)
0.574705 + 0.818360i \(0.305117\pi\)
\(684\) 8.48689e25 0.0990183
\(685\) −4.06943e26 −0.468245
\(686\) 3.33785e27 3.78781
\(687\) 3.32668e26 0.372325
\(688\) −1.77960e26 −0.196441
\(689\) 8.01842e26 0.872984
\(690\) −3.74445e26 −0.402089
\(691\) −6.78820e26 −0.718975 −0.359487 0.933150i \(-0.617048\pi\)
−0.359487 + 0.933150i \(0.617048\pi\)
\(692\) −3.72527e26 −0.389179
\(693\) 2.08145e26 0.214487
\(694\) −2.09035e27 −2.12474
\(695\) −2.03114e26 −0.203650
\(696\) −4.50892e25 −0.0445949
\(697\) 8.75522e26 0.854193
\(698\) −3.52451e26 −0.339212
\(699\) −5.80379e26 −0.551034
\(700\) 9.11417e26 0.853661
\(701\) −1.64884e26 −0.152355 −0.0761776 0.997094i \(-0.524272\pi\)
−0.0761776 + 0.997094i \(0.524272\pi\)
\(702\) 3.73792e26 0.340744
\(703\) −1.33561e26 −0.120117
\(704\) 5.97653e26 0.530285
\(705\) 1.05987e26 0.0927807
\(706\) −2.32588e27 −2.00882
\(707\) −3.49610e27 −2.97920
\(708\) 1.26725e27 1.06548
\(709\) 1.52342e27 1.26381 0.631904 0.775047i \(-0.282274\pi\)
0.631904 + 0.775047i \(0.282274\pi\)
\(710\) 4.39724e26 0.359936
\(711\) −7.00305e26 −0.565622
\(712\) −5.58956e26 −0.445469
\(713\) −2.09321e26 −0.164612
\(714\) −3.34057e27 −2.59232
\(715\) 4.28850e26 0.328396
\(716\) 2.31402e27 1.74861
\(717\) −6.86291e26 −0.511772
\(718\) 1.60330e27 1.17987
\(719\) −2.54571e26 −0.184878 −0.0924390 0.995718i \(-0.529466\pi\)
−0.0924390 + 0.995718i \(0.529466\pi\)
\(720\) −2.13389e26 −0.152937
\(721\) 1.38025e27 0.976274
\(722\) 2.07435e27 1.44803
\(723\) 6.10985e26 0.420936
\(724\) −2.75731e26 −0.187486
\(725\) −8.17768e25 −0.0548806
\(726\) 1.16503e27 0.771684
\(727\) −2.12348e27 −1.38826 −0.694132 0.719847i \(-0.744212\pi\)
−0.694132 + 0.719847i \(0.744212\pi\)
\(728\) −1.63217e27 −1.05322
\(729\) 5.81497e25 0.0370370
\(730\) 2.11938e27 1.33242
\(731\) −8.92955e26 −0.554134
\(732\) 2.91903e26 0.178807
\(733\) −1.37369e27 −0.830619 −0.415309 0.909680i \(-0.636327\pi\)
−0.415309 + 0.909680i \(0.636327\pi\)
\(734\) 3.89538e26 0.232507
\(735\) 1.85878e27 1.09521
\(736\) 1.33035e27 0.773798
\(737\) −7.36336e26 −0.422800
\(738\) 4.76437e26 0.270066
\(739\) 2.36197e27 1.32176 0.660880 0.750492i \(-0.270183\pi\)
0.660880 + 0.750492i \(0.270183\pi\)
\(740\) −1.03413e27 −0.571314
\(741\) −2.75648e26 −0.150342
\(742\) −3.89959e27 −2.09982
\(743\) −2.96849e26 −0.157813 −0.0789063 0.996882i \(-0.525143\pi\)
−0.0789063 + 0.996882i \(0.525143\pi\)
\(744\) 1.58012e26 0.0829365
\(745\) 3.36995e26 0.174638
\(746\) −3.45115e27 −1.76581
\(747\) 5.69492e26 0.287701
\(748\) 1.49947e27 0.747952
\(749\) 3.46580e27 1.70697
\(750\) 1.97003e27 0.958056
\(751\) −2.22426e27 −1.06808 −0.534042 0.845458i \(-0.679327\pi\)
−0.534042 + 0.845458i \(0.679327\pi\)
\(752\) −2.39876e26 −0.113741
\(753\) 4.78989e25 0.0224271
\(754\) 5.97458e26 0.276236
\(755\) 4.66623e26 0.213044
\(756\) −1.03589e27 −0.467040
\(757\) −1.92178e26 −0.0855643 −0.0427822 0.999084i \(-0.513622\pi\)
−0.0427822 + 0.999084i \(0.513622\pi\)
\(758\) −5.72300e26 −0.251632
\(759\) −2.64956e26 −0.115047
\(760\) −2.08444e26 −0.0893840
\(761\) 1.93340e27 0.818778 0.409389 0.912360i \(-0.365742\pi\)
0.409389 + 0.912360i \(0.365742\pi\)
\(762\) −6.40674e26 −0.267957
\(763\) −1.58774e27 −0.655837
\(764\) 8.21607e25 0.0335179
\(765\) −1.07072e27 −0.431414
\(766\) −2.34522e26 −0.0933277
\(767\) −4.11594e27 −1.61776
\(768\) 1.18432e26 0.0459766
\(769\) −1.55642e27 −0.596796 −0.298398 0.954442i \(-0.596452\pi\)
−0.298398 + 0.954442i \(0.596452\pi\)
\(770\) −2.08562e27 −0.789903
\(771\) −1.39611e27 −0.522281
\(772\) 2.61444e27 0.966083
\(773\) 2.79822e27 1.02136 0.510678 0.859772i \(-0.329394\pi\)
0.510678 + 0.859772i \(0.329394\pi\)
\(774\) −4.85924e26 −0.175198
\(775\) 2.86580e26 0.102066
\(776\) 1.30165e27 0.457938
\(777\) 1.63021e27 0.566558
\(778\) 4.90017e27 1.68231
\(779\) −3.51342e26 −0.119158
\(780\) −2.13428e27 −0.715075
\(781\) 3.11146e26 0.102986
\(782\) 4.25234e27 1.39048
\(783\) 9.29448e25 0.0300254
\(784\) −4.20689e27 −1.34264
\(785\) −3.48462e27 −1.09874
\(786\) −2.80526e27 −0.873893
\(787\) 3.80897e27 1.17232 0.586161 0.810194i \(-0.300639\pi\)
0.586161 + 0.810194i \(0.300639\pi\)
\(788\) 3.04194e27 0.925021
\(789\) 1.59468e27 0.479116
\(790\) 7.01707e27 2.08304
\(791\) 8.57244e27 2.51436
\(792\) 2.00009e26 0.0579643
\(793\) −9.48081e26 −0.271488
\(794\) −4.66090e27 −1.31879
\(795\) −1.24990e27 −0.349452
\(796\) −9.17501e27 −2.53474
\(797\) 3.90140e26 0.106504 0.0532521 0.998581i \(-0.483041\pi\)
0.0532521 + 0.998581i \(0.483041\pi\)
\(798\) 1.34055e27 0.361624
\(799\) −1.20363e27 −0.320848
\(800\) −1.82138e27 −0.479784
\(801\) 1.15220e27 0.299930
\(802\) −3.63967e27 −0.936279
\(803\) 1.49966e27 0.381238
\(804\) 3.66455e27 0.920638
\(805\) −3.37036e27 −0.836787
\(806\) −2.09374e27 −0.513736
\(807\) −4.13869e27 −1.00361
\(808\) −3.35944e27 −0.805117
\(809\) −8.85420e26 −0.209719 −0.104860 0.994487i \(-0.533439\pi\)
−0.104860 + 0.994487i \(0.533439\pi\)
\(810\) −5.82662e26 −0.136398
\(811\) −2.17253e27 −0.502651 −0.251326 0.967903i \(-0.580866\pi\)
−0.251326 + 0.967903i \(0.580866\pi\)
\(812\) −1.65573e27 −0.378623
\(813\) −1.90433e27 −0.430410
\(814\) −1.28413e27 −0.286865
\(815\) 6.12338e27 1.35205
\(816\) 2.42332e27 0.528877
\(817\) 3.58338e26 0.0773007
\(818\) −3.75608e27 −0.800900
\(819\) 3.36448e27 0.709122
\(820\) −2.72036e27 −0.566754
\(821\) −2.60443e27 −0.536355 −0.268177 0.963370i \(-0.586421\pi\)
−0.268177 + 0.963370i \(0.586421\pi\)
\(822\) 2.51485e27 0.511953
\(823\) 3.71169e27 0.746919 0.373459 0.927647i \(-0.378172\pi\)
0.373459 + 0.927647i \(0.378172\pi\)
\(824\) 1.32629e27 0.263834
\(825\) 3.62749e26 0.0713336
\(826\) 2.00170e28 3.89124
\(827\) 5.98762e27 1.15067 0.575336 0.817917i \(-0.304871\pi\)
0.575336 + 0.817917i \(0.304871\pi\)
\(828\) 1.31862e27 0.250513
\(829\) 9.15991e27 1.72038 0.860188 0.509977i \(-0.170346\pi\)
0.860188 + 0.509977i \(0.170346\pi\)
\(830\) −5.70632e27 −1.05953
\(831\) −2.95685e27 −0.542774
\(832\) 9.66052e27 1.75319
\(833\) −2.11090e28 −3.78738
\(834\) 1.25521e27 0.222659
\(835\) −8.23393e27 −1.44406
\(836\) −6.01731e26 −0.104338
\(837\) −3.25717e26 −0.0558404
\(838\) −2.79738e27 −0.474169
\(839\) −1.90995e27 −0.320099 −0.160049 0.987109i \(-0.551165\pi\)
−0.160049 + 0.987109i \(0.551165\pi\)
\(840\) 2.54421e27 0.421598
\(841\) −5.95470e27 −0.975659
\(842\) 1.18381e28 1.91786
\(843\) −5.48847e27 −0.879203
\(844\) −1.07985e28 −1.71046
\(845\) 1.79147e27 0.280589
\(846\) −6.54987e26 −0.101441
\(847\) 1.04864e28 1.60595
\(848\) 2.82884e27 0.428398
\(849\) −1.91848e27 −0.287298
\(850\) −5.82185e27 −0.862147
\(851\) −2.07515e27 −0.303892
\(852\) −1.54849e27 −0.224250
\(853\) 2.96003e27 0.423917 0.211958 0.977279i \(-0.432016\pi\)
0.211958 + 0.977279i \(0.432016\pi\)
\(854\) 4.61079e27 0.653018
\(855\) 4.29676e26 0.0601815
\(856\) 3.33032e27 0.461302
\(857\) 6.39793e27 0.876439 0.438219 0.898868i \(-0.355609\pi\)
0.438219 + 0.898868i \(0.355609\pi\)
\(858\) −2.65023e27 −0.359050
\(859\) 1.49963e27 0.200932 0.100466 0.994941i \(-0.467967\pi\)
0.100466 + 0.994941i \(0.467967\pi\)
\(860\) 2.77452e27 0.367666
\(861\) 4.28838e27 0.562035
\(862\) −1.74077e28 −2.25643
\(863\) −1.16811e28 −1.49755 −0.748774 0.662825i \(-0.769357\pi\)
−0.748774 + 0.662825i \(0.769357\pi\)
\(864\) 2.07012e27 0.262491
\(865\) −1.88604e27 −0.236536
\(866\) −8.44260e27 −1.04726
\(867\) 7.45387e27 0.914536
\(868\) 5.80236e27 0.704153
\(869\) 4.96525e27 0.596009
\(870\) −9.31309e26 −0.110576
\(871\) −1.19022e28 −1.39783
\(872\) −1.52567e27 −0.177237
\(873\) −2.68315e27 −0.308326
\(874\) −1.70644e27 −0.193969
\(875\) 1.77321e28 1.99381
\(876\) −7.46344e27 −0.830137
\(877\) 3.36367e27 0.370098 0.185049 0.982729i \(-0.440756\pi\)
0.185049 + 0.982729i \(0.440756\pi\)
\(878\) 7.24914e27 0.789021
\(879\) 5.48265e27 0.590332
\(880\) 1.51295e27 0.161154
\(881\) −8.62862e27 −0.909222 −0.454611 0.890690i \(-0.650222\pi\)
−0.454611 + 0.890690i \(0.650222\pi\)
\(882\) −1.14870e28 −1.19744
\(883\) 3.09180e27 0.318849 0.159425 0.987210i \(-0.449036\pi\)
0.159425 + 0.987210i \(0.449036\pi\)
\(884\) 2.42376e28 2.47283
\(885\) 6.41587e27 0.647581
\(886\) −8.23273e27 −0.822098
\(887\) 1.06571e28 1.05285 0.526423 0.850223i \(-0.323533\pi\)
0.526423 + 0.850223i \(0.323533\pi\)
\(888\) 1.56649e27 0.153110
\(889\) −5.76666e27 −0.557645
\(890\) −1.15451e28 −1.10457
\(891\) −4.12289e26 −0.0390268
\(892\) −7.27876e26 −0.0681697
\(893\) 4.83011e26 0.0447577
\(894\) −2.08258e27 −0.190939
\(895\) 1.17155e28 1.06277
\(896\) −1.91438e28 −1.71831
\(897\) −4.28277e27 −0.380361
\(898\) 2.91522e28 2.56180
\(899\) −5.20616e26 −0.0452690
\(900\) −1.80531e27 −0.155327
\(901\) 1.41943e28 1.20845
\(902\) −3.37800e27 −0.284575
\(903\) −4.37377e27 −0.364605
\(904\) 8.23735e27 0.679497
\(905\) −1.39598e27 −0.113951
\(906\) −2.88366e27 −0.232930
\(907\) −1.19240e28 −0.953133 −0.476567 0.879138i \(-0.658119\pi\)
−0.476567 + 0.879138i \(0.658119\pi\)
\(908\) −3.40555e27 −0.269384
\(909\) 6.92498e27 0.542078
\(910\) −3.37122e28 −2.61152
\(911\) −1.44243e28 −1.10578 −0.552890 0.833254i \(-0.686475\pi\)
−0.552890 + 0.833254i \(0.686475\pi\)
\(912\) −9.72465e26 −0.0737774
\(913\) −4.03777e27 −0.303158
\(914\) −1.45557e28 −1.08154
\(915\) 1.47785e27 0.108675
\(916\) 1.17384e28 0.854284
\(917\) −2.52499e28 −1.81866
\(918\) 6.61692e27 0.471683
\(919\) −2.45481e28 −1.73189 −0.865946 0.500138i \(-0.833283\pi\)
−0.865946 + 0.500138i \(0.833283\pi\)
\(920\) −3.23861e27 −0.226138
\(921\) 9.53693e27 0.659086
\(922\) 3.36080e28 2.29879
\(923\) 5.02940e27 0.340486
\(924\) 7.34455e27 0.492132
\(925\) 2.84108e27 0.188425
\(926\) 4.02897e28 2.64478
\(927\) −2.73395e27 −0.177637
\(928\) 3.30881e27 0.212797
\(929\) 2.24631e27 0.142995 0.0714974 0.997441i \(-0.477222\pi\)
0.0714974 + 0.997441i \(0.477222\pi\)
\(930\) 3.26369e27 0.205647
\(931\) 8.47091e27 0.528333
\(932\) −2.04790e28 −1.26432
\(933\) 1.10926e28 0.677886
\(934\) −3.67924e28 −2.22568
\(935\) 7.59156e27 0.454591
\(936\) 3.23296e27 0.191637
\(937\) 5.69436e27 0.334132 0.167066 0.985946i \(-0.446571\pi\)
0.167066 + 0.985946i \(0.446571\pi\)
\(938\) 5.78838e28 3.36225
\(939\) −1.14034e28 −0.655712
\(940\) 3.73984e27 0.212882
\(941\) −4.99691e27 −0.281579 −0.140790 0.990040i \(-0.544964\pi\)
−0.140790 + 0.990040i \(0.544964\pi\)
\(942\) 2.15344e28 1.20130
\(943\) −5.45884e27 −0.301466
\(944\) −1.45207e28 −0.793879
\(945\) −5.24450e27 −0.283858
\(946\) 3.44526e27 0.184610
\(947\) −1.38781e28 −0.736214 −0.368107 0.929783i \(-0.619994\pi\)
−0.368107 + 0.929783i \(0.619994\pi\)
\(948\) −2.47107e28 −1.29780
\(949\) 2.42407e28 1.26042
\(950\) 2.33628e27 0.120268
\(951\) −2.10681e28 −1.07377
\(952\) −2.88929e28 −1.45794
\(953\) −3.71993e27 −0.185846 −0.0929228 0.995673i \(-0.529621\pi\)
−0.0929228 + 0.995673i \(0.529621\pi\)
\(954\) 7.72419e27 0.382070
\(955\) 4.15965e26 0.0203716
\(956\) −2.42163e28 −1.17424
\(957\) −6.58989e26 −0.0316384
\(958\) −8.94498e27 −0.425213
\(959\) 2.26360e28 1.06542
\(960\) −1.50587e28 −0.701794
\(961\) −1.98462e28 −0.915810
\(962\) −2.07568e28 −0.948414
\(963\) −6.86496e27 −0.310591
\(964\) 2.15590e28 0.965822
\(965\) 1.32364e28 0.587167
\(966\) 2.08283e28 0.914895
\(967\) 1.20501e28 0.524132 0.262066 0.965050i \(-0.415596\pi\)
0.262066 + 0.965050i \(0.415596\pi\)
\(968\) 1.00765e28 0.434002
\(969\) −4.87956e27 −0.208115
\(970\) 2.68853e28 1.13549
\(971\) −8.01489e27 −0.335208 −0.167604 0.985854i \(-0.553603\pi\)
−0.167604 + 0.985854i \(0.553603\pi\)
\(972\) 2.05185e27 0.0849800
\(973\) 1.12981e28 0.463375
\(974\) −5.41478e28 −2.19923
\(975\) 5.86351e27 0.235838
\(976\) −3.34476e27 −0.133227
\(977\) 3.97949e28 1.56975 0.784873 0.619656i \(-0.212728\pi\)
0.784873 + 0.619656i \(0.212728\pi\)
\(978\) −3.78416e28 −1.47826
\(979\) −8.16927e27 −0.316044
\(980\) 6.55882e28 2.51292
\(981\) 3.14495e27 0.119332
\(982\) −4.58713e28 −1.72378
\(983\) 1.67921e28 0.624950 0.312475 0.949926i \(-0.398842\pi\)
0.312475 + 0.949926i \(0.398842\pi\)
\(984\) 4.12075e27 0.151888
\(985\) 1.54008e28 0.562210
\(986\) 1.05763e28 0.382386
\(987\) −5.89549e27 −0.211109
\(988\) −9.72642e27 −0.344955
\(989\) 5.56753e27 0.195568
\(990\) 4.13114e27 0.143726
\(991\) 1.18105e28 0.406975 0.203488 0.979078i \(-0.434772\pi\)
0.203488 + 0.979078i \(0.434772\pi\)
\(992\) −1.15955e28 −0.395755
\(993\) −6.04627e27 −0.204395
\(994\) −2.44594e28 −0.818983
\(995\) −4.64514e28 −1.54056
\(996\) 2.00949e28 0.660119
\(997\) −4.34119e27 −0.141255 −0.0706277 0.997503i \(-0.522500\pi\)
−0.0706277 + 0.997503i \(0.522500\pi\)
\(998\) 2.30998e28 0.744506
\(999\) −3.22908e27 −0.103088
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 \(a_p\))