Properties

Label 6.12.a.a.1.1
Level 6
Weight 12
Character 6.1
Self dual Yes
Analytic conductor 4.610
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6 = 2 \cdot 3 \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 6.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(4.61005908336\)
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

\(f(q)\) \(=\) \(q-32.0000 q^{2} -243.000 q^{3} +1024.00 q^{4} +5766.00 q^{5} +7776.00 q^{6} +72464.0 q^{7} -32768.0 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-32.0000 q^{2} -243.000 q^{3} +1024.00 q^{4} +5766.00 q^{5} +7776.00 q^{6} +72464.0 q^{7} -32768.0 q^{8} +59049.0 q^{9} -184512. q^{10} -408948. q^{11} -248832. q^{12} +1.36756e6 q^{13} -2.31885e6 q^{14} -1.40114e6 q^{15} +1.04858e6 q^{16} +5.42291e6 q^{17} -1.88957e6 q^{18} +1.51661e7 q^{19} +5.90438e6 q^{20} -1.76088e7 q^{21} +1.30863e7 q^{22} -5.21941e7 q^{23} +7.96262e6 q^{24} -1.55814e7 q^{25} -4.37619e7 q^{26} -1.43489e7 q^{27} +7.42031e7 q^{28} +1.18581e8 q^{29} +4.48364e7 q^{30} -5.76524e7 q^{31} -3.35544e7 q^{32} +9.93744e7 q^{33} -1.73533e8 q^{34} +4.17827e8 q^{35} +6.04662e7 q^{36} -3.75985e8 q^{37} -4.85315e8 q^{38} -3.32317e8 q^{39} -1.88940e8 q^{40} +8.56316e8 q^{41} +5.63480e8 q^{42} -1.24519e9 q^{43} -4.18763e8 q^{44} +3.40477e8 q^{45} +1.67021e9 q^{46} -1.30676e9 q^{47} -2.54804e8 q^{48} +3.27370e9 q^{49} +4.98604e8 q^{50} -1.31777e9 q^{51} +1.40038e9 q^{52} +4.09556e8 q^{53} +4.59165e8 q^{54} -2.35799e9 q^{55} -2.37450e9 q^{56} -3.68536e9 q^{57} -3.79460e9 q^{58} -2.88287e9 q^{59} -1.43477e9 q^{60} +5.73177e9 q^{61} +1.84488e9 q^{62} +4.27893e9 q^{63} +1.07374e9 q^{64} +7.88534e9 q^{65} -3.17998e9 q^{66} +3.89327e9 q^{67} +5.55306e9 q^{68} +1.26832e10 q^{69} -1.33705e10 q^{70} -9.07589e9 q^{71} -1.93492e9 q^{72} -1.55718e10 q^{73} +1.20315e10 q^{74} +3.78627e9 q^{75} +1.55301e10 q^{76} -2.96340e10 q^{77} +1.06341e10 q^{78} -3.01968e10 q^{79} +6.04609e9 q^{80} +3.48678e9 q^{81} -2.74021e10 q^{82} +2.31353e10 q^{83} -1.80314e10 q^{84} +3.12685e10 q^{85} +3.98461e10 q^{86} -2.88152e10 q^{87} +1.34004e10 q^{88} -2.56148e10 q^{89} -1.08952e10 q^{90} +9.90987e10 q^{91} -5.34467e10 q^{92} +1.40095e10 q^{93} +4.18164e10 q^{94} +8.74477e10 q^{95} +8.15373e9 q^{96} -6.19376e10 q^{97} -1.04759e11 q^{98} -2.41480e10 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −32.0000 −0.707107
\(3\) −243.000 −0.577350
\(4\) 1024.00 0.500000
\(5\) 5766.00 0.825163 0.412581 0.910921i \(-0.364627\pi\)
0.412581 + 0.910921i \(0.364627\pi\)
\(6\) 7776.00 0.408248
\(7\) 72464.0 1.62961 0.814804 0.579737i \(-0.196845\pi\)
0.814804 + 0.579737i \(0.196845\pi\)
\(8\) −32768.0 −0.353553
\(9\) 59049.0 0.333333
\(10\) −184512. −0.583478
\(11\) −408948. −0.765611 −0.382806 0.923829i \(-0.625042\pi\)
−0.382806 + 0.923829i \(0.625042\pi\)
\(12\) −248832. −0.288675
\(13\) 1.36756e6 1.02154 0.510772 0.859716i \(-0.329360\pi\)
0.510772 + 0.859716i \(0.329360\pi\)
\(14\) −2.31885e6 −1.15231
\(15\) −1.40114e6 −0.476408
\(16\) 1.04858e6 0.250000
\(17\) 5.42291e6 0.926326 0.463163 0.886273i \(-0.346715\pi\)
0.463163 + 0.886273i \(0.346715\pi\)
\(18\) −1.88957e6 −0.235702
\(19\) 1.51661e7 1.40517 0.702585 0.711599i \(-0.252029\pi\)
0.702585 + 0.711599i \(0.252029\pi\)
\(20\) 5.90438e6 0.412581
\(21\) −1.76088e7 −0.940854
\(22\) 1.30863e7 0.541369
\(23\) −5.21941e7 −1.69090 −0.845450 0.534054i \(-0.820668\pi\)
−0.845450 + 0.534054i \(0.820668\pi\)
\(24\) 7.96262e6 0.204124
\(25\) −1.55814e7 −0.319106
\(26\) −4.37619e7 −0.722341
\(27\) −1.43489e7 −0.192450
\(28\) 7.42031e7 0.814804
\(29\) 1.18581e8 1.07356 0.536780 0.843722i \(-0.319640\pi\)
0.536780 + 0.843722i \(0.319640\pi\)
\(30\) 4.48364e7 0.336871
\(31\) −5.76524e7 −0.361683 −0.180842 0.983512i \(-0.557882\pi\)
−0.180842 + 0.983512i \(0.557882\pi\)
\(32\) −3.35544e7 −0.176777
\(33\) 9.93744e7 0.442026
\(34\) −1.73533e8 −0.655011
\(35\) 4.17827e8 1.34469
\(36\) 6.04662e7 0.166667
\(37\) −3.75985e8 −0.891377 −0.445688 0.895188i \(-0.647041\pi\)
−0.445688 + 0.895188i \(0.647041\pi\)
\(38\) −4.85315e8 −0.993606
\(39\) −3.32317e8 −0.589789
\(40\) −1.88940e8 −0.291739
\(41\) 8.56316e8 1.15431 0.577156 0.816634i \(-0.304163\pi\)
0.577156 + 0.816634i \(0.304163\pi\)
\(42\) 5.63480e8 0.665285
\(43\) −1.24519e9 −1.29169 −0.645846 0.763468i \(-0.723495\pi\)
−0.645846 + 0.763468i \(0.723495\pi\)
\(44\) −4.18763e8 −0.382806
\(45\) 3.40477e8 0.275054
\(46\) 1.67021e9 1.19565
\(47\) −1.30676e9 −0.831110 −0.415555 0.909568i \(-0.636413\pi\)
−0.415555 + 0.909568i \(0.636413\pi\)
\(48\) −2.54804e8 −0.144338
\(49\) 3.27370e9 1.65562
\(50\) 4.98604e8 0.225642
\(51\) −1.31777e9 −0.534814
\(52\) 1.40038e9 0.510772
\(53\) 4.09556e8 0.134523 0.0672615 0.997735i \(-0.478574\pi\)
0.0672615 + 0.997735i \(0.478574\pi\)
\(54\) 4.59165e8 0.136083
\(55\) −2.35799e9 −0.631754
\(56\) −2.37450e9 −0.576153
\(57\) −3.68536e9 −0.811276
\(58\) −3.79460e9 −0.759122
\(59\) −2.88287e9 −0.524975 −0.262487 0.964935i \(-0.584543\pi\)
−0.262487 + 0.964935i \(0.584543\pi\)
\(60\) −1.43477e9 −0.238204
\(61\) 5.73177e9 0.868909 0.434455 0.900694i \(-0.356941\pi\)
0.434455 + 0.900694i \(0.356941\pi\)
\(62\) 1.84488e9 0.255749
\(63\) 4.27893e9 0.543203
\(64\) 1.07374e9 0.125000
\(65\) 7.88534e9 0.842941
\(66\) −3.17998e9 −0.312559
\(67\) 3.89327e9 0.352292 0.176146 0.984364i \(-0.443637\pi\)
0.176146 + 0.984364i \(0.443637\pi\)
\(68\) 5.55306e9 0.463163
\(69\) 1.26832e10 0.976242
\(70\) −1.33705e10 −0.950841
\(71\) −9.07589e9 −0.596992 −0.298496 0.954411i \(-0.596485\pi\)
−0.298496 + 0.954411i \(0.596485\pi\)
\(72\) −1.93492e9 −0.117851
\(73\) −1.55718e10 −0.879152 −0.439576 0.898206i \(-0.644871\pi\)
−0.439576 + 0.898206i \(0.644871\pi\)
\(74\) 1.20315e10 0.630298
\(75\) 3.78627e9 0.184236
\(76\) 1.55301e10 0.702585
\(77\) −2.96340e10 −1.24765
\(78\) 1.06341e10 0.417044
\(79\) −3.01968e10 −1.10411 −0.552054 0.833809i \(-0.686156\pi\)
−0.552054 + 0.833809i \(0.686156\pi\)
\(80\) 6.04609e9 0.206291
\(81\) 3.48678e9 0.111111
\(82\) −2.74021e10 −0.816221
\(83\) 2.31353e10 0.644681 0.322340 0.946624i \(-0.395530\pi\)
0.322340 + 0.946624i \(0.395530\pi\)
\(84\) −1.80314e10 −0.470427
\(85\) 3.12685e10 0.764369
\(86\) 3.98461e10 0.913364
\(87\) −2.88152e10 −0.619821
\(88\) 1.34004e10 0.270684
\(89\) −2.56148e10 −0.486235 −0.243118 0.969997i \(-0.578170\pi\)
−0.243118 + 0.969997i \(0.578170\pi\)
\(90\) −1.08952e10 −0.194493
\(91\) 9.90987e10 1.66472
\(92\) −5.34467e10 −0.845450
\(93\) 1.40095e10 0.208818
\(94\) 4.18164e10 0.587684
\(95\) 8.74477e10 1.15949
\(96\) 8.15373e9 0.102062
\(97\) −6.19376e10 −0.732335 −0.366167 0.930549i \(-0.619330\pi\)
−0.366167 + 0.930549i \(0.619330\pi\)
\(98\) −1.04759e11 −1.17070
\(99\) −2.41480e10 −0.255204
\(100\) −1.59553e10 −0.159553
\(101\) −9.49642e10 −0.899067 −0.449534 0.893263i \(-0.648410\pi\)
−0.449534 + 0.893263i \(0.648410\pi\)
\(102\) 4.21686e10 0.378171
\(103\) 5.43719e10 0.462136 0.231068 0.972938i \(-0.425778\pi\)
0.231068 + 0.972938i \(0.425778\pi\)
\(104\) −4.48121e10 −0.361171
\(105\) −1.01532e11 −0.776358
\(106\) −1.31058e10 −0.0951221
\(107\) 5.71348e9 0.0393813 0.0196906 0.999806i \(-0.493732\pi\)
0.0196906 + 0.999806i \(0.493732\pi\)
\(108\) −1.46933e10 −0.0962250
\(109\) −4.96724e10 −0.309221 −0.154611 0.987975i \(-0.549412\pi\)
−0.154611 + 0.987975i \(0.549412\pi\)
\(110\) 7.54558e10 0.446717
\(111\) 9.13644e10 0.514637
\(112\) 7.59840e10 0.407402
\(113\) 1.77803e11 0.907834 0.453917 0.891044i \(-0.350026\pi\)
0.453917 + 0.891044i \(0.350026\pi\)
\(114\) 1.17932e11 0.573659
\(115\) −3.00951e11 −1.39527
\(116\) 1.21427e11 0.536780
\(117\) 8.07529e10 0.340515
\(118\) 9.22517e10 0.371213
\(119\) 3.92966e11 1.50955
\(120\) 4.59125e10 0.168436
\(121\) −1.18073e11 −0.413839
\(122\) −1.83417e11 −0.614412
\(123\) −2.08085e11 −0.666442
\(124\) −5.90361e10 −0.180842
\(125\) −3.71385e11 −1.08848
\(126\) −1.36926e11 −0.384102
\(127\) −4.73708e11 −1.27230 −0.636150 0.771565i \(-0.719474\pi\)
−0.636150 + 0.771565i \(0.719474\pi\)
\(128\) −3.43597e10 −0.0883883
\(129\) 3.02581e11 0.745758
\(130\) −2.52331e11 −0.596049
\(131\) 1.68574e11 0.381767 0.190883 0.981613i \(-0.438865\pi\)
0.190883 + 0.981613i \(0.438865\pi\)
\(132\) 1.01759e11 0.221013
\(133\) 1.09900e12 2.28988
\(134\) −1.24585e11 −0.249108
\(135\) −8.27358e10 −0.158803
\(136\) −1.77698e11 −0.327506
\(137\) −8.01479e11 −1.41883 −0.709413 0.704793i \(-0.751040\pi\)
−0.709413 + 0.704793i \(0.751040\pi\)
\(138\) −4.05861e11 −0.690307
\(139\) 5.24839e11 0.857916 0.428958 0.903324i \(-0.358881\pi\)
0.428958 + 0.903324i \(0.358881\pi\)
\(140\) 4.27855e11 0.672346
\(141\) 3.17543e11 0.479842
\(142\) 2.90428e11 0.422137
\(143\) −5.59260e11 −0.782106
\(144\) 6.19174e10 0.0833333
\(145\) 6.83739e11 0.885862
\(146\) 4.98298e11 0.621654
\(147\) −7.95510e11 −0.955873
\(148\) −3.85009e11 −0.445688
\(149\) 1.25702e12 1.40223 0.701113 0.713051i \(-0.252687\pi\)
0.701113 + 0.713051i \(0.252687\pi\)
\(150\) −1.21161e11 −0.130275
\(151\) −4.92117e11 −0.510147 −0.255074 0.966922i \(-0.582100\pi\)
−0.255074 + 0.966922i \(0.582100\pi\)
\(152\) −4.96963e11 −0.496803
\(153\) 3.20218e11 0.308775
\(154\) 9.48288e11 0.882219
\(155\) −3.32424e11 −0.298447
\(156\) −3.40292e11 −0.294895
\(157\) −9.97092e11 −0.834232 −0.417116 0.908853i \(-0.636959\pi\)
−0.417116 + 0.908853i \(0.636959\pi\)
\(158\) 9.66296e11 0.780722
\(159\) −9.95222e10 −0.0776669
\(160\) −1.93475e11 −0.145870
\(161\) −3.78219e12 −2.75550
\(162\) −1.11577e11 −0.0785674
\(163\) −4.84142e11 −0.329565 −0.164782 0.986330i \(-0.552692\pi\)
−0.164782 + 0.986330i \(0.552692\pi\)
\(164\) 8.76868e11 0.577156
\(165\) 5.72993e11 0.364743
\(166\) −7.40328e11 −0.455858
\(167\) 2.31537e12 1.37937 0.689685 0.724110i \(-0.257749\pi\)
0.689685 + 0.724110i \(0.257749\pi\)
\(168\) 5.77004e11 0.332642
\(169\) 7.80545e10 0.0435533
\(170\) −1.00059e12 −0.540491
\(171\) 8.95543e11 0.468390
\(172\) −1.27507e12 −0.645846
\(173\) 3.37157e12 1.65416 0.827081 0.562083i \(-0.190000\pi\)
0.827081 + 0.562083i \(0.190000\pi\)
\(174\) 9.22087e11 0.438279
\(175\) −1.12909e12 −0.520018
\(176\) −4.28813e11 −0.191403
\(177\) 7.00537e11 0.303094
\(178\) 8.19674e11 0.343820
\(179\) 1.64598e12 0.669472 0.334736 0.942312i \(-0.391353\pi\)
0.334736 + 0.942312i \(0.391353\pi\)
\(180\) 3.48648e11 0.137527
\(181\) 2.74217e12 1.04921 0.524605 0.851346i \(-0.324213\pi\)
0.524605 + 0.851346i \(0.324213\pi\)
\(182\) −3.17116e12 −1.17713
\(183\) −1.39282e12 −0.501665
\(184\) 1.71030e12 0.597824
\(185\) −2.16793e12 −0.735531
\(186\) −4.48305e11 −0.147656
\(187\) −2.21769e12 −0.709205
\(188\) −1.33812e12 −0.415555
\(189\) −1.03978e12 −0.313618
\(190\) −2.79833e12 −0.819886
\(191\) 4.08409e12 1.16255 0.581275 0.813707i \(-0.302554\pi\)
0.581275 + 0.813707i \(0.302554\pi\)
\(192\) −2.60919e11 −0.0721688
\(193\) −4.47239e12 −1.20219 −0.601097 0.799176i \(-0.705269\pi\)
−0.601097 + 0.799176i \(0.705269\pi\)
\(194\) 1.98200e12 0.517839
\(195\) −1.91614e12 −0.486672
\(196\) 3.35227e12 0.827811
\(197\) −7.37025e12 −1.76977 −0.884887 0.465805i \(-0.845765\pi\)
−0.884887 + 0.465805i \(0.845765\pi\)
\(198\) 7.72735e11 0.180456
\(199\) 2.69308e12 0.611728 0.305864 0.952075i \(-0.401055\pi\)
0.305864 + 0.952075i \(0.401055\pi\)
\(200\) 5.10570e11 0.112821
\(201\) −9.46065e11 −0.203396
\(202\) 3.03885e12 0.635736
\(203\) 8.59286e12 1.74948
\(204\) −1.34939e12 −0.267407
\(205\) 4.93752e12 0.952495
\(206\) −1.73990e12 −0.326780
\(207\) −3.08201e12 −0.563634
\(208\) 1.43399e12 0.255386
\(209\) −6.20215e12 −1.07581
\(210\) 3.24903e12 0.548968
\(211\) 6.63458e12 1.09209 0.546047 0.837755i \(-0.316132\pi\)
0.546047 + 0.837755i \(0.316132\pi\)
\(212\) 4.19386e11 0.0672615
\(213\) 2.20544e12 0.344673
\(214\) −1.82831e11 −0.0278468
\(215\) −7.17976e12 −1.06586
\(216\) 4.70185e11 0.0680414
\(217\) −4.17772e12 −0.589401
\(218\) 1.58952e12 0.218652
\(219\) 3.78395e12 0.507578
\(220\) −2.41459e12 −0.315877
\(221\) 7.41615e12 0.946283
\(222\) −2.92366e12 −0.363903
\(223\) −5.99559e12 −0.728040 −0.364020 0.931391i \(-0.618596\pi\)
−0.364020 + 0.931391i \(0.618596\pi\)
\(224\) −2.43149e12 −0.288077
\(225\) −9.20064e11 −0.106369
\(226\) −5.68968e12 −0.641936
\(227\) −7.74930e12 −0.853337 −0.426668 0.904408i \(-0.640313\pi\)
−0.426668 + 0.904408i \(0.640313\pi\)
\(228\) −3.77381e12 −0.405638
\(229\) 3.75804e12 0.394336 0.197168 0.980370i \(-0.436826\pi\)
0.197168 + 0.980370i \(0.436826\pi\)
\(230\) 9.63043e12 0.986604
\(231\) 7.20106e12 0.720329
\(232\) −3.88567e12 −0.379561
\(233\) 9.02676e12 0.861141 0.430570 0.902557i \(-0.358312\pi\)
0.430570 + 0.902557i \(0.358312\pi\)
\(234\) −2.58409e12 −0.240780
\(235\) −7.53479e12 −0.685801
\(236\) −2.95206e12 −0.262487
\(237\) 7.33781e12 0.637457
\(238\) −1.25749e13 −1.06741
\(239\) −4.02269e12 −0.333679 −0.166839 0.985984i \(-0.553356\pi\)
−0.166839 + 0.985984i \(0.553356\pi\)
\(240\) −1.46920e12 −0.119102
\(241\) −1.49997e13 −1.18847 −0.594235 0.804292i \(-0.702545\pi\)
−0.594235 + 0.804292i \(0.702545\pi\)
\(242\) 3.77834e12 0.292629
\(243\) −8.47289e11 −0.0641500
\(244\) 5.86933e12 0.434455
\(245\) 1.88762e13 1.36616
\(246\) 6.65871e12 0.471246
\(247\) 2.07405e13 1.43544
\(248\) 1.88915e12 0.127874
\(249\) −5.62187e12 −0.372207
\(250\) 1.18843e13 0.769670
\(251\) −1.46817e13 −0.930187 −0.465094 0.885262i \(-0.653979\pi\)
−0.465094 + 0.885262i \(0.653979\pi\)
\(252\) 4.38162e12 0.271601
\(253\) 2.13447e13 1.29457
\(254\) 1.51586e13 0.899653
\(255\) −7.59825e12 −0.441309
\(256\) 1.09951e12 0.0625000
\(257\) −1.64476e13 −0.915106 −0.457553 0.889182i \(-0.651274\pi\)
−0.457553 + 0.889182i \(0.651274\pi\)
\(258\) −9.68259e12 −0.527331
\(259\) −2.72454e13 −1.45259
\(260\) 8.07459e12 0.421470
\(261\) 7.00210e12 0.357854
\(262\) −5.39436e12 −0.269950
\(263\) −1.96818e13 −0.964514 −0.482257 0.876030i \(-0.660183\pi\)
−0.482257 + 0.876030i \(0.660183\pi\)
\(264\) −3.25630e12 −0.156280
\(265\) 2.36150e12 0.111003
\(266\) −3.51679e13 −1.61919
\(267\) 6.22440e12 0.280728
\(268\) 3.98671e12 0.176146
\(269\) −1.16174e13 −0.502889 −0.251444 0.967872i \(-0.580906\pi\)
−0.251444 + 0.967872i \(0.580906\pi\)
\(270\) 2.64755e12 0.112290
\(271\) 7.46788e12 0.310360 0.155180 0.987886i \(-0.450404\pi\)
0.155180 + 0.987886i \(0.450404\pi\)
\(272\) 5.68634e12 0.231581
\(273\) −2.40810e13 −0.961125
\(274\) 2.56473e13 1.00326
\(275\) 6.37197e12 0.244311
\(276\) 1.29876e13 0.488121
\(277\) 1.59564e13 0.587892 0.293946 0.955822i \(-0.405031\pi\)
0.293946 + 0.955822i \(0.405031\pi\)
\(278\) −1.67949e13 −0.606638
\(279\) −3.40432e12 −0.120561
\(280\) −1.36914e13 −0.475420
\(281\) 3.96115e13 1.34877 0.674383 0.738382i \(-0.264410\pi\)
0.674383 + 0.738382i \(0.264410\pi\)
\(282\) −1.01614e13 −0.339299
\(283\) 1.50001e13 0.491211 0.245605 0.969370i \(-0.421013\pi\)
0.245605 + 0.969370i \(0.421013\pi\)
\(284\) −9.29371e12 −0.298496
\(285\) −2.12498e13 −0.669435
\(286\) 1.78963e13 0.553032
\(287\) 6.20521e13 1.88107
\(288\) −1.98136e12 −0.0589256
\(289\) −4.86390e12 −0.141921
\(290\) −2.18796e13 −0.626399
\(291\) 1.50508e13 0.422814
\(292\) −1.59455e13 −0.439576
\(293\) 3.88255e13 1.05038 0.525188 0.850986i \(-0.323995\pi\)
0.525188 + 0.850986i \(0.323995\pi\)
\(294\) 2.54563e13 0.675905
\(295\) −1.66226e13 −0.433190
\(296\) 1.23203e13 0.315149
\(297\) 5.86796e12 0.147342
\(298\) −4.02246e13 −0.991523
\(299\) −7.13784e13 −1.72733
\(300\) 3.87714e12 0.0921181
\(301\) −9.02314e13 −2.10495
\(302\) 1.57478e13 0.360729
\(303\) 2.30763e13 0.519077
\(304\) 1.59028e13 0.351293
\(305\) 3.30494e13 0.716992
\(306\) −1.02470e13 −0.218337
\(307\) 7.58194e13 1.58679 0.793394 0.608708i \(-0.208312\pi\)
0.793394 + 0.608708i \(0.208312\pi\)
\(308\) −3.03452e13 −0.623823
\(309\) −1.32124e13 −0.266814
\(310\) 1.06376e13 0.211034
\(311\) −7.99907e13 −1.55904 −0.779520 0.626378i \(-0.784537\pi\)
−0.779520 + 0.626378i \(0.784537\pi\)
\(312\) 1.08894e13 0.208522
\(313\) −6.85614e13 −1.28999 −0.644994 0.764187i \(-0.723140\pi\)
−0.644994 + 0.764187i \(0.723140\pi\)
\(314\) 3.19069e13 0.589891
\(315\) 2.46723e13 0.448231
\(316\) −3.09215e13 −0.552054
\(317\) 6.37891e12 0.111923 0.0559617 0.998433i \(-0.482178\pi\)
0.0559617 + 0.998433i \(0.482178\pi\)
\(318\) 3.18471e12 0.0549188
\(319\) −4.84935e13 −0.821930
\(320\) 6.19120e12 0.103145
\(321\) −1.38838e12 −0.0227368
\(322\) 1.21030e14 1.94844
\(323\) 8.22445e13 1.30165
\(324\) 3.57047e12 0.0555556
\(325\) −2.13084e13 −0.325981
\(326\) 1.54925e13 0.233038
\(327\) 1.20704e13 0.178529
\(328\) −2.80598e13 −0.408111
\(329\) −9.46932e13 −1.35438
\(330\) −1.83358e13 −0.257912
\(331\) 8.90210e13 1.23151 0.615756 0.787937i \(-0.288851\pi\)
0.615756 + 0.787937i \(0.288851\pi\)
\(332\) 2.36905e13 0.322340
\(333\) −2.22015e13 −0.297126
\(334\) −7.40920e13 −0.975361
\(335\) 2.24486e13 0.290699
\(336\) −1.84641e13 −0.235214
\(337\) 1.42601e14 1.78714 0.893568 0.448928i \(-0.148194\pi\)
0.893568 + 0.448928i \(0.148194\pi\)
\(338\) −2.49774e12 −0.0307968
\(339\) −4.32060e13 −0.524138
\(340\) 3.20190e13 0.382185
\(341\) 2.35768e13 0.276909
\(342\) −2.86574e13 −0.331202
\(343\) 9.39407e13 1.06841
\(344\) 4.08024e13 0.456682
\(345\) 7.31311e13 0.805558
\(346\) −1.07890e14 −1.16967
\(347\) −1.33726e14 −1.42693 −0.713467 0.700689i \(-0.752876\pi\)
−0.713467 + 0.700689i \(0.752876\pi\)
\(348\) −2.95068e13 −0.309910
\(349\) −6.30474e13 −0.651820 −0.325910 0.945401i \(-0.605671\pi\)
−0.325910 + 0.945401i \(0.605671\pi\)
\(350\) 3.61308e13 0.367708
\(351\) −1.96230e13 −0.196596
\(352\) 1.37220e13 0.135342
\(353\) −2.89749e13 −0.281359 −0.140680 0.990055i \(-0.544929\pi\)
−0.140680 + 0.990055i \(0.544929\pi\)
\(354\) −2.24172e13 −0.214320
\(355\) −5.23316e13 −0.492615
\(356\) −2.62296e13 −0.243118
\(357\) −9.54907e13 −0.871538
\(358\) −5.26713e13 −0.473388
\(359\) 4.33108e13 0.383334 0.191667 0.981460i \(-0.438611\pi\)
0.191667 + 0.981460i \(0.438611\pi\)
\(360\) −1.11567e13 −0.0972464
\(361\) 1.13520e14 0.974505
\(362\) −8.77495e13 −0.741904
\(363\) 2.86918e13 0.238930
\(364\) 1.01477e14 0.832358
\(365\) −8.97871e13 −0.725443
\(366\) 4.45702e13 0.354731
\(367\) −1.12471e14 −0.881814 −0.440907 0.897553i \(-0.645343\pi\)
−0.440907 + 0.897553i \(0.645343\pi\)
\(368\) −5.47295e13 −0.422725
\(369\) 5.05646e13 0.384770
\(370\) 6.93738e13 0.520099
\(371\) 2.96781e13 0.219220
\(372\) 1.43458e13 0.104409
\(373\) 1.29948e14 0.931900 0.465950 0.884811i \(-0.345713\pi\)
0.465950 + 0.884811i \(0.345713\pi\)
\(374\) 7.09661e13 0.501484
\(375\) 9.02466e13 0.628433
\(376\) 4.28200e13 0.293842
\(377\) 1.62167e14 1.09669
\(378\) 3.32729e13 0.221762
\(379\) −9.45382e13 −0.621000 −0.310500 0.950573i \(-0.600496\pi\)
−0.310500 + 0.950573i \(0.600496\pi\)
\(380\) 8.95465e13 0.579747
\(381\) 1.15111e14 0.734563
\(382\) −1.30691e14 −0.822047
\(383\) 5.45117e13 0.337985 0.168992 0.985617i \(-0.445949\pi\)
0.168992 + 0.985617i \(0.445949\pi\)
\(384\) 8.34942e12 0.0510310
\(385\) −1.70870e14 −1.02951
\(386\) 1.43116e14 0.850079
\(387\) −7.35272e13 −0.430564
\(388\) −6.34241e13 −0.366167
\(389\) −5.11379e13 −0.291085 −0.145543 0.989352i \(-0.546493\pi\)
−0.145543 + 0.989352i \(0.546493\pi\)
\(390\) 6.13164e13 0.344129
\(391\) −2.83044e14 −1.56632
\(392\) −1.07273e14 −0.585351
\(393\) −4.09634e13 −0.220413
\(394\) 2.35848e14 1.25142
\(395\) −1.74115e14 −0.911068
\(396\) −2.47275e13 −0.127602
\(397\) −4.87234e13 −0.247965 −0.123982 0.992284i \(-0.539567\pi\)
−0.123982 + 0.992284i \(0.539567\pi\)
\(398\) −8.61787e13 −0.432557
\(399\) −2.67056e14 −1.32206
\(400\) −1.63382e13 −0.0797766
\(401\) 3.76407e14 1.81286 0.906430 0.422356i \(-0.138797\pi\)
0.906430 + 0.422356i \(0.138797\pi\)
\(402\) 3.02741e13 0.143823
\(403\) −7.88430e13 −0.369475
\(404\) −9.72433e13 −0.449534
\(405\) 2.01048e13 0.0916847
\(406\) −2.74972e14 −1.23707
\(407\) 1.53758e14 0.682448
\(408\) 4.31806e13 0.189085
\(409\) 3.12467e14 1.34998 0.674988 0.737828i \(-0.264149\pi\)
0.674988 + 0.737828i \(0.264149\pi\)
\(410\) −1.58001e14 −0.673515
\(411\) 1.94759e14 0.819160
\(412\) 5.56768e13 0.231068
\(413\) −2.08904e14 −0.855503
\(414\) 9.86242e13 0.398549
\(415\) 1.33398e14 0.531967
\(416\) −4.58876e13 −0.180585
\(417\) −1.27536e14 −0.495318
\(418\) 1.98469e14 0.760716
\(419\) 2.81729e14 1.06575 0.532874 0.846195i \(-0.321112\pi\)
0.532874 + 0.846195i \(0.321112\pi\)
\(420\) −1.03969e14 −0.388179
\(421\) −3.01064e14 −1.10945 −0.554724 0.832034i \(-0.687176\pi\)
−0.554724 + 0.832034i \(0.687176\pi\)
\(422\) −2.12306e14 −0.772227
\(423\) −7.71630e13 −0.277037
\(424\) −1.34203e13 −0.0475610
\(425\) −8.44964e13 −0.295596
\(426\) −7.05741e13 −0.243721
\(427\) 4.15347e14 1.41598
\(428\) 5.85060e12 0.0196906
\(429\) 1.35900e14 0.451549
\(430\) 2.29752e14 0.753674
\(431\) 3.46694e14 1.12285 0.561425 0.827528i \(-0.310253\pi\)
0.561425 + 0.827528i \(0.310253\pi\)
\(432\) −1.50459e13 −0.0481125
\(433\) 4.82345e14 1.52291 0.761456 0.648217i \(-0.224485\pi\)
0.761456 + 0.648217i \(0.224485\pi\)
\(434\) 1.33687e14 0.416770
\(435\) −1.66149e14 −0.511453
\(436\) −5.08645e13 −0.154611
\(437\) −7.91581e14 −2.37600
\(438\) −1.21086e14 −0.358912
\(439\) 1.18934e14 0.348138 0.174069 0.984733i \(-0.444308\pi\)
0.174069 + 0.984733i \(0.444308\pi\)
\(440\) 7.72668e13 0.223359
\(441\) 1.93309e14 0.551874
\(442\) −2.37317e14 −0.669123
\(443\) −1.99914e14 −0.556703 −0.278351 0.960479i \(-0.589788\pi\)
−0.278351 + 0.960479i \(0.589788\pi\)
\(444\) 9.35571e13 0.257318
\(445\) −1.47695e14 −0.401223
\(446\) 1.91859e14 0.514802
\(447\) −3.05456e14 −0.809575
\(448\) 7.78076e13 0.203701
\(449\) −5.06702e14 −1.31038 −0.655191 0.755464i \(-0.727412\pi\)
−0.655191 + 0.755464i \(0.727412\pi\)
\(450\) 2.94421e13 0.0752141
\(451\) −3.50189e14 −0.883754
\(452\) 1.82070e14 0.453917
\(453\) 1.19585e14 0.294534
\(454\) 2.47978e14 0.603400
\(455\) 5.71403e14 1.37366
\(456\) 1.20762e14 0.286829
\(457\) −3.62768e14 −0.851315 −0.425658 0.904884i \(-0.639957\pi\)
−0.425658 + 0.904884i \(0.639957\pi\)
\(458\) −1.20257e14 −0.278838
\(459\) −7.78129e13 −0.178271
\(460\) −3.08174e14 −0.697634
\(461\) 6.56466e13 0.146844 0.0734221 0.997301i \(-0.476608\pi\)
0.0734221 + 0.997301i \(0.476608\pi\)
\(462\) −2.30434e14 −0.509349
\(463\) −2.06748e14 −0.451592 −0.225796 0.974175i \(-0.572498\pi\)
−0.225796 + 0.974175i \(0.572498\pi\)
\(464\) 1.24341e14 0.268390
\(465\) 8.07790e13 0.172309
\(466\) −2.88856e14 −0.608919
\(467\) −3.79401e14 −0.790416 −0.395208 0.918592i \(-0.629327\pi\)
−0.395208 + 0.918592i \(0.629327\pi\)
\(468\) 8.26910e13 0.170257
\(469\) 2.82122e14 0.574099
\(470\) 2.41113e14 0.484935
\(471\) 2.42293e14 0.481644
\(472\) 9.44658e13 0.185607
\(473\) 5.09218e14 0.988934
\(474\) −2.34810e14 −0.450750
\(475\) −2.36309e14 −0.448399
\(476\) 4.02397e14 0.754774
\(477\) 2.41839e13 0.0448410
\(478\) 1.28726e14 0.235946
\(479\) 3.67939e14 0.666701 0.333350 0.942803i \(-0.391821\pi\)
0.333350 + 0.942803i \(0.391821\pi\)
\(480\) 4.70144e13 0.0842178
\(481\) −5.14182e14 −0.910581
\(482\) 4.79989e14 0.840375
\(483\) 9.19072e14 1.59089
\(484\) −1.20907e14 −0.206920
\(485\) −3.57132e14 −0.604295
\(486\) 2.71132e13 0.0453609
\(487\) 6.31645e14 1.04487 0.522437 0.852678i \(-0.325023\pi\)
0.522437 + 0.852678i \(0.325023\pi\)
\(488\) −1.87819e14 −0.307206
\(489\) 1.17647e14 0.190274
\(490\) −6.04038e14 −0.966019
\(491\) 2.78183e14 0.439929 0.219965 0.975508i \(-0.429406\pi\)
0.219965 + 0.975508i \(0.429406\pi\)
\(492\) −2.13079e14 −0.333221
\(493\) 6.43055e14 0.994467
\(494\) −6.63697e14 −1.01501
\(495\) −1.39237e14 −0.210585
\(496\) −6.04529e13 −0.0904208
\(497\) −6.57675e14 −0.972862
\(498\) 1.79900e14 0.263190
\(499\) 4.59050e14 0.664213 0.332106 0.943242i \(-0.392241\pi\)
0.332106 + 0.943242i \(0.392241\pi\)
\(500\) −3.80298e14 −0.544239
\(501\) −5.62636e14 −0.796379
\(502\) 4.69814e14 0.657742
\(503\) −9.15703e14 −1.26803 −0.634017 0.773319i \(-0.718595\pi\)
−0.634017 + 0.773319i \(0.718595\pi\)
\(504\) −1.40212e14 −0.192051
\(505\) −5.47563e14 −0.741877
\(506\) −6.83029e14 −0.915401
\(507\) −1.89672e13 −0.0251455
\(508\) −4.85077e14 −0.636150
\(509\) 1.08562e15 1.40842 0.704208 0.709993i \(-0.251302\pi\)
0.704208 + 0.709993i \(0.251302\pi\)
\(510\) 2.43144e14 0.312052
\(511\) −1.12840e15 −1.43267
\(512\) −3.51844e13 −0.0441942
\(513\) −2.17617e14 −0.270425
\(514\) 5.26324e14 0.647077
\(515\) 3.13508e14 0.381337
\(516\) 3.09843e14 0.372879
\(517\) 5.34398e14 0.636307
\(518\) 8.71852e14 1.02714
\(519\) −8.19291e14 −0.955031
\(520\) −2.58387e14 −0.298024
\(521\) −1.63925e14 −0.187084 −0.0935422 0.995615i \(-0.529819\pi\)
−0.0935422 + 0.995615i \(0.529819\pi\)
\(522\) −2.24067e14 −0.253041
\(523\) 4.69127e13 0.0524241 0.0262121 0.999656i \(-0.491655\pi\)
0.0262121 + 0.999656i \(0.491655\pi\)
\(524\) 1.72620e14 0.190883
\(525\) 2.74368e14 0.300233
\(526\) 6.29818e14 0.682015
\(527\) −3.12644e14 −0.335036
\(528\) 1.04202e14 0.110506
\(529\) 1.77141e15 1.85914
\(530\) −7.55681e13 −0.0784912
\(531\) −1.70230e14 −0.174992
\(532\) 1.12537e15 1.14494
\(533\) 1.17106e15 1.17918
\(534\) −1.99181e14 −0.198505
\(535\) 3.29439e13 0.0324960
\(536\) −1.27575e14 −0.124554
\(537\) −3.99972e14 −0.386520
\(538\) 3.71757e14 0.355596
\(539\) −1.33877e15 −1.26756
\(540\) −8.47215e13 −0.0794013
\(541\) −1.28196e15 −1.18929 −0.594647 0.803987i \(-0.702708\pi\)
−0.594647 + 0.803987i \(0.702708\pi\)
\(542\) −2.38972e14 −0.219458
\(543\) −6.66348e14 −0.605762
\(544\) −1.81963e14 −0.163753
\(545\) −2.86411e14 −0.255158
\(546\) 7.70592e14 0.679618
\(547\) 1.10564e15 0.965347 0.482673 0.875801i \(-0.339666\pi\)
0.482673 + 0.875801i \(0.339666\pi\)
\(548\) −8.20715e14 −0.709413
\(549\) 3.38455e14 0.289636
\(550\) −2.03903e14 −0.172754
\(551\) 1.79841e15 1.50854
\(552\) −4.15602e14 −0.345154
\(553\) −2.18818e15 −1.79926
\(554\) −5.10606e14 −0.415702
\(555\) 5.26807e14 0.424659
\(556\) 5.37435e14 0.428958
\(557\) 2.12161e15 1.67672 0.838362 0.545113i \(-0.183513\pi\)
0.838362 + 0.545113i \(0.183513\pi\)
\(558\) 1.08938e14 0.0852495
\(559\) −1.70287e15 −1.31952
\(560\) 4.38124e14 0.336173
\(561\) 5.38899e14 0.409460
\(562\) −1.26757e15 −0.953721
\(563\) −2.44888e15 −1.82462 −0.912309 0.409503i \(-0.865702\pi\)
−0.912309 + 0.409503i \(0.865702\pi\)
\(564\) 3.25164e14 0.239921
\(565\) 1.02521e15 0.749111
\(566\) −4.80002e14 −0.347338
\(567\) 2.52666e14 0.181068
\(568\) 2.97399e14 0.211068
\(569\) −7.38095e14 −0.518794 −0.259397 0.965771i \(-0.583524\pi\)
−0.259397 + 0.965771i \(0.583524\pi\)
\(570\) 6.79994e14 0.473362
\(571\) −2.10103e13 −0.0144855 −0.00724274 0.999974i \(-0.502305\pi\)
−0.00724274 + 0.999974i \(0.502305\pi\)
\(572\) −5.72682e14 −0.391053
\(573\) −9.92434e14 −0.671199
\(574\) −1.98567e15 −1.33012
\(575\) 8.13255e14 0.539577
\(576\) 6.34034e13 0.0416667
\(577\) 1.13249e15 0.737168 0.368584 0.929594i \(-0.379843\pi\)
0.368584 + 0.929594i \(0.379843\pi\)
\(578\) 1.55645e14 0.100353
\(579\) 1.08679e15 0.694087
\(580\) 7.00149e14 0.442931
\(581\) 1.67647e15 1.05058
\(582\) −4.81626e14 −0.298974
\(583\) −1.67487e14 −0.102992
\(584\) 5.10257e14 0.310827
\(585\) 4.65621e14 0.280980
\(586\) −1.24242e15 −0.742728
\(587\) −2.91255e15 −1.72490 −0.862448 0.506145i \(-0.831070\pi\)
−0.862448 + 0.506145i \(0.831070\pi\)
\(588\) −8.14602e14 −0.477937
\(589\) −8.74362e14 −0.508226
\(590\) 5.31923e14 0.306311
\(591\) 1.79097e15 1.02178
\(592\) −3.94249e14 −0.222844
\(593\) 1.52901e15 0.856270 0.428135 0.903715i \(-0.359171\pi\)
0.428135 + 0.903715i \(0.359171\pi\)
\(594\) −1.87775e14 −0.104186
\(595\) 2.26584e15 1.24562
\(596\) 1.28719e15 0.701113
\(597\) −6.54420e14 −0.353181
\(598\) 2.28411e15 1.22141
\(599\) 2.71517e15 1.43863 0.719315 0.694684i \(-0.244456\pi\)
0.719315 + 0.694684i \(0.244456\pi\)
\(600\) −1.24069e14 −0.0651373
\(601\) −2.59104e15 −1.34792 −0.673960 0.738768i \(-0.735408\pi\)
−0.673960 + 0.738768i \(0.735408\pi\)
\(602\) 2.88740e15 1.48842
\(603\) 2.29894e14 0.117431
\(604\) −5.03928e14 −0.255074
\(605\) −6.80810e14 −0.341485
\(606\) −7.38441e14 −0.367043
\(607\) 1.68761e15 0.831255 0.415628 0.909535i \(-0.363562\pi\)
0.415628 + 0.909535i \(0.363562\pi\)
\(608\) −5.08890e14 −0.248401
\(609\) −2.08807e15 −1.01006
\(610\) −1.05758e15 −0.506990
\(611\) −1.78707e15 −0.849016
\(612\) 3.27903e14 0.154388
\(613\) −5.35764e14 −0.250000 −0.125000 0.992157i \(-0.539893\pi\)
−0.125000 + 0.992157i \(0.539893\pi\)
\(614\) −2.42622e15 −1.12203
\(615\) −1.19982e15 −0.549923
\(616\) 9.71047e14 0.441109
\(617\) −2.84367e15 −1.28030 −0.640148 0.768251i \(-0.721127\pi\)
−0.640148 + 0.768251i \(0.721127\pi\)
\(618\) 4.22796e14 0.188666
\(619\) 8.14487e14 0.360235 0.180117 0.983645i \(-0.442352\pi\)
0.180117 + 0.983645i \(0.442352\pi\)
\(620\) −3.40402e14 −0.149224
\(621\) 7.48928e14 0.325414
\(622\) 2.55970e15 1.10241
\(623\) −1.85615e15 −0.792372
\(624\) −3.48459e14 −0.147447
\(625\) −1.38060e15 −0.579065
\(626\) 2.19397e15 0.912160
\(627\) 1.50712e15 0.621122
\(628\) −1.02102e15 −0.417116
\(629\) −2.03894e15 −0.825705
\(630\) −7.89513e14 −0.316947
\(631\) −1.45868e15 −0.580497 −0.290248 0.956951i \(-0.593738\pi\)
−0.290248 + 0.956951i \(0.593738\pi\)
\(632\) 9.89488e14 0.390361
\(633\) −1.61220e15 −0.630520
\(634\) −2.04125e14 −0.0791417
\(635\) −2.73140e15 −1.04986
\(636\) −1.01911e14 −0.0388334
\(637\) 4.47698e15 1.69129
\(638\) 1.55179e15 0.581192
\(639\) −5.35922e14 −0.198997
\(640\) −1.98118e14 −0.0729348
\(641\) −1.16297e15 −0.424473 −0.212236 0.977218i \(-0.568075\pi\)
−0.212236 + 0.977218i \(0.568075\pi\)
\(642\) 4.44280e13 0.0160773
\(643\) 4.73461e15 1.69873 0.849364 0.527807i \(-0.176985\pi\)
0.849364 + 0.527807i \(0.176985\pi\)
\(644\) −3.87296e15 −1.37775
\(645\) 1.74468e15 0.615372
\(646\) −2.63182e15 −0.920402
\(647\) 5.47527e15 1.89859 0.949297 0.314380i \(-0.101797\pi\)
0.949297 + 0.314380i \(0.101797\pi\)
\(648\) −1.14255e14 −0.0392837
\(649\) 1.17894e15 0.401927
\(650\) 6.81870e14 0.230504
\(651\) 1.01519e15 0.340291
\(652\) −4.95761e14 −0.164782
\(653\) −8.87971e14 −0.292669 −0.146334 0.989235i \(-0.546748\pi\)
−0.146334 + 0.989235i \(0.546748\pi\)
\(654\) −3.86252e14 −0.126239
\(655\) 9.71997e14 0.315020
\(656\) 8.97913e14 0.288578
\(657\) −9.19501e14 −0.293051
\(658\) 3.03018e15 0.957694
\(659\) 3.14454e15 0.985571 0.492785 0.870151i \(-0.335979\pi\)
0.492785 + 0.870151i \(0.335979\pi\)
\(660\) 5.86744e14 0.182372
\(661\) 1.32982e15 0.409907 0.204954 0.978772i \(-0.434296\pi\)
0.204954 + 0.978772i \(0.434296\pi\)
\(662\) −2.84867e15 −0.870810
\(663\) −1.80212e15 −0.546337
\(664\) −7.58096e14 −0.227929
\(665\) 6.33681e15 1.88952
\(666\) 7.10450e14 0.210099
\(667\) −6.18923e15 −1.81528
\(668\) 2.37094e15 0.689685
\(669\) 1.45693e15 0.420334
\(670\) −7.18355e14 −0.205555
\(671\) −2.34399e15 −0.665247
\(672\) 5.90852e14 0.166321
\(673\) −6.84438e15 −1.91096 −0.955479 0.295058i \(-0.904661\pi\)
−0.955479 + 0.295058i \(0.904661\pi\)
\(674\) −4.56323e15 −1.26370
\(675\) 2.23576e14 0.0614121
\(676\) 7.99278e13 0.0217766
\(677\) 8.88820e14 0.240202 0.120101 0.992762i \(-0.461678\pi\)
0.120101 + 0.992762i \(0.461678\pi\)
\(678\) 1.38259e15 0.370622
\(679\) −4.48824e15 −1.19342
\(680\) −1.02461e15 −0.270245
\(681\) 1.88308e15 0.492674
\(682\) −7.54459e14 −0.195804
\(683\) 2.22402e15 0.572565 0.286282 0.958145i \(-0.407580\pi\)
0.286282 + 0.958145i \(0.407580\pi\)
\(684\) 9.17036e14 0.234195
\(685\) −4.62133e15 −1.17076
\(686\) −3.00610e15 −0.755477
\(687\) −9.13204e14 −0.227670
\(688\) −1.30568e15 −0.322923
\(689\) 5.60092e14 0.137421
\(690\) −2.34020e15 −0.569616
\(691\) 4.59721e15 1.11011 0.555053 0.831815i \(-0.312698\pi\)
0.555053 + 0.831815i \(0.312698\pi\)
\(692\) 3.45248e15 0.827081
\(693\) −1.74986e15 −0.415882
\(694\) 4.27923e15 1.00899
\(695\) 3.02622e15 0.707921
\(696\) 9.44217e14 0.219140
\(697\) 4.64373e15 1.06927
\(698\) 2.01752e15 0.460906
\(699\) −2.19350e15 −0.497180
\(700\) −1.15619e15 −0.260009
\(701\) −2.58701e15 −0.577231 −0.288616 0.957445i \(-0.593195\pi\)
−0.288616 + 0.957445i \(0.593195\pi\)
\(702\) 6.27935e14 0.139015
\(703\) −5.70223e15 −1.25254
\(704\) −4.39105e14 −0.0957014
\(705\) 1.83095e15 0.395947
\(706\) 9.27197e14 0.198951
\(707\) −6.88148e15 −1.46513
\(708\) 7.17349e14 0.151547
\(709\) 2.52081e15 0.528427 0.264214 0.964464i \(-0.414888\pi\)
0.264214 + 0.964464i \(0.414888\pi\)
\(710\) 1.67461e15 0.348332
\(711\) −1.78309e15 −0.368036
\(712\) 8.39346e14 0.171910
\(713\) 3.00911e15 0.611570
\(714\) 3.05570e15 0.616270
\(715\) −3.22469e15 −0.645365
\(716\) 1.68548e15 0.334736
\(717\) 9.77514e14 0.192649
\(718\) −1.38595e15 −0.271058
\(719\) 3.03716e15 0.589467 0.294733 0.955580i \(-0.404769\pi\)
0.294733 + 0.955580i \(0.404769\pi\)
\(720\) 3.57016e14 0.0687636
\(721\) 3.94001e15 0.753100
\(722\) −3.63265e15 −0.689079
\(723\) 3.64492e15 0.686163
\(724\) 2.80799e15 0.524605
\(725\) −1.84766e15 −0.342580
\(726\) −9.18137e14 −0.168949
\(727\) 6.52086e15 1.19087 0.595436 0.803402i \(-0.296979\pi\)
0.595436 + 0.803402i \(0.296979\pi\)
\(728\) −3.24727e15 −0.588566
\(729\) 2.05891e14 0.0370370
\(730\) 2.87319e15 0.512966
\(731\) −6.75255e15 −1.19653
\(732\) −1.42625e15 −0.250833
\(733\) −1.48208e15 −0.258703 −0.129351 0.991599i \(-0.541290\pi\)
−0.129351 + 0.991599i \(0.541290\pi\)
\(734\) 3.59907e15 0.623536
\(735\) −4.58691e15 −0.788751
\(736\) 1.75134e15 0.298912
\(737\) −1.59215e15 −0.269719
\(738\) −1.61807e15 −0.272074
\(739\) 5.39343e15 0.900161 0.450081 0.892988i \(-0.351395\pi\)
0.450081 + 0.892988i \(0.351395\pi\)
\(740\) −2.21996e15 −0.367765
\(741\) −5.03995e15 −0.828754
\(742\) −9.49699e14 −0.155012
\(743\) 8.96192e15 1.45199 0.725993 0.687702i \(-0.241380\pi\)
0.725993 + 0.687702i \(0.241380\pi\)
\(744\) −4.59064e14 −0.0738282
\(745\) 7.24798e15 1.15706
\(746\) −4.15832e15 −0.658953
\(747\) 1.36611e15 0.214894
\(748\) −2.27091e15 −0.354603
\(749\) 4.14021e14 0.0641760
\(750\) −2.88789e15 −0.444369
\(751\) −7.78720e15 −1.18949 −0.594746 0.803913i \(-0.702747\pi\)
−0.594746 + 0.803913i \(0.702747\pi\)
\(752\) −1.37024e15 −0.207777
\(753\) 3.56765e15 0.537044
\(754\) −5.18933e15 −0.775477
\(755\) −2.83755e15 −0.420955
\(756\) −1.06473e15 −0.156809
\(757\) −2.41922e15 −0.353711 −0.176856 0.984237i \(-0.556593\pi\)
−0.176856 + 0.984237i \(0.556593\pi\)
\(758\) 3.02522e15 0.439113
\(759\) −5.18675e15 −0.747422
\(760\) −2.86549e15 −0.409943
\(761\) −5.02552e15 −0.713782 −0.356891 0.934146i \(-0.616163\pi\)
−0.356891 + 0.934146i \(0.616163\pi\)
\(762\) −3.68355e15 −0.519415
\(763\) −3.59946e15 −0.503909
\(764\) 4.18211e15 0.581275
\(765\) 1.84637e15 0.254790
\(766\) −1.74438e15 −0.238991
\(767\) −3.94249e15 −0.536285
\(768\) −2.67181e14 −0.0360844
\(769\) 1.21056e16 1.62327 0.811634 0.584166i \(-0.198578\pi\)
0.811634 + 0.584166i \(0.198578\pi\)
\(770\) 5.46783e15 0.727974
\(771\) 3.99678e15 0.528337
\(772\) −4.57973e15 −0.601097
\(773\) −7.45630e15 −0.971709 −0.485854 0.874040i \(-0.661492\pi\)
−0.485854 + 0.874040i \(0.661492\pi\)
\(774\) 2.35287e15 0.304455
\(775\) 8.98303e14 0.115415
\(776\) 2.02957e15 0.258919
\(777\) 6.62063e15 0.838656
\(778\) 1.63641e15 0.205828
\(779\) 1.29870e16 1.62200
\(780\) −1.96212e15 −0.243336
\(781\) 3.71157e15 0.457064
\(782\) 9.05741e15 1.10756
\(783\) −1.70151e15 −0.206607
\(784\) 3.43273e15 0.413905
\(785\) −5.74923e15 −0.688377
\(786\) 1.31083e15 0.155856
\(787\) −1.12580e16 −1.32923 −0.664615 0.747186i \(-0.731404\pi\)
−0.664615 + 0.747186i \(0.731404\pi\)
\(788\) −7.54713e15 −0.884887
\(789\) 4.78268e15 0.556863
\(790\) 5.57167e15 0.644223
\(791\) 1.28843e16 1.47941
\(792\) 7.91281e14 0.0902282
\(793\) 7.83852e15 0.887630
\(794\) 1.55915e15 0.175338
\(795\) −5.73845e14 −0.0640878
\(796\) 2.75772e15 0.305864
\(797\) −1.04669e16 −1.15291 −0.576457 0.817127i \(-0.695565\pi\)
−0.576457 + 0.817127i \(0.695565\pi\)
\(798\) 8.54579e15 0.934838
\(799\) −7.08646e15 −0.769878
\(800\) 5.22824e14 0.0564106
\(801\) −1.51253e15 −0.162078
\(802\) −1.20450e16 −1.28189
\(803\) 6.36807e15 0.673088
\(804\) −9.68771e14 −0.101698
\(805\) −2.18081e16 −2.27374
\(806\) 2.52298e15 0.261259
\(807\) 2.82303e15 0.290343
\(808\) 3.11179e15 0.317868
\(809\) −1.28180e16 −1.30048 −0.650238 0.759730i \(-0.725331\pi\)
−0.650238 + 0.759730i \(0.725331\pi\)
\(810\) −6.43354e14 −0.0648309
\(811\) 9.79295e15 0.980164 0.490082 0.871676i \(-0.336967\pi\)
0.490082 + 0.871676i \(0.336967\pi\)
\(812\) 8.79909e15 0.874742
\(813\) −1.81469e15 −0.179187
\(814\) −4.92027e15 −0.482564
\(815\) −2.79156e15 −0.271945
\(816\) −1.38178e15 −0.133704
\(817\) −1.88847e16 −1.81505
\(818\) −9.99895e15 −0.954578
\(819\) 5.85168e15 0.554906
\(820\) 5.05602e15 0.476247
\(821\) 7.08410e15 0.662823 0.331411 0.943486i \(-0.392475\pi\)
0.331411 + 0.943486i \(0.392475\pi\)
\(822\) −6.23230e15 −0.579233
\(823\) 1.98569e16 1.83321 0.916606 0.399792i \(-0.130918\pi\)
0.916606 + 0.399792i \(0.130918\pi\)
\(824\) −1.78166e15 −0.163390
\(825\) −1.54839e15 −0.141053
\(826\) 6.68493e15 0.604932
\(827\) −2.05537e16 −1.84760 −0.923802 0.382871i \(-0.874935\pi\)
−0.923802 + 0.382871i \(0.874935\pi\)
\(828\) −3.15598e15 −0.281817
\(829\) −1.45920e16 −1.29439 −0.647197 0.762323i \(-0.724059\pi\)
−0.647197 + 0.762323i \(0.724059\pi\)
\(830\) −4.26873e15 −0.376157
\(831\) −3.87742e15 −0.339419
\(832\) 1.46840e15 0.127693
\(833\) 1.77530e16 1.53364
\(834\) 4.08115e15 0.350243
\(835\) 1.33504e16 1.13820
\(836\) −6.35100e15 −0.537907
\(837\) 8.27249e14 0.0696059
\(838\) −9.01533e15 −0.753598
\(839\) 6.54963e15 0.543909 0.271954 0.962310i \(-0.412330\pi\)
0.271954 + 0.962310i \(0.412330\pi\)
\(840\) 3.32700e15 0.274484
\(841\) 1.86098e15 0.152533
\(842\) 9.63404e15 0.784498
\(843\) −9.62559e15 −0.778710
\(844\) 6.79381e15 0.546047
\(845\) 4.50062e14 0.0359386
\(846\) 2.46922e15 0.195895
\(847\) −8.55606e15 −0.674396
\(848\) 4.29451e14 0.0336307
\(849\) −3.64502e15 −0.283601
\(850\) 2.70389e15 0.209018
\(851\) 1.96242e16 1.50723
\(852\) 2.25837e15 0.172337
\(853\) 1.99244e16 1.51066 0.755329 0.655346i \(-0.227477\pi\)
0.755329 + 0.655346i \(0.227477\pi\)
\(854\) −1.32911e16 −1.00125
\(855\) 5.16370e15 0.386498
\(856\) −1.87219e14 −0.0139234
\(857\) 1.59149e16 1.17600 0.588002 0.808859i \(-0.299915\pi\)
0.588002 + 0.808859i \(0.299915\pi\)
\(858\) −4.34881e15 −0.319293
\(859\) −1.19020e15 −0.0868272 −0.0434136 0.999057i \(-0.513823\pi\)
−0.0434136 + 0.999057i \(0.513823\pi\)
\(860\) −7.35208e15 −0.532928
\(861\) −1.50787e16 −1.08604
\(862\) −1.10942e16 −0.793975
\(863\) −1.73343e15 −0.123267 −0.0616336 0.998099i \(-0.519631\pi\)
−0.0616336 + 0.998099i \(0.519631\pi\)
\(864\) 4.81469e14 0.0340207
\(865\) 1.94405e16 1.36495
\(866\) −1.54351e16 −1.07686
\(867\) 1.18193e15 0.0819381
\(868\) −4.27799e15 −0.294701
\(869\) 1.23489e16 0.845317
\(870\) 5.31675e15 0.361652
\(871\) 5.32428e15 0.359882
\(872\) 1.62766e15 0.109326
\(873\) −3.65735e15 −0.244112
\(874\) 2.53306e16 1.68009
\(875\) −2.69121e16 −1.77379
\(876\) 3.87477e15 0.253789
\(877\) 1.16602e16 0.758943 0.379471 0.925203i \(-0.376106\pi\)
0.379471 + 0.925203i \(0.376106\pi\)
\(878\) −3.80589e15 −0.246171
\(879\) −9.43459e15 −0.606435
\(880\) −2.47254e15 −0.157938
\(881\) −1.66091e16 −1.05434 −0.527168 0.849761i \(-0.676746\pi\)
−0.527168 + 0.849761i \(0.676746\pi\)
\(882\) −6.18589e15 −0.390234
\(883\) −1.28205e16 −0.803750 −0.401875 0.915695i \(-0.631641\pi\)
−0.401875 + 0.915695i \(0.631641\pi\)
\(884\) 7.59414e15 0.473141
\(885\) 4.03929e15 0.250102
\(886\) 6.39726e15 0.393648
\(887\) −2.21358e14 −0.0135368 −0.00676840 0.999977i \(-0.502154\pi\)
−0.00676840 + 0.999977i \(0.502154\pi\)
\(888\) −2.99383e15 −0.181951
\(889\) −3.43267e16 −2.07335
\(890\) 4.72624e15 0.283708
\(891\) −1.42591e15 −0.0850679
\(892\) −6.13948e15 −0.364020
\(893\) −1.98185e16 −1.16785
\(894\) 9.77459e15 0.572456
\(895\) 9.49070e15 0.552423
\(896\) −2.48984e15 −0.144038
\(897\) 1.73450e16 0.997275
\(898\) 1.62145e16 0.926579
\(899\) −6.83649e15 −0.388289
\(900\) −9.42146e14 −0.0531844
\(901\) 2.22099e15 0.124612
\(902\) 1.12060e16 0.624908
\(903\) 2.19262e16 1.21529
\(904\) −5.82623e15 −0.320968
\(905\) 1.58114e16 0.865770
\(906\) −3.82671e15 −0.208267
\(907\) −2.48361e16 −1.34352 −0.671758 0.740770i \(-0.734461\pi\)
−0.671758 + 0.740770i \(0.734461\pi\)
\(908\) −7.93529e15 −0.426668
\(909\) −5.60754e15 −0.299689
\(910\) −1.82849e16 −0.971326
\(911\) 8.10295e15 0.427851 0.213925 0.976850i \(-0.431375\pi\)
0.213925 + 0.976850i \(0.431375\pi\)
\(912\) −3.86438e15 −0.202819
\(913\) −9.46112e15 −0.493575
\(914\) 1.16086e16 0.601971
\(915\) −8.03100e15 −0.413955
\(916\) 3.84823e15 0.197168
\(917\) 1.22155e16 0.622130
\(918\) 2.49001e15 0.126057
\(919\) −3.33814e16 −1.67984 −0.839922 0.542707i \(-0.817399\pi\)
−0.839922 + 0.542707i \(0.817399\pi\)
\(920\) 9.86156e15 0.493302
\(921\) −1.84241e16 −0.916133
\(922\) −2.10069e15 −0.103835
\(923\) −1.24118e16 −0.609854
\(924\) 7.37389e15 0.360164
\(925\) 5.85836e15 0.284444
\(926\) 6.61595e15 0.319324
\(927\) 3.21061e15 0.154045
\(928\) −3.97892e15 −0.189781
\(929\) 3.56713e16 1.69134 0.845672 0.533703i \(-0.179200\pi\)
0.845672 + 0.533703i \(0.179200\pi\)
\(930\) −2.58493e15 −0.121841
\(931\) 4.96493e16 2.32643
\(932\) 9.24340e15 0.430570
\(933\) 1.94377e16 0.900112
\(934\) 1.21408e16 0.558908
\(935\) −1.27872e16 −0.585210
\(936\) −2.64611e15 −0.120390
\(937\) 3.96248e16 1.79225 0.896126 0.443800i \(-0.146370\pi\)
0.896126 + 0.443800i \(0.146370\pi\)
\(938\) −9.02791e15 −0.405949
\(939\) 1.66604e16 0.744775
\(940\) −7.71563e15 −0.342900
\(941\) 5.37193e15 0.237349 0.118675 0.992933i \(-0.462135\pi\)
0.118675 + 0.992933i \(0.462135\pi\)
\(942\) −7.75338e15 −0.340574
\(943\) −4.46946e16 −1.95183
\(944\) −3.02290e15 −0.131244
\(945\) −5.99537e15 −0.258786
\(946\) −1.62950e16 −0.699282
\(947\) 2.22241e16 0.948199 0.474099 0.880471i \(-0.342774\pi\)
0.474099 + 0.880471i \(0.342774\pi\)
\(948\) 7.51392e15 0.318728
\(949\) −2.12954e16 −0.898092
\(950\) 7.56188e15 0.317066
\(951\) −1.55008e15 −0.0646190
\(952\) −1.28767e16 −0.533706
\(953\) 7.66867e15 0.316016 0.158008 0.987438i \(-0.449493\pi\)
0.158008 + 0.987438i \(0.449493\pi\)
\(954\) −7.73885e14 −0.0317074
\(955\) 2.35489e16 0.959293
\(956\) −4.11924e15 −0.166839
\(957\) 1.17839e16 0.474542
\(958\) −1.17741e16 −0.471429
\(959\) −5.80784e16 −2.31213
\(960\) −1.50446e15 −0.0595510
\(961\) −2.20847e16 −0.869185
\(962\) 1.64538e16 0.643878
\(963\) 3.37375e14 0.0131271
\(964\) −1.53597e16 −0.594235
\(965\) −2.57878e16 −0.992006
\(966\) −2.94103e16 −1.12493
\(967\) 2.80474e16 1.06671 0.533355 0.845891i \(-0.320931\pi\)
0.533355 + 0.845891i \(0.320931\pi\)
\(968\) 3.86902e15 0.146314
\(969\) −1.99854e16 −0.751505
\(970\) 1.14282e16 0.427301
\(971\) −2.43427e16 −0.905031 −0.452516 0.891757i \(-0.649473\pi\)
−0.452516 + 0.891757i \(0.649473\pi\)
\(972\) −8.67624e14 −0.0320750
\(973\) 3.80320e16 1.39807
\(974\) −2.02126e16 −0.738837
\(975\) 5.17795e15 0.188205
\(976\) 6.01019e15 0.217227
\(977\) −2.19144e16 −0.787608 −0.393804 0.919194i \(-0.628841\pi\)
−0.393804 + 0.919194i \(0.628841\pi\)
\(978\) −3.76469e15 −0.134544
\(979\) 1.04751e16 0.372267
\(980\) 1.93292e16 0.683079
\(981\) −2.93310e15 −0.103074
\(982\) −8.90186e15 −0.311077
\(983\) −7.04586e15 −0.244844 −0.122422 0.992478i \(-0.539066\pi\)
−0.122422 + 0.992478i \(0.539066\pi\)
\(984\) 6.81852e15 0.235623
\(985\) −4.24969e16 −1.46035
\(986\) −2.05778e16 −0.703194
\(987\) 2.30105e16 0.781954
\(988\) 2.12383e16 0.717722
\(989\) 6.49915e16 2.18412
\(990\) 4.45559e15 0.148906
\(991\) 4.04873e16 1.34559 0.672796 0.739828i \(-0.265093\pi\)
0.672796 + 0.739828i \(0.265093\pi\)
\(992\) 1.93449e15 0.0639371
\(993\) −2.16321e16 −0.711013
\(994\) 2.10456e16 0.687918
\(995\) 1.55283e16 0.504775
\(996\) −5.75679e15 −0.186103
\(997\) 1.79607e16 0.577432 0.288716 0.957415i \(-0.406772\pi\)
0.288716 + 0.957415i \(0.406772\pi\)
\(998\) −1.46896e16 −0.469669
\(999\) 5.39498e15 0.171546
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 \(a_p\))