Properties

Label 15.8.a.b.1.1
Level 15
Weight 8
Character 15.1
Self dual Yes
Analytic conductor 4.686
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(4.68577538226\)
Analytic rank: \(0\)
Dimension: \(1\)
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 \(\chi\) = 15.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-13.0000 q^{2}\) \(-27.0000 q^{3}\) \(+41.0000 q^{4}\) \(-125.000 q^{5}\) \(+351.000 q^{6}\) \(+1380.00 q^{7}\) \(+1131.00 q^{8}\) \(+729.000 q^{9}\) \(+O(q^{10})\) \(q\)\(-13.0000 q^{2}\) \(-27.0000 q^{3}\) \(+41.0000 q^{4}\) \(-125.000 q^{5}\) \(+351.000 q^{6}\) \(+1380.00 q^{7}\) \(+1131.00 q^{8}\) \(+729.000 q^{9}\) \(+1625.00 q^{10}\) \(-3304.00 q^{11}\) \(-1107.00 q^{12}\) \(+8506.00 q^{13}\) \(-17940.0 q^{14}\) \(+3375.00 q^{15}\) \(-19951.0 q^{16}\) \(-9994.00 q^{17}\) \(-9477.00 q^{18}\) \(+41236.0 q^{19}\) \(-5125.00 q^{20}\) \(-37260.0 q^{21}\) \(+42952.0 q^{22}\) \(+84120.0 q^{23}\) \(-30537.0 q^{24}\) \(+15625.0 q^{25}\) \(-110578. q^{26}\) \(-19683.0 q^{27}\) \(+56580.0 q^{28}\) \(+132802. q^{29}\) \(-43875.0 q^{30}\) \(-55800.0 q^{31}\) \(+114595. q^{32}\) \(+89208.0 q^{33}\) \(+129922. q^{34}\) \(-172500. q^{35}\) \(+29889.0 q^{36}\) \(+228170. q^{37}\) \(-536068. q^{38}\) \(-229662. q^{39}\) \(-141375. q^{40}\) \(-139670. q^{41}\) \(+484380. q^{42}\) \(-755492. q^{43}\) \(-135464. q^{44}\) \(-91125.0 q^{45}\) \(-1.09356e6 q^{46}\) \(+836984. q^{47}\) \(+538677. q^{48}\) \(+1.08086e6 q^{49}\) \(-203125. q^{50}\) \(+269838. q^{51}\) \(+348746. q^{52}\) \(+1.64165e6 q^{53}\) \(+255879. q^{54}\) \(+413000. q^{55}\) \(+1.56078e6 q^{56}\) \(-1.11337e6 q^{57}\) \(-1.72643e6 q^{58}\) \(-989656. q^{59}\) \(+138375. q^{60}\) \(-1.65816e6 q^{61}\) \(+725400. q^{62}\) \(+1.00602e6 q^{63}\) \(+1.06399e6 q^{64}\) \(-1.06325e6 q^{65}\) \(-1.15970e6 q^{66}\) \(-4.52384e6 q^{67}\) \(-409754. q^{68}\) \(-2.27124e6 q^{69}\) \(+2.24250e6 q^{70}\) \(-389408. q^{71}\) \(+824499. q^{72}\) \(+5.61733e6 q^{73}\) \(-2.96621e6 q^{74}\) \(-421875. q^{75}\) \(+1.69068e6 q^{76}\) \(-4.55952e6 q^{77}\) \(+2.98561e6 q^{78}\) \(+3.90108e6 q^{79}\) \(+2.49388e6 q^{80}\) \(+531441. q^{81}\) \(+1.81571e6 q^{82}\) \(-9.39412e6 q^{83}\) \(-1.52766e6 q^{84}\) \(+1.24925e6 q^{85}\) \(+9.82140e6 q^{86}\) \(-3.58565e6 q^{87}\) \(-3.73682e6 q^{88}\) \(+2.80375e6 q^{89}\) \(+1.18462e6 q^{90}\) \(+1.17383e7 q^{91}\) \(+3.44892e6 q^{92}\) \(+1.50660e6 q^{93}\) \(-1.08808e7 q^{94}\) \(-5.15450e6 q^{95}\) \(-3.09406e6 q^{96}\) \(+5.09943e6 q^{97}\) \(-1.40511e7 q^{98}\) \(-2.40862e6 q^{99}\) \(+O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −13.0000 −1.14905 −0.574524 0.818488i \(-0.694813\pi\)
−0.574524 + 0.818488i \(0.694813\pi\)
\(3\) −27.0000 −0.577350
\(4\) 41.0000 0.320312
\(5\) −125.000 −0.447214
\(6\) 351.000 0.663403
\(7\) 1380.00 1.52067 0.760337 0.649529i \(-0.225034\pi\)
0.760337 + 0.649529i \(0.225034\pi\)
\(8\) 1131.00 0.780994
\(9\) 729.000 0.333333
\(10\) 1625.00 0.513870
\(11\) −3304.00 −0.748455 −0.374227 0.927337i \(-0.622092\pi\)
−0.374227 + 0.927337i \(0.622092\pi\)
\(12\) −1107.00 −0.184933
\(13\) 8506.00 1.07380 0.536900 0.843646i \(-0.319595\pi\)
0.536900 + 0.843646i \(0.319595\pi\)
\(14\) −17940.0 −1.74733
\(15\) 3375.00 0.258199
\(16\) −19951.0 −1.21771
\(17\) −9994.00 −0.493365 −0.246682 0.969096i \(-0.579340\pi\)
−0.246682 + 0.969096i \(0.579340\pi\)
\(18\) −9477.00 −0.383016
\(19\) 41236.0 1.37924 0.689619 0.724173i \(-0.257778\pi\)
0.689619 + 0.724173i \(0.257778\pi\)
\(20\) −5125.00 −0.143248
\(21\) −37260.0 −0.877961
\(22\) 42952.0 0.860011
\(23\) 84120.0 1.44162 0.720812 0.693131i \(-0.243769\pi\)
0.720812 + 0.693131i \(0.243769\pi\)
\(24\) −30537.0 −0.450907
\(25\) 15625.0 0.200000
\(26\) −110578. −1.23385
\(27\) −19683.0 −0.192450
\(28\) 56580.0 0.487091
\(29\) 132802. 1.01114 0.505570 0.862785i \(-0.331282\pi\)
0.505570 + 0.862785i \(0.331282\pi\)
\(30\) −43875.0 −0.296683
\(31\) −55800.0 −0.336410 −0.168205 0.985752i \(-0.553797\pi\)
−0.168205 + 0.985752i \(0.553797\pi\)
\(32\) 114595. 0.618217
\(33\) 89208.0 0.432121
\(34\) 129922. 0.566900
\(35\) −172500. −0.680066
\(36\) 29889.0 0.106771
\(37\) 228170. 0.740547 0.370273 0.928923i \(-0.379264\pi\)
0.370273 + 0.928923i \(0.379264\pi\)
\(38\) −536068. −1.58481
\(39\) −229662. −0.619959
\(40\) −141375. −0.349271
\(41\) −139670. −0.316490 −0.158245 0.987400i \(-0.550584\pi\)
−0.158245 + 0.987400i \(0.550584\pi\)
\(42\) 484380. 1.00882
\(43\) −755492. −1.44907 −0.724537 0.689236i \(-0.757946\pi\)
−0.724537 + 0.689236i \(0.757946\pi\)
\(44\) −135464. −0.239739
\(45\) −91125.0 −0.149071
\(46\) −1.09356e6 −1.65650
\(47\) 836984. 1.17591 0.587956 0.808893i \(-0.299933\pi\)
0.587956 + 0.808893i \(0.299933\pi\)
\(48\) 538677. 0.703047
\(49\) 1.08086e6 1.31245
\(50\) −203125. −0.229810
\(51\) 269838. 0.284844
\(52\) 348746. 0.343952
\(53\) 1.64165e6 1.51466 0.757330 0.653033i \(-0.226504\pi\)
0.757330 + 0.653033i \(0.226504\pi\)
\(54\) 255879. 0.221134
\(55\) 413000. 0.334719
\(56\) 1.56078e6 1.18764
\(57\) −1.11337e6 −0.796303
\(58\) −1.72643e6 −1.16185
\(59\) −989656. −0.627339 −0.313669 0.949532i \(-0.601558\pi\)
−0.313669 + 0.949532i \(0.601558\pi\)
\(60\) 138375. 0.0827043
\(61\) −1.65816e6 −0.935347 −0.467673 0.883901i \(-0.654908\pi\)
−0.467673 + 0.883901i \(0.654908\pi\)
\(62\) 725400. 0.386551
\(63\) 1.00602e6 0.506891
\(64\) 1.06399e6 0.507351
\(65\) −1.06325e6 −0.480218
\(66\) −1.15970e6 −0.496528
\(67\) −4.52384e6 −1.83758 −0.918789 0.394749i \(-0.870832\pi\)
−0.918789 + 0.394749i \(0.870832\pi\)
\(68\) −409754. −0.158031
\(69\) −2.27124e6 −0.832322
\(70\) 2.24250e6 0.781429
\(71\) −389408. −0.129122 −0.0645611 0.997914i \(-0.520565\pi\)
−0.0645611 + 0.997914i \(0.520565\pi\)
\(72\) 824499. 0.260331
\(73\) 5.61733e6 1.69005 0.845026 0.534726i \(-0.179585\pi\)
0.845026 + 0.534726i \(0.179585\pi\)
\(74\) −2.96621e6 −0.850924
\(75\) −421875. −0.115470
\(76\) 1.69068e6 0.441787
\(77\) −4.55952e6 −1.13816
\(78\) 2.98561e6 0.712363
\(79\) 3.90108e6 0.890205 0.445103 0.895480i \(-0.353167\pi\)
0.445103 + 0.895480i \(0.353167\pi\)
\(80\) 2.49388e6 0.544578
\(81\) 531441. 0.111111
\(82\) 1.81571e6 0.363662
\(83\) −9.39412e6 −1.80336 −0.901680 0.432403i \(-0.857666\pi\)
−0.901680 + 0.432403i \(0.857666\pi\)
\(84\) −1.52766e6 −0.281222
\(85\) 1.24925e6 0.220639
\(86\) 9.82140e6 1.66506
\(87\) −3.58565e6 −0.583782
\(88\) −3.73682e6 −0.584539
\(89\) 2.80375e6 0.421574 0.210787 0.977532i \(-0.432397\pi\)
0.210787 + 0.977532i \(0.432397\pi\)
\(90\) 1.18462e6 0.171290
\(91\) 1.17383e7 1.63290
\(92\) 3.44892e6 0.461770
\(93\) 1.50660e6 0.194226
\(94\) −1.08808e7 −1.35118
\(95\) −5.15450e6 −0.616814
\(96\) −3.09406e6 −0.356928
\(97\) 5.09943e6 0.567310 0.283655 0.958926i \(-0.408453\pi\)
0.283655 + 0.958926i \(0.408453\pi\)
\(98\) −1.40511e7 −1.50807
\(99\) −2.40862e6 −0.249485
\(100\) 640625. 0.0640625
\(101\) 1.51723e7 1.46530 0.732648 0.680607i \(-0.238284\pi\)
0.732648 + 0.680607i \(0.238284\pi\)
\(102\) −3.50789e6 −0.327300
\(103\) 4.70527e6 0.424281 0.212141 0.977239i \(-0.431956\pi\)
0.212141 + 0.977239i \(0.431956\pi\)
\(104\) 9.62029e6 0.838632
\(105\) 4.65750e6 0.392636
\(106\) −2.13415e7 −1.74042
\(107\) 2.63120e6 0.207640 0.103820 0.994596i \(-0.466893\pi\)
0.103820 + 0.994596i \(0.466893\pi\)
\(108\) −807003. −0.0616442
\(109\) −4.30059e6 −0.318080 −0.159040 0.987272i \(-0.550840\pi\)
−0.159040 + 0.987272i \(0.550840\pi\)
\(110\) −5.36900e6 −0.384609
\(111\) −6.16059e6 −0.427555
\(112\) −2.75324e7 −1.85174
\(113\) 3.98233e6 0.259635 0.129817 0.991538i \(-0.458561\pi\)
0.129817 + 0.991538i \(0.458561\pi\)
\(114\) 1.44738e7 0.914991
\(115\) −1.05150e7 −0.644714
\(116\) 5.44488e6 0.323881
\(117\) 6.20087e6 0.357934
\(118\) 1.28655e7 0.720843
\(119\) −1.37917e7 −0.750247
\(120\) 3.81713e6 0.201652
\(121\) −8.57075e6 −0.439815
\(122\) 2.15561e7 1.07476
\(123\) 3.77109e6 0.182725
\(124\) −2.28780e6 −0.107756
\(125\) −1.95313e6 −0.0894427
\(126\) −1.30783e7 −0.582443
\(127\) 2.80177e7 1.21372 0.606861 0.794808i \(-0.292429\pi\)
0.606861 + 0.794808i \(0.292429\pi\)
\(128\) −2.85001e7 −1.20119
\(129\) 2.03983e7 0.836623
\(130\) 1.38223e7 0.551794
\(131\) −8.19919e6 −0.318656 −0.159328 0.987226i \(-0.550933\pi\)
−0.159328 + 0.987226i \(0.550933\pi\)
\(132\) 3.65753e6 0.138414
\(133\) 5.69057e7 2.09737
\(134\) 5.88100e7 2.11147
\(135\) 2.46037e6 0.0860663
\(136\) −1.13032e7 −0.385315
\(137\) −1.66646e6 −0.0553697 −0.0276849 0.999617i \(-0.508813\pi\)
−0.0276849 + 0.999617i \(0.508813\pi\)
\(138\) 2.95261e7 0.956378
\(139\) −5.87456e7 −1.85534 −0.927670 0.373401i \(-0.878192\pi\)
−0.927670 + 0.373401i \(0.878192\pi\)
\(140\) −7.07250e6 −0.217834
\(141\) −2.25986e7 −0.678913
\(142\) 5.06230e6 0.148368
\(143\) −2.81038e7 −0.803691
\(144\) −1.45443e7 −0.405904
\(145\) −1.66002e7 −0.452196
\(146\) −7.30253e7 −1.94195
\(147\) −2.91831e7 −0.757742
\(148\) 9.35497e6 0.237206
\(149\) −1.93697e7 −0.479702 −0.239851 0.970810i \(-0.577099\pi\)
−0.239851 + 0.970810i \(0.577099\pi\)
\(150\) 5.48437e6 0.132681
\(151\) −5.33952e7 −1.26207 −0.631034 0.775755i \(-0.717369\pi\)
−0.631034 + 0.775755i \(0.717369\pi\)
\(152\) 4.66379e7 1.07718
\(153\) −7.28563e6 −0.164455
\(154\) 5.92738e7 1.30780
\(155\) 6.97500e6 0.150447
\(156\) −9.41614e6 −0.198581
\(157\) 2.04529e7 0.421800 0.210900 0.977508i \(-0.432361\pi\)
0.210900 + 0.977508i \(0.432361\pi\)
\(158\) −5.07140e7 −1.02289
\(159\) −4.43245e7 −0.874489
\(160\) −1.43244e7 −0.276475
\(161\) 1.16086e8 2.19224
\(162\) −6.90873e6 −0.127672
\(163\) −733588. −0.0132677 −0.00663385 0.999978i \(-0.502112\pi\)
−0.00663385 + 0.999978i \(0.502112\pi\)
\(164\) −5.72647e6 −0.101376
\(165\) −1.11510e7 −0.193250
\(166\) 1.22124e8 2.07215
\(167\) 1.68925e7 0.280664 0.140332 0.990105i \(-0.455183\pi\)
0.140332 + 0.990105i \(0.455183\pi\)
\(168\) −4.21411e7 −0.685682
\(169\) 9.60352e6 0.153048
\(170\) −1.62403e7 −0.253525
\(171\) 3.00610e7 0.459746
\(172\) −3.09752e7 −0.464156
\(173\) 1.18186e7 0.173541 0.0867707 0.996228i \(-0.472345\pi\)
0.0867707 + 0.996228i \(0.472345\pi\)
\(174\) 4.66135e7 0.670794
\(175\) 2.15625e7 0.304135
\(176\) 6.59181e7 0.911403
\(177\) 2.67207e7 0.362194
\(178\) −3.64487e7 −0.484409
\(179\) −3.13746e7 −0.408877 −0.204439 0.978879i \(-0.565537\pi\)
−0.204439 + 0.978879i \(0.565537\pi\)
\(180\) −3.73613e6 −0.0477494
\(181\) −5.83555e7 −0.731488 −0.365744 0.930716i \(-0.619185\pi\)
−0.365744 + 0.930716i \(0.619185\pi\)
\(182\) −1.52598e8 −1.87628
\(183\) 4.47704e7 0.540023
\(184\) 9.51397e7 1.12590
\(185\) −2.85212e7 −0.331183
\(186\) −1.95858e7 −0.223175
\(187\) 3.30202e7 0.369261
\(188\) 3.43163e7 0.376659
\(189\) −2.71625e7 −0.292654
\(190\) 6.70085e7 0.708749
\(191\) 4.06166e6 0.0421780 0.0210890 0.999778i \(-0.493287\pi\)
0.0210890 + 0.999778i \(0.493287\pi\)
\(192\) −2.87278e7 −0.292919
\(193\) −1.33221e8 −1.33389 −0.666946 0.745106i \(-0.732399\pi\)
−0.666946 + 0.745106i \(0.732399\pi\)
\(194\) −6.62925e7 −0.651866
\(195\) 2.87078e7 0.277254
\(196\) 4.43151e7 0.420393
\(197\) 1.30771e7 0.121866 0.0609328 0.998142i \(-0.480592\pi\)
0.0609328 + 0.998142i \(0.480592\pi\)
\(198\) 3.13120e7 0.286670
\(199\) −6.98502e7 −0.628322 −0.314161 0.949370i \(-0.601723\pi\)
−0.314161 + 0.949370i \(0.601723\pi\)
\(200\) 1.76719e7 0.156199
\(201\) 1.22144e8 1.06093
\(202\) −1.97239e8 −1.68370
\(203\) 1.83267e8 1.53761
\(204\) 1.10634e7 0.0912392
\(205\) 1.74588e7 0.141539
\(206\) −6.11685e7 −0.487520
\(207\) 6.13235e7 0.480541
\(208\) −1.69703e8 −1.30758
\(209\) −1.36244e8 −1.03230
\(210\) −6.05475e7 −0.451158
\(211\) 3.28535e7 0.240765 0.120382 0.992728i \(-0.461588\pi\)
0.120382 + 0.992728i \(0.461588\pi\)
\(212\) 6.73076e7 0.485164
\(213\) 1.05140e7 0.0745487
\(214\) −3.42057e7 −0.238589
\(215\) 9.44365e7 0.648045
\(216\) −2.22615e7 −0.150302
\(217\) −7.70040e7 −0.511569
\(218\) 5.59077e7 0.365489
\(219\) −1.51668e8 −0.975752
\(220\) 1.69330e7 0.107215
\(221\) −8.50090e7 −0.529775
\(222\) 8.00877e7 0.491281
\(223\) 6.95194e7 0.419796 0.209898 0.977723i \(-0.432687\pi\)
0.209898 + 0.977723i \(0.432687\pi\)
\(224\) 1.58141e8 0.940106
\(225\) 1.13906e7 0.0666667
\(226\) −5.17703e7 −0.298333
\(227\) −2.30779e8 −1.30950 −0.654750 0.755845i \(-0.727226\pi\)
−0.654750 + 0.755845i \(0.727226\pi\)
\(228\) −4.56483e7 −0.255066
\(229\) 1.46157e8 0.804258 0.402129 0.915583i \(-0.368270\pi\)
0.402129 + 0.915583i \(0.368270\pi\)
\(230\) 1.36695e8 0.740807
\(231\) 1.23107e8 0.657114
\(232\) 1.50199e8 0.789695
\(233\) 3.11907e8 1.61540 0.807700 0.589594i \(-0.200712\pi\)
0.807700 + 0.589594i \(0.200712\pi\)
\(234\) −8.06114e7 −0.411283
\(235\) −1.04623e8 −0.525884
\(236\) −4.05759e7 −0.200944
\(237\) −1.05329e8 −0.513960
\(238\) 1.79292e8 0.862070
\(239\) 2.27310e8 1.07703 0.538513 0.842617i \(-0.318986\pi\)
0.538513 + 0.842617i \(0.318986\pi\)
\(240\) −6.73346e7 −0.314412
\(241\) −1.98483e8 −0.913404 −0.456702 0.889620i \(-0.650969\pi\)
−0.456702 + 0.889620i \(0.650969\pi\)
\(242\) 1.11420e8 0.505369
\(243\) −1.43489e7 −0.0641500
\(244\) −6.79846e7 −0.299603
\(245\) −1.35107e8 −0.586944
\(246\) −4.90242e7 −0.209960
\(247\) 3.50753e8 1.48103
\(248\) −6.31098e7 −0.262734
\(249\) 2.53641e8 1.04117
\(250\) 2.53906e7 0.102774
\(251\) −1.32536e8 −0.529024 −0.264512 0.964382i \(-0.585211\pi\)
−0.264512 + 0.964382i \(0.585211\pi\)
\(252\) 4.12468e7 0.162364
\(253\) −2.77932e8 −1.07899
\(254\) −3.64230e8 −1.39463
\(255\) −3.37297e7 −0.127386
\(256\) 2.34310e8 0.872872
\(257\) −3.58642e7 −0.131794 −0.0658970 0.997826i \(-0.520991\pi\)
−0.0658970 + 0.997826i \(0.520991\pi\)
\(258\) −2.65178e8 −0.961320
\(259\) 3.14875e8 1.12613
\(260\) −4.35933e7 −0.153820
\(261\) 9.68127e7 0.337047
\(262\) 1.06589e8 0.366151
\(263\) −4.79640e8 −1.62581 −0.812907 0.582394i \(-0.802116\pi\)
−0.812907 + 0.582394i \(0.802116\pi\)
\(264\) 1.00894e8 0.337484
\(265\) −2.05206e8 −0.677376
\(266\) −7.39774e8 −2.40998
\(267\) −7.57011e7 −0.243396
\(268\) −1.85478e8 −0.588599
\(269\) −7.08764e7 −0.222008 −0.111004 0.993820i \(-0.535407\pi\)
−0.111004 + 0.993820i \(0.535407\pi\)
\(270\) −3.19849e7 −0.0988944
\(271\) 4.07490e8 1.24373 0.621863 0.783126i \(-0.286376\pi\)
0.621863 + 0.783126i \(0.286376\pi\)
\(272\) 1.99390e8 0.600776
\(273\) −3.16934e8 −0.942755
\(274\) 2.16640e7 0.0636225
\(275\) −5.16250e7 −0.149691
\(276\) −9.31208e7 −0.266603
\(277\) −7.93477e7 −0.224313 −0.112157 0.993691i \(-0.535776\pi\)
−0.112157 + 0.993691i \(0.535776\pi\)
\(278\) 7.63693e8 2.13188
\(279\) −4.06782e7 −0.112137
\(280\) −1.95098e8 −0.531127
\(281\) −8.70068e7 −0.233928 −0.116964 0.993136i \(-0.537316\pi\)
−0.116964 + 0.993136i \(0.537316\pi\)
\(282\) 2.93781e8 0.780104
\(283\) 2.77612e8 0.728091 0.364045 0.931381i \(-0.381395\pi\)
0.364045 + 0.931381i \(0.381395\pi\)
\(284\) −1.59657e7 −0.0413594
\(285\) 1.39171e8 0.356117
\(286\) 3.65350e8 0.923480
\(287\) −1.92745e8 −0.481278
\(288\) 8.35398e7 0.206072
\(289\) −3.10459e8 −0.756591
\(290\) 2.15803e8 0.519595
\(291\) −1.37685e8 −0.327536
\(292\) 2.30311e8 0.541345
\(293\) 2.46490e8 0.572484 0.286242 0.958157i \(-0.407594\pi\)
0.286242 + 0.958157i \(0.407594\pi\)
\(294\) 3.79381e8 0.870682
\(295\) 1.23707e8 0.280554
\(296\) 2.58060e8 0.578363
\(297\) 6.50326e7 0.144040
\(298\) 2.51807e8 0.551201
\(299\) 7.15525e8 1.54802
\(300\) −1.72969e7 −0.0369865
\(301\) −1.04258e9 −2.20357
\(302\) 6.94138e8 1.45018
\(303\) −4.09651e8 −0.845990
\(304\) −8.22699e8 −1.67951
\(305\) 2.07270e8 0.418300
\(306\) 9.47131e7 0.188967
\(307\) 3.84965e8 0.759340 0.379670 0.925122i \(-0.376037\pi\)
0.379670 + 0.925122i \(0.376037\pi\)
\(308\) −1.86940e8 −0.364565
\(309\) −1.27042e8 −0.244959
\(310\) −9.06750e7 −0.172871
\(311\) 4.64435e7 0.0875514 0.0437757 0.999041i \(-0.486061\pi\)
0.0437757 + 0.999041i \(0.486061\pi\)
\(312\) −2.59748e8 −0.484184
\(313\) 2.10558e8 0.388120 0.194060 0.980990i \(-0.437834\pi\)
0.194060 + 0.980990i \(0.437834\pi\)
\(314\) −2.65888e8 −0.484669
\(315\) −1.25752e8 −0.226689
\(316\) 1.59944e8 0.285144
\(317\) −9.60971e8 −1.69435 −0.847175 0.531314i \(-0.821698\pi\)
−0.847175 + 0.531314i \(0.821698\pi\)
\(318\) 5.76219e8 1.00483
\(319\) −4.38778e8 −0.756793
\(320\) −1.32999e8 −0.226894
\(321\) −7.10425e7 −0.119881
\(322\) −1.50911e9 −2.51899
\(323\) −4.12113e8 −0.680467
\(324\) 2.17891e7 0.0355903
\(325\) 1.32906e8 0.214760
\(326\) 9.53664e6 0.0152452
\(327\) 1.16116e8 0.183643
\(328\) −1.57967e8 −0.247177
\(329\) 1.15504e9 1.78818
\(330\) 1.44963e8 0.222054
\(331\) 3.99923e8 0.606147 0.303074 0.952967i \(-0.401987\pi\)
0.303074 + 0.952967i \(0.401987\pi\)
\(332\) −3.85159e8 −0.577639
\(333\) 1.66336e8 0.246849
\(334\) −2.19603e8 −0.322497
\(335\) 5.65480e8 0.821790
\(336\) 7.43374e8 1.06910
\(337\) 2.69185e8 0.383129 0.191565 0.981480i \(-0.438644\pi\)
0.191565 + 0.981480i \(0.438644\pi\)
\(338\) −1.24846e8 −0.175859
\(339\) −1.07523e8 −0.149900
\(340\) 5.12192e7 0.0706736
\(341\) 1.84363e8 0.251787
\(342\) −3.90794e8 −0.528270
\(343\) 3.55093e8 0.475131
\(344\) −8.54461e8 −1.13172
\(345\) 2.83905e8 0.372226
\(346\) −1.53641e8 −0.199407
\(347\) −8.21868e8 −1.05596 −0.527982 0.849256i \(-0.677051\pi\)
−0.527982 + 0.849256i \(0.677051\pi\)
\(348\) −1.47012e8 −0.186993
\(349\) 6.48354e8 0.816438 0.408219 0.912884i \(-0.366150\pi\)
0.408219 + 0.912884i \(0.366150\pi\)
\(350\) −2.80313e8 −0.349466
\(351\) −1.67424e8 −0.206653
\(352\) −3.78622e8 −0.462707
\(353\) 6.52666e8 0.789732 0.394866 0.918739i \(-0.370791\pi\)
0.394866 + 0.918739i \(0.370791\pi\)
\(354\) −3.47369e8 −0.416179
\(355\) 4.86760e7 0.0577452
\(356\) 1.14954e8 0.135035
\(357\) 3.72376e8 0.433155
\(358\) 4.07870e8 0.469820
\(359\) −8.77431e8 −1.00088 −0.500440 0.865771i \(-0.666829\pi\)
−0.500440 + 0.865771i \(0.666829\pi\)
\(360\) −1.03062e8 −0.116424
\(361\) 8.06536e8 0.902295
\(362\) 7.58622e8 0.840515
\(363\) 2.31410e8 0.253927
\(364\) 4.81269e8 0.523038
\(365\) −7.02166e8 −0.755814
\(366\) −5.82015e8 −0.620512
\(367\) 2.86989e8 0.303064 0.151532 0.988452i \(-0.451579\pi\)
0.151532 + 0.988452i \(0.451579\pi\)
\(368\) −1.67828e9 −1.75548
\(369\) −1.01819e8 −0.105497
\(370\) 3.70776e8 0.380545
\(371\) 2.26548e9 2.30330
\(372\) 6.17706e7 0.0622131
\(373\) −1.77013e9 −1.76614 −0.883069 0.469242i \(-0.844527\pi\)
−0.883069 + 0.469242i \(0.844527\pi\)
\(374\) −4.29262e8 −0.424299
\(375\) 5.27344e7 0.0516398
\(376\) 9.46629e8 0.918380
\(377\) 1.12961e9 1.08576
\(378\) 3.53113e8 0.336273
\(379\) 1.46311e9 1.38051 0.690257 0.723565i \(-0.257498\pi\)
0.690257 + 0.723565i \(0.257498\pi\)
\(380\) −2.11335e8 −0.197573
\(381\) −7.56477e8 −0.700742
\(382\) −5.28015e7 −0.0484646
\(383\) −9.90456e8 −0.900823 −0.450412 0.892821i \(-0.648723\pi\)
−0.450412 + 0.892821i \(0.648723\pi\)
\(384\) 7.69502e8 0.693506
\(385\) 5.69940e8 0.508999
\(386\) 1.73187e9 1.53271
\(387\) −5.50754e8 −0.483024
\(388\) 2.09076e8 0.181716
\(389\) −7.96901e8 −0.686406 −0.343203 0.939261i \(-0.611512\pi\)
−0.343203 + 0.939261i \(0.611512\pi\)
\(390\) −3.73201e8 −0.318578
\(391\) −8.40695e8 −0.711246
\(392\) 1.22245e9 1.02501
\(393\) 2.21378e8 0.183976
\(394\) −1.70003e8 −0.140029
\(395\) −4.87635e8 −0.398112
\(396\) −9.87533e7 −0.0799132
\(397\) 7.95584e8 0.638145 0.319073 0.947730i \(-0.396629\pi\)
0.319073 + 0.947730i \(0.396629\pi\)
\(398\) 9.08053e8 0.721972
\(399\) −1.53645e9 −1.21092
\(400\) −3.11734e8 −0.243542
\(401\) −2.01632e9 −1.56154 −0.780771 0.624817i \(-0.785174\pi\)
−0.780771 + 0.624817i \(0.785174\pi\)
\(402\) −1.58787e9 −1.21906
\(403\) −4.74635e8 −0.361237
\(404\) 6.22063e8 0.469353
\(405\) −6.64301e7 −0.0496904
\(406\) −2.38247e9 −1.76679
\(407\) −7.53874e8 −0.554266
\(408\) 3.05187e8 0.222462
\(409\) −5.48030e7 −0.0396070 −0.0198035 0.999804i \(-0.506304\pi\)
−0.0198035 + 0.999804i \(0.506304\pi\)
\(410\) −2.26964e8 −0.162635
\(411\) 4.49944e7 0.0319677
\(412\) 1.92916e8 0.135903
\(413\) −1.36573e9 −0.953978
\(414\) −7.97205e8 −0.552165
\(415\) 1.17426e9 0.806487
\(416\) 9.74745e8 0.663841
\(417\) 1.58613e9 1.07118
\(418\) 1.77117e9 1.18616
\(419\) 1.10925e8 0.0736679 0.0368340 0.999321i \(-0.488273\pi\)
0.0368340 + 0.999321i \(0.488273\pi\)
\(420\) 1.90957e8 0.125766
\(421\) −2.12064e9 −1.38509 −0.692547 0.721373i \(-0.743511\pi\)
−0.692547 + 0.721373i \(0.743511\pi\)
\(422\) −4.27096e8 −0.276650
\(423\) 6.10161e8 0.391971
\(424\) 1.85671e9 1.18294
\(425\) −1.56156e8 −0.0986730
\(426\) −1.36682e8 −0.0856601
\(427\) −2.28826e9 −1.42236
\(428\) 1.07879e8 0.0665097
\(429\) 7.58803e8 0.464011
\(430\) −1.22767e9 −0.744635
\(431\) −2.48533e9 −1.49525 −0.747624 0.664123i \(-0.768805\pi\)
−0.747624 + 0.664123i \(0.768805\pi\)
\(432\) 3.92696e8 0.234349
\(433\) 2.99956e7 0.0177562 0.00887811 0.999961i \(-0.497174\pi\)
0.00887811 + 0.999961i \(0.497174\pi\)
\(434\) 1.00105e9 0.587818
\(435\) 4.48207e8 0.261075
\(436\) −1.76324e8 −0.101885
\(437\) 3.46877e9 1.98834
\(438\) 1.97168e9 1.12119
\(439\) −1.04873e9 −0.591616 −0.295808 0.955247i \(-0.595589\pi\)
−0.295808 + 0.955247i \(0.595589\pi\)
\(440\) 4.67103e8 0.261414
\(441\) 7.87945e8 0.437483
\(442\) 1.10512e9 0.608738
\(443\) 2.04679e8 0.111856 0.0559282 0.998435i \(-0.482188\pi\)
0.0559282 + 0.998435i \(0.482188\pi\)
\(444\) −2.52584e8 −0.136951
\(445\) −3.50468e8 −0.188534
\(446\) −9.03752e8 −0.482366
\(447\) 5.22983e8 0.276956
\(448\) 1.46831e9 0.771516
\(449\) 2.63962e9 1.37619 0.688097 0.725619i \(-0.258446\pi\)
0.688097 + 0.725619i \(0.258446\pi\)
\(450\) −1.48078e8 −0.0766032
\(451\) 4.61470e8 0.236878
\(452\) 1.63276e8 0.0831643
\(453\) 1.44167e9 0.728656
\(454\) 3.00013e9 1.50468
\(455\) −1.46728e9 −0.730255
\(456\) −1.25922e9 −0.621908
\(457\) 1.83738e9 0.900519 0.450260 0.892898i \(-0.351331\pi\)
0.450260 + 0.892898i \(0.351331\pi\)
\(458\) −1.90004e9 −0.924132
\(459\) 1.96712e8 0.0949481
\(460\) −4.31115e8 −0.206510
\(461\) 3.57678e9 1.70035 0.850176 0.526499i \(-0.176495\pi\)
0.850176 + 0.526499i \(0.176495\pi\)
\(462\) −1.60039e9 −0.755056
\(463\) 1.28068e9 0.599662 0.299831 0.953992i \(-0.403070\pi\)
0.299831 + 0.953992i \(0.403070\pi\)
\(464\) −2.64953e9 −1.23128
\(465\) −1.88325e8 −0.0868606
\(466\) −4.05480e9 −1.85617
\(467\) −4.19984e9 −1.90820 −0.954100 0.299490i \(-0.903184\pi\)
−0.954100 + 0.299490i \(0.903184\pi\)
\(468\) 2.54236e8 0.114651
\(469\) −6.24290e9 −2.79436
\(470\) 1.36010e9 0.604266
\(471\) −5.52229e8 −0.243526
\(472\) −1.11930e9 −0.489948
\(473\) 2.49615e9 1.08457
\(474\) 1.36928e9 0.590565
\(475\) 6.44312e8 0.275847
\(476\) −5.65461e8 −0.240313
\(477\) 1.19676e9 0.504887
\(478\) −2.95503e9 −1.23756
\(479\) 2.48202e9 1.03188 0.515942 0.856623i \(-0.327442\pi\)
0.515942 + 0.856623i \(0.327442\pi\)
\(480\) 3.86758e8 0.159623
\(481\) 1.94081e9 0.795200
\(482\) 2.58027e9 1.04955
\(483\) −3.13431e9 −1.26569
\(484\) −3.51401e8 −0.140878
\(485\) −6.37428e8 −0.253709
\(486\) 1.86536e8 0.0737115
\(487\) −1.08065e9 −0.423970 −0.211985 0.977273i \(-0.567993\pi\)
−0.211985 + 0.977273i \(0.567993\pi\)
\(488\) −1.87538e9 −0.730500
\(489\) 1.98069e7 0.00766011
\(490\) 1.75639e9 0.674428
\(491\) −9.47787e8 −0.361348 −0.180674 0.983543i \(-0.557828\pi\)
−0.180674 + 0.983543i \(0.557828\pi\)
\(492\) 1.54615e8 0.0585292
\(493\) −1.32722e9 −0.498861
\(494\) −4.55979e9 −1.70177
\(495\) 3.01077e8 0.111573
\(496\) 1.11327e9 0.409650
\(497\) −5.37383e8 −0.196353
\(498\) −3.29733e9 −1.19636
\(499\) −2.07692e9 −0.748286 −0.374143 0.927371i \(-0.622063\pi\)
−0.374143 + 0.927371i \(0.622063\pi\)
\(500\) −8.00781e7 −0.0286496
\(501\) −4.56098e8 −0.162041
\(502\) 1.72297e9 0.607875
\(503\) 2.73265e9 0.957408 0.478704 0.877976i \(-0.341107\pi\)
0.478704 + 0.877976i \(0.341107\pi\)
\(504\) 1.13781e9 0.395879
\(505\) −1.89653e9 −0.655301
\(506\) 3.61312e9 1.23981
\(507\) −2.59295e8 −0.0883622
\(508\) 1.14872e9 0.388770
\(509\) 4.52470e9 1.52082 0.760409 0.649444i \(-0.224998\pi\)
0.760409 + 0.649444i \(0.224998\pi\)
\(510\) 4.38487e8 0.146373
\(511\) 7.75192e9 2.57002
\(512\) 6.01982e8 0.198216
\(513\) −8.11648e8 −0.265434
\(514\) 4.66235e8 0.151438
\(515\) −5.88159e8 −0.189744
\(516\) 8.36330e8 0.267981
\(517\) −2.76540e9 −0.880117
\(518\) −4.09337e9 −1.29398
\(519\) −3.19101e8 −0.100194
\(520\) −1.20254e9 −0.375048
\(521\) −2.79533e8 −0.0865965 −0.0432983 0.999062i \(-0.513787\pi\)
−0.0432983 + 0.999062i \(0.513787\pi\)
\(522\) −1.25856e9 −0.387283
\(523\) 1.46376e9 0.447419 0.223710 0.974656i \(-0.428183\pi\)
0.223710 + 0.974656i \(0.428183\pi\)
\(524\) −3.36167e8 −0.102069
\(525\) −5.82187e8 −0.175592
\(526\) 6.23533e9 1.86814
\(527\) 5.57665e8 0.165973
\(528\) −1.77979e9 −0.526199
\(529\) 3.67135e9 1.07828
\(530\) 2.66768e9 0.778338
\(531\) −7.21459e8 −0.209113
\(532\) 2.33313e9 0.671814
\(533\) −1.18803e9 −0.339847
\(534\) 9.84115e8 0.279674
\(535\) −3.28901e8 −0.0928595
\(536\) −5.11647e9 −1.43514
\(537\) 8.47115e8 0.236065
\(538\) 9.21393e8 0.255098
\(539\) −3.57115e9 −0.982308
\(540\) 1.00875e8 0.0275681
\(541\) −2.72194e9 −0.739073 −0.369537 0.929216i \(-0.620484\pi\)
−0.369537 + 0.929216i \(0.620484\pi\)
\(542\) −5.29737e9 −1.42910
\(543\) 1.57560e9 0.422325
\(544\) −1.14526e9 −0.305006
\(545\) 5.37574e8 0.142249
\(546\) 4.12014e9 1.08327
\(547\) −6.73048e8 −0.175829 −0.0879145 0.996128i \(-0.528020\pi\)
−0.0879145 + 0.996128i \(0.528020\pi\)
\(548\) −6.83248e7 −0.0177356
\(549\) −1.20880e9 −0.311782
\(550\) 6.71125e8 0.172002
\(551\) 5.47622e9 1.39460
\(552\) −2.56877e9 −0.650038
\(553\) 5.38349e9 1.35371
\(554\) 1.03152e9 0.257747
\(555\) 7.70074e8 0.191208
\(556\) −2.40857e9 −0.594289
\(557\) −7.19994e9 −1.76537 −0.882685 0.469964i \(-0.844267\pi\)
−0.882685 + 0.469964i \(0.844267\pi\)
\(558\) 5.28817e8 0.128850
\(559\) −6.42621e9 −1.55602
\(560\) 3.44155e9 0.828125
\(561\) −8.91545e8 −0.213193
\(562\) 1.13109e9 0.268794
\(563\) 5.80114e9 1.37004 0.685021 0.728524i \(-0.259793\pi\)
0.685021 + 0.728524i \(0.259793\pi\)
\(564\) −9.26541e8 −0.217464
\(565\) −4.97792e8 −0.116112
\(566\) −3.60895e9 −0.836612
\(567\) 7.33389e8 0.168964
\(568\) −4.40420e8 −0.100844
\(569\) −1.67069e9 −0.380192 −0.190096 0.981766i \(-0.560880\pi\)
−0.190096 + 0.981766i \(0.560880\pi\)
\(570\) −1.80923e9 −0.409196
\(571\) 5.70139e9 1.28160 0.640802 0.767706i \(-0.278602\pi\)
0.640802 + 0.767706i \(0.278602\pi\)
\(572\) −1.15226e9 −0.257432
\(573\) −1.09665e8 −0.0243515
\(574\) 2.50568e9 0.553011
\(575\) 1.31438e9 0.288325
\(576\) 7.75651e8 0.169117
\(577\) 2.43063e9 0.526750 0.263375 0.964694i \(-0.415164\pi\)
0.263375 + 0.964694i \(0.415164\pi\)
\(578\) 4.03596e9 0.869360
\(579\) 3.59696e9 0.770123
\(580\) −6.80610e8 −0.144844
\(581\) −1.29639e10 −2.74232
\(582\) 1.78990e9 0.376355
\(583\) −5.42401e9 −1.13365
\(584\) 6.35320e9 1.31992
\(585\) −7.75109e8 −0.160073
\(586\) −3.20438e9 −0.657812
\(587\) −3.33378e9 −0.680305 −0.340153 0.940370i \(-0.610479\pi\)
−0.340153 + 0.940370i \(0.610479\pi\)
\(588\) −1.19651e9 −0.242714
\(589\) −2.30097e9 −0.463988
\(590\) −1.60819e9 −0.322371
\(591\) −3.53083e8 −0.0703591
\(592\) −4.55222e9 −0.901773
\(593\) 3.42280e9 0.674048 0.337024 0.941496i \(-0.390580\pi\)
0.337024 + 0.941496i \(0.390580\pi\)
\(594\) −8.45424e8 −0.165509
\(595\) 1.72396e9 0.335521
\(596\) −7.94159e8 −0.153655
\(597\) 1.88596e9 0.362762
\(598\) −9.30182e9 −1.77875
\(599\) −9.28661e8 −0.176548 −0.0882741 0.996096i \(-0.528135\pi\)
−0.0882741 + 0.996096i \(0.528135\pi\)
\(600\) −4.77141e8 −0.0901814
\(601\) −6.56974e9 −1.23449 −0.617245 0.786771i \(-0.711751\pi\)
−0.617245 + 0.786771i \(0.711751\pi\)
\(602\) 1.35535e10 2.53201
\(603\) −3.29788e9 −0.612526
\(604\) −2.18920e9 −0.404256
\(605\) 1.07134e9 0.196691
\(606\) 5.32547e9 0.972083
\(607\) −3.50790e9 −0.636629 −0.318315 0.947985i \(-0.603117\pi\)
−0.318315 + 0.947985i \(0.603117\pi\)
\(608\) 4.72544e9 0.852667
\(609\) −4.94820e9 −0.887742
\(610\) −2.69451e9 −0.480647
\(611\) 7.11939e9 1.26269
\(612\) −2.98711e8 −0.0526770
\(613\) 3.63970e9 0.638196 0.319098 0.947722i \(-0.396620\pi\)
0.319098 + 0.947722i \(0.396620\pi\)
\(614\) −5.00454e9 −0.872519
\(615\) −4.71386e8 −0.0817173
\(616\) −5.15682e9 −0.888892
\(617\) 7.82559e9 1.34128 0.670639 0.741784i \(-0.266020\pi\)
0.670639 + 0.741784i \(0.266020\pi\)
\(618\) 1.65155e9 0.281470
\(619\) 8.35173e9 1.41533 0.707667 0.706546i \(-0.249748\pi\)
0.707667 + 0.706546i \(0.249748\pi\)
\(620\) 2.85975e8 0.0481900
\(621\) −1.65573e9 −0.277441
\(622\) −6.03765e8 −0.100601
\(623\) 3.86917e9 0.641076
\(624\) 4.58199e9 0.754932
\(625\) 2.44141e8 0.0400000
\(626\) −2.73725e9 −0.445969
\(627\) 3.67858e9 0.595997
\(628\) 8.38570e8 0.135108
\(629\) −2.28033e9 −0.365360
\(630\) 1.63478e9 0.260476
\(631\) −2.16820e7 −0.00343555 −0.00171777 0.999999i \(-0.500547\pi\)
−0.00171777 + 0.999999i \(0.500547\pi\)
\(632\) 4.41212e9 0.695245
\(633\) −8.87045e8 −0.139006
\(634\) 1.24926e10 1.94689
\(635\) −3.50221e9 −0.542793
\(636\) −1.81731e9 −0.280110
\(637\) 9.19377e9 1.40931
\(638\) 5.70411e9 0.869592
\(639\) −2.83878e8 −0.0430407
\(640\) 3.56251e9 0.537188
\(641\) −7.85361e9 −1.17779 −0.588893 0.808211i \(-0.700436\pi\)
−0.588893 + 0.808211i \(0.700436\pi\)
\(642\) 9.23553e8 0.137749
\(643\) −8.81820e9 −1.30810 −0.654051 0.756451i \(-0.726932\pi\)
−0.654051 + 0.756451i \(0.726932\pi\)
\(644\) 4.75951e9 0.702201
\(645\) −2.54979e9 −0.374149
\(646\) 5.35746e9 0.781890
\(647\) −8.71997e9 −1.26576 −0.632878 0.774252i \(-0.718127\pi\)
−0.632878 + 0.774252i \(0.718127\pi\)
\(648\) 6.01060e8 0.0867771
\(649\) 3.26982e9 0.469535
\(650\) −1.72778e9 −0.246770
\(651\) 2.07911e9 0.295354
\(652\) −3.00771e7 −0.00424981
\(653\) −6.65755e8 −0.0935661 −0.0467830 0.998905i \(-0.514897\pi\)
−0.0467830 + 0.998905i \(0.514897\pi\)
\(654\) −1.50951e9 −0.211015
\(655\) 1.02490e9 0.142507
\(656\) 2.78656e9 0.385393
\(657\) 4.09503e9 0.563350
\(658\) −1.50155e10 −2.05470
\(659\) −9.99513e9 −1.36047 −0.680236 0.732994i \(-0.738123\pi\)
−0.680236 + 0.732994i \(0.738123\pi\)
\(660\) −4.57191e8 −0.0619005
\(661\) −2.89160e9 −0.389434 −0.194717 0.980859i \(-0.562379\pi\)
−0.194717 + 0.980859i \(0.562379\pi\)
\(662\) −5.19900e9 −0.696493
\(663\) 2.29524e9 0.305866
\(664\) −1.06247e10 −1.40841
\(665\) −7.11321e9 −0.937972
\(666\) −2.16237e9 −0.283641
\(667\) 1.11713e10 1.45768
\(668\) 6.92593e8 0.0899002
\(669\) −1.87702e9 −0.242370
\(670\) −7.35125e9 −0.944276
\(671\) 5.47857e9 0.700065
\(672\) −4.26981e9 −0.542770
\(673\) −5.83236e9 −0.737550 −0.368775 0.929519i \(-0.620223\pi\)
−0.368775 + 0.929519i \(0.620223\pi\)
\(674\) −3.49940e9 −0.440234
\(675\) −3.07547e8 −0.0384900
\(676\) 3.93744e8 0.0490231
\(677\) −1.22524e10 −1.51762 −0.758808 0.651315i \(-0.774218\pi\)
−0.758808 + 0.651315i \(0.774218\pi\)
\(678\) 1.39780e9 0.172243
\(679\) 7.03721e9 0.862693
\(680\) 1.41290e9 0.172318
\(681\) 6.23103e9 0.756040
\(682\) −2.39672e9 −0.289316
\(683\) −9.69293e9 −1.16408 −0.582040 0.813160i \(-0.697745\pi\)
−0.582040 + 0.813160i \(0.697745\pi\)
\(684\) 1.23250e9 0.147262
\(685\) 2.08307e8 0.0247621
\(686\) −4.61621e9 −0.545948
\(687\) −3.94624e9 −0.464339
\(688\) 1.50728e10 1.76455
\(689\) 1.39639e10 1.62644
\(690\) −3.69077e9 −0.427705
\(691\) 3.33285e9 0.384276 0.192138 0.981368i \(-0.438458\pi\)
0.192138 + 0.981368i \(0.438458\pi\)
\(692\) 4.84561e8 0.0555875
\(693\) −3.32389e9 −0.379385
\(694\) 1.06843e10 1.21335
\(695\) 7.34320e9 0.829733
\(696\) −4.05537e9 −0.455931
\(697\) 1.39586e9 0.156145
\(698\) −8.42860e9 −0.938127
\(699\) −8.42150e9 −0.932651
\(700\) 8.84062e8 0.0974181
\(701\) −2.73199e9 −0.299548 −0.149774 0.988720i \(-0.547855\pi\)
−0.149774 + 0.988720i \(0.547855\pi\)
\(702\) 2.17651e9 0.237454
\(703\) 9.40882e9 1.02139
\(704\) −3.51543e9 −0.379730
\(705\) 2.82482e9 0.303619
\(706\) −8.48466e9 −0.907440
\(707\) 2.09377e10 2.22824
\(708\) 1.09555e9 0.116015
\(709\) 3.44620e8 0.0363144 0.0181572 0.999835i \(-0.494220\pi\)
0.0181572 + 0.999835i \(0.494220\pi\)
\(710\) −6.32788e8 −0.0663520
\(711\) 2.84389e9 0.296735
\(712\) 3.17104e9 0.329247
\(713\) −4.69390e9 −0.484976
\(714\) −4.84089e9 −0.497716
\(715\) 3.51298e9 0.359422
\(716\) −1.28636e9 −0.130969
\(717\) −6.13738e9 −0.621822
\(718\) 1.14066e10 1.15006
\(719\) 3.35749e9 0.336871 0.168436 0.985713i \(-0.446128\pi\)
0.168436 + 0.985713i \(0.446128\pi\)
\(720\) 1.81803e9 0.181526
\(721\) 6.49327e9 0.645194
\(722\) −1.04850e10 −1.03678
\(723\) 5.35903e9 0.527354
\(724\) −2.39258e9 −0.234305
\(725\) 2.07503e9 0.202228
\(726\) −3.00834e9 −0.291775
\(727\) −1.32017e10 −1.27426 −0.637132 0.770755i \(-0.719879\pi\)
−0.637132 + 0.770755i \(0.719879\pi\)
\(728\) 1.32760e10 1.27528
\(729\) 3.87420e8 0.0370370
\(730\) 9.12816e9 0.868467
\(731\) 7.55039e9 0.714922
\(732\) 1.83559e9 0.172976
\(733\) 4.30179e9 0.403446 0.201723 0.979443i \(-0.435346\pi\)
0.201723 + 0.979443i \(0.435346\pi\)
\(734\) −3.73086e9 −0.348235
\(735\) 3.64789e9 0.338873
\(736\) 9.63973e9 0.891236
\(737\) 1.49468e10 1.37534
\(738\) 1.32365e9 0.121221
\(739\) −1.82414e10 −1.66266 −0.831330 0.555780i \(-0.812420\pi\)
−0.831330 + 0.555780i \(0.812420\pi\)
\(740\) −1.16937e9 −0.106082
\(741\) −9.47034e9 −0.855071
\(742\) −2.94512e10 −2.64661
\(743\) −2.36847e8 −0.0211840 −0.0105920 0.999944i \(-0.503372\pi\)
−0.0105920 + 0.999944i \(0.503372\pi\)
\(744\) 1.70396e9 0.151689
\(745\) 2.42122e9 0.214529
\(746\) 2.30117e10 2.02938
\(747\) −6.84831e9 −0.601120
\(748\) 1.35383e9 0.118279
\(749\) 3.63106e9 0.315753
\(750\) −6.85547e8 −0.0593366
\(751\) −1.44326e10 −1.24338 −0.621690 0.783264i \(-0.713553\pi\)
−0.621690 + 0.783264i \(0.713553\pi\)
\(752\) −1.66987e10 −1.43192
\(753\) 3.57847e9 0.305432
\(754\) −1.46850e10 −1.24760
\(755\) 6.67440e9 0.564414
\(756\) −1.11366e9 −0.0937406
\(757\) 1.64934e10 1.38189 0.690945 0.722907i \(-0.257195\pi\)
0.690945 + 0.722907i \(0.257195\pi\)
\(758\) −1.90205e10 −1.58628
\(759\) 7.50418e9 0.622955
\(760\) −5.82974e9 −0.481728
\(761\) −2.96845e9 −0.244165 −0.122083 0.992520i \(-0.538957\pi\)
−0.122083 + 0.992520i \(0.538957\pi\)
\(762\) 9.83420e9 0.805187
\(763\) −5.93482e9 −0.483695
\(764\) 1.66528e8 0.0135102
\(765\) 9.10703e8 0.0735465
\(766\) 1.28759e10 1.03509
\(767\) −8.41801e9 −0.673637
\(768\) −6.32636e9 −0.503953
\(769\) 8.15400e9 0.646590 0.323295 0.946298i \(-0.395209\pi\)
0.323295 + 0.946298i \(0.395209\pi\)
\(770\) −7.40922e9 −0.584864
\(771\) 9.68334e8 0.0760913
\(772\) −5.46204e9 −0.427262
\(773\) −2.78059e9 −0.216525 −0.108263 0.994122i \(-0.534529\pi\)
−0.108263 + 0.994122i \(0.534529\pi\)
\(774\) 7.15980e9 0.555018
\(775\) −8.71875e8 −0.0672819
\(776\) 5.76745e9 0.443065
\(777\) −8.50161e9 −0.650171
\(778\) 1.03597e10 0.788713
\(779\) −5.75943e9 −0.436514
\(780\) 1.17702e9 0.0888080
\(781\) 1.28660e9 0.0966421
\(782\) 1.09290e10 0.817256
\(783\) −2.61394e9 −0.194594
\(784\) −2.15642e10 −1.59818
\(785\) −2.55662e9 −0.188635
\(786\) −2.87792e9 −0.211397
\(787\) −8.20982e9 −0.600374 −0.300187 0.953880i \(-0.597049\pi\)
−0.300187 + 0.953880i \(0.597049\pi\)
\(788\) 5.36163e8 0.0390351
\(789\) 1.29503e10 0.938664
\(790\) 6.33926e9 0.457450
\(791\) 5.49562e9 0.394820
\(792\) −2.72414e9 −0.194846
\(793\) −1.41043e10 −1.00438
\(794\) −1.03426e10 −0.733260
\(795\) 5.54057e9 0.391083
\(796\) −2.86386e9 −0.201259
\(797\) −5.47916e7 −0.00383363 −0.00191681 0.999998i \(-0.500610\pi\)
−0.00191681 + 0.999998i \(0.500610\pi\)
\(798\) 1.99739e10 1.39140
\(799\) −8.36482e9 −0.580153
\(800\) 1.79055e9 0.123643
\(801\) 2.04393e9 0.140525
\(802\) 2.62121e10 1.79429
\(803\) −1.85597e10 −1.26493
\(804\) 5.00790e9 0.339828
\(805\) −1.45107e10 −0.980399
\(806\) 6.17025e9 0.415079
\(807\) 1.91366e9 0.128176
\(808\) 1.71598e10 1.14439
\(809\) 2.04973e9 0.136106 0.0680529 0.997682i \(-0.478321\pi\)
0.0680529 + 0.997682i \(0.478321\pi\)
\(810\) 8.63592e8 0.0570967
\(811\) −1.59471e10 −1.04981 −0.524903 0.851162i \(-0.675899\pi\)
−0.524903 + 0.851162i \(0.675899\pi\)
\(812\) 7.51394e9 0.492517
\(813\) −1.10022e10 −0.718066
\(814\) 9.80036e9 0.636878
\(815\) 9.16985e7 0.00593350
\(816\) −5.38354e9 −0.346858
\(817\) −3.11535e10 −1.99862
\(818\) 7.12439e8 0.0455104
\(819\) 8.55721e9 0.544300
\(820\) 7.15809e8 0.0453366
\(821\) 9.65923e9 0.609174 0.304587 0.952484i \(-0.401482\pi\)
0.304587 + 0.952484i \(0.401482\pi\)
\(822\) −5.84927e8 −0.0367325
\(823\) 3.90398e9 0.244123 0.122061 0.992523i \(-0.461050\pi\)
0.122061 + 0.992523i \(0.461050\pi\)
\(824\) 5.32166e9 0.331361
\(825\) 1.39387e9 0.0864241
\(826\) 1.77544e10 1.09617
\(827\) −1.32224e10 −0.812910 −0.406455 0.913671i \(-0.633235\pi\)
−0.406455 + 0.913671i \(0.633235\pi\)
\(828\) 2.51426e9 0.153923
\(829\) 1.20482e10 0.734484 0.367242 0.930125i \(-0.380302\pi\)
0.367242 + 0.930125i \(0.380302\pi\)
\(830\) −1.52654e10 −0.926693
\(831\) 2.14239e9 0.129507
\(832\) 9.05032e9 0.544794
\(833\) −1.08021e10 −0.647515
\(834\) −2.06197e10 −1.23084
\(835\) −2.11157e9 −0.125517
\(836\) −5.58599e9 −0.330658
\(837\) 1.09831e9 0.0647420
\(838\) −1.44202e9 −0.0846480
\(839\) 3.10603e10 1.81568 0.907839 0.419319i \(-0.137731\pi\)
0.907839 + 0.419319i \(0.137731\pi\)
\(840\) 5.26763e9 0.306646
\(841\) 3.86495e8 0.0224057
\(842\) 2.75683e10 1.59154
\(843\) 2.34918e9 0.135058
\(844\) 1.34699e9 0.0771200
\(845\) −1.20044e9 −0.0684450
\(846\) −7.93210e9 −0.450393
\(847\) −1.18276e10 −0.668815
\(848\) −3.27526e10 −1.84442
\(849\) −7.49552e9 −0.420363
\(850\) 2.03003e9 0.113380
\(851\) 1.91937e10 1.06759
\(852\) 4.31075e8 0.0238789
\(853\) 2.52157e10 1.39107 0.695536 0.718491i \(-0.255167\pi\)
0.695536 + 0.718491i \(0.255167\pi\)
\(854\) 2.97474e10 1.63436
\(855\) −3.75763e9 −0.205605
\(856\) 2.97589e9 0.162166
\(857\) 2.25314e10 1.22280 0.611401 0.791321i \(-0.290606\pi\)
0.611401 + 0.791321i \(0.290606\pi\)
\(858\) −9.86444e9 −0.533172
\(859\) 4.07863e9 0.219552 0.109776 0.993956i \(-0.464987\pi\)
0.109776 + 0.993956i \(0.464987\pi\)
\(860\) 3.87190e9 0.207577
\(861\) 5.20410e9 0.277866
\(862\) 3.23092e10 1.71811
\(863\) −1.10643e10 −0.585986 −0.292993 0.956115i \(-0.594651\pi\)
−0.292993 + 0.956115i \(0.594651\pi\)
\(864\) −2.25557e9 −0.118976
\(865\) −1.47732e9 −0.0776101
\(866\) −3.89943e8 −0.0204028
\(867\) 8.38238e9 0.436818
\(868\) −3.15716e9 −0.163862
\(869\) −1.28892e10 −0.666278
\(870\) −5.82669e9 −0.299988
\(871\) −3.84798e10 −1.97319
\(872\) −4.86397e9 −0.248418
\(873\) 3.71748e9 0.189103
\(874\) −4.50940e10 −2.28470
\(875\) −2.69531e9 −0.136013
\(876\) −6.21838e9 −0.312545
\(877\) 3.60595e10 1.80518 0.902590 0.430501i \(-0.141663\pi\)
0.902590 + 0.430501i \(0.141663\pi\)
\(878\) 1.36336e10 0.679795
\(879\) −6.65524e9 −0.330524
\(880\) −8.23976e9 −0.407592
\(881\) −2.62954e10 −1.29558 −0.647789 0.761820i \(-0.724306\pi\)
−0.647789 + 0.761820i \(0.724306\pi\)
\(882\) −1.02433e10 −0.502689
\(883\) 2.78873e9 0.136315 0.0681575 0.997675i \(-0.478288\pi\)
0.0681575 + 0.997675i \(0.478288\pi\)
\(884\) −3.48537e9 −0.169694
\(885\) −3.34009e9 −0.161978
\(886\) −2.66083e9 −0.128528
\(887\) −1.82970e10 −0.880332 −0.440166 0.897916i \(-0.645080\pi\)
−0.440166 + 0.897916i \(0.645080\pi\)
\(888\) −6.96763e9 −0.333918
\(889\) 3.86644e10 1.84567
\(890\) 4.55609e9 0.216634
\(891\) −1.75588e9 −0.0831617
\(892\) 2.85029e9 0.134466
\(893\) 3.45139e10 1.62186
\(894\) −6.79878e9 −0.318236
\(895\) 3.92183e9 0.182856
\(896\) −3.93301e10 −1.82661
\(897\) −1.93192e10 −0.893748
\(898\) −3.43151e10 −1.58131
\(899\) −7.41035e9 −0.340157
\(900\) 4.67016e8 0.0213542
\(901\) −1.64067e10 −0.747280
\(902\) −5.99911e9 −0.272185
\(903\) 2.81496e10 1.27223
\(904\) 4.50402e9 0.202773
\(905\) 7.29444e9 0.327131
\(906\) −1.87417e10 −0.837261
\(907\) −1.21245e9 −0.0539559 −0.0269780 0.999636i \(-0.508588\pi\)
−0.0269780 + 0.999636i \(0.508588\pi\)
\(908\) −9.46193e9 −0.419449
\(909\) 1.10606e10 0.488432
\(910\) 1.90747e10 0.839099
\(911\) −2.09181e10 −0.916659 −0.458329 0.888782i \(-0.651552\pi\)
−0.458329 + 0.888782i \(0.651552\pi\)
\(912\) 2.22129e10 0.969668
\(913\) 3.10382e10 1.34973
\(914\) −2.38860e10 −1.03474
\(915\) −5.59630e9 −0.241505
\(916\) 5.99244e9 0.257614
\(917\) −1.13149e10 −0.484571
\(918\) −2.55725e9 −0.109100
\(919\) −1.81545e10 −0.771577 −0.385789 0.922587i \(-0.626071\pi\)
−0.385789 + 0.922587i \(0.626071\pi\)
\(920\) −1.18925e10 −0.503517
\(921\) −1.03940e10 −0.438405
\(922\) −4.64981e10 −1.95379
\(923\) −3.31230e9 −0.138651
\(924\) 5.04739e9 0.210482
\(925\) 3.56516e9 0.148109
\(926\) −1.66488e10 −0.689040
\(927\) 3.43014e9 0.141427
\(928\) 1.52184e10 0.625104
\(929\) −3.39225e10 −1.38814 −0.694069 0.719908i \(-0.744184\pi\)
−0.694069 + 0.719908i \(0.744184\pi\)
\(930\) 2.44823e9 0.0998070
\(931\) 4.45702e10 1.81018
\(932\) 1.27882e10 0.517433
\(933\) −1.25397e9 −0.0505478
\(934\) 5.45979e10 2.19261
\(935\) −4.12752e9 −0.165139
\(936\) 7.01319e9 0.279544
\(937\) 3.64023e10 1.44557 0.722786 0.691072i \(-0.242861\pi\)
0.722786 + 0.691072i \(0.242861\pi\)
\(938\) 8.11578e10 3.21085
\(939\) −5.68507e9 −0.224081
\(940\) −4.28954e9 −0.168447
\(941\) 5.07117e10 1.98401 0.992007 0.126181i \(-0.0402719\pi\)
0.992007 + 0.126181i \(0.0402719\pi\)
\(942\) 7.17898e9 0.279824
\(943\) −1.17490e10 −0.456259
\(944\) 1.97446e10 0.763918
\(945\) 3.39532e9 0.130879
\(946\) −3.24499e10 −1.24622
\(947\) 2.30994e10 0.883845 0.441922 0.897053i \(-0.354297\pi\)
0.441922 + 0.897053i \(0.354297\pi\)
\(948\) −4.31850e9 −0.164628
\(949\) 4.77810e10 1.81478
\(950\) −8.37606e9 −0.316962
\(951\) 2.59462e10 0.978233
\(952\) −1.55984e10 −0.585938
\(953\) −4.16368e9 −0.155830 −0.0779151 0.996960i \(-0.524826\pi\)
−0.0779151 + 0.996960i \(0.524826\pi\)
\(954\) −1.55579e10 −0.580139
\(955\) −5.07707e8 −0.0188626
\(956\) 9.31972e9 0.344985
\(957\) 1.18470e10 0.436935
\(958\) −3.22663e10 −1.18569
\(959\) −2.29971e9 −0.0841993
\(960\) 3.59098e9 0.130998
\(961\) −2.43990e10 −0.886829
\(962\) −2.52306e10 −0.913723
\(963\) 1.91815e9 0.0692134
\(964\) −8.13779e9 −0.292575
\(965\) 1.66526e10 0.596535
\(966\) 4.07460e10 1.45434
\(967\) −5.20468e10 −1.85098 −0.925489 0.378775i \(-0.876345\pi\)
−0.925489 + 0.378775i \(0.876345\pi\)
\(968\) −9.69352e9 −0.343493
\(969\) 1.11270e10 0.392868
\(970\) 8.28657e9 0.291524
\(971\) −3.64573e8 −0.0127796 −0.00638979 0.999980i \(-0.502034\pi\)
−0.00638979 + 0.999980i \(0.502034\pi\)
\(972\) −5.88305e8 −0.0205481
\(973\) −8.10689e10 −2.82137
\(974\) 1.40485e10 0.487162
\(975\) −3.58847e9 −0.123992
\(976\) 3.30820e10 1.13898
\(977\) −1.81785e10 −0.623631 −0.311816 0.950143i \(-0.600937\pi\)
−0.311816 + 0.950143i \(0.600937\pi\)
\(978\) −2.57489e8 −0.00880184
\(979\) −9.26358e9 −0.315529
\(980\) −5.53939e9 −0.188006
\(981\) −3.13513e9 −0.106027
\(982\) 1.23212e10 0.415206
\(983\) −1.85778e10 −0.623816 −0.311908 0.950112i \(-0.600968\pi\)
−0.311908 + 0.950112i \(0.600968\pi\)
\(984\) 4.26510e9 0.142707
\(985\) −1.63464e9 −0.0544999
\(986\) 1.72539e10 0.573216
\(987\) −3.11860e10 −1.03240
\(988\) 1.43809e10 0.474391
\(989\) −6.35520e10 −2.08902
\(990\) −3.91400e9 −0.128203
\(991\) 1.82520e10 0.595735 0.297867 0.954607i \(-0.403725\pi\)
0.297867 + 0.954607i \(0.403725\pi\)
\(992\) −6.39440e9 −0.207974
\(993\) −1.07979e10 −0.349959
\(994\) 6.98598e9 0.225619
\(995\) 8.73128e9 0.280994
\(996\) 1.03993e10 0.333500
\(997\) −1.24534e9 −0.0397975 −0.0198987 0.999802i \(-0.506334\pi\)
−0.0198987 + 0.999802i \(0.506334\pi\)
\(998\) 2.70000e10 0.859817
\(999\) −4.49107e9 −0.142518
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 \(a_p\))