Properties

Label 9.12.a.c.1.2
Level 9
Weight 12
Character 9.1
Self dual Yes
Analytic conductor 6.915
Analytic rank 0
Dimension 2
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 9 = 3^{2} \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 9.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(6.91508862504\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{70}) \)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2\cdot 3 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(8.36660\)
Character \(\chi\) = 9.1

$q$-expansion

\(f(q)\) \(=\) \(q+50.1996 q^{2} +472.000 q^{4} +11244.7 q^{5} +58100.0 q^{7} -79114.6 q^{8} +O(q^{10})\) \(q+50.1996 q^{2} +472.000 q^{4} +11244.7 q^{5} +58100.0 q^{7} -79114.6 q^{8} +564480. q^{10} -160639. q^{11} +762650. q^{13} +2.91660e6 q^{14} -4.93818e6 q^{16} -8.97328e6 q^{17} -1.03017e7 q^{19} +5.30750e6 q^{20} -8.06400e6 q^{22} +1.03965e7 q^{23} +7.76154e7 q^{25} +3.82847e7 q^{26} +2.74232e7 q^{28} -1.41001e8 q^{29} +1.06160e8 q^{31} -8.58678e7 q^{32} -4.50455e8 q^{34} +6.53318e8 q^{35} -9.57445e6 q^{37} -5.17141e8 q^{38} -8.89620e8 q^{40} -1.08511e8 q^{41} +1.59070e9 q^{43} -7.58215e7 q^{44} +5.21902e8 q^{46} -1.44049e9 q^{47} +1.39828e9 q^{49} +3.89626e9 q^{50} +3.59971e8 q^{52} +1.05136e9 q^{53} -1.80634e9 q^{55} -4.59656e9 q^{56} -7.07818e9 q^{58} -5.77753e9 q^{59} -3.09262e9 q^{61} +5.32917e9 q^{62} +5.80285e9 q^{64} +8.57578e9 q^{65} -9.11382e9 q^{67} -4.23539e9 q^{68} +3.27963e10 q^{70} +3.35028e9 q^{71} +6.20143e8 q^{73} -4.80634e8 q^{74} -4.86240e9 q^{76} -9.33311e9 q^{77} +1.06185e10 q^{79} -5.55284e10 q^{80} -5.44723e9 q^{82} +6.00030e10 q^{83} -1.00902e11 q^{85} +7.98524e10 q^{86} +1.27089e10 q^{88} -6.14130e10 q^{89} +4.43100e10 q^{91} +4.90717e9 q^{92} -7.23121e10 q^{94} -1.15840e11 q^{95} +1.31873e11 q^{97} +7.01933e10 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 944q^{4} + 116200q^{7} + O(q^{10}) \) \( 2q + 944q^{4} + 116200q^{7} + 1128960q^{10} + 1525300q^{13} - 9876352q^{16} - 20603408q^{19} - 16128000q^{22} + 155230790q^{25} + 54846400q^{28} + 212319016q^{31} - 900910080q^{34} - 19148900q^{37} - 1779240960q^{40} + 3181394800q^{43} + 1043804160q^{46} + 2796566514q^{49} + 719941600q^{52} - 3612672000q^{55} - 14156352000q^{58} - 6185242196q^{61} + 11605707776q^{64} - 18227640800q^{67} + 65592576000q^{70} + 1240285900q^{73} - 9724808576q^{76} + 21236972968q^{79} - 10894464000q^{82} - 201803857920q^{85} + 25417728000q^{88} + 88619930000q^{91} - 144624291840q^{94} + 263745804700q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 50.1996 1.10926 0.554632 0.832095i \(-0.312859\pi\)
0.554632 + 0.832095i \(0.312859\pi\)
\(3\) 0 0
\(4\) 472.000 0.230469
\(5\) 11244.7 1.60921 0.804606 0.593809i \(-0.202377\pi\)
0.804606 + 0.593809i \(0.202377\pi\)
\(6\) 0 0
\(7\) 58100.0 1.30658 0.653291 0.757107i \(-0.273388\pi\)
0.653291 + 0.757107i \(0.273388\pi\)
\(8\) −79114.6 −0.853614
\(9\) 0 0
\(10\) 564480. 1.78504
\(11\) −160639. −0.300740 −0.150370 0.988630i \(-0.548046\pi\)
−0.150370 + 0.988630i \(0.548046\pi\)
\(12\) 0 0
\(13\) 762650. 0.569688 0.284844 0.958574i \(-0.408058\pi\)
0.284844 + 0.958574i \(0.408058\pi\)
\(14\) 2.91660e6 1.44935
\(15\) 0 0
\(16\) −4.93818e6 −1.17735
\(17\) −8.97328e6 −1.53279 −0.766394 0.642371i \(-0.777951\pi\)
−0.766394 + 0.642371i \(0.777951\pi\)
\(18\) 0 0
\(19\) −1.03017e7 −0.954474 −0.477237 0.878775i \(-0.658362\pi\)
−0.477237 + 0.878775i \(0.658362\pi\)
\(20\) 5.30750e6 0.370873
\(21\) 0 0
\(22\) −8.06400e6 −0.333600
\(23\) 1.03965e7 0.336811 0.168405 0.985718i \(-0.446138\pi\)
0.168405 + 0.985718i \(0.446138\pi\)
\(24\) 0 0
\(25\) 7.76154e7 1.58956
\(26\) 3.82847e7 0.631935
\(27\) 0 0
\(28\) 2.74232e7 0.301126
\(29\) −1.41001e8 −1.27653 −0.638267 0.769815i \(-0.720348\pi\)
−0.638267 + 0.769815i \(0.720348\pi\)
\(30\) 0 0
\(31\) 1.06160e8 0.665993 0.332996 0.942928i \(-0.391940\pi\)
0.332996 + 0.942928i \(0.391940\pi\)
\(32\) −8.58678e7 −0.452382
\(33\) 0 0
\(34\) −4.50455e8 −1.70027
\(35\) 6.53318e8 2.10257
\(36\) 0 0
\(37\) −9.57445e6 −0.0226989 −0.0113494 0.999936i \(-0.503613\pi\)
−0.0113494 + 0.999936i \(0.503613\pi\)
\(38\) −5.17141e8 −1.05876
\(39\) 0 0
\(40\) −8.89620e8 −1.37365
\(41\) −1.08511e8 −0.146273 −0.0731365 0.997322i \(-0.523301\pi\)
−0.0731365 + 0.997322i \(0.523301\pi\)
\(42\) 0 0
\(43\) 1.59070e9 1.65010 0.825052 0.565058i \(-0.191146\pi\)
0.825052 + 0.565058i \(0.191146\pi\)
\(44\) −7.58215e7 −0.0693111
\(45\) 0 0
\(46\) 5.21902e8 0.373612
\(47\) −1.44049e9 −0.916163 −0.458082 0.888910i \(-0.651463\pi\)
−0.458082 + 0.888910i \(0.651463\pi\)
\(48\) 0 0
\(49\) 1.39828e9 0.707158
\(50\) 3.89626e9 1.76325
\(51\) 0 0
\(52\) 3.59971e8 0.131295
\(53\) 1.05136e9 0.345331 0.172665 0.984981i \(-0.444762\pi\)
0.172665 + 0.984981i \(0.444762\pi\)
\(54\) 0 0
\(55\) −1.80634e9 −0.483954
\(56\) −4.59656e9 −1.11532
\(57\) 0 0
\(58\) −7.07818e9 −1.41601
\(59\) −5.77753e9 −1.05210 −0.526049 0.850454i \(-0.676327\pi\)
−0.526049 + 0.850454i \(0.676327\pi\)
\(60\) 0 0
\(61\) −3.09262e9 −0.468827 −0.234414 0.972137i \(-0.575317\pi\)
−0.234414 + 0.972137i \(0.575317\pi\)
\(62\) 5.32917e9 0.738763
\(63\) 0 0
\(64\) 5.80285e9 0.675541
\(65\) 8.57578e9 0.916748
\(66\) 0 0
\(67\) −9.11382e9 −0.824687 −0.412343 0.911028i \(-0.635290\pi\)
−0.412343 + 0.911028i \(0.635290\pi\)
\(68\) −4.23539e9 −0.353260
\(69\) 0 0
\(70\) 3.27963e10 2.33231
\(71\) 3.35028e9 0.220374 0.110187 0.993911i \(-0.464855\pi\)
0.110187 + 0.993911i \(0.464855\pi\)
\(72\) 0 0
\(73\) 6.20143e8 0.0350119 0.0175060 0.999847i \(-0.494427\pi\)
0.0175060 + 0.999847i \(0.494427\pi\)
\(74\) −4.80634e8 −0.0251791
\(75\) 0 0
\(76\) −4.86240e9 −0.219977
\(77\) −9.33311e9 −0.392941
\(78\) 0 0
\(79\) 1.06185e10 0.388252 0.194126 0.980977i \(-0.437813\pi\)
0.194126 + 0.980977i \(0.437813\pi\)
\(80\) −5.55284e10 −1.89461
\(81\) 0 0
\(82\) −5.44723e9 −0.162256
\(83\) 6.00030e10 1.67203 0.836014 0.548709i \(-0.184880\pi\)
0.836014 + 0.548709i \(0.184880\pi\)
\(84\) 0 0
\(85\) −1.00902e11 −2.46658
\(86\) 7.98524e10 1.83040
\(87\) 0 0
\(88\) 1.27089e10 0.256715
\(89\) −6.14130e10 −1.16578 −0.582888 0.812552i \(-0.698077\pi\)
−0.582888 + 0.812552i \(0.698077\pi\)
\(90\) 0 0
\(91\) 4.43100e10 0.744344
\(92\) 4.90717e9 0.0776243
\(93\) 0 0
\(94\) −7.23121e10 −1.01627
\(95\) −1.15840e11 −1.53595
\(96\) 0 0
\(97\) 1.31873e11 1.55923 0.779617 0.626257i \(-0.215414\pi\)
0.779617 + 0.626257i \(0.215414\pi\)
\(98\) 7.01933e10 0.784426
\(99\) 0 0
\(100\) 3.66345e10 0.366345
\(101\) 2.72206e9 0.0257710 0.0128855 0.999917i \(-0.495898\pi\)
0.0128855 + 0.999917i \(0.495898\pi\)
\(102\) 0 0
\(103\) 7.95338e10 0.676000 0.338000 0.941146i \(-0.390250\pi\)
0.338000 + 0.941146i \(0.390250\pi\)
\(104\) −6.03367e10 −0.486293
\(105\) 0 0
\(106\) 5.27780e10 0.383063
\(107\) 1.98741e11 1.36986 0.684931 0.728608i \(-0.259832\pi\)
0.684931 + 0.728608i \(0.259832\pi\)
\(108\) 0 0
\(109\) −2.89337e10 −0.180119 −0.0900594 0.995936i \(-0.528706\pi\)
−0.0900594 + 0.995936i \(0.528706\pi\)
\(110\) −9.06773e10 −0.536833
\(111\) 0 0
\(112\) −2.86908e11 −1.53831
\(113\) 2.05831e11 1.05094 0.525471 0.850811i \(-0.323889\pi\)
0.525471 + 0.850811i \(0.323889\pi\)
\(114\) 0 0
\(115\) 1.16906e11 0.542000
\(116\) −6.65523e10 −0.294201
\(117\) 0 0
\(118\) −2.90030e11 −1.16706
\(119\) −5.21348e11 −2.00271
\(120\) 0 0
\(121\) −2.59507e11 −0.909556
\(122\) −1.55248e11 −0.520053
\(123\) 0 0
\(124\) 5.01073e10 0.153491
\(125\) 3.23705e11 0.948732
\(126\) 0 0
\(127\) 4.49318e11 1.20680 0.603398 0.797441i \(-0.293813\pi\)
0.603398 + 0.797441i \(0.293813\pi\)
\(128\) 4.67158e11 1.20174
\(129\) 0 0
\(130\) 4.30501e11 1.01692
\(131\) 4.01940e11 0.910267 0.455134 0.890423i \(-0.349591\pi\)
0.455134 + 0.890423i \(0.349591\pi\)
\(132\) 0 0
\(133\) −5.98529e11 −1.24710
\(134\) −4.57510e11 −0.914796
\(135\) 0 0
\(136\) 7.09917e11 1.30841
\(137\) −4.60579e11 −0.815345 −0.407673 0.913128i \(-0.633659\pi\)
−0.407673 + 0.913128i \(0.633659\pi\)
\(138\) 0 0
\(139\) 7.81318e11 1.27716 0.638581 0.769554i \(-0.279522\pi\)
0.638581 + 0.769554i \(0.279522\pi\)
\(140\) 3.08366e11 0.484576
\(141\) 0 0
\(142\) 1.68183e11 0.244453
\(143\) −1.22511e11 −0.171328
\(144\) 0 0
\(145\) −1.58551e12 −2.05421
\(146\) 3.11309e10 0.0388375
\(147\) 0 0
\(148\) −4.51914e9 −0.00523138
\(149\) −1.45811e12 −1.62654 −0.813272 0.581883i \(-0.802316\pi\)
−0.813272 + 0.581883i \(0.802316\pi\)
\(150\) 0 0
\(151\) −4.60586e11 −0.477461 −0.238730 0.971086i \(-0.576731\pi\)
−0.238730 + 0.971086i \(0.576731\pi\)
\(152\) 8.15015e11 0.814753
\(153\) 0 0
\(154\) −4.68518e11 −0.435876
\(155\) 1.19373e12 1.07172
\(156\) 0 0
\(157\) −4.17640e11 −0.349425 −0.174713 0.984619i \(-0.555900\pi\)
−0.174713 + 0.984619i \(0.555900\pi\)
\(158\) 5.33044e11 0.430674
\(159\) 0 0
\(160\) −9.65559e11 −0.727979
\(161\) 6.04039e11 0.440071
\(162\) 0 0
\(163\) 5.66142e11 0.385384 0.192692 0.981259i \(-0.438278\pi\)
0.192692 + 0.981259i \(0.438278\pi\)
\(164\) −5.12174e10 −0.0337114
\(165\) 0 0
\(166\) 3.01213e12 1.85472
\(167\) −8.35744e11 −0.497889 −0.248945 0.968518i \(-0.580084\pi\)
−0.248945 + 0.968518i \(0.580084\pi\)
\(168\) 0 0
\(169\) −1.21053e12 −0.675456
\(170\) −5.06524e12 −2.73609
\(171\) 0 0
\(172\) 7.50809e11 0.380297
\(173\) 2.25677e12 1.10722 0.553609 0.832777i \(-0.313250\pi\)
0.553609 + 0.832777i \(0.313250\pi\)
\(174\) 0 0
\(175\) 4.50945e12 2.07690
\(176\) 7.93262e11 0.354077
\(177\) 0 0
\(178\) −3.08291e12 −1.29315
\(179\) 1.28902e12 0.524284 0.262142 0.965029i \(-0.415571\pi\)
0.262142 + 0.965029i \(0.415571\pi\)
\(180\) 0 0
\(181\) 1.14166e12 0.436823 0.218411 0.975857i \(-0.429913\pi\)
0.218411 + 0.975857i \(0.429913\pi\)
\(182\) 2.22434e12 0.825675
\(183\) 0 0
\(184\) −8.22518e11 −0.287506
\(185\) −1.07662e11 −0.0365273
\(186\) 0 0
\(187\) 1.44146e12 0.460970
\(188\) −6.79912e11 −0.211147
\(189\) 0 0
\(190\) −5.81511e12 −1.70378
\(191\) −3.96741e12 −1.12934 −0.564668 0.825318i \(-0.690996\pi\)
−0.564668 + 0.825318i \(0.690996\pi\)
\(192\) 0 0
\(193\) −6.13149e12 −1.64817 −0.824083 0.566469i \(-0.808309\pi\)
−0.824083 + 0.566469i \(0.808309\pi\)
\(194\) 6.61997e12 1.72960
\(195\) 0 0
\(196\) 6.59990e11 0.162978
\(197\) 3.47714e11 0.0834945 0.0417472 0.999128i \(-0.486708\pi\)
0.0417472 + 0.999128i \(0.486708\pi\)
\(198\) 0 0
\(199\) 4.26854e12 0.969590 0.484795 0.874628i \(-0.338894\pi\)
0.484795 + 0.874628i \(0.338894\pi\)
\(200\) −6.14051e12 −1.35687
\(201\) 0 0
\(202\) 1.36646e11 0.0285868
\(203\) −8.19214e12 −1.66790
\(204\) 0 0
\(205\) −1.22018e12 −0.235384
\(206\) 3.99257e12 0.749864
\(207\) 0 0
\(208\) −3.76610e12 −0.670723
\(209\) 1.65485e12 0.287048
\(210\) 0 0
\(211\) 6.86132e12 1.12942 0.564708 0.825290i \(-0.308989\pi\)
0.564708 + 0.825290i \(0.308989\pi\)
\(212\) 4.96243e11 0.0795880
\(213\) 0 0
\(214\) 9.97672e12 1.51954
\(215\) 1.78869e13 2.65537
\(216\) 0 0
\(217\) 6.16787e12 0.870175
\(218\) −1.45246e12 −0.199799
\(219\) 0 0
\(220\) −8.52591e11 −0.111536
\(221\) −6.84347e12 −0.873211
\(222\) 0 0
\(223\) −1.10053e13 −1.33637 −0.668183 0.743997i \(-0.732928\pi\)
−0.668183 + 0.743997i \(0.732928\pi\)
\(224\) −4.98892e12 −0.591075
\(225\) 0 0
\(226\) 1.03326e13 1.16577
\(227\) −8.87118e12 −0.976876 −0.488438 0.872599i \(-0.662433\pi\)
−0.488438 + 0.872599i \(0.662433\pi\)
\(228\) 0 0
\(229\) −1.13895e13 −1.19511 −0.597556 0.801827i \(-0.703862\pi\)
−0.597556 + 0.801827i \(0.703862\pi\)
\(230\) 5.86864e12 0.601221
\(231\) 0 0
\(232\) 1.11552e13 1.08967
\(233\) −9.26940e12 −0.884288 −0.442144 0.896944i \(-0.645782\pi\)
−0.442144 + 0.896944i \(0.645782\pi\)
\(234\) 0 0
\(235\) −1.61979e13 −1.47430
\(236\) −2.72700e12 −0.242476
\(237\) 0 0
\(238\) −2.61714e13 −2.22154
\(239\) 2.05536e13 1.70490 0.852452 0.522806i \(-0.175115\pi\)
0.852452 + 0.522806i \(0.175115\pi\)
\(240\) 0 0
\(241\) 1.28698e13 1.01971 0.509857 0.860259i \(-0.329698\pi\)
0.509857 + 0.860259i \(0.329698\pi\)
\(242\) −1.30271e13 −1.00894
\(243\) 0 0
\(244\) −1.45972e12 −0.108050
\(245\) 1.57233e13 1.13797
\(246\) 0 0
\(247\) −7.85659e12 −0.543752
\(248\) −8.39876e12 −0.568501
\(249\) 0 0
\(250\) 1.62498e13 1.05240
\(251\) −3.57196e12 −0.226309 −0.113154 0.993577i \(-0.536095\pi\)
−0.113154 + 0.993577i \(0.536095\pi\)
\(252\) 0 0
\(253\) −1.67009e12 −0.101292
\(254\) 2.25556e13 1.33866
\(255\) 0 0
\(256\) 1.15669e13 0.657503
\(257\) 2.79858e12 0.155706 0.0778530 0.996965i \(-0.475194\pi\)
0.0778530 + 0.996965i \(0.475194\pi\)
\(258\) 0 0
\(259\) −5.56276e11 −0.0296580
\(260\) 4.04777e12 0.211282
\(261\) 0 0
\(262\) 2.01772e13 1.00973
\(263\) −2.99339e13 −1.46692 −0.733460 0.679733i \(-0.762096\pi\)
−0.733460 + 0.679733i \(0.762096\pi\)
\(264\) 0 0
\(265\) 1.18223e13 0.555710
\(266\) −3.00459e13 −1.38336
\(267\) 0 0
\(268\) −4.30172e12 −0.190065
\(269\) −2.64097e13 −1.14321 −0.571606 0.820529i \(-0.693679\pi\)
−0.571606 + 0.820529i \(0.693679\pi\)
\(270\) 0 0
\(271\) 2.96897e13 1.23388 0.616942 0.787009i \(-0.288371\pi\)
0.616942 + 0.787009i \(0.288371\pi\)
\(272\) 4.43116e13 1.80463
\(273\) 0 0
\(274\) −2.31209e13 −0.904434
\(275\) −1.24680e13 −0.478044
\(276\) 0 0
\(277\) 9.53508e12 0.351306 0.175653 0.984452i \(-0.443796\pi\)
0.175653 + 0.984452i \(0.443796\pi\)
\(278\) 3.92218e13 1.41671
\(279\) 0 0
\(280\) −5.16869e13 −1.79478
\(281\) 3.89335e13 1.32568 0.662839 0.748762i \(-0.269351\pi\)
0.662839 + 0.748762i \(0.269351\pi\)
\(282\) 0 0
\(283\) −3.71087e13 −1.21521 −0.607603 0.794241i \(-0.707869\pi\)
−0.607603 + 0.794241i \(0.707869\pi\)
\(284\) 1.58133e12 0.0507893
\(285\) 0 0
\(286\) −6.15001e12 −0.190048
\(287\) −6.30452e12 −0.191118
\(288\) 0 0
\(289\) 4.62478e13 1.34944
\(290\) −7.95920e13 −2.27867
\(291\) 0 0
\(292\) 2.92707e11 0.00806916
\(293\) 3.39516e13 0.918518 0.459259 0.888302i \(-0.348115\pi\)
0.459259 + 0.888302i \(0.348115\pi\)
\(294\) 0 0
\(295\) −6.49667e13 −1.69305
\(296\) 7.57479e11 0.0193761
\(297\) 0 0
\(298\) −7.31966e13 −1.80427
\(299\) 7.92892e12 0.191877
\(300\) 0 0
\(301\) 9.24195e13 2.15600
\(302\) −2.31212e13 −0.529630
\(303\) 0 0
\(304\) 5.08716e13 1.12375
\(305\) −3.47756e13 −0.754442
\(306\) 0 0
\(307\) 3.85370e12 0.0806524 0.0403262 0.999187i \(-0.487160\pi\)
0.0403262 + 0.999187i \(0.487160\pi\)
\(308\) −4.40523e12 −0.0905606
\(309\) 0 0
\(310\) 5.99249e13 1.18883
\(311\) 5.07944e13 0.989996 0.494998 0.868894i \(-0.335169\pi\)
0.494998 + 0.868894i \(0.335169\pi\)
\(312\) 0 0
\(313\) −2.78127e13 −0.523299 −0.261649 0.965163i \(-0.584266\pi\)
−0.261649 + 0.965163i \(0.584266\pi\)
\(314\) −2.09654e13 −0.387605
\(315\) 0 0
\(316\) 5.01193e12 0.0894799
\(317\) −2.62079e13 −0.459840 −0.229920 0.973210i \(-0.573846\pi\)
−0.229920 + 0.973210i \(0.573846\pi\)
\(318\) 0 0
\(319\) 2.26502e13 0.383904
\(320\) 6.52514e13 1.08709
\(321\) 0 0
\(322\) 3.03225e13 0.488155
\(323\) 9.24401e13 1.46301
\(324\) 0 0
\(325\) 5.91934e13 0.905555
\(326\) 2.84201e13 0.427493
\(327\) 0 0
\(328\) 8.58484e12 0.124861
\(329\) −8.36926e13 −1.19704
\(330\) 0 0
\(331\) −1.36923e14 −1.89418 −0.947091 0.320964i \(-0.895993\pi\)
−0.947091 + 0.320964i \(0.895993\pi\)
\(332\) 2.83214e13 0.385350
\(333\) 0 0
\(334\) −4.19540e13 −0.552291
\(335\) −1.02482e14 −1.32710
\(336\) 0 0
\(337\) −5.25144e13 −0.658134 −0.329067 0.944307i \(-0.606734\pi\)
−0.329067 + 0.944307i \(0.606734\pi\)
\(338\) −6.07679e13 −0.749260
\(339\) 0 0
\(340\) −4.76257e13 −0.568470
\(341\) −1.70533e13 −0.200290
\(342\) 0 0
\(343\) −3.36424e13 −0.382622
\(344\) −1.25847e14 −1.40855
\(345\) 0 0
\(346\) 1.13289e14 1.22820
\(347\) 3.79900e13 0.405375 0.202687 0.979243i \(-0.435032\pi\)
0.202687 + 0.979243i \(0.435032\pi\)
\(348\) 0 0
\(349\) −1.48524e14 −1.53552 −0.767760 0.640737i \(-0.778629\pi\)
−0.767760 + 0.640737i \(0.778629\pi\)
\(350\) 2.26373e14 2.30383
\(351\) 0 0
\(352\) 1.37937e13 0.136049
\(353\) 1.45298e14 1.41091 0.705455 0.708755i \(-0.250743\pi\)
0.705455 + 0.708755i \(0.250743\pi\)
\(354\) 0 0
\(355\) 3.76729e13 0.354628
\(356\) −2.89869e13 −0.268675
\(357\) 0 0
\(358\) 6.47081e13 0.581570
\(359\) −1.66188e14 −1.47089 −0.735443 0.677587i \(-0.763026\pi\)
−0.735443 + 0.677587i \(0.763026\pi\)
\(360\) 0 0
\(361\) −1.03652e13 −0.0889787
\(362\) 5.73110e13 0.484552
\(363\) 0 0
\(364\) 2.09143e13 0.171548
\(365\) 6.97333e12 0.0563416
\(366\) 0 0
\(367\) 1.64228e14 1.28761 0.643804 0.765191i \(-0.277355\pi\)
0.643804 + 0.765191i \(0.277355\pi\)
\(368\) −5.13399e13 −0.396545
\(369\) 0 0
\(370\) −5.40459e12 −0.0405185
\(371\) 6.10842e13 0.451203
\(372\) 0 0
\(373\) 1.49640e14 1.07312 0.536561 0.843862i \(-0.319723\pi\)
0.536561 + 0.843862i \(0.319723\pi\)
\(374\) 7.23605e13 0.511338
\(375\) 0 0
\(376\) 1.13964e14 0.782050
\(377\) −1.07534e14 −0.727225
\(378\) 0 0
\(379\) 7.84646e12 0.0515416 0.0257708 0.999668i \(-0.491796\pi\)
0.0257708 + 0.999668i \(0.491796\pi\)
\(380\) −5.46763e13 −0.353989
\(381\) 0 0
\(382\) −1.99162e14 −1.25273
\(383\) −5.62251e13 −0.348608 −0.174304 0.984692i \(-0.555767\pi\)
−0.174304 + 0.984692i \(0.555767\pi\)
\(384\) 0 0
\(385\) −1.04948e14 −0.632325
\(386\) −3.07799e14 −1.82825
\(387\) 0 0
\(388\) 6.22440e13 0.359354
\(389\) 2.38179e14 1.35575 0.677876 0.735177i \(-0.262901\pi\)
0.677876 + 0.735177i \(0.262901\pi\)
\(390\) 0 0
\(391\) −9.32910e13 −0.516259
\(392\) −1.10625e14 −0.603640
\(393\) 0 0
\(394\) 1.74551e13 0.0926175
\(395\) 1.19402e14 0.624780
\(396\) 0 0
\(397\) −1.01185e13 −0.0514956 −0.0257478 0.999668i \(-0.508197\pi\)
−0.0257478 + 0.999668i \(0.508197\pi\)
\(398\) 2.14279e14 1.07553
\(399\) 0 0
\(400\) −3.83278e14 −1.87148
\(401\) 3.13474e14 1.50976 0.754878 0.655865i \(-0.227696\pi\)
0.754878 + 0.655865i \(0.227696\pi\)
\(402\) 0 0
\(403\) 8.09625e13 0.379408
\(404\) 1.28481e12 0.00593940
\(405\) 0 0
\(406\) −4.11242e14 −1.85014
\(407\) 1.53803e12 0.00682645
\(408\) 0 0
\(409\) 9.25258e13 0.399747 0.199873 0.979822i \(-0.435947\pi\)
0.199873 + 0.979822i \(0.435947\pi\)
\(410\) −6.12525e13 −0.261104
\(411\) 0 0
\(412\) 3.75400e13 0.155797
\(413\) −3.35675e14 −1.37465
\(414\) 0 0
\(415\) 6.74716e14 2.69065
\(416\) −6.54871e13 −0.257717
\(417\) 0 0
\(418\) 8.30729e13 0.318412
\(419\) −2.36795e14 −0.895769 −0.447884 0.894091i \(-0.647822\pi\)
−0.447884 + 0.894091i \(0.647822\pi\)
\(420\) 0 0
\(421\) −4.05554e14 −1.49450 −0.747252 0.664541i \(-0.768627\pi\)
−0.747252 + 0.664541i \(0.768627\pi\)
\(422\) 3.44436e14 1.25282
\(423\) 0 0
\(424\) −8.31781e13 −0.294779
\(425\) −6.96465e14 −2.43646
\(426\) 0 0
\(427\) −1.79681e14 −0.612561
\(428\) 9.38058e13 0.315710
\(429\) 0 0
\(430\) 8.97917e14 2.94550
\(431\) 4.86438e14 1.57544 0.787720 0.616033i \(-0.211261\pi\)
0.787720 + 0.616033i \(0.211261\pi\)
\(432\) 0 0
\(433\) 1.85422e14 0.585434 0.292717 0.956199i \(-0.405441\pi\)
0.292717 + 0.956199i \(0.405441\pi\)
\(434\) 3.09624e14 0.965254
\(435\) 0 0
\(436\) −1.36567e13 −0.0415117
\(437\) −1.07102e14 −0.321477
\(438\) 0 0
\(439\) 5.01757e14 1.46872 0.734359 0.678762i \(-0.237483\pi\)
0.734359 + 0.678762i \(0.237483\pi\)
\(440\) 1.42907e14 0.413110
\(441\) 0 0
\(442\) −3.43540e14 −0.968622
\(443\) −1.34268e14 −0.373896 −0.186948 0.982370i \(-0.559860\pi\)
−0.186948 + 0.982370i \(0.559860\pi\)
\(444\) 0 0
\(445\) −6.90571e14 −1.87598
\(446\) −5.52462e14 −1.48238
\(447\) 0 0
\(448\) 3.37146e14 0.882650
\(449\) 6.49358e14 1.67931 0.839653 0.543124i \(-0.182759\pi\)
0.839653 + 0.543124i \(0.182759\pi\)
\(450\) 0 0
\(451\) 1.74311e13 0.0439901
\(452\) 9.71522e13 0.242209
\(453\) 0 0
\(454\) −4.45330e14 −1.08361
\(455\) 4.98253e14 1.19781
\(456\) 0 0
\(457\) −4.64508e14 −1.09007 −0.545035 0.838413i \(-0.683484\pi\)
−0.545035 + 0.838413i \(0.683484\pi\)
\(458\) −5.71748e14 −1.32570
\(459\) 0 0
\(460\) 5.51797e13 0.124914
\(461\) −2.00000e14 −0.447379 −0.223690 0.974660i \(-0.571810\pi\)
−0.223690 + 0.974660i \(0.571810\pi\)
\(462\) 0 0
\(463\) 2.71686e14 0.593433 0.296717 0.954966i \(-0.404108\pi\)
0.296717 + 0.954966i \(0.404108\pi\)
\(464\) 6.96286e14 1.50293
\(465\) 0 0
\(466\) −4.65320e14 −0.980910
\(467\) −8.06950e14 −1.68114 −0.840570 0.541703i \(-0.817780\pi\)
−0.840570 + 0.541703i \(0.817780\pi\)
\(468\) 0 0
\(469\) −5.29513e14 −1.07752
\(470\) −8.13129e14 −1.63539
\(471\) 0 0
\(472\) 4.57087e14 0.898086
\(473\) −2.55528e14 −0.496251
\(474\) 0 0
\(475\) −7.99571e14 −1.51720
\(476\) −2.46076e14 −0.461563
\(477\) 0 0
\(478\) 1.03178e15 1.89119
\(479\) 2.97087e14 0.538317 0.269158 0.963096i \(-0.413255\pi\)
0.269158 + 0.963096i \(0.413255\pi\)
\(480\) 0 0
\(481\) −7.30195e12 −0.0129313
\(482\) 6.46060e14 1.13113
\(483\) 0 0
\(484\) −1.22487e14 −0.209624
\(485\) 1.48287e15 2.50914
\(486\) 0 0
\(487\) −9.67456e13 −0.160038 −0.0800188 0.996793i \(-0.525498\pi\)
−0.0800188 + 0.996793i \(0.525498\pi\)
\(488\) 2.44671e14 0.400197
\(489\) 0 0
\(490\) 7.89303e14 1.26231
\(491\) −4.52873e14 −0.716189 −0.358095 0.933685i \(-0.616574\pi\)
−0.358095 + 0.933685i \(0.616574\pi\)
\(492\) 0 0
\(493\) 1.26524e15 1.95665
\(494\) −3.94398e14 −0.603165
\(495\) 0 0
\(496\) −5.24234e14 −0.784109
\(497\) 1.94651e14 0.287937
\(498\) 0 0
\(499\) 2.84707e14 0.411950 0.205975 0.978557i \(-0.433963\pi\)
0.205975 + 0.978557i \(0.433963\pi\)
\(500\) 1.52789e14 0.218653
\(501\) 0 0
\(502\) −1.79311e14 −0.251036
\(503\) −4.60548e14 −0.637750 −0.318875 0.947797i \(-0.603305\pi\)
−0.318875 + 0.947797i \(0.603305\pi\)
\(504\) 0 0
\(505\) 3.06088e13 0.0414709
\(506\) −8.38377e13 −0.112360
\(507\) 0 0
\(508\) 2.12078e14 0.278129
\(509\) −1.07972e15 −1.40076 −0.700378 0.713772i \(-0.746985\pi\)
−0.700378 + 0.713772i \(0.746985\pi\)
\(510\) 0 0
\(511\) 3.60303e13 0.0457460
\(512\) −3.76086e14 −0.472391
\(513\) 0 0
\(514\) 1.40487e14 0.172719
\(515\) 8.94335e14 1.08783
\(516\) 0 0
\(517\) 2.31399e14 0.275526
\(518\) −2.79248e13 −0.0328985
\(519\) 0 0
\(520\) −6.78469e14 −0.782549
\(521\) 8.11121e12 0.00925717 0.00462859 0.999989i \(-0.498527\pi\)
0.00462859 + 0.999989i \(0.498527\pi\)
\(522\) 0 0
\(523\) −1.00543e15 −1.12355 −0.561774 0.827291i \(-0.689881\pi\)
−0.561774 + 0.827291i \(0.689881\pi\)
\(524\) 1.89716e14 0.209788
\(525\) 0 0
\(526\) −1.50267e15 −1.62720
\(527\) −9.52599e14 −1.02083
\(528\) 0 0
\(529\) −8.44722e14 −0.886559
\(530\) 5.93473e14 0.616430
\(531\) 0 0
\(532\) −2.82506e14 −0.287418
\(533\) −8.27563e13 −0.0833300
\(534\) 0 0
\(535\) 2.23479e15 2.20440
\(536\) 7.21036e14 0.703964
\(537\) 0 0
\(538\) −1.32576e15 −1.26812
\(539\) −2.24618e14 −0.212670
\(540\) 0 0
\(541\) 8.81901e14 0.818153 0.409077 0.912500i \(-0.365851\pi\)
0.409077 + 0.912500i \(0.365851\pi\)
\(542\) 1.49041e15 1.36870
\(543\) 0 0
\(544\) 7.70516e14 0.693406
\(545\) −3.25352e14 −0.289849
\(546\) 0 0
\(547\) −1.79872e15 −1.57048 −0.785241 0.619190i \(-0.787461\pi\)
−0.785241 + 0.619190i \(0.787461\pi\)
\(548\) −2.17393e14 −0.187912
\(549\) 0 0
\(550\) −6.25891e14 −0.530278
\(551\) 1.45255e15 1.21842
\(552\) 0 0
\(553\) 6.16934e14 0.507283
\(554\) 4.78657e14 0.389691
\(555\) 0 0
\(556\) 3.68782e14 0.294346
\(557\) −1.41741e15 −1.12019 −0.560095 0.828428i \(-0.689236\pi\)
−0.560095 + 0.828428i \(0.689236\pi\)
\(558\) 0 0
\(559\) 1.21315e15 0.940043
\(560\) −3.22620e15 −2.47547
\(561\) 0 0
\(562\) 1.95444e15 1.47053
\(563\) 1.42508e15 1.06180 0.530900 0.847435i \(-0.321854\pi\)
0.530900 + 0.847435i \(0.321854\pi\)
\(564\) 0 0
\(565\) 2.31451e15 1.69119
\(566\) −1.86284e15 −1.34799
\(567\) 0 0
\(568\) −2.65056e14 −0.188114
\(569\) −1.45634e15 −1.02364 −0.511819 0.859093i \(-0.671028\pi\)
−0.511819 + 0.859093i \(0.671028\pi\)
\(570\) 0 0
\(571\) −1.56479e15 −1.07884 −0.539421 0.842036i \(-0.681357\pi\)
−0.539421 + 0.842036i \(0.681357\pi\)
\(572\) −5.78253e13 −0.0394857
\(573\) 0 0
\(574\) −3.16484e14 −0.212000
\(575\) 8.06931e14 0.535382
\(576\) 0 0
\(577\) 9.10934e14 0.592952 0.296476 0.955040i \(-0.404188\pi\)
0.296476 + 0.955040i \(0.404188\pi\)
\(578\) 2.32162e15 1.49689
\(579\) 0 0
\(580\) −7.48361e14 −0.473432
\(581\) 3.48617e15 2.18464
\(582\) 0 0
\(583\) −1.68890e14 −0.103855
\(584\) −4.90623e13 −0.0298867
\(585\) 0 0
\(586\) 1.70435e15 1.01888
\(587\) 2.65329e14 0.157136 0.0785680 0.996909i \(-0.474965\pi\)
0.0785680 + 0.996909i \(0.474965\pi\)
\(588\) 0 0
\(589\) −1.09362e15 −0.635673
\(590\) −3.26130e15 −1.87804
\(591\) 0 0
\(592\) 4.72803e13 0.0267246
\(593\) 2.50632e15 1.40358 0.701788 0.712386i \(-0.252385\pi\)
0.701788 + 0.712386i \(0.252385\pi\)
\(594\) 0 0
\(595\) −5.86240e15 −3.22279
\(596\) −6.88228e14 −0.374868
\(597\) 0 0
\(598\) 3.98029e14 0.212842
\(599\) −3.47914e15 −1.84342 −0.921710 0.387881i \(-0.873207\pi\)
−0.921710 + 0.387881i \(0.873207\pi\)
\(600\) 0 0
\(601\) 1.81057e15 0.941901 0.470950 0.882160i \(-0.343911\pi\)
0.470950 + 0.882160i \(0.343911\pi\)
\(602\) 4.63942e15 2.39157
\(603\) 0 0
\(604\) −2.17397e14 −0.110040
\(605\) −2.91808e15 −1.46367
\(606\) 0 0
\(607\) −1.64117e15 −0.808380 −0.404190 0.914675i \(-0.632446\pi\)
−0.404190 + 0.914675i \(0.632446\pi\)
\(608\) 8.84585e14 0.431787
\(609\) 0 0
\(610\) −1.74572e15 −0.836876
\(611\) −1.09859e15 −0.521927
\(612\) 0 0
\(613\) −6.47250e14 −0.302022 −0.151011 0.988532i \(-0.548253\pi\)
−0.151011 + 0.988532i \(0.548253\pi\)
\(614\) 1.93454e14 0.0894649
\(615\) 0 0
\(616\) 7.38385e14 0.335420
\(617\) 1.60917e14 0.0724493 0.0362247 0.999344i \(-0.488467\pi\)
0.0362247 + 0.999344i \(0.488467\pi\)
\(618\) 0 0
\(619\) 1.16338e15 0.514545 0.257272 0.966339i \(-0.417176\pi\)
0.257272 + 0.966339i \(0.417176\pi\)
\(620\) 5.63442e14 0.246999
\(621\) 0 0
\(622\) 2.54986e15 1.09817
\(623\) −3.56809e15 −1.52318
\(624\) 0 0
\(625\) −1.49850e14 −0.0628518
\(626\) −1.39619e15 −0.580477
\(627\) 0 0
\(628\) −1.97126e14 −0.0805315
\(629\) 8.59142e13 0.0347926
\(630\) 0 0
\(631\) 2.12985e15 0.847594 0.423797 0.905757i \(-0.360697\pi\)
0.423797 + 0.905757i \(0.360697\pi\)
\(632\) −8.40077e14 −0.331417
\(633\) 0 0
\(634\) −1.31563e15 −0.510084
\(635\) 5.05245e15 1.94199
\(636\) 0 0
\(637\) 1.06640e15 0.402859
\(638\) 1.13703e15 0.425851
\(639\) 0 0
\(640\) 5.25306e15 1.93385
\(641\) 2.33718e15 0.853046 0.426523 0.904477i \(-0.359738\pi\)
0.426523 + 0.904477i \(0.359738\pi\)
\(642\) 0 0
\(643\) −4.93057e15 −1.76904 −0.884518 0.466505i \(-0.845513\pi\)
−0.884518 + 0.466505i \(0.845513\pi\)
\(644\) 2.85106e14 0.101423
\(645\) 0 0
\(646\) 4.64045e15 1.62286
\(647\) −2.00854e15 −0.696478 −0.348239 0.937406i \(-0.613220\pi\)
−0.348239 + 0.937406i \(0.613220\pi\)
\(648\) 0 0
\(649\) 9.28095e14 0.316408
\(650\) 2.97148e15 1.00450
\(651\) 0 0
\(652\) 2.67219e14 0.0888189
\(653\) 9.77111e14 0.322048 0.161024 0.986950i \(-0.448520\pi\)
0.161024 + 0.986950i \(0.448520\pi\)
\(654\) 0 0
\(655\) 4.51970e15 1.46481
\(656\) 5.35849e14 0.172215
\(657\) 0 0
\(658\) −4.20134e15 −1.32784
\(659\) 1.02367e15 0.320842 0.160421 0.987049i \(-0.448715\pi\)
0.160421 + 0.987049i \(0.448715\pi\)
\(660\) 0 0
\(661\) −1.85889e15 −0.572989 −0.286495 0.958082i \(-0.592490\pi\)
−0.286495 + 0.958082i \(0.592490\pi\)
\(662\) −6.87347e15 −2.10115
\(663\) 0 0
\(664\) −4.74711e15 −1.42727
\(665\) −6.73029e15 −2.00685
\(666\) 0 0
\(667\) −1.46592e15 −0.429950
\(668\) −3.94471e14 −0.114748
\(669\) 0 0
\(670\) −5.14457e15 −1.47210
\(671\) 4.96795e14 0.140995
\(672\) 0 0
\(673\) 1.22633e15 0.342392 0.171196 0.985237i \(-0.445237\pi\)
0.171196 + 0.985237i \(0.445237\pi\)
\(674\) −2.63620e15 −0.730045
\(675\) 0 0
\(676\) −5.71368e14 −0.155671
\(677\) 2.91034e15 0.786513 0.393257 0.919429i \(-0.371348\pi\)
0.393257 + 0.919429i \(0.371348\pi\)
\(678\) 0 0
\(679\) 7.66182e15 2.03727
\(680\) 7.98281e15 2.10551
\(681\) 0 0
\(682\) −8.56070e14 −0.222175
\(683\) −1.19523e15 −0.307707 −0.153854 0.988094i \(-0.549168\pi\)
−0.153854 + 0.988094i \(0.549168\pi\)
\(684\) 0 0
\(685\) −5.17908e15 −1.31206
\(686\) −1.68884e15 −0.424429
\(687\) 0 0
\(688\) −7.85514e15 −1.94275
\(689\) 8.01822e14 0.196731
\(690\) 0 0
\(691\) −2.23559e14 −0.0539836 −0.0269918 0.999636i \(-0.508593\pi\)
−0.0269918 + 0.999636i \(0.508593\pi\)
\(692\) 1.06519e15 0.255179
\(693\) 0 0
\(694\) 1.90708e15 0.449668
\(695\) 8.78569e15 2.05523
\(696\) 0 0
\(697\) 9.73704e14 0.224206
\(698\) −7.45582e15 −1.70330
\(699\) 0 0
\(700\) 2.12846e15 0.478660
\(701\) −1.27005e15 −0.283382 −0.141691 0.989911i \(-0.545254\pi\)
−0.141691 + 0.989911i \(0.545254\pi\)
\(702\) 0 0
\(703\) 9.86331e13 0.0216655
\(704\) −9.32163e14 −0.203162
\(705\) 0 0
\(706\) 7.29391e15 1.56507
\(707\) 1.58152e14 0.0336719
\(708\) 0 0
\(709\) 3.53998e15 0.742073 0.371036 0.928618i \(-0.379003\pi\)
0.371036 + 0.928618i \(0.379003\pi\)
\(710\) 1.89117e15 0.393377
\(711\) 0 0
\(712\) 4.85866e15 0.995123
\(713\) 1.10369e15 0.224313
\(714\) 0 0
\(715\) −1.37760e15 −0.275702
\(716\) 6.08416e14 0.120831
\(717\) 0 0
\(718\) −8.34255e15 −1.63160
\(719\) 6.36514e15 1.23538 0.617688 0.786423i \(-0.288069\pi\)
0.617688 + 0.786423i \(0.288069\pi\)
\(720\) 0 0
\(721\) 4.62091e15 0.883251
\(722\) −5.20327e14 −0.0987010
\(723\) 0 0
\(724\) 5.38864e14 0.100674
\(725\) −1.09438e16 −2.02913
\(726\) 0 0
\(727\) 8.81856e15 1.61049 0.805246 0.592941i \(-0.202033\pi\)
0.805246 + 0.592941i \(0.202033\pi\)
\(728\) −3.50556e15 −0.635383
\(729\) 0 0
\(730\) 3.50058e14 0.0624978
\(731\) −1.42738e16 −2.52926
\(732\) 0 0
\(733\) 1.75733e15 0.306747 0.153374 0.988168i \(-0.450986\pi\)
0.153374 + 0.988168i \(0.450986\pi\)
\(734\) 8.24417e15 1.42830
\(735\) 0 0
\(736\) −8.92728e14 −0.152367
\(737\) 1.46403e15 0.248016
\(738\) 0 0
\(739\) −3.76801e15 −0.628879 −0.314440 0.949277i \(-0.601817\pi\)
−0.314440 + 0.949277i \(0.601817\pi\)
\(740\) −5.08164e13 −0.00841840
\(741\) 0 0
\(742\) 3.06640e15 0.500504
\(743\) −2.68502e15 −0.435019 −0.217510 0.976058i \(-0.569793\pi\)
−0.217510 + 0.976058i \(0.569793\pi\)
\(744\) 0 0
\(745\) −1.63960e16 −2.61746
\(746\) 7.51186e15 1.19038
\(747\) 0 0
\(748\) 6.80367e14 0.106239
\(749\) 1.15469e16 1.78984
\(750\) 0 0
\(751\) 3.28092e15 0.501159 0.250580 0.968096i \(-0.419379\pi\)
0.250580 + 0.968096i \(0.419379\pi\)
\(752\) 7.11341e15 1.07865
\(753\) 0 0
\(754\) −5.39817e15 −0.806685
\(755\) −5.17916e15 −0.768335
\(756\) 0 0
\(757\) −1.15379e16 −1.68695 −0.843473 0.537172i \(-0.819492\pi\)
−0.843473 + 0.537172i \(0.819492\pi\)
\(758\) 3.93889e14 0.0571733
\(759\) 0 0
\(760\) 9.16461e15 1.31111
\(761\) 5.19209e15 0.737440 0.368720 0.929541i \(-0.379796\pi\)
0.368720 + 0.929541i \(0.379796\pi\)
\(762\) 0 0
\(763\) −1.68105e15 −0.235340
\(764\) −1.87262e15 −0.260277
\(765\) 0 0
\(766\) −2.82248e15 −0.386698
\(767\) −4.40624e15 −0.599367
\(768\) 0 0
\(769\) −8.28529e15 −1.11100 −0.555498 0.831518i \(-0.687472\pi\)
−0.555498 + 0.831518i \(0.687472\pi\)
\(770\) −5.26835e15 −0.701416
\(771\) 0 0
\(772\) −2.89406e15 −0.379851
\(773\) 1.13272e15 0.147617 0.0738083 0.997272i \(-0.476485\pi\)
0.0738083 + 0.997272i \(0.476485\pi\)
\(774\) 0 0
\(775\) 8.23961e15 1.05864
\(776\) −1.04331e16 −1.33098
\(777\) 0 0
\(778\) 1.19565e16 1.50389
\(779\) 1.11785e15 0.139614
\(780\) 0 0
\(781\) −5.38185e14 −0.0662752
\(782\) −4.68317e15 −0.572668
\(783\) 0 0
\(784\) −6.90497e15 −0.832575
\(785\) −4.69624e15 −0.562299
\(786\) 0 0
\(787\) −2.83408e15 −0.334619 −0.167309 0.985904i \(-0.553508\pi\)
−0.167309 + 0.985904i \(0.553508\pi\)
\(788\) 1.64121e14 0.0192429
\(789\) 0 0
\(790\) 5.99392e15 0.693046
\(791\) 1.19588e16 1.37314
\(792\) 0 0
\(793\) −2.35859e15 −0.267085
\(794\) −5.07947e14 −0.0571223
\(795\) 0 0
\(796\) 2.01475e15 0.223460
\(797\) 4.32095e15 0.475947 0.237973 0.971272i \(-0.423517\pi\)
0.237973 + 0.971272i \(0.423517\pi\)
\(798\) 0 0
\(799\) 1.29259e16 1.40428
\(800\) −6.66467e15 −0.719090
\(801\) 0 0
\(802\) 1.57362e16 1.67472
\(803\) −9.96190e13 −0.0105295
\(804\) 0 0
\(805\) 6.79224e15 0.708167
\(806\) 4.06429e15 0.420864
\(807\) 0 0
\(808\) −2.15355e14 −0.0219985
\(809\) 4.11714e15 0.417714 0.208857 0.977946i \(-0.433026\pi\)
0.208857 + 0.977946i \(0.433026\pi\)
\(810\) 0 0
\(811\) −1.04760e15 −0.104853 −0.0524266 0.998625i \(-0.516696\pi\)
−0.0524266 + 0.998625i \(0.516696\pi\)
\(812\) −3.86669e15 −0.384398
\(813\) 0 0
\(814\) 7.72084e13 0.00757234
\(815\) 6.36610e15 0.620164
\(816\) 0 0
\(817\) −1.63869e16 −1.57498
\(818\) 4.64476e15 0.443425
\(819\) 0 0
\(820\) −5.75925e14 −0.0542487
\(821\) −7.49519e15 −0.701286 −0.350643 0.936509i \(-0.614037\pi\)
−0.350643 + 0.936509i \(0.614037\pi\)
\(822\) 0 0
\(823\) 6.22230e15 0.574449 0.287225 0.957863i \(-0.407267\pi\)
0.287225 + 0.957863i \(0.407267\pi\)
\(824\) −6.29228e15 −0.577043
\(825\) 0 0
\(826\) −1.68507e16 −1.52485
\(827\) 8.83500e15 0.794193 0.397097 0.917777i \(-0.370018\pi\)
0.397097 + 0.917777i \(0.370018\pi\)
\(828\) 0 0
\(829\) 8.47566e15 0.751837 0.375918 0.926653i \(-0.377327\pi\)
0.375918 + 0.926653i \(0.377327\pi\)
\(830\) 3.38705e16 2.98464
\(831\) 0 0
\(832\) 4.42555e15 0.384847
\(833\) −1.25472e16 −1.08392
\(834\) 0 0
\(835\) −9.39770e15 −0.801209
\(836\) 7.81090e14 0.0661556
\(837\) 0 0
\(838\) −1.18870e16 −0.993645
\(839\) −1.76797e16 −1.46819 −0.734097 0.679044i \(-0.762394\pi\)
−0.734097 + 0.679044i \(0.762394\pi\)
\(840\) 0 0
\(841\) 7.68067e15 0.629537
\(842\) −2.03586e16 −1.65780
\(843\) 0 0
\(844\) 3.23854e15 0.260295
\(845\) −1.36120e16 −1.08695
\(846\) 0 0
\(847\) −1.50773e16 −1.18841
\(848\) −5.19181e15 −0.406576
\(849\) 0 0
\(850\) −3.49622e16 −2.70268
\(851\) −9.95411e13 −0.00764522
\(852\) 0 0
\(853\) 1.41010e16 1.06913 0.534565 0.845127i \(-0.320475\pi\)
0.534565 + 0.845127i \(0.320475\pi\)
\(854\) −9.01993e15 −0.679493
\(855\) 0 0
\(856\) −1.57233e16 −1.16933
\(857\) 1.44396e16 1.06699 0.533494 0.845804i \(-0.320879\pi\)
0.533494 + 0.845804i \(0.320879\pi\)
\(858\) 0 0
\(859\) 1.93032e15 0.140821 0.0704104 0.997518i \(-0.477569\pi\)
0.0704104 + 0.997518i \(0.477569\pi\)
\(860\) 8.44263e15 0.611979
\(861\) 0 0
\(862\) 2.44190e16 1.74758
\(863\) 1.33130e16 0.946709 0.473354 0.880872i \(-0.343043\pi\)
0.473354 + 0.880872i \(0.343043\pi\)
\(864\) 0 0
\(865\) 2.53767e16 1.78175
\(866\) 9.30811e15 0.649401
\(867\) 0 0
\(868\) 2.91123e15 0.200548
\(869\) −1.70574e15 −0.116763
\(870\) 0 0
\(871\) −6.95066e15 −0.469814
\(872\) 2.28908e15 0.153752
\(873\) 0 0
\(874\) −5.37648e15 −0.356603
\(875\) 1.88072e16 1.23960
\(876\) 0 0
\(877\) −2.19539e16 −1.42894 −0.714470 0.699666i \(-0.753332\pi\)
−0.714470 + 0.699666i \(0.753332\pi\)
\(878\) 2.51880e16 1.62920
\(879\) 0 0
\(880\) 8.92001e15 0.569784
\(881\) −2.10443e16 −1.33588 −0.667939 0.744216i \(-0.732823\pi\)
−0.667939 + 0.744216i \(0.732823\pi\)
\(882\) 0 0
\(883\) 2.63651e16 1.65290 0.826449 0.563012i \(-0.190357\pi\)
0.826449 + 0.563012i \(0.190357\pi\)
\(884\) −3.23012e15 −0.201248
\(885\) 0 0
\(886\) −6.74019e15 −0.414750
\(887\) −2.03473e16 −1.24431 −0.622154 0.782895i \(-0.713742\pi\)
−0.622154 + 0.782895i \(0.713742\pi\)
\(888\) 0 0
\(889\) 2.61054e16 1.57678
\(890\) −3.46664e16 −2.08096
\(891\) 0 0
\(892\) −5.19450e15 −0.307991
\(893\) 1.48395e16 0.874454
\(894\) 0 0
\(895\) 1.44946e16 0.843685
\(896\) 2.71419e16 1.57017
\(897\) 0 0
\(898\) 3.25975e16 1.86279
\(899\) −1.49686e16 −0.850162
\(900\) 0 0
\(901\) −9.43417e15 −0.529319
\(902\) 8.75036e14 0.0487967
\(903\) 0 0
\(904\) −1.62842e16 −0.897099
\(905\) 1.28377e16 0.702941
\(906\) 0 0
\(907\) −2.57952e16 −1.39540 −0.697699 0.716391i \(-0.745793\pi\)
−0.697699 + 0.716391i \(0.745793\pi\)
\(908\) −4.18720e15 −0.225139
\(909\) 0 0
\(910\) 2.50121e16 1.32869
\(911\) −2.51182e16 −1.32629 −0.663143 0.748493i \(-0.730778\pi\)
−0.663143 + 0.748493i \(0.730778\pi\)
\(912\) 0 0
\(913\) −9.63880e15 −0.502845
\(914\) −2.33181e16 −1.20918
\(915\) 0 0
\(916\) −5.37584e15 −0.275436
\(917\) 2.33527e16 1.18934
\(918\) 0 0
\(919\) −2.49514e16 −1.25562 −0.627812 0.778365i \(-0.716049\pi\)
−0.627812 + 0.778365i \(0.716049\pi\)
\(920\) −9.24897e15 −0.462658
\(921\) 0 0
\(922\) −1.00399e16 −0.496262
\(923\) 2.55509e15 0.125544
\(924\) 0 0
\(925\) −7.43125e14 −0.0360813
\(926\) 1.36385e16 0.658275
\(927\) 0 0
\(928\) 1.21074e16 0.577481
\(929\) 1.47918e15 0.0701350 0.0350675 0.999385i \(-0.488835\pi\)
0.0350675 + 0.999385i \(0.488835\pi\)
\(930\) 0 0
\(931\) −1.44047e16 −0.674965
\(932\) −4.37516e15 −0.203801
\(933\) 0 0
\(934\) −4.05086e16 −1.86483
\(935\) 1.62088e16 0.741798
\(936\) 0 0
\(937\) 2.25881e16 1.02167 0.510836 0.859678i \(-0.329336\pi\)
0.510836 + 0.859678i \(0.329336\pi\)
\(938\) −2.65813e16 −1.19526
\(939\) 0 0
\(940\) −7.64542e15 −0.339780
\(941\) 1.81217e16 0.800676 0.400338 0.916368i \(-0.368893\pi\)
0.400338 + 0.916368i \(0.368893\pi\)
\(942\) 0 0
\(943\) −1.12814e15 −0.0492663
\(944\) 2.85305e16 1.23869
\(945\) 0 0
\(946\) −1.28274e16 −0.550474
\(947\) 4.12129e16 1.75836 0.879182 0.476487i \(-0.158090\pi\)
0.879182 + 0.476487i \(0.158090\pi\)
\(948\) 0 0
\(949\) 4.72952e14 0.0199459
\(950\) −4.01381e16 −1.68297
\(951\) 0 0
\(952\) 4.12462e16 1.70955
\(953\) 3.38222e16 1.39377 0.696884 0.717184i \(-0.254569\pi\)
0.696884 + 0.717184i \(0.254569\pi\)
\(954\) 0 0
\(955\) −4.46123e16 −1.81734
\(956\) 9.70131e15 0.392927
\(957\) 0 0
\(958\) 1.49136e16 0.597136
\(959\) −2.67597e16 −1.06532
\(960\) 0 0
\(961\) −1.41386e16 −0.556453
\(962\) −3.66555e14 −0.0143442
\(963\) 0 0
\(964\) 6.07455e15 0.235012
\(965\) −6.89469e16 −2.65225
\(966\) 0 0
\(967\) −2.90802e16 −1.10599 −0.552996 0.833184i \(-0.686515\pi\)
−0.552996 + 0.833184i \(0.686515\pi\)
\(968\) 2.05308e16 0.776410
\(969\) 0 0
\(970\) 7.44396e16 2.78330
\(971\) −2.93231e16 −1.09020 −0.545098 0.838373i \(-0.683507\pi\)
−0.545098 + 0.838373i \(0.683507\pi\)
\(972\) 0 0
\(973\) 4.53946e16 1.66872
\(974\) −4.85659e15 −0.177524
\(975\) 0 0
\(976\) 1.52719e16 0.551975
\(977\) −4.17408e16 −1.50017 −0.750086 0.661341i \(-0.769988\pi\)
−0.750086 + 0.661341i \(0.769988\pi\)
\(978\) 0 0
\(979\) 9.86530e15 0.350595
\(980\) 7.42139e15 0.262266
\(981\) 0 0
\(982\) −2.27340e16 −0.794444
\(983\) −9.55672e15 −0.332097 −0.166048 0.986118i \(-0.553101\pi\)
−0.166048 + 0.986118i \(0.553101\pi\)
\(984\) 0 0
\(985\) 3.90994e15 0.134360
\(986\) 6.35144e16 2.17045
\(987\) 0 0
\(988\) −3.70831e15 −0.125318
\(989\) 1.65377e16 0.555772
\(990\) 0 0
\(991\) −2.90356e15 −0.0964997 −0.0482499 0.998835i \(-0.515364\pi\)
−0.0482499 + 0.998835i \(0.515364\pi\)
\(992\) −9.11569e15 −0.301283
\(993\) 0 0
\(994\) 9.77142e15 0.319398
\(995\) 4.79986e16 1.56028
\(996\) 0 0
\(997\) −3.74887e15 −0.120525 −0.0602625 0.998183i \(-0.519194\pi\)
−0.0602625 + 0.998183i \(0.519194\pi\)
\(998\) 1.42922e16 0.456962
\(999\) 0 0
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 \(a_p\))