Properties

Label 16.12.a.d.1.1
Level 16
Weight 12
Character 16.1
Self dual Yes
Analytic conductor 12.293
Analytic rank 0
Dimension 2
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 16.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(12.293490889\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{109}) \)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{7} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(5.72015\)
Character \(\chi\) = 16.1

$q$-expansion

\(f(q)\) \(=\) \(q-696.180 q^{3} -4084.16 q^{5} -73591.5 q^{7} +307519. q^{9} +O(q^{10})\) \(q-696.180 q^{3} -4084.16 q^{5} -73591.5 q^{7} +307519. q^{9} +383508. q^{11} +1.15867e6 q^{13} +2.84331e6 q^{15} -6.51693e6 q^{17} +1.39982e7 q^{19} +5.12329e7 q^{21} -1.37394e6 q^{23} -3.21478e7 q^{25} -9.07624e7 q^{27} -7.46197e7 q^{29} -1.32297e7 q^{31} -2.66991e8 q^{33} +3.00559e8 q^{35} -1.67200e7 q^{37} -8.06644e8 q^{39} +1.03298e9 q^{41} -1.93764e8 q^{43} -1.25596e9 q^{45} +1.16005e9 q^{47} +3.43839e9 q^{49} +4.53696e9 q^{51} +4.44363e8 q^{53} -1.56631e9 q^{55} -9.74529e9 q^{57} +1.28304e8 q^{59} +7.96097e9 q^{61} -2.26308e10 q^{63} -4.73220e9 q^{65} +6.89243e9 q^{67} +9.56509e8 q^{69} +1.12698e10 q^{71} +3.34998e9 q^{73} +2.23806e10 q^{75} -2.82230e10 q^{77} -5.36237e10 q^{79} +8.71083e9 q^{81} +6.31693e10 q^{83} +2.66162e10 q^{85} +5.19487e10 q^{87} +9.62373e10 q^{89} -8.52685e10 q^{91} +9.21027e9 q^{93} -5.71710e10 q^{95} -4.37466e10 q^{97} +1.17936e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 56q^{3} + 7868q^{5} - 91056q^{7} + 540202q^{9} + O(q^{10}) \) \( 2q - 56q^{3} + 7868q^{5} - 91056q^{7} + 540202q^{9} - 159080q^{11} + 1050476q^{13} + 10494832q^{15} + 1430884q^{17} + 21866600q^{19} + 40052544q^{21} - 35806736q^{23} + 61878094q^{25} - 55209392q^{27} - 228827700q^{29} - 64722112q^{31} - 614344864q^{33} + 91821408q^{35} + 75558780q^{37} - 875909072q^{39} + 1201214196q^{41} + 45519832q^{43} + 1525107052q^{45} + 1229079264q^{47} + 1766069074q^{49} + 9624987920q^{51} - 3808549924q^{53} - 8051409968q^{55} - 4708125536q^{57} + 6012926584q^{59} + 9789792908q^{61} - 26694483312q^{63} - 6025376344q^{65} - 14703095224q^{67} - 21086664256q^{69} - 4319991088q^{71} + 11055639476q^{73} + 82574103416q^{75} - 18746968128q^{77} - 51957623264q^{79} - 9747960302q^{81} + 108227975912q^{83} + 121609729720q^{85} - 46772044368q^{87} + 71188291860q^{89} - 83378892576q^{91} - 23754095360q^{93} + 36872875568q^{95} - 1699807676q^{97} - 8314917256q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −696.180 −1.65407 −0.827036 0.562149i \(-0.809975\pi\)
−0.827036 + 0.562149i \(0.809975\pi\)
\(4\) 0 0
\(5\) −4084.16 −0.584477 −0.292238 0.956346i \(-0.594400\pi\)
−0.292238 + 0.956346i \(0.594400\pi\)
\(6\) 0 0
\(7\) −73591.5 −1.65496 −0.827482 0.561492i \(-0.810228\pi\)
−0.827482 + 0.561492i \(0.810228\pi\)
\(8\) 0 0
\(9\) 307519. 1.73595
\(10\) 0 0
\(11\) 383508. 0.717985 0.358992 0.933340i \(-0.383120\pi\)
0.358992 + 0.933340i \(0.383120\pi\)
\(12\) 0 0
\(13\) 1.15867e6 0.865510 0.432755 0.901512i \(-0.357541\pi\)
0.432755 + 0.901512i \(0.357541\pi\)
\(14\) 0 0
\(15\) 2.84331e6 0.966767
\(16\) 0 0
\(17\) −6.51693e6 −1.11320 −0.556601 0.830780i \(-0.687895\pi\)
−0.556601 + 0.830780i \(0.687895\pi\)
\(18\) 0 0
\(19\) 1.39982e7 1.29697 0.648483 0.761229i \(-0.275404\pi\)
0.648483 + 0.761229i \(0.275404\pi\)
\(20\) 0 0
\(21\) 5.12329e7 2.73743
\(22\) 0 0
\(23\) −1.37394e6 −0.0445107 −0.0222554 0.999752i \(-0.507085\pi\)
−0.0222554 + 0.999752i \(0.507085\pi\)
\(24\) 0 0
\(25\) −3.21478e7 −0.658387
\(26\) 0 0
\(27\) −9.07624e7 −1.21732
\(28\) 0 0
\(29\) −7.46197e7 −0.675561 −0.337781 0.941225i \(-0.609676\pi\)
−0.337781 + 0.941225i \(0.609676\pi\)
\(30\) 0 0
\(31\) −1.32297e7 −0.0829969 −0.0414985 0.999139i \(-0.513213\pi\)
−0.0414985 + 0.999139i \(0.513213\pi\)
\(32\) 0 0
\(33\) −2.66991e8 −1.18760
\(34\) 0 0
\(35\) 3.00559e8 0.967288
\(36\) 0 0
\(37\) −1.67200e7 −0.0396394 −0.0198197 0.999804i \(-0.506309\pi\)
−0.0198197 + 0.999804i \(0.506309\pi\)
\(38\) 0 0
\(39\) −8.06644e8 −1.43162
\(40\) 0 0
\(41\) 1.03298e9 1.39245 0.696225 0.717823i \(-0.254861\pi\)
0.696225 + 0.717823i \(0.254861\pi\)
\(42\) 0 0
\(43\) −1.93764e8 −0.201001 −0.100500 0.994937i \(-0.532044\pi\)
−0.100500 + 0.994937i \(0.532044\pi\)
\(44\) 0 0
\(45\) −1.25596e9 −1.01462
\(46\) 0 0
\(47\) 1.16005e9 0.737803 0.368901 0.929469i \(-0.379734\pi\)
0.368901 + 0.929469i \(0.379734\pi\)
\(48\) 0 0
\(49\) 3.43839e9 1.73891
\(50\) 0 0
\(51\) 4.53696e9 1.84132
\(52\) 0 0
\(53\) 4.44363e8 0.145956 0.0729778 0.997334i \(-0.476750\pi\)
0.0729778 + 0.997334i \(0.476750\pi\)
\(54\) 0 0
\(55\) −1.56631e9 −0.419645
\(56\) 0 0
\(57\) −9.74529e9 −2.14528
\(58\) 0 0
\(59\) 1.28304e8 0.0233644 0.0116822 0.999932i \(-0.496281\pi\)
0.0116822 + 0.999932i \(0.496281\pi\)
\(60\) 0 0
\(61\) 7.96097e9 1.20685 0.603423 0.797421i \(-0.293803\pi\)
0.603423 + 0.797421i \(0.293803\pi\)
\(62\) 0 0
\(63\) −2.26308e10 −2.87294
\(64\) 0 0
\(65\) −4.73220e9 −0.505871
\(66\) 0 0
\(67\) 6.89243e9 0.623678 0.311839 0.950135i \(-0.399055\pi\)
0.311839 + 0.950135i \(0.399055\pi\)
\(68\) 0 0
\(69\) 9.56509e8 0.0736240
\(70\) 0 0
\(71\) 1.12698e10 0.741305 0.370652 0.928772i \(-0.379134\pi\)
0.370652 + 0.928772i \(0.379134\pi\)
\(72\) 0 0
\(73\) 3.34998e9 0.189132 0.0945662 0.995519i \(-0.469854\pi\)
0.0945662 + 0.995519i \(0.469854\pi\)
\(74\) 0 0
\(75\) 2.23806e10 1.08902
\(76\) 0 0
\(77\) −2.82230e10 −1.18824
\(78\) 0 0
\(79\) −5.36237e10 −1.96068 −0.980342 0.197304i \(-0.936782\pi\)
−0.980342 + 0.197304i \(0.936782\pi\)
\(80\) 0 0
\(81\) 8.71083e9 0.277583
\(82\) 0 0
\(83\) 6.31693e10 1.76026 0.880130 0.474733i \(-0.157455\pi\)
0.880130 + 0.474733i \(0.157455\pi\)
\(84\) 0 0
\(85\) 2.66162e10 0.650641
\(86\) 0 0
\(87\) 5.19487e10 1.11743
\(88\) 0 0
\(89\) 9.62373e10 1.82683 0.913416 0.407028i \(-0.133435\pi\)
0.913416 + 0.407028i \(0.133435\pi\)
\(90\) 0 0
\(91\) −8.52685e10 −1.43239
\(92\) 0 0
\(93\) 9.21027e9 0.137283
\(94\) 0 0
\(95\) −5.71710e10 −0.758047
\(96\) 0 0
\(97\) −4.37466e10 −0.517250 −0.258625 0.965978i \(-0.583269\pi\)
−0.258625 + 0.965978i \(0.583269\pi\)
\(98\) 0 0
\(99\) 1.17936e11 1.24639
\(100\) 0 0
\(101\) −1.68061e11 −1.59111 −0.795554 0.605882i \(-0.792820\pi\)
−0.795554 + 0.605882i \(0.792820\pi\)
\(102\) 0 0
\(103\) −6.02325e10 −0.511948 −0.255974 0.966684i \(-0.582396\pi\)
−0.255974 + 0.966684i \(0.582396\pi\)
\(104\) 0 0
\(105\) −2.09243e11 −1.59996
\(106\) 0 0
\(107\) −1.39380e11 −0.960701 −0.480351 0.877077i \(-0.659491\pi\)
−0.480351 + 0.877077i \(0.659491\pi\)
\(108\) 0 0
\(109\) 1.19601e11 0.744540 0.372270 0.928124i \(-0.378579\pi\)
0.372270 + 0.928124i \(0.378579\pi\)
\(110\) 0 0
\(111\) 1.16401e10 0.0655664
\(112\) 0 0
\(113\) 2.69277e10 0.137489 0.0687445 0.997634i \(-0.478101\pi\)
0.0687445 + 0.997634i \(0.478101\pi\)
\(114\) 0 0
\(115\) 5.61139e9 0.0260155
\(116\) 0 0
\(117\) 3.56314e11 1.50249
\(118\) 0 0
\(119\) 4.79591e11 1.84231
\(120\) 0 0
\(121\) −1.38233e11 −0.484498
\(122\) 0 0
\(123\) −7.19138e11 −2.30321
\(124\) 0 0
\(125\) 3.30718e11 0.969289
\(126\) 0 0
\(127\) 1.63631e11 0.439486 0.219743 0.975558i \(-0.429478\pi\)
0.219743 + 0.975558i \(0.429478\pi\)
\(128\) 0 0
\(129\) 1.34895e11 0.332469
\(130\) 0 0
\(131\) 2.54332e11 0.575981 0.287991 0.957633i \(-0.407013\pi\)
0.287991 + 0.957633i \(0.407013\pi\)
\(132\) 0 0
\(133\) −1.03015e12 −2.14643
\(134\) 0 0
\(135\) 3.70688e11 0.711496
\(136\) 0 0
\(137\) 1.05270e12 1.86355 0.931776 0.363032i \(-0.118259\pi\)
0.931776 + 0.363032i \(0.118259\pi\)
\(138\) 0 0
\(139\) 9.02335e11 1.47498 0.737491 0.675357i \(-0.236011\pi\)
0.737491 + 0.675357i \(0.236011\pi\)
\(140\) 0 0
\(141\) −8.07607e11 −1.22038
\(142\) 0 0
\(143\) 4.44361e11 0.621423
\(144\) 0 0
\(145\) 3.04759e11 0.394850
\(146\) 0 0
\(147\) −2.39374e12 −2.87628
\(148\) 0 0
\(149\) 1.08288e12 1.20797 0.603986 0.796995i \(-0.293578\pi\)
0.603986 + 0.796995i \(0.293578\pi\)
\(150\) 0 0
\(151\) −8.99725e11 −0.932688 −0.466344 0.884603i \(-0.654429\pi\)
−0.466344 + 0.884603i \(0.654429\pi\)
\(152\) 0 0
\(153\) −2.00408e12 −1.93247
\(154\) 0 0
\(155\) 5.40323e10 0.0485098
\(156\) 0 0
\(157\) −6.05620e11 −0.506701 −0.253351 0.967375i \(-0.581533\pi\)
−0.253351 + 0.967375i \(0.581533\pi\)
\(158\) 0 0
\(159\) −3.09356e11 −0.241421
\(160\) 0 0
\(161\) 1.01110e11 0.0736637
\(162\) 0 0
\(163\) −5.92020e11 −0.402999 −0.201500 0.979489i \(-0.564582\pi\)
−0.201500 + 0.979489i \(0.564582\pi\)
\(164\) 0 0
\(165\) 1.09043e12 0.694124
\(166\) 0 0
\(167\) 5.67821e10 0.0338276 0.0169138 0.999857i \(-0.494616\pi\)
0.0169138 + 0.999857i \(0.494616\pi\)
\(168\) 0 0
\(169\) −4.49639e11 −0.250892
\(170\) 0 0
\(171\) 4.30473e12 2.25147
\(172\) 0 0
\(173\) 2.27930e12 1.11828 0.559138 0.829075i \(-0.311132\pi\)
0.559138 + 0.829075i \(0.311132\pi\)
\(174\) 0 0
\(175\) 2.36581e12 1.08961
\(176\) 0 0
\(177\) −8.93228e10 −0.0386464
\(178\) 0 0
\(179\) 1.91742e12 0.779876 0.389938 0.920841i \(-0.372497\pi\)
0.389938 + 0.920841i \(0.372497\pi\)
\(180\) 0 0
\(181\) −3.61293e12 −1.38238 −0.691190 0.722673i \(-0.742913\pi\)
−0.691190 + 0.722673i \(0.742913\pi\)
\(182\) 0 0
\(183\) −5.54226e12 −1.99621
\(184\) 0 0
\(185\) 6.82871e10 0.0231683
\(186\) 0 0
\(187\) −2.49930e12 −0.799263
\(188\) 0 0
\(189\) 6.67934e12 2.01462
\(190\) 0 0
\(191\) 6.07217e11 0.172846 0.0864232 0.996259i \(-0.472456\pi\)
0.0864232 + 0.996259i \(0.472456\pi\)
\(192\) 0 0
\(193\) 4.64252e12 1.24793 0.623963 0.781454i \(-0.285522\pi\)
0.623963 + 0.781454i \(0.285522\pi\)
\(194\) 0 0
\(195\) 3.29446e12 0.836746
\(196\) 0 0
\(197\) −4.86139e12 −1.16734 −0.583668 0.811992i \(-0.698383\pi\)
−0.583668 + 0.811992i \(0.698383\pi\)
\(198\) 0 0
\(199\) −6.52349e12 −1.48180 −0.740898 0.671618i \(-0.765600\pi\)
−0.740898 + 0.671618i \(0.765600\pi\)
\(200\) 0 0
\(201\) −4.79837e12 −1.03161
\(202\) 0 0
\(203\) 5.49138e12 1.11803
\(204\) 0 0
\(205\) −4.21884e12 −0.813855
\(206\) 0 0
\(207\) −4.22513e11 −0.0772686
\(208\) 0 0
\(209\) 5.36844e12 0.931202
\(210\) 0 0
\(211\) −1.89227e12 −0.311479 −0.155740 0.987798i \(-0.549776\pi\)
−0.155740 + 0.987798i \(0.549776\pi\)
\(212\) 0 0
\(213\) −7.84583e12 −1.22617
\(214\) 0 0
\(215\) 7.91364e11 0.117480
\(216\) 0 0
\(217\) 9.73597e11 0.137357
\(218\) 0 0
\(219\) −2.33219e12 −0.312839
\(220\) 0 0
\(221\) −7.55099e12 −0.963488
\(222\) 0 0
\(223\) −6.33591e12 −0.769365 −0.384682 0.923049i \(-0.625689\pi\)
−0.384682 + 0.923049i \(0.625689\pi\)
\(224\) 0 0
\(225\) −9.88606e12 −1.14293
\(226\) 0 0
\(227\) −4.95535e12 −0.545673 −0.272837 0.962060i \(-0.587962\pi\)
−0.272837 + 0.962060i \(0.587962\pi\)
\(228\) 0 0
\(229\) 1.55285e13 1.62943 0.814714 0.579863i \(-0.196894\pi\)
0.814714 + 0.579863i \(0.196894\pi\)
\(230\) 0 0
\(231\) 1.96483e13 1.96543
\(232\) 0 0
\(233\) 7.75664e12 0.739973 0.369986 0.929037i \(-0.379362\pi\)
0.369986 + 0.929037i \(0.379362\pi\)
\(234\) 0 0
\(235\) −4.73784e12 −0.431229
\(236\) 0 0
\(237\) 3.73317e13 3.24311
\(238\) 0 0
\(239\) −4.18729e12 −0.347332 −0.173666 0.984805i \(-0.555561\pi\)
−0.173666 + 0.984805i \(0.555561\pi\)
\(240\) 0 0
\(241\) 8.28156e12 0.656173 0.328087 0.944648i \(-0.393596\pi\)
0.328087 + 0.944648i \(0.393596\pi\)
\(242\) 0 0
\(243\) 1.00140e13 0.758180
\(244\) 0 0
\(245\) −1.40429e13 −1.01635
\(246\) 0 0
\(247\) 1.62194e13 1.12254
\(248\) 0 0
\(249\) −4.39772e13 −2.91160
\(250\) 0 0
\(251\) 6.31791e11 0.0400284 0.0200142 0.999800i \(-0.493629\pi\)
0.0200142 + 0.999800i \(0.493629\pi\)
\(252\) 0 0
\(253\) −5.26918e11 −0.0319580
\(254\) 0 0
\(255\) −1.85296e13 −1.07621
\(256\) 0 0
\(257\) 1.76085e13 0.979691 0.489845 0.871809i \(-0.337053\pi\)
0.489845 + 0.871809i \(0.337053\pi\)
\(258\) 0 0
\(259\) 1.23045e12 0.0656018
\(260\) 0 0
\(261\) −2.29470e13 −1.17274
\(262\) 0 0
\(263\) 2.18141e13 1.06901 0.534505 0.845165i \(-0.320498\pi\)
0.534505 + 0.845165i \(0.320498\pi\)
\(264\) 0 0
\(265\) −1.81485e12 −0.0853076
\(266\) 0 0
\(267\) −6.69985e13 −3.02171
\(268\) 0 0
\(269\) −1.09453e13 −0.473795 −0.236897 0.971535i \(-0.576131\pi\)
−0.236897 + 0.971535i \(0.576131\pi\)
\(270\) 0 0
\(271\) 4.38029e13 1.82042 0.910210 0.414146i \(-0.135920\pi\)
0.910210 + 0.414146i \(0.135920\pi\)
\(272\) 0 0
\(273\) 5.93622e13 2.36927
\(274\) 0 0
\(275\) −1.23290e13 −0.472712
\(276\) 0 0
\(277\) −3.83236e13 −1.41198 −0.705988 0.708224i \(-0.749497\pi\)
−0.705988 + 0.708224i \(0.749497\pi\)
\(278\) 0 0
\(279\) −4.06840e12 −0.144079
\(280\) 0 0
\(281\) −1.88363e13 −0.641372 −0.320686 0.947186i \(-0.603913\pi\)
−0.320686 + 0.947186i \(0.603913\pi\)
\(282\) 0 0
\(283\) 3.59883e12 0.117852 0.0589258 0.998262i \(-0.481232\pi\)
0.0589258 + 0.998262i \(0.481232\pi\)
\(284\) 0 0
\(285\) 3.98013e13 1.25386
\(286\) 0 0
\(287\) −7.60185e13 −2.30446
\(288\) 0 0
\(289\) 8.19853e12 0.239220
\(290\) 0 0
\(291\) 3.04555e13 0.855568
\(292\) 0 0
\(293\) −1.89960e13 −0.513913 −0.256957 0.966423i \(-0.582720\pi\)
−0.256957 + 0.966423i \(0.582720\pi\)
\(294\) 0 0
\(295\) −5.24015e11 −0.0136560
\(296\) 0 0
\(297\) −3.48081e13 −0.874018
\(298\) 0 0
\(299\) −1.59195e12 −0.0385245
\(300\) 0 0
\(301\) 1.42594e13 0.332649
\(302\) 0 0
\(303\) 1.17001e14 2.63181
\(304\) 0 0
\(305\) −3.25138e13 −0.705373
\(306\) 0 0
\(307\) 5.07622e13 1.06238 0.531189 0.847253i \(-0.321745\pi\)
0.531189 + 0.847253i \(0.321745\pi\)
\(308\) 0 0
\(309\) 4.19326e13 0.846799
\(310\) 0 0
\(311\) −4.89908e13 −0.954844 −0.477422 0.878674i \(-0.658429\pi\)
−0.477422 + 0.878674i \(0.658429\pi\)
\(312\) 0 0
\(313\) 2.02897e13 0.381752 0.190876 0.981614i \(-0.438867\pi\)
0.190876 + 0.981614i \(0.438867\pi\)
\(314\) 0 0
\(315\) 9.24277e13 1.67917
\(316\) 0 0
\(317\) 5.80299e13 1.01818 0.509091 0.860712i \(-0.329982\pi\)
0.509091 + 0.860712i \(0.329982\pi\)
\(318\) 0 0
\(319\) −2.86173e13 −0.485043
\(320\) 0 0
\(321\) 9.70332e13 1.58907
\(322\) 0 0
\(323\) −9.12256e13 −1.44379
\(324\) 0 0
\(325\) −3.72488e13 −0.569841
\(326\) 0 0
\(327\) −8.32636e13 −1.23152
\(328\) 0 0
\(329\) −8.53702e13 −1.22104
\(330\) 0 0
\(331\) 1.94810e13 0.269500 0.134750 0.990880i \(-0.456977\pi\)
0.134750 + 0.990880i \(0.456977\pi\)
\(332\) 0 0
\(333\) −5.14172e12 −0.0688122
\(334\) 0 0
\(335\) −2.81497e13 −0.364526
\(336\) 0 0
\(337\) −1.11994e14 −1.40356 −0.701782 0.712392i \(-0.747612\pi\)
−0.701782 + 0.712392i \(0.747612\pi\)
\(338\) 0 0
\(339\) −1.87465e13 −0.227417
\(340\) 0 0
\(341\) −5.07372e12 −0.0595905
\(342\) 0 0
\(343\) −1.07522e14 −1.22287
\(344\) 0 0
\(345\) −3.90653e12 −0.0430315
\(346\) 0 0
\(347\) 1.43917e14 1.53568 0.767841 0.640640i \(-0.221331\pi\)
0.767841 + 0.640640i \(0.221331\pi\)
\(348\) 0 0
\(349\) 1.17413e14 1.21389 0.606943 0.794745i \(-0.292396\pi\)
0.606943 + 0.794745i \(0.292396\pi\)
\(350\) 0 0
\(351\) −1.05164e14 −1.05360
\(352\) 0 0
\(353\) −3.14959e12 −0.0305839 −0.0152919 0.999883i \(-0.504868\pi\)
−0.0152919 + 0.999883i \(0.504868\pi\)
\(354\) 0 0
\(355\) −4.60278e13 −0.433275
\(356\) 0 0
\(357\) −3.33882e14 −3.04732
\(358\) 0 0
\(359\) 2.16645e14 1.91748 0.958738 0.284291i \(-0.0917583\pi\)
0.958738 + 0.284291i \(0.0917583\pi\)
\(360\) 0 0
\(361\) 7.94605e13 0.682121
\(362\) 0 0
\(363\) 9.62349e13 0.801394
\(364\) 0 0
\(365\) −1.36818e13 −0.110544
\(366\) 0 0
\(367\) 1.32924e14 1.04217 0.521085 0.853505i \(-0.325527\pi\)
0.521085 + 0.853505i \(0.325527\pi\)
\(368\) 0 0
\(369\) 3.17660e14 2.41723
\(370\) 0 0
\(371\) −3.27014e13 −0.241551
\(372\) 0 0
\(373\) 4.97449e13 0.356738 0.178369 0.983964i \(-0.442918\pi\)
0.178369 + 0.983964i \(0.442918\pi\)
\(374\) 0 0
\(375\) −2.30239e14 −1.60327
\(376\) 0 0
\(377\) −8.64598e13 −0.584705
\(378\) 0 0
\(379\) −6.41630e13 −0.421472 −0.210736 0.977543i \(-0.567586\pi\)
−0.210736 + 0.977543i \(0.567586\pi\)
\(380\) 0 0
\(381\) −1.13917e14 −0.726942
\(382\) 0 0
\(383\) −1.53711e14 −0.953040 −0.476520 0.879164i \(-0.658102\pi\)
−0.476520 + 0.879164i \(0.658102\pi\)
\(384\) 0 0
\(385\) 1.15267e14 0.694498
\(386\) 0 0
\(387\) −5.95862e13 −0.348928
\(388\) 0 0
\(389\) 3.08115e14 1.75384 0.876921 0.480635i \(-0.159594\pi\)
0.876921 + 0.480635i \(0.159594\pi\)
\(390\) 0 0
\(391\) 8.95388e12 0.0495495
\(392\) 0 0
\(393\) −1.77061e14 −0.952714
\(394\) 0 0
\(395\) 2.19008e14 1.14597
\(396\) 0 0
\(397\) 2.15252e14 1.09547 0.547734 0.836653i \(-0.315491\pi\)
0.547734 + 0.836653i \(0.315491\pi\)
\(398\) 0 0
\(399\) 7.17171e14 3.55035
\(400\) 0 0
\(401\) −4.29414e13 −0.206815 −0.103407 0.994639i \(-0.532975\pi\)
−0.103407 + 0.994639i \(0.532975\pi\)
\(402\) 0 0
\(403\) −1.53289e13 −0.0718347
\(404\) 0 0
\(405\) −3.55764e13 −0.162241
\(406\) 0 0
\(407\) −6.41227e12 −0.0284605
\(408\) 0 0
\(409\) −1.78142e14 −0.769639 −0.384819 0.922992i \(-0.625736\pi\)
−0.384819 + 0.922992i \(0.625736\pi\)
\(410\) 0 0
\(411\) −7.32869e14 −3.08245
\(412\) 0 0
\(413\) −9.44211e12 −0.0386673
\(414\) 0 0
\(415\) −2.57993e14 −1.02883
\(416\) 0 0
\(417\) −6.28187e14 −2.43972
\(418\) 0 0
\(419\) 3.36601e14 1.27332 0.636662 0.771143i \(-0.280315\pi\)
0.636662 + 0.771143i \(0.280315\pi\)
\(420\) 0 0
\(421\) 6.36951e13 0.234722 0.117361 0.993089i \(-0.462557\pi\)
0.117361 + 0.993089i \(0.462557\pi\)
\(422\) 0 0
\(423\) 3.56739e14 1.28079
\(424\) 0 0
\(425\) 2.09505e14 0.732918
\(426\) 0 0
\(427\) −5.85860e14 −1.99729
\(428\) 0 0
\(429\) −3.09355e14 −1.02788
\(430\) 0 0
\(431\) −1.38853e14 −0.449707 −0.224853 0.974393i \(-0.572190\pi\)
−0.224853 + 0.974393i \(0.572190\pi\)
\(432\) 0 0
\(433\) −3.07253e14 −0.970093 −0.485046 0.874488i \(-0.661197\pi\)
−0.485046 + 0.874488i \(0.661197\pi\)
\(434\) 0 0
\(435\) −2.12167e14 −0.653110
\(436\) 0 0
\(437\) −1.92328e13 −0.0577289
\(438\) 0 0
\(439\) 2.37747e14 0.695921 0.347961 0.937509i \(-0.386874\pi\)
0.347961 + 0.937509i \(0.386874\pi\)
\(440\) 0 0
\(441\) 1.05737e15 3.01866
\(442\) 0 0
\(443\) 6.82803e13 0.190141 0.0950703 0.995471i \(-0.469692\pi\)
0.0950703 + 0.995471i \(0.469692\pi\)
\(444\) 0 0
\(445\) −3.93048e14 −1.06774
\(446\) 0 0
\(447\) −7.53881e14 −1.99807
\(448\) 0 0
\(449\) 7.19557e14 1.86084 0.930422 0.366490i \(-0.119440\pi\)
0.930422 + 0.366490i \(0.119440\pi\)
\(450\) 0 0
\(451\) 3.96156e14 0.999758
\(452\) 0 0
\(453\) 6.26370e14 1.54273
\(454\) 0 0
\(455\) 3.48250e14 0.837198
\(456\) 0 0
\(457\) −5.95803e14 −1.39818 −0.699091 0.715033i \(-0.746412\pi\)
−0.699091 + 0.715033i \(0.746412\pi\)
\(458\) 0 0
\(459\) 5.91492e14 1.35513
\(460\) 0 0
\(461\) −2.48547e14 −0.555973 −0.277987 0.960585i \(-0.589667\pi\)
−0.277987 + 0.960585i \(0.589667\pi\)
\(462\) 0 0
\(463\) 5.55882e14 1.21419 0.607096 0.794629i \(-0.292334\pi\)
0.607096 + 0.794629i \(0.292334\pi\)
\(464\) 0 0
\(465\) −3.76162e13 −0.0802386
\(466\) 0 0
\(467\) −5.11081e13 −0.106475 −0.0532374 0.998582i \(-0.516954\pi\)
−0.0532374 + 0.998582i \(0.516954\pi\)
\(468\) 0 0
\(469\) −5.07224e14 −1.03217
\(470\) 0 0
\(471\) 4.21620e14 0.838121
\(472\) 0 0
\(473\) −7.43103e13 −0.144315
\(474\) 0 0
\(475\) −4.50013e14 −0.853906
\(476\) 0 0
\(477\) 1.36650e14 0.253372
\(478\) 0 0
\(479\) −6.79608e14 −1.23144 −0.615720 0.787965i \(-0.711135\pi\)
−0.615720 + 0.787965i \(0.711135\pi\)
\(480\) 0 0
\(481\) −1.93730e13 −0.0343083
\(482\) 0 0
\(483\) −7.03910e13 −0.121845
\(484\) 0 0
\(485\) 1.78668e14 0.302320
\(486\) 0 0
\(487\) 3.50601e14 0.579967 0.289984 0.957032i \(-0.406350\pi\)
0.289984 + 0.957032i \(0.406350\pi\)
\(488\) 0 0
\(489\) 4.12152e14 0.666590
\(490\) 0 0
\(491\) 5.60616e14 0.886579 0.443289 0.896379i \(-0.353811\pi\)
0.443289 + 0.896379i \(0.353811\pi\)
\(492\) 0 0
\(493\) 4.86292e14 0.752037
\(494\) 0 0
\(495\) −4.81670e14 −0.728485
\(496\) 0 0
\(497\) −8.29365e14 −1.22683
\(498\) 0 0
\(499\) 2.60119e14 0.376374 0.188187 0.982133i \(-0.439739\pi\)
0.188187 + 0.982133i \(0.439739\pi\)
\(500\) 0 0
\(501\) −3.95306e13 −0.0559533
\(502\) 0 0
\(503\) −1.34386e15 −1.86093 −0.930466 0.366377i \(-0.880598\pi\)
−0.930466 + 0.366377i \(0.880598\pi\)
\(504\) 0 0
\(505\) 6.86388e14 0.929966
\(506\) 0 0
\(507\) 3.13029e14 0.414994
\(508\) 0 0
\(509\) 3.28205e14 0.425792 0.212896 0.977075i \(-0.431710\pi\)
0.212896 + 0.977075i \(0.431710\pi\)
\(510\) 0 0
\(511\) −2.46530e14 −0.313007
\(512\) 0 0
\(513\) −1.27051e15 −1.57882
\(514\) 0 0
\(515\) 2.45999e14 0.299222
\(516\) 0 0
\(517\) 4.44891e14 0.529731
\(518\) 0 0
\(519\) −1.58681e15 −1.84971
\(520\) 0 0
\(521\) 3.73999e14 0.426838 0.213419 0.976961i \(-0.431540\pi\)
0.213419 + 0.976961i \(0.431540\pi\)
\(522\) 0 0
\(523\) −7.77988e13 −0.0869388 −0.0434694 0.999055i \(-0.513841\pi\)
−0.0434694 + 0.999055i \(0.513841\pi\)
\(524\) 0 0
\(525\) −1.64703e15 −1.80229
\(526\) 0 0
\(527\) 8.62173e13 0.0923924
\(528\) 0 0
\(529\) −9.50922e14 −0.998019
\(530\) 0 0
\(531\) 3.94560e13 0.0405596
\(532\) 0 0
\(533\) 1.19688e15 1.20518
\(534\) 0 0
\(535\) 5.69248e14 0.561507
\(536\) 0 0
\(537\) −1.33487e15 −1.28997
\(538\) 0 0
\(539\) 1.31865e15 1.24851
\(540\) 0 0
\(541\) −1.17909e15 −1.09386 −0.546929 0.837179i \(-0.684203\pi\)
−0.546929 + 0.837179i \(0.684203\pi\)
\(542\) 0 0
\(543\) 2.51525e15 2.28656
\(544\) 0 0
\(545\) −4.88468e14 −0.435167
\(546\) 0 0
\(547\) −7.58961e14 −0.662658 −0.331329 0.943515i \(-0.607497\pi\)
−0.331329 + 0.943515i \(0.607497\pi\)
\(548\) 0 0
\(549\) 2.44815e15 2.09503
\(550\) 0 0
\(551\) −1.04455e15 −0.876180
\(552\) 0 0
\(553\) 3.94625e15 3.24486
\(554\) 0 0
\(555\) −4.75401e13 −0.0383221
\(556\) 0 0
\(557\) −9.88953e14 −0.781578 −0.390789 0.920480i \(-0.627798\pi\)
−0.390789 + 0.920480i \(0.627798\pi\)
\(558\) 0 0
\(559\) −2.24509e14 −0.173968
\(560\) 0 0
\(561\) 1.73996e15 1.32204
\(562\) 0 0
\(563\) 1.70471e15 1.27015 0.635075 0.772450i \(-0.280969\pi\)
0.635075 + 0.772450i \(0.280969\pi\)
\(564\) 0 0
\(565\) −1.09977e14 −0.0803591
\(566\) 0 0
\(567\) −6.41044e14 −0.459389
\(568\) 0 0
\(569\) 5.26889e14 0.370341 0.185170 0.982706i \(-0.440716\pi\)
0.185170 + 0.982706i \(0.440716\pi\)
\(570\) 0 0
\(571\) 6.85464e14 0.472592 0.236296 0.971681i \(-0.424067\pi\)
0.236296 + 0.971681i \(0.424067\pi\)
\(572\) 0 0
\(573\) −4.22732e14 −0.285900
\(574\) 0 0
\(575\) 4.41692e13 0.0293053
\(576\) 0 0
\(577\) 1.25421e15 0.816402 0.408201 0.912892i \(-0.366156\pi\)
0.408201 + 0.912892i \(0.366156\pi\)
\(578\) 0 0
\(579\) −3.23203e15 −2.06416
\(580\) 0 0
\(581\) −4.64873e15 −2.91317
\(582\) 0 0
\(583\) 1.70417e14 0.104794
\(584\) 0 0
\(585\) −1.45524e15 −0.878168
\(586\) 0 0
\(587\) −2.56777e15 −1.52071 −0.760356 0.649507i \(-0.774975\pi\)
−0.760356 + 0.649507i \(0.774975\pi\)
\(588\) 0 0
\(589\) −1.85193e14 −0.107644
\(590\) 0 0
\(591\) 3.38440e15 1.93086
\(592\) 0 0
\(593\) −1.05019e15 −0.588123 −0.294062 0.955786i \(-0.595007\pi\)
−0.294062 + 0.955786i \(0.595007\pi\)
\(594\) 0 0
\(595\) −1.95873e15 −1.07679
\(596\) 0 0
\(597\) 4.54152e15 2.45100
\(598\) 0 0
\(599\) −1.16345e14 −0.0616455 −0.0308227 0.999525i \(-0.509813\pi\)
−0.0308227 + 0.999525i \(0.509813\pi\)
\(600\) 0 0
\(601\) −9.27714e14 −0.482619 −0.241310 0.970448i \(-0.577577\pi\)
−0.241310 + 0.970448i \(0.577577\pi\)
\(602\) 0 0
\(603\) 2.11955e15 1.08268
\(604\) 0 0
\(605\) 5.64565e14 0.283178
\(606\) 0 0
\(607\) 9.37322e14 0.461691 0.230845 0.972990i \(-0.425851\pi\)
0.230845 + 0.972990i \(0.425851\pi\)
\(608\) 0 0
\(609\) −3.82299e15 −1.84930
\(610\) 0 0
\(611\) 1.34412e15 0.638576
\(612\) 0 0
\(613\) 9.73439e13 0.0454230 0.0227115 0.999742i \(-0.492770\pi\)
0.0227115 + 0.999742i \(0.492770\pi\)
\(614\) 0 0
\(615\) 2.93707e15 1.34618
\(616\) 0 0
\(617\) −2.70501e15 −1.21787 −0.608935 0.793220i \(-0.708403\pi\)
−0.608935 + 0.793220i \(0.708403\pi\)
\(618\) 0 0
\(619\) −5.22797e14 −0.231225 −0.115612 0.993294i \(-0.536883\pi\)
−0.115612 + 0.993294i \(0.536883\pi\)
\(620\) 0 0
\(621\) 1.24702e14 0.0541839
\(622\) 0 0
\(623\) −7.08225e15 −3.02334
\(624\) 0 0
\(625\) 2.19012e14 0.0918603
\(626\) 0 0
\(627\) −3.73740e15 −1.54027
\(628\) 0 0
\(629\) 1.08963e14 0.0441267
\(630\) 0 0
\(631\) 1.58461e15 0.630611 0.315305 0.948990i \(-0.397893\pi\)
0.315305 + 0.948990i \(0.397893\pi\)
\(632\) 0 0
\(633\) 1.31736e15 0.515209
\(634\) 0 0
\(635\) −6.68295e14 −0.256869
\(636\) 0 0
\(637\) 3.98397e15 1.50504
\(638\) 0 0
\(639\) 3.46569e15 1.28687
\(640\) 0 0
\(641\) 3.67621e15 1.34178 0.670890 0.741557i \(-0.265912\pi\)
0.670890 + 0.741557i \(0.265912\pi\)
\(642\) 0 0
\(643\) −1.40268e15 −0.503268 −0.251634 0.967822i \(-0.580968\pi\)
−0.251634 + 0.967822i \(0.580968\pi\)
\(644\) 0 0
\(645\) −5.50931e14 −0.194321
\(646\) 0 0
\(647\) −7.65400e14 −0.265409 −0.132704 0.991156i \(-0.542366\pi\)
−0.132704 + 0.991156i \(0.542366\pi\)
\(648\) 0 0
\(649\) 4.92058e13 0.0167753
\(650\) 0 0
\(651\) −6.77798e14 −0.227198
\(652\) 0 0
\(653\) −3.06409e15 −1.00990 −0.504951 0.863148i \(-0.668490\pi\)
−0.504951 + 0.863148i \(0.668490\pi\)
\(654\) 0 0
\(655\) −1.03873e15 −0.336648
\(656\) 0 0
\(657\) 1.03018e15 0.328325
\(658\) 0 0
\(659\) 5.49550e15 1.72241 0.861207 0.508254i \(-0.169709\pi\)
0.861207 + 0.508254i \(0.169709\pi\)
\(660\) 0 0
\(661\) −4.42413e15 −1.36370 −0.681851 0.731491i \(-0.738825\pi\)
−0.681851 + 0.731491i \(0.738825\pi\)
\(662\) 0 0
\(663\) 5.25685e15 1.59368
\(664\) 0 0
\(665\) 4.20730e15 1.25454
\(666\) 0 0
\(667\) 1.02523e14 0.0300697
\(668\) 0 0
\(669\) 4.41093e15 1.27258
\(670\) 0 0
\(671\) 3.05310e15 0.866497
\(672\) 0 0
\(673\) −3.72652e15 −1.04045 −0.520225 0.854029i \(-0.674152\pi\)
−0.520225 + 0.854029i \(0.674152\pi\)
\(674\) 0 0
\(675\) 2.91781e15 0.801468
\(676\) 0 0
\(677\) 3.80105e15 1.02723 0.513613 0.858022i \(-0.328307\pi\)
0.513613 + 0.858022i \(0.328307\pi\)
\(678\) 0 0
\(679\) 3.21938e15 0.856030
\(680\) 0 0
\(681\) 3.44982e15 0.902582
\(682\) 0 0
\(683\) −4.06733e15 −1.04712 −0.523558 0.851990i \(-0.675396\pi\)
−0.523558 + 0.851990i \(0.675396\pi\)
\(684\) 0 0
\(685\) −4.29939e15 −1.08920
\(686\) 0 0
\(687\) −1.08106e16 −2.69519
\(688\) 0 0
\(689\) 5.14871e14 0.126326
\(690\) 0 0
\(691\) 5.14416e15 1.24218 0.621091 0.783739i \(-0.286690\pi\)
0.621091 + 0.783739i \(0.286690\pi\)
\(692\) 0 0
\(693\) −8.67910e15 −2.06273
\(694\) 0 0
\(695\) −3.68528e15 −0.862092
\(696\) 0 0
\(697\) −6.73185e15 −1.55008
\(698\) 0 0
\(699\) −5.40001e15 −1.22397
\(700\) 0 0
\(701\) −2.86572e15 −0.639417 −0.319708 0.947516i \(-0.603585\pi\)
−0.319708 + 0.947516i \(0.603585\pi\)
\(702\) 0 0
\(703\) −2.34051e14 −0.0514110
\(704\) 0 0
\(705\) 3.29839e15 0.713283
\(706\) 0 0
\(707\) 1.23679e16 2.63323
\(708\) 0 0
\(709\) 5.54221e15 1.16179 0.580896 0.813978i \(-0.302702\pi\)
0.580896 + 0.813978i \(0.302702\pi\)
\(710\) 0 0
\(711\) −1.64903e16 −3.40366
\(712\) 0 0
\(713\) 1.81769e13 0.00369425
\(714\) 0 0
\(715\) −1.81484e15 −0.363207
\(716\) 0 0
\(717\) 2.91511e15 0.574512
\(718\) 0 0
\(719\) −4.73660e15 −0.919301 −0.459651 0.888100i \(-0.652025\pi\)
−0.459651 + 0.888100i \(0.652025\pi\)
\(720\) 0 0
\(721\) 4.43260e15 0.847256
\(722\) 0 0
\(723\) −5.76545e15 −1.08536
\(724\) 0 0
\(725\) 2.39886e15 0.444781
\(726\) 0 0
\(727\) 1.01777e16 1.85870 0.929348 0.369205i \(-0.120370\pi\)
0.929348 + 0.369205i \(0.120370\pi\)
\(728\) 0 0
\(729\) −8.51462e15 −1.53167
\(730\) 0 0
\(731\) 1.26275e15 0.223754
\(732\) 0 0
\(733\) 5.29486e15 0.924235 0.462117 0.886819i \(-0.347090\pi\)
0.462117 + 0.886819i \(0.347090\pi\)
\(734\) 0 0
\(735\) 9.77639e15 1.68112
\(736\) 0 0
\(737\) 2.64330e15 0.447792
\(738\) 0 0
\(739\) −4.55855e15 −0.760821 −0.380411 0.924818i \(-0.624217\pi\)
−0.380411 + 0.924818i \(0.624217\pi\)
\(740\) 0 0
\(741\) −1.12916e16 −1.85676
\(742\) 0 0
\(743\) −9.91668e14 −0.160667 −0.0803337 0.996768i \(-0.525599\pi\)
−0.0803337 + 0.996768i \(0.525599\pi\)
\(744\) 0 0
\(745\) −4.42266e15 −0.706032
\(746\) 0 0
\(747\) 1.94258e16 3.05573
\(748\) 0 0
\(749\) 1.02572e16 1.58993
\(750\) 0 0
\(751\) −5.23831e15 −0.800151 −0.400075 0.916482i \(-0.631016\pi\)
−0.400075 + 0.916482i \(0.631016\pi\)
\(752\) 0 0
\(753\) −4.39840e14 −0.0662098
\(754\) 0 0
\(755\) 3.67461e15 0.545134
\(756\) 0 0
\(757\) −7.31380e15 −1.06934 −0.534670 0.845061i \(-0.679564\pi\)
−0.534670 + 0.845061i \(0.679564\pi\)
\(758\) 0 0
\(759\) 3.66829e14 0.0528609
\(760\) 0 0
\(761\) −7.81344e15 −1.10975 −0.554877 0.831932i \(-0.687235\pi\)
−0.554877 + 0.831932i \(0.687235\pi\)
\(762\) 0 0
\(763\) −8.80161e15 −1.23219
\(764\) 0 0
\(765\) 8.18498e15 1.12948
\(766\) 0 0
\(767\) 1.48663e14 0.0202222
\(768\) 0 0
\(769\) 2.19554e15 0.294405 0.147203 0.989106i \(-0.452973\pi\)
0.147203 + 0.989106i \(0.452973\pi\)
\(770\) 0 0
\(771\) −1.22586e16 −1.62048
\(772\) 0 0
\(773\) 1.32704e16 1.72940 0.864702 0.502286i \(-0.167507\pi\)
0.864702 + 0.502286i \(0.167507\pi\)
\(774\) 0 0
\(775\) 4.25307e14 0.0546441
\(776\) 0 0
\(777\) −8.56615e14 −0.108510
\(778\) 0 0
\(779\) 1.44599e16 1.80596
\(780\) 0 0
\(781\) 4.32208e15 0.532246
\(782\) 0 0
\(783\) 6.77266e15 0.822375
\(784\) 0 0
\(785\) 2.47345e15 0.296155
\(786\) 0 0
\(787\) −1.40226e15 −0.165565 −0.0827826 0.996568i \(-0.526381\pi\)
−0.0827826 + 0.996568i \(0.526381\pi\)
\(788\) 0 0
\(789\) −1.51866e16 −1.76822
\(790\) 0 0
\(791\) −1.98165e15 −0.227539
\(792\) 0 0
\(793\) 9.22415e15 1.04454
\(794\) 0 0
\(795\) 1.26346e15 0.141105
\(796\) 0 0
\(797\) 3.09627e15 0.341049 0.170525 0.985353i \(-0.445454\pi\)
0.170525 + 0.985353i \(0.445454\pi\)
\(798\) 0 0
\(799\) −7.56000e15 −0.821324
\(800\) 0 0
\(801\) 2.95948e16 3.17130
\(802\) 0 0
\(803\) 1.28474e15 0.135794
\(804\) 0 0
\(805\) −4.12951e14 −0.0430547
\(806\) 0 0
\(807\) 7.61990e15 0.783691
\(808\) 0 0
\(809\) −1.62765e16 −1.65137 −0.825683 0.564135i \(-0.809210\pi\)
−0.825683 + 0.564135i \(0.809210\pi\)
\(810\) 0 0
\(811\) −1.55106e16 −1.55244 −0.776219 0.630463i \(-0.782865\pi\)
−0.776219 + 0.630463i \(0.782865\pi\)
\(812\) 0 0
\(813\) −3.04947e16 −3.01111
\(814\) 0 0
\(815\) 2.41790e15 0.235544
\(816\) 0 0
\(817\) −2.71236e15 −0.260691
\(818\) 0 0
\(819\) −2.62217e16 −2.48656
\(820\) 0 0
\(821\) −5.57057e15 −0.521209 −0.260605 0.965446i \(-0.583922\pi\)
−0.260605 + 0.965446i \(0.583922\pi\)
\(822\) 0 0
\(823\) −4.05461e15 −0.374326 −0.187163 0.982329i \(-0.559929\pi\)
−0.187163 + 0.982329i \(0.559929\pi\)
\(824\) 0 0
\(825\) 8.58317e15 0.781899
\(826\) 0 0
\(827\) −9.59579e14 −0.0862582 −0.0431291 0.999070i \(-0.513733\pi\)
−0.0431291 + 0.999070i \(0.513733\pi\)
\(828\) 0 0
\(829\) −1.05269e16 −0.933791 −0.466895 0.884313i \(-0.654627\pi\)
−0.466895 + 0.884313i \(0.654627\pi\)
\(830\) 0 0
\(831\) 2.66801e16 2.33551
\(832\) 0 0
\(833\) −2.24078e16 −1.93576
\(834\) 0 0
\(835\) −2.31907e14 −0.0197714
\(836\) 0 0
\(837\) 1.20076e15 0.101034
\(838\) 0 0
\(839\) −6.15316e15 −0.510984 −0.255492 0.966811i \(-0.582238\pi\)
−0.255492 + 0.966811i \(0.582238\pi\)
\(840\) 0 0
\(841\) −6.63240e15 −0.543617
\(842\) 0 0
\(843\) 1.31134e16 1.06087
\(844\) 0 0
\(845\) 1.83640e15 0.146641
\(846\) 0 0
\(847\) 1.01728e16 0.801827
\(848\) 0 0
\(849\) −2.50543e15 −0.194935
\(850\) 0 0
\(851\) 2.29723e13 0.00176438
\(852\) 0 0
\(853\) 1.77560e16 1.34625 0.673126 0.739528i \(-0.264951\pi\)
0.673126 + 0.739528i \(0.264951\pi\)
\(854\) 0 0
\(855\) −1.75812e16 −1.31593
\(856\) 0 0
\(857\) 2.26793e16 1.67585 0.837925 0.545785i \(-0.183769\pi\)
0.837925 + 0.545785i \(0.183769\pi\)
\(858\) 0 0
\(859\) 1.65429e15 0.120684 0.0603421 0.998178i \(-0.480781\pi\)
0.0603421 + 0.998178i \(0.480781\pi\)
\(860\) 0 0
\(861\) 5.29225e16 3.81174
\(862\) 0 0
\(863\) 2.31182e15 0.164397 0.0821986 0.996616i \(-0.473806\pi\)
0.0821986 + 0.996616i \(0.473806\pi\)
\(864\) 0 0
\(865\) −9.30903e15 −0.653606
\(866\) 0 0
\(867\) −5.70765e15 −0.395688
\(868\) 0 0
\(869\) −2.05651e16 −1.40774
\(870\) 0 0
\(871\) 7.98606e15 0.539800
\(872\) 0 0
\(873\) −1.34529e16 −0.897921
\(874\) 0 0
\(875\) −2.43381e16 −1.60414
\(876\) 0 0
\(877\) 1.39330e16 0.906874 0.453437 0.891288i \(-0.350198\pi\)
0.453437 + 0.891288i \(0.350198\pi\)
\(878\) 0 0
\(879\) 1.32246e16 0.850050
\(880\) 0 0
\(881\) 4.04171e15 0.256565 0.128283 0.991738i \(-0.459054\pi\)
0.128283 + 0.991738i \(0.459054\pi\)
\(882\) 0 0
\(883\) 1.26327e16 0.791975 0.395988 0.918256i \(-0.370402\pi\)
0.395988 + 0.918256i \(0.370402\pi\)
\(884\) 0 0
\(885\) 3.64808e14 0.0225880
\(886\) 0 0
\(887\) 1.96489e16 1.20160 0.600798 0.799401i \(-0.294849\pi\)
0.600798 + 0.799401i \(0.294849\pi\)
\(888\) 0 0
\(889\) −1.20419e16 −0.727334
\(890\) 0 0
\(891\) 3.34068e15 0.199300
\(892\) 0 0
\(893\) 1.62387e16 0.956905
\(894\) 0 0
\(895\) −7.83104e15 −0.455819
\(896\) 0 0
\(897\) 1.10828e15 0.0637223
\(898\) 0 0
\(899\) 9.87200e14 0.0560695
\(900\) 0 0
\(901\) −2.89588e15 −0.162478
\(902\) 0 0
\(903\) −9.92712e15 −0.550225
\(904\) 0 0
\(905\) 1.47558e16 0.807969
\(906\) 0 0
\(907\) −1.75609e15 −0.0949961 −0.0474981 0.998871i \(-0.515125\pi\)
−0.0474981 + 0.998871i \(0.515125\pi\)
\(908\) 0 0
\(909\) −5.16820e16 −2.76209
\(910\) 0 0
\(911\) −2.30636e16 −1.21780 −0.608899 0.793247i \(-0.708389\pi\)
−0.608899 + 0.793247i \(0.708389\pi\)
\(912\) 0 0
\(913\) 2.42260e16 1.26384
\(914\) 0 0
\(915\) 2.26355e16 1.16674
\(916\) 0 0
\(917\) −1.87167e16 −0.953229
\(918\) 0 0
\(919\) −9.41404e14 −0.0473741 −0.0236870 0.999719i \(-0.507541\pi\)
−0.0236870 + 0.999719i \(0.507541\pi\)
\(920\) 0 0
\(921\) −3.53396e16 −1.75725
\(922\) 0 0
\(923\) 1.30581e16 0.641607
\(924\) 0 0
\(925\) 5.37512e14 0.0260981
\(926\) 0 0
\(927\) −1.85226e16 −0.888718
\(928\) 0 0
\(929\) 1.77556e16 0.841876 0.420938 0.907089i \(-0.361701\pi\)
0.420938 + 0.907089i \(0.361701\pi\)
\(930\) 0 0
\(931\) 4.81314e16 2.25530
\(932\) 0 0
\(933\) 3.41064e16 1.57938
\(934\) 0 0
\(935\) 1.02075e16 0.467150
\(936\) 0 0
\(937\) 1.10107e16 0.498020 0.249010 0.968501i \(-0.419895\pi\)
0.249010 + 0.968501i \(0.419895\pi\)
\(938\) 0 0
\(939\) −1.41253e16 −0.631446
\(940\) 0 0
\(941\) −2.50908e16 −1.10859 −0.554295 0.832320i \(-0.687012\pi\)
−0.554295 + 0.832320i \(0.687012\pi\)
\(942\) 0 0
\(943\) −1.41925e15 −0.0619790
\(944\) 0 0
\(945\) −2.72795e16 −1.17750
\(946\) 0 0
\(947\) −1.97365e16 −0.842064 −0.421032 0.907046i \(-0.638332\pi\)
−0.421032 + 0.907046i \(0.638332\pi\)
\(948\) 0 0
\(949\) 3.88152e15 0.163696
\(950\) 0 0
\(951\) −4.03992e16 −1.68415
\(952\) 0 0
\(953\) 1.28343e16 0.528884 0.264442 0.964402i \(-0.414812\pi\)
0.264442 + 0.964402i \(0.414812\pi\)
\(954\) 0 0
\(955\) −2.47997e15 −0.101025
\(956\) 0 0
\(957\) 1.99228e16 0.802296
\(958\) 0 0
\(959\) −7.74699e16 −3.08411
\(960\) 0 0
\(961\) −2.52335e16 −0.993112
\(962\) 0 0
\(963\) −4.28619e16 −1.66773
\(964\) 0 0
\(965\) −1.89608e16 −0.729383
\(966\) 0 0
\(967\) 4.73110e16 1.79935 0.899676 0.436558i \(-0.143803\pi\)
0.899676 + 0.436558i \(0.143803\pi\)
\(968\) 0 0
\(969\) 6.35094e16 2.38813
\(970\) 0 0
\(971\) −2.69052e16 −1.00030 −0.500149 0.865939i \(-0.666722\pi\)
−0.500149 + 0.865939i \(0.666722\pi\)
\(972\) 0 0
\(973\) −6.64042e16 −2.44104
\(974\) 0 0
\(975\) 2.59318e16 0.942557
\(976\) 0 0
\(977\) −1.19615e16 −0.429899 −0.214950 0.976625i \(-0.568959\pi\)
−0.214950 + 0.976625i \(0.568959\pi\)
\(978\) 0 0
\(979\) 3.69078e16 1.31164
\(980\) 0 0
\(981\) 3.67795e16 1.29249
\(982\) 0 0
\(983\) 4.93179e16 1.71380 0.856900 0.515483i \(-0.172387\pi\)
0.856900 + 0.515483i \(0.172387\pi\)
\(984\) 0 0
\(985\) 1.98547e16 0.682281
\(986\) 0 0
\(987\) 5.94330e16 2.01968
\(988\) 0 0
\(989\) 2.66221e14 0.00894669
\(990\) 0 0
\(991\) −4.42856e16 −1.47183 −0.735915 0.677074i \(-0.763247\pi\)
−0.735915 + 0.677074i \(0.763247\pi\)
\(992\) 0 0
\(993\) −1.35623e16 −0.445772
\(994\) 0 0
\(995\) 2.66430e16 0.866075
\(996\) 0 0
\(997\) 2.10581e16 0.677011 0.338506 0.940964i \(-0.390079\pi\)
0.338506 + 0.940964i \(0.390079\pi\)
\(998\) 0 0
\(999\) 1.51755e15 0.0482539
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 \(a_p\))