Properties

Label 20.12.a.b.1.2
Level 20
Weight 12
Character 20.1
Self dual Yes
Analytic conductor 15.367
Analytic rank 0
Dimension 2
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 20.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(15.3668636112\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{46729}) \)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-107.584\)
Character \(\chi\) = 20.1

$q$-expansion

\(f(q)\) \(=\) \(q+542.338 q^{3} +3125.00 q^{5} +49659.5 q^{7} +116983. q^{9} +O(q^{10})\) \(q+542.338 q^{3} +3125.00 q^{5} +49659.5 q^{7} +116983. q^{9} -19451.8 q^{11} -759548. q^{13} +1.69481e6 q^{15} +2.35438e6 q^{17} +1.62826e7 q^{19} +2.69322e7 q^{21} +3.07894e7 q^{23} +9.76562e6 q^{25} -3.26290e7 q^{27} -1.24708e8 q^{29} +2.87600e8 q^{31} -1.05494e7 q^{33} +1.55186e8 q^{35} -6.80788e8 q^{37} -4.11932e8 q^{39} -3.20702e7 q^{41} -1.32076e9 q^{43} +3.65573e8 q^{45} -2.20253e9 q^{47} +4.88739e8 q^{49} +1.27687e9 q^{51} +4.55551e9 q^{53} -6.07867e7 q^{55} +8.83065e9 q^{57} -1.70865e9 q^{59} -6.50342e9 q^{61} +5.80933e9 q^{63} -2.37359e9 q^{65} +6.87165e7 q^{67} +1.66983e10 q^{69} -2.55089e10 q^{71} +1.19267e10 q^{73} +5.29627e9 q^{75} -9.65964e8 q^{77} -9.68170e9 q^{79} -3.84192e10 q^{81} -1.07710e10 q^{83} +7.35742e9 q^{85} -6.76338e10 q^{87} -7.08101e10 q^{89} -3.77188e10 q^{91} +1.55976e11 q^{93} +5.08830e10 q^{95} -1.53217e10 q^{97} -2.27553e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 220q^{3} + 6250q^{5} + 3340q^{7} + 43738q^{9} + O(q^{10}) \) \( 2q + 220q^{3} + 6250q^{5} + 3340q^{7} + 43738q^{9} + 298320q^{11} + 1209820q^{13} + 687500q^{15} + 9056340q^{17} + 19439368q^{19} + 41862752q^{21} + 55926420q^{23} + 19531250q^{25} + 48081880q^{27} + 41841708q^{29} + 62230792q^{31} - 112979280q^{33} + 10437500q^{35} - 729235940q^{37} - 1046733592q^{39} - 608419068q^{41} - 1129440740q^{43} + 136681250q^{45} - 1653072900q^{47} + 656908386q^{49} - 883429896q^{51} + 5724887340q^{53} + 932250000q^{55} + 7813100240q^{57} + 3756433896q^{59} + 4923703564q^{61} + 9202019900q^{63} + 3780687500q^{65} - 5843244140q^{67} + 8595645984q^{69} - 43352162664q^{71} + 33647099620q^{73} + 2148437500q^{75} - 15684992880q^{77} - 54799425296q^{79} - 51460199582q^{81} - 9303032100q^{83} + 28301062500q^{85} - 121318983000q^{87} + 3688968372q^{89} - 128938931512q^{91} + 228621221120q^{93} + 60748025000q^{95} + 65892157780q^{97} - 25550825520q^{99} + O(q^{100}) \)

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
\(3\) 542.338 1.28856 0.644278 0.764792i \(-0.277158\pi\)
0.644278 + 0.764792i \(0.277158\pi\)
\(4\) 0 0
\(5\) 3125.00 0.447214
\(6\) 0 0
\(7\) 49659.5 1.11677 0.558384 0.829582i \(-0.311422\pi\)
0.558384 + 0.829582i \(0.311422\pi\)
\(8\) 0 0
\(9\) 116983. 0.660374
\(10\) 0 0
\(11\) −19451.8 −0.0364166 −0.0182083 0.999834i \(-0.505796\pi\)
−0.0182083 + 0.999834i \(0.505796\pi\)
\(12\) 0 0
\(13\) −759548. −0.567371 −0.283685 0.958917i \(-0.591557\pi\)
−0.283685 + 0.958917i \(0.591557\pi\)
\(14\) 0 0
\(15\) 1.69481e6 0.576259
\(16\) 0 0
\(17\) 2.35438e6 0.402167 0.201084 0.979574i \(-0.435554\pi\)
0.201084 + 0.979574i \(0.435554\pi\)
\(18\) 0 0
\(19\) 1.62826e7 1.50861 0.754307 0.656522i \(-0.227973\pi\)
0.754307 + 0.656522i \(0.227973\pi\)
\(20\) 0 0
\(21\) 2.69322e7 1.43902
\(22\) 0 0
\(23\) 3.07894e7 0.997466 0.498733 0.866756i \(-0.333799\pi\)
0.498733 + 0.866756i \(0.333799\pi\)
\(24\) 0 0
\(25\) 9.76562e6 0.200000
\(26\) 0 0
\(27\) −3.26290e7 −0.437626
\(28\) 0 0
\(29\) −1.24708e8 −1.12903 −0.564514 0.825424i \(-0.690936\pi\)
−0.564514 + 0.825424i \(0.690936\pi\)
\(30\) 0 0
\(31\) 2.87600e8 1.80426 0.902130 0.431464i \(-0.142003\pi\)
0.902130 + 0.431464i \(0.142003\pi\)
\(32\) 0 0
\(33\) −1.05494e7 −0.0469248
\(34\) 0 0
\(35\) 1.55186e8 0.499434
\(36\) 0 0
\(37\) −6.80788e8 −1.61400 −0.806998 0.590554i \(-0.798909\pi\)
−0.806998 + 0.590554i \(0.798909\pi\)
\(38\) 0 0
\(39\) −4.11932e8 −0.731088
\(40\) 0 0
\(41\) −3.20702e7 −0.0432305 −0.0216152 0.999766i \(-0.506881\pi\)
−0.0216152 + 0.999766i \(0.506881\pi\)
\(42\) 0 0
\(43\) −1.32076e9 −1.37008 −0.685040 0.728505i \(-0.740215\pi\)
−0.685040 + 0.728505i \(0.740215\pi\)
\(44\) 0 0
\(45\) 3.65573e8 0.295328
\(46\) 0 0
\(47\) −2.20253e9 −1.40082 −0.700411 0.713740i \(-0.747000\pi\)
−0.700411 + 0.713740i \(0.747000\pi\)
\(48\) 0 0
\(49\) 4.88739e8 0.247172
\(50\) 0 0
\(51\) 1.27687e9 0.518215
\(52\) 0 0
\(53\) 4.55551e9 1.49630 0.748151 0.663528i \(-0.230942\pi\)
0.748151 + 0.663528i \(0.230942\pi\)
\(54\) 0 0
\(55\) −6.07867e7 −0.0162860
\(56\) 0 0
\(57\) 8.83065e9 1.94393
\(58\) 0 0
\(59\) −1.70865e9 −0.311148 −0.155574 0.987824i \(-0.549723\pi\)
−0.155574 + 0.987824i \(0.549723\pi\)
\(60\) 0 0
\(61\) −6.50342e9 −0.985888 −0.492944 0.870061i \(-0.664079\pi\)
−0.492944 + 0.870061i \(0.664079\pi\)
\(62\) 0 0
\(63\) 5.80933e9 0.737485
\(64\) 0 0
\(65\) −2.37359e9 −0.253736
\(66\) 0 0
\(67\) 6.87165e7 0.00621798 0.00310899 0.999995i \(-0.499010\pi\)
0.00310899 + 0.999995i \(0.499010\pi\)
\(68\) 0 0
\(69\) 1.66983e10 1.28529
\(70\) 0 0
\(71\) −2.55089e10 −1.67792 −0.838958 0.544196i \(-0.816835\pi\)
−0.838958 + 0.544196i \(0.816835\pi\)
\(72\) 0 0
\(73\) 1.19267e10 0.673358 0.336679 0.941620i \(-0.390696\pi\)
0.336679 + 0.941620i \(0.390696\pi\)
\(74\) 0 0
\(75\) 5.29627e9 0.257711
\(76\) 0 0
\(77\) −9.65964e8 −0.0406689
\(78\) 0 0
\(79\) −9.68170e9 −0.354000 −0.177000 0.984211i \(-0.556639\pi\)
−0.177000 + 0.984211i \(0.556639\pi\)
\(80\) 0 0
\(81\) −3.84192e10 −1.22428
\(82\) 0 0
\(83\) −1.07710e10 −0.300142 −0.150071 0.988675i \(-0.547950\pi\)
−0.150071 + 0.988675i \(0.547950\pi\)
\(84\) 0 0
\(85\) 7.35742e9 0.179855
\(86\) 0 0
\(87\) −6.76338e10 −1.45481
\(88\) 0 0
\(89\) −7.08101e10 −1.34416 −0.672079 0.740480i \(-0.734598\pi\)
−0.672079 + 0.740480i \(0.734598\pi\)
\(90\) 0 0
\(91\) −3.77188e10 −0.633622
\(92\) 0 0
\(93\) 1.55976e11 2.32489
\(94\) 0 0
\(95\) 5.08830e10 0.674673
\(96\) 0 0
\(97\) −1.53217e10 −0.181160 −0.0905800 0.995889i \(-0.528872\pi\)
−0.0905800 + 0.995889i \(0.528872\pi\)
\(98\) 0 0
\(99\) −2.27553e9 −0.0240486
\(100\) 0 0
\(101\) 2.01154e11 1.90441 0.952207 0.305453i \(-0.0988078\pi\)
0.952207 + 0.305453i \(0.0988078\pi\)
\(102\) 0 0
\(103\) 1.24282e11 1.05634 0.528168 0.849140i \(-0.322879\pi\)
0.528168 + 0.849140i \(0.322879\pi\)
\(104\) 0 0
\(105\) 8.41632e10 0.643548
\(106\) 0 0
\(107\) −1.78965e11 −1.23355 −0.616774 0.787140i \(-0.711561\pi\)
−0.616774 + 0.787140i \(0.711561\pi\)
\(108\) 0 0
\(109\) 8.15715e10 0.507800 0.253900 0.967230i \(-0.418287\pi\)
0.253900 + 0.967230i \(0.418287\pi\)
\(110\) 0 0
\(111\) −3.69217e11 −2.07972
\(112\) 0 0
\(113\) 2.55934e11 1.30676 0.653381 0.757029i \(-0.273350\pi\)
0.653381 + 0.757029i \(0.273350\pi\)
\(114\) 0 0
\(115\) 9.62169e10 0.446080
\(116\) 0 0
\(117\) −8.88545e10 −0.374677
\(118\) 0 0
\(119\) 1.16917e11 0.449128
\(120\) 0 0
\(121\) −2.84933e11 −0.998674
\(122\) 0 0
\(123\) −1.73929e10 −0.0557048
\(124\) 0 0
\(125\) 3.05176e10 0.0894427
\(126\) 0 0
\(127\) 3.21115e11 0.862461 0.431231 0.902242i \(-0.358080\pi\)
0.431231 + 0.902242i \(0.358080\pi\)
\(128\) 0 0
\(129\) −7.16296e11 −1.76542
\(130\) 0 0
\(131\) −6.42126e11 −1.45421 −0.727107 0.686524i \(-0.759136\pi\)
−0.727107 + 0.686524i \(0.759136\pi\)
\(132\) 0 0
\(133\) 8.08584e11 1.68477
\(134\) 0 0
\(135\) −1.01966e11 −0.195713
\(136\) 0 0
\(137\) −4.79216e11 −0.848336 −0.424168 0.905583i \(-0.639433\pi\)
−0.424168 + 0.905583i \(0.639433\pi\)
\(138\) 0 0
\(139\) 6.77838e11 1.10801 0.554006 0.832513i \(-0.313099\pi\)
0.554006 + 0.832513i \(0.313099\pi\)
\(140\) 0 0
\(141\) −1.19451e12 −1.80504
\(142\) 0 0
\(143\) 1.47745e10 0.0206617
\(144\) 0 0
\(145\) −3.89712e11 −0.504917
\(146\) 0 0
\(147\) 2.65062e11 0.318494
\(148\) 0 0
\(149\) −7.05810e11 −0.787342 −0.393671 0.919251i \(-0.628795\pi\)
−0.393671 + 0.919251i \(0.628795\pi\)
\(150\) 0 0
\(151\) 6.42190e11 0.665718 0.332859 0.942977i \(-0.391987\pi\)
0.332859 + 0.942977i \(0.391987\pi\)
\(152\) 0 0
\(153\) 2.75423e11 0.265581
\(154\) 0 0
\(155\) 8.98749e11 0.806890
\(156\) 0 0
\(157\) 1.25437e12 1.04949 0.524743 0.851261i \(-0.324161\pi\)
0.524743 + 0.851261i \(0.324161\pi\)
\(158\) 0 0
\(159\) 2.47062e12 1.92807
\(160\) 0 0
\(161\) 1.52899e12 1.11394
\(162\) 0 0
\(163\) −5.85578e10 −0.0398615 −0.0199307 0.999801i \(-0.506345\pi\)
−0.0199307 + 0.999801i \(0.506345\pi\)
\(164\) 0 0
\(165\) −3.29669e10 −0.0209854
\(166\) 0 0
\(167\) −1.63528e12 −0.974206 −0.487103 0.873344i \(-0.661946\pi\)
−0.487103 + 0.873344i \(0.661946\pi\)
\(168\) 0 0
\(169\) −1.21525e12 −0.678090
\(170\) 0 0
\(171\) 1.90479e12 0.996250
\(172\) 0 0
\(173\) −1.99007e12 −0.976371 −0.488186 0.872740i \(-0.662341\pi\)
−0.488186 + 0.872740i \(0.662341\pi\)
\(174\) 0 0
\(175\) 4.84956e11 0.223354
\(176\) 0 0
\(177\) −9.26664e11 −0.400931
\(178\) 0 0
\(179\) −2.71716e12 −1.10515 −0.552577 0.833462i \(-0.686356\pi\)
−0.552577 + 0.833462i \(0.686356\pi\)
\(180\) 0 0
\(181\) 2.72114e12 1.04116 0.520582 0.853812i \(-0.325715\pi\)
0.520582 + 0.853812i \(0.325715\pi\)
\(182\) 0 0
\(183\) −3.52705e12 −1.27037
\(184\) 0 0
\(185\) −2.12746e12 −0.721801
\(186\) 0 0
\(187\) −4.57967e10 −0.0146455
\(188\) 0 0
\(189\) −1.62034e12 −0.488727
\(190\) 0 0
\(191\) 2.22323e12 0.632850 0.316425 0.948618i \(-0.397518\pi\)
0.316425 + 0.948618i \(0.397518\pi\)
\(192\) 0 0
\(193\) 3.75455e11 0.100924 0.0504618 0.998726i \(-0.483931\pi\)
0.0504618 + 0.998726i \(0.483931\pi\)
\(194\) 0 0
\(195\) −1.28729e12 −0.326953
\(196\) 0 0
\(197\) −3.51030e11 −0.0842907 −0.0421453 0.999111i \(-0.513419\pi\)
−0.0421453 + 0.999111i \(0.513419\pi\)
\(198\) 0 0
\(199\) 4.02056e12 0.913260 0.456630 0.889657i \(-0.349056\pi\)
0.456630 + 0.889657i \(0.349056\pi\)
\(200\) 0 0
\(201\) 3.72675e10 0.00801221
\(202\) 0 0
\(203\) −6.19293e12 −1.26086
\(204\) 0 0
\(205\) −1.00219e11 −0.0193333
\(206\) 0 0
\(207\) 3.60185e12 0.658701
\(208\) 0 0
\(209\) −3.16725e11 −0.0549386
\(210\) 0 0
\(211\) 5.85562e11 0.0963872 0.0481936 0.998838i \(-0.484654\pi\)
0.0481936 + 0.998838i \(0.484654\pi\)
\(212\) 0 0
\(213\) −1.38344e13 −2.16209
\(214\) 0 0
\(215\) −4.12736e12 −0.612719
\(216\) 0 0
\(217\) 1.42821e13 2.01494
\(218\) 0 0
\(219\) 6.46832e12 0.867659
\(220\) 0 0
\(221\) −1.78826e12 −0.228178
\(222\) 0 0
\(223\) 7.67568e12 0.932052 0.466026 0.884771i \(-0.345685\pi\)
0.466026 + 0.884771i \(0.345685\pi\)
\(224\) 0 0
\(225\) 1.14242e12 0.132075
\(226\) 0 0
\(227\) 8.03622e12 0.884931 0.442466 0.896785i \(-0.354104\pi\)
0.442466 + 0.896785i \(0.354104\pi\)
\(228\) 0 0
\(229\) 1.30248e13 1.36671 0.683354 0.730087i \(-0.260521\pi\)
0.683354 + 0.730087i \(0.260521\pi\)
\(230\) 0 0
\(231\) −5.23879e11 −0.0524041
\(232\) 0 0
\(233\) 1.09159e13 1.04136 0.520680 0.853752i \(-0.325678\pi\)
0.520680 + 0.853752i \(0.325678\pi\)
\(234\) 0 0
\(235\) −6.88289e12 −0.626467
\(236\) 0 0
\(237\) −5.25075e12 −0.456148
\(238\) 0 0
\(239\) −1.18735e13 −0.984895 −0.492447 0.870342i \(-0.663898\pi\)
−0.492447 + 0.870342i \(0.663898\pi\)
\(240\) 0 0
\(241\) 2.34520e13 1.85818 0.929088 0.369859i \(-0.120594\pi\)
0.929088 + 0.369859i \(0.120594\pi\)
\(242\) 0 0
\(243\) −1.50561e13 −1.13993
\(244\) 0 0
\(245\) 1.52731e12 0.110539
\(246\) 0 0
\(247\) −1.23674e13 −0.855944
\(248\) 0 0
\(249\) −5.84153e12 −0.386750
\(250\) 0 0
\(251\) −1.53634e13 −0.973378 −0.486689 0.873575i \(-0.661796\pi\)
−0.486689 + 0.873575i \(0.661796\pi\)
\(252\) 0 0
\(253\) −5.98908e11 −0.0363243
\(254\) 0 0
\(255\) 3.99021e12 0.231753
\(256\) 0 0
\(257\) −3.42146e12 −0.190362 −0.0951809 0.995460i \(-0.530343\pi\)
−0.0951809 + 0.995460i \(0.530343\pi\)
\(258\) 0 0
\(259\) −3.38076e13 −1.80246
\(260\) 0 0
\(261\) −1.45887e13 −0.745581
\(262\) 0 0
\(263\) 1.19978e13 0.587954 0.293977 0.955812i \(-0.405021\pi\)
0.293977 + 0.955812i \(0.405021\pi\)
\(264\) 0 0
\(265\) 1.42360e13 0.669167
\(266\) 0 0
\(267\) −3.84030e13 −1.73202
\(268\) 0 0
\(269\) 1.54949e13 0.670734 0.335367 0.942088i \(-0.391140\pi\)
0.335367 + 0.942088i \(0.391140\pi\)
\(270\) 0 0
\(271\) 2.54301e13 1.05686 0.528430 0.848977i \(-0.322781\pi\)
0.528430 + 0.848977i \(0.322781\pi\)
\(272\) 0 0
\(273\) −2.04563e13 −0.816456
\(274\) 0 0
\(275\) −1.89959e11 −0.00728331
\(276\) 0 0
\(277\) 2.18585e12 0.0805345 0.0402672 0.999189i \(-0.487179\pi\)
0.0402672 + 0.999189i \(0.487179\pi\)
\(278\) 0 0
\(279\) 3.36444e13 1.19149
\(280\) 0 0
\(281\) −2.08522e13 −0.710013 −0.355007 0.934864i \(-0.615521\pi\)
−0.355007 + 0.934864i \(0.615521\pi\)
\(282\) 0 0
\(283\) 5.16150e13 1.69025 0.845124 0.534570i \(-0.179526\pi\)
0.845124 + 0.534570i \(0.179526\pi\)
\(284\) 0 0
\(285\) 2.75958e13 0.869353
\(286\) 0 0
\(287\) −1.59259e12 −0.0482784
\(288\) 0 0
\(289\) −2.87288e13 −0.838262
\(290\) 0 0
\(291\) −8.30953e12 −0.233435
\(292\) 0 0
\(293\) 1.44670e13 0.391387 0.195693 0.980665i \(-0.437304\pi\)
0.195693 + 0.980665i \(0.437304\pi\)
\(294\) 0 0
\(295\) −5.33952e12 −0.139149
\(296\) 0 0
\(297\) 6.34692e11 0.0159369
\(298\) 0 0
\(299\) −2.33860e13 −0.565933
\(300\) 0 0
\(301\) −6.55881e13 −1.53006
\(302\) 0 0
\(303\) 1.09094e14 2.45394
\(304\) 0 0
\(305\) −2.03232e13 −0.440902
\(306\) 0 0
\(307\) −1.67889e13 −0.351368 −0.175684 0.984447i \(-0.556214\pi\)
−0.175684 + 0.984447i \(0.556214\pi\)
\(308\) 0 0
\(309\) 6.74026e13 1.36115
\(310\) 0 0
\(311\) 1.98233e13 0.386361 0.193181 0.981163i \(-0.438120\pi\)
0.193181 + 0.981163i \(0.438120\pi\)
\(312\) 0 0
\(313\) 1.94059e13 0.365123 0.182561 0.983194i \(-0.441561\pi\)
0.182561 + 0.983194i \(0.441561\pi\)
\(314\) 0 0
\(315\) 1.81542e13 0.329813
\(316\) 0 0
\(317\) 9.63212e13 1.69004 0.845018 0.534737i \(-0.179589\pi\)
0.845018 + 0.534737i \(0.179589\pi\)
\(318\) 0 0
\(319\) 2.42579e12 0.0411153
\(320\) 0 0
\(321\) −9.70592e13 −1.58949
\(322\) 0 0
\(323\) 3.83353e13 0.606715
\(324\) 0 0
\(325\) −7.41746e12 −0.113474
\(326\) 0 0
\(327\) 4.42393e13 0.654328
\(328\) 0 0
\(329\) −1.09376e14 −1.56439
\(330\) 0 0
\(331\) −1.14888e14 −1.58936 −0.794679 0.607030i \(-0.792361\pi\)
−0.794679 + 0.607030i \(0.792361\pi\)
\(332\) 0 0
\(333\) −7.96409e13 −1.06584
\(334\) 0 0
\(335\) 2.14739e11 0.00278077
\(336\) 0 0
\(337\) −9.51535e13 −1.19251 −0.596253 0.802797i \(-0.703344\pi\)
−0.596253 + 0.802797i \(0.703344\pi\)
\(338\) 0 0
\(339\) 1.38803e14 1.68383
\(340\) 0 0
\(341\) −5.59432e12 −0.0657050
\(342\) 0 0
\(343\) −7.39225e13 −0.840735
\(344\) 0 0
\(345\) 5.21821e13 0.574799
\(346\) 0 0
\(347\) −1.79048e14 −1.91054 −0.955272 0.295727i \(-0.904438\pi\)
−0.955272 + 0.295727i \(0.904438\pi\)
\(348\) 0 0
\(349\) −1.42818e14 −1.47654 −0.738268 0.674507i \(-0.764356\pi\)
−0.738268 + 0.674507i \(0.764356\pi\)
\(350\) 0 0
\(351\) 2.47833e13 0.248296
\(352\) 0 0
\(353\) 8.34518e13 0.810354 0.405177 0.914238i \(-0.367210\pi\)
0.405177 + 0.914238i \(0.367210\pi\)
\(354\) 0 0
\(355\) −7.97152e13 −0.750387
\(356\) 0 0
\(357\) 6.34086e13 0.578726
\(358\) 0 0
\(359\) 1.10422e14 0.977322 0.488661 0.872474i \(-0.337486\pi\)
0.488661 + 0.872474i \(0.337486\pi\)
\(360\) 0 0
\(361\) 1.48632e14 1.27592
\(362\) 0 0
\(363\) −1.54530e14 −1.28685
\(364\) 0 0
\(365\) 3.72711e13 0.301135
\(366\) 0 0
\(367\) 6.35584e13 0.498322 0.249161 0.968462i \(-0.419845\pi\)
0.249161 + 0.968462i \(0.419845\pi\)
\(368\) 0 0
\(369\) −3.75167e12 −0.0285483
\(370\) 0 0
\(371\) 2.26224e14 1.67102
\(372\) 0 0
\(373\) 6.93761e13 0.497521 0.248760 0.968565i \(-0.419977\pi\)
0.248760 + 0.968565i \(0.419977\pi\)
\(374\) 0 0
\(375\) 1.65508e13 0.115252
\(376\) 0 0
\(377\) 9.47216e13 0.640577
\(378\) 0 0
\(379\) −7.64902e13 −0.502447 −0.251224 0.967929i \(-0.580833\pi\)
−0.251224 + 0.967929i \(0.580833\pi\)
\(380\) 0 0
\(381\) 1.74153e14 1.11133
\(382\) 0 0
\(383\) 1.21465e14 0.753110 0.376555 0.926394i \(-0.377109\pi\)
0.376555 + 0.926394i \(0.377109\pi\)
\(384\) 0 0
\(385\) −3.01864e12 −0.0181877
\(386\) 0 0
\(387\) −1.54506e14 −0.904766
\(388\) 0 0
\(389\) −2.85195e14 −1.62338 −0.811688 0.584092i \(-0.801451\pi\)
−0.811688 + 0.584092i \(0.801451\pi\)
\(390\) 0 0
\(391\) 7.24898e13 0.401148
\(392\) 0 0
\(393\) −3.48249e14 −1.87383
\(394\) 0 0
\(395\) −3.02553e13 −0.158313
\(396\) 0 0
\(397\) 1.43169e14 0.728618 0.364309 0.931278i \(-0.381305\pi\)
0.364309 + 0.931278i \(0.381305\pi\)
\(398\) 0 0
\(399\) 4.38526e14 2.17092
\(400\) 0 0
\(401\) 3.83730e14 1.84812 0.924062 0.382242i \(-0.124848\pi\)
0.924062 + 0.382242i \(0.124848\pi\)
\(402\) 0 0
\(403\) −2.18446e14 −1.02368
\(404\) 0 0
\(405\) −1.20060e14 −0.547515
\(406\) 0 0
\(407\) 1.32425e13 0.0587762
\(408\) 0 0
\(409\) −2.42103e13 −0.104598 −0.0522988 0.998631i \(-0.516655\pi\)
−0.0522988 + 0.998631i \(0.516655\pi\)
\(410\) 0 0
\(411\) −2.59897e14 −1.09313
\(412\) 0 0
\(413\) −8.48506e13 −0.347480
\(414\) 0 0
\(415\) −3.36594e13 −0.134228
\(416\) 0 0
\(417\) 3.67617e14 1.42773
\(418\) 0 0
\(419\) 1.87208e14 0.708187 0.354093 0.935210i \(-0.384790\pi\)
0.354093 + 0.935210i \(0.384790\pi\)
\(420\) 0 0
\(421\) −2.90015e14 −1.06873 −0.534366 0.845253i \(-0.679449\pi\)
−0.534366 + 0.845253i \(0.679449\pi\)
\(422\) 0 0
\(423\) −2.57659e14 −0.925067
\(424\) 0 0
\(425\) 2.29919e13 0.0804334
\(426\) 0 0
\(427\) −3.22956e14 −1.10101
\(428\) 0 0
\(429\) 8.01279e12 0.0266237
\(430\) 0 0
\(431\) −1.21836e14 −0.394595 −0.197298 0.980344i \(-0.563217\pi\)
−0.197298 + 0.980344i \(0.563217\pi\)
\(432\) 0 0
\(433\) −6.62337e13 −0.209120 −0.104560 0.994519i \(-0.533343\pi\)
−0.104560 + 0.994519i \(0.533343\pi\)
\(434\) 0 0
\(435\) −2.11356e14 −0.650613
\(436\) 0 0
\(437\) 5.01331e14 1.50479
\(438\) 0 0
\(439\) −1.40333e13 −0.0410776 −0.0205388 0.999789i \(-0.506538\pi\)
−0.0205388 + 0.999789i \(0.506538\pi\)
\(440\) 0 0
\(441\) 5.71743e13 0.163226
\(442\) 0 0
\(443\) −4.34013e14 −1.20860 −0.604299 0.796758i \(-0.706547\pi\)
−0.604299 + 0.796758i \(0.706547\pi\)
\(444\) 0 0
\(445\) −2.21282e14 −0.601126
\(446\) 0 0
\(447\) −3.82788e14 −1.01453
\(448\) 0 0
\(449\) −3.80839e14 −0.984888 −0.492444 0.870344i \(-0.663896\pi\)
−0.492444 + 0.870344i \(0.663896\pi\)
\(450\) 0 0
\(451\) 6.23821e11 0.00157431
\(452\) 0 0
\(453\) 3.48284e14 0.857814
\(454\) 0 0
\(455\) −1.17871e14 −0.283364
\(456\) 0 0
\(457\) 4.71367e14 1.10617 0.553083 0.833126i \(-0.313451\pi\)
0.553083 + 0.833126i \(0.313451\pi\)
\(458\) 0 0
\(459\) −7.68210e13 −0.175999
\(460\) 0 0
\(461\) −3.27142e14 −0.731782 −0.365891 0.930658i \(-0.619236\pi\)
−0.365891 + 0.930658i \(0.619236\pi\)
\(462\) 0 0
\(463\) 4.66836e14 1.01969 0.509846 0.860266i \(-0.329702\pi\)
0.509846 + 0.860266i \(0.329702\pi\)
\(464\) 0 0
\(465\) 4.87426e14 1.03972
\(466\) 0 0
\(467\) −2.78595e13 −0.0580404 −0.0290202 0.999579i \(-0.509239\pi\)
−0.0290202 + 0.999579i \(0.509239\pi\)
\(468\) 0 0
\(469\) 3.41243e12 0.00694404
\(470\) 0 0
\(471\) 6.80291e14 1.35232
\(472\) 0 0
\(473\) 2.56910e13 0.0498936
\(474\) 0 0
\(475\) 1.59009e14 0.301723
\(476\) 0 0
\(477\) 5.32918e14 0.988120
\(478\) 0 0
\(479\) 6.05624e14 1.09738 0.548691 0.836025i \(-0.315126\pi\)
0.548691 + 0.836025i \(0.315126\pi\)
\(480\) 0 0
\(481\) 5.17092e14 0.915734
\(482\) 0 0
\(483\) 8.29227e14 1.43537
\(484\) 0 0
\(485\) −4.78803e13 −0.0810172
\(486\) 0 0
\(487\) −7.89431e14 −1.30588 −0.652942 0.757408i \(-0.726466\pi\)
−0.652942 + 0.757408i \(0.726466\pi\)
\(488\) 0 0
\(489\) −3.17581e13 −0.0513637
\(490\) 0 0
\(491\) −1.81410e14 −0.286889 −0.143444 0.989658i \(-0.545818\pi\)
−0.143444 + 0.989658i \(0.545818\pi\)
\(492\) 0 0
\(493\) −2.93609e14 −0.454058
\(494\) 0 0
\(495\) −7.11103e12 −0.0107548
\(496\) 0 0
\(497\) −1.26676e15 −1.87384
\(498\) 0 0
\(499\) 4.89614e14 0.708436 0.354218 0.935163i \(-0.384747\pi\)
0.354218 + 0.935163i \(0.384747\pi\)
\(500\) 0 0
\(501\) −8.86873e14 −1.25532
\(502\) 0 0
\(503\) 2.37938e14 0.329488 0.164744 0.986336i \(-0.447320\pi\)
0.164744 + 0.986336i \(0.447320\pi\)
\(504\) 0 0
\(505\) 6.28607e14 0.851680
\(506\) 0 0
\(507\) −6.59074e14 −0.873757
\(508\) 0 0
\(509\) −8.23454e14 −1.06830 −0.534148 0.845391i \(-0.679368\pi\)
−0.534148 + 0.845391i \(0.679368\pi\)
\(510\) 0 0
\(511\) 5.92276e14 0.751985
\(512\) 0 0
\(513\) −5.31285e14 −0.660210
\(514\) 0 0
\(515\) 3.88380e14 0.472408
\(516\) 0 0
\(517\) 4.28430e13 0.0510131
\(518\) 0 0
\(519\) −1.07929e15 −1.25811
\(520\) 0 0
\(521\) −9.50125e14 −1.08436 −0.542180 0.840263i \(-0.682401\pi\)
−0.542180 + 0.840263i \(0.682401\pi\)
\(522\) 0 0
\(523\) 1.61137e15 1.80067 0.900337 0.435194i \(-0.143320\pi\)
0.900337 + 0.435194i \(0.143320\pi\)
\(524\) 0 0
\(525\) 2.63010e14 0.287804
\(526\) 0 0
\(527\) 6.77118e14 0.725614
\(528\) 0 0
\(529\) −4.82246e12 −0.00506130
\(530\) 0 0
\(531\) −1.99883e14 −0.205474
\(532\) 0 0
\(533\) 2.43588e13 0.0245277
\(534\) 0 0
\(535\) −5.59264e14 −0.551660
\(536\) 0 0
\(537\) −1.47362e15 −1.42405
\(538\) 0 0
\(539\) −9.50683e12 −0.00900114
\(540\) 0 0
\(541\) −1.03512e15 −0.960294 −0.480147 0.877188i \(-0.659417\pi\)
−0.480147 + 0.877188i \(0.659417\pi\)
\(542\) 0 0
\(543\) 1.47578e15 1.34160
\(544\) 0 0
\(545\) 2.54911e14 0.227095
\(546\) 0 0
\(547\) 5.24788e14 0.458198 0.229099 0.973403i \(-0.426422\pi\)
0.229099 + 0.973403i \(0.426422\pi\)
\(548\) 0 0
\(549\) −7.60791e14 −0.651055
\(550\) 0 0
\(551\) −2.03056e15 −1.70327
\(552\) 0 0
\(553\) −4.80789e14 −0.395336
\(554\) 0 0
\(555\) −1.15380e15 −0.930081
\(556\) 0 0
\(557\) 2.26339e15 1.78878 0.894388 0.447292i \(-0.147612\pi\)
0.894388 + 0.447292i \(0.147612\pi\)
\(558\) 0 0
\(559\) 1.00318e15 0.777344
\(560\) 0 0
\(561\) −2.48373e13 −0.0188716
\(562\) 0 0
\(563\) 6.47720e14 0.482604 0.241302 0.970450i \(-0.422426\pi\)
0.241302 + 0.970450i \(0.422426\pi\)
\(564\) 0 0
\(565\) 7.99794e14 0.584402
\(566\) 0 0
\(567\) −1.90788e15 −1.36724
\(568\) 0 0
\(569\) 2.63615e14 0.185290 0.0926451 0.995699i \(-0.470468\pi\)
0.0926451 + 0.995699i \(0.470468\pi\)
\(570\) 0 0
\(571\) −1.94491e14 −0.134091 −0.0670457 0.997750i \(-0.521357\pi\)
−0.0670457 + 0.997750i \(0.521357\pi\)
\(572\) 0 0
\(573\) 1.20574e15 0.815461
\(574\) 0 0
\(575\) 3.00678e14 0.199493
\(576\) 0 0
\(577\) 7.85826e14 0.511516 0.255758 0.966741i \(-0.417675\pi\)
0.255758 + 0.966741i \(0.417675\pi\)
\(578\) 0 0
\(579\) 2.03624e14 0.130046
\(580\) 0 0
\(581\) −5.34883e14 −0.335189
\(582\) 0 0
\(583\) −8.86126e13 −0.0544902
\(584\) 0 0
\(585\) −2.77670e14 −0.167561
\(586\) 0 0
\(587\) 1.69825e15 1.00576 0.502878 0.864357i \(-0.332274\pi\)
0.502878 + 0.864357i \(0.332274\pi\)
\(588\) 0 0
\(589\) 4.68286e15 2.72193
\(590\) 0 0
\(591\) −1.90377e14 −0.108613
\(592\) 0 0
\(593\) −1.57747e15 −0.883406 −0.441703 0.897161i \(-0.645625\pi\)
−0.441703 + 0.897161i \(0.645625\pi\)
\(594\) 0 0
\(595\) 3.65366e14 0.200856
\(596\) 0 0
\(597\) 2.18050e15 1.17679
\(598\) 0 0
\(599\) 2.36133e14 0.125115 0.0625573 0.998041i \(-0.480074\pi\)
0.0625573 + 0.998041i \(0.480074\pi\)
\(600\) 0 0
\(601\) 2.87143e15 1.49379 0.746893 0.664944i \(-0.231545\pi\)
0.746893 + 0.664944i \(0.231545\pi\)
\(602\) 0 0
\(603\) 8.03868e12 0.00410619
\(604\) 0 0
\(605\) −8.90417e14 −0.446621
\(606\) 0 0
\(607\) −9.22001e14 −0.454144 −0.227072 0.973878i \(-0.572915\pi\)
−0.227072 + 0.973878i \(0.572915\pi\)
\(608\) 0 0
\(609\) −3.35866e15 −1.62469
\(610\) 0 0
\(611\) 1.67292e15 0.794785
\(612\) 0 0
\(613\) −4.25894e14 −0.198732 −0.0993662 0.995051i \(-0.531682\pi\)
−0.0993662 + 0.995051i \(0.531682\pi\)
\(614\) 0 0
\(615\) −5.43527e13 −0.0249120
\(616\) 0 0
\(617\) −2.66401e15 −1.19941 −0.599705 0.800221i \(-0.704715\pi\)
−0.599705 + 0.800221i \(0.704715\pi\)
\(618\) 0 0
\(619\) −1.71903e15 −0.760301 −0.380151 0.924925i \(-0.624128\pi\)
−0.380151 + 0.924925i \(0.624128\pi\)
\(620\) 0 0
\(621\) −1.00463e15 −0.436518
\(622\) 0 0
\(623\) −3.51639e15 −1.50111
\(624\) 0 0
\(625\) 9.53674e13 0.0400000
\(626\) 0 0
\(627\) −1.71772e14 −0.0707914
\(628\) 0 0
\(629\) −1.60283e15 −0.649097
\(630\) 0 0
\(631\) −4.92062e13 −0.0195821 −0.00979103 0.999952i \(-0.503117\pi\)
−0.00979103 + 0.999952i \(0.503117\pi\)
\(632\) 0 0
\(633\) 3.17572e14 0.124200
\(634\) 0 0
\(635\) 1.00348e15 0.385704
\(636\) 0 0
\(637\) −3.71221e14 −0.140238
\(638\) 0 0
\(639\) −2.98411e15 −1.10805
\(640\) 0 0
\(641\) 4.72099e15 1.72311 0.861557 0.507661i \(-0.169490\pi\)
0.861557 + 0.507661i \(0.169490\pi\)
\(642\) 0 0
\(643\) −3.18915e15 −1.14423 −0.572117 0.820172i \(-0.693878\pi\)
−0.572117 + 0.820172i \(0.693878\pi\)
\(644\) 0 0
\(645\) −2.23842e15 −0.789522
\(646\) 0 0
\(647\) −2.51792e15 −0.873110 −0.436555 0.899677i \(-0.643802\pi\)
−0.436555 + 0.899677i \(0.643802\pi\)
\(648\) 0 0
\(649\) 3.32362e13 0.0113309
\(650\) 0 0
\(651\) 7.74570e15 2.59636
\(652\) 0 0
\(653\) −3.80457e15 −1.25396 −0.626979 0.779036i \(-0.715709\pi\)
−0.626979 + 0.779036i \(0.715709\pi\)
\(654\) 0 0
\(655\) −2.00664e15 −0.650344
\(656\) 0 0
\(657\) 1.39523e15 0.444668
\(658\) 0 0
\(659\) 3.23977e15 1.01542 0.507709 0.861529i \(-0.330493\pi\)
0.507709 + 0.861529i \(0.330493\pi\)
\(660\) 0 0
\(661\) −2.71166e15 −0.835848 −0.417924 0.908482i \(-0.637242\pi\)
−0.417924 + 0.908482i \(0.637242\pi\)
\(662\) 0 0
\(663\) −9.69842e14 −0.294020
\(664\) 0 0
\(665\) 2.52683e15 0.753453
\(666\) 0 0
\(667\) −3.83968e15 −1.12617
\(668\) 0 0
\(669\) 4.16281e15 1.20100
\(670\) 0 0
\(671\) 1.26503e14 0.0359026
\(672\) 0 0
\(673\) 3.62755e15 1.01282 0.506409 0.862294i \(-0.330973\pi\)
0.506409 + 0.862294i \(0.330973\pi\)
\(674\) 0 0
\(675\) −3.18643e14 −0.0875253
\(676\) 0 0
\(677\) 4.05118e15 1.09482 0.547412 0.836863i \(-0.315613\pi\)
0.547412 + 0.836863i \(0.315613\pi\)
\(678\) 0 0
\(679\) −7.60868e14 −0.202314
\(680\) 0 0
\(681\) 4.35835e15 1.14028
\(682\) 0 0
\(683\) −4.56724e15 −1.17582 −0.587908 0.808928i \(-0.700048\pi\)
−0.587908 + 0.808928i \(0.700048\pi\)
\(684\) 0 0
\(685\) −1.49755e15 −0.379388
\(686\) 0 0
\(687\) 7.06384e15 1.76108
\(688\) 0 0
\(689\) −3.46013e15 −0.848958
\(690\) 0 0
\(691\) −6.26218e15 −1.51215 −0.756077 0.654482i \(-0.772887\pi\)
−0.756077 + 0.654482i \(0.772887\pi\)
\(692\) 0 0
\(693\) −1.13002e14 −0.0268567
\(694\) 0 0
\(695\) 2.11824e15 0.495518
\(696\) 0 0
\(697\) −7.55052e13 −0.0173859
\(698\) 0 0
\(699\) 5.92009e15 1.34185
\(700\) 0 0
\(701\) −1.12469e15 −0.250949 −0.125474 0.992097i \(-0.540045\pi\)
−0.125474 + 0.992097i \(0.540045\pi\)
\(702\) 0 0
\(703\) −1.10850e16 −2.43490
\(704\) 0 0
\(705\) −3.73285e15 −0.807237
\(706\) 0 0
\(707\) 9.98922e15 2.12679
\(708\) 0 0
\(709\) 4.16576e15 0.873253 0.436626 0.899643i \(-0.356173\pi\)
0.436626 + 0.899643i \(0.356173\pi\)
\(710\) 0 0
\(711\) −1.13260e15 −0.233772
\(712\) 0 0
\(713\) 8.85503e15 1.79969
\(714\) 0 0
\(715\) 4.61705e13 0.00924019
\(716\) 0 0
\(717\) −6.43944e15 −1.26909
\(718\) 0 0
\(719\) −8.31711e14 −0.161422 −0.0807111 0.996738i \(-0.525719\pi\)
−0.0807111 + 0.996738i \(0.525719\pi\)
\(720\) 0 0
\(721\) 6.17176e15 1.17968
\(722\) 0 0
\(723\) 1.27189e16 2.39436
\(724\) 0 0
\(725\) −1.21785e15 −0.225806
\(726\) 0 0
\(727\) 1.54083e15 0.281395 0.140697 0.990053i \(-0.455066\pi\)
0.140697 + 0.990053i \(0.455066\pi\)
\(728\) 0 0
\(729\) −1.35962e15 −0.244577
\(730\) 0 0
\(731\) −3.10956e15 −0.551001
\(732\) 0 0
\(733\) 4.81955e14 0.0841268 0.0420634 0.999115i \(-0.486607\pi\)
0.0420634 + 0.999115i \(0.486607\pi\)
\(734\) 0 0
\(735\) 8.28318e14 0.142435
\(736\) 0 0
\(737\) −1.33666e12 −0.000226438 0
\(738\) 0 0
\(739\) −1.56414e15 −0.261055 −0.130528 0.991445i \(-0.541667\pi\)
−0.130528 + 0.991445i \(0.541667\pi\)
\(740\) 0 0
\(741\) −6.70731e15 −1.10293
\(742\) 0 0
\(743\) −5.48466e14 −0.0888610 −0.0444305 0.999012i \(-0.514147\pi\)
−0.0444305 + 0.999012i \(0.514147\pi\)
\(744\) 0 0
\(745\) −2.20566e15 −0.352110
\(746\) 0 0
\(747\) −1.26003e15 −0.198206
\(748\) 0 0
\(749\) −8.88729e15 −1.37759
\(750\) 0 0
\(751\) −9.51331e15 −1.45315 −0.726577 0.687085i \(-0.758890\pi\)
−0.726577 + 0.687085i \(0.758890\pi\)
\(752\) 0 0
\(753\) −8.33215e15 −1.25425
\(754\) 0 0
\(755\) 2.00684e15 0.297718
\(756\) 0 0
\(757\) −6.27757e15 −0.917834 −0.458917 0.888479i \(-0.651762\pi\)
−0.458917 + 0.888479i \(0.651762\pi\)
\(758\) 0 0
\(759\) −3.24810e14 −0.0468059
\(760\) 0 0
\(761\) −2.56418e15 −0.364193 −0.182097 0.983281i \(-0.558288\pi\)
−0.182097 + 0.983281i \(0.558288\pi\)
\(762\) 0 0
\(763\) 4.05080e15 0.567095
\(764\) 0 0
\(765\) 8.60696e14 0.118771
\(766\) 0 0
\(767\) 1.29780e15 0.176536
\(768\) 0 0
\(769\) 5.83938e14 0.0783018 0.0391509 0.999233i \(-0.487535\pi\)
0.0391509 + 0.999233i \(0.487535\pi\)
\(770\) 0 0
\(771\) −1.85559e15 −0.245292
\(772\) 0 0
\(773\) 2.35645e15 0.307094 0.153547 0.988141i \(-0.450930\pi\)
0.153547 + 0.988141i \(0.450930\pi\)
\(774\) 0 0
\(775\) 2.80859e15 0.360852
\(776\) 0 0
\(777\) −1.83351e16 −2.32257
\(778\) 0 0
\(779\) −5.22185e14 −0.0652181
\(780\) 0 0
\(781\) 4.96192e14 0.0611040
\(782\) 0 0
\(783\) 4.06910e15 0.494093
\(784\) 0 0
\(785\) 3.91990e15 0.469344
\(786\) 0 0
\(787\) −3.54576e15 −0.418647 −0.209324 0.977846i \(-0.567126\pi\)
−0.209324 + 0.977846i \(0.567126\pi\)
\(788\) 0 0
\(789\) 6.50684e15 0.757612
\(790\) 0 0
\(791\) 1.27096e16 1.45935
\(792\) 0 0
\(793\) 4.93966e15 0.559364
\(794\) 0 0
\(795\) 7.72070e15 0.862259
\(796\) 0 0
\(797\) 4.80052e15 0.528771 0.264385 0.964417i \(-0.414831\pi\)
0.264385 + 0.964417i \(0.414831\pi\)
\(798\) 0 0
\(799\) −5.18557e15 −0.563365
\(800\) 0 0
\(801\) −8.28360e15 −0.887647
\(802\) 0 0
\(803\) −2.31996e14 −0.0245214
\(804\) 0 0
\(805\) 4.77808e15 0.498169
\(806\) 0 0
\(807\) 8.40345e15 0.864278
\(808\) 0 0
\(809\) −3.91609e14 −0.0397316 −0.0198658 0.999803i \(-0.506324\pi\)
−0.0198658 + 0.999803i \(0.506324\pi\)
\(810\) 0 0
\(811\) 5.86491e15 0.587012 0.293506 0.955957i \(-0.405178\pi\)
0.293506 + 0.955957i \(0.405178\pi\)
\(812\) 0 0
\(813\) 1.37917e16 1.36182
\(814\) 0 0
\(815\) −1.82993e14 −0.0178266
\(816\) 0 0
\(817\) −2.15053e16 −2.06692
\(818\) 0 0
\(819\) −4.41247e15 −0.418427
\(820\) 0 0
\(821\) −1.66455e15 −0.155743 −0.0778715 0.996963i \(-0.524812\pi\)
−0.0778715 + 0.996963i \(0.524812\pi\)
\(822\) 0 0
\(823\) 1.67289e16 1.54443 0.772216 0.635360i \(-0.219148\pi\)
0.772216 + 0.635360i \(0.219148\pi\)
\(824\) 0 0
\(825\) −1.03022e14 −0.00938495
\(826\) 0 0
\(827\) 1.91438e16 1.72087 0.860435 0.509560i \(-0.170192\pi\)
0.860435 + 0.509560i \(0.170192\pi\)
\(828\) 0 0
\(829\) 1.02576e16 0.909906 0.454953 0.890515i \(-0.349656\pi\)
0.454953 + 0.890515i \(0.349656\pi\)
\(830\) 0 0
\(831\) 1.18547e15 0.103773
\(832\) 0 0
\(833\) 1.15068e15 0.0994043
\(834\) 0 0
\(835\) −5.11024e15 −0.435678
\(836\) 0 0
\(837\) −9.38411e15 −0.789592
\(838\) 0 0
\(839\) −1.89422e16 −1.57304 −0.786519 0.617566i \(-0.788119\pi\)
−0.786519 + 0.617566i \(0.788119\pi\)
\(840\) 0 0
\(841\) 3.35153e15 0.274704
\(842\) 0 0
\(843\) −1.13089e16 −0.914891
\(844\) 0 0
\(845\) −3.79765e15 −0.303251
\(846\) 0 0
\(847\) −1.41496e16 −1.11529
\(848\) 0 0
\(849\) 2.79928e16 2.17798
\(850\) 0 0
\(851\) −2.09611e16 −1.60991
\(852\) 0 0
\(853\) 1.33491e16 1.01212 0.506059 0.862499i \(-0.331102\pi\)
0.506059 + 0.862499i \(0.331102\pi\)
\(854\) 0 0
\(855\) 5.95247e15 0.445537
\(856\) 0 0
\(857\) 2.46363e16 1.82046 0.910231 0.414101i \(-0.135904\pi\)
0.910231 + 0.414101i \(0.135904\pi\)
\(858\) 0 0
\(859\) −2.13423e16 −1.55696 −0.778482 0.627668i \(-0.784010\pi\)
−0.778482 + 0.627668i \(0.784010\pi\)
\(860\) 0 0
\(861\) −8.63721e14 −0.0622094
\(862\) 0 0
\(863\) 9.98852e15 0.710300 0.355150 0.934809i \(-0.384430\pi\)
0.355150 + 0.934809i \(0.384430\pi\)
\(864\) 0 0
\(865\) −6.21897e15 −0.436646
\(866\) 0 0
\(867\) −1.55807e16 −1.08015
\(868\) 0 0
\(869\) 1.88326e14 0.0128915
\(870\) 0 0
\(871\) −5.21935e13 −0.00352790
\(872\) 0 0
\(873\) −1.79238e15 −0.119633
\(874\) 0 0
\(875\) 1.51549e15 0.0998868
\(876\) 0 0
\(877\) 2.31195e16 1.50480 0.752402 0.658705i \(-0.228895\pi\)
0.752402 + 0.658705i \(0.228895\pi\)
\(878\) 0 0
\(879\) 7.84599e15 0.504323
\(880\) 0 0
\(881\) −2.73216e16 −1.73436 −0.867180 0.497995i \(-0.834070\pi\)
−0.867180 + 0.497995i \(0.834070\pi\)
\(882\) 0 0
\(883\) −1.06010e16 −0.664604 −0.332302 0.943173i \(-0.607825\pi\)
−0.332302 + 0.943173i \(0.607825\pi\)
\(884\) 0 0
\(885\) −2.89583e15 −0.179302
\(886\) 0 0
\(887\) 2.11039e16 1.29058 0.645288 0.763939i \(-0.276737\pi\)
0.645288 + 0.763939i \(0.276737\pi\)
\(888\) 0 0
\(889\) 1.59464e16 0.963170
\(890\) 0 0
\(891\) 7.47321e14 0.0445841
\(892\) 0 0
\(893\) −3.58628e16 −2.11330
\(894\) 0 0
\(895\) −8.49112e15 −0.494240
\(896\) 0 0
\(897\) −1.26831e16 −0.729236
\(898\) 0 0
\(899\) −3.58659e16 −2.03706
\(900\) 0 0
\(901\) 1.07254e16 0.601764
\(902\) 0 0
\(903\) −3.55709e16 −1.97157
\(904\) 0 0
\(905\) 8.50357e15 0.465623
\(906\) 0 0
\(907\) 6.86803e15 0.371528 0.185764 0.982594i \(-0.440524\pi\)
0.185764 + 0.982594i \(0.440524\pi\)
\(908\) 0 0
\(909\) 2.35317e16 1.25763
\(910\) 0 0
\(911\) −4.56797e15 −0.241197 −0.120599 0.992701i \(-0.538481\pi\)
−0.120599 + 0.992701i \(0.538481\pi\)
\(912\) 0 0
\(913\) 2.09515e14 0.0109301
\(914\) 0 0
\(915\) −1.10220e16 −0.568127
\(916\) 0 0
\(917\) −3.18877e16 −1.62402
\(918\) 0 0
\(919\) 2.45493e16 1.23539 0.617695 0.786418i \(-0.288067\pi\)
0.617695 + 0.786418i \(0.288067\pi\)
\(920\) 0 0
\(921\) −9.10527e15 −0.452757
\(922\) 0 0
\(923\) 1.93752e16 0.952001
\(924\) 0 0
\(925\) −6.64832e15 −0.322799
\(926\) 0 0
\(927\) 1.45389e16 0.697577
\(928\) 0 0
\(929\) −1.63221e16 −0.773909 −0.386954 0.922099i \(-0.626473\pi\)
−0.386954 + 0.922099i \(0.626473\pi\)
\(930\) 0 0
\(931\) 7.95793e15 0.372887
\(932\) 0 0
\(933\) 1.07509e16 0.497848
\(934\) 0 0
\(935\) −1.43115e14 −0.00654969
\(936\) 0 0
\(937\) 9.76542e15 0.441696 0.220848 0.975308i \(-0.429118\pi\)
0.220848 + 0.975308i \(0.429118\pi\)
\(938\) 0 0
\(939\) 1.05245e16 0.470481
\(940\) 0 0
\(941\) 4.42567e16 1.95540 0.977702 0.209999i \(-0.0673460\pi\)
0.977702 + 0.209999i \(0.0673460\pi\)
\(942\) 0 0
\(943\) −9.87421e14 −0.0431209
\(944\) 0 0
\(945\) −5.06357e15 −0.218566
\(946\) 0 0
\(947\) 2.15494e16 0.919412 0.459706 0.888071i \(-0.347955\pi\)
0.459706 + 0.888071i \(0.347955\pi\)
\(948\) 0 0
\(949\) −9.05893e15 −0.382044
\(950\) 0 0
\(951\) 5.22386e16 2.17771
\(952\) 0 0
\(953\) −3.05469e16 −1.25880 −0.629399 0.777083i \(-0.716699\pi\)
−0.629399 + 0.777083i \(0.716699\pi\)
\(954\) 0 0
\(955\) 6.94759e15 0.283019
\(956\) 0 0
\(957\) 1.31560e15 0.0529794
\(958\) 0 0
\(959\) −2.37976e16 −0.947395
\(960\) 0 0
\(961\) 5.73052e16 2.25536
\(962\) 0 0
\(963\) −2.09359e16 −0.814604
\(964\) 0 0
\(965\) 1.17330e15 0.0451344
\(966\) 0 0
\(967\) −2.67248e15 −0.101641 −0.0508204 0.998708i \(-0.516184\pi\)
−0.0508204 + 0.998708i \(0.516184\pi\)
\(968\) 0 0
\(969\) 2.07907e16 0.781786
\(970\) 0 0
\(971\) 1.05715e16 0.393036 0.196518 0.980500i \(-0.437037\pi\)
0.196518 + 0.980500i \(0.437037\pi\)
\(972\) 0 0
\(973\) 3.36611e16 1.23739
\(974\) 0 0
\(975\) −4.02277e15 −0.146218
\(976\) 0 0
\(977\) 2.22544e16 0.799826 0.399913 0.916553i \(-0.369040\pi\)
0.399913 + 0.916553i \(0.369040\pi\)
\(978\) 0 0
\(979\) 1.37738e15 0.0489496
\(980\) 0 0
\(981\) 9.54251e15 0.335338
\(982\) 0 0
\(983\) −5.53819e15 −0.192453 −0.0962263 0.995359i \(-0.530677\pi\)
−0.0962263 + 0.995359i \(0.530677\pi\)
\(984\) 0 0
\(985\) −1.09697e15 −0.0376959
\(986\) 0 0
\(987\) −5.93189e16 −2.01581
\(988\) 0 0
\(989\) −4.06653e16 −1.36661
\(990\) 0 0
\(991\) −2.34700e16 −0.780024 −0.390012 0.920810i \(-0.627529\pi\)
−0.390012 + 0.920810i \(0.627529\pi\)
\(992\) 0 0
\(993\) −6.23082e16 −2.04798
\(994\) 0 0
\(995\) 1.25642e16 0.408422
\(996\) 0 0
\(997\) −5.95725e16 −1.91524 −0.957618 0.288041i \(-0.906996\pi\)
−0.957618 + 0.288041i \(0.906996\pi\)
\(998\) 0 0
\(999\) 2.22135e16 0.706328
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 \(a_p\))