Properties

Label 20.12.a.b.1.1
Level 20
Weight 12
Character 20.1
Self dual Yes
Analytic conductor 15.367
Analytic rank 0
Dimension 2
CM No
Inner twists 1

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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 1.1
Root \(108.584\)
Character \(\chi\) = 20.1

$q$-expansion

\(f(q)\) \(=\) \(q-322.338 q^{3} +3125.00 q^{5} -46319.5 q^{7} -73245.3 q^{9} +O(q^{10})\) \(q-322.338 q^{3} +3125.00 q^{5} -46319.5 q^{7} -73245.3 q^{9} +317772. q^{11} +1.96937e6 q^{13} -1.00731e6 q^{15} +6.70196e6 q^{17} +3.15680e6 q^{19} +1.49305e7 q^{21} +2.51370e7 q^{23} +9.76562e6 q^{25} +8.07109e7 q^{27} +1.66550e8 q^{29} -2.25369e8 q^{31} -1.02430e8 q^{33} -1.44748e8 q^{35} -4.84476e7 q^{37} -6.34802e8 q^{39} -5.76349e8 q^{41} +1.91315e8 q^{43} -2.28892e8 q^{45} +5.49453e8 q^{47} +1.68169e8 q^{49} -2.16030e9 q^{51} +1.16938e9 q^{53} +9.93037e8 q^{55} -1.01755e9 q^{57} +5.46508e9 q^{59} +1.14271e10 q^{61} +3.39269e9 q^{63} +6.15428e9 q^{65} -5.91196e9 q^{67} -8.10261e9 q^{69} -1.78433e10 q^{71} +2.17204e10 q^{73} -3.14783e9 q^{75} -1.47190e10 q^{77} -4.51177e10 q^{79} -1.30410e10 q^{81} +1.46798e9 q^{83} +2.09436e10 q^{85} -5.36852e10 q^{87} +7.44991e10 q^{89} -9.12201e10 q^{91} +7.26450e10 q^{93} +9.86499e9 q^{95} +8.12138e10 q^{97} -2.32753e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 220q^{3} + 6250q^{5} + 3340q^{7} + 43738q^{9} + O(q^{10}) \) \( 2q + 220q^{3} + 6250q^{5} + 3340q^{7} + 43738q^{9} + 298320q^{11} + 1209820q^{13} + 687500q^{15} + 9056340q^{17} + 19439368q^{19} + 41862752q^{21} + 55926420q^{23} + 19531250q^{25} + 48081880q^{27} + 41841708q^{29} + 62230792q^{31} - 112979280q^{33} + 10437500q^{35} - 729235940q^{37} - 1046733592q^{39} - 608419068q^{41} - 1129440740q^{43} + 136681250q^{45} - 1653072900q^{47} + 656908386q^{49} - 883429896q^{51} + 5724887340q^{53} + 932250000q^{55} + 7813100240q^{57} + 3756433896q^{59} + 4923703564q^{61} + 9202019900q^{63} + 3780687500q^{65} - 5843244140q^{67} + 8595645984q^{69} - 43352162664q^{71} + 33647099620q^{73} + 2148437500q^{75} - 15684992880q^{77} - 54799425296q^{79} - 51460199582q^{81} - 9303032100q^{83} + 28301062500q^{85} - 121318983000q^{87} + 3688968372q^{89} - 128938931512q^{91} + 228621221120q^{93} + 60748025000q^{95} + 65892157780q^{97} - 25550825520q^{99} + O(q^{100}) \)

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
\(3\) −322.338 −0.765851 −0.382926 0.923779i \(-0.625083\pi\)
−0.382926 + 0.923779i \(0.625083\pi\)
\(4\) 0 0
\(5\) 3125.00 0.447214
\(6\) 0 0
\(7\) −46319.5 −1.04166 −0.520828 0.853661i \(-0.674377\pi\)
−0.520828 + 0.853661i \(0.674377\pi\)
\(8\) 0 0
\(9\) −73245.3 −0.413472
\(10\) 0 0
\(11\) 317772. 0.594916 0.297458 0.954735i \(-0.403861\pi\)
0.297458 + 0.954735i \(0.403861\pi\)
\(12\) 0 0
\(13\) 1.96937e6 1.47109 0.735544 0.677477i \(-0.236927\pi\)
0.735544 + 0.677477i \(0.236927\pi\)
\(14\) 0 0
\(15\) −1.00731e6 −0.342499
\(16\) 0 0
\(17\) 6.70196e6 1.14481 0.572405 0.819971i \(-0.306011\pi\)
0.572405 + 0.819971i \(0.306011\pi\)
\(18\) 0 0
\(19\) 3.15680e6 0.292484 0.146242 0.989249i \(-0.453282\pi\)
0.146242 + 0.989249i \(0.453282\pi\)
\(20\) 0 0
\(21\) 1.49305e7 0.797754
\(22\) 0 0
\(23\) 2.51370e7 0.814349 0.407175 0.913350i \(-0.366514\pi\)
0.407175 + 0.913350i \(0.366514\pi\)
\(24\) 0 0
\(25\) 9.76562e6 0.200000
\(26\) 0 0
\(27\) 8.07109e7 1.08251
\(28\) 0 0
\(29\) 1.66550e8 1.50784 0.753919 0.656968i \(-0.228161\pi\)
0.753919 + 0.656968i \(0.228161\pi\)
\(30\) 0 0
\(31\) −2.25369e8 −1.41386 −0.706928 0.707286i \(-0.749919\pi\)
−0.706928 + 0.707286i \(0.749919\pi\)
\(32\) 0 0
\(33\) −1.02430e8 −0.455617
\(34\) 0 0
\(35\) −1.44748e8 −0.465843
\(36\) 0 0
\(37\) −4.84476e7 −0.114858 −0.0574292 0.998350i \(-0.518290\pi\)
−0.0574292 + 0.998350i \(0.518290\pi\)
\(38\) 0 0
\(39\) −6.34802e8 −1.12663
\(40\) 0 0
\(41\) −5.76349e8 −0.776916 −0.388458 0.921466i \(-0.626992\pi\)
−0.388458 + 0.921466i \(0.626992\pi\)
\(42\) 0 0
\(43\) 1.91315e8 0.198460 0.0992300 0.995065i \(-0.468362\pi\)
0.0992300 + 0.995065i \(0.468362\pi\)
\(44\) 0 0
\(45\) −2.28892e8 −0.184910
\(46\) 0 0
\(47\) 5.49453e8 0.349456 0.174728 0.984617i \(-0.444095\pi\)
0.174728 + 0.984617i \(0.444095\pi\)
\(48\) 0 0
\(49\) 1.68169e8 0.0850488
\(50\) 0 0
\(51\) −2.16030e9 −0.876753
\(52\) 0 0
\(53\) 1.16938e9 0.384095 0.192047 0.981386i \(-0.438487\pi\)
0.192047 + 0.981386i \(0.438487\pi\)
\(54\) 0 0
\(55\) 9.93037e8 0.266054
\(56\) 0 0
\(57\) −1.01755e9 −0.223999
\(58\) 0 0
\(59\) 5.46508e9 0.995201 0.497600 0.867406i \(-0.334215\pi\)
0.497600 + 0.867406i \(0.334215\pi\)
\(60\) 0 0
\(61\) 1.14271e10 1.73230 0.866149 0.499786i \(-0.166588\pi\)
0.866149 + 0.499786i \(0.166588\pi\)
\(62\) 0 0
\(63\) 3.39269e9 0.430696
\(64\) 0 0
\(65\) 6.15428e9 0.657890
\(66\) 0 0
\(67\) −5.91196e9 −0.534959 −0.267479 0.963564i \(-0.586191\pi\)
−0.267479 + 0.963564i \(0.586191\pi\)
\(68\) 0 0
\(69\) −8.10261e9 −0.623670
\(70\) 0 0
\(71\) −1.78433e10 −1.17369 −0.586846 0.809699i \(-0.699631\pi\)
−0.586846 + 0.809699i \(0.699631\pi\)
\(72\) 0 0
\(73\) 2.17204e10 1.22628 0.613142 0.789972i \(-0.289905\pi\)
0.613142 + 0.789972i \(0.289905\pi\)
\(74\) 0 0
\(75\) −3.14783e9 −0.153170
\(76\) 0 0
\(77\) −1.47190e10 −0.619698
\(78\) 0 0
\(79\) −4.51177e10 −1.64967 −0.824837 0.565371i \(-0.808733\pi\)
−0.824837 + 0.565371i \(0.808733\pi\)
\(80\) 0 0
\(81\) −1.30410e10 −0.415569
\(82\) 0 0
\(83\) 1.46798e9 0.0409062 0.0204531 0.999791i \(-0.493489\pi\)
0.0204531 + 0.999791i \(0.493489\pi\)
\(84\) 0 0
\(85\) 2.09436e10 0.511974
\(86\) 0 0
\(87\) −5.36852e10 −1.15478
\(88\) 0 0
\(89\) 7.44991e10 1.41418 0.707092 0.707122i \(-0.250007\pi\)
0.707092 + 0.707122i \(0.250007\pi\)
\(90\) 0 0
\(91\) −9.12201e10 −1.53237
\(92\) 0 0
\(93\) 7.26450e10 1.08280
\(94\) 0 0
\(95\) 9.86499e9 0.130803
\(96\) 0 0
\(97\) 8.12138e10 0.960253 0.480126 0.877199i \(-0.340591\pi\)
0.480126 + 0.877199i \(0.340591\pi\)
\(98\) 0 0
\(99\) −2.32753e10 −0.245981
\(100\) 0 0
\(101\) −1.91624e11 −1.81419 −0.907095 0.420926i \(-0.861705\pi\)
−0.907095 + 0.420926i \(0.861705\pi\)
\(102\) 0 0
\(103\) 2.25295e11 1.91490 0.957450 0.288600i \(-0.0931899\pi\)
0.957450 + 0.288600i \(0.0931899\pi\)
\(104\) 0 0
\(105\) 4.66579e10 0.356766
\(106\) 0 0
\(107\) 2.03681e10 0.140391 0.0701955 0.997533i \(-0.477638\pi\)
0.0701955 + 0.997533i \(0.477638\pi\)
\(108\) 0 0
\(109\) 9.40097e10 0.585230 0.292615 0.956230i \(-0.405475\pi\)
0.292615 + 0.956230i \(0.405475\pi\)
\(110\) 0 0
\(111\) 1.56165e10 0.0879644
\(112\) 0 0
\(113\) 3.12193e11 1.59401 0.797006 0.603971i \(-0.206416\pi\)
0.797006 + 0.603971i \(0.206416\pi\)
\(114\) 0 0
\(115\) 7.85532e10 0.364188
\(116\) 0 0
\(117\) −1.44247e11 −0.608253
\(118\) 0 0
\(119\) −3.10432e11 −1.19250
\(120\) 0 0
\(121\) −1.84333e11 −0.646075
\(122\) 0 0
\(123\) 1.85779e11 0.595002
\(124\) 0 0
\(125\) 3.05176e10 0.0894427
\(126\) 0 0
\(127\) −5.10293e11 −1.37056 −0.685282 0.728278i \(-0.740321\pi\)
−0.685282 + 0.728278i \(0.740321\pi\)
\(128\) 0 0
\(129\) −6.16682e10 −0.151991
\(130\) 0 0
\(131\) −6.31604e11 −1.43039 −0.715193 0.698927i \(-0.753661\pi\)
−0.715193 + 0.698927i \(0.753661\pi\)
\(132\) 0 0
\(133\) −1.46221e11 −0.304668
\(134\) 0 0
\(135\) 2.52222e11 0.484113
\(136\) 0 0
\(137\) −3.82398e11 −0.676943 −0.338471 0.940977i \(-0.609910\pi\)
−0.338471 + 0.940977i \(0.609910\pi\)
\(138\) 0 0
\(139\) 9.74280e10 0.159258 0.0796292 0.996825i \(-0.474626\pi\)
0.0796292 + 0.996825i \(0.474626\pi\)
\(140\) 0 0
\(141\) −1.77110e11 −0.267631
\(142\) 0 0
\(143\) 6.25810e11 0.875173
\(144\) 0 0
\(145\) 5.20467e11 0.674325
\(146\) 0 0
\(147\) −5.42073e10 −0.0651347
\(148\) 0 0
\(149\) −1.86847e11 −0.208431 −0.104216 0.994555i \(-0.533233\pi\)
−0.104216 + 0.994555i \(0.533233\pi\)
\(150\) 0 0
\(151\) 1.69395e12 1.75601 0.878005 0.478651i \(-0.158874\pi\)
0.878005 + 0.478651i \(0.158874\pi\)
\(152\) 0 0
\(153\) −4.90888e11 −0.473346
\(154\) 0 0
\(155\) −7.04278e11 −0.632295
\(156\) 0 0
\(157\) 4.67640e11 0.391259 0.195629 0.980678i \(-0.437325\pi\)
0.195629 + 0.980678i \(0.437325\pi\)
\(158\) 0 0
\(159\) −3.76935e11 −0.294159
\(160\) 0 0
\(161\) −1.16433e12 −0.848272
\(162\) 0 0
\(163\) 2.48980e12 1.69486 0.847428 0.530910i \(-0.178150\pi\)
0.847428 + 0.530910i \(0.178150\pi\)
\(164\) 0 0
\(165\) −3.20093e11 −0.203758
\(166\) 0 0
\(167\) 2.71461e12 1.61721 0.808606 0.588351i \(-0.200223\pi\)
0.808606 + 0.588351i \(0.200223\pi\)
\(168\) 0 0
\(169\) 2.08625e12 1.16410
\(170\) 0 0
\(171\) −2.31221e11 −0.120934
\(172\) 0 0
\(173\) −2.77436e12 −1.36116 −0.680579 0.732675i \(-0.738272\pi\)
−0.680579 + 0.732675i \(0.738272\pi\)
\(174\) 0 0
\(175\) −4.52339e11 −0.208331
\(176\) 0 0
\(177\) −1.76160e12 −0.762175
\(178\) 0 0
\(179\) 7.59167e11 0.308778 0.154389 0.988010i \(-0.450659\pi\)
0.154389 + 0.988010i \(0.450659\pi\)
\(180\) 0 0
\(181\) 1.83029e12 0.700305 0.350152 0.936693i \(-0.386130\pi\)
0.350152 + 0.936693i \(0.386130\pi\)
\(182\) 0 0
\(183\) −3.68339e12 −1.32668
\(184\) 0 0
\(185\) −1.51399e11 −0.0513662
\(186\) 0 0
\(187\) 2.12970e12 0.681065
\(188\) 0 0
\(189\) −3.73849e12 −1.12760
\(190\) 0 0
\(191\) −7.81522e11 −0.222463 −0.111231 0.993795i \(-0.535479\pi\)
−0.111231 + 0.993795i \(0.535479\pi\)
\(192\) 0 0
\(193\) −4.70627e12 −1.26506 −0.632530 0.774535i \(-0.717984\pi\)
−0.632530 + 0.774535i \(0.717984\pi\)
\(194\) 0 0
\(195\) −1.98376e12 −0.503846
\(196\) 0 0
\(197\) −8.86812e10 −0.0212945 −0.0106472 0.999943i \(-0.503389\pi\)
−0.0106472 + 0.999943i \(0.503389\pi\)
\(198\) 0 0
\(199\) 2.87053e12 0.652035 0.326017 0.945364i \(-0.394293\pi\)
0.326017 + 0.945364i \(0.394293\pi\)
\(200\) 0 0
\(201\) 1.90565e12 0.409699
\(202\) 0 0
\(203\) −7.71449e12 −1.57065
\(204\) 0 0
\(205\) −1.80109e12 −0.347448
\(206\) 0 0
\(207\) −1.84117e12 −0.336711
\(208\) 0 0
\(209\) 1.00314e12 0.174003
\(210\) 0 0
\(211\) 1.09016e13 1.79447 0.897237 0.441549i \(-0.145571\pi\)
0.897237 + 0.441549i \(0.145571\pi\)
\(212\) 0 0
\(213\) 5.75157e12 0.898873
\(214\) 0 0
\(215\) 5.97860e11 0.0887540
\(216\) 0 0
\(217\) 1.04390e13 1.47275
\(218\) 0 0
\(219\) −7.00129e12 −0.939152
\(220\) 0 0
\(221\) 1.31986e13 1.68411
\(222\) 0 0
\(223\) 1.61507e12 0.196117 0.0980584 0.995181i \(-0.468737\pi\)
0.0980584 + 0.995181i \(0.468737\pi\)
\(224\) 0 0
\(225\) −7.15286e11 −0.0826944
\(226\) 0 0
\(227\) −1.51870e13 −1.67236 −0.836182 0.548452i \(-0.815217\pi\)
−0.836182 + 0.548452i \(0.815217\pi\)
\(228\) 0 0
\(229\) 6.90526e12 0.724578 0.362289 0.932066i \(-0.381995\pi\)
0.362289 + 0.932066i \(0.381995\pi\)
\(230\) 0 0
\(231\) 4.74450e12 0.474597
\(232\) 0 0
\(233\) −1.31428e13 −1.25380 −0.626902 0.779098i \(-0.715678\pi\)
−0.626902 + 0.779098i \(0.715678\pi\)
\(234\) 0 0
\(235\) 1.71704e12 0.156282
\(236\) 0 0
\(237\) 1.45431e13 1.26340
\(238\) 0 0
\(239\) 6.94431e12 0.576024 0.288012 0.957627i \(-0.407006\pi\)
0.288012 + 0.957627i \(0.407006\pi\)
\(240\) 0 0
\(241\) −6.76486e12 −0.536001 −0.268000 0.963419i \(-0.586363\pi\)
−0.268000 + 0.963419i \(0.586363\pi\)
\(242\) 0 0
\(243\) −1.00941e13 −0.764245
\(244\) 0 0
\(245\) 5.25529e11 0.0380350
\(246\) 0 0
\(247\) 6.21689e12 0.430269
\(248\) 0 0
\(249\) −4.73184e11 −0.0313281
\(250\) 0 0
\(251\) −1.68717e13 −1.06894 −0.534471 0.845187i \(-0.679489\pi\)
−0.534471 + 0.845187i \(0.679489\pi\)
\(252\) 0 0
\(253\) 7.98783e12 0.484469
\(254\) 0 0
\(255\) −6.75093e12 −0.392096
\(256\) 0 0
\(257\) −8.55471e12 −0.475963 −0.237982 0.971270i \(-0.576486\pi\)
−0.237982 + 0.971270i \(0.576486\pi\)
\(258\) 0 0
\(259\) 2.24407e12 0.119643
\(260\) 0 0
\(261\) −1.21990e13 −0.623448
\(262\) 0 0
\(263\) 1.13408e13 0.555760 0.277880 0.960616i \(-0.410368\pi\)
0.277880 + 0.960616i \(0.410368\pi\)
\(264\) 0 0
\(265\) 3.65431e12 0.171772
\(266\) 0 0
\(267\) −2.40139e13 −1.08305
\(268\) 0 0
\(269\) −4.07033e13 −1.76194 −0.880972 0.473169i \(-0.843110\pi\)
−0.880972 + 0.473169i \(0.843110\pi\)
\(270\) 0 0
\(271\) −2.46051e13 −1.02257 −0.511286 0.859410i \(-0.670831\pi\)
−0.511286 + 0.859410i \(0.670831\pi\)
\(272\) 0 0
\(273\) 2.94037e13 1.17357
\(274\) 0 0
\(275\) 3.10324e12 0.118983
\(276\) 0 0
\(277\) 1.40213e12 0.0516594 0.0258297 0.999666i \(-0.491777\pi\)
0.0258297 + 0.999666i \(0.491777\pi\)
\(278\) 0 0
\(279\) 1.65072e13 0.584589
\(280\) 0 0
\(281\) −3.18398e12 −0.108414 −0.0542071 0.998530i \(-0.517263\pi\)
−0.0542071 + 0.998530i \(0.517263\pi\)
\(282\) 0 0
\(283\) −1.72628e12 −0.0565310 −0.0282655 0.999600i \(-0.508998\pi\)
−0.0282655 + 0.999600i \(0.508998\pi\)
\(284\) 0 0
\(285\) −3.17986e12 −0.100175
\(286\) 0 0
\(287\) 2.66962e13 0.809280
\(288\) 0 0
\(289\) 1.06444e13 0.310588
\(290\) 0 0
\(291\) −2.61783e13 −0.735411
\(292\) 0 0
\(293\) 5.26240e13 1.42368 0.711839 0.702343i \(-0.247862\pi\)
0.711839 + 0.702343i \(0.247862\pi\)
\(294\) 0 0
\(295\) 1.70784e13 0.445067
\(296\) 0 0
\(297\) 2.56477e13 0.644002
\(298\) 0 0
\(299\) 4.95040e13 1.19798
\(300\) 0 0
\(301\) −8.86163e12 −0.206727
\(302\) 0 0
\(303\) 6.17677e13 1.38940
\(304\) 0 0
\(305\) 3.57098e13 0.774707
\(306\) 0 0
\(307\) −6.51872e13 −1.36427 −0.682137 0.731225i \(-0.738949\pi\)
−0.682137 + 0.731225i \(0.738949\pi\)
\(308\) 0 0
\(309\) −7.26210e13 −1.46653
\(310\) 0 0
\(311\) 3.08407e13 0.601093 0.300546 0.953767i \(-0.402831\pi\)
0.300546 + 0.953767i \(0.402831\pi\)
\(312\) 0 0
\(313\) −2.32028e13 −0.436563 −0.218282 0.975886i \(-0.570045\pi\)
−0.218282 + 0.975886i \(0.570045\pi\)
\(314\) 0 0
\(315\) 1.06021e13 0.192613
\(316\) 0 0
\(317\) −6.76914e13 −1.18770 −0.593851 0.804575i \(-0.702393\pi\)
−0.593851 + 0.804575i \(0.702393\pi\)
\(318\) 0 0
\(319\) 5.29247e13 0.897036
\(320\) 0 0
\(321\) −6.56540e12 −0.107519
\(322\) 0 0
\(323\) 2.11567e13 0.334838
\(324\) 0 0
\(325\) 1.92321e13 0.294217
\(326\) 0 0
\(327\) −3.03029e13 −0.448199
\(328\) 0 0
\(329\) −2.54504e13 −0.364013
\(330\) 0 0
\(331\) −6.49600e13 −0.898653 −0.449326 0.893368i \(-0.648336\pi\)
−0.449326 + 0.893368i \(0.648336\pi\)
\(332\) 0 0
\(333\) 3.54856e12 0.0474907
\(334\) 0 0
\(335\) −1.84749e13 −0.239241
\(336\) 0 0
\(337\) 3.15511e10 0.000395412 0 0.000197706 1.00000i \(-0.499937\pi\)
0.000197706 1.00000i \(0.499937\pi\)
\(338\) 0 0
\(339\) −1.00632e14 −1.22078
\(340\) 0 0
\(341\) −7.16159e13 −0.841125
\(342\) 0 0
\(343\) 8.37993e13 0.953065
\(344\) 0 0
\(345\) −2.53207e13 −0.278914
\(346\) 0 0
\(347\) 2.99274e13 0.319342 0.159671 0.987170i \(-0.448957\pi\)
0.159671 + 0.987170i \(0.448957\pi\)
\(348\) 0 0
\(349\) −1.00661e14 −1.04070 −0.520348 0.853955i \(-0.674198\pi\)
−0.520348 + 0.853955i \(0.674198\pi\)
\(350\) 0 0
\(351\) 1.58950e14 1.59247
\(352\) 0 0
\(353\) −1.54028e14 −1.49568 −0.747840 0.663879i \(-0.768909\pi\)
−0.747840 + 0.663879i \(0.768909\pi\)
\(354\) 0 0
\(355\) −5.57603e13 −0.524891
\(356\) 0 0
\(357\) 1.00064e14 0.913276
\(358\) 0 0
\(359\) 1.71452e14 1.51748 0.758740 0.651393i \(-0.225815\pi\)
0.758740 + 0.651393i \(0.225815\pi\)
\(360\) 0 0
\(361\) −1.06525e14 −0.914453
\(362\) 0 0
\(363\) 5.94174e13 0.494797
\(364\) 0 0
\(365\) 6.78761e13 0.548411
\(366\) 0 0
\(367\) −1.71254e14 −1.34270 −0.671348 0.741142i \(-0.734284\pi\)
−0.671348 + 0.741142i \(0.734284\pi\)
\(368\) 0 0
\(369\) 4.22149e13 0.321233
\(370\) 0 0
\(371\) −5.41651e13 −0.400095
\(372\) 0 0
\(373\) −2.06032e14 −1.47753 −0.738764 0.673964i \(-0.764590\pi\)
−0.738764 + 0.673964i \(0.764590\pi\)
\(374\) 0 0
\(375\) −9.83697e12 −0.0684998
\(376\) 0 0
\(377\) 3.27997e14 2.21816
\(378\) 0 0
\(379\) 2.97286e13 0.195281 0.0976403 0.995222i \(-0.468871\pi\)
0.0976403 + 0.995222i \(0.468871\pi\)
\(380\) 0 0
\(381\) 1.64487e14 1.04965
\(382\) 0 0
\(383\) −6.83277e12 −0.0423647 −0.0211823 0.999776i \(-0.506743\pi\)
−0.0211823 + 0.999776i \(0.506743\pi\)
\(384\) 0 0
\(385\) −4.59970e13 −0.277137
\(386\) 0 0
\(387\) −1.40129e13 −0.0820577
\(388\) 0 0
\(389\) 2.76218e14 1.57228 0.786139 0.618050i \(-0.212077\pi\)
0.786139 + 0.618050i \(0.212077\pi\)
\(390\) 0 0
\(391\) 1.68467e14 0.932274
\(392\) 0 0
\(393\) 2.03590e14 1.09546
\(394\) 0 0
\(395\) −1.40993e14 −0.737757
\(396\) 0 0
\(397\) 2.37045e14 1.20638 0.603188 0.797599i \(-0.293897\pi\)
0.603188 + 0.797599i \(0.293897\pi\)
\(398\) 0 0
\(399\) 4.71326e13 0.233330
\(400\) 0 0
\(401\) 3.12727e13 0.150616 0.0753080 0.997160i \(-0.476006\pi\)
0.0753080 + 0.997160i \(0.476006\pi\)
\(402\) 0 0
\(403\) −4.43835e14 −2.07990
\(404\) 0 0
\(405\) −4.07531e13 −0.185848
\(406\) 0 0
\(407\) −1.53953e13 −0.0683311
\(408\) 0 0
\(409\) −2.62457e14 −1.13391 −0.566956 0.823748i \(-0.691879\pi\)
−0.566956 + 0.823748i \(0.691879\pi\)
\(410\) 0 0
\(411\) 1.23261e14 0.518437
\(412\) 0 0
\(413\) −2.53140e14 −1.03666
\(414\) 0 0
\(415\) 4.58743e12 0.0182938
\(416\) 0 0
\(417\) −3.14047e13 −0.121968
\(418\) 0 0
\(419\) −3.02479e14 −1.14424 −0.572121 0.820169i \(-0.693879\pi\)
−0.572121 + 0.820169i \(0.693879\pi\)
\(420\) 0 0
\(421\) 3.11314e14 1.14722 0.573611 0.819128i \(-0.305542\pi\)
0.573611 + 0.819128i \(0.305542\pi\)
\(422\) 0 0
\(423\) −4.02449e13 −0.144490
\(424\) 0 0
\(425\) 6.54489e13 0.228962
\(426\) 0 0
\(427\) −5.29298e14 −1.80446
\(428\) 0 0
\(429\) −2.01722e14 −0.670252
\(430\) 0 0
\(431\) 1.49970e14 0.485713 0.242856 0.970062i \(-0.421916\pi\)
0.242856 + 0.970062i \(0.421916\pi\)
\(432\) 0 0
\(433\) −2.41783e14 −0.763384 −0.381692 0.924290i \(-0.624658\pi\)
−0.381692 + 0.924290i \(0.624658\pi\)
\(434\) 0 0
\(435\) −1.67766e14 −0.516433
\(436\) 0 0
\(437\) 7.93524e13 0.238184
\(438\) 0 0
\(439\) 2.52346e14 0.738654 0.369327 0.929300i \(-0.379588\pi\)
0.369327 + 0.929300i \(0.379588\pi\)
\(440\) 0 0
\(441\) −1.23176e13 −0.0351653
\(442\) 0 0
\(443\) 1.56538e14 0.435912 0.217956 0.975959i \(-0.430061\pi\)
0.217956 + 0.975959i \(0.430061\pi\)
\(444\) 0 0
\(445\) 2.32810e14 0.632442
\(446\) 0 0
\(447\) 6.02280e13 0.159627
\(448\) 0 0
\(449\) −1.02669e14 −0.265512 −0.132756 0.991149i \(-0.542383\pi\)
−0.132756 + 0.991149i \(0.542383\pi\)
\(450\) 0 0
\(451\) −1.83147e14 −0.462200
\(452\) 0 0
\(453\) −5.46024e14 −1.34484
\(454\) 0 0
\(455\) −2.85063e14 −0.685296
\(456\) 0 0
\(457\) 4.13279e14 0.969850 0.484925 0.874556i \(-0.338847\pi\)
0.484925 + 0.874556i \(0.338847\pi\)
\(458\) 0 0
\(459\) 5.40922e14 1.23927
\(460\) 0 0
\(461\) 2.12155e14 0.474567 0.237284 0.971440i \(-0.423743\pi\)
0.237284 + 0.971440i \(0.423743\pi\)
\(462\) 0 0
\(463\) 3.77488e14 0.824533 0.412267 0.911063i \(-0.364737\pi\)
0.412267 + 0.911063i \(0.364737\pi\)
\(464\) 0 0
\(465\) 2.27016e14 0.484244
\(466\) 0 0
\(467\) −3.60800e14 −0.751664 −0.375832 0.926688i \(-0.622643\pi\)
−0.375832 + 0.926688i \(0.622643\pi\)
\(468\) 0 0
\(469\) 2.73839e14 0.557243
\(470\) 0 0
\(471\) −1.50738e14 −0.299646
\(472\) 0 0
\(473\) 6.07946e13 0.118067
\(474\) 0 0
\(475\) 3.08281e13 0.0584967
\(476\) 0 0
\(477\) −8.56516e13 −0.158812
\(478\) 0 0
\(479\) −2.58776e13 −0.0468899 −0.0234449 0.999725i \(-0.507463\pi\)
−0.0234449 + 0.999725i \(0.507463\pi\)
\(480\) 0 0
\(481\) −9.54111e13 −0.168967
\(482\) 0 0
\(483\) 3.75309e14 0.649650
\(484\) 0 0
\(485\) 2.53793e14 0.429438
\(486\) 0 0
\(487\) 3.54633e14 0.586637 0.293318 0.956015i \(-0.405240\pi\)
0.293318 + 0.956015i \(0.405240\pi\)
\(488\) 0 0
\(489\) −8.02557e14 −1.29801
\(490\) 0 0
\(491\) 1.72416e14 0.272664 0.136332 0.990663i \(-0.456469\pi\)
0.136332 + 0.990663i \(0.456469\pi\)
\(492\) 0 0
\(493\) 1.11621e15 1.72619
\(494\) 0 0
\(495\) −7.27353e13 −0.110006
\(496\) 0 0
\(497\) 8.26492e14 1.22258
\(498\) 0 0
\(499\) 7.01194e14 1.01458 0.507289 0.861776i \(-0.330648\pi\)
0.507289 + 0.861776i \(0.330648\pi\)
\(500\) 0 0
\(501\) −8.75021e14 −1.23854
\(502\) 0 0
\(503\) 7.18922e14 0.995538 0.497769 0.867310i \(-0.334153\pi\)
0.497769 + 0.867310i \(0.334153\pi\)
\(504\) 0 0
\(505\) −5.98825e14 −0.811330
\(506\) 0 0
\(507\) −6.72478e14 −0.891526
\(508\) 0 0
\(509\) −1.13548e15 −1.47309 −0.736547 0.676386i \(-0.763545\pi\)
−0.736547 + 0.676386i \(0.763545\pi\)
\(510\) 0 0
\(511\) −1.00608e15 −1.27737
\(512\) 0 0
\(513\) 2.54788e14 0.316616
\(514\) 0 0
\(515\) 7.04045e14 0.856369
\(516\) 0 0
\(517\) 1.74601e14 0.207897
\(518\) 0 0
\(519\) 8.94280e14 1.04244
\(520\) 0 0
\(521\) −1.52530e15 −1.74079 −0.870396 0.492352i \(-0.836137\pi\)
−0.870396 + 0.492352i \(0.836137\pi\)
\(522\) 0 0
\(523\) 3.67077e14 0.410202 0.205101 0.978741i \(-0.434248\pi\)
0.205101 + 0.978741i \(0.434248\pi\)
\(524\) 0 0
\(525\) 1.45806e14 0.159551
\(526\) 0 0
\(527\) −1.51042e15 −1.61859
\(528\) 0 0
\(529\) −3.20940e14 −0.336835
\(530\) 0 0
\(531\) −4.00292e14 −0.411488
\(532\) 0 0
\(533\) −1.13504e15 −1.14291
\(534\) 0 0
\(535\) 6.36502e13 0.0627847
\(536\) 0 0
\(537\) −2.44708e14 −0.236478
\(538\) 0 0
\(539\) 5.34394e13 0.0505969
\(540\) 0 0
\(541\) 5.85922e14 0.543569 0.271785 0.962358i \(-0.412386\pi\)
0.271785 + 0.962358i \(0.412386\pi\)
\(542\) 0 0
\(543\) −5.89971e14 −0.536329
\(544\) 0 0
\(545\) 2.93780e14 0.261723
\(546\) 0 0
\(547\) −6.35737e14 −0.555069 −0.277535 0.960716i \(-0.589517\pi\)
−0.277535 + 0.960716i \(0.589517\pi\)
\(548\) 0 0
\(549\) −8.36983e14 −0.716257
\(550\) 0 0
\(551\) 5.25763e14 0.441018
\(552\) 0 0
\(553\) 2.08983e15 1.71839
\(554\) 0 0
\(555\) 4.88015e13 0.0393389
\(556\) 0 0
\(557\) −1.06572e15 −0.842246 −0.421123 0.907004i \(-0.638364\pi\)
−0.421123 + 0.907004i \(0.638364\pi\)
\(558\) 0 0
\(559\) 3.76770e14 0.291952
\(560\) 0 0
\(561\) −6.86481e14 −0.521594
\(562\) 0 0
\(563\) 1.14286e15 0.851522 0.425761 0.904836i \(-0.360006\pi\)
0.425761 + 0.904836i \(0.360006\pi\)
\(564\) 0 0
\(565\) 9.75603e14 0.712864
\(566\) 0 0
\(567\) 6.04052e14 0.432880
\(568\) 0 0
\(569\) −4.03257e14 −0.283442 −0.141721 0.989907i \(-0.545264\pi\)
−0.141721 + 0.989907i \(0.545264\pi\)
\(570\) 0 0
\(571\) 1.35092e15 0.931386 0.465693 0.884946i \(-0.345805\pi\)
0.465693 + 0.884946i \(0.345805\pi\)
\(572\) 0 0
\(573\) 2.51914e14 0.170373
\(574\) 0 0
\(575\) 2.45479e14 0.162870
\(576\) 0 0
\(577\) 1.33874e15 0.871421 0.435711 0.900087i \(-0.356497\pi\)
0.435711 + 0.900087i \(0.356497\pi\)
\(578\) 0 0
\(579\) 1.51701e15 0.968848
\(580\) 0 0
\(581\) −6.79959e13 −0.0426103
\(582\) 0 0
\(583\) 3.71596e14 0.228504
\(584\) 0 0
\(585\) −4.50772e14 −0.272019
\(586\) 0 0
\(587\) 1.41689e15 0.839123 0.419562 0.907727i \(-0.362184\pi\)
0.419562 + 0.907727i \(0.362184\pi\)
\(588\) 0 0
\(589\) −7.11444e14 −0.413530
\(590\) 0 0
\(591\) 2.85853e13 0.0163084
\(592\) 0 0
\(593\) −9.36699e14 −0.524565 −0.262282 0.964991i \(-0.584475\pi\)
−0.262282 + 0.964991i \(0.584475\pi\)
\(594\) 0 0
\(595\) −9.70099e14 −0.533301
\(596\) 0 0
\(597\) −9.25281e14 −0.499361
\(598\) 0 0
\(599\) −2.38262e15 −1.26243 −0.631214 0.775609i \(-0.717443\pi\)
−0.631214 + 0.775609i \(0.717443\pi\)
\(600\) 0 0
\(601\) 1.79176e15 0.932114 0.466057 0.884755i \(-0.345674\pi\)
0.466057 + 0.884755i \(0.345674\pi\)
\(602\) 0 0
\(603\) 4.33023e14 0.221190
\(604\) 0 0
\(605\) −5.76040e14 −0.288934
\(606\) 0 0
\(607\) −2.96072e15 −1.45834 −0.729170 0.684332i \(-0.760094\pi\)
−0.729170 + 0.684332i \(0.760094\pi\)
\(608\) 0 0
\(609\) 2.48667e15 1.20288
\(610\) 0 0
\(611\) 1.08208e15 0.514081
\(612\) 0 0
\(613\) −3.04029e14 −0.141867 −0.0709336 0.997481i \(-0.522598\pi\)
−0.0709336 + 0.997481i \(0.522598\pi\)
\(614\) 0 0
\(615\) 5.80560e14 0.266093
\(616\) 0 0
\(617\) 3.93397e15 1.77118 0.885591 0.464467i \(-0.153754\pi\)
0.885591 + 0.464467i \(0.153754\pi\)
\(618\) 0 0
\(619\) 4.65120e14 0.205715 0.102858 0.994696i \(-0.467201\pi\)
0.102858 + 0.994696i \(0.467201\pi\)
\(620\) 0 0
\(621\) 2.02883e15 0.881540
\(622\) 0 0
\(623\) −3.45076e15 −1.47309
\(624\) 0 0
\(625\) 9.53674e13 0.0400000
\(626\) 0 0
\(627\) −3.23350e14 −0.133261
\(628\) 0 0
\(629\) −3.24694e14 −0.131491
\(630\) 0 0
\(631\) −3.11552e15 −1.23985 −0.619925 0.784661i \(-0.712837\pi\)
−0.619925 + 0.784661i \(0.712837\pi\)
\(632\) 0 0
\(633\) −3.51400e15 −1.37430
\(634\) 0 0
\(635\) −1.59467e15 −0.612935
\(636\) 0 0
\(637\) 3.31187e14 0.125114
\(638\) 0 0
\(639\) 1.30694e15 0.485289
\(640\) 0 0
\(641\) −2.68239e15 −0.979047 −0.489523 0.871990i \(-0.662829\pi\)
−0.489523 + 0.871990i \(0.662829\pi\)
\(642\) 0 0
\(643\) −3.24755e15 −1.16519 −0.582594 0.812763i \(-0.697962\pi\)
−0.582594 + 0.812763i \(0.697962\pi\)
\(644\) 0 0
\(645\) −1.92713e14 −0.0679724
\(646\) 0 0
\(647\) 2.20147e15 0.763376 0.381688 0.924291i \(-0.375343\pi\)
0.381688 + 0.924291i \(0.375343\pi\)
\(648\) 0 0
\(649\) 1.73665e15 0.592061
\(650\) 0 0
\(651\) −3.36488e15 −1.12791
\(652\) 0 0
\(653\) 1.76341e15 0.581208 0.290604 0.956843i \(-0.406144\pi\)
0.290604 + 0.956843i \(0.406144\pi\)
\(654\) 0 0
\(655\) −1.97376e15 −0.639688
\(656\) 0 0
\(657\) −1.59091e15 −0.507034
\(658\) 0 0
\(659\) −2.25728e15 −0.707483 −0.353741 0.935343i \(-0.615091\pi\)
−0.353741 + 0.935343i \(0.615091\pi\)
\(660\) 0 0
\(661\) 5.06357e15 1.56081 0.780403 0.625277i \(-0.215014\pi\)
0.780403 + 0.625277i \(0.215014\pi\)
\(662\) 0 0
\(663\) −4.25442e15 −1.28978
\(664\) 0 0
\(665\) −4.56941e14 −0.136252
\(666\) 0 0
\(667\) 4.18656e15 1.22791
\(668\) 0 0
\(669\) −5.20598e14 −0.150196
\(670\) 0 0
\(671\) 3.63122e15 1.03057
\(672\) 0 0
\(673\) −2.34714e15 −0.655323 −0.327662 0.944795i \(-0.606261\pi\)
−0.327662 + 0.944795i \(0.606261\pi\)
\(674\) 0 0
\(675\) 7.88193e14 0.216502
\(676\) 0 0
\(677\) 1.22198e15 0.330237 0.165118 0.986274i \(-0.447199\pi\)
0.165118 + 0.986274i \(0.447199\pi\)
\(678\) 0 0
\(679\) −3.76178e15 −1.00025
\(680\) 0 0
\(681\) 4.89536e15 1.28078
\(682\) 0 0
\(683\) 5.01192e15 1.29030 0.645149 0.764057i \(-0.276795\pi\)
0.645149 + 0.764057i \(0.276795\pi\)
\(684\) 0 0
\(685\) −1.19499e15 −0.302738
\(686\) 0 0
\(687\) −2.22583e15 −0.554919
\(688\) 0 0
\(689\) 2.30294e15 0.565037
\(690\) 0 0
\(691\) 4.25993e15 1.02866 0.514332 0.857591i \(-0.328040\pi\)
0.514332 + 0.857591i \(0.328040\pi\)
\(692\) 0 0
\(693\) 1.07810e15 0.256228
\(694\) 0 0
\(695\) 3.04462e14 0.0712225
\(696\) 0 0
\(697\) −3.86267e15 −0.889421
\(698\) 0 0
\(699\) 4.23642e15 0.960228
\(700\) 0 0
\(701\) 3.06037e15 0.682849 0.341425 0.939909i \(-0.389091\pi\)
0.341425 + 0.939909i \(0.389091\pi\)
\(702\) 0 0
\(703\) −1.52939e14 −0.0335942
\(704\) 0 0
\(705\) −5.53468e14 −0.119688
\(706\) 0 0
\(707\) 8.87594e15 1.88976
\(708\) 0 0
\(709\) 3.38201e15 0.708959 0.354479 0.935064i \(-0.384658\pi\)
0.354479 + 0.935064i \(0.384658\pi\)
\(710\) 0 0
\(711\) 3.30466e15 0.682094
\(712\) 0 0
\(713\) −5.66511e15 −1.15137
\(714\) 0 0
\(715\) 1.95565e15 0.391389
\(716\) 0 0
\(717\) −2.23841e15 −0.441149
\(718\) 0 0
\(719\) −5.50086e15 −1.06763 −0.533816 0.845601i \(-0.679243\pi\)
−0.533816 + 0.845601i \(0.679243\pi\)
\(720\) 0 0
\(721\) −1.04355e16 −1.99467
\(722\) 0 0
\(723\) 2.18057e15 0.410497
\(724\) 0 0
\(725\) 1.62646e15 0.301567
\(726\) 0 0
\(727\) −5.91333e15 −1.07992 −0.539961 0.841690i \(-0.681561\pi\)
−0.539961 + 0.841690i \(0.681561\pi\)
\(728\) 0 0
\(729\) 5.56388e15 1.00087
\(730\) 0 0
\(731\) 1.28219e15 0.227199
\(732\) 0 0
\(733\) 6.66898e14 0.116409 0.0582046 0.998305i \(-0.481462\pi\)
0.0582046 + 0.998305i \(0.481462\pi\)
\(734\) 0 0
\(735\) −1.69398e14 −0.0291291
\(736\) 0 0
\(737\) −1.87865e15 −0.318255
\(738\) 0 0
\(739\) −7.79002e15 −1.30015 −0.650076 0.759869i \(-0.725263\pi\)
−0.650076 + 0.759869i \(0.725263\pi\)
\(740\) 0 0
\(741\) −2.00394e15 −0.329522
\(742\) 0 0
\(743\) 4.40631e14 0.0713898 0.0356949 0.999363i \(-0.488636\pi\)
0.0356949 + 0.999363i \(0.488636\pi\)
\(744\) 0 0
\(745\) −5.83898e14 −0.0932132
\(746\) 0 0
\(747\) −1.07522e14 −0.0169136
\(748\) 0 0
\(749\) −9.43439e14 −0.146239
\(750\) 0 0
\(751\) 2.68780e14 0.0410560 0.0205280 0.999789i \(-0.493465\pi\)
0.0205280 + 0.999789i \(0.493465\pi\)
\(752\) 0 0
\(753\) 5.43840e15 0.818651
\(754\) 0 0
\(755\) 5.29359e15 0.785312
\(756\) 0 0
\(757\) −1.09457e16 −1.60035 −0.800176 0.599766i \(-0.795261\pi\)
−0.800176 + 0.599766i \(0.795261\pi\)
\(758\) 0 0
\(759\) −2.57478e15 −0.371031
\(760\) 0 0
\(761\) −8.77462e15 −1.24627 −0.623136 0.782114i \(-0.714142\pi\)
−0.623136 + 0.782114i \(0.714142\pi\)
\(762\) 0 0
\(763\) −4.35448e15 −0.609609
\(764\) 0 0
\(765\) −1.53402e15 −0.211687
\(766\) 0 0
\(767\) 1.07628e16 1.46403
\(768\) 0 0
\(769\) 3.16898e15 0.424936 0.212468 0.977168i \(-0.431850\pi\)
0.212468 + 0.977168i \(0.431850\pi\)
\(770\) 0 0
\(771\) 2.75751e15 0.364517
\(772\) 0 0
\(773\) −6.13394e15 −0.799378 −0.399689 0.916651i \(-0.630882\pi\)
−0.399689 + 0.916651i \(0.630882\pi\)
\(774\) 0 0
\(775\) −2.20087e15 −0.282771
\(776\) 0 0
\(777\) −7.23348e14 −0.0916287
\(778\) 0 0
\(779\) −1.81942e15 −0.227235
\(780\) 0 0
\(781\) −5.67009e15 −0.698248
\(782\) 0 0
\(783\) 1.34424e16 1.63225
\(784\) 0 0
\(785\) 1.46138e15 0.174976
\(786\) 0 0
\(787\) −1.04791e16 −1.23727 −0.618633 0.785680i \(-0.712313\pi\)
−0.618633 + 0.785680i \(0.712313\pi\)
\(788\) 0 0
\(789\) −3.65557e15 −0.425629
\(790\) 0 0
\(791\) −1.44606e16 −1.66041
\(792\) 0 0
\(793\) 2.25042e16 2.54836
\(794\) 0 0
\(795\) −1.17792e15 −0.131552
\(796\) 0 0
\(797\) 1.44584e15 0.159257 0.0796286 0.996825i \(-0.474627\pi\)
0.0796286 + 0.996825i \(0.474627\pi\)
\(798\) 0 0
\(799\) 3.68242e15 0.400061
\(800\) 0 0
\(801\) −5.45671e15 −0.584725
\(802\) 0 0
\(803\) 6.90212e15 0.729536
\(804\) 0 0
\(805\) −3.63854e15 −0.379359
\(806\) 0 0
\(807\) 1.31202e16 1.34939
\(808\) 0 0
\(809\) −7.03288e15 −0.713537 −0.356768 0.934193i \(-0.616121\pi\)
−0.356768 + 0.934193i \(0.616121\pi\)
\(810\) 0 0
\(811\) −1.18983e16 −1.19088 −0.595441 0.803399i \(-0.703023\pi\)
−0.595441 + 0.803399i \(0.703023\pi\)
\(812\) 0 0
\(813\) 7.93116e15 0.783138
\(814\) 0 0
\(815\) 7.78063e15 0.757963
\(816\) 0 0
\(817\) 6.03943e14 0.0580463
\(818\) 0 0
\(819\) 6.68145e15 0.633591
\(820\) 0 0
\(821\) 7.65247e15 0.716002 0.358001 0.933721i \(-0.383458\pi\)
0.358001 + 0.933721i \(0.383458\pi\)
\(822\) 0 0
\(823\) −7.71911e15 −0.712637 −0.356318 0.934365i \(-0.615968\pi\)
−0.356318 + 0.934365i \(0.615968\pi\)
\(824\) 0 0
\(825\) −1.00029e15 −0.0911234
\(826\) 0 0
\(827\) 9.37712e15 0.842926 0.421463 0.906846i \(-0.361517\pi\)
0.421463 + 0.906846i \(0.361517\pi\)
\(828\) 0 0
\(829\) 1.44345e16 1.28042 0.640209 0.768201i \(-0.278848\pi\)
0.640209 + 0.768201i \(0.278848\pi\)
\(830\) 0 0
\(831\) −4.51959e14 −0.0395634
\(832\) 0 0
\(833\) 1.12706e15 0.0973646
\(834\) 0 0
\(835\) 8.48316e15 0.723239
\(836\) 0 0
\(837\) −1.81897e16 −1.53051
\(838\) 0 0
\(839\) 5.83144e15 0.484268 0.242134 0.970243i \(-0.422153\pi\)
0.242134 + 0.970243i \(0.422153\pi\)
\(840\) 0 0
\(841\) 1.55382e16 1.27357
\(842\) 0 0
\(843\) 1.02632e15 0.0830292
\(844\) 0 0
\(845\) 6.51953e15 0.520601
\(846\) 0 0
\(847\) 8.53820e15 0.672989
\(848\) 0 0
\(849\) 5.56446e14 0.0432943
\(850\) 0 0
\(851\) −1.21783e15 −0.0935348
\(852\) 0 0
\(853\) 8.78821e15 0.666317 0.333158 0.942871i \(-0.391886\pi\)
0.333158 + 0.942871i \(0.391886\pi\)
\(854\) 0 0
\(855\) −7.22564e14 −0.0540832
\(856\) 0 0
\(857\) −1.69999e16 −1.25618 −0.628090 0.778141i \(-0.716163\pi\)
−0.628090 + 0.778141i \(0.716163\pi\)
\(858\) 0 0
\(859\) −8.82248e15 −0.643618 −0.321809 0.946805i \(-0.604291\pi\)
−0.321809 + 0.946805i \(0.604291\pi\)
\(860\) 0 0
\(861\) −8.60519e15 −0.619788
\(862\) 0 0
\(863\) −1.35285e16 −0.962035 −0.481017 0.876711i \(-0.659733\pi\)
−0.481017 + 0.876711i \(0.659733\pi\)
\(864\) 0 0
\(865\) −8.66986e15 −0.608728
\(866\) 0 0
\(867\) −3.43110e15 −0.237864
\(868\) 0 0
\(869\) −1.43371e16 −0.981417
\(870\) 0 0
\(871\) −1.16428e16 −0.786971
\(872\) 0 0
\(873\) −5.94853e15 −0.397038
\(874\) 0 0
\(875\) −1.41356e15 −0.0931686
\(876\) 0 0
\(877\) −6.09366e13 −0.00396625 −0.00198313 0.999998i \(-0.500631\pi\)
−0.00198313 + 0.999998i \(0.500631\pi\)
\(878\) 0 0
\(879\) −1.69627e16 −1.09033
\(880\) 0 0
\(881\) 1.47034e16 0.933362 0.466681 0.884426i \(-0.345450\pi\)
0.466681 + 0.884426i \(0.345450\pi\)
\(882\) 0 0
\(883\) −7.54689e15 −0.473134 −0.236567 0.971615i \(-0.576022\pi\)
−0.236567 + 0.971615i \(0.576022\pi\)
\(884\) 0 0
\(885\) −5.50501e15 −0.340855
\(886\) 0 0
\(887\) 1.09156e16 0.667525 0.333762 0.942657i \(-0.391682\pi\)
0.333762 + 0.942657i \(0.391682\pi\)
\(888\) 0 0
\(889\) 2.36365e16 1.42766
\(890\) 0 0
\(891\) −4.14406e15 −0.247229
\(892\) 0 0
\(893\) 1.73451e15 0.102210
\(894\) 0 0
\(895\) 2.37240e15 0.138090
\(896\) 0 0
\(897\) −1.59570e16 −0.917473
\(898\) 0 0
\(899\) −3.75351e16 −2.13186
\(900\) 0 0
\(901\) 7.83714e15 0.439715
\(902\) 0 0
\(903\) 2.85644e15 0.158322
\(904\) 0 0
\(905\) 5.71965e15 0.313186
\(906\) 0 0
\(907\) −2.62328e16 −1.41907 −0.709535 0.704670i \(-0.751095\pi\)
−0.709535 + 0.704670i \(0.751095\pi\)
\(908\) 0 0
\(909\) 1.40356e16 0.750117
\(910\) 0 0
\(911\) 2.73010e16 1.44154 0.720772 0.693173i \(-0.243788\pi\)
0.720772 + 0.693173i \(0.243788\pi\)
\(912\) 0 0
\(913\) 4.66481e14 0.0243358
\(914\) 0 0
\(915\) −1.15106e16 −0.593311
\(916\) 0 0
\(917\) 2.92556e16 1.48997
\(918\) 0 0
\(919\) 2.05271e16 1.03298 0.516490 0.856293i \(-0.327238\pi\)
0.516490 + 0.856293i \(0.327238\pi\)
\(920\) 0 0
\(921\) 2.10123e16 1.04483
\(922\) 0 0
\(923\) −3.51400e16 −1.72660
\(924\) 0 0
\(925\) −4.73121e14 −0.0229717
\(926\) 0 0
\(927\) −1.65018e16 −0.791757
\(928\) 0 0
\(929\) −2.80839e16 −1.33159 −0.665796 0.746134i \(-0.731908\pi\)
−0.665796 + 0.746134i \(0.731908\pi\)
\(930\) 0 0
\(931\) 5.30876e14 0.0248754
\(932\) 0 0
\(933\) −9.94111e15 −0.460348
\(934\) 0 0
\(935\) 6.65530e15 0.304582
\(936\) 0 0
\(937\) 3.72912e16 1.68670 0.843352 0.537362i \(-0.180579\pi\)
0.843352 + 0.537362i \(0.180579\pi\)
\(938\) 0 0
\(939\) 7.47915e15 0.334342
\(940\) 0 0
\(941\) −1.72223e16 −0.760937 −0.380469 0.924794i \(-0.624237\pi\)
−0.380469 + 0.924794i \(0.624237\pi\)
\(942\) 0 0
\(943\) −1.44877e16 −0.632681
\(944\) 0 0
\(945\) −1.16828e16 −0.504279
\(946\) 0 0
\(947\) 4.57432e16 1.95165 0.975824 0.218557i \(-0.0701349\pi\)
0.975824 + 0.218557i \(0.0701349\pi\)
\(948\) 0 0
\(949\) 4.27754e16 1.80397
\(950\) 0 0
\(951\) 2.18195e16 0.909603
\(952\) 0 0
\(953\) −4.13428e15 −0.170368 −0.0851841 0.996365i \(-0.527148\pi\)
−0.0851841 + 0.996365i \(0.527148\pi\)
\(954\) 0 0
\(955\) −2.44226e15 −0.0994884
\(956\) 0 0
\(957\) −1.70596e16 −0.686996
\(958\) 0 0
\(959\) 1.77125e16 0.705142
\(960\) 0 0
\(961\) 2.53827e16 0.998986
\(962\) 0 0
\(963\) −1.49187e15 −0.0580477
\(964\) 0 0
\(965\) −1.47071e16 −0.565752
\(966\) 0 0
\(967\) 2.48419e16 0.944799 0.472400 0.881385i \(-0.343388\pi\)
0.472400 + 0.881385i \(0.343388\pi\)
\(968\) 0 0
\(969\) −6.81962e15 −0.256436
\(970\) 0 0
\(971\) −3.83204e16 −1.42470 −0.712351 0.701824i \(-0.752369\pi\)
−0.712351 + 0.701824i \(0.752369\pi\)
\(972\) 0 0
\(973\) −4.51281e15 −0.165893
\(974\) 0 0
\(975\) −6.19924e15 −0.225327
\(976\) 0 0
\(977\) 4.89629e15 0.175973 0.0879866 0.996122i \(-0.471957\pi\)
0.0879866 + 0.996122i \(0.471957\pi\)
\(978\) 0 0
\(979\) 2.36737e16 0.841320
\(980\) 0 0
\(981\) −6.88577e15 −0.241976
\(982\) 0 0
\(983\) −4.17672e16 −1.45141 −0.725707 0.688004i \(-0.758487\pi\)
−0.725707 + 0.688004i \(0.758487\pi\)
\(984\) 0 0
\(985\) −2.77129e14 −0.00952319
\(986\) 0 0
\(987\) 8.20363e15 0.278780
\(988\) 0 0
\(989\) 4.80910e15 0.161616
\(990\) 0 0
\(991\) 5.64170e16 1.87502 0.937508 0.347963i \(-0.113127\pi\)
0.937508 + 0.347963i \(0.113127\pi\)
\(992\) 0 0
\(993\) 2.09391e16 0.688234
\(994\) 0 0
\(995\) 8.97041e15 0.291599
\(996\) 0 0
\(997\) −6.38236e15 −0.205191 −0.102595 0.994723i \(-0.532715\pi\)
−0.102595 + 0.994723i \(0.532715\pi\)
\(998\) 0 0
\(999\) −3.91025e15 −0.124335
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 \(a_p\))