Properties

Label 16.12.a.d.1.2
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 1.2
Root \(-4.72015\)
Character \(\chi\) = 16.1

$q$-expansion

\(f(q)\) \(=\) \(q+640.180 q^{3} +11952.2 q^{5} -17464.5 q^{7} +232683. q^{9} +O(q^{10})\) \(q+640.180 q^{3} +11952.2 q^{5} -17464.5 q^{7} +232683. q^{9} -542588. q^{11} -108196. q^{13} +7.65153e6 q^{15} +7.94782e6 q^{17} +7.86836e6 q^{19} -1.11804e7 q^{21} -3.44328e7 q^{23} +9.40259e7 q^{25} +3.55530e7 q^{27} -1.54208e8 q^{29} -5.14924e7 q^{31} -3.47354e8 q^{33} -2.08738e8 q^{35} +9.22788e7 q^{37} -6.92651e7 q^{39} +1.68236e8 q^{41} +2.39284e8 q^{43} +2.78106e9 q^{45} +6.90244e7 q^{47} -1.67232e9 q^{49} +5.08803e9 q^{51} -4.25291e9 q^{53} -6.48510e9 q^{55} +5.03716e9 q^{57} +5.88462e9 q^{59} +1.82883e9 q^{61} -4.06368e9 q^{63} -1.29318e9 q^{65} -2.15955e10 q^{67} -2.20432e10 q^{69} -1.55898e10 q^{71} +7.70566e9 q^{73} +6.01935e10 q^{75} +9.47601e9 q^{77} +1.66608e9 q^{79} -1.84588e10 q^{81} +4.50587e10 q^{83} +9.49936e10 q^{85} -9.87208e10 q^{87} -2.50490e10 q^{89} +1.88959e9 q^{91} -3.29644e10 q^{93} +9.40439e10 q^{95} +4.20468e10 q^{97} -1.26251e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 56q^{3} + 7868q^{5} - 91056q^{7} + 540202q^{9} + O(q^{10}) \) \( 2q - 56q^{3} + 7868q^{5} - 91056q^{7} + 540202q^{9} - 159080q^{11} + 1050476q^{13} + 10494832q^{15} + 1430884q^{17} + 21866600q^{19} + 40052544q^{21} - 35806736q^{23} + 61878094q^{25} - 55209392q^{27} - 228827700q^{29} - 64722112q^{31} - 614344864q^{33} + 91821408q^{35} + 75558780q^{37} - 875909072q^{39} + 1201214196q^{41} + 45519832q^{43} + 1525107052q^{45} + 1229079264q^{47} + 1766069074q^{49} + 9624987920q^{51} - 3808549924q^{53} - 8051409968q^{55} - 4708125536q^{57} + 6012926584q^{59} + 9789792908q^{61} - 26694483312q^{63} - 6025376344q^{65} - 14703095224q^{67} - 21086664256q^{69} - 4319991088q^{71} + 11055639476q^{73} + 82574103416q^{75} - 18746968128q^{77} - 51957623264q^{79} - 9747960302q^{81} + 108227975912q^{83} + 121609729720q^{85} - 46772044368q^{87} + 71188291860q^{89} - 83378892576q^{91} - 23754095360q^{93} + 36872875568q^{95} - 1699807676q^{97} - 8314917256q^{99} + O(q^{100}) \)

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
\(3\) 640.180 1.52102 0.760510 0.649326i \(-0.224949\pi\)
0.760510 + 0.649326i \(0.224949\pi\)
\(4\) 0 0
\(5\) 11952.2 1.71045 0.855227 0.518254i \(-0.173418\pi\)
0.855227 + 0.518254i \(0.173418\pi\)
\(6\) 0 0
\(7\) −17464.5 −0.392750 −0.196375 0.980529i \(-0.562917\pi\)
−0.196375 + 0.980529i \(0.562917\pi\)
\(8\) 0 0
\(9\) 232683. 1.31350
\(10\) 0 0
\(11\) −542588. −1.01581 −0.507903 0.861414i \(-0.669579\pi\)
−0.507903 + 0.861414i \(0.669579\pi\)
\(12\) 0 0
\(13\) −108196. −0.0808209 −0.0404105 0.999183i \(-0.512867\pi\)
−0.0404105 + 0.999183i \(0.512867\pi\)
\(14\) 0 0
\(15\) 7.65153e6 2.60163
\(16\) 0 0
\(17\) 7.94782e6 1.35762 0.678811 0.734313i \(-0.262496\pi\)
0.678811 + 0.734313i \(0.262496\pi\)
\(18\) 0 0
\(19\) 7.86836e6 0.729020 0.364510 0.931199i \(-0.381237\pi\)
0.364510 + 0.931199i \(0.381237\pi\)
\(20\) 0 0
\(21\) −1.11804e7 −0.597380
\(22\) 0 0
\(23\) −3.44328e7 −1.11550 −0.557749 0.830009i \(-0.688335\pi\)
−0.557749 + 0.830009i \(0.688335\pi\)
\(24\) 0 0
\(25\) 9.40259e7 1.92565
\(26\) 0 0
\(27\) 3.55530e7 0.476843
\(28\) 0 0
\(29\) −1.54208e8 −1.39610 −0.698052 0.716047i \(-0.745950\pi\)
−0.698052 + 0.716047i \(0.745950\pi\)
\(30\) 0 0
\(31\) −5.14924e7 −0.323038 −0.161519 0.986870i \(-0.551639\pi\)
−0.161519 + 0.986870i \(0.551639\pi\)
\(32\) 0 0
\(33\) −3.47354e8 −1.54506
\(34\) 0 0
\(35\) −2.08738e8 −0.671780
\(36\) 0 0
\(37\) 9.22788e7 0.218772 0.109386 0.993999i \(-0.465111\pi\)
0.109386 + 0.993999i \(0.465111\pi\)
\(38\) 0 0
\(39\) −6.92651e7 −0.122930
\(40\) 0 0
\(41\) 1.68236e8 0.226782 0.113391 0.993550i \(-0.463829\pi\)
0.113391 + 0.993550i \(0.463829\pi\)
\(42\) 0 0
\(43\) 2.39284e8 0.248220 0.124110 0.992268i \(-0.460392\pi\)
0.124110 + 0.992268i \(0.460392\pi\)
\(44\) 0 0
\(45\) 2.78106e9 2.24668
\(46\) 0 0
\(47\) 6.90244e7 0.0439000 0.0219500 0.999759i \(-0.493013\pi\)
0.0219500 + 0.999759i \(0.493013\pi\)
\(48\) 0 0
\(49\) −1.67232e9 −0.845748
\(50\) 0 0
\(51\) 5.08803e9 2.06497
\(52\) 0 0
\(53\) −4.25291e9 −1.39691 −0.698456 0.715653i \(-0.746129\pi\)
−0.698456 + 0.715653i \(0.746129\pi\)
\(54\) 0 0
\(55\) −6.48510e9 −1.73749
\(56\) 0 0
\(57\) 5.03716e9 1.10885
\(58\) 0 0
\(59\) 5.88462e9 1.07160 0.535800 0.844345i \(-0.320010\pi\)
0.535800 + 0.844345i \(0.320010\pi\)
\(60\) 0 0
\(61\) 1.82883e9 0.277242 0.138621 0.990346i \(-0.455733\pi\)
0.138621 + 0.990346i \(0.455733\pi\)
\(62\) 0 0
\(63\) −4.06368e9 −0.515878
\(64\) 0 0
\(65\) −1.29318e9 −0.138240
\(66\) 0 0
\(67\) −2.15955e10 −1.95412 −0.977062 0.212953i \(-0.931692\pi\)
−0.977062 + 0.212953i \(0.931692\pi\)
\(68\) 0 0
\(69\) −2.20432e10 −1.69670
\(70\) 0 0
\(71\) −1.55898e10 −1.02546 −0.512732 0.858549i \(-0.671367\pi\)
−0.512732 + 0.858549i \(0.671367\pi\)
\(72\) 0 0
\(73\) 7.70566e9 0.435045 0.217523 0.976055i \(-0.430202\pi\)
0.217523 + 0.976055i \(0.430202\pi\)
\(74\) 0 0
\(75\) 6.01935e10 2.92895
\(76\) 0 0
\(77\) 9.47601e9 0.398958
\(78\) 0 0
\(79\) 1.66608e9 0.0609182 0.0304591 0.999536i \(-0.490303\pi\)
0.0304591 + 0.999536i \(0.490303\pi\)
\(80\) 0 0
\(81\) −1.84588e10 −0.588214
\(82\) 0 0
\(83\) 4.50587e10 1.25559 0.627796 0.778378i \(-0.283957\pi\)
0.627796 + 0.778378i \(0.283957\pi\)
\(84\) 0 0
\(85\) 9.49936e10 2.32215
\(86\) 0 0
\(87\) −9.87208e10 −2.12350
\(88\) 0 0
\(89\) −2.50490e10 −0.475495 −0.237748 0.971327i \(-0.576409\pi\)
−0.237748 + 0.971327i \(0.576409\pi\)
\(90\) 0 0
\(91\) 1.88959e9 0.0317424
\(92\) 0 0
\(93\) −3.29644e10 −0.491347
\(94\) 0 0
\(95\) 9.40439e10 1.24695
\(96\) 0 0
\(97\) 4.20468e10 0.497151 0.248576 0.968612i \(-0.420038\pi\)
0.248576 + 0.968612i \(0.420038\pi\)
\(98\) 0 0
\(99\) −1.26251e11 −1.33426
\(100\) 0 0
\(101\) −4.42685e10 −0.419109 −0.209554 0.977797i \(-0.567201\pi\)
−0.209554 + 0.977797i \(0.567201\pi\)
\(102\) 0 0
\(103\) 6.88268e9 0.0584996 0.0292498 0.999572i \(-0.490688\pi\)
0.0292498 + 0.999572i \(0.490688\pi\)
\(104\) 0 0
\(105\) −1.33630e11 −1.02179
\(106\) 0 0
\(107\) 1.12565e11 0.775878 0.387939 0.921685i \(-0.373187\pi\)
0.387939 + 0.921685i \(0.373187\pi\)
\(108\) 0 0
\(109\) −2.47188e11 −1.53880 −0.769399 0.638768i \(-0.779444\pi\)
−0.769399 + 0.638768i \(0.779444\pi\)
\(110\) 0 0
\(111\) 5.90750e10 0.332757
\(112\) 0 0
\(113\) 3.05173e11 1.55817 0.779084 0.626920i \(-0.215685\pi\)
0.779084 + 0.626920i \(0.215685\pi\)
\(114\) 0 0
\(115\) −4.11546e11 −1.90801
\(116\) 0 0
\(117\) −2.51754e10 −0.106158
\(118\) 0 0
\(119\) −1.38804e11 −0.533206
\(120\) 0 0
\(121\) 9.09058e9 0.0318619
\(122\) 0 0
\(123\) 1.07701e11 0.344939
\(124\) 0 0
\(125\) 5.40211e11 1.58328
\(126\) 0 0
\(127\) 6.59571e11 1.77150 0.885750 0.464163i \(-0.153645\pi\)
0.885750 + 0.464163i \(0.153645\pi\)
\(128\) 0 0
\(129\) 1.53185e11 0.377548
\(130\) 0 0
\(131\) 4.08450e11 0.925011 0.462505 0.886616i \(-0.346951\pi\)
0.462505 + 0.886616i \(0.346951\pi\)
\(132\) 0 0
\(133\) −1.37417e11 −0.286322
\(134\) 0 0
\(135\) 4.24935e11 0.815617
\(136\) 0 0
\(137\) −3.28605e11 −0.581717 −0.290858 0.956766i \(-0.593941\pi\)
−0.290858 + 0.956766i \(0.593941\pi\)
\(138\) 0 0
\(139\) −1.06744e12 −1.74487 −0.872435 0.488730i \(-0.837460\pi\)
−0.872435 + 0.488730i \(0.837460\pi\)
\(140\) 0 0
\(141\) 4.41880e10 0.0667728
\(142\) 0 0
\(143\) 5.87061e10 0.0820984
\(144\) 0 0
\(145\) −1.84312e12 −2.38797
\(146\) 0 0
\(147\) −1.07058e12 −1.28640
\(148\) 0 0
\(149\) 5.92629e11 0.661087 0.330543 0.943791i \(-0.392768\pi\)
0.330543 + 0.943791i \(0.392768\pi\)
\(150\) 0 0
\(151\) 1.16984e12 1.21270 0.606352 0.795196i \(-0.292632\pi\)
0.606352 + 0.795196i \(0.292632\pi\)
\(152\) 0 0
\(153\) 1.84932e12 1.78324
\(154\) 0 0
\(155\) −6.15445e11 −0.552541
\(156\) 0 0
\(157\) 3.68743e11 0.308514 0.154257 0.988031i \(-0.450702\pi\)
0.154257 + 0.988031i \(0.450702\pi\)
\(158\) 0 0
\(159\) −2.72263e12 −2.12473
\(160\) 0 0
\(161\) 6.01350e11 0.438112
\(162\) 0 0
\(163\) 1.91683e12 1.30483 0.652413 0.757864i \(-0.273757\pi\)
0.652413 + 0.757864i \(0.273757\pi\)
\(164\) 0 0
\(165\) −4.15163e12 −2.64276
\(166\) 0 0
\(167\) 2.84469e11 0.169471 0.0847354 0.996403i \(-0.472995\pi\)
0.0847354 + 0.996403i \(0.472995\pi\)
\(168\) 0 0
\(169\) −1.78045e12 −0.993468
\(170\) 0 0
\(171\) 1.83083e12 0.957569
\(172\) 0 0
\(173\) 2.16256e12 1.06100 0.530499 0.847686i \(-0.322005\pi\)
0.530499 + 0.847686i \(0.322005\pi\)
\(174\) 0 0
\(175\) −1.64211e12 −0.756299
\(176\) 0 0
\(177\) 3.76722e12 1.62992
\(178\) 0 0
\(179\) 4.61641e12 1.87764 0.938822 0.344404i \(-0.111919\pi\)
0.938822 + 0.344404i \(0.111919\pi\)
\(180\) 0 0
\(181\) −5.43222e10 −0.0207848 −0.0103924 0.999946i \(-0.503308\pi\)
−0.0103924 + 0.999946i \(0.503308\pi\)
\(182\) 0 0
\(183\) 1.17078e12 0.421690
\(184\) 0 0
\(185\) 1.10293e12 0.374200
\(186\) 0 0
\(187\) −4.31239e12 −1.37908
\(188\) 0 0
\(189\) −6.20913e11 −0.187280
\(190\) 0 0
\(191\) 2.32891e12 0.662933 0.331466 0.943467i \(-0.392457\pi\)
0.331466 + 0.943467i \(0.392457\pi\)
\(192\) 0 0
\(193\) 2.49475e12 0.670597 0.335299 0.942112i \(-0.391163\pi\)
0.335299 + 0.942112i \(0.391163\pi\)
\(194\) 0 0
\(195\) −8.27867e11 −0.210266
\(196\) 0 0
\(197\) 6.13716e12 1.47368 0.736839 0.676068i \(-0.236317\pi\)
0.736839 + 0.676068i \(0.236317\pi\)
\(198\) 0 0
\(199\) −7.12259e12 −1.61788 −0.808940 0.587892i \(-0.799958\pi\)
−0.808940 + 0.587892i \(0.799958\pi\)
\(200\) 0 0
\(201\) −1.38250e13 −2.97226
\(202\) 0 0
\(203\) 2.69316e12 0.548319
\(204\) 0 0
\(205\) 2.01078e12 0.387899
\(206\) 0 0
\(207\) −8.01192e12 −1.46521
\(208\) 0 0
\(209\) −4.26928e12 −0.740543
\(210\) 0 0
\(211\) 7.64441e12 1.25832 0.629159 0.777277i \(-0.283400\pi\)
0.629159 + 0.777277i \(0.283400\pi\)
\(212\) 0 0
\(213\) −9.98029e12 −1.55975
\(214\) 0 0
\(215\) 2.85996e12 0.424569
\(216\) 0 0
\(217\) 8.99286e11 0.126873
\(218\) 0 0
\(219\) 4.93301e12 0.661712
\(220\) 0 0
\(221\) −8.59924e11 −0.109724
\(222\) 0 0
\(223\) −2.56098e12 −0.310978 −0.155489 0.987838i \(-0.549695\pi\)
−0.155489 + 0.987838i \(0.549695\pi\)
\(224\) 0 0
\(225\) 2.18782e13 2.52935
\(226\) 0 0
\(227\) −1.15359e13 −1.27031 −0.635156 0.772384i \(-0.719064\pi\)
−0.635156 + 0.772384i \(0.719064\pi\)
\(228\) 0 0
\(229\) 8.77117e12 0.920370 0.460185 0.887823i \(-0.347783\pi\)
0.460185 + 0.887823i \(0.347783\pi\)
\(230\) 0 0
\(231\) 6.06635e12 0.606822
\(232\) 0 0
\(233\) −9.99552e12 −0.953560 −0.476780 0.879023i \(-0.658196\pi\)
−0.476780 + 0.879023i \(0.658196\pi\)
\(234\) 0 0
\(235\) 8.24991e11 0.0750889
\(236\) 0 0
\(237\) 1.06659e12 0.0926578
\(238\) 0 0
\(239\) 9.88633e12 0.820062 0.410031 0.912072i \(-0.365518\pi\)
0.410031 + 0.912072i \(0.365518\pi\)
\(240\) 0 0
\(241\) 1.46080e12 0.115744 0.0578718 0.998324i \(-0.481569\pi\)
0.0578718 + 0.998324i \(0.481569\pi\)
\(242\) 0 0
\(243\) −1.81150e13 −1.37153
\(244\) 0 0
\(245\) −1.99878e13 −1.44661
\(246\) 0 0
\(247\) −8.51327e11 −0.0589201
\(248\) 0 0
\(249\) 2.88456e13 1.90978
\(250\) 0 0
\(251\) 5.71128e12 0.361850 0.180925 0.983497i \(-0.442091\pi\)
0.180925 + 0.983497i \(0.442091\pi\)
\(252\) 0 0
\(253\) 1.86828e13 1.13313
\(254\) 0 0
\(255\) 6.08129e13 3.53204
\(256\) 0 0
\(257\) −3.00608e12 −0.167251 −0.0836254 0.996497i \(-0.526650\pi\)
−0.0836254 + 0.996497i \(0.526650\pi\)
\(258\) 0 0
\(259\) −1.61160e12 −0.0859228
\(260\) 0 0
\(261\) −3.58816e13 −1.83379
\(262\) 0 0
\(263\) −2.94339e13 −1.44242 −0.721210 0.692717i \(-0.756414\pi\)
−0.721210 + 0.692717i \(0.756414\pi\)
\(264\) 0 0
\(265\) −5.08315e13 −2.38935
\(266\) 0 0
\(267\) −1.60359e13 −0.723238
\(268\) 0 0
\(269\) 4.05862e13 1.75688 0.878438 0.477857i \(-0.158586\pi\)
0.878438 + 0.477857i \(0.158586\pi\)
\(270\) 0 0
\(271\) −2.32350e13 −0.965633 −0.482817 0.875721i \(-0.660386\pi\)
−0.482817 + 0.875721i \(0.660386\pi\)
\(272\) 0 0
\(273\) 1.20968e12 0.0482808
\(274\) 0 0
\(275\) −5.10174e13 −1.95609
\(276\) 0 0
\(277\) −1.78412e13 −0.657331 −0.328666 0.944446i \(-0.606599\pi\)
−0.328666 + 0.944446i \(0.606599\pi\)
\(278\) 0 0
\(279\) −1.19814e13 −0.424311
\(280\) 0 0
\(281\) −1.97996e13 −0.674174 −0.337087 0.941473i \(-0.609442\pi\)
−0.337087 + 0.941473i \(0.609442\pi\)
\(282\) 0 0
\(283\) 2.71536e13 0.889207 0.444603 0.895728i \(-0.353345\pi\)
0.444603 + 0.895728i \(0.353345\pi\)
\(284\) 0 0
\(285\) 6.02050e13 1.89664
\(286\) 0 0
\(287\) −2.93815e12 −0.0890684
\(288\) 0 0
\(289\) 2.88959e13 0.843137
\(290\) 0 0
\(291\) 2.69175e13 0.756177
\(292\) 0 0
\(293\) −2.98350e13 −0.807150 −0.403575 0.914947i \(-0.632232\pi\)
−0.403575 + 0.914947i \(0.632232\pi\)
\(294\) 0 0
\(295\) 7.03339e13 1.83292
\(296\) 0 0
\(297\) −1.92906e13 −0.484380
\(298\) 0 0
\(299\) 3.72550e12 0.0901557
\(300\) 0 0
\(301\) −4.17897e12 −0.0974885
\(302\) 0 0
\(303\) −2.83398e13 −0.637473
\(304\) 0 0
\(305\) 2.18584e13 0.474209
\(306\) 0 0
\(307\) 2.24780e13 0.470432 0.235216 0.971943i \(-0.424420\pi\)
0.235216 + 0.971943i \(0.424420\pi\)
\(308\) 0 0
\(309\) 4.40615e12 0.0889790
\(310\) 0 0
\(311\) 2.13685e13 0.416477 0.208239 0.978078i \(-0.433227\pi\)
0.208239 + 0.978078i \(0.433227\pi\)
\(312\) 0 0
\(313\) 2.43422e13 0.458000 0.229000 0.973426i \(-0.426454\pi\)
0.229000 + 0.973426i \(0.426454\pi\)
\(314\) 0 0
\(315\) −4.85697e13 −0.882384
\(316\) 0 0
\(317\) −6.88050e13 −1.20724 −0.603620 0.797272i \(-0.706276\pi\)
−0.603620 + 0.797272i \(0.706276\pi\)
\(318\) 0 0
\(319\) 8.36715e13 1.41817
\(320\) 0 0
\(321\) 7.20620e13 1.18013
\(322\) 0 0
\(323\) 6.25363e13 0.989734
\(324\) 0 0
\(325\) −1.01733e13 −0.155633
\(326\) 0 0
\(327\) −1.58245e14 −2.34054
\(328\) 0 0
\(329\) −1.20547e12 −0.0172417
\(330\) 0 0
\(331\) −1.84782e13 −0.255626 −0.127813 0.991798i \(-0.540796\pi\)
−0.127813 + 0.991798i \(0.540796\pi\)
\(332\) 0 0
\(333\) 2.14717e13 0.287358
\(334\) 0 0
\(335\) −2.58113e14 −3.34244
\(336\) 0 0
\(337\) 1.00646e14 1.26134 0.630669 0.776052i \(-0.282781\pi\)
0.630669 + 0.776052i \(0.282781\pi\)
\(338\) 0 0
\(339\) 1.95365e14 2.37000
\(340\) 0 0
\(341\) 2.79392e13 0.328144
\(342\) 0 0
\(343\) 6.37391e13 0.724917
\(344\) 0 0
\(345\) −2.63463e14 −2.90212
\(346\) 0 0
\(347\) 8.02297e13 0.856097 0.428049 0.903756i \(-0.359201\pi\)
0.428049 + 0.903756i \(0.359201\pi\)
\(348\) 0 0
\(349\) −1.83187e13 −0.189389 −0.0946947 0.995506i \(-0.530187\pi\)
−0.0946947 + 0.995506i \(0.530187\pi\)
\(350\) 0 0
\(351\) −3.84670e12 −0.0385389
\(352\) 0 0
\(353\) −4.56680e13 −0.443456 −0.221728 0.975109i \(-0.571170\pi\)
−0.221728 + 0.975109i \(0.571170\pi\)
\(354\) 0 0
\(355\) −1.86332e14 −1.75401
\(356\) 0 0
\(357\) −8.88597e13 −0.811016
\(358\) 0 0
\(359\) 4.60991e13 0.408012 0.204006 0.978970i \(-0.434604\pi\)
0.204006 + 0.978970i \(0.434604\pi\)
\(360\) 0 0
\(361\) −5.45792e13 −0.468530
\(362\) 0 0
\(363\) 5.81961e12 0.0484626
\(364\) 0 0
\(365\) 9.20993e13 0.744124
\(366\) 0 0
\(367\) −1.36650e14 −1.07139 −0.535693 0.844413i \(-0.679950\pi\)
−0.535693 + 0.844413i \(0.679950\pi\)
\(368\) 0 0
\(369\) 3.91457e13 0.297878
\(370\) 0 0
\(371\) 7.42748e13 0.548637
\(372\) 0 0
\(373\) 9.26839e13 0.664669 0.332335 0.943162i \(-0.392164\pi\)
0.332335 + 0.943162i \(0.392164\pi\)
\(374\) 0 0
\(375\) 3.45832e14 2.40820
\(376\) 0 0
\(377\) 1.66847e13 0.112834
\(378\) 0 0
\(379\) −1.58566e14 −1.04158 −0.520791 0.853684i \(-0.674363\pi\)
−0.520791 + 0.853684i \(0.674363\pi\)
\(380\) 0 0
\(381\) 4.22244e14 2.69449
\(382\) 0 0
\(383\) 2.03453e14 1.26145 0.630727 0.776005i \(-0.282757\pi\)
0.630727 + 0.776005i \(0.282757\pi\)
\(384\) 0 0
\(385\) 1.13259e14 0.682398
\(386\) 0 0
\(387\) 5.56773e13 0.326038
\(388\) 0 0
\(389\) −1.92046e14 −1.09315 −0.546577 0.837409i \(-0.684069\pi\)
−0.546577 + 0.837409i \(0.684069\pi\)
\(390\) 0 0
\(391\) −2.73666e14 −1.51443
\(392\) 0 0
\(393\) 2.61481e14 1.40696
\(394\) 0 0
\(395\) 1.99133e13 0.104198
\(396\) 0 0
\(397\) −3.51854e14 −1.79067 −0.895334 0.445396i \(-0.853063\pi\)
−0.895334 + 0.445396i \(0.853063\pi\)
\(398\) 0 0
\(399\) −8.79713e13 −0.435502
\(400\) 0 0
\(401\) −1.72882e13 −0.0832637 −0.0416318 0.999133i \(-0.513256\pi\)
−0.0416318 + 0.999133i \(0.513256\pi\)
\(402\) 0 0
\(403\) 5.57128e12 0.0261082
\(404\) 0 0
\(405\) −2.20622e14 −1.00611
\(406\) 0 0
\(407\) −5.00694e13 −0.222230
\(408\) 0 0
\(409\) −4.41360e13 −0.190684 −0.0953422 0.995445i \(-0.530395\pi\)
−0.0953422 + 0.995445i \(0.530395\pi\)
\(410\) 0 0
\(411\) −2.10367e14 −0.884803
\(412\) 0 0
\(413\) −1.02772e14 −0.420870
\(414\) 0 0
\(415\) 5.38548e14 2.14763
\(416\) 0 0
\(417\) −6.83355e14 −2.65398
\(418\) 0 0
\(419\) 1.09214e14 0.413144 0.206572 0.978431i \(-0.433769\pi\)
0.206572 + 0.978431i \(0.433769\pi\)
\(420\) 0 0
\(421\) 2.33050e14 0.858811 0.429406 0.903112i \(-0.358723\pi\)
0.429406 + 0.903112i \(0.358723\pi\)
\(422\) 0 0
\(423\) 1.60608e13 0.0576627
\(424\) 0 0
\(425\) 7.47301e14 2.61431
\(426\) 0 0
\(427\) −3.19395e13 −0.108887
\(428\) 0 0
\(429\) 3.75824e13 0.124873
\(430\) 0 0
\(431\) −9.80730e13 −0.317632 −0.158816 0.987308i \(-0.550768\pi\)
−0.158816 + 0.987308i \(0.550768\pi\)
\(432\) 0 0
\(433\) 1.44428e14 0.456003 0.228001 0.973661i \(-0.426781\pi\)
0.228001 + 0.973661i \(0.426781\pi\)
\(434\) 0 0
\(435\) −1.17993e15 −3.63215
\(436\) 0 0
\(437\) −2.70930e14 −0.813221
\(438\) 0 0
\(439\) −1.16021e14 −0.339610 −0.169805 0.985478i \(-0.554314\pi\)
−0.169805 + 0.985478i \(0.554314\pi\)
\(440\) 0 0
\(441\) −3.89120e14 −1.11089
\(442\) 0 0
\(443\) 3.51848e14 0.979795 0.489897 0.871780i \(-0.337034\pi\)
0.489897 + 0.871780i \(0.337034\pi\)
\(444\) 0 0
\(445\) −2.99390e14 −0.813312
\(446\) 0 0
\(447\) 3.79389e14 1.00553
\(448\) 0 0
\(449\) 1.46433e14 0.378690 0.189345 0.981911i \(-0.439364\pi\)
0.189345 + 0.981911i \(0.439364\pi\)
\(450\) 0 0
\(451\) −9.12830e13 −0.230366
\(452\) 0 0
\(453\) 7.48910e14 1.84455
\(454\) 0 0
\(455\) 2.25847e13 0.0542939
\(456\) 0 0
\(457\) −3.55422e14 −0.834076 −0.417038 0.908889i \(-0.636932\pi\)
−0.417038 + 0.908889i \(0.636932\pi\)
\(458\) 0 0
\(459\) 2.82569e14 0.647372
\(460\) 0 0
\(461\) 8.46403e14 1.89331 0.946655 0.322248i \(-0.104438\pi\)
0.946655 + 0.322248i \(0.104438\pi\)
\(462\) 0 0
\(463\) 1.75496e14 0.383330 0.191665 0.981460i \(-0.438611\pi\)
0.191665 + 0.981460i \(0.438611\pi\)
\(464\) 0 0
\(465\) −3.93995e14 −0.840427
\(466\) 0 0
\(467\) 7.53411e13 0.156960 0.0784800 0.996916i \(-0.474993\pi\)
0.0784800 + 0.996916i \(0.474993\pi\)
\(468\) 0 0
\(469\) 3.77154e14 0.767482
\(470\) 0 0
\(471\) 2.36062e14 0.469257
\(472\) 0 0
\(473\) −1.29833e14 −0.252144
\(474\) 0 0
\(475\) 7.39830e14 1.40384
\(476\) 0 0
\(477\) −9.89580e14 −1.83485
\(478\) 0 0
\(479\) 4.09390e14 0.741809 0.370905 0.928671i \(-0.379048\pi\)
0.370905 + 0.928671i \(0.379048\pi\)
\(480\) 0 0
\(481\) −9.98422e12 −0.0176814
\(482\) 0 0
\(483\) 3.84972e14 0.666377
\(484\) 0 0
\(485\) 5.02550e14 0.850354
\(486\) 0 0
\(487\) −8.99264e14 −1.48757 −0.743786 0.668418i \(-0.766972\pi\)
−0.743786 + 0.668418i \(0.766972\pi\)
\(488\) 0 0
\(489\) 1.22712e15 1.98467
\(490\) 0 0
\(491\) 1.50544e14 0.238075 0.119038 0.992890i \(-0.462019\pi\)
0.119038 + 0.992890i \(0.462019\pi\)
\(492\) 0 0
\(493\) −1.22562e15 −1.89538
\(494\) 0 0
\(495\) −1.50897e15 −2.28219
\(496\) 0 0
\(497\) 2.72268e14 0.402751
\(498\) 0 0
\(499\) 7.02134e14 1.01594 0.507969 0.861375i \(-0.330396\pi\)
0.507969 + 0.861375i \(0.330396\pi\)
\(500\) 0 0
\(501\) 1.82112e14 0.257769
\(502\) 0 0
\(503\) −1.24917e15 −1.72981 −0.864903 0.501939i \(-0.832620\pi\)
−0.864903 + 0.501939i \(0.832620\pi\)
\(504\) 0 0
\(505\) −5.29104e14 −0.716866
\(506\) 0 0
\(507\) −1.13981e15 −1.51108
\(508\) 0 0
\(509\) −2.67254e14 −0.346718 −0.173359 0.984859i \(-0.555462\pi\)
−0.173359 + 0.984859i \(0.555462\pi\)
\(510\) 0 0
\(511\) −1.34575e14 −0.170864
\(512\) 0 0
\(513\) 2.79744e14 0.347628
\(514\) 0 0
\(515\) 8.22628e13 0.100061
\(516\) 0 0
\(517\) −3.74519e13 −0.0445939
\(518\) 0 0
\(519\) 1.38443e15 1.61380
\(520\) 0 0
\(521\) −9.63788e14 −1.09995 −0.549976 0.835180i \(-0.685363\pi\)
−0.549976 + 0.835180i \(0.685363\pi\)
\(522\) 0 0
\(523\) −4.44881e14 −0.497146 −0.248573 0.968613i \(-0.579962\pi\)
−0.248573 + 0.968613i \(0.579962\pi\)
\(524\) 0 0
\(525\) −1.05125e15 −1.15035
\(526\) 0 0
\(527\) −4.09252e14 −0.438563
\(528\) 0 0
\(529\) 2.32808e14 0.244338
\(530\) 0 0
\(531\) 1.36925e15 1.40755
\(532\) 0 0
\(533\) −1.82025e13 −0.0183287
\(534\) 0 0
\(535\) 1.34540e15 1.32710
\(536\) 0 0
\(537\) 2.95533e15 2.85593
\(538\) 0 0
\(539\) 9.07381e14 0.859116
\(540\) 0 0
\(541\) 9.18626e14 0.852224 0.426112 0.904671i \(-0.359883\pi\)
0.426112 + 0.904671i \(0.359883\pi\)
\(542\) 0 0
\(543\) −3.47760e13 −0.0316140
\(544\) 0 0
\(545\) −2.95443e15 −2.63204
\(546\) 0 0
\(547\) −1.74722e15 −1.52552 −0.762760 0.646682i \(-0.776156\pi\)
−0.762760 + 0.646682i \(0.776156\pi\)
\(548\) 0 0
\(549\) 4.25537e14 0.364157
\(550\) 0 0
\(551\) −1.21336e15 −1.01779
\(552\) 0 0
\(553\) −2.90972e13 −0.0239256
\(554\) 0 0
\(555\) 7.06074e14 0.569166
\(556\) 0 0
\(557\) −7.28921e14 −0.576072 −0.288036 0.957620i \(-0.593002\pi\)
−0.288036 + 0.957620i \(0.593002\pi\)
\(558\) 0 0
\(559\) −2.58897e13 −0.0200614
\(560\) 0 0
\(561\) −2.76071e15 −2.09761
\(562\) 0 0
\(563\) 1.77150e15 1.31991 0.659956 0.751304i \(-0.270575\pi\)
0.659956 + 0.751304i \(0.270575\pi\)
\(564\) 0 0
\(565\) 3.64747e15 2.66517
\(566\) 0 0
\(567\) 3.22373e14 0.231021
\(568\) 0 0
\(569\) 2.73759e15 1.92420 0.962101 0.272694i \(-0.0879146\pi\)
0.962101 + 0.272694i \(0.0879146\pi\)
\(570\) 0 0
\(571\) −1.04213e15 −0.718491 −0.359245 0.933243i \(-0.616966\pi\)
−0.359245 + 0.933243i \(0.616966\pi\)
\(572\) 0 0
\(573\) 1.49092e15 1.00833
\(574\) 0 0
\(575\) −3.23757e15 −2.14806
\(576\) 0 0
\(577\) 1.89448e15 1.23317 0.616585 0.787288i \(-0.288516\pi\)
0.616585 + 0.787288i \(0.288516\pi\)
\(578\) 0 0
\(579\) 1.59709e15 1.01999
\(580\) 0 0
\(581\) −7.86925e14 −0.493134
\(582\) 0 0
\(583\) 2.30758e15 1.41899
\(584\) 0 0
\(585\) −3.00901e14 −0.181579
\(586\) 0 0
\(587\) −1.08643e15 −0.643419 −0.321709 0.946838i \(-0.604257\pi\)
−0.321709 + 0.946838i \(0.604257\pi\)
\(588\) 0 0
\(589\) −4.05161e14 −0.235501
\(590\) 0 0
\(591\) 3.92888e15 2.24150
\(592\) 0 0
\(593\) −2.51449e15 −1.40815 −0.704075 0.710126i \(-0.748638\pi\)
−0.704075 + 0.710126i \(0.748638\pi\)
\(594\) 0 0
\(595\) −1.65901e15 −0.912023
\(596\) 0 0
\(597\) −4.55974e15 −2.46083
\(598\) 0 0
\(599\) −3.28321e14 −0.173961 −0.0869803 0.996210i \(-0.527722\pi\)
−0.0869803 + 0.996210i \(0.527722\pi\)
\(600\) 0 0
\(601\) −2.14854e15 −1.11772 −0.558861 0.829261i \(-0.688762\pi\)
−0.558861 + 0.829261i \(0.688762\pi\)
\(602\) 0 0
\(603\) −5.02491e15 −2.56675
\(604\) 0 0
\(605\) 1.08652e14 0.0544983
\(606\) 0 0
\(607\) 8.40427e14 0.413964 0.206982 0.978345i \(-0.433636\pi\)
0.206982 + 0.978345i \(0.433636\pi\)
\(608\) 0 0
\(609\) 1.72410e15 0.834005
\(610\) 0 0
\(611\) −7.46819e12 −0.00354804
\(612\) 0 0
\(613\) −9.20771e14 −0.429654 −0.214827 0.976652i \(-0.568919\pi\)
−0.214827 + 0.976652i \(0.568919\pi\)
\(614\) 0 0
\(615\) 1.28726e15 0.590003
\(616\) 0 0
\(617\) −8.78027e14 −0.395312 −0.197656 0.980271i \(-0.563333\pi\)
−0.197656 + 0.980271i \(0.563333\pi\)
\(618\) 0 0
\(619\) −2.73116e15 −1.20795 −0.603975 0.797003i \(-0.706417\pi\)
−0.603975 + 0.797003i \(0.706417\pi\)
\(620\) 0 0
\(621\) −1.22419e15 −0.531918
\(622\) 0 0
\(623\) 4.37468e14 0.186751
\(624\) 0 0
\(625\) 1.86557e15 0.782479
\(626\) 0 0
\(627\) −2.73311e15 −1.12638
\(628\) 0 0
\(629\) 7.33415e14 0.297010
\(630\) 0 0
\(631\) 2.11332e15 0.841016 0.420508 0.907289i \(-0.361852\pi\)
0.420508 + 0.907289i \(0.361852\pi\)
\(632\) 0 0
\(633\) 4.89379e15 1.91393
\(634\) 0 0
\(635\) 7.88329e15 3.03007
\(636\) 0 0
\(637\) 1.80939e14 0.0683541
\(638\) 0 0
\(639\) −3.62749e15 −1.34695
\(640\) 0 0
\(641\) 1.52374e15 0.556149 0.278074 0.960560i \(-0.410304\pi\)
0.278074 + 0.960560i \(0.410304\pi\)
\(642\) 0 0
\(643\) −1.62810e15 −0.584145 −0.292073 0.956396i \(-0.594345\pi\)
−0.292073 + 0.956396i \(0.594345\pi\)
\(644\) 0 0
\(645\) 1.83089e15 0.645779
\(646\) 0 0
\(647\) −2.46240e15 −0.853856 −0.426928 0.904286i \(-0.640404\pi\)
−0.426928 + 0.904286i \(0.640404\pi\)
\(648\) 0 0
\(649\) −3.19293e15 −1.08854
\(650\) 0 0
\(651\) 5.75705e14 0.192976
\(652\) 0 0
\(653\) −5.05508e14 −0.166612 −0.0833059 0.996524i \(-0.526548\pi\)
−0.0833059 + 0.996524i \(0.526548\pi\)
\(654\) 0 0
\(655\) 4.88186e15 1.58219
\(656\) 0 0
\(657\) 1.79298e15 0.571433
\(658\) 0 0
\(659\) −3.21458e15 −1.00752 −0.503761 0.863843i \(-0.668051\pi\)
−0.503761 + 0.863843i \(0.668051\pi\)
\(660\) 0 0
\(661\) 4.00382e15 1.23414 0.617072 0.786906i \(-0.288319\pi\)
0.617072 + 0.786906i \(0.288319\pi\)
\(662\) 0 0
\(663\) −5.50506e14 −0.166893
\(664\) 0 0
\(665\) −1.64242e15 −0.489741
\(666\) 0 0
\(667\) 5.30981e15 1.55735
\(668\) 0 0
\(669\) −1.63949e15 −0.473004
\(670\) 0 0
\(671\) −9.92300e14 −0.281624
\(672\) 0 0
\(673\) −1.69811e15 −0.474115 −0.237058 0.971496i \(-0.576183\pi\)
−0.237058 + 0.971496i \(0.576183\pi\)
\(674\) 0 0
\(675\) 3.34290e15 0.918233
\(676\) 0 0
\(677\) 2.21202e15 0.597793 0.298897 0.954285i \(-0.403381\pi\)
0.298897 + 0.954285i \(0.403381\pi\)
\(678\) 0 0
\(679\) −7.34325e14 −0.195256
\(680\) 0 0
\(681\) −7.38506e15 −1.93217
\(682\) 0 0
\(683\) 2.27584e15 0.585906 0.292953 0.956127i \(-0.405362\pi\)
0.292953 + 0.956127i \(0.405362\pi\)
\(684\) 0 0
\(685\) −3.92754e15 −0.994999
\(686\) 0 0
\(687\) 5.61512e15 1.39990
\(688\) 0 0
\(689\) 4.60149e14 0.112900
\(690\) 0 0
\(691\) −4.62101e14 −0.111586 −0.0557928 0.998442i \(-0.517769\pi\)
−0.0557928 + 0.998442i \(0.517769\pi\)
\(692\) 0 0
\(693\) 2.20491e15 0.524031
\(694\) 0 0
\(695\) −1.27582e16 −2.98452
\(696\) 0 0
\(697\) 1.33711e15 0.307884
\(698\) 0 0
\(699\) −6.39893e15 −1.45038
\(700\) 0 0
\(701\) 8.26266e15 1.84362 0.921808 0.387646i \(-0.126712\pi\)
0.921808 + 0.387646i \(0.126712\pi\)
\(702\) 0 0
\(703\) 7.26083e14 0.159489
\(704\) 0 0
\(705\) 5.28142e14 0.114212
\(706\) 0 0
\(707\) 7.73125e14 0.164605
\(708\) 0 0
\(709\) −4.65932e15 −0.976716 −0.488358 0.872643i \(-0.662404\pi\)
−0.488358 + 0.872643i \(0.662404\pi\)
\(710\) 0 0
\(711\) 3.87668e14 0.0800162
\(712\) 0 0
\(713\) 1.77303e15 0.360349
\(714\) 0 0
\(715\) 7.01664e14 0.140425
\(716\) 0 0
\(717\) 6.32902e15 1.24733
\(718\) 0 0
\(719\) 2.02905e15 0.393808 0.196904 0.980423i \(-0.436911\pi\)
0.196904 + 0.980423i \(0.436911\pi\)
\(720\) 0 0
\(721\) −1.20202e14 −0.0229757
\(722\) 0 0
\(723\) 9.35175e14 0.176048
\(724\) 0 0
\(725\) −1.44995e16 −2.68841
\(726\) 0 0
\(727\) −7.54547e15 −1.37799 −0.688996 0.724765i \(-0.741948\pi\)
−0.688996 + 0.724765i \(0.741948\pi\)
\(728\) 0 0
\(729\) −8.32696e15 −1.49791
\(730\) 0 0
\(731\) 1.90179e15 0.336989
\(732\) 0 0
\(733\) −5.66204e15 −0.988328 −0.494164 0.869369i \(-0.664526\pi\)
−0.494164 + 0.869369i \(0.664526\pi\)
\(734\) 0 0
\(735\) −1.27958e16 −2.20033
\(736\) 0 0
\(737\) 1.17175e16 1.98501
\(738\) 0 0
\(739\) −4.56861e15 −0.762500 −0.381250 0.924472i \(-0.624506\pi\)
−0.381250 + 0.924472i \(0.624506\pi\)
\(740\) 0 0
\(741\) −5.45002e14 −0.0896186
\(742\) 0 0
\(743\) 9.19545e15 1.48982 0.744911 0.667164i \(-0.232492\pi\)
0.744911 + 0.667164i \(0.232492\pi\)
\(744\) 0 0
\(745\) 7.08319e15 1.13076
\(746\) 0 0
\(747\) 1.04844e16 1.64922
\(748\) 0 0
\(749\) −1.96589e15 −0.304726
\(750\) 0 0
\(751\) −2.26878e15 −0.346555 −0.173277 0.984873i \(-0.555436\pi\)
−0.173277 + 0.984873i \(0.555436\pi\)
\(752\) 0 0
\(753\) 3.65625e15 0.550381
\(754\) 0 0
\(755\) 1.39822e16 2.07427
\(756\) 0 0
\(757\) −9.88961e15 −1.44595 −0.722973 0.690877i \(-0.757225\pi\)
−0.722973 + 0.690877i \(0.757225\pi\)
\(758\) 0 0
\(759\) 1.19604e16 1.72351
\(760\) 0 0
\(761\) −1.57459e15 −0.223642 −0.111821 0.993728i \(-0.535668\pi\)
−0.111821 + 0.993728i \(0.535668\pi\)
\(762\) 0 0
\(763\) 4.31701e15 0.604363
\(764\) 0 0
\(765\) 2.21034e16 3.05015
\(766\) 0 0
\(767\) −6.36694e14 −0.0866077
\(768\) 0 0
\(769\) −6.31836e15 −0.847246 −0.423623 0.905839i \(-0.639242\pi\)
−0.423623 + 0.905839i \(0.639242\pi\)
\(770\) 0 0
\(771\) −1.92443e15 −0.254392
\(772\) 0 0
\(773\) 6.47184e15 0.843413 0.421706 0.906732i \(-0.361431\pi\)
0.421706 + 0.906732i \(0.361431\pi\)
\(774\) 0 0
\(775\) −4.84162e15 −0.622058
\(776\) 0 0
\(777\) −1.03171e15 −0.130690
\(778\) 0 0
\(779\) 1.32374e15 0.165328
\(780\) 0 0
\(781\) 8.45886e15 1.04167
\(782\) 0 0
\(783\) −5.48255e15 −0.665722
\(784\) 0 0
\(785\) 4.40727e15 0.527699
\(786\) 0 0
\(787\) −1.32055e15 −0.155918 −0.0779589 0.996957i \(-0.524840\pi\)
−0.0779589 + 0.996957i \(0.524840\pi\)
\(788\) 0 0
\(789\) −1.88430e16 −2.19395
\(790\) 0 0
\(791\) −5.32967e15 −0.611970
\(792\) 0 0
\(793\) −1.97872e14 −0.0224069
\(794\) 0 0
\(795\) −3.25413e16 −3.63425
\(796\) 0 0
\(797\) 2.95580e15 0.325578 0.162789 0.986661i \(-0.447951\pi\)
0.162789 + 0.986661i \(0.447951\pi\)
\(798\) 0 0
\(799\) 5.48594e14 0.0595996
\(800\) 0 0
\(801\) −5.82848e15 −0.624564
\(802\) 0 0
\(803\) −4.18100e15 −0.441921
\(804\) 0 0
\(805\) 7.18743e15 0.749370
\(806\) 0 0
\(807\) 2.59825e16 2.67224
\(808\) 0 0
\(809\) 2.44052e15 0.247608 0.123804 0.992307i \(-0.460491\pi\)
0.123804 + 0.992307i \(0.460491\pi\)
\(810\) 0 0
\(811\) −1.17315e16 −1.17419 −0.587094 0.809518i \(-0.699728\pi\)
−0.587094 + 0.809518i \(0.699728\pi\)
\(812\) 0 0
\(813\) −1.48746e16 −1.46875
\(814\) 0 0
\(815\) 2.29103e16 2.23184
\(816\) 0 0
\(817\) 1.88277e15 0.180958
\(818\) 0 0
\(819\) 4.39675e14 0.0416937
\(820\) 0 0
\(821\) 1.13455e16 1.06154 0.530771 0.847515i \(-0.321902\pi\)
0.530771 + 0.847515i \(0.321902\pi\)
\(822\) 0 0
\(823\) −4.78756e14 −0.0441993 −0.0220997 0.999756i \(-0.507035\pi\)
−0.0220997 + 0.999756i \(0.507035\pi\)
\(824\) 0 0
\(825\) −3.26603e16 −2.97525
\(826\) 0 0
\(827\) 1.04383e16 0.938315 0.469157 0.883115i \(-0.344558\pi\)
0.469157 + 0.883115i \(0.344558\pi\)
\(828\) 0 0
\(829\) 1.91489e16 1.69861 0.849306 0.527902i \(-0.177021\pi\)
0.849306 + 0.527902i \(0.177021\pi\)
\(830\) 0 0
\(831\) −1.14215e16 −0.999814
\(832\) 0 0
\(833\) −1.32913e16 −1.14821
\(834\) 0 0
\(835\) 3.40002e15 0.289872
\(836\) 0 0
\(837\) −1.83071e15 −0.154038
\(838\) 0 0
\(839\) −1.67404e16 −1.39019 −0.695097 0.718916i \(-0.744639\pi\)
−0.695097 + 0.718916i \(0.744639\pi\)
\(840\) 0 0
\(841\) 1.15796e16 0.949107
\(842\) 0 0
\(843\) −1.26753e16 −1.02543
\(844\) 0 0
\(845\) −2.12803e16 −1.69928
\(846\) 0 0
\(847\) −1.58762e14 −0.0125138
\(848\) 0 0
\(849\) 1.73832e16 1.35250
\(850\) 0 0
\(851\) −3.17742e15 −0.244040
\(852\) 0 0
\(853\) −1.25299e16 −0.950009 −0.475005 0.879983i \(-0.657554\pi\)
−0.475005 + 0.879983i \(0.657554\pi\)
\(854\) 0 0
\(855\) 2.18824e16 1.63788
\(856\) 0 0
\(857\) −3.86464e15 −0.285571 −0.142786 0.989754i \(-0.545606\pi\)
−0.142786 + 0.989754i \(0.545606\pi\)
\(858\) 0 0
\(859\) 8.04819e15 0.587132 0.293566 0.955939i \(-0.405158\pi\)
0.293566 + 0.955939i \(0.405158\pi\)
\(860\) 0 0
\(861\) −1.88094e15 −0.135475
\(862\) 0 0
\(863\) −1.48813e16 −1.05823 −0.529116 0.848550i \(-0.677476\pi\)
−0.529116 + 0.848550i \(0.677476\pi\)
\(864\) 0 0
\(865\) 2.58472e16 1.81479
\(866\) 0 0
\(867\) 1.84986e16 1.28243
\(868\) 0 0
\(869\) −9.03996e14 −0.0618811
\(870\) 0 0
\(871\) 2.33656e15 0.157934
\(872\) 0 0
\(873\) 9.78358e15 0.653009
\(874\) 0 0
\(875\) −9.43449e15 −0.621833
\(876\) 0 0
\(877\) −4.76485e15 −0.310136 −0.155068 0.987904i \(-0.549560\pi\)
−0.155068 + 0.987904i \(0.549560\pi\)
\(878\) 0 0
\(879\) −1.90998e16 −1.22769
\(880\) 0 0
\(881\) 1.88870e16 1.19894 0.599468 0.800399i \(-0.295379\pi\)
0.599468 + 0.800399i \(0.295379\pi\)
\(882\) 0 0
\(883\) −2.73933e16 −1.71736 −0.858679 0.512513i \(-0.828715\pi\)
−0.858679 + 0.512513i \(0.828715\pi\)
\(884\) 0 0
\(885\) 4.50263e16 2.78791
\(886\) 0 0
\(887\) 1.46672e16 0.896950 0.448475 0.893795i \(-0.351967\pi\)
0.448475 + 0.893795i \(0.351967\pi\)
\(888\) 0 0
\(889\) −1.15190e16 −0.695756
\(890\) 0 0
\(891\) 1.00155e16 0.597512
\(892\) 0 0
\(893\) 5.43109e14 0.0320040
\(894\) 0 0
\(895\) 5.51761e16 3.21162
\(896\) 0 0
\(897\) 2.38499e15 0.137129
\(898\) 0 0
\(899\) 7.94053e15 0.450995
\(900\) 0 0
\(901\) −3.38014e16 −1.89648
\(902\) 0 0
\(903\) −2.67529e15 −0.148282
\(904\) 0 0
\(905\) −6.49267e14 −0.0355514
\(906\) 0 0
\(907\) 1.51062e15 0.0817175 0.0408588 0.999165i \(-0.486991\pi\)
0.0408588 + 0.999165i \(0.486991\pi\)
\(908\) 0 0
\(909\) −1.03005e16 −0.550500
\(910\) 0 0
\(911\) −1.53728e16 −0.811714 −0.405857 0.913937i \(-0.633027\pi\)
−0.405857 + 0.913937i \(0.633027\pi\)
\(912\) 0 0
\(913\) −2.44483e16 −1.27544
\(914\) 0 0
\(915\) 1.39933e16 0.721281
\(916\) 0 0
\(917\) −7.13336e15 −0.363298
\(918\) 0 0
\(919\) −8.52224e15 −0.428863 −0.214431 0.976739i \(-0.568790\pi\)
−0.214431 + 0.976739i \(0.568790\pi\)
\(920\) 0 0
\(921\) 1.43900e16 0.715536
\(922\) 0 0
\(923\) 1.68676e15 0.0828790
\(924\) 0 0
\(925\) 8.67660e15 0.421279
\(926\) 0 0
\(927\) 1.60148e15 0.0768393
\(928\) 0 0
\(929\) −1.39800e16 −0.662856 −0.331428 0.943480i \(-0.607530\pi\)
−0.331428 + 0.943480i \(0.607530\pi\)
\(930\) 0 0
\(931\) −1.31584e16 −0.616567
\(932\) 0 0
\(933\) 1.36797e16 0.633470
\(934\) 0 0
\(935\) −5.15424e16 −2.35885
\(936\) 0 0
\(937\) −2.51788e16 −1.13885 −0.569426 0.822043i \(-0.692834\pi\)
−0.569426 + 0.822043i \(0.692834\pi\)
\(938\) 0 0
\(939\) 1.55834e16 0.696628
\(940\) 0 0
\(941\) −1.84912e16 −0.817002 −0.408501 0.912758i \(-0.633948\pi\)
−0.408501 + 0.912758i \(0.633948\pi\)
\(942\) 0 0
\(943\) −5.79284e15 −0.252975
\(944\) 0 0
\(945\) −7.42125e15 −0.320333
\(946\) 0 0
\(947\) −2.54291e16 −1.08494 −0.542470 0.840075i \(-0.682511\pi\)
−0.542470 + 0.840075i \(0.682511\pi\)
\(948\) 0 0
\(949\) −8.33724e14 −0.0351608
\(950\) 0 0
\(951\) −4.40475e16 −1.83624
\(952\) 0 0
\(953\) −1.74368e16 −0.718550 −0.359275 0.933232i \(-0.616976\pi\)
−0.359275 + 0.933232i \(0.616976\pi\)
\(954\) 0 0
\(955\) 2.78355e16 1.13392
\(956\) 0 0
\(957\) 5.35648e16 2.15707
\(958\) 0 0
\(959\) 5.73892e15 0.228469
\(960\) 0 0
\(961\) −2.27570e16 −0.895646
\(962\) 0 0
\(963\) 2.61920e16 1.01912
\(964\) 0 0
\(965\) 2.98176e16 1.14703
\(966\) 0 0
\(967\) −2.45449e16 −0.933503 −0.466752 0.884388i \(-0.654576\pi\)
−0.466752 + 0.884388i \(0.654576\pi\)
\(968\) 0 0
\(969\) 4.00345e16 1.50540
\(970\) 0 0
\(971\) 3.90567e16 1.45208 0.726038 0.687655i \(-0.241360\pi\)
0.726038 + 0.687655i \(0.241360\pi\)
\(972\) 0 0
\(973\) 1.86423e16 0.685297
\(974\) 0 0
\(975\) −6.51271e15 −0.236721
\(976\) 0 0
\(977\) −2.20624e16 −0.792925 −0.396462 0.918051i \(-0.629762\pi\)
−0.396462 + 0.918051i \(0.629762\pi\)
\(978\) 0 0
\(979\) 1.35913e16 0.483011
\(980\) 0 0
\(981\) −5.75164e16 −2.02121
\(982\) 0 0
\(983\) 2.11862e16 0.736220 0.368110 0.929782i \(-0.380005\pi\)
0.368110 + 0.929782i \(0.380005\pi\)
\(984\) 0 0
\(985\) 7.33522e16 2.52066
\(986\) 0 0
\(987\) −7.71720e14 −0.0262250
\(988\) 0 0
\(989\) −8.23922e15 −0.276890
\(990\) 0 0
\(991\) 2.97458e16 0.988600 0.494300 0.869292i \(-0.335425\pi\)
0.494300 + 0.869292i \(0.335425\pi\)
\(992\) 0 0
\(993\) −1.18294e16 −0.388813
\(994\) 0 0
\(995\) −8.51303e16 −2.76731
\(996\) 0 0
\(997\) 5.21562e16 1.67680 0.838402 0.545052i \(-0.183490\pi\)
0.838402 + 0.545052i \(0.183490\pi\)
\(998\) 0 0
\(999\) 3.28079e15 0.104320
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 \(a_p\))