Properties

Label 80.10.c.c.49.4
Level 80
Weight 10
Character 80.49
Analytic conductor 41.203
Analytic rank 0
Dimension 4
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) = \( 10 \)
Character orbit: \([\chi]\) = 80.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(41.2028668931\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.0.49740556.1
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{7}\cdot 3^{2}\cdot 5^{2} \)
Twist minimal: no (minimal twist has level 5)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 49.4
Root \(6.05982i\)
Character \(\chi\) = 80.49
Dual form 80.10.c.c.49.1

$q$-expansion

\(f(q)\) \(=\) \(q+179.263i q^{3} +(-568.288 - 1276.78i) q^{5} -8712.99i q^{7} -12452.2 q^{9} +O(q^{10})\) \(q+179.263i q^{3} +(-568.288 - 1276.78i) q^{5} -8712.99i q^{7} -12452.2 q^{9} -44557.8 q^{11} +21430.4i q^{13} +(228880. - 101873. i) q^{15} +300220. i q^{17} +565385. q^{19} +1.56192e6 q^{21} +950727. i q^{23} +(-1.30722e6 + 1.45116e6i) q^{25} +1.29622e6i q^{27} +803167. q^{29} +1.99843e6 q^{31} -7.98755e6i q^{33} +(-1.11246e7 + 4.95149e6i) q^{35} +9.53656e6i q^{37} -3.84168e6 q^{39} -2.54355e7 q^{41} -2.32830e7i q^{43} +(7.07642e6 + 1.58987e7i) q^{45} +3.77353e7i q^{47} -3.55626e7 q^{49} -5.38183e7 q^{51} +4.79297e7i q^{53} +(2.53216e7 + 5.68906e7i) q^{55} +1.01353e8i q^{57} +7.00069e7 q^{59} +1.26942e8 q^{61} +1.08496e8i q^{63} +(2.73620e7 - 1.21787e7i) q^{65} +2.66595e8i q^{67} -1.70430e8 q^{69} -6.59169e7 q^{71} -1.47516e7i q^{73} +(-2.60139e8 - 2.34337e8i) q^{75} +3.88231e8i q^{77} -4.66498e7 q^{79} -4.77460e8 q^{81} +2.01840e8i q^{83} +(3.83316e8 - 1.70611e8i) q^{85} +1.43978e8i q^{87} -5.54039e8 q^{89} +1.86723e8 q^{91} +3.58244e8i q^{93} +(-3.21301e8 - 7.21874e8i) q^{95} +3.39489e8i q^{97} +5.54841e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 1140q^{5} + 11628q^{9} + O(q^{10}) \) \( 4q + 1140q^{5} + 11628q^{9} - 109968q^{11} + 396720q^{15} + 636880q^{19} + 3523968q^{21} - 1337900q^{25} - 3531720q^{29} + 10587712q^{31} - 13629840q^{35} - 1686816q^{39} - 16788552q^{41} + 55737180q^{45} - 46921028q^{49} - 84017088q^{51} + 26907120q^{55} + 460829040q^{59} + 360490568q^{61} + 183895680q^{65} - 286524864q^{69} + 47611872q^{71} - 659239200q^{75} + 728043520q^{79} - 343387836q^{81} + 1275419840q^{85} - 1582700760q^{89} - 473322528q^{91} - 1204791600q^{95} + 728787024q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(21\) \(31\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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
\(3\) 179.263i 1.27775i 0.769312 + 0.638873i \(0.220599\pi\)
−0.769312 + 0.638873i \(0.779401\pi\)
\(4\) 0 0
\(5\) −568.288 1276.78i −0.406634 0.913591i
\(6\) 0 0
\(7\) 8712.99i 1.37160i −0.727792 0.685798i \(-0.759453\pi\)
0.727792 0.685798i \(-0.240547\pi\)
\(8\) 0 0
\(9\) −12452.2 −0.632636
\(10\) 0 0
\(11\) −44557.8 −0.917606 −0.458803 0.888538i \(-0.651722\pi\)
−0.458803 + 0.888538i \(0.651722\pi\)
\(12\) 0 0
\(13\) 21430.4i 0.208107i 0.994572 + 0.104053i \(0.0331813\pi\)
−0.994572 + 0.104053i \(0.966819\pi\)
\(14\) 0 0
\(15\) 228880. 101873.i 1.16734 0.519575i
\(16\) 0 0
\(17\) 300220.i 0.871805i 0.899994 + 0.435903i \(0.143571\pi\)
−0.899994 + 0.435903i \(0.856429\pi\)
\(18\) 0 0
\(19\) 565385. 0.995298 0.497649 0.867379i \(-0.334197\pi\)
0.497649 + 0.867379i \(0.334197\pi\)
\(20\) 0 0
\(21\) 1.56192e6 1.75255
\(22\) 0 0
\(23\) 950727.i 0.708403i 0.935169 + 0.354202i \(0.115247\pi\)
−0.935169 + 0.354202i \(0.884753\pi\)
\(24\) 0 0
\(25\) −1.30722e6 + 1.45116e6i −0.669298 + 0.742994i
\(26\) 0 0
\(27\) 1.29622e6i 0.469398i
\(28\) 0 0
\(29\) 803167. 0.210870 0.105435 0.994426i \(-0.466377\pi\)
0.105435 + 0.994426i \(0.466377\pi\)
\(30\) 0 0
\(31\) 1.99843e6 0.388652 0.194326 0.980937i \(-0.437748\pi\)
0.194326 + 0.980937i \(0.437748\pi\)
\(32\) 0 0
\(33\) 7.98755e6i 1.17247i
\(34\) 0 0
\(35\) −1.11246e7 + 4.95149e6i −1.25308 + 0.557737i
\(36\) 0 0
\(37\) 9.53656e6i 0.836535i 0.908324 + 0.418267i \(0.137363\pi\)
−0.908324 + 0.418267i \(0.862637\pi\)
\(38\) 0 0
\(39\) −3.84168e6 −0.265908
\(40\) 0 0
\(41\) −2.54355e7 −1.40576 −0.702882 0.711306i \(-0.748104\pi\)
−0.702882 + 0.711306i \(0.748104\pi\)
\(42\) 0 0
\(43\) 2.32830e7i 1.03856i −0.854605 0.519279i \(-0.826200\pi\)
0.854605 0.519279i \(-0.173800\pi\)
\(44\) 0 0
\(45\) 7.07642e6 + 1.58987e7i 0.257251 + 0.577971i
\(46\) 0 0
\(47\) 3.77353e7i 1.12800i 0.825776 + 0.563998i \(0.190738\pi\)
−0.825776 + 0.563998i \(0.809262\pi\)
\(48\) 0 0
\(49\) −3.55626e7 −0.881274
\(50\) 0 0
\(51\) −5.38183e7 −1.11395
\(52\) 0 0
\(53\) 4.79297e7i 0.834379i 0.908819 + 0.417190i \(0.136985\pi\)
−0.908819 + 0.417190i \(0.863015\pi\)
\(54\) 0 0
\(55\) 2.53216e7 + 5.68906e7i 0.373129 + 0.838317i
\(56\) 0 0
\(57\) 1.01353e8i 1.27174i
\(58\) 0 0
\(59\) 7.00069e7 0.752154 0.376077 0.926588i \(-0.377273\pi\)
0.376077 + 0.926588i \(0.377273\pi\)
\(60\) 0 0
\(61\) 1.26942e8 1.17387 0.586936 0.809633i \(-0.300334\pi\)
0.586936 + 0.809633i \(0.300334\pi\)
\(62\) 0 0
\(63\) 1.08496e8i 0.867721i
\(64\) 0 0
\(65\) 2.73620e7 1.21787e7i 0.190124 0.0846231i
\(66\) 0 0
\(67\) 2.66595e8i 1.61628i 0.588993 + 0.808138i \(0.299525\pi\)
−0.588993 + 0.808138i \(0.700475\pi\)
\(68\) 0 0
\(69\) −1.70430e8 −0.905160
\(70\) 0 0
\(71\) −6.59169e7 −0.307846 −0.153923 0.988083i \(-0.549191\pi\)
−0.153923 + 0.988083i \(0.549191\pi\)
\(72\) 0 0
\(73\) 1.47516e7i 0.0607977i −0.999538 0.0303989i \(-0.990322\pi\)
0.999538 0.0303989i \(-0.00967775\pi\)
\(74\) 0 0
\(75\) −2.60139e8 2.34337e8i −0.949358 0.855193i
\(76\) 0 0
\(77\) 3.88231e8i 1.25858i
\(78\) 0 0
\(79\) −4.66498e7 −0.134750 −0.0673748 0.997728i \(-0.521462\pi\)
−0.0673748 + 0.997728i \(0.521462\pi\)
\(80\) 0 0
\(81\) −4.77460e8 −1.23241
\(82\) 0 0
\(83\) 2.01840e8i 0.466826i 0.972378 + 0.233413i \(0.0749895\pi\)
−0.972378 + 0.233413i \(0.925011\pi\)
\(84\) 0 0
\(85\) 3.83316e8 1.70611e8i 0.796474 0.354505i
\(86\) 0 0
\(87\) 1.43978e8i 0.269438i
\(88\) 0 0
\(89\) −5.54039e8 −0.936020 −0.468010 0.883723i \(-0.655029\pi\)
−0.468010 + 0.883723i \(0.655029\pi\)
\(90\) 0 0
\(91\) 1.86723e8 0.285438
\(92\) 0 0
\(93\) 3.58244e8i 0.496599i
\(94\) 0 0
\(95\) −3.21301e8 7.21874e8i −0.404722 0.909295i
\(96\) 0 0
\(97\) 3.39489e8i 0.389361i 0.980867 + 0.194681i \(0.0623670\pi\)
−0.980867 + 0.194681i \(0.937633\pi\)
\(98\) 0 0
\(99\) 5.54841e8 0.580511
\(100\) 0 0
\(101\) 1.33921e9 1.28056 0.640282 0.768140i \(-0.278817\pi\)
0.640282 + 0.768140i \(0.278817\pi\)
\(102\) 0 0
\(103\) 3.84306e8i 0.336442i −0.985749 0.168221i \(-0.946198\pi\)
0.985749 0.168221i \(-0.0538022\pi\)
\(104\) 0 0
\(105\) −8.87618e8 1.99423e9i −0.712646 1.60112i
\(106\) 0 0
\(107\) 7.97379e8i 0.588082i 0.955793 + 0.294041i \(0.0950002\pi\)
−0.955793 + 0.294041i \(0.905000\pi\)
\(108\) 0 0
\(109\) 6.63230e8 0.450034 0.225017 0.974355i \(-0.427756\pi\)
0.225017 + 0.974355i \(0.427756\pi\)
\(110\) 0 0
\(111\) −1.70955e9 −1.06888
\(112\) 0 0
\(113\) 1.48164e9i 0.854847i −0.904051 0.427424i \(-0.859421\pi\)
0.904051 0.427424i \(-0.140579\pi\)
\(114\) 0 0
\(115\) 1.21387e9 5.40286e8i 0.647191 0.288060i
\(116\) 0 0
\(117\) 2.66856e8i 0.131656i
\(118\) 0 0
\(119\) 2.61581e9 1.19576
\(120\) 0 0
\(121\) −3.72554e8 −0.157999
\(122\) 0 0
\(123\) 4.55964e9i 1.79621i
\(124\) 0 0
\(125\) 2.59569e9 + 8.44363e8i 0.950952 + 0.309339i
\(126\) 0 0
\(127\) 2.28772e9i 0.780344i 0.920742 + 0.390172i \(0.127584\pi\)
−0.920742 + 0.390172i \(0.872416\pi\)
\(128\) 0 0
\(129\) 4.17378e9 1.32701
\(130\) 0 0
\(131\) 3.83999e9 1.13922 0.569612 0.821914i \(-0.307094\pi\)
0.569612 + 0.821914i \(0.307094\pi\)
\(132\) 0 0
\(133\) 4.92619e9i 1.36515i
\(134\) 0 0
\(135\) 1.65499e9 7.36625e8i 0.428838 0.190873i
\(136\) 0 0
\(137\) 5.82666e9i 1.41311i 0.707657 + 0.706556i \(0.249752\pi\)
−0.707657 + 0.706556i \(0.750248\pi\)
\(138\) 0 0
\(139\) −5.89895e9 −1.34032 −0.670159 0.742217i \(-0.733774\pi\)
−0.670159 + 0.742217i \(0.733774\pi\)
\(140\) 0 0
\(141\) −6.76455e9 −1.44129
\(142\) 0 0
\(143\) 9.54892e8i 0.190960i
\(144\) 0 0
\(145\) −4.56430e8 1.02547e9i −0.0857468 0.192649i
\(146\) 0 0
\(147\) 6.37505e9i 1.12604i
\(148\) 0 0
\(149\) −5.39333e9 −0.896436 −0.448218 0.893924i \(-0.647941\pi\)
−0.448218 + 0.893924i \(0.647941\pi\)
\(150\) 0 0
\(151\) −7.92204e8 −0.124005 −0.0620027 0.998076i \(-0.519749\pi\)
−0.0620027 + 0.998076i \(0.519749\pi\)
\(152\) 0 0
\(153\) 3.73839e9i 0.551536i
\(154\) 0 0
\(155\) −1.13568e9 2.55156e9i −0.158039 0.355069i
\(156\) 0 0
\(157\) 1.18606e10i 1.55797i −0.627042 0.778985i \(-0.715735\pi\)
0.627042 0.778985i \(-0.284265\pi\)
\(158\) 0 0
\(159\) −8.59202e9 −1.06613
\(160\) 0 0
\(161\) 8.28367e9 0.971642
\(162\) 0 0
\(163\) 3.99906e9i 0.443724i 0.975078 + 0.221862i \(0.0712135\pi\)
−0.975078 + 0.221862i \(0.928787\pi\)
\(164\) 0 0
\(165\) −1.01984e10 + 4.53923e9i −1.07116 + 0.476765i
\(166\) 0 0
\(167\) 1.09118e10i 1.08560i 0.839861 + 0.542802i \(0.182637\pi\)
−0.839861 + 0.542802i \(0.817363\pi\)
\(168\) 0 0
\(169\) 1.01452e10 0.956692
\(170\) 0 0
\(171\) −7.04028e9 −0.629662
\(172\) 0 0
\(173\) 1.89328e10i 1.60696i 0.595329 + 0.803482i \(0.297022\pi\)
−0.595329 + 0.803482i \(0.702978\pi\)
\(174\) 0 0
\(175\) 1.26439e10 + 1.13898e10i 1.01909 + 0.918006i
\(176\) 0 0
\(177\) 1.25496e10i 0.961062i
\(178\) 0 0
\(179\) 2.09763e10 1.52718 0.763592 0.645699i \(-0.223434\pi\)
0.763592 + 0.645699i \(0.223434\pi\)
\(180\) 0 0
\(181\) −7.16950e9 −0.496518 −0.248259 0.968694i \(-0.579858\pi\)
−0.248259 + 0.968694i \(0.579858\pi\)
\(182\) 0 0
\(183\) 2.27560e10i 1.49991i
\(184\) 0 0
\(185\) 1.21761e10 5.41951e9i 0.764251 0.340163i
\(186\) 0 0
\(187\) 1.33771e10i 0.799974i
\(188\) 0 0
\(189\) 1.12939e10 0.643824
\(190\) 0 0
\(191\) −1.75301e10 −0.953091 −0.476545 0.879150i \(-0.658111\pi\)
−0.476545 + 0.879150i \(0.658111\pi\)
\(192\) 0 0
\(193\) 3.13528e10i 1.62655i 0.581877 + 0.813277i \(0.302319\pi\)
−0.581877 + 0.813277i \(0.697681\pi\)
\(194\) 0 0
\(195\) 2.18318e9 + 4.90499e9i 0.108127 + 0.242931i
\(196\) 0 0
\(197\) 1.85971e10i 0.879725i −0.898065 0.439862i \(-0.855027\pi\)
0.898065 0.439862i \(-0.144973\pi\)
\(198\) 0 0
\(199\) −1.26662e10 −0.572544 −0.286272 0.958148i \(-0.592416\pi\)
−0.286272 + 0.958148i \(0.592416\pi\)
\(200\) 0 0
\(201\) −4.77906e10 −2.06519
\(202\) 0 0
\(203\) 6.99798e9i 0.289228i
\(204\) 0 0
\(205\) 1.44547e10 + 3.24756e10i 0.571631 + 1.28429i
\(206\) 0 0
\(207\) 1.18386e10i 0.448161i
\(208\) 0 0
\(209\) −2.51923e10 −0.913291
\(210\) 0 0
\(211\) 6.20579e9 0.215539 0.107770 0.994176i \(-0.465629\pi\)
0.107770 + 0.994176i \(0.465629\pi\)
\(212\) 0 0
\(213\) 1.18164e10i 0.393350i
\(214\) 0 0
\(215\) −2.97273e10 + 1.32314e10i −0.948818 + 0.422313i
\(216\) 0 0
\(217\) 1.74123e10i 0.533074i
\(218\) 0 0
\(219\) 2.64442e9 0.0776841
\(220\) 0 0
\(221\) −6.43385e9 −0.181428
\(222\) 0 0
\(223\) 4.30855e10i 1.16670i 0.812221 + 0.583350i \(0.198258\pi\)
−0.812221 + 0.583350i \(0.801742\pi\)
\(224\) 0 0
\(225\) 1.62778e10 1.80701e10i 0.423422 0.470045i
\(226\) 0 0
\(227\) 2.28857e10i 0.572068i −0.958219 0.286034i \(-0.907663\pi\)
0.958219 0.286034i \(-0.0923371\pi\)
\(228\) 0 0
\(229\) 5.26747e9 0.126573 0.0632867 0.997995i \(-0.479842\pi\)
0.0632867 + 0.997995i \(0.479842\pi\)
\(230\) 0 0
\(231\) −6.95955e10 −1.60815
\(232\) 0 0
\(233\) 3.55179e10i 0.789488i −0.918791 0.394744i \(-0.870833\pi\)
0.918791 0.394744i \(-0.129167\pi\)
\(234\) 0 0
\(235\) 4.81798e10 2.14445e10i 1.03053 0.458681i
\(236\) 0 0
\(237\) 8.36257e9i 0.172176i
\(238\) 0 0
\(239\) 5.72471e10 1.13491 0.567457 0.823403i \(-0.307927\pi\)
0.567457 + 0.823403i \(0.307927\pi\)
\(240\) 0 0
\(241\) 3.89830e10 0.744386 0.372193 0.928155i \(-0.378606\pi\)
0.372193 + 0.928155i \(0.378606\pi\)
\(242\) 0 0
\(243\) 6.00774e10i 1.10531i
\(244\) 0 0
\(245\) 2.02098e10 + 4.54057e10i 0.358356 + 0.805124i
\(246\) 0 0
\(247\) 1.21164e10i 0.207128i
\(248\) 0 0
\(249\) −3.61824e10 −0.596486
\(250\) 0 0
\(251\) −4.56895e10 −0.726581 −0.363291 0.931676i \(-0.618347\pi\)
−0.363291 + 0.931676i \(0.618347\pi\)
\(252\) 0 0
\(253\) 4.23622e10i 0.650035i
\(254\) 0 0
\(255\) 3.05843e10 + 6.87143e10i 0.452968 + 1.01769i
\(256\) 0 0
\(257\) 1.29955e10i 0.185821i −0.995674 0.0929104i \(-0.970383\pi\)
0.995674 0.0929104i \(-0.0296170\pi\)
\(258\) 0 0
\(259\) 8.30920e10 1.14739
\(260\) 0 0
\(261\) −1.00012e10 −0.133404
\(262\) 0 0
\(263\) 4.80103e10i 0.618776i −0.950936 0.309388i \(-0.899876\pi\)
0.950936 0.309388i \(-0.100124\pi\)
\(264\) 0 0
\(265\) 6.11958e10 2.72379e10i 0.762282 0.339287i
\(266\) 0 0
\(267\) 9.93185e10i 1.19600i
\(268\) 0 0
\(269\) 9.98823e10 1.16306 0.581531 0.813524i \(-0.302454\pi\)
0.581531 + 0.813524i \(0.302454\pi\)
\(270\) 0 0
\(271\) 4.80217e10 0.540849 0.270424 0.962741i \(-0.412836\pi\)
0.270424 + 0.962741i \(0.412836\pi\)
\(272\) 0 0
\(273\) 3.34725e10i 0.364718i
\(274\) 0 0
\(275\) 5.82469e10 6.46604e10i 0.614152 0.681776i
\(276\) 0 0
\(277\) 1.77838e10i 0.181495i 0.995874 + 0.0907477i \(0.0289257\pi\)
−0.995874 + 0.0907477i \(0.971074\pi\)
\(278\) 0 0
\(279\) −2.48848e10 −0.245875
\(280\) 0 0
\(281\) −1.52044e11 −1.45476 −0.727379 0.686236i \(-0.759262\pi\)
−0.727379 + 0.686236i \(0.759262\pi\)
\(282\) 0 0
\(283\) 1.86733e11i 1.73055i −0.501301 0.865273i \(-0.667145\pi\)
0.501301 0.865273i \(-0.332855\pi\)
\(284\) 0 0
\(285\) 1.29405e11 5.75974e10i 1.16185 0.517132i
\(286\) 0 0
\(287\) 2.21619e11i 1.92814i
\(288\) 0 0
\(289\) 2.84558e10 0.239955
\(290\) 0 0
\(291\) −6.08577e10 −0.497505
\(292\) 0 0
\(293\) 1.28928e11i 1.02198i −0.859586 0.510991i \(-0.829278\pi\)
0.859586 0.510991i \(-0.170722\pi\)
\(294\) 0 0
\(295\) −3.97841e10 8.93836e10i −0.305851 0.687161i
\(296\) 0 0
\(297\) 5.77565e10i 0.430722i
\(298\) 0 0
\(299\) −2.03745e10 −0.147423
\(300\) 0 0
\(301\) −2.02865e11 −1.42448
\(302\) 0 0
\(303\) 2.40070e11i 1.63624i
\(304\) 0 0
\(305\) −7.21396e10 1.62077e11i −0.477336 1.07244i
\(306\) 0 0
\(307\) 8.78331e10i 0.564333i −0.959365 0.282167i \(-0.908947\pi\)
0.959365 0.282167i \(-0.0910531\pi\)
\(308\) 0 0
\(309\) 6.88919e10 0.429887
\(310\) 0 0
\(311\) −2.76204e11 −1.67420 −0.837101 0.547049i \(-0.815751\pi\)
−0.837101 + 0.547049i \(0.815751\pi\)
\(312\) 0 0
\(313\) 1.84107e11i 1.08423i 0.840304 + 0.542115i \(0.182376\pi\)
−0.840304 + 0.542115i \(0.817624\pi\)
\(314\) 0 0
\(315\) 1.38525e11 6.16568e10i 0.792742 0.352845i
\(316\) 0 0
\(317\) 3.48865e11i 1.94040i 0.242313 + 0.970198i \(0.422094\pi\)
−0.242313 + 0.970198i \(0.577906\pi\)
\(318\) 0 0
\(319\) −3.57873e10 −0.193496
\(320\) 0 0
\(321\) −1.42940e11 −0.751419
\(322\) 0 0
\(323\) 1.69740e11i 0.867706i
\(324\) 0 0
\(325\) −3.10990e10 2.80144e10i −0.154622 0.139285i
\(326\) 0 0
\(327\) 1.18893e11i 0.575029i
\(328\) 0 0
\(329\) 3.28788e11 1.54716
\(330\) 0 0
\(331\) −2.88744e11 −1.32217 −0.661084 0.750312i \(-0.729903\pi\)
−0.661084 + 0.750312i \(0.729903\pi\)
\(332\) 0 0
\(333\) 1.18751e11i 0.529222i
\(334\) 0 0
\(335\) 3.40384e11 1.51503e11i 1.47662 0.657232i
\(336\) 0 0
\(337\) 1.25882e11i 0.531654i −0.964021 0.265827i \(-0.914355\pi\)
0.964021 0.265827i \(-0.0856450\pi\)
\(338\) 0 0
\(339\) 2.65602e11 1.09228
\(340\) 0 0
\(341\) −8.90455e10 −0.356630
\(342\) 0 0
\(343\) 4.17441e10i 0.162844i
\(344\) 0 0
\(345\) 9.68533e10 + 2.17602e11i 0.368068 + 0.826946i
\(346\) 0 0
\(347\) 2.95822e11i 1.09534i 0.836695 + 0.547669i \(0.184485\pi\)
−0.836695 + 0.547669i \(0.815515\pi\)
\(348\) 0 0
\(349\) −3.73474e11 −1.34755 −0.673777 0.738934i \(-0.735329\pi\)
−0.673777 + 0.738934i \(0.735329\pi\)
\(350\) 0 0
\(351\) −2.77785e10 −0.0976848
\(352\) 0 0
\(353\) 4.89872e11i 1.67918i 0.543223 + 0.839589i \(0.317204\pi\)
−0.543223 + 0.839589i \(0.682796\pi\)
\(354\) 0 0
\(355\) 3.74598e10 + 8.41615e10i 0.125181 + 0.281246i
\(356\) 0 0
\(357\) 4.68918e11i 1.52788i
\(358\) 0 0
\(359\) −4.27559e11 −1.35854 −0.679268 0.733891i \(-0.737702\pi\)
−0.679268 + 0.733891i \(0.737702\pi\)
\(360\) 0 0
\(361\) −3.02753e9 −0.00938223
\(362\) 0 0
\(363\) 6.67851e10i 0.201883i
\(364\) 0 0
\(365\) −1.88346e10 + 8.38317e9i −0.0555443 + 0.0247224i
\(366\) 0 0
\(367\) 2.54403e10i 0.0732023i −0.999330 0.0366012i \(-0.988347\pi\)
0.999330 0.0366012i \(-0.0116531\pi\)
\(368\) 0 0
\(369\) 3.16727e11 0.889337
\(370\) 0 0
\(371\) 4.17611e11 1.14443
\(372\) 0 0
\(373\) 7.26003e11i 1.94200i −0.239087 0.970998i \(-0.576848\pi\)
0.239087 0.970998i \(-0.423152\pi\)
\(374\) 0 0
\(375\) −1.51363e11 + 4.65312e11i −0.395256 + 1.21508i
\(376\) 0 0
\(377\) 1.72122e10i 0.0438834i
\(378\) 0 0
\(379\) −2.76699e11 −0.688859 −0.344430 0.938812i \(-0.611928\pi\)
−0.344430 + 0.938812i \(0.611928\pi\)
\(380\) 0 0
\(381\) −4.10103e11 −0.997082
\(382\) 0 0
\(383\) 1.71143e11i 0.406410i −0.979136 0.203205i \(-0.934864\pi\)
0.979136 0.203205i \(-0.0651358\pi\)
\(384\) 0 0
\(385\) 4.95687e11 2.20627e11i 1.14983 0.511783i
\(386\) 0 0
\(387\) 2.89924e11i 0.657030i
\(388\) 0 0
\(389\) −3.92384e10 −0.0868837 −0.0434419 0.999056i \(-0.513832\pi\)
−0.0434419 + 0.999056i \(0.513832\pi\)
\(390\) 0 0
\(391\) −2.85427e11 −0.617590
\(392\) 0 0
\(393\) 6.88367e11i 1.45564i
\(394\) 0 0
\(395\) 2.65105e10 + 5.95616e10i 0.0547937 + 0.123106i
\(396\) 0 0
\(397\) 3.91381e11i 0.790756i −0.918519 0.395378i \(-0.870614\pi\)
0.918519 0.395378i \(-0.129386\pi\)
\(398\) 0 0
\(399\) 8.83084e11 1.74431
\(400\) 0 0
\(401\) −5.04969e11 −0.975248 −0.487624 0.873054i \(-0.662136\pi\)
−0.487624 + 0.873054i \(0.662136\pi\)
\(402\) 0 0
\(403\) 4.28272e10i 0.0808811i
\(404\) 0 0
\(405\) 2.71335e11 + 6.09613e11i 0.501138 + 1.12592i
\(406\) 0 0
\(407\) 4.24928e11i 0.767609i
\(408\) 0 0
\(409\) −9.44998e9 −0.0166985 −0.00834923 0.999965i \(-0.502658\pi\)
−0.00834923 + 0.999965i \(0.502658\pi\)
\(410\) 0 0
\(411\) −1.04450e12 −1.80560
\(412\) 0 0
\(413\) 6.09969e11i 1.03165i
\(414\) 0 0
\(415\) 2.57706e11 1.14703e11i 0.426488 0.189827i
\(416\) 0 0
\(417\) 1.05746e12i 1.71259i
\(418\) 0 0
\(419\) −5.77328e10 −0.0915081 −0.0457541 0.998953i \(-0.514569\pi\)
−0.0457541 + 0.998953i \(0.514569\pi\)
\(420\) 0 0
\(421\) 4.38976e9 0.00681038 0.00340519 0.999994i \(-0.498916\pi\)
0.00340519 + 0.999994i \(0.498916\pi\)
\(422\) 0 0
\(423\) 4.69887e11i 0.713612i
\(424\) 0 0
\(425\) −4.35667e11 3.92455e11i −0.647746 0.583498i
\(426\) 0 0
\(427\) 1.10604e12i 1.61008i
\(428\) 0 0
\(429\) 1.71177e11 0.243998
\(430\) 0 0
\(431\) −9.94476e11 −1.38818 −0.694091 0.719887i \(-0.744193\pi\)
−0.694091 + 0.719887i \(0.744193\pi\)
\(432\) 0 0
\(433\) 1.91618e11i 0.261963i −0.991385 0.130982i \(-0.958187\pi\)
0.991385 0.130982i \(-0.0418129\pi\)
\(434\) 0 0
\(435\) 1.83829e11 8.18209e10i 0.246157 0.109563i
\(436\) 0 0
\(437\) 5.37527e11i 0.705072i
\(438\) 0 0
\(439\) 1.38202e12 1.77592 0.887962 0.459917i \(-0.152121\pi\)
0.887962 + 0.459917i \(0.152121\pi\)
\(440\) 0 0
\(441\) 4.42832e11 0.557526
\(442\) 0 0
\(443\) 3.05660e11i 0.377070i 0.982066 + 0.188535i \(0.0603740\pi\)
−0.982066 + 0.188535i \(0.939626\pi\)
\(444\) 0 0
\(445\) 3.14853e11 + 7.07387e11i 0.380617 + 0.855139i
\(446\) 0 0
\(447\) 9.66825e11i 1.14542i
\(448\) 0 0
\(449\) −1.49518e12 −1.73614 −0.868069 0.496444i \(-0.834639\pi\)
−0.868069 + 0.496444i \(0.834639\pi\)
\(450\) 0 0
\(451\) 1.13335e12 1.28994
\(452\) 0 0
\(453\) 1.42013e11i 0.158447i
\(454\) 0 0
\(455\) −1.06112e11 2.38405e11i −0.116069 0.260774i
\(456\) 0 0
\(457\) 1.17977e12i 1.26525i −0.774459 0.632624i \(-0.781978\pi\)
0.774459 0.632624i \(-0.218022\pi\)
\(458\) 0 0
\(459\) −3.89151e11 −0.409223
\(460\) 0 0
\(461\) 1.54415e12 1.59234 0.796170 0.605074i \(-0.206856\pi\)
0.796170 + 0.605074i \(0.206856\pi\)
\(462\) 0 0
\(463\) 4.55769e11i 0.460926i 0.973081 + 0.230463i \(0.0740240\pi\)
−0.973081 + 0.230463i \(0.925976\pi\)
\(464\) 0 0
\(465\) 4.57400e11 2.03586e11i 0.453689 0.201934i
\(466\) 0 0
\(467\) 6.97342e11i 0.678454i 0.940705 + 0.339227i \(0.110165\pi\)
−0.940705 + 0.339227i \(0.889835\pi\)
\(468\) 0 0
\(469\) 2.32284e12 2.21688
\(470\) 0 0
\(471\) 2.12617e12 1.99069
\(472\) 0 0
\(473\) 1.03744e12i 0.952987i
\(474\) 0 0
\(475\) −7.39084e11 + 8.20464e11i −0.666151 + 0.739500i
\(476\) 0 0
\(477\) 5.96829e11i 0.527858i
\(478\) 0 0
\(479\) 2.43471e11 0.211318 0.105659 0.994402i \(-0.466305\pi\)
0.105659 + 0.994402i \(0.466305\pi\)
\(480\) 0 0
\(481\) −2.04373e11 −0.174088
\(482\) 0 0
\(483\) 1.48495e12i 1.24151i
\(484\) 0 0
\(485\) 4.33453e11 1.92927e11i 0.355717 0.158327i
\(486\) 0 0
\(487\) 1.56961e12i 1.26448i −0.774773 0.632239i \(-0.782136\pi\)
0.774773 0.632239i \(-0.217864\pi\)
\(488\) 0 0
\(489\) −7.16882e11 −0.566967
\(490\) 0 0
\(491\) −6.52870e11 −0.506944 −0.253472 0.967343i \(-0.581573\pi\)
−0.253472 + 0.967343i \(0.581573\pi\)
\(492\) 0 0
\(493\) 2.41127e11i 0.183838i
\(494\) 0 0
\(495\) −3.15309e11 7.08412e11i −0.236055 0.530350i
\(496\) 0 0
\(497\) 5.74333e11i 0.422241i
\(498\) 0 0
\(499\) −7.51465e11 −0.542571 −0.271285 0.962499i \(-0.587449\pi\)
−0.271285 + 0.962499i \(0.587449\pi\)
\(500\) 0 0
\(501\) −1.95608e12 −1.38713
\(502\) 0 0
\(503\) 1.31120e12i 0.913299i −0.889647 0.456649i \(-0.849049\pi\)
0.889647 0.456649i \(-0.150951\pi\)
\(504\) 0 0
\(505\) −7.61055e11 1.70988e12i −0.520721 1.16991i
\(506\) 0 0
\(507\) 1.81866e12i 1.22241i
\(508\) 0 0
\(509\) −1.78629e12 −1.17957 −0.589783 0.807561i \(-0.700787\pi\)
−0.589783 + 0.807561i \(0.700787\pi\)
\(510\) 0 0
\(511\) −1.28531e11 −0.0833899
\(512\) 0 0
\(513\) 7.32862e11i 0.467191i
\(514\) 0 0
\(515\) −4.90676e11 + 2.18397e11i −0.307370 + 0.136809i
\(516\) 0 0
\(517\) 1.68140e12i 1.03506i
\(518\) 0 0
\(519\) −3.39394e12 −2.05329
\(520\) 0 0
\(521\) 5.88627e11 0.350002 0.175001 0.984568i \(-0.444007\pi\)
0.175001 + 0.984568i \(0.444007\pi\)
\(522\) 0 0
\(523\) 6.01202e11i 0.351369i −0.984447 0.175684i \(-0.943786\pi\)
0.984447 0.175684i \(-0.0562138\pi\)
\(524\) 0 0
\(525\) −2.04177e12 + 2.26659e12i −1.17298 + 1.30213i
\(526\) 0 0
\(527\) 5.99968e11i 0.338829i
\(528\) 0 0
\(529\) 8.97272e11 0.498165
\(530\) 0 0
\(531\) −8.71739e11 −0.475840
\(532\) 0 0
\(533\) 5.45093e11i 0.292549i
\(534\) 0 0
\(535\) 1.01808e12 4.53141e11i 0.537266 0.239134i
\(536\) 0 0
\(537\) 3.76028e12i 1.95135i
\(538\) 0 0
\(539\) 1.58459e12 0.808662
\(540\) 0 0
\(541\) 1.40863e12 0.706982 0.353491 0.935438i \(-0.384995\pi\)
0.353491 + 0.935438i \(0.384995\pi\)
\(542\) 0 0
\(543\) 1.28522e12i 0.634424i
\(544\) 0 0
\(545\) −3.76905e11 8.46800e11i −0.182999 0.411147i
\(546\) 0 0
\(547\) 8.05933e10i 0.0384907i −0.999815 0.0192454i \(-0.993874\pi\)
0.999815 0.0192454i \(-0.00612636\pi\)
\(548\) 0 0
\(549\) −1.58070e12 −0.742635
\(550\) 0 0
\(551\) 4.54098e11 0.209878
\(552\) 0 0
\(553\) 4.06459e11i 0.184822i
\(554\) 0 0
\(555\) 9.71517e11 + 2.18273e12i 0.434642 + 0.976519i
\(556\) 0 0
\(557\) 3.92066e12i 1.72588i 0.505305 + 0.862941i \(0.331380\pi\)
−0.505305 + 0.862941i \(0.668620\pi\)
\(558\) 0 0
\(559\) 4.98965e11 0.216131
\(560\) 0 0
\(561\) 2.39802e12 1.02216
\(562\) 0 0
\(563\) 3.86627e12i 1.62182i 0.585168 + 0.810912i \(0.301029\pi\)
−0.585168 + 0.810912i \(0.698971\pi\)
\(564\) 0 0
\(565\) −1.89173e12 + 8.41996e11i −0.780981 + 0.347610i
\(566\) 0 0
\(567\) 4.16010e12i 1.69036i
\(568\) 0 0
\(569\) 1.87990e12 0.751849 0.375924 0.926650i \(-0.377325\pi\)
0.375924 + 0.926650i \(0.377325\pi\)
\(570\) 0 0
\(571\) 3.44726e12 1.35710 0.678550 0.734554i \(-0.262609\pi\)
0.678550 + 0.734554i \(0.262609\pi\)
\(572\) 0 0
\(573\) 3.14250e12i 1.21781i
\(574\) 0 0
\(575\) −1.37966e12 1.24281e12i −0.526339 0.474133i
\(576\) 0 0
\(577\) 1.68433e12i 0.632608i 0.948658 + 0.316304i \(0.102442\pi\)
−0.948658 + 0.316304i \(0.897558\pi\)
\(578\) 0 0
\(579\) −5.62039e12 −2.07832
\(580\) 0 0
\(581\) 1.75863e12 0.640297
\(582\) 0 0
\(583\) 2.13564e12i 0.765631i
\(584\) 0 0
\(585\) −3.40717e11 + 1.51651e11i −0.120280 + 0.0535357i
\(586\) 0 0
\(587\) 5.04715e12i 1.75458i 0.479956 + 0.877292i \(0.340652\pi\)
−0.479956 + 0.877292i \(0.659348\pi\)
\(588\) 0 0
\(589\) 1.12988e12 0.386825
\(590\) 0 0
\(591\) 3.33377e12 1.12407
\(592\) 0 0
\(593\) 6.66924e11i 0.221478i −0.993850 0.110739i \(-0.964678\pi\)
0.993850 0.110739i \(-0.0353217\pi\)
\(594\) 0 0
\(595\) −1.48654e12 3.33983e12i −0.486238 1.09244i
\(596\) 0 0
\(597\) 2.27059e12i 0.731566i
\(598\) 0 0
\(599\) 3.36479e12 1.06792 0.533958 0.845511i \(-0.320704\pi\)
0.533958 + 0.845511i \(0.320704\pi\)
\(600\) 0 0
\(601\) −2.79891e12 −0.875092 −0.437546 0.899196i \(-0.644152\pi\)
−0.437546 + 0.899196i \(0.644152\pi\)
\(602\) 0 0
\(603\) 3.31969e12i 1.02251i
\(604\) 0 0
\(605\) 2.11718e11 + 4.75671e11i 0.0642478 + 0.144347i
\(606\) 0 0
\(607\) 3.38683e12i 1.01261i −0.862353 0.506307i \(-0.831010\pi\)
0.862353 0.506307i \(-0.168990\pi\)
\(608\) 0 0
\(609\) 1.25448e12 0.369560
\(610\) 0 0
\(611\) −8.08685e11 −0.234744
\(612\) 0 0
\(613\) 7.53866e11i 0.215636i −0.994171 0.107818i \(-0.965614\pi\)
0.994171 0.107818i \(-0.0343864\pi\)
\(614\) 0 0
\(615\) −5.82166e12 + 2.59119e12i −1.64100 + 0.730399i
\(616\) 0 0
\(617\) 1.42132e11i 0.0394827i −0.999805 0.0197414i \(-0.993716\pi\)
0.999805 0.0197414i \(-0.00628428\pi\)
\(618\) 0 0
\(619\) −1.03073e12 −0.282186 −0.141093 0.989996i \(-0.545062\pi\)
−0.141093 + 0.989996i \(0.545062\pi\)
\(620\) 0 0
\(621\) −1.23235e12 −0.332523
\(622\) 0 0
\(623\) 4.82733e12i 1.28384i
\(624\) 0 0
\(625\) −3.97033e11 3.79398e12i −0.104080 0.994569i
\(626\) 0 0
\(627\) 4.51604e12i 1.16695i
\(628\) 0 0
\(629\) −2.86307e12 −0.729296
\(630\) 0 0
\(631\) 4.61780e12 1.15959 0.579793 0.814764i \(-0.303133\pi\)
0.579793 + 0.814764i \(0.303133\pi\)
\(632\) 0 0
\(633\) 1.11247e12i 0.275404i
\(634\) 0 0
\(635\) 2.92092e12 1.30008e12i 0.712916 0.317314i
\(636\) 0 0
\(637\) 7.62122e11i 0.183399i
\(638\) 0 0
\(639\) 8.20809e11 0.194755
\(640\) 0 0
\(641\) 7.51099e12 1.75726 0.878630 0.477503i \(-0.158458\pi\)
0.878630 + 0.477503i \(0.158458\pi\)
\(642\) 0 0
\(643\) 4.42841e12i 1.02164i −0.859687 0.510821i \(-0.829341\pi\)
0.859687 0.510821i \(-0.170659\pi\)
\(644\) 0 0
\(645\) −2.37191e12 5.32901e12i −0.539609 1.21235i
\(646\) 0 0
\(647\) 1.09396e12i 0.245432i −0.992442 0.122716i \(-0.960840\pi\)
0.992442 0.122716i \(-0.0391604\pi\)
\(648\) 0 0
\(649\) −3.11935e12 −0.690181
\(650\) 0 0
\(651\) 3.12138e12 0.681133
\(652\) 0 0
\(653\) 8.24881e12i 1.77534i 0.460477 + 0.887671i \(0.347678\pi\)
−0.460477 + 0.887671i \(0.652322\pi\)
\(654\) 0 0
\(655\) −2.18222e12 4.90283e12i −0.463247 1.04078i
\(656\) 0 0
\(657\) 1.83690e11i 0.0384628i
\(658\) 0 0
\(659\) −2.64086e12 −0.545458 −0.272729 0.962091i \(-0.587926\pi\)
−0.272729 + 0.962091i \(0.587926\pi\)
\(660\) 0 0
\(661\) 8.94654e12 1.82284 0.911420 0.411478i \(-0.134987\pi\)
0.911420 + 0.411478i \(0.134987\pi\)
\(662\) 0 0
\(663\) 1.15335e12i 0.231820i
\(664\) 0 0
\(665\) −6.28968e12 + 2.79950e12i −1.24719 + 0.555114i
\(666\) 0 0
\(667\) 7.63592e11i 0.149381i
\(668\) 0 0
\(669\) −7.72362e12 −1.49075
\(670\) 0 0
\(671\) −5.65625e12 −1.07715
\(672\) 0 0
\(673\) 6.40541e12i 1.20359i −0.798650 0.601796i \(-0.794452\pi\)
0.798650 0.601796i \(-0.205548\pi\)
\(674\) 0 0
\(675\) −1.88102e12 1.69445e12i −0.348760 0.314167i
\(676\) 0 0
\(677\) 6.41491e12i 1.17366i −0.809711 0.586829i \(-0.800376\pi\)
0.809711 0.586829i \(-0.199624\pi\)
\(678\) 0 0
\(679\) 2.95796e12 0.534046
\(680\) 0 0
\(681\) 4.10256e12 0.730958
\(682\) 0 0
\(683\) 2.15592e12i 0.379088i −0.981872 0.189544i \(-0.939299\pi\)
0.981872 0.189544i \(-0.0607009\pi\)
\(684\) 0 0
\(685\) 7.43937e12 3.31122e12i 1.29101 0.574619i
\(686\) 0 0
\(687\) 9.44262e11i 0.161729i
\(688\) 0 0
\(689\) −1.02715e12 −0.173640
\(690\) 0 0
\(691\) 4.58074e12 0.764336 0.382168 0.924093i \(-0.375178\pi\)
0.382168 + 0.924093i \(0.375178\pi\)
\(692\) 0 0
\(693\) 4.83433e12i 0.796226i
\(694\) 0 0
\(695\) 3.35230e12 + 7.53168e12i 0.545019 + 1.22450i
\(696\) 0 0
\(697\) 7.63624e12i 1.22555i
\(698\) 0 0
\(699\) 6.36704e12 1.00877
\(700\) 0 0
\(701\) −1.22474e12 −0.191564 −0.0957819 0.995402i \(-0.530535\pi\)
−0.0957819 + 0.995402i \(0.530535\pi\)
\(702\) 0 0
\(703\) 5.39183e12i 0.832601i
\(704\) 0 0
\(705\) 3.84421e12 + 8.63686e12i 0.586079 + 1.31675i
\(706\) 0 0
\(707\) 1.16685e13i 1.75642i
\(708\) 0 0
\(709\) 5.65887e12 0.841049 0.420525 0.907281i \(-0.361846\pi\)
0.420525 + 0.907281i \(0.361846\pi\)
\(710\) 0 0
\(711\) 5.80891e11 0.0852475
\(712\) 0 0
\(713\) 1.89996e12i 0.275322i
\(714\) 0 0
\(715\) −1.21919e12 + 5.42653e11i −0.174459 + 0.0776507i
\(716\) 0 0
\(717\) 1.02623e13i 1.45013i
\(718\) 0 0
\(719\) −6.02904e12 −0.841333 −0.420667 0.907215i \(-0.638204\pi\)
−0.420667 + 0.907215i \(0.638204\pi\)
\(720\) 0 0
\(721\) −3.34846e12 −0.461462
\(722\) 0 0
\(723\) 6.98820e12i 0.951137i
\(724\) 0 0
\(725\) −1.04992e12 + 1.16552e12i −0.141135 + 0.156675i
\(726\) 0 0
\(727\) 2.63469e12i 0.349805i 0.984586 + 0.174902i \(0.0559609\pi\)
−0.984586 + 0.174902i \(0.944039\pi\)
\(728\) 0 0
\(729\) 1.37180e12 0.179894
\(730\) 0 0
\(731\) 6.99002e12 0.905421
\(732\) 0 0
\(733\) 5.28609e12i 0.676343i 0.941085 + 0.338171i \(0.109808\pi\)
−0.941085 + 0.338171i \(0.890192\pi\)
\(734\) 0 0
\(735\) −8.13955e12 + 3.62286e12i −1.02874 + 0.457888i
\(736\) 0 0
\(737\) 1.18789e13i 1.48310i
\(738\) 0 0
\(739\) 2.51810e12 0.310580 0.155290 0.987869i \(-0.450369\pi\)
0.155290 + 0.987869i \(0.450369\pi\)
\(740\) 0 0
\(741\) −2.17203e12 −0.264657
\(742\) 0 0
\(743\) 7.02537e11i 0.0845706i −0.999106 0.0422853i \(-0.986536\pi\)
0.999106 0.0422853i \(-0.0134638\pi\)
\(744\) 0 0
\(745\) 3.06497e12 + 6.88612e12i 0.364521 + 0.818976i
\(746\) 0 0
\(747\) 2.51335e12i 0.295331i
\(748\) 0 0
\(749\) 6.94755e12 0.806610
\(750\) 0 0
\(751\) −4.60108e12 −0.527813 −0.263907 0.964548i \(-0.585011\pi\)
−0.263907 + 0.964548i \(0.585011\pi\)
\(752\) 0 0
\(753\) 8.19042e12i 0.928387i
\(754\) 0 0
\(755\) 4.50200e11 + 1.01147e12i 0.0504248 + 0.113290i
\(756\) 0 0
\(757\) 3.05764e12i 0.338419i 0.985580 + 0.169210i \(0.0541215\pi\)
−0.985580 + 0.169210i \(0.945878\pi\)
\(758\) 0 0
\(759\) 7.59398e12 0.830580
\(760\) 0 0
\(761\) −9.86753e12 −1.06654 −0.533270 0.845945i \(-0.679037\pi\)
−0.533270 + 0.845945i \(0.679037\pi\)
\(762\) 0 0
\(763\) 5.77872e12i 0.617264i
\(764\) 0 0
\(765\) −4.77312e12 + 2.12448e12i −0.503878 + 0.224273i
\(766\) 0 0
\(767\) 1.50028e12i 0.156528i
\(768\) 0 0
\(769\) −1.65694e13 −1.70859 −0.854294 0.519790i \(-0.826010\pi\)
−0.854294 + 0.519790i \(0.826010\pi\)
\(770\) 0 0
\(771\) 2.32961e12 0.237432
\(772\) 0 0
\(773\) 1.10674e13i 1.11490i 0.830210 + 0.557451i \(0.188221\pi\)
−0.830210 + 0.557451i \(0.811779\pi\)
\(774\) 0 0
\(775\) −2.61239e12 + 2.90004e12i −0.260124 + 0.288766i
\(776\) 0 0
\(777\) 1.48953e13i 1.46607i
\(778\) 0 0
\(779\) −1.43808e13 −1.39915
\(780\) 0 0
\(781\) 2.93711e12 0.282482
\(782\) 0 0
\(783\) 1.04108e12i 0.0989819i
\(784\) 0 0
\(785\) −1.51434e13 + 6.74025e12i −1.42335 + 0.633523i
\(786\) 0 0
\(787\) 1.67201e12i 0.155365i −0.996978 0.0776825i \(-0.975248\pi\)
0.996978 0.0776825i \(-0.0247520\pi\)
\(788\) 0 0
\(789\) 8.60646e12 0.790638
\(790\) 0 0
\(791\) −1.29095e13 −1.17250
\(792\) 0 0
\(793\) 2.72042e12i 0.244291i
\(794\) 0 0
\(795\) 4.88274e12 + 1.09701e13i 0.433522 + 0.974003i
\(796\) 0 0
\(797\) 6.97864e12i 0.612644i −0.951928 0.306322i \(-0.900902\pi\)
0.951928 0.306322i \(-0.0990985\pi\)
\(798\) 0 0
\(799\) −1.13289e13 −0.983394
\(800\) 0 0
\(801\) 6.89899e12