Properties

Label 177.9.c.a.58.1
Level $177$
Weight $9$
Character 177.58
Analytic conductor $72.106$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(72.1060139808\)
Analytic rank: \(0\)
Dimension: \(80\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.1
Character \(\chi\) \(=\) 177.58
Dual form 177.9.c.a.58.80

$q$-expansion

\(f(q)\) \(=\) \(q-31.6572i q^{2} +46.7654 q^{3} -746.176 q^{4} +733.576 q^{5} -1480.46i q^{6} -1197.79 q^{7} +15517.6i q^{8} +2187.00 q^{9} +O(q^{10})\) \(q-31.6572i q^{2} +46.7654 q^{3} -746.176 q^{4} +733.576 q^{5} -1480.46i q^{6} -1197.79 q^{7} +15517.6i q^{8} +2187.00 q^{9} -23222.9i q^{10} -8187.51i q^{11} -34895.2 q^{12} -19649.3i q^{13} +37918.7i q^{14} +34305.9 q^{15} +300222. q^{16} +39112.0 q^{17} -69234.2i q^{18} +148050. q^{19} -547377. q^{20} -56015.2 q^{21} -259193. q^{22} -347255. i q^{23} +725686. i q^{24} +147508. q^{25} -622042. q^{26} +102276. q^{27} +893763. q^{28} +718866. q^{29} -1.08603e6i q^{30} -540311. i q^{31} -5.53166e6i q^{32} -382892. i q^{33} -1.23818e6i q^{34} -878671. q^{35} -1.63189e6 q^{36} -504723. i q^{37} -4.68684e6i q^{38} -918909. i q^{39} +1.13833e7i q^{40} -2.24431e6 q^{41} +1.77328e6i q^{42} +5.44442e6i q^{43} +6.10932e6i q^{44} +1.60433e6 q^{45} -1.09931e7 q^{46} -6.80833e6i q^{47} +1.40400e7 q^{48} -4.33010e6 q^{49} -4.66969e6i q^{50} +1.82909e6 q^{51} +1.46619e7i q^{52} -1.10727e7 q^{53} -3.23776e6i q^{54} -6.00616e6i q^{55} -1.85868e7i q^{56} +6.92361e6 q^{57} -2.27573e7i q^{58} +(8.67636e6 + 8.45880e6i) q^{59} -2.55983e7 q^{60} -5.93306e6i q^{61} -1.71047e7 q^{62} -2.61957e6 q^{63} -9.82600e7 q^{64} -1.44143e7i q^{65} -1.21213e7 q^{66} -850839. i q^{67} -2.91844e7 q^{68} -1.62395e7i q^{69} +2.78162e7i q^{70} -3.91294e7 q^{71} +3.39370e7i q^{72} -2.01737e7i q^{73} -1.59781e7 q^{74} +6.89827e6 q^{75} -1.10471e8 q^{76} +9.80693e6i q^{77} -2.90900e7 q^{78} -6.48702e6 q^{79} +2.20235e8 q^{80} +4.78297e6 q^{81} +7.10484e7i q^{82} -5.10830e7i q^{83} +4.17972e7 q^{84} +2.86916e7 q^{85} +1.72355e8 q^{86} +3.36180e7 q^{87} +1.27050e8 q^{88} -3.40734e7i q^{89} -5.07885e7i q^{90} +2.35358e7i q^{91} +2.59113e8i q^{92} -2.52678e7i q^{93} -2.15533e8 q^{94} +1.08606e8 q^{95} -2.58690e8i q^{96} +1.35148e8i q^{97} +1.37079e8i q^{98} -1.79061e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} + O(q^{10}) \) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} - 22680q^{12} - 59616q^{15} + 1199848q^{16} - 10608q^{17} - 27516q^{19} - 146436q^{20} - 974696q^{22} + 5718040q^{25} - 797484q^{26} - 3133000q^{28} + 1725924q^{29} + 4318800q^{35} - 22394880q^{36} - 732180q^{41} + 22752084q^{46} + 8703936q^{48} + 55899176q^{49} - 10373832q^{51} - 39265944q^{53} - 11408040q^{57} - 33575112q^{59} - 18034488q^{60} + 13038600q^{62} + 349920q^{63} - 241654260q^{64} - 35711928q^{66} + 36772608q^{68} - 235272660q^{71} - 63050712q^{74} + 74363184q^{75} + 9454680q^{76} - 10865988q^{78} + 17252580q^{79} + 318203976q^{80} + 382637520q^{81} - 20743128q^{84} - 27245820q^{85} + 105666984q^{86} + 29437992q^{87} + 82079788q^{88} + 121215992q^{94} - 690837276q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 31.6572i 1.97857i −0.145988 0.989286i \(-0.546636\pi\)
0.145988 0.989286i \(-0.453364\pi\)
\(3\) 46.7654 0.577350
\(4\) −746.176 −2.91475
\(5\) 733.576 1.17372 0.586860 0.809688i \(-0.300364\pi\)
0.586860 + 0.809688i \(0.300364\pi\)
\(6\) 1480.46i 1.14233i
\(7\) −1197.79 −0.498872 −0.249436 0.968391i \(-0.580245\pi\)
−0.249436 + 0.968391i \(0.580245\pi\)
\(8\) 15517.6i 3.78847i
\(9\) 2187.00 0.333333
\(10\) 23222.9i 2.32229i
\(11\) 8187.51i 0.559218i −0.960114 0.279609i \(-0.909795\pi\)
0.960114 0.279609i \(-0.0902048\pi\)
\(12\) −34895.2 −1.68283
\(13\) 19649.3i 0.687978i −0.938974 0.343989i \(-0.888222\pi\)
0.938974 0.343989i \(-0.111778\pi\)
\(14\) 37918.7i 0.987054i
\(15\) 34305.9 0.677648
\(16\) 300222. 4.58102
\(17\) 39112.0 0.468289 0.234145 0.972202i \(-0.424771\pi\)
0.234145 + 0.972202i \(0.424771\pi\)
\(18\) 69234.2i 0.659524i
\(19\) 148050. 1.13604 0.568021 0.823014i \(-0.307709\pi\)
0.568021 + 0.823014i \(0.307709\pi\)
\(20\) −547377. −3.42110
\(21\) −56015.2 −0.288024
\(22\) −259193. −1.10645
\(23\) 347255.i 1.24090i −0.784246 0.620450i \(-0.786950\pi\)
0.784246 0.620450i \(-0.213050\pi\)
\(24\) 725686.i 2.18728i
\(25\) 147508. 0.377621
\(26\) −622042. −1.36121
\(27\) 102276. 0.192450
\(28\) 893763. 1.45409
\(29\) 718866. 1.01638 0.508190 0.861245i \(-0.330315\pi\)
0.508190 + 0.861245i \(0.330315\pi\)
\(30\) 1.08603e6i 1.34078i
\(31\) 540311.i 0.585055i −0.956257 0.292527i \(-0.905504\pi\)
0.956257 0.292527i \(-0.0944963\pi\)
\(32\) 5.53166e6i 5.27540i
\(33\) 382892.i 0.322865i
\(34\) 1.23818e6i 0.926545i
\(35\) −878671. −0.585536
\(36\) −1.63189e6 −0.971583
\(37\) 504723.i 0.269306i −0.990893 0.134653i \(-0.957008\pi\)
0.990893 0.134653i \(-0.0429920\pi\)
\(38\) 4.68684e6i 2.24774i
\(39\) 918909.i 0.397204i
\(40\) 1.13833e7i 4.44661i
\(41\) −2.24431e6 −0.794231 −0.397115 0.917769i \(-0.629989\pi\)
−0.397115 + 0.917769i \(0.629989\pi\)
\(42\) 1.77328e6i 0.569876i
\(43\) 5.44442e6i 1.59249i 0.604972 + 0.796246i \(0.293184\pi\)
−0.604972 + 0.796246i \(0.706816\pi\)
\(44\) 6.10932e6i 1.62998i
\(45\) 1.60433e6 0.391240
\(46\) −1.09931e7 −2.45521
\(47\) 6.80833e6i 1.39524i −0.716467 0.697621i \(-0.754242\pi\)
0.716467 0.697621i \(-0.245758\pi\)
\(48\) 1.40400e7 2.64485
\(49\) −4.33010e6 −0.751127
\(50\) 4.66969e6i 0.747150i
\(51\) 1.82909e6 0.270367
\(52\) 1.46619e7i 2.00528i
\(53\) −1.10727e7 −1.40330 −0.701648 0.712524i \(-0.747552\pi\)
−0.701648 + 0.712524i \(0.747552\pi\)
\(54\) 3.23776e6i 0.380776i
\(55\) 6.00616e6i 0.656366i
\(56\) 1.85868e7i 1.88996i
\(57\) 6.92361e6 0.655894
\(58\) 2.27573e7i 2.01098i
\(59\) 8.67636e6 + 8.45880e6i 0.716027 + 0.698073i
\(60\) −2.55983e7 −1.97517
\(61\) 5.93306e6i 0.428508i −0.976778 0.214254i \(-0.931268\pi\)
0.976778 0.214254i \(-0.0687321\pi\)
\(62\) −1.71047e7 −1.15757
\(63\) −2.61957e6 −0.166291
\(64\) −9.82600e7 −5.85675
\(65\) 1.44143e7i 0.807494i
\(66\) −1.21213e7 −0.638811
\(67\) 850839.i 0.0422229i −0.999777 0.0211115i \(-0.993280\pi\)
0.999777 0.0211115i \(-0.00672049\pi\)
\(68\) −2.91844e7 −1.36495
\(69\) 1.62395e7i 0.716434i
\(70\) 2.78162e7i 1.15853i
\(71\) −3.91294e7 −1.53982 −0.769910 0.638152i \(-0.779699\pi\)
−0.769910 + 0.638152i \(0.779699\pi\)
\(72\) 3.39370e7i 1.26282i
\(73\) 2.01737e7i 0.710384i −0.934793 0.355192i \(-0.884415\pi\)
0.934793 0.355192i \(-0.115585\pi\)
\(74\) −1.59781e7 −0.532842
\(75\) 6.89827e6 0.218020
\(76\) −1.10471e8 −3.31128
\(77\) 9.80693e6i 0.278978i
\(78\) −2.90900e7 −0.785898
\(79\) −6.48702e6 −0.166547 −0.0832736 0.996527i \(-0.526538\pi\)
−0.0832736 + 0.996527i \(0.526538\pi\)
\(80\) 2.20235e8 5.37684
\(81\) 4.78297e6 0.111111
\(82\) 7.10484e7i 1.57144i
\(83\) 5.10830e7i 1.07638i −0.842825 0.538188i \(-0.819109\pi\)
0.842825 0.538188i \(-0.180891\pi\)
\(84\) 4.17972e7 0.839517
\(85\) 2.86916e7 0.549641
\(86\) 1.72355e8 3.15086
\(87\) 3.36180e7 0.586807
\(88\) 1.27050e8 2.11858
\(89\) 3.40734e7i 0.543070i −0.962429 0.271535i \(-0.912469\pi\)
0.962429 0.271535i \(-0.0875312\pi\)
\(90\) 5.07885e7i 0.774097i
\(91\) 2.35358e7i 0.343213i
\(92\) 2.59113e8i 3.61691i
\(93\) 2.52678e7i 0.337782i
\(94\) −2.15533e8 −2.76059
\(95\) 1.08606e8 1.33340
\(96\) 2.58690e8i 3.04576i
\(97\) 1.35148e8i 1.52659i 0.646052 + 0.763294i \(0.276419\pi\)
−0.646052 + 0.763294i \(0.723581\pi\)
\(98\) 1.37079e8i 1.48616i
\(99\) 1.79061e7i 0.186406i
\(100\) −1.10067e8 −1.10067
\(101\) 1.75070e8i 1.68239i −0.540731 0.841195i \(-0.681852\pi\)
0.540731 0.841195i \(-0.318148\pi\)
\(102\) 5.79037e7i 0.534941i
\(103\) 1.84171e7i 0.163634i −0.996647 0.0818170i \(-0.973928\pi\)
0.996647 0.0818170i \(-0.0260723\pi\)
\(104\) 3.04910e8 2.60639
\(105\) −4.10914e7 −0.338060
\(106\) 3.50530e8i 2.77652i
\(107\) 1.46786e8 1.11982 0.559912 0.828552i \(-0.310835\pi\)
0.559912 + 0.828552i \(0.310835\pi\)
\(108\) −7.63158e7 −0.560944
\(109\) 2.24376e7i 0.158953i 0.996837 + 0.0794767i \(0.0253249\pi\)
−0.996837 + 0.0794767i \(0.974675\pi\)
\(110\) −1.90138e8 −1.29867
\(111\) 2.36036e7i 0.155484i
\(112\) −3.59603e8 −2.28534
\(113\) 1.10893e8i 0.680126i 0.940403 + 0.340063i \(0.110448\pi\)
−0.940403 + 0.340063i \(0.889552\pi\)
\(114\) 2.19182e8i 1.29773i
\(115\) 2.54738e8i 1.45647i
\(116\) −5.36400e8 −2.96249
\(117\) 4.29731e7i 0.229326i
\(118\) 2.67782e8 2.74669e8i 1.38119 1.41671i
\(119\) −4.68480e7 −0.233616
\(120\) 5.32345e8i 2.56725i
\(121\) 1.47324e8 0.687275
\(122\) −1.87824e8 −0.847835
\(123\) −1.04956e8 −0.458549
\(124\) 4.03167e8i 1.70529i
\(125\) −1.78345e8 −0.730499
\(126\) 8.29281e7i 0.329018i
\(127\) 4.05456e8 1.55858 0.779289 0.626664i \(-0.215580\pi\)
0.779289 + 0.626664i \(0.215580\pi\)
\(128\) 1.69453e9i 6.31261i
\(129\) 2.54610e8i 0.919426i
\(130\) −4.56315e8 −1.59769
\(131\) 8.31505e7i 0.282345i −0.989985 0.141172i \(-0.954913\pi\)
0.989985 0.141172i \(-0.0450872\pi\)
\(132\) 2.85705e8i 0.941070i
\(133\) −1.77333e8 −0.566739
\(134\) −2.69352e7 −0.0835411
\(135\) 7.50271e7 0.225883
\(136\) 6.06924e8i 1.77410i
\(137\) −1.03226e8 −0.293027 −0.146514 0.989209i \(-0.546805\pi\)
−0.146514 + 0.989209i \(0.546805\pi\)
\(138\) −5.14096e8 −1.41752
\(139\) 7.82094e7 0.209508 0.104754 0.994498i \(-0.466595\pi\)
0.104754 + 0.994498i \(0.466595\pi\)
\(140\) 6.55643e8 1.70669
\(141\) 3.18394e8i 0.805543i
\(142\) 1.23873e9i 3.04665i
\(143\) −1.60879e8 −0.384730
\(144\) 6.56585e8 1.52701
\(145\) 5.27342e8 1.19295
\(146\) −6.38641e8 −1.40555
\(147\) −2.02499e8 −0.433663
\(148\) 3.76612e8i 0.784960i
\(149\) 8.16267e8i 1.65610i −0.560653 0.828051i \(-0.689450\pi\)
0.560653 0.828051i \(-0.310550\pi\)
\(150\) 2.18380e8i 0.431368i
\(151\) 4.79472e8i 0.922264i −0.887332 0.461132i \(-0.847443\pi\)
0.887332 0.461132i \(-0.152557\pi\)
\(152\) 2.29738e9i 4.30386i
\(153\) 8.55379e7 0.156096
\(154\) 3.10459e8 0.551978
\(155\) 3.96359e8i 0.686691i
\(156\) 6.85668e8i 1.15775i
\(157\) 4.02372e8i 0.662261i −0.943585 0.331130i \(-0.892570\pi\)
0.943585 0.331130i \(-0.107430\pi\)
\(158\) 2.05361e8i 0.329526i
\(159\) −5.17818e8 −0.810194
\(160\) 4.05789e9i 6.19185i
\(161\) 4.15939e8i 0.619050i
\(162\) 1.51415e8i 0.219841i
\(163\) −8.79422e8 −1.24580 −0.622898 0.782303i \(-0.714045\pi\)
−0.622898 + 0.782303i \(0.714045\pi\)
\(164\) 1.67465e9 2.31498
\(165\) 2.80880e8i 0.378953i
\(166\) −1.61714e9 −2.12969
\(167\) −1.26373e9 −1.62476 −0.812380 0.583128i \(-0.801829\pi\)
−0.812380 + 0.583128i \(0.801829\pi\)
\(168\) 8.69220e8i 1.09117i
\(169\) 4.29634e8 0.526686
\(170\) 9.08295e8i 1.08750i
\(171\) 3.23785e8 0.378680
\(172\) 4.06249e9i 4.64172i
\(173\) 3.66882e8i 0.409583i −0.978806 0.204792i \(-0.934348\pi\)
0.978806 0.204792i \(-0.0656517\pi\)
\(174\) 1.06425e9i 1.16104i
\(175\) −1.76684e8 −0.188384
\(176\) 2.45807e9i 2.56179i
\(177\) 4.05753e8 + 3.95579e8i 0.413398 + 0.403032i
\(178\) −1.07867e9 −1.07450
\(179\) 6.49482e8i 0.632638i 0.948653 + 0.316319i \(0.102447\pi\)
−0.948653 + 0.316319i \(0.897553\pi\)
\(180\) −1.19711e9 −1.14037
\(181\) −4.52457e8 −0.421564 −0.210782 0.977533i \(-0.567601\pi\)
−0.210782 + 0.977533i \(0.567601\pi\)
\(182\) 7.45077e8 0.679072
\(183\) 2.77462e8i 0.247399i
\(184\) 5.38855e9 4.70112
\(185\) 3.70252e8i 0.316090i
\(186\) −7.99908e8 −0.668326
\(187\) 3.20230e8i 0.261876i
\(188\) 5.08021e9i 4.06678i
\(189\) −1.22505e8 −0.0960079
\(190\) 3.43815e9i 2.63822i
\(191\) 5.25421e8i 0.394797i 0.980323 + 0.197399i \(0.0632494\pi\)
−0.980323 + 0.197399i \(0.936751\pi\)
\(192\) −4.59517e9 −3.38140
\(193\) 1.33758e9 0.964028 0.482014 0.876164i \(-0.339905\pi\)
0.482014 + 0.876164i \(0.339905\pi\)
\(194\) 4.27839e9 3.02046
\(195\) 6.74089e8i 0.466207i
\(196\) 3.23101e9 2.18935
\(197\) 2.94549e8 0.195565 0.0977827 0.995208i \(-0.468825\pi\)
0.0977827 + 0.995208i \(0.468825\pi\)
\(198\) −5.66856e8 −0.368818
\(199\) 7.82763e8 0.499135 0.249568 0.968357i \(-0.419712\pi\)
0.249568 + 0.968357i \(0.419712\pi\)
\(200\) 2.28897e9i 1.43061i
\(201\) 3.97898e7i 0.0243774i
\(202\) −5.54223e9 −3.32873
\(203\) −8.61051e8 −0.507043
\(204\) −1.36482e9 −0.788052
\(205\) −1.64637e9 −0.932205
\(206\) −5.83035e8 −0.323762
\(207\) 7.59446e8i 0.413633i
\(208\) 5.89916e9i 3.15164i
\(209\) 1.21216e9i 0.635295i
\(210\) 1.30084e9i 0.668875i
\(211\) 3.91593e9i 1.97563i 0.155640 + 0.987814i \(0.450256\pi\)
−0.155640 + 0.987814i \(0.549744\pi\)
\(212\) 8.26217e9 4.09026
\(213\) −1.82990e9 −0.889016
\(214\) 4.64683e9i 2.21565i
\(215\) 3.99389e9i 1.86914i
\(216\) 1.58707e9i 0.729092i
\(217\) 6.47179e8i 0.291867i
\(218\) 7.10310e8 0.314501
\(219\) 9.43429e8i 0.410140i
\(220\) 4.48165e9i 1.91314i
\(221\) 7.68525e8i 0.322173i
\(222\) −7.47222e8 −0.307636
\(223\) −3.32777e9 −1.34565 −0.672827 0.739800i \(-0.734920\pi\)
−0.672827 + 0.739800i \(0.734920\pi\)
\(224\) 6.62578e9i 2.63175i
\(225\) 3.22600e8 0.125874
\(226\) 3.51055e9 1.34568
\(227\) 2.28317e9i 0.859872i 0.902859 + 0.429936i \(0.141464\pi\)
−0.902859 + 0.429936i \(0.858536\pi\)
\(228\) −5.16624e9 −1.91177
\(229\) 4.40320e9i 1.60113i −0.599247 0.800564i \(-0.704533\pi\)
0.599247 0.800564i \(-0.295467\pi\)
\(230\) −8.06427e9 −2.88173
\(231\) 4.58625e8i 0.161068i
\(232\) 1.11551e10i 3.85052i
\(233\) 4.30991e9i 1.46233i −0.682203 0.731163i \(-0.738978\pi\)
0.682203 0.731163i \(-0.261022\pi\)
\(234\) −1.36041e9 −0.453738
\(235\) 4.99443e9i 1.63762i
\(236\) −6.47409e9 6.31175e9i −2.08704 2.03471i
\(237\) −3.03368e8 −0.0961560
\(238\) 1.48308e9i 0.462227i
\(239\) −2.83177e9 −0.867893 −0.433947 0.900939i \(-0.642879\pi\)
−0.433947 + 0.900939i \(0.642879\pi\)
\(240\) 1.02994e10 3.10432
\(241\) −1.47889e9 −0.438396 −0.219198 0.975680i \(-0.570344\pi\)
−0.219198 + 0.975680i \(0.570344\pi\)
\(242\) 4.66385e9i 1.35982i
\(243\) 2.23677e8 0.0641500
\(244\) 4.42711e9i 1.24899i
\(245\) −3.17645e9 −0.881613
\(246\) 3.32260e9i 0.907273i
\(247\) 2.90909e9i 0.781572i
\(248\) 8.38431e9 2.21646
\(249\) 2.38891e9i 0.621446i
\(250\) 5.64588e9i 1.44535i
\(251\) 9.81508e7 0.0247286 0.0123643 0.999924i \(-0.496064\pi\)
0.0123643 + 0.999924i \(0.496064\pi\)
\(252\) 1.95466e9 0.484696
\(253\) −2.84315e9 −0.693934
\(254\) 1.28356e10i 3.08376i
\(255\) 1.34177e9 0.317335
\(256\) 2.84894e10 6.63320
\(257\) 8.52646e9 1.95450 0.977251 0.212086i \(-0.0680256\pi\)
0.977251 + 0.212086i \(0.0680256\pi\)
\(258\) 8.06023e9 1.81915
\(259\) 6.04553e8i 0.134349i
\(260\) 1.07556e10i 2.35364i
\(261\) 1.57216e9 0.338793
\(262\) −2.63231e9 −0.558640
\(263\) −4.65933e9 −0.973868 −0.486934 0.873439i \(-0.661885\pi\)
−0.486934 + 0.873439i \(0.661885\pi\)
\(264\) 5.94156e9 1.22316
\(265\) −8.12265e9 −1.64708
\(266\) 5.61386e9i 1.12133i
\(267\) 1.59346e9i 0.313541i
\(268\) 6.34876e8i 0.123069i
\(269\) 4.27626e9i 0.816687i −0.912828 0.408343i \(-0.866107\pi\)
0.912828 0.408343i \(-0.133893\pi\)
\(270\) 2.37514e9i 0.446925i
\(271\) −8.14416e9 −1.50997 −0.754987 0.655740i \(-0.772357\pi\)
−0.754987 + 0.655740i \(0.772357\pi\)
\(272\) 1.17423e10 2.14524
\(273\) 1.10066e9i 0.198154i
\(274\) 3.26785e9i 0.579775i
\(275\) 1.20772e9i 0.211172i
\(276\) 1.21175e10i 2.08823i
\(277\) 1.03683e10 1.76112 0.880559 0.473936i \(-0.157167\pi\)
0.880559 + 0.473936i \(0.157167\pi\)
\(278\) 2.47589e9i 0.414526i
\(279\) 1.18166e9i 0.195018i
\(280\) 1.36348e10i 2.21829i
\(281\) −2.14005e8 −0.0343241 −0.0171620 0.999853i \(-0.505463\pi\)
−0.0171620 + 0.999853i \(0.505463\pi\)
\(282\) −1.00795e10 −1.59383
\(283\) 9.06708e9i 1.41358i −0.707421 0.706792i \(-0.750142\pi\)
0.707421 0.706792i \(-0.249858\pi\)
\(284\) 2.91974e10 4.48819
\(285\) 5.07899e9 0.769836
\(286\) 5.09298e9i 0.761216i
\(287\) 2.68821e9 0.396219
\(288\) 1.20977e10i 1.75847i
\(289\) −5.44601e9 −0.780705
\(290\) 1.66942e10i 2.36033i
\(291\) 6.32023e9i 0.881376i
\(292\) 1.50531e10i 2.07059i
\(293\) −1.32943e10 −1.80382 −0.901910 0.431923i \(-0.857835\pi\)
−0.901910 + 0.431923i \(0.857835\pi\)
\(294\) 6.41053e9i 0.858034i
\(295\) 6.36476e9 + 6.20517e9i 0.840416 + 0.819343i
\(296\) 7.83208e9 1.02026
\(297\) 8.37385e8i 0.107622i
\(298\) −2.58407e10 −3.27672
\(299\) −6.82333e9 −0.853712
\(300\) −5.14733e9 −0.635472
\(301\) 6.52127e9i 0.794450i
\(302\) −1.51787e10 −1.82477
\(303\) 8.18723e9i 0.971329i
\(304\) 4.44478e10 5.20423
\(305\) 4.35235e9i 0.502949i
\(306\) 2.70789e9i 0.308848i
\(307\) 9.29689e8 0.104661 0.0523304 0.998630i \(-0.483335\pi\)
0.0523304 + 0.998630i \(0.483335\pi\)
\(308\) 7.31769e9i 0.813151i
\(309\) 8.61285e8i 0.0944741i
\(310\) −1.25476e10 −1.35867
\(311\) 2.49791e9 0.267015 0.133508 0.991048i \(-0.457376\pi\)
0.133508 + 0.991048i \(0.457376\pi\)
\(312\) 1.42592e10 1.50480
\(313\) 1.13268e10i 1.18013i −0.807354 0.590067i \(-0.799101\pi\)
0.807354 0.590067i \(-0.200899\pi\)
\(314\) −1.27379e10 −1.31033
\(315\) −1.92165e9 −0.195179
\(316\) 4.84046e9 0.485443
\(317\) 1.91351e10 1.89494 0.947468 0.319850i \(-0.103633\pi\)
0.947468 + 0.319850i \(0.103633\pi\)
\(318\) 1.63927e10i 1.60303i
\(319\) 5.88572e9i 0.568377i
\(320\) −7.20812e10 −6.87419
\(321\) 6.86450e9 0.646530
\(322\) 1.31674e10 1.22484
\(323\) 5.79053e9 0.531996
\(324\) −3.56894e9 −0.323861
\(325\) 2.89844e9i 0.259795i
\(326\) 2.78400e10i 2.46490i
\(327\) 1.04930e9i 0.0917718i
\(328\) 3.48262e10i 3.00892i
\(329\) 8.15496e9i 0.696047i
\(330\) −8.89187e9 −0.749786
\(331\) 7.74326e8 0.0645078 0.0322539 0.999480i \(-0.489731\pi\)
0.0322539 + 0.999480i \(0.489731\pi\)
\(332\) 3.81169e10i 3.13737i
\(333\) 1.10383e9i 0.0897687i
\(334\) 4.00062e10i 3.21471i
\(335\) 6.24155e8i 0.0495579i
\(336\) −1.68170e10 −1.31944
\(337\) 6.97385e8i 0.0540696i 0.999634 + 0.0270348i \(0.00860649\pi\)
−0.999634 + 0.0270348i \(0.991394\pi\)
\(338\) 1.36010e10i 1.04209i
\(339\) 5.18594e9i 0.392671i
\(340\) −2.14090e10 −1.60207
\(341\) −4.42380e9 −0.327173
\(342\) 1.02501e10i 0.749247i
\(343\) 1.20916e10 0.873588
\(344\) −8.44842e10 −6.03311
\(345\) 1.19129e10i 0.840894i
\(346\) −1.16144e10 −0.810390
\(347\) 5.54324e9i 0.382336i 0.981557 + 0.191168i \(0.0612276\pi\)
−0.981557 + 0.191168i \(0.938772\pi\)
\(348\) −2.50850e10 −1.71040
\(349\) 1.82467e10i 1.22994i 0.788552 + 0.614968i \(0.210831\pi\)
−0.788552 + 0.614968i \(0.789169\pi\)
\(350\) 5.59331e9i 0.372732i
\(351\) 2.00965e9i 0.132401i
\(352\) −4.52905e10 −2.95010
\(353\) 2.27785e10i 1.46699i 0.679695 + 0.733494i \(0.262112\pi\)
−0.679695 + 0.733494i \(0.737888\pi\)
\(354\) 1.25229e10 1.28450e10i 0.797429 0.817939i
\(355\) −2.87044e10 −1.80732
\(356\) 2.54248e10i 1.58291i
\(357\) −2.19086e9 −0.134879
\(358\) 2.05608e10 1.25172
\(359\) 2.93931e10 1.76957 0.884786 0.465998i \(-0.154305\pi\)
0.884786 + 0.465998i \(0.154305\pi\)
\(360\) 2.48953e10i 1.48220i
\(361\) 4.93525e9 0.290590
\(362\) 1.43235e10i 0.834094i
\(363\) 6.88964e9 0.396799
\(364\) 1.75619e10i 1.00038i
\(365\) 1.47989e10i 0.833793i
\(366\) −8.78365e9 −0.489498
\(367\) 1.53824e10i 0.847928i 0.905679 + 0.423964i \(0.139362\pi\)
−0.905679 + 0.423964i \(0.860638\pi\)
\(368\) 1.04253e11i 5.68459i
\(369\) −4.90830e9 −0.264744
\(370\) −1.17211e10 −0.625407
\(371\) 1.32628e10 0.700065
\(372\) 1.88542e10i 0.984549i
\(373\) 3.36236e10 1.73704 0.868518 0.495657i \(-0.165073\pi\)
0.868518 + 0.495657i \(0.165073\pi\)
\(374\) −1.01376e10 −0.518140
\(375\) −8.34035e9 −0.421754
\(376\) 1.05649e11 5.28583
\(377\) 1.41252e10i 0.699247i
\(378\) 3.87817e9i 0.189959i
\(379\) −7.79257e9 −0.377680 −0.188840 0.982008i \(-0.560473\pi\)
−0.188840 + 0.982008i \(0.560473\pi\)
\(380\) −8.10391e10 −3.88651
\(381\) 1.89613e10 0.899846
\(382\) 1.66334e10 0.781135
\(383\) −4.04627e9 −0.188044 −0.0940220 0.995570i \(-0.529972\pi\)
−0.0940220 + 0.995570i \(0.529972\pi\)
\(384\) 7.92452e10i 3.64459i
\(385\) 7.19412e9i 0.327442i
\(386\) 4.23439e10i 1.90740i
\(387\) 1.19069e10i 0.530831i
\(388\) 1.00844e11i 4.44962i
\(389\) 2.62751e10 1.14748 0.573742 0.819036i \(-0.305491\pi\)
0.573742 + 0.819036i \(0.305491\pi\)
\(390\) −2.13397e10 −0.922425
\(391\) 1.35818e10i 0.581101i
\(392\) 6.71926e10i 2.84562i
\(393\) 3.88856e9i 0.163012i
\(394\) 9.32457e9i 0.386940i
\(395\) −4.75872e9 −0.195480
\(396\) 1.33611e10i 0.543327i
\(397\) 1.38325e10i 0.556852i −0.960458 0.278426i \(-0.910187\pi\)
0.960458 0.278426i \(-0.0898127\pi\)
\(398\) 2.47801e10i 0.987575i
\(399\) −8.29305e9 −0.327207
\(400\) 4.42851e10 1.72989
\(401\) 1.03051e10i 0.398544i −0.979944 0.199272i \(-0.936142\pi\)
0.979944 0.199272i \(-0.0638577\pi\)
\(402\) −1.25963e9 −0.0482325
\(403\) −1.06167e10 −0.402505
\(404\) 1.30633e11i 4.90375i
\(405\) 3.50867e9 0.130413
\(406\) 2.72584e10i 1.00322i
\(407\) −4.13242e9 −0.150601
\(408\) 2.83830e10i 1.02428i
\(409\) 4.00344e10i 1.43067i 0.698781 + 0.715335i \(0.253726\pi\)
−0.698781 + 0.715335i \(0.746274\pi\)
\(410\) 5.21193e10i 1.84444i
\(411\) −4.82741e9 −0.169179
\(412\) 1.37424e10i 0.476952i
\(413\) −1.03925e10 1.01319e10i −0.357206 0.348249i
\(414\) −2.40419e10 −0.818404
\(415\) 3.74732e10i 1.26336i
\(416\) −1.08694e11 −3.62936
\(417\) 3.65749e9 0.120959
\(418\) −3.83736e10 −1.25698
\(419\) 2.85527e10i 0.926383i 0.886258 + 0.463192i \(0.153296\pi\)
−0.886258 + 0.463192i \(0.846704\pi\)
\(420\) 3.06614e10 0.985359
\(421\) 3.69925e10i 1.17757i 0.808291 + 0.588783i \(0.200393\pi\)
−0.808291 + 0.588783i \(0.799607\pi\)
\(422\) 1.23967e11 3.90892
\(423\) 1.48898e10i 0.465080i
\(424\) 1.71821e11i 5.31635i
\(425\) 5.76934e9 0.176836
\(426\) 5.79295e10i 1.75898i
\(427\) 7.10657e9i 0.213771i
\(428\) −1.09528e11 −3.26400
\(429\) −7.52357e9 −0.222124
\(430\) 1.26435e11 3.69823
\(431\) 2.20682e9i 0.0639525i −0.999489 0.0319763i \(-0.989820\pi\)
0.999489 0.0319763i \(-0.0101801\pi\)
\(432\) 3.07054e10 0.881617
\(433\) 4.65743e10 1.32493 0.662467 0.749091i \(-0.269509\pi\)
0.662467 + 0.749091i \(0.269509\pi\)
\(434\) 2.04879e10 0.577481
\(435\) 2.46614e10 0.688748
\(436\) 1.67424e10i 0.463309i
\(437\) 5.14111e10i 1.40971i
\(438\) −2.98663e10 −0.811493
\(439\) 1.99444e10 0.536985 0.268492 0.963282i \(-0.413475\pi\)
0.268492 + 0.963282i \(0.413475\pi\)
\(440\) 9.32010e10 2.48662
\(441\) −9.46992e9 −0.250376
\(442\) −2.43293e10 −0.637442
\(443\) 2.86671e10i 0.744335i 0.928166 + 0.372167i \(0.121385\pi\)
−0.928166 + 0.372167i \(0.878615\pi\)
\(444\) 1.76124e10i 0.453197i
\(445\) 2.49954e10i 0.637412i
\(446\) 1.05348e11i 2.66247i
\(447\) 3.81730e10i 0.956151i
\(448\) 1.17695e11 2.92177
\(449\) −3.58071e10 −0.881015 −0.440507 0.897749i \(-0.645201\pi\)
−0.440507 + 0.897749i \(0.645201\pi\)
\(450\) 1.02126e10i 0.249050i
\(451\) 1.83753e10i 0.444148i
\(452\) 8.27456e10i 1.98240i
\(453\) 2.24227e10i 0.532469i
\(454\) 7.22785e10 1.70132
\(455\) 1.72653e10i 0.402836i
\(456\) 1.07438e11i 2.48484i
\(457\) 6.09304e10i 1.39691i 0.715653 + 0.698456i \(0.246129\pi\)
−0.715653 + 0.698456i \(0.753871\pi\)
\(458\) −1.39393e11 −3.16795
\(459\) 4.00021e9 0.0901223
\(460\) 1.90079e11i 4.24525i
\(461\) 3.61230e10 0.799797 0.399898 0.916559i \(-0.369045\pi\)
0.399898 + 0.916559i \(0.369045\pi\)
\(462\) 1.45188e10 0.318685
\(463\) 1.00251e10i 0.218155i −0.994033 0.109077i \(-0.965210\pi\)
0.994033 0.109077i \(-0.0347896\pi\)
\(464\) 2.15819e11 4.65605
\(465\) 1.85359e10i 0.396461i
\(466\) −1.36439e11 −2.89332
\(467\) 3.09772e10i 0.651291i −0.945492 0.325646i \(-0.894418\pi\)
0.945492 0.325646i \(-0.105582\pi\)
\(468\) 3.20655e10i 0.668428i
\(469\) 1.01913e9i 0.0210638i
\(470\) −1.58109e11 −3.24016
\(471\) 1.88171e10i 0.382356i
\(472\) −1.31260e11 + 1.34636e11i −2.64463 + 2.71265i
\(473\) 4.45762e10 0.890550
\(474\) 9.60377e9i 0.190252i
\(475\) 2.18386e10 0.428993
\(476\) 3.49569e10 0.680933
\(477\) −2.42160e10 −0.467765
\(478\) 8.96458e10i 1.71719i
\(479\) 5.23904e10 0.995199 0.497599 0.867407i \(-0.334215\pi\)
0.497599 + 0.867407i \(0.334215\pi\)
\(480\) 1.89769e11i 3.57487i
\(481\) −9.91747e9 −0.185277
\(482\) 4.68173e10i 0.867398i
\(483\) 1.94515e10i 0.357409i
\(484\) −1.09929e11 −2.00324
\(485\) 9.91410e10i 1.79179i
\(486\) 7.08099e9i 0.126925i
\(487\) −6.48399e10 −1.15273 −0.576364 0.817193i \(-0.695529\pi\)
−0.576364 + 0.817193i \(0.695529\pi\)
\(488\) 9.20667e10 1.62339
\(489\) −4.11265e10 −0.719261
\(490\) 1.00558e11i 1.74434i
\(491\) 8.45331e10 1.45446 0.727229 0.686395i \(-0.240808\pi\)
0.727229 + 0.686395i \(0.240808\pi\)
\(492\) 7.83155e10 1.33656
\(493\) 2.81163e10 0.475960
\(494\) −9.20934e10 −1.54640
\(495\) 1.31355e10i 0.218789i
\(496\) 1.62213e11i 2.68015i
\(497\) 4.68689e10 0.768173
\(498\) −7.56262e10 −1.22958
\(499\) 3.58704e10 0.578540 0.289270 0.957248i \(-0.406587\pi\)
0.289270 + 0.957248i \(0.406587\pi\)
\(500\) 1.33076e11 2.12922
\(501\) −5.90989e10 −0.938056
\(502\) 3.10717e9i 0.0489272i
\(503\) 3.60231e10i 0.562742i 0.959599 + 0.281371i \(0.0907891\pi\)
−0.959599 + 0.281371i \(0.909211\pi\)
\(504\) 4.06494e10i 0.629987i
\(505\) 1.28427e11i 1.97466i
\(506\) 9.00061e10i 1.37300i
\(507\) 2.00920e10 0.304082
\(508\) −3.02541e11 −4.54287
\(509\) 7.97449e9i 0.118804i −0.998234 0.0594021i \(-0.981081\pi\)
0.998234 0.0594021i \(-0.0189194\pi\)
\(510\) 4.24768e10i 0.627871i
\(511\) 2.41638e10i 0.354391i
\(512\) 4.68094e11i 6.81166i
\(513\) 1.51419e10 0.218631
\(514\) 2.69923e11i 3.86712i
\(515\) 1.35104e10i 0.192061i
\(516\) 1.89984e11i 2.67990i
\(517\) −5.57433e10 −0.780244
\(518\) 1.91384e10 0.265820
\(519\) 1.71574e10i 0.236473i
\(520\) 2.23675e11 3.05917
\(521\) 1.27604e11 1.73186 0.865931 0.500164i \(-0.166727\pi\)
0.865931 + 0.500164i \(0.166727\pi\)
\(522\) 4.97701e10i 0.670327i
\(523\) −6.01563e10 −0.804034 −0.402017 0.915632i \(-0.631691\pi\)
−0.402017 + 0.915632i \(0.631691\pi\)
\(524\) 6.20449e10i 0.822964i
\(525\) −8.26269e9 −0.108764
\(526\) 1.47501e11i 1.92687i
\(527\) 2.11326e10i 0.273975i
\(528\) 1.14952e11i 1.47905i
\(529\) −4.22749e10 −0.539834
\(530\) 2.57140e11i 3.25886i
\(531\) 1.89752e10 + 1.84994e10i 0.238676 + 0.232691i
\(532\) 1.32322e11 1.65190
\(533\) 4.40991e10i 0.546413i
\(534\) −5.04443e10 −0.620364
\(535\) 1.07679e11 1.31436
\(536\) 1.32030e10 0.159960
\(537\) 3.03733e10i 0.365254i
\(538\) −1.35374e11 −1.61587
\(539\) 3.54527e10i 0.420044i
\(540\) −5.59834e10 −0.658392
\(541\) 3.14461e10i 0.367095i −0.983011 0.183547i \(-0.941242\pi\)
0.983011 0.183547i \(-0.0587580\pi\)
\(542\) 2.57821e11i 2.98759i
\(543\) −2.11593e10 −0.243390
\(544\) 2.16354e11i 2.47042i
\(545\) 1.64596e10i 0.186567i
\(546\) 3.48438e10 0.392062
\(547\) 9.18262e10 1.02569 0.512846 0.858480i \(-0.328591\pi\)
0.512846 + 0.858480i \(0.328591\pi\)
\(548\) 7.70249e10 0.854101
\(549\) 1.29756e10i 0.142836i
\(550\) −3.82331e10 −0.417820
\(551\) 1.06428e11 1.15465
\(552\) 2.51998e11 2.71419
\(553\) 7.77010e9 0.0830857
\(554\) 3.28231e11i 3.48450i
\(555\) 1.73150e10i 0.182495i
\(556\) −5.83580e10 −0.610662
\(557\) 1.00723e11 1.04643 0.523215 0.852201i \(-0.324733\pi\)
0.523215 + 0.852201i \(0.324733\pi\)
\(558\) −3.74080e10 −0.385858
\(559\) 1.06979e11 1.09560
\(560\) −2.63796e11 −2.68235
\(561\) 1.49757e10i 0.151194i
\(562\) 6.77479e9i 0.0679126i
\(563\) 1.45204e10i 0.144525i 0.997386 + 0.0722626i \(0.0230220\pi\)
−0.997386 + 0.0722626i \(0.976978\pi\)
\(564\) 2.37578e11i 2.34796i
\(565\) 8.13483e10i 0.798279i
\(566\) −2.87038e11 −2.79688
\(567\) −5.72900e9 −0.0554302
\(568\) 6.07194e11i 5.83357i
\(569\) 2.82153e10i 0.269176i 0.990902 + 0.134588i \(0.0429711\pi\)
−0.990902 + 0.134588i \(0.957029\pi\)
\(570\) 1.60787e11i 1.52318i
\(571\) 3.31259e10i 0.311619i −0.987787 0.155809i \(-0.950201\pi\)
0.987787 0.155809i \(-0.0497985\pi\)
\(572\) 1.20044e11 1.12139
\(573\) 2.45715e10i 0.227936i
\(574\) 8.51011e10i 0.783949i
\(575\) 5.12229e10i 0.468590i
\(576\) −2.14895e11 −1.95225
\(577\) 2.26829e10 0.204643 0.102321 0.994751i \(-0.467373\pi\)
0.102321 + 0.994751i \(0.467373\pi\)
\(578\) 1.72405e11i 1.54468i
\(579\) 6.25523e10 0.556582
\(580\) −3.93490e11 −3.47714
\(581\) 6.11867e10i 0.536973i
\(582\) 2.00081e11 1.74387
\(583\) 9.06577e10i 0.784748i
\(584\) 3.13046e11 2.69127
\(585\) 3.15240e10i 0.269165i
\(586\) 4.20858e11i 3.56899i
\(587\) 2.15182e11i 1.81239i −0.422855 0.906197i \(-0.638972\pi\)
0.422855 0.906197i \(-0.361028\pi\)
\(588\) 1.51100e11 1.26402
\(589\) 7.99930e10i 0.664647i
\(590\) 1.96438e11 2.01490e11i 1.62113 1.66282i
\(591\) 1.37747e10 0.112910
\(592\) 1.51529e11i 1.23370i
\(593\) −1.24514e11 −1.00693 −0.503464 0.864016i \(-0.667941\pi\)
−0.503464 + 0.864016i \(0.667941\pi\)
\(594\) −2.65092e10 −0.212937
\(595\) −3.43666e10 −0.274200
\(596\) 6.09079e11i 4.82712i
\(597\) 3.66062e10 0.288176
\(598\) 2.16007e11i 1.68913i
\(599\) 1.38265e11 1.07400 0.536999 0.843583i \(-0.319558\pi\)
0.536999 + 0.843583i \(0.319558\pi\)
\(600\) 1.07045e11i 0.825961i
\(601\) 1.22659e11i 0.940160i −0.882624 0.470080i \(-0.844225\pi\)
0.882624 0.470080i \(-0.155775\pi\)
\(602\) −2.06445e11 −1.57188
\(603\) 1.86079e9i 0.0140743i
\(604\) 3.57770e11i 2.68817i
\(605\) 1.08073e11 0.806670
\(606\) −2.59184e11 −1.92184
\(607\) −1.20353e11 −0.886546 −0.443273 0.896387i \(-0.646183\pi\)
−0.443273 + 0.896387i \(0.646183\pi\)
\(608\) 8.18963e11i 5.99308i
\(609\) −4.02674e10 −0.292741
\(610\) −1.37783e11 −0.995122
\(611\) −1.33779e11 −0.959896
\(612\) −6.38264e10 −0.454982
\(613\) 6.28488e9i 0.0445097i 0.999752 + 0.0222549i \(0.00708453\pi\)
−0.999752 + 0.0222549i \(0.992915\pi\)
\(614\) 2.94313e10i 0.207079i
\(615\) −7.69930e10 −0.538209
\(616\) −1.52180e11 −1.05690
\(617\) 1.45402e11 1.00330 0.501649 0.865071i \(-0.332727\pi\)
0.501649 + 0.865071i \(0.332727\pi\)
\(618\) −2.72658e10 −0.186924
\(619\) −7.31126e10 −0.498000 −0.249000 0.968503i \(-0.580102\pi\)
−0.249000 + 0.968503i \(0.580102\pi\)
\(620\) 2.95753e11i 2.00153i
\(621\) 3.55158e10i 0.238811i
\(622\) 7.90768e10i 0.528309i
\(623\) 4.08128e10i 0.270922i
\(624\) 2.75876e11i 1.81960i
\(625\) −1.88450e11 −1.23502
\(626\) −3.58576e11 −2.33498
\(627\) 5.66872e10i 0.366787i
\(628\) 3.00240e11i 1.93032i
\(629\) 1.97407e10i 0.126113i
\(630\) 6.08341e10i 0.386175i
\(631\) −2.88787e11 −1.82163 −0.910815 0.412815i \(-0.864545\pi\)
−0.910815 + 0.412815i \(0.864545\pi\)
\(632\) 1.00663e11i 0.630959i
\(633\) 1.83130e11i 1.14063i
\(634\) 6.05764e11i 3.74927i
\(635\) 2.97433e11 1.82934
\(636\) 3.86383e11 2.36151
\(637\) 8.50836e10i 0.516759i
\(638\) −1.86325e11 −1.12458
\(639\) −8.55761e10 −0.513274
\(640\) 1.24306e12i 7.40924i
\(641\) −3.01745e11 −1.78734 −0.893671 0.448723i \(-0.851879\pi\)
−0.893671 + 0.448723i \(0.851879\pi\)
\(642\) 2.17311e11i 1.27921i
\(643\) 1.54047e11 0.901175 0.450588 0.892732i \(-0.351215\pi\)
0.450588 + 0.892732i \(0.351215\pi\)
\(644\) 3.10364e11i 1.80438i
\(645\) 1.86776e11i 1.07915i
\(646\) 1.83312e11i 1.05259i
\(647\) 4.93100e10 0.281396 0.140698 0.990053i \(-0.455065\pi\)
0.140698 + 0.990053i \(0.455065\pi\)
\(648\) 7.42201e10i 0.420941i
\(649\) 6.92565e10 7.10377e10i 0.390375 0.400415i
\(650\) −9.17563e10 −0.514023
\(651\) 3.02656e10i 0.168510i
\(652\) 6.56204e11 3.63119
\(653\) 7.30997e10 0.402034 0.201017 0.979588i \(-0.435575\pi\)
0.201017 + 0.979588i \(0.435575\pi\)
\(654\) 3.32179e10 0.181577
\(655\) 6.09972e10i 0.331394i
\(656\) −6.73789e11 −3.63838
\(657\) 4.41198e10i 0.236795i
\(658\) 2.58163e11 1.37718
\(659\) 2.17792e11i 1.15479i 0.816467 + 0.577393i \(0.195930\pi\)
−0.816467 + 0.577393i \(0.804070\pi\)
\(660\) 2.09586e11i 1.10455i
\(661\) −3.45668e10 −0.181073 −0.0905363 0.995893i \(-0.528858\pi\)
−0.0905363 + 0.995893i \(0.528858\pi\)
\(662\) 2.45130e10i 0.127633i
\(663\) 3.59404e10i 0.186007i
\(664\) 7.92684e11 4.07782
\(665\) −1.30087e11 −0.665193
\(666\) −3.49441e10 −0.177614
\(667\) 2.49630e11i 1.26123i
\(668\) 9.42967e11 4.73577
\(669\) −1.55624e11 −0.776914
\(670\) −1.97590e10 −0.0980540
\(671\) −4.85770e10 −0.239630
\(672\) 3.09857e11i 1.51944i
\(673\) 2.40096e11i 1.17038i −0.810898 0.585188i \(-0.801021\pi\)
0.810898 0.585188i \(-0.198979\pi\)
\(674\) 2.20772e10 0.106981
\(675\) 1.50865e10 0.0726732
\(676\) −3.20583e11 −1.53516
\(677\) 5.36933e10 0.255602 0.127801 0.991800i \(-0.459208\pi\)
0.127801 + 0.991800i \(0.459208\pi\)
\(678\) 1.64172e11 0.776929
\(679\) 1.61879e11i 0.761572i
\(680\) 4.45224e11i 2.08230i
\(681\) 1.06773e11i 0.496447i
\(682\) 1.40045e11i 0.647336i
\(683\) 2.99414e11i 1.37591i 0.725754 + 0.687954i \(0.241491\pi\)
−0.725754 + 0.687954i \(0.758509\pi\)
\(684\) −2.41601e11 −1.10376
\(685\) −7.57242e10 −0.343932
\(686\) 3.82785e11i 1.72846i
\(687\) 2.05917e11i 0.924412i
\(688\) 1.63453e12i 7.29524i
\(689\) 2.17571e11i 0.965437i
\(690\) −3.77129e11 −1.66377
\(691\) 4.19619e11i 1.84053i −0.391296 0.920265i \(-0.627973\pi\)
0.391296 0.920265i \(-0.372027\pi\)
\(692\) 2.73759e11i 1.19383i
\(693\) 2.14477e10i 0.0929927i
\(694\) 1.75483e11 0.756480
\(695\) 5.73725e10 0.245903
\(696\) 5.21670e11i 2.22310i
\(697\) −8.77793e10 −0.371930
\(698\) 5.77639e11 2.43352
\(699\) 2.01554e11i 0.844274i
\(700\) 1.31837e11 0.549094
\(701\) 1.02598e11i 0.424879i −0.977174 0.212439i \(-0.931859\pi\)
0.977174 0.212439i \(-0.0681408\pi\)
\(702\) −6.36199e10 −0.261966
\(703\) 7.47243e10i 0.305943i
\(704\) 8.04505e11i 3.27520i
\(705\) 2.33566e11i 0.945483i
\(706\) 7.21104e11 2.90254
\(707\) 2.09698e11i 0.839297i
\(708\) −3.02763e11 2.95171e11i −1.20495 1.17474i
\(709\) −1.17044e11 −0.463195 −0.231597 0.972812i \(-0.574395\pi\)
−0.231597 + 0.972812i \(0.574395\pi\)
\(710\) 9.08700e11i 3.57591i
\(711\) −1.41871e10 −0.0555157
\(712\) 5.28737e11 2.05740
\(713\) −1.87625e11 −0.725995
\(714\) 6.93566e10i 0.266867i
\(715\) −1.18017e11 −0.451565
\(716\) 4.84628e11i 1.84398i
\(717\) −1.32429e11 −0.501078
\(718\) 9.30503e11i 3.50123i
\(719\) 1.38582e10i 0.0518552i 0.999664 + 0.0259276i \(0.00825394\pi\)
−0.999664 + 0.0259276i \(0.991746\pi\)
\(720\) 4.81654e11 1.79228
\(721\) 2.20599e10i 0.0816324i
\(722\) 1.56236e11i 0.574953i
\(723\) −6.91606e10 −0.253108
\(724\) 3.37613e11 1.22875
\(725\) 1.06039e11 0.383806
\(726\) 2.18107e11i 0.785095i
\(727\) −3.58114e11 −1.28199 −0.640993 0.767547i \(-0.721477\pi\)
−0.640993 + 0.767547i \(0.721477\pi\)
\(728\) −3.65219e11 −1.30025
\(729\) 1.04604e10 0.0370370
\(730\) −4.68491e11 −1.64972
\(731\) 2.12942e11i 0.745748i
\(732\) 2.07035e11i 0.721108i
\(733\) 2.02524e11 0.701552 0.350776 0.936459i \(-0.385918\pi\)
0.350776 + 0.936459i \(0.385918\pi\)
\(734\) 4.86962e11 1.67769
\(735\) −1.48548e11 −0.509000
\(736\) −1.92090e12 −6.54625
\(737\) −6.96625e9 −0.0236118
\(738\) 1.55383e11i 0.523814i
\(739\) 1.94915e11i 0.653532i 0.945105 + 0.326766i \(0.105959\pi\)
−0.945105 + 0.326766i \(0.894041\pi\)
\(740\) 2.76274e11i 0.921324i
\(741\) 1.36044e11i 0.451241i
\(742\) 4.19862e11i 1.38513i
\(743\) 3.03802e11 0.996862 0.498431 0.866929i \(-0.333910\pi\)
0.498431 + 0.866929i \(0.333910\pi\)
\(744\) 3.92096e11 1.27968
\(745\) 5.98794e11i 1.94380i
\(746\) 1.06443e12i 3.43685i
\(747\) 1.11718e11i 0.358792i
\(748\) 2.38948e11i 0.763302i
\(749\) −1.75819e11 −0.558648
\(750\) 2.64032e11i 0.834471i
\(751\) 2.65517e11i 0.834703i 0.908745 + 0.417351i \(0.137042\pi\)
−0.908745 + 0.417351i \(0.862958\pi\)
\(752\) 2.04401e12i 6.39163i
\(753\) 4.59006e9 0.0142770
\(754\) −4.47165e11 −1.38351
\(755\) 3.51729e11i 1.08248i
\(756\) 9.14104e10 0.279839
\(757\) −3.43882e11 −1.04719 −0.523595 0.851967i \(-0.675409\pi\)
−0.523595 + 0.851967i \(0.675409\pi\)
\(758\) 2.46691e11i 0.747268i
\(759\) −1.32961e11 −0.400643
\(760\) 1.68530e12i 5.05153i
\(761\) 1.02985e11 0.307069 0.153534 0.988143i \(-0.450934\pi\)
0.153534 + 0.988143i \(0.450934\pi\)
\(762\) 6.00261e11i 1.78041i
\(763\) 2.68755e10i 0.0792974i
\(764\) 3.92057e11i 1.15074i
\(765\) 6.27486e10 0.183214
\(766\) 1.28093e11i 0.372059i
\(767\) 1.66210e11 1.70485e11i 0.480259 0.492611i
\(768\) 1.33232e12 3.82968
\(769\) 2.68135e11i 0.766741i 0.923595 + 0.383370i \(0.125237\pi\)
−0.923595 + 0.383370i \(0.874763\pi\)
\(770\) 2.27746e11 0.647869
\(771\) 3.98743e11 1.12843
\(772\) −9.98068e11 −2.80990
\(773\) 1.90043e11i 0.532271i 0.963936 + 0.266136i \(0.0857469\pi\)
−0.963936 + 0.266136i \(0.914253\pi\)
\(774\) 3.76940e11 1.05029
\(775\) 7.97002e10i 0.220929i
\(776\) −2.09717e12 −5.78343
\(777\) 2.82721e10i 0.0775666i
\(778\) 8.31796e11i 2.27038i
\(779\) −3.32270e11 −0.902279
\(780\) 5.02989e11i 1.35888i
\(781\) 3.20373e11i 0.861095i
\(782\) −4.29962e11 −1.149