Properties

Label 177.9.c.a.58.11
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 58.11
Character \(\chi\) \(=\) 177.58
Dual form 177.9.c.a.58.70

$q$-expansion

\(f(q)\) \(=\) \(q-25.1007i q^{2} -46.7654 q^{3} -374.043 q^{4} +458.555 q^{5} +1173.84i q^{6} -1157.18 q^{7} +2962.95i q^{8} +2187.00 q^{9} +O(q^{10})\) \(q-25.1007i q^{2} -46.7654 q^{3} -374.043 q^{4} +458.555 q^{5} +1173.84i q^{6} -1157.18 q^{7} +2962.95i q^{8} +2187.00 q^{9} -11510.0i q^{10} -15446.5i q^{11} +17492.3 q^{12} +19712.2i q^{13} +29046.0i q^{14} -21444.5 q^{15} -21382.9 q^{16} -208.117 q^{17} -54895.1i q^{18} -32459.5 q^{19} -171519. q^{20} +54116.1 q^{21} -387717. q^{22} -244303. i q^{23} -138564. i q^{24} -180353. q^{25} +494789. q^{26} -102276. q^{27} +432836. q^{28} -920152. q^{29} +538270. i q^{30} +725461. i q^{31} +1.29524e6i q^{32} +722362. i q^{33} +5223.87i q^{34} -530631. q^{35} -818032. q^{36} +2.65720e6i q^{37} +814755. i q^{38} -921849. i q^{39} +1.35868e6i q^{40} +3.07208e6 q^{41} -1.35835e6i q^{42} +5.98941e6i q^{43} +5.77766e6i q^{44} +1.00286e6 q^{45} -6.13215e6 q^{46} -8.25605e6i q^{47} +999980. q^{48} -4.42573e6 q^{49} +4.52697e6i q^{50} +9732.67 q^{51} -7.37321e6i q^{52} +7.09542e6 q^{53} +2.56719e6i q^{54} -7.08307e6i q^{55} -3.42868e6i q^{56} +1.51798e6 q^{57} +2.30964e7i q^{58} +(1.16388e7 + 3.37193e6i) q^{59} +8.02115e6 q^{60} +7.65261e6i q^{61} +1.82096e7 q^{62} -2.53076e6 q^{63} +2.70374e7 q^{64} +9.03913e6i q^{65} +1.81318e7 q^{66} +1.47421e7i q^{67} +77844.7 q^{68} +1.14249e7i q^{69} +1.33192e7i q^{70} +3.87749e6 q^{71} +6.47998e6i q^{72} -1.72671e7i q^{73} +6.66974e7 q^{74} +8.43426e6 q^{75} +1.21412e7 q^{76} +1.78744e7i q^{77} -2.31390e7 q^{78} -6.10409e7 q^{79} -9.80523e6 q^{80} +4.78297e6 q^{81} -7.71112e7i q^{82} +7.83794e6i q^{83} -2.02417e7 q^{84} -95433.0 q^{85} +1.50338e8 q^{86} +4.30313e7 q^{87} +4.57673e7 q^{88} -8.95553e7i q^{89} -2.51724e7i q^{90} -2.28106e7i q^{91} +9.13796e7i q^{92} -3.39265e7i q^{93} -2.07232e8 q^{94} -1.48845e7 q^{95} -6.05724e7i q^{96} +1.08068e8i q^{97} +1.11089e8i q^{98} -3.37815e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} + O(q^{10}) \) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} - 22680q^{12} - 59616q^{15} + 1199848q^{16} - 10608q^{17} - 27516q^{19} - 146436q^{20} - 974696q^{22} + 5718040q^{25} - 797484q^{26} - 3133000q^{28} + 1725924q^{29} + 4318800q^{35} - 22394880q^{36} - 732180q^{41} + 22752084q^{46} + 8703936q^{48} + 55899176q^{49} - 10373832q^{51} - 39265944q^{53} - 11408040q^{57} - 33575112q^{59} - 18034488q^{60} + 13038600q^{62} + 349920q^{63} - 241654260q^{64} - 35711928q^{66} + 36772608q^{68} - 235272660q^{71} - 63050712q^{74} + 74363184q^{75} + 9454680q^{76} - 10865988q^{78} + 17252580q^{79} + 318203976q^{80} + 382637520q^{81} - 20743128q^{84} - 27245820q^{85} + 105666984q^{86} + 29437992q^{87} + 82079788q^{88} + 121215992q^{94} - 690837276q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 25.1007i 1.56879i −0.620261 0.784395i \(-0.712973\pi\)
0.620261 0.784395i \(-0.287027\pi\)
\(3\) −46.7654 −0.577350
\(4\) −374.043 −1.46110
\(5\) 458.555 0.733687 0.366844 0.930283i \(-0.380438\pi\)
0.366844 + 0.930283i \(0.380438\pi\)
\(6\) 1173.84i 0.905742i
\(7\) −1157.18 −0.481959 −0.240979 0.970530i \(-0.577469\pi\)
−0.240979 + 0.970530i \(0.577469\pi\)
\(8\) 2962.95i 0.723377i
\(9\) 2187.00 0.333333
\(10\) 11510.0i 1.15100i
\(11\) 15446.5i 1.05502i −0.849550 0.527509i \(-0.823126\pi\)
0.849550 0.527509i \(-0.176874\pi\)
\(12\) 17492.3 0.843569
\(13\) 19712.2i 0.690179i 0.938570 + 0.345090i \(0.112151\pi\)
−0.938570 + 0.345090i \(0.887849\pi\)
\(14\) 29046.0i 0.756092i
\(15\) −21444.5 −0.423595
\(16\) −21382.9 −0.326277
\(17\) −208.117 −0.00249179 −0.00124590 0.999999i \(-0.500397\pi\)
−0.00124590 + 0.999999i \(0.500397\pi\)
\(18\) 54895.1i 0.522930i
\(19\) −32459.5 −0.249074 −0.124537 0.992215i \(-0.539744\pi\)
−0.124537 + 0.992215i \(0.539744\pi\)
\(20\) −171519. −1.07199
\(21\) 54116.1 0.278259
\(22\) −387717. −1.65510
\(23\) 244303.i 0.873005i −0.899703 0.436502i \(-0.856217\pi\)
0.899703 0.436502i \(-0.143783\pi\)
\(24\) 138564.i 0.417642i
\(25\) −180353. −0.461703
\(26\) 494789. 1.08275
\(27\) −102276. −0.192450
\(28\) 432836. 0.704192
\(29\) −920152. −1.30097 −0.650485 0.759519i \(-0.725435\pi\)
−0.650485 + 0.759519i \(0.725435\pi\)
\(30\) 538270.i 0.664531i
\(31\) 725461.i 0.785538i 0.919637 + 0.392769i \(0.128483\pi\)
−0.919637 + 0.392769i \(0.871517\pi\)
\(32\) 1.29524e6i 1.23524i
\(33\) 722362.i 0.609115i
\(34\) 5223.87i 0.00390910i
\(35\) −530631. −0.353607
\(36\) −818032. −0.487035
\(37\) 2.65720e6i 1.41781i 0.705306 + 0.708903i \(0.250810\pi\)
−0.705306 + 0.708903i \(0.749190\pi\)
\(38\) 814755.i 0.390744i
\(39\) 921849.i 0.398475i
\(40\) 1.35868e6i 0.530733i
\(41\) 3.07208e6 1.08717 0.543584 0.839355i \(-0.317067\pi\)
0.543584 + 0.839355i \(0.317067\pi\)
\(42\) 1.35835e6i 0.436530i
\(43\) 5.98941e6i 1.75190i 0.482400 + 0.875951i \(0.339765\pi\)
−0.482400 + 0.875951i \(0.660235\pi\)
\(44\) 5.77766e6i 1.54149i
\(45\) 1.00286e6 0.244562
\(46\) −6.13215e6 −1.36956
\(47\) 8.25605e6i 1.69192i −0.533243 0.845962i \(-0.679027\pi\)
0.533243 0.845962i \(-0.320973\pi\)
\(48\) 999980. 0.188376
\(49\) −4.42573e6 −0.767716
\(50\) 4.52697e6i 0.724315i
\(51\) 9732.67 0.00143864
\(52\) 7.37321e6i 1.00842i
\(53\) 7.09542e6 0.899238 0.449619 0.893220i \(-0.351560\pi\)
0.449619 + 0.893220i \(0.351560\pi\)
\(54\) 2.56719e6i 0.301914i
\(55\) 7.08307e6i 0.774053i
\(56\) 3.42868e6i 0.348638i
\(57\) 1.51798e6 0.143803
\(58\) 2.30964e7i 2.04095i
\(59\) 1.16388e7 + 3.37193e6i 0.960502 + 0.278273i
\(60\) 8.02115e6 0.618916
\(61\) 7.65261e6i 0.552701i 0.961057 + 0.276351i \(0.0891251\pi\)
−0.961057 + 0.276351i \(0.910875\pi\)
\(62\) 1.82096e7 1.23235
\(63\) −2.53076e6 −0.160653
\(64\) 2.70374e7 1.61155
\(65\) 9.03913e6i 0.506376i
\(66\) 1.81318e7 0.955573
\(67\) 1.47421e7i 0.731579i 0.930698 + 0.365790i \(0.119201\pi\)
−0.930698 + 0.365790i \(0.880799\pi\)
\(68\) 77844.7 0.00364077
\(69\) 1.14249e7i 0.504030i
\(70\) 1.33192e7i 0.554735i
\(71\) 3.87749e6 0.152587 0.0762935 0.997085i \(-0.475691\pi\)
0.0762935 + 0.997085i \(0.475691\pi\)
\(72\) 6.47998e6i 0.241126i
\(73\) 1.72671e7i 0.608035i −0.952666 0.304018i \(-0.901672\pi\)
0.952666 0.304018i \(-0.0983282\pi\)
\(74\) 6.66974e7 2.22424
\(75\) 8.43426e6 0.266564
\(76\) 1.21412e7 0.363923
\(77\) 1.78744e7i 0.508475i
\(78\) −2.31390e7 −0.625124
\(79\) −6.10409e7 −1.56716 −0.783579 0.621293i \(-0.786608\pi\)
−0.783579 + 0.621293i \(0.786608\pi\)
\(80\) −9.80523e6 −0.239386
\(81\) 4.78297e6 0.111111
\(82\) 7.71112e7i 1.70554i
\(83\) 7.83794e6i 0.165154i 0.996585 + 0.0825771i \(0.0263151\pi\)
−0.996585 + 0.0825771i \(0.973685\pi\)
\(84\) −2.02417e7 −0.406565
\(85\) −95433.0 −0.00182820
\(86\) 1.50338e8 2.74837
\(87\) 4.30313e7 0.751116
\(88\) 4.57673e7 0.763176
\(89\) 8.95553e7i 1.42735i −0.700476 0.713676i \(-0.747029\pi\)
0.700476 0.713676i \(-0.252971\pi\)
\(90\) 2.51724e7i 0.383667i
\(91\) 2.28106e7i 0.332638i
\(92\) 9.13796e7i 1.27555i
\(93\) 3.39265e7i 0.453531i
\(94\) −2.07232e8 −2.65428
\(95\) −1.48845e7 −0.182742
\(96\) 6.05724e7i 0.713165i
\(97\) 1.08068e8i 1.22070i 0.792131 + 0.610351i \(0.208971\pi\)
−0.792131 + 0.610351i \(0.791029\pi\)
\(98\) 1.11089e8i 1.20439i
\(99\) 3.37815e7i 0.351672i
\(100\) 6.74596e7 0.674596
\(101\) 4.86906e7i 0.467907i 0.972248 + 0.233954i \(0.0751664\pi\)
−0.972248 + 0.233954i \(0.924834\pi\)
\(102\) 244296.i 0.00225692i
\(103\) 1.01995e8i 0.906213i −0.891456 0.453106i \(-0.850316\pi\)
0.891456 0.453106i \(-0.149684\pi\)
\(104\) −5.84064e7 −0.499260
\(105\) 2.48152e7 0.204155
\(106\) 1.78100e8i 1.41072i
\(107\) −6.84585e6 −0.0522267 −0.0261133 0.999659i \(-0.508313\pi\)
−0.0261133 + 0.999659i \(0.508313\pi\)
\(108\) 3.82556e7 0.281190
\(109\) 2.20679e8i 1.56334i 0.623690 + 0.781672i \(0.285633\pi\)
−0.623690 + 0.781672i \(0.714367\pi\)
\(110\) −1.77790e8 −1.21433
\(111\) 1.24265e8i 0.818571i
\(112\) 2.47439e7 0.157252
\(113\) 1.71332e8i 1.05081i −0.850851 0.525406i \(-0.823913\pi\)
0.850851 0.525406i \(-0.176087\pi\)
\(114\) 3.81023e7i 0.225596i
\(115\) 1.12026e8i 0.640513i
\(116\) 3.44176e8 1.90086
\(117\) 4.31106e7i 0.230060i
\(118\) 8.46377e7 2.92140e8i 0.436552 1.50683i
\(119\) 240829. 0.00120094
\(120\) 6.35390e7i 0.306419i
\(121\) −2.42358e7 −0.113062
\(122\) 1.92086e8 0.867073
\(123\) −1.43667e8 −0.627677
\(124\) 2.71354e8i 1.14775i
\(125\) −2.61824e8 −1.07243
\(126\) 6.35237e7i 0.252031i
\(127\) 4.65901e8 1.79093 0.895464 0.445133i \(-0.146844\pi\)
0.895464 + 0.445133i \(0.146844\pi\)
\(128\) 3.47074e8i 1.29295i
\(129\) 2.80097e8i 1.01146i
\(130\) 2.26888e8 0.794398
\(131\) 1.18641e6i 0.00402857i −0.999998 0.00201429i \(-0.999359\pi\)
0.999998 0.00201429i \(-0.000641168\pi\)
\(132\) 2.70194e8i 0.889980i
\(133\) 3.75616e7 0.120043
\(134\) 3.70037e8 1.14769
\(135\) −4.68991e7 −0.141198
\(136\) 616641.i 0.00180251i
\(137\) 2.77000e8 0.786317 0.393159 0.919471i \(-0.371382\pi\)
0.393159 + 0.919471i \(0.371382\pi\)
\(138\) 2.86772e8 0.790717
\(139\) 1.50839e8 0.404067 0.202034 0.979379i \(-0.435245\pi\)
0.202034 + 0.979379i \(0.435245\pi\)
\(140\) 1.98479e8 0.516657
\(141\) 3.86097e8i 0.976833i
\(142\) 9.73276e7i 0.239377i
\(143\) 3.04485e8 0.728151
\(144\) −4.67644e7 −0.108759
\(145\) −4.21940e8 −0.954506
\(146\) −4.33416e8 −0.953881
\(147\) 2.06971e8 0.443241
\(148\) 9.93906e8i 2.07156i
\(149\) 4.59699e8i 0.932670i 0.884608 + 0.466335i \(0.154426\pi\)
−0.884608 + 0.466335i \(0.845574\pi\)
\(150\) 2.11705e8i 0.418184i
\(151\) 3.23489e7i 0.0622231i −0.999516 0.0311116i \(-0.990095\pi\)
0.999516 0.0311116i \(-0.00990472\pi\)
\(152\) 9.61760e7i 0.180174i
\(153\) −455152. −0.000830597
\(154\) 4.48660e8 0.797690
\(155\) 3.32664e8i 0.576340i
\(156\) 3.44811e8i 0.582214i
\(157\) 6.79121e8i 1.11776i 0.829249 + 0.558880i \(0.188769\pi\)
−0.829249 + 0.558880i \(0.811231\pi\)
\(158\) 1.53217e9i 2.45854i
\(159\) −3.31820e8 −0.519175
\(160\) 5.93939e8i 0.906279i
\(161\) 2.82703e8i 0.420752i
\(162\) 1.20056e8i 0.174310i
\(163\) 8.90583e8 1.26161 0.630803 0.775943i \(-0.282726\pi\)
0.630803 + 0.775943i \(0.282726\pi\)
\(164\) −1.14909e9 −1.58847
\(165\) 3.31242e8i 0.446900i
\(166\) 1.96737e8 0.259092
\(167\) −1.07002e8 −0.137571 −0.0687853 0.997631i \(-0.521912\pi\)
−0.0687853 + 0.997631i \(0.521912\pi\)
\(168\) 1.60343e8i 0.201286i
\(169\) 4.27159e8 0.523652
\(170\) 2.39543e6i 0.00286806i
\(171\) −7.09889e7 −0.0830245
\(172\) 2.24029e9i 2.55971i
\(173\) 1.00080e9i 1.11728i 0.829410 + 0.558640i \(0.188677\pi\)
−0.829410 + 0.558640i \(0.811323\pi\)
\(174\) 1.08011e9i 1.17834i
\(175\) 2.08701e8 0.222522
\(176\) 3.30291e8i 0.344228i
\(177\) −5.44290e8 1.57690e8i −0.554546 0.160661i
\(178\) −2.24790e9 −2.23922
\(179\) 5.84466e8i 0.569308i 0.958630 + 0.284654i \(0.0918787\pi\)
−0.958630 + 0.284654i \(0.908121\pi\)
\(180\) −3.75112e8 −0.357331
\(181\) 2.10696e9 1.96310 0.981548 0.191215i \(-0.0612428\pi\)
0.981548 + 0.191215i \(0.0612428\pi\)
\(182\) −5.72562e8 −0.521839
\(183\) 3.57877e8i 0.319102i
\(184\) 7.23857e8 0.631512
\(185\) 1.21847e9i 1.04023i
\(186\) −8.51576e8 −0.711495
\(187\) 3.21468e6i 0.00262888i
\(188\) 3.08812e9i 2.47208i
\(189\) 1.18352e8 0.0927530
\(190\) 3.73610e8i 0.286684i
\(191\) 4.70580e8i 0.353590i 0.984248 + 0.176795i \(0.0565730\pi\)
−0.984248 + 0.176795i \(0.943427\pi\)
\(192\) −1.26441e9 −0.930431
\(193\) −1.59781e9 −1.15158 −0.575791 0.817597i \(-0.695306\pi\)
−0.575791 + 0.817597i \(0.695306\pi\)
\(194\) 2.71257e9 1.91502
\(195\) 4.22718e8i 0.292356i
\(196\) 1.65541e9 1.12171
\(197\) −3.39150e8 −0.225178 −0.112589 0.993642i \(-0.535914\pi\)
−0.112589 + 0.993642i \(0.535914\pi\)
\(198\) −8.47938e8 −0.551701
\(199\) −2.20463e9 −1.40580 −0.702898 0.711290i \(-0.748111\pi\)
−0.702898 + 0.711290i \(0.748111\pi\)
\(200\) 5.34376e8i 0.333985i
\(201\) 6.89422e8i 0.422377i
\(202\) 1.22217e9 0.734048
\(203\) 1.06478e9 0.627014
\(204\) −3.64043e6 −0.00210200
\(205\) 1.40872e9 0.797642
\(206\) −2.56014e9 −1.42166
\(207\) 5.34290e8i 0.291002i
\(208\) 4.21504e8i 0.225190i
\(209\) 5.01386e8i 0.262777i
\(210\) 6.22877e8i 0.320277i
\(211\) 1.23787e9i 0.624517i 0.949997 + 0.312259i \(0.101086\pi\)
−0.949997 + 0.312259i \(0.898914\pi\)
\(212\) −2.65399e9 −1.31388
\(213\) −1.81332e8 −0.0880961
\(214\) 1.71835e8i 0.0819327i
\(215\) 2.74647e9i 1.28535i
\(216\) 3.03039e8i 0.139214i
\(217\) 8.39491e8i 0.378597i
\(218\) 5.53918e9 2.45256
\(219\) 8.07504e8i 0.351049i
\(220\) 2.64937e9i 1.13097i
\(221\) 4.10245e6i 0.00171978i
\(222\) −3.11913e9 −1.28417
\(223\) 3.28091e9 1.32671 0.663353 0.748307i \(-0.269133\pi\)
0.663353 + 0.748307i \(0.269133\pi\)
\(224\) 1.49883e9i 0.595334i
\(225\) −3.94431e8 −0.153901
\(226\) −4.30055e9 −1.64851
\(227\) 3.93777e8i 0.148302i 0.997247 + 0.0741509i \(0.0236247\pi\)
−0.997247 + 0.0741509i \(0.976375\pi\)
\(228\) −5.67790e8 −0.210111
\(229\) 1.21372e9i 0.441344i 0.975348 + 0.220672i \(0.0708250\pi\)
−0.975348 + 0.220672i \(0.929175\pi\)
\(230\) −2.81193e9 −1.00483
\(231\) 8.35904e8i 0.293568i
\(232\) 2.72637e9i 0.941093i
\(233\) 3.02094e9i 1.02499i 0.858691 + 0.512493i \(0.171278\pi\)
−0.858691 + 0.512493i \(0.828722\pi\)
\(234\) 1.08210e9 0.360916
\(235\) 3.78585e9i 1.24134i
\(236\) −4.35339e9 1.26125e9i −1.40339 0.406586i
\(237\) 2.85460e9 0.904799
\(238\) 6.04497e6i 0.00188402i
\(239\) 1.27278e8 0.0390087 0.0195043 0.999810i \(-0.493791\pi\)
0.0195043 + 0.999810i \(0.493791\pi\)
\(240\) 4.58545e8 0.138209
\(241\) 2.47599e9 0.733974 0.366987 0.930226i \(-0.380389\pi\)
0.366987 + 0.930226i \(0.380389\pi\)
\(242\) 6.08333e8i 0.177370i
\(243\) −2.23677e8 −0.0641500
\(244\) 2.86241e9i 0.807555i
\(245\) −2.02944e9 −0.563264
\(246\) 3.60613e9i 0.984694i
\(247\) 6.39849e8i 0.171905i
\(248\) −2.14951e9 −0.568241
\(249\) 3.66544e8i 0.0953518i
\(250\) 6.57197e9i 1.68242i
\(251\) 2.75745e9 0.694725 0.347363 0.937731i \(-0.387077\pi\)
0.347363 + 0.937731i \(0.387077\pi\)
\(252\) 9.46612e8 0.234731
\(253\) −3.77362e9 −0.921035
\(254\) 1.16944e10i 2.80959i
\(255\) 4.46296e6 0.00105551
\(256\) −1.79022e9 −0.416818
\(257\) −7.67874e9 −1.76018 −0.880091 0.474805i \(-0.842518\pi\)
−0.880091 + 0.474805i \(0.842518\pi\)
\(258\) −7.03061e9 −1.58677
\(259\) 3.07486e9i 0.683324i
\(260\) 3.38102e9i 0.739868i
\(261\) −2.01237e9 −0.433657
\(262\) −2.97798e7 −0.00631999
\(263\) 1.52171e9 0.318060 0.159030 0.987274i \(-0.449163\pi\)
0.159030 + 0.987274i \(0.449163\pi\)
\(264\) −2.14032e9 −0.440620
\(265\) 3.25364e9 0.659760
\(266\) 9.42820e8i 0.188323i
\(267\) 4.18809e9i 0.824083i
\(268\) 5.51419e9i 1.06891i
\(269\) 1.90338e9i 0.363509i −0.983344 0.181755i \(-0.941822\pi\)
0.983344 0.181755i \(-0.0581777\pi\)
\(270\) 1.17720e9i 0.221510i
\(271\) −9.32770e9 −1.72941 −0.864704 0.502281i \(-0.832494\pi\)
−0.864704 + 0.502281i \(0.832494\pi\)
\(272\) 4.45015e6 0.000813015
\(273\) 1.06675e9i 0.192049i
\(274\) 6.95289e9i 1.23357i
\(275\) 2.78582e9i 0.487104i
\(276\) 4.27340e9i 0.736440i
\(277\) −1.02882e10 −1.74752 −0.873760 0.486357i \(-0.838325\pi\)
−0.873760 + 0.486357i \(0.838325\pi\)
\(278\) 3.78615e9i 0.633897i
\(279\) 1.58658e9i 0.261846i
\(280\) 1.57224e9i 0.255791i
\(281\) −3.50624e9 −0.562362 −0.281181 0.959655i \(-0.590726\pi\)
−0.281181 + 0.959655i \(0.590726\pi\)
\(282\) 9.69130e9 1.53245
\(283\) 6.78254e9i 1.05742i 0.848803 + 0.528709i \(0.177324\pi\)
−0.848803 + 0.528709i \(0.822676\pi\)
\(284\) −1.45035e9 −0.222946
\(285\) 6.96077e8 0.105506
\(286\) 7.64277e9i 1.14232i
\(287\) −3.55495e9 −0.523970
\(288\) 2.83269e9i 0.411746i
\(289\) −6.97571e9 −0.999994
\(290\) 1.05910e10i 1.49742i
\(291\) 5.05383e9i 0.704772i
\(292\) 6.45865e9i 0.888404i
\(293\) −1.05002e9 −0.142471 −0.0712353 0.997460i \(-0.522694\pi\)
−0.0712353 + 0.997460i \(0.522694\pi\)
\(294\) 5.19511e9i 0.695353i
\(295\) 5.33700e9 + 1.54622e9i 0.704708 + 0.204165i
\(296\) −7.87315e9 −1.02561
\(297\) 1.57981e9i 0.203038i
\(298\) 1.15387e10 1.46316
\(299\) 4.81574e9 0.602530
\(300\) −3.15477e9 −0.389478
\(301\) 6.93084e9i 0.844344i
\(302\) −8.11979e8 −0.0976151
\(303\) 2.27703e9i 0.270146i
\(304\) 6.94079e8 0.0812670
\(305\) 3.50914e9i 0.405510i
\(306\) 1.14246e7i 0.00130303i
\(307\) −1.07373e9 −0.120876 −0.0604380 0.998172i \(-0.519250\pi\)
−0.0604380 + 0.998172i \(0.519250\pi\)
\(308\) 6.68580e9i 0.742935i
\(309\) 4.76984e9i 0.523202i
\(310\) 8.35007e9 0.904156
\(311\) 1.79518e9 0.191896 0.0959480 0.995386i \(-0.469412\pi\)
0.0959480 + 0.995386i \(0.469412\pi\)
\(312\) 2.73140e9 0.288248
\(313\) 1.29198e10i 1.34611i 0.739594 + 0.673053i \(0.235017\pi\)
−0.739594 + 0.673053i \(0.764983\pi\)
\(314\) 1.70464e10 1.75353
\(315\) −1.16049e9 −0.117869
\(316\) 2.28319e10 2.28978
\(317\) −1.77264e10 −1.75543 −0.877715 0.479183i \(-0.840933\pi\)
−0.877715 + 0.479183i \(0.840933\pi\)
\(318\) 8.32890e9i 0.814478i
\(319\) 1.42131e10i 1.37255i
\(320\) 1.23981e10 1.18238
\(321\) 3.20149e8 0.0301531
\(322\) 7.09602e9 0.660072
\(323\) 6.75537e6 0.000620639
\(324\) −1.78904e9 −0.162345
\(325\) 3.55515e9i 0.318658i
\(326\) 2.23542e10i 1.97920i
\(327\) 1.03201e10i 0.902597i
\(328\) 9.10242e9i 0.786433i
\(329\) 9.55376e9i 0.815438i
\(330\) 8.31440e9 0.701092
\(331\) 1.70745e10 1.42245 0.711223 0.702967i \(-0.248142\pi\)
0.711223 + 0.702967i \(0.248142\pi\)
\(332\) 2.93173e9i 0.241308i
\(333\) 5.81129e9i 0.472602i
\(334\) 2.68582e9i 0.215820i
\(335\) 6.76008e9i 0.536750i
\(336\) −1.15716e9 −0.0907895
\(337\) 5.55679e9i 0.430828i 0.976523 + 0.215414i \(0.0691102\pi\)
−0.976523 + 0.215414i \(0.930890\pi\)
\(338\) 1.07220e10i 0.821501i
\(339\) 8.01242e9i 0.606687i
\(340\) 3.56960e7 0.00267119
\(341\) 1.12058e10 0.828757
\(342\) 1.78187e9i 0.130248i
\(343\) 1.17923e10 0.851966
\(344\) −1.77463e10 −1.26729
\(345\) 5.23894e9i 0.369800i
\(346\) 2.51207e10 1.75278
\(347\) 6.91524e9i 0.476968i 0.971146 + 0.238484i \(0.0766505\pi\)
−0.971146 + 0.238484i \(0.923349\pi\)
\(348\) −1.60955e10 −1.09746
\(349\) 5.11294e9i 0.344643i −0.985041 0.172321i \(-0.944873\pi\)
0.985041 0.172321i \(-0.0551268\pi\)
\(350\) 5.23853e9i 0.349090i
\(351\) 2.01608e9i 0.132825i
\(352\) 2.00070e10 1.30320
\(353\) 6.28088e9i 0.404503i −0.979334 0.202251i \(-0.935174\pi\)
0.979334 0.202251i \(-0.0648258\pi\)
\(354\) −3.95811e9 + 1.36620e10i −0.252043 + 0.869967i
\(355\) 1.77804e9 0.111951
\(356\) 3.34975e10i 2.08551i
\(357\) −1.12625e7 −0.000693363
\(358\) 1.46705e10 0.893125
\(359\) −4.64931e9 −0.279905 −0.139952 0.990158i \(-0.544695\pi\)
−0.139952 + 0.990158i \(0.544695\pi\)
\(360\) 2.97142e9i 0.176911i
\(361\) −1.59299e10 −0.937962
\(362\) 5.28860e10i 3.07969i
\(363\) 1.13339e9 0.0652761
\(364\) 8.53215e9i 0.486019i
\(365\) 7.91793e9i 0.446108i
\(366\) −8.98296e9 −0.500605
\(367\) 4.38244e9i 0.241575i 0.992678 + 0.120787i \(0.0385419\pi\)
−0.992678 + 0.120787i \(0.961458\pi\)
\(368\) 5.22390e9i 0.284842i
\(369\) 6.71863e9 0.362389
\(370\) 3.05844e10 1.63190
\(371\) −8.21070e9 −0.433395
\(372\) 1.26900e10i 0.662656i
\(373\) 6.57158e9 0.339496 0.169748 0.985488i \(-0.445705\pi\)
0.169748 + 0.985488i \(0.445705\pi\)
\(374\) 8.06906e7 0.00412417
\(375\) 1.22443e10 0.619169
\(376\) 2.44623e10 1.22390
\(377\) 1.81382e10i 0.897903i
\(378\) 2.97071e9i 0.145510i
\(379\) −8.80802e8 −0.0426895 −0.0213448 0.999772i \(-0.506795\pi\)
−0.0213448 + 0.999772i \(0.506795\pi\)
\(380\) 5.56743e9 0.267005
\(381\) −2.17880e10 −1.03399
\(382\) 1.18119e10 0.554709
\(383\) −2.17036e10 −1.00864 −0.504320 0.863517i \(-0.668257\pi\)
−0.504320 + 0.863517i \(0.668257\pi\)
\(384\) 1.62310e10i 0.746486i
\(385\) 8.19640e9i 0.373061i
\(386\) 4.01060e10i 1.80659i
\(387\) 1.30988e10i 0.583968i
\(388\) 4.04220e10i 1.78357i
\(389\) −1.91308e10 −0.835478 −0.417739 0.908567i \(-0.637177\pi\)
−0.417739 + 0.908567i \(0.637177\pi\)
\(390\) −1.06105e10 −0.458646
\(391\) 5.08435e7i 0.00217535i
\(392\) 1.31132e10i 0.555348i
\(393\) 5.54831e7i 0.00232590i
\(394\) 8.51288e9i 0.353258i
\(395\) −2.79906e10 −1.14980
\(396\) 1.26357e10i 0.513830i
\(397\) 2.75869e10i 1.11056i −0.831664 0.555279i \(-0.812611\pi\)
0.831664 0.555279i \(-0.187389\pi\)
\(398\) 5.53375e10i 2.20540i
\(399\) −1.75658e9 −0.0693069
\(400\) 3.85646e9 0.150643
\(401\) 4.26888e10i 1.65096i −0.564433 0.825479i \(-0.690905\pi\)
0.564433 0.825479i \(-0.309095\pi\)
\(402\) −1.73049e10 −0.662622
\(403\) −1.43004e10 −0.542162
\(404\) 1.82124e10i 0.683661i
\(405\) 2.19325e9 0.0815208
\(406\) 2.67268e10i 0.983654i
\(407\) 4.10444e10 1.49581
\(408\) 2.88374e7i 0.00104068i
\(409\) 1.58000e9i 0.0564631i −0.999601 0.0282315i \(-0.991012\pi\)
0.999601 0.0282315i \(-0.00898757\pi\)
\(410\) 3.53597e10i 1.25133i
\(411\) −1.29540e10 −0.453980
\(412\) 3.81505e10i 1.32407i
\(413\) −1.34682e10 3.90194e9i −0.462922 0.134116i
\(414\) −1.34110e10 −0.456521
\(415\) 3.59412e9i 0.121172i
\(416\) −2.55321e10 −0.852536
\(417\) −7.05403e9 −0.233288
\(418\) 1.25851e10 0.412242
\(419\) 1.53991e10i 0.499620i 0.968295 + 0.249810i \(0.0803682\pi\)
−0.968295 + 0.249810i \(0.919632\pi\)
\(420\) −9.28194e9 −0.298292
\(421\) 4.73339e10i 1.50676i 0.657586 + 0.753380i \(0.271578\pi\)
−0.657586 + 0.753380i \(0.728422\pi\)
\(422\) 3.10713e10 0.979737
\(423\) 1.80560e10i 0.563975i
\(424\) 2.10234e10i 0.650488i
\(425\) 3.75344e7 0.00115047
\(426\) 4.55156e9i 0.138204i
\(427\) 8.85547e9i 0.266379i
\(428\) 2.56064e9 0.0763087
\(429\) −1.42393e10 −0.420398
\(430\) 6.89382e10 2.01644
\(431\) 1.05757e10i 0.306478i 0.988189 + 0.153239i \(0.0489704\pi\)
−0.988189 + 0.153239i \(0.951030\pi\)
\(432\) 2.18696e9 0.0627921
\(433\) 1.93675e9 0.0550964 0.0275482 0.999620i \(-0.491230\pi\)
0.0275482 + 0.999620i \(0.491230\pi\)
\(434\) −2.10718e10 −0.593939
\(435\) 1.97322e10 0.551084
\(436\) 8.25433e10i 2.28421i
\(437\) 7.92994e9i 0.217442i
\(438\) 2.02689e10 0.550723
\(439\) 1.52316e9 0.0410097 0.0205048 0.999790i \(-0.493473\pi\)
0.0205048 + 0.999790i \(0.493473\pi\)
\(440\) 2.09868e10 0.559932
\(441\) −9.67907e9 −0.255905
\(442\) −1.02974e8 −0.00269798
\(443\) 5.44692e10i 1.41428i −0.707072 0.707142i \(-0.749984\pi\)
0.707072 0.707142i \(-0.250016\pi\)
\(444\) 4.64804e10i 1.19602i
\(445\) 4.10660e10i 1.04723i
\(446\) 8.23530e10i 2.08132i
\(447\) 2.14980e10i 0.538478i
\(448\) −3.12872e10 −0.776702
\(449\) −3.04171e10 −0.748398 −0.374199 0.927348i \(-0.622082\pi\)
−0.374199 + 0.927348i \(0.622082\pi\)
\(450\) 9.90048e9i 0.241438i
\(451\) 4.74529e10i 1.14698i
\(452\) 6.40856e10i 1.53535i
\(453\) 1.51281e9i 0.0359245i
\(454\) 9.88405e9 0.232655
\(455\) 1.04599e10i 0.244052i
\(456\) 4.49771e9i 0.104024i
\(457\) 6.39260e8i 0.0146559i 0.999973 + 0.00732795i \(0.00233258\pi\)
−0.999973 + 0.00732795i \(0.997667\pi\)
\(458\) 3.04652e10 0.692376
\(459\) 2.12853e7 0.000479546
\(460\) 4.19026e10i 0.935856i
\(461\) −1.63617e10 −0.362263 −0.181132 0.983459i \(-0.557976\pi\)
−0.181132 + 0.983459i \(0.557976\pi\)
\(462\) −2.09817e10 −0.460547
\(463\) 8.06345e10i 1.75468i −0.479874 0.877338i \(-0.659317\pi\)
0.479874 0.877338i \(-0.340683\pi\)
\(464\) 1.96755e10 0.424477
\(465\) 1.55571e10i 0.332750i
\(466\) 7.58275e10 1.60799
\(467\) 1.34566e10i 0.282924i 0.989944 + 0.141462i \(0.0451803\pi\)
−0.989944 + 0.141462i \(0.954820\pi\)
\(468\) 1.61252e10i 0.336141i
\(469\) 1.70593e10i 0.352591i
\(470\) −9.50274e10 −1.94741
\(471\) 3.17593e10i 0.645339i
\(472\) −9.99088e9 + 3.44851e10i −0.201296 + 0.694805i
\(473\) 9.25154e10 1.84829
\(474\) 7.16524e10i 1.41944i
\(475\) 5.85416e9 0.114998
\(476\) −9.00805e7 −0.00175470
\(477\) 1.55177e10 0.299746
\(478\) 3.19476e9i 0.0611964i
\(479\) 1.40052e10 0.266041 0.133021 0.991113i \(-0.457532\pi\)
0.133021 + 0.991113i \(0.457532\pi\)
\(480\) 2.77758e10i 0.523240i
\(481\) −5.23793e10 −0.978541
\(482\) 6.21490e10i 1.15145i
\(483\) 1.32207e10i 0.242921i
\(484\) 9.06521e9 0.165195
\(485\) 4.95550e10i 0.895613i
\(486\) 5.61445e9i 0.100638i
\(487\) 1.25982e10 0.223972 0.111986 0.993710i \(-0.464279\pi\)
0.111986 + 0.993710i \(0.464279\pi\)
\(488\) −2.26743e10 −0.399812
\(489\) −4.16484e10 −0.728389
\(490\) 5.09402e10i 0.883643i
\(491\) −6.06960e9 −0.104432 −0.0522161 0.998636i \(-0.516628\pi\)
−0.0522161 + 0.998636i \(0.516628\pi\)
\(492\) 5.37376e10 0.917102
\(493\) 1.91499e8 0.00324175
\(494\) −1.60606e10 −0.269684
\(495\) 1.54907e10i 0.258018i
\(496\) 1.55125e10i 0.256303i
\(497\) −4.48697e9 −0.0735406
\(498\) −9.20050e9 −0.149587
\(499\) −9.92585e10 −1.60090 −0.800452 0.599397i \(-0.795407\pi\)
−0.800452 + 0.599397i \(0.795407\pi\)
\(500\) 9.79336e10 1.56694
\(501\) 5.00398e9 0.0794264
\(502\) 6.92139e10i 1.08988i
\(503\) 2.23408e10i 0.349001i 0.984657 + 0.174500i \(0.0558310\pi\)
−0.984657 + 0.174500i \(0.944169\pi\)
\(504\) 7.49852e9i 0.116213i
\(505\) 2.23273e10i 0.343298i
\(506\) 9.47204e10i 1.44491i
\(507\) −1.99763e10 −0.302331
\(508\) −1.74267e11 −2.61674
\(509\) 1.18747e11i 1.76909i 0.466456 + 0.884545i \(0.345531\pi\)
−0.466456 + 0.884545i \(0.654469\pi\)
\(510\) 1.12023e8i 0.00165587i
\(511\) 1.99812e10i 0.293048i
\(512\) 4.39153e10i 0.639052i
\(513\) 3.31982e9 0.0479342
\(514\) 1.92741e11i 2.76136i
\(515\) 4.67703e10i 0.664877i
\(516\) 1.04768e11i 1.47785i
\(517\) −1.27527e11 −1.78501
\(518\) −7.71811e10 −1.07199
\(519\) 4.68027e10i 0.645062i
\(520\) −2.67825e10 −0.366301
\(521\) −5.20004e10 −0.705758 −0.352879 0.935669i \(-0.614797\pi\)
−0.352879 + 0.935669i \(0.614797\pi\)
\(522\) 5.05119e10i 0.680317i
\(523\) −1.48520e10 −0.198509 −0.0992543 0.995062i \(-0.531646\pi\)
−0.0992543 + 0.995062i \(0.531646\pi\)
\(524\) 4.43770e8i 0.00588617i
\(525\) −9.75998e9 −0.128473
\(526\) 3.81959e10i 0.498969i
\(527\) 1.50981e8i 0.00195740i
\(528\) 1.54462e10i 0.198740i
\(529\) 1.86272e10 0.237862
\(530\) 8.16685e10i 1.03503i
\(531\) 2.54539e10 + 7.37442e9i 0.320167 + 0.0927576i
\(532\) −1.40496e10 −0.175396
\(533\) 6.05575e10i 0.750341i
\(534\) 1.05124e11 1.29281
\(535\) −3.13920e9 −0.0383181
\(536\) −4.36803e10 −0.529208
\(537\) 2.73328e10i 0.328690i
\(538\) −4.77760e10 −0.570270
\(539\) 6.83621e10i 0.809954i
\(540\) 1.75423e10 0.206305
\(541\) 6.49767e10i 0.758522i −0.925290 0.379261i \(-0.876178\pi\)
0.925290 0.379261i \(-0.123822\pi\)
\(542\) 2.34131e11i 2.71308i
\(543\) −9.85327e10 −1.13339
\(544\) 2.69562e8i 0.00307796i
\(545\) 1.01193e11i 1.14701i
\(546\) 2.67761e10 0.301284
\(547\) −4.70937e10 −0.526034 −0.263017 0.964791i \(-0.584717\pi\)
−0.263017 + 0.964791i \(0.584717\pi\)
\(548\) −1.03610e11 −1.14889
\(549\) 1.67363e10i 0.184234i
\(550\) 6.99259e10 0.764165
\(551\) 2.98677e10 0.324037
\(552\) −3.38514e10 −0.364604
\(553\) 7.06355e10 0.755305
\(554\) 2.58242e11i 2.74149i
\(555\) 5.69822e10i 0.600575i
\(556\) −5.64201e10 −0.590385
\(557\) −4.72589e10 −0.490979 −0.245490 0.969399i \(-0.578949\pi\)
−0.245490 + 0.969399i \(0.578949\pi\)
\(558\) 3.98243e10 0.410782
\(559\) −1.18064e11 −1.20913
\(560\) 1.13464e10 0.115374
\(561\) 1.50336e8i 0.00151779i
\(562\) 8.80089e10i 0.882229i
\(563\) 4.73136e9i 0.0470925i 0.999723 + 0.0235463i \(0.00749570\pi\)
−0.999723 + 0.0235463i \(0.992504\pi\)
\(564\) 1.44417e11i 1.42726i
\(565\) 7.85652e10i 0.770968i
\(566\) 1.70246e11 1.65887
\(567\) −5.53477e9 −0.0535509
\(568\) 1.14888e10i 0.110378i
\(569\) 1.46316e9i 0.0139586i −0.999976 0.00697932i \(-0.997778\pi\)
0.999976 0.00697932i \(-0.00222160\pi\)
\(570\) 1.74720e10i 0.165517i
\(571\) 1.36252e11i 1.28173i 0.767652 + 0.640867i \(0.221425\pi\)
−0.767652 + 0.640867i \(0.778575\pi\)
\(572\) −1.13890e11 −1.06391
\(573\) 2.20069e10i 0.204145i
\(574\) 8.92317e10i 0.821999i
\(575\) 4.40606e10i 0.403069i
\(576\) 5.91307e10 0.537184
\(577\) −2.11877e11 −1.91152 −0.955762 0.294142i \(-0.904966\pi\)
−0.955762 + 0.294142i \(0.904966\pi\)
\(578\) 1.75095e11i 1.56878i
\(579\) 7.47220e10 0.664866
\(580\) 1.57824e11 1.39463
\(581\) 9.06993e9i 0.0795975i
\(582\) −1.26854e11 −1.10564
\(583\) 1.09599e11i 0.948712i
\(584\) 5.11617e10 0.439839
\(585\) 1.97686e10i 0.168792i
\(586\) 2.63561e10i 0.223507i
\(587\) 8.76572e10i 0.738304i 0.929369 + 0.369152i \(0.120352\pi\)
−0.929369 + 0.369152i \(0.879648\pi\)
\(588\) −7.74160e10 −0.647622
\(589\) 2.35481e10i 0.195657i
\(590\) 3.88110e10 1.33962e11i 0.320293 1.10554i
\(591\) 1.58605e10 0.130007
\(592\) 5.68186e10i 0.462598i
\(593\) −3.49038e10 −0.282263 −0.141132 0.989991i \(-0.545074\pi\)
−0.141132 + 0.989991i \(0.545074\pi\)
\(594\) 3.96541e10 0.318524
\(595\) 1.10433e8 0.000881115
\(596\) 1.71947e11i 1.36273i
\(597\) 1.03100e11 0.811637
\(598\) 1.20878e11i 0.945244i
\(599\) 1.94116e10 0.150784 0.0753918 0.997154i \(-0.475979\pi\)
0.0753918 + 0.997154i \(0.475979\pi\)
\(600\) 2.49903e10i 0.192826i
\(601\) 6.35319e10i 0.486960i 0.969906 + 0.243480i \(0.0782891\pi\)
−0.969906 + 0.243480i \(0.921711\pi\)
\(602\) −1.73969e11 −1.32460
\(603\) 3.22411e10i 0.243860i
\(604\) 1.20999e10i 0.0909145i
\(605\) −1.11134e10 −0.0829519
\(606\) −5.71550e10 −0.423803
\(607\) 8.61311e10 0.634462 0.317231 0.948348i \(-0.397247\pi\)
0.317231 + 0.948348i \(0.397247\pi\)
\(608\) 4.20429e10i 0.307665i
\(609\) −4.97950e10 −0.362007
\(610\) 8.80818e10 0.636160
\(611\) 1.62745e11 1.16773
\(612\) 1.70246e8 0.00121359
\(613\) 5.93916e10i 0.420613i −0.977635 0.210307i \(-0.932554\pi\)
0.977635 0.210307i \(-0.0674463\pi\)
\(614\) 2.69512e10i 0.189629i
\(615\) −6.58791e10 −0.460519
\(616\) −5.29611e10 −0.367819
\(617\) 2.34982e11 1.62142 0.810708 0.585450i \(-0.199082\pi\)
0.810708 + 0.585450i \(0.199082\pi\)
\(618\) 1.19726e11 0.820795
\(619\) 1.33083e10 0.0906486 0.0453243 0.998972i \(-0.485568\pi\)
0.0453243 + 0.998972i \(0.485568\pi\)
\(620\) 1.24430e11i 0.842093i
\(621\) 2.49863e10i 0.168010i
\(622\) 4.50601e10i 0.301045i
\(623\) 1.03632e11i 0.687925i
\(624\) 1.97118e10i 0.130013i
\(625\) −4.96106e10 −0.325128
\(626\) 3.24296e11 2.11176
\(627\) 2.34475e10i 0.151714i
\(628\) 2.54020e11i 1.63316i
\(629\) 5.53008e8i 0.00353288i
\(630\) 2.91291e10i 0.184912i
\(631\) 1.02889e10 0.0649009 0.0324505 0.999473i \(-0.489669\pi\)
0.0324505 + 0.999473i \(0.489669\pi\)
\(632\) 1.80861e11i 1.13365i
\(633\) 5.78893e10i 0.360565i
\(634\) 4.44944e11i 2.75390i
\(635\) 2.13641e11 1.31398
\(636\) 1.24115e11 0.758570
\(637\) 8.72409e10i 0.529862i
\(638\) 3.56759e11 2.15324
\(639\) 8.48007e9 0.0508623
\(640\) 1.59152e11i 0.948622i
\(641\) 1.09157e11 0.646574 0.323287 0.946301i \(-0.395212\pi\)
0.323287 + 0.946301i \(0.395212\pi\)
\(642\) 8.03595e9i 0.0473039i
\(643\) 4.76191e10 0.278572 0.139286 0.990252i \(-0.455519\pi\)
0.139286 + 0.990252i \(0.455519\pi\)
\(644\) 1.05743e11i 0.614763i
\(645\) 1.28440e11i 0.742097i
\(646\) 1.69564e8i 0.000973654i
\(647\) −2.74577e11 −1.56692 −0.783461 0.621441i \(-0.786548\pi\)
−0.783461 + 0.621441i \(0.786548\pi\)
\(648\) 1.41717e10i 0.0803753i
\(649\) 5.20846e10 1.79778e11i 0.293583 1.01335i
\(650\) −8.92366e10 −0.499907
\(651\) 3.92591e10i 0.218583i
\(652\) −3.33116e11 −1.84334
\(653\) −2.39958e11 −1.31972 −0.659862 0.751387i \(-0.729385\pi\)
−0.659862 + 0.751387i \(0.729385\pi\)
\(654\) −2.59042e11 −1.41599
\(655\) 5.44036e8i 0.00295571i
\(656\) −6.56900e10 −0.354718
\(657\) 3.77632e10i 0.202678i
\(658\) 2.39806e11 1.27925
\(659\) 2.41605e11i 1.28105i 0.767939 + 0.640523i \(0.221282\pi\)
−0.767939 + 0.640523i \(0.778718\pi\)
\(660\) 1.23899e11i 0.652967i
\(661\) 4.97939e10 0.260838 0.130419 0.991459i \(-0.458368\pi\)
0.130419 + 0.991459i \(0.458368\pi\)
\(662\) 4.28581e11i 2.23152i
\(663\) 1.91852e8i 0.000992917i
\(664\) −2.32235e10 −0.119469
\(665\) 1.72240e10 0.0880741
\(666\) 1.45867e11 0.741414
\(667\) 2.24796e11i 1.13575i
\(668\) 4.00233e10 0.201005
\(669\) −1.53433e11 −0.765974
\(670\) 1.69682e11 0.842049
\(671\) 1.18206e11 0.583109
\(672\) 7.00933e10i 0.343716i
\(673\) 4.04861e11i 1.97354i 0.162128 + 0.986770i \(0.448164\pi\)
−0.162128 + 0.986770i \(0.551836\pi\)
\(674\) 1.39479e11 0.675880
\(675\) 1.84457e10 0.0888547
\(676\) −1.59776e11 −0.765111
\(677\) −4.01952e11 −1.91346 −0.956731 0.290973i \(-0.906021\pi\)
−0.956731 + 0.290973i \(0.906021\pi\)
\(678\) 2.01117e11 0.951765
\(679\) 1.25054e11i 0.588327i
\(680\) 2.82764e8i 0.00132248i
\(681\) 1.84151e10i 0.0856221i
\(682\) 2.81274e11i 1.30015i
\(683\) 1.28178e11i 0.589019i 0.955648 + 0.294510i \(0.0951563\pi\)
−0.955648 + 0.294510i \(0.904844\pi\)
\(684\) 2.65529e10 0.121308
\(685\) 1.27020e11 0.576911
\(686\) 2.95995e11i 1.33656i
\(687\) 5.67601e10i 0.254810i
\(688\) 1.28071e11i 0.571606i
\(689\) 1.39866e11i 0.620636i
\(690\) 1.31501e11 0.580139
\(691\) 1.72925e11i 0.758483i −0.925298 0.379241i \(-0.876185\pi\)
0.925298 0.379241i \(-0.123815\pi\)
\(692\) 3.74342e11i 1.63246i
\(693\) 3.90914e10i 0.169492i
\(694\) 1.73577e11 0.748264
\(695\) 6.91678e10 0.296459
\(696\) 1.27500e11i 0.543340i
\(697\) −6.39352e8 −0.00270900
\(698\) −1.28338e11 −0.540673
\(699\) 1.41275e11i 0.591776i
\(700\) −7.80631e10 −0.325127
\(701\) 5.06019e10i 0.209554i −0.994496 0.104777i \(-0.966587\pi\)
0.994496 0.104777i \(-0.0334128\pi\)
\(702\) −5.06050e10 −0.208375
\(703\) 8.62514e10i 0.353138i
\(704\) 4.17633e11i 1.70022i
\(705\) 1.77047e11i 0.716690i
\(706\) −1.57654e11 −0.634580
\(707\) 5.63439e10i 0.225512i
\(708\) 2.03588e11 + 5.89827e10i 0.810250 + 0.234742i
\(709\) 2.68732e11 1.06349 0.531746 0.846904i \(-0.321536\pi\)
0.531746 + 0.846904i \(0.321536\pi\)
\(710\) 4.46300e10i 0.175628i
\(711\) −1.33496e11 −0.522386
\(712\) 2.65348e11 1.03251
\(713\) 1.77232e11 0.685779
\(714\) 2.82695e8i 0.00108774i
\(715\) 1.39623e11 0.534235
\(716\) 2.18615e11i 0.831819i
\(717\) −5.95219e9 −0.0225217
\(718\) 1.16701e11i 0.439112i
\(719\) 2.69631e11i 1.00891i 0.863437 + 0.504457i \(0.168307\pi\)
−0.863437 + 0.504457i \(0.831693\pi\)
\(720\) −2.14440e10 −0.0797952
\(721\) 1.18027e11i 0.436757i
\(722\) 3.99852e11i 1.47147i
\(723\) −1.15791e11 −0.423760
\(724\) −7.88093e11 −2.86829
\(725\) 1.65952e11 0.600662
\(726\) 2.84489e10i 0.102405i
\(727\) −3.93515e11 −1.40872 −0.704358 0.709845i \(-0.748765\pi\)
−0.704358 + 0.709845i \(0.748765\pi\)
\(728\) 6.75868e10 0.240623
\(729\) 1.04604e10 0.0370370
\(730\) −1.98745e11 −0.699850
\(731\) 1.24650e9i 0.00436538i
\(732\) 1.33861e11i 0.466242i
\(733\) −2.39451e11 −0.829471 −0.414736 0.909942i \(-0.636126\pi\)
−0.414736 + 0.909942i \(0.636126\pi\)
\(734\) 1.10002e11 0.378980
\(735\) 9.49075e10 0.325200
\(736\) 3.16431e11 1.07837
\(737\) 2.27715e11 0.771829
\(738\) 1.68642e11i 0.568513i
\(739\) 3.89964e11i 1.30751i −0.756704 0.653757i \(-0.773192\pi\)
0.756704 0.653757i \(-0.226808\pi\)
\(740\) 4.55760e11i 1.51988i
\(741\) 2.99228e10i 0.0992496i
\(742\) 2.06094e11i 0.679907i
\(743\) 3.43743e11 1.12792 0.563960 0.825802i \(-0.309277\pi\)
0.563960 + 0.825802i \(0.309277\pi\)
\(744\) 1.00523e11 0.328074
\(745\) 2.10797e11i 0.684289i
\(746\) 1.64951e11i 0.532598i
\(747\) 1.71416e10i 0.0550514i
\(748\) 1.20243e9i 0.00384108i
\(749\) 7.92190e9 0.0251711
\(750\) 3.07340e11i 0.971347i
\(751\) 1.75253e10i 0.0550942i 0.999621 + 0.0275471i \(0.00876962\pi\)
−0.999621 + 0.0275471i \(0.991230\pi\)
\(752\) 1.76538e11i 0.552037i
\(753\) −1.28953e11 −0.401100
\(754\) −4.55282e11 −1.40862
\(755\) 1.48337e10i 0.0456523i
\(756\) −4.42687e10 −0.135522
\(757\) −4.13727e11 −1.25988 −0.629942 0.776642i \(-0.716921\pi\)
−0.629942 + 0.776642i \(0.716921\pi\)
\(758\) 2.21087e10i 0.0669709i
\(759\) 1.76475e11 0.531760
\(760\) 4.41020e10i 0.132191i
\(761\) −2.30836e10 −0.0688281 −0.0344141 0.999408i \(-0.510956\pi\)
−0.0344141 + 0.999408i \(0.510956\pi\)
\(762\) 5.46893e11i 1.62212i
\(763\) 2.55366e11i 0.753467i
\(764\) 1.76017e11i 0.516632i
\(765\) −2.08712e8 −0.000609399
\(766\) 5.44774e11i 1.58235i
\(767\) −6.64682e10 + 2.29426e11i −0.192058 + 0.662919i
\(768\) 8.37203e10 0.240650
\(769\) 4.05959e11i 1.16085i 0.814313 + 0.580426i \(0.197114\pi\)
−0.814313 + 0.580426i \(0.802886\pi\)
\(770\) 2.05735e11 0.585255
\(771\) 3.59099e11 1.01624
\(772\) 5.97648e11 1.68258
\(773\) 6.15256e11i 1.72321i −0.507580 0.861604i \(-0.669460\pi\)
0.507580 0.861604i \(-0.330540\pi\)
\(774\) 3.28789e11 0.916123
\(775\) 1.30839e11i 0.362685i
\(776\) −3.20200e11 −0.883027
\(777\) 1.43797e11i 0.394517i
\(778\) 4.80196e11i 1.31069i
\(779\) −9.97181e10 −0.270785
\(780\) 1.58115e11i 0.427163i
\(781\) 5.98937e10i 0.160982i
\(782\) 1.27621e9 0.00341266