Properties

Label 177.9.c.a.58.8
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 58.8
Character \(\chi\) \(=\) 177.58
Dual form 177.9.c.a.58.73

$q$-expansion

\(f(q)\) \(=\) \(q-27.0356i q^{2} +46.7654 q^{3} -474.926 q^{4} +21.6634 q^{5} -1264.33i q^{6} -141.547 q^{7} +5918.81i q^{8} +2187.00 q^{9} +O(q^{10})\) \(q-27.0356i q^{2} +46.7654 q^{3} -474.926 q^{4} +21.6634 q^{5} -1264.33i q^{6} -141.547 q^{7} +5918.81i q^{8} +2187.00 q^{9} -585.684i q^{10} +7994.24i q^{11} -22210.1 q^{12} -55243.6i q^{13} +3826.80i q^{14} +1013.10 q^{15} +38437.8 q^{16} +12422.3 q^{17} -59127.0i q^{18} -130025. q^{19} -10288.5 q^{20} -6619.48 q^{21} +216129. q^{22} +379176. i q^{23} +276795. i q^{24} -390156. q^{25} -1.49355e6 q^{26} +102276. q^{27} +67224.1 q^{28} -149038. q^{29} -27389.7i q^{30} -1.11578e6i q^{31} +476026. i q^{32} +373854. i q^{33} -335844. i q^{34} -3066.38 q^{35} -1.03866e6 q^{36} +2.51615e6i q^{37} +3.51531e6i q^{38} -2.58349e6i q^{39} +128222. i q^{40} +171038. q^{41} +178962. i q^{42} -3.98516e6i q^{43} -3.79667e6i q^{44} +47377.8 q^{45} +1.02513e7 q^{46} +5.38311e6i q^{47} +1.79756e6 q^{48} -5.74477e6 q^{49} +1.05481e7i q^{50} +580931. q^{51} +2.62366e7i q^{52} +6.71423e6 q^{53} -2.76509e6i q^{54} +173182. i q^{55} -837787. i q^{56} -6.08066e6 q^{57} +4.02934e6i q^{58} +(-1.06905e7 + 5.70473e6i) q^{59} -481146. q^{60} +2.35441e7i q^{61} -3.01659e7 q^{62} -309562. q^{63} +2.27097e7 q^{64} -1.19676e6i q^{65} +1.01074e7 q^{66} +3.32648e7i q^{67} -5.89965e6 q^{68} +1.77323e7i q^{69} +82901.5i q^{70} +2.18665e7 q^{71} +1.29444e7i q^{72} -5.20187e6i q^{73} +6.80258e7 q^{74} -1.82458e7 q^{75} +6.17522e7 q^{76} -1.13156e6i q^{77} -6.98462e7 q^{78} -3.31695e7 q^{79} +832693. q^{80} +4.78297e6 q^{81} -4.62413e6i q^{82} +3.11342e7i q^{83} +3.14376e6 q^{84} +269108. q^{85} -1.07741e8 q^{86} -6.96982e6 q^{87} -4.73164e7 q^{88} -8.38935e7i q^{89} -1.28089e6i q^{90} +7.81953e6i q^{91} -1.80081e8i q^{92} -5.21800e7i q^{93} +1.45536e8 q^{94} -2.81678e6 q^{95} +2.22615e7i q^{96} +2.10512e7i q^{97} +1.55313e8i q^{98} +1.74834e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} + O(q^{10}) \) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} - 22680q^{12} - 59616q^{15} + 1199848q^{16} - 10608q^{17} - 27516q^{19} - 146436q^{20} - 974696q^{22} + 5718040q^{25} - 797484q^{26} - 3133000q^{28} + 1725924q^{29} + 4318800q^{35} - 22394880q^{36} - 732180q^{41} + 22752084q^{46} + 8703936q^{48} + 55899176q^{49} - 10373832q^{51} - 39265944q^{53} - 11408040q^{57} - 33575112q^{59} - 18034488q^{60} + 13038600q^{62} + 349920q^{63} - 241654260q^{64} - 35711928q^{66} + 36772608q^{68} - 235272660q^{71} - 63050712q^{74} + 74363184q^{75} + 9454680q^{76} - 10865988q^{78} + 17252580q^{79} + 318203976q^{80} + 382637520q^{81} - 20743128q^{84} - 27245820q^{85} + 105666984q^{86} + 29437992q^{87} + 82079788q^{88} + 121215992q^{94} - 690837276q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 27.0356i 1.68973i −0.534981 0.844864i \(-0.679681\pi\)
0.534981 0.844864i \(-0.320319\pi\)
\(3\) 46.7654 0.577350
\(4\) −474.926 −1.85518
\(5\) 21.6634 0.0346614 0.0173307 0.999850i \(-0.494483\pi\)
0.0173307 + 0.999850i \(0.494483\pi\)
\(6\) 1264.33i 0.975565i
\(7\) −141.547 −0.0589531 −0.0294766 0.999565i \(-0.509384\pi\)
−0.0294766 + 0.999565i \(0.509384\pi\)
\(8\) 5918.81i 1.44502i
\(9\) 2187.00 0.333333
\(10\) 585.684i 0.0585684i
\(11\) 7994.24i 0.546017i 0.962012 + 0.273009i \(0.0880188\pi\)
−0.962012 + 0.273009i \(0.911981\pi\)
\(12\) −22210.1 −1.07109
\(13\) 55243.6i 1.93423i −0.254339 0.967115i \(-0.581858\pi\)
0.254339 0.967115i \(-0.418142\pi\)
\(14\) 3826.80i 0.0996148i
\(15\) 1013.10 0.0200118
\(16\) 38437.8 0.586514
\(17\) 12422.3 0.148732 0.0743661 0.997231i \(-0.476307\pi\)
0.0743661 + 0.997231i \(0.476307\pi\)
\(18\) 59127.0i 0.563243i
\(19\) −130025. −0.997728 −0.498864 0.866680i \(-0.666249\pi\)
−0.498864 + 0.866680i \(0.666249\pi\)
\(20\) −10288.5 −0.0643032
\(21\) −6619.48 −0.0340366
\(22\) 216129. 0.922621
\(23\) 379176.i 1.35497i 0.735536 + 0.677485i \(0.236930\pi\)
−0.735536 + 0.677485i \(0.763070\pi\)
\(24\) 276795.i 0.834284i
\(25\) −390156. −0.998799
\(26\) −1.49355e6 −3.26832
\(27\) 102276. 0.192450
\(28\) 67224.1 0.109369
\(29\) −149038. −0.210720 −0.105360 0.994434i \(-0.533599\pi\)
−0.105360 + 0.994434i \(0.533599\pi\)
\(30\) 27389.7i 0.0338145i
\(31\) 1.11578e6i 1.20818i −0.796915 0.604092i \(-0.793536\pi\)
0.796915 0.604092i \(-0.206464\pi\)
\(32\) 476026.i 0.453973i
\(33\) 373854.i 0.315243i
\(34\) 335844.i 0.251317i
\(35\) −3066.38 −0.00204340
\(36\) −1.03866e6 −0.618393
\(37\) 2.51615e6i 1.34255i 0.741209 + 0.671275i \(0.234253\pi\)
−0.741209 + 0.671275i \(0.765747\pi\)
\(38\) 3.51531e6i 1.68589i
\(39\) 2.58349e6i 1.11673i
\(40\) 128222.i 0.0500865i
\(41\) 171038. 0.0605283 0.0302641 0.999542i \(-0.490365\pi\)
0.0302641 + 0.999542i \(0.490365\pi\)
\(42\) 178962.i 0.0575126i
\(43\) 3.98516e6i 1.16566i −0.812594 0.582831i \(-0.801945\pi\)
0.812594 0.582831i \(-0.198055\pi\)
\(44\) 3.79667e6i 1.01296i
\(45\) 47377.8 0.0115538
\(46\) 1.02513e7 2.28953
\(47\) 5.38311e6i 1.10317i 0.834119 + 0.551584i \(0.185977\pi\)
−0.834119 + 0.551584i \(0.814023\pi\)
\(48\) 1.79756e6 0.338624
\(49\) −5.74477e6 −0.996525
\(50\) 1.05481e7i 1.68770i
\(51\) 580931. 0.0858705
\(52\) 2.62366e7i 3.58835i
\(53\) 6.71423e6 0.850928 0.425464 0.904975i \(-0.360111\pi\)
0.425464 + 0.904975i \(0.360111\pi\)
\(54\) 2.76509e6i 0.325188i
\(55\) 173182.i 0.0189257i
\(56\) 837787.i 0.0851886i
\(57\) −6.08066e6 −0.576038
\(58\) 4.02934e6i 0.356059i
\(59\) −1.06905e7 + 5.70473e6i −0.882246 + 0.470789i
\(60\) −481146. −0.0371255
\(61\) 2.35441e7i 1.70045i 0.526421 + 0.850224i \(0.323534\pi\)
−0.526421 + 0.850224i \(0.676466\pi\)
\(62\) −3.01659e7 −2.04150
\(63\) −309562. −0.0196510
\(64\) 2.27097e7 1.35361
\(65\) 1.19676e6i 0.0670432i
\(66\) 1.01074e7 0.532675
\(67\) 3.32648e7i 1.65077i 0.564571 + 0.825385i \(0.309042\pi\)
−0.564571 + 0.825385i \(0.690958\pi\)
\(68\) −5.89965e6 −0.275925
\(69\) 1.77323e7i 0.782293i
\(70\) 82901.5i 0.00345279i
\(71\) 2.18665e7 0.860490 0.430245 0.902712i \(-0.358427\pi\)
0.430245 + 0.902712i \(0.358427\pi\)
\(72\) 1.29444e7i 0.481674i
\(73\) 5.20187e6i 0.183176i −0.995797 0.0915880i \(-0.970806\pi\)
0.995797 0.0915880i \(-0.0291943\pi\)
\(74\) 6.80258e7 2.26854
\(75\) −1.82458e7 −0.576657
\(76\) 6.17522e7 1.85096
\(77\) 1.13156e6i 0.0321894i
\(78\) −6.98462e7 −1.88697
\(79\) −3.31695e7 −0.851590 −0.425795 0.904820i \(-0.640006\pi\)
−0.425795 + 0.904820i \(0.640006\pi\)
\(80\) 832693. 0.0203294
\(81\) 4.78297e6 0.111111
\(82\) 4.62413e6i 0.102276i
\(83\) 3.11342e7i 0.656033i 0.944672 + 0.328017i \(0.106380\pi\)
−0.944672 + 0.328017i \(0.893620\pi\)
\(84\) 3.14376e6 0.0631441
\(85\) 269108. 0.00515527
\(86\) −1.07741e8 −1.96965
\(87\) −6.96982e6 −0.121659
\(88\) −4.73164e7 −0.789007
\(89\) 8.38935e7i 1.33711i −0.743661 0.668557i \(-0.766912\pi\)
0.743661 0.668557i \(-0.233088\pi\)
\(90\) 1.28089e6i 0.0195228i
\(91\) 7.81953e6i 0.114029i
\(92\) 1.80081e8i 2.51372i
\(93\) 5.21800e7i 0.697545i
\(94\) 1.45536e8 1.86406
\(95\) −2.81678e6 −0.0345827
\(96\) 2.22615e7i 0.262102i
\(97\) 2.10512e7i 0.237787i 0.992907 + 0.118894i \(0.0379348\pi\)
−0.992907 + 0.118894i \(0.962065\pi\)
\(98\) 1.55313e8i 1.68386i
\(99\) 1.74834e7i 0.182006i
\(100\) 1.85295e8 1.85295
\(101\) 1.83997e8i 1.76817i −0.467322 0.884087i \(-0.654781\pi\)
0.467322 0.884087i \(-0.345219\pi\)
\(102\) 1.57059e7i 0.145098i
\(103\) 7.76453e7i 0.689869i 0.938627 + 0.344934i \(0.112099\pi\)
−0.938627 + 0.344934i \(0.887901\pi\)
\(104\) 3.26976e8 2.79501
\(105\) −143400. −0.00117976
\(106\) 1.81524e8i 1.43784i
\(107\) −1.87626e8 −1.43139 −0.715695 0.698413i \(-0.753890\pi\)
−0.715695 + 0.698413i \(0.753890\pi\)
\(108\) −4.85735e7 −0.357030
\(109\) 7.95454e7i 0.563520i 0.959485 + 0.281760i \(0.0909182\pi\)
−0.959485 + 0.281760i \(0.909082\pi\)
\(110\) 4.68210e6 0.0319794
\(111\) 1.17669e8i 0.775121i
\(112\) −5.44073e6 −0.0345768
\(113\) 1.61849e8i 0.992650i −0.868137 0.496325i \(-0.834682\pi\)
0.868137 0.496325i \(-0.165318\pi\)
\(114\) 1.64395e8i 0.973348i
\(115\) 8.21425e6i 0.0469652i
\(116\) 7.07821e7 0.390923
\(117\) 1.20818e8i 0.644743i
\(118\) 1.54231e8 + 2.89024e8i 0.795506 + 1.49075i
\(119\) −1.75833e6 −0.00876823
\(120\) 5.99633e6i 0.0289175i
\(121\) 1.50451e8 0.701865
\(122\) 6.36531e8 2.87329
\(123\) 7.99867e6 0.0349460
\(124\) 5.29915e8i 2.24140i
\(125\) −1.69144e7 −0.0692812
\(126\) 8.36921e6i 0.0332049i
\(127\) 3.43849e8 1.32176 0.660881 0.750491i \(-0.270183\pi\)
0.660881 + 0.750491i \(0.270183\pi\)
\(128\) 4.92110e8i 1.83325i
\(129\) 1.86368e8i 0.672995i
\(130\) −3.23553e7 −0.113285
\(131\) 5.64994e8i 1.91849i 0.282580 + 0.959244i \(0.408810\pi\)
−0.282580 + 0.959244i \(0.591190\pi\)
\(132\) 1.77553e8i 0.584833i
\(133\) 1.84046e7 0.0588192
\(134\) 8.99337e8 2.78935
\(135\) 2.21564e6 0.00667060
\(136\) 7.35250e7i 0.214921i
\(137\) 3.35466e7 0.0952283 0.0476142 0.998866i \(-0.484838\pi\)
0.0476142 + 0.998866i \(0.484838\pi\)
\(138\) 4.79405e8 1.32186
\(139\) −2.60900e8 −0.698899 −0.349450 0.936955i \(-0.613631\pi\)
−0.349450 + 0.936955i \(0.613631\pi\)
\(140\) 1.45630e6 0.00379088
\(141\) 2.51743e8i 0.636915i
\(142\) 5.91175e8i 1.45399i
\(143\) 4.41630e8 1.05612
\(144\) 8.40634e7 0.195505
\(145\) −3.22867e6 −0.00730385
\(146\) −1.40636e8 −0.309517
\(147\) −2.68656e8 −0.575344
\(148\) 1.19499e9i 2.49067i
\(149\) 7.11310e8i 1.44316i −0.692332 0.721579i \(-0.743417\pi\)
0.692332 0.721579i \(-0.256583\pi\)
\(150\) 4.93286e8i 0.974393i
\(151\) 3.12895e8i 0.601853i −0.953647 0.300927i \(-0.902704\pi\)
0.953647 0.300927i \(-0.0972959\pi\)
\(152\) 7.69593e8i 1.44174i
\(153\) 2.71675e7 0.0495774
\(154\) −3.05924e7 −0.0543914
\(155\) 2.41717e7i 0.0418774i
\(156\) 1.22696e9i 2.07173i
\(157\) 1.07100e9i 1.76275i 0.472420 + 0.881374i \(0.343381\pi\)
−0.472420 + 0.881374i \(0.656619\pi\)
\(158\) 8.96759e8i 1.43896i
\(159\) 3.13994e8 0.491284
\(160\) 1.03123e7i 0.0157354i
\(161\) 5.36711e7i 0.0798798i
\(162\) 1.29311e8i 0.187748i
\(163\) −7.32147e8 −1.03717 −0.518583 0.855027i \(-0.673540\pi\)
−0.518583 + 0.855027i \(0.673540\pi\)
\(164\) −8.12306e7 −0.112291
\(165\) 8.09894e6i 0.0109268i
\(166\) 8.41734e8 1.10852
\(167\) −5.61899e8 −0.722424 −0.361212 0.932484i \(-0.617637\pi\)
−0.361212 + 0.932484i \(0.617637\pi\)
\(168\) 3.91794e7i 0.0491837i
\(169\) −2.23612e9 −2.74125
\(170\) 7.27551e6i 0.00871100i
\(171\) −2.84364e8 −0.332576
\(172\) 1.89266e9i 2.16251i
\(173\) 7.34364e7i 0.0819836i 0.999159 + 0.0409918i \(0.0130517\pi\)
−0.999159 + 0.0409918i \(0.986948\pi\)
\(174\) 1.88434e8i 0.205571i
\(175\) 5.52252e7 0.0588823
\(176\) 3.07281e8i 0.320247i
\(177\) −4.99945e8 + 2.66784e8i −0.509365 + 0.271810i
\(178\) −2.26811e9 −2.25936
\(179\) 1.91943e8i 0.186965i 0.995621 + 0.0934824i \(0.0297999\pi\)
−0.995621 + 0.0934824i \(0.970200\pi\)
\(180\) −2.25010e7 −0.0214344
\(181\) −1.53677e9 −1.43184 −0.715919 0.698183i \(-0.753992\pi\)
−0.715919 + 0.698183i \(0.753992\pi\)
\(182\) 2.11406e8 0.192678
\(183\) 1.10105e9i 0.981754i
\(184\) −2.24427e9 −1.95796
\(185\) 5.45084e7i 0.0465347i
\(186\) −1.41072e9 −1.17866
\(187\) 9.93065e7i 0.0812103i
\(188\) 2.55658e9i 2.04658i
\(189\) −1.44768e7 −0.0113455
\(190\) 7.61535e7i 0.0584353i
\(191\) 3.00969e8i 0.226146i 0.993587 + 0.113073i \(0.0360693\pi\)
−0.993587 + 0.113073i \(0.963931\pi\)
\(192\) 1.06203e9 0.781504
\(193\) 1.92053e9 1.38418 0.692090 0.721811i \(-0.256690\pi\)
0.692090 + 0.721811i \(0.256690\pi\)
\(194\) 5.69132e8 0.401796
\(195\) 5.59671e7i 0.0387074i
\(196\) 2.72834e9 1.84873
\(197\) 2.07571e9 1.37817 0.689084 0.724682i \(-0.258013\pi\)
0.689084 + 0.724682i \(0.258013\pi\)
\(198\) 4.72675e8 0.307540
\(199\) −2.89818e9 −1.84805 −0.924024 0.382334i \(-0.875120\pi\)
−0.924024 + 0.382334i \(0.875120\pi\)
\(200\) 2.30926e9i 1.44329i
\(201\) 1.55564e9i 0.953072i
\(202\) −4.97448e9 −2.98773
\(203\) 2.10958e7 0.0124226
\(204\) −2.75899e8 −0.159305
\(205\) 3.70527e6 0.00209800
\(206\) 2.09919e9 1.16569
\(207\) 8.29259e8i 0.451657i
\(208\) 2.12344e9i 1.13445i
\(209\) 1.03945e9i 0.544777i
\(210\) 3.87692e6i 0.00199347i
\(211\) 5.74536e7i 0.0289859i 0.999895 + 0.0144930i \(0.00461342\pi\)
−0.999895 + 0.0144930i \(0.995387\pi\)
\(212\) −3.18877e9 −1.57863
\(213\) 1.02259e9 0.496804
\(214\) 5.07259e9i 2.41866i
\(215\) 8.63322e7i 0.0404035i
\(216\) 6.05351e8i 0.278095i
\(217\) 1.57935e8i 0.0712262i
\(218\) 2.15056e9 0.952195
\(219\) 2.43268e8i 0.105757i
\(220\) 8.22488e7i 0.0351107i
\(221\) 6.86249e8i 0.287682i
\(222\) 3.18125e9 1.30974
\(223\) 3.07934e9 1.24520 0.622598 0.782542i \(-0.286077\pi\)
0.622598 + 0.782542i \(0.286077\pi\)
\(224\) 6.73798e7i 0.0267632i
\(225\) −8.53271e8 −0.332933
\(226\) −4.37569e9 −1.67731
\(227\) 1.63518e9i 0.615831i 0.951414 + 0.307916i \(0.0996314\pi\)
−0.951414 + 0.307916i \(0.900369\pi\)
\(228\) 2.88787e9 1.06865
\(229\) 2.33566e9i 0.849314i −0.905354 0.424657i \(-0.860395\pi\)
0.905354 0.424657i \(-0.139605\pi\)
\(230\) 2.22077e8 0.0793584
\(231\) 5.29177e7i 0.0185846i
\(232\) 8.82128e8i 0.304495i
\(233\) 3.61892e9i 1.22788i 0.789354 + 0.613939i \(0.210416\pi\)
−0.789354 + 0.613939i \(0.789584\pi\)
\(234\) −3.26638e9 −1.08944
\(235\) 1.16616e8i 0.0382374i
\(236\) 5.07719e9 2.70932e9i 1.63672 0.873399i
\(237\) −1.55118e9 −0.491666
\(238\) 4.75375e7i 0.0148159i
\(239\) −4.00604e9 −1.22779 −0.613894 0.789388i \(-0.710398\pi\)
−0.613894 + 0.789388i \(0.710398\pi\)
\(240\) 3.89412e7 0.0117372
\(241\) 2.30136e9 0.682207 0.341103 0.940026i \(-0.389199\pi\)
0.341103 + 0.940026i \(0.389199\pi\)
\(242\) 4.06754e9i 1.18596i
\(243\) 2.23677e8 0.0641500
\(244\) 1.11817e10i 3.15464i
\(245\) −1.24451e8 −0.0345410
\(246\) 2.16249e8i 0.0590492i
\(247\) 7.18303e9i 1.92983i
\(248\) 6.60411e9 1.74585
\(249\) 1.45600e9i 0.378761i
\(250\) 4.57291e8i 0.117066i
\(251\) −4.10510e9 −1.03426 −0.517129 0.855908i \(-0.672999\pi\)
−0.517129 + 0.855908i \(0.672999\pi\)
\(252\) 1.47019e8 0.0364562
\(253\) −3.03123e9 −0.739838
\(254\) 9.29619e9i 2.23342i
\(255\) 1.25849e7 0.00297639
\(256\) −7.49081e9 −1.74409
\(257\) −8.76632e8 −0.200949 −0.100474 0.994940i \(-0.532036\pi\)
−0.100474 + 0.994940i \(0.532036\pi\)
\(258\) −5.03857e9 −1.13718
\(259\) 3.56153e8i 0.0791475i
\(260\) 5.68374e8i 0.124377i
\(261\) −3.25946e8 −0.0702399
\(262\) 1.52750e10 3.24172
\(263\) −6.03710e9 −1.26184 −0.630922 0.775846i \(-0.717323\pi\)
−0.630922 + 0.775846i \(0.717323\pi\)
\(264\) −2.21277e9 −0.455534
\(265\) 1.45453e8 0.0294944
\(266\) 4.97579e8i 0.0993884i
\(267\) 3.92331e9i 0.771983i
\(268\) 1.57983e10i 3.06247i
\(269\) 6.22322e9i 1.18852i 0.804273 + 0.594259i \(0.202555\pi\)
−0.804273 + 0.594259i \(0.797445\pi\)
\(270\) 5.99013e7i 0.0112715i
\(271\) 9.67398e8 0.179361 0.0896805 0.995971i \(-0.471415\pi\)
0.0896805 + 0.995971i \(0.471415\pi\)
\(272\) 4.77484e8 0.0872334
\(273\) 3.65683e8i 0.0658347i
\(274\) 9.06954e8i 0.160910i
\(275\) 3.11900e9i 0.545361i
\(276\) 8.42154e9i 1.45129i
\(277\) 4.68317e9 0.795464 0.397732 0.917502i \(-0.369797\pi\)
0.397732 + 0.917502i \(0.369797\pi\)
\(278\) 7.05359e9i 1.18095i
\(279\) 2.44022e9i 0.402728i
\(280\) 1.81493e7i 0.00295276i
\(281\) −3.92555e9 −0.629616 −0.314808 0.949155i \(-0.601940\pi\)
−0.314808 + 0.949155i \(0.601940\pi\)
\(282\) 6.80604e9 1.07621
\(283\) 2.29831e9i 0.358314i 0.983821 + 0.179157i \(0.0573370\pi\)
−0.983821 + 0.179157i \(0.942663\pi\)
\(284\) −1.03850e10 −1.59636
\(285\) −1.31728e8 −0.0199663
\(286\) 1.19398e10i 1.78456i
\(287\) −2.42099e7 −0.00356833
\(288\) 1.04107e9i 0.151324i
\(289\) −6.82145e9 −0.977879
\(290\) 8.72892e7i 0.0123415i
\(291\) 9.84465e8i 0.137287i
\(292\) 2.47051e9i 0.339824i
\(293\) −1.22364e10 −1.66029 −0.830144 0.557549i \(-0.811742\pi\)
−0.830144 + 0.557549i \(0.811742\pi\)
\(294\) 7.26329e9i 0.972174i
\(295\) −2.31592e8 + 1.23584e8i −0.0305799 + 0.0163182i
\(296\) −1.48926e10 −1.94001
\(297\) 8.17618e8i 0.105081i
\(298\) −1.92307e10 −2.43854
\(299\) 2.09470e10 2.62083
\(300\) 8.66540e9 1.06980
\(301\) 5.64086e8i 0.0687194i
\(302\) −8.45931e9 −1.01697
\(303\) 8.60469e9i 1.02086i
\(304\) −4.99787e9 −0.585181
\(305\) 5.10046e8i 0.0589400i
\(306\) 7.34490e8i 0.0837723i
\(307\) −1.10109e10 −1.23956 −0.619780 0.784776i \(-0.712778\pi\)
−0.619780 + 0.784776i \(0.712778\pi\)
\(308\) 5.37406e8i 0.0597172i
\(309\) 3.63111e9i 0.398296i
\(310\) −6.53496e8 −0.0707614
\(311\) 1.17778e10 1.25899 0.629495 0.777005i \(-0.283262\pi\)
0.629495 + 0.777005i \(0.283262\pi\)
\(312\) 1.52912e10 1.61370
\(313\) 1.32404e9i 0.137951i −0.997618 0.0689756i \(-0.978027\pi\)
0.997618 0.0689756i \(-0.0219731\pi\)
\(314\) 2.89551e10 2.97856
\(315\) −6.70617e6 −0.000681133
\(316\) 1.57531e10 1.57985
\(317\) −5.95561e9 −0.589779 −0.294889 0.955531i \(-0.595283\pi\)
−0.294889 + 0.955531i \(0.595283\pi\)
\(318\) 8.48902e9i 0.830136i
\(319\) 1.19145e9i 0.115057i
\(320\) 4.91970e8 0.0469179
\(321\) −8.77440e9 −0.826413
\(322\) −1.45103e9 −0.134975
\(323\) −1.61520e9 −0.148394
\(324\) −2.27156e9 −0.206131
\(325\) 2.15536e10i 1.93191i
\(326\) 1.97941e10i 1.75253i
\(327\) 3.71997e9i 0.325348i
\(328\) 1.01234e9i 0.0874647i
\(329\) 7.61961e8i 0.0650353i
\(330\) 2.18960e8 0.0184633
\(331\) 7.37192e9 0.614142 0.307071 0.951687i \(-0.400651\pi\)
0.307071 + 0.951687i \(0.400651\pi\)
\(332\) 1.47865e10i 1.21706i
\(333\) 5.50283e9i 0.447516i
\(334\) 1.51913e10i 1.22070i
\(335\) 7.20630e8i 0.0572180i
\(336\) −2.54438e8 −0.0199629
\(337\) 1.48781e10i 1.15353i −0.816911 0.576764i \(-0.804315\pi\)
0.816911 0.576764i \(-0.195685\pi\)
\(338\) 6.04549e10i 4.63196i
\(339\) 7.56893e9i 0.573107i
\(340\) −1.27807e8 −0.00956395
\(341\) 8.91984e9 0.659689
\(342\) 7.68797e9i 0.561963i
\(343\) 1.62914e9 0.117701
\(344\) 2.35874e10 1.68441
\(345\) 3.84142e8i 0.0271154i
\(346\) 1.98540e9 0.138530
\(347\) 6.20527e9i 0.427999i −0.976834 0.213999i \(-0.931351\pi\)
0.976834 0.213999i \(-0.0686491\pi\)
\(348\) 3.31015e9 0.225700
\(349\) 4.68321e9i 0.315676i −0.987465 0.157838i \(-0.949548\pi\)
0.987465 0.157838i \(-0.0504524\pi\)
\(350\) 1.49305e9i 0.0994951i
\(351\) 5.65008e9i 0.372243i
\(352\) −3.80546e9 −0.247877
\(353\) 1.21392e10i 0.781793i −0.920435 0.390897i \(-0.872165\pi\)
0.920435 0.390897i \(-0.127835\pi\)
\(354\) 7.21267e9 + 1.35163e10i 0.459286 + 0.860688i
\(355\) 4.73702e8 0.0298258
\(356\) 3.98432e10i 2.48059i
\(357\) −8.22288e7 −0.00506234
\(358\) 5.18930e9 0.315920
\(359\) −1.60234e10 −0.964665 −0.482333 0.875988i \(-0.660210\pi\)
−0.482333 + 0.875988i \(0.660210\pi\)
\(360\) 2.80420e8i 0.0166955i
\(361\) −7.70990e7 −0.00453962
\(362\) 4.15475e10i 2.41942i
\(363\) 7.03590e9 0.405222
\(364\) 3.71370e9i 0.211544i
\(365\) 1.12690e8i 0.00634914i
\(366\) 2.97676e10 1.65890
\(367\) 4.52398e8i 0.0249377i −0.999922 0.0124688i \(-0.996031\pi\)
0.999922 0.0124688i \(-0.00396906\pi\)
\(368\) 1.45747e10i 0.794709i
\(369\) 3.74061e8 0.0201761
\(370\) 1.47367e9 0.0786310
\(371\) −9.50377e8 −0.0501649
\(372\) 2.47817e10i 1.29407i
\(373\) −1.13079e10 −0.584182 −0.292091 0.956391i \(-0.594351\pi\)
−0.292091 + 0.956391i \(0.594351\pi\)
\(374\) 2.68481e9 0.137223
\(375\) −7.91006e8 −0.0399995
\(376\) −3.18616e10 −1.59410
\(377\) 8.23339e9i 0.407580i
\(378\) 3.91389e8i 0.0191709i
\(379\) −1.45339e9 −0.0704409 −0.0352205 0.999380i \(-0.511213\pi\)
−0.0352205 + 0.999380i \(0.511213\pi\)
\(380\) 1.33776e9 0.0641571
\(381\) 1.60802e10 0.763119
\(382\) 8.13689e9 0.382124
\(383\) −6.96464e9 −0.323671 −0.161835 0.986818i \(-0.551741\pi\)
−0.161835 + 0.986818i \(0.551741\pi\)
\(384\) 2.30137e10i 1.05843i
\(385\) 2.45134e7i 0.00111573i
\(386\) 5.19228e10i 2.33889i
\(387\) 8.71555e9i 0.388554i
\(388\) 9.99774e9i 0.441139i
\(389\) 2.20334e10 0.962240 0.481120 0.876655i \(-0.340230\pi\)
0.481120 + 0.876655i \(0.340230\pi\)
\(390\) −1.51311e9 −0.0654050
\(391\) 4.71023e9i 0.201528i
\(392\) 3.40022e10i 1.44000i
\(393\) 2.64222e10i 1.10764i
\(394\) 5.61182e10i 2.32873i
\(395\) −7.18564e8 −0.0295173
\(396\) 8.30333e9i 0.337654i
\(397\) 2.99959e10i 1.20754i −0.797160 0.603768i \(-0.793665\pi\)
0.797160 0.603768i \(-0.206335\pi\)
\(398\) 7.83542e10i 3.12270i
\(399\) 8.60696e8 0.0339593
\(400\) −1.49967e10 −0.585809
\(401\) 1.42017e10i 0.549241i 0.961553 + 0.274620i \(0.0885522\pi\)
−0.961553 + 0.274620i \(0.911448\pi\)
\(402\) 4.20578e10 1.61043
\(403\) −6.16398e10 −2.33691
\(404\) 8.73850e10i 3.28028i
\(405\) 1.03615e8 0.00385127
\(406\) 5.70339e8i 0.0209908i
\(407\) −2.01147e10 −0.733055
\(408\) 3.43842e9i 0.124085i
\(409\) 1.80649e10i 0.645570i −0.946472 0.322785i \(-0.895381\pi\)
0.946472 0.322785i \(-0.104619\pi\)
\(410\) 1.00174e8i 0.00354504i
\(411\) 1.56882e9 0.0549801
\(412\) 3.68758e10i 1.27983i
\(413\) 1.51320e9 8.07484e8i 0.0520112 0.0277545i
\(414\) 2.24195e10 0.763177
\(415\) 6.74473e8i 0.0227390i
\(416\) 2.62973e10 0.878089
\(417\) −1.22011e10 −0.403510
\(418\) −2.81022e10 −0.920524
\(419\) 2.79122e10i 0.905603i −0.891611 0.452801i \(-0.850425\pi\)
0.891611 0.452801i \(-0.149575\pi\)
\(420\) 6.81046e7 0.00218866
\(421\) 8.74405e9i 0.278346i −0.990268 0.139173i \(-0.955556\pi\)
0.990268 0.139173i \(-0.0444443\pi\)
\(422\) 1.55329e9 0.0489783
\(423\) 1.17729e10i 0.367723i
\(424\) 3.97403e10i 1.22961i
\(425\) −4.84661e9 −0.148553
\(426\) 2.76465e10i 0.839464i
\(427\) 3.33259e9i 0.100247i
\(428\) 8.91085e10 2.65549
\(429\) 2.06530e10 0.609753
\(430\) −2.33405e9 −0.0682709
\(431\) 1.69782e10i 0.492021i 0.969267 + 0.246010i \(0.0791197\pi\)
−0.969267 + 0.246010i \(0.920880\pi\)
\(432\) 3.93126e9 0.112875
\(433\) −7.81317e9 −0.222267 −0.111134 0.993805i \(-0.535448\pi\)
−0.111134 + 0.993805i \(0.535448\pi\)
\(434\) 4.26988e9 0.120353
\(435\) −1.50990e8 −0.00421688
\(436\) 3.77782e10i 1.04543i
\(437\) 4.93024e10i 1.35189i
\(438\) −6.57690e9 −0.178700
\(439\) −9.61070e9 −0.258760 −0.129380 0.991595i \(-0.541299\pi\)
−0.129380 + 0.991595i \(0.541299\pi\)
\(440\) −1.02503e9 −0.0273481
\(441\) −1.25638e10 −0.332175
\(442\) −1.85532e10 −0.486105
\(443\) 6.24996e10i 1.62279i −0.584498 0.811395i \(-0.698708\pi\)
0.584498 0.811395i \(-0.301292\pi\)
\(444\) 5.58840e10i 1.43799i
\(445\) 1.81742e9i 0.0463463i
\(446\) 8.32518e10i 2.10404i
\(447\) 3.32647e10i 0.833208i
\(448\) −3.21448e9 −0.0797993
\(449\) −7.16072e10 −1.76186 −0.880930 0.473247i \(-0.843082\pi\)
−0.880930 + 0.473247i \(0.843082\pi\)
\(450\) 2.30687e10i 0.562566i
\(451\) 1.36732e9i 0.0330495i
\(452\) 7.68663e10i 1.84154i
\(453\) 1.46326e10i 0.347480i
\(454\) 4.42081e10 1.04059
\(455\) 1.69398e8i 0.00395241i
\(456\) 3.59903e10i 0.832388i
\(457\) 5.88145e10i 1.34840i −0.738548 0.674201i \(-0.764488\pi\)
0.738548 0.674201i \(-0.235512\pi\)
\(458\) −6.31462e10 −1.43511
\(459\) 1.27050e9 0.0286235
\(460\) 3.90116e9i 0.0871290i
\(461\) 8.90675e10 1.97204 0.986020 0.166629i \(-0.0532883\pi\)
0.986020 + 0.166629i \(0.0532883\pi\)
\(462\) −1.43066e9 −0.0314029
\(463\) 4.09409e10i 0.890910i 0.895304 + 0.445455i \(0.146958\pi\)
−0.895304 + 0.445455i \(0.853042\pi\)
\(464\) −5.72869e9 −0.123590
\(465\) 1.13040e9i 0.0241779i
\(466\) 9.78397e10 2.07478
\(467\) 9.03824e10i 1.90028i −0.311831 0.950138i \(-0.600942\pi\)
0.311831 0.950138i \(-0.399058\pi\)
\(468\) 5.73795e10i 1.19612i
\(469\) 4.70852e9i 0.0973180i
\(470\) 3.15280e9 0.0646108
\(471\) 5.00856e10i 1.01772i
\(472\) −3.37652e10 6.32750e10i −0.680301 1.27486i
\(473\) 3.18584e10 0.636471
\(474\) 4.19373e10i 0.830782i
\(475\) 5.07299e10 0.996529
\(476\) 8.35075e8 0.0162666
\(477\) 1.46840e10 0.283643
\(478\) 1.08306e11i 2.07463i
\(479\) −3.29316e10 −0.625563 −0.312782 0.949825i \(-0.601261\pi\)
−0.312782 + 0.949825i \(0.601261\pi\)
\(480\) 4.82260e8i 0.00908482i
\(481\) 1.39001e11 2.59680
\(482\) 6.22187e10i 1.15274i
\(483\) 2.50995e9i 0.0461186i
\(484\) −7.14531e10 −1.30209
\(485\) 4.56039e8i 0.00824205i
\(486\) 6.04726e9i 0.108396i
\(487\) −7.35838e10 −1.30818 −0.654089 0.756418i \(-0.726948\pi\)
−0.654089 + 0.756418i \(0.726948\pi\)
\(488\) −1.39353e11 −2.45718
\(489\) −3.42391e10 −0.598808
\(490\) 3.36462e9i 0.0583648i
\(491\) −1.62672e10 −0.279889 −0.139944 0.990159i \(-0.544692\pi\)
−0.139944 + 0.990159i \(0.544692\pi\)
\(492\) −3.79878e9 −0.0648311
\(493\) −1.85139e9 −0.0313408
\(494\) 1.94198e11 3.26090
\(495\) 3.78750e8i 0.00630858i
\(496\) 4.28882e10i 0.708617i
\(497\) −3.09513e9 −0.0507286
\(498\) 3.93640e10 0.640003
\(499\) −2.65185e10 −0.427707 −0.213853 0.976866i \(-0.568601\pi\)
−0.213853 + 0.976866i \(0.568601\pi\)
\(500\) 8.03307e9 0.128529
\(501\) −2.62774e10 −0.417092
\(502\) 1.10984e11i 1.74761i
\(503\) 4.34884e10i 0.679362i 0.940541 + 0.339681i \(0.110319\pi\)
−0.940541 + 0.339681i \(0.889681\pi\)
\(504\) 1.83224e9i 0.0283962i
\(505\) 3.98600e9i 0.0612875i
\(506\) 8.19512e10i 1.25012i
\(507\) −1.04573e11 −1.58266
\(508\) −1.63303e11 −2.45211
\(509\) 9.17675e10i 1.36715i −0.729878 0.683577i \(-0.760423\pi\)
0.729878 0.683577i \(-0.239577\pi\)
\(510\) 3.40242e8i 0.00502930i
\(511\) 7.36307e8i 0.0107988i
\(512\) 7.65389e10i 1.11379i
\(513\) −1.32984e10 −0.192013
\(514\) 2.37003e10i 0.339548i
\(515\) 1.68206e9i 0.0239118i
\(516\) 8.85109e10i 1.24853i
\(517\) −4.30339e10 −0.602349
\(518\) −9.62882e9 −0.133738
\(519\) 3.43428e9i 0.0473332i
\(520\) 7.08341e9 0.0968789
\(521\) 4.07268e10 0.552751 0.276376 0.961050i \(-0.410867\pi\)
0.276376 + 0.961050i \(0.410867\pi\)
\(522\) 8.81217e9i 0.118686i
\(523\) 8.55616e10 1.14359 0.571797 0.820395i \(-0.306246\pi\)
0.571797 + 0.820395i \(0.306246\pi\)
\(524\) 2.68331e11i 3.55914i
\(525\) 2.58263e9 0.0339957
\(526\) 1.63217e11i 2.13217i
\(527\) 1.38605e10i 0.179696i
\(528\) 1.43701e10i 0.184895i
\(529\) −6.54637e10 −0.835946
\(530\) 3.93242e9i 0.0498375i
\(531\) −2.33801e10 + 1.24762e10i −0.294082 + 0.156930i
\(532\) −8.74081e9 −0.109120
\(533\) 9.44877e9i 0.117076i
\(534\) −1.06069e11 −1.30444
\(535\) −4.06462e9 −0.0496140
\(536\) −1.96888e11 −2.38540
\(537\) 8.97628e9i 0.107944i
\(538\) 1.68249e11 2.00827
\(539\) 4.59250e10i 0.544120i
\(540\) −1.05227e9 −0.0123752
\(541\) 1.41371e11i 1.65033i −0.564894 0.825164i \(-0.691083\pi\)
0.564894 0.825164i \(-0.308917\pi\)
\(542\) 2.61542e10i 0.303071i
\(543\) −7.18675e10 −0.826673
\(544\) 5.91331e9i 0.0675204i
\(545\) 1.72322e9i 0.0195324i
\(546\) 9.88648e9 0.111243
\(547\) 2.82315e10 0.315344 0.157672 0.987492i \(-0.449601\pi\)
0.157672 + 0.987492i \(0.449601\pi\)
\(548\) −1.59322e10 −0.176666
\(549\) 5.14910e10i 0.566816i
\(550\) −8.43241e10 −0.921512
\(551\) 1.93787e10 0.210241
\(552\) −1.04954e11 −1.13043
\(553\) 4.69503e9 0.0502039
\(554\) 1.26613e11i 1.34412i
\(555\) 2.54911e9i 0.0268668i
\(556\) 1.23908e11 1.29658
\(557\) −7.13671e10 −0.741442 −0.370721 0.928744i \(-0.620889\pi\)
−0.370721 + 0.928744i \(0.620889\pi\)
\(558\) −6.59729e10 −0.680501
\(559\) −2.20155e11 −2.25466
\(560\) −1.17865e8 −0.00119848
\(561\) 4.64410e9i 0.0468868i
\(562\) 1.06130e11i 1.06388i
\(563\) 2.46340e10i 0.245189i 0.992457 + 0.122595i \(0.0391215\pi\)
−0.992457 + 0.122595i \(0.960879\pi\)
\(564\) 1.19559e11i 1.18159i
\(565\) 3.50620e9i 0.0344067i
\(566\) 6.21364e10 0.605453
\(567\) −6.77013e8 −0.00655035
\(568\) 1.29424e11i 1.24343i
\(569\) 1.72401e11i 1.64472i −0.568970 0.822358i \(-0.692658\pi\)
0.568970 0.822358i \(-0.307342\pi\)
\(570\) 3.56134e9i 0.0337376i
\(571\) 8.92475e9i 0.0839560i 0.999119 + 0.0419780i \(0.0133659\pi\)
−0.999119 + 0.0419780i \(0.986634\pi\)
\(572\) −2.09742e11 −1.95930
\(573\) 1.40749e10i 0.130565i
\(574\) 6.54530e8i 0.00602951i
\(575\) 1.47938e11i 1.35334i
\(576\) 4.96662e10 0.451202
\(577\) −5.89305e10 −0.531663 −0.265832 0.964019i \(-0.585647\pi\)
−0.265832 + 0.964019i \(0.585647\pi\)
\(578\) 1.84422e11i 1.65235i
\(579\) 8.98144e10 0.799156
\(580\) 1.53338e9 0.0135500
\(581\) 4.40694e9i 0.0386752i
\(582\) 2.66156e10 0.231977
\(583\) 5.36752e10i 0.464622i
\(584\) 3.07889e10 0.264693
\(585\) 2.61732e9i 0.0223477i
\(586\) 3.30819e11i 2.80544i
\(587\) 1.15907e11i 0.976243i −0.872776 0.488122i \(-0.837682\pi\)
0.872776 0.488122i \(-0.162318\pi\)
\(588\) 1.27592e11 1.06737
\(589\) 1.45080e11i 1.20544i
\(590\) 3.34117e9 + 6.26125e9i 0.0275734 + 0.0516717i
\(591\) 9.70714e10 0.795685
\(592\) 9.67153e10i 0.787424i
\(593\) −5.41875e10 −0.438208 −0.219104 0.975701i \(-0.570313\pi\)
−0.219104 + 0.975701i \(0.570313\pi\)
\(594\) 2.21048e10 0.177558
\(595\) −3.80913e7 −0.000303919
\(596\) 3.37820e11i 2.67732i
\(597\) −1.35535e11 −1.06697
\(598\) 5.66317e11i 4.42848i
\(599\) −1.14987e11 −0.893188 −0.446594 0.894737i \(-0.647363\pi\)
−0.446594 + 0.894737i \(0.647363\pi\)
\(600\) 1.07993e11i 0.833282i
\(601\) 1.86707e11i 1.43108i 0.698573 + 0.715539i \(0.253819\pi\)
−0.698573 + 0.715539i \(0.746181\pi\)
\(602\) 1.52504e10 0.116117
\(603\) 7.27502e10i 0.550256i
\(604\) 1.48602e11i 1.11655i
\(605\) 3.25928e9 0.0243276
\(606\) −2.32633e11 −1.72497
\(607\) 1.25763e11 0.926398 0.463199 0.886254i \(-0.346702\pi\)
0.463199 + 0.886254i \(0.346702\pi\)
\(608\) 6.18952e10i 0.452942i
\(609\) 9.86554e8 0.00717219
\(610\) 1.37894e10 0.0995925
\(611\) 2.97382e11 2.13378
\(612\) −1.29025e10 −0.0919750
\(613\) 1.57522e11i 1.11558i 0.829983 + 0.557788i \(0.188350\pi\)
−0.829983 + 0.557788i \(0.811650\pi\)
\(614\) 2.97686e11i 2.09452i
\(615\) 1.73278e8 0.00121128
\(616\) 6.69747e9 0.0465145
\(617\) −1.27615e11 −0.880566 −0.440283 0.897859i \(-0.645122\pi\)
−0.440283 + 0.897859i \(0.645122\pi\)
\(618\) 9.81695e10 0.673011
\(619\) 5.27837e10 0.359532 0.179766 0.983709i \(-0.442466\pi\)
0.179766 + 0.983709i \(0.442466\pi\)
\(620\) 1.14798e10i 0.0776901i
\(621\) 3.87806e10i 0.260764i
\(622\) 3.18420e11i 2.12735i
\(623\) 1.18748e10i 0.0788270i
\(624\) 9.93034e10i 0.654977i
\(625\) 1.52038e11 0.996397
\(626\) −3.57964e10 −0.233100
\(627\) 4.86103e10i 0.314527i
\(628\) 5.08645e11i 3.27021i
\(629\) 3.12563e10i 0.199680i
\(630\) 1.81306e8i 0.00115093i
\(631\) −1.41100e11 −0.890038 −0.445019 0.895521i \(-0.646803\pi\)
−0.445019 + 0.895521i \(0.646803\pi\)
\(632\) 1.96324e11i 1.23057i
\(633\) 2.68684e9i 0.0167350i
\(634\) 1.61014e11i 0.996565i
\(635\) 7.44894e9 0.0458142
\(636\) −1.49124e11 −0.911420
\(637\) 3.17361e11i 1.92751i
\(638\) −3.22115e10 −0.194414
\(639\) 4.78220e10 0.286830
\(640\) 1.06608e10i 0.0635431i
\(641\) 1.96649e11 1.16482 0.582411 0.812894i \(-0.302109\pi\)
0.582411 + 0.812894i \(0.302109\pi\)
\(642\) 2.37222e11i 1.39641i
\(643\) −7.88497e10 −0.461271 −0.230635 0.973040i \(-0.574080\pi\)
−0.230635 + 0.973040i \(0.574080\pi\)
\(644\) 2.54898e10i 0.148191i
\(645\) 4.03736e9i 0.0233270i
\(646\) 4.36680e10i 0.250746i
\(647\) 2.18154e11 1.24493 0.622467 0.782646i \(-0.286130\pi\)
0.622467 + 0.782646i \(0.286130\pi\)
\(648\) 2.83095e10i 0.160558i
\(649\) −4.56050e10 8.54623e10i −0.257059 0.481721i
\(650\) 5.82715e11 3.26440
\(651\) 7.38590e9i 0.0411225i
\(652\) 3.47716e11 1.92413
\(653\) −2.06412e11 −1.13522 −0.567612 0.823296i \(-0.692133\pi\)
−0.567612 + 0.823296i \(0.692133\pi\)
\(654\) 1.00572e11 0.549750
\(655\) 1.22397e10i 0.0664975i
\(656\) 6.57433e9 0.0355007
\(657\) 1.13765e10i 0.0610586i
\(658\) −2.06001e10 −0.109892
\(659\) 5.94177e8i 0.00315046i −0.999999 0.00157523i \(-0.999499\pi\)
0.999999 0.00157523i \(-0.000501412\pi\)
\(660\) 3.84640e9i 0.0202712i
\(661\) −9.83164e10 −0.515015 −0.257508 0.966276i \(-0.582901\pi\)
−0.257508 + 0.966276i \(0.582901\pi\)
\(662\) 1.99305e11i 1.03773i
\(663\) 3.20927e10i 0.166093i
\(664\) −1.84278e11 −0.947983
\(665\) 3.98705e8 0.00203876
\(666\) 1.48773e11 0.756181
\(667\) 5.65117e10i 0.285519i
\(668\) 2.66860e11 1.34023
\(669\) 1.44006e11 0.718914
\(670\) 1.94827e10 0.0966829
\(671\) −1.88217e11 −0.928474
\(672\) 3.15104e9i 0.0154517i
\(673\) 8.62581e10i 0.420475i −0.977650 0.210237i \(-0.932576\pi\)
0.977650 0.210237i \(-0.0674236\pi\)
\(674\) −4.02239e11 −1.94915
\(675\) −3.99035e10 −0.192219
\(676\) 1.06199e12 5.08551
\(677\) 1.61084e11 0.766828 0.383414 0.923577i \(-0.374748\pi\)
0.383414 + 0.923577i \(0.374748\pi\)
\(678\) −2.04631e11 −0.968394
\(679\) 2.97972e9i 0.0140183i
\(680\) 1.59280e9i 0.00744948i
\(681\) 7.64697e10i 0.355550i
\(682\) 2.41154e11i 1.11470i
\(683\) 2.63470e11i 1.21073i −0.795947 0.605366i \(-0.793027\pi\)
0.795947 0.605366i \(-0.206973\pi\)
\(684\) 1.35052e11 0.616988
\(685\) 7.26733e8 0.00330075
\(686\) 4.40448e10i 0.198883i
\(687\) 1.09228e11i 0.490352i
\(688\) 1.53181e11i 0.683676i
\(689\) 3.70918e11i 1.64589i
\(690\) 1.03855e10 0.0458176
\(691\) 1.11539e11i 0.489231i −0.969620 0.244615i \(-0.921338\pi\)
0.969620 0.244615i \(-0.0786617\pi\)
\(692\) 3.48768e10i 0.152094i
\(693\) 2.47471e9i 0.0107298i
\(694\) −1.67763e11 −0.723201
\(695\) −5.65198e9 −0.0242248
\(696\) 4.12530e10i 0.175800i
\(697\) 2.12468e9 0.00900249
\(698\) −1.26614e11 −0.533407
\(699\) 1.69240e11i 0.708915i
\(700\) −2.62279e10 −0.109237
\(701\) 2.29404e11i 0.950011i 0.879983 + 0.475005i \(0.157554\pi\)
−0.879983 + 0.475005i \(0.842446\pi\)
\(702\) −1.52754e11 −0.628989
\(703\) 3.27163e11i 1.33950i
\(704\) 1.81547e11i 0.739092i
\(705\) 5.45361e9i 0.0220764i
\(706\) −3.28192e11 −1.32102
\(707\) 2.60441e10i 0.104239i
\(708\) 2.37437e11 1.26703e11i 0.944963 0.504257i
\(709\) 7.40603e10 0.293090 0.146545 0.989204i \(-0.453185\pi\)
0.146545 + 0.989204i \(0.453185\pi\)
\(710\) 1.28069e10i 0.0503975i
\(711\) −7.25417e10 −0.283863
\(712\) 4.96550e11 1.93216
\(713\) 4.23079e11 1.63705
\(714\) 2.22311e9i 0.00855397i
\(715\) 9.56721e9 0.0366067
\(716\) 9.11587e10i 0.346853i
\(717\) −1.87344e11 −0.708864
\(718\) 4.33203e11i 1.63002i
\(719\) 1.90365e11i 0.712315i 0.934426 + 0.356158i \(0.115913\pi\)
−0.934426 + 0.356158i \(0.884087\pi\)
\(720\) 1.82110e9 0.00677647
\(721\) 1.09904e10i 0.0406699i
\(722\) 2.08442e9i 0.00767073i
\(723\) 1.07624e11 0.393872
\(724\) 7.29852e11 2.65632
\(725\) 5.81480e10 0.210467
\(726\) 1.90220e11i 0.684715i
\(727\) −2.66371e11 −0.953562 −0.476781 0.879022i \(-0.658197\pi\)
−0.476781 + 0.879022i \(0.658197\pi\)
\(728\) −4.62823e10 −0.164774
\(729\) 1.04604e10 0.0370370
\(730\) −3.04665e9 −0.0107283
\(731\) 4.95047e10i 0.173371i
\(732\) 5.22917e11i 1.82133i
\(733\) −2.05423e11 −0.711596 −0.355798 0.934563i \(-0.615791\pi\)
−0.355798 + 0.934563i \(0.615791\pi\)
\(734\) −1.22309e10 −0.0421379
\(735\) −5.82000e9 −0.0199422
\(736\) −1.80498e11 −0.615121
\(737\) −2.65927e11 −0.901349
\(738\) 1.01130e10i 0.0340921i
\(739\) 4.75269e11i 1.59353i 0.604287 + 0.796767i \(0.293458\pi\)
−0.604287 + 0.796767i \(0.706542\pi\)
\(740\) 2.58875e10i 0.0863302i
\(741\) 3.35917e11i 1.11419i
\(742\) 2.56940e10i 0.0847651i
\(743\) −4.87871e11 −1.60085 −0.800423 0.599436i \(-0.795392\pi\)
−0.800423 + 0.599436i \(0.795392\pi\)
\(744\) 3.08844e11 1.00797
\(745\) 1.54094e10i 0.0500219i
\(746\) 3.05717e11i 0.987109i
\(747\) 6.80906e10i 0.218678i
\(748\) 4.71632e10i 0.150660i
\(749\) 2.65578e10 0.0843849
\(750\) 2.13854e10i 0.0675883i
\(751\) 1.72924e11i 0.543620i 0.962351 + 0.271810i \(0.0876223\pi\)
−0.962351 + 0.271810i \(0.912378\pi\)
\(752\) 2.06915e11i 0.647024i
\(753\) −1.91976e11 −0.597129
\(754\) 2.22595e11 0.688700
\(755\) 6.77836e9i 0.0208611i
\(756\) 6.87541e9 0.0210480
\(757\) −2.66320e11 −0.811000 −0.405500 0.914095i \(-0.632903\pi\)
−0.405500 + 0.914095i \(0.632903\pi\)
\(758\) 3.92933e10i 0.119026i
\(759\) −1.41756e11 −0.427145
\(760\) 1.66720e10i 0.0499727i
\(761\) 2.54534e11 0.758938 0.379469 0.925204i \(-0.376107\pi\)
0.379469 + 0.925204i \(0.376107\pi\)
\(762\) 4.34740e11i 1.28946i
\(763\) 1.12594e10i 0.0332213i
\(764\) 1.42938e11i 0.419541i
\(765\) 5.88540e8 0.00171842
\(766\) 1.88293e11i 0.546915i
\(767\) 3.15149e11 + 5.90581e11i 0.910615 + 1.70647i
\(768\) −3.50311e11 −1.00695
\(769\) 4.99936e11i 1.42958i 0.699339 + 0.714791i \(0.253478\pi\)
−0.699339 + 0.714791i \(0.746522\pi\)
\(770\) −6.62735e8 −0.00188528
\(771\) −4.09960e10 −0.116018
\(772\) −9.12111e11 −2.56790
\(773\) 5.95523e11i 1.66794i 0.551810 + 0.833970i \(0.313937\pi\)
−0.551810 + 0.833970i \(0.686063\pi\)
\(774\) −2.35631e11 −0.656550
\(775\) 4.35329e11i 1.20673i
\(776\) −1.24598e11 −0.343608
\(777\) 1.66556e10i 0.0456958i
\(778\) 5.95687e11i 1.62592i
\(779\) −2.22392e10 −0.0603907
\(780\) 2.65802e10i 0.0718092i
\(781\) 1.74806e11i 0.469842i
\(782\) 1.27344e11 0.340527