Properties

Label 177.9.c.a.58.17
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 58.17
Character \(\chi\) \(=\) 177.58
Dual form 177.9.c.a.58.64

$q$-expansion

\(f(q)\) \(=\) \(q-20.4347i q^{2} -46.7654 q^{3} -161.576 q^{4} -84.1426 q^{5} +955.636i q^{6} +4222.23 q^{7} -1929.52i q^{8} +2187.00 q^{9} +O(q^{10})\) \(q-20.4347i q^{2} -46.7654 q^{3} -161.576 q^{4} -84.1426 q^{5} +955.636i q^{6} +4222.23 q^{7} -1929.52i q^{8} +2187.00 q^{9} +1719.43i q^{10} +16999.9i q^{11} +7556.18 q^{12} -10850.2i q^{13} -86279.9i q^{14} +3934.96 q^{15} -80792.6 q^{16} +148049. q^{17} -44690.7i q^{18} -234.411 q^{19} +13595.5 q^{20} -197454. q^{21} +347387. q^{22} +436492. i q^{23} +90234.5i q^{24} -383545. q^{25} -221720. q^{26} -102276. q^{27} -682212. q^{28} -448042. q^{29} -80409.6i q^{30} +1.30895e6i q^{31} +1.15702e6i q^{32} -795005. i q^{33} -3.02533e6i q^{34} -355269. q^{35} -353368. q^{36} +2.71698e6i q^{37} +4790.12i q^{38} +507413. i q^{39} +162354. i q^{40} -4.85649e6 q^{41} +4.03491e6i q^{42} +2.79551e6i q^{43} -2.74678e6i q^{44} -184020. q^{45} +8.91959e6 q^{46} +7.12970e6i q^{47} +3.77830e6 q^{48} +1.20624e7 q^{49} +7.83762e6i q^{50} -6.92355e6 q^{51} +1.75313e6i q^{52} +2.15001e6 q^{53} +2.08998e6i q^{54} -1.43041e6i q^{55} -8.14685e6i q^{56} +10962.3 q^{57} +9.15560e6i q^{58} +(1.16333e7 + 3.39063e6i) q^{59} -635797. q^{60} -1.41049e7i q^{61} +2.67480e7 q^{62} +9.23401e6 q^{63} +2.96035e6 q^{64} +912962. i q^{65} -1.62457e7 q^{66} +3.51125e6i q^{67} -2.39212e7 q^{68} -2.04127e7i q^{69} +7.25981e6i q^{70} -7.59726e6 q^{71} -4.21985e6i q^{72} -3.04904e7i q^{73} +5.55206e7 q^{74} +1.79366e7 q^{75} +37875.3 q^{76} +7.17772e7i q^{77} +1.03688e7 q^{78} -6.38797e7 q^{79} +6.79810e6 q^{80} +4.78297e6 q^{81} +9.92409e7i q^{82} +7.86934e7i q^{83} +3.19039e7 q^{84} -1.24572e7 q^{85} +5.71255e7 q^{86} +2.09528e7 q^{87} +3.28015e7 q^{88} -7.28576e6i q^{89} +3.76039e6i q^{90} -4.58119e7i q^{91} -7.05269e7i q^{92} -6.12136e7i q^{93} +1.45693e8 q^{94} +19723.9 q^{95} -5.41083e7i q^{96} -8.07168e7i q^{97} -2.46491e8i q^{98} +3.71787e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} + O(q^{10}) \) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} - 22680q^{12} - 59616q^{15} + 1199848q^{16} - 10608q^{17} - 27516q^{19} - 146436q^{20} - 974696q^{22} + 5718040q^{25} - 797484q^{26} - 3133000q^{28} + 1725924q^{29} + 4318800q^{35} - 22394880q^{36} - 732180q^{41} + 22752084q^{46} + 8703936q^{48} + 55899176q^{49} - 10373832q^{51} - 39265944q^{53} - 11408040q^{57} - 33575112q^{59} - 18034488q^{60} + 13038600q^{62} + 349920q^{63} - 241654260q^{64} - 35711928q^{66} + 36772608q^{68} - 235272660q^{71} - 63050712q^{74} + 74363184q^{75} + 9454680q^{76} - 10865988q^{78} + 17252580q^{79} + 318203976q^{80} + 382637520q^{81} - 20743128q^{84} - 27245820q^{85} + 105666984q^{86} + 29437992q^{87} + 82079788q^{88} + 121215992q^{94} - 690837276q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 20.4347i 1.27717i −0.769552 0.638584i \(-0.779520\pi\)
0.769552 0.638584i \(-0.220480\pi\)
\(3\) −46.7654 −0.577350
\(4\) −161.576 −0.631158
\(5\) −84.1426 −0.134628 −0.0673140 0.997732i \(-0.521443\pi\)
−0.0673140 + 0.997732i \(0.521443\pi\)
\(6\) 955.636i 0.737373i
\(7\) 4222.23 1.75853 0.879264 0.476335i \(-0.158035\pi\)
0.879264 + 0.476335i \(0.158035\pi\)
\(8\) 1929.52i 0.471073i
\(9\) 2187.00 0.333333
\(10\) 1719.43i 0.171943i
\(11\) 16999.9i 1.16111i 0.814220 + 0.580557i \(0.197165\pi\)
−0.814220 + 0.580557i \(0.802835\pi\)
\(12\) 7556.18 0.364399
\(13\) 10850.2i 0.379895i −0.981794 0.189948i \(-0.939168\pi\)
0.981794 0.189948i \(-0.0608318\pi\)
\(14\) 86279.9i 2.24594i
\(15\) 3934.96 0.0777276
\(16\) −80792.6 −1.23280
\(17\) 148049. 1.77259 0.886295 0.463121i \(-0.153270\pi\)
0.886295 + 0.463121i \(0.153270\pi\)
\(18\) 44690.7i 0.425723i
\(19\) −234.411 −0.00179872 −0.000899360 1.00000i \(-0.500286\pi\)
−0.000899360 1.00000i \(0.500286\pi\)
\(20\) 13595.5 0.0849716
\(21\) −197454. −1.01529
\(22\) 347387. 1.48294
\(23\) 436492.i 1.55979i 0.625912 + 0.779894i \(0.284727\pi\)
−0.625912 + 0.779894i \(0.715273\pi\)
\(24\) 90234.5i 0.271974i
\(25\) −383545. −0.981875
\(26\) −221720. −0.485190
\(27\) −102276. −0.192450
\(28\) −682212. −1.10991
\(29\) −448042. −0.633471 −0.316735 0.948514i \(-0.602587\pi\)
−0.316735 + 0.948514i \(0.602587\pi\)
\(30\) 80409.6i 0.0992712i
\(31\) 1.30895e6i 1.41735i 0.705536 + 0.708674i \(0.250706\pi\)
−0.705536 + 0.708674i \(0.749294\pi\)
\(32\) 1.15702e6i 1.10342i
\(33\) 795005.i 0.670369i
\(34\) 3.02533e6i 2.26390i
\(35\) −355269. −0.236747
\(36\) −353368. −0.210386
\(37\) 2.71698e6i 1.44970i 0.688905 + 0.724852i \(0.258092\pi\)
−0.688905 + 0.724852i \(0.741908\pi\)
\(38\) 4790.12i 0.00229727i
\(39\) 507413.i 0.219333i
\(40\) 162354.i 0.0634197i
\(41\) −4.85649e6 −1.71865 −0.859324 0.511431i \(-0.829116\pi\)
−0.859324 + 0.511431i \(0.829116\pi\)
\(42\) 4.03491e6i 1.29669i
\(43\) 2.79551e6i 0.817689i 0.912604 + 0.408844i \(0.134068\pi\)
−0.912604 + 0.408844i \(0.865932\pi\)
\(44\) 2.74678e6i 0.732846i
\(45\) −184020. −0.0448760
\(46\) 8.91959e6 1.99211
\(47\) 7.12970e6i 1.46110i 0.682860 + 0.730549i \(0.260736\pi\)
−0.682860 + 0.730549i \(0.739264\pi\)
\(48\) 3.77830e6 0.711756
\(49\) 1.20624e7 2.09242
\(50\) 7.83762e6i 1.25402i
\(51\) −6.92355e6 −1.02341
\(52\) 1.75313e6i 0.239774i
\(53\) 2.15001e6 0.272482 0.136241 0.990676i \(-0.456498\pi\)
0.136241 + 0.990676i \(0.456498\pi\)
\(54\) 2.08998e6i 0.245791i
\(55\) 1.43041e6i 0.156318i
\(56\) 8.14685e6i 0.828395i
\(57\) 10962.3 0.00103849
\(58\) 9.15560e6i 0.809049i
\(59\) 1.16333e7 + 3.39063e6i 0.960054 + 0.279816i
\(60\) −635797. −0.0490584
\(61\) 1.41049e7i 1.01871i −0.860557 0.509355i \(-0.829884\pi\)
0.860557 0.509355i \(-0.170116\pi\)
\(62\) 2.67480e7 1.81019
\(63\) 9.23401e6 0.586176
\(64\) 2.96035e6 0.176451
\(65\) 912962.i 0.0511446i
\(66\) −1.62457e7 −0.856174
\(67\) 3.51125e6i 0.174246i 0.996198 + 0.0871230i \(0.0277673\pi\)
−0.996198 + 0.0871230i \(0.972233\pi\)
\(68\) −2.39212e7 −1.11878
\(69\) 2.04127e7i 0.900544i
\(70\) 7.25981e6i 0.302366i
\(71\) −7.59726e6 −0.298967 −0.149484 0.988764i \(-0.547761\pi\)
−0.149484 + 0.988764i \(0.547761\pi\)
\(72\) 4.21985e6i 0.157024i
\(73\) 3.04904e7i 1.07367i −0.843687 0.536836i \(-0.819619\pi\)
0.843687 0.536836i \(-0.180381\pi\)
\(74\) 5.55206e7 1.85151
\(75\) 1.79366e7 0.566886
\(76\) 37875.3 0.00113528
\(77\) 7.17772e7i 2.04185i
\(78\) 1.03688e7 0.280125
\(79\) −6.38797e7 −1.64004 −0.820020 0.572335i \(-0.806038\pi\)
−0.820020 + 0.572335i \(0.806038\pi\)
\(80\) 6.79810e6 0.165969
\(81\) 4.78297e6 0.111111
\(82\) 9.92409e7i 2.19500i
\(83\) 7.86934e7i 1.65816i 0.559131 + 0.829079i \(0.311135\pi\)
−0.559131 + 0.829079i \(0.688865\pi\)
\(84\) 3.19039e7 0.640806
\(85\) −1.24572e7 −0.238640
\(86\) 5.71255e7 1.04433
\(87\) 2.09528e7 0.365735
\(88\) 3.28015e7 0.546969
\(89\) 7.28576e6i 0.116122i −0.998313 0.0580611i \(-0.981508\pi\)
0.998313 0.0580611i \(-0.0184918\pi\)
\(90\) 3.76039e6i 0.0573142i
\(91\) 4.58119e7i 0.668056i
\(92\) 7.05269e7i 0.984472i
\(93\) 6.12136e7i 0.818307i
\(94\) 1.45693e8 1.86607
\(95\) 19723.9 0.000242158
\(96\) 5.41083e7i 0.637058i
\(97\) 8.07168e7i 0.911752i −0.890043 0.455876i \(-0.849326\pi\)
0.890043 0.455876i \(-0.150674\pi\)
\(98\) 2.46491e8i 2.67237i
\(99\) 3.71787e7i 0.387038i
\(100\) 6.19718e7 0.619718
\(101\) 8.63367e7i 0.829679i −0.909895 0.414839i \(-0.863838\pi\)
0.909895 0.414839i \(-0.136162\pi\)
\(102\) 1.41480e8i 1.30706i
\(103\) 375851.i 0.00333939i −0.999999 0.00166970i \(-0.999469\pi\)
0.999999 0.00166970i \(-0.000531481\pi\)
\(104\) −2.09356e7 −0.178958
\(105\) 1.66143e7 0.136686
\(106\) 4.39348e7i 0.348005i
\(107\) 6.61773e7 0.504863 0.252432 0.967615i \(-0.418770\pi\)
0.252432 + 0.967615i \(0.418770\pi\)
\(108\) 1.65254e7 0.121466
\(109\) 2.66505e7i 0.188799i 0.995534 + 0.0943995i \(0.0300931\pi\)
−0.995534 + 0.0943995i \(0.969907\pi\)
\(110\) −2.92300e7 −0.199645
\(111\) 1.27060e8i 0.836987i
\(112\) −3.41125e8 −2.16791
\(113\) 5.90478e7i 0.362151i 0.983469 + 0.181076i \(0.0579579\pi\)
−0.983469 + 0.181076i \(0.942042\pi\)
\(114\) 224012.i 0.00132633i
\(115\) 3.67276e7i 0.209991i
\(116\) 7.23930e7 0.399820
\(117\) 2.37294e7i 0.126632i
\(118\) 6.92865e7 2.37723e8i 0.357372 1.22615i
\(119\) 6.25094e8 3.11715
\(120\) 7.59256e6i 0.0366154i
\(121\) −7.46364e7 −0.348184
\(122\) −2.88229e8 −1.30106
\(123\) 2.27116e8 0.992262
\(124\) 2.11496e8i 0.894571i
\(125\) 6.51406e7 0.266816
\(126\) 1.88694e8i 0.748645i
\(127\) −2.53094e8 −0.972898 −0.486449 0.873709i \(-0.661708\pi\)
−0.486449 + 0.873709i \(0.661708\pi\)
\(128\) 2.35702e8i 0.878059i
\(129\) 1.30733e8i 0.472093i
\(130\) 1.86561e7 0.0653202
\(131\) 6.07442e7i 0.206262i 0.994668 + 0.103131i \(0.0328861\pi\)
−0.994668 + 0.103131i \(0.967114\pi\)
\(132\) 1.28454e8i 0.423109i
\(133\) −989736. −0.00316310
\(134\) 7.17513e7 0.222541
\(135\) 8.60575e6 0.0259092
\(136\) 2.85662e8i 0.835020i
\(137\) 2.93273e8 0.832512 0.416256 0.909248i \(-0.363342\pi\)
0.416256 + 0.909248i \(0.363342\pi\)
\(138\) −4.17128e8 −1.15015
\(139\) 6.58855e8 1.76494 0.882472 0.470365i \(-0.155878\pi\)
0.882472 + 0.470365i \(0.155878\pi\)
\(140\) 5.74031e7 0.149425
\(141\) 3.33423e8i 0.843566i
\(142\) 1.55248e8i 0.381831i
\(143\) 1.84452e8 0.441101
\(144\) −1.76693e8 −0.410933
\(145\) 3.76994e7 0.0852830
\(146\) −6.23062e8 −1.37126
\(147\) −5.64102e8 −1.20806
\(148\) 4.39000e8i 0.914992i
\(149\) 5.48129e8i 1.11208i 0.831154 + 0.556042i \(0.187681\pi\)
−0.831154 + 0.556042i \(0.812319\pi\)
\(150\) 3.66529e8i 0.724009i
\(151\) 1.29386e8i 0.248874i 0.992228 + 0.124437i \(0.0397125\pi\)
−0.992228 + 0.124437i \(0.960288\pi\)
\(152\) 452300.i 0.000847329i
\(153\) 3.23782e8 0.590864
\(154\) 1.46675e9 2.60779
\(155\) 1.10139e8i 0.190815i
\(156\) 8.19860e7i 0.138434i
\(157\) 9.49411e8i 1.56263i −0.624138 0.781314i \(-0.714550\pi\)
0.624138 0.781314i \(-0.285450\pi\)
\(158\) 1.30536e9i 2.09461i
\(159\) −1.00546e8 −0.157317
\(160\) 9.73543e7i 0.148551i
\(161\) 1.84297e9i 2.74293i
\(162\) 9.77385e7i 0.141908i
\(163\) 5.58380e8 0.791006 0.395503 0.918465i \(-0.370570\pi\)
0.395503 + 0.918465i \(0.370570\pi\)
\(164\) 7.84695e8 1.08474
\(165\) 6.68937e7i 0.0902505i
\(166\) 1.60808e9 2.11775
\(167\) −4.71534e8 −0.606244 −0.303122 0.952952i \(-0.598029\pi\)
−0.303122 + 0.952952i \(0.598029\pi\)
\(168\) 3.80990e8i 0.478274i
\(169\) 6.98004e8 0.855680
\(170\) 2.54559e8i 0.304784i
\(171\) −512657. −0.000599573
\(172\) 4.51689e8i 0.516091i
\(173\) 1.77517e8i 0.198178i −0.995079 0.0990889i \(-0.968407\pi\)
0.995079 0.0990889i \(-0.0315928\pi\)
\(174\) 4.28165e8i 0.467104i
\(175\) −1.61941e9 −1.72666
\(176\) 1.37346e9i 1.43142i
\(177\) −5.44036e8 1.58564e8i −0.554287 0.161552i
\(178\) −1.48882e8 −0.148307
\(179\) 9.28138e8i 0.904067i 0.892001 + 0.452033i \(0.149301\pi\)
−0.892001 + 0.452033i \(0.850699\pi\)
\(180\) 2.97333e7 0.0283239
\(181\) 2.70900e7 0.0252403 0.0126202 0.999920i \(-0.495983\pi\)
0.0126202 + 0.999920i \(0.495983\pi\)
\(182\) −9.36152e8 −0.853220
\(183\) 6.59621e8i 0.588152i
\(184\) 8.42219e8 0.734774
\(185\) 2.28613e8i 0.195171i
\(186\) −1.25088e9 −1.04512
\(187\) 2.51680e9i 2.05818i
\(188\) 1.15199e9i 0.922184i
\(189\) −4.31832e8 −0.338429
\(190\) 403053.i 0.000309277i
\(191\) 1.66805e9i 1.25336i 0.779277 + 0.626680i \(0.215587\pi\)
−0.779277 + 0.626680i \(0.784413\pi\)
\(192\) −1.38442e8 −0.101874
\(193\) −1.59245e9 −1.14772 −0.573860 0.818953i \(-0.694555\pi\)
−0.573860 + 0.818953i \(0.694555\pi\)
\(194\) −1.64942e9 −1.16446
\(195\) 4.26950e7i 0.0295283i
\(196\) −1.94900e9 −1.32065
\(197\) 2.77911e9 1.84519 0.922593 0.385774i \(-0.126066\pi\)
0.922593 + 0.385774i \(0.126066\pi\)
\(198\) 7.59735e8 0.494312
\(199\) 2.17073e9 1.38418 0.692092 0.721809i \(-0.256689\pi\)
0.692092 + 0.721809i \(0.256689\pi\)
\(200\) 7.40056e8i 0.462535i
\(201\) 1.64205e8i 0.100601i
\(202\) −1.76426e9 −1.05964
\(203\) −1.89173e9 −1.11398
\(204\) 1.11868e9 0.645931
\(205\) 4.08638e8 0.231378
\(206\) −7.68040e6 −0.00426496
\(207\) 9.54609e8i 0.519929i
\(208\) 8.76615e8i 0.468334i
\(209\) 3.98495e6i 0.00208852i
\(210\) 3.39508e8i 0.174571i
\(211\) 2.21937e9i 1.11970i −0.828595 0.559849i \(-0.810859\pi\)
0.828595 0.559849i \(-0.189141\pi\)
\(212\) −3.47391e8 −0.171979
\(213\) 3.55288e8 0.172609
\(214\) 1.35231e9i 0.644795i
\(215\) 2.35222e8i 0.110084i
\(216\) 1.97343e8i 0.0906581i
\(217\) 5.52669e9i 2.49245i
\(218\) 5.44595e8 0.241128
\(219\) 1.42589e9i 0.619885i
\(220\) 2.31121e8i 0.0986617i
\(221\) 1.60635e9i 0.673399i
\(222\) −2.59644e9 −1.06897
\(223\) −2.31335e9 −0.935454 −0.467727 0.883873i \(-0.654927\pi\)
−0.467727 + 0.883873i \(0.654927\pi\)
\(224\) 4.88518e9i 1.94039i
\(225\) −8.38813e8 −0.327292
\(226\) 1.20662e9 0.462528
\(227\) 4.23736e9i 1.59585i 0.602757 + 0.797925i \(0.294069\pi\)
−0.602757 + 0.797925i \(0.705931\pi\)
\(228\) −1.77125e6 −0.000655452
\(229\) 3.99400e9i 1.45233i −0.687518 0.726167i \(-0.741300\pi\)
0.687518 0.726167i \(-0.258700\pi\)
\(230\) −7.50517e8 −0.268194
\(231\) 3.35669e9i 1.17886i
\(232\) 8.64504e8i 0.298411i
\(233\) 2.46144e8i 0.0835151i 0.999128 + 0.0417575i \(0.0132957\pi\)
−0.999128 + 0.0417575i \(0.986704\pi\)
\(234\) −4.84902e8 −0.161730
\(235\) 5.99911e8i 0.196705i
\(236\) −1.87967e9 5.47846e8i −0.605946 0.176608i
\(237\) 2.98736e9 0.946877
\(238\) 1.27736e10i 3.98112i
\(239\) −1.94711e9 −0.596760 −0.298380 0.954447i \(-0.596446\pi\)
−0.298380 + 0.954447i \(0.596446\pi\)
\(240\) −3.17916e8 −0.0958223
\(241\) −7.52200e8 −0.222980 −0.111490 0.993766i \(-0.535562\pi\)
−0.111490 + 0.993766i \(0.535562\pi\)
\(242\) 1.52517e9i 0.444690i
\(243\) −2.23677e8 −0.0641500
\(244\) 2.27902e9i 0.642967i
\(245\) −1.01496e9 −0.281699
\(246\) 4.64104e9i 1.26729i
\(247\) 2.54340e6i 0.000683325i
\(248\) 2.52564e9 0.667675
\(249\) 3.68013e9i 0.957338i
\(250\) 1.33113e9i 0.340769i
\(251\) −6.59545e9 −1.66169 −0.830845 0.556505i \(-0.812142\pi\)
−0.830845 + 0.556505i \(0.812142\pi\)
\(252\) −1.49200e9 −0.369970
\(253\) −7.42031e9 −1.81109
\(254\) 5.17190e9i 1.24255i
\(255\) 5.82565e8 0.137779
\(256\) 5.57435e9 1.29788
\(257\) 7.30477e9 1.67446 0.837228 0.546854i \(-0.184175\pi\)
0.837228 + 0.546854i \(0.184175\pi\)
\(258\) −2.67149e9 −0.602942
\(259\) 1.14717e10i 2.54934i
\(260\) 1.47513e8i 0.0322803i
\(261\) −9.79868e8 −0.211157
\(262\) 1.24129e9 0.263432
\(263\) −3.41679e9 −0.714160 −0.357080 0.934074i \(-0.616228\pi\)
−0.357080 + 0.934074i \(0.616228\pi\)
\(264\) −1.53397e9 −0.315793
\(265\) −1.80907e8 −0.0366837
\(266\) 2.02249e7i 0.00403981i
\(267\) 3.40721e8i 0.0670431i
\(268\) 5.67335e8i 0.109977i
\(269\) 4.46436e9i 0.852610i −0.904580 0.426305i \(-0.859815\pi\)
0.904580 0.426305i \(-0.140185\pi\)
\(270\) 1.75856e8i 0.0330904i
\(271\) −7.44341e9 −1.38005 −0.690025 0.723785i \(-0.742401\pi\)
−0.690025 + 0.723785i \(0.742401\pi\)
\(272\) −1.19612e10 −2.18525
\(273\) 2.14241e9i 0.385702i
\(274\) 5.99295e9i 1.06326i
\(275\) 6.52021e9i 1.14007i
\(276\) 3.29822e9i 0.568385i
\(277\) −3.80187e8 −0.0645770 −0.0322885 0.999479i \(-0.510280\pi\)
−0.0322885 + 0.999479i \(0.510280\pi\)
\(278\) 1.34635e10i 2.25413i
\(279\) 2.86268e9i 0.472450i
\(280\) 6.85497e8i 0.111525i
\(281\) −1.92388e9 −0.308570 −0.154285 0.988026i \(-0.549307\pi\)
−0.154285 + 0.988026i \(0.549307\pi\)
\(282\) −6.81339e9 −1.07738
\(283\) 9.46539e9i 1.47568i −0.674975 0.737841i \(-0.735846\pi\)
0.674975 0.737841i \(-0.264154\pi\)
\(284\) 1.22754e9 0.188695
\(285\) −922397. −0.000139810
\(286\) 3.76921e9i 0.563360i
\(287\) −2.05052e10 −3.02229
\(288\) 2.53039e9i 0.367805i
\(289\) 1.49426e10 2.14208
\(290\) 7.70375e8i 0.108921i
\(291\) 3.77475e9i 0.526400i
\(292\) 4.92653e9i 0.677657i
\(293\) 8.12893e9 1.10297 0.551484 0.834186i \(-0.314062\pi\)
0.551484 + 0.834186i \(0.314062\pi\)
\(294\) 1.15273e10i 1.54290i
\(295\) −9.78857e8 2.85296e8i −0.129250 0.0376711i
\(296\) 5.24245e9 0.682916
\(297\) 1.73868e9i 0.223456i
\(298\) 1.12008e10 1.42032
\(299\) 4.73602e9 0.592556
\(300\) −2.89814e9 −0.357795
\(301\) 1.18033e10i 1.43793i
\(302\) 2.64396e9 0.317854
\(303\) 4.03757e9i 0.479015i
\(304\) 1.89387e7 0.00221746
\(305\) 1.18682e9i 0.137147i
\(306\) 6.61639e9i 0.754632i
\(307\) 4.09629e9 0.461144 0.230572 0.973055i \(-0.425940\pi\)
0.230572 + 0.973055i \(0.425940\pi\)
\(308\) 1.15975e10i 1.28873i
\(309\) 1.75768e7i 0.00192800i
\(310\) −2.25065e9 −0.243703
\(311\) 1.03626e10 1.10771 0.553854 0.832614i \(-0.313157\pi\)
0.553854 + 0.832614i \(0.313157\pi\)
\(312\) 9.79061e8 0.103322
\(313\) 2.85666e9i 0.297633i 0.988865 + 0.148816i \(0.0475464\pi\)
−0.988865 + 0.148816i \(0.952454\pi\)
\(314\) −1.94009e10 −1.99574
\(315\) −7.76973e8 −0.0789158
\(316\) 1.03215e10 1.03512
\(317\) 1.46869e10 1.45443 0.727216 0.686408i \(-0.240814\pi\)
0.727216 + 0.686408i \(0.240814\pi\)
\(318\) 2.05463e9i 0.200921i
\(319\) 7.61665e9i 0.735531i
\(320\) −2.49091e8 −0.0237552
\(321\) −3.09480e9 −0.291483
\(322\) 3.76605e10 3.50318
\(323\) −3.47042e7 −0.00318839
\(324\) −7.72815e8 −0.0701287
\(325\) 4.16153e9i 0.373010i
\(326\) 1.14103e10i 1.01025i
\(327\) 1.24632e9i 0.109003i
\(328\) 9.37067e9i 0.809609i
\(329\) 3.01032e10i 2.56938i
\(330\) 1.36695e9 0.115265
\(331\) 6.01117e9 0.500780 0.250390 0.968145i \(-0.419441\pi\)
0.250390 + 0.968145i \(0.419441\pi\)
\(332\) 1.27150e10i 1.04656i
\(333\) 5.94203e9i 0.483235i
\(334\) 9.63566e9i 0.774275i
\(335\) 2.95446e8i 0.0234584i
\(336\) 1.59528e10 1.25164
\(337\) 9.23729e9i 0.716185i −0.933686 0.358092i \(-0.883427\pi\)
0.933686 0.358092i \(-0.116573\pi\)
\(338\) 1.42635e10i 1.09285i
\(339\) 2.76139e9i 0.209088i
\(340\) 2.01279e9 0.150620
\(341\) −2.22520e10 −1.64570
\(342\) 1.04760e7i 0.000765756i
\(343\) 2.65898e10 1.92105
\(344\) 5.39399e9 0.385191
\(345\) 1.71758e9i 0.121238i
\(346\) −3.62750e9 −0.253106
\(347\) 4.51897e9i 0.311689i −0.987782 0.155844i \(-0.950190\pi\)
0.987782 0.155844i \(-0.0498098\pi\)
\(348\) −3.38549e9 −0.230836
\(349\) 9.56963e9i 0.645050i −0.946561 0.322525i \(-0.895468\pi\)
0.946561 0.322525i \(-0.104532\pi\)
\(350\) 3.30922e10i 2.20523i
\(351\) 1.10971e9i 0.0731109i
\(352\) −1.96691e10 −1.28119
\(353\) 1.43592e10i 0.924765i 0.886680 + 0.462383i \(0.153005\pi\)
−0.886680 + 0.462383i \(0.846995\pi\)
\(354\) −3.24021e9 + 1.11172e10i −0.206329 + 0.707918i
\(355\) 6.39253e8 0.0402494
\(356\) 1.17721e9i 0.0732914i
\(357\) −2.92328e10 −1.79969
\(358\) 1.89662e10 1.15464
\(359\) −1.48076e10 −0.891468 −0.445734 0.895165i \(-0.647057\pi\)
−0.445734 + 0.895165i \(0.647057\pi\)
\(360\) 3.55069e8i 0.0211399i
\(361\) −1.69835e10 −0.999997
\(362\) 5.53576e8i 0.0322361i
\(363\) 3.49040e9 0.201024
\(364\) 7.40213e9i 0.421649i
\(365\) 2.56554e9i 0.144546i
\(366\) 1.34791e10 0.751169
\(367\) 8.19127e9i 0.451530i −0.974182 0.225765i \(-0.927512\pi\)
0.974182 0.225765i \(-0.0724882\pi\)
\(368\) 3.52654e10i 1.92290i
\(369\) −1.06211e10 −0.572883
\(370\) −4.67164e9 −0.249266
\(371\) 9.07783e9 0.479167
\(372\) 9.89068e9i 0.516481i
\(373\) −2.78651e9 −0.143955 −0.0719773 0.997406i \(-0.522931\pi\)
−0.0719773 + 0.997406i \(0.522931\pi\)
\(374\) 5.14301e10 2.62864
\(375\) −3.04633e9 −0.154046
\(376\) 1.37569e10 0.688284
\(377\) 4.86134e9i 0.240652i
\(378\) 8.82435e9i 0.432231i
\(379\) 6.27714e9 0.304232 0.152116 0.988363i \(-0.451391\pi\)
0.152116 + 0.988363i \(0.451391\pi\)
\(380\) −3.18692e6 −0.000152840
\(381\) 1.18360e10 0.561703
\(382\) 3.40861e10 1.60075
\(383\) −2.98388e10 −1.38671 −0.693356 0.720596i \(-0.743868\pi\)
−0.693356 + 0.720596i \(0.743868\pi\)
\(384\) 1.10227e10i 0.506948i
\(385\) 6.03952e9i 0.274890i
\(386\) 3.25412e10i 1.46583i
\(387\) 6.11379e9i 0.272563i
\(388\) 1.30419e10i 0.575460i
\(389\) −7.12005e9 −0.310946 −0.155473 0.987840i \(-0.549690\pi\)
−0.155473 + 0.987840i \(0.549690\pi\)
\(390\) −8.72459e8 −0.0377126
\(391\) 6.46221e10i 2.76486i
\(392\) 2.32746e10i 0.985683i
\(393\) 2.84073e9i 0.119086i
\(394\) 5.67902e10i 2.35661i
\(395\) 5.37500e9 0.220795
\(396\) 6.00720e9i 0.244282i
\(397\) 8.70816e9i 0.350562i 0.984518 + 0.175281i \(0.0560833\pi\)
−0.984518 + 0.175281i \(0.943917\pi\)
\(398\) 4.43582e10i 1.76784i
\(399\) 4.62854e7 0.00182622
\(400\) 3.09876e10 1.21045
\(401\) 4.74740e10i 1.83602i −0.396555 0.918011i \(-0.629794\pi\)
0.396555 0.918011i \(-0.370206\pi\)
\(402\) −3.35548e9 −0.128484
\(403\) 1.42024e10 0.538444
\(404\) 1.39500e10i 0.523658i
\(405\) −4.02451e8 −0.0149587
\(406\) 3.86570e10i 1.42273i
\(407\) −4.61882e10 −1.68327
\(408\) 1.33591e10i 0.482099i
\(409\) 2.06671e10i 0.738563i 0.929318 + 0.369281i \(0.120396\pi\)
−0.929318 + 0.369281i \(0.879604\pi\)
\(410\) 8.35038e9i 0.295509i
\(411\) −1.37150e10 −0.480651
\(412\) 6.07287e7i 0.00210768i
\(413\) 4.91185e10 + 1.43160e10i 1.68828 + 0.492064i
\(414\) 1.95071e10 0.664037
\(415\) 6.62147e9i 0.223235i
\(416\) 1.25538e10 0.419183
\(417\) −3.08116e10 −1.01899
\(418\) −8.14313e7 −0.00266739
\(419\) 5.71901e10i 1.85551i −0.373184 0.927757i \(-0.621734\pi\)
0.373184 0.927757i \(-0.378266\pi\)
\(420\) −2.68448e9 −0.0862705
\(421\) 4.00029e10i 1.27339i −0.771114 0.636697i \(-0.780300\pi\)
0.771114 0.636697i \(-0.219700\pi\)
\(422\) −4.53522e10 −1.43004
\(423\) 1.55926e10i 0.487033i
\(424\) 4.14848e9i 0.128359i
\(425\) −5.67833e10 −1.74046
\(426\) 7.26021e9i 0.220450i
\(427\) 5.95540e10i 1.79143i
\(428\) −1.06927e10 −0.318649
\(429\) −8.62595e9 −0.254670
\(430\) −4.80668e9 −0.140596
\(431\) 1.70819e10i 0.495024i 0.968885 + 0.247512i \(0.0796130\pi\)
−0.968885 + 0.247512i \(0.920387\pi\)
\(432\) 8.26314e9 0.237252
\(433\) 4.49387e10 1.27841 0.639203 0.769038i \(-0.279264\pi\)
0.639203 + 0.769038i \(0.279264\pi\)
\(434\) 1.12936e11 3.18327
\(435\) −1.76303e9 −0.0492381
\(436\) 4.30610e9i 0.119162i
\(437\) 1.02319e8i 0.00280562i
\(438\) 2.91377e10 0.791697
\(439\) −3.55016e10 −0.955850 −0.477925 0.878401i \(-0.658611\pi\)
−0.477925 + 0.878401i \(0.658611\pi\)
\(440\) −2.76000e9 −0.0736374
\(441\) 2.63804e10 0.697474
\(442\) −3.28253e10 −0.860043
\(443\) 3.35104e9i 0.0870092i −0.999053 0.0435046i \(-0.986148\pi\)
0.999053 0.0435046i \(-0.0138523\pi\)
\(444\) 2.05300e10i 0.528271i
\(445\) 6.13043e8i 0.0156333i
\(446\) 4.72726e10i 1.19473i
\(447\) 2.56335e10i 0.642062i
\(448\) 1.24993e10 0.310293
\(449\) −2.40863e10 −0.592632 −0.296316 0.955090i \(-0.595758\pi\)
−0.296316 + 0.955090i \(0.595758\pi\)
\(450\) 1.71409e10i 0.418007i
\(451\) 8.25597e10i 1.99555i
\(452\) 9.54074e9i 0.228575i
\(453\) 6.05079e9i 0.143688i
\(454\) 8.65892e10 2.03817
\(455\) 3.85473e9i 0.0899391i
\(456\) 2.11520e7i 0.000489205i
\(457\) 6.83044e10i 1.56597i −0.622040 0.782985i \(-0.713696\pi\)
0.622040 0.782985i \(-0.286304\pi\)
\(458\) −8.16162e10 −1.85487
\(459\) −1.51418e10 −0.341135
\(460\) 5.93431e9i 0.132538i
\(461\) 4.28118e9 0.0947894 0.0473947 0.998876i \(-0.484908\pi\)
0.0473947 + 0.998876i \(0.484908\pi\)
\(462\) −6.85929e10 −1.50561
\(463\) 6.77595e10i 1.47450i 0.675618 + 0.737252i \(0.263877\pi\)
−0.675618 + 0.737252i \(0.736123\pi\)
\(464\) 3.61985e10 0.780941
\(465\) 5.15067e9i 0.110167i
\(466\) 5.02987e9 0.106663
\(467\) 4.88768e10i 1.02763i 0.857902 + 0.513814i \(0.171768\pi\)
−0.857902 + 0.513814i \(0.828232\pi\)
\(468\) 3.83411e9i 0.0799246i
\(469\) 1.48253e10i 0.306416i
\(470\) −1.22590e10 −0.251225
\(471\) 4.43996e10i 0.902184i
\(472\) 6.54227e9 2.24467e10i 0.131814 0.452255i
\(473\) −4.75234e10 −0.949429
\(474\) 6.10457e10i 1.20932i
\(475\) 8.99072e7 0.00176612
\(476\) −1.01001e11 −1.96741
\(477\) 4.70208e9 0.0908272
\(478\) 3.97887e10i 0.762163i
\(479\) −2.15148e10 −0.408692 −0.204346 0.978899i \(-0.565507\pi\)
−0.204346 + 0.978899i \(0.565507\pi\)
\(480\) 4.55281e9i 0.0857659i
\(481\) 2.94797e10 0.550735
\(482\) 1.53710e10i 0.284782i
\(483\) 8.61872e10i 1.58363i
\(484\) 1.20595e10 0.219759
\(485\) 6.79172e9i 0.122747i
\(486\) 4.57078e9i 0.0819304i
\(487\) −2.81619e10 −0.500663 −0.250332 0.968160i \(-0.580540\pi\)
−0.250332 + 0.968160i \(0.580540\pi\)
\(488\) −2.72156e10 −0.479887
\(489\) −2.61129e10 −0.456688
\(490\) 2.07404e10i 0.359776i
\(491\) 7.94224e10 1.36652 0.683261 0.730174i \(-0.260561\pi\)
0.683261 + 0.730174i \(0.260561\pi\)
\(492\) −3.66965e10 −0.626274
\(493\) −6.63319e10 −1.12288
\(494\) 5.19736e7 0.000872721
\(495\) 3.12831e9i 0.0521062i
\(496\) 1.05754e11i 1.74730i
\(497\) −3.20773e10 −0.525742
\(498\) −7.52022e10 −1.22268
\(499\) 3.92428e10 0.632934 0.316467 0.948604i \(-0.397503\pi\)
0.316467 + 0.948604i \(0.397503\pi\)
\(500\) −1.05252e10 −0.168403
\(501\) 2.20515e10 0.350015
\(502\) 1.34776e11i 2.12226i
\(503\) 1.08109e11i 1.68884i −0.535682 0.844420i \(-0.679945\pi\)
0.535682 0.844420i \(-0.320055\pi\)
\(504\) 1.78172e10i 0.276132i
\(505\) 7.26459e9i 0.111698i
\(506\) 1.51632e11i 2.31307i
\(507\) −3.26424e10 −0.494027
\(508\) 4.08941e10 0.614052
\(509\) 8.80269e10i 1.31143i −0.755010 0.655714i \(-0.772368\pi\)
0.755010 0.655714i \(-0.227632\pi\)
\(510\) 1.19045e10i 0.175967i
\(511\) 1.28737e11i 1.88808i
\(512\) 5.35704e10i 0.779551i
\(513\) 2.39746e7 0.000346164
\(514\) 1.49271e11i 2.13856i
\(515\) 3.16251e7i 0.000449576i
\(516\) 2.11234e10i 0.297965i
\(517\) −1.21204e11 −1.69650
\(518\) 2.34420e11 3.25594
\(519\) 8.30164e9i 0.114418i
\(520\) 1.76157e9 0.0240928
\(521\) 1.43493e10 0.194751 0.0973753 0.995248i \(-0.468955\pi\)
0.0973753 + 0.995248i \(0.468955\pi\)
\(522\) 2.00233e10i 0.269683i
\(523\) 6.50338e10 0.869226 0.434613 0.900617i \(-0.356885\pi\)
0.434613 + 0.900617i \(0.356885\pi\)
\(524\) 9.81484e9i 0.130184i
\(525\) 7.57325e10 0.996885
\(526\) 6.98210e10i 0.912102i
\(527\) 1.93788e11i 2.51238i
\(528\) 6.42305e10i 0.826429i
\(529\) −1.12215e11 −1.43294
\(530\) 3.69679e9i 0.0468512i
\(531\) 2.54421e10 + 7.41531e9i 0.320018 + 0.0932720i
\(532\) 1.59918e8 0.00199642
\(533\) 5.26938e10i 0.652906i
\(534\) 6.96254e9 0.0856254
\(535\) −5.56832e9 −0.0679688
\(536\) 6.77501e9 0.0820826
\(537\) 4.34047e10i 0.521963i
\(538\) −9.12278e10 −1.08893
\(539\) 2.05059e11i 2.42954i
\(540\) −1.39049e9 −0.0163528
\(541\) 9.79103e10i 1.14298i 0.820608 + 0.571491i \(0.193635\pi\)
−0.820608 + 0.571491i \(0.806365\pi\)
\(542\) 1.52104e11i 1.76256i
\(543\) −1.26687e9 −0.0145725
\(544\) 1.71295e11i 1.95591i
\(545\) 2.24244e9i 0.0254176i
\(546\) 4.37795e10 0.492607
\(547\) 8.18786e10 0.914579 0.457290 0.889318i \(-0.348820\pi\)
0.457290 + 0.889318i \(0.348820\pi\)
\(548\) −4.73861e10 −0.525447
\(549\) 3.08474e10i 0.339570i
\(550\) −1.33238e11 −1.45606
\(551\) 1.05026e8 0.00113944
\(552\) −3.93867e10 −0.424222
\(553\) −2.69714e11 −2.88406
\(554\) 7.76900e9i 0.0824757i
\(555\) 1.06912e10i 0.112682i
\(556\) −1.06456e11 −1.11396
\(557\) −5.69753e10 −0.591924 −0.295962 0.955200i \(-0.595640\pi\)
−0.295962 + 0.955200i \(0.595640\pi\)
\(558\) 5.84979e10 0.603398
\(559\) 3.03319e10 0.310636
\(560\) 2.87031e10 0.291861
\(561\) 1.17699e11i 1.18829i
\(562\) 3.93140e10i 0.394096i
\(563\) 4.36537e10i 0.434498i −0.976116 0.217249i \(-0.930292\pi\)
0.976116 0.217249i \(-0.0697083\pi\)
\(564\) 5.38733e10i 0.532423i
\(565\) 4.96843e9i 0.0487557i
\(566\) −1.93422e11 −1.88469
\(567\) 2.01948e10 0.195392
\(568\) 1.46590e10i 0.140835i
\(569\) 2.52046e10i 0.240453i −0.992746 0.120226i \(-0.961638\pi\)
0.992746 0.120226i \(-0.0383621\pi\)
\(570\) 1.88489e7i 0.000178561i
\(571\) 1.02282e11i 0.962173i 0.876673 + 0.481087i \(0.159758\pi\)
−0.876673 + 0.481087i \(0.840242\pi\)
\(572\) −2.98030e10 −0.278405
\(573\) 7.80070e10i 0.723628i
\(574\) 4.19017e11i 3.85997i
\(575\) 1.67414e11i 1.53152i
\(576\) 6.47429e9 0.0588169
\(577\) −1.11183e11 −1.00308 −0.501539 0.865135i \(-0.667233\pi\)
−0.501539 + 0.865135i \(0.667233\pi\)
\(578\) 3.05348e11i 2.73579i
\(579\) 7.44715e10 0.662637
\(580\) −6.09133e9 −0.0538270
\(581\) 3.32261e11i 2.91592i
\(582\) 7.71358e10 0.672302
\(583\) 3.65499e10i 0.316382i
\(584\) −5.88317e10 −0.505778
\(585\) 1.99665e9i 0.0170482i
\(586\) 1.66112e11i 1.40868i
\(587\) 2.19724e11i 1.85066i 0.379166 + 0.925329i \(0.376211\pi\)
−0.379166 + 0.925329i \(0.623789\pi\)
\(588\) 9.11456e10 0.762477
\(589\) 3.06833e8i 0.00254941i
\(590\) −5.82994e9 + 2.00026e10i −0.0481123 + 0.165074i
\(591\) −1.29966e11 −1.06532
\(592\) 2.19512e11i 1.78719i
\(593\) 8.88296e10 0.718354 0.359177 0.933269i \(-0.383057\pi\)
0.359177 + 0.933269i \(0.383057\pi\)
\(594\) −3.55293e10 −0.285391
\(595\) −5.25970e10 −0.419656
\(596\) 8.85648e10i 0.701901i
\(597\) −1.01515e11 −0.799159
\(598\) 9.67792e10i 0.756793i
\(599\) 1.55066e11 1.20451 0.602253 0.798305i \(-0.294270\pi\)
0.602253 + 0.798305i \(0.294270\pi\)
\(600\) 3.46090e10i 0.267045i
\(601\) 2.03126e11i 1.55693i −0.627691 0.778463i \(-0.716000\pi\)
0.627691 0.778463i \(-0.284000\pi\)
\(602\) 2.41197e11 1.83648
\(603\) 7.67910e9i 0.0580820i
\(604\) 2.09057e10i 0.157079i
\(605\) 6.28009e9 0.0468754
\(606\) 8.25064e10 0.611783
\(607\) 6.46251e10 0.476043 0.238022 0.971260i \(-0.423501\pi\)
0.238022 + 0.971260i \(0.423501\pi\)
\(608\) 2.71217e8i 0.00198474i
\(609\) 8.84676e10 0.643154
\(610\) 2.42523e10 0.175160
\(611\) 7.73585e10 0.555064
\(612\) −5.23156e10 −0.372928
\(613\) 9.94284e10i 0.704156i 0.935971 + 0.352078i \(0.114525\pi\)
−0.935971 + 0.352078i \(0.885475\pi\)
\(614\) 8.37063e10i 0.588959i
\(615\) −1.91101e10 −0.133586
\(616\) 1.38495e11 0.961861
\(617\) −8.35450e10 −0.576474 −0.288237 0.957559i \(-0.593069\pi\)
−0.288237 + 0.957559i \(0.593069\pi\)
\(618\) 3.59177e8 0.00246238
\(619\) −2.26233e11 −1.54096 −0.770482 0.637462i \(-0.779984\pi\)
−0.770482 + 0.637462i \(0.779984\pi\)
\(620\) 1.77958e10i 0.120434i
\(621\) 4.46426e10i 0.300181i
\(622\) 2.11755e11i 1.41473i
\(623\) 3.07621e10i 0.204204i
\(624\) 4.09952e10i 0.270393i
\(625\) 1.44341e11 0.945954
\(626\) 5.83749e10 0.380127
\(627\) 1.86358e8i 0.00120581i
\(628\) 1.53402e11i 0.986265i
\(629\) 4.02245e11i 2.56973i
\(630\) 1.58772e10i 0.100789i
\(631\) −3.47458e10 −0.219172 −0.109586 0.993977i \(-0.534952\pi\)
−0.109586 + 0.993977i \(0.534952\pi\)
\(632\) 1.23257e11i 0.772579i
\(633\) 1.03790e11i 0.646457i
\(634\) 3.00123e11i 1.85755i
\(635\) 2.12960e10 0.130979
\(636\) 1.62459e10 0.0992921
\(637\) 1.30879e11i 0.794900i
\(638\) −1.55644e11 −0.939397
\(639\) −1.66152e10 −0.0996557
\(640\) 1.98326e10i 0.118211i
\(641\) −1.29053e11 −0.764424 −0.382212 0.924075i \(-0.624838\pi\)
−0.382212 + 0.924075i \(0.624838\pi\)
\(642\) 6.32414e10i 0.372273i
\(643\) 1.09423e11 0.640123 0.320062 0.947397i \(-0.396296\pi\)
0.320062 + 0.947397i \(0.396296\pi\)
\(644\) 2.97781e11i 1.73122i
\(645\) 1.10002e10i 0.0635569i
\(646\) 7.09170e8i 0.00407211i
\(647\) 2.14235e11 1.22257 0.611283 0.791412i \(-0.290654\pi\)
0.611283 + 0.791412i \(0.290654\pi\)
\(648\) 9.22881e9i 0.0523415i
\(649\) −5.76402e10 + 1.97765e11i −0.324898 + 1.11473i
\(650\) 8.50397e10 0.476396
\(651\) 2.58458e11i 1.43902i
\(652\) −9.02211e10 −0.499250
\(653\) 2.65634e11 1.46093 0.730467 0.682947i \(-0.239302\pi\)
0.730467 + 0.682947i \(0.239302\pi\)
\(654\) −2.54682e10 −0.139215
\(655\) 5.11118e9i 0.0277687i
\(656\) 3.92369e11 2.11875
\(657\) 6.66825e10i 0.357891i
\(658\) 6.15149e11 3.28153
\(659\) 1.38564e11i 0.734698i −0.930083 0.367349i \(-0.880266\pi\)
0.930083 0.367349i \(-0.119734\pi\)
\(660\) 1.08085e10i 0.0569623i
\(661\) −1.59272e11 −0.834319 −0.417160 0.908833i \(-0.636974\pi\)
−0.417160 + 0.908833i \(0.636974\pi\)
\(662\) 1.22836e11i 0.639580i
\(663\) 7.51217e10i 0.388787i
\(664\) 1.51840e11 0.781114
\(665\) 8.32789e7 0.000425842
\(666\) 1.21424e11 0.617172
\(667\) 1.95567e11i 0.988080i
\(668\) 7.61888e10 0.382636
\(669\) 1.08185e11 0.540084
\(670\) −6.03734e9 −0.0299603
\(671\) 2.39781e11 1.18284
\(672\) 2.28457e11i 1.12028i
\(673\) 3.26959e11i 1.59380i 0.604114 + 0.796898i \(0.293527\pi\)
−0.604114 + 0.796898i \(0.706473\pi\)
\(674\) −1.88761e11 −0.914688
\(675\) 3.92274e10 0.188962
\(676\) −1.12781e11 −0.540069
\(677\) −1.41939e11 −0.675690 −0.337845 0.941202i \(-0.609698\pi\)
−0.337845 + 0.941202i \(0.609698\pi\)
\(678\) −5.64282e10 −0.267041
\(679\) 3.40804e11i 1.60334i
\(680\) 2.40363e10i 0.112417i
\(681\) 1.98162e11i 0.921365i
\(682\) 4.54712e11i 2.10184i
\(683\) 9.39417e10i 0.431693i −0.976427 0.215847i \(-0.930749\pi\)
0.976427 0.215847i \(-0.0692512\pi\)
\(684\) 8.28333e7 0.000378426
\(685\) −2.46768e10 −0.112079
\(686\) 5.43355e11i 2.45351i
\(687\) 1.86781e11i 0.838505i
\(688\) 2.25857e11i 1.00804i
\(689\) 2.33280e10i 0.103514i
\(690\) 3.50982e10 0.154842
\(691\) 1.24138e10i 0.0544494i −0.999629 0.0272247i \(-0.991333\pi\)
0.999629 0.0272247i \(-0.00866696\pi\)
\(692\) 2.86825e10i 0.125081i
\(693\) 1.56977e11i 0.680617i
\(694\) −9.23436e10 −0.398079
\(695\) −5.54378e10 −0.237611
\(696\) 4.04288e10i 0.172288i
\(697\) −7.18996e11 −3.04646
\(698\) −1.95552e11 −0.823837
\(699\) 1.15110e10i 0.0482175i
\(700\) 2.61659e11 1.08979
\(701\) 7.13533e10i 0.295489i −0.989026 0.147745i \(-0.952799\pi\)
0.989026 0.147745i \(-0.0472014\pi\)
\(702\) 2.26766e10 0.0933748
\(703\) 6.36889e8i 0.00260761i
\(704\) 5.03255e10i 0.204879i
\(705\) 2.80551e10i 0.113568i
\(706\) 2.93426e11 1.18108
\(707\) 3.64533e11i 1.45901i
\(708\) 8.79035e10 + 2.56202e10i 0.349843 + 0.101965i
\(709\) −2.84497e11 −1.12588 −0.562942 0.826497i \(-0.690330\pi\)
−0.562942 + 0.826497i \(0.690330\pi\)
\(710\) 1.30629e10i 0.0514052i
\(711\) −1.39705e11 −0.546680
\(712\) −1.40580e10 −0.0547020
\(713\) −5.71347e11 −2.21076
\(714\) 5.97363e11i 2.29850i
\(715\) −1.55202e10 −0.0593846
\(716\) 1.49965e11i 0.570609i
\(717\) 9.10575e10 0.344540
\(718\) 3.02588e11i 1.13855i
\(719\) 3.11106e11i 1.16411i −0.813151 0.582053i \(-0.802249\pi\)
0.813151 0.582053i \(-0.197751\pi\)
\(720\) 1.48674e10 0.0553231
\(721\) 1.58693e9i 0.00587241i
\(722\) 3.47053e11i 1.27716i
\(723\) 3.51769e10 0.128737
\(724\) −4.37711e9 −0.0159306
\(725\) 1.71844e11 0.621989
\(726\) 7.13252e10i 0.256742i
\(727\) 4.55240e11 1.62968 0.814840 0.579686i \(-0.196825\pi\)
0.814840 + 0.579686i \(0.196825\pi\)
\(728\) −8.83948e10 −0.314703
\(729\) 1.04604e10 0.0370370
\(730\) 5.24260e10 0.184610
\(731\) 4.13872e11i 1.44943i
\(732\) 1.06579e11i 0.371217i
\(733\) 2.37585e11 0.823005 0.411502 0.911409i \(-0.365004\pi\)
0.411502 + 0.911409i \(0.365004\pi\)
\(734\) −1.67386e11 −0.576680
\(735\) 4.74650e10 0.162639
\(736\) −5.05029e11 −1.72109
\(737\) −5.96908e10 −0.202319
\(738\) 2.17040e11i 0.731668i
\(739\) 1.01236e11i 0.339435i 0.985493 + 0.169718i \(0.0542856\pi\)
−0.985493 + 0.169718i \(0.945714\pi\)
\(740\) 3.69386e10i 0.123184i
\(741\) 1.18943e8i 0.000394518i
\(742\) 1.85503e11i 0.611976i
\(743\) −2.77292e11 −0.909877 −0.454938 0.890523i \(-0.650339\pi\)
−0.454938 + 0.890523i \(0.650339\pi\)
\(744\) −1.18113e11 −0.385482
\(745\) 4.61210e10i 0.149718i
\(746\) 5.69415e10i 0.183854i
\(747\) 1.72103e11i 0.552720i
\(748\) 4.06656e11i 1.29904i
\(749\) 2.79415e11 0.887816
\(750\) 6.22507e10i 0.196743i
\(751\) 2.20002e10i 0.0691619i 0.999402 + 0.0345810i \(0.0110097\pi\)
−0.999402 + 0.0345810i \(0.988990\pi\)
\(752\) 5.76027e11i 1.80124i
\(753\) 3.08439e11 0.959377
\(754\) 9.93399e10 0.307354
\(755\) 1.08869e10i 0.0335054i
\(756\) 6.97739e10 0.213602
\(757\) 3.91803e11 1.19312 0.596560 0.802569i \(-0.296534\pi\)
0.596560 + 0.802569i \(0.296534\pi\)
\(758\) 1.28271e11i 0.388556i
\(759\) 3.47014e11 1.04563
\(760\) 3.80576e7i 0.000114074i
\(761\) 3.95967e11 1.18065 0.590324 0.807167i \(-0.299000\pi\)
0.590324 + 0.807167i \(0.299000\pi\)
\(762\) 2.41866e11i 0.717389i
\(763\) 1.12525e11i 0.332008i
\(764\) 2.69518e11i 0.791068i
\(765\) −2.72439e10 −0.0795468
\(766\) 6.09746e11i 1.77106i
\(767\) 3.67890e10 1.26224e11i 0.106301 0.364720i
\(768\) −2.60687e11 −0.749331
\(769\) 3.19883e11i 0.914714i 0.889283 + 0.457357i \(0.151204\pi\)
−0.889283 + 0.457357i \(0.848796\pi\)
\(770\) −1.23416e11 −0.351081
\(771\) −3.41610e11 −0.966748
\(772\) 2.57302e11 0.724393
\(773\) 1.40067e11i 0.392299i 0.980574 + 0.196150i \(0.0628438\pi\)
−0.980574 + 0.196150i \(0.937156\pi\)
\(774\) 1.24933e11 0.348109
\(775\) 5.02042e11i 1.39166i
\(776\) −1.55744e11 −0.429502
\(777\) 5.36478e11i 1.47186i
\(778\) 1.45496e11i 0.397130i
\(779\) 1.13841e9 0.00309137
\(780\) 6.89851e9i 0.0186370i
\(781\) 1.29152e11i 0.347135i
\(782\) 1.32053e12 3.53120