Properties

Label 177.7.c.a.58.20
Level $177$
Weight $7$
Character 177.58
Analytic conductor $40.720$
Analytic rank $0$
Dimension $60$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(40.7195728007\)
Analytic rank: \(0\)
Dimension: \(60\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.20
Character \(\chi\) \(=\) 177.58
Dual form 177.7.c.a.58.41

$q$-expansion

\(f(q)\) \(=\) \(q-6.65433i q^{2} +15.5885 q^{3} +19.7199 q^{4} +168.519 q^{5} -103.731i q^{6} +568.245 q^{7} -557.100i q^{8} +243.000 q^{9} +O(q^{10})\) \(q-6.65433i q^{2} +15.5885 q^{3} +19.7199 q^{4} +168.519 q^{5} -103.731i q^{6} +568.245 q^{7} -557.100i q^{8} +243.000 q^{9} -1121.38i q^{10} -433.875i q^{11} +307.403 q^{12} -1424.64i q^{13} -3781.29i q^{14} +2626.95 q^{15} -2445.05 q^{16} -3203.72 q^{17} -1617.00i q^{18} -480.820 q^{19} +3323.18 q^{20} +8858.06 q^{21} -2887.14 q^{22} +5842.85i q^{23} -8684.33i q^{24} +12773.6 q^{25} -9480.00 q^{26} +3788.00 q^{27} +11205.7 q^{28} -16081.4 q^{29} -17480.6i q^{30} +48586.3i q^{31} -19384.2i q^{32} -6763.43i q^{33} +21318.6i q^{34} +95759.9 q^{35} +4791.94 q^{36} +27263.4i q^{37} +3199.53i q^{38} -22207.9i q^{39} -93881.7i q^{40} -14615.3 q^{41} -58944.4i q^{42} -68476.3i q^{43} -8555.98i q^{44} +40950.0 q^{45} +38880.2 q^{46} +189784. i q^{47} -38114.5 q^{48} +205253. q^{49} -84999.4i q^{50} -49941.0 q^{51} -28093.8i q^{52} -263394. q^{53} -25206.6i q^{54} -73116.0i q^{55} -316569. i q^{56} -7495.24 q^{57} +107011. i q^{58} +(30685.3 + 203074. i) q^{59} +51803.2 q^{60} +68461.2i q^{61} +323309. q^{62} +138083. q^{63} -285472. q^{64} -240078. i q^{65} -45006.1 q^{66} -381209. i q^{67} -63177.1 q^{68} +91081.0i q^{69} -637218. i q^{70} -330328. q^{71} -135375. i q^{72} +63471.0i q^{73} +181419. q^{74} +199120. q^{75} -9481.73 q^{76} -246547. i q^{77} -147779. q^{78} +49824.6 q^{79} -412036. q^{80} +59049.0 q^{81} +97255.2i q^{82} -57827.2i q^{83} +174680. q^{84} -539887. q^{85} -455664. q^{86} -250685. q^{87} -241711. q^{88} -792215. i q^{89} -272495. i q^{90} -809543. i q^{91} +115221. i q^{92} +757386. i q^{93} +1.26289e6 q^{94} -81027.1 q^{95} -302170. i q^{96} +632824. i q^{97} -1.36582e6i q^{98} -105432. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} + O(q^{10}) \) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} - 1944q^{12} - 4536q^{15} + 56616q^{16} + 8480q^{17} + 11376q^{19} + 40796q^{20} - 8232q^{22} + 197940q^{25} + 147252q^{26} + 71640q^{28} + 63456q^{29} - 364432q^{35} - 466560q^{36} + 99632q^{41} - 470316q^{46} + 171072q^{48} + 1737420q^{49} + 60912q^{51} + 92240q^{53} + 186624q^{57} + 917264q^{59} + 1063368q^{60} - 115768q^{62} - 99144q^{63} - 1107444q^{64} + 1172232q^{66} - 4247232q^{68} + 1498048q^{71} + 1161448q^{74} - 1477440q^{75} - 1045320q^{76} - 1060452q^{78} - 90600q^{79} + 77096q^{80} + 3542940q^{81} - 2225880q^{84} - 693408q^{85} - 1567768q^{86} + 1821528q^{87} + 62892q^{88} + 5268696q^{94} + 296128q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 6.65433i 0.831791i −0.909412 0.415895i \(-0.863468\pi\)
0.909412 0.415895i \(-0.136532\pi\)
\(3\) 15.5885 0.577350
\(4\) 19.7199 0.308124
\(5\) 168.519 1.34815 0.674075 0.738663i \(-0.264543\pi\)
0.674075 + 0.738663i \(0.264543\pi\)
\(6\) 103.731i 0.480235i
\(7\) 568.245 1.65669 0.828345 0.560218i \(-0.189283\pi\)
0.828345 + 0.560218i \(0.189283\pi\)
\(8\) 557.100i 1.08809i
\(9\) 243.000 0.333333
\(10\) 1121.38i 1.12138i
\(11\) 433.875i 0.325976i −0.986628 0.162988i \(-0.947887\pi\)
0.986628 0.162988i \(-0.0521132\pi\)
\(12\) 307.403 0.177895
\(13\) 1424.64i 0.648447i −0.945981 0.324223i \(-0.894897\pi\)
0.945981 0.324223i \(-0.105103\pi\)
\(14\) 3781.29i 1.37802i
\(15\) 2626.95 0.778355
\(16\) −2445.05 −0.596936
\(17\) −3203.72 −0.652090 −0.326045 0.945354i \(-0.605716\pi\)
−0.326045 + 0.945354i \(0.605716\pi\)
\(18\) 1617.00i 0.277264i
\(19\) −480.820 −0.0701006 −0.0350503 0.999386i \(-0.511159\pi\)
−0.0350503 + 0.999386i \(0.511159\pi\)
\(20\) 3323.18 0.415397
\(21\) 8858.06 0.956491
\(22\) −2887.14 −0.271144
\(23\) 5842.85i 0.480221i 0.970746 + 0.240110i \(0.0771837\pi\)
−0.970746 + 0.240110i \(0.922816\pi\)
\(24\) 8684.33i 0.628206i
\(25\) 12773.6 0.817508
\(26\) −9480.00 −0.539372
\(27\) 3788.00 0.192450
\(28\) 11205.7 0.510466
\(29\) −16081.4 −0.659373 −0.329686 0.944090i \(-0.606943\pi\)
−0.329686 + 0.944090i \(0.606943\pi\)
\(30\) 17480.6i 0.647428i
\(31\) 48586.3i 1.63091i 0.578823 + 0.815453i \(0.303512\pi\)
−0.578823 + 0.815453i \(0.696488\pi\)
\(32\) 19384.2i 0.591560i
\(33\) 6763.43i 0.188203i
\(34\) 21318.6i 0.542403i
\(35\) 95759.9 2.23347
\(36\) 4791.94 0.102708
\(37\) 27263.4i 0.538238i 0.963107 + 0.269119i \(0.0867324\pi\)
−0.963107 + 0.269119i \(0.913268\pi\)
\(38\) 3199.53i 0.0583090i
\(39\) 22207.9i 0.374381i
\(40\) 93881.7i 1.46690i
\(41\) −14615.3 −0.212059 −0.106030 0.994363i \(-0.533814\pi\)
−0.106030 + 0.994363i \(0.533814\pi\)
\(42\) 58944.4i 0.795600i
\(43\) 68476.3i 0.861262i −0.902528 0.430631i \(-0.858291\pi\)
0.902528 0.430631i \(-0.141709\pi\)
\(44\) 8555.98i 0.100441i
\(45\) 40950.0 0.449383
\(46\) 38880.2 0.399443
\(47\) 189784.i 1.82796i 0.405762 + 0.913979i \(0.367006\pi\)
−0.405762 + 0.913979i \(0.632994\pi\)
\(48\) −38114.5 −0.344641
\(49\) 205253. 1.74462
\(50\) 84999.4i 0.679995i
\(51\) −49941.0 −0.376484
\(52\) 28093.8i 0.199802i
\(53\) −263394. −1.76921 −0.884604 0.466343i \(-0.845571\pi\)
−0.884604 + 0.466343i \(0.845571\pi\)
\(54\) 25206.6i 0.160078i
\(55\) 73116.0i 0.439465i
\(56\) 316569.i 1.80262i
\(57\) −7495.24 −0.0404726
\(58\) 107011.i 0.548460i
\(59\) 30685.3 + 203074.i 0.149408 + 0.988776i
\(60\) 51803.2 0.239830
\(61\) 68461.2i 0.301617i 0.988563 + 0.150808i \(0.0481876\pi\)
−0.988563 + 0.150808i \(0.951812\pi\)
\(62\) 323309. 1.35657
\(63\) 138083. 0.552230
\(64\) −285472. −1.08899
\(65\) 240078.i 0.874203i
\(66\) −45006.1 −0.156545
\(67\) 381209.i 1.26747i −0.773549 0.633736i \(-0.781520\pi\)
0.773549 0.633736i \(-0.218480\pi\)
\(68\) −63177.1 −0.200925
\(69\) 91081.0i 0.277256i
\(70\) 637218.i 1.85778i
\(71\) −330328. −0.922935 −0.461467 0.887157i \(-0.652677\pi\)
−0.461467 + 0.887157i \(0.652677\pi\)
\(72\) 135375.i 0.362695i
\(73\) 63471.0i 0.163157i 0.996667 + 0.0815787i \(0.0259962\pi\)
−0.996667 + 0.0815787i \(0.974004\pi\)
\(74\) 181419. 0.447701
\(75\) 199120. 0.471988
\(76\) −9481.73 −0.0215997
\(77\) 246547.i 0.540042i
\(78\) −147779. −0.311407
\(79\) 49824.6 0.101056 0.0505281 0.998723i \(-0.483910\pi\)
0.0505281 + 0.998723i \(0.483910\pi\)
\(80\) −412036. −0.804759
\(81\) 59049.0 0.111111
\(82\) 97255.2i 0.176389i
\(83\) 57827.2i 0.101134i −0.998721 0.0505671i \(-0.983897\pi\)
0.998721 0.0505671i \(-0.0161029\pi\)
\(84\) 174680. 0.294718
\(85\) −539887. −0.879115
\(86\) −455664. −0.716389
\(87\) −250685. −0.380689
\(88\) −241711. −0.354690
\(89\) 792215.i 1.12376i −0.827219 0.561879i \(-0.810079\pi\)
0.827219 0.561879i \(-0.189921\pi\)
\(90\) 272495.i 0.373793i
\(91\) 809543.i 1.07428i
\(92\) 115221.i 0.147968i
\(93\) 757386.i 0.941604i
\(94\) 1.26289e6 1.52048
\(95\) −81027.1 −0.0945060
\(96\) 302170.i 0.341537i
\(97\) 632824.i 0.693374i 0.937981 + 0.346687i \(0.112693\pi\)
−0.937981 + 0.346687i \(0.887307\pi\)
\(98\) 1.36582e6i 1.45116i
\(99\) 105432.i 0.108659i
\(100\) 251894. 0.251894
\(101\) 1.61402e6i 1.56655i −0.621675 0.783276i \(-0.713547\pi\)
0.621675 0.783276i \(-0.286453\pi\)
\(102\) 332324.i 0.313156i
\(103\) 801623.i 0.733599i 0.930300 + 0.366799i \(0.119546\pi\)
−0.930300 + 0.366799i \(0.880454\pi\)
\(104\) −793665. −0.705566
\(105\) 1.49275e6 1.28949
\(106\) 1.75271e6i 1.47161i
\(107\) 188639. 0.153985 0.0769927 0.997032i \(-0.475468\pi\)
0.0769927 + 0.997032i \(0.475468\pi\)
\(108\) 74699.0 0.0592985
\(109\) 137612.i 0.106261i −0.998588 0.0531307i \(-0.983080\pi\)
0.998588 0.0531307i \(-0.0169200\pi\)
\(110\) −486538. −0.365543
\(111\) 424994.i 0.310752i
\(112\) −1.38939e6 −0.988938
\(113\) 952885.i 0.660397i −0.943912 0.330198i \(-0.892884\pi\)
0.943912 0.330198i \(-0.107116\pi\)
\(114\) 49875.8i 0.0336647i
\(115\) 984629.i 0.647410i
\(116\) −317125. −0.203169
\(117\) 346187.i 0.216149i
\(118\) 1.35132e6 204190.i 0.822455 0.124276i
\(119\) −1.82050e6 −1.08031
\(120\) 1.46347e6i 0.846916i
\(121\) 1.58331e6 0.893739
\(122\) 455564. 0.250882
\(123\) −227831. −0.122432
\(124\) 958119.i 0.502521i
\(125\) −480522. −0.246027
\(126\) 918853.i 0.459340i
\(127\) 2.83971e6 1.38632 0.693159 0.720785i \(-0.256218\pi\)
0.693159 + 0.720785i \(0.256218\pi\)
\(128\) 659034.i 0.314252i
\(129\) 1.06744e6i 0.497250i
\(130\) −1.59756e6 −0.727154
\(131\) 1.05300e6i 0.468395i 0.972189 + 0.234198i \(0.0752463\pi\)
−0.972189 + 0.234198i \(0.924754\pi\)
\(132\) 133374.i 0.0579897i
\(133\) −273223. −0.116135
\(134\) −2.53669e6 −1.05427
\(135\) 638348. 0.259452
\(136\) 1.78479e6i 0.709530i
\(137\) 3.78035e6 1.47018 0.735090 0.677969i \(-0.237140\pi\)
0.735090 + 0.677969i \(0.237140\pi\)
\(138\) 606083. 0.230619
\(139\) 2.26731e6 0.844240 0.422120 0.906540i \(-0.361286\pi\)
0.422120 + 0.906540i \(0.361286\pi\)
\(140\) 1.88838e6 0.688184
\(141\) 2.95844e6i 1.05537i
\(142\) 2.19811e6i 0.767689i
\(143\) −618114. −0.211378
\(144\) −594147. −0.198979
\(145\) −2.71002e6 −0.888933
\(146\) 422357. 0.135713
\(147\) 3.19958e6 1.00726
\(148\) 537631.i 0.165844i
\(149\) 352053.i 0.106426i 0.998583 + 0.0532132i \(0.0169463\pi\)
−0.998583 + 0.0532132i \(0.983054\pi\)
\(150\) 1.32501e6i 0.392596i
\(151\) 6.04947e6i 1.75706i 0.477687 + 0.878530i \(0.341475\pi\)
−0.477687 + 0.878530i \(0.658525\pi\)
\(152\) 267865.i 0.0762754i
\(153\) −778504. −0.217363
\(154\) −1.64060e6 −0.449202
\(155\) 8.18771e6i 2.19871i
\(156\) 437938.i 0.115356i
\(157\) 4.21637e6i 1.08953i 0.838589 + 0.544765i \(0.183381\pi\)
−0.838589 + 0.544765i \(0.816619\pi\)
\(158\) 331549.i 0.0840576i
\(159\) −4.10591e6 −1.02145
\(160\) 3.26661e6i 0.797511i
\(161\) 3.32017e6i 0.795577i
\(162\) 392931.i 0.0924212i
\(163\) −5.63329e6 −1.30077 −0.650383 0.759606i \(-0.725392\pi\)
−0.650383 + 0.759606i \(0.725392\pi\)
\(164\) −288213. −0.0653405
\(165\) 1.13977e6i 0.253725i
\(166\) −384801. −0.0841225
\(167\) 4.22418e6 0.906971 0.453485 0.891264i \(-0.350180\pi\)
0.453485 + 0.891264i \(0.350180\pi\)
\(168\) 4.93482e6i 1.04074i
\(169\) 2.79722e6 0.579517
\(170\) 3.59258e6i 0.731240i
\(171\) −116839. −0.0233669
\(172\) 1.35035e6i 0.265375i
\(173\) 3.51913e6i 0.679668i 0.940485 + 0.339834i \(0.110371\pi\)
−0.940485 + 0.339834i \(0.889629\pi\)
\(174\) 1.66814e6i 0.316654i
\(175\) 7.25851e6 1.35436
\(176\) 1.06084e6i 0.194587i
\(177\) 478336. + 3.16561e6i 0.0862608 + 0.570870i
\(178\) −5.27166e6 −0.934732
\(179\) 1.00294e7i 1.74871i −0.485291 0.874353i \(-0.661286\pi\)
0.485291 0.874353i \(-0.338714\pi\)
\(180\) 807532. 0.138466
\(181\) −5.10709e6 −0.861266 −0.430633 0.902527i \(-0.641710\pi\)
−0.430633 + 0.902527i \(0.641710\pi\)
\(182\) −5.38696e6 −0.893573
\(183\) 1.06721e6i 0.174138i
\(184\) 3.25505e6 0.522521
\(185\) 4.59439e6i 0.725625i
\(186\) 5.03989e6 0.783218
\(187\) 1.39001e6i 0.212566i
\(188\) 3.74253e6i 0.563238i
\(189\) 2.15251e6 0.318830
\(190\) 539181.i 0.0786093i
\(191\) 1.03251e7i 1.48182i −0.671605 0.740909i \(-0.734395\pi\)
0.671605 0.740909i \(-0.265605\pi\)
\(192\) −4.45007e6 −0.628729
\(193\) 1.65636e6 0.230400 0.115200 0.993342i \(-0.463249\pi\)
0.115200 + 0.993342i \(0.463249\pi\)
\(194\) 4.21102e6 0.576742
\(195\) 3.74245e6i 0.504722i
\(196\) 4.04758e6 0.537560
\(197\) −6.81276e6 −0.891096 −0.445548 0.895258i \(-0.646991\pi\)
−0.445548 + 0.895258i \(0.646991\pi\)
\(198\) −701576. −0.0903814
\(199\) −544506. −0.0690945 −0.0345473 0.999403i \(-0.510999\pi\)
−0.0345473 + 0.999403i \(0.510999\pi\)
\(200\) 7.11615e6i 0.889518i
\(201\) 5.94246e6i 0.731776i
\(202\) −1.07402e7 −1.30304
\(203\) −9.13820e6 −1.09238
\(204\) −984834. −0.116004
\(205\) −2.46296e6 −0.285888
\(206\) 5.33426e6 0.610201
\(207\) 1.41981e6i 0.160074i
\(208\) 3.48331e6i 0.387081i
\(209\) 208615.i 0.0228511i
\(210\) 9.93324e6i 1.07259i
\(211\) 2.00834e6i 0.213791i 0.994270 + 0.106895i \(0.0340910\pi\)
−0.994270 + 0.106895i \(0.965909\pi\)
\(212\) −5.19412e6 −0.545135
\(213\) −5.14931e6 −0.532857
\(214\) 1.25526e6i 0.128084i
\(215\) 1.15395e7i 1.16111i
\(216\) 2.11029e6i 0.209402i
\(217\) 2.76089e7i 2.70191i
\(218\) −915712. −0.0883873
\(219\) 989416.i 0.0941990i
\(220\) 1.44184e6i 0.135410i
\(221\) 4.56414e6i 0.422846i
\(222\) 2.82805e6 0.258480
\(223\) −1.11675e7 −1.00703 −0.503514 0.863987i \(-0.667960\pi\)
−0.503514 + 0.863987i \(0.667960\pi\)
\(224\) 1.10150e7i 0.980031i
\(225\) 3.10397e6 0.272503
\(226\) −6.34081e6 −0.549312
\(227\) 8.43595e6i 0.721201i 0.932720 + 0.360601i \(0.117428\pi\)
−0.932720 + 0.360601i \(0.882572\pi\)
\(228\) −147806. −0.0124706
\(229\) 3.57189e6i 0.297435i −0.988880 0.148718i \(-0.952485\pi\)
0.988880 0.148718i \(-0.0475145\pi\)
\(230\) 6.55204e6 0.538509
\(231\) 3.84329e6i 0.311793i
\(232\) 8.95897e6i 0.717454i
\(233\) 1.49908e7i 1.18511i −0.805530 0.592555i \(-0.798119\pi\)
0.805530 0.592555i \(-0.201881\pi\)
\(234\) −2.30364e6 −0.179791
\(235\) 3.19822e7i 2.46436i
\(236\) 605111. + 4.00460e6i 0.0460362 + 0.304665i
\(237\) 776689. 0.0583448
\(238\) 1.21142e7i 0.898593i
\(239\) −7.08836e6 −0.519221 −0.259610 0.965713i \(-0.583594\pi\)
−0.259610 + 0.965713i \(0.583594\pi\)
\(240\) −6.42301e6 −0.464628
\(241\) 2.47456e7 1.76786 0.883928 0.467622i \(-0.154889\pi\)
0.883928 + 0.467622i \(0.154889\pi\)
\(242\) 1.05359e7i 0.743404i
\(243\) 920483. 0.0641500
\(244\) 1.35005e6i 0.0929353i
\(245\) 3.45890e7 2.35201
\(246\) 1.51606e6i 0.101838i
\(247\) 684994.i 0.0454565i
\(248\) 2.70674e7 1.77457
\(249\) 901437.i 0.0583898i
\(250\) 3.19755e6i 0.204643i
\(251\) 4.72593e6 0.298859 0.149429 0.988772i \(-0.452256\pi\)
0.149429 + 0.988772i \(0.452256\pi\)
\(252\) 2.72300e6 0.170155
\(253\) 2.53506e6 0.156541
\(254\) 1.88964e7i 1.15313i
\(255\) −8.41600e6 −0.507557
\(256\) −1.38848e7 −0.827598
\(257\) −1.93357e7 −1.13910 −0.569549 0.821958i \(-0.692882\pi\)
−0.569549 + 0.821958i \(0.692882\pi\)
\(258\) −7.10310e6 −0.413608
\(259\) 1.54923e7i 0.891693i
\(260\) 4.73432e6i 0.269363i
\(261\) −3.90779e6 −0.219791
\(262\) 7.00697e6 0.389607
\(263\) 3.31759e7 1.82371 0.911855 0.410512i \(-0.134650\pi\)
0.911855 + 0.410512i \(0.134650\pi\)
\(264\) −3.76791e6 −0.204780
\(265\) −4.43869e7 −2.38516
\(266\) 1.81812e6i 0.0966000i
\(267\) 1.23494e7i 0.648802i
\(268\) 7.51741e6i 0.390539i
\(269\) 3.69340e7i 1.89745i −0.316109 0.948723i \(-0.602377\pi\)
0.316109 0.948723i \(-0.397623\pi\)
\(270\) 4.24778e6i 0.215809i
\(271\) 9.48324e6 0.476484 0.238242 0.971206i \(-0.423429\pi\)
0.238242 + 0.971206i \(0.423429\pi\)
\(272\) 7.83325e6 0.389256
\(273\) 1.26195e7i 0.620233i
\(274\) 2.51557e7i 1.22288i
\(275\) 5.54212e6i 0.266488i
\(276\) 1.79611e6i 0.0854291i
\(277\) 2.02819e7 0.954267 0.477134 0.878831i \(-0.341676\pi\)
0.477134 + 0.878831i \(0.341676\pi\)
\(278\) 1.50874e7i 0.702231i
\(279\) 1.18065e7i 0.543635i
\(280\) 5.33478e7i 2.43020i
\(281\) 5.15301e6 0.232243 0.116121 0.993235i \(-0.462954\pi\)
0.116121 + 0.993235i \(0.462954\pi\)
\(282\) 1.96864e7 0.877849
\(283\) 3.44954e7i 1.52196i −0.648778 0.760978i \(-0.724720\pi\)
0.648778 0.760978i \(-0.275280\pi\)
\(284\) −6.51405e6 −0.284378
\(285\) −1.26309e6 −0.0545631
\(286\) 4.11313e6i 0.175823i
\(287\) −8.30509e6 −0.351317
\(288\) 4.71037e6i 0.197187i
\(289\) −1.38738e7 −0.574779
\(290\) 1.80334e7i 0.739407i
\(291\) 9.86475e6i 0.400320i
\(292\) 1.25164e6i 0.0502727i
\(293\) −2.59121e7 −1.03015 −0.515075 0.857145i \(-0.672236\pi\)
−0.515075 + 0.857145i \(0.672236\pi\)
\(294\) 2.12911e7i 0.837828i
\(295\) 5.17104e6 + 3.42217e7i 0.201424 + 1.33302i
\(296\) 1.51884e7 0.585649
\(297\) 1.64351e6i 0.0627342i
\(298\) 2.34268e6 0.0885246
\(299\) 8.32394e6 0.311398
\(300\) 3.92663e6 0.145431
\(301\) 3.89113e7i 1.42684i
\(302\) 4.02552e7 1.46151
\(303\) 2.51601e7i 0.904449i
\(304\) 1.17563e6 0.0418455
\(305\) 1.15370e7i 0.406624i
\(306\) 5.18042e6i 0.180801i
\(307\) −5.13183e7 −1.77361 −0.886804 0.462147i \(-0.847079\pi\)
−0.886804 + 0.462147i \(0.847079\pi\)
\(308\) 4.86189e6i 0.166400i
\(309\) 1.24961e7i 0.423543i
\(310\) 5.44837e7 1.82886
\(311\) −191017. −0.00635025 −0.00317513 0.999995i \(-0.501011\pi\)
−0.00317513 + 0.999995i \(0.501011\pi\)
\(312\) −1.23720e7 −0.407358
\(313\) 5.29245e7i 1.72593i 0.505261 + 0.862966i \(0.331396\pi\)
−0.505261 + 0.862966i \(0.668604\pi\)
\(314\) 2.80571e7 0.906262
\(315\) 2.32697e7 0.744489
\(316\) 982538. 0.0311378
\(317\) −2.57744e7 −0.809117 −0.404558 0.914512i \(-0.632575\pi\)
−0.404558 + 0.914512i \(0.632575\pi\)
\(318\) 2.73221e7i 0.849635i
\(319\) 6.97733e6i 0.214940i
\(320\) −4.81074e7 −1.46812
\(321\) 2.94059e6 0.0889035
\(322\) 2.20935e7 0.661754
\(323\) 1.54041e6 0.0457119
\(324\) 1.16444e6 0.0342360
\(325\) 1.81977e7i 0.530110i
\(326\) 3.74858e7i 1.08197i
\(327\) 2.14515e6i 0.0613500i
\(328\) 8.14220e6i 0.230739i
\(329\) 1.07844e8i 3.02836i
\(330\) −7.58437e6 −0.211046
\(331\) 2.30935e7 0.636803 0.318401 0.947956i \(-0.396854\pi\)
0.318401 + 0.947956i \(0.396854\pi\)
\(332\) 1.14035e6i 0.0311619i
\(333\) 6.62499e6i 0.179413i
\(334\) 2.81091e7i 0.754410i
\(335\) 6.42408e7i 1.70874i
\(336\) −2.16584e7 −0.570963
\(337\) 2.78790e7i 0.728428i −0.931315 0.364214i \(-0.881338\pi\)
0.931315 0.364214i \(-0.118662\pi\)
\(338\) 1.86136e7i 0.482037i
\(339\) 1.48540e7i 0.381280i
\(340\) −1.06465e7 −0.270876
\(341\) 2.10804e7 0.531637
\(342\) 777486.i 0.0194363i
\(343\) 4.97806e7 1.23361
\(344\) −3.81481e7 −0.937126
\(345\) 1.53488e7i 0.373782i
\(346\) 2.34174e7 0.565342
\(347\) 3.17902e7i 0.760859i 0.924810 + 0.380430i \(0.124224\pi\)
−0.924810 + 0.380430i \(0.875776\pi\)
\(348\) −4.94349e6 −0.117299
\(349\) 2.41409e7i 0.567906i −0.958838 0.283953i \(-0.908354\pi\)
0.958838 0.283953i \(-0.0916459\pi\)
\(350\) 4.83005e7i 1.12654i
\(351\) 5.39652e6i 0.124794i
\(352\) −8.41032e6 −0.192835
\(353\) 5.77487e7i 1.31286i 0.754387 + 0.656430i \(0.227934\pi\)
−0.754387 + 0.656430i \(0.772066\pi\)
\(354\) 2.10650e7 3.18300e6i 0.474844 0.0717509i
\(355\) −5.56665e7 −1.24425
\(356\) 1.56224e7i 0.346257i
\(357\) −2.83787e7 −0.623718
\(358\) −6.67390e7 −1.45456
\(359\) −4.80212e7 −1.03789 −0.518943 0.854809i \(-0.673674\pi\)
−0.518943 + 0.854809i \(0.673674\pi\)
\(360\) 2.28133e7i 0.488967i
\(361\) −4.68147e7 −0.995086
\(362\) 3.39842e7i 0.716394i
\(363\) 2.46814e7 0.516001
\(364\) 1.59641e7i 0.331010i
\(365\) 1.06961e7i 0.219961i
\(366\) 7.10153e6 0.144847
\(367\) 7.19741e7i 1.45606i 0.685547 + 0.728028i \(0.259563\pi\)
−0.685547 + 0.728028i \(0.740437\pi\)
\(368\) 1.42860e7i 0.286661i
\(369\) −3.55153e6 −0.0706864
\(370\) 3.05725e7 0.603568
\(371\) −1.49672e8 −2.93103
\(372\) 1.49356e7i 0.290131i
\(373\) −1.33221e6 −0.0256712 −0.0128356 0.999918i \(-0.504086\pi\)
−0.0128356 + 0.999918i \(0.504086\pi\)
\(374\) 9.24959e6 0.176810
\(375\) −7.49059e6 −0.142044
\(376\) 1.05729e8 1.98897
\(377\) 2.29102e7i 0.427568i
\(378\) 1.43235e7i 0.265200i
\(379\) 7.76840e6 0.142697 0.0713484 0.997451i \(-0.477270\pi\)
0.0713484 + 0.997451i \(0.477270\pi\)
\(380\) −1.59785e6 −0.0291196
\(381\) 4.42667e7 0.800391
\(382\) −6.87067e7 −1.23256
\(383\) 9.79995e6 0.174433 0.0872163 0.996189i \(-0.472203\pi\)
0.0872163 + 0.996189i \(0.472203\pi\)
\(384\) 1.02733e7i 0.181433i
\(385\) 4.15478e7i 0.728057i
\(386\) 1.10220e7i 0.191645i
\(387\) 1.66397e7i 0.287087i
\(388\) 1.24792e7i 0.213645i
\(389\) −3.88967e7 −0.660791 −0.330396 0.943843i \(-0.607182\pi\)
−0.330396 + 0.943843i \(0.607182\pi\)
\(390\) −2.49035e7 −0.419823
\(391\) 1.87188e7i 0.313147i
\(392\) 1.14346e8i 1.89830i
\(393\) 1.64146e7i 0.270428i
\(394\) 4.53343e7i 0.741205i
\(395\) 8.39638e6 0.136239
\(396\) 2.07910e6i 0.0334804i
\(397\) 5.11786e7i 0.817932i 0.912550 + 0.408966i \(0.134111\pi\)
−0.912550 + 0.408966i \(0.865889\pi\)
\(398\) 3.62332e6i 0.0574722i
\(399\) −4.25913e6 −0.0670505
\(400\) −3.12320e7 −0.488000
\(401\) 3.02513e7i 0.469148i 0.972098 + 0.234574i \(0.0753696\pi\)
−0.972098 + 0.234574i \(0.924630\pi\)
\(402\) −3.95431e7 −0.608684
\(403\) 6.92179e7 1.05756
\(404\) 3.18283e7i 0.482692i
\(405\) 9.95086e6 0.149794
\(406\) 6.08086e7i 0.908629i
\(407\) 1.18289e7 0.175453
\(408\) 2.78221e7i 0.409647i
\(409\) 4.92500e7i 0.719841i 0.932983 + 0.359921i \(0.117196\pi\)
−0.932983 + 0.359921i \(0.882804\pi\)
\(410\) 1.63893e7i 0.237799i
\(411\) 5.89299e7 0.848809
\(412\) 1.58080e7i 0.226039i
\(413\) 1.74367e7 + 1.15396e8i 0.247523 + 1.63810i
\(414\) 9.44789e6 0.133148
\(415\) 9.74497e6i 0.136344i
\(416\) −2.76155e7 −0.383595
\(417\) 3.53438e7 0.487422
\(418\) 1.38820e6 0.0190074
\(419\) 7.50637e7i 1.02044i 0.860044 + 0.510220i \(0.170436\pi\)
−0.860044 + 0.510220i \(0.829564\pi\)
\(420\) 2.94369e7 0.397323
\(421\) 2.32571e6i 0.0311680i −0.999879 0.0155840i \(-0.995039\pi\)
0.999879 0.0155840i \(-0.00496074\pi\)
\(422\) 1.33641e7 0.177829
\(423\) 4.61175e7i 0.609319i
\(424\) 1.46737e8i 1.92505i
\(425\) −4.09229e7 −0.533089
\(426\) 3.42652e7i 0.443225i
\(427\) 3.89027e7i 0.499685i
\(428\) 3.71994e6 0.0474466
\(429\) −9.63544e6 −0.122039
\(430\) −7.67879e7 −0.965800
\(431\) 2.06821e7i 0.258323i 0.991624 + 0.129161i \(0.0412285\pi\)
−0.991624 + 0.129161i \(0.958771\pi\)
\(432\) −9.26183e6 −0.114880
\(433\) 9.48112e7 1.16787 0.583937 0.811799i \(-0.301511\pi\)
0.583937 + 0.811799i \(0.301511\pi\)
\(434\) 1.83719e8 2.24742
\(435\) −4.22451e7 −0.513226
\(436\) 2.71369e6i 0.0327417i
\(437\) 2.80936e6i 0.0336637i
\(438\) 6.58390e6 0.0783539
\(439\) −1.73231e7 −0.204753 −0.102377 0.994746i \(-0.532645\pi\)
−0.102377 + 0.994746i \(0.532645\pi\)
\(440\) −4.07329e7 −0.478175
\(441\) 4.98765e7 0.581541
\(442\) 3.03713e7 0.351719
\(443\) 3.20560e6i 0.0368722i 0.999830 + 0.0184361i \(0.00586872\pi\)
−0.999830 + 0.0184361i \(0.994131\pi\)
\(444\) 8.38084e6i 0.0957500i
\(445\) 1.33503e8i 1.51499i
\(446\) 7.43123e7i 0.837637i
\(447\) 5.48797e6i 0.0614453i
\(448\) −1.62218e8 −1.80412
\(449\) 3.81575e7 0.421542 0.210771 0.977536i \(-0.432403\pi\)
0.210771 + 0.977536i \(0.432403\pi\)
\(450\) 2.06549e7i 0.226665i
\(451\) 6.34122e6i 0.0691263i
\(452\) 1.87908e7i 0.203484i
\(453\) 9.43019e7i 1.01444i
\(454\) 5.61356e7 0.599889
\(455\) 1.36423e8i 1.44828i
\(456\) 4.17560e6i 0.0440376i
\(457\) 1.22414e7i 0.128258i −0.997942 0.0641289i \(-0.979573\pi\)
0.997942 0.0641289i \(-0.0204269\pi\)
\(458\) −2.37686e7 −0.247404
\(459\) −1.21357e7 −0.125495
\(460\) 1.94168e7i 0.199482i
\(461\) −1.13108e8 −1.15449 −0.577247 0.816570i \(-0.695873\pi\)
−0.577247 + 0.816570i \(0.695873\pi\)
\(462\) −2.55745e7 −0.259347
\(463\) 1.06495e8i 1.07297i −0.843910 0.536485i \(-0.819752\pi\)
0.843910 0.536485i \(-0.180248\pi\)
\(464\) 3.93199e7 0.393603
\(465\) 1.27634e8i 1.26942i
\(466\) −9.97540e7 −0.985763
\(467\) 3.56008e7i 0.349550i −0.984608 0.174775i \(-0.944080\pi\)
0.984608 0.174775i \(-0.0559198\pi\)
\(468\) 6.82678e6i 0.0666006i
\(469\) 2.16620e8i 2.09981i
\(470\) 2.12820e8 2.04983
\(471\) 6.57267e7i 0.629041i
\(472\) 1.13132e8 1.70948e7i 1.07587 0.162569i
\(473\) −2.97101e7 −0.280751
\(474\) 5.16834e6i 0.0485307i
\(475\) −6.14178e6 −0.0573077
\(476\) −3.59001e7 −0.332870
\(477\) −6.40048e7 −0.589736
\(478\) 4.71682e7i 0.431883i
\(479\) −3.29980e7 −0.300249 −0.150124 0.988667i \(-0.547967\pi\)
−0.150124 + 0.988667i \(0.547967\pi\)
\(480\) 5.09213e7i 0.460443i
\(481\) 3.88404e7 0.349018
\(482\) 1.64665e8i 1.47049i
\(483\) 5.17563e7i 0.459327i
\(484\) 3.12228e7 0.275382
\(485\) 1.06643e8i 0.934772i
\(486\) 6.12519e6i 0.0533594i
\(487\) 1.60962e8 1.39359 0.696796 0.717269i \(-0.254608\pi\)
0.696796 + 0.717269i \(0.254608\pi\)
\(488\) 3.81397e7 0.328185
\(489\) −8.78143e7 −0.750998
\(490\) 2.30166e8i 1.95638i
\(491\) −9.28174e7 −0.784125 −0.392062 0.919939i \(-0.628238\pi\)
−0.392062 + 0.919939i \(0.628238\pi\)
\(492\) −4.49280e6 −0.0377244
\(493\) 5.15204e7 0.429971
\(494\) 4.55817e6 0.0378103
\(495\) 1.77672e7i 0.146488i
\(496\) 1.18796e8i 0.973546i
\(497\) −1.87707e8 −1.52902
\(498\) −5.99846e6 −0.0485681
\(499\) 1.69869e8 1.36714 0.683569 0.729886i \(-0.260427\pi\)
0.683569 + 0.729886i \(0.260427\pi\)
\(500\) −9.47585e6 −0.0758068
\(501\) 6.58485e7 0.523640
\(502\) 3.14479e7i 0.248588i
\(503\) 9.91155e7i 0.778821i 0.921064 + 0.389410i \(0.127321\pi\)
−0.921064 + 0.389410i \(0.872679\pi\)
\(504\) 7.69263e7i 0.600874i
\(505\) 2.71992e8i 2.11195i
\(506\) 1.68691e7i 0.130209i
\(507\) 4.36043e7 0.334584
\(508\) 5.59989e7 0.427158
\(509\) 9.96791e6i 0.0755876i 0.999286 + 0.0377938i \(0.0120330\pi\)
−0.999286 + 0.0377938i \(0.987967\pi\)
\(510\) 5.60028e7i 0.422182i
\(511\) 3.60671e7i 0.270301i
\(512\) 1.34572e8i 1.00264i
\(513\) −1.82134e6 −0.0134909
\(514\) 1.28666e8i 0.947491i
\(515\) 1.35089e8i 0.989001i
\(516\) 2.10498e7i 0.153214i
\(517\) 8.23425e7 0.595871
\(518\) 1.03091e8 0.741702
\(519\) 5.48578e7i 0.392407i
\(520\) −1.33747e8 −0.951208
\(521\) 1.51073e8 1.06825 0.534126 0.845405i \(-0.320641\pi\)
0.534126 + 0.845405i \(0.320641\pi\)
\(522\) 2.60037e7i 0.182820i
\(523\) 7.08136e7 0.495007 0.247504 0.968887i \(-0.420390\pi\)
0.247504 + 0.968887i \(0.420390\pi\)
\(524\) 2.07650e7i 0.144324i
\(525\) 1.13149e8 0.781938
\(526\) 2.20764e8i 1.51695i
\(527\) 1.55657e8i 1.06350i
\(528\) 1.65369e7i 0.112345i
\(529\) 1.13897e8 0.769388
\(530\) 2.95365e8i 1.98395i
\(531\) 7.45652e6 + 4.93469e7i 0.0498027 + 0.329592i
\(532\) −5.38794e6 −0.0357839
\(533\) 2.08216e7i 0.137509i
\(534\) −8.21770e7 −0.539668
\(535\) 3.17892e7 0.207595
\(536\) −2.12371e8 −1.37912
\(537\) 1.56343e8i 1.00962i
\(538\) −2.45771e8 −1.57828
\(539\) 8.90541e7i 0.568706i
\(540\) 1.25882e7 0.0799432
\(541\) 2.84621e8i 1.79752i −0.438437 0.898762i \(-0.644468\pi\)
0.438437 0.898762i \(-0.355532\pi\)
\(542\) 6.31046e7i 0.396335i
\(543\) −7.96116e7 −0.497252
\(544\) 6.21016e7i 0.385750i
\(545\) 2.31901e7i 0.143256i
\(546\) −8.39744e7 −0.515904
\(547\) −2.31430e8 −1.41403 −0.707013 0.707200i \(-0.749958\pi\)
−0.707013 + 0.707200i \(0.749958\pi\)
\(548\) 7.45483e7 0.452998
\(549\) 1.66361e7i 0.100539i
\(550\) −3.68791e7 −0.221662
\(551\) 7.73228e6 0.0462224
\(552\) 5.07412e7 0.301678
\(553\) 2.83126e7 0.167419
\(554\) 1.34963e8i 0.793751i
\(555\) 7.16194e7i 0.418940i
\(556\) 4.47111e7 0.260130
\(557\) 3.39669e6 0.0196558 0.00982788 0.999952i \(-0.496872\pi\)
0.00982788 + 0.999952i \(0.496872\pi\)
\(558\) 7.85642e7 0.452191
\(559\) −9.75539e7 −0.558482
\(560\) −2.34138e8 −1.33324
\(561\) 2.16681e7i 0.122725i
\(562\) 3.42898e7i 0.193177i
\(563\) 1.40454e8i 0.787063i 0.919311 + 0.393532i \(0.128747\pi\)
−0.919311 + 0.393532i \(0.871253\pi\)
\(564\) 5.83402e7i 0.325185i
\(565\) 1.60579e8i 0.890314i
\(566\) −2.29544e8 −1.26595
\(567\) 3.35543e7 0.184077
\(568\) 1.84026e8i 1.00423i
\(569\) 3.71990e7i 0.201927i −0.994890 0.100963i \(-0.967808\pi\)
0.994890 0.100963i \(-0.0321925\pi\)
\(570\) 8.40500e6i 0.0453851i
\(571\) 1.77384e8i 0.952810i −0.879226 0.476405i \(-0.841940\pi\)
0.879226 0.476405i \(-0.158060\pi\)
\(572\) −1.21892e7 −0.0651307
\(573\) 1.60953e8i 0.855528i
\(574\) 5.52648e7i 0.292222i
\(575\) 7.46339e7i 0.392584i
\(576\) −6.93697e7 −0.362997
\(577\) 1.78824e8 0.930890 0.465445 0.885077i \(-0.345894\pi\)
0.465445 + 0.885077i \(0.345894\pi\)
\(578\) 9.23205e7i 0.478096i
\(579\) 2.58201e7 0.133022
\(580\) −5.34415e7 −0.273902
\(581\) 3.28600e7i 0.167548i
\(582\) 6.56432e7 0.332982
\(583\) 1.14280e8i 0.576720i
\(584\) 3.53597e7 0.177529
\(585\) 5.83390e7i 0.291401i
\(586\) 1.72428e8i 0.856869i
\(587\) 1.98303e8i 0.980428i −0.871602 0.490214i \(-0.836919\pi\)
0.871602 0.490214i \(-0.163081\pi\)
\(588\) 6.30955e7 0.310360
\(589\) 2.33613e7i 0.114327i
\(590\) 2.27723e8 3.44098e7i 1.10879 0.167543i
\(591\) −1.06200e8 −0.514474
\(592\) 6.66602e7i 0.321293i
\(593\) 1.33160e8 0.638574 0.319287 0.947658i \(-0.396557\pi\)
0.319287 + 0.947658i \(0.396557\pi\)
\(594\) −1.09365e7 −0.0521817
\(595\) −3.06788e8 −1.45642
\(596\) 6.94247e6i 0.0327925i
\(597\) −8.48801e6 −0.0398917
\(598\) 5.53902e7i 0.259018i
\(599\) 2.83893e8 1.32091 0.660457 0.750864i \(-0.270363\pi\)
0.660457 + 0.750864i \(0.270363\pi\)
\(600\) 1.10930e8i 0.513564i
\(601\) 3.04660e8i 1.40344i −0.712455 0.701718i \(-0.752417\pi\)
0.712455 0.701718i \(-0.247583\pi\)
\(602\) −2.58929e8 −1.18684
\(603\) 9.26338e7i 0.422491i
\(604\) 1.19295e8i 0.541392i
\(605\) 2.66818e8 1.20489
\(606\) −1.67423e8 −0.752312
\(607\) −4.18672e8 −1.87201 −0.936005 0.351986i \(-0.885506\pi\)
−0.936005 + 0.351986i \(0.885506\pi\)
\(608\) 9.32032e6i 0.0414687i
\(609\) −1.42450e8 −0.630684
\(610\) 7.67710e7 0.338226
\(611\) 2.70374e8 1.18533
\(612\) −1.53520e7 −0.0669748
\(613\) 9.05013e7i 0.392892i −0.980515 0.196446i \(-0.937060\pi\)
0.980515 0.196446i \(-0.0629401\pi\)
\(614\) 3.41489e8i 1.47527i
\(615\) −3.83937e7 −0.165057
\(616\) −1.37351e8 −0.587612
\(617\) 5.67251e7 0.241501 0.120751 0.992683i \(-0.461470\pi\)
0.120751 + 0.992683i \(0.461470\pi\)
\(618\) 8.31529e7 0.352300
\(619\) −2.52861e8 −1.06613 −0.533065 0.846074i \(-0.678960\pi\)
−0.533065 + 0.846074i \(0.678960\pi\)
\(620\) 1.61461e8i 0.677474i
\(621\) 2.21327e7i 0.0924185i
\(622\) 1.27109e6i 0.00528208i
\(623\) 4.50172e8i 1.86172i
\(624\) 5.42994e7i 0.223481i
\(625\) −2.80564e8 −1.14919
\(626\) 3.52177e8 1.43562
\(627\) 3.25199e6i 0.0131931i
\(628\) 8.31465e7i 0.335710i
\(629\) 8.73441e7i 0.350979i
\(630\) 1.54844e8i 0.619259i
\(631\) 3.87969e8 1.54422 0.772110 0.635489i \(-0.219201\pi\)
0.772110 + 0.635489i \(0.219201\pi\)
\(632\) 2.77573e7i 0.109958i
\(633\) 3.13069e7i 0.123432i
\(634\) 1.71512e8i 0.673016i
\(635\) 4.78544e8 1.86896
\(636\) −8.09683e7 −0.314734
\(637\) 2.92411e8i 1.13130i
\(638\) 4.64294e7 0.178785
\(639\) −8.02698e7 −0.307645
\(640\) 1.11060e8i 0.423659i
\(641\) −7.22759e7 −0.274422 −0.137211 0.990542i \(-0.543814\pi\)
−0.137211 + 0.990542i \(0.543814\pi\)
\(642\) 1.95676e7i 0.0739491i
\(643\) 3.34141e8 1.25689 0.628445 0.777854i \(-0.283692\pi\)
0.628445 + 0.777854i \(0.283692\pi\)
\(644\) 6.54735e7i 0.245136i
\(645\) 1.79884e8i 0.670367i
\(646\) 1.02504e7i 0.0380227i
\(647\) −7.18958e7 −0.265455 −0.132727 0.991153i \(-0.542373\pi\)
−0.132727 + 0.991153i \(0.542373\pi\)
\(648\) 3.28962e7i 0.120898i
\(649\) 8.81085e7 1.33136e7i 0.322317 0.0487035i
\(650\) −1.21093e8 −0.440941
\(651\) 4.30381e8i 1.55995i
\(652\) −1.11088e8 −0.400797
\(653\) −4.95669e8 −1.78013 −0.890065 0.455833i \(-0.849341\pi\)
−0.890065 + 0.455833i \(0.849341\pi\)
\(654\) −1.42745e7 −0.0510304
\(655\) 1.77449e8i 0.631467i
\(656\) 3.57352e7 0.126586
\(657\) 1.54235e7i 0.0543858i
\(658\) 7.17628e8 2.51896
\(659\) 2.59687e8i 0.907391i −0.891157 0.453696i \(-0.850105\pi\)
0.891157 0.453696i \(-0.149895\pi\)
\(660\) 2.24761e7i 0.0781788i
\(661\) −4.06459e8 −1.40738 −0.703691 0.710506i \(-0.748466\pi\)
−0.703691 + 0.710506i \(0.748466\pi\)
\(662\) 1.53671e8i 0.529687i
\(663\) 7.11479e7i 0.244130i
\(664\) −3.22155e7 −0.110043
\(665\) −4.60432e7 −0.156567
\(666\) 4.40849e7 0.149234
\(667\) 9.39614e7i 0.316645i
\(668\) 8.33006e7 0.279459
\(669\) −1.74084e8 −0.581408
\(670\) −4.27479e8 −1.42132
\(671\) 2.97036e7 0.0983199
\(672\) 1.71707e8i 0.565821i
\(673\) 5.55778e7i 0.182329i 0.995836 + 0.0911645i \(0.0290589\pi\)
−0.995836 + 0.0911645i \(0.970941\pi\)
\(674\) −1.85516e8 −0.605900
\(675\) 4.83862e7 0.157329
\(676\) 5.51609e7 0.178563
\(677\) 1.89135e8 0.609545 0.304772 0.952425i \(-0.401420\pi\)
0.304772 + 0.952425i \(0.401420\pi\)
\(678\) −9.88434e7 −0.317146
\(679\) 3.59599e8i 1.14871i
\(680\) 3.00771e8i 0.956552i
\(681\) 1.31503e8i 0.416386i
\(682\) 1.40276e8i 0.442211i
\(683\) 4.05073e8i 1.27137i −0.771949 0.635684i \(-0.780718\pi\)
0.771949 0.635684i \(-0.219282\pi\)
\(684\) −2.30406e6 −0.00719989
\(685\) 6.37060e8 1.98202
\(686\) 3.31256e8i 1.02611i
\(687\) 5.56803e7i 0.171724i
\(688\) 1.67428e8i 0.514118i
\(689\) 3.75242e8i 1.14724i
\(690\) 1.02136e8 0.310909
\(691\) 1.33571e8i 0.404835i 0.979299 + 0.202418i \(0.0648798\pi\)
−0.979299 + 0.202418i \(0.935120\pi\)
\(692\) 6.93970e7i 0.209422i
\(693\) 5.99109e7i 0.180014i
\(694\) 2.11542e8 0.632876
\(695\) 3.82084e8 1.13816
\(696\) 1.39657e8i 0.414222i
\(697\) 4.68234e7 0.138282
\(698\) −1.60641e8 −0.472379
\(699\) 2.33684e8i 0.684223i
\(700\) 1.43137e8 0.417310
\(701\) 1.26831e8i 0.368190i 0.982908 + 0.184095i \(0.0589355\pi\)
−0.982908 + 0.184095i \(0.941065\pi\)
\(702\) −3.59102e7 −0.103802
\(703\) 1.31088e7i 0.0377308i
\(704\) 1.23859e8i 0.354985i
\(705\) 4.98553e8i 1.42280i
\(706\) 3.84279e8 1.09202
\(707\) 9.17158e8i 2.59529i
\(708\) 9.43275e6 + 6.24255e7i 0.0265790 + 0.175899i
\(709\) 4.76626e8 1.33733 0.668666 0.743563i \(-0.266866\pi\)
0.668666 + 0.743563i \(0.266866\pi\)
\(710\) 3.70423e8i 1.03496i
\(711\) 1.21074e7 0.0336854
\(712\) −4.41343e8 −1.22275
\(713\) −2.83883e8 −0.783195
\(714\) 1.88841e8i 0.518803i
\(715\) −1.04164e8 −0.284970
\(716\) 1.97779e8i 0.538818i
\(717\) −1.10497e8 −0.299772
\(718\) 3.19549e8i 0.863304i
\(719\) 2.32671e8i 0.625972i 0.949758 + 0.312986i \(0.101329\pi\)
−0.949758 + 0.312986i \(0.898671\pi\)
\(720\) −1.00125e8 −0.268253
\(721\) 4.55518e8i 1.21535i
\(722\) 3.11520e8i 0.827703i
\(723\) 3.85746e8 1.02067
\(724\) −1.00711e8 −0.265377
\(725\) −2.05417e8 −0.539042
\(726\) 1.64238e8i 0.429205i
\(727\) −2.98682e8 −0.777332 −0.388666 0.921379i \(-0.627064\pi\)
−0.388666 + 0.921379i \(0.627064\pi\)
\(728\) −4.50996e8 −1.16890
\(729\) 1.43489e7 0.0370370
\(730\) 7.11751e7 0.182961
\(731\) 2.19379e8i 0.561620i
\(732\) 2.10452e7i 0.0536562i
\(733\) −3.16957e8 −0.804801 −0.402401 0.915464i \(-0.631824\pi\)
−0.402401 + 0.915464i \(0.631824\pi\)
\(734\) 4.78939e8 1.21113
\(735\) 5.39189e8 1.35794
\(736\) 1.13259e8 0.284079
\(737\) −1.65397e8 −0.413166
\(738\) 2.36330e7i 0.0587963i
\(739\) 3.58559e8i 0.888438i 0.895918 + 0.444219i \(0.146519\pi\)
−0.895918 + 0.444219i \(0.853481\pi\)
\(740\) 9.06010e7i 0.223582i
\(741\) 1.06780e7i 0.0262443i
\(742\) 9.95970e8i 2.43800i
\(743\) −6.56381e8 −1.60026 −0.800128 0.599829i \(-0.795235\pi\)
−0.800128 + 0.599829i \(0.795235\pi\)
\(744\) 4.21940e8 1.02455
\(745\) 5.93276e7i 0.143479i
\(746\) 8.86496e6i 0.0213531i
\(747\) 1.40520e7i 0.0337114i
\(748\) 2.74109e7i 0.0654967i
\(749\) 1.07193e8 0.255106
\(750\) 4.98448e7i 0.118151i
\(751\) 5.00869e8i 1.18251i −0.806485 0.591254i \(-0.798633\pi\)
0.806485 0.591254i \(-0.201367\pi\)
\(752\) 4.64031e8i 1.09117i
\(753\) 7.36700e7 0.172546
\(754\) 1.52452e8 0.355647
\(755\) 1.01945e9i 2.36878i
\(756\) 4.24473e7 0.0982392
\(757\) −4.64421e8 −1.07059 −0.535296 0.844664i \(-0.679800\pi\)
−0.535296 + 0.844664i \(0.679800\pi\)
\(758\) 5.16935e7i 0.118694i
\(759\) 3.95177e7 0.0903788
\(760\) 4.51402e7i 0.102831i
\(761\) 2.78011e8 0.630823 0.315412 0.948955i \(-0.397857\pi\)
0.315412 + 0.948955i \(0.397857\pi\)
\(762\) 2.94565e8i 0.665758i
\(763\) 7.81971e7i 0.176042i
\(764\) 2.03611e8i 0.456584i
\(765\) −1.31192e8 −0.293038
\(766\) 6.52121e7i 0.145091i
\(767\) 2.89306e8 4.37154e7i 0.641168 0.0968831i
\(768\) −2.16442e8 −0.477814
\(769\) 7.91607e8i 1.74073i 0.492410 + 0.870363i \(0.336116\pi\)
−0.492410 + 0.870363i \(0.663884\pi\)
\(770\) −2.76472e8 −0.605591
\(771\) −3.01414e8 −0.657658
\(772\) 3.26633e7 0.0709918
\(773\) 3.12941e8i 0.677523i 0.940872 + 0.338761i \(0.110008\pi\)
−0.940872 + 0.338761i \(0.889992\pi\)
\(774\) −1.10726e8 −0.238796
\(775\) 6.20620e8i 1.33328i
\(776\) 3.52546e8 0.754450
\(777\) 2.41500e8i 0.514819i
\(778\) 2.58832e8i 0.549640i
\(779\) 7.02734e6 0.0148655
\(780\) 7.38008e7i 0.155517i
\(781\) 1.43321e8i 0.300855i
\(782\) −1.24561e8 −0.260473
\(783\) −6.09164e7 −0.126896
\(784\) −5.01854e8 −1.04143
\(785\) 7.10537e8i 1.46885i