Properties

Label 177.5.c.a.58.4
Level $177$
Weight $5$
Character 177.58
Analytic conductor $18.296$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.2964834658\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.4
Character \(\chi\) \(=\) 177.58
Dual form 177.5.c.a.58.37

$q$-expansion

\(f(q)\) \(=\) \(q-6.76718i q^{2} +5.19615 q^{3} -29.7948 q^{4} +6.77685 q^{5} -35.1633i q^{6} +45.8846 q^{7} +93.3518i q^{8} +27.0000 q^{9} +O(q^{10})\) \(q-6.76718i q^{2} +5.19615 q^{3} -29.7948 q^{4} +6.77685 q^{5} -35.1633i q^{6} +45.8846 q^{7} +93.3518i q^{8} +27.0000 q^{9} -45.8602i q^{10} -152.372i q^{11} -154.818 q^{12} -138.574i q^{13} -310.510i q^{14} +35.2135 q^{15} +155.012 q^{16} +61.1978 q^{17} -182.714i q^{18} -184.090 q^{19} -201.915 q^{20} +238.423 q^{21} -1031.13 q^{22} -55.4703i q^{23} +485.070i q^{24} -579.074 q^{25} -937.758 q^{26} +140.296 q^{27} -1367.12 q^{28} +290.483 q^{29} -238.296i q^{30} -681.108i q^{31} +444.632i q^{32} -791.748i q^{33} -414.137i q^{34} +310.953 q^{35} -804.459 q^{36} -1422.17i q^{37} +1245.77i q^{38} -720.053i q^{39} +632.631i q^{40} +1532.90 q^{41} -1613.46i q^{42} +404.708i q^{43} +4539.89i q^{44} +182.975 q^{45} -375.377 q^{46} +1601.56i q^{47} +805.467 q^{48} -295.602 q^{49} +3918.70i q^{50} +317.993 q^{51} +4128.79i q^{52} -1325.56 q^{53} -949.410i q^{54} -1032.60i q^{55} +4283.41i q^{56} -956.562 q^{57} -1965.75i q^{58} +(3430.65 + 589.891i) q^{59} -1049.18 q^{60} +2732.09i q^{61} -4609.19 q^{62} +1238.88 q^{63} +5489.10 q^{64} -939.097i q^{65} -5357.90 q^{66} -2225.52i q^{67} -1823.37 q^{68} -288.232i q^{69} -2104.28i q^{70} -6157.04 q^{71} +2520.50i q^{72} -2816.89i q^{73} -9624.09 q^{74} -3008.96 q^{75} +5484.93 q^{76} -6991.53i q^{77} -4872.73 q^{78} +7747.95 q^{79} +1050.49 q^{80} +729.000 q^{81} -10373.4i q^{82} +648.806i q^{83} -7103.77 q^{84} +414.728 q^{85} +2738.73 q^{86} +1509.40 q^{87} +14224.2 q^{88} +5751.21i q^{89} -1238.22i q^{90} -6358.43i q^{91} +1652.72i q^{92} -3539.14i q^{93} +10838.1 q^{94} -1247.55 q^{95} +2310.38i q^{96} +1510.67i q^{97} +2000.39i q^{98} -4114.04i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + O(q^{10}) \) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + 360q^{12} + 144q^{15} + 3944q^{16} - 528q^{17} + 444q^{19} + 444q^{20} + 1304q^{22} + 4880q^{25} - 1452q^{26} - 1160q^{28} - 996q^{29} + 10320q^{35} - 8640q^{36} - 5196q^{41} - 10476q^{46} + 576q^{48} + 5104q^{49} + 936q^{51} - 2184q^{53} - 2520q^{57} - 11736q^{59} - 11448q^{60} + 15240q^{62} + 2160q^{63} - 81012q^{64} + 17352q^{66} + 29568q^{68} - 5964q^{71} + 14376q^{74} - 2736q^{75} + 3480q^{76} + 37692q^{78} + 19020q^{79} + 33096q^{80} + 29160q^{81} + 25128q^{84} + 20220q^{85} - 65880q^{86} + 1512q^{87} - 14932q^{88} - 17864q^{94} + 11004q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 6.76718i 1.69180i −0.533345 0.845898i \(-0.679065\pi\)
0.533345 0.845898i \(-0.320935\pi\)
\(3\) 5.19615 0.577350
\(4\) −29.7948 −1.86217
\(5\) 6.77685 0.271074 0.135537 0.990772i \(-0.456724\pi\)
0.135537 + 0.990772i \(0.456724\pi\)
\(6\) 35.1633i 0.976759i
\(7\) 45.8846 0.936421 0.468210 0.883617i \(-0.344899\pi\)
0.468210 + 0.883617i \(0.344899\pi\)
\(8\) 93.3518i 1.45862i
\(9\) 27.0000 0.333333
\(10\) 45.8602i 0.458602i
\(11\) 152.372i 1.25927i −0.776890 0.629636i \(-0.783204\pi\)
0.776890 0.629636i \(-0.216796\pi\)
\(12\) −154.818 −1.07513
\(13\) 138.574i 0.819966i −0.912093 0.409983i \(-0.865535\pi\)
0.912093 0.409983i \(-0.134465\pi\)
\(14\) 310.510i 1.58423i
\(15\) 35.2135 0.156505
\(16\) 155.012 0.605517
\(17\) 61.1978 0.211757 0.105878 0.994379i \(-0.466235\pi\)
0.105878 + 0.994379i \(0.466235\pi\)
\(18\) 182.714i 0.563932i
\(19\) −184.090 −0.509946 −0.254973 0.966948i \(-0.582067\pi\)
−0.254973 + 0.966948i \(0.582067\pi\)
\(20\) −201.915 −0.504787
\(21\) 238.423 0.540643
\(22\) −1031.13 −2.13043
\(23\) 55.4703i 0.104859i −0.998625 0.0524294i \(-0.983304\pi\)
0.998625 0.0524294i \(-0.0166964\pi\)
\(24\) 485.070i 0.842136i
\(25\) −579.074 −0.926519
\(26\) −937.758 −1.38722
\(27\) 140.296 0.192450
\(28\) −1367.12 −1.74378
\(29\) 290.483 0.345402 0.172701 0.984974i \(-0.444750\pi\)
0.172701 + 0.984974i \(0.444750\pi\)
\(30\) 238.296i 0.264774i
\(31\) 681.108i 0.708750i −0.935103 0.354375i \(-0.884694\pi\)
0.935103 0.354375i \(-0.115306\pi\)
\(32\) 444.632i 0.434211i
\(33\) 791.748i 0.727041i
\(34\) 414.137i 0.358250i
\(35\) 310.953 0.253839
\(36\) −804.459 −0.620724
\(37\) 1422.17i 1.03884i −0.854519 0.519420i \(-0.826148\pi\)
0.854519 0.519420i \(-0.173852\pi\)
\(38\) 1245.77i 0.862725i
\(39\) 720.053i 0.473408i
\(40\) 632.631i 0.395394i
\(41\) 1532.90 0.911895 0.455948 0.890007i \(-0.349300\pi\)
0.455948 + 0.890007i \(0.349300\pi\)
\(42\) 1613.46i 0.914657i
\(43\) 404.708i 0.218879i 0.993993 + 0.109440i \(0.0349056\pi\)
−0.993993 + 0.109440i \(0.965094\pi\)
\(44\) 4539.89i 2.34498i
\(45\) 182.975 0.0903580
\(46\) −375.377 −0.177400
\(47\) 1601.56i 0.725016i 0.931981 + 0.362508i \(0.118079\pi\)
−0.931981 + 0.362508i \(0.881921\pi\)
\(48\) 805.467 0.349595
\(49\) −295.602 −0.123116
\(50\) 3918.70i 1.56748i
\(51\) 317.993 0.122258
\(52\) 4128.79i 1.52692i
\(53\) −1325.56 −0.471897 −0.235949 0.971766i \(-0.575820\pi\)
−0.235949 + 0.971766i \(0.575820\pi\)
\(54\) 949.410i 0.325586i
\(55\) 1032.60i 0.341356i
\(56\) 4283.41i 1.36588i
\(57\) −956.562 −0.294417
\(58\) 1965.75i 0.584350i
\(59\) 3430.65 + 589.891i 0.985537 + 0.169460i
\(60\) −1049.18 −0.291439
\(61\) 2732.09i 0.734236i 0.930174 + 0.367118i \(0.119656\pi\)
−0.930174 + 0.367118i \(0.880344\pi\)
\(62\) −4609.19 −1.19906
\(63\) 1238.88 0.312140
\(64\) 5489.10 1.34011
\(65\) 939.097i 0.222271i
\(66\) −5357.90 −1.23001
\(67\) 2225.52i 0.495771i −0.968789 0.247885i \(-0.920264\pi\)
0.968789 0.247885i \(-0.0797357\pi\)
\(68\) −1823.37 −0.394328
\(69\) 288.232i 0.0605402i
\(70\) 2104.28i 0.429444i
\(71\) −6157.04 −1.22139 −0.610696 0.791865i \(-0.709110\pi\)
−0.610696 + 0.791865i \(0.709110\pi\)
\(72\) 2520.50i 0.486207i
\(73\) 2816.89i 0.528597i −0.964441 0.264298i \(-0.914860\pi\)
0.964441 0.264298i \(-0.0851404\pi\)
\(74\) −9624.09 −1.75750
\(75\) −3008.96 −0.534926
\(76\) 5484.93 0.949608
\(77\) 6991.53i 1.17921i
\(78\) −4872.73 −0.800909
\(79\) 7747.95 1.24146 0.620730 0.784025i \(-0.286836\pi\)
0.620730 + 0.784025i \(0.286836\pi\)
\(80\) 1050.49 0.164140
\(81\) 729.000 0.111111
\(82\) 10373.4i 1.54274i
\(83\) 648.806i 0.0941800i 0.998891 + 0.0470900i \(0.0149948\pi\)
−0.998891 + 0.0470900i \(0.985005\pi\)
\(84\) −7103.77 −1.00677
\(85\) 414.728 0.0574018
\(86\) 2738.73 0.370299
\(87\) 1509.40 0.199418
\(88\) 14224.2 1.83680
\(89\) 5751.21i 0.726071i 0.931775 + 0.363036i \(0.118260\pi\)
−0.931775 + 0.363036i \(0.881740\pi\)
\(90\) 1238.22i 0.152867i
\(91\) 6358.43i 0.767833i
\(92\) 1652.72i 0.195265i
\(93\) 3539.14i 0.409197i
\(94\) 10838.1 1.22658
\(95\) −1247.55 −0.138233
\(96\) 2310.38i 0.250692i
\(97\) 1510.67i 0.160556i 0.996773 + 0.0802779i \(0.0255808\pi\)
−0.996773 + 0.0802779i \(0.974419\pi\)
\(98\) 2000.39i 0.208287i
\(99\) 4114.04i 0.419758i
\(100\) 17253.4 1.72534
\(101\) 2457.45i 0.240903i 0.992719 + 0.120451i \(0.0384342\pi\)
−0.992719 + 0.120451i \(0.961566\pi\)
\(102\) 2151.92i 0.206835i
\(103\) 8751.92i 0.824952i −0.910968 0.412476i \(-0.864664\pi\)
0.910968 0.412476i \(-0.135336\pi\)
\(104\) 12936.2 1.19602
\(105\) 1615.76 0.146554
\(106\) 8970.31i 0.798354i
\(107\) 21034.2 1.83721 0.918603 0.395182i \(-0.129319\pi\)
0.918603 + 0.395182i \(0.129319\pi\)
\(108\) −4180.09 −0.358375
\(109\) 9627.62i 0.810338i −0.914242 0.405169i \(-0.867213\pi\)
0.914242 0.405169i \(-0.132787\pi\)
\(110\) −6987.81 −0.577505
\(111\) 7389.82i 0.599774i
\(112\) 7112.68 0.567018
\(113\) 23222.8i 1.81869i −0.416044 0.909344i \(-0.636584\pi\)
0.416044 0.909344i \(-0.363416\pi\)
\(114\) 6473.23i 0.498094i
\(115\) 375.914i 0.0284245i
\(116\) −8654.89 −0.643199
\(117\) 3741.51i 0.273322i
\(118\) 3991.90 23215.9i 0.286692 1.66733i
\(119\) 2808.04 0.198294
\(120\) 3287.25i 0.228281i
\(121\) −8576.22 −0.585768
\(122\) 18488.6 1.24218
\(123\) 7965.16 0.526483
\(124\) 20293.5i 1.31981i
\(125\) −8159.83 −0.522229
\(126\) 8383.76i 0.528078i
\(127\) 3258.32 0.202016 0.101008 0.994886i \(-0.467793\pi\)
0.101008 + 0.994886i \(0.467793\pi\)
\(128\) 30031.7i 1.83299i
\(129\) 2102.92i 0.126370i
\(130\) −6355.04 −0.376038
\(131\) 23879.6i 1.39151i 0.718281 + 0.695753i \(0.244929\pi\)
−0.718281 + 0.695753i \(0.755071\pi\)
\(132\) 23590.0i 1.35388i
\(133\) −8446.92 −0.477524
\(134\) −15060.5 −0.838743
\(135\) 950.766 0.0521682
\(136\) 5712.92i 0.308873i
\(137\) 25992.0 1.38483 0.692417 0.721497i \(-0.256546\pi\)
0.692417 + 0.721497i \(0.256546\pi\)
\(138\) −1950.52 −0.102422
\(139\) 10296.8 0.532931 0.266466 0.963844i \(-0.414144\pi\)
0.266466 + 0.963844i \(0.414144\pi\)
\(140\) −9264.78 −0.472693
\(141\) 8321.95i 0.418588i
\(142\) 41665.8i 2.06635i
\(143\) −21114.8 −1.03256
\(144\) 4185.33 0.201839
\(145\) 1968.56 0.0936296
\(146\) −19062.4 −0.894278
\(147\) −1535.99 −0.0710811
\(148\) 42373.3i 1.93450i
\(149\) 34672.4i 1.56175i 0.624687 + 0.780875i \(0.285227\pi\)
−0.624687 + 0.780875i \(0.714773\pi\)
\(150\) 20362.2i 0.904986i
\(151\) 8100.65i 0.355276i −0.984096 0.177638i \(-0.943154\pi\)
0.984096 0.177638i \(-0.0568456\pi\)
\(152\) 17185.2i 0.743818i
\(153\) 1652.34 0.0705857
\(154\) −47313.0 −1.99498
\(155\) 4615.77i 0.192124i
\(156\) 21453.8i 0.881567i
\(157\) 35250.4i 1.43009i 0.699077 + 0.715046i \(0.253594\pi\)
−0.699077 + 0.715046i \(0.746406\pi\)
\(158\) 52431.8i 2.10030i
\(159\) −6887.81 −0.272450
\(160\) 3013.21i 0.117703i
\(161\) 2545.23i 0.0981919i
\(162\) 4933.28i 0.187977i
\(163\) −12118.8 −0.456126 −0.228063 0.973646i \(-0.573239\pi\)
−0.228063 + 0.973646i \(0.573239\pi\)
\(164\) −45672.3 −1.69811
\(165\) 5365.56i 0.197082i
\(166\) 4390.59 0.159333
\(167\) 24887.2 0.892365 0.446182 0.894942i \(-0.352783\pi\)
0.446182 + 0.894942i \(0.352783\pi\)
\(168\) 22257.3i 0.788593i
\(169\) 9358.17 0.327656
\(170\) 2806.54i 0.0971121i
\(171\) −4970.44 −0.169982
\(172\) 12058.2i 0.407591i
\(173\) 6149.40i 0.205466i 0.994709 + 0.102733i \(0.0327588\pi\)
−0.994709 + 0.102733i \(0.967241\pi\)
\(174\) 10214.4i 0.337375i
\(175\) −26570.6 −0.867612
\(176\) 23619.5i 0.762510i
\(177\) 17826.2 + 3065.16i 0.569000 + 0.0978379i
\(178\) 38919.5 1.22836
\(179\) 17529.1i 0.547082i 0.961860 + 0.273541i \(0.0881949\pi\)
−0.961860 + 0.273541i \(0.911805\pi\)
\(180\) −5451.70 −0.168262
\(181\) 20780.3 0.634299 0.317150 0.948376i \(-0.397274\pi\)
0.317150 + 0.948376i \(0.397274\pi\)
\(182\) −43028.6 −1.29902
\(183\) 14196.4i 0.423912i
\(184\) 5178.25 0.152949
\(185\) 9637.84i 0.281602i
\(186\) −23950.0 −0.692277
\(187\) 9324.83i 0.266660i
\(188\) 47718.1i 1.35011i
\(189\) 6437.43 0.180214
\(190\) 8442.42i 0.233862i
\(191\) 13668.6i 0.374676i 0.982296 + 0.187338i \(0.0599860\pi\)
−0.982296 + 0.187338i \(0.940014\pi\)
\(192\) 28522.2 0.773715
\(193\) 24606.0 0.660582 0.330291 0.943879i \(-0.392853\pi\)
0.330291 + 0.943879i \(0.392853\pi\)
\(194\) 10223.0 0.271628
\(195\) 4879.69i 0.128328i
\(196\) 8807.38 0.229263
\(197\) 7657.45 0.197311 0.0986556 0.995122i \(-0.468546\pi\)
0.0986556 + 0.995122i \(0.468546\pi\)
\(198\) −27840.5 −0.710144
\(199\) 50335.0 1.27105 0.635527 0.772079i \(-0.280783\pi\)
0.635527 + 0.772079i \(0.280783\pi\)
\(200\) 54057.6i 1.35144i
\(201\) 11564.1i 0.286233i
\(202\) 16630.0 0.407558
\(203\) 13328.7 0.323442
\(204\) −9474.53 −0.227665
\(205\) 10388.2 0.247191
\(206\) −59225.8 −1.39565
\(207\) 1497.70i 0.0349529i
\(208\) 21480.7i 0.496503i
\(209\) 28050.2i 0.642161i
\(210\) 10934.1i 0.247940i
\(211\) 34304.2i 0.770518i −0.922809 0.385259i \(-0.874112\pi\)
0.922809 0.385259i \(-0.125888\pi\)
\(212\) 39494.7 0.878755
\(213\) −31992.9 −0.705171
\(214\) 142342.i 3.10818i
\(215\) 2742.64i 0.0593324i
\(216\) 13096.9i 0.280712i
\(217\) 31252.4i 0.663688i
\(218\) −65151.9 −1.37093
\(219\) 14637.0i 0.305185i
\(220\) 30766.1i 0.635664i
\(221\) 8480.44i 0.173634i
\(222\) −50008.2 −1.01470
\(223\) 12252.7 0.246390 0.123195 0.992383i \(-0.460686\pi\)
0.123195 + 0.992383i \(0.460686\pi\)
\(224\) 20401.8i 0.406604i
\(225\) −15635.0 −0.308840
\(226\) −157153. −3.07685
\(227\) 83145.6i 1.61357i 0.590846 + 0.806784i \(0.298794\pi\)
−0.590846 + 0.806784i \(0.701206\pi\)
\(228\) 28500.6 0.548256
\(229\) 84147.1i 1.60460i 0.596918 + 0.802302i \(0.296392\pi\)
−0.596918 + 0.802302i \(0.703608\pi\)
\(230\) −2543.88 −0.0480884
\(231\) 36329.1i 0.680817i
\(232\) 27117.1i 0.503811i
\(233\) 10889.2i 0.200578i −0.994958 0.100289i \(-0.968023\pi\)
0.994958 0.100289i \(-0.0319767\pi\)
\(234\) −25319.5 −0.462405
\(235\) 10853.5i 0.196533i
\(236\) −102216. 17575.7i −1.83524 0.315564i
\(237\) 40259.5 0.716757
\(238\) 19002.5i 0.335472i
\(239\) 62954.4 1.10212 0.551061 0.834465i \(-0.314223\pi\)
0.551061 + 0.834465i \(0.314223\pi\)
\(240\) 5458.53 0.0947661
\(241\) −63118.5 −1.08673 −0.543366 0.839496i \(-0.682851\pi\)
−0.543366 + 0.839496i \(0.682851\pi\)
\(242\) 58036.9i 0.990999i
\(243\) 3788.00 0.0641500
\(244\) 81402.1i 1.36728i
\(245\) −2003.25 −0.0333736
\(246\) 53901.7i 0.890702i
\(247\) 25510.2i 0.418138i
\(248\) 63582.7 1.03380
\(249\) 3371.29i 0.0543748i
\(250\) 55219.1i 0.883505i
\(251\) −66048.7 −1.04838 −0.524188 0.851603i \(-0.675631\pi\)
−0.524188 + 0.851603i \(0.675631\pi\)
\(252\) −36912.3 −0.581259
\(253\) −8452.12 −0.132046
\(254\) 22049.6i 0.341770i
\(255\) 2154.99 0.0331409
\(256\) −115404. −1.76093
\(257\) 91076.3 1.37892 0.689460 0.724323i \(-0.257848\pi\)
0.689460 + 0.724323i \(0.257848\pi\)
\(258\) 14230.9 0.213792
\(259\) 65255.8i 0.972791i
\(260\) 27980.2i 0.413908i
\(261\) 7843.05 0.115134
\(262\) 161598. 2.35414
\(263\) −83369.8 −1.20531 −0.602653 0.798003i \(-0.705890\pi\)
−0.602653 + 0.798003i \(0.705890\pi\)
\(264\) 73911.1 1.06048
\(265\) −8983.12 −0.127919
\(266\) 57161.9i 0.807873i
\(267\) 29884.2i 0.419198i
\(268\) 66308.7i 0.923211i
\(269\) 13600.6i 0.187955i 0.995574 + 0.0939775i \(0.0299582\pi\)
−0.995574 + 0.0939775i \(0.970042\pi\)
\(270\) 6434.00i 0.0882580i
\(271\) −374.789 −0.00510327 −0.00255164 0.999997i \(-0.500812\pi\)
−0.00255164 + 0.999997i \(0.500812\pi\)
\(272\) 9486.40 0.128222
\(273\) 33039.4i 0.443309i
\(274\) 175892.i 2.34286i
\(275\) 88234.7i 1.16674i
\(276\) 8587.81i 0.112736i
\(277\) −34517.8 −0.449866 −0.224933 0.974374i \(-0.572216\pi\)
−0.224933 + 0.974374i \(0.572216\pi\)
\(278\) 69680.1i 0.901611i
\(279\) 18389.9i 0.236250i
\(280\) 29028.0i 0.370255i
\(281\) 100630. 1.27442 0.637210 0.770690i \(-0.280088\pi\)
0.637210 + 0.770690i \(0.280088\pi\)
\(282\) 56316.2 0.708166
\(283\) 85403.6i 1.06636i 0.846002 + 0.533179i \(0.179003\pi\)
−0.846002 + 0.533179i \(0.820997\pi\)
\(284\) 183448. 2.27444
\(285\) −6482.48 −0.0798089
\(286\) 142888.i 1.74688i
\(287\) 70336.4 0.853918
\(288\) 12005.1i 0.144737i
\(289\) −79775.8 −0.955159
\(290\) 13321.6i 0.158402i
\(291\) 7849.67i 0.0926969i
\(292\) 83928.7i 0.984339i
\(293\) 133357. 1.55339 0.776696 0.629876i \(-0.216894\pi\)
0.776696 + 0.629876i \(0.216894\pi\)
\(294\) 10394.3i 0.120255i
\(295\) 23249.0 + 3997.60i 0.267153 + 0.0459362i
\(296\) 132762. 1.51527
\(297\) 21377.2i 0.242347i
\(298\) 234635. 2.64216
\(299\) −7686.75 −0.0859806
\(300\) 89651.2 0.996125
\(301\) 18569.9i 0.204963i
\(302\) −54818.6 −0.601055
\(303\) 12769.3i 0.139085i
\(304\) −28536.3 −0.308781
\(305\) 18515.0i 0.199032i
\(306\) 11181.7i 0.119417i
\(307\) 20011.7 0.212328 0.106164 0.994349i \(-0.466143\pi\)
0.106164 + 0.994349i \(0.466143\pi\)
\(308\) 208311.i 2.19589i
\(309\) 45476.3i 0.476286i
\(310\) −31235.8 −0.325034
\(311\) 32402.1 0.335006 0.167503 0.985872i \(-0.446430\pi\)
0.167503 + 0.985872i \(0.446430\pi\)
\(312\) 67218.2 0.690523
\(313\) 191288.i 1.95254i −0.216568 0.976268i \(-0.569486\pi\)
0.216568 0.976268i \(-0.430514\pi\)
\(314\) 238546. 2.41943
\(315\) 8395.73 0.0846131
\(316\) −230848. −2.31181
\(317\) −127089. −1.26470 −0.632351 0.774682i \(-0.717910\pi\)
−0.632351 + 0.774682i \(0.717910\pi\)
\(318\) 46611.1i 0.460930i
\(319\) 44261.5i 0.434956i
\(320\) 37198.8 0.363270
\(321\) 109297. 1.06071
\(322\) −17224.1 −0.166121
\(323\) −11265.9 −0.107985
\(324\) −21720.4 −0.206908
\(325\) 80244.8i 0.759714i
\(326\) 82010.3i 0.771673i
\(327\) 50026.6i 0.467849i
\(328\) 143099.i 1.33011i
\(329\) 73487.0i 0.678920i
\(330\) −36309.7 −0.333422
\(331\) −190707. −1.74064 −0.870321 0.492484i \(-0.836089\pi\)
−0.870321 + 0.492484i \(0.836089\pi\)
\(332\) 19331.0i 0.175379i
\(333\) 38398.6i 0.346280i
\(334\) 168416.i 1.50970i
\(335\) 15082.0i 0.134391i
\(336\) 36958.6 0.327368
\(337\) 121592.i 1.07065i −0.844648 0.535323i \(-0.820190\pi\)
0.844648 0.535323i \(-0.179810\pi\)
\(338\) 63328.5i 0.554326i
\(339\) 120669.i 1.05002i
\(340\) −12356.7 −0.106892
\(341\) −103782. −0.892509
\(342\) 33635.9i 0.287575i
\(343\) −123733. −1.05171
\(344\) −37780.2 −0.319262
\(345\) 1953.30i 0.0164109i
\(346\) 41614.1 0.347607
\(347\) 11383.8i 0.0945426i 0.998882 + 0.0472713i \(0.0150525\pi\)
−0.998882 + 0.0472713i \(0.984947\pi\)
\(348\) −44972.1 −0.371351
\(349\) 133595.i 1.09683i −0.836207 0.548414i \(-0.815232\pi\)
0.836207 0.548414i \(-0.184768\pi\)
\(350\) 179808.i 1.46782i
\(351\) 19441.4i 0.157803i
\(352\) 67749.5 0.546790
\(353\) 152806.i 1.22628i 0.789973 + 0.613141i \(0.210094\pi\)
−0.789973 + 0.613141i \(0.789906\pi\)
\(354\) 20742.5 120633.i 0.165522 0.962632i
\(355\) −41725.3 −0.331088
\(356\) 171356.i 1.35207i
\(357\) 14591.0 0.114485
\(358\) 118622. 0.925551
\(359\) −84352.3 −0.654497 −0.327249 0.944938i \(-0.606121\pi\)
−0.327249 + 0.944938i \(0.606121\pi\)
\(360\) 17081.0i 0.131798i
\(361\) −96431.7 −0.739955
\(362\) 140624.i 1.07310i
\(363\) −44563.4 −0.338193
\(364\) 189448.i 1.42984i
\(365\) 19089.6i 0.143289i
\(366\) 96069.5 0.717172
\(367\) 22612.6i 0.167888i 0.996470 + 0.0839439i \(0.0267517\pi\)
−0.996470 + 0.0839439i \(0.973248\pi\)
\(368\) 8598.57i 0.0634937i
\(369\) 41388.2 0.303965
\(370\) −65221.0 −0.476414
\(371\) −60822.8 −0.441894
\(372\) 105448.i 0.761995i
\(373\) −142008. −1.02069 −0.510347 0.859968i \(-0.670483\pi\)
−0.510347 + 0.859968i \(0.670483\pi\)
\(374\) −63102.8 −0.451134
\(375\) −42399.7 −0.301509
\(376\) −149509. −1.05752
\(377\) 40253.5i 0.283218i
\(378\) 43563.3i 0.304886i
\(379\) −71134.7 −0.495226 −0.247613 0.968859i \(-0.579646\pi\)
−0.247613 + 0.968859i \(0.579646\pi\)
\(380\) 37170.6 0.257414
\(381\) 16930.7 0.116634
\(382\) 92497.6 0.633875
\(383\) 5389.15 0.0367386 0.0183693 0.999831i \(-0.494153\pi\)
0.0183693 + 0.999831i \(0.494153\pi\)
\(384\) 156049.i 1.05828i
\(385\) 47380.5i 0.319653i
\(386\) 166514.i 1.11757i
\(387\) 10927.1i 0.0729597i
\(388\) 45010.1i 0.298983i
\(389\) 227686. 1.50466 0.752329 0.658787i \(-0.228930\pi\)
0.752329 + 0.658787i \(0.228930\pi\)
\(390\) −33021.8 −0.217106
\(391\) 3394.66i 0.0222046i
\(392\) 27594.9i 0.179580i
\(393\) 124082.i 0.803387i
\(394\) 51819.4i 0.333810i
\(395\) 52506.7 0.336527
\(396\) 122577.i 0.781661i
\(397\) 66414.0i 0.421385i −0.977552 0.210692i \(-0.932428\pi\)
0.977552 0.210692i \(-0.0675718\pi\)
\(398\) 340626.i 2.15036i
\(399\) −43891.5 −0.275699
\(400\) −89763.6 −0.561022
\(401\) 185618.i 1.15434i −0.816625 0.577168i \(-0.804158\pi\)
0.816625 0.577168i \(-0.195842\pi\)
\(402\) −78256.5 −0.484249
\(403\) −94384.1 −0.581151
\(404\) 73219.1i 0.448602i
\(405\) 4940.32 0.0301193
\(406\) 90197.9i 0.547198i
\(407\) −216699. −1.30818
\(408\) 29685.2i 0.178328i
\(409\) 69799.6i 0.417260i 0.977995 + 0.208630i \(0.0669004\pi\)
−0.977995 + 0.208630i \(0.933100\pi\)
\(410\) 70298.9i 0.418197i
\(411\) 135058. 0.799535
\(412\) 260761.i 1.53620i
\(413\) 157414. + 27066.9i 0.922877 + 0.158686i
\(414\) −10135.2 −0.0591332
\(415\) 4396.86i 0.0255297i
\(416\) 61614.6 0.356038
\(417\) 53503.5 0.307688
\(418\) 189821. 1.08641
\(419\) 68851.9i 0.392182i −0.980586 0.196091i \(-0.937175\pi\)
0.980586 0.196091i \(-0.0628248\pi\)
\(420\) −48141.2 −0.272909
\(421\) 52611.8i 0.296837i −0.988925 0.148419i \(-0.952582\pi\)
0.988925 0.148419i \(-0.0474183\pi\)
\(422\) −232143. −1.30356
\(423\) 43242.1i 0.241672i
\(424\) 123743.i 0.688320i
\(425\) −35438.1 −0.196197
\(426\) 216502.i 1.19301i
\(427\) 125361.i 0.687554i
\(428\) −626708. −3.42120
\(429\) −109716. −0.596149
\(430\) 18560.0 0.100378
\(431\) 127282.i 0.685193i −0.939483 0.342596i \(-0.888694\pi\)
0.939483 0.342596i \(-0.111306\pi\)
\(432\) 21747.6 0.116532
\(433\) 67016.8 0.357444 0.178722 0.983900i \(-0.442804\pi\)
0.178722 + 0.983900i \(0.442804\pi\)
\(434\) −211491. −1.12282
\(435\) 10229.0 0.0540571
\(436\) 286853.i 1.50899i
\(437\) 10211.5i 0.0534723i
\(438\) −99051.3 −0.516311
\(439\) 131134. 0.680434 0.340217 0.940347i \(-0.389499\pi\)
0.340217 + 0.940347i \(0.389499\pi\)
\(440\) 96395.2 0.497909
\(441\) −7981.24 −0.0410387
\(442\) −57388.7 −0.293753
\(443\) 238014.i 1.21282i −0.795154 0.606408i \(-0.792610\pi\)
0.795154 0.606408i \(-0.207390\pi\)
\(444\) 220178.i 1.11688i
\(445\) 38975.1i 0.196819i
\(446\) 82916.3i 0.416841i
\(447\) 180163.i 0.901677i
\(448\) 251865. 1.25491
\(449\) −140599. −0.697411 −0.348706 0.937232i \(-0.613379\pi\)
−0.348706 + 0.937232i \(0.613379\pi\)
\(450\) 105805.i 0.522494i
\(451\) 233570.i 1.14832i
\(452\) 691919.i 3.38671i
\(453\) 42092.2i 0.205119i
\(454\) 562661. 2.72983
\(455\) 43090.1i 0.208140i
\(456\) 89296.8i 0.429444i
\(457\) 381250.i 1.82548i 0.408539 + 0.912741i \(0.366038\pi\)
−0.408539 + 0.912741i \(0.633962\pi\)
\(458\) 569439. 2.71466
\(459\) 8585.81 0.0407526
\(460\) 11200.3i 0.0529313i
\(461\) −66518.7 −0.312998 −0.156499 0.987678i \(-0.550021\pi\)
−0.156499 + 0.987678i \(0.550021\pi\)
\(462\) −245845. −1.15180
\(463\) 362433.i 1.69070i 0.534216 + 0.845348i \(0.320607\pi\)
−0.534216 + 0.845348i \(0.679393\pi\)
\(464\) 45028.5 0.209147
\(465\) 23984.2i 0.110923i
\(466\) −73689.1 −0.339337
\(467\) 184210.i 0.844656i −0.906443 0.422328i \(-0.861213\pi\)
0.906443 0.422328i \(-0.138787\pi\)
\(468\) 111477.i 0.508973i
\(469\) 102117.i 0.464250i
\(470\) 73447.9 0.332494
\(471\) 183166.i 0.825664i
\(472\) −55067.4 + 320258.i −0.247178 + 1.43753i
\(473\) 61666.1 0.275629
\(474\) 272444.i 1.21261i
\(475\) 106602. 0.472475
\(476\) −83664.8 −0.369257
\(477\) −35790.1 −0.157299
\(478\) 426024.i 1.86457i
\(479\) −348835. −1.52037 −0.760185 0.649707i \(-0.774892\pi\)
−0.760185 + 0.649707i \(0.774892\pi\)
\(480\) 15657.1i 0.0679561i
\(481\) −197076. −0.851813
\(482\) 427135.i 1.83853i
\(483\) 13225.4i 0.0566911i
\(484\) 255527. 1.09080
\(485\) 10237.6i 0.0435225i
\(486\) 25634.1i 0.108529i
\(487\) −451419. −1.90336 −0.951681 0.307087i \(-0.900646\pi\)
−0.951681 + 0.307087i \(0.900646\pi\)
\(488\) −255046. −1.07097
\(489\) −62971.3 −0.263345
\(490\) 13556.3i 0.0564612i
\(491\) −64824.7 −0.268892 −0.134446 0.990921i \(-0.542925\pi\)
−0.134446 + 0.990921i \(0.542925\pi\)
\(492\) −237320. −0.980403
\(493\) 17776.9 0.0731414
\(494\) 172632. 0.707405
\(495\) 27880.3i 0.113785i
\(496\) 105580.i 0.429160i
\(497\) −282513. −1.14374
\(498\) 22814.2 0.0919911
\(499\) −151617. −0.608900 −0.304450 0.952528i \(-0.598473\pi\)
−0.304450 + 0.952528i \(0.598473\pi\)
\(500\) 243120. 0.972481
\(501\) 129317. 0.515207
\(502\) 446964.i 1.77364i
\(503\) 154559.i 0.610883i −0.952211 0.305442i \(-0.901196\pi\)
0.952211 0.305442i \(-0.0988040\pi\)
\(504\) 115652.i 0.455295i
\(505\) 16653.8i 0.0653024i
\(506\) 57197.0i 0.223394i
\(507\) 48626.5 0.189172
\(508\) −97080.8 −0.376189
\(509\) 6251.16i 0.0241282i 0.999927 + 0.0120641i \(0.00384022\pi\)
−0.999927 + 0.0120641i \(0.996160\pi\)
\(510\) 14583.2i 0.0560677i
\(511\) 129252.i 0.494989i
\(512\) 300454.i 1.14614i
\(513\) −25827.2 −0.0981391
\(514\) 616330.i 2.33285i
\(515\) 59310.4i 0.223623i
\(516\) 62656.1i 0.235323i
\(517\) 244033. 0.912993
\(518\) −441598. −1.64576
\(519\) 31953.2i 0.118626i
\(520\) 87666.4 0.324210
\(521\) 351023. 1.29318 0.646591 0.762836i \(-0.276194\pi\)
0.646591 + 0.762836i \(0.276194\pi\)
\(522\) 53075.4i 0.194783i
\(523\) −58841.2 −0.215119 −0.107559 0.994199i \(-0.534304\pi\)
−0.107559 + 0.994199i \(0.534304\pi\)
\(524\) 711489.i 2.59123i
\(525\) −138065. −0.500916
\(526\) 564179.i 2.03913i
\(527\) 41682.3i 0.150083i
\(528\) 122731.i 0.440236i
\(529\) 276764. 0.989005
\(530\) 60790.4i 0.216413i
\(531\) 92627.7 + 15927.1i 0.328512 + 0.0564867i
\(532\) 251674. 0.889233
\(533\) 212420.i 0.747723i
\(534\) 202232. 0.709197
\(535\) 142545. 0.498019
\(536\) 207756. 0.723142
\(537\) 91083.6i 0.315858i
\(538\) 92037.8 0.317981
\(539\) 45041.4i 0.155037i
\(540\) −28327.8 −0.0971462
\(541\) 451192.i 1.54158i 0.637088 + 0.770791i \(0.280139\pi\)
−0.637088 + 0.770791i \(0.719861\pi\)
\(542\) 2536.27i 0.00863369i
\(543\) 107977. 0.366213
\(544\) 27210.5i 0.0919472i
\(545\) 65244.9i 0.219661i
\(546\) −223583. −0.749988
\(547\) −341064. −1.13988 −0.569942 0.821685i \(-0.693034\pi\)
−0.569942 + 0.821685i \(0.693034\pi\)
\(548\) −774425. −2.57880
\(549\) 73766.5i 0.244745i
\(550\) 597100. 1.97389
\(551\) −53475.2 −0.176137
\(552\) 26907.0 0.0883053
\(553\) 355512. 1.16253
\(554\) 233588.i 0.761082i
\(555\) 50079.7i 0.162583i
\(556\) −306790. −0.992410
\(557\) 333403. 1.07463 0.537315 0.843382i \(-0.319439\pi\)
0.537315 + 0.843382i \(0.319439\pi\)
\(558\) −124448. −0.399687
\(559\) 56082.1 0.179474
\(560\) 48201.5 0.153704
\(561\) 48453.2i 0.153956i
\(562\) 680978.i 2.15606i
\(563\) 48980.2i 0.154527i 0.997011 + 0.0772634i \(0.0246182\pi\)
−0.997011 + 0.0772634i \(0.975382\pi\)
\(564\) 247951.i 0.779484i
\(565\) 157378.i 0.492999i
\(566\) 577942. 1.80406
\(567\) 33449.9 0.104047
\(568\) 574771.i 1.78155i
\(569\) 47923.5i 0.148021i 0.997257 + 0.0740106i \(0.0235799\pi\)
−0.997257 + 0.0740106i \(0.976420\pi\)
\(570\) 43868.1i 0.135020i
\(571\) 518303.i 1.58969i 0.606815 + 0.794843i \(0.292447\pi\)
−0.606815 + 0.794843i \(0.707553\pi\)
\(572\) 629112. 1.92281
\(573\) 71023.9i 0.216319i
\(574\) 475979.i 1.44465i
\(575\) 32121.4i 0.0971536i
\(576\) 148206. 0.446704
\(577\) 92997.1 0.279330 0.139665 0.990199i \(-0.455397\pi\)
0.139665 + 0.990199i \(0.455397\pi\)
\(578\) 539858.i 1.61593i
\(579\) 127857. 0.381387
\(580\) −58652.9 −0.174355
\(581\) 29770.2i 0.0881921i
\(582\) 53120.2 0.156824
\(583\) 201978.i 0.594247i
\(584\) 262962. 0.771022
\(585\) 25355.6i 0.0740905i
\(586\) 902452.i 2.62802i
\(587\) 333846.i 0.968881i 0.874824 + 0.484440i \(0.160977\pi\)
−0.874824 + 0.484440i \(0.839023\pi\)
\(588\) 45764.5 0.132365
\(589\) 125386.i 0.361424i
\(590\) 27052.5 157330.i 0.0777147 0.451969i
\(591\) 39789.3 0.113918
\(592\) 220454.i 0.629034i
\(593\) 122051. 0.347081 0.173541 0.984827i \(-0.444479\pi\)
0.173541 + 0.984827i \(0.444479\pi\)
\(594\) −144663. −0.410002
\(595\) 19029.6 0.0537522
\(596\) 1.03306e6i 2.90825i
\(597\) 261548. 0.733843
\(598\) 52017.7i 0.145462i
\(599\) −118410. −0.330015 −0.165008 0.986292i \(-0.552765\pi\)
−0.165008 + 0.986292i \(0.552765\pi\)
\(600\) 280892.i 0.780255i
\(601\) 316761.i 0.876966i 0.898740 + 0.438483i \(0.144484\pi\)
−0.898740 + 0.438483i \(0.855516\pi\)
\(602\) 125666. 0.346756
\(603\) 60088.9i 0.165257i
\(604\) 241357.i 0.661586i
\(605\) −58119.8 −0.158786
\(606\) 86412.0 0.235304
\(607\) −635965. −1.72606 −0.863030 0.505153i \(-0.831436\pi\)
−0.863030 + 0.505153i \(0.831436\pi\)
\(608\) 81852.6i 0.221424i
\(609\) 69258.1 0.186739
\(610\) 125294. 0.336722
\(611\) 221935. 0.594489
\(612\) −49231.1 −0.131443
\(613\) 664506.i 1.76839i −0.467119 0.884195i \(-0.654708\pi\)
0.467119 0.884195i \(-0.345292\pi\)
\(614\) 135423.i 0.359215i
\(615\) 53978.7 0.142716
\(616\) 652672. 1.72002
\(617\) 214690. 0.563952 0.281976 0.959422i \(-0.409010\pi\)
0.281976 + 0.959422i \(0.409010\pi\)
\(618\) −307746. −0.805779
\(619\) −638321. −1.66594 −0.832968 0.553322i \(-0.813360\pi\)
−0.832968 + 0.553322i \(0.813360\pi\)
\(620\) 137526.i 0.357767i
\(621\) 7782.26i 0.0201801i
\(622\) 219271.i 0.566761i
\(623\) 263892.i 0.679908i
\(624\) 111617.i 0.286656i
\(625\) 306624. 0.784956
\(626\) −1.29448e6 −3.30329
\(627\) 145753.i 0.370752i
\(628\) 1.05028e6i 2.66308i
\(629\) 87033.7i 0.219981i
\(630\) 56815.5i 0.143148i
\(631\) −375421. −0.942888 −0.471444 0.881896i \(-0.656267\pi\)
−0.471444 + 0.881896i \(0.656267\pi\)
\(632\) 723285.i 1.81082i
\(633\) 178250.i 0.444859i
\(634\) 860032.i 2.13962i
\(635\) 22081.1 0.0547613
\(636\) 205221. 0.507349
\(637\) 40962.8i 0.100951i
\(638\) −299526. −0.735857
\(639\) −166240. −0.407131
\(640\) 203520.i 0.496875i
\(641\) 704608. 1.71487 0.857435 0.514592i \(-0.172057\pi\)
0.857435 + 0.514592i \(0.172057\pi\)
\(642\) 739631.i 1.79451i
\(643\) −448900. −1.08574 −0.542872 0.839816i \(-0.682663\pi\)
−0.542872 + 0.839816i \(0.682663\pi\)
\(644\) 75834.6i 0.182850i
\(645\) 14251.2i 0.0342556i
\(646\) 76238.6i 0.182688i
\(647\) −211597. −0.505477 −0.252738 0.967535i \(-0.581331\pi\)
−0.252738 + 0.967535i \(0.581331\pi\)
\(648\) 68053.4i 0.162069i
\(649\) 89882.8 522736.i 0.213397 1.24106i
\(650\) 543031. 1.28528
\(651\) 162392.i 0.383180i
\(652\) 361078. 0.849387
\(653\) −171313. −0.401757 −0.200878 0.979616i \(-0.564380\pi\)
−0.200878 + 0.979616i \(0.564380\pi\)
\(654\) −338539. −0.791504
\(655\) 161829.i 0.377201i
\(656\) 237618. 0.552168
\(657\) 76056.1i 0.176199i
\(658\) 497300. 1.14859
\(659\) 123614.i 0.284641i −0.989821 0.142321i \(-0.954544\pi\)
0.989821 0.142321i \(-0.0454564\pi\)
\(660\) 159866.i 0.367001i
\(661\) 759419. 1.73811 0.869057 0.494712i \(-0.164726\pi\)
0.869057 + 0.494712i \(0.164726\pi\)
\(662\) 1.29055e6i 2.94481i
\(663\) 44065.6i 0.100247i
\(664\) −60567.2 −0.137373
\(665\) −57243.5 −0.129444
\(666\) −259850. −0.585835
\(667\) 16113.2i 0.0362185i
\(668\) −741507. −1.66174
\(669\) 63667.0 0.142253
\(670\) −102063. −0.227361
\(671\) 416295. 0.924604
\(672\) 106011.i 0.234753i
\(673\) 366990.i 0.810260i 0.914259 + 0.405130i \(0.132774\pi\)
−0.914259 + 0.405130i \(0.867226\pi\)
\(674\) −822836. −1.81131
\(675\) −81241.9 −0.178309
\(676\) −278825. −0.610152
\(677\) 411628. 0.898105 0.449053 0.893505i \(-0.351762\pi\)
0.449053 + 0.893505i \(0.351762\pi\)
\(678\) −816592. −1.77642
\(679\) 69316.5i 0.150348i
\(680\) 38715.6i 0.0837275i
\(681\) 432037.i 0.931594i
\(682\) 702311.i 1.50994i
\(683\) 654877.i 1.40384i 0.712254 + 0.701921i \(0.247674\pi\)
−0.712254 + 0.701921i \(0.752326\pi\)
\(684\) 148093. 0.316536
\(685\) 176144. 0.375393
\(686\) 837321.i 1.77928i
\(687\) 437241.i 0.926419i
\(688\) 62734.6i 0.132535i
\(689\) 183688.i 0.386940i
\(690\) −13218.4 −0.0277639
\(691\) 628200.i 1.31565i 0.753169 + 0.657827i \(0.228524\pi\)
−0.753169 + 0.657827i \(0.771476\pi\)
\(692\) 183220.i 0.382614i
\(693\) 188771.i 0.393070i
\(694\) 77036.1 0.159947
\(695\) 69779.6 0.144464
\(696\) 140905.i 0.290876i
\(697\) 93809.8 0.193100
\(698\) −904060. −1.85561
\(699\) 56581.9i 0.115804i
\(700\) 791665. 1.61564
\(701\) 517988.i 1.05410i −0.849833 0.527052i \(-0.823297\pi\)
0.849833 0.527052i \(-0.176703\pi\)
\(702\) −131564. −0.266970
\(703\) 261808.i 0.529752i
\(704\) 836386.i 1.68757i
\(705\) 56396.6i 0.113468i
\(706\) 1.03407e6 2.07462
\(707\) 112759.i 0.225586i
\(708\) −531128. 91325.8i −1.05958 0.182191i
\(709\) 417989. 0.831519 0.415759 0.909475i \(-0.363516\pi\)
0.415759 + 0.909475i \(0.363516\pi\)
\(710\) 282363.i 0.560133i
\(711\) 209195. 0.413820
\(712\) −536886. −1.05906
\(713\) −37781.3 −0.0743186
\(714\) 98739.9i 0.193685i
\(715\) −143092. −0.279900
\(716\) 522274.i 1.01876i
\(717\) 327120. 0.636311
\(718\) 570827.i 1.10728i
\(719\) 88171.5i 0.170557i 0.996357 + 0.0852787i \(0.0271781\pi\)
−0.996357 + 0.0852787i \(0.972822\pi\)
\(720\) 28363.3 0.0547132
\(721\) 401578.i 0.772502i
\(722\) 652571.i 1.25185i
\(723\) −327973. −0.627425
\(724\) −619144. −1.18117
\(725\) −168212. −0.320022
\(726\) 301568.i 0.572154i
\(727\) 765157. 1.44771 0.723855 0.689952i \(-0.242368\pi\)
0.723855 + 0.689952i \(0.242368\pi\)
\(728\) 593571. 1.11998
\(729\) 19683.0 0.0370370
\(730\) −129183. −0.242415
\(731\) 24767.2i 0.0463492i
\(732\) 422978.i 0.789397i
\(733\) 45126.1 0.0839885 0.0419943 0.999118i \(-0.486629\pi\)
0.0419943 + 0.999118i \(0.486629\pi\)
\(734\) 153024. 0.284032
\(735\) −10409.2 −0.0192682
\(736\) 24663.9 0.0455308
\(737\) −339106. −0.624311
\(738\) 280082.i 0.514247i
\(739\) 1.03826e6i 1.90116i −0.310476 0.950581i \(-0.600488\pi\)
0.310476 0.950581i \(-0.399512\pi\)
\(740\) 287157.i 0.524392i
\(741\) 132555.i 0.241412i
\(742\) 411599.i 0.747595i
\(743\) −432123. −0.782763 −0.391381 0.920229i \(-0.628003\pi\)
−0.391381 + 0.920229i \(0.628003\pi\)
\(744\) 330385. 0.596863
\(745\) 234970.i 0.423350i
\(746\) 960995.i 1.72681i
\(747\) 17517.8i 0.0313933i
\(748\) 277831.i 0.496567i
\(749\) 965145. 1.72040
\(750\) 286927.i 0.510092i
\(751\) 586786.i 1.04040i −0.854045 0.520200i \(-0.825858\pi\)
0.854045 0.520200i \(-0.174142\pi\)
\(752\) 248262.i 0.439009i
\(753\) −343199. −0.605280
\(754\) −272403. −0.479148
\(755\) 54896.9i 0.0963061i
\(756\) −191802. −0.335590
\(757\) −69647.3 −0.121538 −0.0607690 0.998152i \(-0.519355\pi\)
−0.0607690 + 0.998152i \(0.519355\pi\)
\(758\) 481382.i 0.837821i
\(759\) −43918.5 −0.0762366
\(760\) 116461.i 0.201630i
\(761\) −533970. −0.922035 −0.461017 0.887391i \(-0.652515\pi\)
−0.461017 + 0.887391i \(0.652515\pi\)
\(762\) 114573.i 0.197321i
\(763\) 441760.i 0.758817i
\(764\) 407252.i 0.697712i
\(765\) 11197.7 0.0191339
\(766\) 36469.4i 0.0621542i
\(767\) 81743.7 475400.i 0.138952 0.808107i
\(768\) −599657. −1.01667
\(769\) 316009.i 0.534376i −0.963644 0.267188i \(-0.913905\pi\)
0.963644 0.267188i \(-0.0860945\pi\)
\(770\) −320633. −0.540787
\(771\) 473246. 0.796120
\(772\) −733131. −1.23012
\(773\) 42404.6i 0.0709666i −0.999370 0.0354833i \(-0.988703\pi\)
0.999370 0.0354833i \(-0.0112971\pi\)
\(774\) 73945.7 0.123433
\(775\) 394412.i 0.656670i
\(776\) −141024. −0.234190
\(777\) 339079.i 0.561641i
\(778\) 1.54080e6i 2.54558i
\(779\) −282192. −0.465017
\(780\) 145389.i 0.238970i
\(781\) 938160.i 1.53807i
\(782\) −22972.3 −0.0375656
\(783\) 40753.7 0.0664727
\(784\) −45821.9 −0.0745488
\(785\) 238886.i 0.387661i
\(786\) 839687. 1.35917
\(787\) −952711. −1.53820 −0.769098 0.639131i \(-0.779294\pi\)
−0.769098 + 0.639131i \(0.779294\pi\)
\(788\) −228152. −0.367428
\(789\) −433202. −0.695884