Properties

Label 177.5.c.a.58.19
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 58.19
Character \(\chi\) \(=\) 177.58
Dual form 177.5.c.a.58.22

$q$-expansion

\(f(q)\) \(=\) \(q-0.850217i q^{2} -5.19615 q^{3} +15.2771 q^{4} -11.2738 q^{5} +4.41785i q^{6} -26.4494 q^{7} -26.5923i q^{8} +27.0000 q^{9} +O(q^{10})\) \(q-0.850217i q^{2} -5.19615 q^{3} +15.2771 q^{4} -11.2738 q^{5} +4.41785i q^{6} -26.4494 q^{7} -26.5923i q^{8} +27.0000 q^{9} +9.58520i q^{10} -19.9957i q^{11} -79.3823 q^{12} +190.208i q^{13} +22.4877i q^{14} +58.5805 q^{15} +221.825 q^{16} -159.452 q^{17} -22.9558i q^{18} -294.035 q^{19} -172.232 q^{20} +137.435 q^{21} -17.0007 q^{22} +165.303i q^{23} +138.178i q^{24} -497.901 q^{25} +161.718 q^{26} -140.296 q^{27} -404.071 q^{28} +513.249 q^{29} -49.8061i q^{30} +1627.89i q^{31} -614.077i q^{32} +103.901i q^{33} +135.569i q^{34} +298.186 q^{35} +412.483 q^{36} +1773.75i q^{37} +249.994i q^{38} -988.349i q^{39} +299.797i q^{40} -2060.39 q^{41} -116.850i q^{42} +2180.85i q^{43} -305.478i q^{44} -304.393 q^{45} +140.543 q^{46} +4253.57i q^{47} -1152.64 q^{48} -1701.43 q^{49} +423.323i q^{50} +828.536 q^{51} +2905.83i q^{52} +246.901 q^{53} +119.282i q^{54} +225.429i q^{55} +703.351i q^{56} +1527.85 q^{57} -436.373i q^{58} +(-1203.62 - 3266.29i) q^{59} +894.943 q^{60} -1494.54i q^{61} +1384.06 q^{62} -714.133 q^{63} +3027.10 q^{64} -2144.37i q^{65} +88.3383 q^{66} -3881.60i q^{67} -2435.97 q^{68} -858.939i q^{69} -253.523i q^{70} +1862.97 q^{71} -717.993i q^{72} +619.232i q^{73} +1508.07 q^{74} +2587.17 q^{75} -4492.02 q^{76} +528.875i q^{77} -840.311 q^{78} +2372.28 q^{79} -2500.82 q^{80} +729.000 q^{81} +1751.78i q^{82} -4603.55i q^{83} +2099.61 q^{84} +1797.63 q^{85} +1854.19 q^{86} -2666.92 q^{87} -531.733 q^{88} -8914.96i q^{89} +258.800i q^{90} -5030.88i q^{91} +2525.36i q^{92} -8458.78i q^{93} +3616.46 q^{94} +3314.91 q^{95} +3190.84i q^{96} -1374.52i q^{97} +1446.58i q^{98} -539.885i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + O(q^{10}) \) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + 360q^{12} + 144q^{15} + 3944q^{16} - 528q^{17} + 444q^{19} + 444q^{20} + 1304q^{22} + 4880q^{25} - 1452q^{26} - 1160q^{28} - 996q^{29} + 10320q^{35} - 8640q^{36} - 5196q^{41} - 10476q^{46} + 576q^{48} + 5104q^{49} + 936q^{51} - 2184q^{53} - 2520q^{57} - 11736q^{59} - 11448q^{60} + 15240q^{62} + 2160q^{63} - 81012q^{64} + 17352q^{66} + 29568q^{68} - 5964q^{71} + 14376q^{74} - 2736q^{75} + 3480q^{76} + 37692q^{78} + 19020q^{79} + 33096q^{80} + 29160q^{81} + 25128q^{84} + 20220q^{85} - 65880q^{86} + 1512q^{87} - 14932q^{88} - 17864q^{94} + 11004q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.850217i 0.212554i −0.994337 0.106277i \(-0.966107\pi\)
0.994337 0.106277i \(-0.0338930\pi\)
\(3\) −5.19615 −0.577350
\(4\) 15.2771 0.954821
\(5\) −11.2738 −0.450953 −0.225477 0.974249i \(-0.572394\pi\)
−0.225477 + 0.974249i \(0.572394\pi\)
\(6\) 4.41785i 0.122718i
\(7\) −26.4494 −0.539783 −0.269892 0.962891i \(-0.586988\pi\)
−0.269892 + 0.962891i \(0.586988\pi\)
\(8\) 26.5923i 0.415505i
\(9\) 27.0000 0.333333
\(10\) 9.58520i 0.0958520i
\(11\) 19.9957i 0.165254i −0.996581 0.0826270i \(-0.973669\pi\)
0.996581 0.0826270i \(-0.0263310\pi\)
\(12\) −79.3823 −0.551266
\(13\) 190.208i 1.12549i 0.826630 + 0.562745i \(0.190255\pi\)
−0.826630 + 0.562745i \(0.809745\pi\)
\(14\) 22.4877i 0.114733i
\(15\) 58.5805 0.260358
\(16\) 221.825 0.866503
\(17\) −159.452 −0.551736 −0.275868 0.961195i \(-0.588965\pi\)
−0.275868 + 0.961195i \(0.588965\pi\)
\(18\) 22.9558i 0.0708514i
\(19\) −294.035 −0.814503 −0.407251 0.913316i \(-0.633513\pi\)
−0.407251 + 0.913316i \(0.633513\pi\)
\(20\) −172.232 −0.430579
\(21\) 137.435 0.311644
\(22\) −17.0007 −0.0351254
\(23\) 165.303i 0.312482i 0.987719 + 0.156241i \(0.0499376\pi\)
−0.987719 + 0.156241i \(0.950062\pi\)
\(24\) 138.178i 0.239892i
\(25\) −497.901 −0.796641
\(26\) 161.718 0.239228
\(27\) −140.296 −0.192450
\(28\) −404.071 −0.515396
\(29\) 513.249 0.610284 0.305142 0.952307i \(-0.401296\pi\)
0.305142 + 0.952307i \(0.401296\pi\)
\(30\) 49.8061i 0.0553402i
\(31\) 1627.89i 1.69396i 0.531626 + 0.846979i \(0.321581\pi\)
−0.531626 + 0.846979i \(0.678419\pi\)
\(32\) 614.077i 0.599684i
\(33\) 103.901i 0.0954095i
\(34\) 135.569i 0.117274i
\(35\) 298.186 0.243417
\(36\) 412.483 0.318274
\(37\) 1773.75i 1.29565i 0.761787 + 0.647827i \(0.224322\pi\)
−0.761787 + 0.647827i \(0.775678\pi\)
\(38\) 249.994i 0.173126i
\(39\) 988.349i 0.649802i
\(40\) 299.797i 0.187373i
\(41\) −2060.39 −1.22570 −0.612848 0.790201i \(-0.709976\pi\)
−0.612848 + 0.790201i \(0.709976\pi\)
\(42\) 116.850i 0.0662412i
\(43\) 2180.85i 1.17947i 0.807596 + 0.589736i \(0.200768\pi\)
−0.807596 + 0.589736i \(0.799232\pi\)
\(44\) 305.478i 0.157788i
\(45\) −304.393 −0.150318
\(46\) 140.543 0.0664193
\(47\) 4253.57i 1.92557i 0.270277 + 0.962783i \(0.412885\pi\)
−0.270277 + 0.962783i \(0.587115\pi\)
\(48\) −1152.64 −0.500276
\(49\) −1701.43 −0.708634
\(50\) 423.323i 0.169329i
\(51\) 828.536 0.318545
\(52\) 2905.83i 1.07464i
\(53\) 246.901 0.0878965 0.0439482 0.999034i \(-0.486006\pi\)
0.0439482 + 0.999034i \(0.486006\pi\)
\(54\) 119.282i 0.0409061i
\(55\) 225.429i 0.0745219i
\(56\) 703.351i 0.224283i
\(57\) 1527.85 0.470253
\(58\) 436.373i 0.129718i
\(59\) −1203.62 3266.29i −0.345769 0.938320i
\(60\) 894.943 0.248595
\(61\) 1494.54i 0.401650i −0.979627 0.200825i \(-0.935638\pi\)
0.979627 0.200825i \(-0.0643623\pi\)
\(62\) 1384.06 0.360058
\(63\) −714.133 −0.179928
\(64\) 3027.10 0.739038
\(65\) 2144.37i 0.507543i
\(66\) 88.3383 0.0202797
\(67\) 3881.60i 0.864691i −0.901708 0.432346i \(-0.857686\pi\)
0.901708 0.432346i \(-0.142314\pi\)
\(68\) −2435.97 −0.526809
\(69\) 858.939i 0.180412i
\(70\) 253.523i 0.0517393i
\(71\) 1862.97 0.369564 0.184782 0.982780i \(-0.440842\pi\)
0.184782 + 0.982780i \(0.440842\pi\)
\(72\) 717.993i 0.138502i
\(73\) 619.232i 0.116200i 0.998311 + 0.0581002i \(0.0185043\pi\)
−0.998311 + 0.0581002i \(0.981496\pi\)
\(74\) 1508.07 0.275397
\(75\) 2587.17 0.459941
\(76\) −4492.02 −0.777704
\(77\) 528.875i 0.0892014i
\(78\) −840.311 −0.138118
\(79\) 2372.28 0.380112 0.190056 0.981773i \(-0.439133\pi\)
0.190056 + 0.981773i \(0.439133\pi\)
\(80\) −2500.82 −0.390752
\(81\) 729.000 0.111111
\(82\) 1751.78i 0.260527i
\(83\) 4603.55i 0.668246i −0.942529 0.334123i \(-0.891560\pi\)
0.942529 0.334123i \(-0.108440\pi\)
\(84\) 2099.61 0.297564
\(85\) 1797.63 0.248807
\(86\) 1854.19 0.250702
\(87\) −2666.92 −0.352348
\(88\) −531.733 −0.0686639
\(89\) 8914.96i 1.12548i −0.826633 0.562742i \(-0.809747\pi\)
0.826633 0.562742i \(-0.190253\pi\)
\(90\) 258.800i 0.0319507i
\(91\) 5030.88i 0.607521i
\(92\) 2525.36i 0.298364i
\(93\) 8458.78i 0.978007i
\(94\) 3616.46 0.409287
\(95\) 3314.91 0.367303
\(96\) 3190.84i 0.346228i
\(97\) 1374.52i 0.146085i −0.997329 0.0730427i \(-0.976729\pi\)
0.997329 0.0730427i \(-0.0232709\pi\)
\(98\) 1446.58i 0.150623i
\(99\) 539.885i 0.0550847i
\(100\) −7606.50 −0.760650
\(101\) 3317.53i 0.325216i −0.986691 0.162608i \(-0.948009\pi\)
0.986691 0.162608i \(-0.0519905\pi\)
\(102\) 704.435i 0.0677081i
\(103\) 13068.4i 1.23182i 0.787817 + 0.615910i \(0.211211\pi\)
−0.787817 + 0.615910i \(0.788789\pi\)
\(104\) 5058.07 0.467647
\(105\) −1549.42 −0.140537
\(106\) 209.919i 0.0186828i
\(107\) −12221.9 −1.06751 −0.533754 0.845640i \(-0.679219\pi\)
−0.533754 + 0.845640i \(0.679219\pi\)
\(108\) −2143.32 −0.183755
\(109\) 5683.83i 0.478397i 0.970971 + 0.239198i \(0.0768846\pi\)
−0.970971 + 0.239198i \(0.923115\pi\)
\(110\) 191.663 0.0158399
\(111\) 9216.68i 0.748047i
\(112\) −5867.13 −0.467724
\(113\) 16579.1i 1.29839i −0.760624 0.649193i \(-0.775107\pi\)
0.760624 0.649193i \(-0.224893\pi\)
\(114\) 1299.01i 0.0999543i
\(115\) 1863.60i 0.140915i
\(116\) 7840.97 0.582712
\(117\) 5135.61i 0.375163i
\(118\) −2777.05 + 1023.34i −0.199444 + 0.0734946i
\(119\) 4217.40 0.297818
\(120\) 1557.79i 0.108180i
\(121\) 14241.2 0.972691
\(122\) −1270.68 −0.0853724
\(123\) 10706.1 0.707655
\(124\) 24869.5i 1.61743i
\(125\) 12659.4 0.810201
\(126\) 607.168i 0.0382444i
\(127\) −10677.2 −0.661986 −0.330993 0.943633i \(-0.607384\pi\)
−0.330993 + 0.943633i \(0.607384\pi\)
\(128\) 12398.9i 0.756770i
\(129\) 11332.0i 0.680969i
\(130\) −1823.18 −0.107880
\(131\) 13777.4i 0.802832i −0.915896 0.401416i \(-0.868518\pi\)
0.915896 0.401416i \(-0.131482\pi\)
\(132\) 1587.31i 0.0910990i
\(133\) 7777.06 0.439655
\(134\) −3300.20 −0.183794
\(135\) 1581.67 0.0867860
\(136\) 4240.19i 0.229249i
\(137\) 17518.6 0.933377 0.466689 0.884422i \(-0.345447\pi\)
0.466689 + 0.884422i \(0.345447\pi\)
\(138\) −730.285 −0.0383472
\(139\) −34138.1 −1.76689 −0.883445 0.468535i \(-0.844782\pi\)
−0.883445 + 0.468535i \(0.844782\pi\)
\(140\) 4555.43 0.232420
\(141\) 22102.2i 1.11173i
\(142\) 1583.93i 0.0785524i
\(143\) 3803.35 0.185992
\(144\) 5989.27 0.288834
\(145\) −5786.28 −0.275210
\(146\) 526.481 0.0246989
\(147\) 8840.89 0.409130
\(148\) 27097.8i 1.23712i
\(149\) 21713.6i 0.978045i −0.872271 0.489023i \(-0.837354\pi\)
0.872271 0.489023i \(-0.162646\pi\)
\(150\) 2199.65i 0.0977624i
\(151\) 23115.7i 1.01380i −0.862004 0.506901i \(-0.830791\pi\)
0.862004 0.506901i \(-0.169209\pi\)
\(152\) 7819.09i 0.338430i
\(153\) −4305.20 −0.183912
\(154\) 449.658 0.0189601
\(155\) 18352.6i 0.763896i
\(156\) 15099.1i 0.620445i
\(157\) 27512.2i 1.11616i 0.829787 + 0.558080i \(0.188462\pi\)
−0.829787 + 0.558080i \(0.811538\pi\)
\(158\) 2016.95i 0.0807944i
\(159\) −1282.94 −0.0507470
\(160\) 6922.99i 0.270429i
\(161\) 4372.16i 0.168673i
\(162\) 619.808i 0.0236171i
\(163\) 28943.8 1.08938 0.544691 0.838637i \(-0.316647\pi\)
0.544691 + 0.838637i \(0.316647\pi\)
\(164\) −31476.9 −1.17032
\(165\) 1171.36i 0.0430252i
\(166\) −3914.01 −0.142039
\(167\) 15906.8 0.570362 0.285181 0.958474i \(-0.407946\pi\)
0.285181 + 0.958474i \(0.407946\pi\)
\(168\) 3654.72i 0.129490i
\(169\) −7618.03 −0.266728
\(170\) 1528.38i 0.0528850i
\(171\) −7938.96 −0.271501
\(172\) 33317.1i 1.12619i
\(173\) 31592.5i 1.05558i 0.849375 + 0.527790i \(0.176979\pi\)
−0.849375 + 0.527790i \(0.823021\pi\)
\(174\) 2267.46i 0.0748930i
\(175\) 13169.2 0.430014
\(176\) 4435.55i 0.143193i
\(177\) 6254.20 + 16972.1i 0.199630 + 0.541739i
\(178\) −7579.64 −0.239226
\(179\) 61910.6i 1.93223i 0.258113 + 0.966115i \(0.416899\pi\)
−0.258113 + 0.966115i \(0.583101\pi\)
\(180\) −4650.26 −0.143526
\(181\) 4663.31 0.142343 0.0711717 0.997464i \(-0.477326\pi\)
0.0711717 + 0.997464i \(0.477326\pi\)
\(182\) −4277.34 −0.129131
\(183\) 7765.86i 0.231893i
\(184\) 4395.79 0.129838
\(185\) 19997.0i 0.584280i
\(186\) −7191.80 −0.207879
\(187\) 3188.36i 0.0911767i
\(188\) 64982.4i 1.83857i
\(189\) 3710.75 0.103881
\(190\) 2818.39i 0.0780717i
\(191\) 28272.6i 0.774995i 0.921871 + 0.387497i \(0.126660\pi\)
−0.921871 + 0.387497i \(0.873340\pi\)
\(192\) −15729.3 −0.426684
\(193\) −20835.7 −0.559362 −0.279681 0.960093i \(-0.590229\pi\)
−0.279681 + 0.960093i \(0.590229\pi\)
\(194\) −1168.64 −0.0310511
\(195\) 11142.5i 0.293030i
\(196\) −25993.0 −0.676618
\(197\) −51531.0 −1.32781 −0.663905 0.747817i \(-0.731102\pi\)
−0.663905 + 0.747817i \(0.731102\pi\)
\(198\) −459.019 −0.0117085
\(199\) −32606.5 −0.823374 −0.411687 0.911325i \(-0.635060\pi\)
−0.411687 + 0.911325i \(0.635060\pi\)
\(200\) 13240.3i 0.331009i
\(201\) 20169.4i 0.499230i
\(202\) −2820.62 −0.0691259
\(203\) −13575.1 −0.329421
\(204\) 12657.6 0.304153
\(205\) 23228.5 0.552731
\(206\) 11110.9 0.261828
\(207\) 4463.18i 0.104161i
\(208\) 42192.8i 0.975241i
\(209\) 5879.46i 0.134600i
\(210\) 1317.34i 0.0298717i
\(211\) 16107.1i 0.361787i 0.983503 + 0.180894i \(0.0578989\pi\)
−0.983503 + 0.180894i \(0.942101\pi\)
\(212\) 3771.94 0.0839254
\(213\) −9680.29 −0.213368
\(214\) 10391.3i 0.226903i
\(215\) 24586.5i 0.531887i
\(216\) 3730.80i 0.0799640i
\(217\) 43056.8i 0.914371i
\(218\) 4832.49 0.101685
\(219\) 3217.62i 0.0670883i
\(220\) 3443.90i 0.0711550i
\(221\) 30329.0i 0.620974i
\(222\) −7836.18 −0.159000
\(223\) 15954.1 0.320821 0.160411 0.987050i \(-0.448718\pi\)
0.160411 + 0.987050i \(0.448718\pi\)
\(224\) 16241.9i 0.323700i
\(225\) −13443.3 −0.265547
\(226\) −14095.8 −0.275977
\(227\) 49130.8i 0.953459i 0.879050 + 0.476730i \(0.158178\pi\)
−0.879050 + 0.476730i \(0.841822\pi\)
\(228\) 23341.2 0.449008
\(229\) 32670.4i 0.622993i −0.950247 0.311496i \(-0.899170\pi\)
0.950247 0.311496i \(-0.100830\pi\)
\(230\) −1584.46 −0.0299520
\(231\) 2748.12i 0.0515005i
\(232\) 13648.5i 0.253576i
\(233\) 14015.4i 0.258164i −0.991634 0.129082i \(-0.958797\pi\)
0.991634 0.129082i \(-0.0412030\pi\)
\(234\) 4366.38 0.0797425
\(235\) 47954.1i 0.868340i
\(236\) −18387.9 49899.6i −0.330147 0.895927i
\(237\) −12326.7 −0.219458
\(238\) 3585.70i 0.0633025i
\(239\) 100221. 1.75454 0.877271 0.479996i \(-0.159362\pi\)
0.877271 + 0.479996i \(0.159362\pi\)
\(240\) 12994.6 0.225601
\(241\) 29390.7 0.506030 0.253015 0.967462i \(-0.418578\pi\)
0.253015 + 0.967462i \(0.418578\pi\)
\(242\) 12108.1i 0.206750i
\(243\) −3788.00 −0.0641500
\(244\) 22832.3i 0.383504i
\(245\) 19181.6 0.319561
\(246\) 9102.52i 0.150415i
\(247\) 55927.8i 0.916715i
\(248\) 43289.5 0.703849
\(249\) 23920.7i 0.385812i
\(250\) 10763.2i 0.172212i
\(251\) −100346. −1.59277 −0.796385 0.604790i \(-0.793257\pi\)
−0.796385 + 0.604790i \(0.793257\pi\)
\(252\) −10909.9 −0.171799
\(253\) 3305.36 0.0516389
\(254\) 9077.91i 0.140708i
\(255\) −9340.77 −0.143649
\(256\) 37891.8 0.578184
\(257\) 35228.4 0.533367 0.266684 0.963784i \(-0.414072\pi\)
0.266684 + 0.963784i \(0.414072\pi\)
\(258\) −9634.66 −0.144743
\(259\) 46914.6i 0.699373i
\(260\) 32759.8i 0.484613i
\(261\) 13857.7 0.203428
\(262\) −11713.8 −0.170645
\(263\) −118656. −1.71545 −0.857725 0.514109i \(-0.828123\pi\)
−0.857725 + 0.514109i \(0.828123\pi\)
\(264\) 2762.97 0.0396431
\(265\) −2783.52 −0.0396372
\(266\) 6612.18i 0.0934505i
\(267\) 46323.5i 0.649798i
\(268\) 59299.7i 0.825625i
\(269\) 36762.0i 0.508035i −0.967200 0.254018i \(-0.918248\pi\)
0.967200 0.254018i \(-0.0817522\pi\)
\(270\) 1344.77i 0.0184467i
\(271\) 91224.9 1.24215 0.621076 0.783750i \(-0.286696\pi\)
0.621076 + 0.783750i \(0.286696\pi\)
\(272\) −35370.4 −0.478081
\(273\) 26141.2i 0.350752i
\(274\) 14894.6i 0.198393i
\(275\) 9955.90i 0.131648i
\(276\) 13122.1i 0.172261i
\(277\) 81627.4 1.06384 0.531920 0.846794i \(-0.321471\pi\)
0.531920 + 0.846794i \(0.321471\pi\)
\(278\) 29024.8i 0.375560i
\(279\) 43953.1i 0.564653i
\(280\) 7929.46i 0.101141i
\(281\) 58538.2 0.741355 0.370678 0.928762i \(-0.379125\pi\)
0.370678 + 0.928762i \(0.379125\pi\)
\(282\) −18791.7 −0.236302
\(283\) 45800.4i 0.571869i 0.958249 + 0.285935i \(0.0923040\pi\)
−0.958249 + 0.285935i \(0.907696\pi\)
\(284\) 28460.9 0.352867
\(285\) −17224.8 −0.212062
\(286\) 3233.67i 0.0395333i
\(287\) 54496.1 0.661610
\(288\) 16580.1i 0.199895i
\(289\) −58096.1 −0.695587
\(290\) 4919.59i 0.0584969i
\(291\) 7142.20i 0.0843425i
\(292\) 9460.09i 0.110951i
\(293\) −85610.9 −0.997226 −0.498613 0.866825i \(-0.666157\pi\)
−0.498613 + 0.866825i \(0.666157\pi\)
\(294\) 7516.67i 0.0869623i
\(295\) 13569.4 + 36823.6i 0.155925 + 0.423138i
\(296\) 47168.2 0.538351
\(297\) 2805.32i 0.0318032i
\(298\) −18461.2 −0.207888
\(299\) −31441.9 −0.351695
\(300\) 39524.5 0.439161
\(301\) 57682.0i 0.636660i
\(302\) −19653.3 −0.215488
\(303\) 17238.4i 0.187763i
\(304\) −65224.4 −0.705769
\(305\) 16849.2i 0.181125i
\(306\) 3660.35i 0.0390913i
\(307\) 121584. 1.29002 0.645012 0.764172i \(-0.276852\pi\)
0.645012 + 0.764172i \(0.276852\pi\)
\(308\) 8079.70i 0.0851714i
\(309\) 67905.3i 0.711191i
\(310\) −15603.7 −0.162369
\(311\) −17980.2 −0.185898 −0.0929488 0.995671i \(-0.529629\pi\)
−0.0929488 + 0.995671i \(0.529629\pi\)
\(312\) −26282.5 −0.269996
\(313\) 65025.1i 0.663731i −0.943327 0.331865i \(-0.892322\pi\)
0.943327 0.331865i \(-0.107678\pi\)
\(314\) 23391.3 0.237244
\(315\) 8051.02 0.0811390
\(316\) 36241.6 0.362939
\(317\) −6089.75 −0.0606011 −0.0303006 0.999541i \(-0.509646\pi\)
−0.0303006 + 0.999541i \(0.509646\pi\)
\(318\) 1090.77i 0.0107865i
\(319\) 10262.8i 0.100852i
\(320\) −34127.0 −0.333272
\(321\) 63506.8 0.616326
\(322\) −3717.28 −0.0358521
\(323\) 46884.5 0.449391
\(324\) 11137.0 0.106091
\(325\) 94704.6i 0.896612i
\(326\) 24608.5i 0.231553i
\(327\) 29534.1i 0.276203i
\(328\) 54790.7i 0.509283i
\(329\) 112504.i 1.03939i
\(330\) −995.911 −0.00914519
\(331\) −159934. −1.45977 −0.729884 0.683571i \(-0.760426\pi\)
−0.729884 + 0.683571i \(0.760426\pi\)
\(332\) 70329.0i 0.638055i
\(333\) 47891.3i 0.431885i
\(334\) 13524.3i 0.121233i
\(335\) 43760.5i 0.389935i
\(336\) 30486.5 0.270041
\(337\) 120034.i 1.05693i −0.848956 0.528463i \(-0.822769\pi\)
0.848956 0.528463i \(-0.177231\pi\)
\(338\) 6476.98i 0.0566942i
\(339\) 86147.5i 0.749623i
\(340\) 27462.7 0.237566
\(341\) 32550.9 0.279933
\(342\) 6749.83i 0.0577086i
\(343\) 108507. 0.922292
\(344\) 57993.8 0.490077
\(345\) 9683.54i 0.0813572i
\(346\) 26860.4 0.224368
\(347\) 184056.i 1.52859i 0.644869 + 0.764293i \(0.276912\pi\)
−0.644869 + 0.764293i \(0.723088\pi\)
\(348\) −40742.9 −0.336429
\(349\) 179218.i 1.47140i −0.677305 0.735702i \(-0.736852\pi\)
0.677305 0.735702i \(-0.263148\pi\)
\(350\) 11196.6i 0.0914012i
\(351\) 26685.4i 0.216601i
\(352\) −12278.9 −0.0991002
\(353\) 124737.i 1.00103i 0.865728 + 0.500514i \(0.166856\pi\)
−0.865728 + 0.500514i \(0.833144\pi\)
\(354\) 14430.0 5317.42i 0.115149 0.0424321i
\(355\) −21002.8 −0.166656
\(356\) 136195.i 1.07464i
\(357\) −21914.3 −0.171945
\(358\) 52637.4 0.410703
\(359\) −77449.2 −0.600936 −0.300468 0.953792i \(-0.597143\pi\)
−0.300468 + 0.953792i \(0.597143\pi\)
\(360\) 8094.53i 0.0624578i
\(361\) −43864.2 −0.336586
\(362\) 3964.83i 0.0302557i
\(363\) −73999.3 −0.561583
\(364\) 76857.4i 0.580074i
\(365\) 6981.12i 0.0524009i
\(366\) 6602.66 0.0492898
\(367\) 42555.8i 0.315956i 0.987443 + 0.157978i \(0.0504975\pi\)
−0.987443 + 0.157978i \(0.949502\pi\)
\(368\) 36668.3i 0.270767i
\(369\) −55630.6 −0.408565
\(370\) −17001.8 −0.124191
\(371\) −6530.38 −0.0474451
\(372\) 129226.i 0.933822i
\(373\) 86818.1 0.624012 0.312006 0.950080i \(-0.398999\pi\)
0.312006 + 0.950080i \(0.398999\pi\)
\(374\) 2710.79 0.0193800
\(375\) −65780.1 −0.467770
\(376\) 113112. 0.800082
\(377\) 97624.0i 0.686869i
\(378\) 3154.94i 0.0220804i
\(379\) 45077.2 0.313819 0.156909 0.987613i \(-0.449847\pi\)
0.156909 + 0.987613i \(0.449847\pi\)
\(380\) 50642.2 0.350708
\(381\) 55480.2 0.382198
\(382\) 24037.8 0.164728
\(383\) −275505. −1.87815 −0.939077 0.343707i \(-0.888317\pi\)
−0.939077 + 0.343707i \(0.888317\pi\)
\(384\) 64426.7i 0.436921i
\(385\) 5962.45i 0.0402257i
\(386\) 17714.8i 0.118895i
\(387\) 58882.8i 0.393158i
\(388\) 20998.7i 0.139485i
\(389\) 104159. 0.688333 0.344167 0.938909i \(-0.388161\pi\)
0.344167 + 0.938909i \(0.388161\pi\)
\(390\) 9473.52 0.0622848
\(391\) 26357.9i 0.172408i
\(392\) 45245.0i 0.294441i
\(393\) 71589.5i 0.463516i
\(394\) 43812.5i 0.282232i
\(395\) −26744.7 −0.171413
\(396\) 8247.89i 0.0525960i
\(397\) 30109.0i 0.191036i −0.995428 0.0955181i \(-0.969549\pi\)
0.995428 0.0955181i \(-0.0304508\pi\)
\(398\) 27722.5i 0.175012i
\(399\) −40410.8 −0.253835
\(400\) −110447. −0.690292
\(401\) 80257.6i 0.499111i −0.968360 0.249556i \(-0.919715\pi\)
0.968360 0.249556i \(-0.0802846\pi\)
\(402\) 17148.3 0.106113
\(403\) −309638. −1.90653
\(404\) 50682.3i 0.310523i
\(405\) −8218.62 −0.0501059
\(406\) 11541.8i 0.0700199i
\(407\) 35467.5 0.214112
\(408\) 22032.7i 0.132357i
\(409\) 99079.5i 0.592294i 0.955142 + 0.296147i \(0.0957018\pi\)
−0.955142 + 0.296147i \(0.904298\pi\)
\(410\) 19749.3i 0.117485i
\(411\) −91029.1 −0.538886
\(412\) 199647.i 1.17617i
\(413\) 31835.0 + 86391.4i 0.186640 + 0.506489i
\(414\) 3794.67 0.0221398
\(415\) 51899.6i 0.301348i
\(416\) 116802. 0.674939
\(417\) 177387. 1.02011
\(418\) 4998.81 0.0286098
\(419\) 311022.i 1.77159i 0.464078 + 0.885795i \(0.346386\pi\)
−0.464078 + 0.885795i \(0.653614\pi\)
\(420\) −23670.7 −0.134188
\(421\) 89938.3i 0.507435i 0.967278 + 0.253718i \(0.0816534\pi\)
−0.967278 + 0.253718i \(0.918347\pi\)
\(422\) 13694.5 0.0768993
\(423\) 114846.i 0.641855i
\(424\) 6565.68i 0.0365214i
\(425\) 79391.2 0.439536
\(426\) 8230.34i 0.0453522i
\(427\) 39529.7i 0.216804i
\(428\) −186715. −1.01928
\(429\) −19762.8 −0.107382
\(430\) −20903.8 −0.113055
\(431\) 73388.3i 0.395068i 0.980296 + 0.197534i \(0.0632934\pi\)
−0.980296 + 0.197534i \(0.936707\pi\)
\(432\) −31121.2 −0.166759
\(433\) 68075.2 0.363089 0.181545 0.983383i \(-0.441890\pi\)
0.181545 + 0.983383i \(0.441890\pi\)
\(434\) −36607.6 −0.194353
\(435\) 30066.4 0.158892
\(436\) 86832.7i 0.456783i
\(437\) 48604.9i 0.254517i
\(438\) −2735.68 −0.0142599
\(439\) 137778. 0.714909 0.357454 0.933931i \(-0.383645\pi\)
0.357454 + 0.933931i \(0.383645\pi\)
\(440\) 5994.67 0.0309642
\(441\) −45938.6 −0.236211
\(442\) −25786.2 −0.131991
\(443\) 19727.4i 0.100522i 0.998736 + 0.0502611i \(0.0160054\pi\)
−0.998736 + 0.0502611i \(0.983995\pi\)
\(444\) 140804.i 0.714251i
\(445\) 100506.i 0.507540i
\(446\) 13564.5i 0.0681919i
\(447\) 112827.i 0.564675i
\(448\) −80064.9 −0.398920
\(449\) −279194. −1.38489 −0.692443 0.721473i \(-0.743466\pi\)
−0.692443 + 0.721473i \(0.743466\pi\)
\(450\) 11429.7i 0.0564431i
\(451\) 41199.1i 0.202551i
\(452\) 253281.i 1.23973i
\(453\) 120113.i 0.585318i
\(454\) 41771.8 0.202662
\(455\) 56717.3i 0.273964i
\(456\) 40629.2i 0.195393i
\(457\) 193755.i 0.927728i −0.885906 0.463864i \(-0.846463\pi\)
0.885906 0.463864i \(-0.153537\pi\)
\(458\) −27776.9 −0.132420
\(459\) 22370.5 0.106182
\(460\) 28470.4i 0.134548i
\(461\) 40358.7 0.189905 0.0949524 0.995482i \(-0.469730\pi\)
0.0949524 + 0.995482i \(0.469730\pi\)
\(462\) −2336.49 −0.0109466
\(463\) 219514.i 1.02400i −0.858985 0.512000i \(-0.828905\pi\)
0.858985 0.512000i \(-0.171095\pi\)
\(464\) 113851. 0.528813
\(465\) 95362.9i 0.441035i
\(466\) −11916.2 −0.0548737
\(467\) 321723.i 1.47519i 0.675243 + 0.737596i \(0.264039\pi\)
−0.675243 + 0.737596i \(0.735961\pi\)
\(468\) 78457.4i 0.358214i
\(469\) 102666.i 0.466746i
\(470\) −40771.3 −0.184569
\(471\) 142958.i 0.644415i
\(472\) −86858.3 + 32007.1i −0.389877 + 0.143669i
\(473\) 43607.6 0.194913
\(474\) 10480.4i 0.0466467i
\(475\) 146400. 0.648866
\(476\) 64429.8 0.284363
\(477\) 6666.33 0.0292988
\(478\) 85209.7i 0.372935i
\(479\) 42962.3 0.187248 0.0936238 0.995608i \(-0.470155\pi\)
0.0936238 + 0.995608i \(0.470155\pi\)
\(480\) 35972.9i 0.156133i
\(481\) −337381. −1.45825
\(482\) 24988.5i 0.107559i
\(483\) 22718.4i 0.0973832i
\(484\) 217564. 0.928746
\(485\) 15496.1i 0.0658777i
\(486\) 3220.62i 0.0136354i
\(487\) −268645. −1.13271 −0.566357 0.824160i \(-0.691648\pi\)
−0.566357 + 0.824160i \(0.691648\pi\)
\(488\) −39743.3 −0.166888
\(489\) −150396. −0.628955
\(490\) 16308.5i 0.0679239i
\(491\) 331744. 1.37607 0.688034 0.725678i \(-0.258474\pi\)
0.688034 + 0.725678i \(0.258474\pi\)
\(492\) 163559. 0.675684
\(493\) −81838.5 −0.336716
\(494\) −47550.8 −0.194852
\(495\) 6086.57i 0.0248406i
\(496\) 361107.i 1.46782i
\(497\) −49274.5 −0.199485
\(498\) 20337.8 0.0820060
\(499\) 112576. 0.452111 0.226055 0.974114i \(-0.427417\pi\)
0.226055 + 0.974114i \(0.427417\pi\)
\(500\) 193399. 0.773597
\(501\) −82654.3 −0.329299
\(502\) 85315.9i 0.338550i
\(503\) 350747.i 1.38630i 0.720791 + 0.693152i \(0.243779\pi\)
−0.720791 + 0.693152i \(0.756221\pi\)
\(504\) 18990.5i 0.0747609i
\(505\) 37401.2i 0.146657i
\(506\) 2810.27i 0.0109761i
\(507\) 39584.5 0.153996
\(508\) −163117. −0.632078
\(509\) 95019.3i 0.366755i −0.983043 0.183378i \(-0.941297\pi\)
0.983043 0.183378i \(-0.0587031\pi\)
\(510\) 7941.68i 0.0305332i
\(511\) 16378.3i 0.0627231i
\(512\) 230599.i 0.879665i
\(513\) 41252.0 0.156751
\(514\) 29951.7i 0.113369i
\(515\) 147331.i 0.555493i
\(516\) 173121.i 0.650203i
\(517\) 85053.4 0.318208
\(518\) −39887.6 −0.148655
\(519\) 164159.i 0.609440i
\(520\) −57023.8 −0.210887
\(521\) −131693. −0.485161 −0.242581 0.970131i \(-0.577994\pi\)
−0.242581 + 0.970131i \(0.577994\pi\)
\(522\) 11782.1i 0.0432395i
\(523\) 432940. 1.58280 0.791398 0.611302i \(-0.209354\pi\)
0.791398 + 0.611302i \(0.209354\pi\)
\(524\) 210479.i 0.766561i
\(525\) −68429.0 −0.248269
\(526\) 100883.i 0.364626i
\(527\) 259571.i 0.934618i
\(528\) 23047.8i 0.0826726i
\(529\) 252516. 0.902355
\(530\) 2366.60i 0.00842505i
\(531\) −32497.8 88189.9i −0.115256 0.312773i
\(532\) 118811. 0.419792
\(533\) 391903.i 1.37951i
\(534\) 39385.0 0.138117
\(535\) 137788. 0.481396
\(536\) −103221. −0.359284
\(537\) 321697.i 1.11557i
\(538\) −31255.6 −0.107985
\(539\) 34021.4i 0.117105i
\(540\) 24163.5 0.0828651
\(541\) 369539.i 1.26260i 0.775539 + 0.631300i \(0.217478\pi\)
−0.775539 + 0.631300i \(0.782522\pi\)
\(542\) 77560.9i 0.264024i
\(543\) −24231.3 −0.0821820
\(544\) 97915.6i 0.330867i
\(545\) 64078.6i 0.215735i
\(546\) 22225.7 0.0745539
\(547\) −145339. −0.485745 −0.242873 0.970058i \(-0.578090\pi\)
−0.242873 + 0.970058i \(0.578090\pi\)
\(548\) 267633. 0.891208
\(549\) 40352.6i 0.133883i
\(550\) 8464.67 0.0279824
\(551\) −150913. −0.497078
\(552\) −22841.2 −0.0749619
\(553\) −62745.4 −0.205178
\(554\) 69401.0i 0.226124i
\(555\) 103907.i 0.337334i
\(556\) −521532. −1.68706
\(557\) 120254. 0.387604 0.193802 0.981041i \(-0.437918\pi\)
0.193802 + 0.981041i \(0.437918\pi\)
\(558\) 37369.7 0.120019
\(559\) −414814. −1.32749
\(560\) 66145.0 0.210922
\(561\) 16567.2i 0.0526409i
\(562\) 49770.1i 0.157578i
\(563\) 388859.i 1.22680i 0.789771 + 0.613402i \(0.210200\pi\)
−0.789771 + 0.613402i \(0.789800\pi\)
\(564\) 337658.i 1.06150i
\(565\) 186910.i 0.585511i
\(566\) 38940.3 0.121553
\(567\) −19281.6 −0.0599759
\(568\) 49540.8i 0.153556i
\(569\) 441305.i 1.36306i −0.731792 0.681528i \(-0.761316\pi\)
0.731792 0.681528i \(-0.238684\pi\)
\(570\) 14644.8i 0.0450747i
\(571\) 18999.3i 0.0582726i −0.999575 0.0291363i \(-0.990724\pi\)
0.999575 0.0291363i \(-0.00927569\pi\)
\(572\) 58104.2 0.177589
\(573\) 146909.i 0.447444i
\(574\) 46333.5i 0.140628i
\(575\) 82304.5i 0.248936i
\(576\) 81731.7 0.246346
\(577\) 70278.9 0.211093 0.105546 0.994414i \(-0.466341\pi\)
0.105546 + 0.994414i \(0.466341\pi\)
\(578\) 49394.3i 0.147850i
\(579\) 108265. 0.322948
\(580\) −88397.8 −0.262776
\(581\) 121761.i 0.360708i
\(582\) 6072.42 0.0179273
\(583\) 4936.97i 0.0145252i
\(584\) 16466.8 0.0482819
\(585\) 57898.0i 0.169181i
\(586\) 72787.8i 0.211965i
\(587\) 325818.i 0.945581i −0.881175 0.472790i \(-0.843247\pi\)
0.881175 0.472790i \(-0.156753\pi\)
\(588\) 135063. 0.390646
\(589\) 478658.i 1.37973i
\(590\) 31308.0 11536.9i 0.0899398 0.0331426i
\(591\) 267763. 0.766612
\(592\) 393462.i 1.12269i
\(593\) 607064. 1.72634 0.863168 0.504917i \(-0.168477\pi\)
0.863168 + 0.504917i \(0.168477\pi\)
\(594\) 2385.13 0.00675989
\(595\) −47546.3 −0.134302
\(596\) 331721.i 0.933858i
\(597\) 169428. 0.475375
\(598\) 26732.4i 0.0747543i
\(599\) 23980.8 0.0668360 0.0334180 0.999441i \(-0.489361\pi\)
0.0334180 + 0.999441i \(0.489361\pi\)
\(600\) 68798.8i 0.191108i
\(601\) 226771.i 0.627825i 0.949452 + 0.313913i \(0.101640\pi\)
−0.949452 + 0.313913i \(0.898360\pi\)
\(602\) −49042.2 −0.135325
\(603\) 104803.i 0.288230i
\(604\) 353141.i 0.967999i
\(605\) −160553. −0.438638
\(606\) 14656.3 0.0399099
\(607\) −172250. −0.467499 −0.233749 0.972297i \(-0.575100\pi\)
−0.233749 + 0.972297i \(0.575100\pi\)
\(608\) 180560.i 0.488444i
\(609\) 70538.4 0.190191
\(610\) 14325.5 0.0384989
\(611\) −809063. −2.16721
\(612\) −65771.1 −0.175603
\(613\) 283915.i 0.755559i 0.925896 + 0.377779i \(0.123312\pi\)
−0.925896 + 0.377779i \(0.876688\pi\)
\(614\) 103372.i 0.274200i
\(615\) −120699. −0.319119
\(616\) 14064.0 0.0370637
\(617\) −117535. −0.308743 −0.154372 0.988013i \(-0.549335\pi\)
−0.154372 + 0.988013i \(0.549335\pi\)
\(618\) −57734.2 −0.151167
\(619\) 232785. 0.607537 0.303769 0.952746i \(-0.401755\pi\)
0.303769 + 0.952746i \(0.401755\pi\)
\(620\) 280375.i 0.729384i
\(621\) 23191.4i 0.0601372i
\(622\) 15287.1i 0.0395133i
\(623\) 235795.i 0.607517i
\(624\) 219240.i 0.563056i
\(625\) 168468. 0.431278
\(626\) −55285.4 −0.141079
\(627\) 30550.6i 0.0777113i
\(628\) 420308.i 1.06573i
\(629\) 282828.i 0.714860i
\(630\) 6845.11i 0.0172464i
\(631\) 58189.1 0.146145 0.0730723 0.997327i \(-0.476720\pi\)
0.0730723 + 0.997327i \(0.476720\pi\)
\(632\) 63084.5i 0.157939i
\(633\) 83695.1i 0.208878i
\(634\) 5177.60i 0.0128810i
\(635\) 120373. 0.298525
\(636\) −19599.6 −0.0484543
\(637\) 323625.i 0.797561i
\(638\) −8725.60 −0.0214365
\(639\) 50300.3 0.123188
\(640\) 139783.i 0.341268i
\(641\) 774979. 1.88614 0.943070 0.332595i \(-0.107924\pi\)
0.943070 + 0.332595i \(0.107924\pi\)
\(642\) 53994.5i 0.131003i
\(643\) −69007.6 −0.166907 −0.0834536 0.996512i \(-0.526595\pi\)
−0.0834536 + 0.996512i \(0.526595\pi\)
\(644\) 66794.1i 0.161052i
\(645\) 127755.i 0.307085i
\(646\) 39861.9i 0.0955198i
\(647\) 278274. 0.664760 0.332380 0.943146i \(-0.392148\pi\)
0.332380 + 0.943146i \(0.392148\pi\)
\(648\) 19385.8i 0.0461672i
\(649\) −65311.9 + 24067.3i −0.155061 + 0.0571397i
\(650\) −80519.5 −0.190579
\(651\) 223730.i 0.527912i
\(652\) 442178. 1.04017
\(653\) −158117. −0.370811 −0.185406 0.982662i \(-0.559360\pi\)
−0.185406 + 0.982662i \(0.559360\pi\)
\(654\) −25110.3 −0.0587080
\(655\) 155324.i 0.362040i
\(656\) −457046. −1.06207
\(657\) 16719.3i 0.0387335i
\(658\) −95653.1 −0.220926
\(659\) 619035.i 1.42543i −0.701456 0.712713i \(-0.747466\pi\)
0.701456 0.712713i \(-0.252534\pi\)
\(660\) 17895.0i 0.0410814i
\(661\) −109703. −0.251081 −0.125541 0.992088i \(-0.540067\pi\)
−0.125541 + 0.992088i \(0.540067\pi\)
\(662\) 135978.i 0.310280i
\(663\) 157594.i 0.358519i
\(664\) −122419. −0.277660
\(665\) −87677.2 −0.198264
\(666\) 40718.0 0.0917989
\(667\) 84841.6i 0.190703i
\(668\) 243011. 0.544594
\(669\) −82900.1 −0.185226
\(670\) 37205.9 0.0828824
\(671\) −29884.4 −0.0663743
\(672\) 84395.6i 0.186888i
\(673\) 496628.i 1.09648i −0.836321 0.548240i \(-0.815298\pi\)
0.836321 0.548240i \(-0.184702\pi\)
\(674\) −102055. −0.224654
\(675\) 69853.5 0.153314
\(676\) −116382. −0.254678
\(677\) −273451. −0.596626 −0.298313 0.954468i \(-0.596424\pi\)
−0.298313 + 0.954468i \(0.596424\pi\)
\(678\) 73244.0 0.159336
\(679\) 36355.2i 0.0788545i
\(680\) 47803.2i 0.103381i
\(681\) 255291.i 0.550480i
\(682\) 27675.4i 0.0595010i
\(683\) 80479.6i 0.172522i 0.996273 + 0.0862609i \(0.0274919\pi\)
−0.996273 + 0.0862609i \(0.972508\pi\)
\(684\) −121284. −0.259235
\(685\) −197501. −0.420910
\(686\) 92254.2i 0.196037i
\(687\) 169760.i 0.359685i
\(688\) 483766.i 1.02202i
\(689\) 46962.5i 0.0989266i
\(690\) 8233.10 0.0172928
\(691\) 700168.i 1.46638i 0.680025 + 0.733189i \(0.261969\pi\)
−0.680025 + 0.733189i \(0.738031\pi\)
\(692\) 482642.i 1.00789i
\(693\) 14279.6i 0.0297338i
\(694\) 156487. 0.324907
\(695\) 384867. 0.796785
\(696\) 70919.6i 0.146402i
\(697\) 328533. 0.676260
\(698\) −152375. −0.312753
\(699\) 72826.4i 0.149051i
\(700\) 201187. 0.410586
\(701\) 441649.i 0.898754i 0.893342 + 0.449377i \(0.148354\pi\)
−0.893342 + 0.449377i \(0.851646\pi\)
\(702\) −22688.4 −0.0460394
\(703\) 521546.i 1.05531i
\(704\) 60529.1i 0.122129i
\(705\) 249177.i 0.501336i
\(706\) 106054. 0.212773
\(707\) 87746.5i 0.175546i
\(708\) 95546.2 + 259286.i 0.190610 + 0.517264i
\(709\) 110109. 0.219043 0.109522 0.993984i \(-0.465068\pi\)
0.109522 + 0.993984i \(0.465068\pi\)
\(710\) 17857.0i 0.0354234i
\(711\) 64051.6 0.126704
\(712\) −237069. −0.467644
\(713\) −269096. −0.529331
\(714\) 18631.9i 0.0365477i
\(715\) −42878.3 −0.0838736
\(716\) 945816.i 1.84493i
\(717\) −520764. −1.01298
\(718\) 65848.6i 0.127731i
\(719\) 66331.4i 0.128310i 0.997940 + 0.0641551i \(0.0204353\pi\)
−0.997940 + 0.0641551i \(0.979565\pi\)
\(720\) −67522.0 −0.130251
\(721\) 345651.i 0.664916i
\(722\) 37294.0i 0.0715427i
\(723\) −152719. −0.292156
\(724\) 71242.0 0.135912
\(725\) −255547. −0.486178
\(726\) 62915.4i 0.119367i
\(727\) −199842. −0.378110 −0.189055 0.981967i \(-0.560542\pi\)
−0.189055 + 0.981967i \(0.560542\pi\)
\(728\) −133783. −0.252428
\(729\) 19683.0 0.0370370
\(730\) −5935.46 −0.0111380
\(731\) 347740.i 0.650758i
\(732\) 118640.i 0.221416i
\(733\) −582907. −1.08490 −0.542452 0.840087i \(-0.682504\pi\)
−0.542452 + 0.840087i \(0.682504\pi\)
\(734\) 36181.7 0.0671578
\(735\) −99670.7 −0.184498
\(736\) 101509. 0.187390
\(737\) −77615.5 −0.142894
\(738\) 47298.1i 0.0868422i
\(739\) 45515.8i 0.0833438i 0.999131 + 0.0416719i \(0.0132684\pi\)
−0.999131 + 0.0416719i \(0.986732\pi\)
\(740\) 305496.i 0.557882i
\(741\) 290610.i 0.529265i
\(742\) 5552.24i 0.0100846i
\(743\) −156217. −0.282977 −0.141488 0.989940i \(-0.545189\pi\)
−0.141488 + 0.989940i \(0.545189\pi\)
\(744\) −224939. −0.406367
\(745\) 244795.i 0.441053i
\(746\) 73814.2i 0.132636i
\(747\) 124296.i 0.222749i
\(748\) 48708.9i 0.0870574i
\(749\) 323262. 0.576223
\(750\) 55927.4i 0.0994264i
\(751\) 335449.i 0.594767i 0.954758 + 0.297383i \(0.0961140\pi\)
−0.954758 + 0.297383i \(0.903886\pi\)
\(752\) 943548.i 1.66851i
\(753\) 521414. 0.919586
\(754\) 83001.5 0.145997
\(755\) 260602.i 0.457177i
\(756\) 56689.6 0.0991881
\(757\) 797908. 1.39239 0.696196 0.717852i \(-0.254875\pi\)
0.696196 + 0.717852i \(0.254875\pi\)
\(758\) 38325.4i 0.0667035i
\(759\) −17175.1 −0.0298137
\(760\) 88151.1i 0.152616i
\(761\) −23661.3 −0.0408572 −0.0204286 0.999791i \(-0.506503\pi\)
−0.0204286 + 0.999791i \(0.506503\pi\)
\(762\) 47170.2i 0.0812377i
\(763\) 150334.i 0.258231i
\(764\) 431924.i 0.739981i
\(765\) 48536.1 0.0829357
\(766\) 234239.i 0.399209i
\(767\) 621274. 228938.i 1.05607 0.389159i
\(768\) −196892. −0.333814
\(769\) 698020.i 1.18036i −0.807271 0.590181i \(-0.799056\pi\)
0.807271 0.590181i \(-0.200944\pi\)
\(770\) −5069.37 −0.00855013
\(771\) −183052. −0.307940
\(772\) −318310. −0.534091
\(773\) 531513.i 0.889519i 0.895650 + 0.444759i \(0.146711\pi\)
−0.895650 + 0.444759i \(0.853289\pi\)
\(774\) 50063.2 0.0835673
\(775\) 810530.i 1.34948i
\(776\) −36551.6 −0.0606993
\(777\) 243776.i 0.403783i
\(778\) 88558.0i 0.146308i
\(779\) 605829. 0.998332
\(780\) 170225.i 0.279791i
\(781\) 37251.5i 0.0610720i
\(782\) −22409.9 −0.0366460
\(783\) −72006.8 −0.117449
\(784\) −377419. −0.614034
\(785\) 310168.i 0.503336i
\(786\) 60866.6 0.0985221
\(787\) −127904. −0.206506 −0.103253 0.994655i \(-0.532925\pi\)
−0.103253 + 0.994655i \(0.532925\pi\)
\(788\) −787246. −1.26782
\(789\) 616554. 0.990415