Properties

Label 38.5.b.a.37.3
Level $38$
Weight $5$
Character 38.37
Analytic conductor $3.928$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 38.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.92805859719\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \(x^{8} + 450 x^{6} + 68229 x^{4} + 4001228 x^{2} + 77475204\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 37.3
Root \(8.07810i\) of defining polynomial
Character \(\chi\) \(=\) 38.37
Dual form 38.5.b.a.37.6

$q$-expansion

\(f(q)\) \(=\) \(q-2.82843i q^{2} +6.66389i q^{3} -8.00000 q^{4} +26.7027 q^{5} +18.8483 q^{6} +51.4469 q^{7} +22.6274i q^{8} +36.5926 q^{9} +O(q^{10})\) \(q-2.82843i q^{2} +6.66389i q^{3} -8.00000 q^{4} +26.7027 q^{5} +18.8483 q^{6} +51.4469 q^{7} +22.6274i q^{8} +36.5926 q^{9} -75.5266i q^{10} -25.0891 q^{11} -53.3111i q^{12} -53.2531i q^{13} -145.514i q^{14} +177.944i q^{15} +64.0000 q^{16} -24.4913 q^{17} -103.499i q^{18} +(-78.0101 + 352.470i) q^{19} -213.622 q^{20} +342.837i q^{21} +70.9628i q^{22} -612.242 q^{23} -150.787 q^{24} +88.0343 q^{25} -150.622 q^{26} +783.624i q^{27} -411.576 q^{28} -1345.96i q^{29} +503.301 q^{30} -912.680i q^{31} -181.019i q^{32} -167.191i q^{33} +69.2720i q^{34} +1373.77 q^{35} -292.741 q^{36} +325.059i q^{37} +(996.937 + 220.646i) q^{38} +354.872 q^{39} +604.213i q^{40} -51.7494i q^{41} +969.689 q^{42} -2545.26 q^{43} +200.713 q^{44} +977.121 q^{45} +1731.68i q^{46} +2998.19 q^{47} +426.489i q^{48} +245.788 q^{49} -248.999i q^{50} -163.208i q^{51} +426.024i q^{52} -4067.86i q^{53} +2216.42 q^{54} -669.948 q^{55} +1164.11i q^{56} +(-2348.82 - 519.851i) q^{57} -3806.96 q^{58} +1078.88i q^{59} -1423.55i q^{60} -6530.89 q^{61} -2581.45 q^{62} +1882.58 q^{63} -512.000 q^{64} -1422.00i q^{65} -472.888 q^{66} +7386.18i q^{67} +195.931 q^{68} -4079.92i q^{69} -3885.62i q^{70} +5806.02i q^{71} +827.995i q^{72} +3629.56 q^{73} +919.405 q^{74} +586.651i q^{75} +(624.081 - 2819.76i) q^{76} -1290.76 q^{77} -1003.73i q^{78} +3903.16i q^{79} +1708.97 q^{80} -2257.99 q^{81} -146.369 q^{82} -997.967 q^{83} -2742.69i q^{84} -653.985 q^{85} +7199.08i q^{86} +8969.34 q^{87} -567.702i q^{88} -6152.85i q^{89} -2763.71i q^{90} -2739.71i q^{91} +4897.94 q^{92} +6082.00 q^{93} -8480.16i q^{94} +(-2083.08 + 9411.91i) q^{95} +1206.29 q^{96} +5023.58i q^{97} -695.195i q^{98} -918.076 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 64q^{4} + 18q^{5} - 32q^{6} - 162q^{7} - 268q^{9} + O(q^{10}) \) \( 8q - 64q^{4} + 18q^{5} - 32q^{6} - 162q^{7} - 268q^{9} - 6q^{11} + 512q^{16} + 510q^{17} - 12q^{19} - 144q^{20} - 396q^{23} + 256q^{24} + 3458q^{25} - 192q^{26} + 1296q^{28} - 2752q^{30} + 1002q^{35} + 2144q^{36} - 3216q^{38} - 6588q^{39} + 1376q^{42} - 8654q^{43} + 48q^{44} - 10334q^{45} + 3210q^{47} + 9222q^{49} + 9088q^{54} + 17146q^{55} - 14076q^{57} - 960q^{58} + 1314q^{61} - 15168q^{62} + 29938q^{63} - 4096q^{64} + 4928q^{66} - 4080q^{68} + 23398q^{73} + 13152q^{74} + 96q^{76} - 44622q^{77} + 1152q^{80} - 20368q^{81} + 16512q^{82} - 10440q^{83} + 21274q^{85} - 14316q^{87} + 3168q^{92} + 19416q^{93} - 34686q^{95} - 2048q^{96} - 56798q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).

\(n\) \(21\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.82843i 0.707107i
\(3\) 6.66389i 0.740432i 0.928946 + 0.370216i \(0.120716\pi\)
−0.928946 + 0.370216i \(0.879284\pi\)
\(4\) −8.00000 −0.500000
\(5\) 26.7027 1.06811 0.534054 0.845450i \(-0.320668\pi\)
0.534054 + 0.845450i \(0.320668\pi\)
\(6\) 18.8483 0.523565
\(7\) 51.4469 1.04994 0.524969 0.851121i \(-0.324077\pi\)
0.524969 + 0.851121i \(0.324077\pi\)
\(8\) 22.6274i 0.353553i
\(9\) 36.5926 0.451760
\(10\) 75.5266i 0.755266i
\(11\) −25.0891 −0.207348 −0.103674 0.994611i \(-0.533060\pi\)
−0.103674 + 0.994611i \(0.533060\pi\)
\(12\) 53.3111i 0.370216i
\(13\) 53.2531i 0.315107i −0.987510 0.157553i \(-0.949639\pi\)
0.987510 0.157553i \(-0.0503606\pi\)
\(14\) 145.514i 0.742418i
\(15\) 177.944i 0.790862i
\(16\) 64.0000 0.250000
\(17\) −24.4913 −0.0847451 −0.0423726 0.999102i \(-0.513492\pi\)
−0.0423726 + 0.999102i \(0.513492\pi\)
\(18\) 103.499i 0.319443i
\(19\) −78.0101 + 352.470i −0.216094 + 0.976372i
\(20\) −213.622 −0.534054
\(21\) 342.837i 0.777408i
\(22\) 70.9628i 0.146617i
\(23\) −612.242 −1.15736 −0.578679 0.815555i \(-0.696432\pi\)
−0.578679 + 0.815555i \(0.696432\pi\)
\(24\) −150.787 −0.261782
\(25\) 88.0343 0.140855
\(26\) −150.622 −0.222814
\(27\) 783.624i 1.07493i
\(28\) −411.576 −0.524969
\(29\) 1345.96i 1.60043i −0.599713 0.800215i \(-0.704718\pi\)
0.599713 0.800215i \(-0.295282\pi\)
\(30\) 503.301 0.559224
\(31\) 912.680i 0.949719i −0.880062 0.474860i \(-0.842499\pi\)
0.880062 0.474860i \(-0.157501\pi\)
\(32\) 181.019i 0.176777i
\(33\) 167.191i 0.153527i
\(34\) 69.2720i 0.0599238i
\(35\) 1373.77 1.12145
\(36\) −292.741 −0.225880
\(37\) 325.059i 0.237443i 0.992928 + 0.118721i \(0.0378795\pi\)
−0.992928 + 0.118721i \(0.962120\pi\)
\(38\) 996.937 + 220.646i 0.690400 + 0.152802i
\(39\) 354.872 0.233315
\(40\) 604.213i 0.377633i
\(41\) 51.7494i 0.0307849i −0.999882 0.0153924i \(-0.995100\pi\)
0.999882 0.0153924i \(-0.00489976\pi\)
\(42\) 969.689 0.549710
\(43\) −2545.26 −1.37656 −0.688280 0.725445i \(-0.741634\pi\)
−0.688280 + 0.725445i \(0.741634\pi\)
\(44\) 200.713 0.103674
\(45\) 977.121 0.482529
\(46\) 1731.68i 0.818376i
\(47\) 2998.19 1.35726 0.678630 0.734480i \(-0.262574\pi\)
0.678630 + 0.734480i \(0.262574\pi\)
\(48\) 426.489i 0.185108i
\(49\) 245.788 0.102369
\(50\) 248.999i 0.0995994i
\(51\) 163.208i 0.0627480i
\(52\) 426.024i 0.157553i
\(53\) 4067.86i 1.44815i −0.689720 0.724077i \(-0.742266\pi\)
0.689720 0.724077i \(-0.257734\pi\)
\(54\) 2216.42 0.760090
\(55\) −669.948 −0.221470
\(56\) 1164.11i 0.371209i
\(57\) −2348.82 519.851i −0.722938 0.160003i
\(58\) −3806.96 −1.13168
\(59\) 1078.88i 0.309933i 0.987920 + 0.154966i \(0.0495269\pi\)
−0.987920 + 0.154966i \(0.950473\pi\)
\(60\) 1423.55i 0.395431i
\(61\) −6530.89 −1.75514 −0.877572 0.479445i \(-0.840838\pi\)
−0.877572 + 0.479445i \(0.840838\pi\)
\(62\) −2581.45 −0.671553
\(63\) 1882.58 0.474320
\(64\) −512.000 −0.125000
\(65\) 1422.00i 0.336568i
\(66\) −472.888 −0.108560
\(67\) 7386.18i 1.64540i 0.568478 + 0.822698i \(0.307532\pi\)
−0.568478 + 0.822698i \(0.692468\pi\)
\(68\) 195.931 0.0423726
\(69\) 4079.92i 0.856945i
\(70\) 3885.62i 0.792983i
\(71\) 5806.02i 1.15176i 0.817535 + 0.575879i \(0.195340\pi\)
−0.817535 + 0.575879i \(0.804660\pi\)
\(72\) 827.995i 0.159721i
\(73\) 3629.56 0.681096 0.340548 0.940227i \(-0.389387\pi\)
0.340548 + 0.940227i \(0.389387\pi\)
\(74\) 919.405 0.167897
\(75\) 586.651i 0.104293i
\(76\) 624.081 2819.76i 0.108047 0.488186i
\(77\) −1290.76 −0.217703
\(78\) 1003.73i 0.164979i
\(79\) 3903.16i 0.625407i 0.949851 + 0.312703i \(0.101235\pi\)
−0.949851 + 0.312703i \(0.898765\pi\)
\(80\) 1708.97 0.267027
\(81\) −2257.99 −0.344153
\(82\) −146.369 −0.0217682
\(83\) −997.967 −0.144864 −0.0724319 0.997373i \(-0.523076\pi\)
−0.0724319 + 0.997373i \(0.523076\pi\)
\(84\) 2742.69i 0.388704i
\(85\) −653.985 −0.0905169
\(86\) 7199.08i 0.973375i
\(87\) 8969.34 1.18501
\(88\) 567.702i 0.0733087i
\(89\) 6152.85i 0.776777i −0.921496 0.388389i \(-0.873032\pi\)
0.921496 0.388389i \(-0.126968\pi\)
\(90\) 2763.71i 0.341199i
\(91\) 2739.71i 0.330843i
\(92\) 4897.94 0.578679
\(93\) 6082.00 0.703203
\(94\) 8480.16i 0.959728i
\(95\) −2083.08 + 9411.91i −0.230812 + 1.04287i
\(96\) 1206.29 0.130891
\(97\) 5023.58i 0.533912i 0.963709 + 0.266956i \(0.0860178\pi\)
−0.963709 + 0.266956i \(0.913982\pi\)
\(98\) 695.195i 0.0723860i
\(99\) −918.076 −0.0936717
\(100\) −704.274 −0.0704274
\(101\) 15793.7 1.54825 0.774123 0.633035i \(-0.218191\pi\)
0.774123 + 0.633035i \(0.218191\pi\)
\(102\) −461.621 −0.0443695
\(103\) 13068.7i 1.23185i −0.787806 0.615924i \(-0.788783\pi\)
0.787806 0.615924i \(-0.211217\pi\)
\(104\) 1204.98 0.111407
\(105\) 9154.67i 0.830355i
\(106\) −11505.7 −1.02400
\(107\) 8273.09i 0.722604i −0.932449 0.361302i \(-0.882332\pi\)
0.932449 0.361302i \(-0.117668\pi\)
\(108\) 6268.99i 0.537465i
\(109\) 14219.6i 1.19683i 0.801186 + 0.598416i \(0.204203\pi\)
−0.801186 + 0.598416i \(0.795797\pi\)
\(110\) 1894.90i 0.156603i
\(111\) −2166.16 −0.175810
\(112\) 3292.60 0.262484
\(113\) 20747.4i 1.62483i −0.583080 0.812414i \(-0.698153\pi\)
0.583080 0.812414i \(-0.301847\pi\)
\(114\) −1470.36 + 6643.48i −0.113139 + 0.511194i
\(115\) −16348.5 −1.23618
\(116\) 10767.7i 0.800215i
\(117\) 1948.67i 0.142353i
\(118\) 3051.52 0.219155
\(119\) −1260.00 −0.0889771
\(120\) −4026.41 −0.279612
\(121\) −14011.5 −0.957007
\(122\) 18472.1i 1.24107i
\(123\) 344.852 0.0227941
\(124\) 7301.44i 0.474860i
\(125\) −14338.4 −0.917660
\(126\) 5324.73i 0.335395i
\(127\) 11117.8i 0.689305i −0.938730 0.344653i \(-0.887997\pi\)
0.938730 0.344653i \(-0.112003\pi\)
\(128\) 1448.15i 0.0883883i
\(129\) 16961.3i 1.01925i
\(130\) −4022.02 −0.237990
\(131\) 223.317 0.0130130 0.00650652 0.999979i \(-0.497929\pi\)
0.00650652 + 0.999979i \(0.497929\pi\)
\(132\) 1337.53i 0.0767637i
\(133\) −4013.38 + 18133.5i −0.226886 + 1.02513i
\(134\) 20891.3 1.16347
\(135\) 20924.9i 1.14814i
\(136\) 554.176i 0.0299619i
\(137\) 18953.1 1.00981 0.504903 0.863176i \(-0.331528\pi\)
0.504903 + 0.863176i \(0.331528\pi\)
\(138\) −11539.7 −0.605952
\(139\) −11115.5 −0.575309 −0.287655 0.957734i \(-0.592875\pi\)
−0.287655 + 0.957734i \(0.592875\pi\)
\(140\) −10990.2 −0.560723
\(141\) 19979.6i 1.00496i
\(142\) 16421.9 0.814416
\(143\) 1336.07i 0.0653368i
\(144\) 2341.92 0.112940
\(145\) 35940.8i 1.70943i
\(146\) 10265.9i 0.481608i
\(147\) 1637.91i 0.0757975i
\(148\) 2600.47i 0.118721i
\(149\) −19727.7 −0.888597 −0.444299 0.895879i \(-0.646547\pi\)
−0.444299 + 0.895879i \(0.646547\pi\)
\(150\) 1659.30 0.0737466
\(151\) 770.565i 0.0337952i 0.999857 + 0.0168976i \(0.00537894\pi\)
−0.999857 + 0.0168976i \(0.994621\pi\)
\(152\) −7975.50 1765.17i −0.345200 0.0764009i
\(153\) −896.201 −0.0382845
\(154\) 3650.82i 0.153939i
\(155\) 24371.0i 1.01440i
\(156\) −2838.98 −0.116658
\(157\) 46244.5 1.87612 0.938061 0.346470i \(-0.112620\pi\)
0.938061 + 0.346470i \(0.112620\pi\)
\(158\) 11039.8 0.442229
\(159\) 27107.8 1.07226
\(160\) 4833.71i 0.188817i
\(161\) −31498.0 −1.21515
\(162\) 6386.55i 0.243353i
\(163\) 32951.9 1.24024 0.620119 0.784507i \(-0.287084\pi\)
0.620119 + 0.784507i \(0.287084\pi\)
\(164\) 413.995i 0.0153924i
\(165\) 4464.46i 0.163984i
\(166\) 2822.68i 0.102434i
\(167\) 48049.1i 1.72287i −0.507870 0.861434i \(-0.669567\pi\)
0.507870 0.861434i \(-0.330433\pi\)
\(168\) −7757.51 −0.274855
\(169\) 25725.1 0.900708
\(170\) 1849.75i 0.0640051i
\(171\) −2854.59 + 12897.8i −0.0976228 + 0.441086i
\(172\) 20362.1 0.688280
\(173\) 46219.6i 1.54431i 0.635436 + 0.772153i \(0.280820\pi\)
−0.635436 + 0.772153i \(0.719180\pi\)
\(174\) 25369.1i 0.837929i
\(175\) 4529.10 0.147889
\(176\) −1605.70 −0.0518371
\(177\) −7189.51 −0.229484
\(178\) −17402.9 −0.549264
\(179\) 39826.5i 1.24299i 0.783420 + 0.621493i \(0.213473\pi\)
−0.783420 + 0.621493i \(0.786527\pi\)
\(180\) −7816.96 −0.241264
\(181\) 51844.5i 1.58251i 0.611488 + 0.791254i \(0.290571\pi\)
−0.611488 + 0.791254i \(0.709429\pi\)
\(182\) −7749.06 −0.233941
\(183\) 43521.1i 1.29957i
\(184\) 13853.5i 0.409188i
\(185\) 8679.95i 0.253614i
\(186\) 17202.5i 0.497239i
\(187\) 614.467 0.0175718
\(188\) −23985.5 −0.678630
\(189\) 40315.1i 1.12861i
\(190\) 26620.9 + 5891.84i 0.737421 + 0.163209i
\(191\) −38958.8 −1.06792 −0.533960 0.845509i \(-0.679297\pi\)
−0.533960 + 0.845509i \(0.679297\pi\)
\(192\) 3411.91i 0.0925540i
\(193\) 43058.1i 1.15595i 0.816053 + 0.577977i \(0.196158\pi\)
−0.816053 + 0.577977i \(0.803842\pi\)
\(194\) 14208.8 0.377533
\(195\) 9476.05 0.249206
\(196\) −1966.31 −0.0511846
\(197\) 26311.0 0.677962 0.338981 0.940793i \(-0.389918\pi\)
0.338981 + 0.940793i \(0.389918\pi\)
\(198\) 2596.71i 0.0662359i
\(199\) −11773.1 −0.297293 −0.148647 0.988890i \(-0.547492\pi\)
−0.148647 + 0.988890i \(0.547492\pi\)
\(200\) 1991.99i 0.0497997i
\(201\) −49220.7 −1.21830
\(202\) 44671.2i 1.09478i
\(203\) 69245.7i 1.68035i
\(204\) 1305.66i 0.0313740i
\(205\) 1381.85i 0.0328816i
\(206\) −36963.8 −0.871048
\(207\) −22403.5 −0.522848
\(208\) 3408.20i 0.0787767i
\(209\) 1957.21 8843.18i 0.0448068 0.202449i
\(210\) 25893.3 0.587150
\(211\) 12495.7i 0.280670i −0.990104 0.140335i \(-0.955182\pi\)
0.990104 0.140335i \(-0.0448179\pi\)
\(212\) 32542.9i 0.724077i
\(213\) −38690.7 −0.852799
\(214\) −23399.8 −0.510958
\(215\) −67965.3 −1.47032
\(216\) −17731.4 −0.380045
\(217\) 46954.6i 0.997146i
\(218\) 40219.0 0.846288
\(219\) 24187.0i 0.504305i
\(220\) 5359.58 0.110735
\(221\) 1304.24i 0.0267038i
\(222\) 6126.82i 0.124317i
\(223\) 59706.5i 1.20064i 0.799761 + 0.600319i \(0.204960\pi\)
−0.799761 + 0.600319i \(0.795040\pi\)
\(224\) 9312.89i 0.185605i
\(225\) 3221.40 0.0636326
\(226\) −58682.6 −1.14893
\(227\) 57964.2i 1.12489i −0.826836 0.562443i \(-0.809862\pi\)
0.826836 0.562443i \(-0.190138\pi\)
\(228\) 18790.6 + 4158.80i 0.361469 + 0.0800016i
\(229\) 40157.9 0.765773 0.382886 0.923795i \(-0.374930\pi\)
0.382886 + 0.923795i \(0.374930\pi\)
\(230\) 46240.6i 0.874114i
\(231\) 8601.48i 0.161194i
\(232\) 30455.6 0.565838
\(233\) 71740.1 1.32145 0.660724 0.750629i \(-0.270249\pi\)
0.660724 + 0.750629i \(0.270249\pi\)
\(234\) −5511.66 −0.100659
\(235\) 80059.7 1.44970
\(236\) 8631.00i 0.154966i
\(237\) −26010.2 −0.463071
\(238\) 3563.83i 0.0629163i
\(239\) 44178.4 0.773417 0.386709 0.922202i \(-0.373612\pi\)
0.386709 + 0.922202i \(0.373612\pi\)
\(240\) 11388.4i 0.197715i
\(241\) 33823.7i 0.582353i −0.956669 0.291177i \(-0.905953\pi\)
0.956669 0.291177i \(-0.0940467\pi\)
\(242\) 39630.6i 0.676706i
\(243\) 48426.6i 0.820108i
\(244\) 52247.1 0.877572
\(245\) 6563.22 0.109341
\(246\) 975.390i 0.0161179i
\(247\) 18770.1 + 4154.27i 0.307662 + 0.0680928i
\(248\) 20651.6 0.335777
\(249\) 6650.34i 0.107262i
\(250\) 40555.2i 0.648884i
\(251\) −64952.8 −1.03098 −0.515490 0.856896i \(-0.672390\pi\)
−0.515490 + 0.856896i \(0.672390\pi\)
\(252\) −15060.6 −0.237160
\(253\) 15360.6 0.239976
\(254\) −31445.9 −0.487412
\(255\) 4358.08i 0.0670217i
\(256\) 4096.00 0.0625000
\(257\) 1155.59i 0.0174959i 0.999962 + 0.00874796i \(0.00278460\pi\)
−0.999962 + 0.00874796i \(0.997215\pi\)
\(258\) −47973.9 −0.720718
\(259\) 16723.3i 0.249300i
\(260\) 11376.0i 0.168284i
\(261\) 49252.2i 0.723011i
\(262\) 631.635i 0.00920161i
\(263\) 6732.94 0.0973404 0.0486702 0.998815i \(-0.484502\pi\)
0.0486702 + 0.998815i \(0.484502\pi\)
\(264\) 3783.11 0.0542801
\(265\) 108623.i 1.54678i
\(266\) 51289.4 + 11351.6i 0.724877 + 0.160432i
\(267\) 41001.9 0.575151
\(268\) 59089.5i 0.822698i
\(269\) 22231.5i 0.307230i −0.988131 0.153615i \(-0.950908\pi\)
0.988131 0.153615i \(-0.0490915\pi\)
\(270\) 59184.5 0.811859
\(271\) −46597.6 −0.634490 −0.317245 0.948344i \(-0.602758\pi\)
−0.317245 + 0.948344i \(0.602758\pi\)
\(272\) −1567.45 −0.0211863
\(273\) 18257.1 0.244966
\(274\) 53607.3i 0.714041i
\(275\) −2208.70 −0.0292060
\(276\) 32639.3i 0.428473i
\(277\) 105817. 1.37910 0.689548 0.724240i \(-0.257809\pi\)
0.689548 + 0.724240i \(0.257809\pi\)
\(278\) 31439.5i 0.406805i
\(279\) 33397.3i 0.429045i
\(280\) 31084.9i 0.396491i
\(281\) 20298.2i 0.257067i 0.991705 + 0.128533i \(0.0410269\pi\)
−0.991705 + 0.128533i \(0.958973\pi\)
\(282\) 56510.8 0.710614
\(283\) −55710.6 −0.695609 −0.347804 0.937567i \(-0.613073\pi\)
−0.347804 + 0.937567i \(0.613073\pi\)
\(284\) 46448.1i 0.575879i
\(285\) −62720.0 13881.4i −0.772176 0.170901i
\(286\) 3778.99 0.0462001
\(287\) 2662.35i 0.0323222i
\(288\) 6623.96i 0.0798607i
\(289\) −82921.2 −0.992818
\(290\) −101656. −1.20875
\(291\) −33476.6 −0.395326
\(292\) −29036.5 −0.340548
\(293\) 84053.1i 0.979081i 0.871980 + 0.489541i \(0.162836\pi\)
−0.871980 + 0.489541i \(0.837164\pi\)
\(294\) 4632.70 0.0535969
\(295\) 28808.9i 0.331042i
\(296\) −7355.24 −0.0839486
\(297\) 19660.4i 0.222885i
\(298\) 55798.5i 0.628333i
\(299\) 32603.8i 0.364691i
\(300\) 4693.21i 0.0521467i
\(301\) −130946. −1.44530
\(302\) 2179.49 0.0238968
\(303\) 105247.i 1.14637i
\(304\) −4992.64 + 22558.1i −0.0540236 + 0.244093i
\(305\) −174392. −1.87468
\(306\) 2534.84i 0.0270712i
\(307\) 10396.7i 0.110311i −0.998478 0.0551555i \(-0.982435\pi\)
0.998478 0.0551555i \(-0.0175655\pi\)
\(308\) 10326.1 0.108851
\(309\) 87088.2 0.912100
\(310\) −68931.7 −0.717291
\(311\) 118107. 1.22111 0.610557 0.791973i \(-0.290946\pi\)
0.610557 + 0.791973i \(0.290946\pi\)
\(312\) 8029.85i 0.0824894i
\(313\) −8391.17 −0.0856513 −0.0428257 0.999083i \(-0.513636\pi\)
−0.0428257 + 0.999083i \(0.513636\pi\)
\(314\) 130799.i 1.32662i
\(315\) 50269.9 0.506625
\(316\) 31225.3i 0.312703i
\(317\) 143474.i 1.42776i 0.700270 + 0.713878i \(0.253063\pi\)
−0.700270 + 0.713878i \(0.746937\pi\)
\(318\) 76672.4i 0.758202i
\(319\) 33769.0i 0.331847i
\(320\) −13671.8 −0.133514
\(321\) 55131.0 0.535039
\(322\) 89089.8i 0.859244i
\(323\) 1910.57 8632.47i 0.0183129 0.0827428i
\(324\) 18063.9 0.172076
\(325\) 4688.09i 0.0443843i
\(326\) 93202.1i 0.876981i
\(327\) −94757.6 −0.886173
\(328\) 1170.96 0.0108841
\(329\) 154248. 1.42504
\(330\) −12627.4 −0.115954
\(331\) 16943.3i 0.154647i −0.997006 0.0773237i \(-0.975363\pi\)
0.997006 0.0773237i \(-0.0246375\pi\)
\(332\) 7983.73 0.0724319
\(333\) 11894.7i 0.107267i
\(334\) −135903. −1.21825
\(335\) 197231.i 1.75746i
\(336\) 21941.6i 0.194352i
\(337\) 217168.i 1.91221i −0.293021 0.956106i \(-0.594661\pi\)
0.293021 0.956106i \(-0.405339\pi\)
\(338\) 72761.6i 0.636897i
\(339\) 138259. 1.20308
\(340\) 5231.88 0.0452585
\(341\) 22898.4i 0.196923i
\(342\) 36480.5 + 8074.00i 0.311895 + 0.0690298i
\(343\) −110879. −0.942456
\(344\) 57592.7i 0.486688i
\(345\) 108945.i 0.915310i
\(346\) 130729. 1.09199
\(347\) 64555.0 0.536131 0.268066 0.963401i \(-0.413616\pi\)
0.268066 + 0.963401i \(0.413616\pi\)
\(348\) −71754.8 −0.592505
\(349\) −113275. −0.930001 −0.465001 0.885310i \(-0.653946\pi\)
−0.465001 + 0.885310i \(0.653946\pi\)
\(350\) 12810.2i 0.104573i
\(351\) 41730.4 0.338718
\(352\) 4541.62i 0.0366543i
\(353\) 27685.3 0.222178 0.111089 0.993810i \(-0.464566\pi\)
0.111089 + 0.993810i \(0.464566\pi\)
\(354\) 20335.0i 0.162270i
\(355\) 155036.i 1.23020i
\(356\) 49222.8i 0.388389i
\(357\) 8396.53i 0.0658815i
\(358\) 112646. 0.878923
\(359\) 65336.2 0.506950 0.253475 0.967342i \(-0.418426\pi\)
0.253475 + 0.967342i \(0.418426\pi\)
\(360\) 22109.7i 0.170600i
\(361\) −118150. 54992.5i −0.906606 0.421977i
\(362\) 146638. 1.11900
\(363\) 93371.3i 0.708599i
\(364\) 21917.7i 0.165421i
\(365\) 96919.1 0.727484
\(366\) −123096. −0.918931
\(367\) 177298. 1.31635 0.658176 0.752864i \(-0.271328\pi\)
0.658176 + 0.752864i \(0.271328\pi\)
\(368\) −39183.5 −0.289340
\(369\) 1893.64i 0.0139074i
\(370\) 24550.6 0.179332
\(371\) 209279.i 1.52047i
\(372\) −48656.0 −0.351601
\(373\) 15381.6i 0.110557i 0.998471 + 0.0552783i \(0.0176046\pi\)
−0.998471 + 0.0552783i \(0.982395\pi\)
\(374\) 1737.97i 0.0124251i
\(375\) 95549.8i 0.679465i
\(376\) 67841.3i 0.479864i
\(377\) −71676.6 −0.504307
\(378\) 114028. 0.798047
\(379\) 232626.i 1.61949i 0.586780 + 0.809746i \(0.300395\pi\)
−0.586780 + 0.809746i \(0.699605\pi\)
\(380\) 16664.6 75295.3i 0.115406 0.521436i
\(381\) 74087.8 0.510384
\(382\) 110192.i 0.755134i
\(383\) 52033.6i 0.354721i −0.984146 0.177360i \(-0.943244\pi\)
0.984146 0.177360i \(-0.0567558\pi\)
\(384\) −9650.34 −0.0654456
\(385\) −34466.8 −0.232530
\(386\) 121787. 0.817383
\(387\) −93137.6 −0.621875
\(388\) 40188.6i 0.266956i
\(389\) 57687.6 0.381227 0.190613 0.981665i \(-0.438952\pi\)
0.190613 + 0.981665i \(0.438952\pi\)
\(390\) 26802.3i 0.176215i
\(391\) 14994.6 0.0980804
\(392\) 5561.56i 0.0361930i
\(393\) 1488.16i 0.00963527i
\(394\) 74418.9i 0.479392i
\(395\) 104225.i 0.668002i
\(396\) 7344.61 0.0468358
\(397\) 16914.2 0.107317 0.0536586 0.998559i \(-0.482912\pi\)
0.0536586 + 0.998559i \(0.482912\pi\)
\(398\) 33299.4i 0.210218i
\(399\) −120840. 26744.7i −0.759039 0.167993i
\(400\) 5634.19 0.0352137
\(401\) 23481.6i 0.146029i −0.997331 0.0730144i \(-0.976738\pi\)
0.997331 0.0730144i \(-0.0232619\pi\)
\(402\) 139217.i 0.861471i
\(403\) −48603.0 −0.299263
\(404\) −126349. −0.774123
\(405\) −60294.3 −0.367592
\(406\) −195856. −1.18819
\(407\) 8155.45i 0.0492333i
\(408\) 3692.97 0.0221848
\(409\) 310776.i 1.85781i −0.370321 0.928904i \(-0.620752\pi\)
0.370321 0.928904i \(-0.379248\pi\)
\(410\) −3908.46 −0.0232508
\(411\) 126301.i 0.747693i
\(412\) 104549.i 0.615924i
\(413\) 55504.9i 0.325410i
\(414\) 63366.7i 0.369710i
\(415\) −26648.4 −0.154730
\(416\) −9639.83 −0.0557035
\(417\) 74072.8i 0.425977i
\(418\) −25012.3 5535.81i −0.143153 0.0316832i
\(419\) −271562. −1.54682 −0.773411 0.633905i \(-0.781451\pi\)
−0.773411 + 0.633905i \(0.781451\pi\)
\(420\) 73237.3i 0.415178i
\(421\) 322467.i 1.81937i 0.415299 + 0.909685i \(0.363677\pi\)
−0.415299 + 0.909685i \(0.636323\pi\)
\(422\) −35343.2 −0.198464
\(423\) 109711. 0.613156
\(424\) 92045.2 0.512000
\(425\) −2156.08 −0.0119368
\(426\) 109434.i 0.603020i
\(427\) −335994. −1.84279
\(428\) 66184.7i 0.361302i
\(429\) −8903.44 −0.0483775
\(430\) 192235.i 1.03967i
\(431\) 157951.i 0.850290i −0.905125 0.425145i \(-0.860223\pi\)
0.905125 0.425145i \(-0.139777\pi\)
\(432\) 50151.9i 0.268732i
\(433\) 36946.7i 0.197061i 0.995134 + 0.0985304i \(0.0314142\pi\)
−0.995134 + 0.0985304i \(0.968586\pi\)
\(434\) −132808. −0.705089
\(435\) 239506. 1.26572
\(436\) 113756.i 0.598416i
\(437\) 47761.1 215797.i 0.250099 1.13001i
\(438\) 68411.1 0.356598
\(439\) 194377.i 1.00859i −0.863531 0.504296i \(-0.831752\pi\)
0.863531 0.504296i \(-0.168248\pi\)
\(440\) 15159.2i 0.0783016i
\(441\) 8994.03 0.0462463
\(442\) 3688.94 0.0188824
\(443\) 30671.7 0.156290 0.0781449 0.996942i \(-0.475100\pi\)
0.0781449 + 0.996942i \(0.475100\pi\)
\(444\) 17329.3 0.0879051
\(445\) 164298.i 0.829682i
\(446\) 168875. 0.848979
\(447\) 131464.i 0.657946i
\(448\) −26340.8 −0.131242
\(449\) 236846.i 1.17483i 0.809287 + 0.587413i \(0.199854\pi\)
−0.809287 + 0.587413i \(0.800146\pi\)
\(450\) 9111.50i 0.0449951i
\(451\) 1298.35i 0.00638319i
\(452\) 165980.i 0.812414i
\(453\) −5134.96 −0.0250231
\(454\) −163948. −0.795414
\(455\) 73157.6i 0.353376i
\(456\) 11762.9 53147.8i 0.0565697 0.255597i
\(457\) −82060.7 −0.392919 −0.196459 0.980512i \(-0.562944\pi\)
−0.196459 + 0.980512i \(0.562944\pi\)
\(458\) 113584.i 0.541483i
\(459\) 19192.0i 0.0910951i
\(460\) 130788. 0.618092
\(461\) −16781.0 −0.0789614 −0.0394807 0.999220i \(-0.512570\pi\)
−0.0394807 + 0.999220i \(0.512570\pi\)
\(462\) −24328.7 −0.113981
\(463\) 100169. 0.467274 0.233637 0.972324i \(-0.424937\pi\)
0.233637 + 0.972324i \(0.424937\pi\)
\(464\) 86141.6i 0.400108i
\(465\) 162406. 0.751097
\(466\) 202912.i 0.934405i
\(467\) −216772. −0.993960 −0.496980 0.867762i \(-0.665558\pi\)
−0.496980 + 0.867762i \(0.665558\pi\)
\(468\) 15589.3i 0.0711764i
\(469\) 379997.i 1.72756i
\(470\) 226443.i 1.02509i
\(471\) 308168.i 1.38914i
\(472\) −24412.2 −0.109578
\(473\) 63858.4 0.285427
\(474\) 73568.1i 0.327441i
\(475\) −6867.56 + 31029.5i −0.0304379 + 0.137527i
\(476\) 10080.0 0.0444885
\(477\) 148854.i 0.654218i
\(478\) 124955.i 0.546889i
\(479\) 91676.2 0.399563 0.199782 0.979840i \(-0.435977\pi\)
0.199782 + 0.979840i \(0.435977\pi\)
\(480\) 32211.3 0.139806
\(481\) 17310.4 0.0748198
\(482\) −95667.8 −0.411786
\(483\) 209899.i 0.899739i
\(484\) 112092. 0.478503
\(485\) 134143.i 0.570276i
\(486\) 136971. 0.579904
\(487\) 107326.i 0.452528i −0.974066 0.226264i \(-0.927349\pi\)
0.974066 0.226264i \(-0.0726512\pi\)
\(488\) 147777.i 0.620537i
\(489\) 219588.i 0.918313i
\(490\) 18563.6i 0.0773160i
\(491\) 211818. 0.878619 0.439310 0.898336i \(-0.355223\pi\)
0.439310 + 0.898336i \(0.355223\pi\)
\(492\) −2758.82 −0.0113971
\(493\) 32964.4i 0.135629i
\(494\) 11750.1 53089.9i 0.0481489 0.217550i
\(495\) −24515.1 −0.100051
\(496\) 58411.5i 0.237430i
\(497\) 298702.i 1.20928i
\(498\) −18810.0 −0.0758456
\(499\) 145489. 0.584291 0.292146 0.956374i \(-0.405631\pi\)
0.292146 + 0.956374i \(0.405631\pi\)
\(500\) 114707. 0.458830
\(501\) 320194. 1.27567
\(502\) 183714.i 0.729013i
\(503\) −33735.6 −0.133338 −0.0666689 0.997775i \(-0.521237\pi\)
−0.0666689 + 0.997775i \(0.521237\pi\)
\(504\) 42597.8i 0.167697i
\(505\) 421733. 1.65369
\(506\) 43446.4i 0.169689i
\(507\) 171429.i 0.666913i
\(508\) 88942.4i 0.344653i
\(509\) 128247.i 0.495009i 0.968887 + 0.247505i \(0.0796105\pi\)
−0.968887 + 0.247505i \(0.920389\pi\)
\(510\) −12326.5 −0.0473915
\(511\) 186730. 0.715108
\(512\) 11585.2i 0.0441942i
\(513\) −276204. 61130.6i −1.04953 0.232286i
\(514\) 3268.50 0.0123715
\(515\) 348969.i 1.31575i
\(516\) 135691.i 0.509625i
\(517\) −75222.0 −0.281426
\(518\) 47300.6 0.176282
\(519\) −308002. −1.14345
\(520\) 32176.2 0.118995
\(521\) 38092.9i 0.140336i 0.997535 + 0.0701680i \(0.0223535\pi\)
−0.997535 + 0.0701680i \(0.977646\pi\)
\(522\) −139306. −0.511246
\(523\) 96329.4i 0.352173i −0.984375 0.176086i \(-0.943656\pi\)
0.984375 0.176086i \(-0.0563438\pi\)
\(524\) −1786.53 −0.00650652
\(525\) 30181.4i 0.109502i
\(526\) 19043.6i 0.0688301i
\(527\) 22352.8i 0.0804841i
\(528\) 10700.2i 0.0383818i
\(529\) 94999.8 0.339478
\(530\) −307232. −1.09374
\(531\) 39478.8i 0.140015i
\(532\) 32107.0 145068.i 0.113443 0.512565i
\(533\) −2755.81 −0.00970053
\(534\) 115971.i 0.406693i
\(535\) 220914.i 0.771819i
\(536\) −167130. −0.581735
\(537\) −265399. −0.920346
\(538\) −62880.1 −0.217244
\(539\) −6166.62 −0.0212261
\(540\) 167399.i 0.574071i
\(541\) −163021. −0.556993 −0.278496 0.960437i \(-0.589836\pi\)
−0.278496 + 0.960437i \(0.589836\pi\)
\(542\) 131798.i 0.448652i
\(543\) −345486. −1.17174
\(544\) 4433.41i 0.0149810i
\(545\) 379701.i 1.27835i
\(546\) 51638.9i 0.173217i
\(547\) 450817.i 1.50670i −0.657621 0.753349i \(-0.728437\pi\)
0.657621 0.753349i \(-0.271563\pi\)
\(548\) −151624. −0.504903
\(549\) −238982. −0.792904
\(550\) 6247.16i 0.0206518i
\(551\) 474412. + 104999.i 1.56262 + 0.345844i
\(552\) 92318.0 0.302976
\(553\) 200806.i 0.656638i
\(554\) 299295.i 0.975168i
\(555\) −57842.2 −0.187784
\(556\) 88924.4 0.287655
\(557\) −270930. −0.873268 −0.436634 0.899639i \(-0.643829\pi\)
−0.436634 + 0.899639i \(0.643829\pi\)
\(558\) −94461.9 −0.303381
\(559\) 135543.i 0.433764i
\(560\) 87921.4 0.280362
\(561\) 4094.74i 0.0130107i
\(562\) 57412.1 0.181774
\(563\) 59429.1i 0.187492i 0.995596 + 0.0937459i \(0.0298841\pi\)
−0.995596 + 0.0937459i \(0.970116\pi\)
\(564\) 159837.i 0.502480i
\(565\) 554013.i 1.73549i
\(566\) 157573.i 0.491870i
\(567\) −116166. −0.361339
\(568\) −131375. −0.407208
\(569\) 364145.i 1.12473i 0.826888 + 0.562367i \(0.190109\pi\)
−0.826888 + 0.562367i \(0.809891\pi\)
\(570\) −39262.6 + 177399.i −0.120845 + 0.546011i
\(571\) 410057. 1.25769 0.628843 0.777532i \(-0.283529\pi\)
0.628843 + 0.777532i \(0.283529\pi\)
\(572\) 10688.6i 0.0326684i
\(573\) 259617.i 0.790723i
\(574\) −7530.26 −0.0228553
\(575\) −53898.3 −0.163020
\(576\) −18735.4 −0.0564700
\(577\) −44617.5 −0.134015 −0.0670075 0.997752i \(-0.521345\pi\)
−0.0670075 + 0.997752i \(0.521345\pi\)
\(578\) 234536.i 0.702029i
\(579\) −286935. −0.855906
\(580\) 287527.i 0.854717i
\(581\) −51342.3 −0.152098
\(582\) 94686.0i 0.279537i
\(583\) 102059.i 0.300272i
\(584\) 82127.6i 0.240804i
\(585\) 52034.7i 0.152048i
\(586\) 237738. 0.692315
\(587\) −371422. −1.07793 −0.538966 0.842328i \(-0.681185\pi\)
−0.538966 + 0.842328i \(0.681185\pi\)
\(588\) 13103.3i 0.0378987i
\(589\) 321693. + 71198.3i 0.927280 + 0.205229i
\(590\) 81483.9 0.234082
\(591\) 175334.i 0.501985i
\(592\) 20803.8i 0.0593606i
\(593\) −327963. −0.932644 −0.466322 0.884615i \(-0.654421\pi\)
−0.466322 + 0.884615i \(0.654421\pi\)
\(594\) −55608.1 −0.157603
\(595\) −33645.5 −0.0950372
\(596\) 157822. 0.444299
\(597\) 78454.7i 0.220125i
\(598\) 92217.4 0.257876
\(599\) 81737.2i 0.227806i −0.993492 0.113903i \(-0.963665\pi\)
0.993492 0.113903i \(-0.0363354\pi\)
\(600\) −13274.4 −0.0368733
\(601\) 75524.8i 0.209093i −0.994520 0.104547i \(-0.966661\pi\)
0.994520 0.104547i \(-0.0333392\pi\)
\(602\) 370371.i 1.02198i
\(603\) 270279.i 0.743325i
\(604\) 6164.52i 0.0168976i
\(605\) −374146. −1.02219
\(606\) 297684. 0.810607
\(607\) 97397.5i 0.264345i −0.991227 0.132172i \(-0.957805\pi\)
0.991227 0.132172i \(-0.0421952\pi\)
\(608\) 63804.0 + 14121.3i 0.172600 + 0.0382005i
\(609\) 461445. 1.24419
\(610\) 493256.i 1.32560i
\(611\) 159663.i 0.427682i
\(612\) 7169.61 0.0191422
\(613\) 185283. 0.493078 0.246539 0.969133i \(-0.420707\pi\)
0.246539 + 0.969133i \(0.420707\pi\)
\(614\) −29406.3 −0.0780017
\(615\) 9208.49 0.0243466
\(616\) 29206.6i 0.0769695i
\(617\) 628408. 1.65071 0.825357 0.564612i \(-0.190974\pi\)
0.825357 + 0.564612i \(0.190974\pi\)
\(618\) 246323.i 0.644952i
\(619\) 203791. 0.531867 0.265933 0.963991i \(-0.414320\pi\)
0.265933 + 0.963991i \(0.414320\pi\)
\(620\) 194968.i 0.507201i
\(621\) 479768.i 1.24408i
\(622\) 334058.i 0.863458i
\(623\) 316545.i 0.815568i
\(624\) 22711.8 0.0583288
\(625\) −437896. −1.12101
\(626\) 23733.8i 0.0605646i
\(627\) 58930.0 + 13042.6i 0.149900 + 0.0331764i
\(628\) −369956. −0.938061
\(629\) 7961.13i 0.0201221i
\(630\) 142185.i 0.358238i
\(631\) 496722. 1.24754 0.623771 0.781607i \(-0.285600\pi\)
0.623771 + 0.781607i \(0.285600\pi\)
\(632\) −88318.5 −0.221115
\(633\) 83270.0 0.207817
\(634\) 405805. 1.00958
\(635\) 296875.i 0.736252i
\(636\) −216862. −0.536130
\(637\) 13089.0i 0.0322572i
\(638\) 95513.2 0.234651
\(639\) 212457.i 0.520319i
\(640\) 38669.6i 0.0944083i
\(641\) 44345.5i 0.107928i −0.998543 0.0539639i \(-0.982814\pi\)
0.998543 0.0539639i \(-0.0171856\pi\)
\(642\) 155934.i 0.378330i
\(643\) 139327. 0.336987 0.168494 0.985703i \(-0.446110\pi\)
0.168494 + 0.985703i \(0.446110\pi\)
\(644\) 251984. 0.607577
\(645\) 452913.i 1.08867i
\(646\) −24416.3 5403.91i −0.0585080 0.0129492i
\(647\) −617612. −1.47539 −0.737696 0.675133i \(-0.764086\pi\)
−0.737696 + 0.675133i \(0.764086\pi\)
\(648\) 51092.4i 0.121676i
\(649\) 27068.1i 0.0642640i
\(650\) −13259.9 −0.0313845
\(651\) 312900. 0.738319
\(652\) −263615. −0.620119
\(653\) 570062. 1.33689 0.668446 0.743761i \(-0.266960\pi\)
0.668446 + 0.743761i \(0.266960\pi\)
\(654\) 268015.i 0.626619i
\(655\) 5963.16 0.0138993
\(656\) 3311.96i 0.00769622i
\(657\) 132815. 0.307692
\(658\) 436278.i 1.00765i
\(659\) 716546.i 1.64996i −0.565162 0.824980i \(-0.691186\pi\)
0.565162 0.824980i \(-0.308814\pi\)
\(660\) 35715.7i 0.0819919i
\(661\) 187692.i 0.429579i −0.976660 0.214790i \(-0.931093\pi\)
0.976660 0.214790i \(-0.0689066\pi\)
\(662\) −47923.0 −0.109352
\(663\) −8691.30 −0.0197723
\(664\) 22581.4i 0.0512171i
\(665\) −107168. + 484214.i −0.242338 + 1.09495i
\(666\) 33643.4 0.0758493
\(667\) 824055.i 1.85227i
\(668\) 384393.i 0.861434i
\(669\) −397877. −0.888990
\(670\) 557854. 1.24271
\(671\) 163854. 0.363926
\(672\) 62060.1 0.137428
\(673\) 504263.i 1.11334i 0.830734 + 0.556669i \(0.187921\pi\)
−0.830734 + 0.556669i \(0.812079\pi\)
\(674\) −614244. −1.35214
\(675\) 68985.8i 0.151409i
\(676\) −205801. −0.450354
\(677\) 689926.i 1.50531i −0.658417 0.752653i \(-0.728774\pi\)
0.658417 0.752653i \(-0.271226\pi\)
\(678\) 391055.i 0.850703i
\(679\) 258448.i 0.560574i
\(680\) 14798.0i 0.0320026i
\(681\) 386267. 0.832901
\(682\) 64766.3 0.139245
\(683\) 226300.i 0.485113i 0.970137 + 0.242556i \(0.0779859\pi\)
−0.970137 + 0.242556i \(0.922014\pi\)
\(684\) 22836.7 103182.i 0.0488114 0.220543i
\(685\) 506098. 1.07858
\(686\) 313613.i 0.666417i
\(687\) 267608.i 0.567003i
\(688\) −162897. −0.344140
\(689\) −216626. −0.456323
\(690\) −308142. −0.647222
\(691\) −921891. −1.93074 −0.965370 0.260886i \(-0.915985\pi\)
−0.965370 + 0.260886i \(0.915985\pi\)
\(692\) 369756.i 0.772153i
\(693\) −47232.2 −0.0983494
\(694\) 182589.i 0.379102i
\(695\) −296815. −0.614492
\(696\) 202953.i 0.418964i
\(697\) 1267.41i 0.00260887i
\(698\) 320390.i 0.657610i
\(699\) 478068.i 0.978443i
\(700\) −36232.8 −0.0739444
\(701\) −561368. −1.14238 −0.571191 0.820817i \(-0.693519\pi\)
−0.571191 + 0.820817i \(0.693519\pi\)
\(702\) 118031.i 0.239510i
\(703\) −114574. 25357.9i −0.231832 0.0513100i
\(704\) 12845.6 0.0259185
\(705\) 533509.i 1.07341i
\(706\) 78306.0i 0.157103i
\(707\) 812536. 1.62556
\(708\) 57516.1 0.114742
\(709\) −287728. −0.572386 −0.286193 0.958172i \(-0.592390\pi\)
−0.286193 + 0.958172i \(0.592390\pi\)
\(710\) 438509. 0.869885
\(711\) 142827.i 0.282534i
\(712\) 139223. 0.274632
\(713\) 558782.i 1.09917i
\(714\) −23749.0 −0.0465853
\(715\) 35676.8i 0.0697868i
\(716\) 318612.i 0.621493i
\(717\) 294400.i 0.572663i
\(718\) 184799.i 0.358468i
\(719\) −805860. −1.55884 −0.779420 0.626502i \(-0.784486\pi\)
−0.779420 + 0.626502i \(0.784486\pi\)
\(720\) 62535.7 0.120632
\(721\) 672344.i 1.29336i
\(722\) −155542. + 334178.i −0.298383 + 0.641068i
\(723\) 225397. 0.431193
\(724\) 414756.i 0.791254i
\(725\) 118491.i 0.225428i
\(726\) −264094. −0.501055
\(727\) −348604. −0.659575 −0.329787 0.944055i \(-0.606977\pi\)
−0.329787 + 0.944055i \(0.606977\pi\)
\(728\) 61992.5 0.116970
\(729\) −505606. −0.951387
\(730\) 274129.i 0.514409i
\(731\) 62336.8 0.116657
\(732\) 348169.i 0.649783i
\(733\) 238795. 0.444443 0.222222 0.974996i \(-0.428669\pi\)
0.222222 + 0.974996i \(0.428669\pi\)
\(734\) 501475.i 0.930801i
\(735\) 43736.6i 0.0809599i
\(736\) 110828.i 0.204594i
\(737\) 185313.i 0.341170i
\(738\) −5356.03 −0.00983401
\(739\) 502122. 0.919433 0.459717 0.888066i \(-0.347951\pi\)
0.459717 + 0.888066i \(0.347951\pi\)
\(740\) 69439.6i 0.126807i
\(741\) −27683.6 + 125082.i −0.0504181 + 0.227803i
\(742\) −591931. −1.07514
\(743\) 411861.i 0.746058i −0.927820 0.373029i \(-0.878319\pi\)
0.927820 0.373029i \(-0.121681\pi\)
\(744\) 137620.i 0.248620i
\(745\) −526784. −0.949118
\(746\) 43505.8 0.0781753
\(747\) −36518.2 −0.0654437
\(748\) −4915.73 −0.00878588
\(749\) 425625.i 0.758689i
\(750\) −270256. −0.480454
\(751\) 876407.i 1.55391i 0.629556 + 0.776955i \(0.283237\pi\)
−0.629556 + 0.776955i \(0.716763\pi\)
\(752\) 191884. 0.339315
\(753\) 432838.i 0.763371i
\(754\) 202732.i 0.356599i
\(755\) 20576.2i 0.0360970i
\(756\) 322520.i 0.564305i
\(757\) −447975. −0.781739 −0.390870 0.920446i \(-0.627826\pi\)
−0.390870 + 0.920446i \(0.627826\pi\)
\(758\) 657964. 1.14515
\(759\) 102362.i 0.177686i
\(760\) −212967. 47134.7i −0.368711 0.0816044i
\(761\) 527400. 0.910690 0.455345 0.890315i \(-0.349516\pi\)
0.455345 + 0.890315i \(0.349516\pi\)
\(762\) 209552.i 0.360896i
\(763\) 731553.i 1.25660i
\(764\) 311671. 0.533960
\(765\) −23931.0 −0.0408919
\(766\) −147173. −0.250825
\(767\) 57453.4 0.0976619
\(768\) 27295.3i 0.0462770i
\(769\) 549287. 0.928852 0.464426 0.885612i \(-0.346261\pi\)
0.464426 + 0.885612i \(0.346261\pi\)
\(770\) 97486.7i 0.164424i
\(771\) −7700.71 −0.0129545
\(772\) 344465.i 0.577977i
\(773\) 1.03569e6i 1.73329i −0.498927 0.866644i \(-0.666272\pi\)
0.498927 0.866644i \(-0.333728\pi\)
\(774\) 263433.i 0.439732i
\(775\) 80347.2i 0.133773i
\(776\) −113671. −0.188766
\(777\) −111442. −0.184590
\(778\) 163165.i 0.269568i
\(779\) 18240.1 + 4036.98i 0.0300575 + 0.00665244i
\(780\) −75808.4 −0.124603
\(781\) 145668.i 0.238815i
\(782\) 42411.2i 0.0693533i
\(783\) 1.05473e6 1.72035
\(784\) 15730.5 0.0255923
\(785\) 1.23485e6 2.00390
\(786\) 4209.15 0.00681317
\(787\) 1.04115e6i