Properties

Label 38.5.b.a.37.7
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 37.7
Root \(6.38941i\) of defining polynomial
Character \(\chi\) \(=\) 38.37
Dual form 38.5.b.a.37.2

$q$-expansion

\(f(q)\) \(=\) \(q+2.82843i q^{2} +7.80363i q^{3} -8.00000 q^{4} -33.0971 q^{5} -22.0720 q^{6} +16.0783 q^{7} -22.6274i q^{8} +20.1034 q^{9} +O(q^{10})\) \(q+2.82843i q^{2} +7.80363i q^{3} -8.00000 q^{4} -33.0971 q^{5} -22.0720 q^{6} +16.0783 q^{7} -22.6274i q^{8} +20.1034 q^{9} -93.6127i q^{10} -215.592 q^{11} -62.4290i q^{12} +281.497i q^{13} +45.4764i q^{14} -258.277i q^{15} +64.0000 q^{16} +226.582 q^{17} +56.8610i q^{18} +(13.9969 + 360.729i) q^{19} +264.777 q^{20} +125.469i q^{21} -609.786i q^{22} +414.609 q^{23} +176.576 q^{24} +470.416 q^{25} -796.195 q^{26} +788.973i q^{27} -128.627 q^{28} -606.612i q^{29} +730.518 q^{30} +478.655i q^{31} +181.019i q^{32} -1682.40i q^{33} +640.871i q^{34} -532.145 q^{35} -160.827 q^{36} +104.604i q^{37} +(-1020.29 + 39.5893i) q^{38} -2196.70 q^{39} +748.901i q^{40} -1891.12i q^{41} -354.881 q^{42} +315.912 q^{43} +1724.73 q^{44} -665.364 q^{45} +1172.69i q^{46} -474.327 q^{47} +499.432i q^{48} -2142.49 q^{49} +1330.54i q^{50} +1768.16i q^{51} -2251.98i q^{52} +774.381i q^{53} -2231.55 q^{54} +7135.46 q^{55} -363.811i q^{56} +(-2814.99 + 109.227i) q^{57} +1715.76 q^{58} -567.212i q^{59} +2066.22i q^{60} +4799.51 q^{61} -1353.84 q^{62} +323.229 q^{63} -512.000 q^{64} -9316.74i q^{65} +4758.54 q^{66} -4464.01i q^{67} -1812.66 q^{68} +3235.45i q^{69} -1505.13i q^{70} +7636.34i q^{71} -454.888i q^{72} +8396.65 q^{73} -295.866 q^{74} +3670.95i q^{75} +(-111.975 - 2885.83i) q^{76} -3466.35 q^{77} -6213.21i q^{78} +9706.71i q^{79} -2118.21 q^{80} -4528.48 q^{81} +5348.89 q^{82} -10589.4 q^{83} -1003.75i q^{84} -7499.21 q^{85} +893.533i q^{86} +4733.77 q^{87} +4878.29i q^{88} +10281.7i q^{89} -1881.93i q^{90} +4526.01i q^{91} -3316.87 q^{92} -3735.24 q^{93} -1341.60i q^{94} +(-463.257 - 11939.1i) q^{95} -1412.61 q^{96} -15477.3i q^{97} -6059.87i q^{98} -4334.13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 64q^{4} + 18q^{5} - 32q^{6} - 162q^{7} - 268q^{9} + O(q^{10}) \) \( 8q - 64q^{4} + 18q^{5} - 32q^{6} - 162q^{7} - 268q^{9} - 6q^{11} + 512q^{16} + 510q^{17} - 12q^{19} - 144q^{20} - 396q^{23} + 256q^{24} + 3458q^{25} - 192q^{26} + 1296q^{28} - 2752q^{30} + 1002q^{35} + 2144q^{36} - 3216q^{38} - 6588q^{39} + 1376q^{42} - 8654q^{43} + 48q^{44} - 10334q^{45} + 3210q^{47} + 9222q^{49} + 9088q^{54} + 17146q^{55} - 14076q^{57} - 960q^{58} + 1314q^{61} - 15168q^{62} + 29938q^{63} - 4096q^{64} + 4928q^{66} - 4080q^{68} + 23398q^{73} + 13152q^{74} + 96q^{76} - 44622q^{77} + 1152q^{80} - 20368q^{81} + 16512q^{82} - 10440q^{83} + 21274q^{85} - 14316q^{87} + 3168q^{92} + 19416q^{93} - 34686q^{95} - 2048q^{96} - 56798q^{99} + O(q^{100}) \)

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
\(3\) 7.80363i 0.867070i 0.901137 + 0.433535i \(0.142734\pi\)
−0.901137 + 0.433535i \(0.857266\pi\)
\(4\) −8.00000 −0.500000
\(5\) −33.0971 −1.32388 −0.661941 0.749556i \(-0.730267\pi\)
−0.661941 + 0.749556i \(0.730267\pi\)
\(6\) −22.0720 −0.613111
\(7\) 16.0783 0.328129 0.164064 0.986450i \(-0.447539\pi\)
0.164064 + 0.986450i \(0.447539\pi\)
\(8\) 22.6274i 0.353553i
\(9\) 20.1034 0.248190
\(10\) 93.6127i 0.936127i
\(11\) −215.592 −1.78175 −0.890875 0.454248i \(-0.849908\pi\)
−0.890875 + 0.454248i \(0.849908\pi\)
\(12\) 62.4290i 0.433535i
\(13\) 281.497i 1.66567i 0.553525 + 0.832833i \(0.313282\pi\)
−0.553525 + 0.832833i \(0.686718\pi\)
\(14\) 45.4764i 0.232022i
\(15\) 258.277i 1.14790i
\(16\) 64.0000 0.250000
\(17\) 226.582 0.784022 0.392011 0.919961i \(-0.371780\pi\)
0.392011 + 0.919961i \(0.371780\pi\)
\(18\) 56.8610i 0.175497i
\(19\) 13.9969 + 360.729i 0.0387726 + 0.999248i
\(20\) 264.777 0.661941
\(21\) 125.469i 0.284511i
\(22\) 609.786i 1.25989i
\(23\) 414.609 0.783760 0.391880 0.920016i \(-0.371825\pi\)
0.391880 + 0.920016i \(0.371825\pi\)
\(24\) 176.576 0.306555
\(25\) 470.416 0.752666
\(26\) −796.195 −1.17780
\(27\) 788.973i 1.08227i
\(28\) −128.627 −0.164064
\(29\) 606.612i 0.721298i −0.932702 0.360649i \(-0.882555\pi\)
0.932702 0.360649i \(-0.117445\pi\)
\(30\) 730.518 0.811687
\(31\) 478.655i 0.498080i 0.968493 + 0.249040i \(0.0801151\pi\)
−0.968493 + 0.249040i \(0.919885\pi\)
\(32\) 181.019i 0.176777i
\(33\) 1682.40i 1.54490i
\(34\) 640.871i 0.554387i
\(35\) −532.145 −0.434404
\(36\) −160.827 −0.124095
\(37\) 104.604i 0.0764094i 0.999270 + 0.0382047i \(0.0121639\pi\)
−0.999270 + 0.0382047i \(0.987836\pi\)
\(38\) −1020.29 + 39.5893i −0.706575 + 0.0274164i
\(39\) −2196.70 −1.44425
\(40\) 748.901i 0.468063i
\(41\) 1891.12i 1.12500i −0.826799 0.562498i \(-0.809841\pi\)
0.826799 0.562498i \(-0.190159\pi\)
\(42\) −354.881 −0.201179
\(43\) 315.912 0.170855 0.0854277 0.996344i \(-0.472774\pi\)
0.0854277 + 0.996344i \(0.472774\pi\)
\(44\) 1724.73 0.890875
\(45\) −665.364 −0.328575
\(46\) 1172.69i 0.554202i
\(47\) −474.327 −0.214725 −0.107362 0.994220i \(-0.534241\pi\)
−0.107362 + 0.994220i \(0.534241\pi\)
\(48\) 499.432i 0.216767i
\(49\) −2142.49 −0.892331
\(50\) 1330.54i 0.532215i
\(51\) 1768.16i 0.679801i
\(52\) 2251.98i 0.832833i
\(53\) 774.381i 0.275679i 0.990455 + 0.137839i \(0.0440158\pi\)
−0.990455 + 0.137839i \(0.955984\pi\)
\(54\) −2231.55 −0.765279
\(55\) 7135.46 2.35883
\(56\) 363.811i 0.116011i
\(57\) −2814.99 + 109.227i −0.866418 + 0.0336186i
\(58\) 1715.76 0.510035
\(59\) 567.212i 0.162945i −0.996676 0.0814725i \(-0.974038\pi\)
0.996676 0.0814725i \(-0.0259623\pi\)
\(60\) 2066.22i 0.573949i
\(61\) 4799.51 1.28984 0.644922 0.764248i \(-0.276890\pi\)
0.644922 + 0.764248i \(0.276890\pi\)
\(62\) −1353.84 −0.352196
\(63\) 323.229 0.0814384
\(64\) −512.000 −0.125000
\(65\) 9316.74i 2.20515i
\(66\) 4758.54 1.09241
\(67\) 4464.01i 0.994433i −0.867627 0.497216i \(-0.834356\pi\)
0.867627 0.497216i \(-0.165644\pi\)
\(68\) −1812.66 −0.392011
\(69\) 3235.45i 0.679575i
\(70\) 1505.13i 0.307170i
\(71\) 7636.34i 1.51485i 0.652924 + 0.757423i \(0.273542\pi\)
−0.652924 + 0.757423i \(0.726458\pi\)
\(72\) 454.888i 0.0877484i
\(73\) 8396.65 1.57565 0.787826 0.615898i \(-0.211207\pi\)
0.787826 + 0.615898i \(0.211207\pi\)
\(74\) −295.866 −0.0540296
\(75\) 3670.95i 0.652614i
\(76\) −111.975 2885.83i −0.0193863 0.499624i
\(77\) −3466.35 −0.584644
\(78\) 6213.21i 1.02124i
\(79\) 9706.71i 1.55531i 0.628689 + 0.777657i \(0.283592\pi\)
−0.628689 + 0.777657i \(0.716408\pi\)
\(80\) −2118.21 −0.330971
\(81\) −4528.48 −0.690212
\(82\) 5348.89 0.795492
\(83\) −10589.4 −1.53715 −0.768575 0.639760i \(-0.779034\pi\)
−0.768575 + 0.639760i \(0.779034\pi\)
\(84\) 1003.75i 0.142255i
\(85\) −7499.21 −1.03795
\(86\) 893.533i 0.120813i
\(87\) 4733.77 0.625416
\(88\) 4878.29i 0.629944i
\(89\) 10281.7i 1.29804i 0.760773 + 0.649018i \(0.224820\pi\)
−0.760773 + 0.649018i \(0.775180\pi\)
\(90\) 1881.93i 0.232337i
\(91\) 4526.01i 0.546553i
\(92\) −3316.87 −0.391880
\(93\) −3735.24 −0.431870
\(94\) 1341.60i 0.151833i
\(95\) −463.257 11939.1i −0.0513304 1.32289i
\(96\) −1412.61 −0.153278
\(97\) 15477.3i 1.64494i −0.568806 0.822472i \(-0.692594\pi\)
0.568806 0.822472i \(-0.307406\pi\)
\(98\) 6059.87i 0.630974i
\(99\) −4334.13 −0.442213
\(100\) −3763.33 −0.376333
\(101\) 10464.5 1.02583 0.512914 0.858440i \(-0.328566\pi\)
0.512914 + 0.858440i \(0.328566\pi\)
\(102\) −5001.12 −0.480692
\(103\) 3224.53i 0.303943i 0.988385 + 0.151972i \(0.0485622\pi\)
−0.988385 + 0.151972i \(0.951438\pi\)
\(104\) 6369.56 0.588902
\(105\) 4152.66i 0.376659i
\(106\) −2190.28 −0.194934
\(107\) 7740.93i 0.676123i 0.941124 + 0.338061i \(0.109771\pi\)
−0.941124 + 0.338061i \(0.890229\pi\)
\(108\) 6311.79i 0.541134i
\(109\) 12613.1i 1.06162i −0.847492 0.530809i \(-0.821888\pi\)
0.847492 0.530809i \(-0.178112\pi\)
\(110\) 20182.1i 1.66794i
\(111\) −816.294 −0.0662523
\(112\) 1029.01 0.0820322
\(113\) 900.876i 0.0705518i 0.999378 + 0.0352759i \(0.0112310\pi\)
−0.999378 + 0.0352759i \(0.988769\pi\)
\(114\) −308.940 7962.00i −0.0237719 0.612650i
\(115\) −13722.3 −1.03761
\(116\) 4852.89i 0.360649i
\(117\) 5659.06i 0.413402i
\(118\) 1604.32 0.115220
\(119\) 3643.06 0.257260
\(120\) −5844.15 −0.405843
\(121\) 31838.8 2.17464
\(122\) 13575.1i 0.912058i
\(123\) 14757.6 0.975449
\(124\) 3829.24i 0.249040i
\(125\) 5116.28 0.327442
\(126\) 914.229i 0.0575856i
\(127\) 16688.1i 1.03467i 0.855784 + 0.517334i \(0.173075\pi\)
−0.855784 + 0.517334i \(0.826925\pi\)
\(128\) 1448.15i 0.0883883i
\(129\) 2465.26i 0.148144i
\(130\) 26351.7 1.55927
\(131\) 9365.24 0.545728 0.272864 0.962053i \(-0.412029\pi\)
0.272864 + 0.962053i \(0.412029\pi\)
\(132\) 13459.2i 0.772451i
\(133\) 225.047 + 5799.91i 0.0127224 + 0.327882i
\(134\) 12626.1 0.703170
\(135\) 26112.7i 1.43280i
\(136\) 5126.97i 0.277194i
\(137\) −36021.1 −1.91918 −0.959591 0.281399i \(-0.909201\pi\)
−0.959591 + 0.281399i \(0.909201\pi\)
\(138\) −9151.25 −0.480532
\(139\) −10371.8 −0.536813 −0.268406 0.963306i \(-0.586497\pi\)
−0.268406 + 0.963306i \(0.586497\pi\)
\(140\) 4257.16 0.217202
\(141\) 3701.47i 0.186181i
\(142\) −21598.8 −1.07116
\(143\) 60688.6i 2.96780i
\(144\) 1286.62 0.0620475
\(145\) 20077.1i 0.954914i
\(146\) 23749.3i 1.11415i
\(147\) 16719.2i 0.773714i
\(148\) 836.835i 0.0382047i
\(149\) 1353.29 0.0609562 0.0304781 0.999535i \(-0.490297\pi\)
0.0304781 + 0.999535i \(0.490297\pi\)
\(150\) −10383.0 −0.461468
\(151\) 29132.7i 1.27769i 0.769334 + 0.638847i \(0.220588\pi\)
−0.769334 + 0.638847i \(0.779412\pi\)
\(152\) 8162.36 316.714i 0.353288 0.0137082i
\(153\) 4555.07 0.194586
\(154\) 9804.33i 0.413406i
\(155\) 15842.1i 0.659399i
\(156\) 17573.6 0.722124
\(157\) −11934.0 −0.484156 −0.242078 0.970257i \(-0.577829\pi\)
−0.242078 + 0.970257i \(0.577829\pi\)
\(158\) −27454.7 −1.09977
\(159\) −6042.98 −0.239033
\(160\) 5991.21i 0.234032i
\(161\) 6666.22 0.257174
\(162\) 12808.5i 0.488053i
\(163\) 13818.7 0.520108 0.260054 0.965594i \(-0.416260\pi\)
0.260054 + 0.965594i \(0.416260\pi\)
\(164\) 15128.9i 0.562498i
\(165\) 55682.5i 2.04527i
\(166\) 29951.4i 1.08693i
\(167\) 10267.5i 0.368157i 0.982912 + 0.184079i \(0.0589301\pi\)
−0.982912 + 0.184079i \(0.941070\pi\)
\(168\) 2839.04 0.100590
\(169\) −50679.8 −1.77444
\(170\) 21211.0i 0.733943i
\(171\) 281.386 + 7251.87i 0.00962298 + 0.248003i
\(172\) −2527.29 −0.0854277
\(173\) 29001.7i 0.969015i 0.874787 + 0.484508i \(0.161001\pi\)
−0.874787 + 0.484508i \(0.838999\pi\)
\(174\) 13389.1i 0.442236i
\(175\) 7563.50 0.246971
\(176\) −13797.9 −0.445438
\(177\) 4426.31 0.141285
\(178\) −29081.2 −0.917850
\(179\) 25479.5i 0.795217i −0.917555 0.397608i \(-0.869840\pi\)
0.917555 0.397608i \(-0.130160\pi\)
\(180\) 5322.91 0.164287
\(181\) 31158.1i 0.951073i −0.879696 0.475536i \(-0.842254\pi\)
0.879696 0.475536i \(-0.157746\pi\)
\(182\) −12801.5 −0.386471
\(183\) 37453.6i 1.11839i
\(184\) 9381.53i 0.277101i
\(185\) 3462.10i 0.101157i
\(186\) 10564.9i 0.305378i
\(187\) −48849.3 −1.39693
\(188\) 3794.62 0.107362
\(189\) 12685.4i 0.355123i
\(190\) 33768.8 1310.29i 0.935423 0.0362961i
\(191\) 17888.8 0.490359 0.245179 0.969478i \(-0.421153\pi\)
0.245179 + 0.969478i \(0.421153\pi\)
\(192\) 3995.46i 0.108384i
\(193\) 784.195i 0.0210528i −0.999945 0.0105264i \(-0.996649\pi\)
0.999945 0.0105264i \(-0.00335071\pi\)
\(194\) 43776.4 1.16315
\(195\) 72704.4 1.91202
\(196\) 17139.9 0.446166
\(197\) 42272.4 1.08924 0.544621 0.838682i \(-0.316673\pi\)
0.544621 + 0.838682i \(0.316673\pi\)
\(198\) 12258.8i 0.312692i
\(199\) −15361.7 −0.387911 −0.193955 0.981010i \(-0.562132\pi\)
−0.193955 + 0.981010i \(0.562132\pi\)
\(200\) 10644.3i 0.266108i
\(201\) 34835.5 0.862243
\(202\) 29598.0i 0.725369i
\(203\) 9753.30i 0.236679i
\(204\) 14145.3i 0.339901i
\(205\) 62590.4i 1.48936i
\(206\) −9120.36 −0.214920
\(207\) 8335.05 0.194521
\(208\) 18015.8i 0.416416i
\(209\) −3017.62 77770.1i −0.0690831 1.78041i
\(210\) 11745.5 0.266338
\(211\) 36036.6i 0.809429i −0.914443 0.404714i \(-0.867371\pi\)
0.914443 0.404714i \(-0.132629\pi\)
\(212\) 6195.05i 0.137839i
\(213\) −59591.2 −1.31348
\(214\) −21894.7 −0.478091
\(215\) −10455.8 −0.226193
\(216\) 17852.4 0.382639
\(217\) 7695.96i 0.163434i
\(218\) 35675.2 0.750677
\(219\) 65524.3i 1.36620i
\(220\) −57083.7 −1.17941
\(221\) 63782.3i 1.30592i
\(222\) 2308.83i 0.0468474i
\(223\) 44099.4i 0.886795i −0.896325 0.443398i \(-0.853773\pi\)
0.896325 0.443398i \(-0.146227\pi\)
\(224\) 2910.49i 0.0580056i
\(225\) 9456.96 0.186804
\(226\) −2548.06 −0.0498876
\(227\) 34866.5i 0.676638i −0.941032 0.338319i \(-0.890142\pi\)
0.941032 0.338319i \(-0.109858\pi\)
\(228\) 22519.9 873.814i 0.433209 0.0168093i
\(229\) 26085.5 0.497425 0.248712 0.968577i \(-0.419993\pi\)
0.248712 + 0.968577i \(0.419993\pi\)
\(230\) 38812.7i 0.733699i
\(231\) 27050.1i 0.506927i
\(232\) −13726.1 −0.255017
\(233\) 75466.8 1.39009 0.695047 0.718964i \(-0.255383\pi\)
0.695047 + 0.718964i \(0.255383\pi\)
\(234\) −16006.2 −0.292319
\(235\) 15698.8 0.284271
\(236\) 4537.69i 0.0814725i
\(237\) −75747.5 −1.34856
\(238\) 10304.1i 0.181910i
\(239\) −42891.8 −0.750895 −0.375447 0.926844i \(-0.622511\pi\)
−0.375447 + 0.926844i \(0.622511\pi\)
\(240\) 16529.7i 0.286975i
\(241\) 15629.3i 0.269095i −0.990907 0.134547i \(-0.957042\pi\)
0.990907 0.134547i \(-0.0429580\pi\)
\(242\) 90053.8i 1.53770i
\(243\) 28568.3i 0.483806i
\(244\) −38396.1 −0.644922
\(245\) 70910.1 1.18134
\(246\) 41740.7i 0.689747i
\(247\) −101544. + 3940.10i −1.66441 + 0.0645822i
\(248\) 10830.7 0.176098
\(249\) 82635.9i 1.33282i
\(250\) 14471.0i 0.231536i
\(251\) 76998.8 1.22218 0.611092 0.791560i \(-0.290731\pi\)
0.611092 + 0.791560i \(0.290731\pi\)
\(252\) −2585.83 −0.0407192
\(253\) −89386.3 −1.39646
\(254\) −47201.2 −0.731620
\(255\) 58521.0i 0.899977i
\(256\) 4096.00 0.0625000
\(257\) 8903.45i 0.134801i −0.997726 0.0674003i \(-0.978530\pi\)
0.997726 0.0674003i \(-0.0214705\pi\)
\(258\) −6972.80 −0.104753
\(259\) 1681.86i 0.0250721i
\(260\) 74533.9i 1.10257i
\(261\) 12195.0i 0.179019i
\(262\) 26488.9i 0.385888i
\(263\) −79232.7 −1.14549 −0.572747 0.819732i \(-0.694122\pi\)
−0.572747 + 0.819732i \(0.694122\pi\)
\(264\) −38068.3 −0.546205
\(265\) 25629.8i 0.364966i
\(266\) −16404.6 + 636.529i −0.231848 + 0.00899611i
\(267\) −80234.9 −1.12549
\(268\) 35712.1i 0.497216i
\(269\) 132817.i 1.83548i 0.397177 + 0.917742i \(0.369990\pi\)
−0.397177 + 0.917742i \(0.630010\pi\)
\(270\) 73857.9 1.01314
\(271\) 73016.0 0.994213 0.497106 0.867690i \(-0.334396\pi\)
0.497106 + 0.867690i \(0.334396\pi\)
\(272\) 14501.3 0.196005
\(273\) −35319.3 −0.473900
\(274\) 101883.i 1.35707i
\(275\) −101418. −1.34106
\(276\) 25883.6i 0.339787i
\(277\) 66280.9 0.863831 0.431916 0.901914i \(-0.357838\pi\)
0.431916 + 0.901914i \(0.357838\pi\)
\(278\) 29335.8i 0.379584i
\(279\) 9622.59i 0.123619i
\(280\) 12041.1i 0.153585i
\(281\) 112860.i 1.42932i −0.699473 0.714659i \(-0.746582\pi\)
0.699473 0.714659i \(-0.253418\pi\)
\(282\) 10469.3 0.131650
\(283\) 80766.6 1.00846 0.504230 0.863569i \(-0.331776\pi\)
0.504230 + 0.863569i \(0.331776\pi\)
\(284\) 61090.7i 0.757423i
\(285\) 93168.0 3615.08i 1.14704 0.0445070i
\(286\) 171653. 2.09855
\(287\) 30406.0i 0.369144i
\(288\) 3639.10i 0.0438742i
\(289\) −32181.5 −0.385310
\(290\) −56786.5 −0.675226
\(291\) 120779. 1.42628
\(292\) −67173.2 −0.787826
\(293\) 133666.i 1.55699i 0.627653 + 0.778493i \(0.284016\pi\)
−0.627653 + 0.778493i \(0.715984\pi\)
\(294\) 47289.0 0.547098
\(295\) 18773.0i 0.215720i
\(296\) 2366.93 0.0270148
\(297\) 170096.i 1.92833i
\(298\) 3827.68i 0.0431025i
\(299\) 116711.i 1.30548i
\(300\) 29367.6i 0.326307i
\(301\) 5079.33 0.0560626
\(302\) −82399.8 −0.903467
\(303\) 81660.8i 0.889464i
\(304\) 895.803 + 23086.6i 0.00969316 + 0.249812i
\(305\) −158850. −1.70760
\(306\) 12883.7i 0.137593i
\(307\) 100857.i 1.07011i −0.844816 0.535057i \(-0.820290\pi\)
0.844816 0.535057i \(-0.179710\pi\)
\(308\) 27730.8 0.292322
\(309\) −25163.1 −0.263540
\(310\) 44808.1 0.466266
\(311\) 121531. 1.25651 0.628254 0.778009i \(-0.283770\pi\)
0.628254 + 0.778009i \(0.283770\pi\)
\(312\) 49705.7i 0.510619i
\(313\) 189932. 1.93869 0.969346 0.245700i \(-0.0790180\pi\)
0.969346 + 0.245700i \(0.0790180\pi\)
\(314\) 33754.3i 0.342350i
\(315\) −10697.9 −0.107815
\(316\) 77653.7i 0.777657i
\(317\) 67336.1i 0.670085i −0.942203 0.335042i \(-0.891249\pi\)
0.942203 0.335042i \(-0.108751\pi\)
\(318\) 17092.1i 0.169022i
\(319\) 130781.i 1.28517i
\(320\) 16945.7 0.165485
\(321\) −60407.3 −0.586246
\(322\) 18854.9i 0.181850i
\(323\) 3171.45 + 81734.7i 0.0303986 + 0.783432i
\(324\) 36227.8 0.345106
\(325\) 132421.i 1.25369i
\(326\) 39085.3i 0.367772i
\(327\) 98427.7 0.920496
\(328\) −42791.1 −0.397746
\(329\) −7626.38 −0.0704574
\(330\) −157494. −1.44622
\(331\) 154310.i 1.40844i 0.709984 + 0.704218i \(0.248702\pi\)
−0.709984 + 0.704218i \(0.751298\pi\)
\(332\) 84715.4 0.768575
\(333\) 2102.90i 0.0189640i
\(334\) −29041.0 −0.260327
\(335\) 147746.i 1.31651i
\(336\) 8030.03i 0.0711277i
\(337\) 127543.i 1.12304i −0.827463 0.561521i \(-0.810217\pi\)
0.827463 0.561521i \(-0.189783\pi\)
\(338\) 143344.i 1.25472i
\(339\) −7030.10 −0.0611733
\(340\) 59993.7 0.518976
\(341\) 103194.i 0.887454i
\(342\) −20511.4 + 795.879i −0.175365 + 0.00680447i
\(343\) −73051.6 −0.620929
\(344\) 7148.26i 0.0604065i
\(345\) 107084.i 0.899677i
\(346\) −82029.1 −0.685197
\(347\) −71084.5 −0.590359 −0.295179 0.955442i \(-0.595379\pi\)
−0.295179 + 0.955442i \(0.595379\pi\)
\(348\) −37870.2 −0.312708
\(349\) 83601.6 0.686378 0.343189 0.939266i \(-0.388493\pi\)
0.343189 + 0.939266i \(0.388493\pi\)
\(350\) 21392.8i 0.174635i
\(351\) −222094. −1.80270
\(352\) 39026.3i 0.314972i
\(353\) −40368.7 −0.323963 −0.161981 0.986794i \(-0.551788\pi\)
−0.161981 + 0.986794i \(0.551788\pi\)
\(354\) 12519.5i 0.0999034i
\(355\) 252740.i 2.00548i
\(356\) 82254.0i 0.649018i
\(357\) 28429.1i 0.223063i
\(358\) 72067.0 0.562303
\(359\) 143079. 1.11016 0.555081 0.831796i \(-0.312687\pi\)
0.555081 + 0.831796i \(0.312687\pi\)
\(360\) 15055.5i 0.116169i
\(361\) −129929. + 10098.2i −0.996993 + 0.0774869i
\(362\) 88128.4 0.672510
\(363\) 248458.i 1.88556i
\(364\) 36208.0i 0.273277i
\(365\) −277904. −2.08598
\(366\) −105935. −0.790818
\(367\) −30831.7 −0.228910 −0.114455 0.993428i \(-0.536512\pi\)
−0.114455 + 0.993428i \(0.536512\pi\)
\(368\) 26535.0 0.195940
\(369\) 38017.9i 0.279213i
\(370\) 9792.30 0.0715288
\(371\) 12450.8i 0.0904582i
\(372\) 29882.0 0.215935
\(373\) 199882.i 1.43666i −0.695701 0.718332i \(-0.744906\pi\)
0.695701 0.718332i \(-0.255094\pi\)
\(374\) 138167.i 0.987779i
\(375\) 39925.5i 0.283915i
\(376\) 10732.8i 0.0759167i
\(377\) 170760. 1.20144
\(378\) −35879.6 −0.251110
\(379\) 49499.6i 0.344606i 0.985044 + 0.172303i \(0.0551209\pi\)
−0.985044 + 0.172303i \(0.944879\pi\)
\(380\) 3706.06 + 95512.5i 0.0256652 + 0.661444i
\(381\) −130228. −0.897129
\(382\) 50597.1i 0.346736i
\(383\) 49593.2i 0.338084i −0.985609 0.169042i \(-0.945933\pi\)
0.985609 0.169042i \(-0.0540674\pi\)
\(384\) 11300.9 0.0766389
\(385\) 114726. 0.774000
\(386\) 2218.04 0.0148866
\(387\) 6350.90 0.0424046
\(388\) 123818.i 0.822472i
\(389\) −15826.9 −0.104592 −0.0522958 0.998632i \(-0.516654\pi\)
−0.0522958 + 0.998632i \(0.516654\pi\)
\(390\) 205639.i 1.35200i
\(391\) 93943.1 0.614485
\(392\) 48479.0i 0.315487i
\(393\) 73082.8i 0.473184i
\(394\) 119564.i 0.770211i
\(395\) 321264.i 2.05905i
\(396\) 34673.0 0.221106
\(397\) −2861.99 −0.0181588 −0.00907939 0.999959i \(-0.502890\pi\)
−0.00907939 + 0.999959i \(0.502890\pi\)
\(398\) 43449.3i 0.274294i
\(399\) −45260.3 + 1756.18i −0.284297 + 0.0110312i
\(400\) 30106.6 0.188166
\(401\) 226034.i 1.40567i 0.711351 + 0.702837i \(0.248084\pi\)
−0.711351 + 0.702837i \(0.751916\pi\)
\(402\) 98529.6i 0.609698i
\(403\) −134740. −0.829634
\(404\) −83715.7 −0.512914
\(405\) 149879. 0.913759
\(406\) 27586.5 0.167357
\(407\) 22551.9i 0.136142i
\(408\) 40009.0 0.240346
\(409\) 300321.i 1.79531i 0.440700 + 0.897655i \(0.354730\pi\)
−0.440700 + 0.897655i \(0.645270\pi\)
\(410\) −177032. −1.05314
\(411\) 281095.i 1.66406i
\(412\) 25796.3i 0.151972i
\(413\) 9119.81i 0.0534670i
\(414\) 23575.1i 0.137547i
\(415\) 350479. 2.03501
\(416\) −50956.5 −0.294451
\(417\) 80937.4i 0.465454i
\(418\) 219967. 8535.12i 1.25894 0.0488492i
\(419\) −88915.8 −0.506467 −0.253233 0.967405i \(-0.581494\pi\)
−0.253233 + 0.967405i \(0.581494\pi\)
\(420\) 33221.3i 0.188329i
\(421\) 52919.8i 0.298575i 0.988794 + 0.149288i \(0.0476980\pi\)
−0.988794 + 0.149288i \(0.952302\pi\)
\(422\) 101927. 0.572353
\(423\) −9535.59 −0.0532926
\(424\) 17522.3 0.0974671
\(425\) 106588. 0.590106
\(426\) 168549.i 0.928769i
\(427\) 77168.1 0.423235
\(428\) 61927.4i 0.338061i
\(429\) 473591. 2.57329
\(430\) 29573.3i 0.159942i
\(431\) 18064.2i 0.0972442i −0.998817 0.0486221i \(-0.984517\pi\)
0.998817 0.0486221i \(-0.0154830\pi\)
\(432\) 50494.3i 0.270567i
\(433\) 188974.i 1.00792i −0.863726 0.503961i \(-0.831875\pi\)
0.863726 0.503961i \(-0.168125\pi\)
\(434\) −21767.5 −0.115566
\(435\) −156674. −0.827977
\(436\) 100905.i 0.530809i
\(437\) 5803.25 + 149561.i 0.0303884 + 0.783171i
\(438\) −185331. −0.966049
\(439\) 249410.i 1.29415i −0.762427 0.647074i \(-0.775992\pi\)
0.762427 0.647074i \(-0.224008\pi\)
\(440\) 161457.i 0.833972i
\(441\) −43071.3 −0.221468
\(442\) −180404. −0.923423
\(443\) 43050.1 0.219365 0.109682 0.993967i \(-0.465017\pi\)
0.109682 + 0.993967i \(0.465017\pi\)
\(444\) 6530.35 0.0331261
\(445\) 340296.i 1.71845i
\(446\) 124732. 0.627059
\(447\) 10560.6i 0.0528533i
\(448\) −8232.10 −0.0410161
\(449\) 19223.8i 0.0953556i −0.998863 0.0476778i \(-0.984818\pi\)
0.998863 0.0476778i \(-0.0151821\pi\)
\(450\) 26748.3i 0.132090i
\(451\) 407709.i 2.00446i
\(452\) 7207.01i 0.0352759i
\(453\) −227341. −1.10785
\(454\) 98617.2 0.478455
\(455\) 149798.i 0.723572i
\(456\) 2471.52 + 63696.0i 0.0118860 + 0.306325i
\(457\) 38484.7 0.184271 0.0921353 0.995747i \(-0.470631\pi\)
0.0921353 + 0.995747i \(0.470631\pi\)
\(458\) 73780.8i 0.351732i
\(459\) 178767.i 0.848521i
\(460\) 109779. 0.518803
\(461\) −203940. −0.959623 −0.479812 0.877371i \(-0.659295\pi\)
−0.479812 + 0.877371i \(0.659295\pi\)
\(462\) 76509.3 0.358452
\(463\) −203200. −0.947900 −0.473950 0.880552i \(-0.657172\pi\)
−0.473950 + 0.880552i \(0.657172\pi\)
\(464\) 38823.2i 0.180325i
\(465\) 123626. 0.571745
\(466\) 213452.i 0.982945i
\(467\) −121674. −0.557912 −0.278956 0.960304i \(-0.589988\pi\)
−0.278956 + 0.960304i \(0.589988\pi\)
\(468\) 45272.4i 0.206701i
\(469\) 71773.8i 0.326302i
\(470\) 44403.0i 0.201010i
\(471\) 93128.2i 0.419797i
\(472\) −12834.5 −0.0576098
\(473\) −68108.0 −0.304422
\(474\) 214246.i 0.953579i
\(475\) 6584.37 + 169693.i 0.0291828 + 0.752100i
\(476\) −29144.5 −0.128630
\(477\) 15567.7i 0.0684207i
\(478\) 121316.i 0.530963i
\(479\) −208037. −0.906711 −0.453355 0.891330i \(-0.649773\pi\)
−0.453355 + 0.891330i \(0.649773\pi\)
\(480\) 46753.2 0.202922
\(481\) −29445.9 −0.127272
\(482\) 44206.3 0.190279
\(483\) 52020.7i 0.222988i
\(484\) −254711. −1.08732
\(485\) 512253.i 2.17771i
\(486\) −80803.3 −0.342103
\(487\) 47417.7i 0.199932i 0.994991 + 0.0999660i \(0.0318734\pi\)
−0.994991 + 0.0999660i \(0.968127\pi\)
\(488\) 108601.i 0.456029i
\(489\) 107836.i 0.450970i
\(490\) 200564.i 0.835335i
\(491\) −218823. −0.907676 −0.453838 0.891084i \(-0.649946\pi\)
−0.453838 + 0.891084i \(0.649946\pi\)
\(492\) −118061. −0.487725
\(493\) 137447.i 0.565513i
\(494\) −11144.3 287210.i −0.0456665 1.17692i
\(495\) 143447. 0.585438
\(496\) 30633.9i 0.124520i
\(497\) 122780.i 0.497065i
\(498\) 233730. 0.942443
\(499\) 147213. 0.591214 0.295607 0.955310i \(-0.404478\pi\)
0.295607 + 0.955310i \(0.404478\pi\)
\(500\) −40930.2 −0.163721
\(501\) −80124.1 −0.319218
\(502\) 217786.i 0.864215i
\(503\) 189477. 0.748895 0.374448 0.927248i \(-0.377832\pi\)
0.374448 + 0.927248i \(0.377832\pi\)
\(504\) 7313.83i 0.0287928i
\(505\) −346343. −1.35807
\(506\) 252823.i 0.987450i
\(507\) 395486.i 1.53856i
\(508\) 133505.i 0.517334i
\(509\) 117829.i 0.454797i 0.973802 + 0.227398i \(0.0730220\pi\)
−0.973802 + 0.227398i \(0.926978\pi\)
\(510\) 165522. 0.636380
\(511\) 135004. 0.517017
\(512\) 11585.2i 0.0441942i
\(513\) −284605. + 11043.2i −1.08145 + 0.0419624i
\(514\) 25182.8 0.0953185
\(515\) 106723.i 0.402385i
\(516\) 19722.1i 0.0740718i
\(517\) 102261. 0.382586
\(518\) −4757.03 −0.0177287
\(519\) −226318. −0.840204
\(520\) −210814. −0.779637
\(521\) 254449.i 0.937402i 0.883357 + 0.468701i \(0.155278\pi\)
−0.883357 + 0.468701i \(0.844722\pi\)
\(522\) 34492.6 0.126586
\(523\) 33047.5i 0.120819i 0.998174 + 0.0604094i \(0.0192406\pi\)
−0.998174 + 0.0604094i \(0.980759\pi\)
\(524\) −74921.9 −0.272864
\(525\) 59022.7i 0.214141i
\(526\) 224104.i 0.809987i
\(527\) 108455.i 0.390505i
\(528\) 107673.i 0.386226i
\(529\) −107940. −0.385720
\(530\) 72491.9 0.258070
\(531\) 11402.9i 0.0404414i
\(532\) −1800.38 46399.3i −0.00636121 0.163941i
\(533\) 532345. 1.87387
\(534\) 226939.i 0.795840i
\(535\) 256202.i 0.895107i
\(536\) −101009. −0.351585
\(537\) 198833. 0.689508
\(538\) −375665. −1.29788
\(539\) 461903. 1.58991
\(540\) 208902.i 0.716398i
\(541\) −363239. −1.24108 −0.620538 0.784176i \(-0.713086\pi\)
−0.620538 + 0.784176i \(0.713086\pi\)
\(542\) 206520.i 0.703014i
\(543\) 243146. 0.824647
\(544\) 41015.8i 0.138597i
\(545\) 417456.i 1.40546i
\(546\) 99898.0i 0.335098i
\(547\) 899.921i 0.00300767i −0.999999 0.00150383i \(-0.999521\pi\)
0.999999 0.00150383i \(-0.000478685\pi\)
\(548\) 288169. 0.959591
\(549\) 96486.5 0.320127
\(550\) 286853.i 0.948274i
\(551\) 218822. 8490.69i 0.720756 0.0279666i
\(552\) 73210.0 0.240266
\(553\) 156068.i 0.510343i
\(554\) 187471.i 0.610821i
\(555\) 27016.9 0.0877102
\(556\) 82974.1 0.268406
\(557\) 340311. 1.09690 0.548448 0.836184i \(-0.315219\pi\)
0.548448 + 0.836184i \(0.315219\pi\)
\(558\) −27216.8 −0.0874115
\(559\) 88928.3i 0.284588i
\(560\) −34057.3 −0.108601
\(561\) 381202.i 1.21124i
\(562\) 319217. 1.01068
\(563\) 631686.i 1.99289i −0.0842180 0.996447i \(-0.526839\pi\)
0.0842180 0.996447i \(-0.473161\pi\)
\(564\) 29611.8i 0.0930907i
\(565\) 29816.3i 0.0934023i
\(566\) 228442.i 0.713089i
\(567\) −72810.3 −0.226478
\(568\) 172791. 0.535579
\(569\) 5519.19i 0.0170471i −0.999964 0.00852356i \(-0.997287\pi\)
0.999964 0.00852356i \(-0.00271317\pi\)
\(570\) 10225.0 + 263519.i 0.0314712 + 0.811077i
\(571\) −478673. −1.46814 −0.734068 0.679076i \(-0.762381\pi\)
−0.734068 + 0.679076i \(0.762381\pi\)
\(572\) 485508.i 1.48390i
\(573\) 139597.i 0.425175i
\(574\) 86001.1 0.261024
\(575\) 195039. 0.589909
\(576\) −10292.9 −0.0310238
\(577\) 65914.9 0.197985 0.0989925 0.995088i \(-0.468438\pi\)
0.0989925 + 0.995088i \(0.468438\pi\)
\(578\) 91023.0i 0.272455i
\(579\) 6119.56 0.0182542
\(580\) 160617.i 0.477457i
\(581\) −170260. −0.504383
\(582\) 341614.i 1.00853i
\(583\) 166950.i 0.491191i
\(584\) 189994.i 0.557077i
\(585\) 187298.i 0.547295i
\(586\) −378064. −1.10096
\(587\) 289436. 0.839994 0.419997 0.907526i \(-0.362031\pi\)
0.419997 + 0.907526i \(0.362031\pi\)
\(588\) 133753.i 0.386857i
\(589\) −172664. + 6699.69i −0.497705 + 0.0193119i
\(590\) −53098.2 −0.152537
\(591\) 329878.i 0.944449i
\(592\) 6694.68i 0.0191023i
\(593\) 388285. 1.10418 0.552092 0.833783i \(-0.313830\pi\)
0.552092 + 0.833783i \(0.313830\pi\)
\(594\) 481105. 1.36354
\(595\) −120575. −0.340582
\(596\) −10826.3 −0.0304781
\(597\) 119877.i 0.336346i
\(598\) −330110. −0.923115
\(599\) 601872.i 1.67745i −0.544553 0.838727i \(-0.683301\pi\)
0.544553 0.838727i \(-0.316699\pi\)
\(600\) 83064.2 0.230734
\(601\) 176095.i 0.487527i 0.969835 + 0.243764i \(0.0783821\pi\)
−0.969835 + 0.243764i \(0.921618\pi\)
\(602\) 14366.5i 0.0396423i
\(603\) 89741.7i 0.246808i
\(604\) 233062.i 0.638847i
\(605\) −1.05377e6 −2.87896
\(606\) −230972. −0.628946
\(607\) 607939.i 1.64999i 0.565137 + 0.824997i \(0.308823\pi\)
−0.565137 + 0.824997i \(0.691177\pi\)
\(608\) −65298.8 + 2533.71i −0.176644 + 0.00685410i
\(609\) 76111.1 0.205217
\(610\) 449295.i 1.20746i
\(611\) 133522.i 0.357660i
\(612\) −36440.6 −0.0972932
\(613\) 194933. 0.518757 0.259379 0.965776i \(-0.416482\pi\)
0.259379 + 0.965776i \(0.416482\pi\)
\(614\) 285267. 0.756685
\(615\) −488432. −1.29138
\(616\) 78434.6i 0.206703i
\(617\) 148271. 0.389480 0.194740 0.980855i \(-0.437614\pi\)
0.194740 + 0.980855i \(0.437614\pi\)
\(618\) 71171.9i 0.186351i
\(619\) −572353. −1.49377 −0.746884 0.664955i \(-0.768451\pi\)
−0.746884 + 0.664955i \(0.768451\pi\)
\(620\) 126737.i 0.329700i
\(621\) 327115.i 0.848238i
\(622\) 343741.i 0.888485i
\(623\) 165313.i 0.425923i
\(624\) −140589. −0.361062
\(625\) −463344. −1.18616
\(626\) 537208.i 1.37086i
\(627\) 606889. 23548.4i 1.54374 0.0598999i
\(628\) 95471.7 0.242078
\(629\) 23701.5i 0.0599066i
\(630\) 30258.3i 0.0762366i
\(631\) 236439. 0.593829 0.296914 0.954904i \(-0.404042\pi\)
0.296914 + 0.954904i \(0.404042\pi\)
\(632\) 219638. 0.549886
\(633\) 281216. 0.701831
\(634\) 190455. 0.473821
\(635\) 552329.i 1.36978i
\(636\) 48343.9 0.119516
\(637\) 603105.i 1.48633i
\(638\) −369903. −0.908755
\(639\) 153516.i 0.375970i
\(640\) 47929.7i 0.117016i
\(641\) 247053.i 0.601275i −0.953738 0.300638i \(-0.902801\pi\)
0.953738 0.300638i \(-0.0971995\pi\)
\(642\) 170858.i 0.414538i
\(643\) 543389. 1.31428 0.657142 0.753767i \(-0.271765\pi\)
0.657142 + 0.753767i \(0.271765\pi\)
\(644\) −53329.7 −0.128587
\(645\) 81592.8i 0.196125i
\(646\) −231181. + 8970.22i −0.553970 + 0.0214950i
\(647\) −263444. −0.629332 −0.314666 0.949202i \(-0.601893\pi\)
−0.314666 + 0.949202i \(0.601893\pi\)
\(648\) 102468.i 0.244027i
\(649\) 122286.i 0.290327i
\(650\) −374543. −0.886492
\(651\) −60056.4 −0.141709
\(652\) −110550. −0.260054
\(653\) −261207. −0.612574 −0.306287 0.951939i \(-0.599087\pi\)
−0.306287 + 0.951939i \(0.599087\pi\)
\(654\) 278396.i 0.650889i
\(655\) −309962. −0.722480
\(656\) 121031.i 0.281249i
\(657\) 168801. 0.391061
\(658\) 21570.7i 0.0498209i
\(659\) 532996.i 1.22731i 0.789576 + 0.613653i \(0.210301\pi\)
−0.789576 + 0.613653i \(0.789699\pi\)
\(660\) 445460.i 1.02263i
\(661\) 495346.i 1.13372i −0.823814 0.566860i \(-0.808158\pi\)
0.823814 0.566860i \(-0.191842\pi\)
\(662\) −436454. −0.995915
\(663\) −497734. −1.13232
\(664\) 239611.i 0.543465i
\(665\) −7448.39 191960.i −0.0168430 0.434078i
\(666\) −5947.91 −0.0134096
\(667\) 251507.i 0.565325i
\(668\) 82140.3i 0.184079i
\(669\) 344136. 0.768913
\(670\) −417888. −0.930915
\(671\) −1.03474e6 −2.29818
\(672\) −22712.4 −0.0502949
\(673\) 425648.i 0.939768i 0.882728 + 0.469884i \(0.155704\pi\)
−0.882728 + 0.469884i \(0.844296\pi\)
\(674\) 360745. 0.794110
\(675\) 371146.i 0.814586i
\(676\) 405439. 0.887221
\(677\) 423249.i 0.923461i −0.887020 0.461730i \(-0.847229\pi\)
0.887020 0.461730i \(-0.152771\pi\)
\(678\) 19884.1i 0.0432561i
\(679\) 248849.i 0.539754i
\(680\) 169688.i 0.366972i
\(681\) 272085. 0.586692
\(682\) 291877. 0.627525
\(683\) 310900.i 0.666467i 0.942844 + 0.333233i \(0.108140\pi\)
−0.942844 + 0.333233i \(0.891860\pi\)
\(684\) −2251.08 58015.0i −0.00481149 0.124002i
\(685\) 1.19219e6 2.54077
\(686\) 206621.i 0.439063i
\(687\) 203561.i 0.431302i
\(688\) 20218.3 0.0427139
\(689\) −217986. −0.459188
\(690\) 302879. 0.636168
\(691\) 314072. 0.657769 0.328885 0.944370i \(-0.393327\pi\)
0.328885 + 0.944370i \(0.393327\pi\)
\(692\) 232013.i 0.484508i
\(693\) −69685.5 −0.145103
\(694\) 201057.i 0.417447i
\(695\) 343275. 0.710677
\(696\) 107113.i 0.221118i
\(697\) 428494.i 0.882021i
\(698\) 236461.i 0.485343i
\(699\) 588915.i 1.20531i
\(700\) −60508.0 −0.123486
\(701\) 607472. 1.23620 0.618102 0.786098i \(-0.287902\pi\)
0.618102 + 0.786098i \(0.287902\pi\)
\(702\) 628177.i 1.27470i
\(703\) −37733.8 + 1464.14i −0.0763519 + 0.00296259i
\(704\) 110383. 0.222719
\(705\) 122508.i 0.246482i
\(706\) 114180.i 0.229076i
\(707\) 168251. 0.336604
\(708\) −35410.5 −0.0706424
\(709\) −293984. −0.584833 −0.292416 0.956291i \(-0.594459\pi\)
−0.292416 + 0.956291i \(0.594459\pi\)
\(710\) 714858. 1.41809
\(711\) 195138.i 0.386013i
\(712\) 232649. 0.458925
\(713\) 198455.i 0.390375i
\(714\) −80409.6 −0.157729
\(715\) 2.00861e6i 3.92902i
\(716\) 203836.i 0.397608i
\(717\) 334712.i 0.651078i
\(718\) 404688.i 0.785003i
\(719\) 911462. 1.76312 0.881558 0.472075i \(-0.156495\pi\)
0.881558 + 0.472075i \(0.156495\pi\)
\(720\) −42583.3 −0.0821436
\(721\) 51845.1i 0.0997326i
\(722\) −28562.0 367495.i −0.0547915 0.704981i
\(723\) 121965. 0.233324
\(724\) 249265.i 0.475536i
\(725\) 285360.i 0.542896i
\(726\) −702747. −1.33329
\(727\) −174790. −0.330710 −0.165355 0.986234i \(-0.552877\pi\)
−0.165355 + 0.986234i \(0.552877\pi\)
\(728\) 102412. 0.193236
\(729\) −589743. −1.10971
\(730\) 786032.i 1.47501i
\(731\) 71580.0 0.133954
\(732\) 299629.i 0.559193i
\(733\) −401715. −0.747671 −0.373835 0.927495i \(-0.621958\pi\)
−0.373835 + 0.927495i \(0.621958\pi\)
\(734\) 87205.3i 0.161864i
\(735\) 553356.i 1.02431i
\(736\) 75052.3i 0.138551i
\(737\) 962404.i 1.77183i
\(738\) 107531. 0.197433
\(739\) −302531. −0.553963 −0.276982 0.960875i \(-0.589334\pi\)
−0.276982 + 0.960875i \(0.589334\pi\)
\(740\) 27696.8i 0.0505785i
\(741\) −30747.0 792413.i −0.0559973 1.44316i
\(742\) −35216.0 −0.0639636
\(743\) 909052.i 1.64669i −0.567543 0.823344i \(-0.692106\pi\)
0.567543 0.823344i \(-0.307894\pi\)
\(744\) 84518.9i 0.152689i
\(745\) −44789.9 −0.0806989
\(746\) 565350. 1.01587
\(747\) −212883. −0.381505
\(748\) 390794. 0.698466
\(749\) 124461.i 0.221855i
\(750\) −112926. −0.200758
\(751\) 370317.i 0.656589i 0.944575 + 0.328295i \(0.106474\pi\)
−0.944575 + 0.328295i \(0.893526\pi\)
\(752\) −30356.9 −0.0536812
\(753\) 600870.i 1.05972i
\(754\) 482981.i 0.849547i
\(755\) 964208.i 1.69152i
\(756\) 101483.i 0.177562i
\(757\) 154581. 0.269751 0.134876 0.990863i \(-0.456937\pi\)
0.134876 + 0.990863i \(0.456937\pi\)
\(758\) −140006. −0.243674
\(759\) 697538.i 1.21083i
\(760\) −270150. + 10482.3i −0.467711 + 0.0181480i
\(761\) −722058. −1.24682 −0.623409 0.781896i \(-0.714253\pi\)
−0.623409 + 0.781896i \(0.714253\pi\)
\(762\) 368341.i 0.634366i
\(763\) 202797.i 0.348347i
\(764\) −143110. −0.245179
\(765\) −150760. −0.257610
\(766\) 140271. 0.239062
\(767\) 159669. 0.271412
\(768\) 31963.7i 0.0541919i
\(769\) 496131. 0.838965 0.419482 0.907763i \(-0.362212\pi\)
0.419482 + 0.907763i \(0.362212\pi\)
\(770\) 324495.i 0.547301i
\(771\) 69479.2 0.116882
\(772\) 6273.56i 0.0105264i
\(773\) 317854.i 0.531948i −0.963980 0.265974i \(-0.914306\pi\)
0.963980 0.265974i \(-0.0856935\pi\)
\(774\) 17963.1i 0.0299846i
\(775\) 225167.i 0.374888i
\(776\) −350211. −0.581575
\(777\) −13124.6 −0.0217393
\(778\) 44765.2i 0.0739574i
\(779\) 682180. 26469.8i 1.12415 0.0436190i
\(780\) −581635. −0.956008
\(781\) 1.64633e6i 2.69908i
\(782\) 265711.i 0.434506i
\(783\) 478601. 0.780638
\(784\) −137119. −0.223083
\(785\) 394979. 0.640966
\(786\) −206709. −0.334592
\(787\) 206097.i 0.332752i