Properties

Label 27.10.e.a.4.8
Level $27$
Weight $10$
Character 27.4
Analytic conductor $13.906$
Analytic rank $0$
Dimension $156$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [27,10,Mod(4,27)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(27, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("27.4");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 27 = 3^{3} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 27.e (of order \(9\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(13.9059675764\)
Analytic rank: \(0\)
Dimension: \(156\)
Relative dimension: \(26\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 4.8
Character \(\chi\) \(=\) 27.4
Dual form 27.10.e.a.7.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-20.2233 - 7.36069i) q^{2} +(-95.1961 - 103.057i) q^{3} +(-37.4118 - 31.3922i) q^{4} +(-358.438 + 2032.80i) q^{5} +(1166.61 + 2784.86i) q^{6} +(8116.71 - 6810.73i) q^{7} +(6034.95 + 10452.8i) q^{8} +(-1558.40 + 19621.2i) q^{9} +O(q^{10})\) \(q+(-20.2233 - 7.36069i) q^{2} +(-95.1961 - 103.057i) q^{3} +(-37.4118 - 31.3922i) q^{4} +(-358.438 + 2032.80i) q^{5} +(1166.61 + 2784.86i) q^{6} +(8116.71 - 6810.73i) q^{7} +(6034.95 + 10452.8i) q^{8} +(-1558.40 + 19621.2i) q^{9} +(22211.6 - 38471.7i) q^{10} +(1996.16 + 11320.8i) q^{11} +(326.275 + 6843.95i) q^{12} +(-124301. + 45241.8i) q^{13} +(-214278. + 77991.0i) q^{14} +(243616. - 156575. i) q^{15} +(-40764.6 - 231188. i) q^{16} +(243840. - 422343. i) q^{17} +(175942. - 385335. i) q^{18} +(8347.45 + 14458.2i) q^{19} +(77224.0 - 64798.6i) q^{20} +(-1.47457e6 - 188127. i) q^{21} +(42959.7 - 243637. i) q^{22} +(-292565. - 245491. i) q^{23} +(502733. - 1.61701e6i) q^{24} +(-2.16847e6 - 789259. i) q^{25} +2.84678e6 q^{26} +(2.17045e6 - 1.70726e6i) q^{27} -517464. q^{28} +(1.48849e6 + 541768. i) q^{29} +(-6.07923e6 + 1.37329e6i) q^{30} +(104510. + 87694.3i) q^{31} +(195806. - 1.11047e6i) q^{32} +(976656. - 1.28341e6i) q^{33} +(-8.03999e6 + 6.74636e6i) q^{34} +(1.09355e7 + 1.89409e7i) q^{35} +(674256. - 685143. i) q^{36} +(9.09408e6 - 1.57514e7i) q^{37} +(-62390.9 - 353836. i) q^{38} +(1.64954e7 + 8.50320e6i) q^{39} +(-2.34117e7 + 8.52117e6i) q^{40} +(-1.69679e7 + 6.17580e6i) q^{41} +(2.84360e7 + 1.46584e7i) q^{42} +(643562. + 3.64982e6i) q^{43} +(280704. - 486194. i) q^{44} +(-3.93275e7 - 1.02009e7i) q^{45} +(4.10966e6 + 7.11813e6i) q^{46} +(3.49186e7 - 2.93002e7i) q^{47} +(-1.99448e7 + 2.62092e7i) q^{48} +(1.24876e7 - 7.08209e7i) q^{49} +(3.80442e7 + 3.19229e7i) q^{50} +(-6.67380e7 + 1.50761e7i) q^{51} +(6.07055e6 + 2.20950e6i) q^{52} -2.21455e7 q^{53} +(-5.64604e7 + 1.85504e7i) q^{54} -2.37284e7 q^{55} +(1.20175e8 + 4.37403e7i) q^{56} +(695372. - 2.23663e6i) q^{57} +(-2.61145e7 - 2.19127e7i) q^{58} +(1.26658e7 - 7.18316e7i) q^{59} +(-1.40294e7 - 1.78988e6i) q^{60} +(9.09230e7 - 7.62935e7i) q^{61} +(-1.46805e6 - 2.54274e6i) q^{62} +(1.20986e8 + 1.69874e8i) q^{63} +(-7.22307e7 + 1.25107e8i) q^{64} +(-4.74135e7 - 2.68895e8i) q^{65} +(-2.91980e7 + 1.87660e7i) q^{66} +(2.03580e8 - 7.40972e7i) q^{67} +(-2.23808e7 + 8.14594e6i) q^{68} +(2.55152e6 + 5.35207e7i) q^{69} +(-8.17348e7 - 4.63541e8i) q^{70} +(2.45310e7 - 4.24889e7i) q^{71} +(-2.14502e8 + 1.02123e8i) q^{72} +(-1.87344e8 - 3.24489e8i) q^{73} +(-2.99854e8 + 2.51607e8i) q^{74} +(1.25092e8 + 2.98610e8i) q^{75} +(141582. - 802952. i) q^{76} +(9.33049e7 + 7.82921e7i) q^{77} +(-2.71003e8 - 2.93380e8i) q^{78} +(-5.33276e8 - 1.94097e8i) q^{79} +4.84570e8 q^{80} +(-3.82563e8 - 6.11555e7i) q^{81} +3.88605e8 q^{82} +(7.04727e8 + 2.56500e8i) q^{83} +(4.92606e7 + 5.33282e7i) q^{84} +(7.71139e8 + 6.47063e8i) q^{85} +(1.38502e7 - 7.85486e7i) q^{86} +(-8.58660e7 - 2.04974e8i) q^{87} +(-1.06288e8 + 8.91858e7i) q^{88} +(1.57565e8 + 2.72910e8i) q^{89} +(7.20246e8 + 4.95773e8i) q^{90} +(-7.00784e8 + 1.21379e9i) q^{91} +(3.23887e6 + 1.83685e7i) q^{92} +(-911452. - 1.91186e7i) q^{93} +(-9.21840e8 + 3.35522e8i) q^{94} +(-3.23827e7 + 1.17864e7i) q^{95} +(-1.33081e8 + 8.55332e7i) q^{96} +(-3.05789e7 - 1.73422e8i) q^{97} +(-7.73832e8 + 1.34032e9i) q^{98} +(-2.25238e8 + 2.15247e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 156 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 2382 q^{5} - 6822 q^{6} - 6 q^{7} + 36861 q^{8} + 2538 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 156 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 2382 q^{5} - 6822 q^{6} - 6 q^{7} + 36861 q^{8} + 2538 q^{9} - 3 q^{10} - 121767 q^{11} + 319935 q^{12} - 6 q^{13} - 720417 q^{14} - 706356 q^{15} + 1530 q^{16} + 1002249 q^{17} + 922437 q^{18} - 3 q^{19} - 8448573 q^{20} - 3497394 q^{21} - 1585014 q^{22} + 9316482 q^{23} + 7959258 q^{24} + 2192178 q^{25} - 33129678 q^{26} - 3148155 q^{27} - 12 q^{28} + 19657236 q^{29} + 21174507 q^{30} - 4633692 q^{31} - 37550952 q^{32} - 19055889 q^{33} + 14341770 q^{34} + 34449663 q^{35} + 137733552 q^{36} - 3 q^{37} - 92022060 q^{38} - 89330160 q^{39} + 6645801 q^{40} - 33127221 q^{41} + 227141658 q^{42} + 2356203 q^{43} + 1001541 q^{44} - 78992532 q^{45} - 3 q^{46} - 33488952 q^{47} + 248865393 q^{48} - 93214644 q^{49} - 72027753 q^{50} - 101541537 q^{51} + 160531713 q^{52} + 4841352 q^{53} - 315431874 q^{54} - 12 q^{55} - 91770981 q^{56} - 103852992 q^{57} - 320682489 q^{58} + 538090854 q^{59} + 1127571210 q^{60} + 36683436 q^{61} - 55862958 q^{62} - 419972706 q^{63} - 956301315 q^{64} - 852347310 q^{65} + 472205277 q^{66} - 109026897 q^{67} - 508886217 q^{68} - 1234413090 q^{69} - 815297649 q^{70} + 940878639 q^{71} + 2831326452 q^{72} - 221849931 q^{73} + 838884579 q^{74} - 226667796 q^{75} + 908401146 q^{76} - 967811358 q^{77} - 1247881230 q^{78} - 1228059150 q^{79} - 2497115154 q^{80} - 392600970 q^{81} - 12 q^{82} - 297703284 q^{83} + 1027656618 q^{84} + 1535949369 q^{85} + 2930201574 q^{86} + 2687612040 q^{87} + 2837227002 q^{88} + 1774997208 q^{89} + 7127326206 q^{90} + 551343507 q^{91} - 6896645517 q^{92} - 7299151842 q^{93} + 414852915 q^{94} - 9000269169 q^{95} - 2644638174 q^{96} + 3371772333 q^{97} + 6901039926 q^{98} + 5248107342 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −20.2233 7.36069i −0.893753 0.325299i −0.146006 0.989284i \(-0.546642\pi\)
−0.747747 + 0.663984i \(0.768864\pi\)
\(3\) −95.1961 103.057i −0.678537 0.734566i
\(4\) −37.4118 31.3922i −0.0730699 0.0613129i
\(5\) −358.438 + 2032.80i −0.256477 + 1.45456i 0.535775 + 0.844361i \(0.320020\pi\)
−0.792252 + 0.610194i \(0.791091\pi\)
\(6\) 1166.61 + 2784.86i 0.367490 + 0.877248i
\(7\) 8116.71 6810.73i 1.27773 1.07214i 0.284177 0.958772i \(-0.408280\pi\)
0.993553 0.113370i \(-0.0361646\pi\)
\(8\) 6034.95 + 10452.8i 0.520917 + 0.902255i
\(9\) −1558.40 + 19621.2i −0.0791751 + 0.996861i
\(10\) 22211.6 38471.7i 0.702393 1.21658i
\(11\) 1996.16 + 11320.8i 0.0411081 + 0.233136i 0.998439 0.0558596i \(-0.0177899\pi\)
−0.957331 + 0.288995i \(0.906679\pi\)
\(12\) 326.275 + 6843.95i 0.00454222 + 0.0952777i
\(13\) −124301. + 45241.8i −1.20706 + 0.439334i −0.865683 0.500593i \(-0.833115\pi\)
−0.341377 + 0.939927i \(0.610893\pi\)
\(14\) −214278. + 77991.0i −1.49074 + 0.542586i
\(15\) 243616. 156575.i 1.24250 0.798570i
\(16\) −40764.6 231188.i −0.155505 0.881911i
\(17\) 243840. 422343.i 0.708084 1.22644i −0.257482 0.966283i \(-0.582893\pi\)
0.965567 0.260155i \(-0.0837737\pi\)
\(18\) 175942. 385335.i 0.395041 0.865192i
\(19\) 8347.45 + 14458.2i 0.0146948 + 0.0254521i 0.873279 0.487220i \(-0.161989\pi\)
−0.858585 + 0.512672i \(0.828656\pi\)
\(20\) 77224.0 64798.6i 0.107924 0.0905588i
\(21\) −1.47457e6 188127.i −1.65455 0.211089i
\(22\) 42959.7 243637.i 0.0390984 0.221738i
\(23\) −292565. 245491.i −0.217995 0.182920i 0.527250 0.849710i \(-0.323223\pi\)
−0.745245 + 0.666790i \(0.767668\pi\)
\(24\) 502733. 1.61701e6i 0.309305 0.994862i
\(25\) −2.16847e6 789259.i −1.11026 0.404101i
\(26\) 2.84678e6 1.22173
\(27\) 2.17045e6 1.70726e6i 0.785983 0.618248i
\(28\) −517464. −0.159100
\(29\) 1.48849e6 + 541768.i 0.390802 + 0.142240i 0.529945 0.848032i \(-0.322213\pi\)
−0.139143 + 0.990272i \(0.544435\pi\)
\(30\) −6.07923e6 + 1.37329e6i −1.37026 + 0.309541i
\(31\) 104510. + 87694.3i 0.0203250 + 0.0170547i 0.652894 0.757450i \(-0.273555\pi\)
−0.632569 + 0.774504i \(0.717999\pi\)
\(32\) 195806. 1.11047e6i 0.0330104 0.187211i
\(33\) 976656. 1.28341e6i 0.143360 0.188388i
\(34\) −8.03999e6 + 6.74636e6i −1.03181 + 0.865793i
\(35\) 1.09355e7 + 1.89409e7i 1.23178 + 2.13351i
\(36\) 674256. 685143.i 0.0669057 0.0679860i
\(37\) 9.09408e6 1.57514e7i 0.797721 1.38169i −0.123376 0.992360i \(-0.539372\pi\)
0.921097 0.389333i \(-0.127295\pi\)
\(38\) −62390.9 353836.i −0.00485394 0.0275281i
\(39\) 1.64954e7 + 8.50320e6i 1.14175 + 0.588561i
\(40\) −2.34117e7 + 8.52117e6i −1.44598 + 0.526295i
\(41\) −1.69679e7 + 6.17580e6i −0.937778 + 0.341323i −0.765288 0.643688i \(-0.777403\pi\)
−0.172490 + 0.985011i \(0.555181\pi\)
\(42\) 2.84360e7 + 1.46584e7i 1.41009 + 0.726884i
\(43\) 643562. + 3.64982e6i 0.0287066 + 0.162803i 0.995791 0.0916522i \(-0.0292148\pi\)
−0.967084 + 0.254456i \(0.918104\pi\)
\(44\) 280704. 486194.i 0.0112905 0.0195557i
\(45\) −3.93275e7 1.02009e7i −1.42968 0.370837i
\(46\) 4.10966e6 + 7.11813e6i 0.135330 + 0.234399i
\(47\) 3.49186e7 2.93002e7i 1.04380 0.875851i 0.0513705 0.998680i \(-0.483641\pi\)
0.992428 + 0.122829i \(0.0391966\pi\)
\(48\) −1.99448e7 + 2.62092e7i −0.542306 + 0.712637i
\(49\) 1.24876e7 7.08209e7i 0.309455 1.75501i
\(50\) 3.80442e7 + 3.19229e7i 0.860842 + 0.722333i
\(51\) −6.67380e7 + 1.50761e7i −1.38136 + 0.312049i
\(52\) 6.07055e6 + 2.20950e6i 0.115137 + 0.0419063i
\(53\) −2.21455e7 −0.385518 −0.192759 0.981246i \(-0.561744\pi\)
−0.192759 + 0.981246i \(0.561744\pi\)
\(54\) −5.64604e7 + 1.85504e7i −0.903591 + 0.296881i
\(55\) −2.37284e7 −0.349652
\(56\) 1.20175e8 + 4.37403e7i 1.63294 + 0.594341i
\(57\) 695372. 2.23663e6i 0.00872530 0.0280645i
\(58\) −2.61145e7 2.19127e7i −0.303009 0.254255i
\(59\) 1.26658e7 7.18316e7i 0.136082 0.771758i −0.838019 0.545642i \(-0.816286\pi\)
0.974100 0.226116i \(-0.0726029\pi\)
\(60\) −1.40294e7 1.78988e6i −0.139752 0.0178297i
\(61\) 9.09230e7 7.62935e7i 0.840794 0.705510i −0.116948 0.993138i \(-0.537311\pi\)
0.957742 + 0.287628i \(0.0928668\pi\)
\(62\) −1.46805e6 2.54274e6i −0.0126176 0.0218544i
\(63\) 1.20986e8 + 1.69874e8i 0.967612 + 1.35861i
\(64\) −7.22307e7 + 1.25107e8i −0.538161 + 0.932121i
\(65\) −4.74135e7 2.68895e8i −0.329452 1.86841i
\(66\) −2.91980e7 + 1.87660e7i −0.189411 + 0.121737i
\(67\) 2.03580e8 7.40972e7i 1.23424 0.449226i 0.359192 0.933264i \(-0.383052\pi\)
0.875047 + 0.484038i \(0.160830\pi\)
\(68\) −2.23808e7 + 8.14594e6i −0.126936 + 0.0462010i
\(69\) 2.55152e6 + 5.35207e7i 0.0135512 + 0.284250i
\(70\) −8.17348e7 4.63541e8i −0.406879 2.30753i
\(71\) 2.45310e7 4.24889e7i 0.114565 0.198432i −0.803041 0.595924i \(-0.796786\pi\)
0.917606 + 0.397492i \(0.130119\pi\)
\(72\) −2.14502e8 + 1.02123e8i −0.940667 + 0.447846i
\(73\) −1.87344e8 3.24489e8i −0.772123 1.33736i −0.936398 0.350941i \(-0.885862\pi\)
0.164275 0.986415i \(-0.447472\pi\)
\(74\) −2.99854e8 + 2.51607e8i −1.16243 + 0.975394i
\(75\) 1.25092e8 + 2.98610e8i 0.456512 + 1.08976i
\(76\) 141582. 802952.i 0.000486796 0.00276076i
\(77\) 9.33049e7 + 7.82921e7i 0.302480 + 0.253811i
\(78\) −2.71003e8 2.93380e8i −0.828988 0.897440i
\(79\) −5.33276e8 1.94097e8i −1.54039 0.560656i −0.574251 0.818679i \(-0.694707\pi\)
−0.966139 + 0.258024i \(0.916929\pi\)
\(80\) 4.84570e8 1.32267
\(81\) −3.82563e8 6.11555e7i −0.987463 0.157853i
\(82\) 3.88605e8 0.949174
\(83\) 7.04727e8 + 2.56500e8i 1.62993 + 0.593246i 0.985237 0.171194i \(-0.0547626\pi\)
0.644694 + 0.764441i \(0.276985\pi\)
\(84\) 4.92606e7 + 5.33282e7i 0.107955 + 0.116869i
\(85\) 7.71139e8 + 6.47063e8i 1.60231 + 1.34450i
\(86\) 1.38502e7 7.85486e7i 0.0273032 0.154844i
\(87\) −8.58660e7 2.04974e8i −0.160688 0.383585i
\(88\) −1.06288e8 + 8.91858e7i −0.188934 + 0.158534i
\(89\) 1.57565e8 + 2.72910e8i 0.266198 + 0.461068i 0.967877 0.251425i \(-0.0808992\pi\)
−0.701679 + 0.712493i \(0.747566\pi\)
\(90\) 7.20246e8 + 4.95773e8i 1.15715 + 0.796511i
\(91\) −7.00784e8 + 1.21379e9i −1.07127 + 1.85549i
\(92\) 3.23887e6 + 1.83685e7i 0.00471355 + 0.0267319i
\(93\) −911452. 1.91186e7i −0.00126346 0.0265023i
\(94\) −9.21840e8 + 3.35522e8i −1.21781 + 0.443247i
\(95\) −3.23827e7 + 1.17864e7i −0.0407903 + 0.0148465i
\(96\) −1.33081e8 + 8.55332e7i −0.159918 + 0.102781i
\(97\) −3.05789e7 1.73422e8i −0.0350711 0.198898i 0.962238 0.272210i \(-0.0877544\pi\)
−0.997309 + 0.0733114i \(0.976643\pi\)
\(98\) −7.73832e8 + 1.34032e9i −0.847479 + 1.46788i
\(99\) −2.25238e8 + 2.15247e7i −0.235659 + 0.0225205i
\(100\) 5.63498e7 + 9.76007e7i 0.0563498 + 0.0976007i
\(101\) 1.09530e9 9.19070e8i 1.04734 0.878825i 0.0545310 0.998512i \(-0.482634\pi\)
0.992812 + 0.119687i \(0.0381892\pi\)
\(102\) 1.46063e9 + 1.86349e8i 1.33611 + 0.170462i
\(103\) 1.83735e8 1.04201e9i 0.160851 0.912233i −0.792388 0.610017i \(-0.791163\pi\)
0.953240 0.302216i \(-0.0977263\pi\)
\(104\) −1.22305e9 1.02626e9i −1.02517 0.860219i
\(105\) 9.10968e8 2.93008e9i 0.731394 2.35249i
\(106\) 4.47856e8 + 1.63006e8i 0.344558 + 0.125409i
\(107\) −1.05284e9 −0.776487 −0.388244 0.921557i \(-0.626918\pi\)
−0.388244 + 0.921557i \(0.626918\pi\)
\(108\) −1.34795e8 4.26372e6i −0.0953383 0.00301566i
\(109\) 1.17144e9 0.794880 0.397440 0.917628i \(-0.369899\pi\)
0.397440 + 0.917628i \(0.369899\pi\)
\(110\) 4.79867e8 + 1.74657e8i 0.312503 + 0.113742i
\(111\) −2.48901e9 + 5.62266e8i −1.55623 + 0.351551i
\(112\) −1.90543e9 1.59885e9i −1.14423 0.960120i
\(113\) −5.17745e8 + 2.93628e9i −0.298719 + 1.69412i 0.352972 + 0.935634i \(0.385171\pi\)
−0.651691 + 0.758485i \(0.725940\pi\)
\(114\) −3.05258e7 + 4.01136e7i −0.0169276 + 0.0222444i
\(115\) 6.03902e8 5.06734e8i 0.321978 0.270172i
\(116\) −3.86799e7 6.69956e7i −0.0198347 0.0343546i
\(117\) −6.93988e8 2.50944e9i −0.342386 1.23805i
\(118\) −7.84875e8 + 1.35944e9i −0.372676 + 0.645494i
\(119\) −8.97287e8 5.08877e9i −0.410176 2.32622i
\(120\) 3.10687e9 + 1.60155e9i 1.36775 + 0.705060i
\(121\) 2.09157e9 7.61270e8i 0.887030 0.322853i
\(122\) −2.40034e9 + 8.73651e8i −0.980964 + 0.357042i
\(123\) 2.25173e9 + 1.16074e9i 0.887042 + 0.457260i
\(124\) −1.15699e6 6.56160e6i −0.000439472 0.00249237i
\(125\) 3.65888e8 6.33737e8i 0.134046 0.232174i
\(126\) −1.19635e9 4.32594e9i −0.422853 1.52902i
\(127\) 1.39132e9 + 2.40984e9i 0.474582 + 0.822000i 0.999576 0.0291058i \(-0.00926596\pi\)
−0.524994 + 0.851106i \(0.675933\pi\)
\(128\) 1.93936e9 1.62731e9i 0.638577 0.535830i
\(129\) 3.14874e8 4.13772e8i 0.100111 0.131555i
\(130\) −1.02040e9 + 5.78695e9i −0.313346 + 1.77707i
\(131\) −1.23235e9 1.03406e9i −0.365604 0.306779i 0.441415 0.897303i \(-0.354477\pi\)
−0.807020 + 0.590524i \(0.798921\pi\)
\(132\) −7.68275e7 + 1.73553e7i −0.0220259 + 0.00497564i
\(133\) 1.66225e8 + 6.05009e7i 0.0460642 + 0.0167660i
\(134\) −4.66248e9 −1.24924
\(135\) 2.69255e9 + 5.02405e9i 0.697688 + 1.30182i
\(136\) 5.88625e9 1.47541
\(137\) −4.03797e9 1.46970e9i −0.979311 0.356440i −0.197739 0.980255i \(-0.563360\pi\)
−0.781572 + 0.623815i \(0.785582\pi\)
\(138\) 3.42349e8 1.10115e9i 0.0803550 0.258457i
\(139\) 3.56099e9 + 2.98803e9i 0.809104 + 0.678919i 0.950394 0.311049i \(-0.100680\pi\)
−0.141290 + 0.989968i \(0.545125\pi\)
\(140\) 1.85479e8 1.05190e9i 0.0408055 0.231419i
\(141\) −6.34370e9 8.09336e8i −1.35163 0.172442i
\(142\) −8.08845e8 + 6.78701e8i −0.166943 + 0.140082i
\(143\) −7.60296e8 1.31687e9i −0.152044 0.263349i
\(144\) 4.59971e9 4.39567e8i 0.891454 0.0851911i
\(145\) −1.63484e9 + 2.83163e9i −0.307128 + 0.531961i
\(146\) 1.40025e9 + 7.94122e9i 0.255046 + 1.44644i
\(147\) −8.48735e9 + 5.45494e9i −1.49915 + 0.963522i
\(148\) −8.34697e8 + 3.03805e8i −0.143005 + 0.0520496i
\(149\) 2.28837e9 8.32897e8i 0.380353 0.138437i −0.144766 0.989466i \(-0.546243\pi\)
0.525119 + 0.851029i \(0.324021\pi\)
\(150\) −3.31791e8 6.95965e9i −0.0535123 1.12248i
\(151\) −1.81635e9 1.03010e10i −0.284317 1.61244i −0.707714 0.706499i \(-0.750273\pi\)
0.423396 0.905945i \(-0.360838\pi\)
\(152\) −1.00753e8 + 1.74509e8i −0.0153095 + 0.0265169i
\(153\) 7.90689e9 + 5.44262e9i 1.16653 + 0.802965i
\(154\) −1.31065e9 2.27011e9i −0.187778 0.325240i
\(155\) −2.15726e8 + 1.81015e8i −0.0300199 + 0.0251897i
\(156\) −3.50189e8 8.35947e8i −0.0473415 0.113010i
\(157\) −1.26531e9 + 7.17591e9i −0.166206 + 0.942603i 0.781606 + 0.623773i \(0.214401\pi\)
−0.947812 + 0.318830i \(0.896710\pi\)
\(158\) 9.35594e9 + 7.85056e9i 1.19435 + 1.00218i
\(159\) 2.10817e9 + 2.28225e9i 0.261588 + 0.283188i
\(160\) 2.18718e9 + 7.96069e8i 0.263842 + 0.0960308i
\(161\) −4.04664e9 −0.474655
\(162\) 7.28655e9 + 4.05270e9i 0.831198 + 0.462303i
\(163\) 6.30867e9 0.699993 0.349997 0.936751i \(-0.386183\pi\)
0.349997 + 0.936751i \(0.386183\pi\)
\(164\) 8.28670e8 + 3.01611e8i 0.0894508 + 0.0325574i
\(165\) 2.25885e9 + 2.44537e9i 0.237252 + 0.256843i
\(166\) −1.23639e10 1.03745e10i −1.26377 1.06043i
\(167\) −1.27582e9 + 7.23556e9i −0.126931 + 0.719860i 0.853212 + 0.521565i \(0.174652\pi\)
−0.980142 + 0.198295i \(0.936460\pi\)
\(168\) −6.93250e9 1.65488e10i −0.671426 1.60278i
\(169\) 5.28034e9 4.43073e9i 0.497934 0.417816i
\(170\) −1.08322e10 1.87619e10i −0.994708 1.72288i
\(171\) −2.96696e8 + 1.41255e8i −0.0265356 + 0.0126335i
\(172\) 9.04991e7 1.56749e8i 0.00788436 0.0136561i
\(173\) 1.91429e9 + 1.08565e10i 0.162480 + 0.921469i 0.951625 + 0.307262i \(0.0994129\pi\)
−0.789145 + 0.614207i \(0.789476\pi\)
\(174\) 2.27750e8 + 4.77728e9i 0.0188359 + 0.395102i
\(175\) −2.29763e10 + 8.36269e9i −1.85186 + 0.674023i
\(176\) 2.53585e9 9.22973e8i 0.199212 0.0725074i
\(177\) −8.60847e9 + 5.53278e9i −0.659244 + 0.423705i
\(178\) −1.17768e9 6.67894e9i −0.0879298 0.498675i
\(179\) 1.65732e9 2.87056e9i 0.120661 0.208991i −0.799368 0.600842i \(-0.794832\pi\)
0.920029 + 0.391851i \(0.128165\pi\)
\(180\) 1.15108e9 + 1.61621e9i 0.0817296 + 0.114755i
\(181\) −4.41579e7 7.64837e7i −0.00305812 0.00529682i 0.864492 0.502646i \(-0.167640\pi\)
−0.867550 + 0.497349i \(0.834307\pi\)
\(182\) 2.31065e10 1.93887e10i 1.56104 1.30987i
\(183\) −1.65181e10 2.10739e9i −1.08875 0.138904i
\(184\) 8.00466e8 4.53967e9i 0.0514828 0.291974i
\(185\) 2.87598e10 + 2.41324e10i 1.80515 + 1.51470i
\(186\) −1.22294e8 + 3.93351e8i −0.00749196 + 0.0240975i
\(187\) 5.26800e9 + 1.91739e9i 0.315035 + 0.114663i
\(188\) −2.22617e9 −0.129971
\(189\) 5.98926e9 2.86397e10i 0.341425 1.63264i
\(190\) 7.41642e8 0.0412860
\(191\) 1.16337e10 + 4.23432e9i 0.632511 + 0.230215i 0.638324 0.769768i \(-0.279628\pi\)
−0.00581308 + 0.999983i \(0.501850\pi\)
\(192\) 1.97692e10 4.46586e9i 1.04987 0.237164i
\(193\) −9.54254e9 8.00714e9i −0.495058 0.415403i 0.360777 0.932652i \(-0.382512\pi\)
−0.855835 + 0.517249i \(0.826956\pi\)
\(194\) −6.58096e8 + 3.73225e9i −0.0333566 + 0.189175i
\(195\) −2.31979e10 + 3.04841e10i −1.14893 + 1.50979i
\(196\) −2.69041e9 + 2.25752e9i −0.130216 + 0.109265i
\(197\) −9.21489e8 1.59607e9i −0.0435905 0.0755010i 0.843407 0.537275i \(-0.180546\pi\)
−0.886997 + 0.461774i \(0.847213\pi\)
\(198\) 4.71350e9 + 1.22261e9i 0.217946 + 0.0565318i
\(199\) 1.38449e10 2.39801e10i 0.625822 1.08396i −0.362559 0.931961i \(-0.618097\pi\)
0.988381 0.151995i \(-0.0485699\pi\)
\(200\) −4.83662e9 2.74298e10i −0.213750 1.21224i
\(201\) −2.70163e10 1.39266e10i −1.16746 0.601813i
\(202\) −2.89157e10 + 1.05244e10i −1.22195 + 0.444752i
\(203\) 1.57715e10 5.74036e9i 0.651840 0.237250i
\(204\) 2.97006e9 + 1.53103e9i 0.120069 + 0.0618939i
\(205\) −6.47225e9 3.67060e10i −0.255955 1.45159i
\(206\) −1.13857e10 + 1.97206e10i −0.440510 + 0.762986i
\(207\) 5.27277e9 5.35791e9i 0.199605 0.202828i
\(208\) 1.55264e10 + 2.68925e10i 0.575156 + 0.996200i
\(209\) −1.47015e8 + 1.23360e8i −0.00532972 + 0.00447216i
\(210\) −3.99902e10 + 5.25506e10i −1.41895 + 1.86462i
\(211\) 6.60699e9 3.74701e10i 0.229474 1.30141i −0.624472 0.781047i \(-0.714686\pi\)
0.853946 0.520362i \(-0.174203\pi\)
\(212\) 8.28503e8 + 6.95197e8i 0.0281697 + 0.0236372i
\(213\) −6.71402e9 + 1.51669e9i −0.223498 + 0.0504882i
\(214\) 2.12919e10 + 7.74961e9i 0.693988 + 0.252591i
\(215\) −7.65004e9 −0.244169
\(216\) 3.09443e10 + 1.23842e10i 0.967250 + 0.387102i
\(217\) 1.44554e9 0.0442549
\(218\) −2.36904e10 8.62262e9i −0.710426 0.258574i
\(219\) −1.56064e10 + 5.01971e10i −0.458462 + 1.47462i
\(220\) 8.87721e8 + 7.44887e8i 0.0255490 + 0.0214382i
\(221\) −1.12019e10 + 6.35294e10i −0.315884 + 1.79147i
\(222\) 5.44747e10 + 6.94994e9i 1.50524 + 0.192040i
\(223\) −4.22748e9 + 3.54728e9i −0.114475 + 0.0960557i −0.698228 0.715875i \(-0.746028\pi\)
0.583753 + 0.811931i \(0.301583\pi\)
\(224\) −5.97380e9 1.03469e10i −0.158539 0.274597i
\(225\) 1.88656e10 4.13181e10i 0.490737 1.07478i
\(226\) 3.20835e10 5.55703e10i 0.818077 1.41695i
\(227\) −2.79744e9 1.58651e10i −0.0699269 0.396575i −0.999602 0.0281957i \(-0.991024\pi\)
0.929676 0.368379i \(-0.120087\pi\)
\(228\) −9.62278e7 + 6.18469e7i −0.00235827 + 0.00151569i
\(229\) −2.60243e10 + 9.47207e9i −0.625344 + 0.227607i −0.635204 0.772345i \(-0.719084\pi\)
0.00985928 + 0.999951i \(0.496862\pi\)
\(230\) −1.59428e10 + 5.80271e9i −0.375655 + 0.136727i
\(231\) −8.13730e8 1.70688e10i −0.0188030 0.394411i
\(232\) 3.31998e9 + 1.88285e10i 0.0752384 + 0.426698i
\(233\) 2.61537e10 4.52996e10i 0.581342 1.00691i −0.413978 0.910287i \(-0.635861\pi\)
0.995321 0.0966276i \(-0.0308056\pi\)
\(234\) −4.43644e9 + 5.58574e10i −0.0967304 + 1.21789i
\(235\) 4.70454e10 + 8.14850e10i 1.00626 + 1.74290i
\(236\) −2.72880e9 + 2.28974e9i −0.0572622 + 0.0480487i
\(237\) 3.07629e10 + 7.34350e10i 0.633372 + 1.51194i
\(238\) −1.93107e10 + 1.09516e11i −0.390123 + 2.21250i
\(239\) −5.68809e10 4.77287e10i −1.12765 0.946214i −0.128688 0.991685i \(-0.541077\pi\)
−0.998966 + 0.0454715i \(0.985521\pi\)
\(240\) −4.61292e10 4.99383e10i −0.897481 0.971590i
\(241\) 2.43147e10 + 8.84982e9i 0.464293 + 0.168989i 0.563565 0.826072i \(-0.309429\pi\)
−0.0992725 + 0.995060i \(0.531652\pi\)
\(242\) −4.79020e10 −0.897810
\(243\) 3.01160e10 + 4.52475e10i 0.554076 + 0.832466i
\(244\) −5.79661e9 −0.104694
\(245\) 1.39489e11 + 5.07698e10i 2.47339 + 0.900239i
\(246\) −3.69937e10 4.00484e10i −0.644050 0.697231i
\(247\) −1.69171e9 1.41951e9i −0.0289194 0.0242663i
\(248\) −2.85942e8 + 1.62166e9i −0.00480005 + 0.0272224i
\(249\) −4.06532e10 9.70446e10i −0.670190 1.59983i
\(250\) −1.20642e10 + 1.01231e10i −0.195330 + 0.163901i
\(251\) 1.15077e10 + 1.99319e10i 0.183003 + 0.316970i 0.942902 0.333071i \(-0.108085\pi\)
−0.759899 + 0.650041i \(0.774752\pi\)
\(252\) 8.06418e8 1.01533e10i 0.0125967 0.158600i
\(253\) 2.19514e9 3.80210e9i 0.0336838 0.0583420i
\(254\) −1.03991e10 5.89761e10i −0.156763 0.889046i
\(255\) −6.72525e9 1.41069e11i −0.0996043 2.08930i
\(256\) 1.83052e10 6.66256e9i 0.266376 0.0969529i
\(257\) 3.67307e10 1.33689e10i 0.525206 0.191159i −0.0657905 0.997833i \(-0.520957\pi\)
0.590997 + 0.806674i \(0.298735\pi\)
\(258\) −9.41345e9 + 6.05016e9i −0.132270 + 0.0850116i
\(259\) −3.34646e10 1.89787e11i −0.462100 2.62070i
\(260\) −6.66739e9 + 1.15483e10i −0.0904849 + 0.156724i
\(261\) −1.29498e10 + 2.83618e10i −0.172735 + 0.378313i
\(262\) 1.73107e10 + 2.99830e10i 0.226965 + 0.393115i
\(263\) −6.65835e10 + 5.58702e10i −0.858155 + 0.720077i −0.961570 0.274561i \(-0.911467\pi\)
0.103415 + 0.994638i \(0.467023\pi\)
\(264\) 1.93094e10 + 2.46351e9i 0.244653 + 0.0312131i
\(265\) 7.93780e9 4.50175e10i 0.0988766 0.560757i
\(266\) −2.91629e9 2.44706e9i −0.0357160 0.0299693i
\(267\) 1.31257e10 4.22181e10i 0.158060 0.508392i
\(268\) −9.94237e9 3.61873e9i −0.117729 0.0428499i
\(269\) −1.25195e11 −1.45782 −0.728908 0.684612i \(-0.759972\pi\)
−0.728908 + 0.684612i \(0.759972\pi\)
\(270\) −1.74718e10 1.21422e11i −0.200079 1.39047i
\(271\) −4.95030e10 −0.557532 −0.278766 0.960359i \(-0.589925\pi\)
−0.278766 + 0.960359i \(0.589925\pi\)
\(272\) −1.07581e11 3.91561e10i −1.19172 0.433750i
\(273\) 1.91802e11 4.33279e10i 2.08987 0.472101i
\(274\) 7.08432e10 + 5.94445e10i 0.759312 + 0.637139i
\(275\) 4.60641e9 2.61243e10i 0.0485697 0.275453i
\(276\) 1.58467e9 2.08240e9i 0.0164380 0.0216010i
\(277\) −8.56744e10 + 7.18893e10i −0.874363 + 0.733678i −0.965012 0.262205i \(-0.915550\pi\)
0.0906488 + 0.995883i \(0.471106\pi\)
\(278\) −5.00212e10 8.66392e10i −0.502287 0.869987i
\(279\) −1.88354e9 + 1.91395e9i −0.0186104 + 0.0189109i
\(280\) −1.31991e11 + 2.28615e11i −1.28331 + 2.22276i
\(281\) −6.35247e9 3.60267e10i −0.0607805 0.344704i −0.999999 0.00138357i \(-0.999560\pi\)
0.939219 0.343320i \(-0.111552\pi\)
\(282\) 1.22333e11 + 6.30614e10i 1.15192 + 0.593804i
\(283\) 1.15960e11 4.22059e10i 1.07465 0.391142i 0.256739 0.966481i \(-0.417352\pi\)
0.817915 + 0.575339i \(0.195130\pi\)
\(284\) −2.25157e9 + 8.19503e8i −0.0205377 + 0.00747512i
\(285\) 4.29737e9 + 2.21525e9i 0.0385835 + 0.0198893i
\(286\) 5.68263e9 + 3.22278e10i 0.0502229 + 0.284828i
\(287\) −9.56616e10 + 1.65691e11i −0.832279 + 1.44155i
\(288\) 2.14836e10 + 5.57250e9i 0.184010 + 0.0477292i
\(289\) −5.96221e10 1.03268e11i −0.502767 0.870818i
\(290\) 5.39046e10 4.52313e10i 0.447543 0.375533i
\(291\) −1.49613e10 + 1.96605e10i −0.122307 + 0.160722i
\(292\) −3.17756e9 + 1.80208e10i −0.0255783 + 0.145061i
\(293\) 4.09450e10 + 3.43569e10i 0.324561 + 0.272339i 0.790479 0.612489i \(-0.209831\pi\)
−0.465918 + 0.884828i \(0.654276\pi\)
\(294\) 2.11794e11 4.78442e10i 1.65330 0.373479i
\(295\) 1.41479e11 + 5.14943e10i 1.08766 + 0.395877i
\(296\) 2.19529e11 1.66219
\(297\) 2.36600e10 + 2.11632e10i 0.176446 + 0.157826i
\(298\) −5.24090e10 −0.384975
\(299\) 4.74725e10 + 1.72786e10i 0.343496 + 0.125022i
\(300\) 4.69414e9 1.50984e10i 0.0334588 0.107618i
\(301\) 3.00815e10 + 2.52414e10i 0.211228 + 0.177241i
\(302\) −3.90901e10 + 2.21691e11i −0.270418 + 1.53361i
\(303\) −1.98985e11 2.53867e10i −1.35622 0.173027i
\(304\) 3.00228e9 2.51921e9i 0.0201614 0.0169174i
\(305\) 1.22499e11 + 2.12175e11i 0.810558 + 1.40393i
\(306\) −1.19842e11 1.68268e11i −0.781381 1.09712i
\(307\) −3.63332e10 + 6.29309e10i −0.233443 + 0.404335i −0.958819 0.284018i \(-0.908332\pi\)
0.725376 + 0.688353i \(0.241666\pi\)
\(308\) −1.03294e9 5.85809e9i −0.00654029 0.0370918i
\(309\) −1.24877e11 + 8.02605e10i −0.779239 + 0.500828i
\(310\) 5.69509e9 2.07284e9i 0.0350246 0.0127479i
\(311\) −1.06985e11 + 3.89393e10i −0.648486 + 0.236029i −0.645257 0.763965i \(-0.723250\pi\)
−0.00322837 + 0.999995i \(0.501028\pi\)
\(312\) 1.06665e10 + 2.23740e11i 0.0637274 + 1.33675i
\(313\) −1.93792e10 1.09905e11i −0.114126 0.647242i −0.987179 0.159617i \(-0.948974\pi\)
0.873053 0.487626i \(-0.162137\pi\)
\(314\) 7.84083e10 1.35807e11i 0.455175 0.788387i
\(315\) −3.88685e11 + 1.85051e11i −2.22434 + 1.05899i
\(316\) 1.38577e10 + 2.40022e10i 0.0781806 + 0.135413i
\(317\) 1.64723e11 1.38219e11i 0.916193 0.768777i −0.0570940 0.998369i \(-0.518183\pi\)
0.973287 + 0.229592i \(0.0737390\pi\)
\(318\) −2.58352e10 6.16722e10i −0.141674 0.338195i
\(319\) −3.16196e9 + 1.79324e10i −0.0170961 + 0.0969570i
\(320\) −2.28428e11 1.91674e11i −1.21780 1.02185i
\(321\) 1.00226e11 + 1.08502e11i 0.526875 + 0.570381i
\(322\) 8.18365e10 + 2.97861e10i 0.424225 + 0.154405i
\(323\) 8.14178e9 0.0416206
\(324\) 1.23926e10 + 1.42974e10i 0.0624753 + 0.0720785i
\(325\) 3.05250e11 1.51768
\(326\) −1.27582e11 4.64362e10i −0.625621 0.227707i
\(327\) −1.11517e11 1.20725e11i −0.539356 0.583892i
\(328\) −1.66955e11 1.40092e11i −0.796466 0.668314i
\(329\) 8.38686e10 4.75642e11i 0.394655 2.23820i
\(330\) −2.76818e10 6.60802e10i −0.128494 0.306732i
\(331\) −2.74008e11 + 2.29920e11i −1.25469 + 1.05281i −0.258465 + 0.966021i \(0.583217\pi\)
−0.996227 + 0.0867905i \(0.972339\pi\)
\(332\) −1.83130e10 3.17190e10i −0.0827252 0.143284i
\(333\) 2.94889e11 + 2.02984e11i 1.31420 + 0.904612i
\(334\) 7.90601e10 1.36936e11i 0.347615 0.602087i
\(335\) 7.76540e10 + 4.40398e11i 0.336870 + 1.91048i
\(336\) 1.66176e10 + 3.48571e11i 0.0711283 + 1.49199i
\(337\) 2.23170e11 8.12271e10i 0.942542 0.343057i 0.175373 0.984502i \(-0.443887\pi\)
0.767169 + 0.641445i \(0.221665\pi\)
\(338\) −1.39399e11 + 5.07372e10i −0.580946 + 0.211447i
\(339\) 3.51890e11 2.26165e11i 1.44713 0.930093i
\(340\) −8.53697e9 4.84155e10i −0.0346456 0.196485i
\(341\) −7.84149e8 + 1.35819e9i −0.00314054 + 0.00543957i
\(342\) 7.03992e9 6.72765e8i 0.0278260 0.00265917i
\(343\) −1.67198e11 2.89595e11i −0.652239 1.12971i
\(344\) −3.42671e10 + 2.87535e10i −0.131936 + 0.110708i
\(345\) −1.09711e11 1.39971e10i −0.416933 0.0531927i
\(346\) 4.11978e10 2.33644e11i 0.154537 0.876420i
\(347\) −1.33042e11 1.11636e11i −0.492614 0.413352i 0.362348 0.932043i \(-0.381975\pi\)
−0.854962 + 0.518691i \(0.826420\pi\)
\(348\) −3.22217e9 + 1.03640e10i −0.0117772 + 0.0378808i
\(349\) −1.18532e11 4.31421e10i −0.427682 0.155664i 0.119205 0.992870i \(-0.461965\pi\)
−0.546888 + 0.837206i \(0.684188\pi\)
\(350\) 5.26212e11 1.87437
\(351\) −1.92550e11 + 3.10409e11i −0.677112 + 1.09157i
\(352\) 1.29622e10 0.0450026
\(353\) −2.45907e11 8.95029e10i −0.842918 0.306797i −0.115768 0.993276i \(-0.536933\pi\)
−0.727149 + 0.686479i \(0.759155\pi\)
\(354\) 2.14817e11 4.85270e10i 0.727032 0.164236i
\(355\) 7.75787e10 + 6.50962e10i 0.259248 + 0.217535i
\(356\) 2.67248e9 1.51564e10i 0.00881838 0.0500115i
\(357\) −4.39014e11 + 5.76902e11i −1.43045 + 1.87973i
\(358\) −5.46457e10 + 4.58532e10i −0.175826 + 0.147535i
\(359\) 1.35110e11 + 2.34018e11i 0.429302 + 0.743574i 0.996811 0.0797935i \(-0.0254261\pi\)
−0.567509 + 0.823367i \(0.692093\pi\)
\(360\) −1.30711e11 4.72646e11i −0.410157 1.48311i
\(361\) 1.61204e11 2.79214e11i 0.499568 0.865277i
\(362\) 3.30047e8 + 1.87179e9i 0.00101015 + 0.00572886i
\(363\) −2.77563e11 1.43081e11i −0.839039 0.432515i
\(364\) 6.43212e10 2.34110e10i 0.192043 0.0698979i
\(365\) 7.26773e11 2.64524e11i 2.14329 0.780094i
\(366\) 3.18538e11 + 1.64203e11i 0.927891 + 0.478317i
\(367\) 5.15365e10 + 2.92278e11i 0.148292 + 0.841006i 0.964665 + 0.263480i \(0.0848704\pi\)
−0.816373 + 0.577525i \(0.804018\pi\)
\(368\) −4.48283e10 + 7.76448e10i −0.127420 + 0.220697i
\(369\) −9.47339e10 3.42555e11i −0.266003 0.961858i
\(370\) −4.03989e11 6.99729e11i −1.12063 1.94098i
\(371\) −1.79749e11 + 1.50827e11i −0.492587 + 0.413330i
\(372\) −5.66077e8 + 7.43874e8i −0.00153261 + 0.00201399i
\(373\) 5.50203e10 3.12036e11i 0.147175 0.834669i −0.818421 0.574620i \(-0.805150\pi\)
0.965595 0.260049i \(-0.0837389\pi\)
\(374\) −9.24230e10 7.75521e10i −0.244263 0.204961i
\(375\) −1.00142e11 + 2.26220e10i −0.261503 + 0.0590733i
\(376\) 5.17002e11 + 1.88174e11i 1.33397 + 0.485527i
\(377\) −2.09532e11 −0.534212
\(378\) −3.31931e11 + 5.35105e11i −0.836246 + 1.34811i
\(379\) −5.63064e11 −1.40179 −0.700893 0.713267i \(-0.747215\pi\)
−0.700893 + 0.713267i \(0.747215\pi\)
\(380\) 1.58150e9 + 5.75617e8i 0.00389083 + 0.00141614i
\(381\) 1.15902e11 3.72793e11i 0.281792 0.906369i
\(382\) −2.04105e11 1.71264e11i −0.490419 0.411511i
\(383\) −6.91992e10 + 3.92448e11i −0.164326 + 0.931939i 0.785431 + 0.618950i \(0.212442\pi\)
−0.949757 + 0.312989i \(0.898670\pi\)
\(384\) −3.52325e11 4.49500e10i −0.826900 0.105497i
\(385\) −1.92596e11 + 1.61608e11i −0.446761 + 0.374877i
\(386\) 1.34044e11 + 2.32171e11i 0.307329 + 0.532310i
\(387\) −7.26168e10 + 6.93957e9i −0.164565 + 0.0157265i
\(388\) −4.30008e9 + 7.44796e9i −0.00963239 + 0.0166838i
\(389\) 4.09644e10 + 2.32321e11i 0.0907055 + 0.514416i 0.995979 + 0.0895871i \(0.0285547\pi\)
−0.905274 + 0.424829i \(0.860334\pi\)
\(390\) 6.93522e11 4.45737e11i 1.51799 0.975635i
\(391\) −1.75021e11 + 6.37024e10i −0.378699 + 0.137835i
\(392\) 8.15642e11 2.96869e11i 1.74467 0.635006i
\(393\) 1.07475e10 + 2.25440e11i 0.0227270 + 0.476721i
\(394\) 6.88743e9 + 3.90605e10i 0.0143987 + 0.0816592i
\(395\) 5.85707e11 1.01447e12i 1.21058 2.09679i
\(396\) 9.10226e9 + 6.26544e9i 0.0186003 + 0.0128033i
\(397\) 1.58328e11 + 2.74232e11i 0.319890 + 0.554066i 0.980465 0.196694i \(-0.0630207\pi\)
−0.660575 + 0.750760i \(0.729687\pi\)
\(398\) −4.56500e11 + 3.83049e11i −0.911941 + 0.765209i
\(399\) −9.58893e9 2.28900e10i −0.0189405 0.0452136i
\(400\) −9.40701e10 + 5.33498e11i −0.183731 + 1.04199i
\(401\) −9.47199e10 7.94794e10i −0.182933 0.153499i 0.546723 0.837314i \(-0.315875\pi\)
−0.729656 + 0.683815i \(0.760320\pi\)
\(402\) 4.43850e11 + 4.80500e11i 0.847654 + 0.917648i
\(403\) −1.69581e10 6.17225e9i −0.0320262 0.0116566i
\(404\) −6.98289e10 −0.130412
\(405\) 2.61442e11 7.55755e11i 0.482868 1.39583i
\(406\) −3.61205e11 −0.659762
\(407\) 1.96471e11 + 7.15097e10i 0.354915 + 0.129178i
\(408\) −5.60348e11 6.06618e11i −1.00112 1.08379i
\(409\) 7.53543e11 + 6.32297e11i 1.33154 + 1.11729i 0.983716 + 0.179730i \(0.0575224\pi\)
0.347820 + 0.937561i \(0.386922\pi\)
\(410\) −1.39291e11 + 7.89957e11i −0.243442 + 1.38063i
\(411\) 2.32936e11 + 5.56050e11i 0.402670 + 0.961227i
\(412\) −3.95850e10 + 3.32157e10i −0.0676850 + 0.0567945i
\(413\) −3.86420e11 6.69299e11i −0.653559 1.13200i
\(414\) −1.46071e11 + 6.95435e10i −0.244378 + 0.116347i
\(415\) −7.74014e11 + 1.34063e12i −1.28095 + 2.21867i
\(416\) 2.59008e10 + 1.46891e11i 0.0424027 + 0.240477i
\(417\) −3.10561e10 6.51433e11i −0.0502961 1.05501i
\(418\) 3.88115e9 1.41262e9i 0.00621824 0.00226326i
\(419\) 1.66721e11 6.06813e10i 0.264257 0.0961816i −0.206494 0.978448i \(-0.566205\pi\)
0.470751 + 0.882266i \(0.343983\pi\)
\(420\) −1.26063e11 + 8.10222e10i −0.197681 + 0.127052i
\(421\) 1.93728e10 + 1.09869e11i 0.0300555 + 0.170453i 0.996141 0.0877702i \(-0.0279741\pi\)
−0.966085 + 0.258223i \(0.916863\pi\)
\(422\) −4.09421e11 + 7.09138e11i −0.628440 + 1.08849i
\(423\) 5.20488e11 + 7.30807e11i 0.790458 + 1.10987i
\(424\) −1.33647e11 2.31484e11i −0.200823 0.347836i
\(425\) −8.62099e11 + 7.23387e11i −1.28176 + 1.07553i
\(426\) 1.46944e11 + 1.87472e10i 0.216176 + 0.0275800i
\(427\) 2.18382e11 1.23850e12i 0.317900 1.80290i
\(428\) 3.93885e10 + 3.30509e10i 0.0567378 + 0.0476087i
\(429\) −6.33353e10 + 2.03715e11i −0.0902792 + 0.290378i
\(430\) 1.54709e11 + 5.63096e10i 0.218227 + 0.0794281i
\(431\) −6.03841e10 −0.0842897 −0.0421449 0.999112i \(-0.513419\pi\)
−0.0421449 + 0.999112i \(0.513419\pi\)
\(432\) −4.83175e11 4.32186e11i −0.667463 0.597027i
\(433\) 7.50233e11 1.02565 0.512827 0.858492i \(-0.328598\pi\)
0.512827 + 0.858492i \(0.328598\pi\)
\(434\) −2.92336e10 1.06402e10i −0.0395529 0.0143961i
\(435\) 4.47449e11 1.01078e11i 0.599158 0.135350i
\(436\) −4.38257e10 3.67742e10i −0.0580818 0.0487364i
\(437\) 1.10719e9 6.27920e9i 0.00145230 0.00823641i
\(438\) 6.85098e11 9.00279e11i 0.889445 1.16881i
\(439\) 2.70968e11 2.27369e11i 0.348199 0.292174i −0.451867 0.892085i \(-0.649242\pi\)
0.800066 + 0.599911i \(0.204798\pi\)
\(440\) −1.43200e11 2.48029e11i −0.182140 0.315475i
\(441\) 1.37013e12 + 3.55390e11i 1.72500 + 0.447437i
\(442\) 6.94160e11 1.20232e12i 0.865087 1.49837i
\(443\) 4.86482e10 + 2.75897e11i 0.0600136 + 0.340354i 1.00000 0.000858900i \(-0.000273396\pi\)
−0.939986 + 0.341213i \(0.889162\pi\)
\(444\) 1.10769e11 + 5.71002e10i 0.135268 + 0.0697291i
\(445\) −6.11250e11 + 2.22477e11i −0.738923 + 0.268946i
\(446\) 1.11604e11 4.06206e10i 0.133559 0.0486115i
\(447\) −3.03679e11 1.56543e11i −0.359775 0.185460i
\(448\) 2.65796e11 + 1.50740e12i 0.311743 + 1.76798i
\(449\) −7.97080e10 + 1.38058e11i −0.0925537 + 0.160308i −0.908585 0.417700i \(-0.862836\pi\)
0.816031 + 0.578008i \(0.196170\pi\)
\(450\) −6.85654e11 + 6.96725e11i −0.788222 + 0.800949i
\(451\) −1.03785e11 1.79762e11i −0.118125 0.204598i
\(452\) 1.11546e11 9.35981e10i 0.125699 0.105474i
\(453\) −8.88682e11 + 1.16781e12i −0.991527 + 1.30295i
\(454\) −6.02043e10 + 3.41435e11i −0.0665083 + 0.377187i
\(455\) −2.21621e12 1.85962e12i −2.42416 2.03411i
\(456\) 2.75757e10 6.22932e9i 0.0298665 0.00674682i
\(457\) 2.65483e11 + 9.66279e10i 0.284717 + 0.103629i 0.480431 0.877032i \(-0.340480\pi\)
−0.195714 + 0.980661i \(0.562702\pi\)
\(458\) 5.96019e11 0.632944
\(459\) −1.91806e11 1.33297e12i −0.201700 1.40173i
\(460\) −3.85005e10 −0.0400919
\(461\) −1.20184e12 4.37435e11i −1.23935 0.451086i −0.362560 0.931960i \(-0.618097\pi\)
−0.876790 + 0.480874i \(0.840319\pi\)
\(462\) −1.09182e11 + 3.51178e11i −0.111497 + 0.358623i
\(463\) 7.15490e11 + 6.00367e11i 0.723584 + 0.607159i 0.928374 0.371647i \(-0.121207\pi\)
−0.204790 + 0.978806i \(0.565651\pi\)
\(464\) 6.45721e10 3.66206e11i 0.0646716 0.366771i
\(465\) 3.91911e10 + 5.00004e9i 0.0388731 + 0.00495947i
\(466\) −8.62351e11 + 7.23599e11i −0.847125 + 0.710822i
\(467\) 2.24705e11 + 3.89200e11i 0.218618 + 0.378658i 0.954386 0.298576i \(-0.0965117\pi\)
−0.735768 + 0.677234i \(0.763178\pi\)
\(468\) −5.28134e10 + 1.15668e11i −0.0508907 + 0.111457i
\(469\) 1.14775e12 1.98796e12i 1.09539 1.89727i
\(470\) −3.51628e11 1.99418e12i −0.332386 1.88506i
\(471\) 8.59979e11 5.52720e11i 0.805181 0.517501i
\(472\) 8.27282e11 3.01106e11i 0.767210 0.279242i
\(473\) −4.00341e10 + 1.45712e10i −0.0367752 + 0.0133851i
\(474\) −8.15949e10 1.71154e12i −0.0742439 1.55734i
\(475\) −6.68994e9 3.79405e10i −0.00602978 0.0341966i
\(476\) −1.26179e11 + 2.18548e11i −0.112656 + 0.195126i
\(477\) 3.45116e10 4.34522e11i 0.0305234 0.384308i
\(478\) 7.99004e11 + 1.38392e12i 0.700041 + 1.21251i
\(479\) 2.85894e11 2.39893e11i 0.248139 0.208213i −0.510232 0.860037i \(-0.670440\pi\)
0.758370 + 0.651824i \(0.225996\pi\)
\(480\) −1.26171e11 3.01186e11i −0.108486 0.258970i
\(481\) −4.17779e11 + 2.36934e12i −0.355872 + 2.01825i
\(482\) −4.26583e11 3.57946e11i −0.359991 0.302068i
\(483\) 3.85225e11 + 4.17034e11i 0.322071 + 0.348666i
\(484\) −1.02147e11 3.71786e10i −0.0846102 0.0307956i
\(485\) 3.63493e11 0.298303
\(486\) −2.75994e11 1.13673e12i −0.224407 0.924260i
\(487\) −5.44380e11 −0.438553 −0.219276 0.975663i \(-0.570370\pi\)
−0.219276 + 0.975663i \(0.570370\pi\)
\(488\) 1.34620e12 + 4.89976e11i 1.07453 + 0.391098i
\(489\) −6.00561e11 6.50152e11i −0.474971 0.514191i
\(490\) −2.44723e12 2.05347e12i −1.91775 1.60918i
\(491\) 1.29395e10 7.33835e10i 0.0100473 0.0569812i −0.979372 0.202066i \(-0.935234\pi\)
0.989419 + 0.145085i \(0.0463455\pi\)
\(492\) −4.78031e10 1.14112e11i −0.0367801 0.0877990i
\(493\) 5.91767e11 4.96551e11i 0.451169 0.378576i
\(494\) 2.37634e10 + 4.11594e10i 0.0179530 + 0.0310955i
\(495\) 3.69784e10 4.65580e11i 0.0276837 0.348554i
\(496\) 1.60135e10 2.77363e10i 0.0118801 0.0205769i
\(497\) −9.02695e10 5.11944e11i −0.0663647 0.376373i
\(498\) 1.07828e11 + 2.26180e12i 0.0785596 + 1.64787i
\(499\) 9.80747e11 3.56963e11i 0.708116 0.257733i 0.0372439 0.999306i \(-0.488142\pi\)
0.670872 + 0.741573i \(0.265920\pi\)
\(500\) −3.35829e10 + 1.22232e10i −0.0240300 + 0.00874620i
\(501\) 8.67127e11 5.57315e11i 0.614912 0.395213i
\(502\) −8.60114e10 4.87795e11i −0.0604490 0.342823i
\(503\) −2.08720e11 + 3.61513e11i −0.145381 + 0.251807i −0.929515 0.368784i \(-0.879774\pi\)
0.784134 + 0.620591i \(0.213107\pi\)
\(504\) −1.04552e12 + 2.28982e12i −0.721763 + 1.58075i
\(505\) 1.47569e12 + 2.55597e12i 1.00968 + 1.74882i
\(506\) −7.23792e10 + 6.07334e10i −0.0490836 + 0.0411860i
\(507\) −9.59285e11 1.22387e11i −0.644781 0.0822618i
\(508\) 2.35984e10 1.33833e11i 0.0157216 0.0891614i
\(509\) 3.99625e11 + 3.35325e11i 0.263890 + 0.221430i 0.765126 0.643881i \(-0.222677\pi\)
−0.501236 + 0.865310i \(0.667121\pi\)
\(510\) −9.02358e11 + 2.90239e12i −0.590627 + 1.89972i
\(511\) −3.73062e12 1.35783e12i −2.42040 0.880953i
\(512\) −1.71544e12 −1.10322
\(513\) 4.28017e10 + 1.71296e10i 0.0272855 + 0.0109199i
\(514\) −8.41220e11 −0.531589
\(515\) 2.05235e12 + 7.46994e11i 1.28564 + 0.467934i
\(516\) −2.47692e10 + 5.59535e9i −0.0153811 + 0.00347459i
\(517\) 4.01404e11 + 3.36818e11i 0.247101 + 0.207342i
\(518\) −7.20198e11 + 4.08444e12i −0.439509 + 2.49258i
\(519\) 9.36599e11 1.23077e12i 0.566632 0.744603i
\(520\) 2.52458e12 2.11838e12i 1.51417 1.27054i
\(521\) 2.08413e11 + 3.60982e11i 0.123924 + 0.214643i 0.921312 0.388825i \(-0.127119\pi\)
−0.797388 + 0.603467i \(0.793785\pi\)
\(522\) 4.70650e11 4.78250e11i 0.277448 0.281927i
\(523\) −1.46882e12 + 2.54407e12i −0.858441 + 1.48686i 0.0149738 + 0.999888i \(0.495234\pi\)
−0.873415 + 0.486976i \(0.838100\pi\)
\(524\) 1.36428e10 + 7.73721e10i 0.00790519 + 0.0448325i
\(525\) 3.04909e12 + 1.57177e12i 1.75167 + 0.902966i
\(526\) 1.75778e12 6.39780e11i 1.00122 0.364414i
\(527\) 6.25209e10 2.27557e10i 0.0353083 0.0128512i
\(528\) −3.36522e11 1.73473e11i −0.188434 0.0971358i
\(529\) −2.87438e11 1.63014e12i −0.159586 0.905056i
\(530\) −4.91888e11 + 8.51975e11i −0.270785 + 0.469014i
\(531\) 1.38968e12 + 3.60462e11i 0.758561 + 0.196759i
\(532\) −4.31951e9 7.48161e9i −0.00233793 0.00404942i
\(533\) 1.82972e12 1.53531e12i 0.981999 0.823995i
\(534\) −5.76200e11 + 7.57177e11i −0.306646 + 0.402960i
\(535\) 3.77377e11 2.14021e12i 0.199151 1.12944i
\(536\) 2.00312e12 + 1.68082e12i 1.04825 + 0.879589i
\(537\) −4.53600e11 + 1.02468e11i −0.235391 + 0.0531746i
\(538\) 2.53186e12 + 9.21523e11i 1.30293 + 0.474227i
\(539\) 8.26674e11 0.421876
\(540\) 5.69830e10 2.72484e11i 0.0288385 0.137901i
\(541\) −3.08586e12 −1.54878 −0.774388 0.632711i \(-0.781942\pi\)
−0.774388 + 0.632711i \(0.781942\pi\)
\(542\) 1.00111e12 + 3.64376e11i 0.498296 + 0.181365i
\(543\) −3.67851e9 + 1.18317e10i −0.00181582 + 0.00584049i
\(544\) −4.21254e11 3.53474e11i −0.206229 0.173046i
\(545\) −4.19889e11 + 2.38131e12i −0.203869 + 1.15620i
\(546\) −4.19779e12 5.35558e11i −2.02141 0.257893i
\(547\) 7.06610e11 5.92916e11i 0.337471 0.283172i −0.458265 0.888816i \(-0.651529\pi\)
0.795736 + 0.605644i \(0.207084\pi\)
\(548\) 1.04930e11 + 1.81745e11i 0.0497038 + 0.0860894i
\(549\) 1.35528e12 + 1.90292e12i 0.636725 + 0.894013i
\(550\) −2.85449e11 + 4.94413e11i −0.133014 + 0.230387i
\(551\) 4.59215e9 + 2.60434e10i 0.00212243 + 0.0120369i
\(552\) −5.44045e11 + 3.49665e11i −0.249407 + 0.160297i
\(553\) −5.65039e12 + 2.05657e12i −2.56930 + 0.935150i
\(554\) 2.26178e12 8.23219e11i 1.02013 0.371297i
\(555\) −2.50820e11 5.26121e12i −0.112213 2.35379i
\(556\) −3.94223e10 2.23575e11i −0.0174946 0.0992171i
\(557\) 2.85740e11 4.94916e11i 0.125783 0.217863i −0.796256 0.604960i \(-0.793189\pi\)
0.922039 + 0.387097i \(0.126522\pi\)
\(558\) 5.21794e10 2.48423e10i 0.0227848 0.0108477i
\(559\) −2.45120e11 4.24560e11i −0.106176 0.183902i
\(560\) 3.93312e12 3.30028e12i 1.69002 1.41809i
\(561\) −3.03892e11 7.25431e11i −0.129535 0.309217i
\(562\) −1.36713e11 + 7.75338e11i −0.0578091 + 0.327852i
\(563\) −2.05907e12 1.72777e12i −0.863741 0.724765i 0.0990298 0.995084i \(-0.468426\pi\)
−0.962771 + 0.270320i \(0.912871\pi\)
\(564\) 2.11922e11 + 2.29421e11i 0.0881902 + 0.0954724i
\(565\) −5.78329e12 2.10495e12i −2.38757 0.869006i
\(566\) −2.65576e12 −1.08771
\(567\) −3.52167e12 + 2.10915e12i −1.43095 + 0.857007i
\(568\) 5.92173e11 0.238716
\(569\) −3.85166e12 1.40189e12i −1.54043 0.560671i −0.574282 0.818657i \(-0.694719\pi\)
−0.966149 + 0.257986i \(0.916941\pi\)
\(570\) −7.06015e10 7.64313e10i −0.0280141 0.0303273i
\(571\) 2.74610e12 + 2.30425e12i 1.08107 + 0.907127i 0.996009 0.0892490i \(-0.0284467\pi\)
0.0850621 + 0.996376i \(0.472891\pi\)
\(572\) −1.28955e10 + 7.31338e10i −0.00503680 + 0.0285651i
\(573\) −6.71108e11 1.60202e12i −0.260074 0.620830i
\(574\) 3.15419e12 2.64668e12i 1.21279 1.01765i
\(575\) 4.40663e11 + 7.63251e11i 0.168113 + 0.291180i
\(576\) −2.34219e12 1.61222e12i −0.886586 0.610272i
\(577\) 1.95591e11 3.38774e11i 0.0734613 0.127239i −0.826955 0.562268i \(-0.809929\pi\)
0.900416 + 0.435030i \(0.143262\pi\)
\(578\) 4.45629e11 + 2.52729e12i 0.166073 + 0.941846i
\(579\) 8.32223e10 + 1.74567e12i 0.0307742 + 0.645519i
\(580\) 1.50053e11 5.46149e10i 0.0550579 0.0200394i
\(581\) 7.46701e12 2.71777e12i 2.71866 0.989510i
\(582\) 4.47282e11 2.87474e11i 0.161595 0.103859i
\(583\) −4.42059e10 2.50704e11i −0.0158479 0.0898780i
\(584\) 2.26122e12 3.91655e12i 0.804424 1.39330i
\(585\) 5.34994e12 5.11263e11i 1.88863 0.180486i
\(586\) −5.75153e11 9.96195e11i −0.201486 0.348984i
\(587\) 2.24873e10 1.88691e10i 0.00781745 0.00655962i −0.638871 0.769314i \(-0.720598\pi\)
0.646688 + 0.762755i \(0.276154\pi\)
\(588\) 4.88769e11 + 6.23577e10i 0.168619 + 0.0215125i
\(589\) −3.95511e8 + 2.24305e9i −0.000135406 + 0.000767928i
\(590\) −2.48215e12 2.08277e12i −0.843323 0.707632i
\(591\) −7.67632e10 + 2.46905e11i −0.0258827 + 0.0832503i
\(592\) −4.01225e12 1.46034e12i −1.34258 0.488659i
\(593\) −1.20473e12 −0.400076 −0.200038 0.979788i \(-0.564107\pi\)
−0.200038 + 0.979788i \(0.564107\pi\)
\(594\) −3.22709e11 6.02145e11i −0.106358 0.198455i
\(595\) 1.06661e13 3.48882
\(596\) −1.11758e11 4.06767e10i −0.0362804 0.0132050i
\(597\) −3.78929e12 + 8.55999e11i −1.22088 + 0.275796i
\(598\) −8.32870e11 6.98861e11i −0.266331 0.223478i
\(599\) −8.23667e11 + 4.67125e12i −0.261415 + 1.48256i 0.517637 + 0.855600i \(0.326812\pi\)
−0.779052 + 0.626959i \(0.784299\pi\)
\(600\) −2.36640e12 + 3.10966e12i −0.745432 + 0.979563i
\(601\) −8.87445e11 + 7.44655e11i −0.277464 + 0.232820i −0.770891 0.636968i \(-0.780188\pi\)
0.493427 + 0.869787i \(0.335744\pi\)
\(602\) −4.22555e11 7.31886e11i −0.131129 0.227122i
\(603\) 1.13662e12 + 4.10997e12i 0.350095 + 1.26593i
\(604\) −2.55419e11 + 4.42399e11i −0.0780886 + 0.135253i
\(605\) 7.97812e11 + 4.52462e12i 0.242104 + 1.37304i
\(606\) 3.83728e12 + 1.97807e12i 1.15584 + 0.595820i
\(607\) 1.89938e12 6.91316e11i 0.567887 0.206694i −0.0420891 0.999114i \(-0.513401\pi\)
0.609976 + 0.792420i \(0.291179\pi\)
\(608\) 1.76899e10 6.43859e9i 0.00524999 0.00191084i
\(609\) −2.09297e12 1.07890e12i −0.616574 0.317837i
\(610\) −9.15589e11 5.19256e12i −0.267742 1.51844i
\(611\) −3.01482e12 + 5.22182e12i −0.875136 + 1.51578i
\(612\) −1.24955e11 4.51833e11i −0.0360058 0.130196i
\(613\) −2.38705e12 4.13449e12i −0.682793 1.18263i −0.974125 0.226010i \(-0.927432\pi\)
0.291333 0.956622i \(-0.405901\pi\)
\(614\) 1.19799e12 1.00523e12i 0.340170 0.285437i
\(615\) −3.16667e12 + 4.16128e12i −0.892615 + 1.17297i
\(616\) −2.55285e11 + 1.44779e12i −0.0714350 + 0.405128i
\(617\) −3.79697e12 3.18604e12i −1.05476 0.885050i −0.0611748 0.998127i \(-0.519485\pi\)
−0.993586 + 0.113077i \(0.963929\pi\)
\(618\) 3.11621e12 7.03950e11i 0.859366 0.194130i
\(619\) 5.39510e12 + 1.96366e12i 1.47704 + 0.537598i 0.950002 0.312244i \(-0.101081\pi\)
0.527037 + 0.849842i \(0.323303\pi\)
\(620\) 1.37532e10 0.00373800
\(621\) −1.05412e12 3.33429e10i −0.284431 0.00899686i
\(622\) 2.45021e12 0.656366
\(623\) 3.13763e12 + 1.14200e12i 0.834459 + 0.303718i
\(624\) 1.29340e12 4.16017e12i 0.341510 1.09845i
\(625\) −2.29553e12 1.92618e12i −0.601760 0.504936i
\(626\) −4.17063e11 + 2.36528e12i −0.108547 + 0.615600i
\(627\) 2.67084e10 + 3.40749e9i 0.00690151 + 0.000880502i
\(628\) 2.72605e11 2.28743e11i 0.0699384 0.0586853i
\(629\) −4.43500e12 7.68165e12i −1.12971 1.95671i
\(630\) 9.22261e12 8.81351e11i 2.33250 0.222903i
\(631\) 8.41204e11 1.45701e12i 0.211237 0.365873i −0.740865 0.671654i \(-0.765584\pi\)
0.952102 + 0.305781i \(0.0989176\pi\)
\(632\) −1.18943e12 6.74562e12i −0.296561 1.68188i
\(633\) −4.49051e12 + 2.88611e12i −1.11168 + 0.714491i
\(634\) −4.34863e12 + 1.58277e12i −1.06893 + 0.389060i
\(635\) −5.39744e12 + 1.96451e12i −1.31736 + 0.479481i
\(636\) −7.22553e9 1.51563e11i −0.00175111 0.0367313i
\(637\) 1.65184e12 + 9.36805e12i 0.397503 + 2.25435i
\(638\) 1.95940e11 3.39378e11i 0.0468198 0.0810943i
\(639\) 7.95454e11 + 5.47542e11i 0.188739 + 0.129916i
\(640\) 2.61287e12 + 4.52562e12i 0.615613 + 1.06627i
\(641\) −1.53084e12 + 1.28452e12i −0.358152 + 0.300525i −0.804054 0.594557i \(-0.797328\pi\)
0.445902 + 0.895082i \(0.352883\pi\)
\(642\) −1.22825e12 2.93200e12i −0.285352 0.681172i
\(643\) −6.89388e11 + 3.90971e12i −0.159043 + 0.901977i 0.795953 + 0.605358i \(0.206970\pi\)
−0.954996 + 0.296619i \(0.904141\pi\)
\(644\) 1.51392e11 + 1.27033e11i 0.0346830 + 0.0291025i
\(645\) 7.28254e11 + 7.88389e11i 0.165678 + 0.179358i
\(646\) −1.64654e11 5.99291e10i −0.0371985 0.0135391i
\(647\) 1.84105e12 0.413043 0.206522 0.978442i \(-0.433786\pi\)
0.206522 + 0.978442i \(0.433786\pi\)
\(648\) −1.66950e12 4.36794e12i −0.371963 0.973172i
\(649\) 8.38471e11 0.185518
\(650\) −6.17317e12 2.24685e12i −1.35643 0.493701i
\(651\) −1.37610e11 1.48973e11i −0.0300286 0.0325082i
\(652\) −2.36019e11 1.98043e11i −0.0511484 0.0429186i
\(653\) −8.65790e11 + 4.91014e12i −0.186339 + 1.05678i 0.737884 + 0.674927i \(0.235825\pi\)
−0.924223 + 0.381853i \(0.875286\pi\)
\(654\) 1.36662e12 + 3.26230e12i 0.292111 + 0.697307i
\(655\) 2.54376e12 2.13447e12i 0.539996 0.453110i
\(656\) 2.11946e12 + 3.67101e12i 0.446845 + 0.773959i
\(657\) 6.65882e12 3.17023e12i 1.39429 0.663813i
\(658\) −5.19716e12 + 9.00174e12i −1.08081 + 1.87202i
\(659\) −1.44897e12 8.21749e12i −0.299277 1.69729i −0.649290 0.760541i \(-0.724934\pi\)
0.350012 0.936745i \(-0.386177\pi\)
\(660\) −7.74199e9 1.62396e11i −0.00158820 0.0333141i
\(661\) −5.52723e12 + 2.01175e12i −1.12616 + 0.409889i −0.836897 0.547360i \(-0.815633\pi\)
−0.289264 + 0.957249i \(0.593411\pi\)
\(662\) 7.23372e12 2.63286e12i 1.46386 0.532803i
\(663\) 7.61351e12 4.89331e12i 1.53029 0.983540i
\(664\) 1.57184e12 + 8.91436e12i 0.313800 + 1.77965i
\(665\) −1.82568e11 + 3.16217e11i −0.0362015 + 0.0627028i
\(666\) −4.46954e12 6.27560e12i −0.880297 1.23601i
\(667\) −3.02482e11 5.23915e11i −0.0591744 0.102493i
\(668\) 2.74871e11 2.30644e11i 0.0534115 0.0448176i
\(669\) 7.68011e11 + 9.79836e10i 0.148235 + 0.0189119i
\(670\) 1.67121e12 9.47789e12i 0.320401 1.81708i
\(671\) 1.04520e12 + 8.77025e11i 0.199043 + 0.167017i
\(672\) −4.97639e11 + 1.60063e12i −0.0941353 + 0.302781i
\(673\) 5.28162e12 + 1.92235e12i 0.992428 + 0.361214i 0.786660 0.617386i \(-0.211809\pi\)
0.205768 + 0.978601i \(0.434031\pi\)
\(674\) −5.11112e12 −0.953996
\(675\) −6.05404e12 + 1.98909e12i −1.12248 + 0.368798i
\(676\) −3.36637e11 −0.0620015
\(677\) 5.26169e12 + 1.91510e12i 0.962667 + 0.350382i 0.775078 0.631866i \(-0.217711\pi\)
0.187589 + 0.982248i \(0.439933\pi\)
\(678\) −8.78112e12 + 1.98365e12i −1.59594 + 0.360522i
\(679\) −1.42933e12 1.19935e12i −0.258059 0.216537i
\(680\) −2.10986e12 + 1.19656e13i −0.378410 + 2.14607i
\(681\) −1.36870e12 + 1.79859e12i −0.243863 + 0.320457i
\(682\) 2.58553e10 2.16952e10i 0.00457635 0.00384002i
\(683\) −7.98478e11 1.38301e12i −0.140401 0.243182i 0.787247 0.616638i \(-0.211506\pi\)
−0.927648 + 0.373457i \(0.878172\pi\)
\(684\) 1.55343e10 + 4.02934e9i 0.00271355 + 0.000703852i
\(685\) 4.43498e12 7.68160e12i 0.769633 1.33304i
\(686\) 1.24968e12 + 7.08726e12i 0.215446 + 1.22186i
\(687\) 3.45357e12 + 1.78028e12i 0.591512 + 0.304917i
\(688\) 8.17559e11 2.97567e11i 0.139114 0.0506334i
\(689\) 2.75270e12 1.00190e12i 0.465343 0.169371i
\(690\) 2.11570e12 + 1.09062e12i 0.355331 + 0.183169i
\(691\) −5.52292e11 3.13220e12i −0.0921547 0.522635i −0.995582 0.0938943i \(-0.970068\pi\)
0.903427 0.428741i \(-0.141043\pi\)
\(692\) 2.69191e11 4.66253e11i 0.0446256 0.0772937i
\(693\) −1.68159e12 + 1.70874e12i −0.276963 + 0.281435i
\(694\) 1.86884e12 + 3.23693e12i 0.305812 + 0.529682i
\(695\) −7.35047e12 + 6.16777e12i −1.19504 + 1.00276i
\(696\) 1.62436e12 2.13455e12i 0.262386 0.344798i
\(697\) −1.52914e12 + 8.67218e12i −0.245414 + 1.39181i
\(698\) 2.07956e12 + 1.74495e12i 0.331605 + 0.278250i
\(699\) −7.15816e12 + 1.61702e12i −1.13411 + 0.256194i
\(700\) 1.12211e12 + 4.08414e11i 0.176642 + 0.0642923i
\(701\) 5.90164e12 0.923085 0.461543 0.887118i \(-0.347296\pi\)
0.461543 + 0.887118i \(0.347296\pi\)
\(702\) 6.17881e12 4.86020e12i 0.960258 0.755330i
\(703\) 3.03650e11 0.0468893
\(704\) −1.56049e12 5.67973e11i −0.239434 0.0871467i
\(705\) 3.91904e12 1.26054e13i 0.597488 1.92179i
\(706\) 4.31426e12 + 3.62009e12i 0.653559 + 0.548401i
\(707\) 2.63074e12 1.49196e13i 0.395995 2.24580i
\(708\) 4.95744e11 + 6.32476e10i 0.0741495 + 0.00946006i
\(709\) −7.66212e12 + 6.42928e12i −1.13878 + 0.955552i −0.999398 0.0346867i \(-0.988957\pi\)
−0.139384 + 0.990238i \(0.544512\pi\)
\(710\) −1.08975e12 1.88749e12i −0.160939 0.278755i
\(711\) 4.63947e12 1.01610e13i 0.680856 1.49116i
\(712\) −1.90179e12 + 3.29400e12i −0.277334 + 0.480357i
\(713\) −9.04780e9 5.13126e10i −0.00131111 0.00743569i
\(714\) 1.31247e13 8.43544e12i 1.88994 1.21469i
\(715\) 2.94946e12 1.07351e12i 0.422051 0.153614i
\(716\) −1.52116e11 + 5.53658e10i −0.0216305 + 0.00787286i
\(717\) 4.96069e11 + 1.04055e13i 0.0700980 + 1.47038i
\(718\) −1.00985e12 5.72712e12i −0.141806 0.804223i
\(719\) 3.30047e12 5.71658e12i 0.460570 0.797731i −0.538419 0.842677i \(-0.680978\pi\)
0.998989 + 0.0449463i \(0.0143117\pi\)
\(720\) −7.55156e11 + 9.50786e12i −0.104723 + 1.31852i
\(721\) −5.60555e12 9.70909e12i −0.772519 1.33804i
\(722\) −5.31530e12 + 4.46007e12i −0.727965 + 0.610835i
\(723\) −1.40263e12 3.34826e12i −0.190906 0.455719i
\(724\) −7.48968e8 + 4.24761e9i −0.000101307 + 0.000574541i
\(725\) −2.80016e12 2.34962e12i −0.376411 0.315846i
\(726\) 4.56008e12 + 4.93662e12i 0.609197 + 0.659501i
\(727\) −7.75046e12 2.82094e12i −1.02902 0.374532i −0.228311 0.973588i \(-0.573320\pi\)
−0.800707 + 0.599057i \(0.795542\pi\)
\(728\) −1.69168e13 −2.23217
\(729\) 1.79613e12 7.41105e12i 0.235540 0.971865i
\(730\) −1.66448e13 −2.16934
\(731\) 1.69840e12 + 6.18169e11i 0.219995 + 0.0800716i
\(732\) 5.51815e11 + 5.97380e11i 0.0710384 + 0.0769043i
\(733\) −4.29332e12 3.60252e12i −0.549320 0.460934i 0.325391 0.945580i \(-0.394504\pi\)
−0.874711 + 0.484646i \(0.838949\pi\)
\(734\) 1.10913e12 6.29018e12i 0.141042 0.799891i
\(735\) −8.04662e12 1.92084e13i −1.01700 2.42771i
\(736\) −3.29896e11 + 2.76816e11i −0.0414407 + 0.0347729i
\(737\) 1.24522e12 + 2.15678e12i 0.155468 + 0.269278i
\(738\) −6.05603e11 + 7.62490e12i −0.0751509 + 0.946194i
\(739\) 4.77222e12 8.26573e12i 0.588601 1.01949i −0.405815 0.913955i \(-0.633012\pi\)
0.994416 0.105531i \(-0.0336543\pi\)
\(740\) −3.18388e11 1.80567e12i −0.0390314 0.221358i
\(741\) 1.47537e10 + 3.09474e11i 0.00179771 + 0.0377088i
\(742\) 4.74531e12 1.72715e12i 0.574707 0.209176i
\(743\) 5.99986e12 2.18377e12i 0.722257 0.262880i 0.0453734 0.998970i \(-0.485552\pi\)
0.676884 + 0.736090i \(0.263330\pi\)
\(744\) 1.94343e11 1.24907e11i 0.0232537 0.0149455i
\(745\) 8.72878e11 + 4.95034e12i 0.103813 + 0.588751i
\(746\) −3.40949e12 + 5.90541e12i −0.403055 + 0.698112i
\(747\) −6.13108e12 + 1.34279e13i −0.720434 + 1.57784i
\(748\) −1.36894e11 2.37107e11i −0.0159892 0.0276941i
\(749\) −8.54558e12 + 7.17059e12i −0.992141 + 0.832505i
\(750\) 2.19172e12 + 2.79622e11i 0.252935 + 0.0322697i
\(751\) −4.90563e11 + 2.78212e12i −0.0562750 + 0.319151i −0.999931 0.0117777i \(-0.996251\pi\)
0.943656 + 0.330929i \(0.107362\pi\)
\(752\) −8.19729e12 6.87834e12i −0.934738 0.784338i
\(753\) 9.58633e11 3.08339e12i 0.108661 0.349503i
\(754\) 4.23742e12 + 1.54230e12i 0.477453 + 0.173779i
\(755\) 2.15910e13 2.41831
\(756\) −1.12313e12 + 8.83445e11i −0.125050 + 0.0983630i
\(757\) 1.13228e13 1.25321 0.626605 0.779337i \(-0.284444\pi\)
0.626605 + 0.779337i \(0.284444\pi\)
\(758\) 1.13870e13 + 4.14454e12i 1.25285 + 0.456000i
\(759\) −6.00802e11 + 1.35721e11i −0.0657118 + 0.0148443i
\(760\) −3.18629e11 2.67362e11i −0.0346437 0.0290695i
\(761\) −4.72301e10 + 2.67855e11i −0.00510491 + 0.0289514i −0.987254 0.159154i \(-0.949123\pi\)
0.982149 + 0.188105i \(0.0602346\pi\)
\(762\) −5.08793e12 + 6.68599e12i −0.546694 + 0.718403i
\(763\) 9.50826e12 7.97837e12i 1.01564 0.852224i
\(764\) −3.02313e11 5.23621e11i −0.0321023 0.0556028i
\(765\) −1.38979e13 + 1.41223e13i −1.46714 + 1.49083i
\(766\) 4.28812e12 7.42725e12i 0.450026 0.779468i
\(767\) 1.67541e12 + 9.50174e12i 0.174801 + 0.991343i
\(768\) −2.42921e12 1.25223e12i −0.251964 0.129885i
\(769\) 1.45226e13 5.28580e12i 1.49753 0.545058i 0.542113 0.840306i \(-0.317624\pi\)
0.955421 + 0.295248i \(0.0954022\pi\)
\(770\) 5.08448e12 1.85060e12i 0.521241 0.189716i
\(771\) −4.87437e12 2.51268e12i −0.496791 0.256090i
\(772\) 1.05641e11 + 5.99123e11i 0.0107043 + 0.0607069i
\(773\) 9.37174e12 1.62323e13i 0.944088 1.63521i 0.186520 0.982451i \(-0.440279\pi\)
0.757567 0.652757i \(-0.226388\pi\)
\(774\) 1.51963e12 + 3.94169e11i 0.152196 + 0.0394773i
\(775\) −1.57414e11 2.72648e11i −0.0156742 0.0271485i
\(776\) 1.62821e12 1.36623e12i 0.161188 0.135253i
\(777\) −1.63731e13 + 2.15157e13i −1.61153 + 2.11769i
\(778\) 8.81604e11 4.99982e12i 0.0862711 0.489268i
\(779\) −2.30930e11 1.93773e11i −0.0224678 0.0188527i
\(780\) 1.82484e12 4.12230e11i 0.176522 0.0398762i
\(781\) 5.29974e11 + 1.92895e11i 0.0509712 + 0.0185520i
\(782\) 4.00840e12 0.383301
\(783\) 4.15564e12 1.36536e12i 0.395103 0.129814i
\(784\) −1.68820e13 −1.59588
\(785\) −1.41337e13 5.14424e12i −1.32844 0.483512i
\(786\) 1.44204e12 4.63826e12i 0.134765 0.433464i
\(787\) 1.20410e13 + 1.01036e13i 1.11886 + 0.938838i 0.998546 0.0538970i \(-0.0171643\pi\)
0.120318 + 0.992735i \(0.461609\pi\)
\(788\) −1.56295e10 + 8.86392e10i −0.00144403 + 0.00818951i
\(789\) 1.20963e13 + 1.54326e12i 1.11123 + 0.141772i
\(790\) −1.93122e13 + 1.62048e13i −1.76404 + 1.48021i
\(791\) 1.57958e13 + 2.73591e13i 1.43465 + 2.48489i
\(792\) −1.58429e12 2.22448e12i −0.143078 0.200893i
\(793\) −7.85015e12 + 1.35969e13i −0.704934 + 1.22098i
\(794\) −1.18338e12 6.71129e12i −0.105665 0.599258i
\(795\) −5.39500e12 + 3.46744e12i −0.479005 + 0.307863i
\(796\) −1.27075e12 + 4.62515e11i −0.112189 + 0.0408336i
\(797\) −9.61192e12 + 3.49845e12i −0.843816 + 0.307124i −0.727516 0.686090i \(-0.759325\pi\)
−0.116299 + 0.993214i \(0.537103\pi\)
\(798\) 2.54335e10 + 5.33494e11i 0.00222021 + 0.0465711i
\(799\) −3.86019e12 2.18922e13i −0.335080 1.90033i
\(800\) −1.30105e12 + 2.25348e12i −0.112302 + 0.194513i
\(801\) −5.60038e12 + 2.66631e12i −0.480697 + 0.228857i
\(802\) 1.33053e12 + 2.30454e12i 0.113564 + 0.196698i
\(803\) 3.29950e12 2.76861e12i 0.280045 0.234986i
\(804\) 5.73541e11 + 1.36912e12i 0.0484074 + 0.115555i
\(805\) 1.45047e12 8.22603e12i 0.121738 0.690412i
\(806\) 2.97518e11 + 2.49647e11i 0.0248316 + 0.0208362i
\(807\) 1.19181e13 + 1.29022e13i 0.989182 + 1.07086i
\(808\) 1.62170e13 + 5.90251e12i 1.33850 + 0.487175i
\(809\) 1.29126e13 1.05985 0.529926 0.848044i \(-0.322220\pi\)
0.529926 + 0.848044i \(0.322220\pi\)
\(810\) −1.08501e13 + 1.33595e13i −0.885628 + 1.09045i
\(811\) −4.15809e12 −0.337521 −0.168760 0.985657i \(-0.553976\pi\)
−0.168760 + 0.985657i \(0.553976\pi\)
\(812\) −7.70243e11 2.80345e11i −0.0621764 0.0226304i
\(813\) 4.71249e12 + 5.10162e12i 0.378306 + 0.409544i
\(814\) −3.44694e12 2.89233e12i −0.275185 0.230907i
\(815\) −2.26127e12 + 1.28243e13i −0.179532 + 1.01818i
\(816\) 6.20595e12 + 1.48144e13i 0.490007 + 1.16971i
\(817\) −4.73978e10 + 3.97715e10i −0.00372185 + 0.00312300i
\(818\) −1.05850e13 1.83337e13i −0.826610 1.43173i
\(819\) −2.27240e13 1.56418e13i −1.76485 1.21481i
\(820\) −9.10143e11 + 1.57641e12i −0.0702987 + 0.121761i
\(821\) 1.60090e12 + 9.07914e12i 0.122976 + 0.697430i 0.982490 + 0.186318i \(0.0596553\pi\)
−0.859514 + 0.511112i \(0.829234\pi\)
\(822\) −6.17837e11 1.29598e13i −0.0472009 0.990087i
\(823\) 6.31694e12 2.29918e12i 0.479963 0.174692i −0.0906975 0.995878i \(-0.528910\pi\)
0.570660 + 0.821186i \(0.306687\pi\)
\(824\) 1.20008e13 4.36795e12i 0.906857 0.330069i
\(825\) −3.13080e12 + 2.01221e12i −0.235295 + 0.151227i
\(826\) 2.88820e12 + 1.63798e13i 0.215882 + 1.22433i
\(827\) −8.44409e12 + 1.46256e13i −0.627737 + 1.08727i 0.360267 + 0.932849i \(0.382685\pi\)
−0.988005 + 0.154424i \(0.950648\pi\)
\(828\) −3.65460e11 + 3.49249e10i −0.0270211 + 0.00258225i
\(829\) 2.06589e12 + 3.57823e12i 0.151919 + 0.263132i 0.931933 0.362631i \(-0.118121\pi\)
−0.780014 + 0.625762i \(0.784788\pi\)
\(830\) 2.55211e13 2.14147e13i 1.86659 1.56625i
\(831\) 1.55646e13 + 1.98574e12i 1.13222 + 0.144450i
\(832\) 3.31826e12 1.88188e13i 0.240079 1.36156i
\(833\) −2.68657e13 2.25430e13i −1.93329 1.62222i
\(834\) −4.16694e12 + 1.34027e13i −0.298243 + 0.959282i
\(835\) −1.42512e13 5.18700e12i −1.01452 0.369256i
\(836\) 9.37266e9 0.000663643
\(837\) 3.76551e11 + 1.19107e10i 0.0265191 + 0.000838830i
\(838\) −3.81830e12 −0.267468
\(839\) 7.64227e11 + 2.78156e11i 0.0532468 + 0.0193803i 0.368506 0.929625i \(-0.379869\pi\)
−0.315259 + 0.949006i \(0.602092\pi\)
\(840\) 3.61253e13 8.16069e12i 2.50354 0.565549i
\(841\) −9.19101e12 7.71218e12i −0.633551 0.531612i
\(842\) 4.16926e11 2.36451e12i 0.0285861 0.162120i
\(843\) −3.10806e12 + 4.08426e12i −0.211966 + 0.278541i
\(844\) −1.42345e12 + 1.19442e12i −0.0965608 + 0.0810241i
\(845\) 7.11413e12 + 1.23220e13i 0.480028 + 0.831433i
\(846\) −5.14675e12 1.86105e13i −0.345435 1.24908i
\(847\) 1.17919e13 2.04241e13i 0.787241 1.36354i
\(848\) 9.02753e11 + 5.11977e12i 0.0599498 + 0.339992i
\(849\) −1.53885e13 7.93261e12i −1.01651 0.524000i
\(850\) 2.27591e13 8.28365e12i 1.49545 0.544298i
\(851\) −6.52745e12 + 2.37580e12i −0.426639 + 0.155284i
\(852\) 2.98796e11 + 1.54026e11i 0.0194266 + 0.0100142i
\(853\) −2.60392e12 1.47675e13i −0.168406 0.955075i −0.945483 0.325671i \(-0.894410\pi\)
0.777078 0.629405i \(-0.216701\pi\)
\(854\) −1.35326e13 + 2.34392e13i −0.870607 + 1.50794i
\(855\) −1.80797e11 6.53757e11i −0.0115703 0.0418378i
\(856\) −6.35382e12 1.10051e13i −0.404486 0.700590i
\(857\) −1.32731e12 + 1.11375e12i −0.0840544 + 0.0705300i −0.683847 0.729626i \(-0.739694\pi\)
0.599792 + 0.800156i \(0.295250\pi\)
\(858\) 2.78033e12 3.65359e12i 0.175147 0.230159i
\(859\) −1.78047e12 + 1.00976e13i −0.111575 + 0.632772i 0.876814 + 0.480829i \(0.159664\pi\)
−0.988389 + 0.151943i \(0.951447\pi\)
\(860\) 2.86202e11 + 2.40152e11i 0.0178414 + 0.0149707i
\(861\) 2.61822e13 5.91454e12i 1.62365 0.366781i
\(862\) 1.22117e12 + 4.44468e11i 0.0753342 + 0.0274194i
\(863\) 8.48185e12 0.520525 0.260263 0.965538i \(-0.416191\pi\)
0.260263 + 0.965538i \(0.416191\pi\)
\(864\) −1.47087e12 2.74451e12i −0.0897972 0.167553i
\(865\) −2.27552e13 −1.38200
\(866\) −1.51722e13 5.52223e12i −0.916681 0.333645i
\(867\) −4.96673e12 + 1.59752e13i −0.298527 + 0.960198i
\(868\) −5.40802e10 4.53787e10i −0.00323370 0.00271340i
\(869\) 1.13282e12 6.42455e12i 0.0673864 0.382167i
\(870\) −9.79290e12 1.24939e12i −0.579529 0.0739368i
\(871\) −2.19529e13 + 1.84207e13i −1.29244 + 1.08449i
\(872\) 7.06960e12 + 1.22449e13i 0.414067 + 0.717185i
\(873\) 3.45040e12 3.29735e11i 0.201051 0.0192132i
\(874\) −6.86103e10 + 1.18837e11i −0.00397730 + 0.00688888i
\(875\) −1.34640e12 7.63583e12i −0.0776495 0.440372i
\(876\) 2.15966e12 1.38804e12i 0.123913 0.0796407i
\(877\) −6.44710e12 + 2.34655e12i −0.368016 + 0.133947i −0.519407 0.854527i \(-0.673847\pi\)
0.151391 + 0.988474i \(0.451625\pi\)
\(878\) −7.15346e12 + 2.60365e12i −0.406248 + 0.147862i
\(879\) −3.57089e11 7.49031e12i −0.0201756 0.423204i
\(880\) 9.67279e11 + 5.48571e12i 0.0543725 + 0.308362i
\(881\) 1.22294e13 2.11819e13i 0.683931 1.18460i −0.289841 0.957075i \(-0.593602\pi\)
0.973772 0.227528i \(-0.0730643\pi\)
\(882\) −2.50927e13 1.72723e13i −1.39617 0.961038i
\(883\) −3.97832e12 6.89066e12i −0.220230 0.381450i 0.734648 0.678449i \(-0.237348\pi\)
−0.954878 + 0.296999i \(0.904014\pi\)
\(884\) 2.41341e12 2.02509e12i 0.132922 0.111535i
\(885\) −8.16146e12 1.94825e13i −0.447222 1.06758i
\(886\) 1.04697e12 5.93765e12i 0.0570797 0.323715i
\(887\) 1.48796e13 + 1.24854e13i 0.807113 + 0.677248i 0.949917 0.312503i \(-0.101167\pi\)
−0.142804 + 0.989751i \(0.545612\pi\)
\(888\) −2.08983e13 2.26240e13i −1.12786 1.22099i
\(889\) 2.77057e13 + 1.00841e13i 1.48769 + 0.541474i
\(890\) 1.39991e13 0.747902
\(891\) −7.13289e10 4.45299e12i −0.00379154 0.236702i
\(892\) 2.69514e11 0.0142541
\(893\) 7.15110e11 + 2.60279e11i 0.0376306 + 0.0136964i
\(894\) 4.98914e12 + 5.40111e12i 0.261220 + 0.282790i
\(895\) 5.24123e12 + 4.39791e12i 0.273042 + 0.229109i
\(896\) 4.65801e12 2.64169e13i 0.241443 1.36929i
\(897\) −2.73853e12 6.53722e12i −0.141238 0.337153i
\(898\) 2.62817e12 2.20529e12i 0.134868 0.113168i
\(899\) 1.08053e11 + 1.87153e11i 0.00551718 + 0.00955603i
\(900\) −2.00286e12 + 9.53550e11i −0.101756 + 0.0484454i
\(901\) −5.39997e12 + 9.35302e12i −0.272979 + 0.472814i
\(902\) 7.75716e11 + 4.39931e12i 0.0390188 + 0.221286i
\(903\) −2.62347e11 5.50299e12i −0.0131305 0.275425i
\(904\) −3.38170e13 + 1.23084e13i −1.68414 + 0.612975i
\(905\) 1.71304e11 6.23497e10i 0.00848886 0.00308969i
\(906\) 2.65680e13 1.70756e13i 1.31003 0.841975i
\(907\) 1.60526e11 + 9.10389e11i 0.00787613 + 0.0446678i 0.988493 0.151270i \(-0.0483362\pi\)
−0.980616 + 0.195937i \(0.937225\pi\)
\(908\) −3.93382e11 + 6.81358e11i −0.0192056 + 0.0332651i
\(909\) 1.63263e13 + 2.29235e13i 0.793143 + 1.11364i
\(910\) 3.11311e13 + 5.39206e13i 1.50490 + 2.60657i
\(911\) −1.32517e13 + 1.11195e13i −0.637438 + 0.534874i −0.903230 0.429156i \(-0.858811\pi\)
0.265792 + 0.964030i \(0.414367\pi\)
\(912\) −5.45427e11 6.95861e10i −0.0261072 0.00333078i
\(913\) −1.49703e12 + 8.49006e12i −0.0713035 + 0.404382i
\(914\) −4.65770e12 3.90827e12i −0.220757 0.185237i
\(915\) 1.02046e13 3.28226e13i 0.481284 1.54803i
\(916\) 1.27096e12 + 4.62593e11i 0.0596491 + 0.0217105i
\(917\) −1.70453e13 −0.796054
\(918\) −5.93265e12 + 2.83690e13i −0.275713 + 1.31841i
\(919\) 1.04146e13 0.481639 0.240819 0.970570i \(-0.422584\pi\)
0.240819 + 0.970570i \(0.422584\pi\)
\(920\) 8.94133e12 + 3.25438e12i 0.411488 + 0.149769i
\(921\) 9.94423e12 2.24640e12i 0.455410 0.102877i
\(922\) 2.10855e13 + 1.76928e13i 0.960934 + 0.806320i
\(923\) −1.12695e12 + 6.39122e12i −0.0511087 + 0.289852i
\(924\) −5.05384e11 + 6.64119e11i −0.0228086 + 0.0299724i
\(925\) −3.21522e13 + 2.69789e13i −1.44402 + 1.21168i
\(926\) −1.00505e13 1.74079e13i −0.449197 0.778032i
\(927\) 2.01592e13 + 5.22898e12i 0.896634 + 0.232572i
\(928\) 8.93072e11 1.54685e12i 0.0395294 0.0684670i
\(929\) 3.71622e12 + 2.10757e13i 0.163693 + 0.928350i 0.950402 + 0.311025i \(0.100672\pi\)
−0.786708 + 0.617325i \(0.788216\pi\)
\(930\) −7.55770e11 3.89591e11i −0.0331296 0.0170779i
\(931\) 1.12818e12 4.10625e11i 0.0492160 0.0179132i
\(932\) −2.40051e12 + 8.73714e11i −0.104215 + 0.0379313i
\(933\) 1.41975e13 + 7.31864e12i 0.613401 + 0.316201i
\(934\) −1.67950e12 9.52490e12i −0.0722135 0.409543i
\(935\) −5.78593e12 + 1.00215e13i −0.247583 + 0.428827i
\(936\) 2.20426e13 2.23985e13i 0.938687 0.953843i
\(937\) −1.77409e13 3.07281e13i −0.751877 1.30229i −0.946912 0.321493i \(-0.895815\pi\)
0.195035 0.980796i \(-0.437518\pi\)
\(938\) −3.78440e13 + 3.17549e13i −1.59619 + 1.33936i
\(939\) −9.48161e12 + 1.24597e13i −0.398003 + 0.523011i
\(940\) 7.97942e11 4.52535e12i 0.0333347 0.189050i
\(941\) 2.33619e12 + 1.96030e12i 0.0971304 + 0.0815021i 0.690060 0.723752i \(-0.257584\pi\)
−0.592929 + 0.805254i \(0.702029\pi\)
\(942\) −2.14600e13 + 4.84781e12i −0.887976 + 0.200593i
\(943\) 6.48032e12 + 2.35864e12i 0.266866 + 0.0971313i
\(944\) −1.71229e13 −0.701783
\(945\) 5.60721e13 + 2.24405e13i 2.28720 + 0.915356i
\(946\) 9.16877e11 0.0372221
\(947\) −1.78919e13 6.51213e12i −0.722907 0.263117i −0.0457476 0.998953i \(-0.514567\pi\)
−0.677159 + 0.735836i \(0.736789\pi\)
\(948\) 1.15439e12 3.71305e12i 0.0464212 0.149311i
\(949\) 3.79674e13 + 3.18584e13i 1.51954 + 1.27505i
\(950\) −1.43976e11 + 8.16526e11i −0.00573499 + 0.0325248i
\(951\) −2.99254e13 3.81791e12i −1.18639 0.151361i
\(952\) 4.77770e13 4.00897e13i 1.88518 1.58185i
\(953\) −1.18926e13 2.05985e13i −0.467043 0.808942i 0.532248 0.846588i \(-0.321347\pi\)
−0.999291 + 0.0376460i \(0.988014\pi\)
\(954\) −3.89632e12 + 8.53345e12i −0.152295 + 0.333547i
\(955\) −1.27775e13 + 2.21313e13i −0.497085 + 0.860977i
\(956\) 6.29705e11 + 3.57123e12i 0.0243824 + 0.138279i
\(957\) 2.14906e12 1.38123e12i 0.0828217 0.0532307i
\(958\) −7.54750e12 + 2.74706e12i −0.289506 + 0.105372i
\(959\) −4.27848e13 + 1.55724e13i −1.63345 + 0.594527i
\(960\) 1.99217e12 + 4.17877e13i 0.0757016 + 1.58792i
\(961\) −4.58796e12 2.60196e13i −0.173526 0.984114i
\(962\) 2.58889e13 4.48409e13i 0.974598 1.68805i
\(963\) 1.64075e12 2.06579e13i 0.0614785 0.774050i
\(964\) −6.31840e11 1.09438e12i −0.0235646 0.0408151i
\(965\) 1.96973e13 1.65280e13i 0.731198 0.613548i
\(966\) −4.72086e12 1.12693e13i −0.174431 0.416391i
\(967\) −2.26043e12 + 1.28196e13i −0.0831328 + 0.471470i 0.914611 + 0.404335i \(0.132497\pi\)
−0.997744 + 0.0671350i \(0.978614\pi\)
\(968\) 2.05800e13 + 1.72686e13i 0.753365 + 0.632148i
\(969\) −7.75065e11 8.39065e11i −0.0282411 0.0305731i
\(970\) −7.35104e12 2.67556e12i −0.266610 0.0970380i
\(971\) −4.47113e13 −1.61410 −0.807051 0.590481i \(-0.798938\pi\)
−0.807051 + 0.590481i \(0.798938\pi\)
\(972\) 2.93725e11 2.63820e12i 0.0105546 0.0948002i
\(973\) 4.92542e13 1.76171
\(974\) 1.10092e13 + 4.00701e12i 0.391958 + 0.142661i
\(975\) −2.90586e13 3.14581e13i −1.02980 1.11484i
\(976\) −2.13445e13 1.79102e13i −0.752944 0.631795i
\(977\) 5.02503e12 2.84984e13i 0.176447 1.00068i −0.760014 0.649906i \(-0.774808\pi\)
0.936461 0.350772i \(-0.114081\pi\)
\(978\) 7.35978e12 + 1.75688e13i 0.257241 + 0.614068i
\(979\) −2.77503e12 + 2.32853e12i −0.0965486 + 0.0810139i
\(980\) −3.62475e12 6.27825e12i −0.125534 0.217431i
\(981\) −1.82558e12 + 2.29851e13i −0.0629347 + 0.792385i
\(982\) −8.01832e11 + 1.38881e12i −0.0275158 + 0.0476587i
\(983\) 2.25586e11 + 1.27936e12i 0.00770585 + 0.0437021i 0.988418 0.151754i \(-0.0484923\pi\)
−0.980712 + 0.195456i \(0.937381\pi\)
\(984\) 1.45605e12 + 3.05420e13i 0.0495105 + 1.03853i
\(985\) 3.57478e12 1.30111e12i 0.121000 0.0440405i
\(986\) −1.56224e13 + 5.68611e12i −0.526384 + 0.191588i
\(987\) −5.70021e13 + 3.66361e13i −1.91189 + 1.22880i
\(988\) 1.87282e10 + 1.06213e11i 0.000625303 + 0.00354627i
\(989\) 7.07716e11 1.22580e12i 0.0235221 0.0407414i
\(990\) −4.17481e12 + 9.14338e12i −0.138127 + 0.302516i
\(991\) −1.52985e13 2.64978e13i −0.503869 0.872726i −0.999990 0.00447280i \(-0.998576\pi\)
0.496121 0.868253i \(-0.334757\pi\)
\(992\) 1.17845e11 9.88841e10i 0.00386376 0.00324208i
\(993\) 4.97793e13 + 6.35089e12i 1.62471 + 0.207283i
\(994\) −1.94271e12 + 1.10176e13i −0.0631203 + 0.357973i
\(995\) 4.37842e13 + 3.67393e13i 1.41617 + 1.18830i
\(996\) −1.52554e12 + 4.90681e12i −0.0491197 + 0.157991i
\(997\) 1.02283e13 + 3.72279e12i 0.327850 + 0.119328i 0.500701 0.865620i \(-0.333076\pi\)
−0.172851 + 0.984948i \(0.555298\pi\)
\(998\) −2.24614e13 −0.716721
\(999\) −7.15346e12 4.97136e13i −0.227233 1.57918i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 27.10.e.a.4.8 156
3.2 odd 2 81.10.e.a.64.19 156
27.7 even 9 inner 27.10.e.a.7.8 yes 156
27.20 odd 18 81.10.e.a.19.19 156
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.10.e.a.4.8 156 1.1 even 1 trivial
27.10.e.a.7.8 yes 156 27.7 even 9 inner
81.10.e.a.19.19 156 27.20 odd 18
81.10.e.a.64.19 156 3.2 odd 2