Properties

Label 27.10.e.a.4.7
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 4.7
Character \(\chi\) \(=\) 27.4
Dual form 27.10.e.a.7.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-22.2970 - 8.11544i) q^{2} +(-117.506 + 76.6512i) q^{3} +(39.0810 + 32.7929i) q^{4} +(151.895 - 861.438i) q^{5} +(3242.08 - 755.482i) q^{6} +(4408.97 - 3699.56i) q^{7} +(5469.10 + 9472.76i) q^{8} +(7932.18 - 18013.9i) q^{9} +O(q^{10})\) \(q+(-22.2970 - 8.11544i) q^{2} +(-117.506 + 76.6512i) q^{3} +(39.0810 + 32.7929i) q^{4} +(151.895 - 861.438i) q^{5} +(3242.08 - 755.482i) q^{6} +(4408.97 - 3699.56i) q^{7} +(5469.10 + 9472.76i) q^{8} +(7932.18 - 18013.9i) q^{9} +(-10377.8 + 17974.8i) q^{10} +(-11226.1 - 63666.3i) q^{11} +(-7105.86 - 857.740i) q^{12} +(-2007.46 + 730.657i) q^{13} +(-128330. + 46708.5i) q^{14} +(48181.8 + 112867. i) q^{15} +(-49604.7 - 281322. i) q^{16} +(-273343. + 473443. i) q^{17} +(-323055. + 337283. i) q^{18} +(4584.85 + 7941.20i) q^{19} +(34185.2 - 28684.8i) q^{20} +(-234503. + 772673. i) q^{21} +(-266372. + 1.51067e6i) q^{22} +(-710303. - 596015. i) q^{23} +(-1.36875e6 - 693890. i) q^{24} +(1.11633e6 + 406312. i) q^{25} +50690.0 q^{26} +(448713. + 2.72475e6i) q^{27} +293626. q^{28} +(-6.71518e6 - 2.44413e6i) q^{29} +(-158345. - 2.90761e6i) q^{30} +(-208125. - 174637. i) q^{31} +(-204526. + 1.15992e6i) q^{32} +(6.19923e6 + 6.62066e6i) q^{33} +(9.93693e6 - 8.33807e6i) q^{34} +(-2.51725e6 - 4.36000e6i) q^{35} +(900725. - 443883. i) q^{36} +(5.31071e6 - 9.19842e6i) q^{37} +(-37782.1 - 214273. i) q^{38} +(179883. - 239731. i) q^{39} +(8.99093e6 - 3.27243e6i) q^{40} +(-720374. + 262195. i) q^{41} +(1.14993e7 - 1.53252e7i) q^{42} +(4.99580e6 + 2.83326e7i) q^{43} +(1.64907e6 - 2.85628e6i) q^{44} +(-1.43130e7 - 9.56930e6i) q^{45} +(1.10007e7 + 1.90538e7i) q^{46} +(-1.81087e7 + 1.51950e7i) q^{47} +(2.73925e7 + 2.92547e7i) q^{48} +(-1.25510e6 + 7.11801e6i) q^{49} +(-2.15935e7 - 1.81191e7i) q^{50} +(-4.17070e6 - 7.65844e7i) q^{51} +(-102414. - 37275.7i) q^{52} -7.28654e7 q^{53} +(1.21076e7 - 6.43952e7i) q^{54} -5.65498e7 q^{55} +(5.91582e7 + 2.15318e7i) q^{56} +(-1.14745e6 - 581701. i) q^{57} +(1.29893e8 + 1.08993e8i) q^{58} +(-8.86448e6 + 5.02730e7i) q^{59} +(-1.81823e6 + 5.99097e6i) q^{60} +(2.96204e7 - 2.48544e7i) q^{61} +(3.22330e6 + 5.58292e6i) q^{62} +(-3.16709e7 - 1.08768e8i) q^{63} +(-5.91558e7 + 1.02461e8i) q^{64} +(324493. + 1.84029e6i) q^{65} +(-8.44947e7 - 1.97930e8i) q^{66} +(-2.25674e8 + 8.21387e7i) q^{67} +(-2.62081e7 + 9.53896e6i) q^{68} +(1.29150e8 + 1.55895e7i) q^{69} +(2.07437e7 + 1.17644e8i) q^{70} +(-1.54607e8 + 2.67787e8i) q^{71} +(2.14023e8 - 2.33803e7i) q^{72} +(1.82624e7 + 3.16315e7i) q^{73} +(-1.93062e8 + 1.61998e8i) q^{74} +(-1.62320e8 + 3.78243e7i) q^{75} +(-81233.9 + 460700. i) q^{76} +(-2.85033e8 - 2.39171e8i) q^{77} +(-5.95637e6 + 3.88545e6i) q^{78} +(2.50973e8 + 9.13467e7i) q^{79} -2.49876e8 q^{80} +(-2.61582e8 - 2.85779e8i) q^{81} +1.81900e7 q^{82} +(5.56219e8 + 2.02447e8i) q^{83} +(-3.45028e7 + 2.25068e7i) q^{84} +(3.66323e8 + 3.07382e8i) q^{85} +(1.18540e8 - 6.72275e8i) q^{86} +(9.76417e8 - 2.27528e8i) q^{87} +(5.41699e8 - 4.54540e8i) q^{88} +(-1.70525e8 - 2.95358e8i) q^{89} +(2.41478e8 + 3.29523e8i) q^{90} +(-6.14773e6 + 1.06482e7i) q^{91} +(-8.21432e6 - 4.65857e7i) q^{92} +(3.78420e7 + 4.56787e6i) q^{93} +(5.27085e8 - 1.91843e8i) q^{94} +(7.53727e6 - 2.74334e6i) q^{95} +(-6.48766e7 - 1.51975e8i) q^{96} +(-2.67990e8 - 1.51985e9i) q^{97} +(8.57507e7 - 1.48524e8i) q^{98} +(-1.23593e9 - 3.02787e8i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −22.2970 8.11544i −0.985397 0.358655i −0.201461 0.979497i \(-0.564569\pi\)
−0.783936 + 0.620841i \(0.786791\pi\)
\(3\) −117.506 + 76.6512i −0.837555 + 0.546353i
\(4\) 39.0810 + 32.7929i 0.0763301 + 0.0640486i
\(5\) 151.895 861.438i 0.108687 0.616395i −0.880996 0.473123i \(-0.843127\pi\)
0.989683 0.143272i \(-0.0457623\pi\)
\(6\) 3242.08 755.482i 1.02128 0.237982i
\(7\) 4408.97 3699.56i 0.694058 0.582384i −0.226018 0.974123i \(-0.572571\pi\)
0.920076 + 0.391739i \(0.128126\pi\)
\(8\) 5469.10 + 9472.76i 0.472075 + 0.817658i
\(9\) 7932.18 18013.9i 0.402996 0.915202i
\(10\) −10377.8 + 17974.8i −0.328173 + 0.568413i
\(11\) −11226.1 63666.3i −0.231186 1.31112i −0.850499 0.525977i \(-0.823700\pi\)
0.619313 0.785144i \(-0.287411\pi\)
\(12\) −7105.86 857.740i −0.0989238 0.0119410i
\(13\) −2007.46 + 730.657i −0.0194941 + 0.00709526i −0.351749 0.936094i \(-0.614413\pi\)
0.332255 + 0.943190i \(0.392191\pi\)
\(14\) −128330. + 46708.5i −0.892798 + 0.324952i
\(15\) 48181.8 + 112867.i 0.245738 + 0.575646i
\(16\) −49604.7 281322.i −0.189227 1.07316i
\(17\) −273343. + 473443.i −0.793757 + 1.37483i 0.129869 + 0.991531i \(0.458544\pi\)
−0.923626 + 0.383296i \(0.874789\pi\)
\(18\) −323055. + 337283.i −0.725353 + 0.757301i
\(19\) 4584.85 + 7941.20i 0.00807112 + 0.0139796i 0.870033 0.492994i \(-0.164098\pi\)
−0.861962 + 0.506974i \(0.830764\pi\)
\(20\) 34185.2 28684.8i 0.0477753 0.0400883i
\(21\) −234503. + 772673.i −0.263124 + 0.866980i
\(22\) −266372. + 1.51067e6i −0.242430 + 1.37489i
\(23\) −710303. 596015.i −0.529259 0.444101i 0.338586 0.940935i \(-0.390051\pi\)
−0.867846 + 0.496834i \(0.834496\pi\)
\(24\) −1.36875e6 693890.i −0.842119 0.426914i
\(25\) 1.11633e6 + 406312.i 0.571563 + 0.208032i
\(26\) 50690.0 0.0217542
\(27\) 448713. + 2.72475e6i 0.162492 + 0.986710i
\(28\) 293626. 0.0902784
\(29\) −6.71518e6 2.44413e6i −1.76306 0.641701i −0.763069 0.646317i \(-0.776309\pi\)
−0.999989 + 0.00461569i \(0.998531\pi\)
\(30\) −158345. 2.90761e6i −0.0356911 0.655376i
\(31\) −208125. 174637.i −0.0404759 0.0339633i 0.622325 0.782759i \(-0.286188\pi\)
−0.662801 + 0.748795i \(0.730633\pi\)
\(32\) −204526. + 1.15992e6i −0.0344805 + 0.195548i
\(33\) 6.19923e6 + 6.62066e6i 0.909966 + 0.971826i
\(34\) 9.93693e6 8.33807e6i 1.27525 1.07007i
\(35\) −2.51725e6 4.36000e6i −0.283544 0.491112i
\(36\) 900725. 443883.i 0.0893781 0.0440461i
\(37\) 5.31071e6 9.19842e6i 0.465849 0.806873i −0.533391 0.845869i \(-0.679082\pi\)
0.999239 + 0.0389956i \(0.0124158\pi\)
\(38\) −37782.1 214273.i −0.00293941 0.0166702i
\(39\) 179883. 239731.i 0.0124508 0.0165933i
\(40\) 8.99093e6 3.27243e6i 0.555309 0.202116i
\(41\) −720374. + 262195.i −0.0398135 + 0.0144909i −0.361850 0.932236i \(-0.617855\pi\)
0.322037 + 0.946727i \(0.395633\pi\)
\(42\) 1.14993e7 1.53252e7i 0.570229 0.759949i
\(43\) 4.99580e6 + 2.83326e7i 0.222842 + 1.26380i 0.866768 + 0.498712i \(0.166193\pi\)
−0.643926 + 0.765088i \(0.722695\pi\)
\(44\) 1.64907e6 2.85628e6i 0.0663290 0.114885i
\(45\) −1.43130e7 9.56930e6i −0.520325 0.347876i
\(46\) 1.10007e7 + 1.90538e7i 0.362251 + 0.627438i
\(47\) −1.81087e7 + 1.51950e7i −0.541313 + 0.454215i −0.871987 0.489530i \(-0.837168\pi\)
0.330674 + 0.943745i \(0.392724\pi\)
\(48\) 2.73925e7 + 2.92547e7i 0.744811 + 0.795444i
\(49\) −1.25510e6 + 7.11801e6i −0.0311025 + 0.176391i
\(50\) −2.15935e7 1.81191e7i −0.488605 0.409988i
\(51\) −4.17070e6 7.65844e7i −0.0863264 1.58516i
\(52\) −102414. 37275.7i −0.00194243 0.000706985i
\(53\) −7.28654e7 −1.26847 −0.634235 0.773140i \(-0.718685\pi\)
−0.634235 + 0.773140i \(0.718685\pi\)
\(54\) 1.21076e7 6.43952e7i 0.193770 1.03058i
\(55\) −5.65498e7 −0.833295
\(56\) 5.91582e7 + 2.15318e7i 0.803838 + 0.292573i
\(57\) −1.14745e6 581701.i −0.0143978 0.00729899i
\(58\) 1.29893e8 + 1.08993e8i 1.50716 + 1.26466i
\(59\) −8.86448e6 + 5.02730e7i −0.0952400 + 0.540133i 0.899434 + 0.437057i \(0.143979\pi\)
−0.994674 + 0.103075i \(0.967132\pi\)
\(60\) −1.81823e6 + 5.99097e6i −0.0181121 + 0.0596783i
\(61\) 2.96204e7 2.48544e7i 0.273909 0.229837i −0.495477 0.868621i \(-0.665007\pi\)
0.769386 + 0.638784i \(0.220562\pi\)
\(62\) 3.22330e6 + 5.58292e6i 0.0277037 + 0.0479842i
\(63\) −3.16709e7 1.08768e8i −0.253296 0.869902i
\(64\) −5.91558e7 + 1.02461e8i −0.440745 + 0.763393i
\(65\) 324493. + 1.84029e6i 0.00225473 + 0.0127872i
\(66\) −8.44947e7 1.97930e8i −0.548128 1.28400i
\(67\) −2.25674e8 + 8.21387e7i −1.36819 + 0.497979i −0.918576 0.395245i \(-0.870660\pi\)
−0.449611 + 0.893225i \(0.648437\pi\)
\(68\) −2.62081e7 + 9.53896e6i −0.148643 + 0.0541017i
\(69\) 1.29150e8 + 1.55895e7i 0.685920 + 0.0827966i
\(70\) 2.07437e7 + 1.17644e8i 0.103263 + 0.585635i
\(71\) −1.54607e8 + 2.67787e8i −0.722048 + 1.25062i 0.238130 + 0.971233i \(0.423466\pi\)
−0.960178 + 0.279390i \(0.909868\pi\)
\(72\) 2.14023e8 2.33803e7i 0.938566 0.102531i
\(73\) 1.82624e7 + 3.16315e7i 0.0752672 + 0.130367i 0.901202 0.433398i \(-0.142686\pi\)
−0.825935 + 0.563765i \(0.809352\pi\)
\(74\) −1.93062e8 + 1.61998e8i −0.748435 + 0.628012i
\(75\) −1.62320e8 + 3.78243e7i −0.592374 + 0.138037i
\(76\) −81233.9 + 460700.i −0.000279303 + 0.00158401i
\(77\) −2.85033e8 2.39171e8i −0.924032 0.775355i
\(78\) −5.95637e6 + 3.88545e6i −0.0182203 + 0.0118855i
\(79\) 2.50973e8 + 9.13467e7i 0.724945 + 0.263858i 0.678024 0.735040i \(-0.262837\pi\)
0.0469216 + 0.998899i \(0.485059\pi\)
\(80\) −2.49876e8 −0.682056
\(81\) −2.61582e8 2.85779e8i −0.675188 0.737646i
\(82\) 1.81900e7 0.0444294
\(83\) 5.56219e8 + 2.02447e8i 1.28645 + 0.468231i 0.892562 0.450925i \(-0.148906\pi\)
0.393893 + 0.919156i \(0.371128\pi\)
\(84\) −3.45028e7 + 2.25068e7i −0.0756131 + 0.0493239i
\(85\) 3.66323e8 + 3.07382e8i 0.761165 + 0.638694i
\(86\) 1.18540e8 6.72275e8i 0.233681 1.32527i
\(87\) 9.76417e8 2.27528e8i 1.82725 0.425793i
\(88\) 5.41699e8 4.54540e8i 0.962911 0.807978i
\(89\) −1.70525e8 2.95358e8i −0.288094 0.498993i 0.685261 0.728298i \(-0.259688\pi\)
−0.973355 + 0.229305i \(0.926355\pi\)
\(90\) 2.41478e8 + 3.29523e8i 0.387960 + 0.529413i
\(91\) −6.14773e6 + 1.06482e7i −0.00939786 + 0.0162776i
\(92\) −8.21432e6 4.65857e7i −0.0119544 0.0677966i
\(93\) 3.78420e7 + 4.56787e6i 0.0524567 + 0.00633199i
\(94\) 5.27085e8 1.91843e8i 0.696315 0.253438i
\(95\) 7.53727e6 2.74334e6i 0.00949418 0.00345560i
\(96\) −6.48766e7 1.51975e8i −0.0779593 0.182621i
\(97\) −2.67990e8 1.51985e9i −0.307359 1.74312i −0.612189 0.790711i \(-0.709711\pi\)
0.304830 0.952407i \(-0.401400\pi\)
\(98\) 8.57507e7 1.48524e8i 0.0939118 0.162660i
\(99\) −1.23593e9 3.02787e8i −1.29311 0.316795i
\(100\) 3.03033e7 + 5.24868e7i 0.0303033 + 0.0524868i
\(101\) 1.09404e8 9.18009e7i 0.104613 0.0877811i −0.588981 0.808147i \(-0.700471\pi\)
0.693594 + 0.720366i \(0.256026\pi\)
\(102\) −5.28522e8 + 1.74145e9i −0.483462 + 1.59298i
\(103\) −1.07561e8 + 6.10009e8i −0.0941646 + 0.534034i 0.900836 + 0.434160i \(0.142955\pi\)
−0.995000 + 0.0998734i \(0.968156\pi\)
\(104\) −1.79004e7 1.50202e7i −0.0150042 0.0125900i
\(105\) 6.29990e8 + 3.19375e8i 0.505804 + 0.256418i
\(106\) 1.62468e9 + 5.91335e8i 1.24995 + 0.454944i
\(107\) −1.37614e9 −1.01493 −0.507463 0.861674i \(-0.669416\pi\)
−0.507463 + 0.861674i \(0.669416\pi\)
\(108\) −7.18161e7 + 1.21201e8i −0.0507943 + 0.0857230i
\(109\) −2.88760e9 −1.95938 −0.979689 0.200524i \(-0.935736\pi\)
−0.979689 + 0.200524i \(0.935736\pi\)
\(110\) 1.26089e9 + 4.58927e8i 0.821127 + 0.298866i
\(111\) 8.10316e7 + 1.48794e9i 0.0506642 + 0.930319i
\(112\) −1.25947e9 1.05682e9i −0.756325 0.634632i
\(113\) −1.04844e7 + 5.94600e7i −0.00604910 + 0.0343062i −0.987683 0.156469i \(-0.949989\pi\)
0.981634 + 0.190775i \(0.0611001\pi\)
\(114\) 2.08639e7 + 2.22822e7i 0.0115697 + 0.0123563i
\(115\) −6.21322e8 + 5.21351e8i −0.331265 + 0.277965i
\(116\) −1.82286e8 3.15729e8i −0.0934744 0.161902i
\(117\) −2.76156e6 + 4.19580e7i −0.00136244 + 0.0207004i
\(118\) 6.05639e8 1.04900e9i 0.287571 0.498087i
\(119\) 5.46375e8 + 3.09865e9i 0.249764 + 1.41648i
\(120\) −8.05649e8 + 1.07369e9i −0.354675 + 0.472678i
\(121\) −1.71163e9 + 6.22982e8i −0.725898 + 0.264205i
\(122\) −8.62150e8 + 3.13797e8i −0.352341 + 0.128242i
\(123\) 6.45505e7 8.60269e7i 0.0254288 0.0338892i
\(124\) −2.40687e6 1.36500e7i −0.000914228 0.00518484i
\(125\) 1.37380e9 2.37950e9i 0.503303 0.871747i
\(126\) −1.76537e8 + 2.68223e9i −0.0623978 + 0.948045i
\(127\) −5.82316e8 1.00860e9i −0.198629 0.344035i 0.749455 0.662055i \(-0.230315\pi\)
−0.948084 + 0.318020i \(0.896982\pi\)
\(128\) 2.61247e9 2.19212e9i 0.860214 0.721805i
\(129\) −2.75876e9 2.94631e9i −0.877124 0.936751i
\(130\) 7.69955e6 4.36663e7i 0.00236440 0.0134092i
\(131\) 1.05065e9 + 8.81602e8i 0.311701 + 0.261548i 0.785195 0.619249i \(-0.212563\pi\)
−0.473494 + 0.880797i \(0.657007\pi\)
\(132\) 2.51618e7 + 4.62033e8i 0.00721372 + 0.132462i
\(133\) 4.95934e7 + 1.80505e7i 0.0137433 + 0.00500216i
\(134\) 5.69845e9 1.52681
\(135\) 2.41536e9 + 2.73365e7i 0.625864 + 0.00708340i
\(136\) −5.97975e9 −1.49885
\(137\) 4.30632e9 + 1.56737e9i 1.04439 + 0.380127i 0.806543 0.591175i \(-0.201336\pi\)
0.237848 + 0.971302i \(0.423558\pi\)
\(138\) −2.75314e9 1.39571e9i −0.646208 0.327596i
\(139\) −2.37882e9 1.99607e9i −0.540499 0.453533i 0.331209 0.943557i \(-0.392543\pi\)
−0.871709 + 0.490025i \(0.836988\pi\)
\(140\) 4.46003e7 2.52941e8i 0.00981210 0.0556472i
\(141\) 9.63162e8 3.17356e9i 0.205217 0.676178i
\(142\) 5.62048e9 4.71614e9i 1.16005 0.973395i
\(143\) 6.90542e7 + 1.19605e8i 0.0138095 + 0.0239188i
\(144\) −5.46118e9 1.33792e9i −1.05841 0.259298i
\(145\) −3.12547e9 + 5.41347e9i −0.587163 + 1.01700i
\(146\) −1.50494e8 8.53494e8i −0.0274114 0.155458i
\(147\) −3.98123e8 9.32611e8i −0.0703217 0.164730i
\(148\) 5.09190e8 1.85330e8i 0.0872373 0.0317518i
\(149\) 6.57123e8 2.39173e8i 0.109222 0.0397534i −0.286831 0.957981i \(-0.592602\pi\)
0.396053 + 0.918228i \(0.370380\pi\)
\(150\) 3.92621e9 + 4.73928e8i 0.633231 + 0.0764367i
\(151\) −2.28019e8 1.29316e9i −0.0356924 0.202422i 0.961747 0.273940i \(-0.0883268\pi\)
−0.997439 + 0.0715179i \(0.977216\pi\)
\(152\) −5.01500e7 + 8.68624e7i −0.00762035 + 0.0131988i
\(153\) 6.36037e9 + 8.67941e9i 0.938363 + 1.28050i
\(154\) 4.41440e9 + 7.64597e9i 0.632454 + 1.09544i
\(155\) −1.82053e8 + 1.52760e8i −0.0253340 + 0.0212578i
\(156\) 1.48915e7 3.47006e6i 0.00201315 0.000469112i
\(157\) 1.57956e9 8.95814e9i 0.207486 1.17671i −0.685994 0.727607i \(-0.740632\pi\)
0.893480 0.449103i \(-0.148256\pi\)
\(158\) −4.85463e9 4.07352e9i −0.619725 0.520011i
\(159\) 8.56210e9 5.58523e9i 1.06241 0.693033i
\(160\) 9.68136e8 + 3.52373e8i 0.116788 + 0.0425072i
\(161\) −5.33670e9 −0.625974
\(162\) 3.51326e9 + 8.49487e9i 0.400768 + 0.969034i
\(163\) 1.47674e10 1.63855 0.819273 0.573403i \(-0.194377\pi\)
0.819273 + 0.573403i \(0.194377\pi\)
\(164\) −3.67511e7 1.33763e7i −0.00396709 0.00144390i
\(165\) 6.64492e9 4.33461e9i 0.697931 0.455274i
\(166\) −1.07591e10 9.02793e9i −1.09974 0.922787i
\(167\) −1.83713e9 + 1.04189e10i −0.182775 + 1.03657i 0.746007 + 0.665939i \(0.231969\pi\)
−0.928781 + 0.370628i \(0.879142\pi\)
\(168\) −8.60186e9 + 2.00444e9i −0.833107 + 0.194134i
\(169\) −8.12002e9 + 6.81351e9i −0.765715 + 0.642511i
\(170\) −5.67337e9 9.82656e9i −0.520980 0.902363i
\(171\) 1.79420e8 1.96002e7i 0.0160468 0.00175298i
\(172\) −7.33866e8 + 1.27109e9i −0.0639350 + 0.110739i
\(173\) 1.69786e9 + 9.62902e9i 0.144110 + 0.817287i 0.968078 + 0.250650i \(0.0806444\pi\)
−0.823968 + 0.566636i \(0.808244\pi\)
\(174\) −2.36177e10 2.85086e9i −1.95328 0.235779i
\(175\) 6.42506e9 2.33853e9i 0.517852 0.188483i
\(176\) −1.73539e10 + 6.31629e9i −1.36329 + 0.496198i
\(177\) −2.81186e9 6.58683e9i −0.215335 0.504425i
\(178\) 1.40524e9 + 7.96950e9i 0.104920 + 0.595033i
\(179\) 1.20072e10 2.07971e10i 0.874186 1.51414i 0.0165596 0.999863i \(-0.494729\pi\)
0.857627 0.514273i \(-0.171938\pi\)
\(180\) −2.45563e8 8.43343e8i −0.0174356 0.0598795i
\(181\) 6.67484e9 + 1.15612e10i 0.462261 + 0.800659i 0.999073 0.0430423i \(-0.0137050\pi\)
−0.536812 + 0.843702i \(0.680372\pi\)
\(182\) 2.23491e8 1.87531e8i 0.0150987 0.0126693i
\(183\) −1.57544e9 + 5.19098e9i −0.103842 + 0.342152i
\(184\) 1.76119e9 9.98820e9i 0.113273 0.642402i
\(185\) −7.11720e9 5.97204e9i −0.446721 0.374843i
\(186\) −8.06693e8 4.08955e8i −0.0494197 0.0250534i
\(187\) 3.32110e10 + 1.20878e10i 1.98607 + 0.722870i
\(188\) −1.20600e9 −0.0704103
\(189\) 1.20587e10 + 1.03533e10i 0.687423 + 0.590201i
\(190\) −1.90322e8 −0.0105949
\(191\) −2.73224e10 9.94455e9i −1.48549 0.540673i −0.533230 0.845970i \(-0.679022\pi\)
−0.952257 + 0.305297i \(0.901244\pi\)
\(192\) −9.02608e8 1.65741e10i −0.0479340 0.880186i
\(193\) −6.32551e9 5.30773e9i −0.328161 0.275360i 0.463789 0.885946i \(-0.346490\pi\)
−0.791950 + 0.610586i \(0.790934\pi\)
\(194\) −6.35886e9 + 3.60629e10i −0.322308 + 1.82790i
\(195\) −1.79190e8 1.91372e8i −0.00887480 0.00947811i
\(196\) −2.82470e8 + 2.37021e8i −0.0136716 + 0.0114719i
\(197\) −7.38377e9 1.27891e10i −0.349285 0.604980i 0.636837 0.770998i \(-0.280242\pi\)
−0.986123 + 0.166018i \(0.946909\pi\)
\(198\) 2.51002e10 + 1.67813e10i 1.16060 + 0.775949i
\(199\) −1.87054e10 + 3.23988e10i −0.845530 + 1.46450i 0.0396310 + 0.999214i \(0.487382\pi\)
−0.885161 + 0.465286i \(0.845952\pi\)
\(200\) 2.25644e9 + 1.27969e10i 0.0997216 + 0.565549i
\(201\) 2.02220e10 2.69500e10i 0.873859 1.16460i
\(202\) −3.18439e9 + 1.15902e9i −0.134569 + 0.0489791i
\(203\) −3.86492e10 + 1.40672e10i −1.59738 + 0.581399i
\(204\) 2.34843e9 3.12976e9i 0.0949382 0.126525i
\(205\) 1.16443e8 + 6.60384e8i 0.00460493 + 0.0261158i
\(206\) 7.34878e9 1.27285e10i 0.284324 0.492463i
\(207\) −1.63708e10 + 8.06764e9i −0.619732 + 0.305408i
\(208\) 3.05129e8 + 5.28500e8i 0.0113031 + 0.0195776i
\(209\) 4.54117e8 3.81049e8i 0.0164630 0.0138141i
\(210\) −1.14550e10 1.22338e10i −0.406452 0.434083i
\(211\) 1.43138e9 8.11777e9i 0.0497147 0.281946i −0.949808 0.312833i \(-0.898722\pi\)
0.999523 + 0.0308869i \(0.00983317\pi\)
\(212\) −2.84766e9 2.38947e9i −0.0968225 0.0812437i
\(213\) −2.35901e9 4.33173e10i −0.0785276 1.44196i
\(214\) 3.06837e10 + 1.11679e10i 1.00010 + 0.364008i
\(215\) 2.51656e10 0.803220
\(216\) −2.33568e10 + 1.91525e10i −0.730083 + 0.598664i
\(217\) −1.56370e9 −0.0478723
\(218\) 6.43849e10 + 2.34342e10i 1.93077 + 0.702741i
\(219\) −4.57053e9 2.31704e9i −0.134267 0.0680667i
\(220\) −2.21002e9 1.85443e9i −0.0636055 0.0533714i
\(221\) 2.02801e8 1.15014e9i 0.00571879 0.0324329i
\(222\) 1.02685e10 3.38342e10i 0.283739 0.934905i
\(223\) −1.46162e10 + 1.22645e10i −0.395789 + 0.332106i −0.818863 0.573989i \(-0.805395\pi\)
0.423075 + 0.906095i \(0.360951\pi\)
\(224\) 3.38946e9 + 5.87072e9i 0.0899529 + 0.155803i
\(225\) 1.61742e10 1.68866e10i 0.420729 0.439259i
\(226\) 7.16315e8 1.24069e9i 0.0182649 0.0316357i
\(227\) −4.50093e9 2.55261e10i −0.112509 0.638069i −0.987954 0.154751i \(-0.950543\pi\)
0.875445 0.483318i \(-0.160569\pi\)
\(228\) −2.57678e7 6.03616e7i −0.000631496 0.00147929i
\(229\) −5.63083e10 + 2.04945e10i −1.35305 + 0.492468i −0.913897 0.405946i \(-0.866942\pi\)
−0.439149 + 0.898414i \(0.644720\pi\)
\(230\) 1.80846e10 6.58226e9i 0.426122 0.155096i
\(231\) 5.18258e10 + 6.25584e9i 1.19755 + 0.144554i
\(232\) −1.35734e10 7.69785e10i −0.307604 1.74451i
\(233\) 5.49051e9 9.50985e9i 0.122043 0.211384i −0.798530 0.601954i \(-0.794389\pi\)
0.920573 + 0.390570i \(0.127722\pi\)
\(234\) 4.02082e8 9.13126e8i 0.00876685 0.0199094i
\(235\) 1.03390e10 + 1.79076e10i 0.221142 + 0.383030i
\(236\) −1.99503e9 + 1.67403e9i −0.0418644 + 0.0351284i
\(237\) −3.64926e10 + 8.50364e9i −0.751341 + 0.175080i
\(238\) 1.29644e10 7.35246e10i 0.261912 1.48538i
\(239\) 1.01925e10 + 8.55255e9i 0.202065 + 0.169553i 0.738205 0.674576i \(-0.235674\pi\)
−0.536140 + 0.844129i \(0.680118\pi\)
\(240\) 2.93619e10 1.91533e10i 0.571259 0.372644i
\(241\) 6.82856e10 + 2.48539e10i 1.30392 + 0.474590i 0.898273 0.439438i \(-0.144822\pi\)
0.405651 + 0.914028i \(0.367045\pi\)
\(242\) 4.32200e10 0.810057
\(243\) 5.26427e10 + 1.35301e10i 0.968522 + 0.248928i
\(244\) 1.97264e9 0.0356282
\(245\) 5.94108e9 + 2.16238e9i 0.105346 + 0.0383428i
\(246\) −2.13743e9 + 1.39429e9i −0.0372121 + 0.0242741i
\(247\) −1.50062e7 1.25917e7i −0.000256528 0.000215253i
\(248\) 5.16043e8 2.92663e9i 0.00866270 0.0491286i
\(249\) −8.08767e10 + 1.88462e10i −1.33330 + 0.310689i
\(250\) −4.99424e10 + 4.19066e10i −0.808610 + 0.678505i
\(251\) −3.06999e10 5.31738e10i −0.488209 0.845602i 0.511699 0.859165i \(-0.329016\pi\)
−0.999908 + 0.0135625i \(0.995683\pi\)
\(252\) 2.32910e9 5.28936e9i 0.0363819 0.0826229i
\(253\) −2.99722e10 + 5.19133e10i −0.459913 + 0.796593i
\(254\) 4.79866e9 + 2.72145e10i 0.0723382 + 0.410251i
\(255\) −6.66062e10 8.03996e9i −0.986470 0.119076i
\(256\) −1.91179e10 + 6.95834e9i −0.278202 + 0.101257i
\(257\) 3.10164e10 1.12890e10i 0.443498 0.161420i −0.110612 0.993864i \(-0.535281\pi\)
0.554110 + 0.832444i \(0.313059\pi\)
\(258\) 3.76016e10 + 8.80824e10i 0.528345 + 1.23766i
\(259\) −1.06154e10 6.02029e10i −0.146584 0.831320i
\(260\) −4.76669e7 + 8.25614e7i −0.000646899 + 0.00112046i
\(261\) −9.72943e10 + 1.01579e11i −1.29779 + 1.35495i
\(262\) −1.62718e10 2.81836e10i −0.213344 0.369522i
\(263\) −4.63109e10 + 3.88594e10i −0.596873 + 0.500836i −0.890439 0.455103i \(-0.849603\pi\)
0.293566 + 0.955939i \(0.405158\pi\)
\(264\) −2.88117e10 + 9.49329e10i −0.365049 + 1.20282i
\(265\) −1.10679e10 + 6.27691e10i −0.137866 + 0.781879i
\(266\) −9.59297e8 8.04946e8i −0.0117486 0.00985823i
\(267\) 4.26773e10 + 2.16353e10i 0.513921 + 0.260533i
\(268\) −1.15131e10 4.19044e9i −0.136329 0.0496196i
\(269\) −1.69022e11 −1.96815 −0.984075 0.177753i \(-0.943117\pi\)
−0.984075 + 0.177753i \(0.943117\pi\)
\(270\) −5.36334e10 2.02112e10i −0.614184 0.231449i
\(271\) −7.95062e10 −0.895445 −0.447723 0.894173i \(-0.647765\pi\)
−0.447723 + 0.894173i \(0.647765\pi\)
\(272\) 1.46749e11 + 5.34123e10i 1.62561 + 0.591672i
\(273\) −9.38030e7 1.72245e9i −0.00102208 0.0187679i
\(274\) −8.32980e10 6.98953e10i −0.892806 0.749153i
\(275\) 1.33363e10 7.56341e10i 0.140618 0.797482i
\(276\) 4.53608e9 + 4.84445e9i 0.0470533 + 0.0502521i
\(277\) 6.80684e10 5.71162e10i 0.694683 0.582908i −0.225572 0.974226i \(-0.572425\pi\)
0.920255 + 0.391318i \(0.127981\pi\)
\(278\) 3.68416e10 + 6.38115e10i 0.369945 + 0.640763i
\(279\) −4.79679e9 + 2.36389e9i −0.0473949 + 0.0233565i
\(280\) 2.75342e10 4.76906e10i 0.267708 0.463683i
\(281\) 3.56770e9 + 2.02335e10i 0.0341358 + 0.193594i 0.997107 0.0760104i \(-0.0242182\pi\)
−0.962971 + 0.269604i \(0.913107\pi\)
\(282\) −4.72305e10 + 6.29444e10i −0.444735 + 0.592702i
\(283\) 1.82105e11 6.62809e10i 1.68765 0.614256i 0.693327 0.720623i \(-0.256144\pi\)
0.994327 + 0.106367i \(0.0339220\pi\)
\(284\) −1.48237e10 + 5.39538e9i −0.135215 + 0.0492141i
\(285\) −6.75391e8 + 9.00099e8i −0.00606392 + 0.00808143i
\(286\) −5.69051e8 3.22725e9i −0.00502926 0.0285223i
\(287\) −2.20610e9 + 3.82108e9i −0.0191936 + 0.0332443i
\(288\) 1.92724e10 + 1.28850e10i 0.165071 + 0.110362i
\(289\) −9.01385e10 1.56125e11i −0.760099 1.31653i
\(290\) 1.13621e11 9.53395e10i 0.943340 0.791556i
\(291\) 1.47988e11 + 1.58049e11i 1.20979 + 1.29203i
\(292\) −3.23572e8 + 1.83507e9i −0.00260464 + 0.0147717i
\(293\) −1.88246e11 1.57957e11i −1.49218 1.25209i −0.891844 0.452342i \(-0.850588\pi\)
−0.600337 0.799747i \(-0.704967\pi\)
\(294\) 1.30840e9 + 2.40254e10i 0.0102135 + 0.187546i
\(295\) 4.19606e10 + 1.52724e10i 0.322584 + 0.117411i
\(296\) 1.16179e11 0.879662
\(297\) 1.68437e11 5.91562e10i 1.25613 0.441160i
\(298\) −1.65929e10 −0.121884
\(299\) 1.86139e9 + 6.77491e8i 0.0134684 + 0.00490211i
\(300\) −7.58399e9 3.84472e9i −0.0540570 0.0274043i
\(301\) 1.26845e11 + 1.06435e11i 0.890682 + 0.747371i
\(302\) −5.41044e9 + 3.06841e10i −0.0374284 + 0.212267i
\(303\) −5.81895e9 + 1.91731e10i −0.0396600 + 0.130677i
\(304\) 2.00660e9 1.68374e9i 0.0134750 0.0113069i
\(305\) −1.69114e10 2.92914e10i −0.111900 0.193816i
\(306\) −7.13799e10 2.45142e11i −0.465403 1.59835i
\(307\) −2.42335e10 + 4.19737e10i −0.155702 + 0.269683i −0.933314 0.359060i \(-0.883097\pi\)
0.777613 + 0.628744i \(0.216431\pi\)
\(308\) −3.29628e9 1.86941e10i −0.0208711 0.118366i
\(309\) −3.41189e10 7.99242e10i −0.212903 0.498730i
\(310\) 5.29894e9 1.92866e9i 0.0325883 0.0118612i
\(311\) 2.35292e11 8.56394e10i 1.42622 0.519101i 0.490373 0.871512i \(-0.336860\pi\)
0.935845 + 0.352411i \(0.114638\pi\)
\(312\) 3.25471e9 + 3.92872e8i 0.0194454 + 0.00234723i
\(313\) −4.27002e10 2.42165e11i −0.251467 1.42614i −0.804982 0.593299i \(-0.797825\pi\)
0.553516 0.832839i \(-0.313286\pi\)
\(314\) −1.07919e11 + 1.86921e11i −0.626490 + 1.08511i
\(315\) −9.85079e10 + 1.07612e10i −0.563733 + 0.0615833i
\(316\) 6.81276e9 + 1.18000e10i 0.0384354 + 0.0665720i
\(317\) 9.58123e10 8.03961e10i 0.532911 0.447165i −0.336194 0.941793i \(-0.609140\pi\)
0.869105 + 0.494627i \(0.164695\pi\)
\(318\) −2.36236e11 + 5.50485e10i −1.29546 + 0.301873i
\(319\) −8.02233e10 + 4.54969e11i −0.433753 + 2.45994i
\(320\) 7.92783e10 + 6.65224e10i 0.422648 + 0.354644i
\(321\) 1.61704e11 1.05482e11i 0.850056 0.554508i
\(322\) 1.18992e11 + 4.33097e10i 0.616833 + 0.224509i
\(323\) −5.01294e9 −0.0256260
\(324\) −8.51364e8 1.97465e10i −0.00429203 0.0995494i
\(325\) −2.53787e9 −0.0126181
\(326\) −3.29268e11 1.19844e11i −1.61462 0.587674i
\(327\) 3.39310e11 2.21338e11i 1.64109 1.07051i
\(328\) −6.42350e9 5.38996e9i −0.0306436 0.0257130i
\(329\) −2.36259e10 + 1.33989e11i −0.111175 + 0.630504i
\(330\) −1.83339e11 + 4.27223e10i −0.851025 + 0.198309i
\(331\) −2.47890e11 + 2.08004e11i −1.13510 + 0.952459i −0.999267 0.0382729i \(-0.987814\pi\)
−0.135829 + 0.990732i \(0.543370\pi\)
\(332\) 1.50988e10 + 2.61519e10i 0.0682057 + 0.118136i
\(333\) −1.23574e11 1.68630e11i −0.550717 0.751512i
\(334\) 1.25516e11 2.17401e11i 0.551876 0.955877i
\(335\) 3.64787e10 + 2.06881e11i 0.158248 + 0.897467i
\(336\) 2.29002e11 + 2.76426e10i 0.980196 + 0.118318i
\(337\) −2.34667e11 + 8.54118e10i −0.991100 + 0.360731i −0.786146 0.618041i \(-0.787927\pi\)
−0.204954 + 0.978772i \(0.565704\pi\)
\(338\) 2.36347e11 8.60232e10i 0.984973 0.358501i
\(339\) −3.32571e9 7.79054e9i −0.0136768 0.0320382i
\(340\) 4.23636e9 + 2.40256e10i 0.0171924 + 0.0975031i
\(341\) −8.78210e9 + 1.52110e10i −0.0351725 + 0.0609206i
\(342\) −4.15959e9 1.01905e9i −0.0164412 0.00402788i
\(343\) 1.36927e11 + 2.37165e11i 0.534155 + 0.925183i
\(344\) −2.41065e11 + 2.02278e11i −0.928158 + 0.778817i
\(345\) 3.30466e10 1.08887e11i 0.125586 0.413799i
\(346\) 4.02867e10 2.28477e11i 0.151119 0.857038i
\(347\) 1.80082e11 + 1.51107e11i 0.666789 + 0.559503i 0.912113 0.409939i \(-0.134450\pi\)
−0.245324 + 0.969441i \(0.578894\pi\)
\(348\) 4.56207e10 + 2.31275e10i 0.166746 + 0.0845321i
\(349\) 1.69174e11 + 6.15744e10i 0.610407 + 0.222170i 0.628681 0.777663i \(-0.283595\pi\)
−0.0182742 + 0.999833i \(0.505817\pi\)
\(350\) −1.62238e11 −0.577890
\(351\) −2.89163e9 5.14198e9i −0.0101686 0.0180821i
\(352\) 7.61441e10 0.264359
\(353\) −3.23489e11 1.17740e11i −1.10885 0.403589i −0.278279 0.960500i \(-0.589764\pi\)
−0.830572 + 0.556911i \(0.811986\pi\)
\(354\) 9.24092e9 + 1.69686e11i 0.0312752 + 0.574290i
\(355\) 2.07198e11 + 1.73860e11i 0.692401 + 0.580993i
\(356\) 3.02135e9 1.71349e10i 0.00996956 0.0565402i
\(357\) −3.01717e11 3.22228e11i −0.983090 1.04992i
\(358\) −4.36503e11 + 3.66270e11i −1.40447 + 1.17849i
\(359\) 1.14041e11 + 1.97525e11i 0.362358 + 0.627622i 0.988348 0.152209i \(-0.0486386\pi\)
−0.625991 + 0.779830i \(0.715305\pi\)
\(360\) 1.23683e10 1.87919e11i 0.0388106 0.589671i
\(361\) 1.61302e11 2.79383e11i 0.499870 0.865800i
\(362\) −5.50049e10 3.11948e11i −0.168350 0.954760i
\(363\) 1.53374e11 2.04403e11i 0.463630 0.617883i
\(364\) −5.89444e8 + 2.14540e8i −0.00175989 + 0.000640549i
\(365\) 3.00225e10 1.09273e10i 0.0885379 0.0322252i
\(366\) 7.72546e10 1.02958e11i 0.225040 0.299912i
\(367\) −4.52408e10 2.56573e11i −0.130177 0.738269i −0.978098 0.208146i \(-0.933257\pi\)
0.847921 0.530123i \(-0.177854\pi\)
\(368\) −1.32438e11 + 2.29389e11i −0.376441 + 0.652015i
\(369\) −9.90980e8 + 1.50565e10i −0.00278257 + 0.0422772i
\(370\) 1.10226e11 + 1.90918e11i 0.305758 + 0.529589i
\(371\) −3.21262e11 + 2.69570e11i −0.880392 + 0.738737i
\(372\) 1.32911e9 + 1.41947e9i 0.00359847 + 0.00384310i
\(373\) −6.72680e9 + 3.81496e10i −0.0179936 + 0.102047i −0.992482 0.122391i \(-0.960944\pi\)
0.974488 + 0.224438i \(0.0720548\pi\)
\(374\) −6.42407e11 5.39044e11i −1.69781 1.42463i
\(375\) 2.09617e10 + 3.84908e11i 0.0547376 + 1.00512i
\(376\) −2.42978e11 8.84366e10i −0.626933 0.228185i
\(377\) 1.52663e10 0.0389222
\(378\) −1.84852e11 3.28709e11i −0.465706 0.828131i
\(379\) −8.58744e10 −0.213790 −0.106895 0.994270i \(-0.534091\pi\)
−0.106895 + 0.994270i \(0.534091\pi\)
\(380\) 3.84526e8 + 1.39956e8i 0.000946018 + 0.000344322i
\(381\) 1.45736e11 + 7.38811e10i 0.354327 + 0.179627i
\(382\) 5.28503e11 + 4.43467e11i 1.26988 + 1.06556i
\(383\) −7.54514e10 + 4.27906e11i −0.179173 + 1.01614i 0.754043 + 0.656825i \(0.228101\pi\)
−0.933216 + 0.359316i \(0.883010\pi\)
\(384\) −1.38951e11 + 4.57836e11i −0.326116 + 1.07453i
\(385\) −2.49326e11 + 2.09210e11i −0.578356 + 0.485298i
\(386\) 9.79652e10 + 1.69681e11i 0.224610 + 0.389036i
\(387\) 5.50009e11 + 1.34745e11i 1.24644 + 0.305361i
\(388\) 3.93668e10 6.81853e10i 0.0881835 0.152738i
\(389\) −1.05692e11 5.99410e11i −0.234029 1.32724i −0.844649 0.535320i \(-0.820191\pi\)
0.610620 0.791924i \(-0.290920\pi\)
\(390\) 2.44234e9 + 5.72122e9i 0.00534583 + 0.0125227i
\(391\) 4.76336e11 1.73372e11i 1.03067 0.375131i
\(392\) −7.42914e10 + 2.70399e10i −0.158910 + 0.0578385i
\(393\) −1.91034e11 2.30595e10i −0.403965 0.0487621i
\(394\) 6.08470e10 + 3.45081e11i 0.127206 + 0.721419i
\(395\) 1.16811e11 2.02323e11i 0.241433 0.418175i
\(396\) −3.83720e10 5.23628e10i −0.0784127 0.107003i
\(397\) −6.26424e10 1.08500e11i −0.126564 0.219216i 0.795779 0.605587i \(-0.207062\pi\)
−0.922343 + 0.386371i \(0.873728\pi\)
\(398\) 6.80005e11 5.70592e11i 1.35843 1.13986i
\(399\) −7.21111e9 + 1.68036e9i −0.0142437 + 0.00331913i
\(400\) 5.89292e10 3.34204e11i 0.115096 0.652742i
\(401\) 4.22849e11 + 3.54812e11i 0.816649 + 0.685250i 0.952185 0.305522i \(-0.0988311\pi\)
−0.135536 + 0.990772i \(0.543276\pi\)
\(402\) −6.69600e11 + 4.36793e11i −1.27879 + 0.834178i
\(403\) 5.45403e8 + 1.98511e8i 0.00103002 + 0.000374896i
\(404\) 7.28604e9 0.0136074
\(405\) −2.85914e11 + 1.81928e11i −0.528065 + 0.336010i
\(406\) 9.75923e11 1.78258
\(407\) −6.45248e11 2.34851e11i −1.16561 0.424246i
\(408\) 7.02655e11 4.58356e11i 1.25537 0.818902i
\(409\) −4.54913e11 3.81717e11i −0.803847 0.674507i 0.145284 0.989390i \(-0.453590\pi\)
−0.949131 + 0.314883i \(0.898035\pi\)
\(410\) 2.76297e9 1.56696e10i 0.00482890 0.0273861i
\(411\) −6.26158e11 + 1.45909e11i −1.08242 + 0.252229i
\(412\) −2.42075e10 + 2.03125e10i −0.0413917 + 0.0347318i
\(413\) 1.46905e11 + 2.54447e11i 0.248463 + 0.430350i
\(414\) 4.30492e11 4.70278e10i 0.720218 0.0786780i
\(415\) 2.58883e11 4.48398e11i 0.428436 0.742073i
\(416\) −4.36928e8 2.47794e9i −0.000715303 0.00405668i
\(417\) 4.32526e11 + 5.22097e10i 0.700487 + 0.0845550i
\(418\) −1.32178e10 + 4.81089e9i −0.0211771 + 0.00770784i
\(419\) 1.02237e12 3.72111e11i 1.62048 0.589807i 0.637007 0.770858i \(-0.280172\pi\)
0.983474 + 0.181052i \(0.0579502\pi\)
\(420\) 1.41474e10 + 3.31407e10i 0.0221848 + 0.0519684i
\(421\) −7.85148e10 4.45280e11i −0.121810 0.690817i −0.983152 0.182792i \(-0.941487\pi\)
0.861342 0.508026i \(-0.169625\pi\)
\(422\) −9.77948e10 + 1.69386e11i −0.150110 + 0.259998i
\(423\) 1.30080e11 + 4.46739e11i 0.197552 + 0.678457i
\(424\) −3.98508e11 6.90237e11i −0.598813 1.03717i
\(425\) −4.97507e11 + 4.17458e11i −0.739689 + 0.620673i
\(426\) −2.98940e11 + 9.84990e11i −0.439785 + 1.44907i
\(427\) 3.86447e10 2.19165e11i 0.0562554 0.319040i
\(428\) −5.37808e10 4.51274e10i −0.0774694 0.0650045i
\(429\) −1.72822e10 8.76123e9i −0.0246343 0.0124884i
\(430\) −5.61118e11 2.04230e11i −0.791491 0.288079i
\(431\) 3.23263e11 0.451241 0.225620 0.974215i \(-0.427559\pi\)
0.225620 + 0.974215i \(0.427559\pi\)
\(432\) 7.44273e11 2.61393e11i 1.02815 0.361091i
\(433\) 9.86284e10 0.134836 0.0674181 0.997725i \(-0.478524\pi\)
0.0674181 + 0.997725i \(0.478524\pi\)
\(434\) 3.48658e10 + 1.26901e10i 0.0471732 + 0.0171697i
\(435\) −4.76888e10 8.75684e11i −0.0638579 1.17259i
\(436\) −1.12850e11 9.46928e10i −0.149559 0.125495i
\(437\) 1.47644e9 8.37330e9i 0.00193664 0.0109832i
\(438\) 8.31053e10 + 8.87549e10i 0.107893 + 0.115228i
\(439\) −1.67490e11 + 1.40541e11i −0.215228 + 0.180598i −0.744028 0.668149i \(-0.767087\pi\)
0.528799 + 0.848747i \(0.322642\pi\)
\(440\) −3.09277e11 5.35683e11i −0.393378 0.681350i
\(441\) 1.18267e11 + 7.90705e10i 0.148899 + 0.0995499i
\(442\) −1.38557e10 + 2.39989e10i −0.0172675 + 0.0299082i
\(443\) −4.85196e10 2.75168e11i −0.0598550 0.339455i 0.940144 0.340777i \(-0.110690\pi\)
−0.999999 + 0.00132255i \(0.999579\pi\)
\(444\) −4.56270e10 + 6.08074e10i −0.0557184 + 0.0742563i
\(445\) −2.80335e11 + 1.02034e11i −0.338889 + 0.123345i
\(446\) 4.25430e11 1.54844e11i 0.509121 0.185305i
\(447\) −5.88827e10 + 7.84735e10i −0.0697596 + 0.0929692i
\(448\) 1.18244e11 + 6.70598e11i 0.138685 + 0.786522i
\(449\) 1.50042e11 2.59881e11i 0.174223 0.301763i −0.765669 0.643234i \(-0.777592\pi\)
0.939892 + 0.341472i \(0.110925\pi\)
\(450\) −4.97679e11 + 2.45259e11i −0.572127 + 0.281948i
\(451\) 2.47800e10 + 4.29201e10i 0.0282037 + 0.0488502i
\(452\) −2.35961e9 + 1.97994e9i −0.00265899 + 0.00223116i
\(453\) 1.25916e11 + 1.34476e11i 0.140488 + 0.150039i
\(454\) −1.06798e11 + 6.05682e11i −0.117981 + 0.669103i
\(455\) 8.23895e9 + 6.91330e9i 0.00901199 + 0.00756195i
\(456\) −7.65196e8 1.40509e10i −0.000828764 0.0152182i
\(457\) −1.33541e12 4.86048e11i −1.43216 0.521262i −0.494607 0.869116i \(-0.664688\pi\)
−0.937549 + 0.347854i \(0.886910\pi\)
\(458\) 1.42183e12 1.50991
\(459\) −1.41267e12 5.32350e11i −1.48553 0.559809i
\(460\) −4.13785e10 −0.0430888
\(461\) 9.27676e11 + 3.37647e11i 0.956626 + 0.348183i 0.772711 0.634759i \(-0.218900\pi\)
0.183916 + 0.982942i \(0.441123\pi\)
\(462\) −1.10479e12 5.60076e11i −1.12821 0.571950i
\(463\) −3.93681e11 3.30337e11i −0.398134 0.334074i 0.421638 0.906764i \(-0.361455\pi\)
−0.819772 + 0.572690i \(0.805900\pi\)
\(464\) −3.54482e11 + 2.01037e12i −0.355029 + 2.01347i
\(465\) 9.68295e9 3.19047e10i 0.00960438 0.0316459i
\(466\) −1.99599e11 + 1.67483e11i −0.196074 + 0.164526i
\(467\) 6.89524e11 + 1.19429e12i 0.670847 + 1.16194i 0.977664 + 0.210172i \(0.0674025\pi\)
−0.306817 + 0.951768i \(0.599264\pi\)
\(468\) −1.48385e9 + 1.54920e9i −0.00142982 + 0.00149280i
\(469\) −6.91113e11 + 1.19704e12i −0.659586 + 1.14244i
\(470\) −8.51997e10 4.83192e11i −0.0805374 0.456750i
\(471\) 5.01045e11 + 1.17371e12i 0.469119 + 1.09892i
\(472\) −5.24704e11 + 1.90977e11i −0.486604 + 0.177109i
\(473\) 1.74775e12 6.36129e11i 1.60548 0.584346i
\(474\) 8.82686e11 + 1.06548e11i 0.803163 + 0.0969490i
\(475\) 1.89162e9 + 1.07279e10i 0.00170495 + 0.00966926i
\(476\) −8.02606e10 + 1.39015e11i −0.0716591 + 0.124117i
\(477\) −5.77981e11 + 1.31259e12i −0.511189 + 1.16091i
\(478\) −1.57855e11 2.73413e11i −0.138303 0.239549i
\(479\) −4.83136e11 + 4.05399e11i −0.419334 + 0.351863i −0.827910 0.560862i \(-0.810470\pi\)
0.408576 + 0.912724i \(0.366026\pi\)
\(480\) −1.40771e11 + 3.28030e10i −0.121040 + 0.0282052i
\(481\) −3.94017e9 + 2.23458e10i −0.00335631 + 0.0190346i
\(482\) −1.32086e12 1.10834e12i −1.11467 0.935319i
\(483\) 6.27093e11 4.09065e11i 0.524288 0.342003i
\(484\) −8.73216e10 3.17825e10i −0.0723299 0.0263259i
\(485\) −1.34996e12 −1.10786
\(486\) −1.06397e12 7.28899e11i −0.865100 0.592658i
\(487\) −1.35575e12 −1.09219 −0.546097 0.837722i \(-0.683887\pi\)
−0.546097 + 0.837722i \(0.683887\pi\)
\(488\) 3.97437e11 + 1.44655e11i 0.317233 + 0.115464i
\(489\) −1.73525e12 + 1.13194e12i −1.37237 + 0.895225i
\(490\) −1.14920e11 9.64290e10i −0.0900558 0.0755658i
\(491\) 1.08359e11 6.14534e11i 0.0841391 0.477177i −0.913400 0.407063i \(-0.866553\pi\)
0.997539 0.0701133i \(-0.0223361\pi\)
\(492\) 5.34377e9 1.24522e9i 0.00411154 0.000958086i
\(493\) 2.99270e12 2.51117e12i 2.28167 1.91455i
\(494\) 2.32406e8 + 4.02539e8i 0.000175581 + 0.000304114i
\(495\) −4.48563e11 + 1.01868e12i −0.335815 + 0.762633i
\(496\) −3.88054e10 + 6.72129e10i −0.0287889 + 0.0498638i
\(497\) 3.09038e11 + 1.75264e12i 0.227200 + 1.28851i
\(498\) 1.95625e12 + 2.36137e11i 1.42526 + 0.172041i
\(499\) −3.41705e11 + 1.24370e11i −0.246717 + 0.0897976i −0.462419 0.886662i \(-0.653018\pi\)
0.215702 + 0.976459i \(0.430796\pi\)
\(500\) 1.31720e11 4.79422e10i 0.0942513 0.0343047i
\(501\) −5.82748e11 1.36510e12i −0.413248 0.968041i
\(502\) 2.52987e11 + 1.43476e12i 0.177800 + 1.00835i
\(503\) 1.11783e11 1.93614e11i 0.0778610 0.134859i −0.824466 0.565912i \(-0.808524\pi\)
0.902327 + 0.431053i \(0.141858\pi\)
\(504\) 8.57125e11 8.94876e11i 0.591707 0.617768i
\(505\) −6.24629e10 1.08189e11i −0.0427377 0.0740239i
\(506\) 1.08959e12 9.14274e11i 0.738899 0.620010i
\(507\) 4.31885e11 1.42304e12i 0.290290 0.956489i
\(508\) 1.03174e10 5.85130e10i 0.00687360 0.0389821i
\(509\) −1.09210e12 9.16384e11i −0.721164 0.605128i 0.206543 0.978437i \(-0.433779\pi\)
−0.927707 + 0.373309i \(0.878223\pi\)
\(510\) 1.41987e12 + 7.19806e11i 0.929358 + 0.471140i
\(511\) 1.97541e11 + 7.18991e10i 0.128163 + 0.0466476i
\(512\) −1.26335e12 −0.812474
\(513\) −1.95805e10 + 1.60559e10i −0.0124823 + 0.0102354i
\(514\) −7.83188e11 −0.494916
\(515\) 5.09147e11 + 1.85314e11i 0.318941 + 0.116085i
\(516\) −1.11974e10 2.05612e11i −0.00695336 0.127681i
\(517\) 1.17070e12 + 9.82337e11i 0.720675 + 0.604718i
\(518\) −2.51882e11 + 1.42849e12i −0.153714 + 0.871754i
\(519\) −9.37584e11 1.00132e12i −0.567227 0.605788i
\(520\) −1.56579e10 + 1.31386e10i −0.00939116 + 0.00788012i
\(521\) −1.52682e12 2.64452e12i −0.907856 1.57245i −0.817037 0.576585i \(-0.804385\pi\)
−0.0908193 0.995867i \(-0.528949\pi\)
\(522\) 2.99373e12 1.47533e12i 1.76480 0.869706i
\(523\) 5.36074e11 9.28507e11i 0.313305 0.542660i −0.665771 0.746156i \(-0.731897\pi\)
0.979076 + 0.203496i \(0.0652305\pi\)
\(524\) 1.21503e10 + 6.89078e10i 0.00704039 + 0.0399280i
\(525\) −5.75730e11 + 7.67279e11i −0.330751 + 0.440795i
\(526\) 1.34796e12 4.90616e11i 0.767785 0.279451i
\(527\) 1.39570e11 5.07995e10i 0.0788216 0.0286887i
\(528\) 1.55503e12 2.07240e12i 0.870734 1.16043i
\(529\) −1.63470e11 9.27086e11i −0.0907587 0.514718i
\(530\) 7.56180e11 1.30974e12i 0.416278 0.721015i
\(531\) 8.35298e11 + 5.58458e11i 0.455949 + 0.304835i
\(532\) 1.34623e9 + 2.33174e9i 0.000728648 + 0.00126206i
\(533\) 1.25455e9 1.05269e9i 0.000673311 0.000564975i
\(534\) −7.75995e11 8.28748e11i −0.412975 0.441049i
\(535\) −2.09028e11 + 1.18546e12i −0.110309 + 0.625595i
\(536\) −2.01231e12 1.68853e12i −1.05306 0.883625i
\(537\) 1.83208e11 + 3.36415e12i 0.0950737 + 1.74579i
\(538\) 3.76869e12 + 1.37169e12i 1.93941 + 0.705888i
\(539\) 4.67267e11 0.238460
\(540\) 9.34983e10 + 8.02749e10i 0.0473186 + 0.0406264i
\(541\) 2.23544e12 1.12195 0.560977 0.827832i \(-0.310426\pi\)
0.560977 + 0.827832i \(0.310426\pi\)
\(542\) 1.77275e12 + 6.45228e11i 0.882369 + 0.321156i
\(543\) −1.67051e12 8.46867e11i −0.824612 0.418038i
\(544\) −4.93253e11 4.13888e11i −0.241476 0.202623i
\(545\) −4.38612e11 + 2.48749e12i −0.212959 + 1.20775i
\(546\) −1.18870e10 + 3.91668e10i −0.00572405 + 0.0188604i
\(547\) 1.61476e12 1.35494e12i 0.771195 0.647109i −0.169820 0.985475i \(-0.554319\pi\)
0.941015 + 0.338366i \(0.109874\pi\)
\(548\) 1.16897e11 + 2.02471e11i 0.0553719 + 0.0959069i
\(549\) −2.12772e11 7.30729e11i −0.0999628 0.343305i
\(550\) −9.11165e11 + 1.57818e12i −0.424585 + 0.735403i
\(551\) −1.13788e10 6.45325e10i −0.00525915 0.0298261i
\(552\) 5.58658e11 + 1.30867e12i 0.256106 + 0.599934i
\(553\) 1.44448e12 5.25746e11i 0.656821 0.239063i
\(554\) −1.98124e12 + 7.21114e11i −0.893602 + 0.325245i
\(555\) 1.29408e12 + 1.56207e11i 0.578950 + 0.0698845i
\(556\) −2.75099e10 1.56017e11i −0.0122082 0.0692364i
\(557\) −1.25471e12 + 2.17322e12i −0.552326 + 0.956656i 0.445781 + 0.895142i \(0.352926\pi\)
−0.998106 + 0.0615137i \(0.980407\pi\)
\(558\) 1.26138e11 1.37795e10i 0.0550797 0.00601701i
\(559\) −3.07303e10 5.32264e10i −0.0133111 0.0230555i
\(560\) −1.10170e12 + 9.24433e11i −0.473387 + 0.397219i
\(561\) −4.82902e12 + 1.12528e12i −2.05838 + 0.479652i
\(562\) 8.46544e10 4.80099e11i 0.0357961 0.203010i
\(563\) −3.49371e12 2.93157e12i −1.46554 1.22974i −0.920156 0.391552i \(-0.871938\pi\)
−0.545387 0.838184i \(-0.683617\pi\)
\(564\) 1.41712e11 9.24412e10i 0.0589725 0.0384689i
\(565\) 4.96286e10 + 1.80633e10i 0.0204887 + 0.00745727i
\(566\) −4.59830e12 −1.88332
\(567\) −2.21056e12 2.92253e11i −0.898213 0.118750i
\(568\) −3.38224e12 −1.36344
\(569\) −2.34120e11 8.52126e10i −0.0936338 0.0340799i 0.294778 0.955566i \(-0.404754\pi\)
−0.388412 + 0.921486i \(0.626976\pi\)
\(570\) 2.23639e10 1.45884e10i 0.00887382 0.00578857i
\(571\) −1.93473e12 1.62343e12i −0.761656 0.639105i 0.176902 0.984229i \(-0.443393\pi\)
−0.938557 + 0.345123i \(0.887837\pi\)
\(572\) −1.22350e9 + 6.93879e9i −0.000477881 + 0.00271020i
\(573\) 3.97280e12 9.25756e11i 1.53958 0.358757i
\(574\) 8.01992e10 6.72951e10i 0.0308366 0.0258750i
\(575\) −5.50767e11 9.53956e11i −0.210118 0.363934i
\(576\) 1.37649e12 + 1.87837e12i 0.521040 + 0.711015i
\(577\) −2.35385e12 + 4.07699e12i −0.884072 + 1.53126i −0.0372978 + 0.999304i \(0.511875\pi\)
−0.846774 + 0.531953i \(0.821458\pi\)
\(578\) 7.42799e11 + 4.21262e12i 0.276819 + 1.56992i
\(579\) 1.15013e12 + 1.38831e11i 0.425297 + 0.0513371i
\(580\) −2.99669e11 + 1.09071e11i −0.109955 + 0.0400205i
\(581\) 3.20132e12 1.16518e12i 1.16556 0.424231i
\(582\) −2.01706e12 4.72501e12i −0.728728 1.70706i
\(583\) 8.17994e11 + 4.63908e12i 0.293252 + 1.66312i
\(584\) −1.99758e11 + 3.45991e11i −0.0710635 + 0.123086i
\(585\) 3.57247e10 + 8.75211e9i 0.0126115 + 0.00308967i
\(586\) 2.91543e12 + 5.04967e12i 1.02132 + 1.76898i
\(587\) 1.57495e12 1.32154e12i 0.547513 0.459418i −0.326585 0.945168i \(-0.605898\pi\)
0.874098 + 0.485750i \(0.161453\pi\)
\(588\) 1.50239e10 4.95030e10i 0.00518305 0.0170779i
\(589\) 4.32609e8 2.45345e9i 0.000148107 0.000839958i
\(590\) −8.11653e11 6.81058e11i −0.275763 0.231393i
\(591\) 1.84793e12 + 9.36813e11i 0.623078 + 0.315871i
\(592\) −2.85115e12 1.03773e12i −0.954054 0.347247i
\(593\) 5.03859e12 1.67326 0.836628 0.547771i \(-0.184523\pi\)
0.836628 + 0.547771i \(0.184523\pi\)
\(594\) −4.23573e12 4.79391e10i −1.39601 0.0157998i
\(595\) 2.75229e12 0.900258
\(596\) 3.35242e10 + 1.22018e10i 0.0108830 + 0.00396110i
\(597\) −2.85410e11 5.24083e12i −0.0919570 1.68856i
\(598\) −3.60053e10 3.02120e10i −0.0115136 0.00966105i
\(599\) −2.21300e11 + 1.25506e12i −0.0702362 + 0.398329i 0.929340 + 0.369225i \(0.120377\pi\)
−0.999576 + 0.0291046i \(0.990734\pi\)
\(600\) −1.24604e12 1.33075e12i −0.392512 0.419195i
\(601\) 3.57897e12 3.00311e12i 1.11898 0.938937i 0.120429 0.992722i \(-0.461573\pi\)
0.998553 + 0.0537849i \(0.0171285\pi\)
\(602\) −1.96449e12 3.40259e12i −0.609627 1.05591i
\(603\) −3.10448e11 + 4.71681e12i −0.0956227 + 1.45285i
\(604\) 3.34953e10 5.80155e10i 0.0102404 0.0177369i
\(605\) 2.76673e11 + 1.56909e12i 0.0839591 + 0.476156i
\(606\) 2.85343e11 3.80279e11i 0.0859490 0.114545i
\(607\) −3.36490e12 + 1.22473e12i −1.00606 + 0.366176i −0.791918 0.610627i \(-0.790917\pi\)
−0.214141 + 0.976803i \(0.568695\pi\)
\(608\) −1.01489e10 + 3.69390e9i −0.00301199 + 0.00109627i
\(609\) 3.46324e12 4.61548e12i 1.02025 1.35969i
\(610\) 1.39361e11 + 7.90353e11i 0.0407527 + 0.231120i
\(611\) 2.52503e10 4.37348e10i 0.00732961 0.0126953i
\(612\) −3.60531e10 + 5.47775e11i −0.0103887 + 0.157841i
\(613\) −8.06728e11 1.39729e12i −0.230757 0.399683i 0.727274 0.686347i \(-0.240787\pi\)
−0.958031 + 0.286664i \(0.907454\pi\)
\(614\) 8.80970e11 7.39221e11i 0.250152 0.209902i
\(615\) −6.43020e10 6.86733e10i −0.0181254 0.0193575i
\(616\) 7.06737e11 4.00810e12i 0.197763 1.12157i
\(617\) 1.42050e12 + 1.19195e12i 0.394602 + 0.331111i 0.818403 0.574645i \(-0.194860\pi\)
−0.423801 + 0.905755i \(0.639304\pi\)
\(618\) 1.12129e11 + 2.05896e12i 0.0309221 + 0.567806i
\(619\) −2.64304e12 9.61986e11i −0.723594 0.263367i −0.0461433 0.998935i \(-0.514693\pi\)
−0.677451 + 0.735568i \(0.736915\pi\)
\(620\) −1.21242e10 −0.00329528
\(621\) 1.30527e12 2.20284e12i 0.352199 0.594388i
\(622\) −5.94132e12 −1.59157
\(623\) −1.84454e12 6.71357e11i −0.490559 0.178549i
\(624\) −7.63646e10 3.87132e10i −0.0201633 0.0102218i
\(625\) −6.36897e10 5.34420e10i −0.0166959 0.0140095i
\(626\) −1.01319e12 + 5.74608e12i −0.263697 + 1.49550i
\(627\) −2.41534e10 + 7.95841e10i −0.00624129 + 0.0205647i
\(628\) 3.55494e11 2.98295e11i 0.0912040 0.0765293i
\(629\) 2.90329e12 + 5.02864e12i 0.739541 + 1.28092i
\(630\) 2.28376e12 + 5.59493e11i 0.577589 + 0.141502i
\(631\) 7.73874e11 1.34039e12i 0.194329 0.336588i −0.752351 0.658762i \(-0.771080\pi\)
0.946680 + 0.322174i \(0.104414\pi\)
\(632\) 5.07291e11 + 2.87699e12i 0.126483 + 0.717318i
\(633\) 4.54042e11 + 1.06360e12i 0.112403 + 0.263307i
\(634\) −2.78878e12 + 1.01503e12i −0.685508 + 0.249504i
\(635\) −9.57298e11 + 3.48428e11i −0.233650 + 0.0850416i
\(636\) 5.17771e11 + 6.24996e10i 0.125482 + 0.0151468i
\(637\) −2.68126e9 1.52062e10i −0.000645225 0.00365926i
\(638\) 5.48101e12 9.49339e12i 1.30969 2.26845i
\(639\) 3.59752e12 + 4.90920e12i 0.853590 + 1.16482i
\(640\) −1.49156e12 2.58345e12i −0.351423 0.608683i
\(641\) 1.58481e12 1.32981e12i 0.370780 0.311121i −0.438290 0.898834i \(-0.644416\pi\)
0.809070 + 0.587712i \(0.199971\pi\)
\(642\) −4.46154e12 + 1.03964e12i −1.03652 + 0.241534i
\(643\) 3.85428e11 2.18587e12i 0.0889188 0.504283i −0.907523 0.420002i \(-0.862029\pi\)
0.996442 0.0842815i \(-0.0268595\pi\)
\(644\) −2.08564e11 1.75006e11i −0.0477807 0.0400927i
\(645\) −2.95710e12 + 1.92898e12i −0.672741 + 0.438842i
\(646\) 1.11774e11 + 4.06823e10i 0.0252518 + 0.00919091i
\(647\) 2.41867e12 0.542633 0.271317 0.962490i \(-0.412541\pi\)
0.271317 + 0.962490i \(0.412541\pi\)
\(648\) 1.27650e12 4.04085e12i 0.284402 0.900297i
\(649\) 3.30021e12 0.730197
\(650\) 5.65870e10 + 2.05960e10i 0.0124339 + 0.00452556i
\(651\) 1.83744e11 1.19859e11i 0.0400957 0.0261552i
\(652\) 5.77124e11 + 4.84264e11i 0.125070 + 0.104947i
\(653\) −8.01429e11 + 4.54513e12i −0.172487 + 0.978221i 0.768518 + 0.639828i \(0.220994\pi\)
−0.941005 + 0.338393i \(0.890117\pi\)
\(654\) −9.36185e12 + 2.18153e12i −2.00107 + 0.466296i
\(655\) 9.19035e11 7.71162e11i 0.195095 0.163704i
\(656\) 1.09495e11 + 1.89651e11i 0.0230848 + 0.0399841i
\(657\) 7.14667e11 7.80716e10i 0.149644 0.0163474i
\(658\) 1.61417e12 2.79582e12i 0.335685 0.581423i
\(659\) −1.47288e12 8.35314e12i −0.304217 1.72530i −0.627166 0.778886i \(-0.715785\pi\)
0.322948 0.946417i \(-0.395326\pi\)
\(660\) 4.01835e11 + 4.85050e10i 0.0824327 + 0.00995037i
\(661\) −3.60104e12 + 1.31067e12i −0.733705 + 0.267047i −0.681732 0.731602i \(-0.738773\pi\)
−0.0519728 + 0.998649i \(0.516551\pi\)
\(662\) 7.21525e12 2.62614e12i 1.46013 0.531442i
\(663\) 6.43294e10 + 1.50693e11i 0.0129300 + 0.0302888i
\(664\) 1.12428e12 + 6.37613e12i 0.224450 + 1.27292i
\(665\) 2.30824e10 3.99799e10i 0.00457703 0.00792765i
\(666\) 1.38682e12 + 4.76280e12i 0.273141 + 0.938056i
\(667\) 3.31308e12 + 5.73842e12i 0.648135 + 1.12260i
\(668\) −4.13462e11 + 3.46936e11i −0.0803418 + 0.0674148i
\(669\) 7.77403e11 2.56150e12i 0.150047 0.494397i
\(670\) 8.65565e11 4.90886e12i 0.165945 0.941118i
\(671\) −1.91491e12 1.60680e12i −0.364668 0.305993i
\(672\) −8.48280e11 4.30037e11i −0.160464 0.0813475i
\(673\) −1.64780e12 5.99749e11i −0.309625 0.112694i 0.182534 0.983199i \(-0.441570\pi\)
−0.492159 + 0.870505i \(0.663792\pi\)
\(674\) 5.92552e12 1.10601
\(675\) −6.06185e11 + 3.22404e12i −0.112393 + 0.597770i
\(676\) −5.40773e11 −0.0995990
\(677\) 3.37602e12 + 1.22877e12i 0.617669 + 0.224813i 0.631856 0.775086i \(-0.282294\pi\)
−0.0141863 + 0.999899i \(0.504516\pi\)
\(678\) 1.09296e10 + 2.00695e11i 0.00198643 + 0.0364757i
\(679\) −6.80433e12 5.70951e12i −1.22849 1.03082i
\(680\) −9.08294e11 + 5.15119e12i −0.162906 + 0.923884i
\(681\) 2.48549e12 + 2.65446e12i 0.442843 + 0.472948i
\(682\) 3.19259e11 2.67890e11i 0.0565084 0.0474162i
\(683\) −1.62740e12 2.81874e12i −0.286155 0.495635i 0.686733 0.726909i \(-0.259044\pi\)
−0.972889 + 0.231274i \(0.925711\pi\)
\(684\) 7.65466e9 + 5.11770e9i 0.00133713 + 0.000893968i
\(685\) 2.00430e12 3.47155e12i 0.347821 0.602443i
\(686\) −1.12837e12 6.39930e12i −0.194533 1.10325i
\(687\) 5.04561e12 6.72432e12i 0.864188 1.15171i
\(688\) 7.72277e12 2.81086e12i 1.31409 0.478290i
\(689\) 1.46275e11 5.32397e10i 0.0247276 0.00900013i
\(690\) −1.62051e12 + 2.15966e12i −0.272163 + 0.362714i
\(691\) −6.09285e11 3.45543e12i −0.101665 0.576568i −0.992500 0.122243i \(-0.960991\pi\)
0.890836 0.454326i \(-0.150120\pi\)
\(692\) −2.49409e11 + 4.31989e11i −0.0413461 + 0.0716136i
\(693\) −6.56934e12 + 3.23742e12i −1.08199 + 0.533211i
\(694\) −2.78900e12 4.83068e12i −0.456384 0.790480i
\(695\) −2.08082e12 + 1.74601e12i −0.338301 + 0.283868i
\(696\) 7.49544e12 + 8.00499e12i 1.21075 + 1.29306i
\(697\) 7.27746e10 4.12725e11i 0.0116797 0.0662390i
\(698\) −3.27237e12 2.74585e12i −0.521811 0.437852i
\(699\) 8.37751e10 + 1.53832e12i 0.0132730 + 0.243724i
\(700\) 3.27785e11 + 1.19304e11i 0.0515998 + 0.0187808i
\(701\) −2.33825e12 −0.365730 −0.182865 0.983138i \(-0.558537\pi\)
−0.182865 + 0.983138i \(0.558537\pi\)
\(702\) 2.27453e10 + 1.38118e11i 0.00353488 + 0.0214650i
\(703\) 9.73952e10 0.0150397
\(704\) 7.18740e12 + 2.61600e12i 1.10279 + 0.401384i
\(705\) −2.58753e12 1.31175e12i −0.394488 0.199987i
\(706\) 6.25732e12 + 5.25051e12i 0.947910 + 0.795391i
\(707\) 1.42736e11 8.09495e11i 0.0214855 0.121850i
\(708\) 1.06111e11 3.49629e11i 0.0158712 0.0522947i
\(709\) −6.45500e12 + 5.41639e12i −0.959375 + 0.805011i −0.980851 0.194758i \(-0.937608\pi\)
0.0214765 + 0.999769i \(0.493163\pi\)
\(710\) −3.20894e12 5.55805e12i −0.473914 0.820843i
\(711\) 3.63627e12 3.79643e12i 0.533634 0.557137i
\(712\) 1.86524e12 3.23069e12i 0.272004 0.471124i
\(713\) 4.37451e10 + 2.48091e11i 0.00633909 + 0.0359508i
\(714\) 4.11236e12 + 9.63330e12i 0.592174 + 1.38718i
\(715\) 1.13522e11 4.13185e10i 0.0162443 0.00591245i
\(716\) 1.15125e12 4.19021e11i 0.163705 0.0595837i
\(717\) −1.85324e12 2.23703e11i −0.261876 0.0316108i
\(718\) −9.39773e11 5.32972e12i −0.131966 0.748418i
\(719\) −3.05242e12 + 5.28695e12i −0.425956 + 0.737777i −0.996509 0.0834837i \(-0.973395\pi\)
0.570554 + 0.821260i \(0.306729\pi\)
\(720\) −1.98206e12 + 4.50125e12i −0.274866 + 0.624219i
\(721\) 1.78253e12 + 3.08744e12i 0.245657 + 0.425491i
\(722\) −5.86386e12 + 4.92037e12i −0.803094 + 0.673876i
\(723\) −9.92903e12 + 2.31370e12i −1.35140 + 0.314908i
\(724\) −1.18264e11 + 6.70709e11i −0.0159967 + 0.0907216i
\(725\) −6.50330e12 5.45692e12i −0.874204 0.733544i
\(726\) −5.07859e12 + 3.31287e12i −0.678467 + 0.442577i
\(727\) −8.04855e12 2.92943e12i −1.06859 0.388936i −0.252943 0.967481i \(-0.581399\pi\)
−0.815651 + 0.578545i \(0.803621\pi\)
\(728\) −1.34490e11 −0.0177460
\(729\) −7.22291e12 + 2.44526e12i −0.947193 + 0.320665i
\(730\) −7.58092e11 −0.0988028
\(731\) −1.47795e13 5.37928e12i −1.91439 0.696780i
\(732\) −2.31797e11 + 1.51205e11i −0.0298406 + 0.0194656i
\(733\) −5.57220e12 4.67564e12i −0.712950 0.598236i 0.212475 0.977166i \(-0.431848\pi\)
−0.925425 + 0.378930i \(0.876292\pi\)
\(734\) −1.07347e12 + 6.08797e12i −0.136508 + 0.774177i
\(735\) −8.63860e11 + 2.01300e11i −0.109182 + 0.0254419i
\(736\) 8.36607e11 7.01997e11i 0.105092 0.0881830i
\(737\) 7.76291e12 + 1.34457e13i 0.969216 + 1.67873i
\(738\) 1.44286e11 3.27673e11i 0.0179049 0.0406619i
\(739\) −5.47159e12 + 9.47708e12i −0.674860 + 1.16889i 0.301650 + 0.953419i \(0.402463\pi\)
−0.976510 + 0.215473i \(0.930871\pi\)
\(740\) −8.23071e10 4.66787e11i −0.0100901 0.0572237i
\(741\) 2.72849e9 + 3.29352e8i 0.000332460 + 4.01309e-5i
\(742\) 9.35085e12 3.40343e12i 1.13249 0.412192i
\(743\) 9.36887e12 3.40999e12i 1.12781 0.410491i 0.290316 0.956931i \(-0.406240\pi\)
0.837498 + 0.546440i \(0.184017\pi\)
\(744\) 1.63692e11 + 3.83451e11i 0.0195861 + 0.0458808i
\(745\) −1.06219e11 6.02400e11i −0.0126328 0.0716443i
\(746\) 4.59589e11 7.96031e11i 0.0543306 0.0941034i
\(747\) 8.05889e12 8.41383e12i 0.946962 0.988670i
\(748\) 9.01525e11 + 1.56149e12i 0.105298 + 0.182382i
\(749\) −6.06734e12 + 5.09110e12i −0.704417 + 0.591076i
\(750\) 2.65632e12 8.75242e12i 0.306552 1.01007i
\(751\) −2.13031e12 + 1.20816e13i −0.244378 + 1.38594i 0.577554 + 0.816352i \(0.304007\pi\)
−0.821932 + 0.569585i \(0.807104\pi\)
\(752\) 5.17298e12 + 4.34064e12i 0.589875 + 0.494964i
\(753\) 7.68325e12 + 3.89504e12i 0.870899 + 0.441504i
\(754\) −3.40393e11 1.23893e11i −0.0383539 0.0139597i
\(755\) −1.14862e12 −0.128651
\(756\) 1.31754e11 + 8.00058e11i 0.0146695 + 0.0890786i
\(757\) 1.34182e13 1.48512 0.742561 0.669779i \(-0.233611\pi\)
0.742561 + 0.669779i \(0.233611\pi\)
\(758\) 1.91474e12 + 6.96909e11i 0.210668 + 0.0766769i
\(759\) −4.57320e11 8.39751e12i −0.0500186 0.918465i
\(760\) 6.72091e10 + 5.63951e10i 0.00730746 + 0.00613169i
\(761\) 1.30766e12 7.41611e12i 0.141340 0.801577i −0.828894 0.559406i \(-0.811029\pi\)
0.970234 0.242171i \(-0.0778595\pi\)
\(762\) −2.64990e12 2.83004e12i −0.284729 0.304085i
\(763\) −1.27314e13 + 1.06829e13i −1.35992 + 1.14111i
\(764\) −7.41678e11 1.28462e12i −0.0787581 0.136413i
\(765\) 8.44288e12 4.16071e12i 0.891280 0.439229i
\(766\) 5.15499e12 8.92870e12i 0.541001 0.937042i
\(767\) −1.89372e10 1.07398e11i −0.00197577 0.0112051i
\(768\) 1.71310e12 2.28306e12i 0.177687 0.236805i
\(769\) −2.78527e12 + 1.01376e12i −0.287210 + 0.104536i −0.481608 0.876387i \(-0.659947\pi\)
0.194398 + 0.980923i \(0.437725\pi\)
\(770\) 7.25706e12 2.64135e12i 0.743965 0.270781i
\(771\) −2.77928e12 + 3.70397e12i −0.283262 + 0.377505i
\(772\) −7.31515e10 4.14863e11i −0.00741217 0.0420365i
\(773\) −7.60990e12 + 1.31807e13i −0.766605 + 1.32780i 0.172789 + 0.984959i \(0.444722\pi\)
−0.939394 + 0.342839i \(0.888611\pi\)
\(774\) −1.11700e13 7.46798e12i −1.11872 0.747943i
\(775\) −1.61379e11 2.79517e11i −0.0160691 0.0278324i
\(776\) 1.29315e13 1.08508e13i 1.28018 1.07420i
\(777\) 5.86199e12 + 6.26050e12i 0.576967 + 0.616189i
\(778\) −2.50786e12 + 1.42228e13i −0.245412 + 1.39180i
\(779\) −5.38495e9 4.51851e9i −0.000523917 0.000439619i
\(780\) −7.27308e8 1.33552e10i −7.03546e−5 0.00129188i
\(781\) 1.87846e13 + 6.83705e12i 1.80665 + 0.657565i
\(782\) −1.20278e13 −1.15016
\(783\) 3.64644e12 1.93939e13i 0.346690 1.84390i
\(784\) 2.06471e12 0.195181
\(785\) −7.47696e12 2.72139e12i −0.702768 0.255786i
\(786\) 4.07234e12 + 2.06448e12i 0.380577 + 0.192934i
\(787\) 5.64672e12 + 4.73816e12i 0.524699 + 0.440275i 0.866266 0.499583i \(-0.166513\pi\)
−0.341567 + 0.939857i \(0.610958\pi\)
\(788\) 1.30825e11 7.41945e11i 0.0120871 0.0685494i
\(789\) 2.46317e12 8.11599e12i 0.226281 0.745582i
\(790\) −4.24648e12 + 3.56322e12i −0.387888 + 0.325477i
\(791\) 1.73751e11 + 3.00945e11i 0.0157809 + 0.0273334i
\(792\) −3.89118e12 1.33636e13i −0.351413 1.20687i
\(793\) −4.13017e10 + 7.15367e10i −0.00370885 + 0.00642391i
\(794\) 5.16213e11 + 2.92759e12i 0.0460932 + 0.261407i
\(795\) −3.51079e12 8.22409e12i −0.311711 0.730190i
\(796\) −1.79347e12 + 6.52772e11i −0.158338 + 0.0576305i
\(797\) 8.54503e12 3.11014e12i 0.750155 0.273034i 0.0614841 0.998108i \(-0.480417\pi\)
0.688671 + 0.725074i \(0.258194\pi\)
\(798\) 1.74423e11 + 2.10544e10i 0.0152262 + 0.00183793i
\(799\) −2.24410e12 1.27269e13i −0.194797 1.10475i
\(800\) −6.99610e11 + 1.21176e12i −0.0603880 + 0.104595i
\(801\) −6.67320e12 + 7.28993e11i −0.572780 + 0.0625715i
\(802\) −6.54880e12 1.13429e13i −0.558955 0.968139i
\(803\) 1.80884e12 1.51780e12i 0.153526 0.128823i
\(804\) 1.67406e12 3.90096e11i 0.141293 0.0329245i
\(805\) −8.10617e11 + 4.59724e12i −0.0680353 + 0.385847i
\(806\) −1.05499e10 8.85238e9i −0.000880519 0.000738843i
\(807\) 1.98611e13 1.29558e13i 1.64843 1.07531i
\(808\) 1.46795e12 + 5.34290e11i 0.121160 + 0.0440987i
\(809\) −2.35878e12 −0.193606 −0.0968030 0.995304i \(-0.530862\pi\)
−0.0968030 + 0.995304i \(0.530862\pi\)
\(810\) 7.85145e12 1.73613e12i 0.640866 0.141710i
\(811\) 6.33918e12 0.514564 0.257282 0.966336i \(-0.417173\pi\)
0.257282 + 0.966336i \(0.417173\pi\)
\(812\) −1.97175e12 7.17660e11i −0.159166 0.0579317i
\(813\) 9.34243e12 6.09425e12i 0.749984 0.489229i
\(814\) 1.24812e13 + 1.04729e13i 0.996427 + 0.836102i
\(815\) 2.24309e12 1.27212e13i 0.178089 1.00999i
\(816\) −2.13380e13 + 4.97225e12i −1.68480 + 0.392597i
\(817\) −2.02090e11 + 1.69573e11i −0.0158688 + 0.0133155i
\(818\) 7.04539e12 + 1.22030e13i 0.550193 + 0.952962i
\(819\) 1.43051e11 + 1.95208e11i 0.0111100 + 0.0151607i
\(820\) −1.71051e10 + 2.96270e10i −0.00132119 + 0.00228836i
\(821\) −1.48263e12 8.40839e12i −0.113890 0.645905i −0.987294 0.158907i \(-0.949203\pi\)
0.873403 0.486998i \(-0.161908\pi\)
\(822\) 1.51456e13 + 1.82820e12i 1.15708 + 0.139669i
\(823\) −5.80187e12 + 2.11171e12i −0.440828 + 0.160448i −0.552892 0.833253i \(-0.686476\pi\)
0.112064 + 0.993701i \(0.464254\pi\)
\(824\) −6.36673e12 + 2.31730e12i −0.481110 + 0.175110i
\(825\) 4.23035e12 + 9.90969e12i 0.317932 + 0.744761i
\(826\) −1.21059e12 6.86560e12i −0.0904871 0.513178i
\(827\) −1.10185e12 + 1.90846e12i −0.0819120 + 0.141876i −0.904071 0.427382i \(-0.859436\pi\)
0.822159 + 0.569258i \(0.192769\pi\)
\(828\) −9.04349e11 2.21554e11i −0.0668651 0.0163811i
\(829\) −9.34340e12 1.61833e13i −0.687084 1.19006i −0.972777 0.231743i \(-0.925557\pi\)
0.285693 0.958321i \(-0.407776\pi\)
\(830\) −9.41125e12 + 7.89698e12i −0.688329 + 0.577576i
\(831\) −3.62040e12 + 1.19290e13i −0.263361 + 0.867760i
\(832\) 4.38894e10 2.48909e11i 0.00317545 0.0180088i
\(833\) −3.02690e12 2.53987e12i −0.217819 0.182772i
\(834\) −9.22033e12 4.67426e12i −0.659932 0.334554i
\(835\) 8.69618e12 + 3.16515e12i 0.619070 + 0.225323i
\(836\) 3.02430e10 0.00214140
\(837\) 3.82455e11 6.45450e11i 0.0269349 0.0454567i
\(838\) −2.58156e13 −1.80835
\(839\) −2.10778e12 7.67169e11i −0.146858 0.0534518i 0.267546 0.963545i \(-0.413787\pi\)
−0.414403 + 0.910093i \(0.636010\pi\)
\(840\) 4.20120e11 + 7.71444e12i 0.0291150 + 0.534623i
\(841\) 2.80068e13 + 2.35005e13i 1.93055 + 1.61993i
\(842\) −1.86300e12 + 1.05656e13i −0.127734 + 0.724418i
\(843\) −1.97014e12 2.10408e12i −0.134361 0.143495i
\(844\) 3.22145e11 2.70312e11i 0.0218530 0.0183368i
\(845\) 4.63603e12 + 8.02984e12i 0.312817 + 0.541816i
\(846\) 7.25083e11 1.10166e13i 0.0486655 0.739403i
\(847\) −5.24176e12 + 9.07900e12i −0.349947 + 0.606125i
\(848\) 3.61447e12 + 2.04987e13i 0.240028 + 1.36127i
\(849\) −1.63179e13 + 2.17470e13i −1.07790 + 1.43653i
\(850\) 1.44808e13 5.27057e12i 0.951496 0.346316i
\(851\) −9.25461e12 + 3.36840e12i −0.604888 + 0.220161i
\(852\) 1.32830e12 1.77024e12i 0.0863614 0.115094i
\(853\) −1.35439e12 7.68113e12i −0.0875938 0.496769i −0.996767 0.0803503i \(-0.974396\pi\)
0.909173 0.416419i \(-0.136715\pi\)
\(854\) −2.64028e12 + 4.57310e12i −0.169860 + 0.294205i
\(855\) 1.03686e10 1.57536e11i 0.000663549 0.0100817i
\(856\) −7.52622e12 1.30358e13i −0.479121 0.829861i
\(857\) 3.68822e12 3.09478e12i 0.233563 0.195982i −0.518493 0.855082i \(-0.673507\pi\)
0.752056 + 0.659100i \(0.229062\pi\)
\(858\) 3.14239e11 + 3.35602e11i 0.0197956 + 0.0211413i
\(859\) −3.32620e11 + 1.88638e12i −0.0208439 + 0.118212i −0.993454 0.114229i \(-0.963560\pi\)
0.972610 + 0.232441i \(0.0746713\pi\)
\(860\) 9.83498e11 + 8.25253e11i 0.0613099 + 0.0514451i
\(861\) −3.36610e10 6.18099e11i −0.00208743 0.0383304i
\(862\) −7.20779e12 2.62342e12i −0.444651 0.161840i
\(863\) −1.46100e13 −0.896608 −0.448304 0.893881i \(-0.647972\pi\)
−0.448304 + 0.893881i \(0.647972\pi\)
\(864\) −3.25227e12 3.68086e10i −0.198552 0.00224718i
\(865\) 8.55270e12 0.519434
\(866\) −2.19912e12 8.00413e11i −0.132867 0.0483597i
\(867\) 2.25589e13 + 1.14363e13i 1.35592 + 0.687384i
\(868\) −6.11109e10 5.12782e10i −0.00365410 0.00306615i
\(869\) 2.99826e12 1.70040e13i 0.178353 1.01149i
\(870\) −6.04325e12 + 1.99121e13i −0.357630 + 1.17837i
\(871\) 3.93018e11 3.29781e11i 0.0231382 0.0194153i
\(872\) −1.57926e13 2.73536e13i −0.924973 1.60210i
\(873\) −2.95041e13 7.22814e12i −1.71917 0.421175i
\(874\) −1.00873e11 + 1.74717e11i −0.00584755 + 0.0101283i
\(875\) −2.74605e12 1.55736e13i −0.158370 0.898159i
\(876\) −1.02639e11 2.40433e11i −0.00588901 0.0137951i
\(877\) −1.91357e13 + 6.96483e12i −1.09231 + 0.397569i −0.824477 0.565896i \(-0.808530\pi\)
−0.267835 + 0.963465i \(0.586308\pi\)
\(878\) 4.87509e12 1.77439e12i 0.276858 0.100768i
\(879\) 3.42276e13 + 4.13158e12i 1.93387 + 0.233435i
\(880\) 2.80513e12 + 1.59087e13i 0.157682 + 0.894258i
\(881\) −8.70739e12 + 1.50816e13i −0.486963 + 0.843445i −0.999888 0.0149885i \(-0.995229\pi\)
0.512924 + 0.858434i \(0.328562\pi\)
\(882\) −1.99532e12 2.72283e12i −0.111021 0.151500i
\(883\) 1.11410e13 + 1.92968e13i 0.616738 + 1.06822i 0.990077 + 0.140527i \(0.0448796\pi\)
−0.373339 + 0.927695i \(0.621787\pi\)
\(884\) 4.56421e10 3.82982e10i 0.00251380 0.00210933i
\(885\) −6.10126e12 + 1.42174e12i −0.334329 + 0.0779066i
\(886\) −1.15127e12 + 6.52918e12i −0.0627662 + 0.355965i
\(887\) −2.61023e12 2.19025e12i −0.141587 0.118806i 0.569243 0.822169i \(-0.307236\pi\)
−0.710830 + 0.703363i \(0.751681\pi\)
\(888\) −1.36517e13 + 8.90528e12i −0.736765 + 0.480606i
\(889\) −6.29880e12 2.29258e12i −0.338220 0.123102i
\(890\) 7.07868e12 0.378179
\(891\) −1.52580e13 + 1.98621e13i −0.811049 + 1.05579i
\(892\) −9.73404e11 −0.0514815
\(893\) −2.03693e11 7.41381e10i −0.0107187 0.00390130i
\(894\) 1.94976e12 1.27186e12i 0.102085 0.0665919i
\(895\) −1.60916e13 1.35025e13i −0.838293 0.703411i
\(896\) 3.40840e12 1.93300e13i 0.176671 1.00195i
\(897\) −2.70654e11 + 6.30689e10i −0.0139588 + 0.00325274i
\(898\) −5.45454e12 + 4.57690e12i −0.279907 + 0.234870i
\(899\) 9.70760e11 + 1.68141e12i 0.0495671 + 0.0858527i
\(900\) 1.18586e12 1.29546e11i 0.0602482 0.00658162i
\(901\) 1.99172e13 3.44977e13i 1.00686 1.74393i
\(902\) −2.04203e11 1.15809e12i −0.0102715 0.0582523i
\(903\) −2.30634e13 2.78395e12i −1.15432 0.139337i
\(904\) −6.20591e11 + 2.25877e11i −0.0309063 + 0.0112490i
\(905\) 1.09731e13 3.99388e12i 0.543764 0.197914i
\(906\) −1.71622e12 4.02028e12i −0.0846244 0.198234i
\(907\) −1.16315e12 6.59654e12i −0.0570692 0.323656i 0.942886 0.333115i \(-0.108100\pi\)
−0.999955 + 0.00945984i \(0.996989\pi\)
\(908\) 6.61172e11 1.14518e12i 0.0322796 0.0559099i
\(909\) −7.85882e11 2.69898e12i −0.0381786 0.131118i
\(910\) −1.27599e11 2.21009e11i −0.00616825 0.0106837i
\(911\) −5.69266e12 + 4.77671e12i −0.273831 + 0.229771i −0.769353 0.638824i \(-0.779421\pi\)
0.495522 + 0.868595i \(0.334977\pi\)
\(912\) −1.06727e11 + 3.51658e11i −0.00510853 + 0.0168323i
\(913\) 6.64490e12 3.76851e13i 0.316497 1.79495i
\(914\) 2.58310e13 + 2.16748e13i 1.22429 + 1.02730i
\(915\) 4.23241e12 + 2.14563e12i 0.199615 + 0.101195i
\(916\) −2.87266e12 1.04556e12i −0.134820 0.0490705i
\(917\) 7.89384e12 0.368660
\(918\) 2.71780e13 + 2.33342e13i 1.26306 + 1.08443i
\(919\) 3.16558e13 1.46397 0.731986 0.681320i \(-0.238594\pi\)
0.731986 + 0.681320i \(0.238594\pi\)
\(920\) −8.33670e12 3.03431e12i −0.383662 0.139642i
\(921\) −3.69759e11 6.78967e12i −0.0169336 0.310943i
\(922\) −1.79442e13 1.50570e13i −0.817779 0.686198i
\(923\) 1.14707e11 6.50537e11i 0.00520215 0.0295029i
\(924\) 1.82026e12 + 1.94400e12i 0.0821503 + 0.0877349i
\(925\) 9.66595e12 8.11069e12i 0.434117 0.364267i
\(926\) 6.09707e12 + 1.05604e13i 0.272503 + 0.471989i
\(927\) 1.01355e13 + 6.77629e12i 0.450801 + 0.301393i
\(928\) 4.20843e12 7.28921e12i 0.186275 0.322637i
\(929\) 1.85507e12 + 1.05206e13i 0.0817129 + 0.463417i 0.998018 + 0.0629351i \(0.0200461\pi\)
−0.916305 + 0.400482i \(0.868843\pi\)
\(930\) −4.74822e11 + 6.32799e11i −0.0208141 + 0.0277391i
\(931\) −6.22799e10 + 2.26680e10i −0.00271690 + 0.000988872i
\(932\) 5.26430e11 1.91605e11i 0.0228544 0.00831831i
\(933\) −2.10838e13 + 2.80986e13i −0.910924 + 1.21399i
\(934\) −5.68212e12 3.22249e13i −0.244314 1.38558i
\(935\) 1.54575e13 2.67731e13i 0.661434 1.14564i
\(936\) −4.12561e11 + 2.03313e11i −0.0175690 + 0.00865811i
\(937\) 8.82822e12 + 1.52909e13i 0.374149 + 0.648046i 0.990199 0.139661i \(-0.0446014\pi\)
−0.616050 + 0.787707i \(0.711268\pi\)
\(938\) 2.51243e13 2.10818e13i 1.05970 0.889190i
\(939\) 2.35797e13 + 2.51827e13i 0.989792 + 1.05708i
\(940\) −1.83185e11 + 1.03889e12i −0.00765269 + 0.0434005i
\(941\) 4.17615e12 + 3.50420e12i 0.173629 + 0.145692i 0.725461 0.688263i \(-0.241627\pi\)
−0.551832 + 0.833955i \(0.686071\pi\)
\(942\) −1.64664e12 3.02364e13i −0.0681350 1.25113i
\(943\) 6.67956e11 + 2.43116e11i 0.0275071 + 0.0100118i
\(944\) 1.45826e13 0.597670
\(945\) 1.07504e13 8.81526e12i 0.438511 0.359577i
\(946\) −4.41320e13 −1.79161
\(947\) 1.21514e13 + 4.42275e12i 0.490967 + 0.178697i 0.575627 0.817713i \(-0.304758\pi\)
−0.0846599 + 0.996410i \(0.526980\pi\)
\(948\) −1.70503e12 8.64366e11i −0.0685636 0.0347584i
\(949\) −5.97729e10 5.01554e10i −0.00239225 0.00200734i
\(950\) 4.48843e10 2.54551e11i 0.00178788 0.0101396i
\(951\) −5.09603e12 + 1.67911e13i −0.202032 + 0.665683i
\(952\) −2.63646e13 + 2.21225e13i −1.04029 + 0.872907i
\(953\) 7.52593e12 + 1.30353e13i 0.295558 + 0.511921i 0.975114 0.221702i \(-0.0711612\pi\)
−0.679557 + 0.733623i \(0.737828\pi\)
\(954\) 2.35395e13 2.45763e13i 0.920089 0.960613i
\(955\) −1.27167e13 + 2.20261e13i −0.494722 + 0.856883i
\(956\) 1.17872e11 + 6.68485e11i 0.00456404 + 0.0258840i
\(957\) −2.54472e13 5.96107e13i −0.980702 2.29731i
\(958\) 1.40625e13 5.11833e12i 0.539408 0.196328i
\(959\) 2.47850e13 9.02101e12i 0.946249 0.344406i
\(960\) −1.44147e13 1.73998e12i −0.547752 0.0661186i
\(961\) −4.57837e12 2.59653e13i −0.173163 0.982058i
\(962\) 2.69200e11 4.66268e11i 0.0101341 0.0175529i
\(963\) −1.09157e13 + 2.47896e13i −0.409011 + 0.928861i
\(964\) 1.85364e12 + 3.21060e12i 0.0691319 + 0.119740i
\(965\) −5.53309e12 + 4.64282e12i −0.205397 + 0.172349i
\(966\) −1.73020e13 + 4.03178e12i −0.639293 + 0.148970i
\(967\) −6.89028e12 + 3.90767e13i −0.253406 + 1.43714i 0.546724 + 0.837313i \(0.315875\pi\)
−0.800131 + 0.599826i \(0.795237\pi\)
\(968\) −1.52624e13 1.28067e13i −0.558708 0.468812i
\(969\) 5.89049e11 3.84248e11i 0.0214632 0.0140009i
\(970\) 3.01001e13 + 1.09555e13i 1.09168 + 0.397338i
\(971\) 1.66895e13 0.602499 0.301250 0.953545i \(-0.402596\pi\)
0.301250 + 0.953545i \(0.402596\pi\)
\(972\) 1.61364e12 + 2.25507e12i 0.0579839 + 0.0810331i
\(973\) −1.78727e13 −0.639268
\(974\) 3.02292e13 + 1.10025e13i 1.07625 + 0.391722i
\(975\) 2.98215e11 1.94531e11i 0.0105684 0.00689395i
\(976\) −8.46141e12 7.09997e12i −0.298482 0.250456i
\(977\) −4.63459e12 + 2.62841e13i −0.162737 + 0.922927i 0.788630 + 0.614868i \(0.210791\pi\)
−0.951367 + 0.308059i \(0.900321\pi\)
\(978\) 4.78770e13 1.11565e13i 1.67341 0.389944i
\(979\) −1.68901e13 + 1.41724e13i −0.587637 + 0.493086i
\(980\) 1.61273e11 + 2.79333e11i 0.00558527 + 0.00967397i
\(981\) −2.29050e13 + 5.20170e13i −0.789622 + 1.79323i
\(982\) −7.40330e12 + 1.28229e13i −0.254052 + 0.440032i
\(983\) −3.20706e12 1.81881e13i −0.109551 0.621294i −0.989305 0.145864i \(-0.953404\pi\)
0.879754 0.475430i \(-0.157707\pi\)
\(984\) 1.16795e12 + 1.40981e11i 0.0397141 + 0.00479384i
\(985\) −1.21386e13 + 4.41807e12i −0.410870 + 0.149544i
\(986\) −8.71076e13 + 3.17046e13i −2.93501 + 1.06826i
\(987\) −7.49425e12 1.75554e13i −0.251363 0.588822i
\(988\) −1.73540e8 9.84193e8i −5.79419e−6 3.28605e-5i
\(989\) 1.33381e13 2.31023e13i 0.443314 0.767842i
\(990\) 1.82687e13 1.90733e13i 0.604434 0.631055i
\(991\) −7.05130e12 1.22132e13i −0.232240 0.402252i 0.726227 0.687455i \(-0.241272\pi\)
−0.958467 + 0.285203i \(0.907939\pi\)
\(992\) 2.45133e11 2.05691e11i 0.00803710 0.00674393i
\(993\) 1.31847e13 4.34428e13i 0.430327 1.41790i
\(994\) 7.33284e12 4.15866e13i 0.238250 1.35119i
\(995\) 2.50683e13 + 2.10348e13i 0.810813 + 0.680353i
\(996\) −3.77876e12 1.91565e12i −0.121670 0.0616807i
\(997\) −1.36357e13 4.96298e12i −0.437067 0.159079i 0.114109 0.993468i \(-0.463599\pi\)
−0.551176 + 0.834389i \(0.685821\pi\)
\(998\) 8.62832e12 0.275321
\(999\) 2.74464e13 + 1.03429e13i 0.871847 + 0.328547i
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.4.7 156
3.2 odd 2 81.10.e.a.64.20 156
27.7 even 9 inner 27.10.e.a.7.7 yes 156
27.20 odd 18 81.10.e.a.19.20 156
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.10.e.a.4.7 156 1.1 even 1 trivial
27.10.e.a.7.7 yes 156 27.7 even 9 inner
81.10.e.a.19.20 156 27.20 odd 18
81.10.e.a.64.20 156 3.2 odd 2