Properties

Label 27.9.f.a.2.14
Level $27$
Weight $9$
Character 27.2
Analytic conductor $10.999$
Analytic rank $0$
Dimension $138$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [27,9,Mod(2,27)]
 
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([1]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("27.2");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 27 = 3^{3} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 27.f (of order \(18\), 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: \(10.9992224717\)
Analytic rank: \(0\)
Dimension: \(138\)
Relative dimension: \(23\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 2.14
Character \(\chi\) \(=\) 27.2
Dual form 27.9.f.a.14.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(7.08460 + 1.24921i) q^{2} +(14.6630 + 79.6618i) q^{3} +(-191.930 - 69.8569i) q^{4} +(349.559 + 416.588i) q^{5} +(4.36750 + 582.689i) q^{6} +(22.4234 - 8.16143i) q^{7} +(-2867.39 - 1655.49i) q^{8} +(-6130.99 + 2336.16i) q^{9} +(1956.08 + 3388.03i) q^{10} +(-15469.2 + 18435.5i) q^{11} +(2750.65 - 16313.8i) q^{12} +(-8798.06 - 49896.3i) q^{13} +(169.056 - 29.8091i) q^{14} +(-28060.6 + 33954.9i) q^{15} +(21808.2 + 18299.3i) q^{16} +(-37540.0 + 21673.7i) q^{17} +(-46354.0 + 8891.89i) q^{18} +(-75167.3 + 130194. i) q^{19} +(-37989.4 - 104375. i) q^{20} +(978.948 + 1666.61i) q^{21} +(-132623. + 111284. i) q^{22} +(-108972. + 299398. i) q^{23} +(89834.6 - 252696. i) q^{24} +(16477.1 - 93446.3i) q^{25} -364486. i q^{26} +(-276001. - 454151. i) q^{27} -4873.85 q^{28} +(945594. + 166734. i) q^{29} +(-241215. + 205504. i) q^{30} +(736394. + 268025. i) q^{31} +(676476. + 806193. i) q^{32} +(-1.69543e6 - 961988. i) q^{33} +(-293031. + 106655. i) q^{34} +(11238.2 + 6488.40i) q^{35} +(1.33992e6 - 20087.6i) q^{36} +(1.21793e6 + 2.10952e6i) q^{37} +(-695170. + 828471. i) q^{38} +(3.84582e6 - 1.43250e6i) q^{39} +(-312665. - 1.77321e6i) q^{40} +(2.52414e6 - 445074. i) q^{41} +(4853.51 + 13030.2i) q^{42} +(-2.24939e6 - 1.88746e6i) q^{43} +(4.25687e6 - 2.45770e6i) q^{44} +(-3.11636e6 - 1.73747e6i) q^{45} +(-1.14603e6 + 1.98499e6i) q^{46} +(-569539. - 1.56479e6i) q^{47} +(-1.13798e6 + 2.00561e6i) q^{48} +(-4.41566e6 + 3.70518e6i) q^{49} +(233468. - 641447. i) q^{50} +(-2.27702e6 - 2.67270e6i) q^{51} +(-1.79699e6 + 1.01912e7i) q^{52} +3.88995e6i q^{53} +(-1.38803e6 - 3.56226e6i) q^{54} -1.30874e7 q^{55} +(-77807.6 - 13719.6i) q^{56} +(-1.14736e7 - 4.07893e6i) q^{57} +(6.49088e6 + 2.36249e6i) q^{58} +(6.87370e6 + 8.19175e6i) q^{59} +(7.75765e6 - 4.55675e6i) q^{60} +(-1.49222e7 + 5.43124e6i) q^{61} +(4.88224e6 + 2.81876e6i) q^{62} +(-118411. + 102422. i) q^{63} +(141478. + 245047. i) q^{64} +(1.77108e7 - 2.11069e7i) q^{65} +(-1.08097e7 - 8.93325e6i) q^{66} +(1.45408e6 + 8.24651e6i) q^{67} +(8.71913e6 - 1.53742e6i) q^{68} +(-2.54484e7 - 4.29083e6i) q^{69} +(71513.1 + 60006.6i) q^{70} +(-9.42132e6 + 5.43940e6i) q^{71} +(2.14474e7 + 3.45110e6i) q^{72} +(1.18791e7 - 2.05752e7i) q^{73} +(5.99334e6 + 1.64666e7i) q^{74} +(7.68570e6 - 57607.5i) q^{75} +(2.35218e7 - 1.97371e7i) q^{76} +(-196412. + 539638. i) q^{77} +(2.90356e7 - 5.34446e6i) q^{78} +(-7.07994e6 + 4.01523e7i) q^{79} +1.54817e7i q^{80} +(3.21314e7 - 2.86460e7i) q^{81} +1.84385e7 q^{82} +(-5.20151e7 - 9.17167e6i) q^{83} +(-71465.3 - 388260. i) q^{84} +(-2.21515e7 - 8.06248e6i) q^{85} +(-1.35782e7 - 1.61819e7i) q^{86} +(582937. + 7.77725e7i) q^{87} +(7.48761e7 - 2.72527e7i) q^{88} +(3.60266e7 + 2.07999e7i) q^{89} +(-1.99077e7 - 1.62023e7i) q^{90} +(-604507. - 1.04704e6i) q^{91} +(4.18301e7 - 4.98511e7i) q^{92} +(-1.05536e7 + 6.25925e7i) q^{93} +(-2.08020e6 - 1.17974e7i) q^{94} +(-8.05126e7 + 1.41965e7i) q^{95} +(-5.43036e7 + 6.57105e7i) q^{96} +(-7.44489e7 - 6.24700e7i) q^{97} +(-3.59117e7 + 2.07336e7i) q^{98} +(5.17735e7 - 1.49167e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 138 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 447 q^{5} - 774 q^{6} - 6 q^{7} - 9 q^{8} - 12960 q^{9} - 3 q^{10} + 28668 q^{11} + 77421 q^{12} - 6 q^{13} - 120975 q^{14} + 105507 q^{15} - 774 q^{16} - 9 q^{17}+ \cdots + 228876057 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.08460 + 1.24921i 0.442788 + 0.0780754i 0.390597 0.920562i \(-0.372269\pi\)
0.0521906 + 0.998637i \(0.483380\pi\)
\(3\) 14.6630 + 79.6618i 0.181025 + 0.983479i
\(4\) −191.930 69.8569i −0.749727 0.272878i
\(5\) 349.559 + 416.588i 0.559294 + 0.666541i 0.969397 0.245498i \(-0.0789516\pi\)
−0.410103 + 0.912039i \(0.634507\pi\)
\(6\) 4.36750 + 582.689i 0.00336998 + 0.449606i
\(7\) 22.4234 8.16143i 0.00933917 0.00339918i −0.337346 0.941381i \(-0.609529\pi\)
0.346686 + 0.937981i \(0.387307\pi\)
\(8\) −2867.39 1655.49i −0.700046 0.404172i
\(9\) −6130.99 + 2336.16i −0.934460 + 0.356068i
\(10\) 1956.08 + 3388.03i 0.195608 + 0.338803i
\(11\) −15469.2 + 18435.5i −1.05657 + 1.25917i −0.0918844 + 0.995770i \(0.529289\pi\)
−0.964686 + 0.263402i \(0.915155\pi\)
\(12\) 2750.65 16313.8i 0.132651 0.786739i
\(13\) −8798.06 49896.3i −0.308045 1.74701i −0.608815 0.793312i \(-0.708355\pi\)
0.300771 0.953696i \(-0.402756\pi\)
\(14\) 169.056 29.8091i 0.00440066 0.000775956i
\(15\) −28060.6 + 33954.9i −0.554283 + 0.670714i
\(16\) 21808.2 + 18299.3i 0.332767 + 0.279225i
\(17\) −37540.0 + 21673.7i −0.449468 + 0.259501i −0.707606 0.706608i \(-0.750225\pi\)
0.258137 + 0.966108i \(0.416891\pi\)
\(18\) −46354.0 + 8891.89i −0.441568 + 0.0847040i
\(19\) −75167.3 + 130194.i −0.576786 + 0.999023i 0.419059 + 0.907959i \(0.362360\pi\)
−0.995845 + 0.0910639i \(0.970973\pi\)
\(20\) −37989.4 104375.i −0.237434 0.652343i
\(21\) 978.948 + 1666.61i 0.00503364 + 0.00856954i
\(22\) −132623. + 111284.i −0.566147 + 0.475054i
\(23\) −108972. + 299398.i −0.389407 + 1.06989i 0.577862 + 0.816134i \(0.303887\pi\)
−0.967269 + 0.253753i \(0.918335\pi\)
\(24\) 89834.6 252696.i 0.270769 0.761645i
\(25\) 16477.1 93446.3i 0.0421814 0.239223i
\(26\) 364486.i 0.797605i
\(27\) −276001. 454151.i −0.519345 0.854565i
\(28\) −4873.85 −0.00792940
\(29\) 945594. + 166734.i 1.33694 + 0.235739i 0.795988 0.605312i \(-0.206952\pi\)
0.540955 + 0.841052i \(0.318063\pi\)
\(30\) −241215. + 205504.i −0.297796 + 0.253708i
\(31\) 736394. + 268025.i 0.797376 + 0.290221i 0.708399 0.705813i \(-0.249418\pi\)
0.0889773 + 0.996034i \(0.471640\pi\)
\(32\) 676476. + 806193.i 0.645138 + 0.768845i
\(33\) −1.69543e6 961988.i −1.42963 0.811173i
\(34\) −293031. + 106655.i −0.219280 + 0.0798113i
\(35\) 11238.2 + 6488.40i 0.00748904 + 0.00432380i
\(36\) 1.33992e6 20087.6i 0.797754 0.0119597i
\(37\) 1.21793e6 + 2.10952e6i 0.649855 + 1.12558i 0.983157 + 0.182761i \(0.0585035\pi\)
−0.333303 + 0.942820i \(0.608163\pi\)
\(38\) −695170. + 828471.i −0.333393 + 0.397322i
\(39\) 3.84582e6 1.43250e6i 1.66238 0.619207i
\(40\) −312665. 1.77321e6i −0.122135 0.692660i
\(41\) 2.52414e6 445074.i 0.893261 0.157506i 0.291867 0.956459i \(-0.405723\pi\)
0.601394 + 0.798953i \(0.294612\pi\)
\(42\) 4853.51 + 13030.2i 0.00155976 + 0.00418749i
\(43\) −2.24939e6 1.88746e6i −0.657948 0.552084i 0.251523 0.967851i \(-0.419068\pi\)
−0.909471 + 0.415768i \(0.863513\pi\)
\(44\) 4.25687e6 2.45770e6i 1.13574 0.655720i
\(45\) −3.11636e6 1.73747e6i −0.759972 0.423709i
\(46\) −1.14603e6 + 1.98499e6i −0.255957 + 0.443330i
\(47\) −569539. 1.56479e6i −0.116716 0.320676i 0.867554 0.497342i \(-0.165691\pi\)
−0.984271 + 0.176667i \(0.943468\pi\)
\(48\) −1.13798e6 + 2.00561e6i −0.214373 + 0.377816i
\(49\) −4.41566e6 + 3.70518e6i −0.765969 + 0.642724i
\(50\) 233468. 641447.i 0.0373548 0.102631i
\(51\) −2.27702e6 2.67270e6i −0.336578 0.395066i
\(52\) −1.79699e6 + 1.01912e7i −0.245771 + 1.39384i
\(53\) 3.88995e6i 0.492993i 0.969144 + 0.246496i \(0.0792793\pi\)
−0.969144 + 0.246496i \(0.920721\pi\)
\(54\) −1.38803e6 3.56226e6i −0.163239 0.418939i
\(55\) −1.30874e7 −1.43022
\(56\) −77807.6 13719.6i −0.00791170 0.00139505i
\(57\) −1.14736e7 4.07893e6i −1.08693 0.386409i
\(58\) 6.49088e6 + 2.36249e6i 0.573577 + 0.208765i
\(59\) 6.87370e6 + 8.19175e6i 0.567260 + 0.676034i 0.971066 0.238810i \(-0.0767574\pi\)
−0.403806 + 0.914845i \(0.632313\pi\)
\(60\) 7.75765e6 4.55675e6i 0.598584 0.351601i
\(61\) −1.49222e7 + 5.43124e6i −1.07774 + 0.392265i −0.819065 0.573700i \(-0.805508\pi\)
−0.258673 + 0.965965i \(0.583285\pi\)
\(62\) 4.88224e6 + 2.81876e6i 0.330409 + 0.190762i
\(63\) −118411. + 102422.i −0.00751675 + 0.00650178i
\(64\) 141478. + 245047.i 0.00843275 + 0.0146060i
\(65\) 1.77108e7 2.11069e7i 0.992165 1.18242i
\(66\) −1.08097e7 8.93325e6i −0.569692 0.470797i
\(67\) 1.45408e6 + 8.24651e6i 0.0721588 + 0.409233i 0.999396 + 0.0347579i \(0.0110660\pi\)
−0.927237 + 0.374475i \(0.877823\pi\)
\(68\) 8.71913e6 1.53742e6i 0.407791 0.0719045i
\(69\) −2.54484e7 4.29083e6i −1.12270 0.189298i
\(70\) 71513.1 + 60006.6i 0.00297847 + 0.00249924i
\(71\) −9.42132e6 + 5.43940e6i −0.370747 + 0.214051i −0.673785 0.738927i \(-0.735333\pi\)
0.303037 + 0.952979i \(0.401999\pi\)
\(72\) 2.14474e7 + 3.45110e6i 0.798078 + 0.128419i
\(73\) 1.18791e7 2.05752e7i 0.418305 0.724525i −0.577464 0.816416i \(-0.695958\pi\)
0.995769 + 0.0918908i \(0.0292911\pi\)
\(74\) 5.99334e6 + 1.64666e7i 0.199867 + 0.549131i
\(75\) 7.68570e6 57607.5i 0.242906 0.00182068i
\(76\) 2.35218e7 1.97371e7i 0.705044 0.591602i
\(77\) −196412. + 539638.i −0.00558734 + 0.0153511i
\(78\) 2.90356e7 5.34446e6i 0.784427 0.144386i
\(79\) −7.07994e6 + 4.01523e7i −0.181770 + 1.03087i 0.748266 + 0.663398i \(0.230886\pi\)
−0.930036 + 0.367468i \(0.880225\pi\)
\(80\) 1.54817e7i 0.377972i
\(81\) 3.21314e7 2.86460e7i 0.746432 0.665462i
\(82\) 1.84385e7 0.407822
\(83\) −5.20151e7 9.17167e6i −1.09602 0.193257i −0.403729 0.914879i \(-0.632286\pi\)
−0.692288 + 0.721621i \(0.743397\pi\)
\(84\) −71465.3 388260.i −0.00143542 0.00779839i
\(85\) −2.21515e7 8.06248e6i −0.424353 0.154452i
\(86\) −1.35782e7 1.61819e7i −0.248227 0.295825i
\(87\) 582937. + 7.77725e7i 0.0101752 + 1.35753i
\(88\) 7.48761e7 2.72527e7i 1.24857 0.454442i
\(89\) 3.60266e7 + 2.07999e7i 0.574199 + 0.331514i 0.758825 0.651295i \(-0.225774\pi\)
−0.184625 + 0.982809i \(0.559107\pi\)
\(90\) −1.99077e7 1.62023e7i −0.303425 0.246948i
\(91\) −604507. 1.04704e6i −0.00881528 0.0152685i
\(92\) 4.18301e7 4.98511e7i 0.583898 0.695863i
\(93\) −1.05536e7 + 6.25925e7i −0.141082 + 0.836739i
\(94\) −2.08020e6 1.17974e7i −0.0266437 0.151104i
\(95\) −8.05126e7 + 1.41965e7i −0.988483 + 0.174296i
\(96\) −5.43036e7 + 6.57105e7i −0.639357 + 0.773659i
\(97\) −7.44489e7 6.24700e7i −0.840952 0.705642i 0.116826 0.993152i \(-0.462728\pi\)
−0.957778 + 0.287510i \(0.907172\pi\)
\(98\) −3.59117e7 + 2.07336e7i −0.389343 + 0.224787i
\(99\) 5.17735e7 1.49167e8i 0.538973 1.55286i
\(100\) −9.69032e6 + 1.67841e7i −0.0969032 + 0.167841i
\(101\) −2.31756e7 6.36744e7i −0.222713 0.611898i 0.777135 0.629334i \(-0.216672\pi\)
−0.999848 + 0.0174353i \(0.994450\pi\)
\(102\) −1.27930e7 2.17795e7i −0.118188 0.201209i
\(103\) 8.20157e7 6.88194e7i 0.728699 0.611451i −0.201077 0.979575i \(-0.564444\pi\)
0.929777 + 0.368124i \(0.120000\pi\)
\(104\) −5.73752e7 + 1.57637e8i −0.490446 + 1.34749i
\(105\) −352091. + 990397.i −0.00289666 + 0.00814802i
\(106\) −4.85935e6 + 2.75588e7i −0.0384906 + 0.218291i
\(107\) 6.59985e7i 0.503499i −0.967792 0.251750i \(-0.918994\pi\)
0.967792 0.251750i \(-0.0810060\pi\)
\(108\) 2.12475e7 + 1.06446e8i 0.156175 + 0.782409i
\(109\) 1.44628e8 1.02458 0.512290 0.858813i \(-0.328797\pi\)
0.512290 + 0.858813i \(0.328797\pi\)
\(110\) −9.27193e7 1.63489e7i −0.633285 0.111665i
\(111\) −1.50190e8 + 1.27954e8i −0.989345 + 0.842876i
\(112\) 638362. + 232345.i 0.00405691 + 0.00147659i
\(113\) 4.25133e7 + 5.06654e7i 0.260742 + 0.310740i 0.880494 0.474058i \(-0.157211\pi\)
−0.619752 + 0.784798i \(0.712767\pi\)
\(114\) −7.61907e7 4.32306e7i −0.451110 0.255960i
\(115\) −1.62818e8 + 5.92609e7i −0.930917 + 0.338826i
\(116\) −1.69841e8 9.80575e7i −0.938015 0.541563i
\(117\) 1.70507e8 + 2.85360e8i 0.909909 + 1.52282i
\(118\) 3.84642e7 + 6.66220e7i 0.198394 + 0.343629i
\(119\) −664884. + 792378.i −0.00331557 + 0.00395134i
\(120\) 1.36672e8 5.09080e7i 0.659107 0.245505i
\(121\) −6.33482e7 3.59265e8i −0.295524 1.67600i
\(122\) −1.12503e8 + 1.98372e7i −0.507836 + 0.0895451i
\(123\) 7.24669e7 + 1.94551e8i 0.316606 + 0.849991i
\(124\) −1.22613e8 1.02884e8i −0.518620 0.435173i
\(125\) 2.28657e8 1.32015e8i 0.936579 0.540734i
\(126\) −966842. + 577701.i −0.00383595 + 0.00229203i
\(127\) −8.82421e7 + 1.52840e8i −0.339204 + 0.587519i −0.984283 0.176597i \(-0.943491\pi\)
0.645079 + 0.764116i \(0.276824\pi\)
\(128\) −9.14498e7 2.51256e8i −0.340677 0.936003i
\(129\) 1.17376e8 2.06866e8i 0.423858 0.747018i
\(130\) 1.51841e8 1.27409e8i 0.531636 0.446096i
\(131\) −1.40625e7 + 3.86363e7i −0.0477503 + 0.131193i −0.961275 0.275589i \(-0.911127\pi\)
0.913525 + 0.406782i \(0.133349\pi\)
\(132\) 2.58203e8 + 3.03072e8i 0.850484 + 0.998275i
\(133\) −622937. + 3.53285e6i −0.00199085 + 0.0112906i
\(134\) 6.02397e7i 0.186837i
\(135\) 9.27150e7 2.73731e8i 0.279135 0.824118i
\(136\) 1.43522e8 0.419531
\(137\) −3.79891e8 6.69850e7i −1.07839 0.190150i −0.393888 0.919159i \(-0.628870\pi\)
−0.684504 + 0.729009i \(0.739981\pi\)
\(138\) −1.74932e8 6.21892e7i −0.482340 0.171474i
\(139\) 4.70756e8 + 1.71341e8i 1.26106 + 0.458989i 0.884126 0.467249i \(-0.154755\pi\)
0.376938 + 0.926239i \(0.376977\pi\)
\(140\) −1.70370e6 2.03039e6i −0.00443487 0.00528527i
\(141\) 1.16303e8 6.83150e7i 0.294249 0.172838i
\(142\) −7.35412e7 + 2.67668e7i −0.180875 + 0.0658330i
\(143\) 1.05596e9 + 6.09661e8i 2.52525 + 1.45796i
\(144\) −1.76456e8 6.12453e7i −0.410381 0.142437i
\(145\) 2.61082e8 + 4.52207e8i 0.590615 + 1.02297i
\(146\) 1.09862e8 1.30928e8i 0.241788 0.288152i
\(147\) −3.59908e8 2.97430e8i −0.770765 0.636965i
\(148\) −8.63934e7 4.89962e8i −0.180067 1.02121i
\(149\) −1.35585e8 + 2.39072e7i −0.275084 + 0.0485048i −0.309488 0.950903i \(-0.600158\pi\)
0.0344041 + 0.999408i \(0.489047\pi\)
\(150\) 5.45221e7 + 9.19290e6i 0.107698 + 0.0181588i
\(151\) −2.29217e8 1.92336e8i −0.440900 0.369959i 0.395146 0.918618i \(-0.370694\pi\)
−0.836046 + 0.548659i \(0.815138\pi\)
\(152\) 4.31068e8 2.48877e8i 0.807554 0.466241i
\(153\) 1.79524e8 2.20581e8i 0.327610 0.402534i
\(154\) −2.06562e6 + 3.57776e6i −0.00367255 + 0.00636104i
\(155\) 1.45757e8 + 4.00463e8i 0.252524 + 0.693803i
\(156\) −8.38199e8 + 6.28265e6i −1.41530 + 0.0106083i
\(157\) −6.09281e8 + 5.11248e8i −1.00281 + 0.841459i −0.987372 0.158422i \(-0.949359\pi\)
−0.0154401 + 0.999881i \(0.504915\pi\)
\(158\) −1.00317e8 + 2.75619e8i −0.160971 + 0.442263i
\(159\) −3.09880e8 + 5.70383e7i −0.484848 + 0.0892438i
\(160\) −9.93821e7 + 5.63624e8i −0.151645 + 0.860022i
\(161\) 7.60288e6i 0.0113155i
\(162\) 2.63423e8 1.62807e8i 0.382467 0.236381i
\(163\) 5.37083e8 0.760836 0.380418 0.924815i \(-0.375780\pi\)
0.380418 + 0.924815i \(0.375780\pi\)
\(164\) −5.15551e8 9.09055e7i −0.712682 0.125665i
\(165\) −1.91901e8 1.04257e9i −0.258906 1.40659i
\(166\) −3.57049e8 1.29955e8i −0.470214 0.171144i
\(167\) 1.24169e8 + 1.47979e8i 0.159642 + 0.190254i 0.839936 0.542685i \(-0.182592\pi\)
−0.680294 + 0.732939i \(0.738148\pi\)
\(168\) −47966.6 6.39946e6i −6.02146e−5 0.00803353i
\(169\) −1.64570e9 + 5.98985e8i −2.01745 + 0.734293i
\(170\) −1.46863e8 8.47913e7i −0.175839 0.101521i
\(171\) 1.56697e8 9.73819e8i 0.183264 1.13892i
\(172\) 2.99874e8 + 5.19397e8i 0.342630 + 0.593452i
\(173\) 8.68042e8 1.03449e9i 0.969072 1.15490i −0.0188306 0.999823i \(-0.505994\pi\)
0.987903 0.155073i \(-0.0495612\pi\)
\(174\) −9.30241e7 + 5.51716e8i −0.101484 + 0.601892i
\(175\) −393184. 2.22986e6i −0.000419221 0.00237752i
\(176\) −6.74714e8 + 1.18970e8i −0.703184 + 0.123990i
\(177\) −5.51781e8 + 6.67686e8i −0.562177 + 0.680267i
\(178\) 2.29250e8 + 1.92364e8i 0.228365 + 0.191621i
\(179\) 2.84475e8 1.64242e8i 0.277097 0.159982i −0.355011 0.934862i \(-0.615523\pi\)
0.632109 + 0.774880i \(0.282190\pi\)
\(180\) 4.76749e8 + 5.51173e8i 0.454151 + 0.525047i
\(181\) −4.80709e8 + 8.32613e8i −0.447887 + 0.775762i −0.998248 0.0591641i \(-0.981156\pi\)
0.550362 + 0.834926i \(0.314490\pi\)
\(182\) −2.97473e6 8.17300e6i −0.00271120 0.00744897i
\(183\) −6.51466e8 1.10909e9i −0.580881 0.988923i
\(184\) 8.08115e8 6.78089e8i 0.705021 0.591583i
\(185\) −4.53062e8 + 1.24478e9i −0.386786 + 1.06269i
\(186\) −1.52959e8 + 4.30259e8i −0.127798 + 0.359483i
\(187\) 1.81149e8 1.02735e9i 0.148139 0.840138i
\(188\) 3.40117e8i 0.272269i
\(189\) −9.89540e6 7.93101e6i −0.00775507 0.00621558i
\(190\) −5.88134e8 −0.451296
\(191\) 1.19301e9 + 2.10360e8i 0.896419 + 0.158063i 0.602831 0.797869i \(-0.294039\pi\)
0.293588 + 0.955932i \(0.405150\pi\)
\(192\) −1.74464e7 + 1.48635e7i −0.0128381 + 0.0109375i
\(193\) −1.71398e9 6.23836e8i −1.23531 0.449615i −0.359896 0.932992i \(-0.617188\pi\)
−0.875412 + 0.483377i \(0.839410\pi\)
\(194\) −4.49403e8 5.35577e8i −0.317270 0.378107i
\(195\) 1.94110e9 + 1.10138e9i 1.34249 + 0.761727i
\(196\) 1.10633e9 4.02671e8i 0.749653 0.272851i
\(197\) 1.52700e9 + 8.81617e8i 1.01385 + 0.585349i 0.912318 0.409483i \(-0.134291\pi\)
0.101536 + 0.994832i \(0.467624\pi\)
\(198\) 5.53135e8 9.92112e8i 0.359890 0.645505i
\(199\) 7.74048e8 + 1.34069e9i 0.493578 + 0.854902i 0.999973 0.00739959i \(-0.00235539\pi\)
−0.506395 + 0.862302i \(0.669022\pi\)
\(200\) −2.01945e8 + 2.40669e8i −0.126216 + 0.150418i
\(201\) −6.35610e8 + 2.36753e8i −0.389409 + 0.145048i
\(202\) −8.46474e7 4.80059e8i −0.0508403 0.288330i
\(203\) 2.25642e7 3.97867e6i 0.0132873 0.00234290i
\(204\) 2.50322e8 + 6.72038e8i 0.144537 + 0.388037i
\(205\) 1.06775e9 + 8.95948e8i 0.604580 + 0.507303i
\(206\) 6.67019e8 3.85103e8i 0.370398 0.213850i
\(207\) −3.13354e7 2.09018e9i −0.0170668 1.13842i
\(208\) 7.21197e8 1.24915e9i 0.385301 0.667361i
\(209\) −1.23741e9 3.39975e9i −0.648526 1.78181i
\(210\) −3.73164e6 + 6.57674e6i −0.00191877 + 0.00338169i
\(211\) 2.15590e8 1.80902e8i 0.108768 0.0912668i −0.586782 0.809745i \(-0.699605\pi\)
0.695549 + 0.718478i \(0.255161\pi\)
\(212\) 2.71740e8 7.46599e8i 0.134527 0.369610i
\(213\) −5.71457e8 6.70761e8i −0.277629 0.325874i
\(214\) 8.24458e7 4.67573e8i 0.0393109 0.222943i
\(215\) 1.59685e9i 0.747326i
\(216\) 3.95625e7 + 1.75914e9i 0.0181747 + 0.808139i
\(217\) 1.86999e7 0.00843335
\(218\) 1.02463e9 + 1.80670e8i 0.453671 + 0.0799945i
\(219\) 1.81324e9 + 6.44617e8i 0.788278 + 0.280237i
\(220\) 2.51187e9 + 9.14248e8i 1.07228 + 0.390277i
\(221\) 1.41172e9 + 1.68242e9i 0.591806 + 0.705287i
\(222\) −1.22388e9 + 7.18889e8i −0.503878 + 0.295972i
\(223\) −3.57572e9 + 1.30146e9i −1.44592 + 0.526272i −0.941449 0.337156i \(-0.890535\pi\)
−0.504472 + 0.863428i \(0.668313\pi\)
\(224\) 2.17486e7 + 1.25565e7i 0.00863850 + 0.00498744i
\(225\) 1.17285e8 + 6.11412e8i 0.0457626 + 0.238563i
\(226\) 2.37898e8 + 4.12052e8i 0.0911922 + 0.157950i
\(227\) −2.91521e9 + 3.47421e9i −1.09791 + 1.30844i −0.150431 + 0.988621i \(0.548066\pi\)
−0.947479 + 0.319818i \(0.896378\pi\)
\(228\) 1.91720e9 + 1.58438e9i 0.709459 + 0.586301i
\(229\) −4.94015e8 2.80170e9i −0.179638 1.01878i −0.932653 0.360775i \(-0.882512\pi\)
0.753015 0.658004i \(-0.228599\pi\)
\(230\) −1.22753e9 + 2.16447e8i −0.438652 + 0.0773463i
\(231\) −4.58685e7 7.73383e6i −0.0161089 0.00271610i
\(232\) −2.43536e9 2.04351e9i −0.840643 0.705383i
\(233\) −3.07386e9 + 1.77469e9i −1.04294 + 0.602143i −0.920665 0.390353i \(-0.872353\pi\)
−0.122277 + 0.992496i \(0.539020\pi\)
\(234\) 8.51498e8 + 2.23466e9i 0.284001 + 0.745330i
\(235\) 4.52787e8 7.84251e8i 0.148465 0.257148i
\(236\) −7.47020e8 2.05242e9i −0.240815 0.661635i
\(237\) −3.30242e9 + 2.47530e7i −1.04674 + 0.00784575i
\(238\) −5.70029e6 + 4.78311e6i −0.00177660 + 0.00149074i
\(239\) −2.51801e8 + 6.91818e8i −0.0771731 + 0.212031i −0.972280 0.233821i \(-0.924877\pi\)
0.895107 + 0.445852i \(0.147099\pi\)
\(240\) −1.23330e9 + 2.27009e8i −0.371727 + 0.0684223i
\(241\) −2.07614e8 + 1.17744e9i −0.0615445 + 0.349036i 0.938449 + 0.345418i \(0.112263\pi\)
−0.999993 + 0.00361833i \(0.998848\pi\)
\(242\) 2.62439e9i 0.765185i
\(243\) 2.75313e9 + 2.13961e9i 0.789590 + 0.613634i
\(244\) 3.24343e9 0.915051
\(245\) −3.08707e9 5.44333e8i −0.856804 0.151078i
\(246\) 2.70364e8 + 1.46885e9i 0.0738259 + 0.401085i
\(247\) 7.15751e9 + 2.60512e9i 1.92298 + 0.699906i
\(248\) −1.66781e9 1.98762e9i −0.440901 0.525445i
\(249\) −3.20661e7 4.27810e9i −0.00834160 1.11289i
\(250\) 1.78486e9 6.49635e8i 0.456924 0.166307i
\(251\) −1.64288e9 9.48514e8i −0.413914 0.238973i 0.278556 0.960420i \(-0.410144\pi\)
−0.692470 + 0.721447i \(0.743477\pi\)
\(252\) 2.98815e7 1.13861e7i 0.00740971 0.00282340i
\(253\) −3.83385e9 6.64042e9i −0.935735 1.62074i
\(254\) −8.16089e8 + 9.72577e8i −0.196066 + 0.233663i
\(255\) 3.17464e8 1.88285e9i 0.0750817 0.445301i
\(256\) −3.46593e8 1.96563e9i −0.0806975 0.457658i
\(257\) 1.74694e9 3.08032e8i 0.400447 0.0706095i 0.0302019 0.999544i \(-0.490385\pi\)
0.370245 + 0.928934i \(0.379274\pi\)
\(258\) 1.08998e9 1.31894e9i 0.246003 0.297678i
\(259\) 4.45268e7 + 3.73624e7i 0.00989516 + 0.00830302i
\(260\) −4.87369e9 + 2.81383e9i −1.06651 + 0.615749i
\(261\) −6.18695e9 + 1.18682e9i −1.33326 + 0.255753i
\(262\) −1.47892e8 + 2.56156e8i −0.0313862 + 0.0543624i
\(263\) 9.56007e8 + 2.62661e9i 0.199819 + 0.549000i 0.998616 0.0526024i \(-0.0167516\pi\)
−0.798796 + 0.601602i \(0.794529\pi\)
\(264\) 3.26891e9 + 5.56516e9i 0.672956 + 1.14568i
\(265\) −1.62051e9 + 1.35977e9i −0.328600 + 0.275728i
\(266\) −8.82653e6 + 2.42507e7i −0.00176304 + 0.00484392i
\(267\) −1.12870e9 + 3.17493e9i −0.222093 + 0.624725i
\(268\) 2.96993e8 1.68433e9i 0.0575714 0.326504i
\(269\) 3.73774e9i 0.713839i 0.934135 + 0.356919i \(0.116173\pi\)
−0.934135 + 0.356919i \(0.883827\pi\)
\(270\) 9.98796e8 1.82346e9i 0.187941 0.343116i
\(271\) −4.23327e9 −0.784873 −0.392436 0.919779i \(-0.628368\pi\)
−0.392436 + 0.919779i \(0.628368\pi\)
\(272\) −1.21530e9 2.14290e8i −0.222027 0.0391494i
\(273\) 7.45450e7 6.35088e7i 0.0134205 0.0114336i
\(274\) −2.60770e9 9.49124e8i −0.462653 0.168392i
\(275\) 1.46784e9 + 1.74931e9i 0.256655 + 0.305869i
\(276\) 4.58458e9 + 2.60129e9i 0.790066 + 0.448283i
\(277\) 9.61877e9 3.50095e9i 1.63381 0.594657i 0.647866 0.761754i \(-0.275662\pi\)
0.985940 + 0.167097i \(0.0534394\pi\)
\(278\) 3.12108e9 + 1.80196e9i 0.522548 + 0.301693i
\(279\) −5.14097e9 + 7.70718e7i −0.848455 + 0.0127198i
\(280\) −2.14829e7 3.72095e7i −0.00349512 0.00605372i
\(281\) 3.70155e9 4.41134e9i 0.593688 0.707530i −0.382622 0.923905i \(-0.624979\pi\)
0.976310 + 0.216375i \(0.0694233\pi\)
\(282\) 9.09301e8 3.38698e8i 0.143784 0.0535570i
\(283\) 5.45231e8 + 3.09216e9i 0.0850031 + 0.482077i 0.997356 + 0.0726717i \(0.0231525\pi\)
−0.912353 + 0.409405i \(0.865736\pi\)
\(284\) 2.18821e9 3.85841e8i 0.336369 0.0593110i
\(285\) −2.31148e9 6.20561e9i −0.350356 0.940600i
\(286\) 6.71950e9 + 5.63833e9i 1.00432 + 0.842726i
\(287\) 5.29673e7 3.05807e7i 0.00780693 0.00450733i
\(288\) −6.03087e9 3.36241e9i −0.876617 0.488743i
\(289\) −2.54838e9 + 4.41392e9i −0.365319 + 0.632751i
\(290\) 1.28476e9 + 3.52985e9i 0.181648 + 0.499073i
\(291\) 3.88483e9 6.84672e9i 0.541751 0.954797i
\(292\) −3.71728e9 + 3.11917e9i −0.511322 + 0.429050i
\(293\) 2.74172e9 7.53280e9i 0.372008 1.02208i −0.602576 0.798061i \(-0.705859\pi\)
0.974584 0.224022i \(-0.0719186\pi\)
\(294\) −2.17825e9 2.55677e9i −0.291554 0.342218i
\(295\) −1.00982e9 + 5.72700e9i −0.133339 + 0.756204i
\(296\) 8.06509e9i 1.05061i
\(297\) 1.26420e10 + 1.93714e9i 1.62477 + 0.248963i
\(298\) −9.90429e8 −0.125591
\(299\) 1.58976e10 + 2.80318e9i 1.98906 + 0.350724i
\(300\) −1.47914e9 5.25842e8i −0.182610 0.0649188i
\(301\) −6.58433e7 2.39650e7i −0.00802132 0.00291952i
\(302\) −1.38365e9 1.64897e9i −0.166340 0.198237i
\(303\) 4.73259e9 2.77987e9i 0.561473 0.329802i
\(304\) −4.02172e9 + 1.46379e9i −0.470888 + 0.171389i
\(305\) −7.47878e9 4.31787e9i −0.864234 0.498966i
\(306\) 1.54741e9 1.33847e9i 0.176490 0.152659i
\(307\) −2.44162e9 4.22901e9i −0.274868 0.476086i 0.695234 0.718784i \(-0.255301\pi\)
−0.970102 + 0.242698i \(0.921968\pi\)
\(308\) 7.53948e7 8.98520e7i 0.00837797 0.00998447i
\(309\) 6.68487e9 + 5.52442e9i 0.733262 + 0.605972i
\(310\) 5.32367e8 + 3.01921e9i 0.0576454 + 0.326923i
\(311\) 1.23151e10 2.17148e9i 1.31643 0.232121i 0.529048 0.848592i \(-0.322549\pi\)
0.787378 + 0.616471i \(0.211438\pi\)
\(312\) −1.33989e10 2.25918e9i −1.41401 0.238414i
\(313\) −7.17480e9 6.02037e9i −0.747536 0.627258i 0.187314 0.982300i \(-0.440022\pi\)
−0.934850 + 0.355043i \(0.884466\pi\)
\(314\) −4.95517e9 + 2.86087e9i −0.509730 + 0.294293i
\(315\) −8.40595e7 1.35260e7i −0.00853777 0.00137381i
\(316\) 4.16377e9 7.21186e9i 0.417579 0.723268i
\(317\) 3.76140e9 + 1.03344e10i 0.372488 + 1.02340i 0.974396 + 0.224838i \(0.0721852\pi\)
−0.601908 + 0.798565i \(0.705593\pi\)
\(318\) −2.26663e9 + 1.69893e7i −0.221652 + 0.00166138i
\(319\) −1.77015e10 + 1.48533e10i −1.70941 + 1.43437i
\(320\) −5.26288e7 + 1.44597e8i −0.00501908 + 0.0137898i
\(321\) 5.25756e9 9.67736e8i 0.495181 0.0911458i
\(322\) −9.49757e6 + 5.38634e7i −0.000883464 + 0.00501038i
\(323\) 6.51663e9i 0.598705i
\(324\) −8.16811e9 + 3.25342e9i −0.741210 + 0.295230i
\(325\) −4.80759e9 −0.430917
\(326\) 3.80502e9 + 6.70928e8i 0.336889 + 0.0594026i
\(327\) 2.12068e9 + 1.15213e10i 0.185474 + 1.00765i
\(328\) −7.97451e9 2.90248e9i −0.688983 0.250769i
\(329\) −2.55419e7 3.04397e7i −0.00218007 0.00259810i
\(330\) −5.71594e7 7.62591e9i −0.00481983 0.643037i
\(331\) 1.70860e10 6.21880e9i 1.42341 0.518077i 0.488371 0.872636i \(-0.337591\pi\)
0.935034 + 0.354559i \(0.115369\pi\)
\(332\) 9.34257e9 + 5.39393e9i 0.768978 + 0.443970i
\(333\) −1.23953e10 1.00882e10i −1.00805 0.820418i
\(334\) 6.94831e8 + 1.20348e9i 0.0558333 + 0.0967061i
\(335\) −2.92711e9 + 3.48839e9i −0.232413 + 0.276979i
\(336\) −9.14870e6 + 5.42599e7i −0.000717798 + 0.00425718i
\(337\) 3.85980e9 + 2.18900e10i 0.299257 + 1.69717i 0.649376 + 0.760468i \(0.275030\pi\)
−0.350118 + 0.936705i \(0.613859\pi\)
\(338\) −1.24074e10 + 2.18776e9i −0.950634 + 0.167622i
\(339\) −3.41272e9 + 4.12959e9i −0.258406 + 0.312686i
\(340\) 3.68832e9 + 3.09487e9i 0.276002 + 0.231593i
\(341\) −1.63326e10 + 9.42966e9i −1.20792 + 0.697394i
\(342\) 2.32664e9 6.70338e9i 0.170069 0.489992i
\(343\) −1.37555e8 + 2.38253e8i −0.00993805 + 0.0172132i
\(344\) 3.32521e9 + 9.13593e9i 0.237457 + 0.652408i
\(345\) −7.10822e9 1.21014e10i −0.501747 0.854201i
\(346\) 7.44203e9 6.24460e9i 0.519262 0.435713i
\(347\) 5.16122e9 1.41803e10i 0.355987 0.978067i −0.624421 0.781088i \(-0.714665\pi\)
0.980408 0.196979i \(-0.0631129\pi\)
\(348\) 5.32106e9 1.49676e10i 0.362812 1.02055i
\(349\) 9.91134e8 5.62100e9i 0.0668083 0.378889i −0.933010 0.359849i \(-0.882828\pi\)
0.999819 0.0190395i \(-0.00606082\pi\)
\(350\) 1.62888e7i 0.00108547i
\(351\) −2.02322e10 + 1.77671e10i −1.33295 + 1.17054i
\(352\) −2.53272e10 −1.64974
\(353\) −1.45465e10 2.56494e9i −0.936827 0.165188i −0.315666 0.948870i \(-0.602228\pi\)
−0.621162 + 0.783683i \(0.713339\pi\)
\(354\) −4.74323e9 + 4.04101e9i −0.302037 + 0.257322i
\(355\) −5.55930e9 2.02342e9i −0.350031 0.127401i
\(356\) −5.46157e9 6.50884e9i −0.340030 0.405232i
\(357\) −7.28715e7 4.13472e7i −0.00448626 0.00254550i
\(358\) 2.22057e9 8.08220e8i 0.135186 0.0492037i
\(359\) 2.51153e10 + 1.45003e10i 1.51203 + 0.872972i 0.999901 + 0.0140646i \(0.00447704\pi\)
0.512131 + 0.858907i \(0.328856\pi\)
\(360\) 6.05945e9 + 1.01411e10i 0.360764 + 0.603775i
\(361\) −2.80848e9 4.86443e9i −0.165365 0.286420i
\(362\) −4.44574e9 + 5.29823e9i −0.258887 + 0.308529i
\(363\) 2.76908e10 1.03143e10i 1.59481 0.594039i
\(364\) 4.28805e7 + 2.43187e8i 0.00244261 + 0.0138527i
\(365\) 1.27239e10 2.24356e9i 0.716881 0.126405i
\(366\) −3.22990e9 8.67128e9i −0.179997 0.483236i
\(367\) 1.36601e9 + 1.14621e9i 0.0752988 + 0.0631832i 0.679660 0.733527i \(-0.262127\pi\)
−0.604361 + 0.796710i \(0.706572\pi\)
\(368\) −7.85526e9 + 4.53524e9i −0.428321 + 0.247291i
\(369\) −1.44357e10 + 8.62555e9i −0.778634 + 0.465244i
\(370\) −4.76475e9 + 8.25279e9i −0.254234 + 0.440346i
\(371\) 3.17476e7 + 8.72257e7i 0.00167577 + 0.00460414i
\(372\) 6.39808e9 1.12761e10i 0.334101 0.588828i
\(373\) 9.68547e9 8.12708e9i 0.500363 0.419855i −0.357360 0.933967i \(-0.616323\pi\)
0.857723 + 0.514112i \(0.171878\pi\)
\(374\) 2.56674e9 7.05205e9i 0.131188 0.360437i
\(375\) 1.38694e10 + 1.62795e10i 0.701344 + 0.823219i
\(376\) −9.57409e8 + 5.42974e9i −0.0479012 + 0.271661i
\(377\) 4.86486e10i 2.40827i
\(378\) −6.01975e7 6.85495e7i −0.00294857 0.00335766i
\(379\) 2.90826e10 1.40954 0.704768 0.709438i \(-0.251051\pi\)
0.704768 + 0.709438i \(0.251051\pi\)
\(380\) 1.64445e10 + 2.89961e9i 0.788654 + 0.139061i
\(381\) −1.34694e10 4.78843e9i −0.639216 0.227245i
\(382\) 8.18923e9 + 2.98064e9i 0.384583 + 0.139977i
\(383\) 3.45256e9 + 4.11460e9i 0.160452 + 0.191220i 0.840281 0.542152i \(-0.182390\pi\)
−0.679828 + 0.733371i \(0.737946\pi\)
\(384\) 1.86746e10 1.09692e10i 0.858868 0.504488i
\(385\) −2.93464e8 + 1.06812e8i −0.0133571 + 0.00486159i
\(386\) −1.13635e10 6.56074e9i −0.511876 0.295531i
\(387\) 1.82004e10 + 6.31709e9i 0.811405 + 0.281626i
\(388\) 9.92502e9 + 1.71906e10i 0.437930 + 0.758517i
\(389\) −1.48272e10 + 1.76703e10i −0.647530 + 0.771697i −0.985539 0.169446i \(-0.945802\pi\)
0.338009 + 0.941143i \(0.390247\pi\)
\(390\) 1.23761e10 + 1.02277e10i 0.534965 + 0.442099i
\(391\) −2.39827e9 1.36013e10i −0.102610 0.581931i
\(392\) 1.87953e10 3.31412e9i 0.795984 0.140354i
\(393\) −3.28403e9 5.53716e8i −0.137669 0.0232122i
\(394\) 9.71690e9 + 8.15345e9i 0.403221 + 0.338342i
\(395\) −1.92018e10 + 1.10862e10i −0.788778 + 0.455401i
\(396\) −2.03572e10 + 2.50129e10i −0.827824 + 1.01714i
\(397\) 1.33126e10 2.30581e10i 0.535921 0.928242i −0.463198 0.886255i \(-0.653298\pi\)
0.999118 0.0419866i \(-0.0133687\pi\)
\(398\) 3.80903e9 + 1.04652e10i 0.151803 + 0.417077i
\(399\) −2.90567e8 + 2.17792e6i −0.0114645 + 8.59312e-5i
\(400\) 2.06934e9 1.73638e9i 0.0808335 0.0678274i
\(401\) −6.68098e9 + 1.83559e10i −0.258382 + 0.709900i 0.740885 + 0.671632i \(0.234406\pi\)
−0.999268 + 0.0382681i \(0.987816\pi\)
\(402\) −4.79880e9 + 8.83294e8i −0.183750 + 0.0338221i
\(403\) 6.89464e9 3.91014e10i 0.261391 1.48242i
\(404\) 1.38400e10i 0.519531i
\(405\) 2.31654e10 + 3.37212e9i 0.861033 + 0.125338i
\(406\) 1.64829e8 0.00606636
\(407\) −5.77306e10 1.01795e10i −2.10392 0.370977i
\(408\) 2.10447e9 + 1.14333e10i 0.0759455 + 0.412600i
\(409\) 2.91511e10 + 1.06101e10i 1.04174 + 0.379164i 0.805541 0.592539i \(-0.201875\pi\)
0.236203 + 0.971704i \(0.424097\pi\)
\(410\) 6.44536e9 + 7.68128e9i 0.228093 + 0.271830i
\(411\) −2.34194e8 3.12450e10i −0.00820745 1.09500i
\(412\) −2.05488e10 + 7.47915e9i −0.713178 + 0.259575i
\(413\) 2.20988e8 + 1.27587e8i 0.00759570 + 0.00438538i
\(414\) 2.38907e9 1.48473e10i 0.0813258 0.505412i
\(415\) −1.43615e10 2.48749e10i −0.484182 0.838628i
\(416\) 3.42744e10 4.08466e10i 1.14445 1.36390i
\(417\) −6.74665e9 + 4.00136e10i −0.223123 + 1.32332i
\(418\) −4.51955e9 2.56317e10i −0.148044 0.839598i
\(419\) −5.06009e10 + 8.92230e9i −1.64173 + 0.289481i −0.916802 0.399342i \(-0.869239\pi\)
−0.724929 + 0.688824i \(0.758127\pi\)
\(420\) 1.36763e8 1.65491e8i 0.00439513 0.00531836i
\(421\) −4.57824e9 3.84160e9i −0.145737 0.122288i 0.567004 0.823715i \(-0.308102\pi\)
−0.712741 + 0.701427i \(0.752547\pi\)
\(422\) 1.75335e9 1.01230e9i 0.0552866 0.0319197i
\(423\) 7.14745e9 + 8.26321e9i 0.223249 + 0.258100i
\(424\) 6.43976e9 1.11540e10i 0.199254 0.345118i
\(425\) 1.40678e9 + 3.86510e9i 0.0431192 + 0.118469i
\(426\) −3.21063e9 5.46594e9i −0.0974881 0.165969i
\(427\) −2.90279e8 + 2.43573e8i −0.00873181 + 0.00732686i
\(428\) −4.61045e9 + 1.26671e10i −0.137394 + 0.377487i
\(429\) −3.30831e10 + 9.30595e10i −0.976736 + 2.74746i
\(430\) 1.99480e9 1.13130e10i 0.0583478 0.330907i
\(431\) 2.95889e10i 0.857473i −0.903430 0.428736i \(-0.858959\pi\)
0.903430 0.428736i \(-0.141041\pi\)
\(432\) 2.29153e9 1.49549e10i 0.0657946 0.429385i
\(433\) −6.02354e9 −0.171356 −0.0856782 0.996323i \(-0.527306\pi\)
−0.0856782 + 0.996323i \(0.527306\pi\)
\(434\) 1.32481e8 + 2.33600e7i 0.00373418 + 0.000658437i
\(435\) −3.21953e10 + 2.74289e10i −0.899158 + 0.766041i
\(436\) −2.77584e10 1.01032e10i −0.768155 0.279586i
\(437\) −3.07886e10 3.66924e10i −0.844237 1.00612i
\(438\) 1.20409e10 + 6.83197e9i 0.327160 + 0.185631i
\(439\) 3.27196e9 1.19090e9i 0.0880948 0.0320639i −0.297597 0.954692i \(-0.596185\pi\)
0.385692 + 0.922628i \(0.373963\pi\)
\(440\) 3.75268e10 + 2.16661e10i 1.00122 + 0.578056i
\(441\) 1.84165e10 3.30321e10i 0.486914 0.873337i
\(442\) 7.89978e9 + 1.36828e10i 0.206979 + 0.358498i
\(443\) 9.32868e9 1.11175e10i 0.242217 0.288664i −0.631216 0.775607i \(-0.717444\pi\)
0.873433 + 0.486944i \(0.161888\pi\)
\(444\) 3.77644e10 1.40666e10i 0.971742 0.361956i
\(445\) 3.92840e9 + 2.22790e10i 0.100179 + 0.568141i
\(446\) −2.69584e10 + 4.75349e9i −0.681325 + 0.120136i
\(447\) −3.89257e9 1.04504e10i −0.0975004 0.261759i
\(448\) 5.17235e6 + 4.34012e6i 0.000128403 + 0.000107743i
\(449\) −5.23161e10 + 3.02047e10i −1.28721 + 0.743171i −0.978156 0.207873i \(-0.933346\pi\)
−0.309055 + 0.951044i \(0.600013\pi\)
\(450\) 6.71345e7 + 4.47812e9i 0.00163718 + 0.109206i
\(451\) −3.08414e10 + 5.34189e10i −0.745466 + 1.29119i
\(452\) −4.62026e9 1.26941e10i −0.110691 0.304121i
\(453\) 1.19608e10 2.10801e10i 0.284033 0.500587i
\(454\) −2.49931e10 + 2.09717e10i −0.588298 + 0.493641i
\(455\) 2.24872e8 6.17832e8i 0.00524675 0.0144153i
\(456\) 2.61467e10 + 3.06904e10i 0.604726 + 0.709811i
\(457\) −2.85275e9 + 1.61788e10i −0.0654033 + 0.370920i 0.934485 + 0.356001i \(0.115860\pi\)
−0.999889 + 0.0149190i \(0.995251\pi\)
\(458\) 2.04661e10i 0.465128i
\(459\) 2.02042e10 + 1.10668e10i 0.455189 + 0.249329i
\(460\) 3.53895e10 0.790392
\(461\) −1.19496e9 2.10704e8i −0.0264576 0.00466519i 0.160404 0.987051i \(-0.448720\pi\)
−0.186861 + 0.982386i \(0.559832\pi\)
\(462\) −3.15299e8 1.12090e8i −0.00692077 0.00246037i
\(463\) −3.29010e10 1.19750e10i −0.715953 0.260586i −0.0417465 0.999128i \(-0.513292\pi\)
−0.674207 + 0.738543i \(0.735514\pi\)
\(464\) 1.75706e10 + 2.09399e10i 0.379067 + 0.451754i
\(465\) −2.97644e10 + 1.74832e10i −0.636627 + 0.373947i
\(466\) −2.39940e10 + 8.73312e9i −0.508815 + 0.185193i
\(467\) 5.50338e10 + 3.17738e10i 1.15708 + 0.668039i 0.950602 0.310413i \(-0.100467\pi\)
0.206475 + 0.978452i \(0.433801\pi\)
\(468\) −1.27910e10 6.66803e10i −0.266637 1.39000i
\(469\) 9.99087e7 + 1.73047e8i 0.00206496 + 0.00357662i
\(470\) 4.18751e9 4.99048e9i 0.0858153 0.102271i
\(471\) −4.96608e10 4.10400e10i −1.00909 0.833919i
\(472\) −6.14822e9 3.48683e10i −0.123874 0.702526i
\(473\) 6.95928e10 1.22711e10i 1.39034 0.245154i
\(474\) −2.34273e10 3.95004e9i −0.464096 0.0782507i
\(475\) 1.09276e10 + 9.16932e9i 0.214659 + 0.180120i
\(476\) 1.82965e8 1.05635e8i 0.00356401 0.00205768i
\(477\) −9.08755e9 2.38493e10i −0.175539 0.460682i
\(478\) −2.64814e9 + 4.58671e9i −0.0507258 + 0.0878596i
\(479\) −1.69332e10 4.65236e10i −0.321660 0.883754i −0.990147 0.140030i \(-0.955280\pi\)
0.668487 0.743724i \(-0.266942\pi\)
\(480\) −4.63565e10 + 3.47461e8i −0.873265 + 0.00654548i
\(481\) 9.45418e10 7.93300e10i 1.76622 1.48203i
\(482\) −2.94173e9 + 8.08234e9i −0.0545023 + 0.149744i
\(483\) −6.05659e8 + 1.11481e8i −0.0111286 + 0.00204839i
\(484\) −1.29387e10 + 7.33792e10i −0.235782 + 1.33719i
\(485\) 5.28515e10i 0.955191i
\(486\) 1.68320e10 + 1.85975e10i 0.301711 + 0.333357i
\(487\) 8.96707e9 0.159417 0.0797085 0.996818i \(-0.474601\pi\)
0.0797085 + 0.996818i \(0.474601\pi\)
\(488\) 5.17791e10 + 9.13005e9i 0.913009 + 0.160988i
\(489\) 7.87525e9 + 4.27850e10i 0.137730 + 0.748266i
\(490\) −2.11907e10 7.71277e9i −0.367587 0.133791i
\(491\) 4.41641e10 + 5.26328e10i 0.759878 + 0.905587i 0.997840 0.0656873i \(-0.0209240\pi\)
−0.237962 + 0.971274i \(0.576480\pi\)
\(492\) −3.17825e8 4.24026e10i −0.00542410 0.723656i
\(493\) −3.91114e10 + 1.42354e10i −0.662088 + 0.240980i
\(494\) 4.74538e10 + 2.73975e10i 0.796825 + 0.460047i
\(495\) 8.02390e10 3.05744e10i 1.33649 0.509256i
\(496\) 1.11548e10 + 1.93206e10i 0.184304 + 0.319223i
\(497\) −1.66864e8 + 1.98861e8i −0.00273488 + 0.00325930i
\(498\) 5.11706e9 3.03487e10i 0.0831961 0.493427i
\(499\) 1.11840e10 + 6.34274e10i 0.180382 + 1.02300i 0.931746 + 0.363110i \(0.118285\pi\)
−0.751364 + 0.659888i \(0.770604\pi\)
\(500\) −5.31083e10 + 9.36443e9i −0.849733 + 0.149831i
\(501\) −9.96755e9 + 1.20613e10i −0.158211 + 0.191445i
\(502\) −1.04542e10 8.77214e9i −0.164618 0.138131i
\(503\) −1.39660e10 + 8.06327e9i −0.218173 + 0.125962i −0.605104 0.796147i \(-0.706868\pi\)
0.386931 + 0.922109i \(0.373535\pi\)
\(504\) 5.09089e8 9.76564e7i 0.00788990 0.00151349i
\(505\) 1.84248e10 3.19126e10i 0.283293 0.490679i
\(506\) −1.88660e10 5.18340e10i −0.287792 0.790702i
\(507\) −7.18471e10 1.22316e11i −1.08737 1.85120i
\(508\) 2.76132e10 2.31703e10i 0.414632 0.347917i
\(509\) −2.93576e10 + 8.06594e10i −0.437371 + 1.20167i 0.503825 + 0.863806i \(0.331926\pi\)
−0.941196 + 0.337861i \(0.890297\pi\)
\(510\) 4.60117e9 1.29426e10i 0.0680124 0.191312i
\(511\) 9.84463e7 5.58316e8i 0.00144383 0.00818836i
\(512\) 5.40910e10i 0.787127i
\(513\) 7.98738e10 1.79633e9i 1.15328 0.0259368i
\(514\) 1.27611e10 0.182826
\(515\) 5.73387e10 + 1.01104e10i 0.815115 + 0.143727i
\(516\) −3.69790e10 + 3.15044e10i −0.521623 + 0.444398i
\(517\) 3.76581e10 + 1.37064e10i 0.527105 + 0.191850i
\(518\) 2.68782e8 + 3.20321e8i 0.00373319 + 0.00444905i
\(519\) 9.51375e10 + 5.39810e10i 1.31124 + 0.743997i
\(520\) −8.57258e10 + 3.12016e10i −1.17246 + 0.426741i
\(521\) 1.02555e11 + 5.92104e10i 1.39190 + 0.803614i 0.993526 0.113609i \(-0.0362411\pi\)
0.398374 + 0.917223i \(0.369574\pi\)
\(522\) −4.53147e10 + 6.79343e8i −0.610319 + 0.00914970i
\(523\) 1.60296e10 + 2.77642e10i 0.214248 + 0.371089i 0.953040 0.302845i \(-0.0979365\pi\)
−0.738792 + 0.673934i \(0.764603\pi\)
\(524\) 5.39802e9 6.43311e9i 0.0715994 0.0853288i
\(525\) 1.71869e8 6.40181e7i 0.00226235 0.000842685i
\(526\) 3.49175e9 + 1.98027e10i 0.0456143 + 0.258691i
\(527\) −3.34533e10 + 5.89873e9i −0.433708 + 0.0764744i
\(528\) −1.93707e10 5.20045e10i −0.249236 0.669122i
\(529\) −1.77747e10 1.49147e10i −0.226976 0.190455i
\(530\) −1.31793e10 + 7.60906e9i −0.167028 + 0.0964334i
\(531\) −6.12798e10 3.41655e10i −0.770796 0.429744i
\(532\) 3.66354e8 6.34545e8i 0.00457357 0.00792165i
\(533\) −4.44151e10 1.22030e11i −0.550329 1.51202i
\(534\) −1.19626e10 + 2.10831e10i −0.147116 + 0.259281i
\(535\) 2.74942e10 2.30704e10i 0.335603 0.281604i
\(536\) 9.48257e9 2.60532e10i 0.114886 0.315647i
\(537\) 1.72551e10 + 2.02535e10i 0.207500 + 0.243559i
\(538\) −4.66921e9 + 2.64804e10i −0.0557333 + 0.316079i
\(539\) 1.38721e11i 1.64357i
\(540\) −3.69168e10 + 4.60605e10i −0.434160 + 0.541694i
\(541\) −4.07582e10 −0.475801 −0.237901 0.971290i \(-0.576459\pi\)
−0.237901 + 0.971290i \(0.576459\pi\)
\(542\) −2.99911e10 5.28824e9i −0.347532 0.0612793i
\(543\) −7.33760e10 2.60855e10i −0.844024 0.300055i
\(544\) −4.28682e10 1.56027e10i −0.489485 0.178158i
\(545\) 5.05559e10 + 6.02502e10i 0.573041 + 0.682924i
\(546\) 6.07457e8 3.56813e8i 0.00683511 0.00401486i
\(547\) −3.74514e8 + 1.36312e8i −0.00418330 + 0.00152260i −0.344111 0.938929i \(-0.611820\pi\)
0.339928 + 0.940452i \(0.389597\pi\)
\(548\) 6.82332e10 + 3.93944e10i 0.756612 + 0.436830i
\(549\) 7.87997e10 6.81595e10i 0.867431 0.750304i
\(550\) 8.21385e9 + 1.42268e10i 0.0897627 + 0.155473i
\(551\) −9.27855e10 + 1.10577e11i −1.00664 + 1.19967i
\(552\) 6.58672e10 + 5.44331e10i 0.709435 + 0.586282i
\(553\) 1.68945e8 + 9.58133e8i 0.00180652 + 0.0102453i
\(554\) 7.25186e10 1.27870e10i 0.769858 0.135747i
\(555\) −1.05804e11 1.78396e10i −1.11515 0.188023i
\(556\) −7.83830e10 6.57711e10i −0.820205 0.688234i
\(557\) 4.33094e10 2.50047e10i 0.449947 0.259777i −0.257861 0.966182i \(-0.583018\pi\)
0.707808 + 0.706405i \(0.249684\pi\)
\(558\) −3.65180e10 5.87612e9i −0.376678 0.0606113i
\(559\) −7.43872e10 + 1.28842e11i −0.761817 + 1.31951i
\(560\) 1.26353e8 + 3.47152e8i 0.00128480 + 0.00352995i
\(561\) 8.44965e10 6.33336e8i 0.853075 0.00639415i
\(562\) 3.17347e10 2.66286e10i 0.318119 0.266933i
\(563\) 4.03175e9 1.10771e10i 0.0401292 0.110254i −0.918010 0.396558i \(-0.870205\pi\)
0.958139 + 0.286304i \(0.0924268\pi\)
\(564\) −2.70944e10 + 4.98714e9i −0.267770 + 0.0492873i
\(565\) −6.24569e9 + 3.54211e10i −0.0612896 + 0.347590i
\(566\) 2.25878e10i 0.220094i
\(567\) 4.86702e8 9.04577e8i 0.00470903 0.00875212i
\(568\) 3.60194e10 0.346054
\(569\) −1.00783e11 1.77708e10i −0.961476 0.169534i −0.329185 0.944265i \(-0.606774\pi\)
−0.632291 + 0.774731i \(0.717885\pi\)
\(570\) −8.62381e9 4.68518e10i −0.0816958 0.443840i
\(571\) −7.58711e10 2.76148e10i −0.713726 0.259775i −0.0404663 0.999181i \(-0.512884\pi\)
−0.673260 + 0.739406i \(0.735107\pi\)
\(572\) −1.60082e11 1.90779e11i −1.49541 1.78216i
\(573\) 7.35464e8 + 9.81219e10i 0.00682249 + 0.910222i
\(574\) 4.13454e8 1.50485e8i 0.00380872 0.00138626i
\(575\) 2.61821e10 + 1.51162e10i 0.239515 + 0.138284i
\(576\) −1.43987e9 1.17187e9i −0.0130808 0.0106460i
\(577\) 6.69536e10 + 1.15967e11i 0.604047 + 1.04624i 0.992201 + 0.124646i \(0.0397794\pi\)
−0.388154 + 0.921594i \(0.626887\pi\)
\(578\) −2.35681e10 + 2.80874e10i −0.211161 + 0.251652i
\(579\) 2.45639e10 1.45686e11i 0.218566 1.29629i
\(580\) −1.85197e10 1.05030e11i −0.163652 0.928118i
\(581\) −1.24121e9 + 2.18858e8i −0.0108928 + 0.00192070i
\(582\) 3.60754e10 4.36534e10i 0.314427 0.380475i
\(583\) −7.17133e10 6.01746e10i −0.620763 0.520882i
\(584\) −6.81241e10 + 3.93315e10i −0.585665 + 0.338134i
\(585\) −5.92756e10 + 1.70781e11i −0.506118 + 1.45820i
\(586\) 2.88340e10 4.99420e10i 0.244520 0.423521i
\(587\) 4.47539e10 + 1.22960e11i 0.376946 + 1.03565i 0.972615 + 0.232420i \(0.0746645\pi\)
−0.595670 + 0.803229i \(0.703113\pi\)
\(588\) 4.82996e10 + 8.22278e10i 0.404049 + 0.687875i
\(589\) −9.02479e10 + 7.57270e10i −0.749853 + 0.629201i
\(590\) −1.43084e10 + 3.93121e10i −0.118082 + 0.324428i
\(591\) −4.78407e10 + 1.34571e11i −0.392146 + 1.10307i
\(592\) −1.20418e10 + 6.82922e10i −0.0980400 + 0.556012i
\(593\) 1.64843e11i 1.33307i −0.745474 0.666535i \(-0.767777\pi\)
0.745474 0.666535i \(-0.232223\pi\)
\(594\) 8.71440e10 + 2.95164e10i 0.699990 + 0.237092i
\(595\) −5.62512e8 −0.00448811
\(596\) 2.76929e10 + 4.88300e9i 0.219474 + 0.0386992i
\(597\) −9.54520e10 + 8.13206e10i −0.751428 + 0.640182i
\(598\) 1.09127e11 + 3.97188e10i 0.853347 + 0.310593i
\(599\) 1.35576e11 + 1.61573e11i 1.05311 + 1.25505i 0.965914 + 0.258861i \(0.0833473\pi\)
0.0871995 + 0.996191i \(0.472208\pi\)
\(600\) −2.21333e10 1.25584e10i −0.170781 0.0969012i
\(601\) 2.01380e11 7.32965e10i 1.54355 0.561805i 0.576653 0.816989i \(-0.304358\pi\)
0.966892 + 0.255185i \(0.0821363\pi\)
\(602\) −4.36537e8 2.52035e8i −0.00332380 0.00191900i
\(603\) −2.81801e10 4.71623e10i −0.213144 0.356719i
\(604\) 3.05577e10 + 5.29275e10i 0.229601 + 0.397680i
\(605\) 1.27522e11 1.51975e11i 0.951838 1.13436i
\(606\) 3.70012e10 1.37823e10i 0.274363 0.102195i
\(607\) −2.96670e10 1.68250e11i −0.218534 1.23937i −0.874668 0.484722i \(-0.838921\pi\)
0.656135 0.754644i \(-0.272190\pi\)
\(608\) −1.55810e11 + 2.74735e10i −1.14020 + 0.201048i
\(609\) 6.47807e8 + 1.73916e9i 0.00470952 + 0.0126436i
\(610\) −4.75903e10 3.99330e10i −0.343715 0.288411i
\(611\) −7.30666e10 + 4.21850e10i −0.524269 + 0.302687i
\(612\) −4.98652e10 + 2.97952e10i −0.355461 + 0.212393i
\(613\) 8.94848e10 1.54992e11i 0.633734 1.09766i −0.353047 0.935605i \(-0.614855\pi\)
0.986782 0.162055i \(-0.0518121\pi\)
\(614\) −1.20150e10 3.30109e10i −0.0845377 0.232265i
\(615\) −5.57164e10 + 9.81961e10i −0.389478 + 0.686426i
\(616\) 1.45655e9 1.22219e9i 0.0101159 0.00848823i
\(617\) −2.07969e10 + 5.71390e10i −0.143502 + 0.394268i −0.990533 0.137275i \(-0.956166\pi\)
0.847031 + 0.531543i \(0.178388\pi\)
\(618\) 4.04585e10 + 4.74891e10i 0.277368 + 0.325567i
\(619\) 3.90616e10 2.21529e11i 0.266065 1.50893i −0.499921 0.866071i \(-0.666637\pi\)
0.765985 0.642858i \(-0.222251\pi\)
\(620\) 8.70431e10i 0.589071i
\(621\) 1.66048e11 3.31446e10i 1.11652 0.222867i
\(622\) 8.99602e10 0.601020
\(623\) 9.77593e8 + 1.72376e8i 0.00648942 + 0.00114426i
\(624\) 1.10084e11 + 3.91355e10i 0.726084 + 0.258127i
\(625\) 1.00095e11 + 3.64315e10i 0.655981 + 0.238758i
\(626\) −4.33099e10 5.16148e10i −0.282027 0.336106i
\(627\) 2.52686e11 1.48425e11i 1.63497 0.960363i
\(628\) 1.52654e11 5.55614e10i 0.981451 0.357219i
\(629\) −9.14424e10 5.27943e10i −0.584178 0.337275i
\(630\) −5.78632e8 2.00834e8i −0.00367316 0.00127490i
\(631\) −1.08103e11 1.87240e11i −0.681901 1.18109i −0.974400 0.224821i \(-0.927820\pi\)
0.292499 0.956266i \(-0.405513\pi\)
\(632\) 8.67726e10 1.03412e11i 0.543894 0.648188i
\(633\) 1.75721e10 + 1.45217e10i 0.109449 + 0.0904490i
\(634\) 1.37383e10 + 7.79137e10i 0.0850306 + 0.482233i
\(635\) −9.45171e10 + 1.66659e10i −0.581320 + 0.102502i
\(636\) 6.34599e10 + 1.06999e10i 0.387856 + 0.0653960i
\(637\) 2.23724e11 + 1.87727e11i 1.35880 + 1.14017i
\(638\) −1.43963e11 + 8.31169e10i −0.868895 + 0.501657i
\(639\) 4.50547e10 5.53586e10i 0.270232 0.332033i
\(640\) 7.27033e10 1.25926e11i 0.433345 0.750576i
\(641\) 5.67063e10 + 1.55799e11i 0.335892 + 0.922854i 0.986547 + 0.163481i \(0.0522722\pi\)
−0.650655 + 0.759373i \(0.725506\pi\)
\(642\) 3.84566e10 2.88248e8i 0.226376 0.00169678i
\(643\) −9.87208e10 + 8.28366e10i −0.577517 + 0.484594i −0.884131 0.467240i \(-0.845249\pi\)
0.306614 + 0.951834i \(0.400804\pi\)
\(644\) 5.31113e8 1.45922e9i 0.00308776 0.00848356i
\(645\) 1.27208e11 2.34146e10i 0.734979 0.135284i
\(646\) 8.14062e9 4.61678e10i 0.0467442 0.265099i
\(647\) 8.44054e8i 0.00481674i −0.999997 0.00240837i \(-0.999233\pi\)
0.999997 0.00240837i \(-0.000766609\pi\)
\(648\) −1.39556e11 + 2.89459e10i −0.791498 + 0.164168i
\(649\) −2.57350e11 −1.45059
\(650\) −3.40599e10 6.00568e9i −0.190805 0.0336441i
\(651\) 2.74196e8 + 1.48967e9i 0.00152664 + 0.00829402i
\(652\) −1.03083e11 3.75190e10i −0.570420 0.207616i
\(653\) −1.57212e11 1.87359e11i −0.864638 1.03044i −0.999218 0.0395325i \(-0.987413\pi\)
0.134580 0.990903i \(-0.457031\pi\)
\(654\) 6.31661e8 + 8.42730e10i 0.00345281 + 0.460657i
\(655\) −2.10111e10 + 7.64740e9i −0.114152 + 0.0415479i
\(656\) 6.31917e10 + 3.64837e10i 0.341228 + 0.197008i
\(657\) −2.47637e10 + 1.53898e11i −0.132909 + 0.825985i
\(658\) −1.42929e8 2.47560e8i −0.000762459 0.00132062i
\(659\) −2.08795e11 + 2.48832e11i −1.10708 + 1.31936i −0.164122 + 0.986440i \(0.552479\pi\)
−0.942954 + 0.332922i \(0.891965\pi\)
\(660\) −3.59990e10 + 2.13506e11i −0.189721 + 1.12521i
\(661\) 2.43729e10 + 1.38226e11i 0.127674 + 0.724074i 0.979684 + 0.200548i \(0.0642724\pi\)
−0.852010 + 0.523526i \(0.824616\pi\)
\(662\) 1.28816e11 2.27138e10i 0.670715 0.118265i
\(663\) −1.13325e11 + 1.37129e11i −0.586503 + 0.709703i
\(664\) 1.33964e11 + 1.12409e11i 0.689153 + 0.578268i
\(665\) −1.68950e9 + 9.75432e8i −0.00863915 + 0.00498781i
\(666\) −7.52137e10 8.69550e10i −0.382296 0.441975i
\(667\) −1.52963e11 + 2.64940e11i −0.772829 + 1.33858i
\(668\) −1.34944e10 3.70756e10i −0.0677717 0.186201i
\(669\) −1.56107e11 2.65765e11i −0.779324 1.32676i
\(670\) −2.50951e10 + 2.10573e10i −0.124535 + 0.104497i
\(671\) 1.30707e11 3.59116e11i 0.644778 1.77151i
\(672\) −6.81377e8 + 1.91664e9i −0.00334126 + 0.00939863i
\(673\) 5.61098e9 3.18215e10i 0.0273513 0.155117i −0.968073 0.250667i \(-0.919350\pi\)
0.995425 + 0.0955502i \(0.0304611\pi\)
\(674\) 1.59904e11i 0.774852i
\(675\) −4.69864e10 + 1.83082e10i −0.226338 + 0.0881924i
\(676\) 3.57703e11 1.71291
\(677\) 9.66599e10 + 1.70437e10i 0.460142 + 0.0811354i 0.398914 0.916988i \(-0.369387\pi\)
0.0612279 + 0.998124i \(0.480498\pi\)
\(678\) −2.93365e10 + 2.49933e10i −0.138832 + 0.118278i
\(679\) −2.17924e9 7.93178e8i −0.0102524 0.00373157i
\(680\) 5.01696e10 + 5.97898e10i 0.234641 + 0.279635i
\(681\) −3.19508e11 1.81289e11i −1.48557 0.842911i
\(682\) −1.27490e11 + 4.64025e10i −0.589303 + 0.214489i
\(683\) −6.47335e10 3.73739e10i −0.297472 0.171746i 0.343835 0.939030i \(-0.388274\pi\)
−0.641307 + 0.767285i \(0.721607\pi\)
\(684\) −9.81029e10 + 1.75959e11i −0.448185 + 0.803872i
\(685\) −1.04889e11 1.81673e11i −0.476396 0.825142i
\(686\) −1.27215e9 + 1.51609e9i −0.00574437 + 0.00684588i
\(687\) 2.15945e11 8.04354e10i 0.969428 0.361094i
\(688\) −1.45160e10 8.23245e10i −0.0647880 0.367431i
\(689\) 1.94094e11 3.42240e10i 0.861262 0.151864i
\(690\) −3.52418e10 9.46134e10i −0.155475 0.417404i
\(691\) −1.56712e11 1.31497e11i −0.687371 0.576772i 0.230779 0.973006i \(-0.425873\pi\)
−0.918150 + 0.396234i \(0.870317\pi\)
\(692\) −2.38870e11 + 1.37912e11i −1.04169 + 0.601418i
\(693\) −5.64791e7 3.76737e9i −0.000244881 0.0163345i
\(694\) 5.42794e10 9.40146e10i 0.233990 0.405282i
\(695\) 9.31783e10 + 2.56005e11i 0.399370 + 1.09726i
\(696\) 1.27080e11 2.23969e11i 0.541552 0.954446i
\(697\) −8.51099e10 + 7.14157e10i −0.360619 + 0.302596i
\(698\) 1.40436e10 3.85844e10i 0.0591638 0.162551i
\(699\) −1.86447e11 2.18847e11i −0.780993 0.916709i
\(700\) −8.03069e7 + 4.55443e8i −0.000334473 + 0.00189689i
\(701\) 1.17559e11i 0.486835i 0.969922 + 0.243418i \(0.0782686\pi\)
−0.969922 + 0.243418i \(0.921731\pi\)
\(702\) −1.65532e11 + 1.00599e11i −0.681605 + 0.414232i
\(703\) −3.66195e11 −1.49931
\(704\) −6.70613e9 1.18247e9i −0.0273012 0.00481394i
\(705\) 6.91140e10 + 2.45704e10i 0.279776 + 0.0994616i
\(706\) −9.98520e10 3.63432e10i −0.401919 0.146286i
\(707\) −1.03935e9 1.23865e9i −0.00415991 0.00495758i
\(708\) 1.52546e11 8.96035e10i 0.607110 0.356609i
\(709\) 2.17824e11 7.92814e10i 0.862026 0.313752i 0.127092 0.991891i \(-0.459436\pi\)
0.734934 + 0.678139i \(0.237213\pi\)
\(710\) −3.68577e10 2.12798e10i −0.145043 0.0837403i
\(711\) −5.03952e10 2.62714e11i −0.197202 1.02803i
\(712\) −6.88681e10 1.19283e11i −0.267977 0.464150i
\(713\) −1.60493e11 + 1.91268e11i −0.621008 + 0.740088i
\(714\) −4.64614e8 3.83960e8i −0.00178772 0.00147738i
\(715\) 1.15144e11 + 6.53015e11i 0.440573 + 2.49861i
\(716\) −6.60728e10 + 1.16504e10i −0.251403 + 0.0443292i
\(717\) −5.88036e10 9.91480e9i −0.222499 0.0375152i
\(718\) 1.59818e11 + 1.34103e11i 0.601352 + 0.504594i
\(719\) 3.61669e11 2.08810e11i 1.35331 0.781332i 0.364595 0.931166i \(-0.381207\pi\)
0.988711 + 0.149835i \(0.0478741\pi\)
\(720\) −3.61678e10 9.49184e10i −0.134584 0.353200i
\(721\) 1.27740e9 2.21253e9i 0.00472701 0.00818743i
\(722\) −1.38203e10 3.79709e10i −0.0508590 0.139734i
\(723\) −9.68412e10 + 7.25865e8i −0.354411 + 0.00265646i
\(724\) 1.50426e11 1.26223e11i 0.547482 0.459392i
\(725\) 3.11613e10 8.56150e10i 0.112788 0.309883i
\(726\) 2.09063e11 3.84814e10i 0.752543 0.138517i
\(727\) −5.38552e10 + 3.05428e11i −0.192792 + 1.09338i 0.722735 + 0.691125i \(0.242885\pi\)
−0.915528 + 0.402255i \(0.868226\pi\)
\(728\) 4.00302e9i 0.0142515i
\(729\) −1.30076e11 + 2.50692e11i −0.460561 + 0.887628i
\(730\) 9.29461e10 0.327295
\(731\) 1.25351e11 + 2.21027e10i 0.438992 + 0.0774062i
\(732\) 4.75584e10 + 2.58377e11i 0.165647 + 0.899933i
\(733\) 9.20818e10 + 3.35150e10i 0.318976 + 0.116098i 0.496546 0.868010i \(-0.334601\pi\)
−0.177570 + 0.984108i \(0.556824\pi\)
\(734\) 8.24575e9 + 9.82690e9i 0.0284083 + 0.0338558i
\(735\) −1.90311e9 2.53903e11i −0.00652099 0.869997i
\(736\) −3.15090e11 + 1.14683e11i −1.07380 + 0.390831i
\(737\) −1.74522e11 1.00760e11i −0.591536 0.341523i
\(738\) −1.13047e11 + 4.30754e10i −0.381094 + 0.145212i
\(739\) −1.88472e11 3.26443e11i −0.631931 1.09454i −0.987157 0.159755i \(-0.948929\pi\)
0.355226 0.934780i \(-0.384404\pi\)
\(740\) 1.73913e11 2.07261e11i 0.579968 0.691179i
\(741\) −1.02578e11 + 6.08379e11i −0.340237 + 2.01791i
\(742\) 1.15956e8 + 6.57619e8i 0.000382541 + 0.00216950i
\(743\) 5.58247e11 9.84340e10i 1.83177 0.322991i 0.852066 0.523434i \(-0.175349\pi\)
0.979705 + 0.200443i \(0.0642382\pi\)
\(744\) 1.33882e11 1.62005e11i 0.436950 0.528735i
\(745\) −5.73543e10 4.81260e10i −0.186183 0.156227i
\(746\) 7.87701e10 4.54780e10i 0.254335 0.146840i
\(747\) 3.40331e11 6.52842e10i 1.09300 0.209665i
\(748\) −1.06535e11 + 1.84524e11i −0.340320 + 0.589451i
\(749\) −5.38642e8 1.47991e9i −0.00171149 0.00470227i
\(750\) 7.79224e10 + 1.32659e11i 0.246273 + 0.419269i
\(751\) −3.50924e11 + 2.94460e11i −1.10320 + 0.925692i −0.997636 0.0687214i \(-0.978108\pi\)
−0.105560 + 0.994413i \(0.533664\pi\)
\(752\) 1.62140e10 4.45476e10i 0.0507012 0.139300i
\(753\) 5.14709e10 1.44782e11i 0.160096 0.450335i
\(754\) 6.07722e10 3.44656e11i 0.188027 1.06635i
\(755\) 1.62722e11i 0.500794i
\(756\) 1.34519e9 + 2.21346e9i 0.00411809 + 0.00677618i
\(757\) −2.66800e11 −0.812460 −0.406230 0.913771i \(-0.633157\pi\)
−0.406230 + 0.913771i \(0.633157\pi\)
\(758\) 2.06039e11 + 3.63302e10i 0.624125 + 0.110050i
\(759\) 4.72772e11 4.02780e11i 1.42457 1.21367i
\(760\) 2.54363e11 + 9.25806e10i 0.762429 + 0.277502i
\(761\) 3.48504e11 + 4.15330e11i 1.03913 + 1.23838i 0.970591 + 0.240735i \(0.0773884\pi\)
0.0685361 + 0.997649i \(0.478167\pi\)
\(762\) −8.94435e10 5.07502e10i −0.265295 0.150528i
\(763\) 3.24304e9 1.18037e9i 0.00956872 0.00348273i
\(764\) −2.14280e11 1.23715e11i −0.628938 0.363118i
\(765\) 1.54646e11 2.31840e9i 0.451536 0.00676928i
\(766\) 1.93200e10 + 3.34633e10i 0.0561167 + 0.0971971i
\(767\) 3.48263e11 4.15044e11i 1.00630 1.19926i
\(768\) 1.51503e11 5.64322e10i 0.435489 0.162212i
\(769\) −5.95729e10 3.37855e11i −0.170351 0.966106i −0.943375 0.331729i \(-0.892368\pi\)
0.773024 0.634377i \(-0.218743\pi\)
\(770\) −2.21251e9 + 3.90125e8i −0.00629393 + 0.00110979i
\(771\) 5.01537e10 + 1.34647e11i 0.141934 + 0.381049i
\(772\) 2.85384e11 + 2.39466e11i 0.803454 + 0.674178i
\(773\) −3.94669e11 + 2.27862e11i −1.10539 + 0.638197i −0.937631 0.347631i \(-0.886986\pi\)
−0.167758 + 0.985828i \(0.553653\pi\)
\(774\) 1.21051e11 + 6.74902e10i 0.337292 + 0.188051i
\(775\) 3.71796e10 6.43970e10i 0.103062 0.178508i
\(776\) 1.10055e11 + 3.02375e11i 0.303504 + 0.833871i
\(777\) −2.32346e9 + 4.09493e9i −0.00637458 + 0.0112347i
\(778\) −1.27119e11 + 1.06665e11i −0.346969 + 0.291142i
\(779\) −1.31787e11 + 3.62082e11i −0.357868 + 0.983235i
\(780\) −2.95617e11 3.46988e11i −0.798641 0.937423i
\(781\) 4.54625e10 2.57830e11i 0.122194 0.692995i
\(782\) 9.93554e10i 0.265683i
\(783\) −1.85263e11 4.75461e11i −0.492881 1.26493i
\(784\) −1.64100e11 −0.434354
\(785\) −4.25960e11 7.51082e10i −1.12173 0.197792i
\(786\) −2.25744e10 8.02530e9i −0.0591460 0.0210267i
\(787\) 3.14201e11 + 1.14360e11i 0.819048 + 0.298109i 0.717356 0.696707i \(-0.245352\pi\)
0.101692 + 0.994816i \(0.467574\pi\)
\(788\) −2.31491e11 2.75881e11i −0.600385 0.715511i
\(789\) −1.95222e11 + 1.14671e11i −0.503757 + 0.295901i
\(790\) −1.49886e11 + 5.45542e10i −0.384817 + 0.140062i
\(791\) 1.36679e9 + 7.89118e8i 0.00349138 + 0.00201575i
\(792\) −3.95398e11 + 3.42009e11i −1.00493 + 0.869233i
\(793\) 4.02285e11 + 6.96778e11i 1.01728 + 1.76198i
\(794\) 1.23119e11 1.46727e11i 0.309772 0.369172i
\(795\) −1.32083e11 1.09154e11i −0.330657 0.273257i
\(796\) −5.49068e10 3.11392e11i −0.136765 0.775630i
\(797\) 2.18436e11 3.85161e10i 0.541365 0.0954573i 0.103722 0.994606i \(-0.466925\pi\)
0.437643 + 0.899149i \(0.355814\pi\)
\(798\) −2.06128e9 3.47549e8i −0.00508305 0.000857047i
\(799\) 5.52954e10 + 4.63984e10i 0.135676 + 0.113845i
\(800\) 8.64821e10 4.99305e10i 0.211138 0.121901i
\(801\) −2.69471e11 4.33605e10i −0.654608 0.105333i
\(802\) −7.02624e10 + 1.21698e11i −0.169834 + 0.294162i
\(803\) 1.95554e11 + 5.37281e11i 0.470333 + 1.29223i
\(804\) 1.38532e11 1.03835e9i 0.331531 0.00248497i
\(805\) −3.16727e9 + 2.65765e9i −0.00754226 + 0.00632871i
\(806\) 9.76915e10 2.68405e11i 0.231482 0.635991i
\(807\) −2.97755e11 + 5.48065e10i −0.702045 + 0.129222i
\(808\) −3.89588e10 + 2.20946e11i −0.0914029 + 0.518371i
\(809\) 2.04827e11i 0.478181i −0.970997 0.239091i \(-0.923151\pi\)
0.970997 0.239091i \(-0.0768493\pi\)
\(810\) 1.59905e11 + 5.28285e10i 0.371469 + 0.122724i
\(811\) −5.70557e9 −0.0131891 −0.00659456 0.999978i \(-0.502099\pi\)
−0.00659456 + 0.999978i \(0.502099\pi\)
\(812\) −4.60869e9 8.12636e8i −0.0106012 0.00186927i
\(813\) −6.20725e10 3.37230e11i −0.142081 0.771906i
\(814\) −3.96282e11 1.44235e11i −0.902625 0.328528i
\(815\) 1.87742e11 + 2.23743e11i 0.425532 + 0.507129i
\(816\) −7.49203e8 9.99548e10i −0.00168981 0.225446i
\(817\) 4.14817e11 1.50981e11i 0.931039 0.338871i
\(818\) 1.93270e11 + 1.11584e11i 0.431668 + 0.249224i
\(819\) 6.15228e9 + 5.00715e9i 0.0136742 + 0.0111290i
\(820\) −1.42345e11 2.46549e11i −0.314838 0.545316i
\(821\) −3.53407e11 + 4.21174e11i −0.777861 + 0.927019i −0.998835 0.0482606i \(-0.984632\pi\)
0.220973 + 0.975280i \(0.429077\pi\)
\(822\) 3.73723e10 2.21651e11i 0.0818582 0.485492i
\(823\) −3.62341e10 2.05494e11i −0.0789802 0.447919i −0.998494 0.0548611i \(-0.982528\pi\)
0.919514 0.393058i \(-0.128583\pi\)
\(824\) −3.49101e11 + 6.15559e10i −0.757254 + 0.133524i
\(825\) −1.17830e11 + 1.42581e11i −0.254355 + 0.307784i
\(826\) 1.40623e9 + 1.17997e9i 0.00302089 + 0.00253483i
\(827\) 2.10222e11 1.21372e11i 0.449424 0.259475i −0.258163 0.966101i \(-0.583117\pi\)
0.707587 + 0.706626i \(0.249784\pi\)
\(828\) −1.40000e11 + 4.03359e11i −0.297855 + 0.858163i
\(829\) 3.10954e11 5.38589e11i 0.658383 1.14035i −0.322651 0.946518i \(-0.604574\pi\)
0.981034 0.193835i \(-0.0620926\pi\)
\(830\) −7.06719e10 1.94169e11i −0.148914 0.409137i
\(831\) 4.19932e11 + 7.14914e11i 0.880592 + 1.49917i
\(832\) 1.09822e10 9.21517e9i 0.0229191 0.0192314i
\(833\) 8.54589e10 2.34796e11i 0.177491 0.487653i
\(834\) −9.77827e10 + 2.75053e11i −0.202115 + 0.568528i
\(835\) −1.82418e10 + 1.03455e11i −0.0375251 + 0.212816i
\(836\) 7.38956e11i 1.51284i
\(837\) −8.15217e10 4.08409e11i −0.166101 0.832134i
\(838\) −3.69633e11 −0.749540
\(839\) −9.66564e10 1.70431e10i −0.195066 0.0343955i 0.0752612 0.997164i \(-0.476021\pi\)
−0.270328 + 0.962768i \(0.587132\pi\)
\(840\) 2.64917e9 2.25697e9i 0.00532100 0.00453324i
\(841\) 3.96271e11 + 1.44231e11i 0.792151 + 0.288319i
\(842\) −2.76361e10 3.29354e10i −0.0549829 0.0655261i
\(843\) 4.05691e11 + 2.30189e11i 0.803313 + 0.455799i
\(844\) −5.40155e10 + 1.96600e10i −0.106451 + 0.0387449i
\(845\) −8.24799e11 4.76198e11i −1.61779 0.934030i
\(846\) 4.03144e10 + 6.74702e10i 0.0787007 + 0.131714i
\(847\) −4.35260e9 7.53892e9i −0.00845698 0.0146479i
\(848\) −7.11833e10 + 8.48330e10i −0.137656 + 0.164052i
\(849\) −2.38332e11 + 8.87744e10i −0.458724 + 0.170866i
\(850\) 5.13818e9 + 2.91400e10i 0.00984313 + 0.0558232i
\(851\) −7.64307e11 + 1.34768e11i −1.45730 + 0.256962i
\(852\) 6.28226e10 + 1.68659e11i 0.119222 + 0.320075i
\(853\) −2.23404e11 1.87458e11i −0.421982 0.354085i 0.406934 0.913457i \(-0.366598\pi\)
−0.828916 + 0.559372i \(0.811042\pi\)
\(854\) −2.36079e9 + 1.36300e9i −0.00443839 + 0.00256250i
\(855\) 4.60457e11 2.75129e11i 0.861637 0.514840i
\(856\) −1.09260e11 + 1.89243e11i −0.203500 + 0.352473i
\(857\) −2.91419e11 8.00668e11i −0.540250 1.48433i −0.846508 0.532377i \(-0.821299\pi\)
0.306257 0.951949i \(-0.400923\pi\)
\(858\) −3.50631e11 + 6.17962e11i −0.646996 + 1.14028i
\(859\) −1.76996e11 + 1.48517e11i −0.325081 + 0.272775i −0.790692 0.612214i \(-0.790279\pi\)
0.465611 + 0.884989i \(0.345835\pi\)
\(860\) −1.11551e11 + 3.06484e11i −0.203929 + 0.560291i
\(861\) 3.21277e9 + 3.77106e9i 0.00584611 + 0.00686201i
\(862\) 3.69627e10 2.09626e11i 0.0669475 0.379678i
\(863\) 9.48191e11i 1.70944i 0.519093 + 0.854718i \(0.326270\pi\)
−0.519093 + 0.854718i \(0.673730\pi\)
\(864\) 1.79425e11 5.29732e11i 0.321979 0.950608i
\(865\) 7.34389e11 1.31178
\(866\) −4.26744e10 7.52465e9i −0.0758745 0.0133787i
\(867\) −3.88987e11 1.38287e11i −0.688429 0.244740i
\(868\) −3.58907e9 1.30632e9i −0.00632271 0.00230128i
\(869\) −6.30708e11 7.51649e11i −1.10599 1.31806i
\(870\) −2.62356e11 + 1.54104e11i −0.457945 + 0.268991i
\(871\) 3.98677e11 1.45107e11i 0.692706 0.252124i
\(872\) −4.14704e11 2.39429e11i −0.717253 0.414106i
\(873\) 6.02385e11 + 2.09079e11i 1.03709 + 0.359959i
\(874\) −1.72289e11 2.98413e11i −0.295264 0.511413i
\(875\) 4.04982e9 4.82639e9i 0.00690882 0.00823361i
\(876\) −3.02985e11 2.50389e11i −0.514523 0.425205i
\(877\) 3.40749e10 + 1.93249e11i 0.0576019 + 0.326677i 0.999969 0.00790482i \(-0.00251621\pi\)
−0.942367 + 0.334581i \(0.891405\pi\)
\(878\) 2.46682e10 4.34968e9i 0.0415107 0.00731946i
\(879\) 6.40278e11 + 1.07956e11i 1.07254 + 0.180839i
\(880\) −2.85414e11 2.39491e11i −0.475932 0.399354i
\(881\) 5.35098e11 3.08939e11i 0.888238 0.512825i 0.0148725 0.999889i \(-0.495266\pi\)
0.873366 + 0.487065i \(0.161932\pi\)
\(882\) 1.71737e11 2.11013e11i 0.283786 0.348687i
\(883\) 4.02882e11 6.97813e11i 0.662728 1.14788i −0.317168 0.948369i \(-0.602732\pi\)
0.979896 0.199509i \(-0.0639348\pi\)
\(884\) −1.53423e11 4.21526e11i −0.251236 0.690264i
\(885\) −4.71030e11 + 3.53057e9i −0.767849 + 0.00575534i
\(886\) 7.99781e10 6.71096e10i 0.129788 0.108905i
\(887\) −1.44487e11 + 3.96974e11i −0.233418 + 0.641310i −1.00000 0.000836512i \(-0.999734\pi\)
0.766582 + 0.642147i \(0.221956\pi\)
\(888\) 6.42479e11 1.18258e11i 1.03325 0.190187i
\(889\) −7.31292e8 + 4.14736e9i −0.00117080 + 0.00663995i
\(890\) 1.62746e11i 0.259388i
\(891\) 3.10545e10 + 1.03549e12i 0.0492735 + 1.64299i
\(892\) 7.77205e11 1.22765
\(893\) 2.46537e11 + 4.34711e10i 0.387683 + 0.0683589i
\(894\) −1.45227e10 7.88994e10i −0.0227351 0.123516i
\(895\) 1.67862e11 + 6.10968e10i 0.261614 + 0.0952196i
\(896\) −4.10122e9 4.88765e9i −0.00636329 0.00758347i
\(897\) 9.80051e9 + 1.30753e12i 0.0151384 + 2.01968i
\(898\) −4.08370e11 + 1.48635e11i −0.627985 + 0.228568i
\(899\) 6.51641e11 + 3.76225e11i 0.997630 + 0.575982i
\(900\) 2.02009e10 1.25542e11i 0.0307893 0.191345i
\(901\) −8.43098e10 1.46029e11i −0.127932 0.221585i
\(902\) −2.85230e11 + 3.39924e11i −0.430893 + 0.513518i
\(903\) 9.43634e8 5.59659e9i 0.00141923 0.00841730i
\(904\) −3.80262e10 2.15658e11i −0.0569390 0.322917i
\(905\) −5.14893e11 + 9.07895e10i −0.767578 + 0.135345i
\(906\) 1.11071e11 1.34403e11i 0.164850 0.199478i
\(907\) −4.22135e11 3.54213e11i −0.623767 0.523402i 0.275218 0.961382i \(-0.411250\pi\)
−0.898985 + 0.437979i \(0.855694\pi\)
\(908\) 8.02215e11 4.63159e11i 1.18018 0.681376i
\(909\) 2.90843e11 + 3.36245e11i 0.425994 + 0.492494i
\(910\) 2.36493e9 4.09618e9i 0.00344868 0.00597329i
\(911\) −1.83317e11 5.03660e11i −0.266152 0.731247i −0.998721 0.0505544i \(-0.983901\pi\)
0.732569 0.680693i \(-0.238321\pi\)
\(912\) −1.75578e11 2.98914e11i −0.253800 0.432082i
\(913\) 9.73719e11 8.17047e11i 1.40136 1.17588i
\(914\) −4.04213e10 + 1.11057e11i −0.0579195 + 0.159133i
\(915\) 2.34308e11 6.59086e11i 0.334274 0.940280i
\(916\) −1.00902e11 + 5.72241e11i −0.143323 + 0.812825i
\(917\) 9.81125e8i 0.00138754i
\(918\) 1.29314e11 + 1.03643e11i 0.182086 + 0.145939i
\(919\) −4.66590e11 −0.654144 −0.327072 0.944999i \(-0.606062\pi\)
−0.327072 + 0.944999i \(0.606062\pi\)
\(920\) 5.64968e11 + 9.96191e10i 0.788628 + 0.139056i
\(921\) 3.01089e11 2.56514e11i 0.418462 0.356510i
\(922\) −8.20262e9 2.98551e9i −0.0113509 0.00413138i
\(923\) 3.54295e11 + 4.22233e11i 0.488156 + 0.581762i
\(924\) 8.26329e9 + 4.68858e9i 0.0113361 + 0.00643212i
\(925\) 2.17195e11 7.90525e10i 0.296676 0.107981i
\(926\) −2.18131e11 1.25938e11i −0.296670 0.171283i
\(927\) −3.42065e11 + 6.13533e11i −0.463222 + 0.830843i
\(928\) 5.05252e11 + 8.75123e11i 0.681266 + 1.17999i
\(929\) −2.51335e11 + 2.99530e11i −0.337435 + 0.402140i −0.907903 0.419180i \(-0.862318\pi\)
0.570468 + 0.821320i \(0.306762\pi\)
\(930\) −2.32709e11 + 8.66799e10i −0.311087 + 0.115874i
\(931\) −1.50477e11 8.53399e11i −0.200296 1.13593i
\(932\) 7.13941e11 1.25887e11i 0.946235 0.166847i
\(933\) 3.53560e11 + 9.49202e11i 0.466592 + 1.25266i
\(934\) 3.50201e11 + 2.93853e11i 0.460182 + 0.386139i
\(935\) 4.91303e11 2.83654e11i 0.642840 0.371144i
\(936\) −1.64985e10 1.10051e12i −0.0214952 1.43381i
\(937\) −6.00089e11 + 1.03938e12i −0.778497 + 1.34840i 0.154311 + 0.988022i \(0.450684\pi\)
−0.932808 + 0.360374i \(0.882649\pi\)
\(938\) 4.91642e8 + 1.35078e9i 0.000635094 + 0.00174491i
\(939\) 3.74389e11 6.59834e11i 0.481572 0.848735i
\(940\) −1.41689e11 + 1.18891e11i −0.181478 + 0.152278i
\(941\) 2.70127e11 7.42169e11i 0.344517 0.946551i −0.639550 0.768750i \(-0.720879\pi\)
0.984066 0.177802i \(-0.0568986\pi\)
\(942\) −3.00560e11 3.52789e11i −0.381704 0.448034i
\(943\) −1.41806e11 + 8.04224e11i −0.179328 + 1.01702i
\(944\) 3.04432e11i 0.383355i
\(945\) −1.55058e8 6.89466e9i −0.000194432 0.00864541i
\(946\) 5.08367e11 0.634764
\(947\) −5.11065e11 9.01145e10i −0.635442 0.112046i −0.153358 0.988171i \(-0.549009\pi\)
−0.482084 + 0.876125i \(0.660120\pi\)
\(948\) 6.35563e11 + 2.25946e11i 0.786911 + 0.279751i
\(949\) −1.13114e12 4.11702e11i −1.39461 0.507596i
\(950\) 6.59632e10 + 7.86118e10i 0.0809855 + 0.0965147i
\(951\) −7.68100e11 + 4.51173e11i −0.939065 + 0.551595i
\(952\) 3.21825e9 1.17135e9i 0.00391807 0.00142606i
\(953\) −3.61729e11 2.08844e11i −0.438543 0.253193i 0.264437 0.964403i \(-0.414814\pi\)
−0.702979 + 0.711210i \(0.748147\pi\)
\(954\) −3.45890e10 1.80315e11i −0.0417585 0.217690i
\(955\) 3.29394e11 + 5.70528e11i 0.396007 + 0.685904i
\(956\) 9.66565e10 1.15191e11i 0.115718 0.137907i
\(957\) −1.44280e12 1.19234e12i −1.72011 1.42151i
\(958\) −6.18474e10 3.50754e11i −0.0734277 0.416429i
\(959\) −9.06512e9 + 1.59842e9i −0.0107176 + 0.00188981i
\(960\) −1.22905e10 2.07229e9i −0.0144705 0.00243986i
\(961\) −1.82915e11 1.53484e11i −0.214464 0.179957i
\(962\) 7.68891e11 4.43919e11i 0.897769 0.518327i
\(963\) 1.54183e11 + 4.04636e11i 0.179280 + 0.470500i
\(964\) 1.22100e11 2.11483e11i 0.141386 0.244888i
\(965\) −3.39253e11 9.32089e11i −0.391214 1.07485i
\(966\) −4.43012e9 + 3.32056e7i −0.00508753 + 3.81331e-5i
\(967\) 4.30878e11 3.61550e11i 0.492775 0.413487i −0.362245 0.932083i \(-0.617990\pi\)
0.855020 + 0.518596i \(0.173545\pi\)
\(968\) −4.13116e11 + 1.13503e12i −0.470511 + 1.29272i
\(969\) 5.19126e11 9.55533e10i 0.588814 0.108380i
\(970\) 6.60224e10 3.74432e11i 0.0745769 0.422947i
\(971\) 4.33654e11i 0.487828i 0.969797 + 0.243914i \(0.0784315\pi\)
−0.969797 + 0.243914i \(0.921569\pi\)
\(972\) −3.78942e11 6.02981e11i −0.424530 0.675521i
\(973\) 1.19543e10 0.0133375
\(974\) 6.35282e10 + 1.12017e10i 0.0705879 + 0.0124466i
\(975\) −7.04937e10 3.82981e11i −0.0780067 0.423798i
\(976\) −4.24815e11 1.54620e11i −0.468166 0.170399i
\(977\) −2.82117e11 3.36214e11i −0.309636 0.369010i 0.588675 0.808370i \(-0.299650\pi\)
−0.898311 + 0.439360i \(0.855205\pi\)
\(978\) 2.34571e9 + 3.12953e11i 0.00256401 + 0.342077i
\(979\) −9.40762e11 + 3.42409e11i −1.02412 + 0.372748i
\(980\) 5.54476e11 + 3.20127e11i 0.601144 + 0.347070i
\(981\) −8.86711e11 + 3.37873e11i −0.957428 + 0.364820i
\(982\) 2.47136e11 + 4.28052e11i 0.265760 + 0.460311i
\(983\) 1.59758e11 1.90392e11i 0.171100 0.203909i −0.673680 0.739023i \(-0.735287\pi\)
0.844779 + 0.535115i \(0.179732\pi\)
\(984\) 1.14287e11 6.77823e11i 0.121903 0.722996i
\(985\) 1.66507e11 + 9.44309e11i 0.176884 + 1.00316i
\(986\) −2.94872e11 + 5.19938e10i −0.311979 + 0.0550103i
\(987\) 2.05036e9 2.48105e9i 0.00216053 0.00261437i
\(988\) −1.19176e12 1.00000e12i −1.25072 1.04948i
\(989\) 8.10224e11 4.67783e11i 0.846876 0.488944i
\(990\) 6.06655e11 1.16372e11i 0.631540 0.121146i
\(991\) −9.46761e11 + 1.63984e12i −0.981625 + 1.70022i −0.325557 + 0.945522i \(0.605552\pi\)
−0.656068 + 0.754702i \(0.727782\pi\)
\(992\) 2.82073e11 + 7.74988e11i 0.291282 + 0.800292i
\(993\) 7.45932e11 + 1.26991e12i 0.767189 + 1.30610i
\(994\) −1.43059e9 + 1.20040e9i −0.00146544 + 0.00122965i
\(995\) −2.87941e11 + 7.91110e11i −0.293772 + 0.807132i
\(996\) −2.92700e11 + 8.23337e11i −0.297431 + 0.836643i
\(997\) 1.58879e11 9.01049e11i 0.160800 0.911943i −0.792489 0.609886i \(-0.791215\pi\)
0.953290 0.302058i \(-0.0976735\pi\)
\(998\) 4.63329e11i 0.467054i
\(999\) 6.21889e11 1.13536e12i 0.624383 1.13991i
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 27.9.f.a.2.14 138
3.2 odd 2 81.9.f.a.8.10 138
27.13 even 9 81.9.f.a.71.10 138
27.14 odd 18 inner 27.9.f.a.14.14 yes 138
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.9.f.a.2.14 138 1.1 even 1 trivial
27.9.f.a.14.14 yes 138 27.14 odd 18 inner
81.9.f.a.8.10 138 3.2 odd 2
81.9.f.a.71.10 138 27.13 even 9