Properties

Label 27.9.f.a.2.15
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 2.15
Character \(\chi\) \(=\) 27.2
Dual form 27.9.f.a.14.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(13.3375 + 2.35175i) q^{2} +(34.9288 + 73.0820i) q^{3} +(-68.2042 - 24.8243i) q^{4} +(-636.805 - 758.914i) q^{5} +(293.990 + 1056.87i) q^{6} +(-2502.00 + 910.653i) q^{7} +(-3853.85 - 2225.02i) q^{8} +(-4120.96 + 5105.33i) q^{9} +(-6708.58 - 11619.6i) q^{10} +(15349.9 - 18293.3i) q^{11} +(-568.081 - 5851.58i) q^{12} +(4780.28 + 27110.3i) q^{13} +(-35511.9 + 6261.71i) q^{14} +(33220.2 - 73046.9i) q^{15} +(-31934.2 - 26796.0i) q^{16} +(-105956. + 61173.5i) q^{17} +(-66969.6 + 58400.7i) q^{18} +(-547.495 + 948.289i) q^{19} +(24593.2 + 67569.4i) q^{20} +(-153944. - 151043. i) q^{21} +(247750. - 207887. i) q^{22} +(50471.0 - 138668. i) q^{23} +(27998.7 - 359365. i) q^{24} +(-102599. + 581870. i) q^{25} +372825. i q^{26} +(-517048. - 122845. i) q^{27} +193253. q^{28} +(-924074. - 162939. i) q^{29} +(614861. - 896135. i) q^{30} +(131238. + 47766.6i) q^{31} +(369368. + 440196. i) q^{32} +(1.87306e6 + 482838. i) q^{33} +(-1.55704e6 + 566717. i) q^{34} +(2.28439e6 + 1.31889e6i) q^{35} +(407803. - 245905. i) q^{36} +(-379045. - 656525. i) q^{37} +(-9532.34 + 11360.2i) q^{38} +(-1.81431e6 + 1.29628e6i) q^{39} +(765550. + 4.34165e6i) q^{40} +(4.60079e6 - 811243. i) q^{41} +(-1.69801e6 - 2.37657e6i) q^{42} +(-1.82392e6 - 1.53045e6i) q^{43} +(-1.50104e6 + 866629. i) q^{44} +(6.49876e6 - 123645. i) q^{45} +(999268. - 1.73078e6i) q^{46} +(425686. + 1.16956e6i) q^{47} +(842880. - 3.26976e6i) q^{48} +(1.01461e6 - 851361. i) q^{49} +(-2.73683e6 + 7.51938e6i) q^{50} +(-8.17158e6 - 5.60673e6i) q^{51} +(346960. - 1.96771e6i) q^{52} -6.96711e6i q^{53} +(-6.60721e6 - 2.85441e6i) q^{54} -2.36579e7 q^{55} +(1.16686e7 + 2.05748e6i) q^{56} +(-88426.2 - 6889.44i) q^{57} +(-1.19416e7 - 4.34639e6i) q^{58} +(4.48304e6 + 5.34268e6i) q^{59} +(-4.07909e6 + 4.15744e6i) q^{60} +(-2.36882e7 + 8.62179e6i) q^{61} +(1.63804e6 + 945725. i) q^{62} +(5.66145e6 - 1.65263e7i) q^{63} +(9.22715e6 + 1.59819e7i) q^{64} +(1.75303e7 - 2.08918e7i) q^{65} +(2.38464e7 + 1.08448e7i) q^{66} +(-3.60777e6 - 2.04607e7i) q^{67} +(8.74520e6 - 1.54201e6i) q^{68} +(1.18970e7 - 1.15498e6i) q^{69} +(2.73663e7 + 2.29630e7i) q^{70} +(-1.06620e7 + 6.15572e6i) q^{71} +(2.72411e7 - 1.05060e7i) q^{72} +(3.50114e6 - 6.06416e6i) q^{73} +(-3.51151e6 - 9.64780e6i) q^{74} +(-4.61079e7 + 1.28258e7i) q^{75} +(60882.1 - 51086.1i) q^{76} +(-2.17466e7 + 5.97482e7i) q^{77} +(-2.72468e7 + 1.30223e7i) q^{78} +(2.79249e6 - 1.58370e7i) q^{79} +4.12991e7i q^{80} +(-9.08211e6 - 4.20777e7i) q^{81} +6.32706e7 q^{82} +(4.48356e6 + 790573. i) q^{83} +(6.75010e6 + 1.41233e7i) q^{84} +(1.13898e8 + 4.14556e7i) q^{85} +(-2.07272e7 - 2.47018e7i) q^{86} +(-2.03689e7 - 7.32244e7i) q^{87} +(-9.98592e7 + 3.63458e7i) q^{88} +(-3.86601e7 - 2.23204e7i) q^{89} +(8.69677e7 + 1.36344e7i) q^{90} +(-3.66484e7 - 6.34768e7i) q^{91} +(-6.88467e6 + 8.20483e6i) q^{92} +(1.09309e6 + 1.12595e7i) q^{93} +(2.92705e6 + 1.66001e7i) q^{94} +(1.06832e6 - 188373. i) q^{95} +(-1.92688e7 + 4.23697e7i) q^{96} +(1.19186e7 + 1.00009e7i) q^{97} +(1.55345e7 - 8.96887e6i) q^{98} +(3.01370e7 + 1.53752e8i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 13.3375 + 2.35175i 0.833591 + 0.146985i 0.574125 0.818768i \(-0.305342\pi\)
0.259466 + 0.965752i \(0.416453\pi\)
\(3\) 34.9288 + 73.0820i 0.431220 + 0.902247i
\(4\) −68.2042 24.8243i −0.266423 0.0969699i
\(5\) −636.805 758.914i −1.01889 1.21426i −0.976579 0.215158i \(-0.930973\pi\)
−0.0423083 0.999105i \(-0.513471\pi\)
\(6\) 293.990 + 1056.87i 0.226844 + 0.815488i
\(7\) −2502.00 + 910.653i −1.04207 + 0.379281i −0.805663 0.592375i \(-0.798191\pi\)
−0.236402 + 0.971655i \(0.575968\pi\)
\(8\) −3853.85 2225.02i −0.940882 0.543219i
\(9\) −4120.96 + 5105.33i −0.628099 + 0.778133i
\(10\) −6708.58 11619.6i −0.670858 1.16196i
\(11\) 15349.9 18293.3i 1.04842 1.24946i 0.0808814 0.996724i \(-0.474227\pi\)
0.967536 0.252732i \(-0.0813290\pi\)
\(12\) −568.081 5851.58i −0.0273959 0.282194i
\(13\) 4780.28 + 27110.3i 0.167371 + 0.949208i 0.946586 + 0.322451i \(0.104507\pi\)
−0.779215 + 0.626757i \(0.784382\pi\)
\(14\) −35511.9 + 6261.71i −0.924405 + 0.162997i
\(15\) 33220.2 73046.9i 0.656201 1.44290i
\(16\) −31934.2 26796.0i −0.487277 0.408874i
\(17\) −105956. + 61173.5i −1.26861 + 0.732432i −0.974725 0.223409i \(-0.928281\pi\)
−0.293885 + 0.955841i \(0.594948\pi\)
\(18\) −66969.6 + 58400.7i −0.637952 + 0.556324i
\(19\) −547.495 + 948.289i −0.00420113 + 0.00727656i −0.868118 0.496357i \(-0.834671\pi\)
0.863917 + 0.503634i \(0.168004\pi\)
\(20\) 24593.2 + 67569.4i 0.153708 + 0.422309i
\(21\) −153944. 151043.i −0.791564 0.776647i
\(22\) 247750. 207887.i 1.05760 0.887434i
\(23\) 50471.0 138668.i 0.180356 0.495524i −0.816264 0.577680i \(-0.803958\pi\)
0.996619 + 0.0821558i \(0.0261805\pi\)
\(24\) 27998.7 359365.i 0.0843905 1.08315i
\(25\) −102599. + 581870.i −0.262654 + 1.48959i
\(26\) 372825.i 0.815853i
\(27\) −517048. 122845.i −0.972917 0.231154i
\(28\) 193253. 0.314409
\(29\) −924074. 162939.i −1.30652 0.230374i −0.523313 0.852140i \(-0.675304\pi\)
−0.783203 + 0.621766i \(0.786415\pi\)
\(30\) 614861. 896135.i 0.759088 1.10634i
\(31\) 131238. + 47766.6i 0.142106 + 0.0517223i 0.412094 0.911141i \(-0.364798\pi\)
−0.269988 + 0.962864i \(0.587020\pi\)
\(32\) 369368. + 440196.i 0.352257 + 0.419804i
\(33\) 1.87306e6 + 482838.i 1.57942 + 0.407142i
\(34\) −1.55704e6 + 566717.i −1.16516 + 0.424083i
\(35\) 2.28439e6 + 1.31889e6i 1.52229 + 0.878897i
\(36\) 407803. 245905.i 0.242795 0.146406i
\(37\) −379045. 656525.i −0.202248 0.350303i 0.747005 0.664819i \(-0.231491\pi\)
−0.949252 + 0.314515i \(0.898158\pi\)
\(38\) −9532.34 + 11360.2i −0.00457157 + 0.00544818i
\(39\) −1.81431e6 + 1.29628e6i −0.784247 + 0.560327i
\(40\) 765550. + 4.34165e6i 0.299043 + 1.69596i
\(41\) 4.60079e6 811243.i 1.62816 0.287088i 0.716361 0.697730i \(-0.245806\pi\)
0.911797 + 0.410641i \(0.134695\pi\)
\(42\) −1.69801e6 2.37657e6i −0.545685 0.763754i
\(43\) −1.82392e6 1.53045e6i −0.533498 0.447658i 0.335810 0.941930i \(-0.390990\pi\)
−0.869307 + 0.494272i \(0.835435\pi\)
\(44\) −1.50104e6 + 866629.i −0.400482 + 0.231218i
\(45\) 6.49876e6 123645.i 1.58482 0.0301527i
\(46\) 999268. 1.73078e6i 0.223178 0.386555i
\(47\) 425686. + 1.16956e6i 0.0872365 + 0.239680i 0.975638 0.219387i \(-0.0704058\pi\)
−0.888401 + 0.459068i \(0.848184\pi\)
\(48\) 842880. 3.26976e6i 0.158782 0.615958i
\(49\) 1.01461e6 851361.i 0.176001 0.147683i
\(50\) −2.73683e6 + 7.51938e6i −0.437893 + 1.20310i
\(51\) −8.17158e6 5.60673e6i −1.20788 0.828760i
\(52\) 346960. 1.96771e6i 0.0474532 0.269121i
\(53\) 6.96711e6i 0.882977i −0.897267 0.441489i \(-0.854451\pi\)
0.897267 0.441489i \(-0.145549\pi\)
\(54\) −6.60721e6 2.85441e6i −0.777039 0.335692i
\(55\) −2.36579e7 −2.58539
\(56\) 1.16686e7 + 2.05748e6i 1.18649 + 0.209211i
\(57\) −88426.2 6889.44i −0.00837687 0.000652656i
\(58\) −1.19416e7 4.34639e6i −1.05524 0.384076i
\(59\) 4.48304e6 + 5.34268e6i 0.369968 + 0.440911i 0.918621 0.395139i \(-0.129304\pi\)
−0.548653 + 0.836050i \(0.684859\pi\)
\(60\) −4.07909e6 + 4.15744e6i −0.314745 + 0.320790i
\(61\) −2.36882e7 + 8.62179e6i −1.71085 + 0.622699i −0.996986 0.0775852i \(-0.975279\pi\)
−0.713865 + 0.700284i \(0.753057\pi\)
\(62\) 1.63804e6 + 945725.i 0.110856 + 0.0640026i
\(63\) 5.66145e6 1.65263e7i 0.359389 1.04909i
\(64\) 9.22715e6 + 1.59819e7i 0.549981 + 0.952595i
\(65\) 1.75303e7 2.08918e7i 0.982056 1.17037i
\(66\) 2.38464e7 + 1.08448e7i 1.25674 + 0.571540i
\(67\) −3.60777e6 2.04607e7i −0.179036 1.01536i −0.933382 0.358885i \(-0.883157\pi\)
0.754346 0.656477i \(-0.227954\pi\)
\(68\) 8.74520e6 1.54201e6i 0.409010 0.0721195i
\(69\) 1.18970e7 1.15498e6i 0.524858 0.0509540i
\(70\) 2.73663e7 + 2.29630e7i 1.13979 + 0.956394i
\(71\) −1.06620e7 + 6.15572e6i −0.419571 + 0.242240i −0.694894 0.719112i \(-0.744549\pi\)
0.275323 + 0.961352i \(0.411215\pi\)
\(72\) 2.72411e7 1.05060e7i 1.01366 0.390937i
\(73\) 3.50114e6 6.06416e6i 0.123287 0.213540i −0.797775 0.602956i \(-0.793990\pi\)
0.921062 + 0.389415i \(0.127323\pi\)
\(74\) −3.51151e6 9.64780e6i −0.117103 0.321737i
\(75\) −4.61079e7 + 1.28258e7i −1.45724 + 0.405360i
\(76\) 60882.1 51086.1i 0.00182488 0.00153126i
\(77\) −2.17466e7 + 5.97482e7i −0.618625 + 1.69966i
\(78\) −2.72468e7 + 1.30223e7i −0.736101 + 0.351812i
\(79\) 2.79249e6 1.58370e7i 0.0716941 0.406598i −0.927748 0.373207i \(-0.878258\pi\)
0.999442 0.0333910i \(-0.0106306\pi\)
\(80\) 4.12991e7i 1.00828i
\(81\) −9.08211e6 4.20777e7i −0.210983 0.977490i
\(82\) 6.32706e7 1.39942
\(83\) 4.48356e6 + 790573.i 0.0944737 + 0.0166583i 0.220685 0.975345i \(-0.429171\pi\)
−0.126211 + 0.992003i \(0.540282\pi\)
\(84\) 6.75010e6 + 1.41233e7i 0.135579 + 0.283674i
\(85\) 1.13898e8 + 4.14556e7i 2.18194 + 0.794159i
\(86\) −2.07272e7 2.47018e7i −0.378920 0.451579i
\(87\) −2.03689e7 7.32244e7i −0.355541 1.27814i
\(88\) −9.98592e7 + 3.63458e7i −1.66517 + 0.606071i
\(89\) −3.86601e7 2.23204e7i −0.616174 0.355748i 0.159204 0.987246i \(-0.449107\pi\)
−0.775378 + 0.631497i \(0.782441\pi\)
\(90\) 8.69677e7 + 1.36344e7i 1.32552 + 0.207809i
\(91\) −3.66484e7 6.34768e7i −0.534428 0.925656i
\(92\) −6.88467e6 + 8.20483e6i −0.0961018 + 0.114530i
\(93\) 1.09309e6 + 1.12595e7i 0.0146125 + 0.150518i
\(94\) 2.92705e6 + 1.66001e7i 0.0374903 + 0.212618i
\(95\) 1.06832e6 188373.i 0.0131161 0.00231273i
\(96\) −1.92688e7 + 4.23697e7i −0.226866 + 0.498850i
\(97\) 1.19186e7 + 1.00009e7i 0.134629 + 0.112967i 0.707616 0.706598i \(-0.249771\pi\)
−0.572987 + 0.819565i \(0.694215\pi\)
\(98\) 1.55345e7 8.96887e6i 0.168420 0.0972374i
\(99\) 3.01370e7 + 1.53752e8i 0.313733 + 1.60059i
\(100\) 2.14422e7 3.71390e7i 0.214422 0.371390i
\(101\) −5.97338e7 1.64117e8i −0.574030 1.57714i −0.798076 0.602557i \(-0.794149\pi\)
0.224046 0.974579i \(-0.428073\pi\)
\(102\) −9.58024e7 9.39970e7i −0.885066 0.868387i
\(103\) 6.03092e7 5.06054e7i 0.535839 0.449623i −0.334273 0.942476i \(-0.608491\pi\)
0.870112 + 0.492854i \(0.164046\pi\)
\(104\) 4.18986e7 1.15116e8i 0.358151 0.984012i
\(105\) −1.65964e7 + 2.13015e8i −0.136539 + 1.75248i
\(106\) 1.63849e7 9.29236e7i 0.129784 0.736042i
\(107\) 6.15134e7i 0.469283i 0.972082 + 0.234641i \(0.0753916\pi\)
−0.972082 + 0.234641i \(0.924608\pi\)
\(108\) 3.22153e7 + 2.12139e7i 0.236792 + 0.155928i
\(109\) −2.02005e7 −0.143105 −0.0715526 0.997437i \(-0.522795\pi\)
−0.0715526 + 0.997437i \(0.522795\pi\)
\(110\) −3.15536e8 5.56376e7i −2.15516 0.380012i
\(111\) 3.47406e7 5.06330e7i 0.228847 0.333535i
\(112\) 1.04301e8 + 3.79625e7i 0.662852 + 0.241258i
\(113\) 7.22019e7 + 8.60469e7i 0.442828 + 0.527742i 0.940578 0.339579i \(-0.110285\pi\)
−0.497750 + 0.867321i \(0.665840\pi\)
\(114\) −1.16318e6 299844.i −0.00688695 0.00177532i
\(115\) −1.37377e8 + 5.00012e7i −0.785459 + 0.285884i
\(116\) 5.89809e7 + 3.40526e7i 0.325746 + 0.188070i
\(117\) −1.58107e8 8.73156e7i −0.843736 0.465960i
\(118\) 4.72277e7 + 8.18007e7i 0.243595 + 0.421919i
\(119\) 2.09393e8 2.49545e8i 1.04418 1.24440i
\(120\) −2.90557e8 + 2.07597e8i −1.40122 + 1.00114i
\(121\) −6.18021e7 3.50497e8i −0.288311 1.63510i
\(122\) −3.36216e8 + 5.92840e7i −1.51768 + 0.267607i
\(123\) 2.19987e8 + 3.07899e8i 0.961118 + 1.34520i
\(124\) −7.76519e6 6.51577e6i −0.0328447 0.0275600i
\(125\) 1.71783e8 9.91787e7i 0.703622 0.406236i
\(126\) 1.14375e8 2.07104e8i 0.453784 0.821689i
\(127\) −1.22668e8 + 2.12467e8i −0.471536 + 0.816725i −0.999470 0.0325610i \(-0.989634\pi\)
0.527934 + 0.849286i \(0.322967\pi\)
\(128\) 3.51679e7 + 9.66229e7i 0.131011 + 0.359948i
\(129\) 4.81411e7 1.86753e8i 0.173843 0.674385i
\(130\) 2.82942e8 2.37417e8i 0.990660 0.831262i
\(131\) −1.43812e8 + 3.95121e8i −0.488327 + 1.34167i 0.413867 + 0.910337i \(0.364178\pi\)
−0.902194 + 0.431330i \(0.858045\pi\)
\(132\) −1.15765e8 7.94291e7i −0.381312 0.261628i
\(133\) 506269. 2.87120e6i 0.00161799 0.00917606i
\(134\) 2.81378e8i 0.872713i
\(135\) 2.36030e8 + 4.70623e8i 0.710611 + 1.41690i
\(136\) 5.44450e8 1.59148
\(137\) 3.65675e8 + 6.44783e7i 1.03804 + 0.183034i 0.666593 0.745422i \(-0.267752\pi\)
0.371444 + 0.928456i \(0.378863\pi\)
\(138\) 1.61392e8 + 1.25743e7i 0.445006 + 0.0346712i
\(139\) −3.96654e8 1.44370e8i −1.06256 0.386739i −0.249169 0.968460i \(-0.580158\pi\)
−0.813389 + 0.581721i \(0.802380\pi\)
\(140\) −1.23064e8 1.46663e8i −0.320347 0.381775i
\(141\) −7.06054e7 + 7.19615e7i −0.178633 + 0.182064i
\(142\) −1.56681e8 + 5.70272e7i −0.385357 + 0.140258i
\(143\) 5.69314e8 + 3.28693e8i 1.36147 + 0.786044i
\(144\) 2.68402e8 5.26095e7i 0.624216 0.122353i
\(145\) 4.64798e8 + 8.05053e8i 1.05146 + 1.82118i
\(146\) 6.09578e7 7.26467e7i 0.134158 0.159884i
\(147\) 9.76583e7 + 4.44129e7i 0.209141 + 0.0951129i
\(148\) 9.55468e6 + 5.41873e7i 0.0199145 + 0.112941i
\(149\) −4.73599e8 + 8.35083e7i −0.960873 + 0.169428i −0.632019 0.774953i \(-0.717773\pi\)
−0.328854 + 0.944381i \(0.606662\pi\)
\(150\) −6.45125e8 + 6.26298e7i −1.27432 + 0.123713i
\(151\) −3.88229e8 3.25763e8i −0.746758 0.626605i 0.187885 0.982191i \(-0.439837\pi\)
−0.934643 + 0.355586i \(0.884281\pi\)
\(152\) 4.21993e6 2.43638e6i 0.00790553 0.00456426i
\(153\) 1.24328e8 7.93031e8i 0.226883 1.44719i
\(154\) −4.30557e8 + 7.45746e8i −0.765504 + 1.32589i
\(155\) −4.73220e7 1.30016e8i −0.0819854 0.225253i
\(156\) 1.55923e8 4.33731e7i 0.263276 0.0732356i
\(157\) −3.53896e8 + 2.96954e8i −0.582475 + 0.488755i −0.885759 0.464146i \(-0.846361\pi\)
0.303284 + 0.952900i \(0.401917\pi\)
\(158\) 7.44895e7 2.04658e8i 0.119527 0.328398i
\(159\) 5.09171e8 2.43353e8i 0.796663 0.380757i
\(160\) 9.88555e7 5.60638e8i 0.150842 0.855465i
\(161\) 3.92908e8i 0.584774i
\(162\) −2.21759e7 5.82569e8i −0.0321974 0.845838i
\(163\) −4.56114e8 −0.646134 −0.323067 0.946376i \(-0.604714\pi\)
−0.323067 + 0.946376i \(0.604714\pi\)
\(164\) −3.33932e8 5.88811e7i −0.461617 0.0813956i
\(165\) −8.26342e8 1.72897e9i −1.11487 2.33266i
\(166\) 5.79401e7 + 2.10885e7i 0.0763040 + 0.0277724i
\(167\) 1.61471e8 + 1.92434e8i 0.207601 + 0.247409i 0.859791 0.510647i \(-0.170594\pi\)
−0.652190 + 0.758056i \(0.726150\pi\)
\(168\) 2.57204e8 + 9.24627e8i 0.322879 + 1.16073i
\(169\) 5.44170e7 1.98062e7i 0.0667095 0.0242803i
\(170\) 1.42162e9 + 8.20774e8i 1.70211 + 0.982715i
\(171\) −2.58513e6 6.70300e6i −0.00302341 0.00783944i
\(172\) 8.64068e7 + 1.49661e8i 0.0987265 + 0.170999i
\(173\) −7.42345e8 + 8.84693e8i −0.828746 + 0.987661i 0.171251 + 0.985227i \(0.445219\pi\)
−0.999997 + 0.00243395i \(0.999225\pi\)
\(174\) −9.94630e7 1.02453e9i −0.108509 1.11771i
\(175\) −2.73178e8 1.54927e9i −0.291269 1.65187i
\(176\) −9.80372e8 + 1.72866e8i −1.02174 + 0.180160i
\(177\) −2.33866e8 + 5.14243e8i −0.238273 + 0.523932i
\(178\) −4.63136e8 3.88617e8i −0.461348 0.387117i
\(179\) 6.53835e8 3.77492e8i 0.636878 0.367702i −0.146533 0.989206i \(-0.546811\pi\)
0.783411 + 0.621504i \(0.213478\pi\)
\(180\) −4.46312e8 1.52894e8i −0.425156 0.145647i
\(181\) 1.14593e8 1.98480e8i 0.106768 0.184928i −0.807691 0.589606i \(-0.799283\pi\)
0.914459 + 0.404678i \(0.132616\pi\)
\(182\) −3.39514e8 9.32808e8i −0.309437 0.850171i
\(183\) −1.45750e9 1.43003e9i −1.29958 1.27509i
\(184\) −5.03047e8 + 4.22107e8i −0.438872 + 0.368257i
\(185\) −2.56869e8 + 7.05741e8i −0.219293 + 0.602502i
\(186\) −1.19006e7 + 1.52744e8i −0.00994298 + 0.127619i
\(187\) −5.07342e8 + 2.87728e9i −0.414891 + 2.35297i
\(188\) 9.03366e7i 0.0723156i
\(189\) 1.40552e9 1.63494e8i 1.10152 0.128131i
\(190\) 1.46916e7 0.0112734
\(191\) −9.71028e7 1.71218e7i −0.0729623 0.0128652i 0.137048 0.990564i \(-0.456239\pi\)
−0.210010 + 0.977699i \(0.567350\pi\)
\(192\) −8.45696e8 + 1.23257e9i −0.622313 + 0.906996i
\(193\) 2.38182e9 + 8.66911e8i 1.71664 + 0.624806i 0.997540 0.0700985i \(-0.0223314\pi\)
0.719102 + 0.694905i \(0.244554\pi\)
\(194\) 1.35444e8 + 1.61416e8i 0.0956211 + 0.113957i
\(195\) 2.13913e9 + 5.51425e8i 1.47944 + 0.381371i
\(196\) −9.03352e7 + 3.28793e7i −0.0612115 + 0.0222792i
\(197\) 3.70754e8 + 2.14055e8i 0.246162 + 0.142122i 0.618006 0.786174i \(-0.287941\pi\)
−0.371843 + 0.928295i \(0.621274\pi\)
\(198\) 4.03642e7 + 2.12154e9i 0.0262625 + 1.38035i
\(199\) 4.87197e8 + 8.43850e8i 0.310665 + 0.538088i 0.978507 0.206216i \(-0.0661149\pi\)
−0.667842 + 0.744303i \(0.732782\pi\)
\(200\) 1.69008e9 2.01416e9i 1.05630 1.25885i
\(201\) 1.36929e9 9.78331e8i 0.838904 0.599379i
\(202\) −4.10734e8 2.32939e9i −0.246692 1.39906i
\(203\) 2.46041e9 4.33837e8i 1.44885 0.255472i
\(204\) 4.18153e8 + 5.85256e8i 0.241443 + 0.337929i
\(205\) −3.54547e9 2.97500e9i −2.00751 1.68450i
\(206\) 9.23383e8 5.33115e8i 0.512759 0.296041i
\(207\) 4.99957e8 + 8.29116e8i 0.272302 + 0.451579i
\(208\) 5.73793e8 9.93838e8i 0.306550 0.530961i
\(209\) 8.94333e6 + 2.45716e7i 0.00468721 + 0.0128780i
\(210\) −7.22313e8 + 2.80205e9i −0.371406 + 1.44078i
\(211\) −1.10978e9 + 9.31219e8i −0.559897 + 0.469809i −0.878276 0.478154i \(-0.841306\pi\)
0.318379 + 0.947964i \(0.396862\pi\)
\(212\) −1.72954e8 + 4.75187e8i −0.0856222 + 0.235245i
\(213\) −8.22283e8 5.64190e8i −0.399487 0.274099i
\(214\) −1.44664e8 + 8.20432e8i −0.0689773 + 0.391190i
\(215\) 2.35880e9i 1.10392i
\(216\) 1.71930e9 + 1.62387e9i 0.789833 + 0.745996i
\(217\) −3.71855e8 −0.167701
\(218\) −2.69423e8 4.75066e7i −0.119291 0.0210343i
\(219\) 5.65472e8 + 4.40569e7i 0.245830 + 0.0191530i
\(220\) 1.61357e9 + 5.87291e8i 0.688806 + 0.250705i
\(221\) −2.16493e9 2.58006e9i −0.907559 1.08159i
\(222\) 5.82427e8 5.93614e8i 0.239789 0.244395i
\(223\) 9.28127e8 3.37811e8i 0.375308 0.136601i −0.147477 0.989065i \(-0.547115\pi\)
0.522785 + 0.852464i \(0.324893\pi\)
\(224\) −1.32502e9 7.65003e8i −0.526298 0.303858i
\(225\) −2.54783e9 2.92167e9i −0.994124 1.13999i
\(226\) 7.60629e8 + 1.31745e9i 0.291568 + 0.505010i
\(227\) 4.10560e8 4.89286e8i 0.154623 0.184272i −0.683172 0.730257i \(-0.739400\pi\)
0.837795 + 0.545985i \(0.183845\pi\)
\(228\) 5.86001e6 + 2.66501e6i 0.00216850 + 0.000986187i
\(229\) 1.06279e8 + 6.02738e8i 0.0386460 + 0.219173i 0.998015 0.0629834i \(-0.0200615\pi\)
−0.959369 + 0.282156i \(0.908950\pi\)
\(230\) −1.94985e9 + 3.43812e8i −0.696772 + 0.122860i
\(231\) −5.12610e9 + 4.97649e8i −1.80028 + 0.174774i
\(232\) 3.19870e9 + 2.68403e9i 1.10413 + 0.926479i
\(233\) −3.04859e9 + 1.76010e9i −1.03437 + 0.597192i −0.918233 0.396041i \(-0.870384\pi\)
−0.116134 + 0.993234i \(0.537050\pi\)
\(234\) −1.90340e9 1.53640e9i −0.634842 0.512436i
\(235\) 6.16520e8 1.06784e9i 0.202151 0.350135i
\(236\) −1.73134e8 4.75681e8i −0.0558128 0.153344i
\(237\) 1.25494e9 3.49087e8i 0.397767 0.110647i
\(238\) 3.37963e9 2.83585e9i 1.05332 0.883844i
\(239\) −1.07538e9 + 2.95458e9i −0.329587 + 0.905533i 0.658629 + 0.752468i \(0.271137\pi\)
−0.988216 + 0.153065i \(0.951086\pi\)
\(240\) −3.01822e9 + 1.44253e9i −0.909716 + 0.434789i
\(241\) 6.25199e8 3.54568e9i 0.185332 1.05107i −0.740196 0.672391i \(-0.765267\pi\)
0.925528 0.378679i \(-0.123622\pi\)
\(242\) 4.82009e9i 1.40538i
\(243\) 2.75790e9 2.13346e9i 0.790957 0.611871i
\(244\) 1.82966e9 0.516192
\(245\) −1.29222e9 2.27853e8i −0.358651 0.0632398i
\(246\) 2.20997e9 + 4.62395e9i 0.603456 + 1.26262i
\(247\) −2.83256e7 1.03097e7i −0.00761012 0.00276986i
\(248\) −3.99489e8 4.76093e8i −0.105608 0.125859i
\(249\) 9.88288e7 + 3.55282e8i 0.0257091 + 0.0924220i
\(250\) 2.52439e9 9.18802e8i 0.646243 0.235213i
\(251\) −1.40741e9 8.12567e8i −0.354589 0.204722i 0.312116 0.950044i \(-0.398962\pi\)
−0.666705 + 0.745322i \(0.732296\pi\)
\(252\) −7.96388e8 + 9.86621e8i −0.197480 + 0.244652i
\(253\) −1.76197e9 3.05182e9i −0.430047 0.744863i
\(254\) −2.13574e9 + 2.54528e9i −0.513114 + 0.611506i
\(255\) 9.48673e8 + 9.77192e9i 0.224365 + 2.31110i
\(256\) −5.78550e8 3.28112e9i −0.134704 0.763945i
\(257\) 5.64879e8 9.96034e7i 0.129486 0.0228319i −0.108530 0.994093i \(-0.534614\pi\)
0.238016 + 0.971261i \(0.423503\pi\)
\(258\) 1.08128e9 2.37759e9i 0.244038 0.536609i
\(259\) 1.54624e9 + 1.29745e9i 0.343619 + 0.288330i
\(260\) −1.71427e9 + 9.89732e8i −0.375133 + 0.216583i
\(261\) 4.63993e9 4.04624e9i 0.999883 0.871946i
\(262\) −2.84732e9 + 4.93170e9i −0.604269 + 1.04663i
\(263\) −2.40422e9 6.60554e9i −0.502517 1.38065i −0.888809 0.458278i \(-0.848466\pi\)
0.386292 0.922377i \(-0.373756\pi\)
\(264\) −6.14418e9 6.02840e9i −1.26488 1.24104i
\(265\) −5.28744e9 + 4.43669e9i −1.07217 + 0.899654i
\(266\) 1.35047e7 3.71038e7i 0.00269748 0.00741126i
\(267\) 2.80871e8 3.60499e9i 0.0552664 0.709347i
\(268\) −2.61857e8 + 1.48507e9i −0.0507604 + 0.287877i
\(269\) 8.50405e9i 1.62411i −0.583578 0.812057i \(-0.698348\pi\)
0.583578 0.812057i \(-0.301652\pi\)
\(270\) 2.04125e9 + 6.83200e9i 0.384097 + 1.28556i
\(271\) 3.66496e9 0.679504 0.339752 0.940515i \(-0.389657\pi\)
0.339752 + 0.940515i \(0.389657\pi\)
\(272\) 5.02280e9 + 8.85656e8i 0.917636 + 0.161804i
\(273\) 3.35893e9 4.89550e9i 0.604715 0.881347i
\(274\) 4.72554e9 + 1.71995e9i 0.838395 + 0.305151i
\(275\) 9.06942e9 + 1.08085e10i 1.58580 + 1.88988i
\(276\) −8.40098e8 2.16561e8i −0.144775 0.0373201i
\(277\) −7.34026e9 + 2.67163e9i −1.24679 + 0.453793i −0.879315 0.476241i \(-0.841999\pi\)
−0.367472 + 0.930035i \(0.619777\pi\)
\(278\) −4.95083e9 2.85836e9i −0.828894 0.478562i
\(279\) −7.84690e8 + 4.73168e8i −0.129503 + 0.0780906i
\(280\) −5.86914e9 1.01657e10i −0.954866 1.65388i
\(281\) −1.00634e9 + 1.19931e9i −0.161405 + 0.192356i −0.840686 0.541524i \(-0.817848\pi\)
0.679280 + 0.733879i \(0.262292\pi\)
\(282\) −1.11093e9 + 7.93737e8i −0.175667 + 0.125511i
\(283\) 1.38681e9 + 7.86497e9i 0.216207 + 1.22617i 0.878799 + 0.477192i \(0.158345\pi\)
−0.662592 + 0.748980i \(0.730544\pi\)
\(284\) 8.80006e8 1.55169e8i 0.135273 0.0238523i
\(285\) 5.10817e7 + 7.14951e7i 0.00774259 + 0.0108367i
\(286\) 6.82019e9 + 5.72282e9i 1.01937 + 0.855354i
\(287\) −1.07724e10 + 6.21945e9i −1.58776 + 0.916693i
\(288\) −3.76950e9 + 7.17182e7i −0.547915 + 0.0104246i
\(289\) 3.99650e9 6.92215e9i 0.572913 0.992315i
\(290\) 4.30593e9 + 1.18305e10i 0.608801 + 1.67267i
\(291\) −3.14583e8 + 1.22036e9i −0.0438696 + 0.170182i
\(292\) −3.89331e8 + 3.26688e8i −0.0535535 + 0.0449367i
\(293\) 3.64627e9 1.00180e10i 0.494741 1.35929i −0.401555 0.915835i \(-0.631530\pi\)
0.896296 0.443456i \(-0.146248\pi\)
\(294\) 1.19807e9 + 8.22023e8i 0.160358 + 0.110026i
\(295\) 1.19981e9 6.80448e9i 0.158426 0.898477i
\(296\) 3.37354e9i 0.439459i
\(297\) −1.01839e10 + 7.57285e9i −1.30884 + 0.973270i
\(298\) −6.51300e9 −0.825878
\(299\) 4.00060e9 + 7.05414e8i 0.500542 + 0.0882590i
\(300\) 3.46314e9 + 2.69820e8i 0.427549 + 0.0333111i
\(301\) 5.95716e9 + 2.16823e9i 0.725727 + 0.264143i
\(302\) −4.41187e9 5.25787e9i −0.530390 0.632094i
\(303\) 9.90759e9 1.00979e10i 1.17543 1.19801i
\(304\) 4.28941e7 1.56122e7i 0.00502231 0.00182797i
\(305\) 2.16279e10 + 1.24869e10i 2.49928 + 1.44296i
\(306\) 3.52323e9 1.02846e10i 0.401842 1.17301i
\(307\) −1.42521e9 2.46854e9i −0.160445 0.277899i 0.774583 0.632472i \(-0.217960\pi\)
−0.935028 + 0.354573i \(0.884626\pi\)
\(308\) 2.96641e9 3.53523e9i 0.329632 0.392840i
\(309\) 5.80487e9 + 2.63993e9i 0.636735 + 0.289573i
\(310\) −3.25390e8 1.84538e9i −0.0352336 0.199820i
\(311\) 1.12462e10 1.98300e9i 1.20216 0.211974i 0.463529 0.886082i \(-0.346583\pi\)
0.738633 + 0.674108i \(0.235472\pi\)
\(312\) 9.87634e9 9.58811e8i 1.04226 0.101185i
\(313\) 3.45161e9 + 2.89625e9i 0.359621 + 0.301758i 0.804639 0.593764i \(-0.202359\pi\)
−0.445019 + 0.895521i \(0.646803\pi\)
\(314\) −5.41844e9 + 3.12834e9i −0.557386 + 0.321807i
\(315\) −1.61473e10 + 6.22747e9i −1.64005 + 0.632513i
\(316\) −5.83602e8 + 1.01083e9i −0.0585287 + 0.101375i
\(317\) 1.83180e9 + 5.03284e9i 0.181402 + 0.498398i 0.996749 0.0805754i \(-0.0256758\pi\)
−0.815347 + 0.578973i \(0.803454\pi\)
\(318\) 7.36335e9 2.04827e9i 0.720057 0.200298i
\(319\) −1.71651e10 + 1.44032e10i −1.65762 + 1.39091i
\(320\) 6.25299e9 1.71800e10i 0.596332 1.63841i
\(321\) −4.49552e9 + 2.14859e9i −0.423409 + 0.202364i
\(322\) −9.24024e8 + 5.24040e9i −0.0859527 + 0.487462i
\(323\) 1.33969e8i 0.0123082i
\(324\) −4.25112e8 + 3.09534e9i −0.0385765 + 0.280884i
\(325\) −1.62651e10 −1.45789
\(326\) −6.08340e9 1.07267e9i −0.538612 0.0949718i
\(327\) −7.05578e8 1.47629e9i −0.0617098 0.129116i
\(328\) −1.95358e10 7.11045e9i −1.68786 0.614330i
\(329\) −2.13013e9 2.53859e9i −0.181812 0.216675i
\(330\) −6.95520e9 2.50034e10i −0.586481 2.10835i
\(331\) −3.90947e9 + 1.42293e9i −0.325691 + 0.118542i −0.499691 0.866204i \(-0.666553\pi\)
0.174000 + 0.984746i \(0.444331\pi\)
\(332\) −2.86173e8 1.65222e8i −0.0235546 0.0135992i
\(333\) 4.91381e9 + 7.70362e8i 0.399614 + 0.0626496i
\(334\) 1.70106e9 + 2.94632e9i 0.136689 + 0.236752i
\(335\) −1.32305e10 + 1.57675e10i −1.05050 + 1.25194i
\(336\) 8.68736e8 + 8.94851e9i 0.0681601 + 0.702092i
\(337\) −1.67135e9 9.47871e9i −0.129583 0.734902i −0.978480 0.206343i \(-0.933844\pi\)
0.848897 0.528559i \(-0.177267\pi\)
\(338\) 7.72364e8 1.36189e8i 0.0591773 0.0104346i
\(339\) −3.76656e9 + 8.28218e9i −0.285197 + 0.627113i
\(340\) −6.73924e9 5.65490e9i −0.504307 0.423164i
\(341\) 2.88829e9 1.66756e9i 0.213611 0.123328i
\(342\) −1.87152e7 9.54806e7i −0.00136801 0.00697928i
\(343\) 5.91133e9 1.02387e10i 0.427080 0.739724i
\(344\) 3.62384e9 + 9.95641e9i 0.258782 + 0.710999i
\(345\) −8.45261e9 8.29332e9i −0.596643 0.585399i
\(346\) −1.19816e10 + 1.00537e10i −0.836007 + 0.701493i
\(347\) −6.87957e7 + 1.89015e8i −0.00474508 + 0.0130370i −0.942043 0.335493i \(-0.891097\pi\)
0.937297 + 0.348530i \(0.113319\pi\)
\(348\) −4.28503e8 + 5.49986e9i −0.0292171 + 0.375003i
\(349\) 2.82255e9 1.60075e10i 0.190257 1.07900i −0.728756 0.684773i \(-0.759901\pi\)
0.919013 0.394227i \(-0.128988\pi\)
\(350\) 2.13058e10i 1.41979i
\(351\) 8.58729e8 1.46046e10i 0.0565754 0.962189i
\(352\) 1.37224e10 0.893838
\(353\) 5.10574e9 + 9.00279e8i 0.328821 + 0.0579800i 0.335622 0.941997i \(-0.391054\pi\)
−0.00680064 + 0.999977i \(0.502165\pi\)
\(354\) −4.32856e9 + 6.30869e9i −0.275632 + 0.401723i
\(355\) 1.14613e10 + 4.17157e9i 0.721639 + 0.262655i
\(356\) 2.08270e9 + 2.48206e9i 0.129666 + 0.154530i
\(357\) 2.55511e10 + 6.58655e9i 1.57303 + 0.405495i
\(358\) 9.60827e9 3.49712e9i 0.584942 0.212902i
\(359\) −2.29627e10 1.32575e10i −1.38244 0.798151i −0.389991 0.920819i \(-0.627522\pi\)
−0.992448 + 0.122668i \(0.960855\pi\)
\(360\) −2.53204e10 1.39834e10i −1.50751 0.832534i
\(361\) 8.49118e9 + 1.47072e10i 0.499965 + 0.865964i
\(362\) 1.99515e9 2.37773e9i 0.116183 0.138461i
\(363\) 2.34564e10 1.67591e10i 1.35093 0.965213i
\(364\) 9.23805e8 + 5.23916e9i 0.0526229 + 0.298439i
\(365\) −6.83172e9 + 1.20462e9i −0.384910 + 0.0678700i
\(366\) −1.60762e10 2.25006e10i −0.895900 1.25392i
\(367\) 2.18128e10 + 1.83031e10i 1.20239 + 1.00893i 0.999558 + 0.0297143i \(0.00945975\pi\)
0.202834 + 0.979213i \(0.434985\pi\)
\(368\) −5.32749e9 + 3.07583e9i −0.290490 + 0.167714i
\(369\) −1.48180e10 + 2.68316e10i −0.799252 + 1.44724i
\(370\) −5.08570e9 + 8.80870e9i −0.271359 + 0.470007i
\(371\) 6.34462e9 + 1.74317e10i 0.334896 + 0.920120i
\(372\) 2.04957e8 7.95084e8i 0.0107026 0.0415185i
\(373\) 2.43295e9 2.04149e9i 0.125689 0.105466i −0.577776 0.816195i \(-0.696079\pi\)
0.703465 + 0.710729i \(0.251635\pi\)
\(374\) −1.35333e10 + 3.71825e10i −0.691700 + 1.90043i
\(375\) 1.32483e10 + 9.09002e9i 0.669941 + 0.459663i
\(376\) 9.61774e8 5.45449e9i 0.0481196 0.272900i
\(377\) 2.58308e10i 1.27871i
\(378\) 1.91306e10 + 1.12485e9i 0.937047 + 0.0550971i
\(379\) −2.63613e10 −1.27764 −0.638822 0.769354i \(-0.720578\pi\)
−0.638822 + 0.769354i \(0.720578\pi\)
\(380\) −7.75400e7 1.36724e7i −0.00371870 0.000655707i
\(381\) −1.98121e10 1.54360e9i −0.940223 0.0732544i
\(382\) −1.25484e9 4.56724e8i −0.0589297 0.0214487i
\(383\) 5.71089e9 + 6.80598e9i 0.265405 + 0.316297i 0.882244 0.470792i \(-0.156032\pi\)
−0.616839 + 0.787089i \(0.711587\pi\)
\(384\) −5.83303e9 + 5.94506e9i −0.268268 + 0.273421i
\(385\) 5.91920e10 2.15441e10i 2.69414 0.980587i
\(386\) 2.97287e10 + 1.71639e10i 1.33914 + 0.773153i
\(387\) 1.53298e10 3.00480e9i 0.683427 0.133959i
\(388\) −5.64634e8 9.77975e8i −0.0249138 0.0431520i
\(389\) 3.83291e9 4.56788e9i 0.167390 0.199488i −0.675828 0.737059i \(-0.736214\pi\)
0.843218 + 0.537572i \(0.180658\pi\)
\(390\) 2.72337e10 + 1.23853e10i 1.17720 + 0.535363i
\(391\) 3.13511e9 + 1.77801e10i 0.134136 + 0.760725i
\(392\) −5.80446e9 + 1.02348e9i −0.245820 + 0.0433448i
\(393\) −3.38994e10 + 3.29101e9i −1.42109 + 0.137962i
\(394\) 4.44152e9 + 3.72688e9i 0.184309 + 0.154654i
\(395\) −1.37972e10 + 7.96582e9i −0.566765 + 0.327222i
\(396\) 1.76132e9 1.12347e10i 0.0716237 0.456856i
\(397\) −1.60190e9 + 2.77457e9i −0.0644871 + 0.111695i −0.896466 0.443112i \(-0.853874\pi\)
0.831979 + 0.554807i \(0.187208\pi\)
\(398\) 4.51344e9 + 1.24006e10i 0.179877 + 0.494208i
\(399\) 2.27516e8 6.32882e7i 0.00897678 0.00249707i
\(400\) 1.88682e10 1.58323e10i 0.737038 0.618449i
\(401\) 1.33575e10 3.66996e10i 0.516594 1.41933i −0.357656 0.933853i \(-0.616424\pi\)
0.874250 0.485477i \(-0.161354\pi\)
\(402\) 2.05637e10 9.82820e9i 0.787403 0.376331i
\(403\) −6.67616e8 + 3.78624e9i −0.0253108 + 0.143545i
\(404\) 1.26763e10i 0.475848i
\(405\) −2.61499e10 + 3.36878e10i −0.971962 + 1.25214i
\(406\) 3.38359e10 1.24530
\(407\) −1.78283e10 3.14361e9i −0.649729 0.114565i
\(408\) 1.90170e10 + 3.97895e10i 0.686279 + 1.43591i
\(409\) −3.94804e10 1.43697e10i −1.41087 0.513516i −0.479488 0.877548i \(-0.659178\pi\)
−0.931386 + 0.364032i \(0.881400\pi\)
\(410\) −4.02910e10 4.80170e10i −1.42585 1.69926i
\(411\) 8.06037e9 + 2.89764e10i 0.282480 + 1.01549i
\(412\) −5.36959e9 + 1.95437e9i −0.186360 + 0.0678294i
\(413\) −1.60819e10 9.28487e9i −0.552760 0.319136i
\(414\) 4.71828e9 + 1.22341e10i 0.160614 + 0.416457i
\(415\) −2.25518e9 3.90608e9i −0.0760306 0.131689i
\(416\) −1.01682e10 + 1.21180e10i −0.339523 + 0.404628i
\(417\) −3.30378e9 3.40309e10i −0.109261 1.12546i
\(418\) 6.14950e7 + 3.48755e8i 0.00201435 + 0.0114239i
\(419\) 2.44273e10 4.30720e9i 0.792538 0.139746i 0.237299 0.971437i \(-0.423738\pi\)
0.555239 + 0.831691i \(0.312627\pi\)
\(420\) 6.41990e9 1.41165e10i 0.206315 0.453661i
\(421\) −4.34557e10 3.64636e10i −1.38331 1.16073i −0.967971 0.251062i \(-0.919220\pi\)
−0.415335 0.909669i \(-0.636335\pi\)
\(422\) −1.69917e10 + 9.81015e9i −0.535780 + 0.309333i
\(423\) −7.72525e9 2.64645e9i −0.241297 0.0826614i
\(424\) −1.55020e10 + 2.68502e10i −0.479650 + 0.830778i
\(425\) −2.47240e10 6.79287e10i −0.757815 2.08208i
\(426\) −9.64034e9 9.45867e9i −0.292721 0.287205i
\(427\) 5.14163e10 4.31434e10i 1.54664 1.29778i
\(428\) 1.52703e9 4.19547e9i 0.0455063 0.125028i
\(429\) −4.13613e9 + 5.30875e10i −0.122114 + 1.56734i
\(430\) −5.54732e9 + 3.14604e10i −0.162259 + 0.920217i
\(431\) 6.46311e10i 1.87298i −0.350698 0.936489i \(-0.614055\pi\)
0.350698 0.936489i \(-0.385945\pi\)
\(432\) 1.32198e10 + 1.77777e10i 0.379567 + 0.510436i
\(433\) 2.65628e10 0.755653 0.377826 0.925876i \(-0.376672\pi\)
0.377826 + 0.925876i \(0.376672\pi\)
\(434\) −4.95961e9 8.74513e8i −0.139794 0.0246494i
\(435\) −4.26001e10 + 6.20879e10i −1.18974 + 1.73400i
\(436\) 1.37776e9 + 5.01463e8i 0.0381265 + 0.0138769i
\(437\) 1.03865e8 + 1.23781e8i 0.00284801 + 0.00339413i
\(438\) 7.43835e9 + 1.91746e9i 0.202106 + 0.0520990i
\(439\) −5.28937e10 + 1.92517e10i −1.42412 + 0.518337i −0.935240 0.354015i \(-0.884816\pi\)
−0.488878 + 0.872352i \(0.662594\pi\)
\(440\) 9.11741e10 + 5.26394e10i 2.43255 + 1.40443i
\(441\) 1.65304e8 + 8.68835e9i 0.00437048 + 0.229712i
\(442\) −2.28070e10 3.95029e10i −0.597557 1.03500i
\(443\) 2.12742e10 2.53536e10i 0.552381 0.658302i −0.415534 0.909577i \(-0.636405\pi\)
0.967916 + 0.251275i \(0.0808498\pi\)
\(444\) −3.62638e9 + 2.59097e9i −0.0933129 + 0.0666701i
\(445\) 7.67966e9 + 4.35535e10i 0.195840 + 1.11066i
\(446\) 1.31733e10 2.32281e9i 0.332932 0.0587049i
\(447\) −2.26452e10 3.16947e10i −0.567213 0.793884i
\(448\) −3.76403e10 3.15839e10i −0.934417 0.784069i
\(449\) −6.27975e10 + 3.62562e10i −1.54510 + 0.892065i −0.546597 + 0.837396i \(0.684077\pi\)
−0.998505 + 0.0546691i \(0.982590\pi\)
\(450\) −2.71106e10 4.49595e10i −0.661132 1.09641i
\(451\) 5.57812e10 9.66159e10i 1.34829 2.33530i
\(452\) −2.78842e9 7.66113e9i −0.0668043 0.183543i
\(453\) 1.02470e10 3.97510e10i 0.243335 0.943965i
\(454\) 6.62650e9 5.56030e9i 0.155977 0.130880i
\(455\) −2.48356e10 + 6.82353e10i −0.579468 + 1.59208i
\(456\) 3.25453e8 + 2.23301e8i 0.00752711 + 0.00516454i
\(457\) −9.23518e9 + 5.23753e10i −0.211729 + 1.20078i 0.674764 + 0.738033i \(0.264245\pi\)
−0.886493 + 0.462742i \(0.846866\pi\)
\(458\) 8.28893e9i 0.188381i
\(459\) 6.22989e10 1.86135e10i 1.40356 0.419351i
\(460\) 1.06110e10 0.236986
\(461\) −3.01751e10 5.32068e9i −0.668104 0.117805i −0.170699 0.985323i \(-0.554603\pi\)
−0.497405 + 0.867518i \(0.665714\pi\)
\(462\) −6.95395e10 5.41794e9i −1.52638 0.118923i
\(463\) 3.02920e10 + 1.10254e10i 0.659181 + 0.239922i 0.649883 0.760035i \(-0.274818\pi\)
0.00929829 + 0.999957i \(0.497040\pi\)
\(464\) 2.51434e10 + 2.99648e10i 0.542441 + 0.646456i
\(465\) 7.84895e9 7.99970e9i 0.167880 0.171105i
\(466\) −4.47997e10 + 1.63058e10i −0.950017 + 0.345778i
\(467\) 4.49907e10 + 2.59754e10i 0.945922 + 0.546129i 0.891812 0.452406i \(-0.149434\pi\)
0.0541106 + 0.998535i \(0.482768\pi\)
\(468\) 8.61599e9 + 9.88018e9i 0.179606 + 0.205959i
\(469\) 2.76592e10 + 4.79072e10i 0.571674 + 0.990169i
\(470\) 1.07341e10 1.27924e10i 0.219976 0.262157i
\(471\) −3.40632e10 1.54912e10i −0.692152 0.314776i
\(472\) −5.38939e9 3.05648e10i −0.108585 0.615819i
\(473\) −5.59940e10 + 9.87325e9i −1.11866 + 0.197249i
\(474\) 1.75587e10 1.70462e9i 0.347839 0.0337687i
\(475\) −4.95608e8 4.15865e8i −0.00973563 0.00816916i
\(476\) −2.04762e10 + 1.18220e10i −0.398862 + 0.230283i
\(477\) 3.55694e10 + 2.87112e10i 0.687074 + 0.554597i
\(478\) −2.12913e10 + 3.68776e10i −0.407840 + 0.706400i
\(479\) −7.77313e9 2.13565e10i −0.147657 0.405684i 0.843710 0.536799i \(-0.180367\pi\)
−0.991367 + 0.131115i \(0.958144\pi\)
\(480\) 4.44254e10 1.23578e10i 0.836887 0.232797i
\(481\) 1.59867e10 1.34144e10i 0.298660 0.250606i
\(482\) 1.66771e10 4.58201e10i 0.308982 0.848922i
\(483\) −2.87145e10 + 1.37238e10i −0.527610 + 0.252166i
\(484\) −4.48568e9 + 2.54396e10i −0.0817424 + 0.463584i
\(485\) 1.54138e10i 0.278576i
\(486\) 4.18007e10 2.19691e10i 0.749271 0.393792i
\(487\) −6.87683e10 −1.22257 −0.611283 0.791412i \(-0.709346\pi\)
−0.611283 + 0.791412i \(0.709346\pi\)
\(488\) 1.10474e11 + 1.94796e10i 1.94797 + 0.343480i
\(489\) −1.59315e10 3.33337e10i −0.278626 0.582973i
\(490\) −1.66991e10 6.07796e9i −0.289673 0.105432i
\(491\) 4.69265e10 + 5.59248e10i 0.807406 + 0.962229i 0.999818 0.0190855i \(-0.00607549\pi\)
−0.192412 + 0.981314i \(0.561631\pi\)
\(492\) −7.36067e9 2.64610e10i −0.125620 0.451592i
\(493\) 1.07878e11 3.92645e10i 1.82619 0.664679i
\(494\) −3.53546e8 2.04120e8i −0.00593660 0.00342750i
\(495\) 9.74933e10 1.20781e11i 1.62388 2.01178i
\(496\) −2.91102e9 5.04203e9i −0.0480970 0.0833064i
\(497\) 2.10706e10 2.51110e10i 0.345344 0.411565i
\(498\) 4.82590e8 + 4.97098e9i 0.00784623 + 0.0808210i
\(499\) 6.66714e9 + 3.78112e10i 0.107532 + 0.609844i 0.990179 + 0.139807i \(0.0446482\pi\)
−0.882647 + 0.470037i \(0.844241\pi\)
\(500\) −1.41783e10 + 2.50002e9i −0.226853 + 0.0400004i
\(501\) −8.42345e9 + 1.85221e10i −0.133702 + 0.293995i
\(502\) −1.68603e10 1.41475e10i −0.265491 0.222774i
\(503\) 1.37684e9 7.94918e8i 0.0215085 0.0124180i −0.489207 0.872168i \(-0.662714\pi\)
0.510716 + 0.859750i \(0.329380\pi\)
\(504\) −5.85898e10 + 5.10931e10i −0.908029 + 0.791845i
\(505\) −8.65122e10 + 1.49844e11i −1.33018 + 2.30395i
\(506\) −1.63230e10 4.48472e10i −0.249000 0.684121i
\(507\) 3.34820e9 + 3.28510e9i 0.0506733 + 0.0497183i
\(508\) 1.36408e10 1.14460e10i 0.204826 0.171869i
\(509\) −2.97231e10 + 8.16637e10i −0.442816 + 1.21663i 0.494816 + 0.868998i \(0.335236\pi\)
−0.937632 + 0.347630i \(0.886987\pi\)
\(510\) −1.03283e10 + 1.32564e11i −0.152667 + 1.95949i
\(511\) −3.23751e9 + 1.83608e10i −0.0474819 + 0.269283i
\(512\) 7.14453e10i 1.03967i
\(513\) 3.99574e8 4.23054e8i 0.00576936 0.00610839i
\(514\) 7.76829e9 0.111294
\(515\) −7.68104e10 1.35437e10i −1.09192 0.192535i
\(516\) −7.91943e9 + 1.15423e10i −0.111711 + 0.162814i
\(517\) 2.79294e10 + 1.01655e10i 0.390930 + 0.142287i
\(518\) 1.75716e10 + 2.09410e10i 0.244057 + 0.290856i
\(519\) −9.05844e10 2.33508e10i −1.24849 0.321835i
\(520\) −1.14044e11 + 4.15086e10i −1.55977 + 0.567708i
\(521\) 1.18023e11 + 6.81406e10i 1.60183 + 0.924815i 0.991122 + 0.132956i \(0.0424470\pi\)
0.610704 + 0.791859i \(0.290886\pi\)
\(522\) 7.14006e10 4.30546e10i 0.961657 0.579879i
\(523\) −1.68568e10 2.91969e10i −0.225304 0.390238i 0.731107 0.682263i \(-0.239004\pi\)
−0.956411 + 0.292025i \(0.905671\pi\)
\(524\) 1.96172e10 2.33789e10i 0.260203 0.310098i
\(525\) 1.03682e11 7.40785e10i 1.36479 0.975113i
\(526\) −1.65316e10 9.37552e10i −0.215959 1.22476i
\(527\) −1.68274e10 + 2.96713e9i −0.218160 + 0.0384675i
\(528\) −4.68766e10 6.56095e10i −0.603143 0.844173i
\(529\) 4.33082e10 + 3.63399e10i 0.553029 + 0.464046i
\(530\) −8.09551e10 + 4.67394e10i −1.02598 + 0.592352i
\(531\) −4.57505e10 + 8.70447e8i −0.575464 + 0.0109487i
\(532\) −1.05805e8 + 1.83260e8i −0.00132087 + 0.00228781i
\(533\) 4.39861e10 + 1.20851e11i 0.545013 + 1.49741i
\(534\) 1.22241e10 4.74208e10i 0.150333 0.583182i
\(535\) 4.66834e10 3.91720e10i 0.569832 0.478146i
\(536\) −3.16217e10 + 8.68799e10i −0.383112 + 1.05259i
\(537\) 5.04255e10 + 3.45982e10i 0.606392 + 0.416061i
\(538\) 1.99994e10 1.13422e11i 0.238720 1.35385i
\(539\) 3.16289e10i 0.374739i
\(540\) −4.41534e9 3.79578e10i −0.0519265 0.446402i
\(541\) 1.02849e11 1.20064 0.600319 0.799760i \(-0.295040\pi\)
0.600319 + 0.799760i \(0.295040\pi\)
\(542\) 4.88813e10 + 8.61908e9i 0.566429 + 0.0998767i
\(543\) 1.85079e10 + 1.44198e9i 0.212892 + 0.0165868i
\(544\) −6.60649e10 2.40457e10i −0.754354 0.274562i
\(545\) 1.28638e10 + 1.53304e10i 0.145808 + 0.173767i
\(546\) 5.63126e10 5.73942e10i 0.633629 0.645799i
\(547\) −1.29316e11 + 4.70673e10i −1.44446 + 0.525739i −0.941037 0.338304i \(-0.890147\pi\)
−0.503418 + 0.864043i \(0.667925\pi\)
\(548\) −2.33399e10 1.34753e10i −0.258808 0.149423i
\(549\) 5.36009e10 1.56466e11i 0.590041 1.72239i
\(550\) 9.55441e10 + 1.65487e11i 1.04413 + 1.80848i
\(551\) 6.60439e8 7.87081e8i 0.00716517 0.00853912i
\(552\) −4.84192e10 2.20200e10i −0.521509 0.237171i
\(553\) 7.43521e9 + 4.21672e10i 0.0795047 + 0.450893i
\(554\) −1.04183e11 + 1.83703e10i −1.10601 + 0.195020i
\(555\) −6.05491e10 + 5.87820e9i −0.638169 + 0.0619544i
\(556\) 2.34696e10 + 1.96933e10i 0.245587 + 0.206072i
\(557\) 1.34913e11 7.78922e10i 1.40163 0.809232i 0.407071 0.913397i \(-0.366550\pi\)
0.994560 + 0.104165i \(0.0332169\pi\)
\(558\) −1.15785e10 + 4.46546e9i −0.119431 + 0.0460606i
\(559\) 3.27722e10 5.67631e10i 0.335628 0.581325i
\(560\) −3.76091e10 1.03330e11i −0.382421 1.05069i
\(561\) −2.27998e11 + 6.34223e10i −2.30187 + 0.640311i
\(562\) −1.62425e10 + 1.36290e10i −0.162820 + 0.136622i
\(563\) 3.49849e10 9.61202e10i 0.348214 0.956711i −0.634718 0.772744i \(-0.718884\pi\)
0.982932 0.183967i \(-0.0588941\pi\)
\(564\) 6.60198e9 3.15535e9i 0.0652466 0.0311839i
\(565\) 1.93237e10 1.09590e11i 0.189625 1.07542i
\(566\) 1.08160e11i 1.05391i
\(567\) 6.10416e10 + 9.70077e10i 0.590601 + 0.938586i
\(568\) 5.47865e10 0.526356
\(569\) −8.94456e10 1.57717e10i −0.853316 0.150463i −0.270152 0.962818i \(-0.587074\pi\)
−0.583163 + 0.812355i \(0.698185\pi\)
\(570\) 5.13162e8 + 1.07370e9i 0.00486133 + 0.0101714i
\(571\) −1.14927e11 4.18298e10i −1.08113 0.393497i −0.260799 0.965393i \(-0.583986\pi\)
−0.820326 + 0.571896i \(0.806208\pi\)
\(572\) −3.06700e10 3.65511e10i −0.286503 0.341441i
\(573\) −2.14039e9 7.69451e9i −0.0198552 0.0713777i
\(574\) −1.58303e11 + 5.76176e10i −1.45828 + 0.530771i
\(575\) 7.55084e10 + 4.35948e10i 0.690755 + 0.398807i
\(576\) −1.19618e11 1.87531e10i −1.08669 0.170366i
\(577\) −1.35572e9 2.34817e9i −0.0122311 0.0211849i 0.859845 0.510555i \(-0.170560\pi\)
−0.872076 + 0.489370i \(0.837227\pi\)
\(578\) 6.95824e10 8.29251e10i 0.623431 0.742976i
\(579\) 1.98385e10 + 2.04348e11i 0.176520 + 1.81826i
\(580\) −1.17163e10 6.64463e10i −0.103533 0.587163i
\(581\) −1.19378e10 + 2.10496e9i −0.104766 + 0.0184731i
\(582\) −7.06572e9 + 1.55366e10i −0.0615835 + 0.135414i
\(583\) −1.27451e11 1.06944e11i −1.10324 0.925729i
\(584\) −2.69858e10 + 1.55803e10i −0.231998 + 0.133944i
\(585\) 3.44179e10 + 1.75592e11i 0.293874 + 1.49928i
\(586\) 7.21919e10 1.25040e11i 0.612207 1.06037i
\(587\) −4.01800e10 1.10394e11i −0.338421 0.929805i −0.985843 0.167673i \(-0.946375\pi\)
0.647421 0.762132i \(-0.275847\pi\)
\(588\) −5.55819e9 5.45345e9i −0.0464969 0.0456207i
\(589\) −1.17149e8 + 9.82993e7i −0.000973365 + 0.000816751i
\(590\) 3.20049e10 8.79328e10i 0.264125 0.725677i
\(591\) −2.69358e9 + 3.45722e10i −0.0220790 + 0.283385i
\(592\) −5.48773e9 + 3.11224e10i −0.0446792 + 0.253389i
\(593\) 1.69673e11i 1.37212i −0.727544 0.686061i \(-0.759338\pi\)
0.727544 0.686061i \(-0.240662\pi\)
\(594\) −1.53636e11 + 7.70526e10i −1.23409 + 0.618930i
\(595\) −3.22725e11 −2.57493
\(596\) 3.43745e10 + 6.06115e9i 0.272428 + 0.0480364i
\(597\) −4.46530e10 + 6.50800e10i −0.351523 + 0.512330i
\(598\) 5.16989e10 + 1.88168e10i 0.404274 + 0.147144i
\(599\) −1.03440e11 1.23275e11i −0.803493 0.957566i 0.196243 0.980555i \(-0.437126\pi\)
−0.999736 + 0.0229897i \(0.992681\pi\)
\(600\) 2.06231e11 + 5.31622e10i 1.59129 + 0.410202i
\(601\) 1.59242e11 5.79593e10i 1.22056 0.444248i 0.350206 0.936673i \(-0.386112\pi\)
0.870355 + 0.492425i \(0.163889\pi\)
\(602\) 7.43542e10 + 4.29284e10i 0.566135 + 0.326858i
\(603\) 1.19326e11 + 6.58988e10i 0.902540 + 0.498435i
\(604\) 1.83920e10 + 3.18559e10i 0.138192 + 0.239355i
\(605\) −2.26641e11 + 2.70101e11i −1.69168 + 2.01606i
\(606\) 1.55890e11 1.11380e11i 1.15592 0.825879i
\(607\) 3.08833e10 + 1.75148e11i 0.227494 + 1.29018i 0.857860 + 0.513883i \(0.171794\pi\)
−0.630366 + 0.776298i \(0.717095\pi\)
\(608\) −6.19660e8 + 1.09263e8i −0.00453460 + 0.000799573i
\(609\) 1.17645e11 + 1.64658e11i 0.855271 + 1.19706i
\(610\) 2.59096e11 + 2.17407e11i 1.87129 + 1.57020i
\(611\) −2.96724e10 + 1.71314e10i −0.212906 + 0.122921i
\(612\) −2.81661e10 + 5.10017e10i −0.200780 + 0.363563i
\(613\) −2.91010e10 + 5.04044e10i −0.206094 + 0.356966i −0.950481 0.310783i \(-0.899409\pi\)
0.744387 + 0.667749i \(0.232742\pi\)
\(614\) −1.32033e10 3.62758e10i −0.0928987 0.255237i
\(615\) 9.35801e10 3.63023e11i 0.654158 2.53766i
\(616\) 2.16749e11 1.81874e11i 1.50534 1.26313i
\(617\) 4.57298e10 1.25641e11i 0.315543 0.866947i −0.675969 0.736930i \(-0.736275\pi\)
0.991512 0.130017i \(-0.0415031\pi\)
\(618\) 7.12138e10 + 4.88616e10i 0.488214 + 0.334976i
\(619\) 2.33487e10 1.32417e11i 0.159038 0.901948i −0.795963 0.605345i \(-0.793035\pi\)
0.955001 0.296603i \(-0.0958538\pi\)
\(620\) 1.00424e10i 0.0679627i
\(621\) −4.31306e10 + 6.54979e10i −0.290014 + 0.440414i
\(622\) 1.54659e11 1.03327
\(623\) 1.17054e11 + 2.06397e10i 0.777022 + 0.137010i
\(624\) 9.26736e10 + 7.22036e9i 0.611248 + 0.0476234i
\(625\) 3.22202e10 + 1.17272e10i 0.211158 + 0.0768554i
\(626\) 3.92245e10 + 4.67459e10i 0.255423 + 0.304401i
\(627\) −1.48336e9 + 1.51185e9i −0.00959792 + 0.00978227i
\(628\) 3.15089e10 1.14683e10i 0.202579 0.0737328i
\(629\) 8.03238e10 + 4.63750e10i 0.513147 + 0.296265i
\(630\) −2.30009e11 + 4.50842e10i −1.46010 + 0.286195i
\(631\) −1.52481e10 2.64105e10i −0.0961831 0.166594i 0.813919 0.580979i \(-0.197330\pi\)
−0.910102 + 0.414385i \(0.863997\pi\)
\(632\) −4.59996e10 + 5.48202e10i −0.288327 + 0.343615i
\(633\) −1.06819e11 4.85788e10i −0.665323 0.302574i
\(634\) 1.25956e10 + 7.14333e10i 0.0779583 + 0.442123i
\(635\) 2.39359e11 4.22055e10i 1.47216 0.259582i
\(636\) −4.07686e10 + 3.95788e9i −0.249171 + 0.0241899i
\(637\) 2.79308e10 + 2.34367e10i 0.169639 + 0.142344i
\(638\) −2.62812e11 + 1.51735e11i −1.58622 + 0.915802i
\(639\) 1.25107e10 7.98006e10i 0.0750377 0.478633i
\(640\) 5.09334e10 8.82193e10i 0.303587 0.525828i
\(641\) 7.45477e10 + 2.04818e11i 0.441572 + 1.21321i 0.938458 + 0.345394i \(0.112255\pi\)
−0.496885 + 0.867816i \(0.665523\pi\)
\(642\) −6.50118e10 + 1.80843e10i −0.382694 + 0.106454i
\(643\) −1.17314e11 + 9.84380e10i −0.686286 + 0.575863i −0.917836 0.396961i \(-0.870065\pi\)
0.231549 + 0.972823i \(0.425621\pi\)
\(644\) 9.75368e9 2.67980e10i 0.0567055 0.155797i
\(645\) −1.72386e11 + 8.23900e10i −0.996008 + 0.476032i
\(646\) 3.15061e8 1.78680e9i 0.00180911 0.0102600i
\(647\) 1.23404e11i 0.704226i −0.935957 0.352113i \(-0.885463\pi\)
0.935957 0.352113i \(-0.114537\pi\)
\(648\) −5.86228e10 + 1.82369e11i −0.332481 + 1.03431i
\(649\) 1.66549e11 0.938780
\(650\) −2.16936e11 3.82516e10i −1.21528 0.214287i
\(651\) −1.29885e10 2.71759e10i −0.0723159 0.151308i
\(652\) 3.11089e10 + 1.13227e10i 0.172145 + 0.0626556i
\(653\) −4.83237e10 5.75899e10i −0.265771 0.316733i 0.616610 0.787268i \(-0.288505\pi\)
−0.882381 + 0.470535i \(0.844061\pi\)
\(654\) −5.93875e9 2.13493e10i −0.0324626 0.116701i
\(655\) 3.91443e11 1.42474e11i 2.12669 0.774051i
\(656\) −1.68660e11 9.73761e10i −0.910747 0.525820i
\(657\) 1.65315e10 + 4.28647e10i 0.0887259 + 0.230058i
\(658\) −2.24404e10 3.88680e10i −0.119709 0.207342i
\(659\) 4.53931e10 5.40973e10i 0.240684 0.286836i −0.632157 0.774840i \(-0.717830\pi\)
0.872842 + 0.488004i \(0.162275\pi\)
\(660\) 1.34396e10 + 1.38436e11i 0.0708289 + 0.729582i
\(661\) −2.47641e10 1.40444e11i −0.129723 0.735696i −0.978390 0.206768i \(-0.933705\pi\)
0.848667 0.528928i \(-0.177406\pi\)
\(662\) −5.54888e10 + 9.78418e9i −0.288917 + 0.0509439i
\(663\) 1.12938e11 2.48336e11i 0.584501 1.28524i
\(664\) −1.55200e10 1.30228e10i −0.0798396 0.0669934i
\(665\) −2.50139e9 + 1.44418e9i −0.0127907 + 0.00738471i
\(666\) 6.37260e10 + 2.18307e10i 0.323907 + 0.110961i
\(667\) −6.92334e10 + 1.19916e11i −0.349794 + 0.605861i
\(668\) −6.23597e9 1.71332e10i −0.0313183 0.0860464i
\(669\) 5.71062e10 + 5.60301e10i 0.285088 + 0.279716i
\(670\) −2.13542e11 + 1.79183e11i −1.05970 + 0.889196i
\(671\) −2.05890e11 + 5.65678e11i −1.01565 + 2.79048i
\(672\) 9.62647e9 1.23556e11i 0.0472052 0.605881i
\(673\) −1.33595e10 + 7.57657e10i −0.0651225 + 0.369328i 0.934778 + 0.355232i \(0.115598\pi\)
−0.999901 + 0.0140960i \(0.995513\pi\)
\(674\) 1.30353e11i 0.631655i
\(675\) 1.24529e11 2.88251e11i 0.599865 1.38853i
\(676\) −4.20314e9 −0.0201274
\(677\) −2.24167e11 3.95267e10i −1.06713 0.188164i −0.387612 0.921823i \(-0.626700\pi\)
−0.679518 + 0.733659i \(0.737811\pi\)
\(678\) −6.97139e10 + 1.01605e11i −0.329914 + 0.480836i
\(679\) −3.89277e10 1.41685e10i −0.183138 0.0666569i
\(680\) −3.46708e11 4.13191e11i −1.62154 1.93248i
\(681\) 5.00984e10 + 1.29144e10i 0.232935 + 0.0600460i
\(682\) 4.24442e10 1.54484e10i 0.196192 0.0714079i
\(683\) −6.00315e10 3.46592e10i −0.275865 0.159271i 0.355685 0.934606i \(-0.384248\pi\)
−0.631550 + 0.775335i \(0.717581\pi\)
\(684\) 9.91912e6 + 5.21347e8i 4.53157e−5 + 0.00238178i
\(685\) −1.83930e11 3.18576e11i −0.835392 1.44694i
\(686\) 1.02921e11 1.22657e11i 0.464738 0.553853i
\(687\) −4.03371e10 + 2.88200e10i −0.181083 + 0.129380i
\(688\) 1.72355e10 + 9.77475e10i 0.0769255 + 0.436266i
\(689\) 1.88881e11 3.33048e10i 0.838129 0.147785i
\(690\) −9.32325e10 1.30490e11i −0.411312 0.575681i
\(691\) −6.29010e10 5.27802e10i −0.275896 0.231504i 0.494331 0.869274i \(-0.335413\pi\)
−0.770228 + 0.637769i \(0.779857\pi\)
\(692\) 7.25930e10 4.19116e10i 0.316570 0.182772i
\(693\) −2.15418e11 3.57243e11i −0.934003 1.54893i
\(694\) −1.36208e9 + 2.35919e9i −0.00587170 + 0.0101701i
\(695\) 1.43026e11 + 3.92962e11i 0.613024 + 1.68427i
\(696\) −8.44275e10 + 3.27518e11i −0.359788 + 1.39572i
\(697\) −4.37852e11 + 3.67402e11i −1.85522 + 1.55672i
\(698\) 7.52914e10 2.06861e11i 0.317193 0.871480i
\(699\) −2.35115e11 1.61319e11i −0.984854 0.675734i
\(700\) −1.98276e10 + 1.12448e11i −0.0825808 + 0.468339i
\(701\) 3.67111e11i 1.52029i −0.649755 0.760144i \(-0.725129\pi\)
0.649755 0.760144i \(-0.274871\pi\)
\(702\) 4.57996e10 1.92768e11i 0.188588 0.793757i
\(703\) 8.30101e8 0.00339867
\(704\) 4.33997e11 + 7.65254e10i 1.76684 + 0.311541i
\(705\) 9.95744e10 + 7.75801e9i 0.403080 + 0.0314047i
\(706\) 6.59803e10 + 2.40149e10i 0.265580 + 0.0966633i
\(707\) 2.98908e11 + 3.56224e11i 1.19635 + 1.42576i
\(708\) 2.87164e10 2.92679e10i 0.114287 0.116482i
\(709\) −2.03327e10 + 7.40048e9i −0.0804654 + 0.0292870i −0.381939 0.924187i \(-0.624744\pi\)
0.301474 + 0.953474i \(0.402521\pi\)
\(710\) 1.43054e11 + 8.25922e10i 0.562945 + 0.325017i
\(711\) 6.93455e10 + 7.95203e10i 0.271356 + 0.311171i
\(712\) 9.93270e10 + 1.72039e11i 0.386498 + 0.669435i
\(713\) 1.32474e10 1.57876e10i 0.0512593 0.0610884i
\(714\) 3.25296e11 + 1.47938e11i 1.25166 + 0.569228i
\(715\) −1.13092e11 6.41374e11i −0.432719 2.45407i
\(716\) −5.39653e10 + 9.51553e9i −0.205335 + 0.0362060i
\(717\) −2.53488e11 + 2.46090e10i −0.959138 + 0.0931147i
\(718\) −2.75086e11 2.30825e11i −1.03507 0.868529i
\(719\) −2.85002e11 + 1.64546e11i −1.06643 + 0.615703i −0.927204 0.374557i \(-0.877795\pi\)
−0.139226 + 0.990261i \(0.544461\pi\)
\(720\) −2.10846e11 1.70192e11i −0.784575 0.633299i
\(721\) −1.04810e11 + 1.81535e11i −0.387846 + 0.671770i
\(722\) 7.86632e10 + 2.16125e11i 0.289483 + 0.795347i
\(723\) 2.80963e11 7.81556e10i 1.02824 0.286027i
\(724\) −1.27428e10 + 1.06925e10i −0.0463780 + 0.0389158i
\(725\) 1.89619e11 5.20973e11i 0.686324 1.88566i
\(726\) 3.52261e11 1.68360e11i 1.26800 0.606027i
\(727\) −6.75215e10 + 3.82933e11i −0.241715 + 1.37084i 0.586283 + 0.810106i \(0.300590\pi\)
−0.827999 + 0.560730i \(0.810521\pi\)
\(728\) 3.26174e11i 1.16124i
\(729\) 2.52248e11 + 1.27033e11i 0.893135 + 0.449788i
\(730\) −9.39508e10 −0.330833
\(731\) 2.86878e11 + 5.05843e10i 1.00468 + 0.177152i
\(732\) 6.39079e10 + 1.33715e11i 0.222592 + 0.465733i
\(733\) 2.34914e11 + 8.55016e10i 0.813753 + 0.296182i 0.715173 0.698947i \(-0.246348\pi\)
0.0985795 + 0.995129i \(0.468570\pi\)
\(734\) 2.47882e11 + 2.95415e11i 0.854007 + 1.01777i
\(735\) −2.84837e10 1.02397e11i −0.0975994 0.350862i
\(736\) 7.96834e10 2.90024e10i 0.271554 0.0988377i
\(737\) −4.29672e11 2.48071e11i −1.45635 0.840827i
\(738\) −2.60736e11 + 3.23018e11i −0.878972 + 1.08893i
\(739\) −2.59650e11 4.49726e11i −0.870582 1.50789i −0.861395 0.507935i \(-0.830409\pi\)
−0.00918707 0.999958i \(-0.502924\pi\)
\(740\) 3.50390e10 4.17579e10i 0.116849 0.139255i
\(741\) −2.35927e8 2.43020e9i −0.000782538 0.00806063i
\(742\) 4.36261e10 + 2.47416e11i 0.143923 + 0.816228i
\(743\) −1.13404e11 + 1.99962e10i −0.372112 + 0.0656133i −0.356577 0.934266i \(-0.616056\pi\)
−0.0155348 + 0.999879i \(0.504945\pi\)
\(744\) 2.08401e10 4.58248e10i 0.0680157 0.149558i
\(745\) 3.64966e11 + 3.06243e11i 1.18475 + 0.994124i
\(746\) 3.72504e10 2.15065e10i 0.120275 0.0694409i
\(747\) −2.25127e10 + 1.96322e10i −0.0723012 + 0.0630501i
\(748\) 1.06029e11 1.83648e11i 0.338703 0.586652i
\(749\) −5.60173e10 1.53906e11i −0.177990 0.489023i
\(750\) 1.55322e11 + 1.52395e11i 0.490893 + 0.481642i
\(751\) −2.06886e11 + 1.73598e11i −0.650387 + 0.545740i −0.907188 0.420725i \(-0.861776\pi\)
0.256801 + 0.966464i \(0.417331\pi\)
\(752\) 1.77456e10 4.87557e10i 0.0554907 0.152459i
\(753\) 1.02250e10 1.31238e11i 0.0318041 0.408207i
\(754\) 6.07478e10 3.44518e11i 0.187951 1.06592i
\(755\) 5.02080e11i 1.54520i
\(756\) −9.99212e10 2.37402e10i −0.305893 0.0726769i
\(757\) −3.18441e11 −0.969719 −0.484859 0.874592i \(-0.661129\pi\)
−0.484859 + 0.874592i \(0.661129\pi\)
\(758\) −3.51593e11 6.19953e10i −1.06503 0.187794i
\(759\) 1.61489e11 2.35364e11i 0.486606 0.709208i
\(760\) −4.53627e9 1.65107e9i −0.0135971 0.00494892i
\(761\) 2.11330e11 + 2.51853e11i 0.630118 + 0.750946i 0.982775 0.184807i \(-0.0591660\pi\)
−0.352656 + 0.935753i \(0.614722\pi\)
\(762\) −2.60613e11 6.71809e10i −0.772995 0.199263i
\(763\) 5.05416e10 1.83956e10i 0.149125 0.0542771i
\(764\) 6.19778e9 + 3.57829e9i 0.0181913 + 0.0105027i
\(765\) −6.81015e11 + 4.10652e11i −1.98843 + 1.19903i
\(766\) 6.01628e10 + 1.04205e11i 0.174748 + 0.302673i
\(767\) −1.23412e11 + 1.47076e11i −0.356594 + 0.424972i
\(768\) 2.19583e11 1.56887e11i 0.631180 0.450964i
\(769\) 5.37175e10 + 3.04647e11i 0.153607 + 0.871148i 0.960048 + 0.279834i \(0.0902794\pi\)
−0.806442 + 0.591314i \(0.798609\pi\)
\(770\) 8.40138e11 1.48139e11i 2.38994 0.421412i
\(771\) 2.70098e10 + 3.78035e10i 0.0764369 + 0.106983i
\(772\) −1.40930e11 1.18254e11i −0.396765 0.332925i
\(773\) 4.97453e11 2.87205e11i 1.39327 0.804403i 0.399591 0.916694i \(-0.369152\pi\)
0.993675 + 0.112291i \(0.0358189\pi\)
\(774\) 2.11527e11 4.02450e9i 0.589388 0.0112137i
\(775\) −4.12589e10 + 7.14625e10i −0.114370 + 0.198094i
\(776\) −2.36803e10 6.50612e10i −0.0653042 0.179422i
\(777\) −4.08118e10 + 1.58320e11i −0.111970 + 0.434363i
\(778\) 6.18638e10 5.19099e10i 0.168857 0.141688i
\(779\) −1.74961e9 + 4.80703e9i −0.00475108 + 0.0130535i
\(780\) −1.32209e11 9.07119e10i −0.357176 0.245067i
\(781\) −5.10524e10 + 2.89533e11i −0.137218 + 0.778204i
\(782\) 2.44515e11i 0.653849i
\(783\) 4.57774e11 + 1.97765e11i 1.21788 + 0.526142i
\(784\) −5.52138e10 −0.146145
\(785\) 4.50726e11 + 7.94751e10i 1.18695 + 0.209292i
\(786\) −4.59872e11 3.58294e10i −1.20489 0.0938749i
\(787\) 4.88907e11 + 1.77948e11i 1.27446 + 0.463867i 0.888598 0.458687i \(-0.151680\pi\)
0.385867 + 0.922555i \(0.373902\pi\)
\(788\) −1.99732e10 2.38032e10i −0.0518017 0.0617348i
\(789\) 3.98769e11 4.06428e11i 1.02900 1.04876i
\(790\) −2.02753e11 + 7.37962e10i −0.520547 + 0.189463i
\(791\) −2.59008e11 1.49538e11i −0.661618 0.381985i
\(792\) 2.25958e11 6.59594e11i 0.574285 1.67639i
\(793\) −3.46976e11 6.00979e11i −0.877417 1.51973i
\(794\) −2.78904e10 + 3.32384e10i −0.0701733 + 0.0836293i
\(795\) −5.08926e11 2.31449e11i −1.27405 0.579410i
\(796\) −1.22809e10 6.96484e10i −0.0305899 0.173484i
\(797\) −2.25157e11 + 3.97012e10i −0.558023 + 0.0983945i −0.445545 0.895260i \(-0.646990\pi\)
−0.112478 + 0.993654i \(0.535879\pi\)
\(798\) 3.18333e9 3.09042e8i 0.00785000 0.000762090i
\(799\) −1.16650e11 9.78811e10i −0.286219 0.240166i
\(800\) −2.94034e11 + 1.69760e11i −0.717856 + 0.414454i
\(801\) 2.73270e11 1.05391e11i 0.663838 0.256020i
\(802\) 2.64464e11 4.58065e11i 0.639248 1.10721i
\(803\) −5.71912e10 1.57132e11i −0.137552 0.377921i
\(804\) −1.17678e11 + 3.27345e10i −0.281625 + 0.0783397i
\(805\) 2.98184e11 2.50206e11i 0.710069 0.595819i
\(806\) −1.78086e10 + 4.89287e10i −0.0421978 + 0.115937i
\(807\) 6.21493e11 2.97036e11i 1.46535 0.700350i
\(808\) −1.34960e11 + 7.65393e11i −0.316634 + 1.79572i
\(809\) 2.80231e11i 0.654218i −0.944987 0.327109i \(-0.893926\pi\)
0.944987 0.327109i \(-0.106074\pi\)
\(810\) −4.27998e11 + 3.87812e11i −0.994264 + 0.900910i
\(811\) −6.94464e11 −1.60534 −0.802668 0.596426i \(-0.796587\pi\)
−0.802668 + 0.596426i \(0.796587\pi\)
\(812\) −1.78580e11 3.14885e10i −0.410780 0.0724316i
\(813\) 1.28013e11 + 2.67843e11i 0.293015 + 0.613080i
\(814\) −2.30391e11 8.38555e10i −0.524769 0.191000i
\(815\) 2.90455e11 + 3.46151e11i 0.658338 + 0.784577i
\(816\) 1.10715e11 + 3.98011e11i 0.249716 + 0.897707i
\(817\) 2.44990e9 8.91690e8i 0.00549870 0.00200136i
\(818\) −4.92774e11 2.84503e11i −1.10061 0.635440i
\(819\) 4.75097e11 + 7.44833e10i 1.05596 + 0.165548i
\(820\) 1.67963e11 + 2.90921e11i 0.371500 + 0.643458i
\(821\) 9.00287e10 1.07292e11i 0.198157 0.236154i −0.657811 0.753183i \(-0.728518\pi\)
0.855968 + 0.517029i \(0.172962\pi\)
\(822\) 3.93595e10 + 4.05428e11i 0.0862110 + 0.888027i
\(823\) 1.32353e11 + 7.50609e11i 0.288492 + 1.63612i 0.692540 + 0.721379i \(0.256492\pi\)
−0.404048 + 0.914738i \(0.632397\pi\)
\(824\) −3.45021e11 + 6.08365e10i −0.748405 + 0.131964i
\(825\) −4.73124e11 + 1.04034e12i −1.02131 + 2.24574i
\(826\) −1.92656e11 1.61657e11i −0.413868 0.347276i
\(827\) 1.73429e11 1.00129e11i 0.370765 0.214061i −0.303028 0.952982i \(-0.597997\pi\)
0.673793 + 0.738921i \(0.264664\pi\)
\(828\) −1.35169e10 6.89603e10i −0.0287579 0.146716i
\(829\) 3.02214e11 5.23449e11i 0.639876 1.10830i −0.345584 0.938388i \(-0.612319\pi\)
0.985460 0.169910i \(-0.0543476\pi\)
\(830\) −2.08922e10 5.74008e10i −0.0440222 0.120950i
\(831\) −4.51635e11 4.43124e11i −0.947072 0.929225i
\(832\) −3.89166e11 + 3.26549e11i −0.812160 + 0.681483i
\(833\) −5.54231e10 + 1.52274e11i −0.115109 + 0.316260i
\(834\) 3.59684e10 4.61656e11i 0.0743459 0.954233i
\(835\) 4.32152e10 2.45085e11i 0.0888976 0.504164i
\(836\) 1.89790e9i 0.00388551i
\(837\) −6.19883e10 4.08195e10i −0.126301 0.0831699i
\(838\) 3.35928e11 0.681193
\(839\) −8.98602e11 1.58448e11i −1.81351 0.319771i −0.839002 0.544129i \(-0.816860\pi\)
−0.974507 + 0.224358i \(0.927972\pi\)
\(840\) 5.37924e11 7.84003e11i 1.08045 1.57471i
\(841\) 3.57286e11 + 1.30041e11i 0.714219 + 0.259955i
\(842\) −4.93835e11 5.88529e11i −0.982502 1.17090i
\(843\) −1.22798e11 3.16548e10i −0.243153 0.0626801i
\(844\) 9.88087e10 3.59634e10i 0.194727 0.0708747i
\(845\) −4.96842e10 2.86852e10i −0.0974521 0.0562640i
\(846\) −9.68114e10 5.34649e10i −0.188993 0.104373i
\(847\) 4.73810e11 + 8.20663e11i 0.920599 + 1.59452i
\(848\) −1.86690e11 + 2.22489e11i −0.361026 + 0.430254i
\(849\) −5.26348e11 + 3.76065e11i −1.01308 + 0.723822i
\(850\) −1.70004e11 9.64141e11i −0.325674 1.84699i
\(851\) −1.10170e11 + 1.94259e10i −0.210060 + 0.0370393i
\(852\) 4.20776e10 + 5.88927e10i 0.0798532 + 0.111764i
\(853\) 4.59900e10 + 3.85902e10i 0.0868695 + 0.0728922i 0.685188 0.728366i \(-0.259720\pi\)
−0.598319 + 0.801258i \(0.704164\pi\)
\(854\) 7.87225e11 4.54505e11i 1.48002 0.854490i
\(855\) −3.44078e9 + 6.23039e9i −0.00643862 + 0.0116587i
\(856\) 1.36869e11 2.37064e11i 0.254923 0.441540i
\(857\) −1.56719e11 4.30581e11i −0.290535 0.798237i −0.995988 0.0894815i \(-0.971479\pi\)
0.705454 0.708756i \(-0.250743\pi\)
\(858\) −1.80014e11 + 6.98325e11i −0.332168 + 1.28857i
\(859\) 2.76176e11 2.31740e11i 0.507241 0.425625i −0.352916 0.935655i \(-0.614810\pi\)
0.860157 + 0.510030i \(0.170366\pi\)
\(860\) 5.85556e10 1.60880e11i 0.107047 0.294109i
\(861\) −8.30796e11 5.70031e11i −1.51176 1.03726i
\(862\) 1.51996e11 8.62015e11i 0.275299 1.56130i
\(863\) 8.65609e11i 1.56055i 0.625435 + 0.780276i \(0.284922\pi\)
−0.625435 + 0.780276i \(0.715078\pi\)
\(864\) −1.36905e11 2.72977e11i −0.245677 0.489860i
\(865\) 1.14414e12 2.04368
\(866\) 3.54280e11 + 6.24692e10i 0.629906 + 0.111069i
\(867\) 6.45477e11 + 5.02903e10i 1.14236 + 0.0890036i
\(868\) 2.53621e10 + 9.23105e9i 0.0446793 + 0.0162619i
\(869\) −2.46846e11 2.94180e11i −0.432860 0.515863i
\(870\) −7.14192e11 + 7.27910e11i −1.24663 + 1.27058i
\(871\) 5.37450e11 1.95616e11i 0.933825 0.339885i
\(872\) 7.78497e10 + 4.49465e10i 0.134645 + 0.0777375i
\(873\) −1.00174e11 + 1.96352e10i −0.172464 + 0.0338047i
\(874\) 1.09419e9 + 1.89519e9i 0.00187519 + 0.00324793i
\(875\) −3.39482e11 + 4.04579e11i −0.579142 + 0.690195i
\(876\) −3.74739e10 1.70423e10i −0.0636374 0.0289409i
\(877\) −5.54872e10 3.14683e11i −0.0937981 0.531956i −0.995109 0.0987829i \(-0.968505\pi\)
0.901311 0.433173i \(-0.142606\pi\)
\(878\) −7.50743e11 + 1.32376e11i −1.26332 + 0.222757i
\(879\) 8.59498e11 8.34414e10i 1.43976 0.139774i
\(880\) 7.55496e11 + 6.33936e11i 1.25980 + 1.05710i
\(881\) −7.29538e11 + 4.21199e11i −1.21100 + 0.699172i −0.962977 0.269582i \(-0.913114\pi\)
−0.248024 + 0.968754i \(0.579781\pi\)
\(882\) −1.82281e10 + 1.16269e11i −0.0301209 + 0.192128i
\(883\) −5.44619e11 + 9.43307e11i −0.895880 + 1.55171i −0.0631678 + 0.998003i \(0.520120\pi\)
−0.832712 + 0.553706i \(0.813213\pi\)
\(884\) 8.36091e10 + 2.29714e11i 0.136913 + 0.376165i
\(885\) 5.39193e11 1.49988e11i 0.878965 0.244502i
\(886\) 3.43370e11 2.88121e11i 0.557221 0.467564i
\(887\) 1.25823e11 3.45697e11i 0.203267 0.558471i −0.795612 0.605806i \(-0.792851\pi\)
0.998879 + 0.0473352i \(0.0150729\pi\)
\(888\) −2.46545e11 + 1.17834e11i −0.396501 + 0.189503i
\(889\) 1.13431e11 6.43299e11i 0.181604 1.02992i
\(890\) 5.98954e11i 0.954626i
\(891\) −9.09149e11 4.79747e11i −1.44253 0.761204i
\(892\) −7.16881e10 −0.113237
\(893\) −1.34215e9 2.36657e8i −0.00211054 0.000372145i
\(894\) −2.27491e11 4.75983e11i −0.356135 0.745146i
\(895\) −7.02849e11 2.55816e11i −1.09539 0.398690i
\(896\) −1.75980e11 2.09725e11i −0.273043 0.325400i
\(897\) 8.81831e10 + 3.17011e11i 0.136212 + 0.489671i
\(898\) −9.22825e11 + 3.35881e11i −1.41910 + 0.516511i
\(899\) −1.13490e11 6.55237e10i −0.173748 0.100314i
\(900\) 1.01245e11 + 2.62518e11i 0.154313 + 0.400119i
\(901\) 4.26202e11 + 7.38204e11i 0.646721 + 1.12015i
\(902\) 9.71197e11 1.15743e12i 1.46717 1.74851i
\(903\) 4.96179e10 + 5.11095e11i 0.0746255 + 0.768689i
\(904\) −8.67993e10 4.92263e11i −0.129970 0.737096i
\(905\) −2.23603e11 + 3.94272e10i −0.333337 + 0.0587762i
\(906\) 2.30154e11 5.06079e11i 0.341590 0.751114i
\(907\) −1.47819e11 1.24035e11i −0.218425 0.183280i 0.527009 0.849860i \(-0.323313\pi\)
−0.745434 + 0.666579i \(0.767758\pi\)
\(908\) −4.01481e10 + 2.31795e10i −0.0590638 + 0.0341005i
\(909\) 1.08403e12 + 3.71360e11i 1.58777 + 0.543925i
\(910\) −4.91717e11 + 8.51678e11i −0.717050 + 1.24197i
\(911\) 3.85785e10 + 1.05994e11i 0.0560109 + 0.153889i 0.964543 0.263927i \(-0.0850179\pi\)
−0.908532 + 0.417816i \(0.862796\pi\)
\(912\) 2.63921e9 + 2.58947e9i 0.00381500 + 0.00374310i
\(913\) 8.32844e10 6.98839e10i 0.119862 0.100576i
\(914\) −2.46348e11 + 6.76834e11i −0.352991 + 0.969835i
\(915\) −1.57130e11 + 2.01676e12i −0.224168 + 2.87720i
\(916\) 7.71387e9 4.37475e10i 0.0109570 0.0621401i
\(917\) 1.11955e12i 1.58332i
\(918\) 8.74684e11 1.01745e11i 1.23163 0.143266i
\(919\) 3.60073e11 0.504811 0.252405 0.967622i \(-0.418778\pi\)
0.252405 + 0.967622i \(0.418778\pi\)
\(920\) 6.40686e11 + 1.12970e11i 0.894322 + 0.157693i
\(921\) 1.30625e11 1.90381e11i 0.181546 0.264597i
\(922\) −3.89946e11 1.41929e11i −0.539610 0.196402i
\(923\) −2.17851e11 2.59625e11i −0.300160 0.357717i
\(924\) 3.61975e11 + 9.33100e10i 0.496582 + 0.128009i
\(925\) 4.20902e11 1.53196e11i 0.574929 0.209257i
\(926\) 3.78090e11 + 2.18290e11i 0.514223 + 0.296887i
\(927\) 9.82578e9 + 5.16441e11i 0.0133060 + 0.699362i
\(928\) −2.69598e11 4.66958e11i −0.363518 0.629631i
\(929\) −4.96330e10 + 5.91503e10i −0.0666358 + 0.0794135i −0.798333 0.602217i \(-0.794284\pi\)
0.731697 + 0.681630i \(0.238729\pi\)
\(930\) 1.23498e11 8.82369e10i 0.165093 0.117956i
\(931\) 2.51841e8 + 1.42826e9i 0.000335218 + 0.00190112i
\(932\) 2.51620e11 4.43673e10i 0.333489 0.0588030i
\(933\) 5.37737e11 + 7.52629e11i 0.709649 + 0.993240i
\(934\) 5.38974e11 + 4.52253e11i 0.708240 + 0.594284i
\(935\) 2.50669e12 1.44724e12i 3.27985 1.89362i
\(936\) 4.15040e11 + 6.88293e11i 0.540738 + 0.896747i
\(937\) −5.46345e10 + 9.46298e10i −0.0708776 + 0.122764i −0.899286 0.437361i \(-0.855913\pi\)
0.828409 + 0.560124i \(0.189247\pi\)
\(938\) 2.56238e11 + 7.04008e11i 0.331003 + 0.909424i
\(939\) −9.11028e10 + 3.53413e11i −0.117184 + 0.454590i
\(940\) −6.85577e10 + 5.75267e10i −0.0878102 + 0.0736815i
\(941\) −1.51783e11 + 4.17019e11i −0.193581 + 0.531860i −0.998069 0.0621085i \(-0.980218\pi\)
0.804488 + 0.593969i \(0.202440\pi\)
\(942\) −4.17885e11 2.86721e11i −0.530705 0.364130i
\(943\) 1.19713e11 6.78926e11i 0.151389 0.858569i
\(944\) 2.90741e11i 0.366116i
\(945\) −1.01912e12 9.62557e11i −1.27790 1.20698i
\(946\) −7.70037e11 −0.961495
\(947\) 5.80418e11 + 1.02343e11i 0.721673 + 0.127250i 0.522409 0.852695i \(-0.325034\pi\)
0.199265 + 0.979946i \(0.436145\pi\)
\(948\) −9.42580e10 7.34380e9i −0.116704 0.00909259i
\(949\) 1.81138e11 + 6.59288e10i 0.223329 + 0.0812850i
\(950\) −5.63214e9 6.71213e9i −0.00691479 0.00824073i
\(951\) −3.03827e11 + 3.09663e11i −0.371454 + 0.378588i
\(952\) −1.36221e12 + 4.95805e11i −1.65843 + 0.603619i
\(953\) 1.23865e10 + 7.15133e9i 0.0150168 + 0.00866992i 0.507490 0.861658i \(-0.330574\pi\)
−0.492473 + 0.870328i \(0.663907\pi\)
\(954\) 4.06884e11 + 4.66585e11i 0.491221 + 0.563297i
\(955\) 4.88415e10 + 8.45960e10i 0.0587186 + 0.101704i
\(956\) 1.46691e11 1.74819e11i 0.175619 0.209294i
\(957\) −1.65217e12 7.51373e11i −1.96974 0.895794i
\(958\) −5.34486e10 3.03122e11i −0.0634562 0.359878i
\(959\) −9.73635e11 + 1.71678e11i −1.15112 + 0.202974i
\(960\) 1.47396e12 1.43094e11i 1.73540 0.168475i
\(961\) −6.38411e11 5.35690e11i −0.748526 0.628088i
\(962\) 2.44769e11 1.41317e11i 0.285796 0.165004i
\(963\) −3.14046e11 2.53494e11i −0.365164 0.294756i
\(964\) −1.30660e11 + 2.26310e11i −0.151299 + 0.262057i
\(965\) −8.58842e11 2.35965e12i −0.990385 2.72106i
\(966\) −4.15254e11 + 1.15511e11i −0.476876 + 0.132653i
\(967\) −1.09840e11 + 9.21663e10i −0.125618 + 0.105406i −0.703433 0.710762i \(-0.748350\pi\)
0.577814 + 0.816168i \(0.303906\pi\)
\(968\) −5.41688e11 + 1.48828e12i −0.616947 + 1.69505i
\(969\) 9.79070e9 4.67936e9i 0.0111050 0.00530752i
\(970\) 3.62495e10 2.05581e11i 0.0409464 0.232218i
\(971\) 1.68081e12i 1.89078i 0.325944 + 0.945389i \(0.394318\pi\)
−0.325944 + 0.945389i \(0.605682\pi\)
\(972\) −2.41062e11 + 7.70483e10i −0.270062 + 0.0863173i
\(973\) 1.12390e12 1.25394
\(974\) −9.17194e11 1.61726e11i −1.01912 0.179698i
\(975\) −5.68122e11 1.18869e12i −0.628670 1.31538i
\(976\) 9.87491e11 + 3.59417e11i 1.08826 + 0.396095i
\(977\) 3.78131e11 + 4.50639e11i 0.415015 + 0.494596i 0.932537 0.361074i \(-0.117590\pi\)
−0.517522 + 0.855670i \(0.673145\pi\)
\(978\) −1.34093e11 4.82054e11i −0.146572 0.526915i
\(979\) −1.00174e12 + 3.64605e11i −1.09050 + 0.396909i
\(980\) 8.24785e10 + 4.76190e10i 0.0894204 + 0.0516269i
\(981\) 8.32453e10 1.03130e11i 0.0898843 0.111355i
\(982\) 4.94358e11 + 8.56254e11i 0.531614 + 0.920782i
\(983\) −5.44055e11 + 6.48380e11i −0.582678 + 0.694409i −0.974181 0.225768i \(-0.927511\pi\)
0.391503 + 0.920177i \(0.371955\pi\)
\(984\) −1.62716e11 1.67607e12i −0.173560 1.78778i
\(985\) −7.36486e10 4.17682e11i −0.0782384 0.443712i
\(986\) 1.53116e12 2.69985e11i 1.62000 0.285649i
\(987\) 1.11123e11 2.44344e11i 0.117094 0.257474i
\(988\) 1.67600e9 + 1.40633e9i 0.00175892 + 0.00147591i
\(989\) −3.04280e11 + 1.75676e11i −0.318045 + 0.183623i
\(990\) 1.58436e12 1.38164e12i 1.64935 1.43831i
\(991\) 4.81519e11 8.34015e11i 0.499251 0.864728i −0.500749 0.865593i \(-0.666942\pi\)
1.00000 0.000864758i \(0.000275261\pi\)
\(992\) 2.74484e10 + 7.54138e10i 0.0283446 + 0.0778761i
\(993\) −2.40544e11 2.36011e11i −0.247399 0.242736i
\(994\) 3.40083e11 2.85364e11i 0.348369 0.292317i
\(995\) 3.30160e11 9.07108e11i 0.336847 0.925480i
\(996\) 2.07908e9 2.66851e10i 0.00211268 0.0271163i
\(997\) −1.22891e11 + 6.96951e11i −0.124377 + 0.705378i 0.857299 + 0.514819i \(0.172141\pi\)
−0.981676 + 0.190559i \(0.938970\pi\)
\(998\) 5.19985e11i 0.524166i
\(999\) 1.15334e11 + 3.86019e11i 0.115796 + 0.387567i
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.2.15 138
3.2 odd 2 81.9.f.a.8.9 138
27.13 even 9 81.9.f.a.71.9 138
27.14 odd 18 inner 27.9.f.a.14.15 yes 138
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.9.f.a.2.15 138 1.1 even 1 trivial
27.9.f.a.14.15 yes 138 27.14 odd 18 inner
81.9.f.a.8.9 138 3.2 odd 2
81.9.f.a.71.9 138 27.13 even 9