Properties

Label 27.9.f.a.2.12
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 2.12
Character \(\chi\) \(=\) 27.2
Dual form 27.9.f.a.14.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.46646 - 0.434904i) q^{2} +(-52.6972 - 61.5143i) q^{3} +(-234.667 - 85.4118i) q^{4} +(-411.949 - 490.942i) q^{5} +(103.223 + 174.641i) q^{6} +(243.334 - 88.5664i) q^{7} +(1096.91 + 633.301i) q^{8} +(-1007.01 + 6483.26i) q^{9} +(802.546 + 1390.05i) q^{10} +(4355.96 - 5191.23i) q^{11} +(7112.24 + 18936.3i) q^{12} +(-733.507 - 4159.93i) q^{13} +(-638.693 + 112.619i) q^{14} +(-8491.39 + 51212.1i) q^{15} +(46543.3 + 39054.5i) q^{16} +(-27580.9 + 15923.8i) q^{17} +(5303.36 - 15552.8i) q^{18} +(-31761.5 + 55012.5i) q^{19} +(54738.7 + 150393. i) q^{20} +(-18271.1 - 10301.3i) q^{21} +(-13001.5 + 10909.6i) q^{22} +(-67576.8 + 185666. i) q^{23} +(-18847.0 - 100849. i) q^{24} +(-3490.62 + 19796.3i) q^{25} +10579.3i q^{26} +(451880. - 279704. i) q^{27} -64667.1 q^{28} +(1.01674e6 + 179279. i) q^{29} +(43216.0 - 122620. i) q^{30} +(-1.67239e6 - 608702. i) q^{31} +(-306236. - 364958. i) q^{32} +(-548882. + 5609.45i) q^{33} +(74952.5 - 27280.5i) q^{34} +(-143722. - 82978.2i) q^{35} +(790060. - 1.43540e6i) q^{36} +(-711454. - 1.23227e6i) q^{37} +(102264. - 121873. i) q^{38} +(-217241. + 264338. i) q^{39} +(-140957. - 799407. i) q^{40} +(47826.5 - 8433.11i) q^{41} +(40585.0 + 33354.1i) q^{42} +(670492. + 562610. i) q^{43} +(-1.46559e6 + 846160. i) q^{44} +(3.59774e6 - 2.17639e6i) q^{45} +(247423. - 428549. i) q^{46} +(2.11724e6 + 5.81707e6i) q^{47} +(-50293.0 - 4.92114e6i) q^{48} +(-4.36473e6 + 3.66244e6i) q^{49} +(17219.0 - 47308.8i) q^{50} +(2.43298e6 + 857477. i) q^{51} +(-183177. + 1.03885e6i) q^{52} +9.95902e6i q^{53} +(-1.23619e6 + 493355. i) q^{54} -4.34303e6 q^{55} +(323005. + 56954.4i) q^{56} +(5.05780e6 - 945219. i) q^{57} +(-2.42979e6 - 884370. i) q^{58} +(9.92151e6 + 1.18240e7i) q^{59} +(6.36676e6 - 1.12925e7i) q^{60} +(-2.00776e7 + 7.30764e6i) q^{61} +(3.86018e6 + 2.22867e6i) q^{62} +(329158. + 1.66679e6i) q^{63} +(-7.18042e6 - 1.24369e7i) q^{64} +(-1.74012e6 + 2.07379e6i) q^{65} +(1.35624e6 + 224875. i) q^{66} +(2.15182e6 + 1.22036e7i) q^{67} +(7.83240e6 - 1.38106e6i) q^{68} +(1.49822e7 - 5.62712e6i) q^{69} +(318399. + 267168. i) q^{70} +(-2.36946e6 + 1.36801e6i) q^{71} +(-5.21046e6 + 6.47380e6i) q^{72} +(874977. - 1.51550e6i) q^{73} +(1.21886e6 + 3.34878e6i) q^{74} +(1.40170e6 - 828486. i) q^{75} +(1.21521e7 - 1.01968e7i) q^{76} +(600185. - 1.64900e6i) q^{77} +(650779. - 557500. i) q^{78} +(7.53737e6 - 4.27466e7i) q^{79} -3.89386e7i q^{80} +(-4.10186e7 - 1.30575e7i) q^{81} -121630. q^{82} +(-5.86063e7 - 1.03339e7i) q^{83} +(3.40778e6 + 3.97795e6i) q^{84} +(1.91796e7 + 6.98080e6i) q^{85} +(-1.40906e6 - 1.67926e6i) q^{86} +(-4.25512e7 - 7.19916e7i) q^{87} +(8.06570e6 - 2.93568e6i) q^{88} +(-3.32007e7 - 1.91684e7i) q^{89} +(-9.82023e6 + 3.80331e6i) q^{90} +(-546917. - 947288. i) q^{91} +(3.17161e7 - 3.77978e7i) q^{92} +(5.06866e7 + 1.34953e8i) q^{93} +(-2.69223e6 - 1.52684e7i) q^{94} +(4.00921e7 - 7.06932e6i) q^{95} +(-6.31236e6 + 3.80702e7i) q^{96} +(1.06250e8 + 8.91546e7i) q^{97} +(1.23583e7 - 7.13504e6i) q^{98} +(2.92696e7 + 3.34685e7i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.46646 0.434904i −0.154154 0.0271815i 0.0960385 0.995378i \(-0.469383\pi\)
−0.250193 + 0.968196i \(0.580494\pi\)
\(3\) −52.6972 61.5143i −0.650582 0.759436i
\(4\) −234.667 85.4118i −0.916668 0.333640i
\(5\) −411.949 490.942i −0.659119 0.785508i 0.328140 0.944629i \(-0.393578\pi\)
−0.987259 + 0.159122i \(0.949134\pi\)
\(6\) 103.223 + 174.641i 0.0796473 + 0.134754i
\(7\) 243.334 88.5664i 0.101347 0.0368873i −0.290849 0.956769i \(-0.593938\pi\)
0.392196 + 0.919882i \(0.371715\pi\)
\(8\) 1096.91 + 633.301i 0.267800 + 0.154614i
\(9\) −1007.01 + 6483.26i −0.153485 + 0.988151i
\(10\) 802.546 + 1390.05i 0.0802546 + 0.139005i
\(11\) 4355.96 5191.23i 0.297518 0.354568i −0.596489 0.802621i \(-0.703438\pi\)
0.894007 + 0.448053i \(0.147882\pi\)
\(12\) 7112.24 + 18936.3i 0.342990 + 0.913211i
\(13\) −733.507 4159.93i −0.0256821 0.145651i 0.969270 0.245998i \(-0.0791157\pi\)
−0.994952 + 0.100347i \(0.968005\pi\)
\(14\) −638.693 + 112.619i −0.0166257 + 0.00293156i
\(15\) −8491.39 + 51212.1i −0.167731 + 1.01160i
\(16\) 46543.3 + 39054.5i 0.710195 + 0.595924i
\(17\) −27580.9 + 15923.8i −0.330227 + 0.190656i −0.655942 0.754812i \(-0.727728\pi\)
0.325715 + 0.945468i \(0.394395\pi\)
\(18\) 5303.36 15552.8i 0.0505198 0.148156i
\(19\) −31761.5 + 55012.5i −0.243717 + 0.422131i −0.961770 0.273858i \(-0.911700\pi\)
0.718053 + 0.695989i \(0.245034\pi\)
\(20\) 54738.7 + 150393.i 0.342117 + 0.939958i
\(21\) −18271.1 10301.3i −0.0939481 0.0529683i
\(22\) −13001.5 + 10909.6i −0.0555013 + 0.0465711i
\(23\) −67576.8 + 185666.i −0.241483 + 0.663469i 0.758448 + 0.651733i \(0.225958\pi\)
−0.999931 + 0.0117355i \(0.996264\pi\)
\(24\) −18847.0 100849.i −0.0568063 0.303966i
\(25\) −3490.62 + 19796.3i −0.00893599 + 0.0506785i
\(26\) 10579.3i 0.0231507i
\(27\) 451880. 279704.i 0.850292 0.526312i
\(28\) −64667.1 −0.105209
\(29\) 1.01674e6 + 179279.i 1.43753 + 0.253476i 0.837474 0.546478i \(-0.184032\pi\)
0.600061 + 0.799954i \(0.295143\pi\)
\(30\) 43216.0 122620.i 0.0533531 0.151382i
\(31\) −1.67239e6 608702.i −1.81089 0.659110i −0.996940 0.0781752i \(-0.975091\pi\)
−0.813950 0.580935i \(-0.802687\pi\)
\(32\) −306236. 364958.i −0.292050 0.348051i
\(33\) −548882. + 5609.45i −0.462832 + 0.00473004i
\(34\) 74952.5 27280.5i 0.0560881 0.0204144i
\(35\) −143722. 82978.2i −0.0957750 0.0552957i
\(36\) 790060. 1.43540e6i 0.470381 0.854598i
\(37\) −711454. 1.23227e6i −0.379612 0.657507i 0.611394 0.791327i \(-0.290609\pi\)
−0.991006 + 0.133819i \(0.957276\pi\)
\(38\) 102264. 121873.i 0.0490442 0.0584486i
\(39\) −217241. + 264338.i −0.0939039 + 0.114262i
\(40\) −140957. 799407.i −0.0550613 0.312268i
\(41\) 47826.5 8433.11i 0.0169252 0.00298437i −0.165179 0.986264i \(-0.552820\pi\)
0.182104 + 0.983279i \(0.441709\pi\)
\(42\) 40585.0 + 33354.1i 0.0130427 + 0.0107189i
\(43\) 670492. + 562610.i 0.196119 + 0.164564i 0.735559 0.677461i \(-0.236920\pi\)
−0.539440 + 0.842024i \(0.681364\pi\)
\(44\) −1.46559e6 + 846160.i −0.391023 + 0.225757i
\(45\) 3.59774e6 2.17639e6i 0.877365 0.530746i
\(46\) 247423. 428549.i 0.0552597 0.0957125i
\(47\) 2.11724e6 + 5.81707e6i 0.433889 + 1.19210i 0.943406 + 0.331639i \(0.107602\pi\)
−0.509517 + 0.860460i \(0.670176\pi\)
\(48\) −50293.0 4.92114e6i −0.00947420 0.927045i
\(49\) −4.36473e6 + 3.66244e6i −0.757134 + 0.635311i
\(50\) 17219.0 47308.8i 0.00275504 0.00756941i
\(51\) 2.43298e6 + 857477.i 0.359631 + 0.126748i
\(52\) −183177. + 1.03885e6i −0.0250529 + 0.142082i
\(53\) 9.95902e6i 1.26216i 0.775719 + 0.631078i \(0.217387\pi\)
−0.775719 + 0.631078i \(0.782613\pi\)
\(54\) −1.23619e6 + 493355.i −0.145382 + 0.0580209i
\(55\) −4.34303e6 −0.474616
\(56\) 323005. + 56954.4i 0.0328440 + 0.00579129i
\(57\) 5.05780e6 945219.i 0.479140 0.0895433i
\(58\) −2.42979e6 884370.i −0.214712 0.0781487i
\(59\) 9.92151e6 + 1.18240e7i 0.818785 + 0.975790i 0.999971 0.00765928i \(-0.00243805\pi\)
−0.181186 + 0.983449i \(0.557994\pi\)
\(60\) 6.36676e6 1.12925e7i 0.491263 0.871336i
\(61\) −2.00776e7 + 7.30764e6i −1.45008 + 0.527786i −0.942613 0.333886i \(-0.891640\pi\)
−0.507466 + 0.861672i \(0.669418\pi\)
\(62\) 3.86018e6 + 2.22867e6i 0.261240 + 0.150827i
\(63\) 329158. + 1.66679e6i 0.0208950 + 0.105808i
\(64\) −7.18042e6 1.24369e7i −0.427987 0.741295i
\(65\) −1.74012e6 + 2.07379e6i −0.0974821 + 0.116175i
\(66\) 1.35624e6 + 224875.i 0.0714759 + 0.0118513i
\(67\) 2.15182e6 + 1.22036e7i 0.106784 + 0.605602i 0.990493 + 0.137565i \(0.0439276\pi\)
−0.883709 + 0.468037i \(0.844961\pi\)
\(68\) 7.83240e6 1.38106e6i 0.366319 0.0645919i
\(69\) 1.49822e7 5.62712e6i 0.660966 0.248250i
\(70\) 318399. + 267168.i 0.0132611 + 0.0111274i
\(71\) −2.36946e6 + 1.36801e6i −0.0932429 + 0.0538338i −0.545896 0.837853i \(-0.683811\pi\)
0.452654 + 0.891686i \(0.350477\pi\)
\(72\) −5.21046e6 + 6.47380e6i −0.193886 + 0.240896i
\(73\) 874977. 1.51550e6i 0.0308109 0.0533661i −0.850209 0.526446i \(-0.823524\pi\)
0.881020 + 0.473080i \(0.156858\pi\)
\(74\) 1.21886e6 + 3.34878e6i 0.0406467 + 0.111676i
\(75\) 1.40170e6 828486.i 0.0443007 0.0261843i
\(76\) 1.21521e7 1.01968e7i 0.364248 0.305640i
\(77\) 600185. 1.64900e6i 0.0170735 0.0469091i
\(78\) 650779. 557500.i 0.0175815 0.0150614i
\(79\) 7.53737e6 4.27466e7i 0.193514 1.09747i −0.721006 0.692929i \(-0.756320\pi\)
0.914520 0.404542i \(-0.132569\pi\)
\(80\) 3.89386e7i 0.950648i
\(81\) −4.10186e7 1.30575e7i −0.952885 0.303333i
\(82\) −121630. −0.00269020
\(83\) −5.86063e7 1.03339e7i −1.23490 0.217746i −0.482172 0.876077i \(-0.660152\pi\)
−0.752729 + 0.658330i \(0.771263\pi\)
\(84\) 3.40778e6 + 3.97795e6i 0.0684469 + 0.0798992i
\(85\) 1.91796e7 + 6.98080e6i 0.367421 + 0.133730i
\(86\) −1.40906e6 1.67926e6i −0.0257595 0.0306990i
\(87\) −4.25512e7 7.19916e7i −0.742736 1.25662i
\(88\) 8.06570e6 2.93568e6i 0.134497 0.0489528i
\(89\) −3.32007e7 1.91684e7i −0.529161 0.305511i 0.211514 0.977375i \(-0.432161\pi\)
−0.740675 + 0.671864i \(0.765494\pi\)
\(90\) −9.82023e6 + 3.80331e6i −0.149676 + 0.0579685i
\(91\) −546917. 947288.i −0.00797547 0.0138139i
\(92\) 3.17161e7 3.77978e7i 0.442719 0.527612i
\(93\) 5.06866e7 + 1.34953e8i 0.677581 + 1.80406i
\(94\) −2.69223e6 1.52684e7i −0.0344826 0.195561i
\(95\) 4.00921e7 7.06932e6i 0.492226 0.0867927i
\(96\) −6.31236e6 + 3.80702e7i −0.0743201 + 0.448229i
\(97\) 1.06250e8 + 8.91546e7i 1.20017 + 1.00706i 0.999625 + 0.0273787i \(0.00871601\pi\)
0.200546 + 0.979684i \(0.435728\pi\)
\(98\) 1.23583e7 7.13504e6i 0.133984 0.0773557i
\(99\) 2.92696e7 + 3.34685e7i 0.304702 + 0.348413i
\(100\) 2.50997e6 4.34740e6i 0.0250997 0.0434740i
\(101\) 4.55685e7 + 1.25198e8i 0.437904 + 1.20313i 0.940853 + 0.338816i \(0.110026\pi\)
−0.502949 + 0.864316i \(0.667751\pi\)
\(102\) −5.62793e6 3.17305e6i −0.0519933 0.0293140i
\(103\) −9.13908e7 + 7.66860e7i −0.811995 + 0.681345i −0.951083 0.308935i \(-0.900027\pi\)
0.139088 + 0.990280i \(0.455583\pi\)
\(104\) 1.82989e6 5.02759e6i 0.0156420 0.0429761i
\(105\) 2.46942e6 + 1.32137e7i 0.0203160 + 0.108709i
\(106\) 4.33122e6 2.45636e7i 0.0343073 0.194567i
\(107\) 1.15116e8i 0.878216i −0.898434 0.439108i \(-0.855295\pi\)
0.898434 0.439108i \(-0.144705\pi\)
\(108\) −1.29931e8 + 2.70413e7i −0.955034 + 0.198762i
\(109\) 3.18734e7 0.225799 0.112900 0.993606i \(-0.463986\pi\)
0.112900 + 0.993606i \(0.463986\pi\)
\(110\) 1.07119e7 + 1.88880e6i 0.0731639 + 0.0129008i
\(111\) −3.83109e7 + 1.08702e8i −0.252366 + 0.716054i
\(112\) 1.47845e7 + 5.38112e6i 0.0939582 + 0.0341980i
\(113\) −4.45785e7 5.31266e7i −0.273408 0.325835i 0.611816 0.791000i \(-0.290439\pi\)
−0.885224 + 0.465165i \(0.845995\pi\)
\(114\) −1.28860e7 + 131692.i −0.0762952 + 0.000779721i
\(115\) 1.18989e8 4.33086e7i 0.680326 0.247618i
\(116\) −2.23283e8 1.28913e8i −1.23317 0.711972i
\(117\) 2.77085e7 566410.i 0.147867 0.00302264i
\(118\) −1.93287e7 3.34784e7i −0.0996955 0.172678i
\(119\) −5.30105e6 + 6.31755e6i −0.0264347 + 0.0315036i
\(120\) −4.17469e7 + 5.07974e7i −0.201326 + 0.244972i
\(121\) 2.92485e7 + 1.65877e8i 0.136447 + 0.773827i
\(122\) 5.26987e7 9.29221e6i 0.237882 0.0419449i
\(123\) −3.03908e6 2.49761e6i −0.0132777 0.0109120i
\(124\) 3.40466e8 + 2.85685e8i 1.44008 + 1.20837i
\(125\) −2.05647e8 + 1.18730e8i −0.842331 + 0.486320i
\(126\) −86963.5 4.25422e6i −0.000345029 0.0168787i
\(127\) 2.33645e8 4.04684e8i 0.898133 1.55561i 0.0682548 0.997668i \(-0.478257\pi\)
0.829878 0.557944i \(-0.188410\pi\)
\(128\) 5.40153e7 + 1.48406e8i 0.201223 + 0.552855i
\(129\) −724509. 7.08928e7i −0.00261629 0.256002i
\(130\) 5.19383e6 4.35814e6i 0.0181851 0.0152591i
\(131\) 1.80234e8 4.95187e8i 0.611998 1.68145i −0.113765 0.993508i \(-0.536291\pi\)
0.725763 0.687944i \(-0.241487\pi\)
\(132\) 1.29284e8 + 4.55646e7i 0.425841 + 0.150083i
\(133\) −2.85640e6 + 1.61994e7i −0.00912876 + 0.0517718i
\(134\) 3.10355e7i 0.0962586i
\(135\) −3.23470e8 1.06623e8i −0.973865 0.321008i
\(136\) −4.03382e7 −0.117913
\(137\) −3.13130e8 5.52133e7i −0.888879 0.156733i −0.289480 0.957184i \(-0.593482\pi\)
−0.599399 + 0.800451i \(0.704594\pi\)
\(138\) −3.94003e7 + 7.36327e6i −0.108638 + 0.0203027i
\(139\) −5.17739e8 1.88442e8i −1.38692 0.504798i −0.462652 0.886540i \(-0.653102\pi\)
−0.924269 + 0.381742i \(0.875324\pi\)
\(140\) 2.66396e7 + 3.17478e7i 0.0693450 + 0.0826422i
\(141\) 2.46260e8 4.36783e8i 0.623043 1.10507i
\(142\) 6.43914e6 2.34365e6i 0.0158370 0.00576421i
\(143\) −2.47903e7 1.43127e7i −0.0592839 0.0342276i
\(144\) −3.00070e8 + 2.62424e8i −0.697867 + 0.610314i
\(145\) −3.30830e8 5.73015e8i −0.748399 1.29627i
\(146\) −2.81720e6 + 3.35741e6i −0.00620020 + 0.00738912i
\(147\) 4.55301e8 + 7.54928e7i 0.975056 + 0.161672i
\(148\) 6.17040e7 + 3.49941e8i 0.128608 + 0.729370i
\(149\) 6.98309e8 1.23131e8i 1.41678 0.249817i 0.587761 0.809035i \(-0.300010\pi\)
0.829021 + 0.559218i \(0.188899\pi\)
\(150\) −3.81756e6 + 1.43383e6i −0.00754086 + 0.00283225i
\(151\) −2.61562e8 2.19476e8i −0.503114 0.422163i 0.355584 0.934644i \(-0.384282\pi\)
−0.858698 + 0.512481i \(0.828726\pi\)
\(152\) −6.96789e7 + 4.02291e7i −0.130535 + 0.0753644i
\(153\) −7.54639e7 1.94849e8i −0.137712 0.355577i
\(154\) −2.19749e6 + 3.80617e6i −0.00390701 + 0.00676714i
\(155\) 3.90105e8 + 1.07180e9i 0.675856 + 1.85690i
\(156\) 7.35569e7 4.34763e7i 0.124201 0.0734099i
\(157\) −6.89517e8 + 5.78573e8i −1.13487 + 0.952269i −0.999259 0.0384927i \(-0.987744\pi\)
−0.135612 + 0.990762i \(0.543300\pi\)
\(158\) −3.71813e7 + 1.02155e8i −0.0596618 + 0.163920i
\(159\) 6.12622e8 5.24812e8i 0.958527 0.821137i
\(160\) −5.30195e7 + 3.00689e8i −0.0809014 + 0.458815i
\(161\) 5.11639e7i 0.0761483i
\(162\) 9.54921e7 + 5.00449e7i 0.138646 + 0.0726608i
\(163\) −5.07912e8 −0.719512 −0.359756 0.933046i \(-0.617140\pi\)
−0.359756 + 0.933046i \(0.617140\pi\)
\(164\) −1.19436e7 2.10598e6i −0.0165105 0.00291124i
\(165\) 2.28865e8 + 2.67158e8i 0.308777 + 0.360440i
\(166\) 1.40056e8 + 5.09763e7i 0.184446 + 0.0671330i
\(167\) 5.64103e8 + 6.72272e8i 0.725258 + 0.864329i 0.995130 0.0985671i \(-0.0314259\pi\)
−0.269872 + 0.962896i \(0.586981\pi\)
\(168\) −1.35179e7 2.28707e7i −0.0169696 0.0287107i
\(169\) 7.49769e8 2.72894e8i 0.919138 0.334539i
\(170\) −4.42698e7 2.55592e7i −0.0530044 0.0306021i
\(171\) −3.24676e8 2.61316e8i −0.379722 0.305620i
\(172\) −1.09289e8 1.89294e8i −0.124871 0.216283i
\(173\) −9.08559e8 + 1.08278e9i −1.01430 + 1.20880i −0.0364893 + 0.999334i \(0.511617\pi\)
−0.977816 + 0.209467i \(0.932827\pi\)
\(174\) 7.36415e7 + 1.96070e8i 0.0803389 + 0.213902i
\(175\) 903900. + 5.12627e6i 0.000963758 + 0.00546574i
\(176\) 4.05482e8 7.14974e7i 0.422591 0.0745143i
\(177\) 2.04509e8 1.23341e9i 0.208362 1.25665i
\(178\) 7.35520e7 + 6.17174e7i 0.0732680 + 0.0614792i
\(179\) −1.09594e8 + 6.32741e7i −0.106752 + 0.0616330i −0.552425 0.833562i \(-0.686298\pi\)
0.445674 + 0.895196i \(0.352964\pi\)
\(180\) −1.03016e9 + 2.03437e8i −0.981330 + 0.193794i
\(181\) −2.30450e8 + 3.99152e8i −0.214715 + 0.371898i −0.953185 0.302389i \(-0.902216\pi\)
0.738469 + 0.674287i \(0.235549\pi\)
\(182\) 936972. + 2.57431e6i 0.000853967 + 0.00234626i
\(183\) 1.50755e9 + 8.49965e8i 1.34422 + 0.757874i
\(184\) −1.91708e8 + 1.60862e8i −0.167251 + 0.140340i
\(185\) −3.11893e8 + 8.56918e8i −0.266268 + 0.731564i
\(186\) −6.63251e7 3.54901e8i −0.0554148 0.296521i
\(187\) −3.74769e7 + 2.12542e8i −0.0306477 + 0.173811i
\(188\) 1.54591e9i 1.23752i
\(189\) 8.51855e7 1.08083e8i 0.0667603 0.0847051i
\(190\) −1.01960e8 −0.0782378
\(191\) 7.37923e8 + 1.30116e8i 0.554469 + 0.0977679i 0.443860 0.896096i \(-0.353609\pi\)
0.110609 + 0.993864i \(0.464720\pi\)
\(192\) −3.86656e8 + 1.09709e9i −0.284525 + 0.807302i
\(193\) −1.25557e9 4.56992e8i −0.904927 0.329366i −0.152701 0.988272i \(-0.548797\pi\)
−0.752225 + 0.658906i \(0.771019\pi\)
\(194\) −2.23289e8 2.66105e8i −0.157638 0.187865i
\(195\) 2.19267e8 2.24086e6i 0.151647 0.00154980i
\(196\) 1.33707e9 4.86655e8i 0.906005 0.329759i
\(197\) −8.27317e8 4.77652e8i −0.549297 0.317137i 0.199541 0.979889i \(-0.436055\pi\)
−0.748838 + 0.662753i \(0.769388\pi\)
\(198\) −5.76368e7 9.52782e7i −0.0375007 0.0619916i
\(199\) −4.23487e8 7.33501e8i −0.270040 0.467723i 0.698832 0.715286i \(-0.253704\pi\)
−0.968872 + 0.247563i \(0.920370\pi\)
\(200\) −1.63659e7 + 1.95041e7i −0.0102287 + 0.0121901i
\(201\) 6.37299e8 7.75461e8i 0.390444 0.475090i
\(202\) −5.79438e7 3.28615e8i −0.0348018 0.197371i
\(203\) 2.63286e8 4.64244e7i 0.155040 0.0273377i
\(204\) −4.97700e8 4.09026e8i −0.287374 0.236173i
\(205\) −2.38423e7 2.00060e7i −0.0135000 0.0113278i
\(206\) 2.58763e8 1.49397e8i 0.143692 0.0829608i
\(207\) −1.13567e9 6.25086e8i −0.618543 0.340454i
\(208\) 1.28324e8 2.22264e8i 0.0685574 0.118745i
\(209\) 1.47231e8 + 4.04514e8i 0.0771638 + 0.212006i
\(210\) −344050. 3.36651e7i −0.000176907 0.0173102i
\(211\) −1.74069e8 + 1.46061e8i −0.0878195 + 0.0736893i −0.685641 0.727940i \(-0.740478\pi\)
0.597821 + 0.801630i \(0.296033\pi\)
\(212\) 8.50618e8 2.33705e9i 0.421106 1.15698i
\(213\) 2.09016e8 + 7.36654e7i 0.101545 + 0.0357886i
\(214\) −5.00645e7 + 2.83930e8i −0.0238712 + 0.135381i
\(215\) 5.60940e8i 0.262520i
\(216\) 6.72808e8 2.06336e7i 0.309084 0.00947894i
\(217\) −4.60861e8 −0.207841
\(218\) −7.86146e7 1.38619e7i −0.0348079 0.00613757i
\(219\) −1.39334e8 + 2.60392e7i −0.0605732 + 0.0113201i
\(220\) 1.01917e9 + 3.70946e8i 0.435065 + 0.158351i
\(221\) 8.64727e7 + 1.03054e8i 0.0362501 + 0.0432012i
\(222\) 1.41767e8 2.51448e8i 0.0583666 0.103523i
\(223\) 6.09381e8 2.21796e8i 0.246416 0.0896882i −0.215859 0.976424i \(-0.569255\pi\)
0.462276 + 0.886736i \(0.347033\pi\)
\(224\) −1.06841e8 6.16846e7i −0.0424371 0.0245010i
\(225\) −1.24829e8 4.25658e7i −0.0487065 0.0166085i
\(226\) 8.68463e7 + 1.50422e8i 0.0332903 + 0.0576605i
\(227\) −6.84046e8 + 8.15215e8i −0.257622 + 0.307021i −0.879316 0.476238i \(-0.842000\pi\)
0.621695 + 0.783260i \(0.286444\pi\)
\(228\) −1.26763e9 2.10184e8i −0.469087 0.0777786i
\(229\) 3.42445e8 + 1.94210e9i 0.124523 + 0.706205i 0.981590 + 0.191000i \(0.0611731\pi\)
−0.857067 + 0.515205i \(0.827716\pi\)
\(230\) −3.12318e8 + 5.50701e7i −0.111606 + 0.0196791i
\(231\) −1.33065e8 + 4.99775e7i −0.0467321 + 0.0175520i
\(232\) 1.00173e9 + 8.40555e8i 0.345781 + 0.290145i
\(233\) −3.99283e9 + 2.30526e9i −1.35474 + 0.782161i −0.988910 0.148519i \(-0.952549\pi\)
−0.365833 + 0.930680i \(0.619216\pi\)
\(234\) −6.85884e7 1.06535e7i −0.0228764 0.00355329i
\(235\) 1.98365e9 3.43578e9i 0.650419 1.12656i
\(236\) −1.31834e9 3.62212e9i −0.424991 1.16765i
\(237\) −3.02672e9 + 1.78897e9i −0.959355 + 0.567034i
\(238\) 1.58224e7 1.32766e7i 0.00493133 0.00413788i
\(239\) 4.79266e8 1.31677e9i 0.146888 0.403570i −0.844328 0.535827i \(-0.820000\pi\)
0.991216 + 0.132256i \(0.0422222\pi\)
\(240\) −2.39528e9 + 2.05195e9i −0.721956 + 0.618475i
\(241\) −5.55644e8 + 3.15122e9i −0.164713 + 0.934136i 0.784646 + 0.619944i \(0.212845\pi\)
−0.949359 + 0.314192i \(0.898266\pi\)
\(242\) 4.21849e8i 0.122997i
\(243\) 1.35834e9 + 3.21132e9i 0.389568 + 0.920998i
\(244\) 5.33570e9 1.50533
\(245\) 3.59609e9 + 6.34088e8i 0.998083 + 0.175989i
\(246\) 6.40956e6 + 7.48198e6i 0.00175020 + 0.00204304i
\(247\) 2.52145e8 + 9.17734e7i 0.0677428 + 0.0246564i
\(248\) −1.44897e9 1.72682e9i −0.383048 0.456499i
\(249\) 2.45271e9 + 4.14969e9i 0.638041 + 1.07949i
\(250\) 5.58858e8 2.03408e8i 0.143068 0.0520723i
\(251\) 2.82883e9 + 1.63323e9i 0.712709 + 0.411483i 0.812063 0.583569i \(-0.198344\pi\)
−0.0993540 + 0.995052i \(0.531678\pi\)
\(252\) 6.51208e7 4.19254e8i 0.0161479 0.103962i
\(253\) 6.69472e8 + 1.15956e9i 0.163399 + 0.283016i
\(254\) −7.52275e8 + 8.96526e8i −0.180735 + 0.215391i
\(255\) −5.81291e8 1.54769e9i −0.137478 0.366035i
\(256\) 5.69712e8 + 3.23100e9i 0.132646 + 0.752275i
\(257\) −1.01335e9 + 1.78680e8i −0.232287 + 0.0409585i −0.288580 0.957456i \(-0.593183\pi\)
0.0562927 + 0.998414i \(0.482072\pi\)
\(258\) −2.90446e7 + 1.75170e8i −0.00655521 + 0.0395349i
\(259\) −2.82259e8 2.36844e8i −0.0627262 0.0526336i
\(260\) 5.85474e8 3.38023e8i 0.128119 0.0739696i
\(261\) −2.18618e9 + 6.41126e9i −0.471113 + 1.38160i
\(262\) −6.59899e8 + 1.14298e9i −0.140046 + 0.242568i
\(263\) −1.69620e9 4.66027e9i −0.354531 0.974066i −0.980895 0.194536i \(-0.937680\pi\)
0.626364 0.779530i \(-0.284542\pi\)
\(264\) −6.05626e8 3.41454e8i −0.124678 0.0702937i
\(265\) 4.88931e9 4.10261e9i 0.991434 0.831912i
\(266\) 1.40904e7 3.87131e7i 0.00281447 0.00773270i
\(267\) 5.70451e8 + 3.05244e9i 0.112247 + 0.600624i
\(268\) 5.37368e8 3.04756e9i 0.104168 0.590764i
\(269\) 1.08134e9i 0.206516i −0.994655 0.103258i \(-0.967073\pi\)
0.994655 0.103258i \(-0.0329267\pi\)
\(270\) 7.51456e8 + 4.03661e8i 0.141400 + 0.0759559i
\(271\) −4.66467e9 −0.864855 −0.432428 0.901669i \(-0.642343\pi\)
−0.432428 + 0.901669i \(0.642343\pi\)
\(272\) −1.90560e9 3.36009e8i −0.348142 0.0613868i
\(273\) −2.94508e7 + 8.35627e7i −0.00530208 + 0.0150439i
\(274\) 7.48312e8 + 2.72363e8i 0.132764 + 0.0483221i
\(275\) 8.75622e7 + 1.04353e8i 0.0153104 + 0.0182462i
\(276\) −3.99645e9 + 4.08429e7i −0.688713 + 0.00703850i
\(277\) −8.24991e9 + 3.00272e9i −1.40130 + 0.510030i −0.928563 0.371175i \(-0.878955\pi\)
−0.472734 + 0.881205i \(0.656733\pi\)
\(278\) 1.19503e9 + 6.89951e8i 0.200078 + 0.115515i
\(279\) 5.63050e9 1.02296e10i 0.929245 1.68827i
\(280\) −1.05100e8 1.82039e8i −0.0170990 0.0296164i
\(281\) 3.27244e9 3.89994e9i 0.524864 0.625508i −0.436860 0.899530i \(-0.643909\pi\)
0.961724 + 0.274021i \(0.0883539\pi\)
\(282\) −7.97351e8 + 9.70211e8i −0.126082 + 0.153416i
\(283\) −1.36212e9 7.72497e9i −0.212359 1.20435i −0.885432 0.464770i \(-0.846137\pi\)
0.673073 0.739576i \(-0.264974\pi\)
\(284\) 6.72878e8 1.18646e8i 0.103434 0.0182382i
\(285\) −2.54760e9 2.09370e9i −0.386147 0.317348i
\(286\) 5.49197e7 + 4.60831e7i 0.00820850 + 0.00688775i
\(287\) 1.08909e7 6.28789e6i 0.00160523 0.000926781i
\(288\) 2.67450e9 1.61789e9i 0.388752 0.235169i
\(289\) −2.98074e9 + 5.16280e9i −0.427300 + 0.740106i
\(290\) 5.66775e8 + 1.55720e9i 0.0801343 + 0.220167i
\(291\) −1.14810e8 1.12341e10i −0.0160106 1.56663i
\(292\) −3.34770e8 + 2.80905e8i −0.0460485 + 0.0386393i
\(293\) −4.13715e9 + 1.13667e10i −0.561347 + 1.54229i 0.256318 + 0.966592i \(0.417490\pi\)
−0.817665 + 0.575695i \(0.804732\pi\)
\(294\) −1.09015e9 3.84213e8i −0.145914 0.0514259i
\(295\) 1.71774e9 9.74178e9i 0.226813 1.28632i
\(296\) 1.80226e9i 0.234774i
\(297\) 5.16364e8 3.56419e9i 0.0663637 0.458073i
\(298\) −1.77591e9 −0.225193
\(299\) 8.21924e8 + 1.44927e8i 0.102836 + 0.0181328i
\(300\) −3.99696e8 + 7.46965e7i −0.0493451 + 0.00922179i
\(301\) 2.12982e8 + 7.75192e7i 0.0259464 + 0.00944372i
\(302\) 5.49682e8 + 6.55085e8i 0.0660820 + 0.0787535i
\(303\) 5.30016e9 9.40072e9i 0.628809 1.11530i
\(304\) −3.62677e9 + 1.32004e9i −0.424645 + 0.154558i
\(305\) 1.18586e10 + 6.84655e9i 1.37035 + 0.791175i
\(306\) 1.01388e8 + 5.13409e8i 0.0115638 + 0.0585568i
\(307\) 6.47222e9 + 1.12102e10i 0.728618 + 1.26200i 0.957467 + 0.288542i \(0.0931705\pi\)
−0.228849 + 0.973462i \(0.573496\pi\)
\(308\) −2.81687e8 + 3.35702e8i −0.0313015 + 0.0373036i
\(309\) 9.53332e9 + 1.58070e9i 1.04571 + 0.173387i
\(310\) −4.96047e8 2.81322e9i −0.0537126 0.304619i
\(311\) −1.24197e10 + 2.18993e9i −1.32761 + 0.234093i −0.792076 0.610423i \(-0.791000\pi\)
−0.535531 + 0.844516i \(0.679888\pi\)
\(312\) −4.05699e8 + 1.52375e8i −0.0428140 + 0.0160804i
\(313\) −6.91530e9 5.80262e9i −0.720499 0.604571i 0.207024 0.978336i \(-0.433622\pi\)
−0.927523 + 0.373765i \(0.878067\pi\)
\(314\) 1.95229e9 1.12716e9i 0.200829 0.115949i
\(315\) 6.82700e8 8.48229e8i 0.0693406 0.0861531i
\(316\) −5.41983e9 + 9.38743e9i −0.543548 + 0.941452i
\(317\) −8.52565e8 2.34240e9i −0.0844287 0.231966i 0.890293 0.455388i \(-0.150499\pi\)
−0.974722 + 0.223422i \(0.928277\pi\)
\(318\) −1.73925e9 + 1.02800e9i −0.170081 + 0.100527i
\(319\) 5.35956e9 4.49721e9i 0.517567 0.434290i
\(320\) −3.14781e9 + 8.64853e9i −0.300198 + 0.824788i
\(321\) −7.08129e9 + 6.06630e9i −0.666949 + 0.571352i
\(322\) 2.22514e7 1.26194e8i 0.00206983 0.0117386i
\(323\) 2.02306e9i 0.185865i
\(324\) 8.51044e9 + 6.56763e9i 0.772275 + 0.595976i
\(325\) 8.49116e7 0.00761085
\(326\) 1.25275e9 + 2.20893e8i 0.110916 + 0.0195574i
\(327\) −1.67964e9 1.96067e9i −0.146901 0.171480i
\(328\) 5.78020e7 + 2.10382e7i 0.00499399 + 0.00181766i
\(329\) 1.03039e9 + 1.22798e9i 0.0879467 + 0.104811i
\(330\) −4.48300e8 7.58471e8i −0.0378019 0.0639563i
\(331\) −1.23169e10 + 4.48300e9i −1.02610 + 0.373471i −0.799596 0.600539i \(-0.794953\pi\)
−0.226507 + 0.974010i \(0.572731\pi\)
\(332\) 1.28703e10 + 7.43069e9i 1.05935 + 0.611614i
\(333\) 8.70560e9 3.37162e9i 0.707981 0.274197i
\(334\) −1.09897e9 1.90347e9i −0.0883077 0.152953i
\(335\) 5.10481e9 6.08367e9i 0.405322 0.483044i
\(336\) −4.48086e8 1.19303e9i −0.0351564 0.0936038i
\(337\) −2.91787e8 1.65481e9i −0.0226228 0.128300i 0.971405 0.237430i \(-0.0763049\pi\)
−0.994028 + 0.109129i \(0.965194\pi\)
\(338\) −1.96796e9 + 3.47005e8i −0.150782 + 0.0265870i
\(339\) −9.18883e8 + 5.54183e9i −0.0695763 + 0.419619i
\(340\) −3.90457e9 3.27633e9i −0.292185 0.245172i
\(341\) −1.04448e10 + 6.03031e9i −0.772472 + 0.445987i
\(342\) 6.87155e8 + 7.85731e8i 0.0502285 + 0.0574340i
\(343\) −1.48412e9 + 2.57057e9i −0.107224 + 0.185717i
\(344\) 3.79168e8 + 1.04176e9i 0.0270768 + 0.0743930i
\(345\) −8.93450e9 5.03731e9i −0.630658 0.355568i
\(346\) 2.71183e9 2.27550e9i 0.189216 0.158771i
\(347\) 2.77675e9 7.62907e9i 0.191522 0.526203i −0.806347 0.591442i \(-0.798559\pi\)
0.997870 + 0.0652390i \(0.0207810\pi\)
\(348\) 3.83642e9 + 2.05284e10i 0.261583 + 1.39971i
\(349\) 1.80498e7 1.02366e8i 0.00121667 0.00690006i −0.984193 0.177097i \(-0.943329\pi\)
0.985410 + 0.170197i \(0.0544404\pi\)
\(350\) 1.30369e7i 0.000868763i
\(351\) −1.49500e9 1.67462e9i −0.0984949 0.110329i
\(352\) −3.22854e9 −0.210298
\(353\) −9.42955e9 1.66268e9i −0.607285 0.107081i −0.138454 0.990369i \(-0.544213\pi\)
−0.468830 + 0.883288i \(0.655324\pi\)
\(354\) −1.04083e9 + 2.95321e9i −0.0662774 + 0.188053i
\(355\) 1.64771e9 + 5.99717e8i 0.103745 + 0.0377601i
\(356\) 6.15390e9 + 7.33394e9i 0.383134 + 0.456601i
\(357\) 6.67970e8 6.82651e6i 0.0411229 0.000420267i
\(358\) 2.97828e8 1.08400e8i 0.0181315 0.00659931i
\(359\) 2.20697e10 + 1.27419e10i 1.32867 + 0.767109i 0.985094 0.172015i \(-0.0550276\pi\)
0.343578 + 0.939124i \(0.388361\pi\)
\(360\) 5.32471e9 1.08846e8i 0.317019 0.00648041i
\(361\) 6.47420e9 + 1.12136e10i 0.381204 + 0.660264i
\(362\) 7.41991e8 8.84270e8i 0.0432080 0.0514933i
\(363\) 8.66247e9 1.05404e10i 0.498902 0.607061i
\(364\) 4.74338e7 + 2.69011e8i 0.00270198 + 0.0153237i
\(365\) −1.10447e9 + 1.94748e8i −0.0622276 + 0.0109724i
\(366\) −3.34868e9 2.75205e9i −0.186616 0.153367i
\(367\) −4.98172e8 4.18016e8i −0.0274609 0.0230424i 0.628954 0.777443i \(-0.283483\pi\)
−0.656415 + 0.754400i \(0.727928\pi\)
\(368\) −1.03963e10 + 6.00232e9i −0.566877 + 0.327287i
\(369\) 6.51199e6 + 3.18564e8i 0.000351243 + 0.0171827i
\(370\) 1.14195e9 1.97791e9i 0.0609312 0.105536i
\(371\) 8.82035e8 + 2.42337e9i 0.0465576 + 0.127916i
\(372\) −3.67894e8 3.59983e10i −0.0192111 1.87979i
\(373\) 9.77422e8 8.20154e8i 0.0504948 0.0423702i −0.617191 0.786813i \(-0.711729\pi\)
0.667686 + 0.744443i \(0.267285\pi\)
\(374\) 1.84871e8 5.07929e8i 0.00944892 0.0259607i
\(375\) 1.81406e10 + 6.39348e9i 0.917334 + 0.323305i
\(376\) −1.36153e9 + 7.72164e9i −0.0681204 + 0.386330i
\(377\) 4.36107e9i 0.215888i
\(378\) −2.57113e8 + 2.29535e8i −0.0125938 + 0.0112430i
\(379\) 2.22343e10 1.07762 0.538811 0.842427i \(-0.318874\pi\)
0.538811 + 0.842427i \(0.318874\pi\)
\(380\) −1.00121e10 1.76540e9i −0.480165 0.0846661i
\(381\) −3.72063e10 + 6.95324e9i −1.76570 + 0.329980i
\(382\) −1.76347e9 6.41851e8i −0.0828162 0.0301426i
\(383\) −2.13080e10 2.53939e10i −0.990258 1.18014i −0.983636 0.180166i \(-0.942337\pi\)
−0.00662182 0.999978i \(-0.502108\pi\)
\(384\) 6.28263e9 1.11433e10i 0.288946 0.512494i
\(385\) −1.05681e9 + 3.84647e8i −0.0481009 + 0.0175073i
\(386\) 2.89808e9 + 1.67321e9i 0.130545 + 0.0753704i
\(387\) −4.32274e9 + 3.78042e9i −0.192715 + 0.168537i
\(388\) −1.73186e10 2.99967e10i −0.764162 1.32357i
\(389\) 2.54213e10 3.02959e10i 1.11019 1.32308i 0.168845 0.985643i \(-0.445996\pi\)
0.941349 0.337435i \(-0.109559\pi\)
\(390\) −5.41789e8 8.98331e7i −0.0234192 0.00388309i
\(391\) −1.09268e9 6.19690e9i −0.0467505 0.265135i
\(392\) −7.10713e9 + 1.25318e9i −0.300989 + 0.0530724i
\(393\) −3.99589e10 + 1.50080e10i −1.67511 + 0.629150i
\(394\) 1.83282e9 + 1.53792e9i 0.0760561 + 0.0638186i
\(395\) −2.40911e10 + 1.39090e10i −0.989620 + 0.571357i
\(396\) −4.01000e9 1.03539e10i −0.163066 0.421040i
\(397\) 1.01278e10 1.75419e10i 0.407712 0.706179i −0.586921 0.809645i \(-0.699660\pi\)
0.994633 + 0.103466i \(0.0329932\pi\)
\(398\) 7.25513e8 + 1.99333e9i 0.0289143 + 0.0794414i
\(399\) 1.14702e9 6.77955e8i 0.0452564 0.0267491i
\(400\) −9.35600e8 + 7.85061e8i −0.0365469 + 0.0306665i
\(401\) 9.60582e9 2.63918e10i 0.371498 1.02068i −0.603284 0.797526i \(-0.706142\pi\)
0.974783 0.223157i \(-0.0716363\pi\)
\(402\) −1.90913e9 + 1.63548e9i −0.0731022 + 0.0626242i
\(403\) −1.30544e9 + 7.40353e9i −0.0494923 + 0.280685i
\(404\) 3.32720e10i 1.24897i
\(405\) 1.04871e10 + 2.55168e10i 0.389794 + 0.948431i
\(406\) −6.69576e8 −0.0246431
\(407\) −9.49609e9 1.67442e9i −0.346073 0.0610219i
\(408\) 2.12571e9 + 2.48138e9i 0.0767121 + 0.0895473i
\(409\) 2.22849e10 + 8.11103e9i 0.796374 + 0.289856i 0.707983 0.706229i \(-0.249605\pi\)
0.0883910 + 0.996086i \(0.471828\pi\)
\(410\) 5.01054e7 + 5.97133e7i 0.00177317 + 0.00211318i
\(411\) 1.31047e10 + 2.21716e10i 0.459260 + 0.777014i
\(412\) 2.79963e10 1.01898e10i 0.971654 0.353653i
\(413\) 3.46145e9 + 1.99847e9i 0.118976 + 0.0686906i
\(414\) 2.52923e9 + 2.03566e9i 0.0860969 + 0.0692953i
\(415\) 1.90695e10 + 3.30294e10i 0.642906 + 1.11355i
\(416\) −1.29357e9 + 1.54162e9i −0.0431934 + 0.0514759i
\(417\) 1.56915e10 + 4.17787e10i 0.518945 + 1.38169i
\(418\) −1.87215e8 1.06175e9i −0.00613248 0.0347790i
\(419\) 1.55067e10 2.73425e9i 0.503111 0.0887120i 0.0836677 0.996494i \(-0.473337\pi\)
0.419443 + 0.907782i \(0.362225\pi\)
\(420\) 5.49114e8 3.31174e9i 0.0176468 0.106429i
\(421\) 3.24333e9 + 2.72148e9i 0.103244 + 0.0866316i 0.692948 0.720987i \(-0.256311\pi\)
−0.589705 + 0.807619i \(0.700756\pi\)
\(422\) 4.92857e8 2.84551e8i 0.0155407 0.00897244i
\(423\) −3.98456e10 + 7.86873e9i −1.24457 + 0.245778i
\(424\) −6.30706e9 + 1.09241e10i −0.195148 + 0.338006i
\(425\) −2.18958e8 6.01583e8i −0.00671128 0.0184391i
\(426\) −4.83492e8 2.72595e8i −0.0146809 0.00827712i
\(427\) −4.23835e9 + 3.55640e9i −0.127493 + 0.106979i
\(428\) −9.83228e9 + 2.70140e10i −0.293008 + 0.805033i
\(429\) 4.25944e8 + 2.27919e9i 0.0125754 + 0.0672902i
\(430\) −2.43955e8 + 1.38354e9i −0.00713569 + 0.0404685i
\(431\) 5.43801e10i 1.57591i −0.615734 0.787954i \(-0.711140\pi\)
0.615734 0.787954i \(-0.288860\pi\)
\(432\) 3.19557e10 + 4.62960e9i 0.917515 + 0.132926i
\(433\) 1.01330e10 0.288261 0.144130 0.989559i \(-0.453962\pi\)
0.144130 + 0.989559i \(0.453962\pi\)
\(434\) 1.13670e9 + 2.00431e8i 0.0320395 + 0.00564944i
\(435\) −1.78148e10 + 5.05471e10i −0.497535 + 1.41169i
\(436\) −7.47964e9 2.72237e9i −0.206983 0.0753356i
\(437\) −8.06760e9 9.61459e9i −0.221217 0.263636i
\(438\) 3.54987e8 3.62789e6i 0.00964530 9.85729e-5i
\(439\) 4.09720e10 1.49126e10i 1.10314 0.401509i 0.274665 0.961540i \(-0.411433\pi\)
0.828471 + 0.560031i \(0.189211\pi\)
\(440\) −4.76391e9 2.75044e9i −0.127102 0.0733824i
\(441\) −1.93492e10 3.19858e10i −0.511574 0.845673i
\(442\) −1.68463e8 2.91787e8i −0.00441383 0.00764498i
\(443\) −2.87742e10 + 3.42918e10i −0.747117 + 0.890379i −0.996961 0.0779071i \(-0.975176\pi\)
0.249844 + 0.968286i \(0.419621\pi\)
\(444\) 1.82747e10 2.22366e10i 0.470240 0.572184i
\(445\) 4.26642e9 + 2.41961e10i 0.108799 + 0.617028i
\(446\) −1.59948e9 + 2.82031e8i −0.0404239 + 0.00712783i
\(447\) −4.43732e10 3.64674e10i −1.11145 0.913428i
\(448\) −2.84873e9 2.39037e9i −0.0707195 0.0593407i
\(449\) −3.94571e10 + 2.27806e10i −0.970823 + 0.560505i −0.899487 0.436947i \(-0.856060\pi\)
−0.0713360 + 0.997452i \(0.522726\pi\)
\(450\) 2.89375e8 + 1.59276e8i 0.00705686 + 0.00388418i
\(451\) 1.64552e8 2.85013e8i 0.00397738 0.00688903i
\(452\) 5.92346e9 + 1.62746e10i 0.141913 + 0.389903i
\(453\) 2.82634e8 + 2.76556e10i 0.00671168 + 0.656734i
\(454\) 2.04172e9 1.71320e9i 0.0480587 0.0403260i
\(455\) −2.39762e8 + 6.58740e8i −0.00559415 + 0.0153698i
\(456\) 6.14655e9 + 2.16629e9i 0.142158 + 0.0501022i
\(457\) −7.31714e9 + 4.14976e10i −0.167755 + 0.951388i 0.778422 + 0.627741i \(0.216020\pi\)
−0.946178 + 0.323647i \(0.895091\pi\)
\(458\) 4.93906e9i 0.112249i
\(459\) −8.00928e9 + 1.49101e10i −0.180444 + 0.335916i
\(460\) −3.16220e10 −0.706248
\(461\) 1.81731e10 + 3.20440e9i 0.402369 + 0.0709484i 0.371170 0.928565i \(-0.378957\pi\)
0.0311982 + 0.999513i \(0.490068\pi\)
\(462\) 3.49935e8 6.53971e7i 0.00768104 0.00143546i
\(463\) −2.73595e10 9.95805e9i −0.595367 0.216696i 0.0267215 0.999643i \(-0.491493\pi\)
−0.622088 + 0.782947i \(0.713715\pi\)
\(464\) 4.03209e10 + 4.80525e10i 0.869877 + 1.03668i
\(465\) 4.53738e10 8.04780e10i 0.970496 1.72134i
\(466\) 1.08507e10 3.94934e9i 0.230099 0.0837493i
\(467\) 4.63413e10 + 2.67552e10i 0.974319 + 0.562523i 0.900550 0.434752i \(-0.143164\pi\)
0.0737688 + 0.997275i \(0.476497\pi\)
\(468\) −6.55066e9 2.23372e9i −0.136553 0.0465634i
\(469\) 1.60444e9 + 2.77897e9i 0.0331613 + 0.0574370i
\(470\) −6.38683e9 + 7.61153e9i −0.130886 + 0.155984i
\(471\) 7.19261e10 + 1.19260e10i 1.46151 + 0.242331i
\(472\) 3.39485e9 + 1.92531e10i 0.0683994 + 0.387912i
\(473\) 5.84128e9 1.02997e9i 0.116698 0.0205770i
\(474\) 8.24334e9 3.09609e9i 0.163301 0.0613339i
\(475\) −9.78177e8 8.20788e8i −0.0192151 0.0161234i
\(476\) 1.78357e9 1.02975e9i 0.0347427 0.0200587i
\(477\) −6.45669e10 1.00289e10i −1.24720 0.193722i
\(478\) −1.75476e9 + 3.03934e9i −0.0336130 + 0.0582194i
\(479\) 9.54151e9 + 2.62151e10i 0.181249 + 0.497977i 0.996730 0.0808069i \(-0.0257497\pi\)
−0.815481 + 0.578784i \(0.803527\pi\)
\(480\) 2.12906e10 1.25840e10i 0.401073 0.237057i
\(481\) −4.60432e9 + 3.86348e9i −0.0860171 + 0.0721769i
\(482\) 2.74095e9 7.53071e9i 0.0507825 0.139524i
\(483\) 3.14731e9 2.69619e9i 0.0578297 0.0495407i
\(484\) 7.30416e9 4.14240e10i 0.133103 0.754867i
\(485\) 8.88899e10i 1.60652i
\(486\) −1.95368e9 8.51135e9i −0.0350194 0.152565i
\(487\) −5.43062e10 −0.965458 −0.482729 0.875770i \(-0.660354\pi\)
−0.482729 + 0.875770i \(0.660354\pi\)
\(488\) −2.66512e10 4.69932e9i −0.469934 0.0828621i
\(489\) 2.67655e10 + 3.12438e10i 0.468102 + 0.546423i
\(490\) −8.59387e9 3.12791e9i −0.149075 0.0542588i
\(491\) 2.12598e10 + 2.53364e10i 0.365791 + 0.435933i 0.917276 0.398252i \(-0.130383\pi\)
−0.551485 + 0.834185i \(0.685939\pi\)
\(492\) 4.99846e8 + 8.45681e8i 0.00853052 + 0.0144326i
\(493\) −3.08974e10 + 1.12457e10i −0.523039 + 0.190371i
\(494\) −5.81995e8 3.36015e8i −0.00977263 0.00564223i
\(495\) 4.37350e9 2.81570e10i 0.0728464 0.468992i
\(496\) −5.40663e10 9.36455e10i −0.893305 1.54725i
\(497\) −4.55411e8 + 5.42737e8i −0.00746410 + 0.00889537i
\(498\) −4.24480e9 1.13018e10i −0.0690144 0.183751i
\(499\) −7.01014e9 3.97565e10i −0.113064 0.641218i −0.987691 0.156421i \(-0.950004\pi\)
0.874626 0.484798i \(-0.161107\pi\)
\(500\) 5.83996e10 1.02974e10i 0.934393 0.164759i
\(501\) 1.16277e10 7.01272e10i 0.184562 1.11310i
\(502\) −6.26692e9 5.25857e9i −0.0986823 0.0828043i
\(503\) −1.03883e11 + 5.99768e10i −1.62283 + 0.936940i −0.636668 + 0.771138i \(0.719688\pi\)
−0.986159 + 0.165801i \(0.946979\pi\)
\(504\) −6.94521e8 + 2.03677e9i −0.0107637 + 0.0315660i
\(505\) 4.26933e10 7.39469e10i 0.656438 1.13698i
\(506\) −1.14693e9 3.15117e9i −0.0174959 0.0480695i
\(507\) −5.62976e10 3.17408e10i −0.852036 0.480381i
\(508\) −8.93935e10 + 7.50100e10i −1.34230 + 1.12633i
\(509\) 1.99802e10 5.48952e10i 0.297666 0.817830i −0.697223 0.716854i \(-0.745581\pi\)
0.994889 0.100976i \(-0.0321966\pi\)
\(510\) 7.60639e8 + 4.07012e9i 0.0112434 + 0.0601626i
\(511\) 7.86890e7 4.46268e8i 0.00115407 0.00654503i
\(512\) 4.86471e10i 0.707908i
\(513\) 1.03482e9 + 3.37429e10i 0.0149416 + 0.487206i
\(514\) 2.57709e9 0.0369213
\(515\) 7.52968e10 + 1.32768e10i 1.07040 + 0.188741i
\(516\) −5.88507e9 + 1.66981e10i −0.0830142 + 0.235542i
\(517\) 3.94203e10 + 1.43478e10i 0.551770 + 0.200828i
\(518\) 5.93178e8 + 7.06922e8i 0.00823884 + 0.00981867i
\(519\) 1.14485e11 1.17001e9i 1.57790 0.0161258i
\(520\) −3.22208e9 + 1.17274e9i −0.0440680 + 0.0160394i
\(521\) 6.93877e9 + 4.00610e9i 0.0941741 + 0.0543715i 0.546347 0.837559i \(-0.316018\pi\)
−0.452173 + 0.891930i \(0.649351\pi\)
\(522\) 8.18043e9 1.48624e10i 0.110178 0.200173i
\(523\) −2.54192e10 4.40273e10i −0.339746 0.588457i 0.644639 0.764487i \(-0.277008\pi\)
−0.984385 + 0.176030i \(0.943674\pi\)
\(524\) −8.45897e10 + 1.00810e11i −1.12200 + 1.33715i
\(525\) 2.67706e8 3.25743e8i 0.00352388 0.00428783i
\(526\) 2.15685e9 + 1.22321e10i 0.0281758 + 0.159793i
\(527\) 5.58189e10 9.84238e9i 0.723667 0.127602i
\(528\) −2.57659e10 2.11752e10i −0.331519 0.272453i
\(529\) 3.00845e10 + 2.52439e10i 0.384168 + 0.322355i
\(530\) −1.38435e10 + 7.99257e9i −0.175446 + 0.101294i
\(531\) −8.66491e10 + 5.24168e10i −1.08990 + 0.659314i
\(532\) 2.05392e9 3.55750e9i 0.0256412 0.0444118i
\(533\) −7.01622e7 1.92769e8i −0.000869349 0.00238852i
\(534\) −7.94775e7 7.77683e9i −0.000977416 0.0956396i
\(535\) −5.65154e10 + 4.74221e10i −0.689845 + 0.578849i
\(536\) −5.36818e9 + 1.47489e10i −0.0650381 + 0.178691i
\(537\) 9.66755e9 + 3.40723e9i 0.116257 + 0.0409736i
\(538\) −4.70280e8 + 2.66709e9i −0.00561342 + 0.0318353i
\(539\) 3.86117e10i 0.457472i
\(540\) 6.68009e10 + 5.26491e10i 0.785610 + 0.619179i
\(541\) 4.99438e10 0.583032 0.291516 0.956566i \(-0.405840\pi\)
0.291516 + 0.956566i \(0.405840\pi\)
\(542\) 1.15052e10 + 2.02868e9i 0.133321 + 0.0235081i
\(543\) 3.66976e10 6.85818e9i 0.422123 0.0788878i
\(544\) 1.42578e10 + 5.18941e9i 0.162801 + 0.0592546i
\(545\) −1.31302e10 1.56480e10i −0.148829 0.177367i
\(546\) 1.08981e8 1.93296e8i 0.00122625 0.00217497i
\(547\) −2.21042e10 + 8.04528e9i −0.246903 + 0.0898653i −0.462507 0.886616i \(-0.653050\pi\)
0.215604 + 0.976481i \(0.430828\pi\)
\(548\) 6.87654e10 + 3.97017e10i 0.762514 + 0.440238i
\(549\) −2.71589e10 1.37527e11i −0.298967 1.51390i
\(550\) −1.70586e8 2.95463e8i −0.00186420 0.00322888i
\(551\) −4.21558e10 + 5.02393e10i −0.457352 + 0.545051i
\(552\) 1.99978e10 + 3.31580e9i 0.215390 + 0.0357135i
\(553\) −1.95181e9 1.10693e10i −0.0208707 0.118364i
\(554\) 2.16540e10 3.81819e9i 0.229879 0.0405339i
\(555\) 6.91486e10 2.59713e10i 0.728805 0.273730i
\(556\) 1.05401e11 + 8.84420e10i 1.10293 + 0.925464i
\(557\) −1.24286e11 + 7.17563e10i −1.29122 + 0.745486i −0.978870 0.204482i \(-0.934449\pi\)
−0.312349 + 0.949968i \(0.601116\pi\)
\(558\) −1.83363e10 + 2.27822e10i −0.189137 + 0.234995i
\(559\) 1.84861e9 3.20188e9i 0.0189320 0.0327912i
\(560\) −3.44865e9 9.47509e9i −0.0350669 0.0963454i
\(561\) 1.50493e10 8.89500e9i 0.151937 0.0898038i
\(562\) −9.76746e9 + 8.19588e9i −0.0979121 + 0.0821580i
\(563\) 1.27931e10 3.51488e10i 0.127334 0.349846i −0.859601 0.510965i \(-0.829288\pi\)
0.986935 + 0.161119i \(0.0515103\pi\)
\(564\) −9.50956e10 + 8.14651e10i −0.939818 + 0.805110i
\(565\) −7.71799e9 + 4.37709e10i −0.0757375 + 0.429528i
\(566\) 1.96458e10i 0.191427i
\(567\) −1.11377e10 + 4.55536e8i −0.107761 + 0.00440749i
\(568\) −3.46544e9 −0.0332939
\(569\) 1.61367e11 + 2.84534e10i 1.53945 + 0.271447i 0.878043 0.478581i \(-0.158849\pi\)
0.661407 + 0.750028i \(0.269960\pi\)
\(570\) 5.37302e9 + 6.27201e9i 0.0509001 + 0.0594165i
\(571\) −1.72062e11 6.26253e10i −1.61860 0.589122i −0.635486 0.772112i \(-0.719200\pi\)
−0.983115 + 0.182990i \(0.941422\pi\)
\(572\) 4.59499e9 + 5.47609e9i 0.0429240 + 0.0511548i
\(573\) −3.08825e10 5.22495e10i −0.286479 0.484690i
\(574\) −2.95967e7 + 1.07723e7i −0.000272644 + 9.92344e-5i
\(575\) −3.43961e9 1.98586e9i −0.0314657 0.0181668i
\(576\) 8.78622e10 3.40284e10i 0.798201 0.309138i
\(577\) −1.38743e10 2.40309e10i −0.125172 0.216804i 0.796628 0.604470i \(-0.206615\pi\)
−0.921800 + 0.387665i \(0.873282\pi\)
\(578\) 9.59722e9 1.14375e10i 0.0859873 0.102476i
\(579\) 3.80537e10 + 1.01318e11i 0.338597 + 0.901513i
\(580\) 2.86927e10 + 1.62725e11i 0.253548 + 1.43794i
\(581\) −1.51762e10 + 2.67597e9i −0.133186 + 0.0234842i
\(582\) −4.60258e9 + 2.77585e10i −0.0401153 + 0.241938i
\(583\) 5.16996e10 + 4.33811e10i 0.447520 + 0.375514i
\(584\) 1.91954e9 1.10825e9i 0.0165023 0.00952763i
\(585\) −1.16926e10 1.33700e10i −0.0998360 0.114158i
\(586\) 1.51476e10 2.62364e10i 0.128456 0.222492i
\(587\) 1.84410e10 + 5.06662e10i 0.155322 + 0.426743i 0.992808 0.119715i \(-0.0381981\pi\)
−0.837487 + 0.546458i \(0.815976\pi\)
\(588\) −1.00396e11 5.66038e10i −0.839862 0.473517i
\(589\) 8.66040e10 7.26694e10i 0.719576 0.603796i
\(590\) −8.47348e9 + 2.32807e10i −0.0699284 + 0.192127i
\(591\) 1.42149e10 + 7.60627e10i 0.116518 + 0.623479i
\(592\) 1.50124e10 8.51396e10i 0.122226 0.693178i
\(593\) 1.98579e11i 1.60589i −0.596054 0.802945i \(-0.703265\pi\)
0.596054 0.802945i \(-0.296735\pi\)
\(594\) −2.82368e9 + 8.56638e9i −0.0226814 + 0.0688100i
\(595\) 5.28532e9 0.0421700
\(596\) −1.74387e11 3.07491e10i −1.38207 0.243696i
\(597\) −2.28042e10 + 6.47039e10i −0.179522 + 0.509370i
\(598\) −1.96422e9 7.14917e8i −0.0153598 0.00559050i
\(599\) −1.00906e11 1.20255e11i −0.783808 0.934105i 0.215291 0.976550i \(-0.430930\pi\)
−0.999099 + 0.0424444i \(0.986485\pi\)
\(600\) 2.06222e9 2.10754e7i 0.0159122 0.000162619i
\(601\) 1.23406e10 4.49162e9i 0.0945887 0.0344275i −0.294292 0.955715i \(-0.595084\pi\)
0.388881 + 0.921288i \(0.372862\pi\)
\(602\) −4.91599e8 2.83825e8i −0.00374305 0.00216105i
\(603\) −8.12858e10 + 1.66162e9i −0.614816 + 0.0125679i
\(604\) 4.26340e10 + 7.38443e10i 0.320338 + 0.554842i
\(605\) 6.93870e10 8.26922e10i 0.517912 0.617224i
\(606\) −1.71611e10 + 2.08815e10i −0.127249 + 0.154836i
\(607\) −2.69000e10 1.52558e11i −0.198152 1.12377i −0.907858 0.419277i \(-0.862284\pi\)
0.709706 0.704497i \(-0.248828\pi\)
\(608\) 2.98038e10 5.25521e9i 0.218101 0.0384571i
\(609\) −1.67302e10 1.37494e10i −0.121628 0.0999574i
\(610\) −2.62711e10 2.20441e10i −0.189740 0.159211i
\(611\) 2.26456e10 1.30744e10i 0.162487 0.0938118i
\(612\) 1.06645e9 + 5.21702e10i 0.00760211 + 0.371892i
\(613\) −6.82522e10 + 1.18216e11i −0.483364 + 0.837212i −0.999818 0.0191038i \(-0.993919\pi\)
0.516453 + 0.856315i \(0.327252\pi\)
\(614\) −1.10881e10 3.04644e10i −0.0780163 0.214348i
\(615\) 2.57631e7 + 2.52090e9i 0.000180093 + 0.0176220i
\(616\) 1.70266e9 1.42870e9i 0.0118251 0.00992244i
\(617\) 1.05167e10 2.88945e10i 0.0725672 0.199377i −0.898106 0.439778i \(-0.855057\pi\)
0.970673 + 0.240402i \(0.0772792\pi\)
\(618\) −2.28261e10 8.04483e9i −0.156487 0.0551522i
\(619\) 2.29396e10 1.30097e11i 0.156251 0.886143i −0.801382 0.598152i \(-0.795902\pi\)
0.957633 0.287991i \(-0.0929872\pi\)
\(620\) 2.84837e11i 1.92765i
\(621\) 2.13948e10 + 1.02800e11i 0.143861 + 0.691237i
\(622\) 3.15852e10 0.211019
\(623\) −9.77655e9 1.72387e9i −0.0648983 0.0114433i
\(624\) −2.04347e10 + 3.81891e9i −0.134781 + 0.0251884i
\(625\) 1.50385e11 + 5.47355e10i 0.985561 + 0.358715i
\(626\) 1.45327e10 + 1.73195e10i 0.0946347 + 0.112781i
\(627\) 1.71247e10 3.03735e10i 0.110803 0.196528i
\(628\) 2.11224e11 7.68792e10i 1.35801 0.494277i
\(629\) 3.92450e10 + 2.26581e10i 0.250716 + 0.144751i
\(630\) −2.05275e9 + 1.79522e9i −0.0130309 + 0.0113961i
\(631\) 6.47545e10 + 1.12158e11i 0.408463 + 0.707478i 0.994718 0.102648i \(-0.0327316\pi\)
−0.586255 + 0.810127i \(0.699398\pi\)
\(632\) 3.53392e10 4.21157e10i 0.221508 0.263983i
\(633\) 1.81578e10 + 3.01071e9i 0.113096 + 0.0187523i
\(634\) 1.08410e9 + 6.14824e9i 0.00670984 + 0.0380534i
\(635\) −2.94926e11 + 5.20035e10i −1.81392 + 0.319843i
\(636\) −1.88587e11 + 7.08310e10i −1.15261 + 0.432907i
\(637\) 1.84370e10 + 1.54705e10i 0.111978 + 0.0939609i
\(638\) −1.51750e10 + 8.76130e9i −0.0915897 + 0.0528793i
\(639\) −6.48306e9 1.67394e10i −0.0388845 0.100401i
\(640\) 5.06071e10 8.76541e10i 0.301642 0.522459i
\(641\) −5.46839e10 1.50243e11i −0.323912 0.889941i −0.989617 0.143726i \(-0.954092\pi\)
0.665706 0.746215i \(-0.268131\pi\)
\(642\) 2.01040e10 1.18826e10i 0.118343 0.0699475i
\(643\) 1.61080e11 1.35162e11i 0.942318 0.790699i −0.0356691 0.999364i \(-0.511356\pi\)
0.977987 + 0.208665i \(0.0669118\pi\)
\(644\) 4.37000e9 1.20065e10i 0.0254061 0.0698027i
\(645\) −3.45058e10 + 2.95600e10i −0.199367 + 0.170791i
\(646\) −8.79836e8 + 4.98980e9i −0.00505210 + 0.0286519i
\(647\) 1.78264e11i 1.01730i 0.860974 + 0.508648i \(0.169855\pi\)
−0.860974 + 0.508648i \(0.830145\pi\)
\(648\) −3.67243e10 4.02999e10i −0.208283 0.228562i
\(649\) 1.04599e11 0.589587
\(650\) −2.09431e8 3.69284e7i −0.00117324 0.000206875i
\(651\) 2.42861e10 + 2.83496e10i 0.135218 + 0.157842i
\(652\) 1.19190e11 + 4.33817e10i 0.659554 + 0.240058i
\(653\) 6.49968e10 + 7.74602e10i 0.357470 + 0.426016i 0.914569 0.404430i \(-0.132530\pi\)
−0.557099 + 0.830446i \(0.688086\pi\)
\(654\) 3.29007e9 + 5.56641e9i 0.0179843 + 0.0304273i
\(655\) −3.17356e11 + 1.15508e11i −1.72417 + 0.627548i
\(656\) 2.55536e9 + 1.47534e9i 0.0137986 + 0.00796664i
\(657\) 8.94429e9 + 7.19884e9i 0.0480048 + 0.0386368i
\(658\) −2.00738e9 3.47688e9i −0.0107084 0.0185475i
\(659\) −1.04978e9 + 1.25108e9i −0.00556616 + 0.00663349i −0.768820 0.639465i \(-0.779156\pi\)
0.763254 + 0.646098i \(0.223600\pi\)
\(660\) −3.08887e10 8.22411e10i −0.162788 0.433424i
\(661\) −1.54225e10 8.74653e10i −0.0807884 0.458174i −0.998186 0.0602023i \(-0.980825\pi\)
0.917398 0.397971i \(-0.130286\pi\)
\(662\) 3.23290e10 5.70047e9i 0.168329 0.0296810i
\(663\) 1.78243e9 1.07500e10i 0.00922485 0.0556356i
\(664\) −5.77414e10 4.84508e10i −0.297040 0.249246i
\(665\) 9.12968e9 5.27102e9i 0.0466841 0.0269531i
\(666\) −2.29384e10 + 4.52988e9i −0.116591 + 0.0230245i
\(667\) −1.01994e11 + 1.76659e11i −0.515314 + 0.892549i
\(668\) −7.49564e10 2.05941e11i −0.376446 1.03428i
\(669\) −4.57563e10 2.57976e10i −0.228426 0.128788i
\(670\) −1.52366e10 + 1.27851e10i −0.0756119 + 0.0634459i
\(671\) −4.95214e10 + 1.36059e11i −0.244289 + 0.671177i
\(672\) 1.83573e9 + 9.82284e9i 0.00900184 + 0.0481682i
\(673\) −1.34793e10 + 7.64450e10i −0.0657064 + 0.372640i 0.934169 + 0.356832i \(0.116143\pi\)
−0.999875 + 0.0158078i \(0.994968\pi\)
\(674\) 4.20842e9i 0.0203929i
\(675\) 3.95976e9 + 9.92189e9i 0.0190745 + 0.0477947i
\(676\) −1.99254e11 −0.954160
\(677\) −1.68693e11 2.97451e10i −0.803050 0.141599i −0.242965 0.970035i \(-0.578120\pi\)
−0.560084 + 0.828436i \(0.689231\pi\)
\(678\) 4.67656e9 1.32691e10i 0.0221313 0.0627947i
\(679\) 3.37504e10 + 1.22842e10i 0.158782 + 0.0577918i
\(680\) 1.66173e10 + 1.98037e10i 0.0777187 + 0.0926215i
\(681\) 8.61947e10 8.80891e8i 0.400767 0.00409575i
\(682\) 2.83843e10 1.03311e10i 0.131202 0.0477537i
\(683\) 3.58504e11 + 2.06982e11i 1.64744 + 0.951153i 0.978083 + 0.208216i \(0.0667657\pi\)
0.669362 + 0.742937i \(0.266568\pi\)
\(684\) 5.38713e10 + 8.90535e10i 0.246112 + 0.406843i
\(685\) 1.01887e11 + 1.76474e11i 0.462762 + 0.801527i
\(686\) 4.77848e9 5.69477e9i 0.0215771 0.0257146i
\(687\) 1.01421e11 1.23409e11i 0.455305 0.554012i
\(688\) 9.23450e9 + 5.23715e10i 0.0412154 + 0.233744i
\(689\) 4.14288e10 7.30502e9i 0.183834 0.0324149i
\(690\) 1.98459e10 + 1.63100e10i 0.0875536 + 0.0719544i
\(691\) −3.19102e11 2.67758e11i −1.39964 1.17444i −0.961258 0.275650i \(-0.911107\pi\)
−0.438383 0.898788i \(-0.644449\pi\)
\(692\) 3.05691e11 1.76491e11i 1.33309 0.769657i
\(693\) 1.00865e10 + 5.55172e9i 0.0437327 + 0.0240710i
\(694\) −1.01667e10 + 1.76092e10i −0.0438269 + 0.0759105i
\(695\) 1.20768e11 + 3.31808e11i 0.517623 + 1.42216i
\(696\) −1.08244e9 1.05916e11i −0.00461281 0.451361i
\(697\) −1.18481e9 + 9.94173e8i −0.00502016 + 0.00421241i
\(698\) −8.90386e7 + 2.44632e8i −0.000375108 + 0.00103060i
\(699\) 3.52217e11 + 1.24135e11i 1.47537 + 0.519980i
\(700\) 2.25729e8 1.28017e9i 0.000940144 0.00533182i
\(701\) 4.23591e11i 1.75418i 0.480326 + 0.877090i \(0.340518\pi\)
−0.480326 + 0.877090i \(0.659482\pi\)
\(702\) 2.95907e9 + 4.78058e9i 0.0121845 + 0.0196849i
\(703\) 9.03874e10 0.370072
\(704\) −9.58403e10 1.68992e10i −0.390173 0.0687980i
\(705\) −3.15882e11 + 5.90332e10i −1.27870 + 0.238968i
\(706\) 2.25345e10 + 8.20191e9i 0.0907048 + 0.0330138i
\(707\) 2.21767e10 + 2.64292e10i 0.0887606 + 0.105781i
\(708\) −1.53339e11 + 2.71972e11i −0.610266 + 1.08241i
\(709\) −1.98886e11 + 7.23886e10i −0.787081 + 0.286474i −0.704122 0.710079i \(-0.748659\pi\)
−0.0829588 + 0.996553i \(0.526437\pi\)
\(710\) −3.80320e9 2.19578e9i −0.0149663 0.00864082i
\(711\) 2.69547e11 + 9.19132e10i 1.05477 + 0.359666i
\(712\) −2.42788e10 4.20521e10i −0.0944728 0.163632i
\(713\) 2.26030e11 2.69372e11i 0.874598 1.04231i
\(714\) −1.65049e9 2.73666e8i −0.00635069 0.00105300i
\(715\) 3.18564e9 + 1.80667e10i 0.0121891 + 0.0691281i
\(716\) 3.11224e10 5.48772e9i 0.118419 0.0208805i
\(717\) −1.06256e11 + 3.99085e10i −0.402048 + 0.151004i
\(718\) −4.88925e10 4.10257e10i −0.183969 0.154368i
\(719\) −3.55351e11 + 2.05162e11i −1.32966 + 0.767681i −0.985247 0.171137i \(-0.945256\pi\)
−0.344415 + 0.938817i \(0.611923\pi\)
\(720\) 2.52449e11 + 3.92117e10i 0.939384 + 0.145910i
\(721\) −1.54467e10 + 2.67545e10i −0.0571603 + 0.0990046i
\(722\) −1.10915e10 3.04737e10i −0.0408171 0.112144i
\(723\) 2.23126e11 1.31880e11i 0.816576 0.482643i
\(724\) 8.81714e10 7.39846e10i 0.320903 0.269269i
\(725\) −7.09812e9 + 1.95019e10i −0.0256916 + 0.0705871i
\(726\) −2.59498e10 + 2.22303e10i −0.0934086 + 0.0800199i
\(727\) −5.40742e10 + 3.06670e11i −0.193576 + 1.09783i 0.720855 + 0.693086i \(0.243749\pi\)
−0.914432 + 0.404741i \(0.867362\pi\)
\(728\) 1.38545e9i 0.00493249i
\(729\) 1.25961e11 2.52785e11i 0.445992 0.895037i
\(730\) 2.80884e9 0.00989088
\(731\) −2.74517e10 4.84047e9i −0.0961389 0.0169519i
\(732\) −2.81176e11 3.28222e11i −0.979342 1.14320i
\(733\) −1.43090e11 5.20803e10i −0.495669 0.180409i 0.0820759 0.996626i \(-0.473845\pi\)
−0.577745 + 0.816217i \(0.696067\pi\)
\(734\) 1.04693e9 + 1.24768e9i 0.00360688 + 0.00429851i
\(735\) −1.50498e11 2.54626e11i −0.515683 0.872475i
\(736\) 8.84547e10 3.21949e10i 0.301446 0.109717i
\(737\) 7.27248e10 + 4.19877e10i 0.246497 + 0.142315i
\(738\) 1.22483e8 7.88559e8i 0.000412906 0.00265833i
\(739\) −3.62658e10 6.28143e10i −0.121596 0.210611i 0.798801 0.601595i \(-0.205468\pi\)
−0.920397 + 0.390984i \(0.872135\pi\)
\(740\) 1.46382e11 1.74451e11i 0.488158 0.581764i
\(741\) −7.64197e9 2.03467e10i −0.0253474 0.0674873i
\(742\) −1.12157e9 6.36076e9i −0.00370009 0.0209842i
\(743\) −2.97391e11 + 5.24380e10i −0.975826 + 0.172064i −0.638751 0.769413i \(-0.720549\pi\)
−0.337075 + 0.941478i \(0.609438\pi\)
\(744\) −2.98672e10 + 1.80131e11i −0.0974773 + 0.587891i
\(745\) −3.48118e11 2.92106e11i −1.13006 0.948234i
\(746\) −2.76746e9 + 1.59780e9i −0.00893566 + 0.00515901i
\(747\) 1.26015e11 3.69554e11i 0.404705 1.18685i
\(748\) 2.69482e10 4.66756e10i 0.0860842 0.149102i
\(749\) −1.01954e10 2.80117e10i −0.0323950 0.0890046i
\(750\) −4.19627e10 2.36587e10i −0.132623 0.0747733i
\(751\) 1.35125e11 1.13384e11i 0.424793 0.356443i −0.405190 0.914232i \(-0.632795\pi\)
0.829983 + 0.557789i \(0.188350\pi\)
\(752\) −1.28639e11 + 3.53433e11i −0.402255 + 1.10519i
\(753\) −4.86047e10 2.60080e11i −0.151181 0.808961i
\(754\) −1.89665e9 + 1.07564e10i −0.00586815 + 0.0332799i
\(755\) 2.18825e11i 0.673455i
\(756\) −2.92218e10 + 1.80876e10i −0.0894581 + 0.0553726i
\(757\) 1.08704e11 0.331025 0.165513 0.986208i \(-0.447072\pi\)
0.165513 + 0.986208i \(0.447072\pi\)
\(758\) −5.48401e10 9.66979e9i −0.166120 0.0292914i
\(759\) 3.60502e10 1.02288e11i 0.108628 0.308217i
\(760\) 4.84544e10 + 1.76360e10i 0.145237 + 0.0528621i
\(761\) −3.21895e11 3.83619e11i −0.959788 1.14383i −0.989538 0.144273i \(-0.953916\pi\)
0.0297499 0.999557i \(-0.490529\pi\)
\(762\) 9.47919e10 9.68753e8i 0.281159 0.00287338i
\(763\) 7.75589e9 2.82291e9i 0.0228841 0.00832913i
\(764\) −1.62053e11 9.35612e10i −0.475645 0.274614i
\(765\) −6.45725e10 + 1.17316e11i −0.188539 + 0.342542i
\(766\) 4.15116e10 + 7.19002e10i 0.120574 + 0.208841i
\(767\) 4.19094e10 4.99457e10i 0.121096 0.144317i
\(768\) 1.68730e11 2.05310e11i 0.485007 0.590153i
\(769\) −7.36249e10 4.17547e11i −0.210533 1.19399i −0.888493 0.458891i \(-0.848247\pi\)
0.677960 0.735099i \(-0.262864\pi\)
\(770\) 2.77386e9 4.89107e8i 0.00789082 0.00139136i
\(771\) 6.43919e10 + 5.29193e10i 0.182227 + 0.149760i
\(772\) 2.55609e11 + 2.14482e11i 0.719627 + 0.603839i
\(773\) 2.87823e11 1.66175e11i 0.806134 0.465422i −0.0394773 0.999220i \(-0.512569\pi\)
0.845612 + 0.533799i \(0.179236\pi\)
\(774\) 1.23060e10 7.44429e9i 0.0342889 0.0207424i
\(775\) 1.78877e10 3.09825e10i 0.0495848 0.0858834i
\(776\) 6.00852e10 + 1.65083e11i 0.165699 + 0.455255i
\(777\) 3.04999e8 + 2.98440e10i 0.000836786 + 0.0818790i
\(778\) −7.58765e10 + 6.36679e10i −0.207104 + 0.173781i
\(779\) −1.05512e9 + 2.89891e9i −0.00286517 + 0.00787198i
\(780\) −5.16461e10 1.82021e10i −0.139527 0.0491749i
\(781\) −3.21962e9 + 1.82594e10i −0.00865368 + 0.0490775i
\(782\) 1.57596e10i 0.0421424i
\(783\) 5.09590e11 2.03374e11i 1.35573 0.541063i
\(784\) −3.46184e11 −0.916310
\(785\) 5.68092e11 + 1.00170e11i 1.49603 + 0.263790i
\(786\) 1.05084e11 1.96385e10i 0.275326 0.0514539i
\(787\) −4.41598e11 1.60728e11i −1.15114 0.418980i −0.305215 0.952283i \(-0.598728\pi\)
−0.845924 + 0.533303i \(0.820951\pi\)
\(788\) 1.53347e11 + 1.82752e11i 0.397714 + 0.473977i
\(789\) −1.97288e11 + 3.49924e11i −0.509089 + 0.902954i
\(790\) 6.54690e10 2.38288e10i 0.168084 0.0611777i
\(791\) −1.55527e10 8.97936e9i −0.0397283 0.0229371i
\(792\) 1.09105e10 + 5.52483e10i 0.0277295 + 0.140417i
\(793\) 4.51263e10 + 7.81610e10i 0.114113 + 0.197650i
\(794\) −3.26090e10 + 3.88618e10i −0.0820455 + 0.0977781i
\(795\) −5.10022e11 8.45659e10i −1.27679 0.211703i
\(796\) 3.67288e10 + 2.08299e11i 0.0914859 + 0.518842i
\(797\) −4.55285e10 + 8.02790e9i −0.112837 + 0.0198961i −0.229781 0.973242i \(-0.573801\pi\)
0.116945 + 0.993138i \(0.462690\pi\)
\(798\) −3.12393e9 + 1.17331e9i −0.00770353 + 0.00289335i
\(799\) −1.51025e11 1.26725e11i −0.370563 0.310939i
\(800\) 8.29378e9 4.78842e9i 0.0202485 0.0116905i
\(801\) 1.57708e11 1.95946e11i 0.383109 0.475999i
\(802\) −3.51703e10 + 6.09168e10i −0.0850117 + 0.147245i
\(803\) −4.05597e9 1.11437e10i −0.00975512 0.0268020i
\(804\) −2.15787e11 + 1.27542e11i −0.516417 + 0.305232i
\(805\) 2.51185e10 2.10769e10i 0.0598150 0.0501908i
\(806\) 6.43965e9 1.76928e10i 0.0152589 0.0419234i
\(807\) −6.65180e10 + 5.69837e10i −0.156836 + 0.134356i
\(808\) −2.93037e10 + 1.66190e11i −0.0687508 + 0.389905i
\(809\) 1.18357e11i 0.276312i 0.990410 + 0.138156i \(0.0441175\pi\)
−0.990410 + 0.138156i \(0.955882\pi\)
\(810\) −1.47687e10 6.74971e10i −0.0343086 0.156800i
\(811\) 9.39449e10 0.217165 0.108582 0.994087i \(-0.465369\pi\)
0.108582 + 0.994087i \(0.465369\pi\)
\(812\) −6.57497e10 1.15935e10i −0.151241 0.0266679i
\(813\) 2.45815e11 + 2.86944e11i 0.562660 + 0.656802i
\(814\) 2.26936e10 + 8.25978e9i 0.0516898 + 0.0188136i
\(815\) 2.09234e11 + 2.49355e11i 0.474244 + 0.565182i
\(816\) 7.97505e10 + 1.34928e11i 0.179876 + 0.304329i
\(817\) −5.22464e10 + 1.90161e10i −0.117265 + 0.0426810i
\(818\) −5.14373e10 2.96974e10i −0.114886 0.0663292i
\(819\) 6.69227e9 2.59187e9i 0.0148743 0.00576074i
\(820\) 3.88624e9 + 6.73117e9i 0.00859557 + 0.0148880i
\(821\) 1.46122e11 1.74141e11i 0.321619 0.383291i −0.580875 0.813993i \(-0.697290\pi\)
0.902494 + 0.430702i \(0.141734\pi\)
\(822\) −2.26797e10 6.03846e10i −0.0496764 0.132263i
\(823\) 6.39160e9 + 3.62485e10i 0.0139319 + 0.0790117i 0.990981 0.134003i \(-0.0427830\pi\)
−0.977049 + 0.213014i \(0.931672\pi\)
\(824\) −1.48813e11 + 2.62397e10i −0.322798 + 0.0569180i
\(825\) 1.80489e9 1.08854e10i 0.00389615 0.0234979i
\(826\) −7.66841e9 6.43456e9i −0.0164735 0.0138229i
\(827\) 3.00935e11 1.73745e11i 0.643354 0.371441i −0.142551 0.989787i \(-0.545531\pi\)
0.785906 + 0.618347i \(0.212197\pi\)
\(828\) 2.13114e11 + 2.43687e11i 0.453410 + 0.518454i
\(829\) −2.97922e11 + 5.16016e11i −0.630790 + 1.09256i 0.356601 + 0.934257i \(0.383936\pi\)
−0.987391 + 0.158303i \(0.949398\pi\)
\(830\) −3.26697e10 8.97592e10i −0.0688387 0.189133i
\(831\) 6.19457e11 + 3.49252e11i 1.29899 + 0.732378i
\(832\) −4.64695e10 + 3.89926e10i −0.0969784 + 0.0813745i
\(833\) 6.20629e10 1.70516e11i 0.128900 0.354149i
\(834\) −2.05329e10 1.09870e11i −0.0424410 0.227099i
\(835\) 9.76647e10 5.53884e11i 0.200905 1.13939i
\(836\) 1.07501e11i 0.220084i
\(837\) −9.25978e11 + 1.92715e11i −1.88668 + 0.392657i
\(838\) −3.94359e10 −0.0799678
\(839\) −3.77521e11 6.65672e10i −0.761892 0.134342i −0.220816 0.975316i \(-0.570872\pi\)
−0.541077 + 0.840973i \(0.681983\pi\)
\(840\) −5.65951e9 + 1.60581e10i −0.0113674 + 0.0322535i
\(841\) 5.31543e11 + 1.93466e11i 1.06256 + 0.386741i
\(842\) −6.81598e9 8.12297e9i −0.0135606 0.0161609i
\(843\) −4.12351e11 + 4.21414e9i −0.816501 + 0.00834446i
\(844\) 5.33235e10 1.94082e10i 0.105087 0.0382486i
\(845\) −4.42842e11 2.55675e11i −0.868604 0.501489i
\(846\) 1.01700e11 2.07892e9i 0.198536 0.00405842i
\(847\) 2.18083e10 + 3.77730e10i 0.0423729 + 0.0733919i
\(848\) −3.88945e11 + 4.63526e11i −0.752150 + 0.896377i
\(849\) −4.03416e11 + 4.90874e11i −0.776466 + 0.944799i
\(850\) 2.78422e8 + 1.57901e9i 0.000533369 + 0.00302489i
\(851\) 2.76869e11 4.88195e10i 0.527906 0.0930840i
\(852\) −4.27572e10 3.51392e10i −0.0811430 0.0666859i
\(853\) 6.58027e11 + 5.52150e11i 1.24293 + 1.04294i 0.997289 + 0.0735846i \(0.0234439\pi\)
0.245644 + 0.969360i \(0.421001\pi\)
\(854\) 1.20004e10 6.92845e9i 0.0225614 0.0130258i
\(855\) 5.45888e9 + 2.67046e11i 0.0102150 + 0.499715i
\(856\) 7.29032e10 1.26272e11i 0.135785 0.235186i
\(857\) −1.21489e11 3.33788e11i −0.225223 0.618795i 0.774685 0.632347i \(-0.217908\pi\)
−0.999908 + 0.0135519i \(0.995686\pi\)
\(858\) −5.93442e7 5.80679e9i −0.000109504 0.0107149i
\(859\) 3.20921e11 2.69285e11i 0.589421 0.494583i −0.298605 0.954377i \(-0.596521\pi\)
0.888026 + 0.459794i \(0.152077\pi\)
\(860\) −4.79109e10 + 1.31634e11i −0.0875872 + 0.240644i
\(861\) −9.60717e8 3.38594e8i −0.00174817 0.000616123i
\(862\) −2.36501e10 + 1.34127e11i −0.0428356 + 0.242933i
\(863\) 3.69630e11i 0.666383i 0.942859 + 0.333191i \(0.108125\pi\)
−0.942859 + 0.333191i \(0.891875\pi\)
\(864\) −2.40462e11 7.92619e10i −0.431511 0.142236i
\(865\) 9.05862e11 1.61807
\(866\) −2.49926e10 4.40687e9i −0.0444365 0.00783536i
\(867\) 4.74663e11 8.87066e10i 0.840057 0.156993i
\(868\) 1.08149e11 + 3.93630e10i 0.190521 + 0.0693441i
\(869\) −1.89075e11 2.25331e11i −0.331554 0.395131i
\(870\) 6.59227e10 1.16925e11i 0.115069 0.204094i
\(871\) 4.91876e10 1.79028e10i 0.0854639 0.0311063i
\(872\) 3.49622e10 + 2.01855e10i 0.0604691 + 0.0349118i
\(873\) −6.85008e11 + 5.99068e11i −1.17934 + 1.03138i
\(874\) 1.57170e10 + 2.72227e10i 0.0269355 + 0.0466536i
\(875\) −3.95255e10 + 4.71046e10i −0.0674287 + 0.0803584i
\(876\) 3.49211e10 + 5.79022e9i 0.0593024 + 0.00983283i
\(877\) 1.45845e11 + 8.27127e11i 0.246543 + 1.39821i 0.816882 + 0.576805i \(0.195701\pi\)
−0.570339 + 0.821409i \(0.693188\pi\)
\(878\) −1.07542e11 + 1.89625e10i −0.180967 + 0.0319093i
\(879\) 9.17233e11 3.44501e11i 1.53647 0.577078i
\(880\) −2.02139e11 1.69615e11i −0.337070 0.282835i
\(881\) 6.57619e11 3.79677e11i 1.09162 0.630246i 0.157612 0.987501i \(-0.449621\pi\)
0.934007 + 0.357255i \(0.116287\pi\)
\(882\) 3.38134e10 + 8.73068e10i 0.0558746 + 0.144269i
\(883\) 5.00897e11 8.67579e11i 0.823959 1.42714i −0.0787530 0.996894i \(-0.525094\pi\)
0.902712 0.430245i \(-0.141573\pi\)
\(884\) −1.14902e10 3.15692e10i −0.0188157 0.0516957i
\(885\) −6.89778e11 + 4.07699e11i −1.12444 + 0.664609i
\(886\) 8.58842e10 7.20654e10i 0.139373 0.116948i
\(887\) 2.56509e11 7.04753e11i 0.414389 1.13853i −0.540443 0.841380i \(-0.681743\pi\)
0.954832 0.297145i \(-0.0960344\pi\)
\(888\) −1.10865e11 + 9.49739e10i −0.178296 + 0.152740i
\(889\) 2.10123e10 1.19167e11i 0.0336408 0.190786i
\(890\) 6.15342e10i 0.0980747i
\(891\) −2.46460e11 + 1.56059e11i −0.391052 + 0.247616i
\(892\) −1.61946e11 −0.255805
\(893\) −3.87258e11 6.82841e10i −0.608968 0.107378i
\(894\) 9.35852e10 + 1.09244e11i 0.146507 + 0.171020i
\(895\) 7.62111e10 + 2.77386e10i 0.118775 + 0.0432306i
\(896\) 2.62876e10 + 3.13283e10i 0.0407867 + 0.0486077i
\(897\) −3.43980e10 5.81973e10i −0.0531328 0.0898945i
\(898\) 1.07227e11 3.90274e10i 0.164892 0.0600157i
\(899\) −1.59126e12 9.18717e11i −2.43615 1.40651i
\(900\) 2.56577e10 + 2.06507e10i 0.0391064 + 0.0314749i
\(901\) −1.58586e11 2.74678e11i −0.240638 0.416798i
\(902\) −5.29815e8 + 6.31409e8i −0.000800384 + 0.000953861i
\(903\) −6.45502e9 1.71865e10i −0.00970838 0.0258485i
\(904\) −1.52534e10 8.65066e10i −0.0228399 0.129532i
\(905\) 2.90895e11 5.12925e10i 0.433652 0.0764645i
\(906\) 1.13304e10 6.83344e10i 0.0168164 0.101421i
\(907\) 1.50108e11 + 1.25956e11i 0.221807 + 0.186118i 0.746919 0.664915i \(-0.231532\pi\)
−0.525112 + 0.851033i \(0.675977\pi\)
\(908\) 2.30152e11 1.32878e11i 0.338588 0.195484i
\(909\) −8.57582e11 + 1.69356e11i −1.25609 + 0.248053i
\(910\) 8.77852e8 1.52049e9i 0.00128014 0.00221726i
\(911\) −2.20777e11 6.06578e11i −0.320538 0.880671i −0.990406 0.138190i \(-0.955871\pi\)
0.669868 0.742480i \(-0.266351\pi\)
\(912\) 2.72322e11 + 1.53536e11i 0.393643 + 0.221938i
\(913\) −3.08932e11 + 2.59225e11i −0.444611 + 0.373073i
\(914\) 3.60949e10 9.91700e10i 0.0517204 0.142101i
\(915\) −2.03753e11 1.09027e12i −0.290682 1.55542i
\(916\) 8.55180e10 4.84997e11i 0.121472 0.688901i
\(917\) 1.36459e11i 0.192985i
\(918\) 2.62391e10 3.32920e10i 0.0369469 0.0468780i
\(919\) −6.41781e11 −0.899756 −0.449878 0.893090i \(-0.648532\pi\)
−0.449878 + 0.893090i \(0.648532\pi\)
\(920\) 1.57948e11 + 2.78505e10i 0.220477 + 0.0388760i
\(921\) 3.48521e11 9.88881e11i 0.484384 1.37438i
\(922\) −4.34296e10 1.58071e10i −0.0600983 0.0218740i
\(923\) 7.42882e9 + 8.85333e9i 0.0102356 + 0.0121983i
\(924\) 3.54946e10 3.62747e8i 0.0486939 0.000497641i
\(925\) 2.68779e10 9.78276e9i 0.0367137 0.0133627i
\(926\) 6.31505e10 + 3.64600e10i 0.0858881 + 0.0495875i
\(927\) −4.05143e11 6.69734e11i −0.548642 0.906950i
\(928\) −2.45934e11 4.25970e11i −0.331609 0.574363i
\(929\) −8.58049e11 + 1.02258e12i −1.15199 + 1.37289i −0.235970 + 0.971760i \(0.575827\pi\)
−0.916021 + 0.401129i \(0.868618\pi\)
\(930\) −1.46913e11 + 1.78763e11i −0.196394 + 0.238971i
\(931\) −6.28498e10 3.56439e11i −0.0836576 0.474446i
\(932\) 1.13388e12 1.99934e11i 1.50281 0.264986i
\(933\) 7.89195e11 + 6.48586e11i 1.04150 + 0.855935i
\(934\) −1.02663e11 8.61448e10i −0.134905 0.113199i
\(935\) 1.19784e11 6.91576e10i 0.156731 0.0904885i
\(936\) 3.07524e10 + 1.69265e10i 0.0400660 + 0.0220528i
\(937\) −2.84345e11 + 4.92500e11i −0.368882 + 0.638922i −0.989391 0.145277i \(-0.953593\pi\)
0.620509 + 0.784199i \(0.286926\pi\)
\(938\) −2.74870e9 7.55200e9i −0.00355072 0.00975552i
\(939\) 7.47241e9 + 7.31171e11i 0.00961166 + 0.940496i
\(940\) −7.58953e11 + 6.36837e11i −0.972083 + 0.815675i
\(941\) 1.33808e11 3.67635e11i 0.170657 0.468876i −0.824650 0.565643i \(-0.808628\pi\)
0.995307 + 0.0967671i \(0.0308502\pi\)
\(942\) −1.72217e11 6.06959e10i −0.218711 0.0770825i
\(943\) −1.66622e9 + 9.44963e9i −0.00210711 + 0.0119500i
\(944\) 9.37807e11i 1.18093i
\(945\) −8.81546e10 + 2.70351e9i −0.110540 + 0.00339001i
\(946\) −1.48552e10 −0.0185488
\(947\) 1.36936e12 + 2.41455e11i 1.70262 + 0.300218i 0.938608 0.344986i \(-0.112116\pi\)
0.764011 + 0.645203i \(0.223227\pi\)
\(948\) 8.63071e11 1.61294e11i 1.06860 0.199703i
\(949\) −6.94619e9 2.52821e9i −0.00856410 0.00311708i
\(950\) 2.05568e9 + 2.44986e9i 0.00252383 + 0.00300778i
\(951\) −9.91635e10 + 1.75883e11i −0.121235 + 0.215031i
\(952\) −9.81568e9 + 3.57261e9i −0.0119501 + 0.00434949i
\(953\) −2.09625e11 1.21027e11i −0.254139 0.146727i 0.367519 0.930016i \(-0.380207\pi\)
−0.621658 + 0.783289i \(0.713541\pi\)
\(954\) 1.54890e11 + 5.28163e10i 0.186995 + 0.0637639i
\(955\) −2.40108e11 4.15879e11i −0.288664 0.499980i
\(956\) −2.24936e11 + 2.68068e11i −0.269294 + 0.320932i
\(957\) −5.59076e11 9.26995e10i −0.666535 0.110517i
\(958\) −1.21327e10 6.88082e10i −0.0144045 0.0816918i
\(959\) −8.10853e10 + 1.42975e10i −0.0958667 + 0.0169039i
\(960\) 6.97889e11 2.62118e11i 0.821677 0.308611i
\(961\) 1.77303e12 + 1.48775e12i 2.07885 + 1.74436i
\(962\) 1.30366e10 7.52670e9i 0.0152218 0.00878829i
\(963\) 7.46328e11 + 1.15924e11i 0.867810 + 0.134793i
\(964\) 3.99542e11 6.92028e11i 0.462652 0.801337i
\(965\) 2.92877e11 + 8.04672e11i 0.337735 + 0.927918i
\(966\) −8.93531e9 + 5.28128e9i −0.0102613 + 0.00606500i
\(967\) −2.96716e11 + 2.48974e11i −0.339340 + 0.284740i −0.796492 0.604648i \(-0.793314\pi\)
0.457153 + 0.889388i \(0.348869\pi\)
\(968\) −7.29668e10 + 2.00475e11i −0.0831044 + 0.228328i
\(969\) −1.24447e11 + 1.06609e11i −0.141153 + 0.120921i
\(970\) −3.86586e10 + 2.19244e11i −0.0436676 + 0.247651i
\(971\) 4.12689e11i 0.464243i 0.972687 + 0.232122i \(0.0745668\pi\)
−0.972687 + 0.232122i \(0.925433\pi\)
\(972\) −4.44732e10 8.69609e11i −0.0498235 0.974225i
\(973\) −1.42673e11 −0.159181
\(974\) 1.33944e11 + 2.36180e10i 0.148829 + 0.0262426i
\(975\) −4.47460e9 5.22327e9i −0.00495149 0.00577995i
\(976\) −1.21987e12 4.43997e11i −1.34436 0.489307i
\(977\) 2.63596e11 + 3.14142e11i 0.289308 + 0.344784i 0.891049 0.453907i \(-0.149970\pi\)
−0.601741 + 0.798692i \(0.705526\pi\)
\(978\) −5.24281e10 8.87023e10i −0.0573072 0.0969570i
\(979\) −2.44129e11 + 8.88556e10i −0.265759 + 0.0967285i
\(980\) −7.89726e11 4.55948e11i −0.856194 0.494324i
\(981\) −3.20970e10 + 2.06644e11i −0.0346568 + 0.223124i
\(982\) −4.14176e10 7.17374e10i −0.0445389 0.0771436i
\(983\) −1.47538e11 + 1.75829e11i −0.158012 + 0.188311i −0.839242 0.543758i \(-0.817001\pi\)
0.681230 + 0.732069i \(0.261445\pi\)
\(984\) −1.75185e9 4.66430e9i −0.00186860 0.00497515i
\(985\) 1.06313e11 + 6.02934e11i 0.112939 + 0.640508i
\(986\) 8.10981e10 1.42998e10i 0.0858031 0.0151294i
\(987\) 2.12392e10 1.28095e11i 0.0223805 0.134978i
\(988\) −5.13317e10 4.30724e10i −0.0538713 0.0452034i
\(989\) −1.49767e11 + 8.64681e10i −0.156542 + 0.0903797i
\(990\) −2.30327e10 + 6.75462e10i −0.0239775 + 0.0703169i
\(991\) 2.92488e11 5.06604e11i 0.303259 0.525260i −0.673613 0.739084i \(-0.735259\pi\)
0.976872 + 0.213824i \(0.0685920\pi\)
\(992\) 2.89997e11 + 7.96761e11i 0.299466 + 0.822775i
\(993\) 9.24836e11 + 5.21426e11i 0.951191 + 0.536285i
\(994\) 1.35929e9 1.14058e9i 0.00139241 0.00116837i
\(995\) −1.85651e11 + 5.10073e11i −0.189411 + 0.520403i
\(996\) −2.21137e11 1.18329e12i −0.224711 1.20241i
\(997\) −5.61372e10 + 3.18370e11i −0.0568160 + 0.322219i −0.999948 0.0101990i \(-0.996753\pi\)
0.943132 + 0.332418i \(0.107865\pi\)
\(998\) 1.01107e11i 0.101920i
\(999\) −6.66164e11 3.57844e11i −0.668835 0.359279i
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.2.12 138
3.2 odd 2 81.9.f.a.8.12 138
27.13 even 9 81.9.f.a.71.12 138
27.14 odd 18 inner 27.9.f.a.14.12 yes 138
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.9.f.a.2.12 138 1.1 even 1 trivial
27.9.f.a.14.12 yes 138 27.14 odd 18 inner
81.9.f.a.8.12 138 3.2 odd 2
81.9.f.a.71.12 138 27.13 even 9