Properties

Label 27.9.f.a.2.11
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 2.11
Character \(\chi\) \(=\) 27.2
Dual form 27.9.f.a.14.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.24198 - 0.571649i) q^{2} +(-71.7460 + 37.5966i) q^{3} +(-230.378 - 83.8506i) q^{4} +(387.667 + 462.003i) q^{5} +(254.092 - 80.8741i) q^{6} +(-3862.15 + 1405.71i) q^{7} +(1428.79 + 824.913i) q^{8} +(3733.99 - 5394.82i) q^{9} +(-992.706 - 1719.42i) q^{10} +(11423.3 - 13613.8i) q^{11} +(19681.2 - 2645.47i) q^{12} +(-882.859 - 5006.94i) q^{13} +(13324.6 - 2349.49i) q^{14} +(-45183.3 - 18571.9i) q^{15} +(43917.7 + 36851.3i) q^{16} +(23746.9 - 13710.3i) q^{17} +(-15189.5 + 15355.4i) q^{18} +(92857.3 - 160834. i) q^{19} +(-50570.5 - 138941. i) q^{20} +(224244. - 246058. i) q^{21} +(-44816.5 + 37605.5i) q^{22} +(-88410.2 + 242905. i) q^{23} +(-133524. - 5466.51i) q^{24} +(4669.78 - 26483.6i) q^{25} +16737.1i q^{26} +(-65071.9 + 527442. i) q^{27} +1.00762e6 q^{28} +(-234351. - 41322.5i) q^{29} +(135867. + 86039.0i) q^{30} +(-618503. - 225117. i) q^{31} +(-392799. - 468120. i) q^{32} +(-307745. + 1.40621e6i) q^{33} +(-84824.4 + 30873.6i) q^{34} +(-2.14667e6 - 1.23938e6i) q^{35} +(-1.31259e6 + 929748. i) q^{36} +(779022. + 1.34931e6i) q^{37} +(-392982. + 468338. i) q^{38} +(251586. + 326036. i) q^{39} +(172782. + 979898. i) q^{40} +(3.82274e6 - 674052. i) q^{41} +(-867655. + 669527. i) q^{42} +(-1.19676e6 - 1.00420e6i) q^{43} +(-3.77320e6 + 2.17846e6i) q^{44} +(3.93997e6 - 366277. i) q^{45} +(425481. - 736954. i) q^{46} +(407155. + 1.11865e6i) q^{47} +(-4.53640e6 - 992779. i) q^{48} +(8.52411e6 - 7.15258e6i) q^{49} +(-30278.7 + 83190.0i) q^{50} +(-1.18828e6 + 1.87646e6i) q^{51} +(-216444. + 1.22752e6i) q^{52} -1.29944e7i q^{53} +(512474. - 1.67276e6i) q^{54} +1.07180e7 q^{55} +(-6.67780e6 - 1.17748e6i) q^{56} +(-615344. + 1.50303e7i) q^{57} +(736141. + 267934. i) q^{58} +(-1.38268e7 - 1.64782e7i) q^{59} +(8.85196e6 + 8.06721e6i) q^{60} +(1.39731e7 - 5.08578e6i) q^{61} +(1.87649e6 + 1.08339e6i) q^{62} +(-6.83769e6 + 2.60845e7i) q^{63} +(-6.33245e6 - 1.09681e7i) q^{64} +(1.97097e6 - 2.34891e6i) q^{65} +(1.80156e6 - 4.38299e6i) q^{66} +(-1.06177e6 - 6.02157e6i) q^{67} +(-6.62036e6 + 1.16735e6i) q^{68} +(-2.78933e6 - 2.07514e7i) q^{69} +(6.25098e6 + 5.24520e6i) q^{70} +(3.07395e7 - 1.77475e7i) q^{71} +(9.78534e6 - 4.62785e6i) q^{72} +(6.89919e6 - 1.19498e7i) q^{73} +(-1.75425e6 - 4.81975e6i) q^{74} +(660657. + 2.07566e6i) q^{75} +(-3.48782e7 + 2.92663e7i) q^{76} +(-2.49816e7 + 6.86363e7i) q^{77} +(-629259. - 1.20082e6i) q^{78} +(-7.76297e6 + 4.40260e7i) q^{79} +3.45761e7i q^{80} +(-1.51614e7 - 4.02884e7i) q^{81} -1.27786e7 q^{82} +(-4.57442e7 - 8.06593e6i) q^{83} +(-7.22930e7 + 3.78832e7i) q^{84} +(1.55401e7 + 5.65612e6i) q^{85} +(3.30581e6 + 3.93971e6i) q^{86} +(1.83674e7 - 5.84610e6i) q^{87} +(2.75517e7 - 1.00280e7i) q^{88} +(-3.60126e6 - 2.07919e6i) q^{89} +(-1.29827e7 - 1.06481e6i) q^{90} +(1.04480e7 + 1.80965e7i) q^{91} +(4.07355e7 - 4.85466e7i) q^{92} +(5.28388e7 - 7.10240e6i) q^{93} +(-680516. - 3.85940e6i) q^{94} +(1.10303e8 - 1.94495e7i) q^{95} +(4.57815e7 + 1.88178e7i) q^{96} +(-1.08572e8 - 9.11031e7i) q^{97} +(-3.17238e7 + 1.83157e7i) q^{98} +(-3.07893e7 - 1.12460e8i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.24198 0.571649i −0.202624 0.0357281i 0.0714149 0.997447i \(-0.477249\pi\)
−0.274039 + 0.961719i \(0.588360\pi\)
\(3\) −71.7460 + 37.5966i −0.885754 + 0.464156i
\(4\) −230.378 83.8506i −0.899913 0.327541i
\(5\) 387.667 + 462.003i 0.620267 + 0.739206i 0.981116 0.193419i \(-0.0619576\pi\)
−0.360849 + 0.932624i \(0.617513\pi\)
\(6\) 254.092 80.8741i 0.196058 0.0624028i
\(7\) −3862.15 + 1405.71i −1.60856 + 0.585468i −0.981155 0.193225i \(-0.938105\pi\)
−0.627405 + 0.778693i \(0.715883\pi\)
\(8\) 1428.79 + 824.913i 0.348826 + 0.201395i
\(9\) 3733.99 5394.82i 0.569119 0.822255i
\(10\) −992.706 1719.42i −0.0992706 0.171942i
\(11\) 11423.3 13613.8i 0.780227 0.929839i −0.218716 0.975788i \(-0.570187\pi\)
0.998944 + 0.0459497i \(0.0146314\pi\)
\(12\) 19681.2 2645.47i 0.949131 0.127579i
\(13\) −882.859 5006.94i −0.0309113 0.175307i 0.965443 0.260612i \(-0.0839245\pi\)
−0.996355 + 0.0853055i \(0.972813\pi\)
\(14\) 13324.6 2349.49i 0.346850 0.0611591i
\(15\) −45183.3 18571.9i −0.892510 0.366853i
\(16\) 43917.7 + 36851.3i 0.670130 + 0.562306i
\(17\) 23746.9 13710.3i 0.284322 0.164153i −0.351056 0.936354i \(-0.614177\pi\)
0.635378 + 0.772201i \(0.280844\pi\)
\(18\) −15189.5 + 15355.4i −0.144695 + 0.146275i
\(19\) 92857.3 160834.i 0.712528 1.23413i −0.251378 0.967889i \(-0.580884\pi\)
0.963905 0.266245i \(-0.0857831\pi\)
\(20\) −50570.5 138941.i −0.316066 0.868384i
\(21\) 224244. 246058.i 1.15304 1.26520i
\(22\) −44816.5 + 37605.5i −0.191314 + 0.160532i
\(23\) −88410.2 + 242905.i −0.315930 + 0.868011i 0.675498 + 0.737361i \(0.263928\pi\)
−0.991429 + 0.130650i \(0.958294\pi\)
\(24\) −133524. 5466.51i −0.402452 0.0164765i
\(25\) 4669.78 26483.6i 0.0119546 0.0677981i
\(26\) 16737.1i 0.0366258i
\(27\) −65071.9 + 527442.i −0.122444 + 0.992475i
\(28\) 1.00762e6 1.63933
\(29\) −234351. 41322.5i −0.331341 0.0584244i 0.00550273 0.999985i \(-0.498248\pi\)
−0.336844 + 0.941560i \(0.609360\pi\)
\(30\) 135867. + 86039.0i 0.167737 + 0.106221i
\(31\) −618503. 225117.i −0.669723 0.243759i −0.0152945 0.999883i \(-0.504869\pi\)
−0.654429 + 0.756124i \(0.727091\pi\)
\(32\) −392799. 468120.i −0.374602 0.446434i
\(33\) −307745. + 1.40621e6i −0.259499 + 1.18576i
\(34\) −84824.4 + 30873.6i −0.0634754 + 0.0231031i
\(35\) −2.14667e6 1.23938e6i −1.43052 0.825910i
\(36\) −1.31259e6 + 929748.i −0.781480 + 0.553548i
\(37\) 779022. + 1.34931e6i 0.415664 + 0.719952i 0.995498 0.0947831i \(-0.0302158\pi\)
−0.579834 + 0.814735i \(0.696882\pi\)
\(38\) −392982. + 468338.i −0.188468 + 0.224608i
\(39\) 251586. + 326036.i 0.108750 + 0.140931i
\(40\) 172782. + 979898.i 0.0674931 + 0.382773i
\(41\) 3.82274e6 674052.i 1.35282 0.238538i 0.550201 0.835033i \(-0.314551\pi\)
0.802617 + 0.596494i \(0.203440\pi\)
\(42\) −867655. + 669527.i −0.278837 + 0.215165i
\(43\) −1.19676e6 1.00420e6i −0.350051 0.293728i 0.450759 0.892645i \(-0.351153\pi\)
−0.800811 + 0.598918i \(0.795598\pi\)
\(44\) −3.77320e6 + 2.17846e6i −1.00670 + 0.581217i
\(45\) 3.93997e6 366277.i 0.960821 0.0893223i
\(46\) 425481. 736954.i 0.0950274 0.164592i
\(47\) 407155. + 1.11865e6i 0.0834390 + 0.229247i 0.974395 0.224843i \(-0.0721869\pi\)
−0.890956 + 0.454089i \(0.849965\pi\)
\(48\) −4.53640e6 992779.i −0.854568 0.187020i
\(49\) 8.52411e6 7.15258e6i 1.47865 1.24073i
\(50\) −30278.7 + 83190.0i −0.00484459 + 0.0133104i
\(51\) −1.18828e6 + 1.87646e6i −0.175647 + 0.277369i
\(52\) −216444. + 1.22752e6i −0.0296028 + 0.167886i
\(53\) 1.29944e7i 1.64684i −0.567432 0.823420i \(-0.692063\pi\)
0.567432 0.823420i \(-0.307937\pi\)
\(54\) 512474. 1.67276e6i 0.0602694 0.196725i
\(55\) 1.07180e7 1.17129
\(56\) −6.67780e6 1.17748e6i −0.679018 0.119729i
\(57\) −615344. + 1.50303e7i −0.0582933 + 1.42386i
\(58\) 736141. + 267934.i 0.0650503 + 0.0236764i
\(59\) −1.38268e7 1.64782e7i −1.14107 1.35988i −0.923391 0.383861i \(-0.874594\pi\)
−0.217684 0.976019i \(-0.569850\pi\)
\(60\) 8.85196e6 + 8.06721e6i 0.683022 + 0.622470i
\(61\) 1.39731e7 5.08578e6i 1.00919 0.367315i 0.216068 0.976378i \(-0.430677\pi\)
0.793121 + 0.609064i \(0.208455\pi\)
\(62\) 1.87649e6 + 1.08339e6i 0.126993 + 0.0733194i
\(63\) −6.83769e6 + 2.60845e7i −0.434057 + 1.65585i
\(64\) −6.33245e6 1.09681e7i −0.377443 0.653751i
\(65\) 1.97097e6 2.34891e6i 0.110415 0.131587i
\(66\) 1.80156e6 4.38299e6i 0.0949455 0.230991i
\(67\) −1.06177e6 6.02157e6i −0.0526901 0.298821i 0.947063 0.321048i \(-0.104035\pi\)
−0.999753 + 0.0222278i \(0.992924\pi\)
\(68\) −6.62036e6 + 1.16735e6i −0.309632 + 0.0545965i
\(69\) −2.78933e6 2.07514e7i −0.123056 0.915485i
\(70\) 6.25098e6 + 5.24520e6i 0.260349 + 0.218459i
\(71\) 3.07395e7 1.77475e7i 1.20966 0.698398i 0.246975 0.969022i \(-0.420563\pi\)
0.962685 + 0.270624i \(0.0872300\pi\)
\(72\) 9.78534e6 4.62785e6i 0.364121 0.172207i
\(73\) 6.89919e6 1.19498e7i 0.242944 0.420792i −0.718607 0.695416i \(-0.755220\pi\)
0.961552 + 0.274624i \(0.0885534\pi\)
\(74\) −1.75425e6 4.81975e6i −0.0585011 0.160730i
\(75\) 660657. + 2.07566e6i 0.0208800 + 0.0656012i
\(76\) −3.48782e7 + 2.92663e7i −1.04544 + 0.877231i
\(77\) −2.49816e7 + 6.86363e7i −0.710652 + 1.95250i
\(78\) −629259. 1.20082e6i −0.0170001 0.0324414i
\(79\) −7.76297e6 + 4.40260e7i −0.199306 + 1.13032i 0.706846 + 0.707367i \(0.250117\pi\)
−0.906152 + 0.422952i \(0.860994\pi\)
\(80\) 3.45761e7i 0.844144i
\(81\) −1.51614e7 4.02884e7i −0.352208 0.935922i
\(82\) −1.27786e7 −0.282636
\(83\) −4.57442e7 8.06593e6i −0.963881 0.169958i −0.330506 0.943804i \(-0.607220\pi\)
−0.633374 + 0.773846i \(0.718331\pi\)
\(84\) −7.22930e7 + 3.78832e7i −1.45204 + 0.760904i
\(85\) 1.55401e7 + 5.65612e6i 0.297699 + 0.108354i
\(86\) 3.30581e6 + 3.93971e6i 0.0604344 + 0.0720230i
\(87\) 1.83674e7 5.84610e6i 0.320605 0.102044i
\(88\) 2.75517e7 1.00280e7i 0.459428 0.167218i
\(89\) −3.60126e6 2.07919e6i −0.0573977 0.0331386i 0.471027 0.882119i \(-0.343884\pi\)
−0.528424 + 0.848980i \(0.677217\pi\)
\(90\) −1.29827e7 1.06481e6i −0.197877 0.0162295i
\(91\) 1.04480e7 + 1.80965e7i 0.152359 + 0.263894i
\(92\) 4.07355e7 4.85466e7i 0.568619 0.677654i
\(93\) 5.28388e7 7.10240e6i 0.706352 0.0949453i
\(94\) −680516. 3.85940e6i −0.00871619 0.0494320i
\(95\) 1.10303e8 1.94495e7i 1.35424 0.238788i
\(96\) 4.57815e7 + 1.88178e7i 0.539020 + 0.221556i
\(97\) −1.08572e8 9.11031e7i −1.22640 1.02907i −0.998464 0.0553970i \(-0.982358\pi\)
−0.227937 0.973676i \(-0.573198\pi\)
\(98\) −3.17238e7 + 1.83157e7i −0.343938 + 0.198573i
\(99\) −3.07893e7 1.12460e8i −0.320523 1.17073i
\(100\) −3.29648e6 + 5.70967e6i −0.0329648 + 0.0570967i
\(101\) 4.07022e7 + 1.11828e8i 0.391140 + 1.07465i 0.966482 + 0.256735i \(0.0826467\pi\)
−0.575342 + 0.817913i \(0.695131\pi\)
\(102\) 4.92507e6 5.40417e6i 0.0455001 0.0499262i
\(103\) −2.77608e7 + 2.32941e7i −0.246651 + 0.206965i −0.757729 0.652570i \(-0.773691\pi\)
0.511077 + 0.859535i \(0.329247\pi\)
\(104\) 2.86887e6 7.88216e6i 0.0245232 0.0673770i
\(105\) 2.00612e8 + 8.21309e6i 1.65044 + 0.0675693i
\(106\) −7.42821e6 + 4.21275e7i −0.0588384 + 0.333689i
\(107\) 1.86649e8i 1.42394i −0.702212 0.711968i \(-0.747804\pi\)
0.702212 0.711968i \(-0.252196\pi\)
\(108\) 5.92174e7 1.16055e8i 0.435266 0.853036i
\(109\) 1.05606e8 0.748138 0.374069 0.927401i \(-0.377962\pi\)
0.374069 + 0.927401i \(0.377962\pi\)
\(110\) −3.47477e7 6.12696e6i −0.237332 0.0418480i
\(111\) −1.06621e8 6.75187e7i −0.702346 0.444767i
\(112\) −2.21419e8 8.05899e7i −1.40716 0.512163i
\(113\) 1.87685e8 + 2.23674e8i 1.15110 + 1.37183i 0.916643 + 0.399708i \(0.130888\pi\)
0.234462 + 0.972125i \(0.424667\pi\)
\(114\) 1.05870e7 4.83762e7i 0.0626835 0.286426i
\(115\) −1.46497e8 + 5.33204e7i −0.837599 + 0.304861i
\(116\) 5.05244e7 + 2.91703e7i 0.279042 + 0.161105i
\(117\) −3.03081e7 1.39330e7i −0.161739 0.0743534i
\(118\) 3.54066e7 + 6.13260e7i 0.182623 + 0.316313i
\(119\) −7.24414e7 + 8.63323e7i −0.361243 + 0.430512i
\(120\) −4.92373e7 6.38077e7i −0.237448 0.307715i
\(121\) −1.76197e7 9.99263e7i −0.0821972 0.466164i
\(122\) −4.82078e7 + 8.50033e6i −0.217609 + 0.0383704i
\(123\) −2.48924e8 + 1.92083e8i −1.08754 + 0.839205i
\(124\) 1.23613e8 + 1.03724e8i 0.522851 + 0.438724i
\(125\) 2.18070e8 1.25903e8i 0.893215 0.515698i
\(126\) 3.70789e7 8.06568e7i 0.147111 0.320006i
\(127\) 1.44951e8 2.51062e8i 0.557192 0.965085i −0.440537 0.897734i \(-0.645212\pi\)
0.997729 0.0673506i \(-0.0214546\pi\)
\(128\) 6.77648e7 + 1.86182e8i 0.252444 + 0.693583i
\(129\) 1.23617e8 + 2.70532e7i 0.446395 + 0.0976922i
\(130\) −7.73260e6 + 6.48842e6i −0.0270740 + 0.0227178i
\(131\) 5.14222e7 1.41281e8i 0.174609 0.479733i −0.821258 0.570556i \(-0.806728\pi\)
0.995867 + 0.0908232i \(0.0289498\pi\)
\(132\) 1.88809e8 2.98155e8i 0.621910 0.982079i
\(133\) −1.32544e8 + 7.51694e8i −0.423598 + 2.40234i
\(134\) 2.01288e7i 0.0624307i
\(135\) −2.68906e8 + 1.74408e8i −0.809591 + 0.525088i
\(136\) 4.52391e7 0.132239
\(137\) −6.49465e8 1.14518e8i −1.84363 0.325082i −0.860707 0.509101i \(-0.829978\pi\)
−0.982923 + 0.184020i \(0.941089\pi\)
\(138\) −2.81956e6 + 6.88702e7i −0.00777438 + 0.189896i
\(139\) −4.91164e8 1.78769e8i −1.31573 0.478887i −0.413643 0.910439i \(-0.635744\pi\)
−0.902088 + 0.431552i \(0.857966\pi\)
\(140\) 3.90622e8 + 4.65525e8i 1.01682 + 1.21180i
\(141\) −7.12693e7 6.49511e7i −0.180313 0.164327i
\(142\) −1.09802e8 + 3.99648e7i −0.270059 + 0.0982933i
\(143\) −7.82485e7 4.51768e7i −0.187125 0.108037i
\(144\) 3.62794e8 9.93255e7i 0.843743 0.230999i
\(145\) −7.17592e7 1.24291e8i −0.162332 0.281168i
\(146\) −2.91981e7 + 3.47970e7i −0.0642604 + 0.0765826i
\(147\) −3.42658e8 + 8.33647e8i −0.733824 + 1.78531i
\(148\) −6.63292e7 3.76171e8i −0.138248 0.784041i
\(149\) −5.15210e8 + 9.08454e7i −1.04530 + 0.184314i −0.669824 0.742520i \(-0.733630\pi\)
−0.375472 + 0.926834i \(0.622519\pi\)
\(150\) −955287. 7.10693e6i −0.00188699 0.0140384i
\(151\) 5.15851e8 + 4.32850e8i 0.992239 + 0.832588i 0.985890 0.167392i \(-0.0535346\pi\)
0.00634899 + 0.999980i \(0.497979\pi\)
\(152\) 2.65347e8 1.53198e8i 0.497096 0.286999i
\(153\) 1.47062e7 1.79304e8i 0.0268370 0.327208i
\(154\) 1.20226e8 2.08237e8i 0.213754 0.370233i
\(155\) −1.35769e8 3.73021e8i −0.235219 0.646259i
\(156\) −3.06214e7 9.62070e7i −0.0517044 0.162446i
\(157\) 4.46343e8 3.74526e8i 0.734633 0.616430i −0.196758 0.980452i \(-0.563041\pi\)
0.931390 + 0.364022i \(0.118597\pi\)
\(158\) 5.03349e7 1.38294e8i 0.0807682 0.221909i
\(159\) 4.88544e8 + 9.32294e8i 0.764390 + 1.45869i
\(160\) 6.39977e7 3.62949e8i 0.0976528 0.553816i
\(161\) 1.06242e9i 1.58121i
\(162\) 2.61222e7 + 1.39281e8i 0.0379271 + 0.202224i
\(163\) 1.04960e9 1.48687 0.743437 0.668806i \(-0.233194\pi\)
0.743437 + 0.668806i \(0.233194\pi\)
\(164\) −9.37194e8 1.65253e8i −1.29555 0.228440i
\(165\) −7.68977e8 + 4.02962e8i −1.03748 + 0.543662i
\(166\) 1.43691e8 + 5.22992e7i 0.189233 + 0.0688752i
\(167\) −1.58207e8 1.88544e8i −0.203404 0.242407i 0.654693 0.755895i \(-0.272798\pi\)
−0.858097 + 0.513487i \(0.828353\pi\)
\(168\) 5.23375e8 1.66583e8i 0.657015 0.209120i
\(169\) 7.42246e8 2.70155e8i 0.909916 0.331182i
\(170\) −4.71473e7 2.72205e7i −0.0564496 0.0325912i
\(171\) −5.20940e8 1.10150e9i −0.609261 1.28825i
\(172\) 1.91503e8 + 3.31693e8i 0.218808 + 0.378986i
\(173\) −2.45942e8 + 2.93102e8i −0.274567 + 0.327216i −0.885653 0.464348i \(-0.846289\pi\)
0.611086 + 0.791564i \(0.290733\pi\)
\(174\) −6.28886e7 + 8.45326e6i −0.0686081 + 0.00922205i
\(175\) 1.91929e7 + 1.08848e8i 0.0204639 + 0.116056i
\(176\) 1.00337e9 1.76921e8i 1.04571 0.184387i
\(177\) 1.61154e9 + 6.62401e8i 1.64191 + 0.674882i
\(178\) 1.04867e7 + 8.79935e6i 0.0104462 + 0.00876538i
\(179\) −1.76049e8 + 1.01642e8i −0.171483 + 0.0990057i −0.583285 0.812268i \(-0.698233\pi\)
0.411802 + 0.911273i \(0.364900\pi\)
\(180\) −9.38393e8 2.45987e8i −0.893912 0.234327i
\(181\) 3.05406e8 5.28979e8i 0.284553 0.492861i −0.687948 0.725760i \(-0.741488\pi\)
0.972501 + 0.232900i \(0.0748214\pi\)
\(182\) −2.35275e7 6.46413e7i −0.0214432 0.0589148i
\(183\) −8.11304e8 + 8.90225e8i −0.723402 + 0.793772i
\(184\) −3.26695e8 + 2.74130e8i −0.285017 + 0.239158i
\(185\) −3.21383e8 + 8.82992e8i −0.274369 + 0.753824i
\(186\) −1.75363e8 7.17939e6i −0.146516 0.00599841i
\(187\) 8.46195e7 4.79901e8i 0.0691997 0.392451i
\(188\) 2.91852e8i 0.233632i
\(189\) −4.90112e8 2.12853e9i −0.384104 1.66814i
\(190\) −3.68720e8 −0.282932
\(191\) 1.58410e8 + 2.79319e7i 0.119028 + 0.0209878i 0.232845 0.972514i \(-0.425197\pi\)
−0.113817 + 0.993502i \(0.536308\pi\)
\(192\) 8.66693e8 + 5.48841e8i 0.637764 + 0.403870i
\(193\) −1.24511e8 4.53181e7i −0.0897381 0.0326620i 0.296761 0.954952i \(-0.404094\pi\)
−0.386499 + 0.922290i \(0.626316\pi\)
\(194\) 2.99911e8 + 3.57420e8i 0.211731 + 0.252332i
\(195\) −5.30982e7 + 2.42627e8i −0.0367232 + 0.167803i
\(196\) −2.56351e9 + 9.33042e8i −1.73705 + 0.632233i
\(197\) −5.26529e7 3.03991e7i −0.0349588 0.0201835i 0.482419 0.875941i \(-0.339758\pi\)
−0.517378 + 0.855757i \(0.673092\pi\)
\(198\) 3.55306e7 + 3.82195e8i 0.0231175 + 0.248671i
\(199\) −3.16579e8 5.48332e8i −0.201869 0.349648i 0.747261 0.664530i \(-0.231368\pi\)
−0.949131 + 0.314882i \(0.898035\pi\)
\(200\) 2.85188e7 3.39874e7i 0.0178243 0.0212421i
\(201\) 3.02568e8 + 3.92105e8i 0.185370 + 0.240225i
\(202\) −6.80292e7 3.85813e8i −0.0408592 0.231724i
\(203\) 9.63188e8 1.69836e8i 0.567188 0.100011i
\(204\) 4.31096e8 3.32656e8i 0.248916 0.192077i
\(205\) 1.79336e9 + 1.50481e9i 1.01544 + 0.852053i
\(206\) 1.03316e8 5.96496e7i 0.0573719 0.0331237i
\(207\) 9.80306e8 + 1.38396e9i 0.533925 + 0.753776i
\(208\) 1.45739e8 2.52428e8i 0.0778616 0.134860i
\(209\) −1.12881e9 3.10139e9i −0.591612 1.62544i
\(210\) −6.45685e8 1.41306e8i −0.332004 0.0726581i
\(211\) −1.27463e9 + 1.06955e9i −0.643067 + 0.539597i −0.904958 0.425500i \(-0.860098\pi\)
0.261892 + 0.965097i \(0.415654\pi\)
\(212\) −1.08958e9 + 2.99361e9i −0.539408 + 1.48201i
\(213\) −1.53819e9 + 2.42901e9i −0.747296 + 1.18008i
\(214\) −1.06698e8 + 6.05112e8i −0.0508745 + 0.288523i
\(215\) 9.42199e8i 0.440950i
\(216\) −5.28068e8 + 6.99926e8i −0.242591 + 0.321542i
\(217\) 2.70520e9 1.22000
\(218\) −3.42372e8 6.03695e7i −0.151591 0.0267295i
\(219\) −4.57194e7 + 1.11673e9i −0.0198758 + 0.485482i
\(220\) −2.46920e9 8.98715e8i −1.05406 0.383646i
\(221\) −8.96116e7 1.06795e8i −0.0375660 0.0447695i
\(222\) 3.07067e8 + 2.79844e8i 0.126421 + 0.115214i
\(223\) −9.28099e7 + 3.37800e7i −0.0375297 + 0.0136597i −0.360717 0.932675i \(-0.617468\pi\)
0.323187 + 0.946335i \(0.395246\pi\)
\(224\) 2.17509e9 + 1.25579e9i 0.863943 + 0.498798i
\(225\) −1.25437e8 1.24082e8i −0.0489437 0.0484149i
\(226\) −4.80607e8 8.32436e8i −0.184228 0.319093i
\(227\) −2.09551e9 + 2.49733e9i −0.789198 + 0.940529i −0.999310 0.0371480i \(-0.988173\pi\)
0.210112 + 0.977677i \(0.432617\pi\)
\(228\) 1.40206e9 3.41105e9i 0.518833 1.26226i
\(229\) −2.35578e8 1.33603e9i −0.0856630 0.485819i −0.997212 0.0746264i \(-0.976224\pi\)
0.911549 0.411192i \(-0.134888\pi\)
\(230\) 5.05420e8 8.91192e7i 0.180610 0.0318464i
\(231\) −7.88165e8 5.86360e9i −0.276802 2.05929i
\(232\) −3.00752e8 2.52361e8i −0.103814 0.0871104i
\(233\) 6.27753e8 3.62433e8i 0.212993 0.122972i −0.389709 0.920938i \(-0.627424\pi\)
0.602702 + 0.797967i \(0.294091\pi\)
\(234\) 9.02936e7 + 6.24962e7i 0.0301158 + 0.0208444i
\(235\) −3.58980e8 + 6.21771e8i −0.117706 + 0.203873i
\(236\) 1.80369e9 + 4.95559e9i 0.581451 + 1.59752i
\(237\) −1.09827e9 3.45055e9i −0.348108 1.09369i
\(238\) 2.84206e8 2.38477e8i 0.0885778 0.0743256i
\(239\) 7.45604e8 2.04853e9i 0.228516 0.627842i −0.771448 0.636292i \(-0.780467\pi\)
0.999964 + 0.00844956i \(0.00268961\pi\)
\(240\) −1.29995e9 2.48070e9i −0.391814 0.747704i
\(241\) −2.83147e8 + 1.60581e9i −0.0839352 + 0.476020i 0.913646 + 0.406511i \(0.133255\pi\)
−0.997581 + 0.0695097i \(0.977857\pi\)
\(242\) 3.34032e8i 0.0973927i
\(243\) 2.60248e9 + 2.32051e9i 0.746383 + 0.665517i
\(244\) −3.64553e9 −1.02849
\(245\) 6.60903e9 + 1.16535e9i 1.83431 + 0.323439i
\(246\) 9.16813e8 4.80432e8i 0.250346 0.131187i
\(247\) −8.87265e8 3.22938e8i −0.238378 0.0867623i
\(248\) −6.98010e8 8.31856e8i −0.184525 0.219908i
\(249\) 3.58521e9 1.14113e9i 0.932648 0.296850i
\(250\) −7.78952e8 + 2.83515e8i −0.199412 + 0.0725799i
\(251\) −5.80211e8 3.34985e8i −0.146181 0.0843977i 0.425126 0.905134i \(-0.360230\pi\)
−0.571307 + 0.820737i \(0.693563\pi\)
\(252\) 3.76245e9 5.43594e9i 0.932972 1.34795i
\(253\) 2.29692e9 + 3.97838e9i 0.560613 + 0.971010i
\(254\) −6.13446e8 + 7.31077e8i −0.147381 + 0.175642i
\(255\) −1.32759e9 + 1.78450e8i −0.313981 + 0.0422042i
\(256\) 4.49743e8 + 2.55062e9i 0.104714 + 0.593862i
\(257\) 3.70746e9 6.53725e8i 0.849853 0.149852i 0.268275 0.963343i \(-0.413547\pi\)
0.581578 + 0.813491i \(0.302435\pi\)
\(258\) −3.85299e8 1.58371e8i −0.0869599 0.0357436i
\(259\) −4.90543e9 4.11615e9i −1.09013 0.914728i
\(260\) −6.51025e8 + 3.75869e8i −0.142464 + 0.0822514i
\(261\) −1.09799e9 + 1.10999e9i −0.236612 + 0.239197i
\(262\) −2.47473e8 + 4.28636e8i −0.0525198 + 0.0909670i
\(263\) −8.27508e8 2.27356e9i −0.172961 0.475207i 0.822676 0.568510i \(-0.192480\pi\)
−0.995638 + 0.0933024i \(0.970258\pi\)
\(264\) −1.59971e9 + 1.75532e9i −0.329325 + 0.361360i
\(265\) 6.00344e9 5.03748e9i 1.21735 1.02148i
\(266\) 8.59411e8 2.36121e9i 0.171662 0.471638i
\(267\) 3.36547e8 + 1.37783e7i 0.0662217 + 0.00271113i
\(268\) −2.60305e8 + 1.47626e9i −0.0504596 + 0.286171i
\(269\) 2.83899e9i 0.542195i −0.962552 0.271097i \(-0.912613\pi\)
0.962552 0.271097i \(-0.0873865\pi\)
\(270\) 9.71490e8 4.11709e8i 0.182803 0.0774703i
\(271\) −4.82586e9 −0.894741 −0.447370 0.894349i \(-0.647639\pi\)
−0.447370 + 0.894349i \(0.647639\pi\)
\(272\) 1.54815e9 + 2.72980e8i 0.282837 + 0.0498719i
\(273\) −1.42997e9 9.05544e8i −0.257441 0.163027i
\(274\) 2.04009e9 + 7.42532e8i 0.361949 + 0.131739i
\(275\) −3.07198e8 3.66104e8i −0.0537139 0.0640138i
\(276\) −1.09742e9 + 5.01455e9i −0.189119 + 0.864162i
\(277\) 1.86396e9 6.78426e8i 0.316605 0.115235i −0.178830 0.983880i \(-0.557231\pi\)
0.495434 + 0.868645i \(0.335009\pi\)
\(278\) 1.49015e9 + 8.60339e8i 0.249489 + 0.144043i
\(279\) −3.52395e9 + 2.49613e9i −0.581584 + 0.411956i
\(280\) −2.04476e9 3.54163e9i −0.332668 0.576198i
\(281\) −7.81636e8 + 9.31518e8i −0.125366 + 0.149405i −0.825076 0.565021i \(-0.808868\pi\)
0.699710 + 0.714427i \(0.253312\pi\)
\(282\) 1.93925e8 + 2.51311e8i 0.0306645 + 0.0397389i
\(283\) 1.67891e9 + 9.52155e9i 0.261746 + 1.48444i 0.778143 + 0.628087i \(0.216162\pi\)
−0.516396 + 0.856350i \(0.672727\pi\)
\(284\) −8.56983e9 + 1.51109e9i −1.31734 + 0.232283i
\(285\) −7.18260e9 + 5.54246e9i −1.08868 + 0.840084i
\(286\) 2.27855e8 + 1.91193e8i 0.0340561 + 0.0285764i
\(287\) −1.38165e10 + 7.97695e9i −2.03643 + 1.17573i
\(288\) −3.99213e9 + 3.71126e8i −0.580276 + 0.0539451i
\(289\) −3.11194e9 + 5.39003e9i −0.446107 + 0.772680i
\(290\) 1.61591e8 + 4.43969e8i 0.0228469 + 0.0627712i
\(291\) 1.12148e10 + 2.45433e9i 1.56394 + 0.342264i
\(292\) −2.59141e9 + 2.17445e9i −0.356456 + 0.299102i
\(293\) 1.75048e8 4.80940e8i 0.0237512 0.0652560i −0.927250 0.374442i \(-0.877834\pi\)
0.951002 + 0.309186i \(0.100057\pi\)
\(294\) 1.58745e9 2.50679e9i 0.212476 0.335528i
\(295\) 2.25277e9 1.27761e10i 0.297460 1.68698i
\(296\) 2.57050e9i 0.334850i
\(297\) 6.43714e9 + 6.91101e9i 0.827308 + 0.888210i
\(298\) 1.72223e9 0.218387
\(299\) 1.29427e9 + 2.28214e8i 0.161934 + 0.0285534i
\(300\) 2.18450e7 5.33583e8i 0.00269692 0.0658744i
\(301\) 6.03366e9 + 2.19607e9i 0.735047 + 0.267535i
\(302\) −1.42494e9 1.69818e9i −0.171305 0.204153i
\(303\) −7.12458e9 6.49297e9i −0.845257 0.770323i
\(304\) 1.00050e10 3.64152e9i 1.17145 0.426372i
\(305\) 7.76655e9 + 4.48402e9i 0.897488 + 0.518165i
\(306\) −1.50176e8 + 5.72894e8i −0.0171283 + 0.0653414i
\(307\) 3.72843e8 + 6.45783e8i 0.0419733 + 0.0726998i 0.886249 0.463209i \(-0.153302\pi\)
−0.844276 + 0.535909i \(0.819969\pi\)
\(308\) 1.15104e10 1.37175e10i 1.27905 1.52431i
\(309\) 1.11595e9 2.71497e9i 0.122408 0.297805i
\(310\) 2.26922e8 + 1.28694e9i 0.0245714 + 0.139351i
\(311\) −1.43070e10 + 2.52271e9i −1.52935 + 0.269666i −0.874101 0.485745i \(-0.838548\pi\)
−0.655252 + 0.755411i \(0.727437\pi\)
\(312\) 9.05124e7 + 6.73373e8i 0.00955190 + 0.0710620i
\(313\) −4.83723e9 4.05892e9i −0.503988 0.422896i 0.355020 0.934859i \(-0.384474\pi\)
−0.859008 + 0.511963i \(0.828919\pi\)
\(314\) −1.66113e9 + 9.59056e8i −0.170878 + 0.0986565i
\(315\) −1.47019e10 + 6.95307e9i −1.49324 + 0.706210i
\(316\) 5.48002e9 9.49168e9i 0.549584 0.951907i
\(317\) −3.91673e9 1.07611e10i −0.387870 1.06566i −0.967958 0.251110i \(-0.919204\pi\)
0.580089 0.814553i \(-0.303018\pi\)
\(318\) −1.05091e9 3.30176e9i −0.102767 0.322877i
\(319\) −3.23962e9 + 2.71837e9i −0.312847 + 0.262510i
\(320\) 2.61243e9 7.17759e9i 0.249141 0.684509i
\(321\) 7.01737e9 + 1.33913e10i 0.660928 + 1.26126i
\(322\) −6.07329e8 + 3.44433e9i −0.0564937 + 0.320392i
\(323\) 5.09239e9i 0.467856i
\(324\) 1.14643e8 + 1.05528e10i 0.0104032 + 0.957611i
\(325\) −1.36725e8 −0.0122550
\(326\) −3.40279e9 6.00004e8i −0.301276 0.0531232i
\(327\) −7.57680e9 + 3.97042e9i −0.662666 + 0.347253i
\(328\) 6.01793e9 + 2.19035e9i 0.519938 + 0.189242i
\(329\) −3.14499e9 3.74806e9i −0.268433 0.319906i
\(330\) 2.72336e9 8.66812e8i 0.229641 0.0730919i
\(331\) 1.41536e10 5.15148e9i 1.17911 0.429161i 0.323223 0.946323i \(-0.395234\pi\)
0.855888 + 0.517162i \(0.173011\pi\)
\(332\) 9.86210e9 + 5.69389e9i 0.811740 + 0.468658i
\(333\) 1.01881e10 + 8.35609e8i 0.828547 + 0.0679557i
\(334\) 4.05123e8 + 7.01694e8i 0.0325538 + 0.0563848i
\(335\) 2.37038e9 2.82490e9i 0.188208 0.224297i
\(336\) 1.89158e10 2.54260e9i 1.48412 0.199490i
\(337\) −9.05604e8 5.13594e9i −0.0702132 0.398199i −0.999578 0.0290371i \(-0.990756\pi\)
0.929365 0.369162i \(-0.120355\pi\)
\(338\) −2.56078e9 + 4.51535e8i −0.196203 + 0.0345959i
\(339\) −2.18750e10 8.99140e9i −1.65634 0.680814i
\(340\) −3.10581e9 2.60609e9i −0.232413 0.195017i
\(341\) −1.01300e10 + 5.84858e9i −0.749193 + 0.432547i
\(342\) 1.05921e9 + 3.86884e9i 0.0774242 + 0.282798i
\(343\) −1.10203e10 + 1.90877e10i −0.796188 + 1.37904i
\(344\) −8.81538e8 2.42201e9i −0.0629517 0.172958i
\(345\) 8.50589e9 9.33331e9i 0.600404 0.658809i
\(346\) 9.64890e8 8.09639e8i 0.0673246 0.0564920i
\(347\) 5.88556e9 1.61705e10i 0.405948 1.11533i −0.553353 0.832947i \(-0.686652\pi\)
0.959301 0.282386i \(-0.0911257\pi\)
\(348\) −4.72163e9 1.93305e8i −0.321940 0.0131803i
\(349\) 1.33644e9 7.57932e9i 0.0900840 0.510891i −0.906059 0.423151i \(-0.860924\pi\)
0.996143 0.0877409i \(-0.0279648\pi\)
\(350\) 3.63855e8i 0.0242469i
\(351\) 2.69832e9 1.39846e8i 0.177773 0.00921343i
\(352\) −1.08599e10 −0.707387
\(353\) 1.16353e10 + 2.05161e9i 0.749337 + 0.132128i 0.535259 0.844688i \(-0.320214\pi\)
0.214078 + 0.976817i \(0.431325\pi\)
\(354\) −4.84593e9 3.06873e9i −0.308578 0.195409i
\(355\) 2.01161e10 + 7.32165e9i 1.26657 + 0.460995i
\(356\) 6.55309e8 + 7.80966e8i 0.0407987 + 0.0486219i
\(357\) 1.95158e9 8.91755e9i 0.120147 0.549001i
\(358\) 6.28850e8 2.28883e8i 0.0382838 0.0139342i
\(359\) −7.89075e9 4.55572e9i −0.475051 0.274271i 0.243301 0.969951i \(-0.421770\pi\)
−0.718352 + 0.695680i \(0.755103\pi\)
\(360\) 5.93154e9 + 2.72680e9i 0.353148 + 0.162346i
\(361\) −8.75319e9 1.51610e10i −0.515392 0.892684i
\(362\) −1.29251e9 + 1.54036e9i −0.0752662 + 0.0896988i
\(363\) 5.02104e9 + 6.50687e9i 0.289179 + 0.374754i
\(364\) −8.89589e8 5.04511e9i −0.0506739 0.287386i
\(365\) 8.19542e9 1.44507e9i 0.461742 0.0814176i
\(366\) 3.13913e9 2.42231e9i 0.174938 0.134991i
\(367\) 4.80686e9 + 4.03344e9i 0.264971 + 0.222337i 0.765587 0.643333i \(-0.222449\pi\)
−0.500616 + 0.865669i \(0.666893\pi\)
\(368\) −1.28341e10 + 7.40979e9i −0.699802 + 0.404031i
\(369\) 1.06377e10 2.31399e10i 0.573775 1.24812i
\(370\) 1.54668e9 2.67893e9i 0.0825265 0.142940i
\(371\) 1.82663e10 + 5.01862e10i 0.964172 + 2.64904i
\(372\) −1.27684e10 2.79433e9i −0.666754 0.145917i
\(373\) 1.92922e10 1.61881e10i 0.996660 0.836297i 0.0101421 0.999949i \(-0.496772\pi\)
0.986518 + 0.163651i \(0.0523272\pi\)
\(374\) −5.48670e8 + 1.50746e9i −0.0280430 + 0.0770476i
\(375\) −1.09121e10 + 1.72317e10i −0.551804 + 0.871373i
\(376\) −3.41049e8 + 1.93419e9i −0.0170634 + 0.0967713i
\(377\) 1.20987e9i 0.0598924i
\(378\) 3.72162e8 + 7.18084e9i 0.0182291 + 0.351729i
\(379\) −4.03794e9 −0.195705 −0.0978527 0.995201i \(-0.531197\pi\)
−0.0978527 + 0.995201i \(0.531197\pi\)
\(380\) −2.70423e10 4.76828e9i −1.29691 0.228680i
\(381\) −9.60554e8 + 2.34623e10i −0.0455850 + 1.11345i
\(382\) −4.97594e8 1.81109e8i −0.0233680 0.00850526i
\(383\) −1.68071e10 2.00299e10i −0.781082 0.930857i 0.217900 0.975971i \(-0.430079\pi\)
−0.998982 + 0.0451138i \(0.985635\pi\)
\(384\) −1.18617e10 1.08101e10i −0.545533 0.497171i
\(385\) −4.13947e10 + 1.50665e10i −1.88409 + 0.685754i
\(386\) 3.77755e8 + 2.18097e8i 0.0170161 + 0.00982427i
\(387\) −9.88613e9 + 2.70662e9i −0.440740 + 0.120666i
\(388\) 1.73736e10 + 3.00920e10i 0.766590 + 1.32777i
\(389\) 5.81049e8 6.92467e8i 0.0253755 0.0302413i −0.753207 0.657783i \(-0.771494\pi\)
0.778583 + 0.627542i \(0.215939\pi\)
\(390\) 3.10841e8 7.56238e8i 0.0134363 0.0326889i
\(391\) 1.23083e9 + 6.98036e9i 0.0526611 + 0.298656i
\(392\) 1.80794e10 3.18789e9i 0.765668 0.135008i
\(393\) 1.62236e9 + 1.20697e10i 0.0680108 + 0.505971i
\(394\) 1.53322e8 + 1.28652e8i 0.00636238 + 0.00533867i
\(395\) −2.33496e10 + 1.34809e10i −0.959161 + 0.553772i
\(396\) −2.33670e9 + 2.84900e10i −0.0950214 + 1.15854i
\(397\) −1.45975e10 + 2.52837e10i −0.587648 + 1.01784i 0.406892 + 0.913476i \(0.366613\pi\)
−0.994540 + 0.104360i \(0.966721\pi\)
\(398\) 7.12892e8 + 1.95865e9i 0.0284113 + 0.0780594i
\(399\) −1.87517e10 5.89143e10i −0.739858 2.32450i
\(400\) 1.18104e9 9.91012e8i 0.0461344 0.0387114i
\(401\) −7.29919e9 + 2.00544e10i −0.282291 + 0.775589i 0.714797 + 0.699332i \(0.246519\pi\)
−0.997088 + 0.0762567i \(0.975703\pi\)
\(402\) −7.56774e8 1.44416e9i −0.0289776 0.0552982i
\(403\) −5.81096e8 + 3.29556e9i −0.0220307 + 0.124942i
\(404\) 2.91756e10i 1.09520i
\(405\) 1.27358e10 2.26231e10i 0.473376 0.840875i
\(406\) −3.21973e9 −0.118499
\(407\) 2.72681e10 + 4.80811e9i 0.993752 + 0.175225i
\(408\) −3.24573e9 + 1.70084e9i −0.117131 + 0.0613793i
\(409\) −4.86243e10 1.76978e10i −1.73764 0.632450i −0.738516 0.674236i \(-0.764473\pi\)
−0.999127 + 0.0417856i \(0.986695\pi\)
\(410\) −4.95383e9 5.90375e9i −0.175310 0.208926i
\(411\) 5.09021e10 1.62015e10i 1.78389 0.567789i
\(412\) 8.34869e9 3.03868e9i 0.289754 0.105462i
\(413\) 7.65648e10 + 4.42047e10i 2.63165 + 1.51939i
\(414\) −2.38699e9 5.04717e9i −0.0812550 0.171809i
\(415\) −1.40070e10 2.42609e10i −0.472229 0.817925i
\(416\) −1.99706e9 + 2.38001e9i −0.0666835 + 0.0794703i
\(417\) 4.19602e10 5.64013e9i 1.38769 0.186529i
\(418\) 1.88669e9 + 1.06999e10i 0.0618009 + 0.350490i
\(419\) 3.61100e10 6.36717e9i 1.17158 0.206581i 0.446202 0.894932i \(-0.352776\pi\)
0.725378 + 0.688351i \(0.241665\pi\)
\(420\) −4.55278e10 1.87135e10i −1.46312 0.601393i
\(421\) −6.06361e9 5.08797e9i −0.193020 0.161963i 0.541156 0.840922i \(-0.317987\pi\)
−0.734176 + 0.678959i \(0.762431\pi\)
\(422\) 4.74375e9 2.73881e9i 0.149579 0.0863597i
\(423\) 7.55523e9 + 1.98050e9i 0.235986 + 0.0618604i
\(424\) 1.07192e10 1.85662e10i 0.331665 0.574460i
\(425\) −2.52205e8 6.92927e8i −0.00773032 0.0212389i
\(426\) 6.37534e9 6.99551e9i 0.193582 0.212413i
\(427\) −4.68170e10 + 3.92841e10i −1.40829 + 1.18170i
\(428\) −1.56506e10 + 4.29997e10i −0.466398 + 1.28142i
\(429\) 7.31252e9 + 2.99376e8i 0.215893 + 0.00883870i
\(430\) −5.38607e8 + 3.05459e9i −0.0157543 + 0.0893469i
\(431\) 5.13707e10i 1.48870i −0.667791 0.744349i \(-0.732760\pi\)
0.667791 0.744349i \(-0.267240\pi\)
\(432\) −2.22947e10 + 2.07660e10i −0.640129 + 0.596237i
\(433\) −1.87525e9 −0.0533468 −0.0266734 0.999644i \(-0.508491\pi\)
−0.0266734 + 0.999644i \(0.508491\pi\)
\(434\) −8.77022e9 1.54643e9i −0.247202 0.0435884i
\(435\) 9.82134e9 + 6.21945e9i 0.274292 + 0.173698i
\(436\) −2.43292e10 8.85511e9i −0.673259 0.245046i
\(437\) 3.08578e10 + 3.67748e10i 0.846133 + 1.00838i
\(438\) 7.86601e8 3.59430e9i 0.0213726 0.0976602i
\(439\) −1.43069e10 + 5.20730e9i −0.385202 + 0.140202i −0.527360 0.849642i \(-0.676818\pi\)
0.142158 + 0.989844i \(0.454596\pi\)
\(440\) 1.53139e10 + 8.84146e9i 0.408577 + 0.235892i
\(441\) −6.75793e9 7.26937e10i −0.178673 1.92195i
\(442\) 2.29470e8 + 3.97454e8i 0.00601225 + 0.0104135i
\(443\) 2.80078e10 3.33784e10i 0.727217 0.866663i −0.268094 0.963393i \(-0.586394\pi\)
0.995311 + 0.0967298i \(0.0308383\pi\)
\(444\) 1.89016e10 + 2.44950e10i 0.486371 + 0.630299i
\(445\) −4.35497e8 2.46983e9i −0.0111057 0.0629835i
\(446\) 3.20198e8 5.64596e7i 0.00809245 0.00142692i
\(447\) 3.35488e10 2.58880e10i 0.840324 0.648437i
\(448\) 3.98749e10 + 3.34590e10i 0.989891 + 0.830617i
\(449\) −4.37682e10 + 2.52696e10i −1.07690 + 0.621746i −0.930057 0.367415i \(-0.880243\pi\)
−0.146838 + 0.989161i \(0.546910\pi\)
\(450\) 3.35735e8 + 4.73978e8i 0.00818740 + 0.0115587i
\(451\) 3.44920e10 5.97418e10i 0.833703 1.44402i
\(452\) −2.44832e10 6.72669e10i −0.586562 1.61156i
\(453\) −5.32840e10 1.16610e10i −1.26533 0.276914i
\(454\) 8.22120e9 6.89840e9i 0.193514 0.162377i
\(455\) −4.31030e9 + 1.18425e10i −0.100569 + 0.276310i
\(456\) −1.32779e10 + 2.09675e10i −0.307093 + 0.484940i
\(457\) 6.63960e9 3.76550e10i 0.152222 0.863293i −0.809060 0.587726i \(-0.800023\pi\)
0.961282 0.275567i \(-0.0888656\pi\)
\(458\) 4.46605e9i 0.101499i
\(459\) 5.68612e9 + 1.34173e10i 0.128105 + 0.302282i
\(460\) 3.82205e10 0.853621
\(461\) −5.77035e10 1.01747e10i −1.27761 0.225277i −0.506646 0.862154i \(-0.669115\pi\)
−0.770965 + 0.636877i \(0.780226\pi\)
\(462\) −7.96708e8 + 1.94603e10i −0.0174876 + 0.427150i
\(463\) 6.30183e10 + 2.29368e10i 1.37133 + 0.499124i 0.919539 0.392999i \(-0.128562\pi\)
0.451793 + 0.892123i \(0.350785\pi\)
\(464\) −8.76938e9 1.04509e10i −0.189190 0.225467i
\(465\) 2.37652e10 + 2.16583e10i 0.508311 + 0.463248i
\(466\) −2.24235e9 + 8.16148e8i −0.0475510 + 0.0173071i
\(467\) −7.50725e9 4.33431e9i −0.157839 0.0911281i 0.419000 0.907986i \(-0.362381\pi\)
−0.576839 + 0.816858i \(0.695714\pi\)
\(468\) 5.81402e9 + 5.75121e9i 0.121197 + 0.119888i
\(469\) 1.25653e10 + 2.17637e10i 0.259705 + 0.449823i
\(470\) 1.51924e9 1.81056e9i 0.0311340 0.0371041i
\(471\) −1.79424e10 + 4.36518e10i −0.364584 + 0.886989i
\(472\) −6.16259e9 3.49498e10i −0.124164 0.704168i
\(473\) −2.73418e10 + 4.82110e9i −0.546239 + 0.0963167i
\(474\) 1.58806e9 + 1.18145e10i 0.0314596 + 0.234046i
\(475\) −3.82583e9 3.21026e9i −0.0751539 0.0630616i
\(476\) 2.39279e10 1.38148e10i 0.466097 0.269101i
\(477\) −7.01022e10 4.85208e10i −1.35412 0.937247i
\(478\) −3.58827e9 + 6.21507e9i −0.0687344 + 0.119051i
\(479\) 1.03071e10 + 2.83185e10i 0.195792 + 0.537933i 0.998273 0.0587442i \(-0.0187096\pi\)
−0.802482 + 0.596677i \(0.796487\pi\)
\(480\) 9.05408e9 + 2.84463e10i 0.170561 + 0.535871i
\(481\) 6.06813e9 5.09176e9i 0.113364 0.0951235i
\(482\) 1.83592e9 5.04414e9i 0.0340146 0.0934543i
\(483\) 3.99432e10 + 7.62241e10i 0.733930 + 1.40057i
\(484\) −4.31970e9 + 2.44982e10i −0.0787176 + 0.446429i
\(485\) 8.54785e10i 1.54486i
\(486\) −7.11067e9 9.01077e9i −0.127457 0.161516i
\(487\) 2.41067e10 0.428570 0.214285 0.976771i \(-0.431258\pi\)
0.214285 + 0.976771i \(0.431258\pi\)
\(488\) 2.41599e10 + 4.26005e9i 0.426007 + 0.0751165i
\(489\) −7.53048e10 + 3.94615e10i −1.31700 + 0.690141i
\(490\) −2.07602e10 7.55609e9i −0.360120 0.131073i
\(491\) 3.30867e10 + 3.94312e10i 0.569282 + 0.678444i 0.971483 0.237108i \(-0.0761994\pi\)
−0.402202 + 0.915551i \(0.631755\pi\)
\(492\) 7.34529e10 2.33791e10i 1.25357 0.398995i
\(493\) −6.13166e9 + 2.23174e9i −0.103798 + 0.0377795i
\(494\) 2.69189e9 + 1.55416e9i 0.0452011 + 0.0260969i
\(495\) 4.00211e10 5.78219e10i 0.666604 0.963101i
\(496\) −1.88674e10 3.26793e10i −0.311735 0.539940i
\(497\) −9.37729e10 + 1.11754e11i −1.53692 + 1.83163i
\(498\) −1.22755e10 + 1.65003e9i −0.199583 + 0.0268272i
\(499\) −5.22963e9 2.96587e10i −0.0843468 0.478355i −0.997496 0.0707282i \(-0.977468\pi\)
0.913149 0.407626i \(-0.133643\pi\)
\(500\) −6.07955e10 + 1.07199e10i −0.972728 + 0.171518i
\(501\) 1.84393e10 + 7.57921e9i 0.292681 + 0.120302i
\(502\) 1.68954e9 + 1.41769e9i 0.0266044 + 0.0223238i
\(503\) −1.24574e10 + 7.19230e9i −0.194606 + 0.112356i −0.594137 0.804364i \(-0.702506\pi\)
0.399531 + 0.916720i \(0.369173\pi\)
\(504\) −3.12871e10 + 3.16288e10i −0.484890 + 0.490186i
\(505\) −3.58862e10 + 6.21567e10i −0.551774 + 0.955701i
\(506\) −5.17233e9 1.42109e10i −0.0789013 0.216779i
\(507\) −4.30963e10 + 4.72885e10i −0.652241 + 0.715688i
\(508\) −5.44450e10 + 4.56848e10i −0.817529 + 0.685989i
\(509\) 2.93880e10 8.07429e10i 0.437824 1.20291i −0.503081 0.864239i \(-0.667800\pi\)
0.940905 0.338671i \(-0.109977\pi\)
\(510\) 4.40603e9 + 1.80384e8i 0.0651279 + 0.00266635i
\(511\) −9.84787e9 + 5.58500e10i −0.144430 + 0.819105i
\(512\) 5.92477e10i 0.862168i
\(513\) 7.87880e10 + 5.94426e10i 1.13760 + 0.858279i
\(514\) −1.23932e10 −0.177554
\(515\) −2.15239e10 3.79524e9i −0.305979 0.0539524i
\(516\) −2.62101e10 1.65978e10i −0.369718 0.234127i
\(517\) 1.98801e10 + 7.23577e9i 0.278264 + 0.101280i
\(518\) 1.35503e10 + 1.61487e10i 0.188205 + 0.224294i
\(519\) 6.62570e9 3.02755e10i 0.0913192 0.417274i
\(520\) 4.75375e9 1.73022e9i 0.0650164 0.0236640i
\(521\) 3.91268e8 + 2.25899e8i 0.00531036 + 0.00306594i 0.502653 0.864488i \(-0.332357\pi\)
−0.497342 + 0.867554i \(0.665691\pi\)
\(522\) 4.19420e9 2.97089e9i 0.0564894 0.0400133i
\(523\) 3.63173e10 + 6.29034e10i 0.485408 + 0.840751i 0.999859 0.0167684i \(-0.00533780\pi\)
−0.514452 + 0.857519i \(0.672004\pi\)
\(524\) −2.36931e10 + 2.82363e10i −0.314265 + 0.374526i
\(525\) −5.46933e9 7.08783e9i −0.0719942 0.0932989i
\(526\) 1.38309e9 + 7.84388e9i 0.0180679 + 0.102468i
\(527\) −1.77739e10 + 3.13402e9i −0.230431 + 0.0406312i
\(528\) −6.53362e10 + 5.04167e10i −0.840656 + 0.648693i
\(529\) 8.80320e9 + 7.38676e9i 0.112413 + 0.0943260i
\(530\) −2.23427e10 + 1.28996e10i −0.283160 + 0.163483i
\(531\) −1.40526e11 + 1.30639e10i −1.76758 + 0.164322i
\(532\) 9.35652e10 1.62060e11i 1.16807 2.02315i
\(533\) −6.74988e9 1.85451e10i −0.0836349 0.229785i
\(534\) −1.08320e9 2.37056e8i −0.0133212 0.00291531i
\(535\) 8.62324e10 7.23576e10i 1.05258 0.883220i
\(536\) 3.45023e9 9.47943e9i 0.0418012 0.114848i
\(537\) 8.80941e9 1.39112e10i 0.105937 0.167289i
\(538\) −1.62291e9 + 9.20397e9i −0.0193716 + 0.109862i
\(539\) 1.97751e11i 2.34296i
\(540\) 7.65742e10 1.76318e10i 0.900550 0.207359i
\(541\) 1.03907e11 1.21298 0.606491 0.795091i \(-0.292577\pi\)
0.606491 + 0.795091i \(0.292577\pi\)
\(542\) 1.56453e10 + 2.75870e9i 0.181296 + 0.0319674i
\(543\) −2.02386e9 + 4.94344e10i −0.0232799 + 0.568630i
\(544\) −1.57458e10 5.73100e9i −0.179791 0.0654387i
\(545\) 4.09399e10 + 4.87902e10i 0.464045 + 0.553028i
\(546\) 4.11830e9 + 3.75320e9i 0.0463391 + 0.0422310i
\(547\) 2.07308e10 7.54538e9i 0.231561 0.0842814i −0.223633 0.974673i \(-0.571792\pi\)
0.455195 + 0.890392i \(0.349570\pi\)
\(548\) 1.40020e11 + 8.08405e10i 1.55263 + 0.896410i
\(549\) 2.47384e10 9.43724e10i 0.272322 1.03886i
\(550\) 7.86646e8 + 1.36251e9i 0.00859664 + 0.0148898i
\(551\) −2.84073e10 + 3.38545e10i −0.308193 + 0.367291i
\(552\) 1.31327e10 3.19504e10i 0.141449 0.344128i
\(553\) −3.19060e10 1.80948e11i −0.341170 1.93487i
\(554\) −6.43075e9 + 1.13391e9i −0.0682688 + 0.0120376i
\(555\) −1.01396e10 7.54341e10i −0.106868 0.795052i
\(556\) 9.81633e10 + 8.23688e10i 1.02719 + 0.861913i
\(557\) −1.00807e11 + 5.82008e10i −1.04729 + 0.604656i −0.921891 0.387450i \(-0.873356\pi\)
−0.125404 + 0.992106i \(0.540023\pi\)
\(558\) 1.28515e10 6.07795e9i 0.132561 0.0626932i
\(559\) −3.97139e9 + 6.87865e9i −0.0406720 + 0.0704459i
\(560\) −4.86040e10 1.33538e11i −0.494219 1.35786i
\(561\) 1.19715e10 + 3.76124e10i 0.120864 + 0.379734i
\(562\) 3.06655e9 2.57314e9i 0.0307401 0.0257940i
\(563\) −1.04359e10 + 2.86725e10i −0.103872 + 0.285386i −0.980731 0.195361i \(-0.937412\pi\)
0.876860 + 0.480747i \(0.159634\pi\)
\(564\) 1.09727e10 + 2.09392e10i 0.108442 + 0.206940i
\(565\) −3.05790e10 + 1.73422e11i −0.300074 + 1.70181i
\(566\) 3.18284e10i 0.310134i
\(567\) 1.15189e11 + 1.34287e11i 1.11450 + 1.29928i
\(568\) 5.85604e10 0.562615
\(569\) −7.50849e10 1.32395e10i −0.716314 0.126305i −0.196400 0.980524i \(-0.562925\pi\)
−0.519914 + 0.854219i \(0.674036\pi\)
\(570\) 2.64542e10 1.38626e10i 0.250608 0.131325i
\(571\) −1.53807e11 5.59810e10i −1.44687 0.526619i −0.505157 0.863027i \(-0.668566\pi\)
−0.941716 + 0.336408i \(0.890788\pi\)
\(572\) 1.42386e10 + 1.69689e10i 0.133010 + 0.158515i
\(573\) −1.24154e10 + 3.95166e9i −0.115171 + 0.0366574i
\(574\) 4.93528e10 1.79630e10i 0.454637 0.165474i
\(575\) 6.02015e9 + 3.47573e9i 0.0550726 + 0.0317962i
\(576\) −8.28163e10 6.79243e9i −0.752360 0.0617071i
\(577\) −3.03217e10 5.25187e10i −0.273559 0.473818i 0.696212 0.717836i \(-0.254867\pi\)
−0.969770 + 0.244019i \(0.921534\pi\)
\(578\) 1.31701e10 1.56955e10i 0.117998 0.140625i
\(579\) 1.06369e10 1.42978e9i 0.0946461 0.0127220i
\(580\) 6.10987e9 + 3.46508e10i 0.0539909 + 0.306197i
\(581\) 1.88009e11 3.31511e10i 1.64996 0.290933i
\(582\) −3.49552e10 1.43678e10i −0.304663 0.125227i
\(583\) −1.76902e11 1.48439e11i −1.53130 1.28491i
\(584\) 1.97150e10 1.13825e10i 0.169491 0.0978554i
\(585\) −5.31237e9 1.94038e10i −0.0453591 0.165678i
\(586\) −8.42431e8 + 1.45913e9i −0.00714404 + 0.0123738i
\(587\) 2.20481e10 + 6.05765e10i 0.185703 + 0.510214i 0.997253 0.0740686i \(-0.0235984\pi\)
−0.811551 + 0.584282i \(0.801376\pi\)
\(588\) 1.48843e11 1.63322e11i 1.24514 1.36626i
\(589\) −9.36389e10 + 7.85724e10i −0.778028 + 0.652843i
\(590\) −1.46069e10 + 4.01320e10i −0.120545 + 0.331194i
\(591\) 4.92054e9 + 2.01448e8i 0.0403332 + 0.00165125i
\(592\) −1.55108e10 + 8.79663e10i −0.126284 + 0.716192i
\(593\) 8.45828e10i 0.684011i 0.939698 + 0.342006i \(0.111106\pi\)
−0.939698 + 0.342006i \(0.888894\pi\)
\(594\) −1.69184e10 2.60852e10i −0.135898 0.209531i
\(595\) −6.79690e10 −0.542304
\(596\) 1.26310e11 + 2.22719e10i 1.00105 + 0.176511i
\(597\) 4.33287e10 + 2.74383e10i 0.341098 + 0.216003i
\(598\) −4.06553e9 1.47973e9i −0.0317916 0.0115712i
\(599\) 1.36255e10 + 1.62383e10i 0.105839 + 0.126134i 0.816364 0.577538i \(-0.195987\pi\)
−0.710524 + 0.703673i \(0.751542\pi\)
\(600\) −7.68300e8 + 3.51067e9i −0.00592824 + 0.0270885i
\(601\) 8.36696e9 3.04533e9i 0.0641313 0.0233419i −0.309755 0.950816i \(-0.600247\pi\)
0.373887 + 0.927474i \(0.378025\pi\)
\(602\) −1.83056e10 1.05688e10i −0.139380 0.0804708i
\(603\) −3.64499e10 1.67564e10i −0.275694 0.126740i
\(604\) −8.25458e10 1.42973e11i −0.620222 1.07426i
\(605\) 3.93357e10 4.68785e10i 0.293606 0.349907i
\(606\) 1.93861e10 + 2.51229e10i 0.143747 + 0.186285i
\(607\) 3.13171e10 + 1.77608e11i 0.230689 + 1.30830i 0.851506 + 0.524345i \(0.175690\pi\)
−0.620817 + 0.783955i \(0.713199\pi\)
\(608\) −1.11764e11 + 1.97070e10i −0.817874 + 0.144213i
\(609\) −6.27197e10 + 4.83977e10i −0.455968 + 0.351848i
\(610\) −2.26157e10 1.89769e10i −0.163340 0.137058i
\(611\) 5.24156e9 3.02621e9i 0.0376093 0.0217138i
\(612\) −1.84227e10 + 4.00745e10i −0.131325 + 0.285669i
\(613\) −9.37926e10 + 1.62454e11i −0.664243 + 1.15050i 0.315248 + 0.949009i \(0.397912\pi\)
−0.979490 + 0.201492i \(0.935421\pi\)
\(614\) −8.39590e8 2.30675e9i −0.00590736 0.0162303i
\(615\) −1.85243e11 4.05398e10i −1.29491 0.283388i
\(616\) −9.23124e10 + 7.74593e10i −0.641117 + 0.537961i
\(617\) 6.58893e9 1.81029e10i 0.0454647 0.124913i −0.914882 0.403720i \(-0.867717\pi\)
0.960347 + 0.278807i \(0.0899391\pi\)
\(618\) −5.16990e9 + 8.16396e9i −0.0354428 + 0.0559689i
\(619\) 3.75319e10 2.12854e11i 0.255646 1.44984i −0.538764 0.842457i \(-0.681109\pi\)
0.794410 0.607382i \(-0.207780\pi\)
\(620\) 9.73200e10i 0.658621i
\(621\) −1.22365e11 6.24375e10i −0.822796 0.419836i
\(622\) 4.78252e10 0.319518
\(623\) 1.68313e10 + 2.96782e9i 0.111729 + 0.0197009i
\(624\) −9.65781e8 + 2.35900e10i −0.00637001 + 0.155593i
\(625\) 1.32835e11 + 4.83479e10i 0.870547 + 0.316853i
\(626\) 1.33620e10 + 1.59242e10i 0.0870107 + 0.103695i
\(627\) 1.97590e11 + 1.80073e11i 1.27848 + 1.16514i
\(628\) −1.34232e11 + 4.88563e10i −0.863011 + 0.314110i
\(629\) 3.69987e10 + 2.13612e10i 0.236365 + 0.136466i
\(630\) 5.16380e10 1.41374e10i 0.327798 0.0897444i
\(631\) 1.52109e11 + 2.63460e11i 0.959482 + 1.66187i 0.723760 + 0.690052i \(0.242412\pi\)
0.235722 + 0.971820i \(0.424254\pi\)
\(632\) −4.74093e10 + 5.65002e10i −0.297163 + 0.354145i
\(633\) 5.12387e10 1.24658e11i 0.319141 0.776433i
\(634\) 6.54638e9 + 3.71263e10i 0.0405176 + 0.229787i
\(635\) 1.72184e11 3.03607e10i 1.05900 0.186731i
\(636\) −3.43762e10 2.55744e11i −0.210102 1.56307i
\(637\) −4.33381e10 3.63650e10i −0.263216 0.220865i
\(638\) 1.20568e10 6.96097e9i 0.0727692 0.0420133i
\(639\) 1.90366e10 2.32103e11i 0.114179 1.39212i
\(640\) −5.97467e10 + 1.03484e11i −0.356118 + 0.616814i
\(641\) 7.60783e10 + 2.09023e11i 0.450639 + 1.23812i 0.932276 + 0.361749i \(0.117820\pi\)
−0.481637 + 0.876371i \(0.659958\pi\)
\(642\) −1.50951e10 4.74259e10i −0.0888576 0.279174i
\(643\) 2.07474e11 1.74091e11i 1.21372 1.01844i 0.214595 0.976703i \(-0.431157\pi\)
0.999129 0.0417321i \(-0.0132876\pi\)
\(644\) −8.90842e10 + 2.44757e11i −0.517913 + 1.42295i
\(645\) 3.54235e10 + 6.75991e10i 0.204669 + 0.390573i
\(646\) −2.91106e9 + 1.65095e10i −0.0167156 + 0.0947988i
\(647\) 2.00279e9i 0.0114293i −0.999984 0.00571463i \(-0.998181\pi\)
0.999984 0.00571463i \(-0.00181903\pi\)
\(648\) 1.15719e10 7.00705e10i 0.0656305 0.397407i
\(649\) −3.82278e11 −2.15477
\(650\) 4.43259e8 + 7.81586e7i 0.00248316 + 0.000437848i
\(651\) −1.94088e11 + 1.01707e11i −1.08062 + 0.566272i
\(652\) −2.41805e11 8.80098e10i −1.33806 0.487013i
\(653\) −1.92647e11 2.29588e11i −1.05952 1.26269i −0.963614 0.267299i \(-0.913869\pi\)
−0.0959083 0.995390i \(-0.530576\pi\)
\(654\) 2.68335e10 8.54077e9i 0.146679 0.0466859i
\(655\) 8.52072e10 3.10129e10i 0.462925 0.168491i
\(656\) 1.92726e11 + 1.11270e11i 1.04070 + 0.600846i
\(657\) −3.87052e10 8.18401e10i −0.207734 0.439243i
\(658\) 8.05344e9 + 1.39490e10i 0.0429614 + 0.0744112i
\(659\) 1.37639e11 1.64032e11i 0.729794 0.869734i −0.265749 0.964042i \(-0.585619\pi\)
0.995543 + 0.0943079i \(0.0300638\pi\)
\(660\) 2.10944e11 2.83543e10i 1.11171 0.149432i
\(661\) 3.06780e10 + 1.73984e11i 0.160702 + 0.911386i 0.953386 + 0.301753i \(0.0975719\pi\)
−0.792684 + 0.609633i \(0.791317\pi\)
\(662\) −4.88305e10 + 8.61014e9i −0.254249 + 0.0448310i
\(663\) 1.04444e10 + 4.29302e9i 0.0540542 + 0.0222182i
\(664\) −5.87052e10 4.92595e10i −0.301998 0.253406i
\(665\) −3.98668e11 + 2.30171e11i −2.03857 + 1.17697i
\(666\) −3.25520e10 8.53306e9i −0.165455 0.0433718i
\(667\) 3.07565e10 5.32718e10i 0.155394 0.269150i
\(668\) 2.06378e10 + 5.67020e10i 0.103647 + 0.284769i
\(669\) 5.38873e9 5.91292e9i 0.0269018 0.0295187i
\(670\) −9.29957e9 + 7.80327e9i −0.0461491 + 0.0387237i
\(671\) 9.03821e10 2.48323e11i 0.445853 1.22497i
\(672\) −2.03268e11 8.32183e9i −0.996761 0.0408076i
\(673\) 5.10778e10 2.89676e11i 0.248984 1.41206i −0.562071 0.827089i \(-0.689995\pi\)
0.811055 0.584970i \(-0.198894\pi\)
\(674\) 1.71683e10i 0.0831932i
\(675\) 1.36647e10 + 4.18638e9i 0.0658241 + 0.0201662i
\(676\) −1.93650e11 −0.927320
\(677\) 1.66165e11 + 2.92994e10i 0.791015 + 0.139477i 0.554537 0.832159i \(-0.312896\pi\)
0.236479 + 0.971637i \(0.424007\pi\)
\(678\) 6.57785e10 + 4.16548e10i 0.311290 + 0.197127i
\(679\) 5.47388e11 + 1.99233e11i 2.57523 + 0.937307i
\(680\) 1.75377e10 + 2.09006e10i 0.0820232 + 0.0977515i
\(681\) 5.64532e10 2.57957e11i 0.262483 1.19939i
\(682\) 3.61848e10 1.31702e10i 0.167259 0.0608771i
\(683\) 5.30164e10 + 3.06090e10i 0.243628 + 0.140659i 0.616843 0.787086i \(-0.288411\pi\)
−0.373215 + 0.927745i \(0.621745\pi\)
\(684\) 2.76515e10 + 2.97442e11i 0.126327 + 1.35887i
\(685\) −1.98868e11 3.44450e11i −0.903240 1.56446i
\(686\) 4.66389e10 5.55821e10i 0.210597 0.250980i
\(687\) 6.71320e10 + 8.69979e10i 0.301372 + 0.390555i
\(688\) −1.55527e10 8.82040e10i −0.0694150 0.393672i
\(689\) −6.50620e10 + 1.14722e10i −0.288703 + 0.0509060i
\(690\) −3.29113e10 + 2.53961e10i −0.145194 + 0.112039i
\(691\) 2.97075e11 + 2.49275e11i 1.30303 + 1.09337i 0.989613 + 0.143754i \(0.0459173\pi\)
0.313414 + 0.949616i \(0.398527\pi\)
\(692\) 8.12362e10 4.69018e10i 0.354263 0.204534i
\(693\) 2.76999e11 + 3.91058e11i 1.20101 + 1.69554i
\(694\) −2.83247e10 + 4.90599e10i −0.122103 + 0.211489i
\(695\) −1.07816e11 2.96222e11i −0.462109 1.26963i
\(696\) 3.10657e10 + 6.79863e9i 0.132386 + 0.0289724i
\(697\) 8.15367e10 6.84174e10i 0.345479 0.289892i
\(698\) −8.66543e9 + 2.38081e10i −0.0365063 + 0.100300i
\(699\) −3.14125e10 + 4.96046e10i −0.131581 + 0.207784i
\(700\) 4.70537e9 2.66855e10i 0.0195976 0.111143i
\(701\) 5.50796e10i 0.228096i −0.993475 0.114048i \(-0.963618\pi\)
0.993475 0.114048i \(-0.0363818\pi\)
\(702\) −8.82786e9 1.08911e9i −0.0363502 0.00448462i
\(703\) 2.89352e11 1.18469
\(704\) −2.21655e11 3.90838e10i −0.902375 0.159113i
\(705\) 2.37888e9 5.81060e10i 0.00962976 0.235215i
\(706\) −3.65485e10 1.33026e10i −0.147113 0.0535447i
\(707\) −3.14396e11 3.74682e11i −1.25834 1.49964i
\(708\) −3.15721e11 2.87731e11i −1.25652 1.14513i
\(709\) 9.30404e10 3.38639e10i 0.368202 0.134015i −0.151291 0.988489i \(-0.548343\pi\)
0.519493 + 0.854475i \(0.326121\pi\)
\(710\) −6.10306e10 3.52360e10i −0.240167 0.138661i
\(711\) 2.08525e11 + 2.06272e11i 0.815982 + 0.807166i
\(712\) −3.43030e9 5.94145e9i −0.0133479 0.0231192i
\(713\) 1.09364e11 1.30335e11i 0.423171 0.504316i
\(714\) −1.14247e10 + 2.77949e10i −0.0439594 + 0.106948i
\(715\) −9.46253e9 5.36646e10i −0.0362062 0.205336i
\(716\) 4.90804e10 8.65420e9i 0.186748 0.0329287i
\(717\) 2.35237e10 + 1.75006e11i 0.0890079 + 0.662181i
\(718\) 2.29774e10 + 1.92803e10i 0.0864576 + 0.0725465i
\(719\) 2.21541e11 1.27907e11i 0.828968 0.478605i −0.0245313 0.999699i \(-0.507809\pi\)
0.853499 + 0.521094i \(0.174476\pi\)
\(720\) 1.86532e11 + 1.29107e11i 0.694102 + 0.480418i
\(721\) 7.44718e10 1.28989e11i 0.275582 0.477322i
\(722\) 1.97109e10 + 5.41553e10i 0.0725368 + 0.199293i
\(723\) −4.00583e10 1.25856e11i −0.146602 0.460596i
\(724\) −1.14714e11 + 9.62564e10i −0.417505 + 0.350329i
\(725\) −2.18874e9 + 6.01351e9i −0.00792213 + 0.0217659i
\(726\) −1.25585e10 2.39654e10i −0.0452054 0.0862659i
\(727\) 1.05428e10 5.97912e10i 0.0377414 0.214042i −0.960105 0.279641i \(-0.909785\pi\)
0.997846 + 0.0655987i \(0.0208957\pi\)
\(728\) 3.44749e10i 0.122738i
\(729\) −2.73961e11 6.86433e10i −0.970015 0.243046i
\(730\) −2.73955e10 −0.0964689
\(731\) −4.21870e10 7.43871e9i −0.147744 0.0260512i
\(732\) 2.61552e11 1.37060e11i 0.910991 0.477381i
\(733\) −4.73428e10 1.72314e10i −0.163998 0.0596903i 0.258717 0.965953i \(-0.416700\pi\)
−0.422714 + 0.906263i \(0.638923\pi\)
\(734\) −1.32781e10 1.58242e10i −0.0457457 0.0545176i
\(735\) −5.17985e11 + 1.64868e11i −1.77488 + 0.564920i
\(736\) 1.48436e11 5.40263e10i 0.505858 0.184117i
\(737\) −9.41051e10 5.43316e10i −0.318965 0.184155i
\(738\) −4.77151e10 + 6.89381e10i −0.160853 + 0.232399i
\(739\) 2.34907e11 + 4.06871e11i 0.787624 + 1.36420i 0.927419 + 0.374024i \(0.122022\pi\)
−0.139796 + 0.990180i \(0.544645\pi\)
\(740\) 1.48079e11 1.76473e11i 0.493817 0.588508i
\(741\) 7.57991e10 1.01886e10i 0.251415 0.0337943i
\(742\) −3.05301e10 1.73145e11i −0.100719 0.571207i
\(743\) −5.04740e11 + 8.89993e10i −1.65620 + 0.292033i −0.922083 0.386991i \(-0.873514\pi\)
−0.734116 + 0.679024i \(0.762403\pi\)
\(744\) 8.13545e10 + 3.34396e10i 0.265515 + 0.109136i
\(745\) −2.41701e11 2.02811e11i −0.784608 0.658364i
\(746\) −7.17990e10 + 4.14532e10i −0.231827 + 0.133845i
\(747\) −2.14322e11 + 2.16663e11i −0.688311 + 0.695830i
\(748\) −5.97344e10 + 1.03463e11i −0.190818 + 0.330506i
\(749\) 2.62374e11 + 7.20866e11i 0.833668 + 2.29049i
\(750\) 4.52275e10 4.96271e10i 0.142941 0.156846i
\(751\) 2.12965e10 1.78699e10i 0.0669498 0.0561776i −0.608699 0.793401i \(-0.708308\pi\)
0.675649 + 0.737224i \(0.263864\pi\)
\(752\) −2.33424e10 + 6.41327e10i −0.0729918 + 0.200543i
\(753\) 5.42222e10 + 2.21987e9i 0.168654 + 0.00690475i
\(754\) 6.91619e8 3.92237e9i 0.00213984 0.0121356i
\(755\) 4.06127e11i 1.24990i
\(756\) −6.55679e10 + 5.31463e11i −0.200726 + 1.62699i
\(757\) −3.59044e11 −1.09336 −0.546681 0.837341i \(-0.684109\pi\)
−0.546681 + 0.837341i \(0.684109\pi\)
\(758\) 1.30909e10 + 2.30828e9i 0.0396546 + 0.00699218i
\(759\) −3.14368e11 1.99076e11i −0.947265 0.599864i
\(760\) 1.73645e11 + 6.32015e10i 0.520484 + 0.189441i
\(761\) 4.75589e10 + 5.66785e10i 0.141806 + 0.168997i 0.832273 0.554367i \(-0.187039\pi\)
−0.690467 + 0.723364i \(0.742595\pi\)
\(762\) 1.65263e10 7.55154e10i 0.0490181 0.223983i
\(763\) −4.07866e11 + 1.48451e11i −1.20343 + 0.438011i
\(764\) −3.41519e10 1.97176e10i −0.100240 0.0578737i
\(765\) 8.85401e10 6.27159e10i 0.258520 0.183118i
\(766\) 4.30381e10 + 7.45443e10i 0.125008 + 0.216521i
\(767\) −7.02981e10 + 8.37780e10i −0.203124 + 0.242074i
\(768\) −1.28162e11 1.66088e11i −0.368396 0.477412i
\(769\) 6.71441e10 + 3.80793e11i 0.192000 + 1.08889i 0.916626 + 0.399746i \(0.130902\pi\)
−0.724626 + 0.689143i \(0.757987\pi\)
\(770\) 1.42814e11 2.51819e10i 0.406263 0.0716351i
\(771\) −2.41418e11 + 1.86290e11i −0.683205 + 0.527196i
\(772\) 2.48845e10 + 2.08806e10i 0.0700583 + 0.0587859i
\(773\) −3.24557e11 + 1.87383e11i −0.909020 + 0.524823i −0.880116 0.474759i \(-0.842535\pi\)
−0.0289045 + 0.999582i \(0.509202\pi\)
\(774\) 3.35979e10 3.12341e9i 0.0936156 0.00870293i
\(775\) −8.85018e9 + 1.53290e10i −0.0245327 + 0.0424919i
\(776\) −7.99752e10 2.19730e11i −0.220551 0.605958i
\(777\) 5.06699e11 + 1.10889e11i 1.39016 + 0.304233i
\(778\) −2.27960e9 + 1.91281e9i −0.00622214 + 0.00522100i
\(779\) 2.46559e11 6.77416e11i 0.669532 1.83952i
\(780\) 3.25770e10 5.14435e10i 0.0880102 0.138980i
\(781\) 1.09537e11 6.21215e11i 0.294413 1.66970i
\(782\) 2.33338e10i 0.0623963i
\(783\) 3.70449e10 1.20918e11i 0.0985556 0.321694i
\(784\) 6.37941e11 1.68856
\(785\) 3.46065e11 + 6.10206e10i 0.911337 + 0.160693i
\(786\) 1.63995e9 4.00571e10i 0.00429675 0.104952i
\(787\) 1.64892e11 + 6.00158e10i 0.429834 + 0.156447i 0.547872 0.836562i \(-0.315438\pi\)
−0.118038 + 0.993009i \(0.537660\pi\)
\(788\) 9.58105e9 + 1.14183e10i 0.0248490 + 0.0296139i
\(789\) 1.44849e11 + 1.32007e11i 0.373771 + 0.340636i
\(790\) 8.34054e10 3.03571e10i 0.214134 0.0779384i
\(791\) −1.03929e12 6.00032e11i −2.65479 1.53274i
\(792\) 4.87785e10 1.86081e11i 0.123973 0.472934i
\(793\) −3.78005e10 6.54723e10i −0.0955883 0.165564i
\(794\) 6.17783e10 7.36245e10i 0.155437 0.185242i
\(795\) −2.41331e11 + 5.87128e11i −0.604149 + 1.46982i
\(796\) 2.69549e10 + 1.52869e11i 0.0671406 + 0.380773i
\(797\) 1.75652e10 3.09722e9i 0.0435331 0.00767606i −0.151839 0.988405i \(-0.548520\pi\)
0.195372 + 0.980729i \(0.437408\pi\)
\(798\) 2.71143e10 + 2.01719e11i 0.0668631 + 0.497433i
\(799\) 2.50057e10 + 2.09822e10i 0.0613552 + 0.0514831i
\(800\) −1.42318e10 + 8.21673e9i −0.0347456 + 0.0200604i
\(801\) −2.46639e10 + 1.16645e10i −0.0599145 + 0.0283358i
\(802\) 3.51279e10 6.08433e10i 0.0849092 0.147067i
\(803\) −8.38696e10 2.30430e11i −0.201717 0.554213i
\(804\) −3.68267e10 1.15703e11i −0.0881330 0.276898i
\(805\) 4.90840e11 4.11863e11i 1.16884 0.980775i
\(806\) 3.76781e9 1.03520e10i 0.00892788 0.0245291i
\(807\) 1.06737e11 + 2.03686e11i 0.251663 + 0.480251i
\(808\) −3.40937e10 + 1.93355e11i −0.0799887 + 0.453638i
\(809\) 1.94607e11i 0.454323i −0.973857 0.227161i \(-0.927056\pi\)
0.973857 0.227161i \(-0.0729445\pi\)
\(810\) −5.42217e10 + 6.60632e10i −0.125960 + 0.153469i
\(811\) −8.64952e10 −0.199944 −0.0999720 0.994990i \(-0.531875\pi\)
−0.0999720 + 0.994990i \(0.531875\pi\)
\(812\) −2.36138e11 4.16375e10i −0.543177 0.0957768i
\(813\) 3.46236e11 1.81436e11i 0.792520 0.415299i
\(814\) −8.56543e10 3.11756e10i −0.195097 0.0710097i
\(815\) 4.06896e11 + 4.84920e11i 0.922259 + 1.09911i
\(816\) −1.21337e11 + 3.86199e10i −0.273673 + 0.0871065i
\(817\) −2.72636e11 + 9.92315e10i −0.611921 + 0.222721i
\(818\) 1.47522e11 + 8.51721e10i 0.329492 + 0.190232i
\(819\) 1.36640e11 + 1.12070e10i 0.303699 + 0.0249088i
\(820\) −2.86972e11 4.97050e11i −0.634722 1.09937i
\(821\) −1.63679e11 + 1.95065e11i −0.360264 + 0.429346i −0.915482 0.402359i \(-0.868190\pi\)
0.555218 + 0.831705i \(0.312635\pi\)
\(822\) −1.74285e11 + 2.34268e10i −0.381745 + 0.0513128i
\(823\) 4.26800e10 + 2.42050e11i 0.0930304 + 0.527602i 0.995333 + 0.0964986i \(0.0307643\pi\)
−0.902303 + 0.431103i \(0.858125\pi\)
\(824\) −5.88800e10 + 1.03821e10i −0.127720 + 0.0225205i
\(825\) 3.58045e10 + 1.47169e10i 0.0772897 + 0.0317688i
\(826\) −2.22952e11 1.87079e11i −0.478951 0.401888i
\(827\) 5.42919e11 3.13454e11i 1.16068 0.670120i 0.209214 0.977870i \(-0.432909\pi\)
0.951467 + 0.307750i \(0.0995760\pi\)
\(828\) −1.09795e11 4.01033e11i −0.233593 0.853215i
\(829\) −3.00938e11 + 5.21239e11i −0.637174 + 1.10362i 0.348876 + 0.937169i \(0.386564\pi\)
−0.986050 + 0.166449i \(0.946770\pi\)
\(830\) 3.15418e10 + 8.66604e10i 0.0664621 + 0.182603i
\(831\) −1.08225e11 + 1.18753e11i −0.226947 + 0.249023i
\(832\) −4.93261e10 + 4.13895e10i −0.102940 + 0.0863768i
\(833\) 1.04357e11 2.86719e11i 0.216742 0.595493i
\(834\) −1.39258e11 5.70127e9i −0.287844 0.0117844i
\(835\) 2.57762e10 1.46184e11i 0.0530241 0.300715i
\(836\) 8.09143e11i 1.65653i
\(837\) 1.58983e11 3.11576e11i 0.323929 0.634837i
\(838\) −1.20708e11 −0.244771
\(839\) 2.19890e11 + 3.87726e10i 0.443770 + 0.0782486i 0.391068 0.920362i \(-0.372106\pi\)
0.0527018 + 0.998610i \(0.483217\pi\)
\(840\) 2.79857e11 + 1.77222e11i 0.562107 + 0.355959i
\(841\) −4.16865e11 1.51726e11i −0.833319 0.303303i
\(842\) 1.67496e10 + 1.99614e10i 0.0333239 + 0.0397138i
\(843\) 2.10574e10 9.62196e10i 0.0416960 0.190526i
\(844\) 3.83329e11 1.39520e11i 0.755444 0.274959i
\(845\) 4.12557e11 + 2.38190e11i 0.809202 + 0.467193i
\(846\) −2.33618e10 1.07397e10i −0.0456063 0.0209657i
\(847\) 2.08517e11 + 3.61162e11i 0.405143 + 0.701728i
\(848\) 4.78859e11 5.70682e11i 0.926028 1.10360i
\(849\) −4.78433e11 6.20012e11i −0.920853 1.19335i
\(850\) 4.21533e8 + 2.39063e9i 0.000807524 + 0.00457970i
\(851\) −3.96627e11 + 6.99360e10i −0.756247 + 0.133347i
\(852\) 5.58039e11 4.30612e11i 1.05903 0.817198i
\(853\) 1.07390e10 + 9.01105e9i 0.0202846 + 0.0170208i 0.652874 0.757467i \(-0.273563\pi\)
−0.632589 + 0.774488i \(0.718008\pi\)
\(854\) 1.74237e11 1.00596e11i 0.327573 0.189124i
\(855\) 3.06945e11 6.67691e11i 0.574376 1.24943i
\(856\) 1.53969e11 2.66682e11i 0.286773 0.496706i
\(857\) −3.56164e10 9.78554e10i −0.0660279 0.181410i 0.902291 0.431128i \(-0.141884\pi\)
−0.968319 + 0.249718i \(0.919662\pi\)
\(858\) −2.35359e10 5.15077e9i −0.0434292 0.00950436i
\(859\) −2.94212e11 + 2.46873e11i −0.540365 + 0.453420i −0.871663 0.490106i \(-0.836958\pi\)
0.331298 + 0.943526i \(0.392514\pi\)
\(860\) −7.90040e10 + 2.17062e11i −0.144429 + 0.396816i
\(861\) 6.91372e11 1.09177e12i 1.25805 1.98663i
\(862\) −2.93660e10 + 1.66543e11i −0.0531883 + 0.301646i
\(863\) 2.17241e11i 0.391650i 0.980639 + 0.195825i \(0.0627384\pi\)
−0.980639 + 0.195825i \(0.937262\pi\)
\(864\) 2.72466e11 1.76717e11i 0.488942 0.317120i
\(865\) −2.30758e11 −0.412184
\(866\) 6.07954e9 + 1.07199e9i 0.0108093 + 0.00190598i
\(867\) 2.06221e10 5.03712e11i 0.0364969 0.891468i
\(868\) −6.23218e11 2.26833e11i −1.09790 0.399602i
\(869\) 5.10681e11 + 6.08606e11i 0.895511 + 1.06723i
\(870\) −2.82853e10 2.57777e10i −0.0493723 0.0449953i
\(871\) −2.92123e10 + 1.06324e10i −0.0507566 + 0.0184739i
\(872\) 1.50889e11 + 8.71156e10i 0.260970 + 0.150671i
\(873\) −8.96893e11 + 2.45551e11i −1.54413 + 0.422751i
\(874\) −7.90180e10 1.36863e11i −0.135419 0.234553i
\(875\) −6.65237e11 + 7.92799e11i −1.13487 + 1.35248i
\(876\) 1.04172e11 2.53437e11i 0.176902 0.430381i
\(877\) −2.14413e10 1.21600e11i −0.0362454 0.205558i 0.961307 0.275479i \(-0.0888364\pi\)
−0.997553 + 0.0699210i \(0.977725\pi\)
\(878\) 4.93596e10 8.70343e9i 0.0830603 0.0146458i
\(879\) 5.52273e9 + 4.10868e10i 0.00925121 + 0.0688250i
\(880\) 4.70712e11 + 3.94974e11i 0.784918 + 0.658624i
\(881\) 7.64992e11 4.41668e11i 1.26985 0.733150i 0.294893 0.955530i \(-0.404716\pi\)
0.974960 + 0.222381i \(0.0713828\pi\)
\(882\) −1.96462e10 + 2.39535e11i −0.0324641 + 0.395817i
\(883\) 8.16461e10 1.41415e11i 0.134305 0.232623i −0.791027 0.611782i \(-0.790453\pi\)
0.925332 + 0.379158i \(0.123786\pi\)
\(884\) 1.16897e10 + 3.21172e10i 0.0191423 + 0.0525930i
\(885\) 3.18710e11 + 1.00133e12i 0.519545 + 1.63231i
\(886\) −1.09881e11 + 9.22015e10i −0.178316 + 0.149625i
\(887\) −3.73853e11 + 1.02715e12i −0.603957 + 1.65936i 0.139218 + 0.990262i \(0.455541\pi\)
−0.743175 + 0.669097i \(0.766681\pi\)
\(888\) −9.66422e10 1.84423e11i −0.155423 0.296595i
\(889\) −2.06901e11 + 1.17340e12i −0.331251 + 1.87862i
\(890\) 8.25609e9i 0.0131587i
\(891\) −7.21670e11 2.53823e11i −1.14506 0.402735i
\(892\) 2.42138e10 0.0382475
\(893\) 2.17724e11 + 3.83906e10i 0.342374 + 0.0603697i
\(894\) −1.23563e11 + 6.47502e10i −0.193437 + 0.101366i
\(895\) −1.15207e11 4.19320e10i −0.179551 0.0653511i
\(896\) −5.23436e11 6.23807e11i −0.812141 0.967872i
\(897\) −1.01438e11 + 3.22866e10i −0.156687 + 0.0498715i
\(898\) 1.56341e11 5.69035e10i 0.240419 0.0875052i
\(899\) 1.35645e11 + 7.83146e10i 0.207665 + 0.119896i
\(900\) 1.84936e10 + 3.91037e10i 0.0281872 + 0.0596003i
\(901\) −1.78156e11 3.08575e11i −0.270334 0.468233i
\(902\) −1.45974e11 + 1.73965e11i −0.220520 + 0.262806i
\(903\) −5.15456e11 + 6.92858e10i −0.775248 + 0.104206i
\(904\) 8.36507e10 + 4.74407e11i 0.125255 + 0.710357i
\(905\) 3.62786e11 6.39690e10i 0.540824 0.0953619i
\(906\) 1.66080e11 + 6.82646e10i 0.246493 + 0.101317i
\(907\) −2.36599e11 1.98531e11i −0.349611 0.293358i 0.451023 0.892512i \(-0.351059\pi\)
−0.800634 + 0.599154i \(0.795504\pi\)
\(908\) 6.92161e11 3.99619e11i 1.01827 0.587899i
\(909\) 7.55274e11 + 1.97985e11i 1.10624 + 0.289985i
\(910\) 2.07437e10 3.59291e10i 0.0302496 0.0523939i
\(911\) −2.99551e11 8.23009e11i −0.434907 1.19490i −0.942765 0.333457i \(-0.891785\pi\)
0.507858 0.861441i \(-0.330437\pi\)
\(912\) −5.80910e11 + 6.37419e11i −0.839711 + 0.921395i
\(913\) −6.32357e11 + 5.30611e11i −0.910080 + 0.763648i
\(914\) −4.30509e10 + 1.18282e11i −0.0616876 + 0.169485i
\(915\) −7.25803e11 2.97146e10i −1.03546 0.0423921i
\(916\) −5.77550e10 + 3.27545e11i −0.0820366 + 0.465253i
\(917\) 6.17935e11i 0.873907i
\(918\) −1.07643e10 4.67490e10i −0.0151571 0.0658266i
\(919\) −5.59623e11 −0.784574 −0.392287 0.919843i \(-0.628316\pi\)
−0.392287 + 0.919843i \(0.628316\pi\)
\(920\) −2.53298e11 4.46632e10i −0.353574 0.0623446i
\(921\) −5.10293e10 3.23147e10i −0.0709220 0.0449120i
\(922\) 1.81258e11 + 6.59723e10i 0.250826 + 0.0912932i
\(923\) −1.15999e11 1.38242e11i −0.159826 0.190474i
\(924\) −3.10091e11 + 1.41693e12i −0.425404 + 1.94384i
\(925\) 3.93724e10 1.43304e10i 0.0537805 0.0195745i
\(926\) −1.91192e11 1.10385e11i −0.260032 0.150130i
\(927\) 2.20088e10 + 2.36744e11i 0.0298042 + 0.320598i
\(928\) 7.27092e10 + 1.25936e11i 0.0980386 + 0.169808i
\(929\) −4.11643e11 + 4.90577e11i −0.552660 + 0.658634i −0.967976 0.251043i \(-0.919226\pi\)
0.415316 + 0.909677i \(0.363671\pi\)
\(930\) −6.46654e10 8.38013e10i −0.0864450 0.112026i
\(931\) −3.58849e11 2.03513e12i −0.477653 2.70891i
\(932\) −1.75011e11 + 3.08591e10i −0.231953 + 0.0408996i
\(933\) 9.31626e11 7.18890e11i 1.22946 0.948716i
\(934\) 2.18607e10 + 1.83433e10i 0.0287260 + 0.0241040i
\(935\) 2.54520e11 1.46947e11i 0.333024 0.192272i
\(936\) −3.18105e10 4.49089e10i −0.0414445 0.0585099i
\(937\) 1.69447e11 2.93491e11i 0.219824 0.380747i −0.734930 0.678143i \(-0.762785\pi\)
0.954754 + 0.297396i \(0.0961182\pi\)
\(938\) −2.82952e10 7.77404e10i −0.0365512 0.100424i
\(939\) 4.99654e11 + 1.09348e11i 0.642698 + 0.140653i
\(940\) 1.34837e11 1.13141e11i 0.172702 0.144914i
\(941\) −2.45934e11 + 6.75699e11i −0.313661 + 0.861777i 0.678249 + 0.734833i \(0.262739\pi\)
−0.991910 + 0.126945i \(0.959483\pi\)
\(942\) 8.31225e10 1.31262e11i 0.105564 0.166699i
\(943\) −1.74239e11 + 9.88156e11i −0.220342 + 1.24962i
\(944\) 1.23322e12i 1.55293i
\(945\) 7.93390e11 1.05160e12i 0.994854 1.31863i
\(946\) 9.13977e10 0.114122
\(947\) −4.79075e11 8.44739e10i −0.595667 0.105032i −0.132317 0.991207i \(-0.542242\pi\)
−0.463350 + 0.886175i \(0.653353\pi\)
\(948\) −3.63149e10 + 8.87021e11i −0.0449626 + 1.09825i
\(949\) −6.59227e10 2.39939e10i −0.0812775 0.0295826i
\(950\) 1.05681e10 + 1.25946e10i 0.0129749 + 0.0154629i
\(951\) 6.85591e11 + 6.24812e11i 0.838191 + 0.763883i
\(952\) −1.74720e11 + 6.35930e10i −0.212714 + 0.0774215i
\(953\) −7.27038e11 4.19755e11i −0.881425 0.508891i −0.0102969 0.999947i \(-0.503278\pi\)
−0.871128 + 0.491056i \(0.836611\pi\)
\(954\) 1.99533e11 + 1.97377e11i 0.240892 + 0.238289i
\(955\) 4.85055e10 + 8.40140e10i 0.0583147 + 0.101004i
\(956\) −3.43541e11 + 4.09416e11i −0.411289 + 0.490155i
\(957\) 1.30229e11 3.16831e11i 0.155260 0.377729i
\(958\) −1.72272e10 9.77001e10i −0.0204527 0.115993i
\(959\) 2.66931e12 4.70672e11i 3.15591 0.556473i
\(960\) 8.24218e10 + 6.13182e11i 0.0970414 + 0.721946i
\(961\) −3.21484e11 2.69757e11i −0.376934 0.316285i
\(962\) −2.25835e10 + 1.30386e10i −0.0263688 + 0.0152240i
\(963\) −1.00694e12 6.96944e11i −1.17084 0.810388i
\(964\) 1.99879e11 3.46200e11i 0.231451 0.400884i
\(965\) −2.73315e10 7.50926e10i −0.0315177 0.0865940i
\(966\) −8.59218e10 2.69951e11i −0.0986723 0.310010i
\(967\) 3.58024e11 3.00417e11i 0.409455 0.343573i −0.414680 0.909967i \(-0.636106\pi\)
0.824135 + 0.566394i \(0.191662\pi\)
\(968\) 5.72556e10 1.57309e11i 0.0652104 0.179164i
\(969\) 1.91457e11 + 3.65359e11i 0.217158 + 0.414405i
\(970\) −4.88637e10 + 2.77120e11i −0.0551950 + 0.313026i
\(971\) 9.07616e11i 1.02100i 0.859878 + 0.510500i \(0.170539\pi\)
−0.859878 + 0.510500i \(0.829461\pi\)
\(972\) −4.04976e11 7.52814e11i −0.453695 0.843378i
\(973\) 2.14825e12 2.39681
\(974\) −7.81535e10 1.37806e10i −0.0868386 0.0153120i
\(975\) 9.80946e9 5.14039e9i 0.0108549 0.00568823i
\(976\) 8.01083e11 + 2.91570e11i 0.882832 + 0.321325i
\(977\) 1.09047e11 + 1.29957e11i 0.119684 + 0.142634i 0.822559 0.568679i \(-0.192545\pi\)
−0.702876 + 0.711313i \(0.748101\pi\)
\(978\) 2.66695e11 8.48856e10i 0.291514 0.0927852i
\(979\) −6.94439e10 + 2.52755e10i −0.0755968 + 0.0275150i
\(980\) −1.42486e12 8.22642e11i −1.54478 0.891880i
\(981\) 3.94331e11 5.69724e11i 0.425779 0.615161i
\(982\) −8.47257e10 1.46749e11i −0.0911106 0.157808i
\(983\) −2.30885e11 + 2.75158e11i −0.247276 + 0.294692i −0.875378 0.483439i \(-0.839387\pi\)
0.628102 + 0.778131i \(0.283832\pi\)
\(984\) −5.14112e11 + 6.91051e10i −0.548375 + 0.0737106i
\(985\) −6.36726e9 3.61105e10i −0.00676407 0.0383609i
\(986\) 2.11545e10 3.73011e9i 0.0223818 0.00394652i
\(987\) 3.66555e11 + 1.50667e11i 0.386252 + 0.158763i
\(988\) 1.77327e11 + 1.48795e11i 0.186101 + 0.156157i
\(989\) 3.49730e11 2.01917e11i 0.365551 0.211051i
\(990\) −1.62801e11 + 1.64580e11i −0.169480 + 0.171331i
\(991\) 1.75783e11 3.04465e11i 0.182256 0.315677i −0.760392 0.649464i \(-0.774993\pi\)
0.942648 + 0.333787i \(0.108327\pi\)
\(992\) 1.37566e11 + 3.77959e11i 0.142058 + 0.390300i
\(993\) −8.21785e11 + 9.01725e11i −0.845203 + 0.927422i
\(994\) 3.67894e11 3.08700e11i 0.376858 0.316221i
\(995\) 1.30604e11 3.58831e11i 0.133249 0.366098i
\(996\) −9.21637e11 3.77321e10i −0.936532 0.0383419i
\(997\) 2.09430e11 1.18774e12i 0.211962 1.20210i −0.674139 0.738604i \(-0.735485\pi\)
0.886101 0.463492i \(-0.153404\pi\)
\(998\) 9.91425e10i 0.0999397i
\(999\) −7.62373e11 + 3.23087e11i −0.765430 + 0.324383i
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.2.11 138
3.2 odd 2 81.9.f.a.8.13 138
27.13 even 9 81.9.f.a.71.13 138
27.14 odd 18 inner 27.9.f.a.14.11 yes 138
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.9.f.a.2.11 138 1.1 even 1 trivial
27.9.f.a.14.11 yes 138 27.14 odd 18 inner
81.9.f.a.8.13 138 3.2 odd 2
81.9.f.a.71.13 138 27.13 even 9