Properties

Label 27.9.f.a.2.10
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 2.10
Character \(\chi\) \(=\) 27.2
Dual form 27.9.f.a.14.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-7.66670 - 1.35185i) q^{2} +(72.7671 - 35.5802i) q^{3} +(-183.611 - 66.8288i) q^{4} +(-24.0534 - 28.6657i) q^{5} +(-605.982 + 174.413i) q^{6} +(-2598.90 + 945.921i) q^{7} +(3043.29 + 1757.05i) q^{8} +(4029.09 - 5178.14i) q^{9} +(145.659 + 252.288i) q^{10} +(-4786.80 + 5704.68i) q^{11} +(-15738.6 + 1669.97i) q^{12} +(2684.14 + 15222.5i) q^{13} +(21203.7 - 3738.78i) q^{14} +(-2770.23 - 1230.10i) q^{15} +(17361.5 + 14568.0i) q^{16} +(-124728. + 72011.7i) q^{17} +(-37889.9 + 34252.5i) q^{18} +(-101393. + 175618. i) q^{19} +(2500.76 + 6870.79i) q^{20} +(-155458. + 161301. i) q^{21} +(44410.8 - 37265.1i) q^{22} +(-39698.1 + 109070. i) q^{23} +(283967. + 19574.0i) q^{24} +(67588.2 - 383312. i) q^{25} -120335. i q^{26} +(108946. - 520154. i) q^{27} +540399. q^{28} +(-609347. - 107444. i) q^{29} +(19575.6 + 13175.7i) q^{30} +(1.01617e6 + 369854. i) q^{31} +(-691668. - 824298. i) q^{32} +(-145347. + 585428. i) q^{33} +(1.05360e6 - 383479. i) q^{34} +(89627.8 + 51746.6i) q^{35} +(-1.08583e6 + 681502. i) q^{36} +(-978631. - 1.69504e6i) q^{37} +(1.01476e6 - 1.20934e6i) q^{38} +(736937. + 1.01219e6i) q^{39} +(-22834.5 - 129501. i) q^{40} +(-1.39463e6 + 245911. i) q^{41} +(1.40990e6 - 1.02649e6i) q^{42} +(2.04961e6 + 1.71982e6i) q^{43} +(1.26014e6 - 727544. i) q^{44} +(-245349. + 9054.95i) q^{45} +(451799. - 782539. i) q^{46} +(-1.82238e6 - 5.00694e6i) q^{47} +(1.78168e6 + 442347. i) q^{48} +(1.44340e6 - 1.21116e6i) q^{49} +(-1.03636e6 + 2.84736e6i) q^{50} +(-6.51389e6 + 9.67792e6i) q^{51} +(524465. - 2.97439e6i) q^{52} +3.45452e6i q^{53} +(-1.53842e6 + 3.84059e6i) q^{54} +278668. q^{55} +(-9.57122e6 - 1.68767e6i) q^{56} +(-1.12955e6 + 1.63868e7i) q^{57} +(4.52643e6 + 1.64749e6i) q^{58} +(-1.16111e7 - 1.38375e7i) q^{59} +(426437. + 410989. i) q^{60} +(1.16719e7 - 4.24821e6i) q^{61} +(-7.29065e6 - 4.20926e6i) q^{62} +(-5.57309e6 + 1.72687e7i) q^{63} +(1.28751e6 + 2.23004e6i) q^{64} +(371801. - 443096. i) q^{65} +(1.90574e6 - 4.29181e6i) q^{66} +(-1.92937e6 - 1.09420e7i) q^{67} +(2.77138e7 - 4.88669e6i) q^{68} +(992009. + 9.34915e6i) q^{69} +(-617196. - 517889. i) q^{70} +(-2.34487e7 + 1.35381e7i) q^{71} +(2.13599e7 - 8.67929e6i) q^{72} +(-1.28556e7 + 2.22665e7i) q^{73} +(5.21144e6 + 1.43183e7i) q^{74} +(-8.72012e6 - 3.02973e7i) q^{75} +(3.03531e7 - 2.54693e7i) q^{76} +(7.04421e6 - 1.93538e7i) q^{77} +(-4.28154e6 - 8.75641e6i) q^{78} +(-981583. + 5.56684e6i) q^{79} -848091. i q^{80} +(-1.05795e7 - 4.17264e7i) q^{81} +1.10246e7 q^{82} +(5.90784e6 + 1.04171e6i) q^{83} +(3.93233e7 - 1.92275e7i) q^{84} +(5.06440e6 + 1.84329e6i) q^{85} +(-1.33888e7 - 1.59561e7i) q^{86} +(-4.81633e7 + 1.38623e7i) q^{87} +(-2.45910e7 + 8.95039e6i) q^{88} +(3.29258e7 + 1.90097e7i) q^{89} +(1.89325e6 + 262252. i) q^{90} +(-2.13751e7 - 3.70227e7i) q^{91} +(1.45780e7 - 1.73734e7i) q^{92} +(8.71029e7 - 9.24222e6i) q^{93} +(7.20300e6 + 4.08503e7i) q^{94} +(7.47305e6 - 1.31770e6i) q^{95} +(-7.96594e7 - 3.53720e7i) q^{96} +(9.92181e6 + 8.32538e6i) q^{97} +(-1.27034e7 + 7.33433e6i) q^{98} +(1.02532e7 + 4.77714e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 138 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 447 q^{5} - 774 q^{6} - 6 q^{7} - 9 q^{8} - 12960 q^{9} - 3 q^{10} + 28668 q^{11} + 77421 q^{12} - 6 q^{13} - 120975 q^{14} + 105507 q^{15} - 774 q^{16} - 9 q^{17}+ \cdots + 228876057 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −7.66670 1.35185i −0.479169 0.0844904i −0.0711532 0.997465i \(-0.522668\pi\)
−0.408015 + 0.912975i \(0.633779\pi\)
\(3\) 72.7671 35.5802i 0.898359 0.439262i
\(4\) −183.611 66.8288i −0.717229 0.261050i
\(5\) −24.0534 28.6657i −0.0384854 0.0458652i 0.746458 0.665432i \(-0.231753\pi\)
−0.784944 + 0.619567i \(0.787308\pi\)
\(6\) −605.982 + 174.413i −0.467579 + 0.134578i
\(7\) −2598.90 + 945.921i −1.08242 + 0.393970i −0.820809 0.571203i \(-0.806477\pi\)
−0.261614 + 0.965173i \(0.584255\pi\)
\(8\) 3043.29 + 1757.05i 0.742991 + 0.428966i
\(9\) 4029.09 5178.14i 0.614098 0.789230i
\(10\) 145.659 + 252.288i 0.0145659 + 0.0252288i
\(11\) −4786.80 + 5704.68i −0.326945 + 0.389637i −0.904330 0.426835i \(-0.859629\pi\)
0.577385 + 0.816472i \(0.304073\pi\)
\(12\) −15738.6 + 1669.97i −0.758998 + 0.0805349i
\(13\) 2684.14 + 15222.5i 0.0939791 + 0.532982i 0.995055 + 0.0993213i \(0.0316672\pi\)
−0.901076 + 0.433661i \(0.857222\pi\)
\(14\) 21203.7 3738.78i 0.551949 0.0973236i
\(15\) −2770.23 1230.10i −0.0547206 0.0242982i
\(16\) 17361.5 + 14568.0i 0.264916 + 0.222291i
\(17\) −124728. + 72011.7i −1.49337 + 0.862198i −0.999971 0.00760413i \(-0.997580\pi\)
−0.493400 + 0.869802i \(0.664246\pi\)
\(18\) −37889.9 + 34252.5i −0.360939 + 0.326289i
\(19\) −101393. + 175618.i −0.778024 + 1.34758i 0.155054 + 0.987906i \(0.450445\pi\)
−0.933079 + 0.359672i \(0.882889\pi\)
\(20\) 2500.76 + 6870.79i 0.0156298 + 0.0429424i
\(21\) −155458. + 161301.i −0.799348 + 0.829393i
\(22\) 44410.8 37265.1i 0.189582 0.159078i
\(23\) −39698.1 + 109070.i −0.141860 + 0.389756i −0.990193 0.139707i \(-0.955384\pi\)
0.848333 + 0.529462i \(0.177606\pi\)
\(24\) 283967. + 19574.0i 0.855901 + 0.0589977i
\(25\) 67588.2 383312.i 0.173026 0.981277i
\(26\) 120335.i 0.263329i
\(27\) 108946. 520154.i 0.205001 0.978762i
\(28\) 540399. 0.879190
\(29\) −609347. 107444.i −0.861534 0.151912i −0.274612 0.961555i \(-0.588549\pi\)
−0.586922 + 0.809643i \(0.699660\pi\)
\(30\) 19575.6 + 13175.7i 0.0241674 + 0.0162663i
\(31\) 1.01617e6 + 369854.i 1.10032 + 0.400483i 0.827433 0.561564i \(-0.189800\pi\)
0.272884 + 0.962047i \(0.412022\pi\)
\(32\) −691668. 824298.i −0.659626 0.786112i
\(33\) −145347. + 585428.i −0.122561 + 0.493649i
\(34\) 1.05360e6 383479.i 0.788424 0.286963i
\(35\) 89627.8 + 51746.6i 0.0597270 + 0.0344834i
\(36\) −1.08583e6 + 681502.i −0.646477 + 0.405748i
\(37\) −978631. 1.69504e6i −0.522170 0.904426i −0.999667 0.0257923i \(-0.991789\pi\)
0.477497 0.878633i \(-0.341544\pi\)
\(38\) 1.01476e6 1.20934e6i 0.486662 0.579982i
\(39\) 736937. + 1.01219e6i 0.318546 + 0.437528i
\(40\) −22834.5 129501.i −0.00891974 0.0505864i
\(41\) −1.39463e6 + 245911.i −0.493541 + 0.0870247i −0.414879 0.909877i \(-0.636176\pi\)
−0.0786625 + 0.996901i \(0.525065\pi\)
\(42\) 1.40990e6 1.02649e6i 0.453098 0.329882i
\(43\) 2.04961e6 + 1.71982e6i 0.599510 + 0.503049i 0.891288 0.453437i \(-0.149802\pi\)
−0.291778 + 0.956486i \(0.594247\pi\)
\(44\) 1.26014e6 727544.i 0.336209 0.194110i
\(45\) −245349. + 9054.95i −0.0598320 + 0.00220819i
\(46\) 451799. 782539.i 0.100905 0.174773i
\(47\) −1.82238e6 5.00694e6i −0.373462 1.02608i −0.974013 0.226492i \(-0.927274\pi\)
0.600551 0.799587i \(-0.294948\pi\)
\(48\) 1.78168e6 + 442347.i 0.335633 + 0.0833293i
\(49\) 1.44340e6 1.21116e6i 0.250382 0.210095i
\(50\) −1.03636e6 + 2.84736e6i −0.165817 + 0.455578i
\(51\) −6.51389e6 + 9.67792e6i −0.962852 + 1.43055i
\(52\) 524465. 2.97439e6i 0.0717304 0.406803i
\(53\) 3.45452e6i 0.437809i 0.975746 + 0.218905i \(0.0702483\pi\)
−0.975746 + 0.218905i \(0.929752\pi\)
\(54\) −1.53842e6 + 3.84059e6i −0.180926 + 0.451671i
\(55\) 278668. 0.0304534
\(56\) −9.57122e6 1.68767e6i −0.973230 0.171607i
\(57\) −1.12955e6 + 1.63868e7i −0.107005 + 1.55237i
\(58\) 4.52643e6 + 1.64749e6i 0.399985 + 0.145583i
\(59\) −1.16111e7 1.38375e7i −0.958217 1.14196i −0.989801 0.142458i \(-0.954499\pi\)
0.0315836 0.999501i \(-0.489945\pi\)
\(60\) 426437. + 410989.i 0.0329041 + 0.0317122i
\(61\) 1.16719e7 4.24821e6i 0.842987 0.306822i 0.115810 0.993271i \(-0.463054\pi\)
0.727178 + 0.686449i \(0.240832\pi\)
\(62\) −7.29065e6 4.20926e6i −0.493401 0.284865i
\(63\) −5.57309e6 + 1.72687e7i −0.353780 + 1.09622i
\(64\) 1.28751e6 + 2.23004e6i 0.0767418 + 0.132921i
\(65\) 371801. 443096.i 0.0208285 0.0248224i
\(66\) 1.90574e6 4.29181e6i 0.100436 0.226186i
\(67\) −1.92937e6 1.09420e7i −0.0957452 0.542998i −0.994516 0.104580i \(-0.966650\pi\)
0.898771 0.438418i \(-0.144461\pi\)
\(68\) 2.77138e7 4.88669e6i 1.29617 0.228549i
\(69\) 992009. + 9.34915e6i 0.0437642 + 0.412454i
\(70\) −617196. 517889.i −0.0257058 0.0215697i
\(71\) −2.34487e7 + 1.35381e7i −0.922752 + 0.532751i −0.884512 0.466518i \(-0.845508\pi\)
−0.0382397 + 0.999269i \(0.512175\pi\)
\(72\) 2.13599e7 8.67929e6i 0.794822 0.322964i
\(73\) −1.28556e7 + 2.22665e7i −0.452690 + 0.784082i −0.998552 0.0537933i \(-0.982869\pi\)
0.545862 + 0.837875i \(0.316202\pi\)
\(74\) 5.21144e6 + 1.43183e7i 0.173792 + 0.477491i
\(75\) −8.72012e6 3.02973e7i −0.275599 0.957543i
\(76\) 3.03531e7 2.54693e7i 0.909807 0.763418i
\(77\) 7.04421e6 1.93538e7i 0.200387 0.550558i
\(78\) −4.28154e6 8.75641e6i −0.115670 0.236564i
\(79\) −981583. + 5.56684e6i −0.0252011 + 0.142922i −0.994812 0.101729i \(-0.967562\pi\)
0.969611 + 0.244652i \(0.0786736\pi\)
\(80\) 848091.i 0.0207054i
\(81\) −1.05795e7 4.17264e7i −0.245768 0.969329i
\(82\) 1.10246e7 0.243842
\(83\) 5.90784e6 + 1.04171e6i 0.124485 + 0.0219500i 0.235543 0.971864i \(-0.424313\pi\)
−0.111059 + 0.993814i \(0.535424\pi\)
\(84\) 3.93233e7 1.92275e7i 0.789828 0.386195i
\(85\) 5.06440e6 + 1.84329e6i 0.0970179 + 0.0353116i
\(86\) −1.33888e7 1.59561e7i −0.244764 0.291698i
\(87\) −4.81633e7 + 1.38623e7i −0.840696 + 0.241968i
\(88\) −2.45910e7 + 8.95039e6i −0.410058 + 0.149249i
\(89\) 3.29258e7 + 1.90097e7i 0.524779 + 0.302981i 0.738888 0.673829i \(-0.235351\pi\)
−0.214109 + 0.976810i \(0.568685\pi\)
\(90\) 1.89325e6 + 262252.i 0.0288562 + 0.00399713i
\(91\) −2.13751e7 3.70227e7i −0.311704 0.539887i
\(92\) 1.45780e7 1.73734e7i 0.203491 0.242512i
\(93\) 8.71029e7 9.24222e6i 1.16440 0.123551i
\(94\) 7.20300e6 + 4.08503e7i 0.0922576 + 0.523219i
\(95\) 7.47305e6 1.31770e6i 0.0917495 0.0161779i
\(96\) −7.96594e7 3.53720e7i −0.937890 0.416462i
\(97\) 9.92181e6 + 8.32538e6i 0.112074 + 0.0940410i 0.697102 0.716972i \(-0.254472\pi\)
−0.585029 + 0.811013i \(0.698917\pi\)
\(98\) −1.27034e7 + 7.33433e6i −0.137726 + 0.0795162i
\(99\) 1.02532e7 + 4.77714e7i 0.106738 + 0.497310i
\(100\) −3.80261e7 + 6.58632e7i −0.380261 + 0.658632i
\(101\) 2.54486e7 + 6.99195e7i 0.244556 + 0.671912i 0.999863 + 0.0165413i \(0.00526549\pi\)
−0.755307 + 0.655371i \(0.772512\pi\)
\(102\) 6.30231e7 6.53920e7i 0.582236 0.604121i
\(103\) −3.98778e7 + 3.34615e7i −0.354309 + 0.297301i −0.802518 0.596628i \(-0.796507\pi\)
0.448209 + 0.893929i \(0.352062\pi\)
\(104\) −1.85780e7 + 5.10426e7i −0.158806 + 0.436315i
\(105\) 8.36311e6 + 576473.i 0.0688035 + 0.00474266i
\(106\) 4.66998e6 2.64848e7i 0.0369906 0.209784i
\(107\) 2.19636e8i 1.67559i 0.545986 + 0.837795i \(0.316155\pi\)
−0.545986 + 0.837795i \(0.683845\pi\)
\(108\) −5.47649e7 + 8.82251e7i −0.402538 + 0.648480i
\(109\) −2.65997e8 −1.88439 −0.942194 0.335067i \(-0.891241\pi\)
−0.942194 + 0.335067i \(0.891241\pi\)
\(110\) −2.13646e6 376716.i −0.0145923 0.00257302i
\(111\) −1.31522e8 8.85231e7i −0.866376 0.583129i
\(112\) −5.89010e7 2.14382e7i −0.374326 0.136244i
\(113\) −7.63601e6 9.10024e6i −0.0468331 0.0558135i 0.742119 0.670268i \(-0.233821\pi\)
−0.788953 + 0.614454i \(0.789376\pi\)
\(114\) 3.08123e7 1.24105e8i 0.182433 0.734804i
\(115\) 4.08144e6 1.48552e6i 0.0233357 0.00849352i
\(116\) 1.04702e8 + 6.04498e7i 0.578260 + 0.333859i
\(117\) 8.96388e7 + 4.74340e7i 0.478358 + 0.253132i
\(118\) 7.03123e7 + 1.21785e8i 0.362663 + 0.628151i
\(119\) 2.56037e8 3.05134e8i 1.27678 1.52161i
\(120\) −6.26928e6 8.61096e6i −0.0302338 0.0415266i
\(121\) 2.75931e7 + 1.56488e8i 0.128724 + 0.730028i
\(122\) −9.52276e7 + 1.67912e7i −0.429857 + 0.0757953i
\(123\) −9.27336e7 + 6.75155e7i −0.405151 + 0.294973i
\(124\) −1.61862e8 1.35818e8i −0.684633 0.574476i
\(125\) −2.52726e7 + 1.45912e7i −0.103517 + 0.0597654i
\(126\) 6.60717e7 1.24860e8i 0.262140 0.495381i
\(127\) −1.66357e7 + 2.88139e7i −0.0639479 + 0.110761i −0.896227 0.443596i \(-0.853702\pi\)
0.832279 + 0.554357i \(0.187036\pi\)
\(128\) 8.73591e7 + 2.40017e8i 0.325438 + 0.894133i
\(129\) 2.10336e8 + 5.22211e7i 0.759546 + 0.188576i
\(130\) −3.44948e6 + 2.89446e6i −0.0120776 + 0.0101343i
\(131\) 1.61936e8 4.44915e8i 0.549867 1.51075i −0.284022 0.958818i \(-0.591669\pi\)
0.833890 0.551931i \(-0.186109\pi\)
\(132\) 6.58107e7 9.77774e7i 0.216771 0.322064i
\(133\) 9.73893e7 5.52322e8i 0.311246 1.76517i
\(134\) 8.64974e7i 0.268277i
\(135\) −1.75311e7 + 9.38846e6i −0.0527806 + 0.0282657i
\(136\) −5.06111e8 −1.47942
\(137\) 2.76763e8 + 4.88007e7i 0.785643 + 0.138530i 0.552057 0.833806i \(-0.313843\pi\)
0.233586 + 0.972336i \(0.424954\pi\)
\(138\) 5.03317e6 7.30181e7i 0.0138780 0.201333i
\(139\) 6.76410e8 + 2.46193e8i 1.81197 + 0.659503i 0.996769 + 0.0803220i \(0.0255949\pi\)
0.815199 + 0.579180i \(0.196627\pi\)
\(140\) −1.29984e7 1.54909e7i −0.0338360 0.0403242i
\(141\) −3.10757e8 2.99500e8i −0.786221 0.757739i
\(142\) 1.98075e8 7.20935e7i 0.487166 0.177314i
\(143\) −9.96879e7 5.75548e7i −0.238396 0.137638i
\(144\) 1.45386e8 3.12043e7i 0.338123 0.0725713i
\(145\) 1.15769e7 + 2.00518e7i 0.0261891 + 0.0453608i
\(146\) 1.28661e8 1.53332e8i 0.283162 0.337459i
\(147\) 6.19388e7 1.39489e8i 0.132646 0.298724i
\(148\) 6.64097e7 + 3.76628e8i 0.138415 + 0.784993i
\(149\) −8.91020e8 + 1.57111e8i −1.80777 + 0.318758i −0.972819 0.231569i \(-0.925614\pi\)
−0.834949 + 0.550327i \(0.814503\pi\)
\(150\) 2.58973e7 + 2.44068e8i 0.0511552 + 0.482110i
\(151\) −2.47852e8 2.07973e8i −0.476744 0.400036i 0.372503 0.928031i \(-0.378500\pi\)
−0.849247 + 0.527995i \(0.822944\pi\)
\(152\) −6.17136e8 + 3.56304e8i −1.15613 + 0.667492i
\(153\) −1.29654e8 + 9.36000e8i −0.236603 + 1.70809i
\(154\) −8.01692e7 + 1.38857e8i −0.142536 + 0.246880i
\(155\) −1.38401e7 3.80254e7i −0.0239780 0.0658790i
\(156\) −6.76656e7 2.35098e8i −0.114254 0.396964i
\(157\) 5.95886e8 5.00008e8i 0.980764 0.822959i −0.00344009 0.999994i \(-0.501095\pi\)
0.984205 + 0.177035i \(0.0566506\pi\)
\(158\) 1.50510e7 4.13523e7i 0.0241511 0.0663546i
\(159\) 1.22913e8 + 2.51376e8i 0.192313 + 0.393310i
\(160\) −6.99213e6 + 3.96543e7i −0.0106691 + 0.0605077i
\(161\) 3.21012e8i 0.477769i
\(162\) 2.47024e7 + 3.34206e8i 0.0358656 + 0.485237i
\(163\) 1.09107e9 1.54561 0.772806 0.634642i \(-0.218852\pi\)
0.772806 + 0.634642i \(0.218852\pi\)
\(164\) 2.72503e8 + 4.80496e7i 0.376700 + 0.0664223i
\(165\) 2.02778e7 9.91506e6i 0.0273581 0.0133770i
\(166\) −4.38854e7 1.59730e7i −0.0577947 0.0210355i
\(167\) −8.88832e8 1.05927e9i −1.14276 1.36188i −0.922294 0.386488i \(-0.873688\pi\)
−0.220462 0.975396i \(-0.570757\pi\)
\(168\) −7.56518e8 + 2.17740e8i −0.949690 + 0.273339i
\(169\) 5.42016e8 1.97278e8i 0.664455 0.241842i
\(170\) −3.63354e7 2.09782e7i −0.0435045 0.0251173i
\(171\) 5.00851e8 + 1.23261e9i 0.585766 + 1.44158i
\(172\) −2.61396e8 4.52751e8i −0.298665 0.517303i
\(173\) 2.53987e7 3.02690e7i 0.0283548 0.0337920i −0.751681 0.659527i \(-0.770757\pi\)
0.780035 + 0.625735i \(0.215201\pi\)
\(174\) 3.87993e8 4.11687e7i 0.423279 0.0449128i
\(175\) 1.86928e8 + 1.06012e9i 0.199307 + 1.13032i
\(176\) −1.66212e8 + 2.93077e7i −0.173225 + 0.0305443i
\(177\) −1.33725e9 5.93792e8i −1.36244 0.604980i
\(178\) −2.26734e8 1.90252e8i −0.225858 0.189518i
\(179\) −5.49026e8 + 3.16980e8i −0.534787 + 0.308759i −0.742963 0.669332i \(-0.766580\pi\)
0.208177 + 0.978091i \(0.433247\pi\)
\(180\) 4.56537e7 + 1.47338e7i 0.0434897 + 0.0140354i
\(181\) −4.29163e8 + 7.43332e8i −0.399860 + 0.692578i −0.993708 0.111999i \(-0.964275\pi\)
0.593848 + 0.804577i \(0.297608\pi\)
\(182\) 1.13827e8 + 3.12738e8i 0.103743 + 0.285033i
\(183\) 6.98175e8 7.24418e8i 0.622530 0.645929i
\(184\) −3.12453e8 + 2.62179e8i −0.272592 + 0.228732i
\(185\) −2.50501e7 + 6.88246e7i −0.0213857 + 0.0587567i
\(186\) −6.80286e8 4.68924e7i −0.568381 0.0391788i
\(187\) 1.86243e8 1.05624e9i 0.152305 0.863764i
\(188\) 1.04111e9i 0.833425i
\(189\) 2.08885e8 + 1.45488e9i 0.163705 + 1.14020i
\(190\) −5.90750e7 −0.0453304
\(191\) 6.61152e8 + 1.16579e8i 0.496784 + 0.0875965i 0.416426 0.909170i \(-0.363282\pi\)
0.0803582 + 0.996766i \(0.474394\pi\)
\(192\) 1.73034e8 + 1.16463e8i 0.127329 + 0.0857008i
\(193\) −2.97918e7 1.08433e7i −0.0214718 0.00781508i 0.331262 0.943539i \(-0.392526\pi\)
−0.352734 + 0.935724i \(0.614748\pi\)
\(194\) −6.48129e7 7.72410e7i −0.0457567 0.0545307i
\(195\) 1.12894e7 4.54715e7i 0.00780790 0.0314486i
\(196\) −3.45964e8 + 1.25921e8i −0.234426 + 0.0853242i
\(197\) −8.67018e8 5.00573e8i −0.575656 0.332355i 0.183749 0.982973i \(-0.441177\pi\)
−0.759405 + 0.650618i \(0.774510\pi\)
\(198\) −1.40285e7 3.80109e8i −0.00912747 0.247314i
\(199\) 1.45511e8 + 2.52033e8i 0.0927865 + 0.160711i 0.908683 0.417488i \(-0.137089\pi\)
−0.815896 + 0.578198i \(0.803756\pi\)
\(200\) 8.79186e8 1.04777e9i 0.549491 0.654858i
\(201\) −5.29715e8 7.27571e8i −0.324532 0.445750i
\(202\) −1.00586e8 5.70454e8i −0.0604135 0.342622i
\(203\) 1.68526e9 2.97157e8i 0.992392 0.174986i
\(204\) 1.84278e9 1.34165e9i 1.06403 0.774675i
\(205\) 4.05948e7 + 3.40631e7i 0.0229856 + 0.0192872i
\(206\) 3.50966e8 2.02630e8i 0.194893 0.112521i
\(207\) 4.04830e8 + 6.45014e8i 0.220491 + 0.351308i
\(208\) −1.75161e8 + 3.03388e8i −0.0935803 + 0.162086i
\(209\) −5.16496e8 1.41906e9i −0.270696 0.743731i
\(210\) −6.33381e7 1.57253e7i −0.0325678 0.00808577i
\(211\) 2.57792e9 2.16313e9i 1.30059 1.09132i 0.310543 0.950559i \(-0.399489\pi\)
0.990043 0.140762i \(-0.0449553\pi\)
\(212\) 2.30862e8 6.34287e8i 0.114290 0.314009i
\(213\) −1.22460e9 + 1.81944e9i −0.594945 + 0.883931i
\(214\) 2.96913e8 1.68388e9i 0.141571 0.802890i
\(215\) 1.00121e8i 0.0468567i
\(216\) 1.24549e9 1.39156e9i 0.572170 0.639273i
\(217\) −2.99076e9 −1.34879
\(218\) 2.03932e9 + 3.59587e8i 0.902940 + 0.159213i
\(219\) −1.43215e8 + 2.07768e9i −0.0622605 + 0.903236i
\(220\) −5.11663e7 1.86230e7i −0.0218420 0.00794985i
\(221\) −1.43098e9 1.70538e9i −0.599882 0.714911i
\(222\) 8.88670e8 + 8.56478e8i 0.365872 + 0.352618i
\(223\) −3.84150e8 + 1.39819e8i −0.155339 + 0.0565388i −0.418519 0.908208i \(-0.637451\pi\)
0.263180 + 0.964747i \(0.415229\pi\)
\(224\) 2.57729e9 + 1.48800e9i 1.02370 + 0.591032i
\(225\) −1.71252e9 1.89438e9i −0.668199 0.739157i
\(226\) 4.62409e7 + 8.00915e7i 0.0177252 + 0.0307010i
\(227\) −1.70797e9 + 2.03548e9i −0.643246 + 0.766591i −0.984879 0.173243i \(-0.944575\pi\)
0.341633 + 0.939833i \(0.389020\pi\)
\(228\) 1.30250e9 2.93330e9i 0.481992 1.08547i
\(229\) 7.47013e8 + 4.23652e9i 0.271635 + 1.54052i 0.749451 + 0.662060i \(0.230318\pi\)
−0.477816 + 0.878460i \(0.658571\pi\)
\(230\) −3.32993e7 + 5.87157e6i −0.0118994 + 0.00209818i
\(231\) −1.76026e8 1.65895e9i −0.0618201 0.582621i
\(232\) −1.66563e9 1.39763e9i −0.574947 0.482438i
\(233\) −2.49677e9 + 1.44151e9i −0.847138 + 0.489095i −0.859684 0.510826i \(-0.829340\pi\)
0.0125463 + 0.999921i \(0.496006\pi\)
\(234\) −6.23110e8 4.84840e8i −0.207827 0.161709i
\(235\) −9.96932e7 + 1.72674e8i −0.0326884 + 0.0566180i
\(236\) 1.20717e9 + 3.31667e9i 0.389153 + 1.06919i
\(237\) 1.26642e8 + 4.40007e8i 0.0401408 + 0.139465i
\(238\) −2.37546e9 + 1.99324e9i −0.740353 + 0.621230i
\(239\) −6.28233e8 + 1.72606e9i −0.192544 + 0.529010i −0.997970 0.0636865i \(-0.979714\pi\)
0.805426 + 0.592696i \(0.201936\pi\)
\(240\) −3.01753e7 6.17131e7i −0.00909508 0.0186008i
\(241\) −7.37356e8 + 4.18175e9i −0.218579 + 1.23962i 0.656007 + 0.754755i \(0.272244\pi\)
−0.874586 + 0.484870i \(0.838867\pi\)
\(242\) 1.23705e9i 0.360682i
\(243\) −2.25448e9 2.65989e9i −0.646578 0.762848i
\(244\) −2.42698e9 −0.684711
\(245\) −6.94374e7 1.22437e7i −0.0192721 0.00339819i
\(246\) 8.02231e8 3.92259e8i 0.219058 0.107111i
\(247\) −2.94549e9 1.07207e9i −0.791353 0.288029i
\(248\) 2.44264e9 + 2.91102e9i 0.645733 + 0.769554i
\(249\) 4.66961e8 1.34400e8i 0.121474 0.0349625i
\(250\) 2.13483e8 7.77013e7i 0.0546516 0.0198915i
\(251\) 6.55995e9 + 3.78739e9i 1.65274 + 0.954212i 0.975937 + 0.218052i \(0.0699704\pi\)
0.676807 + 0.736160i \(0.263363\pi\)
\(252\) 2.17732e9 2.79826e9i 0.539908 0.693883i
\(253\) −4.32181e8 7.48559e8i −0.105483 0.182702i
\(254\) 1.66493e8 1.98419e8i 0.0400001 0.0476703i
\(255\) 4.34106e8 4.60616e7i 0.102668 0.0108938i
\(256\) −4.59760e8 2.60743e9i −0.107046 0.607089i
\(257\) −1.33863e8 + 2.36037e7i −0.0306852 + 0.00541062i −0.188970 0.981983i \(-0.560515\pi\)
0.158285 + 0.987394i \(0.449404\pi\)
\(258\) −1.54198e9 6.84705e8i −0.348018 0.154534i
\(259\) 4.14673e9 + 3.47952e9i 0.921525 + 0.773251i
\(260\) −9.78782e7 + 5.65100e7i −0.0214187 + 0.0123661i
\(261\) −3.01148e9 + 2.72238e9i −0.648959 + 0.586660i
\(262\) −1.84297e9 + 3.19212e9i −0.391123 + 0.677445i
\(263\) −3.23234e9 8.88079e9i −0.675608 1.85622i −0.484899 0.874570i \(-0.661144\pi\)
−0.190709 0.981647i \(-0.561079\pi\)
\(264\) −1.47096e9 + 1.52625e9i −0.302820 + 0.314202i
\(265\) 9.90265e7 8.30931e7i 0.0200802 0.0168493i
\(266\) −1.49331e9 + 4.10283e9i −0.298279 + 0.819515i
\(267\) 3.07228e9 + 2.11774e8i 0.604528 + 0.0416704i
\(268\) −3.76989e8 + 2.13801e9i −0.0730784 + 0.414448i
\(269\) 1.18549e8i 0.0226407i 0.999936 + 0.0113204i \(0.00360346\pi\)
−0.999936 + 0.0113204i \(0.996397\pi\)
\(270\) 1.47098e8 4.82791e7i 0.0276790 0.00908457i
\(271\) 3.58270e9 0.664252 0.332126 0.943235i \(-0.392234\pi\)
0.332126 + 0.943235i \(0.392234\pi\)
\(272\) −3.21453e9 5.66809e8i −0.587276 0.103553i
\(273\) −2.87268e9 1.93350e9i −0.517174 0.348092i
\(274\) −2.05589e9 7.48281e8i −0.364751 0.132759i
\(275\) 1.86314e9 + 2.22040e9i 0.325773 + 0.388241i
\(276\) 4.42649e8 1.78290e9i 0.0762822 0.307249i
\(277\) 1.39013e9 5.05965e8i 0.236122 0.0859412i −0.221249 0.975217i \(-0.571013\pi\)
0.457371 + 0.889276i \(0.348791\pi\)
\(278\) −4.85301e9 2.80189e9i −0.812517 0.469107i
\(279\) 6.00939e9 3.77167e9i 0.991775 0.622468i
\(280\) 1.81842e8 + 3.14960e8i 0.0295844 + 0.0512417i
\(281\) −3.91017e9 + 4.65996e9i −0.627149 + 0.747407i −0.982282 0.187409i \(-0.939991\pi\)
0.355133 + 0.934816i \(0.384435\pi\)
\(282\) 1.97760e9 + 2.71627e9i 0.312711 + 0.429513i
\(283\) −8.05969e8 4.57088e9i −0.125653 0.712613i −0.980918 0.194422i \(-0.937717\pi\)
0.855265 0.518191i \(-0.173394\pi\)
\(284\) 5.21016e9 9.18691e8i 0.800898 0.141220i
\(285\) 4.96908e8 3.61778e8i 0.0753176 0.0548357i
\(286\) 6.86472e8 + 5.76018e8i 0.102603 + 0.0860938i
\(287\) 3.39189e9 1.95831e9i 0.499935 0.288638i
\(288\) −7.05512e9 + 2.60380e8i −1.02550 + 0.0378475i
\(289\) 6.88348e9 1.19225e10i 0.986772 1.70914i
\(290\) −6.16496e7 1.69381e8i −0.00871643 0.0239482i
\(291\) 1.01820e9 + 2.52794e8i 0.141991 + 0.0352528i
\(292\) 3.84847e9 3.22925e9i 0.529366 0.444191i
\(293\) 3.86218e9 1.06113e10i 0.524037 1.43978i −0.341952 0.939717i \(-0.611088\pi\)
0.865989 0.500063i \(-0.166690\pi\)
\(294\) −6.63434e8 + 9.85688e8i −0.0887991 + 0.131932i
\(295\) −1.17377e8 + 6.65679e8i −0.0154987 + 0.0878976i
\(296\) 6.87800e9i 0.895974i
\(297\) 2.44581e9 + 3.11137e9i 0.314338 + 0.399877i
\(298\) 7.04357e9 0.893158
\(299\) −1.76687e9 3.11546e8i −0.221065 0.0389797i
\(300\) −4.23623e8 + 6.14565e9i −0.0522991 + 0.758722i
\(301\) −6.95353e9 2.53088e9i −0.847109 0.308323i
\(302\) 1.61906e9 + 1.92952e9i 0.194642 + 0.231965i
\(303\) 4.33957e9 + 4.18237e9i 0.514845 + 0.496194i
\(304\) −4.31874e9 + 1.57189e9i −0.505665 + 0.184047i
\(305\) −4.02526e8 2.32399e8i −0.0465152 0.0268556i
\(306\) 2.25934e9 7.00076e9i 0.257690 0.798471i
\(307\) 1.60427e9 + 2.77868e9i 0.180603 + 0.312813i 0.942086 0.335372i \(-0.108862\pi\)
−0.761483 + 0.648185i \(0.775529\pi\)
\(308\) −2.58678e9 + 3.08281e9i −0.287446 + 0.342565i
\(309\) −1.71123e9 + 3.85375e9i −0.187704 + 0.422717i
\(310\) 5.47035e7 + 3.10239e8i 0.00592336 + 0.0335931i
\(311\) −5.93601e9 + 1.04668e9i −0.634531 + 0.111885i −0.481656 0.876361i \(-0.659964\pi\)
−0.152875 + 0.988245i \(0.548853\pi\)
\(312\) 4.64242e8 + 4.37523e9i 0.0489921 + 0.461724i
\(313\) 2.47074e9 + 2.07320e9i 0.257425 + 0.216005i 0.762362 0.647151i \(-0.224040\pi\)
−0.504937 + 0.863156i \(0.668484\pi\)
\(314\) −5.24441e9 + 3.02786e9i −0.539484 + 0.311471i
\(315\) 6.29070e8 2.55613e8i 0.0638935 0.0259622i
\(316\) 5.52254e8 9.56532e8i 0.0553848 0.0959292i
\(317\) 1.44241e9 + 3.96300e9i 0.142841 + 0.392452i 0.990397 0.138254i \(-0.0441490\pi\)
−0.847556 + 0.530706i \(0.821927\pi\)
\(318\) −6.02514e8 2.09338e9i −0.0589195 0.204710i
\(319\) 3.52975e9 2.96181e9i 0.340864 0.286019i
\(320\) 3.29566e7 9.05476e7i 0.00314299 0.00863529i
\(321\) 7.81468e9 + 1.59822e10i 0.736023 + 1.50528i
\(322\) −4.33959e8 + 2.46110e9i −0.0403669 + 0.228932i
\(323\) 2.92059e10i 2.68325i
\(324\) −8.46013e8 + 8.36843e9i −0.0767709 + 0.759388i
\(325\) 6.01637e9 0.539264
\(326\) −8.36487e9 1.47495e9i −0.740609 0.130589i
\(327\) −1.93558e10 + 9.46423e9i −1.69286 + 0.827741i
\(328\) −4.67634e9 1.70205e9i −0.404028 0.147054i
\(329\) 9.47233e9 + 1.12887e10i 0.808488 + 0.963518i
\(330\) −1.68868e8 + 4.86033e7i −0.0142394 + 0.00409836i
\(331\) −5.24937e9 + 1.91061e9i −0.437316 + 0.159170i −0.551290 0.834314i \(-0.685864\pi\)
0.113974 + 0.993484i \(0.463642\pi\)
\(332\) −1.01513e9 5.86083e8i −0.0835541 0.0482400i
\(333\) −1.27201e10 1.76198e9i −1.03446 0.143293i
\(334\) 5.38244e9 + 9.32265e9i 0.432507 + 0.749124i
\(335\) −2.67253e8 + 3.18500e8i −0.0212199 + 0.0252889i
\(336\) −5.04883e9 + 5.35715e8i −0.396126 + 0.0420317i
\(337\) −3.28023e8 1.86031e9i −0.0254322 0.144233i 0.969448 0.245299i \(-0.0788860\pi\)
−0.994880 + 0.101065i \(0.967775\pi\)
\(338\) −4.42217e9 + 7.79747e8i −0.338819 + 0.0597430i
\(339\) −8.79439e8 3.90507e8i −0.0665897 0.0295686i
\(340\) −8.06692e8 6.76895e8i −0.0603659 0.0506530i
\(341\) −6.97408e9 + 4.02649e9i −0.515786 + 0.297789i
\(342\) −2.17358e9 1.01271e10i −0.158881 0.740254i
\(343\) 5.36623e9 9.29458e9i 0.387697 0.671511i
\(344\) 3.21574e9 + 8.83518e9i 0.229640 + 0.630931i
\(345\) 2.44139e8 2.53315e8i 0.0172330 0.0178807i
\(346\) −2.35643e8 + 1.97728e8i −0.0164418 + 0.0137963i
\(347\) −4.26463e9 + 1.17170e10i −0.294146 + 0.808160i 0.701303 + 0.712864i \(0.252602\pi\)
−0.995449 + 0.0952965i \(0.969620\pi\)
\(348\) 9.76968e9 + 6.73429e8i 0.666137 + 0.0459171i
\(349\) −2.62191e9 + 1.48696e10i −0.176733 + 1.00230i 0.759392 + 0.650633i \(0.225496\pi\)
−0.936125 + 0.351667i \(0.885615\pi\)
\(350\) 8.38032e9i 0.558455i
\(351\) 8.21047e9 + 2.62265e8i 0.540928 + 0.0172787i
\(352\) 8.01323e9 0.521960
\(353\) −1.77537e10 3.13045e9i −1.14338 0.201608i −0.430295 0.902688i \(-0.641591\pi\)
−0.713083 + 0.701080i \(0.752702\pi\)
\(354\) 9.44954e9 + 6.36017e9i 0.601725 + 0.405001i
\(355\) 9.52100e8 + 3.46536e8i 0.0599472 + 0.0218190i
\(356\) −4.77513e9 5.69077e9i −0.297293 0.354300i
\(357\) 7.77437e9 3.13135e10i 0.478622 1.92779i
\(358\) 4.63772e9 1.68799e9i 0.282340 0.102763i
\(359\) 2.52845e10 + 1.45980e10i 1.52222 + 0.878852i 0.999655 + 0.0262509i \(0.00835688\pi\)
0.522562 + 0.852602i \(0.324976\pi\)
\(360\) −7.62577e8 4.03532e8i −0.0454019 0.0240252i
\(361\) −1.20693e10 2.09046e10i −0.710644 1.23087i
\(362\) 4.29513e9 5.11874e9i 0.250117 0.298077i
\(363\) 7.57575e9 + 1.04054e10i 0.436314 + 0.599284i
\(364\) 1.45051e9 + 8.22623e9i 0.0826255 + 0.468592i
\(365\) 9.47507e8 1.67071e8i 0.0533840 0.00941304i
\(366\) −6.33200e9 + 4.61007e9i −0.352872 + 0.256911i
\(367\) 6.35266e9 + 5.33051e9i 0.350180 + 0.293836i 0.800862 0.598849i \(-0.204375\pi\)
−0.450682 + 0.892684i \(0.648819\pi\)
\(368\) −2.27815e9 + 1.31529e9i −0.124220 + 0.0717184i
\(369\) −4.34573e9 + 8.21239e9i −0.234400 + 0.442959i
\(370\) 2.85092e8 4.93794e8i 0.0152117 0.0263475i
\(371\) −3.26771e9 8.97795e9i −0.172483 0.473894i
\(372\) −1.66107e10 4.12401e9i −0.867392 0.215352i
\(373\) −2.11366e10 + 1.77357e10i −1.09194 + 0.916248i −0.996857 0.0792207i \(-0.974757\pi\)
−0.0950853 + 0.995469i \(0.530312\pi\)
\(374\) −2.85574e9 + 7.84608e9i −0.145960 + 0.401020i
\(375\) −1.31986e9 + 1.96096e9i −0.0667425 + 0.0991618i
\(376\) 3.25139e9 1.84396e10i 0.162674 0.922570i
\(377\) 9.56417e9i 0.473458i
\(378\) 3.65313e8 1.14365e10i 0.0178936 0.560178i
\(379\) 2.32513e10 1.12691 0.563457 0.826145i \(-0.309471\pi\)
0.563457 + 0.826145i \(0.309471\pi\)
\(380\) −1.46019e9 2.57471e8i −0.0700286 0.0123479i
\(381\) −1.85327e8 + 2.68861e9i −0.00879505 + 0.127593i
\(382\) −4.91126e9 1.78755e9i −0.230642 0.0839470i
\(383\) 3.20145e9 + 3.81534e9i 0.148782 + 0.177312i 0.835288 0.549812i \(-0.185301\pi\)
−0.686506 + 0.727124i \(0.740856\pi\)
\(384\) 1.48967e10 + 1.43571e10i 0.685119 + 0.660300i
\(385\) −7.24228e8 + 2.63597e8i −0.0329634 + 0.0119977i
\(386\) 2.13746e8 + 1.23406e8i 0.00962829 + 0.00555890i
\(387\) 1.71635e10 3.68382e9i 0.765179 0.164231i
\(388\) −1.26537e9 2.19169e9i −0.0558331 0.0967057i
\(389\) 6.62163e9 7.89136e9i 0.289179 0.344630i −0.601823 0.798630i \(-0.705559\pi\)
0.891002 + 0.453999i \(0.150003\pi\)
\(390\) −1.48023e8 + 3.33355e8i −0.00639840 + 0.0144095i
\(391\) −2.90283e9 1.64628e10i −0.124198 0.704361i
\(392\) 6.52075e9 1.14978e9i 0.276155 0.0486936i
\(393\) −4.04659e9 3.81369e10i −0.169636 1.59873i
\(394\) 5.97047e9 + 5.00982e9i 0.247756 + 0.207892i
\(395\) 1.83188e8 1.05764e8i 0.00752503 0.00434458i
\(396\) 1.30991e9 9.45654e9i 0.0532673 0.384549i
\(397\) −1.12454e10 + 1.94777e10i −0.452704 + 0.784107i −0.998553 0.0537771i \(-0.982874\pi\)
0.545849 + 0.837884i \(0.316207\pi\)
\(398\) −7.74882e8 2.12897e9i −0.0308818 0.0848472i
\(399\) −1.25650e10 4.36560e10i −0.495760 1.72247i
\(400\) 6.75753e9 5.67024e9i 0.263966 0.221494i
\(401\) −1.26623e10 + 3.47894e10i −0.489705 + 1.34545i 0.411242 + 0.911526i \(0.365095\pi\)
−0.900947 + 0.433928i \(0.857127\pi\)
\(402\) 3.07760e9 + 6.29416e9i 0.117844 + 0.241009i
\(403\) −2.90258e9 + 1.64613e10i −0.110043 + 0.624086i
\(404\) 1.45386e10i 0.545756i
\(405\) −9.41645e8 + 1.30693e9i −0.0349999 + 0.0485772i
\(406\) −1.33221e10 −0.490308
\(407\) 1.43542e10 + 2.53103e9i 0.523119 + 0.0922400i
\(408\) −3.68282e10 + 1.80075e10i −1.32905 + 0.649851i
\(409\) −1.04727e10 3.81173e9i −0.374251 0.136216i 0.148044 0.988981i \(-0.452702\pi\)
−0.522296 + 0.852764i \(0.674924\pi\)
\(410\) −2.65180e8 3.16029e8i −0.00938438 0.0111839i
\(411\) 2.18756e10 6.29620e9i 0.766641 0.220654i
\(412\) 9.55817e9 3.47889e9i 0.331731 0.120740i
\(413\) 4.32652e10 + 2.49792e10i 1.48709 + 0.858574i
\(414\) −2.23175e9 5.49240e9i −0.0759705 0.186965i
\(415\) −1.12242e8 1.94409e8i −0.00378411 0.00655428i
\(416\) 1.06913e10 1.27414e10i 0.356992 0.425447i
\(417\) 5.79800e10 6.15207e9i 1.91749 0.203459i
\(418\) 2.04147e9 + 1.15777e10i 0.0668709 + 0.379244i
\(419\) 2.88812e10 5.09254e9i 0.937044 0.165226i 0.315784 0.948831i \(-0.397732\pi\)
0.621259 + 0.783605i \(0.286621\pi\)
\(420\) −1.49703e9 6.64743e8i −0.0481098 0.0213627i
\(421\) −3.97225e10 3.33311e10i −1.26447 1.06102i −0.995191 0.0979530i \(-0.968771\pi\)
−0.269278 0.963062i \(-0.586785\pi\)
\(422\) −2.26883e10 + 1.30991e10i −0.715406 + 0.413040i
\(423\) −3.32691e10 1.07369e10i −1.03915 0.335365i
\(424\) −6.06976e9 + 1.05131e10i −0.187805 + 0.325288i
\(425\) 1.91728e10 + 5.26768e10i 0.587664 + 1.61459i
\(426\) 1.18483e10 1.22936e10i 0.359763 0.373285i
\(427\) −2.63155e10 + 2.20813e10i −0.791590 + 0.664223i
\(428\) 1.46780e10 4.03274e10i 0.437412 1.20178i
\(429\) −9.30181e9 6.41178e8i −0.274624 0.0189299i
\(430\) −1.35348e8 + 7.67598e8i −0.00395894 + 0.0224523i
\(431\) 2.99834e9i 0.0868905i 0.999056 + 0.0434452i \(0.0138334\pi\)
−0.999056 + 0.0434452i \(0.986167\pi\)
\(432\) 9.46909e9 7.44353e9i 0.271878 0.213719i
\(433\) −6.72699e10 −1.91368 −0.956839 0.290617i \(-0.906139\pi\)
−0.956839 + 0.290617i \(0.906139\pi\)
\(434\) 2.29293e10 + 4.04305e9i 0.646296 + 0.113959i
\(435\) 1.55586e9 + 1.04720e9i 0.0434525 + 0.0292464i
\(436\) 4.88398e10 + 1.77762e10i 1.35154 + 0.491919i
\(437\) −1.51295e10 1.80306e10i −0.414856 0.494406i
\(438\) 3.90668e9 1.57353e10i 0.106148 0.427542i
\(439\) −4.83773e10 + 1.76079e10i −1.30252 + 0.474078i −0.897816 0.440371i \(-0.854847\pi\)
−0.404702 + 0.914449i \(0.632625\pi\)
\(440\) 8.48067e8 + 4.89631e8i 0.0226266 + 0.0130635i
\(441\) −4.55943e8 1.23540e10i −0.0120547 0.326628i
\(442\) 8.66551e9 + 1.50091e10i 0.227041 + 0.393247i
\(443\) −1.96213e10 + 2.33837e10i −0.509463 + 0.607154i −0.958056 0.286582i \(-0.907481\pi\)
0.448593 + 0.893736i \(0.351925\pi\)
\(444\) 1.82329e10 + 2.50432e10i 0.469164 + 0.644404i
\(445\) −2.47050e8 1.40109e9i −0.00630006 0.0357294i
\(446\) 3.13417e9 5.52639e8i 0.0792107 0.0139670i
\(447\) −5.92469e10 + 4.31352e10i −1.48401 + 1.08044i
\(448\) −5.45556e9 4.57776e9i −0.135434 0.113642i
\(449\) −4.45495e10 + 2.57207e10i −1.09612 + 0.632845i −0.935199 0.354123i \(-0.884780\pi\)
−0.160920 + 0.986967i \(0.551446\pi\)
\(450\) 1.05685e10 + 1.68387e10i 0.257728 + 0.410637i
\(451\) 5.27297e9 9.13304e9i 0.127453 0.220754i
\(452\) 7.93894e8 + 2.18121e9i 0.0190199 + 0.0522568i
\(453\) −2.54352e10 6.31493e9i −0.604008 0.149960i
\(454\) 1.58462e10 1.32965e10i 0.372993 0.312978i
\(455\) −5.47140e8 + 1.50325e9i −0.0127659 + 0.0350741i
\(456\) −3.22298e10 + 4.78851e10i −0.745416 + 1.10749i
\(457\) 1.83947e9 1.04321e10i 0.0421723 0.239171i −0.956434 0.291949i \(-0.905696\pi\)
0.998606 + 0.0527778i \(0.0168075\pi\)
\(458\) 3.34900e10i 0.761120i
\(459\) 2.38686e10 + 7.27231e10i 0.537744 + 1.63841i
\(460\) −8.48670e8 −0.0189543
\(461\) −1.61670e10 2.85068e9i −0.357953 0.0631168i −0.00822026 0.999966i \(-0.502617\pi\)
−0.349733 + 0.936849i \(0.613728\pi\)
\(462\) −8.93109e8 + 1.29567e10i −0.0196036 + 0.284397i
\(463\) 2.17181e10 + 7.90475e9i 0.472605 + 0.172014i 0.567332 0.823489i \(-0.307976\pi\)
−0.0947270 + 0.995503i \(0.530198\pi\)
\(464\) −9.01393e9 1.07424e10i −0.194465 0.231755i
\(465\) −2.36006e9 2.27456e9i −0.0504790 0.0486504i
\(466\) 2.10906e10 7.67637e9i 0.447246 0.162784i
\(467\) 3.17397e10 + 1.83249e10i 0.667322 + 0.385278i 0.795061 0.606529i \(-0.207439\pi\)
−0.127739 + 0.991808i \(0.540772\pi\)
\(468\) −1.32887e10 1.46998e10i −0.277012 0.306429i
\(469\) 1.53645e10 + 2.66121e10i 0.317562 + 0.550033i
\(470\) 9.97745e8 1.18907e9i 0.0204469 0.0243677i
\(471\) 2.55705e10 5.75859e10i 0.519584 1.17013i
\(472\) −1.10227e10 6.25128e10i −0.222085 1.25951i
\(473\) −1.96221e10 + 3.45990e9i −0.392013 + 0.0691225i
\(474\) −3.76107e8 3.54460e9i −0.00745071 0.0702189i
\(475\) 6.04633e10 + 5.07348e10i 1.18773 + 0.996624i
\(476\) −6.74029e10 + 3.89151e10i −1.31296 + 0.758036i
\(477\) 1.78880e10 + 1.39186e10i 0.345532 + 0.268858i
\(478\) 7.14984e9 1.23839e10i 0.136957 0.237217i
\(479\) −3.04605e10 8.36895e10i −0.578622 1.58975i −0.790505 0.612456i \(-0.790182\pi\)
0.211883 0.977295i \(-0.432040\pi\)
\(480\) 9.02114e8 + 3.13431e9i 0.0169940 + 0.0590442i
\(481\) 2.31759e10 1.94469e10i 0.432969 0.363304i
\(482\) 1.13062e10 3.10634e10i 0.209473 0.575521i
\(483\) −1.14217e10 2.33591e10i −0.209866 0.429208i
\(484\) 5.39153e9 3.05769e10i 0.0982495 0.557200i
\(485\) 4.84670e8i 0.00875949i
\(486\) 1.36886e10 + 2.34403e10i 0.245366 + 0.420162i
\(487\) −2.06487e10 −0.367093 −0.183547 0.983011i \(-0.558758\pi\)
−0.183547 + 0.983011i \(0.558758\pi\)
\(488\) 4.29852e10 + 7.57945e9i 0.757948 + 0.133647i
\(489\) 7.93937e10 3.88204e10i 1.38851 0.678929i
\(490\) 5.15804e8 + 1.87737e8i 0.00894748 + 0.00325662i
\(491\) −1.51222e10 1.80220e10i −0.260190 0.310082i 0.620096 0.784526i \(-0.287094\pi\)
−0.880286 + 0.474444i \(0.842649\pi\)
\(492\) 2.15388e10 6.19928e9i 0.367588 0.105799i
\(493\) 8.37397e10 3.04788e10i 1.41757 0.515953i
\(494\) 2.11329e10 + 1.22011e10i 0.354856 + 0.204876i
\(495\) 1.12278e9 1.44298e9i 0.0187013 0.0240347i
\(496\) 1.22541e10 + 2.12248e10i 0.202468 + 0.350684i
\(497\) 4.81347e10 5.73647e10i 0.788919 0.940198i
\(498\) −3.76174e9 + 3.99146e8i −0.0611605 + 0.00648955i
\(499\) 4.39743e9 + 2.49391e10i 0.0709246 + 0.402233i 0.999515 + 0.0311280i \(0.00990996\pi\)
−0.928591 + 0.371105i \(0.878979\pi\)
\(500\) 5.61543e9 9.90152e8i 0.0898469 0.0158424i
\(501\) −1.02367e11 4.54550e10i −1.62483 0.721491i
\(502\) −4.51732e10 3.79048e10i −0.711322 0.596870i
\(503\) −8.07649e10 + 4.66296e10i −1.26168 + 0.728434i −0.973400 0.229111i \(-0.926418\pi\)
−0.288284 + 0.957545i \(0.593085\pi\)
\(504\) −4.73023e10 + 4.27614e10i −0.733095 + 0.662719i
\(505\) 1.39217e9 2.41130e9i 0.0214055 0.0370754i
\(506\) 2.30146e9 + 6.32322e9i 0.0351077 + 0.0964575i
\(507\) 3.24218e10 3.36404e10i 0.490687 0.509131i
\(508\) 4.98009e9 4.17879e9i 0.0747795 0.0627474i
\(509\) 2.18961e10 6.01590e10i 0.326208 0.896250i −0.662854 0.748749i \(-0.730655\pi\)
0.989062 0.147501i \(-0.0471230\pi\)
\(510\) −3.39043e9 2.33704e8i −0.0501157 0.00345450i
\(511\) 1.23480e10 7.00288e10i 0.181097 1.02705i
\(512\) 4.47759e10i 0.651575i
\(513\) 8.03019e10 + 7.18728e10i 1.15946 + 1.03776i
\(514\) 1.05820e9 0.0151605
\(515\) 1.91839e9 + 3.38265e8i 0.0272715 + 0.00480870i
\(516\) −3.51300e10 2.36448e10i −0.495540 0.333532i
\(517\) 3.72863e10 + 1.35711e10i 0.521900 + 0.189956i
\(518\) −2.70880e10 3.22822e10i −0.376234 0.448378i
\(519\) 7.71211e8 3.10628e9i 0.0106293 0.0428125i
\(520\) 1.91004e9 6.95197e8i 0.0261233 0.00950812i
\(521\) 9.62836e10 + 5.55894e10i 1.30678 + 0.754468i 0.981557 0.191170i \(-0.0612283\pi\)
0.325220 + 0.945638i \(0.394562\pi\)
\(522\) 2.67683e10 1.68006e10i 0.360528 0.226278i
\(523\) −3.92357e10 6.79583e10i −0.524415 0.908313i −0.999596 0.0284250i \(-0.990951\pi\)
0.475181 0.879888i \(-0.342383\pi\)
\(524\) −5.94663e10 + 7.08692e10i −0.788761 + 0.940009i
\(525\) 5.13215e10 + 7.04909e10i 0.675557 + 0.927888i
\(526\) 1.27759e10 + 7.24560e10i 0.166898 + 0.946523i
\(527\) −1.53378e11 + 2.70447e10i −1.98848 + 0.350622i
\(528\) −1.10520e10 + 8.04649e9i −0.142202 + 0.103531i
\(529\) 4.96694e10 + 4.16776e10i 0.634259 + 0.532206i
\(530\) −8.71535e8 + 5.03181e8i −0.0110454 + 0.00637706i
\(531\) −1.18435e11 + 4.37101e9i −1.48971 + 0.0549798i
\(532\) −5.47927e10 + 9.49037e10i −0.684031 + 1.18478i
\(533\) −7.48676e9 2.05697e10i −0.0927651 0.254870i
\(534\) −2.32680e10 5.77686e9i −0.286150 0.0710439i
\(535\) 6.29601e9 5.28298e9i 0.0768512 0.0644858i
\(536\) 1.33540e10 3.66898e10i 0.161790 0.444514i
\(537\) −2.86728e10 + 4.26002e10i −0.344804 + 0.512288i
\(538\) 1.60261e8 9.08883e8i 0.00191292 0.0108487i
\(539\) 1.40317e10i 0.166248i
\(540\) 3.84632e9 5.52237e8i 0.0452345 0.00649457i
\(541\) 5.30837e10 0.619687 0.309844 0.950788i \(-0.399723\pi\)
0.309844 + 0.950788i \(0.399723\pi\)
\(542\) −2.74675e10 4.84326e9i −0.318289 0.0561229i
\(543\) −4.78100e9 + 6.93598e10i −0.0549946 + 0.797827i
\(544\) 1.45629e11 + 5.30047e10i 1.66285 + 0.605228i
\(545\) 6.39813e9 + 7.62499e9i 0.0725215 + 0.0864278i
\(546\) 1.94102e10 + 1.87070e10i 0.218403 + 0.210491i
\(547\) 2.28786e10 8.32712e9i 0.255552 0.0930134i −0.211067 0.977472i \(-0.567694\pi\)
0.466620 + 0.884458i \(0.345472\pi\)
\(548\) −4.75553e10 2.74560e10i −0.527323 0.304450i
\(549\) 2.50292e10 7.75550e10i 0.275523 0.853730i
\(550\) −1.12825e10 1.95418e10i −0.123297 0.213557i
\(551\) 8.06525e10 9.61180e10i 0.875007 1.04279i
\(552\) −1.34079e10 + 3.01952e10i −0.144412 + 0.325223i
\(553\) −2.71475e9 1.53961e10i −0.0290288 0.164631i
\(554\) −1.13417e10 + 1.99984e9i −0.120403 + 0.0212303i
\(555\) 6.25973e8 + 5.89946e9i 0.00659756 + 0.0621785i
\(556\) −1.07743e11 9.04073e10i −1.12743 0.946028i
\(557\) −5.15104e10 + 2.97396e10i −0.535149 + 0.308968i −0.743111 0.669169i \(-0.766650\pi\)
0.207962 + 0.978137i \(0.433317\pi\)
\(558\) −5.11709e10 + 2.07925e10i −0.527820 + 0.214472i
\(559\) −2.06786e10 + 3.58164e10i −0.211775 + 0.366804i
\(560\) 8.02227e8 + 2.20410e9i 0.00815728 + 0.0224119i
\(561\) −2.40288e10 8.34859e10i −0.242594 0.842872i
\(562\) 3.62776e10 3.04406e10i 0.363659 0.305146i
\(563\) −8.78895e9 + 2.41474e10i −0.0874789 + 0.240346i −0.975716 0.219039i \(-0.929708\pi\)
0.888237 + 0.459385i \(0.151930\pi\)
\(564\) 3.70431e10 + 7.57588e10i 0.366092 + 0.748715i
\(565\) −7.71931e7 + 4.37784e8i −0.000757503 + 0.00429601i
\(566\) 3.61331e10i 0.352078i
\(567\) 6.69650e10 + 9.84352e10i 0.647911 + 0.952398i
\(568\) −9.51482e10 −0.914128
\(569\) 1.36983e11 + 2.41538e10i 1.30683 + 0.230429i 0.783334 0.621601i \(-0.213517\pi\)
0.523493 + 0.852030i \(0.324629\pi\)
\(570\) −4.29871e9 + 2.10190e9i −0.0407229 + 0.0199119i
\(571\) −3.21798e10 1.17125e10i −0.302719 0.110181i 0.186195 0.982513i \(-0.440384\pi\)
−0.488913 + 0.872332i \(0.662607\pi\)
\(572\) 1.44574e10 + 1.72297e10i 0.135054 + 0.160951i
\(573\) 5.22580e10 1.50408e10i 0.484768 0.139525i
\(574\) −2.86519e10 + 1.04284e10i −0.263940 + 0.0960664i
\(575\) 3.91245e10 + 2.25886e10i 0.357913 + 0.206641i
\(576\) 1.67350e10 + 2.31811e9i 0.152032 + 0.0210593i
\(577\) −4.06482e10 7.04048e10i −0.366723 0.635183i 0.622328 0.782756i \(-0.286187\pi\)
−0.989051 + 0.147574i \(0.952854\pi\)
\(578\) −6.88910e10 + 8.21011e10i −0.617236 + 0.735593i
\(579\) −2.55367e9 + 2.70962e8i −0.0227222 + 0.00241098i
\(580\) −7.85604e8 4.45538e9i −0.00694212 0.0393707i
\(581\) −1.63392e10 + 2.88105e9i −0.143393 + 0.0252840i
\(582\) −7.46449e9 3.31454e9i −0.0650591 0.0288889i
\(583\) −1.97070e10 1.65361e10i −0.170587 0.143139i
\(584\) −7.82466e10 + 4.51757e10i −0.672689 + 0.388377i
\(585\) −7.96388e8 3.71051e9i −0.00679988 0.0316818i
\(586\) −4.39549e10 + 7.61322e10i −0.372750 + 0.645621i
\(587\) 1.12180e10 + 3.08212e10i 0.0944850 + 0.259595i 0.977928 0.208944i \(-0.0670026\pi\)
−0.883443 + 0.468539i \(0.844780\pi\)
\(588\) −2.06945e10 + 2.14724e10i −0.173119 + 0.179626i
\(589\) −1.67985e11 + 1.40956e11i −1.39576 + 1.17118i
\(590\) 1.79979e9 4.94489e9i 0.0148530 0.0408083i
\(591\) −8.09008e10 5.57653e9i −0.663137 0.0457103i
\(592\) 7.70288e9 4.36852e10i 0.0627142 0.355670i
\(593\) 1.79096e11i 1.44833i −0.689628 0.724164i \(-0.742226\pi\)
0.689628 0.724164i \(-0.257774\pi\)
\(594\) −1.45452e10 2.71603e10i −0.116835 0.218167i
\(595\) −1.49054e10 −0.118926
\(596\) 1.74100e11 + 3.06986e10i 1.37979 + 0.243295i
\(597\) 1.95558e10 + 1.31624e10i 0.153950 + 0.103618i
\(598\) 1.31249e10 + 4.77706e9i 0.102634 + 0.0373557i
\(599\) −3.31382e10 3.94926e10i −0.257408 0.306767i 0.621828 0.783154i \(-0.286390\pi\)
−0.879235 + 0.476387i \(0.841946\pi\)
\(600\) 2.66958e10 1.07525e11i 0.205986 0.829669i
\(601\) −1.52122e10 + 5.53680e9i −0.116599 + 0.0424386i −0.399661 0.916663i \(-0.630872\pi\)
0.283062 + 0.959102i \(0.408650\pi\)
\(602\) 4.98893e10 + 2.88036e10i 0.379858 + 0.219311i
\(603\) −6.44329e10 3.40959e10i −0.487347 0.257889i
\(604\) 3.16097e10 + 5.47497e10i 0.237505 + 0.411371i
\(605\) 3.82214e9 4.55504e9i 0.0285289 0.0339994i
\(606\) −2.76163e10 3.79314e10i −0.204774 0.281260i
\(607\) 6.49937e9 + 3.68597e10i 0.0478758 + 0.271517i 0.999343 0.0362316i \(-0.0115354\pi\)
−0.951468 + 0.307749i \(0.900424\pi\)
\(608\) 2.14892e11 3.78912e10i 1.57255 0.277283i
\(609\) 1.12059e11 8.15853e10i 0.814660 0.593120i
\(610\) 2.77188e9 + 2.32588e9i 0.0200196 + 0.0167984i
\(611\) 7.13266e10 4.11804e10i 0.511784 0.295479i
\(612\) 8.63575e10 1.63195e11i 0.615594 1.16332i
\(613\) 1.05930e11 1.83475e11i 0.750197 1.29938i −0.197530 0.980297i \(-0.563292\pi\)
0.947727 0.319083i \(-0.103375\pi\)
\(614\) −8.54311e9 2.34720e10i −0.0601094 0.165149i
\(615\) 4.16594e9 + 1.03430e9i 0.0291214 + 0.00723012i
\(616\) 5.54431e10 4.65223e10i 0.385057 0.323101i
\(617\) −5.33383e10 + 1.46546e11i −0.368043 + 1.01119i 0.608062 + 0.793889i \(0.291947\pi\)
−0.976105 + 0.217300i \(0.930275\pi\)
\(618\) 1.83291e10 2.72323e10i 0.125657 0.186694i
\(619\) 7.73618e9 4.38741e10i 0.0526944 0.298845i −0.947059 0.321060i \(-0.895961\pi\)
0.999753 + 0.0222154i \(0.00707198\pi\)
\(620\) 7.90678e9i 0.0535098i
\(621\) 5.24081e10 + 3.25318e10i 0.352397 + 0.218747i
\(622\) 4.69245e10 0.313501
\(623\) −1.03552e11 1.82591e10i −0.687397 0.121207i
\(624\) −1.95135e9 + 2.83089e10i −0.0128705 + 0.186718i
\(625\) −1.41846e11 5.16276e10i −0.929599 0.338346i
\(626\) −1.61398e10 1.92347e10i −0.105100 0.125253i
\(627\) −8.80744e10 8.48838e10i −0.569875 0.549231i
\(628\) −1.42826e11 + 5.19844e10i −0.918266 + 0.334221i
\(629\) 2.44125e11 + 1.40946e11i 1.55959 + 0.900429i
\(630\) −5.16844e9 + 1.10930e9i −0.0328093 + 0.00704187i
\(631\) 9.52325e10 + 1.64948e11i 0.600714 + 1.04047i 0.992713 + 0.120502i \(0.0384503\pi\)
−0.391999 + 0.919966i \(0.628216\pi\)
\(632\) −1.27684e10 + 1.52168e10i −0.0800330 + 0.0953796i
\(633\) 1.10623e11 2.49128e11i 0.689017 1.55170i
\(634\) −5.70119e9 3.23330e10i −0.0352865 0.200120i
\(635\) 1.22612e9 2.16198e8i 0.00754114 0.00132971i
\(636\) −5.76896e9 5.43693e10i −0.0352589 0.332296i
\(637\) 2.23111e10 + 1.87213e10i 0.135508 + 0.113704i
\(638\) −3.10655e10 + 1.79357e10i −0.187497 + 0.108252i
\(639\) −2.43747e10 + 1.75967e11i −0.146196 + 1.05542i
\(640\) 4.77898e9 8.27744e9i 0.0284850 0.0493374i
\(641\) −1.00079e10 2.74965e10i −0.0592804 0.162871i 0.906517 0.422169i \(-0.138731\pi\)
−0.965797 + 0.259298i \(0.916509\pi\)
\(642\) −3.83073e10 1.33095e11i −0.225497 0.783470i
\(643\) −8.94608e10 + 7.50665e10i −0.523346 + 0.439139i −0.865796 0.500397i \(-0.833188\pi\)
0.342450 + 0.939536i \(0.388743\pi\)
\(644\) −2.14528e10 + 5.89412e10i −0.124721 + 0.342670i
\(645\) −3.56233e9 7.28552e9i −0.0205824 0.0420941i
\(646\) −3.94819e10 + 2.23913e11i −0.226708 + 1.28573i
\(647\) 2.25850e11i 1.28885i −0.764667 0.644425i \(-0.777097\pi\)
0.764667 0.644425i \(-0.222903\pi\)
\(648\) 4.11186e10 1.45574e11i 0.233205 0.825629i
\(649\) 1.34518e11 0.758234
\(650\) −4.61257e10 8.13321e9i −0.258398 0.0455626i
\(651\) −2.17629e11 + 1.06412e11i −1.21169 + 0.592471i
\(652\) −2.00331e11 7.29146e10i −1.10856 0.403482i
\(653\) 1.81964e11 + 2.16856e11i 1.00077 + 1.19267i 0.981227 + 0.192858i \(0.0617757\pi\)
0.0195398 + 0.999809i \(0.493780\pi\)
\(654\) 1.61189e11 4.63933e10i 0.881100 0.253597i
\(655\) −1.66489e10 + 6.05972e9i −0.0904526 + 0.0329221i
\(656\) −2.77953e10 1.60476e10i −0.150092 0.0866554i
\(657\) 6.35028e10 + 1.56282e11i 0.340825 + 0.838779i
\(658\) −5.73610e10 9.93521e10i −0.305994 0.529997i
\(659\) 3.52316e10 4.19873e10i 0.186806 0.222626i −0.664511 0.747278i \(-0.731360\pi\)
0.851317 + 0.524652i \(0.175805\pi\)
\(660\) −4.38583e9 + 4.65367e8i −0.0231141 + 0.00245256i
\(661\) −1.81789e10 1.03098e11i −0.0952276 0.540063i −0.994677 0.103038i \(-0.967144\pi\)
0.899450 0.437024i \(-0.143968\pi\)
\(662\) 4.28282e10 7.55176e9i 0.222996 0.0393202i
\(663\) −1.64806e11 7.31808e10i −0.852943 0.378742i
\(664\) 1.61490e10 + 1.35506e10i 0.0830753 + 0.0697085i
\(665\) −1.81753e10 + 1.04935e10i −0.0929381 + 0.0536578i
\(666\) 9.51396e10 + 3.07043e10i 0.483576 + 0.156064i
\(667\) 3.59088e10 6.21959e10i 0.181425 0.314238i
\(668\) 9.24093e10 + 2.53892e11i 0.464098 + 1.27510i
\(669\) −2.29787e10 + 2.38424e10i −0.114715 + 0.119027i
\(670\) 2.47951e9 2.08056e9i 0.0123046 0.0103248i
\(671\) −3.16361e10 + 8.69196e10i −0.156061 + 0.428773i
\(672\) 2.40486e11 + 1.65768e10i 1.17927 + 0.0812874i
\(673\) −3.36410e10 + 1.90788e11i −0.163987 + 0.930015i 0.786116 + 0.618079i \(0.212089\pi\)
−0.950103 + 0.311936i \(0.899022\pi\)
\(674\) 1.47059e10i 0.0712609i
\(675\) −1.92018e11 7.69165e10i −0.924966 0.370514i
\(676\) −1.12704e11 −0.539699
\(677\) −3.16004e11 5.57200e10i −1.50431 0.265250i −0.640065 0.768321i \(-0.721092\pi\)
−0.864245 + 0.503071i \(0.832204\pi\)
\(678\) 6.21449e9 + 4.18277e9i 0.0294094 + 0.0197945i
\(679\) −3.36609e10 1.22516e10i −0.158360 0.0576385i
\(680\) 1.21737e10 + 1.45080e10i 0.0569360 + 0.0678536i
\(681\) −5.18612e10 + 2.08886e11i −0.241131 + 0.971227i
\(682\) 5.89114e10 2.14420e10i 0.272309 0.0991123i
\(683\) −3.37083e11 1.94615e11i −1.54901 0.894321i −0.998218 0.0596780i \(-0.980993\pi\)
−0.550792 0.834643i \(-0.685674\pi\)
\(684\) −9.58796e9 2.59791e11i −0.0438028 1.18686i
\(685\) −5.25818e9 9.10743e9i −0.0238821 0.0413650i
\(686\) −5.37061e10 + 6.40044e10i −0.242509 + 0.289010i
\(687\) 2.05094e11 + 2.81700e11i 0.920718 + 1.26462i
\(688\) 1.05298e10 + 5.97175e10i 0.0469966 + 0.266531i
\(689\) −5.25865e10 + 9.27242e9i −0.233344 + 0.0411449i
\(690\) −2.21418e9 + 1.61206e9i −0.00976826 + 0.00711187i
\(691\) 2.64622e11 + 2.22045e11i 1.16069 + 0.973930i 0.999915 0.0130614i \(-0.00415771\pi\)
0.160770 + 0.986992i \(0.448602\pi\)
\(692\) −6.68630e9 + 3.86034e9i −0.0291583 + 0.0168345i
\(693\) −7.18349e10 1.14454e11i −0.311460 0.496248i
\(694\) 4.85352e10 8.40654e10i 0.209227 0.362392i
\(695\) −9.21265e9 2.53116e10i −0.0394862 0.108487i
\(696\) −1.70932e11 4.24380e10i −0.728426 0.180850i
\(697\) 1.56241e11 1.31102e11i 0.662008 0.555491i
\(698\) 4.02028e10 1.10456e11i 0.169369 0.465339i
\(699\) −1.30393e11 + 1.93730e11i −0.546193 + 0.811499i
\(700\) 3.65246e10 2.07141e11i 0.152122 0.862729i
\(701\) 7.99935e9i 0.0331271i −0.999863 0.0165635i \(-0.994727\pi\)
0.999863 0.0165635i \(-0.00527258\pi\)
\(702\) −6.25926e10 1.31100e10i −0.257736 0.0539826i
\(703\) 3.96905e11 1.62505
\(704\) −1.88847e10 3.32989e9i −0.0768812 0.0135562i
\(705\) −1.11061e9 + 1.61121e10i −0.00449579 + 0.0652221i
\(706\) 1.31880e11 + 4.80005e10i 0.530837 + 0.193209i
\(707\) −1.32277e11 1.57641e11i −0.529426 0.630945i
\(708\) 2.05850e11 + 1.98393e11i 0.819253 + 0.789575i
\(709\) −2.58748e11 + 9.41764e10i −1.02398 + 0.372698i −0.798786 0.601616i \(-0.794524\pi\)
−0.225194 + 0.974314i \(0.572302\pi\)
\(710\) −6.83100e9 3.94388e9i −0.0268813 0.0155199i
\(711\) 2.48710e10 + 2.75121e10i 0.0973227 + 0.107658i
\(712\) 6.68018e10 + 1.15704e11i 0.259937 + 0.450224i
\(713\) −8.06798e10 + 9.61504e10i −0.312181 + 0.372043i
\(714\) −1.01935e11 + 2.29562e11i −0.392220 + 0.883297i
\(715\) 7.47982e8 + 4.24201e9i 0.00286198 + 0.0162311i
\(716\) 1.21990e11 2.15102e10i 0.464166 0.0818450i
\(717\) 1.56988e10 + 1.47953e11i 0.0594005 + 0.559818i
\(718\) −1.74114e11 1.46099e11i −0.655144 0.549731i
\(719\) 2.56982e11 1.48369e11i 0.961585 0.555172i 0.0649248 0.997890i \(-0.479319\pi\)
0.896661 + 0.442719i \(0.145986\pi\)
\(720\) −4.39153e9 3.41704e9i −0.0163413 0.0127151i
\(721\) 7.19864e10 1.24684e11i 0.266385 0.461392i
\(722\) 6.42717e10 + 1.76585e11i 0.236522 + 0.649838i
\(723\) 9.51325e10 + 3.30529e11i 0.348157 + 1.20964i
\(724\) 1.28475e11 1.07803e11i 0.467588 0.392353i
\(725\) −8.23692e10 + 2.26308e11i −0.298135 + 0.819119i
\(726\) −4.40145e10 9.00164e10i −0.158434 0.324022i
\(727\) −4.88255e10 + 2.76903e11i −0.174787 + 0.991267i 0.763602 + 0.645687i \(0.223429\pi\)
−0.938389 + 0.345580i \(0.887682\pi\)
\(728\) 1.50228e11i 0.534841i
\(729\) −2.58691e11 1.13337e11i −0.915949 0.401294i
\(730\) −7.49011e9 −0.0263752
\(731\) −3.79490e11 6.69144e10i −1.32902 0.234342i
\(732\) −1.76604e11 + 8.63526e10i −0.615116 + 0.300767i
\(733\) −3.89034e11 1.41597e11i −1.34763 0.490498i −0.435424 0.900225i \(-0.643402\pi\)
−0.912208 + 0.409728i \(0.865624\pi\)
\(734\) −4.14979e10 4.94552e10i −0.142969 0.170384i
\(735\) −5.48839e9 + 1.57966e9i −0.0188060 + 0.00541271i
\(736\) 1.17364e11 4.27169e10i 0.399966 0.145576i
\(737\) 7.16562e10 + 4.13708e10i 0.242876 + 0.140224i
\(738\) 4.44193e10 5.70871e10i 0.149743 0.192448i
\(739\) −7.10244e10 1.23018e11i −0.238139 0.412468i 0.722042 0.691850i \(-0.243204\pi\)
−0.960180 + 0.279382i \(0.909871\pi\)
\(740\) 9.19893e9 1.09629e10i 0.0306768 0.0365592i
\(741\) −2.52479e11 + 2.67898e10i −0.837439 + 0.0888580i
\(742\) 1.29157e10 + 7.32487e10i 0.0426092 + 0.241649i
\(743\) 1.74447e11 3.07596e10i 0.572410 0.100931i 0.120052 0.992768i \(-0.461694\pi\)
0.452358 + 0.891836i \(0.350583\pi\)
\(744\) 2.81319e11 + 1.24917e11i 0.918136 + 0.407690i
\(745\) 2.59358e10 + 2.17627e10i 0.0841926 + 0.0706460i
\(746\) 1.86024e11 1.07401e11i 0.600639 0.346779i
\(747\) 2.91974e10 2.63945e10i 0.0937695 0.0847678i
\(748\) −1.04783e11 + 1.81490e11i −0.334723 + 0.579757i
\(749\) −2.07758e11 5.70810e11i −0.660131 1.81370i
\(750\) 1.27699e10 1.32499e10i 0.0403591 0.0418761i
\(751\) 1.35565e11 1.13753e11i 0.426175 0.357603i −0.404331 0.914613i \(-0.632496\pi\)
0.830506 + 0.557009i \(0.188051\pi\)
\(752\) 4.13021e10 1.13476e11i 0.129152 0.354841i
\(753\) 6.12105e11 + 4.21927e10i 1.90391 + 0.131237i
\(754\) −1.29293e10 + 7.33256e10i −0.0400027 + 0.226866i
\(755\) 1.21073e10i 0.0372615i
\(756\) 5.88743e10 2.81091e11i 0.180235 0.860518i
\(757\) −2.71823e11 −0.827755 −0.413878 0.910333i \(-0.635826\pi\)
−0.413878 + 0.910333i \(0.635826\pi\)
\(758\) −1.78261e11 3.14322e10i −0.539982 0.0952134i
\(759\) −5.80825e10 3.90934e10i −0.175016 0.117797i
\(760\) 2.50579e10 + 9.12035e9i 0.0751088 + 0.0273374i
\(761\) 2.67176e11 + 3.18408e11i 0.796634 + 0.949391i 0.999556 0.0298038i \(-0.00948826\pi\)
−0.202922 + 0.979195i \(0.565044\pi\)
\(762\) 5.05543e9 2.03622e10i 0.0149947 0.0603955i
\(763\) 6.91298e11 2.51612e11i 2.03970 0.742392i
\(764\) −1.13604e11 6.55891e10i −0.333441 0.192512i
\(765\) 2.99497e10 1.87974e10i 0.0874475 0.0548847i
\(766\) −1.93868e10 3.35789e10i −0.0563107 0.0975330i
\(767\) 1.79476e11 2.13891e11i 0.518591 0.618033i
\(768\) −1.26228e11 1.73376e11i −0.362837 0.498362i
\(769\) −5.30732e10 3.00993e11i −0.151765 0.860699i −0.961684 0.274159i \(-0.911601\pi\)
0.809920 0.586540i \(-0.199511\pi\)
\(770\) 5.90878e9 1.04188e9i 0.0168087 0.00296383i
\(771\) −8.90101e9 + 6.48045e9i −0.0251896 + 0.0183395i
\(772\) 4.74544e9 + 3.98190e9i 0.0133600 + 0.0112104i
\(773\) 1.31306e11 7.58097e10i 0.367763 0.212328i −0.304718 0.952443i \(-0.598562\pi\)
0.672481 + 0.740115i \(0.265229\pi\)
\(774\) −1.36568e11 + 5.04023e9i −0.380526 + 0.0140439i
\(775\) 2.10450e11 3.64510e11i 0.583368 1.01042i
\(776\) 1.55669e10 + 4.27696e10i 0.0429294 + 0.117947i
\(777\) 4.25548e11 + 1.05653e11i 1.16752 + 0.289866i
\(778\) −6.14340e10 + 5.15492e10i −0.167683 + 0.140703i
\(779\) 9.82193e10 2.69855e11i 0.266715 0.732793i
\(780\) −5.11167e9 + 7.59459e9i −0.0138097 + 0.0205176i
\(781\) 3.50135e10 1.98571e11i 0.0941090 0.533718i
\(782\) 1.30139e11i 0.348001i
\(783\) −1.22273e11 + 3.05249e11i −0.325301 + 0.812094i
\(784\) 4.27038e10 0.113032
\(785\) −2.86662e10 5.05462e9i −0.0754903 0.0133110i
\(786\) −2.05312e10 + 2.97854e11i −0.0537929 + 0.780394i
\(787\) −1.69477e11 6.16845e10i −0.441786 0.160797i 0.111543 0.993760i \(-0.464421\pi\)
−0.553329 + 0.832963i \(0.686643\pi\)
\(788\) 1.25741e11 + 1.49852e11i 0.326116 + 0.388650i
\(789\) −5.51189e11 5.31222e11i −1.42230 1.37078i
\(790\) −1.54742e9 + 5.63215e8i −0.00397283 + 0.00144599i
\(791\) 2.84533e10 + 1.64275e10i 0.0726820 + 0.0419630i
\(792\) −5.27331e10 + 1.63398e11i −0.134024 + 0.415284i
\(793\) 9.59973e10 + 1.66272e11i 0.242754 + 0.420462i
\(794\) 1.12546e11 1.34127e11i 0.283171 0.337470i
\(795\) 4.24940e9 9.56982e9i 0.0106380 0.0239572i
\(796\) −9.87436e9 5.60003e10i −0.0245956 0.139488i
\(797\) −5.56877e11 + 9.81924e10i −1.38015 + 0.243357i −0.813961 0.580919i \(-0.802693\pi\)
−0.566187 + 0.824277i \(0.691582\pi\)
\(798\) 3.73160e10 + 3.51683e11i 0.0920203 + 0.867241i
\(799\) 5.87859e11 + 4.93272e11i 1.44240 + 1.21032i
\(800\) −3.62711e11 + 2.09412e11i −0.885526 + 0.511259i
\(801\) 2.31096e11 9.39024e10i 0.561387 0.228111i
\(802\) 1.44108e11 2.49602e11i 0.348329 0.603324i
\(803\) −6.54864e10 1.79922e11i −0.157503 0.432736i
\(804\) 4.86385e10 + 1.68990e11i 0.116401 + 0.404424i
\(805\) −9.20204e9 + 7.72143e9i −0.0219129 + 0.0183871i
\(806\) 4.45063e10 1.22280e11i 0.105459 0.289745i
\(807\) 4.21802e9 + 8.62650e9i 0.00994522 + 0.0203395i
\(808\) −4.54041e10 + 2.57500e11i −0.106525 + 0.604131i
\(809\) 5.05250e10i 0.117954i 0.998259 + 0.0589769i \(0.0187838\pi\)
−0.998259 + 0.0589769i \(0.981216\pi\)
\(810\) 8.98607e9 8.74690e9i 0.0208752 0.0203195i
\(811\) 3.28251e11 0.758791 0.379396 0.925235i \(-0.376132\pi\)
0.379396 + 0.925235i \(0.376132\pi\)
\(812\) −3.29291e11 5.80628e10i −0.757452 0.133559i
\(813\) 2.60703e11 1.27473e11i 0.596737 0.291781i
\(814\) −1.06628e11 3.88092e10i −0.242869 0.0883970i
\(815\) −2.62439e10 3.12762e10i −0.0594836 0.0708898i
\(816\) −2.54079e11 + 7.31288e10i −0.573071 + 0.164941i
\(817\) −5.09847e11 + 1.85569e11i −1.14433 + 0.416503i
\(818\) 7.51378e10 + 4.33808e10i 0.167821 + 0.0968913i
\(819\) −2.77831e11 3.84849e10i −0.617511 0.0855371i
\(820\) −5.17724e9 8.96724e9i −0.0114510 0.0198337i
\(821\) −4.35639e11 + 5.19174e11i −0.958857 + 1.14272i 0.0308373 + 0.999524i \(0.490183\pi\)
−0.989694 + 0.143197i \(0.954262\pi\)
\(822\) −1.76225e11 + 1.86987e10i −0.385993 + 0.0409565i
\(823\) 1.04516e11 + 5.92737e11i 0.227815 + 1.29200i 0.857231 + 0.514933i \(0.172183\pi\)
−0.629416 + 0.777069i \(0.716706\pi\)
\(824\) −1.80153e11 + 3.17658e10i −0.390780 + 0.0689051i
\(825\) 2.14578e11 + 9.52813e10i 0.463200 + 0.205680i
\(826\) −2.97933e11 2.49995e11i −0.640027 0.537047i
\(827\) 3.13017e11 1.80720e11i 0.669184 0.386353i −0.126584 0.991956i \(-0.540401\pi\)
0.795767 + 0.605603i \(0.207068\pi\)
\(828\) −3.12256e10 1.45486e11i −0.0664339 0.309527i
\(829\) −1.85216e11 + 3.20803e11i −0.392157 + 0.679235i −0.992734 0.120332i \(-0.961604\pi\)
0.600577 + 0.799567i \(0.294938\pi\)
\(830\) 5.97716e8 + 1.64221e9i 0.00125946 + 0.00346032i
\(831\) 8.31532e10 8.62787e10i 0.174371 0.180925i
\(832\) −3.04909e10 + 2.55849e10i −0.0636322 + 0.0533938i
\(833\) −9.28149e10 + 2.55007e11i −0.192769 + 0.529629i
\(834\) −4.52831e11 3.12139e10i −0.935993 0.0645184i
\(835\) −8.98527e9 + 5.09580e10i −0.0184835 + 0.104825i
\(836\) 2.95071e11i 0.604090i
\(837\) 3.03088e11 4.88269e11i 0.617544 0.994849i
\(838\) −2.28308e11 −0.462962
\(839\) 4.93790e11 + 8.70685e10i 0.996539 + 0.175717i 0.648051 0.761597i \(-0.275584\pi\)
0.348488 + 0.937313i \(0.386695\pi\)
\(840\) 2.44385e10 + 1.64487e10i 0.0490860 + 0.0330381i
\(841\) −1.10319e11 4.01528e10i −0.220529 0.0802660i
\(842\) 2.59482e11 + 3.09238e11i 0.516248 + 0.615241i
\(843\) −1.18729e11 + 4.78216e11i −0.235097 + 0.946922i
\(844\) −6.17892e11 + 2.24894e11i −1.21771 + 0.443209i
\(845\) −1.86925e10 1.07921e10i −0.0366640 0.0211679i
\(846\) 2.40550e11 + 1.27291e11i 0.469595 + 0.248495i
\(847\) −2.19737e11 3.80595e11i −0.426942 0.739486i
\(848\) −5.03256e10 + 5.99758e10i −0.0973209 + 0.115982i
\(849\) −2.21281e11 3.03933e11i −0.425905 0.584988i
\(850\) −7.57810e10 4.29775e11i −0.145173 0.823315i
\(851\) 2.23727e11 3.94491e10i 0.426580 0.0752176i
\(852\) 3.46441e11 2.52229e11i 0.657462 0.478671i
\(853\) −1.25556e11 1.05354e11i −0.237160 0.199001i 0.516460 0.856312i \(-0.327250\pi\)
−0.753620 + 0.657310i \(0.771694\pi\)
\(854\) 2.31604e11 1.33716e11i 0.435425 0.251393i
\(855\) 2.32864e10 4.40057e10i 0.0435750 0.0823463i
\(856\) −3.85910e11 + 6.68415e11i −0.718771 + 1.24495i
\(857\) 2.24707e11 + 6.17377e11i 0.416575 + 1.14453i 0.953630 + 0.300982i \(0.0973145\pi\)
−0.537055 + 0.843547i \(0.680463\pi\)
\(858\) 7.04474e10 + 1.74903e10i 0.129992 + 0.0322737i
\(859\) −2.05655e11 + 1.72565e11i −0.377717 + 0.316943i −0.811806 0.583928i \(-0.801515\pi\)
0.434088 + 0.900870i \(0.357071\pi\)
\(860\) −6.69097e9 + 1.83833e10i −0.0122319 + 0.0336070i
\(861\) 1.77141e11 2.63184e11i 0.322334 0.478903i
\(862\) 4.05330e9 2.29874e10i 0.00734141 0.0416352i
\(863\) 7.75412e11i 1.39794i 0.715150 + 0.698971i \(0.246358\pi\)
−0.715150 + 0.698971i \(0.753642\pi\)
\(864\) −5.04116e11 + 2.69970e11i −0.904640 + 0.484463i
\(865\) −1.47861e9 −0.00264112
\(866\) 5.15738e11 + 9.09385e10i 0.916975 + 0.161687i
\(867\) 7.66840e10 1.11248e12i 0.135715 1.96887i
\(868\) 5.49136e11 + 1.99869e11i 0.967388 + 0.352101i
\(869\) −2.70584e10 3.22469e10i −0.0474485 0.0565469i
\(870\) −1.05127e10 1.01318e10i −0.0183500 0.0176853i
\(871\) 1.61386e11 5.87398e10i 0.280410 0.102061i
\(872\) −8.09506e11 4.67368e11i −1.40008 0.808339i
\(873\) 8.30859e10 1.78327e10i 0.143044 0.0307016i
\(874\) 9.16184e10 + 1.58688e11i 0.157014 + 0.271955i
\(875\) 5.18789e10 6.18268e10i 0.0885031 0.105474i
\(876\) 1.65144e11 3.71912e11i 0.280445 0.631574i
\(877\) 5.75848e10 + 3.26579e11i 0.0973440 + 0.552065i 0.994004 + 0.109345i \(0.0348754\pi\)
−0.896660 + 0.442720i \(0.854014\pi\)
\(878\) 3.94698e11 6.95958e10i 0.664181 0.117113i
\(879\) −9.65113e10 9.09567e11i −0.161667 1.52363i
\(880\) 4.83809e9 + 4.05964e9i 0.00806758 + 0.00676950i
\(881\) 3.43576e11 1.98364e11i 0.570320 0.329275i −0.186957 0.982368i \(-0.559862\pi\)
0.757277 + 0.653094i \(0.226529\pi\)
\(882\) −1.32051e10 + 9.53308e10i −0.0218207 + 0.157528i
\(883\) −2.25631e11 + 3.90804e11i −0.371155 + 0.642860i −0.989744 0.142856i \(-0.954372\pi\)
0.618588 + 0.785715i \(0.287705\pi\)
\(884\) 1.48775e11 + 4.08757e11i 0.243625 + 0.669354i
\(885\) 1.51438e10 + 5.26158e10i 0.0246867 + 0.0857716i
\(886\) 1.82042e11 1.52751e11i 0.295417 0.247885i
\(887\) 1.74390e11 4.79133e11i 0.281726 0.774037i −0.715431 0.698684i \(-0.753769\pi\)
0.997157 0.0753529i \(-0.0240083\pi\)
\(888\) −2.44721e11 5.00492e11i −0.393567 0.804906i
\(889\) 1.59788e10 9.06204e10i 0.0255822 0.145084i
\(890\) 1.10757e10i 0.0176527i
\(891\) 2.88678e11 + 1.39383e11i 0.458039 + 0.221156i
\(892\) 7.98779e10 0.126173
\(893\) 1.06408e12 + 1.87627e11i 1.67328 + 0.295045i
\(894\) 5.12540e11 2.50612e11i 0.802376 0.392330i
\(895\) 2.22924e10 + 8.11377e9i 0.0347428 + 0.0126453i
\(896\) −4.54074e11 5.41145e11i −0.704523 0.839617i
\(897\) −1.39655e11 + 4.01952e10i −0.215718 + 0.0620876i
\(898\) 3.76318e11 1.36969e11i 0.578695 0.210628i
\(899\) −5.79459e11 3.34551e11i −0.887123 0.512181i
\(900\) 1.87838e11 + 4.62274e11i 0.286295 + 0.704578i
\(901\) −2.48766e11 4.30875e11i −0.377478 0.653812i
\(902\) −5.27727e10 + 6.28921e10i −0.0797229 + 0.0950101i
\(903\) −5.96037e11 + 6.32437e10i −0.896443 + 0.0951187i
\(904\) −7.24907e9 4.11115e10i −0.0108545 0.0615587i
\(905\) 3.16310e10 5.57740e9i 0.0471540 0.00831452i
\(906\) 1.86467e11 + 8.27991e10i 0.276751 + 0.122889i
\(907\) −8.86132e11 7.43553e11i −1.30939 1.09871i −0.988440 0.151614i \(-0.951553\pi\)
−0.320952 0.947096i \(-0.604003\pi\)
\(908\) 4.49630e11 2.59594e11i 0.661473 0.381901i
\(909\) 4.64587e11 + 1.49936e11i 0.680475 + 0.219609i
\(910\) 6.22692e9 1.07853e10i 0.00908046 0.0157278i
\(911\) −1.13732e11 3.12476e11i −0.165124 0.453673i 0.829341 0.558742i \(-0.188716\pi\)
−0.994465 + 0.105069i \(0.966494\pi\)
\(912\) −2.58334e11 + 2.68044e11i −0.373424 + 0.387460i
\(913\) −3.42223e10 + 2.87159e10i −0.0492522 + 0.0413275i
\(914\) −2.82053e10 + 7.74933e10i −0.0404153 + 0.111040i
\(915\) −3.75595e10 2.58899e9i −0.0535840 0.00369357i
\(916\) 1.45962e11 8.27792e11i 0.207328 1.17582i
\(917\) 1.30947e12i 1.85190i
\(918\) −8.46827e10 5.89813e11i −0.119241 0.830507i
\(919\) −1.61529e11 −0.226459 −0.113229 0.993569i \(-0.536120\pi\)
−0.113229 + 0.993569i \(0.536120\pi\)
\(920\) 1.50311e10 + 2.65039e9i 0.0209817 + 0.00369964i
\(921\) 2.15604e11 + 1.45116e11i 0.299653 + 0.201686i
\(922\) 1.20094e11 + 4.37107e10i 0.166187 + 0.0604872i
\(923\) −2.69023e11 3.20609e11i −0.370666 0.441742i
\(924\) −7.85456e10 + 3.16365e11i −0.107754 + 0.434011i
\(925\) −7.15872e11 + 2.60556e11i −0.977842 + 0.355905i
\(926\) −1.55820e11 8.99629e10i −0.211924 0.122354i
\(927\) 1.25966e10 + 3.41312e11i 0.0170583 + 0.462203i
\(928\) 3.32899e11 + 5.76599e11i 0.448871 + 0.777467i
\(929\) 4.01736e11 4.78770e11i 0.539359 0.642783i −0.425685 0.904872i \(-0.639967\pi\)
0.965044 + 0.262088i \(0.0844112\pi\)
\(930\) 1.50190e10 + 2.06288e10i 0.0200775 + 0.0275767i
\(931\) 6.63500e10 + 3.76290e11i 0.0883166 + 0.500868i
\(932\) 5.54767e11 9.78203e10i 0.735270 0.129648i
\(933\) −3.94705e11 + 2.87368e11i −0.520890 + 0.379238i
\(934\) −2.18566e11 1.83399e11i −0.287207 0.240996i
\(935\) −3.47576e10 + 2.00673e10i −0.0454782 + 0.0262569i
\(936\) 1.89453e11 + 3.01855e11i 0.246831 + 0.393274i
\(937\) −2.07728e10 + 3.59796e10i −0.0269487 + 0.0466765i −0.879185 0.476480i \(-0.841912\pi\)
0.852237 + 0.523157i \(0.175246\pi\)
\(938\) −8.18197e10 2.24798e11i −0.105693 0.290389i
\(939\) 2.53554e11 + 6.29511e10i 0.326143 + 0.0809731i
\(940\) 2.98443e10 2.50423e10i 0.0382252 0.0320747i
\(941\) −1.12104e11 + 3.08003e11i −0.142976 + 0.392822i −0.990425 0.138055i \(-0.955915\pi\)
0.847449 + 0.530877i \(0.178137\pi\)
\(942\) −2.73889e11 + 4.06926e11i −0.347833 + 0.516788i
\(943\) 2.85428e10 1.61874e11i 0.0360952 0.204706i
\(944\) 4.09391e11i 0.515526i
\(945\) 3.66808e10 4.09827e10i 0.0459951 0.0513894i
\(946\) 1.55114e11 0.193681
\(947\) 1.83765e11 + 3.24028e10i 0.228488 + 0.0402886i 0.286720 0.958014i \(-0.407435\pi\)
−0.0582317 + 0.998303i \(0.518546\pi\)
\(948\) 6.15227e9 8.92533e10i 0.00761732 0.110507i
\(949\) −3.73458e11 1.35928e11i −0.460445 0.167588i
\(950\) −3.94969e11 4.70705e11i −0.484918 0.577902i
\(951\) 2.45965e11 + 2.37054e11i 0.300712 + 0.289819i
\(952\) 1.31533e12 4.78741e11i 1.60135 0.582845i
\(953\) 2.43325e11 + 1.40483e11i 0.294995 + 0.170315i 0.640192 0.768215i \(-0.278855\pi\)
−0.345197 + 0.938530i \(0.612188\pi\)
\(954\) −1.18326e11 1.30892e11i −0.142852 0.158022i
\(955\) −1.25611e10 2.17565e10i −0.0151013 0.0261563i
\(956\) 2.30701e11 2.74938e11i 0.276196 0.329157i
\(957\) 1.51468e11 3.41112e11i 0.180581 0.406677i
\(958\) 1.20396e11 + 6.82800e11i 0.142939 + 0.810647i
\(959\) −7.65439e11 + 1.34968e11i −0.904974 + 0.159571i
\(960\) −8.23547e8 7.76149e9i −0.000969624 0.00913819i
\(961\) 2.42449e11 + 2.03439e11i 0.284268 + 0.238529i
\(962\) −2.03972e11 + 1.17763e11i −0.238161 + 0.137502i
\(963\) 1.13730e12 + 8.84932e11i 1.32243 + 1.02898i
\(964\) 4.14848e11 7.18537e11i 0.480375 0.832034i
\(965\) 4.05762e8 + 1.11482e9i 0.000467910 + 0.00128557i
\(966\) 5.59887e10 + 1.94528e11i 0.0642972 + 0.223395i
\(967\) 3.59916e11 3.02005e11i 0.411619 0.345389i −0.413345 0.910574i \(-0.635640\pi\)
0.824964 + 0.565185i \(0.191195\pi\)
\(968\) −1.90983e11 + 5.24721e11i −0.217517 + 0.597622i
\(969\) −1.03915e12 2.12523e12i −1.17865 2.41052i
\(970\) −6.55198e8 + 3.71582e9i −0.000740092 + 0.00419727i
\(971\) 1.13211e12i 1.27354i 0.771056 + 0.636768i \(0.219729\pi\)
−0.771056 + 0.636768i \(0.780271\pi\)
\(972\) 2.36189e11 + 6.39047e11i 0.264603 + 0.715926i
\(973\) −1.99080e12 −2.22114
\(974\) 1.58307e11 + 2.79138e10i 0.175899 + 0.0310158i
\(975\) 4.37794e11 2.14064e11i 0.484453 0.236878i
\(976\) 2.64529e11 + 9.62808e10i 0.291524 + 0.106106i
\(977\) −1.01318e11 1.20746e11i −0.111201 0.132524i 0.707573 0.706640i \(-0.249790\pi\)
−0.818774 + 0.574117i \(0.805346\pi\)
\(978\) −6.61167e11 + 1.90296e11i −0.722696 + 0.208005i
\(979\) −2.66053e11 + 9.68355e10i −0.289626 + 0.105415i
\(980\) 1.19312e10 + 6.88849e9i 0.0129354 + 0.00746827i
\(981\) −1.07173e12 + 1.37737e12i −1.15720 + 1.48722i
\(982\) 9.15746e10 + 1.58612e11i 0.0984757 + 0.170565i
\(983\) 2.32916e11 2.77578e11i 0.249451 0.297284i −0.626760 0.779213i \(-0.715619\pi\)
0.876210 + 0.481929i \(0.160064\pi\)
\(984\) −4.00843e11 + 4.25322e10i −0.427557 + 0.0453667i
\(985\) 6.50544e9 + 3.68942e10i 0.00691085 + 0.0391934i
\(986\) −6.83210e11 + 1.20468e11i −0.722847 + 0.127457i
\(987\) 1.09093e12 + 4.84417e11i 1.14955 + 0.510447i
\(988\) 4.69178e11 + 3.93687e11i 0.492391 + 0.413165i
\(989\) −2.68946e11 + 1.55276e11i −0.281113 + 0.162300i
\(990\) −1.05587e10 + 9.54506e9i −0.0109918 + 0.00993661i
\(991\) 2.02286e11 3.50370e11i 0.209735 0.363272i −0.741896 0.670515i \(-0.766073\pi\)
0.951631 + 0.307243i \(0.0994064\pi\)
\(992\) −3.97980e11 1.09344e12i −0.410974 1.12914i
\(993\) −3.14001e11 + 3.25803e11i −0.322949 + 0.335088i
\(994\) −4.46582e11 + 3.74727e11i −0.457463 + 0.383857i
\(995\) 3.72467e9 1.02334e10i 0.00380010 0.0104407i
\(996\) −9.47207e10 6.52914e9i −0.0962515 0.00663466i
\(997\) 2.68798e11 1.52443e12i 0.272048 1.54286i −0.476137 0.879371i \(-0.657963\pi\)
0.748185 0.663490i \(-0.230926\pi\)
\(998\) 1.97145e11i 0.198730i
\(999\) −9.88300e11 + 3.24371e11i −0.992263 + 0.325672i
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.2.10 138
3.2 odd 2 81.9.f.a.8.14 138
27.13 even 9 81.9.f.a.71.14 138
27.14 odd 18 inner 27.9.f.a.14.10 yes 138
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.9.f.a.2.10 138 1.1 even 1 trivial
27.9.f.a.14.10 yes 138 27.14 odd 18 inner
81.9.f.a.8.14 138 3.2 odd 2
81.9.f.a.71.14 138 27.13 even 9