Properties

Label 162.11.d.d.107.2
Level $162$
Weight $11$
Character 162.107
Analytic conductor $102.928$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [162,11,Mod(53,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 11, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.53");
 
S:= CuspForms(chi, 11);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 162.d (of order \(6\), degree \(2\), not 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: \(102.927874933\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.17318914560000.97
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 4x^{7} - 82x^{6} + 260x^{5} + 2477x^{4} - 5392x^{3} - 31616x^{2} + 34356x + 161859 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 2^{24}\cdot 3^{16} \)
Twist minimal: no (minimal twist has level 6)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 107.2
Root \(3.88503 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 162.107
Dual form 162.11.d.d.53.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-19.5959 - 11.3137i) q^{2} +(256.000 + 443.405i) q^{4} +(4172.87 - 2409.21i) q^{5} +(-335.265 + 580.696i) q^{7} -11585.2i q^{8} +O(q^{10})\) \(q+(-19.5959 - 11.3137i) q^{2} +(256.000 + 443.405i) q^{4} +(4172.87 - 2409.21i) q^{5} +(-335.265 + 580.696i) q^{7} -11585.2i q^{8} -109028. q^{10} +(202016. + 116634. i) q^{11} +(-153890. - 266546. i) q^{13} +(13139.6 - 7586.18i) q^{14} +(-131072. + 227023. i) q^{16} -672324. i q^{17} -1.55119e6 q^{19} +(2.13651e6 + 1.23351e6i) q^{20} +(-2.63913e6 - 4.57111e6i) q^{22} +(-4.82854e6 + 2.78776e6i) q^{23} +(6.72574e6 - 1.16493e7i) q^{25} +6.96428e6i q^{26} -343311. q^{28} +(-2.57481e7 - 1.48657e7i) q^{29} +(-1.54684e7 - 2.67921e7i) q^{31} +(5.13695e6 - 2.96582e6i) q^{32} +(-7.60648e6 + 1.31748e7i) q^{34} +3.23089e6i q^{35} -8.56690e7 q^{37} +(3.03970e7 + 1.75497e7i) q^{38} +(-2.79112e7 - 4.83437e7i) q^{40} +(-3.10950e7 + 1.79527e7i) q^{41} +(1.83126e7 - 3.17184e7i) q^{43} +1.19433e8i q^{44} +1.26159e8 q^{46} +(2.84816e7 + 1.64438e7i) q^{47} +(1.41013e8 + 2.44241e8i) q^{49} +(-2.63594e8 + 1.52186e8i) q^{50} +(7.87918e7 - 1.36471e8i) q^{52} -4.59194e8i q^{53} +1.12398e9 q^{55} +(6.72750e6 + 3.88412e6i) q^{56} +(3.36372e8 + 5.82613e8i) q^{58} +(4.23189e8 - 2.44328e8i) q^{59} +(3.06464e7 - 5.30811e7i) q^{61} +7.00020e8i q^{62} -1.34218e8 q^{64} +(-1.28433e9 - 7.41507e8i) q^{65} +(3.35388e8 + 5.80909e8i) q^{67} +(2.98112e8 - 1.72115e8i) q^{68} +(3.65533e7 - 6.33122e7i) q^{70} -1.23330e9i q^{71} +1.08126e9 q^{73} +(1.67876e9 + 9.69234e8i) q^{74} +(-3.97104e8 - 6.87805e8i) q^{76} +(-1.35458e8 + 7.82067e7i) q^{77} +(9.33141e8 - 1.61625e9i) q^{79} +1.26312e9i q^{80} +8.12446e8 q^{82} +(-9.48838e8 - 5.47812e8i) q^{83} +(-1.61977e9 - 2.80552e9i) q^{85} +(-7.17706e8 + 4.14368e8i) q^{86} +(1.35123e9 - 2.34041e9i) q^{88} -5.19876e9i q^{89} +2.06376e8 q^{91} +(-2.47221e9 - 1.42733e9i) q^{92} +(-3.72082e8 - 6.44464e8i) q^{94} +(-6.47291e9 + 3.73714e9i) q^{95} +(5.37353e9 - 9.30722e9i) q^{97} -6.38151e9i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2048 q^{4} + 45112 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2048 q^{4} + 45112 q^{7} - 107520 q^{10} - 275240 q^{13} - 1048576 q^{16} - 3137456 q^{19} - 7730688 q^{22} + 33732380 q^{25} + 46194688 q^{28} + 21785848 q^{31} - 151087104 q^{34} - 142028336 q^{37} - 27525120 q^{40} + 470688664 q^{43} + 377628672 q^{46} + 50058420 q^{49} + 140922880 q^{52} + 5402718720 q^{55} + 1564177920 q^{58} + 1184038744 q^{61} - 1073741824 q^{64} + 297365848 q^{67} + 3962250240 q^{70} + 13068538000 q^{73} - 803188736 q^{76} - 199282568 q^{79} + 16757336064 q^{82} + 12880512000 q^{85} + 3958112256 q^{88} + 16634464160 q^{91} - 8505477120 q^{94} + 39176355064 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −19.5959 11.3137i −0.612372 0.353553i
\(3\) 0 0
\(4\) 256.000 + 443.405i 0.250000 + 0.433013i
\(5\) 4172.87 2409.21i 1.33532 0.770946i 0.349209 0.937045i \(-0.386450\pi\)
0.986109 + 0.166099i \(0.0531171\pi\)
\(6\) 0 0
\(7\) −335.265 + 580.696i −0.0199479 + 0.0345508i −0.875827 0.482625i \(-0.839683\pi\)
0.855879 + 0.517176i \(0.173017\pi\)
\(8\) 11585.2i 0.353553i
\(9\) 0 0
\(10\) −109028. −1.09028
\(11\) 202016. + 116634.i 1.25436 + 0.724206i 0.971973 0.235093i \(-0.0755396\pi\)
0.282390 + 0.959300i \(0.408873\pi\)
\(12\) 0 0
\(13\) −153890. 266546.i −0.414471 0.717885i 0.580901 0.813974i \(-0.302700\pi\)
−0.995373 + 0.0960885i \(0.969367\pi\)
\(14\) 13139.6 7586.18i 0.0244311 0.0141053i
\(15\) 0 0
\(16\) −131072. + 227023.i −0.125000 + 0.216506i
\(17\) 672324.i 0.473515i −0.971569 0.236758i \(-0.923915\pi\)
0.971569 0.236758i \(-0.0760847\pi\)
\(18\) 0 0
\(19\) −1.55119e6 −0.626465 −0.313233 0.949676i \(-0.601412\pi\)
−0.313233 + 0.949676i \(0.601412\pi\)
\(20\) 2.13651e6 + 1.23351e6i 0.667659 + 0.385473i
\(21\) 0 0
\(22\) −2.63913e6 4.57111e6i −0.512091 0.886968i
\(23\) −4.82854e6 + 2.78776e6i −0.750199 + 0.433127i −0.825766 0.564013i \(-0.809257\pi\)
0.0755670 + 0.997141i \(0.475923\pi\)
\(24\) 0 0
\(25\) 6.72574e6 1.16493e7i 0.688716 1.19289i
\(26\) 6.96428e6i 0.586151i
\(27\) 0 0
\(28\) −343311. −0.0199479
\(29\) −2.57481e7 1.48657e7i −1.25532 0.724760i −0.283160 0.959073i \(-0.591383\pi\)
−0.972161 + 0.234313i \(0.924716\pi\)
\(30\) 0 0
\(31\) −1.54684e7 2.67921e7i −0.540303 0.935832i −0.998886 0.0471804i \(-0.984976\pi\)
0.458584 0.888651i \(-0.348357\pi\)
\(32\) 5.13695e6 2.96582e6i 0.153093 0.0883883i
\(33\) 0 0
\(34\) −7.60648e6 + 1.31748e7i −0.167413 + 0.289968i
\(35\) 3.23089e6i 0.0615151i
\(36\) 0 0
\(37\) −8.56690e7 −1.23542 −0.617711 0.786406i \(-0.711940\pi\)
−0.617711 + 0.786406i \(0.711940\pi\)
\(38\) 3.03970e7 + 1.75497e7i 0.383630 + 0.221489i
\(39\) 0 0
\(40\) −2.79112e7 4.83437e7i −0.272571 0.472106i
\(41\) −3.10950e7 + 1.79527e7i −0.268393 + 0.154957i −0.628157 0.778087i \(-0.716190\pi\)
0.359764 + 0.933043i \(0.382857\pi\)
\(42\) 0 0
\(43\) 1.83126e7 3.17184e7i 0.124569 0.215759i −0.796996 0.603985i \(-0.793579\pi\)
0.921564 + 0.388226i \(0.126912\pi\)
\(44\) 1.19433e8i 0.724206i
\(45\) 0 0
\(46\) 1.26159e8 0.612535
\(47\) 2.84816e7 + 1.64438e7i 0.124187 + 0.0716992i 0.560806 0.827947i \(-0.310491\pi\)
−0.436620 + 0.899646i \(0.643825\pi\)
\(48\) 0 0
\(49\) 1.41013e8 + 2.44241e8i 0.499204 + 0.864647i
\(50\) −2.63594e8 + 1.52186e8i −0.843501 + 0.486996i
\(51\) 0 0
\(52\) 7.87918e7 1.36471e8i 0.207236 0.358943i
\(53\) 4.59194e8i 1.09804i −0.835810 0.549019i \(-0.815002\pi\)
0.835810 0.549019i \(-0.184998\pi\)
\(54\) 0 0
\(55\) 1.12398e9 2.23330
\(56\) 6.72750e6 + 3.88412e6i 0.0122156 + 0.00705266i
\(57\) 0 0
\(58\) 3.36372e8 + 5.82613e8i 0.512483 + 0.887646i
\(59\) 4.23189e8 2.44328e8i 0.591936 0.341754i −0.173927 0.984759i \(-0.555646\pi\)
0.765863 + 0.643004i \(0.222312\pi\)
\(60\) 0 0
\(61\) 3.06464e7 5.30811e7i 0.0362852 0.0628479i −0.847312 0.531095i \(-0.821781\pi\)
0.883598 + 0.468247i \(0.155114\pi\)
\(62\) 7.00020e8i 0.764103i
\(63\) 0 0
\(64\) −1.34218e8 −0.125000
\(65\) −1.28433e9 7.41507e8i −1.10690 0.639070i
\(66\) 0 0
\(67\) 3.35388e8 + 5.80909e8i 0.248413 + 0.430263i 0.963086 0.269196i \(-0.0867578\pi\)
−0.714673 + 0.699459i \(0.753424\pi\)
\(68\) 2.98112e8 1.72115e8i 0.205038 0.118379i
\(69\) 0 0
\(70\) 3.65533e7 6.33122e7i 0.0217489 0.0376702i
\(71\) 1.23330e9i 0.683561i −0.939780 0.341781i \(-0.888970\pi\)
0.939780 0.341781i \(-0.111030\pi\)
\(72\) 0 0
\(73\) 1.08126e9 0.521573 0.260787 0.965396i \(-0.416018\pi\)
0.260787 + 0.965396i \(0.416018\pi\)
\(74\) 1.67876e9 + 9.69234e8i 0.756538 + 0.436787i
\(75\) 0 0
\(76\) −3.97104e8 6.87805e8i −0.156616 0.271267i
\(77\) −1.35458e8 + 7.82067e7i −0.0500439 + 0.0288928i
\(78\) 0 0
\(79\) 9.33141e8 1.61625e9i 0.303258 0.525258i −0.673614 0.739083i \(-0.735259\pi\)
0.976872 + 0.213826i \(0.0685924\pi\)
\(80\) 1.26312e9i 0.385473i
\(81\) 0 0
\(82\) 8.12446e8 0.219142
\(83\) −9.48838e8 5.47812e8i −0.240880 0.139072i 0.374701 0.927146i \(-0.377745\pi\)
−0.615581 + 0.788073i \(0.711079\pi\)
\(84\) 0 0
\(85\) −1.61977e9 2.80552e9i −0.365055 0.632293i
\(86\) −7.17706e8 + 4.14368e8i −0.152565 + 0.0880833i
\(87\) 0 0
\(88\) 1.35123e9 2.34041e9i 0.256046 0.443484i
\(89\) 5.19876e9i 0.931000i −0.885048 0.465500i \(-0.845874\pi\)
0.885048 0.465500i \(-0.154126\pi\)
\(90\) 0 0
\(91\) 2.06376e8 0.0330714
\(92\) −2.47221e9 1.42733e9i −0.375099 0.216564i
\(93\) 0 0
\(94\) −3.72082e8 6.44464e8i −0.0506990 0.0878132i
\(95\) −6.47291e9 + 3.73714e9i −0.836530 + 0.482971i
\(96\) 0 0
\(97\) 5.37353e9 9.30722e9i 0.625750 1.08383i −0.362645 0.931927i \(-0.618126\pi\)
0.988395 0.151904i \(-0.0485403\pi\)
\(98\) 6.38151e9i 0.705981i
\(99\) 0 0
\(100\) 6.88716e9 0.688716
\(101\) −9.36643e9 5.40771e9i −0.891183 0.514525i −0.0168540 0.999858i \(-0.505365\pi\)
−0.874329 + 0.485333i \(0.838698\pi\)
\(102\) 0 0
\(103\) 1.41723e9 + 2.45471e9i 0.122251 + 0.211746i 0.920655 0.390377i \(-0.127655\pi\)
−0.798404 + 0.602122i \(0.794322\pi\)
\(104\) −3.08800e9 + 1.78286e9i −0.253811 + 0.146538i
\(105\) 0 0
\(106\) −5.19519e9 + 8.99834e9i −0.388215 + 0.672408i
\(107\) 2.41202e10i 1.71974i 0.510515 + 0.859869i \(0.329455\pi\)
−0.510515 + 0.859869i \(0.670545\pi\)
\(108\) 0 0
\(109\) −5.43424e9 −0.353188 −0.176594 0.984284i \(-0.556508\pi\)
−0.176594 + 0.984284i \(0.556508\pi\)
\(110\) −2.20255e10 1.27164e10i −1.36761 0.789590i
\(111\) 0 0
\(112\) −8.78877e7 1.52226e8i −0.00498698 0.00863771i
\(113\) −1.20642e10 + 6.96526e9i −0.654795 + 0.378046i −0.790291 0.612732i \(-0.790071\pi\)
0.135496 + 0.990778i \(0.456737\pi\)
\(114\) 0 0
\(115\) −1.34326e10 + 2.32659e10i −0.667836 + 1.15673i
\(116\) 1.52224e10i 0.724760i
\(117\) 0 0
\(118\) −1.10570e10 −0.483313
\(119\) 3.90416e8 + 2.25407e8i 0.0163603 + 0.00944565i
\(120\) 0 0
\(121\) 1.42383e10 + 2.46615e10i 0.548950 + 0.950809i
\(122\) −1.20109e9 + 6.93449e8i −0.0444402 + 0.0256575i
\(123\) 0 0
\(124\) 7.91982e9 1.37175e10i 0.270151 0.467916i
\(125\) 1.77600e10i 0.581958i
\(126\) 0 0
\(127\) 4.08412e10 1.23617 0.618087 0.786110i \(-0.287908\pi\)
0.618087 + 0.786110i \(0.287908\pi\)
\(128\) 2.63012e9 + 1.51850e9i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 1.67784e10 + 2.90610e10i 0.451891 + 0.782698i
\(131\) −3.59831e10 + 2.07749e10i −0.932701 + 0.538495i −0.887665 0.460490i \(-0.847674\pi\)
−0.0450365 + 0.998985i \(0.514340\pi\)
\(132\) 0 0
\(133\) 5.20059e8 9.00769e8i 0.0124967 0.0216449i
\(134\) 1.51779e10i 0.351308i
\(135\) 0 0
\(136\) −7.78903e9 −0.167413
\(137\) −8.01534e10 4.62766e10i −1.66081 0.958867i −0.972331 0.233609i \(-0.924946\pi\)
−0.688477 0.725259i \(-0.741720\pi\)
\(138\) 0 0
\(139\) −3.97788e10 6.88989e10i −0.766615 1.32782i −0.939388 0.342855i \(-0.888606\pi\)
0.172773 0.984962i \(-0.444727\pi\)
\(140\) −1.43259e9 + 8.27107e8i −0.0266368 + 0.0153788i
\(141\) 0 0
\(142\) −1.39532e10 + 2.41677e10i −0.241675 + 0.418594i
\(143\) 7.17955e10i 1.20065i
\(144\) 0 0
\(145\) −1.43258e11 −2.23500
\(146\) −2.11883e10 1.22330e10i −0.319397 0.184404i
\(147\) 0 0
\(148\) −2.19313e10 3.79861e10i −0.308855 0.534953i
\(149\) −6.99579e10 + 4.03902e10i −0.952589 + 0.549977i −0.893884 0.448298i \(-0.852030\pi\)
−0.0587047 + 0.998275i \(0.518697\pi\)
\(150\) 0 0
\(151\) −1.54327e10 + 2.67302e10i −0.196588 + 0.340501i −0.947420 0.319993i \(-0.896320\pi\)
0.750832 + 0.660493i \(0.229653\pi\)
\(152\) 1.79709e10i 0.221489i
\(153\) 0 0
\(154\) 3.53923e9 0.0408606
\(155\) −1.29095e11 7.45332e10i −1.44295 0.833088i
\(156\) 0 0
\(157\) −4.85661e10 8.41190e10i −0.509138 0.881852i −0.999944 0.0105835i \(-0.996631\pi\)
0.490806 0.871269i \(-0.336702\pi\)
\(158\) −3.65715e10 + 2.11146e10i −0.371413 + 0.214435i
\(159\) 0 0
\(160\) 1.42905e10 2.47520e10i 0.136285 0.236053i
\(161\) 3.73855e9i 0.0345600i
\(162\) 0 0
\(163\) −1.39440e11 −1.21185 −0.605927 0.795520i \(-0.707198\pi\)
−0.605927 + 0.795520i \(0.707198\pi\)
\(164\) −1.59206e10 9.19178e9i −0.134196 0.0774784i
\(165\) 0 0
\(166\) 1.23956e10 + 2.14698e10i 0.0983390 + 0.170328i
\(167\) 1.08981e11 6.29200e10i 0.839009 0.484402i −0.0179180 0.999839i \(-0.505704\pi\)
0.856927 + 0.515437i \(0.172370\pi\)
\(168\) 0 0
\(169\) 2.15648e10 3.73513e10i 0.156427 0.270940i
\(170\) 7.33023e10i 0.516265i
\(171\) 0 0
\(172\) 1.87521e10 0.124569
\(173\) −1.09342e11 6.31284e10i −0.705594 0.407375i 0.103833 0.994595i \(-0.466889\pi\)
−0.809428 + 0.587220i \(0.800222\pi\)
\(174\) 0 0
\(175\) 4.50981e9 + 7.81121e9i 0.0274769 + 0.0475914i
\(176\) −5.29574e10 + 3.05749e10i −0.313591 + 0.181052i
\(177\) 0 0
\(178\) −5.88173e10 + 1.01875e11i −0.329158 + 0.570119i
\(179\) 2.96543e11i 1.61370i −0.590758 0.806848i \(-0.701171\pi\)
0.590758 0.806848i \(-0.298829\pi\)
\(180\) 0 0
\(181\) 2.48451e11 1.27893 0.639466 0.768819i \(-0.279155\pi\)
0.639466 + 0.768819i \(0.279155\pi\)
\(182\) −4.04413e9 2.33488e9i −0.0202520 0.0116925i
\(183\) 0 0
\(184\) 3.22968e10 + 5.59397e10i 0.153134 + 0.265235i
\(185\) −3.57485e11 + 2.06394e11i −1.64968 + 0.952443i
\(186\) 0 0
\(187\) 7.84159e10 1.35820e11i 0.342923 0.593960i
\(188\) 1.68385e10i 0.0716992i
\(189\) 0 0
\(190\) 1.69123e11 0.683024
\(191\) −1.36876e11 7.90252e10i −0.538468 0.310884i 0.205990 0.978554i \(-0.433959\pi\)
−0.744458 + 0.667670i \(0.767292\pi\)
\(192\) 0 0
\(193\) 1.89185e11 + 3.27677e11i 0.706479 + 1.22366i 0.966155 + 0.257962i \(0.0830508\pi\)
−0.259676 + 0.965696i \(0.583616\pi\)
\(194\) −2.10598e11 + 1.21589e11i −0.766384 + 0.442472i
\(195\) 0 0
\(196\) −7.21986e10 + 1.25052e11i −0.249602 + 0.432323i
\(197\) 1.89406e11i 0.638356i 0.947695 + 0.319178i \(0.103407\pi\)
−0.947695 + 0.319178i \(0.896593\pi\)
\(198\) 0 0
\(199\) 5.02942e10 0.161158 0.0805791 0.996748i \(-0.474323\pi\)
0.0805791 + 0.996748i \(0.474323\pi\)
\(200\) −1.34960e11 7.79193e10i −0.421750 0.243498i
\(201\) 0 0
\(202\) 1.22362e11 + 2.11938e11i 0.363824 + 0.630162i
\(203\) 1.72649e10 9.96787e9i 0.0500821 0.0289149i
\(204\) 0 0
\(205\) −8.65035e10 + 1.49828e11i −0.238927 + 0.413833i
\(206\) 6.41365e10i 0.172890i
\(207\) 0 0
\(208\) 8.06828e10 0.207236
\(209\) −3.13366e11 1.80922e11i −0.785814 0.453690i
\(210\) 0 0
\(211\) −2.37485e11 4.11336e11i −0.567837 0.983522i −0.996780 0.0801907i \(-0.974447\pi\)
0.428943 0.903332i \(-0.358886\pi\)
\(212\) 2.03609e11 1.17554e11i 0.475464 0.274509i
\(213\) 0 0
\(214\) 2.72889e11 4.72658e11i 0.608019 1.05312i
\(215\) 1.76476e11i 0.384143i
\(216\) 0 0
\(217\) 2.07440e10 0.0431117
\(218\) 1.06489e11 + 6.14814e10i 0.216283 + 0.124871i
\(219\) 0 0
\(220\) 2.87740e11 + 4.98380e11i 0.558324 + 0.967046i
\(221\) −1.79205e11 + 1.03464e11i −0.339930 + 0.196258i
\(222\) 0 0
\(223\) 1.17790e11 2.04018e11i 0.213592 0.369951i −0.739244 0.673437i \(-0.764817\pi\)
0.952836 + 0.303486i \(0.0981505\pi\)
\(224\) 3.97734e9i 0.00705266i
\(225\) 0 0
\(226\) 3.15211e11 0.534638
\(227\) 3.69815e11 + 2.13513e11i 0.613557 + 0.354238i 0.774356 0.632750i \(-0.218074\pi\)
−0.160799 + 0.986987i \(0.551407\pi\)
\(228\) 0 0
\(229\) −5.18356e11 8.97819e11i −0.823096 1.42564i −0.903366 0.428871i \(-0.858911\pi\)
0.0802696 0.996773i \(-0.474422\pi\)
\(230\) 5.26447e11 3.03944e11i 0.817928 0.472231i
\(231\) 0 0
\(232\) −1.72222e11 + 2.98298e11i −0.256241 + 0.443823i
\(233\) 1.03766e12i 1.51103i 0.655130 + 0.755516i \(0.272614\pi\)
−0.655130 + 0.755516i \(0.727386\pi\)
\(234\) 0 0
\(235\) 1.58466e11 0.221105
\(236\) 2.16673e11 + 1.25096e11i 0.295968 + 0.170877i
\(237\) 0 0
\(238\) −5.10037e9 8.83410e9i −0.00667908 0.0115685i
\(239\) 1.07116e12 6.18437e11i 1.37362 0.793060i 0.382238 0.924064i \(-0.375153\pi\)
0.991382 + 0.131004i \(0.0418202\pi\)
\(240\) 0 0
\(241\) 5.19560e11 8.99904e11i 0.639072 1.10691i −0.346564 0.938026i \(-0.612652\pi\)
0.985637 0.168880i \(-0.0540149\pi\)
\(242\) 6.44354e11i 0.776333i
\(243\) 0 0
\(244\) 3.13819e10 0.0362852
\(245\) 1.17686e12 + 6.79458e11i 1.33319 + 0.769719i
\(246\) 0 0
\(247\) 2.38713e11 + 4.13463e11i 0.259652 + 0.449730i
\(248\) −3.10392e11 + 1.79205e11i −0.330866 + 0.191026i
\(249\) 0 0
\(250\) −2.00931e11 + 3.48023e11i −0.205753 + 0.356375i
\(251\) 5.66781e11i 0.568914i −0.958689 0.284457i \(-0.908187\pi\)
0.958689 0.284457i \(-0.0918133\pi\)
\(252\) 0 0
\(253\) −1.30059e12 −1.25469
\(254\) −8.00320e11 4.62065e11i −0.756999 0.437053i
\(255\) 0 0
\(256\) −3.43597e10 5.95128e10i −0.0312500 0.0541266i
\(257\) −1.10802e12 + 6.39713e11i −0.988281 + 0.570584i −0.904760 0.425922i \(-0.859950\pi\)
−0.0835208 + 0.996506i \(0.526617\pi\)
\(258\) 0 0
\(259\) 2.87218e10 4.97476e10i 0.0246441 0.0426848i
\(260\) 7.59303e11i 0.639070i
\(261\) 0 0
\(262\) 9.40164e11 0.761548
\(263\) 1.45997e12 + 8.42915e11i 1.16029 + 0.669892i 0.951373 0.308042i \(-0.0996737\pi\)
0.208914 + 0.977934i \(0.433007\pi\)
\(264\) 0 0
\(265\) −1.10629e12 1.91616e12i −0.846528 1.46623i
\(266\) −2.03821e10 + 1.17676e10i −0.0153052 + 0.00883649i
\(267\) 0 0
\(268\) −1.71719e11 + 2.97426e11i −0.124206 + 0.215132i
\(269\) 1.34023e12i 0.951523i 0.879574 + 0.475761i \(0.157827\pi\)
−0.879574 + 0.475761i \(0.842173\pi\)
\(270\) 0 0
\(271\) −1.75349e12 −1.19966 −0.599829 0.800129i \(-0.704765\pi\)
−0.599829 + 0.800129i \(0.704765\pi\)
\(272\) 1.52633e11 + 8.81228e10i 0.102519 + 0.0591894i
\(273\) 0 0
\(274\) 1.04712e12 + 1.81366e12i 0.678022 + 1.17437i
\(275\) 2.71742e12 1.56890e12i 1.72780 0.997545i
\(276\) 0 0
\(277\) −8.47898e11 + 1.46860e12i −0.519930 + 0.900545i 0.479802 + 0.877377i \(0.340709\pi\)
−0.999732 + 0.0231681i \(0.992625\pi\)
\(278\) 1.80018e12i 1.08416i
\(279\) 0 0
\(280\) 3.74306e10 0.0217489
\(281\) 2.11462e11 + 1.22088e11i 0.120698 + 0.0696851i 0.559134 0.829078i \(-0.311134\pi\)
−0.438435 + 0.898763i \(0.644467\pi\)
\(282\) 0 0
\(283\) 4.98205e11 + 8.62916e11i 0.274458 + 0.475375i 0.969998 0.243112i \(-0.0781683\pi\)
−0.695540 + 0.718487i \(0.744835\pi\)
\(284\) 5.46852e11 3.15725e11i 0.295991 0.170890i
\(285\) 0 0
\(286\) −8.12273e11 + 1.40690e12i −0.424494 + 0.735246i
\(287\) 2.40756e10i 0.0123643i
\(288\) 0 0
\(289\) 1.56397e12 0.775783
\(290\) 2.80727e12 + 1.62078e12i 1.36865 + 0.790193i
\(291\) 0 0
\(292\) 2.76802e11 + 4.79435e11i 0.130393 + 0.225848i
\(293\) 1.36461e12 7.87855e11i 0.631930 0.364845i −0.149569 0.988751i \(-0.547789\pi\)
0.781499 + 0.623906i \(0.214455\pi\)
\(294\) 0 0
\(295\) 1.17728e12 2.03910e12i 0.526948 0.912701i
\(296\) 9.92496e11i 0.436787i
\(297\) 0 0
\(298\) 1.82785e12 0.777786
\(299\) 1.48613e12 + 8.58017e11i 0.621872 + 0.359038i
\(300\) 0 0
\(301\) 1.22792e10 + 2.12681e10i 0.00496977 + 0.00860790i
\(302\) 6.04836e11 3.49202e11i 0.240770 0.139009i
\(303\) 0 0
\(304\) 2.03317e11 3.52156e11i 0.0783081 0.135634i
\(305\) 2.95334e11i 0.111896i
\(306\) 0 0
\(307\) −3.29823e12 −1.20945 −0.604726 0.796434i \(-0.706717\pi\)
−0.604726 + 0.796434i \(0.706717\pi\)
\(308\) −6.93545e10 4.00418e10i −0.0250219 0.0144464i
\(309\) 0 0
\(310\) 1.68649e12 + 2.92109e12i 0.589082 + 1.02032i
\(311\) −1.44887e12 + 8.36504e11i −0.497997 + 0.287519i −0.727886 0.685698i \(-0.759497\pi\)
0.229889 + 0.973217i \(0.426164\pi\)
\(312\) 0 0
\(313\) −8.66592e11 + 1.50098e12i −0.288465 + 0.499636i −0.973444 0.228927i \(-0.926478\pi\)
0.684979 + 0.728563i \(0.259812\pi\)
\(314\) 2.19785e12i 0.720029i
\(315\) 0 0
\(316\) 9.55536e11 0.303258
\(317\) −1.15268e12 6.65501e11i −0.360092 0.207899i 0.309029 0.951053i \(-0.399996\pi\)
−0.669121 + 0.743154i \(0.733329\pi\)
\(318\) 0 0
\(319\) −3.46769e12 6.00621e12i −1.04975 1.81822i
\(320\) −5.60073e11 + 3.23358e11i −0.166915 + 0.0963683i
\(321\) 0 0
\(322\) −4.22968e10 + 7.32603e10i −0.0122188 + 0.0211636i
\(323\) 1.04290e12i 0.296641i
\(324\) 0 0
\(325\) −4.14010e12 −1.14181
\(326\) 2.73246e12 + 1.57759e12i 0.742107 + 0.428455i
\(327\) 0 0
\(328\) 2.07986e11 + 3.60243e11i 0.0547855 + 0.0948912i
\(329\) −1.90977e10 + 1.10261e10i −0.00495453 + 0.00286050i
\(330\) 0 0
\(331\) −2.35980e12 + 4.08730e12i −0.593931 + 1.02872i 0.399766 + 0.916617i \(0.369092\pi\)
−0.993697 + 0.112102i \(0.964242\pi\)
\(332\) 5.60959e11i 0.139072i
\(333\) 0 0
\(334\) −2.84743e12 −0.685048
\(335\) 2.79906e12 + 1.61604e12i 0.663420 + 0.383025i
\(336\) 0 0
\(337\) −2.07642e12 3.59646e12i −0.477711 0.827419i 0.521963 0.852968i \(-0.325200\pi\)
−0.999674 + 0.0255489i \(0.991867\pi\)
\(338\) −8.45164e11 + 4.87956e11i −0.191583 + 0.110611i
\(339\) 0 0
\(340\) 8.29321e11 1.43643e12i 0.182527 0.316147i
\(341\) 7.21658e12i 1.56516i
\(342\) 0 0
\(343\) −3.78515e11 −0.0797282
\(344\) −3.67466e11 2.12156e11i −0.0762824 0.0440417i
\(345\) 0 0
\(346\) 1.42843e12 + 2.47412e12i 0.288058 + 0.498931i
\(347\) 3.80998e12 2.19969e12i 0.757313 0.437235i −0.0710170 0.997475i \(-0.522624\pi\)
0.828330 + 0.560240i \(0.189291\pi\)
\(348\) 0 0
\(349\) 4.62001e12 8.00209e12i 0.892310 1.54553i 0.0552116 0.998475i \(-0.482417\pi\)
0.837099 0.547052i \(-0.184250\pi\)
\(350\) 2.04091e11i 0.0388582i
\(351\) 0 0
\(352\) 1.38366e12 0.256046
\(353\) 7.97378e11 + 4.60367e11i 0.145476 + 0.0839905i 0.570971 0.820970i \(-0.306567\pi\)
−0.425495 + 0.904961i \(0.639900\pi\)
\(354\) 0 0
\(355\) −2.97128e12 5.14640e12i −0.526989 0.912771i
\(356\) 2.30516e12 1.33088e12i 0.403135 0.232750i
\(357\) 0 0
\(358\) −3.35500e12 + 5.81103e12i −0.570528 + 0.988184i
\(359\) 6.17595e12i 1.03569i 0.855473 + 0.517847i \(0.173267\pi\)
−0.855473 + 0.517847i \(0.826733\pi\)
\(360\) 0 0
\(361\) −3.72488e12 −0.607542
\(362\) −4.86862e12 2.81090e12i −0.783183 0.452171i
\(363\) 0 0
\(364\) 5.28323e10 + 9.15082e10i 0.00826784 + 0.0143203i
\(365\) 4.51195e12 2.60497e12i 0.696466 0.402105i
\(366\) 0 0
\(367\) 4.09689e12 7.09603e12i 0.615353 1.06582i −0.374969 0.927037i \(-0.622347\pi\)
0.990322 0.138786i \(-0.0443199\pi\)
\(368\) 1.46159e12i 0.216564i
\(369\) 0 0
\(370\) 9.34034e12 1.34696
\(371\) 2.66652e11 + 1.53952e11i 0.0379381 + 0.0219036i
\(372\) 0 0
\(373\) 4.53661e12 + 7.85764e12i 0.628329 + 1.08830i 0.987887 + 0.155176i \(0.0495943\pi\)
−0.359557 + 0.933123i \(0.617072\pi\)
\(374\) −3.07326e12 + 1.77435e12i −0.419993 + 0.242483i
\(375\) 0 0
\(376\) 1.90506e11 3.29966e11i 0.0253495 0.0439066i
\(377\) 9.15072e12i 1.20157i
\(378\) 0 0
\(379\) 1.17817e13 1.50665 0.753324 0.657650i \(-0.228449\pi\)
0.753324 + 0.657650i \(0.228449\pi\)
\(380\) −3.31413e12 1.91341e12i −0.418265 0.241485i
\(381\) 0 0
\(382\) 1.78814e12 + 3.09714e12i 0.219828 + 0.380754i
\(383\) −5.90920e12 + 3.41168e12i −0.717026 + 0.413975i −0.813657 0.581345i \(-0.802527\pi\)
0.0966310 + 0.995320i \(0.469193\pi\)
\(384\) 0 0
\(385\) −3.76832e11 + 6.52692e11i −0.0445496 + 0.0771622i
\(386\) 8.56152e12i 0.999112i
\(387\) 0 0
\(388\) 5.50249e12 0.625750
\(389\) 6.12985e11 + 3.53907e11i 0.0688180 + 0.0397321i 0.534014 0.845476i \(-0.320683\pi\)
−0.465196 + 0.885208i \(0.654016\pi\)
\(390\) 0 0
\(391\) 1.87428e12 + 3.24634e12i 0.205092 + 0.355230i
\(392\) 2.82959e12 1.63367e12i 0.305699 0.176495i
\(393\) 0 0
\(394\) 2.14289e12 3.71159e12i 0.225693 0.390912i
\(395\) 8.99251e12i 0.935181i
\(396\) 0 0
\(397\) 1.26553e12 0.128328 0.0641639 0.997939i \(-0.479562\pi\)
0.0641639 + 0.997939i \(0.479562\pi\)
\(398\) −9.85560e11 5.69013e11i −0.0986888 0.0569780i
\(399\) 0 0
\(400\) 1.76311e12 + 3.05380e12i 0.172179 + 0.298223i
\(401\) −1.30128e13 + 7.51294e12i −1.25501 + 0.724583i −0.972101 0.234562i \(-0.924634\pi\)
−0.282914 + 0.959145i \(0.591301\pi\)
\(402\) 0 0
\(403\) −4.76087e12 + 8.24608e12i −0.447880 + 0.775751i
\(404\) 5.53749e12i 0.514525i
\(405\) 0 0
\(406\) −4.51094e11 −0.0408919
\(407\) −1.73065e13 9.99193e12i −1.54967 0.894700i
\(408\) 0 0
\(409\) 8.51808e11 + 1.47537e12i 0.0744261 + 0.128910i 0.900837 0.434158i \(-0.142954\pi\)
−0.826410 + 0.563068i \(0.809621\pi\)
\(410\) 3.39023e12 1.95735e12i 0.292624 0.168947i
\(411\) 0 0
\(412\) −7.25622e11 + 1.25681e12i −0.0611257 + 0.105873i
\(413\) 3.27659e11i 0.0272692i
\(414\) 0 0
\(415\) −5.27917e12 −0.428869
\(416\) −1.58105e12 9.12822e11i −0.126905 0.0732689i
\(417\) 0 0
\(418\) 4.09379e12 + 7.09065e12i 0.320807 + 0.555655i
\(419\) −1.92646e13 + 1.11224e13i −1.49173 + 0.861248i −0.999955 0.00947693i \(-0.996983\pi\)
−0.491770 + 0.870725i \(0.663650\pi\)
\(420\) 0 0
\(421\) −9.14739e10 + 1.58437e11i −0.00691650 + 0.0119797i −0.869463 0.493998i \(-0.835535\pi\)
0.862546 + 0.505978i \(0.168868\pi\)
\(422\) 1.07473e13i 0.803043i
\(423\) 0 0
\(424\) −5.31988e12 −0.388215
\(425\) −7.83212e12 4.52187e12i −0.564852 0.326117i
\(426\) 0 0
\(427\) 2.05493e10 + 3.55924e10i 0.00144763 + 0.00250737i
\(428\) −1.06950e13 + 6.17477e12i −0.744668 + 0.429934i
\(429\) 0 0
\(430\) −1.99660e12 + 3.45820e12i −0.135815 + 0.235239i
\(431\) 6.64491e12i 0.446789i −0.974728 0.223395i \(-0.928286\pi\)
0.974728 0.223395i \(-0.0717139\pi\)
\(432\) 0 0
\(433\) 7.28337e12 0.478512 0.239256 0.970956i \(-0.423096\pi\)
0.239256 + 0.970956i \(0.423096\pi\)
\(434\) −4.06499e11 2.34692e11i −0.0264004 0.0152423i
\(435\) 0 0
\(436\) −1.39116e12 2.40957e12i −0.0882970 0.152935i
\(437\) 7.48997e12 4.32434e12i 0.469973 0.271339i
\(438\) 0 0
\(439\) 7.63002e12 1.32156e13i 0.467954 0.810520i −0.531376 0.847136i \(-0.678325\pi\)
0.999329 + 0.0366167i \(0.0116581\pi\)
\(440\) 1.30216e13i 0.789590i
\(441\) 0 0
\(442\) 4.68225e12 0.277551
\(443\) −1.58746e13 9.16520e12i −0.930430 0.537184i −0.0434825 0.999054i \(-0.513845\pi\)
−0.886948 + 0.461870i \(0.847179\pi\)
\(444\) 0 0
\(445\) −1.25249e13 2.16937e13i −0.717751 1.24318i
\(446\) −4.61641e12 + 2.66528e12i −0.261595 + 0.151032i
\(447\) 0 0
\(448\) 4.49985e10 7.79397e10i 0.00249349 0.00431885i
\(449\) 8.33876e12i 0.456951i −0.973550 0.228475i \(-0.926626\pi\)
0.973550 0.228475i \(-0.0733741\pi\)
\(450\) 0 0
\(451\) −8.37559e12 −0.448883
\(452\) −6.17686e12 3.56621e12i −0.327398 0.189023i
\(453\) 0 0
\(454\) −4.83124e12 8.36796e12i −0.250484 0.433851i
\(455\) 8.61180e11 4.97202e11i 0.0441608 0.0254962i
\(456\) 0 0
\(457\) −2.06144e11 + 3.57052e11i −0.0103416 + 0.0179123i −0.871150 0.491017i \(-0.836625\pi\)
0.860808 + 0.508929i \(0.169959\pi\)
\(458\) 2.34581e13i 1.16403i
\(459\) 0 0
\(460\) −1.37549e13 −0.667836
\(461\) 1.43974e11 + 8.31235e10i 0.00691480 + 0.00399226i 0.503453 0.864022i \(-0.332063\pi\)
−0.496539 + 0.868015i \(0.665396\pi\)
\(462\) 0 0
\(463\) −6.36616e12 1.10265e13i −0.299208 0.518243i 0.676747 0.736216i \(-0.263389\pi\)
−0.975955 + 0.217972i \(0.930056\pi\)
\(464\) 6.74970e12 3.89694e12i 0.313830 0.181190i
\(465\) 0 0
\(466\) 1.17397e13 2.03338e13i 0.534230 0.925314i
\(467\) 2.26689e13i 1.02058i 0.860004 + 0.510288i \(0.170461\pi\)
−0.860004 + 0.510288i \(0.829539\pi\)
\(468\) 0 0
\(469\) −4.49775e11 −0.0198213
\(470\) −3.10530e12 1.79284e12i −0.135398 0.0781723i
\(471\) 0 0
\(472\) −2.83060e12 4.90275e12i −0.120828 0.209281i
\(473\) 7.39891e12 4.27176e12i 0.312508 0.180427i
\(474\) 0 0
\(475\) −1.04329e13 + 1.80703e13i −0.431456 + 0.747304i
\(476\) 2.30816e11i 0.00944565i
\(477\) 0 0
\(478\) −2.79873e13 −1.12156
\(479\) −2.07547e13 1.19827e13i −0.823073 0.475201i 0.0284023 0.999597i \(-0.490958\pi\)
−0.851475 + 0.524395i \(0.824291\pi\)
\(480\) 0 0
\(481\) 1.31836e13 + 2.28347e13i 0.512047 + 0.886891i
\(482\) −2.03625e13 + 1.17563e13i −0.782701 + 0.451892i
\(483\) 0 0
\(484\) −7.29004e12 + 1.26267e13i −0.274475 + 0.475405i
\(485\) 5.17838e13i 1.92968i
\(486\) 0 0
\(487\) −1.13824e13 −0.415516 −0.207758 0.978180i \(-0.566617\pi\)
−0.207758 + 0.978180i \(0.566617\pi\)
\(488\) −6.14957e11 3.55046e11i −0.0222201 0.0128288i
\(489\) 0 0
\(490\) −1.53744e13 2.66292e13i −0.544273 0.942709i
\(491\) −3.11346e13 + 1.79756e13i −1.09103 + 0.629906i −0.933850 0.357664i \(-0.883573\pi\)
−0.157179 + 0.987570i \(0.550240\pi\)
\(492\) 0 0
\(493\) −9.99454e12 + 1.73110e13i −0.343185 + 0.594414i
\(494\) 1.08029e13i 0.367203i
\(495\) 0 0
\(496\) 8.10990e12 0.270151
\(497\) 7.16172e11 + 4.13482e11i 0.0236176 + 0.0136356i
\(498\) 0 0
\(499\) 6.68148e12 + 1.15727e13i 0.215958 + 0.374051i 0.953569 0.301176i \(-0.0973791\pi\)
−0.737610 + 0.675227i \(0.764046\pi\)
\(500\) 7.87485e12 4.54655e12i 0.251995 0.145490i
\(501\) 0 0
\(502\) −6.41239e12 + 1.11066e13i −0.201141 + 0.348387i
\(503\) 3.54934e13i 1.10232i −0.834399 0.551160i \(-0.814185\pi\)
0.834399 0.551160i \(-0.185815\pi\)
\(504\) 0 0
\(505\) −5.21132e13 −1.58668
\(506\) 2.54863e13 + 1.47145e13i 0.768340 + 0.443602i
\(507\) 0 0
\(508\) 1.04553e13 + 1.81092e13i 0.309043 + 0.535279i
\(509\) 5.25969e13 3.03668e13i 1.53947 0.888813i 0.540600 0.841280i \(-0.318197\pi\)
0.998870 0.0475339i \(-0.0151362\pi\)
\(510\) 0 0
\(511\) −3.62508e11 + 6.27882e11i −0.0104043 + 0.0180208i
\(512\) 1.55494e12i 0.0441942i
\(513\) 0 0
\(514\) 2.89501e13 0.806928
\(515\) 1.18278e13 + 6.82880e12i 0.326489 + 0.188499i
\(516\) 0 0
\(517\) 3.83583e12 + 6.64385e12i 0.103850 + 0.179873i
\(518\) −1.12566e12 + 6.49900e11i −0.0301827 + 0.0174260i
\(519\) 0 0
\(520\) −8.59053e12 + 1.48792e13i −0.225945 + 0.391349i
\(521\) 2.06244e13i 0.537270i 0.963242 + 0.268635i \(0.0865726\pi\)
−0.963242 + 0.268635i \(0.913427\pi\)
\(522\) 0 0
\(523\) 5.24376e13 1.34009 0.670045 0.742320i \(-0.266275\pi\)
0.670045 + 0.742320i \(0.266275\pi\)
\(524\) −1.84234e13 1.06367e13i −0.466351 0.269248i
\(525\) 0 0
\(526\) −1.90730e13 3.30354e13i −0.473685 0.820447i
\(527\) −1.80129e13 + 1.03998e13i −0.443130 + 0.255841i
\(528\) 0 0
\(529\) −5.17008e12 + 8.95484e12i −0.124801 + 0.216162i
\(530\) 5.00652e13i 1.19717i
\(531\) 0 0
\(532\) 5.32541e11 0.0124967
\(533\) 9.57043e12 + 5.52549e12i 0.222482 + 0.128450i
\(534\) 0 0
\(535\) 5.81106e13 + 1.00650e14i 1.32582 + 2.29640i
\(536\) 6.72997e12 3.88555e12i 0.152121 0.0878271i
\(537\) 0 0
\(538\) 1.51630e13 2.62631e13i 0.336414 0.582686i
\(539\) 6.57877e13i 1.44611i
\(540\) 0 0
\(541\) 8.20249e13 1.76994 0.884972 0.465645i \(-0.154178\pi\)
0.884972 + 0.465645i \(0.154178\pi\)
\(542\) 3.43613e13 + 1.98385e13i 0.734637 + 0.424143i
\(543\) 0 0
\(544\) −1.99399e12 3.45370e12i −0.0418532 0.0724919i
\(545\) −2.26764e13 + 1.30922e13i −0.471618 + 0.272289i
\(546\) 0 0
\(547\) 8.11661e12 1.40584e13i 0.165744 0.287077i −0.771175 0.636623i \(-0.780331\pi\)
0.936919 + 0.349546i \(0.113664\pi\)
\(548\) 4.73872e13i 0.958867i
\(549\) 0 0
\(550\) −7.10004e13 −1.41074
\(551\) 3.99401e13 + 2.30595e13i 0.786415 + 0.454037i
\(552\) 0 0
\(553\) 6.25698e11 + 1.08374e12i 0.0120987 + 0.0209556i
\(554\) 3.32307e13 1.91857e13i 0.636782 0.367646i
\(555\) 0 0
\(556\) 2.03667e13 3.52762e13i 0.383308 0.663908i
\(557\) 1.12168e13i 0.209215i 0.994514 + 0.104608i \(0.0333587\pi\)
−0.994514 + 0.104608i \(0.966641\pi\)
\(558\) 0 0
\(559\) −1.12726e13 −0.206521
\(560\) −7.33487e11 4.23479e11i −0.0133184 0.00768939i
\(561\) 0 0
\(562\) −2.76253e12 4.78484e12i −0.0492748 0.0853465i
\(563\) 6.91540e13 3.99261e13i 1.22258 0.705854i 0.257109 0.966382i \(-0.417230\pi\)
0.965466 + 0.260528i \(0.0838968\pi\)
\(564\) 0 0
\(565\) −3.35615e13 + 5.81302e13i −0.582906 + 1.00962i
\(566\) 2.25462e13i 0.388142i
\(567\) 0 0
\(568\) −1.42881e13 −0.241675
\(569\) −8.62210e11 4.97797e11i −0.0144561 0.00834624i 0.492755 0.870168i \(-0.335990\pi\)
−0.507211 + 0.861822i \(0.669323\pi\)
\(570\) 0 0
\(571\) −5.39178e13 9.33883e13i −0.888283 1.53855i −0.841904 0.539627i \(-0.818565\pi\)
−0.0463786 0.998924i \(-0.514768\pi\)
\(572\) 3.18345e13 1.83796e13i 0.519897 0.300163i
\(573\) 0 0
\(574\) −2.72385e11 + 4.71784e11i −0.00437143 + 0.00757153i
\(575\) 7.49989e13i 1.19321i
\(576\) 0 0
\(577\) 3.31000e13 0.517546 0.258773 0.965938i \(-0.416682\pi\)
0.258773 + 0.965938i \(0.416682\pi\)
\(578\) −3.06475e13 1.76944e13i −0.475068 0.274281i
\(579\) 0 0
\(580\) −3.66740e13 6.35212e13i −0.558751 0.967785i
\(581\) 6.36224e11 3.67324e11i 0.00961013 0.00554841i
\(582\) 0 0
\(583\) 5.35578e13 9.27648e13i 0.795206 1.37734i
\(584\) 1.25266e13i 0.184404i
\(585\) 0 0
\(586\) −3.56543e13 −0.515969
\(587\) 1.04808e14 + 6.05110e13i 1.50385 + 0.868248i 0.999990 + 0.00446213i \(0.00142035\pi\)
0.503859 + 0.863786i \(0.331913\pi\)
\(588\) 0 0
\(589\) 2.39944e13 + 4.15596e13i 0.338481 + 0.586266i
\(590\) −4.61396e13 + 2.66387e13i −0.645377 + 0.372609i
\(591\) 0 0
\(592\) 1.12288e13 1.94489e13i 0.154428 0.267477i
\(593\) 8.43944e12i 0.115091i 0.998343 + 0.0575453i \(0.0183274\pi\)
−0.998343 + 0.0575453i \(0.981673\pi\)
\(594\) 0 0
\(595\) 2.17220e12 0.0291283
\(596\) −3.58185e13 2.06798e13i −0.476294 0.274989i
\(597\) 0 0
\(598\) −1.94147e13 3.36273e13i −0.253878 0.439730i
\(599\) −2.70098e13 + 1.55941e13i −0.350258 + 0.202221i −0.664799 0.747023i \(-0.731483\pi\)
0.314541 + 0.949244i \(0.398149\pi\)
\(600\) 0 0
\(601\) −1.43700e13 + 2.48896e13i −0.183267 + 0.317428i −0.942991 0.332817i \(-0.892001\pi\)
0.759724 + 0.650246i \(0.225334\pi\)
\(602\) 5.55692e11i 0.00702832i
\(603\) 0 0
\(604\) −1.58031e13 −0.196588
\(605\) 1.18830e14 + 6.86062e13i 1.46605 + 0.846422i
\(606\) 0 0
\(607\) 2.23768e13 + 3.87578e13i 0.271553 + 0.470344i 0.969260 0.246040i \(-0.0791295\pi\)
−0.697707 + 0.716384i \(0.745796\pi\)
\(608\) −7.96839e12 + 4.60055e12i −0.0959075 + 0.0553722i
\(609\) 0 0
\(610\) −3.34132e12 + 5.78734e12i −0.0395612 + 0.0685219i
\(611\) 1.01222e13i 0.118869i
\(612\) 0 0
\(613\) 6.78051e13 0.783358 0.391679 0.920102i \(-0.371894\pi\)
0.391679 + 0.920102i \(0.371894\pi\)
\(614\) 6.46318e13 + 3.73152e13i 0.740635 + 0.427606i
\(615\) 0 0
\(616\) 9.06043e11 + 1.56931e12i 0.0102152 + 0.0176932i
\(617\) 2.15001e12 1.24131e12i 0.0240444 0.0138820i −0.487930 0.872883i \(-0.662248\pi\)
0.511974 + 0.859001i \(0.328914\pi\)
\(618\) 0 0
\(619\) −8.20000e12 + 1.42028e13i −0.0902320 + 0.156286i −0.907609 0.419817i \(-0.862094\pi\)
0.817377 + 0.576104i \(0.195428\pi\)
\(620\) 7.63220e13i 0.833088i
\(621\) 0 0
\(622\) 3.78559e13 0.406613
\(623\) 3.01890e12 + 1.74296e12i 0.0321668 + 0.0185715i
\(624\) 0 0
\(625\) 2.28936e13 + 3.96529e13i 0.240057 + 0.415791i
\(626\) 3.39633e13 1.96087e13i 0.353296 0.203976i
\(627\) 0 0
\(628\) 2.48659e13 4.30689e13i 0.254569 0.440926i
\(629\) 5.75973e13i 0.584991i
\(630\) 0 0
\(631\) −1.37258e13 −0.137211 −0.0686056 0.997644i \(-0.521855\pi\)
−0.0686056 + 0.997644i \(0.521855\pi\)
\(632\) −1.87246e13 1.08107e13i −0.185707 0.107218i
\(633\) 0 0
\(634\) 1.50586e13 + 2.60822e13i 0.147007 + 0.254623i
\(635\) 1.70425e14 9.83948e13i 1.65068 0.953023i
\(636\) 0 0
\(637\) 4.34010e13 7.51728e13i 0.413812 0.716743i
\(638\) 1.56930e14i 1.48457i
\(639\) 0 0
\(640\) 1.46335e13 0.136285
\(641\) −4.69687e13 2.71174e13i −0.434029 0.250587i 0.267033 0.963687i \(-0.413957\pi\)
−0.701061 + 0.713101i \(0.747290\pi\)
\(642\) 0 0
\(643\) 2.77346e13 + 4.80378e13i 0.252329 + 0.437047i 0.964167 0.265297i \(-0.0854700\pi\)
−0.711837 + 0.702344i \(0.752137\pi\)
\(644\) 1.65769e12 9.57068e11i 0.0149649 0.00863999i
\(645\) 0 0
\(646\) 1.17991e13 2.04366e13i 0.104878 0.181655i
\(647\) 5.56652e13i 0.490979i −0.969399 0.245489i \(-0.921051\pi\)
0.969399 0.245489i \(-0.0789486\pi\)
\(648\) 0 0
\(649\) 1.13988e14 0.990002
\(650\) 8.11291e13 + 4.68399e13i 0.699214 + 0.403691i
\(651\) 0 0
\(652\) −3.56967e13 6.18286e13i −0.302964 0.524749i
\(653\) 4.82196e13 2.78396e13i 0.406123 0.234475i −0.283000 0.959120i \(-0.591329\pi\)
0.689123 + 0.724645i \(0.257996\pi\)
\(654\) 0 0
\(655\) −1.00102e14 + 1.73382e14i −0.830302 + 1.43813i
\(656\) 9.41238e12i 0.0774784i
\(657\) 0 0
\(658\) 4.98984e11 0.00404536
\(659\) 1.32241e14 + 7.63495e13i 1.06399 + 0.614298i 0.926535 0.376210i \(-0.122773\pi\)
0.137460 + 0.990507i \(0.456106\pi\)
\(660\) 0 0
\(661\) 1.04018e14 + 1.80164e14i 0.824329 + 1.42778i 0.902431 + 0.430834i \(0.141780\pi\)
−0.0781026 + 0.996945i \(0.524886\pi\)
\(662\) 9.24851e13 5.33963e13i 0.727414 0.419973i
\(663\) 0 0
\(664\) −6.34653e12 + 1.09925e13i −0.0491695 + 0.0851641i
\(665\) 5.01172e12i 0.0385371i
\(666\) 0 0
\(667\) 1.65767e14 1.25565
\(668\) 5.57981e13 + 3.22150e13i 0.419505 + 0.242201i
\(669\) 0 0
\(670\) −3.65668e13 6.33355e13i −0.270840 0.469108i
\(671\) 1.23821e13 7.14883e12i 0.0910297 0.0525560i
\(672\) 0 0
\(673\) 4.72630e13 8.18619e13i 0.342331 0.592934i −0.642534 0.766257i \(-0.722117\pi\)
0.984865 + 0.173323i \(0.0554503\pi\)
\(674\) 9.39679e13i 0.675585i
\(675\) 0 0
\(676\) 2.20824e13 0.156427
\(677\) −1.47316e14 8.50528e13i −1.03587 0.598060i −0.117210 0.993107i \(-0.537395\pi\)
−0.918661 + 0.395047i \(0.870728\pi\)
\(678\) 0 0
\(679\) 3.60311e12 + 6.24077e12i 0.0249648 + 0.0432404i
\(680\) −3.25026e13 + 1.87654e13i −0.223549 + 0.129066i
\(681\) 0 0
\(682\) −8.16463e13 + 1.41415e14i −0.553369 + 0.958462i
\(683\) 2.23578e14i 1.50427i −0.659009 0.752135i \(-0.729024\pi\)
0.659009 0.752135i \(-0.270976\pi\)
\(684\) 0 0
\(685\) −4.45960e14 −2.95694
\(686\) 7.41734e12 + 4.28240e12i 0.0488234 + 0.0281882i
\(687\) 0 0
\(688\) 4.80055e12 + 8.31480e12i 0.0311422 + 0.0539398i
\(689\) −1.22396e14 + 7.06656e13i −0.788265 + 0.455105i
\(690\) 0 0
\(691\) 5.50672e12 9.53792e12i 0.0349545 0.0605429i −0.848019 0.529966i \(-0.822205\pi\)
0.882973 + 0.469423i \(0.155538\pi\)
\(692\) 6.46435e13i 0.407375i
\(693\) 0 0
\(694\) −9.95468e13 −0.618344
\(695\) −3.31983e14 1.91671e14i −2.04735 1.18204i
\(696\) 0 0
\(697\) 1.20700e13 + 2.09059e13i 0.0733744 + 0.127088i
\(698\) −1.81067e14 + 1.04539e14i −1.09285 + 0.630959i
\(699\) 0 0
\(700\) −2.30902e12 + 3.99934e12i −0.0137384 + 0.0237957i
\(701\) 1.10962e14i 0.655516i 0.944762 + 0.327758i \(0.106293\pi\)
−0.944762 + 0.327758i \(0.893707\pi\)
\(702\) 0 0
\(703\) 1.32889e14 0.773948
\(704\) −2.71142e13 1.56544e13i −0.156795 0.0905258i
\(705\) 0 0
\(706\) −1.04169e13 1.80426e13i −0.0593903 0.102867i
\(707\) 6.28047e12 3.62603e12i 0.0355545 0.0205274i
\(708\) 0 0
\(709\) −1.04110e14 + 1.80323e14i −0.581112 + 1.00652i 0.414236 + 0.910169i \(0.364049\pi\)
−0.995348 + 0.0963458i \(0.969285\pi\)
\(710\) 1.34465e14i 0.745275i
\(711\) 0 0
\(712\) −6.02289e13 −0.329158
\(713\) 1.49380e14 + 8.62443e13i 0.810669 + 0.468040i
\(714\) 0 0
\(715\) −1.72970e14 2.99593e14i −0.925637 1.60325i
\(716\) 1.31488e14 7.59149e13i 0.698751 0.403424i
\(717\) 0 0
\(718\) 6.98730e13 1.21024e14i 0.366173 0.634231i
\(719\) 2.74910e14i 1.43069i −0.698771 0.715346i \(-0.746269\pi\)
0.698771 0.715346i \(-0.253731\pi\)
\(720\) 0 0
\(721\) −1.90059e12 −0.00975465
\(722\) 7.29924e13 + 4.21422e13i 0.372042 + 0.214798i
\(723\) 0 0
\(724\) 6.36034e13 + 1.10164e14i 0.319733 + 0.553794i
\(725\) −3.46350e14 + 1.99965e14i −1.72912 + 0.998307i
\(726\) 0 0
\(727\) 1.49536e14 2.59003e14i 0.736330 1.27536i −0.217807 0.975992i \(-0.569890\pi\)
0.954137 0.299370i \(-0.0967764\pi\)
\(728\) 2.39092e12i 0.0116925i
\(729\) 0 0
\(730\) −1.17888e14 −0.568662
\(731\) −2.13251e13 1.23120e13i −0.102165 0.0589852i
\(732\) 0 0
\(733\) −5.99610e13 1.03856e14i −0.283367 0.490806i 0.688845 0.724909i \(-0.258118\pi\)
−0.972212 + 0.234103i \(0.924785\pi\)
\(734\) −1.60565e14 + 9.27021e13i −0.753651 + 0.435120i
\(735\) 0 0
\(736\) −1.65360e13 + 2.86411e13i −0.0765668 + 0.132618i
\(737\) 1.56471e14i 0.719608i
\(738\) 0 0
\(739\) −7.29345e13 −0.330911 −0.165455 0.986217i \(-0.552909\pi\)
−0.165455 + 0.986217i \(0.552909\pi\)
\(740\) −1.83033e14 1.05674e14i −0.824840 0.476221i
\(741\) 0 0
\(742\) −3.48353e12 6.03365e12i −0.0154882 0.0268263i
\(743\) 9.27173e13 5.35303e13i 0.409465 0.236405i −0.281095 0.959680i \(-0.590698\pi\)
0.690560 + 0.723275i \(0.257364\pi\)
\(744\) 0 0
\(745\) −1.94617e14 + 3.37086e14i −0.848006 + 1.46879i
\(746\) 2.05304e14i 0.888592i
\(747\) 0 0
\(748\) 8.02979e13 0.342923
\(749\) −1.40065e13 8.08666e12i −0.0594183 0.0343052i
\(750\) 0 0
\(751\) −9.18885e13 1.59156e14i −0.384646 0.666227i 0.607074 0.794645i \(-0.292343\pi\)
−0.991720 + 0.128419i \(0.959010\pi\)
\(752\) −7.46627e12 + 4.31065e12i −0.0310466 + 0.0179248i
\(753\) 0 0
\(754\) 1.03529e14 1.79317e14i 0.424819 0.735808i
\(755\) 1.48722e14i 0.606236i
\(756\) 0 0
\(757\) −1.73049e14 −0.696130 −0.348065 0.937470i \(-0.613161\pi\)
−0.348065 + 0.937470i \(0.613161\pi\)
\(758\) −2.30873e14 1.33295e14i −0.922629 0.532680i
\(759\) 0 0
\(760\) 4.32956e13 + 7.49902e13i 0.170756 + 0.295758i
\(761\) 9.53979e13 5.50780e13i 0.373780 0.215802i −0.301329 0.953520i \(-0.597430\pi\)
0.675108 + 0.737719i \(0.264097\pi\)
\(762\) 0 0
\(763\) 1.82191e12 3.15564e12i 0.00704537 0.0122029i
\(764\) 8.09218e13i 0.310884i
\(765\) 0 0
\(766\) 1.54395e14 0.585449
\(767\) −1.30249e14 7.51995e13i −0.490681 0.283295i
\(768\) 0 0
\(769\) −1.15229e14 1.99583e14i −0.428480 0.742149i 0.568259 0.822850i \(-0.307617\pi\)
−0.996738 + 0.0807014i \(0.974284\pi\)
\(770\) 1.47687e13 8.52674e12i 0.0545619 0.0315013i
\(771\) 0 0
\(772\) −9.68625e13 + 1.67771e14i −0.353239 + 0.611829i
\(773\) 1.50965e14i 0.546991i 0.961873 + 0.273495i \(0.0881798\pi\)
−0.961873 + 0.273495i \(0.911820\pi\)
\(774\) 0 0
\(775\) −4.16146e14 −1.48846
\(776\) −1.07826e14 6.22536e13i −0.383192 0.221236i
\(777\) 0 0
\(778\) −8.00801e12 1.38703e13i −0.0280948 0.0486617i
\(779\) 4.82342e13 2.78480e13i 0.168139 0.0970750i
\(780\) 0 0
\(781\) 1.43845e14 2.49147e14i 0.495039 0.857433i
\(782\) 8.48200e13i 0.290044i
\(783\) 0 0
\(784\) −7.39313e13 −0.249602
\(785\) −4.05320e14 2.34012e14i −1.35972 0.785035i
\(786\) 0 0
\(787\) 1.71040e14 + 2.96250e14i 0.566532 + 0.981263i 0.996905 + 0.0786117i \(0.0250487\pi\)
−0.430373 + 0.902651i \(0.641618\pi\)
\(788\) −8.39837e13 + 4.84880e13i −0.276416 + 0.159589i
\(789\) 0 0
\(790\) −1.01739e14 + 1.76217e14i −0.330636 + 0.572679i
\(791\) 9.34082e12i 0.0301649i
\(792\) 0 0
\(793\) −1.88647e13 −0.0601568
\(794\) −2.47993e13 1.43179e13i −0.0785844 0.0453707i
\(795\) 0 0
\(796\) 1.28753e13 + 2.23007e13i 0.0402895 + 0.0697835i
\(797\) −4.52919e14 + 2.61493e14i −1.40841 + 0.813146i −0.995235 0.0975050i \(-0.968914\pi\)
−0.413176 + 0.910651i \(0.635580\pi\)
\(798\) 0 0
\(799\) 1.10556e13 1.91488e13i 0.0339506 0.0588042i
\(800\) 7.97893e13i 0.243498i
\(801\) 0 0
\(802\) 3.39997e14 1.02472
\(803\) 2.18432e14 + 1.26112e14i 0.654242 + 0.377727i
\(804\) 0 0
\(805\) −9.00693e12 1.56005e13i −0.0266439 0.0461486i
\(806\) 1.86587e14 1.07726e14i 0.548539 0.316699i
\(807\) 0 0
\(808\) −6.26496e13 + 1.08512e14i −0.181912 + 0.315081i
\(809\) 3.45374e14i 0.996661i −0.866987 0.498331i \(-0.833947\pi\)
0.866987 0.498331i \(-0.166053\pi\)
\(810\) 0 0
\(811\) 3.60870e14 1.02860 0.514301 0.857610i \(-0.328052\pi\)
0.514301 + 0.857610i \(0.328052\pi\)
\(812\) 8.83960e12 + 5.10355e12i 0.0250411 + 0.0144575i
\(813\) 0 0
\(814\) 2.26092e14 + 3.91602e14i 0.632648 + 1.09578i
\(815\) −5.81866e14 + 3.35941e14i −1.61821 + 0.934275i
\(816\) 0 0
\(817\) −2.84064e13 + 4.92013e13i −0.0780379 + 0.135166i
\(818\) 3.85484e13i 0.105254i
\(819\) 0 0
\(820\) −8.85796e13 −0.238927
\(821\) −5.78784e14 3.34161e14i −1.55168 0.895860i −0.998006 0.0631235i \(-0.979894\pi\)
−0.553669 0.832737i \(-0.686773\pi\)
\(822\) 0 0
\(823\) −2.17665e13 3.77008e13i −0.0576488 0.0998506i 0.835761 0.549094i \(-0.185027\pi\)
−0.893410 + 0.449243i \(0.851694\pi\)
\(824\) 2.84384e13 1.64189e13i 0.0748634 0.0432224i
\(825\) 0 0
\(826\) 3.70704e12 6.42078e12i 0.00964110 0.0166989i
\(827\) 2.21008e13i 0.0571321i 0.999592 + 0.0285661i \(0.00909409\pi\)
−0.999592 + 0.0285661i \(0.990906\pi\)
\(828\) 0 0
\(829\) 7.62973e14 1.94866 0.974331 0.225119i \(-0.0722770\pi\)
0.974331 + 0.225119i \(0.0722770\pi\)
\(830\) 1.03450e14 + 5.97270e13i 0.262628 + 0.151628i
\(831\) 0 0
\(832\) 2.06548e13 + 3.57752e13i 0.0518089 + 0.0897357i
\(833\) 1.64209e14 9.48063e13i 0.409423 0.236381i
\(834\) 0 0
\(835\) 3.03174e14 5.25113e14i 0.746896 1.29366i
\(836\) 1.85264e14i 0.453690i
\(837\) 0 0
\(838\) 5.03342e14 1.21799
\(839\) −7.40702e13 4.27644e13i −0.178170 0.102866i 0.408263 0.912864i \(-0.366135\pi\)
−0.586432 + 0.809998i \(0.699468\pi\)
\(840\) 0 0
\(841\) 2.31622e14 + 4.01181e14i 0.550554 + 0.953588i
\(842\) 3.58503e12 2.06982e12i 0.00847095 0.00489071i
\(843\) 0 0
\(844\) 1.21592e14 2.10604e14i 0.283918 0.491761i
\(845\) 2.07816e14i 0.482387i
\(846\) 0 0
\(847\) −1.90945e13 −0.0438017
\(848\) 1.04248e14 + 6.01875e13i 0.237732 + 0.137255i
\(849\) 0 0
\(850\) 1.02318e14 + 1.77221e14i 0.230600 + 0.399411i
\(851\) 4.13656e14 2.38824e14i 0.926811 0.535095i
\(852\) 0 0
\(853\) −9.10893e13 + 1.57771e14i −0.201708 + 0.349368i −0.949079 0.315039i \(-0.897982\pi\)
0.747371 + 0.664407i \(0.231316\pi\)
\(854\) 9.29956e11i 0.00204726i
\(855\) 0 0
\(856\) 2.79438e14 0.608019
\(857\) 7.38198e14 + 4.26199e14i 1.59687 + 0.921952i 0.992086 + 0.125560i \(0.0400727\pi\)
0.604781 + 0.796392i \(0.293261\pi\)
\(858\) 0 0
\(859\) −1.30031e14 2.25220e14i −0.278023 0.481550i 0.692870 0.721062i \(-0.256346\pi\)
−0.970893 + 0.239512i \(0.923013\pi\)
\(860\) 7.82502e13 4.51778e13i 0.166339 0.0960357i
\(861\) 0 0
\(862\) −7.51786e13 + 1.30213e14i −0.157964 + 0.273601i
\(863\) 2.71494e14i 0.567161i 0.958948 + 0.283580i \(0.0915223\pi\)
−0.958948 + 0.283580i \(0.908478\pi\)
\(864\) 0 0
\(865\) −6.08358e14 −1.25626
\(866\) −1.42724e14 8.24020e13i −0.293028 0.169180i
\(867\) 0 0
\(868\) 5.31048e12 + 9.19801e12i 0.0107779 + 0.0186679i
\(869\) 3.77019e14 2.17672e14i 0.760790 0.439242i
\(870\) 0 0
\(871\) 1.03226e14 1.78793e14i 0.205920 0.356664i
\(872\) 6.29569e13i 0.124871i
\(873\) 0 0
\(874\) −1.95697e14 −0.383732
\(875\) 1.03131e13 + 5.95429e12i 0.0201071 + 0.0116089i
\(876\) 0 0
\(877\) −9.50609e13 1.64650e14i −0.183233 0.317369i 0.759747 0.650219i \(-0.225323\pi\)
−0.942980 + 0.332850i \(0.891990\pi\)
\(878\) −2.99034e14 + 1.72648e14i −0.573124 + 0.330893i
\(879\) 0 0
\(880\) −1.47323e14 + 2.55170e14i −0.279162 + 0.483523i
\(881\) 6.12829e14i 1.15468i −0.816506 0.577338i \(-0.804092\pi\)
0.816506 0.577338i \(-0.195908\pi\)
\(882\) 0 0
\(883\) −4.57367e14 −0.852042 −0.426021 0.904713i \(-0.640085\pi\)
−0.426021 + 0.904713i \(0.640085\pi\)
\(884\) −9.17530e13 5.29736e13i −0.169965 0.0981292i
\(885\) 0 0
\(886\) 2.07385e14 + 3.59201e14i 0.379847 + 0.657913i
\(887\) −5.17143e14 + 2.98573e14i −0.941874 + 0.543791i −0.890547 0.454891i \(-0.849678\pi\)
−0.0513267 + 0.998682i \(0.516345\pi\)
\(888\) 0 0
\(889\) −1.36926e13 + 2.37163e13i −0.0246591 + 0.0427108i
\(890\) 5.66812e14i 1.01505i
\(891\) 0 0
\(892\) 1.20617e14 0.213592
\(893\) −4.41803e13 2.55075e13i −0.0777985 0.0449170i
\(894\) 0 0
\(895\) −7.14432e14 1.23743e15i −1.24407 2.15480i
\(896\) −1.76357e12 + 1.01820e12i −0.00305389 + 0.00176316i
\(897\) 0 0
\(898\) −9.43423e13 + 1.63406e14i −0.161557 + 0.279824i
\(899\) 9.19792e14i 1.56636i
\(900\) 0 0
\(901\) −3.08727e14 −0.519938
\(902\) 1.64127e14 + 9.47590e13i 0.274883 + 0.158704i
\(903\) 0 0
\(904\) 8.06941e13 + 1.39766e14i 0.133659 + 0.231505i
\(905\) 1.03675e15 5.98569e14i 1.70778 0.985988i
\(906\) 0 0
\(907\) 3.98099e14 6.89528e14i 0.648567 1.12335i −0.334898 0.942254i \(-0.608702\pi\)
0.983465 0.181097i \(-0.0579647\pi\)
\(908\) 2.18637e14i 0.354238i
\(909\) 0 0
\(910\) −2.25008e13 −0.0360571
\(911\) −5.15739e14 2.97762e14i −0.821936 0.474545i 0.0291479 0.999575i \(-0.490721\pi\)
−0.851083 + 0.525030i \(0.824054\pi\)
\(912\) 0 0
\(913\) −1.27787e14 2.21334e14i −0.201434 0.348894i
\(914\) 8.07916e12 4.66451e12i 0.0126659 0.00731265i
\(915\) 0 0
\(916\) 2.65398e14 4.59683e14i 0.411548 0.712822i
\(917\) 2.78603e13i 0.0429675i
\(918\) 0 0
\(919\) 5.55318e14 0.847157 0.423579 0.905859i \(-0.360774\pi\)
0.423579 + 0.905859i \(0.360774\pi\)
\(920\) 2.69541e14 + 1.55619e14i 0.408964 + 0.236116i
\(921\) 0 0
\(922\) −1.88087e12 3.25776e12i −0.00282296 0.00488950i
\(923\) −3.28731e14 + 1.89793e14i −0.490718 + 0.283316i
\(924\) 0 0
\(925\) −5.76187e14 + 9.97986e14i −0.850854 + 1.47372i
\(926\) 2.88100e14i 0.423144i
\(927\) 0 0
\(928\) −1.76356e14 −0.256241
\(929\) −1.29291e14 7.46462e13i −0.186849 0.107877i 0.403658 0.914910i \(-0.367739\pi\)
−0.590506 + 0.807033i \(0.701072\pi\)
\(930\) 0 0
\(931\) −2.18738e14 3.78865e14i −0.312734 0.541671i
\(932\) −4.60102e14 + 2.65640e14i −0.654296 + 0.377758i
\(933\) 0 0
\(934\) 2.56469e14 4.44217e14i 0.360828 0.624972i
\(935\) 7.55681e14i 1.05750i
\(936\) 0 0
\(937\) −3.07315e14 −0.425487 −0.212743 0.977108i \(-0.568240\pi\)
−0.212743 + 0.977108i \(0.568240\pi\)
\(938\) 8.81376e12 + 5.08863e12i 0.0121380 + 0.00700788i
\(939\) 0 0
\(940\) 4.05674e13 + 7.02648e13i 0.0552762 + 0.0957412i
\(941\) −2.27895e14 + 1.31575e14i −0.308877 + 0.178330i −0.646424 0.762978i \(-0.723736\pi\)
0.337547 + 0.941309i \(0.390403\pi\)
\(942\) 0 0
\(943\) 1.00096e14 1.73371e14i 0.134232 0.232497i
\(944\) 1.28098e14i 0.170877i
\(945\) 0 0
\(946\) −1.93318e14 −0.255162
\(947\) 1.04028e15 + 6.00604e14i 1.36584 + 0.788566i 0.990393 0.138279i \(-0.0441572\pi\)
0.375443 + 0.926845i \(0.377491\pi\)
\(948\) 0 0
\(949\) −1.66395e14 2.88205e14i −0.216177 0.374430i
\(950\) 4.08884e14 2.36069e14i 0.528424 0.305086i
\(951\) 0 0
\(952\) 2.61139e12 4.52306e12i 0.00333954 0.00578425i
\(953\) 3.27942e13i 0.0417189i −0.999782 0.0208594i \(-0.993360\pi\)
0.999782 0.0208594i \(-0.00664025\pi\)
\(954\) 0 0
\(955\) −7.61552e14 −0.958700
\(956\) 5.48436e14 + 3.16640e14i 0.686810 + 0.396530i
\(957\) 0 0
\(958\) 2.71138e14 + 4.69624e14i 0.336018 + 0.582000i
\(959\) 5.37452e13 3.10298e13i 0.0662593 0.0382548i
\(960\) 0 0
\(961\) −6.87290e13 + 1.19042e14i −0.0838538 + 0.145239i
\(962\) 5.96623e14i 0.724143i
\(963\) 0 0
\(964\) 5.32029e14 0.639072
\(965\) 1.57888e15 + 9.11569e14i 1.88675 + 1.08931i
\(966\) 0 0
\(967\) 4.93527e14 + 8.54813e14i 0.583684 + 1.01097i 0.995038 + 0.0994953i \(0.0317228\pi\)
−0.411354 + 0.911476i \(0.634944\pi\)
\(968\) 2.85710e14 1.64955e14i 0.336162 0.194083i
\(969\) 0 0
\(970\) −5.85866e14 + 1.01475e15i −0.682244 + 1.18168i
\(971\) 5.42431e14i 0.628418i 0.949354 + 0.314209i \(0.101739\pi\)
−0.949354 + 0.314209i \(0.898261\pi\)
\(972\) 0 0
\(973\) 5.33457e13 0.0611695
\(974\) 2.23048e14 + 1.28777e14i 0.254451 + 0.146907i
\(975\) 0 0
\(976\) 8.03377e12 + 1.39149e13i 0.00907131 + 0.0157120i
\(977\) 8.26067e14 4.76930e14i 0.927988 0.535774i 0.0418131 0.999125i \(-0.486687\pi\)
0.886175 + 0.463352i \(0.153353\pi\)
\(978\) 0 0
\(979\) 6.06353e14 1.05023e15i 0.674237 1.16781i
\(980\) 6.95765e14i 0.769719i
\(981\) 0 0
\(982\) 8.13482e14 0.890821
\(983\) −5.46361e14 3.15442e14i −0.595268 0.343678i 0.171910 0.985113i \(-0.445006\pi\)
−0.767178 + 0.641435i \(0.778340\pi\)
\(984\) 0 0
\(985\) 4.56319e14 + 7.90367e14i 0.492138 + 0.852409i
\(986\) 3.91704e14 2.26151e14i 0.420314 0.242668i
\(987\) 0 0
\(988\) −1.22221e14 + 2.11693e14i −0.129826 + 0.224865i
\(989\) 2.04205e14i 0.215816i
\(990\) 0 0
\(991\) 4.94498e14 0.517364 0.258682 0.965963i \(-0.416712\pi\)
0.258682 + 0.965963i \(0.416712\pi\)
\(992\) −1.58921e14 9.17530e13i −0.165433 0.0955129i
\(993\) 0 0
\(994\) −9.35604e12 1.62051e13i −0.00964184 0.0167002i
\(995\) 2.09871e14 1.21169e14i 0.215197 0.124244i
\(996\) 0 0
\(997\) −8.14965e14 + 1.41156e15i −0.827301 + 1.43293i 0.0728476 + 0.997343i \(0.476791\pi\)
−0.900148 + 0.435584i \(0.856542\pi\)
\(998\) 3.02369e14i 0.305411i
\(999\) 0 0
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 162.11.d.d.107.2 8
3.2 odd 2 inner 162.11.d.d.107.3 8
9.2 odd 6 6.11.b.a.5.2 4
9.4 even 3 inner 162.11.d.d.53.3 8
9.5 odd 6 inner 162.11.d.d.53.2 8
9.7 even 3 6.11.b.a.5.4 yes 4
36.7 odd 6 48.11.e.d.17.1 4
36.11 even 6 48.11.e.d.17.2 4
45.2 even 12 150.11.b.a.149.5 8
45.7 odd 12 150.11.b.a.149.3 8
45.29 odd 6 150.11.d.a.101.3 4
45.34 even 6 150.11.d.a.101.1 4
45.38 even 12 150.11.b.a.149.4 8
45.43 odd 12 150.11.b.a.149.6 8
72.11 even 6 192.11.e.h.65.3 4
72.29 odd 6 192.11.e.g.65.2 4
72.43 odd 6 192.11.e.h.65.4 4
72.61 even 6 192.11.e.g.65.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6.11.b.a.5.2 4 9.2 odd 6
6.11.b.a.5.4 yes 4 9.7 even 3
48.11.e.d.17.1 4 36.7 odd 6
48.11.e.d.17.2 4 36.11 even 6
150.11.b.a.149.3 8 45.7 odd 12
150.11.b.a.149.4 8 45.38 even 12
150.11.b.a.149.5 8 45.2 even 12
150.11.b.a.149.6 8 45.43 odd 12
150.11.d.a.101.1 4 45.34 even 6
150.11.d.a.101.3 4 45.29 odd 6
162.11.d.d.53.2 8 9.5 odd 6 inner
162.11.d.d.53.3 8 9.4 even 3 inner
162.11.d.d.107.2 8 1.1 even 1 trivial
162.11.d.d.107.3 8 3.2 odd 2 inner
192.11.e.g.65.1 4 72.61 even 6
192.11.e.g.65.2 4 72.29 odd 6
192.11.e.h.65.3 4 72.11 even 6
192.11.e.h.65.4 4 72.43 odd 6