Properties

Label 81.9.d.g.26.15
Level $81$
Weight $9$
Character 81.26
Analytic conductor $32.998$
Analytic rank $0$
Dimension $32$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [81,9,Mod(26,81)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(81, base_ring=CyclotomicField(6))
 
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("81.26");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 81 = 3^{4} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 81.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: \(32.9976674150\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 26.15
Character \(\chi\) \(=\) 81.26
Dual form 81.9.d.g.53.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(22.2403 + 12.8404i) q^{2} +(201.753 + 349.447i) q^{4} +(-176.989 + 102.185i) q^{5} +(1851.21 - 3206.39i) q^{7} +3788.08i q^{8} -5248.38 q^{10} +(13951.7 + 8054.99i) q^{11} +(18463.8 + 31980.2i) q^{13} +(82342.9 - 47540.7i) q^{14} +(3008.19 - 5210.35i) q^{16} +47526.9i q^{17} +213962. q^{19} +(-71416.2 - 41232.2i) q^{20} +(206859. + 358290. i) q^{22} +(-143902. + 83082.0i) q^{23} +(-174429. + 302120. i) q^{25} +948331. i q^{26} +1.49395e6 q^{28} +(-1.17848e6 - 680393. i) q^{29} +(109298. + 189309. i) q^{31} +(973633. - 562128. i) q^{32} +(-610265. + 1.05701e6i) q^{34} +756662. i q^{35} +1.15091e6 q^{37} +(4.75857e6 + 2.74736e6i) q^{38} +(-387084. - 670449. i) q^{40} +(643528. - 371541. i) q^{41} +(1.46517e6 - 2.53774e6i) q^{43} +6.50048e6i q^{44} -4.26723e6 q^{46} +(6.31706e6 + 3.64716e6i) q^{47} +(-3.97156e6 - 6.87895e6i) q^{49} +(-7.75870e6 + 4.47949e6i) q^{50} +(-7.45025e6 + 1.29042e7i) q^{52} -2.55324e6i q^{53} -3.29239e6 q^{55} +(1.21461e7 + 7.01254e6i) q^{56} +(-1.74731e7 - 3.02643e7i) q^{58} +(-4.44279e6 + 2.56505e6i) q^{59} +(1.34768e6 - 2.33425e6i) q^{61} +5.61372e6i q^{62} +2.73316e7 q^{64} +(-6.53578e6 - 3.77343e6i) q^{65} +(-319308. - 553057. i) q^{67} +(-1.66081e7 + 9.58869e6i) q^{68} +(-9.71586e6 + 1.68284e7i) q^{70} +3.72932e7i q^{71} -2.13898e7 q^{73} +(2.55965e7 + 1.47782e7i) q^{74} +(4.31675e7 + 7.47683e7i) q^{76} +(5.16549e7 - 2.98230e7i) q^{77} +(2.50309e7 - 4.33548e7i) q^{79} +1.22957e6i q^{80} +1.90830e7 q^{82} +(-2.83851e7 - 1.63882e7i) q^{83} +(-4.85652e6 - 8.41174e6i) q^{85} +(6.51714e7 - 3.76267e7i) q^{86} +(-3.05130e7 + 5.28500e7i) q^{88} +6.85873e6i q^{89} +1.36721e8 q^{91} +(-5.80654e7 - 3.35241e7i) q^{92} +(9.36621e7 + 1.62228e8i) q^{94} +(-3.78689e7 + 2.18636e7i) q^{95} +(4.14058e7 - 7.17170e7i) q^{97} -2.03986e8i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 2048 q^{4} - 3692 q^{7} + 21504 q^{10} - 63860 q^{13} - 95116 q^{16} + 370216 q^{19} + 691980 q^{22} + 541712 q^{25} - 1994264 q^{28} - 571136 q^{31} - 1027656 q^{34} + 8708536 q^{37} + 2973768 q^{40}+ \cdots + 133878688 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 22.2403 + 12.8404i 1.39002 + 0.802527i 0.993317 0.115422i \(-0.0368219\pi\)
0.396700 + 0.917948i \(0.370155\pi\)
\(3\) 0 0
\(4\) 201.753 + 349.447i 0.788098 + 1.36503i
\(5\) −176.989 + 102.185i −0.283183 + 0.163496i −0.634863 0.772624i \(-0.718944\pi\)
0.351681 + 0.936120i \(0.385610\pi\)
\(6\) 0 0
\(7\) 1851.21 3206.39i 0.771017 1.33544i −0.165990 0.986127i \(-0.553082\pi\)
0.937006 0.349312i \(-0.113585\pi\)
\(8\) 3788.08i 0.924825i
\(9\) 0 0
\(10\) −5248.38 −0.524838
\(11\) 13951.7 + 8054.99i 0.952917 + 0.550167i 0.893986 0.448095i \(-0.147897\pi\)
0.0589310 + 0.998262i \(0.481231\pi\)
\(12\) 0 0
\(13\) 18463.8 + 31980.2i 0.646468 + 1.11972i 0.983960 + 0.178387i \(0.0570880\pi\)
−0.337492 + 0.941328i \(0.609579\pi\)
\(14\) 82342.9 47540.7i 2.14345 1.23752i
\(15\) 0 0
\(16\) 3008.19 5210.35i 0.0459014 0.0795036i
\(17\) 47526.9i 0.569041i 0.958670 + 0.284520i \(0.0918344\pi\)
−0.958670 + 0.284520i \(0.908166\pi\)
\(18\) 0 0
\(19\) 213962. 1.64181 0.820904 0.571066i \(-0.193470\pi\)
0.820904 + 0.571066i \(0.193470\pi\)
\(20\) −71416.2 41232.2i −0.446351 0.257701i
\(21\) 0 0
\(22\) 206859. + 358290.i 0.883047 + 1.52948i
\(23\) −143902. + 83082.0i −0.514229 + 0.296890i −0.734570 0.678533i \(-0.762616\pi\)
0.220342 + 0.975423i \(0.429283\pi\)
\(24\) 0 0
\(25\) −174429. + 302120.i −0.446538 + 0.773427i
\(26\) 948331.i 2.07523i
\(27\) 0 0
\(28\) 1.49395e6 2.43055
\(29\) −1.17848e6 680393.i −1.66621 0.961984i −0.969655 0.244476i \(-0.921384\pi\)
−0.696550 0.717508i \(-0.745283\pi\)
\(30\) 0 0
\(31\) 109298. + 189309.i 0.118349 + 0.204986i 0.919114 0.393993i \(-0.128907\pi\)
−0.800765 + 0.598979i \(0.795573\pi\)
\(32\) 973633. 562128.i 0.928529 0.536087i
\(33\) 0 0
\(34\) −610265. + 1.05701e6i −0.456670 + 0.790976i
\(35\) 756662.i 0.504231i
\(36\) 0 0
\(37\) 1.15091e6 0.614093 0.307046 0.951695i \(-0.400659\pi\)
0.307046 + 0.951695i \(0.400659\pi\)
\(38\) 4.75857e6 + 2.74736e6i 2.28214 + 1.31759i
\(39\) 0 0
\(40\) −387084. 670449.i −0.151205 0.261894i
\(41\) 643528. 371541.i 0.227736 0.131484i −0.381791 0.924249i \(-0.624693\pi\)
0.609527 + 0.792765i \(0.291359\pi\)
\(42\) 0 0
\(43\) 1.46517e6 2.53774e6i 0.428562 0.742291i −0.568184 0.822902i \(-0.692354\pi\)
0.996746 + 0.0806110i \(0.0256871\pi\)
\(44\) 6.50048e6i 1.73434i
\(45\) 0 0
\(46\) −4.26723e6 −0.953048
\(47\) 6.31706e6 + 3.64716e6i 1.29456 + 0.747417i 0.979460 0.201640i \(-0.0646270\pi\)
0.315105 + 0.949057i \(0.397960\pi\)
\(48\) 0 0
\(49\) −3.97156e6 6.87895e6i −0.688933 1.19327i
\(50\) −7.75870e6 + 4.47949e6i −1.24139 + 0.716718i
\(51\) 0 0
\(52\) −7.45025e6 + 1.29042e7i −1.01896 + 1.76489i
\(53\) 2.55324e6i 0.323585i −0.986825 0.161792i \(-0.948273\pi\)
0.986825 0.161792i \(-0.0517275\pi\)
\(54\) 0 0
\(55\) −3.29239e6 −0.359799
\(56\) 1.21461e7 + 7.01254e6i 1.23505 + 0.713055i
\(57\) 0 0
\(58\) −1.74731e7 3.02643e7i −1.54404 2.67435i
\(59\) −4.44279e6 + 2.56505e6i −0.366647 + 0.211684i −0.671993 0.740558i \(-0.734561\pi\)
0.305346 + 0.952242i \(0.401228\pi\)
\(60\) 0 0
\(61\) 1.34768e6 2.33425e6i 0.0973346 0.168588i −0.813246 0.581920i \(-0.802302\pi\)
0.910581 + 0.413332i \(0.135635\pi\)
\(62\) 5.61372e6i 0.379913i
\(63\) 0 0
\(64\) 2.73316e7 1.62909
\(65\) −6.53578e6 3.77343e6i −0.366137 0.211389i
\(66\) 0 0
\(67\) −319308. 553057.i −0.0158456 0.0274455i 0.857994 0.513660i \(-0.171711\pi\)
−0.873839 + 0.486214i \(0.838377\pi\)
\(68\) −1.66081e7 + 9.58869e6i −0.776755 + 0.448460i
\(69\) 0 0
\(70\) −9.71586e6 + 1.68284e7i −0.404659 + 0.700890i
\(71\) 3.72932e7i 1.46756i 0.679387 + 0.733780i \(0.262246\pi\)
−0.679387 + 0.733780i \(0.737754\pi\)
\(72\) 0 0
\(73\) −2.13898e7 −0.753209 −0.376604 0.926374i \(-0.622908\pi\)
−0.376604 + 0.926374i \(0.622908\pi\)
\(74\) 2.55965e7 + 1.47782e7i 0.853599 + 0.492826i
\(75\) 0 0
\(76\) 4.31675e7 + 7.47683e7i 1.29391 + 2.24111i
\(77\) 5.16549e7 2.98230e7i 1.46943 0.848375i
\(78\) 0 0
\(79\) 2.50309e7 4.33548e7i 0.642641 1.11309i −0.342200 0.939627i \(-0.611172\pi\)
0.984841 0.173460i \(-0.0554946\pi\)
\(80\) 1.22957e6i 0.0300187i
\(81\) 0 0
\(82\) 1.90830e7 0.422076
\(83\) −2.83851e7 1.63882e7i −0.598106 0.345317i 0.170190 0.985411i \(-0.445562\pi\)
−0.768296 + 0.640094i \(0.778895\pi\)
\(84\) 0 0
\(85\) −4.85652e6 8.41174e6i −0.0930357 0.161142i
\(86\) 6.51714e7 3.76267e7i 1.19142 0.687864i
\(87\) 0 0
\(88\) −3.05130e7 + 5.28500e7i −0.508808 + 0.881281i
\(89\) 6.85873e6i 0.109316i 0.998505 + 0.0546580i \(0.0174069\pi\)
−0.998505 + 0.0546580i \(0.982593\pi\)
\(90\) 0 0
\(91\) 1.36721e8 1.99375
\(92\) −5.80654e7 3.35241e7i −0.810525 0.467957i
\(93\) 0 0
\(94\) 9.36621e7 + 1.62228e8i 1.19964 + 2.07785i
\(95\) −3.78689e7 + 2.18636e7i −0.464931 + 0.268428i
\(96\) 0 0
\(97\) 4.14058e7 7.17170e7i 0.467708 0.810093i −0.531612 0.846988i \(-0.678413\pi\)
0.999319 + 0.0368950i \(0.0117467\pi\)
\(98\) 2.03986e8i 2.21155i
\(99\) 0 0
\(100\) −1.40766e8 −1.40766
\(101\) −1.71673e8 9.91154e7i −1.64974 0.952480i −0.977173 0.212447i \(-0.931857\pi\)
−0.672571 0.740033i \(-0.734810\pi\)
\(102\) 0 0
\(103\) −1.05983e8 1.83567e8i −0.941641 1.63097i −0.762340 0.647177i \(-0.775950\pi\)
−0.179302 0.983794i \(-0.557384\pi\)
\(104\) −1.21144e8 + 6.99423e7i −1.03554 + 0.597870i
\(105\) 0 0
\(106\) 3.27847e7 5.67847e7i 0.259685 0.449788i
\(107\) 1.63763e8i 1.24934i 0.780887 + 0.624672i \(0.214767\pi\)
−0.780887 + 0.624672i \(0.785233\pi\)
\(108\) 0 0
\(109\) −2.21458e8 −1.56887 −0.784434 0.620213i \(-0.787046\pi\)
−0.784434 + 0.620213i \(0.787046\pi\)
\(110\) −7.32236e7 4.22757e7i −0.500127 0.288748i
\(111\) 0 0
\(112\) −1.11376e7 1.92909e7i −0.0707815 0.122597i
\(113\) −6.14338e7 + 3.54688e7i −0.376785 + 0.217537i −0.676418 0.736518i \(-0.736469\pi\)
0.299634 + 0.954054i \(0.403136\pi\)
\(114\) 0 0
\(115\) 1.69794e7 2.94092e7i 0.0970804 0.168148i
\(116\) 5.49086e8i 3.03255i
\(117\) 0 0
\(118\) −1.31745e8 −0.679527
\(119\) 1.52390e8 + 8.79822e7i 0.759920 + 0.438740i
\(120\) 0 0
\(121\) 2.25863e7 + 3.91207e7i 0.105367 + 0.182501i
\(122\) 5.99455e7 3.46096e7i 0.270593 0.156227i
\(123\) 0 0
\(124\) −4.41023e7 + 7.63875e7i −0.186541 + 0.323099i
\(125\) 1.51128e8i 0.619019i
\(126\) 0 0
\(127\) −2.24298e8 −0.862205 −0.431102 0.902303i \(-0.641875\pi\)
−0.431102 + 0.902303i \(0.641875\pi\)
\(128\) 3.58613e8 + 2.07045e8i 1.33594 + 0.771303i
\(129\) 0 0
\(130\) −9.69049e7 1.67844e8i −0.339291 0.587669i
\(131\) 3.07378e8 1.77465e8i 1.04373 0.602596i 0.122841 0.992426i \(-0.460800\pi\)
0.920887 + 0.389830i \(0.127466\pi\)
\(132\) 0 0
\(133\) 3.96089e8 6.86046e8i 1.26586 2.19254i
\(134\) 1.64002e7i 0.0508662i
\(135\) 0 0
\(136\) −1.80036e8 −0.526263
\(137\) −6.45816e7 3.72862e7i −0.183327 0.105844i 0.405528 0.914083i \(-0.367088\pi\)
−0.588855 + 0.808239i \(0.700421\pi\)
\(138\) 0 0
\(139\) −4.16583e6 7.21542e6i −0.0111594 0.0193287i 0.860392 0.509633i \(-0.170219\pi\)
−0.871551 + 0.490305i \(0.836886\pi\)
\(140\) −2.64413e8 + 1.52659e8i −0.688288 + 0.397383i
\(141\) 0 0
\(142\) −4.78860e8 + 8.29410e8i −1.17776 + 2.03993i
\(143\) 5.94902e8i 1.42266i
\(144\) 0 0
\(145\) 2.78103e8 0.629121
\(146\) −4.75715e8 2.74654e8i −1.04697 0.604470i
\(147\) 0 0
\(148\) 2.32199e8 + 4.02181e8i 0.483965 + 0.838252i
\(149\) −5.91209e8 + 3.41334e8i −1.19949 + 0.692524i −0.960441 0.278484i \(-0.910168\pi\)
−0.239046 + 0.971008i \(0.576835\pi\)
\(150\) 0 0
\(151\) −6.08390e7 + 1.05376e8i −0.117024 + 0.202691i −0.918587 0.395219i \(-0.870669\pi\)
0.801563 + 0.597910i \(0.204002\pi\)
\(152\) 8.10506e8i 1.51838i
\(153\) 0 0
\(154\) 1.53176e9 2.72338
\(155\) −3.86890e7 2.23371e7i −0.0670288 0.0386991i
\(156\) 0 0
\(157\) 3.73425e7 + 6.46792e7i 0.0614618 + 0.106455i 0.895119 0.445827i \(-0.147090\pi\)
−0.833657 + 0.552282i \(0.813757\pi\)
\(158\) 1.11339e9 6.42815e8i 1.78656 1.03147i
\(159\) 0 0
\(160\) −1.14882e8 + 1.98981e8i −0.175296 + 0.303621i
\(161\) 6.15209e8i 0.915628i
\(162\) 0 0
\(163\) 5.65546e8 0.801157 0.400578 0.916262i \(-0.368809\pi\)
0.400578 + 0.916262i \(0.368809\pi\)
\(164\) 2.59667e8 + 1.49919e8i 0.358957 + 0.207244i
\(165\) 0 0
\(166\) −4.20862e8 7.28954e8i −0.554252 0.959992i
\(167\) −2.18287e8 + 1.26028e8i −0.280648 + 0.162032i −0.633717 0.773565i \(-0.718471\pi\)
0.353069 + 0.935597i \(0.385138\pi\)
\(168\) 0 0
\(169\) −2.73957e8 + 4.74507e8i −0.335842 + 0.581696i
\(170\) 2.49439e8i 0.298654i
\(171\) 0 0
\(172\) 1.18241e9 1.35099
\(173\) −2.42772e8 1.40164e8i −0.271028 0.156478i 0.358327 0.933596i \(-0.383347\pi\)
−0.629355 + 0.777118i \(0.716681\pi\)
\(174\) 0 0
\(175\) 6.45810e8 + 1.11858e9i 0.688577 + 1.19265i
\(176\) 8.39386e7 4.84620e7i 0.0874804 0.0505069i
\(177\) 0 0
\(178\) −8.80690e7 + 1.52540e8i −0.0877290 + 0.151951i
\(179\) 4.01384e8i 0.390974i 0.980706 + 0.195487i \(0.0626287\pi\)
−0.980706 + 0.195487i \(0.937371\pi\)
\(180\) 0 0
\(181\) −1.39158e9 −1.29657 −0.648284 0.761399i \(-0.724513\pi\)
−0.648284 + 0.761399i \(0.724513\pi\)
\(182\) 3.04072e9 + 1.75556e9i 2.77135 + 1.60004i
\(183\) 0 0
\(184\) −3.14721e8 5.45113e8i −0.274571 0.475571i
\(185\) −2.03698e8 + 1.17605e8i −0.173900 + 0.100401i
\(186\) 0 0
\(187\) −3.82829e8 + 6.63078e8i −0.313067 + 0.542249i
\(188\) 2.94330e9i 2.35615i
\(189\) 0 0
\(190\) −1.12295e9 −0.861683
\(191\) −1.47287e8 8.50360e7i −0.110670 0.0638953i 0.443643 0.896203i \(-0.353686\pi\)
−0.554313 + 0.832308i \(0.687019\pi\)
\(192\) 0 0
\(193\) 2.90945e8 + 5.03932e8i 0.209692 + 0.363198i 0.951618 0.307285i \(-0.0994205\pi\)
−0.741925 + 0.670483i \(0.766087\pi\)
\(194\) 1.84175e9 1.06334e9i 1.30024 0.750695i
\(195\) 0 0
\(196\) 1.60255e9 2.77570e9i 1.08589 1.88082i
\(197\) 1.19043e9i 0.790385i −0.918598 0.395193i \(-0.870678\pi\)
0.918598 0.395193i \(-0.129322\pi\)
\(198\) 0 0
\(199\) −1.88525e9 −1.20214 −0.601071 0.799196i \(-0.705259\pi\)
−0.601071 + 0.799196i \(0.705259\pi\)
\(200\) −1.14446e9 6.60752e8i −0.715285 0.412970i
\(201\) 0 0
\(202\) −2.54537e9 4.40871e9i −1.52878 2.64793i
\(203\) −4.36321e9 + 2.51910e9i −2.56934 + 1.48341i
\(204\) 0 0
\(205\) −7.59316e7 + 1.31517e8i −0.0429939 + 0.0744677i
\(206\) 5.44345e9i 3.02277i
\(207\) 0 0
\(208\) 2.22171e8 0.118695
\(209\) 2.98512e9 + 1.72346e9i 1.56451 + 0.903268i
\(210\) 0 0
\(211\) 1.98576e8 + 3.43944e8i 0.100184 + 0.173524i 0.911760 0.410723i \(-0.134724\pi\)
−0.811576 + 0.584246i \(0.801390\pi\)
\(212\) 8.92220e8 5.15123e8i 0.441701 0.255016i
\(213\) 0 0
\(214\) −2.10279e9 + 3.64214e9i −1.00263 + 1.73661i
\(215\) 5.98871e8i 0.280272i
\(216\) 0 0
\(217\) 8.09333e8 0.364996
\(218\) −4.92530e9 2.84362e9i −2.18075 1.25906i
\(219\) 0 0
\(220\) −6.64249e8 1.15051e9i −0.283557 0.491135i
\(221\) −1.51992e9 + 8.77526e8i −0.637164 + 0.367867i
\(222\) 0 0
\(223\) 9.30529e8 1.61172e9i 0.376279 0.651735i −0.614238 0.789121i \(-0.710537\pi\)
0.990518 + 0.137386i \(0.0438699\pi\)
\(224\) 4.16247e9i 1.65333i
\(225\) 0 0
\(226\) −1.82174e9 −0.698316
\(227\) −1.89595e9 1.09463e9i −0.714041 0.412252i 0.0985143 0.995136i \(-0.468591\pi\)
−0.812556 + 0.582884i \(0.801924\pi\)
\(228\) 0 0
\(229\) 1.07525e9 + 1.86238e9i 0.390990 + 0.677215i 0.992580 0.121590i \(-0.0387993\pi\)
−0.601590 + 0.798805i \(0.705466\pi\)
\(230\) 7.55254e8 4.36046e8i 0.269887 0.155819i
\(231\) 0 0
\(232\) 2.57739e9 4.46416e9i 0.889667 1.54095i
\(233\) 3.41313e9i 1.15805i 0.815308 + 0.579027i \(0.196567\pi\)
−0.815308 + 0.579027i \(0.803433\pi\)
\(234\) 0 0
\(235\) −1.49074e9 −0.488798
\(236\) −1.79269e9 1.03501e9i −0.577907 0.333655i
\(237\) 0 0
\(238\) 2.25946e9 + 3.91350e9i 0.704201 + 1.21971i
\(239\) 2.84547e9 1.64283e9i 0.872091 0.503502i 0.00404838 0.999992i \(-0.498711\pi\)
0.868042 + 0.496490i \(0.165378\pi\)
\(240\) 0 0
\(241\) −2.01741e9 + 3.49426e9i −0.598035 + 1.03583i 0.395076 + 0.918648i \(0.370718\pi\)
−0.993111 + 0.117178i \(0.962615\pi\)
\(242\) 1.16007e9i 0.338239i
\(243\) 0 0
\(244\) 1.08759e9 0.306837
\(245\) 1.40585e9 + 8.11666e8i 0.390188 + 0.225275i
\(246\) 0 0
\(247\) 3.95055e9 + 6.84255e9i 1.06138 + 1.83836i
\(248\) −7.17119e8 + 4.14029e8i −0.189577 + 0.109452i
\(249\) 0 0
\(250\) 1.94054e9 3.36112e9i 0.496779 0.860447i
\(251\) 4.69477e9i 1.18282i −0.806371 0.591411i \(-0.798571\pi\)
0.806371 0.591411i \(-0.201429\pi\)
\(252\) 0 0
\(253\) −2.67690e9 −0.653356
\(254\) −4.98845e9 2.88008e9i −1.19848 0.691942i
\(255\) 0 0
\(256\) 1.81865e9 + 3.14999e9i 0.423437 + 0.733414i
\(257\) 1.10426e8 6.37546e7i 0.0253128 0.0146143i −0.487290 0.873240i \(-0.662015\pi\)
0.512603 + 0.858626i \(0.328681\pi\)
\(258\) 0 0
\(259\) 2.13057e9 3.69026e9i 0.473476 0.820084i
\(260\) 3.04521e9i 0.666382i
\(261\) 0 0
\(262\) 9.11488e9 1.93440
\(263\) 2.01039e9 + 1.16070e9i 0.420201 + 0.242603i 0.695163 0.718852i \(-0.255332\pi\)
−0.274962 + 0.961455i \(0.588665\pi\)
\(264\) 0 0
\(265\) 2.60902e8 + 4.51895e8i 0.0529046 + 0.0916335i
\(266\) 1.76182e10 1.01719e10i 3.51914 2.03177i
\(267\) 0 0
\(268\) 1.28843e8 2.23162e8i 0.0249758 0.0432594i
\(269\) 7.86019e9i 1.50115i 0.660785 + 0.750575i \(0.270223\pi\)
−0.660785 + 0.750575i \(0.729777\pi\)
\(270\) 0 0
\(271\) 2.14381e9 0.397474 0.198737 0.980053i \(-0.436316\pi\)
0.198737 + 0.980053i \(0.436316\pi\)
\(272\) 2.47631e8 + 1.42970e8i 0.0452408 + 0.0261198i
\(273\) 0 0
\(274\) −9.57541e8 1.65851e9i −0.169885 0.294249i
\(275\) −4.86715e9 + 2.81005e9i −0.851028 + 0.491341i
\(276\) 0 0
\(277\) −3.87519e8 + 6.71202e8i −0.0658224 + 0.114008i −0.897059 0.441912i \(-0.854300\pi\)
0.831236 + 0.555920i \(0.187634\pi\)
\(278\) 2.13964e8i 0.0358229i
\(279\) 0 0
\(280\) −2.86630e9 −0.466325
\(281\) −6.89145e9 3.97878e9i −1.10531 0.638153i −0.167702 0.985838i \(-0.553634\pi\)
−0.937611 + 0.347685i \(0.886968\pi\)
\(282\) 0 0
\(283\) −9.79004e8 1.69568e9i −0.152630 0.264362i 0.779564 0.626323i \(-0.215441\pi\)
−0.932193 + 0.361961i \(0.882107\pi\)
\(284\) −1.30320e10 + 7.52401e9i −2.00326 + 1.15658i
\(285\) 0 0
\(286\) −7.63880e9 + 1.32308e10i −1.14172 + 1.97752i
\(287\) 2.75120e9i 0.405504i
\(288\) 0 0
\(289\) 4.71695e9 0.676192
\(290\) 6.18509e9 + 3.57096e9i 0.874488 + 0.504886i
\(291\) 0 0
\(292\) −4.31546e9 7.47459e9i −0.593602 1.02815i
\(293\) −1.07304e10 + 6.19523e9i −1.45595 + 0.840595i −0.998809 0.0487979i \(-0.984461\pi\)
−0.457144 + 0.889393i \(0.651128\pi\)
\(294\) 0 0
\(295\) 5.24217e8 9.07971e8i 0.0692187 0.119890i
\(296\) 4.35974e9i 0.567928i
\(297\) 0 0
\(298\) −1.75315e10 −2.22308
\(299\) −5.31396e9 3.06801e9i −0.664865 0.383860i
\(300\) 0 0
\(301\) −5.42467e9 9.39580e9i −0.660856 1.14464i
\(302\) −2.70615e9 + 1.56240e9i −0.325330 + 0.187829i
\(303\) 0 0
\(304\) 6.43639e8 1.11482e9i 0.0753613 0.130530i
\(305\) 5.50849e8i 0.0636551i
\(306\) 0 0
\(307\) −3.61263e8 −0.0406696 −0.0203348 0.999793i \(-0.506473\pi\)
−0.0203348 + 0.999793i \(0.506473\pi\)
\(308\) 2.08431e10 + 1.20338e10i 2.31611 + 1.33721i
\(309\) 0 0
\(310\) −5.73636e8 9.93567e8i −0.0621141 0.107585i
\(311\) 4.51507e9 2.60677e9i 0.482639 0.278652i −0.238876 0.971050i \(-0.576779\pi\)
0.721516 + 0.692398i \(0.243446\pi\)
\(312\) 0 0
\(313\) 7.25733e9 1.25701e10i 0.756136 1.30967i −0.188672 0.982040i \(-0.560418\pi\)
0.944808 0.327625i \(-0.106248\pi\)
\(314\) 1.91798e9i 0.197299i
\(315\) 0 0
\(316\) 2.02003e10 2.02586
\(317\) 9.91318e9 + 5.72338e9i 0.981694 + 0.566781i 0.902781 0.430100i \(-0.141522\pi\)
0.0789126 + 0.996882i \(0.474855\pi\)
\(318\) 0 0
\(319\) −1.09611e10 1.89852e10i −1.05850 1.83338i
\(320\) −4.83740e9 + 2.79287e9i −0.461331 + 0.266349i
\(321\) 0 0
\(322\) −7.89955e9 + 1.36824e10i −0.734816 + 1.27274i
\(323\) 1.01689e10i 0.934256i
\(324\) 0 0
\(325\) −1.28825e10 −1.15469
\(326\) 1.25779e10 + 7.26185e9i 1.11362 + 0.642950i
\(327\) 0 0
\(328\) 1.40743e9 + 2.43774e9i 0.121599 + 0.210616i
\(329\) 2.33884e10 1.35033e10i 1.99626 1.15254i
\(330\) 0 0
\(331\) −6.60298e9 + 1.14367e10i −0.550083 + 0.952771i 0.448185 + 0.893941i \(0.352071\pi\)
−0.998268 + 0.0588306i \(0.981263\pi\)
\(332\) 1.32254e10i 1.08857i
\(333\) 0 0
\(334\) −6.47301e9 −0.520140
\(335\) 1.13028e8 + 6.52567e7i 0.00897442 + 0.00518139i
\(336\) 0 0
\(337\) 5.96753e9 + 1.03361e10i 0.462674 + 0.801375i 0.999093 0.0425770i \(-0.0135568\pi\)
−0.536419 + 0.843952i \(0.680223\pi\)
\(338\) −1.21857e10 + 7.03544e9i −0.933653 + 0.539045i
\(339\) 0 0
\(340\) 1.95964e9 3.39419e9i 0.146642 0.253992i
\(341\) 3.52157e9i 0.260447i
\(342\) 0 0
\(343\) −8.06507e9 −0.582682
\(344\) 9.61318e9 + 5.55017e9i 0.686489 + 0.396344i
\(345\) 0 0
\(346\) −3.59954e9 6.23458e9i −0.251155 0.435014i
\(347\) 7.95396e9 4.59222e9i 0.548612 0.316741i −0.199950 0.979806i \(-0.564078\pi\)
0.748562 + 0.663065i \(0.230745\pi\)
\(348\) 0 0
\(349\) 1.04434e10 1.80886e10i 0.703950 1.21928i −0.263119 0.964763i \(-0.584751\pi\)
0.967069 0.254514i \(-0.0819155\pi\)
\(350\) 3.31699e10i 2.21041i
\(351\) 0 0
\(352\) 1.81117e10 1.17975
\(353\) −9.50403e9 5.48716e9i −0.612081 0.353385i 0.161698 0.986840i \(-0.448303\pi\)
−0.773780 + 0.633455i \(0.781636\pi\)
\(354\) 0 0
\(355\) −3.81079e9 6.60049e9i −0.239940 0.415588i
\(356\) −2.39676e9 + 1.38377e9i −0.149219 + 0.0861517i
\(357\) 0 0
\(358\) −5.15394e9 + 8.92688e9i −0.313767 + 0.543460i
\(359\) 1.19761e10i 0.721001i 0.932759 + 0.360501i \(0.117394\pi\)
−0.932759 + 0.360501i \(0.882606\pi\)
\(360\) 0 0
\(361\) 2.87962e10 1.69553
\(362\) −3.09492e10 1.78685e10i −1.80225 1.04053i
\(363\) 0 0
\(364\) 2.75840e10 + 4.77768e10i 1.57127 + 2.72152i
\(365\) 3.78576e9 2.18571e9i 0.213296 0.123146i
\(366\) 0 0
\(367\) 3.11074e9 5.38796e9i 0.171474 0.297002i −0.767461 0.641096i \(-0.778480\pi\)
0.938936 + 0.344093i \(0.111814\pi\)
\(368\) 9.99707e8i 0.0545107i
\(369\) 0 0
\(370\) −6.04041e9 −0.322299
\(371\) −8.18668e9 4.72658e9i −0.432128 0.249489i
\(372\) 0 0
\(373\) 6.15140e9 + 1.06545e10i 0.317789 + 0.550427i 0.980026 0.198867i \(-0.0637263\pi\)
−0.662237 + 0.749294i \(0.730393\pi\)
\(374\) −1.70284e10 + 9.83136e9i −0.870338 + 0.502490i
\(375\) 0 0
\(376\) −1.38157e10 + 2.39296e10i −0.691230 + 1.19725i
\(377\) 5.02505e10i 2.48757i
\(378\) 0 0
\(379\) 2.26268e10 1.09665 0.548324 0.836266i \(-0.315266\pi\)
0.548324 + 0.836266i \(0.315266\pi\)
\(380\) −1.52804e10 8.82212e9i −0.732823 0.423095i
\(381\) 0 0
\(382\) −2.18380e9 3.78245e9i −0.102555 0.177631i
\(383\) −9.94555e9 + 5.74206e9i −0.462204 + 0.266854i −0.712971 0.701194i \(-0.752651\pi\)
0.250767 + 0.968048i \(0.419317\pi\)
\(384\) 0 0
\(385\) −6.09490e9 + 1.05567e10i −0.277411 + 0.480490i
\(386\) 1.49435e10i 0.673134i
\(387\) 0 0
\(388\) 3.34150e10 1.47440
\(389\) −6.51932e8 3.76393e8i −0.0284711 0.0164378i 0.485697 0.874127i \(-0.338566\pi\)
−0.514168 + 0.857690i \(0.671899\pi\)
\(390\) 0 0
\(391\) −3.94863e9 6.83922e9i −0.168943 0.292617i
\(392\) 2.60580e10 1.50446e10i 1.10356 0.637142i
\(393\) 0 0
\(394\) 1.52856e10 2.64755e10i 0.634305 1.09865i
\(395\) 1.02311e10i 0.420276i
\(396\) 0 0
\(397\) −5.67666e9 −0.228524 −0.114262 0.993451i \(-0.536450\pi\)
−0.114262 + 0.993451i \(0.536450\pi\)
\(398\) −4.19284e10 2.42074e10i −1.67100 0.964751i
\(399\) 0 0
\(400\) 1.04943e9 + 1.81767e9i 0.0409935 + 0.0710028i
\(401\) 3.63092e10 2.09631e10i 1.40423 0.810735i 0.409410 0.912350i \(-0.365734\pi\)
0.994824 + 0.101615i \(0.0324011\pi\)
\(402\) 0 0
\(403\) −4.03610e9 + 6.99073e9i −0.153018 + 0.265034i
\(404\) 7.99874e10i 3.00259i
\(405\) 0 0
\(406\) −1.29385e11 −4.76191
\(407\) 1.60571e10 + 9.27056e9i 0.585179 + 0.337853i
\(408\) 0 0
\(409\) −1.25068e10 2.16625e10i −0.446946 0.774133i 0.551240 0.834347i \(-0.314155\pi\)
−0.998185 + 0.0602143i \(0.980822\pi\)
\(410\) −3.37748e9 + 1.94999e9i −0.119525 + 0.0690075i
\(411\) 0 0
\(412\) 4.27646e10 7.40705e10i 1.48421 2.57073i
\(413\) 1.89938e10i 0.652846i
\(414\) 0 0
\(415\) 6.69848e9 0.225831
\(416\) 3.59539e10 + 2.07580e10i 1.20053 + 0.693126i
\(417\) 0 0
\(418\) 4.42600e10 + 7.66605e10i 1.44979 + 2.51112i
\(419\) 4.37377e9 2.52520e9i 0.141906 0.0819294i −0.427366 0.904079i \(-0.640558\pi\)
0.569272 + 0.822149i \(0.307225\pi\)
\(420\) 0 0
\(421\) −7.11594e9 + 1.23252e10i −0.226519 + 0.392342i −0.956774 0.290832i \(-0.906068\pi\)
0.730255 + 0.683174i \(0.239401\pi\)
\(422\) 1.01992e10i 0.321601i
\(423\) 0 0
\(424\) 9.67187e9 0.299259
\(425\) −1.43588e10 8.29007e9i −0.440112 0.254099i
\(426\) 0 0
\(427\) −4.98968e9 8.64237e9i −0.150093 0.259969i
\(428\) −5.72266e10 + 3.30398e10i −1.70539 + 0.984605i
\(429\) 0 0
\(430\) −7.68975e9 + 1.33190e10i −0.224925 + 0.389582i
\(431\) 3.72124e10i 1.07840i −0.842179 0.539199i \(-0.818727\pi\)
0.842179 0.539199i \(-0.181273\pi\)
\(432\) 0 0
\(433\) −3.76284e10 −1.07044 −0.535222 0.844711i \(-0.679772\pi\)
−0.535222 + 0.844711i \(0.679772\pi\)
\(434\) 1.79998e10 + 1.03922e10i 0.507351 + 0.292919i
\(435\) 0 0
\(436\) −4.46799e10 7.73879e10i −1.23642 2.14154i
\(437\) −3.07896e10 + 1.77764e10i −0.844264 + 0.487436i
\(438\) 0 0
\(439\) −2.68277e9 + 4.64669e9i −0.0722312 + 0.125108i −0.899879 0.436140i \(-0.856345\pi\)
0.827648 + 0.561248i \(0.189679\pi\)
\(440\) 1.24718e10i 0.332751i
\(441\) 0 0
\(442\) −4.50712e10 −1.18089
\(443\) 2.08109e10 + 1.20152e10i 0.540350 + 0.311971i 0.745221 0.666818i \(-0.232344\pi\)
−0.204871 + 0.978789i \(0.565677\pi\)
\(444\) 0 0
\(445\) −7.00857e8 1.21392e9i −0.0178727 0.0309564i
\(446\) 4.13904e10 2.38968e10i 1.04607 0.603949i
\(447\) 0 0
\(448\) 5.05966e10 8.76359e10i 1.25606 2.17555i
\(449\) 7.28050e10i 1.79133i −0.444729 0.895665i \(-0.646700\pi\)
0.444729 0.895665i \(-0.353300\pi\)
\(450\) 0 0
\(451\) 1.19710e10 0.289351
\(452\) −2.47889e10 1.43119e10i −0.593886 0.342881i
\(453\) 0 0
\(454\) −2.81110e10 4.86896e10i −0.661686 1.14607i
\(455\) −2.41982e10 + 1.39708e10i −0.564595 + 0.325969i
\(456\) 0 0
\(457\) −3.09877e10 + 5.36723e10i −0.710436 + 1.23051i 0.254258 + 0.967137i \(0.418169\pi\)
−0.964694 + 0.263375i \(0.915164\pi\)
\(458\) 5.52265e10i 1.25512i
\(459\) 0 0
\(460\) 1.37026e10 0.306035
\(461\) 1.04284e10 + 6.02087e9i 0.230896 + 0.133308i 0.610985 0.791642i \(-0.290773\pi\)
−0.380090 + 0.924950i \(0.624107\pi\)
\(462\) 0 0
\(463\) 2.96311e9 + 5.13225e9i 0.0644797 + 0.111682i 0.896463 0.443118i \(-0.146128\pi\)
−0.831983 + 0.554801i \(0.812795\pi\)
\(464\) −7.09017e9 + 4.09351e9i −0.152962 + 0.0883129i
\(465\) 0 0
\(466\) −4.38260e10 + 7.59089e10i −0.929369 + 1.60971i
\(467\) 5.80782e10i 1.22109i −0.791983 0.610543i \(-0.790951\pi\)
0.791983 0.610543i \(-0.209049\pi\)
\(468\) 0 0
\(469\) −2.36442e9 −0.0488690
\(470\) −3.31544e10 1.91417e10i −0.679437 0.392273i
\(471\) 0 0
\(472\) −9.71661e9 1.68297e10i −0.195770 0.339084i
\(473\) 4.08830e10 2.36038e10i 0.816767 0.471561i
\(474\) 0 0
\(475\) −3.73212e10 + 6.46422e10i −0.733130 + 1.26982i
\(476\) 7.10027e10i 1.38308i
\(477\) 0 0
\(478\) 8.43786e10 1.61629
\(479\) −3.99551e10 2.30681e10i −0.758980 0.438197i 0.0699495 0.997551i \(-0.477716\pi\)
−0.828929 + 0.559353i \(0.811050\pi\)
\(480\) 0 0
\(481\) 2.12501e10 + 3.68063e10i 0.396991 + 0.687609i
\(482\) −8.97356e10 + 5.18088e10i −1.66256 + 0.959877i
\(483\) 0 0
\(484\) −9.11372e9 + 1.57854e10i −0.166079 + 0.287657i
\(485\) 1.69242e10i 0.305872i
\(486\) 0 0
\(487\) 8.55813e10 1.52147 0.760735 0.649063i \(-0.224839\pi\)
0.760735 + 0.649063i \(0.224839\pi\)
\(488\) 8.84233e9 + 5.10512e9i 0.155915 + 0.0900174i
\(489\) 0 0
\(490\) 2.08443e10 + 3.61033e10i 0.361578 + 0.626272i
\(491\) 2.58098e10 1.49013e10i 0.444077 0.256388i −0.261248 0.965272i \(-0.584134\pi\)
0.705326 + 0.708884i \(0.250801\pi\)
\(492\) 0 0
\(493\) 3.23370e10 5.60093e10i 0.547408 0.948139i
\(494\) 2.02907e11i 3.40713i
\(495\) 0 0
\(496\) 1.31516e9 0.0217295
\(497\) 1.19576e11 + 6.90375e10i 1.95984 + 1.13151i
\(498\) 0 0
\(499\) 2.57266e10 + 4.45598e10i 0.414936 + 0.718690i 0.995422 0.0955806i \(-0.0304708\pi\)
−0.580486 + 0.814270i \(0.697137\pi\)
\(500\) 5.28111e10 3.04905e10i 0.844977 0.487848i
\(501\) 0 0
\(502\) 6.02828e10 1.04413e11i 0.949246 1.64414i
\(503\) 1.97425e10i 0.308412i 0.988039 + 0.154206i \(0.0492819\pi\)
−0.988039 + 0.154206i \(0.950718\pi\)
\(504\) 0 0
\(505\) 4.05123e10 0.622905
\(506\) −5.95350e10 3.43725e10i −0.908176 0.524336i
\(507\) 0 0
\(508\) −4.52528e10 7.83801e10i −0.679502 1.17693i
\(509\) 2.46734e10 1.42452e10i 0.367586 0.212226i −0.304817 0.952411i \(-0.598595\pi\)
0.672403 + 0.740185i \(0.265262\pi\)
\(510\) 0 0
\(511\) −3.95970e10 + 6.85841e10i −0.580736 + 1.00586i
\(512\) 1.25983e10i 0.183330i
\(513\) 0 0
\(514\) 3.27455e9 0.0469136
\(515\) 3.75155e10 + 2.16596e10i 0.533313 + 0.307908i
\(516\) 0 0
\(517\) 5.87557e10 + 1.01768e11i 0.822408 + 1.42445i
\(518\) 9.47691e10 5.47150e10i 1.31628 0.759954i
\(519\) 0 0
\(520\) 1.42941e10 2.47581e10i 0.195498 0.338613i
\(521\) 1.19310e11i 1.61929i 0.586919 + 0.809646i \(0.300341\pi\)
−0.586919 + 0.809646i \(0.699659\pi\)
\(522\) 0 0
\(523\) −8.33461e10 −1.11398 −0.556992 0.830518i \(-0.688044\pi\)
−0.556992 + 0.830518i \(0.688044\pi\)
\(524\) 1.24029e11 + 7.16081e10i 1.64512 + 0.949810i
\(525\) 0 0
\(526\) 2.98077e10 + 5.16285e10i 0.389391 + 0.674445i
\(527\) −8.99728e9 + 5.19458e9i −0.116646 + 0.0673454i
\(528\) 0 0
\(529\) −2.53503e10 + 4.39079e10i −0.323713 + 0.560687i
\(530\) 1.34004e10i 0.169829i
\(531\) 0 0
\(532\) 3.19648e11 3.99049
\(533\) 2.37639e10 + 1.37201e10i 0.294448 + 0.170000i
\(534\) 0 0
\(535\) −1.67341e10 2.89843e10i −0.204262 0.353792i
\(536\) 2.09503e9 1.20956e9i 0.0253822 0.0146544i
\(537\) 0 0
\(538\) −1.00928e11 + 1.74813e11i −1.20471 + 2.08662i
\(539\) 1.27964e11i 1.51611i
\(540\) 0 0
\(541\) −1.38210e11 −1.61343 −0.806717 0.590937i \(-0.798758\pi\)
−0.806717 + 0.590937i \(0.798758\pi\)
\(542\) 4.76789e10 + 2.75274e10i 0.552495 + 0.318983i
\(543\) 0 0
\(544\) 2.67162e10 + 4.62737e10i 0.305055 + 0.528371i
\(545\) 3.91957e10 2.26297e10i 0.444276 0.256503i
\(546\) 0 0
\(547\) 3.95682e10 6.85341e10i 0.441974 0.765522i −0.555862 0.831275i \(-0.687612\pi\)
0.997836 + 0.0657529i \(0.0209449\pi\)
\(548\) 3.00904e10i 0.333661i
\(549\) 0 0
\(550\) −1.44329e11 −1.57726
\(551\) −2.52149e11 1.45578e11i −2.73559 1.57939i
\(552\) 0 0
\(553\) −9.26750e10 1.60518e11i −0.990974 1.71642i
\(554\) −1.72370e10 + 9.95182e9i −0.182989 + 0.105648i
\(555\) 0 0
\(556\) 1.68094e9 2.91147e9i 0.0175894 0.0304658i
\(557\) 1.12395e11i 1.16769i 0.811865 + 0.583846i \(0.198453\pi\)
−0.811865 + 0.583846i \(0.801547\pi\)
\(558\) 0 0
\(559\) 1.08210e11 1.10821
\(560\) 3.94247e9 + 2.27619e9i 0.0400882 + 0.0231449i
\(561\) 0 0
\(562\) −1.02178e11 1.76978e11i −1.02427 1.77409i
\(563\) −1.03943e11 + 6.00113e10i −1.03457 + 0.597310i −0.918291 0.395906i \(-0.870430\pi\)
−0.116280 + 0.993216i \(0.537097\pi\)
\(564\) 0 0
\(565\) 7.24874e9 1.25552e10i 0.0711326 0.123205i
\(566\) 5.02833e10i 0.489957i
\(567\) 0 0
\(568\) −1.41270e11 −1.35724
\(569\) 1.32890e11 + 7.67240e10i 1.26778 + 0.731951i 0.974567 0.224097i \(-0.0719432\pi\)
0.293210 + 0.956048i \(0.405277\pi\)
\(570\) 0 0
\(571\) −2.33391e10 4.04245e10i −0.219553 0.380277i 0.735118 0.677939i \(-0.237127\pi\)
−0.954671 + 0.297662i \(0.903793\pi\)
\(572\) −2.07887e11 + 1.20023e11i −1.94197 + 1.12120i
\(573\) 0 0
\(574\) 3.53266e10 6.11875e10i 0.325428 0.563657i
\(575\) 5.79677e10i 0.530291i
\(576\) 0 0
\(577\) 9.25710e10 0.835164 0.417582 0.908639i \(-0.362878\pi\)
0.417582 + 0.908639i \(0.362878\pi\)
\(578\) 1.04906e11 + 6.05677e10i 0.939919 + 0.542662i
\(579\) 0 0
\(580\) 5.61082e10 + 9.71822e10i 0.495809 + 0.858766i
\(581\) −1.05094e11 + 6.06759e10i −0.922300 + 0.532490i
\(582\) 0 0
\(583\) 2.05663e10 3.56219e10i 0.178025 0.308349i
\(584\) 8.10263e10i 0.696586i
\(585\) 0 0
\(586\) −3.18197e11 −2.69840
\(587\) −6.72211e10 3.88101e10i −0.566178 0.326883i 0.189443 0.981892i \(-0.439332\pi\)
−0.755621 + 0.655009i \(0.772665\pi\)
\(588\) 0 0
\(589\) 2.33856e10 + 4.05050e10i 0.194306 + 0.336548i
\(590\) 2.33175e10 1.34623e10i 0.192430 0.111100i
\(591\) 0 0
\(592\) 3.46216e9 5.99663e9i 0.0281877 0.0488226i
\(593\) 2.09190e11i 1.69169i −0.533427 0.845846i \(-0.679096\pi\)
0.533427 0.845846i \(-0.320904\pi\)
\(594\) 0 0
\(595\) −3.59618e10 −0.286928
\(596\) −2.38556e11 1.37731e11i −1.89063 1.09155i
\(597\) 0 0
\(598\) −7.87892e10 1.36467e11i −0.616116 1.06714i
\(599\) −8.07861e10 + 4.66419e10i −0.627523 + 0.362300i −0.779792 0.626039i \(-0.784675\pi\)
0.152269 + 0.988339i \(0.451342\pi\)
\(600\) 0 0
\(601\) 4.06269e10 7.03678e10i 0.311398 0.539357i −0.667267 0.744818i \(-0.732536\pi\)
0.978665 + 0.205461i \(0.0658695\pi\)
\(602\) 2.78620e11i 2.12142i
\(603\) 0 0
\(604\) −4.90978e10 −0.368905
\(605\) −7.99507e9 4.61596e9i −0.0596762 0.0344540i
\(606\) 0 0
\(607\) −2.06162e10 3.57084e10i −0.151864 0.263036i 0.780049 0.625719i \(-0.215194\pi\)
−0.931913 + 0.362683i \(0.881861\pi\)
\(608\) 2.08321e11 1.20274e11i 1.52447 0.880151i
\(609\) 0 0
\(610\) −7.07313e9 + 1.22510e10i −0.0510849 + 0.0884816i
\(611\) 2.69361e11i 1.93273i
\(612\) 0 0
\(613\) 2.01264e10 0.142536 0.0712681 0.997457i \(-0.477295\pi\)
0.0712681 + 0.997457i \(0.477295\pi\)
\(614\) −8.03459e9 4.63877e9i −0.0565315 0.0326385i
\(615\) 0 0
\(616\) 1.12972e11 + 1.95673e11i 0.784599 + 1.35896i
\(617\) 1.18902e11 6.86484e10i 0.820446 0.473685i −0.0301240 0.999546i \(-0.509590\pi\)
0.850570 + 0.525861i \(0.176257\pi\)
\(618\) 0 0
\(619\) 4.85200e10 8.40391e10i 0.330490 0.572425i −0.652118 0.758117i \(-0.726119\pi\)
0.982608 + 0.185692i \(0.0594527\pi\)
\(620\) 1.80263e10i 0.121995i
\(621\) 0 0
\(622\) 1.33888e11 0.894502
\(623\) 2.19918e10 + 1.26970e10i 0.145985 + 0.0842845i
\(624\) 0 0
\(625\) −5.26934e10 9.12677e10i −0.345332 0.598132i
\(626\) 3.22810e11 1.86375e11i 2.10208 1.21364i
\(627\) 0 0
\(628\) −1.50679e10 + 2.60984e10i −0.0968758 + 0.167794i
\(629\) 5.46991e10i 0.349444i
\(630\) 0 0
\(631\) −2.86142e11 −1.80495 −0.902473 0.430747i \(-0.858250\pi\)
−0.902473 + 0.430747i \(0.858250\pi\)
\(632\) 1.64232e11 + 9.48192e10i 1.02941 + 0.594330i
\(633\) 0 0
\(634\) 1.46981e11 + 2.54579e11i 0.909714 + 1.57567i
\(635\) 3.96983e10 2.29198e10i 0.244161 0.140967i
\(636\) 0 0
\(637\) 1.46660e11 2.54023e11i 0.890747 1.54282i
\(638\) 5.62982e11i 3.39791i
\(639\) 0 0
\(640\) −8.46274e10 −0.504418
\(641\) 4.96090e10 + 2.86417e10i 0.293852 + 0.169655i 0.639678 0.768643i \(-0.279068\pi\)
−0.345826 + 0.938299i \(0.612401\pi\)
\(642\) 0 0
\(643\) 6.72328e10 + 1.16451e11i 0.393312 + 0.681236i 0.992884 0.119084i \(-0.0379959\pi\)
−0.599572 + 0.800321i \(0.704663\pi\)
\(644\) −2.14983e11 + 1.24120e11i −1.24986 + 0.721605i
\(645\) 0 0
\(646\) −1.30574e11 + 2.26160e11i −0.749765 + 1.29863i
\(647\) 2.98401e11i 1.70288i 0.524454 + 0.851439i \(0.324269\pi\)
−0.524454 + 0.851439i \(0.675731\pi\)
\(648\) 0 0
\(649\) −8.26457e10 −0.465845
\(650\) −2.86510e11 1.65417e11i −1.60504 0.926671i
\(651\) 0 0
\(652\) 1.14101e11 + 1.97628e11i 0.631390 + 1.09360i
\(653\) 8.81880e10 5.09154e10i 0.485017 0.280025i −0.237488 0.971390i \(-0.576324\pi\)
0.722505 + 0.691366i \(0.242991\pi\)
\(654\) 0 0
\(655\) −3.62683e10 + 6.28186e10i −0.197044 + 0.341290i
\(656\) 4.47067e9i 0.0241411i
\(657\) 0 0
\(658\) 6.93553e11 3.69978
\(659\) −2.09636e11 1.21033e11i −1.11154 0.641746i −0.172310 0.985043i \(-0.555123\pi\)
−0.939227 + 0.343296i \(0.888456\pi\)
\(660\) 0 0
\(661\) 1.53401e11 + 2.65699e11i 0.803570 + 1.39182i 0.917252 + 0.398307i \(0.130402\pi\)
−0.113682 + 0.993517i \(0.536265\pi\)
\(662\) −2.93704e11 + 1.69570e11i −1.52925 + 0.882912i
\(663\) 0 0
\(664\) 6.20797e10 1.07525e11i 0.319358 0.553143i
\(665\) 1.61897e11i 0.827850i
\(666\) 0 0
\(667\) 2.26114e11 1.14241
\(668\) −8.80800e10 5.08530e10i −0.442356 0.255394i
\(669\) 0 0
\(670\) 1.67585e9 + 2.90265e9i 0.00831640 + 0.0144044i
\(671\) 3.76047e10 2.17111e10i 0.185504 0.107101i
\(672\) 0 0
\(673\) 8.97126e10 1.55387e11i 0.437314 0.757450i −0.560168 0.828379i \(-0.689263\pi\)
0.997481 + 0.0709297i \(0.0225966\pi\)
\(674\) 3.06502e11i 1.48523i
\(675\) 0 0
\(676\) −2.21086e11 −1.05871
\(677\) −1.27199e11 7.34384e10i −0.605521 0.349597i 0.165690 0.986178i \(-0.447015\pi\)
−0.771210 + 0.636580i \(0.780348\pi\)
\(678\) 0 0
\(679\) −1.53302e11 2.65526e11i −0.721220 1.24919i
\(680\) 3.18644e10 1.83969e10i 0.149029 0.0860417i
\(681\) 0 0
\(682\) −4.52185e10 + 7.83207e10i −0.209015 + 0.362025i
\(683\) 5.39354e10i 0.247851i 0.992291 + 0.123926i \(0.0395485\pi\)
−0.992291 + 0.123926i \(0.960452\pi\)
\(684\) 0 0
\(685\) 1.52403e10 0.0692200
\(686\) −1.79369e11 1.03559e11i −0.809938 0.467618i
\(687\) 0 0
\(688\) −8.81501e9 1.52681e10i −0.0393432 0.0681444i
\(689\) 8.16531e10 4.71424e10i 0.362323 0.209187i
\(690\) 0 0
\(691\) −5.19287e10 + 8.99432e10i −0.227769 + 0.394508i −0.957147 0.289603i \(-0.906477\pi\)
0.729377 + 0.684112i \(0.239810\pi\)
\(692\) 1.13114e11i 0.493279i
\(693\) 0 0
\(694\) 2.35864e11 1.01677
\(695\) 1.47461e9 + 8.51367e8i 0.00632031 + 0.00364903i
\(696\) 0 0
\(697\) 1.76582e10 + 3.05849e10i 0.0748195 + 0.129591i
\(698\) 4.64530e11 2.68196e11i 1.95700 1.12988i
\(699\) 0 0
\(700\) −2.60588e11 + 4.51352e11i −1.08533 + 1.87985i
\(701\) 1.65918e11i 0.687103i 0.939134 + 0.343552i \(0.111630\pi\)
−0.939134 + 0.343552i \(0.888370\pi\)
\(702\) 0 0
\(703\) 2.46251e11 1.00822
\(704\) 3.81321e11 + 2.20156e11i 1.55239 + 0.896272i
\(705\) 0 0
\(706\) −1.40915e11 2.44072e11i −0.567202 0.982423i
\(707\) −6.35606e11 + 3.66967e11i −2.54396 + 1.46876i
\(708\) 0 0
\(709\) 7.63444e10 1.32232e11i 0.302129 0.523303i −0.674489 0.738285i \(-0.735636\pi\)
0.976618 + 0.214982i \(0.0689693\pi\)
\(710\) 1.95729e11i 0.770232i
\(711\) 0 0
\(712\) −2.59814e10 −0.101098
\(713\) −3.14564e10 1.81614e10i −0.121717 0.0702733i
\(714\) 0 0
\(715\) −6.07899e10 1.05291e11i −0.232599 0.402873i
\(716\) −1.40262e11 + 8.09804e10i −0.533689 + 0.308125i
\(717\) 0 0
\(718\) −1.53778e11 + 2.66351e11i −0.578623 + 1.00220i
\(719\) 2.64075e11i 0.988125i −0.869427 0.494062i \(-0.835511\pi\)
0.869427 0.494062i \(-0.164489\pi\)
\(720\) 0 0
\(721\) −7.84784e11 −2.90408
\(722\) 6.40435e11 + 3.69755e11i 2.35682 + 1.36071i
\(723\) 0 0
\(724\) −2.80756e11 4.86284e11i −1.02182 1.76985i
\(725\) 4.11121e11 2.37361e11i 1.48805 0.859126i
\(726\) 0 0
\(727\) 1.28330e11 2.22274e11i 0.459399 0.795703i −0.539530 0.841966i \(-0.681398\pi\)
0.998929 + 0.0462634i \(0.0147314\pi\)
\(728\) 5.17912e11i 1.84387i
\(729\) 0 0
\(730\) 1.12262e11 0.395313
\(731\) 1.20611e11 + 6.96348e10i 0.422394 + 0.243869i
\(732\) 0 0
\(733\) 1.38206e11 + 2.39380e11i 0.478752 + 0.829223i 0.999703 0.0243635i \(-0.00775591\pi\)
−0.520951 + 0.853587i \(0.674423\pi\)
\(734\) 1.38367e11 7.98864e10i 0.476705 0.275226i
\(735\) 0 0
\(736\) −9.34053e10 + 1.61783e11i −0.318317 + 0.551342i
\(737\) 1.02881e10i 0.0348710i
\(738\) 0 0
\(739\) 3.69193e11 1.23787 0.618935 0.785442i \(-0.287564\pi\)
0.618935 + 0.785442i \(0.287564\pi\)
\(740\) −8.21935e10 4.74545e10i −0.274101 0.158252i
\(741\) 0 0
\(742\) −1.21383e11 2.10241e11i −0.400443 0.693588i
\(743\) −4.52457e11 + 2.61226e11i −1.48464 + 0.857160i −0.999847 0.0174674i \(-0.994440\pi\)
−0.484797 + 0.874627i \(0.661106\pi\)
\(744\) 0 0
\(745\) 6.97583e10 1.20825e11i 0.226449 0.392222i
\(746\) 3.15947e11i 1.02014i
\(747\) 0 0
\(748\) −3.08947e11 −0.986911
\(749\) 5.25090e11 + 3.03161e11i 1.66842 + 0.963265i
\(750\) 0 0
\(751\) −1.11747e11 1.93552e11i −0.351300 0.608469i 0.635178 0.772366i \(-0.280927\pi\)
−0.986477 + 0.163897i \(0.947594\pi\)
\(752\) 3.80059e10 2.19427e10i 0.118845 0.0686150i
\(753\) 0 0
\(754\) 6.45238e11 1.11758e12i 1.99634 3.45776i
\(755\) 2.48673e10i 0.0765315i
\(756\) 0 0
\(757\) −2.44183e11 −0.743588 −0.371794 0.928315i \(-0.621257\pi\)
−0.371794 + 0.928315i \(0.621257\pi\)
\(758\) 5.03227e11 + 2.90538e11i 1.52436 + 0.880089i
\(759\) 0 0
\(760\) −8.28213e10 1.43451e11i −0.248249 0.429980i
\(761\) −1.94881e11 + 1.12515e11i −0.581073 + 0.335483i −0.761560 0.648095i \(-0.775566\pi\)
0.180487 + 0.983577i \(0.442233\pi\)
\(762\) 0 0
\(763\) −4.09966e11 + 7.10082e11i −1.20962 + 2.09513i
\(764\) 6.86251e10i 0.201423i
\(765\) 0 0
\(766\) −2.94922e11 −0.856628
\(767\) −1.64061e11 9.47209e10i −0.474051 0.273693i
\(768\) 0 0
\(769\) 2.41526e11 + 4.18336e11i 0.690652 + 1.19624i 0.971625 + 0.236528i \(0.0760095\pi\)
−0.280973 + 0.959716i \(0.590657\pi\)
\(770\) −2.71105e11 + 1.56522e11i −0.771212 + 0.445260i
\(771\) 0 0
\(772\) −1.17398e11 + 2.03340e11i −0.330516 + 0.572470i
\(773\) 1.32482e10i 0.0371056i 0.999828 + 0.0185528i \(0.00590588\pi\)
−0.999828 + 0.0185528i \(0.994094\pi\)
\(774\) 0 0
\(775\) −7.62588e10 −0.211390
\(776\) 2.71670e11 + 1.56849e11i 0.749194 + 0.432547i
\(777\) 0 0
\(778\) −9.66609e9 1.67422e10i −0.0263835 0.0456976i
\(779\) 1.37691e11 7.94957e10i 0.373899 0.215871i
\(780\) 0 0
\(781\) −3.00396e11 + 5.20301e11i −0.807403 + 1.39846i
\(782\) 2.02808e11i 0.542324i
\(783\) 0 0
\(784\) −4.77889e10 −0.126492
\(785\) −1.32184e10 7.63167e9i −0.0348098 0.0200975i
\(786\) 0 0
\(787\) −2.37300e11 4.11015e11i −0.618584 1.07142i −0.989744 0.142850i \(-0.954373\pi\)
0.371161 0.928569i \(-0.378960\pi\)
\(788\) 4.15992e11 2.40173e11i 1.07890 0.622901i
\(789\) 0 0
\(790\) −1.31372e11 + 2.27543e11i −0.337282 + 0.584190i
\(791\) 2.62641e11i 0.670898i
\(792\) 0 0
\(793\) 9.95330e10 0.251695
\(794\) −1.26250e11 7.28907e10i −0.317652 0.183396i
\(795\) 0 0
\(796\) −3.80354e11 6.58792e11i −0.947405 1.64095i
\(797\) −2.58248e11 + 1.49100e11i −0.640035 + 0.369524i −0.784628 0.619967i \(-0.787146\pi\)
0.144593 + 0.989491i \(0.453813\pi\)
\(798\) 0 0
\(799\) −1.73338e11 + 3.00230e11i −0.425311 + 0.736660i
\(800\) 3.92206e11i 0.957533i
\(801\) 0 0
\(802\) 1.07670e12 2.60255
\(803\) −2.98423e11 1.72295e11i −0.717745 0.414390i
\(804\) 0 0
\(805\) −6.28650e10 1.08885e11i −0.149701 0.259290i
\(806\) −1.79528e11 + 1.03650e11i −0.425394 + 0.245602i
\(807\) 0 0
\(808\) 3.75457e11 6.50311e11i 0.880877 1.52572i
\(809\) 3.19136e11i 0.745044i −0.928023 0.372522i \(-0.878493\pi\)
0.928023 0.372522i \(-0.121507\pi\)
\(810\) 0 0
\(811\) 2.94415e11 0.680575 0.340288 0.940321i \(-0.389476\pi\)
0.340288 + 0.940321i \(0.389476\pi\)
\(812\) −1.76058e12 1.01647e12i −4.04979 2.33815i
\(813\) 0 0
\(814\) 2.38076e11 + 4.12360e11i 0.542273 + 0.939244i
\(815\) −1.00095e11 + 5.77902e10i −0.226874 + 0.130986i
\(816\) 0 0
\(817\) 3.13490e11 5.42981e11i 0.703616 1.21870i
\(818\) 6.42373e11i 1.43474i
\(819\) 0 0
\(820\) −6.12777e10 −0.135534
\(821\) 5.33500e10 + 3.08016e10i 0.117425 + 0.0677956i 0.557562 0.830135i \(-0.311737\pi\)
−0.440137 + 0.897931i \(0.645070\pi\)
\(822\) 0 0
\(823\) 2.35526e11 + 4.07944e11i 0.513381 + 0.889203i 0.999880 + 0.0155212i \(0.00494074\pi\)
−0.486498 + 0.873682i \(0.661726\pi\)
\(824\) 6.95368e11 4.01471e11i 1.50836 0.870853i
\(825\) 0 0
\(826\) −2.43888e11 + 4.22427e11i −0.523927 + 0.907467i
\(827\) 4.35038e11i 0.930048i −0.885298 0.465024i \(-0.846046\pi\)
0.885298 0.465024i \(-0.153954\pi\)
\(828\) 0 0
\(829\) 2.07438e11 0.439208 0.219604 0.975589i \(-0.429524\pi\)
0.219604 + 0.975589i \(0.429524\pi\)
\(830\) 1.48976e11 + 8.60113e10i 0.313909 + 0.181235i
\(831\) 0 0
\(832\) 5.04645e11 + 8.74071e11i 1.05316 + 1.82412i
\(833\) 3.26935e11 1.88756e11i 0.679018 0.392031i
\(834\) 0 0
\(835\) 2.57562e10 4.46111e10i 0.0529830 0.0917693i
\(836\) 1.39086e12i 2.84745i
\(837\) 0 0
\(838\) 1.29699e11 0.263002
\(839\) 2.06839e11 + 1.19419e11i 0.417431 + 0.241004i 0.693978 0.719996i \(-0.255857\pi\)
−0.276546 + 0.961001i \(0.589190\pi\)
\(840\) 0 0
\(841\) 6.75747e11 + 1.17043e12i 1.35083 + 2.33970i
\(842\) −3.16521e11 + 1.82743e11i −0.629730 + 0.363575i
\(843\) 0 0
\(844\) −8.01268e10 + 1.38784e11i −0.157909 + 0.273507i
\(845\) 1.11977e11i 0.219635i
\(846\) 0 0
\(847\) 1.67248e11 0.324959
\(848\) −1.33033e10 7.68064e9i −0.0257261 0.0148530i
\(849\) 0 0
\(850\) −2.12896e11 3.68747e11i −0.407842 0.706403i
\(851\) −1.65618e11 + 9.56198e10i −0.315784 + 0.182318i
\(852\) 0 0
\(853\) 1.57842e11 2.73391e11i 0.298144 0.516401i −0.677567 0.735461i \(-0.736966\pi\)
0.975711 + 0.219060i \(0.0702990\pi\)
\(854\) 2.56278e11i 0.481815i
\(855\) 0 0
\(856\) −6.20349e11 −1.15542
\(857\) 4.18908e11 + 2.41857e11i 0.776597 + 0.448369i 0.835223 0.549911i \(-0.185339\pi\)
−0.0586257 + 0.998280i \(0.518672\pi\)
\(858\) 0 0
\(859\) 2.84594e11 + 4.92930e11i 0.522700 + 0.905343i 0.999651 + 0.0264130i \(0.00840849\pi\)
−0.476951 + 0.878930i \(0.658258\pi\)
\(860\) −2.09273e11 + 1.20824e11i −0.382578 + 0.220882i
\(861\) 0 0
\(862\) 4.77823e11 8.27614e11i 0.865443 1.49899i
\(863\) 1.70442e11i 0.307279i −0.988127 0.153639i \(-0.950901\pi\)
0.988127 0.153639i \(-0.0490994\pi\)
\(864\) 0 0
\(865\) 5.72906e10 0.102334
\(866\) −8.36865e11 4.83164e11i −1.48793 0.859060i
\(867\) 0 0
\(868\) 1.63285e11 + 2.82819e11i 0.287653 + 0.498229i
\(869\) 6.98445e11 4.03248e11i 1.22477 0.707119i
\(870\) 0 0
\(871\) 1.17912e10 2.04230e10i 0.0204874 0.0354852i
\(872\) 8.38903e11i 1.45093i
\(873\) 0 0
\(874\) −9.13026e11 −1.56472
\(875\) −4.84575e11 2.79769e11i −0.826663 0.477274i
\(876\) 0 0
\(877\) −3.49396e11 6.05172e11i −0.590636 1.02301i −0.994147 0.108037i \(-0.965544\pi\)
0.403511 0.914975i \(-0.367790\pi\)
\(878\) −1.19331e11 + 6.88957e10i −0.200805 + 0.115935i
\(879\) 0 0
\(880\) −9.90414e9 + 1.71545e10i −0.0165153 + 0.0286053i
\(881\) 2.05065e11i 0.340399i 0.985410 + 0.170199i \(0.0544412\pi\)
−0.985410 + 0.170199i \(0.945559\pi\)
\(882\) 0 0
\(883\) −7.79882e11 −1.28288 −0.641440 0.767173i \(-0.721663\pi\)
−0.641440 + 0.767173i \(0.721663\pi\)
\(884\) −6.13296e11 3.54087e11i −1.00430 0.579830i
\(885\) 0 0
\(886\) 3.08559e11 + 5.34441e11i 0.500730 + 0.867290i
\(887\) 4.20319e11 2.42671e11i 0.679023 0.392034i −0.120464 0.992718i \(-0.538438\pi\)
0.799487 + 0.600684i \(0.205105\pi\)
\(888\) 0 0
\(889\) −4.15223e11 + 7.19187e11i −0.664774 + 1.15142i
\(890\) 3.59972e10i 0.0573732i
\(891\) 0 0
\(892\) 7.50948e11 1.18618
\(893\) 1.35161e12 + 7.80353e11i 2.12543 + 1.22712i
\(894\) 0 0
\(895\) −4.10153e10 7.10405e10i −0.0639224 0.110717i
\(896\) 1.32774e12 7.66568e11i 2.06006 1.18938i
\(897\) 0 0
\(898\) 9.34847e11 1.61920e12i 1.43759 2.48998i
\(899\) 2.97462e11i 0.455400i
\(900\) 0 0
\(901\) 1.21347e11 0.184133
\(902\) 2.66239e11 + 1.53713e11i 0.402203 + 0.232212i
\(903\) 0 0
\(904\) −1.34359e11 2.32716e11i −0.201183 0.348460i
\(905\) 2.46295e11 1.42199e11i 0.367165 0.211983i
\(906\) 0 0
\(907\) −3.68722e11 + 6.38645e11i −0.544841 + 0.943693i 0.453776 + 0.891116i \(0.350077\pi\)
−0.998617 + 0.0525767i \(0.983257\pi\)
\(908\) 8.83377e11i 1.29958i
\(909\) 0 0
\(910\) −7.17566e11 −1.04640
\(911\) −5.44603e11 3.14427e11i −0.790691 0.456506i 0.0495146 0.998773i \(-0.484233\pi\)
−0.840206 + 0.542268i \(0.817566\pi\)
\(912\) 0 0
\(913\) −2.64013e11 4.57284e11i −0.379964 0.658116i
\(914\) −1.37835e12 + 7.95791e11i −1.97504 + 1.14029i
\(915\) 0 0
\(916\) −4.33868e11 + 7.51482e11i −0.616277 + 1.06742i
\(917\) 1.31410e12i 1.85845i
\(918\) 0 0
\(919\) 3.48346e11 0.488370 0.244185 0.969729i \(-0.421480\pi\)
0.244185 + 0.969729i \(0.421480\pi\)
\(920\) 1.11405e11 + 6.43194e10i 0.155508 + 0.0897823i
\(921\) 0 0
\(922\) 1.54621e11 + 2.67811e11i 0.213966 + 0.370600i
\(923\) −1.19264e12 + 6.88573e11i −1.64325 + 0.948731i
\(924\) 0 0
\(925\) −2.00752e11 + 3.47713e11i −0.274216 + 0.474956i
\(926\) 1.52190e11i 0.206987i
\(927\) 0 0
\(928\) −1.52987e12 −2.06283
\(929\) −5.27095e8 3.04319e8i −0.000707663 0.000408569i 0.499646 0.866230i \(-0.333463\pi\)
−0.500354 + 0.865821i \(0.666797\pi\)
\(930\) 0 0
\(931\) −8.49763e11 1.47183e12i −1.13110 1.95912i
\(932\) −1.19271e12 + 6.88609e11i −1.58077 + 0.912660i
\(933\) 0 0
\(934\) 7.45749e11 1.29168e12i 0.979953 1.69733i
\(935\) 1.56477e11i 0.204740i
\(936\) 0 0
\(937\) 5.98470e10 0.0776398 0.0388199 0.999246i \(-0.487640\pi\)
0.0388199 + 0.999246i \(0.487640\pi\)
\(938\) −5.25854e10 3.03602e10i −0.0679288 0.0392187i
\(939\) 0 0
\(940\) −3.00760e11 5.20932e11i −0.385220 0.667221i
\(941\) 1.12529e12 6.49688e11i 1.43518 0.828603i 0.437673 0.899134i \(-0.355803\pi\)
0.997510 + 0.0705309i \(0.0224694\pi\)
\(942\) 0 0
\(943\) −6.17367e10 + 1.06931e11i −0.0780723 + 0.135225i
\(944\) 3.08646e10i 0.0388663i
\(945\) 0 0
\(946\) 1.21233e12 1.51376
\(947\) −1.13710e12 6.56502e11i −1.41383 0.816275i −0.418083 0.908409i \(-0.637298\pi\)
−0.995747 + 0.0921343i \(0.970631\pi\)
\(948\) 0 0
\(949\) −3.94937e11 6.84050e11i −0.486925 0.843380i
\(950\) −1.66007e12 + 9.58440e11i −2.03813 + 1.17671i
\(951\) 0 0
\(952\) −3.33284e11 + 5.77265e11i −0.405758 + 0.702793i
\(953\) 1.49915e12i 1.81750i 0.417341 + 0.908750i \(0.362962\pi\)
−0.417341 + 0.908750i \(0.637038\pi\)
\(954\) 0 0
\(955\) 3.47575e10 0.0417864
\(956\) 1.14816e12 + 6.62892e11i 1.37459 + 0.793618i
\(957\) 0 0
\(958\) −5.92408e11 1.02608e12i −0.703330 1.21820i
\(959\) −2.39108e11 + 1.38049e11i −0.282696 + 0.163215i
\(960\) 0 0
\(961\) 4.02554e11 6.97243e11i 0.471987 0.817506i
\(962\) 1.09144e12i 1.27438i
\(963\) 0 0
\(964\) −1.62808e12 −1.88524
\(965\) −1.02988e11 5.94604e10i −0.118762 0.0685675i
\(966\) 0 0
\(967\) 1.29701e11 + 2.24648e11i 0.148332 + 0.256919i 0.930611 0.366009i \(-0.119276\pi\)
−0.782279 + 0.622928i \(0.785943\pi\)
\(968\) −1.48192e11 + 8.55589e10i −0.168781 + 0.0974459i
\(969\) 0 0
\(970\) −2.17313e11 + 3.76398e11i −0.245471 + 0.425168i
\(971\) 1.15804e12i 1.30271i −0.758772 0.651356i \(-0.774200\pi\)
0.758772 0.651356i \(-0.225800\pi\)
\(972\) 0 0
\(973\) −3.08473e10 −0.0344164
\(974\) 1.90335e12 + 1.09890e12i 2.11487 + 1.22102i
\(975\) 0 0
\(976\) −8.10816e9 1.40437e10i −0.00893559 0.0154769i
\(977\) −7.79343e10 + 4.49954e10i −0.0855363 + 0.0493844i −0.542158 0.840277i \(-0.682393\pi\)
0.456622 + 0.889661i \(0.349059\pi\)
\(978\) 0 0
\(979\) −5.52470e10 + 9.56907e10i −0.0601420 + 0.104169i
\(980\) 6.55024e11i 0.710155i
\(981\) 0 0
\(982\) 7.65356e11 0.823033
\(983\) −1.42514e12 8.22805e11i −1.52631 0.881217i −0.999512 0.0312278i \(-0.990058\pi\)
−0.526800 0.849989i \(-0.676608\pi\)
\(984\) 0 0
\(985\) 1.21644e11 + 2.10693e11i 0.129224 + 0.223823i
\(986\) 1.43837e12 8.30441e11i 1.52181 0.878620i
\(987\) 0 0
\(988\) −1.59407e12 + 2.76101e12i −1.67294 + 2.89761i
\(989\) 4.86916e11i 0.508943i
\(990\) 0 0
\(991\) 6.39028e11 0.662560 0.331280 0.943533i \(-0.392520\pi\)
0.331280 + 0.943533i \(0.392520\pi\)
\(992\) 2.12832e11 + 1.22879e11i 0.219781 + 0.126891i
\(993\) 0 0
\(994\) 1.77294e12 + 3.07083e12i 1.81614 + 3.14564i
\(995\) 3.33668e11 1.92643e11i 0.340426 0.196545i
\(996\) 0 0
\(997\) 4.46173e11 7.72795e11i 0.451568 0.782139i −0.546916 0.837188i \(-0.684198\pi\)
0.998484 + 0.0550490i \(0.0175315\pi\)
\(998\) 1.32136e12i 1.33199i
\(999\) 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 81.9.d.g.26.15 32
3.2 odd 2 inner 81.9.d.g.26.2 32
9.2 odd 6 81.9.b.b.80.15 yes 16
9.4 even 3 inner 81.9.d.g.53.2 32
9.5 odd 6 inner 81.9.d.g.53.15 32
9.7 even 3 81.9.b.b.80.2 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.9.b.b.80.2 16 9.7 even 3
81.9.b.b.80.15 yes 16 9.2 odd 6
81.9.d.g.26.2 32 3.2 odd 2 inner
81.9.d.g.26.15 32 1.1 even 1 trivial
81.9.d.g.53.2 32 9.4 even 3 inner
81.9.d.g.53.15 32 9.5 odd 6 inner