Properties

Label 81.9.f.a.8.9
Level $81$
Weight $9$
Character 81.8
Analytic conductor $32.998$
Analytic rank $0$
Dimension $138$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [81,9,Mod(8,81)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(81, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("81.8");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 81 = 3^{4} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 81.f (of order \(18\), degree \(6\), 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: \(138\)
Relative dimension: \(23\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 27)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 8.9
Character \(\chi\) \(=\) 81.8
Dual form 81.9.f.a.71.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-13.3375 - 2.35175i) q^{2} +(-68.2042 - 24.8243i) q^{4} +(636.805 + 758.914i) q^{5} +(-2502.00 + 910.653i) q^{7} +(3853.85 + 2225.02i) q^{8} +(-6708.58 - 11619.6i) q^{10} +(-15349.9 + 18293.3i) q^{11} +(4780.28 + 27110.3i) q^{13} +(35511.9 - 6261.71i) q^{14} +(-31934.2 - 26796.0i) q^{16} +(105956. - 61173.5i) q^{17} +(-547.495 + 948.289i) q^{19} +(-24593.2 - 67569.4i) q^{20} +(247750. - 207887. i) q^{22} +(-50471.0 + 138668. i) q^{23} +(-102599. + 581870. i) q^{25} -372825. i q^{26} +193253. q^{28} +(924074. + 162939. i) q^{29} +(131238. + 47766.6i) q^{31} +(-369368. - 440196. i) q^{32} +(-1.55704e6 + 566717. i) q^{34} +(-2.28439e6 - 1.31889e6i) q^{35} +(-379045. - 656525. i) q^{37} +(9532.34 - 11360.2i) q^{38} +(765550. + 4.34165e6i) q^{40} +(-4.60079e6 + 811243. i) q^{41} +(-1.82392e6 - 1.53045e6i) q^{43} +(1.50104e6 - 866629. i) q^{44} +(999268. - 1.73078e6i) q^{46} +(-425686. - 1.16956e6i) q^{47} +(1.01461e6 - 851361. i) q^{49} +(2.73683e6 - 7.51938e6i) q^{50} +(346960. - 1.96771e6i) q^{52} +6.96711e6i q^{53} -2.36579e7 q^{55} +(-1.16686e7 - 2.05748e6i) q^{56} +(-1.19416e7 - 4.34639e6i) q^{58} +(-4.48304e6 - 5.34268e6i) q^{59} +(-2.36882e7 + 8.62179e6i) q^{61} +(-1.63804e6 - 945725. i) q^{62} +(9.22715e6 + 1.59819e7i) q^{64} +(-1.75303e7 + 2.08918e7i) q^{65} +(-3.60777e6 - 2.04607e7i) q^{67} +(-8.74520e6 + 1.54201e6i) q^{68} +(2.73663e7 + 2.29630e7i) q^{70} +(1.06620e7 - 6.15572e6i) q^{71} +(3.50114e6 - 6.06416e6i) q^{73} +(3.51151e6 + 9.64780e6i) q^{74} +(60882.1 - 51086.1i) q^{76} +(2.17466e7 - 5.97482e7i) q^{77} +(2.79249e6 - 1.58370e7i) q^{79} -4.12991e7i q^{80} +6.32706e7 q^{82} +(-4.48356e6 - 790573. i) q^{83} +(1.13898e8 + 4.14556e7i) q^{85} +(2.07272e7 + 2.47018e7i) q^{86} +(-9.98592e7 + 3.63458e7i) q^{88} +(3.86601e7 + 2.23204e7i) q^{89} +(-3.66484e7 - 6.34768e7i) q^{91} +(6.88467e6 - 8.20483e6i) q^{92} +(2.92705e6 + 1.66001e7i) q^{94} +(-1.06832e6 + 188373. i) q^{95} +(1.19186e7 + 1.00009e7i) q^{97} +(-1.55345e7 + 8.96887e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 138 q + 6 q^{2} - 6 q^{4} + 447 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} - 28668 q^{11} - 6 q^{13} + 120975 q^{14} - 774 q^{16} + 9 q^{17} - 3 q^{19} - 137913 q^{20} - 185478 q^{22} - 68376 q^{23} + 507585 q^{25}+ \cdots - 1293135102 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −13.3375 2.35175i −0.833591 0.146985i −0.259466 0.965752i \(-0.583547\pi\)
−0.574125 + 0.818768i \(0.694658\pi\)
\(3\) 0 0
\(4\) −68.2042 24.8243i −0.266423 0.0969699i
\(5\) 636.805 + 758.914i 1.01889 + 1.21426i 0.976579 + 0.215158i \(0.0690267\pi\)
0.0423083 + 0.999105i \(0.486529\pi\)
\(6\) 0 0
\(7\) −2502.00 + 910.653i −1.04207 + 0.379281i −0.805663 0.592375i \(-0.798191\pi\)
−0.236402 + 0.971655i \(0.575968\pi\)
\(8\) 3853.85 + 2225.02i 0.940882 + 0.543219i
\(9\) 0 0
\(10\) −6708.58 11619.6i −0.670858 1.16196i
\(11\) −15349.9 + 18293.3i −1.04842 + 1.24946i −0.0808814 + 0.996724i \(0.525773\pi\)
−0.967536 + 0.252732i \(0.918671\pi\)
\(12\) 0 0
\(13\) 4780.28 + 27110.3i 0.167371 + 0.949208i 0.946586 + 0.322451i \(0.104507\pi\)
−0.779215 + 0.626757i \(0.784382\pi\)
\(14\) 35511.9 6261.71i 0.924405 0.162997i
\(15\) 0 0
\(16\) −31934.2 26796.0i −0.487277 0.408874i
\(17\) 105956. 61173.5i 1.26861 0.732432i 0.293885 0.955841i \(-0.405052\pi\)
0.974725 + 0.223409i \(0.0717185\pi\)
\(18\) 0 0
\(19\) −547.495 + 948.289i −0.00420113 + 0.00727656i −0.868118 0.496357i \(-0.834671\pi\)
0.863917 + 0.503634i \(0.168004\pi\)
\(20\) −24593.2 67569.4i −0.153708 0.422309i
\(21\) 0 0
\(22\) 247750. 207887.i 1.05760 0.887434i
\(23\) −50471.0 + 138668.i −0.180356 + 0.495524i −0.996619 0.0821558i \(-0.973819\pi\)
0.816264 + 0.577680i \(0.196042\pi\)
\(24\) 0 0
\(25\) −102599. + 581870.i −0.262654 + 1.48959i
\(26\) 372825.i 0.815853i
\(27\) 0 0
\(28\) 193253. 0.314409
\(29\) 924074. + 162939.i 1.30652 + 0.230374i 0.783203 0.621766i \(-0.213585\pi\)
0.523313 + 0.852140i \(0.324696\pi\)
\(30\) 0 0
\(31\) 131238. + 47766.6i 0.142106 + 0.0517223i 0.412094 0.911141i \(-0.364798\pi\)
−0.269988 + 0.962864i \(0.587020\pi\)
\(32\) −369368. 440196.i −0.352257 0.419804i
\(33\) 0 0
\(34\) −1.55704e6 + 566717.i −1.16516 + 0.424083i
\(35\) −2.28439e6 1.31889e6i −1.52229 0.878897i
\(36\) 0 0
\(37\) −379045. 656525.i −0.202248 0.350303i 0.747005 0.664819i \(-0.231491\pi\)
−0.949252 + 0.314515i \(0.898158\pi\)
\(38\) 9532.34 11360.2i 0.00457157 0.00544818i
\(39\) 0 0
\(40\) 765550. + 4.34165e6i 0.299043 + 1.69596i
\(41\) −4.60079e6 + 811243.i −1.62816 + 0.287088i −0.911797 0.410641i \(-0.865305\pi\)
−0.716361 + 0.697730i \(0.754194\pi\)
\(42\) 0 0
\(43\) −1.82392e6 1.53045e6i −0.533498 0.447658i 0.335810 0.941930i \(-0.390990\pi\)
−0.869307 + 0.494272i \(0.835435\pi\)
\(44\) 1.50104e6 866629.i 0.400482 0.231218i
\(45\) 0 0
\(46\) 999268. 1.73078e6i 0.223178 0.386555i
\(47\) −425686. 1.16956e6i −0.0872365 0.239680i 0.888401 0.459068i \(-0.151816\pi\)
−0.975638 + 0.219387i \(0.929594\pi\)
\(48\) 0 0
\(49\) 1.01461e6 851361.i 0.176001 0.147683i
\(50\) 2.73683e6 7.51938e6i 0.437893 1.20310i
\(51\) 0 0
\(52\) 346960. 1.96771e6i 0.0474532 0.269121i
\(53\) 6.96711e6i 0.882977i 0.897267 + 0.441489i \(0.145549\pi\)
−0.897267 + 0.441489i \(0.854451\pi\)
\(54\) 0 0
\(55\) −2.36579e7 −2.58539
\(56\) −1.16686e7 2.05748e6i −1.18649 0.209211i
\(57\) 0 0
\(58\) −1.19416e7 4.34639e6i −1.05524 0.384076i
\(59\) −4.48304e6 5.34268e6i −0.369968 0.440911i 0.548653 0.836050i \(-0.315141\pi\)
−0.918621 + 0.395139i \(0.870696\pi\)
\(60\) 0 0
\(61\) −2.36882e7 + 8.62179e6i −1.71085 + 0.622699i −0.996986 0.0775852i \(-0.975279\pi\)
−0.713865 + 0.700284i \(0.753057\pi\)
\(62\) −1.63804e6 945725.i −0.110856 0.0640026i
\(63\) 0 0
\(64\) 9.22715e6 + 1.59819e7i 0.549981 + 0.952595i
\(65\) −1.75303e7 + 2.08918e7i −0.982056 + 1.17037i
\(66\) 0 0
\(67\) −3.60777e6 2.04607e7i −0.179036 1.01536i −0.933382 0.358885i \(-0.883157\pi\)
0.754346 0.656477i \(-0.227954\pi\)
\(68\) −8.74520e6 + 1.54201e6i −0.409010 + 0.0721195i
\(69\) 0 0
\(70\) 2.73663e7 + 2.29630e7i 1.13979 + 0.956394i
\(71\) 1.06620e7 6.15572e6i 0.419571 0.242240i −0.275323 0.961352i \(-0.588785\pi\)
0.694894 + 0.719112i \(0.255451\pi\)
\(72\) 0 0
\(73\) 3.50114e6 6.06416e6i 0.123287 0.213540i −0.797775 0.602956i \(-0.793990\pi\)
0.921062 + 0.389415i \(0.127323\pi\)
\(74\) 3.51151e6 + 9.64780e6i 0.117103 + 0.321737i
\(75\) 0 0
\(76\) 60882.1 51086.1i 0.00182488 0.00153126i
\(77\) 2.17466e7 5.97482e7i 0.618625 1.69966i
\(78\) 0 0
\(79\) 2.79249e6 1.58370e7i 0.0716941 0.406598i −0.927748 0.373207i \(-0.878258\pi\)
0.999442 0.0333910i \(-0.0106306\pi\)
\(80\) 4.12991e7i 1.00828i
\(81\) 0 0
\(82\) 6.32706e7 1.39942
\(83\) −4.48356e6 790573.i −0.0944737 0.0166583i 0.126211 0.992003i \(-0.459718\pi\)
−0.220685 + 0.975345i \(0.570829\pi\)
\(84\) 0 0
\(85\) 1.13898e8 + 4.14556e7i 2.18194 + 0.794159i
\(86\) 2.07272e7 + 2.47018e7i 0.378920 + 0.451579i
\(87\) 0 0
\(88\) −9.98592e7 + 3.63458e7i −1.66517 + 0.606071i
\(89\) 3.86601e7 + 2.23204e7i 0.616174 + 0.355748i 0.775378 0.631497i \(-0.217559\pi\)
−0.159204 + 0.987246i \(0.550893\pi\)
\(90\) 0 0
\(91\) −3.66484e7 6.34768e7i −0.534428 0.925656i
\(92\) 6.88467e6 8.20483e6i 0.0961018 0.114530i
\(93\) 0 0
\(94\) 2.92705e6 + 1.66001e7i 0.0374903 + 0.212618i
\(95\) −1.06832e6 + 188373.i −0.0131161 + 0.00231273i
\(96\) 0 0
\(97\) 1.19186e7 + 1.00009e7i 0.134629 + 0.112967i 0.707616 0.706598i \(-0.249771\pi\)
−0.572987 + 0.819565i \(0.694215\pi\)
\(98\) −1.55345e7 + 8.96887e6i −0.168420 + 0.0972374i
\(99\) 0 0
\(100\) 2.14422e7 3.71390e7i 0.214422 0.371390i
\(101\) 5.97338e7 + 1.64117e8i 0.574030 + 1.57714i 0.798076 + 0.602557i \(0.205851\pi\)
−0.224046 + 0.974579i \(0.571927\pi\)
\(102\) 0 0
\(103\) 6.03092e7 5.06054e7i 0.535839 0.449623i −0.334273 0.942476i \(-0.608491\pi\)
0.870112 + 0.492854i \(0.164046\pi\)
\(104\) −4.18986e7 + 1.15116e8i −0.358151 + 0.984012i
\(105\) 0 0
\(106\) 1.63849e7 9.29236e7i 0.129784 0.736042i
\(107\) 6.15134e7i 0.469283i −0.972082 0.234641i \(-0.924608\pi\)
0.972082 0.234641i \(-0.0753916\pi\)
\(108\) 0 0
\(109\) −2.02005e7 −0.143105 −0.0715526 0.997437i \(-0.522795\pi\)
−0.0715526 + 0.997437i \(0.522795\pi\)
\(110\) 3.15536e8 + 5.56376e7i 2.15516 + 0.380012i
\(111\) 0 0
\(112\) 1.04301e8 + 3.79625e7i 0.662852 + 0.241258i
\(113\) −7.22019e7 8.60469e7i −0.442828 0.527742i 0.497750 0.867321i \(-0.334160\pi\)
−0.940578 + 0.339579i \(0.889715\pi\)
\(114\) 0 0
\(115\) −1.37377e8 + 5.00012e7i −0.785459 + 0.285884i
\(116\) −5.89809e7 3.40526e7i −0.325746 0.188070i
\(117\) 0 0
\(118\) 4.72277e7 + 8.18007e7i 0.243595 + 0.421919i
\(119\) −2.09393e8 + 2.49545e8i −1.04418 + 1.24440i
\(120\) 0 0
\(121\) −6.18021e7 3.50497e8i −0.288311 1.63510i
\(122\) 3.36216e8 5.92840e7i 1.51768 0.267607i
\(123\) 0 0
\(124\) −7.76519e6 6.51577e6i −0.0328447 0.0275600i
\(125\) −1.71783e8 + 9.91787e7i −0.703622 + 0.406236i
\(126\) 0 0
\(127\) −1.22668e8 + 2.12467e8i −0.471536 + 0.816725i −0.999470 0.0325610i \(-0.989634\pi\)
0.527934 + 0.849286i \(0.322967\pi\)
\(128\) −3.51679e7 9.66229e7i −0.131011 0.359948i
\(129\) 0 0
\(130\) 2.82942e8 2.37417e8i 0.990660 0.831262i
\(131\) 1.43812e8 3.95121e8i 0.488327 1.34167i −0.413867 0.910337i \(-0.635822\pi\)
0.902194 0.431330i \(-0.141955\pi\)
\(132\) 0 0
\(133\) 506269. 2.87120e6i 0.00161799 0.00917606i
\(134\) 2.81378e8i 0.872713i
\(135\) 0 0
\(136\) 5.44450e8 1.59148
\(137\) −3.65675e8 6.44783e7i −1.03804 0.183034i −0.371444 0.928456i \(-0.621137\pi\)
−0.666593 + 0.745422i \(0.732248\pi\)
\(138\) 0 0
\(139\) −3.96654e8 1.44370e8i −1.06256 0.386739i −0.249169 0.968460i \(-0.580158\pi\)
−0.813389 + 0.581721i \(0.802380\pi\)
\(140\) 1.23064e8 + 1.46663e8i 0.320347 + 0.381775i
\(141\) 0 0
\(142\) −1.56681e8 + 5.70272e7i −0.385357 + 0.140258i
\(143\) −5.69314e8 3.28693e8i −1.36147 0.786044i
\(144\) 0 0
\(145\) 4.64798e8 + 8.05053e8i 1.05146 + 1.82118i
\(146\) −6.09578e7 + 7.26467e7i −0.134158 + 0.159884i
\(147\) 0 0
\(148\) 9.55468e6 + 5.41873e7i 0.0199145 + 0.112941i
\(149\) 4.73599e8 8.35083e7i 0.960873 0.169428i 0.328854 0.944381i \(-0.393338\pi\)
0.632019 + 0.774953i \(0.282227\pi\)
\(150\) 0 0
\(151\) −3.88229e8 3.25763e8i −0.746758 0.626605i 0.187885 0.982191i \(-0.439837\pi\)
−0.934643 + 0.355586i \(0.884281\pi\)
\(152\) −4.21993e6 + 2.43638e6i −0.00790553 + 0.00456426i
\(153\) 0 0
\(154\) −4.30557e8 + 7.45746e8i −0.765504 + 1.32589i
\(155\) 4.73220e7 + 1.30016e8i 0.0819854 + 0.225253i
\(156\) 0 0
\(157\) −3.53896e8 + 2.96954e8i −0.582475 + 0.488755i −0.885759 0.464146i \(-0.846361\pi\)
0.303284 + 0.952900i \(0.401917\pi\)
\(158\) −7.44895e7 + 2.04658e8i −0.119527 + 0.328398i
\(159\) 0 0
\(160\) 9.88555e7 5.60638e8i 0.150842 0.855465i
\(161\) 3.92908e8i 0.584774i
\(162\) 0 0
\(163\) −4.56114e8 −0.646134 −0.323067 0.946376i \(-0.604714\pi\)
−0.323067 + 0.946376i \(0.604714\pi\)
\(164\) 3.33932e8 + 5.88811e7i 0.461617 + 0.0813956i
\(165\) 0 0
\(166\) 5.79401e7 + 2.10885e7i 0.0763040 + 0.0277724i
\(167\) −1.61471e8 1.92434e8i −0.207601 0.247409i 0.652190 0.758056i \(-0.273850\pi\)
−0.859791 + 0.510647i \(0.829406\pi\)
\(168\) 0 0
\(169\) 5.44170e7 1.98062e7i 0.0667095 0.0242803i
\(170\) −1.42162e9 8.20774e8i −1.70211 0.982715i
\(171\) 0 0
\(172\) 8.64068e7 + 1.49661e8i 0.0987265 + 0.170999i
\(173\) 7.42345e8 8.84693e8i 0.828746 0.987661i −0.171251 0.985227i \(-0.554781\pi\)
0.999997 0.00243395i \(-0.000774751\pi\)
\(174\) 0 0
\(175\) −2.73178e8 1.54927e9i −0.291269 1.65187i
\(176\) 9.80372e8 1.72866e8i 1.02174 0.180160i
\(177\) 0 0
\(178\) −4.63136e8 3.88617e8i −0.461348 0.387117i
\(179\) −6.53835e8 + 3.77492e8i −0.636878 + 0.367702i −0.783411 0.621504i \(-0.786522\pi\)
0.146533 + 0.989206i \(0.453189\pi\)
\(180\) 0 0
\(181\) 1.14593e8 1.98480e8i 0.106768 0.184928i −0.807691 0.589606i \(-0.799283\pi\)
0.914459 + 0.404678i \(0.132616\pi\)
\(182\) 3.39514e8 + 9.32808e8i 0.309437 + 0.850171i
\(183\) 0 0
\(184\) −5.03047e8 + 4.22107e8i −0.438872 + 0.368257i
\(185\) 2.56869e8 7.05741e8i 0.219293 0.602502i
\(186\) 0 0
\(187\) −5.07342e8 + 2.87728e9i −0.414891 + 2.35297i
\(188\) 9.03366e7i 0.0723156i
\(189\) 0 0
\(190\) 1.46916e7 0.0112734
\(191\) 9.71028e7 + 1.71218e7i 0.0729623 + 0.0128652i 0.210010 0.977699i \(-0.432650\pi\)
−0.137048 + 0.990564i \(0.543761\pi\)
\(192\) 0 0
\(193\) 2.38182e9 + 8.66911e8i 1.71664 + 0.624806i 0.997540 0.0700985i \(-0.0223314\pi\)
0.719102 + 0.694905i \(0.244554\pi\)
\(194\) −1.35444e8 1.61416e8i −0.0956211 0.113957i
\(195\) 0 0
\(196\) −9.03352e7 + 3.28793e7i −0.0612115 + 0.0222792i
\(197\) −3.70754e8 2.14055e8i −0.246162 0.142122i 0.371843 0.928295i \(-0.378726\pi\)
−0.618006 + 0.786174i \(0.712059\pi\)
\(198\) 0 0
\(199\) 4.87197e8 + 8.43850e8i 0.310665 + 0.538088i 0.978507 0.206216i \(-0.0661149\pi\)
−0.667842 + 0.744303i \(0.732782\pi\)
\(200\) −1.69008e9 + 2.01416e9i −1.05630 + 1.25885i
\(201\) 0 0
\(202\) −4.10734e8 2.32939e9i −0.246692 1.39906i
\(203\) −2.46041e9 + 4.33837e8i −1.44885 + 0.255472i
\(204\) 0 0
\(205\) −3.54547e9 2.97500e9i −2.00751 1.68450i
\(206\) −9.23383e8 + 5.33115e8i −0.512759 + 0.296041i
\(207\) 0 0
\(208\) 5.73793e8 9.93838e8i 0.306550 0.530961i
\(209\) −8.94333e6 2.45716e7i −0.00468721 0.0128780i
\(210\) 0 0
\(211\) −1.10978e9 + 9.31219e8i −0.559897 + 0.469809i −0.878276 0.478154i \(-0.841306\pi\)
0.318379 + 0.947964i \(0.396862\pi\)
\(212\) 1.72954e8 4.75187e8i 0.0856222 0.235245i
\(213\) 0 0
\(214\) −1.44664e8 + 8.20432e8i −0.0689773 + 0.391190i
\(215\) 2.35880e9i 1.10392i
\(216\) 0 0
\(217\) −3.71855e8 −0.167701
\(218\) 2.69423e8 + 4.75066e7i 0.119291 + 0.0210343i
\(219\) 0 0
\(220\) 1.61357e9 + 5.87291e8i 0.688806 + 0.250705i
\(221\) 2.16493e9 + 2.58006e9i 0.907559 + 1.08159i
\(222\) 0 0
\(223\) 9.28127e8 3.37811e8i 0.375308 0.136601i −0.147477 0.989065i \(-0.547115\pi\)
0.522785 + 0.852464i \(0.324893\pi\)
\(224\) 1.32502e9 + 7.65003e8i 0.526298 + 0.303858i
\(225\) 0 0
\(226\) 7.60629e8 + 1.31745e9i 0.291568 + 0.505010i
\(227\) −4.10560e8 + 4.89286e8i −0.154623 + 0.184272i −0.837795 0.545985i \(-0.816155\pi\)
0.683172 + 0.730257i \(0.260600\pi\)
\(228\) 0 0
\(229\) 1.06279e8 + 6.02738e8i 0.0386460 + 0.219173i 0.998015 0.0629834i \(-0.0200615\pi\)
−0.959369 + 0.282156i \(0.908950\pi\)
\(230\) 1.94985e9 3.43812e8i 0.696772 0.122860i
\(231\) 0 0
\(232\) 3.19870e9 + 2.68403e9i 1.10413 + 0.926479i
\(233\) 3.04859e9 1.76010e9i 1.03437 0.597192i 0.116134 0.993234i \(-0.462950\pi\)
0.918233 + 0.396041i \(0.129616\pi\)
\(234\) 0 0
\(235\) 6.16520e8 1.06784e9i 0.202151 0.350135i
\(236\) 1.73134e8 + 4.75681e8i 0.0558128 + 0.153344i
\(237\) 0 0
\(238\) 3.37963e9 2.83585e9i 1.05332 0.883844i
\(239\) 1.07538e9 2.95458e9i 0.329587 0.905533i −0.658629 0.752468i \(-0.728863\pi\)
0.988216 0.153065i \(-0.0489144\pi\)
\(240\) 0 0
\(241\) 6.25199e8 3.54568e9i 0.185332 1.05107i −0.740196 0.672391i \(-0.765267\pi\)
0.925528 0.378679i \(-0.123622\pi\)
\(242\) 4.82009e9i 1.40538i
\(243\) 0 0
\(244\) 1.82966e9 0.516192
\(245\) 1.29222e9 + 2.27853e8i 0.358651 + 0.0632398i
\(246\) 0 0
\(247\) −2.83256e7 1.03097e7i −0.00761012 0.00276986i
\(248\) 3.99489e8 + 4.76093e8i 0.105608 + 0.125859i
\(249\) 0 0
\(250\) 2.52439e9 9.18802e8i 0.646243 0.235213i
\(251\) 1.40741e9 + 8.12567e8i 0.354589 + 0.204722i 0.666705 0.745322i \(-0.267704\pi\)
−0.312116 + 0.950044i \(0.601038\pi\)
\(252\) 0 0
\(253\) −1.76197e9 3.05182e9i −0.430047 0.744863i
\(254\) 2.13574e9 2.54528e9i 0.513114 0.611506i
\(255\) 0 0
\(256\) −5.78550e8 3.28112e9i −0.134704 0.763945i
\(257\) −5.64879e8 + 9.96034e7i −0.129486 + 0.0228319i −0.238016 0.971261i \(-0.576497\pi\)
0.108530 + 0.994093i \(0.465386\pi\)
\(258\) 0 0
\(259\) 1.54624e9 + 1.29745e9i 0.343619 + 0.288330i
\(260\) 1.71427e9 9.89732e8i 0.375133 0.216583i
\(261\) 0 0
\(262\) −2.84732e9 + 4.93170e9i −0.604269 + 1.04663i
\(263\) 2.40422e9 + 6.60554e9i 0.502517 + 1.38065i 0.888809 + 0.458278i \(0.151534\pi\)
−0.386292 + 0.922377i \(0.626244\pi\)
\(264\) 0 0
\(265\) −5.28744e9 + 4.43669e9i −1.07217 + 0.899654i
\(266\) −1.35047e7 + 3.71038e7i −0.00269748 + 0.00741126i
\(267\) 0 0
\(268\) −2.61857e8 + 1.48507e9i −0.0507604 + 0.287877i
\(269\) 8.50405e9i 1.62411i 0.583578 + 0.812057i \(0.301652\pi\)
−0.583578 + 0.812057i \(0.698348\pi\)
\(270\) 0 0
\(271\) 3.66496e9 0.679504 0.339752 0.940515i \(-0.389657\pi\)
0.339752 + 0.940515i \(0.389657\pi\)
\(272\) −5.02280e9 8.85656e8i −0.917636 0.161804i
\(273\) 0 0
\(274\) 4.72554e9 + 1.71995e9i 0.838395 + 0.305151i
\(275\) −9.06942e9 1.08085e10i −1.58580 1.88988i
\(276\) 0 0
\(277\) −7.34026e9 + 2.67163e9i −1.24679 + 0.453793i −0.879315 0.476241i \(-0.841999\pi\)
−0.367472 + 0.930035i \(0.619777\pi\)
\(278\) 4.95083e9 + 2.85836e9i 0.828894 + 0.478562i
\(279\) 0 0
\(280\) −5.86914e9 1.01657e10i −0.954866 1.65388i
\(281\) 1.00634e9 1.19931e9i 0.161405 0.192356i −0.679280 0.733879i \(-0.737708\pi\)
0.840686 + 0.541524i \(0.182152\pi\)
\(282\) 0 0
\(283\) 1.38681e9 + 7.86497e9i 0.216207 + 1.22617i 0.878799 + 0.477192i \(0.158345\pi\)
−0.662592 + 0.748980i \(0.730544\pi\)
\(284\) −8.80006e8 + 1.55169e8i −0.135273 + 0.0238523i
\(285\) 0 0
\(286\) 6.82019e9 + 5.72282e9i 1.01937 + 0.855354i
\(287\) 1.07724e10 6.21945e9i 1.58776 0.916693i
\(288\) 0 0
\(289\) 3.99650e9 6.92215e9i 0.572913 0.992315i
\(290\) −4.30593e9 1.18305e10i −0.608801 1.67267i
\(291\) 0 0
\(292\) −3.89331e8 + 3.26688e8i −0.0535535 + 0.0449367i
\(293\) −3.64627e9 + 1.00180e10i −0.494741 + 1.35929i 0.401555 + 0.915835i \(0.368470\pi\)
−0.896296 + 0.443456i \(0.853752\pi\)
\(294\) 0 0
\(295\) 1.19981e9 6.80448e9i 0.158426 0.898477i
\(296\) 3.37354e9i 0.439459i
\(297\) 0 0
\(298\) −6.51300e9 −0.825878
\(299\) −4.00060e9 7.05414e8i −0.500542 0.0882590i
\(300\) 0 0
\(301\) 5.95716e9 + 2.16823e9i 0.725727 + 0.264143i
\(302\) 4.41187e9 + 5.25787e9i 0.530390 + 0.632094i
\(303\) 0 0
\(304\) 4.28941e7 1.56122e7i 0.00502231 0.00182797i
\(305\) −2.16279e10 1.24869e10i −2.49928 1.44296i
\(306\) 0 0
\(307\) −1.42521e9 2.46854e9i −0.160445 0.277899i 0.774583 0.632472i \(-0.217960\pi\)
−0.935028 + 0.354573i \(0.884626\pi\)
\(308\) −2.96641e9 + 3.53523e9i −0.329632 + 0.392840i
\(309\) 0 0
\(310\) −3.25390e8 1.84538e9i −0.0352336 0.199820i
\(311\) −1.12462e10 + 1.98300e9i −1.20216 + 0.211974i −0.738633 0.674108i \(-0.764528\pi\)
−0.463529 + 0.886082i \(0.653417\pi\)
\(312\) 0 0
\(313\) 3.45161e9 + 2.89625e9i 0.359621 + 0.301758i 0.804639 0.593764i \(-0.202359\pi\)
−0.445019 + 0.895521i \(0.646803\pi\)
\(314\) 5.41844e9 3.12834e9i 0.557386 0.321807i
\(315\) 0 0
\(316\) −5.83602e8 + 1.01083e9i −0.0585287 + 0.101375i
\(317\) −1.83180e9 5.03284e9i −0.181402 0.498398i 0.815347 0.578973i \(-0.196546\pi\)
−0.996749 + 0.0805754i \(0.974324\pi\)
\(318\) 0 0
\(319\) −1.71651e10 + 1.44032e10i −1.65762 + 1.39091i
\(320\) −6.25299e9 + 1.71800e10i −0.596332 + 1.63841i
\(321\) 0 0
\(322\) −9.24024e8 + 5.24040e9i −0.0859527 + 0.487462i
\(323\) 1.33969e8i 0.0123082i
\(324\) 0 0
\(325\) −1.62651e10 −1.45789
\(326\) 6.08340e9 + 1.07267e9i 0.538612 + 0.0949718i
\(327\) 0 0
\(328\) −1.95358e10 7.11045e9i −1.68786 0.614330i
\(329\) 2.13013e9 + 2.53859e9i 0.181812 + 0.216675i
\(330\) 0 0
\(331\) −3.90947e9 + 1.42293e9i −0.325691 + 0.118542i −0.499691 0.866204i \(-0.666553\pi\)
0.174000 + 0.984746i \(0.444331\pi\)
\(332\) 2.86173e8 + 1.65222e8i 0.0235546 + 0.0135992i
\(333\) 0 0
\(334\) 1.70106e9 + 2.94632e9i 0.136689 + 0.236752i
\(335\) 1.32305e10 1.57675e10i 1.05050 1.25194i
\(336\) 0 0
\(337\) −1.67135e9 9.47871e9i −0.129583 0.734902i −0.978480 0.206343i \(-0.933844\pi\)
0.848897 0.528559i \(-0.177267\pi\)
\(338\) −7.72364e8 + 1.36189e8i −0.0591773 + 0.0104346i
\(339\) 0 0
\(340\) −6.73924e9 5.65490e9i −0.504307 0.423164i
\(341\) −2.88829e9 + 1.66756e9i −0.213611 + 0.123328i
\(342\) 0 0
\(343\) 5.91133e9 1.02387e10i 0.427080 0.739724i
\(344\) −3.62384e9 9.95641e9i −0.258782 0.710999i
\(345\) 0 0
\(346\) −1.19816e10 + 1.00537e10i −0.836007 + 0.701493i
\(347\) 6.87957e7 1.89015e8i 0.00474508 0.0130370i −0.937297 0.348530i \(-0.886681\pi\)
0.942043 + 0.335493i \(0.108903\pi\)
\(348\) 0 0
\(349\) 2.82255e9 1.60075e10i 0.190257 1.07900i −0.728756 0.684773i \(-0.759901\pi\)
0.919013 0.394227i \(-0.128988\pi\)
\(350\) 2.13058e10i 1.41979i
\(351\) 0 0
\(352\) 1.37224e10 0.893838
\(353\) −5.10574e9 9.00279e8i −0.328821 0.0579800i 0.00680064 0.999977i \(-0.497835\pi\)
−0.335622 + 0.941997i \(0.608946\pi\)
\(354\) 0 0
\(355\) 1.14613e10 + 4.17157e9i 0.721639 + 0.262655i
\(356\) −2.08270e9 2.48206e9i −0.129666 0.154530i
\(357\) 0 0
\(358\) 9.60827e9 3.49712e9i 0.584942 0.212902i
\(359\) 2.29627e10 + 1.32575e10i 1.38244 + 0.798151i 0.992448 0.122668i \(-0.0391449\pi\)
0.389991 + 0.920819i \(0.372478\pi\)
\(360\) 0 0
\(361\) 8.49118e9 + 1.47072e10i 0.499965 + 0.865964i
\(362\) −1.99515e9 + 2.37773e9i −0.116183 + 0.138461i
\(363\) 0 0
\(364\) 9.23805e8 + 5.23916e9i 0.0526229 + 0.298439i
\(365\) 6.83172e9 1.20462e9i 0.384910 0.0678700i
\(366\) 0 0
\(367\) 2.18128e10 + 1.83031e10i 1.20239 + 1.00893i 0.999558 + 0.0297143i \(0.00945975\pi\)
0.202834 + 0.979213i \(0.434985\pi\)
\(368\) 5.32749e9 3.07583e9i 0.290490 0.167714i
\(369\) 0 0
\(370\) −5.08570e9 + 8.80870e9i −0.271359 + 0.470007i
\(371\) −6.34462e9 1.74317e10i −0.334896 0.920120i
\(372\) 0 0
\(373\) 2.43295e9 2.04149e9i 0.125689 0.105466i −0.577776 0.816195i \(-0.696079\pi\)
0.703465 + 0.710729i \(0.251635\pi\)
\(374\) 1.35333e10 3.71825e10i 0.691700 1.90043i
\(375\) 0 0
\(376\) 9.61774e8 5.45449e9i 0.0481196 0.272900i
\(377\) 2.58308e10i 1.27871i
\(378\) 0 0
\(379\) −2.63613e10 −1.27764 −0.638822 0.769354i \(-0.720578\pi\)
−0.638822 + 0.769354i \(0.720578\pi\)
\(380\) 7.75400e7 + 1.36724e7i 0.00371870 + 0.000655707i
\(381\) 0 0
\(382\) −1.25484e9 4.56724e8i −0.0589297 0.0214487i
\(383\) −5.71089e9 6.80598e9i −0.265405 0.316297i 0.616839 0.787089i \(-0.288413\pi\)
−0.882244 + 0.470792i \(0.843968\pi\)
\(384\) 0 0
\(385\) 5.91920e10 2.15441e10i 2.69414 0.980587i
\(386\) −2.97287e10 1.71639e10i −1.33914 0.773153i
\(387\) 0 0
\(388\) −5.64634e8 9.77975e8i −0.0249138 0.0431520i
\(389\) −3.83291e9 + 4.56788e9i −0.167390 + 0.199488i −0.843218 0.537572i \(-0.819342\pi\)
0.675828 + 0.737059i \(0.263786\pi\)
\(390\) 0 0
\(391\) 3.13511e9 + 1.77801e10i 0.134136 + 0.760725i
\(392\) 5.80446e9 1.02348e9i 0.245820 0.0433448i
\(393\) 0 0
\(394\) 4.44152e9 + 3.72688e9i 0.184309 + 0.154654i
\(395\) 1.37972e10 7.96582e9i 0.566765 0.327222i
\(396\) 0 0
\(397\) −1.60190e9 + 2.77457e9i −0.0644871 + 0.111695i −0.896466 0.443112i \(-0.853874\pi\)
0.831979 + 0.554807i \(0.187208\pi\)
\(398\) −4.51344e9 1.24006e10i −0.179877 0.494208i
\(399\) 0 0
\(400\) 1.88682e10 1.58323e10i 0.737038 0.618449i
\(401\) −1.33575e10 + 3.66996e10i −0.516594 + 1.41933i 0.357656 + 0.933853i \(0.383576\pi\)
−0.874250 + 0.485477i \(0.838646\pi\)
\(402\) 0 0
\(403\) −6.67616e8 + 3.78624e9i −0.0253108 + 0.143545i
\(404\) 1.26763e10i 0.475848i
\(405\) 0 0
\(406\) 3.38359e10 1.24530
\(407\) 1.78283e10 + 3.14361e9i 0.649729 + 0.114565i
\(408\) 0 0
\(409\) −3.94804e10 1.43697e10i −1.41087 0.513516i −0.479488 0.877548i \(-0.659178\pi\)
−0.931386 + 0.364032i \(0.881400\pi\)
\(410\) 4.02910e10 + 4.80170e10i 1.42585 + 1.69926i
\(411\) 0 0
\(412\) −5.36959e9 + 1.95437e9i −0.186360 + 0.0678294i
\(413\) 1.60819e10 + 9.28487e9i 0.552760 + 0.319136i
\(414\) 0 0
\(415\) −2.25518e9 3.90608e9i −0.0760306 0.131689i
\(416\) 1.01682e10 1.21180e10i 0.339523 0.404628i
\(417\) 0 0
\(418\) 6.14950e7 + 3.48755e8i 0.00201435 + 0.0114239i
\(419\) −2.44273e10 + 4.30720e9i −0.792538 + 0.139746i −0.555239 0.831691i \(-0.687373\pi\)
−0.237299 + 0.971437i \(0.576262\pi\)
\(420\) 0 0
\(421\) −4.34557e10 3.64636e10i −1.38331 1.16073i −0.967971 0.251062i \(-0.919220\pi\)
−0.415335 0.909669i \(-0.636335\pi\)
\(422\) 1.69917e10 9.81015e9i 0.535780 0.309333i
\(423\) 0 0
\(424\) −1.55020e10 + 2.68502e10i −0.479650 + 0.830778i
\(425\) 2.47240e10 + 6.79287e10i 0.757815 + 2.08208i
\(426\) 0 0
\(427\) 5.14163e10 4.31434e10i 1.54664 1.29778i
\(428\) −1.52703e9 + 4.19547e9i −0.0455063 + 0.125028i
\(429\) 0 0
\(430\) −5.54732e9 + 3.14604e10i −0.162259 + 0.920217i
\(431\) 6.46311e10i 1.87298i 0.350698 + 0.936489i \(0.385945\pi\)
−0.350698 + 0.936489i \(0.614055\pi\)
\(432\) 0 0
\(433\) 2.65628e10 0.755653 0.377826 0.925876i \(-0.376672\pi\)
0.377826 + 0.925876i \(0.376672\pi\)
\(434\) 4.95961e9 + 8.74513e8i 0.139794 + 0.0246494i
\(435\) 0 0
\(436\) 1.37776e9 + 5.01463e8i 0.0381265 + 0.0138769i
\(437\) −1.03865e8 1.23781e8i −0.00284801 0.00339413i
\(438\) 0 0
\(439\) −5.28937e10 + 1.92517e10i −1.42412 + 0.518337i −0.935240 0.354015i \(-0.884816\pi\)
−0.488878 + 0.872352i \(0.662594\pi\)
\(440\) −9.11741e10 5.26394e10i −2.43255 1.40443i
\(441\) 0 0
\(442\) −2.28070e10 3.95029e10i −0.597557 1.03500i
\(443\) −2.12742e10 + 2.53536e10i −0.552381 + 0.658302i −0.967916 0.251275i \(-0.919150\pi\)
0.415534 + 0.909577i \(0.363595\pi\)
\(444\) 0 0
\(445\) 7.67966e9 + 4.35535e10i 0.195840 + 1.11066i
\(446\) −1.31733e10 + 2.32281e9i −0.332932 + 0.0587049i
\(447\) 0 0
\(448\) −3.76403e10 3.15839e10i −0.934417 0.784069i
\(449\) 6.27975e10 3.62562e10i 1.54510 0.892065i 0.546597 0.837396i \(-0.315923\pi\)
0.998505 0.0546691i \(-0.0174104\pi\)
\(450\) 0 0
\(451\) 5.57812e10 9.66159e10i 1.34829 2.33530i
\(452\) 2.78842e9 + 7.66113e9i 0.0668043 + 0.183543i
\(453\) 0 0
\(454\) 6.62650e9 5.56030e9i 0.155977 0.130880i
\(455\) 2.48356e10 6.82353e10i 0.579468 1.59208i
\(456\) 0 0
\(457\) −9.23518e9 + 5.23753e10i −0.211729 + 1.20078i 0.674764 + 0.738033i \(0.264245\pi\)
−0.886493 + 0.462742i \(0.846866\pi\)
\(458\) 8.28893e9i 0.188381i
\(459\) 0 0
\(460\) 1.06110e10 0.236986
\(461\) 3.01751e10 + 5.32068e9i 0.668104 + 0.117805i 0.497405 0.867518i \(-0.334286\pi\)
0.170699 + 0.985323i \(0.445397\pi\)
\(462\) 0 0
\(463\) 3.02920e10 + 1.10254e10i 0.659181 + 0.239922i 0.649883 0.760035i \(-0.274818\pi\)
0.00929829 + 0.999957i \(0.497040\pi\)
\(464\) −2.51434e10 2.99648e10i −0.542441 0.646456i
\(465\) 0 0
\(466\) −4.47997e10 + 1.63058e10i −0.950017 + 0.345778i
\(467\) −4.49907e10 2.59754e10i −0.945922 0.546129i −0.0541106 0.998535i \(-0.517232\pi\)
−0.891812 + 0.452406i \(0.850566\pi\)
\(468\) 0 0
\(469\) 2.76592e10 + 4.79072e10i 0.571674 + 0.990169i
\(470\) −1.07341e10 + 1.27924e10i −0.219976 + 0.262157i
\(471\) 0 0
\(472\) −5.38939e9 3.05648e10i −0.108585 0.615819i
\(473\) 5.59940e10 9.87325e9i 1.11866 0.197249i
\(474\) 0 0
\(475\) −4.95608e8 4.15865e8i −0.00973563 0.00816916i
\(476\) 2.04762e10 1.18220e10i 0.398862 0.230283i
\(477\) 0 0
\(478\) −2.12913e10 + 3.68776e10i −0.407840 + 0.706400i
\(479\) 7.77313e9 + 2.13565e10i 0.147657 + 0.405684i 0.991367 0.131115i \(-0.0418556\pi\)
−0.843710 + 0.536799i \(0.819633\pi\)
\(480\) 0 0
\(481\) 1.59867e10 1.34144e10i 0.298660 0.250606i
\(482\) −1.66771e10 + 4.58201e10i −0.308982 + 0.848922i
\(483\) 0 0
\(484\) −4.48568e9 + 2.54396e10i −0.0817424 + 0.463584i
\(485\) 1.54138e10i 0.278576i
\(486\) 0 0
\(487\) −6.87683e10 −1.22257 −0.611283 0.791412i \(-0.709346\pi\)
−0.611283 + 0.791412i \(0.709346\pi\)
\(488\) −1.10474e11 1.94796e10i −1.94797 0.343480i
\(489\) 0 0
\(490\) −1.66991e10 6.07796e9i −0.289673 0.105432i
\(491\) −4.69265e10 5.59248e10i −0.807406 0.962229i 0.192412 0.981314i \(-0.438369\pi\)
−0.999818 + 0.0190855i \(0.993925\pi\)
\(492\) 0 0
\(493\) 1.07878e11 3.92645e10i 1.82619 0.664679i
\(494\) 3.53546e8 + 2.04120e8i 0.00593660 + 0.00342750i
\(495\) 0 0
\(496\) −2.91102e9 5.04203e9i −0.0480970 0.0833064i
\(497\) −2.10706e10 + 2.51110e10i −0.345344 + 0.411565i
\(498\) 0 0
\(499\) 6.66714e9 + 3.78112e10i 0.107532 + 0.609844i 0.990179 + 0.139807i \(0.0446482\pi\)
−0.882647 + 0.470037i \(0.844241\pi\)
\(500\) 1.41783e10 2.50002e9i 0.226853 0.0400004i
\(501\) 0 0
\(502\) −1.68603e10 1.41475e10i −0.265491 0.222774i
\(503\) −1.37684e9 + 7.94918e8i −0.0215085 + 0.0124180i −0.510716 0.859750i \(-0.670620\pi\)
0.489207 + 0.872168i \(0.337286\pi\)
\(504\) 0 0
\(505\) −8.65122e10 + 1.49844e11i −1.33018 + 2.30395i
\(506\) 1.63230e10 + 4.48472e10i 0.249000 + 0.684121i
\(507\) 0 0
\(508\) 1.36408e10 1.14460e10i 0.204826 0.171869i
\(509\) 2.97231e10 8.16637e10i 0.442816 1.21663i −0.494816 0.868998i \(-0.664764\pi\)
0.937632 0.347630i \(-0.113013\pi\)
\(510\) 0 0
\(511\) −3.23751e9 + 1.83608e10i −0.0474819 + 0.269283i
\(512\) 7.14453e10i 1.03967i
\(513\) 0 0
\(514\) 7.76829e9 0.111294
\(515\) 7.68104e10 + 1.35437e10i 1.09192 + 0.192535i
\(516\) 0 0
\(517\) 2.79294e10 + 1.01655e10i 0.390930 + 0.142287i
\(518\) −1.75716e10 2.09410e10i −0.244057 0.290856i
\(519\) 0 0
\(520\) −1.14044e11 + 4.15086e10i −1.55977 + 0.567708i
\(521\) −1.18023e11 6.81406e10i −1.60183 0.924815i −0.991122 0.132956i \(-0.957553\pi\)
−0.610704 0.791859i \(-0.709114\pi\)
\(522\) 0 0
\(523\) −1.68568e10 2.91969e10i −0.225304 0.390238i 0.731107 0.682263i \(-0.239004\pi\)
−0.956411 + 0.292025i \(0.905671\pi\)
\(524\) −1.96172e10 + 2.33789e10i −0.260203 + 0.310098i
\(525\) 0 0
\(526\) −1.65316e10 9.37552e10i −0.215959 1.22476i
\(527\) 1.68274e10 2.96713e9i 0.218160 0.0384675i
\(528\) 0 0
\(529\) 4.33082e10 + 3.63399e10i 0.553029 + 0.464046i
\(530\) 8.09551e10 4.67394e10i 1.02598 0.592352i
\(531\) 0 0
\(532\) −1.05805e8 + 1.83260e8i −0.00132087 + 0.00228781i
\(533\) −4.39861e10 1.20851e11i −0.545013 1.49741i
\(534\) 0 0
\(535\) 4.66834e10 3.91720e10i 0.569832 0.478146i
\(536\) 3.16217e10 8.68799e10i 0.383112 1.05259i
\(537\) 0 0
\(538\) 1.99994e10 1.13422e11i 0.238720 1.35385i
\(539\) 3.16289e10i 0.374739i
\(540\) 0 0
\(541\) 1.02849e11 1.20064 0.600319 0.799760i \(-0.295040\pi\)
0.600319 + 0.799760i \(0.295040\pi\)
\(542\) −4.88813e10 8.61908e9i −0.566429 0.0998767i
\(543\) 0 0
\(544\) −6.60649e10 2.40457e10i −0.754354 0.274562i
\(545\) −1.28638e10 1.53304e10i −0.145808 0.173767i
\(546\) 0 0
\(547\) −1.29316e11 + 4.70673e10i −1.44446 + 0.525739i −0.941037 0.338304i \(-0.890147\pi\)
−0.503418 + 0.864043i \(0.667925\pi\)
\(548\) 2.33399e10 + 1.34753e10i 0.258808 + 0.149423i
\(549\) 0 0
\(550\) 9.55441e10 + 1.65487e11i 1.04413 + 1.80848i
\(551\) −6.60439e8 + 7.87081e8i −0.00716517 + 0.00853912i
\(552\) 0 0
\(553\) 7.43521e9 + 4.21672e10i 0.0795047 + 0.450893i
\(554\) 1.04183e11 1.83703e10i 1.10601 0.195020i
\(555\) 0 0
\(556\) 2.34696e10 + 1.96933e10i 0.245587 + 0.206072i
\(557\) −1.34913e11 + 7.78922e10i −1.40163 + 0.809232i −0.994560 0.104165i \(-0.966783\pi\)
−0.407071 + 0.913397i \(0.633450\pi\)
\(558\) 0 0
\(559\) 3.27722e10 5.67631e10i 0.335628 0.581325i
\(560\) 3.76091e10 + 1.03330e11i 0.382421 + 1.05069i
\(561\) 0 0
\(562\) −1.62425e10 + 1.36290e10i −0.162820 + 0.136622i
\(563\) −3.49849e10 + 9.61202e10i −0.348214 + 0.956711i 0.634718 + 0.772744i \(0.281116\pi\)
−0.982932 + 0.183967i \(0.941106\pi\)
\(564\) 0 0
\(565\) 1.93237e10 1.09590e11i 0.189625 1.07542i
\(566\) 1.08160e11i 1.05391i
\(567\) 0 0
\(568\) 5.47865e10 0.526356
\(569\) 8.94456e10 + 1.57717e10i 0.853316 + 0.150463i 0.583163 0.812355i \(-0.301815\pi\)
0.270152 + 0.962818i \(0.412926\pi\)
\(570\) 0 0
\(571\) −1.14927e11 4.18298e10i −1.08113 0.393497i −0.260799 0.965393i \(-0.583986\pi\)
−0.820326 + 0.571896i \(0.806208\pi\)
\(572\) 3.06700e10 + 3.65511e10i 0.286503 + 0.341441i
\(573\) 0 0
\(574\) −1.58303e11 + 5.76176e10i −1.45828 + 0.530771i
\(575\) −7.55084e10 4.35948e10i −0.690755 0.398807i
\(576\) 0 0
\(577\) −1.35572e9 2.34817e9i −0.0122311 0.0211849i 0.859845 0.510555i \(-0.170560\pi\)
−0.872076 + 0.489370i \(0.837227\pi\)
\(578\) −6.95824e10 + 8.29251e10i −0.623431 + 0.742976i
\(579\) 0 0
\(580\) −1.17163e10 6.64463e10i −0.103533 0.587163i
\(581\) 1.19378e10 2.10496e9i 0.104766 0.0184731i
\(582\) 0 0
\(583\) −1.27451e11 1.06944e11i −1.10324 0.925729i
\(584\) 2.69858e10 1.55803e10i 0.231998 0.133944i
\(585\) 0 0
\(586\) 7.21919e10 1.25040e11i 0.612207 1.06037i
\(587\) 4.01800e10 + 1.10394e11i 0.338421 + 0.929805i 0.985843 + 0.167673i \(0.0536253\pi\)
−0.647421 + 0.762132i \(0.724153\pi\)
\(588\) 0 0
\(589\) −1.17149e8 + 9.82993e7i −0.000973365 + 0.000816751i
\(590\) −3.20049e10 + 8.79328e10i −0.264125 + 0.725677i
\(591\) 0 0
\(592\) −5.48773e9 + 3.11224e10i −0.0446792 + 0.253389i
\(593\) 1.69673e11i 1.37212i 0.727544 + 0.686061i \(0.240662\pi\)
−0.727544 + 0.686061i \(0.759338\pi\)
\(594\) 0 0
\(595\) −3.22725e11 −2.57493
\(596\) −3.43745e10 6.06115e9i −0.272428 0.0480364i
\(597\) 0 0
\(598\) 5.16989e10 + 1.88168e10i 0.404274 + 0.147144i
\(599\) 1.03440e11 + 1.23275e11i 0.803493 + 0.957566i 0.999736 0.0229897i \(-0.00731850\pi\)
−0.196243 + 0.980555i \(0.562874\pi\)
\(600\) 0 0
\(601\) 1.59242e11 5.79593e10i 1.22056 0.444248i 0.350206 0.936673i \(-0.386112\pi\)
0.870355 + 0.492425i \(0.163889\pi\)
\(602\) −7.43542e10 4.29284e10i −0.566135 0.326858i
\(603\) 0 0
\(604\) 1.83920e10 + 3.18559e10i 0.138192 + 0.239355i
\(605\) 2.26641e11 2.70101e11i 1.69168 2.01606i
\(606\) 0 0
\(607\) 3.08833e10 + 1.75148e11i 0.227494 + 1.29018i 0.857860 + 0.513883i \(0.171794\pi\)
−0.630366 + 0.776298i \(0.717095\pi\)
\(608\) 6.19660e8 1.09263e8i 0.00453460 0.000799573i
\(609\) 0 0
\(610\) 2.59096e11 + 2.17407e11i 1.87129 + 1.57020i
\(611\) 2.96724e10 1.71314e10i 0.212906 0.122921i
\(612\) 0 0
\(613\) −2.91010e10 + 5.04044e10i −0.206094 + 0.356966i −0.950481 0.310783i \(-0.899409\pi\)
0.744387 + 0.667749i \(0.232742\pi\)
\(614\) 1.32033e10 + 3.62758e10i 0.0928987 + 0.255237i
\(615\) 0 0
\(616\) 2.16749e11 1.81874e11i 1.50534 1.26313i
\(617\) −4.57298e10 + 1.25641e11i −0.315543 + 0.866947i 0.675969 + 0.736930i \(0.263725\pi\)
−0.991512 + 0.130017i \(0.958497\pi\)
\(618\) 0 0
\(619\) 2.33487e10 1.32417e11i 0.159038 0.901948i −0.795963 0.605345i \(-0.793035\pi\)
0.955001 0.296603i \(-0.0958538\pi\)
\(620\) 1.00424e10i 0.0679627i
\(621\) 0 0
\(622\) 1.54659e11 1.03327
\(623\) −1.17054e11 2.06397e10i −0.777022 0.137010i
\(624\) 0 0
\(625\) 3.22202e10 + 1.17272e10i 0.211158 + 0.0768554i
\(626\) −3.92245e10 4.67459e10i −0.255423 0.304401i
\(627\) 0 0
\(628\) 3.15089e10 1.14683e10i 0.202579 0.0737328i
\(629\) −8.03238e10 4.63750e10i −0.513147 0.296265i
\(630\) 0 0
\(631\) −1.52481e10 2.64105e10i −0.0961831 0.166594i 0.813919 0.580979i \(-0.197330\pi\)
−0.910102 + 0.414385i \(0.863997\pi\)
\(632\) 4.59996e10 5.48202e10i 0.288327 0.343615i
\(633\) 0 0
\(634\) 1.25956e10 + 7.14333e10i 0.0779583 + 0.442123i
\(635\) −2.39359e11 + 4.22055e10i −1.47216 + 0.259582i
\(636\) 0 0
\(637\) 2.79308e10 + 2.34367e10i 0.169639 + 0.142344i
\(638\) 2.62812e11 1.51735e11i 1.58622 0.915802i
\(639\) 0 0
\(640\) 5.09334e10 8.82193e10i 0.303587 0.525828i
\(641\) −7.45477e10 2.04818e11i −0.441572 1.21321i −0.938458 0.345394i \(-0.887745\pi\)
0.496885 0.867816i \(-0.334477\pi\)
\(642\) 0 0
\(643\) −1.17314e11 + 9.84380e10i −0.686286 + 0.575863i −0.917836 0.396961i \(-0.870065\pi\)
0.231549 + 0.972823i \(0.425621\pi\)
\(644\) −9.75368e9 + 2.67980e10i −0.0567055 + 0.155797i
\(645\) 0 0
\(646\) 3.15061e8 1.78680e9i 0.00180911 0.0102600i
\(647\) 1.23404e11i 0.704226i 0.935957 + 0.352113i \(0.114537\pi\)
−0.935957 + 0.352113i \(0.885463\pi\)
\(648\) 0 0
\(649\) 1.66549e11 0.938780
\(650\) 2.16936e11 + 3.82516e10i 1.21528 + 0.214287i
\(651\) 0 0
\(652\) 3.11089e10 + 1.13227e10i 0.172145 + 0.0626556i
\(653\) 4.83237e10 + 5.75899e10i 0.265771 + 0.316733i 0.882381 0.470535i \(-0.155939\pi\)
−0.616610 + 0.787268i \(0.711495\pi\)
\(654\) 0 0
\(655\) 3.91443e11 1.42474e11i 2.12669 0.774051i
\(656\) 1.68660e11 + 9.73761e10i 0.910747 + 0.525820i
\(657\) 0 0
\(658\) −2.24404e10 3.88680e10i −0.119709 0.207342i
\(659\) −4.53931e10 + 5.40973e10i −0.240684 + 0.286836i −0.872842 0.488004i \(-0.837725\pi\)
0.632157 + 0.774840i \(0.282170\pi\)
\(660\) 0 0
\(661\) −2.47641e10 1.40444e11i −0.129723 0.735696i −0.978390 0.206768i \(-0.933705\pi\)
0.848667 0.528928i \(-0.177406\pi\)
\(662\) 5.54888e10 9.78418e9i 0.288917 0.0509439i
\(663\) 0 0
\(664\) −1.55200e10 1.30228e10i −0.0798396 0.0669934i
\(665\) 2.50139e9 1.44418e9i 0.0127907 0.00738471i
\(666\) 0 0
\(667\) −6.92334e10 + 1.19916e11i −0.349794 + 0.605861i
\(668\) 6.23597e9 + 1.71332e10i 0.0313183 + 0.0860464i
\(669\) 0 0
\(670\) −2.13542e11 + 1.79183e11i −1.05970 + 0.889196i
\(671\) 2.05890e11 5.65678e11i 1.01565 2.79048i
\(672\) 0 0
\(673\) −1.33595e10 + 7.57657e10i −0.0651225 + 0.369328i 0.934778 + 0.355232i \(0.115598\pi\)
−0.999901 + 0.0140960i \(0.995513\pi\)
\(674\) 1.30353e11i 0.631655i
\(675\) 0 0
\(676\) −4.20314e9 −0.0201274
\(677\) 2.24167e11 + 3.95267e10i 1.06713 + 0.188164i 0.679518 0.733659i \(-0.262189\pi\)
0.387612 + 0.921823i \(0.373300\pi\)
\(678\) 0 0
\(679\) −3.89277e10 1.41685e10i −0.183138 0.0666569i
\(680\) 3.46708e11 + 4.13191e11i 1.62154 + 1.93248i
\(681\) 0 0
\(682\) 4.24442e10 1.54484e10i 0.196192 0.0714079i
\(683\) 6.00315e10 + 3.46592e10i 0.275865 + 0.159271i 0.631550 0.775335i \(-0.282419\pi\)
−0.355685 + 0.934606i \(0.615752\pi\)
\(684\) 0 0
\(685\) −1.83930e11 3.18576e11i −0.835392 1.44694i
\(686\) −1.02921e11 + 1.22657e11i −0.464738 + 0.553853i
\(687\) 0 0
\(688\) 1.72355e10 + 9.77475e10i 0.0769255 + 0.436266i
\(689\) −1.88881e11 + 3.33048e10i −0.838129 + 0.147785i
\(690\) 0 0
\(691\) −6.29010e10 5.27802e10i −0.275896 0.231504i 0.494331 0.869274i \(-0.335413\pi\)
−0.770228 + 0.637769i \(0.779857\pi\)
\(692\) −7.25930e10 + 4.19116e10i −0.316570 + 0.182772i
\(693\) 0 0
\(694\) −1.36208e9 + 2.35919e9i −0.00587170 + 0.0101701i
\(695\) −1.43026e11 3.92962e11i −0.613024 1.68427i
\(696\) 0 0
\(697\) −4.37852e11 + 3.67402e11i −1.85522 + 1.55672i
\(698\) −7.52914e10 + 2.06861e11i −0.317193 + 0.871480i
\(699\) 0 0
\(700\) −1.98276e10 + 1.12448e11i −0.0825808 + 0.468339i
\(701\) 3.67111e11i 1.52029i 0.649755 + 0.760144i \(0.274871\pi\)
−0.649755 + 0.760144i \(0.725129\pi\)
\(702\) 0 0
\(703\) 8.30101e8 0.00339867
\(704\) −4.33997e11 7.65254e10i −1.76684 0.311541i
\(705\) 0 0
\(706\) 6.59803e10 + 2.40149e10i 0.265580 + 0.0966633i
\(707\) −2.98908e11 3.56224e11i −1.19635 1.42576i
\(708\) 0 0
\(709\) −2.03327e10 + 7.40048e9i −0.0804654 + 0.0292870i −0.381939 0.924187i \(-0.624744\pi\)
0.301474 + 0.953474i \(0.402521\pi\)
\(710\) −1.43054e11 8.25922e10i −0.562945 0.325017i
\(711\) 0 0
\(712\) 9.93270e10 + 1.72039e11i 0.386498 + 0.669435i
\(713\) −1.32474e10 + 1.57876e10i −0.0512593 + 0.0610884i
\(714\) 0 0
\(715\) −1.13092e11 6.41374e11i −0.432719 2.45407i
\(716\) 5.39653e10 9.51553e9i 0.205335 0.0362060i
\(717\) 0 0
\(718\) −2.75086e11 2.30825e11i −1.03507 0.868529i
\(719\) 2.85002e11 1.64546e11i 1.06643 0.615703i 0.139226 0.990261i \(-0.455539\pi\)
0.927204 + 0.374557i \(0.122205\pi\)
\(720\) 0 0
\(721\) −1.04810e11 + 1.81535e11i −0.387846 + 0.671770i
\(722\) −7.86632e10 2.16125e11i −0.289483 0.795347i
\(723\) 0 0
\(724\) −1.27428e10 + 1.06925e10i −0.0463780 + 0.0389158i
\(725\) −1.89619e11 + 5.20973e11i −0.686324 + 1.88566i
\(726\) 0 0
\(727\) −6.75215e10 + 3.82933e11i −0.241715 + 1.37084i 0.586283 + 0.810106i \(0.300590\pi\)
−0.827999 + 0.560730i \(0.810521\pi\)
\(728\) 3.26174e11i 1.16124i
\(729\) 0 0
\(730\) −9.39508e10 −0.330833
\(731\) −2.86878e11 5.05843e10i −1.00468 0.177152i
\(732\) 0 0
\(733\) 2.34914e11 + 8.55016e10i 0.813753 + 0.296182i 0.715173 0.698947i \(-0.246348\pi\)
0.0985795 + 0.995129i \(0.468570\pi\)
\(734\) −2.47882e11 2.95415e11i −0.854007 1.01777i
\(735\) 0 0
\(736\) 7.96834e10 2.90024e10i 0.271554 0.0988377i
\(737\) 4.29672e11 + 2.48071e11i 1.45635 + 0.840827i
\(738\) 0 0
\(739\) −2.59650e11 4.49726e11i −0.870582 1.50789i −0.861395 0.507935i \(-0.830409\pi\)
−0.00918707 0.999958i \(-0.502924\pi\)
\(740\) −3.50390e10 + 4.17579e10i −0.116849 + 0.139255i
\(741\) 0 0
\(742\) 4.36261e10 + 2.47416e11i 0.143923 + 0.816228i
\(743\) 1.13404e11 1.99962e10i 0.372112 0.0656133i 0.0155348 0.999879i \(-0.495055\pi\)
0.356577 + 0.934266i \(0.383944\pi\)
\(744\) 0 0
\(745\) 3.64966e11 + 3.06243e11i 1.18475 + 0.994124i
\(746\) −3.72504e10 + 2.15065e10i −0.120275 + 0.0694409i
\(747\) 0 0
\(748\) 1.06029e11 1.83648e11i 0.338703 0.586652i
\(749\) 5.60173e10 + 1.53906e11i 0.177990 + 0.489023i
\(750\) 0 0
\(751\) −2.06886e11 + 1.73598e11i −0.650387 + 0.545740i −0.907188 0.420725i \(-0.861776\pi\)
0.256801 + 0.966464i \(0.417331\pi\)
\(752\) −1.77456e10 + 4.87557e10i −0.0554907 + 0.152459i
\(753\) 0 0
\(754\) 6.07478e10 3.44518e11i 0.187951 1.06592i
\(755\) 5.02080e11i 1.54520i
\(756\) 0 0
\(757\) −3.18441e11 −0.969719 −0.484859 0.874592i \(-0.661129\pi\)
−0.484859 + 0.874592i \(0.661129\pi\)
\(758\) 3.51593e11 + 6.19953e10i 1.06503 + 0.187794i
\(759\) 0 0
\(760\) −4.53627e9 1.65107e9i −0.0135971 0.00494892i
\(761\) −2.11330e11 2.51853e11i −0.630118 0.750946i 0.352656 0.935753i \(-0.385278\pi\)
−0.982775 + 0.184807i \(0.940834\pi\)
\(762\) 0 0
\(763\) 5.05416e10 1.83956e10i 0.149125 0.0542771i
\(764\) −6.19778e9 3.57829e9i −0.0181913 0.0105027i
\(765\) 0 0
\(766\) 6.01628e10 + 1.04205e11i 0.174748 + 0.302673i
\(767\) 1.23412e11 1.47076e11i 0.356594 0.424972i
\(768\) 0 0
\(769\) 5.37175e10 + 3.04647e11i 0.153607 + 0.871148i 0.960048 + 0.279834i \(0.0902794\pi\)
−0.806442 + 0.591314i \(0.798609\pi\)
\(770\) −8.40138e11 + 1.48139e11i −2.38994 + 0.421412i
\(771\) 0 0
\(772\) −1.40930e11 1.18254e11i −0.396765 0.332925i
\(773\) −4.97453e11 + 2.87205e11i −1.39327 + 0.804403i −0.993675 0.112291i \(-0.964181\pi\)
−0.399591 + 0.916694i \(0.630848\pi\)
\(774\) 0 0
\(775\) −4.12589e10 + 7.14625e10i −0.114370 + 0.198094i
\(776\) 2.36803e10 + 6.50612e10i 0.0653042 + 0.179422i
\(777\) 0 0
\(778\) 6.18638e10 5.19099e10i 0.168857 0.141688i
\(779\) 1.74961e9 4.80703e9i 0.00475108 0.0130535i
\(780\) 0 0
\(781\) −5.10524e10 + 2.89533e11i −0.137218 + 0.778204i
\(782\) 2.44515e11i 0.653849i
\(783\) 0 0
\(784\) −5.52138e10 −0.146145
\(785\) −4.50726e11 7.94751e10i −1.18695 0.209292i
\(786\) 0 0
\(787\) 4.88907e11 + 1.77948e11i 1.27446 + 0.463867i 0.888598 0.458687i \(-0.151680\pi\)
0.385867 + 0.922555i \(0.373902\pi\)
\(788\) 1.99732e10 + 2.38032e10i 0.0518017 + 0.0617348i
\(789\) 0 0
\(790\) −2.02753e11 + 7.37962e10i −0.520547 + 0.189463i
\(791\) 2.59008e11 + 1.49538e11i 0.661618 + 0.381985i
\(792\) 0 0
\(793\) −3.46976e11 6.00979e11i −0.877417 1.51973i
\(794\) 2.78904e10 3.32384e10i 0.0701733 0.0836293i
\(795\) 0 0
\(796\) −1.22809e10 6.96484e10i −0.0305899 0.173484i
\(797\) 2.25157e11 3.97012e10i 0.558023 0.0983945i 0.112478 0.993654i \(-0.464121\pi\)
0.445545 + 0.895260i \(0.353010\pi\)
\(798\) 0 0
\(799\) −1.16650e11 9.78811e10i −0.286219 0.240166i
\(800\) 2.94034e11 1.69760e11i 0.717856 0.414454i
\(801\) 0 0
\(802\) 2.64464e11 4.58065e11i 0.639248 1.10721i
\(803\) 5.71912e10 + 1.57132e11i 0.137552 + 0.377921i
\(804\) 0 0
\(805\) 2.98184e11 2.50206e11i 0.710069 0.595819i
\(806\) 1.78086e10 4.89287e10i 0.0421978 0.115937i
\(807\) 0 0
\(808\) −1.34960e11 + 7.65393e11i −0.316634 + 1.79572i
\(809\) 2.80231e11i 0.654218i 0.944987 + 0.327109i \(0.106074\pi\)
−0.944987 + 0.327109i \(0.893926\pi\)
\(810\) 0 0
\(811\) −6.94464e11 −1.60534 −0.802668 0.596426i \(-0.796587\pi\)
−0.802668 + 0.596426i \(0.796587\pi\)
\(812\) 1.78580e11 + 3.14885e10i 0.410780 + 0.0724316i
\(813\) 0 0
\(814\) −2.30391e11 8.38555e10i −0.524769 0.191000i
\(815\) −2.90455e11 3.46151e11i −0.658338 0.784577i
\(816\) 0 0
\(817\) 2.44990e9 8.91690e8i 0.00549870 0.00200136i
\(818\) 4.92774e11 + 2.84503e11i 1.10061 + 0.635440i
\(819\) 0 0
\(820\) 1.67963e11 + 2.90921e11i 0.371500 + 0.643458i
\(821\) −9.00287e10 + 1.07292e11i −0.198157 + 0.236154i −0.855968 0.517029i \(-0.827038\pi\)
0.657811 + 0.753183i \(0.271482\pi\)
\(822\) 0 0
\(823\) 1.32353e11 + 7.50609e11i 0.288492 + 1.63612i 0.692540 + 0.721379i \(0.256492\pi\)
−0.404048 + 0.914738i \(0.632397\pi\)
\(824\) 3.45021e11 6.08365e10i 0.748405 0.131964i
\(825\) 0 0
\(826\) −1.92656e11 1.61657e11i −0.413868 0.347276i
\(827\) −1.73429e11 + 1.00129e11i −0.370765 + 0.214061i −0.673793 0.738921i \(-0.735336\pi\)
0.303028 + 0.952982i \(0.402003\pi\)
\(828\) 0 0
\(829\) 3.02214e11 5.23449e11i 0.639876 1.10830i −0.345584 0.938388i \(-0.612319\pi\)
0.985460 0.169910i \(-0.0543476\pi\)
\(830\) 2.08922e10 + 5.74008e10i 0.0440222 + 0.120950i
\(831\) 0 0
\(832\) −3.89166e11 + 3.26549e11i −0.812160 + 0.681483i
\(833\) 5.54231e10 1.52274e11i 0.115109 0.316260i
\(834\) 0 0
\(835\) 4.32152e10 2.45085e11i 0.0888976 0.504164i
\(836\) 1.89790e9i 0.00388551i
\(837\) 0 0
\(838\) 3.35928e11 0.681193
\(839\) 8.98602e11 + 1.58448e11i 1.81351 + 0.319771i 0.974507 0.224358i \(-0.0720285\pi\)
0.839002 + 0.544129i \(0.183140\pi\)
\(840\) 0 0
\(841\) 3.57286e11 + 1.30041e11i 0.714219 + 0.259955i
\(842\) 4.93835e11 + 5.88529e11i 0.982502 + 1.17090i
\(843\) 0 0
\(844\) 9.88087e10 3.59634e10i 0.194727 0.0708747i
\(845\) 4.96842e10 + 2.86852e10i 0.0974521 + 0.0562640i
\(846\) 0 0
\(847\) 4.73810e11 + 8.20663e11i 0.920599 + 1.59452i
\(848\) 1.86690e11 2.22489e11i 0.361026 0.430254i
\(849\) 0 0
\(850\) −1.70004e11 9.64141e11i −0.325674 1.84699i
\(851\) 1.10170e11 1.94259e10i 0.210060 0.0370393i
\(852\) 0 0
\(853\) 4.59900e10 + 3.85902e10i 0.0868695 + 0.0728922i 0.685188 0.728366i \(-0.259720\pi\)
−0.598319 + 0.801258i \(0.704164\pi\)
\(854\) −7.87225e11 + 4.54505e11i −1.48002 + 0.854490i
\(855\) 0 0
\(856\) 1.36869e11 2.37064e11i 0.254923 0.441540i
\(857\) 1.56719e11 + 4.30581e11i 0.290535 + 0.798237i 0.995988 + 0.0894815i \(0.0285210\pi\)
−0.705454 + 0.708756i \(0.749257\pi\)
\(858\) 0 0
\(859\) 2.76176e11 2.31740e11i 0.507241 0.425625i −0.352916 0.935655i \(-0.614810\pi\)
0.860157 + 0.510030i \(0.170366\pi\)
\(860\) −5.85556e10 + 1.60880e11i −0.107047 + 0.294109i
\(861\) 0 0
\(862\) 1.51996e11 8.62015e11i 0.275299 1.56130i
\(863\) 8.65609e11i 1.56055i −0.625435 0.780276i \(-0.715078\pi\)
0.625435 0.780276i \(-0.284922\pi\)
\(864\) 0 0
\(865\) 1.14414e12 2.04368
\(866\) −3.54280e11 6.24692e10i −0.629906 0.111069i
\(867\) 0 0
\(868\) 2.53621e10 + 9.23105e9i 0.0446793 + 0.0162619i
\(869\) 2.46846e11 + 2.94180e11i 0.432860 + 0.515863i
\(870\) 0 0
\(871\) 5.37450e11 1.95616e11i 0.933825 0.339885i
\(872\) −7.78497e10 4.49465e10i −0.134645 0.0777375i
\(873\) 0 0
\(874\) 1.09419e9 + 1.89519e9i 0.00187519 + 0.00324793i
\(875\) 3.39482e11 4.04579e11i 0.579142 0.690195i
\(876\) 0 0
\(877\) −5.54872e10 3.14683e11i −0.0937981 0.531956i −0.995109 0.0987829i \(-0.968505\pi\)
0.901311 0.433173i \(-0.142606\pi\)
\(878\) 7.50743e11 1.32376e11i 1.26332 0.222757i
\(879\) 0 0
\(880\) 7.55496e11 + 6.33936e11i 1.25980 + 1.05710i
\(881\) 7.29538e11 4.21199e11i 1.21100 0.699172i 0.248024 0.968754i \(-0.420219\pi\)
0.962977 + 0.269582i \(0.0868856\pi\)
\(882\) 0 0
\(883\) −5.44619e11 + 9.43307e11i −0.895880 + 1.55171i −0.0631678 + 0.998003i \(0.520120\pi\)
−0.832712 + 0.553706i \(0.813213\pi\)
\(884\) −8.36091e10 2.29714e11i −0.136913 0.376165i
\(885\) 0 0
\(886\) 3.43370e11 2.88121e11i 0.557221 0.467564i
\(887\) −1.25823e11 + 3.45697e11i −0.203267 + 0.558471i −0.998879 0.0473352i \(-0.984927\pi\)
0.795612 + 0.605806i \(0.207149\pi\)
\(888\) 0 0
\(889\) 1.13431e11 6.43299e11i 0.181604 1.02992i
\(890\) 5.98954e11i 0.954626i
\(891\) 0 0
\(892\) −7.16881e10 −0.113237
\(893\) 1.34215e9 + 2.36657e8i 0.00211054 + 0.000372145i
\(894\) 0 0
\(895\) −7.02849e11 2.55816e11i −1.09539 0.398690i
\(896\) 1.75980e11 + 2.09725e11i 0.273043 + 0.325400i
\(897\) 0 0
\(898\) −9.22825e11 + 3.35881e11i −1.41910 + 0.516511i
\(899\) 1.13490e11 + 6.55237e10i 0.173748 + 0.100314i
\(900\) 0 0
\(901\) 4.26202e11 + 7.38204e11i 0.646721 + 1.12015i
\(902\) −9.71197e11 + 1.15743e12i −1.46717 + 1.74851i
\(903\) 0 0
\(904\) −8.67993e10 4.92263e11i −0.129970 0.737096i
\(905\) 2.23603e11 3.94272e10i 0.333337 0.0587762i
\(906\) 0 0
\(907\) −1.47819e11 1.24035e11i −0.218425 0.183280i 0.527009 0.849860i \(-0.323313\pi\)
−0.745434 + 0.666579i \(0.767758\pi\)
\(908\) 4.01481e10 2.31795e10i 0.0590638 0.0341005i
\(909\) 0 0
\(910\) −4.91717e11 + 8.51678e11i −0.717050 + 1.24197i
\(911\) −3.85785e10 1.05994e11i −0.0560109 0.153889i 0.908532 0.417816i \(-0.137204\pi\)
−0.964543 + 0.263927i \(0.914982\pi\)
\(912\) 0 0
\(913\) 8.32844e10 6.98839e10i 0.119862 0.100576i
\(914\) 2.46348e11 6.76834e11i 0.352991 0.969835i
\(915\) 0 0
\(916\) 7.71387e9 4.37475e10i 0.0109570 0.0621401i
\(917\) 1.11955e12i 1.58332i
\(918\) 0 0
\(919\) 3.60073e11 0.504811 0.252405 0.967622i \(-0.418778\pi\)
0.252405 + 0.967622i \(0.418778\pi\)
\(920\) −6.40686e11 1.12970e11i −0.894322 0.157693i
\(921\) 0 0
\(922\) −3.89946e11 1.41929e11i −0.539610 0.196402i
\(923\) 2.17851e11 + 2.59625e11i 0.300160 + 0.357717i
\(924\) 0 0
\(925\) 4.20902e11 1.53196e11i 0.574929 0.209257i
\(926\) −3.78090e11 2.18290e11i −0.514223 0.296887i
\(927\) 0 0
\(928\) −2.69598e11 4.66958e11i −0.363518 0.629631i
\(929\) 4.96330e10 5.91503e10i 0.0666358 0.0794135i −0.731697 0.681630i \(-0.761271\pi\)
0.798333 + 0.602217i \(0.205716\pi\)
\(930\) 0 0
\(931\) 2.51841e8 + 1.42826e9i 0.000335218 + 0.00190112i
\(932\) −2.51620e11 + 4.43673e10i −0.333489 + 0.0588030i
\(933\) 0 0
\(934\) 5.38974e11 + 4.52253e11i 0.708240 + 0.594284i
\(935\) −2.50669e12 + 1.44724e12i −3.27985 + 1.89362i
\(936\) 0 0
\(937\) −5.46345e10 + 9.46298e10i −0.0708776 + 0.122764i −0.899286 0.437361i \(-0.855913\pi\)
0.828409 + 0.560124i \(0.189247\pi\)
\(938\) −2.56238e11 7.04008e11i −0.331003 0.909424i
\(939\) 0 0
\(940\) −6.85577e10 + 5.75267e10i −0.0878102 + 0.0736815i
\(941\) 1.51783e11 4.17019e11i 0.193581 0.531860i −0.804488 0.593969i \(-0.797560\pi\)
0.998069 + 0.0621085i \(0.0197825\pi\)
\(942\) 0 0
\(943\) 1.19713e11 6.78926e11i 0.151389 0.858569i
\(944\) 2.90741e11i 0.366116i
\(945\) 0 0
\(946\) −7.70037e11 −0.961495
\(947\) −5.80418e11 1.02343e11i −0.721673 0.127250i −0.199265 0.979946i \(-0.563855\pi\)
−0.522409 + 0.852695i \(0.674966\pi\)
\(948\) 0 0
\(949\) 1.81138e11 + 6.59288e10i 0.223329 + 0.0812850i
\(950\) 5.63214e9 + 6.71213e9i 0.00691479 + 0.00824073i
\(951\) 0 0
\(952\) −1.36221e12 + 4.95805e11i −1.65843 + 0.603619i
\(953\) −1.23865e10 7.15133e9i −0.0150168 0.00866992i 0.492473 0.870328i \(-0.336093\pi\)
−0.507490 + 0.861658i \(0.669426\pi\)
\(954\) 0 0
\(955\) 4.88415e10 + 8.45960e10i 0.0587186 + 0.101704i
\(956\) −1.46691e11 + 1.74819e11i −0.175619 + 0.209294i
\(957\) 0 0
\(958\) −5.34486e10 3.03122e11i −0.0634562 0.359878i
\(959\) 9.73635e11 1.71678e11i 1.15112 0.202974i
\(960\) 0 0
\(961\) −6.38411e11 5.35690e11i −0.748526 0.628088i
\(962\) −2.44769e11 + 1.41317e11i −0.285796 + 0.165004i
\(963\) 0 0
\(964\) −1.30660e11 + 2.26310e11i −0.151299 + 0.262057i
\(965\) 8.58842e11 + 2.35965e12i 0.990385 + 2.72106i
\(966\) 0 0
\(967\) −1.09840e11 + 9.21663e10i −0.125618 + 0.105406i −0.703433 0.710762i \(-0.748350\pi\)
0.577814 + 0.816168i \(0.303906\pi\)
\(968\) 5.41688e11 1.48828e12i 0.616947 1.69505i
\(969\) 0 0
\(970\) 3.62495e10 2.05581e11i 0.0409464 0.232218i
\(971\) 1.68081e12i 1.89078i −0.325944 0.945389i \(-0.605682\pi\)
0.325944 0.945389i \(-0.394318\pi\)
\(972\) 0 0
\(973\) 1.12390e12 1.25394
\(974\) 9.17194e11 + 1.61726e11i 1.01912 + 0.179698i
\(975\) 0 0
\(976\) 9.87491e11 + 3.59417e11i 1.08826 + 0.396095i
\(977\) −3.78131e11 4.50639e11i −0.415015 0.494596i 0.517522 0.855670i \(-0.326855\pi\)
−0.932537 + 0.361074i \(0.882410\pi\)
\(978\) 0 0
\(979\) −1.00174e12 + 3.64605e11i −1.09050 + 0.396909i
\(980\) −8.24785e10 4.76190e10i −0.0894204 0.0516269i
\(981\) 0 0
\(982\) 4.94358e11 + 8.56254e11i 0.531614 + 0.920782i
\(983\) 5.44055e11 6.48380e11i 0.582678 0.694409i −0.391503 0.920177i \(-0.628045\pi\)
0.974181 + 0.225768i \(0.0724891\pi\)
\(984\) 0 0
\(985\) −7.36486e10 4.17682e11i −0.0782384 0.443712i
\(986\) −1.53116e12 + 2.69985e11i −1.62000 + 0.285649i
\(987\) 0 0
\(988\) 1.67600e9 + 1.40633e9i 0.00175892 + 0.00147591i
\(989\) 3.04280e11 1.75676e11i 0.318045 0.183623i
\(990\) 0 0
\(991\) 4.81519e11 8.34015e11i 0.499251 0.864728i −0.500749 0.865593i \(-0.666942\pi\)
1.00000 0.000864758i \(0.000275261\pi\)
\(992\) −2.74484e10 7.54138e10i −0.0283446 0.0778761i
\(993\) 0 0
\(994\) 3.40083e11 2.85364e11i 0.348369 0.292317i
\(995\) −3.30160e11 + 9.07108e11i −0.336847 + 0.925480i
\(996\) 0 0
\(997\) −1.22891e11 + 6.96951e11i −0.124377 + 0.705378i 0.857299 + 0.514819i \(0.172141\pi\)
−0.981676 + 0.190559i \(0.938970\pi\)
\(998\) 5.19985e11i 0.524166i
\(999\) 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.f.a.8.9 138
3.2 odd 2 27.9.f.a.2.15 138
27.13 even 9 27.9.f.a.14.15 yes 138
27.14 odd 18 inner 81.9.f.a.71.9 138
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.9.f.a.2.15 138 3.2 odd 2
27.9.f.a.14.15 yes 138 27.13 even 9
81.9.f.a.8.9 138 1.1 even 1 trivial
81.9.f.a.71.9 138 27.14 odd 18 inner