Properties

Label 81.9.d.e.26.2
Level $81$
Weight $9$
Character 81.26
Analytic conductor $32.998$
Analytic rank $0$
Dimension $4$
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: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{3} \)
Twist minimal: no (minimal twist has level 27)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 26.2
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 81.26
Dual form 81.9.d.e.53.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(25.4558 + 14.6969i) q^{2} +(304.000 + 526.543i) q^{4} +(712.764 - 411.514i) q^{5} +(-983.500 + 1703.47i) q^{7} +10346.6i q^{8} +O(q^{10})\) \(q+(25.4558 + 14.6969i) q^{2} +(304.000 + 526.543i) q^{4} +(712.764 - 411.514i) q^{5} +(-983.500 + 1703.47i) q^{7} +10346.6i q^{8} +24192.0 q^{10} +(-10895.1 - 6290.29i) q^{11} +(22752.5 + 39408.5i) q^{13} +(-50071.6 + 28908.9i) q^{14} +(-74240.0 + 128587. i) q^{16} +59610.8i q^{17} +152399. q^{19} +(433360. + 250201. i) q^{20} +(-184896. - 320249. i) q^{22} +(113737. - 65665.9i) q^{23} +(143376. - 248334. i) q^{25} +1.33757e6i q^{26} -1.19594e6 q^{28} +(-509728. - 294291. i) q^{29} +(82175.0 + 142331. i) q^{31} +(-1.48581e6 + 857831. i) q^{32} +(-876096. + 1.51744e6i) q^{34} +1.61890e6i q^{35} -663937. q^{37} +(3.87945e6 + 2.23980e6i) q^{38} +(4.25779e6 + 7.37471e6i) q^{40} +(812347. - 469009. i) q^{41} +(-287665. + 498250. i) q^{43} -7.64899e6i q^{44} +3.86035e6 q^{46} +(-7.99711e6 - 4.61713e6i) q^{47} +(947856. + 1.64173e6i) q^{49} +(7.29949e6 - 4.21436e6i) q^{50} +(-1.38335e7 + 2.39604e7i) q^{52} -1.03765e7i q^{53} -1.03542e7 q^{55} +(-1.76252e7 - 1.01759e7i) q^{56} +(-8.65037e6 - 1.49829e7i) q^{58} +(4.36466e6 - 2.51994e6i) q^{59} +(9.60648e6 - 1.66389e7i) q^{61} +4.83088e6i q^{62} -1.24191e7 q^{64} +(3.24343e7 + 1.87260e7i) q^{65} +(299016. + 517912. i) q^{67} +(-3.13877e7 + 1.81217e7i) q^{68} +(-2.37928e7 + 4.12104e7i) q^{70} -2.92721e7i q^{71} +1.28502e7 q^{73} +(-1.69011e7 - 9.75784e6i) q^{74} +(4.63293e7 + 8.02447e7i) q^{76} +(2.14307e7 - 1.23730e7i) q^{77} +(1.17923e7 - 2.04249e7i) q^{79} +1.22203e8i q^{80} +2.75720e7 q^{82} +(2.89694e7 + 1.67255e7i) q^{83} +(2.45307e7 + 4.24884e7i) q^{85} +(-1.46455e7 + 8.45559e6i) q^{86} +(6.50834e7 - 1.12728e8i) q^{88} +2.82848e7i q^{89} -8.95083e7 q^{91} +(6.91519e7 + 3.99249e7i) q^{92} +(-1.35715e8 - 2.35066e8i) q^{94} +(1.08624e8 - 6.27144e7i) q^{95} +(-6.82448e7 + 1.18203e8i) q^{97} +5.57223e7i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 1216 q^{4} - 3934 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 1216 q^{4} - 3934 q^{7} + 96768 q^{10} + 91010 q^{13} - 296960 q^{16} + 609596 q^{19} - 739584 q^{22} + 573502 q^{25} - 4783744 q^{28} + 328700 q^{31} - 3504384 q^{34} - 2655748 q^{37} + 17031168 q^{40} - 1150660 q^{43} + 15441408 q^{46} + 3791424 q^{49} - 55334080 q^{52} - 41416704 q^{55} - 34601472 q^{58} + 38425922 q^{61} - 49676288 q^{64} + 1196066 q^{67} - 95171328 q^{70} + 51400700 q^{73} + 185317184 q^{76} + 47169314 q^{79} + 110287872 q^{82} + 98122752 q^{85} + 260333568 q^{88} - 358033340 q^{91} - 542861568 q^{94} - 272979262 q^{97}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 25.4558 + 14.6969i 1.59099 + 0.918559i 0.993137 + 0.116953i \(0.0373126\pi\)
0.597853 + 0.801606i \(0.296021\pi\)
\(3\) 0 0
\(4\) 304.000 + 526.543i 1.18750 + 2.05681i
\(5\) 712.764 411.514i 1.14042 0.658423i 0.193887 0.981024i \(-0.437891\pi\)
0.946535 + 0.322601i \(0.104557\pi\)
\(6\) 0 0
\(7\) −983.500 + 1703.47i −0.409621 + 0.709484i −0.994847 0.101386i \(-0.967672\pi\)
0.585226 + 0.810870i \(0.301006\pi\)
\(8\) 10346.6i 2.52604i
\(9\) 0 0
\(10\) 24192.0 2.41920
\(11\) −10895.1 6290.29i −0.744150 0.429635i 0.0794262 0.996841i \(-0.474691\pi\)
−0.823576 + 0.567205i \(0.808025\pi\)
\(12\) 0 0
\(13\) 22752.5 + 39408.5i 0.796628 + 1.37980i 0.921800 + 0.387666i \(0.126718\pi\)
−0.125172 + 0.992135i \(0.539948\pi\)
\(14\) −50071.6 + 28908.9i −1.30341 + 0.752522i
\(15\) 0 0
\(16\) −74240.0 + 128587.i −1.13281 + 1.96209i
\(17\) 59610.8i 0.713722i 0.934157 + 0.356861i \(0.116153\pi\)
−0.934157 + 0.356861i \(0.883847\pi\)
\(18\) 0 0
\(19\) 152399. 1.16941 0.584706 0.811245i \(-0.301210\pi\)
0.584706 + 0.811245i \(0.301210\pi\)
\(20\) 433360. + 250201.i 2.70850 + 1.56375i
\(21\) 0 0
\(22\) −184896. 320249.i −0.789290 1.36709i
\(23\) 113737. 65665.9i 0.406433 0.234654i −0.282823 0.959172i \(-0.591271\pi\)
0.689256 + 0.724518i \(0.257937\pi\)
\(24\) 0 0
\(25\) 143376. 248334.i 0.367041 0.635734i
\(26\) 1.33757e6i 2.92700i
\(27\) 0 0
\(28\) −1.19594e6 −1.94570
\(29\) −509728. 294291.i −0.720686 0.416089i 0.0943188 0.995542i \(-0.469933\pi\)
−0.815005 + 0.579454i \(0.803266\pi\)
\(30\) 0 0
\(31\) 82175.0 + 142331.i 0.0889801 + 0.154118i 0.907080 0.420958i \(-0.138306\pi\)
−0.818100 + 0.575076i \(0.804973\pi\)
\(32\) −1.48581e6 + 857831.i −1.41698 + 0.818091i
\(33\) 0 0
\(34\) −876096. + 1.51744e6i −0.655596 + 1.13552i
\(35\) 1.61890e6i 1.07882i
\(36\) 0 0
\(37\) −663937. −0.354258 −0.177129 0.984188i \(-0.556681\pi\)
−0.177129 + 0.984188i \(0.556681\pi\)
\(38\) 3.87945e6 + 2.23980e6i 1.86052 + 1.07417i
\(39\) 0 0
\(40\) 4.25779e6 + 7.37471e6i 1.66320 + 2.88075i
\(41\) 812347. 469009.i 0.287479 0.165976i −0.349325 0.937001i \(-0.613589\pi\)
0.636804 + 0.771025i \(0.280256\pi\)
\(42\) 0 0
\(43\) −287665. + 498250.i −0.0841421 + 0.145738i −0.905025 0.425358i \(-0.860148\pi\)
0.820883 + 0.571096i \(0.193482\pi\)
\(44\) 7.64899e6i 2.04077i
\(45\) 0 0
\(46\) 3.86035e6 0.862175
\(47\) −7.99711e6 4.61713e6i −1.63886 0.946195i −0.981227 0.192855i \(-0.938225\pi\)
−0.657631 0.753340i \(-0.728441\pi\)
\(48\) 0 0
\(49\) 947856. + 1.64173e6i 0.164421 + 0.284786i
\(50\) 7.29949e6 4.21436e6i 1.16792 0.674298i
\(51\) 0 0
\(52\) −1.38335e7 + 2.39604e7i −1.89199 + 3.27703i
\(53\) 1.03765e7i 1.31507i −0.753425 0.657533i \(-0.771600\pi\)
0.753425 0.657533i \(-0.228400\pi\)
\(54\) 0 0
\(55\) −1.03542e7 −1.13153
\(56\) −1.76252e7 1.01759e7i −1.79218 1.03472i
\(57\) 0 0
\(58\) −8.65037e6 1.49829e7i −0.764403 1.32399i
\(59\) 4.36466e6 2.51994e6i 0.360199 0.207961i −0.308969 0.951072i \(-0.599984\pi\)
0.669168 + 0.743111i \(0.266651\pi\)
\(60\) 0 0
\(61\) 9.60648e6 1.66389e7i 0.693817 1.20173i −0.276761 0.960939i \(-0.589261\pi\)
0.970578 0.240788i \(-0.0774057\pi\)
\(62\) 4.83088e6i 0.326934i
\(63\) 0 0
\(64\) −1.24191e7 −0.740234
\(65\) 3.24343e7 + 1.87260e7i 1.81698 + 1.04904i
\(66\) 0 0
\(67\) 299016. + 517912.i 0.0148387 + 0.0257014i 0.873349 0.487094i \(-0.161943\pi\)
−0.858511 + 0.512796i \(0.828610\pi\)
\(68\) −3.13877e7 + 1.81217e7i −1.46799 + 0.847545i
\(69\) 0 0
\(70\) −2.37928e7 + 4.12104e7i −0.990955 + 1.71638i
\(71\) 2.92721e7i 1.15191i −0.817480 0.575957i \(-0.804630\pi\)
0.817480 0.575957i \(-0.195370\pi\)
\(72\) 0 0
\(73\) 1.28502e7 0.452499 0.226249 0.974069i \(-0.427354\pi\)
0.226249 + 0.974069i \(0.427354\pi\)
\(74\) −1.69011e7 9.75784e6i −0.563621 0.325407i
\(75\) 0 0
\(76\) 4.63293e7 + 8.02447e7i 1.38868 + 2.40526i
\(77\) 2.14307e7 1.23730e7i 0.609639 0.351975i
\(78\) 0 0
\(79\) 1.17923e7 2.04249e7i 0.302755 0.524387i −0.674004 0.738728i \(-0.735427\pi\)
0.976759 + 0.214341i \(0.0687603\pi\)
\(80\) 1.22203e8i 2.98348i
\(81\) 0 0
\(82\) 2.75720e7 0.609835
\(83\) 2.89694e7 + 1.67255e7i 0.610417 + 0.352424i 0.773129 0.634249i \(-0.218691\pi\)
−0.162712 + 0.986674i \(0.552024\pi\)
\(84\) 0 0
\(85\) 2.45307e7 + 4.24884e7i 0.469931 + 0.813944i
\(86\) −1.46455e7 + 8.45559e6i −0.267738 + 0.154579i
\(87\) 0 0
\(88\) 6.50834e7 1.12728e8i 1.08527 1.87975i
\(89\) 2.82848e7i 0.450809i 0.974265 + 0.225405i \(0.0723704\pi\)
−0.974265 + 0.225405i \(0.927630\pi\)
\(90\) 0 0
\(91\) −8.95083e7 −1.30526
\(92\) 6.91519e7 + 3.99249e7i 0.965279 + 0.557304i
\(93\) 0 0
\(94\) −1.35715e8 2.35066e8i −1.73827 3.01078i
\(95\) 1.08624e8 6.27144e7i 1.33362 0.769968i
\(96\) 0 0
\(97\) −6.82448e7 + 1.18203e8i −0.770873 + 1.33519i 0.166212 + 0.986090i \(0.446846\pi\)
−0.937085 + 0.349101i \(0.886487\pi\)
\(98\) 5.57223e7i 0.604122i
\(99\) 0 0
\(100\) 1.74345e8 1.74345
\(101\) 3.48570e7 + 2.01247e7i 0.334969 + 0.193394i 0.658045 0.752979i \(-0.271384\pi\)
−0.323076 + 0.946373i \(0.604717\pi\)
\(102\) 0 0
\(103\) −1.67954e7 2.90904e7i −0.149225 0.258465i 0.781716 0.623634i \(-0.214344\pi\)
−0.930941 + 0.365169i \(0.881011\pi\)
\(104\) −4.07746e8 + 2.35412e8i −3.48543 + 2.01231i
\(105\) 0 0
\(106\) 1.52503e8 2.64143e8i 1.20797 2.09226i
\(107\) 1.95483e8i 1.49133i −0.666322 0.745664i \(-0.732132\pi\)
0.666322 0.745664i \(-0.267868\pi\)
\(108\) 0 0
\(109\) −1.01182e8 −0.716800 −0.358400 0.933568i \(-0.616678\pi\)
−0.358400 + 0.933568i \(0.616678\pi\)
\(110\) −2.63574e8 1.52175e8i −1.80025 1.03937i
\(111\) 0 0
\(112\) −1.46030e8 2.52932e8i −0.928048 1.60743i
\(113\) 2.72369e8 1.57252e8i 1.67049 0.964457i 0.703126 0.711066i \(-0.251787\pi\)
0.967364 0.253392i \(-0.0815462\pi\)
\(114\) 0 0
\(115\) 5.40449e7 9.36086e7i 0.309004 0.535210i
\(116\) 3.57858e8i 1.97642i
\(117\) 0 0
\(118\) 1.48141e8 0.764097
\(119\) −1.01545e8 5.86272e7i −0.506375 0.292356i
\(120\) 0 0
\(121\) −2.80440e7 4.85736e7i −0.130827 0.226599i
\(122\) 4.89082e8 2.82372e8i 2.20771 1.27462i
\(123\) 0 0
\(124\) −4.99624e7 + 8.65374e7i −0.211328 + 0.366030i
\(125\) 8.54913e7i 0.350172i
\(126\) 0 0
\(127\) 4.30869e8 1.65627 0.828133 0.560532i \(-0.189403\pi\)
0.828133 + 0.560532i \(0.189403\pi\)
\(128\) 6.42286e7 + 3.70824e7i 0.239270 + 0.138143i
\(129\) 0 0
\(130\) 5.50428e8 + 9.53370e8i 1.92720 + 3.33801i
\(131\) 1.63621e8 9.44664e7i 0.555588 0.320769i −0.195785 0.980647i \(-0.562725\pi\)
0.751373 + 0.659878i \(0.229392\pi\)
\(132\) 0 0
\(133\) −1.49884e8 + 2.59607e8i −0.479016 + 0.829680i
\(134\) 1.75785e7i 0.0545209i
\(135\) 0 0
\(136\) −6.16772e8 −1.80289
\(137\) −1.06519e8 6.14989e7i −0.302375 0.174576i 0.341134 0.940015i \(-0.389189\pi\)
−0.643509 + 0.765438i \(0.722522\pi\)
\(138\) 0 0
\(139\) −8.60360e7 1.49019e8i −0.230474 0.399192i 0.727474 0.686135i \(-0.240694\pi\)
−0.957948 + 0.286943i \(0.907361\pi\)
\(140\) −8.52420e8 + 4.92145e8i −2.21892 + 1.28109i
\(141\) 0 0
\(142\) 4.30210e8 7.45145e8i 1.05810 1.83268i
\(143\) 5.72479e8i 1.36904i
\(144\) 0 0
\(145\) −4.84421e8 −1.09585
\(146\) 3.27112e8 + 1.88858e8i 0.719921 + 0.415647i
\(147\) 0 0
\(148\) −2.01837e8 3.49592e8i −0.420682 0.728642i
\(149\) −6.33642e8 + 3.65834e8i −1.28558 + 0.742230i −0.977863 0.209248i \(-0.932898\pi\)
−0.307717 + 0.951478i \(0.599565\pi\)
\(150\) 0 0
\(151\) −9.29762e7 + 1.61039e8i −0.178840 + 0.309759i −0.941483 0.337059i \(-0.890568\pi\)
0.762644 + 0.646819i \(0.223901\pi\)
\(152\) 1.57682e9i 2.95398i
\(153\) 0 0
\(154\) 7.27381e8 1.29324
\(155\) 1.17143e8 + 6.76324e7i 0.202950 + 0.117173i
\(156\) 0 0
\(157\) −4.87004e8 8.43515e8i −0.801556 1.38834i −0.918592 0.395207i \(-0.870673\pi\)
0.117036 0.993128i \(-0.462661\pi\)
\(158\) 6.00367e8 3.46622e8i 0.963360 0.556196i
\(159\) 0 0
\(160\) −7.06019e8 + 1.22286e9i −1.07730 + 1.86594i
\(161\) 2.58330e8i 0.384477i
\(162\) 0 0
\(163\) −1.15499e9 −1.63616 −0.818082 0.575102i \(-0.804962\pi\)
−0.818082 + 0.575102i \(0.804962\pi\)
\(164\) 4.93907e8 + 2.85157e8i 0.682763 + 0.394193i
\(165\) 0 0
\(166\) 4.91626e8 + 8.51522e8i 0.647445 + 1.12141i
\(167\) −9.89881e7 + 5.71508e7i −0.127267 + 0.0734779i −0.562282 0.826945i \(-0.690076\pi\)
0.435015 + 0.900423i \(0.356743\pi\)
\(168\) 0 0
\(169\) −6.27487e8 + 1.08684e9i −0.769233 + 1.33235i
\(170\) 1.44210e9i 1.72664i
\(171\) 0 0
\(172\) −3.49801e8 −0.399675
\(173\) 1.43173e9 + 8.26610e8i 1.59837 + 0.922819i 0.991802 + 0.127786i \(0.0407872\pi\)
0.606567 + 0.795032i \(0.292546\pi\)
\(174\) 0 0
\(175\) 2.82020e8 + 4.88472e8i 0.300696 + 0.520820i
\(176\) 1.61770e9 9.33982e8i 1.68597 0.973392i
\(177\) 0 0
\(178\) −4.15700e8 + 7.20013e8i −0.414095 + 0.717233i
\(179\) 4.17229e8i 0.406408i 0.979136 + 0.203204i \(0.0651355\pi\)
−0.979136 + 0.203204i \(0.934865\pi\)
\(180\) 0 0
\(181\) 1.16424e9 1.08475 0.542374 0.840137i \(-0.317526\pi\)
0.542374 + 0.840137i \(0.317526\pi\)
\(182\) −2.27851e9 1.31550e9i −2.07666 1.19896i
\(183\) 0 0
\(184\) 6.79422e8 + 1.17679e9i 0.592746 + 1.02667i
\(185\) −4.73230e8 + 2.73220e8i −0.404004 + 0.233252i
\(186\) 0 0
\(187\) 3.74969e8 6.49466e8i 0.306640 0.531116i
\(188\) 5.61443e9i 4.49443i
\(189\) 0 0
\(190\) 3.68684e9 2.82904
\(191\) −1.39478e9 8.05276e8i −1.04803 0.605078i −0.125930 0.992039i \(-0.540191\pi\)
−0.922096 + 0.386961i \(0.873525\pi\)
\(192\) 0 0
\(193\) 3.55139e8 + 6.15120e8i 0.255959 + 0.443333i 0.965155 0.261677i \(-0.0842756\pi\)
−0.709197 + 0.705010i \(0.750942\pi\)
\(194\) −3.47446e9 + 2.00598e9i −2.45290 + 1.41618i
\(195\) 0 0
\(196\) −5.76296e8 + 9.98175e8i −0.390501 + 0.676367i
\(197\) 1.41623e9i 0.940303i 0.882586 + 0.470152i \(0.155801\pi\)
−0.882586 + 0.470152i \(0.844199\pi\)
\(198\) 0 0
\(199\) −2.34324e9 −1.49419 −0.747093 0.664720i \(-0.768551\pi\)
−0.747093 + 0.664720i \(0.768551\pi\)
\(200\) 2.56942e9 + 1.48346e9i 1.60589 + 0.927160i
\(201\) 0 0
\(202\) 5.91543e8 + 1.02458e9i 0.355288 + 0.615377i
\(203\) 1.00263e9 5.78871e8i 0.590417 0.340877i
\(204\) 0 0
\(205\) 3.86008e8 6.68585e8i 0.218565 0.378565i
\(206\) 9.87362e8i 0.548286i
\(207\) 0 0
\(208\) −6.75658e9 −3.60972
\(209\) −1.66040e9 9.58634e8i −0.870218 0.502421i
\(210\) 0 0
\(211\) −5.32585e8 9.22464e8i −0.268695 0.465393i 0.699830 0.714309i \(-0.253259\pi\)
−0.968525 + 0.248916i \(0.919926\pi\)
\(212\) 5.46368e9 3.15446e9i 2.70484 1.56164i
\(213\) 0 0
\(214\) 2.87300e9 4.97618e9i 1.36987 2.37269i
\(215\) 4.73513e8i 0.221604i
\(216\) 0 0
\(217\) −3.23276e8 −0.145792
\(218\) −2.57568e9 1.48707e9i −1.14042 0.658423i
\(219\) 0 0
\(220\) −3.14767e9 5.45192e9i −1.34369 2.32734i
\(221\) −2.34917e9 + 1.35629e9i −0.984794 + 0.568571i
\(222\) 0 0
\(223\) −9.97928e8 + 1.72846e9i −0.403534 + 0.698941i −0.994150 0.108012i \(-0.965552\pi\)
0.590616 + 0.806953i \(0.298885\pi\)
\(224\) 3.37471e9i 1.34043i
\(225\) 0 0
\(226\) 9.24451e9 3.54364
\(227\) −1.55818e9 8.99614e8i −0.586831 0.338807i 0.177012 0.984209i \(-0.443357\pi\)
−0.763844 + 0.645401i \(0.776690\pi\)
\(228\) 0 0
\(229\) −7.98936e8 1.38380e9i −0.290516 0.503188i 0.683416 0.730029i \(-0.260494\pi\)
−0.973932 + 0.226841i \(0.927160\pi\)
\(230\) 2.75152e9 1.58859e9i 0.983244 0.567676i
\(231\) 0 0
\(232\) 3.04493e9 5.27397e9i 1.05105 1.82048i
\(233\) 4.98411e9i 1.69108i 0.533912 + 0.845540i \(0.320721\pi\)
−0.533912 + 0.845540i \(0.679279\pi\)
\(234\) 0 0
\(235\) −7.60006e9 −2.49199
\(236\) 2.65371e9 + 1.53212e9i 0.855472 + 0.493907i
\(237\) 0 0
\(238\) −1.72328e9 2.98481e9i −0.537091 0.930270i
\(239\) −5.10742e9 + 2.94877e9i −1.56535 + 0.903753i −0.568645 + 0.822583i \(0.692532\pi\)
−0.996700 + 0.0811700i \(0.974134\pi\)
\(240\) 0 0
\(241\) −1.13087e9 + 1.95873e9i −0.335231 + 0.580638i −0.983529 0.180749i \(-0.942148\pi\)
0.648298 + 0.761387i \(0.275481\pi\)
\(242\) 1.64864e9i 0.480689i
\(243\) 0 0
\(244\) 1.16815e10 3.29563
\(245\) 1.35119e9 + 7.80113e8i 0.375019 + 0.216517i
\(246\) 0 0
\(247\) 3.46746e9 + 6.00581e9i 0.931587 + 1.61356i
\(248\) −1.47265e9 + 8.50236e8i −0.389308 + 0.224767i
\(249\) 0 0
\(250\) −1.25646e9 + 2.17625e9i −0.321654 + 0.557121i
\(251\) 3.31815e9i 0.835989i −0.908450 0.417994i \(-0.862733\pi\)
0.908450 0.417994i \(-0.137267\pi\)
\(252\) 0 0
\(253\) −1.65223e9 −0.403263
\(254\) 1.09681e10 + 6.33245e9i 2.63510 + 1.52138i
\(255\) 0 0
\(256\) 2.67964e9 + 4.64127e9i 0.623901 + 1.08063i
\(257\) 2.64153e9 1.52509e9i 0.605512 0.349593i −0.165695 0.986177i \(-0.552987\pi\)
0.771207 + 0.636584i \(0.219653\pi\)
\(258\) 0 0
\(259\) 6.52982e8 1.13100e9i 0.145112 0.251341i
\(260\) 2.27708e10i 4.98292i
\(261\) 0 0
\(262\) 5.55347e9 1.17858
\(263\) 1.70972e9 + 9.87108e8i 0.357357 + 0.206320i 0.667921 0.744232i \(-0.267184\pi\)
−0.310564 + 0.950553i \(0.600518\pi\)
\(264\) 0 0
\(265\) −4.27008e9 7.39600e9i −0.865870 1.49973i
\(266\) −7.63087e9 + 4.40568e9i −1.52422 + 0.880008i
\(267\) 0 0
\(268\) −1.81802e8 + 3.14890e8i −0.0352419 + 0.0610408i
\(269\) 3.49334e9i 0.667163i −0.942721 0.333581i \(-0.891743\pi\)
0.942721 0.333581i \(-0.108257\pi\)
\(270\) 0 0
\(271\) 1.43226e9 0.265549 0.132774 0.991146i \(-0.457611\pi\)
0.132774 + 0.991146i \(0.457611\pi\)
\(272\) −7.66520e9 4.42550e9i −1.40039 0.808513i
\(273\) 0 0
\(274\) −1.80769e9 3.13101e9i −0.320717 0.555498i
\(275\) −3.12418e9 + 1.80375e9i −0.546268 + 0.315388i
\(276\) 0 0
\(277\) −1.67547e9 + 2.90201e9i −0.284589 + 0.492923i −0.972510 0.232863i \(-0.925191\pi\)
0.687920 + 0.725786i \(0.258524\pi\)
\(278\) 5.05787e9i 0.846814i
\(279\) 0 0
\(280\) −1.67502e10 −2.72513
\(281\) −3.71560e9 2.14520e9i −0.595941 0.344067i 0.171502 0.985184i \(-0.445138\pi\)
−0.767443 + 0.641117i \(0.778471\pi\)
\(282\) 0 0
\(283\) 4.95573e7 + 8.58357e7i 0.00772612 + 0.0133820i 0.869863 0.493294i \(-0.164207\pi\)
−0.862136 + 0.506676i \(0.830874\pi\)
\(284\) 1.54130e10 8.89871e9i 2.36927 1.36790i
\(285\) 0 0
\(286\) 8.41369e9 1.45729e10i 1.25754 2.17813i
\(287\) 1.84508e9i 0.271949i
\(288\) 0 0
\(289\) 3.42231e9 0.490601
\(290\) −1.23313e10 7.11950e9i −1.74348 1.00660i
\(291\) 0 0
\(292\) 3.90645e9 + 6.76618e9i 0.537343 + 0.930705i
\(293\) −7.81997e8 + 4.51486e8i −0.106105 + 0.0612596i −0.552113 0.833769i \(-0.686178\pi\)
0.446009 + 0.895029i \(0.352845\pi\)
\(294\) 0 0
\(295\) 2.07398e9 3.59224e9i 0.273852 0.474326i
\(296\) 6.86952e9i 0.894869i
\(297\) 0 0
\(298\) −2.15065e10 −2.72713
\(299\) 5.17559e9 + 2.98813e9i 0.647553 + 0.373865i
\(300\) 0 0
\(301\) −5.65837e8 9.80059e8i −0.0689327 0.119395i
\(302\) −4.73357e9 + 2.73293e9i −0.569064 + 0.328549i
\(303\) 0 0
\(304\) −1.13141e10 + 1.95966e10i −1.32473 + 2.29449i
\(305\) 1.58128e10i 1.82730i
\(306\) 0 0
\(307\) 3.36397e9 0.378703 0.189352 0.981909i \(-0.439361\pi\)
0.189352 + 0.981909i \(0.439361\pi\)
\(308\) 1.30298e10 + 7.52278e9i 1.44789 + 0.835941i
\(309\) 0 0
\(310\) 1.98798e9 + 3.44328e9i 0.215261 + 0.372842i
\(311\) 1.15202e10 6.65116e9i 1.23145 0.710978i 0.264117 0.964491i \(-0.414919\pi\)
0.967332 + 0.253513i \(0.0815860\pi\)
\(312\) 0 0
\(313\) −6.56247e9 + 1.13665e10i −0.683738 + 1.18427i 0.290094 + 0.956998i \(0.406314\pi\)
−0.973832 + 0.227271i \(0.927020\pi\)
\(314\) 2.86299e10i 2.94510i
\(315\) 0 0
\(316\) 1.43395e10 1.43809
\(317\) 6.04936e9 + 3.49260e9i 0.599063 + 0.345869i 0.768673 0.639642i \(-0.220917\pi\)
−0.169610 + 0.985511i \(0.554251\pi\)
\(318\) 0 0
\(319\) 3.70236e9 + 6.41267e9i 0.357533 + 0.619265i
\(320\) −8.85186e9 + 5.11063e9i −0.844179 + 0.487387i
\(321\) 0 0
\(322\) −3.79666e9 + 6.57600e9i −0.353165 + 0.611700i
\(323\) 9.08462e9i 0.834635i
\(324\) 0 0
\(325\) 1.30486e10 1.16958
\(326\) −2.94012e10 1.69748e10i −2.60312 1.50291i
\(327\) 0 0
\(328\) 4.85267e9 + 8.40506e9i 0.419262 + 0.726182i
\(329\) 1.57303e10 9.08190e9i 1.34262 0.775163i
\(330\) 0 0
\(331\) 5.93663e9 1.02825e10i 0.494570 0.856620i −0.505410 0.862879i \(-0.668659\pi\)
0.999980 + 0.00625875i \(0.00199223\pi\)
\(332\) 2.03382e10i 1.67402i
\(333\) 0 0
\(334\) −3.35977e9 −0.269975
\(335\) 4.26256e8 + 2.46099e8i 0.0338448 + 0.0195403i
\(336\) 0 0
\(337\) −4.57709e9 7.92776e9i −0.354871 0.614654i 0.632225 0.774785i \(-0.282142\pi\)
−0.987096 + 0.160131i \(0.948808\pi\)
\(338\) −3.19464e10 + 1.84443e10i −2.44769 + 1.41317i
\(339\) 0 0
\(340\) −1.49147e10 + 2.58329e10i −1.11609 + 1.93312i
\(341\) 2.06762e9i 0.152916i
\(342\) 0 0
\(343\) −1.50682e10 −1.08864
\(344\) −5.15522e9 2.97637e9i −0.368140 0.212546i
\(345\) 0 0
\(346\) 2.42973e10 + 4.20841e10i 1.69533 + 2.93639i
\(347\) 1.77605e10 1.02540e10i 1.22500 0.707257i 0.259024 0.965871i \(-0.416599\pi\)
0.965981 + 0.258614i \(0.0832659\pi\)
\(348\) 0 0
\(349\) −6.73994e9 + 1.16739e10i −0.454312 + 0.786892i −0.998648 0.0519753i \(-0.983448\pi\)
0.544336 + 0.838867i \(0.316782\pi\)
\(350\) 1.65793e10i 1.10483i
\(351\) 0 0
\(352\) 2.15840e10 1.40592
\(353\) −8.47197e9 4.89130e9i −0.545614 0.315011i 0.201737 0.979440i \(-0.435341\pi\)
−0.747351 + 0.664429i \(0.768675\pi\)
\(354\) 0 0
\(355\) −1.20459e10 2.08641e10i −0.758446 1.31367i
\(356\) −1.48932e10 + 8.59858e9i −0.927229 + 0.535336i
\(357\) 0 0
\(358\) −6.13199e9 + 1.06209e10i −0.373310 + 0.646591i
\(359\) 1.67338e10i 1.00743i 0.863868 + 0.503717i \(0.168035\pi\)
−0.863868 + 0.503717i \(0.831965\pi\)
\(360\) 0 0
\(361\) 6.24189e9 0.367525
\(362\) 2.96368e10 + 1.71108e10i 1.72582 + 0.996405i
\(363\) 0 0
\(364\) −2.72105e10 4.71300e10i −1.55000 2.68468i
\(365\) 9.15914e9 5.28803e9i 0.516040 0.297936i
\(366\) 0 0
\(367\) 7.49396e9 1.29799e10i 0.413092 0.715497i −0.582134 0.813093i \(-0.697782\pi\)
0.995226 + 0.0975963i \(0.0311154\pi\)
\(368\) 1.95002e10i 1.06328i
\(369\) 0 0
\(370\) −1.60620e10 −0.857022
\(371\) 1.76761e10 + 1.02053e10i 0.933019 + 0.538679i
\(372\) 0 0
\(373\) 9.89819e9 + 1.71442e10i 0.511353 + 0.885689i 0.999913 + 0.0131590i \(0.00418876\pi\)
−0.488561 + 0.872530i \(0.662478\pi\)
\(374\) 1.90903e10 1.10218e10i 0.975723 0.563334i
\(375\) 0 0
\(376\) 4.77718e10 8.27432e10i 2.39012 4.13982i
\(377\) 2.67835e10i 1.32587i
\(378\) 0 0
\(379\) −5.34899e9 −0.259248 −0.129624 0.991563i \(-0.541377\pi\)
−0.129624 + 0.991563i \(0.541377\pi\)
\(380\) 6.60437e10 + 3.81303e10i 3.16736 + 1.82867i
\(381\) 0 0
\(382\) −2.36702e10 4.09980e10i −1.11160 1.92535i
\(383\) −1.25520e10 + 7.24690e9i −0.583335 + 0.336788i −0.762457 0.647038i \(-0.776007\pi\)
0.179123 + 0.983827i \(0.442674\pi\)
\(384\) 0 0
\(385\) 1.01833e10 1.76380e10i 0.463497 0.802800i
\(386\) 2.08778e10i 0.940452i
\(387\) 0 0
\(388\) −8.29857e10 −3.66165
\(389\) −1.56324e10 9.02536e9i −0.682695 0.394154i 0.118175 0.992993i \(-0.462296\pi\)
−0.800870 + 0.598839i \(0.795629\pi\)
\(390\) 0 0
\(391\) 3.91440e9 + 6.77993e9i 0.167478 + 0.290080i
\(392\) −1.69864e10 + 9.80713e9i −0.719380 + 0.415334i
\(393\) 0 0
\(394\) −2.08142e10 + 3.60513e10i −0.863724 + 1.49601i
\(395\) 1.94108e10i 0.797363i
\(396\) 0 0
\(397\) 3.82640e10 1.54038 0.770191 0.637814i \(-0.220161\pi\)
0.770191 + 0.637814i \(0.220161\pi\)
\(398\) −5.96491e10 3.44384e10i −2.37723 1.37250i
\(399\) 0 0
\(400\) 2.12884e10 + 3.68726e10i 0.831578 + 1.44034i
\(401\) −3.69448e10 + 2.13301e10i −1.42881 + 0.824926i −0.997027 0.0770497i \(-0.975450\pi\)
−0.431787 + 0.901976i \(0.642117\pi\)
\(402\) 0 0
\(403\) −3.73937e9 + 6.47678e9i −0.141768 + 0.245550i
\(404\) 2.44716e10i 0.918623i
\(405\) 0 0
\(406\) 3.40305e10 1.25246
\(407\) 7.23366e9 + 4.17636e9i 0.263621 + 0.152202i
\(408\) 0 0
\(409\) 1.76976e10 + 3.06532e10i 0.632444 + 1.09542i 0.987051 + 0.160409i \(0.0512813\pi\)
−0.354607 + 0.935015i \(0.615385\pi\)
\(410\) 1.96523e10 1.13463e10i 0.695469 0.401529i
\(411\) 0 0
\(412\) 1.02116e10 1.76870e10i 0.354409 0.613854i
\(413\) 9.91343e9i 0.340741i
\(414\) 0 0
\(415\) 2.75311e10 0.928177
\(416\) −6.76116e10 3.90356e10i −2.25761 1.30343i
\(417\) 0 0
\(418\) −2.81780e10 4.88057e10i −0.923006 1.59869i
\(419\) −1.26376e10 + 7.29630e9i −0.410022 + 0.236726i −0.690799 0.723047i \(-0.742741\pi\)
0.280777 + 0.959773i \(0.409408\pi\)
\(420\) 0 0
\(421\) 1.32550e10 2.29583e10i 0.421939 0.730820i −0.574190 0.818722i \(-0.694683\pi\)
0.996129 + 0.0879018i \(0.0280162\pi\)
\(422\) 3.13095e10i 0.987247i
\(423\) 0 0
\(424\) 1.07362e11 3.32191
\(425\) 1.48034e10 + 8.54673e9i 0.453738 + 0.261965i
\(426\) 0 0
\(427\) 1.88959e10 + 3.27287e10i 0.568404 + 0.984505i
\(428\) 1.02930e11 5.94268e10i 3.06738 1.77095i
\(429\) 0 0
\(430\) −6.95919e9 + 1.20537e10i −0.203557 + 0.352570i
\(431\) 4.61676e9i 0.133791i −0.997760 0.0668957i \(-0.978691\pi\)
0.997760 0.0668957i \(-0.0213095\pi\)
\(432\) 0 0
\(433\) −1.64494e10 −0.467948 −0.233974 0.972243i \(-0.575173\pi\)
−0.233974 + 0.972243i \(0.575173\pi\)
\(434\) −8.22927e9 4.75117e9i −0.231954 0.133919i
\(435\) 0 0
\(436\) −3.07594e10 5.32768e10i −0.851200 1.47432i
\(437\) 1.73334e10 1.00074e10i 0.475288 0.274408i
\(438\) 0 0
\(439\) 1.30737e10 2.26444e10i 0.351999 0.609681i −0.634600 0.772840i \(-0.718835\pi\)
0.986600 + 0.163160i \(0.0521686\pi\)
\(440\) 1.07131e11i 2.85828i
\(441\) 0 0
\(442\) −7.97335e10 −2.08906
\(443\) −3.73651e10 2.15728e10i −0.970179 0.560133i −0.0708880 0.997484i \(-0.522583\pi\)
−0.899291 + 0.437351i \(0.855917\pi\)
\(444\) 0 0
\(445\) 1.16396e10 + 2.01604e10i 0.296823 + 0.514113i
\(446\) −5.08062e10 + 2.93330e10i −1.28404 + 0.741339i
\(447\) 0 0
\(448\) 1.22142e10 2.11555e10i 0.303216 0.525185i
\(449\) 2.18287e10i 0.537084i 0.963268 + 0.268542i \(0.0865418\pi\)
−0.963268 + 0.268542i \(0.913458\pi\)
\(450\) 0 0
\(451\) −1.18008e10 −0.285237
\(452\) 1.65600e11 + 9.56094e10i 3.96741 + 2.29059i
\(453\) 0 0
\(454\) −2.64431e10 4.58009e10i −0.622429 1.07808i
\(455\) −6.37983e10 + 3.68340e10i −1.48855 + 0.859415i
\(456\) 0 0
\(457\) −1.23453e10 + 2.13826e10i −0.283032 + 0.490226i −0.972130 0.234442i \(-0.924674\pi\)
0.689098 + 0.724668i \(0.258007\pi\)
\(458\) 4.69676e10i 1.06742i
\(459\) 0 0
\(460\) 6.57186e10 1.46777
\(461\) −2.26667e10 1.30866e10i −0.501862 0.289750i 0.227620 0.973750i \(-0.426906\pi\)
−0.729482 + 0.684000i \(0.760239\pi\)
\(462\) 0 0
\(463\) −3.52051e10 6.09770e10i −0.766093 1.32691i −0.939667 0.342092i \(-0.888865\pi\)
0.173573 0.984821i \(-0.444469\pi\)
\(464\) 7.56844e10 4.36964e10i 1.63281 0.942701i
\(465\) 0 0
\(466\) −7.32512e10 + 1.26875e11i −1.55336 + 2.69049i
\(467\) 1.07220e10i 0.225428i −0.993627 0.112714i \(-0.964046\pi\)
0.993627 0.112714i \(-0.0359543\pi\)
\(468\) 0 0
\(469\) −1.17633e9 −0.0243130
\(470\) −1.93466e11 1.11698e11i −3.96473 2.28904i
\(471\) 0 0
\(472\) 2.60729e10 + 4.51596e10i 0.525317 + 0.909875i
\(473\) 6.26828e9 3.61899e9i 0.125229 0.0723008i
\(474\) 0 0
\(475\) 2.18503e10 3.78458e10i 0.429223 0.743435i
\(476\) 7.12907e10i 1.38869i
\(477\) 0 0
\(478\) −1.73352e11 −3.32060
\(479\) −1.21273e10 7.00168e9i −0.230367 0.133003i 0.380374 0.924833i \(-0.375795\pi\)
−0.610742 + 0.791830i \(0.709129\pi\)
\(480\) 0 0
\(481\) −1.51062e10 2.61648e10i −0.282212 0.488806i
\(482\) −5.75745e10 + 3.32407e10i −1.06670 + 0.615860i
\(483\) 0 0
\(484\) 1.70507e10 2.95327e10i 0.310714 0.538173i
\(485\) 1.12335e11i 2.03024i
\(486\) 0 0
\(487\) 1.72271e9 0.0306264 0.0153132 0.999883i \(-0.495125\pi\)
0.0153132 + 0.999883i \(0.495125\pi\)
\(488\) 1.72157e11 + 9.93948e10i 3.03560 + 1.75261i
\(489\) 0 0
\(490\) 2.29305e10 + 3.97168e10i 0.397768 + 0.688954i
\(491\) 3.20792e10 1.85209e10i 0.551947 0.318667i −0.197960 0.980210i \(-0.563432\pi\)
0.749907 + 0.661543i \(0.230098\pi\)
\(492\) 0 0
\(493\) 1.75429e10 3.03853e10i 0.296972 0.514370i
\(494\) 2.03844e11i 3.42287i
\(495\) 0 0
\(496\) −2.44027e10 −0.403191
\(497\) 4.98641e10 + 2.87891e10i 0.817265 + 0.471848i
\(498\) 0 0
\(499\) 6.67483e9 + 1.15612e10i 0.107656 + 0.186466i 0.914820 0.403861i \(-0.132332\pi\)
−0.807164 + 0.590327i \(0.798999\pi\)
\(500\) −4.50149e10 + 2.59893e10i −0.720238 + 0.415830i
\(501\) 0 0
\(502\) 4.87666e10 8.44662e10i 0.767905 1.33005i
\(503\) 5.91175e10i 0.923516i 0.887006 + 0.461758i \(0.152781\pi\)
−0.887006 + 0.461758i \(0.847219\pi\)
\(504\) 0 0
\(505\) 3.31264e10 0.509341
\(506\) −4.20589e10 2.42827e10i −0.641588 0.370421i
\(507\) 0 0
\(508\) 1.30984e11 + 2.26871e11i 1.96682 + 3.40663i
\(509\) −2.87565e10 + 1.66026e10i −0.428415 + 0.247345i −0.698671 0.715443i \(-0.746225\pi\)
0.270256 + 0.962788i \(0.412892\pi\)
\(510\) 0 0
\(511\) −1.26381e10 + 2.18899e10i −0.185353 + 0.321041i
\(512\) 1.38544e11i 2.01607i
\(513\) 0 0
\(514\) 8.96565e10 1.28449
\(515\) −2.39423e10 1.38231e10i −0.340358 0.196506i
\(516\) 0 0
\(517\) 5.80862e10 + 1.00608e11i 0.813038 + 1.40822i
\(518\) 3.32444e10 1.91937e10i 0.461742 0.266587i
\(519\) 0 0
\(520\) −1.93751e11 + 3.35586e11i −2.64990 + 4.58977i
\(521\) 2.53746e10i 0.344388i 0.985063 + 0.172194i \(0.0550856\pi\)
−0.985063 + 0.172194i \(0.944914\pi\)
\(522\) 0 0
\(523\) 1.27775e11 1.70781 0.853903 0.520432i \(-0.174229\pi\)
0.853903 + 0.520432i \(0.174229\pi\)
\(524\) 9.94813e10 + 5.74356e10i 1.31952 + 0.761826i
\(525\) 0 0
\(526\) 2.90149e10 + 5.02553e10i 0.379034 + 0.656507i
\(527\) −8.48448e9 + 4.89852e9i −0.109997 + 0.0635071i
\(528\) 0 0
\(529\) −3.05315e10 + 5.28821e10i −0.389875 + 0.675283i
\(530\) 2.51029e11i 3.18141i
\(531\) 0 0
\(532\) −1.82259e11 −2.27533
\(533\) 3.69658e10 + 2.13422e10i 0.458028 + 0.264442i
\(534\) 0 0
\(535\) −8.04440e10 1.39333e11i −0.981925 1.70074i
\(536\) −5.35865e9 + 3.09382e9i −0.0649226 + 0.0374831i
\(537\) 0 0
\(538\) 5.13414e10 8.89259e10i 0.612828 1.06145i
\(539\) 2.38492e10i 0.282565i
\(540\) 0 0
\(541\) 6.16835e9 0.0720078 0.0360039 0.999352i \(-0.488537\pi\)
0.0360039 + 0.999352i \(0.488537\pi\)
\(542\) 3.64594e10 + 2.10498e10i 0.422486 + 0.243922i
\(543\) 0 0
\(544\) −5.11360e10 8.85701e10i −0.583890 1.01133i
\(545\) −7.21190e10 + 4.16379e10i −0.817454 + 0.471958i
\(546\) 0 0
\(547\) −5.11547e10 + 8.86025e10i −0.571394 + 0.989684i 0.425029 + 0.905180i \(0.360264\pi\)
−0.996423 + 0.0845041i \(0.973069\pi\)
\(548\) 7.47826e10i 0.829237i
\(549\) 0 0
\(550\) −1.06038e11 −1.15881
\(551\) −7.76820e10 4.48497e10i −0.842780 0.486579i
\(552\) 0 0
\(553\) 2.31955e10 + 4.01758e10i 0.248030 + 0.429600i
\(554\) −8.53012e10 + 4.92487e10i −0.905558 + 0.522824i
\(555\) 0 0
\(556\) 5.23099e10 9.06034e10i 0.547375 0.948081i
\(557\) 1.00553e11i 1.04466i −0.852743 0.522331i \(-0.825063\pi\)
0.852743 0.522331i \(-0.174937\pi\)
\(558\) 0 0
\(559\) −2.61804e10 −0.268120
\(560\) −2.08170e11 1.20187e11i −2.11673 1.22210i
\(561\) 0 0
\(562\) −6.30558e10 1.09216e11i −0.632091 1.09481i
\(563\) 1.11721e11 6.45022e10i 1.11199 0.642009i 0.172648 0.984984i \(-0.444768\pi\)
0.939345 + 0.342974i \(0.111434\pi\)
\(564\) 0 0
\(565\) 1.29423e11 2.24167e11i 1.27004 2.19978i
\(566\) 2.91336e9i 0.0283876i
\(567\) 0 0
\(568\) 3.02868e11 2.90978
\(569\) 1.19625e10 + 6.90655e9i 0.114123 + 0.0658889i 0.555975 0.831199i \(-0.312345\pi\)
−0.441852 + 0.897088i \(0.645678\pi\)
\(570\) 0 0
\(571\) −3.91580e10 6.78237e10i −0.368363 0.638024i 0.620946 0.783853i \(-0.286748\pi\)
−0.989310 + 0.145829i \(0.953415\pi\)
\(572\) 3.01435e11 1.74034e11i 2.81585 1.62573i
\(573\) 0 0
\(574\) −2.71170e10 + 4.69681e10i −0.249801 + 0.432668i
\(575\) 3.76595e10i 0.344511i
\(576\) 0 0
\(577\) −6.44834e10 −0.581761 −0.290880 0.956759i \(-0.593948\pi\)
−0.290880 + 0.956759i \(0.593948\pi\)
\(578\) 8.71178e10 + 5.02975e10i 0.780541 + 0.450646i
\(579\) 0 0
\(580\) −1.47264e11 2.55068e11i −1.30132 2.25395i
\(581\) −5.69827e10 + 3.28990e10i −0.500079 + 0.288721i
\(582\) 0 0
\(583\) −6.52712e10 + 1.13053e11i −0.564999 + 0.978607i
\(584\) 1.32956e11i 1.14303i
\(585\) 0 0
\(586\) −2.65418e10 −0.225082
\(587\) 9.52651e10 + 5.50013e10i 0.802383 + 0.463256i 0.844304 0.535865i \(-0.180014\pi\)
−0.0419210 + 0.999121i \(0.513348\pi\)
\(588\) 0 0
\(589\) 1.25234e10 + 2.16911e10i 0.104054 + 0.180228i
\(590\) 1.05590e11 6.09623e10i 0.871393 0.503099i
\(591\) 0 0
\(592\) 4.92907e10 8.53740e10i 0.401308 0.695086i
\(593\) 9.33048e9i 0.0754545i 0.999288 + 0.0377273i \(0.0120118\pi\)
−0.999288 + 0.0377273i \(0.987988\pi\)
\(594\) 0 0
\(595\) −9.65037e10 −0.769974
\(596\) −3.85255e11 2.22427e11i −3.05325 1.76280i
\(597\) 0 0
\(598\) 8.78327e10 + 1.52131e11i 0.686833 + 1.18963i
\(599\) −7.03813e10 + 4.06347e10i −0.546701 + 0.315638i −0.747790 0.663935i \(-0.768885\pi\)
0.201089 + 0.979573i \(0.435552\pi\)
\(600\) 0 0
\(601\) −9.02916e10 + 1.56390e11i −0.692069 + 1.19870i 0.279090 + 0.960265i \(0.409967\pi\)
−0.971159 + 0.238434i \(0.923366\pi\)
\(602\) 3.32643e10i 0.253275i
\(603\) 0 0
\(604\) −1.13059e11 −0.849488
\(605\) −3.99774e10 2.30810e10i −0.298396 0.172279i
\(606\) 0 0
\(607\) −5.78752e10 1.00243e11i −0.426322 0.738411i 0.570221 0.821491i \(-0.306858\pi\)
−0.996543 + 0.0830800i \(0.973524\pi\)
\(608\) −2.26435e11 + 1.30733e11i −1.65703 + 0.956686i
\(609\) 0 0
\(610\) 2.32400e11 4.02529e11i 1.67848 2.90722i
\(611\) 4.20205e11i 3.01506i
\(612\) 0 0
\(613\) 7.01257e10 0.496632 0.248316 0.968679i \(-0.420123\pi\)
0.248316 + 0.968679i \(0.420123\pi\)
\(614\) 8.56328e10 + 4.94401e10i 0.602513 + 0.347861i
\(615\) 0 0
\(616\) 1.28019e11 + 2.21735e11i 0.889102 + 1.53997i
\(617\) 1.55050e10 8.95183e9i 0.106987 0.0617691i −0.445552 0.895256i \(-0.646992\pi\)
0.552539 + 0.833487i \(0.313659\pi\)
\(618\) 0 0
\(619\) −6.79961e10 + 1.17773e11i −0.463150 + 0.802199i −0.999116 0.0420404i \(-0.986614\pi\)
0.535966 + 0.844240i \(0.319948\pi\)
\(620\) 8.22410e10i 0.556572i
\(621\) 0 0
\(622\) 3.91007e11 2.61230
\(623\) −4.81823e10 2.78181e10i −0.319842 0.184661i
\(624\) 0 0
\(625\) 9.11869e10 + 1.57940e11i 0.597603 + 1.03508i
\(626\) −3.34106e11 + 1.92896e11i −2.17564 + 1.25611i
\(627\) 0 0
\(628\) 2.96098e11 5.12857e11i 1.90369 3.29730i
\(629\) 3.95778e10i 0.252842i
\(630\) 0 0
\(631\) −2.50988e11 −1.58320 −0.791600 0.611040i \(-0.790752\pi\)
−0.791600 + 0.611040i \(0.790752\pi\)
\(632\) 2.11329e11 + 1.22011e11i 1.32462 + 0.764770i
\(633\) 0 0
\(634\) 1.02661e11 + 1.77814e11i 0.635402 + 1.10055i
\(635\) 3.07108e11 1.77309e11i 1.88884 1.09052i
\(636\) 0 0
\(637\) −4.31322e10 + 7.47071e10i −0.261965 + 0.453737i
\(638\) 2.17653e11i 1.31366i
\(639\) 0 0
\(640\) 6.10397e10 0.363825
\(641\) 2.22817e10 + 1.28643e10i 0.131982 + 0.0761999i 0.564537 0.825408i \(-0.309055\pi\)
−0.432555 + 0.901607i \(0.642388\pi\)
\(642\) 0 0
\(643\) −2.14853e10 3.72136e10i −0.125689 0.217700i 0.796313 0.604885i \(-0.206781\pi\)
−0.922002 + 0.387185i \(0.873448\pi\)
\(644\) −1.36022e11 + 7.85322e10i −0.790797 + 0.456567i
\(645\) 0 0
\(646\) −1.33516e11 + 2.31257e11i −0.766662 + 1.32790i
\(647\) 2.20975e11i 1.26103i 0.776177 + 0.630516i \(0.217157\pi\)
−0.776177 + 0.630516i \(0.782843\pi\)
\(648\) 0 0
\(649\) −6.34045e10 −0.357389
\(650\) 3.32163e11 + 1.91775e11i 1.86079 + 1.07433i
\(651\) 0 0
\(652\) −3.51116e11 6.08151e11i −1.94294 3.36528i
\(653\) 2.58951e11 1.49505e11i 1.42418 0.822251i 0.427527 0.904002i \(-0.359385\pi\)
0.996653 + 0.0817518i \(0.0260515\pi\)
\(654\) 0 0
\(655\) 7.77485e10 1.34664e11i 0.422403 0.731624i
\(656\) 1.39277e11i 0.752079i
\(657\) 0 0
\(658\) 5.33904e11 2.84813
\(659\) 2.59640e11 + 1.49903e11i 1.37667 + 0.794820i 0.991757 0.128134i \(-0.0408987\pi\)
0.384911 + 0.922954i \(0.374232\pi\)
\(660\) 0 0
\(661\) 1.05724e11 + 1.83120e11i 0.553820 + 0.959244i 0.997994 + 0.0633036i \(0.0201636\pi\)
−0.444175 + 0.895940i \(0.646503\pi\)
\(662\) 3.02244e11 1.74500e11i 1.57371 0.908583i
\(663\) 0 0
\(664\) −1.73052e11 + 2.99736e11i −0.890237 + 1.54194i
\(665\) 2.46718e11i 1.26158i
\(666\) 0 0
\(667\) −7.72997e10 −0.390548
\(668\) −6.01848e10 3.47477e10i −0.302260 0.174510i
\(669\) 0 0
\(670\) 7.23381e9 + 1.25293e10i 0.0358978 + 0.0621768i
\(671\) −2.09327e11 + 1.20855e11i −1.03261 + 0.596177i
\(672\) 0 0
\(673\) 9.50831e10 1.64689e11i 0.463493 0.802793i −0.535639 0.844447i \(-0.679929\pi\)
0.999132 + 0.0416539i \(0.0132627\pi\)
\(674\) 2.69077e11i 1.30388i
\(675\) 0 0
\(676\) −7.63024e11 −3.65386
\(677\) −9.94331e10 5.74077e10i −0.473343 0.273285i 0.244295 0.969701i \(-0.421443\pi\)
−0.717638 + 0.696416i \(0.754777\pi\)
\(678\) 0 0
\(679\) −1.34238e11 2.32506e11i −0.631531 1.09384i
\(680\) −4.39612e11 + 2.53810e11i −2.05605 + 1.18706i
\(681\) 0 0
\(682\) 3.03877e10 5.26330e10i 0.140462 0.243288i
\(683\) 3.07050e11i 1.41100i 0.708710 + 0.705500i \(0.249277\pi\)
−0.708710 + 0.705500i \(0.750723\pi\)
\(684\) 0 0
\(685\) −1.01231e11 −0.459780
\(686\) −3.83574e11 2.21457e11i −1.73202 0.999983i
\(687\) 0 0
\(688\) −4.27125e10 7.39802e10i −0.190634 0.330188i
\(689\) 4.08923e11 2.36092e11i 1.81453 1.04762i
\(690\) 0 0
\(691\) 1.10299e11 1.91043e11i 0.483791 0.837951i −0.516036 0.856567i \(-0.672593\pi\)
0.999827 + 0.0186164i \(0.00592614\pi\)
\(692\) 1.00516e12i 4.38339i
\(693\) 0 0
\(694\) 6.02812e11 2.59863
\(695\) −1.22647e11 7.08101e10i −0.525674 0.303498i
\(696\) 0 0
\(697\) 2.79580e10 + 4.84246e10i 0.118461 + 0.205180i
\(698\) −3.43142e11 + 1.98113e11i −1.44561 + 0.834625i
\(699\) 0 0
\(700\) −1.71468e11 + 2.96991e11i −0.714152 + 1.23695i
\(701\) 4.11156e11i 1.70269i −0.524609 0.851343i \(-0.675788\pi\)
0.524609 0.851343i \(-0.324212\pi\)
\(702\) 0 0
\(703\) −1.01183e11 −0.414274
\(704\) 1.35307e11 + 7.81196e10i 0.550845 + 0.318031i
\(705\) 0 0
\(706\) −1.43774e11 2.49024e11i −0.578711 1.00236i
\(707\) −6.85637e10 + 3.95853e10i −0.274421 + 0.158437i
\(708\) 0 0
\(709\) −7.05213e10 + 1.22146e11i −0.279084 + 0.483388i −0.971157 0.238439i \(-0.923364\pi\)
0.692073 + 0.721827i \(0.256698\pi\)
\(710\) 7.08150e11i 2.78671i
\(711\) 0 0
\(712\) −2.92653e11 −1.13876
\(713\) 1.86926e10 + 1.07922e10i 0.0723290 + 0.0417591i
\(714\) 0 0
\(715\) −2.35583e11 4.08042e11i −0.901406 1.56128i
\(716\) −2.19689e11 + 1.26838e11i −0.835904 + 0.482610i
\(717\) 0 0
\(718\) −2.45936e11 + 4.25973e11i −0.925388 + 1.60282i
\(719\) 1.87514e11i 0.701645i −0.936442 0.350823i \(-0.885902\pi\)
0.936442 0.350823i \(-0.114098\pi\)
\(720\) 0 0
\(721\) 6.60730e10 0.244502
\(722\) 1.58893e11 + 9.17367e10i 0.584729 + 0.337594i
\(723\) 0 0
\(724\) 3.53929e11 + 6.13024e11i 1.28814 + 2.23112i
\(725\) −1.46165e11 + 8.43884e10i −0.529043 + 0.305443i
\(726\) 0 0
\(727\) −3.37310e10 + 5.84239e10i −0.120751 + 0.209148i −0.920064 0.391768i \(-0.871864\pi\)
0.799313 + 0.600915i \(0.205197\pi\)
\(728\) 9.26111e11i 3.29714i
\(729\) 0 0
\(730\) 3.10871e11 1.09469
\(731\) −2.97011e10 1.71479e10i −0.104017 0.0600541i
\(732\) 0 0
\(733\) 2.75674e11 + 4.77481e11i 0.954948 + 1.65402i 0.734487 + 0.678623i \(0.237423\pi\)
0.220461 + 0.975396i \(0.429244\pi\)
\(734\) 3.81530e11 2.20276e11i 1.31445 0.758899i
\(735\) 0 0
\(736\) −1.12661e11 + 1.95134e11i −0.383937 + 0.664999i
\(737\) 7.52360e9i 0.0255009i
\(738\) 0 0
\(739\) −3.53894e11 −1.18658 −0.593288 0.804990i \(-0.702171\pi\)
−0.593288 + 0.804990i \(0.702171\pi\)
\(740\) −2.87724e11 1.66117e11i −0.959509 0.553973i
\(741\) 0 0
\(742\) 2.99973e11 + 5.19569e11i 0.989616 + 1.71407i
\(743\) −3.99633e10 + 2.30728e10i −0.131131 + 0.0757086i −0.564131 0.825686i \(-0.690789\pi\)
0.432999 + 0.901394i \(0.357455\pi\)
\(744\) 0 0
\(745\) −3.01092e11 + 5.21506e11i −0.977402 + 1.69291i
\(746\) 5.81893e11i 1.87883i
\(747\) 0 0
\(748\) 4.55962e11 1.45654
\(749\) 3.32999e11 + 1.92257e11i 1.05807 + 0.610880i
\(750\) 0 0
\(751\) 1.39277e11 + 2.41235e11i 0.437845 + 0.758370i 0.997523 0.0703401i \(-0.0224085\pi\)
−0.559678 + 0.828710i \(0.689075\pi\)
\(752\) 1.18741e12 6.85552e11i 3.71304 2.14372i
\(753\) 0 0
\(754\) 3.93635e11 6.81796e11i 1.21789 2.10945i
\(755\) 1.53044e11i 0.471008i
\(756\) 0 0
\(757\) −2.54100e11 −0.773786 −0.386893 0.922125i \(-0.626452\pi\)
−0.386893 + 0.922125i \(0.626452\pi\)
\(758\) −1.36163e11 7.86138e10i −0.412461 0.238134i
\(759\) 0 0
\(760\) 6.48883e11 + 1.12390e12i 1.94497 + 3.36878i
\(761\) −4.36794e11 + 2.52183e11i −1.30238 + 0.751930i −0.980812 0.194956i \(-0.937543\pi\)
−0.321569 + 0.946886i \(0.604210\pi\)
\(762\) 0 0
\(763\) 9.95127e10 1.72361e11i 0.293616 0.508558i
\(764\) 9.79216e11i 2.87412i
\(765\) 0 0
\(766\) −4.26029e11 −1.23744
\(767\) 1.98614e11 + 1.14670e11i 0.573889 + 0.331335i
\(768\) 0 0
\(769\) −1.08224e11 1.87449e11i −0.309468 0.536015i 0.668778 0.743462i \(-0.266818\pi\)
−0.978246 + 0.207447i \(0.933484\pi\)