Properties

Label 99.8.j.a.8.8
Level $99$
Weight $8$
Character 99.8
Analytic conductor $30.926$
Analytic rank $0$
Dimension $112$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [99,8,Mod(8,99)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(99, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 3]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("99.8");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 99.j (of order \(10\), degree \(4\), 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: \(30.9261175229\)
Analytic rank: \(0\)
Dimension: \(112\)
Relative dimension: \(28\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 8.8
Character \(\chi\) \(=\) 99.8
Dual form 99.8.j.a.62.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-10.9960 + 7.98908i) q^{2} +(17.5330 - 53.9610i) q^{4} +(47.9158 - 65.9504i) q^{5} +(-905.136 - 294.096i) q^{7} +(-299.308 - 921.176i) q^{8} +O(q^{10})\) \(q+(-10.9960 + 7.98908i) q^{2} +(17.5330 - 53.9610i) q^{4} +(47.9158 - 65.9504i) q^{5} +(-905.136 - 294.096i) q^{7} +(-299.308 - 921.176i) q^{8} +1108.00i q^{10} +(-3576.27 + 2587.94i) q^{11} +(846.767 + 1165.48i) q^{13} +(12302.5 - 3997.31i) q^{14} +(16526.0 + 12006.8i) q^{16} +(-29596.9 - 21503.4i) q^{17} +(21779.0 - 7076.41i) q^{19} +(-2718.64 - 3741.89i) q^{20} +(18649.5 - 57028.2i) q^{22} -25983.7i q^{23} +(22088.4 + 67981.2i) q^{25} +(-18622.1 - 6050.70i) q^{26} +(-31739.5 + 43685.6i) q^{28} +(56158.7 - 172839. i) q^{29} +(200024. - 145326. i) q^{31} -153665. q^{32} +497240. q^{34} +(-62766.1 + 45602.2i) q^{35} +(-148801. + 457962. i) q^{37} +(-182948. + 251806. i) q^{38} +(-75093.6 - 24399.4i) q^{40} +(140768. + 433240. i) q^{41} +389553. i q^{43} +(76945.2 + 238353. i) q^{44} +(207586. + 285717. i) q^{46} +(-782981. + 254406. i) q^{47} +(66517.7 + 48327.9i) q^{49} +(-785992. - 571056. i) q^{50} +(77736.5 - 25258.1i) q^{52} +(816540. + 1.12387e6i) q^{53} +(-683.937 + 359860. i) q^{55} +921815. i q^{56} +(763300. + 2.34920e6i) q^{58} +(1.53223e6 + 497851. i) q^{59} +(375155. - 516357. i) q^{61} +(-1.03845e6 + 3.19601e6i) q^{62} +(-425620. + 309231. i) q^{64} +117437. q^{65} +144363. q^{67} +(-1.67926e6 + 1.22006e6i) q^{68} +(325857. - 1.00289e6i) q^{70} +(-1.88721e6 + 2.59752e6i) q^{71} +(3.11417e6 + 1.01186e6i) q^{73} +(-2.02248e6 - 6.22455e6i) q^{74} -1.29928e6i q^{76} +(3.99812e6 - 1.29067e6i) q^{77} +(1.88249e6 + 2.59103e6i) q^{79} +(1.58371e6 - 514579. i) q^{80} +(-5.00908e6 - 3.63931e6i) q^{82} +(901996. + 655339. i) q^{83} +(-2.83631e6 + 921574. i) q^{85} +(-3.11217e6 - 4.28353e6i) q^{86} +(3.45436e6 + 2.51978e6i) q^{88} -1.06756e7i q^{89} +(-423677. - 1.30394e6i) q^{91} +(-1.40211e6 - 455572. i) q^{92} +(6.57721e6 - 9.05275e6i) q^{94} +(576864. - 1.77540e6i) q^{95} +(434523. - 315699. i) q^{97} -1.11753e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 112 q - 1792 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 112 q - 1792 q^{4} - 134096 q^{16} + 401484 q^{22} - 68552 q^{25} + 1493020 q^{28} - 398144 q^{31} - 729944 q^{34} + 685476 q^{37} - 399360 q^{40} - 1410880 q^{46} + 2923872 q^{49} + 6472520 q^{52} + 1445488 q^{55} + 13215936 q^{58} - 7843440 q^{61} - 12806712 q^{64} + 1864032 q^{67} - 1233728 q^{70} + 53841940 q^{73} - 53845440 q^{79} - 36360204 q^{82} + 41703500 q^{85} + 21474024 q^{88} + 27611736 q^{91} - 94707560 q^{94} - 27695460 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{3}{10}\right)\) \(-1\)

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −10.9960 + 7.98908i −0.971920 + 0.706141i −0.955888 0.293730i \(-0.905103\pi\)
−0.0160319 + 0.999871i \(0.505103\pi\)
\(3\) 0 0
\(4\) 17.5330 53.9610i 0.136976 0.421570i
\(5\) 47.9158 65.9504i 0.171429 0.235951i −0.714654 0.699478i \(-0.753416\pi\)
0.886083 + 0.463526i \(0.153416\pi\)
\(6\) 0 0
\(7\) −905.136 294.096i −0.997403 0.324076i −0.235576 0.971856i \(-0.575697\pi\)
−0.761827 + 0.647780i \(0.775697\pi\)
\(8\) −299.308 921.176i −0.206683 0.636104i
\(9\) 0 0
\(10\) 1108.00i 0.350379i
\(11\) −3576.27 + 2587.94i −0.810133 + 0.586247i
\(12\) 0 0
\(13\) 846.767 + 1165.48i 0.106896 + 0.147130i 0.859113 0.511785i \(-0.171016\pi\)
−0.752217 + 0.658915i \(0.771016\pi\)
\(14\) 12302.5 3997.31i 1.19824 0.389332i
\(15\) 0 0
\(16\) 16526.0 + 12006.8i 1.00867 + 0.732840i
\(17\) −29596.9 21503.4i −1.46108 1.06154i −0.983080 0.183179i \(-0.941361\pi\)
−0.478002 0.878359i \(-0.658639\pi\)
\(18\) 0 0
\(19\) 21779.0 7076.41i 0.728450 0.236688i 0.0787670 0.996893i \(-0.474902\pi\)
0.649683 + 0.760205i \(0.274902\pi\)
\(20\) −2718.64 3741.89i −0.0759884 0.104589i
\(21\) 0 0
\(22\) 18649.5 57028.2i 0.373411 1.14185i
\(23\) 25983.7i 0.445301i −0.974898 0.222651i \(-0.928529\pi\)
0.974898 0.222651i \(-0.0714709\pi\)
\(24\) 0 0
\(25\) 22088.4 + 67981.2i 0.282732 + 0.870159i
\(26\) −18622.1 6050.70i −0.207789 0.0675148i
\(27\) 0 0
\(28\) −31739.5 + 43685.6i −0.273241 + 0.376084i
\(29\) 56158.7 172839.i 0.427587 1.31598i −0.472909 0.881111i \(-0.656796\pi\)
0.900496 0.434865i \(-0.143204\pi\)
\(30\) 0 0
\(31\) 200024. 145326.i 1.20591 0.876146i 0.211058 0.977474i \(-0.432309\pi\)
0.994853 + 0.101328i \(0.0323091\pi\)
\(32\) −153665. −0.828994
\(33\) 0 0
\(34\) 497240. 2.16965
\(35\) −62766.1 + 45602.2i −0.247450 + 0.179783i
\(36\) 0 0
\(37\) −148801. + 457962.i −0.482947 + 1.48636i 0.351985 + 0.936006i \(0.385507\pi\)
−0.834932 + 0.550353i \(0.814493\pi\)
\(38\) −182948. + 251806.i −0.540860 + 0.744430i
\(39\) 0 0
\(40\) −75093.6 24399.4i −0.185521 0.0602794i
\(41\) 140768. + 433240.i 0.318978 + 0.981714i 0.974086 + 0.226178i \(0.0726232\pi\)
−0.655108 + 0.755535i \(0.727377\pi\)
\(42\) 0 0
\(43\) 389553.i 0.747182i 0.927593 + 0.373591i \(0.121874\pi\)
−0.927593 + 0.373591i \(0.878126\pi\)
\(44\) 76945.2 + 238353.i 0.136175 + 0.421830i
\(45\) 0 0
\(46\) 207586. + 285717.i 0.314446 + 0.432797i
\(47\) −782981. + 254406.i −1.10004 + 0.357425i −0.802118 0.597165i \(-0.796294\pi\)
−0.297922 + 0.954590i \(0.596294\pi\)
\(48\) 0 0
\(49\) 66517.7 + 48327.9i 0.0807701 + 0.0586829i
\(50\) −785992. 571056.i −0.889248 0.646076i
\(51\) 0 0
\(52\) 77736.5 25258.1i 0.0766679 0.0249109i
\(53\) 816540. + 1.12387e6i 0.753376 + 1.03693i 0.997736 + 0.0672485i \(0.0214220\pi\)
−0.244360 + 0.969684i \(0.578578\pi\)
\(54\) 0 0
\(55\) −683.937 + 359860.i −0.000554302 + 0.291651i
\(56\) 921815.i 0.701432i
\(57\) 0 0
\(58\) 763300. + 2.34920e6i 0.513685 + 1.58096i
\(59\) 1.53223e6 + 497851.i 0.971272 + 0.315585i 0.751329 0.659927i \(-0.229413\pi\)
0.219943 + 0.975513i \(0.429413\pi\)
\(60\) 0 0
\(61\) 375155. 516357.i 0.211620 0.291270i −0.689991 0.723818i \(-0.742385\pi\)
0.901611 + 0.432548i \(0.142385\pi\)
\(62\) −1.03845e6 + 3.19601e6i −0.553367 + 1.70309i
\(63\) 0 0
\(64\) −425620. + 309231.i −0.202951 + 0.147453i
\(65\) 117437. 0.0530406
\(66\) 0 0
\(67\) 144363. 0.0586398 0.0293199 0.999570i \(-0.490666\pi\)
0.0293199 + 0.999570i \(0.490666\pi\)
\(68\) −1.67926e6 + 1.22006e6i −0.647646 + 0.470543i
\(69\) 0 0
\(70\) 325857. 1.00289e6i 0.113549 0.349469i
\(71\) −1.88721e6 + 2.59752e6i −0.625771 + 0.861299i −0.997757 0.0669387i \(-0.978677\pi\)
0.371986 + 0.928238i \(0.378677\pi\)
\(72\) 0 0
\(73\) 3.11417e6 + 1.01186e6i 0.936942 + 0.304431i 0.737398 0.675458i \(-0.236054\pi\)
0.199543 + 0.979889i \(0.436054\pi\)
\(74\) −2.02248e6 6.22455e6i −0.580193 1.78565i
\(75\) 0 0
\(76\) 1.29928e6i 0.339513i
\(77\) 3.99812e6 1.29067e6i 0.998017 0.322180i
\(78\) 0 0
\(79\) 1.88249e6 + 2.59103e6i 0.429574 + 0.591258i 0.967855 0.251507i \(-0.0809262\pi\)
−0.538281 + 0.842765i \(0.680926\pi\)
\(80\) 1.58371e6 514579.i 0.345829 0.112367i
\(81\) 0 0
\(82\) −5.00908e6 3.63931e6i −1.00325 0.728904i
\(83\) 901996. + 655339.i 0.173154 + 0.125803i 0.670987 0.741469i \(-0.265871\pi\)
−0.497833 + 0.867273i \(0.665871\pi\)
\(84\) 0 0
\(85\) −2.83631e6 + 921574.i −0.500943 + 0.162766i
\(86\) −3.11217e6 4.28353e6i −0.527616 0.726202i
\(87\) 0 0
\(88\) 3.45436e6 + 2.51978e6i 0.540354 + 0.394161i
\(89\) 1.06756e7i 1.60519i −0.596524 0.802595i \(-0.703452\pi\)
0.596524 0.802595i \(-0.296548\pi\)
\(90\) 0 0
\(91\) −423677. 1.30394e6i −0.0589373 0.181390i
\(92\) −1.40211e6 455572.i −0.187726 0.0609957i
\(93\) 0 0
\(94\) 6.57721e6 9.05275e6i 0.816759 1.12417i
\(95\) 576864. 1.77540e6i 0.0690304 0.212454i
\(96\) 0 0
\(97\) 434523. 315699.i 0.0483406 0.0351215i −0.563353 0.826217i \(-0.690489\pi\)
0.611693 + 0.791095i \(0.290489\pi\)
\(98\) −1.11753e6 −0.119941
\(99\) 0 0
\(100\) 4.05561e6 0.405561
\(101\) 5.67786e6 4.12521e6i 0.548353 0.398402i −0.278825 0.960342i \(-0.589945\pi\)
0.827178 + 0.561940i \(0.189945\pi\)
\(102\) 0 0
\(103\) −2.12733e6 + 6.54724e6i −0.191824 + 0.590375i 0.808174 + 0.588943i \(0.200456\pi\)
−0.999999 + 0.00143195i \(0.999544\pi\)
\(104\) 820164. 1.12886e6i 0.0714964 0.0984063i
\(105\) 0 0
\(106\) −1.79574e7 5.83471e6i −1.46444 0.475826i
\(107\) 303151. + 933003.i 0.0239230 + 0.0736274i 0.962305 0.271972i \(-0.0876757\pi\)
−0.938382 + 0.345599i \(0.887676\pi\)
\(108\) 0 0
\(109\) 9.01952e6i 0.667100i −0.942732 0.333550i \(-0.891753\pi\)
0.942732 0.333550i \(-0.108247\pi\)
\(110\) −2.86743e6 3.96249e6i −0.205408 0.283853i
\(111\) 0 0
\(112\) −1.14271e7 1.57281e7i −0.768552 1.05782i
\(113\) 1.51500e7 4.92254e6i 0.987732 0.320934i 0.229779 0.973243i \(-0.426200\pi\)
0.757953 + 0.652309i \(0.226200\pi\)
\(114\) 0 0
\(115\) −1.71364e6 1.24503e6i −0.105069 0.0763374i
\(116\) −8.34192e6 6.06076e6i −0.496207 0.360515i
\(117\) 0 0
\(118\) −2.08258e7 + 6.76670e6i −1.16685 + 0.379132i
\(119\) 2.04651e7 + 2.81678e7i 1.11327 + 1.53228i
\(120\) 0 0
\(121\) 6.09227e6 1.85104e7i 0.312630 0.949875i
\(122\) 8.67502e6i 0.432525i
\(123\) 0 0
\(124\) −4.33490e6 1.33415e7i −0.204175 0.628387i
\(125\) 1.15988e7 + 3.76866e6i 0.531161 + 0.172585i
\(126\) 0 0
\(127\) −1.93966e7 + 2.66972e7i −0.840260 + 1.15652i 0.145666 + 0.989334i \(0.453468\pi\)
−0.985926 + 0.167185i \(0.946532\pi\)
\(128\) 8.28776e6 2.55071e7i 0.349303 1.07504i
\(129\) 0 0
\(130\) −1.29134e6 + 938214.i −0.0515513 + 0.0374542i
\(131\) 3.73191e6 0.145038 0.0725190 0.997367i \(-0.476896\pi\)
0.0725190 + 0.997367i \(0.476896\pi\)
\(132\) 0 0
\(133\) −2.17941e7 −0.803263
\(134\) −1.58741e6 + 1.15332e6i −0.0569933 + 0.0414080i
\(135\) 0 0
\(136\) −1.09498e7 + 3.37001e7i −0.373268 + 1.14880i
\(137\) −2.03181e7 + 2.79655e7i −0.675091 + 0.929183i −0.999862 0.0166100i \(-0.994713\pi\)
0.324771 + 0.945793i \(0.394713\pi\)
\(138\) 0 0
\(139\) 2.11333e7 + 6.86662e6i 0.667445 + 0.216866i 0.623090 0.782150i \(-0.285877\pi\)
0.0443545 + 0.999016i \(0.485877\pi\)
\(140\) 1.36026e6 + 4.18646e6i 0.0418962 + 0.128943i
\(141\) 0 0
\(142\) 4.36394e7i 1.27900i
\(143\) −6.04445e6 1.97667e6i −0.172855 0.0565273i
\(144\) 0 0
\(145\) −8.70790e6 1.19854e7i −0.237206 0.326486i
\(146\) −4.23273e7 + 1.37530e7i −1.12560 + 0.365731i
\(147\) 0 0
\(148\) 2.21032e7 + 1.60589e7i 0.560452 + 0.407192i
\(149\) 4.67549e7 + 3.39694e7i 1.15791 + 0.841272i 0.989512 0.144447i \(-0.0461404\pi\)
0.168399 + 0.985719i \(0.446140\pi\)
\(150\) 0 0
\(151\) 6.12940e7 1.99156e7i 1.44877 0.470733i 0.524149 0.851627i \(-0.324383\pi\)
0.924619 + 0.380893i \(0.124383\pi\)
\(152\) −1.30373e7 1.79442e7i −0.301116 0.414450i
\(153\) 0 0
\(154\) −3.36521e7 + 4.61335e7i −0.742489 + 1.01787i
\(155\) 2.01550e7i 0.434733i
\(156\) 0 0
\(157\) 1.82709e7 + 5.62320e7i 0.376800 + 1.15967i 0.942256 + 0.334893i \(0.108700\pi\)
−0.565456 + 0.824778i \(0.691300\pi\)
\(158\) −4.13999e7 1.34516e7i −0.835024 0.271316i
\(159\) 0 0
\(160\) −7.36300e6 + 1.01343e7i −0.142113 + 0.195602i
\(161\) −7.64172e6 + 2.35188e7i −0.144311 + 0.444144i
\(162\) 0 0
\(163\) 3.13782e7 2.27976e7i 0.567507 0.412318i −0.266692 0.963782i \(-0.585931\pi\)
0.834199 + 0.551464i \(0.185931\pi\)
\(164\) 2.58461e7 0.457554
\(165\) 0 0
\(166\) −1.51539e7 −0.257127
\(167\) 2.79236e7 2.02877e7i 0.463942 0.337074i −0.331134 0.943584i \(-0.607431\pi\)
0.795076 + 0.606510i \(0.207431\pi\)
\(168\) 0 0
\(169\) 1.87490e7 5.77036e7i 0.298797 0.919601i
\(170\) 2.38256e7 3.27932e7i 0.371940 0.511932i
\(171\) 0 0
\(172\) 2.10206e7 + 6.83002e6i 0.314990 + 0.102346i
\(173\) −1.79011e7 5.50940e7i −0.262857 0.808990i −0.992179 0.124820i \(-0.960165\pi\)
0.729323 0.684170i \(-0.239835\pi\)
\(174\) 0 0
\(175\) 6.80283e7i 0.959525i
\(176\) −9.01745e7 171383.i −1.24678 0.00236958i
\(177\) 0 0
\(178\) 8.52881e7 + 1.17389e8i 1.13349 + 1.56012i
\(179\) −6.96827e7 + 2.26413e7i −0.908111 + 0.295063i −0.725581 0.688137i \(-0.758429\pi\)
−0.182531 + 0.983200i \(0.558429\pi\)
\(180\) 0 0
\(181\) 9.35580e7 + 6.79739e7i 1.17275 + 0.852054i 0.991336 0.131353i \(-0.0419320\pi\)
0.181416 + 0.983406i \(0.441932\pi\)
\(182\) 1.50761e7 + 1.09534e7i 0.185370 + 0.134679i
\(183\) 0 0
\(184\) −2.39356e7 + 7.77714e6i −0.283258 + 0.0920360i
\(185\) 2.30729e7 + 3.17571e7i 0.267917 + 0.368757i
\(186\) 0 0
\(187\) 1.61496e8 + 306934.i 1.80599 + 0.00343241i
\(188\) 4.67109e7i 0.512703i
\(189\) 0 0
\(190\) 7.84063e6 + 2.41310e7i 0.0829304 + 0.255233i
\(191\) −5.99955e7 1.94937e7i −0.623020 0.202431i −0.0195393 0.999809i \(-0.506220\pi\)
−0.603481 + 0.797378i \(0.706220\pi\)
\(192\) 0 0
\(193\) 5.16054e7 7.10288e7i 0.516708 0.711187i −0.468325 0.883556i \(-0.655142\pi\)
0.985032 + 0.172369i \(0.0551422\pi\)
\(194\) −2.25588e6 + 6.94288e6i −0.0221824 + 0.0682706i
\(195\) 0 0
\(196\) 3.77407e6 2.74203e6i 0.0358026 0.0260121i
\(197\) 2.33594e7 0.217686 0.108843 0.994059i \(-0.465285\pi\)
0.108843 + 0.994059i \(0.465285\pi\)
\(198\) 0 0
\(199\) −1.49101e8 −1.34120 −0.670600 0.741819i \(-0.733963\pi\)
−0.670600 + 0.741819i \(0.733963\pi\)
\(200\) 5.60114e7 4.06947e7i 0.495075 0.359693i
\(201\) 0 0
\(202\) −2.94773e7 + 9.07218e7i −0.251627 + 0.774429i
\(203\) −1.01662e8 + 1.39926e8i −0.852952 + 1.17399i
\(204\) 0 0
\(205\) 3.53174e7 + 1.14753e7i 0.286319 + 0.0930306i
\(206\) −2.89143e7 8.89890e7i −0.230450 0.709253i
\(207\) 0 0
\(208\) 2.94277e7i 0.226743i
\(209\) −5.95741e7 + 8.16699e7i −0.451384 + 0.618800i
\(210\) 0 0
\(211\) −8.53544e6 1.17480e7i −0.0625514 0.0860947i 0.776595 0.630000i \(-0.216945\pi\)
−0.839147 + 0.543905i \(0.816945\pi\)
\(212\) 7.49615e7 2.43565e7i 0.540335 0.175565i
\(213\) 0 0
\(214\) −1.07873e7 7.83742e6i −0.0752426 0.0546670i
\(215\) 2.56912e7 + 1.86657e7i 0.176299 + 0.128088i
\(216\) 0 0
\(217\) −2.23788e8 + 7.27132e7i −1.48672 + 0.483064i
\(218\) 7.20577e7 + 9.91789e7i 0.471067 + 0.648368i
\(219\) 0 0
\(220\) 1.94064e7 + 6.34632e6i 0.122876 + 0.0401830i
\(221\) 5.27028e7i 0.328443i
\(222\) 0 0
\(223\) −2.02580e7 6.23478e7i −0.122329 0.376491i 0.871076 0.491149i \(-0.163423\pi\)
−0.993405 + 0.114658i \(0.963423\pi\)
\(224\) 1.39088e8 + 4.51924e7i 0.826841 + 0.268657i
\(225\) 0 0
\(226\) −1.27264e8 + 1.75163e8i −0.733372 + 1.00940i
\(227\) 4.78857e7 1.47377e8i 0.271716 0.836257i −0.718353 0.695678i \(-0.755104\pi\)
0.990070 0.140578i \(-0.0448961\pi\)
\(228\) 0 0
\(229\) 2.60142e8 1.89004e8i 1.43148 1.04003i 0.441743 0.897142i \(-0.354360\pi\)
0.989739 0.142890i \(-0.0456396\pi\)
\(230\) 2.87898e7 0.156024
\(231\) 0 0
\(232\) −1.76024e8 −0.925472
\(233\) −1.70860e8 + 1.24137e8i −0.884900 + 0.642917i −0.934543 0.355850i \(-0.884192\pi\)
0.0496433 + 0.998767i \(0.484192\pi\)
\(234\) 0 0
\(235\) −2.07390e7 + 6.38280e7i −0.104244 + 0.320829i
\(236\) 5.37290e7 7.39516e7i 0.266083 0.366231i
\(237\) 0 0
\(238\) −4.50070e8 1.46237e8i −2.16402 0.703131i
\(239\) 6.31895e7 + 1.94477e8i 0.299400 + 0.921459i 0.981708 + 0.190394i \(0.0609765\pi\)
−0.682308 + 0.731065i \(0.739024\pi\)
\(240\) 0 0
\(241\) 3.98267e8i 1.83280i −0.400266 0.916399i \(-0.631082\pi\)
0.400266 0.916399i \(-0.368918\pi\)
\(242\) 8.08901e7 + 2.52212e8i 0.366895 + 1.14396i
\(243\) 0 0
\(244\) −2.12855e7 2.92970e7i −0.0938037 0.129110i
\(245\) 6.37449e6 2.07120e6i 0.0276926 0.00899788i
\(246\) 0 0
\(247\) 2.66891e7 + 1.93908e7i 0.112692 + 0.0818758i
\(248\) −1.93739e8 1.40760e8i −0.806560 0.586000i
\(249\) 0 0
\(250\) −1.57648e8 + 5.12230e7i −0.638115 + 0.207336i
\(251\) 2.59305e8 + 3.56903e8i 1.03503 + 1.42460i 0.901102 + 0.433607i \(0.142759\pi\)
0.133929 + 0.990991i \(0.457241\pi\)
\(252\) 0 0
\(253\) 6.72444e7 + 9.29248e7i 0.261056 + 0.360753i
\(254\) 4.48524e8i 1.71739i
\(255\) 0 0
\(256\) 9.18367e7 + 2.82644e8i 0.342118 + 1.05293i
\(257\) −7.75368e7 2.51932e7i −0.284933 0.0925802i 0.163064 0.986615i \(-0.447862\pi\)
−0.447996 + 0.894035i \(0.647862\pi\)
\(258\) 0 0
\(259\) 2.69370e8 3.70756e8i 0.963386 1.32599i
\(260\) 2.05902e6 6.33702e6i 0.00726531 0.0223603i
\(261\) 0 0
\(262\) −4.10362e7 + 2.98145e7i −0.140965 + 0.102417i
\(263\) 2.55717e8 0.866790 0.433395 0.901204i \(-0.357316\pi\)
0.433395 + 0.901204i \(0.357316\pi\)
\(264\) 0 0
\(265\) 1.13245e8 0.373816
\(266\) 2.39648e8 1.74115e8i 0.780707 0.567217i
\(267\) 0 0
\(268\) 2.53111e6 7.78994e6i 0.00803228 0.0247208i
\(269\) 3.12392e8 4.29971e8i 0.978515 1.34681i 0.0408890 0.999164i \(-0.486981\pi\)
0.937626 0.347646i \(-0.113019\pi\)
\(270\) 0 0
\(271\) −4.99126e8 1.62176e8i −1.52341 0.494987i −0.576670 0.816977i \(-0.695648\pi\)
−0.946743 + 0.321990i \(0.895648\pi\)
\(272\) −2.30930e8 7.10730e8i −0.695808 2.14148i
\(273\) 0 0
\(274\) 4.69833e8i 1.37980i
\(275\) −2.54926e8 1.85956e8i −0.739178 0.539194i
\(276\) 0 0
\(277\) −1.29198e8 1.77826e8i −0.365239 0.502709i 0.586360 0.810051i \(-0.300560\pi\)
−0.951599 + 0.307342i \(0.900560\pi\)
\(278\) −2.87240e8 + 9.33300e7i −0.801841 + 0.260534i
\(279\) 0 0
\(280\) 6.07941e7 + 4.41695e7i 0.165504 + 0.120246i
\(281\) −1.88857e8 1.37212e8i −0.507762 0.368911i 0.304212 0.952604i \(-0.401607\pi\)
−0.811974 + 0.583694i \(0.801607\pi\)
\(282\) 0 0
\(283\) −1.89449e7 + 6.15556e6i −0.0496866 + 0.0161442i −0.333755 0.942660i \(-0.608316\pi\)
0.284068 + 0.958804i \(0.408316\pi\)
\(284\) 1.07076e8 + 1.47378e8i 0.277382 + 0.381784i
\(285\) 0 0
\(286\) 8.22567e7 2.65541e7i 0.207917 0.0671198i
\(287\) 4.33540e8i 1.08254i
\(288\) 0 0
\(289\) 2.86777e8 + 8.82610e8i 0.698880 + 2.15093i
\(290\) 1.91504e8 + 6.22236e7i 0.461090 + 0.149817i
\(291\) 0 0
\(292\) 1.09201e8 1.50303e8i 0.256678 0.353287i
\(293\) −9.51103e7 + 2.92720e8i −0.220898 + 0.679853i 0.777785 + 0.628531i \(0.216343\pi\)
−0.998682 + 0.0513220i \(0.983657\pi\)
\(294\) 0 0
\(295\) 1.06251e8 7.71961e7i 0.240967 0.175073i
\(296\) 4.66401e8 1.04529
\(297\) 0 0
\(298\) −7.85502e8 −1.71945
\(299\) 3.02834e7 2.20022e7i 0.0655172 0.0476010i
\(300\) 0 0
\(301\) 1.14566e8 3.52598e8i 0.242144 0.745242i
\(302\) −5.14883e8 + 7.08676e8i −1.07568 + 1.48055i
\(303\) 0 0
\(304\) 4.44885e8 + 1.44552e8i 0.908217 + 0.295098i
\(305\) −1.60781e7 4.94833e7i −0.0324478 0.0998640i
\(306\) 0 0
\(307\) 5.03613e8i 0.993373i −0.867930 0.496686i \(-0.834550\pi\)
0.867930 0.496686i \(-0.165450\pi\)
\(308\) 453041. 2.38372e8i 0.000883506 0.464865i
\(309\) 0 0
\(310\) 1.61020e8 + 2.21625e8i 0.306983 + 0.422526i
\(311\) 6.15580e7 2.00014e7i 0.116044 0.0377050i −0.250419 0.968137i \(-0.580568\pi\)
0.366463 + 0.930432i \(0.380568\pi\)
\(312\) 0 0
\(313\) 4.98052e8 + 3.61856e8i 0.918057 + 0.667008i 0.943040 0.332680i \(-0.107953\pi\)
−0.0249823 + 0.999688i \(0.507953\pi\)
\(314\) −6.50149e8 4.72361e8i −1.18511 0.861034i
\(315\) 0 0
\(316\) 1.72820e8 5.61526e7i 0.308098 0.100107i
\(317\) 3.07192e8 + 4.22814e8i 0.541630 + 0.745489i 0.988847 0.148936i \(-0.0475849\pi\)
−0.447217 + 0.894425i \(0.647585\pi\)
\(318\) 0 0
\(319\) 2.46458e8 + 7.63454e8i 0.425085 + 1.31679i
\(320\) 4.28868e7i 0.0731643i
\(321\) 0 0
\(322\) −1.03865e8 3.19663e8i −0.173370 0.533577i
\(323\) −7.96756e8 2.58882e8i −1.31558 0.427457i
\(324\) 0 0
\(325\) −6.05266e7 + 8.33077e7i −0.0978035 + 0.134615i
\(326\) −1.62903e8 + 5.01365e8i −0.260417 + 0.801480i
\(327\) 0 0
\(328\) 3.56957e8 2.59345e8i 0.558544 0.405806i
\(329\) 7.83524e8 1.21302
\(330\) 0 0
\(331\) −1.75659e8 −0.266240 −0.133120 0.991100i \(-0.542500\pi\)
−0.133120 + 0.991100i \(0.542500\pi\)
\(332\) 5.11774e7 3.71826e7i 0.0767529 0.0557643i
\(333\) 0 0
\(334\) −1.44969e8 + 4.46168e8i −0.212893 + 0.655217i
\(335\) 6.91725e6 9.52077e6i 0.0100526 0.0138362i
\(336\) 0 0
\(337\) −7.90824e8 2.56954e8i −1.12558 0.365722i −0.313684 0.949528i \(-0.601563\pi\)
−0.811894 + 0.583805i \(0.801563\pi\)
\(338\) 2.54834e8 + 7.84298e8i 0.358962 + 1.10477i
\(339\) 0 0
\(340\) 1.69208e8i 0.233478i
\(341\) −3.39244e8 + 1.03737e9i −0.463311 + 1.41676i
\(342\) 0 0
\(343\) 4.14699e8 + 5.70785e8i 0.554886 + 0.763735i
\(344\) 3.58847e8 1.16596e8i 0.475285 0.154430i
\(345\) 0 0
\(346\) 6.36992e8 + 4.62801e8i 0.826737 + 0.600660i
\(347\) 7.92011e8 + 5.75429e8i 1.01760 + 0.739331i 0.965790 0.259326i \(-0.0835003\pi\)
0.0518120 + 0.998657i \(0.483500\pi\)
\(348\) 0 0
\(349\) −1.17163e9 + 3.80687e8i −1.47538 + 0.479379i −0.932728 0.360581i \(-0.882579\pi\)
−0.542649 + 0.839960i \(0.682579\pi\)
\(350\) 5.43483e8 + 7.48041e8i 0.677561 + 0.932582i
\(351\) 0 0
\(352\) 5.49549e8 3.97677e8i 0.671595 0.485995i
\(353\) 1.84044e8i 0.222695i −0.993782 0.111347i \(-0.964483\pi\)
0.993782 0.111347i \(-0.0355166\pi\)
\(354\) 0 0
\(355\) 8.08803e7 + 2.48924e8i 0.0959497 + 0.295303i
\(356\) −5.76065e8 1.87175e8i −0.676700 0.219873i
\(357\) 0 0
\(358\) 5.85349e8 8.05664e8i 0.674256 0.928033i
\(359\) −2.82686e8 + 8.70017e8i −0.322458 + 0.992424i 0.650117 + 0.759834i \(0.274720\pi\)
−0.972575 + 0.232590i \(0.925280\pi\)
\(360\) 0 0
\(361\) −2.98910e8 + 2.17171e8i −0.334399 + 0.242955i
\(362\) −1.57181e9 −1.74149
\(363\) 0 0
\(364\) −7.77904e7 −0.0845418
\(365\) 2.15950e8 1.56897e8i 0.232450 0.168884i
\(366\) 0 0
\(367\) −3.47305e8 + 1.06890e9i −0.366759 + 1.12877i 0.582114 + 0.813107i \(0.302226\pi\)
−0.948872 + 0.315660i \(0.897774\pi\)
\(368\) 3.11982e8 4.29407e8i 0.326334 0.449161i
\(369\) 0 0
\(370\) −5.07420e8 1.64871e8i −0.520789 0.169214i
\(371\) −4.08553e8 1.25740e9i −0.415374 1.27839i
\(372\) 0 0
\(373\) 7.87433e8i 0.785657i −0.919612 0.392828i \(-0.871497\pi\)
0.919612 0.392828i \(-0.128503\pi\)
\(374\) −1.77827e9 + 1.28683e9i −1.75771 + 1.27195i
\(375\) 0 0
\(376\) 4.68706e8 + 6.45118e8i 0.454719 + 0.625866i
\(377\) 2.48993e8 8.09026e7i 0.239327 0.0777621i
\(378\) 0 0
\(379\) 1.56447e9 + 1.13666e9i 1.47615 + 1.07249i 0.978771 + 0.204955i \(0.0657047\pi\)
0.497380 + 0.867533i \(0.334295\pi\)
\(380\) −8.56884e7 6.22562e7i −0.0801086 0.0582023i
\(381\) 0 0
\(382\) 8.15449e8 2.64955e8i 0.748471 0.243193i
\(383\) 5.60901e8 + 7.72014e8i 0.510141 + 0.702149i 0.983943 0.178482i \(-0.0571187\pi\)
−0.473802 + 0.880632i \(0.657119\pi\)
\(384\) 0 0
\(385\) 1.06453e8 3.25521e8i 0.0950700 0.290714i
\(386\) 1.19331e9i 1.05609i
\(387\) 0 0
\(388\) −9.41696e6 2.89824e7i −0.00818465 0.0251898i
\(389\) 5.21422e8 + 1.69420e8i 0.449124 + 0.145929i 0.524841 0.851200i \(-0.324125\pi\)
−0.0757175 + 0.997129i \(0.524125\pi\)
\(390\) 0 0
\(391\) −5.58738e8 + 7.69036e8i −0.472704 + 0.650621i
\(392\) 2.46092e7 7.57394e7i 0.0206346 0.0635069i
\(393\) 0 0
\(394\) −2.56861e8 + 1.86620e8i −0.211573 + 0.153717i
\(395\) 2.61080e8 0.213150
\(396\) 0 0
\(397\) −2.20403e8 −0.176787 −0.0883935 0.996086i \(-0.528173\pi\)
−0.0883935 + 0.996086i \(0.528173\pi\)
\(398\) 1.63951e9 1.19118e9i 1.30354 0.947077i
\(399\) 0 0
\(400\) −4.51206e8 + 1.38867e9i −0.352505 + 1.08490i
\(401\) 8.55634e7 1.17768e8i 0.0662648 0.0912056i −0.774598 0.632454i \(-0.782048\pi\)
0.840863 + 0.541248i \(0.182048\pi\)
\(402\) 0 0
\(403\) 3.38747e8 + 1.10066e8i 0.257815 + 0.0837691i
\(404\) −1.23050e8 3.78710e8i −0.0928428 0.285741i
\(405\) 0 0
\(406\) 2.35082e9i 1.74333i
\(407\) −6.53027e8 2.02289e9i −0.480121 1.48727i
\(408\) 0 0
\(409\) −4.32334e8 5.95057e8i −0.312455 0.430058i 0.623690 0.781672i \(-0.285633\pi\)
−0.936145 + 0.351614i \(0.885633\pi\)
\(410\) −4.80028e8 + 1.55970e8i −0.343972 + 0.111763i
\(411\) 0 0
\(412\) 3.15997e8 + 2.29585e8i 0.222609 + 0.161735i
\(413\) −1.24046e9 9.01245e8i −0.866476 0.629531i
\(414\) 0 0
\(415\) 8.64397e7 2.80860e7i 0.0593670 0.0192895i
\(416\) −1.30119e8 1.79093e8i −0.0886163 0.121970i
\(417\) 0 0
\(418\) 2.61135e6 1.37399e9i 0.00174883 0.920165i
\(419\) 2.22040e8i 0.147462i −0.997278 0.0737312i \(-0.976509\pi\)
0.997278 0.0737312i \(-0.0234907\pi\)
\(420\) 0 0
\(421\) −1.20100e8 3.69630e8i −0.0784434 0.241424i 0.904143 0.427230i \(-0.140510\pi\)
−0.982586 + 0.185806i \(0.940510\pi\)
\(422\) 1.87712e8 + 6.09913e7i 0.121590 + 0.0395070i
\(423\) 0 0
\(424\) 7.90886e8 1.08856e9i 0.503887 0.693541i
\(425\) 8.08077e8 2.48700e9i 0.510612 1.57150i
\(426\) 0 0
\(427\) −4.91425e8 + 3.57041e8i −0.305464 + 0.221932i
\(428\) 5.56609e7 0.0343160
\(429\) 0 0
\(430\) −4.31622e8 −0.261797
\(431\) −8.53454e7 + 6.20071e7i −0.0513464 + 0.0373053i −0.613162 0.789957i \(-0.710103\pi\)
0.561816 + 0.827262i \(0.310103\pi\)
\(432\) 0 0
\(433\) 9.00005e8 2.76993e9i 0.532767 1.63969i −0.215659 0.976469i \(-0.569190\pi\)
0.748426 0.663219i \(-0.230810\pi\)
\(434\) 1.87987e9 2.58742e9i 1.10386 1.51933i
\(435\) 0 0
\(436\) −4.86702e8 1.58139e8i −0.281229 0.0913770i
\(437\) −1.83871e8 5.65898e8i −0.105397 0.324379i
\(438\) 0 0
\(439\) 7.68123e8i 0.433316i 0.976248 + 0.216658i \(0.0695157\pi\)
−0.976248 + 0.216658i \(0.930484\pi\)
\(440\) 3.31699e8 1.07079e8i 0.185635 0.0599267i
\(441\) 0 0
\(442\) 4.21047e8 + 5.79521e8i 0.231927 + 0.319221i
\(443\) −7.72690e8 + 2.51062e8i −0.422272 + 0.137205i −0.512442 0.858722i \(-0.671259\pi\)
0.0901698 + 0.995926i \(0.471259\pi\)
\(444\) 0 0
\(445\) −7.04059e8 5.11529e8i −0.378747 0.275176i
\(446\) 7.20859e8 + 5.23735e8i 0.384750 + 0.279537i
\(447\) 0 0
\(448\) 4.76187e8 1.54723e8i 0.250210 0.0812982i
\(449\) 8.53615e8 + 1.17490e9i 0.445041 + 0.612546i 0.971323 0.237764i \(-0.0764145\pi\)
−0.526282 + 0.850310i \(0.676415\pi\)
\(450\) 0 0
\(451\) −1.62462e9 1.18508e9i −0.833941 0.608318i
\(452\) 9.03818e8i 0.460359i
\(453\) 0 0
\(454\) 6.50855e8 + 2.00313e9i 0.326429 + 1.00464i
\(455\) −1.06297e8 3.45378e7i −0.0529029 0.0171892i
\(456\) 0 0
\(457\) −7.17862e8 + 9.88053e8i −0.351831 + 0.484254i −0.947850 0.318716i \(-0.896748\pi\)
0.596019 + 0.802970i \(0.296748\pi\)
\(458\) −1.35056e9 + 4.15658e9i −0.656876 + 2.02166i
\(459\) 0 0
\(460\) −9.72282e7 + 7.06404e7i −0.0465736 + 0.0338377i
\(461\) −1.57062e9 −0.746651 −0.373325 0.927701i \(-0.621782\pi\)
−0.373325 + 0.927701i \(0.621782\pi\)
\(462\) 0 0
\(463\) −3.15854e9 −1.47895 −0.739475 0.673184i \(-0.764926\pi\)
−0.739475 + 0.673184i \(0.764926\pi\)
\(464\) 3.00333e9 2.18204e9i 1.39569 1.01403i
\(465\) 0 0
\(466\) 8.87039e8 2.73002e9i 0.406062 1.24973i
\(467\) 2.04073e8 2.80883e8i 0.0927207 0.127619i −0.760136 0.649764i \(-0.774868\pi\)
0.852857 + 0.522145i \(0.174868\pi\)
\(468\) 0 0
\(469\) −1.30668e8 4.24565e7i −0.0584875 0.0190038i
\(470\) −2.81881e8 8.67539e8i −0.125234 0.385431i
\(471\) 0 0
\(472\) 1.56046e9i 0.683056i
\(473\) −1.00814e9 1.39315e9i −0.438033 0.605317i
\(474\) 0 0
\(475\) 9.62126e8 + 1.32425e9i 0.411912 + 0.566948i
\(476\) 1.87878e9 6.10452e8i 0.798456 0.259434i
\(477\) 0 0
\(478\) −2.24853e9 1.63365e9i −0.941674 0.684166i
\(479\) −7.72118e8 5.60977e8i −0.321003 0.233222i 0.415600 0.909547i \(-0.363572\pi\)
−0.736603 + 0.676325i \(0.763572\pi\)
\(480\) 0 0
\(481\) −6.59743e8 + 2.14364e8i −0.270313 + 0.0878301i
\(482\) 3.18179e9 + 4.37935e9i 1.29421 + 1.78133i
\(483\) 0 0
\(484\) −8.92022e8 6.53287e8i −0.357616 0.261906i
\(485\) 4.37840e7i 0.0174269i
\(486\) 0 0
\(487\) 2.14210e8 + 6.59271e8i 0.0840405 + 0.258650i 0.984243 0.176822i \(-0.0565816\pi\)
−0.900202 + 0.435472i \(0.856582\pi\)
\(488\) −5.87943e8 1.91034e8i −0.229016 0.0744118i
\(489\) 0 0
\(490\) −5.35471e7 + 7.37012e7i −0.0205613 + 0.0283001i
\(491\) −1.45884e9 + 4.48986e9i −0.556190 + 1.71178i 0.136589 + 0.990628i \(0.456386\pi\)
−0.692779 + 0.721150i \(0.743614\pi\)
\(492\) 0 0
\(493\) −5.37874e9 + 3.90788e9i −2.02170 + 1.46885i
\(494\) −4.48388e8 −0.167344
\(495\) 0 0
\(496\) 5.05049e9 1.85844
\(497\) 2.47210e9 1.79608e9i 0.903272 0.656265i
\(498\) 0 0
\(499\) −8.52220e8 + 2.62286e9i −0.307043 + 0.944982i 0.671864 + 0.740675i \(0.265494\pi\)
−0.978907 + 0.204307i \(0.934506\pi\)
\(500\) 4.06721e8 5.59804e8i 0.145513 0.200282i
\(501\) 0 0
\(502\) −5.70265e9 1.85290e9i −2.01194 0.653717i
\(503\) −2.34566e8 7.21921e8i −0.0821821 0.252931i 0.901520 0.432738i \(-0.142453\pi\)
−0.983702 + 0.179807i \(0.942453\pi\)
\(504\) 0 0
\(505\) 5.72120e8i 0.197682i
\(506\) −1.48180e9 4.84583e8i −0.508468 0.166280i
\(507\) 0 0
\(508\) 1.10053e9 + 1.51474e9i 0.372458 + 0.512644i
\(509\) 1.47407e9 4.78956e8i 0.495458 0.160984i −0.0506206 0.998718i \(-0.516120\pi\)
0.546079 + 0.837734i \(0.316120\pi\)
\(510\) 0 0
\(511\) −2.52116e9 1.83173e9i −0.835849 0.607280i
\(512\) −4.90606e8 3.56446e8i −0.161543 0.117368i
\(513\) 0 0
\(514\) 1.05387e9 3.42422e8i 0.342306 0.111222i
\(515\) 3.29861e8 + 4.54014e8i 0.106416 + 0.146468i
\(516\) 0 0
\(517\) 2.14176e9 2.93614e9i 0.681640 0.934457i
\(518\) 6.22886e9i 1.96904i
\(519\) 0 0
\(520\) −3.51499e7 1.08180e8i −0.0109626 0.0337393i
\(521\) 2.23060e9 + 7.24764e8i 0.691017 + 0.224525i 0.633412 0.773814i \(-0.281654\pi\)
0.0576047 + 0.998339i \(0.481654\pi\)
\(522\) 0 0
\(523\) 1.74729e9 2.40494e9i 0.534083 0.735102i −0.453663 0.891173i \(-0.649883\pi\)
0.987746 + 0.156071i \(0.0498829\pi\)
\(524\) 6.54315e7 2.01378e8i 0.0198668 0.0611437i
\(525\) 0 0
\(526\) −2.81187e9 + 2.04294e9i −0.842451 + 0.612076i
\(527\) −9.04506e9 −2.69200
\(528\) 0 0
\(529\) 2.72967e9 0.801707
\(530\) −1.24524e9 + 9.04722e8i −0.363319 + 0.263967i
\(531\) 0 0
\(532\) −3.82115e8 + 1.17603e9i −0.110028 + 0.338631i
\(533\) −3.85732e8 + 5.30915e8i −0.110342 + 0.151873i
\(534\) 0 0
\(535\) 7.60576e7 + 2.47126e7i 0.0214736 + 0.00697719i
\(536\) −4.32089e7 1.32983e8i −0.0121198 0.0373010i
\(537\) 0 0
\(538\) 7.22370e9i 1.99996i
\(539\) −3.62955e8 689820.i −0.0998372 0.000189747i
\(540\) 0 0
\(541\) −1.44674e8 1.99127e8i −0.0392827 0.0540680i 0.788924 0.614491i \(-0.210639\pi\)
−0.828207 + 0.560423i \(0.810639\pi\)
\(542\) 6.78404e9 2.20427e9i 1.83017 0.594658i
\(543\) 0 0
\(544\) 4.54801e9 + 3.30433e9i 1.21123 + 0.880008i
\(545\) −5.94841e8 4.32177e8i −0.157403 0.114360i
\(546\) 0 0
\(547\) 6.65514e9 2.16239e9i 1.73861 0.564908i 0.743958 0.668226i \(-0.232946\pi\)
0.994648 + 0.103318i \(0.0329460\pi\)
\(548\) 1.15281e9 + 1.58671e9i 0.299244 + 0.411874i
\(549\) 0 0
\(550\) 4.28878e9 + 8.15111e6i 1.09917 + 0.00208904i
\(551\) 4.16165e9i 1.05983i
\(552\) 0 0
\(553\) −9.41899e8 2.89887e9i −0.236846 0.728937i
\(554\) 2.84133e9 + 9.23206e8i 0.709967 + 0.230682i
\(555\) 0 0
\(556\) 7.41059e8 1.01998e9i 0.182848 0.251669i
\(557\) −1.09907e9 + 3.38260e9i −0.269485 + 0.829388i 0.721142 + 0.692788i \(0.243618\pi\)
−0.990626 + 0.136601i \(0.956382\pi\)
\(558\) 0 0
\(559\) −4.54014e8 + 3.29860e8i −0.109933 + 0.0798710i
\(560\) −1.58481e9 −0.381346
\(561\) 0 0
\(562\) 3.17287e9 0.754008
\(563\) −3.69987e9 + 2.68811e9i −0.873789 + 0.634845i −0.931601 0.363482i \(-0.881588\pi\)
0.0578118 + 0.998327i \(0.481588\pi\)
\(564\) 0 0
\(565\) 4.01282e8 1.23502e9i 0.0936009 0.288074i
\(566\) 1.59141e8 2.19039e8i 0.0368914 0.0507766i
\(567\) 0 0
\(568\) 2.95763e9 + 9.60992e8i 0.677212 + 0.220039i
\(569\) −1.85685e8 5.71480e8i −0.0422556 0.130049i 0.927703 0.373319i \(-0.121780\pi\)
−0.969959 + 0.243269i \(0.921780\pi\)
\(570\) 0 0
\(571\) 3.83669e9i 0.862444i 0.902246 + 0.431222i \(0.141917\pi\)
−0.902246 + 0.431222i \(0.858083\pi\)
\(572\) −2.12640e8 + 2.91508e8i −0.0475072 + 0.0651274i
\(573\) 0 0
\(574\) 3.46359e9 + 4.76722e9i 0.764424 + 1.05214i
\(575\) 1.76640e9 5.73939e8i 0.387483 0.125901i
\(576\) 0 0
\(577\) 1.60961e9 + 1.16945e9i 0.348824 + 0.253435i 0.748375 0.663275i \(-0.230834\pi\)
−0.399552 + 0.916711i \(0.630834\pi\)
\(578\) −1.02047e10 7.41411e9i −2.19812 1.59703i
\(579\) 0 0
\(580\) −7.99419e8 + 2.59747e8i −0.170128 + 0.0552780i
\(581\) −6.23696e8 8.58444e8i −0.131934 0.181592i
\(582\) 0 0
\(583\) −5.82868e9 1.90611e9i −1.21823 0.398389i
\(584\) 3.17156e9i 0.658912i
\(585\) 0 0
\(586\) −1.29272e9 3.97859e9i −0.265377 0.816748i
\(587\) 7.92439e8 + 2.57479e8i 0.161708 + 0.0525422i 0.388752 0.921342i \(-0.372906\pi\)
−0.227044 + 0.973884i \(0.572906\pi\)
\(588\) 0 0
\(589\) 3.32792e9 4.58049e9i 0.671073 0.923653i
\(590\) −5.51616e8 + 1.69770e9i −0.110574 + 0.340313i
\(591\) 0 0
\(592\) −7.95776e9 + 5.78165e9i −1.57640 + 1.14532i
\(593\) −7.87395e9 −1.55061 −0.775303 0.631590i \(-0.782403\pi\)
−0.775303 + 0.631590i \(0.782403\pi\)
\(594\) 0 0
\(595\) 2.83828e9 0.552390
\(596\) 2.65278e9 1.92735e9i 0.513261 0.372906i
\(597\) 0 0
\(598\) −1.57220e8 + 4.83872e8i −0.0300644 + 0.0925288i
\(599\) 5.29380e9 7.28628e9i 1.00641 1.38520i 0.0850950 0.996373i \(-0.472881\pi\)
0.921311 0.388826i \(-0.127119\pi\)
\(600\) 0 0
\(601\) 3.88434e9 + 1.26210e9i 0.729889 + 0.237155i 0.650305 0.759673i \(-0.274641\pi\)
0.0795837 + 0.996828i \(0.474641\pi\)
\(602\) 1.55716e9 + 4.79245e9i 0.290902 + 0.895303i
\(603\) 0 0
\(604\) 3.65667e9i 0.675237i
\(605\) −9.28851e8 1.28873e9i −0.170531 0.236601i
\(606\) 0 0
\(607\) 4.12073e9 + 5.67170e9i 0.747849 + 1.02933i 0.998128 + 0.0611525i \(0.0194776\pi\)
−0.250279 + 0.968174i \(0.580522\pi\)
\(608\) −3.34667e9 + 1.08740e9i −0.603880 + 0.196213i
\(609\) 0 0
\(610\) 5.72121e8 + 4.15670e8i 0.102055 + 0.0741472i
\(611\) −9.59507e8 6.97122e8i −0.170178 0.123642i
\(612\) 0 0
\(613\) 5.63558e9 1.83111e9i 0.988160 0.321073i 0.230035 0.973182i \(-0.426116\pi\)
0.758125 + 0.652110i \(0.226116\pi\)
\(614\) 4.02340e9 + 5.53774e9i 0.701462 + 0.965479i
\(615\) 0 0
\(616\) −2.38561e9 3.29666e9i −0.411212 0.568253i
\(617\) 9.74311e9i 1.66994i 0.550299 + 0.834968i \(0.314514\pi\)
−0.550299 + 0.834968i \(0.685486\pi\)
\(618\) 0 0
\(619\) 2.52204e9 + 7.76206e9i 0.427401 + 1.31541i 0.900676 + 0.434491i \(0.143072\pi\)
−0.473275 + 0.880915i \(0.656928\pi\)
\(620\) −1.08759e9 3.53378e8i −0.183270 0.0595482i
\(621\) 0 0
\(622\) −5.17100e8 + 7.11727e8i −0.0861605 + 0.118590i
\(623\) −3.13965e9 + 9.66285e9i −0.520203 + 1.60102i
\(624\) 0 0
\(625\) −3.71352e9 + 2.69803e9i −0.608423 + 0.442046i
\(626\) −8.36749e9 −1.36328
\(627\) 0 0
\(628\) 3.35468e9 0.540496
\(629\) 1.42518e10 1.03545e10i 2.28345 1.65902i
\(630\) 0 0
\(631\) 6.16236e8 1.89658e9i 0.0976436 0.300516i −0.890290 0.455394i \(-0.849498\pi\)
0.987934 + 0.154878i \(0.0494984\pi\)
\(632\) 1.82335e9 2.50962e9i 0.287316 0.395457i
\(633\) 0 0
\(634\) −6.75578e9 2.19509e9i −1.05284 0.342089i
\(635\) 8.31285e8 + 2.55843e9i 0.128837 + 0.396521i
\(636\) 0 0
\(637\) 1.18447e8i 0.0181567i
\(638\) −8.80935e9 6.42598e9i −1.34299 0.979642i
\(639\) 0 0
\(640\) −1.28509e9 1.76877e9i −0.193778 0.266712i
\(641\) 3.46870e9 1.12705e9i 0.520192 0.169021i −0.0371402 0.999310i \(-0.511825\pi\)
0.557333 + 0.830289i \(0.311825\pi\)
\(642\) 0 0
\(643\) −2.18782e9 1.58954e9i −0.324544 0.235795i 0.413568 0.910473i \(-0.364282\pi\)
−0.738112 + 0.674678i \(0.764282\pi\)
\(644\) 1.13511e9 + 8.24709e8i 0.167471 + 0.121675i
\(645\) 0 0
\(646\) 1.08294e10 3.51868e9i 1.58048 0.513530i
\(647\) −1.49552e9 2.05841e9i −0.217084 0.298791i 0.686561 0.727072i \(-0.259119\pi\)
−0.903646 + 0.428281i \(0.859119\pi\)
\(648\) 0 0
\(649\) −6.76807e9 + 2.18487e9i −0.971870 + 0.313739i
\(650\) 1.39961e9i 0.199898i
\(651\) 0 0
\(652\) −6.80026e8 2.09291e9i −0.0960858 0.295722i
\(653\) 5.13384e9 + 1.66809e9i 0.721517 + 0.234435i 0.646681 0.762761i \(-0.276157\pi\)
0.0748361 + 0.997196i \(0.476157\pi\)
\(654\) 0 0
\(655\) 1.78817e8 2.46121e8i 0.0248637 0.0342219i
\(656\) −2.87551e9 + 8.84990e9i −0.397696 + 1.22398i
\(657\) 0 0
\(658\) −8.61565e9 + 6.25963e9i −1.17896 + 0.856561i
\(659\) 8.25592e9 1.12374 0.561871 0.827225i \(-0.310082\pi\)
0.561871 + 0.827225i \(0.310082\pi\)
\(660\) 0 0
\(661\) −1.59869e9 −0.215308 −0.107654 0.994188i \(-0.534334\pi\)
−0.107654 + 0.994188i \(0.534334\pi\)
\(662\) 1.93155e9 1.40335e9i 0.258764 0.188003i
\(663\) 0 0
\(664\) 3.33708e8 1.02705e9i 0.0442362 0.136145i
\(665\) −1.04428e9 + 1.43733e9i −0.137702 + 0.189531i
\(666\) 0 0
\(667\) −4.49099e9 1.45921e9i −0.586006 0.190405i
\(668\) −6.05159e8 1.86249e9i −0.0785510 0.241755i
\(669\) 0 0
\(670\) 1.59953e8i 0.0205462i
\(671\) −5.35487e6 + 2.81751e9i −0.000684258 + 0.360029i
\(672\) 0 0
\(673\) −6.58584e9 9.06463e9i −0.832834 1.14630i −0.987389 0.158313i \(-0.949394\pi\)
0.154555 0.987984i \(-0.450606\pi\)
\(674\) 1.07488e10 3.49248e9i 1.35222 0.439364i
\(675\) 0 0
\(676\) −2.78502e9 2.02343e9i −0.346748 0.251927i
\(677\) 4.44437e9 + 3.22902e9i 0.550490 + 0.399954i 0.827966 0.560778i \(-0.189498\pi\)
−0.277476 + 0.960733i \(0.589498\pi\)
\(678\) 0 0
\(679\) −4.86148e8 + 1.57959e8i −0.0595970 + 0.0193642i
\(680\) 1.69786e9 + 2.33691e9i 0.207072 + 0.285011i
\(681\) 0 0
\(682\) −4.55732e9 1.41172e10i −0.550129 1.70414i
\(683\) 1.15384e10i 1.38571i 0.721077 + 0.692855i \(0.243648\pi\)
−0.721077 + 0.692855i \(0.756352\pi\)
\(684\) 0 0
\(685\) 8.70778e8 + 2.67998e9i 0.103512 + 0.318577i
\(686\) −9.12009e9 2.96330e9i −1.07861 0.350462i
\(687\) 0 0
\(688\) −4.67730e9 + 6.43775e9i −0.547565 + 0.753658i
\(689\) −6.18424e8 + 1.90331e9i −0.0720309 + 0.221688i
\(690\) 0 0
\(691\) −4.22081e9 + 3.06660e9i −0.486656 + 0.353577i −0.803897 0.594769i \(-0.797244\pi\)
0.317241 + 0.948345i \(0.397244\pi\)
\(692\) −3.28679e9 −0.377051
\(693\) 0 0
\(694\) −1.33061e10 −1.51110
\(695\) 1.46547e9 1.06473e9i 0.165589 0.120307i
\(696\) 0 0
\(697\) 5.14982e9 1.58495e10i 0.576073 1.77297i
\(698\) 9.84198e9 1.35463e10i 1.09544 1.50774i
\(699\) 0 0
\(700\) −3.67087e9 1.19274e9i −0.404507 0.131432i
\(701\) 1.91991e9 + 5.90889e9i 0.210508 + 0.647877i 0.999442 + 0.0333992i \(0.0106333\pi\)
−0.788934 + 0.614478i \(0.789367\pi\)
\(702\) 0 0
\(703\) 1.10269e10i 1.19705i
\(704\) 7.21860e8 2.20737e9i 0.0779738 0.238436i
\(705\) 0 0
\(706\) 1.47034e9 + 2.02375e9i 0.157254 + 0.216442i
\(707\) −6.35245e9 + 2.06403e9i −0.676041 + 0.219659i
\(708\) 0 0
\(709\) −5.10956e9 3.71231e9i −0.538421 0.391185i 0.285078 0.958504i \(-0.407981\pi\)
−0.823498 + 0.567319i \(0.807981\pi\)
\(710\) −2.87804e9 2.09102e9i −0.301781 0.219257i
\(711\) 0 0
\(712\) −9.83409e9 + 3.19529e9i −1.02107 + 0.331765i
\(713\) −3.77610e9 5.19736e9i −0.390149 0.536994i
\(714\) 0 0
\(715\) −4.19987e8 + 3.03921e8i −0.0429699 + 0.0310949i
\(716\) 4.15711e9i 0.423249i
\(717\) 0 0
\(718\) −3.84222e9 1.18251e10i −0.387388 1.19226i
\(719\) 1.84505e9 + 5.99492e8i 0.185121 + 0.0601496i 0.400111 0.916467i \(-0.368972\pi\)
−0.214989 + 0.976616i \(0.568972\pi\)
\(720\) 0 0
\(721\) 3.85104e9 5.30050e9i 0.382653 0.526676i
\(722\) 1.55183e9 4.77603e9i 0.153448 0.472266i
\(723\) 0 0
\(724\) 5.30829e9 3.85670e9i 0.519840 0.377686i
\(725\) 1.29902e10 1.26600
\(726\) 0 0
\(727\) 1.44854e10 1.39817 0.699085 0.715039i \(-0.253591\pi\)
0.699085 + 0.715039i \(0.253591\pi\)
\(728\) −1.07435e9 + 7.80563e8i −0.103202 + 0.0749805i
\(729\) 0 0
\(730\) −1.12113e9 + 3.45049e9i −0.106666 + 0.328285i
\(731\) 8.37670e9 1.15295e10i 0.793162 1.09169i
\(732\) 0 0
\(733\) −1.78243e9 5.79147e8i −0.167166 0.0543156i 0.224238 0.974534i \(-0.428011\pi\)
−0.391404 + 0.920219i \(0.628011\pi\)
\(734\) −4.72052e9 1.45283e10i −0.440609 1.35606i
\(735\) 0 0
\(736\) 3.99280e9i 0.369152i
\(737\) −5.16280e8 + 3.73602e8i −0.0475061 + 0.0343774i
\(738\) 0 0
\(739\) 1.19120e10 + 1.63954e10i 1.08575 + 1.49440i 0.853033 + 0.521857i \(0.174761\pi\)
0.232714 + 0.972545i \(0.425239\pi\)
\(740\) 2.11818e9 6.88238e8i 0.192155 0.0624350i
\(741\) 0 0
\(742\) 1.45379e10 + 1.05624e10i 1.30644 + 0.949181i
\(743\) −7.80489e9 5.67059e9i −0.698081 0.507186i 0.181225 0.983442i \(-0.441994\pi\)
−0.879307 + 0.476256i \(0.841994\pi\)
\(744\) 0 0
\(745\) 4.48059e9 1.45583e9i 0.396998 0.128993i
\(746\) 6.29087e9 + 8.65864e9i 0.554785 + 0.763596i
\(747\) 0 0
\(748\) 2.84807e9 8.70910e9i 0.248825 0.760882i
\(749\) 9.33650e8i 0.0811891i
\(750\) 0 0
\(751\) −2.98733e9 9.19404e9i −0.257361 0.792076i −0.993355 0.115088i \(-0.963285\pi\)
0.735994 0.676988i \(-0.236715\pi\)
\(752\) −1.59942e10 5.19682e9i −1.37151 0.445631i
\(753\) 0 0
\(754\) −2.09159e9 + 2.87883e9i −0.177696 + 0.244577i
\(755\) 1.62351e9 4.99664e9i 0.137290 0.422536i
\(756\) 0 0
\(757\) −4.17835e9 + 3.03575e9i −0.350081 + 0.254349i −0.748903 0.662679i \(-0.769419\pi\)
0.398822 + 0.917028i \(0.369419\pi\)
\(758\) −2.62838e10 −2.19203
\(759\) 0 0
\(760\) −1.80812e9 −0.149410
\(761\) 1.02486e10 7.44603e9i 0.842981 0.612461i −0.0802211 0.996777i \(-0.525563\pi\)
0.923202 + 0.384316i \(0.125563\pi\)
\(762\) 0 0
\(763\) −2.65261e9 + 8.16389e9i −0.216191 + 0.665367i
\(764\) −2.10380e9 + 2.89563e9i −0.170678 + 0.234918i
\(765\) 0 0
\(766\) −1.23354e10 4.00800e9i −0.991634 0.322201i
\(767\) 7.17207e8 + 2.20734e9i 0.0573932 + 0.176638i
\(768\) 0 0
\(769\) 1.70413e10i 1.35133i −0.737209 0.675664i \(-0.763857\pi\)
0.737209 0.675664i \(-0.236143\pi\)
\(770\) 1.43006e9 + 4.42989e9i 0.112885 + 0.349684i
\(771\) 0 0
\(772\) −2.92799e9 4.03003e9i −0.229038 0.315244i
\(773\) 1.15213e10 3.74349e9i 0.897166 0.291507i 0.176099 0.984372i \(-0.443652\pi\)
0.721067