Properties

Label 99.8.j.a.8.20
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 8.20
Character \(\chi\) \(=\) 99.8
Dual form 99.8.j.a.62.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(7.62018 - 5.53639i) q^{2} +(-12.1386 + 37.3586i) q^{4} +(208.552 - 287.047i) q^{5} +(-1358.87 - 441.525i) q^{7} +(486.897 + 1498.52i) q^{8} +O(q^{10})\) \(q+(7.62018 - 5.53639i) q^{2} +(-12.1386 + 37.3586i) q^{4} +(208.552 - 287.047i) q^{5} +(-1358.87 - 441.525i) q^{7} +(486.897 + 1498.52i) q^{8} -3341.97i q^{10} +(-1862.20 + 4002.42i) q^{11} +(617.277 + 849.609i) q^{13} +(-12799.3 + 4158.75i) q^{14} +(7938.88 + 5767.93i) q^{16} +(6748.26 + 4902.90i) q^{17} +(-24116.4 + 7835.88i) q^{19} +(8192.16 + 11275.5i) q^{20} +(7968.65 + 40809.1i) q^{22} -9951.54i q^{23} +(-14760.1 - 45427.0i) q^{25} +(9407.53 + 3056.69i) q^{26} +(32989.5 - 45406.2i) q^{28} +(-35993.4 + 110776. i) q^{29} +(-224599. + 163181. i) q^{31} -109252. q^{32} +78567.4 q^{34} +(-410134. + 297980. i) q^{35} +(-91703.1 + 282233. i) q^{37} +(-140389. + 193228. i) q^{38} +(531688. + 172756. i) q^{40} +(-2950.31 - 9080.11i) q^{41} +299983. i q^{43} +(-126921. - 118153. i) q^{44} +(-55095.6 - 75832.6i) q^{46} +(745002. - 242066. i) q^{47} +(985335. + 715888. i) q^{49} +(-363977. - 264444. i) q^{50} +(-39233.1 + 12747.6i) q^{52} +(34907.1 + 48045.6i) q^{53} +(760518. + 1.36925e6i) q^{55} -2.25127e6i q^{56} +(339024. + 1.04341e6i) q^{58} +(-2.43396e6 - 790842. i) q^{59} +(527255. - 725705. i) q^{61} +(-808054. + 2.48693e6i) q^{62} +(-1.84869e6 + 1.34316e6i) q^{64} +372612. q^{65} +4.31366e6 q^{67} +(-265080. + 192592. i) q^{68} +(-1.47557e6 + 4.54132e6i) q^{70} +(-3.21492e6 + 4.42496e6i) q^{71} +(-981628. - 318950. i) q^{73} +(863758. + 2.65837e6i) q^{74} -996071. i q^{76} +(4.29767e6 - 4.61658e6i) q^{77} +(-4.56320e6 - 6.28071e6i) q^{79} +(3.31134e6 - 1.07592e6i) q^{80} +(-72752.9 - 52858.1i) q^{82} +(-6.22978e6 - 4.52620e6i) q^{83} +(2.81473e6 - 914560. i) q^{85} +(1.66082e6 + 2.28592e6i) q^{86} +(-6.90439e6 - 841768. i) q^{88} +3.43387e6i q^{89} +(-463678. - 1.42706e6i) q^{91} +(371776. + 120797. i) q^{92} +(4.33688e6 - 5.96920e6i) q^{94} +(-2.78025e6 + 8.55672e6i) q^{95} +(189559. - 137723. i) q^{97} +1.14719e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 112 q - 1792 q^{4}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.62018 5.53639i 0.673536 0.489352i −0.197671 0.980268i \(-0.563338\pi\)
0.871207 + 0.490916i \(0.163338\pi\)
\(3\) 0 0
\(4\) −12.1386 + 37.3586i −0.0948325 + 0.291864i
\(5\) 208.552 287.047i 0.746138 1.02697i −0.252104 0.967700i \(-0.581123\pi\)
0.998242 0.0592702i \(-0.0188774\pi\)
\(6\) 0 0
\(7\) −1358.87 441.525i −1.49739 0.486533i −0.558138 0.829748i \(-0.688484\pi\)
−0.939257 + 0.343215i \(0.888484\pi\)
\(8\) 486.897 + 1498.52i 0.336219 + 1.03478i
\(9\) 0 0
\(10\) 3341.97i 1.05683i
\(11\) −1862.20 + 4002.42i −0.421844 + 0.906668i
\(12\) 0 0
\(13\) 617.277 + 849.609i 0.0779253 + 0.107255i 0.846200 0.532865i \(-0.178885\pi\)
−0.768275 + 0.640120i \(0.778885\pi\)
\(14\) −12799.3 + 4158.75i −1.24663 + 0.405056i
\(15\) 0 0
\(16\) 7938.88 + 5767.93i 0.484551 + 0.352047i
\(17\) 6748.26 + 4902.90i 0.333135 + 0.242037i 0.741760 0.670666i \(-0.233991\pi\)
−0.408624 + 0.912703i \(0.633991\pi\)
\(18\) 0 0
\(19\) −24116.4 + 7835.88i −0.806630 + 0.262090i −0.683170 0.730260i \(-0.739399\pi\)
−0.123460 + 0.992350i \(0.539399\pi\)
\(20\) 8192.16 + 11275.5i 0.228978 + 0.315161i
\(21\) 0 0
\(22\) 7968.65 + 40809.1i 0.159553 + 0.817104i
\(23\) 9951.54i 0.170547i −0.996358 0.0852733i \(-0.972824\pi\)
0.996358 0.0852733i \(-0.0271763\pi\)
\(24\) 0 0
\(25\) −14760.1 45427.0i −0.188930 0.581466i
\(26\) 9407.53 + 3056.69i 0.104971 + 0.0341071i
\(27\) 0 0
\(28\) 32989.5 45406.2i 0.284003 0.390897i
\(29\) −35993.4 + 110776.i −0.274050 + 0.843439i 0.715419 + 0.698696i \(0.246236\pi\)
−0.989469 + 0.144744i \(0.953764\pi\)
\(30\) 0 0
\(31\) −224599. + 163181.i −1.35407 + 0.983791i −0.355275 + 0.934762i \(0.615613\pi\)
−0.998797 + 0.0490292i \(0.984387\pi\)
\(32\) −109252. −0.589391
\(33\) 0 0
\(34\) 78567.4 0.342820
\(35\) −410134. + 297980.i −1.61692 + 1.17476i
\(36\) 0 0
\(37\) −91703.1 + 282233.i −0.297631 + 0.916014i 0.684694 + 0.728831i \(0.259936\pi\)
−0.982325 + 0.187183i \(0.940064\pi\)
\(38\) −140389. + 193228.i −0.415040 + 0.571253i
\(39\) 0 0
\(40\) 531688. + 172756.i 1.31355 + 0.426798i
\(41\) −2950.31 9080.11i −0.00668534 0.0205754i 0.947658 0.319287i \(-0.103443\pi\)
−0.954344 + 0.298711i \(0.903443\pi\)
\(42\) 0 0
\(43\) 299983.i 0.575383i 0.957723 + 0.287691i \(0.0928877\pi\)
−0.957723 + 0.287691i \(0.907112\pi\)
\(44\) −126921. 118153.i −0.224620 0.209103i
\(45\) 0 0
\(46\) −55095.6 75832.6i −0.0834573 0.114869i
\(47\) 745002. 242066.i 1.04668 0.340088i 0.265317 0.964161i \(-0.414524\pi\)
0.781365 + 0.624074i \(0.214524\pi\)
\(48\) 0 0
\(49\) 985335. + 715888.i 1.19646 + 0.869278i
\(50\) −363977. 264444.i −0.411792 0.299185i
\(51\) 0 0
\(52\) −39233.1 + 12747.6i −0.0386937 + 0.0125724i
\(53\) 34907.1 + 48045.6i 0.0322069 + 0.0443290i 0.824817 0.565400i \(-0.191278\pi\)
−0.792610 + 0.609729i \(0.791278\pi\)
\(54\) 0 0
\(55\) 760518. + 1.36925e6i 0.616368 + 1.10972i
\(56\) 2.25127e6i 1.71305i
\(57\) 0 0
\(58\) 339024. + 1.04341e6i 0.228156 + 0.702193i
\(59\) −2.43396e6 790842.i −1.54288 0.501311i −0.590709 0.806885i \(-0.701152\pi\)
−0.952168 + 0.305573i \(0.901152\pi\)
\(60\) 0 0
\(61\) 527255. 725705.i 0.297418 0.409360i −0.633988 0.773343i \(-0.718583\pi\)
0.931406 + 0.363983i \(0.118583\pi\)
\(62\) −808054. + 2.48693e6i −0.430595 + 1.32524i
\(63\) 0 0
\(64\) −1.84869e6 + 1.34316e6i −0.881526 + 0.640466i
\(65\) 372612. 0.168291
\(66\) 0 0
\(67\) 4.31366e6 1.75220 0.876102 0.482126i \(-0.160135\pi\)
0.876102 + 0.482126i \(0.160135\pi\)
\(68\) −265080. + 192592.i −0.102234 + 0.0742774i
\(69\) 0 0
\(70\) −1.47557e6 + 4.54132e6i −0.514180 + 1.58248i
\(71\) −3.21492e6 + 4.42496e6i −1.06602 + 1.46725i −0.191984 + 0.981398i \(0.561492\pi\)
−0.874039 + 0.485856i \(0.838508\pi\)
\(72\) 0 0
\(73\) −981628. 318950.i −0.295336 0.0959606i 0.157601 0.987503i \(-0.449624\pi\)
−0.452938 + 0.891542i \(0.649624\pi\)
\(74\) 863758. + 2.65837e6i 0.247788 + 0.762614i
\(75\) 0 0
\(76\) 996071.i 0.260281i
\(77\) 4.29767e6 4.61658e6i 1.07279 1.15240i
\(78\) 0 0
\(79\) −4.56320e6 6.28071e6i −1.04130 1.43322i −0.896116 0.443819i \(-0.853623\pi\)
−0.145182 0.989405i \(-0.546377\pi\)
\(80\) 3.31134e6 1.07592e6i 0.723083 0.234944i
\(81\) 0 0
\(82\) −72752.9 52858.1i −0.0145714 0.0105868i
\(83\) −6.22978e6 4.52620e6i −1.19591 0.868881i −0.202036 0.979378i \(-0.564756\pi\)
−0.993876 + 0.110497i \(0.964756\pi\)
\(84\) 0 0
\(85\) 2.81473e6 914560.i 0.497130 0.161527i
\(86\) 1.66082e6 + 2.28592e6i 0.281565 + 0.387541i
\(87\) 0 0
\(88\) −6.90439e6 841768.i −1.08003 0.131675i
\(89\) 3.43387e6i 0.516320i 0.966102 + 0.258160i \(0.0831162\pi\)
−0.966102 + 0.258160i \(0.916884\pi\)
\(90\) 0 0
\(91\) −463678. 1.42706e6i −0.0645018 0.198516i
\(92\) 371776. + 120797.i 0.0497764 + 0.0161733i
\(93\) 0 0
\(94\) 4.33688e6 5.96920e6i 0.538555 0.741257i
\(95\) −2.78025e6 + 8.55672e6i −0.332698 + 1.02394i
\(96\) 0 0
\(97\) 189559. 137723.i 0.0210884 0.0153216i −0.577191 0.816609i \(-0.695851\pi\)
0.598280 + 0.801287i \(0.295851\pi\)
\(98\) 1.14719e7 1.23124
\(99\) 0 0
\(100\) 1.87626e6 0.187626
\(101\) 3.78082e6 2.74692e6i 0.365141 0.265291i −0.390052 0.920793i \(-0.627543\pi\)
0.755193 + 0.655502i \(0.227543\pi\)
\(102\) 0 0
\(103\) −3.10532e6 + 9.55720e6i −0.280012 + 0.861788i 0.707838 + 0.706375i \(0.249671\pi\)
−0.987850 + 0.155413i \(0.950329\pi\)
\(104\) −972602. + 1.33867e6i −0.0847849 + 0.116696i
\(105\) 0 0
\(106\) 531998. + 172857.i 0.0433850 + 0.0140966i
\(107\) −4.03531e6 1.24194e7i −0.318445 0.980072i −0.974313 0.225197i \(-0.927697\pi\)
0.655868 0.754875i \(-0.272303\pi\)
\(108\) 0 0
\(109\) 2.17651e7i 1.60978i −0.593421 0.804892i \(-0.702223\pi\)
0.593421 0.804892i \(-0.297777\pi\)
\(110\) 1.33760e7 + 6.22342e6i 0.958190 + 0.445815i
\(111\) 0 0
\(112\) −8.24126e6 1.13431e7i −0.554281 0.762903i
\(113\) 7.07932e6 2.30021e6i 0.461548 0.149966i −0.0690077 0.997616i \(-0.521983\pi\)
0.530556 + 0.847650i \(0.321983\pi\)
\(114\) 0 0
\(115\) −2.85656e6 2.07541e6i −0.175146 0.127251i
\(116\) −3.70154e6 2.68933e6i −0.220181 0.159971i
\(117\) 0 0
\(118\) −2.29256e7 + 7.44899e6i −1.28450 + 0.417360i
\(119\) −7.00529e6 9.64196e6i −0.381076 0.524506i
\(120\) 0 0
\(121\) −1.25516e7 1.49066e7i −0.644095 0.764945i
\(122\) 8.44910e6i 0.421261i
\(123\) 0 0
\(124\) −3.36990e6 1.03715e7i −0.158723 0.488501i
\(125\) 1.02449e7 + 3.32876e6i 0.469160 + 0.152439i
\(126\) 0 0
\(127\) 1.90374e7 2.62027e7i 0.824696 1.13510i −0.164191 0.986429i \(-0.552501\pi\)
0.988887 0.148668i \(-0.0474987\pi\)
\(128\) −2.32981e6 + 7.17040e6i −0.0981940 + 0.302210i
\(129\) 0 0
\(130\) 2.83937e6 2.06292e6i 0.113350 0.0823534i
\(131\) −7.11909e6 −0.276678 −0.138339 0.990385i \(-0.544176\pi\)
−0.138339 + 0.990385i \(0.544176\pi\)
\(132\) 0 0
\(133\) 3.62309e7 1.33536
\(134\) 3.28709e7 2.38821e7i 1.18017 0.857445i
\(135\) 0 0
\(136\) −4.06136e6 + 1.24996e7i −0.138448 + 0.426098i
\(137\) 1.95722e7 2.69389e7i 0.650307 0.895071i −0.348805 0.937195i \(-0.613412\pi\)
0.999112 + 0.0421239i \(0.0134124\pi\)
\(138\) 0 0
\(139\) 4.69607e7 + 1.52585e7i 1.48314 + 0.481903i 0.935050 0.354515i \(-0.115354\pi\)
0.548093 + 0.836417i \(0.315354\pi\)
\(140\) −6.15368e6 1.89391e7i −0.189534 0.583326i
\(141\) 0 0
\(142\) 5.15181e7i 1.50991i
\(143\) −4.54999e6 + 888462.i −0.130117 + 0.0254075i
\(144\) 0 0
\(145\) 2.42915e7 + 3.34344e7i 0.661708 + 0.910763i
\(146\) −9.24602e6 + 3.00421e6i −0.245878 + 0.0798906i
\(147\) 0 0
\(148\) −9.43070e6 6.85180e6i −0.239127 0.173736i
\(149\) 3.42366e7 + 2.48743e7i 0.847888 + 0.616027i 0.924563 0.381030i \(-0.124430\pi\)
−0.0766751 + 0.997056i \(0.524430\pi\)
\(150\) 0 0
\(151\) −3.96080e7 + 1.28694e7i −0.936190 + 0.304187i −0.737092 0.675793i \(-0.763801\pi\)
−0.199099 + 0.979979i \(0.563801\pi\)
\(152\) −2.34844e7 3.23235e7i −0.542409 0.746561i
\(153\) 0 0
\(154\) 7.18982e6 5.89728e7i 0.158634 1.30115i
\(155\) 9.85021e7i 2.12464i
\(156\) 0 0
\(157\) −2.80082e6 8.62002e6i −0.0577611 0.177771i 0.918013 0.396550i \(-0.129793\pi\)
−0.975774 + 0.218779i \(0.929793\pi\)
\(158\) −6.95449e7 2.25965e7i −1.40270 0.455766i
\(159\) 0 0
\(160\) −2.27846e7 + 3.13604e7i −0.439767 + 0.605287i
\(161\) −4.39385e6 + 1.35229e7i −0.0829765 + 0.255375i
\(162\) 0 0
\(163\) −1.43925e7 + 1.04567e7i −0.260303 + 0.189121i −0.710280 0.703919i \(-0.751432\pi\)
0.449978 + 0.893040i \(0.351432\pi\)
\(164\) 375033. 0.00663920
\(165\) 0 0
\(166\) −7.25309e7 −1.23068
\(167\) −7.54130e7 + 5.47907e7i −1.25296 + 0.910331i −0.998390 0.0567222i \(-0.981935\pi\)
−0.254574 + 0.967053i \(0.581935\pi\)
\(168\) 0 0
\(169\) 1.90496e7 5.86285e7i 0.303586 0.934341i
\(170\) 1.63854e7 2.25525e7i 0.255791 0.352066i
\(171\) 0 0
\(172\) −1.12069e7 3.64136e6i −0.167934 0.0545650i
\(173\) 8.35515e6 + 2.57145e7i 0.122685 + 0.377587i 0.993472 0.114074i \(-0.0363900\pi\)
−0.870787 + 0.491661i \(0.836390\pi\)
\(174\) 0 0
\(175\) 6.82466e7i 0.962604i
\(176\) −3.78695e7 + 2.10337e7i −0.523595 + 0.290818i
\(177\) 0 0
\(178\) 1.90113e7 + 2.61667e7i 0.252662 + 0.347760i
\(179\) −6.01556e7 + 1.95458e7i −0.783954 + 0.254722i −0.673528 0.739162i \(-0.735222\pi\)
−0.110427 + 0.993884i \(0.535222\pi\)
\(180\) 0 0
\(181\) 9.16356e7 + 6.65771e7i 1.14865 + 0.834546i 0.988301 0.152514i \(-0.0487370\pi\)
0.160352 + 0.987060i \(0.448737\pi\)
\(182\) −1.14340e7 8.30732e6i −0.140589 0.102144i
\(183\) 0 0
\(184\) 1.49125e7 4.84538e6i 0.176477 0.0573410i
\(185\) 6.18893e7 + 8.51833e7i 0.718645 + 0.989130i
\(186\) 0 0
\(187\) −3.21901e7 + 1.78792e7i −0.359979 + 0.199942i
\(188\) 3.07706e7i 0.337740i
\(189\) 0 0
\(190\) 2.61873e7 + 8.05963e7i 0.276983 + 0.852467i
\(191\) −4.52027e7 1.46873e7i −0.469405 0.152519i 0.0647569 0.997901i \(-0.479373\pi\)
−0.534162 + 0.845382i \(0.679373\pi\)
\(192\) 0 0
\(193\) −1.06319e8 + 1.46336e8i −1.06454 + 1.46521i −0.189057 + 0.981966i \(0.560543\pi\)
−0.875484 + 0.483248i \(0.839457\pi\)
\(194\) 681988. 2.09894e6i 0.00670611 0.0206393i
\(195\) 0 0
\(196\) −3.87051e7 + 2.81209e7i −0.367174 + 0.266768i
\(197\) −1.64736e8 −1.53517 −0.767586 0.640946i \(-0.778542\pi\)
−0.767586 + 0.640946i \(0.778542\pi\)
\(198\) 0 0
\(199\) 2.07137e8 1.86325 0.931627 0.363415i \(-0.118389\pi\)
0.931627 + 0.363415i \(0.118389\pi\)
\(200\) 6.08864e7 4.42366e7i 0.538165 0.391000i
\(201\) 0 0
\(202\) 1.36025e7 4.18641e7i 0.116115 0.357365i
\(203\) 9.78210e7 1.34639e8i 0.820722 1.12963i
\(204\) 0 0
\(205\) −3.22171e6 1.04680e6i −0.0261185 0.00848640i
\(206\) 2.92493e7 + 9.00199e7i 0.233120 + 0.717470i
\(207\) 0 0
\(208\) 1.03054e7i 0.0794038i
\(209\) 1.35470e7 1.11116e8i 0.102643 0.841907i
\(210\) 0 0
\(211\) −2.24474e7 3.08961e7i −0.164504 0.226420i 0.718805 0.695212i \(-0.244690\pi\)
−0.883309 + 0.468792i \(0.844690\pi\)
\(212\) −2.21864e6 + 720879.i −0.0159923 + 0.00519621i
\(213\) 0 0
\(214\) −9.95086e7 7.22972e7i −0.694085 0.504282i
\(215\) 8.61092e7 + 6.25620e7i 0.590901 + 0.429315i
\(216\) 0 0
\(217\) 3.77250e8 1.22576e8i 2.50623 0.814322i
\(218\) −1.20500e8 1.65854e8i −0.787752 1.08425i
\(219\) 0 0
\(220\) −6.03849e7 + 1.17912e7i −0.382339 + 0.0746582i
\(221\) 8.75984e6i 0.0545912i
\(222\) 0 0
\(223\) −5.25866e7 1.61845e8i −0.317547 0.977309i −0.974693 0.223546i \(-0.928237\pi\)
0.657146 0.753763i \(-0.271763\pi\)
\(224\) 1.48459e8 + 4.82374e7i 0.882550 + 0.286758i
\(225\) 0 0
\(226\) 4.12109e7 5.67219e7i 0.237483 0.326867i
\(227\) 1.73740e7 5.34717e7i 0.0985846 0.303412i −0.889587 0.456766i \(-0.849008\pi\)
0.988171 + 0.153354i \(0.0490075\pi\)
\(228\) 0 0
\(229\) −1.99842e8 + 1.45193e8i −1.09967 + 0.798955i −0.981006 0.193979i \(-0.937861\pi\)
−0.118662 + 0.992935i \(0.537861\pi\)
\(230\) −3.32578e7 −0.180238
\(231\) 0 0
\(232\) −1.83525e8 −0.964912
\(233\) −6.04388e7 + 4.39114e7i −0.313019 + 0.227421i −0.733191 0.680023i \(-0.761970\pi\)
0.420172 + 0.907444i \(0.361970\pi\)
\(234\) 0 0
\(235\) 8.58872e7 2.64334e8i 0.431709 1.32866i
\(236\) 5.90895e7 8.13297e7i 0.292630 0.402770i
\(237\) 0 0
\(238\) −1.06763e8 3.46895e7i −0.513337 0.166793i
\(239\) 7.99078e7 + 2.45931e8i 0.378614 + 1.16525i 0.941008 + 0.338384i \(0.109880\pi\)
−0.562394 + 0.826869i \(0.690120\pi\)
\(240\) 0 0
\(241\) 3.17817e8i 1.46257i 0.682071 + 0.731286i \(0.261079\pi\)
−0.682071 + 0.731286i \(0.738921\pi\)
\(242\) −1.78174e8 4.41007e7i −0.808149 0.200028i
\(243\) 0 0
\(244\) 2.07112e7 + 2.85065e7i 0.0912728 + 0.125626i
\(245\) 4.10987e8 1.33538e8i 1.78545 0.580126i
\(246\) 0 0
\(247\) −2.15439e7 1.56526e7i −0.0909673 0.0660916i
\(248\) −3.53885e8 2.57113e8i −1.47327 1.07039i
\(249\) 0 0
\(250\) 9.64971e7 3.13538e7i 0.390593 0.126911i
\(251\) 1.18984e8 + 1.63767e8i 0.474930 + 0.653685i 0.977521 0.210839i \(-0.0676197\pi\)
−0.502591 + 0.864524i \(0.667620\pi\)
\(252\) 0 0
\(253\) 3.98303e7 + 1.85318e7i 0.154629 + 0.0719440i
\(254\) 3.05068e8i 1.16810i
\(255\) 0 0
\(256\) −6.84412e7 2.10640e8i −0.254963 0.784696i
\(257\) 4.00047e8 + 1.29983e8i 1.47009 + 0.477662i 0.931137 0.364671i \(-0.118818\pi\)
0.538957 + 0.842333i \(0.318818\pi\)
\(258\) 0 0
\(259\) 2.49226e8 3.43030e8i 0.891342 1.22683i
\(260\) −4.52297e6 + 1.39203e7i −0.0159594 + 0.0491180i
\(261\) 0 0
\(262\) −5.42488e7 + 3.94141e7i −0.186353 + 0.135393i
\(263\) −1.78654e8 −0.605574 −0.302787 0.953058i \(-0.597917\pi\)
−0.302787 + 0.953058i \(0.597917\pi\)
\(264\) 0 0
\(265\) 2.10713e7 0.0695553
\(266\) 2.76086e8 2.00588e8i 0.899411 0.653461i
\(267\) 0 0
\(268\) −5.23616e7 + 1.61153e8i −0.166166 + 0.511406i
\(269\) −1.95714e8 + 2.69378e8i −0.613042 + 0.843779i −0.996823 0.0796445i \(-0.974621\pi\)
0.383782 + 0.923424i \(0.374621\pi\)
\(270\) 0 0
\(271\) −2.34036e8 7.60429e7i −0.714316 0.232095i −0.0707588 0.997493i \(-0.522542\pi\)
−0.643557 + 0.765398i \(0.722542\pi\)
\(272\) 2.52941e7 + 7.78471e7i 0.0762127 + 0.234559i
\(273\) 0 0
\(274\) 3.13639e8i 0.921092i
\(275\) 2.09304e8 + 2.55179e7i 0.606896 + 0.0739913i
\(276\) 0 0
\(277\) −3.84867e7 5.29725e7i −0.108801 0.149751i 0.751144 0.660138i \(-0.229502\pi\)
−0.859945 + 0.510387i \(0.829502\pi\)
\(278\) 4.42326e8 1.43721e8i 1.23477 0.401201i
\(279\) 0 0
\(280\) −6.46221e8 4.69507e8i −1.75925 1.27817i
\(281\) −1.28885e8 9.36405e7i −0.346522 0.251763i 0.400887 0.916128i \(-0.368702\pi\)
−0.747408 + 0.664365i \(0.768702\pi\)
\(282\) 0 0
\(283\) 3.22475e8 1.04779e8i 0.845754 0.274802i 0.146087 0.989272i \(-0.453332\pi\)
0.699666 + 0.714470i \(0.253332\pi\)
\(284\) −1.26286e8 1.73818e8i −0.327146 0.450277i
\(285\) 0 0
\(286\) −2.97529e7 + 3.19607e7i −0.0752052 + 0.0807859i
\(287\) 1.36414e7i 0.0340621i
\(288\) 0 0
\(289\) −1.05301e8 3.24083e8i −0.256620 0.789794i
\(290\) 3.70212e8 + 1.20289e8i 0.891368 + 0.289623i
\(291\) 0 0
\(292\) 2.38311e7 3.28007e7i 0.0560150 0.0770980i
\(293\) −2.47019e8 + 7.60246e8i −0.573711 + 1.76570i 0.0668151 + 0.997765i \(0.478716\pi\)
−0.640526 + 0.767936i \(0.721284\pi\)
\(294\) 0 0
\(295\) −7.34615e8 + 5.33729e8i −1.66603 + 1.21044i
\(296\) −4.67581e8 −1.04794
\(297\) 0 0
\(298\) 3.98603e8 0.872537
\(299\) 8.45492e6 6.14286e6i 0.0182920 0.0132899i
\(300\) 0 0
\(301\) 1.32450e8 4.07639e8i 0.279943 0.861575i
\(302\) −2.30570e8 + 3.17353e8i −0.481703 + 0.663007i
\(303\) 0 0
\(304\) −2.36654e8 7.68935e7i −0.483121 0.156976i
\(305\) −9.83513e7 3.02694e8i −0.198486 0.610878i
\(306\) 0 0
\(307\) 8.79282e8i 1.73438i 0.497980 + 0.867189i \(0.334075\pi\)
−0.497980 + 0.867189i \(0.665925\pi\)
\(308\) 1.20302e8 + 2.16594e8i 0.234609 + 0.422394i
\(309\) 0 0
\(310\) 5.45346e8 + 7.50604e8i 1.03970 + 1.43102i
\(311\) −5.93586e7 + 1.92868e7i −0.111898 + 0.0363579i −0.364431 0.931230i \(-0.618736\pi\)
0.252533 + 0.967588i \(0.418736\pi\)
\(312\) 0 0
\(313\) 2.32559e7 + 1.68964e7i 0.0428675 + 0.0311451i 0.609013 0.793160i \(-0.291566\pi\)
−0.566145 + 0.824306i \(0.691566\pi\)
\(314\) −6.90665e7 5.01798e7i −0.125897 0.0914692i
\(315\) 0 0
\(316\) 2.90030e8 9.42363e7i 0.517056 0.168002i
\(317\) 1.46072e8 + 2.01051e8i 0.257550 + 0.354487i 0.918137 0.396262i \(-0.129693\pi\)
−0.660588 + 0.750749i \(0.729693\pi\)
\(318\) 0 0
\(319\) −3.76347e8 3.50348e8i −0.649113 0.604272i
\(320\) 8.10780e8i 1.38318i
\(321\) 0 0
\(322\) 4.13860e7 + 1.27373e8i 0.0690809 + 0.212609i
\(323\) −2.01162e8 6.53615e7i −0.332152 0.107923i
\(324\) 0 0
\(325\) 2.94841e7 4.05814e7i 0.0476427 0.0655745i
\(326\) −5.17807e7 + 1.59365e8i −0.0827763 + 0.254759i
\(327\) 0 0
\(328\) 1.21702e7 8.84216e6i 0.0190431 0.0138357i
\(329\) −1.11924e9 −1.73276
\(330\) 0 0
\(331\) 9.73914e8 1.47612 0.738062 0.674733i \(-0.235741\pi\)
0.738062 + 0.674733i \(0.235741\pi\)
\(332\) 2.44713e8 1.77794e8i 0.367007 0.266646i
\(333\) 0 0
\(334\) −2.71318e8 + 8.35031e8i −0.398443 + 1.22628i
\(335\) 8.99622e8 1.23822e9i 1.30738 1.79946i
\(336\) 0 0
\(337\) 3.99622e8 + 1.29845e8i 0.568780 + 0.184808i 0.579268 0.815137i \(-0.303338\pi\)
−0.0104879 + 0.999945i \(0.503338\pi\)
\(338\) −1.79429e8 5.52226e8i −0.252746 0.777872i
\(339\) 0 0
\(340\) 1.16256e8i 0.160412i
\(341\) −2.34870e8 1.20281e9i −0.320765 1.64270i
\(342\) 0 0
\(343\) −3.31228e8 4.55896e8i −0.443198 0.610009i
\(344\) −4.49529e8 + 1.46061e8i −0.595392 + 0.193455i
\(345\) 0 0
\(346\) 2.06033e8 + 1.49692e8i 0.267406 + 0.194282i
\(347\) −4.23861e8 3.07953e8i −0.544590 0.395668i 0.281197 0.959650i \(-0.409269\pi\)
−0.825787 + 0.563982i \(0.809269\pi\)
\(348\) 0 0
\(349\) −1.48823e8 + 4.83556e7i −0.187405 + 0.0608916i −0.401216 0.915983i \(-0.631412\pi\)
0.213811 + 0.976875i \(0.431412\pi\)
\(350\) 3.77840e8 + 5.20052e8i 0.471052 + 0.648348i
\(351\) 0 0
\(352\) 2.03449e8 4.37271e8i 0.248631 0.534382i
\(353\) 1.74748e8i 0.211447i −0.994396 0.105724i \(-0.966284\pi\)
0.994396 0.105724i \(-0.0337159\pi\)
\(354\) 0 0
\(355\) 5.99694e8 + 1.84567e9i 0.711427 + 2.18955i
\(356\) −1.28285e8 4.16822e7i −0.150695 0.0489639i
\(357\) 0 0
\(358\) −3.50184e8 + 4.81987e8i −0.403372 + 0.555194i
\(359\) −1.89357e7 + 5.82781e7i −0.0215998 + 0.0664775i −0.961275 0.275589i \(-0.911127\pi\)
0.939676 + 0.342067i \(0.111127\pi\)
\(360\) 0 0
\(361\) −2.02959e8 + 1.47459e8i −0.227057 + 0.164966i
\(362\) 1.06688e9 1.18205
\(363\) 0 0
\(364\) 5.89412e7 0.0640567
\(365\) −2.96274e8 + 2.15256e8i −0.318910 + 0.231702i
\(366\) 0 0
\(367\) 3.44710e7 1.06091e8i 0.0364018 0.112033i −0.931205 0.364497i \(-0.881241\pi\)
0.967606 + 0.252464i \(0.0812409\pi\)
\(368\) 5.73998e7 7.90041e7i 0.0600404 0.0826385i
\(369\) 0 0
\(370\) 9.43216e8 + 3.06469e8i 0.968066 + 0.314544i
\(371\) −2.62211e7 8.07003e7i −0.0266589 0.0820477i
\(372\) 0 0
\(373\) 1.53423e8i 0.153077i −0.997067 0.0765384i \(-0.975613\pi\)
0.997067 0.0765384i \(-0.0243868\pi\)
\(374\) −1.46308e8 + 3.14460e8i −0.144617 + 0.310824i
\(375\) 0 0
\(376\) 7.25479e8 + 9.98536e8i 0.703829 + 0.968737i
\(377\) −1.16334e8 + 3.77994e7i −0.111818 + 0.0363320i
\(378\) 0 0
\(379\) 1.31360e9 + 9.54384e8i 1.23944 + 0.900505i 0.997561 0.0698020i \(-0.0222368\pi\)
0.241878 + 0.970307i \(0.422237\pi\)
\(380\) −2.85919e8 2.07732e8i −0.267301 0.194205i
\(381\) 0 0
\(382\) −4.25768e8 + 1.38340e8i −0.390797 + 0.126978i
\(383\) 7.16014e8 + 9.85508e8i 0.651217 + 0.896323i 0.999151 0.0411957i \(-0.0131167\pi\)
−0.347934 + 0.937519i \(0.613117\pi\)
\(384\) 0 0
\(385\) −4.28889e8 2.19643e9i −0.383030 1.96157i
\(386\) 1.70373e9i 1.50781i
\(387\) 0 0
\(388\) 2.84415e6 + 8.75341e6i 0.00247196 + 0.00760792i
\(389\) −1.81674e9 5.90295e8i −1.56484 0.508447i −0.606744 0.794897i \(-0.707525\pi\)
−0.958095 + 0.286450i \(0.907525\pi\)
\(390\) 0 0
\(391\) 4.87914e7 6.71556e7i 0.0412786 0.0568151i
\(392\) −5.93012e8 + 1.82510e9i −0.497236 + 1.53033i
\(393\) 0 0
\(394\) −1.25532e9 + 9.12043e8i −1.03399 + 0.751240i
\(395\) −2.75452e9 −2.24883
\(396\) 0 0
\(397\) 3.12073e7 0.0250317 0.0125158 0.999922i \(-0.496016\pi\)
0.0125158 + 0.999922i \(0.496016\pi\)
\(398\) 1.57842e9 1.14679e9i 1.25497 0.911788i
\(399\) 0 0
\(400\) 1.44841e8 4.45775e8i 0.113157 0.348262i
\(401\) 3.21254e8 4.42168e8i 0.248796 0.342438i −0.666293 0.745690i \(-0.732120\pi\)
0.915089 + 0.403252i \(0.132120\pi\)
\(402\) 0 0
\(403\) −2.77280e8 9.00936e7i −0.211033 0.0685688i
\(404\) 5.67277e7 + 1.74590e8i 0.0428016 + 0.131730i
\(405\) 0 0
\(406\) 1.56755e9i 1.16247i
\(407\) −9.58847e8 8.92609e8i −0.704967 0.656267i
\(408\) 0 0
\(409\) −5.18590e8 7.13777e8i −0.374794 0.515859i 0.579402 0.815042i \(-0.303286\pi\)
−0.954196 + 0.299183i \(0.903286\pi\)
\(410\) −3.03455e7 + 9.85984e6i −0.0217446 + 0.00706523i
\(411\) 0 0
\(412\) −3.19350e8 2.32021e8i −0.224971 0.163451i
\(413\) 2.95827e9 + 2.14931e9i 2.06639 + 1.50132i
\(414\) 0 0
\(415\) −2.59846e9 + 8.44292e8i −1.78463 + 0.579861i
\(416\) −6.74386e7 9.28212e7i −0.0459284 0.0632151i
\(417\) 0 0
\(418\) −5.11950e8 9.21725e8i −0.342855 0.617283i
\(419\) 3.00048e8i 0.199270i 0.995024 + 0.0996349i \(0.0317675\pi\)
−0.995024 + 0.0996349i \(0.968233\pi\)
\(420\) 0 0
\(421\) −8.34933e8 2.56966e9i −0.545336 1.67837i −0.720190 0.693777i \(-0.755945\pi\)
0.174854 0.984594i \(-0.444055\pi\)
\(422\) −3.42106e8 1.11157e8i −0.221599 0.0720018i
\(423\) 0 0
\(424\) −5.50008e7 + 7.57021e7i −0.0350420 + 0.0482312i
\(425\) 1.23119e8 3.78921e8i 0.0777971 0.239435i
\(426\) 0 0
\(427\) −1.03689e9 + 7.53345e8i −0.644519 + 0.468270i
\(428\) 5.12955e8 0.316247
\(429\) 0 0
\(430\) 1.00254e9 0.608079
\(431\) 1.71587e9 1.24665e9i 1.03232 0.750024i 0.0635483 0.997979i \(-0.479758\pi\)
0.968772 + 0.247954i \(0.0797583\pi\)
\(432\) 0 0
\(433\) −1.21726e8 + 3.74634e8i −0.0720569 + 0.221768i −0.980599 0.196025i \(-0.937197\pi\)
0.908542 + 0.417794i \(0.137197\pi\)
\(434\) 2.19609e9 3.02266e9i 1.28954 1.77490i
\(435\) 0 0
\(436\) 8.13114e8 + 2.64197e8i 0.469839 + 0.152660i
\(437\) 7.79791e7 + 2.39995e8i 0.0446985 + 0.137568i
\(438\) 0 0
\(439\) 7.30240e8i 0.411946i 0.978558 + 0.205973i \(0.0660358\pi\)
−0.978558 + 0.205973i \(0.933964\pi\)
\(440\) −1.68155e9 + 1.80633e9i −0.941078 + 1.01091i
\(441\) 0 0
\(442\) 4.84979e7 + 6.67516e7i 0.0267143 + 0.0367691i
\(443\) 3.00712e9 9.77072e8i 1.64338 0.533966i 0.666088 0.745873i \(-0.267968\pi\)
0.977290 + 0.211907i \(0.0679676\pi\)
\(444\) 0 0
\(445\) 9.85683e8 + 7.16140e8i 0.530246 + 0.385246i
\(446\) −1.29676e9 9.42148e8i −0.692128 0.502860i
\(447\) 0 0
\(448\) 3.10518e9 1.00893e9i 1.63160 0.530139i
\(449\) 4.63996e8 + 6.38636e8i 0.241909 + 0.332959i 0.912657 0.408726i \(-0.134027\pi\)
−0.670748 + 0.741685i \(0.734027\pi\)
\(450\) 0 0
\(451\) 4.18365e7 + 5.10061e6i 0.0214752 + 0.00261821i
\(452\) 2.92395e8i 0.148931i
\(453\) 0 0
\(454\) −1.63647e8 5.03653e8i −0.0820752 0.252602i
\(455\) −5.06333e8 1.64518e8i −0.251998 0.0818790i
\(456\) 0 0
\(457\) 1.39350e9 1.91799e9i 0.682970 0.940027i −0.316995 0.948427i \(-0.602674\pi\)
0.999965 + 0.00839982i \(0.00267378\pi\)
\(458\) −7.18982e8 + 2.21280e9i −0.349695 + 1.07625i
\(459\) 0 0
\(460\) 1.12209e8 8.15246e7i 0.0537496 0.0390514i
\(461\) 2.40257e9 1.14215 0.571074 0.820899i \(-0.306527\pi\)
0.571074 + 0.820899i \(0.306527\pi\)
\(462\) 0 0
\(463\) −3.33982e9 −1.56383 −0.781915 0.623385i \(-0.785757\pi\)
−0.781915 + 0.623385i \(0.785757\pi\)
\(464\) −9.24698e8 + 6.71832e8i −0.429721 + 0.312211i
\(465\) 0 0
\(466\) −2.17445e8 + 6.69226e8i −0.0995401 + 0.306353i
\(467\) −6.82859e8 + 9.39875e8i −0.310257 + 0.427032i −0.935461 0.353429i \(-0.885016\pi\)
0.625204 + 0.780461i \(0.285016\pi\)
\(468\) 0 0
\(469\) −5.86173e9 1.90459e9i −2.62374 0.852505i
\(470\) −8.08977e8 2.48978e9i −0.359413 1.10616i
\(471\) 0 0
\(472\) 4.03239e9i 1.76508i
\(473\) −1.20066e9 5.58628e8i −0.521681 0.242722i
\(474\) 0 0
\(475\) 7.11921e8 + 9.79876e8i 0.304793 + 0.419511i
\(476\) 4.45244e8 1.44669e8i 0.189223 0.0614823i
\(477\) 0 0
\(478\) 1.97048e9 + 1.43164e9i 0.825229 + 0.599564i
\(479\) −2.69936e9 1.96120e9i −1.12224 0.815356i −0.137694 0.990475i \(-0.543969\pi\)
−0.984547 + 0.175118i \(0.943969\pi\)
\(480\) 0 0
\(481\) −2.96394e8 + 9.63043e7i −0.121440 + 0.0394582i
\(482\) 1.75956e9 + 2.42182e9i 0.715712 + 0.985094i
\(483\) 0 0
\(484\) 7.09249e8 2.87965e8i 0.284341 0.115447i
\(485\) 8.31345e7i 0.0330891i
\(486\) 0 0
\(487\) −2.01657e7 6.20637e7i −0.00791156 0.0243493i 0.947023 0.321166i \(-0.104075\pi\)
−0.954934 + 0.296817i \(0.904075\pi\)
\(488\) 1.34420e9 + 4.36757e8i 0.523594 + 0.170126i
\(489\) 0 0
\(490\) 2.39248e9 3.29297e9i 0.918675 1.26445i
\(491\) −6.86799e8 + 2.11375e9i −0.261845 + 0.805876i 0.730558 + 0.682850i \(0.239260\pi\)
−0.992403 + 0.123026i \(0.960740\pi\)
\(492\) 0 0
\(493\) −7.86018e8 + 5.71076e8i −0.295439 + 0.214649i
\(494\) −2.50827e8 −0.0936118
\(495\) 0 0
\(496\) −2.72428e9 −1.00246
\(497\) 6.32241e9 4.59350e9i 2.31012 1.67840i
\(498\) 0 0
\(499\) 1.47827e8 4.54964e8i 0.0532600 0.163917i −0.920888 0.389826i \(-0.872535\pi\)
0.974148 + 0.225909i \(0.0725351\pi\)
\(500\) −2.48716e8 + 3.42328e8i −0.0889833 + 0.122475i
\(501\) 0 0
\(502\) 1.81336e9 + 5.89195e8i 0.639764 + 0.207872i
\(503\) −1.16148e9 3.57467e9i −0.406934 1.25241i −0.919270 0.393628i \(-0.871220\pi\)
0.512336 0.858785i \(-0.328780\pi\)
\(504\) 0 0
\(505\) 1.65815e9i 0.572933i
\(506\) 4.06113e8 7.93004e7i 0.139354 0.0272112i
\(507\) 0 0
\(508\) 7.47811e8 + 1.02927e9i 0.253086 + 0.348343i
\(509\) 1.57098e9 5.10443e8i 0.528030 0.171567i −0.0328563 0.999460i \(-0.510460\pi\)
0.560887 + 0.827893i \(0.310460\pi\)
\(510\) 0 0
\(511\) 1.19308e9 + 8.66827e8i 0.395547 + 0.287382i
\(512\) −2.46846e9 1.79344e9i −0.812795 0.590530i
\(513\) 0 0
\(514\) 3.76807e9 1.22432e9i 1.22391 0.397671i
\(515\) 2.09575e9 + 2.88455e9i 0.676103 + 0.930577i
\(516\) 0 0
\(517\) −4.18493e8 + 3.43259e9i −0.133190 + 1.09246i
\(518\) 3.99377e9i 1.26249i
\(519\) 0 0
\(520\) 1.81424e8 + 5.58365e8i 0.0565825 + 0.174143i
\(521\) 2.48110e9 + 8.06157e8i 0.768620 + 0.249740i 0.666974 0.745081i \(-0.267589\pi\)
0.101646 + 0.994821i \(0.467589\pi\)
\(522\) 0 0
\(523\) −7.59251e8 + 1.04502e9i −0.232076 + 0.319425i −0.909133 0.416505i \(-0.863255\pi\)
0.677058 + 0.735930i \(0.263255\pi\)
\(524\) 8.64155e7 2.65960e8i 0.0262381 0.0807525i
\(525\) 0 0
\(526\) −1.36138e9 + 9.89098e8i −0.407876 + 0.296339i
\(527\) −2.31571e9 −0.689203
\(528\) 0 0
\(529\) 3.30579e9 0.970914
\(530\) 1.60567e8 1.16659e8i 0.0468480 0.0340370i
\(531\) 0 0
\(532\) −4.39790e8 + 1.35353e9i −0.126635 + 0.389743i
\(533\) 5.89338e6 8.11155e6i 0.00168585 0.00232038i
\(534\) 0 0
\(535\) −4.40653e9 1.43177e9i −1.24411 0.404235i
\(536\) 2.10031e9 + 6.46409e9i 0.589124 + 1.81314i
\(537\) 0 0
\(538\) 3.13626e9i 0.868309i
\(539\) −4.70018e9 + 2.61060e9i −1.29287 + 0.718092i
\(540\) 0 0
\(541\) 2.99505e9 + 4.12233e9i 0.813230 + 1.11932i 0.990817 + 0.135210i \(0.0431710\pi\)
−0.177587 + 0.984105i \(0.556829\pi\)
\(542\) −2.20440e9 + 7.16253e8i −0.594693 + 0.193228i
\(543\) 0 0
\(544\) −7.37259e8 5.35650e8i −0.196347 0.142654i
\(545\) −6.24760e9 4.53915e9i −1.65320 1.20112i
\(546\) 0 0
\(547\) 2.15829e9 7.01271e8i 0.563838 0.183202i −0.0132096 0.999913i \(-0.504205\pi\)
0.577047 + 0.816711i \(0.304205\pi\)
\(548\) 7.68821e8 + 1.05819e9i 0.199569 + 0.274683i
\(549\) 0 0
\(550\) 1.73622e9 9.64339e8i 0.444974 0.247150i
\(551\) 2.95356e9i 0.752169i
\(552\) 0 0
\(553\) 3.42773e9 + 1.05495e10i 0.861923 + 2.65273i
\(554\) −5.86552e8 1.90582e8i −0.146562 0.0476210i
\(555\) 0 0
\(556\) −1.14007e9 + 1.56917e9i −0.281300 + 0.387177i
\(557\) −1.08755e9 + 3.34713e9i −0.266658 + 0.820690i 0.724649 + 0.689119i \(0.242002\pi\)
−0.991307 + 0.131571i \(0.957998\pi\)
\(558\) 0 0
\(559\) −2.54868e8 + 1.85173e8i −0.0617127 + 0.0448369i
\(560\) −4.97473e9 −1.19705
\(561\) 0 0
\(562\) −1.50056e9 −0.356595
\(563\) −2.83699e9 + 2.06119e9i −0.670005 + 0.486787i −0.870027 0.493004i \(-0.835899\pi\)
0.200022 + 0.979791i \(0.435899\pi\)
\(564\) 0 0
\(565\) 8.16136e8 2.51181e9i 0.190368 0.585891i
\(566\) 1.87723e9 2.58378e9i 0.435170 0.598961i
\(567\) 0 0
\(568\) −8.19621e9 2.66311e9i −1.87670 0.609776i
\(569\) 5.03984e8 + 1.55110e9i 0.114690 + 0.352978i 0.991882 0.127160i \(-0.0405863\pi\)
−0.877193 + 0.480139i \(0.840586\pi\)
\(570\) 0 0
\(571\) 5.19511e9i 1.16780i −0.811826 0.583899i \(-0.801526\pi\)
0.811826 0.583899i \(-0.198474\pi\)
\(572\) 2.20386e7 1.80766e8i 0.00492376 0.0403860i
\(573\) 0 0
\(574\) 7.55239e7 + 1.03950e8i 0.0166683 + 0.0229420i
\(575\) −4.52069e8 + 1.46886e8i −0.0991670 + 0.0322213i
\(576\) 0 0
\(577\) 1.89636e9 + 1.37779e9i 0.410966 + 0.298584i 0.773993 0.633195i \(-0.218257\pi\)
−0.363027 + 0.931779i \(0.618257\pi\)
\(578\) −2.59666e9 1.88659e9i −0.559330 0.406377i
\(579\) 0 0
\(580\) −1.54393e9 + 5.01652e8i −0.328571 + 0.106759i
\(581\) 6.46706e9 + 8.90114e9i 1.36801 + 1.88291i
\(582\) 0 0
\(583\) −2.57303e8 + 5.02427e7i −0.0537780 + 0.0105011i
\(584\) 1.62628e9i 0.337871i
\(585\) 0 0
\(586\) 2.32669e9 + 7.16080e9i 0.477635 + 1.47001i
\(587\) 3.64098e9 + 1.18303e9i 0.742994 + 0.241413i 0.655964 0.754792i \(-0.272262\pi\)
0.0870300 + 0.996206i \(0.472262\pi\)
\(588\) 0 0
\(589\) 4.13785e9 5.69526e9i 0.834393 1.14844i
\(590\) −2.64297e9 + 8.13423e9i −0.529798 + 1.63055i
\(591\) 0 0
\(592\) −2.35592e9 + 1.71168e9i −0.466697 + 0.339075i
\(593\) 1.29933e9 0.255876 0.127938 0.991782i \(-0.459164\pi\)
0.127938 + 0.991782i \(0.459164\pi\)
\(594\) 0 0
\(595\) −4.22866e9 −0.822988
\(596\) −1.34485e9 + 9.77093e8i −0.260203 + 0.189049i
\(597\) 0 0
\(598\) 3.04188e7 9.36194e7i 0.00581685 0.0179024i
\(599\) −4.70771e9 + 6.47961e9i −0.894985 + 1.23184i 0.0770550 + 0.997027i \(0.475448\pi\)
−0.972040 + 0.234815i \(0.924552\pi\)
\(600\) 0 0
\(601\) −6.67906e9 2.17016e9i −1.25503 0.407784i −0.395310 0.918548i \(-0.629363\pi\)
−0.859721 + 0.510764i \(0.829363\pi\)
\(602\) −1.24755e9 3.83958e9i −0.233062 0.717292i
\(603\) 0 0
\(604\) 1.63592e9i 0.302087i
\(605\) −6.89656e9 + 4.94094e8i −1.26616 + 0.0907121i
\(606\) 0 0
\(607\) 3.54239e9 + 4.87569e9i 0.642890 + 0.884861i 0.998766 0.0496717i \(-0.0158175\pi\)
−0.355876 + 0.934533i \(0.615817\pi\)
\(608\) 2.63475e9 8.56083e8i 0.475420 0.154473i
\(609\) 0 0
\(610\) −2.42529e9 1.76207e9i −0.432622 0.314318i
\(611\) 6.65534e8 + 4.83539e8i 0.118039 + 0.0857604i
\(612\) 0 0
\(613\) −5.37610e9 + 1.74680e9i −0.942662 + 0.306289i −0.739730 0.672903i \(-0.765047\pi\)
−0.202932 + 0.979193i \(0.565047\pi\)
\(614\) 4.86804e9 + 6.70029e9i 0.848722 + 1.16816i
\(615\) 0 0
\(616\) 9.01054e9 + 4.19232e9i 1.55317 + 0.722640i
\(617\) 2.68661e9i 0.460475i −0.973134 0.230237i \(-0.926050\pi\)
0.973134 0.230237i \(-0.0739503\pi\)
\(618\) 0 0
\(619\) −8.75262e7 2.69378e8i −0.0148327 0.0456504i 0.943366 0.331753i \(-0.107640\pi\)
−0.958199 + 0.286103i \(0.907640\pi\)
\(620\) −3.67990e9 1.19567e9i −0.620105 0.201484i
\(621\) 0 0
\(622\) −3.45545e8 + 4.75601e8i −0.0575755 + 0.0792459i
\(623\) 1.51614e9 4.66620e9i 0.251207 0.773135i
\(624\) 0 0
\(625\) 6.11104e9 4.43993e9i 1.00123 0.727439i
\(626\) 2.70759e8 0.0441137
\(627\) 0 0
\(628\) 3.56030e8 0.0573625
\(629\) −2.00260e9 + 1.45497e9i −0.320861 + 0.233119i
\(630\) 0 0
\(631\) −7.75127e8 + 2.38560e9i −0.122820 + 0.378002i −0.993498 0.113852i \(-0.963681\pi\)
0.870677 + 0.491855i \(0.163681\pi\)
\(632\) 7.18993e9 9.89610e9i 1.13296 1.55939i
\(633\) 0 0
\(634\) 2.22620e9 + 7.23336e8i 0.346938 + 0.112727i
\(635\) −3.55113e9 1.09292e10i −0.550374 1.69388i
\(636\) 0 0
\(637\) 1.27905e9i 0.196065i
\(638\) −4.80749e9 5.86119e8i −0.732903 0.0893538i
\(639\) 0 0
\(640\) 1.57236e9 + 2.16416e9i 0.237094 + 0.326333i
\(641\) 1.23993e9 4.02879e8i 0.185950 0.0604187i −0.214562 0.976710i \(-0.568832\pi\)
0.400512 + 0.916292i \(0.368832\pi\)
\(642\) 0 0
\(643\) 8.11137e9 + 5.89325e9i 1.20325 + 0.874212i 0.994600 0.103779i \(-0.0330933\pi\)
0.208649 + 0.977991i \(0.433093\pi\)
\(644\) −4.51862e8 3.28297e8i −0.0666661 0.0484357i
\(645\) 0 0
\(646\) −1.89476e9 + 6.15645e8i −0.276529 + 0.0898497i
\(647\) 3.89936e9 + 5.36701e9i 0.566015 + 0.779053i 0.992076 0.125641i \(-0.0400988\pi\)
−0.426060 + 0.904695i \(0.640099\pi\)
\(648\) 0 0
\(649\) 7.69780e9 8.26903e9i 1.10538 1.18740i
\(650\) 4.72473e8i 0.0674808i
\(651\) 0 0
\(652\) −2.15946e8 6.64612e8i −0.0305125 0.0939079i
\(653\) 3.13289e9 + 1.01794e9i 0.440300 + 0.143062i 0.520774 0.853695i \(-0.325643\pi\)
−0.0804742 + 0.996757i \(0.525643\pi\)
\(654\) 0 0
\(655\) −1.48470e9 + 2.04351e9i −0.206440 + 0.284140i
\(656\) 2.89513e7 8.91031e7i 0.00400410 0.0123234i
\(657\) 0 0
\(658\) −8.52883e9 + 6.19656e9i −1.16708 + 0.847930i
\(659\) −5.97728e9 −0.813588 −0.406794 0.913520i \(-0.633353\pi\)
−0.406794 + 0.913520i \(0.633353\pi\)
\(660\) 0 0
\(661\) −5.91083e9 −0.796055 −0.398028 0.917373i \(-0.630305\pi\)
−0.398028 + 0.917373i \(0.630305\pi\)
\(662\) 7.42141e9 5.39197e9i 0.994222 0.722344i
\(663\) 0 0
\(664\) 3.74932e9 1.15392e10i 0.497009 1.52964i
\(665\) 7.55601e9 1.04000e10i 0.996361 1.37137i
\(666\) 0 0
\(667\) 1.10239e9 + 3.58190e8i 0.143846 + 0.0467383i
\(668\) −1.13150e9 3.48241e9i −0.146872 0.452024i
\(669\) 0 0
\(670\) 1.44162e10i 1.85177i
\(671\) 1.92272e9 + 3.46171e9i 0.245690 + 0.442345i
\(672\) 0 0
\(673\) 2.98812e9 + 4.11280e9i 0.377873 + 0.520098i 0.955019 0.296543i \(-0.0958338\pi\)
−0.577146 + 0.816641i \(0.695834\pi\)
\(674\) 3.76406e9 1.22302e9i 0.473530 0.153859i
\(675\) 0 0
\(676\) 1.95905e9 + 1.42333e9i 0.243911 + 0.177212i
\(677\) 3.98720e9 + 2.89687e9i 0.493864 + 0.358813i 0.806668 0.591004i \(-0.201268\pi\)
−0.312804 + 0.949818i \(0.601268\pi\)
\(678\) 0 0
\(679\) −3.18395e8 + 1.03453e8i −0.0390321 + 0.0126823i
\(680\) 2.74096e9 + 3.77261e9i 0.334289 + 0.460109i
\(681\) 0 0
\(682\) −8.44900e9 7.86534e9i −1.01991 0.949450i
\(683\) 5.09550e9i 0.611948i 0.952040 + 0.305974i \(0.0989820\pi\)
−0.952040 + 0.305974i \(0.901018\pi\)
\(684\) 0 0
\(685\) −3.65090e9 1.12363e10i −0.433993 1.33569i
\(686\) −5.04803e9 1.64021e9i −0.597019 0.193983i
\(687\) 0 0
\(688\) −1.73028e9 + 2.38153e9i −0.202562 + 0.278802i
\(689\) −1.92726e7 + 5.93148e7i −0.00224477 + 0.00690870i
\(690\) 0 0
\(691\) −1.20085e9 + 8.72469e8i −0.138457 + 0.100595i −0.654858 0.755752i \(-0.727272\pi\)
0.516401 + 0.856347i \(0.327272\pi\)
\(692\) −1.06208e9 −0.121839
\(693\) 0 0
\(694\) −4.93484e9 −0.560422
\(695\) 1.41736e10 1.02978e10i 1.60153 1.16358i
\(696\) 0 0
\(697\) 2.46094e7 7.57400e7i 0.00275288 0.00847248i
\(698\) −8.66345e8 + 1.19242e9i −0.0964266 + 0.132720i
\(699\) 0 0
\(700\) −2.54960e9 8.28415e8i −0.280950 0.0912861i
\(701\) −1.01181e9 3.11403e9i −0.110940 0.341437i 0.880139 0.474716i \(-0.157449\pi\)
−0.991079 + 0.133279i \(0.957449\pi\)
\(702\) 0 0
\(703\) 7.52501e9i 0.816890i
\(704\) −1.93324e9 9.90048e9i −0.208824 1.06943i
\(705\) 0 0
\(706\) −9.67475e8 1.33162e9i −0.103472 0.142417i
\(707\) −6.35049e9 + 2.06340e9i −0.675833 + 0.219591i
\(708\) 0 0
\(709\) 1.26098e9 + 9.16155e8i 0.132876 + 0.0965399i 0.652238 0.758014i \(-0.273830\pi\)
−0.519362 + 0.854554i \(0.673830\pi\)
\(710\) 1.47881e10 + 1.07442e10i 1.55063 + 1.12660i
\(711\) 0 0
\(712\) −5.14571e9 + 1.67194e9i −0.534276 + 0.173597i
\(713\) 1.62390e9 + 2.23511e9i 0.167782 + 0.230932i
\(714\) 0 0
\(715\) −6.93878e8 + 1.49135e9i −0.0709924 + 0.152584i
\(716\) 2.48459e9i 0.252964i
\(717\) 0 0
\(718\) 1.78357e8 + 5.48925e8i 0.0179826 + 0.0553449i
\(719\) −1.16975e10 3.80075e9i −1.17366 0.381345i −0.343651 0.939097i \(-0.611664\pi\)
−0.830007 + 0.557753i \(0.811664\pi\)
\(720\) 0 0
\(721\) 8.43949e9 1.16160e10i 0.838577 1.15420i
\(722\) −7.30200e8 + 2.24732e9i −0.0722041 + 0.222221i
\(723\) 0 0
\(724\) −3.59955e9 + 2.61523e9i −0.352504 + 0.256109i
\(725\) 5.56350e9 0.542207
\(726\) 0 0
\(727\) 3.22482e9 0.311269 0.155634 0.987815i \(-0.450258\pi\)
0.155634 + 0.987815i \(0.450258\pi\)
\(728\) 1.91270e9 1.38966e9i 0.183733 0.133490i
\(729\) 0 0
\(730\) −1.06592e9 + 3.28058e9i −0.101414 + 0.312119i
\(731\) −1.47079e9 + 2.02436e9i −0.139264 + 0.191680i
\(732\) 0 0
\(733\) −5.53027e9 1.79689e9i −0.518659 0.168523i 0.0379775 0.999279i \(-0.487908\pi\)
−0.556637 + 0.830756i \(0.687908\pi\)
\(734\) −3.24685e8 9.99277e8i −0.0303058 0.0932717i
\(735\) 0 0
\(736\) 1.08722e9i 0.100519i
\(737\) −8.03291e9 + 1.72651e10i −0.739157 + 1.58867i
\(738\) 0 0
\(739\) −2.14679e9 2.95480e9i −0.195674 0.269322i 0.699894 0.714247i \(-0.253231\pi\)
−0.895568 + 0.444924i \(0.853231\pi\)
\(740\) −3.93358e9 + 1.27810e9i −0.356843 + 0.115945i
\(741\) 0 0
\(742\) −6.46598e8 4.69781e8i −0.0581059 0.0422164i
\(743\) −1.04254e10 7.57452e9i −0.932466 0.677476i 0.0141294 0.999900i \(-0.495502\pi\)
−0.946595 + 0.322424i \(0.895502\pi\)
\(744\) 0 0
\(745\) 1.42802e10 4.63992e9i 1.26528 0.411115i
\(746\) −8.49409e8 1.16911e9i −0.0749085 0.103103i
\(747\) 0 0
\(748\) −2.77202e8 1.41961e9i −0.0242181 0.124026i
\(749\) 1.86581e10i 1.62249i
\(750\) 0 0
\(751\) 1.32157e9 + 4.06738e9i 0.113855 + 0.350409i 0.991706 0.128524i \(-0.0410239\pi\)
−0.877852 + 0.478932i \(0.841024\pi\)
\(752\) 7.31070e9 + 2.37539e9i 0.626897 + 0.203691i
\(753\) 0 0
\(754\) −6.77218e8 + 9.32111e8i −0.0575346 + 0.0791895i
\(755\) −4.56620e9 + 1.40533e10i −0.386136 + 1.18840i
\(756\) 0 0
\(757\) 1.90567e10 1.38455e10i 1.59666 1.16004i 0.703096 0.711095i \(-0.251800\pi\)
0.893560 0.448944i \(-0.148200\pi\)
\(758\) 1.52937e10 1.27547
\(759\) 0 0
\(760\) −1.41761e10 −1.17141
\(761\) 1.64926e10 1.19826e10i 1.35657 0.985607i 0.357917 0.933754i \(-0.383487\pi\)
0.998655 0.0518533i \(-0.0165128\pi\)
\(762\) 0 0
\(763\) −9.60983e9 + 2.95760e10i −0.783213 + 2.41048i
\(764\) 1.09739e9 1.51043e9i 0.0890297 0.122539i
\(765\) 0 0
\(766\) 1.09123e10 + 3.54563e9i 0.877236 + 0.285031i
\(767\) −8.30522e8 2.55608e9i −0.0664611 0.204546i
\(768\) 0 0
\(769\) 2.33312e10i 1.85010i −0.379843 0.925051i \(-0.624022\pi\)
0.379843 0.925051i \(-0.375978\pi\)
\(770\) −1.54285e10 1.43627e10i −1.21788 1.13375i
\(771\) 0 0
\(772\) −4.17635e9 5.74826e9i −0.326691 0.449651i
\(773\) 1.21945e10 3.96222e9i 0.949585 0.308539i 0.207038 0.978333i \(-0