Properties

Label 99.8.j.a.8.2
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 8.2
Character \(\chi\) \(=\) 99.8
Dual form 99.8.j.a.62.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-16.8891 + 12.2707i) q^{2} +(95.1191 - 292.746i) q^{4} +(-112.238 + 154.483i) q^{5} +(-161.473 - 52.4657i) q^{7} +(1159.98 + 3570.05i) q^{8} +O(q^{10})\) \(q+(-16.8891 + 12.2707i) q^{2} +(95.1191 - 292.746i) q^{4} +(-112.238 + 154.483i) q^{5} +(-161.473 - 52.4657i) q^{7} +(1159.98 + 3570.05i) q^{8} -3986.32i q^{10} +(-3990.11 - 1888.44i) q^{11} +(-7512.00 - 10339.4i) q^{13} +(3370.92 - 1095.28i) q^{14} +(-31522.7 - 22902.6i) q^{16} +(12943.8 + 9404.22i) q^{17} +(13042.0 - 4237.60i) q^{19} +(34548.3 + 47551.6i) q^{20} +(90561.9 - 17067.1i) q^{22} -18569.8i q^{23} +(12874.5 + 39623.5i) q^{25} +(253742. + 82445.9i) q^{26} +(-30718.3 + 42280.1i) q^{28} +(46697.9 - 143721. i) q^{29} +(73885.5 - 53681.0i) q^{31} +332938. q^{32} -334005. q^{34} +(26228.5 - 19056.1i) q^{35} +(81151.2 - 249758. i) q^{37} +(-168270. + 231604. i) q^{38} +(-681705. - 221499. i) q^{40} +(237716. + 731614. i) q^{41} +462838. i q^{43} +(-932370. + 988462. i) q^{44} +(227863. + 313627. i) q^{46} +(-246363. + 80048.1i) q^{47} +(-642939. - 467123. i) q^{49} +(-703645. - 511228. i) q^{50} +(-3.74135e6 + 1.21564e6i) q^{52} +(-480284. - 661055. i) q^{53} +(739575. - 404447. i) q^{55} -637324. i q^{56} +(974870. + 3.00034e6i) q^{58} +(-1.96455e6 - 638320. i) q^{59} +(-1.62720e6 + 2.23965e6i) q^{61} +(-589161. + 1.81325e6i) q^{62} +(-1.58812e6 + 1.15384e6i) q^{64} +2.44039e6 q^{65} +3.75516e6 q^{67} +(3.98425e6 - 2.89473e6i) q^{68} +(-209145. + 643682. i) q^{70} +(-2.62729e6 + 3.61616e6i) q^{71} +(4.56184e6 + 1.48223e6i) q^{73} +(1.69412e6 + 5.21397e6i) q^{74} -4.22108e6i q^{76} +(545215. + 514276. i) q^{77} +(870296. + 1.19786e6i) q^{79} +(7.07611e6 - 2.29917e6i) q^{80} +(-1.29922e7 - 9.43939e6i) q^{82} +(-687365. - 499400. i) q^{83} +(-2.90558e6 + 944080. i) q^{85} +(-5.67933e6 - 7.81692e6i) q^{86} +(2.11339e6 - 1.64354e7i) q^{88} +7.55415e6i q^{89} +(670521. + 2.06365e6i) q^{91} +(-5.43623e6 - 1.76634e6i) q^{92} +(3.17861e6 - 4.37498e6i) q^{94} +(-809176. + 2.49039e6i) q^{95} +(6.87572e6 - 4.99550e6i) q^{97} +1.65906e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 112 q - 1792 q^{4}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −16.8891 + 12.2707i −1.49280 + 1.08458i −0.519661 + 0.854372i \(0.673942\pi\)
−0.973141 + 0.230211i \(0.926058\pi\)
\(3\) 0 0
\(4\) 95.1191 292.746i 0.743118 2.28708i
\(5\) −112.238 + 154.483i −0.401556 + 0.552695i −0.961134 0.276083i \(-0.910963\pi\)
0.559578 + 0.828778i \(0.310963\pi\)
\(6\) 0 0
\(7\) −161.473 52.4657i −0.177933 0.0578139i 0.218696 0.975793i \(-0.429820\pi\)
−0.396628 + 0.917979i \(0.629820\pi\)
\(8\) 1159.98 + 3570.05i 0.801004 + 2.46524i
\(9\) 0 0
\(10\) 3986.32i 1.26058i
\(11\) −3990.11 1888.44i −0.903879 0.427789i
\(12\) 0 0
\(13\) −7512.00 10339.4i −0.948318 1.30525i −0.952270 0.305256i \(-0.901258\pi\)
0.00395243 0.999992i \(-0.498742\pi\)
\(14\) 3370.92 1095.28i 0.328322 0.106678i
\(15\) 0 0
\(16\) −31522.7 22902.6i −1.92399 1.39786i
\(17\) 12943.8 + 9404.22i 0.638985 + 0.464249i 0.859501 0.511134i \(-0.170774\pi\)
−0.220517 + 0.975383i \(0.570774\pi\)
\(18\) 0 0
\(19\) 13042.0 4237.60i 0.436221 0.141737i −0.0826703 0.996577i \(-0.526345\pi\)
0.518892 + 0.854840i \(0.326345\pi\)
\(20\) 34548.3 + 47551.6i 0.965654 + 1.32911i
\(21\) 0 0
\(22\) 90561.9 17067.1i 1.81328 0.341728i
\(23\) 18569.8i 0.318243i −0.987259 0.159121i \(-0.949134\pi\)
0.987259 0.159121i \(-0.0508661\pi\)
\(24\) 0 0
\(25\) 12874.5 + 39623.5i 0.164793 + 0.507181i
\(26\) 253742. + 82445.9i 2.83130 + 0.919946i
\(27\) 0 0
\(28\) −30718.3 + 42280.1i −0.264450 + 0.363984i
\(29\) 46697.9 143721.i 0.355553 1.09428i −0.600135 0.799899i \(-0.704887\pi\)
0.955688 0.294381i \(-0.0951134\pi\)
\(30\) 0 0
\(31\) 73885.5 53681.0i 0.445444 0.323634i −0.342350 0.939572i \(-0.611223\pi\)
0.787795 + 0.615938i \(0.211223\pi\)
\(32\) 332938. 1.79613
\(33\) 0 0
\(34\) −334005. −1.45739
\(35\) 26228.5 19056.1i 0.103403 0.0751270i
\(36\) 0 0
\(37\) 81151.2 249758.i 0.263384 0.810612i −0.728677 0.684857i \(-0.759865\pi\)
0.992061 0.125755i \(-0.0401354\pi\)
\(38\) −168270. + 231604.i −0.497466 + 0.684704i
\(39\) 0 0
\(40\) −681705. 221499.i −1.68417 0.547221i
\(41\) 237716. + 731614.i 0.538660 + 1.65782i 0.735605 + 0.677410i \(0.236898\pi\)
−0.196946 + 0.980414i \(0.563102\pi\)
\(42\) 0 0
\(43\) 462838.i 0.887747i 0.896089 + 0.443874i \(0.146396\pi\)
−0.896089 + 0.443874i \(0.853604\pi\)
\(44\) −932370. + 988462.i −1.65008 + 1.74935i
\(45\) 0 0
\(46\) 227863. + 313627.i 0.345161 + 0.475073i
\(47\) −246363. + 80048.1i −0.346125 + 0.112463i −0.476920 0.878947i \(-0.658247\pi\)
0.130795 + 0.991409i \(0.458247\pi\)
\(48\) 0 0
\(49\) −642939. 467123.i −0.780699 0.567211i
\(50\) −703645. 511228.i −0.796083 0.578388i
\(51\) 0 0
\(52\) −3.74135e6 + 1.21564e6i −3.68992 + 1.19893i
\(53\) −480284. 661055.i −0.443132 0.609918i 0.527773 0.849386i \(-0.323027\pi\)
−0.970904 + 0.239467i \(0.923027\pi\)
\(54\) 0 0
\(55\) 739575. 404447.i 0.599395 0.327788i
\(56\) 637324.i 0.484956i
\(57\) 0 0
\(58\) 974870. + 3.00034e6i 0.656068 + 2.01917i
\(59\) −1.96455e6 638320.i −1.24532 0.404629i −0.389078 0.921205i \(-0.627206\pi\)
−0.856241 + 0.516576i \(0.827206\pi\)
\(60\) 0 0
\(61\) −1.62720e6 + 2.23965e6i −0.917881 + 1.26335i 0.0465217 + 0.998917i \(0.485186\pi\)
−0.964403 + 0.264438i \(0.914814\pi\)
\(62\) −589161. + 1.81325e6i −0.313952 + 0.966244i
\(63\) 0 0
\(64\) −1.58812e6 + 1.15384e6i −0.757276 + 0.550193i
\(65\) 2.44039e6 1.10221
\(66\) 0 0
\(67\) 3.75516e6 1.52534 0.762670 0.646788i \(-0.223888\pi\)
0.762670 + 0.646788i \(0.223888\pi\)
\(68\) 3.98425e6 2.89473e6i 1.53662 1.11642i
\(69\) 0 0
\(70\) −209145. + 643682.i −0.0728793 + 0.224299i
\(71\) −2.62729e6 + 3.61616e6i −0.871173 + 1.19907i 0.107616 + 0.994193i \(0.465678\pi\)
−0.978788 + 0.204874i \(0.934322\pi\)
\(72\) 0 0
\(73\) 4.56184e6 + 1.48223e6i 1.37249 + 0.445950i 0.900195 0.435488i \(-0.143424\pi\)
0.472299 + 0.881438i \(0.343424\pi\)
\(74\) 1.69412e6 + 5.21397e6i 0.485997 + 1.49575i
\(75\) 0 0
\(76\) 4.22108e6i 1.10300i
\(77\) 545215. + 514276.i 0.136098 + 0.128374i
\(78\) 0 0
\(79\) 870296. + 1.19786e6i 0.198597 + 0.273345i 0.896687 0.442664i \(-0.145967\pi\)
−0.698091 + 0.716009i \(0.745967\pi\)
\(80\) 7.07611e6 2.29917e6i 1.54518 0.502060i
\(81\) 0 0
\(82\) −1.29922e7 9.43939e6i −2.60216 1.89058i
\(83\) −687365. 499400.i −0.131952 0.0958684i 0.519852 0.854257i \(-0.325987\pi\)
−0.651803 + 0.758388i \(0.725987\pi\)
\(84\) 0 0
\(85\) −2.90558e6 + 944080.i −0.513176 + 0.166741i
\(86\) −5.67933e6 7.81692e6i −0.962836 1.32523i
\(87\) 0 0
\(88\) 2.11339e6 1.64354e7i 0.330591 2.57094i
\(89\) 7.55415e6i 1.13585i 0.823081 + 0.567925i \(0.192253\pi\)
−0.823081 + 0.567925i \(0.807747\pi\)
\(90\) 0 0
\(91\) 670521. + 2.06365e6i 0.0932755 + 0.287072i
\(92\) −5.43623e6 1.76634e6i −0.727847 0.236492i
\(93\) 0 0
\(94\) 3.17861e6 4.37498e6i 0.394720 0.543286i
\(95\) −809176. + 2.49039e6i −0.0968301 + 0.298012i
\(96\) 0 0
\(97\) 6.87572e6 4.99550e6i 0.764922 0.555749i −0.135494 0.990778i \(-0.543262\pi\)
0.900416 + 0.435030i \(0.143262\pi\)
\(98\) 1.65906e7 1.78062
\(99\) 0 0
\(100\) 1.28242e7 1.28242
\(101\) −1.11242e7 + 8.08218e6i −1.07434 + 0.780555i −0.976688 0.214665i \(-0.931134\pi\)
−0.0976546 + 0.995220i \(0.531134\pi\)
\(102\) 0 0
\(103\) −1.40557e6 + 4.32590e6i −0.126742 + 0.390073i −0.994215 0.107413i \(-0.965743\pi\)
0.867472 + 0.497486i \(0.165743\pi\)
\(104\) 2.81983e7 3.88117e7i 2.45814 3.38334i
\(105\) 0 0
\(106\) 1.62232e7 + 5.27122e6i 1.32302 + 0.429874i
\(107\) 6.65956e6 + 2.04960e7i 0.525536 + 1.61743i 0.763253 + 0.646099i \(0.223601\pi\)
−0.237717 + 0.971334i \(0.576399\pi\)
\(108\) 0 0
\(109\) 1.06299e7i 0.786203i 0.919495 + 0.393101i \(0.128598\pi\)
−0.919495 + 0.393101i \(0.871402\pi\)
\(110\) −7.52794e6 + 1.59058e7i −0.539264 + 1.13942i
\(111\) 0 0
\(112\) 3.88845e6 + 5.35200e6i 0.261525 + 0.359959i
\(113\) 1.42159e6 461903.i 0.0926831 0.0301146i −0.262308 0.964984i \(-0.584484\pi\)
0.354991 + 0.934870i \(0.384484\pi\)
\(114\) 0 0
\(115\) 2.86871e6 + 2.08424e6i 0.175891 + 0.127792i
\(116\) −3.76320e7 2.73413e7i −2.23849 1.62636i
\(117\) 0 0
\(118\) 4.10121e7 1.33256e7i 2.29787 0.746623i
\(119\) −1.59667e6 2.19763e6i −0.0868563 0.119547i
\(120\) 0 0
\(121\) 1.23547e7 + 1.50702e7i 0.633993 + 0.773339i
\(122\) 5.77925e7i 2.88146i
\(123\) 0 0
\(124\) −8.68699e6 2.67358e7i −0.409160 1.25927i
\(125\) −2.17541e7 7.06833e6i −0.996221 0.323692i
\(126\) 0 0
\(127\) −1.72439e7 + 2.37342e7i −0.747003 + 1.02816i 0.251182 + 0.967940i \(0.419181\pi\)
−0.998185 + 0.0602215i \(0.980819\pi\)
\(128\) −505444. + 1.55560e6i −0.0213029 + 0.0655635i
\(129\) 0 0
\(130\) −4.12161e7 + 2.99452e7i −1.64538 + 1.19544i
\(131\) 2.28719e6 0.0888901 0.0444451 0.999012i \(-0.485848\pi\)
0.0444451 + 0.999012i \(0.485848\pi\)
\(132\) 0 0
\(133\) −2.32826e6 −0.0858124
\(134\) −6.34214e7 + 4.60783e7i −2.27703 + 1.65436i
\(135\) 0 0
\(136\) −1.85590e7 + 5.71186e7i −0.632656 + 1.94712i
\(137\) 2.53505e7 3.48920e7i 0.842296 1.15932i −0.143212 0.989692i \(-0.545743\pi\)
0.985508 0.169629i \(-0.0542569\pi\)
\(138\) 0 0
\(139\) 1.70153e7 + 5.52861e6i 0.537389 + 0.174608i 0.565122 0.825007i \(-0.308829\pi\)
−0.0277336 + 0.999615i \(0.508829\pi\)
\(140\) −3.08378e6 9.49089e6i −0.0949806 0.292320i
\(141\) 0 0
\(142\) 9.33124e7i 2.73483i
\(143\) 1.04483e7 + 5.54412e7i 0.298794 + 1.58547i
\(144\) 0 0
\(145\) 1.69612e7 + 2.33451e7i 0.462028 + 0.635927i
\(146\) −9.52335e7 + 3.09432e7i −2.53253 + 0.822869i
\(147\) 0 0
\(148\) −6.53967e7 4.75135e7i −1.65821 1.20476i
\(149\) −1.40423e7 1.02023e7i −0.347766 0.252667i 0.400165 0.916443i \(-0.368953\pi\)
−0.747931 + 0.663776i \(0.768953\pi\)
\(150\) 0 0
\(151\) 7.01160e7 2.27821e7i 1.65729 0.538485i 0.676987 0.735995i \(-0.263285\pi\)
0.980301 + 0.197510i \(0.0632854\pi\)
\(152\) 3.02569e7 + 4.16450e7i 0.698830 + 0.961857i
\(153\) 0 0
\(154\) −1.55187e7 1.99552e6i −0.342400 0.0440284i
\(155\) 1.74391e7i 0.376152i
\(156\) 0 0
\(157\) −2.38706e7 7.34660e7i −0.492282 1.51509i −0.821150 0.570712i \(-0.806667\pi\)
0.328868 0.944376i \(-0.393333\pi\)
\(158\) −2.93971e7 9.55169e6i −0.592931 0.192655i
\(159\) 0 0
\(160\) −3.73684e7 + 5.14331e7i −0.721247 + 0.992712i
\(161\) −974275. + 2.99851e6i −0.0183989 + 0.0566259i
\(162\) 0 0
\(163\) −7.41435e7 + 5.38684e7i −1.34096 + 0.974266i −0.341554 + 0.939862i \(0.610953\pi\)
−0.999408 + 0.0344038i \(0.989047\pi\)
\(164\) 2.36789e8 4.19187
\(165\) 0 0
\(166\) 1.77370e7 0.300955
\(167\) 6.38964e7 4.64234e7i 1.06162 0.771311i 0.0872318 0.996188i \(-0.472198\pi\)
0.974387 + 0.224877i \(0.0721979\pi\)
\(168\) 0 0
\(169\) −3.10823e7 + 9.56616e7i −0.495348 + 1.52452i
\(170\) 3.74882e7 5.15981e7i 0.585226 0.805494i
\(171\) 0 0
\(172\) 1.35494e8 + 4.40247e7i 2.03035 + 0.659700i
\(173\) −7.11159e6 2.18872e7i −0.104425 0.321388i 0.885170 0.465268i \(-0.154042\pi\)
−0.989595 + 0.143880i \(0.954042\pi\)
\(174\) 0 0
\(175\) 7.07358e6i 0.0997714i
\(176\) 8.25286e7 + 1.50912e8i 1.14106 + 2.08656i
\(177\) 0 0
\(178\) −9.26945e7 1.27583e8i −1.23192 1.69560i
\(179\) 1.12159e8 3.64428e7i 1.46167 0.474926i 0.533093 0.846057i \(-0.321030\pi\)
0.928581 + 0.371130i \(0.121030\pi\)
\(180\) 0 0
\(181\) 6.34250e7 + 4.60809e7i 0.795033 + 0.577625i 0.909453 0.415807i \(-0.136501\pi\)
−0.114420 + 0.993433i \(0.536501\pi\)
\(182\) −3.66469e7 2.66255e7i −0.450596 0.327377i
\(183\) 0 0
\(184\) 6.62949e7 2.15405e7i 0.784544 0.254914i
\(185\) 2.94750e7 + 4.05689e7i 0.342258 + 0.471077i
\(186\) 0 0
\(187\) −3.38878e7 6.19675e7i −0.378964 0.692976i
\(188\) 7.97359e7i 0.875188i
\(189\) 0 0
\(190\) −1.68924e7 5.19896e7i −0.178671 0.549894i
\(191\) −4.35147e7 1.41388e7i −0.451876 0.146823i 0.0742324 0.997241i \(-0.476349\pi\)
−0.526108 + 0.850418i \(0.676349\pi\)
\(192\) 0 0
\(193\) −2.40696e7 + 3.31289e7i −0.241000 + 0.331708i −0.912334 0.409447i \(-0.865722\pi\)
0.671334 + 0.741155i \(0.265722\pi\)
\(194\) −5.48268e7 + 1.68739e8i −0.539121 + 1.65924i
\(195\) 0 0
\(196\) −1.97904e8 + 1.43786e8i −1.87741 + 1.36402i
\(197\) 1.20287e8 1.12095 0.560475 0.828171i \(-0.310619\pi\)
0.560475 + 0.828171i \(0.310619\pi\)
\(198\) 0 0
\(199\) 4.75770e7 0.427968 0.213984 0.976837i \(-0.431356\pi\)
0.213984 + 0.976837i \(0.431356\pi\)
\(200\) −1.26524e8 + 9.19248e7i −1.11832 + 0.812508i
\(201\) 0 0
\(202\) 8.87037e7 2.73002e8i 0.757202 2.33043i
\(203\) −1.50809e7 + 2.07570e7i −0.126529 + 0.174152i
\(204\) 0 0
\(205\) −1.39703e8 4.53921e7i −1.13257 0.367995i
\(206\) −2.93428e7 9.03079e7i −0.233866 0.719765i
\(207\) 0 0
\(208\) 4.97969e8i 3.83690i
\(209\) −6.00415e7 7.72060e6i −0.454924 0.0584977i
\(210\) 0 0
\(211\) 2.79758e7 + 3.85054e7i 0.205019 + 0.282184i 0.899128 0.437685i \(-0.144202\pi\)
−0.694109 + 0.719870i \(0.744202\pi\)
\(212\) −2.39205e8 + 7.77226e7i −1.72423 + 0.560237i
\(213\) 0 0
\(214\) −3.63974e8 2.64443e8i −2.53876 1.84452i
\(215\) −7.15005e7 5.19481e7i −0.490653 0.356480i
\(216\) 0 0
\(217\) −1.47469e7 + 4.79156e6i −0.0979698 + 0.0318323i
\(218\) −1.30435e8 1.79529e8i −0.852703 1.17365i
\(219\) 0 0
\(220\) −4.80528e7 2.54979e8i −0.304256 1.61445i
\(221\) 2.04475e8i 1.27429i
\(222\) 0 0
\(223\) 4.37823e7 + 1.34748e8i 0.264382 + 0.813684i 0.991835 + 0.127527i \(0.0407039\pi\)
−0.727453 + 0.686157i \(0.759296\pi\)
\(224\) −5.37604e7 1.74678e7i −0.319591 0.103841i
\(225\) 0 0
\(226\) −1.83416e7 + 2.52450e7i −0.105696 + 0.145478i
\(227\) 7.94800e7 2.44614e8i 0.450991 1.38801i −0.424787 0.905293i \(-0.639651\pi\)
0.875778 0.482714i \(-0.160349\pi\)
\(228\) 0 0
\(229\) −8.45659e7 + 6.14407e7i −0.465341 + 0.338090i −0.795623 0.605793i \(-0.792856\pi\)
0.330282 + 0.943882i \(0.392856\pi\)
\(230\) −7.40250e7 −0.401172
\(231\) 0 0
\(232\) 5.67260e8 2.98246
\(233\) 2.24038e8 1.62773e8i 1.16032 0.843019i 0.170499 0.985358i \(-0.445462\pi\)
0.989818 + 0.142339i \(0.0454622\pi\)
\(234\) 0 0
\(235\) 1.52853e7 4.70433e7i 0.0768310 0.236461i
\(236\) −3.73732e8 + 5.14398e8i −1.85084 + 2.54746i
\(237\) 0 0
\(238\) 5.39328e7 + 1.75238e7i 0.259318 + 0.0842577i
\(239\) 7.62765e7 + 2.34755e8i 0.361408 + 1.11230i 0.952200 + 0.305476i \(0.0988156\pi\)
−0.590791 + 0.806824i \(0.701184\pi\)
\(240\) 0 0
\(241\) 2.70798e8i 1.24619i 0.782145 + 0.623097i \(0.214126\pi\)
−0.782145 + 0.623097i \(0.785874\pi\)
\(242\) −3.93582e8 1.02921e8i −1.78518 0.466823i
\(243\) 0 0
\(244\) 5.00871e8 + 6.89390e8i 2.20730 + 3.03809i
\(245\) 1.44325e8 4.68940e7i 0.626989 0.203721i
\(246\) 0 0
\(247\) −1.41786e8 1.03013e8i −0.598678 0.434965i
\(248\) 2.77349e8 + 2.01506e8i 1.15464 + 0.838894i
\(249\) 0 0
\(250\) 4.54141e8 1.47559e8i 1.83823 0.597278i
\(251\) 1.67191e7 + 2.30118e7i 0.0667350 + 0.0918529i 0.841080 0.540911i \(-0.181920\pi\)
−0.774345 + 0.632764i \(0.781920\pi\)
\(252\) 0 0
\(253\) −3.50679e7 + 7.40953e7i −0.136141 + 0.287653i
\(254\) 6.12444e8i 2.34503i
\(255\) 0 0
\(256\) −8.81976e7 2.71444e8i −0.328562 1.01121i
\(257\) 2.38263e7 + 7.74162e6i 0.0875568 + 0.0284489i 0.352468 0.935824i \(-0.385343\pi\)
−0.264911 + 0.964273i \(0.585343\pi\)
\(258\) 0 0
\(259\) −2.62074e7 + 3.60714e7i −0.0937293 + 0.129007i
\(260\) 2.32128e8 7.14416e8i 0.819069 2.52084i
\(261\) 0 0
\(262\) −3.86287e7 + 2.80654e7i −0.132695 + 0.0964088i
\(263\) 1.92223e8 0.651569 0.325785 0.945444i \(-0.394372\pi\)
0.325785 + 0.945444i \(0.394372\pi\)
\(264\) 0 0
\(265\) 1.56028e8 0.515041
\(266\) 3.93222e7 2.85693e7i 0.128101 0.0930708i
\(267\) 0 0
\(268\) 3.57187e8 1.09931e9i 1.13351 3.48858i
\(269\) −1.43564e8 + 1.97599e8i −0.449690 + 0.618945i −0.972331 0.233608i \(-0.924947\pi\)
0.522641 + 0.852553i \(0.324947\pi\)
\(270\) 0 0
\(271\) 6.85550e7 + 2.22749e7i 0.209241 + 0.0679865i 0.411762 0.911291i \(-0.364913\pi\)
−0.202521 + 0.979278i \(0.564913\pi\)
\(272\) −1.92642e8 5.92892e8i −0.580444 1.78642i
\(273\) 0 0
\(274\) 9.00363e8i 2.64418i
\(275\) 2.34563e7 1.82415e8i 0.0680135 0.528926i
\(276\) 0 0
\(277\) −3.18623e8 4.38547e8i −0.900738 1.23976i −0.970232 0.242177i \(-0.922139\pi\)
0.0694941 0.997582i \(-0.477861\pi\)
\(278\) −3.55214e8 + 1.15416e8i −0.991592 + 0.322188i
\(279\) 0 0
\(280\) 9.84557e7 + 7.15322e7i 0.268033 + 0.194737i
\(281\) 4.10187e8 + 2.98019e8i 1.10283 + 0.801256i 0.981520 0.191358i \(-0.0612893\pi\)
0.121314 + 0.992614i \(0.461289\pi\)
\(282\) 0 0
\(283\) −4.08433e8 + 1.32708e8i −1.07119 + 0.348052i −0.790952 0.611878i \(-0.790414\pi\)
−0.280241 + 0.959930i \(0.590414\pi\)
\(284\) 8.08711e8 + 1.11310e9i 2.09498 + 2.88349i
\(285\) 0 0
\(286\) −8.56764e8 8.08146e8i −2.16561 2.04272i
\(287\) 1.30608e8i 0.326123i
\(288\) 0 0
\(289\) −4.76991e7 1.46803e8i −0.116243 0.357760i
\(290\) −5.72919e8 1.86153e8i −1.37943 0.448205i
\(291\) 0 0
\(292\) 8.67837e8 1.19447e9i 2.03985 2.80761i
\(293\) −4.94300e7 + 1.52130e8i −0.114803 + 0.353328i −0.991906 0.126975i \(-0.959473\pi\)
0.877103 + 0.480303i \(0.159473\pi\)
\(294\) 0 0
\(295\) 3.19107e8 2.31845e8i 0.723702 0.525800i
\(296\) 9.85781e8 2.20932
\(297\) 0 0
\(298\) 3.62352e8 0.793184
\(299\) −1.92000e8 + 1.39496e8i −0.415386 + 0.301795i
\(300\) 0 0
\(301\) 2.42831e7 7.47357e7i 0.0513241 0.157959i
\(302\) −9.04647e8 + 1.24514e9i −1.88997 + 2.60132i
\(303\) 0 0
\(304\) −5.08171e8 1.65115e8i −1.03741 0.337076i
\(305\) −1.63353e8 5.02749e8i −0.329669 1.01462i
\(306\) 0 0
\(307\) 6.42943e8i 1.26820i 0.773250 + 0.634101i \(0.218630\pi\)
−0.773250 + 0.634101i \(0.781370\pi\)
\(308\) 2.02413e8 1.10692e8i 0.394739 0.215869i
\(309\) 0 0
\(310\) −2.13990e8 2.94531e8i −0.407969 0.561520i
\(311\) −8.14841e7 + 2.64758e7i −0.153607 + 0.0499100i −0.384811 0.922995i \(-0.625733\pi\)
0.231204 + 0.972905i \(0.425733\pi\)
\(312\) 0 0
\(313\) 6.38210e8 + 4.63687e8i 1.17641 + 0.854712i 0.991762 0.128093i \(-0.0408856\pi\)
0.184648 + 0.982805i \(0.440886\pi\)
\(314\) 1.30463e9 + 9.47869e8i 2.37812 + 1.72780i
\(315\) 0 0
\(316\) 4.33451e8 1.40837e8i 0.772743 0.251079i
\(317\) −1.91045e7 2.62951e7i −0.0336844 0.0463626i 0.791843 0.610725i \(-0.209122\pi\)
−0.825527 + 0.564363i \(0.809122\pi\)
\(318\) 0 0
\(319\) −4.57739e8 + 4.85277e8i −0.789497 + 0.836994i
\(320\) 3.74843e8i 0.639476i
\(321\) 0 0
\(322\) −2.03391e7 6.25972e7i −0.0339497 0.104486i
\(323\) 2.08664e8 + 6.77992e7i 0.344540 + 0.111948i
\(324\) 0 0
\(325\) 3.12970e8 4.30766e8i 0.505720 0.696064i
\(326\) 5.91218e8 1.81958e9i 0.945117 2.90877i
\(327\) 0 0
\(328\) −2.33615e9 + 1.69731e9i −3.65546 + 2.65585i
\(329\) 4.39807e7 0.0680889
\(330\) 0 0
\(331\) 4.47188e7 0.0677786 0.0338893 0.999426i \(-0.489211\pi\)
0.0338893 + 0.999426i \(0.489211\pi\)
\(332\) −2.11579e8 + 1.53721e8i −0.317314 + 0.230542i
\(333\) 0 0
\(334\) −5.09507e8 + 1.56810e9i −0.748235 + 2.30283i
\(335\) −4.21473e8 + 5.80108e8i −0.612510 + 0.843047i
\(336\) 0 0
\(337\) 7.63618e8 + 2.48115e8i 1.08686 + 0.353141i 0.797030 0.603939i \(-0.206403\pi\)
0.289825 + 0.957080i \(0.406403\pi\)
\(338\) −6.48878e8 1.99704e9i −0.914018 2.81306i
\(339\) 0 0
\(340\) 9.40398e8i 1.29758i
\(341\) −3.96185e8 + 7.46642e7i −0.541075 + 0.101970i
\(342\) 0 0
\(343\) 1.61495e8 + 2.22279e8i 0.216088 + 0.297419i
\(344\) −1.65235e9 + 5.36882e8i −2.18851 + 0.711089i
\(345\) 0 0
\(346\) 3.88680e8 + 2.82392e8i 0.504458 + 0.366510i
\(347\) −5.60324e8 4.07099e8i −0.719923 0.523055i 0.166436 0.986052i \(-0.446774\pi\)
−0.886360 + 0.462997i \(0.846774\pi\)
\(348\) 0 0
\(349\) 1.09894e9 3.57067e8i 1.38384 0.449636i 0.479908 0.877319i \(-0.340670\pi\)
0.903929 + 0.427683i \(0.140670\pi\)
\(350\) 8.67976e7 + 1.19467e8i 0.108210 + 0.148939i
\(351\) 0 0
\(352\) −1.32846e9 6.28734e8i −1.62348 0.768365i
\(353\) 4.99455e8i 0.604345i 0.953253 + 0.302172i \(0.0977118\pi\)
−0.953253 + 0.302172i \(0.902288\pi\)
\(354\) 0 0
\(355\) −2.63751e8 8.11743e8i −0.312893 0.962985i
\(356\) 2.21145e9 + 7.18544e8i 2.59778 + 0.844070i
\(357\) 0 0
\(358\) −1.44710e9 + 1.99176e9i −1.66689 + 2.29428i
\(359\) −2.97389e8 + 9.15268e8i −0.339230 + 1.04404i 0.625371 + 0.780327i \(0.284948\pi\)
−0.964601 + 0.263714i \(0.915052\pi\)
\(360\) 0 0
\(361\) −5.71021e8 + 4.14871e8i −0.638817 + 0.464128i
\(362\) −1.63664e9 −1.81331
\(363\) 0 0
\(364\) 6.67906e8 0.725872
\(365\) −7.40993e8 + 5.38363e8i −0.797608 + 0.579496i
\(366\) 0 0
\(367\) 1.60583e8 4.94223e8i 0.169577 0.521905i −0.829767 0.558110i \(-0.811527\pi\)
0.999344 + 0.0362048i \(0.0115269\pi\)
\(368\) −4.25295e8 + 5.85368e8i −0.444859 + 0.612297i
\(369\) 0 0
\(370\) −9.95614e8 3.23495e8i −1.02185 0.332018i
\(371\) 4.28701e7 + 1.31941e8i 0.0435859 + 0.134144i
\(372\) 0 0
\(373\) 2.34504e8i 0.233975i 0.993133 + 0.116987i \(0.0373237\pi\)
−0.993133 + 0.116987i \(0.962676\pi\)
\(374\) 1.33272e9 + 6.30750e8i 1.31731 + 0.623458i
\(375\) 0 0
\(376\) −5.71551e8 7.86672e8i −0.554495 0.763197i
\(377\) −1.83678e9 + 5.96808e8i −1.76548 + 0.573640i
\(378\) 0 0
\(379\) −3.89167e6 2.82746e6i −0.00367197 0.00266784i 0.585948 0.810349i \(-0.300722\pi\)
−0.589620 + 0.807681i \(0.700722\pi\)
\(380\) 6.52084e8 + 4.73767e8i 0.609622 + 0.442917i
\(381\) 0 0
\(382\) 9.08417e8 2.95163e8i 0.833803 0.270919i
\(383\) 2.04748e8 + 2.81811e8i 0.186219 + 0.256308i 0.891912 0.452210i \(-0.149364\pi\)
−0.705693 + 0.708518i \(0.749364\pi\)
\(384\) 0 0
\(385\) −1.40641e8 + 2.65049e7i −0.125603 + 0.0236708i
\(386\) 8.54867e8i 0.756560i
\(387\) 0 0
\(388\) −8.08404e8 2.48801e9i −0.702615 2.16243i
\(389\) 6.88801e8 + 2.23805e8i 0.593294 + 0.192773i 0.590247 0.807222i \(-0.299030\pi\)
0.00304678 + 0.999995i \(0.499030\pi\)
\(390\) 0 0
\(391\) 1.74634e8 2.40363e8i 0.147744 0.203352i
\(392\) 9.21854e8 2.83718e9i 0.772967 2.37895i
\(393\) 0 0
\(394\) −2.03154e9 + 1.47600e9i −1.67336 + 1.21576i
\(395\) −2.82729e8 −0.230824
\(396\) 0 0
\(397\) 8.55964e8 0.686576 0.343288 0.939230i \(-0.388459\pi\)
0.343288 + 0.939230i \(0.388459\pi\)
\(398\) −8.03534e8 + 5.83802e8i −0.638872 + 0.464167i
\(399\) 0 0
\(400\) 5.01642e8 1.54390e9i 0.391908 1.20617i
\(401\) 7.09443e8 9.76465e8i 0.549430 0.756225i −0.440505 0.897750i \(-0.645201\pi\)
0.989935 + 0.141525i \(0.0452005\pi\)
\(402\) 0 0
\(403\) −1.11006e9 3.60679e8i −0.844846 0.274507i
\(404\) 1.30791e9 + 4.02533e9i 0.986831 + 3.03715i
\(405\) 0 0
\(406\) 5.35621e8i 0.397206i
\(407\) −7.95456e8 + 8.43311e8i −0.584838 + 0.620022i
\(408\) 0 0
\(409\) −2.35018e8 3.23474e8i −0.169851 0.233780i 0.715602 0.698508i \(-0.246152\pi\)
−0.885454 + 0.464727i \(0.846152\pi\)
\(410\) 2.91645e9 9.47611e8i 2.08983 0.679026i
\(411\) 0 0
\(412\) 1.13270e9 + 8.22951e8i 0.797945 + 0.579741i
\(413\) 2.83731e8 + 2.06143e8i 0.198190 + 0.143993i
\(414\) 0 0
\(415\) 1.54298e8 5.01343e7i 0.105972 0.0344323i
\(416\) −2.50103e9 3.44237e9i −1.70330 2.34440i
\(417\) 0 0
\(418\) 1.10878e9 6.06355e8i 0.742558 0.406078i
\(419\) 8.72987e8i 0.579774i −0.957061 0.289887i \(-0.906382\pi\)
0.957061 0.289887i \(-0.0936177\pi\)
\(420\) 0 0
\(421\) 5.35931e8 + 1.64942e9i 0.350043 + 1.07732i 0.958828 + 0.283986i \(0.0916570\pi\)
−0.608786 + 0.793335i \(0.708343\pi\)
\(422\) −9.44973e8 3.07040e8i −0.612105 0.198885i
\(423\) 0 0
\(424\) 1.80288e9 2.48145e9i 1.14864 1.58097i
\(425\) −2.05984e8 + 6.33953e8i −0.130158 + 0.400586i
\(426\) 0 0
\(427\) 3.80253e8 2.76270e8i 0.236361 0.171726i
\(428\) 6.63359e9 4.08974
\(429\) 0 0
\(430\) 1.84502e9 1.11908
\(431\) 1.03101e9 7.49071e8i 0.620285 0.450664i −0.232736 0.972540i \(-0.574768\pi\)
0.853021 + 0.521876i \(0.174768\pi\)
\(432\) 0 0
\(433\) 3.58181e8 1.10237e9i 0.212029 0.652557i −0.787322 0.616541i \(-0.788533\pi\)
0.999351 0.0360160i \(-0.0114667\pi\)
\(434\) 1.90267e8 2.61880e8i 0.111725 0.153776i
\(435\) 0 0
\(436\) 3.11185e9 + 1.01110e9i 1.79811 + 0.584241i
\(437\) −7.86913e7 2.42187e8i −0.0451067 0.138824i
\(438\) 0 0
\(439\) 2.54514e8i 0.143577i −0.997420 0.0717886i \(-0.977129\pi\)
0.997420 0.0717886i \(-0.0228707\pi\)
\(440\) 2.30179e9 + 2.17117e9i 1.28819 + 1.21509i
\(441\) 0 0
\(442\) 2.50905e9 + 3.45341e9i 1.38207 + 1.90226i
\(443\) −6.67263e8 + 2.16807e8i −0.364656 + 0.118484i −0.485613 0.874174i \(-0.661404\pi\)
0.120957 + 0.992658i \(0.461404\pi\)
\(444\) 0 0
\(445\) −1.16699e9 8.47865e8i −0.627778 0.456107i
\(446\) −2.39290e9 1.73854e9i −1.27718 0.927925i
\(447\) 0 0
\(448\) 3.16975e8 1.02992e8i 0.166553 0.0541164i
\(449\) −5.19228e8 7.14657e8i −0.270705 0.372593i 0.651923 0.758286i \(-0.273963\pi\)
−0.922628 + 0.385692i \(0.873963\pi\)
\(450\) 0 0
\(451\) 4.33101e8 3.36813e9i 0.222316 1.72891i
\(452\) 4.60102e8i 0.234352i
\(453\) 0 0
\(454\) 1.65923e9 + 5.10660e9i 0.832170 + 2.56116i
\(455\) −3.94057e8 1.28037e8i −0.196119 0.0637228i
\(456\) 0 0
\(457\) 6.52094e8 8.97530e8i 0.319598 0.439888i −0.618747 0.785591i \(-0.712359\pi\)
0.938344 + 0.345702i \(0.112359\pi\)
\(458\) 6.74325e8 2.07536e9i 0.327975 1.00940i
\(459\) 0 0
\(460\) 8.83022e8 6.41553e8i 0.422979 0.307312i
\(461\) 5.45480e8 0.259314 0.129657 0.991559i \(-0.458612\pi\)
0.129657 + 0.991559i \(0.458612\pi\)
\(462\) 0 0
\(463\) −2.56341e9 −1.20029 −0.600143 0.799893i \(-0.704890\pi\)
−0.600143 + 0.799893i \(0.704890\pi\)
\(464\) −4.76363e9 + 3.46098e9i −2.21373 + 1.60837i
\(465\) 0 0
\(466\) −1.78647e9 + 5.49820e9i −0.817797 + 2.51692i
\(467\) 1.30090e9 1.79053e9i 0.591062 0.813528i −0.403791 0.914851i \(-0.632308\pi\)
0.994854 + 0.101324i \(0.0323077\pi\)
\(468\) 0 0
\(469\) −6.06356e8 1.97017e8i −0.271408 0.0881858i
\(470\) 3.19097e8 + 9.82081e8i 0.141769 + 0.436320i
\(471\) 0 0
\(472\) 7.75397e9i 3.39412i
\(473\) 8.74043e8 1.84677e9i 0.379768 0.802416i
\(474\) 0 0
\(475\) 3.35817e8 + 4.62213e8i 0.143772 + 0.197886i
\(476\) −7.95222e8 + 2.58383e8i −0.337959 + 0.109810i
\(477\) 0 0
\(478\) −4.16884e9 3.02884e9i −1.74589 1.26847i
\(479\) −2.30215e9 1.67261e9i −0.957103 0.695376i −0.00462662 0.999989i \(-0.501473\pi\)
−0.952476 + 0.304614i \(0.901473\pi\)
\(480\) 0 0
\(481\) −3.19195e9 + 1.03713e9i −1.30782 + 0.424937i
\(482\) −3.32287e9 4.57354e9i −1.35160 1.86032i
\(483\) 0 0
\(484\) 5.58691e9 2.18334e9i 2.23982 0.875312i
\(485\) 1.62287e9i 0.645933i
\(486\) 0 0
\(487\) −6.45924e8 1.98795e9i −0.253414 0.779927i −0.994138 0.108118i \(-0.965518\pi\)
0.740724 0.671809i \(-0.234482\pi\)
\(488\) −9.88316e9 3.21123e9i −3.84970 1.25084i
\(489\) 0 0
\(490\) −1.86210e9 + 2.56296e9i −0.715018 + 0.984138i
\(491\) −1.38217e9 + 4.25388e9i −0.526958 + 1.62181i 0.233453 + 0.972368i \(0.424998\pi\)
−0.760411 + 0.649442i \(0.775002\pi\)
\(492\) 0 0
\(493\) 1.95603e9 1.42114e9i 0.735211 0.534162i
\(494\) 3.65868e9 1.36546
\(495\) 0 0
\(496\) −3.55850e9 −1.30943
\(497\) 6.13960e8 4.46068e8i 0.224333 0.162987i
\(498\) 0 0
\(499\) −8.51296e7 + 2.62002e8i −0.0306711 + 0.0943958i −0.965220 0.261438i \(-0.915803\pi\)
0.934549 + 0.355834i \(0.115803\pi\)
\(500\) −4.13846e9 + 5.69610e9i −1.48062 + 2.03790i
\(501\) 0 0
\(502\) −5.64741e8 1.83495e8i −0.199244 0.0647384i
\(503\) 1.60077e7 + 4.92668e7i 0.00560844 + 0.0172610i 0.953822 0.300374i \(-0.0971114\pi\)
−0.948213 + 0.317635i \(0.897111\pi\)
\(504\) 0 0
\(505\) 2.62562e9i 0.907220i
\(506\) −3.16932e8 1.68171e9i −0.108753 0.577065i
\(507\) 0 0
\(508\) 5.30787e9 + 7.30566e9i 1.79638 + 2.47250i
\(509\) 2.20949e9 7.17907e8i 0.742643 0.241299i 0.0868302 0.996223i \(-0.472326\pi\)
0.655812 + 0.754924i \(0.272326\pi\)
\(510\) 0 0
\(511\) −6.58847e8 4.78680e8i −0.218430 0.158698i
\(512\) 4.65101e9 + 3.37915e9i 1.53145 + 1.11266i
\(513\) 0 0
\(514\) −4.97400e8 + 1.61615e8i −0.161560 + 0.0524941i
\(515\) −5.10518e8 7.02668e8i −0.164697 0.226686i
\(516\) 0 0
\(517\) 1.13418e9 + 1.45842e8i 0.360965 + 0.0464157i
\(518\) 9.30798e8i 0.294240i
\(519\) 0 0
\(520\) 2.83080e9 + 8.71231e9i 0.882872 + 2.71720i
\(521\) −5.56492e9 1.80815e9i −1.72396 0.560149i −0.731405 0.681944i \(-0.761135\pi\)
−0.992555 + 0.121795i \(0.961135\pi\)
\(522\) 0 0
\(523\) −2.83357e9 + 3.90008e9i −0.866121 + 1.19211i 0.113954 + 0.993486i \(0.463648\pi\)
−0.980075 + 0.198628i \(0.936352\pi\)
\(524\) 2.17556e8 6.69568e8i 0.0660558 0.203299i
\(525\) 0 0
\(526\) −3.24648e9 + 2.35871e9i −0.972664 + 0.706682i
\(527\) 1.46119e9 0.434879
\(528\) 0 0
\(529\) 3.05999e9 0.898721
\(530\) −2.63517e9 + 1.91457e9i −0.768854 + 0.558605i
\(531\) 0 0
\(532\) −2.21462e8 + 6.81589e8i −0.0637687 + 0.196260i
\(533\) 5.77872e9 7.95372e9i 1.65305 2.27523i
\(534\) 0 0
\(535\) −3.91374e9 1.27165e9i −1.10498 0.359029i
\(536\) 4.35590e9 + 1.34061e10i 1.22180 + 3.76033i
\(537\) 0 0
\(538\) 5.09891e9i 1.41169i
\(539\) 1.68326e9 + 3.07803e9i 0.463011 + 0.846665i
\(540\) 0 0
\(541\) −7.60925e8 1.04732e9i −0.206610 0.284375i 0.693119 0.720823i \(-0.256236\pi\)
−0.899729 + 0.436449i \(0.856236\pi\)
\(542\) −1.43116e9 + 4.65013e8i −0.386092 + 0.125449i
\(543\) 0 0
\(544\) 4.30948e9 + 3.13102e9i 1.14770 + 0.833853i
\(545\) −1.64213e9 1.19308e9i −0.434530 0.315705i
\(546\) 0 0
\(547\) −2.97477e9 + 9.66561e8i −0.777137 + 0.252507i −0.670617 0.741803i \(-0.733971\pi\)
−0.106520 + 0.994311i \(0.533971\pi\)
\(548\) −7.80318e9 1.07402e10i −2.02554 2.78791i
\(549\) 0 0
\(550\) 1.84219e9 + 3.36865e9i 0.472135 + 0.863349i
\(551\) 2.07230e9i 0.527743i
\(552\) 0 0
\(553\) −7.76826e7 2.39082e8i −0.0195338 0.0601187i
\(554\) 1.07625e10 + 3.49696e9i 2.68925 + 0.873789i
\(555\) 0 0
\(556\) 3.23696e9 4.45530e9i 0.798686 1.09930i
\(557\) 1.68380e9 5.18222e9i 0.412856 1.27064i −0.501299 0.865274i \(-0.667144\pi\)
0.914155 0.405366i \(-0.132856\pi\)
\(558\) 0 0
\(559\) 4.78546e9 3.47684e9i 1.15873 0.841866i
\(560\) −1.26323e9 −0.303964
\(561\) 0 0
\(562\) −1.05846e10 −2.51534
\(563\) −3.91480e9 + 2.84427e9i −0.924551 + 0.671725i −0.944653 0.328073i \(-0.893601\pi\)
0.0201019 + 0.999798i \(0.493601\pi\)
\(564\) 0 0
\(565\) −8.82010e7 + 2.71455e8i −0.0205733 + 0.0633181i
\(566\) 5.26965e9 7.25306e9i 1.22159 1.68137i
\(567\) 0 0
\(568\) −1.59575e10 5.18489e9i −3.65380 1.18719i
\(569\) 5.67099e8 + 1.74535e9i 0.129052 + 0.397182i 0.994618 0.103614i \(-0.0330406\pi\)
−0.865565 + 0.500796i \(0.833041\pi\)
\(570\) 0 0
\(571\) 2.40660e9i 0.540975i 0.962724 + 0.270487i \(0.0871848\pi\)
−0.962724 + 0.270487i \(0.912815\pi\)
\(572\) 1.72241e10 + 2.21480e9i 3.84813 + 0.494822i
\(573\) 0 0
\(574\) 1.60264e9 + 2.20585e9i 0.353708 + 0.486838i
\(575\) 7.35798e8 2.39075e8i 0.161407 0.0524442i
\(576\) 0 0
\(577\) 1.00060e9 + 7.26982e8i 0.216844 + 0.157546i 0.690905 0.722946i \(-0.257212\pi\)
−0.474061 + 0.880492i \(0.657212\pi\)
\(578\) 2.60696e9 + 1.89407e9i 0.561549 + 0.407989i
\(579\) 0 0
\(580\) 8.44751e9 2.74476e9i 1.79776 0.584127i
\(581\) 8.47894e7 + 1.16703e8i 0.0179360 + 0.0246868i
\(582\) 0 0
\(583\) 6.68021e8 + 3.54467e9i 0.139621 + 0.740859i
\(584\) 1.80054e10i 3.74073i
\(585\) 0 0
\(586\) −1.03191e9 3.17588e9i −0.211836 0.651963i
\(587\) 8.88547e9 + 2.88706e9i 1.81321 + 0.589146i 0.999974 + 0.00720517i \(0.00229350\pi\)
0.813231 + 0.581941i \(0.197707\pi\)
\(588\) 0 0
\(589\) 7.36137e8 1.01321e9i 0.148441 0.204312i
\(590\) −2.54455e9 + 7.83132e9i −0.510069 + 1.56983i
\(591\) 0 0
\(592\) −8.27820e9 + 6.01446e9i −1.63987 + 1.19144i
\(593\) −5.50413e8 −0.108392 −0.0541960 0.998530i \(-0.517260\pi\)
−0.0541960 + 0.998530i \(0.517260\pi\)
\(594\) 0 0
\(595\) 5.18704e8 0.100951
\(596\) −4.32239e9 + 3.14040e9i −0.836300 + 0.607608i
\(597\) 0 0
\(598\) 1.53100e9 4.71193e9i 0.292766 0.901042i
\(599\) −5.67085e9 + 7.80526e9i −1.07809 + 1.48386i −0.216482 + 0.976287i \(0.569458\pi\)
−0.861607 + 0.507575i \(0.830542\pi\)
\(600\) 0 0
\(601\) 4.38353e8 + 1.42429e8i 0.0823688 + 0.0267633i 0.349912 0.936783i \(-0.386212\pi\)
−0.267543 + 0.963546i \(0.586212\pi\)
\(602\) 5.06936e8 + 1.56019e9i 0.0947035 + 0.291467i
\(603\) 0 0
\(604\) 2.26932e10i 4.19051i
\(605\) −3.71476e9 + 2.17141e8i −0.682004 + 0.0398656i
\(606\) 0 0
\(607\) −4.27021e9 5.87745e9i −0.774978 1.06667i −0.995818 0.0913556i \(-0.970880\pi\)
0.220840 0.975310i \(-0.429120\pi\)
\(608\) 4.34217e9 1.41086e9i 0.783510 0.254578i
\(609\) 0 0
\(610\) 8.92795e9 + 6.48654e9i 1.59257 + 1.15707i
\(611\) 2.67833e9 + 1.94592e9i 0.475028 + 0.345128i
\(612\) 0 0
\(613\) 3.32144e9 1.07920e9i 0.582391 0.189230i −0.00298046 0.999996i \(-0.500949\pi\)
0.585371 + 0.810765i \(0.300949\pi\)
\(614\) −7.88934e9 1.08587e10i −1.37547 1.89317i
\(615\) 0 0
\(616\) −1.20355e9 + 2.54299e9i −0.207459 + 0.438341i
\(617\) 2.74124e9i 0.469838i −0.972015 0.234919i \(-0.924517\pi\)
0.972015 0.234919i \(-0.0754826\pi\)
\(618\) 0 0
\(619\) −3.21856e9 9.90570e9i −0.545436 1.67868i −0.719950 0.694025i \(-0.755835\pi\)
0.174514 0.984655i \(-0.444165\pi\)
\(620\) 5.10524e9 + 1.65879e9i 0.860290 + 0.279525i
\(621\) 0 0
\(622\) 1.05132e9 1.44702e9i 0.175173 0.241106i
\(623\) 3.96334e8 1.21979e9i 0.0656678 0.202105i
\(624\) 0 0
\(625\) 9.00316e8 6.54118e8i 0.147508 0.107171i
\(626\) −1.64686e10 −2.68315
\(627\) 0 0
\(628\) −2.37775e10 −3.83095
\(629\) 3.39918e9 2.46965e9i 0.544625 0.395693i
\(630\) 0 0
\(631\) −2.89926e9 + 8.92301e9i −0.459393 + 1.41387i 0.406506 + 0.913648i \(0.366747\pi\)
−0.865899 + 0.500219i \(0.833253\pi\)
\(632\) −3.26689e9 + 4.49649e9i −0.514784 + 0.708539i
\(633\) 0 0
\(634\) 6.45317e8 + 2.09676e8i 0.100568 + 0.0326766i
\(635\) −1.73110e9 5.32777e9i −0.268296 0.825729i
\(636\) 0 0
\(637\) 1.01566e10i 1.55690i
\(638\) 1.77614e9 1.38127e10i 0.270773 2.10574i
\(639\) 0 0
\(640\) −1.83583e8 2.52680e8i −0.0276823 0.0381014i
\(641\) −5.21602e9 + 1.69479e9i −0.782233 + 0.254163i −0.672793 0.739830i \(-0.734906\pi\)
−0.109440 + 0.993993i \(0.534906\pi\)
\(642\) 0 0
\(643\) 5.40319e9 + 3.92564e9i 0.801515 + 0.582335i 0.911358 0.411614i \(-0.135035\pi\)
−0.109843 + 0.993949i \(0.535035\pi\)
\(644\) 7.85131e8 + 5.70431e8i 0.115835 + 0.0841593i
\(645\) 0 0
\(646\) −4.35610e9 + 1.41538e9i −0.635747 + 0.206567i
\(647\) 1.91756e9 + 2.63930e9i 0.278346 + 0.383110i 0.925185 0.379516i \(-0.123910\pi\)
−0.646839 + 0.762626i \(0.723910\pi\)
\(648\) 0 0
\(649\) 6.63332e9 + 6.25691e9i 0.952522 + 0.898469i
\(650\) 1.11156e10i 1.58758i
\(651\) 0 0
\(652\) 8.71732e9 + 2.68292e10i 1.23173 + 3.79088i
\(653\) 6.64335e8 + 2.15856e8i 0.0933665 + 0.0303366i 0.355328 0.934742i \(-0.384369\pi\)
−0.261961 + 0.965078i \(0.584369\pi\)
\(654\) 0 0
\(655\) −2.56711e8 + 3.53332e8i −0.0356944 + 0.0491291i
\(656\) 9.26240e9 2.85067e10i 1.28103 3.94261i
\(657\) 0 0
\(658\) −7.42795e8 + 5.39672e8i −0.101643 + 0.0738481i
\(659\) −7.18896e9 −0.978514 −0.489257 0.872140i \(-0.662732\pi\)
−0.489257 + 0.872140i \(0.662732\pi\)
\(660\) 0 0
\(661\) 4.65098e9 0.626382 0.313191 0.949690i \(-0.398602\pi\)
0.313191 + 0.949690i \(0.398602\pi\)
\(662\) −7.55262e8 + 5.48730e8i −0.101180 + 0.0735116i
\(663\) 0 0
\(664\) 9.85553e8 3.03322e9i 0.130645 0.402083i
\(665\) 2.61320e8 3.59676e8i 0.0344585 0.0474281i
\(666\) 0 0
\(667\) −2.66887e9 8.67168e8i −0.348247 0.113152i
\(668\) −7.51253e9 2.31212e10i −0.975144 3.00118i
\(669\) 0 0
\(670\) 1.49693e10i 1.92282i
\(671\) 1.07221e10 5.86356e9i 1.37010 0.749260i
\(672\) 0 0
\(673\) 2.44819e9 + 3.36965e9i 0.309594 + 0.426120i 0.935255 0.353976i \(-0.115170\pi\)
−0.625660 + 0.780096i \(0.715170\pi\)
\(674\) −1.59414e10 + 5.17967e9i −2.00547 + 0.651617i
\(675\) 0 0
\(676\) 2.50481e10 + 1.81985e10i 3.11861 + 2.26580i
\(677\) 6.27316e9 + 4.55772e9i 0.777009 + 0.564530i 0.904080 0.427364i \(-0.140558\pi\)
−0.127071 + 0.991894i \(0.540558\pi\)
\(678\) 0 0
\(679\) −1.37233e9 + 4.45898e8i −0.168235 + 0.0546628i
\(680\) −6.74082e9 9.27794e9i −0.822113 1.13154i
\(681\) 0 0
\(682\) 5.77503e9 6.12246e9i 0.697123 0.739062i
\(683\) 1.18721e10i 1.42579i 0.701272 + 0.712893i \(0.252616\pi\)
−0.701272 + 0.712893i \(0.747384\pi\)
\(684\) 0 0
\(685\) 2.54491e9 + 7.83244e9i 0.302521 + 0.931065i
\(686\) −5.45503e9 1.77245e9i −0.645153 0.209623i
\(687\) 0 0
\(688\) 1.06002e10 1.45899e10i 1.24095 1.70802i
\(689\) −3.22700e9 + 9.93169e9i −0.375865 + 1.15679i
\(690\) 0 0
\(691\) 2.62053e9 1.90392e9i 0.302145 0.219521i −0.426374 0.904547i \(-0.640209\pi\)
0.728519 + 0.685026i \(0.240209\pi\)
\(692\) −7.08386e9 −0.812640
\(693\) 0 0
\(694\) 1.44588e10 1.64200
\(695\) −2.76385e9 + 2.00805e9i −0.312297 + 0.226897i
\(696\) 0 0
\(697\) −3.80331e9 + 1.17054e10i −0.425449 + 1.30940i
\(698\) −1.41787e10 + 1.95153e10i −1.57813 + 2.17210i
\(699\) 0 0
\(700\) −2.07077e9 6.72832e8i −0.228185 0.0741419i
\(701\) 6.87023e8 + 2.11444e9i 0.0753283 + 0.231837i 0.981630 0.190795i \(-0.0611065\pi\)
−0.906302 + 0.422631i \(0.861106\pi\)
\(702\) 0 0
\(703\) 3.60123e9i 0.390937i
\(704\) 8.51574e9 1.60486e9i 0.919852 0.173353i
\(705\) 0 0
\(706\) −6.12864e9 8.43535e9i −0.655462 0.902167i
\(707\) 2.22029e9 7.21415e8i 0.236288 0.0767745i
\(708\) 0 0
\(709\) 9.86868e9 + 7.17002e9i 1.03991 + 0.755542i 0.970269 0.242030i \(-0.0778133\pi\)
0.0696452 + 0.997572i \(0.477813\pi\)
\(710\) 1.44152e10 + 1.04732e10i 1.51152 + 1.09819i
\(711\) 0 0
\(712\) −2.69687e10 + 8.76265e9i −2.80014 + 0.909820i
\(713\) −9.96843e8 1.37204e9i −0.102994 0.141760i
\(714\) 0 0
\(715\) −9.73743e9 4.60854e9i −0.996261 0.471512i
\(716\) 3.63007e10i 3.69589i
\(717\) 0 0
\(718\) −6.20832e9 1.91072e10i −0.625948 1.92647i
\(719\) 1.63224e9 + 5.30348e8i 0.163770 + 0.0532120i 0.389754 0.920919i \(-0.372560\pi\)
−0.225985 + 0.974131i \(0.572560\pi\)
\(720\) 0 0
\(721\) 4.53923e8 6.24771e8i 0.0451033 0.0620794i
\(722\) 4.55330e9 1.40136e10i 0.450242 1.38570i
\(723\) 0 0
\(724\) 1.95229e10 1.41843e10i 1.91188 1.38906i
\(725\) 6.29595e9 0.613590
\(726\) 0 0
\(727\) −1.10578e10 −1.06733 −0.533667 0.845695i \(-0.679186\pi\)
−0.533667 + 0.845695i \(0.679186\pi\)
\(728\) −6.58954e9 + 4.78758e9i −0.632988 + 0.459893i
\(729\) 0 0
\(730\) 5.90865e9 1.81850e10i 0.562158 1.73014i
\(731\) −4.35263e9 + 5.99088e9i −0.412136 + 0.567257i
\(732\) 0 0
\(733\) −1.84211e10 5.98539e9i −1.72764 0.561344i −0.734533 0.678573i \(-0.762599\pi\)
−0.993105 + 0.117229i \(0.962599\pi\)
\(734\) 3.35234e9 + 1.03174e10i 0.312905 + 0.963021i
\(735\) 0 0
\(736\) 6.18257e9i 0.571606i
\(737\) −1.49835e10 7.09141e9i −1.37872 0.652524i
\(738\) 0 0
\(739\) 1.08095e10 + 1.48781e10i 0.985262 + 1.35610i 0.933946 + 0.357414i \(0.116341\pi\)
0.0513154 + 0.998682i \(0.483659\pi\)
\(740\) 1.46800e10 4.76983e9i 1.33173 0.432705i
\(741\) 0 0
\(742\) −2.34304e9 1.70232e9i −0.210555 0.152977i
\(743\) −1.10768e10 8.04780e9i −0.990730 0.719807i −0.0306490 0.999530i \(-0.509757\pi\)
−0.960081 + 0.279723i \(0.909757\pi\)
\(744\) 0 0
\(745\) 3.15217e9 1.02420e9i 0.279295 0.0907485i
\(746\) −2.87752e9 3.96057e9i −0.253765 0.349278i
\(747\) 0 0
\(748\) −2.13641e10 + 4.02624e9i −1.86651 + 0.351758i
\(749\) 3.65895e9i 0.318178i
\(750\) 0 0
\(751\) 5.90818e8 + 1.81835e9i 0.0508995 + 0.156653i 0.973275 0.229641i \(-0.0737552\pi\)
−0.922376 + 0.386294i \(0.873755\pi\)
\(752\) 9.59932e9 + 3.11901e9i 0.823148 + 0.267457i
\(753\) 0 0
\(754\) 2.36985e10 3.26181e10i 2.01336 2.77115i
\(755\) −4.35027e9 + 1.33887e10i −0.367876 + 1.13221i
\(756\) 0 0
\(757\) 1.02215e10 7.42635e9i 0.856404 0.622214i −0.0705002 0.997512i \(-0.522460\pi\)
0.926904 + 0.375298i \(0.122460\pi\)
\(758\) 1.00422e8 0.00837501
\(759\) 0 0
\(760\) −9.82943e9 −0.812233
\(761\) 1.42474e10 1.03514e10i 1.17190 0.851434i 0.180664 0.983545i \(-0.442175\pi\)
0.991235 + 0.132111i \(0.0421755\pi\)
\(762\) 0 0
\(763\) 5.57703e8 1.71643e9i 0.0454534 0.139891i
\(764\) −8.27815e9 + 1.13939e10i −0.671594 + 0.924370i
\(765\) 0 0
\(766\) −6.91602e9 2.24715e9i −0.555976 0.180647i
\(767\) 8.15785e9 + 2.51073e10i 0.652818 + 2.00917i
\(768\) 0 0
\(769\) 1.01982e10i 0.808687i 0.914607 + 0.404344i \(0.132500\pi\)
−0.914607 + 0.404344i \(0.867500\pi\)
\(770\) 2.05007e9 2.17340e9i 0.161827 0.171562i
\(771\) 0 0
\(772\) 7.40889e9 + 1.01975e10i 0.579552 + 0.797685i
\(773\) −4.95979e8 + 1.61153e8i −0.0386221 + 0.0125491i −0.328264 0.944586i \(-0.606464\pi\)
0.289642 + 0.957135i \(0.406464\pi\)