Properties

Label 99.8.j.a.8.3
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 8.3
Character \(\chi\) \(=\) 99.8
Dual form 99.8.j.a.62.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-16.1346 + 11.7225i) q^{2} +(83.3550 - 256.540i) q^{4} +(233.551 - 321.456i) q^{5} +(1297.08 + 421.447i) q^{7} +(873.541 + 2688.48i) q^{8} +O(q^{10})\) \(q+(-16.1346 + 11.7225i) q^{2} +(83.3550 - 256.540i) q^{4} +(233.551 - 321.456i) q^{5} +(1297.08 + 421.447i) q^{7} +(873.541 + 2688.48i) q^{8} +7924.37i q^{10} +(-4333.78 - 839.967i) q^{11} +(3296.70 + 4537.52i) q^{13} +(-25868.3 + 8405.12i) q^{14} +(-17677.0 - 12843.1i) q^{16} +(18271.1 + 13274.7i) q^{17} +(40920.9 - 13296.0i) q^{19} +(-62998.7 - 86710.3i) q^{20} +(79770.3 - 37250.1i) q^{22} -70493.3i q^{23} +(-24645.7 - 75851.7i) q^{25} +(-106382. - 34565.6i) q^{26} +(216236. - 297624. i) q^{28} +(-75321.1 + 231815. i) q^{29} +(-30902.9 + 22452.3i) q^{31} +73928.6 q^{32} -450410. q^{34} +(438412. - 318525. i) q^{35} +(26832.5 - 82582.1i) q^{37} +(-504380. + 694220. i) q^{38} +(1.06825e6 + 347094. i) q^{40} +(-138158. - 425206. i) q^{41} +161530. i q^{43} +(-576727. + 1.04177e6i) q^{44} +(826356. + 1.13738e6i) q^{46} +(704857. - 229022. i) q^{47} +(838539. + 609234. i) q^{49} +(1.28682e6 + 934930. i) q^{50} +(1.43885e6 - 467512. i) q^{52} +(-613121. - 843889. i) q^{53} +(-1.28217e6 + 1.19694e6i) q^{55} +3.85533e6i q^{56} +(-1.50216e6 - 4.62319e6i) q^{58} +(2.39611e6 + 778543. i) q^{59} +(-531908. + 732108. i) q^{61} +(235410. - 724518. i) q^{62} +(1.06984e6 - 777286. i) q^{64} +2.22856e6 q^{65} +2.05587e6 q^{67} +(4.92849e6 - 3.58075e6i) q^{68} +(-3.33970e6 + 1.02785e7i) q^{70} +(-2.09425e6 + 2.88249e6i) q^{71} +(2.13520e6 + 693770. i) q^{73} +(535134. + 1.64697e6i) q^{74} -1.16061e7i q^{76} +(-5.26726e6 - 2.91596e6i) q^{77} +(-2.59597e6 - 3.57305e6i) q^{79} +(-8.25696e6 + 2.68285e6i) q^{80} +(7.21359e6 + 5.24098e6i) q^{82} +(1.35902e6 + 987387. i) q^{83} +(8.53448e6 - 2.77302e6i) q^{85} +(-1.89353e6 - 2.60622e6i) q^{86} +(-1.52750e6 - 1.23850e7i) q^{88} +1.87524e6i q^{89} +(2.36376e6 + 7.27491e6i) q^{91} +(-1.80844e7 - 5.87597e6i) q^{92} +(-8.68788e6 + 1.19578e7i) q^{94} +(5.28305e6 - 1.62596e7i) q^{95} +(-1.97370e6 + 1.43398e6i) q^{97} -2.06712e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 112 q - 1792 q^{4}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −16.1346 + 11.7225i −1.42611 + 1.03613i −0.435388 + 0.900243i \(0.643389\pi\)
−0.990724 + 0.135888i \(0.956611\pi\)
\(3\) 0 0
\(4\) 83.3550 256.540i 0.651211 2.00422i
\(5\) 233.551 321.456i 0.835579 1.15008i −0.151280 0.988491i \(-0.548339\pi\)
0.986859 0.161585i \(-0.0516606\pi\)
\(6\) 0 0
\(7\) 1297.08 + 421.447i 1.42930 + 0.464408i 0.918545 0.395317i \(-0.129365\pi\)
0.510756 + 0.859725i \(0.329365\pi\)
\(8\) 873.541 + 2688.48i 0.603209 + 1.85649i
\(9\) 0 0
\(10\) 7924.37i 2.50591i
\(11\) −4333.78 839.967i −0.981730 0.190278i
\(12\) 0 0
\(13\) 3296.70 + 4537.52i 0.416177 + 0.572818i 0.964711 0.263310i \(-0.0848141\pi\)
−0.548535 + 0.836128i \(0.684814\pi\)
\(14\) −25868.3 + 8405.12i −2.51953 + 0.818645i
\(15\) 0 0
\(16\) −17677.0 12843.1i −1.07892 0.783879i
\(17\) 18271.1 + 13274.7i 0.901972 + 0.655321i 0.938972 0.343994i \(-0.111780\pi\)
−0.0369998 + 0.999315i \(0.511780\pi\)
\(18\) 0 0
\(19\) 40920.9 13296.0i 1.36870 0.444717i 0.469760 0.882794i \(-0.344341\pi\)
0.898937 + 0.438078i \(0.144341\pi\)
\(20\) −62998.7 86710.3i −1.76087 2.42363i
\(21\) 0 0
\(22\) 79770.3 37250.1i 1.59721 0.745844i
\(23\) 70493.3i 1.20809i −0.796949 0.604046i \(-0.793554\pi\)
0.796949 0.604046i \(-0.206446\pi\)
\(24\) 0 0
\(25\) −24645.7 75851.7i −0.315465 0.970902i
\(26\) −106382. 34565.6i −1.18703 0.385689i
\(27\) 0 0
\(28\) 216236. 297624.i 1.86155 2.56221i
\(29\) −75321.1 + 231815.i −0.573487 + 1.76501i 0.0677869 + 0.997700i \(0.478406\pi\)
−0.641274 + 0.767312i \(0.721594\pi\)
\(30\) 0 0
\(31\) −30902.9 + 22452.3i −0.186309 + 0.135361i −0.677030 0.735955i \(-0.736733\pi\)
0.490721 + 0.871317i \(0.336733\pi\)
\(32\) 73928.6 0.398830
\(33\) 0 0
\(34\) −450410. −1.96531
\(35\) 438412. 318525.i 1.72840 1.25576i
\(36\) 0 0
\(37\) 26832.5 82582.1i 0.0870875 0.268028i −0.898023 0.439948i \(-0.854997\pi\)
0.985111 + 0.171920i \(0.0549970\pi\)
\(38\) −504380. + 694220.i −1.49113 + 2.05236i
\(39\) 0 0
\(40\) 1.06825e6 + 347094.i 2.63913 + 0.857506i
\(41\) −138158. 425206.i −0.313063 0.963509i −0.976544 0.215316i \(-0.930922\pi\)
0.663481 0.748193i \(-0.269078\pi\)
\(42\) 0 0
\(43\) 161530.i 0.309822i 0.987928 + 0.154911i \(0.0495091\pi\)
−0.987928 + 0.154911i \(0.950491\pi\)
\(44\) −576727. + 1.04177e6i −1.02067 + 1.84369i
\(45\) 0 0
\(46\) 826356. + 1.13738e6i 1.25174 + 1.72288i
\(47\) 704857. 229022.i 0.990280 0.321762i 0.231305 0.972881i \(-0.425700\pi\)
0.758975 + 0.651120i \(0.225700\pi\)
\(48\) 0 0
\(49\) 838539. + 609234.i 1.01821 + 0.739772i
\(50\) 1.28682e6 + 934930.i 1.45587 + 1.05775i
\(51\) 0 0
\(52\) 1.43885e6 467512.i 1.41907 0.461085i
\(53\) −613121. 843889.i −0.565693 0.778610i 0.426343 0.904561i \(-0.359802\pi\)
−0.992036 + 0.125952i \(0.959802\pi\)
\(54\) 0 0
\(55\) −1.28217e6 + 1.19694e6i −1.03915 + 0.970072i
\(56\) 3.85533e6i 2.93361i
\(57\) 0 0
\(58\) −1.50216e6 4.62319e6i −1.01093 3.11131i
\(59\) 2.39611e6 + 778543.i 1.51888 + 0.493515i 0.945458 0.325743i \(-0.105614\pi\)
0.573425 + 0.819258i \(0.305614\pi\)
\(60\) 0 0
\(61\) −531908. + 732108.i −0.300042 + 0.412972i −0.932243 0.361832i \(-0.882151\pi\)
0.632202 + 0.774804i \(0.282151\pi\)
\(62\) 235410. 724518.i 0.125445 0.386081i
\(63\) 0 0
\(64\) 1.06984e6 777286.i 0.510140 0.370639i
\(65\) 2.22856e6 1.00653
\(66\) 0 0
\(67\) 2.05587e6 0.835092 0.417546 0.908656i \(-0.362890\pi\)
0.417546 + 0.908656i \(0.362890\pi\)
\(68\) 4.92849e6 3.58075e6i 1.90078 1.38100i
\(69\) 0 0
\(70\) −3.33970e6 + 1.02785e7i −1.16376 + 3.58169i
\(71\) −2.09425e6 + 2.88249e6i −0.694424 + 0.955793i 0.305569 + 0.952170i \(0.401153\pi\)
−0.999993 + 0.00362331i \(0.998847\pi\)
\(72\) 0 0
\(73\) 2.13520e6 + 693770.i 0.642406 + 0.208730i 0.612063 0.790809i \(-0.290340\pi\)
0.0303431 + 0.999540i \(0.490340\pi\)
\(74\) 535134. + 1.64697e6i 0.153515 + 0.472471i
\(75\) 0 0
\(76\) 1.16061e7i 3.03277i
\(77\) −5.26726e6 2.91596e6i −1.31482 0.727887i
\(78\) 0 0
\(79\) −2.59597e6 3.57305e6i −0.592387 0.815351i 0.402598 0.915377i \(-0.368107\pi\)
−0.994985 + 0.100026i \(0.968107\pi\)
\(80\) −8.25696e6 + 2.68285e6i −1.80304 + 0.585843i
\(81\) 0 0
\(82\) 7.21359e6 + 5.24098e6i 1.44478 + 1.04970i
\(83\) 1.35902e6 + 987387.i 0.260887 + 0.189546i 0.710538 0.703659i \(-0.248452\pi\)
−0.449651 + 0.893204i \(0.648452\pi\)
\(84\) 0 0
\(85\) 8.53448e6 2.77302e6i 1.50734 0.489764i
\(86\) −1.89353e6 2.60622e6i −0.321016 0.441841i
\(87\) 0 0
\(88\) −1.52750e6 1.23850e7i −0.238941 1.93735i
\(89\) 1.87524e6i 0.281962i 0.990012 + 0.140981i \(0.0450257\pi\)
−0.990012 + 0.140981i \(0.954974\pi\)
\(90\) 0 0
\(91\) 2.36376e6 + 7.27491e6i 0.328820 + 1.01201i
\(92\) −1.80844e7 5.87597e6i −2.42128 0.786723i
\(93\) 0 0
\(94\) −8.68788e6 + 1.19578e7i −1.07886 + 1.48493i
\(95\) 5.28305e6 1.62596e7i 0.632197 1.94570i
\(96\) 0 0
\(97\) −1.97370e6 + 1.43398e6i −0.219573 + 0.159529i −0.692135 0.721768i \(-0.743330\pi\)
0.472561 + 0.881298i \(0.343330\pi\)
\(98\) −2.06712e7 −2.21858
\(99\) 0 0
\(100\) −2.15134e7 −2.15134
\(101\) 1.28900e7 9.36511e6i 1.24488 0.904457i 0.246966 0.969024i \(-0.420567\pi\)
0.997913 + 0.0645668i \(0.0205666\pi\)
\(102\) 0 0
\(103\) 212696. 654612.i 0.0191792 0.0590274i −0.941009 0.338382i \(-0.890120\pi\)
0.960188 + 0.279354i \(0.0901205\pi\)
\(104\) −9.31923e6 + 1.28268e7i −0.812388 + 1.11816i
\(105\) 0 0
\(106\) 1.97850e7 + 6.42852e6i 1.61348 + 0.524253i
\(107\) −3.19166e6 9.82293e6i −0.251869 0.775172i −0.994431 0.105394i \(-0.966390\pi\)
0.742562 0.669777i \(-0.233610\pi\)
\(108\) 0 0
\(109\) 1.44776e7i 1.07079i −0.844603 0.535394i \(-0.820163\pi\)
0.844603 0.535394i \(-0.179837\pi\)
\(110\) 6.65621e6 3.43425e7i 0.476818 2.46012i
\(111\) 0 0
\(112\) −1.75158e7 2.41084e7i −1.17806 1.62146i
\(113\) 1.82867e7 5.94170e6i 1.19223 0.387379i 0.355333 0.934740i \(-0.384368\pi\)
0.836897 + 0.547361i \(0.184368\pi\)
\(114\) 0 0
\(115\) −2.26605e7 1.64638e7i −1.38940 1.00946i
\(116\) 5.31914e7 + 3.86458e7i 3.16401 + 2.29879i
\(117\) 0 0
\(118\) −4.77867e7 + 1.55269e7i −2.67744 + 0.869954i
\(119\) 1.81045e7 + 2.49187e7i 0.984853 + 1.35553i
\(120\) 0 0
\(121\) 1.80761e7 + 7.28046e6i 0.927589 + 0.373603i
\(122\) 1.80476e7i 0.899827i
\(123\) 0 0
\(124\) 3.18400e6 + 9.79935e6i 0.149968 + 0.461553i
\(125\) −616061. 200170.i −0.0282123 0.00916674i
\(126\) 0 0
\(127\) −1.29347e7 + 1.78031e7i −0.560328 + 0.771226i −0.991368 0.131107i \(-0.958147\pi\)
0.431040 + 0.902333i \(0.358147\pi\)
\(128\) −1.10740e7 + 3.40821e7i −0.466732 + 1.43645i
\(129\) 0 0
\(130\) −3.59570e7 + 2.61243e7i −1.43543 + 1.04290i
\(131\) 3.12372e7 1.21401 0.607005 0.794698i \(-0.292371\pi\)
0.607005 + 0.794698i \(0.292371\pi\)
\(132\) 0 0
\(133\) 5.86812e7 2.16281
\(134\) −3.31707e7 + 2.40999e7i −1.19093 + 0.865264i
\(135\) 0 0
\(136\) −1.97283e7 + 6.07175e7i −0.672517 + 2.06980i
\(137\) −1.50523e7 + 2.07177e7i −0.500127 + 0.688366i −0.982216 0.187757i \(-0.939878\pi\)
0.482089 + 0.876123i \(0.339878\pi\)
\(138\) 0 0
\(139\) 5.08915e6 + 1.65357e6i 0.160729 + 0.0522240i 0.388276 0.921543i \(-0.373071\pi\)
−0.227547 + 0.973767i \(0.573071\pi\)
\(140\) −4.51706e7 1.39021e8i −1.39126 4.28185i
\(141\) 0 0
\(142\) 7.10578e7i 2.08258i
\(143\) −1.04758e7 2.24337e7i −0.299579 0.641542i
\(144\) 0 0
\(145\) 5.69268e7 + 7.83530e7i 1.55070 + 2.13436i
\(146\) −4.25834e7 + 1.38362e7i −1.13241 + 0.367944i
\(147\) 0 0
\(148\) −1.89490e7 1.37673e7i −0.480474 0.349085i
\(149\) 2.30366e7 + 1.67371e7i 0.570514 + 0.414502i 0.835292 0.549807i \(-0.185299\pi\)
−0.264778 + 0.964309i \(0.585299\pi\)
\(150\) 0 0
\(151\) −7.51976e7 + 2.44332e7i −1.77740 + 0.577512i −0.998752 0.0499504i \(-0.984094\pi\)
−0.778647 + 0.627462i \(0.784094\pi\)
\(152\) 7.14921e7 + 9.84004e7i 1.65122 + 2.27271i
\(153\) 0 0
\(154\) 1.19167e8 1.46974e7i 2.62927 0.324279i
\(155\) 1.51777e7i 0.327375i
\(156\) 0 0
\(157\) −1.16491e7 3.58521e7i −0.240238 0.739377i −0.996383 0.0849728i \(-0.972920\pi\)
0.756145 0.654404i \(-0.227080\pi\)
\(158\) 8.37701e7 + 2.72185e7i 1.68962 + 0.548991i
\(159\) 0 0
\(160\) 1.72661e7 2.37648e7i 0.333254 0.458685i
\(161\) 2.97092e7 9.14354e7i 0.561048 1.72673i
\(162\) 0 0
\(163\) 6.08360e7 4.41999e7i 1.10028 0.799402i 0.119176 0.992873i \(-0.461975\pi\)
0.981106 + 0.193471i \(0.0619746\pi\)
\(164\) −1.20599e8 −2.13496
\(165\) 0 0
\(166\) −3.35019e7 −0.568449
\(167\) −2.91873e6 + 2.12058e6i −0.0484939 + 0.0352329i −0.611768 0.791037i \(-0.709541\pi\)
0.563274 + 0.826270i \(0.309541\pi\)
\(168\) 0 0
\(169\) 9.66952e6 2.97597e7i 0.154100 0.474270i
\(170\) −1.05194e8 + 1.44787e8i −1.64217 + 2.26026i
\(171\) 0 0
\(172\) 4.14389e7 + 1.34643e7i 0.620952 + 0.201760i
\(173\) −32900.8 101258.i −0.000483110 0.00148686i 0.950815 0.309760i \(-0.100249\pi\)
−0.951298 + 0.308273i \(0.900249\pi\)
\(174\) 0 0
\(175\) 1.08773e8i 1.53422i
\(176\) 6.58203e7 + 7.05071e7i 0.910050 + 0.974851i
\(177\) 0 0
\(178\) −2.19824e7 3.02562e7i −0.292150 0.402110i
\(179\) 8.63413e6 2.80540e6i 0.112521 0.0365603i −0.252215 0.967671i \(-0.581159\pi\)
0.364736 + 0.931111i \(0.381159\pi\)
\(180\) 0 0
\(181\) −9.60496e7 6.97842e7i −1.20398 0.874746i −0.209313 0.977849i \(-0.567123\pi\)
−0.994671 + 0.103103i \(0.967123\pi\)
\(182\) −1.23418e8 8.96687e7i −1.51750 1.10253i
\(183\) 0 0
\(184\) 1.89520e8 6.15787e7i 2.24281 0.728733i
\(185\) −2.02797e7 2.79126e7i −0.235484 0.324116i
\(186\) 0 0
\(187\) −6.80325e7 7.28768e7i −0.760800 0.814974i
\(188\) 1.99914e8i 2.19428i
\(189\) 0 0
\(190\) 1.05362e8 + 3.24272e8i 1.11442 + 3.42983i
\(191\) 1.03326e8 + 3.35726e7i 1.07298 + 0.348632i 0.791647 0.610978i \(-0.209224\pi\)
0.281332 + 0.959610i \(0.409224\pi\)
\(192\) 0 0
\(193\) 9.48272e7 1.30518e8i 0.949472 1.30684i −0.00228959 0.999997i \(-0.500729\pi\)
0.951762 0.306839i \(-0.0992712\pi\)
\(194\) 1.50351e7 4.62733e7i 0.147843 0.455013i
\(195\) 0 0
\(196\) 2.26190e8 1.64336e8i 2.14574 1.55897i
\(197\) 6.38266e6 0.0594799 0.0297399 0.999558i \(-0.490532\pi\)
0.0297399 + 0.999558i \(0.490532\pi\)
\(198\) 0 0
\(199\) −5.16750e7 −0.464830 −0.232415 0.972617i \(-0.574663\pi\)
−0.232415 + 0.972617i \(0.574663\pi\)
\(200\) 1.82397e8 1.32519e8i 1.61218 1.17131i
\(201\) 0 0
\(202\) −9.81923e7 + 3.02205e8i −0.838200 + 2.57972i
\(203\) −1.95395e8 + 2.68938e8i −1.63937 + 2.25640i
\(204\) 0 0
\(205\) −1.68952e8 5.48958e7i −1.36970 0.445042i
\(206\) 4.24190e6 + 1.30552e7i 0.0338085 + 0.104052i
\(207\) 0 0
\(208\) 1.22549e8i 0.944255i
\(209\) −1.88510e8 + 2.32497e7i −1.42831 + 0.176159i
\(210\) 0 0
\(211\) 3.11587e7 + 4.28863e7i 0.228344 + 0.314289i 0.907781 0.419446i \(-0.137775\pi\)
−0.679436 + 0.733735i \(0.737775\pi\)
\(212\) −2.67598e8 + 8.69480e7i −1.92889 + 0.626735i
\(213\) 0 0
\(214\) 1.66645e8 + 1.21075e8i 1.16237 + 0.844513i
\(215\) 5.19247e7 + 3.77255e7i 0.356319 + 0.258881i
\(216\) 0 0
\(217\) −4.95460e7 + 1.60985e7i −0.329154 + 0.106949i
\(218\) 1.69713e8 + 2.33590e8i 1.10948 + 1.52706i
\(219\) 0 0
\(220\) 2.00189e8 + 4.28700e8i 1.26754 + 2.71440i
\(221\) 1.26668e8i 0.789395i
\(222\) 0 0
\(223\) 1.95379e7 + 6.01316e7i 0.117981 + 0.363108i 0.992557 0.121780i \(-0.0388603\pi\)
−0.874576 + 0.484888i \(0.838860\pi\)
\(224\) 9.58913e7 + 3.11570e7i 0.570048 + 0.185220i
\(225\) 0 0
\(226\) −2.25397e8 + 3.10232e8i −1.29888 + 1.78775i
\(227\) −7.40744e7 + 2.27978e8i −0.420318 + 1.29361i 0.487089 + 0.873352i \(0.338059\pi\)
−0.907407 + 0.420253i \(0.861941\pi\)
\(228\) 0 0
\(229\) 1.17543e8 8.54002e7i 0.646806 0.469932i −0.215376 0.976531i \(-0.569098\pi\)
0.862182 + 0.506599i \(0.169098\pi\)
\(230\) 5.58615e8 3.02737
\(231\) 0 0
\(232\) −6.89025e8 −3.62266
\(233\) 2.34251e8 1.70194e8i 1.21321 0.881450i 0.217693 0.976017i \(-0.430147\pi\)
0.995518 + 0.0945676i \(0.0301469\pi\)
\(234\) 0 0
\(235\) 9.09998e7 2.80069e8i 0.457407 1.40776i
\(236\) 3.99455e8 5.49803e8i 1.97823 2.72279i
\(237\) 0 0
\(238\) −5.84217e8 1.89824e8i −2.80902 0.912706i
\(239\) 6.80895e7 + 2.09558e8i 0.322617 + 0.992914i 0.972505 + 0.232883i \(0.0748160\pi\)
−0.649888 + 0.760030i \(0.725184\pi\)
\(240\) 0 0
\(241\) 3.74963e8i 1.72556i −0.505582 0.862778i \(-0.668722\pi\)
0.505582 0.862778i \(-0.331278\pi\)
\(242\) −3.76996e8 + 9.44292e7i −1.70995 + 0.428304i
\(243\) 0 0
\(244\) 1.43478e8 + 1.97481e8i 0.632297 + 0.870282i
\(245\) 3.91684e8 1.27266e8i 1.70159 0.552880i
\(246\) 0 0
\(247\) 1.95235e8 + 1.41846e8i 0.824361 + 0.598934i
\(248\) −8.73575e7 6.34690e7i −0.363680 0.264229i
\(249\) 0 0
\(250\) 1.22864e7 3.99210e6i 0.0497319 0.0161589i
\(251\) −1.76197e8 2.42514e8i −0.703299 0.968008i −0.999915 0.0130113i \(-0.995858\pi\)
0.296616 0.954997i \(-0.404142\pi\)
\(252\) 0 0
\(253\) −5.92120e7 + 3.05502e8i −0.229873 + 1.18602i
\(254\) 4.38872e8i 1.68043i
\(255\) 0 0
\(256\) −1.68547e8 5.18734e8i −0.627886 1.93243i
\(257\) −3.44506e8 1.11937e8i −1.26599 0.411346i −0.402366 0.915479i \(-0.631812\pi\)
−0.863626 + 0.504133i \(0.831812\pi\)
\(258\) 0 0
\(259\) 6.96079e7 9.58071e7i 0.248948 0.342648i
\(260\) 1.85762e8 5.71716e8i 0.655465 2.01731i
\(261\) 0 0
\(262\) −5.04000e8 + 3.66177e8i −1.73131 + 1.25787i
\(263\) 2.35460e8 0.798128 0.399064 0.916923i \(-0.369335\pi\)
0.399064 + 0.916923i \(0.369335\pi\)
\(264\) 0 0
\(265\) −4.14469e8 −1.36814
\(266\) −9.46799e8 + 6.87889e8i −3.08441 + 2.24095i
\(267\) 0 0
\(268\) 1.71367e8 5.27414e8i 0.543821 1.67371i
\(269\) −1.64874e8 + 2.26930e8i −0.516440 + 0.710819i −0.984989 0.172619i \(-0.944777\pi\)
0.468548 + 0.883438i \(0.344777\pi\)
\(270\) 0 0
\(271\) 1.78882e8 + 5.81222e7i 0.545976 + 0.177398i 0.569002 0.822336i \(-0.307330\pi\)
−0.0230253 + 0.999735i \(0.507330\pi\)
\(272\) −1.52489e8 4.69314e8i −0.459460 1.41407i
\(273\) 0 0
\(274\) 5.10722e8i 1.49988i
\(275\) 4.30962e7 + 3.49426e8i 0.124961 + 1.01319i
\(276\) 0 0
\(277\) −2.02106e8 2.78175e8i −0.571348 0.786393i 0.421366 0.906891i \(-0.361551\pi\)
−0.992714 + 0.120498i \(0.961551\pi\)
\(278\) −1.01495e8 + 3.29779e7i −0.283328 + 0.0920589i
\(279\) 0 0
\(280\) 1.23932e9 + 9.00417e8i 3.37388 + 2.45127i
\(281\) −2.43673e8 1.77039e8i −0.655142 0.475989i 0.209877 0.977728i \(-0.432694\pi\)
−0.865019 + 0.501739i \(0.832694\pi\)
\(282\) 0 0
\(283\) −6.35365e8 + 2.06443e8i −1.66637 + 0.541436i −0.982192 0.187881i \(-0.939838\pi\)
−0.684176 + 0.729317i \(0.739838\pi\)
\(284\) 5.64909e8 + 7.77530e8i 1.46340 + 2.01420i
\(285\) 0 0
\(286\) 4.32002e8 + 2.39157e8i 1.09195 + 0.604508i
\(287\) 6.09752e8i 1.52253i
\(288\) 0 0
\(289\) 3.08127e7 + 9.48316e7i 0.0750908 + 0.231106i
\(290\) −1.83698e9 5.96872e8i −4.42295 1.43710i
\(291\) 0 0
\(292\) 3.55960e8 4.89937e8i 0.836683 1.15160i
\(293\) 2.60475e7 8.01660e7i 0.0604964 0.186189i −0.916241 0.400627i \(-0.868792\pi\)
0.976737 + 0.214439i \(0.0687922\pi\)
\(294\) 0 0
\(295\) 8.09882e8 5.88414e8i 1.83673 1.33446i
\(296\) 2.45460e8 0.550122
\(297\) 0 0
\(298\) −5.67886e8 −1.24309
\(299\) 3.19865e8 2.32395e8i 0.692017 0.502780i
\(300\) 0 0
\(301\) −6.80762e7 + 2.09517e8i −0.143884 + 0.442829i
\(302\) 9.26867e8 1.27572e9i 1.93639 2.66521i
\(303\) 0 0
\(304\) −8.94118e8 2.90517e8i −1.82531 0.593080i
\(305\) 1.11113e8 + 3.41970e8i 0.224241 + 0.690142i
\(306\) 0 0
\(307\) 9.59911e8i 1.89342i 0.322091 + 0.946709i \(0.395614\pi\)
−0.322091 + 0.946709i \(0.604386\pi\)
\(308\) −1.18711e9 + 1.10820e9i −2.31507 + 2.16118i
\(309\) 0 0
\(310\) −1.77920e8 2.44886e8i −0.339203 0.466873i
\(311\) −4.77925e8 + 1.55287e8i −0.900945 + 0.292735i −0.722627 0.691238i \(-0.757066\pi\)
−0.178318 + 0.983973i \(0.557066\pi\)
\(312\) 0 0
\(313\) 4.30773e8 + 3.12975e8i 0.794042 + 0.576905i 0.909160 0.416446i \(-0.136725\pi\)
−0.115118 + 0.993352i \(0.536725\pi\)
\(314\) 6.08229e8 + 4.41904e8i 1.10870 + 0.805516i
\(315\) 0 0
\(316\) −1.13302e9 + 3.68140e8i −2.01991 + 0.656309i
\(317\) 5.54463e7 + 7.63153e7i 0.0977609 + 0.134556i 0.855095 0.518471i \(-0.173499\pi\)
−0.757334 + 0.653027i \(0.773499\pi\)
\(318\) 0 0
\(319\) 5.21141e8 9.41365e8i 0.898852 1.62364i
\(320\) 5.25443e8i 0.896398i
\(321\) 0 0
\(322\) 5.92504e8 + 1.82354e9i 0.988999 + 3.04383i
\(323\) 9.24169e8 + 3.00281e8i 1.52596 + 0.495814i
\(324\) 0 0
\(325\) 2.62929e8 3.61891e8i 0.424861 0.584771i
\(326\) −4.63432e8 + 1.42630e9i −0.740841 + 2.28007i
\(327\) 0 0
\(328\) 1.02247e9 7.42869e8i 1.59990 1.16240i
\(329\) 1.01078e9 1.56484
\(330\) 0 0
\(331\) −5.87605e8 −0.890610 −0.445305 0.895379i \(-0.646905\pi\)
−0.445305 + 0.895379i \(0.646905\pi\)
\(332\) 3.66586e8 2.66340e8i 0.549784 0.399442i
\(333\) 0 0
\(334\) 2.22341e7 6.84296e7i 0.0326518 0.100492i
\(335\) 4.80152e8 6.60872e8i 0.697785 0.960419i
\(336\) 0 0
\(337\) −6.46480e8 2.10054e8i −0.920133 0.298969i −0.189612 0.981859i \(-0.560723\pi\)
−0.730521 + 0.682890i \(0.760723\pi\)
\(338\) 1.92844e8 + 5.93512e8i 0.271642 + 0.836029i
\(339\) 0 0
\(340\) 2.42058e9i 3.33998i
\(341\) 1.52786e8 7.13458e7i 0.208661 0.0974379i
\(342\) 0 0
\(343\) 1.70708e8 + 2.34959e8i 0.228415 + 0.314386i
\(344\) −4.34269e8 + 1.41103e8i −0.575181 + 0.186888i
\(345\) 0 0
\(346\) 1.71784e6 + 1.24809e6i 0.00222955 + 0.00161986i
\(347\) −8.93278e8 6.49004e8i −1.14771 0.833863i −0.159538 0.987192i \(-0.551001\pi\)
−0.988175 + 0.153329i \(0.951001\pi\)
\(348\) 0 0
\(349\) 3.02642e8 9.83342e7i 0.381100 0.123827i −0.112201 0.993686i \(-0.535790\pi\)
0.493301 + 0.869858i \(0.335790\pi\)
\(350\) 1.27509e9 + 1.75500e9i 1.58965 + 2.18796i
\(351\) 0 0
\(352\) −3.20390e8 6.20976e7i −0.391543 0.0758884i
\(353\) 5.64214e8i 0.682704i 0.939936 + 0.341352i \(0.110885\pi\)
−0.939936 + 0.341352i \(0.889115\pi\)
\(354\) 0 0
\(355\) 4.37479e8 + 1.34642e9i 0.518988 + 1.59728i
\(356\) 4.81074e8 + 1.56310e8i 0.565115 + 0.183617i
\(357\) 0 0
\(358\) −1.06422e8 + 1.46478e8i −0.122586 + 0.168725i
\(359\) −6.52917e6 + 2.00947e7i −0.00744779 + 0.0229219i −0.954711 0.297534i \(-0.903836\pi\)
0.947264 + 0.320456i \(0.103836\pi\)
\(360\) 0 0
\(361\) 7.74577e8 5.62763e8i 0.866541 0.629579i
\(362\) 2.36777e9 2.62337
\(363\) 0 0
\(364\) 2.06334e9 2.24241
\(365\) 7.21697e8 5.24343e8i 0.776837 0.564405i
\(366\) 0 0
\(367\) −2.27020e8 + 6.98695e8i −0.239736 + 0.737831i 0.756722 + 0.653737i \(0.226800\pi\)
−0.996458 + 0.0840939i \(0.973200\pi\)
\(368\) −9.05350e8 + 1.24611e9i −0.946998 + 1.30343i
\(369\) 0 0
\(370\) 6.54411e8 + 2.12631e8i 0.671652 + 0.218233i
\(371\) −4.39613e8 1.35299e9i −0.446953 1.37558i
\(372\) 0 0
\(373\) 1.34792e9i 1.34488i 0.740153 + 0.672439i \(0.234753\pi\)
−0.740153 + 0.672439i \(0.765247\pi\)
\(374\) 1.95197e9 + 3.78329e8i 1.92941 + 0.373955i
\(375\) 0 0
\(376\) 1.23144e9 + 1.69493e9i 1.19469 + 1.64435i
\(377\) −1.30017e9 + 4.22452e8i −1.24970 + 0.406053i
\(378\) 0 0
\(379\) 3.66935e8 + 2.66594e8i 0.346220 + 0.251543i 0.747281 0.664508i \(-0.231359\pi\)
−0.401062 + 0.916051i \(0.631359\pi\)
\(380\) −3.73086e9 2.71063e9i −3.48792 2.53412i
\(381\) 0 0
\(382\) −2.06067e9 + 6.69554e8i −1.89142 + 0.614559i
\(383\) −8.88225e6 1.22254e7i −0.00807844 0.0111190i 0.804959 0.593331i \(-0.202187\pi\)
−0.813037 + 0.582212i \(0.802187\pi\)
\(384\) 0 0
\(385\) −2.16753e9 + 1.01216e9i −1.93576 + 0.903937i
\(386\) 3.21747e9i 2.84747i
\(387\) 0 0
\(388\) 2.03355e8 + 6.25862e8i 0.176744 + 0.543961i
\(389\) −1.53166e8 4.97665e7i −0.131928 0.0428661i 0.242309 0.970199i \(-0.422095\pi\)
−0.374237 + 0.927333i \(0.622095\pi\)
\(390\) 0 0
\(391\) 9.35778e8 1.28799e9i 0.791689 1.08967i
\(392\) −9.05417e8 + 2.78659e9i −0.759185 + 2.33653i
\(393\) 0 0
\(394\) −1.02982e8 + 7.48206e7i −0.0848249 + 0.0616289i
\(395\) −1.75487e9 −1.43270
\(396\) 0 0
\(397\) −1.08749e9 −0.872287 −0.436144 0.899877i \(-0.643656\pi\)
−0.436144 + 0.899877i \(0.643656\pi\)
\(398\) 8.33755e8 6.05759e8i 0.662900 0.481625i
\(399\) 0 0
\(400\) −5.38507e8 + 1.65736e9i −0.420709 + 1.29481i
\(401\) −9.25850e8 + 1.27432e9i −0.717027 + 0.986903i 0.282591 + 0.959241i \(0.408806\pi\)
−0.999617 + 0.0276621i \(0.991194\pi\)
\(402\) 0 0
\(403\) −2.03755e8 6.62041e7i −0.155075 0.0503869i
\(404\) −1.32808e9 4.08743e9i −1.00205 3.08400i
\(405\) 0 0
\(406\) 6.62973e9i 4.91648i
\(407\) −1.85652e8 + 3.35354e8i −0.136496 + 0.246560i
\(408\) 0 0
\(409\) 7.98054e8 + 1.09843e9i 0.576768 + 0.793853i 0.993336 0.115252i \(-0.0367674\pi\)
−0.416569 + 0.909104i \(0.636767\pi\)
\(410\) 3.36949e9 1.09481e9i 2.41446 0.784507i
\(411\) 0 0
\(412\) −1.50205e8 1.09130e8i −0.105814 0.0768785i
\(413\) 2.77983e9 + 2.01966e9i 1.94175 + 1.41076i
\(414\) 0 0
\(415\) 6.34803e8 2.06260e8i 0.435984 0.141660i
\(416\) 2.43720e8 + 3.35452e8i 0.165984 + 0.228457i
\(417\) 0 0
\(418\) 2.76899e9 2.58493e9i 1.85441 1.73114i
\(419\) 2.38608e9i 1.58466i −0.610095 0.792328i \(-0.708869\pi\)
0.610095 0.792328i \(-0.291131\pi\)
\(420\) 0 0
\(421\) −5.10840e7 1.57220e8i −0.0333655 0.102688i 0.932987 0.359911i \(-0.117193\pi\)
−0.966352 + 0.257222i \(0.917193\pi\)
\(422\) −1.00547e9 3.26696e8i −0.651290 0.211617i
\(423\) 0 0
\(424\) 1.73319e9 2.38554e9i 1.10425 1.51987i
\(425\) 5.56606e8 1.71306e9i 0.351712 1.08246i
\(426\) 0 0
\(427\) −9.98471e8 + 7.25432e8i −0.620638 + 0.450920i
\(428\) −2.78602e9 −1.71763
\(429\) 0 0
\(430\) −1.28002e9 −0.776386
\(431\) 7.18280e8 5.21861e8i 0.432139 0.313967i −0.350365 0.936613i \(-0.613942\pi\)
0.782504 + 0.622646i \(0.213942\pi\)
\(432\) 0 0
\(433\) 1.10008e7 3.38571e7i 0.00651205 0.0200420i −0.947748 0.319021i \(-0.896646\pi\)
0.954260 + 0.298979i \(0.0966460\pi\)
\(434\) 6.10692e8 8.40545e8i 0.358598 0.493568i
\(435\) 0 0
\(436\) −3.71408e9 1.20678e9i −2.14609 0.697308i
\(437\) −9.37279e8 2.88465e9i −0.537259 1.65351i
\(438\) 0 0
\(439\) 1.03073e9i 0.581457i 0.956806 + 0.290728i \(0.0938976\pi\)
−0.956806 + 0.290728i \(0.906102\pi\)
\(440\) −4.33799e9 2.40152e9i −2.42775 1.34401i
\(441\) 0 0
\(442\) −1.48487e9 2.04374e9i −0.817917 1.12577i
\(443\) −2.53543e9 + 8.23812e8i −1.38560 + 0.450210i −0.904508 0.426458i \(-0.859761\pi\)
−0.481097 + 0.876668i \(0.659761\pi\)
\(444\) 0 0
\(445\) 6.02806e8 + 4.37964e8i 0.324278 + 0.235602i
\(446\) −1.02013e9 7.41167e8i −0.544481 0.395589i
\(447\) 0 0
\(448\) 1.71526e9 5.57320e8i 0.901272 0.292841i
\(449\) −4.61426e7 6.35099e7i −0.0240569 0.0331115i 0.796819 0.604218i \(-0.206514\pi\)
−0.820876 + 0.571106i \(0.806514\pi\)
\(450\) 0 0
\(451\) 2.41586e8 + 1.95880e9i 0.124009 + 1.00548i
\(452\) 5.18653e9i 2.64176i
\(453\) 0 0
\(454\) −1.47730e9 4.54667e9i −0.740924 2.28033i
\(455\) 2.89062e9 + 9.39220e8i 1.43864 + 0.467442i
\(456\) 0 0
\(457\) 2.59483e8 3.57148e8i 0.127175 0.175042i −0.740681 0.671857i \(-0.765497\pi\)
0.867857 + 0.496815i \(0.165497\pi\)
\(458\) −8.95413e8 + 2.75580e9i −0.435506 + 1.34035i
\(459\) 0 0
\(460\) −6.11249e9 + 4.44099e9i −2.92797 + 2.12729i
\(461\) −2.55192e9 −1.21315 −0.606573 0.795028i \(-0.707456\pi\)
−0.606573 + 0.795028i \(0.707456\pi\)
\(462\) 0 0
\(463\) 1.31061e9 0.613677 0.306839 0.951762i \(-0.400729\pi\)
0.306839 + 0.951762i \(0.400729\pi\)
\(464\) 4.30866e9 3.13042e9i 2.00230 1.45476i
\(465\) 0 0
\(466\) −1.78446e9 + 5.49202e9i −0.816878 + 2.51409i
\(467\) −1.50667e9 + 2.07375e9i −0.684556 + 0.942211i −0.999977 0.00674094i \(-0.997854\pi\)
0.315421 + 0.948952i \(0.397854\pi\)
\(468\) 0 0
\(469\) 2.66663e9 + 8.66441e8i 1.19360 + 0.387823i
\(470\) 1.81485e9 + 5.58554e9i 0.806305 + 2.48155i
\(471\) 0 0
\(472\) 7.12198e9i 3.11748i
\(473\) 1.35679e8 7.00033e8i 0.0589522 0.304162i
\(474\) 0 0
\(475\) −2.01705e9 2.77623e9i −0.863553 1.18858i
\(476\) 7.90174e9 2.56743e9i 3.35814 1.09112i
\(477\) 0 0
\(478\) −3.55514e9 2.58296e9i −1.48888 1.08173i
\(479\) 2.11291e9 + 1.53512e9i 0.878429 + 0.638216i 0.932835 0.360303i \(-0.117327\pi\)
−0.0544061 + 0.998519i \(0.517327\pi\)
\(480\) 0 0
\(481\) 4.63176e8 1.50495e8i 0.189775 0.0616616i
\(482\) 4.39550e9 + 6.04989e9i 1.78790 + 2.46084i
\(483\) 0 0
\(484\) 3.37446e9 4.03038e9i 1.35284 1.61580i
\(485\) 9.69364e8i 0.385825i
\(486\) 0 0
\(487\) −3.85262e8 1.18571e9i −0.151149 0.465188i 0.846602 0.532227i \(-0.178645\pi\)
−0.997750 + 0.0670390i \(0.978645\pi\)
\(488\) −2.43290e9 7.90498e8i −0.947666 0.307915i
\(489\) 0 0
\(490\) −4.82780e9 + 6.64490e9i −1.85380 + 2.55154i
\(491\) −8.17925e8 + 2.51731e9i −0.311837 + 0.959737i 0.665199 + 0.746666i \(0.268347\pi\)
−0.977037 + 0.213071i \(0.931653\pi\)
\(492\) 0 0
\(493\) −4.45347e9 + 3.23564e9i −1.67392 + 1.21617i
\(494\) −4.81283e9 −1.79621
\(495\) 0 0
\(496\) 8.34626e8 0.307119
\(497\) −3.93123e9 + 2.85621e9i −1.43642 + 1.04362i
\(498\) 0 0
\(499\) −5.06137e8 + 1.55773e9i −0.182354 + 0.561229i −0.999893 0.0146449i \(-0.995338\pi\)
0.817538 + 0.575874i \(0.195338\pi\)
\(500\) −1.02704e8 + 1.41359e8i −0.0367443 + 0.0505742i
\(501\) 0 0
\(502\) 5.68573e9 + 1.84741e9i 2.00597 + 0.651778i
\(503\) 1.47633e8 + 4.54368e8i 0.0517245 + 0.159192i 0.973582 0.228337i \(-0.0733288\pi\)
−0.921858 + 0.387529i \(0.873329\pi\)
\(504\) 0 0
\(505\) 6.33079e9i 2.18745i
\(506\) −2.62588e9 5.62327e9i −0.901049 1.92958i
\(507\) 0 0
\(508\) 3.48903e9 + 4.80224e9i 1.18081 + 1.62525i
\(509\) 2.13018e9 6.92138e8i 0.715985 0.232638i 0.0717036 0.997426i \(-0.477156\pi\)
0.644282 + 0.764788i \(0.277156\pi\)
\(510\) 0 0
\(511\) 2.47714e9 + 1.79975e9i 0.821255 + 0.596677i
\(512\) 5.08931e9 + 3.69760e9i 1.67577 + 1.21752i
\(513\) 0 0
\(514\) 6.87065e9 2.23241e9i 2.23165 0.725108i
\(515\) −1.60753e8 2.21258e8i −0.0518603 0.0713795i
\(516\) 0 0
\(517\) −3.24706e9 + 4.00473e8i −1.03341 + 0.127455i
\(518\) 2.36179e9i 0.746598i
\(519\) 0 0
\(520\) 1.94674e9 + 5.99145e9i 0.607150 + 1.86862i
\(521\) −2.53294e8 8.23003e7i −0.0784681 0.0254958i 0.269520 0.962995i \(-0.413135\pi\)
−0.347988 + 0.937499i \(0.613135\pi\)
\(522\) 0 0
\(523\) −1.93002e9 + 2.65644e9i −0.589936 + 0.811978i −0.994741 0.102426i \(-0.967340\pi\)
0.404804 + 0.914403i \(0.367340\pi\)
\(524\) 2.60377e9 8.01359e9i 0.790576 2.43314i
\(525\) 0 0
\(526\) −3.79906e9 + 2.76018e9i −1.13822 + 0.826965i
\(527\) −8.62678e8 −0.256751
\(528\) 0 0
\(529\) −1.56448e9 −0.459488
\(530\) 6.68729e9 4.85860e9i 1.95112 1.41757i
\(531\) 0 0
\(532\) 4.89137e9 1.50541e10i 1.40845 4.33475i
\(533\) 1.47392e9 2.02867e9i 0.421626 0.580318i
\(534\) 0 0
\(535\) −3.90306e9 1.26818e9i −1.10196 0.358049i
\(536\) 1.79589e9 + 5.52717e9i 0.503735 + 1.55034i
\(537\) 0 0
\(538\) 5.59417e9i 1.54881i
\(539\) −3.12231e9 3.34463e9i −0.858845 0.919999i
\(540\) 0 0
\(541\) 1.12819e9 + 1.55282e9i 0.306332 + 0.421630i 0.934233 0.356664i \(-0.116086\pi\)
−0.627901 + 0.778293i \(0.716086\pi\)
\(542\) −3.56753e9 + 1.15916e9i −0.962431 + 0.312713i
\(543\) 0 0
\(544\) 1.35076e9 + 9.81382e8i 0.359733 + 0.261362i
\(545\) −4.65390e9 3.38126e9i −1.23149 0.894727i
\(546\) 0 0
\(547\) 8.70977e8 2.82998e8i 0.227537 0.0739311i −0.193030 0.981193i \(-0.561831\pi\)
0.420566 + 0.907262i \(0.361831\pi\)
\(548\) 4.06024e9 + 5.58844e9i 1.05395 + 1.45064i
\(549\) 0 0
\(550\) −4.79148e9 5.13266e9i −1.22801 1.31545i
\(551\) 1.04875e10i 2.67081i
\(552\) 0 0
\(553\) −1.86133e9 5.72860e9i −0.468044 1.44049i
\(554\) 6.52181e9 + 2.11907e9i 1.62961 + 0.529493i
\(555\) 0 0
\(556\) 8.48413e8 1.16774e9i 0.209337 0.288127i
\(557\) 5.40993e8 1.66500e9i 0.132647 0.408246i −0.862569 0.505939i \(-0.831146\pi\)
0.995217 + 0.0976924i \(0.0311461\pi\)
\(558\) 0 0
\(559\) −7.32944e8 + 5.32515e8i −0.177472 + 0.128941i
\(560\) −1.18406e10 −2.84916
\(561\) 0 0
\(562\) 6.00691e9 1.42749
\(563\) −2.96091e9 + 2.15122e9i −0.699271 + 0.508050i −0.879695 0.475539i \(-0.842253\pi\)
0.180424 + 0.983589i \(0.442253\pi\)
\(564\) 0 0
\(565\) 2.36088e9 7.26605e9i 0.550687 1.69484i
\(566\) 7.83135e9 1.07789e10i 1.81543 2.49872i
\(567\) 0 0
\(568\) −9.57894e9 3.11239e9i −2.19330 0.712647i
\(569\) −2.21700e9 6.82324e9i −0.504514 1.55274i −0.801585 0.597880i \(-0.796010\pi\)
0.297071 0.954855i \(-0.403990\pi\)
\(570\) 0 0
\(571\) 4.09294e9i 0.920046i 0.887907 + 0.460023i \(0.152159\pi\)
−0.887907 + 0.460023i \(0.847841\pi\)
\(572\) −6.62836e9 + 8.17503e8i −1.48088 + 0.182643i
\(573\) 0 0
\(574\) 7.14781e9 + 9.83812e9i 1.57754 + 2.17130i
\(575\) −5.34704e9 + 1.73736e9i −1.17294 + 0.381111i
\(576\) 0 0
\(577\) −3.74087e9 2.71790e9i −0.810694 0.589003i 0.103338 0.994646i \(-0.467048\pi\)
−0.914032 + 0.405643i \(0.867048\pi\)
\(578\) −1.60881e9 1.16887e9i −0.346544 0.251779i
\(579\) 0 0
\(580\) 2.48458e10 8.07290e9i 5.28757 1.71803i
\(581\) 1.34663e9 + 1.85348e9i 0.284860 + 0.392076i
\(582\) 0 0
\(583\) 1.94829e9 + 4.17223e9i 0.407206 + 0.872024i
\(584\) 6.34649e9i 1.31853i
\(585\) 0 0
\(586\) 5.19478e8 + 1.59879e9i 0.106641 + 0.328208i
\(587\) 3.02266e9 + 9.82120e8i 0.616816 + 0.200416i 0.600726 0.799455i \(-0.294878\pi\)
0.0160897 + 0.999871i \(0.494878\pi\)
\(588\) 0 0
\(589\) −9.66049e8 + 1.32965e9i −0.194803 + 0.268123i
\(590\) −6.16946e9 + 1.89877e10i −1.23670 + 3.80618i
\(591\) 0 0
\(592\) −1.53492e9 + 1.11519e9i −0.304061 + 0.220913i
\(593\) −6.05663e9 −1.19272 −0.596362 0.802716i \(-0.703388\pi\)
−0.596362 + 0.802716i \(0.703388\pi\)
\(594\) 0 0
\(595\) 1.22386e10 2.38189
\(596\) 6.21394e9 4.51469e9i 1.20228 0.873507i
\(597\) 0 0
\(598\) −2.43664e9 + 7.49921e9i −0.465948 + 1.43404i
\(599\) −3.03706e9 + 4.18015e9i −0.577377 + 0.794691i −0.993405 0.114661i \(-0.963422\pi\)
0.416028 + 0.909352i \(0.363422\pi\)
\(600\) 0 0
\(601\) 2.53607e9 + 8.24018e8i 0.476541 + 0.154838i 0.537432 0.843307i \(-0.319394\pi\)
−0.0608914 + 0.998144i \(0.519394\pi\)
\(602\) −1.35768e9 4.17850e9i −0.253634 0.780607i
\(603\) 0 0
\(604\) 2.13278e10i 3.93838i
\(605\) 6.56204e9 4.11030e9i 1.20475 0.754623i
\(606\) 0 0
\(607\) −2.03621e9 2.80261e9i −0.369541 0.508630i 0.583235 0.812303i \(-0.301787\pi\)
−0.952776 + 0.303674i \(0.901787\pi\)
\(608\) 3.02522e9 9.82955e8i 0.545877 0.177366i
\(609\) 0 0
\(610\) −5.80150e9 4.21503e9i −1.03487 0.751877i
\(611\) 3.36289e9 + 2.44328e9i 0.596442 + 0.433341i
\(612\) 0 0
\(613\) −6.19578e9 + 2.01313e9i −1.08639 + 0.352988i −0.796849 0.604178i \(-0.793502\pi\)
−0.289538 + 0.957167i \(0.593502\pi\)
\(614\) −1.12525e10 1.54878e10i −1.96183 2.70023i
\(615\) 0 0
\(616\) 3.23835e9 1.67081e10i 0.558201 2.88002i
\(617\) 1.53248e9i 0.262662i −0.991339 0.131331i \(-0.958075\pi\)
0.991339 0.131331i \(-0.0419251\pi\)
\(618\) 0 0
\(619\) 1.92493e9 + 5.92433e9i 0.326210 + 1.00397i 0.970891 + 0.239520i \(0.0769902\pi\)
−0.644681 + 0.764452i \(0.723010\pi\)
\(620\) 3.89369e9 + 1.26514e9i 0.656131 + 0.213190i
\(621\) 0 0
\(622\) 5.89078e9 8.10796e9i 0.981537 1.35097i
\(623\) −7.90313e8 + 2.43233e9i −0.130946 + 0.403009i
\(624\) 0 0
\(625\) 4.83266e9 3.51113e9i 0.791783 0.575264i
\(626\) −1.06192e10 −1.73014
\(627\) 0 0
\(628\) −1.01685e10 −1.63832
\(629\) 1.58651e9 1.15267e9i 0.254195 0.184683i
\(630\) 0 0
\(631\) 2.22013e9 6.83285e9i 0.351783 1.08268i −0.606068 0.795413i \(-0.707254\pi\)
0.957851 0.287265i \(-0.0927459\pi\)
\(632\) 7.33839e9 1.01004e10i 1.15636 1.59159i
\(633\) 0 0
\(634\) −1.78921e9 5.81349e8i −0.278836 0.0905993i
\(635\) 2.70199e9 + 8.31586e9i 0.418770 + 1.28884i
\(636\) 0 0
\(637\) 5.81335e9i 0.891125i
\(638\) 2.62672e9 + 2.12976e10i 0.400444 + 3.24683i
\(639\) 0 0
\(640\) 8.36957e9 + 1.15197e10i 1.26204 + 1.73705i
\(641\) 6.39156e9 2.07674e9i 0.958526 0.311444i 0.212351 0.977194i \(-0.431888\pi\)
0.746175 + 0.665750i \(0.231888\pi\)
\(642\) 0 0
\(643\) −1.03739e8 7.53707e7i −0.0153887 0.0111806i 0.580064 0.814571i \(-0.303027\pi\)
−0.595453 + 0.803390i \(0.703027\pi\)
\(644\) −2.09805e10 1.52432e10i −3.09538 2.24893i
\(645\) 0 0
\(646\) −1.84312e10 + 5.98864e9i −2.68992 + 0.874006i
\(647\) −1.49228e9 2.05395e9i −0.216614 0.298143i 0.686857 0.726792i \(-0.258990\pi\)
−0.903471 + 0.428649i \(0.858990\pi\)
\(648\) 0 0
\(649\) −9.73025e9 5.38668e9i −1.39723 0.773508i
\(650\) 8.92115e9i 1.27416i
\(651\) 0 0
\(652\) −6.26808e9 1.92912e10i −0.885662 2.72579i
\(653\) 6.69399e9 + 2.17501e9i 0.940781 + 0.305678i 0.738964 0.673745i \(-0.235315\pi\)
0.201817 + 0.979423i \(0.435315\pi\)
\(654\) 0 0
\(655\) 7.29549e9 1.00414e10i 1.01440 1.39620i
\(656\) −3.01874e9 + 9.29072e9i −0.417505 + 1.28495i
\(657\) 0 0
\(658\) −1.63085e10 + 1.18488e10i −2.23163 + 1.62138i
\(659\) 3.04568e9 0.414558 0.207279 0.978282i \(-0.433539\pi\)
0.207279 + 0.978282i \(0.433539\pi\)
\(660\) 0 0
\(661\) −1.20808e10 −1.62701 −0.813504 0.581560i \(-0.802443\pi\)
−0.813504 + 0.581560i \(0.802443\pi\)
\(662\) 9.48078e9 6.88819e9i 1.27011 0.922789i
\(663\) 0 0
\(664\) −1.46741e9 + 4.51623e9i −0.194520 + 0.598670i
\(665\) 1.37051e10 1.88634e10i 1.80720 2.48740i
\(666\) 0 0
\(667\) 1.63414e10 + 5.30963e9i 2.13230 + 0.692826i
\(668\) 3.00724e8 + 9.25534e8i 0.0390347 + 0.120136i
\(669\) 0 0
\(670\) 1.62915e10i 2.09266i
\(671\) 2.92012e9 2.72601e9i 0.373139 0.348336i
\(672\) 0 0
\(673\) 9.77881e8 + 1.34594e9i 0.123661 + 0.170205i 0.866359 0.499422i \(-0.166454\pi\)
−0.742698 + 0.669627i \(0.766454\pi\)
\(674\) 1.28931e10 4.18921e9i 1.62198 0.527015i
\(675\) 0 0
\(676\) −6.82856e9 4.96124e9i −0.850190 0.617699i
\(677\) 4.94961e9 + 3.59610e9i 0.613071 + 0.445422i 0.850494 0.525984i \(-0.176303\pi\)
−0.237423 + 0.971406i \(0.576303\pi\)
\(678\) 0 0
\(679\) −3.16439e9 + 1.02817e9i −0.387923 + 0.126044i
\(680\) 1.49104e10 + 2.05224e10i 1.81848 + 2.50292i
\(681\) 0 0
\(682\) −1.62879e9 + 2.94216e9i −0.196616 + 0.355158i
\(683\) 1.02138e10i 1.22664i −0.789836 0.613318i \(-0.789834\pi\)
0.789836 0.613318i \(-0.210166\pi\)
\(684\) 0 0
\(685\) 3.14434e9 + 9.67729e9i 0.373777 + 1.15037i
\(686\) −5.50861e9 1.78986e9i −0.651490 0.211682i
\(687\) 0 0
\(688\) 2.07454e9 2.85535e9i 0.242863 0.334272i
\(689\) 1.80789e9 5.56410e9i 0.210573 0.648078i
\(690\) 0 0
\(691\) −2.49364e9 + 1.81174e9i −0.287515 + 0.208892i −0.722189 0.691696i \(-0.756864\pi\)
0.434674 + 0.900588i \(0.356864\pi\)
\(692\) −2.87193e7 −0.00329460
\(693\) 0 0
\(694\) 2.20206e10 2.50076
\(695\) 1.72013e9 1.24975e9i 0.194363 0.141213i
\(696\) 0 0
\(697\) 3.12020e9 9.60298e9i 0.349034 1.07422i
\(698\) −3.73028e9 + 5.13429e9i −0.415191 + 0.571461i
\(699\) 0 0
\(700\) −2.79046e10 9.06674e9i −3.07491 0.999098i
\(701\) 2.55707e9 + 7.86985e9i 0.280369 + 0.862886i 0.987749 + 0.156052i \(0.0498769\pi\)
−0.707380 + 0.706833i \(0.750123\pi\)
\(702\) 0 0
\(703\) 3.73609e9i 0.405578i
\(704\) −5.28935e9 + 2.46995e9i −0.571345 + 0.266799i
\(705\) 0 0
\(706\) −6.61399e9 9.10338e9i −0.707371 0.973612i
\(707\) 2.06662e10 6.71486e9i 2.19934 0.714610i
\(708\) 0 0
\(709\) 7.20373e9 + 5.23382e9i 0.759094 + 0.551514i 0.898632 0.438703i \(-0.144562\pi\)
−0.139538 + 0.990217i \(0.544562\pi\)
\(710\) −2.28419e10 1.65956e10i −2.39513 1.74016i
\(711\) 0 0
\(712\) −5.04154e9 + 1.63810e9i −0.523460 + 0.170082i
\(713\) 1.58274e9 + 2.17845e9i 0.163529 + 0.225078i
\(714\) 0 0
\(715\) −9.65809e9 1.87192e9i −0.988144 0.191521i
\(716\) 2.44885e9i 0.249325i
\(717\) 0 0
\(718\) −1.30214e8 4.00759e8i −0.0131287 0.0404061i
\(719\) −1.10622e10 3.59434e9i −1.10992 0.360635i −0.304008 0.952670i \(-0.598325\pi\)
−0.805912 + 0.592035i \(0.798325\pi\)
\(720\) 0 0
\(721\) 5.51768e8 7.59444e8i 0.0548256 0.0754609i
\(722\) −5.90052e9 + 1.81599e10i −0.583458 + 1.79570i
\(723\) 0 0
\(724\) −2.59087e10 + 1.88237e10i −2.53723 + 1.84341i
\(725\) 1.94399e10 1.89457
\(726\) 0 0
\(727\) 4.00323e9 0.386403 0.193201 0.981159i \(-0.438113\pi\)
0.193201 + 0.981159i \(0.438113\pi\)
\(728\) −1.74936e10 + 1.27099e10i −1.68043 + 1.22090i
\(729\) 0 0
\(730\) −5.49769e9 + 1.69202e10i −0.523059 + 1.60981i
\(731\) −2.14426e9 + 2.95132e9i −0.203033 + 0.279451i
\(732\) 0 0
\(733\) −7.55070e9 2.45337e9i −0.708147 0.230091i −0.0672701 0.997735i \(-0.521429\pi\)
−0.640876 + 0.767644i \(0.721429\pi\)
\(734\) −4.52757e9 1.39344e10i −0.422599 1.30063i
\(735\) 0 0
\(736\) 5.21147e9i 0.481824i
\(737\) −8.90969e9 1.72686e9i −0.819835 0.158899i
\(738\) 0 0
\(739\) 4.03855e9 + 5.55859e9i 0.368104 + 0.506651i 0.952384 0.304901i \(-0.0986232\pi\)
−0.584281 + 0.811552i \(0.698623\pi\)
\(740\) −8.85113e9 + 2.87591e9i −0.802949 + 0.260894i
\(741\) 0 0
\(742\) 2.29534e10 + 1.66766e10i 2.06269 + 1.49863i
\(743\) −5.85788e9 4.25600e9i −0.523938 0.380663i 0.294147 0.955760i \(-0.404964\pi\)
−0.818085 + 0.575097i \(0.804964\pi\)
\(744\) 0 0
\(745\) 1.07605e10 3.49628e9i 0.953418 0.309784i
\(746\) −1.58009e10 2.17481e10i −1.39347 1.91795i
\(747\) 0 0
\(748\) −2.43667e10 + 1.13784e10i −2.12883 + 0.994092i
\(749\) 1.40862e10i 1.22492i
\(750\) 0 0
\(751\) 4.18520e9 + 1.28807e10i 0.360559 + 1.10969i 0.952715 + 0.303864i \(0.0982768\pi\)
−0.592156 + 0.805823i \(0.701723\pi\)
\(752\) −1.54011e10 5.00411e9i −1.32065 0.429106i
\(753\) 0 0
\(754\) 1.60256e10 2.20574e10i 1.36149 1.87393i
\(755\) −9.70832e9 + 2.98791e10i −0.820975 + 2.52670i
\(756\) 0 0
\(757\) −6.52660e9 + 4.74185e9i −0.546829 + 0.397295i −0.826615 0.562768i \(-0.809736\pi\)
0.279786 + 0.960062i \(0.409736\pi\)
\(758\) −9.04549e9 −0.754379
\(759\) 0 0
\(760\) 4.83285e10 3.99352
\(761\) −1.10669e10 + 8.04058e9i −0.910290 + 0.661364i −0.941088 0.338161i \(-0.890195\pi\)
0.0307981 + 0.999526i \(0.490195\pi\)
\(762\) 0 0
\(763\) 6.10153e9 1.87786e10i 0.497282 1.53048i
\(764\) 1.72254e10 2.37088e10i 1.39747 1.92346i
\(765\) 0 0
\(766\) 2.86623e8 + 9.31296e7i 0.0230415 + 0.00748664i
\(767\) 4.36660e9 + 1.34390e10i 0.349429 + 1.07543i
\(768\) 0 0
\(769\) 7.57152e9i 0.600401i −0.953876 0.300200i \(-0.902946\pi\)
0.953876 0.300200i \(-0.0970535\pi\)
\(770\) 2.31072e10 4.17397e10i 1.82402 3.29482i
\(771\) 0 0
\(772\) −2.55789e10 3.52063e10i −2.00088 2.75398i
\(773\) −1.53865e10 + 4.99938e9i −1.19815 + 0.389303i −0.839080 0.544007i \(-0.816906\pi\)
−0.359071 + 0.933310i \(0.616906\pi\)