Properties

Label 99.8.j.a.8.12
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 8.12
Character \(\chi\) \(=\) 99.8
Dual form 99.8.j.a.62.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.02244 + 2.92248i) q^{2} +(-31.9150 + 98.2243i) q^{4} +(-62.7155 + 86.3205i) q^{5} +(522.505 + 169.772i) q^{7} +(-355.346 - 1093.64i) q^{8} +O(q^{10})\) \(q+(-4.02244 + 2.92248i) q^{2} +(-31.9150 + 98.2243i) q^{4} +(-62.7155 + 86.3205i) q^{5} +(522.505 + 169.772i) q^{7} +(-355.346 - 1093.64i) q^{8} -530.504i q^{10} +(2359.01 + 3731.25i) q^{11} +(7244.34 + 9970.97i) q^{13} +(-2597.90 + 844.109i) q^{14} +(-6069.49 - 4409.74i) q^{16} +(13260.5 + 9634.35i) q^{17} +(5470.54 - 1777.49i) q^{19} +(-6477.21 - 8915.11i) q^{20} +(-20393.5 - 8114.61i) q^{22} -67520.8i q^{23} +(20624.0 + 63474.0i) q^{25} +(-58279.8 - 18936.3i) q^{26} +(-33351.5 + 45904.4i) q^{28} +(4970.94 - 15299.0i) q^{29} +(-209670. + 152334. i) q^{31} +184492. q^{32} -81495.9 q^{34} +(-47424.0 + 34455.6i) q^{35} +(32368.4 - 99619.6i) q^{37} +(-16810.3 + 23137.3i) q^{38} +(116689. + 37914.7i) q^{40} +(-202479. - 623167. i) q^{41} +990652. i q^{43} +(-441787. + 112629. i) q^{44} +(197328. + 271598. i) q^{46} +(-997288. + 324038. i) q^{47} +(-422071. - 306653. i) q^{49} +(-268460. - 195048. i) q^{50} +(-1.21059e6 + 393346. i) q^{52} +(275492. + 379182. i) q^{53} +(-470030. - 30376.8i) q^{55} -631761. i q^{56} +(24715.6 + 76066.7i) q^{58} +(-1.50482e6 - 488946. i) q^{59} +(-1.25749e6 + 1.73079e6i) q^{61} +(398193. - 1.22551e6i) q^{62} +(34787.6 - 25274.7i) q^{64} -1.31503e6 q^{65} -301833. q^{67} +(-1.36954e6 + 995027. i) q^{68} +(90064.8 - 277191. i) q^{70} +(2.46871e6 - 3.39788e6i) q^{71} +(-2.18986e6 - 711530. i) q^{73} +(160936. + 495310. i) q^{74} +594068. i q^{76} +(599131. + 2.35009e6i) q^{77} +(1.39018e6 + 1.91342e6i) q^{79} +(761302. - 247362. i) q^{80} +(2.63565e6 + 1.91491e6i) q^{82} +(399457. + 290223. i) q^{83} +(-1.66328e6 + 540434. i) q^{85} +(-2.89516e6 - 3.98484e6i) q^{86} +(3.24239e6 - 3.90579e6i) q^{88} +8.78877e6i q^{89} +(2.09241e6 + 6.43977e6i) q^{91} +(6.63218e6 + 2.15492e6i) q^{92} +(3.06454e6 - 4.21797e6i) q^{94} +(-189654. + 583696. i) q^{95} +(1.01865e7 - 7.40089e6i) q^{97} +2.59394e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 112 q - 1792 q^{4}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.02244 + 2.92248i −0.355537 + 0.258313i −0.751188 0.660088i \(-0.770519\pi\)
0.395651 + 0.918401i \(0.370519\pi\)
\(3\) 0 0
\(4\) −31.9150 + 98.2243i −0.249336 + 0.767377i
\(5\) −62.7155 + 86.3205i −0.224378 + 0.308830i −0.906333 0.422564i \(-0.861130\pi\)
0.681955 + 0.731394i \(0.261130\pi\)
\(6\) 0 0
\(7\) 522.505 + 169.772i 0.575768 + 0.187078i 0.582404 0.812900i \(-0.302112\pi\)
−0.00663590 + 0.999978i \(0.502112\pi\)
\(8\) −355.346 1093.64i −0.245378 0.755196i
\(9\) 0 0
\(10\) 530.504i 0.167760i
\(11\) 2359.01 + 3731.25i 0.534386 + 0.845241i
\(12\) 0 0
\(13\) 7244.34 + 9970.97i 0.914528 + 1.25874i 0.965597 + 0.260044i \(0.0837372\pi\)
−0.0510690 + 0.998695i \(0.516263\pi\)
\(14\) −2597.90 + 844.109i −0.253031 + 0.0822149i
\(15\) 0 0
\(16\) −6069.49 4409.74i −0.370452 0.269149i
\(17\) 13260.5 + 9634.35i 0.654621 + 0.475610i 0.864842 0.502044i \(-0.167418\pi\)
−0.210221 + 0.977654i \(0.567418\pi\)
\(18\) 0 0
\(19\) 5470.54 1777.49i 0.182975 0.0594523i −0.216096 0.976372i \(-0.569333\pi\)
0.399072 + 0.916920i \(0.369333\pi\)
\(20\) −6477.21 8915.11i −0.181043 0.249185i
\(21\) 0 0
\(22\) −20393.5 8114.61i −0.408330 0.162476i
\(23\) 67520.8i 1.15715i −0.815629 0.578575i \(-0.803609\pi\)
0.815629 0.578575i \(-0.196391\pi\)
\(24\) 0 0
\(25\) 20624.0 + 63474.0i 0.263987 + 0.812467i
\(26\) −58279.8 18936.3i −0.650297 0.211294i
\(27\) 0 0
\(28\) −33351.5 + 45904.4i −0.287119 + 0.395186i
\(29\) 4970.94 15299.0i 0.0378482 0.116485i −0.930347 0.366679i \(-0.880495\pi\)
0.968196 + 0.250195i \(0.0804946\pi\)
\(30\) 0 0
\(31\) −209670. + 152334.i −1.26407 + 0.918401i −0.998950 0.0458148i \(-0.985412\pi\)
−0.265120 + 0.964215i \(0.585412\pi\)
\(32\) 184492. 0.995295
\(33\) 0 0
\(34\) −81495.9 −0.355598
\(35\) −47424.0 + 34455.6i −0.186965 + 0.135838i
\(36\) 0 0
\(37\) 32368.4 99619.6i 0.105055 0.323325i −0.884689 0.466182i \(-0.845629\pi\)
0.989743 + 0.142858i \(0.0456291\pi\)
\(38\) −16810.3 + 23137.3i −0.0496972 + 0.0684023i
\(39\) 0 0
\(40\) 116689. + 37914.7i 0.288285 + 0.0936693i
\(41\) −202479. 623167.i −0.458815 1.41209i −0.866598 0.499007i \(-0.833698\pi\)
0.407783 0.913079i \(-0.366302\pi\)
\(42\) 0 0
\(43\) 990652.i 1.90012i 0.312065 + 0.950061i \(0.398979\pi\)
−0.312065 + 0.950061i \(0.601021\pi\)
\(44\) −441787. + 112629.i −0.781860 + 0.199327i
\(45\) 0 0
\(46\) 197328. + 271598.i 0.298907 + 0.411410i
\(47\) −997288. + 324038.i −1.40113 + 0.455254i −0.909556 0.415582i \(-0.863578\pi\)
−0.491573 + 0.870837i \(0.663578\pi\)
\(48\) 0 0
\(49\) −422071. 306653.i −0.512507 0.372358i
\(50\) −268460. 195048.i −0.303728 0.220671i
\(51\) 0 0
\(52\) −1.21059e6 + 393346.i −1.19395 + 0.387939i
\(53\) 275492. + 379182.i 0.254181 + 0.349850i 0.916970 0.398956i \(-0.130627\pi\)
−0.662789 + 0.748806i \(0.730627\pi\)
\(54\) 0 0
\(55\) −470030. 30376.8i −0.380940 0.0246191i
\(56\) 631761.i 0.480723i
\(57\) 0 0
\(58\) 24715.6 + 76066.7i 0.0166331 + 0.0511913i
\(59\) −1.50482e6 488946.i −0.953900 0.309941i −0.209601 0.977787i \(-0.567216\pi\)
−0.744299 + 0.667846i \(0.767216\pi\)
\(60\) 0 0
\(61\) −1.25749e6 + 1.73079e6i −0.709333 + 0.976313i 0.290478 + 0.956882i \(0.406186\pi\)
−0.999811 + 0.0194312i \(0.993814\pi\)
\(62\) 398193. 1.22551e6i 0.212189 0.653051i
\(63\) 0 0
\(64\) 34787.6 25274.7i 0.0165880 0.0120519i
\(65\) −1.31503e6 −0.593936
\(66\) 0 0
\(67\) −301833. −0.122604 −0.0613021 0.998119i \(-0.519525\pi\)
−0.0613021 + 0.998119i \(0.519525\pi\)
\(68\) −1.36954e6 + 995027.i −0.528193 + 0.383755i
\(69\) 0 0
\(70\) 90064.8 277191.i 0.0313843 0.0965909i
\(71\) 2.46871e6 3.39788e6i 0.818587 1.12669i −0.171354 0.985210i \(-0.554814\pi\)
0.989941 0.141479i \(-0.0451858\pi\)
\(72\) 0 0
\(73\) −2.18986e6 711530.i −0.658851 0.214074i −0.0395381 0.999218i \(-0.512589\pi\)
−0.619313 + 0.785145i \(0.712589\pi\)
\(74\) 160936. + 495310.i 0.0461681 + 0.142091i
\(75\) 0 0
\(76\) 594068.i 0.155235i
\(77\) 599131. + 2.35009e6i 0.149556 + 0.586634i
\(78\) 0 0
\(79\) 1.39018e6 + 1.91342e6i 0.317232 + 0.436632i 0.937619 0.347663i \(-0.113025\pi\)
−0.620388 + 0.784295i \(0.713025\pi\)
\(80\) 761302. 247362.i 0.166243 0.0540155i
\(81\) 0 0
\(82\) 2.63565e6 + 1.91491e6i 0.527885 + 0.383531i
\(83\) 399457. + 290223.i 0.0766826 + 0.0557132i 0.625466 0.780251i \(-0.284909\pi\)
−0.548783 + 0.835965i \(0.684909\pi\)
\(84\) 0 0
\(85\) −1.66328e6 + 540434.i −0.293765 + 0.0954501i
\(86\) −2.89516e6 3.98484e6i −0.490826 0.675564i
\(87\) 0 0
\(88\) 3.24239e6 3.90579e6i 0.507196 0.610970i
\(89\) 8.78877e6i 1.32149i 0.750612 + 0.660743i \(0.229759\pi\)
−0.750612 + 0.660743i \(0.770241\pi\)
\(90\) 0 0
\(91\) 2.09241e6 + 6.43977e6i 0.291073 + 0.895830i
\(92\) 6.63218e6 + 2.15492e6i 0.887971 + 0.288519i
\(93\) 0 0
\(94\) 3.06454e6 4.21797e6i 0.380555 0.523789i
\(95\) −189654. + 583696.i −0.0226950 + 0.0698480i
\(96\) 0 0
\(97\) 1.01865e7 7.40089e6i 1.13324 0.823347i 0.147077 0.989125i \(-0.453013\pi\)
0.986163 + 0.165778i \(0.0530135\pi\)
\(98\) 2.59394e6 0.278400
\(99\) 0 0
\(100\) −6.89290e6 −0.689290
\(101\) 1.73397e6 1.25980e6i 0.167462 0.121669i −0.500898 0.865507i \(-0.666997\pi\)
0.668360 + 0.743838i \(0.266997\pi\)
\(102\) 0 0
\(103\) 4.86869e6 1.49843e7i 0.439017 1.35116i −0.449896 0.893081i \(-0.648539\pi\)
0.888913 0.458075i \(-0.151461\pi\)
\(104\) 8.33042e6 1.14658e7i 0.726190 0.999515i
\(105\) 0 0
\(106\) −2.21630e6 720119.i −0.180741 0.0587265i
\(107\) 5.31756e6 + 1.63658e7i 0.419632 + 1.29150i 0.908041 + 0.418881i \(0.137577\pi\)
−0.488409 + 0.872615i \(0.662423\pi\)
\(108\) 0 0
\(109\) 5.66270e6i 0.418823i −0.977828 0.209412i \(-0.932845\pi\)
0.977828 0.209412i \(-0.0671548\pi\)
\(110\) 1.97944e6 1.25146e6i 0.141798 0.0896486i
\(111\) 0 0
\(112\) −2.42269e6 3.33454e6i −0.162942 0.224271i
\(113\) −1.14660e6 + 372554.i −0.0747548 + 0.0242893i −0.346156 0.938177i \(-0.612513\pi\)
0.271401 + 0.962466i \(0.412513\pi\)
\(114\) 0 0
\(115\) 5.82843e6 + 4.23460e6i 0.357363 + 0.259639i
\(116\) 1.34408e6 + 976533.i 0.0799509 + 0.0580877i
\(117\) 0 0
\(118\) 7.48199e6 2.43105e6i 0.419209 0.136209i
\(119\) 5.29306e6 + 7.28527e6i 0.287933 + 0.396306i
\(120\) 0 0
\(121\) −8.35733e6 + 1.76041e7i −0.428863 + 0.903369i
\(122\) 1.06370e7i 0.530345i
\(123\) 0 0
\(124\) −8.27131e6 2.54565e7i −0.389581 1.19901i
\(125\) −1.47004e7 4.77644e6i −0.673198 0.218735i
\(126\) 0 0
\(127\) 1.25456e7 1.72675e7i 0.543473 0.748027i −0.445635 0.895215i \(-0.647022\pi\)
0.989109 + 0.147188i \(0.0470222\pi\)
\(128\) −7.36348e6 + 2.26625e7i −0.310347 + 0.955151i
\(129\) 0 0
\(130\) 5.28964e6 3.84315e6i 0.211166 0.153421i
\(131\) 2.57846e7 1.00210 0.501051 0.865418i \(-0.332947\pi\)
0.501051 + 0.865418i \(0.332947\pi\)
\(132\) 0 0
\(133\) 3.16015e6 0.116474
\(134\) 1.21411e6 882101.i 0.0435903 0.0316702i
\(135\) 0 0
\(136\) 5.82444e6 1.79258e7i 0.198549 0.611072i
\(137\) −4.53268e6 + 6.23870e6i −0.150603 + 0.207287i −0.877652 0.479298i \(-0.840891\pi\)
0.727049 + 0.686585i \(0.240891\pi\)
\(138\) 0 0
\(139\) −1.05337e6 342260.i −0.0332681 0.0108095i 0.292336 0.956316i \(-0.405568\pi\)
−0.325604 + 0.945506i \(0.605568\pi\)
\(140\) −1.87084e6 5.75784e6i −0.0576219 0.177342i
\(141\) 0 0
\(142\) 2.08825e7i 0.612031i
\(143\) −2.01148e7 + 5.05521e7i −0.575227 + 1.44565i
\(144\) 0 0
\(145\) 1.00886e6 + 1.38858e6i 0.0274817 + 0.0378253i
\(146\) 1.08880e7 3.53773e6i 0.289544 0.0940785i
\(147\) 0 0
\(148\) 8.75203e6 + 6.35872e6i 0.221918 + 0.161233i
\(149\) −4.64780e7 3.37683e7i −1.15105 0.836290i −0.162434 0.986719i \(-0.551934\pi\)
−0.988621 + 0.150429i \(0.951934\pi\)
\(150\) 0 0
\(151\) 2.02320e7 6.57378e6i 0.478212 0.155380i −0.0599858 0.998199i \(-0.519106\pi\)
0.538197 + 0.842819i \(0.319106\pi\)
\(152\) −3.88786e6 5.35118e6i −0.0897963 0.123594i
\(153\) 0 0
\(154\) −9.27806e6 7.70217e6i −0.204708 0.169938i
\(155\) 2.76526e7i 0.596451i
\(156\) 0 0
\(157\) 1.06707e7 + 3.28410e7i 0.220061 + 0.677279i 0.998755 + 0.0498754i \(0.0158824\pi\)
−0.778694 + 0.627404i \(0.784118\pi\)
\(158\) −1.11838e7 3.63385e6i −0.225575 0.0732938i
\(159\) 0 0
\(160\) −1.15705e7 + 1.59254e7i −0.223322 + 0.307377i
\(161\) 1.14631e7 3.52799e7i 0.216478 0.666250i
\(162\) 0 0
\(163\) −5.83562e7 + 4.23983e7i −1.05543 + 0.766817i −0.973238 0.229800i \(-0.926193\pi\)
−0.0821947 + 0.996616i \(0.526193\pi\)
\(164\) 6.76723e7 1.19800
\(165\) 0 0
\(166\) −2.45496e6 −0.0416549
\(167\) −3.98206e7 + 2.89314e7i −0.661607 + 0.480686i −0.867205 0.497951i \(-0.834086\pi\)
0.205598 + 0.978636i \(0.434086\pi\)
\(168\) 0 0
\(169\) −2.75495e7 + 8.47888e7i −0.439047 + 1.35125i
\(170\) 5.11106e6 7.03477e6i 0.0797884 0.109819i
\(171\) 0 0
\(172\) −9.73060e7 3.16166e7i −1.45811 0.473769i
\(173\) −2.70065e6 8.31174e6i −0.0396558 0.122048i 0.929269 0.369404i \(-0.120438\pi\)
−0.968925 + 0.247356i \(0.920438\pi\)
\(174\) 0 0
\(175\) 3.66669e7i 0.517179i
\(176\) 2.13589e6 3.30494e7i 0.0295314 0.456951i
\(177\) 0 0
\(178\) −2.56849e7 3.53523e7i −0.341357 0.469837i
\(179\) 9.76633e6 3.17327e6i 0.127276 0.0413544i −0.244687 0.969602i \(-0.578685\pi\)
0.371962 + 0.928248i \(0.378685\pi\)
\(180\) 0 0
\(181\) 8.33240e7 + 6.05384e7i 1.04447 + 0.758851i 0.971153 0.238458i \(-0.0766420\pi\)
0.0733155 + 0.997309i \(0.476642\pi\)
\(182\) −2.72367e7 1.97886e7i −0.334891 0.243313i
\(183\) 0 0
\(184\) −7.38435e7 + 2.39932e7i −0.873876 + 0.283940i
\(185\) 6.56922e6 + 9.04175e6i 0.0762803 + 0.104991i
\(186\) 0 0
\(187\) −4.66647e6 + 7.22059e7i −0.0521846 + 0.807472i
\(188\) 1.08300e8i 1.18870i
\(189\) 0 0
\(190\) −942963. 2.90214e6i −0.00997372 0.0306959i
\(191\) −7.55063e7 2.45335e7i −0.784091 0.254767i −0.110505 0.993876i \(-0.535247\pi\)
−0.673586 + 0.739109i \(0.735247\pi\)
\(192\) 0 0
\(193\) 2.96666e7 4.08325e7i 0.297041 0.408842i −0.634244 0.773133i \(-0.718689\pi\)
0.931285 + 0.364291i \(0.118689\pi\)
\(194\) −1.93455e7 + 5.95393e7i −0.190228 + 0.585461i
\(195\) 0 0
\(196\) 4.35911e7 3.16708e7i 0.413525 0.300444i
\(197\) −9.93802e7 −0.926121 −0.463061 0.886327i \(-0.653249\pi\)
−0.463061 + 0.886327i \(0.653249\pi\)
\(198\) 0 0
\(199\) −6.47610e7 −0.582542 −0.291271 0.956641i \(-0.594078\pi\)
−0.291271 + 0.956641i \(0.594078\pi\)
\(200\) 6.20892e7 4.51104e7i 0.548796 0.398723i
\(201\) 0 0
\(202\) −3.29305e6 + 1.01350e7i −0.0281105 + 0.0865153i
\(203\) 5.19468e6 7.14987e6i 0.0435836 0.0599876i
\(204\) 0 0
\(205\) 6.64908e7 + 2.16042e7i 0.539042 + 0.175145i
\(206\) 2.42072e7 + 7.45020e7i 0.192934 + 0.593790i
\(207\) 0 0
\(208\) 9.24643e7i 0.712447i
\(209\) 1.95373e7 + 1.62189e7i 0.148031 + 0.122888i
\(210\) 0 0
\(211\) 7.03862e7 + 9.68783e7i 0.515821 + 0.709967i 0.984887 0.173196i \(-0.0554095\pi\)
−0.469066 + 0.883163i \(0.655409\pi\)
\(212\) −4.60372e7 + 1.49584e7i −0.331843 + 0.107822i
\(213\) 0 0
\(214\) −6.92181e7 5.02899e7i −0.482805 0.350778i
\(215\) −8.55136e7 6.21293e7i −0.586814 0.426345i
\(216\) 0 0
\(217\) −1.35416e8 + 4.39993e7i −0.899624 + 0.292305i
\(218\) 1.65491e7 + 2.27779e7i 0.108187 + 0.148907i
\(219\) 0 0
\(220\) 1.79848e7 4.51989e7i 0.113874 0.286186i
\(221\) 2.02015e8i 1.25896i
\(222\) 0 0
\(223\) 7.43830e7 + 2.28927e8i 0.449166 + 1.38239i 0.877850 + 0.478936i \(0.158977\pi\)
−0.428684 + 0.903455i \(0.641023\pi\)
\(224\) 9.63978e7 + 3.13215e7i 0.573059 + 0.186198i
\(225\) 0 0
\(226\) 3.52337e6 4.84950e6i 0.0203038 0.0279458i
\(227\) −5.21424e7 + 1.60478e8i −0.295870 + 0.910594i 0.687058 + 0.726602i \(0.258902\pi\)
−0.982928 + 0.183991i \(0.941098\pi\)
\(228\) 0 0
\(229\) 1.65121e8 1.19967e8i 0.908611 0.660145i −0.0320518 0.999486i \(-0.510204\pi\)
0.940663 + 0.339341i \(0.110204\pi\)
\(230\) −3.58200e7 −0.194124
\(231\) 0 0
\(232\) −1.84980e7 −0.0972560
\(233\) 2.22697e7 1.61799e7i 0.115337 0.0837972i −0.528622 0.848858i \(-0.677291\pi\)
0.643959 + 0.765060i \(0.277291\pi\)
\(234\) 0 0
\(235\) 3.45743e7 1.06409e8i 0.173786 0.534859i
\(236\) 9.60528e7 1.32205e8i 0.475683 0.654722i
\(237\) 0 0
\(238\) −4.25820e7 1.38357e7i −0.204742 0.0665247i
\(239\) −9.36313e7 2.88168e8i −0.443638 1.36538i −0.883971 0.467542i \(-0.845140\pi\)
0.440333 0.897834i \(-0.354860\pi\)
\(240\) 0 0
\(241\) 3.98774e8i 1.83513i −0.397582 0.917567i \(-0.630151\pi\)
0.397582 0.917567i \(-0.369849\pi\)
\(242\) −1.78307e7 9.52356e7i −0.0808750 0.431962i
\(243\) 0 0
\(244\) −1.29872e8 1.78754e8i −0.572338 0.787756i
\(245\) 5.29409e7 1.72015e7i 0.229990 0.0747284i
\(246\) 0 0
\(247\) 5.73537e7 + 4.16699e7i 0.242171 + 0.175947i
\(248\) 2.41105e8 + 1.75173e8i 1.00375 + 0.729266i
\(249\) 0 0
\(250\) 7.30903e7 2.37485e7i 0.295849 0.0961271i
\(251\) 1.34314e8 + 1.84868e8i 0.536122 + 0.737909i 0.988048 0.154147i \(-0.0492628\pi\)
−0.451926 + 0.892056i \(0.649263\pi\)
\(252\) 0 0
\(253\) 2.51937e8 1.59282e8i 0.978071 0.618365i
\(254\) 1.06122e8i 0.406337i
\(255\) 0 0
\(256\) −3.49105e7 1.07443e8i −0.130052 0.400258i
\(257\) 2.07079e7 + 6.72841e6i 0.0760975 + 0.0247256i 0.346818 0.937932i \(-0.387262\pi\)
−0.270721 + 0.962658i \(0.587262\pi\)
\(258\) 0 0
\(259\) 3.38253e7 4.65565e7i 0.120974 0.166506i
\(260\) 4.19693e7 1.29168e8i 0.148090 0.455773i
\(261\) 0 0
\(262\) −1.03717e8 + 7.53550e7i −0.356284 + 0.258856i
\(263\) 2.55504e8 0.866068 0.433034 0.901378i \(-0.357443\pi\)
0.433034 + 0.901378i \(0.357443\pi\)
\(264\) 0 0
\(265\) −5.00088e7 −0.165077
\(266\) −1.27115e7 + 9.23546e6i −0.0414106 + 0.0300866i
\(267\) 0 0
\(268\) 9.63301e6 2.96474e7i 0.0305696 0.0940837i
\(269\) −1.84859e8 + 2.54436e8i −0.579037 + 0.796977i −0.993589 0.113049i \(-0.963938\pi\)
0.414552 + 0.910026i \(0.363938\pi\)
\(270\) 0 0
\(271\) 1.99405e7 + 6.47907e6i 0.0608617 + 0.0197752i 0.339290 0.940682i \(-0.389813\pi\)
−0.278428 + 0.960457i \(0.589813\pi\)
\(272\) −3.79997e7 1.16951e8i −0.114496 0.352381i
\(273\) 0 0
\(274\) 3.83415e7i 0.112601i
\(275\) −1.88186e8 + 2.26689e8i −0.545660 + 0.657303i
\(276\) 0 0
\(277\) 3.58592e8 + 4.93560e8i 1.01373 + 1.39528i 0.916509 + 0.400014i \(0.130995\pi\)
0.0972190 + 0.995263i \(0.469005\pi\)
\(278\) 5.23735e6 1.70172e6i 0.0146203 0.00475041i
\(279\) 0 0
\(280\) 5.45339e7 + 3.96212e7i 0.148461 + 0.107864i
\(281\) 2.70813e8 + 1.96757e8i 0.728110 + 0.529003i 0.888965 0.457975i \(-0.151425\pi\)
−0.160855 + 0.986978i \(0.551425\pi\)
\(282\) 0 0
\(283\) 1.14375e8 3.71626e7i 0.299970 0.0974662i −0.155165 0.987889i \(-0.549591\pi\)
0.455135 + 0.890422i \(0.349591\pi\)
\(284\) 2.54966e8 + 3.50930e8i 0.660492 + 0.909089i
\(285\) 0 0
\(286\) −6.68266e7 2.62128e8i −0.168915 0.662570i
\(287\) 3.59984e8i 0.898868i
\(288\) 0 0
\(289\) −4.37803e7 1.34742e8i −0.106693 0.328368i
\(290\) −8.11617e6 2.63710e6i −0.0195415 0.00634942i
\(291\) 0 0
\(292\) 1.39779e8 1.92389e8i 0.328550 0.452211i
\(293\) 4.66040e7 1.43432e8i 0.108240 0.333127i −0.882238 0.470805i \(-0.843964\pi\)
0.990477 + 0.137677i \(0.0439637\pi\)
\(294\) 0 0
\(295\) 1.36582e8 9.92325e7i 0.309753 0.225049i
\(296\) −1.20450e8 −0.269952
\(297\) 0 0
\(298\) 2.85642e8 0.625267
\(299\) 6.73248e8 4.89143e8i 1.45655 1.05825i
\(300\) 0 0
\(301\) −1.68185e8 + 5.17621e8i −0.355472 + 1.09403i
\(302\) −6.21704e7 + 8.55703e7i −0.129885 + 0.178772i
\(303\) 0 0
\(304\) −4.10416e7 1.33352e7i −0.0837851 0.0272234i
\(305\) −7.05382e7 2.17094e8i −0.142356 0.438126i
\(306\) 0 0
\(307\) 1.90006e8i 0.374785i −0.982285 0.187393i \(-0.939996\pi\)
0.982285 0.187393i \(-0.0600036\pi\)
\(308\) −2.49957e8 1.61541e7i −0.487459 0.0315032i
\(309\) 0 0
\(310\) 8.08140e7 + 1.11231e8i 0.154071 + 0.212061i
\(311\) −6.73627e8 + 2.18875e8i −1.26987 + 0.412605i −0.865001 0.501771i \(-0.832682\pi\)
−0.404867 + 0.914376i \(0.632682\pi\)
\(312\) 0 0
\(313\) 7.58465e7 + 5.51057e7i 0.139807 + 0.101576i 0.655491 0.755203i \(-0.272462\pi\)
−0.515683 + 0.856779i \(0.672462\pi\)
\(314\) −1.38899e8 1.00916e8i −0.253190 0.183953i
\(315\) 0 0
\(316\) −2.32312e8 + 7.54827e7i −0.414158 + 0.134568i
\(317\) 5.07216e8 + 6.98124e8i 0.894306 + 1.23091i 0.972249 + 0.233948i \(0.0751646\pi\)
−0.0779434 + 0.996958i \(0.524835\pi\)
\(318\) 0 0
\(319\) 6.88108e7 1.75426e7i 0.118683 0.0302570i
\(320\) 4.58800e6i 0.00782705i
\(321\) 0 0
\(322\) 5.69949e7 + 1.75412e8i 0.0951350 + 0.292796i
\(323\) 8.96672e7 + 2.91346e7i 0.148056 + 0.0481062i
\(324\) 0 0
\(325\) −4.83491e8 + 6.65468e8i −0.781262 + 1.07531i
\(326\) 1.10827e8 3.41089e8i 0.177167 0.545263i
\(327\) 0 0
\(328\) −6.09571e8 + 4.42880e8i −0.953819 + 0.692990i
\(329\) −5.76101e8 −0.891893
\(330\) 0 0
\(331\) −8.83832e8 −1.33959 −0.669795 0.742546i \(-0.733618\pi\)
−0.669795 + 0.742546i \(0.733618\pi\)
\(332\) −4.12556e7 + 2.99739e7i −0.0618727 + 0.0449532i
\(333\) 0 0
\(334\) 7.56249e7 2.32749e8i 0.111059 0.341803i
\(335\) 1.89296e7 2.60544e7i 0.0275097 0.0378638i
\(336\) 0 0
\(337\) −3.32549e8 1.08052e8i −0.473316 0.153790i 0.0626392 0.998036i \(-0.480048\pi\)
−0.535955 + 0.844247i \(0.680048\pi\)
\(338\) −1.36977e8 4.21571e8i −0.192947 0.593830i
\(339\) 0 0
\(340\) 1.80623e8i 0.249228i
\(341\) −1.06301e9 4.22975e8i −1.45177 0.577663i
\(342\) 0 0
\(343\) −4.34417e8 5.97923e8i −0.581269 0.800048i
\(344\) 1.08342e9 3.52024e8i 1.43497 0.466248i
\(345\) 0 0
\(346\) 3.51541e7 + 2.55409e7i 0.0456257 + 0.0331490i
\(347\) −7.30955e8 5.31070e8i −0.939155 0.682336i 0.00906197 0.999959i \(-0.497115\pi\)
−0.948217 + 0.317623i \(0.897115\pi\)
\(348\) 0 0
\(349\) 4.54869e8 1.47796e8i 0.572793 0.186112i −0.00827654 0.999966i \(-0.502635\pi\)
0.581069 + 0.813854i \(0.302635\pi\)
\(350\) −1.07158e8 1.47490e8i −0.133594 0.183876i
\(351\) 0 0
\(352\) 4.35217e8 + 6.88385e8i 0.531871 + 0.841263i
\(353\) 3.87310e8i 0.468649i −0.972158 0.234325i \(-0.924712\pi\)
0.972158 0.234325i \(-0.0752878\pi\)
\(354\) 0 0
\(355\) 1.38481e8 + 4.26200e8i 0.164282 + 0.505608i
\(356\) −8.63270e8 2.80493e8i −1.01408 0.329494i
\(357\) 0 0
\(358\) −3.00107e7 + 4.13062e7i −0.0345689 + 0.0475800i
\(359\) −4.38160e8 + 1.34852e9i −0.499806 + 1.53825i 0.309524 + 0.950892i \(0.399830\pi\)
−0.809330 + 0.587354i \(0.800170\pi\)
\(360\) 0 0
\(361\) −6.96390e8 + 5.05957e8i −0.779072 + 0.566029i
\(362\) −5.12088e8 −0.567368
\(363\) 0 0
\(364\) −6.99321e8 −0.760014
\(365\) 1.98758e8 1.44406e8i 0.213944 0.155439i
\(366\) 0 0
\(367\) −3.45614e8 + 1.06369e9i −0.364972 + 1.12327i 0.585026 + 0.811015i \(0.301084\pi\)
−0.949998 + 0.312255i \(0.898916\pi\)
\(368\) −2.97749e8 + 4.09816e8i −0.311446 + 0.428669i
\(369\) 0 0
\(370\) −5.28486e7 1.71716e7i −0.0542410 0.0176240i
\(371\) 7.95713e7 + 2.44895e8i 0.0808999 + 0.248984i
\(372\) 0 0
\(373\) 1.48070e9i 1.47736i −0.674056 0.738680i \(-0.735449\pi\)
0.674056 0.738680i \(-0.264551\pi\)
\(374\) −1.92249e8 3.04082e8i −0.190027 0.300566i
\(375\) 0 0
\(376\) 7.08763e8 + 9.75529e8i 0.687613 + 0.946418i
\(377\) 1.88557e8 6.12658e7i 0.181237 0.0588876i
\(378\) 0 0
\(379\) 3.75058e8 + 2.72496e8i 0.353884 + 0.257112i 0.750497 0.660874i \(-0.229814\pi\)
−0.396613 + 0.917986i \(0.629814\pi\)
\(380\) −5.12803e7 3.72573e7i −0.0479411 0.0348312i
\(381\) 0 0
\(382\) 3.75418e8 1.21981e8i 0.344583 0.111962i
\(383\) −2.12243e8 2.92127e8i −0.193035 0.265690i 0.701518 0.712652i \(-0.252506\pi\)
−0.894553 + 0.446961i \(0.852506\pi\)
\(384\) 0 0
\(385\) −2.40436e8 9.56701e7i −0.214727 0.0854405i
\(386\) 2.50946e8i 0.222088i
\(387\) 0 0
\(388\) 4.01846e8 + 1.23676e9i 0.349260 + 1.07491i
\(389\) 1.68289e9 + 5.46804e8i 1.44955 + 0.470987i 0.924860 0.380308i \(-0.124182\pi\)
0.524688 + 0.851295i \(0.324182\pi\)
\(390\) 0 0
\(391\) 6.50518e8 8.95362e8i 0.550352 0.757495i
\(392\) −1.85387e8 + 5.70562e8i −0.155445 + 0.478412i
\(393\) 0 0
\(394\) 3.99751e8 2.90436e8i 0.329270 0.239229i
\(395\) −2.52353e8 −0.206025
\(396\) 0 0
\(397\) 1.09879e8 0.0881347 0.0440674 0.999029i \(-0.485968\pi\)
0.0440674 + 0.999029i \(0.485968\pi\)
\(398\) 2.60497e8 1.89262e8i 0.207115 0.150478i
\(399\) 0 0
\(400\) 1.54727e8 4.76201e8i 0.120881 0.372032i
\(401\) 1.08934e9 1.49935e9i 0.843643 1.16118i −0.141585 0.989926i \(-0.545220\pi\)
0.985228 0.171249i \(-0.0547802\pi\)
\(402\) 0 0
\(403\) −3.03785e9 9.87056e8i −2.31205 0.751232i
\(404\) 6.84036e7 + 2.10525e8i 0.0516112 + 0.158843i
\(405\) 0 0
\(406\) 4.39412e7i 0.0325860i
\(407\) 4.48063e8 1.14229e8i 0.329427 0.0839838i
\(408\) 0 0
\(409\) 9.76214e8 + 1.34364e9i 0.705527 + 0.971074i 0.999882 + 0.0153779i \(0.00489513\pi\)
−0.294355 + 0.955696i \(0.595105\pi\)
\(410\) −3.30593e8 + 1.07416e8i −0.236892 + 0.0769708i
\(411\) 0 0
\(412\) 1.31644e9 + 9.56447e8i 0.927384 + 0.673784i
\(413\) −7.03268e8 5.10954e8i −0.491242 0.356908i
\(414\) 0 0
\(415\) −5.01043e7 + 1.62799e7i −0.0344118 + 0.0111811i
\(416\) 1.33652e9 + 1.83956e9i 0.910224 + 1.25282i
\(417\) 0 0
\(418\) −1.25987e8 8.14218e6i −0.0843739 0.00545285i
\(419\) 3.09054e8i 0.205251i −0.994720 0.102626i \(-0.967276\pi\)
0.994720 0.102626i \(-0.0327243\pi\)
\(420\) 0 0
\(421\) −1.76149e8 5.42132e8i −0.115052 0.354093i 0.876906 0.480662i \(-0.159604\pi\)
−0.991958 + 0.126569i \(0.959604\pi\)
\(422\) −5.66249e8 1.83985e8i −0.366787 0.119176i
\(423\) 0 0
\(424\) 3.16794e8 4.36030e8i 0.201835 0.277802i
\(425\) −3.38046e8 + 1.04040e9i −0.213606 + 0.657413i
\(426\) 0 0
\(427\) −9.50884e8 + 6.90858e8i −0.591058 + 0.429429i
\(428\) −1.77722e9 −1.09569
\(429\) 0 0
\(430\) 5.25545e8 0.318765
\(431\) 1.49843e9 1.08867e9i 0.901498 0.654977i −0.0373521 0.999302i \(-0.511892\pi\)
0.938850 + 0.344325i \(0.111892\pi\)
\(432\) 0 0
\(433\) 6.58379e8 2.02628e9i 0.389734 1.19948i −0.543254 0.839569i \(-0.682808\pi\)
0.932987 0.359909i \(-0.117192\pi\)
\(434\) 4.16116e8 5.72735e8i 0.244343 0.336310i
\(435\) 0 0
\(436\) 5.56214e8 + 1.80725e8i 0.321395 + 0.104428i
\(437\) −1.20017e8 3.69375e8i −0.0687952 0.211730i
\(438\) 0 0
\(439\) 2.61260e8i 0.147383i −0.997281 0.0736914i \(-0.976522\pi\)
0.997281 0.0736914i \(-0.0234780\pi\)
\(440\) 1.33802e8 + 5.24839e8i 0.0748821 + 0.293725i
\(441\) 0 0
\(442\) −5.90384e8 8.12593e8i −0.325204 0.447605i
\(443\) 3.00676e9 9.76957e8i 1.64318 0.533903i 0.665938 0.746007i \(-0.268032\pi\)
0.977247 + 0.212104i \(0.0680317\pi\)
\(444\) 0 0
\(445\) −7.58651e8 5.51192e8i −0.408114 0.296513i
\(446\) −9.68236e8 7.03465e8i −0.516784 0.375466i
\(447\) 0 0
\(448\) 2.24676e7 7.30018e6i 0.0118055 0.00383584i
\(449\) 1.98044e9 + 2.72584e9i 1.03252 + 1.42115i 0.903036 + 0.429564i \(0.141333\pi\)
0.129486 + 0.991581i \(0.458667\pi\)
\(450\) 0 0
\(451\) 1.84755e9 2.22556e9i 0.948369 1.14241i
\(452\) 1.24514e8i 0.0634213i
\(453\) 0 0
\(454\) −2.59253e8 7.97898e8i −0.130025 0.400177i
\(455\) −6.87111e8 2.23256e8i −0.341969 0.111113i
\(456\) 0 0
\(457\) 2.07094e9 2.85040e9i 1.01499 1.39701i 0.0993250 0.995055i \(-0.468332\pi\)
0.915660 0.401953i \(-0.131668\pi\)
\(458\) −3.13588e8 + 9.65124e8i −0.152521 + 0.469412i
\(459\) 0 0
\(460\) −6.01955e8 + 4.37346e8i −0.288344 + 0.209494i
\(461\) 3.06840e9 1.45868 0.729338 0.684153i \(-0.239828\pi\)
0.729338 + 0.684153i \(0.239828\pi\)
\(462\) 0 0
\(463\) 9.23554e8 0.432443 0.216221 0.976344i \(-0.430627\pi\)
0.216221 + 0.976344i \(0.430627\pi\)
\(464\) −9.76355e7 + 7.09364e7i −0.0453727 + 0.0329652i
\(465\) 0 0
\(466\) −4.22932e7 + 1.30165e8i −0.0193607 + 0.0595860i
\(467\) 9.89025e8 1.36128e9i 0.449364 0.618496i −0.522897 0.852396i \(-0.675149\pi\)
0.972261 + 0.233900i \(0.0751487\pi\)
\(468\) 0 0
\(469\) −1.57709e8 5.12429e7i −0.0705916 0.0229366i
\(470\) 1.71904e8 + 5.29065e8i 0.0763735 + 0.235053i
\(471\) 0 0
\(472\) 1.81948e9i 0.796435i
\(473\) −3.69637e9 + 2.33696e9i −1.60606 + 1.01540i
\(474\) 0 0
\(475\) 2.25648e8 + 3.10578e8i 0.0966060 + 0.132967i
\(476\) −8.84518e8 + 2.87397e8i −0.375909 + 0.122140i
\(477\) 0 0
\(478\) 1.21879e9 + 8.85502e8i 0.510424 + 0.370845i
\(479\) −1.50652e9 1.09455e9i −0.626328 0.455054i 0.228798 0.973474i \(-0.426520\pi\)
−0.855126 + 0.518420i \(0.826520\pi\)
\(480\) 0 0
\(481\) 1.22779e9 3.98934e8i 0.503057 0.163453i
\(482\) 1.16541e9 + 1.60405e9i 0.474038 + 0.652458i
\(483\) 0 0
\(484\) −1.46243e9 1.38273e9i −0.586294 0.554342i
\(485\) 1.34345e9i 0.534719i
\(486\) 0 0
\(487\) 3.01827e8 + 9.28929e8i 0.118415 + 0.364444i 0.992644 0.121070i \(-0.0386324\pi\)
−0.874229 + 0.485514i \(0.838632\pi\)
\(488\) 2.33970e9 + 7.60215e8i 0.911363 + 0.296120i
\(489\) 0 0
\(490\) −1.62681e8 + 2.23911e8i −0.0624668 + 0.0859782i
\(491\) −9.38771e8 + 2.88924e9i −0.357910 + 1.10153i 0.596392 + 0.802693i \(0.296600\pi\)
−0.954303 + 0.298842i \(0.903400\pi\)
\(492\) 0 0
\(493\) 2.13313e8 1.54981e8i 0.0801776 0.0582524i
\(494\) −3.52481e8 −0.131550
\(495\) 0 0
\(496\) 1.94435e9 0.715464
\(497\) 1.86678e9 1.35629e9i 0.682095 0.495571i
\(498\) 0 0
\(499\) 4.17712e8 1.28558e9i 0.150496 0.463179i −0.847181 0.531305i \(-0.821702\pi\)
0.997677 + 0.0681259i \(0.0217020\pi\)
\(500\) 9.38324e8 1.29149e9i 0.335705 0.462058i
\(501\) 0 0
\(502\) −1.08054e9 3.51089e8i −0.381223 0.123867i
\(503\) −1.03043e9 3.17133e9i −0.361018 1.11110i −0.952437 0.304735i \(-0.901432\pi\)
0.591419 0.806365i \(-0.298568\pi\)
\(504\) 0 0
\(505\) 2.28687e8i 0.0790171i
\(506\) −5.47905e8 + 1.37698e9i −0.188009 + 0.472500i
\(507\) 0 0
\(508\) 1.29570e9 + 1.78337e9i 0.438511 + 0.603559i
\(509\) −6.82900e8 + 2.21888e8i −0.229533 + 0.0745798i −0.421525 0.906817i \(-0.638505\pi\)
0.191992 + 0.981396i \(0.438505\pi\)
\(510\) 0 0
\(511\) −1.02342e9 7.43556e8i −0.339297 0.246513i
\(512\) −2.01314e9 1.46263e9i −0.662870 0.481603i
\(513\) 0 0
\(514\) −1.02960e8 + 3.34537e7i −0.0334424 + 0.0108661i
\(515\) 9.88109e8 + 1.36002e9i 0.318772 + 0.438751i
\(516\) 0 0
\(517\) −3.56168e9 2.95672e9i −1.13354 0.941009i
\(518\) 2.86124e8i 0.0904484i
\(519\) 0 0
\(520\) 4.67291e8 + 1.43817e9i 0.145739 + 0.448538i
\(521\) −3.65924e9 1.18896e9i −1.13360 0.368328i −0.318655 0.947871i \(-0.603231\pi\)
−0.814942 + 0.579543i \(0.803231\pi\)
\(522\) 0 0
\(523\) 3.37554e8 4.64604e8i 0.103178 0.142013i −0.754306 0.656523i \(-0.772026\pi\)
0.857484 + 0.514511i \(0.172026\pi\)
\(524\) −8.22917e8 + 2.53268e9i −0.249860 + 0.768990i
\(525\) 0 0
\(526\) −1.02775e9 + 7.46703e8i −0.307919 + 0.223716i
\(527\) −4.24798e9 −1.26429
\(528\) 0 0
\(529\) −1.15423e9 −0.338998
\(530\) 2.01158e8 1.46149e8i 0.0586909 0.0426414i
\(531\) 0 0
\(532\) −1.00856e8 + 3.10404e8i −0.0290410 + 0.0893791i
\(533\) 4.74676e9 6.53335e9i 1.35785 1.86892i
\(534\) 0 0
\(535\) −1.74619e9 5.67373e8i −0.493009 0.160188i
\(536\) 1.07255e8 + 3.30097e8i 0.0300844 + 0.0925903i
\(537\) 0 0
\(538\) 1.56370e9i 0.432927i
\(539\) 1.48530e8 2.29825e9i 0.0408557 0.632174i
\(540\) 0 0
\(541\) 2.27912e9 + 3.13694e9i 0.618838 + 0.851757i 0.997268 0.0738729i \(-0.0235359\pi\)
−0.378430 + 0.925630i \(0.623536\pi\)
\(542\) −9.91445e7 + 3.22140e7i −0.0267468 + 0.00869055i
\(543\) 0 0
\(544\) 2.44646e9 + 1.77746e9i 0.651541 + 0.473372i
\(545\) 4.88807e8 + 3.55139e8i 0.129345 + 0.0939747i
\(546\) 0 0
\(547\) −2.61894e9 + 8.50944e8i −0.684178 + 0.222303i −0.630424 0.776251i \(-0.717119\pi\)
−0.0537544 + 0.998554i \(0.517119\pi\)
\(548\) −4.68132e8 6.44328e8i −0.121517 0.167253i
\(549\) 0 0
\(550\) 9.44728e7 1.46181e9i 0.0242124 0.374646i
\(551\) 9.25294e7i 0.0235640i
\(552\) 0 0
\(553\) 4.01531e8 + 1.23579e9i 0.100967 + 0.310746i
\(554\) −2.88483e9 9.37339e8i −0.720836 0.234214i
\(555\) 0 0
\(556\) 6.72364e7 9.25430e7i 0.0165899 0.0228340i
\(557\) −1.38404e9 + 4.25964e9i −0.339357 + 1.04443i 0.625180 + 0.780481i \(0.285026\pi\)
−0.964536 + 0.263951i \(0.914974\pi\)
\(558\) 0 0
\(559\) −9.87776e9 + 7.17661e9i −2.39176 + 1.73771i
\(560\) 4.39780e8 0.105822
\(561\) 0 0
\(562\) −1.66435e9 −0.395518
\(563\) 4.16183e9 3.02375e9i 0.982891 0.714112i 0.0245382 0.999699i \(-0.492188\pi\)
0.958353 + 0.285587i \(0.0921885\pi\)
\(564\) 0 0
\(565\) 3.97508e7 1.22340e8i 0.00927206 0.0285365i
\(566\) −3.51459e8 + 4.83742e8i −0.0814737 + 0.112139i
\(567\) 0 0
\(568\) −4.59331e9 1.49246e9i −1.05173 0.341729i
\(569\) 4.50072e8 + 1.38518e9i 0.102421 + 0.315219i 0.989116 0.147135i \(-0.0470050\pi\)
−0.886696 + 0.462354i \(0.847005\pi\)
\(570\) 0 0
\(571\) 6.99471e8i 0.157233i −0.996905 0.0786165i \(-0.974950\pi\)
0.996905 0.0786165i \(-0.0250502\pi\)
\(572\) −4.32348e9 3.58913e9i −0.965933 0.801868i
\(573\) 0 0
\(574\) 1.05204e9 + 1.44801e9i 0.232189 + 0.319581i
\(575\) 4.28581e9 1.39255e9i 0.940147 0.305472i
\(576\) 0 0
\(577\) 6.56396e9 + 4.76900e9i 1.42250 + 1.03350i 0.991353 + 0.131219i \(0.0418891\pi\)
0.431142 + 0.902284i \(0.358111\pi\)
\(578\) 5.69884e8 + 4.14045e8i 0.122755 + 0.0891867i
\(579\) 0 0
\(580\) −1.68590e8 + 5.47781e7i −0.0358784 + 0.0116576i
\(581\) 1.59447e8 + 2.19459e8i 0.0337286 + 0.0464235i
\(582\) 0 0
\(583\) −7.64936e8 + 1.92242e9i −0.159877 + 0.401799i
\(584\) 2.64776e9i 0.550091i
\(585\) 0 0
\(586\) 2.31715e8 + 7.13147e8i 0.0475678 + 0.146399i
\(587\) 1.01774e9 + 3.30682e8i 0.207683 + 0.0674804i 0.411011 0.911630i \(-0.365176\pi\)
−0.203328 + 0.979111i \(0.565176\pi\)
\(588\) 0 0
\(589\) −8.76237e8 + 1.20604e9i −0.176693 + 0.243196i
\(590\) −2.59388e8 + 7.98314e8i −0.0519957 + 0.160026i
\(591\) 0 0
\(592\) −6.35756e8 + 4.61904e8i −0.125940 + 0.0915009i
\(593\) −9.77682e9 −1.92534 −0.962668 0.270686i \(-0.912749\pi\)
−0.962668 + 0.270686i \(0.912749\pi\)
\(594\) 0 0
\(595\) −9.60825e8 −0.186997
\(596\) 4.80021e9 3.48756e9i 0.928749 0.674776i
\(597\) 0 0
\(598\) −1.27859e9 + 3.93510e9i −0.244499 + 0.752491i
\(599\) 1.23412e9 1.69863e9i 0.234620 0.322927i −0.675431 0.737423i \(-0.736042\pi\)
0.910051 + 0.414497i \(0.136042\pi\)
\(600\) 0 0
\(601\) 4.23944e9 + 1.37748e9i 0.796614 + 0.258836i 0.678918 0.734214i \(-0.262449\pi\)
0.117696 + 0.993050i \(0.462449\pi\)
\(602\) −8.36218e8 2.57362e9i −0.156218 0.480791i
\(603\) 0 0
\(604\) 2.19708e9i 0.405710i
\(605\) −9.95462e8 1.82546e9i −0.182760 0.335142i
\(606\) 0 0
\(607\) −2.67567e8 3.68275e8i −0.0485593 0.0668362i 0.784047 0.620702i \(-0.213152\pi\)
−0.832606 + 0.553865i \(0.813152\pi\)
\(608\) 1.00927e9 3.27931e8i 0.182114 0.0591725i
\(609\) 0 0
\(610\) 9.18189e8 + 6.67103e8i 0.163786 + 0.118998i
\(611\) −1.04557e10 7.59648e9i −1.85442 1.34731i
\(612\) 0 0
\(613\) 7.20021e9 2.33949e9i 1.26251 0.410213i 0.400119 0.916463i \(-0.368969\pi\)
0.862387 + 0.506250i \(0.168969\pi\)
\(614\) 5.55287e8 + 7.64287e8i 0.0968118 + 0.133250i
\(615\) 0 0
\(616\) 2.35726e9 1.49033e9i 0.406326 0.256891i
\(617\) 1.06436e10i 1.82428i 0.409880 + 0.912140i \(0.365571\pi\)
−0.409880 + 0.912140i \(0.634429\pi\)
\(618\) 0 0
\(619\) 4.81512e8 + 1.48194e9i 0.0815999 + 0.251139i 0.983530 0.180742i \(-0.0578500\pi\)
−0.901931 + 0.431881i \(0.857850\pi\)
\(620\) 2.71616e9 + 8.82533e8i 0.457703 + 0.148717i
\(621\) 0 0
\(622\) 2.06997e9 2.84907e9i 0.344904 0.474719i
\(623\) −1.49209e9 + 4.59217e9i −0.247222 + 0.760870i
\(624\) 0 0
\(625\) −2.88405e9 + 2.09539e9i −0.472523 + 0.343308i
\(626\) −4.66133e8 −0.0759451
\(627\) 0 0
\(628\) −3.56634e9 −0.574598
\(629\) 1.38899e9 1.00916e9i 0.222547 0.161690i
\(630\) 0 0
\(631\) −1.25665e9 + 3.86758e9i −0.199119 + 0.612825i 0.800785 + 0.598952i \(0.204416\pi\)
−0.999904 + 0.0138730i \(0.995584\pi\)
\(632\) 1.59860e9 2.20028e9i 0.251901 0.346712i
\(633\) 0 0
\(634\) −4.08050e9 1.32583e9i −0.635917 0.206622i
\(635\) 7.03738e8 + 2.16588e9i 0.109069 + 0.335681i
\(636\) 0 0
\(637\) 6.42996e9i 0.985644i
\(638\) −2.25520e8 + 2.71662e8i −0.0343805 + 0.0414149i
\(639\) 0 0
\(640\) −1.49443e9 2.05691e9i −0.225344 0.310159i
\(641\) 8.39651e9 2.72819e9i 1.25920 0.409140i 0.397992 0.917389i \(-0.369707\pi\)
0.861210 + 0.508249i \(0.169707\pi\)
\(642\) 0 0
\(643\) −3.09641e9 2.24967e9i −0.459324 0.333719i 0.333942 0.942594i \(-0.391621\pi\)
−0.793266 + 0.608875i \(0.791621\pi\)
\(644\) 3.09950e9 + 2.25192e9i 0.457289 + 0.332240i
\(645\) 0 0
\(646\) −4.45826e8 + 1.44858e8i −0.0650657 + 0.0211411i
\(647\) 7.27301e9 + 1.00104e10i 1.05572 + 1.45308i 0.883742 + 0.467975i \(0.155016\pi\)
0.171980 + 0.985101i \(0.444984\pi\)
\(648\) 0 0
\(649\) −1.72550e9 6.76830e9i −0.247776 0.971903i
\(650\) 4.08980e9i 0.584124i
\(651\) 0 0
\(652\) −2.30210e9 7.08514e9i −0.325280 1.00111i
\(653\) −5.23074e9 1.69957e9i −0.735135 0.238860i −0.0825623 0.996586i \(-0.526310\pi\)
−0.652573 + 0.757726i \(0.726310\pi\)
\(654\) 0 0
\(655\) −1.61710e9 + 2.22574e9i −0.224849 + 0.309479i
\(656\) −1.51906e9 + 4.67519e9i −0.210093 + 0.646600i
\(657\) 0 0
\(658\) 2.31733e9 1.68364e9i 0.317101 0.230387i
\(659\) −9.55087e9 −1.30000 −0.650001 0.759934i \(-0.725231\pi\)
−0.650001 + 0.759934i \(0.725231\pi\)
\(660\) 0 0
\(661\) 1.04063e10 1.40149 0.700744 0.713412i \(-0.252851\pi\)
0.700744 + 0.713412i \(0.252851\pi\)
\(662\) 3.55516e9 2.58298e9i 0.476273 0.346033i
\(663\) 0 0
\(664\) 1.75454e8 5.39992e8i 0.0232581 0.0715812i
\(665\) −1.98191e8 + 2.72786e8i −0.0261341 + 0.0359705i
\(666\) 0 0
\(667\) −1.03300e9 3.35642e8i −0.134790 0.0437961i
\(668\) −1.57089e9 4.83469e9i −0.203905 0.627554i
\(669\) 0 0
\(670\) 1.60124e8i 0.0205681i
\(671\) −9.42443e9 6.09075e8i −1.20428 0.0778291i
\(672\) 0 0
\(673\) 3.45295e9 + 4.75258e9i 0.436654 + 0.601003i 0.969464 0.245232i \(-0.0788640\pi\)
−0.532810 + 0.846235i \(0.678864\pi\)
\(674\) 1.65344e9 5.37234e8i 0.208007 0.0675856i
\(675\) 0 0
\(676\) −7.44907e9 5.41207e9i −0.927446 0.673829i
\(677\) 6.62226e9 + 4.81136e9i 0.820250 + 0.595946i 0.916784 0.399383i \(-0.130776\pi\)
−0.0965344 + 0.995330i \(0.530776\pi\)
\(678\) 0 0
\(679\) 6.57894e9 2.13763e9i 0.806514 0.262052i
\(680\) 1.18208e9 + 1.62700e9i 0.144167 + 0.198429i
\(681\) 0 0
\(682\) 5.51204e9 1.40523e9i 0.665376 0.169630i
\(683\) 1.49778e10i 1.79877i −0.437162 0.899383i \(-0.644016\pi\)
0.437162 0.899383i \(-0.355984\pi\)
\(684\) 0 0
\(685\) −2.54259e8 7.82528e8i −0.0302245 0.0930214i
\(686\) 3.49483e9 + 1.13554e9i 0.413325 + 0.134297i
\(687\) 0 0
\(688\) 4.36852e9 6.01275e9i 0.511416 0.703904i
\(689\) −1.78506e9 + 5.49384e9i −0.207915 + 0.639895i
\(690\) 0 0
\(691\) −1.08108e10 + 7.85450e9i −1.24648 + 0.905619i −0.998012 0.0630218i \(-0.979926\pi\)
−0.248465 + 0.968641i \(0.579926\pi\)
\(692\) 9.02606e8 0.103544
\(693\) 0 0
\(694\) 4.49226e9 0.510161
\(695\) 9.56065e7 6.94622e7i 0.0108029 0.00784877i
\(696\) 0 0
\(697\) 3.31882e9 1.02143e10i 0.371253 1.14260i
\(698\) −1.39775e9 + 1.92384e9i −0.155574 + 0.214129i
\(699\) 0 0
\(700\) −3.60158e9 1.17022e9i −0.396871 0.128951i
\(701\) 1.57726e9 + 4.85432e9i 0.172938 + 0.532249i 0.999533 0.0305480i \(-0.00972525\pi\)
−0.826595 + 0.562797i \(0.809725\pi\)
\(702\) 0 0
\(703\) 6.02507e8i 0.0654061i
\(704\) 1.76370e8 + 7.01782e7i 0.0190512 + 0.00758050i
\(705\) 0 0
\(706\) 1.13191e9 + 1.55793e9i 0.121058 + 0.166622i
\(707\) 1.11989e9 3.63874e8i 0.119181 0.0387242i
\(708\) 0 0
\(709\) 6.79294e9 + 4.93536e9i 0.715807 + 0.520064i 0.885042 0.465512i \(-0.154130\pi\)
−0.169235 + 0.985576i \(0.554130\pi\)
\(710\) −1.80259e9 1.30966e9i −0.189013 0.137326i
\(711\) 0 0
\(712\) 9.61176e9 3.12305e9i 0.997982 0.324264i
\(713\) 1.02857e10 + 1.41571e10i 1.06273 + 1.46272i
\(714\) 0 0
\(715\) −3.10217e9 4.90672e9i −0.317391 0.502019i
\(716\) 1.06057e9i 0.107980i
\(717\) 0 0
\(718\) −2.17853e9 6.70484e9i −0.219649 0.676010i
\(719\) 1.59643e10 + 5.18710e9i 1.60176 + 0.520443i 0.967542 0.252711i \(-0.0813221\pi\)
0.634218 + 0.773154i \(0.281322\pi\)
\(720\) 0 0
\(721\) 5.08783e9 7.00280e9i 0.505544 0.695822i
\(722\) 1.32254e9 4.07037e9i 0.130776 0.402488i
\(723\) 0 0
\(724\) −8.60563e9 + 6.25236e9i −0.842748 + 0.612292i
\(725\) 1.07361e9 0.104632
\(726\) 0 0
\(727\) 6.26269e9 0.604492 0.302246 0.953230i \(-0.402264\pi\)
0.302246 + 0.953230i \(0.402264\pi\)
\(728\) 6.29927e9 4.57669e9i 0.605105 0.439634i
\(729\) 0 0
\(730\) −3.77469e8 + 1.16173e9i −0.0359130 + 0.110529i
\(731\) −9.54428e9 + 1.31366e10i −0.903717 + 1.24386i
\(732\) 0 0
\(733\) 2.88905e9 + 9.38708e8i 0.270951 + 0.0880373i 0.441341 0.897339i \(-0.354503\pi\)
−0.170390 + 0.985377i \(0.554503\pi\)
\(734\) −1.71840e9 5.28868e9i −0.160394 0.493641i
\(735\) 0 0
\(736\) 1.24570e10i 1.15171i
\(737\) −7.12027e8 1.12622e9i −0.0655180 0.103630i
\(738\) 0 0
\(739\) 4.99971e9 + 6.88151e9i 0.455711 + 0.627232i 0.973612 0.228208i \(-0.0732866\pi\)
−0.517901 + 0.855440i \(0.673287\pi\)
\(740\) −1.09778e9 + 3.56689e8i −0.0995870 + 0.0323578i
\(741\) 0 0
\(742\) −1.03577e9 7.52532e8i −0.0930787 0.0676256i
\(743\) −3.09446e9 2.24826e9i −0.276773 0.201088i 0.440735 0.897637i \(-0.354718\pi\)
−0.717509 + 0.696549i \(0.754718\pi\)
\(744\) 0 0
\(745\) 5.82979e9 1.89421e9i 0.516543 0.167835i
\(746\) 4.32731e9 + 5.95603e9i 0.381621 + 0.525256i
\(747\) 0 0
\(748\) −6.94344e9 2.76281e9i −0.606624 0.241377i
\(749\) 9.45397e9i 0.822106i
\(750\) 0 0
\(751\) 6.62110e9 + 2.03776e10i 0.570414 + 1.75555i 0.651289 + 0.758830i \(0.274229\pi\)
−0.0808748 + 0.996724i \(0.525771\pi\)
\(752\) 7.48195e9 + 2.43103e9i 0.641582 + 0.208463i
\(753\) 0 0
\(754\) −5.79411e8 + 7.97491e8i −0.0492251 + 0.0677526i
\(755\) −7.01410e8 + 2.15872e9i −0.0593141 + 0.182550i
\(756\) 0 0
\(757\) 4.48701e9 3.26000e9i 0.375942 0.273138i −0.383728 0.923446i \(-0.625360\pi\)
0.759671 + 0.650308i \(0.225360\pi\)
\(758\) −2.30501e9 −0.192234
\(759\) 0 0
\(760\) 7.05746e8 0.0583178
\(761\) 2.82352e9 2.05140e9i 0.232244 0.168735i −0.465577 0.885007i \(-0.654153\pi\)
0.697821 + 0.716272i \(0.254153\pi\)
\(762\) 0 0
\(763\) 9.61369e8 2.95879e9i 0.0783527 0.241145i
\(764\) 4.81957e9 6.63357e9i 0.391004 0.538171i
\(765\) 0 0
\(766\) 1.70747e9 + 5.54790e8i 0.137262 + 0.0445993i
\(767\) −6.02616e9 1.85466e10i −0.482233 1.48416i
\(768\) 0 0
\(769\) 8.62193e9i 0.683695i 0.939755 + 0.341848i \(0.111053\pi\)
−0.939755 + 0.341848i \(0.888947\pi\)
\(770\) 1.24673e9 3.17841e8i 0.0984138 0.0250895i
\(771\) 0 0
\(772\) 3.06394e9 + 4.21715e9i 0.239673 + 0.329882i
\(773\) −1.28237e10 + 4.16667e9i −0.998584 + 0.324459i −0.762299 0.647225i \(-0.775930\pi\)