Properties

Label 588.8.i.f.361.1
Level $588$
Weight $8$
Character 588.361
Analytic conductor $183.682$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [588,8,Mod(361,588)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(588, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("588.361");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 588.i (of order \(3\), degree \(2\), not 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: \(183.682394985\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 588.361
Dual form 588.8.i.f.373.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(13.5000 - 23.3827i) q^{3} +(-50.0000 - 86.6025i) q^{5} +(-364.500 - 631.333i) q^{9} +(-1387.00 + 2402.35i) q^{11} -3294.00 q^{13} -2700.00 q^{15} +(-2950.00 + 5109.55i) q^{17} +(-3322.00 - 5753.87i) q^{19} +(-991.000 - 1716.46i) q^{23} +(34062.5 - 58998.0i) q^{25} -19683.0 q^{27} -208106. q^{29} +(58896.0 - 102011. i) q^{31} +(37449.0 + 64863.6i) q^{33} +(167843. + 290713. i) q^{37} +(-44469.0 + 77022.6i) q^{39} -265488. q^{41} -93292.0 q^{43} +(-36450.0 + 63133.3i) q^{45} +(328758. + 569426. i) q^{47} +(79650.0 + 137958. i) q^{51} +(304359. - 527165. i) q^{53} +277400. q^{55} -179388. q^{57} +(268060. - 464294. i) q^{59} +(898545. + 1.55633e6i) q^{61} +(164700. + 285269. i) q^{65} +(-1.06159e6 + 1.83872e6i) q^{67} -53514.0 q^{69} -1.19121e6 q^{71} +(-528215. + 914895. i) q^{73} +(-919688. - 1.59295e6i) q^{75} +(-499242. - 864713. i) q^{79} +(-265720. + 460241. i) q^{81} +3.89800e6 q^{83} +590000. q^{85} +(-2.80943e6 + 4.86608e6i) q^{87} +(2.31118e6 + 4.00307e6i) q^{89} +(-1.59019e6 - 2.75429e6i) q^{93} +(-332200. + 575387. i) q^{95} +1.52877e7 q^{97} +2.02225e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 27 q^{3} - 100 q^{5} - 729 q^{9} - 2774 q^{11} - 6588 q^{13} - 5400 q^{15} - 5900 q^{17} - 6644 q^{19} - 1982 q^{23} + 68125 q^{25} - 39366 q^{27} - 416212 q^{29} + 117792 q^{31} + 74898 q^{33} + 335686 q^{37}+ \cdots + 4044492 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(493\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 13.5000 23.3827i 0.288675 0.500000i
\(4\) 0 0
\(5\) −50.0000 86.6025i −0.178885 0.309839i 0.762614 0.646854i \(-0.223916\pi\)
−0.941499 + 0.337016i \(0.890582\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −364.500 631.333i −0.166667 0.288675i
\(10\) 0 0
\(11\) −1387.00 + 2402.35i −0.314197 + 0.544205i −0.979266 0.202576i \(-0.935069\pi\)
0.665069 + 0.746782i \(0.268402\pi\)
\(12\) 0 0
\(13\) −3294.00 −0.415836 −0.207918 0.978146i \(-0.566669\pi\)
−0.207918 + 0.978146i \(0.566669\pi\)
\(14\) 0 0
\(15\) −2700.00 −0.206559
\(16\) 0 0
\(17\) −2950.00 + 5109.55i −0.145630 + 0.252239i −0.929608 0.368550i \(-0.879854\pi\)
0.783978 + 0.620789i \(0.213188\pi\)
\(18\) 0 0
\(19\) −3322.00 5753.87i −0.111112 0.192452i 0.805107 0.593130i \(-0.202108\pi\)
−0.916219 + 0.400678i \(0.868775\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −991.000 1716.46i −0.0169835 0.0294162i 0.857409 0.514636i \(-0.172073\pi\)
−0.874392 + 0.485220i \(0.838740\pi\)
\(24\) 0 0
\(25\) 34062.5 58998.0i 0.436000 0.755174i
\(26\) 0 0
\(27\) −19683.0 −0.192450
\(28\) 0 0
\(29\) −208106. −1.58450 −0.792249 0.610198i \(-0.791090\pi\)
−0.792249 + 0.610198i \(0.791090\pi\)
\(30\) 0 0
\(31\) 58896.0 102011.i 0.355075 0.615008i −0.632056 0.774923i \(-0.717789\pi\)
0.987131 + 0.159915i \(0.0511221\pi\)
\(32\) 0 0
\(33\) 37449.0 + 64863.6i 0.181402 + 0.314197i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 167843. + 290713.i 0.544750 + 0.943535i 0.998623 + 0.0524680i \(0.0167088\pi\)
−0.453873 + 0.891067i \(0.649958\pi\)
\(38\) 0 0
\(39\) −44469.0 + 77022.6i −0.120041 + 0.207918i
\(40\) 0 0
\(41\) −265488. −0.601591 −0.300796 0.953689i \(-0.597252\pi\)
−0.300796 + 0.953689i \(0.597252\pi\)
\(42\) 0 0
\(43\) −93292.0 −0.178939 −0.0894695 0.995990i \(-0.528517\pi\)
−0.0894695 + 0.995990i \(0.528517\pi\)
\(44\) 0 0
\(45\) −36450.0 + 63133.3i −0.0596285 + 0.103280i
\(46\) 0 0
\(47\) 328758. + 569426.i 0.461885 + 0.800008i 0.999055 0.0434658i \(-0.0138400\pi\)
−0.537170 + 0.843474i \(0.680507\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 79650.0 + 137958.i 0.0840795 + 0.145630i
\(52\) 0 0
\(53\) 304359. 527165.i 0.280815 0.486386i −0.690771 0.723074i \(-0.742729\pi\)
0.971586 + 0.236688i \(0.0760619\pi\)
\(54\) 0 0
\(55\) 277400. 0.224821
\(56\) 0 0
\(57\) −179388. −0.128301
\(58\) 0 0
\(59\) 268060. 464294.i 0.169922 0.294314i −0.768470 0.639886i \(-0.778982\pi\)
0.938392 + 0.345572i \(0.112315\pi\)
\(60\) 0 0
\(61\) 898545. + 1.55633e6i 0.506857 + 0.877902i 0.999969 + 0.00793591i \(0.00252610\pi\)
−0.493112 + 0.869966i \(0.664141\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 164700. + 285269.i 0.0743870 + 0.128842i
\(66\) 0 0
\(67\) −1.06159e6 + 1.83872e6i −0.431215 + 0.746887i −0.996978 0.0776811i \(-0.975248\pi\)
0.565763 + 0.824568i \(0.308582\pi\)
\(68\) 0 0
\(69\) −53514.0 −0.0196108
\(70\) 0 0
\(71\) −1.19121e6 −0.394990 −0.197495 0.980304i \(-0.563281\pi\)
−0.197495 + 0.980304i \(0.563281\pi\)
\(72\) 0 0
\(73\) −528215. + 914895.i −0.158921 + 0.275259i −0.934480 0.356016i \(-0.884135\pi\)
0.775559 + 0.631275i \(0.217468\pi\)
\(74\) 0 0
\(75\) −919688. 1.59295e6i −0.251725 0.436000i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −499242. 864713.i −0.113924 0.197323i 0.803425 0.595406i \(-0.203009\pi\)
−0.917349 + 0.398083i \(0.869675\pi\)
\(80\) 0 0
\(81\) −265720. + 460241.i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 3.89800e6 0.748288 0.374144 0.927371i \(-0.377937\pi\)
0.374144 + 0.927371i \(0.377937\pi\)
\(84\) 0 0
\(85\) 590000. 0.104204
\(86\) 0 0
\(87\) −2.80943e6 + 4.86608e6i −0.457405 + 0.792249i
\(88\) 0 0
\(89\) 2.31118e6 + 4.00307e6i 0.347511 + 0.601906i 0.985807 0.167885i \(-0.0536938\pi\)
−0.638296 + 0.769791i \(0.720360\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −1.59019e6 2.75429e6i −0.205003 0.355075i
\(94\) 0 0
\(95\) −332200. + 575387.i −0.0397527 + 0.0688538i
\(96\) 0 0
\(97\) 1.52877e7 1.70075 0.850377 0.526174i \(-0.176374\pi\)
0.850377 + 0.526174i \(0.176374\pi\)
\(98\) 0 0
\(99\) 2.02225e6 0.209465
\(100\) 0 0
\(101\) −1.11934e6 + 1.93876e6i −0.108103 + 0.187240i −0.915002 0.403450i \(-0.867811\pi\)
0.806899 + 0.590690i \(0.201144\pi\)
\(102\) 0 0
\(103\) −6.22511e6 1.07822e7i −0.561328 0.972249i −0.997381 0.0723279i \(-0.976957\pi\)
0.436053 0.899921i \(-0.356376\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.79430e6 + 6.57192e6i 0.299425 + 0.518620i 0.976005 0.217750i \(-0.0698717\pi\)
−0.676579 + 0.736370i \(0.736538\pi\)
\(108\) 0 0
\(109\) −2.58548e6 + 4.47819e6i −0.191227 + 0.331215i −0.945657 0.325166i \(-0.894580\pi\)
0.754430 + 0.656380i \(0.227913\pi\)
\(110\) 0 0
\(111\) 9.06352e6 0.629023
\(112\) 0 0
\(113\) −9.63868e6 −0.628410 −0.314205 0.949355i \(-0.601738\pi\)
−0.314205 + 0.949355i \(0.601738\pi\)
\(114\) 0 0
\(115\) −99100.0 + 171646.i −0.00607619 + 0.0105243i
\(116\) 0 0
\(117\) 1.20066e6 + 2.07961e6i 0.0693060 + 0.120041i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 5.89605e6 + 1.02123e7i 0.302560 + 0.524050i
\(122\) 0 0
\(123\) −3.58409e6 + 6.20782e6i −0.173664 + 0.300796i
\(124\) 0 0
\(125\) −1.46250e7 −0.669747
\(126\) 0 0
\(127\) 8.08309e6 0.350158 0.175079 0.984554i \(-0.443982\pi\)
0.175079 + 0.984554i \(0.443982\pi\)
\(128\) 0 0
\(129\) −1.25944e6 + 2.18142e6i −0.0516552 + 0.0894695i
\(130\) 0 0
\(131\) 9.87927e6 + 1.71114e7i 0.383951 + 0.665022i 0.991623 0.129166i \(-0.0412299\pi\)
−0.607672 + 0.794188i \(0.707897\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 984150. + 1.70460e6i 0.0344265 + 0.0596285i
\(136\) 0 0
\(137\) 2.40448e7 4.16468e7i 0.798913 1.38376i −0.121412 0.992602i \(-0.538742\pi\)
0.920325 0.391155i \(-0.127924\pi\)
\(138\) 0 0
\(139\) 1.37173e7 0.433229 0.216615 0.976257i \(-0.430499\pi\)
0.216615 + 0.976257i \(0.430499\pi\)
\(140\) 0 0
\(141\) 1.77529e7 0.533339
\(142\) 0 0
\(143\) 4.56878e6 7.91336e6i 0.130654 0.226300i
\(144\) 0 0
\(145\) 1.04053e7 + 1.80225e7i 0.283444 + 0.490939i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 3.53552e7 + 6.12370e7i 0.875591 + 1.51657i 0.856132 + 0.516758i \(0.172861\pi\)
0.0194598 + 0.999811i \(0.493805\pi\)
\(150\) 0 0
\(151\) 1.28485e7 2.22542e7i 0.303691 0.526009i −0.673278 0.739390i \(-0.735114\pi\)
0.976969 + 0.213381i \(0.0684475\pi\)
\(152\) 0 0
\(153\) 4.30110e6 0.0970867
\(154\) 0 0
\(155\) −1.17792e7 −0.254071
\(156\) 0 0
\(157\) −1.04590e7 + 1.81155e7i −0.215695 + 0.373595i −0.953487 0.301433i \(-0.902535\pi\)
0.737792 + 0.675028i \(0.235868\pi\)
\(158\) 0 0
\(159\) −8.21769e6 1.42335e7i −0.162129 0.280815i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −2.72080e7 4.71256e7i −0.492084 0.852315i 0.507874 0.861431i \(-0.330432\pi\)
−0.999958 + 0.00911613i \(0.997098\pi\)
\(164\) 0 0
\(165\) 3.74490e6 6.48636e6i 0.0649003 0.112411i
\(166\) 0 0
\(167\) 6.41888e6 0.106648 0.0533238 0.998577i \(-0.483018\pi\)
0.0533238 + 0.998577i \(0.483018\pi\)
\(168\) 0 0
\(169\) −5.18981e7 −0.827081
\(170\) 0 0
\(171\) −2.42174e6 + 4.19457e6i −0.0370374 + 0.0641507i
\(172\) 0 0
\(173\) 2.73266e7 + 4.73311e7i 0.401259 + 0.695000i 0.993878 0.110482i \(-0.0352395\pi\)
−0.592619 + 0.805483i \(0.701906\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −7.23762e6 1.25359e7i −0.0981046 0.169922i
\(178\) 0 0
\(179\) 1.88329e7 3.26196e7i 0.245433 0.425102i −0.716821 0.697258i \(-0.754403\pi\)
0.962253 + 0.272156i \(0.0877367\pi\)
\(180\) 0 0
\(181\) 1.76788e7 0.221604 0.110802 0.993842i \(-0.464658\pi\)
0.110802 + 0.993842i \(0.464658\pi\)
\(182\) 0 0
\(183\) 4.85214e7 0.585268
\(184\) 0 0
\(185\) 1.67843e7 2.90713e7i 0.194896 0.337569i
\(186\) 0 0
\(187\) −8.18330e6 1.41739e7i −0.0915130 0.158505i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2.04588e7 3.54357e7i −0.212454 0.367980i 0.740028 0.672576i \(-0.234812\pi\)
−0.952482 + 0.304595i \(0.901479\pi\)
\(192\) 0 0
\(193\) 8.19134e7 1.41878e8i 0.820171 1.42058i −0.0853830 0.996348i \(-0.527211\pi\)
0.905554 0.424230i \(-0.139455\pi\)
\(194\) 0 0
\(195\) 8.89380e6 0.0858947
\(196\) 0 0
\(197\) 8.02076e7 0.747453 0.373726 0.927539i \(-0.378080\pi\)
0.373726 + 0.927539i \(0.378080\pi\)
\(198\) 0 0
\(199\) −4.91610e7 + 8.51493e7i −0.442216 + 0.765941i −0.997854 0.0654838i \(-0.979141\pi\)
0.555637 + 0.831425i \(0.312474\pi\)
\(200\) 0 0
\(201\) 2.86629e7 + 4.96456e7i 0.248962 + 0.431215i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 1.32744e7 + 2.29919e7i 0.107616 + 0.186396i
\(206\) 0 0
\(207\) −722439. + 1.25130e6i −0.00566115 + 0.00980541i
\(208\) 0 0
\(209\) 1.84305e7 0.139645
\(210\) 0 0
\(211\) 1.36321e8 0.999021 0.499510 0.866308i \(-0.333513\pi\)
0.499510 + 0.866308i \(0.333513\pi\)
\(212\) 0 0
\(213\) −1.60814e7 + 2.78538e7i −0.114024 + 0.197495i
\(214\) 0 0
\(215\) 4.66460e6 + 8.07932e6i 0.0320096 + 0.0554422i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 1.42618e7 + 2.47022e7i 0.0917530 + 0.158921i
\(220\) 0 0
\(221\) 9.71730e6 1.68309e7i 0.0605582 0.104890i
\(222\) 0 0
\(223\) 1.26358e8 0.763019 0.381510 0.924365i \(-0.375404\pi\)
0.381510 + 0.924365i \(0.375404\pi\)
\(224\) 0 0
\(225\) −4.96631e7 −0.290667
\(226\) 0 0
\(227\) −1.17004e8 + 2.02656e8i −0.663909 + 1.14992i 0.315671 + 0.948869i \(0.397770\pi\)
−0.979580 + 0.201055i \(0.935563\pi\)
\(228\) 0 0
\(229\) −3.41803e7 5.92020e7i −0.188084 0.325771i 0.756527 0.653962i \(-0.226894\pi\)
−0.944611 + 0.328191i \(0.893561\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −9.01923e7 1.56218e8i −0.467115 0.809067i 0.532179 0.846632i \(-0.321373\pi\)
−0.999294 + 0.0375648i \(0.988040\pi\)
\(234\) 0 0
\(235\) 3.28758e7 5.69426e7i 0.165249 0.286220i
\(236\) 0 0
\(237\) −2.69591e7 −0.131548
\(238\) 0 0
\(239\) 2.61131e8 1.23727 0.618637 0.785677i \(-0.287685\pi\)
0.618637 + 0.785677i \(0.287685\pi\)
\(240\) 0 0
\(241\) −9.88781e6 + 1.71262e7i −0.0455031 + 0.0788136i −0.887880 0.460075i \(-0.847822\pi\)
0.842377 + 0.538889i \(0.181156\pi\)
\(242\) 0 0
\(243\) 7.17445e6 + 1.24265e7i 0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 1.09427e7 + 1.89533e7i 0.0462045 + 0.0800285i
\(248\) 0 0
\(249\) 5.26231e7 9.11458e7i 0.216012 0.374144i
\(250\) 0 0
\(251\) 1.53770e8 0.613779 0.306890 0.951745i \(-0.400712\pi\)
0.306890 + 0.951745i \(0.400712\pi\)
\(252\) 0 0
\(253\) 5.49807e6 0.0213446
\(254\) 0 0
\(255\) 7.96500e6 1.37958e7i 0.0300812 0.0521022i
\(256\) 0 0
\(257\) 7.16802e7 + 1.24154e8i 0.263411 + 0.456241i 0.967146 0.254222i \(-0.0818192\pi\)
−0.703735 + 0.710462i \(0.748486\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 7.58546e7 + 1.31384e8i 0.264083 + 0.457405i
\(262\) 0 0
\(263\) 2.53650e8 4.39336e8i 0.859786 1.48919i −0.0123459 0.999924i \(-0.503930\pi\)
0.872132 0.489270i \(-0.162737\pi\)
\(264\) 0 0
\(265\) −6.08718e7 −0.200935
\(266\) 0 0
\(267\) 1.24804e8 0.401271
\(268\) 0 0
\(269\) −2.63943e8 + 4.57163e8i −0.826755 + 1.43198i 0.0738149 + 0.997272i \(0.476483\pi\)
−0.900570 + 0.434710i \(0.856851\pi\)
\(270\) 0 0
\(271\) 2.52918e8 + 4.38067e8i 0.771947 + 1.33705i 0.936495 + 0.350682i \(0.114050\pi\)
−0.164548 + 0.986369i \(0.552616\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 9.44894e7 + 1.63660e8i 0.273980 + 0.474547i
\(276\) 0 0
\(277\) 2.94293e8 5.09730e8i 0.831956 1.44099i −0.0645284 0.997916i \(-0.520554\pi\)
0.896485 0.443075i \(-0.146112\pi\)
\(278\) 0 0
\(279\) −8.58704e7 −0.236717
\(280\) 0 0
\(281\) 8.65142e7 0.232603 0.116301 0.993214i \(-0.462896\pi\)
0.116301 + 0.993214i \(0.462896\pi\)
\(282\) 0 0
\(283\) 7.86504e7 1.36227e8i 0.206276 0.357280i −0.744263 0.667887i \(-0.767199\pi\)
0.950538 + 0.310607i \(0.100532\pi\)
\(284\) 0 0
\(285\) 8.96940e6 + 1.55355e7i 0.0229513 + 0.0397527i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 1.87764e8 + 3.25217e8i 0.457584 + 0.792558i
\(290\) 0 0
\(291\) 2.06384e8 3.57468e8i 0.490965 0.850377i
\(292\) 0 0
\(293\) 6.80964e8 1.58157 0.790783 0.612097i \(-0.209674\pi\)
0.790783 + 0.612097i \(0.209674\pi\)
\(294\) 0 0
\(295\) −5.36120e7 −0.121586
\(296\) 0 0
\(297\) 2.73003e7 4.72855e7i 0.0604672 0.104732i
\(298\) 0 0
\(299\) 3.26435e6 + 5.65403e6i 0.00706233 + 0.0122323i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 3.02223e7 + 5.23465e7i 0.0624134 + 0.108103i
\(304\) 0 0
\(305\) 8.98545e7 1.55633e8i 0.181339 0.314088i
\(306\) 0 0
\(307\) 2.81734e8 0.555718 0.277859 0.960622i \(-0.410375\pi\)
0.277859 + 0.960622i \(0.410375\pi\)
\(308\) 0 0
\(309\) −3.36156e8 −0.648166
\(310\) 0 0
\(311\) 2.09860e8 3.63487e8i 0.395610 0.685217i −0.597569 0.801818i \(-0.703866\pi\)
0.993179 + 0.116601i \(0.0371998\pi\)
\(312\) 0 0
\(313\) 1.14342e8 + 1.98046e8i 0.210766 + 0.365057i 0.951954 0.306240i \(-0.0990709\pi\)
−0.741188 + 0.671297i \(0.765738\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.33001e8 2.30365e8i −0.234503 0.406171i 0.724625 0.689143i \(-0.242013\pi\)
−0.959128 + 0.282972i \(0.908680\pi\)
\(318\) 0 0
\(319\) 2.88643e8 4.99944e8i 0.497844 0.862292i
\(320\) 0 0
\(321\) 2.04892e8 0.345747
\(322\) 0 0
\(323\) 3.91996e7 0.0647251
\(324\) 0 0
\(325\) −1.12202e8 + 1.94339e8i −0.181304 + 0.314028i
\(326\) 0 0
\(327\) 6.98080e7 + 1.20911e8i 0.110405 + 0.191227i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 3.58054e8 + 6.20167e8i 0.542688 + 0.939963i 0.998749 + 0.0500141i \(0.0159266\pi\)
−0.456061 + 0.889949i \(0.650740\pi\)
\(332\) 0 0
\(333\) 1.22358e8 2.11929e8i 0.181583 0.314512i
\(334\) 0 0
\(335\) 2.12318e8 0.308553
\(336\) 0 0
\(337\) 5.70266e8 0.811657 0.405829 0.913949i \(-0.366983\pi\)
0.405829 + 0.913949i \(0.366983\pi\)
\(338\) 0 0
\(339\) −1.30122e8 + 2.25378e8i −0.181406 + 0.314205i
\(340\) 0 0
\(341\) 1.63378e8 + 2.82978e8i 0.223127 + 0.386467i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 2.67570e6 + 4.63445e6i 0.00350809 + 0.00607619i
\(346\) 0 0
\(347\) 8.23203e7 1.42583e8i 0.105768 0.183195i −0.808284 0.588793i \(-0.799603\pi\)
0.914052 + 0.405598i \(0.132937\pi\)
\(348\) 0 0
\(349\) 1.31564e9 1.65671 0.828357 0.560200i \(-0.189276\pi\)
0.828357 + 0.560200i \(0.189276\pi\)
\(350\) 0 0
\(351\) 6.48358e7 0.0800276
\(352\) 0 0
\(353\) −7.80588e8 + 1.35202e9i −0.944518 + 1.63595i −0.187805 + 0.982206i \(0.560137\pi\)
−0.756713 + 0.653747i \(0.773196\pi\)
\(354\) 0 0
\(355\) 5.95607e7 + 1.03162e8i 0.0706579 + 0.122383i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 4.30358e8 + 7.45402e8i 0.490907 + 0.850276i 0.999945 0.0104681i \(-0.00333215\pi\)
−0.509038 + 0.860744i \(0.669999\pi\)
\(360\) 0 0
\(361\) 4.24865e8 7.35887e8i 0.475308 0.823258i
\(362\) 0 0
\(363\) 3.18387e8 0.349367
\(364\) 0 0
\(365\) 1.05643e8 0.113714
\(366\) 0 0
\(367\) −4.56066e8 + 7.89930e8i −0.481612 + 0.834176i −0.999777 0.0211045i \(-0.993282\pi\)
0.518166 + 0.855280i \(0.326615\pi\)
\(368\) 0 0
\(369\) 9.67704e7 + 1.67611e8i 0.100265 + 0.173664i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −1.18002e8 2.04386e8i −0.117736 0.203925i 0.801134 0.598485i \(-0.204230\pi\)
−0.918870 + 0.394560i \(0.870897\pi\)
\(374\) 0 0
\(375\) −1.97438e8 + 3.41972e8i −0.193339 + 0.334874i
\(376\) 0 0
\(377\) 6.85501e8 0.658891
\(378\) 0 0
\(379\) 8.29313e8 0.782495 0.391247 0.920286i \(-0.372044\pi\)
0.391247 + 0.920286i \(0.372044\pi\)
\(380\) 0 0
\(381\) 1.09122e8 1.89004e8i 0.101082 0.175079i
\(382\) 0 0
\(383\) 6.08316e8 + 1.05363e9i 0.553265 + 0.958284i 0.998036 + 0.0626393i \(0.0199518\pi\)
−0.444771 + 0.895644i \(0.646715\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 3.40049e7 + 5.88983e7i 0.0298232 + 0.0516552i
\(388\) 0 0
\(389\) 5.91064e7 1.02375e8i 0.0509109 0.0881803i −0.839447 0.543442i \(-0.817121\pi\)
0.890358 + 0.455261i \(0.150454\pi\)
\(390\) 0 0
\(391\) 1.16938e7 0.00989321
\(392\) 0 0
\(393\) 5.33481e8 0.443348
\(394\) 0 0
\(395\) −4.99242e7 + 8.64713e7i −0.0407588 + 0.0705963i
\(396\) 0 0
\(397\) −1.81283e7 3.13991e7i −0.0145408 0.0251855i 0.858663 0.512540i \(-0.171295\pi\)
−0.873204 + 0.487354i \(0.837962\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2.53425e8 4.38945e8i −0.196265 0.339942i 0.751049 0.660246i \(-0.229548\pi\)
−0.947315 + 0.320305i \(0.896215\pi\)
\(402\) 0 0
\(403\) −1.94003e8 + 3.36024e8i −0.147653 + 0.255742i
\(404\) 0 0
\(405\) 5.31441e7 0.0397523
\(406\) 0 0
\(407\) −9.31193e8 −0.684635
\(408\) 0 0
\(409\) −8.40605e8 + 1.45597e9i −0.607519 + 1.05225i 0.384128 + 0.923280i \(0.374502\pi\)
−0.991648 + 0.128975i \(0.958831\pi\)
\(410\) 0 0
\(411\) −6.49210e8 1.12446e9i −0.461252 0.798913i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −1.94900e8 3.37577e8i −0.133858 0.231849i
\(416\) 0 0
\(417\) 1.85184e8 3.20748e8i 0.125062 0.216615i
\(418\) 0 0
\(419\) 4.94962e8 0.328718 0.164359 0.986401i \(-0.447444\pi\)
0.164359 + 0.986401i \(0.447444\pi\)
\(420\) 0 0
\(421\) −6.57487e7 −0.0429437 −0.0214719 0.999769i \(-0.506835\pi\)
−0.0214719 + 0.999769i \(0.506835\pi\)
\(422\) 0 0
\(423\) 2.39665e8 4.15111e8i 0.153962 0.266669i
\(424\) 0 0
\(425\) 2.00969e8 + 3.48088e8i 0.126989 + 0.219952i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −1.23357e8 2.13661e8i −0.0754333 0.130654i
\(430\) 0 0
\(431\) 6.67089e8 1.15543e9i 0.401341 0.695143i −0.592547 0.805536i \(-0.701878\pi\)
0.993888 + 0.110393i \(0.0352109\pi\)
\(432\) 0 0
\(433\) −2.47903e7 −0.0146749 −0.00733745 0.999973i \(-0.502336\pi\)
−0.00733745 + 0.999973i \(0.502336\pi\)
\(434\) 0 0
\(435\) 5.61886e8 0.327292
\(436\) 0 0
\(437\) −6.58420e6 + 1.14042e7i −0.00377414 + 0.00653701i
\(438\) 0 0
\(439\) 3.44664e8 + 5.96975e8i 0.194433 + 0.336768i 0.946714 0.322074i \(-0.104380\pi\)
−0.752282 + 0.658842i \(0.771047\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 2.87308e8 + 4.97633e8i 0.157013 + 0.271954i 0.933790 0.357821i \(-0.116480\pi\)
−0.776777 + 0.629775i \(0.783147\pi\)
\(444\) 0 0
\(445\) 2.31118e8 4.00307e8i 0.124329 0.215344i
\(446\) 0 0
\(447\) 1.90918e9 1.01105
\(448\) 0 0
\(449\) 9.56884e7 0.0498881 0.0249440 0.999689i \(-0.492059\pi\)
0.0249440 + 0.999689i \(0.492059\pi\)
\(450\) 0 0
\(451\) 3.68232e8 6.37796e8i 0.189018 0.327389i
\(452\) 0 0
\(453\) −3.46909e8 6.00864e8i −0.175336 0.303691i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 2.36545e7 + 4.09707e7i 0.0115933 + 0.0200802i 0.871764 0.489926i \(-0.162976\pi\)
−0.860171 + 0.510006i \(0.829643\pi\)
\(458\) 0 0
\(459\) 5.80648e7 1.00571e8i 0.0280265 0.0485433i
\(460\) 0 0
\(461\) −2.13567e9 −1.01527 −0.507634 0.861573i \(-0.669480\pi\)
−0.507634 + 0.861573i \(0.669480\pi\)
\(462\) 0 0
\(463\) 2.92675e8 0.137042 0.0685208 0.997650i \(-0.478172\pi\)
0.0685208 + 0.997650i \(0.478172\pi\)
\(464\) 0 0
\(465\) −1.59019e8 + 2.75429e8i −0.0733439 + 0.127035i
\(466\) 0 0
\(467\) 1.76917e9 + 3.06429e9i 0.803824 + 1.39226i 0.917082 + 0.398698i \(0.130538\pi\)
−0.113259 + 0.993566i \(0.536129\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 2.82392e8 + 4.89118e8i 0.124532 + 0.215695i
\(472\) 0 0
\(473\) 1.29396e8 2.24120e8i 0.0562221 0.0973795i
\(474\) 0 0
\(475\) −4.52622e8 −0.193780
\(476\) 0 0
\(477\) −4.43755e8 −0.187210
\(478\) 0 0
\(479\) 2.07849e9 3.60005e9i 0.864120 1.49670i −0.00379880 0.999993i \(-0.501209\pi\)
0.867919 0.496707i \(-0.165457\pi\)
\(480\) 0 0
\(481\) −5.52875e8 9.57607e8i −0.226527 0.392355i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −7.64386e8 1.32395e9i −0.304240 0.526959i
\(486\) 0 0
\(487\) −6.20460e7 + 1.07467e8i −0.0243423 + 0.0421622i −0.877940 0.478771i \(-0.841083\pi\)
0.853598 + 0.520933i \(0.174416\pi\)
\(488\) 0 0
\(489\) −1.46923e9 −0.568210
\(490\) 0 0
\(491\) −3.29218e9 −1.25516 −0.627578 0.778554i \(-0.715954\pi\)
−0.627578 + 0.778554i \(0.715954\pi\)
\(492\) 0 0
\(493\) 6.13913e8 1.06333e9i 0.230750 0.399671i
\(494\) 0 0
\(495\) −1.01112e8 1.75132e8i −0.0374702 0.0649003i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 1.80219e8 + 3.12149e8i 0.0649306 + 0.112463i 0.896663 0.442713i \(-0.145984\pi\)
−0.831733 + 0.555176i \(0.812651\pi\)
\(500\) 0 0
\(501\) 8.66548e7 1.50091e8i 0.0307865 0.0533238i
\(502\) 0 0
\(503\) −4.29760e9 −1.50570 −0.752849 0.658193i \(-0.771321\pi\)
−0.752849 + 0.658193i \(0.771321\pi\)
\(504\) 0 0
\(505\) 2.23869e8 0.0773524
\(506\) 0 0
\(507\) −7.00624e8 + 1.21352e9i −0.238758 + 0.413540i
\(508\) 0 0
\(509\) 2.71294e8 + 4.69895e8i 0.0911860 + 0.157939i 0.908010 0.418948i \(-0.137601\pi\)
−0.816824 + 0.576886i \(0.804268\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 6.53869e7 + 1.13253e8i 0.0213836 + 0.0370374i
\(514\) 0 0
\(515\) −6.22511e8 + 1.07822e9i −0.200827 + 0.347842i
\(516\) 0 0
\(517\) −1.82395e9 −0.580492
\(518\) 0 0
\(519\) 1.47564e9 0.463334
\(520\) 0 0
\(521\) 1.18378e8 2.05036e8i 0.0366722 0.0635182i −0.847107 0.531423i \(-0.821658\pi\)
0.883779 + 0.467905i \(0.154991\pi\)
\(522\) 0 0
\(523\) −3.24162e9 5.61465e9i −0.990846 1.71619i −0.612337 0.790597i \(-0.709770\pi\)
−0.378509 0.925598i \(-0.623563\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 3.47486e8 + 6.01864e8i 0.103419 + 0.179127i
\(528\) 0 0
\(529\) 1.70045e9 2.94526e9i 0.499423 0.865026i
\(530\) 0 0
\(531\) −3.90831e8 −0.113281
\(532\) 0 0
\(533\) 8.74517e8 0.250163
\(534\) 0 0
\(535\) 3.79430e8 6.57192e8i 0.107126 0.185547i
\(536\) 0 0
\(537\) −5.08489e8 8.80729e8i −0.141701 0.245433i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 7.50494e7 + 1.29989e8i 0.0203778 + 0.0352954i 0.876034 0.482248i \(-0.160180\pi\)
−0.855657 + 0.517544i \(0.826846\pi\)
\(542\) 0 0
\(543\) 2.38664e8 4.13378e8i 0.0639716 0.110802i
\(544\) 0 0
\(545\) 5.17097e8 0.136831
\(546\) 0 0
\(547\) 3.32631e9 0.868974 0.434487 0.900678i \(-0.356930\pi\)
0.434487 + 0.900678i \(0.356930\pi\)
\(548\) 0 0
\(549\) 6.55039e8 1.13456e9i 0.168952 0.292634i
\(550\) 0 0
\(551\) 6.91328e8 + 1.19742e9i 0.176057 + 0.304940i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −4.53176e8 7.84924e8i −0.112523 0.194896i
\(556\) 0 0
\(557\) −2.36256e9 + 4.09208e9i −0.579282 + 1.00335i 0.416280 + 0.909236i \(0.363334\pi\)
−0.995562 + 0.0941092i \(0.970000\pi\)
\(558\) 0 0
\(559\) 3.07304e8 0.0744092
\(560\) 0 0
\(561\) −4.41898e8 −0.105670
\(562\) 0 0
\(563\) −3.55522e9 + 6.15782e9i −0.839628 + 1.45428i 0.0505779 + 0.998720i \(0.483894\pi\)
−0.890206 + 0.455558i \(0.849440\pi\)
\(564\) 0 0
\(565\) 4.81934e8 + 8.34734e8i 0.112413 + 0.194706i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −3.27657e9 5.67519e9i −0.745636 1.29148i −0.949897 0.312564i \(-0.898812\pi\)
0.204260 0.978917i \(-0.434521\pi\)
\(570\) 0 0
\(571\) −4.14639e9 + 7.18175e9i −0.932059 + 1.61437i −0.152263 + 0.988340i \(0.548656\pi\)
−0.779796 + 0.626034i \(0.784677\pi\)
\(572\) 0 0
\(573\) −1.10478e9 −0.245320
\(574\) 0 0
\(575\) −1.35024e8 −0.0296192
\(576\) 0 0
\(577\) 2.94000e9 5.09223e9i 0.637135 1.10355i −0.348923 0.937151i \(-0.613453\pi\)
0.986058 0.166400i \(-0.0532141\pi\)
\(578\) 0 0
\(579\) −2.21166e9 3.83071e9i −0.473526 0.820171i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 8.44292e8 + 1.46236e9i 0.176463 + 0.305642i
\(584\) 0 0
\(585\) 1.20066e8 2.07961e8i 0.0247957 0.0429473i
\(586\) 0 0
\(587\) −1.43194e9 −0.292207 −0.146103 0.989269i \(-0.546673\pi\)
−0.146103 + 0.989269i \(0.546673\pi\)
\(588\) 0 0
\(589\) −7.82610e8 −0.157813
\(590\) 0 0
\(591\) 1.08280e9 1.87547e9i 0.215771 0.373726i
\(592\) 0 0
\(593\) −1.74069e9 3.01497e9i −0.342792 0.593733i 0.642158 0.766572i \(-0.278039\pi\)
−0.984950 + 0.172839i \(0.944706\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 1.32735e9 + 2.29903e9i 0.255314 + 0.442216i
\(598\) 0 0
\(599\) −3.96799e9 + 6.87275e9i −0.754356 + 1.30658i 0.191338 + 0.981524i \(0.438717\pi\)
−0.945694 + 0.325058i \(0.894616\pi\)
\(600\) 0 0
\(601\) −4.05169e9 −0.761335 −0.380668 0.924712i \(-0.624306\pi\)
−0.380668 + 0.924712i \(0.624306\pi\)
\(602\) 0 0
\(603\) 1.54780e9 0.287477
\(604\) 0 0
\(605\) 5.89605e8 1.02123e9i 0.108247 0.187490i
\(606\) 0 0
\(607\) −2.59580e9 4.49605e9i −0.471097 0.815964i 0.528356 0.849023i \(-0.322808\pi\)
−0.999453 + 0.0330588i \(0.989475\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.08293e9 1.87569e9i −0.192068 0.332672i
\(612\) 0 0
\(613\) −1.84903e9 + 3.20262e9i −0.324215 + 0.561557i −0.981353 0.192213i \(-0.938434\pi\)
0.657138 + 0.753770i \(0.271767\pi\)
\(614\) 0 0
\(615\) 7.16818e8 0.124264
\(616\) 0 0
\(617\) −6.19879e9 −1.06245 −0.531226 0.847230i \(-0.678268\pi\)
−0.531226 + 0.847230i \(0.678268\pi\)
\(618\) 0 0
\(619\) 1.42569e9 2.46936e9i 0.241605 0.418473i −0.719566 0.694424i \(-0.755659\pi\)
0.961172 + 0.275951i \(0.0889927\pi\)
\(620\) 0 0
\(621\) 1.95059e7 + 3.37851e7i 0.00326847 + 0.00566115i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −1.92988e9 3.34266e9i −0.316192 0.547661i
\(626\) 0 0
\(627\) 2.48811e8 4.30954e8i 0.0403119 0.0698223i
\(628\) 0 0
\(629\) −1.98055e9 −0.317328
\(630\) 0 0
\(631\) −7.56414e9 −1.19855 −0.599276 0.800543i \(-0.704545\pi\)
−0.599276 + 0.800543i \(0.704545\pi\)
\(632\) 0 0
\(633\) 1.84033e9 3.18755e9i 0.288392 0.499510i
\(634\) 0 0
\(635\) −4.04155e8 7.00016e8i −0.0626382 0.108493i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 4.34198e8 + 7.52052e8i 0.0658316 + 0.114024i
\(640\) 0 0
\(641\) −5.60093e9 + 9.70109e9i −0.839957 + 1.45485i 0.0499734 + 0.998751i \(0.484086\pi\)
−0.889930 + 0.456097i \(0.849247\pi\)
\(642\) 0 0
\(643\) 7.87742e9 1.16855 0.584273 0.811557i \(-0.301380\pi\)
0.584273 + 0.811557i \(0.301380\pi\)
\(644\) 0 0
\(645\) 2.51888e8 0.0369615
\(646\) 0 0
\(647\) −6.24724e8 + 1.08205e9i −0.0906825 + 0.157067i −0.907798 0.419407i \(-0.862238\pi\)
0.817116 + 0.576473i \(0.195572\pi\)
\(648\) 0 0
\(649\) 7.43598e8 + 1.28795e9i 0.106778 + 0.184945i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −3.76348e9 6.51854e9i −0.528924 0.916124i −0.999431 0.0337275i \(-0.989262\pi\)
0.470507 0.882396i \(-0.344071\pi\)
\(654\) 0 0
\(655\) 9.87927e8 1.71114e9i 0.137366 0.237926i
\(656\) 0 0
\(657\) 7.70137e8 0.105947
\(658\) 0 0
\(659\) 2.29417e9 0.312268 0.156134 0.987736i \(-0.450097\pi\)
0.156134 + 0.987736i \(0.450097\pi\)
\(660\) 0 0
\(661\) 2.54192e9 4.40274e9i 0.342339 0.592949i −0.642527 0.766263i \(-0.722114\pi\)
0.984867 + 0.173314i \(0.0554474\pi\)
\(662\) 0 0
\(663\) −2.62367e8 4.54433e8i −0.0349633 0.0605582i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 2.06233e8 + 3.57206e8i 0.0269103 + 0.0466099i
\(668\) 0 0
\(669\) 1.70583e9 2.95459e9i 0.220265 0.381510i
\(670\) 0 0
\(671\) −4.98513e9 −0.637012
\(672\) 0 0
\(673\) −5.62649e9 −0.711516 −0.355758 0.934578i \(-0.615777\pi\)
−0.355758 + 0.934578i \(0.615777\pi\)
\(674\) 0 0
\(675\) −6.70452e8 + 1.16126e9i −0.0839082 + 0.145333i
\(676\) 0 0
\(677\) 5.13727e9 + 8.89801e9i 0.636314 + 1.10213i 0.986235 + 0.165349i \(0.0528752\pi\)
−0.349921 + 0.936779i \(0.613791\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 3.15909e9 + 5.47171e9i 0.383308 + 0.663909i
\(682\) 0 0
\(683\) −7.76228e9 + 1.34447e10i −0.932217 + 1.61465i −0.152693 + 0.988274i \(0.548795\pi\)
−0.779524 + 0.626373i \(0.784539\pi\)
\(684\) 0 0
\(685\) −4.80896e9 −0.571655
\(686\) 0 0
\(687\) −1.84574e9 −0.217181
\(688\) 0 0
\(689\) −1.00256e9 + 1.73648e9i −0.116773 + 0.202257i
\(690\) 0 0
\(691\) −4.11725e9 7.13128e9i −0.474716 0.822232i 0.524865 0.851186i \(-0.324116\pi\)
−0.999581 + 0.0289536i \(0.990782\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −6.85866e8 1.18796e9i −0.0774984 0.134231i
\(696\) 0 0
\(697\) 7.83190e8 1.35652e9i 0.0876097 0.151744i
\(698\) 0 0
\(699\) −4.87039e9 −0.539378
\(700\) 0 0
\(701\) −4.88820e9 −0.535964 −0.267982 0.963424i \(-0.586357\pi\)
−0.267982 + 0.963424i \(0.586357\pi\)
\(702\) 0 0
\(703\) 1.11515e9 1.93149e9i 0.121057 0.209677i
\(704\) 0 0
\(705\) −8.87647e8 1.53745e9i −0.0954065 0.165249i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 3.97553e9 + 6.88582e9i 0.418922 + 0.725594i 0.995831 0.0912141i \(-0.0290748\pi\)
−0.576909 + 0.816808i \(0.695741\pi\)
\(710\) 0 0
\(711\) −3.63947e8 + 6.30375e8i −0.0379748 + 0.0657742i
\(712\) 0 0
\(713\) −2.33464e8 −0.0241216
\(714\) 0 0
\(715\) −9.13756e8 −0.0934887
\(716\) 0 0
\(717\) 3.52527e9 6.10594e9i 0.357170 0.618637i
\(718\) 0 0
\(719\) 6.50173e9 + 1.12613e10i 0.652346 + 1.12990i 0.982552 + 0.185987i \(0.0595484\pi\)
−0.330206 + 0.943909i \(0.607118\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 2.66971e8 + 4.62407e8i 0.0262712 + 0.0455031i
\(724\) 0 0
\(725\) −7.08861e9 + 1.22778e10i −0.690841 + 1.19657i
\(726\) 0 0
\(727\) −1.73805e10 −1.67761 −0.838805 0.544431i \(-0.816745\pi\)
−0.838805 + 0.544431i \(0.816745\pi\)
\(728\) 0 0
\(729\) 3.87420e8 0.0370370
\(730\) 0 0
\(731\) 2.75211e8 4.76680e8i 0.0260589 0.0451353i
\(732\) 0 0
\(733\) −4.73557e9 8.20225e9i −0.444128 0.769253i 0.553863 0.832608i \(-0.313153\pi\)
−0.997991 + 0.0633553i \(0.979820\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −2.94485e9 5.10062e9i −0.270973 0.469339i
\(738\) 0 0
\(739\) −2.76457e9 + 4.78837e9i −0.251983 + 0.436448i −0.964072 0.265642i \(-0.914416\pi\)
0.712088 + 0.702090i \(0.247749\pi\)
\(740\) 0 0
\(741\) 5.90904e8 0.0533523
\(742\) 0 0
\(743\) −1.53701e10 −1.37472 −0.687362 0.726315i \(-0.741231\pi\)
−0.687362 + 0.726315i \(0.741231\pi\)
\(744\) 0 0
\(745\) 3.53552e9 6.12370e9i 0.313261 0.542584i
\(746\) 0 0
\(747\) −1.42082e9 2.46094e9i −0.124715 0.216012i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 4.25975e9 + 7.37811e9i 0.366982 + 0.635631i 0.989092 0.147299i \(-0.0470578\pi\)
−0.622110 + 0.782930i \(0.713724\pi\)
\(752\) 0 0
\(753\) 2.07589e9 3.59555e9i 0.177183 0.306890i
\(754\) 0 0
\(755\) −2.56970e9 −0.217304
\(756\) 0 0
\(757\) −4.72648e8 −0.0396006 −0.0198003 0.999804i \(-0.506303\pi\)
−0.0198003 + 0.999804i \(0.506303\pi\)
\(758\) 0 0
\(759\) 7.42239e7 1.28560e8i 0.00616166 0.0106723i
\(760\) 0 0
\(761\) 7.17326e9 + 1.24245e10i 0.590025 + 1.02195i 0.994228 + 0.107284i \(0.0342154\pi\)
−0.404203 + 0.914669i \(0.632451\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −2.15055e8 3.72486e8i −0.0173674 0.0300812i
\(766\) 0 0
\(767\) −8.82990e8 + 1.52938e9i −0.0706597 + 0.122386i
\(768\) 0 0
\(769\) 1.39480e10 1.10603 0.553017 0.833170i \(-0.313476\pi\)
0.553017 + 0.833170i \(0.313476\pi\)
\(770\) 0 0
\(771\) 3.87073e9 0.304160
\(772\) 0 0
\(773\) 2.16169e9 3.74415e9i 0.168331 0.291558i −0.769502 0.638644i \(-0.779496\pi\)
0.937833 + 0.347086i \(0.112829\pi\)
\(774\) 0 0
\(775\) −4.01229e9 6.94949e9i −0.309625 0.536287i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 8.81951e8 + 1.52758e9i 0.0668442 + 0.115777i
\(780\) 0 0
\(781\) 1.65221e9 2.86172e9i 0.124105 0.214955i
\(782\) 0 0
\(783\) 4.09615e9 0.304937
\(784\) 0 0
\(785\) 2.09180e9 0.154339