Properties

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

Related objects

Downloads

Learn more

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.c.373.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-13.5000 + 23.3827i) q^{3} +(50.0000 + 86.6025i) q^{5} +(-364.500 - 631.333i) q^{9} +O(q^{10})\) \(q+(-13.5000 + 23.3827i) q^{3} +(50.0000 + 86.6025i) q^{5} +(-364.500 - 631.333i) q^{9} +(-1387.00 + 2402.35i) q^{11} +3294.00 q^{13} -2700.00 q^{15} +(2950.00 - 5109.55i) q^{17} +(3322.00 + 5753.87i) q^{19} +(-991.000 - 1716.46i) q^{23} +(34062.5 - 58998.0i) q^{25} +19683.0 q^{27} -208106. q^{29} +(-58896.0 + 102011. i) q^{31} +(-37449.0 - 64863.6i) q^{33} +(167843. + 290713. i) q^{37} +(-44469.0 + 77022.6i) q^{39} +265488. q^{41} -93292.0 q^{43} +(36450.0 - 63133.3i) q^{45} +(-328758. - 569426. i) q^{47} +(79650.0 + 137958. i) q^{51} +(304359. - 527165. i) q^{53} -277400. q^{55} -179388. q^{57} +(-268060. + 464294. i) q^{59} +(-898545. - 1.55633e6i) q^{61} +(164700. + 285269. i) q^{65} +(-1.06159e6 + 1.83872e6i) q^{67} +53514.0 q^{69} -1.19121e6 q^{71} +(528215. - 914895. i) q^{73} +(919688. + 1.59295e6i) q^{75} +(-499242. - 864713. i) q^{79} +(-265720. + 460241. i) q^{81} -3.89800e6 q^{83} +590000. q^{85} +(2.80943e6 - 4.86608e6i) q^{87} +(-2.31118e6 - 4.00307e6i) q^{89} +(-1.59019e6 - 2.75429e6i) q^{93} +(-332200. + 575387. i) q^{95} -1.52877e7 q^{97} +2.02225e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 27 q^{3} + 100 q^{5} - 729 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 27 q^{3} + 100 q^{5} - 729 q^{9} - 2774 q^{11} + 6588 q^{13} - 5400 q^{15} + 5900 q^{17} + 6644 q^{19} - 1982 q^{23} + 68125 q^{25} + 39366 q^{27} - 416212 q^{29} - 117792 q^{31} - 74898 q^{33} + 335686 q^{37} - 88938 q^{39} + 530976 q^{41} - 186584 q^{43} + 72900 q^{45} - 657516 q^{47} + 159300 q^{51} + 608718 q^{53} - 554800 q^{55} - 358776 q^{57} - 536120 q^{59} - 1797090 q^{61} + 329400 q^{65} - 2123176 q^{67} + 107028 q^{69} - 2382428 q^{71} + 1056430 q^{73} + 1839375 q^{75} - 998484 q^{79} - 531441 q^{81} - 7796008 q^{83} + 1180000 q^{85} + 5618862 q^{87} - 4622352 q^{89} - 3180384 q^{93} - 664400 q^{95} - 30575420 q^{97} + 4044492 q^{99}+O(q^{100}) \) 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 0.941499 0.337016i \(-0.109418\pi\)
−0.762614 + 0.646854i \(0.776084\pi\)
\(6\) 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 \(-0.433331\pi\)
0.207918 + 0.978146i \(0.433331\pi\)
\(14\) 0 0
\(15\) −2700.00 −0.206559
\(16\) 0 0
\(17\) 2950.00 5109.55i 0.145630 0.252239i −0.783978 0.620789i \(-0.786812\pi\)
0.929608 + 0.368550i \(0.120146\pi\)
\(18\) 0 0
\(19\) 3322.00 + 5753.87i 0.111112 + 0.192452i 0.916219 0.400678i \(-0.131225\pi\)
−0.805107 + 0.593130i \(0.797892\pi\)
\(20\) 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 −0.987131 0.159915i \(-0.948878\pi\)
0.632056 + 0.774923i \(0.282211\pi\)
\(32\) 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 \(-0.402748\pi\)
0.300796 + 0.953689i \(0.402748\pi\)
\(42\) 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 0.537170 0.843474i \(-0.319493\pi\)
−0.999055 + 0.0434658i \(0.986160\pi\)
\(48\) 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 −0.938392 0.345572i \(-0.887685\pi\)
0.768470 + 0.639886i \(0.221018\pi\)
\(60\) 0 0
\(61\) −898545. 1.55633e6i −0.506857 0.877902i −0.999969 0.00793591i \(-0.997474\pi\)
0.493112 0.869966i \(-0.335859\pi\)
\(62\) 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 −0.775559 0.631275i \(-0.782532\pi\)
0.934480 + 0.356016i \(0.115865\pi\)
\(74\) 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 \(-0.622063\pi\)
−0.374144 + 0.927371i \(0.622063\pi\)
\(84\) 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 0.638296 0.769791i \(-0.279640\pi\)
−0.985807 + 0.167885i \(0.946306\pi\)
\(90\) 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 \(-0.823626\pi\)
−0.850377 + 0.526174i \(0.823626\pi\)
\(98\) 0 0
\(99\) 2.02225e6 0.209465
\(100\) 0 0
\(101\) 1.11934e6 1.93876e6i 0.108103 0.187240i −0.806899 0.590690i \(-0.798856\pi\)
0.915002 + 0.403450i \(0.132189\pi\)
\(102\) 0 0
\(103\) 6.22511e6 + 1.07822e7i 0.561328 + 0.972249i 0.997381 + 0.0723279i \(0.0230428\pi\)
−0.436053 + 0.899921i \(0.643624\pi\)
\(104\) 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 0.607672 0.794188i \(-0.292103\pi\)
−0.991623 + 0.129166i \(0.958770\pi\)
\(132\) 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 \(-0.569501\pi\)
−0.216615 + 0.976257i \(0.569501\pi\)
\(140\) 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 −0.737792 0.675028i \(-0.764132\pi\)
0.953487 + 0.301433i \(0.0974649\pi\)
\(158\) 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 \(-0.516982\pi\)
−0.0533238 + 0.998577i \(0.516982\pi\)
\(168\) 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 0.592619 0.805483i \(-0.298094\pi\)
−0.993878 + 0.110482i \(0.964760\pi\)
\(174\) 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 \(-0.535342\pi\)
−0.110802 + 0.993842i \(0.535342\pi\)
\(182\) 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 −0.555637 0.831425i \(-0.687526\pi\)
0.997854 + 0.0654838i \(0.0208591\pi\)
\(200\) 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 \(-0.624596\pi\)
−0.381510 + 0.924365i \(0.624596\pi\)
\(224\) 0 0
\(225\) −4.96631e7 −0.290667
\(226\) 0 0
\(227\) 1.17004e8 2.02656e8i 0.663909 1.14992i −0.315671 0.948869i \(-0.602230\pi\)
0.979580 0.201055i \(-0.0644370\pi\)
\(228\) 0 0
\(229\) 3.41803e7 + 5.92020e7i 0.188084 + 0.325771i 0.944611 0.328191i \(-0.106439\pi\)
−0.756527 + 0.653962i \(0.773106\pi\)
\(230\) 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 −0.842377 0.538889i \(-0.818844\pi\)
0.887880 + 0.460075i \(0.152178\pi\)
\(242\) 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 \(-0.599288\pi\)
−0.306890 + 0.951745i \(0.599288\pi\)
\(252\) 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 0.703735 0.710462i \(-0.251514\pi\)
−0.967146 + 0.254222i \(0.918181\pi\)
\(258\) 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 \(-0.523517\pi\)
0.900570 0.434710i \(-0.143149\pi\)
\(270\) 0 0
\(271\) −2.52918e8 4.38067e8i −0.771947 1.33705i −0.936495 0.350682i \(-0.885950\pi\)
0.164548 0.986369i \(-0.447384\pi\)
\(272\) 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 −0.950538 0.310607i \(-0.899468\pi\)
0.744263 + 0.667887i \(0.232801\pi\)
\(284\) 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 \(-0.790326\pi\)
−0.790783 + 0.612097i \(0.790326\pi\)
\(294\) 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 \(-0.589625\pi\)
−0.277859 + 0.960622i \(0.589625\pi\)
\(308\) 0 0
\(309\) −3.36156e8 −0.648166
\(310\) 0 0
\(311\) −2.09860e8 + 3.63487e8i −0.395610 + 0.685217i −0.993179 0.116601i \(-0.962800\pi\)
0.597569 + 0.801818i \(0.296134\pi\)
\(312\) 0 0
\(313\) −1.14342e8 1.98046e8i −0.210766 0.365057i 0.741188 0.671297i \(-0.234262\pi\)
−0.951954 + 0.306240i \(0.900929\pi\)
\(314\) 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 \(-0.810724\pi\)
−0.828357 + 0.560200i \(0.810724\pi\)
\(350\) 0 0
\(351\) 6.48358e7 0.0800276
\(352\) 0 0
\(353\) 7.80588e8 1.35202e9i 0.944518 1.63595i 0.187805 0.982206i \(-0.439863\pi\)
0.756713 0.653747i \(-0.226804\pi\)
\(354\) 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 −0.518166 0.855280i \(-0.673385\pi\)
0.999777 + 0.0211045i \(0.00671828\pi\)
\(368\) 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 \(-0.980048\pi\)
0.444771 0.895644i \(-0.353285\pi\)
\(384\) 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 0.873204 0.487354i \(-0.162038\pi\)
−0.858663 + 0.512540i \(0.828705\pi\)
\(398\) 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 \(-0.625498\pi\)
0.991648 0.128975i \(-0.0411687\pi\)
\(410\) 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 \(-0.552556\pi\)
−0.164359 + 0.986401i \(0.552556\pi\)
\(420\) 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 \(-0.497664\pi\)
0.00733745 + 0.999973i \(0.497664\pi\)
\(434\) 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 0.752282 0.658842i \(-0.228953\pi\)
−0.946714 + 0.322074i \(0.895620\pi\)
\(440\) 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 \(-0.330520\pi\)
0.507634 + 0.861573i \(0.330520\pi\)
\(462\) 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 \(-0.869462\pi\)
0.113259 0.993566i \(-0.463871\pi\)
\(468\) 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 \(0.498791\pi\)
−0.867919 + 0.496707i \(0.834543\pi\)
\(480\) 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 \(-0.228679\pi\)
0.752849 + 0.658193i \(0.228679\pi\)
\(504\) 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 0.816824 0.576886i \(-0.195732\pi\)
−0.908010 + 0.418948i \(0.862399\pi\)
\(510\) 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 −0.883779 0.467905i \(-0.845009\pi\)
0.847107 + 0.531423i \(0.178342\pi\)
\(522\) 0 0
\(523\) 3.24162e9 + 5.61465e9i 0.990846 + 1.71619i 0.612337 + 0.790597i \(0.290230\pi\)
0.378509 + 0.925598i \(0.376437\pi\)
\(524\) 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 \(-0.516106\pi\)
0.890206 0.455558i \(-0.150560\pi\)
\(564\) 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 \(0.386547\pi\)
−0.986058 + 0.166400i \(0.946786\pi\)
\(578\) 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 \(-0.453327\pi\)
0.146103 + 0.989269i \(0.453327\pi\)
\(588\) 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 0.984950 0.172839i \(-0.0552941\pi\)
−0.642158 + 0.766572i \(0.721961\pi\)
\(594\) 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 \(-0.375694\pi\)
0.380668 + 0.924712i \(0.375694\pi\)
\(602\) 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 0.999453 0.0330588i \(-0.0105249\pi\)
−0.528356 + 0.849023i \(0.677192\pi\)
\(608\) 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 −0.961172 0.275951i \(-0.911007\pi\)
0.719566 + 0.694424i \(0.244341\pi\)
\(620\) 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 \(-0.698620\pi\)
−0.584273 + 0.811557i \(0.698620\pi\)
\(644\) 0 0
\(645\) 2.51888e8 0.0369615
\(646\) 0 0
\(647\) 6.24724e8 1.08205e9i 0.0906825 0.157067i −0.817116 0.576473i \(-0.804428\pi\)
0.907798 + 0.419407i \(0.137762\pi\)
\(648\) 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 −0.984867 0.173314i \(-0.944553\pi\)
0.642527 + 0.766263i \(0.277886\pi\)
\(662\) 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 \(-0.947125\pi\)
0.349921 0.936779i \(-0.386209\pi\)
\(678\) 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 0.999581 0.0289536i \(-0.00921751\pi\)
−0.524865 + 0.851186i \(0.675884\pi\)
\(692\) 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 \(-0.940452\pi\)
0.330206 0.943909i \(-0.392882\pi\)
\(720\) 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 \(-0.183255\pi\)
0.838805 + 0.544431i \(0.183255\pi\)
\(728\) 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 0.997991 0.0633553i \(-0.0201801\pi\)
−0.553863 + 0.832608i \(0.686847\pi\)
\(734\) 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 \(-0.965785\pi\)
0.404203 0.914669i \(-0.367549\pi\)
\(762\) 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 \(-0.686524\pi\)
−0.553017 + 0.833170i \(0.686524\pi\)
\(770\) 0 0
\(771\) 3.87073e9 0.304160
\(772\) 0 0
\(773\) −2.16169e9 + 3.74415e9i −0.168331 + 0.291558i −0.937833 0.347086i \(-0.887171\pi\)
0.769502 + 0.638644i \(0.220504\pi\)
\(774\) 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