Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [81,8,Mod(28,81)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(81, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("81.28");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 81 = 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 81.c (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: | \(25.3031870642\) |
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: |
\( x^{2} - x + 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 55.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 81.55 |
Dual form | 81.8.c.c.28.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.00000 | − | 5.19615i | 0.265165 | − | 0.459279i | −0.702442 | − | 0.711741i | \(-0.747907\pi\) |
0.967607 | + | 0.252462i | \(0.0812402\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 46.0000 | + | 79.6743i | 0.359375 | + | 0.622456i | ||||
\(5\) | 195.000 | + | 337.750i | 0.697653 | + | 1.20837i | 0.969278 | + | 0.245968i | \(0.0791057\pi\) |
−0.271625 | + | 0.962403i | \(0.587561\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 32.0000 | − | 55.4256i | 0.0352620 | − | 0.0610756i | −0.847856 | − | 0.530227i | \(-0.822107\pi\) |
0.883118 | + | 0.469151i | \(0.155440\pi\) | |||||||
\(8\) | 1320.00 | 0.911505 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2340.00 | 0.739973 | ||||||||
\(11\) | −474.000 | + | 820.992i | −0.107375 | + | 0.185979i | −0.914706 | − | 0.404120i | \(-0.867578\pi\) |
0.807331 | + | 0.590099i | \(0.200911\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2549.00 | + | 4415.00i | 0.321787 | + | 0.557351i | 0.980857 | − | 0.194731i | \(-0.0623833\pi\) |
−0.659070 | + | 0.752082i | \(0.729050\pi\) | |||||||
\(14\) | −192.000 | − | 332.554i | −0.0187005 | − | 0.0323902i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1928.00 | + | 3339.39i | −0.117676 | + | 0.203820i | ||||
\(17\) | −28386.0 | −1.40131 | −0.700653 | − | 0.713502i | \(-0.747108\pi\) | ||||
−0.700653 | + | 0.713502i | \(0.747108\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8620.00 | −0.288317 | −0.144158 | − | 0.989555i | \(-0.546047\pi\) | ||||
−0.144158 | + | 0.989555i | \(0.546047\pi\) | |||||||
\(20\) | −17940.0 | + | 31073.0i | −0.501438 | + | 0.868517i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2844.00 | + | 4925.95i | 0.0569443 | + | 0.0986304i | ||||
\(23\) | −7644.00 | − | 13239.8i | −0.131001 | − | 0.226900i | 0.793062 | − | 0.609141i | \(-0.208486\pi\) |
−0.924063 | + | 0.382241i | \(0.875152\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −36987.5 | + | 64064.2i | −0.473440 | + | 0.820022i | ||||
\(26\) | 30588.0 | 0.341306 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5888.00 | 0.0506891 | ||||||||
\(29\) | 18255.0 | − | 31618.6i | 0.138992 | − | 0.240741i | −0.788124 | − | 0.615517i | \(-0.788947\pi\) |
0.927115 | + | 0.374776i | \(0.122281\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 138404. | + | 239723.i | 0.834416 | + | 1.44525i | 0.894505 | + | 0.447058i | \(0.147528\pi\) |
−0.0600887 | + | 0.998193i | \(0.519138\pi\) | |||||||
\(32\) | 96048.0 | + | 166360.i | 0.518159 | + | 0.897478i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −85158.0 | + | 147498.i | −0.371577 | + | 0.643591i | ||||
\(35\) | 24960.0 | 0.0984026 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 268526. | 0.871526 | 0.435763 | − | 0.900061i | \(-0.356479\pi\) | ||||
0.435763 | + | 0.900061i | \(0.356479\pi\) | |||||||
\(38\) | −25860.0 | + | 44790.8i | −0.0764515 | + | 0.132418i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 257400. | + | 445830.i | 0.635914 | + | 1.10144i | ||||
\(41\) | −314859. | − | 545352.i | −0.713465 | − | 1.23576i | −0.963549 | − | 0.267533i | \(-0.913791\pi\) |
0.250084 | − | 0.968224i | \(-0.419542\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −342886. | + | 593896.i | −0.657673 | + | 1.13912i | 0.323543 | + | 0.946213i | \(0.395126\pi\) |
−0.981216 | + | 0.192910i | \(0.938207\pi\) | |||||||
\(44\) | −87216.0 | −0.154352 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −91728.0 | −0.138947 | ||||||||
\(47\) | 291648. | − | 505149.i | 0.409748 | − | 0.709704i | −0.585114 | − | 0.810951i | \(-0.698950\pi\) |
0.994861 | + | 0.101248i | \(0.0322834\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 409724. | + | 709662.i | 0.497513 | + | 0.861718i | ||||
\(50\) | 221925. | + | 384385.i | 0.251079 | + | 0.434882i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −234508. | + | 406180.i | −0.231284 | + | 0.400596i | ||||
\(53\) | 428058. | 0.394945 | 0.197473 | − | 0.980308i | \(-0.436727\pi\) | ||||
0.197473 | + | 0.980308i | \(0.436727\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −369720. | −0.299643 | ||||||||
\(56\) | 42240.0 | − | 73161.8i | 0.0321415 | − | 0.0556707i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −109530. | − | 189712.i | −0.0737115 | − | 0.127672i | ||||
\(59\) | 653190. | + | 1.13136e6i | 0.414054 | + | 0.717163i | 0.995329 | − | 0.0965444i | \(-0.0307790\pi\) |
−0.581274 | + | 0.813708i | \(0.697446\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −150331. | + | 260381.i | −0.0847997 | + | 0.146877i | −0.905306 | − | 0.424760i | \(-0.860358\pi\) |
0.820506 | + | 0.571638i | \(0.193692\pi\) | |||||||
\(62\) | 1.66085e6 | 0.885032 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 659008. | 0.314240 | ||||||||
\(65\) | −994110. | + | 1.72185e6i | −0.448991 | + | 0.777675i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 253622. | + | 439286.i | 0.103021 | + | 0.178437i | 0.912928 | − | 0.408121i | \(-0.133816\pi\) |
−0.809907 | + | 0.586558i | \(0.800482\pi\) | |||||||
\(68\) | −1.30576e6 | − | 2.26164e6i | −0.503594 | − | 0.872251i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 74880.0 | − | 129696.i | 0.0260929 | − | 0.0451943i | ||||
\(71\) | −5.56063e6 | −1.84383 | −0.921913 | − | 0.387397i | \(-0.873374\pi\) | ||||
−0.921913 | + | 0.387397i | \(0.873374\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.36908e6 | 0.411907 | 0.205954 | − | 0.978562i | \(-0.433970\pi\) | ||||
0.205954 | + | 0.978562i | \(0.433970\pi\) | |||||||
\(74\) | 805578. | − | 1.39530e6i | 0.231098 | − | 0.400274i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −396520. | − | 686793.i | −0.103614 | − | 0.179464i | ||||
\(77\) | 30336.0 | + | 52543.5i | 0.00757253 | + | 0.0131160i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.45686e6 | − | 5.98746e6i | 0.788836 | − | 1.36630i | −0.137844 | − | 0.990454i | \(-0.544017\pi\) |
0.926680 | − | 0.375851i | \(-0.122649\pi\) | |||||||
\(80\) | −1.50384e6 | −0.328388 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.77831e6 | −0.756744 | ||||||||
\(83\) | −2.18837e6 | + | 3.79037e6i | −0.420096 | + | 0.727627i | −0.995948 | − | 0.0899264i | \(-0.971337\pi\) |
0.575853 | + | 0.817553i | \(0.304670\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.53527e6 | − | 9.58737e6i | −0.977626 | − | 1.69330i | ||||
\(86\) | 2.05732e6 | + | 3.56338e6i | 0.348784 | + | 0.604111i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −625680. | + | 1.08371e6i | −0.0978730 | + | 0.169521i | ||||
\(89\) | 8.52831e6 | 1.28232 | 0.641162 | − | 0.767405i | \(-0.278453\pi\) | ||||
0.641162 | + | 0.767405i | \(0.278453\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 326272. | 0.0453874 | ||||||||
\(92\) | 703248. | − | 1.21806e6i | 0.0941567 | − | 0.163084i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.74989e6 | − | 3.03089e6i | −0.217302 | − | 0.376377i | ||||
\(95\) | −1.68090e6 | − | 2.91140e6i | −0.201145 | − | 0.348393i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.41341e6 | − | 7.64425e6i | 0.490990 | − | 0.850420i | −0.508956 | − | 0.860793i | \(-0.669968\pi\) |
0.999946 | + | 0.0103725i | \(0.00330171\pi\) | |||||||
\(98\) | 4.91668e6 | 0.527692 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −6.80570e6 | −0.680570 | ||||||||
\(101\) | 5.99321e6 | − | 1.03805e7i | 0.578808 | − | 1.00253i | −0.416808 | − | 0.908995i | \(-0.636851\pi\) |
0.995616 | − | 0.0935309i | \(-0.0298154\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.60470e6 | − | 6.24352e6i | −0.325041 | − | 0.562988i | 0.656480 | − | 0.754344i | \(-0.272045\pi\) |
−0.981521 | + | 0.191356i | \(0.938711\pi\) | |||||||
\(104\) | 3.36468e6 | + | 5.82780e6i | 0.293310 | + | 0.508028i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.28417e6 | − | 2.22425e6i | 0.104726 | − | 0.181390i | ||||
\(107\) | −1.14261e7 | −0.901683 | −0.450842 | − | 0.892604i | \(-0.648876\pi\) | ||||
−0.450842 | + | 0.892604i | \(0.648876\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.02095e6 | 0.297397 | 0.148698 | − | 0.988883i | \(-0.452492\pi\) | ||||
0.148698 | + | 0.988883i | \(0.452492\pi\) | |||||||
\(110\) | −1.10916e6 | + | 1.92112e6i | −0.0794547 | + | 0.137620i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 123392. | + | 213721.i | 0.00829896 | + | 0.0143742i | ||||
\(113\) | −8.85316e6 | − | 1.53341e7i | −0.577197 | − | 0.999734i | −0.995799 | − | 0.0915642i | \(-0.970813\pi\) |
0.418603 | − | 0.908169i | \(-0.362520\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.98116e6 | − | 5.16352e6i | 0.182786 | − | 0.316595i | ||||
\(116\) | 3.35892e6 | 0.199801 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.83828e6 | 0.439171 | ||||||||
\(119\) | −908352. | + | 1.57331e6i | −0.0494128 | + | 0.0855855i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.29423e6 | + | 1.60981e7i | 0.476941 | + | 0.826086i | ||||
\(122\) | 901986. | + | 1.56229e6i | 0.0449718 | + | 0.0778935i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.27332e7 | + | 2.20545e7i | −0.599737 | + | 1.03877i | ||||
\(125\) | 1.61850e6 | 0.0741187 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.67883e7 | 0.727267 | 0.363633 | − | 0.931542i | \(-0.381536\pi\) | ||||
0.363633 | + | 0.931542i | \(0.381536\pi\) | |||||||
\(128\) | −1.03171e7 | + | 1.78698e7i | −0.434834 | + | 0.753155i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.96466e6 | + | 1.03311e7i | 0.238113 | + | 0.412425i | ||||
\(131\) | 8.41339e6 | + | 1.45724e7i | 0.326980 | + | 0.566346i | 0.981911 | − | 0.189343i | \(-0.0606357\pi\) |
−0.654931 | + | 0.755689i | \(0.727302\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −275840. | + | 477769.i | −0.0101666 | + | 0.0176091i | ||||
\(134\) | 3.04346e6 | 0.109270 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.74695e7 | −1.27730 | ||||||||
\(137\) | 1.40225e7 | − | 2.42876e7i | 0.465910 | − | 0.806980i | −0.533332 | − | 0.845906i | \(-0.679060\pi\) |
0.999242 | + | 0.0389262i | \(0.0123937\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.91365e6 | + | 1.02427e7i | 0.186769 | + | 0.323493i | 0.944171 | − | 0.329456i | \(-0.106865\pi\) |
−0.757402 | + | 0.652948i | \(0.773532\pi\) | |||||||
\(140\) | 1.14816e6 | + | 1.98867e6i | 0.0353634 | + | 0.0612512i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.66819e7 | + | 2.88939e7i | −0.488918 | + | 0.846831i | ||||
\(143\) | −4.83290e6 | −0.138208 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.42389e7 | 0.387872 | ||||||||
\(146\) | 4.10725e6 | − | 7.11396e6i | 0.109223 | − | 0.189180i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.23522e7 | + | 2.13946e7i | 0.313205 | + | 0.542486i | ||||
\(149\) | 1.03923e7 | + | 1.80000e7i | 0.257371 | + | 0.445780i | 0.965537 | − | 0.260266i | \(-0.0838103\pi\) |
−0.708165 | + | 0.706046i | \(0.750477\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −38056.0 | + | 65914.9i | −0.000899505 | + | 0.00155799i | −0.866475 | − | 0.499221i | \(-0.833620\pi\) |
0.865575 | + | 0.500779i | \(0.166953\pi\) | |||||||
\(152\) | −1.13784e7 | −0.262802 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 364032. | 0.00803188 | ||||||||
\(155\) | −5.39776e7 | + | 9.34919e7i | −1.16427 | + | 2.01657i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.60912e7 | + | 2.78708e7i | 0.331849 | + | 0.574780i | 0.982874 | − | 0.184276i | \(-0.0589942\pi\) |
−0.651025 | + | 0.759056i | \(0.725661\pi\) | |||||||
\(158\) | −2.07412e7 | − | 3.59247e7i | −0.418344 | − | 0.724593i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.74587e7 | + | 6.48804e7i | −0.722991 | + | 1.25226i | ||||
\(161\) | −978432. | −0.0184774 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.83435e7 | 1.05520 | 0.527601 | − | 0.849492i | \(-0.323092\pi\) | ||||
0.527601 | + | 0.849492i | \(0.323092\pi\) | |||||||
\(164\) | 2.89670e7 | − | 5.01724e7i | 0.512803 | − | 0.888201i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.31302e7 | + | 2.27422e7i | 0.222789 | + | 0.385883i | ||||
\(167\) | −1.29183e7 | − | 2.23751e7i | −0.214633 | − | 0.371755i | 0.738526 | − | 0.674225i | \(-0.235522\pi\) |
−0.953159 | + | 0.302470i | \(0.902189\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.83795e7 | − | 3.18342e7i | 0.292907 | − | 0.507329i | ||||
\(170\) | −6.64232e7 | −1.03693 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.30910e7 | −0.945405 | ||||||||
\(173\) | 3.17600e7 | − | 5.50100e7i | 0.466358 | − | 0.807756i | −0.532904 | − | 0.846176i | \(-0.678899\pi\) |
0.999262 | + | 0.0384200i | \(0.0122325\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.36720e6 | + | 4.10011e6i | 0.0333889 | + | 0.0578312i | ||||
\(176\) | −1.82774e6 | − | 3.16575e6i | −0.0252709 | − | 0.0437705i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.55849e7 | − | 4.43144e7i | 0.340028 | − | 0.588945i | ||||
\(179\) | 8.09559e7 | 1.05503 | 0.527513 | − | 0.849547i | \(-0.323125\pi\) | ||||
0.527513 | + | 0.849547i | \(0.323125\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.45032e7 | 0.808549 | 0.404274 | − | 0.914638i | \(-0.367524\pi\) | ||||
0.404274 | + | 0.914638i | \(0.367524\pi\) | |||||||
\(182\) | 978816. | − | 1.69536e6i | 0.0120351 | − | 0.0208455i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.00901e7 | − | 1.74765e7i | −0.119408 | − | 0.206820i | ||||
\(185\) | 5.23626e7 | + | 9.06946e7i | 0.608023 | + | 1.05313i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.34550e7 | − | 2.33047e7i | 0.150465 | − | 0.260614i | ||||
\(188\) | 5.36632e7 | 0.589012 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.01708e7 | −0.213346 | ||||||||
\(191\) | 2.84137e7 | − | 4.92140e7i | 0.295060 | − | 0.511060i | −0.679939 | − | 0.733269i | \(-0.737994\pi\) |
0.974999 | + | 0.222209i | \(0.0713269\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.81885e7 | − | 1.00785e8i | −0.582621 | − | 1.00913i | −0.995167 | − | 0.0981931i | \(-0.968694\pi\) |
0.412546 | − | 0.910937i | \(-0.364640\pi\) | |||||||
\(194\) | −2.64804e7 | − | 4.58655e7i | −0.260387 | − | 0.451003i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.76946e7 | + | 6.52889e7i | −0.357588 | + | 0.619360i | ||||
\(197\) | 1.18816e8 | 1.10724 | 0.553622 | − | 0.832768i | \(-0.313245\pi\) | ||||
0.553622 | + | 0.832768i | \(0.313245\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.50106e7 | −0.854646 | −0.427323 | − | 0.904099i | \(-0.640543\pi\) | ||||
−0.427323 | + | 0.904099i | \(0.640543\pi\) | |||||||
\(200\) | −4.88235e7 | + | 8.45648e7i | −0.431543 | + | 0.747454i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.59593e7 | − | 6.22833e7i | −0.306959 | − | 0.531669i | ||||
\(203\) | −1.16832e6 | − | 2.02359e6i | −0.00980225 | − | 0.0169780i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.22795e8 | − | 2.12687e8i | 0.995502 | − | 1.72426i | ||||
\(206\) | −4.32564e7 | −0.344758 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.96579e7 | −0.151466 | ||||||||
\(209\) | 4.08588e6 | − | 7.07695e6i | 0.0309581 | − | 0.0536209i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.96232e7 | − | 1.55232e8i | −0.656798 | − | 1.13761i | −0.981440 | − | 0.191770i | \(-0.938577\pi\) |
0.324642 | − | 0.945837i | \(-0.394756\pi\) | |||||||
\(212\) | 1.96907e7 | + | 3.41052e7i | 0.141934 | + | 0.245836i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.42782e7 | + | 5.93716e7i | −0.239095 | + | 0.414124i | ||||
\(215\) | −2.67451e8 | −1.83531 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.77157e7 | 0.117693 | ||||||||
\(218\) | 1.20628e7 | − | 2.08935e7i | 0.0788592 | − | 0.136588i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.70071e7 | − | 2.94572e7i | −0.107684 | − | 0.186514i | ||||
\(221\) | −7.23559e7 | − | 1.25324e8i | −0.450922 | − | 0.781019i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.03268e8 | − | 1.78866e8i | 0.623592 | − | 1.08009i | −0.365219 | − | 0.930922i | \(-0.619006\pi\) |
0.988811 | − | 0.149172i | \(-0.0476607\pi\) | |||||||
\(224\) | 1.22941e7 | 0.0730853 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.06238e8 | −0.612209 | ||||||||
\(227\) | 2.16977e7 | − | 3.75815e7i | 0.123118 | − | 0.213247i | −0.797877 | − | 0.602820i | \(-0.794044\pi\) |
0.920996 | + | 0.389572i | \(0.127377\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.80965e7 | + | 3.13441e7i | 0.0995799 | + | 0.172477i | 0.911511 | − | 0.411276i | \(-0.134917\pi\) |
−0.811931 | + | 0.583753i | \(0.801583\pi\) | |||||||
\(230\) | −1.78870e7 | − | 3.09811e7i | −0.0969369 | − | 0.167900i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.40966e7 | − | 4.17365e7i | 0.126692 | − | 0.219436i | ||||
\(233\) | −9.22347e7 | −0.477693 | −0.238846 | − | 0.971057i | \(-0.576769\pi\) | ||||
−0.238846 | + | 0.971057i | \(0.576769\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.27485e8 | 1.14345 | ||||||||
\(236\) | −6.00935e7 | + | 1.04085e8i | −0.297602 | + | 0.515461i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.45011e6 | + | 9.43987e6i | 0.0262051 | + | 0.0453886i | ||||
\(239\) | 2.49234e7 | + | 4.31686e7i | 0.118090 | + | 0.204539i | 0.919011 | − | 0.394232i | \(-0.128989\pi\) |
−0.800920 | + | 0.598771i | \(0.795656\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.96870e7 | + | 1.72663e8i | −0.458753 | + | 0.794583i | −0.998895 | − | 0.0469902i | \(-0.985037\pi\) |
0.540142 | + | 0.841574i | \(0.318370\pi\) | |||||||
\(242\) | 1.11531e8 | 0.505872 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.76609e7 | −0.121900 | ||||||||
\(245\) | −1.59792e8 | + | 2.76768e8i | −0.694183 | + | 1.20236i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.19724e7 | − | 3.80573e7i | −0.0927765 | − | 0.160694i | ||||
\(248\) | 1.82693e8 | + | 3.16434e8i | 0.760574 | + | 1.31735i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.85550e6 | − | 8.40997e6i | 0.0196537 | − | 0.0340412i | ||||
\(251\) | 3.94678e8 | 1.57538 | 0.787689 | − | 0.616073i | \(-0.211277\pi\) | ||||
0.787689 | + | 0.616073i | \(0.211277\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.44930e7 | 0.0562649 | ||||||||
\(254\) | 5.03649e7 | − | 8.72345e7i | 0.192846 | − | 0.334018i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.04079e8 | + | 1.80271e8i | 0.387725 | + | 0.671560i | ||||
\(257\) | −7.14427e7 | − | 1.23742e8i | −0.262538 | − | 0.454729i | 0.704378 | − | 0.709825i | \(-0.251226\pi\) |
−0.966916 | + | 0.255096i | \(0.917893\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.59283e6 | − | 1.48832e7i | 0.0307317 | − | 0.0532289i | ||||
\(260\) | −1.82916e8 | −0.645425 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.00961e8 | 0.346815 | ||||||||
\(263\) | 2.20120e8 | − | 3.81260e8i | 0.746131 | − | 1.29234i | −0.203533 | − | 0.979068i | \(-0.565243\pi\) |
0.949664 | − | 0.313269i | \(-0.101424\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.34713e7 | + | 1.44577e8i | 0.275535 | + | 0.477241i | ||||
\(266\) | 1.65504e6 | + | 2.86661e6i | 0.00539166 | + | 0.00933863i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.33332e7 | + | 4.04143e7i | −0.0740462 | + | 0.128252i | ||||
\(269\) | −2.75405e8 | −0.862657 | −0.431329 | − | 0.902195i | \(-0.641955\pi\) | ||||
−0.431329 | + | 0.902195i | \(0.641955\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.24670e8 | −1.29616 | −0.648080 | − | 0.761572i | \(-0.724428\pi\) | ||||
−0.648080 | + | 0.761572i | \(0.724428\pi\) | |||||||
\(272\) | 5.47282e7 | − | 9.47920e7i | 0.164900 | − | 0.285615i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.41347e7 | − | 1.45726e8i | −0.247086 | − | 0.427966i | ||||
\(275\) | −3.50642e7 | − | 6.07329e7i | −0.101671 | − | 0.176100i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.58079e8 | + | 4.47006e8i | −0.729581 | + | 1.26367i | 0.227479 | + | 0.973783i | \(0.426952\pi\) |
−0.957060 | + | 0.289889i | \(0.906382\pi\) | |||||||
\(278\) | 7.09638e7 | 0.198098 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.29472e7 | 0.0896944 | ||||||||
\(281\) | −1.55521e8 | + | 2.69371e8i | −0.418137 | + | 0.724234i | −0.995752 | − | 0.0920753i | \(-0.970650\pi\) |
0.577616 | + | 0.816309i | \(0.303983\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.97154e8 | + | 5.14686e8i | 0.779344 | + | 1.34986i | 0.932320 | + | 0.361634i | \(0.117781\pi\) |
−0.152976 | + | 0.988230i | \(0.548886\pi\) | |||||||
\(284\) | −2.55789e8 | − | 4.43040e8i | −0.662625 | − | 1.14770i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.44987e7 | + | 2.51125e7i | −0.0366478 | + | 0.0634759i | ||||
\(287\) | −4.03020e7 | −0.100633 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.95426e8 | 0.963658 | ||||||||
\(290\) | 4.27167e7 | − | 7.39875e7i | 0.102850 | − | 0.178142i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.29778e7 | + | 1.09081e8i | 0.148029 | + | 0.256394i | ||||
\(293\) | 5.77574e7 | + | 1.00039e8i | 0.134144 | + | 0.232344i | 0.925270 | − | 0.379309i | \(-0.123838\pi\) |
−0.791126 | + | 0.611653i | \(0.790505\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.54744e8 | + | 4.41230e8i | −0.577733 | + | 1.00066i | ||||
\(296\) | 3.54454e8 | 0.794400 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.24708e8 | 0.272984 | ||||||||
\(299\) | 3.89691e7 | − | 6.74965e7i | 0.0843085 | − | 0.146027i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.19447e7 | + | 3.80093e7i | 0.0463817 | + | 0.0803355i | ||||
\(302\) | 228336. | + | 395490.i | 0.000477035 | + | 0.000826249i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.66194e7 | − | 2.87856e7i | 0.0339279 | − | 0.0587648i | ||||
\(305\) | −1.17258e8 | −0.236643 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.60600e8 | −0.514032 | −0.257016 | − | 0.966407i | \(-0.582739\pi\) | ||||
−0.257016 | + | 0.966407i | \(0.582739\pi\) | |||||||
\(308\) | −2.79091e6 | + | 4.83400e6i | −0.00544275 | + | 0.00942712i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.23865e8 | + | 5.60951e8i | 0.617445 | + | 1.06945i | ||||
\(311\) | 2.88397e8 | + | 4.99519e8i | 0.543663 | + | 0.941652i | 0.998690 | + | 0.0511744i | \(0.0162964\pi\) |
−0.455027 | + | 0.890478i | \(0.650370\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.30037e8 | − | 3.98436e8i | 0.424026 | − | 0.734435i | −0.572303 | − | 0.820043i | \(-0.693950\pi\) |
0.996329 | + | 0.0856073i | \(0.0272831\pi\) | |||||||
\(314\) | 1.93095e8 | 0.351979 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.36062e8 | 1.13395 | ||||||||
\(317\) | 3.12781e7 | − | 5.41752e7i | 0.0551483 | − | 0.0955197i | −0.837133 | − | 0.546999i | \(-0.815770\pi\) |
0.892282 | + | 0.451479i | \(0.149103\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.73057e7 | + | 2.99744e7i | 0.0298485 | + | 0.0516992i | ||||
\(320\) | 1.28507e8 | + | 2.22580e8i | 0.219230 | + | 0.379718i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.93530e6 | + | 5.08408e6i | −0.00489955 | + | 0.00848627i | ||||
\(323\) | 2.44687e8 | 0.404020 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.77125e8 | −0.609387 | ||||||||
\(326\) | 1.75030e8 | − | 3.03162e8i | 0.279803 | − | 0.484633i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.15614e8 | − | 7.19864e8i | −0.650327 | − | 1.12640i | ||||
\(329\) | −1.86655e7 | − | 3.23295e7i | −0.0288970 | − | 0.0500511i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.42118e8 | + | 5.92566e8i | −0.518535 | + | 0.898128i | 0.481233 | + | 0.876593i | \(0.340189\pi\) |
−0.999768 | + | 0.0215359i | \(0.993144\pi\) | |||||||
\(332\) | −4.02661e8 | −0.603888 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.55019e8 | −0.227652 | ||||||||
\(335\) | −9.89126e7 | + | 1.71322e8i | −0.143746 | + | 0.248975i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.13156e8 | + | 5.42403e8i | 0.445714 | + | 0.772000i | 0.998102 | − | 0.0615875i | \(-0.0196163\pi\) |
−0.552387 | + | 0.833588i | \(0.686283\pi\) | |||||||
\(338\) | −1.10277e8 | − | 1.91005e8i | −0.155337 | − | 0.269052i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.09245e8 | − | 8.82038e8i | 0.702668 | − | 1.21706i | ||||
\(341\) | −2.62414e8 | −0.358382 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.05151e8 | 0.140697 | ||||||||
\(344\) | −4.52610e8 | + | 7.83943e8i | −0.599472 | + | 1.03832i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.90560e8 | − | 3.30060e8i | −0.247324 | − | 0.428377i | ||||
\(347\) | −6.26698e8 | − | 1.08547e9i | −0.805203 | − | 1.39465i | −0.916154 | − | 0.400826i | \(-0.868723\pi\) |
0.110952 | − | 0.993826i | \(-0.464610\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.32675e8 | + | 2.29800e8i | −0.167071 | + | 0.289375i | −0.937389 | − | 0.348285i | \(-0.886764\pi\) |
0.770318 | + | 0.637660i | \(0.220098\pi\) | |||||||
\(350\) | 2.84064e7 | 0.0354142 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.82107e8 | −0.222550 | ||||||||
\(353\) | −2.84818e8 | + | 4.93319e8i | −0.344632 | + | 0.596920i | −0.985287 | − | 0.170909i | \(-0.945330\pi\) |
0.640655 | + | 0.767829i | \(0.278663\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.08432e9 | − | 1.87810e9i | −1.28635 | − | 2.22803i | ||||
\(356\) | 3.92302e8 | + | 6.79487e8i | 0.460835 | + | 0.798190i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.42868e8 | − | 4.20659e8i | 0.279756 | − | 0.484551i | ||||
\(359\) | −9.32541e8 | −1.06374 | −0.531872 | − | 0.846825i | \(-0.678511\pi\) | ||||
−0.531872 | + | 0.846825i | \(0.678511\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.19567e8 | −0.916874 | ||||||||
\(362\) | 1.93510e8 | − | 3.35168e8i | 0.214399 | − | 0.371350i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.50085e7 | + | 2.59955e7i | 0.0163111 | + | 0.0282516i | ||||
\(365\) | 2.66971e8 | + | 4.62407e8i | 0.287368 | + | 0.497737i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.26282e8 | − | 7.38343e8i | 0.450159 | − | 0.779699i | −0.548236 | − | 0.836323i | \(-0.684701\pi\) |
0.998396 | + | 0.0566249i | \(0.0180339\pi\) | |||||||
\(368\) | 5.89505e7 | 0.0616624 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.28351e8 | 0.644906 | ||||||||
\(371\) | 1.36979e7 | − | 2.37254e7i | 0.0139266 | − | 0.0241215i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.90592e8 | − | 3.30115e8i | −0.190162 | − | 0.329370i | 0.755142 | − | 0.655561i | \(-0.227568\pi\) |
−0.945304 | + | 0.326192i | \(0.894235\pi\) | |||||||
\(374\) | −8.07298e7 | − | 1.39828e8i | −0.0797964 | − | 0.138211i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.84975e8 | − | 6.66797e8i | 0.373487 | − | 0.646898i | ||||
\(377\) | 1.86128e8 | 0.178903 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.48353e9 | −1.39978 | −0.699889 | − | 0.714251i | \(-0.746767\pi\) | ||||
−0.699889 | + | 0.714251i | \(0.746767\pi\) | |||||||
\(380\) | 1.54643e8 | − | 2.67849e8i | 0.144573 | − | 0.250408i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.70482e8 | − | 2.95284e8i | −0.156479 | − | 0.271030i | ||||
\(383\) | −3.80965e8 | − | 6.59851e8i | −0.346489 | − | 0.600136i | 0.639134 | − | 0.769095i | \(-0.279293\pi\) |
−0.985623 | + | 0.168959i | \(0.945959\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.18310e7 | + | 2.04920e7i | −0.0105660 | + | 0.0183008i | ||||
\(386\) | −6.98262e8 | −0.617963 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8.12067e8 | 0.705799 | ||||||||
\(389\) | 8.04509e8 | − | 1.39345e9i | 0.692959 | − | 1.20024i | −0.277905 | − | 0.960608i | \(-0.589640\pi\) |
0.970864 | − | 0.239631i | \(-0.0770265\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.16983e8 | + | 3.75825e8i | 0.183572 | + | 0.317956i | ||||
\(392\) | 5.40835e8 | + | 9.36754e8i | 0.453486 | + | 0.785460i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.56448e8 | − | 6.17386e8i | 0.293602 | − | 0.508534i | ||||
\(395\) | 2.69635e9 | 2.20134 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.88016e9 | 1.50809 | 0.754046 | − | 0.656822i | \(-0.228100\pi\) | ||||
0.754046 | + | 0.656822i | \(0.228100\pi\) | |||||||
\(398\) | −2.85032e8 | + | 4.93690e8i | −0.226622 | + | 0.392521i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.42624e8 | − | 2.47032e8i | −0.111425 | − | 0.192993i | ||||
\(401\) | 1.34296e8 | + | 2.32608e8i | 0.104006 | + | 0.180144i | 0.913332 | − | 0.407217i | \(-0.133501\pi\) |
−0.809326 | + | 0.587360i | \(0.800167\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.05584e8 | + | 1.22211e9i | −0.537008 | + | 0.930125i | ||||
\(404\) | 1.10275e9 | 0.832037 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.40198e7 | −0.0103969 | ||||||||
\(407\) | −1.27281e8 | + | 2.20458e8i | −0.0935803 | + | 0.162086i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.49739e7 | − | 7.78971e7i | −0.0325034 | − | 0.0562976i | 0.849316 | − | 0.527885i | \(-0.177015\pi\) |
−0.881820 | + | 0.471587i | \(0.843681\pi\) | |||||||
\(410\) | −7.36770e8 | − | 1.27612e9i | −0.527945 | − | 0.914427i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.31632e8 | − | 5.74404e8i | 0.233623 | − | 0.404647i | ||||
\(413\) | 8.36083e7 | 0.0584015 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.70693e9 | −1.17232 | ||||||||
\(416\) | −4.89653e8 | + | 8.48103e8i | −0.333474 | + | 0.577593i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.45153e7 | − | 4.24617e7i | −0.0164180 | − | 0.0284368i | ||||
\(419\) | 8.45271e8 | + | 1.46405e9i | 0.561367 | + | 0.972317i | 0.997377 | + | 0.0723749i | \(0.0230578\pi\) |
−0.436010 | + | 0.899942i | \(0.643609\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.66664e8 | − | 9.81490e8i | 0.370116 | − | 0.641060i | −0.619467 | − | 0.785023i | \(-0.712651\pi\) |
0.989583 | + | 0.143963i | \(0.0459845\pi\) | |||||||
\(422\) | −1.07548e9 | −0.696639 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.65037e8 | 0.359995 | ||||||||
\(425\) | 1.04993e9 | − | 1.81853e9i | 0.663434 | − | 1.14910i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.62118e6 | + | 1.66644e7i | 0.00598041 | + | 0.0103584i | ||||
\(428\) | −5.25599e8 | − | 9.10365e8i | −0.324042 | − | 0.561258i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.02353e8 | + | 1.38972e9i | −0.486660 | + | 0.842921i | ||||
\(431\) | −2.19943e9 | −1.32324 | −0.661621 | − | 0.749839i | \(-0.730131\pi\) | ||||
−0.661621 | + | 0.749839i | \(0.730131\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.51738e8 | −0.0898227 | −0.0449114 | − | 0.998991i | \(-0.514301\pi\) | ||||
−0.0449114 | + | 0.998991i | \(0.514301\pi\) | |||||||
\(434\) | 5.31471e7 | − | 9.20535e7i | 0.0312080 | − | 0.0540538i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.84964e8 | + | 3.20367e8i | 0.106877 | + | 0.185116i | ||||
\(437\) | 6.58913e7 | + | 1.14127e8i | 0.0377696 | + | 0.0654189i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.95381e8 | + | 8.58026e8i | −0.279456 | + | 0.484032i | −0.971250 | − | 0.238063i | \(-0.923488\pi\) |
0.691793 | + | 0.722095i | \(0.256821\pi\) | |||||||
\(440\) | −4.88030e8 | −0.273126 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.68271e8 | −0.478275 | ||||||||
\(443\) | −8.86878e8 | + | 1.53612e9i | −0.484675 | + | 0.839482i | −0.999845 | − | 0.0176059i | \(-0.994396\pi\) |
0.515170 | + | 0.857088i | \(0.327729\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.66302e9 | + | 2.88044e9i | 0.894618 | + | 1.54952i | ||||
\(446\) | −6.19611e8 | − | 1.07320e9i | −0.330710 | − | 0.572806i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.10883e7 | − | 3.65259e7i | 0.0110807 | − | 0.0191924i | ||||
\(449\) | 2.77010e8 | 0.144422 | 0.0722110 | − | 0.997389i | \(-0.476994\pi\) | ||||
0.0722110 | + | 0.997389i | \(0.476994\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.96973e8 | 0.306434 | ||||||||
\(452\) | 8.14491e8 | − | 1.41074e9i | 0.414860 | − | 0.718559i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.30186e8 | − | 2.25489e8i | −0.0652934 | − | 0.113092i | ||||
\(455\) | 6.36230e7 | + | 1.10198e8i | 0.0316646 | + | 0.0548448i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.47379e9 | + | 2.55268e9i | −0.722320 | + | 1.25109i | 0.237748 | + | 0.971327i | \(0.423591\pi\) |
−0.960068 | + | 0.279768i | \(0.909742\pi\) | |||||||
\(458\) | 2.17159e8 | 0.105620 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.48533e8 | 0.262755 | ||||||||
\(461\) | −1.38344e9 | + | 2.39618e9i | −0.657667 | + | 1.13911i | 0.323551 | + | 0.946211i | \(0.395123\pi\) |
−0.981218 | + | 0.192902i | \(0.938210\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.31776e8 | − | 4.01449e8i | −0.108527 | − | 0.187973i | 0.806647 | − | 0.591034i | \(-0.201280\pi\) |
−0.915174 | + | 0.403060i | \(0.867947\pi\) | |||||||
\(464\) | 7.03913e7 | + | 1.21921e8i | 0.0327119 | + | 0.0566587i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.76704e8 | + | 4.79265e8i | −0.126667 | + | 0.219394i | ||||
\(467\) | 4.17922e8 | 0.189883 | 0.0949415 | − | 0.995483i | \(-0.469734\pi\) | ||||
0.0949415 | + | 0.995483i | \(0.469734\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.24636e7 | 0.0145309 | ||||||||
\(470\) | 6.82456e8 | − | 1.18205e9i | 0.303202 | − | 0.525162i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.62211e8 | + | 1.49339e9i | 0.377413 | + | 0.653698i | ||||
\(473\) | −3.25056e8 | − | 5.63013e8i | −0.141236 | − | 0.244627i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.18832e8 | − | 5.52234e8i | 0.136501 | − | 0.236426i | ||||
\(476\) | −1.67137e8 | −0.0710310 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.99081e8 | 0.125254 | ||||||||
\(479\) | −7.54864e8 | + | 1.30746e9i | −0.313830 | + | 0.543570i | −0.979188 | − | 0.202955i | \(-0.934946\pi\) |
0.665358 | + | 0.746524i | \(0.268279\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.84473e8 | + | 1.18554e9i | 0.280445 | + | 0.485746i | ||||
\(482\) | 5.98122e8 | + | 1.03598e9i | 0.243290 | + | 0.421392i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.55069e8 | + | 1.48102e9i | −0.342801 | + | 0.593750i | ||||
\(485\) | 3.44246e9 | 1.37016 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.29460e8 | 0.364653 | 0.182326 | − | 0.983238i | \(-0.441637\pi\) | ||||
0.182326 | + | 0.983238i | \(0.441637\pi\) | |||||||
\(488\) | −1.98437e8 | + | 3.43703e8i | −0.0772953 | + | 0.133879i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 9.58753e8 | + | 1.66061e9i | 0.368146 | + | 0.637648i | ||||
\(491\) | 2.56401e9 | + | 4.44100e9i | 0.977541 | + | 1.69315i | 0.671280 | + | 0.741204i | \(0.265745\pi\) |
0.306262 | + | 0.951947i | \(0.400922\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.18186e8 | + | 8.97525e8i | −0.194770 | + | 0.337351i | ||||
\(494\) | −2.63669e8 | −0.0984043 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.06737e9 | −0.392762 | ||||||||
\(497\) | −1.77940e8 | + | 3.08202e8i | −0.0650170 | + | 0.112613i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.05325e8 | + | 3.55633e8i | 0.0739757 | + | 0.128130i | 0.900640 | − | 0.434565i | \(-0.143098\pi\) |
−0.826665 | + | 0.562695i | \(0.809765\pi\) | |||||||
\(500\) | 7.44510e7 | + | 1.28953e8i | 0.0266364 | + | 0.0461356i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.18403e9 | − | 2.05081e9i | 0.417735 | − | 0.723538i | ||||
\(503\) | −5.02041e9 | −1.75894 | −0.879470 | − | 0.475954i | \(-0.842103\pi\) | ||||
−0.879470 | + | 0.475954i | \(0.842103\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.67470e9 | 1.61523 | ||||||||
\(506\) | 4.34791e7 | − | 7.53080e7i | 0.0149195 | − | 0.0258413i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.72262e8 | + | 1.33760e9i | 0.261361 | + | 0.452691i | ||||
\(509\) | −1.62463e9 | − | 2.81394e9i | −0.546062 | − | 0.945807i | −0.998539 | − | 0.0540314i | \(-0.982793\pi\) |
0.452477 | − | 0.891776i | \(-0.350540\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.38106e7 | − | 7.58822e7i | 0.0145247 | − | 0.0251575i | ||||
\(512\) | −1.39223e9 | −0.458423 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −8.57312e8 | −0.278463 | ||||||||
\(515\) | 1.40583e9 | − | 2.43497e9i | 0.453532 | − | 0.785540i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.76482e8 | + | 4.78881e8i | 0.0879935 | + | 0.152409i | ||||
\(518\) | −5.15570e7 | − | 8.92993e7i | −0.0162980 | − | 0.0282289i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.31223e9 | + | 2.27284e9i | −0.409258 | + | 0.708855i | ||||
\(521\) | 2.10950e9 | 0.653503 | 0.326752 | − | 0.945110i | \(-0.394046\pi\) | ||||
0.326752 | + | 0.945110i | \(0.394046\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.28911e9 | −1.61669 | −0.808345 | − | 0.588709i | \(-0.799636\pi\) | ||||
−0.808345 | + | 0.588709i | \(0.799636\pi\) | |||||||
\(524\) | −7.74032e8 | + | 1.34066e9i | −0.235017 | + | 0.407061i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.32072e9 | − | 2.28756e9i | −0.395696 | − | 0.685365i | ||||
\(527\) | −3.92874e9 | − | 6.80477e9i | −1.16927 | − | 2.02524i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.58555e9 | − | 2.74626e9i | 0.465678 | − | 0.806577i | ||||
\(530\) | 1.00166e9 | 0.292249 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.07546e7 | −0.0146145 | ||||||||
\(533\) | 1.60515e9 | − | 2.78020e9i | 0.459167 | − | 0.795301i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.22808e9 | − | 3.85916e9i | −0.629062 | − | 1.08957i | ||||
\(536\) | 3.34781e8 | + | 5.79858e8i | 0.0939040 | + | 0.162646i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.26214e8 | + | 1.43104e9i | −0.228747 | + | 0.396201i | ||||
\(539\) | −7.76836e8 | −0.213682 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.04614e9 | 0.827101 | 0.413551 | − | 0.910481i | \(-0.364288\pi\) | ||||
0.413551 | + | 0.910481i | \(0.364288\pi\) | |||||||
\(542\) | −1.27401e9 | + | 2.20665e9i | −0.343696 | + | 0.595300i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.72642e9 | − | 4.72230e9i | −0.726100 | − | 1.25764i | ||||
\(545\) | 7.84085e8 | + | 1.35808e9i | 0.207480 | + | 0.359365i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.42768e9 | − | 4.20487e9i | 0.634215 | − | 1.09849i | −0.352466 | − | 0.935825i | \(-0.614657\pi\) |
0.986681 | − | 0.162668i | \(-0.0520100\pi\) | |||||||
\(548\) | 2.58013e9 | 0.669746 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.20770e8 | −0.107839 | ||||||||
\(551\) | −1.57358e8 | + | 2.72552e8i | −0.0400736 | + | 0.0694095i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.21239e8 | − | 3.83197e8i | −0.0556319 | − | 0.0963573i | ||||
\(554\) | 1.54847e9 | + | 2.68204e9i | 0.386919 | + | 0.670163i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.44056e8 | + | 9.42332e8i | −0.134240 | + | 0.232510i | ||||
\(557\) | −1.27762e9 | −0.313263 | −0.156631 | − | 0.987657i | \(-0.550063\pi\) | ||||
−0.156631 | + | 0.987657i | \(0.550063\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.49607e9 | −0.846522 | ||||||||
\(560\) | −4.81229e7 | + | 8.33513e7i | −0.0115796 | + | 0.0200565i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.33129e8 | + | 1.61623e9i | 0.221750 | + | 0.384083i | ||||
\(563\) | 2.35632e9 | + | 4.08127e9i | 0.556487 | + | 0.963865i | 0.997786 | + | 0.0665042i | \(0.0211846\pi\) |
−0.441299 | + | 0.897360i | \(0.645482\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.45273e9 | − | 5.98031e9i | 0.805366 | − | 1.39493i | ||||
\(566\) | 3.56585e9 | 0.826619 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.34003e9 | −1.68066 | ||||||||
\(569\) | 2.28900e9 | − | 3.96466e9i | 0.520898 | − | 0.902222i | −0.478807 | − | 0.877920i | \(-0.658931\pi\) |
0.999705 | − | 0.0243013i | \(-0.00773611\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.47560e9 | − | 4.28786e9i | −0.556485 | − | 0.963860i | −0.997786 | − | 0.0665012i | \(-0.978816\pi\) |
0.441301 | − | 0.897359i | \(-0.354517\pi\) | |||||||
\(572\) | −2.22314e8 | − | 3.85058e8i | −0.0496684 | − | 0.0860281i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.20906e8 | + | 2.09415e8i | −0.0266843 | + | 0.0462186i | ||||
\(575\) | 1.13093e9 | 0.248084 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.51847e9 | 1.84606 | 0.923031 | − | 0.384725i | \(-0.125704\pi\) | ||||
0.923031 | + | 0.384725i | \(0.125704\pi\) | |||||||
\(578\) | 1.18628e9 | − | 2.05470e9i | 0.255529 | − | 0.442588i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.54989e8 | + | 1.13447e9i | 0.139392 | + | 0.241433i | ||||
\(581\) | 1.40056e8 | + | 2.42584e8i | 0.0296268 | + | 0.0513152i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.02899e8 | + | 3.51432e8i | −0.0424073 | + | 0.0734517i | ||||
\(584\) | 1.80719e9 | 0.375455 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.93088e8 | 0.142281 | ||||||||
\(587\) | −2.81124e8 | + | 4.86921e8i | −0.0573673 | + | 0.0993630i | −0.893283 | − | 0.449495i | \(-0.851604\pi\) |
0.835916 | + | 0.548858i | \(0.184937\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.19304e9 | − | 2.06641e9i | −0.240576 | − | 0.416690i | ||||
\(590\) | 1.52846e9 | + | 2.64738e9i | 0.306389 | + | 0.530682i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.17718e8 | + | 8.96714e8i | −0.102557 | + | 0.177635i | ||||
\(593\) | −3.62110e9 | −0.713099 | −0.356549 | − | 0.934277i | \(-0.616047\pi\) | ||||
−0.356549 | + | 0.934277i | \(0.616047\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.08515e8 | −0.137892 | ||||||||
\(596\) | −9.56093e8 | + | 1.65600e9i | −0.184986 | + | 0.320405i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.33815e8 | − | 4.04979e8i | −0.0447113 | − | 0.0774423i | ||||
\(599\) | −3.74052e9 | − | 6.47877e9i | −0.711112 | − | 1.23168i | −0.964440 | − | 0.264301i | \(-0.914859\pi\) |
0.253328 | − | 0.967380i | \(-0.418475\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.90635e9 | − | 5.03395e9i | 0.546119 | − | 0.945906i | −0.452416 | − | 0.891807i | \(-0.649438\pi\) |
0.998536 | − | 0.0540994i | \(-0.0172288\pi\) | |||||||
\(602\) | 2.63336e8 | 0.0491953 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7.00230e6 | −0.00129304 | ||||||||
\(605\) | −3.62475e9 | + | 6.27825e9i | −0.665479 | + | 1.15264i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.92026e9 | − | 3.32598e9i | −0.348497 | − | 0.603614i | 0.637486 | − | 0.770462i | \(-0.279974\pi\) |
−0.985983 | + | 0.166848i | \(0.946641\pi\) | |||||||
\(608\) | −8.27934e8 | − | 1.43402e9i | −0.149394 | − | 0.258758i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.51775e8 | + | 6.09291e8i | −0.0627495 | + | 0.108685i | ||||
\(611\) | 2.97364e9 | 0.527405 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.70484e9 | 0.298932 | 0.149466 | − | 0.988767i | \(-0.452245\pi\) | ||||
0.149466 | + | 0.988767i | \(0.452245\pi\) | |||||||
\(614\) | −7.81799e8 | + | 1.35412e9i | −0.136303 | + | 0.236084i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.00435e7 | + | 6.93574e7i | 0.00690239 | + | 0.0119553i | ||||
\(617\) | −1.40405e9 | − | 2.43188e9i | −0.240649 | − | 0.416816i | 0.720251 | − | 0.693714i | \(-0.244027\pi\) |
−0.960899 | + | 0.276898i | \(0.910693\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.27183e9 | − | 2.20287e9i | 0.215532 | − | 0.373312i | −0.737905 | − | 0.674904i | \(-0.764185\pi\) |
0.953437 | + | 0.301593i | \(0.0975182\pi\) | |||||||
\(620\) | −9.93187e9 | −1.67363 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.46077e9 | 0.576642 | ||||||||
\(623\) | 2.72906e8 | − | 4.72687e8i | 0.0452173 | − | 0.0783187i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.20526e9 | + | 5.55167e9i | 0.525149 | + | 0.909585i | ||||
\(626\) | −1.38022e9 | − | 2.39062e9i | −0.224874 | − | 0.389493i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.48039e9 | + | 2.56412e9i | −0.238517 | + | 0.413123i | ||||
\(629\) | −7.62238e9 | −1.22127 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.51146e8 | −0.0239494 | −0.0119747 | − | 0.999928i | \(-0.503812\pi\) | ||||
−0.0119747 | + | 0.999928i | \(0.503812\pi\) | |||||||
\(632\) | 4.56306e9 | − | 7.90344e9i | 0.719028 | − | 1.24539i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.87668e8 | − | 3.25051e8i | −0.0292468 | − | 0.0506570i | ||||
\(635\) | 3.27372e9 | + | 5.67025e9i | 0.507380 | + | 0.878808i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.08877e9 | + | 3.61786e9i | −0.320186 | + | 0.554579i | ||||
\(638\) | 2.07669e8 | 0.0316591 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8.04735e9 | −1.21345 | ||||||||
\(641\) | −6.18126e9 | + | 1.07062e10i | −0.926987 | + | 1.60559i | −0.138653 | + | 0.990341i | \(0.544277\pi\) |
−0.788334 | + | 0.615247i | \(0.789056\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.43372e9 | − | 2.48328e9i | −0.212680 | − | 0.368372i | 0.739873 | − | 0.672747i | \(-0.234886\pi\) |
−0.952552 | + | 0.304375i | \(0.901552\pi\) | |||||||
\(644\) | −4.50079e7 | − | 7.79559e7i | −0.00664030 | − | 0.0115013i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.34062e8 | − | 1.27143e9i | 0.107132 | − | 0.185558i | ||||
\(647\) | 4.10640e9 | 0.596068 | 0.298034 | − | 0.954555i | \(-0.403669\pi\) | ||||
0.298034 | + | 0.954555i | \(0.403669\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.23845e9 | −0.177837 | ||||||||
\(650\) | −1.13137e9 | + | 1.95960e9i | −0.161588 | + | 0.279879i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.68380e9 | + | 4.64848e9i | 0.379213 | + | 0.656817i | ||||
\(653\) | 3.45550e9 | + | 5.98510e9i | 0.485640 | + | 0.841153i | 0.999864 | − | 0.0165027i | \(-0.00525320\pi\) |
−0.514224 | + | 0.857656i | \(0.671920\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.28122e9 | + | 5.68324e9i | −0.456237 | + | 0.790226i | ||||
\(656\) | 2.42819e9 | 0.335830 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.23986e8 | −0.0306499 | ||||||||
\(659\) | 1.71222e9 | − | 2.96565e9i | 0.233056 | − | 0.403665i | −0.725650 | − | 0.688064i | \(-0.758461\pi\) |
0.958706 | + | 0.284399i | \(0.0917941\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.38219e9 | + | 5.85812e9i | 0.455504 | + | 0.788956i | 0.998717 | − | 0.0506388i | \(-0.0161257\pi\) |
−0.543213 | + | 0.839595i | \(0.682792\pi\) | |||||||
\(662\) | 2.05271e9 | + | 3.55539e9i | 0.274995 | + | 0.476305i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.88865e9 | + | 5.00329e9i | −0.382919 | + | 0.663236i | ||||
\(665\) | −2.15155e8 | −0.0283711 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.58165e8 | −0.0728320 | ||||||||
\(668\) | 1.18848e9 | − | 2.05851e9i | 0.154267 | − | 0.267199i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.93475e8 | + | 1.02793e9i | 0.0762326 | + | 0.132039i | ||||
\(671\) | −1.42514e8 | − | 2.46841e8i | −0.0182108 | − | 0.0315420i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.74796e8 | − | 1.51519e9i | 0.110625 | − | 0.191608i | −0.805397 | − | 0.592735i | \(-0.798048\pi\) |
0.916023 | + | 0.401127i | \(0.131381\pi\) | |||||||
\(674\) | 3.75788e9 | 0.472752 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.38182e9 | 0.421053 | ||||||||
\(677\) | 4.15006e9 | − | 7.18811e9i | 0.514036 | − | 0.890337i | −0.485831 | − | 0.874053i | \(-0.661483\pi\) |
0.999867 | − | 0.0162840i | \(-0.00518358\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.82458e8 | − | 4.89232e8i | −0.0346266 | − | 0.0599750i | ||||
\(680\) | −7.30656e9 | − | 1.26553e10i | −0.891110 | − | 1.54345i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.87242e8 | + | 1.36354e9i | −0.0950305 | + | 0.164598i | ||||
\(683\) | 1.21232e10 | 1.45594 | 0.727969 | − | 0.685610i | \(-0.240464\pi\) | ||||
0.727969 | + | 0.685610i | \(0.240464\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.09375e10 | 1.30017 | ||||||||
\(686\) | 3.15454e8 | − | 5.46382e8i | 0.0373080 | − | 0.0646193i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.32217e9 | − | 2.29006e9i | −0.154784 | − | 0.268094i | ||||
\(689\) | 1.09112e9 | + | 1.88988e9i | 0.127088 | + | 0.220123i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.10923e9 | + | 7.11739e9i | −0.473791 | + | 0.820631i | −0.999550 | − | 0.0300033i | \(-0.990448\pi\) |
0.525758 | + | 0.850634i | \(0.323782\pi\) | |||||||
\(692\) | 5.84385e9 | 0.670390 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.52038e9 | −0.854046 | ||||||||
\(695\) | −2.30632e9 | + | 3.99467e9i | −0.260599 | + | 0.451371i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.93759e9 | + | 1.54804e10i | 0.999783 | + | 1.73167i | ||||
\(698\) | 7.96051e8 | + | 1.37880e9i | 0.0886027 | + | 0.153464i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.17782e8 | + | 3.77210e8i | −0.0239983 | + | 0.0415662i | ||||
\(701\) | −4.72231e9 | −0.517775 | −0.258888 | − | 0.965907i | \(-0.583356\pi\) | ||||
−0.258888 | + | 0.965907i | \(0.583356\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.31469e9 | −0.251275 | ||||||||
\(704\) | −3.12370e8 | + | 5.41040e8i | −0.0337415 | + | 0.0584420i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.70891e9 | + | 2.95991e9i | 0.182769 | + | 0.316565i | ||||
\(707\) | −3.83566e8 | − | 6.64355e8i | −0.0408199 | − | 0.0707021i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.39487e9 | + | 2.41599e9i | −0.146985 | + | 0.254585i | −0.930112 | − | 0.367277i | \(-0.880290\pi\) |
0.783127 | + | 0.621862i | \(0.213624\pi\) | |||||||
\(710\) | −1.30119e10 | −1.36438 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.12574e10 | 1.16885 | ||||||||
\(713\) | 2.11592e9 | − | 3.66488e9i | 0.218618 | − | 0.378658i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.42416e8 | − | 1.63231e9i | −0.0964210 | − | 0.167006i | ||||
\(716\) | 3.72397e9 | + | 6.45011e9i | 0.379150 | + | 0.656707i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.79762e9 | + | 4.84562e9i | −0.282068 | + | 0.488556i | ||||
\(719\) | −1.51985e9 | −0.152493 | −0.0762463 | − | 0.997089i | \(-0.524294\pi\) | ||||
−0.0762463 | + | 0.997089i | \(0.524294\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.61401e8 | −0.0458464 | ||||||||
\(722\) | −2.45870e9 | + | 4.25860e9i | −0.243123 | + | 0.421101i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.96715e9 | + | 5.13925e9i | 0.290572 | + | 0.503286i | ||||
\(725\) | 1.35041e9 | + | 2.33899e9i | 0.131608 | + | 0.227953i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.05880e9 | − | 7.03005e9i | 0.391767 | − | 0.678560i | −0.600916 | − | 0.799312i | \(-0.705197\pi\) |
0.992683 | + | 0.120752i | \(0.0385307\pi\) | |||||||
\(728\) | 4.30679e8 | 0.0413708 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.20365e9 | 0.304800 | ||||||||
\(731\) | 9.73316e9 | − | 1.68583e10i | 0.921601 | − | 1.59626i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.16203e9 | + | 8.94090e9i | 0.484124 | + | 0.838528i | 0.999834 | − | 0.0182357i | \(-0.00580493\pi\) |
−0.515709 | + | 0.856764i | \(0.672472\pi\) | |||||||
\(734\) | −2.55769e9 | − | 4.43006e9i | −0.238733 | − | 0.413498i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.46838e9 | − | 2.54331e9i | 0.135758 | − | 0.235140i | ||||
\(737\) | −4.80867e8 | −0.0442475 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.35365e10 | −1.23382 | −0.616908 | − | 0.787035i | \(-0.711615\pi\) | ||||
−0.616908 | + | 0.787035i | \(0.711615\pi\) | |||||||
\(740\) | −4.81736e9 | + | 8.34391e9i | −0.437016 | + | 0.756935i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.21871e7 | − | 1.42352e8i | −0.00738567 | − | 0.0127924i | ||||
\(743\) | −8.59680e9 | − | 1.48901e10i | −0.768910 | − | 1.33179i | −0.938154 | − | 0.346218i | \(-0.887466\pi\) |
0.169244 | − | 0.985574i | \(-0.445868\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.05300e9 | + | 7.02001e9i | −0.359112 | + | 0.622000i | ||||
\(746\) | −2.28710e9 | −0.201697 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.47571e9 | 0.216294 | ||||||||
\(749\) | −3.65634e8 | + | 6.33297e8i | −0.0317951 | + | 0.0550708i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.62392e9 | − | 9.74092e9i | −0.484506 | − | 0.839190i | 0.515335 | − | 0.856989i | \(-0.327667\pi\) |
−0.999842 | + | 0.0177991i | \(0.994334\pi\) | |||||||
\(752\) | 1.12459e9 | + | 1.94786e9i | 0.0964348 | + | 0.167030i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.58384e8 | − | 9.67149e8i | 0.0474387 | − | 0.0821663i | ||||
\(755\) | −2.96837e7 | −0.00251017 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.63068e10 | 1.36626 | 0.683131 | − | 0.730296i | \(-0.260618\pi\) | ||||
0.683131 | + | 0.730296i | \(0.260618\pi\) | |||||||
\(758\) | −4.45059e9 | + | 7.70865e9i | −0.371172 | + | 0.642889i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.21879e9 | − | 3.84305e9i | −0.183345 | − | 0.317562i | ||||
\(761\) | 3.07035e9 | + | 5.31800e9i | 0.252546 | + | 0.437423i | 0.964226 | − | 0.265081i | \(-0.0853986\pi\) |
−0.711680 | + | 0.702504i | \(0.752065\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.28670e8 | − | 2.22864e8i | 0.0104868 | − | 0.0181637i | ||||
\(764\) | 5.22812e9 | 0.424149 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.57158e9 | −0.367507 | ||||||||
\(767\) | −3.32996e9 | + | 5.76766e9i | −0.266474 | + | 0.461547i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.22534e10 | − | 2.12236e10i | −0.971664 | − | 1.68297i | −0.690532 | − | 0.723302i | \(-0.742624\pi\) |
−0.281132 | − | 0.959669i | \(-0.590710\pi\) | |||||||
\(770\) | 7.09862e7 | + | 1.22952e8i | 0.00560346 | + | 0.00970549i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.35334e9 | − | 9.27226e9i | 0.418759 | − | 0.725312i | ||||
\(773\) | 1.01722e10 | 0.792110 | 0.396055 | − | 0.918227i | \(-0.370379\pi\) | ||||
0.396055 | + | 0.918227i | \(0.370379\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.04769e10 | −1.58018 | ||||||||
\(776\) | 5.82570e9 | − | 1.00904e10i | 0.447540 | − | 0.775162i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.82705e9 | − | 8.36070e9i | −0.367497 | − | 0.636523i | ||||
\(779\) | 2.71408e9 | + | 4.70093e9i | 0.205704 | + | 0.356289i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.63574e9 | − | 4.56523e9i | 0.197981 | − | 0.342913i | ||||
\(782\) | 2.60379e9 | 0.194707 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.15979e9 | −0.234181 | ||||||||
\(785\) | −6.27558e9 | + | 1.08696e10i | −0.463031 | + | 0.801994i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.89567e9 | + | 8.47956e9i | 0.358015 | + | 0.620100i | 0.987629 | − | 0.156808i | \(-0.0501204\pi\) |
−0.629614 | + | 0.776908i | \(0.716787\pi\) | |||||||
\(788\) | 5.46554e9 | + | 9.46659e9i | 0.397916 | + | 0.689211i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.08905e9 | − | 1.40106e10i | 0.583718 | − | 1.01103i | ||||
\(791\) | −1.13320e9 | −0.0814124 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.53277e9 | −0.109150 | ||||||||
\(794\) | 5.64047e9 | − | 9.76959e9i | 0.399893 | − | 0.692635i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.37049e9 | − | 7.56991e9i | −0.307139 | − | 0.531980i | ||||
\(797\) | −4.87891e9 | − | 8.45052e9i | −0.341365 | − | 0.591261i | 0.643322 | − | 0.765596i | \(-0.277556\pi\) |
−0.984686 | + | 0.174335i | \(0.944222\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.27872e9 | + | 1.43392e10i | −0.574182 | + | 0.994512i | ||||
\(800\) | −1.42103e10 | −0.981270 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.61155e9 | 0.110315 | ||||||||
\(803\) | −6.48945e8 | + | 1.12401e9i | −0.0442286 | + | 0.0766062i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.90794e8 | − | 3.30465e8i | −0.0128908 | − | 0.0223275i | ||||
\(806\) | 4.23350e9 | + | 7.33264e9i | 0.284792 | + | 0.493273i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.91104e9 | − | 1.37023e10i | 0.527587 | − | 0.913807i | ||||
\(809\) | 2.78706e9 | 0.185066 | 0.0925330 | − | 0.995710i | \(-0.470504\pi\) | ||||
0.0925330 | + | 0.995710i | \(0.470504\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.99983e9 | −0.526633 | −0.263316 | − | 0.964710i | \(-0.584816\pi\) | ||||
−0.263316 | + | 0.964710i | \(0.584816\pi\) | |||||||
\(812\) | 1.07485e8 | − | 1.86170e8i | 0.00704537 | − | 0.0122029i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.63688e8 | + | 1.32275e9i | 0.0496284 | + | 0.0859590i | ||||
\(815\) | 1.13770e10 | + | 1.97055e10i | 0.736165 | + | 1.27508i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.95568e9 | − | 5.11938e9i | 0.189618 | − | 0.328428i | ||||
\(818\) | −5.39687e8 | −0.0344751 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.25943e10 | 1.43103 | ||||||||
\(821\) | −5.12009e9 | + | 8.86826e9i | −0.322906 | + | 0.559290i | −0.981086 | − | 0.193570i | \(-0.937993\pi\) |
0.658180 | + | 0.752861i | \(0.271327\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.39341e10 | − | 2.41346e10i | −0.871324 | − | 1.50918i | −0.860627 | − | 0.509236i | \(-0.829928\pi\) |
−0.0106973 | − | 0.999943i | \(-0.503405\pi\) | |||||||
\(824\) | −4.75820e9 | − | 8.24144e9i | −0.296277 | − | 0.513166i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.50825e8 | − | 4.34442e8i | 0.0154860 | − | 0.0268226i | ||||
\(827\) | −2.35125e10 | −1.44554 | −0.722769 | − | 0.691090i | \(-0.757131\pi\) | ||||
−0.722769 | + | 0.691090i | \(0.757131\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.28598e10 | −0.783960 | −0.391980 | − | 0.919974i | \(-0.628210\pi\) | ||||
−0.391980 | + | 0.919974i | \(0.628210\pi\) | |||||||
\(830\) | −5.12080e9 | + | 8.86948e9i | −0.310859 | + | 0.538424i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.67981e9 | + | 2.90952e9i | 0.101118 | + | 0.175142i | ||||
\(833\) | −1.16304e10 | − | 2.01445e10i | −0.697168 | − | 1.20753i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.03812e9 | − | 8.72628e9i | 0.299479 | − | 0.518712i | ||||
\(836\) | 7.51802e8 | 0.0445022 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.01433e10 | 0.595420 | ||||||||
\(839\) | −3.99916e9 | + | 6.92675e9i | −0.233777 | + | 0.404914i | −0.958917 | − | 0.283688i | \(-0.908442\pi\) |
0.725139 | + | 0.688602i | \(0.241775\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.95845e9 | + | 1.37844e10i | 0.461363 | + | 0.799103i | ||||
\(842\) | −3.39998e9 | − | 5.88894e9i | −0.196284 | − | 0.339973i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.24533e9 | − | 1.42813e10i | 0.472074 | − | 0.817655i | ||||
\(845\) | 1.43360e10 | 0.817389 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.18966e9 | 0.0672716 | ||||||||
\(848\) | −8.25296e8 | + | 1.42945e9i | −0.0464755 | + | 0.0804979i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6.29956e9 | − | 1.09112e10i | −0.351839 | − | 0.609403i | ||||
\(851\) | −2.05261e9 | − | 3.55523e9i | −0.114170 | − | 0.197749i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.10414e9 | + | 3.64447e9i | −0.116079 | + | 0.201054i | −0.918210 | − | 0.396093i | \(-0.870366\pi\) |
0.802132 | + | 0.597147i | \(0.203699\pi\) | |||||||
\(854\) | 1.15454e8 | 0.00634318 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.50824e10 | −0.821888 | ||||||||
\(857\) | 1.59653e10 | − | 2.76528e10i | 0.866453 | − | 1.50074i | 0.000855933 | − | 1.00000i | \(-0.499728\pi\) |
0.865597 | − | 0.500741i | \(-0.166939\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.09001e10 | − | 1.88795e10i | −0.586752 | − | 1.01628i | −0.994655 | − | 0.103259i | \(-0.967073\pi\) |
0.407903 | − | 0.913025i | \(-0.366260\pi\) | |||||||
\(860\) | −1.23027e10 | − | 2.13090e10i | −0.659565 | − | 1.14240i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.59828e9 | + | 1.14286e10i | −0.350877 | + | 0.607737i | ||||
\(863\) | −1.04728e10 | −0.554657 | −0.277329 | − | 0.960775i | \(-0.589449\pi\) | ||||
−0.277329 | + | 0.960775i | \(0.589449\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.47728e10 | 1.30142 | ||||||||
\(866\) | −4.55214e8 | + | 7.88453e8i | −0.0238178 | + | 0.0412537i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.14923e8 | + | 1.41149e9i | 0.0422958 | + | 0.0732585i | ||||
\(869\) | 3.27710e9 | + | 5.67611e9i | 0.169403 | + | 0.293414i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.29296e9 | + | 2.23948e9i | −0.0663015 | + | 0.114838i | ||||
\(872\) | 5.30765e9 | 0.271078 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7.90695e8 | 0.0400608 | ||||||||
\(875\) | 5.17920e7 | − | 8.97064e7i | 0.00261357 | − | 0.00452684i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.88935e9 | + | 1.53968e10i | 0.445012 | + | 0.770783i | 0.998053 | − | 0.0623707i | \(-0.0198661\pi\) |
−0.553041 | + | 0.833154i | \(0.686533\pi\) | |||||||
\(878\) | 2.97229e9 | + | 5.14815e9i | 0.148204 | + | 0.256697i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.12820e8 | − | 1.23464e9i | 0.0352607 | − | 0.0610733i | ||||
\(881\) | 7.64253e9 | 0.376549 | 0.188274 | − | 0.982116i | \(-0.439711\pi\) | ||||
0.188274 | + | 0.982116i | \(0.439711\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.76375e10 | −1.35094 | −0.675472 | − | 0.737386i | \(-0.736060\pi\) | ||||
−0.675472 | + | 0.737386i | \(0.736060\pi\) | |||||||
\(884\) | 6.65674e9 | − | 1.15298e10i | 0.324100 | − | 0.561358i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.32127e9 | + | 9.21671e9i | 0.257038 | + | 0.445203i | ||||
\(887\) | 1.61544e10 | + | 2.79802e10i | 0.777243 | + | 1.34622i | 0.933525 | + | 0.358512i | \(0.116716\pi\) |
−0.156282 | + | 0.987713i | \(0.549951\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.37225e8 | − | 9.30502e8i | 0.0256449 | − | 0.0444182i | ||||
\(890\) | 1.99562e10 | 0.948886 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.90014e10 | 0.896414 | ||||||||
\(893\) | −2.51401e9 | + | 4.35439e9i | −0.118137 | + | 0.204619i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.57864e10 | + | 2.73428e10i | 0.736042 | + | 1.27486i | ||||
\(896\) | 6.60296e8 | + | 1.14367e9i | 0.0306662 | + | 0.0531155i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.31031e8 | − | 1.43939e9i | 0.0382957 | − | 0.0663301i | ||||
\(899\) | 1.01063e10 | 0.463908 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.21509e10 | −0.553439 | ||||||||
\(902\) | 1.79092e9 | − | 3.10196e9i | 0.0812555 | − | 0.140739i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.16862e10 | − | 2.02410e10i | −0.526117 | − | 0.911262i | ||||
\(905\) | 1.25781e10 | + | 2.17859e10i | 0.564087 | + | 0.977027i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.13571e10 | + | 1.96711e10i | −0.505409 | + | 0.875394i | 0.494572 | + | 0.869137i | \(0.335325\pi\) |
−0.999980 | + | 0.00625673i | \(0.998008\pi\) | |||||||
\(908\) | 3.99238e9 | 0.176983 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 7.63476e8 | 0.0335854 | ||||||||
\(911\) | 3.75463e9 | − | 6.50320e9i | 0.164533 | − | 0.284979i | −0.771957 | − | 0.635675i | \(-0.780722\pi\) |
0.936489 | + | 0.350696i | \(0.114055\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.07458e9 | − | 3.59328e9i | −0.0902157 | − | 0.156258i | ||||
\(914\) | 8.84275e9 | + | 1.53161e10i | 0.383068 | + | 0.663493i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.66488e9 | + | 2.88366e9i | −0.0715730 | + | 0.123968i | ||||
\(917\) | 1.07691e9 | 0.0461199 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.49374e10 | −1.05986 | −0.529928 | − | 0.848043i | \(-0.677781\pi\) | ||||
−0.529928 | + | 0.848043i | \(0.677781\pi\) | |||||||
\(920\) | 3.93513e9 | − | 6.81585e9i | 0.166610 | − | 0.288577i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8.30062e9 | + | 1.43771e10i | 0.348781 | + | 0.604106i | ||||
\(923\) | −1.41741e10 | − | 2.45502e10i | −0.593319 | − | 1.02766i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.93211e9 | + | 1.72029e10i | −0.412615 | + | 0.714671i | ||||
\(926\) | −2.78132e9 | −0.115110 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.01342e9 | 0.288079 | ||||||||
\(929\) | −4.33103e9 | + | 7.50156e9i | −0.177229 | + | 0.306970i | −0.940931 | − | 0.338600i | \(-0.890047\pi\) |
0.763701 | + | 0.645570i | \(0.223380\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.53182e9 | − | 6.11729e9i | −0.143441 | − | 0.248448i | ||||
\(932\) | −4.24280e9 | − | 7.34874e9i | −0.171671 | − | 0.297343i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.25377e9 | − | 2.17159e9i | 0.0503503 | − | 0.0872093i | ||||
\(935\) | 1.04949e10 | 0.419891 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.82655e10 | 1.12245 | 0.561226 | − | 0.827663i | \(-0.310330\pi\) | ||||
0.561226 | + | 0.827663i | \(0.310330\pi\) | |||||||
\(938\) | 9.73908e7 | − | 1.68686e8i | 0.00385308 | − | 0.00667373i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.04643e10 | + | 1.81248e10i | 0.410926 | + | 0.711745i | ||||
\(941\) | −2.33541e10 | − | 4.04505e10i | −0.913691 | − | 1.58256i | −0.808807 | − | 0.588074i | \(-0.799886\pi\) |
−0.104884 | − | 0.994484i | \(-0.533447\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.81356e9 | + | 8.33734e9i | −0.186929 | + | 0.323770i | ||||
\(944\) | −5.03740e9 | −0.194897 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.90067e9 | −0.149803 | ||||||||
\(947\) | −2.33696e10 | + | 4.04774e10i | −0.894184 | + | 1.54877i | −0.0593718 | + | 0.998236i | \(0.518910\pi\) |
−0.834812 | + | 0.550535i | \(0.814424\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.48979e9 | + | 6.04449e9i | 0.132546 | + | 0.229577i | ||||
\(950\) | −1.91299e9 | − | 3.31340e9i | −0.0723904 | − | 0.125384i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.19902e9 | + | 2.07677e9i | −0.0450400 | + | 0.0780116i | ||||
\(953\) | −3.82420e10 | −1.43125 | −0.715625 | − | 0.698484i | \(-0.753858\pi\) | ||||
−0.715625 | + | 0.698484i | \(0.753858\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.21627e10 | 0.823399 | ||||||||
\(956\) | −2.29295e9 | + | 3.97151e9i | −0.0848775 | + | 0.147012i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.52919e9 | + | 7.84478e9i | 0.166434 | + | 0.288271i | ||||
\(959\) | −8.97437e8 | − | 1.55441e9i | −0.0328578 | − | 0.0569114i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.45550e10 | + | 4.25306e10i | −0.892501 | + | 1.54586i | ||||
\(962\) | 8.21367e9 | 0.297457 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.83424e10 | −0.659457 | ||||||||
\(965\) | 2.26935e10 | − | 3.93063e10i | 0.812935 | − | 1.40805i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.45006e10 | + | 4.24363e10i | 0.871333 | + | 1.50919i | 0.860618 | + | 0.509250i | \(0.170077\pi\) |
0.0107146 | + | 0.999943i | \(0.496589\pi\) | |||||||
\(968\) | 1.22684e10 | + | 2.12495e10i | 0.434734 | + | 0.752982i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.03274e10 | − | 1.78875e10i | 0.363320 | − | 0.629288i | ||||
\(971\) | −2.72929e10 | −0.956713 | −0.478357 | − | 0.878166i | \(-0.658767\pi\) | ||||
−0.478357 | + | 0.878166i | \(0.658767\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.56947e8 | 0.0263433 | ||||||||
\(974\) | 2.78838e9 | − | 4.82962e9i | 0.0966931 | − | 0.167477i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.79676e8 | − | 1.00403e9i | −0.0199577 | − | 0.0345678i | ||||
\(977\) | 1.97241e9 | + | 3.41631e9i | 0.0676653 | + | 0.117200i | 0.897873 | − | 0.440254i | \(-0.145112\pi\) |
−0.830208 | + | 0.557454i | \(0.811778\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.04242e9 | + | 7.00167e9i | −0.137690 | + | 0.238486i | ||||
\(980\) | −2.94018e10 | −0.997889 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.07682e10 | 1.03684 | ||||||||
\(983\) | 2.37160e8 | − | 4.10774e8i | 0.00796351 | − | 0.0137932i | −0.862016 | − | 0.506881i | \(-0.830798\pi\) |
0.869980 | + | 0.493088i | \(0.164132\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.31691e10 | + | 4.01301e10i | 0.772472 | + | 1.33796i | ||||
\(986\) | 3.10912e9 | + | 5.38515e9i | 0.103292 | + | 0.178908i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.02146e9 | − | 3.50127e9i | 0.0666831 | − | 0.115498i | ||||
\(989\) | 1.04841e10 | 0.344622 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.22197e10 | 0.398843 | 0.199421 | − | 0.979914i | \(-0.436094\pi\) | ||||
0.199421 | + | 0.979914i | \(0.436094\pi\) | |||||||
\(992\) | −2.65869e10 | + | 4.60498e10i | −0.864721 | + | 1.49774i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.06764e9 | + | 1.84921e9i | 0.0344805 | + | 0.0597219i | ||||
\(995\) | −1.85271e10 | − | 3.20898e10i | −0.596247 | − | 1.03273i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.80345e10 | − | 3.12367e10i | 0.576330 | − | 0.998233i | −0.419566 | − | 0.907725i | \(-0.637818\pi\) |
0.995896 | − | 0.0905079i | \(-0.0288490\pi\) | |||||||
\(998\) | 2.46390e9 | 0.0784631 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 81.8.c.c.55.1 | 2 | ||
3.2 | odd | 2 | 81.8.c.a.55.1 | 2 | |||
9.2 | odd | 6 | 3.8.a.a.1.1 | ✓ | 1 | ||
9.4 | even | 3 | inner | 81.8.c.c.28.1 | 2 | ||
9.5 | odd | 6 | 81.8.c.a.28.1 | 2 | |||
9.7 | even | 3 | 9.8.a.a.1.1 | 1 | |||
36.7 | odd | 6 | 144.8.a.b.1.1 | 1 | |||
36.11 | even | 6 | 48.8.a.g.1.1 | 1 | |||
45.2 | even | 12 | 75.8.b.c.49.2 | 2 | |||
45.7 | odd | 12 | 225.8.b.f.199.1 | 2 | |||
45.29 | odd | 6 | 75.8.a.a.1.1 | 1 | |||
45.34 | even | 6 | 225.8.a.i.1.1 | 1 | |||
45.38 | even | 12 | 75.8.b.c.49.1 | 2 | |||
45.43 | odd | 12 | 225.8.b.f.199.2 | 2 | |||
63.2 | odd | 6 | 147.8.e.b.67.1 | 2 | |||
63.11 | odd | 6 | 147.8.e.b.79.1 | 2 | |||
63.20 | even | 6 | 147.8.a.b.1.1 | 1 | |||
63.34 | odd | 6 | 441.8.a.a.1.1 | 1 | |||
63.38 | even | 6 | 147.8.e.a.79.1 | 2 | |||
63.47 | even | 6 | 147.8.e.a.67.1 | 2 | |||
72.11 | even | 6 | 192.8.a.a.1.1 | 1 | |||
72.29 | odd | 6 | 192.8.a.i.1.1 | 1 | |||
72.43 | odd | 6 | 576.8.a.x.1.1 | 1 | |||
72.61 | even | 6 | 576.8.a.w.1.1 | 1 | |||
99.65 | even | 6 | 363.8.a.b.1.1 | 1 | |||
117.38 | odd | 6 | 507.8.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.8.a.a.1.1 | ✓ | 1 | 9.2 | odd | 6 | ||
9.8.a.a.1.1 | 1 | 9.7 | even | 3 | |||
48.8.a.g.1.1 | 1 | 36.11 | even | 6 | |||
75.8.a.a.1.1 | 1 | 45.29 | odd | 6 | |||
75.8.b.c.49.1 | 2 | 45.38 | even | 12 | |||
75.8.b.c.49.2 | 2 | 45.2 | even | 12 | |||
81.8.c.a.28.1 | 2 | 9.5 | odd | 6 | |||
81.8.c.a.55.1 | 2 | 3.2 | odd | 2 | |||
81.8.c.c.28.1 | 2 | 9.4 | even | 3 | inner | ||
81.8.c.c.55.1 | 2 | 1.1 | even | 1 | trivial | ||
144.8.a.b.1.1 | 1 | 36.7 | odd | 6 | |||
147.8.a.b.1.1 | 1 | 63.20 | even | 6 | |||
147.8.e.a.67.1 | 2 | 63.47 | even | 6 | |||
147.8.e.a.79.1 | 2 | 63.38 | even | 6 | |||
147.8.e.b.67.1 | 2 | 63.2 | odd | 6 | |||
147.8.e.b.79.1 | 2 | 63.11 | odd | 6 | |||
192.8.a.a.1.1 | 1 | 72.11 | even | 6 | |||
192.8.a.i.1.1 | 1 | 72.29 | odd | 6 | |||
225.8.a.i.1.1 | 1 | 45.34 | even | 6 | |||
225.8.b.f.199.1 | 2 | 45.7 | odd | 12 | |||
225.8.b.f.199.2 | 2 | 45.43 | odd | 12 | |||
363.8.a.b.1.1 | 1 | 99.65 | even | 6 | |||
441.8.a.a.1.1 | 1 | 63.34 | odd | 6 | |||
507.8.a.a.1.1 | 1 | 117.38 | odd | 6 | |||
576.8.a.w.1.1 | 1 | 72.61 | even | 6 | |||
576.8.a.x.1.1 | 1 | 72.43 | odd | 6 |