Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,7,Mod(13,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.13");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.j (of order \(18\), degree \(6\), 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: | \(17.4841103551\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 13.8 | ||
Character | \(\chi\) | \(=\) | 76.13 |
Dual form | 76.7.j.a.41.8 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{5}{18}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 9.61067 | − | 26.4051i | 0.355951 | − | 0.977967i | −0.624469 | − | 0.781049i | \(-0.714685\pi\) |
0.980420 | − | 0.196917i | \(-0.0630931\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 26.4812 | + | 150.182i | 0.211849 | + | 1.20146i | 0.886291 | + | 0.463129i | \(0.153273\pi\) |
−0.674442 | + | 0.738328i | \(0.735616\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 197.423 | − | 341.946i | 0.575577 | − | 0.996928i | −0.420402 | − | 0.907338i | \(-0.638111\pi\) |
0.995979 | − | 0.0895901i | \(-0.0285557\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −46.4181 | − | 38.9494i | −0.0636737 | − | 0.0534286i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 403.111 | + | 698.209i | 0.302863 | + | 0.524575i | 0.976783 | − | 0.214230i | \(-0.0687241\pi\) |
−0.673920 | + | 0.738804i | \(0.735391\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 674.923 | + | 1854.34i | 0.307202 | + | 0.844031i | 0.993199 | + | 0.116427i | \(0.0371440\pi\) |
−0.685997 | + | 0.727604i | \(0.740634\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4220.07 | + | 744.113i | 1.25039 | + | 0.220478i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −722.165 | + | 605.969i | −0.146991 | + | 0.123340i | −0.713318 | − | 0.700841i | \(-0.752808\pi\) |
0.566327 | + | 0.824181i | \(0.308364\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6573.76 | − | 1957.42i | 0.958414 | − | 0.285380i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7131.76 | − | 8499.30i | −0.770086 | − | 0.917752i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3876.04 | − | 21982.1i | 0.318570 | − | 1.80670i | −0.232898 | − | 0.972501i | \(-0.574821\pi\) |
0.551467 | − | 0.834196i | \(-0.314068\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7170.71 | + | 2609.92i | −0.458925 | + | 0.167035i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 16265.7 | − | 9391.00i | 0.826383 | − | 0.477112i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6965.80 | − | 8301.52i | 0.285612 | − | 0.340380i | −0.604094 | − | 0.796913i | \(-0.706465\pi\) |
0.889706 | + | 0.456534i | \(0.150909\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 19159.1 | + | 11061.5i | 0.643119 | + | 0.371305i | 0.785815 | − | 0.618462i | \(-0.212244\pi\) |
−0.142696 | + | 0.989767i | \(0.545577\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 22310.5 | − | 3933.93i | 0.620821 | − | 0.109468i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 56582.2 | + | 20594.2i | 1.31970 | + | 0.480332i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 63273.4i | 1.24915i | 0.780963 | + | 0.624577i | \(0.214729\pi\) | ||||
−0.780963 | + | 0.624577i | \(0.785271\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 55450.4 | 0.934783 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 24822.9 | − | 68200.3i | 0.360164 | − | 0.989543i | −0.618807 | − | 0.785543i | \(-0.712384\pi\) |
0.978971 | − | 0.204000i | \(-0.0653942\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2093.79 | + | 11874.4i | 0.0263346 | + | 0.149351i | 0.995140 | − | 0.0984728i | \(-0.0313957\pi\) |
−0.968805 | + | 0.247824i | \(0.920285\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4620.30 | − | 8002.59i | 0.0507029 | − | 0.0878200i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −110893. | − | 93050.5i | −1.06810 | − | 0.896242i | −0.0732206 | − | 0.997316i | \(-0.523328\pi\) |
−0.994879 | + | 0.101074i | \(0.967772\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −19127.0 | − | 33129.0i | −0.162577 | − | 0.281592i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9060.17 | + | 24892.6i | 0.0683008 | + | 0.187655i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 23048.9 | + | 4064.15i | 0.154819 | + | 0.0272987i | 0.250520 | − | 0.968111i | \(-0.419398\pi\) |
−0.0957016 | + | 0.995410i | \(0.530509\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −94183.6 | + | 79029.5i | −0.566092 | + | 0.475008i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11492.4 | − | 192393.i | 0.0620562 | − | 1.03888i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −35824.8 | − | 42694.4i | −0.174433 | − | 0.207881i | 0.671744 | − | 0.740784i | \(-0.265546\pi\) |
−0.846176 | + | 0.532903i | \(0.821101\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −67722.4 | + | 384073.i | −0.298362 | + | 1.69209i | 0.354855 | + | 0.934921i | \(0.384530\pi\) |
−0.653216 | + | 0.757171i | \(0.726581\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −22482.6 | + | 8183.00i | −0.0899135 | + | 0.0327258i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −260615. | + | 150466.i | −0.948986 | + | 0.547897i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −142739. | + | 170110.i | −0.474591 | + | 0.565595i | −0.949229 | − | 0.314586i | \(-0.898134\pi\) |
0.474638 | + | 0.880181i | \(0.342579\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −543188. | − | 313610.i | −1.65350 | − | 0.954646i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 100843. | − | 17781.3i | 0.281753 | − | 0.0496807i | −0.0309857 | − | 0.999520i | \(-0.509865\pi\) |
0.312739 | + | 0.949839i | \(0.398754\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 122731. | + | 44670.3i | 0.315489 | + | 0.114829i | 0.494911 | − | 0.868944i | \(-0.335201\pi\) |
−0.179422 | + | 0.983772i | \(0.557423\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 214426.i | 0.508270i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 318333. | 0.697284 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −44636.7 | + | 122638.i | −0.0905337 | + | 0.248739i | −0.976693 | − | 0.214642i | \(-0.931142\pi\) |
0.886159 | + | 0.463381i | \(0.153364\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −99316.8 | − | 563254.i | −0.186882 | − | 1.05986i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −490002. | + | 848709.i | −0.856967 | + | 1.48431i | 0.0178420 | + | 0.999841i | \(0.494320\pi\) |
−0.874809 | + | 0.484469i | \(0.839013\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −110129. | − | 92409.6i | −0.179327 | − | 0.150474i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −152256. | − | 263716.i | −0.231216 | − | 0.400478i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 219248. | + | 602378.i | 0.311003 | + | 0.854475i | 0.992455 | + | 0.122611i | \(0.0391269\pi\) |
−0.681451 | + | 0.731863i | \(0.738651\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 767328. | + | 135301.i | 1.01826 | + | 0.179546i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 476213. | − | 399590.i | 0.592042 | − | 0.496782i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 468050. | + | 935427.i | 0.545911 | + | 1.09104i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.02042e6 | − | 1.21609e6i | −1.11806 | − | 1.33245i | −0.937142 | − | 0.348948i | \(-0.886539\pi\) |
−0.180913 | − | 0.983499i | \(-0.557905\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8483.18 | − | 48110.5i | 0.00874285 | − | 0.0495832i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 76505.6 | − | 27845.7i | 0.0742555 | − | 0.0270268i | −0.304625 | − | 0.952472i | \(-0.598531\pi\) |
0.378881 | + | 0.925445i | \(0.376309\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.21817e6 | + | 703313.i | −1.11480 | + | 0.643631i | −0.940069 | − | 0.340984i | \(-0.889240\pi\) |
−0.174733 | + | 0.984616i | \(0.555906\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.08759e6 | − | 1.29613e6i | 0.939497 | − | 1.11965i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.71778e6 | − | 991759.i | −1.40222 | − | 0.809571i | −0.407598 | − | 0.913162i | \(-0.633633\pi\) |
−0.994620 | + | 0.103591i | \(0.966967\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 365117. | − | 64380.0i | 0.281937 | − | 0.0497131i | −0.0308913 | − | 0.999523i | \(-0.509835\pi\) |
0.312829 | + | 0.949810i | \(0.398723\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.67074e6 | + | 608100.i | 1.22163 | + | 0.444638i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.51843e6i | − | 1.05235i | −0.850377 | − | 0.526174i | \(-0.823626\pi\) | ||
0.850377 | − | 0.526174i | \(-0.176374\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.40396e6 | 2.23816 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 40896.6 | − | 112363.i | 0.0255347 | − | 0.0701559i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 64636.9 | + | 366574.i | 0.0383565 | + | 0.217531i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 560783. | − | 971305.i | 0.316548 | − | 0.548276i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.56227e6 | − | 1.31090e6i | −0.839539 | − | 0.704457i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 609545. | + | 1.05576e6i | 0.312087 | + | 0.540551i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 944399. | + | 2.59472e6i | 0.461046 | + | 1.26671i | 0.924700 | + | 0.380697i | \(0.124316\pi\) |
−0.463654 | + | 0.886017i | \(0.653462\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 333669. | + | 58834.8i | 0.155434 | + | 0.0274072i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.29984e6 | − | 1.09069e6i | 0.578197 | − | 0.485165i | −0.306158 | − | 0.951981i | \(-0.599043\pi\) |
0.884354 | + | 0.466816i | \(0.154599\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 628478. | − | 2.63431e6i | 0.267138 | − | 1.11973i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.84109e6 | + | 2.19413e6i | 0.748299 | + | 0.891787i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11429.8 | − | 64821.8i | 0.00444506 | − | 0.0252092i | −0.982505 | − | 0.186239i | \(-0.940370\pi\) |
0.986950 | + | 0.161029i | \(0.0514814\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.00228e6 | − | 364798.i | 0.373201 | − | 0.135834i | −0.148609 | − | 0.988896i | \(-0.547479\pi\) |
0.521809 | + | 0.853062i | \(0.325257\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.52277e6 | + | 2.03387e6i | −1.25669 | + | 0.725548i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.02264e6 | + | 1.21874e6i | −0.349717 | + | 0.416776i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.43120e6 | + | 826305.i | 0.469458 | + | 0.271042i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.05860e6 | + | 186659.i | −0.333257 | + | 0.0587622i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 680757. | + | 247775.i | 0.205794 | + | 0.0749030i | 0.442861 | − | 0.896590i | \(-0.353964\pi\) |
−0.237066 | + | 0.971493i | \(0.576186\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 58611.7i | 0.0170237i | 0.999964 | + | 0.00851185i | \(0.00270944\pi\) | ||||
−0.999964 | + | 0.00851185i | \(0.997291\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 57123.7 | 0.0159493 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.15389e6 | + | 3.17028e6i | −0.309862 | + | 0.851340i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 202162. | + | 1.14652e6i | 0.0522396 | + | 0.296265i | 0.999723 | − | 0.0235398i | \(-0.00749366\pi\) |
−0.947483 | + | 0.319805i | \(0.896383\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 328830. | − | 569550.i | 0.0818050 | − | 0.141690i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.75148e6 | − | 5.66516e6i | −1.61779 | − | 1.35748i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.90764e6 | − | 6.76822e6i | −0.902301 | − | 1.56283i | −0.824500 | − | 0.565862i | \(-0.808544\pi\) |
−0.0778007 | − | 0.996969i | \(-0.524790\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.18161e6 | + | 3.24645e6i | 0.263041 | + | 0.722699i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.69691e6 | − | 475538.i | −0.579051 | − | 0.102102i | −0.123551 | − | 0.992338i | \(-0.539428\pi\) |
−0.455500 | + | 0.890236i | \(0.650539\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 714511. | − | 599546.i | 0.148030 | − | 0.124212i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −381382. | − | 165185.i | −0.0762732 | − | 0.0330355i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.92508e6 | − | 5.86948e6i | −0.951207 | − | 1.13360i | −0.990928 | − | 0.134394i | \(-0.957091\pi\) |
0.0397206 | − | 0.999211i | \(-0.487353\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −523207. | + | 2.96726e6i | −0.0976247 | + | 0.553657i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.47165e6 | + | 535637.i | −0.265390 | + | 0.0965941i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.15677e6 | + | 2.97726e6i | −0.899123 | + | 0.519109i | −0.876915 | − | 0.480645i | \(-0.840403\pi\) |
−0.0222073 | + | 0.999753i | \(0.507069\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.04070e6 | + | 3.62376e6i | −0.512787 | + | 0.611116i | −0.958860 | − | 0.283881i | \(-0.908378\pi\) |
0.446072 | + | 0.894997i | \(0.352822\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.49063e6 | + | 5.47942e6i | 1.54861 | + | 0.894090i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.50254e6 | + | 1.67555e6i | −1.50081 | + | 0.264632i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −714206. | − | 259950.i | −0.109219 | − | 0.0397525i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 7.41599e6i | − | 1.09846i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.83569e6 | 0.837514 | 0.418757 | − | 0.908098i | \(-0.362466\pi\) | ||||
0.418757 | + | 0.908098i | \(0.362466\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.84465e6 | + | 1.33106e7i | −0.673893 | + | 1.85150i | −0.175686 | + | 0.984446i | \(0.556214\pi\) |
−0.498207 | + | 0.867058i | \(0.666008\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.46839e6 | + | 8.32765e6i | 0.198033 | + | 1.12310i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.72438e6 | − | 8.18286e6i | 0.617940 | − | 1.07030i | −0.371921 | − | 0.928264i | \(-0.621301\pi\) |
0.989861 | − | 0.142039i | \(-0.0453657\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.54781e6 | + | 4.65516e6i | 0.703983 | + | 0.590712i | 0.922904 | − | 0.385031i | \(-0.125809\pi\) |
−0.218921 | + | 0.975743i | \(0.570254\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.11995e6 | + | 5.40392e6i | 0.384202 | + | 0.665458i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.46347e6 | − | 4.02084e6i | −0.174942 | − | 0.480650i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.08998e7 | + | 1.92193e6i | 1.26519 | + | 0.223088i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.03611e6 | + | 869398.i | −0.116814 | + | 0.0980184i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.01665e6 | + | 3.80080e6i | 0.439972 | + | 0.416329i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.68456e6 | − | 9.15810e6i | −0.818034 | − | 0.974895i | 0.181930 | − | 0.983311i | \(-0.441765\pi\) |
−0.999965 | + | 0.00841610i | \(0.997321\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 499649. | − | 2.83365e6i | 0.0517042 | − | 0.293229i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.72788e6 | + | 628898.i | −0.173860 | + | 0.0632798i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.56490e6 | − | 4.36760e6i | 0.740328 | − | 0.427429i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.35905e6 | − | 2.81140e6i | 0.224597 | − | 0.267664i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.61108e6 | − | 930155.i | −0.149259 | − | 0.0861744i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.42826e7 | + | 2.51841e6i | −1.28793 | + | 0.227097i | −0.775345 | − | 0.631538i | \(-0.782424\pi\) |
−0.512587 | + | 0.858635i | \(0.671313\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 434506. | + | 158147.i | 0.0381459 | + | 0.0138840i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 1.61867e7i | − | 1.38383i | −0.721980 | − | 0.691914i | \(-0.756768\pi\) | ||
0.721980 | − | 0.691914i | \(-0.243232\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.21678e6 | 0.351135 | 0.175568 | − | 0.984467i | \(-0.443824\pi\) | ||||
0.175568 | + | 0.984467i | \(0.443824\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.05940e6 | − | 8.40563e6i | 0.248199 | − | 0.681921i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −644840. | − | 3.65707e6i | −0.0509782 | − | 0.289112i | 0.948652 | − | 0.316323i | \(-0.102448\pi\) |
−0.999630 | + | 0.0272114i | \(0.991337\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.10379e7 | − | 1.91183e7i | 0.850520 | − | 1.47314i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.80929e6 | + | 2.35727e6i | 0.211033 | + | 0.177078i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.49683e6 | − | 4.32464e6i | −0.182892 | − | 0.316779i | 0.759972 | − | 0.649956i | \(-0.225213\pi\) |
−0.942864 | + | 0.333177i | \(0.891879\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.75072e6 | − | 7.55753e6i | −0.196515 | − | 0.539919i | 0.801823 | − | 0.597562i | \(-0.203864\pi\) |
−0.998337 | + | 0.0576427i | \(0.981642\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.34320e6 | − | 413170.i | −0.163302 | − | 0.0287945i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.46887e6 | − | 3.74983e6i | 0.303878 | − | 0.254984i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.06650e6 | + | 1.08689e7i | 0.535296 | + | 0.721262i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.77010e7 | + | 2.10952e7i | 1.14657 | + | 1.36643i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.79221e6 | + | 2.15067e7i | −0.239812 | + | 1.36004i | 0.592427 | + | 0.805624i | \(0.298170\pi\) |
−0.832239 | + | 0.554417i | \(0.812941\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.69106e7 | − | 6.15494e6i | 1.04423 | − | 0.380069i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.49850e6 | + | 2.01986e6i | −0.210990 | + | 0.121815i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.92917e6 | + | 1.06414e7i | −0.526031 | + | 0.626900i | −0.961996 | − | 0.273064i | \(-0.911963\pi\) |
0.435965 | + | 0.899964i | \(0.356407\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.16361e7 | + | 1.24916e7i | 1.24532 | + | 0.718984i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −646679. | + | 114027.i | −0.0363720 | + | 0.00641336i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.44268e7 | − | 8.89064e6i | −1.34277 | − | 0.488727i | −0.432083 | − | 0.901834i | \(-0.642221\pi\) |
−0.910682 | + | 0.413107i | \(0.864443\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.56916e6i | 0.191791i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.80130e7 | 0.946350 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.76324e6 | − | 7.59193e6i | 0.141958 | − | 0.390028i | −0.848255 | − | 0.529588i | \(-0.822347\pi\) |
0.990214 | + | 0.139560i | \(0.0445688\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.07065e6 | − | 3.44283e7i | −0.305019 | − | 1.72985i | −0.623415 | − | 0.781891i | \(-0.714255\pi\) |
0.318395 | − | 0.947958i | \(-0.396856\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.09472e7 | − | 1.89611e7i | 0.538039 | − | 0.931911i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.71286e6 | − | 3.95456e6i | −0.226614 | − | 0.190152i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.40991e7 | + | 2.44203e7i | 0.663364 | + | 1.14898i | 0.979726 | + | 0.200341i | \(0.0642051\pi\) |
−0.316362 | + | 0.948638i | \(0.602462\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −458491. | − | 1.25969e6i | −0.0211115 | − | 0.0580032i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.54569e7 | − | 2.72546e6i | −0.696630 | − | 0.122835i | −0.185891 | − | 0.982570i | \(-0.559517\pi\) |
−0.510739 | + | 0.859736i | \(0.670628\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.54762e7 | + | 1.29861e7i | −0.682818 | + | 0.572952i | −0.916828 | − | 0.399282i | \(-0.869260\pi\) |
0.234010 | + | 0.972234i | \(0.424815\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.91983e7 | − | 3.36884e6i | 1.26131 | − | 0.145528i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.84202e7 | − | 2.19524e7i | −0.779201 | − | 0.928616i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.03712e6 | + | 2.28956e7i | −0.167255 | + | 0.948548i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.19178e7 | + | 1.52568e7i | −1.70106 | + | 0.619136i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.77132e7 | + | 2.17737e7i | −1.49931 | + | 0.865625i | −1.00000 | 0.000800815i | \(-0.999745\pi\) | |
−0.499306 | + | 0.866426i | \(0.666412\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.46324e6 | − | 6.51084e6i | 0.212806 | − | 0.253613i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.31138e7 | + | 7.57124e6i | 0.500562 | + | 0.289000i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.33782e7 | − | 7.64875e6i | 1.62277 | − | 0.286139i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.47378e6 | + | 1.62832e6i | 0.164050 | + | 0.0597092i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 2.28775e6i | − | 0.0822397i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.94742e7 | −2.09618 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.34301e6 | − | 1.46798e7i | 0.184659 | − | 0.507347i | −0.812475 | − | 0.582996i | \(-0.801880\pi\) |
0.997135 | + | 0.0756485i | \(0.0241027\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.86359e6 | + | 3.89253e7i | 0.232635 | + | 1.31934i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −187666. | + | 325047.i | −0.00623885 | + | 0.0108060i | −0.869128 | − | 0.494587i | \(-0.835319\pi\) |
0.862889 | + | 0.505393i | \(0.168653\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −269242. | − | 225921.i | −0.00878032 | − | 0.00736756i | 0.638387 | − | 0.769716i | \(-0.279602\pi\) |
−0.647167 | + | 0.762348i | \(0.724046\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.82431e6 | − | 3.15979e6i | −0.0583668 | − | 0.101094i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.78808e6 | − | 1.59026e7i | −0.181701 | − | 0.499219i | 0.815084 | − | 0.579343i | \(-0.196691\pi\) |
−0.996785 | + | 0.0801237i | \(0.974468\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.60419e6 | + | 1.51715e6i | 0.265056 | + | 0.0467366i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.26965e7 | + | 3.58266e7i | −1.29085 | + | 1.08315i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.56121e6 | + | 5.39708e6i | −0.105679 | + | 0.160159i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.67935e6 | − | 1.15354e7i | −0.281966 | − | 0.336033i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.80906e6 | − | 1.02597e7i | 0.0517380 | − | 0.293421i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.37111e7 | + | 1.95493e7i | −1.50826 | + | 0.548962i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.66583e7 | − | 9.61765e6i | 0.459352 | − | 0.265207i | −0.252420 | − | 0.967618i | \(-0.581226\pi\) |
0.711772 | + | 0.702411i | \(0.247893\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.46446e6 | − | 2.93703e6i | 0.0667406 | − | 0.0795383i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.93274e7 | − | 1.69322e7i | −0.780080 | − | 0.450379i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.42452e7 | + | 6.03835e6i | −0.894766 | + | 0.157771i | −0.602079 | − | 0.798437i | \(-0.705661\pi\) |
−0.292687 | + | 0.956208i | \(0.594550\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.00943e7 | − | 1.45931e7i | −1.02916 | − | 0.374584i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.78361e7i | 0.449818i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.13487e7 | 0.776851 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.27143e7 | − | 8.98819e7i | 0.796674 | − | 2.18884i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.54383e6 | + | 8.75552e6i | 0.0369498 | + | 0.209553i | 0.997693 | − | 0.0678862i | \(-0.0216255\pi\) |
−0.960743 | + | 0.277439i | \(0.910514\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.45519e7 | + | 4.25251e7i | −0.577575 | + | 1.00039i | 0.418181 | + | 0.908363i | \(0.362668\pi\) |
−0.995757 | + | 0.0920259i | \(0.970666\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.83922e7 | + | 2.38239e7i | 0.656564 | + | 0.550923i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.50131e6 | + | 1.64567e7i | 0.216003 | + | 0.374128i | 0.953582 | − | 0.301132i | \(-0.0973646\pi\) |
−0.737580 | + | 0.675260i | \(0.764031\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.34086e6 | + | 1.46739e7i | 0.119378 | + | 0.327990i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.03006e7 | + | 1.81628e6i | 0.226391 | + | 0.0399188i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.94956e7 | − | 4.15317e7i | 1.06975 | − | 0.897628i | 0.0747220 | − | 0.997204i | \(-0.476193\pi\) |
0.995030 | + | 0.0995759i | \(0.0317486\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.93829e7 | − | 2.57353e7i | 0.837117 | − | 0.547025i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.02579e7 | − | 2.41424e7i | −0.423521 | − | 0.504732i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.45863e6 | + | 1.96149e7i | −0.0711255 | + | 0.403373i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.93940e6 | − | 1.06985e6i | 0.0594649 | − | 0.0216434i | −0.312116 | − | 0.950044i | \(-0.601038\pi\) |
0.371581 | + | 0.928400i | \(0.378816\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.80859e6 | + | 2.19889e6i | −0.0758028 | + | 0.0437648i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.94010e6 | − | 7.07914e6i | 0.116325 | − | 0.138630i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.02387e6 | + | 5.20994e6i | 0.173887 | + | 0.100394i | 0.584417 | − | 0.811453i | \(-0.301323\pi\) |
−0.410531 | + | 0.911847i | \(0.634656\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.37357e7 | − | 5.94851e6i | 0.639728 | − | 0.112801i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.00952e7 | + | 7.31405e6i | 0.375032 | + | 0.136500i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.68127e7i | 1.41096i | 0.708729 | + | 0.705481i | \(0.249269\pi\) | ||||
−0.708729 | + | 0.705481i | \(0.750731\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.75900e7 | 1.40291 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.51356e6 | + | 1.24009e7i | −0.0803384 | + | 0.220728i | −0.973358 | − | 0.229289i | \(-0.926360\pi\) |
0.893020 | + | 0.450017i | \(0.148582\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.42983e6 | + | 4.78080e7i | 0.147719 | + | 0.837757i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 365313. | − | 632741.i | 0.00630279 | − | 0.0109167i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.02447e7 | + | 4.21603e7i | 0.853575 | + | 0.716234i | 0.960574 | − | 0.278025i | \(-0.0896797\pi\) |
−0.106999 | + | 0.994259i | \(0.534124\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.05213e7 | + | 1.82235e7i | 0.176011 | + | 0.304860i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.63076e7 | − | 4.48047e7i | −0.268665 | − | 0.738152i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.96001e7 | − | 3.45602e6i | −0.318029 | − | 0.0560771i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.25176e7 | − | 7.76315e7i | 1.47861 | − | 1.24070i | 0.570951 | − | 0.820984i | \(-0.306575\pi\) |
0.907656 | − | 0.419714i | \(-0.137870\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.35192e7 | − | 4.19126e7i | −0.999969 | − | 0.659820i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.13892e7 | − | 4.93257e7i | −0.641880 | − | 0.764963i | 0.342786 | − | 0.939414i | \(-0.388630\pi\) |
−0.984666 | + | 0.174450i | \(0.944185\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.58086e6 | + | 4.29932e7i | −0.115825 | + | 0.656877i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.19606e7 | − | 2.98312e7i | 1.23379 | − | 0.449061i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.41781e7 | + | 2.55062e7i | −0.655275 | + | 0.378323i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.82871e7 | − | 6.94639e7i | 0.851928 | − | 1.01529i | −0.147727 | − | 0.989028i | \(-0.547196\pi\) |
0.999655 | − | 0.0262600i | \(-0.00835978\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.60178e6 | − | 924787.i | −0.0230715 | − | 0.0133204i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.16718e7 | + | 3.82133e6i | −0.307642 | + | 0.0542455i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.40437e8 | − | 5.11148e7i | −1.96488 | − | 0.715158i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 2.99711e7i | − | 0.413328i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.67979e7 | −0.228356 | −0.114178 | − | 0.993460i | \(-0.536423\pi\) | ||||
−0.114178 | + | 0.993460i | \(0.536423\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.37748e7 | − | 1.20270e8i | 0.586648 | − | 1.61180i | −0.189941 | − | 0.981796i | \(-0.560830\pi\) |
0.776589 | − | 0.630008i | \(-0.216948\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.52319e6 | + | 8.63846e6i | 0.0201249 | + | 0.114134i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.59690e6 | − | 6.23002e6i | 0.0468557 | − | 0.0811564i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.17962e8 | + | 9.89822e7i | 1.51516 | + | 1.27137i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.23527e7 | + | 3.87160e7i | 0.283112 | + | 0.490364i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.72172e7 | + | 1.02254e8i | 0.464850 | + | 1.27716i | 0.921798 | + | 0.387670i | \(0.126720\pi\) |
−0.456948 | + | 0.889493i | \(0.651058\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.88860e7 | − | 1.39097e7i | −0.971709 | − | 0.171339i | −0.334810 | − | 0.942286i | \(-0.608672\pi\) |
−0.636899 | + | 0.770947i | \(0.719783\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.55735e7 | − | 2.98497e7i | 0.432174 | − | 0.362637i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.75481e7 | − | 1.52092e8i | −0.210274 | − | 1.82248i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.92893e7 | − | 3.49056e7i | −0.346190 | − | 0.412574i | 0.564651 | − | 0.825330i | \(-0.309011\pi\) |
−0.910842 | + | 0.412756i | \(0.864566\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −402514. | + | 2.28277e6i | −0.00469316 | + | 0.0266162i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.16177e8 | − | 4.22851e7i | 1.33632 | − | 0.486381i | 0.427669 | − | 0.903936i | \(-0.359335\pi\) |
0.908652 | + | 0.417555i | \(0.137113\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.46605e7 | + | 4.88788e7i | −0.960729 | + | 0.554677i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.30851e7 | − | 1.55942e7i | 0.146505 | − | 0.174598i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.62254e7 | − | 3.82353e7i | −0.731620 | − | 0.422401i | 0.0873946 | − | 0.996174i | \(-0.472146\pi\) |
−0.819015 | + | 0.573773i | \(0.805479\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.76244e7 | − | 1.01607e7i | 0.628170 | − | 0.110763i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.54765e6 | + | 563298.i | 0.0166486 | + | 0.00605960i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.18822e8i | 1.26143i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.66101e8 | −1.74030 | −0.870150 | − | 0.492788i | \(-0.835978\pi\) | ||||
−0.870150 | + | 0.492788i | \(0.835978\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.05587e6 | + | 1.66384e7i | −0.0626237 | + | 0.172057i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.86876e7 | + | 1.62695e8i | 0.292813 | + | 1.66063i | 0.675959 | + | 0.736939i | \(0.263729\pi\) |
−0.383146 | + | 0.923688i | \(0.625159\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.22060e7 | + | 7.31030e7i | −0.425238 | + | 0.736533i | −0.996443 | − | 0.0842743i | \(-0.973143\pi\) |
0.571205 | + | 0.820807i | \(0.306476\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.26220e7 | + | 6.09371e7i | 0.722286 | + | 0.606070i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.35463e7 | − | 4.07834e7i | −0.231192 | − | 0.400436i | 0.726967 | − | 0.686672i | \(-0.240929\pi\) |
−0.958159 | + | 0.286236i | \(0.907596\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.99885e7 | + | 8.23928e7i | 0.290694 | + | 0.798676i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.22168e7 | + | 5.68068e6i | 0.308332 | + | 0.0543673i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.44682e6 | + | 6.24862e6i | −0.0703700 | + | 0.0590474i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.20298e7 | + | 3.11931e7i | −0.392172 | + | 0.291057i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −911591. | − | 1.08639e6i | −0.00839934 | − | 0.0100099i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.15066e7 | − | 1.21970e8i | 0.195689 | − | 1.10981i | −0.715745 | − | 0.698361i | \(-0.753913\pi\) |
0.911434 | − | 0.411446i | \(-0.134976\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.17330e8 | + | 4.27047e7i | −1.05433 | + | 0.383743i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.14475e8 | + | 1.23827e8i | −1.90343 | + | 1.09894i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.55613e8 | − | 1.85452e8i | 1.36402 | − | 1.62557i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.42317e8 | + | 8.21666e7i | 1.23217 | + | 0.711391i | 0.967481 | − | 0.252944i | \(-0.0813989\pi\) |
0.264684 | + | 0.964335i | \(0.414732\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.16271e8 | + | 3.81344e7i | −1.84957 | + | 0.326129i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.55454e6 | + | 565806.i | 0.0131328 | + | 0.00477995i | 0.348578 | − | 0.937280i | \(-0.386665\pi\) |
−0.335445 | + | 0.942060i | \(0.608887\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.02161e7i | 0.0852601i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.44998e6 | 0.0614242 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.38284e7 | − | 3.79932e7i | 0.112643 | − | 0.309483i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.76476e7 | + | 1.00085e8i | 0.142032 | + | 0.805501i | 0.969703 | + | 0.244288i | \(0.0785542\pi\) |
−0.827671 | + | 0.561213i | \(0.810335\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.84757e7 | + | 6.66419e7i | −0.305966 | + | 0.529949i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.47556e8 | + | 1.23814e8i | 1.15946 | + | 0.972898i | 0.999898 | − | 0.0142904i | \(-0.00454893\pi\) |
0.159557 | + | 0.987189i | \(0.448993\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.20789e6 | + | 1.07524e7i | 0.0482025 | + | 0.0834892i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.96414e6 | − | 2.46288e7i | −0.0687836 | − | 0.188981i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.53662e8 | − | 4.47275e7i | −1.92355 | − | 0.339173i | −0.924436 | − | 0.381338i | \(-0.875463\pi\) |
−0.999111 | + | 0.0421649i | \(0.986575\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.95047e7 | − | 3.31483e7i | 0.296064 | − | 0.248427i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.85447e7 | − | 9.35731e7i | 0.655859 | − | 0.693105i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.37884e8 | − | 1.64323e8i | −1.00947 | − | 1.20303i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.02664e7 | − | 1.14936e8i | 0.146658 | − | 0.831737i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.02318e8 | + | 7.36376e7i | −1.44721 | + | 0.526742i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.46169e7 | + | 3.73066e7i | −0.456912 | + | 0.263798i | −0.710745 | − | 0.703450i | \(-0.751642\pi\) |
0.253833 | + | 0.967248i | \(0.418309\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.91069e7 | − | 2.27707e7i | 0.133562 | − | 0.159174i | −0.695118 | − | 0.718896i | \(-0.744648\pi\) |
0.828680 | + | 0.559722i | \(0.189092\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7.33223e7 | + | 4.23327e7i | 0.506709 | + | 0.292548i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.05390e7 | + | 3.62158e6i | −0.140329 | + | 0.0247438i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.29080e8 | − | 1.19775e8i | −2.22298 | − | 0.809097i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.37715e6i | 0.0225562i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.43220e8 | 0.945848 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.03456e8 | − | 2.84242e8i | 0.675605 | − | 1.85621i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.90549e7 | + | 1.64779e8i | 0.187628 | + | 1.06409i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.54206e7 | − | 2.67093e7i | 0.0984773 | − | 0.170568i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.88357e8 | − | 1.58050e8i | −1.18957 | − | 0.998168i | −0.999867 | − | 0.0163264i | \(-0.994803\pi\) |
−0.189703 | − | 0.981841i | \(-0.560753\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.64626e7 | + | 1.15117e8i | 0.415124 | + | 0.719016i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.93374e7 | + | 5.31291e7i | 0.119456 | + | 0.328204i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.53339e7 | + | 6.23032e6i | 0.215889 | + | 0.0380670i | 0.280546 | − | 0.959841i | \(-0.409484\pi\) |
−0.0646575 | + | 0.997908i | \(0.520596\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.81030e7 | − | 1.51902e7i | 0.109404 | − | 0.0918007i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.95420e7 | − | 6.82073e7i | 0.176598 | − | 0.407733i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.31234e7 | + | 3.94749e7i | 0.195866 | + | 0.233424i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.70826e7 | + | 2.67019e8i | −0.275411 | + | 1.56193i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.51561e8 | − | 5.51638e7i | 0.877047 | − | 0.319219i | 0.136029 | − | 0.990705i | \(-0.456566\pi\) |
0.741017 | + | 0.671486i | \(0.234344\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.06061e7 | + | 1.18969e7i | −0.117967 | + | 0.0681081i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.37280e7 | + | 1.63604e7i | −0.0777533 | + | 0.0926627i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.11851e7 | − | 6.45775e6i | −0.0626782 | − | 0.0361873i | 0.468333 | − | 0.883552i | \(-0.344855\pi\) |
−0.531012 | + | 0.847365i | \(0.678188\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.28041e8 | − | 4.02097e7i | 1.26435 | − | 0.222939i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.12210e8 | − | 7.72381e7i | −1.16417 | − | 0.423723i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.45400e8i | 0.789274i | 0.918837 | + | 0.394637i | \(0.129130\pi\) | ||||
−0.918837 | + | 0.394637i | \(0.870870\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.58822e6 | 0.0192740 | 0.00963699 | − | 0.999954i | \(-0.496932\pi\) | ||||
0.00963699 | + | 0.999954i | \(0.496932\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.60849e7 | − | 1.54092e8i | 0.298114 | − | 0.819061i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.95777e7 | + | 1.67743e8i | 0.155582 | + | 0.882351i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.41871e8 | − | 2.45728e8i | 0.738528 | − | 1.27917i | −0.214629 | − | 0.976696i | \(-0.568854\pi\) |
0.953158 | − | 0.302473i | \(-0.0978123\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.04907e8 | + | 2.55847e8i | 1.57084 | + | 1.31809i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.93475e8 | + | 3.35109e8i | 0.986500 | + | 1.70867i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.45365e6 | + | 1.77313e7i | 0.0325687 | + | 0.0894817i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.79578e7 | + | 3.16645e6i | 0.0896988 | + | 0.0158163i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.02834e8 | − | 2.54108e8i | 1.49724 | − | 1.25633i | 0.612292 | − | 0.790632i | \(-0.290248\pi\) |
0.884944 | − | 0.465698i | \(-0.154197\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.47600e8 | + | 3.52134e7i | 0.722337 | + | 0.172331i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.70665e8 | − | 2.03391e8i | −0.826765 | − | 0.985300i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.67942e7 | + | 2.08670e8i | −0.176447 | + | 1.00068i | 0.760013 | + | 0.649908i | \(0.225193\pi\) |
−0.936460 | + | 0.350774i | \(0.885918\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.33412e7 | + | 1.94146e7i | −0.253228 | + | 0.0921674i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.76238e8 | − | 1.01751e8i | 0.828280 | − | 0.478207i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.23827e8 | + | 1.47571e8i | −0.576149 | + | 0.686628i | −0.972881 | − | 0.231307i | \(-0.925700\pi\) |
0.396732 | + | 0.917935i | \(0.370144\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.31929e8 | + | 7.61690e7i | 0.607737 | + | 0.350877i | 0.772079 | − | 0.635526i | \(-0.219217\pi\) |
−0.164343 | + | 0.986403i | \(0.552550\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.32514e7 | − | 2.33658e6i | 0.0604379 | − | 0.0106568i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.60723e8 | + | 5.84983e7i | 0.725791 | + | 0.264166i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 2.68257e8i | − | 1.19946i | −0.800204 | − | 0.599728i | \(-0.795275\pi\) | ||
0.800204 | − | 0.599728i | \(-0.204725\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.20236e8 | −0.532330 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.77025e7 | − | 2.68435e8i | 0.428333 | − | 1.17684i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.12482e7 | − | 1.77217e8i | −0.135657 | − | 0.769351i | −0.974400 | − | 0.224823i | \(-0.927820\pi\) |
0.838742 | − | 0.544528i | \(-0.183291\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.55503e8 | − | 2.69339e8i | 0.668519 | − | 1.15791i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.87601e7 | + | 4.09146e7i | 0.207591 | + | 0.174190i | 0.740656 | − | 0.671885i | \(-0.234515\pi\) |
−0.533064 | + | 0.846075i | \(0.678960\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.18613e8 | − | 2.05444e8i | −0.500105 | − | 0.866207i | −1.00000 | 0.000121168i | \(-0.999961\pi\) | |
0.499895 | − | 0.866086i | \(-0.333372\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.43387e8 | − | 3.93954e8i | −0.598737 | − | 1.64502i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.49266e8 | + | 4.39522e7i | 1.03086 | + | 0.181768i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.33753e8 | + | 1.96142e8i | −0.957452 | + | 0.803398i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.38963e8 | − | 6.95317e7i | 0.563764 | − | 0.282085i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.83417e7 | − | 4.56939e7i | −0.154071 | − | 0.183614i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.70815e7 | + | 4.37151e8i | −0.306805 | + | 1.73998i | 0.308081 | + | 0.951360i | \(0.400313\pi\) |
−0.614886 | + | 0.788616i | \(0.710798\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.15674e8 | + | 1.14896e8i | −1.24460 | + | 0.452996i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.64671e8 | + | 2.10543e8i | −1.42423 | + | 0.822279i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.85230e7 | − | 5.78274e7i | 0.187728 | − | 0.223726i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.37349e6 | − | 3.10239e6i | −0.0205946 | − | 0.0118903i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.11928e8 | − | 1.97359e7i | 0.424975 | − | 0.0749346i | 0.0429296 | − | 0.999078i | \(-0.486331\pi\) |
0.382045 | + | 0.924144i | \(0.375220\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.31162e8 | − | 8.41362e7i | −0.869529 | − | 0.316483i | −0.131553 | − | 0.991309i | \(-0.541996\pi\) |
−0.737976 | + | 0.674826i | \(0.764218\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.16691e7i | 0.192554i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.86637e8 | 1.79677 | 0.898385 | − | 0.439208i | \(-0.144741\pi\) | ||||
0.898385 | + | 0.439208i | \(0.144741\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.53682e7 | − | 4.22238e7i | 0.0562198 | − | 0.154463i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.26231e7 | − | 2.41728e8i | −0.154491 | − | 0.876160i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.51687e7 | + | 7.82345e7i | −0.162218 | + | 0.280969i | −0.935664 | − | 0.352893i | \(-0.885198\pi\) |
0.773446 | + | 0.633862i | \(0.218531\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.98224e8 | + | 1.66330e8i | 0.705395 | + | 0.591897i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.95704e6 | − | 6.85380e6i | −0.0139532 | − | 0.0241677i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.80641e7 | − | 1.59530e8i | −0.202886 | − | 0.557424i | 0.795966 | − | 0.605342i | \(-0.206964\pi\) |
−0.998851 | + | 0.0479180i | \(0.984741\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.84249e7 | + | 1.73550e7i | 0.340801 | + | 0.0600924i | 0.341429 | − | 0.939907i | \(-0.389089\pi\) |
−0.000628625 | 1.00000i | \(0.500200\pi\) | ||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.00444e7 | + | 3.36012e7i | −0.137404 | + | 0.115296i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.12270e8 | + | 2.46265e7i | 1.40190 | + | 0.0837408i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.55485e8 | − | 1.85300e8i | −0.523976 | − | 0.624450i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.07666e7 | + | 4.01337e8i | −0.236347 | + | 1.34039i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.95463e8 | + | 1.07540e8i | −0.977992 | + | 0.355960i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.64893e8 | + | 2.10671e8i | −1.19707 | + | 0.691130i | −0.959901 | − | 0.280338i | \(-0.909553\pi\) |
−0.237171 | + | 0.971468i | \(0.576220\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9.21267e7 | + | 1.09792e8i | −0.299553 | + | 0.356994i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.08379e8 | + | 2.93513e8i | 1.63841 | + | 0.945934i | 0.981383 | + | 0.192063i | \(0.0615178\pi\) |
0.657023 | + | 0.753871i | \(0.271816\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.17291e8 | + | 1.08845e8i | −1.97188 | + | 0.347696i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.27413e8 | − | 1.55566e8i | −1.35334 | − | 0.492575i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 3.41997e8i | − | 1.07340i | −0.843775 | − | 0.536698i | \(-0.819672\pi\) | ||
0.843775 | − | 0.536698i | \(-0.180328\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.00377e7 | 0.0312295 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.05261e7 | − | 1.11345e8i | 0.124987 | − | 0.343399i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.01995e6 | + | 4.54834e7i | 0.0245196 | + | 0.139058i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.86643e8 | − | 3.23275e8i | 0.565689 | − | 0.979802i | −0.431296 | − | 0.902210i | \(-0.641944\pi\) |
0.996985 | − | 0.0775919i | \(-0.0247231\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.47764e7 | − | 1.23989e7i | −0.0443987 | − | 0.0372549i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.13276e7 | + | 1.40863e8i | 0.242261 | + | 0.419608i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.34010e7 | + | 6.42938e7i | 0.0691093 | + | 0.189876i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.02763e8 | − | 1.81198e7i | −0.300887 | − | 0.0530546i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.64738e8 | + | 3.06052e8i | −1.05883 | + | 0.888466i | −0.993995 | − | 0.109430i | \(-0.965097\pi\) |
−0.0648379 | + | 0.997896i | \(0.520653\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.23853e8 | + | 4.15945e8i | 0.356484 | + | 1.19721i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.98738e8 | − | 4.75197e8i | −1.13794 | − | 1.35615i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.58219e6 | − | 3.16582e7i | 0.0157960 | − | 0.0895834i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.68509e7 | + | 1.34126e7i | −0.103397 | + | 0.0376336i | −0.393201 | − | 0.919453i | \(-0.628632\pi\) |
0.289803 | + | 0.957086i | \(0.406410\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.84864e6 | − | 3.95406e6i | 0.0190544 | − | 0.0110011i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.17417e8 | − | 3.78283e8i | 0.875713 | − | 1.04363i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.10114e8 | − | 1.21309e8i | −0.574826 | − | 0.331876i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.38189e8 | + | 2.43664e7i | −0.374900 | + | 0.0661049i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.06321e7 | + | 2.93477e7i | 0.216931 | + | 0.0789564i | 0.448200 | − | 0.893934i | \(-0.352065\pi\) |
−0.231269 | + | 0.972890i | \(0.574288\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.55400e8i | 1.48184i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.25994e8 | −0.597973 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.82834e7 | + | 7.77080e7i | −0.0742194 | + | 0.203916i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.32733e7 | + | 2.45415e8i | 0.112620 | + | 0.638702i | 0.987901 | + | 0.155087i | \(0.0495657\pi\) |
−0.875280 | + | 0.483616i | \(0.839323\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.75044e8 | − | 3.03184e8i | 0.451818 | − | 0.782572i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.70760e6 | − | 7.30655e6i | −0.0222919 | − | 0.0187051i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.03466e8 | + | 3.52413e8i | 0.516630 | + | 0.894830i | 0.999814 | + | 0.0193107i | \(0.00614716\pi\) |
−0.483183 | + | 0.875519i | \(0.660520\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.60658e7 | − | 1.54039e8i | −0.141200 | − | 0.387945i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.76312e8 | − | 3.10886e7i | −0.440433 | − | 0.0776602i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.67822e8 | + | 3.92550e8i | −1.15917 | + | 0.972661i | −0.999894 | − | 0.0145732i | \(-0.995361\pi\) |
−0.159278 | + | 0.987234i | \(0.550917\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.64518e8 | − | 1.08540e8i | 0.895909 | − | 0.266768i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.12282e7 | − | 1.33812e7i | −0.0273743 | − | 0.0326234i | 0.752184 | − | 0.658954i | \(-0.229001\pi\) |
−0.779558 | + | 0.626330i | \(0.784556\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.91842e7 | + | 1.08799e8i | −0.0463953 | + | 0.263121i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.58017e7 | − | 2.03102e7i | 0.133871 | − | 0.0487250i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.78257e8 | + | 3.91592e8i | −1.61417 | + | 0.931940i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.87795e7 | + | 1.05803e8i | −0.209601 | + | 0.249792i | −0.860595 | − | 0.509291i | \(-0.829908\pi\) |
0.650994 | + | 0.759083i | \(0.274352\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.31440e8 | + | 3.06827e8i | 1.24471 | + | 0.718636i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.80243e6 | + | 1.55211e6i | −0.0204532 | + | 0.00360646i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.16441e8 | − | 4.23810e7i | −0.268422 | − | 0.0976975i | 0.204303 | − | 0.978908i | \(-0.434507\pi\) |
−0.472725 | + | 0.881210i | \(0.656729\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 5.05678e8i | − | 1.15651i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.97285e8 | 1.35528 | 0.677638 | − | 0.735396i | \(-0.263004\pi\) | ||||
0.677638 | + | 0.735396i | \(0.263004\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.00679e7 | − | 1.37560e8i | 0.112716 | − | 0.309685i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.51270e6 | + | 8.57895e6i | 0.00337885 | + | 0.0191624i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.49907e7 | − | 9.52466e7i | 0.121872 | − | 0.211088i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.60060e8 | − | 2.18216e8i | −0.571866 | − | 0.479853i | 0.310398 | − | 0.950607i | \(-0.399538\pi\) |
−0.882265 | + | 0.470754i | \(0.843982\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.95171e8 | + | 3.38046e8i | 0.425846 | + | 0.737586i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.72755e8 | + | 7.49390e8i | 0.590521 | + | 1.62244i | 0.769542 | + | 0.638597i | \(0.220485\pi\) |
−0.179021 | + | 0.983845i | \(0.557293\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.66254e8 | − | 2.93151e7i | −0.357164 | − | 0.0629777i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.37780e8 | − | 4.51251e8i | 1.14641 | − | 0.961956i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.96830e7 | − | 4.96921e8i | 0.0627908 | − | 1.05118i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.30658e7 | + | 6.32414e7i | 0.111394 | + | 0.132754i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.53440e7 | − | 2.00446e8i | 0.0736259 | − | 0.417553i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.66833e8 | + | 6.07221e7i | −0.344883 | + | 0.125527i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.50568e8 | − | 8.69306e7i | 0.308894 | − | 0.178340i | −0.337538 | − | 0.941312i | \(-0.609594\pi\) |
0.646431 | + | 0.762972i | \(0.276261\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.69517e8 | + | 5.59548e8i | −0.955917 | + | 1.13922i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.19221e8 | − | 2.99772e8i | −1.04911 | − | 0.605707i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.57907e8 | + | 1.33640e8i | −1.51984 | + | 0.267988i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.42440e7 | + | 3.43020e7i | 0.187565 | + | 0.0682681i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 3.01357e8i | − | 0.595259i | −0.954681 | − | 0.297630i | \(-0.903804\pi\) | ||
0.954681 | − | 0.297630i | \(-0.0961960\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.36469e8 | 0.267543 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.32852e7 | − | 3.65008e7i | 0.0258506 | − | 0.0710240i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.82849e7 | + | 1.03699e8i | 0.0353139 | + | 0.200275i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.72019e8 | − | 1.16397e9i | 1.28823 | − | 2.23128i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.73909e8 | − | 1.45927e8i | −0.330904 | − | 0.277661i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.33002e8 | − | 5.76777e8i | −0.628929 | − | 1.08934i | −0.987767 | − | 0.155937i | \(-0.950160\pi\) |
0.358838 | − | 0.933400i | \(-0.383173\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.06082e6 | + | 2.21469e7i | 0.0151118 | + | 0.0415193i | 0.947019 | − | 0.321177i | \(-0.104078\pi\) |
−0.931907 | + | 0.362696i | \(0.881856\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.67427e8 | − | 1.70583e8i | −1.80031 | − | 0.317443i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.12987e8 | − | 7.66087e8i | 1.68652 | − | 1.41516i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.70073e7 | + | 7.39614e7i | 0.0678612 | + | 0.135625i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.03481e7 | − | 3.61674e7i | −0.0552432 | − | 0.0658363i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.71094e6 | + | 4.37309e7i | −0.0139341 | + | 0.0790240i | −0.990982 | − | 0.133996i | \(-0.957219\pi\) |
0.977048 | + | 0.213020i | \(0.0683301\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.13893e8 | − | 3.32630e8i | 1.63944 | − | 0.596708i | 0.652500 | − | 0.757789i | \(-0.273720\pi\) |
0.986941 | + | 0.161082i | \(0.0514982\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.49714e8 | + | 8.64377e7i | −0.266626 | + | 0.153936i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.37395e8 | − | 1.63741e8i | 0.242915 | − | 0.289495i | −0.630787 | − | 0.775956i | \(-0.717268\pi\) |
0.873702 | + | 0.486461i | \(0.161712\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.24510e8 | + | 5.33766e8i | 1.62274 | + | 0.936887i | 0.986184 | + | 0.165654i | \(0.0529736\pi\) |
0.636553 | + | 0.771233i | \(0.280360\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.80323e8 | − | 1.37592e8i | 1.35979 | − | 0.239767i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.38880e7 | + | 1.23342e7i | 0.0586288 | + | 0.0213391i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 4.17620e8i | − | 0.717335i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.15516e8 | 0.708616 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.34263e8 | + | 6.43632e8i | −0.396659 | + | 1.08981i | 0.567242 | + | 0.823551i | \(0.308010\pi\) |
−0.963901 | + | 0.266261i | \(0.914212\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.28972e7 | + | 4.70133e8i | 0.139364 | + | 0.790374i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.20517e8 | + | 3.81946e8i | −0.368094 | + | 0.637558i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.08962e8 | + | 9.14300e7i | 0.180595 | + | 0.151537i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.21423e8 | − | 3.83516e8i | −0.364395 | − | 0.631150i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.94162e8 | + | 5.33456e8i | 0.317279 | + | 0.871716i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.39088e9 | + | 2.45250e8i | 2.25685 | + | 0.397943i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.49397e8 | − | 2.09269e8i | 0.401831 | − | 0.337176i | −0.419370 | − | 0.907816i | \(-0.637749\pi\) |
0.821201 | + | 0.570639i | \(0.193304\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.47083e7 | − | 6.16510e7i | 0.0235323 | − | 0.0986375i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.08265e7 | + | 9.63252e7i | 0.128414 | + | 0.153037i | 0.826420 | − | 0.563054i | \(-0.190374\pi\) |
−0.698006 | + | 0.716092i | \(0.745929\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.62744e8 | + | 9.22968e8i | −0.256759 | + | 1.45615i | 0.534757 | + | 0.845006i | \(0.320403\pi\) |
−0.791517 | + | 0.611148i | \(0.790708\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.56686e8 | + | 2.75411e8i | −1.18551 | + | 0.431491i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.69158e8 | + | 4.44074e8i | −1.19669 | + | 0.690912i | −0.959817 | − | 0.280627i | \(-0.909457\pi\) |
−0.236878 | + | 0.971539i | \(0.576124\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.51070e8 | − | 8.95090e8i | 1.16046 | − | 1.38299i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.65762e8 | + | 3.26643e8i | 0.868114 | + | 0.501206i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.03621e8 | + | 1.82711e7i | −0.157902 | + | 0.0278423i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.11779e8 | − | 1.49875e8i | −0.623175 | − | 0.226817i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.61932e7i | 0.144578i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.81352e8 | 0.718520 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.70849e8 | − | 1.01890e9i | 0.549792 | − | 1.51054i | −0.284200 | − | 0.958765i | \(-0.591728\pi\) |
0.833992 | − | 0.551777i | \(-0.186050\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.12488e8 | + | 1.20508e9i | 0.312873 | + | 1.77439i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.14430e8 | + | 8.91019e8i | −0.752313 | + | 1.30304i | 0.194386 | + | 0.980925i | \(0.437729\pi\) |
−0.946699 | + | 0.322120i | \(0.895605\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.04914e8 | + | 2.55853e8i | 0.442889 | + | 0.371628i | 0.836789 | − | 0.547525i | \(-0.184430\pi\) |
−0.393900 | + | 0.919153i | \(0.628874\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.19414e8 | − | 2.06831e8i | −0.172276 | − | 0.298391i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.87811e6 | + | 2.43924e7i | 0.0127218 | + | 0.0349529i | 0.945891 | − | 0.324485i | \(-0.105191\pi\) |
−0.933169 | + | 0.359437i | \(0.882969\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.07370e9 | + | 1.89322e8i | 1.52819 | + | 0.269461i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.53233e8 | − | 2.96398e8i | 0.499377 | − | 0.419027i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.11126e8 | − | 3.94627e8i | −1.27945 | − | 0.554157i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.83689e8 | − | 6.95614e8i | −0.814165 | − | 0.970284i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.14928e8 | − | 1.21892e9i | 0.297793 | − | 1.68887i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.25286e8 | − | 8.19976e7i | 0.310067 | − | 0.112855i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.91079e7 | + | 1.10319e7i | −0.0261239 | + | 0.0150826i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.59921e7 | − | 1.02481e8i | 0.116787 | − | 0.139182i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.24745e8 | − | 3.60697e8i | −0.842863 | − | 0.486627i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.54701e8 | + | 1.68340e8i | −1.27952 | + | 0.225613i | −0.771775 | − | 0.635896i | \(-0.780631\pi\) |
−0.507742 | + | 0.861509i | \(0.669519\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.63582e6 | − | 1.68730e6i | −0.00617213 | − | 0.00224647i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 4.88876e8i | − | 0.646612i | −0.946294 | − | 0.323306i | \(-0.895206\pi\) | ||
0.946294 | − | 0.323306i | \(-0.104794\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.90102e8 | −1.03818 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.71587e8 | + | 1.57042e9i | −0.746138 | + | 2.05000i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.16341e8 | − | 6.59803e8i | −0.150878 | − | 0.855670i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.98571e8 | + | 8.63551e8i | −0.642363 | + | 1.11261i | 0.342541 | + | 0.939503i | \(0.388713\pi\) |
−0.984904 | + | 0.173103i | \(0.944621\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.36272e8 | − | 2.82166e8i | −0.430439 | − | 0.361181i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.01033e8 | + | 1.74995e8i | 0.128487 | + | 0.222546i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.65139e8 | − | 4.53715e8i | −0.208653 | − | 0.573269i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.39390e7 | + | 1.48007e7i | 0.105372 | + | 0.0185799i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.62920e8 | + | 1.36706e8i | −0.203201 | + | 0.170506i | −0.738710 | − | 0.674024i | \(-0.764564\pi\) |
0.535508 | + | 0.844530i | \(0.320120\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.90584e8 | − | 1.80342e8i | −0.236177 | − | 0.223485i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.77931e6 | + | 8.07927e6i | 0.00834719 | + | 0.00994780i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.01268e7 | − | 1.14145e8i | 0.0246229 | − | 0.139644i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.42179e8 | − | 2.33734e8i | 0.780616 | − | 0.284121i | 0.0791862 | − | 0.996860i | \(-0.474768\pi\) |
0.701429 | + | 0.712739i | \(0.252546\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.55307e6 | + | 4.93812e6i | −0.0103306 | + | 0.00596437i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.00500e8 | + | 3.58122e8i | −0.360641 | + | 0.429796i | −0.915605 | − | 0.402079i | \(-0.868288\pi\) |
0.554964 | + | 0.831875i | \(0.312732\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.40297e9 | − | 8.10005e8i | −1.67307 | − | 0.965946i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.11375e9 | − | 1.96384e8i | 1.31975 | − | 0.232708i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.30602e6 | − | 1.56726e6i | −0.00507022 | − | 0.00184541i | 0.339484 | − | 0.940612i | \(-0.389748\pi\) |
−0.344554 | + | 0.938766i | \(0.611970\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.57733e8i | 0.301558i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.75538e8 | −0.552896 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.12984e8 | + | 3.10421e8i | −0.130538 | + | 0.358651i | −0.987692 | − | 0.156409i | \(-0.950008\pi\) |
0.857154 | + | 0.515060i | \(0.172230\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.54536e8 | + | 8.76416e8i | 0.177427 | + | 1.00624i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.22753e8 | − | 2.12614e8i | 0.140054 | − | 0.242580i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.99091e7 | − | 1.67057e7i | −0.0225733 | − | 0.0189412i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.99037e8 | − | 3.44741e8i | −0.224266 | − | 0.388439i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.11075e7 | + | 1.12942e8i | 0.0460302 | + | 0.126467i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.12730e9 | − | 3.75101e8i | −2.36727 | − | 0.417413i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.84061e8 | − | 3.22265e8i | 0.424737 | − | 0.356397i | −0.405224 | − | 0.914217i | \(-0.632807\pi\) |
0.829962 | + | 0.557820i | \(0.188362\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.08285e8 | + | 1.45904e8i | 0.119013 | + | 0.160360i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.49281e8 | − | 1.77906e8i | −0.163059 | − | 0.194327i | 0.678328 | − | 0.734759i | \(-0.262705\pi\) |
−0.841387 | + | 0.540433i | \(0.818260\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.31305e7 | − | 4.14744e8i | 0.0793890 | − | 0.450237i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.97618e8 | + | 1.44721e8i | −0.428995 | + | 0.156142i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.80735e8 | + | 1.04347e8i | −0.193802 | + | 0.111892i | −0.593761 | − | 0.804641i | \(-0.702358\pi\) |
0.399959 | + | 0.916533i | \(0.369024\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.32205e8 | + | 3.95906e8i | −0.354044 | + | 0.421934i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.94556e7 | − | 1.12327e7i | −0.0206081 | − | 0.0118981i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.06226e9 | + | 1.87305e8i | −1.11833 | + | 0.197192i | −0.702108 | − | 0.712070i | \(-0.747758\pi\) |
−0.416223 | + | 0.909262i | \(0.636647\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.35403e9 | + | 4.92825e8i | 1.41683 | + | 0.515685i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.60613e9i | 1.67043i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.69141e8 | 0.278221 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.26899e8 | − | 6.23400e8i | 0.233137 | − | 0.640539i | −0.766862 | − | 0.641812i | \(-0.778183\pi\) |
0.999999 | + | 0.00127277i | \(0.000405134\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.38580e7 | − | 5.32295e8i | −0.0958570 | − | 0.543632i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.52210e8 | + | 9.56455e8i | −0.560576 | + | 0.970946i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.78322e8 | + | 2.33540e8i | 0.280842 | + | 0.235655i | 0.772317 | − | 0.635237i | \(-0.219098\pi\) |
−0.491475 | + | 0.870892i | \(0.663542\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.94201e8 | + | 1.02919e9i | 0.595987 | + | 1.03228i |
(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 | 76.7.j.a.13.8 | ✓ | 60 | |
19.3 | odd | 18 | inner | 76.7.j.a.41.8 | yes | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.7.j.a.13.8 | ✓ | 60 | 1.1 | even | 1 | trivial | |
76.7.j.a.41.8 | yes | 60 | 19.3 | odd | 18 | inner |