Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,8,Mod(45,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.45");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.e (of order \(3\), degree \(2\), 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: | \(23.7412619368\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 45.5 | ||
Character | \(\chi\) | \(=\) | 76.45 |
Dual form | 76.8.e.a.49.5 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −3.42876 | − | 5.93879i | −0.0733184 | − | 0.126991i | 0.827035 | − | 0.562150i | \(-0.190026\pi\) |
−0.900354 | + | 0.435159i | \(0.856692\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −200.054 | − | 346.504i | −0.715735 | − | 1.23969i | −0.962675 | − | 0.270659i | \(-0.912758\pi\) |
0.246940 | − | 0.969031i | \(-0.420575\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1032.75 | −1.13802 | −0.569010 | − | 0.822331i | \(-0.692673\pi\) | ||||
−0.569010 | + | 0.822331i | \(0.692673\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1069.99 | − | 1853.27i | 0.489249 | − | 0.847404i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 309.913 | 0.0702047 | 0.0351023 | − | 0.999384i | \(-0.488824\pi\) | ||||
0.0351023 | + | 0.999384i | \(0.488824\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4892.02 | + | 8473.22i | −0.617570 | + | 1.06966i | 0.372358 | + | 0.928089i | \(0.378549\pi\) |
−0.989928 | + | 0.141573i | \(0.954784\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1371.88 | + | 2376.16i | −0.104953 | + | 0.181784i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 9807.53 | + | 16987.1i | 0.484159 | + | 0.838589i | 0.999834 | − | 0.0181957i | \(-0.00579218\pi\) |
−0.515675 | + | 0.856784i | \(0.672459\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 19379.0 | − | 22766.8i | 0.648177 | − | 0.761490i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3541.04 | + | 6133.25i | 0.0834378 | + | 0.144518i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2635.65 | + | 4565.08i | −0.0451690 | + | 0.0782351i | −0.887726 | − | 0.460372i | \(-0.847716\pi\) |
0.842557 | + | 0.538607i | \(0.181049\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −40980.8 | + | 70980.9i | −0.524554 | + | 0.908555i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −29672.3 | −0.290120 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −94034.0 | + | 162872.i | −0.715965 | + | 1.24009i | 0.246621 | + | 0.969112i | \(0.420680\pi\) |
−0.962586 | + | 0.270976i | \(0.912654\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −59256.8 | −0.357250 | −0.178625 | − | 0.983917i | \(-0.557165\pi\) | ||||
−0.178625 | + | 0.983917i | \(0.557165\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1062.62 | − | 1840.51i | −0.00514729 | − | 0.00891537i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 206605. | + | 357850.i | 0.814521 | + | 1.41079i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 61832.4 | 0.200683 | 0.100341 | − | 0.994953i | \(-0.468006\pi\) | ||||
0.100341 | + | 0.994953i | \(0.468006\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 67094.2 | 0.181117 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 188128. | + | 325847.i | 0.426295 | + | 0.738364i | 0.996540 | − | 0.0831103i | \(-0.0264854\pi\) |
−0.570246 | + | 0.821474i | \(0.693152\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 276316. | + | 478594.i | 0.529989 | + | 0.917968i | 0.999388 | + | 0.0349820i | \(0.0111374\pi\) |
−0.469399 | + | 0.882986i | \(0.655529\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −856221. | −1.40069 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −390472. | + | 676317.i | −0.548589 | + | 0.950184i | 0.449782 | + | 0.893138i | \(0.351502\pi\) |
−0.998372 | + | 0.0570461i | \(0.981832\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 243019. | 0.295090 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 67255.3 | − | 116490.i | 0.0709955 | − | 0.122968i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −505468. | + | 875497.i | −0.466368 | + | 0.807773i | −0.999262 | − | 0.0384091i | \(-0.987771\pi\) |
0.532894 | + | 0.846182i | \(0.321104\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −61999.5 | − | 107386.i | −0.0502480 | − | 0.0870321i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −201653. | − | 37025.9i | −0.144226 | − | 0.0264816i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −884350. | − | 1.53174e6i | −0.560586 | − | 0.970963i | −0.997445 | − | 0.0714335i | \(-0.977243\pi\) |
0.436859 | − | 0.899530i | \(-0.356091\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 795991. | − | 1.37870e6i | 0.449008 | − | 0.777704i | −0.549314 | − | 0.835616i | \(-0.685111\pi\) |
0.998322 | + | 0.0579120i | \(0.0184443\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.10502e6 | + | 1.91396e6i | −0.556775 | + | 0.964363i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.91467e6 | 1.76807 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 557626. | − | 965836.i | 0.226507 | − | 0.392321i | −0.730264 | − | 0.683165i | \(-0.760603\pi\) |
0.956770 | + | 0.290844i | \(0.0939362\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 36148.1 | 0.0132469 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.33615e6 | − | 2.31428e6i | −0.443048 | − | 0.767381i | 0.554866 | − | 0.831940i | \(-0.312769\pi\) |
−0.997914 | + | 0.0645583i | \(0.979436\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.07183e6 | + | 3.58851e6i | 0.623338 | + | 1.07965i | 0.988860 | + | 0.148850i | \(0.0475573\pi\) |
−0.365522 | + | 0.930803i | \(0.619109\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 562054. | 0.153838 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −320062. | −0.0798943 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.55161e6 | − | 2.68747e6i | −0.354070 | − | 0.613267i | 0.632889 | − | 0.774243i | \(-0.281869\pi\) |
−0.986958 | + | 0.160976i | \(0.948536\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.23832e6 | − | 3.87689e6i | −0.467978 | − | 0.810561i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.31855e6 | −1.02099 | −0.510493 | − | 0.859882i | \(-0.670537\pi\) | ||||
−0.510493 | + | 0.859882i | \(0.670537\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.92407e6 | − | 6.79669e6i | 0.693060 | − | 1.20042i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.28968e6 | 0.209974 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.01342e6 | − | 6.95144e6i | 0.603461 | − | 1.04522i | −0.388832 | − | 0.921309i | \(-0.627121\pi\) |
0.992293 | − | 0.123916i | \(-0.0395454\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.05221e6 | − | 8.75068e6i | 0.702807 | − | 1.21730i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 203177. | + | 351914.i | 0.0261930 | + | 0.0453676i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.17656e7 | − | 2.16031e6i | −1.40793 | − | 0.258513i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.68244e6 | − | 6.37817e6i | −0.409670 | − | 0.709570i | 0.585182 | − | 0.810902i | \(-0.301023\pi\) |
−0.994853 | + | 0.101332i | \(0.967690\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 331603. | − | 574354.i | 0.0343476 | − | 0.0594917i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.41116e6 | + | 1.63006e7i | −0.908905 | + | 1.57427i | −0.0933167 | + | 0.995636i | \(0.529747\pi\) |
−0.815588 | + | 0.578633i | \(0.803586\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.64481e6 | 0.779517 | 0.389758 | − | 0.920917i | \(-0.372559\pi\) | ||||
0.389758 | + | 0.920917i | \(0.372559\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.41680e6 | − | 2.45397e6i | 0.119439 | − | 0.206874i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.53786e7 | 1.21359 | 0.606797 | − | 0.794857i | \(-0.292454\pi\) | ||||
0.606797 | + | 0.794857i | \(0.292454\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.06313e7 | + | 1.84140e7i | 0.786310 | + | 1.36193i | 0.928213 | + | 0.372049i | \(0.121345\pi\) |
−0.141903 | + | 0.989881i | \(0.545322\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −212009. | − | 367210.i | −0.0147137 | − | 0.0254849i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.30223e6 | −0.150098 | −0.0750490 | − | 0.997180i | \(-0.523911\pi\) | ||||
−0.0750490 | + | 0.997180i | \(0.523911\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.10909e6 | 0.129316 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.04688e7 | + | 1.81325e7i | 0.604291 | + | 1.04666i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.01287e7 | − | 1.75434e7i | −0.550983 | − | 0.954331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.93911e7 | −0.995071 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.29009e6 | − | 2.23450e6i | 0.0625104 | − | 0.108271i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.53507e6 | 0.0702980 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.09606e7 | + | 1.89843e7i | −0.474810 | + | 0.822395i | −0.999584 | − | 0.0288466i | \(-0.990817\pi\) |
0.524774 | + | 0.851242i | \(0.324150\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.89485e6 | − | 3.28197e6i | 0.0777159 | − | 0.134608i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.33047e7 | − | 2.30444e7i | −0.517077 | − | 0.895604i | −0.999803 | − | 0.0198325i | \(-0.993687\pi\) |
0.482726 | − | 0.875771i | \(-0.339647\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.00136e7 | + | 2.35123e7i | −0.737639 | + | 0.866591i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.93607e6 | + | 1.02816e7i | 0.207649 | + | 0.359659i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −698694. | + | 1.21017e6i | −0.0232148 | + | 0.0402092i | −0.877399 | − | 0.479761i | \(-0.840723\pi\) |
0.854185 | + | 0.519970i | \(0.174057\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.62493e7 | + | 4.54652e7i | −0.829022 | + | 1.43591i | 0.0697835 | + | 0.997562i | \(0.477769\pi\) |
−0.898806 | + | 0.438347i | \(0.855564\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.35534e6 | 0.160887 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.51610e6 | + | 2.62597e6i | −0.0433563 | + | 0.0750953i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.52476e7 | 2.04977 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −833255. | − | 1.44324e6i | −0.0216355 | − | 0.0374738i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.17294e7 | + | 5.49570e7i | 0.785797 | + | 1.36104i | 0.928522 | + | 0.371278i | \(0.121080\pi\) |
−0.142725 | + | 0.989762i | \(0.545586\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.06708e7 | −1.90676 | −0.953382 | − | 0.301765i | \(-0.902424\pi\) | ||||
−0.953382 | + | 0.301765i | \(0.902424\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.19757e7 | 0.947498 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.18546e7 | + | 2.05327e7i | 0.255697 | + | 0.442879i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.81104e7 | + | 3.13681e7i | 0.373490 | + | 0.646904i | 0.990100 | − | 0.140365i | \(-0.0448276\pi\) |
−0.616609 | + | 0.787269i | \(0.711494\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.93252e6 | 0.136773 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.72196e6 | − | 4.71457e6i | 0.0514033 | − | 0.0890331i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.29480e7 | −1.68106 | −0.840530 | − | 0.541764i | \(-0.817756\pi\) | ||||
−0.840530 | + | 0.541764i | \(0.817756\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −425163. | + | 736404.i | −0.00736820 | + | 0.0127621i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.19347e7 | − | 5.53124e7i | 0.530584 | − | 0.918999i | −0.468779 | − | 0.883316i | \(-0.655306\pi\) |
0.999363 | − | 0.0356836i | \(-0.0113608\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.64894e7 | − | 2.85605e7i | −0.262786 | − | 0.455158i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.14578e7 | − | 6.02747e7i | −0.328169 | − | 0.921826i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.20485e7 | + | 3.81890e7i | 0.323755 | + | 0.560761i | 0.981260 | − | 0.192690i | \(-0.0617212\pi\) |
−0.657504 | + | 0.753451i | \(0.728388\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.23227e7 | − | 7.33051e7i | 0.596954 | − | 1.03395i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.06445e6 | + | 1.05039e7i | −0.0822025 | + | 0.142379i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.53869e7 | −1.11277 | −0.556386 | − | 0.830924i | \(-0.687812\pi\) | ||||
−0.556386 | + | 0.830924i | \(0.687812\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.01761e7 | − | 8.69076e7i | 0.628959 | − | 1.08939i | −0.358802 | − | 0.933414i | \(-0.616815\pi\) |
0.987761 | − | 0.155975i | \(-0.0498519\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.09170e7 | −0.131682 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.23698e7 | − | 2.14252e7i | −0.143636 | − | 0.248785i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.03948e6 | + | 5.26454e6i | 0.0339903 | + | 0.0588728i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.06439e7 | 0.330163 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.76457e7 | 0.494774 | 0.247387 | − | 0.968917i | \(-0.420428\pi\) | ||||
0.247387 | + | 0.968917i | \(0.420428\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.96096e7 | + | 3.39648e7i | 0.196344 | + | 0.340078i | 0.947340 | − | 0.320229i | \(-0.103760\pi\) |
−0.750996 | + | 0.660306i | \(0.770426\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.34225e7 | − | 2.32484e7i | −0.129632 | − | 0.224529i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.97786e7 | −0.836644 | −0.418322 | − | 0.908299i | \(-0.637382\pi\) | ||||
−0.418322 | + | 0.908299i | \(0.637382\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.75156e7 | + | 4.76585e7i | −0.247511 | + | 0.428701i | −0.962835 | − | 0.270092i | \(-0.912946\pi\) |
0.715324 | + | 0.698793i | \(0.246279\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.64786e6 | −0.0664284 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.71132e7 | − | 1.68205e8i | 0.814783 | − | 1.41125i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.52715e7 | − | 1.30374e8i | 0.610228 | − | 1.05695i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.64023e6 | + | 9.76916e6i | 0.0441978 | + | 0.0765528i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.00581e6 | − | 7.05573e6i | 0.0455051 | − | 0.0534601i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.72518e7 | + | 1.16484e8i | 0.492850 | + | 0.853642i | 0.999966 | − | 0.00823595i | \(-0.00262161\pi\) |
−0.507116 | + | 0.861878i | \(0.669288\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.16267e6 | + | 1.58702e7i | −0.0649671 | + | 0.112526i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.10556e8 | − | 1.91489e8i | 0.758664 | − | 1.31405i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.11972e7 | 0.406558 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.42076e7 | − | 2.46083e7i | 0.0914043 | − | 0.158317i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.91914e8 | −1.19601 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.00298e8 | − | 1.73722e8i | −0.605657 | − | 1.04903i | −0.991947 | − | 0.126651i | \(-0.959577\pi\) |
0.386291 | − | 0.922377i | \(-0.373756\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.76979e7 | + | 1.51897e8i | 0.513275 | + | 0.889019i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.02654e8 | −1.71734 | −0.858670 | − | 0.512528i | \(-0.828709\pi\) | ||||
−0.858670 | + | 0.512528i | \(0.828709\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.02274e7 | −0.111306 | −0.0556528 | − | 0.998450i | \(-0.517724\pi\) | ||||
−0.0556528 | + | 0.998450i | \(0.517724\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.09741e6 | + | 1.90078e6i | 0.00585772 | + | 0.0101459i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.72219e7 | − | 4.71496e7i | −0.140985 | − | 0.244193i | 0.786883 | − | 0.617102i | \(-0.211694\pi\) |
−0.927868 | + | 0.372910i | \(0.878360\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.12462e8 | 1.57058 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.06402e7 | + | 1.84294e7i | −0.0519196 | + | 0.0899274i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.18021e7 | −0.434970 | −0.217485 | − | 0.976064i | \(-0.569785\pi\) | ||||
−0.217485 | + | 0.976064i | \(0.569785\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.72321e7 | + | 8.18084e7i | −0.217359 | + | 0.376477i | −0.954000 | − | 0.299808i | \(-0.903078\pi\) |
0.736641 | + | 0.676284i | \(0.236411\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.77960e7 | + | 8.27852e7i | −0.213683 | + | 0.370110i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.86170e7 | − | 8.42071e7i | −0.211206 | − | 0.365820i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.81056e7 | + | 2.75578e8i | 0.414242 | + | 1.16360i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.82360e7 | + | 3.15857e7i | 0.0748570 | + | 0.129656i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.06661e8 | + | 1.84742e8i | −0.425743 | + | 0.737409i | −0.996490 | − | 0.0837176i | \(-0.973321\pi\) |
0.570746 | + | 0.821126i | \(0.306654\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −816824. | + | 1.41478e6i | −0.00317108 | + | 0.00549247i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.38188e7 | −0.203256 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.94297e7 | + | 1.72217e8i | −0.365385 | + | 0.632865i | −0.988838 | − | 0.148996i | \(-0.952396\pi\) |
0.623453 | + | 0.781861i | \(0.285729\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.38571e7 | −0.228381 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.01230e8 | + | 3.48541e8i | 0.700570 | + | 1.21342i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.15071e7 | − | 3.72514e7i | −0.0729016 | − | 0.126269i | 0.827270 | − | 0.561804i | \(-0.189893\pi\) |
−0.900172 | + | 0.435535i | \(0.856559\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.04484e8 | 1.33518 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.50442e7 | −0.176979 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.78542e8 | − | 3.09244e8i | −0.559253 | − | 0.968654i | −0.997559 | − | 0.0698285i | \(-0.977755\pi\) |
0.438306 | − | 0.898826i | \(-0.355579\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.93309e8 | + | 3.34821e8i | 0.590010 | + | 1.02193i | 0.994230 | + | 0.107265i | \(0.0342095\pi\) |
−0.404221 | + | 0.914662i | \(0.632457\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.92912e7 | −0.206115 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.27005e7 | + | 2.19979e7i | −0.0368262 | + | 0.0637848i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.54226e8 | 1.28408 | 0.642042 | − | 0.766670i | \(-0.278088\pi\) | ||||
0.642042 | + | 0.766670i | \(0.278088\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.34040e7 | + | 1.09819e8i | −0.174784 | + | 0.302735i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.53164e8 | + | 2.65289e8i | −0.411800 | + | 0.713258i | −0.995087 | − | 0.0990084i | \(-0.968433\pi\) |
0.583287 | + | 0.812266i | \(0.301766\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.15788e8 | + | 3.73756e8i | 0.565946 | + | 0.980247i | 0.996961 | + | 0.0779020i | \(0.0248221\pi\) |
−0.431015 | + | 0.902345i | \(0.641845\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.75119e7 | + | 7.72808e7i | 0.0703985 | + | 0.197749i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.94288e8 | − | 3.36517e8i | −0.485132 | − | 0.840273i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.27942e7 | − | 2.21601e7i | 0.0311795 | − | 0.0540045i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.52524e7 | + | 4.37385e7i | −0.0600727 | + | 0.104049i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.86914e8 | −1.36313 | −0.681565 | − | 0.731757i | \(-0.738700\pi\) | ||||
−0.681565 | + | 0.731757i | \(0.738700\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.53836e8 | + | 6.12862e8i | −0.802462 | + | 1.38991i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.19585e6 | −0.0203678 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.57873e7 | − | 4.46649e7i | −0.0557901 | − | 0.0966313i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.85364e8 | − | 4.94266e8i | −0.603139 | − | 1.04467i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.29074e8 | 0.266558 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.36965e8 | −1.28548 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.69068e8 | − | 4.66039e8i | −0.530735 | − | 0.919260i | −0.999357 | − | 0.0358608i | \(-0.988583\pi\) |
0.468622 | − | 0.883399i | \(-0.344751\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.96410e7 | − | 5.13397e7i | −0.0571529 | − | 0.0989917i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.78266e8 | 0.901589 | 0.450794 | − | 0.892628i | \(-0.351141\pi\) | ||||
0.450794 | + | 0.892628i | \(0.351141\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.75443e7 | − | 8.23492e7i | 0.0876382 | − | 0.151794i | −0.818874 | − | 0.573973i | \(-0.805401\pi\) |
0.906512 | + | 0.422179i | \(0.138735\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.84258e8 | 1.59401 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.70472e7 | − | 6.41676e7i | 0.0653202 | − | 0.113138i | −0.831516 | − | 0.555501i | \(-0.812526\pi\) |
0.896836 | + | 0.442363i | \(0.145860\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.91424e7 | + | 5.04761e7i | −0.0502641 | + | 0.0870600i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.27295e7 | − | 9.13302e7i | −0.0889787 | − | 0.154116i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.76802e8 | + | 1.05908e8i | 0.952397 | + | 0.174871i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.00958e8 | − | 6.94479e8i | −0.647898 | − | 1.12219i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.29044e7 | − | 1.26274e8i | 0.115302 | − | 0.199709i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.03258e8 | − | 6.98463e8i | 0.624305 | − | 1.08133i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.16278e8 | 1.23720 | 0.618601 | − | 0.785706i | \(-0.287700\pi\) | ||||
0.618601 | + | 0.785706i | \(0.287700\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.61599e7 | − | 1.14592e8i | 0.0981839 | − | 0.170059i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.46221e8 | −0.648475 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.17261e8 | + | 7.22717e8i | 0.593886 | + | 1.02864i | 0.993703 | + | 0.112045i | \(0.0357402\pi\) |
−0.399818 | + | 0.916595i | \(0.630927\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.89381e6 | + | 1.36725e7i | 0.0110049 | + | 0.0190611i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.83645e7 | −0.0250806 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.99533e8 | 0.802202 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.23158e6 | − | 1.25255e7i | −0.00948126 | − | 0.0164220i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.55250e8 | − | 7.88517e8i | −0.584921 | − | 1.01311i | −0.994885 | − | 0.101011i | \(-0.967792\pi\) |
0.409965 | − | 0.912101i | \(-0.365541\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.50247e9 | −1.89199 | −0.945993 | − | 0.324187i | \(-0.894909\pi\) | ||||
−0.945993 | + | 0.324187i | \(0.894909\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.45158e8 | − | 2.51420e8i | 0.179170 | − | 0.310331i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.97618e7 | −0.0723123 | −0.0361561 | − | 0.999346i | \(-0.511511\pi\) | ||||
−0.0361561 | + | 0.999346i | \(0.511511\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.34604e8 | + | 9.25962e8i | −0.634210 | + | 1.09848i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.94576e7 | + | 1.20304e8i | −0.0807944 | + | 0.139940i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.57575e8 | + | 4.46133e8i | 0.293814 | + | 0.508902i | 0.974708 | − | 0.223480i | \(-0.0717419\pi\) |
−0.680894 | + | 0.732382i | \(0.738409\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.42781e8 | − | 8.82395e8i | −0.159733 | − | 0.987160i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.64875e7 | + | 1.15160e8i | 0.0729570 | + | 0.126365i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.28955e8 | − | 1.43579e9i | 0.892290 | − | 1.54549i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.77565e7 | − | 1.34678e8i | 0.0821118 | − | 0.142222i | −0.822045 | − | 0.569422i | \(-0.807167\pi\) |
0.904157 | + | 0.427201i | \(0.140500\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.05178e8 | 0.834256 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.22020e8 | − | 9.04165e8i | 0.530736 | − | 0.919262i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.06099e9 | −1.05860 | −0.529298 | − | 0.848436i | \(-0.677545\pi\) | ||||
−0.529298 | + | 0.848436i | \(0.677545\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.26339e6 | − | 9.11645e6i | −0.00515414 | − | 0.00892722i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.20032e8 | − | 1.59354e9i | −0.884318 | − | 1.53168i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.33602e8 | 0.126060 | 0.0630298 | − | 0.998012i | \(-0.479924\pi\) | ||||
0.0630298 | + | 0.998012i | \(0.479924\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.50325e8 | 0.139249 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.70073e8 | − | 1.50701e9i | −0.791334 | − | 1.37063i | −0.925141 | − | 0.379624i | \(-0.876053\pi\) |
0.133806 | − | 0.991007i | \(-0.457280\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.40296e7 | + | 1.10903e8i | 0.0571832 | + | 0.0990442i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.18262e9 | 1.03719 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.04123e8 | + | 1.21958e9i | −0.606492 | + | 1.05047i | 0.385322 | + | 0.922782i | \(0.374090\pi\) |
−0.991814 | + | 0.127693i | \(0.959243\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.03397e8 | −0.0874760 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.12372e7 | + | 1.58028e8i | −0.0758225 | + | 0.131328i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.20813e8 | + | 1.07528e9i | −0.506840 | + | 0.877873i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.05321e9 | + | 1.82422e9i | 0.844791 | + | 1.46322i | 0.885802 | + | 0.464063i | \(0.153609\pi\) |
−0.0410111 | + | 0.999159i | \(0.513058\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.08256e8 | + | 3.82383e7i | 0.164132 | + | 0.0301365i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.95631e8 | − | 3.38844e8i | −0.151507 | − | 0.262418i | 0.780275 | − | 0.625437i | \(-0.215079\pi\) |
−0.931782 | + | 0.363019i | \(0.881746\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.89885e8 | − | 5.02096e8i | 0.220627 | − | 0.382137i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.95571e8 | + | 1.55118e9i | −0.669896 | + | 1.16029i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.91627e7 | 0.0140889 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.98307e8 | − | 1.20950e9i | 0.504678 | − | 0.874128i | −0.495307 | − | 0.868718i | \(-0.664944\pi\) |
0.999985 | − | 0.00541045i | \(-0.00172221\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.58262e6 | 0.00680829 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.13308e8 | + | 1.58190e9i | 0.637958 | + | 1.10498i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.06400e9 | + | 1.84290e9i | 0.730755 | + | 1.26571i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.60011e8 | 0.243130 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.68975e9 | −1.12221 | −0.561103 | − | 0.827746i | \(-0.689623\pi\) | ||||
−0.561103 | + | 0.827746i | \(0.689623\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.77764e8 | + | 1.00072e9i | 0.377366 | + | 0.653618i | 0.990678 | − | 0.136223i | \(-0.0434964\pi\) |
−0.613312 | + | 0.789841i | \(0.710163\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.35600e8 | + | 1.44730e9i | 0.536793 | + | 0.929753i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.60768e9 | −1.01587 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.22056e8 | + | 1.42384e9i | −0.510980 | + | 0.885043i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.07934e7 | 0.0127153 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.49150e7 | + | 7.77950e7i | −0.0270222 | + | 0.0468038i | −0.879220 | − | 0.476416i | \(-0.841936\pi\) |
0.852198 | + | 0.523219i | \(0.175269\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.37930e9 | − | 2.38903e9i | 0.816493 | − | 1.41421i | −0.0917580 | − | 0.995781i | \(-0.529249\pi\) |
0.908251 | − | 0.418426i | \(-0.137418\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.58006e8 | − | 4.46879e8i | −0.150286 | − | 0.260302i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.28560e7 | + | 1.48472e8i | 0.0302977 | + | 0.0851059i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.01886e9 | + | 1.76472e9i | 0.574762 | + | 0.995517i | 0.996067 | + | 0.0885983i | \(0.0282388\pi\) |
−0.421305 | + | 0.906919i | \(0.638428\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.60027e8 | − | 4.50381e8i | 0.144372 | − | 0.250060i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.65429e8 | + | 9.79352e8i | −0.309005 | + | 0.535212i | −0.978145 | − | 0.207924i | \(-0.933329\pi\) |
0.669140 | + | 0.743136i | \(0.266663\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.21160e9 | −1.72767 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.17585e8 | − | 3.76869e8i | 0.115227 | − | 0.199579i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.23894e8 | 0.168865 | 0.0844326 | − | 0.996429i | \(-0.473092\pi\) | ||||
0.0844326 | + | 0.996429i | \(0.473092\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.83034e7 | + | 1.00984e8i | 0.0299279 | + | 0.0518366i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.76601e8 | + | 4.79087e8i | 0.139801 | + | 0.242142i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.04286e9 | −2.01210 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.60252e9 | 1.76563 | 0.882815 | − | 0.469721i | \(-0.155646\pi\) | ||||
0.882815 | + | 0.469721i | \(0.155646\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.91012e8 | − | 5.04048e8i | −0.140465 | − | 0.243292i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.12127e9 | − | 1.94210e9i | −0.533038 | − | 0.923248i | −0.999256 | − | 0.0385785i | \(-0.987717\pi\) |
0.466218 | − | 0.884670i | \(-0.345616\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.97166e8 | 0.326440 | 0.163220 | − | 0.986590i | \(-0.447812\pi\) | ||||
0.163220 | + | 0.986590i | \(0.447812\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.12930e7 | − | 1.40804e8i | 0.0374945 | − | 0.0649424i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.42577e9 | −0.647798 | −0.323899 | − | 0.946092i | \(-0.604994\pi\) | ||||
−0.323899 | + | 0.946092i | \(0.604994\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.75885e8 | + | 9.97462e8i | −0.257769 | + | 0.446469i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.24193e8 | − | 2.15108e8i | 0.0547674 | − | 0.0948599i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.56342e7 | + | 1.48323e8i | 0.0372077 | + | 0.0644457i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.21839e8 | + | 2.30854e9i | 0.351851 | + | 0.988347i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.08169e9 | + | 1.87354e9i | 0.456340 | + | 0.790404i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.32428e9 | − | 2.29372e9i | 0.550562 | − | 0.953601i | −0.447672 | − | 0.894198i | \(-0.647747\pi\) |
0.998234 | − | 0.0594031i | \(-0.0189197\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.02485e8 | + | 5.23920e8i | −0.123936 | + | 0.214663i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.73318e7 | −0.0150752 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.47337e9 | + | 2.55196e9i | −0.586431 | + | 1.01573i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.84312e9 | 1.11543 | 0.557717 | − | 0.830031i | \(-0.311678\pi\) | ||||
0.557717 | + | 0.830031i | \(0.311678\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.18696e8 | + | 5.51998e8i | 0.123253 | + | 0.213480i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.76747e8 | + | 1.51857e9i | 0.334264 | + | 0.578962i | 0.983343 | − | 0.181759i | \(-0.0581790\pi\) |
−0.649079 | + | 0.760721i | \(0.724846\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.68896e9 | −1.38657 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.65355e8 | −0.0983351 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.37990e9 | + | 2.39006e9i | 0.504197 | + | 0.873295i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.62927e9 | − | 2.82198e9i | −0.587005 | − | 1.01672i | −0.994622 | − | 0.103569i | \(-0.966974\pi\) |
0.407617 | − | 0.913153i | \(-0.366360\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.37985e8 | −0.155606 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.24667e8 | − | 1.25516e9i | 0.253893 | − | 0.439756i | −0.710701 | − | 0.703494i | \(-0.751622\pi\) |
0.964594 | + | 0.263738i | \(0.0849556\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.53097e9 | 2.60214 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.13076e8 | + | 1.95854e8i | −0.0385340 | + | 0.0667429i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.51350e9 | − | 4.35350e9i | 0.844824 | − | 1.46328i | −0.0409504 | − | 0.999161i | \(-0.513039\pi\) |
0.885774 | − | 0.464117i | \(-0.153628\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.13967e9 | − | 3.70602e9i | −0.709371 | − | 1.22867i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.75020e8 | + | 6.75543e8i | −0.188049 | + | 0.220924i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.72943e9 | − | 2.99546e9i | −0.557928 | − | 0.966359i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.21012e8 | + | 2.09600e8i | −0.0385135 | + | 0.0667074i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.51198e8 | − | 2.61882e8i | 0.0474744 | − | 0.0822281i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.39494e9 | −0.741930 | −0.370965 | − | 0.928647i | \(-0.620973\pi\) | ||||
−0.370965 | + | 0.928647i | \(0.620973\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.02362e9 | − | 5.23707e9i | 0.924213 | − | 1.60078i | 0.131391 | − | 0.991331i | \(-0.458056\pi\) |
0.792822 | − | 0.609453i | \(-0.208611\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.80458e8 | −0.175071 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.81163e8 | − | 1.00660e9i | −0.172966 | − | 0.299586i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.68852e9 | + | 2.92460e9i | 0.495920 | + | 0.858958i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.78497e9 | −1.09706 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.68130e9 | −1.05307 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.07655e9 | − | 5.32874e9i | −0.868612 | − | 1.50448i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.92771e8 | + | 5.07095e8i | 0.0815866 | + | 0.141312i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.53149e7 | 0.0207167 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.58330e9 | + | 2.74236e9i | −0.429906 | + | 0.744618i | −0.996864 | − | 0.0791278i | \(-0.974786\pi\) |
0.566959 | + | 0.823746i | \(0.308120\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.88168e8 | −0.184457 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.25368e9 | − | 7.36758e9i | 1.12558 | − | 1.94956i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.08848e9 | − | 5.34941e9i | 0.806844 | − | 1.39749i | −0.108195 | − | 0.994130i | \(-0.534507\pi\) |
0.915039 | − | 0.403365i | \(-0.132159\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.70340e9 | − | 2.95038e9i | −0.439353 | − | 0.760981i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.88578e9 | + | 5.29714e9i | 0.480242 | + | 1.34900i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.60242e9 | + | 2.77547e9i | 0.402938 | + | 0.697910i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.48264e7 | + | 1.46924e8i | −0.0210623 | + | 0.0364810i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.51752e7 | + | 9.55662e7i | −0.0135285 | + | 0.0234321i | −0.872710 | − | 0.488238i | \(-0.837640\pi\) |
0.859182 | + | 0.511670i | \(0.170973\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.40698e9 | −1.30922 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.08433e7 | − | 3.61017e7i | 0.00498422 | − | 0.00863292i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.31030e9 | 0.309451 | 0.154725 | − | 0.987958i | \(-0.450551\pi\) | ||||
0.154725 | + | 0.987958i | \(0.450551\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.60571e8 | + | 7.97733e8i | 0.107430 | + | 0.186075i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.31162e9 | + | 4.00384e9i | 0.532568 | + | 0.922435i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.76132e8 | −0.199378 | −0.0996889 | − | 0.995019i | \(-0.531785\pi\) | ||||
−0.0996889 | + | 0.995019i | \(0.531785\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.88405e8 | −0.132267 | −0.0661333 | − | 0.997811i | \(-0.521066\pi\) | ||||
−0.0661333 | + | 0.997811i | \(0.521066\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.63366e8 | − | 2.82958e8i | −0.0362760 | − | 0.0628319i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.16022e8 | − | 3.74162e8i | −0.0473872 | − | 0.0820771i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.83427e9 | 0.614222 | 0.307111 | − | 0.951674i | \(-0.400638\pi\) | ||||
0.307111 | + | 0.951674i | \(0.400638\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.34473e8 | − | 2.32914e8i | 0.0287912 | − | 0.0498679i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.49270e9 | 1.16190 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.56651e8 | + | 2.71328e8i | −0.0327412 | + | 0.0567094i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.18865e9 | − | 7.25495e9i | 0.865025 | − | 1.49827i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.48056e9 | + | 7.76056e9i | 0.914322 | + | 1.58365i | 0.807891 | + | 0.589332i | \(0.200609\pi\) |
0.106430 | + | 0.994320i | \(0.466058\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.14834e9 | + | 1.34909e9i | −0.231561 | + | 0.272042i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.07829e8 | + | 5.33176e8i | 0.0613414 | + | 0.106246i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.23594e9 | − | 3.87277e9i | 0.440321 | − | 0.762658i | −0.557392 | − | 0.830249i | \(-0.688198\pi\) |
0.997713 | + | 0.0675913i | \(0.0215314\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.05257e9 | + | 7.01925e9i | −0.788716 | + | 1.36610i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.77378e8 | 0.0725883 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.07531e9 | − | 3.59454e9i | 0.394538 | − | 0.683359i | −0.598504 | − | 0.801120i | \(-0.704238\pi\) |
0.993042 | + | 0.117760i | \(0.0375714\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.71806e9 | −0.886549 | −0.443274 | − | 0.896386i | \(-0.646183\pi\) | ||||
−0.443274 | + | 0.896386i | \(0.646183\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.19330e9 | − | 2.06686e9i | −0.221636 | − | 0.383885i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.87927e9 | + | 6.71910e9i | 0.712208 | + | 1.23358i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.08059e9 | −1.64799 | −0.823993 | − | 0.566599i | \(-0.808259\pi\) | ||||
−0.823993 | + | 0.566599i | \(0.808259\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.33191e9 | −0.238954 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.82039e9 | − | 6.61711e9i | −0.677584 | − | 1.17361i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.14764e9 | − | 1.98778e9i | −0.201231 | − | 0.348543i | 0.747694 | − | 0.664043i | \(-0.231161\pi\) |
−0.948925 | + | 0.315500i | \(0.897828\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.03235e9 | −0.178964 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.24054e9 | + | 5.61278e9i | −0.555417 | + | 0.962010i | 0.442454 | + | 0.896791i | \(0.354108\pi\) |
−0.997871 | + | 0.0652190i | \(0.979225\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.59214e9 | −0.608746 | −0.304373 | − | 0.952553i | \(-0.598447\pi\) | ||||
−0.304373 | + | 0.952553i | \(0.598447\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.82059e7 | − | 1.35457e8i | 0.0131045 | − | 0.0226976i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.14483e9 | + | 7.17906e9i | −0.686751 | + | 1.18949i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.89453e9 | + | 5.01347e9i | 0.474240 | + | 0.821407i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.24950e7 | − | 1.14748e7i | −0.0101253 | − | 0.00185913i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.06423e8 | + | 1.05036e9i | 0.0971625 | + | 0.168290i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.87462e9 | − | 8.44309e9i | 0.772393 | − | 1.33782i | −0.163856 | − | 0.986484i | \(-0.552393\pi\) |
0.936248 | − | 0.351339i | \(-0.114274\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.61181e8 | − | 7.98788e8i | 0.0722700 | − | 0.125175i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.77083e9 | 1.35935 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.18885e9 | + | 2.05916e9i | −0.182239 | + | 0.315647i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.71865e9 | −0.867043 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.87557e9 | + | 1.01768e10i | 0.881144 | + | 1.52619i | 0.850071 | + | 0.526668i | \(0.176559\pi\) |
0.0310726 | + | 0.999517i | \(0.490108\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.74384e8 | − | 1.34127e9i | −0.114873 | − | 0.198966i | 0.802856 | − | 0.596173i | \(-0.203313\pi\) |
−0.917729 | + | 0.397207i | \(0.869979\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.51629e9 | −0.222496 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.16031e9 | 0.168426 | 0.0842131 | − | 0.996448i | \(-0.473162\pi\) | ||||
0.0842131 | + | 0.996448i | \(0.473162\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.74072e8 | − | 4.74707e8i | −0.0393558 | − | 0.0681662i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.09830e8 | − | 3.63437e8i | −0.0298082 | − | 0.0516292i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.03338e10 | −1.45233 | −0.726164 | − | 0.687522i | \(-0.758698\pi\) | ||||
−0.726164 | + | 0.687522i | \(0.758698\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.32332e9 | + | 9.22026e9i | −0.740181 | + | 1.28203i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.86732e9 | 1.21987 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.82319e9 | + | 1.00861e10i | −0.792614 | + | 1.37285i | 0.131729 | + | 0.991286i | \(0.457947\pi\) |
−0.924343 | + | 0.381562i | \(0.875386\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.29073e8 | − | 9.16381e8i | 0.0712542 | − | 0.123416i | −0.828197 | − | 0.560437i | \(-0.810633\pi\) |
0.899451 | + | 0.437021i | \(0.143967\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.58028e8 | + | 1.13974e9i | 0.0876894 | + | 0.151883i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.21509e10 | + | 2.23105e9i | 1.60226 | + | 0.294194i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.95682e8 | − | 8.58546e8i | −0.0646789 | − | 0.112027i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.87798e8 | + | 1.19130e9i | −0.0888115 | + | 0.153826i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.46688e8 | − | 4.27277e8i | 0.0315224 | − | 0.0545985i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.15132e9 | −0.777886 | −0.388943 | − | 0.921262i | \(-0.627160\pi\) | ||||
−0.388943 | + | 0.921262i | \(0.627160\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.21600e9 | − | 2.10617e9i | 0.152184 | − | 0.263590i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.01802e10 | −1.26095 | −0.630474 | − | 0.776210i | \(-0.717140\pi\) | ||||
−0.630474 | + | 0.776210i | \(0.717140\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.80302e9 | + | 6.58702e9i | 0.466213 | + | 0.807505i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.03773e9 | + | 1.79740e9i | 0.125913 | + | 0.218087i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.10947e9 | 0.373435 | 0.186717 | − | 0.982414i | \(-0.440215\pi\) | ||||
0.186717 | + | 0.982414i | \(0.440215\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.59107e8 | 0.0664626 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.93551e7 | + | 1.20127e8i | 0.00816074 | + | 0.0141348i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.94552e9 | − | 8.56589e9i | −0.576030 | − | 0.997712i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.68784e9 | 0.309907 | 0.154953 | − | 0.987922i | \(-0.450477\pi\) | ||||
0.154953 | + | 0.987922i | \(0.450477\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.42462e8 | + | 5.93161e8i | −0.0390882 | + | 0.0677028i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.10051e10 | 2.37344 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.69014e9 | + | 6.39151e9i | −0.412789 | + | 0.714971i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.86674e8 | + | 3.23330e8i | −0.0206735 | + | 0.0358076i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.86197e9 | + | 1.01532e10i | 0.642733 | + | 1.11325i | 0.984820 | + | 0.173577i | \(0.0555327\pi\) |
−0.342088 | + | 0.939668i | \(0.611134\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.19825e9 | − | 1.40773e9i | 0.130078 | − | 0.152818i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.07136e9 | − | 1.85565e9i | −0.115152 | − | 0.199450i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.71933e9 | − | 1.68344e10i | 1.03435 | − | 1.79155i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.19422e9 | − | 3.80050e9i | 0.231216 | − | 0.400479i | −0.726950 | − | 0.686690i | \(-0.759063\pi\) |
0.958166 | + | 0.286212i | \(0.0923961\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.64083e9 | −0.692913 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.56180e8 | − | 2.70512e8i | 0.0161366 | − | 0.0279495i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.21321e9 | 0.124127 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.14767e8 | + | 5.45193e8i | 0.0318913 | + | 0.0552374i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.26409e9 | − | 1.60459e10i | −0.929505 | − | 1.60995i | −0.784151 | − | 0.620570i | \(-0.786901\pi\) |
−0.145354 | − | 0.989380i | \(-0.546432\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.92789e9 | −0.887106 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.47790e8 | 0.0637456 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.70718e9 | − | 1.33492e10i | −0.751126 | − | 1.30099i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.79368e9 | + | 1.34990e10i | 0.752267 | + | 1.30296i | 0.946722 | + | 0.322053i | \(0.104373\pi\) |
−0.194455 | + | 0.980911i | \(0.562294\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.13490e9 | −0.873288 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.41996e9 | + | 9.38765e9i | −0.513198 | + | 0.888886i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.52039e9 | −0.423948 | −0.211974 | − | 0.977275i | \(-0.567989\pi\) | ||||
−0.211974 | + | 0.977275i | \(0.567989\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.33392e8 | + | 5.77452e8i | −0.0309706 | + | 0.0536427i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.72816e8 | − | 2.99326e8i | 0.0159018 | − | 0.0275428i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.41317e8 | − | 1.45720e9i | −0.0766839 | − | 0.132820i | 0.825133 | − | 0.564938i | \(-0.191100\pi\) |
−0.901817 | + | 0.432118i | \(0.857767\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.30022e9 | − | 1.52752e9i | 0.117396 | − | 0.137919i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.92734e9 | − | 8.53440e9i | −0.440709 | − | 0.763330i | 0.557033 | − | 0.830490i | \(-0.311940\pi\) |
−0.997742 | + | 0.0671601i | \(0.978606\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.26952e10 | − | 2.19887e10i | 1.12485 | − | 1.94829i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.69078e9 | + | 9.85671e9i | −0.499516 | + | 0.865187i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.58822e10 | −1.38109 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.43842e9 | − | 1.46158e10i | 0.726979 | − | 1.25916i | −0.231176 | − | 0.972912i | \(-0.574257\pi\) |
0.958154 | − | 0.286252i | \(-0.0924094\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.46286e9 | 0.124859 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.61385e10 | + | 2.79528e10i | 1.36474 | + | 2.36380i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.68849e9 | − | 1.33168e10i | −0.644177 | − | 1.11575i | −0.984491 | − | 0.175435i | \(-0.943867\pi\) |
0.340314 | − | 0.940312i | \(-0.389467\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.12028e7 | 0.000929993 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.94746e9 | 0.324692 | 0.162346 | − | 0.986734i | \(-0.448094\pi\) | ||||
0.162346 | + | 0.986734i | \(0.448094\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.09794e10 | − | 1.90169e10i | −0.894837 | − | 1.54990i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.39742e9 | − | 1.45447e10i | −0.678158 | − | 1.17460i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.73050e10 | 1.38480 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.06474e9 | − | 1.22365e10i | 0.560214 | − | 0.970320i | −0.437263 | − | 0.899334i | \(-0.644052\pi\) |
0.997477 | − | 0.0709859i | \(-0.0226145\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.36368e9 | 0.107158 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.44191e9 | + | 1.63539e10i | −0.735244 | + | 1.27348i | 0.219372 | + | 0.975641i | \(0.429599\pi\) |
−0.954616 | + | 0.297839i | \(0.903734\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.42839e9 | − | 4.20610e9i | 0.187397 | − | 0.324581i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.18951e8 | + | 3.79234e8i | 0.0167445 | + | 0.0290024i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.10642e10 | + | 2.03152e9i | 0.838571 | + | 0.153972i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.14091e8 | − | 7.17226e8i | −0.0311040 | − | 0.0538738i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.79021e9 | − | 4.83278e9i | 0.207716 | − | 0.359775i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.24612e9 | − | 1.25507e10i | 0.534641 | − | 0.926025i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.09229e10 | 0.798779 | 0.399390 | − | 0.916781i | \(-0.369222\pi\) | ||||
0.399390 | + | 0.916781i | \(0.369222\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.47485e8 | + | 2.55452e8i | −0.0106900 | + | 0.0185157i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.37762e9 | 0.170815 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.78800e9 | + | 1.34892e10i | 0.554587 | + | 0.960573i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.38688e9 | − | 2.40215e9i | −0.0978935 | − | 0.169557i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.26385e9 | −0.0884280 | −0.0442140 | − | 0.999022i | \(-0.514078\pi\) | ||||
−0.0442140 | + | 0.999022i | \(0.514078\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.53183e10 | −1.06242 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.58861e9 | − | 1.48759e10i | −0.590485 | − | 1.02275i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.42087e8 | + | 1.11213e9i | 0.0437612 | + | 0.0757967i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.17816e9 | −0.147165 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.22436e9 | + | 2.12065e9i | −0.0820070 | + | 0.142040i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.99516e10 | 1.32482 | 0.662412 | − | 0.749140i | \(-0.269533\pi\) | ||||
0.662412 | + | 0.749140i | \(0.269533\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.42506e9 | + | 7.66442e9i | −0.291303 | + | 0.504552i | −0.974118 | − | 0.226039i | \(-0.927422\pi\) |
0.682815 | + | 0.730592i | \(0.260756\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.32562e9 | − | 2.29604e9i | 0.0865171 | − | 0.149852i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.85946e10 | + | 3.22068e10i | 1.20319 | + | 2.08399i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.62508e10 | + | 2.98384e9i | 1.04255 | + | 0.191425i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.08116e10 | − | 1.87262e10i | −0.687695 | − | 1.19112i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.44573e9 | + | 9.43229e9i | −0.343444 | + | 0.594862i | −0.985070 | − | 0.172156i | \(-0.944927\pi\) |
0.641626 | + | 0.767018i | \(0.278260\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.20282e8 | − | 3.81540e8i | 0.0137746 | − | 0.0238583i | −0.859056 | − | 0.511882i | \(-0.828949\pi\) |
0.872831 | + | 0.488023i | \(0.162282\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.74188e8 | 0.0108001 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.60272e9 | + | 1.31683e10i | −0.467412 | + | 0.809581i | −0.999307 | − | 0.0372295i | \(-0.988147\pi\) |
0.531895 | + | 0.846810i | \(0.321480\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.34670e10 | −1.43060 | −0.715298 | − | 0.698820i | \(-0.753709\pi\) | ||||
−0.715298 | + | 0.698820i | \(0.753709\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.55743e9 | − | 2.69755e9i | −0.0941469 | − | 0.163067i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.38342e9 | + | 4.12820e9i | 0.142871 | + | 0.247459i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.55546e10 | −1.51903 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.75829e9 | 0.103646 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.84074e9 | − | 1.35806e10i | −0.458343 | − | 0.793873i | 0.540531 | − | 0.841324i | \(-0.318223\pi\) |
−0.998874 | + | 0.0474514i | \(0.984890\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.05985e9 | − | 1.56921e10i | −0.525213 | − | 0.909695i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.10066e9 | 0.120770 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.59755e9 | + | 1.14273e10i | −0.376170 | + | 0.651545i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.00261e10 | 1.13241 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.47977e9 | − | 2.56304e9i | 0.0829884 | − | 0.143740i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.62969e8 | + | 2.82270e8i | −0.00906465 | + | 0.0157004i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.96010e9 | − | 3.39499e9i | −0.108133 | − | 0.187291i | 0.806881 | − | 0.590714i | \(-0.201154\pi\) |
−0.915014 | + | 0.403423i | \(0.867820\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.65927e10 | + | 1.94934e10i | −0.907896 | + | 1.06661i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.16873e9 | + | 1.58807e10i | 0.497595 | + | 0.861861i | 0.999996 | − | 0.00277432i | \(-0.000883094\pi\) |
−0.502401 | + | 0.864635i | \(0.667550\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.89177e9 | − | 1.19369e10i | 0.370984 | − | 0.642562i | −0.618734 | − | 0.785601i | \(-0.712354\pi\) |
0.989717 | + | 0.143038i | \(0.0456873\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.33234e9 | + | 2.30767e9i | −0.0711381 | + | 0.123215i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.63513e9 | −0.351408 | −0.175704 | − | 0.984443i | \(-0.556220\pi\) | ||||
−0.175704 | + | 0.984443i | \(0.556220\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.82177e9 | − | 1.52798e10i | 0.463446 | − | 0.802712i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.75473e8 | −0.00914413 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.80866e8 | − | 8.32884e8i | −0.0248573 | − | 0.0430542i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.45583e9 | + | 9.44977e9i | 0.279767 | + | 0.484571i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.57607e10 | −0.801723 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.58534e9 | −0.0800006 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.03218e10 | + | 1.78779e10i | 0.516722 | + | 0.894989i | 0.999811 | + | 0.0194178i | \(0.00618128\pi\) |
−0.483089 | + | 0.875571i | \(0.660485\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.01239e9 | + | 3.48556e9i | 0.0999425 | + | 0.173106i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.87740e9 | 0.486661 | 0.243331 | − | 0.969943i | \(-0.421760\pi\) | ||||
0.243331 | + | 0.969943i | \(0.421760\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.85403e10 | + | 3.21128e10i | −0.906264 | + | 1.56969i | −0.0870520 | + | 0.996204i | \(0.527745\pi\) |
−0.819212 | + | 0.573491i | \(0.805589\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.85287e9 | 0.235341 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.21684e10 | − | 2.10763e10i | 0.585466 | − | 1.01406i | −0.409351 | − | 0.912377i | \(-0.634245\pi\) |
0.994817 | − | 0.101680i | \(-0.0324218\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.13195e10 | − | 1.96059e10i | 0.540343 | − | 0.935902i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.93686e8 | − | 1.20150e9i | −0.0328542 | − | 0.0569052i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.83061e9 | + | 2.19961e10i | 0.367973 | + | 1.03363i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.70820e10 | + | 2.95869e10i | 0.796450 | + | 1.37949i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.76837e8 | + | 3.06291e8i | −0.00818088 | + | 0.0141697i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.57216e9 | − | 9.65126e9i | 0.255779 | − | 0.443022i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.98296e10 | −0.903185 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.95689e9 | + | 3.38944e9i | −0.0884423 | + | 0.153187i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.01518e10 | −1.80067 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.43237e10 | + | 2.48094e10i | 0.637426 | + | 1.10405i | 0.985996 | + | 0.166771i | \(0.0533342\pi\) |
−0.348570 | + | 0.937283i | \(0.613332\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.01396e10 | + | 3.48829e10i | 0.889361 | + | 1.54042i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.21467e9 | 0.403799 | 0.201900 | − | 0.979406i | \(-0.435288\pi\) | ||||
0.201900 | + | 0.979406i | \(0.435288\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.64829e9 | −0.0716780 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.18400e9 | + | 3.78280e9i | 0.0942495 | + | 0.163245i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.37404e10 | + | 2.37990e10i | 0.588444 | + | 1.01922i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.19815e10 | −1.78424 | −0.892120 | − | 0.451798i | \(-0.850783\pi\) | ||||
−0.892120 | + | 0.451798i | \(0.850783\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.84514e9 | + | 3.19587e9i | −0.0778252 | + | 0.134797i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.61459e10 | 1.09445 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.53394e9 | + | 4.38892e9i | −0.105269 | + | 0.182331i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.24984e9 | − | 1.60212e10i | 0.381378 | − | 0.660565i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.67307e9 | − | 9.82605e9i | −0.232147 | − | 0.402091i | 0.726293 | − | 0.687386i | \(-0.241242\pi\) |
−0.958440 | + | 0.285295i | \(0.907908\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.70947e9 | − | 5.53277e9i | 0.191271 | − | 0.224708i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.63986e9 | − | 2.84032e9i | −0.0661030 | − | 0.114494i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.21612e9 | − | 2.10639e9i | 0.0486561 | − | 0.0842748i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.35639e10 | + | 2.34934e10i | −0.538638 | + | 0.932948i | 0.460340 | + | 0.887743i | \(0.347728\pi\) |
−0.998978 | + | 0.0452054i | \(0.985606\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.52072e8 | −0.0257020 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.68415e9 | + | 4.64909e9i | −0.105013 | + | 0.181888i | −0.913744 | − | 0.406291i | \(-0.866822\pi\) |
0.808730 | + | 0.588179i | \(0.200155\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.98336e9 | −0.0770212 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.13045e9 | − | 1.06182e10i | −0.236309 | − | 0.409300i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.31120e10 | + | 4.00312e10i | 0.884327 | + | 1.53170i | 0.846483 | + | 0.532416i | \(0.178716\pi\) |
0.0378444 | + | 0.999284i | \(0.487951\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.05417e10 | −1.53982 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.08103e8 | −0.0191567 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.31060e10 | − | 4.00208e10i | −0.864769 | − | 1.49782i | −0.867276 | − | 0.497827i | \(-0.834132\pi\) |
0.00250756 | − | 0.999997i | \(-0.499202\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.53171e9 | − | 1.65094e10i | −0.354127 | − | 0.613366i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.99689e8 | 0.0147411 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.21573e8 | − | 1.24980e9i | 0.0264189 | − | 0.0457589i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.40012e10 | −0.872372 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.64549e10 | − | 2.85007e10i | 0.593749 | − | 1.02840i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.84595e9 | − | 1.35896e10i | 0.281061 | − | 0.486811i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.91059e9 | + | 5.04128e9i | 0.103511 | + | 0.179287i | 0.913129 | − | 0.407671i | \(-0.133659\pi\) |
−0.809618 | + | 0.586958i | \(0.800326\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.34875e9 | − | 3.78864e9i | −0.0476211 | − | 0.133767i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.77878e10 | − | 3.08094e10i | −0.623526 | − | 1.07998i | −0.988824 | − | 0.149088i | \(-0.952366\pi\) |
0.365298 | − | 0.930891i | \(-0.380967\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.71089e10 | − | 4.69539e10i | 0.943444 | − | 1.63409i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.74958e9 | + | 4.76241e9i | −0.0950057 | + | 0.164555i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.86368e10 | 0.639353 | 0.319677 | − | 0.947527i | \(-0.396426\pi\) | ||||
0.319677 | + | 0.947527i | \(0.396426\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.24381e9 | − | 2.15434e9i | 0.0423658 | − | 0.0733797i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.55015e10 | 1.53881 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.54863e10 | − | 4.41437e10i | −0.855796 | − | 1.48228i | −0.875904 | − | 0.482485i | \(-0.839734\pi\) |
0.0201083 | − | 0.999798i | \(-0.493599\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.79606e10 | + | 3.11086e10i | 0.598816 | + | 1.03718i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.53070e9 | −0.183092 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.91310e9 | −0.0957564 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.57841e9 | + | 2.73389e9i | 0.0515185 | + | 0.0892326i | 0.890635 | − | 0.454720i | \(-0.150261\pi\) |
−0.839116 | + | 0.543952i | \(0.816927\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.79882e9 | − | 4.84770e9i | −0.0907096 | − | 0.157114i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.20185e10 | 0.708609 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.66012e9 | − | 6.33951e9i | 0.116967 | − | 0.202592i | −0.801598 | − | 0.597864i | \(-0.796016\pi\) |
0.918564 | + | 0.395272i | \(0.129350\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.83471e9 | −0.0582222 |
(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 | 76.8.e.a.45.5 | ✓ | 22 | |
19.11 | even | 3 | inner | 76.8.e.a.49.5 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.8.e.a.45.5 | ✓ | 22 | 1.1 | even | 1 | trivial | |
76.8.e.a.49.5 | yes | 22 | 19.11 | even | 3 | inner |