Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,8,Mod(75,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.75");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.d (of order \(2\), degree \(1\), 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: | \(68\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 75.4 | ||
Character | \(\chi\) | \(=\) | 76.75 |
Dual form | 76.8.d.a.75.3 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −11.1927 | + | 1.65015i | −0.989306 | + | 0.145854i | ||||
\(3\) | −65.7104 | −1.40511 | −0.702554 | − | 0.711630i | \(-0.747957\pi\) | ||||
−0.702554 | + | 0.711630i | \(0.747957\pi\) | |||||||
\(4\) | 122.554 | − | 36.9394i | 0.957453 | − | 0.288589i | ||||
\(5\) | −95.9690 | −0.343349 | −0.171675 | − | 0.985154i | \(-0.554918\pi\) | ||||
−0.171675 | + | 0.985154i | \(0.554918\pi\) | |||||||
\(6\) | 735.478 | − | 108.432i | 1.39008 | − | 0.204941i | ||||
\(7\) | − | 851.669i | − | 0.938486i | −0.883069 | − | 0.469243i | \(-0.844527\pi\) | ||
0.883069 | − | 0.469243i | \(-0.155473\pi\) | |||||||
\(8\) | −1310.76 | + | 615.686i | −0.905122 | + | 0.425152i | ||||
\(9\) | 2130.86 | 0.974329 | ||||||||
\(10\) | 1074.15 | − | 158.364i | 0.339677 | − | 0.0500790i | ||||
\(11\) | 2279.40i | 0.516353i | 0.966098 | + | 0.258176i | \(0.0831216\pi\) | ||||
−0.966098 | + | 0.258176i | \(0.916878\pi\) | |||||||
\(12\) | −8053.07 | + | 2427.30i | −1.34533 | + | 0.405499i | ||||
\(13\) | 12626.0i | 1.59391i | 0.604038 | + | 0.796956i | \(0.293558\pi\) | ||||
−0.604038 | + | 0.796956i | \(0.706442\pi\) | |||||||
\(14\) | 1405.38 | + | 9532.49i | 0.136882 | + | 0.928450i | ||||
\(15\) | 6306.16 | 0.482443 | ||||||||
\(16\) | 13655.0 | − | 9054.15i | 0.833432 | − | 0.552621i | ||||
\(17\) | 23515.2 | 1.16085 | 0.580427 | − | 0.814312i | \(-0.302886\pi\) | ||||
0.580427 | + | 0.814312i | \(0.302886\pi\) | |||||||
\(18\) | −23850.1 | + | 3516.24i | −0.963910 | + | 0.142110i | ||||
\(19\) | −15823.4 | + | 25367.2i | −0.529251 | + | 0.848466i | ||||
\(20\) | −11761.4 | + | 3545.04i | −0.328741 | + | 0.0990869i | ||||
\(21\) | 55963.5i | 1.31867i | ||||||||
\(22\) | −3761.36 | − | 25512.7i | −0.0753123 | − | 0.510831i | ||||
\(23\) | 37267.2i | 0.638673i | 0.947641 | + | 0.319337i | \(0.103460\pi\) | ||||
−0.947641 | + | 0.319337i | \(0.896540\pi\) | |||||||
\(24\) | 86130.4 | − | 40457.0i | 1.27179 | − | 0.597384i | ||||
\(25\) | −68915.0 | −0.882111 | ||||||||
\(26\) | −20834.9 | − | 141319.i | −0.232479 | − | 1.57687i | ||||
\(27\) | 3689.15 | 0.0360706 | ||||||||
\(28\) | −31460.2 | − | 104375.i | −0.270837 | − | 0.898556i | ||||
\(29\) | − | 262235.i | − | 1.99663i | −0.0580455 | − | 0.998314i | \(-0.518487\pi\) | ||
0.0580455 | − | 0.998314i | \(-0.481513\pi\) | |||||||
\(30\) | −70583.1 | + | 10406.1i | −0.477283 | + | 0.0703664i | ||||
\(31\) | 67159.0 | 0.404891 | 0.202445 | − | 0.979294i | \(-0.435111\pi\) | ||||
0.202445 | + | 0.979294i | \(0.435111\pi\) | |||||||
\(32\) | −137895. | + | 123873.i | −0.743918 | + | 0.668271i | ||||
\(33\) | − | 149780.i | − | 0.725532i | ||||||
\(34\) | −263199. | + | 38803.7i | −1.14844 | + | 0.169316i | ||||
\(35\) | 81733.8i | 0.322228i | ||||||||
\(36\) | 261145. | − | 78712.7i | 0.932874 | − | 0.281181i | ||||
\(37\) | 295883.i | 0.960317i | 0.877182 | + | 0.480159i | \(0.159421\pi\) | ||||
−0.877182 | + | 0.480159i | \(0.840579\pi\) | |||||||
\(38\) | 135247. | − | 310039.i | 0.399838 | − | 0.916586i | ||||
\(39\) | − | 829660.i | − | 2.23962i | ||||||
\(40\) | 125792. | − | 59086.7i | 0.310773 | − | 0.145975i | ||||
\(41\) | − | 438259.i | − | 0.993086i | −0.868012 | − | 0.496543i | \(-0.834602\pi\) | ||
0.868012 | − | 0.496543i | \(-0.165398\pi\) | |||||||
\(42\) | −92348.4 | − | 626384.i | −0.192334 | − | 1.30457i | ||||
\(43\) | 230063.i | 0.441272i | 0.975356 | + | 0.220636i | \(0.0708133\pi\) | ||||
−0.975356 | + | 0.220636i | \(0.929187\pi\) | |||||||
\(44\) | 84199.8 | + | 279350.i | 0.149014 | + | 0.494384i | ||||
\(45\) | −204496. | −0.334535 | ||||||||
\(46\) | −61496.6 | − | 417121.i | −0.0931533 | − | 0.631844i | ||||
\(47\) | − | 712136.i | − | 1.00051i | −0.865879 | − | 0.500254i | \(-0.833240\pi\) | ||
0.865879 | − | 0.500254i | \(-0.166760\pi\) | |||||||
\(48\) | −897273. | + | 594952.i | −1.17106 | + | 0.776493i | ||||
\(49\) | 98203.2 | 0.119245 | ||||||||
\(50\) | 771346. | − | 113720.i | 0.872678 | − | 0.128660i | ||||
\(51\) | −1.54519e6 | −1.63113 | ||||||||
\(52\) | 466397. | + | 1.54737e6i | 0.459986 | + | 1.52610i | ||||
\(53\) | − | 154721.i | − | 0.142753i | −0.997449 | − | 0.0713763i | \(-0.977261\pi\) | ||
0.997449 | − | 0.0713763i | \(-0.0227391\pi\) | |||||||
\(54\) | −41291.7 | + | 6087.67i | −0.0356849 | + | 0.00526106i | ||||
\(55\) | − | 218752.i | − | 0.177289i | ||||||
\(56\) | 524360. | + | 1.11633e6i | 0.398999 | + | 0.849444i | ||||
\(57\) | 1.03976e6 | − | 1.66689e6i | 0.743654 | − | 1.19219i | ||||
\(58\) | 432728. | + | 2.93512e6i | 0.291217 | + | 1.97528i | ||||
\(59\) | 707384. | 0.448408 | 0.224204 | − | 0.974542i | \(-0.428022\pi\) | ||||
0.224204 | + | 0.974542i | \(0.428022\pi\) | |||||||
\(60\) | 772845. | − | 232946.i | 0.461916 | − | 0.139228i | ||||
\(61\) | −3.10918e6 | −1.75385 | −0.876923 | − | 0.480630i | \(-0.840408\pi\) | ||||
−0.876923 | + | 0.480630i | \(0.840408\pi\) | |||||||
\(62\) | −751692. | + | 110823.i | −0.400561 | + | 0.0590551i | ||||
\(63\) | − | 1.81478e6i | − | 0.914394i | ||||||
\(64\) | 1.33901e6 | − | 1.61403e6i | 0.638492 | − | 0.769629i | ||||
\(65\) | − | 1.21170e6i | − | 0.547268i | ||||||
\(66\) | 247161. | + | 1.67645e6i | 0.105822 | + | 0.717773i | ||||
\(67\) | −155450. | −0.0631436 | −0.0315718 | − | 0.999501i | \(-0.510051\pi\) | ||||
−0.0315718 | + | 0.999501i | \(0.510051\pi\) | |||||||
\(68\) | 2.88188e6 | − | 868638.i | 1.11146 | − | 0.335010i | ||||
\(69\) | − | 2.44884e6i | − | 0.897405i | ||||||
\(70\) | −134873. | − | 914823.i | −0.0469984 | − | 0.318782i | ||||
\(71\) | −3.51389e6 | −1.16516 | −0.582578 | − | 0.812775i | \(-0.697956\pi\) | ||||
−0.582578 | + | 0.812775i | \(0.697956\pi\) | |||||||
\(72\) | −2.79304e6 | + | 1.31194e6i | −0.881887 | + | 0.414238i | ||||
\(73\) | −933723. | −0.280924 | −0.140462 | − | 0.990086i | \(-0.544859\pi\) | ||||
−0.140462 | + | 0.990086i | \(0.544859\pi\) | |||||||
\(74\) | −488253. | − | 3.31174e6i | −0.140066 | − | 0.950048i | ||||
\(75\) | 4.52843e6 | 1.23946 | ||||||||
\(76\) | −1.00217e6 | + | 3.69335e6i | −0.261874 | + | 0.965102i | ||||
\(77\) | 1.94130e6 | 0.484590 | ||||||||
\(78\) | 1.36907e6 | + | 9.28615e6i | 0.326658 | + | 2.21567i | ||||
\(79\) | 4.27796e6 | 0.976207 | 0.488103 | − | 0.872786i | \(-0.337689\pi\) | ||||
0.488103 | + | 0.872786i | \(0.337689\pi\) | |||||||
\(80\) | −1.31045e6 | + | 868917.i | −0.286158 | + | 0.189742i | ||||
\(81\) | −4.90260e6 | −1.02501 | ||||||||
\(82\) | 723194. | + | 4.90531e6i | 0.144846 | + | 0.982466i | ||||
\(83\) | 3.72571e6i | 0.715214i | 0.933872 | + | 0.357607i | \(0.116407\pi\) | ||||
−0.933872 | + | 0.357607i | \(0.883593\pi\) | |||||||
\(84\) | 2.06726e6 | + | 6.85855e6i | 0.380555 | + | 1.26257i | ||||
\(85\) | −2.25673e6 | −0.398578 | ||||||||
\(86\) | −379639. | − | 2.57503e6i | −0.0643615 | − | 0.436553i | ||||
\(87\) | 1.72315e7i | 2.80548i | ||||||||
\(88\) | −1.40340e6 | − | 2.98774e6i | −0.219528 | − | 0.467362i | ||||
\(89\) | − | 3.99893e6i | − | 0.601282i | −0.953737 | − | 0.300641i | \(-0.902799\pi\) | ||
0.953737 | − | 0.300641i | \(-0.0972006\pi\) | |||||||
\(90\) | 2.28887e6 | − | 337450.i | 0.330957 | − | 0.0487934i | ||||
\(91\) | 1.07532e7 | 1.49586 | ||||||||
\(92\) | 1.37663e6 | + | 4.56724e6i | 0.184314 | + | 0.611500i | ||||
\(93\) | −4.41304e6 | −0.568916 | ||||||||
\(94\) | 1.17513e6 | + | 7.97074e6i | 0.145928 | + | 0.989808i | ||||
\(95\) | 1.51855e6 | − | 2.43446e6i | 0.181718 | − | 0.291320i | ||||
\(96\) | 9.06116e6 | − | 8.13977e6i | 1.04528 | − | 0.938994i | ||||
\(97\) | − | 5.49101e6i | − | 0.610873i | −0.952212 | − | 0.305437i | \(-0.901198\pi\) | ||
0.952212 | − | 0.305437i | \(-0.0988024\pi\) | |||||||
\(98\) | −1.09916e6 | + | 162050.i | −0.117970 | + | 0.0173924i | ||||
\(99\) | 4.85708e6i | 0.503097i | ||||||||
\(100\) | −8.44580e6 | + | 2.54568e6i | −0.844580 | + | 0.254568i | ||||
\(101\) | −1.16288e7 | −1.12308 | −0.561539 | − | 0.827450i | \(-0.689791\pi\) | ||||
−0.561539 | + | 0.827450i | \(0.689791\pi\) | |||||||
\(102\) | 1.72949e7 | − | 2.54981e6i | 1.61368 | − | 0.237907i | ||||
\(103\) | 1.03356e6 | 0.0931977 | 0.0465989 | − | 0.998914i | \(-0.485162\pi\) | ||||
0.0465989 | + | 0.998914i | \(0.485162\pi\) | |||||||
\(104\) | −7.77365e6 | − | 1.65496e7i | −0.677654 | − | 1.44268i | ||||
\(105\) | − | 5.37076e6i | − | 0.452765i | ||||||
\(106\) | 255314. | + | 1.73175e6i | 0.0208211 | + | 0.141226i | ||||
\(107\) | −9.71657e6 | −0.766779 | −0.383389 | − | 0.923587i | \(-0.625243\pi\) | ||||
−0.383389 | + | 0.923587i | \(0.625243\pi\) | |||||||
\(108\) | 452120. | − | 136275.i | 0.0345359 | − | 0.0104096i | ||||
\(109\) | − | 1.69381e7i | − | 1.25277i | −0.779513 | − | 0.626386i | \(-0.784534\pi\) | ||
0.779513 | − | 0.626386i | \(-0.215466\pi\) | |||||||
\(110\) | 360974. | + | 2.44843e6i | 0.0258584 | + | 0.175393i | ||||
\(111\) | − | 1.94426e7i | − | 1.34935i | ||||||
\(112\) | −7.71114e6 | − | 1.16295e7i | −0.518627 | − | 0.782164i | ||||
\(113\) | − | 1.04311e7i | − | 0.680071i | −0.940413 | − | 0.340035i | \(-0.889561\pi\) | ||
0.940413 | − | 0.340035i | \(-0.110439\pi\) | |||||||
\(114\) | −8.88712e6 | + | 2.03728e7i | −0.561816 | + | 1.28790i | ||||
\(115\) | − | 3.57649e6i | − | 0.219288i | ||||||
\(116\) | −9.68680e6 | − | 3.21379e7i | −0.576205 | − | 1.91168i | ||||
\(117\) | 2.69042e7i | 1.55299i | ||||||||
\(118\) | −7.91755e6 | + | 1.16729e6i | −0.443612 | + | 0.0654022i | ||||
\(119\) | − | 2.00272e7i | − | 1.08944i | ||||||
\(120\) | −8.26584e6 | + | 3.88261e6i | −0.436669 | + | 0.205111i | ||||
\(121\) | 1.42915e7 | 0.733380 | ||||||||
\(122\) | 3.48002e7 | − | 5.13063e6i | 1.73509 | − | 0.255806i | ||||
\(123\) | 2.87982e7i | 1.39539i | ||||||||
\(124\) | 8.23060e6 | − | 2.48081e6i | 0.387664 | − | 0.116847i | ||||
\(125\) | 1.41113e7 | 0.646221 | ||||||||
\(126\) | 2.99467e6 | + | 2.03124e7i | 0.133368 | + | 0.904615i | ||||
\(127\) | −1.49746e7 | −0.648699 | −0.324349 | − | 0.945937i | \(-0.605145\pi\) | ||||
−0.324349 | + | 0.945937i | \(0.605145\pi\) | |||||||
\(128\) | −1.23238e7 | + | 2.02749e7i | −0.519410 | + | 0.854525i | ||||
\(129\) | − | 1.51175e7i | − | 0.620035i | ||||||
\(130\) | 1.99950e6 | + | 1.35623e7i | 0.0798214 | + | 0.541416i | ||||
\(131\) | − | 4.01857e7i | − | 1.56179i | −0.624664 | − | 0.780893i | \(-0.714764\pi\) | ||
0.624664 | − | 0.780893i | \(-0.285236\pi\) | |||||||
\(132\) | −5.53280e6 | − | 1.83562e7i | −0.209381 | − | 0.694662i | ||||
\(133\) | 2.16044e7 | + | 1.34763e7i | 0.796273 | + | 0.496694i | ||||
\(134\) | 1.73991e6 | − | 256517.i | 0.0624683 | − | 0.00920977i | ||||
\(135\) | −354044. | −0.0123848 | ||||||||
\(136\) | −3.08227e7 | + | 1.44780e7i | −1.05071 | + | 0.493539i | ||||
\(137\) | −4.32227e7 | −1.43612 | −0.718059 | − | 0.695982i | \(-0.754969\pi\) | ||||
−0.718059 | + | 0.695982i | \(0.754969\pi\) | |||||||
\(138\) | 4.04096e6 | + | 2.74092e7i | 0.130891 | + | 0.887809i | ||||
\(139\) | − | 3.49442e7i | − | 1.10363i | −0.833967 | − | 0.551815i | \(-0.813936\pi\) | ||
0.833967 | − | 0.551815i | \(-0.186064\pi\) | |||||||
\(140\) | 3.01920e6 | + | 1.00168e7i | 0.0929916 | + | 0.308518i | ||||
\(141\) | 4.67947e7i | 1.40582i | ||||||||
\(142\) | 3.93300e7 | − | 5.79846e6i | 1.15270 | − | 0.169943i | ||||
\(143\) | −2.87797e7 | −0.823021 | ||||||||
\(144\) | 2.90968e7 | − | 1.92931e7i | 0.812037 | − | 0.538435i | ||||
\(145\) | 2.51664e7i | 0.685540i | ||||||||
\(146\) | 1.04509e7 | − | 1.54079e6i | 0.277919 | − | 0.0409739i | ||||
\(147\) | −6.45297e6 | −0.167552 | ||||||||
\(148\) | 1.09298e7 | + | 3.62617e7i | 0.277137 | + | 0.919459i | ||||
\(149\) | 3.06096e7 | 0.758063 | 0.379032 | − | 0.925384i | \(-0.376257\pi\) | ||||
0.379032 | + | 0.925384i | \(0.376257\pi\) | |||||||
\(150\) | −5.06854e7 | + | 7.47261e6i | −1.22621 | + | 0.180781i | ||||
\(151\) | −6.53382e7 | −1.54436 | −0.772178 | − | 0.635406i | \(-0.780833\pi\) | ||||
−0.772178 | + | 0.635406i | \(0.780833\pi\) | |||||||
\(152\) | 5.12239e6 | − | 4.29924e7i | 0.118310 | − | 0.992977i | ||||
\(153\) | 5.01075e7 | 1.13105 | ||||||||
\(154\) | −2.17284e7 | + | 3.20344e6i | −0.479408 | + | 0.0706795i | ||||
\(155\) | −6.44518e6 | −0.139019 | ||||||||
\(156\) | −3.06472e7 | − | 1.01678e8i | −0.646330 | − | 2.14433i | ||||
\(157\) | 5.69477e7 | 1.17443 | 0.587216 | − | 0.809431i | \(-0.300224\pi\) | ||||
0.587216 | + | 0.809431i | \(0.300224\pi\) | |||||||
\(158\) | −4.78820e7 | + | 7.05929e6i | −0.965767 | + | 0.142384i | ||||
\(159\) | 1.01668e7i | 0.200583i | ||||||||
\(160\) | 1.32337e7 | − | 1.18880e7i | 0.255423 | − | 0.229450i | ||||
\(161\) | 3.17393e7 | 0.599386 | ||||||||
\(162\) | 5.48734e7 | − | 8.09005e6i | 1.01405 | − | 0.149503i | ||||
\(163\) | − | 3.31661e6i | − | 0.0599843i | −0.999550 | − | 0.0299921i | \(-0.990452\pi\) | ||
0.999550 | − | 0.0299921i | \(-0.00954822\pi\) | |||||||
\(164\) | −1.61890e7 | − | 5.37103e7i | −0.286594 | − | 0.950833i | ||||
\(165\) | 1.43743e7i | 0.249111i | ||||||||
\(166\) | −6.14800e6 | − | 4.17009e7i | −0.104317 | − | 0.707566i | ||||
\(167\) | 1.02027e8 | 1.69515 | 0.847574 | − | 0.530677i | \(-0.178062\pi\) | ||||
0.847574 | + | 0.530677i | \(0.178062\pi\) | |||||||
\(168\) | −3.44559e7 | − | 7.33545e7i | −0.560637 | − | 1.19356i | ||||
\(169\) | −9.66675e7 | −1.54055 | ||||||||
\(170\) | 2.52589e7 | − | 3.72395e6i | 0.394316 | − | 0.0581344i | ||||
\(171\) | −3.37173e7 | + | 5.40538e7i | −0.515664 | + | 0.826685i | ||||
\(172\) | 8.49839e6 | + | 2.81951e7i | 0.127346 | + | 0.422498i | ||||
\(173\) | − | 4.55355e6i | − | 0.0668634i | −0.999441 | − | 0.0334317i | \(-0.989356\pi\) | ||
0.999441 | − | 0.0334317i | \(-0.0106436\pi\) | |||||||
\(174\) | −2.84347e7 | − | 1.92868e8i | −0.409191 | − | 2.77548i | ||||
\(175\) | 5.86927e7i | 0.827849i | ||||||||
\(176\) | 2.06380e7 | + | 3.11251e7i | 0.285348 | + | 0.430345i | ||||
\(177\) | −4.64825e7 | −0.630061 | ||||||||
\(178\) | 6.59884e6 | + | 4.47589e7i | 0.0876997 | + | 0.594852i | ||||
\(179\) | 3.41444e7 | 0.444974 | 0.222487 | − | 0.974936i | \(-0.428583\pi\) | ||||
0.222487 | + | 0.974936i | \(0.428583\pi\) | |||||||
\(180\) | −2.50618e7 | + | 7.55397e6i | −0.320301 | + | 0.0965432i | ||||
\(181\) | 1.15782e8i | 1.45133i | 0.688047 | + | 0.725666i | \(0.258468\pi\) | ||||
−0.688047 | + | 0.725666i | \(0.741532\pi\) | |||||||
\(182\) | −1.20357e8 | + | 1.77444e7i | −1.47987 | + | 0.218178i | ||||
\(183\) | 2.04306e8 | 2.46434 | ||||||||
\(184\) | −2.29449e7 | − | 4.88482e7i | −0.271533 | − | 0.578077i | ||||
\(185\) | − | 2.83956e7i | − | 0.329724i | ||||||
\(186\) | 4.93940e7 | − | 7.28220e6i | 0.562832 | − | 0.0829789i | ||||
\(187\) | 5.36006e7i | 0.599410i | ||||||||
\(188\) | −2.63059e7 | − | 8.72751e7i | −0.288736 | − | 0.957939i | ||||
\(189\) | − | 3.14194e6i | − | 0.0338518i | ||||||
\(190\) | −1.29795e7 | + | 2.97541e7i | −0.137284 | + | 0.314709i | ||||
\(191\) | 7.47997e7i | 0.776754i | 0.921501 | + | 0.388377i | \(0.126964\pi\) | ||||
−0.921501 | + | 0.388377i | \(0.873036\pi\) | |||||||
\(192\) | −8.79872e7 | + | 1.06058e8i | −0.897150 | + | 1.08141i | ||||
\(193\) | 3.87375e7i | 0.387865i | 0.981015 | + | 0.193933i | \(0.0621243\pi\) | ||||
−0.981015 | + | 0.193933i | \(0.937876\pi\) | |||||||
\(194\) | 9.06101e6 | + | 6.14593e7i | 0.0890985 | + | 0.604340i | ||||
\(195\) | 7.96216e7i | 0.768971i | ||||||||
\(196\) | 1.20352e7 | − | 3.62757e6i | 0.114171 | − | 0.0344128i | ||||
\(197\) | 4.01567e7 | 0.374219 | 0.187110 | − | 0.982339i | \(-0.440088\pi\) | ||||
0.187110 | + | 0.982339i | \(0.440088\pi\) | |||||||
\(198\) | −8.01493e6 | − | 5.43639e7i | −0.0733790 | − | 0.497717i | ||||
\(199\) | − | 1.08568e8i | − | 0.976596i | −0.872677 | − | 0.488298i | \(-0.837618\pi\) | ||
0.872677 | − | 0.488298i | \(-0.162382\pi\) | |||||||
\(200\) | 9.03307e7 | − | 4.24300e7i | 0.798419 | − | 0.375031i | ||||
\(201\) | 1.02147e7 | 0.0887235 | ||||||||
\(202\) | 1.30158e8 | − | 1.91893e7i | 1.11107 | − | 0.163806i | ||||
\(203\) | −2.23337e8 | −1.87381 | ||||||||
\(204\) | −1.89370e8 | + | 5.70786e7i | −1.56173 | + | 0.470725i | ||||
\(205\) | 4.20592e7i | 0.340975i | ||||||||
\(206\) | −1.15683e7 | + | 1.70553e6i | −0.0922011 | + | 0.0135933i | ||||
\(207\) | 7.94110e7i | 0.622278i | ||||||||
\(208\) | 1.14318e8 | + | 1.72408e8i | 0.880830 | + | 1.32842i | ||||
\(209\) | −5.78220e7 | − | 3.60678e7i | −0.438108 | − | 0.273280i | ||||
\(210\) | 8.86258e6 | + | 6.01134e7i | 0.0660378 | + | 0.447924i | ||||
\(211\) | 1.61640e8 | 1.18457 | 0.592283 | − | 0.805730i | \(-0.298227\pi\) | ||||
0.592283 | + | 0.805730i | \(0.298227\pi\) | |||||||
\(212\) | −5.71531e6 | − | 1.89617e7i | −0.0411969 | − | 0.136679i | ||||
\(213\) | 2.30899e8 | 1.63717 | ||||||||
\(214\) | 1.08755e8 | − | 1.60338e7i | 0.758579 | − | 0.111838i | ||||
\(215\) | − | 2.20789e7i | − | 0.151510i | ||||||
\(216\) | −4.83558e6 | + | 2.27136e6i | −0.0326483 | + | 0.0153355i | ||||
\(217\) | − | 5.71972e7i | − | 0.379984i | ||||||
\(218\) | 2.79505e7 | + | 1.89583e8i | 0.182722 | + | 1.23937i | ||||
\(219\) | 6.13553e7 | 0.394728 | ||||||||
\(220\) | −8.08057e6 | − | 2.68089e7i | −0.0511638 | − | 0.169746i | ||||
\(221\) | 2.96903e8i | 1.85030i | ||||||||
\(222\) | 3.20833e7 | + | 2.17616e8i | 0.196809 | + | 1.33492i | ||||
\(223\) | −3.08329e8 | −1.86186 | −0.930931 | − | 0.365196i | \(-0.881002\pi\) | ||||
−0.930931 | + | 0.365196i | \(0.881002\pi\) | |||||||
\(224\) | 1.05499e8 | + | 1.17441e8i | 0.627163 | + | 0.698156i | ||||
\(225\) | −1.46848e8 | −0.859467 | ||||||||
\(226\) | 1.72129e7 | + | 1.16752e8i | 0.0991913 | + | 0.672798i | ||||
\(227\) | −3.74342e7 | −0.212412 | −0.106206 | − | 0.994344i | \(-0.533870\pi\) | ||||
−0.106206 | + | 0.994344i | \(0.533870\pi\) | |||||||
\(228\) | 6.58529e7 | − | 2.42692e8i | 0.367962 | − | 1.35607i | ||||
\(229\) | 1.46709e8 | 0.807294 | 0.403647 | − | 0.914915i | \(-0.367742\pi\) | ||||
0.403647 | + | 0.914915i | \(0.367742\pi\) | |||||||
\(230\) | 5.90176e6 | + | 4.00307e7i | 0.0319841 | + | 0.216943i | ||||
\(231\) | −1.27563e8 | −0.680901 | ||||||||
\(232\) | 1.61454e8 | + | 3.43726e8i | 0.848870 | + | 1.80719i | ||||
\(233\) | 8.76843e7 | 0.454126 | 0.227063 | − | 0.973880i | \(-0.427088\pi\) | ||||
0.227063 | + | 0.973880i | \(0.427088\pi\) | |||||||
\(234\) | −4.43961e7 | − | 3.01131e8i | −0.226511 | − | 1.53639i | ||||
\(235\) | 6.83429e7i | 0.343523i | ||||||||
\(236\) | 8.66927e7 | − | 2.61304e7i | 0.429329 | − | 0.129406i | ||||
\(237\) | −2.81106e8 | −1.37168 | ||||||||
\(238\) | 3.30479e7 | + | 2.24158e8i | 0.158900 | + | 1.07779i | ||||
\(239\) | − | 2.63970e8i | − | 1.25072i | −0.780334 | − | 0.625362i | \(-0.784951\pi\) | ||
0.780334 | − | 0.625362i | \(-0.215049\pi\) | |||||||
\(240\) | 8.61103e7 | − | 5.70969e7i | 0.402083 | − | 0.266608i | ||||
\(241\) | − | 1.44649e8i | − | 0.665667i | −0.942986 | − | 0.332834i | \(-0.891995\pi\) | ||
0.942986 | − | 0.332834i | \(-0.108005\pi\) | |||||||
\(242\) | −1.59961e8 | + | 2.35832e7i | −0.725537 | + | 0.106967i | ||||
\(243\) | 3.14084e8 | 1.40418 | ||||||||
\(244\) | −3.81043e8 | + | 1.14851e8i | −1.67923 | + | 0.506141i | ||||
\(245\) | −9.42446e6 | −0.0409426 | ||||||||
\(246\) | −4.75214e7 | − | 3.22330e8i | −0.203524 | − | 1.38047i | ||||
\(247\) | −3.20286e8 | − | 1.99786e8i | −1.35238 | − | 0.843579i | ||||
\(248\) | −8.80291e7 | + | 4.13488e7i | −0.366476 | + | 0.172140i | ||||
\(249\) | − | 2.44818e8i | − | 1.00495i | ||||||
\(250\) | −1.57944e8 | + | 2.32858e7i | −0.639310 | + | 0.0942542i | ||||
\(251\) | − | 4.87124e8i | − | 1.94438i | −0.234193 | − | 0.972190i | \(-0.575245\pi\) | ||
0.234193 | − | 0.972190i | \(-0.424755\pi\) | |||||||
\(252\) | −6.70371e7 | − | 2.22409e8i | −0.263884 | − | 0.875489i | ||||
\(253\) | −8.49468e7 | −0.329781 | ||||||||
\(254\) | 1.67607e8 | − | 2.47104e7i | 0.641762 | − | 0.0946156i | ||||
\(255\) | 1.48291e8 | 0.560045 | ||||||||
\(256\) | 1.04480e8 | − | 2.47268e8i | 0.389219 | − | 0.921145i | ||||
\(257\) | − | 4.07775e8i | − | 1.49849i | −0.662291 | − | 0.749247i | \(-0.730416\pi\) | ||
0.662291 | − | 0.749247i | \(-0.269584\pi\) | |||||||
\(258\) | 2.49462e7 | + | 1.69206e8i | 0.0904349 | + | 0.613405i | ||||
\(259\) | 2.51995e8 | 0.901244 | ||||||||
\(260\) | −4.47597e7 | − | 1.48499e8i | −0.157936 | − | 0.523983i | ||||
\(261\) | − | 5.58785e8i | − | 1.94537i | ||||||
\(262\) | 6.63126e7 | + | 4.49787e8i | 0.227794 | + | 1.54509i | ||||
\(263\) | − | 1.84282e8i | − | 0.624650i | −0.949975 | − | 0.312325i | \(-0.898892\pi\) | ||
0.949975 | − | 0.312325i | \(-0.101108\pi\) | |||||||
\(264\) | 9.22177e7 | + | 1.96326e8i | 0.308461 | + | 0.656695i | ||||
\(265\) | 1.48484e7i | 0.0490139i | ||||||||
\(266\) | −2.64050e8 | − | 1.15186e8i | −0.860202 | − | 0.375243i | ||||
\(267\) | 2.62771e8i | 0.844867i | ||||||||
\(268\) | −1.90510e7 | + | 5.74224e6i | −0.0604570 | + | 0.0182226i | ||||
\(269\) | − | 1.19232e7i | − | 0.0373474i | −0.999826 | − | 0.0186737i | \(-0.994056\pi\) | ||
0.999826 | − | 0.0186737i | \(-0.00594436\pi\) | |||||||
\(270\) | 3.96272e6 | − | 584228.i | 0.0122524 | − | 0.00180638i | ||||
\(271\) | 4.62328e8i | 1.41110i | 0.708661 | + | 0.705549i | \(0.249300\pi\) | ||||
−0.708661 | + | 0.705549i | \(0.750700\pi\) | |||||||
\(272\) | 3.21099e8 | − | 2.12910e8i | 0.967493 | − | 0.641513i | ||||
\(273\) | −7.06596e8 | −2.10185 | ||||||||
\(274\) | 4.83780e8 | − | 7.13242e7i | 1.42076 | − | 0.209464i | ||||
\(275\) | − | 1.57085e8i | − | 0.455481i | ||||||
\(276\) | −9.04588e7 | − | 3.00115e8i | −0.258982 | − | 0.859223i | ||||
\(277\) | 1.26408e8 | 0.357350 | 0.178675 | − | 0.983908i | \(-0.442819\pi\) | ||||
0.178675 | + | 0.983908i | \(0.442819\pi\) | |||||||
\(278\) | 5.76633e7 | + | 3.91121e8i | 0.160969 | + | 1.09183i | ||||
\(279\) | 1.43106e8 | 0.394497 | ||||||||
\(280\) | −5.03223e7 | − | 1.07133e8i | −0.136996 | − | 0.291656i | ||||
\(281\) | − | 3.46415e8i | − | 0.931374i | −0.884950 | − | 0.465687i | \(-0.845807\pi\) | ||
0.884950 | − | 0.465687i | \(-0.154193\pi\) | |||||||
\(282\) | −7.72185e7 | − | 5.23760e8i | −0.205045 | − | 1.39079i | ||||
\(283\) | − | 4.43927e7i | − | 0.116428i | −0.998304 | − | 0.0582142i | \(-0.981459\pi\) | ||
0.998304 | − | 0.0582142i | \(-0.0185406\pi\) | |||||||
\(284\) | −4.30642e8 | + | 1.29801e8i | −1.11558 | + | 0.336252i | ||||
\(285\) | −9.97847e7 | + | 1.59969e8i | −0.255333 | + | 0.409336i | ||||
\(286\) | 3.22124e8 | − | 4.74910e7i | 0.814219 | − | 0.120041i | ||||
\(287\) | −3.73251e8 | −0.931997 | ||||||||
\(288\) | −2.93835e8 | + | 2.63956e8i | −0.724820 | + | 0.651116i | ||||
\(289\) | 1.42626e8 | 0.347581 | ||||||||
\(290\) | −4.15284e7 | − | 2.81680e8i | −0.0999891 | − | 0.678209i | ||||
\(291\) | 3.60816e8i | 0.858343i | ||||||||
\(292\) | −1.14432e8 | + | 3.44912e7i | −0.268971 | + | 0.0810715i | ||||
\(293\) | 5.69115e8i | 1.32179i | 0.750477 | + | 0.660897i | \(0.229824\pi\) | ||||
−0.750477 | + | 0.660897i | \(0.770176\pi\) | |||||||
\(294\) | 7.22263e7 | − | 1.06484e7i | 0.165760 | − | 0.0244382i | ||||
\(295\) | −6.78869e7 | −0.153960 | ||||||||
\(296\) | −1.82171e8 | − | 3.87831e8i | −0.408281 | − | 0.869204i | ||||
\(297\) | 8.40906e6i | 0.0186252i | ||||||||
\(298\) | −3.42604e8 | + | 5.05105e7i | −0.749956 | + | 0.110567i | ||||
\(299\) | −4.70535e8 | −1.01799 | ||||||||
\(300\) | 5.54977e8 | − | 1.67278e8i | 1.18673 | − | 0.357695i | ||||
\(301\) | 1.95937e8 | 0.414128 | ||||||||
\(302\) | 7.31312e8 | − | 1.07818e8i | 1.52784 | − | 0.225251i | ||||
\(303\) | 7.64133e8 | 1.57805 | ||||||||
\(304\) | 1.36106e7 | + | 4.89655e8i | 0.0277856 | + | 0.999614i | ||||
\(305\) | 2.98385e8 | 0.602182 | ||||||||
\(306\) | −5.60840e8 | + | 8.26852e7i | −1.11896 | + | 0.164969i | ||||
\(307\) | −1.55277e8 | −0.306283 | −0.153141 | − | 0.988204i | \(-0.548939\pi\) | ||||
−0.153141 | + | 0.988204i | \(0.548939\pi\) | |||||||
\(308\) | 2.37914e8 | − | 7.17104e7i | 0.463972 | − | 0.139847i | ||||
\(309\) | −6.79156e7 | −0.130953 | ||||||||
\(310\) | 7.21391e7 | − | 1.06355e7i | 0.137532 | − | 0.0202765i | ||||
\(311\) | − | 7.16865e8i | − | 1.35138i | −0.737188 | − | 0.675688i | \(-0.763847\pi\) | ||
0.737188 | − | 0.675688i | \(-0.236153\pi\) | |||||||
\(312\) | 5.10810e8 | + | 1.08748e9i | 0.952178 | + | 2.02713i | ||||
\(313\) | −4.06883e8 | −0.750006 | −0.375003 | − | 0.927024i | \(-0.622358\pi\) | ||||
−0.375003 | + | 0.927024i | \(0.622358\pi\) | |||||||
\(314\) | −6.37400e8 | + | 9.39725e7i | −1.16187 | + | 0.171296i | ||||
\(315\) | 1.74163e8i | 0.313956i | ||||||||
\(316\) | 5.24281e8 | − | 1.58025e8i | 0.934672 | − | 0.281723i | ||||
\(317\) | − | 5.67181e8i | − | 1.00003i | −0.866016 | − | 0.500017i | \(-0.833327\pi\) | ||
0.866016 | − | 0.500017i | \(-0.166673\pi\) | |||||||
\(318\) | −1.67768e7 | − | 1.13794e8i | −0.0292559 | − | 0.198438i | ||||
\(319\) | 5.97738e8 | 1.03096 | ||||||||
\(320\) | −1.28504e8 | + | 1.54897e8i | −0.219226 | + | 0.264251i | ||||
\(321\) | 6.38480e8 | 1.07741 | ||||||||
\(322\) | −3.55249e8 | + | 5.23747e7i | −0.592976 | + | 0.0874231i | ||||
\(323\) | −3.72090e8 | + | 5.96514e8i | −0.614383 | + | 0.984944i | ||||
\(324\) | −6.00833e8 | + | 1.81099e8i | −0.981401 | + | 0.295808i | ||||
\(325\) | − | 8.70121e8i | − | 1.40601i | ||||||
\(326\) | 5.47291e6 | + | 3.71219e7i | 0.00874897 | + | 0.0593428i | ||||
\(327\) | 1.11301e9i | 1.76028i | ||||||||
\(328\) | 2.69830e8 | + | 5.74450e8i | 0.422212 | + | 0.898864i | ||||
\(329\) | −6.06504e8 | −0.938962 | ||||||||
\(330\) | −2.37198e7 | − | 1.60887e8i | −0.0363339 | − | 0.246447i | ||||
\(331\) | 4.02076e8 | 0.609410 | 0.304705 | − | 0.952447i | \(-0.401442\pi\) | ||||
0.304705 | + | 0.952447i | \(0.401442\pi\) | |||||||
\(332\) | 1.37626e8 | + | 4.56601e8i | 0.206403 | + | 0.684784i | ||||
\(333\) | 6.30485e8i | 0.935665i | ||||||||
\(334\) | −1.14196e9 | + | 1.68360e8i | −1.67702 | + | 0.247245i | ||||
\(335\) | 1.49184e7 | 0.0216803 | ||||||||
\(336\) | 5.06702e8 | + | 7.64179e8i | 0.728727 | + | 1.09903i | ||||
\(337\) | 8.59668e8i | 1.22356i | 0.791027 | + | 0.611781i | \(0.209547\pi\) | ||||
−0.791027 | + | 0.611781i | \(0.790453\pi\) | |||||||
\(338\) | 1.08197e9 | − | 1.59516e8i | 1.52408 | − | 0.224697i | ||||
\(339\) | 6.85430e8i | 0.955573i | ||||||||
\(340\) | −2.76571e8 | + | 8.33623e7i | −0.381620 | + | 0.115025i | ||||
\(341\) | 1.53082e8i | 0.209067i | ||||||||
\(342\) | 2.88192e8 | − | 6.60648e8i | 0.389574 | − | 0.893056i | ||||
\(343\) | − | 7.85023e8i | − | 1.05040i | ||||||
\(344\) | −1.41646e8 | − | 3.01556e8i | −0.187608 | − | 0.399405i | ||||
\(345\) | 2.35013e8i | 0.308123i | ||||||||
\(346\) | 7.51406e6 | + | 5.09666e7i | 0.00975233 | + | 0.0661484i | ||||
\(347\) | − | 1.28212e9i | − | 1.64731i | −0.567088 | − | 0.823657i | \(-0.691930\pi\) | ||
0.567088 | − | 0.823657i | \(-0.308070\pi\) | |||||||
\(348\) | 6.36524e8 | + | 2.11179e9i | 0.809631 | + | 2.68611i | ||||
\(349\) | −1.14608e9 | −1.44320 | −0.721598 | − | 0.692312i | \(-0.756592\pi\) | ||||
−0.721598 | + | 0.692312i | \(0.756592\pi\) | |||||||
\(350\) | −9.68520e7 | − | 6.56931e8i | −0.120745 | − | 0.818996i | ||||
\(351\) | 4.65793e7i | 0.0574934i | ||||||||
\(352\) | −2.82357e8 | − | 3.14319e8i | −0.345064 | − | 0.384124i | ||||
\(353\) | 5.84728e8 | 0.707526 | 0.353763 | − | 0.935335i | \(-0.384902\pi\) | ||||
0.353763 | + | 0.935335i | \(0.384902\pi\) | |||||||
\(354\) | 5.20265e8 | − | 7.67033e7i | 0.623323 | − | 0.0918972i | ||||
\(355\) | 3.37225e8 | 0.400055 | ||||||||
\(356\) | −1.47718e8 | − | 4.90084e8i | −0.173524 | − | 0.575699i | ||||
\(357\) | 1.31599e9i | 1.53079i | ||||||||
\(358\) | −3.82169e8 | + | 5.63436e7i | −0.440215 | + | 0.0649014i | ||||
\(359\) | 2.14308e8i | 0.244460i | 0.992502 | + | 0.122230i | \(0.0390045\pi\) | ||||
−0.992502 | + | 0.122230i | \(0.960995\pi\) | |||||||
\(360\) | 2.68045e8 | − | 1.25905e8i | 0.302795 | − | 0.142228i | ||||
\(361\) | −3.93114e8 | − | 8.02788e8i | −0.439788 | − | 0.898102i | ||||
\(362\) | −1.91058e8 | − | 1.29592e9i | −0.211683 | − | 1.43581i | ||||
\(363\) | −9.39100e8 | −1.03048 | ||||||||
\(364\) | 1.31784e9 | − | 3.97216e8i | 1.43222 | − | 0.431690i | ||||
\(365\) | 8.96085e7 | 0.0964548 | ||||||||
\(366\) | −2.28673e9 | + | 3.37136e8i | −2.43799 | + | 0.359435i | ||||
\(367\) | − | 7.04524e8i | − | 0.743985i | −0.928236 | − | 0.371993i | \(-0.878675\pi\) | ||
0.928236 | − | 0.371993i | \(-0.121325\pi\) | |||||||
\(368\) | 3.37422e8 | + | 5.08881e8i | 0.352945 | + | 0.532291i | ||||
\(369\) | − | 9.33867e8i | − | 0.967593i | ||||||
\(370\) | 4.68572e7 | + | 3.17824e8i | 0.0480917 | + | 0.326198i | ||||
\(371\) | −1.31771e8 | −0.133971 | ||||||||
\(372\) | −5.40836e8 | + | 1.63015e8i | −0.544710 | + | 0.164183i | ||||
\(373\) | 2.79872e7i | 0.0279241i | 0.999903 | + | 0.0139620i | \(0.00444440\pi\) | ||||
−0.999903 | + | 0.0139620i | \(0.995556\pi\) | |||||||
\(374\) | −8.84493e7 | − | 5.99937e8i | −0.0874266 | − | 0.593000i | ||||
\(375\) | −9.27257e8 | −0.908011 | ||||||||
\(376\) | 4.38452e8 | + | 9.33437e8i | 0.425368 | + | 0.905581i | ||||
\(377\) | 3.31098e9 | 3.18245 | ||||||||
\(378\) | 5.18468e6 | + | 3.51668e7i | 0.00493743 | + | 0.0334897i | ||||
\(379\) | 1.12336e9 | 1.05994 | 0.529972 | − | 0.848015i | \(-0.322202\pi\) | ||||
0.529972 | + | 0.848015i | \(0.322202\pi\) | |||||||
\(380\) | 9.61771e7 | − | 3.54447e8i | 0.0899143 | − | 0.331367i | ||||
\(381\) | 9.83989e8 | 0.911492 | ||||||||
\(382\) | −1.23431e8 | − | 8.37213e8i | −0.113293 | − | 0.768447i | ||||
\(383\) | −1.05996e8 | −0.0964039 | −0.0482020 | − | 0.998838i | \(-0.515349\pi\) | ||||
−0.0482020 | + | 0.998838i | \(0.515349\pi\) | |||||||
\(384\) | 8.09803e8 | − | 1.33227e9i | 0.729827 | − | 1.20070i | ||||
\(385\) | −1.86304e8 | −0.166383 | ||||||||
\(386\) | −6.39228e7 | − | 4.33578e8i | −0.0565718 | − | 0.383717i | ||||
\(387\) | 4.90231e8i | 0.429944i | ||||||||
\(388\) | −2.02835e8 | − | 6.72945e8i | −0.176291 | − | 0.584882i | ||||
\(389\) | −1.49288e8 | −0.128588 | −0.0642939 | − | 0.997931i | \(-0.520480\pi\) | ||||
−0.0642939 | + | 0.997931i | \(0.520480\pi\) | |||||||
\(390\) | −1.31388e8 | − | 8.91182e8i | −0.112158 | − | 0.760747i | ||||
\(391\) | 8.76345e8i | 0.741407i | ||||||||
\(392\) | −1.28720e8 | + | 6.04623e7i | −0.107931 | + | 0.0506971i | ||||
\(393\) | 2.64062e9i | 2.19448i | ||||||||
\(394\) | −4.49463e8 | + | 6.62648e7i | −0.370218 | + | 0.0545816i | ||||
\(395\) | −4.10551e8 | −0.335180 | ||||||||
\(396\) | 1.79418e8 | + | 5.95255e8i | 0.145189 | + | 0.481692i | ||||
\(397\) | −1.94958e9 | −1.56378 | −0.781889 | − | 0.623417i | \(-0.785744\pi\) | ||||
−0.781889 | + | 0.623417i | \(0.785744\pi\) | |||||||
\(398\) | 1.79153e8 | + | 1.21517e9i | 0.142441 | + | 0.966152i | ||||
\(399\) | −1.41964e9 | − | 8.85531e8i | −1.11885 | − | 0.697909i | ||||
\(400\) | −9.41031e8 | + | 6.23966e8i | −0.735180 | + | 0.487474i | ||||
\(401\) | 2.46897e9i | 1.91210i | 0.293201 | + | 0.956051i | \(0.405280\pi\) | ||||
−0.293201 | + | 0.956051i | \(0.594720\pi\) | |||||||
\(402\) | −1.14330e8 | + | 1.68558e7i | −0.0877747 | + | 0.0129407i | ||||
\(403\) | 8.47950e8i | 0.645360i | ||||||||
\(404\) | −1.42516e9 | + | 4.29561e8i | −1.07529 | + | 0.324108i | ||||
\(405\) | 4.70498e8 | 0.351937 | ||||||||
\(406\) | 2.49975e9 | − | 3.68541e8i | 1.85377 | − | 0.273303i | ||||
\(407\) | −6.74437e8 | −0.495862 | ||||||||
\(408\) | 2.02537e9 | − | 9.51354e8i | 1.47637 | − | 0.693476i | ||||
\(409\) | − | 1.79791e9i | − | 1.29938i | −0.760199 | − | 0.649690i | \(-0.774899\pi\) | ||
0.760199 | − | 0.649690i | \(-0.225101\pi\) | |||||||
\(410\) | −6.94042e7 | − | 4.70757e8i | −0.0497327 | − | 0.337329i | ||||
\(411\) | 2.84018e9 | 2.01790 | ||||||||
\(412\) | 1.26667e8 | − | 3.81791e7i | 0.0892325 | − | 0.0268959i | ||||
\(413\) | − | 6.02457e8i | − | 0.420824i | ||||||
\(414\) | −1.31040e8 | − | 8.88825e8i | −0.0907620 | − | 0.615623i | ||||
\(415\) | − | 3.57553e8i | − | 0.245568i | ||||||
\(416\) | −1.56403e9 | − | 1.74107e9i | −1.06517 | − | 1.18574i | ||||
\(417\) | 2.29620e9i | 1.55072i | ||||||||
\(418\) | 7.06702e8 | + | 3.08282e8i | 0.473282 | + | 0.206458i | ||||
\(419\) | 6.78355e8i | 0.450514i | 0.974299 | + | 0.225257i | \(0.0723221\pi\) | ||||
−0.974299 | + | 0.225257i | \(0.927678\pi\) | |||||||
\(420\) | −1.98393e8 | − | 6.58208e8i | −0.130663 | − | 0.433502i | ||||
\(421\) | − | 2.06412e9i | − | 1.34818i | −0.738651 | − | 0.674088i | \(-0.764537\pi\) | ||
0.738651 | − | 0.674088i | \(-0.235463\pi\) | |||||||
\(422\) | −1.80919e9 | + | 2.66730e8i | −1.17190 | + | 0.172774i | ||||
\(423\) | − | 1.51746e9i | − | 0.974823i | ||||||
\(424\) | 9.52595e7 | + | 2.02802e8i | 0.0606915 | + | 0.129208i | ||||
\(425\) | −1.62055e9 | −1.02400 | ||||||||
\(426\) | −2.58439e9 | + | 3.81019e8i | −1.61966 | + | 0.238789i | ||||
\(427\) | 2.64799e9i | 1.64596i | ||||||||
\(428\) | −1.19080e9 | + | 3.58925e8i | −0.734154 | + | 0.221284i | ||||
\(429\) | 1.89113e9 | 1.15643 | ||||||||
\(430\) | 3.64336e7 | + | 2.47123e8i | 0.0220985 | + | 0.149890i | ||||
\(431\) | 1.09723e9 | 0.660128 | 0.330064 | − | 0.943959i | \(-0.392930\pi\) | ||||
0.330064 | + | 0.943959i | \(0.392930\pi\) | |||||||
\(432\) | 5.03752e7 | − | 3.34021e7i | 0.0300624 | − | 0.0199334i | ||||
\(433\) | 6.96119e8i | 0.412074i | 0.978544 | + | 0.206037i | \(0.0660568\pi\) | ||||
−0.978544 | + | 0.206037i | \(0.933943\pi\) | |||||||
\(434\) | 9.43842e7 | + | 6.40192e8i | 0.0554224 | + | 0.375921i | ||||
\(435\) | − | 1.65369e9i | − | 0.963258i | ||||||
\(436\) | −6.25683e8 | − | 2.07583e9i | −0.361536 | − | 1.19947i | ||||
\(437\) | −9.45362e8 | − | 5.89692e8i | −0.541892 | − | 0.338018i | ||||
\(438\) | −6.86733e8 | + | 1.01246e8i | −0.390507 | + | 0.0575728i | ||||
\(439\) | 3.36456e8 | 0.189803 | 0.0949014 | − | 0.995487i | \(-0.469746\pi\) | ||||
0.0949014 | + | 0.995487i | \(0.469746\pi\) | |||||||
\(440\) | 1.34682e8 | + | 2.86730e8i | 0.0753748 | + | 0.160468i | ||||
\(441\) | 2.09257e8 | 0.116184 | ||||||||
\(442\) | −4.89936e8 | − | 3.32315e9i | −0.269874 | − | 1.83051i | ||||
\(443\) | − | 2.21727e8i | − | 0.121173i | −0.998163 | − | 0.0605863i | \(-0.980703\pi\) | ||
0.998163 | − | 0.0605863i | \(-0.0192970\pi\) | |||||||
\(444\) | −7.18199e8 | − | 2.38277e9i | −0.389408 | − | 1.29194i | ||||
\(445\) | 3.83773e8i | 0.206450i | ||||||||
\(446\) | 3.45104e9 | − | 5.08790e8i | 1.84195 | − | 0.271561i | ||||
\(447\) | −2.01137e9 | −1.06516 | ||||||||
\(448\) | −1.37462e9 | − | 1.14040e9i | −0.722285 | − | 0.599215i | ||||
\(449\) | 1.22306e9i | 0.637656i | 0.947813 | + | 0.318828i | \(0.103289\pi\) | ||||
−0.947813 | + | 0.318828i | \(0.896711\pi\) | |||||||
\(450\) | 1.64363e9 | − | 2.42322e8i | 0.850276 | − | 0.125357i | ||||
\(451\) | 9.98968e8 | 0.512783 | ||||||||
\(452\) | −3.85318e8 | − | 1.27837e9i | −0.196261 | − | 0.651136i | ||||
\(453\) | 4.29340e9 | 2.16999 | ||||||||
\(454\) | 4.18991e8 | − | 6.17723e7i | 0.210140 | − | 0.0309812i | ||||
\(455\) | −1.03197e9 | −0.513603 | ||||||||
\(456\) | −3.36594e8 | + | 2.82505e9i | −0.166238 | + | 1.39524i | ||||
\(457\) | 2.73191e9 | 1.33894 | 0.669469 | − | 0.742840i | \(-0.266522\pi\) | ||||
0.669469 | + | 0.742840i | \(0.266522\pi\) | |||||||
\(458\) | −1.64207e9 | + | 2.42092e8i | −0.798661 | + | 0.117747i | ||||
\(459\) | 8.67512e7 | 0.0418727 | ||||||||
\(460\) | −1.32114e8 | − | 4.38313e8i | −0.0632841 | − | 0.209958i | ||||
\(461\) | −1.69276e9 | −0.804715 | −0.402357 | − | 0.915483i | \(-0.631809\pi\) | ||||
−0.402357 | + | 0.915483i | \(0.631809\pi\) | |||||||
\(462\) | 1.42778e9 | − | 2.10499e8i | 0.673619 | − | 0.0993124i | ||||
\(463\) | − | 1.38820e9i | − | 0.650007i | −0.945713 | − | 0.325003i | \(-0.894635\pi\) | ||
0.945713 | − | 0.325003i | \(-0.105365\pi\) | |||||||
\(464\) | −2.37431e9 | − | 3.58080e9i | −1.10338 | − | 1.66405i | ||||
\(465\) | 4.23515e8 | 0.195337 | ||||||||
\(466\) | −9.81426e8 | + | 1.44693e8i | −0.449269 | + | 0.0662363i | ||||
\(467\) | 2.94927e9i | 1.34000i | 0.742360 | + | 0.670001i | \(0.233706\pi\) | ||||
−0.742360 | + | 0.670001i | \(0.766294\pi\) | |||||||
\(468\) | 9.93826e8 | + | 3.29722e9i | 0.448177 | + | 1.48692i | ||||
\(469\) | 1.32392e8i | 0.0592593i | ||||||||
\(470\) | −1.12776e8 | − | 7.64943e8i | −0.0501044 | − | 0.339850i | ||||
\(471\) | −3.74206e9 | −1.65020 | ||||||||
\(472\) | −9.27208e8 | + | 4.35526e8i | −0.405864 | + | 0.190641i | ||||
\(473\) | −5.24406e8 | −0.227852 | ||||||||
\(474\) | 3.14635e9 | − | 4.63869e8i | 1.35701 | − | 0.200065i | ||||
\(475\) | 1.09047e9 | − | 1.74818e9i | 0.466858 | − | 0.748441i | ||||
\(476\) | −7.39792e8 | − | 2.45441e9i | −0.314402 | − | 1.04309i | ||||
\(477\) | − | 3.29688e8i | − | 0.139088i | ||||||
\(478\) | 4.35591e8 | + | 2.95454e9i | 0.182424 | + | 1.23735i | ||||
\(479\) | − | 3.36401e9i | − | 1.39857i | −0.714845 | − | 0.699283i | \(-0.753503\pi\) | ||
0.714845 | − | 0.699283i | \(-0.246497\pi\) | |||||||
\(480\) | −8.69590e8 | + | 7.81165e8i | −0.358897 | + | 0.322403i | ||||
\(481\) | −3.73583e9 | −1.53066 | ||||||||
\(482\) | 2.38694e8 | + | 1.61902e9i | 0.0970905 | + | 0.658549i | ||||
\(483\) | −2.08560e9 | −0.842202 | ||||||||
\(484\) | 1.75148e9 | − | 5.27920e8i | 0.702177 | − | 0.211646i | ||||
\(485\) | 5.26966e8i | 0.209743i | ||||||||
\(486\) | −3.51545e9 | + | 5.18287e8i | −1.38917 | + | 0.204806i | ||||
\(487\) | 4.06977e8 | 0.159668 | 0.0798341 | − | 0.996808i | \(-0.474561\pi\) | ||||
0.0798341 | + | 0.996808i | \(0.474561\pi\) | |||||||
\(488\) | 4.07538e9 | − | 1.91428e9i | 1.58745 | − | 0.745651i | ||||
\(489\) | 2.17936e8i | 0.0842844i | ||||||||
\(490\) | 1.05485e8 | − | 1.55518e7i | 0.0405047 | − | 0.00597165i | ||||
\(491\) | 1.83223e9i | 0.698547i | 0.937021 | + | 0.349274i | \(0.113572\pi\) | ||||
−0.937021 | + | 0.349274i | \(0.886428\pi\) | |||||||
\(492\) | 1.06379e9 | + | 3.52933e9i | 0.402696 | + | 1.33602i | ||||
\(493\) | − | 6.16650e9i | − | 2.31779i | ||||||
\(494\) | 3.91455e9 | + | 1.70763e9i | 1.46096 | + | 0.637307i | ||||
\(495\) | − | 4.66129e8i | − | 0.172738i | ||||||
\(496\) | 9.17053e8 | − | 6.08067e8i | 0.337449 | − | 0.223751i | ||||
\(497\) | 2.99267e9i | 1.09348i | ||||||||
\(498\) | 4.03988e8 | + | 2.74018e9i | 0.146577 | + | 0.994207i | ||||
\(499\) | 3.10292e9i | 1.11794i | 0.829188 | + | 0.558969i | \(0.188803\pi\) | ||||
−0.829188 | + | 0.558969i | \(0.811197\pi\) | |||||||
\(500\) | 1.72939e9 | − | 5.21262e8i | 0.618726 | − | 0.186492i | ||||
\(501\) | −6.70424e9 | −2.38187 | ||||||||
\(502\) | 8.03829e8 | + | 5.45224e9i | 0.283596 | + | 1.92359i | ||||
\(503\) | − | 3.92897e9i | − | 1.37654i | −0.725452 | − | 0.688272i | \(-0.758369\pi\) | ||
0.725452 | − | 0.688272i | \(-0.241631\pi\) | |||||||
\(504\) | 1.11734e9 | + | 2.37874e9i | 0.388756 | + | 0.827638i | ||||
\(505\) | 1.11600e9 | 0.385608 | ||||||||
\(506\) | 9.50786e8 | − | 1.40175e8i | 0.326254 | − | 0.0481000i | ||||
\(507\) | 6.35206e9 | 2.16465 | ||||||||
\(508\) | −1.83520e9 | + | 5.53154e8i | −0.621099 | + | 0.187208i | ||||
\(509\) | − | 1.02125e8i | − | 0.0343256i | −0.999853 | − | 0.0171628i | \(-0.994537\pi\) | ||
0.999853 | − | 0.0171628i | \(-0.00546336\pi\) | |||||||
\(510\) | −1.65978e9 | + | 2.44702e8i | −0.554056 | + | 0.0816851i | ||||
\(511\) | 7.95223e8i | 0.263643i | ||||||||
\(512\) | −7.61388e8 | + | 2.94001e9i | −0.250704 | + | 0.968064i | ||||
\(513\) | −5.83748e7 | + | 9.35833e7i | −0.0190904 | + | 0.0306047i | ||||
\(514\) | 6.72892e8 | + | 4.56412e9i | 0.218562 | + | 1.48247i | ||||
\(515\) | −9.91897e7 | −0.0319994 | ||||||||
\(516\) | −5.58432e8 | − | 1.85271e9i | −0.178936 | − | 0.593655i | ||||
\(517\) | 1.62324e9 | 0.516615 | ||||||||
\(518\) | −2.82051e9 | + | 4.15830e8i | −0.891606 | + | 0.131450i | ||||
\(519\) | 2.99216e8i | 0.0939504i | ||||||||
\(520\) | 7.46029e8 | + | 1.58825e9i | 0.232672 | + | 0.495344i | ||||
\(521\) | − | 6.06005e9i | − | 1.87735i | −0.344810 | − | 0.938673i | \(-0.612057\pi\) | ||
0.344810 | − | 0.938673i | \(-0.387943\pi\) | |||||||
\(522\) | 9.22081e8 | + | 6.25432e9i | 0.283741 | + | 1.92457i | ||||
\(523\) | −6.20968e9 | −1.89807 | −0.949037 | − | 0.315164i | \(-0.897941\pi\) | ||||
−0.949037 | + | 0.315164i | \(0.897941\pi\) | |||||||
\(524\) | −1.48444e9 | − | 4.92492e9i | −0.450715 | − | 1.49534i | ||||
\(525\) | − | 3.85672e9i | − | 1.16322i | ||||||
\(526\) | 3.04093e8 | + | 2.06261e9i | 0.0911080 | + | 0.617970i | ||||
\(527\) | 1.57926e9 | 0.470019 | ||||||||
\(528\) | −1.35613e9 | − | 2.04525e9i | −0.400944 | − | 0.604682i | ||||
\(529\) | 2.01598e9 | 0.592096 | ||||||||
\(530\) | −2.45022e7 | − | 1.66194e8i | −0.00714890 | − | 0.0484898i | ||||
\(531\) | 1.50733e9 | 0.436897 | ||||||||
\(532\) | 3.14551e9 | + | 8.53516e8i | 0.905734 | + | 0.245765i | ||||
\(533\) | 5.53346e9 | 1.58289 | ||||||||
\(534\) | −4.33613e8 | − | 2.94112e9i | −0.123227 | − | 0.835832i | ||||
\(535\) | 9.32490e8 | 0.263273 | ||||||||
\(536\) | 2.03757e8 | − | 9.57084e7i | 0.0571526 | − | 0.0268456i | ||||
\(537\) | −2.24365e9 | −0.625236 | ||||||||
\(538\) | 1.96751e7 | + | 1.33453e8i | 0.00544728 | + | 0.0369480i | ||||
\(539\) | 2.23845e8i | 0.0615724i | ||||||||
\(540\) | −4.33895e7 | + | 1.30782e7i | −0.0118579 | + | 0.00357412i | ||||
\(541\) | −7.04766e9 | −1.91362 | −0.956808 | − | 0.290722i | \(-0.906105\pi\) | ||||
−0.956808 | + | 0.290722i | \(0.906105\pi\) | |||||||
\(542\) | −7.62912e8 | − | 5.17470e9i | −0.205815 | − | 1.39601i | ||||
\(543\) | − | 7.60809e9i | − | 2.03928i | ||||||
\(544\) | −3.24264e9 | + | 2.91291e9i | −0.863579 | + | 0.775765i | ||||
\(545\) | 1.62553e9i | 0.430138i | ||||||||
\(546\) | 7.90873e9 | − | 1.16599e9i | 2.07937 | − | 0.306564i | ||||
\(547\) | 5.59729e9 | 1.46225 | 0.731126 | − | 0.682243i | \(-0.238995\pi\) | ||||
0.731126 | + | 0.682243i | \(0.238995\pi\) | |||||||
\(548\) | −5.29712e9 | + | 1.59662e9i | −1.37502 | + | 0.414448i | ||||
\(549\) | −6.62522e9 | −1.70882 | ||||||||
\(550\) | 2.59214e8 | + | 1.75821e9i | 0.0664339 | + | 0.450610i | ||||
\(551\) | 6.65215e9 | + | 4.14944e9i | 1.69407 | + | 1.05672i | ||||
\(552\) | 1.50772e9 | + | 3.20983e9i | 0.381534 | + | 0.812261i | ||||
\(553\) | − | 3.64341e9i | − | 0.916156i | ||||||
\(554\) | −1.41484e9 | + | 2.08592e8i | −0.353529 | + | 0.0521211i | ||||
\(555\) | 1.86589e9i | 0.463298i | ||||||||
\(556\) | −1.29082e9 | − | 4.28255e9i | −0.318496 | − | 1.05667i | ||||
\(557\) | 1.32642e9 | 0.325228 | 0.162614 | − | 0.986690i | \(-0.448007\pi\) | ||||
0.162614 | + | 0.986690i | \(0.448007\pi\) | |||||||
\(558\) | −1.60175e9 | + | 2.36147e8i | −0.390278 | + | 0.0575391i | ||||
\(559\) | −2.90477e9 | −0.703349 | ||||||||
\(560\) | 7.40030e8 | + | 1.11607e9i | 0.178070 | + | 0.268555i | ||||
\(561\) | − | 3.52212e9i | − | 0.842236i | ||||||
\(562\) | 5.71637e8 | + | 3.87732e9i | 0.135845 | + | 0.921414i | ||||
\(563\) | −4.44310e9 | −1.04932 | −0.524659 | − | 0.851313i | \(-0.675807\pi\) | ||||
−0.524659 | + | 0.851313i | \(0.675807\pi\) | |||||||
\(564\) | 1.72857e9 | + | 5.73488e9i | 0.405705 | + | 1.34601i | ||||
\(565\) | 1.00106e9i | 0.233502i | ||||||||
\(566\) | 7.32547e7 | + | 4.96875e8i | 0.0169816 | + | 0.115183i | ||||
\(567\) | 4.17539e9i | 0.961959i | ||||||||
\(568\) | 4.60586e9 | − | 2.16345e9i | 1.05461 | − | 0.495368i | ||||
\(569\) | 5.62317e9i | 1.27964i | 0.768525 | + | 0.639820i | \(0.220991\pi\) | ||||
−0.768525 | + | 0.639820i | \(0.779009\pi\) | |||||||
\(570\) | 8.52888e8 | − | 1.95515e9i | 0.192899 | − | 0.442200i | ||||
\(571\) | 7.89864e9i | 1.77552i | 0.460305 | + | 0.887761i | \(0.347740\pi\) | ||||
−0.460305 | + | 0.887761i | \(0.652260\pi\) | |||||||
\(572\) | −3.52707e9 | + | 1.06311e9i | −0.788004 | + | 0.237515i | ||||
\(573\) | − | 4.91512e9i | − | 1.09142i | ||||||
\(574\) | 4.17770e9 | − | 6.15922e8i | 0.922030 | − | 0.135936i | ||||
\(575\) | − | 2.56826e9i | − | 0.563381i | ||||||
\(576\) | 2.85325e9 | − | 3.43926e9i | 0.622101 | − | 0.749871i | ||||
\(577\) | −8.57711e9 | −1.85877 | −0.929385 | − | 0.369112i | \(-0.879662\pi\) | ||||
−0.929385 | + | 0.369112i | \(0.879662\pi\) | |||||||
\(578\) | −1.59637e9 | + | 2.35355e8i | −0.343864 | + | 0.0506963i | ||||
\(579\) | − | 2.54546e9i | − | 0.544993i | ||||||
\(580\) | 9.29632e8 | + | 3.08424e9i | 0.197840 | + | 0.656373i | ||||
\(581\) | 3.17308e9 | 0.671218 | ||||||||
\(582\) | −5.95403e8 | − | 4.03852e9i | −0.125193 | − | 0.849164i | ||||
\(583\) | 3.52671e8 | 0.0737107 | ||||||||
\(584\) | 1.22388e9 | − | 5.74880e8i | 0.254270 | − | 0.119435i | ||||
\(585\) | − | 2.58197e9i | − | 0.533219i | ||||||
\(586\) | −9.39128e8 | − | 6.36995e9i | −0.192789 | − | 1.30766i | ||||
\(587\) | 6.85625e9i | 1.39912i | 0.714576 | + | 0.699558i | \(0.246620\pi\) | ||||
−0.714576 | + | 0.699558i | \(0.753380\pi\) | |||||||
\(588\) | −7.90837e8 | + | 2.38369e8i | −0.160423 | + | 0.0483536i | ||||
\(589\) | −1.06268e9 | + | 1.70363e9i | −0.214289 | + | 0.343536i | ||||
\(590\) | 7.59839e8 | − | 1.12024e8i | 0.152314 | − | 0.0224558i | ||||
\(591\) | −2.63871e9 | −0.525819 | ||||||||
\(592\) | 2.67897e9 | + | 4.04028e9i | 0.530692 | + | 0.800359i | ||||
\(593\) | 4.59277e9 | 0.904448 | 0.452224 | − | 0.891904i | \(-0.350631\pi\) | ||||
0.452224 | + | 0.891904i | \(0.350631\pi\) | |||||||
\(594\) | −1.38763e7 | − | 9.41203e7i | −0.00271656 | − | 0.0184260i | ||||
\(595\) | 1.92199e9i | 0.374060i | ||||||||
\(596\) | 3.75133e9 | − | 1.13070e9i | 0.725810 | − | 0.218769i | ||||
\(597\) | 7.13403e9i | 1.37222i | ||||||||
\(598\) | 5.26657e9 | − | 7.76456e8i | 1.00710 | − | 0.148478i | ||||
\(599\) | −2.63520e9 | −0.500980 | −0.250490 | − | 0.968119i | \(-0.580592\pi\) | ||||
−0.250490 | + | 0.968119i | \(0.580592\pi\) | |||||||
\(600\) | −5.93567e9 | + | 2.78809e9i | −1.12186 | + | 0.526960i | ||||
\(601\) | − | 8.74575e7i | − | 0.0164337i | −0.999966 | − | 0.00821687i | \(-0.997384\pi\) | ||
0.999966 | − | 0.00821687i | \(-0.00261554\pi\) | |||||||
\(602\) | −2.19307e9 | + | 3.23327e8i | −0.409699 | + | 0.0604024i | ||||
\(603\) | −3.31242e8 | −0.0615226 | ||||||||
\(604\) | −8.00745e9 | + | 2.41355e9i | −1.47865 | + | 0.445685i | ||||
\(605\) | −1.37154e9 | −0.251805 | ||||||||
\(606\) | −8.55273e9 | + | 1.26094e9i | −1.56117 | + | 0.230165i | ||||
\(607\) | −1.28108e9 | −0.232496 | −0.116248 | − | 0.993220i | \(-0.537087\pi\) | ||||
−0.116248 | + | 0.993220i | \(0.537087\pi\) | |||||||
\(608\) | −9.60345e8 | − | 5.45811e9i | −0.173287 | − | 0.984871i | ||||
\(609\) | 1.46756e10 | 2.63290 | ||||||||
\(610\) | −3.33974e9 | + | 4.92381e8i | −0.595742 | + | 0.0878308i | ||||
\(611\) | 8.99143e9 | 1.59472 | ||||||||
\(612\) | 6.14088e9 | − | 1.85094e9i | 1.08293 | − | 0.326410i | ||||
\(613\) | 2.05372e9 | 0.360105 | 0.180053 | − | 0.983657i | \(-0.442373\pi\) | ||||
0.180053 | + | 0.983657i | \(0.442373\pi\) | |||||||
\(614\) | 1.73797e9 | − | 2.56231e8i | 0.303008 | − | 0.0446727i | ||||
\(615\) | − | 2.76373e9i | − | 0.479107i | ||||||
\(616\) | −2.54457e9 | + | 1.19523e9i | −0.438613 | + | 0.206024i | ||||
\(617\) | 2.58182e8 | 0.0442514 | 0.0221257 | − | 0.999755i | \(-0.492957\pi\) | ||||
0.0221257 | + | 0.999755i | \(0.492957\pi\) | |||||||
\(618\) | 7.60161e8 | − | 1.12071e8i | 0.129553 | − | 0.0191001i | ||||
\(619\) | − | 5.13102e9i | − | 0.869533i | −0.900543 | − | 0.434766i | \(-0.856831\pi\) | ||
0.900543 | − | 0.434766i | \(-0.143169\pi\) | |||||||
\(620\) | −7.89882e8 | + | 2.38081e8i | −0.133104 | + | 0.0401194i | ||||
\(621\) | 1.37484e8i | 0.0230373i | ||||||||
\(622\) | 1.18294e9 | + | 8.02367e9i | 0.197104 | + | 1.33692i | ||||
\(623\) | −3.40576e9 | −0.564295 | ||||||||
\(624\) | −7.51186e9 | − | 1.13290e10i | −1.23766 | − | 1.86657i | ||||
\(625\) | 4.02974e9 | 0.660232 | ||||||||
\(626\) | 4.55413e9 | − | 6.71420e8i | 0.741985 | − | 0.109392i | ||||
\(627\) | 3.79950e9 | + | 2.37003e9i | 0.615589 | + | 0.383988i | ||||
\(628\) | 6.97917e9 | − | 2.10362e9i | 1.12446 | − | 0.338928i | ||||
\(629\) | 6.95776e9i | 1.11479i | ||||||||
\(630\) | −2.87396e8 | − | 1.94936e9i | −0.0457919 | − | 0.310599i | ||||
\(631\) | 1.83720e9i | 0.291108i | 0.989350 | + | 0.145554i | \(0.0464965\pi\) | ||||
−0.989350 | + | 0.145554i | \(0.953504\pi\) | |||||||
\(632\) | −5.60736e9 | + | 2.63388e9i | −0.883586 | + | 0.415036i | ||||
\(633\) | −1.06214e10 | −1.66444 | ||||||||
\(634\) | 9.35937e8 | + | 6.34830e9i | 0.145859 | + | 0.989339i | ||||
\(635\) | 1.43710e9 | 0.222730 | ||||||||
\(636\) | 3.75555e8 | + | 1.24598e9i | 0.0578860 | + | 0.192049i | ||||
\(637\) | 1.23991e9i | 0.190066i | ||||||||
\(638\) | −6.69032e9 | + | 9.86360e8i | −1.01994 | + | 0.150371i | ||||
\(639\) | −7.48760e9 | −1.13525 | ||||||||
\(640\) | 1.18270e9 | − | 1.94577e9i | 0.178339 | − | 0.293400i | ||||
\(641\) | − | 1.97789e9i | − | 0.296619i | −0.988941 | − | 0.148309i | \(-0.952617\pi\) | ||
0.988941 | − | 0.148309i | \(-0.0473832\pi\) | |||||||
\(642\) | −7.14633e9 | + | 1.05359e9i | −1.06589 | + | 0.157145i | ||||
\(643\) | − | 9.86193e9i | − | 1.46293i | −0.681879 | − | 0.731465i | \(-0.738837\pi\) | ||
0.681879 | − | 0.731465i | \(-0.261163\pi\) | |||||||
\(644\) | 3.88978e9 | − | 1.17243e9i | 0.573884 | − | 0.172976i | ||||
\(645\) | 1.45081e9i | 0.212889i | ||||||||
\(646\) | 3.18036e9 | − | 7.29062e9i | 0.464154 | − | 1.06402i | ||||
\(647\) | − | 9.10174e8i | − | 0.132117i | −0.997816 | − | 0.0660586i | \(-0.978958\pi\) | ||
0.997816 | − | 0.0660586i | \(-0.0210424\pi\) | |||||||
\(648\) | 6.42612e9 | − | 3.01846e9i | 0.927761 | − | 0.435786i | ||||
\(649\) | 1.61241e9i | 0.231537i | ||||||||
\(650\) | 1.43583e9 | + | 9.73902e9i | 0.205072 | + | 1.39097i | ||||
\(651\) | 3.75845e9i | 0.533919i | ||||||||
\(652\) | −1.22514e8 | − | 4.06463e8i | −0.0173108 | − | 0.0574321i | ||||
\(653\) | −9.48723e9 | −1.33335 | −0.666674 | − | 0.745350i | \(-0.732282\pi\) | ||||
−0.666674 | + | 0.745350i | \(0.732282\pi\) | |||||||
\(654\) | −1.83664e9 | − | 1.24576e10i | −0.256744 | − | 1.74145i | ||||
\(655\) | 3.85658e9i | 0.536238i | ||||||||
\(656\) | −3.96806e9 | − | 5.98440e9i | −0.548801 | − | 0.827670i | ||||
\(657\) | −1.98963e9 | −0.273712 | ||||||||
\(658\) | 6.78843e9 | − | 1.00082e9i | 0.928920 | − | 0.136952i | ||||
\(659\) | −7.74112e9 | −1.05367 | −0.526836 | − | 0.849967i | \(-0.676622\pi\) | ||||
−0.526836 | + | 0.849967i | \(0.676622\pi\) | |||||||
\(660\) | 5.30977e8 | + | 1.76162e9i | 0.0718906 | + | 0.238512i | ||||
\(661\) | 1.37129e9i | 0.184682i | 0.995727 | + | 0.0923411i | \(0.0294350\pi\) | ||||
−0.995727 | + | 0.0923411i | \(0.970565\pi\) | |||||||
\(662\) | −4.50032e9 | + | 6.63487e8i | −0.602893 | + | 0.0888852i | ||||
\(663\) | − | 1.95096e10i | − | 2.59987i | ||||||
\(664\) | −2.29387e9 | − | 4.88351e9i | −0.304075 | − | 0.647356i | ||||
\(665\) | −2.07335e9 | − | 1.29330e9i | −0.273399 | − | 0.170539i | ||||
\(666\) | −1.04040e9 | − | 7.05685e9i | −0.136471 | − | 0.925659i | ||||
\(667\) | 9.77274e9 | 1.27519 | ||||||||
\(668\) | 1.25038e10 | − | 3.76882e9i | 1.62302 | − | 0.489202i | ||||
\(669\) | 2.02604e10 | 2.61612 | ||||||||
\(670\) | −1.66977e8 | + | 2.46176e7i | −0.0214484 | + | 0.00316216i | ||||
\(671\) | − | 7.08707e9i | − | 0.905604i | ||||||
\(672\) | −6.93239e9 | − | 7.71711e9i | −0.881232 | − | 0.980985i | ||||
\(673\) | − | 1.80224e9i | − | 0.227908i | −0.993486 | − | 0.113954i | \(-0.963648\pi\) | ||
0.993486 | − | 0.113954i | \(-0.0363517\pi\) | |||||||
\(674\) | −1.41858e9 | − | 9.62202e9i | −0.178462 | − | 1.21048i | ||||
\(675\) | −2.54238e8 | −0.0318183 | ||||||||
\(676\) | −1.18470e10 | + | 3.57084e9i | −1.47501 | + | 0.444587i | ||||
\(677\) | − | 4.95318e9i | − | 0.613513i | −0.951788 | − | 0.306756i | \(-0.900756\pi\) | ||
0.951788 | − | 0.306756i | \(-0.0992437\pi\) | |||||||
\(678\) | −1.13106e9 | − | 7.67182e9i | −0.139375 | − | 0.945354i | ||||
\(679\) | −4.67652e9 | −0.573296 | ||||||||
\(680\) | 2.95802e9 | − | 1.38944e9i | 0.360762 | − | 0.169456i | ||||
\(681\) | 2.45982e9 | 0.298461 | ||||||||
\(682\) | −2.52609e8 | − | 1.71341e9i | −0.0304933 | − | 0.206831i | ||||
\(683\) | −2.87179e9 | −0.344890 | −0.172445 | − | 0.985019i | \(-0.555167\pi\) | ||||
−0.172445 | + | 0.985019i | \(0.555167\pi\) | |||||||
\(684\) | −2.13548e9 | + | 7.87001e9i | −0.255152 | + | 0.940327i | ||||
\(685\) | 4.14804e9 | 0.493090 | ||||||||
\(686\) | 1.29541e9 | + | 8.78654e9i | 0.153205 | + | 1.03916i | ||||
\(687\) | −9.64029e9 | −1.13434 | ||||||||
\(688\) | 2.08302e9 | + | 3.14150e9i | 0.243857 | + | 0.367771i | ||||
\(689\) | 1.95351e9 | 0.227535 | ||||||||
\(690\) | −3.87807e8 | − | 2.63043e9i | −0.0449411 | − | 0.304828i | ||||
\(691\) | − | 1.28787e10i | − | 1.48490i | −0.669901 | − | 0.742451i | \(-0.733663\pi\) | ||
0.669901 | − | 0.742451i | \(-0.266337\pi\) | |||||||
\(692\) | −1.68206e8 | − | 5.58056e8i | −0.0192961 | − | 0.0640186i | ||||
\(693\) | 4.13662e9 | 0.472150 | ||||||||
\(694\) | 2.11570e9 | + | 1.43504e10i | 0.240268 | + | 1.62970i | ||||
\(695\) | 3.35356e9i | 0.378930i | ||||||||
\(696\) | −1.06092e10 | − | 2.25864e10i | −1.19275 | − | 2.53930i | ||||
\(697\) | − | 1.03057e10i | − | 1.15283i | ||||||
\(698\) | 1.28277e10 | − | 1.89121e9i | 1.42776 | − | 0.210497i | ||||
\(699\) | −5.76177e9 | −0.638096 | ||||||||
\(700\) | 2.16808e9 | + | 7.19303e9i | 0.238908 | + | 0.792626i | ||||
\(701\) | −1.05229e9 | −0.115378 | −0.0576891 | − | 0.998335i | \(-0.518373\pi\) | ||||
−0.0576891 | + | 0.998335i | \(0.518373\pi\) | |||||||
\(702\) | −7.68630e7 | − | 5.21349e8i | −0.00838566 | − | 0.0568785i | ||||
\(703\) | −7.50572e9 | − | 4.68187e9i | −0.814796 | − | 0.508248i | ||||
\(704\) | 3.67902e9 | + | 3.05215e9i | 0.397400 | + | 0.329687i | ||||
\(705\) | − | 4.49084e9i | − | 0.482687i | ||||||
\(706\) | −6.54470e9 | + | 9.64892e8i | −0.699960 | + | 0.103196i | ||||
\(707\) | 9.90389e9i | 1.05399i | ||||||||
\(708\) | −5.69661e9 | + | 1.71704e9i | −0.603254 | + | 0.181829i | ||||
\(709\) | −3.13967e9 | −0.330844 | −0.165422 | − | 0.986223i | \(-0.552899\pi\) | ||||
−0.165422 | + | 0.986223i | \(0.552899\pi\) | |||||||
\(710\) | −3.77446e9 | + | 5.56473e8i | −0.395777 | + | 0.0583498i | ||||
\(711\) | 9.11572e9 | 0.951147 | ||||||||
\(712\) | 2.46208e9 | + | 5.24162e9i | 0.255636 | + | 0.544234i | ||||
\(713\) | 2.50282e9i | 0.258593i | ||||||||
\(714\) | −2.17159e9 | − | 1.47295e10i | −0.223272 | − | 1.51442i | ||||
\(715\) | 2.76196e9 | 0.282583 | ||||||||
\(716\) | 4.18454e9 | − | 1.26128e9i | 0.426041 | − | 0.128415i | ||||
\(717\) | 1.73456e10i | 1.75740i | ||||||||
\(718\) | −3.53641e8 | − | 2.39869e9i | −0.0356555 | − | 0.241845i | ||||
\(719\) | 4.36867e9i | 0.438327i | 0.975688 | + | 0.219163i | \(0.0703328\pi\) | ||||
−0.975688 | + | 0.219163i | \(0.929667\pi\) | |||||||
\(720\) | −2.79239e9 | + | 1.85154e9i | −0.278812 | + | 0.184871i | ||||
\(721\) | − | 8.80251e8i | − | 0.0874647i | ||||||
\(722\) | 5.72474e9 | + | 8.33668e9i | 0.566077 | + | 0.824353i | ||||
\(723\) | 9.50498e9i | 0.935335i | ||||||||
\(724\) | 4.27693e9 | + | 1.41896e10i | 0.418839 | + | 1.38958i | ||||
\(725\) | 1.80719e10i | 1.76125i | ||||||||
\(726\) | 1.05111e10 | − | 1.54966e9i | 1.01946 | − | 0.150300i | ||||
\(727\) | − | 3.06737e9i | − | 0.296071i | −0.988982 | − | 0.148035i | \(-0.952705\pi\) | ||
0.988982 | − | 0.148035i | \(-0.0472949\pi\) | |||||||
\(728\) | −1.40948e10 | + | 6.62058e9i | −1.35394 | + | 0.635969i | ||||
\(729\) | −9.91658e9 | −0.948016 | ||||||||
\(730\) | −1.00296e9 | + | 1.47868e8i | −0.0954234 | + | 0.0140684i | ||||
\(731\) | 5.40997e9i | 0.512253i | ||||||||
\(732\) | 2.50385e10 | − | 7.54693e9i | 2.35949 | − | 0.711183i | ||||
\(733\) | −1.22662e10 | −1.15039 | −0.575196 | − | 0.818015i | \(-0.695074\pi\) | ||||
−0.575196 | + | 0.818015i | \(0.695074\pi\) | |||||||
\(734\) | 1.16257e9 | + | 7.88554e9i | 0.108514 | + | 0.736029i | ||||
\(735\) | 6.19285e8 | 0.0575287 | ||||||||
\(736\) | −4.61641e9 | − | 5.13897e9i | −0.426807 | − | 0.475120i | ||||
\(737\) | − | 3.54333e8i | − | 0.0326044i | ||||||
\(738\) | 1.54102e9 | + | 1.04525e10i | 0.141128 | + | 0.957245i | ||||
\(739\) | 8.36331e9i | 0.762294i | 0.924514 | + | 0.381147i | \(0.124471\pi\) | ||||
−0.924514 | + | 0.381147i | \(0.875529\pi\) | |||||||
\(740\) | −1.04892e9 | − | 3.48000e9i | −0.0951548 | − | 0.315695i | ||||
\(741\) | 2.10461e10 | + | 1.31280e10i | 1.90024 | + | 1.18532i | ||||
\(742\) | 1.47488e9 | − | 2.17443e8i | 0.132539 | − | 0.0195403i | ||||
\(743\) | 8.14455e9 | 0.728461 | 0.364230 | − | 0.931309i | \(-0.381332\pi\) | ||||
0.364230 | + | 0.931309i | \(0.381332\pi\) | |||||||
\(744\) | 5.78443e9 | − | 2.71705e9i | 0.514938 | − | 0.241876i | ||||
\(745\) | −2.93757e9 | −0.260280 | ||||||||
\(746\) | −4.61833e7 | − | 3.13253e8i | −0.00407285 | − | 0.0276255i | ||||
\(747\) | 7.93897e9i | 0.696854i | ||||||||
\(748\) | 1.97998e9 | + | 6.56897e9i | 0.172983 | + | 0.573907i | ||||
\(749\) | 8.27530e9i | 0.719611i | ||||||||
\(750\) | 1.03785e10 | − | 1.53012e9i | 0.898300 | − | 0.132437i | ||||
\(751\) | 5.78813e9 | 0.498653 | 0.249327 | − | 0.968419i | \(-0.419791\pi\) | ||||
0.249327 | + | 0.968419i | \(0.419791\pi\) | |||||||
\(752\) | −6.44778e9 | − | 9.72418e9i | −0.552902 | − | 0.833855i | ||||
\(753\) | 3.20091e10i | 2.73206i | ||||||||
\(754\) | −3.70588e10 | + | 5.46362e9i | −3.14842 | + | 0.464174i | ||||
\(755\) | 6.27044e9 | 0.530253 | ||||||||
\(756\) | −1.16061e8 | − | 3.85057e8i | −0.00976925 | − | 0.0324115i | ||||
\(757\) | 1.85609e10 | 1.55512 | 0.777558 | − | 0.628812i | \(-0.216458\pi\) | ||||
0.777558 | + | 0.628812i | \(0.216458\pi\) | |||||||
\(758\) | −1.25735e10 | + | 1.85372e9i | −1.04861 | + | 0.154598i | ||||
\(759\) | 5.58189e9 | 0.463378 | ||||||||
\(760\) | −4.91591e8 | + | 4.12594e9i | −0.0406215 | + | 0.340938i | ||||
\(761\) | 1.40157e10 | 1.15284 | 0.576420 | − | 0.817154i | \(-0.304449\pi\) | ||||
0.576420 | + | 0.817154i | \(0.304449\pi\) | |||||||
\(762\) | −1.10135e10 | + | 1.62373e9i | −0.901745 | + | 0.132945i | ||||
\(763\) | −1.44256e10 | −1.17571 | ||||||||
\(764\) | 2.76306e9 | + | 9.16701e9i | 0.224163 | + | 0.743705i | ||||
\(765\) | −4.80877e9 | −0.388346 | ||||||||
\(766\) | 1.18639e9 | − | 1.74910e8i | 0.0953730 | − | 0.0140609i | ||||
\(767\) | 8.93143e9i | 0.714722i | ||||||||
\(768\) | −6.86544e9 | + | 1.62481e10i | −0.546895 | + | 1.29431i | ||||
\(769\) | 9.93943e9 | 0.788169 | 0.394084 | − | 0.919074i | \(-0.371062\pi\) | ||||
0.394084 | + | 0.919074i | \(0.371062\pi\) | |||||||
\(770\) | 2.08525e9 | − | 3.07431e8i | 0.164604 | − | 0.0242677i | ||||
\(771\) | 2.67951e10i | 2.10555i | ||||||||
\(772\) | 1.43094e9 | + | 4.74743e9i | 0.111934 | + | 0.371363i | ||||
\(773\) | − | 3.46341e9i | − | 0.269697i | −0.990866 | − | 0.134848i | \(-0.956945\pi\) | ||
0.990866 | − | 0.134848i | \(-0.0430548\pi\) | |||||||
\(774\) | −8.08957e8 | − | 5.48702e9i | −0.0627093 | − | 0.425347i | ||||
\(775\) | −4.62826e9 | −0.357159 | ||||||||
\(776\) | 3.38073e9 | + | 7.19738e9i | 0.259714 | + | 0.552915i | ||||
\(777\) | −1.65587e10 | −1.26635 | ||||||||
\(778\) | 1.67093e9 | − | 2.46347e8i | 0.127213 | − | 0.0187551i | ||||
\(779\) | 1.11174e10 | + | 6.93473e9i | 0.842599 | + | 0.525591i | ||||
\(780\) | 2.94118e9 | + | 9.75795e9i | 0.221917 | + | 0.736253i | ||||
\(781\) | − | 8.00957e9i | − | 0.601632i | ||||||
\(782\) | −1.44610e9 | − | 9.80868e9i | −0.108137 | − | 0.733478i | ||||
\(783\) | − | 9.67424e8i | − | 0.0720196i | ||||||
\(784\) | 1.34096e9 | − | 8.89146e8i | 0.0993824 | − | 0.0658972i | ||||
\(785\) | −5.46521e9 | −0.403240 | ||||||||
\(786\) | −4.35743e9 | − | 2.95557e10i | −0.320075 | − | 2.17101i | ||||
\(787\) | 2.30979e10 | 1.68912 | 0.844562 | − | 0.535457i | \(-0.179861\pi\) | ||||
0.844562 | + | 0.535457i | \(0.179861\pi\) | |||||||
\(788\) | 4.92137e9 | − | 1.48337e9i | 0.358298 | − | 0.107996i | ||||
\(789\) | 1.21092e10i | 0.877701i | ||||||||
\(790\) | 4.59519e9 | − | 6.77473e8i | 0.331595 | − | 0.0488874i | ||||
\(791\) | −8.88381e9 | −0.638237 | ||||||||
\(792\) | −2.99043e9 | − | 6.36645e9i | −0.213893 | − | 0.455365i | ||||
\(793\) | − | 3.92565e10i | − | 2.79548i | ||||||
\(794\) | 2.18212e10 | − | 3.21712e9i | 1.54706 | − | 0.228084i | ||||
\(795\) | − | 9.75696e8i | − | 0.0688699i | ||||||
\(796\) | −4.01043e9 | − | 1.33054e10i | −0.281835 | − | 0.935044i | ||||
\(797\) | − | 2.97700e9i | − | 0.208293i | −0.994562 | − | 0.104146i | \(-0.966789\pi\) | ||
0.994562 | − | 0.104146i | \(-0.0332111\pi\) | |||||||
\(798\) | 1.73508e10 | + | 7.56889e9i | 1.20868 | + | 0.527256i | ||||
\(799\) | − | 1.67460e10i | − | 1.16144i | ||||||
\(800\) | 9.50305e9 | − | 8.53673e9i | 0.656218 | − | 0.589490i | ||||
\(801\) | − | 8.52114e9i | − | 0.585847i | ||||||
\(802\) | −4.07419e9 | − | 2.76345e10i | −0.278888 | − | 1.89165i | ||||
\(803\) | − | 2.12833e9i | − | 0.145056i | ||||||
\(804\) | 1.25185e9 | − | 3.77325e8i | 0.0849486 | − | 0.0256047i | ||||
\(805\) | −3.04599e9 | −0.205799 | ||||||||
\(806\) | −1.39925e9 | − | 9.49086e9i | −0.0941287 | − | 0.638459i | ||||
\(807\) | 7.83479e8i | 0.0524771i | ||||||||
\(808\) | 1.52425e10 | − | 7.15968e9i | 1.01652 | − | 0.477479i | ||||
\(809\) | −1.83177e10 | −1.21633 | −0.608165 | − | 0.793811i | \(-0.708094\pi\) | ||||
−0.608165 | + | 0.793811i | \(0.708094\pi\) | |||||||
\(810\) | −5.26615e9 | + | 7.76394e8i | −0.348173 | + | 0.0513315i | ||||
\(811\) | −4.72596e9 | −0.311112 | −0.155556 | − | 0.987827i | \(-0.549717\pi\) | ||||
−0.155556 | + | 0.987827i | \(0.549717\pi\) | |||||||
\(812\) | −2.73709e10 | + | 8.24995e9i | −1.79408 | + | 0.540761i | ||||
\(813\) | − | 3.03797e10i | − | 1.98275i | ||||||
\(814\) | 7.54879e9 | − | 1.11293e9i | 0.490560 | − | 0.0723237i | ||||
\(815\) | 3.18291e8i | 0.0205955i | ||||||||
\(816\) | −2.10996e10 | + | 1.39904e10i | −1.35943 | + | 0.901395i | ||||
\(817\) | −5.83604e9 | − | 3.64037e9i | −0.374404 | − | 0.233544i | ||||
\(818\) | 2.96683e9 | + | 2.01235e10i | 0.189520 | + | 1.28548i | ||||
\(819\) | 2.29135e10 | 1.45746 | ||||||||
\(820\) | 1.55364e9 | + | 5.15453e9i | 0.0984018 | + | 0.326468i | ||||
\(821\) | −8.26532e9 | −0.521265 | −0.260633 | − | 0.965438i | \(-0.583931\pi\) | ||||
−0.260633 | + | 0.965438i | \(0.583931\pi\) | |||||||
\(822\) | −3.17894e10 | + | 4.68674e9i | −1.99632 | + | 0.294320i | ||||
\(823\) | − | 1.64112e10i | − | 1.02622i | −0.858322 | − | 0.513111i | \(-0.828493\pi\) | ||
0.858322 | − | 0.513111i | \(-0.171507\pi\) | |||||||
\(824\) | −1.35475e9 | + | 6.36348e8i | −0.0843553 | + | 0.0396232i | ||||
\(825\) | 1.03221e10i | 0.640000i | ||||||||
\(826\) | 9.94147e8 | + | 6.74313e9i | 0.0613791 | + | 0.416324i | ||||
\(827\) | 2.37954e10 | 1.46293 | 0.731464 | − | 0.681880i | \(-0.238837\pi\) | ||||
0.731464 | + | 0.681880i | \(0.238837\pi\) | |||||||
\(828\) | 2.93340e9 | + | 9.73214e9i | 0.179583 | + | 0.595802i | ||||
\(829\) | − | 2.69057e10i | − | 1.64023i | −0.572202 | − | 0.820113i | \(-0.693911\pi\) | ||
0.572202 | − | 0.820113i | \(-0.306089\pi\) | |||||||
\(830\) | 5.90018e8 | + | 4.00199e9i | 0.0358172 | + | 0.242942i | ||||
\(831\) | −8.30629e9 | −0.502116 | ||||||||
\(832\) | 2.03787e10 | + | 1.69064e10i | 1.22672 | + | 1.01770i | ||||
\(833\) | 2.30927e9 | 0.138426 | ||||||||
\(834\) | −3.78908e9 | − | 2.57007e10i | −0.226179 | − | 1.53414i | ||||
\(835\) | −9.79143e9 | −0.582027 | ||||||||
\(836\) | −8.41864e9 | − | 2.28434e9i | −0.498333 | − | 0.135220i | ||||
\(837\) | 2.47760e8 | 0.0146047 | ||||||||
\(838\) | −1.11939e9 | − | 7.59264e9i | −0.0657094 | − | 0.445696i | ||||
\(839\) | −3.18793e10 | −1.86356 | −0.931778 | − | 0.363028i | \(-0.881743\pi\) | ||||
−0.931778 | + | 0.363028i | \(0.881743\pi\) | |||||||
\(840\) | 3.30670e9 | + | 7.03976e9i | 0.192494 | + | 0.409808i | ||||
\(841\) | −5.15172e10 | −2.98652 | ||||||||
\(842\) | 3.40611e9 | + | 2.31031e10i | 0.196637 | + | 1.33376i | ||||
\(843\) | 2.27630e10i | 1.30868i | ||||||||
\(844\) | 1.98096e10 | − | 5.97087e9i | 1.13417 | − | 0.341853i | ||||
\(845\) | 9.27708e9 | 0.528948 | ||||||||
\(846\) | 2.50404e9 | + | 1.69845e10i | 0.142182 | + | 0.964398i | ||||
\(847\) | − | 1.21716e10i | − | 0.688266i | ||||||
\(848\) | −1.40087e9 | − | 2.11271e9i | −0.0788881 | − | 0.118975i | ||||
\(849\) | 2.91706e9i | 0.163594i | ||||||||
\(850\) | 1.81384e10 | − | 2.67416e9i | 1.01305 | − | 0.149355i | ||||
\(851\) | −1.10267e10 | −0.613329 | ||||||||
\(852\) | 2.82976e10 | − | 8.52929e9i | 1.56751 | − | 0.472470i | ||||
\(853\) | −1.80521e10 | −0.995878 | −0.497939 | − | 0.867212i | \(-0.665910\pi\) | ||||
−0.497939 | + | 0.867212i | \(0.665910\pi\) | |||||||
\(854\) | −4.36960e9 | − | 2.96382e10i | −0.240070 | − | 1.62836i | ||||
\(855\) | 3.23582e9 | − | 5.18749e9i | 0.177053 | − | 0.283841i | ||||
\(856\) | 1.27361e10 | − | 5.98236e9i | 0.694028 | − | 0.325997i | ||||
\(857\) | − | 4.39427e9i | − | 0.238481i | −0.992865 | − | 0.119240i | \(-0.961954\pi\) | ||
0.992865 | − | 0.119240i | \(-0.0380459\pi\) | |||||||
\(858\) | −2.11669e10 | + | 3.12065e9i | −1.14407 | + | 0.168671i | ||||
\(859\) | 1.06603e10i | 0.573841i | 0.957954 | + | 0.286920i | \(0.0926315\pi\) | ||||
−0.957954 | + | 0.286920i | \(0.907368\pi\) | |||||||
\(860\) | −8.15581e8 | − | 2.70586e9i | −0.0437243 | − | 0.145064i | ||||
\(861\) | 2.45265e10 | 1.30956 | ||||||||
\(862\) | −1.22810e10 | + | 1.81060e9i | −0.653069 | + | 0.0962826i | ||||
\(863\) | 2.19935e10 | 1.16481 | 0.582407 | − | 0.812898i | \(-0.302111\pi\) | ||||
0.582407 | + | 0.812898i | \(0.302111\pi\) | |||||||
\(864\) | −5.08717e8 | + | 4.56988e8i | −0.0268336 | + | 0.0241050i | ||||
\(865\) | 4.36999e8i | 0.0229575i | ||||||||
\(866\) | −1.14870e9 | − | 7.79146e9i | −0.0601029 | − | 0.407668i | ||||
\(867\) | −9.37202e9 | −0.488389 | ||||||||
\(868\) | −2.11283e9 | − | 7.00975e9i | −0.109659 | − | 0.363817i | ||||
\(869\) | 9.75119e9i | 0.504067i | ||||||||
\(870\) | 2.72885e9 | + | 1.85093e10i | 0.140495 | + | 0.952957i | ||||
\(871\) | − | 1.96271e9i | − | 0.100645i | ||||||
\(872\) | 1.04285e10 | + | 2.22017e10i | 0.532618 | + | 1.13391i | ||||
\(873\) | − | 1.17006e10i | − | 0.595191i | ||||||
\(874\) | 1.15543e10 | + | 5.04027e9i | 0.585399 | + | 0.255366i | ||||
\(875\) | − | 1.20181e10i | − | 0.606469i | ||||||
\(876\) | 7.51934e9 | − | 2.26643e9i | 0.377934 | − | 0.113914i | ||||
\(877\) | − | 2.98444e10i | − | 1.49405i | −0.664797 | − | 0.747024i | \(-0.731482\pi\) | ||
0.664797 | − | 0.747024i | \(-0.268518\pi\) | |||||||
\(878\) | −3.76586e9 | + | 5.55205e8i | −0.187773 | + | 0.0276836i | ||||
\(879\) | − | 3.73968e10i | − | 1.85726i | ||||||
\(880\) | −1.98061e9 | − | 2.98705e9i | −0.0979738 | − | 0.147759i | ||||
\(881\) | 2.62000e10 | 1.29088 | 0.645440 | − | 0.763811i | \(-0.276674\pi\) | ||||
0.645440 | + | 0.763811i | \(0.276674\pi\) | |||||||
\(882\) | −2.34215e9 | + | 3.45306e8i | −0.114941 | + | 0.0169459i | ||||
\(883\) | − | 5.98290e9i | − | 0.292448i | −0.989251 | − | 0.146224i | \(-0.953288\pi\) | ||
0.989251 | − | 0.146224i | \(-0.0467121\pi\) | |||||||
\(884\) | 1.09674e10 | + | 3.63867e10i | 0.533976 | + | 1.77157i | ||||
\(885\) | 4.46088e9 | 0.216331 | ||||||||
\(886\) | 3.65883e8 | + | 2.48172e9i | 0.0176736 | + | 0.119877i | ||||
\(887\) | −1.61623e10 | −0.777626 | −0.388813 | − | 0.921317i | \(-0.627115\pi\) | ||||
−0.388813 | + | 0.921317i | \(0.627115\pi\) | |||||||
\(888\) | 1.19705e10 | + | 2.54845e10i | 0.573678 | + | 1.22133i | ||||
\(889\) | 1.27534e10i | 0.608794i | ||||||||
\(890\) | −6.33284e8 | − | 4.29546e9i | −0.0301116 | − | 0.204242i | ||||
\(891\) | − | 1.11750e10i | − | 0.529268i | ||||||
\(892\) | −3.77870e10 | + | 1.13895e10i | −1.78265 | + | 0.537313i | ||||
\(893\) | 1.80649e10 | + | 1.12684e10i | 0.848896 | + | 0.529519i | ||||
\(894\) | 2.25127e10 | − | 3.31907e9i | 1.05377 | − | 0.155358i | ||||
\(895\) | −3.27681e9 | −0.152781 | ||||||||
\(896\) | 1.72675e10 | + | 1.04958e10i | 0.801960 | + | 0.487459i | ||||
\(897\) | 3.09191e10 | 1.43038 | ||||||||
\(898\) | −2.01824e9 | − | 1.36894e10i | −0.0930049 | − | 0.630837i | ||||
\(899\) | − | 1.76114e10i | − | 0.808417i | ||||||
\(900\) | −1.79968e10 | + | 5.42448e9i | −0.822899 | + | 0.248033i | ||||
\(901\) | − | 3.63830e9i | − | 0.165715i | ||||||
\(902\) | −1.11812e10 | + | 1.64845e9i | −0.507299 | + | 0.0747916i | ||||
\(903\) | −1.28751e10 | −0.581894 | ||||||||
\(904\) | 6.42226e9 | + | 1.36726e10i | 0.289133 | + | 0.615547i | ||||
\(905\) | − | 1.11115e10i | − | 0.498313i | ||||||
\(906\) | −4.80548e10 | + | 7.08477e9i | −2.14678 | + | 0.316502i | ||||
\(907\) | −3.91266e10 | −1.74119 | −0.870597 | − | 0.491997i | \(-0.836267\pi\) | ||||
−0.870597 | + | 0.491997i | \(0.836267\pi\) | |||||||
\(908\) | −4.58771e9 | + | 1.38280e9i | −0.203374 | + | 0.0612997i | ||||
\(909\) | −2.47793e10 | −1.09425 | ||||||||
\(910\) | 1.15506e10 | − | 1.70291e9i | 0.508111 | − | 0.0749113i | ||||
\(911\) | 1.27769e10 | 0.559900 | 0.279950 | − | 0.960015i | \(-0.409682\pi\) | ||||
0.279950 | + | 0.960015i | \(0.409682\pi\) | |||||||
\(912\) | −8.94357e8 | − | 3.21754e10i | −0.0390417 | − | 1.40457i | ||||
\(913\) | −8.49240e9 | −0.369303 | ||||||||
\(914\) | −3.05776e10 | + | 4.50808e9i | −1.32462 | + | 0.195290i | ||||
\(915\) | −1.96070e10 | −0.846130 | ||||||||
\(916\) | 1.79797e10 | − | 5.41934e9i | 0.772946 | − | 0.232977i | ||||
\(917\) | −3.42249e10 | −1.46571 | ||||||||
\(918\) | −9.70982e8 | + | 1.43153e8i | −0.0414249 | + | 0.00610732i | ||||
\(919\) | − | 3.67168e10i | − | 1.56049i | −0.625476 | − | 0.780243i | \(-0.715095\pi\) | ||
0.625476 | − | 0.780243i | \(-0.284905\pi\) | |||||||
\(920\) | 2.20199e9 | + | 4.68791e9i | 0.0932307 | + | 0.198482i | ||||
\(921\) | 1.02033e10 | 0.430361 | ||||||||
\(922\) | 1.89466e10 | − | 2.79331e9i | 0.796109 | − | 0.117371i | ||||
\(923\) | − | 4.43664e10i | − | 1.85716i | ||||||
\(924\) | −1.56334e10 | + | 4.71212e9i | −0.651931 | + | 0.196501i | ||||
\(925\) | − | 2.03908e10i | − | 0.847107i | ||||||
\(926\) | 2.29074e9 | + | 1.55377e10i | 0.0948064 | + | 0.643056i | ||||
\(927\) | 2.20237e9 | 0.0908053 | ||||||||
\(928\) | 3.24839e10 | + | 3.61610e10i | 1.33429 | + | 1.48533i | ||||
\(929\) | 2.94042e10 | 1.20324 | 0.601622 | − | 0.798781i | \(-0.294521\pi\) | ||||
0.601622 | + | 0.798781i | \(0.294521\pi\) | |||||||
\(930\) | −4.74029e9 | + | 6.98865e8i | −0.193248 | + | 0.0284907i | ||||
\(931\) | −1.55390e9 | + | 2.49114e9i | −0.0631103 | + | 0.101175i | ||||
\(932\) | 1.07461e10 | − | 3.23901e9i | 0.434804 | − | 0.131056i | ||||
\(933\) | 4.71055e10i | 1.89883i | ||||||||
\(934\) | −4.86675e9 | − | 3.30104e10i | −0.195445 | − | 1.32567i | ||||
\(935\) | − | 5.14399e9i | − | 0.205807i | ||||||
\(936\) | −1.65645e10 | − | 3.52649e10i | −0.660258 | − | 1.40565i | ||||
\(937\) | 3.19605e9 | 0.126918 | 0.0634592 | − | 0.997984i | \(-0.479787\pi\) | ||||
0.0634592 | + | 0.997984i | \(0.479787\pi\) | |||||||
\(938\) | −2.18467e8 | − | 1.48183e9i | −0.00864323 | − | 0.0586256i | ||||
\(939\) | 2.67365e10 | 1.05384 | ||||||||
\(940\) | 2.52455e9 | + | 8.37570e9i | 0.0991371 | + | 0.328907i | ||||
\(941\) | 1.08078e10i | 0.422836i | 0.977396 | + | 0.211418i | \(0.0678082\pi\) | ||||
−0.977396 | + | 0.211418i | \(0.932192\pi\) | |||||||
\(942\) | 4.18838e10 | − | 6.17497e9i | 1.63256 | − | 0.240689i | ||||
\(943\) | 1.63327e10 | 0.634258 | ||||||||
\(944\) | 9.65930e9 | − | 6.40476e9i | 0.373718 | − | 0.247800i | ||||
\(945\) | 3.01528e8i | 0.0116230i | ||||||||
\(946\) | 5.86952e9 | − | 8.65350e8i | 0.225416 | − | 0.0332332i | ||||
\(947\) | 3.36631e10i | 1.28804i | 0.765009 | + | 0.644020i | \(0.222735\pi\) | ||||
−0.765009 | + | 0.644020i | \(0.777265\pi\) | |||||||
\(948\) | −3.44507e10 | + | 1.03839e10i | −1.31332 | + | 0.395851i | ||||
\(949\) | − | 1.17892e10i | − | 0.447767i | ||||||
\(950\) | −9.32053e9 | + | 2.13663e10i | −0.352702 | + | 0.808531i | ||||
\(951\) | 3.72697e10i | 1.40516i | ||||||||
\(952\) | 1.23304e10 | + | 2.62507e10i | 0.463179 | + | 0.986080i | ||||
\(953\) | − | 4.55999e9i | − | 0.170663i | −0.996353 | − | 0.0853313i | \(-0.972805\pi\) | ||
0.996353 | − | 0.0853313i | \(-0.0271949\pi\) | |||||||
\(954\) | 5.44037e8 | + | 3.69011e9i | 0.0202866 | + | 0.137601i | ||||
\(955\) | − | 7.17845e9i | − | 0.266698i | ||||||
\(956\) | −9.75090e9 | − | 3.23506e10i | −0.360946 | − | 1.19751i | ||||
\(957\) | −3.92776e10 | −1.44862 | ||||||||
\(958\) | 5.55113e9 | + | 3.76524e10i | 0.203987 | + | 1.38361i | ||||
\(959\) | 3.68114e10i | 1.34778i | ||||||||
\(960\) | 8.44404e9 | − | 1.01783e10i | 0.308036 | − | 0.371302i | ||||
\(961\) | −2.30023e10 | −0.836063 | ||||||||
\(962\) | 4.18141e10 | − | 6.16469e9i | 1.51429 | − | 0.223254i | ||||
\(963\) | −2.07046e10 | −0.747094 | ||||||||
\(964\) | −5.34327e9 | − | 1.77274e10i | −0.192104 | − | 0.637345i | ||||
\(965\) | − | 3.71760e9i | − | 0.133173i | ||||||
\(966\) | 2.33435e10 | − | 3.44156e9i | 0.833196 | − | 0.122839i | ||||
\(967\) | 3.80903e10i | 1.35463i | 0.735691 | + | 0.677317i | \(0.236857\pi\) | ||||
−0.735691 | + | 0.677317i | \(0.763143\pi\) | |||||||
\(968\) | −1.87327e10 | + | 8.79907e9i | −0.663798 | + | 0.311798i | ||||
\(969\) | 2.44502e10 | − | 3.91972e10i | 0.863274 | − | 1.38395i | ||||
\(970\) | −8.69576e8 | − | 5.89819e9i | −0.0305919 | − | 0.207500i | ||||
\(971\) | 3.45775e10 | 1.21207 | 0.606033 | − | 0.795440i | \(-0.292760\pi\) | ||||
0.606033 | + | 0.795440i | \(0.292760\pi\) | |||||||
\(972\) | 3.84922e10 | − | 1.16021e10i | 1.34444 | − | 0.405232i | ||||
\(973\) | −2.97609e10 | −1.03574 | ||||||||
\(974\) | −4.55518e9 | + | 6.71575e8i | −0.157961 | + | 0.0232883i | ||||
\(975\) | 5.71760e10i | 1.97559i | ||||||||
\(976\) | −4.24557e10 | + | 2.81510e10i | −1.46171 | + | 0.969213i | ||||
\(977\) | 1.31226e10i | 0.450182i | 0.974338 | + | 0.225091i | \(0.0722680\pi\) | ||||
−0.974338 | + | 0.225091i | \(0.927732\pi\) | |||||||
\(978\) | −3.59627e8 | − | 2.43929e9i | −0.0122932 | − | 0.0833831i | ||||
\(979\) | 9.11516e9 | 0.310474 | ||||||||
\(980\) | −1.15500e9 | + | 3.48134e8i | −0.0392006 | + | 0.0118156i | ||||
\(981\) | − | 3.60927e10i | − | 1.22061i | ||||||
\(982\) | −3.02347e9 | − | 2.05077e10i | −0.101886 | − | 0.691077i | ||||
\(983\) | −3.08571e10 | −1.03614 | −0.518069 | − | 0.855339i | \(-0.673349\pi\) | ||||
−0.518069 | + | 0.855339i | \(0.673349\pi\) | |||||||
\(984\) | −1.77306e10 | − | 3.77474e10i | −0.593254 | − | 1.26300i | ||||
\(985\) | −3.85380e9 | −0.128488 | ||||||||
\(986\) | 1.01757e10 | + | 6.90199e10i | 0.338060 | + | 2.29301i | ||||
\(987\) | 3.98536e10 | 1.31934 | ||||||||
\(988\) | −4.66323e10 | − | 1.26534e10i | −1.53829 | − | 0.417405i | ||||
\(989\) | −8.57379e9 | −0.281829 | ||||||||
\(990\) | 7.69185e8 | + | 5.21725e9i | 0.0251946 | + | 0.170891i | ||||
\(991\) | 1.42619e10 | 0.465500 | 0.232750 | − | 0.972537i | \(-0.425228\pi\) | ||||
0.232750 | + | 0.972537i | \(0.425228\pi\) | |||||||
\(992\) | −9.26091e9 | + | 8.31921e9i | −0.301206 | + | 0.270577i | ||||
\(993\) | −2.64206e10 | −0.856288 | ||||||||
\(994\) | −4.93837e9 | − | 3.34961e10i | −0.159489 | − | 1.08179i | ||||
\(995\) | 1.04191e10i | 0.335313i | ||||||||
\(996\) | −9.04345e9 | − | 3.00034e10i | −0.290019 | − | 0.962196i | ||||
\(997\) | 4.57776e10 | 1.46292 | 0.731460 | − | 0.681885i | \(-0.238839\pi\) | ||||
0.731460 | + | 0.681885i | \(0.238839\pi\) | |||||||
\(998\) | −5.12029e9 | − | 3.47301e10i | −0.163056 | − | 1.10598i | ||||
\(999\) | 1.09156e9i | 0.0346392i |
(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.d.a.75.4 | yes | 68 | |
4.3 | odd | 2 | inner | 76.8.d.a.75.66 | yes | 68 | |
19.18 | odd | 2 | inner | 76.8.d.a.75.65 | yes | 68 | |
76.75 | even | 2 | inner | 76.8.d.a.75.3 | ✓ | 68 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.8.d.a.75.3 | ✓ | 68 | 76.75 | even | 2 | inner | |
76.8.d.a.75.4 | yes | 68 | 1.1 | even | 1 | trivial | |
76.8.d.a.75.65 | yes | 68 | 19.18 | odd | 2 | inner | |
76.8.d.a.75.66 | yes | 68 | 4.3 | odd | 2 | inner |