Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,9,Mod(26,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.26");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.c (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: | \(30.5533957546\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 64 x^{10} + 385774 x^{8} - 323639784 x^{6} - 48708595080 x^{4} + 21531002169600 x^{2} + 82\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{16}\cdot 3^{18}\cdot 5^{8} \) |
Twist minimal: | no (minimal twist has level 15) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 26.4 | ||
Root | \(20.6227 + 2.01276i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.26 |
Dual form | 75.9.c.h.26.10 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 17.5844i | − | 1.09903i | −0.835485 | − | 0.549514i | \(-0.814813\pi\) | ||
0.835485 | − | 0.549514i | \(-0.185187\pi\) | |||||||
\(3\) | 31.2287 | − | 74.7380i | 0.385540 | − | 0.922691i | ||||
\(4\) | −53.2123 | −0.207860 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1314.22 | − | 549.140i | −1.01406 | − | 0.423719i | ||||
\(7\) | −3426.92 | −1.42729 | −0.713644 | − | 0.700508i | \(-0.752957\pi\) | ||||
−0.713644 | + | 0.700508i | \(0.752957\pi\) | |||||||
\(8\) | − | 3565.91i | − | 0.870583i | ||||||
\(9\) | −4610.53 | − | 4667.95i | −0.702718 | − | 0.711469i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 15724.8i | 1.07402i | 0.843575 | + | 0.537011i | \(0.180447\pi\) | ||||
−0.843575 | + | 0.537011i | \(0.819553\pi\) | |||||||
\(12\) | −1661.75 | + | 3976.98i | −0.0801385 | + | 0.191791i | ||||
\(13\) | 27065.2 | 0.947628 | 0.473814 | − | 0.880625i | \(-0.342877\pi\) | ||||
0.473814 | + | 0.880625i | \(0.342877\pi\) | |||||||
\(14\) | 60260.4i | 1.56863i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −76326.8 | −1.16465 | ||||||||
\(17\) | − | 14218.4i | − | 0.170238i | −0.996371 | − | 0.0851189i | \(-0.972873\pi\) | ||
0.996371 | − | 0.0851189i | \(-0.0271270\pi\) | |||||||
\(18\) | −82083.2 | + | 81073.6i | −0.781923 | + | 0.772306i | ||||
\(19\) | −210073. | −1.61196 | −0.805981 | − | 0.591941i | \(-0.798362\pi\) | ||||
−0.805981 | + | 0.591941i | \(0.798362\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −107018. | + | 256121.i | −0.550277 | + | 1.31695i | ||||
\(22\) | 276511. | 1.18038 | ||||||||
\(23\) | 60230.4i | 0.215231i | 0.994193 | + | 0.107615i | \(0.0343215\pi\) | ||||
−0.994193 | + | 0.107615i | \(0.965678\pi\) | |||||||
\(24\) | −266509. | − | 111359.i | −0.803279 | − | 0.335645i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 475926.i | − | 1.04147i | ||||||
\(27\) | −492854. | + | 198808.i | −0.927392 | + | 0.374092i | ||||
\(28\) | 182354. | 0.296677 | ||||||||
\(29\) | 758209.i | 1.07201i | 0.844216 | + | 0.536003i | \(0.180066\pi\) | ||||
−0.844216 | + | 0.536003i | \(0.819934\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 333379. | 0.360987 | 0.180493 | − | 0.983576i | \(-0.442231\pi\) | ||||
0.180493 | + | 0.983576i | \(0.442231\pi\) | |||||||
\(32\) | 429291.i | 0.409404i | ||||||||
\(33\) | 1.17524e6 | + | 491064.i | 0.990990 | + | 0.414078i | ||||
\(34\) | −250023. | −0.187096 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 245337. | + | 248392.i | 0.146067 | + | 0.147886i | ||||
\(37\) | −683328. | −0.364605 | −0.182302 | − | 0.983243i | \(-0.558355\pi\) | ||||
−0.182302 | + | 0.983243i | \(0.558355\pi\) | |||||||
\(38\) | 3.69401e6i | 1.77159i | ||||||||
\(39\) | 845213. | − | 2.02280e6i | 0.365349 | − | 0.874368i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.23950e6i | − | 0.438644i | −0.975653 | − | 0.219322i | \(-0.929615\pi\) | ||
0.975653 | − | 0.219322i | \(-0.0703846\pi\) | |||||||
\(42\) | 4.50374e6 | + | 1.88186e6i | 1.44736 | + | 0.604769i | ||||
\(43\) | 1.15567e6 | 0.338033 | 0.169016 | − | 0.985613i | \(-0.445941\pi\) | ||||
0.169016 | + | 0.985613i | \(0.445941\pi\) | |||||||
\(44\) | − | 836750.i | − | 0.223247i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.05912e6 | 0.236545 | ||||||||
\(47\) | − | 1.52165e6i | − | 0.311833i | −0.987770 | − | 0.155917i | \(-0.950167\pi\) | ||
0.987770 | − | 0.155917i | \(-0.0498331\pi\) | |||||||
\(48\) | −2.38359e6 | + | 5.70451e6i | −0.449021 | + | 1.07462i | ||||
\(49\) | 5.97898e6 | 1.03715 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.06266e6 | − | 444024.i | −0.157077 | − | 0.0656335i | ||||
\(52\) | −1.44020e6 | −0.196974 | ||||||||
\(53\) | 4.73392e6i | 0.599954i | 0.953947 | + | 0.299977i | \(0.0969789\pi\) | ||||
−0.953947 | + | 0.299977i | \(0.903021\pi\) | |||||||
\(54\) | 3.49592e6 | + | 8.66656e6i | 0.411137 | + | 1.01923i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.22201e7i | 1.24257i | ||||||||
\(57\) | −6.56030e6 | + | 1.57004e7i | −0.621476 | + | 1.48734i | ||||
\(58\) | 1.33327e7 | 1.17816 | ||||||||
\(59\) | − | 1.30629e7i | − | 1.07803i | −0.842296 | − | 0.539016i | \(-0.818796\pi\) | ||
0.842296 | − | 0.539016i | \(-0.181204\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.62861e6 | −0.478744 | −0.239372 | − | 0.970928i | \(-0.576941\pi\) | ||||
−0.239372 | + | 0.970928i | \(0.576941\pi\) | |||||||
\(62\) | − | 5.86228e6i | − | 0.396734i | ||||||
\(63\) | 1.57999e7 | + | 1.59967e7i | 1.00298 | + | 1.01547i | ||||
\(64\) | −1.19908e7 | −0.714709 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 8.63509e6 | − | 2.06659e7i | 0.455083 | − | 1.08913i | ||||
\(67\) | 2.47970e7 | 1.23055 | 0.615276 | − | 0.788312i | \(-0.289045\pi\) | ||||
0.615276 | + | 0.788312i | \(0.289045\pi\) | |||||||
\(68\) | 756595.i | 0.0353857i | ||||||||
\(69\) | 4.50150e6 | + | 1.88092e6i | 0.198592 | + | 0.0829801i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.07106e7i | − | 0.421485i | −0.977542 | − | 0.210742i | \(-0.932412\pi\) | ||
0.977542 | − | 0.210742i | \(-0.0675881\pi\) | |||||||
\(72\) | −1.66455e7 | + | 1.64407e7i | −0.619392 | + | 0.611774i | ||||
\(73\) | −3.48665e7 | −1.22777 | −0.613885 | − | 0.789395i | \(-0.710394\pi\) | ||||
−0.613885 | + | 0.789395i | \(0.710394\pi\) | |||||||
\(74\) | 1.20159e7i | 0.400711i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.11784e7 | 0.335063 | ||||||||
\(77\) | − | 5.38875e7i | − | 1.53294i | ||||||
\(78\) | −3.55698e7 | − | 1.48626e7i | −0.960954 | − | 0.401528i | ||||
\(79\) | −5.01757e7 | −1.28820 | −0.644102 | − | 0.764939i | \(-0.722769\pi\) | ||||
−0.644102 | + | 0.764939i | \(0.722769\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −532723. | + | 4.30434e7i | −0.0123754 | + | 0.999923i | ||||
\(82\) | −2.17960e7 | −0.482082 | ||||||||
\(83\) | − | 4.50568e7i | − | 0.949398i | −0.880148 | − | 0.474699i | \(-0.842557\pi\) | ||
0.880148 | − | 0.474699i | \(-0.157443\pi\) | |||||||
\(84\) | 5.69469e6 | − | 1.36288e7i | 0.114381 | − | 0.273741i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 2.03217e7i | − | 0.371507i | ||||||
\(87\) | 5.66670e7 | + | 2.36779e7i | 0.989130 | + | 0.413301i | ||||
\(88\) | 5.60730e7 | 0.935025 | ||||||||
\(89\) | 7.30781e7i | 1.16473i | 0.812926 | + | 0.582367i | \(0.197873\pi\) | ||||
−0.812926 | + | 0.582367i | \(0.802127\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.27503e7 | −1.35254 | ||||||||
\(92\) | − | 3.20500e6i | − | 0.0447380i | ||||||
\(93\) | 1.04110e7 | − | 2.49161e7i | 0.139175 | − | 0.333079i | ||||
\(94\) | −2.67573e7 | −0.342713 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.20843e7 | + | 1.34062e7i | 0.377753 | + | 0.157842i | ||||
\(97\) | −1.45948e8 | −1.64858 | −0.824292 | − | 0.566165i | \(-0.808426\pi\) | ||||
−0.824292 | + | 0.566165i | \(0.808426\pi\) | |||||||
\(98\) | − | 1.05137e8i | − | 1.13986i | ||||||
\(99\) | 7.34023e7 | − | 7.24995e7i | 0.764133 | − | 0.754734i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.21312e7i | 0.116579i | 0.998300 | + | 0.0582893i | \(0.0185646\pi\) | ||||
−0.998300 | + | 0.0582893i | \(0.981435\pi\) | |||||||
\(102\) | −7.80790e6 | + | 1.86862e7i | −0.0721330 | + | 0.172632i | ||||
\(103\) | −1.23716e8 | −1.09920 | −0.549602 | − | 0.835427i | \(-0.685220\pi\) | ||||
−0.549602 | + | 0.835427i | \(0.685220\pi\) | |||||||
\(104\) | − | 9.65120e7i | − | 0.824989i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.32433e7 | 0.659365 | ||||||||
\(107\) | − | 1.35805e8i | − | 1.03605i | −0.855366 | − | 0.518024i | \(-0.826668\pi\) | ||
0.855366 | − | 0.518024i | \(-0.173332\pi\) | |||||||
\(108\) | 2.62259e7 | − | 1.05790e7i | 0.192768 | − | 0.0777589i | ||||
\(109\) | −2.65155e7 | −0.187843 | −0.0939214 | − | 0.995580i | \(-0.529940\pi\) | ||||
−0.0939214 | + | 0.995580i | \(0.529940\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.13395e7 | + | 5.10706e7i | −0.140570 | + | 0.336418i | ||||
\(112\) | 2.61566e8 | 1.66230 | ||||||||
\(113\) | − | 1.84493e8i | − | 1.13153i | −0.824567 | − | 0.565764i | \(-0.808581\pi\) | ||
0.824567 | − | 0.565764i | \(-0.191419\pi\) | |||||||
\(114\) | 2.76083e8 | + | 1.15359e8i | 1.63463 | + | 0.683019i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 4.03460e7i | − | 0.222827i | ||||||
\(117\) | −1.24785e8 | − | 1.26339e8i | −0.665915 | − | 0.674208i | ||||
\(118\) | −2.29704e8 | −1.18479 | ||||||||
\(119\) | 4.87254e7i | 0.242978i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.29090e7 | −0.153523 | ||||||||
\(122\) | 1.16560e8i | 0.526152i | ||||||||
\(123\) | −9.26380e7 | − | 3.87081e7i | −0.404733 | − | 0.169115i | ||||
\(124\) | −1.77398e7 | −0.0750348 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.81293e8 | − | 2.77833e8i | 1.11603 | − | 1.10230i | ||||
\(127\) | −3.35553e7 | −0.128987 | −0.0644936 | − | 0.997918i | \(-0.520543\pi\) | ||||
−0.0644936 | + | 0.997918i | \(0.520543\pi\) | |||||||
\(128\) | 3.20750e8i | 1.19489i | ||||||||
\(129\) | 3.60900e7 | − | 8.63722e7i | 0.130325 | − | 0.311900i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 2.26563e7i | − | 0.0769315i | −0.999260 | − | 0.0384658i | \(-0.987753\pi\) | ||
0.999260 | − | 0.0384658i | \(-0.0122471\pi\) | |||||||
\(132\) | −6.25370e7 | − | 2.61306e7i | −0.205988 | − | 0.0860705i | ||||
\(133\) | 7.19902e8 | 2.30074 | ||||||||
\(134\) | − | 4.36041e8i | − | 1.35241i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.07016e7 | −0.148206 | ||||||||
\(137\) | 4.06245e8i | 1.15320i | 0.817025 | + | 0.576602i | \(0.195622\pi\) | ||||
−0.817025 | + | 0.576602i | \(0.804378\pi\) | |||||||
\(138\) | 3.30749e7 | − | 7.91563e7i | 0.0911974 | − | 0.218258i | ||||
\(139\) | −7.13135e8 | −1.91035 | −0.955174 | − | 0.296046i | \(-0.904332\pi\) | ||||
−0.955174 | + | 0.296046i | \(0.904332\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.13725e8 | − | 4.75191e7i | −0.287726 | − | 0.120224i | ||||
\(142\) | −1.88340e8 | −0.463223 | ||||||||
\(143\) | 4.25594e8i | 1.01777i | ||||||||
\(144\) | 3.51907e8 | + | 3.56289e8i | 0.818423 | + | 0.828615i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.13108e8i | 1.34935i | ||||||||
\(147\) | 1.86716e8 | − | 4.46857e8i | 0.399864 | − | 0.956972i | ||||
\(148\) | 3.63614e7 | 0.0757869 | ||||||||
\(149\) | 6.69006e8i | 1.35733i | 0.734448 | + | 0.678665i | \(0.237441\pi\) | ||||
−0.734448 | + | 0.678665i | \(0.762559\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.63219e8 | −1.08335 | −0.541676 | − | 0.840587i | \(-0.682210\pi\) | ||||
−0.541676 | + | 0.840587i | \(0.682210\pi\) | |||||||
\(152\) | 7.49100e8i | 1.40335i | ||||||||
\(153\) | −6.63709e7 | + | 6.55545e7i | −0.121119 | + | 0.119629i | ||||
\(154\) | −9.47581e8 | −1.68474 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.49757e7 | + | 1.07638e8i | −0.0759415 | + | 0.181747i | ||||
\(157\) | 1.50502e8 | 0.247710 | 0.123855 | − | 0.992300i | \(-0.460474\pi\) | ||||
0.123855 | + | 0.992300i | \(0.460474\pi\) | |||||||
\(158\) | 8.82311e8i | 1.41577i | ||||||||
\(159\) | 3.53804e8 | + | 1.47834e8i | 0.553572 | + | 0.231306i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 2.06405e8i | − | 0.307197i | ||||||
\(162\) | 7.56894e8 | + | 9.36762e6i | 1.09894 | + | 0.0136010i | ||||
\(163\) | −1.13070e9 | −1.60175 | −0.800876 | − | 0.598830i | \(-0.795633\pi\) | ||||
−0.800876 | + | 0.598830i | \(0.795633\pi\) | |||||||
\(164\) | 6.59568e7i | 0.0911768i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.92299e8 | −1.04341 | ||||||||
\(167\) | − | 5.40340e8i | − | 0.694707i | −0.937734 | − | 0.347353i | \(-0.887080\pi\) | ||
0.937734 | − | 0.347353i | \(-0.112920\pi\) | |||||||
\(168\) | 9.13304e8 | + | 3.81618e8i | 1.14651 | + | 0.479062i | ||||
\(169\) | −8.32048e7 | −0.102000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.68546e8 | + | 9.80608e8i | 1.13276 | + | 1.14686i | ||||
\(172\) | −6.14956e7 | −0.0702636 | ||||||||
\(173\) | − | 2.02228e8i | − | 0.225765i | −0.993608 | − | 0.112883i | \(-0.963992\pi\) | ||
0.993608 | − | 0.112883i | \(-0.0360084\pi\) | |||||||
\(174\) | 4.16363e8 | − | 9.96457e8i | 0.454229 | − | 1.08708i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 1.20022e9i | − | 1.25086i | ||||||
\(177\) | −9.76295e8 | − | 4.07938e8i | −0.994690 | − | 0.415624i | ||||
\(178\) | 1.28504e9 | 1.28008 | ||||||||
\(179\) | − | 8.47838e8i | − | 0.825850i | −0.910765 | − | 0.412925i | \(-0.864507\pi\) | ||
0.910765 | − | 0.412925i | \(-0.135493\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.41633e9 | 1.31962 | 0.659810 | − | 0.751432i | \(-0.270637\pi\) | ||||
0.659810 | + | 0.751432i | \(0.270637\pi\) | |||||||
\(182\) | 1.63096e9i | 1.48648i | ||||||||
\(183\) | −2.07003e8 | + | 4.95409e8i | −0.184575 | + | 0.441733i | ||||
\(184\) | 2.14776e8 | 0.187376 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.38135e8 | − | 1.83072e8i | −0.366063 | − | 0.152957i | ||||
\(187\) | 2.23581e8 | 0.182839 | ||||||||
\(188\) | 8.09702e7i | 0.0648177i | ||||||||
\(189\) | 1.68897e9 | − | 6.81298e8i | 1.32366 | − | 0.533937i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 6.78044e8i | − | 0.509476i | −0.967010 | − | 0.254738i | \(-0.918011\pi\) | ||
0.967010 | − | 0.254738i | \(-0.0819893\pi\) | |||||||
\(192\) | −3.74458e8 | + | 8.96170e8i | −0.275549 | + | 0.659455i | ||||
\(193\) | 7.99869e8 | 0.576487 | 0.288244 | − | 0.957557i | \(-0.406929\pi\) | ||||
0.288244 | + | 0.957557i | \(0.406929\pi\) | |||||||
\(194\) | 2.56641e9i | 1.81184i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.18155e8 | −0.215583 | ||||||||
\(197\) | − | 2.31570e9i | − | 1.53751i | −0.639546 | − | 0.768753i | \(-0.720878\pi\) | ||
0.639546 | − | 0.768753i | \(-0.279122\pi\) | |||||||
\(198\) | −1.27486e9 | − | 1.29074e9i | −0.829473 | − | 0.839803i | ||||
\(199\) | 1.43493e9 | 0.914997 | 0.457498 | − | 0.889210i | \(-0.348746\pi\) | ||||
0.457498 | + | 0.889210i | \(0.348746\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.74379e8 | − | 1.85328e9i | 0.474427 | − | 1.13542i | ||||
\(202\) | 2.13320e8 | 0.128123 | ||||||||
\(203\) | − | 2.59832e9i | − | 1.53006i | ||||||
\(204\) | 5.65464e7 | + | 2.36275e7i | 0.0326501 | + | 0.0136426i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.17548e9i | 1.20805i | ||||||||
\(207\) | 2.81152e8 | − | 2.77694e8i | 0.153130 | − | 0.151247i | ||||
\(208\) | −2.06580e9 | −1.10366 | ||||||||
\(209\) | − | 3.30334e9i | − | 1.73128i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.19293e8 | 0.362891 | 0.181445 | − | 0.983401i | \(-0.441922\pi\) | ||||
0.181445 | + | 0.983401i | \(0.441922\pi\) | |||||||
\(212\) | − | 2.51903e8i | − | 0.124707i | ||||||
\(213\) | −8.00491e8 | − | 3.34480e8i | −0.388900 | − | 0.162499i | ||||
\(214\) | −2.38805e9 | −1.13865 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 7.08930e8 | + | 1.75747e9i | 0.325678 | + | 0.807371i | ||||
\(217\) | −1.14246e9 | −0.515232 | ||||||||
\(218\) | 4.66261e8i | 0.206444i | ||||||||
\(219\) | −1.08884e9 | + | 2.60585e9i | −0.473355 | + | 1.13285i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 3.84825e8i | − | 0.161322i | ||||||
\(222\) | 8.98047e8 | + | 3.75243e8i | 0.369732 | + | 0.154490i | ||||
\(223\) | −1.26189e9 | −0.510274 | −0.255137 | − | 0.966905i | \(-0.582121\pi\) | ||||
−0.255137 | + | 0.966905i | \(0.582121\pi\) | |||||||
\(224\) | − | 1.47115e9i | − | 0.584338i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.24420e9 | −1.24358 | ||||||||
\(227\) | − | 4.20903e9i | − | 1.58518i | −0.609755 | − | 0.792590i | \(-0.708732\pi\) | ||
0.609755 | − | 0.792590i | \(-0.291268\pi\) | |||||||
\(228\) | 3.49089e8 | − | 8.35454e8i | 0.129180 | − | 0.309160i | ||||
\(229\) | −7.15398e8 | −0.260139 | −0.130070 | − | 0.991505i | \(-0.541520\pi\) | ||||
−0.130070 | + | 0.991505i | \(0.541520\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.02744e9 | − | 1.68284e9i | −1.41443 | − | 0.591009i | ||||
\(232\) | 2.70370e9 | 0.933269 | ||||||||
\(233\) | − | 3.80229e9i | − | 1.29009i | −0.764143 | − | 0.645047i | \(-0.776838\pi\) | ||
0.764143 | − | 0.645047i | \(-0.223162\pi\) | |||||||
\(234\) | −2.22160e9 | + | 2.19427e9i | −0.740973 | + | 0.731859i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.95106e8i | 0.224080i | ||||||||
\(237\) | −1.56692e9 | + | 3.75003e9i | −0.496654 | + | 1.18861i | ||||
\(238\) | 8.56809e8 | 0.267040 | ||||||||
\(239\) | 3.64896e9i | 1.11835i | 0.829050 | + | 0.559175i | \(0.188882\pi\) | ||||
−0.829050 | + | 0.559175i | \(0.811118\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.36444e9 | 0.404471 | 0.202235 | − | 0.979337i | \(-0.435179\pi\) | ||||
0.202235 | + | 0.979337i | \(0.435179\pi\) | |||||||
\(242\) | 5.78686e8i | 0.168726i | ||||||||
\(243\) | 3.20034e9 | + | 1.38401e9i | 0.917849 | + | 0.396929i | ||||
\(244\) | 3.52723e8 | 0.0995119 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.80661e8 | + | 1.62899e9i | −0.185862 | + | 0.444813i | ||||
\(247\) | −5.68566e9 | −1.52754 | ||||||||
\(248\) | − | 1.18880e9i | − | 0.314269i | ||||||
\(249\) | −3.36746e9 | − | 1.40707e9i | −0.876001 | − | 0.366031i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.18506e9i | 1.81024i | 0.425160 | + | 0.905118i | \(0.360218\pi\) | ||||
−0.425160 | + | 0.905118i | \(0.639782\pi\) | |||||||
\(252\) | −8.40750e8 | − | 8.51219e8i | −0.208480 | − | 0.211076i | ||||
\(253\) | −9.47109e8 | −0.231163 | ||||||||
\(254\) | 5.90051e8i | 0.141760i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.57056e9 | 0.598506 | ||||||||
\(257\) | − | 3.06178e9i | − | 0.701846i | −0.936404 | − | 0.350923i | \(-0.885868\pi\) | ||
0.936404 | − | 0.350923i | \(-0.114132\pi\) | |||||||
\(258\) | −1.51881e9 | − | 6.34622e8i | −0.342786 | − | 0.143231i | ||||
\(259\) | 2.34171e9 | 0.520396 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.53928e9 | − | 3.49575e9i | 0.762698 | − | 0.753317i | ||||
\(262\) | −3.98399e8 | −0.0845498 | ||||||||
\(263\) | − | 3.51144e9i | − | 0.733943i | −0.930232 | − | 0.366971i | \(-0.880395\pi\) | ||
0.930232 | − | 0.366971i | \(-0.119605\pi\) | |||||||
\(264\) | 1.75109e9 | − | 4.19078e9i | 0.360490 | − | 0.862739i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 1.26591e10i | − | 2.52857i | ||||||
\(267\) | 5.46171e9 | + | 2.28214e9i | 1.07469 | + | 0.449052i | ||||
\(268\) | −1.31950e9 | −0.255783 | ||||||||
\(269\) | − | 1.89915e9i | − | 0.362703i | −0.983418 | − | 0.181352i | \(-0.941953\pi\) | ||
0.983418 | − | 0.181352i | \(-0.0580472\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.54442e7 | 0.0121337 | 0.00606686 | − | 0.999982i | \(-0.498069\pi\) | ||||
0.00606686 | + | 0.999982i | \(0.498069\pi\) | |||||||
\(272\) | 1.08525e9i | 0.198268i | ||||||||
\(273\) | −2.89648e9 | + | 6.93197e9i | −0.521458 | + | 1.24798i | ||||
\(274\) | 7.14359e9 | 1.26740 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.39535e8 | − | 1.00088e8i | −0.0412793 | − | 0.0172483i | ||||
\(277\) | 6.90961e9 | 1.17364 | 0.586820 | − | 0.809718i | \(-0.300380\pi\) | ||||
0.586820 | + | 0.809718i | \(0.300380\pi\) | |||||||
\(278\) | 1.25401e10i | 2.09952i | ||||||||
\(279\) | −1.53705e9 | − | 1.55619e9i | −0.253672 | − | 0.256831i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.73863e9i | − | 0.278857i | −0.990232 | − | 0.139428i | \(-0.955474\pi\) | ||
0.990232 | − | 0.139428i | \(-0.0445265\pi\) | |||||||
\(282\) | −8.35596e8 | + | 1.99978e9i | −0.132130 | + | 0.316218i | ||||
\(283\) | 4.14006e9 | 0.645448 | 0.322724 | − | 0.946493i | \(-0.395401\pi\) | ||||
0.322724 | + | 0.946493i | \(0.395401\pi\) | |||||||
\(284\) | 5.69937e8i | 0.0876100i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.48383e9 | 1.11856 | ||||||||
\(287\) | 4.24768e9i | 0.626072i | ||||||||
\(288\) | 2.00391e9 | − | 1.97926e9i | 0.291278 | − | 0.287695i | ||||
\(289\) | 6.77359e9 | 0.971019 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.55777e9 | + | 1.09079e10i | −0.635595 | + | 1.52113i | ||||
\(292\) | 1.85533e9 | 0.255205 | ||||||||
\(293\) | 6.87312e9i | 0.932575i | 0.884633 | + | 0.466287i | \(0.154409\pi\) | ||||
−0.884633 | + | 0.466287i | \(0.845591\pi\) | |||||||
\(294\) | −7.85772e9 | − | 3.28330e9i | −1.05174 | − | 0.439461i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.43668e9i | 0.317419i | ||||||||
\(297\) | −3.12620e9 | − | 7.75001e9i | −0.401783 | − | 0.996039i | ||||
\(298\) | 1.17641e10 | 1.49174 | ||||||||
\(299\) | 1.63015e9i | 0.203959i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.96038e9 | −0.482470 | ||||||||
\(302\) | 9.90389e9i | 1.19063i | ||||||||
\(303\) | 9.06662e8 | + | 3.78842e8i | 0.107566 | + | 0.0449457i | ||||
\(304\) | 1.60342e10 | 1.87738 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.15274e9 | + | 1.16709e9i | 0.131476 | + | 0.133113i | ||||
\(307\) | −2.34414e9 | −0.263894 | −0.131947 | − | 0.991257i | \(-0.542123\pi\) | ||||
−0.131947 | + | 0.991257i | \(0.542123\pi\) | |||||||
\(308\) | 2.86747e9i | 0.318637i | ||||||||
\(309\) | −3.86350e9 | + | 9.24630e9i | −0.423787 | + | 1.01422i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 6.18587e9i | − | 0.661240i | −0.943764 | − | 0.330620i | \(-0.892742\pi\) | ||
0.943764 | − | 0.330620i | \(-0.107258\pi\) | |||||||
\(312\) | −7.21312e9 | − | 3.01395e9i | −0.761210 | − | 0.318066i | ||||
\(313\) | −6.33696e9 | −0.660243 | −0.330121 | − | 0.943939i | \(-0.607090\pi\) | ||||
−0.330121 | + | 0.943939i | \(0.607090\pi\) | |||||||
\(314\) | − | 2.64649e9i | − | 0.272240i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.66996e9 | 0.267767 | ||||||||
\(317\) | 2.63659e9i | 0.261099i | 0.991442 | + | 0.130550i | \(0.0416742\pi\) | ||||
−0.991442 | + | 0.130550i | \(0.958326\pi\) | |||||||
\(318\) | 2.59958e9 | − | 6.22144e9i | 0.254212 | − | 0.608390i | ||||
\(319\) | −1.19226e10 | −1.15136 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.01498e10 | − | 4.24101e9i | −0.955953 | − | 0.399438i | ||||
\(322\) | −3.62951e9 | −0.337617 | ||||||||
\(323\) | 2.98690e9i | 0.274417i | ||||||||
\(324\) | 2.83474e7 | − | 2.29044e9i | 0.00257237 | − | 0.207844i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.98826e10i | 1.76037i | ||||||||
\(327\) | −8.28047e8 | + | 1.98172e9i | −0.0724209 | + | 0.173321i | ||||
\(328\) | −4.41996e9 | −0.381876 | ||||||||
\(329\) | 5.21456e9i | 0.445076i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.06785e9 | −0.505502 | −0.252751 | − | 0.967531i | \(-0.581335\pi\) | ||||
−0.252751 | + | 0.967531i | \(0.581335\pi\) | |||||||
\(332\) | 2.39758e9i | 0.197342i | ||||||||
\(333\) | 3.15051e9 | + | 3.18974e9i | 0.256214 | + | 0.259405i | ||||
\(334\) | −9.50158e9 | −0.763501 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 8.16837e9 | − | 1.95489e10i | 0.640882 | − | 1.53379i | ||||
\(337\) | 1.29810e10 | 1.00644 | 0.503220 | − | 0.864158i | \(-0.332149\pi\) | ||||
0.503220 | + | 0.864158i | \(0.332149\pi\) | |||||||
\(338\) | 1.46311e9i | 0.112101i | ||||||||
\(339\) | −1.37886e10 | − | 5.76148e9i | −1.04405 | − | 0.436249i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.24230e9i | 0.387708i | ||||||||
\(342\) | 1.72434e10 | − | 1.70313e10i | 1.26043 | − | 1.24493i | ||||
\(343\) | −7.33974e8 | −0.0530279 | ||||||||
\(344\) | − | 4.12100e9i | − | 0.294285i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.55607e9 | −0.248122 | ||||||||
\(347\) | 1.27979e10i | 0.882718i | 0.897331 | + | 0.441359i | \(0.145504\pi\) | ||||
−0.897331 | + | 0.441359i | \(0.854496\pi\) | |||||||
\(348\) | −3.01538e9 | − | 1.25996e9i | −0.205601 | − | 0.0859089i | ||||
\(349\) | 7.93032e9 | 0.534551 | 0.267275 | − | 0.963620i | \(-0.413877\pi\) | ||||
0.267275 | + | 0.963620i | \(0.413877\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.33392e10 | + | 5.38077e9i | −0.878823 | + | 0.354500i | ||||
\(352\) | −6.75050e9 | −0.439709 | ||||||||
\(353\) | − | 1.11540e10i | − | 0.718342i | −0.933272 | − | 0.359171i | \(-0.883059\pi\) | ||
0.933272 | − | 0.359171i | \(-0.116941\pi\) | |||||||
\(354\) | −7.17336e9 | + | 1.71676e10i | −0.456782 | + | 1.09319i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 3.88865e9i | − | 0.242102i | ||||||
\(357\) | 3.64164e9 | + | 1.52163e9i | 0.224194 | + | 0.0936779i | ||||
\(358\) | −1.49088e10 | −0.907631 | ||||||||
\(359\) | − | 3.89548e9i | − | 0.234522i | −0.993101 | − | 0.117261i | \(-0.962589\pi\) | ||
0.993101 | − | 0.117261i | \(-0.0374114\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.71469e10 | 1.59842 | ||||||||
\(362\) | − | 2.49053e10i | − | 1.45030i | ||||||
\(363\) | −1.02771e9 | + | 2.45955e9i | −0.0591893 | + | 0.141654i | ||||
\(364\) | 4.93545e9 | 0.281139 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 8.71148e9 | + | 3.64003e9i | 0.485476 | + | 0.202853i | ||||
\(367\) | −2.72657e10 | −1.50298 | −0.751488 | − | 0.659747i | \(-0.770663\pi\) | ||||
−0.751488 | + | 0.659747i | \(0.770663\pi\) | |||||||
\(368\) | − | 4.59720e9i | − | 0.250670i | ||||||
\(369\) | −5.78594e9 | + | 5.71477e9i | −0.312082 | + | 0.308243i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 1.62228e10i | − | 0.856307i | ||||||
\(372\) | −5.53993e8 | + | 1.32584e9i | −0.0289289 | + | 0.0692340i | ||||
\(373\) | 8.68516e9 | 0.448686 | 0.224343 | − | 0.974510i | \(-0.427976\pi\) | ||||
0.224343 | + | 0.974510i | \(0.427976\pi\) | |||||||
\(374\) | − | 3.93155e9i | − | 0.200945i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.42605e9 | −0.271476 | ||||||||
\(377\) | 2.05211e10i | 1.01586i | ||||||||
\(378\) | −1.19802e10 | − | 2.96996e10i | −0.586811 | − | 1.45473i | ||||
\(379\) | 2.18982e10 | 1.06133 | 0.530666 | − | 0.847581i | \(-0.321942\pi\) | ||||
0.530666 | + | 0.847581i | \(0.321942\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.04789e9 | + | 2.50786e9i | −0.0497297 | + | 0.119015i | ||||
\(382\) | −1.19230e10 | −0.559928 | ||||||||
\(383\) | − | 3.16884e10i | − | 1.47267i | −0.676618 | − | 0.736334i | \(-0.736555\pi\) | ||
0.676618 | − | 0.736334i | \(-0.263445\pi\) | |||||||
\(384\) | 2.39722e10 | + | 1.00166e10i | 1.10251 | + | 0.460677i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 1.40652e10i | − | 0.633575i | ||||||
\(387\) | −5.32824e9 | − | 5.39459e9i | −0.237542 | − | 0.240500i | ||||
\(388\) | 7.76622e9 | 0.342675 | ||||||||
\(389\) | − | 9.57908e9i | − | 0.418336i | −0.977880 | − | 0.209168i | \(-0.932924\pi\) | ||
0.977880 | − | 0.209168i | \(-0.0670756\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.56382e8 | 0.0366404 | ||||||||
\(392\) | − | 2.13205e10i | − | 0.902928i | ||||||
\(393\) | −1.69329e9 | − | 7.07528e8i | −0.0709840 | − | 0.0296602i | ||||
\(394\) | −4.07202e10 | −1.68976 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.90590e9 | + | 3.85786e9i | −0.158833 | + | 0.156879i | ||||
\(397\) | 4.45553e10 | 1.79365 | 0.896824 | − | 0.442388i | \(-0.145868\pi\) | ||||
0.896824 | + | 0.442388i | \(0.145868\pi\) | |||||||
\(398\) | − | 2.52325e10i | − | 1.00561i | ||||||
\(399\) | 2.24816e10 | − | 5.38040e10i | 0.887026 | − | 2.12287i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.51147e10i | 0.971293i | 0.874155 | + | 0.485647i | \(0.161416\pi\) | ||||
−0.874155 | + | 0.485647i | \(0.838584\pi\) | |||||||
\(402\) | −3.25888e10 | − | 1.36170e10i | −1.24786 | − | 0.521408i | ||||
\(403\) | 9.02297e9 | 0.342081 | ||||||||
\(404\) | − | 6.45529e8i | − | 0.0242321i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.56900e10 | −1.68158 | ||||||||
\(407\) | − | 1.07452e10i | − | 0.391594i | ||||||
\(408\) | −1.58335e9 | + | 3.78933e9i | −0.0571394 | + | 0.136748i | ||||
\(409\) | 1.11563e10 | 0.398683 | 0.199341 | − | 0.979930i | \(-0.436120\pi\) | ||||
0.199341 | + | 0.979930i | \(0.436120\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.03620e10 | + | 1.26865e10i | 1.06405 | + | 0.444606i | ||||
\(412\) | 6.58322e9 | 0.228481 | ||||||||
\(413\) | 4.47655e10i | 1.53866i | ||||||||
\(414\) | −4.88310e9 | − | 4.94391e9i | −0.166224 | − | 0.168294i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.16189e10i | 0.387963i | ||||||||
\(417\) | −2.22703e10 | + | 5.32982e10i | −0.736515 | + | 1.76266i | ||||
\(418\) | −5.80874e10 | −1.90273 | ||||||||
\(419\) | 5.51814e10i | 1.79034i | 0.445720 | + | 0.895172i | \(0.352948\pi\) | ||||
−0.445720 | + | 0.895172i | \(0.647052\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.21829e10 | 0.706139 | 0.353070 | − | 0.935597i | \(-0.385138\pi\) | ||||
0.353070 | + | 0.935597i | \(0.385138\pi\) | |||||||
\(422\) | − | 1.26484e10i | − | 0.398827i | ||||||
\(423\) | −7.10296e9 | + | 7.01559e9i | −0.221859 | + | 0.219131i | ||||
\(424\) | 1.68807e10 | 0.522309 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.88163e9 | + | 1.40762e10i | −0.178591 | + | 0.427412i | ||||
\(427\) | 2.27157e10 | 0.683305 | ||||||||
\(428\) | 7.22648e9i | 0.215354i | ||||||||
\(429\) | 3.18080e10 | + | 1.32908e10i | 0.939091 | + | 0.392392i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 4.91950e10i | − | 1.42565i | −0.701343 | − | 0.712824i | \(-0.747416\pi\) | ||
0.701343 | − | 0.712824i | \(-0.252584\pi\) | |||||||
\(432\) | 3.76180e10 | − | 1.51744e10i | 1.08009 | − | 0.435688i | ||||
\(433\) | 1.97041e10 | 0.560537 | 0.280268 | − | 0.959922i | \(-0.409577\pi\) | ||||
0.280268 | + | 0.959922i | \(0.409577\pi\) | |||||||
\(434\) | 2.00896e10i | 0.566254i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.41095e9 | 0.0390451 | ||||||||
\(437\) | − | 1.26528e10i | − | 0.346944i | ||||||
\(438\) | 4.58224e10 | + | 1.91466e10i | 1.24504 | + | 0.520230i | ||||
\(439\) | −1.74433e10 | −0.469647 | −0.234824 | − | 0.972038i | \(-0.575451\pi\) | ||||
−0.234824 | + | 0.972038i | \(0.575451\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.75663e10 | − | 2.79096e10i | −0.728826 | − | 0.737902i | ||||
\(442\) | −6.76693e9 | −0.177297 | ||||||||
\(443\) | − | 2.46881e10i | − | 0.641022i | −0.947245 | − | 0.320511i | \(-0.896145\pi\) | ||
0.947245 | − | 0.320511i | \(-0.103855\pi\) | |||||||
\(444\) | 1.13552e9 | − | 2.71758e9i | 0.0292189 | − | 0.0699279i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.21897e10i | 0.560805i | ||||||||
\(447\) | 5.00002e10 | + | 2.08922e10i | 1.25240 | + | 0.523305i | ||||
\(448\) | 4.10916e10 | 1.02010 | ||||||||
\(449\) | − | 4.94885e10i | − | 1.21764i | −0.793308 | − | 0.608820i | \(-0.791643\pi\) | ||
0.793308 | − | 0.608820i | \(-0.208357\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.94909e10 | 0.471114 | ||||||||
\(452\) | 9.81727e9i | 0.235200i | ||||||||
\(453\) | −1.75886e10 | + | 4.20939e10i | −0.417676 | + | 0.999599i | ||||
\(454\) | −7.40134e10 | −1.74216 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.59862e10 | + | 2.33934e10i | 1.29486 | + | 0.541047i | ||||
\(457\) | −7.51747e10 | −1.72348 | −0.861741 | − | 0.507349i | \(-0.830626\pi\) | ||||
−0.861741 | + | 0.507349i | \(0.830626\pi\) | |||||||
\(458\) | 1.25799e10i | 0.285900i | ||||||||
\(459\) | 2.82673e9 | + | 7.00761e9i | 0.0636845 | + | 0.157877i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 1.73856e10i | − | 0.384933i | −0.981304 | − | 0.192466i | \(-0.938351\pi\) | ||
0.981304 | − | 0.192466i | \(-0.0616487\pi\) | |||||||
\(462\) | −2.95918e10 | + | 7.08203e10i | −0.649535 | + | 1.55450i | ||||
\(463\) | −2.11164e10 | −0.459511 | −0.229755 | − | 0.973248i | \(-0.573793\pi\) | ||||
−0.229755 | + | 0.973248i | \(0.573793\pi\) | |||||||
\(464\) | − | 5.78717e10i | − | 1.24852i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.68610e10 | −1.41785 | ||||||||
\(467\) | − | 1.49113e10i | − | 0.313508i | −0.987638 | − | 0.156754i | \(-0.949897\pi\) | ||
0.987638 | − | 0.156754i | \(-0.0501030\pi\) | |||||||
\(468\) | 6.64009e9 | + | 6.72278e9i | 0.138417 | + | 0.140141i | ||||
\(469\) | −8.49774e10 | −1.75635 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.69999e9 | − | 1.12482e10i | 0.0955022 | − | 0.228560i | ||||
\(472\) | −4.65811e10 | −0.938516 | ||||||||
\(473\) | 1.81726e10i | 0.363054i | ||||||||
\(474\) | 6.59421e10 | + | 2.75535e10i | 1.30632 | + | 0.545837i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 2.59279e9i | − | 0.0505056i | ||||||
\(477\) | 2.20977e10 | − | 2.18259e10i | 0.426848 | − | 0.421598i | ||||
\(478\) | 6.41649e10 | 1.22910 | ||||||||
\(479\) | 5.15755e9i | 0.0979718i | 0.998799 | + | 0.0489859i | \(0.0155989\pi\) | ||||
−0.998799 | + | 0.0489859i | \(0.984401\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.84944e10 | −0.345510 | ||||||||
\(482\) | − | 2.39929e10i | − | 0.444524i | ||||||
\(483\) | −1.54263e10 | − | 6.44576e9i | −0.283448 | − | 0.118437i | ||||
\(484\) | 1.75116e9 | 0.0319114 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.43370e10 | − | 5.62762e10i | 0.436236 | − | 1.00874i | ||||
\(487\) | 3.79969e10 | 0.675510 | 0.337755 | − | 0.941234i | \(-0.390332\pi\) | ||||
0.337755 | + | 0.941234i | \(0.390332\pi\) | |||||||
\(488\) | 2.36370e10i | 0.416786i | ||||||||
\(489\) | −3.53102e10 | + | 8.45059e10i | −0.617540 | + | 1.47792i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.21946e10i | 1.24216i | 0.783746 | + | 0.621081i | \(0.213306\pi\) | ||||
−0.783746 | + | 0.621081i | \(0.786694\pi\) | |||||||
\(492\) | 4.92948e9 | + | 2.05975e9i | 0.0841280 | + | 0.0351523i | ||||
\(493\) | 1.07805e10 | 0.182496 | ||||||||
\(494\) | 9.99791e10i | 1.67881i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.54457e10 | −0.420425 | ||||||||
\(497\) | 3.67045e10i | 0.601580i | ||||||||
\(498\) | −2.47425e10 | + | 5.92148e10i | −0.402278 | + | 0.962749i | ||||
\(499\) | 2.25403e10 | 0.363544 | 0.181772 | − | 0.983341i | \(-0.441817\pi\) | ||||
0.181772 | + | 0.983341i | \(0.441817\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.03839e10 | − | 1.68741e10i | −0.641000 | − | 0.267837i | ||||
\(502\) | 1.26345e11 | 1.98950 | ||||||||
\(503\) | 1.10303e11i | 1.72312i | 0.507657 | + | 0.861559i | \(0.330512\pi\) | ||||
−0.507657 | + | 0.861559i | \(0.669488\pi\) | |||||||
\(504\) | 5.70427e10 | − | 5.63411e10i | 0.884052 | − | 0.873178i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.66544e10i | 0.254054i | ||||||||
\(507\) | −2.59838e9 | + | 6.21856e9i | −0.0393252 | + | 0.0941148i | ||||
\(508\) | 1.78555e9 | 0.0268113 | ||||||||
\(509\) | − | 9.85205e10i | − | 1.46776i | −0.679278 | − | 0.733881i | \(-0.737707\pi\) | ||
0.679278 | − | 0.733881i | \(-0.262293\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.19485e11 | 1.75238 | ||||||||
\(512\) | 3.69102e10i | 0.537114i | ||||||||
\(513\) | 1.03535e11 | − | 4.17641e10i | 1.49492 | − | 0.603022i | ||||
\(514\) | −5.38397e10 | −0.771348 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.92043e9 | + | 4.59606e9i | −0.0270894 | + | 0.0648316i | ||||
\(517\) | 2.39275e10 | 0.334915 | ||||||||
\(518\) | − | 4.11777e10i | − | 0.571930i | ||||||
\(519\) | −1.51141e10 | − | 6.31533e9i | −0.208312 | − | 0.0870416i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.84071e10i | 1.06415i | 0.846696 | + | 0.532077i | \(0.178588\pi\) | ||||
−0.846696 | + | 0.532077i | \(0.821412\pi\) | |||||||
\(522\) | −6.14707e10 | − | 6.22362e10i | −0.827916 | − | 0.838226i | ||||
\(523\) | −1.26646e11 | −1.69272 | −0.846359 | − | 0.532613i | \(-0.821210\pi\) | ||||
−0.846359 | + | 0.532613i | \(0.821210\pi\) | |||||||
\(524\) | 1.20559e9i | 0.0159910i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.17467e10 | −0.806623 | ||||||||
\(527\) | − | 4.74012e9i | − | 0.0614536i | ||||||
\(528\) | −8.97020e10 | − | 3.74814e10i | −1.15416 | − | 0.482258i | ||||
\(529\) | 7.46833e10 | 0.953676 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.09769e10 | + | 6.02269e10i | −0.766986 | + | 0.757552i | ||||
\(532\) | −3.83076e10 | −0.478232 | ||||||||
\(533\) | − | 3.35474e10i | − | 0.415672i | ||||||
\(534\) | 4.01301e10 | − | 9.60410e10i | 0.493520 | − | 1.18111i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 8.84238e10i | − | 1.07130i | ||||||
\(537\) | −6.33657e10 | − | 2.64769e10i | −0.762004 | − | 0.318398i | ||||
\(538\) | −3.33956e10 | −0.398620 | ||||||||
\(539\) | 9.40180e10i | 1.11392i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.35314e10 | −0.975126 | −0.487563 | − | 0.873088i | \(-0.662114\pi\) | ||||
−0.487563 | + | 0.873088i | \(0.662114\pi\) | |||||||
\(542\) | − | 1.15080e9i | − | 0.0133353i | ||||||
\(543\) | 4.42301e10 | − | 1.05853e11i | 0.508767 | − | 1.21760i | ||||
\(544\) | 6.10384e9 | 0.0696960 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.21895e11 | + | 5.09329e10i | 1.37156 | + | 0.573096i | ||||
\(547\) | −2.75997e10 | −0.308287 | −0.154144 | − | 0.988048i | \(-0.549262\pi\) | ||||
−0.154144 | + | 0.988048i | \(0.549262\pi\) | |||||||
\(548\) | − | 2.16172e10i | − | 0.239705i | ||||||
\(549\) | 3.05614e10 | + | 3.09420e10i | 0.336422 | + | 0.340611i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1.59279e11i | − | 1.72803i | ||||||
\(552\) | 6.70719e9 | − | 1.60519e10i | 0.0722411 | − | 0.172890i | ||||
\(553\) | 1.71948e11 | 1.83864 | ||||||||
\(554\) | − | 1.21502e11i | − | 1.28986i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.79475e10 | 0.397086 | ||||||||
\(557\) | 1.06328e11i | 1.10465i | 0.833628 | + | 0.552326i | \(0.186260\pi\) | ||||
−0.833628 | + | 0.552326i | \(0.813740\pi\) | |||||||
\(558\) | −2.73648e10 | + | 2.70282e10i | −0.282264 | + | 0.278792i | ||||
\(559\) | 3.12784e10 | 0.320329 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.98216e9 | − | 1.67100e10i | 0.0704918 | − | 0.168704i | ||||
\(562\) | −3.05728e10 | −0.306471 | ||||||||
\(563\) | − | 1.35823e11i | − | 1.35188i | −0.736956 | − | 0.675941i | \(-0.763737\pi\) | ||
0.736956 | − | 0.675941i | \(-0.236263\pi\) | |||||||
\(564\) | 6.05155e9 | + | 2.52860e9i | 0.0598067 | + | 0.0249898i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 7.28006e10i | − | 0.709364i | ||||||
\(567\) | 1.82560e9 | − | 1.47506e11i | 0.0176633 | − | 1.42718i | ||||
\(568\) | −3.81931e10 | −0.366937 | ||||||||
\(569\) | 6.61732e10i | 0.631296i | 0.948876 | + | 0.315648i | \(0.102222\pi\) | ||||
−0.948876 | + | 0.315648i | \(0.897778\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.17754e10 | 0.863340 | 0.431670 | − | 0.902032i | \(-0.357925\pi\) | ||||
0.431670 | + | 0.902032i | \(0.357925\pi\) | |||||||
\(572\) | − | 2.26468e10i | − | 0.211555i | ||||||
\(573\) | −5.06756e10 | − | 2.11744e10i | −0.470089 | − | 0.196424i | ||||
\(574\) | 7.46931e10 | 0.688070 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 5.52840e10 | + | 5.59725e10i | 0.502238 | + | 0.508493i | ||||
\(577\) | −1.35583e11 | −1.22321 | −0.611607 | − | 0.791162i | \(-0.709476\pi\) | ||||
−0.611607 | + | 0.791162i | \(0.709476\pi\) | |||||||
\(578\) | − | 1.19110e11i | − | 1.06718i | ||||||
\(579\) | 2.49789e10 | − | 5.97806e10i | 0.222259 | − | 0.531920i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.54406e11i | 1.35506i | ||||||||
\(582\) | 1.91808e11 | + | 8.01458e10i | 1.67177 | + | 0.698536i | ||||
\(583\) | −7.44398e10 | −0.644363 | ||||||||
\(584\) | 1.24331e11i | 1.06888i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.20860e11 | 1.02492 | ||||||||
\(587\) | − | 6.90011e10i | − | 0.581171i | −0.956849 | − | 0.290585i | \(-0.906150\pi\) | ||
0.956849 | − | 0.290585i | \(-0.0938500\pi\) | |||||||
\(588\) | −9.93558e9 | + | 2.37783e10i | −0.0831159 | + | 0.198917i | ||||
\(589\) | −7.00338e10 | −0.581897 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.73071e11 | − | 7.23163e10i | −1.41864 | − | 0.592770i | ||||
\(592\) | 5.21562e10 | 0.424639 | ||||||||
\(593\) | 2.17447e11i | 1.75847i | 0.476391 | + | 0.879234i | \(0.341945\pi\) | ||||
−0.476391 | + | 0.879234i | \(0.658055\pi\) | |||||||
\(594\) | −1.36279e11 | + | 5.49725e10i | −1.09467 | + | 0.441570i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 3.55993e10i | − | 0.282135i | ||||||
\(597\) | 4.48112e10 | − | 1.07244e11i | 0.352768 | − | 0.844260i | ||||
\(598\) | 2.86653e10 | 0.224156 | ||||||||
\(599\) | − | 1.17194e11i | − | 0.910327i | −0.890408 | − | 0.455163i | \(-0.849581\pi\) | ||
0.890408 | − | 0.455163i | \(-0.150419\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.03470e10 | −0.309253 | −0.154626 | − | 0.987973i | \(-0.549417\pi\) | ||||
−0.154626 | + | 0.987973i | \(0.549417\pi\) | |||||||
\(602\) | 6.96410e10i | 0.530248i | ||||||||
\(603\) | −1.14327e11 | − | 1.15751e11i | −0.864731 | − | 0.875499i | ||||
\(604\) | 2.99702e10 | 0.225186 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 6.66173e9 | − | 1.59431e10i | 0.0493965 | − | 0.118218i | ||||
\(607\) | 4.42279e10 | 0.325793 | 0.162896 | − | 0.986643i | \(-0.447916\pi\) | ||||
0.162896 | + | 0.986643i | \(0.447916\pi\) | |||||||
\(608\) | − | 9.01823e10i | − | 0.659944i | ||||||
\(609\) | −1.94193e11 | − | 8.11423e10i | −1.41177 | − | 0.589900i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 4.11837e10i | − | 0.295502i | ||||||
\(612\) | 3.53174e9 | − | 3.48830e9i | 0.0251758 | − | 0.0248662i | ||||
\(613\) | −2.22935e11 | −1.57883 | −0.789416 | − | 0.613858i | \(-0.789617\pi\) | ||||
−0.789416 | + | 0.613858i | \(0.789617\pi\) | |||||||
\(614\) | 4.12204e10i | 0.290027i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.92158e11 | −1.33455 | ||||||||
\(617\) | − | 1.00709e11i | − | 0.694906i | −0.937697 | − | 0.347453i | \(-0.887047\pi\) | ||
0.937697 | − | 0.347453i | \(-0.112953\pi\) | |||||||
\(618\) | 1.62591e11 | + | 6.79375e10i | 1.11466 | + | 0.465753i | ||||
\(619\) | −9.16635e10 | −0.624358 | −0.312179 | − | 0.950023i | \(-0.601059\pi\) | ||||
−0.312179 | + | 0.950023i | \(0.601059\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.19743e10 | − | 2.96848e10i | −0.0805161 | − | 0.199603i | ||||
\(622\) | −1.08775e11 | −0.726721 | ||||||||
\(623\) | − | 2.50433e11i | − | 1.66241i | ||||||
\(624\) | −6.45124e10 | + | 1.54394e11i | −0.425505 | + | 1.01834i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.11432e11i | 0.725624i | ||||||||
\(627\) | −2.46885e11 | − | 1.03159e11i | −1.59744 | − | 0.667479i | ||||
\(628\) | −8.00855e9 | −0.0514891 | ||||||||
\(629\) | 9.71585e9i | 0.0620695i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.69834e10 | −0.548680 | −0.274340 | − | 0.961633i | \(-0.588459\pi\) | ||||
−0.274340 | + | 0.961633i | \(0.588459\pi\) | |||||||
\(632\) | 1.78922e11i | 1.12149i | ||||||||
\(633\) | 2.24626e10 | − | 5.37585e10i | 0.139909 | − | 0.334836i | ||||
\(634\) | 4.63629e10 | 0.286955 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.88267e10 | − | 7.86660e9i | −0.115066 | − | 0.0480794i | ||||
\(637\) | 1.61822e11 | 0.982836 | ||||||||
\(638\) | 2.09653e11i | 1.26537i | ||||||||
\(639\) | −4.99967e10 | + | 4.93817e10i | −0.299873 | + | 0.296185i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.68189e11i | 0.996243i | 0.867107 | + | 0.498122i | \(0.165977\pi\) | ||||
−0.867107 | + | 0.498122i | \(0.834023\pi\) | |||||||
\(642\) | −7.45758e10 | + | 1.78478e11i | −0.438993 | + | 1.05062i | ||||
\(643\) | 1.47717e11 | 0.864144 | 0.432072 | − | 0.901839i | \(-0.357783\pi\) | ||||
0.432072 | + | 0.901839i | \(0.357783\pi\) | |||||||
\(644\) | 1.09833e10i | 0.0638540i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.25230e10 | 0.301592 | ||||||||
\(647\) | − | 5.56399e10i | − | 0.317518i | −0.987317 | − | 0.158759i | \(-0.949251\pi\) | ||
0.987317 | − | 0.158759i | \(-0.0507493\pi\) | |||||||
\(648\) | 1.53489e11 | + | 1.89964e9i | 0.870516 | + | 0.0107739i | ||||
\(649\) | 2.05411e11 | 1.15783 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.56777e10 | + | 8.53853e10i | −0.198643 | + | 0.475400i | ||||
\(652\) | 6.01669e10 | 0.332941 | ||||||||
\(653\) | 3.03168e11i | 1.66737i | 0.552243 | + | 0.833683i | \(0.313772\pi\) | ||||
−0.552243 | + | 0.833683i | \(0.686228\pi\) | |||||||
\(654\) | 3.48474e10 | + | 1.45607e10i | 0.190484 | + | 0.0795925i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9.46074e10i | 0.510869i | ||||||||
\(657\) | 1.60753e11 | + | 1.62755e11i | 0.862776 | + | 0.873520i | ||||
\(658\) | 9.16950e10 | 0.489150 | ||||||||
\(659\) | − | 4.09785e10i | − | 0.217278i | −0.994081 | − | 0.108639i | \(-0.965351\pi\) | ||
0.994081 | − | 0.108639i | \(-0.0346492\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.42879e11 | 1.27229 | 0.636143 | − | 0.771571i | \(-0.280529\pi\) | ||||
0.636143 | + | 0.771571i | \(0.280529\pi\) | |||||||
\(662\) | 1.06700e11i | 0.555560i | ||||||||
\(663\) | −2.87610e10 | − | 1.20176e10i | −0.148851 | − | 0.0621961i | ||||
\(664\) | −1.60668e11 | −0.826530 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.60898e10 | − | 5.53999e10i | 0.285093 | − | 0.281586i | ||||
\(667\) | −4.56673e10 | −0.230729 | ||||||||
\(668\) | 2.87527e10i | 0.144402i | ||||||||
\(669\) | −3.94074e10 | + | 9.43114e10i | −0.196731 | + | 0.470825i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1.04233e11i | − | 0.514181i | ||||||
\(672\) | −1.09950e11 | − | 4.59420e10i | −0.539163 | − | 0.225286i | ||||
\(673\) | 2.34992e11 | 1.14549 | 0.572747 | − | 0.819732i | \(-0.305878\pi\) | ||||
0.572747 | + | 0.819732i | \(0.305878\pi\) | |||||||
\(674\) | − | 2.28263e11i | − | 1.10610i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.42752e9 | 0.0212018 | ||||||||
\(677\) | − | 2.35523e11i | − | 1.12119i | −0.828090 | − | 0.560595i | \(-0.810573\pi\) | ||
0.828090 | − | 0.560595i | \(-0.189427\pi\) | |||||||
\(678\) | −1.01312e11 | + | 2.42465e11i | −0.479450 | + | 1.14744i | ||||
\(679\) | 5.00152e11 | 2.35300 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.14574e11 | − | 1.31443e11i | −1.46263 | − | 0.611150i | ||||
\(682\) | 9.21829e10 | 0.426101 | ||||||||
\(683\) | 1.13979e11i | 0.523772i | 0.965099 | + | 0.261886i | \(0.0843444\pi\) | ||||
−0.965099 | + | 0.261886i | \(0.915656\pi\) | |||||||
\(684\) | −5.15385e10 | − | 5.21804e10i | −0.235455 | − | 0.238387i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.29065e10i | 0.0582791i | ||||||||
\(687\) | −2.23410e10 | + | 5.34674e10i | −0.100294 | + | 0.240028i | ||||
\(688\) | −8.82083e10 | −0.393691 | ||||||||
\(689\) | 1.28125e11i | 0.568533i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.47931e11 | 1.08747 | 0.543737 | − | 0.839256i | \(-0.317009\pi\) | ||||
0.543737 | + | 0.839256i | \(0.317009\pi\) | |||||||
\(692\) | 1.07610e10i | 0.0469277i | ||||||||
\(693\) | −2.51544e11 | + | 2.48450e11i | −1.09064 | + | 1.07722i | ||||
\(694\) | 2.25044e11 | 0.970131 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8.44332e10 | − | 2.02069e11i | 0.359813 | − | 0.861119i | ||||
\(697\) | −1.76238e10 | −0.0746738 | ||||||||
\(698\) | − | 1.39450e11i | − | 0.587485i | ||||||
\(699\) | −2.84175e11 | − | 1.18741e11i | −1.19036 | − | 0.497383i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 3.48469e11i | − | 1.44308i | −0.692370 | − | 0.721542i | \(-0.743434\pi\) | ||
0.692370 | − | 0.721542i | \(-0.256566\pi\) | |||||||
\(702\) | 9.46178e10 | + | 2.34562e11i | 0.389605 | + | 0.965850i | ||||
\(703\) | 1.43549e11 | 0.587730 | ||||||||
\(704\) | − | 1.88553e11i | − | 0.767613i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.96137e11 | −0.789477 | ||||||||
\(707\) | − | 4.15727e10i | − | 0.166391i | ||||||
\(708\) | 5.19508e10 | + | 2.17073e10i | 0.206757 | + | 0.0863918i | ||||
\(709\) | 3.19932e11 | 1.26611 | 0.633057 | − | 0.774105i | \(-0.281800\pi\) | ||||
0.633057 | + | 0.774105i | \(0.281800\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.31337e11 | + | 2.34217e11i | 0.905244 | + | 0.916517i | ||||
\(712\) | 2.60590e11 | 1.01400 | ||||||||
\(713\) | 2.00795e10i | 0.0776955i | ||||||||
\(714\) | 2.67571e10 | − | 6.40362e10i | 0.102955 | − | 0.246395i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.51154e10i | 0.171661i | ||||||||
\(717\) | 2.72716e11 | + | 1.13952e11i | 1.03189 | + | 0.431169i | ||||
\(718\) | −6.84998e10 | −0.257746 | ||||||||
\(719\) | − | 2.06854e11i | − | 0.774014i | −0.922077 | − | 0.387007i | \(-0.873509\pi\) | ||
0.922077 | − | 0.387007i | \(-0.126491\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.23966e11 | 1.56888 | ||||||||
\(722\) | − | 4.77364e11i | − | 1.75671i | ||||||
\(723\) | 4.26098e10 | − | 1.01976e11i | 0.155940 | − | 0.373201i | ||||
\(724\) | −7.53659e10 | −0.274297 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4.32499e10 | + | 1.80716e10i | 0.155682 | + | 0.0650506i | ||||
\(727\) | −3.61835e11 | −1.29531 | −0.647654 | − | 0.761934i | \(-0.724250\pi\) | ||||
−0.647654 | + | 0.761934i | \(0.724250\pi\) | |||||||
\(728\) | 3.30739e11i | 1.17750i | ||||||||
\(729\) | 2.03381e11 | − | 1.95966e11i | 0.720111 | − | 0.693859i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 1.64318e10i | − | 0.0575459i | ||||||
\(732\) | 1.10151e10 | − | 2.63618e10i | 0.0383658 | − | 0.0918187i | ||||
\(733\) | −2.04728e11 | −0.709188 | −0.354594 | − | 0.935020i | \(-0.615381\pi\) | ||||
−0.354594 | + | 0.935020i | \(0.615381\pi\) | |||||||
\(734\) | 4.79451e11i | 1.65181i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.58564e10 | −0.0881164 | ||||||||
\(737\) | 3.89927e11i | 1.32164i | ||||||||
\(738\) | 1.00491e11 | + | 1.01742e11i | 0.338768 | + | 0.342986i | ||||
\(739\) | −4.92586e11 | −1.65160 | −0.825798 | − | 0.563966i | \(-0.809275\pi\) | ||||
−0.825798 | + | 0.563966i | \(0.809275\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.77556e11 | + | 4.24935e11i | −0.588929 | + | 1.40945i | ||||
\(742\) | −2.85268e11 | −0.941104 | ||||||||
\(743\) | − | 5.52619e11i | − | 1.81330i | −0.421880 | − | 0.906652i | \(-0.638630\pi\) | ||
0.421880 | − | 0.906652i | \(-0.361370\pi\) | |||||||
\(744\) | −8.88484e10 | − | 3.71247e10i | −0.289973 | − | 0.121163i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 1.52724e11i | − | 0.493118i | ||||||
\(747\) | −2.10323e11 | + | 2.07736e11i | −0.675467 | + | 0.667159i | ||||
\(748\) | −1.18973e10 | −0.0380050 | ||||||||
\(749\) | 4.65392e11i | 1.47874i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.05834e11 | −0.647079 | −0.323540 | − | 0.946215i | \(-0.604873\pi\) | ||||
−0.323540 | + | 0.946215i | \(0.604873\pi\) | |||||||
\(752\) | 1.16142e11i | 0.363178i | ||||||||
\(753\) | 5.36997e11 | + | 2.24380e11i | 1.67029 | + | 0.697919i | ||||
\(754\) | 3.60852e11 | 1.11646 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −8.98740e10 | + | 3.62534e10i | −0.275136 | + | 0.110984i | ||||
\(757\) | −1.27946e10 | −0.0389622 | −0.0194811 | − | 0.999810i | \(-0.506201\pi\) | ||||
−0.0194811 | + | 0.999810i | \(0.506201\pi\) | |||||||
\(758\) | − | 3.85067e11i | − | 1.16643i | ||||||
\(759\) | −2.95770e10 | + | 7.07850e10i | −0.0891225 | + | 0.213292i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 2.92493e11i | − | 0.872120i | −0.899918 | − | 0.436060i | \(-0.856373\pi\) | ||
0.899918 | − | 0.436060i | \(-0.143627\pi\) | |||||||
\(762\) | 4.40992e10 | + | 1.84266e10i | 0.130801 | + | 0.0546543i | ||||
\(763\) | 9.08667e10 | 0.268106 | ||||||||
\(764\) | 3.60802e10i | 0.105900i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.57222e11 | −1.61850 | ||||||||
\(767\) | − | 3.53550e11i | − | 1.02157i | ||||||
\(768\) | 8.02754e10 | − | 1.92119e11i | 0.230748 | − | 0.552236i | ||||
\(769\) | −4.81512e11 | −1.37690 | −0.688449 | − | 0.725285i | \(-0.741708\pi\) | ||||
−0.688449 | + | 0.725285i | \(0.741708\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.28831e11 | − | 9.56156e10i | −0.647587 | − | 0.270590i | ||||
\(772\) | −4.25628e10 | −0.119829 | ||||||||
\(773\) | 4.38699e11i | 1.22871i | 0.789030 | + | 0.614354i | \(0.210583\pi\) | ||||
−0.789030 | + | 0.614354i | \(0.789417\pi\) | |||||||
\(774\) | −9.48608e10 | + | 9.36940e10i | −0.264316 | + | 0.261065i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5.20437e11i | 1.43523i | ||||||||
\(777\) | 7.31287e10 | − | 1.75015e11i | 0.200634 | − | 0.480165i | ||||
\(778\) | −1.68443e11 | −0.459763 | ||||||||
\(779\) | 2.60386e11i | 0.707078i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.68422e11 | 0.452684 | ||||||||
\(782\) | − | 1.50590e10i | − | 0.0402688i | ||||||
\(783\) | −1.50738e11 | − | 3.73686e11i | −0.401028 | − | 0.994169i | ||||
\(784\) | −4.56356e11 | −1.20792 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.24415e10 | + | 2.97755e10i | −0.0325973 | + | 0.0780134i | ||||
\(787\) | 3.97244e11 | 1.03552 | 0.517760 | − | 0.855526i | \(-0.326766\pi\) | ||||
0.517760 | + | 0.855526i | \(0.326766\pi\) | |||||||
\(788\) | 1.23223e11i | 0.319587i | ||||||||
\(789\) | −2.62438e11 | − | 1.09658e11i | −0.677202 | − | 0.282964i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.32242e11i | 1.61502i | ||||||||
\(792\) | −2.58526e11 | − | 2.61746e11i | −0.657059 | − | 0.665241i | ||||
\(793\) | −1.79405e11 | −0.453671 | ||||||||
\(794\) | − | 7.83479e11i | − | 1.97127i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.63561e10 | −0.190192 | ||||||||
\(797\) | − | 5.24995e10i | − | 0.130113i | −0.997882 | − | 0.0650567i | \(-0.979277\pi\) | ||
0.997882 | − | 0.0650567i | \(-0.0207228\pi\) | |||||||
\(798\) | −9.46113e11 | − | 3.95327e11i | −2.33309 | − | 0.974866i | ||||
\(799\) | −2.16354e10 | −0.0530858 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.41125e11 | − | 3.36929e11i | 0.828672 | − | 0.818480i | ||||
\(802\) | 4.41628e11 | 1.06748 | ||||||||
\(803\) | − | 5.48267e11i | − | 1.31865i | ||||||
\(804\) | −4.12065e10 | + | 9.86171e10i | −0.0986146 | + | 0.236009i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 1.58664e11i | − | 0.375957i | ||||||
\(807\) | −1.41939e11 | − | 5.93082e10i | −0.334663 | − | 0.139837i | ||||
\(808\) | 4.32588e10 | 0.101491 | ||||||||
\(809\) | − | 3.82829e11i | − | 0.893739i | −0.894599 | − | 0.446870i | \(-0.852539\pi\) | ||
0.894599 | − | 0.446870i | \(-0.147461\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.50313e11 | −1.04095 | −0.520477 | − | 0.853876i | \(-0.674246\pi\) | ||||
−0.520477 | + | 0.853876i | \(0.674246\pi\) | |||||||
\(812\) | 1.38263e11i | 0.318039i | ||||||||
\(813\) | 2.04374e9 | − | 4.89117e9i | 0.00467803 | − | 0.0111957i | ||||
\(814\) | −1.88948e11 | −0.430372 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 8.11092e10 | + | 3.38909e10i | 0.182940 | + | 0.0764403i | ||||
\(817\) | −2.42774e11 | −0.544896 | ||||||||
\(818\) | − | 1.96178e11i | − | 0.438163i | ||||||
\(819\) | 4.27628e11 | + | 4.32954e11i | 0.950453 | + | 0.962289i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 4.00560e11i | − | 0.881648i | −0.897593 | − | 0.440824i | \(-0.854686\pi\) | ||
0.897593 | − | 0.440824i | \(-0.145314\pi\) | |||||||
\(822\) | 2.23085e11 | − | 5.33898e11i | 0.488634 | − | 1.16942i | ||||
\(823\) | −5.98531e11 | −1.30463 | −0.652315 | − | 0.757948i | \(-0.726202\pi\) | ||||
−0.652315 | + | 0.757948i | \(0.726202\pi\) | |||||||
\(824\) | 4.41161e11i | 0.956947i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.87176e11 | 1.69103 | ||||||||
\(827\) | 1.33008e11i | 0.284352i | 0.989841 | + | 0.142176i | \(0.0454098\pi\) | ||||
−0.989841 | + | 0.142176i | \(0.954590\pi\) | |||||||
\(828\) | −1.49608e10 | + | 1.47767e10i | −0.0318297 | + | 0.0314382i | ||||
\(829\) | 3.30572e11 | 0.699920 | 0.349960 | − | 0.936765i | \(-0.386195\pi\) | ||||
0.349960 | + | 0.936765i | \(0.386195\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.15779e11 | − | 5.16411e11i | 0.452485 | − | 1.08291i | ||||
\(832\) | −3.24534e11 | −0.677278 | ||||||||
\(833\) | − | 8.50117e10i | − | 0.176563i | ||||||
\(834\) | 9.37219e11 | + | 3.91611e11i | 1.93721 | + | 0.809450i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.75778e11i | 0.359865i | ||||||||
\(837\) | −1.64307e11 | + | 6.62783e10i | −0.334776 | + | 0.135042i | ||||
\(838\) | 9.70334e11 | 1.96764 | ||||||||
\(839\) | 6.49466e10i | 0.131072i | 0.997850 | + | 0.0655358i | \(0.0208757\pi\) | ||||
−0.997850 | + | 0.0655358i | \(0.979124\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.46344e10 | −0.149195 | ||||||||
\(842\) | − | 3.90074e11i | − | 0.776066i | ||||||
\(843\) | −1.29941e11 | − | 5.42951e10i | −0.257299 | − | 0.107510i | ||||
\(844\) | −3.82752e10 | −0.0754306 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.23365e11 | + | 1.24902e11i | 0.240830 | + | 0.243830i | ||||
\(847\) | 1.12777e11 | 0.219122 | ||||||||
\(848\) | − | 3.61325e11i | − | 0.698739i | ||||||
\(849\) | 1.29289e11 | − | 3.09420e11i | 0.248846 | − | 0.595549i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 4.11571e10i | − | 0.0784742i | ||||||
\(852\) | 4.25959e10 | + | 1.77984e10i | 0.0808369 | + | 0.0337772i | ||||
\(853\) | 4.77389e10 | 0.0901730 | 0.0450865 | − | 0.998983i | \(-0.485644\pi\) | ||||
0.0450865 | + | 0.998983i | \(0.485644\pi\) | |||||||
\(854\) | − | 3.99443e11i | − | 0.750971i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.84268e11 | −0.901966 | ||||||||
\(857\) | 8.80902e11i | 1.63307i | 0.577297 | + | 0.816534i | \(0.304108\pi\) | ||||
−0.577297 | + | 0.816534i | \(0.695892\pi\) | |||||||
\(858\) | 2.33710e11 | − | 5.59326e11i | 0.431250 | − | 1.03209i | ||||
\(859\) | 7.72690e9 | 0.0141916 | 0.00709582 | − | 0.999975i | \(-0.497741\pi\) | ||||
0.00709582 | + | 0.999975i | \(0.497741\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.17463e11 | + | 1.32650e11i | 0.577671 | + | 0.241376i | ||||
\(862\) | −8.65067e11 | −1.56683 | ||||||||
\(863\) | 4.51506e11i | 0.813993i | 0.913430 | + | 0.406996i | \(0.133424\pi\) | ||||
−0.913430 | + | 0.406996i | \(0.866576\pi\) | |||||||
\(864\) | −8.53464e10 | − | 2.11578e11i | −0.153155 | − | 0.379678i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 3.46485e11i | − | 0.616045i | ||||||
\(867\) | 2.11531e11 | − | 5.06245e11i | 0.374367 | − | 0.895951i | ||||
\(868\) | 6.07930e10 | 0.107096 | ||||||||
\(869\) | − | 7.89000e11i | − | 1.38356i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.71136e11 | 1.16611 | ||||||||
\(872\) | 9.45520e10i | 0.163533i | ||||||||
\(873\) | 6.72897e11 | + | 6.81277e11i | 1.15849 | + | 1.17292i | ||||
\(874\) | −2.22492e11 | −0.381301 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5.79395e10 | − | 1.38663e11i | 0.0983917 | − | 0.235475i | ||||
\(877\) | 6.13569e11 | 1.03721 | 0.518603 | − | 0.855015i | \(-0.326452\pi\) | ||||
0.518603 | + | 0.855015i | \(0.326452\pi\) | |||||||
\(878\) | 3.06731e11i | 0.516155i | ||||||||
\(879\) | 5.13683e11 | + | 2.14639e11i | 0.860478 | + | 0.359545i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.49493e11i | 0.912134i | 0.889945 | + | 0.456067i | \(0.150742\pi\) | ||||
−0.889945 | + | 0.456067i | \(0.849258\pi\) | |||||||
\(882\) | −4.90774e11 | + | 4.84737e11i | −0.810974 | + | 0.800999i | ||||
\(883\) | −2.86999e11 | −0.472104 | −0.236052 | − | 0.971740i | \(-0.575854\pi\) | ||||
−0.236052 | + | 0.971740i | \(0.575854\pi\) | |||||||
\(884\) | 2.04774e10i | 0.0335325i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.34127e11 | −0.704501 | ||||||||
\(887\) | 6.67473e11i | 1.07830i | 0.842210 | + | 0.539150i | \(0.181254\pi\) | ||||
−0.842210 | + | 0.539150i | \(0.818746\pi\) | |||||||
\(888\) | 1.82113e11 | + | 7.60946e10i | 0.292879 | + | 0.122378i | ||||
\(889\) | 1.14991e11 | 0.184102 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.76847e11 | − | 8.37693e9i | −1.07394 | − | 0.0132915i | ||||
\(892\) | 6.71482e10 | 0.106066 | ||||||||
\(893\) | 3.19656e11i | 0.502663i | ||||||||
\(894\) | 3.67378e11 | − | 8.79225e11i | 0.575126 | − | 1.37642i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 1.09919e12i | − | 1.70545i | ||||||
\(897\) | 1.21834e11 | + | 5.09075e10i | 0.188191 | + | 0.0786343i | ||||
\(898\) | −8.70228e11 | −1.33822 | ||||||||
\(899\) | 2.52771e11i | 0.386980i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.73089e10 | 0.102135 | ||||||||
\(902\) | − | 3.42736e11i | − | 0.517767i | ||||||
\(903\) | −1.23678e11 | + | 2.95991e11i | −0.186012 | + | 0.445171i | ||||
\(904\) | −6.57884e11 | −0.985089 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 7.40197e11 | + | 3.09286e11i | 1.09859 | + | 0.459037i | ||||
\(907\) | 8.49166e11 | 1.25477 | 0.627384 | − | 0.778710i | \(-0.284126\pi\) | ||||
0.627384 | + | 0.778710i | \(0.284126\pi\) | |||||||
\(908\) | 2.23972e11i | 0.329496i | ||||||||
\(909\) | 5.66278e10 | − | 5.59313e10i | 0.0829420 | − | 0.0819218i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.01144e12i | 1.46847i | 0.678895 | + | 0.734235i | \(0.262459\pi\) | ||||
−0.678895 | + | 0.734235i | \(0.737541\pi\) | |||||||
\(912\) | 5.00727e11 | − | 1.19836e12i | 0.723805 | − | 1.73224i | ||||
\(913\) | 7.08508e11 | 1.01967 | ||||||||
\(914\) | 1.32190e12i | 1.89415i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.80679e10 | 0.0540726 | ||||||||
\(917\) | 7.76414e10i | 0.109803i | ||||||||
\(918\) | 1.23225e11 | − | 4.97065e10i | 0.173511 | − | 0.0699910i | ||||
\(919\) | −2.59912e11 | −0.364389 | −0.182194 | − | 0.983263i | \(-0.558320\pi\) | ||||
−0.182194 | + | 0.983263i | \(0.558320\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.32046e10 | + | 1.75196e11i | −0.101742 | + | 0.243493i | ||||
\(922\) | −3.05715e11 | −0.423052 | ||||||||
\(923\) | − | 2.89886e11i | − | 0.399411i | ||||||
\(924\) | 2.14309e11 | + | 8.95476e10i | 0.294004 | + | 0.122847i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.71320e11i | 0.505015i | ||||||||
\(927\) | 5.70398e11 | + | 5.77501e11i | 0.772430 | + | 0.782049i | ||||
\(928\) | −3.25492e11 | −0.438883 | ||||||||
\(929\) | 4.58599e11i | 0.615701i | 0.951435 | + | 0.307851i | \(0.0996097\pi\) | ||||
−0.951435 | + | 0.307851i | \(0.900390\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.25602e12 | −1.67185 | ||||||||
\(932\) | 2.02328e11i | 0.268159i | ||||||||
\(933\) | −4.62319e11 | − | 1.93177e11i | −0.610120 | − | 0.254935i | ||||
\(934\) | −2.62207e11 | −0.344554 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.50513e11 | + | 4.44972e11i | −0.586954 | + | 0.579734i | ||||
\(937\) | −7.74108e11 | −1.00425 | −0.502126 | − | 0.864794i | \(-0.667449\pi\) | ||||
−0.502126 | + | 0.864794i | \(0.667449\pi\) | |||||||
\(938\) | 1.49428e12i | 1.93028i | ||||||||
\(939\) | −1.97895e11 | + | 4.73612e11i | −0.254550 | + | 0.609200i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 6.66336e11i | − | 0.849836i | −0.905232 | − | 0.424918i | \(-0.860303\pi\) | ||
0.905232 | − | 0.424918i | \(-0.139697\pi\) | |||||||
\(942\) | −1.97794e11 | − | 8.26466e10i | −0.251194 | − | 0.104959i | ||||
\(943\) | 7.46558e10 | 0.0944098 | ||||||||
\(944\) | 9.97049e11i | 1.25553i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.19554e11 | 0.399007 | ||||||||
\(947\) | − | 2.31471e11i | − | 0.287804i | −0.989592 | − | 0.143902i | \(-0.954035\pi\) | ||
0.989592 | − | 0.143902i | \(-0.0459649\pi\) | |||||||
\(948\) | 8.33795e10 | − | 1.99547e11i | 0.103235 | − | 0.247066i | ||||
\(949\) | −9.43670e11 | −1.16347 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.97053e11 | + | 8.23374e10i | 0.240914 | + | 0.100664i | ||||
\(952\) | 1.73750e11 | 0.211533 | ||||||||
\(953\) | 7.87320e11i | 0.954509i | 0.878765 | + | 0.477254i | \(0.158368\pi\) | ||||
−0.878765 | + | 0.477254i | \(0.841632\pi\) | |||||||
\(954\) | −3.83796e11 | − | 3.88575e11i | −0.463348 | − | 0.469118i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 1.94169e11i | − | 0.232461i | ||||||
\(957\) | −3.72329e11 | + | 8.91075e11i | −0.443894 | + | 1.06235i | ||||
\(958\) | 9.06926e10 | 0.107674 | ||||||||
\(959\) | − | 1.39217e12i | − | 1.64595i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.41750e11 | −0.869689 | ||||||||
\(962\) | 3.25214e11i | 0.379725i | ||||||||
\(963\) | −6.33930e11 | + | 6.26133e11i | −0.737116 | + | 0.728050i | ||||
\(964\) | −7.26050e10 | −0.0840734 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.13345e11 | + | 2.71262e11i | −0.130165 | + | 0.311517i | ||||
\(967\) | −6.73055e11 | −0.769741 | −0.384871 | − | 0.922971i | \(-0.625754\pi\) | ||||
−0.384871 | + | 0.922971i | \(0.625754\pi\) | |||||||
\(968\) | 1.17351e11i | 0.133654i | ||||||||
\(969\) | 2.23235e11 | + | 9.32772e10i | 0.253202 | + | 0.105799i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.86603e10i | 0.110985i | 0.998459 | + | 0.0554927i | \(0.0176729\pi\) | ||||
−0.998459 | + | 0.0554927i | \(0.982327\pi\) | |||||||
\(972\) | −1.70297e11 | − | 7.36461e10i | −0.190785 | − | 0.0825059i | ||||
\(973\) | 2.44386e12 | 2.72662 | ||||||||
\(974\) | − | 6.68153e11i | − | 0.742404i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.05940e11 | 0.557571 | ||||||||
\(977\) | 2.61518e11i | 0.287028i | 0.989648 | + | 0.143514i | \(0.0458402\pi\) | ||||
−0.989648 | + | 0.143514i | \(0.954160\pi\) | |||||||
\(978\) | 1.48599e12 | + | 6.20910e11i | 1.62428 | + | 0.678693i | ||||
\(979\) | −1.14913e12 | −1.25095 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.22251e11 | + | 1.23773e11i | 0.132000 | + | 0.133644i | ||||
\(982\) | 1.26950e12 | 1.36517 | ||||||||
\(983\) | − | 9.90776e11i | − | 1.06111i | −0.847650 | − | 0.530556i | \(-0.821983\pi\) | ||
0.847650 | − | 0.530556i | \(-0.178017\pi\) | |||||||
\(984\) | −1.38030e11 | + | 3.30339e11i | −0.147229 | + | 0.352354i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 1.89570e11i | − | 0.200568i | ||||||
\(987\) | 3.89726e11 | + | 1.62844e11i | 0.410667 | + | 0.171595i | ||||
\(988\) | 3.02547e11 | 0.317515 | ||||||||
\(989\) | 6.96063e10i | 0.0727551i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.03368e11 | 0.314540 | 0.157270 | − | 0.987556i | \(-0.449731\pi\) | ||||
0.157270 | + | 0.987556i | \(0.449731\pi\) | |||||||
\(992\) | 1.43117e11i | 0.147789i | ||||||||
\(993\) | −1.89491e11 | + | 4.53499e11i | −0.194891 | + | 0.466422i | ||||
\(994\) | 6.45428e11 | 0.661153 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.79190e11 | + | 7.48733e10i | 0.182086 | + | 0.0760833i | ||||
\(997\) | 2.24125e11 | 0.226835 | 0.113417 | − | 0.993547i | \(-0.463820\pi\) | ||||
0.113417 | + | 0.993547i | \(0.463820\pi\) | |||||||
\(998\) | − | 3.96358e11i | − | 0.399545i | ||||||
\(999\) | 3.36781e11 | − | 1.35851e11i | 0.338132 | − | 0.136396i |
(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 | 75.9.c.h.26.4 | 12 | ||
3.2 | odd | 2 | inner | 75.9.c.h.26.10 | 12 | ||
5.2 | odd | 4 | 15.9.d.c.14.9 | yes | 12 | ||
5.3 | odd | 4 | 15.9.d.c.14.4 | yes | 12 | ||
5.4 | even | 2 | inner | 75.9.c.h.26.9 | 12 | ||
15.2 | even | 4 | 15.9.d.c.14.3 | ✓ | 12 | ||
15.8 | even | 4 | 15.9.d.c.14.10 | yes | 12 | ||
15.14 | odd | 2 | inner | 75.9.c.h.26.3 | 12 | ||
20.3 | even | 4 | 240.9.c.c.209.1 | 12 | |||
20.7 | even | 4 | 240.9.c.c.209.12 | 12 | |||
60.23 | odd | 4 | 240.9.c.c.209.11 | 12 | |||
60.47 | odd | 4 | 240.9.c.c.209.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.9.d.c.14.3 | ✓ | 12 | 15.2 | even | 4 | ||
15.9.d.c.14.4 | yes | 12 | 5.3 | odd | 4 | ||
15.9.d.c.14.9 | yes | 12 | 5.2 | odd | 4 | ||
15.9.d.c.14.10 | yes | 12 | 15.8 | even | 4 | ||
75.9.c.h.26.3 | 12 | 15.14 | odd | 2 | inner | ||
75.9.c.h.26.4 | 12 | 1.1 | even | 1 | trivial | ||
75.9.c.h.26.9 | 12 | 5.4 | even | 2 | inner | ||
75.9.c.h.26.10 | 12 | 3.2 | odd | 2 | inner | ||
240.9.c.c.209.1 | 12 | 20.3 | even | 4 | |||
240.9.c.c.209.2 | 12 | 60.47 | odd | 4 | |||
240.9.c.c.209.11 | 12 | 60.23 | odd | 4 | |||
240.9.c.c.209.12 | 12 | 20.7 | even | 4 |