Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [49,10,Mod(18,49)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(49, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("49.18");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 49 = 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 49.c (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(25.2367559720\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{193})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 49x^{2} + 48x + 2304 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 7) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 30.2 | ||
Root | \(3.72311 - 6.44862i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 49.30 |
Dual form | 49.10.c.b.18.2 |
$q$-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 \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.44622 | − | 14.6293i | 0.373274 | − | 0.646529i | −0.616793 | − | 0.787125i | \(-0.711569\pi\) |
0.990067 | + | 0.140596i | \(0.0449019\pi\) | |||||||
\(3\) | 54.9084 | + | 95.1042i | 0.391375 | + | 0.677882i | 0.992631 | − | 0.121175i | \(-0.0386661\pi\) |
−0.601256 | + | 0.799057i | \(0.705333\pi\) | |||||||
\(4\) | 113.323 | + | 196.281i | 0.221333 | + | 0.383361i | ||||
\(5\) | −1219.39 | + | 2112.05i | −0.872525 | + | 1.51126i | −0.0131494 | + | 0.999914i | \(0.504186\pi\) |
−0.859376 | + | 0.511344i | \(0.829148\pi\) | |||||||
\(6\) | 1855.08 | 0.584361 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 12477.5 | 1.07702 | ||||||||
\(9\) | 3811.63 | − | 6601.93i | 0.193651 | − | 0.335413i | ||||
\(10\) | 20598.5 | + | 35677.6i | 0.651382 | + | 1.12823i | ||||
\(11\) | 14274.1 | + | 24723.5i | 0.293956 | + | 0.509147i | 0.974742 | − | 0.223336i | \(-0.0716947\pi\) |
−0.680785 | + | 0.732483i | \(0.738361\pi\) | |||||||
\(12\) | −12444.7 | + | 21554.9i | −0.173249 | + | 0.300076i | ||||
\(13\) | −138149. | −1.34153 | −0.670767 | − | 0.741668i | \(-0.734035\pi\) | ||||
−0.670767 | + | 0.741668i | \(0.734035\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −267819. | −1.36594 | ||||||||
\(16\) | 47366.7 | − | 82041.6i | 0.180690 | − | 0.312964i | ||||
\(17\) | −50504.9 | − | 87477.1i | −0.146661 | − | 0.254024i | 0.783331 | − | 0.621605i | \(-0.213519\pi\) |
−0.929991 | + | 0.367582i | \(0.880186\pi\) | |||||||
\(18\) | −64387.7 | − | 111523.i | −0.144569 | − | 0.250402i | ||||
\(19\) | −244464. | + | 423424.i | −0.430352 | + | 0.745391i | −0.996903 | − | 0.0786349i | \(-0.974944\pi\) |
0.566552 | + | 0.824026i | \(0.308277\pi\) | |||||||
\(20\) | −552739. | −0.772476 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 482250. | 0.438905 | ||||||||
\(23\) | 70035.7 | − | 121305.i | 0.0521848 | − | 0.0903868i | −0.838753 | − | 0.544512i | \(-0.816715\pi\) |
0.890938 | + | 0.454125i | \(0.150048\pi\) | |||||||
\(24\) | 685121. | + | 1.18667e6i | 0.421519 | + | 0.730092i | ||||
\(25\) | −1.99727e6 | − | 3.45937e6i | −1.02260 | − | 1.77120i | ||||
\(26\) | −1.16683e6 | + | 2.02102e6i | −0.500760 | + | 0.867341i | ||||
\(27\) | 2.99869e6 | 1.08591 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.31716e6 | −1.65856 | −0.829279 | − | 0.558835i | \(-0.811249\pi\) | ||||
−0.829279 | + | 0.558835i | \(0.811249\pi\) | |||||||
\(30\) | −2.26206e6 | + | 3.91801e6i | −0.509869 | + | 0.883120i | ||||
\(31\) | −504514. | − | 873843.i | −0.0981172 | − | 0.169944i | 0.812788 | − | 0.582559i | \(-0.197949\pi\) |
−0.910905 | + | 0.412615i | \(0.864615\pi\) | |||||||
\(32\) | 2.39411e6 | + | 4.14671e6i | 0.403616 | + | 0.699084i | ||||
\(33\) | −1.56754e6 | + | 2.71506e6i | −0.230094 | + | 0.398535i | ||||
\(34\) | −1.70630e6 | −0.218978 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.72777e6 | 0.171445 | ||||||||
\(37\) | −5.96032e6 | + | 1.03236e7i | −0.522832 | + | 0.905571i | 0.476815 | + | 0.879004i | \(0.341791\pi\) |
−0.999647 | + | 0.0265676i | \(0.991542\pi\) | |||||||
\(38\) | 4.12959e6 | + | 7.15267e6i | 0.321278 | + | 0.556470i | ||||
\(39\) | −7.58553e6 | − | 1.31385e7i | −0.525044 | − | 0.909402i | ||||
\(40\) | −1.52150e7 | + | 2.63531e7i | −0.939727 | + | 1.62765i | ||||
\(41\) | 2.15106e7 | 1.18884 | 0.594422 | − | 0.804153i | \(-0.297381\pi\) | ||||
0.594422 | + | 0.804153i | \(0.297381\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.65957e7 | 0.740265 | 0.370133 | − | 0.928979i | \(-0.379312\pi\) | ||||
0.370133 | + | 0.928979i | \(0.379312\pi\) | |||||||
\(44\) | −3.23517e6 | + | 5.60347e6i | −0.130125 | + | 0.225382i | ||||
\(45\) | 9.29573e6 | + | 1.61007e7i | 0.337930 | + | 0.585312i | ||||
\(46\) | −1.18307e6 | − | 2.04914e6i | −0.0389585 | − | 0.0674780i | ||||
\(47\) | −1.33720e7 | + | 2.31611e7i | −0.399721 | + | 0.692338i | −0.993691 | − | 0.112149i | \(-0.964226\pi\) |
0.593970 | + | 0.804487i | \(0.297560\pi\) | |||||||
\(48\) | 1.04033e7 | 0.282870 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −6.74774e7 | −1.52684 | ||||||||
\(51\) | 5.54629e6 | − | 9.60646e6i | 0.114799 | − | 0.198837i | ||||
\(52\) | −1.56554e7 | − | 2.71159e7i | −0.296926 | − | 0.514291i | ||||
\(53\) | −1.87495e7 | − | 3.24752e7i | −0.326399 | − | 0.565340i | 0.655395 | − | 0.755286i | \(-0.272502\pi\) |
−0.981795 | + | 0.189946i | \(0.939169\pi\) | |||||||
\(54\) | 2.53276e7 | − | 4.38687e7i | 0.405342 | − | 0.702073i | ||||
\(55\) | −6.96230e7 | −1.02594 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.36926e7 | −0.673717 | ||||||||
\(58\) | −5.33561e7 | + | 9.24155e7i | −0.619096 | + | 1.07231i | ||||
\(59\) | 9.09537e6 | + | 1.57536e7i | 0.0977207 | + | 0.169257i | 0.910741 | − | 0.412978i | \(-0.135511\pi\) |
−0.813020 | + | 0.582236i | \(0.802178\pi\) | |||||||
\(60\) | −3.03500e7 | − | 5.25678e7i | −0.302328 | − | 0.523647i | ||||
\(61\) | −1.25055e7 | + | 2.16602e7i | −0.115643 | + | 0.200299i | −0.918036 | − | 0.396496i | \(-0.870226\pi\) |
0.802394 | + | 0.596795i | \(0.203559\pi\) | |||||||
\(62\) | −1.70449e7 | −0.146498 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.29388e8 | 0.964017 | ||||||||
\(65\) | 1.68457e8 | − | 2.91777e8i | 1.17052 | − | 2.02740i | ||||
\(66\) | 2.64796e7 | + | 4.58640e7i | 0.171776 | + | 0.297526i | ||||
\(67\) | 1.09286e8 | + | 1.89289e8i | 0.662564 | + | 1.14759i | 0.979940 | + | 0.199295i | \(0.0638651\pi\) |
−0.317376 | + | 0.948300i | \(0.602802\pi\) | |||||||
\(68\) | 1.14467e7 | − | 1.98263e7i | 0.0649218 | − | 0.112448i | ||||
\(69\) | 1.53822e7 | 0.0816954 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.12688e8 | 1.46032 | 0.730161 | − | 0.683275i | \(-0.239445\pi\) | ||||
0.730161 | + | 0.683275i | \(0.239445\pi\) | |||||||
\(72\) | 4.75597e7 | − | 8.23757e7i | 0.208566 | − | 0.361246i | ||||
\(73\) | −1.44519e8 | − | 2.50314e8i | −0.595624 | − | 1.03165i | −0.993459 | − | 0.114193i | \(-0.963572\pi\) |
0.397835 | − | 0.917457i | \(-0.369762\pi\) | |||||||
\(74\) | 1.00684e8 | + | 1.74391e8i | 0.390319 | + | 0.676052i | ||||
\(75\) | 2.19334e8 | − | 3.79897e8i | 0.800441 | − | 1.38641i | ||||
\(76\) | −1.10813e8 | −0.381005 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.56276e8 | −0.783940 | ||||||||
\(79\) | −2.34342e8 | + | 4.05893e8i | −0.676907 | + | 1.17244i | 0.299001 | + | 0.954253i | \(0.403347\pi\) |
−0.975908 | + | 0.218184i | \(0.929987\pi\) | |||||||
\(80\) | 1.15517e8 | + | 2.00082e8i | 0.315313 | + | 0.546138i | ||||
\(81\) | 8.96290e7 | + | 1.55242e8i | 0.231348 | + | 0.400707i | ||||
\(82\) | 1.81683e8 | − | 3.14685e8i | 0.443764 | − | 0.768623i | ||||
\(83\) | 7.75407e7 | 0.179341 | 0.0896703 | − | 0.995972i | \(-0.471419\pi\) | ||||
0.0896703 | + | 0.995972i | \(0.471419\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.46341e8 | 0.511860 | ||||||||
\(86\) | 1.40171e8 | − | 2.42783e8i | 0.276322 | − | 0.478603i | ||||
\(87\) | −3.46865e8 | − | 6.00788e8i | −0.649119 | − | 1.12431i | ||||
\(88\) | 1.78106e8 | + | 3.08488e8i | 0.316597 | + | 0.548361i | ||||
\(89\) | 1.68840e8 | − | 2.92439e8i | 0.285246 | − | 0.494061i | −0.687422 | − | 0.726258i | \(-0.741258\pi\) |
0.972669 | + | 0.232196i | \(0.0745912\pi\) | |||||||
\(90\) | 3.14055e8 | 0.504562 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.17465e7 | 0.0462010 | ||||||||
\(93\) | 5.54041e7 | − | 9.59627e7i | 0.0768013 | − | 0.133024i | ||||
\(94\) | 2.25886e8 | + | 3.91247e8i | 0.298411 | + | 0.516863i | ||||
\(95\) | −5.96194e8 | − | 1.03264e9i | −0.750986 | − | 1.30075i | ||||
\(96\) | −2.62913e8 | + | 4.55379e8i | −0.315931 | + | 0.547208i | ||||
\(97\) | 7.36733e8 | 0.844962 | 0.422481 | − | 0.906372i | \(-0.361159\pi\) | ||||
0.422481 | + | 0.906372i | \(0.361159\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.17631e8 | 0.227699 | ||||||||
\(100\) | 4.52671e8 | − | 7.84050e8i | 0.452671 | − | 0.784050i | ||||
\(101\) | 9.87140e7 | + | 1.70978e8i | 0.0943914 | + | 0.163491i | 0.909354 | − | 0.416022i | \(-0.136576\pi\) |
−0.814963 | + | 0.579513i | \(0.803243\pi\) | |||||||
\(102\) | −9.36904e7 | − | 1.62277e8i | −0.0857027 | − | 0.148441i | ||||
\(103\) | −6.37247e8 | + | 1.10374e9i | −0.557879 | + | 0.966276i | 0.439794 | + | 0.898099i | \(0.355052\pi\) |
−0.997673 | + | 0.0681767i | \(0.978282\pi\) | |||||||
\(104\) | −1.72375e9 | −1.44486 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.33451e8 | −0.487345 | ||||||||
\(107\) | −9.09683e8 | + | 1.57562e9i | −0.670908 | + | 1.16205i | 0.306739 | + | 0.951794i | \(0.400762\pi\) |
−0.977647 | + | 0.210253i | \(0.932571\pi\) | |||||||
\(108\) | 3.39819e8 | + | 5.88584e8i | 0.240348 | + | 0.416296i | ||||
\(109\) | 1.15713e8 | + | 2.00420e8i | 0.0785167 | + | 0.135995i | 0.902610 | − | 0.430459i | \(-0.141648\pi\) |
−0.824093 | + | 0.566454i | \(0.808315\pi\) | |||||||
\(110\) | −5.88051e8 | + | 1.01853e9i | −0.382955 | + | 0.663298i | ||||
\(111\) | −1.30909e9 | −0.818494 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.51983e9 | −0.876885 | −0.438443 | − | 0.898759i | \(-0.644470\pi\) | ||||
−0.438443 | + | 0.898759i | \(0.644470\pi\) | |||||||
\(114\) | −4.53499e8 | + | 7.85484e8i | −0.251481 | + | 0.435577i | ||||
\(115\) | 1.70802e8 | + | 2.95837e8i | 0.0910652 | + | 0.157729i | ||||
\(116\) | −7.15877e8 | − | 1.23994e9i | −0.367094 | − | 0.635826i | ||||
\(117\) | −5.26571e8 | + | 9.12048e8i | −0.259789 | + | 0.449968i | ||||
\(118\) | 3.07286e8 | 0.145906 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.34172e9 | −1.47114 | ||||||||
\(121\) | 7.71472e8 | − | 1.33623e9i | 0.327179 | − | 0.566691i | ||||
\(122\) | 2.11249e8 | + | 3.65894e8i | 0.0863328 | + | 0.149533i | ||||
\(123\) | 1.18111e9 | + | 2.04575e9i | 0.465284 | + | 0.805896i | ||||
\(124\) | 1.14346e8 | − | 1.98052e8i | 0.0434332 | − | 0.0752286i | ||||
\(125\) | 4.97855e9 | 1.82393 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.20951e9 | 1.43587 | 0.717934 | − | 0.696111i | \(-0.245088\pi\) | ||||
0.717934 | + | 0.696111i | \(0.245088\pi\) | |||||||
\(128\) | −1.32941e8 | + | 2.30261e8i | −0.0437739 | + | 0.0758186i | ||||
\(129\) | 9.11244e8 | + | 1.57832e9i | 0.289722 | + | 0.501812i | ||||
\(130\) | −2.84566e9 | − | 4.92882e9i | −0.873851 | − | 1.51355i | ||||
\(131\) | −2.06065e9 | + | 3.56915e9i | −0.611342 | + | 1.05887i | 0.379673 | + | 0.925121i | \(0.376037\pi\) |
−0.991015 | + | 0.133754i | \(0.957297\pi\) | |||||||
\(132\) | −7.10552e8 | −0.203710 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.69221e9 | 0.989271 | ||||||||
\(135\) | −3.65657e9 | + | 6.33337e9i | −0.947485 | + | 1.64109i | ||||
\(136\) | −6.30176e8 | − | 1.09150e9i | −0.157956 | − | 0.273588i | ||||
\(137\) | 6.39710e8 | + | 1.10801e9i | 0.155146 | + | 0.268721i | 0.933112 | − | 0.359585i | \(-0.117082\pi\) |
−0.777966 | + | 0.628306i | \(0.783749\pi\) | |||||||
\(138\) | 1.29922e8 | − | 2.25031e8i | 0.0304948 | − | 0.0528185i | ||||
\(139\) | 4.02340e9 | 0.914170 | 0.457085 | − | 0.889423i | \(-0.348893\pi\) | ||||
0.457085 | + | 0.889423i | \(0.348893\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.93695e9 | −0.625764 | ||||||||
\(142\) | 2.64103e9 | − | 4.57440e9i | 0.545100 | − | 0.944141i | ||||
\(143\) | −1.97195e9 | − | 3.41552e9i | −0.394352 | − | 0.683039i | ||||
\(144\) | −3.61089e8 | − | 6.25424e8i | −0.0699814 | − | 0.121211i | ||||
\(145\) | 7.70308e9 | − | 1.33421e10i | 1.44713 | − | 2.50651i | ||||
\(146\) | −4.88256e9 | −0.889323 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.70176e9 | −0.462880 | ||||||||
\(149\) | 3.83893e8 | − | 6.64922e8i | 0.0638075 | − | 0.110518i | −0.832357 | − | 0.554240i | \(-0.813009\pi\) |
0.896164 | + | 0.443722i | \(0.146342\pi\) | |||||||
\(150\) | −3.70508e9 | − | 6.41739e9i | −0.597568 | − | 1.03502i | ||||
\(151\) | 4.92376e9 | + | 8.52821e9i | 0.770727 | + | 1.33494i | 0.937165 | + | 0.348887i | \(0.113440\pi\) |
−0.166437 | + | 0.986052i | \(0.553226\pi\) | |||||||
\(152\) | −3.05031e9 | + | 5.28328e9i | −0.463497 | + | 0.802801i | ||||
\(153\) | −7.70023e8 | −0.113604 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.46080e9 | 0.342439 | ||||||||
\(156\) | 1.71923e9 | − | 2.97779e9i | 0.232419 | − | 0.402562i | ||||
\(157\) | 4.02048e9 | + | 6.96368e9i | 0.528116 | + | 0.914724i | 0.999463 | + | 0.0327762i | \(0.0104349\pi\) |
−0.471346 | + | 0.881948i | \(0.656232\pi\) | |||||||
\(158\) | 3.95862e9 | + | 6.85652e9i | 0.505343 | + | 0.875280i | ||||
\(159\) | 2.05902e9 | − | 3.56632e9i | 0.255489 | − | 0.442520i | ||||
\(160\) | −1.16774e10 | −1.40866 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 3.02811e9 | 0.345425 | ||||||||
\(163\) | 4.53674e9 | − | 7.85787e9i | 0.503384 | − | 0.871888i | −0.496608 | − | 0.867975i | \(-0.665421\pi\) |
0.999992 | − | 0.00391250i | \(-0.00124539\pi\) | |||||||
\(164\) | 2.43764e9 | + | 4.22211e9i | 0.263131 | + | 0.455756i | ||||
\(165\) | −3.82289e9 | − | 6.62144e9i | −0.401526 | − | 0.695464i | ||||
\(166\) | 6.54926e8 | − | 1.13437e9i | 0.0669431 | − | 0.115949i | ||||
\(167\) | 8.83471e9 | 0.878958 | 0.439479 | − | 0.898253i | \(-0.355163\pi\) | ||||
0.439479 | + | 0.898253i | \(0.355163\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.48058e9 | 0.799715 | ||||||||
\(170\) | 2.08065e9 | − | 3.60379e9i | 0.191064 | − | 0.330933i | ||||
\(171\) | 1.86361e9 | + | 3.22787e9i | 0.166676 | + | 0.288691i | ||||
\(172\) | 1.88067e9 | + | 3.25741e9i | 0.163845 | + | 0.283789i | ||||
\(173\) | 3.94936e9 | − | 6.84049e9i | 0.335211 | − | 0.580603i | −0.648314 | − | 0.761373i | \(-0.724526\pi\) |
0.983525 | + | 0.180770i | \(0.0578589\pi\) | |||||||
\(174\) | −1.17188e10 | −0.969196 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.70448e9 | 0.212460 | ||||||||
\(177\) | −9.98825e8 | + | 1.73002e9i | −0.0764909 | + | 0.132486i | ||||
\(178\) | −2.85212e9 | − | 4.94002e9i | −0.212950 | − | 0.368840i | ||||
\(179\) | −2.29936e9 | − | 3.98260e9i | −0.167405 | − | 0.289954i | 0.770102 | − | 0.637921i | \(-0.220205\pi\) |
−0.937507 | + | 0.347967i | \(0.886872\pi\) | |||||||
\(180\) | −2.10683e9 | + | 3.64914e9i | −0.149590 | + | 0.259098i | ||||
\(181\) | 6.70993e8 | 0.0464691 | 0.0232346 | − | 0.999730i | \(-0.492604\pi\) | ||||
0.0232346 | + | 0.999730i | \(0.492604\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.74664e9 | −0.181039 | ||||||||
\(184\) | 8.73872e8 | − | 1.51359e9i | 0.0562041 | − | 0.0973483i | ||||
\(185\) | −1.45359e10 | − | 2.51770e10i | −0.912368 | − | 1.58027i | ||||
\(186\) | −9.35911e8 | − | 1.62105e9i | −0.0573358 | − | 0.0993086i | ||||
\(187\) | 1.44183e9 | − | 2.49732e9i | 0.0862236 | − | 0.149344i | ||||
\(188\) | −6.06142e9 | −0.353887 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.01424e10 | −1.12129 | ||||||||
\(191\) | −5.03429e9 | + | 8.71964e9i | −0.273708 | + | 0.474076i | −0.969808 | − | 0.243868i | \(-0.921584\pi\) |
0.696100 | + | 0.717945i | \(0.254917\pi\) | |||||||
\(192\) | 7.10450e9 | + | 1.23054e10i | 0.377292 | + | 0.653490i | ||||
\(193\) | 9.89379e9 | + | 1.71365e10i | 0.513281 | + | 0.889028i | 0.999881 | + | 0.0154035i | \(0.00490329\pi\) |
−0.486601 | + | 0.873624i | \(0.661763\pi\) | |||||||
\(194\) | 6.22261e9 | − | 1.07779e10i | 0.315402 | − | 0.546293i | ||||
\(195\) | 3.69989e10 | 1.83246 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.07508e10 | −0.508560 | −0.254280 | − | 0.967131i | \(-0.581839\pi\) | ||||
−0.254280 | + | 0.967131i | \(0.581839\pi\) | |||||||
\(198\) | 1.83816e9 | − | 3.18378e9i | 0.0849942 | − | 0.147214i | ||||
\(199\) | −7.90300e8 | − | 1.36884e9i | −0.0357234 | − | 0.0618748i | 0.847611 | − | 0.530618i | \(-0.178040\pi\) |
−0.883334 | + | 0.468743i | \(0.844707\pi\) | |||||||
\(200\) | −2.49209e10 | − | 4.31643e10i | −1.10136 | − | 1.90761i | ||||
\(201\) | −1.20014e10 | + | 2.07871e10i | −0.518622 | + | 0.898281i | ||||
\(202\) | 3.33504e9 | 0.140935 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.51408e9 | 0.101635 | ||||||||
\(205\) | −2.62298e10 | + | 4.54314e10i | −1.03730 | + | 1.79665i | ||||
\(206\) | 1.07647e10 | + | 1.86449e10i | 0.416484 | + | 0.721371i | ||||
\(207\) | −5.33900e8 | − | 9.24742e8i | −0.0202113 | − | 0.0350069i | ||||
\(208\) | −6.54366e9 | + | 1.13339e10i | −0.242402 | + | 0.419852i | ||||
\(209\) | −1.39580e10 | −0.506019 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.44247e10 | 1.54295 | 0.771477 | − | 0.636257i | \(-0.219518\pi\) | ||||
0.771477 | + | 0.636257i | \(0.219518\pi\) | |||||||
\(212\) | 4.24950e9 | − | 7.36034e9i | 0.144486 | − | 0.250257i | ||||
\(213\) | 1.71692e10 | + | 2.97379e10i | 0.571534 | + | 0.989926i | ||||
\(214\) | 1.53668e10 | + | 2.66160e10i | 0.500865 | + | 0.867523i | ||||
\(215\) | −2.02366e10 | + | 3.50509e10i | −0.645900 | + | 1.11873i | ||||
\(216\) | 3.74162e10 | 1.16955 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3.90934e9 | 0.117233 | ||||||||
\(219\) | 1.58706e10 | − | 2.74887e10i | 0.466225 | − | 0.807525i | ||||
\(220\) | −7.88987e9 | − | 1.36656e10i | −0.227074 | − | 0.393304i | ||||
\(221\) | 6.97719e9 | + | 1.20848e10i | 0.196750 | + | 0.340781i | ||||
\(222\) | −1.10568e10 | + | 1.91510e10i | −0.305522 | + | 0.529180i | ||||
\(223\) | −2.40745e10 | −0.651907 | −0.325954 | − | 0.945386i | \(-0.605685\pi\) | ||||
−0.325954 | + | 0.945386i | \(0.605685\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.04513e10 | −0.792109 | ||||||||
\(226\) | −1.28368e10 | + | 2.22341e10i | −0.327318 | + | 0.566932i | ||||
\(227\) | −8.57942e7 | − | 1.48600e8i | −0.00214458 | − | 0.00371452i | 0.864951 | − | 0.501856i | \(-0.167349\pi\) |
−0.867096 | + | 0.498142i | \(0.834016\pi\) | |||||||
\(228\) | −6.08458e9 | − | 1.05388e10i | −0.149116 | − | 0.258276i | ||||
\(229\) | −5.58886e9 | + | 9.68019e9i | −0.134296 | + | 0.232608i | −0.925328 | − | 0.379167i | \(-0.876211\pi\) |
0.791032 | + | 0.611775i | \(0.209544\pi\) | |||||||
\(230\) | 5.77052e9 | 0.135969 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.88225e10 | −1.78630 | ||||||||
\(233\) | −3.27243e9 | + | 5.66802e9i | −0.0727393 | + | 0.125988i | −0.900101 | − | 0.435681i | \(-0.856507\pi\) |
0.827362 | + | 0.561670i | \(0.189841\pi\) | |||||||
\(234\) | 8.89508e9 | + | 1.54067e10i | 0.193945 | + | 0.335922i | ||||
\(235\) | −3.26115e10 | − | 5.64848e10i | −0.697534 | − | 1.20816i | ||||
\(236\) | −2.06142e9 | + | 3.57049e9i | −0.0432577 | + | 0.0749245i | ||||
\(237\) | −5.14695e10 | −1.05970 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.08610e9 | −0.180130 | −0.0900651 | − | 0.995936i | \(-0.528708\pi\) | ||||
−0.0900651 | + | 0.995936i | \(0.528708\pi\) | |||||||
\(240\) | −1.26857e10 | + | 2.19723e10i | −0.246811 | + | 0.427490i | ||||
\(241\) | −2.68200e10 | − | 4.64536e10i | −0.512132 | − | 0.887039i | −0.999901 | − | 0.0140665i | \(-0.995522\pi\) |
0.487769 | − | 0.872973i | \(-0.337811\pi\) | |||||||
\(242\) | −1.30320e10 | − | 2.25722e10i | −0.244255 | − | 0.423062i | ||||
\(243\) | 1.96688e10 | − | 3.40674e10i | 0.361868 | − | 0.626773i | ||||
\(244\) | −5.66865e9 | −0.102382 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.99038e10 | 0.694714 | ||||||||
\(247\) | 3.37724e10 | − | 5.84955e10i | 0.577332 | − | 0.999968i | ||||
\(248\) | −6.29508e9 | − | 1.09034e10i | −0.105674 | − | 0.183033i | ||||
\(249\) | 4.25764e9 | + | 7.37445e9i | 0.0701895 | + | 0.121572i | ||||
\(250\) | 4.20499e10 | − | 7.28326e10i | 0.680825 | − | 1.17922i | ||||
\(251\) | −3.92651e10 | −0.624418 | −0.312209 | − | 0.950013i | \(-0.601069\pi\) | ||||
−0.312209 | + | 0.950013i | \(0.601069\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.99880e9 | 0.0613602 | ||||||||
\(254\) | 3.55544e10 | − | 6.15821e10i | 0.535972 | − | 0.928331i | ||||
\(255\) | 1.35262e10 | + | 2.34281e10i | 0.200330 | + | 0.346981i | ||||
\(256\) | 3.53691e10 | + | 6.12610e10i | 0.514688 | + | 0.891465i | ||||
\(257\) | −3.85393e9 | + | 6.67520e9i | −0.0551067 | + | 0.0954477i | −0.892263 | − | 0.451516i | \(-0.850883\pi\) |
0.837156 | + | 0.546964i | \(0.184217\pi\) | |||||||
\(258\) | 3.07863e10 | 0.432582 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 7.63601e10 | 1.03630 | ||||||||
\(261\) | −2.40786e10 | + | 4.17054e10i | −0.321181 | + | 0.556302i | ||||
\(262\) | 3.48095e10 | + | 6.02918e10i | 0.456396 | + | 0.790500i | ||||
\(263\) | −1.82939e10 | − | 3.16860e10i | −0.235779 | − | 0.408382i | 0.723720 | − | 0.690094i | \(-0.242431\pi\) |
−0.959499 | + | 0.281712i | \(0.909098\pi\) | |||||||
\(264\) | −1.95590e10 | + | 3.38772e10i | −0.247816 | + | 0.429230i | ||||
\(265\) | 9.14521e10 | 1.13917 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.70830e10 | 0.446554 | ||||||||
\(268\) | −2.47692e10 | + | 4.29014e10i | −0.293295 | + | 0.508002i | ||||
\(269\) | −8.27391e10 | − | 1.43308e11i | −0.963442 | − | 1.66873i | −0.713743 | − | 0.700408i | \(-0.753002\pi\) |
−0.249699 | − | 0.968323i | \(-0.580332\pi\) | |||||||
\(270\) | 6.17685e10 | + | 1.06986e11i | 0.707343 | + | 1.22515i | ||||
\(271\) | 2.73624e10 | − | 4.73931e10i | 0.308171 | − | 0.533769i | −0.669791 | − | 0.742550i | \(-0.733616\pi\) |
0.977962 | + | 0.208781i | \(0.0669496\pi\) | |||||||
\(272\) | −9.56901e9 | −0.106000 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.16125e10 | 0.231648 | ||||||||
\(275\) | 5.70185e10 | − | 9.87590e10i | 0.601200 | − | 1.04131i | ||||
\(276\) | 1.74315e9 | + | 3.01923e9i | 0.0180819 | + | 0.0313188i | ||||
\(277\) | 1.27510e10 | + | 2.20853e10i | 0.130132 | + | 0.225395i | 0.923727 | − | 0.383051i | \(-0.125127\pi\) |
−0.793595 | + | 0.608446i | \(0.791793\pi\) | |||||||
\(278\) | 3.39826e10 | − | 5.88595e10i | 0.341236 | − | 0.591038i | ||||
\(279\) | −7.69207e9 | −0.0760019 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.44664e10 | −0.234095 | −0.117047 | − | 0.993126i | \(-0.537343\pi\) | ||||
−0.117047 | + | 0.993126i | \(0.537343\pi\) | |||||||
\(282\) | −2.48062e10 | + | 4.29655e10i | −0.233581 | + | 0.404575i | ||||
\(283\) | 9.19688e10 | + | 1.59295e11i | 0.852318 | + | 1.47626i | 0.879111 | + | 0.476617i | \(0.158137\pi\) |
−0.0267930 | + | 0.999641i | \(0.508530\pi\) | |||||||
\(284\) | 3.54346e10 | + | 6.13746e10i | 0.323218 | + | 0.559830i | ||||
\(285\) | 6.54722e10 | − | 1.13401e11i | 0.587835 | − | 1.01816i | ||||
\(286\) | −6.66222e10 | −0.588806 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 3.65018e10 | 0.312642 | ||||||||
\(289\) | 5.41924e10 | − | 9.38641e10i | 0.456981 | − | 0.791515i | ||||
\(290\) | −1.30124e11 | − | 2.25381e11i | −1.08035 | − | 1.87123i | ||||
\(291\) | 4.04529e10 | + | 7.00664e10i | 0.330697 | + | 0.572785i | ||||
\(292\) | 3.27545e10 | − | 5.67325e10i | 0.263663 | − | 0.456677i | ||||
\(293\) | −1.39840e11 | −1.10848 | −0.554241 | − | 0.832356i | \(-0.686991\pi\) | ||||
−0.554241 | + | 0.832356i | \(0.686991\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.43633e10 | −0.341055 | ||||||||
\(296\) | −7.43701e10 | + | 1.28813e11i | −0.563100 | + | 0.975318i | ||||
\(297\) | 4.28037e10 | + | 7.41381e10i | 0.319210 | + | 0.552889i | ||||
\(298\) | −6.48489e9 | − | 1.12322e10i | −0.0476353 | − | 0.0825068i | ||||
\(299\) | −9.67534e9 | + | 1.67582e10i | −0.0700077 | + | 0.121257i | ||||
\(300\) | 9.94219e10 | 0.708657 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.66349e11 | 1.15077 | ||||||||
\(303\) | −1.08405e10 | + | 1.87762e10i | −0.0738849 | + | 0.127972i | ||||
\(304\) | 2.31589e10 | + | 4.01124e10i | 0.155520 | + | 0.269369i | ||||
\(305\) | −3.04983e10 | − | 5.28246e10i | −0.201802 | − | 0.349532i | ||||
\(306\) | −6.50379e9 | + | 1.12649e10i | −0.0424053 | + | 0.0734481i | ||||
\(307\) | 1.22633e11 | 0.787922 | 0.393961 | − | 0.919127i | \(-0.371105\pi\) | ||||
0.393961 | + | 0.919127i | \(0.371105\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.39961e11 | −0.873361 | ||||||||
\(310\) | 2.07844e10 | − | 3.59997e10i | 0.127824 | − | 0.221397i | ||||
\(311\) | −7.20587e10 | − | 1.24809e11i | −0.436782 | − | 0.756529i | 0.560657 | − | 0.828048i | \(-0.310549\pi\) |
−0.997439 | + | 0.0715193i | \(0.977215\pi\) | |||||||
\(312\) | −9.46487e10 | − | 1.63936e11i | −0.565482 | − | 0.979444i | ||||
\(313\) | −1.37377e11 | + | 2.37943e11i | −0.809027 | + | 1.40128i | 0.104511 | + | 0.994524i | \(0.466672\pi\) |
−0.913538 | + | 0.406753i | \(0.866661\pi\) | |||||||
\(314\) | 1.35832e11 | 0.788528 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.06225e11 | −0.599288 | ||||||||
\(317\) | 6.15696e10 | − | 1.06642e11i | 0.342452 | − | 0.593144i | −0.642435 | − | 0.766340i | \(-0.722076\pi\) |
0.984887 | + | 0.173195i | \(0.0554092\pi\) | |||||||
\(318\) | −3.47818e10 | − | 6.02439e10i | −0.190735 | − | 0.330363i | ||||
\(319\) | −9.01719e10 | − | 1.56182e11i | −0.487543 | − | 0.844450i | ||||
\(320\) | −1.57775e11 | + | 2.73274e11i | −0.841129 | + | 1.45688i | ||||
\(321\) | −1.99797e11 | −1.05031 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.93865e10 | 0.252463 | ||||||||
\(324\) | −2.03140e10 | + | 3.51849e10i | −0.102410 | + | 0.177380i | ||||
\(325\) | 2.75920e11 | + | 4.77907e11i | 1.37185 | + | 2.37612i | ||||
\(326\) | −7.66367e10 | − | 1.32739e11i | −0.375800 | − | 0.650906i | ||||
\(327\) | −1.27072e10 | + | 2.20095e10i | −0.0614590 | + | 0.106450i | ||||
\(328\) | 2.68399e11 | 1.28041 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.29156e11 | −0.599517 | ||||||||
\(331\) | −1.68623e11 | + | 2.92063e11i | −0.772129 | + | 1.33737i | 0.164265 | + | 0.986416i | \(0.447475\pi\) |
−0.936394 | + | 0.350950i | \(0.885859\pi\) | |||||||
\(332\) | 8.78712e9 | + | 1.52197e10i | 0.0396940 | + | 0.0687521i | ||||
\(333\) | 4.54370e10 | + | 7.86993e10i | 0.202493 | + | 0.350729i | ||||
\(334\) | 7.46199e10 | − | 1.29245e11i | 0.328092 | − | 0.568272i | ||||
\(335\) | −5.33049e11 | −2.31242 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.84144e11 | −1.20006 | −0.600032 | − | 0.799976i | \(-0.704846\pi\) | ||||
−0.600032 | + | 0.799976i | \(0.704846\pi\) | |||||||
\(338\) | 7.16288e10 | − | 1.24065e11i | 0.298513 | − | 0.517039i | ||||
\(339\) | −8.34516e10 | − | 1.44542e11i | −0.343191 | − | 0.594425i | ||||
\(340\) | 2.79160e10 | + | 4.83520e10i | 0.113292 | + | 0.196227i | ||||
\(341\) | 1.44030e10 | − | 2.49467e10i | 0.0576843 | − | 0.0999122i | ||||
\(342\) | 6.29619e10 | 0.248863 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.07073e11 | 0.797280 | ||||||||
\(345\) | −1.87569e10 | + | 3.24879e10i | −0.0712813 | + | 0.123463i | ||||
\(346\) | −6.67143e10 | − | 1.15553e11i | −0.250251 | − | 0.433448i | ||||
\(347\) | −6.93882e10 | − | 1.20184e11i | −0.256923 | − | 0.445004i | 0.708493 | − | 0.705718i | \(-0.249375\pi\) |
−0.965416 | + | 0.260714i | \(0.916042\pi\) | |||||||
\(348\) | 7.86154e10 | − | 1.36166e11i | 0.287343 | − | 0.497693i | ||||
\(349\) | 1.52561e11 | 0.550463 | 0.275231 | − | 0.961378i | \(-0.411246\pi\) | ||||
0.275231 | + | 0.961378i | \(0.411246\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.14265e11 | −1.45679 | ||||||||
\(352\) | −6.83476e10 | + | 1.18382e11i | −0.237291 | + | 0.411000i | ||||
\(353\) | 6.23141e10 | + | 1.07931e11i | 0.213599 | + | 0.369965i | 0.952838 | − | 0.303478i | \(-0.0981479\pi\) |
−0.739239 | + | 0.673443i | \(0.764815\pi\) | |||||||
\(354\) | 1.68726e10 | + | 2.92242e10i | 0.0571041 | + | 0.0989072i | ||||
\(355\) | −3.81289e11 | + | 6.60412e11i | −1.27417 | + | 2.20692i | ||||
\(356\) | 7.65336e10 | 0.252538 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.76835e10 | −0.249951 | ||||||||
\(359\) | 3.84689e10 | − | 6.66301e10i | 0.122232 | − | 0.211712i | −0.798416 | − | 0.602107i | \(-0.794328\pi\) |
0.920648 | + | 0.390395i | \(0.127661\pi\) | |||||||
\(360\) | 1.15988e11 | + | 2.00896e11i | 0.363957 | + | 0.630393i | ||||
\(361\) | 4.18185e10 | + | 7.24318e10i | 0.129594 | + | 0.224464i | ||||
\(362\) | 5.66736e9 | − | 9.81615e9i | 0.0173457 | − | 0.0300437i | ||||
\(363\) | 1.69441e11 | 0.512200 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.04900e11 | 2.07879 | ||||||||
\(366\) | −2.31987e10 | + | 4.01814e10i | −0.0675771 | + | 0.117047i | ||||
\(367\) | −2.18303e11 | − | 3.78113e11i | −0.628150 | − | 1.08799i | −0.987923 | − | 0.154947i | \(-0.950479\pi\) |
0.359773 | − | 0.933040i | \(-0.382854\pi\) | |||||||
\(368\) | −6.63473e9 | − | 1.14917e10i | −0.0188585 | − | 0.0326639i | ||||
\(369\) | 8.19903e10 | − | 1.42011e11i | 0.230220 | − | 0.398754i | ||||
\(370\) | −4.91095e11 | −1.36225 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.51142e10 | 0.0679948 | ||||||||
\(373\) | −8.32727e10 | + | 1.44232e11i | −0.222747 | + | 0.385810i | −0.955641 | − | 0.294533i | \(-0.904836\pi\) |
0.732894 | + | 0.680343i | \(0.238169\pi\) | |||||||
\(374\) | −2.43560e10 | − | 4.21858e10i | −0.0643700 | − | 0.111492i | ||||
\(375\) | 2.73364e11 | + | 4.73481e11i | 0.713841 | + | 1.23641i | ||||
\(376\) | −1.66850e11 | + | 2.88993e11i | −0.430508 | + | 0.745661i | ||||
\(377\) | 8.72707e11 | 2.22501 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.10213e11 | 1.02125 | 0.510627 | − | 0.859803i | \(-0.329413\pi\) | ||||
0.510627 | + | 0.859803i | \(0.329413\pi\) | |||||||
\(380\) | 1.35125e11 | − | 2.34043e11i | 0.332436 | − | 0.575797i | ||||
\(381\) | 2.31138e11 | + | 4.00342e11i | 0.561964 | + | 0.973349i | ||||
\(382\) | 8.50414e10 | + | 1.47296e11i | 0.204336 | + | 0.353921i | ||||
\(383\) | 3.50583e11 | − | 6.07228e11i | 0.832523 | − | 1.44197i | −0.0635077 | − | 0.997981i | \(-0.520229\pi\) |
0.896031 | − | 0.443991i | \(-0.146438\pi\) | |||||||
\(384\) | −2.91984e10 | −0.0685281 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.34261e11 | 0.766377 | ||||||||
\(387\) | 6.32566e10 | − | 1.09564e11i | 0.143353 | − | 0.248294i | ||||
\(388\) | 8.34886e10 | + | 1.44606e11i | 0.187018 | + | 0.323925i | ||||
\(389\) | −4.23376e11 | − | 7.33309e11i | −0.937461 | − | 1.62373i | −0.770186 | − | 0.637820i | \(-0.779836\pi\) |
−0.167275 | − | 0.985910i | \(-0.553497\pi\) | |||||||
\(390\) | 3.12501e11 | − | 5.41268e11i | 0.684007 | − | 1.18474i | ||||
\(391\) | −1.41486e10 | −0.0306138 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.52589e11 | −0.957056 | ||||||||
\(394\) | −9.08036e10 | + | 1.57276e11i | −0.189832 | + | 0.328799i | ||||
\(395\) | −5.71510e11 | − | 9.89884e11i | −1.18124 | − | 2.04596i | ||||
\(396\) | 2.46625e10 | + | 4.27167e10i | 0.0503974 | + | 0.0872909i | ||||
\(397\) | 4.37644e11 | − | 7.58021e11i | 0.884226 | − | 1.53152i | 0.0376278 | − | 0.999292i | \(-0.488020\pi\) |
0.846598 | − | 0.532233i | \(-0.178647\pi\) | |||||||
\(398\) | −2.67002e10 | −0.0533385 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.78416e11 | −0.739094 | ||||||||
\(401\) | 1.23745e11 | − | 2.14333e11i | 0.238990 | − | 0.413943i | −0.721435 | − | 0.692482i | \(-0.756517\pi\) |
0.960425 | + | 0.278540i | \(0.0898504\pi\) | |||||||
\(402\) | 2.02734e11 | + | 3.51145e11i | 0.387176 | + | 0.670609i | ||||
\(403\) | 6.96979e10 | + | 1.20720e11i | 0.131628 | + | 0.227986i | ||||
\(404\) | −2.23731e10 | + | 3.87513e10i | −0.0417839 | + | 0.0723719i | ||||
\(405\) | −4.37171e11 | −0.807428 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.40314e11 | −0.614759 | ||||||||
\(408\) | 6.92040e10 | − | 1.19865e11i | 0.123640 | − | 0.214151i | ||||
\(409\) | −4.74213e10 | − | 8.21361e10i | −0.0837951 | − | 0.145137i | 0.821082 | − | 0.570810i | \(-0.193371\pi\) |
−0.904877 | + | 0.425673i | \(0.860037\pi\) | |||||||
\(410\) | 4.43086e11 | + | 7.67447e11i | 0.774391 | + | 1.34129i | ||||
\(411\) | −7.02509e10 | + | 1.21678e11i | −0.121441 | + | 0.210341i | ||||
\(412\) | −2.88858e11 | −0.493909 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.80377e10 | −0.0301773 | ||||||||
\(415\) | −9.45525e10 | + | 1.63770e11i | −0.156479 | + | 0.271030i | ||||
\(416\) | −3.30743e11 | − | 5.72863e11i | −0.541465 | − | 0.937845i | ||||
\(417\) | 2.20919e11 | + | 3.82643e11i | 0.357784 | + | 0.619700i | ||||
\(418\) | −1.17893e11 | + | 2.04196e11i | −0.188883 | + | 0.327156i | ||||
\(419\) | −9.93237e11 | −1.57431 | −0.787154 | − | 0.616756i | \(-0.788446\pi\) | ||||
−0.787154 | + | 0.616756i | \(0.788446\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.88328e11 | 0.602461 | 0.301230 | − | 0.953551i | \(-0.402603\pi\) | ||||
0.301230 | + | 0.953551i | \(0.402603\pi\) | |||||||
\(422\) | 3.75221e11 | − | 6.49901e11i | 0.575945 | − | 0.997565i | ||||
\(423\) | 1.01938e11 | + | 1.76563e11i | 0.154813 | + | 0.268143i | ||||
\(424\) | −2.33948e11 | − | 4.05210e11i | −0.351538 | − | 0.608882i | ||||
\(425\) | −2.01744e11 | + | 3.49430e11i | −0.299950 | + | 0.519529i | ||||
\(426\) | 5.80060e11 | 0.853355 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −4.12351e11 | −0.593977 | ||||||||
\(429\) | 2.16554e11 | − | 3.75082e11i | 0.308680 | − | 0.534649i | ||||
\(430\) | 3.41846e11 | + | 5.92095e11i | 0.482195 | + | 0.835187i | ||||
\(431\) | −1.04247e11 | − | 1.80562e11i | −0.145518 | − | 0.252045i | 0.784048 | − | 0.620700i | \(-0.213152\pi\) |
−0.929566 | + | 0.368655i | \(0.879818\pi\) | |||||||
\(432\) | 1.42038e11 | − | 2.46017e11i | 0.196213 | − | 0.339851i | ||||
\(433\) | 3.43270e11 | 0.469289 | 0.234645 | − | 0.972081i | \(-0.424607\pi\) | ||||
0.234645 | + | 0.972081i | \(0.424607\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.69186e12 | 2.26549 | ||||||||
\(436\) | −2.62257e10 | + | 4.54243e10i | −0.0347567 | + | 0.0602004i | ||||
\(437\) | 3.42424e10 | + | 5.93096e10i | 0.0449157 | + | 0.0777962i | ||||
\(438\) | −2.68094e11 | − | 4.64352e11i | −0.348059 | − | 0.602856i | ||||
\(439\) | 2.99428e11 | − | 5.18625e11i | 0.384771 | − | 0.666444i | −0.606966 | − | 0.794728i | \(-0.707614\pi\) |
0.991737 | + | 0.128284i | \(0.0409470\pi\) | |||||||
\(440\) | −8.68723e11 | −1.10495 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.35724e11 | 0.293767 | ||||||||
\(443\) | 1.52584e11 | − | 2.64284e11i | 0.188232 | − | 0.326027i | −0.756429 | − | 0.654076i | \(-0.773058\pi\) |
0.944661 | + | 0.328049i | \(0.106391\pi\) | |||||||
\(444\) | −1.48349e11 | − | 2.56949e11i | −0.181160 | − | 0.313778i | ||||
\(445\) | 4.11764e11 | + | 7.13196e11i | 0.497769 | + | 0.862162i | ||||
\(446\) | −2.03339e11 | + | 3.52193e11i | −0.243340 | + | 0.421477i | ||||
\(447\) | 8.43158e10 | 0.0998907 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.40802e11 | 0.279610 | 0.139805 | − | 0.990179i | \(-0.455352\pi\) | ||||
0.139805 | + | 0.990179i | \(0.455352\pi\) | |||||||
\(450\) | −2.57199e11 | + | 4.45481e11i | −0.295674 | + | 0.512122i | ||||
\(451\) | 3.07045e11 | + | 5.31818e11i | 0.349468 | + | 0.605297i | ||||
\(452\) | −1.72231e11 | − | 2.98314e11i | −0.194084 | − | 0.336163i | ||||
\(453\) | −5.40712e11 | + | 9.36541e11i | −0.603287 | + | 1.04492i | ||||
\(454\) | −2.89855e9 | −0.00320206 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.69950e11 | −0.725606 | ||||||||
\(457\) | −1.18113e11 | + | 2.04578e11i | −0.126671 | + | 0.219400i | −0.922385 | − | 0.386273i | \(-0.873762\pi\) |
0.795714 | + | 0.605672i | \(0.207096\pi\) | |||||||
\(458\) | 9.44095e10 | + | 1.63522e11i | 0.100259 | + | 0.173653i | ||||
\(459\) | −1.51448e11 | − | 2.62316e11i | −0.159260 | − | 0.275847i | ||||
\(460\) | −3.87114e10 | + | 6.70502e10i | −0.0403115 | + | 0.0698216i | ||||
\(461\) | 1.17120e12 | 1.20775 | 0.603873 | − | 0.797081i | \(-0.293624\pi\) | ||||
0.603873 | + | 0.797081i | \(0.293624\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.78934e12 | −1.80958 | −0.904791 | − | 0.425856i | \(-0.859973\pi\) | ||||
−0.904791 | + | 0.425856i | \(0.859973\pi\) | |||||||
\(464\) | −2.99223e11 | + | 5.18270e11i | −0.299684 | + | 0.519069i | ||||
\(465\) | 1.35119e11 | + | 2.34032e11i | 0.134022 | + | 0.232133i | ||||
\(466\) | 5.52794e10 | + | 9.57468e10i | 0.0543034 | + | 0.0940562i | ||||
\(467\) | −1.90601e11 | + | 3.30131e11i | −0.185438 | + | 0.321189i | −0.943724 | − | 0.330734i | \(-0.892704\pi\) |
0.758286 | + | 0.651922i | \(0.226037\pi\) | |||||||
\(468\) | −2.38690e11 | −0.230000 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.10178e12 | −1.04148 | ||||||||
\(471\) | −4.41517e11 | + | 7.64729e11i | −0.413383 | + | 0.716001i | ||||
\(472\) | 1.13488e11 | + | 1.96566e11i | 0.105247 | + | 0.182293i | ||||
\(473\) | 2.36889e11 | + | 4.10304e11i | 0.217606 | + | 0.376904i | ||||
\(474\) | −4.34723e11 | + | 7.52962e11i | −0.395558 | + | 0.685126i | ||||
\(475\) | 1.95304e12 | 1.76031 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.85865e11 | −0.252830 | ||||||||
\(478\) | −7.67432e10 | + | 1.32923e11i | −0.0672379 | + | 0.116459i | ||||
\(479\) | −8.55732e11 | − | 1.48217e12i | −0.742725 | − | 1.28644i | −0.951250 | − | 0.308420i | \(-0.900200\pi\) |
0.208526 | − | 0.978017i | \(-0.433133\pi\) | |||||||
\(480\) | −6.41188e11 | − | 1.11057e12i | −0.551315 | − | 0.954906i | ||||
\(481\) | 8.23411e11 | − | 1.42619e12i | 0.701397 | − | 1.21486i | ||||
\(482\) | −9.06111e11 | −0.764663 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.49701e11 | 0.289663 | ||||||||
\(485\) | −8.98366e11 | + | 1.55602e12i | −0.737251 | + | 1.27696i | ||||
\(486\) | −3.32254e11 | − | 5.75481e11i | −0.270151 | − | 0.467916i | ||||
\(487\) | −3.69357e11 | − | 6.39744e11i | −0.297554 | − | 0.515378i | 0.678022 | − | 0.735042i | \(-0.262837\pi\) |
−0.975576 | + | 0.219663i | \(0.929504\pi\) | |||||||
\(488\) | −1.56038e11 | + | 2.70266e11i | −0.124549 | + | 0.215726i | ||||
\(489\) | 9.96422e11 | 0.788049 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.52117e12 | 1.18116 | 0.590582 | − | 0.806978i | \(-0.298898\pi\) | ||||
0.590582 | + | 0.806978i | \(0.298898\pi\) | |||||||
\(492\) | −2.67694e11 | + | 4.63659e11i | −0.205966 | + | 0.356743i | ||||
\(493\) | 3.19047e11 | + | 5.52606e11i | 0.243245 | + | 0.421313i | ||||
\(494\) | −5.70498e11 | − | 9.88132e11i | −0.431006 | − | 0.746524i | ||||
\(495\) | −2.65377e11 | + | 4.59646e11i | −0.198673 | + | 0.344112i | ||||
\(496\) | −9.55887e10 | −0.0709151 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.43844e11 | 0.104800 | ||||||||
\(499\) | 8.38601e11 | − | 1.45250e12i | 0.605484 | − | 1.04873i | −0.386491 | − | 0.922293i | \(-0.626313\pi\) |
0.991975 | − | 0.126436i | \(-0.0403538\pi\) | |||||||
\(500\) | 5.64183e11 | + | 9.77193e11i | 0.403696 | + | 0.699222i | ||||
\(501\) | 4.85100e11 | + | 8.40218e11i | 0.344003 | + | 0.595830i | ||||
\(502\) | −3.31642e11 | + | 5.74421e11i | −0.233079 | + | 0.403704i | ||||
\(503\) | −2.93328e11 | −0.204314 | −0.102157 | − | 0.994768i | \(-0.532574\pi\) | ||||
−0.102157 | + | 0.994768i | \(0.532574\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.81484e11 | −0.329436 | ||||||||
\(506\) | 3.37747e10 | − | 5.84995e10i | 0.0229042 | − | 0.0396712i | ||||
\(507\) | 4.65655e11 | + | 8.06539e11i | 0.312989 | + | 0.542112i | ||||
\(508\) | 4.77033e11 | + | 8.26245e11i | 0.317806 | + | 0.550455i | ||||
\(509\) | −1.43749e12 | + | 2.48981e12i | −0.949238 | + | 1.64413i | −0.202203 | + | 0.979344i | \(0.564810\pi\) |
−0.747035 | + | 0.664785i | \(0.768523\pi\) | |||||||
\(510\) | 4.56981e11 | 0.299111 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.05881e12 | 0.680930 | ||||||||
\(513\) | −7.33071e11 | + | 1.26972e12i | −0.467324 | + | 0.809429i | ||||
\(514\) | 6.51023e10 | + | 1.12760e11i | 0.0411398 | + | 0.0712562i | ||||
\(515\) | −1.55411e12 | − | 2.69179e12i | −0.973528 | − | 1.68620i | ||||
\(516\) | −2.06529e11 | + | 3.57719e11i | −0.128250 | + | 0.222136i | ||||
\(517\) | −7.63497e11 | −0.470002 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.67412e11 | 0.524774 | ||||||||
\(520\) | 2.10193e12 | − | 3.64065e12i | 1.26068 | − | 2.18355i | ||||
\(521\) | 8.46666e11 | + | 1.46647e12i | 0.503434 | + | 0.871973i | 0.999992 | + | 0.00396961i | \(0.00126357\pi\) |
−0.496558 | + | 0.868003i | \(0.665403\pi\) | |||||||
\(522\) | 4.06747e11 | + | 7.04507e11i | 0.239777 | + | 0.415306i | ||||
\(523\) | 4.74232e11 | − | 8.21395e11i | 0.277162 | − | 0.480059i | −0.693516 | − | 0.720441i | \(-0.743939\pi\) |
0.970678 | + | 0.240382i | \(0.0772728\pi\) | |||||||
\(524\) | −9.34075e11 | −0.541241 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.18058e11 | −0.352041 | ||||||||
\(527\) | −5.09608e10 | + | 8.82667e10i | −0.0287799 | + | 0.0498482i | ||||
\(528\) | 1.48499e11 | + | 2.57207e11i | 0.0831514 | + | 0.144023i | ||||
\(529\) | 8.90766e11 | + | 1.54285e12i | 0.494553 | + | 0.856592i | ||||
\(530\) | 7.72425e11 | − | 1.33788e12i | 0.425221 | − | 0.736504i | ||||
\(531\) | 1.38673e11 | 0.0756947 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.97166e12 | −1.59488 | ||||||||
\(534\) | 3.13211e11 | − | 5.42497e11i | 0.166687 | − | 0.288710i | ||||
\(535\) | −2.21852e12 | − | 3.84259e12i | −1.17077 | − | 2.02783i | ||||
\(536\) | 1.36362e12 | + | 2.36186e12i | 0.713594 | + | 1.23598i | ||||
\(537\) | 2.52508e11 | − | 4.37357e11i | 0.131036 | − | 0.226961i | ||||
\(538\) | −2.79533e12 | −1.43851 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.65749e12 | −0.838840 | ||||||||
\(541\) | −1.30244e12 | + | 2.25589e12i | −0.653688 | + | 1.13222i | 0.328533 | + | 0.944492i | \(0.393446\pi\) |
−0.982221 | + | 0.187728i | \(0.939888\pi\) | |||||||
\(542\) | −4.62218e11 | − | 8.00585e11i | −0.230065 | − | 0.398484i | ||||
\(543\) | 3.68432e10 | + | 6.38143e10i | 0.0181869 | + | 0.0315006i | ||||
\(544\) | 2.41828e11 | − | 4.18859e11i | 0.118389 | − | 0.205056i | ||||
\(545\) | −5.64396e11 | −0.274031 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.01576e12 | 0.962711 | 0.481356 | − | 0.876525i | \(-0.340145\pi\) | ||||
0.481356 | + | 0.876525i | \(0.340145\pi\) | |||||||
\(548\) | −1.44987e11 | + | 2.51125e11i | −0.0686779 | + | 0.118954i | ||||
\(549\) | 9.53329e10 | + | 1.65121e11i | 0.0447886 | + | 0.0775761i | ||||
\(550\) | −9.63182e11 | − | 1.66828e12i | −0.448824 | − | 0.777386i | ||||
\(551\) | 1.54432e12 | − | 2.67484e12i | 0.713764 | − | 1.23627i | ||||
\(552\) | 1.91932e11 | 0.0879875 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 4.30790e11 | 0.194300 | ||||||||
\(555\) | 1.59629e12 | − | 2.76486e12i | 0.714157 | − | 1.23696i | ||||
\(556\) | 4.55943e11 | + | 7.89716e11i | 0.202336 | + | 0.350457i | ||||
\(557\) | 1.52097e12 | + | 2.63440e12i | 0.669534 | + | 1.15967i | 0.978035 | + | 0.208442i | \(0.0668393\pi\) |
−0.308501 | + | 0.951224i | \(0.599827\pi\) | |||||||
\(558\) | −6.49689e10 | + | 1.12529e11i | −0.0283695 | + | 0.0491374i | ||||
\(559\) | −2.29267e12 | −0.993091 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.16674e11 | 0.134983 | ||||||||
\(562\) | −2.06649e11 | + | 3.57926e11i | −0.0873814 | + | 0.151349i | ||||
\(563\) | 2.11956e12 | + | 3.67119e12i | 0.889115 | + | 1.53999i | 0.840923 | + | 0.541154i | \(0.182013\pi\) |
0.0481917 | + | 0.998838i | \(0.484654\pi\) | |||||||
\(564\) | −3.32823e11 | − | 5.76467e11i | −0.138503 | − | 0.239893i | ||||
\(565\) | 1.85327e12 | − | 3.20996e12i | 0.765104 | − | 1.32520i | ||||
\(566\) | 3.10716e12 | 1.27259 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.90157e12 | 1.57280 | ||||||||
\(569\) | −6.70597e10 | + | 1.16151e11i | −0.0268199 | + | 0.0464534i | −0.879124 | − | 0.476593i | \(-0.841871\pi\) |
0.852304 | + | 0.523047i | \(0.175205\pi\) | |||||||
\(570\) | −1.10599e12 | − | 1.91562e12i | −0.438847 | − | 0.760105i | ||||
\(571\) | 7.56052e10 | + | 1.30952e11i | 0.0297638 | + | 0.0515525i | 0.880524 | − | 0.474002i | \(-0.157191\pi\) |
−0.850760 | + | 0.525555i | \(0.823858\pi\) | |||||||
\(572\) | 4.46934e11 | − | 7.74113e11i | 0.174567 | − | 0.302358i | ||||
\(573\) | −1.10570e12 | −0.428491 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.59520e11 | −0.213457 | ||||||||
\(576\) | 4.93179e11 | − | 8.54212e11i | 0.186683 | − | 0.323344i | ||||
\(577\) | −9.23403e11 | − | 1.59938e12i | −0.346817 | − | 0.600704i | 0.638865 | − | 0.769319i | \(-0.279404\pi\) |
−0.985682 | + | 0.168614i | \(0.946071\pi\) | |||||||
\(578\) | −9.15443e11 | − | 1.58559e12i | −0.341158 | − | 0.590904i | ||||
\(579\) | −1.08651e12 | + | 1.88188e12i | −0.401771 | + | 0.695887i | ||||
\(580\) | 3.49174e12 | 1.28120 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.36670e12 | 0.493763 | ||||||||
\(583\) | 5.35267e11 | − | 9.27110e11i | 0.191894 | − | 0.332371i | ||||
\(584\) | −1.80324e12 | − | 3.12330e12i | −0.641498 | − | 1.11111i | ||||
\(585\) | −1.28419e12 | − | 2.22429e12i | −0.453345 | − | 0.785217i | ||||
\(586\) | −1.18112e12 | + | 2.04577e12i | −0.413767 | + | 0.716666i | ||||
\(587\) | 2.97730e12 | 1.03503 | 0.517513 | − | 0.855675i | \(-0.326858\pi\) | ||||
0.517513 | + | 0.855675i | \(0.326858\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.93342e11 | 0.168900 | ||||||||
\(590\) | −3.74702e11 | + | 6.49003e11i | −0.127307 | + | 0.220502i | ||||
\(591\) | −5.90309e11 | − | 1.02245e12i | −0.199038 | − | 0.344744i | ||||
\(592\) | 5.64642e11 | + | 9.77989e11i | 0.188941 | + | 0.327255i | ||||
\(593\) | 5.30464e11 | − | 9.18790e11i | 0.176161 | − | 0.305120i | −0.764401 | − | 0.644741i | \(-0.776965\pi\) |
0.940562 | + | 0.339621i | \(0.110299\pi\) | |||||||
\(594\) | 1.44612e12 | 0.476611 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.74015e11 | 0.0564909 | ||||||||
\(597\) | 8.67882e10 | − | 1.50322e11i | 0.0279625 | − | 0.0484325i | ||||
\(598\) | 1.63440e11 | + | 2.83087e11i | 0.0522641 | + | 0.0905241i | ||||
\(599\) | 2.26554e12 | + | 3.92403e12i | 0.719037 | + | 1.24541i | 0.961382 | + | 0.275219i | \(0.0887503\pi\) |
−0.242344 | + | 0.970190i | \(0.577916\pi\) | |||||||
\(600\) | 2.73674e12 | − | 4.74017e12i | 0.862091 | − | 1.49319i | ||||
\(601\) | 1.05588e12 | 0.330127 | 0.165063 | − | 0.986283i | \(-0.447217\pi\) | ||||
0.165063 | + | 0.986283i | \(0.447217\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.66623e12 | 0.513224 | ||||||||
\(604\) | −1.11595e12 | + | 1.93288e12i | −0.341175 | + | 0.590933i | ||||
\(605\) | 1.88145e12 | + | 3.25877e12i | 0.570945 | + | 0.988905i | ||||
\(606\) | 1.83122e11 | + | 3.17176e11i | 0.0551586 | + | 0.0955376i | ||||
\(607\) | −1.62521e12 | + | 2.81495e12i | −0.485916 | + | 0.841630i | −0.999869 | − | 0.0161877i | \(-0.994847\pi\) |
0.513953 | + | 0.857818i | \(0.328180\pi\) | |||||||
\(608\) | −2.34109e12 | −0.694788 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.03038e12 | −0.301310 | ||||||||
\(611\) | 1.84733e12 | − | 3.19967e12i | 0.536240 | − | 0.928795i | ||||
\(612\) | −8.72611e10 | − | 1.51141e11i | −0.0251443 | − | 0.0435512i | ||||
\(613\) | 1.24335e12 | + | 2.15355e12i | 0.355649 | + | 0.616003i | 0.987229 | − | 0.159308i | \(-0.0509264\pi\) |
−0.631579 | + | 0.775311i | \(0.717593\pi\) | |||||||
\(614\) | 1.03578e12 | − | 1.79403e12i | 0.294111 | − | 0.509415i | ||||
\(615\) | −5.76095e12 | −1.62389 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.06622e12 | −1.12956 | −0.564778 | − | 0.825243i | \(-0.691038\pi\) | ||||
−0.564778 | + | 0.825243i | \(0.691038\pi\) | |||||||
\(618\) | −1.18214e12 | + | 2.04753e12i | −0.326003 | + | 0.564653i | ||||
\(619\) | −2.12365e12 | − | 3.67827e12i | −0.581400 | − | 1.00701i | −0.995314 | − | 0.0966976i | \(-0.969172\pi\) |
0.413914 | − | 0.910316i | \(-0.364161\pi\) | |||||||
\(620\) | 2.78864e11 | + | 4.83007e11i | 0.0757932 | + | 0.131278i | ||||
\(621\) | 2.10015e11 | − | 3.63757e11i | 0.0566681 | − | 0.0981520i | ||||
\(622\) | −2.43450e12 | −0.652157 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.43721e12 | −0.379480 | ||||||||
\(625\) | −2.16989e12 | + | 3.75836e12i | −0.568823 | + | 0.985231i | ||||
\(626\) | 2.32063e12 | + | 4.01944e12i | 0.603978 | + | 1.04612i | ||||
\(627\) | −7.66415e11 | − | 1.32747e12i | −0.198043 | − | 0.343021i | ||||
\(628\) | −9.11223e11 | + | 1.57829e12i | −0.233780 | + | 0.404918i | ||||
\(629\) | 1.20410e12 | 0.306715 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.44130e12 | 0.361929 | 0.180965 | − | 0.983490i | \(-0.442078\pi\) | ||||
0.180965 | + | 0.983490i | \(0.442078\pi\) | |||||||
\(632\) | −2.92401e12 | + | 5.06454e12i | −0.729042 | + | 1.26274i | ||||
\(633\) | 2.43929e12 | + | 4.22497e12i | 0.603874 | + | 1.04594i | ||||
\(634\) | −1.04006e12 | − | 1.80144e12i | −0.255657 | − | 0.442811i | ||||
\(635\) | −5.13304e12 | + | 8.89068e12i | −1.25283 | + | 2.16997i | ||||
\(636\) | 9.33333e11 | 0.226193 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −3.04645e12 | −0.727949 | ||||||||
\(639\) | 1.19185e12 | − | 2.06434e12i | 0.282792 | − | 0.489811i | ||||
\(640\) | −3.24215e11 | − | 5.61557e11i | −0.0763877 | − | 0.132307i | ||||
\(641\) | −3.00490e12 | − | 5.20464e12i | −0.703022 | − | 1.21767i | −0.967401 | − | 0.253251i | \(-0.918500\pi\) |
0.264378 | − | 0.964419i | \(-0.414833\pi\) | |||||||
\(642\) | −1.68753e12 | + | 2.92289e12i | −0.392052 | + | 0.679054i | ||||
\(643\) | −2.09069e12 | −0.482327 | −0.241163 | − | 0.970485i | \(-0.577529\pi\) | ||||
−0.241163 | + | 0.970485i | \(0.577529\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.44465e12 | −1.01116 | ||||||||
\(646\) | 4.17130e11 | − | 7.22490e11i | 0.0942377 | − | 0.163224i | ||||
\(647\) | −6.74470e11 | − | 1.16822e12i | −0.151319 | − | 0.262092i | 0.780394 | − | 0.625289i | \(-0.215019\pi\) |
−0.931713 | + | 0.363196i | \(0.881685\pi\) | |||||||
\(648\) | 1.11835e12 | + | 1.93704e12i | 0.249166 | + | 0.431569i | ||||
\(649\) | −2.59657e11 | + | 4.49739e11i | −0.0574512 | + | 0.0995084i | ||||
\(650\) | 9.32192e12 | 2.04831 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.05646e12 | 0.445663 | ||||||||
\(653\) | 3.69147e12 | − | 6.39382e12i | 0.794494 | − | 1.37610i | −0.128666 | − | 0.991688i | \(-0.541070\pi\) |
0.923160 | − | 0.384416i | \(-0.125597\pi\) | |||||||
\(654\) | 2.14656e11 | + | 3.71795e11i | 0.0458820 | + | 0.0794700i | ||||
\(655\) | −5.02548e12 | − | 8.70439e12i | −1.06682 | − | 1.84779i | ||||
\(656\) | 1.01889e12 | − | 1.76476e12i | 0.214812 | − | 0.372065i | ||||
\(657\) | −2.20341e12 | −0.461372 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.34345e12 | 0.690574 | 0.345287 | − | 0.938497i | \(-0.387782\pi\) | ||||
0.345287 | + | 0.938497i | \(0.387782\pi\) | |||||||
\(660\) | 8.66440e11 | − | 1.50072e12i | 0.177742 | − | 0.307859i | ||||
\(661\) | 4.07404e12 | + | 7.05644e12i | 0.830078 | + | 1.43774i | 0.897976 | + | 0.440044i | \(0.145037\pi\) |
−0.0678985 | + | 0.997692i | \(0.521629\pi\) | |||||||
\(662\) | 2.84845e12 | + | 4.93366e12i | 0.576431 | + | 0.998408i | ||||
\(663\) | −7.66213e11 | + | 1.32712e12i | −0.154006 | + | 0.266747i | ||||
\(664\) | 9.67516e11 | 0.193153 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.53509e12 | 0.302342 | ||||||||
\(667\) | −4.42426e11 | + | 7.66305e11i | −0.0865516 | + | 0.149912i | ||||
\(668\) | 1.00117e12 | + | 1.73408e12i | 0.194543 | + | 0.336958i | ||||
\(669\) | −1.32189e12 | − | 2.28959e12i | −0.255141 | − | 0.441916i | ||||
\(670\) | −4.50225e12 | + | 7.79813e12i | −0.863164 | + | 1.49504i | ||||
\(671\) | −7.14023e11 | −0.135976 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.60403e12 | −1.24091 | −0.620457 | − | 0.784241i | \(-0.713053\pi\) | ||||
−0.620457 | + | 0.784241i | \(0.713053\pi\) | |||||||
\(674\) | −2.39995e12 | + | 4.15683e12i | −0.447953 | + | 0.775877i | ||||
\(675\) | −5.98918e12 | − | 1.03736e13i | −1.11045 | − | 1.92336i | ||||
\(676\) | 9.61042e11 | + | 1.66457e12i | 0.177004 | + | 0.306579i | ||||
\(677\) | 1.58161e12 | − | 2.73942e12i | 0.289367 | − | 0.501199i | −0.684291 | − | 0.729209i | \(-0.739888\pi\) |
0.973659 | + | 0.228010i | \(0.0732217\pi\) | |||||||
\(678\) | −2.81940e12 | −0.512417 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3.07373e12 | 0.551283 | ||||||||
\(681\) | 9.42165e9 | − | 1.63188e10i | 0.00167867 | − | 0.00290754i | ||||
\(682\) | −2.43302e11 | − | 4.21411e11i | −0.0430641 | − | 0.0745892i | ||||
\(683\) | −3.92938e12 | − | 6.80588e12i | −0.690925 | − | 1.19672i | −0.971535 | − | 0.236895i | \(-0.923870\pi\) |
0.280610 | − | 0.959822i | \(-0.409463\pi\) | |||||||
\(684\) | −4.22379e11 | + | 7.31581e11i | −0.0737819 | + | 0.127794i | ||||
\(685\) | −3.12022e12 | −0.541475 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.22750e12 | −0.210241 | ||||||||
\(688\) | 7.86084e11 | − | 1.36154e12i | 0.133758 | − | 0.231676i | ||||
\(689\) | 2.59023e12 | + | 4.48640e12i | 0.437876 | + | 0.758423i | ||||
\(690\) | 3.16850e11 | + | 5.48801e11i | 0.0532149 | + | 0.0921709i | ||||
\(691\) | 1.60762e12 | − | 2.78448e12i | 0.268246 | − | 0.464615i | −0.700163 | − | 0.713983i | \(-0.746889\pi\) |
0.968409 | + | 0.249368i | \(0.0802227\pi\) | |||||||
\(692\) | 1.79021e12 | 0.296774 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.34427e12 | −0.383611 | ||||||||
\(695\) | −4.90610e12 | + | 8.49762e12i | −0.797637 | + | 1.38155i | ||||
\(696\) | −4.32802e12 | − | 7.49635e12i | −0.699113 | − | 1.21090i | ||||
\(697\) | −1.08639e12 | − | 1.88168e12i | −0.174357 | − | 0.301995i | ||||
\(698\) | 1.28856e12 | − | 2.23185e12i | 0.205473 | − | 0.355890i | ||||
\(699\) | −7.18737e11 | −0.113874 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.07789e12 | −0.950652 | −0.475326 | − | 0.879810i | \(-0.657670\pi\) | ||||
−0.475326 | + | 0.879810i | \(0.657670\pi\) | |||||||
\(702\) | −3.49897e12 | + | 6.06040e12i | −0.543781 | + | 0.941855i | ||||
\(703\) | −2.91417e12 | − | 5.04749e12i | −0.450003 | − | 0.779429i | ||||
\(704\) | 1.84690e12 | + | 3.19893e12i | 0.283379 | + | 0.490826i | ||||
\(705\) | 3.58129e12 | − | 6.20298e12i | 0.545995 | − | 0.945692i | ||||
\(706\) | 2.10528e12 | 0.318924 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −4.52758e11 | −0.0677200 | ||||||||
\(709\) | 3.39960e12 | − | 5.88829e12i | 0.505266 | − | 0.875147i | −0.494715 | − | 0.869055i | \(-0.664728\pi\) |
0.999981 | − | 0.00609177i | \(-0.00193908\pi\) | |||||||
\(710\) | 6.44090e12 | + | 1.11560e13i | 0.951227 | + | 1.64757i | ||||
\(711\) | 1.78645e12 | + | 3.09422e12i | 0.262167 | + | 0.454086i | ||||
\(712\) | 2.10670e12 | − | 3.64892e12i | 0.307216 | − | 0.532114i | ||||
\(713\) | −1.41336e11 | −0.0204809 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.61833e12 | 1.37633 | ||||||||
\(716\) | 5.21139e11 | − | 9.02639e11i | 0.0741045 | − | 0.128353i | ||||
\(717\) | −4.98903e11 | − | 8.64126e11i | −0.0704986 | − | 0.122107i | ||||
\(718\) | −6.49834e11 | − | 1.12555e12i | −0.0912520 | − | 0.158053i | ||||
\(719\) | 4.31619e11 | − | 7.47586e11i | 0.0602311 | − | 0.104323i | −0.834338 | − | 0.551254i | \(-0.814150\pi\) |
0.894569 | + | 0.446931i | \(0.147483\pi\) | |||||||
\(720\) | 1.76123e12 | 0.244242 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.41283e12 | 0.193497 | ||||||||
\(723\) | 2.94529e12 | − | 5.10139e12i | 0.400872 | − | 0.694331i | ||||
\(724\) | 7.60388e10 | + | 1.31703e11i | 0.0102852 | + | 0.0178144i | ||||
\(725\) | 1.26170e13 | + | 2.18534e13i | 1.69604 | + | 2.93763i | ||||
\(726\) | 1.43114e12 | − | 2.47881e12i | 0.191191 | − | 0.331152i | ||||
\(727\) | 9.34730e12 | 1.24103 | 0.620514 | − | 0.784195i | \(-0.286924\pi\) | ||||
0.620514 | + | 0.784195i | \(0.286924\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.84827e12 | 1.02920 | ||||||||
\(730\) | 5.95375e12 | − | 1.03122e13i | 0.775956 | − | 1.34400i | ||||
\(731\) | −8.38164e11 | − | 1.45174e12i | −0.108568 | − | 0.188045i | ||||
\(732\) | −3.11257e11 | − | 5.39112e11i | −0.0400699 | − | 0.0694032i | ||||
\(733\) | −5.60224e12 | + | 9.70336e12i | −0.716793 | + | 1.24152i | 0.245471 | + | 0.969404i | \(0.421057\pi\) |
−0.962264 | + | 0.272118i | \(0.912276\pi\) | |||||||
\(734\) | −7.37536e12 | −0.937887 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.70692e11 | 0.0842506 | ||||||||
\(737\) | −3.11993e12 | + | 5.40387e12i | −0.389530 | + | 0.674685i | ||||
\(738\) | −1.38502e12 | − | 2.39892e12i | −0.171871 | − | 0.297689i | ||||
\(739\) | 2.27884e12 | + | 3.94707e12i | 0.281070 | + | 0.486827i | 0.971649 | − | 0.236430i | \(-0.0759774\pi\) |
−0.690579 | + | 0.723257i | \(0.742644\pi\) | |||||||
\(740\) | 3.29450e12 | − | 5.70624e12i | 0.403875 | − | 0.699532i | ||||
\(741\) | 7.41756e12 | 0.903814 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.57016e12 | 0.429772 | 0.214886 | − | 0.976639i | \(-0.431062\pi\) | ||||
0.214886 | + | 0.976639i | \(0.431062\pi\) | |||||||
\(744\) | 6.91306e11 | − | 1.19738e12i | 0.0827165 | − | 0.143269i | ||||
\(745\) | 9.36231e11 | + | 1.62160e12i | 0.111347 | + | 0.192859i | ||||
\(746\) | 1.40668e12 | + | 2.43644e12i | 0.166292 | + | 0.288025i | ||||
\(747\) | 2.95556e11 | − | 5.11918e11i | 0.0347294 | − | 0.0601531i | ||||
\(748\) | 6.53567e11 | 0.0763366 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 9.23559e12 | 1.06583 | ||||||||
\(751\) | 1.19156e12 | − | 2.06385e12i | 0.136690 | − | 0.236754i | −0.789552 | − | 0.613684i | \(-0.789687\pi\) |
0.926242 | + | 0.376930i | \(0.123020\pi\) | |||||||
\(752\) | 1.26678e12 | + | 2.19413e12i | 0.144451 | + | 0.250197i | ||||
\(753\) | −2.15599e12 | − | 3.73428e12i | −0.244382 | − | 0.423282i | ||||
\(754\) | 7.37108e12 | − | 1.27671e13i | 0.830539 | − | 1.43854i | ||||
\(755\) | −2.40160e13 | −2.68992 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.96674e12 | 0.549718 | 0.274859 | − | 0.961484i | \(-0.411369\pi\) | ||||
0.274859 | + | 0.961484i | \(0.411369\pi\) | |||||||
\(758\) | 3.46475e12 | − | 6.00113e12i | 0.381207 | − | 0.660270i | ||||
\(759\) | 2.19568e11 | + | 3.80302e11i | 0.0240149 | + | 0.0415950i | ||||
\(760\) | −7.43903e12 | − | 1.28848e13i | −0.808826 | − | 1.40093i | ||||
\(761\) | 5.08300e12 | − | 8.80402e12i | 0.549401 | − | 0.951590i | −0.448915 | − | 0.893575i | \(-0.648189\pi\) |
0.998316 | − | 0.0580158i | \(-0.0184774\pi\) | |||||||
\(762\) | 7.80896e12 | 0.839065 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.28200e12 | −0.242323 | ||||||||
\(765\) | 9.38960e11 | − | 1.62633e12i | 0.0991221 | − | 0.171684i | ||||
\(766\) | −5.92220e12 | − | 1.02576e13i | −0.621518 | − | 1.07650i | ||||
\(767\) | −1.25651e12 | − | 2.17635e12i | −0.131096 | − | 0.227064i | ||||
\(768\) | −3.88412e12 | + | 6.72750e12i | −0.402872 | + | 0.697795i | ||||
\(769\) | 4.53519e12 | 0.467656 | 0.233828 | − | 0.972278i | \(-0.424875\pi\) | ||||
0.233828 | + | 0.972278i | \(0.424875\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.46453e11 | −0.0862697 | ||||||||
\(772\) | −2.24238e12 | + | 3.88392e12i | −0.227212 | + | 0.393543i | ||||
\(773\) | −1.82380e12 | − | 3.15891e12i | −0.183725 | − | 0.318222i | 0.759421 | − | 0.650600i | \(-0.225482\pi\) |
−0.943146 | + | 0.332378i | \(0.892149\pi\) | |||||||
\(774\) | −1.06856e12 | − | 1.85080e12i | −0.107020 | − | 0.185364i | ||||
\(775\) | −2.01530e12 | + | 3.49060e12i | −0.200669 | + | 0.347570i | ||||
\(776\) | 9.19261e12 | 0.910041 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.43037e13 | −1.39972 | ||||||||
\(779\) | −5.25857e12 | + | 9.10810e12i | −0.511621 | + | 0.886154i | ||||
\(780\) | 4.19282e12 | + | 7.26217e12i | 0.405583 | + | 0.702491i | ||||
\(781\) | 4.46335e12 | + | 7.73075e12i | 0.429271 | + | 0.743519i | ||||
\(782\) | −1.19502e11 | + | 2.06984e11i | −0.0114273 | + | 0.0197927i | ||||
\(783\) | −1.89432e13 | −1.80105 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.96102e13 | −1.84318 | ||||||||
\(786\) | −3.82267e12 | + | 6.62105e12i | −0.357244 | + | 0.618765i | ||||
\(787\) | −1.34042e12 | − | 2.32168e12i | −0.124553 | − | 0.215733i | 0.797005 | − | 0.603973i | \(-0.206416\pi\) |
−0.921558 | + | 0.388240i | \(0.873083\pi\) | |||||||
\(788\) | −1.21831e12 | − | 2.11017e12i | −0.112561 | − | 0.194962i | ||||
\(789\) | 2.00898e12 | − | 3.47966e12i | 0.184556 | − | 0.319661i | ||||
\(790\) | −1.93084e13 | −1.76370 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2.71549e12 | 0.245237 | ||||||||
\(793\) | 1.72763e12 | − | 2.99233e12i | 0.155139 | − | 0.268708i | ||||
\(794\) | −7.39287e12 | − | 1.28048e13i | −0.660117 | − | 1.14336i | ||||
\(795\) | 5.02149e12 | + | 8.69748e12i | 0.445842 | + | 0.772221i | ||||
\(796\) | 1.79118e11 | − | 3.10241e11i | 0.0158136 | − | 0.0273899i | ||||
\(797\) | 9.88359e12 | 0.867665 | 0.433833 | − | 0.900994i | \(-0.357161\pi\) | ||||
0.433833 | + | 0.900994i | \(0.357161\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.70142e12 | 0.234494 | ||||||||
\(800\) | 9.56334e12 | − | 1.65642e13i | 0.825476 | − | 1.42977i | ||||
\(801\) | −1.28711e12 | − | 2.22934e12i | −0.110476 | − | 0.191351i | ||||
\(802\) | −2.09036e12 | − | 3.62061e12i | −0.178417 | − | 0.309028i | ||||
\(803\) | 4.12577e12 | − | 7.14604e12i | 0.350175 | − | 0.606520i | ||||
\(804\) | −5.44014e12 | −0.459154 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.35474e12 | 0.196533 | ||||||||
\(807\) | 9.08615e12 | − | 1.57377e13i | 0.754135 | − | 1.30620i | ||||
\(808\) | 1.23171e12 | + | 2.13338e12i | 0.101661 | + | 0.176083i | ||||
\(809\) | −8.12026e12 | − | 1.40647e13i | −0.666502 | − | 1.15442i | −0.978876 | − | 0.204456i | \(-0.934457\pi\) |
0.312374 | − | 0.949959i | \(-0.398876\pi\) | |||||||
\(810\) | −3.69245e12 | + | 6.39550e12i | −0.301392 | + | 0.522026i | ||||
\(811\) | 2.28548e13 | 1.85517 | 0.927584 | − | 0.373614i | \(-0.121882\pi\) | ||||
0.927584 | + | 0.373614i | \(0.121882\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.00971e12 | 0.482443 | ||||||||
\(814\) | −2.87437e12 | + | 4.97855e12i | −0.229473 | + | 0.397459i | ||||
\(815\) | 1.10641e13 | + | 1.91636e13i | 0.878431 | + | 1.52149i | ||||
\(816\) | −5.25420e11 | − | 9.10053e11i | −0.0414859 | − | 0.0718557i | ||||
\(817\) | −4.05705e12 | + | 7.02702e12i | −0.318575 | + | 0.551787i | ||||
\(818\) | −1.60212e12 | −0.125114 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.18897e13 | −0.918353 | ||||||||
\(821\) | −8.29498e12 | + | 1.43673e13i | −0.637193 | + | 1.10365i | 0.348853 | + | 0.937177i | \(0.386571\pi\) |
−0.986046 | + | 0.166473i | \(0.946762\pi\) | |||||||
\(822\) | 1.18671e12 | + | 2.05544e12i | 0.0906612 | + | 0.157030i | ||||
\(823\) | −4.93808e12 | − | 8.55301e12i | −0.375197 | − | 0.649860i | 0.615160 | − | 0.788402i | \(-0.289091\pi\) |
−0.990356 | + | 0.138543i | \(0.955758\pi\) | |||||||
\(824\) | −7.95127e12 | + | 1.37720e13i | −0.600847 | + | 1.04070i | ||||
\(825\) | 1.25232e13 | 0.941179 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.15367e12 | −0.234445 | −0.117223 | − | 0.993106i | \(-0.537399\pi\) | ||||
−0.117223 | + | 0.993106i | \(0.537399\pi\) | |||||||
\(828\) | 1.21006e11 | − | 2.09588e11i | 0.00894685 | − | 0.0154964i | ||||
\(829\) | 1.01164e13 | + | 1.75221e13i | 0.743927 | + | 1.28852i | 0.950694 | + | 0.310129i | \(0.100372\pi\) |
−0.206767 | + | 0.978390i | \(0.566294\pi\) | |||||||
\(830\) | 1.59722e12 | + | 2.76647e12i | 0.116819 | + | 0.202337i | ||||
\(831\) | −1.40027e12 | + | 2.42534e12i | −0.101861 | + | 0.176428i | ||||
\(832\) | −1.78748e13 | −1.29326 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 7.46372e12 | 0.534205 | ||||||||
\(835\) | −1.07730e13 | + | 1.86593e13i | −0.766913 | + | 1.32833i | ||||
\(836\) | −1.58176e12 | − | 2.73969e12i | −0.111999 | − | 0.193988i | ||||
\(837\) | −1.51288e12 | − | 2.62038e12i | −0.106547 | − | 0.184544i | ||||
\(838\) | −8.38910e12 | + | 1.45303e13i | −0.587648 | + | 1.01784i | ||||
\(839\) | 2.38915e13 | 1.66462 | 0.832310 | − | 0.554311i | \(-0.187018\pi\) | ||||
0.832310 | + | 0.554311i | \(0.187018\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.53993e13 | 1.75081 | ||||||||
\(842\) | 3.27990e12 | − | 5.68096e12i | 0.224883 | − | 0.389509i | ||||
\(843\) | −1.34341e12 | − | 2.32686e12i | −0.0916189 | − | 0.158689i | ||||
\(844\) | 5.03432e12 | + | 8.71970e12i | 0.341507 | + | 0.591508i | ||||
\(845\) | −1.03411e13 | + | 1.79114e13i | −0.697771 | + | 1.20858i | ||||
\(846\) | 3.44398e12 | 0.231150 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.55242e12 | −0.235908 | ||||||||
\(849\) | −1.00997e13 | + | 1.74932e13i | −0.667153 | + | 1.15554i | ||||
\(850\) | 3.40794e12 | + | 5.90273e12i | 0.223927 | + | 0.387853i | ||||
\(851\) | 8.34871e11 | + | 1.44604e12i | 0.0545678 | + | 0.0945141i | ||||
\(852\) | −3.89132e12 | + | 6.73997e12i | −0.252999 | + | 0.438207i | ||||
\(853\) | −1.68078e13 | −1.08703 | −0.543514 | − | 0.839400i | \(-0.682906\pi\) | ||||
−0.543514 | + | 0.839400i | \(0.682906\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.08988e12 | −0.581716 | ||||||||
\(856\) | −1.13506e13 | + | 1.96598e13i | −0.722581 | + | 1.25155i | ||||
\(857\) | −3.34139e12 | − | 5.78746e12i | −0.211599 | − | 0.366500i | 0.740616 | − | 0.671928i | \(-0.234534\pi\) |
−0.952215 | + | 0.305428i | \(0.901200\pi\) | |||||||
\(858\) | −3.65812e12 | − | 6.33606e12i | −0.230444 | − | 0.399141i | ||||
\(859\) | 1.02271e13 | − | 1.77138e13i | 0.640887 | − | 1.11005i | −0.344348 | − | 0.938842i | \(-0.611900\pi\) |
0.985235 | − | 0.171207i | \(-0.0547667\pi\) | |||||||
\(860\) | −9.17308e12 | −0.571837 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.52198e12 | −0.217272 | ||||||||
\(863\) | 9.37526e12 | − | 1.62384e13i | 0.575353 | − | 0.996541i | −0.420650 | − | 0.907223i | \(-0.638198\pi\) |
0.996003 | − | 0.0893182i | \(-0.0284688\pi\) | |||||||
\(864\) | 7.17918e12 | + | 1.24347e13i | 0.438291 | + | 0.759143i | ||||
\(865\) | 9.63162e12 | + | 1.66825e13i | 0.584961 | + | 1.01318i | ||||
\(866\) | 2.89934e12 | − | 5.02180e12i | 0.175173 | − | 0.303409i | ||||
\(867\) | 1.19025e13 | 0.715405 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.33801e13 | −0.795924 | ||||||||
\(870\) | 1.42898e13 | − | 2.47507e13i | 0.845648 | − | 1.46471i | ||||
\(871\) | −1.50977e13 | − | 2.61500e13i | −0.888853 | − | 1.53954i | ||||
\(872\) | 1.44381e12 | + | 2.50075e12i | 0.0845640 | + | 0.146469i | ||||
\(873\) | 2.80815e12 | − | 4.86386e12i | 0.163628 | − | 0.283411i | ||||
\(874\) | 1.15688e12 | 0.0670634 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.19400e12 | 0.412764 | ||||||||
\(877\) | −1.01380e13 | + | 1.75595e13i | −0.578699 | + | 1.00234i | 0.416930 | + | 0.908938i | \(0.363106\pi\) |
−0.995629 | + | 0.0933968i | \(0.970227\pi\) | |||||||
\(878\) | −5.05808e12 | − | 8.76085e12i | −0.287250 | − | 0.497532i | ||||
\(879\) | −7.67842e12 | − | 1.32994e13i | −0.433833 | − | 0.751420i | ||||
\(880\) | −3.29781e12 | + | 5.71198e12i | −0.185376 | + | 0.321081i | ||||
\(881\) | 2.17613e13 | 1.21701 | 0.608505 | − | 0.793550i | \(-0.291770\pi\) | ||||
0.608505 | + | 0.793550i | \(0.291770\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.44540e13 | −1.90729 | −0.953645 | − | 0.300933i | \(-0.902702\pi\) | ||||
−0.953645 | + | 0.300933i | \(0.902702\pi\) | |||||||
\(884\) | −1.58135e12 | + | 2.73897e12i | −0.0870948 | + | 0.150853i | ||||
\(885\) | −2.43592e12 | − | 4.21913e12i | −0.133481 | − | 0.231195i | ||||
\(886\) | −2.57752e12 | − | 4.46440e12i | −0.140524 | − | 0.243395i | ||||
\(887\) | 2.99034e12 | − | 5.17943e12i | 0.162205 | − | 0.280948i | −0.773454 | − | 0.633852i | \(-0.781473\pi\) |
0.935659 | + | 0.352905i | \(0.114806\pi\) | |||||||
\(888\) | −1.63342e13 | −0.881534 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.39114e13 | 0.743217 | ||||||||
\(891\) | −2.55875e12 | + | 4.43189e12i | −0.136012 | + | 0.235581i | ||||
\(892\) | −2.72819e12 | − | 4.72536e12i | −0.144289 | − | 0.249916i | ||||
\(893\) | −6.53797e12 | − | 1.13241e13i | −0.344042 | − | 0.595898i | ||||
\(894\) | 7.12150e11 | − | 1.23348e12i | 0.0372866 | − | 0.0645823i | ||||
\(895\) | 1.12153e13 | 0.584260 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.12503e12 | −0.109597 | ||||||||
\(898\) | 2.03387e12 | − | 3.52277e12i | 0.104371 | − | 0.180776i | ||||
\(899\) | 3.18709e12 | + | 5.52020e12i | 0.162733 | + | 0.281862i | ||||
\(900\) | −3.45083e12 | − | 5.97701e12i | −0.175320 | − | 0.303663i | ||||
\(901\) | −1.89389e12 | + | 3.28031e12i | −0.0957398 | + | 0.165826i | ||||
\(902\) | 1.03735e13 | 0.521789 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.89637e13 | −0.944422 | ||||||||
\(905\) | −8.18203e11 | + | 1.41717e12i | −0.0405455 | + | 0.0702269i | ||||
\(906\) | 9.13395e12 | + | 1.58205e13i | 0.450383 | + | 0.780086i | ||||
\(907\) | 1.25841e12 | + | 2.17964e12i | 0.0617434 | + | 0.106943i | 0.895245 | − | 0.445575i | \(-0.147001\pi\) |
−0.833501 | + | 0.552517i | \(0.813667\pi\) | |||||||
\(908\) | 1.94449e10 | − | 3.36795e10i | 0.000949333 | − | 0.00164429i | ||||
\(909\) | 1.50504e12 | 0.0731158 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.96021e13 | 1.90496 | 0.952478 | − | 0.304607i | \(-0.0985252\pi\) | ||||
0.952478 | + | 0.304607i | \(0.0985252\pi\) | |||||||
\(912\) | −2.54324e12 | + | 4.40502e12i | −0.121734 | + | 0.210849i | ||||
\(913\) | 1.10683e12 | + | 1.91708e12i | 0.0527183 | + | 0.0913107i | ||||
\(914\) | 1.99522e12 | + | 3.45582e12i | 0.0945656 | + | 0.163792i | ||||
\(915\) | 3.34923e12 | − | 5.80103e12i | 0.157961 | − | 0.273596i | ||||
\(916\) | −2.53338e12 | −0.118897 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −5.11667e12 | −0.237791 | ||||||||
\(919\) | 2.00425e13 | − | 3.47147e13i | 0.926899 | − | 1.60544i | 0.138422 | − | 0.990373i | \(-0.455797\pi\) |
0.788478 | − | 0.615063i | \(-0.210870\pi\) | |||||||
\(920\) | 2.13118e12 | + | 3.69132e12i | 0.0980789 | + | 0.169878i | ||||
\(921\) | 6.73356e12 | + | 1.16629e13i | 0.308373 | + | 0.534118i | ||||
\(922\) | 9.89218e12 | − | 1.71338e13i | 0.450820 | − | 0.780843i | ||||
\(923\) | −4.31975e13 | −1.95907 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.76174e13 | 2.13859 | ||||||||
\(926\) | −1.51132e13 | + | 2.61768e13i | −0.675469 | + | 1.16995i | ||||
\(927\) | 4.85790e12 | + | 8.41412e12i | 0.216067 | + | 0.374240i | ||||
\(928\) | −1.51239e13 | − | 2.61954e13i | −0.669421 | − | 1.15947i | ||||
\(929\) | −4.19235e12 | + | 7.26136e12i | −0.184666 | + | 0.319851i | −0.943464 | − | 0.331475i | \(-0.892454\pi\) |
0.758798 | + | 0.651326i | \(0.225787\pi\) | |||||||
\(930\) | 4.56497e12 | 0.200108 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.48336e12 | −0.0643986 | ||||||||
\(933\) | 7.91326e12 | − | 1.37062e13i | 0.341891 | − | 0.592173i | ||||
\(934\) | 3.21972e12 | + | 5.57672e12i | 0.138439 | + | 0.239783i | ||||
\(935\) | 3.51630e12 | + | 6.09042e12i | 0.150465 | + | 0.260612i | ||||
\(936\) | −6.57031e12 | + | 1.13801e13i | −0.279798 | + | 0.484624i | ||||
\(937\) | −2.33983e12 | −0.0991645 | −0.0495822 | − | 0.998770i | \(-0.515789\pi\) | ||||
−0.0495822 | + | 0.998770i | \(0.515789\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.01725e13 | −1.26653 | ||||||||
\(940\) | 7.39124e12 | − | 1.28020e13i | 0.308775 | − | 0.534814i | ||||
\(941\) | −3.22947e12 | − | 5.59360e12i | −0.134270 | − | 0.232562i | 0.791049 | − | 0.611753i | \(-0.209535\pi\) |
−0.925318 | + | 0.379192i | \(0.876202\pi\) | |||||||
\(942\) | 7.45830e12 | + | 1.29182e13i | 0.308610 | + | 0.534529i | ||||
\(943\) | 1.50651e12 | − | 2.60935e12i | 0.0620396 | − | 0.107456i | ||||
\(944\) | 1.72327e12 | 0.0706285 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.00327e12 | 0.324906 | ||||||||
\(947\) | 1.21661e13 | − | 2.10724e13i | 0.491561 | − | 0.851409i | −0.508391 | − | 0.861126i | \(-0.669760\pi\) |
0.999953 | + | 0.00971684i | \(0.00309302\pi\) | |||||||
\(948\) | −5.83266e12 | − | 1.01025e13i | −0.234547 | − | 0.406247i | ||||
\(949\) | 1.99651e13 | + | 3.45806e13i | 0.799050 | + | 1.38399i | ||||
\(950\) | 1.64958e13 | − | 2.85716e13i | 0.657079 | − | 1.13809i | ||||
\(951\) | 1.35228e13 | 0.536109 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.50351e12 | 0.0983177 | 0.0491589 | − | 0.998791i | \(-0.484346\pi\) | ||||
0.0491589 | + | 0.998791i | \(0.484346\pi\) | |||||||
\(954\) | −2.41448e12 | + | 4.18200e12i | −0.0943747 | + | 0.163462i | ||||
\(955\) | −1.22775e13 | − | 2.12653e13i | −0.477635 | − | 0.827287i | ||||
\(956\) | −1.02966e12 | − | 1.78342e12i | −0.0398688 | − | 0.0690548i | ||||
\(957\) | 9.90240e12 | − | 1.71515e13i | 0.381625 | − | 0.660994i | ||||
\(958\) | −2.89108e13 | −1.10896 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.46527e13 | −1.31679 | ||||||||
\(961\) | 1.27107e13 | − | 2.20157e13i | 0.480746 | − | 0.832677i | ||||
\(962\) | −1.39094e13 | − | 2.40918e13i | −0.523626 | − | 0.906947i | ||||
\(963\) | 6.93474e12 | + | 1.20113e13i | 0.259844 | + | 0.450062i | ||||
\(964\) | 6.07863e12 | − | 1.05285e13i | 0.226704 | − | 0.392663i | ||||
\(965\) | −4.82576e13 | −1.79140 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.19887e13 | 0.808686 | 0.404343 | − | 0.914607i | \(-0.367500\pi\) | ||||
0.404343 | + | 0.914607i | \(0.367500\pi\) | |||||||
\(968\) | 9.62606e12 | − | 1.66728e13i | 0.352379 | − | 0.610338i | ||||
\(969\) | 2.71174e12 | + | 4.69687e12i | 0.0988077 | + | 0.171140i | ||||
\(970\) | 1.51756e13 | + | 2.62849e13i | 0.550393 | + | 0.953309i | ||||
\(971\) | −4.53872e12 | + | 7.86129e12i | −0.163850 | + | 0.283797i | −0.936246 | − | 0.351344i | \(-0.885725\pi\) |
0.772396 | + | 0.635141i | \(0.219058\pi\) | |||||||
\(972\) | 8.91568e12 | 0.320373 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.24787e13 | −0.444276 | ||||||||
\(975\) | −3.03007e13 | + | 5.24823e13i | −1.07382 | + | 1.85991i | ||||
\(976\) | 1.18469e12 | + | 2.05195e12i | 0.0417909 | + | 0.0723840i | ||||
\(977\) | −1.36576e13 | − | 2.36557e13i | −0.479567 | − | 0.830634i | 0.520158 | − | 0.854070i | \(-0.325873\pi\) |
−0.999725 | + | 0.0234354i | \(0.992540\pi\) | |||||||
\(978\) | 8.41600e12 | − | 1.45769e13i | 0.294158 | − | 0.509497i | ||||
\(979\) | 9.64018e12 | 0.335400 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.76421e12 | 0.0608192 | ||||||||
\(982\) | 1.28481e13 | − | 2.22536e13i | 0.440897 | − | 0.763656i | ||||
\(983\) | 5.37703e12 | + | 9.31329e12i | 0.183676 | + | 0.318135i | 0.943129 | − | 0.332426i | \(-0.107867\pi\) |
−0.759454 | + | 0.650561i | \(0.774534\pi\) | |||||||
\(984\) | 1.47374e13 | + | 2.55259e13i | 0.501120 | + | 0.867966i | ||||
\(985\) | 1.31094e13 | − | 2.27062e13i | 0.443732 | − | 0.768566i | ||||
\(986\) | 1.07790e13 | 0.363188 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.53087e13 | 0.511131 | ||||||||
\(989\) | 1.16229e12 | − | 2.01315e12i | 0.0386306 | − | 0.0669102i | ||||
\(990\) | 4.48286e12 | + | 7.76455e12i | 0.148319 | + | 0.256896i | ||||
\(991\) | 1.03024e13 | + | 1.78442e13i | 0.339317 | + | 0.587714i | 0.984304 | − | 0.176479i | \(-0.0564708\pi\) |
−0.644988 | + | 0.764193i | \(0.723137\pi\) | |||||||
\(992\) | 2.41572e12 | − | 4.18415e12i | 0.0792034 | − | 0.137184i | ||||
\(993\) | −3.70352e13 | −1.20877 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.85474e12 | 0.124678 | ||||||||
\(996\) | −9.64974e11 | + | 1.67138e12i | −0.0310705 | + | 0.0538157i | ||||
\(997\) | 1.15190e13 | + | 1.99515e13i | 0.369222 | + | 0.639511i | 0.989444 | − | 0.144915i | \(-0.0462909\pi\) |
−0.620222 | + | 0.784426i | \(0.712958\pi\) | |||||||
\(998\) | −1.41660e13 | − | 2.45363e13i | −0.452023 | − | 0.782926i | ||||
\(999\) | −1.78731e13 | + | 3.09572e13i | −0.567749 | + | 0.983370i |
(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 | 49.10.c.b.30.2 | 4 | ||
7.2 | even | 3 | 49.10.a.b.1.1 | 2 | |||
7.3 | odd | 6 | 49.10.c.c.18.2 | 4 | |||
7.4 | even | 3 | inner | 49.10.c.b.18.2 | 4 | ||
7.5 | odd | 6 | 7.10.a.a.1.1 | ✓ | 2 | ||
7.6 | odd | 2 | 49.10.c.c.30.2 | 4 | |||
21.5 | even | 6 | 63.10.a.d.1.2 | 2 | |||
28.19 | even | 6 | 112.10.a.e.1.1 | 2 | |||
35.12 | even | 12 | 175.10.b.b.99.1 | 4 | |||
35.19 | odd | 6 | 175.10.a.b.1.2 | 2 | |||
35.33 | even | 12 | 175.10.b.b.99.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.10.a.a.1.1 | ✓ | 2 | 7.5 | odd | 6 | ||
49.10.a.b.1.1 | 2 | 7.2 | even | 3 | |||
49.10.c.b.18.2 | 4 | 7.4 | even | 3 | inner | ||
49.10.c.b.30.2 | 4 | 1.1 | even | 1 | trivial | ||
49.10.c.c.18.2 | 4 | 7.3 | odd | 6 | |||
49.10.c.c.30.2 | 4 | 7.6 | odd | 2 | |||
63.10.a.d.1.2 | 2 | 21.5 | even | 6 | |||
112.10.a.e.1.1 | 2 | 28.19 | even | 6 | |||
175.10.a.b.1.2 | 2 | 35.19 | odd | 6 | |||
175.10.b.b.99.1 | 4 | 35.12 | even | 12 | |||
175.10.b.b.99.4 | 4 | 35.33 | even | 12 |