Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [15,9,Mod(14,15)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("15.14");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.11067915092\) |
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: | \( x^{12} + 2096 x^{10} + 1966565 x^{8} + 942732880 x^{6} + 407378811520 x^{4} + 58185108489824 x^{2} + 32\!\cdots\!64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{13}\cdot 3^{18}\cdot 5^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 14.8 | ||
Root | \(-2.83292 + 10.0603i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 15.14 |
Dual form | 15.9.d.c.14.7 |
$q$-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 \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(11\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.66585 | 0.354116 | 0.177058 | − | 0.984200i | \(-0.443342\pi\) | ||||
0.177058 | + | 0.984200i | \(0.443342\pi\) | |||||||
\(3\) | 35.3550 | + | 72.8768i | 0.436481 | + | 0.899713i | ||||
\(4\) | −223.898 | −0.874602 | ||||||||
\(5\) | −531.836 | + | 328.291i | −0.850938 | + | 0.525266i | ||||
\(6\) | 200.316 | + | 412.909i | 0.154565 | + | 0.318602i | ||||
\(7\) | − | 1674.62i | − | 0.697469i | −0.937222 | − | 0.348734i | \(-0.886612\pi\) | ||
0.937222 | − | 0.348734i | \(-0.113388\pi\) | |||||||
\(8\) | −2719.03 | −0.663826 | ||||||||
\(9\) | −4061.05 | + | 5153.12i | −0.618968 | + | 0.785416i | ||||
\(10\) | −3013.30 | + | 1860.05i | −0.301330 | + | 0.186005i | ||||
\(11\) | 21417.9i | 1.46287i | 0.681910 | + | 0.731436i | \(0.261150\pi\) | ||||
−0.681910 | + | 0.731436i | \(0.738850\pi\) | |||||||
\(12\) | −7915.92 | − | 16317.0i | −0.381748 | − | 0.786891i | ||||
\(13\) | 5980.82i | 0.209405i | 0.994504 | + | 0.104703i | \(0.0333890\pi\) | ||||
−0.994504 | + | 0.104703i | \(0.966611\pi\) | |||||||
\(14\) | − | 9488.16i | − | 0.246985i | ||||||
\(15\) | −42727.9 | − | 27151.8i | −0.844007 | − | 0.536332i | ||||
\(16\) | 41912.3 | 0.639531 | ||||||||
\(17\) | 69210.3 | 0.828657 | 0.414329 | − | 0.910127i | \(-0.364016\pi\) | ||||
0.414329 | + | 0.910127i | \(0.364016\pi\) | |||||||
\(18\) | −23009.3 | + | 29196.8i | −0.219186 | + | 0.278128i | ||||
\(19\) | −18044.8 | −0.138464 | −0.0692320 | − | 0.997601i | \(-0.522055\pi\) | ||||
−0.0692320 | + | 0.997601i | \(0.522055\pi\) | |||||||
\(20\) | 119077. | − | 73503.8i | 0.744233 | − | 0.459399i | ||||
\(21\) | 122041. | − | 59206.3i | 0.627522 | − | 0.304432i | ||||
\(22\) | 121351.i | 0.518026i | ||||||||
\(23\) | 91800.0 | 0.328043 | 0.164022 | − | 0.986457i | \(-0.447553\pi\) | ||||
0.164022 | + | 0.986457i | \(0.447553\pi\) | |||||||
\(24\) | −96131.3 | − | 198154.i | −0.289748 | − | 0.597253i | ||||
\(25\) | 175075. | − | 349194.i | 0.448192 | − | 0.893937i | ||||
\(26\) | 33886.4i | 0.0741536i | ||||||||
\(27\) | −519121. | − | 113768.i | −0.976817 | − | 0.214074i | ||||
\(28\) | 374945.i | 0.610008i | ||||||||
\(29\) | 1.12754e6i | 1.59419i | 0.603854 | + | 0.797095i | \(0.293631\pi\) | ||||
−0.603854 | + | 0.797095i | \(0.706369\pi\) | |||||||
\(30\) | −242090. | − | 153838.i | −0.298876 | − | 0.189923i | ||||
\(31\) | −1.27927e6 | −1.38521 | −0.692607 | − | 0.721316i | \(-0.743538\pi\) | ||||
−0.692607 | + | 0.721316i | \(0.743538\pi\) | |||||||
\(32\) | 933541. | 0.890294 | ||||||||
\(33\) | −1.56087e6 | + | 757230.i | −1.31617 | + | 0.638517i | ||||
\(34\) | 392135. | 0.293440 | ||||||||
\(35\) | 549764. | + | 890626.i | 0.366356 | + | 0.593503i | ||||
\(36\) | 909261. | − | 1.15377e6i | 0.541351 | − | 0.686927i | ||||
\(37\) | − | 2.19804e6i | − | 1.17281i | −0.810018 | − | 0.586405i | \(-0.800543\pi\) | ||
0.810018 | − | 0.586405i | \(-0.199457\pi\) | |||||||
\(38\) | −102239. | −0.0490322 | ||||||||
\(39\) | −435863. | + | 211452.i | −0.188404 | + | 0.0914014i | ||||
\(40\) | 1.44608e6 | − | 892633.i | 0.564875 | − | 0.348685i | ||||
\(41\) | − | 29007.4i | − | 0.0102653i | −0.999987 | − | 0.00513267i | \(-0.998366\pi\) | ||
0.999987 | − | 0.00513267i | \(-0.00163379\pi\) | |||||||
\(42\) | 691466. | − | 335454.i | 0.222215 | − | 0.107804i | ||||
\(43\) | 6.78169e6i | 1.98365i | 0.127625 | + | 0.991823i | \(0.459265\pi\) | ||||
−0.127625 | + | 0.991823i | \(0.540735\pi\) | |||||||
\(44\) | − | 4.79543e6i | − | 1.27943i | ||||||
\(45\) | 468092. | − | 4.07382e6i | 0.114151 | − | 0.993463i | ||||
\(46\) | 520125. | 0.116165 | ||||||||
\(47\) | 1.96089e6 | 0.401847 | 0.200924 | − | 0.979607i | \(-0.435606\pi\) | ||||
0.200924 | + | 0.979607i | \(0.435606\pi\) | |||||||
\(48\) | 1.48181e6 | + | 3.05443e6i | 0.279143 | + | 0.575395i | ||||
\(49\) | 2.96044e6 | 0.513537 | ||||||||
\(50\) | 991948. | − | 1.97848e6i | 0.158712 | − | 0.316557i | ||||
\(51\) | 2.44693e6 | + | 5.04382e6i | 0.361694 | + | 0.745554i | ||||
\(52\) | − | 1.33909e6i | − | 0.183146i | ||||||
\(53\) | −1.23039e7 | −1.55933 | −0.779664 | − | 0.626198i | \(-0.784610\pi\) | ||||
−0.779664 | + | 0.626198i | \(0.784610\pi\) | |||||||
\(54\) | −2.94126e6 | − | 644591.i | −0.345906 | − | 0.0758070i | ||||
\(55\) | −7.03131e6 | − | 1.13908e7i | −0.768397 | − | 1.24481i | ||||
\(56\) | 4.55335e6i | 0.462998i | ||||||||
\(57\) | −637973. | − | 1.31504e6i | −0.0604370 | − | 0.124578i | ||||
\(58\) | 6.38847e6i | 0.564527i | ||||||||
\(59\) | 5.58621e6i | 0.461009i | 0.973071 | + | 0.230504i | \(0.0740376\pi\) | ||||
−0.973071 | + | 0.230504i | \(0.925962\pi\) | |||||||
\(60\) | 9.56669e6 | + | 6.07924e6i | 0.738171 | + | 0.469077i | ||||
\(61\) | 312034. | 0.0225363 | 0.0112681 | − | 0.999937i | \(-0.496413\pi\) | ||||
0.0112681 | + | 0.999937i | \(0.496413\pi\) | |||||||
\(62\) | −7.24817e6 | −0.490525 | ||||||||
\(63\) | 8.62953e6 | + | 6.80073e6i | 0.547803 | + | 0.431711i | ||||
\(64\) | −5.44025e6 | −0.324264 | ||||||||
\(65\) | −1.96345e6 | − | 3.18082e6i | −0.109993 | − | 0.178191i | ||||
\(66\) | −8.84365e6 | + | 4.29035e6i | −0.466075 | + | 0.226109i | ||||
\(67\) | − | 853503.i | − | 0.0423551i | −0.999776 | − | 0.0211775i | \(-0.993258\pi\) | ||
0.999776 | − | 0.0211775i | \(-0.00674153\pi\) | |||||||
\(68\) | −1.54961e7 | −0.724746 | ||||||||
\(69\) | 3.24559e6 | + | 6.69009e6i | 0.143185 | + | 0.295145i | ||||
\(70\) | 3.11488e6 | + | 5.04615e6i | 0.129733 | + | 0.210169i | ||||
\(71\) | − | 3.18282e7i | − | 1.25250i | −0.779621 | − | 0.626252i | \(-0.784588\pi\) | ||
0.779621 | − | 0.626252i | \(-0.215412\pi\) | |||||||
\(72\) | 1.10421e7 | − | 1.40115e7i | 0.410887 | − | 0.521379i | ||||
\(73\) | 2.36800e6i | 0.0833855i | 0.999130 | + | 0.0416927i | \(0.0132751\pi\) | ||||
−0.999130 | + | 0.0416927i | \(0.986725\pi\) | |||||||
\(74\) | − | 1.24537e7i | − | 0.415310i | ||||||
\(75\) | 3.16379e7 | + | 413140.i | 0.999915 | + | 0.0130573i | ||||
\(76\) | 4.04019e6 | 0.121101 | ||||||||
\(77\) | 3.58669e7 | 1.02031 | ||||||||
\(78\) | −2.46953e6 | + | 1.19805e6i | −0.0667170 | + | 0.0323667i | ||||
\(79\) | 2.92328e7 | 0.750520 | 0.375260 | − | 0.926920i | \(-0.377553\pi\) | ||||
0.375260 | + | 0.926920i | \(0.377553\pi\) | |||||||
\(80\) | −2.22905e7 | + | 1.37594e7i | −0.544202 | + | 0.335924i | ||||
\(81\) | −1.00625e7 | − | 4.18541e7i | −0.233757 | − | 0.972295i | ||||
\(82\) | − | 164351.i | − | 0.00363512i | ||||||
\(83\) | 6.73076e7 | 1.41825 | 0.709124 | − | 0.705084i | \(-0.249091\pi\) | ||||
0.709124 | + | 0.705084i | \(0.249091\pi\) | |||||||
\(84\) | −2.73248e7 | + | 1.32562e7i | −0.548832 | + | 0.266257i | ||||
\(85\) | −3.68086e7 | + | 2.27211e7i | −0.705136 | + | 0.435265i | ||||
\(86\) | 3.84240e7i | 0.702439i | ||||||||
\(87\) | −8.21715e7 | + | 3.98642e7i | −1.43431 | + | 0.695834i | ||||
\(88\) | − | 5.82360e7i | − | 0.971093i | ||||||
\(89\) | 4.90240e7i | 0.781355i | 0.920528 | + | 0.390678i | \(0.127759\pi\) | ||||
−0.920528 | + | 0.390678i | \(0.872241\pi\) | |||||||
\(90\) | 2.65214e6 | − | 2.30816e7i | 0.0404228 | − | 0.351801i | ||||
\(91\) | 1.00156e7 | 0.146054 | ||||||||
\(92\) | −2.05539e7 | −0.286908 | ||||||||
\(93\) | −4.52287e7 | − | 9.32293e7i | −0.604620 | − | 1.24629i | ||||
\(94\) | 1.11101e7 | 0.142300 | ||||||||
\(95\) | 9.59686e6 | − | 5.92394e6i | 0.117824 | − | 0.0727304i | ||||
\(96\) | 3.30053e7 | + | 6.80334e7i | 0.388597 | + | 0.801009i | ||||
\(97\) | 7.18400e7i | 0.811483i | 0.913988 | + | 0.405741i | \(0.132987\pi\) | ||||
−0.913988 | + | 0.405741i | \(0.867013\pi\) | |||||||
\(98\) | 1.67734e7 | 0.181851 | ||||||||
\(99\) | −1.10369e8 | − | 8.69792e7i | −1.14896 | − | 0.905471i | ||||
\(100\) | −3.91990e7 | + | 7.81840e7i | −0.391990 | + | 0.781840i | ||||
\(101\) | 1.12197e8i | 1.07819i | 0.842244 | + | 0.539097i | \(0.181234\pi\) | ||||
−0.842244 | + | 0.539097i | \(0.818766\pi\) | |||||||
\(102\) | 1.38639e7 | + | 2.85775e7i | 0.128081 | + | 0.264012i | ||||
\(103\) | − | 1.33889e8i | − | 1.18959i | −0.803877 | − | 0.594795i | \(-0.797233\pi\) | ||
0.803877 | − | 0.594795i | \(-0.202767\pi\) | |||||||
\(104\) | − | 1.62620e7i | − | 0.139008i | ||||||
\(105\) | −4.54690e7 | + | 7.15531e7i | −0.374075 | + | 0.588669i | ||||
\(106\) | −6.97118e7 | −0.552183 | ||||||||
\(107\) | 3.67153e7 | 0.280100 | 0.140050 | − | 0.990144i | \(-0.455274\pi\) | ||||
0.140050 | + | 0.990144i | \(0.455274\pi\) | |||||||
\(108\) | 1.16230e8 | + | 2.54724e7i | 0.854327 | + | 0.187230i | ||||
\(109\) | 1.68006e8 | 1.19020 | 0.595099 | − | 0.803652i | \(-0.297113\pi\) | ||||
0.595099 | + | 0.803652i | \(0.297113\pi\) | |||||||
\(110\) | −3.98383e7 | − | 6.45387e7i | −0.272101 | − | 0.440808i | ||||
\(111\) | 1.60186e8 | − | 7.77115e7i | 1.05519 | − | 0.511910i | ||||
\(112\) | − | 7.01873e7i | − | 0.446053i | ||||||
\(113\) | 9.78362e7 | 0.600048 | 0.300024 | − | 0.953932i | \(-0.403005\pi\) | ||||
0.300024 | + | 0.953932i | \(0.403005\pi\) | |||||||
\(114\) | −3.61466e6 | − | 7.45084e6i | −0.0214017 | − | 0.0441150i | ||||
\(115\) | −4.88226e7 | + | 3.01371e7i | −0.279145 | + | 0.172310i | ||||
\(116\) | − | 2.52454e8i | − | 1.39428i | ||||||
\(117\) | −3.08198e7 | − | 2.42884e7i | −0.164470 | − | 0.129615i | ||||
\(118\) | 3.16506e7i | 0.163250i | ||||||||
\(119\) | − | 1.15901e8i | − | 0.577963i | ||||||
\(120\) | 1.16178e8 | + | 7.38266e7i | 0.560274 | + | 0.356031i | ||||
\(121\) | −2.44368e8 | −1.14000 | ||||||||
\(122\) | 1.76793e6 | 0.00798044 | ||||||||
\(123\) | 2.11397e6 | − | 1.02556e6i | 0.00923586 | − | 0.00448063i | ||||
\(124\) | 2.86427e8 | 1.21151 | ||||||||
\(125\) | 2.15261e7 | + | 2.43190e8i | 0.0881709 | + | 0.996105i | ||||
\(126\) | 4.88936e7 | + | 3.85319e7i | 0.193986 | + | 0.152876i | ||||
\(127\) | 1.37799e8i | 0.529701i | 0.964289 | + | 0.264851i | \(0.0853227\pi\) | ||||
−0.964289 | + | 0.264851i | \(0.914677\pi\) | |||||||
\(128\) | −2.69810e8 | −1.00512 | ||||||||
\(129\) | −4.94228e8 | + | 2.39767e8i | −1.78471 | + | 0.865824i | ||||
\(130\) | −1.11246e7 | − | 1.80220e7i | −0.0389503 | − | 0.0631001i | ||||
\(131\) | 7.11572e7i | 0.241620i | 0.992676 | + | 0.120810i | \(0.0385492\pi\) | ||||
−0.992676 | + | 0.120810i | \(0.961451\pi\) | |||||||
\(132\) | 3.49476e8 | − | 1.69543e8i | 1.15112 | − | 0.558448i | ||||
\(133\) | 3.02182e7i | 0.0965743i | ||||||||
\(134\) | − | 4.83582e6i | − | 0.0149986i | ||||||
\(135\) | 3.13436e8 | − | 1.09917e8i | 0.943657 | − | 0.330925i | ||||
\(136\) | −1.88185e8 | −0.550084 | ||||||||
\(137\) | −5.04740e8 | −1.43280 | −0.716400 | − | 0.697689i | \(-0.754212\pi\) | ||||
−0.716400 | + | 0.697689i | \(0.754212\pi\) | |||||||
\(138\) | 1.83890e7 | + | 3.79050e7i | 0.0507040 | + | 0.104515i | ||||
\(139\) | 2.09113e8 | 0.560171 | 0.280086 | − | 0.959975i | \(-0.409637\pi\) | ||||
0.280086 | + | 0.959975i | \(0.409637\pi\) | |||||||
\(140\) | −1.23091e8 | − | 1.99409e8i | −0.320416 | − | 0.519079i | ||||
\(141\) | 6.93271e7 | + | 1.42903e8i | 0.175399 | + | 0.361547i | ||||
\(142\) | − | 1.80334e8i | − | 0.443531i | ||||||
\(143\) | −1.28097e8 | −0.306333 | ||||||||
\(144\) | −1.70208e8 | + | 2.15979e8i | −0.395849 | + | 0.502298i | ||||
\(145\) | −3.70161e8 | − | 5.99667e8i | −0.837373 | − | 1.35656i | ||||
\(146\) | 1.34167e7i | 0.0295281i | ||||||||
\(147\) | 1.04666e8 | + | 2.15747e8i | 0.224149 | + | 0.462036i | ||||
\(148\) | 4.92136e8i | 1.02574i | ||||||||
\(149\) | 2.19726e8i | 0.445796i | 0.974842 | + | 0.222898i | \(0.0715517\pi\) | ||||
−0.974842 | + | 0.222898i | \(0.928448\pi\) | |||||||
\(150\) | 1.79256e8 | + | 2.34079e6i | 0.354085 | + | 0.00462378i | ||||
\(151\) | 3.50620e8 | 0.674418 | 0.337209 | − | 0.941430i | \(-0.390517\pi\) | ||||
0.337209 | + | 0.941430i | \(0.390517\pi\) | |||||||
\(152\) | 4.90643e7 | 0.0919160 | ||||||||
\(153\) | −2.81066e8 | + | 3.56649e8i | −0.512912 | + | 0.650841i | ||||
\(154\) | 2.03217e8 | 0.361307 | ||||||||
\(155\) | 6.80364e8 | − | 4.19974e8i | 1.17873 | − | 0.727605i | ||||
\(156\) | 9.75889e7 | − | 4.73437e7i | 0.164779 | − | 0.0799399i | ||||
\(157\) | 7.08761e7i | 0.116654i | 0.998298 | + | 0.0583272i | \(0.0185767\pi\) | ||||
−0.998298 | + | 0.0583272i | \(0.981423\pi\) | |||||||
\(158\) | 1.65629e8 | 0.265771 | ||||||||
\(159\) | −4.35003e8 | − | 8.96665e8i | −0.680618 | − | 1.40295i | ||||
\(160\) | −4.96491e8 | + | 3.06473e8i | −0.757585 | + | 0.467641i | ||||
\(161\) | − | 1.53730e8i | − | 0.228800i | ||||||
\(162\) | −5.70125e7 | − | 2.37139e8i | −0.0827771 | − | 0.344305i | ||||
\(163\) | 7.30934e8i | 1.03545i | 0.855548 | + | 0.517724i | \(0.173220\pi\) | ||||
−0.855548 | + | 0.517724i | \(0.826780\pi\) | |||||||
\(164\) | 6.49470e6i | 0.00897809i | ||||||||
\(165\) | 5.81535e8 | − | 9.15142e8i | 0.784585 | − | 1.23468i | ||||
\(166\) | 3.81355e8 | 0.502223 | ||||||||
\(167\) | 1.02725e9 | 1.32072 | 0.660361 | − | 0.750948i | \(-0.270403\pi\) | ||||
0.660361 | + | 0.750948i | \(0.270403\pi\) | |||||||
\(168\) | −3.31833e8 | + | 1.60984e8i | −0.416565 | + | 0.202090i | ||||
\(169\) | 7.79961e8 | 0.956150 | ||||||||
\(170\) | −2.08552e8 | + | 1.28734e8i | −0.249700 | + | 0.154134i | ||||
\(171\) | 7.32807e7 | − | 9.29868e7i | 0.0857048 | − | 0.108752i | ||||
\(172\) | − | 1.51841e9i | − | 1.73490i | ||||||
\(173\) | −1.07140e8 | −0.119610 | −0.0598050 | − | 0.998210i | \(-0.519048\pi\) | ||||
−0.0598050 | + | 0.998210i | \(0.519048\pi\) | |||||||
\(174\) | −4.65571e8 | + | 2.25864e8i | −0.507913 | + | 0.246406i | ||||
\(175\) | −5.84769e8 | − | 2.93185e8i | −0.623494 | − | 0.312600i | ||||
\(176\) | 8.97675e8i | 0.935553i | ||||||||
\(177\) | −4.07105e8 | + | 1.97500e8i | −0.414776 | + | 0.201222i | ||||
\(178\) | 2.77763e8i | 0.276690i | ||||||||
\(179\) | − | 1.76590e8i | − | 0.172010i | −0.996295 | − | 0.0860051i | \(-0.972590\pi\) | ||
0.996295 | − | 0.0860051i | \(-0.0274101\pi\) | |||||||
\(180\) | −1.04805e8 | + | 9.12121e8i | −0.0998371 | + | 0.868885i | ||||
\(181\) | −1.03775e9 | −0.966896 | −0.483448 | − | 0.875373i | \(-0.660616\pi\) | ||||
−0.483448 | + | 0.875373i | \(0.660616\pi\) | |||||||
\(182\) | 5.67469e7 | 0.0517198 | ||||||||
\(183\) | 1.10319e7 | + | 2.27400e7i | 0.00983666 | + | 0.0202762i | ||||
\(184\) | −2.49607e8 | −0.217764 | ||||||||
\(185\) | 7.21595e8 | + | 1.16900e9i | 0.616037 | + | 0.997989i | ||||
\(186\) | −2.56259e8 | − | 5.28223e8i | −0.214105 | − | 0.441332i | ||||
\(187\) | 1.48234e9i | 1.21222i | ||||||||
\(188\) | −4.39039e8 | −0.351456 | ||||||||
\(189\) | −1.90518e8 | + | 8.69332e8i | −0.149310 | + | 0.681300i | ||||
\(190\) | 5.43744e7 | − | 3.35641e7i | 0.0417234 | − | 0.0257550i | ||||
\(191\) | − | 4.41653e8i | − | 0.331854i | −0.986138 | − | 0.165927i | \(-0.946938\pi\) | ||
0.986138 | − | 0.165927i | \(-0.0530617\pi\) | |||||||
\(192\) | −1.92340e8 | − | 3.96468e8i | −0.141535 | − | 0.291745i | ||||
\(193\) | − | 1.80470e9i | − | 1.30070i | −0.759635 | − | 0.650349i | \(-0.774623\pi\) | ||
0.759635 | − | 0.650349i | \(-0.225377\pi\) | |||||||
\(194\) | 4.07034e8i | 0.287359i | ||||||||
\(195\) | 1.62390e8 | − | 2.55548e8i | 0.112311 | − | 0.176739i | ||||
\(196\) | −6.62837e8 | −0.449141 | ||||||||
\(197\) | −1.84458e9 | −1.22471 | −0.612355 | − | 0.790583i | \(-0.709778\pi\) | ||||
−0.612355 | + | 0.790583i | \(0.709778\pi\) | |||||||
\(198\) | −6.25334e8 | − | 4.92811e8i | −0.406866 | − | 0.320641i | ||||
\(199\) | 1.80610e9 | 1.15167 | 0.575837 | − | 0.817564i | \(-0.304676\pi\) | ||||
0.575837 | + | 0.817564i | \(0.304676\pi\) | |||||||
\(200\) | −4.76034e8 | + | 9.49470e8i | −0.297521 | + | 0.593419i | ||||
\(201\) | 6.22005e7 | − | 3.01756e7i | 0.0381074 | − | 0.0184872i | ||||
\(202\) | 6.35693e8i | 0.381805i | ||||||||
\(203\) | 1.88820e9 | 1.11190 | ||||||||
\(204\) | −5.47863e8 | − | 1.12930e9i | −0.316338 | − | 0.652063i | ||||
\(205\) | 9.52287e6 | + | 1.54272e7i | 0.00539203 | + | 0.00873517i | ||||
\(206\) | − | 7.58597e8i | − | 0.421253i | ||||||
\(207\) | −3.72804e8 | + | 4.73056e8i | −0.203048 | + | 0.257651i | ||||
\(208\) | 2.50670e8i | 0.133921i | ||||||||
\(209\) | − | 3.86481e8i | − | 0.202555i | ||||||
\(210\) | −2.57621e8 | + | 4.05409e8i | −0.132466 | + | 0.208457i | ||||
\(211\) | 2.94285e8 | 0.148470 | 0.0742350 | − | 0.997241i | \(-0.476349\pi\) | ||||
0.0742350 | + | 0.997241i | \(0.476349\pi\) | |||||||
\(212\) | 2.75481e9 | 1.36379 | ||||||||
\(213\) | 2.31954e9 | − | 1.12529e9i | 1.12689 | − | 0.546695i | ||||
\(214\) | 2.08024e8 | 0.0991876 | ||||||||
\(215\) | −2.22637e9 | − | 3.60675e9i | −1.04194 | − | 1.68796i | ||||
\(216\) | 1.41151e9 | + | 3.09338e8i | 0.648437 | + | 0.142108i | ||||
\(217\) | 2.14230e9i | 0.966143i | ||||||||
\(218\) | 9.51897e8 | 0.421468 | ||||||||
\(219\) | −1.72572e8 | + | 8.37207e7i | −0.0750230 | + | 0.0363962i | ||||
\(220\) | 1.57430e9 | + | 2.55039e9i | 0.672042 | + | 1.08872i | ||||
\(221\) | 4.13934e8i | 0.173525i | ||||||||
\(222\) | 9.07588e8 | − | 4.40302e8i | 0.373660 | − | 0.181275i | ||||
\(223\) | − | 3.54930e9i | − | 1.43523i | −0.696438 | − | 0.717617i | \(-0.745233\pi\) | ||
0.696438 | − | 0.717617i | \(-0.254767\pi\) | |||||||
\(224\) | − | 1.56333e9i | − | 0.620952i | ||||||
\(225\) | 1.08845e9 | + | 2.32028e9i | 0.424696 | + | 0.905336i | ||||
\(226\) | 5.54325e8 | 0.212486 | ||||||||
\(227\) | −3.07376e9 | −1.15762 | −0.578811 | − | 0.815461i | \(-0.696483\pi\) | ||||
−0.578811 | + | 0.815461i | \(0.696483\pi\) | |||||||
\(228\) | 1.42841e8 | + | 2.94436e8i | 0.0528583 | + | 0.108956i | ||||
\(229\) | −2.58716e9 | −0.940767 | −0.470383 | − | 0.882462i | \(-0.655884\pi\) | ||||
−0.470383 | + | 0.882462i | \(0.655884\pi\) | |||||||
\(230\) | −2.76621e8 | + | 1.70752e8i | −0.0988495 | + | 0.0610176i | ||||
\(231\) | 1.26808e9 | + | 2.61387e9i | 0.445346 | + | 0.917985i | ||||
\(232\) | − | 3.06582e9i | − | 1.05826i | ||||||
\(233\) | −4.46492e9 | −1.51492 | −0.757460 | − | 0.652882i | \(-0.773560\pi\) | ||||
−0.757460 | + | 0.652882i | \(0.773560\pi\) | |||||||
\(234\) | −1.74621e8 | − | 1.37614e8i | −0.0582414 | − | 0.0458987i | ||||
\(235\) | −1.04287e9 | + | 6.43741e8i | −0.341947 | + | 0.211077i | ||||
\(236\) | − | 1.25074e9i | − | 0.403199i | ||||||
\(237\) | 1.03353e9 | + | 2.13039e9i | 0.327588 | + | 0.675253i | ||||
\(238\) | − | 6.56678e8i | − | 0.204666i | ||||||
\(239\) | 2.49405e9i | 0.764388i | 0.924082 | + | 0.382194i | \(0.124831\pi\) | ||||
−0.924082 | + | 0.382194i | \(0.875169\pi\) | |||||||
\(240\) | −1.79082e9 | − | 1.13799e9i | −0.539769 | − | 0.343001i | ||||
\(241\) | −1.06935e9 | −0.316993 | −0.158497 | − | 0.987360i | \(-0.550665\pi\) | ||||
−0.158497 | + | 0.987360i | \(0.550665\pi\) | |||||||
\(242\) | −1.38455e9 | −0.403691 | ||||||||
\(243\) | 2.69443e9 | − | 2.21307e9i | 0.772756 | − | 0.634703i | ||||
\(244\) | −6.98637e7 | −0.0197103 | ||||||||
\(245\) | −1.57447e9 | + | 9.71886e8i | −0.436988 | + | 0.269743i | ||||
\(246\) | 1.19774e7 | − | 5.81065e6i | 0.00327056 | − | 0.00158666i | ||||
\(247\) | − | 1.07922e8i | − | 0.0289951i | ||||||
\(248\) | 3.47838e9 | 0.919540 | ||||||||
\(249\) | 2.37966e9 | + | 4.90516e9i | 0.619039 | + | 1.27602i | ||||
\(250\) | 1.21964e8 | + | 1.37788e9i | 0.0312227 | + | 0.352736i | ||||
\(251\) | 2.58790e9i | 0.652007i | 0.945369 | + | 0.326003i | \(0.105702\pi\) | ||||
−0.945369 | + | 0.326003i | \(0.894298\pi\) | |||||||
\(252\) | −1.93214e9 | − | 1.52267e9i | −0.479110 | − | 0.377575i | ||||
\(253\) | 1.96617e9i | 0.479886i | ||||||||
\(254\) | 7.80748e8i | 0.187575i | ||||||||
\(255\) | −2.95721e9 | − | 1.87918e9i | −0.699393 | − | 0.444435i | ||||
\(256\) | −1.35998e8 | −0.0316644 | ||||||||
\(257\) | 3.99995e9 | 0.916900 | 0.458450 | − | 0.888720i | \(-0.348405\pi\) | ||||
0.458450 | + | 0.888720i | \(0.348405\pi\) | |||||||
\(258\) | −2.80022e9 | + | 1.35848e9i | −0.631994 | + | 0.306602i | ||||
\(259\) | −3.68088e9 | −0.817999 | ||||||||
\(260\) | 4.39613e8 | + | 7.12179e8i | 0.0962004 | + | 0.155846i | ||||
\(261\) | −5.81035e9 | − | 4.57900e9i | −1.25210 | − | 0.986753i | ||||
\(262\) | 4.03166e8i | 0.0855615i | ||||||||
\(263\) | −2.61772e9 | −0.547142 | −0.273571 | − | 0.961852i | \(-0.588205\pi\) | ||||
−0.273571 | + | 0.961852i | \(0.588205\pi\) | |||||||
\(264\) | 4.24405e9 | − | 2.05893e9i | 0.873705 | − | 0.423864i | ||||
\(265\) | 6.54364e9 | − | 4.03925e9i | 1.32689 | − | 0.819062i | ||||
\(266\) | 1.71212e8i | 0.0341985i | ||||||||
\(267\) | −3.57271e9 | + | 1.73324e9i | −0.702996 | + | 0.341047i | ||||
\(268\) | 1.91098e8i | 0.0370439i | ||||||||
\(269\) | − | 6.21608e9i | − | 1.18715i | −0.804777 | − | 0.593577i | \(-0.797715\pi\) | ||
0.804777 | − | 0.593577i | \(-0.202285\pi\) | |||||||
\(270\) | 1.77588e9 | − | 6.22772e8i | 0.334164 | − | 0.117186i | ||||
\(271\) | 5.31021e9 | 0.984543 | 0.492271 | − | 0.870442i | \(-0.336167\pi\) | ||||
0.492271 | + | 0.870442i | \(0.336167\pi\) | |||||||
\(272\) | 2.90076e9 | 0.529952 | ||||||||
\(273\) | 3.54102e8 | + | 7.29906e8i | 0.0637496 | + | 0.131406i | ||||
\(274\) | −2.85978e9 | −0.507377 | ||||||||
\(275\) | 7.47902e9 | + | 3.74974e9i | 1.30772 | + | 0.655648i | ||||
\(276\) | −7.26681e8 | − | 1.49790e9i | −0.125230 | − | 0.258135i | ||||
\(277\) | 2.24918e9i | 0.382037i | 0.981586 | + | 0.191018i | \(0.0611790\pi\) | ||||
−0.981586 | + | 0.191018i | \(0.938821\pi\) | |||||||
\(278\) | 1.18480e9 | 0.198365 | ||||||||
\(279\) | 5.19519e9 | − | 6.59224e9i | 0.857403 | − | 1.08797i | ||||
\(280\) | −1.49482e9 | − | 2.42164e9i | −0.243197 | − | 0.393983i | ||||
\(281\) | − | 7.68684e9i | − | 1.23289i | −0.787400 | − | 0.616443i | \(-0.788573\pi\) | ||
0.787400 | − | 0.616443i | \(-0.211427\pi\) | |||||||
\(282\) | 3.92797e8 | + | 8.09667e8i | 0.0621114 | + | 0.128029i | ||||
\(283\) | 7.20498e9i | 1.12328i | 0.827382 | + | 0.561639i | \(0.189829\pi\) | ||||
−0.827382 | + | 0.561639i | \(0.810171\pi\) | |||||||
\(284\) | 7.12628e9i | 1.09544i | ||||||||
\(285\) | 7.71014e8 | + | 4.89948e8i | 0.116865 | + | 0.0742626i | ||||
\(286\) | −7.25776e8 | −0.108477 | ||||||||
\(287\) | −4.85765e7 | −0.00715976 | ||||||||
\(288\) | −3.79115e9 | + | 4.81064e9i | −0.551063 | + | 0.699251i | ||||
\(289\) | −2.18569e9 | −0.313327 | ||||||||
\(290\) | −2.09728e9 | − | 3.39762e9i | −0.296527 | − | 0.480378i | ||||
\(291\) | −5.23547e9 | + | 2.53990e9i | −0.730102 | + | 0.354197i | ||||
\(292\) | − | 5.30191e8i | − | 0.0729291i | ||||||
\(293\) | 3.98677e9 | 0.540942 | 0.270471 | − | 0.962728i | \(-0.412821\pi\) | ||||
0.270471 | + | 0.962728i | \(0.412821\pi\) | |||||||
\(294\) | 5.93023e8 | + | 1.22239e9i | 0.0793748 | + | 0.163614i | ||||
\(295\) | −1.83390e9 | − | 2.97095e9i | −0.242152 | − | 0.392290i | ||||
\(296\) | 5.97653e9i | 0.778542i | ||||||||
\(297\) | 2.43667e9 | − | 1.11185e10i | 0.313163 | − | 1.42896i | ||||
\(298\) | 1.24493e9i | 0.157863i | ||||||||
\(299\) | 5.49039e8i | 0.0686940i | ||||||||
\(300\) | −7.08367e9 | − | 9.25012e7i | −0.874528 | − | 0.0114199i | ||||
\(301\) | 1.13568e10 | 1.38353 | ||||||||
\(302\) | 1.98656e9 | 0.238822 | ||||||||
\(303\) | −8.17658e9 | + | 3.96674e9i | −0.970066 | + | 0.470612i | ||||
\(304\) | −7.56298e8 | −0.0885520 | ||||||||
\(305\) | −1.65951e8 | + | 1.02438e8i | −0.0191770 | + | 0.0118375i | ||||
\(306\) | −1.59248e9 | + | 2.02072e9i | −0.181630 | + | 0.230473i | ||||
\(307\) | − | 9.29130e9i | − | 1.04598i | −0.852339 | − | 0.522990i | \(-0.824817\pi\) | ||
0.852339 | − | 0.522990i | \(-0.175183\pi\) | |||||||
\(308\) | −8.03054e9 | −0.892364 | ||||||||
\(309\) | 9.75743e9 | − | 4.73366e9i | 1.07029 | − | 0.519234i | ||||
\(310\) | 3.85484e9 | − | 2.37951e9i | 0.417407 | − | 0.257656i | ||||
\(311\) | 1.12048e10i | 1.19774i | 0.800847 | + | 0.598869i | \(0.204383\pi\) | ||||
−0.800847 | + | 0.598869i | \(0.795617\pi\) | |||||||
\(312\) | 1.18512e9 | − | 5.74944e8i | 0.125068 | − | 0.0606746i | ||||
\(313\) | 9.45147e9i | 0.984741i | 0.870386 | + | 0.492371i | \(0.163870\pi\) | ||||
−0.870386 | + | 0.492371i | \(0.836130\pi\) | |||||||
\(314\) | 4.01573e8i | 0.0413092i | ||||||||
\(315\) | −6.82211e9 | − | 7.83878e8i | −0.692910 | − | 0.0796170i | ||||
\(316\) | −6.54518e9 | −0.656407 | ||||||||
\(317\) | −8.48385e8 | −0.0840148 | −0.0420074 | − | 0.999117i | \(-0.513375\pi\) | ||||
−0.0420074 | + | 0.999117i | \(0.513375\pi\) | |||||||
\(318\) | −2.46466e9 | − | 5.08037e9i | −0.241017 | − | 0.496806i | ||||
\(319\) | −2.41496e10 | −2.33210 | ||||||||
\(320\) | 2.89333e9 | − | 1.78599e9i | 0.275929 | − | 0.170325i | ||||
\(321\) | 1.29807e9 | + | 2.67570e9i | 0.122258 | + | 0.252009i | ||||
\(322\) | − | 8.71013e8i | − | 0.0810217i | ||||||
\(323\) | −1.24888e9 | −0.114739 | ||||||||
\(324\) | 2.25297e9 | + | 9.37106e9i | 0.204445 | + | 0.850371i | ||||
\(325\) | 2.08847e9 | + | 1.04709e9i | 0.187195 | + | 0.0938537i | ||||
\(326\) | 4.14136e9i | 0.366668i | ||||||||
\(327\) | 5.93986e9 | + | 1.22437e10i | 0.519499 | + | 1.07084i | ||||
\(328\) | 7.88720e7i | 0.00681440i | ||||||||
\(329\) | − | 3.28374e9i | − | 0.280276i | ||||||
\(330\) | 3.29489e9 | − | 5.18506e9i | 0.277834 | − | 0.437218i | ||||
\(331\) | 4.71539e9 | 0.392831 | 0.196415 | − | 0.980521i | \(-0.437070\pi\) | ||||
0.196415 | + | 0.980521i | \(0.437070\pi\) | |||||||
\(332\) | −1.50701e10 | −1.24040 | ||||||||
\(333\) | 1.13267e10 | + | 8.92633e9i | 0.921144 | + | 0.725932i | ||||
\(334\) | 5.82026e9 | 0.467688 | ||||||||
\(335\) | 2.80197e8 | + | 4.53924e8i | 0.0222477 | + | 0.0360416i | ||||
\(336\) | 5.11503e9 | − | 2.48147e9i | 0.401320 | − | 0.194694i | ||||
\(337\) | − | 3.45801e8i | − | 0.0268106i | −0.999910 | − | 0.0134053i | \(-0.995733\pi\) | ||
0.999910 | − | 0.0134053i | \(-0.00426716\pi\) | |||||||
\(338\) | 4.41914e9 | 0.338587 | ||||||||
\(339\) | 3.45900e9 | + | 7.12999e9i | 0.261910 | + | 0.539871i | ||||
\(340\) | 8.24137e9 | − | 5.08722e9i | 0.616714 | − | 0.380684i | ||||
\(341\) | − | 2.73994e10i | − | 2.02639i | ||||||
\(342\) | 4.15197e8 | − | 5.26849e8i | 0.0303494 | − | 0.0385107i | ||||
\(343\) | − | 1.46115e10i | − | 1.05565i | ||||||
\(344\) | − | 1.84396e10i | − | 1.31679i | ||||||
\(345\) | −3.92242e9 | − | 2.49254e9i | −0.276871 | − | 0.175940i | ||||
\(346\) | −6.07040e8 | −0.0423558 | ||||||||
\(347\) | 3.52962e9 | 0.243450 | 0.121725 | − | 0.992564i | \(-0.461157\pi\) | ||||
0.121725 | + | 0.992564i | \(0.461157\pi\) | |||||||
\(348\) | 1.83980e10 | − | 8.92552e9i | 1.25445 | − | 0.608578i | ||||
\(349\) | 8.25013e9 | 0.556108 | 0.278054 | − | 0.960565i | \(-0.410311\pi\) | ||||
0.278054 | + | 0.960565i | \(0.410311\pi\) | |||||||
\(350\) | −3.31321e9 | − | 1.66114e9i | −0.220789 | − | 0.110697i | ||||
\(351\) | 6.80424e8 | − | 3.10477e9i | 0.0448282 | − | 0.204550i | ||||
\(352\) | 1.99945e10i | 1.30239i | ||||||||
\(353\) | −1.08036e10 | −0.695776 | −0.347888 | − | 0.937536i | \(-0.613101\pi\) | ||||
−0.347888 | + | 0.937536i | \(0.613101\pi\) | |||||||
\(354\) | −2.30659e9 | + | 1.11901e9i | −0.146878 | + | 0.0712557i | ||||
\(355\) | 1.04489e10 | + | 1.69274e10i | 0.657897 | + | 1.06580i | ||||
\(356\) | − | 1.09764e10i | − | 0.683375i | ||||||
\(357\) | 8.44650e9 | − | 4.09768e9i | 0.520001 | − | 0.252270i | ||||
\(358\) | − | 1.00053e9i | − | 0.0609115i | ||||||
\(359\) | 1.78116e10i | 1.07232i | 0.844115 | + | 0.536162i | \(0.180126\pi\) | ||||
−0.844115 | + | 0.536162i | \(0.819874\pi\) | |||||||
\(360\) | −1.27276e9 | + | 1.10768e10i | −0.0757766 | + | 0.659487i | ||||
\(361\) | −1.66579e10 | −0.980828 | ||||||||
\(362\) | −5.87975e9 | −0.342393 | ||||||||
\(363\) | −8.63965e9 | − | 1.78088e10i | −0.497587 | − | 1.02567i | ||||
\(364\) | −2.24248e9 | −0.127739 | ||||||||
\(365\) | −7.77394e8 | − | 1.25939e9i | −0.0437995 | − | 0.0709559i | ||||
\(366\) | 6.25053e7 | + | 1.28841e8i | 0.00348331 | + | 0.00718011i | ||||
\(367\) | − | 7.25059e9i | − | 0.399677i | −0.979829 | − | 0.199839i | \(-0.935958\pi\) | ||
0.979829 | − | 0.199839i | \(-0.0640418\pi\) | |||||||
\(368\) | 3.84755e9 | 0.209794 | ||||||||
\(369\) | 1.49478e8 | + | 1.17800e8i | 0.00806256 | + | 0.00635392i | ||||
\(370\) | 4.08845e9 | + | 6.62335e9i | 0.218148 | + | 0.353404i | ||||
\(371\) | 2.06043e10i | 1.08758i | ||||||||
\(372\) | 1.01266e10 | + | 2.08739e10i | 0.528802 | + | 1.09001i | ||||
\(373\) | − | 1.40594e10i | − | 0.726325i | −0.931726 | − | 0.363163i | \(-0.881697\pi\) | ||
0.931726 | − | 0.363163i | \(-0.118303\pi\) | |||||||
\(374\) | 8.39872e9i | 0.429266i | ||||||||
\(375\) | −1.69618e10 | + | 1.01667e10i | −0.857724 | + | 0.514110i | ||||
\(376\) | −5.33171e9 | −0.266757 | ||||||||
\(377\) | −6.74361e9 | −0.333831 | ||||||||
\(378\) | −1.07945e9 | + | 4.92550e9i | −0.0528730 | + | 0.241259i | ||||
\(379\) | 9.41156e9 | 0.456147 | 0.228073 | − | 0.973644i | \(-0.426757\pi\) | ||||
0.228073 | + | 0.973644i | \(0.426757\pi\) | |||||||
\(380\) | −2.14872e9 | + | 1.32636e9i | −0.103049 | + | 0.0636102i | ||||
\(381\) | −1.00423e10 | + | 4.87188e9i | −0.476579 | + | 0.231205i | ||||
\(382\) | − | 2.50234e9i | − | 0.117515i | ||||||
\(383\) | 2.22515e10 | 1.03410 | 0.517052 | − | 0.855954i | \(-0.327029\pi\) | ||||
0.517052 | + | 0.855954i | \(0.327029\pi\) | |||||||
\(384\) | −9.53913e9 | − | 1.96629e10i | −0.438716 | − | 0.904320i | ||||
\(385\) | −1.90753e10 | + | 1.17748e10i | −0.868219 | + | 0.535933i | ||||
\(386\) | − | 1.02252e10i | − | 0.460598i | ||||||
\(387\) | −3.49468e10 | − | 2.75408e10i | −1.55799 | − | 1.22781i | ||||
\(388\) | − | 1.60848e10i | − | 0.709725i | ||||||
\(389\) | 1.67518e10i | 0.731582i | 0.930697 | + | 0.365791i | \(0.119202\pi\) | ||||
−0.930697 | + | 0.365791i | \(0.880798\pi\) | |||||||
\(390\) | 9.20077e8 | − | 1.44789e9i | 0.0397709 | − | 0.0625862i | ||||
\(391\) | 6.35351e9 | 0.271836 | ||||||||
\(392\) | −8.04952e9 | −0.340899 | ||||||||
\(393\) | −5.18570e9 | + | 2.51576e9i | −0.217389 | + | 0.105463i | ||||
\(394\) | −1.04511e10 | −0.433689 | ||||||||
\(395\) | −1.55471e10 | + | 9.59687e9i | −0.638646 | + | 0.394223i | ||||
\(396\) | 2.47114e10 | + | 1.94745e10i | 1.00489 | + | 0.791927i | ||||
\(397\) | − | 3.88428e9i | − | 0.156368i | −0.996939 | − | 0.0781840i | \(-0.975088\pi\) | ||
0.996939 | − | 0.0781840i | \(-0.0249122\pi\) | |||||||
\(398\) | 1.02331e10 | 0.407826 | ||||||||
\(399\) | −2.20220e9 | + | 1.06836e9i | −0.0868892 | + | 0.0421529i | ||||
\(400\) | 7.33780e9 | − | 1.46355e10i | 0.286633 | − | 0.571701i | ||||
\(401\) | 3.28950e10i | 1.27219i | 0.771610 | + | 0.636096i | \(0.219452\pi\) | ||||
−0.771610 | + | 0.636096i | \(0.780548\pi\) | |||||||
\(402\) | 3.52419e8 | − | 1.70970e8i | 0.0134944 | − | 0.00654661i | ||||
\(403\) | − | 7.65110e9i | − | 0.290071i | ||||||
\(404\) | − | 2.51208e10i | − | 0.942991i | ||||||
\(405\) | 1.90919e10 | + | 1.89561e10i | 0.709626 | + | 0.704578i | ||||
\(406\) | 1.06983e10 | 0.393740 | ||||||||
\(407\) | 4.70774e10 | 1.71567 | ||||||||
\(408\) | −6.65327e9 | − | 1.37143e10i | −0.240101 | − | 0.494918i | ||||
\(409\) | −1.08495e9 | −0.0387718 | −0.0193859 | − | 0.999812i | \(-0.506171\pi\) | ||||
−0.0193859 | + | 0.999812i | \(0.506171\pi\) | |||||||
\(410\) | 5.39551e7 | + | 8.74081e7i | 0.00190940 | + | 0.00309326i | ||||
\(411\) | −1.78451e10 | − | 3.67838e10i | −0.625391 | − | 1.28911i | ||||
\(412\) | 2.99776e10i | 1.04042i | ||||||||
\(413\) | 9.35479e9 | 0.321539 | ||||||||
\(414\) | −2.11225e9 | + | 2.68026e9i | −0.0719026 | + | 0.0912381i | ||||
\(415\) | −3.57967e10 | + | 2.20965e10i | −1.20684 | + | 0.744957i | ||||
\(416\) | 5.58334e9i | 0.186432i | ||||||||
\(417\) | 7.39317e9 | + | 1.52395e10i | 0.244504 | + | 0.503994i | ||||
\(418\) | − | 2.18974e9i | − | 0.0717279i | ||||||
\(419\) | − | 3.39202e10i | − | 1.10053i | −0.834990 | − | 0.550266i | \(-0.814526\pi\) | ||
0.834990 | − | 0.550266i | \(-0.185474\pi\) | |||||||
\(420\) | 1.01804e10 | − | 1.60206e10i | 0.327167 | − | 0.514851i | ||||
\(421\) | 2.88554e10 | 0.918542 | 0.459271 | − | 0.888296i | \(-0.348111\pi\) | ||||
0.459271 | + | 0.888296i | \(0.348111\pi\) | |||||||
\(422\) | 1.66738e9 | 0.0525755 | ||||||||
\(423\) | −7.96325e9 | + | 1.01047e10i | −0.248731 | + | 0.315617i | ||||
\(424\) | 3.34546e10 | 1.03512 | ||||||||
\(425\) | 1.21170e10 | − | 2.41678e10i | 0.371398 | − | 0.740768i | ||||
\(426\) | 1.31422e10 | − | 6.37570e9i | 0.399051 | − | 0.193593i | ||||
\(427\) | − | 5.22539e8i | − | 0.0157183i | ||||||
\(428\) | −8.22050e9 | −0.244976 | ||||||||
\(429\) | −4.52886e9 | − | 9.33527e9i | −0.133709 | − | 0.275612i | ||||
\(430\) | −1.26143e10 | − | 2.04353e10i | −0.368967 | − | 0.597733i | ||||
\(431\) | − | 7.99799e8i | − | 0.0231778i | −0.999933 | − | 0.0115889i | \(-0.996311\pi\) | ||
0.999933 | − | 0.0115889i | \(-0.00368894\pi\) | |||||||
\(432\) | −2.17576e10 | − | 4.76827e9i | −0.624705 | − | 0.136907i | ||||
\(433\) | 2.02420e10i | 0.575839i | 0.957655 | + | 0.287920i | \(0.0929636\pi\) | ||||
−0.957655 | + | 0.287920i | \(0.907036\pi\) | |||||||
\(434\) | 1.21380e10i | 0.342126i | ||||||||
\(435\) | 3.06147e10 | − | 4.81774e10i | 0.855015 | − | 1.34551i | ||||
\(436\) | −3.76163e10 | −1.04095 | ||||||||
\(437\) | −1.65651e9 | −0.0454222 | ||||||||
\(438\) | −9.77768e8 | + | 4.74349e8i | −0.0265668 | + | 0.0128885i | ||||
\(439\) | 4.16160e10 | 1.12048 | 0.560238 | − | 0.828332i | \(-0.310710\pi\) | ||||
0.560238 | + | 0.828332i | \(0.310710\pi\) | |||||||
\(440\) | 1.91183e10 | + | 3.09720e10i | 0.510082 | + | 0.826340i | ||||
\(441\) | −1.20225e10 | + | 1.52555e10i | −0.317863 | + | 0.403340i | ||||
\(442\) | 2.34529e9i | 0.0614479i | ||||||||
\(443\) | 1.00330e10 | 0.260504 | 0.130252 | − | 0.991481i | \(-0.458421\pi\) | ||||
0.130252 | + | 0.991481i | \(0.458421\pi\) | |||||||
\(444\) | −3.58653e10 | + | 1.73995e10i | −0.922874 | + | 0.447718i | ||||
\(445\) | −1.60941e10 | − | 2.60727e10i | −0.410419 | − | 0.664885i | ||||
\(446\) | − | 2.01098e10i | − | 0.508239i | ||||||
\(447\) | −1.60129e10 | + | 7.76841e9i | −0.401088 | + | 0.194582i | ||||
\(448\) | 9.11037e9i | 0.226164i | ||||||||
\(449\) | 2.59211e10i | 0.637775i | 0.947793 | + | 0.318888i | \(0.103309\pi\) | ||||
−0.947793 | + | 0.318888i | \(0.896691\pi\) | |||||||
\(450\) | 6.16699e9 | + | 1.31463e10i | 0.150392 | + | 0.320593i | ||||
\(451\) | 6.21278e8 | 0.0150169 | ||||||||
\(452\) | −2.19054e10 | −0.524803 | ||||||||
\(453\) | 1.23962e10 | + | 2.55521e10i | 0.294371 | + | 0.606783i | ||||
\(454\) | −1.74155e10 | −0.409932 | ||||||||
\(455\) | −5.32667e9 | + | 3.28804e9i | −0.124283 | + | 0.0767169i | ||||
\(456\) | 1.73467e9 | + | 3.57565e9i | 0.0401196 | + | 0.0826980i | ||||
\(457\) | − | 5.83258e10i | − | 1.33720i | −0.743623 | − | 0.668599i | \(-0.766894\pi\) | ||
0.743623 | − | 0.668599i | \(-0.233106\pi\) | |||||||
\(458\) | −1.46585e10 | −0.333140 | ||||||||
\(459\) | −3.59285e10 | − | 7.87390e9i | −0.809447 | − | 0.177394i | ||||
\(460\) | 1.09313e10 | − | 6.74765e9i | 0.244141 | − | 0.150703i | ||||
\(461\) | − | 2.73170e10i | − | 0.604825i | −0.953177 | − | 0.302412i | \(-0.902208\pi\) | ||
0.953177 | − | 0.302412i | \(-0.0977920\pi\) | |||||||
\(462\) | 7.18472e9 | + | 1.48098e10i | 0.157704 | + | 0.325073i | ||||
\(463\) | 5.50831e10i | 1.19866i | 0.800504 | + | 0.599328i | \(0.204565\pi\) | ||||
−0.800504 | + | 0.599328i | \(0.795435\pi\) | |||||||
\(464\) | 4.72578e10i | 1.01953i | ||||||||
\(465\) | 5.46606e10 | + | 3.47346e10i | 1.16913 | + | 0.742934i | ||||
\(466\) | −2.52975e10 | −0.536456 | ||||||||
\(467\) | 4.06476e10 | 0.854610 | 0.427305 | − | 0.904108i | \(-0.359463\pi\) | ||||
0.427305 | + | 0.904108i | \(0.359463\pi\) | |||||||
\(468\) | 6.90051e9 | + | 5.43813e9i | 0.143846 | + | 0.113362i | ||||
\(469\) | −1.42929e9 | −0.0295414 | ||||||||
\(470\) | −5.90875e9 | + | 3.64734e9i | −0.121089 | + | 0.0747455i | ||||
\(471\) | −5.16522e9 | + | 2.50582e9i | −0.104956 | + | 0.0509175i | ||||
\(472\) | − | 1.51891e10i | − | 0.306029i | ||||||
\(473\) | −1.45250e11 | −2.90182 | ||||||||
\(474\) | 5.85580e9 | + | 1.20705e10i | 0.116004 | + | 0.239118i | ||||
\(475\) | −3.15919e9 | + | 6.30113e9i | −0.0620585 | + | 0.123778i | ||||
\(476\) | 2.59501e10i | 0.505488i | ||||||||
\(477\) | 4.99666e10 | − | 6.34032e10i | 0.965175 | − | 1.22472i | ||||
\(478\) | 1.41309e10i | 0.270682i | ||||||||
\(479\) | − | 1.08547e10i | − | 0.206194i | −0.994671 | − | 0.103097i | \(-0.967125\pi\) | ||
0.994671 | − | 0.103097i | \(-0.0328752\pi\) | |||||||
\(480\) | −3.98882e10 | − | 2.53473e10i | −0.751414 | − | 0.477493i | ||||
\(481\) | 1.31460e10 | 0.245592 | ||||||||
\(482\) | −6.05876e9 | −0.112252 | ||||||||
\(483\) | 1.12034e10 | − | 5.43514e9i | 0.205855 | − | 0.0998670i | ||||
\(484\) | 5.47137e10 | 0.997044 | ||||||||
\(485\) | −2.35844e10 | − | 3.82071e10i | −0.426244 | − | 0.690522i | ||||
\(486\) | 1.52663e10 | − | 1.25389e10i | 0.273645 | − | 0.224758i | ||||
\(487\) | − | 1.77991e10i | − | 0.316433i | −0.987404 | − | 0.158216i | \(-0.949426\pi\) | ||
0.987404 | − | 0.158216i | \(-0.0505743\pi\) | |||||||
\(488\) | −8.48429e8 | −0.0149602 | ||||||||
\(489\) | −5.32681e10 | + | 2.58422e10i | −0.931606 | + | 0.451953i | ||||
\(490\) | −8.92070e9 | + | 5.50656e9i | −0.154744 | + | 0.0955203i | ||||
\(491\) | − | 7.93615e10i | − | 1.36547i | −0.730664 | − | 0.682737i | \(-0.760789\pi\) | ||
0.730664 | − | 0.682737i | \(-0.239211\pi\) | |||||||
\(492\) | −4.73313e8 | + | 2.29620e8i | −0.00807771 | + | 0.00391877i | ||||
\(493\) | 7.80374e10i | 1.32104i | ||||||||
\(494\) | − | 6.11472e8i | − | 0.0102676i | ||||||
\(495\) | 8.72528e10 | + | 1.00256e10i | 1.45331 | + | 0.166989i | ||||
\(496\) | −5.36173e10 | −0.885887 | ||||||||
\(497\) | −5.33003e10 | −0.873582 | ||||||||
\(498\) | 1.34828e10 | + | 2.77919e10i | 0.219211 | + | 0.451857i | ||||
\(499\) | 6.54034e10 | 1.05487 | 0.527434 | − | 0.849596i | \(-0.323154\pi\) | ||||
0.527434 | + | 0.849596i | \(0.323154\pi\) | |||||||
\(500\) | −4.81965e9 | − | 5.44497e10i | −0.0771144 | − | 0.871196i | ||||
\(501\) | 3.63185e10 | + | 7.48629e10i | 0.576471 | + | 1.18827i | ||||
\(502\) | 1.46626e10i | 0.230886i | ||||||||
\(503\) | 1.01074e11 | 1.57894 | 0.789471 | − | 0.613788i | \(-0.210355\pi\) | ||||
0.789471 | + | 0.613788i | \(0.210355\pi\) | |||||||
\(504\) | −2.34639e10 | − | 1.84914e10i | −0.363646 | − | 0.286581i | ||||
\(505\) | −3.68334e10 | − | 5.96706e10i | −0.566339 | − | 0.917477i | ||||
\(506\) | 1.11400e10i | 0.169935i | ||||||||
\(507\) | 2.75755e10 | + | 5.68410e10i | 0.417341 | + | 0.860260i | ||||
\(508\) | − | 3.08529e10i | − | 0.463278i | ||||||
\(509\) | − | 1.19907e11i | − | 1.78638i | −0.449681 | − | 0.893189i | \(-0.648462\pi\) | ||
0.449681 | − | 0.893189i | \(-0.351538\pi\) | |||||||
\(510\) | −1.67551e10 | − | 1.06472e10i | −0.247666 | − | 0.157381i | ||||
\(511\) | 3.96551e9 | 0.0581588 | ||||||||
\(512\) | 6.83008e10 | 0.993908 | ||||||||
\(513\) | 9.36741e9 | + | 2.05291e9i | 0.135254 | + | 0.0296416i | ||||
\(514\) | 2.26631e10 | 0.324689 | ||||||||
\(515\) | 4.39547e10 | + | 7.12073e10i | 0.624851 | + | 1.01227i | ||||
\(516\) | 1.10657e11 | − | 5.36833e10i | 1.56091 | − | 0.757252i | ||||
\(517\) | 4.19981e10i | 0.587851i | ||||||||
\(518\) | −2.08553e10 | −0.289666 | ||||||||
\(519\) | −3.78794e9 | − | 7.80802e9i | −0.0522076 | − | 0.107615i | ||||
\(520\) | 5.33868e9 | + | 8.64874e9i | 0.0730164 | + | 0.118288i | ||||
\(521\) | 1.21461e11i | 1.64849i | 0.566230 | + | 0.824247i | \(0.308401\pi\) | ||||
−0.566230 | + | 0.824247i | \(0.691599\pi\) | |||||||
\(522\) | −3.29205e10 | − | 2.59439e10i | −0.443389 | − | 0.349424i | ||||
\(523\) | − | 8.02894e10i | − | 1.07313i | −0.843860 | − | 0.536564i | \(-0.819722\pi\) | ||
0.843860 | − | 0.536564i | \(-0.180278\pi\) | |||||||
\(524\) | − | 1.59320e10i | − | 0.211322i | ||||||
\(525\) | 6.91853e8 | − | 5.29816e10i | 0.00910703 | − | 0.697409i | ||||
\(526\) | −1.48316e10 | −0.193751 | ||||||||
\(527\) | −8.85389e10 | −1.14787 | ||||||||
\(528\) | −6.54196e10 | + | 3.17373e10i | −0.841729 | + | 0.408351i | ||||
\(529\) | −6.98837e10 | −0.892387 | ||||||||
\(530\) | 3.70753e10 | − | 2.28858e10i | 0.469873 | − | 0.290043i | ||||
\(531\) | −2.87864e10 | − | 2.26859e10i | −0.362084 | − | 0.285350i | ||||
\(532\) | − | 6.76580e9i | − | 0.0844641i | ||||||
\(533\) | 1.73488e8 | 0.00214961 | ||||||||
\(534\) | −2.02424e10 | + | 9.82029e9i | −0.248942 | + | 0.120770i | ||||
\(535\) | −1.95266e10 | + | 1.20533e10i | −0.238347 | + | 0.147127i | ||||
\(536\) | 2.32070e9i | 0.0281164i | ||||||||
\(537\) | 1.28693e10 | − | 6.24334e9i | 0.154760 | − | 0.0750793i | ||||
\(538\) | − | 3.52193e10i | − | 0.420390i | ||||||
\(539\) | 6.34064e10i | 0.751239i | ||||||||
\(540\) | −7.01778e10 | + | 2.46102e10i | −0.825325 | + | 0.289428i | ||||
\(541\) | 2.31499e10 | 0.270246 | 0.135123 | − | 0.990829i | \(-0.456857\pi\) | ||||
0.135123 | + | 0.990829i | \(0.456857\pi\) | |||||||
\(542\) | 3.00868e10 | 0.348642 | ||||||||
\(543\) | −3.66897e10 | − | 7.56281e10i | −0.422032 | − | 0.869929i | ||||
\(544\) | 6.46106e10 | 0.737748 | ||||||||
\(545\) | −8.93518e10 | + | 5.51549e10i | −1.01279 | + | 0.625170i | ||||
\(546\) | 2.00629e9 | + | 4.13553e9i | 0.0225747 | + | 0.0465330i | ||||
\(547\) | 1.06905e11i | 1.19412i | 0.802196 | + | 0.597061i | \(0.203665\pi\) | ||||
−0.802196 | + | 0.597061i | \(0.796335\pi\) | |||||||
\(548\) | 1.13010e11 | 1.25313 | ||||||||
\(549\) | −1.26718e9 | + | 1.60794e9i | −0.0139492 | + | 0.0177003i | ||||
\(550\) | 4.23750e10 | + | 2.12455e10i | 0.463083 | + | 0.232175i | ||||
\(551\) | − | 2.03462e10i | − | 0.220738i | ||||||
\(552\) | −8.82485e9 | − | 1.81906e10i | −0.0950498 | − | 0.195925i | ||||
\(553\) | − | 4.89540e10i | − | 0.523465i | ||||||
\(554\) | 1.27435e10i | 0.135285i | ||||||||
\(555\) | −5.96806e10 | + | 9.39174e10i | −0.629016 | + | 0.989861i | ||||
\(556\) | −4.68199e10 | −0.489927 | ||||||||
\(557\) | −3.49063e10 | −0.362646 | −0.181323 | − | 0.983424i | \(-0.558038\pi\) | ||||
−0.181323 | + | 0.983424i | \(0.558038\pi\) | |||||||
\(558\) | 2.94352e10 | − | 3.73507e10i | 0.303620 | − | 0.385267i | ||||
\(559\) | −4.05600e10 | −0.415385 | ||||||||
\(560\) | 2.30419e10 | + | 3.73282e10i | 0.234296 | + | 0.379564i | ||||
\(561\) | −1.08028e11 | + | 5.24081e10i | −1.09065 | + | 0.529112i | ||||
\(562\) | − | 4.35525e10i | − | 0.436584i | ||||||
\(563\) | 1.11294e10 | 0.110775 | 0.0553873 | − | 0.998465i | \(-0.482361\pi\) | ||||
0.0553873 | + | 0.998465i | \(0.482361\pi\) | |||||||
\(564\) | −1.55222e10 | − | 3.19957e10i | −0.153404 | − | 0.316210i | ||||
\(565\) | −5.20329e10 | + | 3.21188e10i | −0.510604 | + | 0.315185i | ||||
\(566\) | 4.08223e10i | 0.397770i | ||||||||
\(567\) | −7.00899e10 | + | 1.68509e10i | −0.678146 | + | 0.163038i | ||||
\(568\) | 8.65419e10i | 0.831444i | ||||||||
\(569\) | 1.10613e11i | 1.05526i | 0.849475 | + | 0.527629i | \(0.176919\pi\) | ||||
−0.849475 | + | 0.527629i | \(0.823081\pi\) | |||||||
\(570\) | 4.36845e9 | + | 2.77597e9i | 0.0413836 | + | 0.0262976i | ||||
\(571\) | −3.15777e10 | −0.297055 | −0.148527 | − | 0.988908i | \(-0.547453\pi\) | ||||
−0.148527 | + | 0.988908i | \(0.547453\pi\) | |||||||
\(572\) | 2.86806e10 | 0.267919 | ||||||||
\(573\) | 3.21862e10 | − | 1.56146e10i | 0.298574 | − | 0.144848i | ||||
\(574\) | −2.75227e8 | −0.00253538 | ||||||||
\(575\) | 1.60719e10 | − | 3.20560e10i | 0.147026 | − | 0.293250i | ||||
\(576\) | 2.20931e10 | − | 2.80343e10i | 0.200709 | − | 0.254683i | ||||
\(577\) | − | 3.66049e10i | − | 0.330245i | −0.986273 | − | 0.165123i | \(-0.947198\pi\) | ||
0.986273 | − | 0.165123i | \(-0.0528020\pi\) | |||||||
\(578\) | −1.23838e10 | −0.110954 | ||||||||
\(579\) | 1.31521e11 | − | 6.38053e10i | 1.17026 | − | 0.567731i | ||||
\(580\) | 8.28785e10 | + | 1.34264e11i | 0.732368 | + | 1.18645i | ||||
\(581\) | − | 1.12715e11i | − | 0.989184i | ||||||
\(582\) | −2.96634e10 | + | 1.43907e10i | −0.258540 | + | 0.125427i | ||||
\(583\) | − | 2.63523e11i | − | 2.28110i | ||||||
\(584\) | − | 6.43867e9i | − | 0.0553534i | ||||||
\(585\) | 2.43648e10 | + | 2.79957e9i | 0.208036 | + | 0.0239039i | ||||
\(586\) | 2.25884e10 | 0.191556 | ||||||||
\(587\) | 5.45783e10 | 0.459693 | 0.229846 | − | 0.973227i | \(-0.426178\pi\) | ||||
0.229846 | + | 0.973227i | \(0.426178\pi\) | |||||||
\(588\) | −2.34346e10 | − | 4.83054e10i | −0.196042 | − | 0.404098i | ||||
\(589\) | 2.30842e10 | 0.191802 | ||||||||
\(590\) | −1.03906e10 | − | 1.68329e10i | −0.0857498 | − | 0.138916i | ||||
\(591\) | −6.52152e10 | − | 1.34427e11i | −0.534563 | − | 1.10189i | ||||
\(592\) | − | 9.21248e10i | − | 0.750049i | ||||||
\(593\) | 8.35997e10 | 0.676061 | 0.338031 | − | 0.941135i | \(-0.390239\pi\) | ||||
0.338031 | + | 0.941135i | \(0.390239\pi\) | |||||||
\(594\) | 1.38058e10 | − | 6.29957e10i | 0.110896 | − | 0.506017i | ||||
\(595\) | 3.80493e10 | + | 6.16405e10i | 0.303584 | + | 0.491811i | ||||
\(596\) | − | 4.91962e10i | − | 0.389894i | ||||||
\(597\) | 6.38547e10 | + | 1.31623e11i | 0.502684 | + | 1.03618i | ||||
\(598\) | 3.11077e9i | 0.0243256i | ||||||||
\(599\) | 1.39529e10i | 0.108382i | 0.998531 | + | 0.0541909i | \(0.0172579\pi\) | ||||
−0.998531 | + | 0.0541909i | \(0.982742\pi\) | |||||||
\(600\) | −8.60245e10 | − | 1.12334e9i | −0.663769 | − | 0.00866774i | ||||
\(601\) | 2.42138e11 | 1.85595 | 0.927974 | − | 0.372645i | \(-0.121549\pi\) | ||||
0.927974 | + | 0.372645i | \(0.121549\pi\) | |||||||
\(602\) | 6.43457e10 | 0.489930 | ||||||||
\(603\) | 4.39820e9 | + | 3.46612e9i | 0.0332664 | + | 0.0262164i | ||||
\(604\) | −7.85032e10 | −0.589847 | ||||||||
\(605\) | 1.29964e11 | − | 8.02240e10i | 0.970067 | − | 0.598801i | ||||
\(606\) | −4.63273e10 | + | 2.24749e10i | −0.343515 | + | 0.166651i | ||||
\(607\) | 1.24176e11i | 0.914712i | 0.889284 | + | 0.457356i | \(0.151203\pi\) | ||||
−0.889284 | + | 0.457356i | \(0.848797\pi\) | |||||||
\(608\) | −1.68455e10 | −0.123274 | ||||||||
\(609\) | 6.67575e10 | + | 1.37606e11i | 0.485323 | + | 1.00039i | ||||
\(610\) | −9.40252e8 | + | 5.80397e8i | −0.00679086 | + | 0.00419185i | ||||
\(611\) | 1.17277e10i | 0.0841488i | ||||||||
\(612\) | 6.29302e10 | − | 7.98530e10i | 0.448594 | − | 0.569227i | ||||
\(613\) | 1.73317e11i | 1.22743i | 0.789526 | + | 0.613717i | \(0.210327\pi\) | ||||
−0.789526 | + | 0.613717i | \(0.789673\pi\) | |||||||
\(614\) | − | 5.26431e10i | − | 0.370397i | ||||||
\(615\) | −7.87603e8 | + | 1.23942e9i | −0.00550563 | + | 0.00866402i | ||||
\(616\) | −9.75233e10 | −0.677307 | ||||||||
\(617\) | −1.52659e11 | −1.05337 | −0.526687 | − | 0.850060i | \(-0.676566\pi\) | ||||
−0.526687 | + | 0.850060i | \(0.676566\pi\) | |||||||
\(618\) | 5.52841e10 | − | 2.68202e10i | 0.379006 | − | 0.183869i | ||||
\(619\) | −2.41342e11 | −1.64388 | −0.821942 | − | 0.569571i | \(-0.807109\pi\) | ||||
−0.821942 | + | 0.569571i | \(0.807109\pi\) | |||||||
\(620\) | −1.52332e11 | + | 9.40314e10i | −1.03092 | + | 0.636365i | ||||
\(621\) | −4.76553e10 | − | 1.04439e10i | −0.320439 | − | 0.0702256i | ||||
\(622\) | 6.34846e10i | 0.424137i | ||||||||
\(623\) | 8.20967e10 | 0.544971 | ||||||||
\(624\) | −1.82680e10 | + | 8.86243e9i | −0.120491 | + | 0.0584541i | ||||
\(625\) | −9.12854e10 | − | 1.22270e11i | −0.598248 | − | 0.801311i | ||||
\(626\) | 5.35506e10i | 0.348712i | ||||||||
\(627\) | 2.81655e10 | − | 1.36640e10i | 0.182242 | − | 0.0884116i | ||||
\(628\) | − | 1.58690e10i | − | 0.102026i | ||||||
\(629\) | − | 1.52127e11i | − | 0.971858i | ||||||
\(630\) | −3.86531e10 | − | 4.44133e9i | −0.245370 | − | 0.0281936i | ||||
\(631\) | 1.68033e11 | 1.05993 | 0.529966 | − | 0.848019i | \(-0.322205\pi\) | ||||
0.529966 | + | 0.848019i | \(0.322205\pi\) | |||||||
\(632\) | −7.94849e10 | −0.498215 | ||||||||
\(633\) | 1.04045e10 | + | 2.14466e10i | 0.0648044 | + | 0.133580i | ||||
\(634\) | −4.80682e9 | −0.0297510 | ||||||||
\(635\) | −4.52382e10 | − | 7.32865e10i | −0.278234 | − | 0.450743i | ||||
\(636\) | 9.73963e10 | + | 2.00762e11i | 0.595270 | + | 1.22702i | ||||
\(637\) | 1.77058e10i | 0.107537i | ||||||||
\(638\) | −1.36828e11 | −0.825832 | ||||||||
\(639\) | 1.64015e11 | + | 1.29256e11i | 0.983737 | + | 0.775260i | ||||
\(640\) | 1.43495e11 | − | 8.85762e10i | 0.855296 | − | 0.527955i | ||||
\(641\) | 1.07087e11i | 0.634313i | 0.948373 | + | 0.317156i | \(0.102728\pi\) | ||||
−0.948373 | + | 0.317156i | \(0.897272\pi\) | |||||||
\(642\) | 7.35467e9 | + | 1.51601e10i | 0.0432935 | + | 0.0892404i | ||||
\(643\) | − | 1.21734e11i | − | 0.712142i | −0.934459 | − | 0.356071i | \(-0.884116\pi\) | ||
0.934459 | − | 0.356071i | \(-0.115884\pi\) | |||||||
\(644\) | 3.44200e10i | 0.200109i | ||||||||
\(645\) | 1.84135e11 | − | 2.89767e11i | 1.06389 | − | 1.67421i | ||||
\(646\) | −7.07598e9 | −0.0406309 | ||||||||
\(647\) | −1.91646e11 | −1.09366 | −0.546829 | − | 0.837244i | \(-0.684165\pi\) | ||||
−0.546829 | + | 0.837244i | \(0.684165\pi\) | |||||||
\(648\) | 2.73602e10 | + | 1.13803e11i | 0.155174 | + | 0.645434i | ||||
\(649\) | −1.19645e11 | −0.674397 | ||||||||
\(650\) | 1.18329e10 | + | 5.93266e9i | 0.0662886 | + | 0.0332350i | ||||
\(651\) | −1.56124e11 | + | 7.57410e10i | −0.869252 | + | 0.421704i | ||||
\(652\) | − | 1.63655e11i | − | 0.905604i | ||||||
\(653\) | −1.71426e11 | −0.942811 | −0.471406 | − | 0.881917i | \(-0.656253\pi\) | ||||
−0.471406 | + | 0.881917i | \(0.656253\pi\) | |||||||
\(654\) | 3.36543e10 | + | 6.93712e10i | 0.183963 | + | 0.379200i | ||||
\(655\) | −2.33603e10 | − | 3.78440e10i | −0.126915 | − | 0.205604i | ||||
\(656\) | − | 1.21577e9i | − | 0.00656500i | ||||||
\(657\) | −1.22026e10 | − | 9.61657e9i | −0.0654923 | − | 0.0516129i | ||||
\(658\) | − | 1.86052e10i | − | 0.0992501i | ||||||
\(659\) | 6.16692e10i | 0.326984i | 0.986545 | + | 0.163492i | \(0.0522758\pi\) | ||||
−0.986545 | + | 0.163492i | \(0.947724\pi\) | |||||||
\(660\) | −1.30205e11 | + | 2.04899e11i | −0.686200 | + | 1.07985i | ||||
\(661\) | 2.25974e10 | 0.118373 | 0.0591864 | − | 0.998247i | \(-0.481149\pi\) | ||||
0.0591864 | + | 0.998247i | \(0.481149\pi\) | |||||||
\(662\) | 2.67167e10 | 0.139107 | ||||||||
\(663\) | −3.01662e10 | + | 1.46346e10i | −0.156123 | + | 0.0757404i | ||||
\(664\) | −1.83012e11 | −0.941469 | ||||||||
\(665\) | −9.92036e9 | − | 1.60711e10i | −0.0507272 | − | 0.0821788i | ||||
\(666\) | 6.41755e10 | + | 5.05752e10i | 0.326192 | + | 0.257064i | ||||
\(667\) | 1.03508e11i | 0.522964i | ||||||||
\(668\) | −2.30000e11 | −1.15511 | ||||||||
\(669\) | 2.58661e11 | − | 1.25485e11i | 1.29130 | − | 0.626453i | ||||
\(670\) | 1.58756e9 | + | 2.57186e9i | 0.00787825 | + | 0.0127629i | ||||
\(671\) | 6.68311e9i | 0.0329677i | ||||||||
\(672\) | 1.13930e11 | − | 5.52715e10i | 0.558679 | − | 0.271034i | ||||
\(673\) | 3.18816e11i | 1.55410i | 0.629437 | + | 0.777051i | \(0.283285\pi\) | ||||
−0.629437 | + | 0.777051i | \(0.716715\pi\) | |||||||
\(674\) | − | 1.95925e9i | − | 0.00949404i | ||||||
\(675\) | −1.30612e11 | + | 1.61356e11i | −0.629171 | + | 0.777267i | ||||
\(676\) | −1.74632e11 | −0.836250 | ||||||||
\(677\) | 3.75454e11 | 1.78732 | 0.893660 | − | 0.448745i | \(-0.148129\pi\) | ||||
0.893660 | + | 0.448745i | \(0.148129\pi\) | |||||||
\(678\) | 1.95982e10 | + | 4.03974e10i | 0.0927463 | + | 0.191177i | ||||
\(679\) | 1.20305e11 | 0.565984 | ||||||||
\(680\) | 1.00084e11 | − | 6.17794e10i | 0.468088 | − | 0.288940i | ||||
\(681\) | −1.08673e11 | − | 2.24006e11i | −0.505281 | − | 1.04153i | ||||
\(682\) | − | 1.55241e11i | − | 0.717576i | ||||||
\(683\) | 1.83700e11 | 0.844162 | 0.422081 | − | 0.906558i | \(-0.361300\pi\) | ||||
0.422081 | + | 0.906558i | \(0.361300\pi\) | |||||||
\(684\) | −1.64074e10 | + | 2.08196e10i | −0.0749576 | + | 0.0951146i | ||||
\(685\) | 2.68439e11 | − | 1.65702e11i | 1.21922 | − | 0.752601i | ||||
\(686\) | − | 8.27865e10i | − | 0.373820i | ||||||
\(687\) | −9.14692e10 | − | 1.88544e11i | −0.410627 | − | 0.846420i | ||||
\(688\) | 2.84236e11i | 1.26860i | ||||||||
\(689\) | − | 7.35871e10i | − | 0.326531i | ||||||
\(690\) | −2.22238e10 | − | 1.41223e10i | −0.0980443 | − | 0.0623031i | ||||
\(691\) | 1.46577e11 | 0.642916 | 0.321458 | − | 0.946924i | \(-0.395827\pi\) | ||||
0.321458 | + | 0.946924i | \(0.395827\pi\) | |||||||
\(692\) | 2.39885e10 | 0.104611 | ||||||||
\(693\) | −1.45657e11 | + | 1.84827e11i | −0.631538 | + | 0.801367i | ||||
\(694\) | 1.99983e10 | 0.0862095 | ||||||||
\(695\) | −1.11214e11 | + | 6.86498e10i | −0.476671 | + | 0.294239i | ||||
\(696\) | 2.23427e11 | − | 1.08392e11i | 0.952134 | − | 0.461913i | ||||
\(697\) | − | 2.00761e9i | − | 0.00850645i | ||||||
\(698\) | 4.67440e10 | 0.196926 | ||||||||
\(699\) | −1.57857e11 | − | 3.25389e11i | −0.661234 | − | 1.36299i | ||||
\(700\) | 1.30929e11 | + | 6.56435e10i | 0.545309 | + | 0.273401i | ||||
\(701\) | − | 3.90726e11i | − | 1.61808i | −0.587753 | − | 0.809041i | \(-0.699987\pi\) | ||
0.587753 | − | 0.809041i | \(-0.300013\pi\) | |||||||
\(702\) | 3.85518e9 | − | 1.75911e10i | 0.0158744 | − | 0.0724345i | ||||
\(703\) | 3.96630e10i | 0.162392i | ||||||||
\(704\) | − | 1.16519e11i | − | 0.474358i | ||||||
\(705\) | −8.37845e10 | − | 5.32416e10i | −0.339162 | − | 0.215523i | ||||
\(706\) | −6.12115e10 | −0.246385 | ||||||||
\(707\) | 1.87888e11 | 0.752007 | ||||||||
\(708\) | 9.11500e10 | − | 4.42200e10i | 0.362764 | − | 0.175989i | ||||
\(709\) | −3.36760e10 | −0.133271 | −0.0666354 | − | 0.997777i | \(-0.521226\pi\) | ||||
−0.0666354 | + | 0.997777i | \(0.521226\pi\) | |||||||
\(710\) | 5.92020e10 | + | 9.59081e10i | 0.232972 | + | 0.377417i | ||||
\(711\) | −1.18716e11 | + | 1.50640e11i | −0.464548 | + | 0.589471i | ||||
\(712\) | − | 1.33298e11i | − | 0.518684i | ||||||
\(713\) | −1.17437e11 | −0.454410 | ||||||||
\(714\) | 4.78566e10 | − | 2.32169e10i | 0.184140 | − | 0.0893327i | ||||
\(715\) | 6.81265e10 | − | 4.20530e10i | 0.260670 | − | 0.160906i | ||||
\(716\) | 3.95382e10i | 0.150441i | ||||||||
\(717\) | −1.81758e11 | + | 8.81772e10i | −0.687730 | + | 0.333641i | ||||
\(718\) | 1.00918e11i | 0.379726i | ||||||||
\(719\) | 3.34576e11i | 1.25193i | 0.779852 | + | 0.625964i | \(0.215294\pi\) | ||||
−0.779852 | + | 0.625964i | \(0.784706\pi\) | |||||||
\(720\) | 1.96188e10 | − | 1.70743e11i | 0.0730034 | − | 0.635351i | ||||
\(721\) | −2.24214e11 | −0.829703 | ||||||||
\(722\) | −9.43814e10 | −0.347326 | ||||||||
\(723\) | −3.78067e10 | − | 7.79305e10i | −0.138362 | − | 0.285203i | ||||
\(724\) | 2.32351e11 | 0.845649 | ||||||||
\(725\) | 3.93731e11 | + | 1.97404e11i | 1.42511 | + | 0.714503i | ||||
\(726\) | −4.89509e10 | − | 1.00902e11i | −0.176203 | − | 0.363206i | ||||
\(727\) | 7.75537e10i | 0.277629i | 0.990318 | + | 0.138815i | \(0.0443292\pi\) | ||||
−0.990318 | + | 0.138815i | \(0.955671\pi\) | |||||||
\(728\) | −2.72328e10 | −0.0969541 | ||||||||
\(729\) | 2.56543e11 | + | 1.18118e11i | 0.908345 | + | 0.418223i | ||||
\(730\) | −4.40459e9 | − | 7.13551e9i | −0.0155101 | − | 0.0251266i | ||||
\(731\) | 4.69363e11i | 1.64376i | ||||||||
\(732\) | −2.47003e9 | − | 5.09144e9i | −0.00860316 | − | 0.0177336i | ||||
\(733\) | − | 1.83371e10i | − | 0.0635205i | −0.999496 | − | 0.0317603i | \(-0.989889\pi\) | ||
0.999496 | − | 0.0317603i | \(-0.0101113\pi\) | |||||||
\(734\) | − | 4.10808e10i | − | 0.141532i | ||||||
\(735\) | −1.26493e11 | − | 8.03812e10i | −0.433429 | − | 0.275426i | ||||
\(736\) | 8.56990e10 | 0.292055 | ||||||||
\(737\) | 1.82803e10 | 0.0619601 | ||||||||
\(738\) | 8.46922e8 | + | 6.67439e8i | 0.00285508 | + | 0.00225002i | ||||
\(739\) | −4.44324e11 | −1.48978 | −0.744890 | − | 0.667187i | \(-0.767498\pi\) | ||||
−0.744890 | + | 0.667187i | \(0.767498\pi\) | |||||||
\(740\) | −1.61564e11 | − | 2.61736e11i | −0.538787 | − | 0.872844i | ||||
\(741\) | 7.86504e9 | − | 3.81560e9i | 0.0260872 | − | 0.0126558i | ||||
\(742\) | 1.16741e11i | 0.385130i | ||||||||
\(743\) | 5.92783e10 | 0.194509 | 0.0972547 | − | 0.995260i | \(-0.468994\pi\) | ||||
0.0972547 | + | 0.995260i | \(0.468994\pi\) | |||||||
\(744\) | 1.22978e11 | + | 2.53493e11i | 0.401362 | + | 0.827323i | ||||
\(745\) | −7.21340e10 | − | 1.16858e11i | −0.234161 | − | 0.379345i | ||||
\(746\) | − | 7.96584e10i | − | 0.257203i | ||||||
\(747\) | −2.73340e11 | + | 3.46844e11i | −0.877850 | + | 1.11391i | ||||
\(748\) | − | 3.31893e11i | − | 1.06021i | ||||||
\(749\) | − | 6.14843e10i | − | 0.195361i | ||||||
\(750\) | −9.61032e10 | + | 5.76031e10i | −0.303733 | + | 0.182054i | ||||
\(751\) | −1.35059e11 | −0.424585 | −0.212292 | − | 0.977206i | \(-0.568093\pi\) | ||||
−0.212292 | + | 0.977206i | \(0.568093\pi\) | |||||||
\(752\) | 8.21853e10 | 0.256994 | ||||||||
\(753\) | −1.88598e11 | + | 9.14950e10i | −0.586619 | + | 0.284589i | ||||
\(754\) | −3.82083e10 | −0.118215 | ||||||||
\(755\) | −1.86473e11 | + | 1.15105e11i | −0.573888 | + | 0.354249i | ||||
\(756\) | 4.26567e10 | − | 1.94642e11i | 0.130587 | − | 0.595866i | ||||
\(757\) | − | 3.52798e11i | − | 1.07434i | −0.843473 | − | 0.537171i | \(-0.819493\pi\) | ||
0.843473 | − | 0.537171i | \(-0.180507\pi\) | |||||||
\(758\) | 5.33245e10 | 0.161529 | ||||||||
\(759\) | −1.43288e11 | + | 6.95138e10i | −0.431760 | + | 0.209461i | ||||
\(760\) | −2.60942e10 | + | 1.61074e10i | −0.0782148 | + | 0.0482803i | ||||
\(761\) | 4.67185e11i | 1.39300i | 0.717558 | + | 0.696499i | \(0.245260\pi\) | ||||
−0.717558 | + | 0.696499i | \(0.754740\pi\) | |||||||
\(762\) | −5.68984e10 | + | 2.76033e10i | −0.168764 | + | 0.0818732i | ||||
\(763\) | − | 2.81347e11i | − | 0.830126i | ||||||
\(764\) | 9.88853e10i | 0.290241i | ||||||||
\(765\) | 3.23968e10 | − | 2.81950e11i | 0.0945924 | − | 0.823241i | ||||
\(766\) | 1.26074e11 | 0.366193 | ||||||||
\(767\) | −3.34101e10 | −0.0965375 | ||||||||
\(768\) | −4.80819e9 | − | 9.91106e9i | −0.0138209 | − | 0.0284889i | ||||
\(769\) | −1.44792e11 | −0.414038 | −0.207019 | − | 0.978337i | \(-0.566376\pi\) | ||||
−0.207019 | + | 0.978337i | \(0.566376\pi\) | |||||||
\(770\) | −1.08078e11 | + | 6.67142e10i | −0.307450 | + | 0.189782i | ||||
\(771\) | 1.41418e11 | + | 2.91503e11i | 0.400210 | + | 0.824947i | ||||
\(772\) | 4.04070e11i | 1.13759i | ||||||||
\(773\) | 1.13132e11 | 0.316860 | 0.158430 | − | 0.987370i | \(-0.449357\pi\) | ||||
0.158430 | + | 0.987370i | \(0.449357\pi\) | |||||||
\(774\) | −1.98003e11 | − | 1.56042e11i | −0.551707 | − | 0.434788i | ||||
\(775\) | −2.23969e11 | + | 4.46715e11i | −0.620841 | + | 1.23829i | ||||
\(776\) | − | 1.95335e11i | − | 0.538683i | ||||||
\(777\) | −1.30138e11 | − | 2.68251e11i | −0.357041 | − | 0.735964i | ||||
\(778\) | 9.49132e10i | 0.259065i | ||||||||
\(779\) | 5.23432e8i | 0.00142138i | ||||||||
\(780\) | −3.63588e10 | + | 5.72166e10i | −0.0982271 | + | 0.154577i | ||||
\(781\) | 6.81694e11 | 1.83225 | ||||||||
\(782\) | 3.59980e10 | 0.0962612 | ||||||||
\(783\) | 1.28278e11 | − | 5.85330e11i | 0.341275 | − | 1.55723i | ||||
\(784\) | 1.24079e11 | 0.328423 | ||||||||
\(785\) | −2.32680e10 | − | 3.76945e10i | −0.0612746 | − | 0.0992657i | ||||
\(786\) | −2.93814e10 | + | 1.42539e10i | −0.0769808 | + | 0.0373460i | ||||
\(787\) | 4.10788e10i | 0.107083i | 0.998566 | + | 0.0535413i | \(0.0170509\pi\) | ||||
−0.998566 | + | 0.0535413i | \(0.982949\pi\) | |||||||
\(788\) | 4.12999e11 | 1.07113 | ||||||||
\(789\) | −9.25494e10 | − | 1.90771e11i | −0.238817 | − | 0.492271i | ||||
\(790\) | −8.80874e10 | + | 5.43744e10i | −0.226155 | + | 0.139600i | ||||
\(791\) | − | 1.63839e11i | − | 0.418515i | ||||||
\(792\) | 3.00097e11 | + | 2.36499e11i | 0.762712 | + | 0.601075i | ||||
\(793\) | 1.86622e9i | 0.00471921i | ||||||||
\(794\) | − | 2.20077e10i | − | 0.0553723i | ||||||
\(795\) | 5.25717e11 | + | 3.34072e11i | 1.31608 | + | 0.836318i | ||||
\(796\) | −4.04383e11 | −1.00726 | ||||||||
\(797\) | 1.01477e11 | 0.251498 | 0.125749 | − | 0.992062i | \(-0.459867\pi\) | ||||
0.125749 | + | 0.992062i | \(0.459867\pi\) | |||||||
\(798\) | −1.24774e10 | + | 6.05319e9i | −0.0307688 | + | 0.0149270i | ||||
\(799\) | 1.35713e11 | 0.332994 | ||||||||
\(800\) | 1.63440e11 | − | 3.25987e11i | 0.399022 | − | 0.795867i | ||||
\(801\) | −2.52626e11 | − | 1.99089e11i | −0.613689 | − | 0.483634i | ||||
\(802\) | 1.86378e11i | 0.450503i | ||||||||
\(803\) | −5.07177e10 | −0.121982 | ||||||||
\(804\) | −1.39266e10 | + | 6.75626e9i | −0.0333288 | + | 0.0161690i | ||||
\(805\) | 5.04683e10 | + | 8.17594e10i | 0.120181 | + | 0.194695i | ||||
\(806\) | − | 4.33500e10i | − | 0.102719i | ||||||
\(807\) | 4.53008e11 | − | 2.19769e11i | 1.06810 | − | 0.518171i | ||||
\(808\) | − | 3.05068e11i | − | 0.715733i | ||||||
\(809\) | − | 2.81290e11i | − | 0.656689i | −0.944558 | − | 0.328344i | \(-0.893509\pi\) | ||
0.944558 | − | 0.328344i | \(-0.106491\pi\) | |||||||
\(810\) | 1.08172e11 | + | 1.07402e11i | 0.251290 | + | 0.249502i | ||||
\(811\) | 3.06605e11 | 0.708754 | 0.354377 | − | 0.935103i | \(-0.384693\pi\) | ||||
0.354377 | + | 0.935103i | \(0.384693\pi\) | |||||||
\(812\) | −4.22766e11 | −0.972468 | ||||||||
\(813\) | 1.87742e11 | + | 3.86991e11i | 0.429735 | + | 0.885806i | ||||
\(814\) | 2.66733e11 | 0.607546 | ||||||||
\(815\) | −2.39959e11 | − | 3.88738e11i | −0.543885 | − | 0.881102i | ||||
\(816\) | 1.02556e11 | + | 2.11398e11i | 0.231314 | + | 0.476805i | ||||
\(817\) | − | 1.22374e11i | − | 0.274663i | ||||||
\(818\) | −6.14716e9 | −0.0137297 | ||||||||
\(819\) | −4.06739e10 | + | 5.16116e10i | −0.0904024 | + | 0.114713i | ||||
\(820\) | −2.13215e9 | − | 3.45412e9i | −0.00471588 | − | 0.00763980i | ||||
\(821\) | − | 5.33533e11i | − | 1.17433i | −0.809469 | − | 0.587163i | \(-0.800245\pi\) | ||
0.809469 | − | 0.587163i | \(-0.199755\pi\) | |||||||
\(822\) | −1.01108e11 | − | 2.08412e11i | −0.221461 | − | 0.456494i | ||||
\(823\) | − | 5.45096e11i | − | 1.18816i | −0.804407 | − | 0.594078i | \(-0.797517\pi\) | ||
0.804407 | − | 0.594078i | \(-0.202483\pi\) | |||||||
\(824\) | 3.64050e11i | 0.789681i | ||||||||
\(825\) | −8.84859e9 | + | 6.77619e11i | −0.0191011 | + | 1.46275i | ||||
\(826\) | 5.30028e10 | 0.113862 | ||||||||
\(827\) | −7.10494e11 | −1.51893 | −0.759466 | − | 0.650547i | \(-0.774540\pi\) | ||||
−0.759466 | + | 0.650547i | \(0.774540\pi\) | |||||||
\(828\) | 8.34702e10 | − | 1.05916e11i | 0.177587 | − | 0.225342i | ||||
\(829\) | 3.64341e11 | 0.771419 | 0.385710 | − | 0.922620i | \(-0.373957\pi\) | ||||
0.385710 | + | 0.922620i | \(0.373957\pi\) | |||||||
\(830\) | −2.02818e11 | + | 1.25195e11i | −0.427361 | + | 0.263801i | ||||
\(831\) | −1.63913e11 | + | 7.95198e10i | −0.343724 | + | 0.166752i | ||||
\(832\) | − | 3.25372e10i | − | 0.0679026i | ||||||
\(833\) | 2.04893e11 | 0.425546 | ||||||||
\(834\) | 4.18886e10 | + | 8.63444e10i | 0.0865828 | + | 0.178472i | ||||
\(835\) | −5.46331e11 | + | 3.37238e11i | −1.12385 | + | 0.693730i | ||||
\(836\) | 8.65325e10i | 0.177155i | ||||||||
\(837\) | 6.64098e11 | + | 1.45540e11i | 1.35310 | + | 0.296538i | ||||
\(838\) | − | 1.92187e11i | − | 0.389715i | ||||||
\(839\) | − | 3.80877e11i | − | 0.768665i | −0.923195 | − | 0.384333i | \(-0.874432\pi\) | ||
0.923195 | − | 0.384333i | \(-0.125568\pi\) | |||||||
\(840\) | 1.23632e11 | − | 1.94555e11i | 0.248320 | − | 0.390774i | ||||
\(841\) | −7.71101e11 | −1.54144 | ||||||||
\(842\) | 1.63490e11 | 0.325270 | ||||||||
\(843\) | 5.60192e11 | − | 2.71768e11i | 1.10924 | − | 0.538132i | ||||
\(844\) | −6.58899e10 | −0.129852 | ||||||||
\(845\) | −4.14811e11 | + | 2.56054e11i | −0.813624 | + | 0.502233i | ||||
\(846\) | −4.51186e10 | + | 5.72515e10i | −0.0880793 | + | 0.111765i | ||||
\(847\) | 4.09225e11i | 0.795112i | ||||||||
\(848\) | −5.15683e11 | −0.997240 | ||||||||
\(849\) | −5.25076e11 | + | 2.54732e11i | −1.01063 | + | 0.490290i | ||||
\(850\) | 6.86530e10 | − | 1.36931e11i | 0.131518 | − | 0.262317i | ||||
\(851\) | − | 2.01780e11i | − | 0.384733i | ||||||
\(852\) | −5.19340e11 | + | 2.51950e11i | −0.985584 | + | 0.478140i | ||||
\(853\) | 8.33398e11i | 1.57419i | 0.616834 | + | 0.787093i | \(0.288415\pi\) | ||||
−0.616834 | + | 0.787093i | \(0.711585\pi\) | |||||||
\(854\) | − | 2.96062e9i | − | 0.00556611i | ||||||
\(855\) | −8.44661e9 | + | 7.35111e10i | −0.0158059 | + | 0.137559i | ||||
\(856\) | −9.98301e10 | −0.185937 | ||||||||
\(857\) | 2.81549e11 | 0.521952 | 0.260976 | − | 0.965345i | \(-0.415956\pi\) | ||||
0.260976 | + | 0.965345i | \(0.415956\pi\) | |||||||
\(858\) | −2.56598e10 | − | 5.28922e10i | −0.0473483 | − | 0.0975984i | ||||
\(859\) | 6.11769e11 | 1.12361 | 0.561804 | − | 0.827271i | \(-0.310108\pi\) | ||||
0.561804 | + | 0.827271i | \(0.310108\pi\) | |||||||
\(860\) | 4.98480e11 | + | 8.07544e11i | 0.911284 | + | 1.47629i | ||||
\(861\) | −1.71742e9 | − | 3.54010e9i | −0.00312510 | − | 0.00644173i | ||||
\(862\) | − | 4.53154e9i | − | 0.00820761i | ||||||
\(863\) | −4.91320e11 | −0.885771 | −0.442886 | − | 0.896578i | \(-0.646045\pi\) | ||||
−0.442886 | + | 0.896578i | \(0.646045\pi\) | |||||||
\(864\) | −4.84620e11 | − | 1.06207e11i | −0.869654 | − | 0.190589i | ||||
\(865\) | 5.69810e10 | − | 3.51731e10i | 0.101781 | − | 0.0628270i | ||||
\(866\) | 1.14688e11i | 0.203914i | ||||||||
\(867\) | −7.72752e10 | − | 1.59286e11i | −0.136761 | − | 0.281904i | ||||
\(868\) | − | 4.79657e11i | − | 0.844991i | ||||||
\(869\) | 6.26106e11i | 1.09792i | ||||||||
\(870\) | 1.73458e11 | − | 2.72966e11i | 0.302774 | − | 0.476465i | ||||
\(871\) | 5.10464e9 | 0.00886937 | ||||||||
\(872\) | −4.56814e11 | −0.790084 | ||||||||
\(873\) | −3.70200e11 | − | 2.91746e11i | −0.637352 | − | 0.502282i | ||||
\(874\) | −9.38553e9 | −0.0160847 | ||||||||
\(875\) | 4.07251e11 | − | 3.60481e10i | 0.694753 | − | 0.0614964i | ||||
\(876\) | 3.86386e10 | − | 1.87449e10i | 0.0656153 | − | 0.0318322i | ||||
\(877\) | − | 2.91940e11i | − | 0.493509i | −0.969078 | − | 0.246755i | \(-0.920636\pi\) | ||
0.969078 | − | 0.246755i | \(-0.0793641\pi\) | |||||||
\(878\) | 2.35790e11 | 0.396778 | ||||||||
\(879\) | 1.40952e11 | + | 2.90543e11i | 0.236111 | + | 0.486693i | ||||
\(880\) | −2.94699e11 | − | 4.77416e11i | −0.491414 | − | 0.796098i | ||||
\(881\) | 3.04364e11i | 0.505230i | 0.967567 | + | 0.252615i | \(0.0812906\pi\) | ||||
−0.967567 | + | 0.252615i | \(0.918709\pi\) | |||||||
\(882\) | −6.81176e10 | + | 8.64353e10i | −0.112560 | + | 0.142829i | ||||
\(883\) | − | 4.35514e11i | − | 0.716407i | −0.933644 | − | 0.358203i | \(-0.883389\pi\) | ||
0.933644 | − | 0.358203i | \(-0.116611\pi\) | |||||||
\(884\) | − | 9.26791e10i | − | 0.151765i | ||||||
\(885\) | 1.51676e11 | − | 2.38687e11i | 0.247254 | − | 0.389095i | ||||
\(886\) | 5.68453e10 | 0.0922486 | ||||||||
\(887\) | 1.80753e11 | 0.292006 | 0.146003 | − | 0.989284i | \(-0.453359\pi\) | ||||
0.146003 | + | 0.989284i | \(0.453359\pi\) | |||||||
\(888\) | −4.35550e11 | + | 2.11300e11i | −0.700464 | + | 0.339819i | ||||
\(889\) | 2.30761e11 | 0.369450 | ||||||||
\(890\) | −9.11869e10 | − | 1.47724e11i | −0.145336 | − | 0.235446i | ||||
\(891\) | 8.96428e11 | − | 2.15518e11i | 1.42234 | − | 0.341957i | ||||
\(892\) | 7.94681e11i | 1.25526i | ||||||||
\(893\) | −3.53837e10 | −0.0556414 | ||||||||
\(894\) | −9.07267e10 | + | 4.40146e10i | −0.142032 | + | 0.0689044i | ||||
\(895\) | 5.79730e10 | + | 9.39171e10i | 0.0903511 | + | 0.146370i | ||||
\(896\) | 4.51830e11i | 0.701040i | ||||||||
\(897\) | −4.00122e10 | + | 1.94113e10i | −0.0618049 | + | 0.0299836i | ||||
\(898\) | 1.46865e11i | 0.225846i | ||||||||
\(899\) | − | 1.44243e12i | − | 2.20829i | ||||||
\(900\) | −2.43702e11 | − | 5.19506e11i | −0.371440 | − | 0.791809i | ||||
\(901\) | −8.51553e11 | −1.29215 | ||||||||
\(902\) | 3.52007e9 | 0.00531771 | ||||||||
\(903\) | 4.01519e11 | + | 8.27645e11i | 0.603885 | + | 1.24478i | ||||
\(904\) | −2.66020e11 | −0.398327 | ||||||||
\(905\) | 5.51915e11 | − | 3.40685e11i | 0.822769 | − | 0.507877i | ||||
\(906\) | 7.02348e10 | + | 1.44774e11i | 0.104241 | + | 0.214871i | ||||
\(907\) | − | 1.24264e12i | − | 1.83618i | −0.396374 | − | 0.918089i | \(-0.629732\pi\) | ||
0.396374 | − | 0.918089i | \(-0.370268\pi\) | |||||||
\(908\) | 6.88210e11 | 1.01246 | ||||||||
\(909\) | −5.78166e11 | − | 4.55639e11i | −0.846832 | − | 0.667368i | ||||
\(910\) | −3.01801e10 | + | 1.86295e10i | −0.0440104 | + | 0.0271666i | ||||
\(911\) | − | 3.34146e10i | − | 0.0485135i | −0.999706 | − | 0.0242568i | \(-0.992278\pi\) | ||
0.999706 | − | 0.0242568i | \(-0.00772193\pi\) | |||||||
\(912\) | −2.67389e10 | − | 5.51166e10i | −0.0386513 | − | 0.0796715i | ||||
\(913\) | 1.44159e12i | 2.07472i | ||||||||
\(914\) | − | 3.30465e11i | − | 0.473523i | ||||||
\(915\) | −1.33325e10 | − | 8.47227e9i | −0.0190208 | − | 0.0120869i | ||||
\(916\) | 5.79261e11 | 0.822797 | ||||||||
\(917\) | 1.19161e11 | 0.168523 | ||||||||
\(918\) | −2.03565e11 | − | 4.46123e10i | −0.286638 | − | 0.0628180i | ||||
\(919\) | 1.22601e12 | 1.71882 | 0.859412 | − | 0.511283i | \(-0.170830\pi\) | ||||
0.859412 | + | 0.511283i | \(0.170830\pi\) | |||||||
\(920\) | 1.32750e11 | − | 8.19437e10i | 0.185303 | − | 0.114384i | ||||
\(921\) | 6.77120e11 | − | 3.28494e11i | 0.941081 | − | 0.456550i | ||||
\(922\) | − | 1.54774e11i | − | 0.214178i | ||||||
\(923\) | 1.90359e11 | 0.262281 | ||||||||
\(924\) | −2.83920e11 | − | 5.85240e11i | −0.389500 | − | 0.802872i | ||||
\(925\) | −7.67541e11 | − | 3.84821e11i | −1.04842 | − | 0.525644i | ||||
\(926\) | 3.12093e11i | 0.424463i | ||||||||
\(927\) | 6.89948e11 | + | 5.43732e11i | 0.934324 | + | 0.736319i | ||||
\(928\) | 1.05260e12i | 1.41930i | ||||||||
\(929\) | 1.46087e12i | 1.96133i | 0.195701 | + | 0.980664i | \(0.437302\pi\) | ||||
−0.195701 | + | 0.980664i | \(0.562698\pi\) | |||||||
\(930\) | 3.09699e11 | + | 1.96801e11i | 0.414007 | + | 0.263084i | ||||
\(931\) | −5.34204e10 | −0.0711064 | ||||||||
\(932\) | 9.99686e11 | 1.32495 | ||||||||
\(933\) | −8.16568e11 | + | 3.96145e11i | −1.07762 | + | 0.522790i | ||||
\(934\) | 2.30303e11 | 0.302631 | ||||||||
\(935\) | −4.86639e11 | − | 7.88363e11i | −0.636738 | − | 1.03152i | ||||
\(936\) | 8.38001e10 | + | 6.60409e10i | 0.109179 | + | 0.0860418i | ||||
\(937\) | − | 1.02495e12i | − | 1.32968i | −0.746987 | − | 0.664838i | \(-0.768500\pi\) | ||
0.746987 | − | 0.664838i | \(-0.231500\pi\) | |||||||
\(938\) | −8.09817e9 | −0.0104611 | ||||||||
\(939\) | −6.88793e11 | + | 3.34157e11i | −0.885985 | + | 0.429821i | ||||
\(940\) | 2.33497e11 | − | 1.44133e11i | 0.299068 | − | 0.184608i | ||||
\(941\) | − | 1.83735e11i | − | 0.234333i | −0.993112 | − | 0.117166i | \(-0.962619\pi\) | ||
0.993112 | − | 0.117166i | \(-0.0373811\pi\) | |||||||
\(942\) | −2.92654e10 | + | 1.41976e10i | −0.0371664 | + | 0.0180307i | ||||
\(943\) | − | 2.66288e9i | − | 0.00336748i | ||||||
\(944\) | 2.34131e11i | 0.294829i | ||||||||
\(945\) | −1.84069e11 | − | 5.24888e11i | −0.230810 | − | 0.658172i | ||||
\(946\) | −8.22962e11 | −1.02758 | ||||||||
\(947\) | 2.26053e11 | 0.281067 | 0.140533 | − | 0.990076i | \(-0.455118\pi\) | ||||
0.140533 | + | 0.990076i | \(0.455118\pi\) | |||||||
\(948\) | −2.31405e11 | − | 4.76991e11i | −0.286509 | − | 0.590578i | ||||
\(949\) | −1.41626e10 | −0.0174613 | ||||||||
\(950\) | −1.78995e10 | + | 3.57012e10i | −0.0219759 | + | 0.0438318i | ||||
\(951\) | −2.99946e10 | − | 6.18276e10i | −0.0366709 | − | 0.0755893i | ||||
\(952\) | 3.15139e11i | 0.383667i | ||||||||
\(953\) | −1.49255e12 | −1.80949 | −0.904745 | − | 0.425953i | \(-0.859939\pi\) | ||||
−0.904745 | + | 0.425953i | \(0.859939\pi\) | |||||||
\(954\) | 2.83103e11 | − | 3.59233e11i | 0.341783 | − | 0.433693i | ||||
\(955\) | 1.44991e11 | + | 2.34887e11i | 0.174312 | + | 0.282388i | ||||
\(956\) | − | 5.58414e11i | − | 0.668535i | ||||||
\(957\) | −8.53808e11 | − | 1.75994e12i | −1.01792 | − | 2.09822i | ||||
\(958\) | − | 6.15012e10i | − | 0.0730166i | ||||||
\(959\) | 8.45250e11i | 0.999334i | ||||||||
\(960\) | 2.32450e11 | + | 1.47713e11i | 0.273682 | + | 0.173913i | ||||
\(961\) | 7.83650e11 | 0.918816 | ||||||||
\(962\) | 7.44835e10 | 0.0869681 | ||||||||
\(963\) | −1.49103e11 | + | 1.89198e11i | −0.173373 | + | 0.219995i | ||||
\(964\) | 2.39425e11 | 0.277243 | ||||||||
\(965\) | 5.92468e11 | + | 9.59807e11i | 0.683212 | + | 1.10681i | ||||
\(966\) | 6.34766e10 | − | 3.07947e10i | 0.0728963 | − | 0.0353645i | ||||
\(967\) | 7.94256e11i | 0.908352i | 0.890912 | + | 0.454176i | \(0.150066\pi\) | ||||
−0.890912 | + | 0.454176i | \(0.849934\pi\) | |||||||
\(968\) | 6.64445e11 | 0.756759 | ||||||||
\(969\) | −4.41543e10 | − | 9.10146e10i | −0.0500815 | − | 0.103232i | ||||
\(970\) | −1.33626e11 | − | 2.16476e11i | −0.150940 | − | 0.244524i | ||||
\(971\) | 7.55855e10i | 0.0850279i | 0.999096 | + | 0.0425139i | \(0.0135367\pi\) | ||||
−0.999096 | + | 0.0425139i | \(0.986463\pi\) | |||||||
\(972\) | −6.03279e11 | + | 4.95503e11i | −0.675854 | + | 0.555113i | ||||
\(973\) | − | 3.50185e11i | − | 0.390702i | ||||||
\(974\) | − | 1.00847e11i | − | 0.112054i | ||||||
\(975\) | −2.47091e9 | + | 1.89221e11i | −0.00273425 | + | 0.209387i | ||||
\(976\) | 1.30780e10 | 0.0144126 | ||||||||
\(977\) | 1.31247e11 | 0.144049 | 0.0720244 | − | 0.997403i | \(-0.477054\pi\) | ||||
0.0720244 | + | 0.997403i | \(0.477054\pi\) | |||||||
\(978\) | −3.01809e11 | + | 1.46418e11i | −0.329896 | + | 0.160044i | ||||
\(979\) | −1.04999e12 | −1.14302 | ||||||||
\(980\) | 3.52521e11 | − | 2.17603e11i | 0.382191 | − | 0.235918i | ||||
\(981\) | −6.82281e11 | + | 8.65755e11i | −0.736694 | + | 0.934801i | ||||
\(982\) | − | 4.49650e11i | − | 0.483536i | ||||||
\(983\) | 2.55150e11 | 0.273264 | 0.136632 | − | 0.990622i | \(-0.456372\pi\) | ||||
0.136632 | + | 0.990622i | \(0.456372\pi\) | |||||||
\(984\) | −5.74794e9 | + | 2.78852e9i | −0.00613100 | + | 0.00297436i | ||||
\(985\) | 9.81017e11 | − | 6.05560e11i | 1.04215 | − | 0.643298i | ||||
\(986\) | 4.42148e11i | 0.467800i | ||||||||
\(987\) | 2.39309e11 | − | 1.16097e11i | 0.252168 | − | 0.122335i | ||||
\(988\) | 2.41636e10i | 0.0253591i | ||||||||
\(989\) | 6.22559e11i | 0.650722i | ||||||||
\(990\) | 4.94361e11 | + | 5.68033e10i | 0.514640 | + | 0.0591334i | ||||
\(991\) | −1.00441e12 | −1.04139 | −0.520697 | − | 0.853742i | \(-0.674328\pi\) | ||||
−0.520697 | + | 0.853742i | \(0.674328\pi\) | |||||||
\(992\) | −1.19425e12 | −1.23325 | ||||||||
\(993\) | 1.66713e11 | + | 3.43642e11i | 0.171463 | + | 0.353435i | ||||
\(994\) | −3.01991e11 | −0.309349 | ||||||||
\(995\) | −9.60550e11 | + | 5.92927e11i | −0.980004 | + | 0.604935i | ||||
\(996\) | −5.32802e11 | − | 1.09826e12i | −0.541413 | − | 1.11601i | ||||
\(997\) | 1.22258e12i | 1.23737i | 0.785641 | + | 0.618683i | \(0.212333\pi\) | ||||
−0.785641 | + | 0.618683i | \(0.787667\pi\) | |||||||
\(998\) | 3.70566e11 | 0.373545 | ||||||||
\(999\) | −2.50066e11 | + | 1.14105e12i | −0.251068 | + | 1.14562i |
(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 | 15.9.d.c.14.8 | yes | 12 | |
3.2 | odd | 2 | inner | 15.9.d.c.14.6 | yes | 12 | |
4.3 | odd | 2 | 240.9.c.c.209.3 | 12 | |||
5.2 | odd | 4 | 75.9.c.h.26.8 | 12 | |||
5.3 | odd | 4 | 75.9.c.h.26.5 | 12 | |||
5.4 | even | 2 | inner | 15.9.d.c.14.5 | ✓ | 12 | |
12.11 | even | 2 | 240.9.c.c.209.9 | 12 | |||
15.2 | even | 4 | 75.9.c.h.26.6 | 12 | |||
15.8 | even | 4 | 75.9.c.h.26.7 | 12 | |||
15.14 | odd | 2 | inner | 15.9.d.c.14.7 | yes | 12 | |
20.19 | odd | 2 | 240.9.c.c.209.10 | 12 | |||
60.59 | even | 2 | 240.9.c.c.209.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.9.d.c.14.5 | ✓ | 12 | 5.4 | even | 2 | inner | |
15.9.d.c.14.6 | yes | 12 | 3.2 | odd | 2 | inner | |
15.9.d.c.14.7 | yes | 12 | 15.14 | odd | 2 | inner | |
15.9.d.c.14.8 | yes | 12 | 1.1 | even | 1 | trivial | |
75.9.c.h.26.5 | 12 | 5.3 | odd | 4 | |||
75.9.c.h.26.6 | 12 | 15.2 | even | 4 | |||
75.9.c.h.26.7 | 12 | 15.8 | even | 4 | |||
75.9.c.h.26.8 | 12 | 5.2 | odd | 4 | |||
240.9.c.c.209.3 | 12 | 4.3 | odd | 2 | |||
240.9.c.c.209.4 | 12 | 60.59 | even | 2 | |||
240.9.c.c.209.9 | 12 | 12.11 | even | 2 | |||
240.9.c.c.209.10 | 12 | 20.19 | odd | 2 |