Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,11,Mod(42,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.42");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.b (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: | \(27.3203618650\) |
Analytic rank: | \(0\) |
Dimension: | \(34\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 42.3 | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.11.b.b.42.32 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 57.1045i | − | 1.78451i | −0.451528 | − | 0.892257i | \(-0.649121\pi\) | ||
0.451528 | − | 0.892257i | \(-0.350879\pi\) | |||||||
\(3\) | 18.6474i | 0.0767382i | 0.999264 | + | 0.0383691i | \(0.0122163\pi\) | ||||
−0.999264 | + | 0.0383691i | \(0.987784\pi\) | |||||||
\(4\) | −2236.92 | −2.18449 | ||||||||
\(5\) | 2202.14i | 0.704683i | 0.935871 | + | 0.352342i | \(0.114615\pi\) | ||||
−0.935871 | + | 0.352342i | \(0.885385\pi\) | |||||||
\(6\) | 1064.85 | 0.136940 | ||||||||
\(7\) | 1818.95i | 0.108226i | 0.998535 | + | 0.0541128i | \(0.0172331\pi\) | ||||
−0.998535 | + | 0.0541128i | \(0.982767\pi\) | |||||||
\(8\) | 69263.1i | 2.11374i | ||||||||
\(9\) | 58701.3 | 0.994111 | ||||||||
\(10\) | 125752. | 1.25752 | ||||||||
\(11\) | 84875.6 | 0.527011 | 0.263505 | − | 0.964658i | \(-0.415121\pi\) | ||||
0.263505 | + | 0.964658i | \(0.415121\pi\) | |||||||
\(12\) | − | 41712.7i | − | 0.167634i | ||||||
\(13\) | −196611. | −0.529530 | −0.264765 | − | 0.964313i | \(-0.585294\pi\) | ||||
−0.264765 | + | 0.964313i | \(0.585294\pi\) | |||||||
\(14\) | 103870. | 0.193130 | ||||||||
\(15\) | −41064.1 | −0.0540761 | ||||||||
\(16\) | 1.66462e6 | 1.58751 | ||||||||
\(17\) | 562240. | 0.395983 | 0.197992 | − | 0.980204i | \(-0.436558\pi\) | ||||
0.197992 | + | 0.980204i | \(0.436558\pi\) | |||||||
\(18\) | − | 3.35210e6i | − | 1.77401i | ||||||
\(19\) | − | 2.47979e6i | − | 1.00149i | −0.865595 | − | 0.500745i | \(-0.833059\pi\) | ||
0.865595 | − | 0.500745i | \(-0.166941\pi\) | |||||||
\(20\) | − | 4.92600e6i | − | 1.53937i | ||||||
\(21\) | −33918.6 | −0.00830503 | ||||||||
\(22\) | − | 4.84678e6i | − | 0.940458i | ||||||
\(23\) | 4.25931e6 | 0.661759 | 0.330879 | − | 0.943673i | \(-0.392655\pi\) | ||||
0.330879 | + | 0.943673i | \(0.392655\pi\) | |||||||
\(24\) | −1.29157e6 | −0.162205 | ||||||||
\(25\) | 4.91622e6 | 0.503421 | ||||||||
\(26\) | 1.12273e7i | 0.944953i | ||||||||
\(27\) | 2.19573e6i | 0.153024i | ||||||||
\(28\) | − | 4.06884e6i | − | 0.236418i | ||||||
\(29\) | 7153.04i | 0.000348739i | 1.00000 | 0.000174370i | \(5.55036e-5\pi\) | |||||
−1.00000 | 0.000174370i | \(0.999944\pi\) | ||||||||
\(30\) | 2.34494e6i | 0.0964996i | ||||||||
\(31\) | 9.25813e6 | 0.323381 | 0.161691 | − | 0.986841i | \(-0.448305\pi\) | ||||
0.161691 | + | 0.986841i | \(0.448305\pi\) | |||||||
\(32\) | − | 2.41321e7i | − | 0.719192i | ||||||
\(33\) | 1.58271e6i | 0.0404419i | ||||||||
\(34\) | − | 3.21064e7i | − | 0.706638i | ||||||
\(35\) | −4.00557e6 | −0.0762648 | ||||||||
\(36\) | −1.31310e8 | −2.17163 | ||||||||
\(37\) | − | 2.64139e7i | − | 0.380911i | −0.981696 | − | 0.190455i | \(-0.939004\pi\) | ||
0.981696 | − | 0.190455i | \(-0.0609964\pi\) | |||||||
\(38\) | −1.41607e8 | −1.78717 | ||||||||
\(39\) | − | 3.66627e6i | − | 0.0406352i | ||||||
\(40\) | −1.52527e8 | −1.48952 | ||||||||
\(41\) | −1.16242e8 | −1.00333 | −0.501664 | − | 0.865063i | \(-0.667279\pi\) | ||||
−0.501664 | + | 0.865063i | \(0.667279\pi\) | |||||||
\(42\) | 1.93690e6i | 0.0148204i | ||||||||
\(43\) | 8.45157e7 | − | 1.20285e8i | 0.574904 | − | 0.818221i | ||||
\(44\) | −1.89860e8 | −1.15125 | ||||||||
\(45\) | 1.29268e8i | 0.700534i | ||||||||
\(46\) | − | 2.43225e8i | − | 1.18092i | ||||||
\(47\) | 3.14889e7 | 0.137299 | 0.0686496 | − | 0.997641i | \(-0.478131\pi\) | ||||
0.0686496 | + | 0.997641i | \(0.478131\pi\) | |||||||
\(48\) | 3.10409e7i | 0.121823i | ||||||||
\(49\) | 2.79167e8 | 0.988287 | ||||||||
\(50\) | − | 2.80738e8i | − | 0.898362i | ||||||
\(51\) | 1.04843e7i | 0.0303870i | ||||||||
\(52\) | 4.39802e8 | 1.15675 | ||||||||
\(53\) | 2.99781e8 | 0.716844 | 0.358422 | − | 0.933560i | \(-0.383315\pi\) | ||||
0.358422 | + | 0.933560i | \(0.383315\pi\) | |||||||
\(54\) | 1.25386e8 | 0.273074 | ||||||||
\(55\) | 1.86908e8i | 0.371376i | ||||||||
\(56\) | −1.25986e8 | −0.228761 | ||||||||
\(57\) | 4.62416e7 | 0.0768526 | ||||||||
\(58\) | 408471. | 0.000622330 | ||||||||
\(59\) | 6.98652e6 | 0.00977239 | 0.00488620 | − | 0.999988i | \(-0.498445\pi\) | ||||
0.00488620 | + | 0.999988i | \(0.498445\pi\) | |||||||
\(60\) | 9.18569e7 | 0.118129 | ||||||||
\(61\) | − | 1.07131e9i | − | 1.26843i | −0.773158 | − | 0.634214i | \(-0.781324\pi\) | ||
0.773158 | − | 0.634214i | \(-0.218676\pi\) | |||||||
\(62\) | − | 5.28681e8i | − | 0.577079i | ||||||
\(63\) | 1.06775e8i | 0.107588i | ||||||||
\(64\) | 3.26525e8 | 0.304100 | ||||||||
\(65\) | − | 4.32964e8i | − | 0.373151i | ||||||
\(66\) | 9.03797e7 | 0.0721691 | ||||||||
\(67\) | 1.30677e9 | 0.967888 | 0.483944 | − | 0.875099i | \(-0.339204\pi\) | ||||
0.483944 | + | 0.875099i | \(0.339204\pi\) | |||||||
\(68\) | −1.25768e9 | −0.865022 | ||||||||
\(69\) | 7.94249e7i | 0.0507822i | ||||||||
\(70\) | 2.28736e8i | 0.136096i | ||||||||
\(71\) | − | 1.39477e9i | − | 0.773055i | −0.922278 | − | 0.386528i | \(-0.873674\pi\) | ||
0.922278 | − | 0.386528i | \(-0.126326\pi\) | |||||||
\(72\) | 4.06583e9i | 2.10129i | ||||||||
\(73\) | 7.73274e8i | 0.373009i | 0.982454 | + | 0.186504i | \(0.0597158\pi\) | ||||
−0.982454 | + | 0.186504i | \(0.940284\pi\) | |||||||
\(74\) | −1.50835e9 | −0.679741 | ||||||||
\(75\) | 9.16747e7i | 0.0386316i | ||||||||
\(76\) | 5.54709e9i | 2.18775i | ||||||||
\(77\) | 1.54384e8i | 0.0570361i | ||||||||
\(78\) | −2.09361e8 | −0.0725140 | ||||||||
\(79\) | −2.98734e8 | −0.0970844 | −0.0485422 | − | 0.998821i | \(-0.515458\pi\) | ||||
−0.0485422 | + | 0.998821i | \(0.515458\pi\) | |||||||
\(80\) | 3.66573e9i | 1.11869i | ||||||||
\(81\) | 3.42531e9 | 0.982368 | ||||||||
\(82\) | 6.63792e9i | 1.79045i | ||||||||
\(83\) | 3.52379e9 | 0.894582 | 0.447291 | − | 0.894389i | \(-0.352389\pi\) | ||||
0.447291 | + | 0.894389i | \(0.352389\pi\) | |||||||
\(84\) | 7.58731e7 | 0.0181423 | ||||||||
\(85\) | 1.23813e9i | 0.279043i | ||||||||
\(86\) | −6.86883e9 | − | 4.82622e9i | −1.46013 | − | 1.02592i | ||||
\(87\) | −133385. | −2.67616e−5 | ||||||||
\(88\) | 5.87875e9i | 1.11396i | ||||||||
\(89\) | − | 8.07639e9i | − | 1.44633i | −0.690676 | − | 0.723164i | \(-0.742687\pi\) | ||
0.690676 | − | 0.723164i | \(-0.257313\pi\) | |||||||
\(90\) | 7.38179e9 | 1.25011 | ||||||||
\(91\) | − | 3.57625e8i | − | 0.0573087i | ||||||
\(92\) | −9.52772e9 | −1.44561 | ||||||||
\(93\) | 1.72640e8i | 0.0248157i | ||||||||
\(94\) | − | 1.79815e9i | − | 0.245012i | ||||||
\(95\) | 5.46083e9 | 0.705734 | ||||||||
\(96\) | 4.50000e8 | 0.0551895 | ||||||||
\(97\) | −7.54869e9 | −0.879049 | −0.439524 | − | 0.898231i | \(-0.644853\pi\) | ||||
−0.439524 | + | 0.898231i | \(0.644853\pi\) | |||||||
\(98\) | − | 1.59417e10i | − | 1.76361i | ||||||
\(99\) | 4.98231e9 | 0.523907 | ||||||||
\(100\) | −1.09972e10 | −1.09972 | ||||||||
\(101\) | 3.95675e9 | 0.376471 | 0.188236 | − | 0.982124i | \(-0.439723\pi\) | ||||
0.188236 | + | 0.982124i | \(0.439723\pi\) | |||||||
\(102\) | 5.98700e8 | 0.0542261 | ||||||||
\(103\) | 1.14870e10 | 0.990876 | 0.495438 | − | 0.868643i | \(-0.335008\pi\) | ||||
0.495438 | + | 0.868643i | \(0.335008\pi\) | |||||||
\(104\) | − | 1.36179e10i | − | 1.11929i | ||||||
\(105\) | − | 7.46934e7i | − | 0.00585242i | ||||||
\(106\) | − | 1.71188e10i | − | 1.27922i | ||||||
\(107\) | 7.45115e9 | 0.531257 | 0.265628 | − | 0.964076i | \(-0.414421\pi\) | ||||
0.265628 | + | 0.964076i | \(0.414421\pi\) | |||||||
\(108\) | − | 4.91168e9i | − | 0.334281i | ||||||
\(109\) | 1.68687e10 | 1.09635 | 0.548175 | − | 0.836363i | \(-0.315323\pi\) | ||||
0.548175 | + | 0.836363i | \(0.315323\pi\) | |||||||
\(110\) | 1.06733e10 | 0.662725 | ||||||||
\(111\) | 4.92549e8 | 0.0292304 | ||||||||
\(112\) | 3.02786e9i | 0.171809i | ||||||||
\(113\) | 1.10472e10i | 0.599596i | 0.954003 | + | 0.299798i | \(0.0969192\pi\) | ||||
−0.954003 | + | 0.299798i | \(0.903081\pi\) | |||||||
\(114\) | − | 2.64060e9i | − | 0.137144i | ||||||
\(115\) | 9.37957e9i | 0.466331i | ||||||||
\(116\) | − | 1.60008e7i | − | 0.000761818i | ||||||
\(117\) | −1.15413e10 | −0.526412 | ||||||||
\(118\) | − | 3.98961e8i | − | 0.0174390i | ||||||
\(119\) | 1.02268e9i | 0.0428555i | ||||||||
\(120\) | − | 2.84422e9i | − | 0.114303i | ||||||
\(121\) | −1.87336e10 | −0.722260 | ||||||||
\(122\) | −6.11765e10 | −2.26353 | ||||||||
\(123\) | − | 2.16760e9i | − | 0.0769935i | ||||||
\(124\) | −2.07097e10 | −0.706424 | ||||||||
\(125\) | 3.23314e10i | 1.05944i | ||||||||
\(126\) | 6.09730e9 | 0.191993 | ||||||||
\(127\) | −4.21274e10 | −1.27510 | −0.637552 | − | 0.770407i | \(-0.720053\pi\) | ||||
−0.637552 | + | 0.770407i | \(0.720053\pi\) | |||||||
\(128\) | − | 4.33573e10i | − | 1.26186i | ||||||
\(129\) | 2.24301e9 | + | 1.57600e9i | 0.0627888 | + | 0.0441170i | ||||
\(130\) | −2.47241e10 | −0.665893 | ||||||||
\(131\) | 2.65584e9i | 0.0688407i | 0.999407 | + | 0.0344203i | \(0.0109585\pi\) | ||||
−0.999407 | + | 0.0344203i | \(0.989042\pi\) | |||||||
\(132\) | − | 3.54039e9i | − | 0.0883449i | ||||||
\(133\) | 4.51061e9 | 0.108387 | ||||||||
\(134\) | − | 7.46224e10i | − | 1.72721i | ||||||
\(135\) | −4.83530e9 | −0.107834 | ||||||||
\(136\) | 3.89424e10i | 0.837006i | ||||||||
\(137\) | 1.39044e10i | 0.288104i | 0.989570 | + | 0.144052i | \(0.0460133\pi\) | ||||
−0.989570 | + | 0.144052i | \(0.953987\pi\) | |||||||
\(138\) | 4.53552e9 | 0.0906215 | ||||||||
\(139\) | 2.23725e10 | 0.431162 | 0.215581 | − | 0.976486i | \(-0.430835\pi\) | ||||
0.215581 | + | 0.976486i | \(0.430835\pi\) | |||||||
\(140\) | 8.96013e9 | 0.166600 | ||||||||
\(141\) | 5.87185e8i | 0.0105361i | ||||||||
\(142\) | −7.96475e10 | −1.37953 | ||||||||
\(143\) | −1.66875e10 | −0.279068 | ||||||||
\(144\) | 9.77156e10 | 1.57816 | ||||||||
\(145\) | −1.57520e7 | −0.000245751 | ||||||||
\(146\) | 4.41574e10 | 0.665639 | ||||||||
\(147\) | 5.20573e9i | 0.0758394i | ||||||||
\(148\) | 5.90856e10i | 0.832096i | ||||||||
\(149\) | 9.63861e10i | 1.31245i | 0.754565 | + | 0.656225i | \(0.227848\pi\) | ||||
−0.754565 | + | 0.656225i | \(0.772152\pi\) | |||||||
\(150\) | 5.23503e9 | 0.0689387 | ||||||||
\(151\) | 8.29933e10i | 1.05720i | 0.848870 | + | 0.528601i | \(0.177283\pi\) | ||||
−0.848870 | + | 0.528601i | \(0.822717\pi\) | |||||||
\(152\) | 1.71758e11 | 2.11689 | ||||||||
\(153\) | 3.30042e10 | 0.393651 | ||||||||
\(154\) | 8.81603e9 | 0.101782 | ||||||||
\(155\) | 2.03877e10i | 0.227882i | ||||||||
\(156\) | 8.20116e9i | 0.0887671i | ||||||||
\(157\) | 1.42899e11i | 1.49807i | 0.662532 | + | 0.749034i | \(0.269482\pi\) | ||||
−0.662532 | + | 0.749034i | \(0.730518\pi\) | |||||||
\(158\) | 1.70591e10i | 0.173249i | ||||||||
\(159\) | 5.59013e9i | 0.0550093i | ||||||||
\(160\) | 5.31421e10 | 0.506803 | ||||||||
\(161\) | 7.74746e9i | 0.0716192i | ||||||||
\(162\) | − | 1.95600e11i | − | 1.75305i | ||||||
\(163\) | − | 1.25418e11i | − | 1.08999i | −0.838440 | − | 0.544993i | \(-0.816532\pi\) | ||
0.838440 | − | 0.544993i | \(-0.183468\pi\) | |||||||
\(164\) | 2.60023e11 | 2.19176 | ||||||||
\(165\) | −3.48534e9 | −0.0284987 | ||||||||
\(166\) | − | 2.01224e11i | − | 1.59639i | ||||||
\(167\) | 5.76436e10 | 0.443781 | 0.221891 | − | 0.975072i | \(-0.428777\pi\) | ||||
0.221891 | + | 0.975072i | \(0.428777\pi\) | |||||||
\(168\) | − | 2.34931e9i | − | 0.0175547i | ||||||
\(169\) | −9.92027e10 | −0.719598 | ||||||||
\(170\) | 7.07026e10 | 0.497956 | ||||||||
\(171\) | − | 1.45567e11i | − | 0.995593i | ||||||
\(172\) | −1.89055e11 | + | 2.69069e11i | −1.25587 | + | 1.78740i | ||||
\(173\) | 1.26919e11 | 0.819021 | 0.409511 | − | 0.912305i | \(-0.365699\pi\) | ||||
0.409511 | + | 0.912305i | \(0.365699\pi\) | |||||||
\(174\) | 7.61690e6i | 4.77565e-5i | ||||||||
\(175\) | 8.94235e9i | 0.0544831i | ||||||||
\(176\) | 1.41286e11 | 0.836635 | ||||||||
\(177\) | 1.30280e8i | 0.000749915i | ||||||||
\(178\) | −4.61198e11 | −2.58099 | ||||||||
\(179\) | 2.41061e11i | 1.31179i | 0.754854 | + | 0.655893i | \(0.227708\pi\) | ||||
−0.754854 | + | 0.655893i | \(0.772292\pi\) | |||||||
\(180\) | − | 2.89162e11i | − | 1.53031i | ||||||
\(181\) | −2.48789e11 | −1.28067 | −0.640336 | − | 0.768095i | \(-0.721205\pi\) | ||||
−0.640336 | + | 0.768095i | \(0.721205\pi\) | |||||||
\(182\) | −2.04220e10 | −0.102268 | ||||||||
\(183\) | 1.99771e10 | 0.0973368 | ||||||||
\(184\) | 2.95013e11i | 1.39879i | ||||||||
\(185\) | 5.81669e10 | 0.268421 | ||||||||
\(186\) | 9.85851e9 | 0.0442840 | ||||||||
\(187\) | 4.77204e10 | 0.208688 | ||||||||
\(188\) | −7.04380e10 | −0.299929 | ||||||||
\(189\) | −3.99392e9 | −0.0165612 | ||||||||
\(190\) | − | 3.11838e11i | − | 1.25939i | ||||||
\(191\) | 1.27186e11i | 0.500347i | 0.968201 | + | 0.250174i | \(0.0804877\pi\) | ||||
−0.968201 | + | 0.250174i | \(0.919512\pi\) | |||||||
\(192\) | 6.08884e9i | 0.0233361i | ||||||||
\(193\) | −1.33168e11 | −0.497293 | −0.248647 | − | 0.968594i | \(-0.579986\pi\) | ||||
−0.248647 | + | 0.968594i | \(0.579986\pi\) | |||||||
\(194\) | 4.31064e11i | 1.56867i | ||||||||
\(195\) | 8.07363e9 | 0.0286349 | ||||||||
\(196\) | −6.24473e11 | −2.15890 | ||||||||
\(197\) | 3.13724e11 | 1.05734 | 0.528672 | − | 0.848826i | \(-0.322690\pi\) | ||||
0.528672 | + | 0.848826i | \(0.322690\pi\) | |||||||
\(198\) | − | 2.84512e11i | − | 0.934920i | ||||||
\(199\) | 4.99495e11i | 1.60054i | 0.599642 | + | 0.800268i | \(0.295310\pi\) | ||||
−0.599642 | + | 0.800268i | \(0.704690\pi\) | |||||||
\(200\) | 3.40513e11i | 1.06410i | ||||||||
\(201\) | 2.43678e10i | 0.0742739i | ||||||||
\(202\) | − | 2.25948e11i | − | 0.671818i | ||||||
\(203\) | −1.30110e7 | −3.77425e−5 | ||||||||
\(204\) | − | 2.34525e10i | − | 0.0663802i | ||||||
\(205\) | − | 2.55980e11i | − | 0.707028i | ||||||
\(206\) | − | 6.55957e11i | − | 1.76823i | ||||||
\(207\) | 2.50027e11 | 0.657862 | ||||||||
\(208\) | −3.27283e11 | −0.840634 | ||||||||
\(209\) | − | 2.10474e11i | − | 0.527796i | ||||||
\(210\) | −4.26532e9 | −0.0104437 | ||||||||
\(211\) | 4.50429e11i | 1.07700i | 0.842627 | + | 0.538498i | \(0.181008\pi\) | ||||
−0.842627 | + | 0.538498i | \(0.818992\pi\) | |||||||
\(212\) | −6.70586e11 | −1.56594 | ||||||||
\(213\) | 2.60088e10 | 0.0593228 | ||||||||
\(214\) | − | 4.25494e11i | − | 0.948035i | ||||||
\(215\) | 2.64885e11 | + | 1.86115e11i | 0.576587 | + | 0.405125i | ||||
\(216\) | −1.52083e11 | −0.323454 | ||||||||
\(217\) | 1.68401e10i | 0.0349981i | ||||||||
\(218\) | − | 9.63279e11i | − | 1.95645i | ||||||
\(219\) | −1.44195e10 | −0.0286240 | ||||||||
\(220\) | − | 4.18097e11i | − | 0.811267i | ||||||
\(221\) | −1.10542e11 | −0.209685 | ||||||||
\(222\) | − | 2.81267e10i | − | 0.0521620i | ||||||
\(223\) | − | 7.34909e11i | − | 1.33263i | −0.745671 | − | 0.666315i | \(-0.767871\pi\) | ||
0.745671 | − | 0.666315i | \(-0.232129\pi\) | |||||||
\(224\) | 4.38950e10 | 0.0778350 | ||||||||
\(225\) | 2.88589e11 | 0.500457 | ||||||||
\(226\) | 6.30842e11 | 1.06999 | ||||||||
\(227\) | − | 8.22389e11i | − | 1.36442i | −0.731156 | − | 0.682210i | \(-0.761019\pi\) | ||
0.731156 | − | 0.682210i | \(-0.238981\pi\) | |||||||
\(228\) | −1.03439e11 | −0.167884 | ||||||||
\(229\) | 8.77283e11 | 1.39304 | 0.696518 | − | 0.717539i | \(-0.254732\pi\) | ||||
0.696518 | + | 0.717539i | \(0.254732\pi\) | |||||||
\(230\) | 5.35615e11 | 0.832173 | ||||||||
\(231\) | −2.87886e9 | −0.00437684 | ||||||||
\(232\) | −4.95442e8 | −0.000737144 | ||||||||
\(233\) | − | 6.34864e11i | − | 0.924488i | −0.886753 | − | 0.462244i | \(-0.847044\pi\) | ||
0.886753 | − | 0.462244i | \(-0.152956\pi\) | |||||||
\(234\) | 6.59060e11i | 0.939389i | ||||||||
\(235\) | 6.93428e10i | 0.0967524i | ||||||||
\(236\) | −1.56283e10 | −0.0213477 | ||||||||
\(237\) | − | 5.57061e9i | − | 0.00745008i | ||||||
\(238\) | 5.83998e10 | 0.0764763 | ||||||||
\(239\) | −7.00573e9 | −0.00898388 | −0.00449194 | − | 0.999990i | \(-0.501430\pi\) | ||||
−0.00449194 | + | 0.999990i | \(0.501430\pi\) | |||||||
\(240\) | −6.83562e10 | −0.0858464 | ||||||||
\(241\) | − | 1.92126e11i | − | 0.236321i | −0.992995 | − | 0.118160i | \(-0.962300\pi\) | ||
0.992995 | − | 0.118160i | \(-0.0376997\pi\) | |||||||
\(242\) | 1.06977e12i | 1.28888i | ||||||||
\(243\) | 1.93529e11i | 0.228410i | ||||||||
\(244\) | 2.39643e12i | 2.77087i | ||||||||
\(245\) | 6.14763e11i | 0.696430i | ||||||||
\(246\) | −1.23780e11 | −0.137396 | ||||||||
\(247\) | 4.87553e11i | 0.530319i | ||||||||
\(248\) | 6.41247e11i | 0.683544i | ||||||||
\(249\) | 6.57095e10i | 0.0686486i | ||||||||
\(250\) | 1.84627e12 | 1.89058 | ||||||||
\(251\) | −7.65495e11 | −0.768375 | −0.384188 | − | 0.923255i | \(-0.625518\pi\) | ||||
−0.384188 | + | 0.923255i | \(0.625518\pi\) | |||||||
\(252\) | − | 2.38846e11i | − | 0.235026i | ||||||
\(253\) | 3.61511e11 | 0.348754 | ||||||||
\(254\) | 2.40566e12i | 2.27544i | ||||||||
\(255\) | −2.30878e10 | −0.0214132 | ||||||||
\(256\) | −2.14153e12 | −1.94771 | ||||||||
\(257\) | − | 2.15015e12i | − | 1.91780i | −0.283745 | − | 0.958900i | \(-0.591577\pi\) | ||
0.283745 | − | 0.958900i | \(-0.408423\pi\) | |||||||
\(258\) | 8.99964e10 | − | 1.28086e11i | 0.0787275 | − | 0.112048i | ||||
\(259\) | 4.80454e10 | 0.0412243 | ||||||||
\(260\) | 9.68504e11i | 0.815145i | ||||||||
\(261\) | 4.19893e8i | 0.000346686i | ||||||||
\(262\) | 1.51660e11 | 0.122847 | ||||||||
\(263\) | − | 9.92900e11i | − | 0.789090i | −0.918877 | − | 0.394545i | \(-0.870902\pi\) | ||
0.918877 | − | 0.394545i | \(-0.129098\pi\) | |||||||
\(264\) | −1.09623e11 | −0.0854836 | ||||||||
\(265\) | 6.60158e11i | 0.505148i | ||||||||
\(266\) | − | 2.57576e11i | − | 0.193418i | ||||||
\(267\) | 1.50603e11 | 0.110989 | ||||||||
\(268\) | −2.92314e12 | −2.11434 | ||||||||
\(269\) | 3.87961e11 | 0.275440 | 0.137720 | − | 0.990471i | \(-0.456023\pi\) | ||||
0.137720 | + | 0.990471i | \(0.456023\pi\) | |||||||
\(270\) | 2.76117e11i | 0.192431i | ||||||||
\(271\) | 1.29080e11 | 0.0883107 | 0.0441554 | − | 0.999025i | \(-0.485940\pi\) | ||||
0.0441554 | + | 0.999025i | \(0.485940\pi\) | |||||||
\(272\) | 9.35918e11 | 0.628627 | ||||||||
\(273\) | 6.66876e9 | 0.00439776 | ||||||||
\(274\) | 7.94004e11 | 0.514126 | ||||||||
\(275\) | 4.17268e11 | 0.265308 | ||||||||
\(276\) | − | 1.77667e11i | − | 0.110933i | ||||||
\(277\) | 1.08344e12i | 0.664364i | 0.943215 | + | 0.332182i | \(0.107785\pi\) | ||||
−0.943215 | + | 0.332182i | \(0.892215\pi\) | |||||||
\(278\) | − | 1.27757e12i | − | 0.769415i | ||||||
\(279\) | 5.43464e11 | 0.321477 | ||||||||
\(280\) | − | 2.77438e11i | − | 0.161204i | ||||||
\(281\) | −5.74014e11 | −0.327635 | −0.163818 | − | 0.986491i | \(-0.552381\pi\) | ||||
−0.163818 | + | 0.986491i | \(0.552381\pi\) | |||||||
\(282\) | 3.35309e10 | 0.0188018 | ||||||||
\(283\) | −2.28530e12 | −1.25896 | −0.629478 | − | 0.777018i | \(-0.716731\pi\) | ||||
−0.629478 | + | 0.777018i | \(0.716731\pi\) | |||||||
\(284\) | 3.11998e12i | 1.68873i | ||||||||
\(285\) | 1.01830e11i | 0.0541567i | ||||||||
\(286\) | 9.52928e11i | 0.498001i | ||||||||
\(287\) | − | 2.11438e11i | − | 0.108586i | ||||||
\(288\) | − | 1.41658e12i | − | 0.714957i | ||||||
\(289\) | −1.69988e12 | −0.843197 | ||||||||
\(290\) | 8.99508e8i | 0.000438546i | ||||||||
\(291\) | − | 1.40763e11i | − | 0.0674566i | ||||||
\(292\) | − | 1.72975e12i | − | 0.814834i | ||||||
\(293\) | −1.26450e12 | −0.585572 | −0.292786 | − | 0.956178i | \(-0.594582\pi\) | ||||
−0.292786 | + | 0.956178i | \(0.594582\pi\) | |||||||
\(294\) | 2.97270e11 | 0.135336 | ||||||||
\(295\) | 1.53853e10i | 0.00688644i | ||||||||
\(296\) | 1.82950e12 | 0.805146 | ||||||||
\(297\) | 1.86364e11i | 0.0806456i | ||||||||
\(298\) | 5.50407e12 | 2.34209 | ||||||||
\(299\) | −8.37425e11 | −0.350421 | ||||||||
\(300\) | − | 2.05069e11i | − | 0.0843904i | ||||||
\(301\) | 2.18793e11 | + | 1.53730e11i | 0.0885525 | + | 0.0622193i | ||||
\(302\) | 4.73929e12 | 1.88659 | ||||||||
\(303\) | 7.37830e10i | 0.0288897i | ||||||||
\(304\) | − | 4.12792e12i | − | 1.58988i | ||||||
\(305\) | 2.35917e12 | 0.893840 | ||||||||
\(306\) | − | 1.88469e12i | − | 0.702477i | ||||||
\(307\) | 2.50470e11 | 0.0918469 | 0.0459235 | − | 0.998945i | \(-0.485377\pi\) | ||||
0.0459235 | + | 0.998945i | \(0.485377\pi\) | |||||||
\(308\) | − | 3.45345e11i | − | 0.124595i | ||||||
\(309\) | 2.14202e11i | 0.0760380i | ||||||||
\(310\) | 1.16423e12 | 0.406658 | ||||||||
\(311\) | −4.53328e12 | −1.55815 | −0.779077 | − | 0.626928i | \(-0.784312\pi\) | ||||
−0.779077 | + | 0.626928i | \(0.784312\pi\) | |||||||
\(312\) | 2.53937e11 | 0.0858922 | ||||||||
\(313\) | − | 3.19354e12i | − | 1.06304i | −0.847045 | − | 0.531522i | \(-0.821620\pi\) | ||
0.847045 | − | 0.531522i | \(-0.178380\pi\) | |||||||
\(314\) | 8.16018e12 | 2.67332 | ||||||||
\(315\) | −2.35132e11 | −0.0758157 | ||||||||
\(316\) | 6.68244e11 | 0.212080 | ||||||||
\(317\) | −4.16251e12 | −1.30035 | −0.650173 | − | 0.759786i | \(-0.725304\pi\) | ||||
−0.650173 | + | 0.759786i | \(0.725304\pi\) | |||||||
\(318\) | 3.19221e11 | 0.0981649 | ||||||||
\(319\) | 6.07119e8i | 0.000183789i | ||||||||
\(320\) | 7.19053e11i | 0.214295i | ||||||||
\(321\) | 1.38944e11i | 0.0407677i | ||||||||
\(322\) | 4.42414e11 | 0.127806 | ||||||||
\(323\) | − | 1.39424e12i | − | 0.396574i | ||||||
\(324\) | −7.66213e12 | −2.14597 | ||||||||
\(325\) | −9.66582e11 | −0.266577 | ||||||||
\(326\) | −7.16192e12 | −1.94510 | ||||||||
\(327\) | 3.14557e11i | 0.0841320i | ||||||||
\(328\) | − | 8.05126e12i | − | 2.12077i | ||||||
\(329\) | 5.72766e10i | 0.0148593i | ||||||||
\(330\) | 1.99028e11i | 0.0508563i | ||||||||
\(331\) | − | 2.33766e12i | − | 0.588358i | −0.955750 | − | 0.294179i | \(-0.904954\pi\) | ||
0.955750 | − | 0.294179i | \(-0.0950461\pi\) | |||||||
\(332\) | −7.88244e12 | −1.95421 | ||||||||
\(333\) | − | 1.55053e12i | − | 0.378668i | ||||||
\(334\) | − | 3.29171e12i | − | 0.791934i | ||||||
\(335\) | 2.87768e12i | 0.682055i | ||||||||
\(336\) | −5.64617e10 | −0.0131843 | ||||||||
\(337\) | −6.43508e12 | −1.48049 | −0.740244 | − | 0.672339i | \(-0.765290\pi\) | ||||
−0.740244 | + | 0.672339i | \(0.765290\pi\) | |||||||
\(338\) | 5.66492e12i | 1.28413i | ||||||||
\(339\) | −2.06001e11 | −0.0460119 | ||||||||
\(340\) | − | 2.76959e12i | − | 0.609567i | ||||||
\(341\) | 7.85790e11 | 0.170426 | ||||||||
\(342\) | −8.31251e12 | −1.77665 | ||||||||
\(343\) | 1.02160e12i | 0.215184i | ||||||||
\(344\) | 8.33134e12 | + | 5.85381e12i | 1.72951 | + | 1.21520i | ||||
\(345\) | −1.74904e11 | −0.0357854 | ||||||||
\(346\) | − | 7.24762e12i | − | 1.46155i | ||||||
\(347\) | 6.74519e12i | 1.34075i | 0.742024 | + | 0.670373i | \(0.233866\pi\) | ||||
−0.742024 | + | 0.670373i | \(0.766134\pi\) | |||||||
\(348\) | 2.98372e8 | 5.84605e−5 | ||||||||
\(349\) | 3.87004e12i | 0.747462i | 0.927537 | + | 0.373731i | \(0.121922\pi\) | ||||
−0.927537 | + | 0.373731i | \(0.878078\pi\) | |||||||
\(350\) | 5.10648e11 | 0.0972258 | ||||||||
\(351\) | − | 4.31705e11i | − | 0.0810310i | ||||||
\(352\) | − | 2.04823e12i | − | 0.379022i | ||||||
\(353\) | 2.15226e12 | 0.392665 | 0.196332 | − | 0.980537i | \(-0.437097\pi\) | ||||
0.196332 | + | 0.980537i | \(0.437097\pi\) | |||||||
\(354\) | 7.43958e9 | 0.00133823 | ||||||||
\(355\) | 3.07147e12 | 0.544759 | ||||||||
\(356\) | 1.80662e13i | 3.15949i | ||||||||
\(357\) | −1.90704e10 | −0.00328865 | ||||||||
\(358\) | 1.37657e13 | 2.34090 | ||||||||
\(359\) | 6.07414e12 | 1.01862 | 0.509310 | − | 0.860583i | \(-0.329901\pi\) | ||||
0.509310 | + | 0.860583i | \(0.329901\pi\) | |||||||
\(360\) | −8.95351e12 | −1.48075 | ||||||||
\(361\) | −1.82909e10 | −0.00298331 | ||||||||
\(362\) | 1.42070e13i | 2.28538i | ||||||||
\(363\) | − | 3.49332e11i | − | 0.0554249i | ||||||
\(364\) | 7.99977e11i | 0.125190i | ||||||||
\(365\) | −1.70285e12 | −0.262853 | ||||||||
\(366\) | − | 1.14078e12i | − | 0.173699i | ||||||
\(367\) | −2.68441e12 | −0.403198 | −0.201599 | − | 0.979468i | \(-0.564614\pi\) | ||||
−0.201599 | + | 0.979468i | \(0.564614\pi\) | |||||||
\(368\) | 7.09015e12 | 1.05055 | ||||||||
\(369\) | −6.82354e12 | −0.997419 | ||||||||
\(370\) | − | 3.32159e12i | − | 0.479002i | ||||||
\(371\) | 5.45286e11i | 0.0775809i | ||||||||
\(372\) | − | 3.86181e11i | − | 0.0542097i | ||||||
\(373\) | − | 8.55286e12i | − | 1.18459i | −0.805722 | − | 0.592294i | \(-0.798222\pi\) | ||
0.805722 | − | 0.592294i | \(-0.201778\pi\) | |||||||
\(374\) | − | 2.72505e12i | − | 0.372406i | ||||||
\(375\) | −6.02896e11 | −0.0812992 | ||||||||
\(376\) | 2.18102e12i | 0.290215i | ||||||||
\(377\) | − | 1.40636e9i | − | 0.000184668i | ||||||
\(378\) | 2.28071e11i | 0.0295536i | ||||||||
\(379\) | 1.36576e13 | 1.74654 | 0.873269 | − | 0.487238i | \(-0.161996\pi\) | ||||
0.873269 | + | 0.487238i | \(0.161996\pi\) | |||||||
\(380\) | −1.22154e13 | −1.54167 | ||||||||
\(381\) | − | 7.85565e11i | − | 0.0978492i | ||||||
\(382\) | 7.26287e12 | 0.892877 | ||||||||
\(383\) | − | 5.32035e12i | − | 0.645574i | −0.946472 | − | 0.322787i | \(-0.895380\pi\) | ||
0.946472 | − | 0.322787i | \(-0.104620\pi\) | |||||||
\(384\) | 8.08500e11 | 0.0968331 | ||||||||
\(385\) | −3.39975e11 | −0.0401924 | ||||||||
\(386\) | 7.60447e12i | 0.887427i | ||||||||
\(387\) | 4.96118e12 | − | 7.06091e12i | 0.571518 | − | 0.813403i | ||||
\(388\) | 1.68858e13 | 1.92027 | ||||||||
\(389\) | − | 7.76096e12i | − | 0.871299i | −0.900116 | − | 0.435650i | \(-0.856519\pi\) | ||
0.900116 | − | 0.435650i | \(-0.143481\pi\) | |||||||
\(390\) | − | 4.61040e11i | − | 0.0510994i | ||||||
\(391\) | 2.39475e12 | 0.262045 | ||||||||
\(392\) | 1.93359e13i | 2.08898i | ||||||||
\(393\) | −4.95244e10 | −0.00528271 | ||||||||
\(394\) | − | 1.79150e13i | − | 1.88685i | ||||||
\(395\) | − | 6.57853e11i | − | 0.0684138i | ||||||
\(396\) | −1.11450e13 | −1.14447 | ||||||||
\(397\) | −8.18970e12 | −0.830454 | −0.415227 | − | 0.909718i | \(-0.636298\pi\) | ||||
−0.415227 | + | 0.909718i | \(0.636298\pi\) | |||||||
\(398\) | 2.85234e13 | 2.85618 | ||||||||
\(399\) | 8.41110e10i | 0.00831741i | ||||||||
\(400\) | 8.18366e12 | 0.799186 | ||||||||
\(401\) | 1.19369e13 | 1.15125 | 0.575626 | − | 0.817713i | \(-0.304758\pi\) | ||||
0.575626 | + | 0.817713i | \(0.304758\pi\) | |||||||
\(402\) | 1.39151e12 | 0.132543 | ||||||||
\(403\) | −1.82025e12 | −0.171240 | ||||||||
\(404\) | −8.85093e12 | −0.822398 | ||||||||
\(405\) | 7.54299e12i | 0.692259i | ||||||||
\(406\) | 7.42986e8i | 6.73520e-5i | ||||||||
\(407\) | − | 2.24189e12i | − | 0.200744i | ||||||
\(408\) | −7.26174e11 | −0.0642303 | ||||||||
\(409\) | − | 2.10211e13i | − | 1.83670i | −0.395766 | − | 0.918351i | \(-0.629521\pi\) | ||
0.395766 | − | 0.918351i | \(-0.370479\pi\) | |||||||
\(410\) | −1.46176e13 | −1.26170 | ||||||||
\(411\) | −2.59281e11 | −0.0221086 | ||||||||
\(412\) | −2.56954e13 | −2.16456 | ||||||||
\(413\) | 1.27081e10i | 0.00105762i | ||||||||
\(414\) | − | 1.42776e13i | − | 1.17396i | ||||||
\(415\) | 7.75987e12i | 0.630397i | ||||||||
\(416\) | 4.74463e12i | 0.380834i | ||||||||
\(417\) | 4.17189e11i | 0.0330866i | ||||||||
\(418\) | −1.20190e13 | −0.941860 | ||||||||
\(419\) | 1.65091e13i | 1.27836i | 0.769056 | + | 0.639181i | \(0.220727\pi\) | ||||
−0.769056 | + | 0.639181i | \(0.779273\pi\) | |||||||
\(420\) | 1.67083e11i | 0.0127846i | ||||||||
\(421\) | 2.29197e13i | 1.73300i | 0.499176 | + | 0.866501i | \(0.333636\pi\) | ||||
−0.499176 | + | 0.866501i | \(0.666364\pi\) | |||||||
\(422\) | 2.57215e13 | 1.92192 | ||||||||
\(423\) | 1.84844e12 | 0.136491 | ||||||||
\(424\) | 2.07637e13i | 1.51522i | ||||||||
\(425\) | 2.76410e12 | 0.199346 | ||||||||
\(426\) | − | 1.48522e12i | − | 0.105862i | ||||||
\(427\) | 1.94866e12 | 0.137276 | ||||||||
\(428\) | −1.66676e13 | −1.16053 | ||||||||
\(429\) | − | 3.11177e11i | − | 0.0214152i | ||||||
\(430\) | 1.06280e13 | − | 1.51261e13i | 0.722951 | − | 1.02893i | ||||
\(431\) | 2.74183e13 | 1.84355 | 0.921773 | − | 0.387731i | \(-0.126741\pi\) | ||||
0.921773 | + | 0.387731i | \(0.126741\pi\) | |||||||
\(432\) | 3.65507e12i | 0.242928i | ||||||||
\(433\) | 1.02469e13i | 0.673216i | 0.941645 | + | 0.336608i | \(0.109280\pi\) | ||||
−0.941645 | + | 0.336608i | \(0.890720\pi\) | |||||||
\(434\) | 9.61642e11 | 0.0624547 | ||||||||
\(435\) | − | 2.93733e8i | − | 1.88585e-5i | ||||||
\(436\) | −3.77340e13 | −2.39497 | ||||||||
\(437\) | − | 1.05622e13i | − | 0.662745i | ||||||
\(438\) | 8.23419e11i | 0.0510799i | ||||||||
\(439\) | −2.04098e13 | −1.25175 | −0.625873 | − | 0.779925i | \(-0.715257\pi\) | ||||
−0.625873 | + | 0.779925i | \(0.715257\pi\) | |||||||
\(440\) | −1.29458e13 | −0.784992 | ||||||||
\(441\) | 1.63874e13 | 0.982467 | ||||||||
\(442\) | 6.31246e12i | 0.374186i | ||||||||
\(443\) | 1.64922e13 | 0.966630 | 0.483315 | − | 0.875447i | \(-0.339433\pi\) | ||||
0.483315 | + | 0.875447i | \(0.339433\pi\) | |||||||
\(444\) | −1.10179e12 | −0.0638535 | ||||||||
\(445\) | 1.77853e13 | 1.01920 | ||||||||
\(446\) | −4.19666e13 | −2.37810 | ||||||||
\(447\) | −1.79735e12 | −0.100715 | ||||||||
\(448\) | 5.93932e11i | 0.0329114i | ||||||||
\(449\) | − | 4.44530e11i | − | 0.0243596i | −0.999926 | − | 0.0121798i | \(-0.996123\pi\) | ||
0.999926 | − | 0.0121798i | \(-0.00387704\pi\) | |||||||
\(450\) | − | 1.64797e13i | − | 0.893072i | ||||||
\(451\) | −9.86609e12 | −0.528764 | ||||||||
\(452\) | − | 2.47116e13i | − | 1.30981i | ||||||
\(453\) | −1.54761e12 | −0.0811278 | ||||||||
\(454\) | −4.69621e13 | −2.43483 | ||||||||
\(455\) | 7.87538e11 | 0.0403845 | ||||||||
\(456\) | 3.20283e12i | 0.162446i | ||||||||
\(457\) | − | 3.80983e12i | − | 0.191128i | −0.995423 | − | 0.0955641i | \(-0.969534\pi\) | ||
0.995423 | − | 0.0955641i | \(-0.0304655\pi\) | |||||||
\(458\) | − | 5.00968e13i | − | 2.48589i | ||||||
\(459\) | 1.23453e12i | 0.0605951i | ||||||||
\(460\) | − | 2.09813e13i | − | 1.01869i | ||||||
\(461\) | −3.28817e13 | −1.57924 | −0.789622 | − | 0.613594i | \(-0.789723\pi\) | ||||
−0.789622 | + | 0.613594i | \(0.789723\pi\) | |||||||
\(462\) | 1.64396e11i | 0.00781054i | ||||||||
\(463\) | 3.09113e13i | 1.45282i | 0.687262 | + | 0.726410i | \(0.258812\pi\) | ||||
−0.687262 | + | 0.726410i | \(0.741188\pi\) | |||||||
\(464\) | 1.19071e10i | 0.000553627i | ||||||||
\(465\) | −3.80177e11 | −0.0174872 | ||||||||
\(466\) | −3.62536e13 | −1.64976 | ||||||||
\(467\) | − | 2.24409e11i | − | 0.0101031i | −0.999987 | − | 0.00505156i | \(-0.998392\pi\) | ||
0.999987 | − | 0.00505156i | \(-0.00160797\pi\) | |||||||
\(468\) | 2.58169e13 | 1.14994 | ||||||||
\(469\) | 2.37695e12i | 0.104750i | ||||||||
\(470\) | 3.95978e12 | 0.172656 | ||||||||
\(471\) | −2.66470e12 | −0.114959 | ||||||||
\(472\) | 4.83908e11i | 0.0206563i | ||||||||
\(473\) | 7.17332e12 | − | 1.02093e13i | 0.302980 | − | 0.431211i | ||||
\(474\) | −3.18107e11 | −0.0132948 | ||||||||
\(475\) | − | 1.21912e13i | − | 0.504172i | ||||||
\(476\) | − | 2.28766e12i | − | 0.0936175i | ||||||
\(477\) | 1.75975e13 | 0.712623 | ||||||||
\(478\) | 4.00058e11i | 0.0160319i | ||||||||
\(479\) | −1.96576e13 | −0.779566 | −0.389783 | − | 0.920907i | \(-0.627450\pi\) | ||||
−0.389783 | + | 0.920907i | \(0.627450\pi\) | |||||||
\(480\) | 9.90962e11i | 0.0388911i | ||||||||
\(481\) | 5.19325e12i | 0.201704i | ||||||||
\(482\) | −1.09713e13 | −0.421718 | ||||||||
\(483\) | −1.44470e11 | −0.00549593 | ||||||||
\(484\) | 4.19054e13 | 1.57777 | ||||||||
\(485\) | − | 1.66232e13i | − | 0.619451i | ||||||
\(486\) | 1.10514e13 | 0.407600 | ||||||||
\(487\) | 3.32804e13 | 1.21491 | 0.607454 | − | 0.794355i | \(-0.292191\pi\) | ||||
0.607454 | + | 0.794355i | \(0.292191\pi\) | |||||||
\(488\) | 7.42022e13 | 2.68113 | ||||||||
\(489\) | 2.33871e12 | 0.0836436 | ||||||||
\(490\) | 3.51057e13 | 1.24279 | ||||||||
\(491\) | 2.31126e13i | 0.809918i | 0.914335 | + | 0.404959i | \(0.132714\pi\) | ||||
−0.914335 | + | 0.404959i | \(0.867286\pi\) | |||||||
\(492\) | 4.84875e12i | 0.168192i | ||||||||
\(493\) | 4.02172e9i | 0.000138095i | ||||||||
\(494\) | 2.78415e13 | 0.946362 | ||||||||
\(495\) | 1.09717e13i | 0.369189i | ||||||||
\(496\) | 1.54113e13 | 0.513371 | ||||||||
\(497\) | 2.53701e12 | 0.0836643 | ||||||||
\(498\) | 3.75231e12 | 0.122504 | ||||||||
\(499\) | 8.58315e11i | 0.0277424i | 0.999904 | + | 0.0138712i | \(0.00441548\pi\) | ||||
−0.999904 | + | 0.0138712i | \(0.995585\pi\) | |||||||
\(500\) | − | 7.23228e13i | − | 2.31433i | ||||||
\(501\) | 1.07490e12i | 0.0340550i | ||||||||
\(502\) | 4.37131e13i | 1.37118i | ||||||||
\(503\) | − | 3.88625e12i | − | 0.120696i | −0.998177 | − | 0.0603478i | \(-0.980779\pi\) | ||
0.998177 | − | 0.0603478i | \(-0.0192210\pi\) | |||||||
\(504\) | −7.39553e12 | −0.227414 | ||||||||
\(505\) | 8.71330e12i | 0.265293i | ||||||||
\(506\) | − | 2.06439e13i | − | 0.622357i | ||||||
\(507\) | − | 1.84987e12i | − | 0.0552206i | ||||||
\(508\) | 9.42355e13 | 2.78545 | ||||||||
\(509\) | −5.83701e13 | −1.70845 | −0.854223 | − | 0.519906i | \(-0.825967\pi\) | ||||
−0.854223 | + | 0.519906i | \(0.825967\pi\) | |||||||
\(510\) | 1.31842e12i | 0.0382122i | ||||||||
\(511\) | −1.40654e12 | −0.0403691 | ||||||||
\(512\) | 7.78932e13i | 2.21386i | ||||||||
\(513\) | 5.44496e12 | 0.153253 | ||||||||
\(514\) | −1.22783e14 | −3.42234 | ||||||||
\(515\) | 2.52959e13i | 0.698254i | ||||||||
\(516\) | −5.01743e12 | − | 3.52537e12i | −0.137162 | − | 0.0963733i | ||||
\(517\) | 2.67264e12 | 0.0723581 | ||||||||
\(518\) | − | 2.74361e12i | − | 0.0735653i | ||||||
\(519\) | 2.36670e12i | 0.0628502i | ||||||||
\(520\) | 2.99884e13 | 0.788744 | ||||||||
\(521\) | − | 1.80423e13i | − | 0.470006i | −0.971995 | − | 0.235003i | \(-0.924490\pi\) | ||
0.971995 | − | 0.235003i | \(-0.0755100\pi\) | |||||||
\(522\) | 2.39777e10 | 0.000618665 | ||||||||
\(523\) | 6.85020e13i | 1.75063i | 0.483552 | + | 0.875316i | \(0.339347\pi\) | ||||
−0.483552 | + | 0.875316i | \(0.660653\pi\) | |||||||
\(524\) | − | 5.94089e12i | − | 0.150382i | ||||||
\(525\) | −1.66751e11 | −0.00418093 | ||||||||
\(526\) | −5.66990e13 | −1.40814 | ||||||||
\(527\) | 5.20529e12 | 0.128054 | ||||||||
\(528\) | 2.63461e12i | 0.0642018i | ||||||||
\(529\) | −2.32848e13 | −0.562075 | ||||||||
\(530\) | 3.76980e13 | 0.901444 | ||||||||
\(531\) | 4.10118e11 | 0.00971484 | ||||||||
\(532\) | −1.00899e13 | −0.236770 | ||||||||
\(533\) | 2.28544e13 | 0.531292 | ||||||||
\(534\) | − | 8.60013e12i | − | 0.198061i | ||||||
\(535\) | 1.64084e13i | 0.374368i | ||||||||
\(536\) | 9.05109e13i | 2.04586i | ||||||||
\(537\) | −4.49516e12 | −0.100664 | ||||||||
\(538\) | − | 2.21543e13i | − | 0.491526i | ||||||
\(539\) | 2.36944e13 | 0.520838 | ||||||||
\(540\) | 1.08162e13 | 0.235562 | ||||||||
\(541\) | −6.10736e13 | −1.31785 | −0.658926 | − | 0.752207i | \(-0.728989\pi\) | ||||
−0.658926 | + | 0.752207i | \(0.728989\pi\) | |||||||
\(542\) | − | 7.37106e12i | − | 0.157592i | ||||||
\(543\) | − | 4.63926e12i | − | 0.0982765i | ||||||
\(544\) | − | 1.35680e13i | − | 0.284788i | ||||||
\(545\) | 3.71472e13i | 0.772580i | ||||||||
\(546\) | − | 3.80816e11i | − | 0.00784787i | ||||||
\(547\) | −7.67144e13 | −1.56653 | −0.783267 | − | 0.621685i | \(-0.786448\pi\) | ||||
−0.783267 | + | 0.621685i | \(0.786448\pi\) | |||||||
\(548\) | − | 3.11030e13i | − | 0.629362i | ||||||
\(549\) | − | 6.28872e13i | − | 1.26096i | ||||||
\(550\) | − | 2.38278e13i | − | 0.473447i | ||||||
\(551\) | 1.77380e10 | 0.000349259 | ||||||||
\(552\) | −5.50121e12 | −0.107340 | ||||||||
\(553\) | − | 5.43382e11i | − | 0.0105070i | ||||||
\(554\) | 6.18693e13 | 1.18557 | ||||||||
\(555\) | 1.08466e12i | 0.0205982i | ||||||||
\(556\) | −5.00455e13 | −0.941870 | ||||||||
\(557\) | −2.21154e13 | −0.412496 | −0.206248 | − | 0.978500i | \(-0.566125\pi\) | ||||
−0.206248 | + | 0.978500i | \(0.566125\pi\) | |||||||
\(558\) | − | 3.10342e13i | − | 0.573680i | ||||||
\(559\) | −1.66167e13 | + | 2.36494e13i | −0.304429 | + | 0.433273i | ||||
\(560\) | −6.66777e12 | −0.121071 | ||||||||
\(561\) | 8.89861e11i | 0.0160143i | ||||||||
\(562\) | 3.27787e13i | 0.584670i | ||||||||
\(563\) | 2.34950e13 | 0.415369 | 0.207685 | − | 0.978196i | \(-0.433407\pi\) | ||||
0.207685 | + | 0.978196i | \(0.433407\pi\) | |||||||
\(564\) | − | 1.31348e12i | − | 0.0230160i | ||||||
\(565\) | −2.43273e13 | −0.422525 | ||||||||
\(566\) | 1.30501e14i | 2.24662i | ||||||||
\(567\) | 6.23045e12i | 0.106317i | ||||||||
\(568\) | 9.66059e13 | 1.63404 | ||||||||
\(569\) | 1.92419e11 | 0.00322616 | 0.00161308 | − | 0.999999i | \(-0.499487\pi\) | ||||
0.00161308 | + | 0.999999i | \(0.499487\pi\) | |||||||
\(570\) | 5.81496e12 | 0.0966434 | ||||||||
\(571\) | 6.65935e13i | 1.09711i | 0.836114 | + | 0.548556i | \(0.184822\pi\) | ||||
−0.836114 | + | 0.548556i | \(0.815178\pi\) | |||||||
\(572\) | 3.73285e13 | 0.609621 | ||||||||
\(573\) | −2.37168e12 | −0.0383957 | ||||||||
\(574\) | −1.20740e13 | −0.193773 | ||||||||
\(575\) | 2.09397e13 | 0.333143 | ||||||||
\(576\) | 1.91675e13 | 0.302310 | ||||||||
\(577\) | − | 6.72009e13i | − | 1.05074i | −0.850873 | − | 0.525371i | \(-0.823926\pi\) | ||
0.850873 | − | 0.525371i | \(-0.176074\pi\) | |||||||
\(578\) | 9.70707e13i | 1.50470i | ||||||||
\(579\) | − | 2.48323e12i | − | 0.0381614i | ||||||
\(580\) | 3.52359e10 | 0.000536840 | ||||||||
\(581\) | 6.40960e12i | 0.0968166i | ||||||||
\(582\) | −8.03821e12 | −0.120377 | ||||||||
\(583\) | 2.54441e13 | 0.377785 | ||||||||
\(584\) | −5.35593e13 | −0.788444 | ||||||||
\(585\) | − | 2.54155e13i | − | 0.370954i | ||||||
\(586\) | 7.22085e13i | 1.04496i | ||||||||
\(587\) | − | 9.27329e12i | − | 0.133059i | −0.997784 | − | 0.0665293i | \(-0.978807\pi\) | ||
0.997784 | − | 0.0665293i | \(-0.0211926\pi\) | |||||||
\(588\) | − | 1.16448e13i | − | 0.165670i | ||||||
\(589\) | − | 2.29582e13i | − | 0.323863i | ||||||
\(590\) | 8.78567e11 | 0.0122890 | ||||||||
\(591\) | 5.85012e12i | 0.0811386i | ||||||||
\(592\) | − | 4.39691e13i | − | 0.604699i | ||||||
\(593\) | − | 1.26589e14i | − | 1.72632i | −0.504927 | − | 0.863162i | \(-0.668481\pi\) | ||
0.504927 | − | 0.863162i | \(-0.331519\pi\) | |||||||
\(594\) | 1.06422e13 | 0.143913 | ||||||||
\(595\) | −2.25209e12 | −0.0301996 | ||||||||
\(596\) | − | 2.15608e14i | − | 2.86704i | ||||||
\(597\) | −9.31427e12 | −0.122822 | ||||||||
\(598\) | 4.78207e13i | 0.625331i | ||||||||
\(599\) | 9.12594e13 | 1.18343 | 0.591716 | − | 0.806146i | \(-0.298451\pi\) | ||||
0.591716 | + | 0.806146i | \(0.298451\pi\) | |||||||
\(600\) | −6.34967e12 | −0.0816572 | ||||||||
\(601\) | − | 8.65963e13i | − | 1.10440i | −0.833711 | − | 0.552201i | \(-0.813788\pi\) | ||
0.833711 | − | 0.552201i | \(-0.186212\pi\) | |||||||
\(602\) | 8.77864e12 | − | 1.24940e13i | 0.111031 | − | 0.158023i | ||||
\(603\) | 7.67090e13 | 0.962188 | ||||||||
\(604\) | − | 1.85649e14i | − | 2.30945i | ||||||
\(605\) | − | 4.12538e13i | − | 0.508964i | ||||||
\(606\) | 4.21334e12 | 0.0515541 | ||||||||
\(607\) | − | 2.96451e13i | − | 0.359758i | −0.983689 | − | 0.179879i | \(-0.942429\pi\) | ||
0.983689 | − | 0.179879i | \(-0.0575706\pi\) | |||||||
\(608\) | −5.98425e13 | −0.720264 | ||||||||
\(609\) | − | 2.42621e8i | − | 2.89629e-6i | ||||||
\(610\) | − | 1.34719e14i | − | 1.59507i | ||||||
\(611\) | −6.19105e12 | −0.0727040 | ||||||||
\(612\) | −7.38277e13 | −0.859928 | ||||||||
\(613\) | −2.80351e13 | −0.323891 | −0.161946 | − | 0.986800i | \(-0.551777\pi\) | ||||
−0.161946 | + | 0.986800i | \(0.551777\pi\) | |||||||
\(614\) | − | 1.43030e13i | − | 0.163902i | ||||||
\(615\) | 4.77336e12 | 0.0542561 | ||||||||
\(616\) | −1.06931e13 | −0.120559 | ||||||||
\(617\) | 1.75598e13 | 0.196378 | 0.0981891 | − | 0.995168i | \(-0.468695\pi\) | ||||
0.0981891 | + | 0.995168i | \(0.468695\pi\) | |||||||
\(618\) | 1.22319e13 | 0.135691 | ||||||||
\(619\) | −4.13205e13 | −0.454686 | −0.227343 | − | 0.973815i | \(-0.573004\pi\) | ||||
−0.227343 | + | 0.973815i | \(0.573004\pi\) | |||||||
\(620\) | − | 4.56056e13i | − | 0.497805i | ||||||
\(621\) | 9.35230e12i | 0.101265i | ||||||||
\(622\) | 2.58870e14i | 2.78055i | ||||||||
\(623\) | 1.46905e13 | 0.156530 | ||||||||
\(624\) | − | 6.10297e12i | − | 0.0645087i | ||||||
\(625\) | −2.31882e13 | −0.243146 | ||||||||
\(626\) | −1.82366e14 | −1.89702 | ||||||||
\(627\) | 3.92478e12 | 0.0405021 | ||||||||
\(628\) | − | 3.19654e14i | − | 3.27252i | ||||||
\(629\) | − | 1.48509e13i | − | 0.150834i | ||||||
\(630\) | 1.34271e13i | 0.135294i | ||||||||
\(631\) | 1.03967e14i | 1.03932i | 0.854373 | + | 0.519660i | \(0.173941\pi\) | ||||
−0.854373 | + | 0.519660i | \(0.826059\pi\) | |||||||
\(632\) | − | 2.06912e13i | − | 0.205211i | ||||||
\(633\) | −8.39932e12 | −0.0826467 | ||||||||
\(634\) | 2.37698e14i | 2.32049i | ||||||||
\(635\) | − | 9.27702e13i | − | 0.898545i | ||||||
\(636\) | − | 1.25047e13i | − | 0.120167i | ||||||
\(637\) | −5.48872e13 | −0.523328 | ||||||||
\(638\) | 3.46692e10 | 0.000327975 | ||||||||
\(639\) | − | 8.18747e13i | − | 0.768503i | ||||||
\(640\) | 9.54787e13 | 0.889215 | ||||||||
\(641\) | 8.81924e13i | 0.814969i | 0.913212 | + | 0.407484i | \(0.133594\pi\) | ||||
−0.913212 | + | 0.407484i | \(0.866406\pi\) | |||||||
\(642\) | 7.93434e12 | 0.0727505 | ||||||||
\(643\) | 1.86707e14 | 1.69866 | 0.849329 | − | 0.527865i | \(-0.177007\pi\) | ||||
0.849329 | + | 0.527865i | \(0.177007\pi\) | |||||||
\(644\) | − | 1.73304e13i | − | 0.156452i | ||||||
\(645\) | −3.47056e12 | + | 4.93941e12i | −0.0310886 | + | 0.0442462i | ||||
\(646\) | −7.96171e13 | −0.707691 | ||||||||
\(647\) | 4.89851e13i | 0.432058i | 0.976387 | + | 0.216029i | \(0.0693106\pi\) | ||||
−0.976387 | + | 0.216029i | \(0.930689\pi\) | |||||||
\(648\) | 2.37247e14i | 2.07647i | ||||||||
\(649\) | 5.92985e11 | 0.00515016 | ||||||||
\(650\) | 5.51961e13i | 0.475710i | ||||||||
\(651\) | −3.14023e11 | −0.00268569 | ||||||||
\(652\) | 2.80549e14i | 2.38107i | ||||||||
\(653\) | − | 1.63337e14i | − | 1.37569i | −0.725859 | − | 0.687844i | \(-0.758558\pi\) | ||
0.725859 | − | 0.687844i | \(-0.241442\pi\) | |||||||
\(654\) | 1.79626e13 | 0.150135 | ||||||||
\(655\) | −5.84852e12 | −0.0485109 | ||||||||
\(656\) | −1.93499e14 | −1.59279 | ||||||||
\(657\) | 4.53921e13i | 0.370812i | ||||||||
\(658\) | 3.27075e12 | 0.0265166 | ||||||||
\(659\) | 1.48601e14 | 1.19562 | 0.597811 | − | 0.801637i | \(-0.296037\pi\) | ||||
0.597811 | + | 0.801637i | \(0.296037\pi\) | |||||||
\(660\) | 7.79642e12 | 0.0622552 | ||||||||
\(661\) | −2.25306e13 | −0.178552 | −0.0892761 | − | 0.996007i | \(-0.528455\pi\) | ||||
−0.0892761 | + | 0.996007i | \(0.528455\pi\) | |||||||
\(662\) | −1.33491e14 | −1.04993 | ||||||||
\(663\) | − | 2.06132e12i | − | 0.0160908i | ||||||
\(664\) | 2.44069e14i | 1.89091i | ||||||||
\(665\) | 9.93297e12i | 0.0763785i | ||||||||
\(666\) | −8.85420e13 | −0.675738 | ||||||||
\(667\) | 3.04670e10i | 0.000230781i | ||||||||
\(668\) | −1.28944e14 | −0.969436 | ||||||||
\(669\) | 1.37041e13 | 0.102264 | ||||||||
\(670\) | 1.64329e14 | 1.21714 | ||||||||
\(671\) | − | 9.09281e13i | − | 0.668475i | ||||||
\(672\) | 8.18527e11i | 0.00597292i | ||||||||
\(673\) | − | 1.63307e14i | − | 1.18285i | −0.806361 | − | 0.591424i | \(-0.798566\pi\) | ||
0.806361 | − | 0.591424i | \(-0.201434\pi\) | |||||||
\(674\) | 3.67472e14i | 2.64195i | ||||||||
\(675\) | 1.07947e13i | 0.0770358i | ||||||||
\(676\) | 2.21908e14 | 1.57196 | ||||||||
\(677\) | − | 2.03834e13i | − | 0.143329i | −0.997429 | − | 0.0716643i | \(-0.977169\pi\) | ||
0.997429 | − | 0.0716643i | \(-0.0228310\pi\) | |||||||
\(678\) | 1.17635e13i | 0.0821088i | ||||||||
\(679\) | − | 1.37307e13i | − | 0.0951356i | ||||||
\(680\) | −8.57565e13 | −0.589824 | ||||||||
\(681\) | 1.53354e13 | 0.104703 | ||||||||
\(682\) | − | 4.48721e13i | − | 0.304127i | ||||||
\(683\) | −2.61360e14 | −1.75847 | −0.879235 | − | 0.476389i | \(-0.841946\pi\) | ||||
−0.879235 | + | 0.476389i | \(0.841946\pi\) | |||||||
\(684\) | 3.25621e14i | 2.17486i | ||||||||
\(685\) | −3.06194e13 | −0.203022 | ||||||||
\(686\) | 5.83377e13 | 0.383998 | ||||||||
\(687\) | 1.63590e13i | 0.106899i | ||||||||
\(688\) | 1.40687e14 | − | 2.00230e14i | 0.912665 | − | 1.29893i | ||||
\(689\) | −5.89401e13 | −0.379590 | ||||||||
\(690\) | 9.98782e12i | 0.0638595i | ||||||||
\(691\) | − | 1.06175e14i | − | 0.673957i | −0.941512 | − | 0.336979i | \(-0.890595\pi\) | ||
0.941512 | − | 0.336979i | \(-0.109405\pi\) | |||||||
\(692\) | −2.83907e14 | −1.78914 | ||||||||
\(693\) | 9.06256e12i | 0.0567002i | ||||||||
\(694\) | 3.85180e14 | 2.39258 | ||||||||
\(695\) | 4.92673e13i | 0.303833i | ||||||||
\(696\) | − | 9.23868e9i | − | 5.65671e-5i | ||||||
\(697\) | −6.53557e13 | −0.397301 | ||||||||
\(698\) | 2.20997e14 | 1.33386 | ||||||||
\(699\) | 1.18385e13 | 0.0709435 | ||||||||
\(700\) | − | 2.00033e13i | − | 0.119018i | ||||||
\(701\) | −1.75520e14 | −1.03690 | −0.518449 | − | 0.855109i | \(-0.673490\pi\) | ||||
−0.518449 | + | 0.855109i | \(0.673490\pi\) | |||||||
\(702\) | −2.46523e13 | −0.144601 | ||||||||
\(703\) | −6.55008e13 | −0.381478 | ||||||||
\(704\) | 2.77140e13 | 0.160264 | ||||||||
\(705\) | −1.29306e12 | −0.00742460 | ||||||||
\(706\) | − | 1.22904e14i | − | 0.700716i | ||||||
\(707\) | 7.19712e12i | 0.0407438i | ||||||||
\(708\) | − | 2.91426e11i | − | 0.00163818i | ||||||
\(709\) | −1.11019e14 | −0.619678 | −0.309839 | − | 0.950789i | \(-0.600275\pi\) | ||||
−0.309839 | + | 0.950789i | \(0.600275\pi\) | |||||||
\(710\) | − | 1.75395e14i | − | 0.972130i | ||||||
\(711\) | −1.75361e13 | −0.0965127 | ||||||||
\(712\) | 5.59395e14 | 3.05716 | ||||||||
\(713\) | 3.94332e13 | 0.214001 | ||||||||
\(714\) | 1.08900e12i | 0.00586865i | ||||||||
\(715\) | − | 3.67481e13i | − | 0.196655i | ||||||
\(716\) | − | 5.39235e14i | − | 2.86558i | ||||||
\(717\) | − | 1.30638e11i | − | 0.000689406i | ||||||
\(718\) | − | 3.46860e14i | − | 1.81774i | ||||||
\(719\) | 2.29173e14 | 1.19267 | 0.596333 | − | 0.802737i | \(-0.296624\pi\) | ||||
0.596333 | + | 0.802737i | \(0.296624\pi\) | |||||||
\(720\) | 2.15183e14i | 1.11210i | ||||||||
\(721\) | 2.08942e13i | 0.107238i | ||||||||
\(722\) | 1.04449e12i | 0.00532377i | ||||||||
\(723\) | 3.58265e12 | 0.0181348 | ||||||||
\(724\) | 5.56521e14 | 2.79762 | ||||||||
\(725\) | 3.51659e10i | 0.000175563i | ||||||||
\(726\) | −1.99484e13 | −0.0989065 | ||||||||
\(727\) | 2.63433e14i | 1.29717i | 0.761142 | + | 0.648586i | \(0.224639\pi\) | ||||
−0.761142 | + | 0.648586i | \(0.775361\pi\) | |||||||
\(728\) | 2.47702e13 | 0.121136 | ||||||||
\(729\) | 1.98652e14 | 0.964841 | ||||||||
\(730\) | 9.72405e13i | 0.469065i | ||||||||
\(731\) | 4.75181e13 | − | 6.76292e13i | 0.227652 | − | 0.324002i | ||||
\(732\) | −4.46872e13 | −0.212631 | ||||||||
\(733\) | − | 6.84831e13i | − | 0.323641i | −0.986820 | − | 0.161820i | \(-0.948263\pi\) | ||
0.986820 | − | 0.161820i | \(-0.0517365\pi\) | |||||||
\(734\) | 1.53292e14i | 0.719512i | ||||||||
\(735\) | −1.14637e13 | −0.0534427 | ||||||||
\(736\) | − | 1.02786e14i | − | 0.475932i | ||||||
\(737\) | 1.10913e14 | 0.510087 | ||||||||
\(738\) | 3.89654e14i | 1.77991i | ||||||||
\(739\) | 3.18534e14i | 1.44522i | 0.691256 | + | 0.722610i | \(0.257058\pi\) | ||||
−0.691256 | + | 0.722610i | \(0.742942\pi\) | |||||||
\(740\) | −1.30115e14 | −0.586364 | ||||||||
\(741\) | −9.09159e12 | −0.0406957 | ||||||||
\(742\) | 3.11382e13 | 0.138444 | ||||||||
\(743\) | 1.06741e14i | 0.471396i | 0.971826 | + | 0.235698i | \(0.0757376\pi\) | ||||
−0.971826 | + | 0.235698i | \(0.924262\pi\) | |||||||
\(744\) | −1.19576e13 | −0.0524539 | ||||||||
\(745\) | −2.12255e14 | −0.924862 | ||||||||
\(746\) | −4.88406e14 | −2.11391 | ||||||||
\(747\) | 2.06851e14 | 0.889314 | ||||||||
\(748\) | −1.06747e14 | −0.455876 | ||||||||
\(749\) | 1.35532e13i | 0.0574956i | ||||||||
\(750\) | 3.44281e13i | 0.145080i | ||||||||
\(751\) | 3.69630e14i | 1.54728i | 0.633628 | + | 0.773638i | \(0.281565\pi\) | ||||
−0.633628 | + | 0.773638i | \(0.718435\pi\) | |||||||
\(752\) | 5.24171e13 | 0.217964 | ||||||||
\(753\) | − | 1.42745e13i | − | 0.0589637i | ||||||
\(754\) | −8.03097e10 | −0.000329542 | ||||||||
\(755\) | −1.82762e14 | −0.744993 | ||||||||
\(756\) | 8.93408e12 | 0.0361777 | ||||||||
\(757\) | − | 7.07825e13i | − | 0.284739i | −0.989814 | − | 0.142369i | \(-0.954528\pi\) | ||
0.989814 | − | 0.142369i | \(-0.0454721\pi\) | |||||||
\(758\) | − | 7.79909e14i | − | 3.11672i | ||||||
\(759\) | 6.74124e12i | 0.0267628i | ||||||||
\(760\) | 3.78234e14i | 1.49174i | ||||||||
\(761\) | − | 2.27363e14i | − | 0.890833i | −0.895323 | − | 0.445417i | \(-0.853056\pi\) | ||
0.895323 | − | 0.445417i | \(-0.146944\pi\) | |||||||
\(762\) | −4.48593e13 | −0.174613 | ||||||||
\(763\) | 3.06833e13i | 0.118653i | ||||||||
\(764\) | − | 2.84504e14i | − | 1.09300i | ||||||
\(765\) | 7.26797e13i | 0.277400i | ||||||||
\(766\) | −3.03816e14 | −1.15204 | ||||||||
\(767\) | −1.37362e12 | −0.00517477 | ||||||||
\(768\) | − | 3.99340e13i | − | 0.149464i | ||||||
\(769\) | −2.60420e14 | −0.968374 | −0.484187 | − | 0.874965i | \(-0.660885\pi\) | ||||
−0.484187 | + | 0.874965i | \(0.660885\pi\) | |||||||
\(770\) | 1.94141e13i | 0.0717238i | ||||||||
\(771\) | 4.00947e13 | 0.147168 | ||||||||
\(772\) | 2.97885e14 | 1.08633 | ||||||||
\(773\) | 1.78304e14i | 0.646045i | 0.946391 | + | 0.323023i | \(0.104699\pi\) | ||||
−0.946391 | + | 0.323023i | \(0.895301\pi\) | |||||||
\(774\) | −4.03209e14 | − | 2.83305e14i | −1.45153 | − | 1.01988i | ||||
\(775\) | 4.55151e13 | 0.162797 | ||||||||
\(776\) | − | 5.22845e14i | − | 1.85808i | ||||||
\(777\) | 8.95921e11i | 0.00316348i | ||||||||
\(778\) | −4.43185e14 | −1.55485 | ||||||||
\(779\) | 2.88255e14i | 1.00482i | ||||||||
\(780\) | −1.80601e13 | −0.0625527 | ||||||||
\(781\) | − | 1.18382e14i | − | 0.407408i | ||||||
\(782\) | − | 1.36751e14i | − | 0.467624i | ||||||
\(783\) | −1.57062e10 | −5.33656e−5 | ||||||||
\(784\) | 4.64708e14 | 1.56892 | ||||||||
\(785\) | −3.14683e14 | −1.05566 | ||||||||
\(786\) | 2.82806e12i | 0.00942707i | ||||||||
\(787\) | −3.33113e14 | −1.10336 | −0.551680 | − | 0.834056i | \(-0.686013\pi\) | ||||
−0.551680 | + | 0.834056i | \(0.686013\pi\) | |||||||
\(788\) | −7.01775e14 | −2.30976 | ||||||||
\(789\) | 1.85150e13 | 0.0605534 | ||||||||
\(790\) | −3.75664e13 | −0.122085 | ||||||||
\(791\) | −2.00942e13 | −0.0648916 | ||||||||
\(792\) | 3.45090e14i | 1.10740i | ||||||||
\(793\) | 2.10631e14i | 0.671670i | ||||||||
\(794\) | 4.67669e14i | 1.48196i | ||||||||
\(795\) | −1.23102e13 | −0.0387641 | ||||||||
\(796\) | − | 1.11733e15i | − | 3.49636i | ||||||
\(797\) | 3.13392e14 | 0.974532 | 0.487266 | − | 0.873254i | \(-0.337994\pi\) | ||||
0.487266 | + | 0.873254i | \(0.337994\pi\) | |||||||
\(798\) | 4.80311e12 | 0.0148425 | ||||||||
\(799\) | 1.77043e13 | 0.0543682 | ||||||||
\(800\) | − | 1.18639e14i | − | 0.362057i | ||||||
\(801\) | − | 4.74094e14i | − | 1.43781i | ||||||
\(802\) | − | 6.81651e14i | − | 2.05442i | ||||||
\(803\) | 6.56321e13i | 0.196580i | ||||||||
\(804\) | − | 5.45088e13i | − | 0.162251i | ||||||
\(805\) | −1.70609e13 | −0.0504689 | ||||||||
\(806\) | 1.03944e14i | 0.305580i | ||||||||
\(807\) | 7.23445e12i | 0.0211367i | ||||||||
\(808\) | 2.74057e14i | 0.795763i | ||||||||
\(809\) | −5.35034e14 | −1.54397 | −0.771984 | − | 0.635642i | \(-0.780736\pi\) | ||||
−0.771984 | + | 0.635642i | \(0.780736\pi\) | |||||||
\(810\) | 4.30738e14 | 1.23535 | ||||||||
\(811\) | 4.81889e14i | 1.37354i | 0.726873 | + | 0.686772i | \(0.240973\pi\) | ||||
−0.726873 | + | 0.686772i | \(0.759027\pi\) | |||||||
\(812\) | 2.91046e10 | 8.24481e−5 | ||||||||
\(813\) | 2.40701e12i | 0.00677680i | ||||||||
\(814\) | −1.28022e14 | −0.358231 | ||||||||
\(815\) | 2.76187e14 | 0.768096 | ||||||||
\(816\) | 1.74524e13i | 0.0482397i | ||||||||
\(817\) | −2.98283e14 | − | 2.09581e14i | −0.819441 | − | 0.575760i | ||||
\(818\) | −1.20040e15 | −3.27762 | ||||||||
\(819\) | − | 2.09930e13i | − | 0.0569712i | ||||||
\(820\) | 5.72606e14i | 1.54450i | ||||||||
\(821\) | 3.85049e14 | 1.03229 | 0.516143 | − | 0.856503i | \(-0.327367\pi\) | ||||
0.516143 | + | 0.856503i | \(0.327367\pi\) | |||||||
\(822\) | 1.48061e13i | 0.0394531i | ||||||||
\(823\) | 8.97443e13 | 0.237688 | 0.118844 | − | 0.992913i | \(-0.462081\pi\) | ||||
0.118844 | + | 0.992913i | \(0.462081\pi\) | |||||||
\(824\) | 7.95622e14i | 2.09445i | ||||||||
\(825\) | 7.78094e12i | 0.0203593i | ||||||||
\(826\) | 7.25690e11 | 0.00188734 | ||||||||
\(827\) | 6.58096e14 | 1.70123 | 0.850613 | − | 0.525793i | \(-0.176231\pi\) | ||||
0.850613 | + | 0.525793i | \(0.176231\pi\) | |||||||
\(828\) | −5.59290e14 | −1.43709 | ||||||||
\(829\) | 4.31626e14i | 1.10239i | 0.834377 | + | 0.551194i | \(0.185828\pi\) | ||||
−0.834377 | + | 0.551194i | \(0.814172\pi\) | |||||||
\(830\) | 4.43123e14 | 1.12495 | ||||||||
\(831\) | −2.02033e13 | −0.0509821 | ||||||||
\(832\) | −6.41984e13 | −0.161030 | ||||||||
\(833\) | 1.56959e14 | 0.391345 | ||||||||
\(834\) | 2.38233e13 | 0.0590435 | ||||||||
\(835\) | 1.26939e14i | 0.312725i | ||||||||
\(836\) | 4.70813e14i | 1.15297i | ||||||||
\(837\) | 2.03284e13i | 0.0494853i | ||||||||
\(838\) | 9.42745e14 | 2.28126 | ||||||||
\(839\) | − | 3.83588e14i | − | 0.922688i | −0.887221 | − | 0.461344i | \(-0.847367\pi\) | ||
0.887221 | − | 0.461344i | \(-0.152633\pi\) | |||||||
\(840\) | 5.17349e12 | 0.0123705 | ||||||||
\(841\) | 4.20707e14 | 1.00000 | ||||||||
\(842\) | 1.30882e15 | 3.09257 | ||||||||
\(843\) | − | 1.07038e13i | − | 0.0251421i | ||||||
\(844\) | − | 1.00757e15i | − | 2.35269i | ||||||
\(845\) | − | 2.18458e14i | − | 0.507089i | ||||||
\(846\) | − | 1.05554e14i | − | 0.243569i | ||||||
\(847\) | − | 3.40753e13i | − | 0.0781670i | ||||||
\(848\) | 4.99023e14 | 1.13800 | ||||||||
\(849\) | − | 4.26148e13i | − | 0.0966100i | ||||||
\(850\) | − | 1.57842e14i | − | 0.355736i | ||||||
\(851\) | − | 1.12505e14i | − | 0.252071i | ||||||
\(852\) | −5.81795e13 | −0.129590 | ||||||||
\(853\) | −1.46909e14 | −0.325314 | −0.162657 | − | 0.986683i | \(-0.552006\pi\) | ||||
−0.162657 | + | 0.986683i | \(0.552006\pi\) | |||||||
\(854\) | − | 1.11277e14i | − | 0.244972i | ||||||
\(855\) | 3.20558e14 | 0.701578 | ||||||||
\(856\) | 5.16089e14i | 1.12294i | ||||||||
\(857\) | 4.19235e14 | 0.906888 | 0.453444 | − | 0.891285i | \(-0.350195\pi\) | ||||
0.453444 | + | 0.891285i | \(0.350195\pi\) | |||||||
\(858\) | −1.77696e13 | −0.0382157 | ||||||||
\(859\) | 3.29596e14i | 0.704719i | 0.935865 | + | 0.352360i | \(0.114621\pi\) | ||||
−0.935865 | + | 0.352360i | \(0.885379\pi\) | |||||||
\(860\) | −5.92526e14 | − | 4.16324e14i | −1.25955 | − | 0.884992i | ||||
\(861\) | 3.94276e12 | 0.00833267 | ||||||||
\(862\) | − | 1.56571e15i | − | 3.28983i | ||||||
\(863\) | 6.83525e14i | 1.42791i | 0.700192 | + | 0.713954i | \(0.253098\pi\) | ||||
−0.700192 | + | 0.713954i | \(0.746902\pi\) | |||||||
\(864\) | 5.29876e13 | 0.110054 | ||||||||
\(865\) | 2.79492e14i | 0.577151i | ||||||||
\(866\) | 5.85145e14 | 1.20136 | ||||||||
\(867\) | − | 3.16983e13i | − | 0.0647054i | ||||||
\(868\) | − | 3.76698e13i | − | 0.0764531i | ||||||
\(869\) | −2.53553e13 | −0.0511645 | ||||||||
\(870\) | −1.67735e10 | −3.36532e−5 | ||||||||
\(871\) | −2.56925e14 | −0.512525 | ||||||||
\(872\) | 1.16838e15i | 2.31740i | ||||||||
\(873\) | −4.43118e14 | −0.873872 | ||||||||
\(874\) | −6.03148e14 | −1.18268 | ||||||||
\(875\) | −5.88092e13 | −0.114658 | ||||||||
\(876\) | 3.22553e13 | 0.0625289 | ||||||||
\(877\) | 3.46402e14 | 0.667701 | 0.333851 | − | 0.942626i | \(-0.391652\pi\) | ||||
0.333851 | + | 0.942626i | \(0.391652\pi\) | |||||||
\(878\) | 1.16549e15i | 2.23376i | ||||||||
\(879\) | − | 2.35796e13i | − | 0.0449357i | ||||||
\(880\) | 3.11131e14i | 0.589563i | ||||||||
\(881\) | 2.94182e14 | 0.554289 | 0.277144 | − | 0.960828i | \(-0.410612\pi\) | ||||
0.277144 | + | 0.960828i | \(0.410612\pi\) | |||||||
\(882\) | − | 9.35796e14i | − | 1.75323i | ||||||
\(883\) | −1.25729e14 | −0.234224 | −0.117112 | − | 0.993119i | \(-0.537364\pi\) | ||||
−0.117112 | + | 0.993119i | \(0.537364\pi\) | |||||||
\(884\) | 2.47274e14 | 0.458055 | ||||||||
\(885\) | −2.86895e11 | −0.000528453 | ||||||||
\(886\) | − | 9.41779e14i | − | 1.72496i | ||||||
\(887\) | − | 4.57414e14i | − | 0.833090i | −0.909115 | − | 0.416545i | \(-0.863241\pi\) | ||
0.909115 | − | 0.416545i | \(-0.136759\pi\) | |||||||
\(888\) | 3.41155e13i | 0.0617855i | ||||||||
\(889\) | − | 7.66275e13i | − | 0.137999i | ||||||
\(890\) | − | 1.01562e15i | − | 1.81878i | ||||||
\(891\) | 2.90725e14 | 0.517719 | ||||||||
\(892\) | 1.64393e15i | 2.91112i | ||||||||
\(893\) | − | 7.80858e13i | − | 0.137504i | ||||||
\(894\) | 1.02637e14i | 0.179727i | ||||||||
\(895\) | −5.30850e14 | −0.924393 | ||||||||
\(896\) | 7.88647e13 | 0.136566 | ||||||||
\(897\) | − | 1.56158e13i | − | 0.0268907i | ||||||
\(898\) | −2.53847e13 | −0.0434700 | ||||||||
\(899\) | 6.62238e10i | 0.000112776i | ||||||||
\(900\) | −6.45549e14 | −1.09324 | ||||||||
\(901\) | 1.68549e14 | 0.283858 | ||||||||
\(902\) | 5.63398e14i | 0.943588i | ||||||||
\(903\) | −2.86665e12 | + | 4.07991e12i | −0.00477459 | + | 0.00679535i | ||||
\(904\) | −7.65160e14 | −1.26739 | ||||||||
\(905\) | − | 5.47867e14i | − | 0.902469i | ||||||
\(906\) | 8.83753e13i | 0.144774i | ||||||||
\(907\) | −2.39048e14 | −0.389447 | −0.194724 | − | 0.980858i | \(-0.562381\pi\) | ||||
−0.194724 | + | 0.980858i | \(0.562381\pi\) | |||||||
\(908\) | 1.83962e15i | 2.98056i | ||||||||
\(909\) | 2.32266e14 | 0.374254 | ||||||||
\(910\) | − | 4.49719e13i | − | 0.0720667i | ||||||
\(911\) | − | 5.26630e14i | − | 0.839294i | −0.907687 | − | 0.419647i | \(-0.862154\pi\) | ||
0.907687 | − | 0.419647i | \(-0.137846\pi\) | |||||||
\(912\) | 7.69748e13 | 0.122004 | ||||||||
\(913\) | 2.99084e14 | 0.471454 | ||||||||
\(914\) | −2.17558e14 | −0.341071 | ||||||||
\(915\) | 4.39923e13i | 0.0685916i | ||||||||
\(916\) | −1.96241e15 | −3.04307 | ||||||||
\(917\) | −4.83083e12 | −0.00745032 | ||||||||
\(918\) | 7.04971e13 | 0.108133 | ||||||||
\(919\) | 7.60464e14 | 1.16012 | 0.580058 | − | 0.814575i | \(-0.303030\pi\) | ||||
0.580058 | + | 0.814575i | \(0.303030\pi\) | |||||||
\(920\) | −6.49658e14 | −0.985702 | ||||||||
\(921\) | 4.67062e12i | 0.00704816i | ||||||||
\(922\) | 1.87769e15i | 2.81818i | ||||||||
\(923\) | 2.74226e14i | 0.409356i | ||||||||
\(924\) | 6.43978e12 | 0.00956117 | ||||||||
\(925\) | − | 1.29856e14i | − | 0.191759i | ||||||
\(926\) | 1.76517e15 | 2.59258 | ||||||||
\(927\) | 6.74300e14 | 0.985041 | ||||||||
\(928\) | 1.72618e11 | 0.000250811 | ||||||||
\(929\) | − | 3.27786e14i | − | 0.473709i | −0.971545 | − | 0.236855i | \(-0.923883\pi\) | ||
0.971545 | − | 0.236855i | \(-0.0761165\pi\) | |||||||
\(930\) | 2.17098e13i | 0.0312062i | ||||||||
\(931\) | − | 6.92275e14i | − | 0.989760i | ||||||
\(932\) | 1.42014e15i | 2.01954i | ||||||||
\(933\) | − | 8.45338e13i | − | 0.119570i | ||||||
\(934\) | −1.28147e13 | −0.0180292 | ||||||||
\(935\) | 1.05087e14i | 0.147059i | ||||||||
\(936\) | − | 7.99386e14i | − | 1.11270i | ||||||
\(937\) | 9.81273e14i | 1.35860i | 0.733860 | + | 0.679300i | \(0.237717\pi\) | ||||
−0.733860 | + | 0.679300i | \(0.762283\pi\) | |||||||
\(938\) | 1.35734e14 | 0.186928 | ||||||||
\(939\) | 5.95512e13 | 0.0815760 | ||||||||
\(940\) | − | 1.55114e14i | − | 0.211355i | ||||||
\(941\) | −3.45253e14 | −0.467939 | −0.233969 | − | 0.972244i | \(-0.575172\pi\) | ||||
−0.233969 | + | 0.972244i | \(0.575172\pi\) | |||||||
\(942\) | 1.52166e14i | 0.205146i | ||||||||
\(943\) | −4.95109e14 | −0.663961 | ||||||||
\(944\) | 1.16299e13 | 0.0155138 | ||||||||
\(945\) | − | 8.79516e12i | − | 0.0116704i | ||||||
\(946\) | −5.82997e14 | − | 4.09629e14i | −0.769503 | − | 0.540673i | ||||
\(947\) | −7.34535e13 | −0.0964412 | −0.0482206 | − | 0.998837i | \(-0.515355\pi\) | ||||
−0.0482206 | + | 0.998837i | \(0.515355\pi\) | |||||||
\(948\) | 1.24610e13i | 0.0162746i | ||||||||
\(949\) | − | 1.52034e14i | − | 0.197519i | ||||||
\(950\) | −6.96172e14 | −0.899701 | ||||||||
\(951\) | − | 7.76199e13i | − | 0.0997862i | ||||||
\(952\) | −7.08342e13 | −0.0905855 | ||||||||
\(953\) | 2.74344e14i | 0.349005i | 0.984657 | + | 0.174502i | \(0.0558316\pi\) | ||||
−0.984657 | + | 0.174502i | \(0.944168\pi\) | |||||||
\(954\) | − | 1.00490e15i | − | 1.27169i | ||||||
\(955\) | −2.80080e14 | −0.352586 | ||||||||
\(956\) | 1.56712e13 | 0.0196252 | ||||||||
\(957\) | −1.13212e10 | −1.41037e−5 | ||||||||
\(958\) | 1.12254e15i | 1.39115i | ||||||||
\(959\) | −2.52914e13 | −0.0311803 | ||||||||
\(960\) | −1.34085e13 | −0.0164446 | ||||||||
\(961\) | −7.33915e14 | −0.895424 | ||||||||
\(962\) | 2.96558e14 | 0.359943 | ||||||||
\(963\) | 4.37392e14 | 0.528128 | ||||||||
\(964\) | 4.29771e14i | 0.516241i | ||||||||
\(965\) | − | 2.93254e14i | − | 0.350434i | ||||||
\(966\) | 8.24986e12i | 0.00980756i | ||||||||
\(967\) | −8.62206e14 | −1.01971 | −0.509857 | − | 0.860259i | \(-0.670302\pi\) | ||||
−0.509857 | + | 0.860259i | \(0.670302\pi\) | |||||||
\(968\) | − | 1.29754e15i | − | 1.52667i | ||||||
\(969\) | 2.59988e13 | 0.0304323 | ||||||||
\(970\) | −9.49261e14 | −1.10542 | ||||||||
\(971\) | 8.55599e14 | 0.991230 | 0.495615 | − | 0.868542i | \(-0.334943\pi\) | ||||
0.495615 | + | 0.868542i | \(0.334943\pi\) | |||||||
\(972\) | − | 4.32908e14i | − | 0.498959i | ||||||
\(973\) | 4.06944e13i | 0.0466628i | ||||||||
\(974\) | − | 1.90046e15i | − | 2.16802i | ||||||
\(975\) | − | 1.80242e13i | − | 0.0204566i | ||||||
\(976\) | − | 1.78333e15i | − | 2.01364i | ||||||
\(977\) | 2.37846e14 | 0.267192 | 0.133596 | − | 0.991036i | \(-0.457348\pi\) | ||||
0.133596 | + | 0.991036i | \(0.457348\pi\) | |||||||
\(978\) | − | 1.33551e14i | − | 0.149263i | ||||||
\(979\) | − | 6.85488e14i | − | 0.762231i | ||||||
\(980\) | − | 1.37517e15i | − | 1.52134i | ||||||
\(981\) | 9.90215e14 | 1.08989 | ||||||||
\(982\) | 1.31983e15 | 1.44531 | ||||||||
\(983\) | − | 3.50277e14i | − | 0.381631i | −0.981626 | − | 0.190816i | \(-0.938887\pi\) | ||
0.981626 | − | 0.190816i | \(-0.0611133\pi\) | |||||||
\(984\) | 1.50135e14 | 0.162744 | ||||||||
\(985\) | 6.90862e14i | 0.745093i | ||||||||
\(986\) | 2.29658e11 | 0.000246432 | ||||||||
\(987\) | −1.06806e12 | −0.00114027 | ||||||||
\(988\) | − | 1.09062e15i | − | 1.15848i | ||||||
\(989\) | 3.59978e14 | − | 5.12333e14i | 0.380448 | − | 0.541465i | ||||
\(990\) | 6.26534e14 | 0.658823 | ||||||||
\(991\) | − | 2.02632e14i | − | 0.212002i | −0.994366 | − | 0.106001i | \(-0.966195\pi\) | ||
0.994366 | − | 0.106001i | \(-0.0338047\pi\) | |||||||
\(992\) | − | 2.23418e14i | − | 0.232573i | ||||||
\(993\) | 4.35912e13 | 0.0451495 | ||||||||
\(994\) | − | 1.44875e14i | − | 0.149300i | ||||||
\(995\) | −1.09996e15 | −1.12787 | ||||||||
\(996\) | − | 1.46987e14i | − | 0.149962i | ||||||
\(997\) | − | 2.81153e14i | − | 0.285408i | −0.989765 | − | 0.142704i | \(-0.954420\pi\) | ||
0.989765 | − | 0.142704i | \(-0.0455797\pi\) | |||||||
\(998\) | 4.90136e13 | 0.0495067 | ||||||||
\(999\) | 5.79978e13 | 0.0582886 |
(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 | 43.11.b.b.42.3 | ✓ | 34 | |
43.42 | odd | 2 | inner | 43.11.b.b.42.32 | yes | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.11.b.b.42.3 | ✓ | 34 | 1.1 | even | 1 | trivial | |
43.11.b.b.42.32 | yes | 34 | 43.42 | odd | 2 | inner |