Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,10,Mod(49,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.49");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(38.6276877123\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 15) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.49 |
Dual form | 75.10.b.d.49.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 4.00000i | − 0.176777i | −0.996086 | − | 0.0883883i | \(-0.971828\pi\) | ||||
0.996086 | − | 0.0883883i | \(-0.0281716\pi\) | |||||||
\(3\) | − 81.0000i | − 0.577350i | ||||||||
\(4\) | 496.000 | 0.968750 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −324.000 | −0.102062 | ||||||||
\(7\) | − 7680.00i | − 1.20898i | −0.796612 | − | 0.604491i | \(-0.793376\pi\) | ||||
0.796612 | − | 0.604491i | \(-0.206624\pi\) | |||||||
\(8\) | − 4032.00i | − 0.348029i | ||||||||
\(9\) | −6561.00 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −86404.0 | −1.77937 | −0.889686 | − | 0.456573i | \(-0.849077\pi\) | ||||
−0.889686 | + | 0.456573i | \(0.849077\pi\) | |||||||
\(12\) | − 40176.0i | − 0.559308i | ||||||||
\(13\) | 149978.i | 1.45641i | 0.685361 | + | 0.728203i | \(0.259644\pi\) | ||||
−0.685361 | + | 0.728203i | \(0.740356\pi\) | |||||||
\(14\) | −30720.0 | −0.213720 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 237824. | 0.907227 | ||||||||
\(17\) | − 207622.i | − 0.602911i | −0.953480 | − | 0.301456i | \(-0.902528\pi\) | ||||
0.953480 | − | 0.301456i | \(-0.0974725\pi\) | |||||||
\(18\) | 26244.0i | 0.0589256i | ||||||||
\(19\) | −716284. | −1.26094 | −0.630469 | − | 0.776214i | \(-0.717138\pi\) | ||||
−0.630469 | + | 0.776214i | \(0.717138\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −622080. | −0.698006 | ||||||||
\(22\) | 345616.i | 0.314552i | ||||||||
\(23\) | − 1.36992e6i | − 1.02075i | −0.859952 | − | 0.510376i | \(-0.829506\pi\) | ||||
0.859952 | − | 0.510376i | \(-0.170494\pi\) | |||||||
\(24\) | −326592. | −0.200935 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 599912. | 0.257459 | ||||||||
\(27\) | 531441.i | 0.192450i | ||||||||
\(28\) | − 3.80928e6i | − 1.17120i | ||||||||
\(29\) | 3.19440e6 | 0.838684 | 0.419342 | − | 0.907828i | \(-0.362261\pi\) | ||||
0.419342 | + | 0.907828i | \(0.362261\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.34900e6 | −0.456831 | −0.228415 | − | 0.973564i | \(-0.573354\pi\) | ||||
−0.228415 | + | 0.973564i | \(0.573354\pi\) | |||||||
\(32\) | − 3.01568e6i | − 0.508406i | ||||||||
\(33\) | 6.99872e6i | 1.02732i | ||||||||
\(34\) | −830488. | −0.106581 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.25426e6 | −0.322917 | ||||||||
\(37\) | 1.87357e7i | 1.64347i | 0.569868 | + | 0.821736i | \(0.306994\pi\) | ||||
−0.569868 | + | 0.821736i | \(0.693006\pi\) | |||||||
\(38\) | 2.86514e6i | 0.222905i | ||||||||
\(39\) | 1.21482e7 | 0.840856 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.92826e7 | −1.61839 | −0.809194 | − | 0.587541i | \(-0.800096\pi\) | ||||
−0.809194 | + | 0.587541i | \(0.800096\pi\) | |||||||
\(42\) | 2.48832e6i | 0.123391i | ||||||||
\(43\) | 1.51672e6i | 0.0676548i | 0.999428 | + | 0.0338274i | \(0.0107696\pi\) | ||||
−0.999428 | + | 0.0338274i | \(0.989230\pi\) | |||||||
\(44\) | −4.28564e7 | −1.72377 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.47968e6 | −0.180445 | ||||||||
\(47\) | 615752.i | 0.0184063i | 0.999958 | + | 0.00920313i | \(0.00292949\pi\) | ||||
−0.999958 | + | 0.00920313i | \(0.997071\pi\) | |||||||
\(48\) | − 1.92637e7i | − 0.523788i | ||||||||
\(49\) | −1.86288e7 | −0.461639 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.68174e7 | −0.348091 | ||||||||
\(52\) | 7.43891e7i | 1.41089i | ||||||||
\(53\) | − 4.74743e6i | − 0.0826451i | −0.999146 | − | 0.0413226i | \(-0.986843\pi\) | ||||
0.999146 | − | 0.0413226i | \(-0.0131571\pi\) | |||||||
\(54\) | 2.12576e6 | 0.0340207 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.09658e7 | −0.420761 | ||||||||
\(57\) | 5.80190e7i | 0.728003i | ||||||||
\(58\) | − 1.27776e7i | − 0.148260i | ||||||||
\(59\) | −6.06161e7 | −0.651259 | −0.325630 | − | 0.945497i | \(-0.605576\pi\) | ||||
−0.325630 | + | 0.945497i | \(0.605576\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.26746e8 | −1.17206 | −0.586029 | − | 0.810290i | \(-0.699309\pi\) | ||||
−0.586029 | + | 0.810290i | \(0.699309\pi\) | |||||||
\(62\) | 9.39600e6i | 0.0807570i | ||||||||
\(63\) | 5.03885e7i | 0.402994i | ||||||||
\(64\) | 1.09703e8 | 0.817352 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.79949e7 | 0.181606 | ||||||||
\(67\) | − 1.11183e8i | − 0.674063i | −0.941493 | − | 0.337031i | \(-0.890577\pi\) | ||||
0.941493 | − | 0.337031i | \(-0.109423\pi\) | |||||||
\(68\) | − 1.02981e8i | − 0.584070i | ||||||||
\(69\) | −1.10964e8 | −0.589331 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.75552e8 | −0.819865 | −0.409932 | − | 0.912116i | \(-0.634448\pi\) | ||||
−0.409932 | + | 0.912116i | \(0.634448\pi\) | |||||||
\(72\) | 2.64540e7i | 0.116010i | ||||||||
\(73\) | 6.12334e7i | 0.252369i | 0.992007 | + | 0.126184i | \(0.0402731\pi\) | ||||
−0.992007 | + | 0.126184i | \(0.959727\pi\) | |||||||
\(74\) | 7.49428e7 | 0.290528 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.55277e8 | −1.22153 | ||||||||
\(77\) | 6.63583e8i | 2.15123i | ||||||||
\(78\) | − 4.85929e7i | − 0.148644i | ||||||||
\(79\) | −2.34431e8 | −0.677163 | −0.338582 | − | 0.940937i | \(-0.609947\pi\) | ||||
−0.338582 | + | 0.940937i | \(0.609947\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 1.17131e8i | 0.286093i | ||||||||
\(83\) | − 1.18910e8i | − 0.275023i | −0.990500 | − | 0.137511i | \(-0.956090\pi\) | ||||
0.990500 | − | 0.137511i | \(-0.0439103\pi\) | |||||||
\(84\) | −3.08552e8 | −0.676194 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.06690e6 | 0.0119598 | ||||||||
\(87\) | − 2.58747e8i | − 0.484215i | ||||||||
\(88\) | 3.48381e8i | 0.619273i | ||||||||
\(89\) | 3.16534e8 | 0.534768 | 0.267384 | − | 0.963590i | \(-0.413841\pi\) | ||||
0.267384 | + | 0.963590i | \(0.413841\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.15183e9 | 1.76077 | ||||||||
\(92\) | − 6.79480e8i | − 0.988853i | ||||||||
\(93\) | 1.90269e8i | 0.263751i | ||||||||
\(94\) | 2.46301e6 | 0.00325380 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.44270e8 | −0.293528 | ||||||||
\(97\) | 2.42912e8i | 0.278597i | 0.990250 | + | 0.139299i | \(0.0444848\pi\) | ||||
−0.990250 | + | 0.139299i | \(0.955515\pi\) | |||||||
\(98\) | 7.45152e7i | 0.0816070i | ||||||||
\(99\) | 5.66897e8 | 0.593124 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.53803e8 | −0.625173 | −0.312587 | − | 0.949889i | \(-0.601195\pi\) | ||||
−0.312587 | + | 0.949889i | \(0.601195\pi\) | |||||||
\(102\) | 6.72695e7i | 0.0615343i | ||||||||
\(103\) | − 1.40420e9i | − 1.22931i | −0.788795 | − | 0.614656i | \(-0.789295\pi\) | ||||
0.788795 | − | 0.614656i | \(-0.210705\pi\) | |||||||
\(104\) | 6.04711e8 | 0.506872 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.89897e7 | −0.0146097 | ||||||||
\(107\) | − 1.83854e9i | − 1.35595i | −0.735083 | − | 0.677977i | \(-0.762857\pi\) | ||||
0.735083 | − | 0.677977i | \(-0.237143\pi\) | |||||||
\(108\) | 2.63595e8i | 0.186436i | ||||||||
\(109\) | 9.33452e8 | 0.633392 | 0.316696 | − | 0.948527i | \(-0.397426\pi\) | ||||
0.316696 | + | 0.948527i | \(0.397426\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.51759e9 | 0.948859 | ||||||||
\(112\) | − 1.82649e9i | − 1.09682i | ||||||||
\(113\) | 9.28534e7i | 0.0535728i | 0.999641 | + | 0.0267864i | \(0.00852740\pi\) | ||||
−0.999641 | + | 0.0267864i | \(0.991473\pi\) | |||||||
\(114\) | 2.32076e8 | 0.128694 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.58442e9 | 0.812476 | ||||||||
\(117\) | − 9.84006e8i | − 0.485469i | ||||||||
\(118\) | 2.42464e8i | 0.115127i | ||||||||
\(119\) | −1.59454e9 | −0.728909 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.10770e9 | 2.16616 | ||||||||
\(122\) | 5.06983e8i | 0.207192i | ||||||||
\(123\) | 2.37189e9i | 0.934377i | ||||||||
\(124\) | −1.16510e9 | −0.442555 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.01554e8 | 0.0712400 | ||||||||
\(127\) | 1.73819e9i | 0.592900i | 0.955048 | + | 0.296450i | \(0.0958028\pi\) | ||||
−0.955048 | + | 0.296450i | \(0.904197\pi\) | |||||||
\(128\) | − 1.98284e9i | − 0.652894i | ||||||||
\(129\) | 1.22855e8 | 0.0390605 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.49730e9 | −0.740882 | −0.370441 | − | 0.928856i | \(-0.620793\pi\) | ||||
−0.370441 | + | 0.928856i | \(0.620793\pi\) | |||||||
\(132\) | 3.47137e9i | 0.995217i | ||||||||
\(133\) | 5.50106e9i | 1.52445i | ||||||||
\(134\) | −4.44731e8 | −0.119159 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.37132e8 | −0.209831 | ||||||||
\(137\) | − 7.96226e9i | − 1.93105i | −0.260306 | − | 0.965526i | \(-0.583823\pi\) | ||||
0.260306 | − | 0.965526i | \(-0.416177\pi\) | |||||||
\(138\) | 4.43854e8i | 0.104180i | ||||||||
\(139\) | 2.85565e9 | 0.648842 | 0.324421 | − | 0.945913i | \(-0.394831\pi\) | ||||
0.324421 | + | 0.945913i | \(0.394831\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.98759e7 | 0.0106269 | ||||||||
\(142\) | 7.02206e8i | 0.144933i | ||||||||
\(143\) | − 1.29587e10i | − 2.59149i | ||||||||
\(144\) | −1.56036e9 | −0.302409 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.44933e8 | 0.0446129 | ||||||||
\(147\) | 1.50893e9i | 0.266527i | ||||||||
\(148\) | 9.29291e9i | 1.59211i | ||||||||
\(149\) | 9.63383e9 | 1.60126 | 0.800628 | − | 0.599161i | \(-0.204499\pi\) | ||||
0.800628 | + | 0.599161i | \(0.204499\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.38292e9 | −0.842601 | −0.421300 | − | 0.906921i | \(-0.638426\pi\) | ||||
−0.421300 | + | 0.906921i | \(0.638426\pi\) | |||||||
\(152\) | 2.88806e9i | 0.438843i | ||||||||
\(153\) | 1.36221e9i | 0.200970i | ||||||||
\(154\) | 2.65433e9 | 0.380287 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.02552e9 | 0.814580 | ||||||||
\(157\) | 5.19434e8i | 0.0682310i | 0.999418 | + | 0.0341155i | \(0.0108614\pi\) | ||||
−0.999418 | + | 0.0341155i | \(0.989139\pi\) | |||||||
\(158\) | 9.37725e8i | 0.119707i | ||||||||
\(159\) | −3.84542e8 | −0.0477152 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.05210e10 | −1.23407 | ||||||||
\(162\) | − 1.72187e8i | − 0.0196419i | ||||||||
\(163\) | − 9.41239e9i | − 1.04437i | −0.852831 | − | 0.522187i | \(-0.825116\pi\) | ||||
0.852831 | − | 0.522187i | \(-0.174884\pi\) | |||||||
\(164\) | −1.45242e10 | −1.56781 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.75642e8 | −0.0486176 | ||||||||
\(167\) | 9.37241e9i | 0.932453i | 0.884665 | + | 0.466227i | \(0.154387\pi\) | ||||
−0.884665 | + | 0.466227i | \(0.845613\pi\) | |||||||
\(168\) | 2.50823e9i | 0.242927i | ||||||||
\(169\) | −1.18889e10 | −1.12112 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.69954e9 | 0.420313 | ||||||||
\(172\) | 7.52295e8i | 0.0655406i | ||||||||
\(173\) | − 1.23573e10i | − 1.04886i | −0.851455 | − | 0.524428i | \(-0.824279\pi\) | ||||
0.851455 | − | 0.524428i | \(-0.175721\pi\) | |||||||
\(174\) | −1.03499e9 | −0.0855979 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.05489e10 | −1.61429 | ||||||||
\(177\) | 4.90990e9i | 0.376005i | ||||||||
\(178\) | − 1.26614e9i | − 0.0945346i | ||||||||
\(179\) | 6.66040e8 | 0.0484910 | 0.0242455 | − | 0.999706i | \(-0.492282\pi\) | ||||
0.0242455 | + | 0.999706i | \(0.492282\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.27207e9 | 0.365113 | 0.182557 | − | 0.983195i | \(-0.441563\pi\) | ||||
0.182557 | + | 0.983195i | \(0.441563\pi\) | |||||||
\(182\) | − 4.60732e9i | − 0.311263i | ||||||||
\(183\) | 1.02664e10i | 0.676688i | ||||||||
\(184\) | −5.52352e9 | −0.355251 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 7.61076e8 | 0.0466251 | ||||||||
\(187\) | 1.79394e10i | 1.07280i | ||||||||
\(188\) | 3.05413e8i | 0.0178311i | ||||||||
\(189\) | 4.08147e9 | 0.232669 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.93896e10 | −1.59788 | −0.798939 | − | 0.601412i | \(-0.794605\pi\) | ||||
−0.798939 | + | 0.601412i | \(0.794605\pi\) | |||||||
\(192\) | − 8.88596e9i | − 0.471899i | ||||||||
\(193\) | 1.48746e10i | 0.771681i | 0.922565 | + | 0.385841i | \(0.126089\pi\) | ||||
−0.922565 | + | 0.385841i | \(0.873911\pi\) | |||||||
\(194\) | 9.71649e8 | 0.0492495 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.23988e9 | −0.447213 | ||||||||
\(197\) | 4.98675e9i | 0.235895i | 0.993020 | + | 0.117948i | \(0.0376315\pi\) | ||||
−0.993020 | + | 0.117948i | \(0.962368\pi\) | |||||||
\(198\) | − 2.26759e9i | − 0.104851i | ||||||||
\(199\) | −1.45527e10 | −0.657816 | −0.328908 | − | 0.944362i | \(-0.606681\pi\) | ||||
−0.328908 | + | 0.944362i | \(0.606681\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.00579e9 | −0.389170 | ||||||||
\(202\) | 2.61521e9i | 0.110516i | ||||||||
\(203\) | − 2.45330e10i | − 1.01395i | ||||||||
\(204\) | −8.34142e9 | −0.337213 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.61681e9 | −0.217314 | ||||||||
\(207\) | 8.98805e9i | 0.340250i | ||||||||
\(208\) | 3.56684e10i | 1.32129i | ||||||||
\(209\) | 6.18898e10 | 2.24368 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.15407e10 | 1.79011 | 0.895054 | − | 0.445959i | \(-0.147137\pi\) | ||||
0.895054 | + | 0.445959i | \(0.147137\pi\) | |||||||
\(212\) | − 2.35473e9i | − 0.0800624i | ||||||||
\(213\) | 1.42197e10i | 0.473349i | ||||||||
\(214\) | −7.35414e9 | −0.239701 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.14277e9 | 0.0669782 | ||||||||
\(217\) | 1.80403e10i | 0.552300i | ||||||||
\(218\) | − 3.73381e9i | − 0.111969i | ||||||||
\(219\) | 4.95990e9 | 0.145705 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.11387e10 | 0.878083 | ||||||||
\(222\) | − 6.07037e9i | − 0.167736i | ||||||||
\(223\) | − 4.61272e10i | − 1.24907i | −0.780998 | − | 0.624533i | \(-0.785289\pi\) | ||||
0.780998 | − | 0.624533i | \(-0.214711\pi\) | |||||||
\(224\) | −2.31604e10 | −0.614654 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.71414e8 | 0.00947043 | ||||||||
\(227\) | − 3.75833e10i | − 0.939460i | −0.882810 | − | 0.469730i | \(-0.844351\pi\) | ||||
0.882810 | − | 0.469730i | \(-0.155649\pi\) | |||||||
\(228\) | 2.87774e10i | 0.705253i | ||||||||
\(229\) | 6.41082e10 | 1.54047 | 0.770236 | − | 0.637759i | \(-0.220138\pi\) | ||||
0.770236 | + | 0.637759i | \(0.220138\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.37502e10 | 1.24201 | ||||||||
\(232\) | − 1.28798e10i | − 0.291887i | ||||||||
\(233\) | − 6.96578e10i | − 1.54835i | −0.632973 | − | 0.774174i | \(-0.718166\pi\) | ||||
0.632973 | − | 0.774174i | \(-0.281834\pi\) | |||||||
\(234\) | −3.93602e9 | −0.0858195 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.00656e10 | −0.630907 | ||||||||
\(237\) | 1.89889e10i | 0.390960i | ||||||||
\(238\) | 6.37815e9i | 0.128854i | ||||||||
\(239\) | −6.65825e10 | −1.31999 | −0.659993 | − | 0.751272i | \(-0.729441\pi\) | ||||
−0.659993 | + | 0.751272i | \(0.729441\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.41659e10 | −0.843354 | −0.421677 | − | 0.906746i | \(-0.638558\pi\) | ||||
−0.421677 | + | 0.906746i | \(0.638558\pi\) | |||||||
\(242\) | − 2.04308e10i | − 0.382927i | ||||||||
\(243\) | − 3.48678e9i | − 0.0641500i | ||||||||
\(244\) | −6.28659e10 | −1.13543 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.48757e9 | 0.165176 | ||||||||
\(247\) | − 1.07427e11i | − 1.83644i | ||||||||
\(248\) | 9.47117e9i | 0.158990i | ||||||||
\(249\) | −9.63174e9 | −0.158784 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.36236e10 | 1.32983 | 0.664916 | − | 0.746918i | \(-0.268467\pi\) | ||||
0.664916 | + | 0.746918i | \(0.268467\pi\) | |||||||
\(252\) | 2.49927e10i | 0.390401i | ||||||||
\(253\) | 1.18367e11i | 1.81630i | ||||||||
\(254\) | 6.95277e9 | 0.104811 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.82367e10 | 0.701936 | ||||||||
\(257\) | − 8.65274e10i | − 1.23724i | −0.785690 | − | 0.618621i | \(-0.787692\pi\) | ||||
0.785690 | − | 0.618621i | \(-0.212308\pi\) | |||||||
\(258\) | − 4.91419e8i | − 0.00690499i | ||||||||
\(259\) | 1.43890e11 | 1.98693 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.09585e10 | −0.279561 | ||||||||
\(262\) | 9.98919e9i | 0.130971i | ||||||||
\(263\) | 9.61535e10i | 1.23927i | 0.784892 | + | 0.619633i | \(0.212718\pi\) | ||||
−0.784892 | + | 0.619633i | \(0.787282\pi\) | |||||||
\(264\) | 2.82189e10 | 0.357538 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.20042e10 | 0.269488 | ||||||||
\(267\) | − 2.56393e10i | − 0.308749i | ||||||||
\(268\) | − 5.51466e10i | − 0.652998i | ||||||||
\(269\) | 1.09505e10 | 0.127511 | 0.0637557 | − | 0.997966i | \(-0.479692\pi\) | ||||
0.0637557 | + | 0.997966i | \(0.479692\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.80287e10 | 0.878805 | 0.439403 | − | 0.898290i | \(-0.355190\pi\) | ||||
0.439403 | + | 0.898290i | \(0.355190\pi\) | |||||||
\(272\) | − 4.93775e10i | − 0.546977i | ||||||||
\(273\) | − 9.32983e10i | − 1.01658i | ||||||||
\(274\) | −3.18491e10 | −0.341365 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.50379e10 | −0.570914 | ||||||||
\(277\) | 6.56840e10i | 0.670349i | 0.942156 | + | 0.335174i | \(0.108795\pi\) | ||||
−0.942156 | + | 0.335174i | \(0.891205\pi\) | |||||||
\(278\) | − 1.14226e10i | − 0.114700i | ||||||||
\(279\) | 1.54118e10 | 0.152277 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.44906e10 | −0.617046 | −0.308523 | − | 0.951217i | \(-0.599835\pi\) | ||||
−0.308523 | + | 0.951217i | \(0.599835\pi\) | |||||||
\(282\) | − 1.99504e8i | − 0.00187858i | ||||||||
\(283\) | − 9.63133e10i | − 0.892580i | −0.894888 | − | 0.446290i | \(-0.852745\pi\) | ||||
0.894888 | − | 0.446290i | \(-0.147255\pi\) | |||||||
\(284\) | −8.70736e10 | −0.794244 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.18348e10 | −0.458115 | ||||||||
\(287\) | 2.24891e11i | 1.95660i | ||||||||
\(288\) | 1.97859e10i | 0.169469i | ||||||||
\(289\) | 7.54810e10 | 0.636498 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.96759e10 | 0.160848 | ||||||||
\(292\) | 3.03717e10i | 0.244482i | ||||||||
\(293\) | − 8.16308e10i | − 0.647068i | −0.946217 | − | 0.323534i | \(-0.895129\pi\) | ||||
0.946217 | − | 0.323534i | \(-0.104871\pi\) | |||||||
\(294\) | 6.03573e9 | 0.0471158 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7.55424e10 | 0.571976 | ||||||||
\(297\) | − 4.59186e10i | − 0.342440i | ||||||||
\(298\) | − 3.85353e10i | − 0.283065i | ||||||||
\(299\) | 2.05458e11 | 1.48663 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.16484e10 | 0.0817935 | ||||||||
\(302\) | 2.15317e10i | 0.148952i | ||||||||
\(303\) | 5.29580e10i | 0.360944i | ||||||||
\(304\) | −1.70350e11 | −1.14396 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 5.44883e9 | 0.0355269 | ||||||||
\(307\) | − 2.95582e10i | − 0.189914i | −0.995481 | − | 0.0949568i | \(-0.969729\pi\) | ||||
0.995481 | − | 0.0949568i | \(-0.0302713\pi\) | |||||||
\(308\) | 3.29137e11i | 2.08400i | ||||||||
\(309\) | −1.13740e11 | −0.709744 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.99071e10 | −0.241896 | −0.120948 | − | 0.992659i | \(-0.538593\pi\) | ||||
−0.120948 | + | 0.992659i | \(0.538593\pi\) | |||||||
\(312\) | − 4.89816e10i | − 0.292643i | ||||||||
\(313\) | − 1.85371e11i | − 1.09167i | −0.837892 | − | 0.545836i | \(-0.816212\pi\) | ||||
0.837892 | − | 0.545836i | \(-0.183788\pi\) | |||||||
\(314\) | 2.07774e9 | 0.0120617 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.16278e11 | −0.656002 | ||||||||
\(317\) | 2.68895e11i | 1.49560i | 0.663924 | + | 0.747800i | \(0.268890\pi\) | ||||
−0.663924 | + | 0.747800i | \(0.731110\pi\) | |||||||
\(318\) | 1.53817e9i | 0.00843493i | ||||||||
\(319\) | −2.76009e11 | −1.49233 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.48921e11 | −0.782860 | ||||||||
\(322\) | 4.20839e10i | 0.218155i | ||||||||
\(323\) | 1.48716e11i | 0.760234i | ||||||||
\(324\) | 2.13512e10 | 0.107639 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.76496e10 | −0.184621 | ||||||||
\(327\) | − 7.56096e10i | − 0.365689i | ||||||||
\(328\) | 1.18068e11i | 0.563246i | ||||||||
\(329\) | 4.72898e9 | 0.0222528 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.29099e11 | −1.96486 | −0.982430 | − | 0.186629i | \(-0.940244\pi\) | ||||
−0.982430 | + | 0.186629i | \(0.940244\pi\) | |||||||
\(332\) | − 5.89796e10i | − 0.266428i | ||||||||
\(333\) | − 1.22925e11i | − 0.547824i | ||||||||
\(334\) | 3.74896e10 | 0.164836 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.47946e11 | −0.633250 | ||||||||
\(337\) | − 2.02598e10i | − 0.0855657i | −0.999084 | − | 0.0427828i | \(-0.986378\pi\) | ||||
0.999084 | − | 0.0427828i | \(-0.0136224\pi\) | |||||||
\(338\) | 4.75556e10i | 0.198188i | ||||||||
\(339\) | 7.52112e9 | 0.0309303 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.02963e11 | 0.812872 | ||||||||
\(342\) | − 1.87982e10i | − 0.0743015i | ||||||||
\(343\) | − 1.66847e11i | − 0.650869i | ||||||||
\(344\) | 6.11543e9 | 0.0235458 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.94292e10 | −0.185413 | ||||||||
\(347\) | 2.92783e10i | 0.108409i | 0.998530 | + | 0.0542043i | \(0.0172622\pi\) | ||||
−0.998530 | + | 0.0542043i | \(0.982738\pi\) | |||||||
\(348\) | − 1.28338e11i | − 0.469083i | ||||||||
\(349\) | −7.05132e10 | −0.254423 | −0.127211 | − | 0.991876i | \(-0.540603\pi\) | ||||
−0.127211 | + | 0.991876i | \(0.540603\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.97045e10 | −0.280285 | ||||||||
\(352\) | 2.60567e11i | 0.904643i | ||||||||
\(353\) | 6.57350e10i | 0.225325i | 0.993633 | + | 0.112663i | \(0.0359380\pi\) | ||||
−0.993633 | + | 0.112663i | \(0.964062\pi\) | |||||||
\(354\) | 1.96396e10 | 0.0664688 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.57001e11 | 0.518057 | ||||||||
\(357\) | 1.29157e11i | 0.420836i | ||||||||
\(358\) | − 2.66416e9i | − 0.00857209i | ||||||||
\(359\) | −5.81702e11 | −1.84831 | −0.924157 | − | 0.382013i | \(-0.875231\pi\) | ||||
−0.924157 | + | 0.382013i | \(0.875231\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.90375e11 | 0.589967 | ||||||||
\(362\) | − 2.10883e10i | − 0.0645435i | ||||||||
\(363\) | − 4.13724e11i | − 1.25064i | ||||||||
\(364\) | 5.71308e11 | 1.70575 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.10656e10 | 0.119623 | ||||||||
\(367\) | − 4.17070e11i | − 1.20008i | −0.799969 | − | 0.600042i | \(-0.795151\pi\) | ||||
0.799969 | − | 0.600042i | \(-0.204849\pi\) | |||||||
\(368\) | − 3.25800e11i | − 0.926053i | ||||||||
\(369\) | 1.92123e11 | 0.539463 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.64603e10 | −0.0999165 | ||||||||
\(372\) | 9.43734e10i | 0.255509i | ||||||||
\(373\) | 7.60417e10i | 0.203405i | 0.994815 | + | 0.101703i | \(0.0324290\pi\) | ||||
−0.994815 | + | 0.101703i | \(0.967571\pi\) | |||||||
\(374\) | 7.17575e10 | 0.189647 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.48271e9 | 0.00640591 | ||||||||
\(377\) | 4.79090e11i | 1.22147i | ||||||||
\(378\) | − 1.63259e10i | − 0.0411304i | ||||||||
\(379\) | 1.79180e11 | 0.446080 | 0.223040 | − | 0.974809i | \(-0.428402\pi\) | ||||
0.223040 | + | 0.974809i | \(0.428402\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.40794e11 | 0.342311 | ||||||||
\(382\) | 1.17558e11i | 0.282467i | ||||||||
\(383\) | 7.95018e11i | 1.88792i | 0.330066 | + | 0.943958i | \(0.392929\pi\) | ||||
−0.330066 | + | 0.943958i | \(0.607071\pi\) | |||||||
\(384\) | −1.60610e11 | −0.376949 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.94985e10 | 0.136415 | ||||||||
\(387\) | − 9.95123e9i | − 0.0225516i | ||||||||
\(388\) | 1.20484e11i | 0.269891i | ||||||||
\(389\) | 1.79533e11 | 0.397532 | 0.198766 | − | 0.980047i | \(-0.436307\pi\) | ||||
0.198766 | + | 0.980047i | \(0.436307\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.84426e11 | −0.615422 | ||||||||
\(392\) | 7.51113e10i | 0.160664i | ||||||||
\(393\) | 2.02281e11i | 0.427749i | ||||||||
\(394\) | 1.99470e10 | 0.0417008 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.81181e11 | 0.574589 | ||||||||
\(397\) | − 3.43730e11i | − 0.694480i | −0.937776 | − | 0.347240i | \(-0.887119\pi\) | ||||
0.937776 | − | 0.347240i | \(-0.112881\pi\) | |||||||
\(398\) | 5.82108e10i | 0.116287i | ||||||||
\(399\) | 4.45586e11 | 0.880143 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.72080e11 | 1.49112 | 0.745560 | − | 0.666438i | \(-0.232182\pi\) | ||||
0.745560 | + | 0.666438i | \(0.232182\pi\) | |||||||
\(402\) | 3.60232e10i | 0.0687963i | ||||||||
\(403\) | − 3.52298e11i | − 0.665331i | ||||||||
\(404\) | −3.24286e11 | −0.605637 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.81320e10 | −0.179244 | ||||||||
\(407\) | − 1.61884e12i | − 2.92435i | ||||||||
\(408\) | 6.78077e10i | 0.121146i | ||||||||
\(409\) | −2.60632e11 | −0.460546 | −0.230273 | − | 0.973126i | \(-0.573962\pi\) | ||||
−0.230273 | + | 0.973126i | \(0.573962\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.44943e11 | −1.11489 | ||||||||
\(412\) | − 6.96484e11i | − 1.19090i | ||||||||
\(413\) | 4.65531e11i | 0.787361i | ||||||||
\(414\) | 3.59522e10 | 0.0601483 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.52286e11 | 0.740445 | ||||||||
\(417\) | − 2.31308e11i | − 0.374609i | ||||||||
\(418\) | − 2.47559e11i | − 0.396630i | ||||||||
\(419\) | 5.60166e11 | 0.887879 | 0.443939 | − | 0.896057i | \(-0.353581\pi\) | ||||
0.443939 | + | 0.896057i | \(0.353581\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.68321e11 | 0.261137 | 0.130569 | − | 0.991439i | \(-0.458320\pi\) | ||||
0.130569 | + | 0.991439i | \(0.458320\pi\) | |||||||
\(422\) | − 2.06163e11i | − 0.316449i | ||||||||
\(423\) | − 4.03995e9i | − 0.00613542i | ||||||||
\(424\) | −1.91416e10 | −0.0287629 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.68787e10 | 0.0836771 | ||||||||
\(427\) | 9.73407e11i | 1.41700i | ||||||||
\(428\) | − 9.11913e11i | − 1.31358i | ||||||||
\(429\) | −1.04965e12 | −1.49620 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.48383e11 | 0.625895 | 0.312948 | − | 0.949770i | \(-0.398684\pi\) | ||||
0.312948 | + | 0.949770i | \(0.398684\pi\) | |||||||
\(432\) | 1.26389e11i | 0.174596i | ||||||||
\(433\) | 1.08485e12i | 1.48311i | 0.670891 | + | 0.741556i | \(0.265912\pi\) | ||||
−0.670891 | + | 0.741556i | \(0.734088\pi\) | |||||||
\(434\) | 7.21613e10 | 0.0976339 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.62992e11 | 0.613599 | ||||||||
\(437\) | 9.81252e11i | 1.28711i | ||||||||
\(438\) | − 1.98396e10i | − 0.0257573i | ||||||||
\(439\) | −4.60548e11 | −0.591814 | −0.295907 | − | 0.955217i | \(-0.595622\pi\) | ||||
−0.295907 | + | 0.955217i | \(0.595622\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.22224e11 | 0.153880 | ||||||||
\(442\) | − 1.24555e11i | − 0.155225i | ||||||||
\(443\) | 1.32095e10i | 0.0162956i | 0.999967 | + | 0.00814779i | \(0.00259355\pi\) | ||||
−0.999967 | + | 0.00814779i | \(0.997406\pi\) | |||||||
\(444\) | 7.52726e11 | 0.919207 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.84509e11 | −0.220806 | ||||||||
\(447\) | − 7.80341e11i | − 0.924486i | ||||||||
\(448\) | − 8.42520e11i | − 0.988165i | ||||||||
\(449\) | 6.91889e11 | 0.803393 | 0.401696 | − | 0.915773i | \(-0.368421\pi\) | ||||
0.401696 | + | 0.915773i | \(0.368421\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.53014e12 | 2.87971 | ||||||||
\(452\) | 4.60553e10i | 0.0518987i | ||||||||
\(453\) | 4.36017e11i | 0.486476i | ||||||||
\(454\) | −1.50333e11 | −0.166075 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.33933e11 | 0.253366 | ||||||||
\(457\) | − 3.73135e11i | − 0.400168i | −0.979779 | − | 0.200084i | \(-0.935878\pi\) | ||||
0.979779 | − | 0.200084i | \(-0.0641216\pi\) | |||||||
\(458\) | − 2.56433e11i | − 0.272320i | ||||||||
\(459\) | 1.10339e11 | 0.116030 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.45940e12 | −1.50494 | −0.752470 | − | 0.658627i | \(-0.771138\pi\) | ||||
−0.752470 | + | 0.658627i | \(0.771138\pi\) | |||||||
\(462\) | − 2.15001e11i | − 0.219559i | ||||||||
\(463\) | − 1.34213e11i | − 0.135732i | −0.997694 | − | 0.0678658i | \(-0.978381\pi\) | ||||
0.997694 | − | 0.0678658i | \(-0.0216190\pi\) | |||||||
\(464\) | 7.59705e11 | 0.760877 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.78631e11 | −0.273712 | ||||||||
\(467\) | − 3.64531e10i | − 0.0354657i | −0.999843 | − | 0.0177329i | \(-0.994355\pi\) | ||||
0.999843 | − | 0.0177329i | \(-0.00564484\pi\) | |||||||
\(468\) | − 4.88067e11i | − 0.470298i | ||||||||
\(469\) | −8.53883e11 | −0.814930 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.20741e10 | 0.0393932 | ||||||||
\(472\) | 2.44404e11i | 0.226657i | ||||||||
\(473\) | − 1.31051e11i | − 0.120383i | ||||||||
\(474\) | 7.59557e10 | 0.0691127 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.90890e11 | −0.706131 | ||||||||
\(477\) | 3.11479e10i | 0.0275484i | ||||||||
\(478\) | 2.66330e11i | 0.233343i | ||||||||
\(479\) | −8.82280e11 | −0.765767 | −0.382883 | − | 0.923797i | \(-0.625069\pi\) | ||||
−0.382883 | + | 0.923797i | \(0.625069\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.80994e12 | −2.39356 | ||||||||
\(482\) | 1.76663e11i | 0.149085i | ||||||||
\(483\) | 8.52200e11i | 0.712491i | ||||||||
\(484\) | 2.53342e12 | 2.09847 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.39471e10 | −0.0113402 | ||||||||
\(487\) | 5.09840e11i | 0.410727i | 0.978686 | + | 0.205364i | \(0.0658377\pi\) | ||||
−0.978686 | + | 0.205364i | \(0.934162\pi\) | |||||||
\(488\) | 5.11039e11i | 0.407910i | ||||||||
\(489\) | −7.62404e11 | −0.602969 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.52131e12 | −1.18128 | −0.590638 | − | 0.806937i | \(-0.701124\pi\) | ||||
−0.590638 | + | 0.806937i | \(0.701124\pi\) | |||||||
\(492\) | 1.17646e12i | 0.905178i | ||||||||
\(493\) | − 6.63228e11i | − 0.505652i | ||||||||
\(494\) | −4.29707e11 | −0.324640 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.58649e11 | −0.414449 | ||||||||
\(497\) | 1.34824e12i | 0.991202i | ||||||||
\(498\) | 3.85270e10i | 0.0280694i | ||||||||
\(499\) | −7.03413e11 | −0.507876 | −0.253938 | − | 0.967220i | \(-0.581726\pi\) | ||||
−0.253938 | + | 0.967220i | \(0.581726\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.59165e11 | 0.538352 | ||||||||
\(502\) | − 3.34494e11i | − 0.235083i | ||||||||
\(503\) | − 3.78018e8i | 0 0.000263304i | −1.00000 | 0.000131652i | \(-0.999958\pi\) | |||||
1.00000 | 0.000131652i | \(-4.19061e-5\pi\) | ||||||||
\(504\) | 2.03166e11 | 0.140254 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.73466e11 | 0.321079 | ||||||||
\(507\) | 9.63001e11i | 0.647278i | ||||||||
\(508\) | 8.62144e11i | 0.574372i | ||||||||
\(509\) | −1.32057e12 | −0.872027 | −0.436013 | − | 0.899940i | \(-0.643610\pi\) | ||||
−0.436013 | + | 0.899940i | \(0.643610\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.70272e11 | 0.305109 | ||||||||
\(512\) | − 1.20816e12i | − 0.776980i | ||||||||
\(513\) | − 3.80663e11i | − 0.242668i | ||||||||
\(514\) | −3.46110e11 | −0.218715 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 6.09359e10 | 0.0378399 | ||||||||
\(517\) | − 5.32034e10i | − 0.0327516i | ||||||||
\(518\) | − 5.75561e11i | − 0.351243i | ||||||||
\(519\) | −1.00094e12 | −0.605558 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.31853e12 | −0.784009 | −0.392005 | − | 0.919963i | \(-0.628218\pi\) | ||||
−0.392005 | + | 0.919963i | \(0.628218\pi\) | |||||||
\(522\) | 8.38339e10i | 0.0494200i | ||||||||
\(523\) | 1.69211e12i | 0.988945i | 0.869193 | + | 0.494472i | \(0.164639\pi\) | ||||
−0.869193 | + | 0.494472i | \(0.835361\pi\) | |||||||
\(524\) | −1.23866e12 | −0.717730 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.84614e11 | 0.219073 | ||||||||
\(527\) | 4.87704e11i | 0.275428i | ||||||||
\(528\) | 1.66446e12i | 0.932013i | ||||||||
\(529\) | −7.55281e10 | −0.0419332 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.97702e11 | 0.217086 | ||||||||
\(532\) | 2.72853e12i | 1.47681i | ||||||||
\(533\) | − 4.39175e12i | − 2.35703i | ||||||||
\(534\) | −1.02557e11 | −0.0545796 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.48288e11 | −0.234594 | ||||||||
\(537\) | − 5.39492e10i | − 0.0279963i | ||||||||
\(538\) | − 4.38021e10i | − 0.0225411i | ||||||||
\(539\) | 1.60960e12 | 0.821427 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.86369e12 | −0.935373 | −0.467687 | − | 0.883894i | \(-0.654912\pi\) | ||||
−0.467687 | + | 0.883894i | \(0.654912\pi\) | |||||||
\(542\) | − 3.12115e11i | − 0.155352i | ||||||||
\(543\) | − 4.27037e11i | − 0.210798i | ||||||||
\(544\) | −6.26122e11 | −0.306523 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.73193e11 | −0.179708 | ||||||||
\(547\) | 4.37242e11i | 0.208823i | 0.994534 | + | 0.104412i | \(0.0332959\pi\) | ||||
−0.994534 | + | 0.104412i | \(0.966704\pi\) | |||||||
\(548\) | − 3.94928e12i | − 1.87071i | ||||||||
\(549\) | 8.31578e11 | 0.390686 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.28810e12 | −1.05753 | ||||||||
\(552\) | 4.47405e11i | 0.205104i | ||||||||
\(553\) | 1.80043e12i | 0.818679i | ||||||||
\(554\) | 2.62736e11 | 0.118502 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.41640e12 | 0.628565 | ||||||||
\(557\) | − 7.09146e11i | − 0.312167i | −0.987744 | − | 0.156084i | \(-0.950113\pi\) | ||||
0.987744 | − | 0.156084i | \(-0.0498869\pi\) | |||||||
\(558\) | − 6.16472e10i | − 0.0269190i | ||||||||
\(559\) | −2.27475e11 | −0.0985328 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.45309e12 | 0.619383 | ||||||||
\(562\) | 2.57962e11i | 0.109079i | ||||||||
\(563\) | − 3.77472e10i | − 0.0158342i | −0.999969 | − | 0.00791711i | \(-0.997480\pi\) | ||||
0.999969 | − | 0.00791711i | \(-0.00252012\pi\) | |||||||
\(564\) | 2.47385e10 | 0.0102948 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.85253e11 | −0.157787 | ||||||||
\(567\) | − 3.30599e11i | − 0.134331i | ||||||||
\(568\) | 7.07824e11i | 0.285337i | ||||||||
\(569\) | 3.56270e11 | 0.142487 | 0.0712433 | − | 0.997459i | \(-0.477303\pi\) | ||||
0.0712433 | + | 0.997459i | \(0.477303\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.87932e12 | 1.52719 | 0.763596 | − | 0.645694i | \(-0.223432\pi\) | ||||
0.763596 | + | 0.645694i | \(0.223432\pi\) | |||||||
\(572\) | − 6.42751e12i | − 2.51050i | ||||||||
\(573\) | 2.38056e12i | 0.922535i | ||||||||
\(574\) | 8.99562e11 | 0.345882 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −7.19762e11 | −0.272451 | ||||||||
\(577\) | − 4.28876e12i | − 1.61080i | −0.592734 | − | 0.805399i | \(-0.701951\pi\) | ||||
0.592734 | − | 0.805399i | \(-0.298049\pi\) | |||||||
\(578\) | − 3.01924e11i | − 0.112518i | ||||||||
\(579\) | 1.20484e12 | 0.445530 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.13232e11 | −0.332498 | ||||||||
\(582\) | − 7.87036e10i | − 0.0284342i | ||||||||
\(583\) | 4.10197e11i | 0.147056i | ||||||||
\(584\) | 2.46893e11 | 0.0878316 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.26523e11 | −0.114387 | ||||||||
\(587\) | 4.43245e12i | 1.54089i | 0.637504 | + | 0.770447i | \(0.279967\pi\) | ||||
−0.637504 | + | 0.770447i | \(0.720033\pi\) | |||||||
\(588\) | 7.48430e11i | 0.258198i | ||||||||
\(589\) | 1.68255e12 | 0.576036 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.03927e11 | 0.136194 | ||||||||
\(592\) | 4.45580e12i | 1.49100i | ||||||||
\(593\) | 5.10104e12i | 1.69400i | 0.531596 | + | 0.846998i | \(0.321593\pi\) | ||||
−0.531596 | + | 0.846998i | \(0.678407\pi\) | |||||||
\(594\) | −1.83675e11 | −0.0605355 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.77838e12 | 1.55122 | ||||||||
\(597\) | 1.17877e12i | 0.379790i | ||||||||
\(598\) | − 8.21831e11i | − 0.262801i | ||||||||
\(599\) | 7.04599e11 | 0.223626 | 0.111813 | − | 0.993729i | \(-0.464334\pi\) | ||||
0.111813 | + | 0.993729i | \(0.464334\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.73879e12 | −0.543641 | −0.271821 | − | 0.962348i | \(-0.587626\pi\) | ||||
−0.271821 | + | 0.962348i | \(0.587626\pi\) | |||||||
\(602\) | − 4.65938e10i | − 0.0144592i | ||||||||
\(603\) | 7.29469e11i | 0.224688i | ||||||||
\(604\) | −2.66993e12 | −0.816269 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.11832e11 | 0.0638065 | ||||||||
\(607\) | − 5.78292e11i | − 0.172901i | −0.996256 | − | 0.0864507i | \(-0.972447\pi\) | ||||
0.996256 | − | 0.0864507i | \(-0.0275525\pi\) | |||||||
\(608\) | 2.16008e12i | 0.641068i | ||||||||
\(609\) | −1.98717e12 | −0.585407 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.23493e10 | −0.0268070 | ||||||||
\(612\) | 6.75655e11i | 0.194690i | ||||||||
\(613\) | − 3.74595e12i | − 1.07150i | −0.844378 | − | 0.535748i | \(-0.820030\pi\) | ||||
0.844378 | − | 0.535748i | \(-0.179970\pi\) | |||||||
\(614\) | −1.18233e11 | −0.0335723 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.67557e12 | 0.748691 | ||||||||
\(617\) | − 3.94875e12i | − 1.09692i | −0.836176 | − | 0.548461i | \(-0.815214\pi\) | ||||
0.836176 | − | 0.548461i | \(-0.184786\pi\) | |||||||
\(618\) | 4.54962e11i | 0.125466i | ||||||||
\(619\) | −3.42253e12 | −0.937000 | −0.468500 | − | 0.883463i | \(-0.655205\pi\) | ||||
−0.468500 | + | 0.883463i | \(0.655205\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.28032e11 | 0.196444 | ||||||||
\(622\) | 1.59628e11i | 0.0427615i | ||||||||
\(623\) | − 2.43098e12i | − 0.646526i | ||||||||
\(624\) | 2.88914e12 | 0.762847 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −7.41484e11 | −0.192982 | ||||||||
\(627\) | − 5.01307e12i | − 1.29539i | ||||||||
\(628\) | 2.57639e11i | 0.0660988i | ||||||||
\(629\) | 3.88995e12 | 0.990868 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.84755e12 | 1.46839 | 0.734196 | − | 0.678938i | \(-0.237560\pi\) | ||||
0.734196 | + | 0.678938i | \(0.237560\pi\) | |||||||
\(632\) | 9.45226e11i | 0.235673i | ||||||||
\(633\) | − 4.17479e12i | − 1.03352i | ||||||||
\(634\) | 1.07558e12 | 0.264387 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.90733e11 | −0.0462241 | ||||||||
\(637\) | − 2.79391e12i | − 0.672334i | ||||||||
\(638\) | 1.10404e12i | 0.263809i | ||||||||
\(639\) | 1.15179e12 | 0.273288 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.66671e12 | 0.623899 | 0.311950 | − | 0.950099i | \(-0.399018\pi\) | ||||
0.311950 | + | 0.950099i | \(0.399018\pi\) | |||||||
\(642\) | 5.95685e11i | 0.138391i | ||||||||
\(643\) | − 9.68716e10i | − 0.0223484i | −0.999938 | − | 0.0111742i | \(-0.996443\pi\) | ||||
0.999938 | − | 0.0111742i | \(-0.00355694\pi\) | |||||||
\(644\) | −5.21841e12 | −1.19551 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.94865e11 | 0.134392 | ||||||||
\(647\) | 4.47368e10i | 0.0100368i | 0.999987 | + | 0.00501840i | \(0.00159741\pi\) | ||||
−0.999987 | + | 0.00501840i | \(0.998403\pi\) | |||||||
\(648\) | − 1.73564e11i | − 0.0386699i | ||||||||
\(649\) | 5.23747e12 | 1.15883 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.46127e12 | 0.318871 | ||||||||
\(652\) | − 4.66855e12i | − 1.01174i | ||||||||
\(653\) | − 4.95385e12i | − 1.06619i | −0.846056 | − | 0.533094i | \(-0.821029\pi\) | ||||
0.846056 | − | 0.533094i | \(-0.178971\pi\) | |||||||
\(654\) | −3.02438e11 | −0.0646453 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.96411e12 | −1.46824 | ||||||||
\(657\) | − 4.01752e11i | − 0.0841228i | ||||||||
\(658\) | − 1.89159e10i | − 0.00393378i | ||||||||
\(659\) | 5.85077e12 | 1.20845 | 0.604225 | − | 0.796814i | \(-0.293483\pi\) | ||||
0.604225 | + | 0.796814i | \(0.293483\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.81007e11 | −0.179503 | −0.0897517 | − | 0.995964i | \(-0.528607\pi\) | ||||
−0.0897517 | + | 0.995964i | \(0.528607\pi\) | |||||||
\(662\) | 1.71640e12i | 0.347342i | ||||||||
\(663\) | − 2.52224e12i | − 0.506962i | ||||||||
\(664\) | −4.79447e11 | −0.0957159 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.91700e11 | −0.0968425 | ||||||||
\(667\) | − 4.37608e12i | − 0.856088i | ||||||||
\(668\) | 4.64872e12i | 0.903314i | ||||||||
\(669\) | −3.73630e12 | −0.721149 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.09513e13 | 2.08553 | ||||||||
\(672\) | 1.87599e12i | 0.354870i | ||||||||
\(673\) | 8.66521e12i | 1.62821i | 0.580715 | + | 0.814107i | \(0.302773\pi\) | ||||
−0.580715 | + | 0.814107i | \(0.697227\pi\) | |||||||
\(674\) | −8.10390e10 | −0.0151260 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.89689e12 | −1.08608 | ||||||||
\(677\) | 8.98549e12i | 1.64397i | 0.569512 | + | 0.821983i | \(0.307132\pi\) | ||||
−0.569512 | + | 0.821983i | \(0.692868\pi\) | |||||||
\(678\) | − 3.00845e10i | − 0.00546776i | ||||||||
\(679\) | 1.86557e12 | 0.336819 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.04425e12 | −0.542397 | ||||||||
\(682\) | − 8.11852e11i | − 0.143697i | ||||||||
\(683\) | 3.86477e12i | 0.679564i | 0.940504 | + | 0.339782i | \(0.110353\pi\) | ||||
−0.940504 | + | 0.339782i | \(0.889647\pi\) | |||||||
\(684\) | 2.33097e12 | 0.407178 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.67386e11 | −0.115059 | ||||||||
\(687\) | − 5.19276e12i | − 0.889392i | ||||||||
\(688\) | 3.60713e11i | 0.0613782i | ||||||||
\(689\) | 7.12010e11 | 0.120365 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.08564e12 | −1.18230 | −0.591150 | − | 0.806561i | \(-0.701326\pi\) | ||||
−0.591150 | + | 0.806561i | \(0.701326\pi\) | |||||||
\(692\) | − 6.12922e12i | − 1.01608i | ||||||||
\(693\) | − 4.35377e12i | − 0.717077i | ||||||||
\(694\) | 1.17113e11 | 0.0191641 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.04327e12 | −0.168521 | ||||||||
\(697\) | 6.07972e12i | 0.975744i | ||||||||
\(698\) | 2.82053e11i | 0.0449760i | ||||||||
\(699\) | −5.64229e12 | −0.893939 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.69380e12 | 0.734165 | 0.367083 | − | 0.930188i | \(-0.380357\pi\) | ||||
0.367083 | + | 0.930188i | \(0.380357\pi\) | |||||||
\(702\) | 3.18818e11i | 0.0495479i | ||||||||
\(703\) | − 1.34201e13i | − 2.07232i | ||||||||
\(704\) | −9.47879e12 | −1.45437 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.62940e11 | 0.0398323 | ||||||||
\(707\) | 5.02120e12i | 0.755824i | ||||||||
\(708\) | 2.43531e12i | 0.364254i | ||||||||
\(709\) | −1.06645e13 | −1.58501 | −0.792503 | − | 0.609868i | \(-0.791223\pi\) | ||||
−0.792503 | + | 0.609868i | \(0.791223\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.53810e12 | 0.225721 | ||||||||
\(712\) | − 1.27627e12i | − 0.186115i | ||||||||
\(713\) | 3.21794e12i | 0.466311i | ||||||||
\(714\) | 5.16630e11 | 0.0743940 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.30356e11 | 0.0469757 | ||||||||
\(717\) | 5.39318e12i | 0.762095i | ||||||||
\(718\) | 2.32681e12i | 0.326739i | ||||||||
\(719\) | 8.15663e12 | 1.13823 | 0.569116 | − | 0.822257i | \(-0.307285\pi\) | ||||
0.569116 | + | 0.822257i | \(0.307285\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.07843e13 | −1.48622 | ||||||||
\(722\) | − 7.61500e11i | − 0.104292i | ||||||||
\(723\) | 3.57743e12i | 0.486911i | ||||||||
\(724\) | 2.61495e12 | 0.353703 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.65490e12 | −0.221083 | ||||||||
\(727\) | 6.64771e12i | 0.882606i | 0.897358 | + | 0.441303i | \(0.145484\pi\) | ||||
−0.897358 | + | 0.441303i | \(0.854516\pi\) | |||||||
\(728\) | − 4.64418e12i | − 0.612799i | ||||||||
\(729\) | −2.82430e11 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.14905e11 | 0.0407898 | ||||||||
\(732\) | 5.09213e12i | 0.655541i | ||||||||
\(733\) | − 7.07821e12i | − 0.905640i | −0.891602 | − | 0.452820i | \(-0.850418\pi\) | ||||
0.891602 | − | 0.452820i | \(-0.149582\pi\) | |||||||
\(734\) | −1.66828e12 | −0.212147 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.13124e12 | −0.518956 | ||||||||
\(737\) | 9.60663e12i | 1.19941i | ||||||||
\(738\) | − 7.68493e11i | − 0.0953644i | ||||||||
\(739\) | 2.61052e12 | 0.321979 | 0.160989 | − | 0.986956i | \(-0.448532\pi\) | ||||
0.160989 | + | 0.986956i | \(0.448532\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.70157e12 | −1.06027 | ||||||||
\(742\) | 1.45841e11i | 0.0176629i | ||||||||
\(743\) | 1.41841e13i | 1.70747i | 0.520709 | + | 0.853734i | \(0.325667\pi\) | ||||
−0.520709 | + | 0.853734i | \(0.674333\pi\) | |||||||
\(744\) | 7.67165e11 | 0.0917932 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.04167e11 | 0.0359573 | ||||||||
\(747\) | 7.80171e11i | 0.0916742i | ||||||||
\(748\) | 8.89793e12i | 1.03928i | ||||||||
\(749\) | −1.41199e13 | −1.63932 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.44355e11 | 0.0968603 | 0.0484301 | − | 0.998827i | \(-0.484578\pi\) | ||||
0.0484301 | + | 0.998827i | \(0.484578\pi\) | |||||||
\(752\) | 1.46441e11i | 0.0166986i | ||||||||
\(753\) | − 6.77351e12i | − 0.767779i | ||||||||
\(754\) | 1.91636e12 | 0.215927 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.02441e12 | 0.225398 | ||||||||
\(757\) | 9.05305e12i | 1.00199i | 0.865450 | + | 0.500995i | \(0.167032\pi\) | ||||
−0.865450 | + | 0.500995i | \(0.832968\pi\) | |||||||
\(758\) | − 7.16719e11i | − 0.0788565i | ||||||||
\(759\) | 9.58769e12 | 1.04864 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.97701e12 | −0.754116 | −0.377058 | − | 0.926190i | \(-0.623064\pi\) | ||||
−0.377058 | + | 0.926190i | \(0.623064\pi\) | |||||||
\(762\) | − 5.63174e11i | − 0.0605126i | ||||||||
\(763\) | − 7.16891e12i | − 0.765760i | ||||||||
\(764\) | −1.45772e13 | −1.54794 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.18007e12 | 0.333739 | ||||||||
\(767\) | − 9.09108e12i | − 0.948498i | ||||||||
\(768\) | − 3.90717e12i | − 0.405263i | ||||||||
\(769\) | 1.07233e13 | 1.10576 | 0.552879 | − | 0.833261i | \(-0.313529\pi\) | ||||
0.552879 | + | 0.833261i | \(0.313529\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.00872e12 | −0.714322 | ||||||||
\(772\) | 7.37781e12i | 0.747566i | ||||||||
\(773\) | 1.37568e13i | 1.38583i | 0.721019 | + | 0.692916i | \(0.243674\pi\) | ||||
−0.721019 | + | 0.692916i | \(0.756326\pi\) | |||||||
\(774\) | −3.98049e10 | −0.00398660 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.79422e11 | 0.0969599 | ||||||||
\(777\) | − 1.16551e13i | − 1.14715i | ||||||||
\(778\) | − 7.18134e11i | − 0.0702744i | ||||||||
\(779\) | 2.09747e13 | 2.04069 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.51684e13 | 1.45884 | ||||||||
\(782\) | 1.13770e12i | 0.108792i | ||||||||
\(783\) | 1.69764e12i | 0.161405i | ||||||||
\(784\) | −4.43037e12 | −0.418811 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 8.09124e11 | 0.0756160 | ||||||||
\(787\) | − 1.27539e13i | − 1.18510i | −0.805533 | − | 0.592551i | \(-0.798121\pi\) | ||||
0.805533 | − | 0.592551i | \(-0.201879\pi\) | |||||||
\(788\) | 2.47343e12i | 0.228524i | ||||||||
\(789\) | 7.78843e12 | 0.715490 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.13114e11 | 0.0647686 | ||||||||
\(792\) | − 2.28573e12i | − 0.206424i | ||||||||
\(793\) | − 1.90091e13i | − 1.70699i | ||||||||
\(794\) | −1.37492e12 | −0.122768 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.21814e12 | −0.637260 | ||||||||
\(797\) | 1.27845e13i | 1.12233i | 0.827704 | + | 0.561164i | \(0.189646\pi\) | ||||
−0.827704 | + | 0.561164i | \(0.810354\pi\) | |||||||
\(798\) | − 1.78234e12i | − 0.155589i | ||||||||
\(799\) | 1.27844e11 | 0.0110973 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.07678e12 | −0.178256 | ||||||||
\(802\) | − 3.08832e12i | − 0.263595i | ||||||||
\(803\) | − 5.29081e12i | − 0.449057i | ||||||||
\(804\) | −4.46687e12 | −0.377009 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.40919e12 | −0.117615 | ||||||||
\(807\) | − 8.86992e11i | − 0.0736188i | ||||||||
\(808\) | 2.63613e12i | 0.217579i | ||||||||
\(809\) | −6.03746e12 | −0.495548 | −0.247774 | − | 0.968818i | \(-0.579699\pi\) | ||||
−0.247774 | + | 0.968818i | \(0.579699\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.50043e12 | −0.202965 | −0.101482 | − | 0.994837i | \(-0.532359\pi\) | ||||
−0.101482 | + | 0.994837i | \(0.532359\pi\) | |||||||
\(812\) | − 1.21684e13i | − 0.982269i | ||||||||
\(813\) | − 6.32033e12i | − 0.507379i | ||||||||
\(814\) | −6.47536e12 | −0.516957 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.99958e12 | −0.315797 | ||||||||
\(817\) | − 1.08641e12i | − 0.0853085i | ||||||||
\(818\) | 1.04253e12i | 0.0814138i | ||||||||
\(819\) | −7.55716e12 | −0.586923 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.21082e12 | −0.323461 | −0.161731 | − | 0.986835i | \(-0.551708\pi\) | ||||
−0.161731 | + | 0.986835i | \(0.551708\pi\) | |||||||
\(822\) | 2.57977e12i | 0.197087i | ||||||||
\(823\) | − 2.08206e11i | − 0.0158196i | −0.999969 | − | 0.00790978i | \(-0.997482\pi\) | ||||
0.999969 | − | 0.00790978i | \(-0.00251779\pi\) | |||||||
\(824\) | −5.66174e12 | −0.427836 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.86213e12 | 0.139187 | ||||||||
\(827\) | − 9.26106e12i | − 0.688472i | −0.938883 | − | 0.344236i | \(-0.888138\pi\) | ||||
0.938883 | − | 0.344236i | \(-0.111862\pi\) | |||||||
\(828\) | 4.45807e12i | 0.329618i | ||||||||
\(829\) | −2.42762e13 | −1.78519 | −0.892597 | − | 0.450856i | \(-0.851119\pi\) | ||||
−0.892597 | + | 0.450856i | \(0.851119\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.32041e12 | 0.387026 | ||||||||
\(832\) | 1.64531e13i | 1.19040i | ||||||||
\(833\) | 3.86775e12i | 0.278327i | ||||||||
\(834\) | −9.25231e11 | −0.0662221 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.06973e13 | 2.17356 | ||||||||
\(837\) | − 1.24835e12i | − 0.0879171i | ||||||||
\(838\) | − 2.24066e12i | − 0.156956i | ||||||||
\(839\) | 1.25546e13 | 0.874728 | 0.437364 | − | 0.899285i | \(-0.355912\pi\) | ||||
0.437364 | + | 0.899285i | \(0.355912\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.30294e12 | −0.296608 | ||||||||
\(842\) | − 6.73284e11i | − 0.0461630i | ||||||||
\(843\) | 5.22374e12i | 0.356252i | ||||||||
\(844\) | 2.55642e13 | 1.73417 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.61598e10 | −0.00108460 | ||||||||
\(847\) | − 3.92272e13i | − 2.61886i | ||||||||
\(848\) | − 1.12905e12i | − 0.0749778i | ||||||||
\(849\) | −7.80137e12 | −0.515331 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.56664e13 | 1.67758 | ||||||||
\(852\) | 7.05296e12i | 0.458557i | ||||||||
\(853\) | 1.36320e13i | 0.881632i | 0.897597 | + | 0.440816i | \(0.145311\pi\) | ||||
−0.897597 | + | 0.440816i | \(0.854689\pi\) | |||||||
\(854\) | 3.89363e12 | 0.250492 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.41297e12 | −0.471911 | ||||||||
\(857\) | 1.73987e13i | 1.10180i | 0.834570 | + | 0.550901i | \(0.185716\pi\) | ||||
−0.834570 | + | 0.550901i | \(0.814284\pi\) | |||||||
\(858\) | 4.19862e12i | 0.264493i | ||||||||
\(859\) | 6.43355e10 | 0.00403163 | 0.00201582 | − | 0.999998i | \(-0.499358\pi\) | ||||
0.00201582 | + | 0.999998i | \(0.499358\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.82161e13 | 1.12965 | ||||||||
\(862\) | − 1.79353e12i | − 0.110644i | ||||||||
\(863\) | − 3.32120e12i | − 0.203820i | −0.994794 | − | 0.101910i | \(-0.967505\pi\) | ||||
0.994794 | − | 0.101910i | \(-0.0324953\pi\) | |||||||
\(864\) | 1.60266e12 | 0.0978427 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.33940e12 | 0.262180 | ||||||||
\(867\) | − 6.11396e12i | − 0.367482i | ||||||||
\(868\) | 8.94800e12i | 0.535041i | ||||||||
\(869\) | 2.02558e13 | 1.20493 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.66750e13 | 0.981709 | ||||||||
\(872\) | − 3.76368e12i | − 0.220439i | ||||||||
\(873\) | − 1.59375e12i | − 0.0928657i | ||||||||
\(874\) | 3.92501e12 | 0.227530 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.46011e12 | 0.141152 | ||||||||
\(877\) | 1.95832e12i | 0.111786i | 0.998437 | + | 0.0558928i | \(0.0178005\pi\) | ||||
−0.998437 | + | 0.0558928i | \(0.982200\pi\) | |||||||
\(878\) | 1.84219e12i | 0.104619i | ||||||||
\(879\) | −6.61210e12 | −0.373585 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.02253e13 | −1.69036 | −0.845179 | − | 0.534483i | \(-0.820506\pi\) | ||||
−0.845179 | + | 0.534483i | \(0.820506\pi\) | |||||||
\(882\) | − 4.88894e11i | − 0.0272023i | ||||||||
\(883\) | 9.30097e12i | 0.514879i | 0.966294 | + | 0.257439i | \(0.0828788\pi\) | ||||
−0.966294 | + | 0.257439i | \(0.917121\pi\) | |||||||
\(884\) | 1.54448e13 | 0.850643 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.28380e10 | 0.00288068 | ||||||||
\(887\) | 9.27171e12i | 0.502925i | 0.967867 | + | 0.251463i | \(0.0809115\pi\) | ||||
−0.967867 | + | 0.251463i | \(0.919088\pi\) | |||||||
\(888\) | − 6.11893e12i | − 0.330231i | ||||||||
\(889\) | 1.33493e13 | 0.716805 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.71941e12 | −0.197708 | ||||||||
\(892\) | − 2.28791e13i | − 1.21003i | ||||||||
\(893\) | − 4.41053e11i | − 0.0232092i | ||||||||
\(894\) | −3.12136e12 | −0.163428 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.52282e13 | −0.789338 | ||||||||
\(897\) | − 1.66421e13i | − 0.858305i | ||||||||
\(898\) | − 2.76756e12i | − 0.142021i | ||||||||
\(899\) | −7.50365e12 | −0.383137 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.85671e11 | −0.0498276 | ||||||||
\(902\) | − 1.01205e13i | − 0.509066i | ||||||||
\(903\) | − 9.43524e11i | − 0.0472235i | ||||||||
\(904\) | 3.74385e11 | 0.0186449 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.74407e12 | 0.0859976 | ||||||||
\(907\) | 1.32868e12i | 0.0651908i | 0.999469 | + | 0.0325954i | \(0.0103773\pi\) | ||||
−0.999469 | + | 0.0325954i | \(0.989623\pi\) | |||||||
\(908\) | − 1.86413e13i | − 0.910102i | ||||||||
\(909\) | 4.28960e12 | 0.208391 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.71297e12 | 0.130501 | 0.0652503 | − | 0.997869i | \(-0.479215\pi\) | ||||
0.0652503 | + | 0.997869i | \(0.479215\pi\) | |||||||
\(912\) | 1.37983e13i | 0.660464i | ||||||||
\(913\) | 1.02743e13i | 0.489368i | ||||||||
\(914\) | −1.49254e12 | −0.0707404 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.17977e13 | 1.49233 | ||||||||
\(917\) | 1.91792e13i | 0.895714i | ||||||||
\(918\) | − 4.41355e11i | − 0.0205114i | ||||||||
\(919\) | −1.32139e12 | −0.0611100 | −0.0305550 | − | 0.999533i | \(-0.509727\pi\) | ||||
−0.0305550 | + | 0.999533i | \(0.509727\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.39422e12 | −0.109647 | ||||||||
\(922\) | 5.83758e12i | 0.266038i | ||||||||
\(923\) | − 2.63289e13i | − 1.19406i | ||||||||
\(924\) | 2.66601e13 | 1.20320 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.36853e11 | −0.0239942 | ||||||||
\(927\) | 9.21297e12i | 0.409771i | ||||||||
\(928\) | − 9.63329e12i | − 0.426392i | ||||||||
\(929\) | −1.16124e12 | −0.0511507 | −0.0255754 | − | 0.999673i | \(-0.508142\pi\) | ||||
−0.0255754 | + | 0.999673i | \(0.508142\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.33435e13 | 0.582098 | ||||||||
\(932\) | − 3.45503e13i | − 1.49996i | ||||||||
\(933\) | 3.23247e12i | 0.139659i | ||||||||
\(934\) | −1.45813e11 | −0.00626952 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.96751e12 | −0.168957 | ||||||||
\(937\) | 3.40914e13i | 1.44483i | 0.691460 | + | 0.722415i | \(0.256968\pi\) | ||||
−0.691460 | + | 0.722415i | \(0.743032\pi\) | |||||||
\(938\) | 3.41553e12i | 0.144061i | ||||||||
\(939\) | −1.50151e13 | −0.630277 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.60215e12 | −0.0666114 | −0.0333057 | − | 0.999445i | \(-0.510603\pi\) | ||||
−0.0333057 | + | 0.999445i | \(0.510603\pi\) | |||||||
\(942\) | − 1.68297e11i | − 0.00696380i | ||||||||
\(943\) | 4.01149e13i | 1.65197i | ||||||||
\(944\) | −1.44160e13 | −0.590840 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.24204e11 | −0.0212809 | ||||||||
\(947\) | − 3.38850e13i | − 1.36909i | −0.728969 | − | 0.684546i | \(-0.760000\pi\) | ||||
0.728969 | − | 0.684546i | \(-0.240000\pi\) | |||||||
\(948\) | 9.41851e12i | 0.378743i | ||||||||
\(949\) | −9.18366e12 | −0.367551 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.17805e13 | 0.863485 | ||||||||
\(952\) | 6.42917e12i | 0.253682i | ||||||||
\(953\) | − 2.15757e13i | − 0.847320i | −0.905821 | − | 0.423660i | \(-0.860745\pi\) | ||||
0.905821 | − | 0.423660i | \(-0.139255\pi\) | |||||||
\(954\) | 1.24592e11 | 0.00486991 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.30249e13 | −1.27874 | ||||||||
\(957\) | 2.23567e13i | 0.861598i | ||||||||
\(958\) | 3.52912e12i | 0.135370i | ||||||||
\(959\) | −6.11502e13 | −2.33461 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.09218e13 | −0.791306 | ||||||||
\(962\) | 1.12398e13i | 0.423126i | ||||||||
\(963\) | 1.20626e13i | 0.451985i | ||||||||
\(964\) | −2.19063e13 | −0.816999 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.40880e12 | 0.125952 | ||||||||
\(967\) | 3.06249e13i | 1.12630i | 0.826353 | + | 0.563152i | \(0.190411\pi\) | ||||
−0.826353 | + | 0.563152i | \(0.809589\pi\) | |||||||
\(968\) | − 2.05943e13i | − 0.753888i | ||||||||
\(969\) | 1.20460e13 | 0.438921 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.92365e12 | 0.0694447 | 0.0347224 | − | 0.999397i | \(-0.488945\pi\) | ||||
0.0347224 | + | 0.999397i | \(0.488945\pi\) | |||||||
\(972\) | − 1.72945e12i | − 0.0621453i | ||||||||
\(973\) | − 2.19314e13i | − 0.784438i | ||||||||
\(974\) | 2.03936e12 | 0.0726070 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.01432e13 | −1.06332 | ||||||||
\(977\) | − 1.83893e13i | − 0.645714i | −0.946448 | − | 0.322857i | \(-0.895357\pi\) | ||||
0.946448 | − | 0.322857i | \(-0.104643\pi\) | |||||||
\(978\) | 3.04962e12i | 0.106591i | ||||||||
\(979\) | −2.73498e13 | −0.951552 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.12438e12 | −0.211131 | ||||||||
\(982\) | 6.08524e12i | 0.208822i | ||||||||
\(983\) | 4.63273e13i | 1.58251i | 0.611488 | + | 0.791254i | \(0.290571\pi\) | ||||
−0.611488 | + | 0.791254i | \(0.709429\pi\) | |||||||
\(984\) | 9.56347e12 | 0.325190 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.65291e12 | −0.0893875 | ||||||||
\(987\) | − 3.83047e11i | − 0.0128477i | ||||||||
\(988\) | − 5.32837e13i | − 1.77905i | ||||||||
\(989\) | 2.07779e12 | 0.0690587 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.76252e12 | 0.0909857 | 0.0454929 | − | 0.998965i | \(-0.485514\pi\) | ||||
0.0454929 | + | 0.998965i | \(0.485514\pi\) | |||||||
\(992\) | 7.08383e12i | 0.232255i | ||||||||
\(993\) | 3.47570e13i | 1.13441i | ||||||||
\(994\) | 5.39295e12 | 0.175221 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4.77734e12 | −0.153822 | ||||||||
\(997\) | − 1.74502e13i | − 0.559337i | −0.960097 | − | 0.279668i | \(-0.909776\pi\) | ||||
0.960097 | − | 0.279668i | \(-0.0902245\pi\) | |||||||
\(998\) | 2.81365e12i | 0.0897807i | ||||||||
\(999\) | −9.95692e12 | −0.316286 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 75.10.b.d.49.1 | 2 | ||
3.2 | odd | 2 | 225.10.b.e.199.2 | 2 | |||
5.2 | odd | 4 | 75.10.a.c.1.1 | 1 | |||
5.3 | odd | 4 | 15.10.a.a.1.1 | ✓ | 1 | ||
5.4 | even | 2 | inner | 75.10.b.d.49.2 | 2 | ||
15.2 | even | 4 | 225.10.a.c.1.1 | 1 | |||
15.8 | even | 4 | 45.10.a.b.1.1 | 1 | |||
15.14 | odd | 2 | 225.10.b.e.199.1 | 2 | |||
20.3 | even | 4 | 240.10.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.10.a.a.1.1 | ✓ | 1 | 5.3 | odd | 4 | ||
45.10.a.b.1.1 | 1 | 15.8 | even | 4 | |||
75.10.a.c.1.1 | 1 | 5.2 | odd | 4 | |||
75.10.b.d.49.1 | 2 | 1.1 | even | 1 | trivial | ||
75.10.b.d.49.2 | 2 | 5.4 | even | 2 | inner | ||
225.10.a.c.1.1 | 1 | 15.2 | even | 4 | |||
225.10.b.e.199.1 | 2 | 15.14 | odd | 2 | |||
225.10.b.e.199.2 | 2 | 3.2 | odd | 2 | |||
240.10.a.c.1.1 | 1 | 20.3 | even | 4 |