Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,34,Mod(24,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 34, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.24");
S:= CuspForms(chi, 34);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 34 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.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: | \(172.457072203\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 20265063301 x^{10} + \cdots + 39\!\cdots\!96 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{47}\cdot 3^{10}\cdot 5^{36}\cdot 7^{2}\cdot 11^{4} \) |
Twist minimal: | no (minimal twist has level 5) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 24.2 | ||
Root | \(-66460.8i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 25.24 |
Dual form | 25.34.b.c.24.11 |
$q$-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 \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 132922.i | − 1.43417i | −0.696986 | − | 0.717085i | \(-0.745476\pi\) | ||||
0.696986 | − | 0.717085i | \(-0.254524\pi\) | |||||||
\(3\) | − 1.17526e8i | − 1.57627i | −0.615499 | − | 0.788137i | \(-0.711046\pi\) | ||||
0.615499 | − | 0.788137i | \(-0.288954\pi\) | |||||||
\(4\) | −9.07819e9 | −1.05684 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.56217e13 | −2.26064 | ||||||||
\(7\) | 1.34853e13i | 0.153371i | 0.997055 | + | 0.0766854i | \(0.0244337\pi\) | ||||
−0.997055 | + | 0.0766854i | \(0.975566\pi\) | |||||||
\(8\) | 6.49000e13i | 0.0815192i | ||||||||
\(9\) | −8.25322e15 | −1.48464 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −7.96470e16 | −0.522625 | −0.261313 | − | 0.965254i | \(-0.584155\pi\) | ||||
−0.261313 | + | 0.965254i | \(0.584155\pi\) | |||||||
\(12\) | 1.06692e18i | 1.66587i | ||||||||
\(13\) | − 1.16823e18i | − 0.486928i | −0.969910 | − | 0.243464i | \(-0.921716\pi\) | ||||
0.969910 | − | 0.243464i | \(-0.0782838\pi\) | |||||||
\(14\) | 1.79249e18 | 0.219960 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −6.93545e19 | −0.939928 | ||||||||
\(17\) | − 3.27833e20i | − 1.63398i | −0.576654 | − | 0.816988i | \(-0.695642\pi\) | ||||
0.576654 | − | 0.816988i | \(-0.304358\pi\) | |||||||
\(18\) | 1.09703e21i | 2.12923i | ||||||||
\(19\) | −2.21358e21 | −1.76060 | −0.880301 | − | 0.474416i | \(-0.842659\pi\) | ||||
−0.880301 | + | 0.474416i | \(0.842659\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.58487e21 | 0.241755 | ||||||||
\(22\) | 1.05868e22i | 0.749533i | ||||||||
\(23\) | 3.93052e22i | 1.33641i | 0.743975 | + | 0.668207i | \(0.232938\pi\) | ||||
−0.743975 | + | 0.668207i | \(0.767062\pi\) | |||||||
\(24\) | 7.62742e21 | 0.128497 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.55283e23 | −0.698337 | ||||||||
\(27\) | 3.16633e23i | 0.763930i | ||||||||
\(28\) | − 1.22422e23i | − 0.162089i | ||||||||
\(29\) | −1.59428e24 | −1.18303 | −0.591516 | − | 0.806293i | \(-0.701470\pi\) | ||||
−0.591516 | + | 0.806293i | \(0.701470\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.07133e24 | 0.511425 | 0.255712 | − | 0.966753i | \(-0.417690\pi\) | ||||
0.255712 | + | 0.966753i | \(0.417690\pi\) | |||||||
\(32\) | 9.77619e24i | 1.42954i | ||||||||
\(33\) | 9.36057e24i | 0.823801i | ||||||||
\(34\) | −4.35761e25 | −2.34340 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 7.49243e25 | 1.56903 | ||||||||
\(37\) | 4.76387e25i | 0.634792i | 0.948293 | + | 0.317396i | \(0.102808\pi\) | ||||
−0.948293 | + | 0.317396i | \(0.897192\pi\) | |||||||
\(38\) | 2.94233e26i | 2.52500i | ||||||||
\(39\) | −1.37297e26 | −0.767532 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.39281e26 | −1.56588 | −0.782940 | − | 0.622097i | \(-0.786281\pi\) | ||||
−0.782940 | + | 0.622097i | \(0.786281\pi\) | |||||||
\(42\) | − 2.10663e26i | − 0.346717i | ||||||||
\(43\) | − 2.16469e26i | − 0.241639i | −0.992674 | − | 0.120819i | \(-0.961448\pi\) | ||||
0.992674 | − | 0.120819i | \(-0.0385522\pi\) | |||||||
\(44\) | 7.23051e26 | 0.552331 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.22451e27 | 1.91664 | ||||||||
\(47\) | − 7.45743e27i | − 1.91856i | −0.282462 | − | 0.959278i | \(-0.591151\pi\) | ||||
0.282462 | − | 0.959278i | \(-0.408849\pi\) | |||||||
\(48\) | 8.15093e27i | 1.48159i | ||||||||
\(49\) | 7.54914e27 | 0.976477 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.85288e28 | −2.57560 | ||||||||
\(52\) | 1.06055e28i | 0.514605i | ||||||||
\(53\) | 1.70592e28i | 0.604513i | 0.953227 | + | 0.302257i | \(0.0977399\pi\) | ||||
−0.953227 | + | 0.302257i | \(0.902260\pi\) | |||||||
\(54\) | 4.20873e28 | 1.09560 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −8.75196e26 | −0.0125027 | ||||||||
\(57\) | 2.60153e29i | 2.77519i | ||||||||
\(58\) | 2.11913e29i | 1.69667i | ||||||||
\(59\) | 5.91397e28 | 0.357126 | 0.178563 | − | 0.983928i | \(-0.442855\pi\) | ||||
0.178563 | + | 0.983928i | \(0.442855\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.18117e29 | 0.759884 | 0.379942 | − | 0.925010i | \(-0.375944\pi\) | ||||
0.379942 | + | 0.925010i | \(0.375944\pi\) | |||||||
\(62\) | − 2.75325e29i | − 0.733470i | ||||||||
\(63\) | − 1.11297e29i | − 0.227701i | ||||||||
\(64\) | 7.03715e29 | 1.11027 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.24422e30 | 1.18147 | ||||||||
\(67\) | − 2.21631e30i | − 1.64209i | −0.570865 | − | 0.821044i | \(-0.693392\pi\) | ||||
0.570865 | − | 0.821044i | \(-0.306608\pi\) | |||||||
\(68\) | 2.97613e30i | 1.72685i | ||||||||
\(69\) | 4.61937e30 | 2.10656 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.87498e30 | 0.818223 | 0.409112 | − | 0.912484i | \(-0.365839\pi\) | ||||
0.409112 | + | 0.912484i | \(0.365839\pi\) | |||||||
\(72\) | − 5.35634e29i | − 0.121027i | ||||||||
\(73\) | − 3.41825e30i | − 0.615143i | −0.951525 | − | 0.307571i | \(-0.900484\pi\) | ||||
0.951525 | − | 0.307571i | \(-0.0995163\pi\) | |||||||
\(74\) | 6.33220e30 | 0.910398 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00953e31 | 1.86068 | ||||||||
\(77\) | − 1.07406e30i | − 0.0801555i | ||||||||
\(78\) | 1.82498e31i | 1.10077i | ||||||||
\(79\) | −5.87385e30 | −0.287128 | −0.143564 | − | 0.989641i | \(-0.545856\pi\) | ||||
−0.143564 | + | 0.989641i | \(0.545856\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.66769e30 | −0.280479 | ||||||||
\(82\) | 8.49743e31i | 2.24574i | ||||||||
\(83\) | − 2.11211e31i | − 0.457013i | −0.973542 | − | 0.228507i | \(-0.926616\pi\) | ||||
0.973542 | − | 0.228507i | \(-0.0733843\pi\) | |||||||
\(84\) | −1.43877e31 | −0.255496 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.87734e31 | −0.346551 | ||||||||
\(87\) | 1.87368e32i | 1.86478i | ||||||||
\(88\) | − 5.16909e30i | − 0.0426040i | ||||||||
\(89\) | 2.67672e32 | 1.83092 | 0.915458 | − | 0.402413i | \(-0.131828\pi\) | ||||
0.915458 | + | 0.402413i | \(0.131828\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.57540e31 | 0.0746806 | ||||||||
\(92\) | − 3.56821e32i | − 1.41238i | ||||||||
\(93\) | − 2.43435e32i | − 0.806146i | ||||||||
\(94\) | −9.91253e32 | −2.75153 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.14895e33 | 2.25334 | ||||||||
\(97\) | − 1.07066e31i | − 0.0176977i | −0.999961 | − | 0.00884885i | \(-0.997183\pi\) | ||||
0.999961 | − | 0.00884885i | \(-0.00281671\pi\) | |||||||
\(98\) | − 1.00344e33i | − 1.40043i | ||||||||
\(99\) | 6.57344e32 | 0.775911 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.55093e33 | 1.31610 | 0.658051 | − | 0.752974i | \(-0.271381\pi\) | ||||
0.658051 | + | 0.752974i | \(0.271381\pi\) | |||||||
\(102\) | 5.12131e33i | 3.69384i | ||||||||
\(103\) | 6.99665e32i | 0.429612i | 0.976657 | + | 0.214806i | \(0.0689119\pi\) | ||||
−0.976657 | + | 0.214806i | \(0.931088\pi\) | |||||||
\(104\) | 7.58184e31 | 0.0396940 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.26753e33 | 0.866974 | ||||||||
\(107\) | 6.35208e32i | 0.208010i | 0.994577 | + | 0.104005i | \(0.0331658\pi\) | ||||
−0.994577 | + | 0.104005i | \(0.966834\pi\) | |||||||
\(108\) | − 2.87445e33i | − 0.807352i | ||||||||
\(109\) | −2.09396e33 | −0.505163 | −0.252581 | − | 0.967576i | \(-0.581280\pi\) | ||||
−0.252581 | + | 0.967576i | \(0.581280\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.59876e33 | 1.00061 | ||||||||
\(112\) | − 9.35266e32i | − 0.144158i | ||||||||
\(113\) | 7.28662e33i | 0.969910i | 0.874539 | + | 0.484955i | \(0.161164\pi\) | ||||
−0.874539 | + | 0.484955i | \(0.838836\pi\) | |||||||
\(114\) | 3.45799e34 | 3.98009 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.44731e34 | 1.25028 | ||||||||
\(117\) | 9.64169e33i | 0.722914i | ||||||||
\(118\) | − 7.86094e33i | − 0.512179i | ||||||||
\(119\) | 4.42093e33 | 0.250604 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.68815e34 | −0.726863 | ||||||||
\(122\) | − 2.89924e34i | − 1.08980i | ||||||||
\(123\) | 7.51320e34i | 2.46826i | ||||||||
\(124\) | −1.88040e34 | −0.540495 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.47938e34 | −0.326562 | ||||||||
\(127\) | 4.47086e34i | 0.866222i | 0.901341 | + | 0.433111i | \(0.142584\pi\) | ||||
−0.901341 | + | 0.433111i | \(0.857416\pi\) | |||||||
\(128\) | − 9.56208e33i | − 0.162775i | ||||||||
\(129\) | −2.54407e34 | −0.380889 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.63964e34 | −0.306597 | −0.153298 | − | 0.988180i | \(-0.548990\pi\) | ||||
−0.153298 | + | 0.988180i | \(0.548990\pi\) | |||||||
\(132\) | − 8.49770e34i | − 0.870626i | ||||||||
\(133\) | − 2.98508e34i | − 0.270025i | ||||||||
\(134\) | −2.94595e35 | −2.35503 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.12764e34 | 0.133201 | ||||||||
\(137\) | − 1.03805e35i | − 0.575874i | −0.957649 | − | 0.287937i | \(-0.907031\pi\) | ||||
0.957649 | − | 0.287937i | \(-0.0929694\pi\) | |||||||
\(138\) | − 6.14014e35i | − 3.02116i | ||||||||
\(139\) | 1.77157e34 | 0.0773774 | 0.0386887 | − | 0.999251i | \(-0.487682\pi\) | ||||
0.0386887 | + | 0.999251i | \(0.487682\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.76440e35 | −3.02417 | ||||||||
\(142\) | − 3.82147e35i | − 1.17347i | ||||||||
\(143\) | 9.30464e34i | 0.254481i | ||||||||
\(144\) | 5.72398e35 | 1.39546 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.54358e35 | −0.882219 | ||||||||
\(147\) | − 8.87218e35i | − 1.53920i | ||||||||
\(148\) | − 4.32473e35i | − 0.670874i | ||||||||
\(149\) | −9.39618e35 | −1.30430 | −0.652151 | − | 0.758089i | \(-0.726133\pi\) | ||||
−0.652151 | + | 0.758089i | \(0.726133\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.46650e35 | 0.497563 | 0.248781 | − | 0.968560i | \(-0.419970\pi\) | ||||
0.248781 | + | 0.968560i | \(0.419970\pi\) | |||||||
\(152\) | − 1.43661e35i | − 0.143523i | ||||||||
\(153\) | 2.70568e36i | 2.42587i | ||||||||
\(154\) | −1.42766e35 | −0.114956 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.24641e36 | 0.811159 | ||||||||
\(157\) | 7.30629e35i | 0.427910i | 0.976843 | + | 0.213955i | \(0.0686346\pi\) | ||||
−0.976843 | + | 0.213955i | \(0.931365\pi\) | |||||||
\(158\) | 7.80761e35i | 0.411791i | ||||||||
\(159\) | 2.00489e36 | 0.952879 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.30043e35 | −0.204967 | ||||||||
\(162\) | 1.15212e36i | 0.402254i | ||||||||
\(163\) | − 2.77089e35i | − 0.0874026i | −0.999045 | − | 0.0437013i | \(-0.986085\pi\) | ||||
0.999045 | − | 0.0437013i | \(-0.0139150\pi\) | |||||||
\(164\) | 5.80352e36 | 1.65489 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.80745e36 | −0.655434 | ||||||||
\(167\) | − 5.22919e36i | − 1.10564i | −0.833302 | − | 0.552818i | \(-0.813552\pi\) | ||||
0.833302 | − | 0.552818i | \(-0.186448\pi\) | |||||||
\(168\) | 1.02858e35i | 0.0197077i | ||||||||
\(169\) | 4.39136e36 | 0.762901 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.82692e37 | 2.61386 | ||||||||
\(172\) | 1.96515e36i | 0.255374i | ||||||||
\(173\) | − 5.38814e36i | − 0.636324i | −0.948036 | − | 0.318162i | \(-0.896934\pi\) | ||||
0.948036 | − | 0.318162i | \(-0.103066\pi\) | |||||||
\(174\) | 2.49053e37 | 2.67441 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.52388e36 | 0.491230 | ||||||||
\(177\) | − 6.95044e36i | − 0.562928i | ||||||||
\(178\) | − 3.55794e37i | − 2.62584i | ||||||||
\(179\) | −2.52793e37 | −1.70094 | −0.850472 | − | 0.526020i | \(-0.823684\pi\) | ||||
−0.850472 | + | 0.526020i | \(0.823684\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.65835e36 | 0.0928924 | 0.0464462 | − | 0.998921i | \(-0.485210\pi\) | ||||
0.0464462 | + | 0.998921i | \(0.485210\pi\) | |||||||
\(182\) | − 2.09404e36i | − 0.107105i | ||||||||
\(183\) | − 2.56343e37i | − 1.19779i | ||||||||
\(184\) | −2.55091e36 | −0.108943 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.23577e37 | −1.15615 | ||||||||
\(187\) | 2.61109e37i | 0.853957i | ||||||||
\(188\) | 6.77000e37i | 2.02761i | ||||||||
\(189\) | −4.26989e36 | −0.117165 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.04480e37 | 1.39422 | 0.697110 | − | 0.716964i | \(-0.254469\pi\) | ||||
0.697110 | + | 0.716964i | \(0.254469\pi\) | |||||||
\(192\) | − 8.27046e37i | − 1.75009i | ||||||||
\(193\) | 6.49082e36i | 0.126068i | 0.998011 | + | 0.0630339i | \(0.0200776\pi\) | ||||
−0.998011 | + | 0.0630339i | \(0.979922\pi\) | |||||||
\(194\) | −1.42313e36 | −0.0253815 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.85326e37 | −1.03198 | ||||||||
\(197\) | − 9.24040e37i | − 1.27938i | −0.768635 | − | 0.639688i | \(-0.779064\pi\) | ||||
0.768635 | − | 0.639688i | \(-0.220936\pi\) | |||||||
\(198\) | − 8.73752e37i | − 1.11279i | ||||||||
\(199\) | 1.09203e38 | 1.27985 | 0.639925 | − | 0.768437i | \(-0.278965\pi\) | ||||
0.639925 | + | 0.768437i | \(0.278965\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.60473e38 | −2.58838 | ||||||||
\(202\) | − 2.06152e38i | − 1.88751i | ||||||||
\(203\) | − 2.14993e37i | − 0.181443i | ||||||||
\(204\) | 3.49772e38 | 2.72200 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 9.30006e37 | 0.616136 | ||||||||
\(207\) | − 3.24395e38i | − 1.98410i | ||||||||
\(208\) | 8.10223e37i | 0.457677i | ||||||||
\(209\) | 1.76305e38 | 0.920134 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.11672e37 | −0.272808 | −0.136404 | − | 0.990653i | \(-0.543555\pi\) | ||||
−0.136404 | + | 0.990653i | \(0.543555\pi\) | |||||||
\(212\) | − 1.54866e38i | − 0.638874i | ||||||||
\(213\) | − 3.37884e38i | − 1.28974i | ||||||||
\(214\) | 8.44328e37 | 0.298321 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.05495e37 | −0.0622750 | ||||||||
\(217\) | 2.79325e37i | 0.0784377i | ||||||||
\(218\) | 2.78332e38i | 0.724489i | ||||||||
\(219\) | −4.01731e38 | −0.969634 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.82986e38 | −0.795629 | ||||||||
\(222\) | − 7.44196e38i | − 1.43504i | ||||||||
\(223\) | 9.45280e38i | 1.69251i | 0.532781 | + | 0.846253i | \(0.321147\pi\) | ||||
−0.532781 | + | 0.846253i | \(0.678853\pi\) | |||||||
\(224\) | −1.31835e38 | −0.219249 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.68548e38 | 1.39102 | ||||||||
\(227\) | − 4.90469e38i | − 0.654914i | −0.944866 | − | 0.327457i | \(-0.893808\pi\) | ||||
0.944866 | − | 0.327457i | \(-0.106192\pi\) | |||||||
\(228\) | − 2.36172e39i | − 2.93294i | ||||||||
\(229\) | 4.57241e38 | 0.528275 | 0.264137 | − | 0.964485i | \(-0.414913\pi\) | ||||
0.264137 | + | 0.964485i | \(0.414913\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.26230e38 | −0.126347 | ||||||||
\(232\) | − 1.03468e38i | − 0.0964398i | ||||||||
\(233\) | − 8.69571e38i | − 0.754975i | −0.926015 | − | 0.377487i | \(-0.876788\pi\) | ||||
0.926015 | − | 0.377487i | \(-0.123212\pi\) | |||||||
\(234\) | 1.28159e39 | 1.03678 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −5.36882e38 | −0.377425 | ||||||||
\(237\) | 6.90328e38i | 0.452593i | ||||||||
\(238\) | − 5.87637e38i | − 0.359409i | ||||||||
\(239\) | 1.38618e39 | 0.791140 | 0.395570 | − | 0.918436i | \(-0.370547\pi\) | ||||
0.395570 | + | 0.918436i | \(0.370547\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.94732e39 | −1.46604 | −0.733019 | − | 0.680208i | \(-0.761890\pi\) | ||||
−0.733019 | + | 0.680208i | \(0.761890\pi\) | |||||||
\(242\) | 2.24392e39i | 1.04244i | ||||||||
\(243\) | 2.77886e39i | 1.20604i | ||||||||
\(244\) | −1.98011e39 | −0.803076 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.98665e39 | 3.53990 | ||||||||
\(247\) | 2.58598e39i | 0.857286i | ||||||||
\(248\) | 1.34430e38i | 0.0416910i | ||||||||
\(249\) | −2.48228e39 | −0.720379 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.17168e39 | −1.31527 | −0.657636 | − | 0.753336i | \(-0.728444\pi\) | ||||
−0.657636 | + | 0.753336i | \(0.728444\pi\) | |||||||
\(252\) | 1.01038e39i | 0.240644i | ||||||||
\(253\) | − 3.13055e39i | − 0.698444i | ||||||||
\(254\) | 5.94273e39 | 1.24231 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.77386e39 | 0.876820 | ||||||||
\(257\) | 4.09624e39i | 0.705488i | 0.935720 | + | 0.352744i | \(0.114751\pi\) | ||||
−0.935720 | + | 0.352744i | \(0.885249\pi\) | |||||||
\(258\) | 3.38162e39i | 0.546260i | ||||||||
\(259\) | −6.42422e38 | −0.0973585 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.31579e40 | 1.75638 | ||||||||
\(262\) | 3.50865e39i | 0.439712i | ||||||||
\(263\) | 2.59968e39i | 0.305950i | 0.988230 | + | 0.152975i | \(0.0488854\pi\) | ||||
−0.988230 | + | 0.152975i | \(0.951115\pi\) | |||||||
\(264\) | −6.07501e38 | −0.0671556 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.96781e39 | −0.387262 | ||||||||
\(267\) | − 3.14584e40i | − 2.88603i | ||||||||
\(268\) | 2.01201e40i | 1.73543i | ||||||||
\(269\) | −7.20422e39 | −0.584351 | −0.292176 | − | 0.956365i | \(-0.594379\pi\) | ||||
−0.292176 | + | 0.956365i | \(0.594379\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.89743e40 | −1.36199 | −0.680993 | − | 0.732290i | \(-0.738451\pi\) | ||||
−0.680993 | + | 0.732290i | \(0.738451\pi\) | |||||||
\(272\) | 2.27367e40i | 1.53582i | ||||||||
\(273\) | − 1.85150e39i | − 0.117717i | ||||||||
\(274\) | −1.37979e40 | −0.825901 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.19356e40 | −2.22629 | ||||||||
\(277\) | − 3.08340e40i | − 1.54211i | −0.636771 | − | 0.771053i | \(-0.719730\pi\) | ||||
0.636771 | − | 0.771053i | \(-0.280270\pi\) | |||||||
\(278\) | − 2.35480e39i | − 0.110972i | ||||||||
\(279\) | −1.70952e40 | −0.759283 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.56575e40 | −0.618112 | −0.309056 | − | 0.951044i | \(-0.600013\pi\) | ||||
−0.309056 | + | 0.951044i | \(0.600013\pi\) | |||||||
\(282\) | 1.16498e41i | 4.33718i | ||||||||
\(283\) | 7.24188e39i | 0.254317i | 0.991882 | + | 0.127158i | \(0.0405857\pi\) | ||||
−0.991882 | + | 0.127158i | \(0.959414\pi\) | |||||||
\(284\) | −2.60996e40 | −0.864732 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.23679e40 | 0.364968 | ||||||||
\(287\) | − 8.62090e39i | − 0.240160i | ||||||||
\(288\) | − 8.06850e40i | − 2.12235i | ||||||||
\(289\) | −6.72202e40 | −1.66988 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.25830e39 | −0.0278964 | ||||||||
\(292\) | 3.10315e40i | 0.650108i | ||||||||
\(293\) | 7.67091e40i | 1.51891i | 0.650562 | + | 0.759453i | \(0.274533\pi\) | ||||
−0.650562 | + | 0.759453i | \(0.725467\pi\) | |||||||
\(294\) | −1.17930e41 | −2.20747 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.09175e39 | −0.0517477 | ||||||||
\(297\) | − 2.52188e40i | − 0.399249i | ||||||||
\(298\) | 1.24895e41i | 1.87059i | ||||||||
\(299\) | 4.59177e40 | 0.650737 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.91915e39 | 0.0370604 | ||||||||
\(302\) | − 5.93694e40i | − 0.713589i | ||||||||
\(303\) | − 1.82274e41i | − 2.07454i | ||||||||
\(304\) | 1.53522e41 | 1.65484 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.59643e41 | 3.47911 | ||||||||
\(307\) | 1.29298e41i | 1.18525i | 0.805478 | + | 0.592625i | \(0.201909\pi\) | ||||
−0.805478 | + | 0.592625i | \(0.798091\pi\) | |||||||
\(308\) | 9.75056e39i | 0.0847116i | ||||||||
\(309\) | 8.22286e40 | 0.677186 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.39990e40 | −0.399797 | −0.199898 | − | 0.979817i | \(-0.564061\pi\) | ||||
−0.199898 | + | 0.979817i | \(0.564061\pi\) | |||||||
\(312\) | − 8.91061e39i | − 0.0625686i | ||||||||
\(313\) | 1.08588e41i | 0.723270i | 0.932320 | + | 0.361635i | \(0.117781\pi\) | ||||
−0.932320 | + | 0.361635i | \(0.882219\pi\) | |||||||
\(314\) | 9.71163e40 | 0.613696 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.33240e40 | 0.303449 | ||||||||
\(317\) | 1.38129e41i | 0.746117i | 0.927808 | + | 0.373059i | \(0.121691\pi\) | ||||
−0.927808 | + | 0.373059i | \(0.878309\pi\) | |||||||
\(318\) | − 2.66493e41i | − 1.36659i | ||||||||
\(319\) | 1.26979e41 | 0.618282 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.46533e40 | 0.327881 | ||||||||
\(322\) | 7.04541e40i | 0.293957i | ||||||||
\(323\) | 7.25686e41i | 2.87678i | ||||||||
\(324\) | 7.86869e40 | 0.296422 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.68311e40 | −0.125350 | ||||||||
\(327\) | 2.46094e41i | 0.796275i | ||||||||
\(328\) | − 4.14894e40i | − 0.127649i | ||||||||
\(329\) | 1.00566e41 | 0.294251 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.29457e41 | −1.13699 | −0.568496 | − | 0.822686i | \(-0.692474\pi\) | ||||
−0.568496 | + | 0.822686i | \(0.692474\pi\) | |||||||
\(332\) | 1.91742e41i | 0.482990i | ||||||||
\(333\) | − 3.93172e41i | − 0.942439i | ||||||||
\(334\) | −6.95072e41 | −1.58567 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.09918e41 | −0.227232 | ||||||||
\(337\) | − 6.97107e41i | − 1.37216i | −0.727524 | − | 0.686082i | \(-0.759329\pi\) | ||||
0.727524 | − | 0.686082i | \(-0.240671\pi\) | |||||||
\(338\) | − 5.83706e41i | − 1.09413i | ||||||||
\(339\) | 8.56364e41 | 1.52885 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.64975e41 | −0.267284 | ||||||||
\(342\) | − 2.42837e42i | − 3.74872i | ||||||||
\(343\) | 2.06057e41i | 0.303134i | ||||||||
\(344\) | 1.40489e40 | 0.0196982 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.16200e41 | −0.912596 | ||||||||
\(347\) | − 7.56830e41i | − 0.919522i | −0.888043 | − | 0.459761i | \(-0.847935\pi\) | ||||
0.888043 | − | 0.459761i | \(-0.152065\pi\) | |||||||
\(348\) | − 1.70096e42i | − 1.97078i | ||||||||
\(349\) | −4.06051e41 | −0.448705 | −0.224353 | − | 0.974508i | \(-0.572027\pi\) | ||||
−0.224353 | + | 0.974508i | \(0.572027\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.69901e41 | 0.371979 | ||||||||
\(352\) | − 7.78644e41i | − 0.747111i | ||||||||
\(353\) | − 1.97994e42i | − 1.81288i | −0.422336 | − | 0.906439i | \(-0.638790\pi\) | ||||
0.422336 | − | 0.906439i | \(-0.361210\pi\) | |||||||
\(354\) | −9.23863e41 | −0.807335 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.42998e42 | −1.93499 | ||||||||
\(357\) | − 5.19573e41i | − 0.395022i | ||||||||
\(358\) | 3.36016e42i | 2.43944i | ||||||||
\(359\) | 6.70289e41 | 0.464733 | 0.232366 | − | 0.972628i | \(-0.425353\pi\) | ||||
0.232366 | + | 0.972628i | \(0.425353\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.31917e42 | 2.09972 | ||||||||
\(362\) | − 2.20431e41i | − 0.133223i | ||||||||
\(363\) | 1.98401e42i | 1.14574i | ||||||||
\(364\) | −1.43018e41 | −0.0789255 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.40736e42 | −1.71783 | ||||||||
\(367\) | 1.36571e42i | 0.658215i | 0.944292 | + | 0.329108i | \(0.106748\pi\) | ||||
−0.944292 | + | 0.329108i | \(0.893252\pi\) | |||||||
\(368\) | − 2.72599e42i | − 1.25613i | ||||||||
\(369\) | 5.27613e42 | 2.32477 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.30048e41 | −0.0927147 | ||||||||
\(372\) | 2.20995e42i | 0.851968i | ||||||||
\(373\) | 3.32617e41i | 0.122673i | 0.998117 | + | 0.0613364i | \(0.0195363\pi\) | ||||
−0.998117 | + | 0.0613364i | \(0.980464\pi\) | |||||||
\(374\) | 3.47071e42 | 1.22472 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.83988e41 | 0.156399 | ||||||||
\(377\) | 1.86249e42i | 0.576051i | ||||||||
\(378\) | 5.67560e41i | 0.168034i | ||||||||
\(379\) | −1.32387e42 | −0.375230 | −0.187615 | − | 0.982243i | \(-0.560076\pi\) | ||||
−0.187615 | + | 0.982243i | \(0.560076\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.25440e42 | 1.36540 | ||||||||
\(382\) | − 8.03484e42i | − 1.99955i | ||||||||
\(383\) | 5.38010e42i | 1.28236i | 0.767390 | + | 0.641181i | \(0.221555\pi\) | ||||
−0.767390 | + | 0.641181i | \(0.778445\pi\) | |||||||
\(384\) | −1.12379e42 | −0.256578 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.62770e41 | 0.180803 | ||||||||
\(387\) | 1.78657e42i | 0.358747i | ||||||||
\(388\) | 9.71963e40i | 0.0187036i | ||||||||
\(389\) | 6.93155e42 | 1.27839 | 0.639193 | − | 0.769046i | \(-0.279269\pi\) | ||||
0.639193 | + | 0.769046i | \(0.279269\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.28856e43 | 2.18367 | ||||||||
\(392\) | 4.89939e41i | 0.0796017i | ||||||||
\(393\) | 3.10225e42i | 0.483281i | ||||||||
\(394\) | −1.22825e43 | −1.83484 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5.96750e42 | −0.820015 | ||||||||
\(397\) | 9.33530e42i | 1.23051i | 0.788329 | + | 0.615254i | \(0.210947\pi\) | ||||
−0.788329 | + | 0.615254i | \(0.789053\pi\) | |||||||
\(398\) | − 1.45154e43i | − 1.83552i | ||||||||
\(399\) | −3.50824e42 | −0.425634 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.40931e42 | 0.380877 | 0.190438 | − | 0.981699i | \(-0.439009\pi\) | ||||
0.190438 | + | 0.981699i | \(0.439009\pi\) | |||||||
\(402\) | 3.46225e43i | 3.71218i | ||||||||
\(403\) | − 2.41980e42i | − 0.249027i | ||||||||
\(404\) | −1.40796e43 | −1.39091 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.85772e42 | −0.260219 | ||||||||
\(407\) | − 3.79428e42i | − 0.331758i | ||||||||
\(408\) | − 2.50052e42i | − 0.209961i | ||||||||
\(409\) | −3.12051e42 | −0.251646 | −0.125823 | − | 0.992053i | \(-0.540157\pi\) | ||||
−0.125823 | + | 0.992053i | \(0.540157\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.21997e43 | −0.907736 | ||||||||
\(412\) | − 6.35170e42i | − 0.454031i | ||||||||
\(413\) | 7.97517e41i | 0.0547727i | ||||||||
\(414\) | −4.31190e43 | −2.84553 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.14209e43 | 0.696081 | ||||||||
\(417\) | − 2.08205e42i | − 0.121968i | ||||||||
\(418\) | − 2.34347e43i | − 1.31963i | ||||||||
\(419\) | 3.20466e43 | 1.73480 | 0.867402 | − | 0.497608i | \(-0.165788\pi\) | ||||
0.867402 | + | 0.497608i | \(0.165788\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.44061e42 | 0.272266 | 0.136133 | − | 0.990691i | \(-0.456533\pi\) | ||||
0.136133 | + | 0.990691i | \(0.456533\pi\) | |||||||
\(422\) | 8.13043e42i | 0.391253i | ||||||||
\(423\) | 6.15478e43i | 2.84837i | ||||||||
\(424\) | −1.10714e42 | −0.0492794 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.49120e43 | −1.84971 | ||||||||
\(427\) | 2.94137e42i | 0.116544i | ||||||||
\(428\) | − 5.76654e42i | − 0.219833i | ||||||||
\(429\) | 1.09353e43 | 0.401132 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.50771e43 | −1.19165 | −0.595826 | − | 0.803114i | \(-0.703175\pi\) | ||||
−0.595826 | + | 0.803114i | \(0.703175\pi\) | |||||||
\(432\) | − 2.19599e43i | − 0.718039i | ||||||||
\(433\) | 4.30567e43i | 1.35516i | 0.735449 | + | 0.677580i | \(0.236971\pi\) | ||||
−0.735449 | + | 0.677580i | \(0.763029\pi\) | |||||||
\(434\) | 3.71284e42 | 0.112493 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.90094e43 | 0.533876 | ||||||||
\(437\) | − 8.70054e43i | − 2.35289i | ||||||||
\(438\) | 5.33988e43i | 1.39062i | ||||||||
\(439\) | 1.81689e43 | 0.455685 | 0.227843 | − | 0.973698i | \(-0.426833\pi\) | ||||
0.227843 | + | 0.973698i | \(0.426833\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.23047e43 | −1.44972 | ||||||||
\(442\) | 5.09071e43i | 1.14107i | ||||||||
\(443\) | − 2.81575e43i | − 0.608040i | −0.952666 | − | 0.304020i | \(-0.901671\pi\) | ||||
0.952666 | − | 0.304020i | \(-0.0983290\pi\) | |||||||
\(444\) | −5.08267e43 | −1.05748 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.25648e44 | 2.42734 | ||||||||
\(447\) | 1.10429e44i | 2.05594i | ||||||||
\(448\) | 9.48981e42i | 0.170283i | ||||||||
\(449\) | −2.21288e43 | −0.382731 | −0.191365 | − | 0.981519i | \(-0.561292\pi\) | ||||
−0.191365 | + | 0.981519i | \(0.561292\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.09169e43 | 0.818368 | ||||||||
\(452\) | − 6.61493e43i | − 1.02504i | ||||||||
\(453\) | − 5.24928e43i | − 0.784295i | ||||||||
\(454\) | −6.51938e43 | −0.939258 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.68839e43 | −0.226231 | ||||||||
\(457\) | 6.39404e43i | 0.826339i | 0.910654 | + | 0.413169i | \(0.135578\pi\) | ||||
−0.910654 | + | 0.413169i | \(0.864422\pi\) | |||||||
\(458\) | − 6.07772e43i | − 0.757636i | ||||||||
\(459\) | 1.03803e44 | 1.24824 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.79013e42 | 0.0983853 | 0.0491926 | − | 0.998789i | \(-0.484335\pi\) | ||||
0.0491926 | + | 0.998789i | \(0.484335\pi\) | |||||||
\(462\) | 1.67787e43i | 0.181203i | ||||||||
\(463\) | − 1.18763e44i | − 1.23764i | −0.785532 | − | 0.618821i | \(-0.787611\pi\) | ||||
0.785532 | − | 0.618821i | \(-0.212389\pi\) | |||||||
\(464\) | 1.10570e44 | 1.11196 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.15585e44 | −1.08276 | ||||||||
\(467\) | − 1.78679e44i | − 1.61564i | −0.589431 | − | 0.807819i | \(-0.700648\pi\) | ||||
0.589431 | − | 0.807819i | \(-0.299352\pi\) | |||||||
\(468\) | − 8.75291e43i | − 0.764005i | ||||||||
\(469\) | 2.98876e43 | 0.251849 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.58677e43 | 0.674504 | ||||||||
\(472\) | 3.83817e42i | 0.0291126i | ||||||||
\(473\) | 1.72411e43i | 0.126287i | ||||||||
\(474\) | 9.17595e43 | 0.649095 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.01341e43 | −0.264849 | ||||||||
\(477\) | − 1.40793e44i | − 0.897486i | ||||||||
\(478\) | − 1.84253e44i | − 1.13463i | ||||||||
\(479\) | −1.06259e44 | −0.632165 | −0.316082 | − | 0.948732i | \(-0.602368\pi\) | ||||
−0.316082 | + | 0.948732i | \(0.602368\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.56531e43 | 0.309098 | ||||||||
\(482\) | 3.91762e44i | 2.10255i | ||||||||
\(483\) | 6.22936e43i | 0.323084i | ||||||||
\(484\) | 1.53254e44 | 0.768178 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 3.69370e44 | 1.72967 | ||||||||
\(487\) | − 1.85504e44i | − 0.839700i | −0.907593 | − | 0.419850i | \(-0.862083\pi\) | ||||
0.907593 | − | 0.419850i | \(-0.137917\pi\) | |||||||
\(488\) | 1.41558e43i | 0.0619451i | ||||||||
\(489\) | −3.25651e43 | −0.137771 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.88210e43 | 0.351294 | 0.175647 | − | 0.984453i | \(-0.443798\pi\) | ||||
0.175647 | + | 0.984453i | \(0.443798\pi\) | |||||||
\(492\) | − 6.82062e44i | − 2.60855i | ||||||||
\(493\) | 5.22657e44i | 1.93305i | ||||||||
\(494\) | 3.43733e44 | 1.22949 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.43656e44 | −0.480703 | ||||||||
\(497\) | 3.87700e43i | 0.125492i | ||||||||
\(498\) | 3.29948e44i | 1.03314i | ||||||||
\(499\) | −2.77853e44 | −0.841699 | −0.420849 | − | 0.907131i | \(-0.638268\pi\) | ||||
−0.420849 | + | 0.907131i | \(0.638268\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.14564e44 | −1.74279 | ||||||||
\(502\) | 6.87428e44i | 1.88632i | ||||||||
\(503\) | 8.80760e41i | 0.00233876i | 0.999999 | + | 0.00116938i | \(0.000372226\pi\) | ||||
−0.999999 | + | 0.00116938i | \(0.999628\pi\) | |||||||
\(504\) | 7.22319e42 | 0.0185620 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.16117e44 | −1.00169 | ||||||||
\(507\) | − 5.16097e44i | − 1.20254i | ||||||||
\(508\) | − 4.05873e44i | − 0.915459i | ||||||||
\(509\) | 8.68803e44 | 1.89705 | 0.948523 | − | 0.316709i | \(-0.102578\pi\) | ||||
0.948523 | + | 0.316709i | \(0.102578\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.60961e43 | 0.0943450 | ||||||||
\(512\) | − 7.16687e44i | − 1.42028i | ||||||||
\(513\) | − 7.00892e44i | − 1.34498i | ||||||||
\(514\) | 5.44479e44 | 1.01179 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.30956e44 | 0.402539 | ||||||||
\(517\) | 5.93962e44i | 1.00269i | ||||||||
\(518\) | 8.53917e43i | 0.139629i | ||||||||
\(519\) | −6.33245e44 | −1.00302 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.56437e44 | −0.381205 | −0.190602 | − | 0.981667i | \(-0.561044\pi\) | ||||
−0.190602 | + | 0.981667i | \(0.561044\pi\) | |||||||
\(522\) | − 1.74897e45i | − 2.51894i | ||||||||
\(523\) | − 6.37079e43i | − 0.0889028i | −0.999012 | − | 0.0444514i | \(-0.985846\pi\) | ||||
0.999012 | − | 0.0444514i | \(-0.0141540\pi\) | |||||||
\(524\) | 2.39631e44 | 0.324024 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.45554e44 | 0.438784 | ||||||||
\(527\) | − 6.79052e44i | − 0.835657i | ||||||||
\(528\) | − 6.49197e44i | − 0.774314i | ||||||||
\(529\) | −6.79897e44 | −0.786004 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.88093e44 | −0.530204 | ||||||||
\(532\) | 2.70991e44i | 0.285373i | ||||||||
\(533\) | 7.46830e44i | 0.762471i | ||||||||
\(534\) | −4.18149e45 | −4.13905 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.43839e44 | 0.133862 | ||||||||
\(537\) | 2.97097e45i | 2.68116i | ||||||||
\(538\) | 9.57595e44i | 0.838059i | ||||||||
\(539\) | −6.01267e44 | −0.510332 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.56706e45 | −1.25121 | −0.625605 | − | 0.780140i | \(-0.715148\pi\) | ||||
−0.625605 | + | 0.780140i | \(0.715148\pi\) | |||||||
\(542\) | 2.52209e45i | 1.95332i | ||||||||
\(543\) | − 1.94899e44i | − 0.146424i | ||||||||
\(544\) | 3.20496e45 | 2.33583 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.46104e44 | −0.168826 | ||||||||
\(547\) | 2.05395e45i | 1.36710i | 0.729905 | + | 0.683548i | \(0.239564\pi\) | ||||
−0.729905 | + | 0.683548i | \(0.760436\pi\) | |||||||
\(548\) | 9.42359e44i | 0.608607i | ||||||||
\(549\) | −1.80017e45 | −1.12816 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.52906e45 | 2.08285 | ||||||||
\(552\) | 2.99797e44i | 0.171725i | ||||||||
\(553\) | − 7.92107e43i | − 0.0440371i | ||||||||
\(554\) | −4.09851e45 | −2.21164 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.60827e44 | −0.0817756 | ||||||||
\(557\) | − 3.02985e44i | − 0.149558i | −0.997200 | − | 0.0747792i | \(-0.976175\pi\) | ||||
0.997200 | − | 0.0747792i | \(-0.0238252\pi\) | |||||||
\(558\) | 2.27231e45i | 1.08894i | ||||||||
\(559\) | −2.52887e44 | −0.117661 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.06871e45 | 1.34607 | ||||||||
\(562\) | 2.08122e45i | 0.886478i | ||||||||
\(563\) | − 2.25447e45i | − 0.932514i | −0.884649 | − | 0.466257i | \(-0.845602\pi\) | ||||
0.884649 | − | 0.466257i | \(-0.154398\pi\) | |||||||
\(564\) | 7.95649e45 | 3.19607 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 9.62602e44 | 0.364733 | ||||||||
\(567\) | − 1.16886e44i | − 0.0430173i | ||||||||
\(568\) | 1.86586e44i | 0.0667009i | ||||||||
\(569\) | 3.27232e45 | 1.13633 | 0.568163 | − | 0.822916i | \(-0.307654\pi\) | ||||
0.568163 | + | 0.822916i | \(0.307654\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.07381e45 | 1.00735 | 0.503675 | − | 0.863893i | \(-0.331981\pi\) | ||||
0.503675 | + | 0.863893i | \(0.331981\pi\) | |||||||
\(572\) | − 8.44693e44i | − 0.268946i | ||||||||
\(573\) | − 7.10419e45i | − 2.19768i | ||||||||
\(574\) | −1.14590e45 | −0.344431 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −5.80792e45 | −1.64835 | ||||||||
\(577\) | 6.81899e43i | 0.0188070i | 0.999956 | + | 0.00940349i | \(0.00299327\pi\) | ||||
−0.999956 | + | 0.00940349i | \(0.997007\pi\) | |||||||
\(578\) | 8.93501e45i | 2.39489i | ||||||||
\(579\) | 7.62838e44 | 0.198718 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.84825e44 | 0.0700926 | ||||||||
\(582\) | 1.67255e44i | 0.0400082i | ||||||||
\(583\) | − 1.35871e45i | − 0.315934i | ||||||||
\(584\) | 2.21844e44 | 0.0501460 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.01963e46 | 2.17837 | ||||||||
\(587\) | 8.96797e45i | 1.86280i | 0.364002 | + | 0.931398i | \(0.381410\pi\) | ||||
−0.364002 | + | 0.931398i | \(0.618590\pi\) | |||||||
\(588\) | 8.05433e45i | 1.62669i | ||||||||
\(589\) | −4.58506e45 | −0.900416 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.08598e46 | −2.01665 | ||||||||
\(592\) | − 3.30395e45i | − 0.596659i | ||||||||
\(593\) | − 3.75910e45i | − 0.660209i | −0.943944 | − | 0.330104i | \(-0.892916\pi\) | ||||
0.943944 | − | 0.330104i | \(-0.107084\pi\) | |||||||
\(594\) | −3.35213e45 | −0.572590 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.53004e45 | 1.37844 | ||||||||
\(597\) | − 1.28342e46i | − 2.01740i | ||||||||
\(598\) | − 6.10345e45i | − 0.933268i | ||||||||
\(599\) | −8.80446e45 | −1.30966 | −0.654832 | − | 0.755774i | \(-0.727261\pi\) | ||||
−0.654832 | + | 0.755774i | \(0.727261\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.53048e45 | −0.637846 | −0.318923 | − | 0.947781i | \(-0.603321\pi\) | ||||
−0.318923 | + | 0.947781i | \(0.603321\pi\) | |||||||
\(602\) | − 3.88018e44i | − 0.0531508i | ||||||||
\(603\) | 1.82917e46i | 2.43791i | ||||||||
\(604\) | −4.05477e45 | −0.525844 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.42281e46 | −2.97524 | ||||||||
\(607\) | − 1.02463e46i | − 1.22448i | −0.790671 | − | 0.612242i | \(-0.790268\pi\) | ||||
0.790671 | − | 0.612242i | \(-0.209732\pi\) | |||||||
\(608\) | − 2.16404e46i | − 2.51684i | ||||||||
\(609\) | −2.52672e45 | −0.286003 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.71203e45 | −0.934199 | ||||||||
\(612\) | − 2.45627e46i | − 2.56376i | ||||||||
\(613\) | − 4.85425e45i | − 0.493201i | −0.969117 | − | 0.246601i | \(-0.920686\pi\) | ||||
0.969117 | − | 0.246601i | \(-0.0793136\pi\) | |||||||
\(614\) | 1.71865e46 | 1.69985 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.97068e43 | 0.00653421 | ||||||||
\(617\) | 1.62668e46i | 1.48455i | 0.670093 | + | 0.742277i | \(0.266254\pi\) | ||||
−0.670093 | + | 0.742277i | \(0.733746\pi\) | |||||||
\(618\) | − 1.09300e46i | − 0.971200i | ||||||||
\(619\) | 2.50157e45 | 0.216430 | 0.108215 | − | 0.994128i | \(-0.465486\pi\) | ||||
0.108215 | + | 0.994128i | \(0.465486\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.24453e46 | −1.02093 | ||||||||
\(622\) | 7.17763e45i | 0.573376i | ||||||||
\(623\) | 3.60964e45i | 0.280809i | ||||||||
\(624\) | 9.52220e45 | 0.721425 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.44337e46 | 1.03729 | ||||||||
\(627\) | − 2.07204e46i | − 1.45038i | ||||||||
\(628\) | − 6.63279e45i | − 0.452233i | ||||||||
\(629\) | 1.56175e46 | 1.03723 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.94339e45 | 0.437610 | 0.218805 | − | 0.975769i | \(-0.429784\pi\) | ||||
0.218805 | + | 0.975769i | \(0.429784\pi\) | |||||||
\(632\) | − 3.81213e44i | − 0.0234065i | ||||||||
\(633\) | 7.18871e45i | 0.430021i | ||||||||
\(634\) | 1.83603e46 | 1.07006 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.82008e46 | −1.00704 | ||||||||
\(637\) | − 8.81916e45i | − 0.475474i | ||||||||
\(638\) | − 1.68783e46i | − 0.886721i | ||||||||
\(639\) | −2.37278e46 | −1.21477 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.34529e45 | 0.211282 | 0.105641 | − | 0.994404i | \(-0.466311\pi\) | ||||
0.105641 | + | 0.994404i | \(0.466311\pi\) | |||||||
\(642\) | − 9.92303e45i | − 0.470236i | ||||||||
\(643\) | 2.56764e46i | 1.18591i | 0.805235 | + | 0.592956i | \(0.202039\pi\) | ||||
−0.805235 | + | 0.592956i | \(0.797961\pi\) | |||||||
\(644\) | 4.81183e45 | 0.216618 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.64592e46 | 4.12579 | ||||||||
\(647\) | 1.55928e46i | 0.650136i | 0.945691 | + | 0.325068i | \(0.105387\pi\) | ||||
−0.945691 | + | 0.325068i | \(0.894613\pi\) | |||||||
\(648\) | − 5.62533e44i | − 0.0228644i | ||||||||
\(649\) | −4.71030e45 | −0.186643 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.28279e45 | 0.123639 | ||||||||
\(652\) | 2.51547e45i | 0.0923706i | ||||||||
\(653\) | 1.54838e45i | 0.0554384i | 0.999616 | + | 0.0277192i | \(0.00882442\pi\) | ||||
−0.999616 | + | 0.0277192i | \(0.991176\pi\) | |||||||
\(654\) | 3.27112e46 | 1.14199 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.43370e46 | 1.47182 | ||||||||
\(657\) | 2.82115e46i | 0.913267i | ||||||||
\(658\) | − 1.33673e46i | − 0.422005i | ||||||||
\(659\) | 1.05260e46 | 0.324080 | 0.162040 | − | 0.986784i | \(-0.448193\pi\) | ||||
0.162040 | + | 0.986784i | \(0.448193\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.48865e46 | −0.435981 | −0.217990 | − | 0.975951i | \(-0.569950\pi\) | ||||
−0.217990 | + | 0.975951i | \(0.569950\pi\) | |||||||
\(662\) | 5.70840e46i | 1.63064i | ||||||||
\(663\) | 4.50107e46i | 1.25413i | ||||||||
\(664\) | 1.37076e45 | 0.0372554 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.22611e46 | −1.35162 | ||||||||
\(667\) | − 6.26634e46i | − 1.58102i | ||||||||
\(668\) | 4.74716e46i | 1.16848i | ||||||||
\(669\) | 1.11095e47 | 2.66786 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.73724e46 | −0.397134 | ||||||||
\(672\) | 1.54940e46i | 0.345597i | ||||||||
\(673\) | − 2.78172e46i | − 0.605432i | −0.953081 | − | 0.302716i | \(-0.902107\pi\) | ||||
0.953081 | − | 0.302716i | \(-0.0978933\pi\) | |||||||
\(674\) | −9.26605e46 | −1.96791 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.98656e46 | −0.806265 | ||||||||
\(677\) | 9.09948e45i | 0.179599i | 0.995960 | + | 0.0897995i | \(0.0286226\pi\) | ||||
−0.995960 | + | 0.0897995i | \(0.971377\pi\) | |||||||
\(678\) | − 1.13829e47i | − 2.19262i | ||||||||
\(679\) | 1.44381e44 | 0.00271431 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.76426e46 | −1.03233 | ||||||||
\(682\) | 2.19288e46i | 0.383330i | ||||||||
\(683\) | 2.07397e46i | 0.353883i | 0.984221 | + | 0.176942i | \(0.0566204\pi\) | ||||
−0.984221 | + | 0.176942i | \(0.943380\pi\) | |||||||
\(684\) | −1.65851e47 | −2.76244 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.73894e46 | 0.434746 | ||||||||
\(687\) | − 5.37376e46i | − 0.832707i | ||||||||
\(688\) | 1.50131e46i | 0.227123i | ||||||||
\(689\) | 1.99291e46 | 0.294354 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.80876e46 | 1.09950 | 0.549749 | − | 0.835330i | \(-0.314723\pi\) | ||||
0.549749 | + | 0.835330i | \(0.314723\pi\) | |||||||
\(692\) | 4.89146e46i | 0.672493i | ||||||||
\(693\) | 8.86448e45i | 0.119002i | ||||||||
\(694\) | −1.00599e47 | −1.31875 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.21602e46 | −0.152016 | ||||||||
\(697\) | 2.09578e47i | 2.55861i | ||||||||
\(698\) | 5.39729e46i | 0.643519i | ||||||||
\(699\) | −1.02197e47 | −1.19005 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.28838e46 | −0.809624 | −0.404812 | − | 0.914400i | \(-0.632663\pi\) | ||||
−0.404812 | + | 0.914400i | \(0.632663\pi\) | |||||||
\(702\) | − 4.91678e46i | − 0.533480i | ||||||||
\(703\) | − 1.05452e47i | − 1.11761i | ||||||||
\(704\) | −5.60488e46 | −0.580253 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.63176e47 | −2.59997 | ||||||||
\(707\) | 2.09147e46i | 0.201852i | ||||||||
\(708\) | 6.30974e46i | 0.594926i | ||||||||
\(709\) | −4.67334e46 | −0.430491 | −0.215246 | − | 0.976560i | \(-0.569055\pi\) | ||||
−0.215246 | + | 0.976560i | \(0.569055\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.84782e46 | 0.426283 | ||||||||
\(712\) | 1.73719e46i | 0.149255i | ||||||||
\(713\) | 8.14142e46i | 0.683476i | ||||||||
\(714\) | −6.90624e46 | −0.566528 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.29490e47 | 1.79763 | ||||||||
\(717\) | − 1.62911e47i | − 1.24705i | ||||||||
\(718\) | − 8.90958e46i | − 0.666506i | ||||||||
\(719\) | 1.27931e47 | 0.935299 | 0.467649 | − | 0.883914i | \(-0.345101\pi\) | ||||
0.467649 | + | 0.883914i | \(0.345101\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.43520e45 | −0.0658899 | ||||||||
\(722\) | − 4.41189e47i | − 3.01135i | ||||||||
\(723\) | 3.46385e47i | 2.31088i | ||||||||
\(724\) | −1.50548e46 | −0.0981725 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.63718e47 | 1.64318 | ||||||||
\(727\) | 1.68652e47i | 1.02724i | 0.858017 | + | 0.513621i | \(0.171696\pi\) | ||||
−0.858017 | + | 0.513621i | \(0.828304\pi\) | |||||||
\(728\) | 1.02243e45i | 0.00608790i | ||||||||
\(729\) | 2.78403e47 | 1.62057 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.09659e46 | −0.394832 | ||||||||
\(732\) | 2.32713e47i | 1.26587i | ||||||||
\(733\) | 3.19951e47i | 1.70164i | 0.525456 | + | 0.850821i | \(0.323895\pi\) | ||||
−0.525456 | + | 0.850821i | \(0.676105\pi\) | |||||||
\(734\) | 1.81532e47 | 0.943992 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.84255e47 | −1.91045 | ||||||||
\(737\) | 1.76523e47i | 0.858196i | ||||||||
\(738\) | − 7.01311e47i | − 3.33412i | ||||||||
\(739\) | 1.33356e47 | 0.619980 | 0.309990 | − | 0.950740i | \(-0.399674\pi\) | ||||
0.309990 | + | 0.950740i | \(0.399674\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.03919e47 | 1.35132 | ||||||||
\(742\) | 3.05783e46i | 0.132969i | ||||||||
\(743\) | 3.22840e46i | 0.137300i | 0.997641 | + | 0.0686502i | \(0.0218692\pi\) | ||||
−0.997641 | + | 0.0686502i | \(0.978131\pi\) | |||||||
\(744\) | 1.57989e46 | 0.0657164 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 4.42119e46 | 0.175934 | ||||||||
\(747\) | 1.74317e47i | 0.678502i | ||||||||
\(748\) | − 2.37040e47i | − 0.902497i | ||||||||
\(749\) | −8.56597e45 | −0.0319027 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.39672e46 | 0.0854196 | 0.0427098 | − | 0.999088i | \(-0.486401\pi\) | ||||
0.0427098 | + | 0.999088i | \(0.486401\pi\) | |||||||
\(752\) | 5.17206e47i | 1.80331i | ||||||||
\(753\) | 6.07806e47i | 2.07323i | ||||||||
\(754\) | 2.47565e47 | 0.826154 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3.87628e46 | 0.123824 | ||||||||
\(757\) | 6.92584e46i | 0.216466i | 0.994126 | + | 0.108233i | \(0.0345193\pi\) | ||||
−0.994126 | + | 0.108233i | \(0.965481\pi\) | |||||||
\(758\) | 1.75970e47i | 0.538143i | ||||||||
\(759\) | −3.67919e47 | −1.10094 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.97287e47 | −1.42482 | −0.712411 | − | 0.701763i | \(-0.752397\pi\) | ||||
−0.712411 | + | 0.701763i | \(0.752397\pi\) | |||||||
\(762\) | − 6.98423e47i | − 1.95822i | ||||||||
\(763\) | − 2.82377e46i | − 0.0774773i | ||||||||
\(764\) | −5.48759e47 | −1.47347 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.15131e47 | 1.83912 | ||||||||
\(767\) | − 6.90891e46i | − 0.173895i | ||||||||
\(768\) | − 5.61051e47i | − 1.38211i | ||||||||
\(769\) | −2.89778e47 | −0.698683 | −0.349342 | − | 0.936995i | \(-0.613595\pi\) | ||||
−0.349342 | + | 0.936995i | \(0.613595\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.81414e47 | 1.11204 | ||||||||
\(772\) | − 5.89249e46i | − 0.133234i | ||||||||
\(773\) | − 5.10656e47i | − 1.13023i | −0.825012 | − | 0.565115i | \(-0.808832\pi\) | ||||
0.825012 | − | 0.565115i | \(-0.191168\pi\) | |||||||
\(774\) | 2.37473e47 | 0.514504 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.94857e44 | 0.00144270 | ||||||||
\(777\) | 7.55010e46i | 0.153464i | ||||||||
\(778\) | − 9.21352e47i | − 1.83342i | ||||||||
\(779\) | 1.41510e48 | 2.75689 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.28983e47 | −0.427624 | ||||||||
\(782\) | − 1.71277e48i | − 3.13175i | ||||||||
\(783\) | − 5.04799e47i | − 0.903753i | ||||||||
\(784\) | −5.23567e47 | −0.917819 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4.12356e47 | 0.693107 | ||||||||
\(787\) | − 3.90010e47i | − 0.641938i | −0.947090 | − | 0.320969i | \(-0.895991\pi\) | ||||
0.947090 | − | 0.320969i | \(-0.104009\pi\) | |||||||
\(788\) | 8.38862e47i | 1.35210i | ||||||||
\(789\) | 3.05529e47 | 0.482261 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.82622e46 | −0.148756 | ||||||||
\(792\) | 4.26617e46i | 0.0632517i | ||||||||
\(793\) | − 2.54812e47i | − 0.370009i | ||||||||
\(794\) | 1.24086e48 | 1.76476 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.91367e47 | −1.35260 | ||||||||
\(797\) | − 6.38986e47i | − 0.853943i | −0.904265 | − | 0.426972i | \(-0.859580\pi\) | ||||
0.904265 | − | 0.426972i | \(-0.140420\pi\) | |||||||
\(798\) | 4.66320e47i | 0.610431i | ||||||||
\(799\) | −2.44479e48 | −3.13488 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.20916e48 | −2.71826 | ||||||||
\(802\) | − 4.53171e47i | − 0.546242i | ||||||||
\(803\) | 2.72253e47i | 0.321489i | ||||||||
\(804\) | 2.36463e48 | 2.73551 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.21644e47 | −0.357147 | ||||||||
\(807\) | 8.46680e47i | 0.921098i | ||||||||
\(808\) | 1.00655e47i | 0.107288i | ||||||||
\(809\) | 3.00339e47 | 0.313661 | 0.156831 | − | 0.987626i | \(-0.449872\pi\) | ||||
0.156831 | + | 0.987626i | \(0.449872\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.57205e48 | −1.57624 | −0.788121 | − | 0.615521i | \(-0.788946\pi\) | ||||
−0.788121 | + | 0.615521i | \(0.788946\pi\) | |||||||
\(812\) | 1.95175e47i | 0.191756i | ||||||||
\(813\) | 2.22997e48i | 2.14686i | ||||||||
\(814\) | −5.04341e47 | −0.475797 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.67215e48 | 2.42088 | ||||||||
\(817\) | 4.79172e47i | 0.425430i | ||||||||
\(818\) | 4.14782e47i | 0.360903i | ||||||||
\(819\) | −1.30021e47 | −0.110874 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.23751e48 | 1.83275 | 0.916374 | − | 0.400324i | \(-0.131102\pi\) | ||||
0.916374 | + | 0.400324i | \(0.131102\pi\) | |||||||
\(822\) | 1.62160e48i | 1.30185i | ||||||||
\(823\) | − 5.02472e47i | − 0.395380i | −0.980265 | − | 0.197690i | \(-0.936656\pi\) | ||||
0.980265 | − | 0.197690i | \(-0.0633439\pi\) | |||||||
\(824\) | −4.54083e46 | −0.0350216 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.06007e47 | 0.0785533 | ||||||||
\(827\) | − 1.52395e48i | − 1.10695i | −0.832865 | − | 0.553475i | \(-0.813301\pi\) | ||||
0.832865 | − | 0.553475i | \(-0.186699\pi\) | |||||||
\(828\) | 2.94492e48i | 2.09688i | ||||||||
\(829\) | −7.14872e47 | −0.498975 | −0.249487 | − | 0.968378i | \(-0.580262\pi\) | ||||
−0.249487 | + | 0.968378i | \(0.580262\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.62379e48 | −2.43078 | ||||||||
\(832\) | − 8.22104e47i | − 0.540620i | ||||||||
\(833\) | − 2.47486e48i | − 1.59554i | ||||||||
\(834\) | −2.76749e47 | −0.174923 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.60053e48 | −0.972436 | ||||||||
\(837\) | 6.55851e47i | 0.390693i | ||||||||
\(838\) | − 4.25968e48i | − 2.48800i | ||||||||
\(839\) | −2.41800e48 | −1.38479 | −0.692394 | − | 0.721519i | \(-0.743444\pi\) | ||||
−0.692394 | + | 0.721519i | \(0.743444\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.25637e47 | 0.399563 | ||||||||
\(842\) | − 7.23174e47i | − 0.390475i | ||||||||
\(843\) | 1.84015e48i | 0.974315i | ||||||||
\(844\) | 5.55287e47 | 0.288315 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 8.18103e48 | 4.08505 | ||||||||
\(847\) | − 2.27652e47i | − 0.111480i | ||||||||
\(848\) | − 1.18313e48i | − 0.568199i | ||||||||
\(849\) | 8.51107e47 | 0.400873 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.87245e48 | −0.848345 | ||||||||
\(852\) | 3.06737e48i | 1.36306i | ||||||||
\(853\) | 5.58595e47i | 0.243466i | 0.992563 | + | 0.121733i | \(0.0388452\pi\) | ||||
−0.992563 | + | 0.121733i | \(0.961155\pi\) | |||||||
\(854\) | 3.90972e47 | 0.167144 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.12250e46 | −0.0169568 | ||||||||
\(857\) | 7.99378e47i | 0.322529i | 0.986911 | + | 0.161264i | \(0.0515572\pi\) | ||||
−0.986911 | + | 0.161264i | \(0.948443\pi\) | |||||||
\(858\) | − 1.45354e48i | − 0.575290i | ||||||||
\(859\) | −3.21299e48 | −1.24745 | −0.623723 | − | 0.781646i | \(-0.714381\pi\) | ||||
−0.623723 | + | 0.781646i | \(0.714381\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.01318e48 | −0.378559 | ||||||||
\(862\) | 4.66251e48i | 1.70903i | ||||||||
\(863\) | 2.15382e48i | 0.774519i | 0.921971 | + | 0.387259i | \(0.126578\pi\) | ||||
−0.921971 | + | 0.387259i | \(0.873422\pi\) | |||||||
\(864\) | −3.09546e48 | −1.09206 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 5.72316e48 | 1.94353 | ||||||||
\(867\) | 7.90010e48i | 2.63219i | ||||||||
\(868\) | − 2.53577e47i | − 0.0828962i | ||||||||
\(869\) | 4.67835e47 | 0.150060 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.58917e48 | −0.799578 | ||||||||
\(872\) | − 1.35898e47i | − 0.0411805i | ||||||||
\(873\) | 8.83637e46i | 0.0262748i | ||||||||
\(874\) | −1.15649e49 | −3.37445 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.64700e48 | 1.02475 | ||||||||
\(877\) | − 4.36089e48i | − 1.20249i | −0.799064 | − | 0.601245i | \(-0.794671\pi\) | ||||
0.799064 | − | 0.601245i | \(-0.205329\pi\) | |||||||
\(878\) | − 2.41504e48i | − 0.653530i | ||||||||
\(879\) | 9.01528e48 | 2.39421 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.71885e48 | −1.20707 | −0.603537 | − | 0.797335i | \(-0.706242\pi\) | ||||
−0.603537 | + | 0.797335i | \(0.706242\pi\) | |||||||
\(882\) | 8.28163e48i | 2.07914i | ||||||||
\(883\) | − 2.47214e48i | − 0.609146i | −0.952489 | − | 0.304573i | \(-0.901486\pi\) | ||||
0.952489 | − | 0.304573i | \(-0.0985138\pi\) | |||||||
\(884\) | 3.47682e48 | 0.840853 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.74274e48 | −0.872033 | ||||||||
\(887\) | 6.65983e48i | 1.52308i | 0.648116 | + | 0.761542i | \(0.275557\pi\) | ||||
−0.648116 | + | 0.761542i | \(0.724443\pi\) | |||||||
\(888\) | 3.63360e47i | 0.0815686i | ||||||||
\(889\) | −6.02908e47 | −0.132853 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.90355e47 | 0.146585 | ||||||||
\(892\) | − 8.58144e48i | − 1.78871i | ||||||||
\(893\) | 1.65076e49i | 3.37781i | ||||||||
\(894\) | 1.46784e49 | 2.94856 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.28948e47 | 0.0249650 | ||||||||
\(897\) | − 5.39651e48i | − 1.02574i | ||||||||
\(898\) | 2.94139e48i | 0.548901i | ||||||||
\(899\) | −3.30227e48 | −0.605032 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.59256e48 | 0.987760 | ||||||||
\(902\) | − 6.76795e48i | − 1.17368i | ||||||||
\(903\) | − 3.43075e47i | − 0.0584173i | ||||||||
\(904\) | −4.72902e47 | −0.0790663 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6.97743e48 | −1.12481 | ||||||||
\(907\) | − 4.30056e48i | − 0.680777i | −0.940285 | − | 0.340388i | \(-0.889441\pi\) | ||||
0.940285 | − | 0.340388i | \(-0.110559\pi\) | |||||||
\(908\) | 4.45257e48i | 0.692140i | ||||||||
\(909\) | −1.28002e49 | −1.95394 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.43257e48 | −0.358106 | −0.179053 | − | 0.983839i | \(-0.557303\pi\) | ||||
−0.179053 | + | 0.983839i | \(0.557303\pi\) | |||||||
\(912\) | − 1.80427e49i | − 2.60848i | ||||||||
\(913\) | 1.68224e48i | 0.238847i | ||||||||
\(914\) | 8.49906e48 | 1.18511 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.15093e48 | −0.558303 | ||||||||
\(917\) | − 3.55963e47i | − 0.0470230i | ||||||||
\(918\) | − 1.37976e49i | − 1.79019i | ||||||||
\(919\) | −1.59035e48 | −0.202669 | −0.101334 | − | 0.994852i | \(-0.532311\pi\) | ||||
−0.101334 | + | 0.994852i | \(0.532311\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.51959e49 | 1.86828 | ||||||||
\(922\) | − 1.16840e48i | − 0.141101i | ||||||||
\(923\) | − 3.35865e48i | − 0.398416i | ||||||||
\(924\) | 1.14594e48 | 0.133529 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.57862e49 | −1.77499 | ||||||||
\(927\) | − 5.77449e48i | − 0.637820i | ||||||||
\(928\) | − 1.55859e49i | − 1.69119i | ||||||||
\(929\) | 1.48456e49 | 1.58248 | 0.791239 | − | 0.611507i | \(-0.209436\pi\) | ||||
0.791239 | + | 0.611507i | \(0.209436\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.67106e49 | −1.71919 | ||||||||
\(932\) | 7.89414e48i | 0.797888i | ||||||||
\(933\) | 6.34627e48i | 0.630190i | ||||||||
\(934\) | −2.37502e49 | −2.31710 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.25746e47 | −0.0589314 | ||||||||
\(937\) | 1.00831e49i | 0.933020i | 0.884516 | + | 0.466510i | \(0.154489\pi\) | ||||
−0.884516 | + | 0.466510i | \(0.845511\pi\) | |||||||
\(938\) | − 3.97271e48i | − 0.361193i | ||||||||
\(939\) | 1.27619e49 | 1.14007 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.04832e48 | 0.780440 | 0.390220 | − | 0.920722i | \(-0.372399\pi\) | ||||
0.390220 | + | 0.920722i | \(0.372399\pi\) | |||||||
\(942\) | − 1.14137e49i | − 0.967353i | ||||||||
\(943\) | − 2.51271e49i | − 2.09266i | ||||||||
\(944\) | −4.10161e48 | −0.335673 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.29172e48 | 0.181116 | ||||||||
\(947\) | 9.36347e48i | 0.727214i | 0.931552 | + | 0.363607i | \(0.118455\pi\) | ||||
−0.931552 | + | 0.363607i | \(0.881545\pi\) | |||||||
\(948\) | − 6.26693e48i | − 0.478319i | ||||||||
\(949\) | −3.99331e48 | −0.299530 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.62337e49 | 1.17609 | ||||||||
\(952\) | 2.86919e47i | 0.0204291i | ||||||||
\(953\) | 1.92193e49i | 1.34494i | 0.740123 | + | 0.672472i | \(0.234767\pi\) | ||||
−0.740123 | + | 0.672472i | \(0.765233\pi\) | |||||||
\(954\) | −1.87144e49 | −1.28715 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.25840e49 | −0.836109 | ||||||||
\(957\) | − 1.49233e49i | − 0.974582i | ||||||||
\(958\) | 1.41241e49i | 0.906631i | ||||||||
\(959\) | 1.39984e48 | 0.0883223 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.21131e49 | −0.738444 | ||||||||
\(962\) | − 7.39750e48i | − 0.443298i | ||||||||
\(963\) | − 5.24251e48i | − 0.308820i | ||||||||
\(964\) | 2.67563e49 | 1.54937 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 8.28017e48 | 0.463358 | ||||||||
\(967\) | 1.11182e49i | 0.611642i | 0.952089 | + | 0.305821i | \(0.0989309\pi\) | ||||
−0.952089 | + | 0.305821i | \(0.901069\pi\) | |||||||
\(968\) | − 1.09561e48i | − 0.0592533i | ||||||||
\(969\) | 8.52867e49 | 4.53460 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.55536e49 | 0.799308 | 0.399654 | − | 0.916666i | \(-0.369130\pi\) | ||||
0.399654 | + | 0.916666i | \(0.369130\pi\) | |||||||
\(972\) | − 2.52270e49i | − 1.27459i | ||||||||
\(973\) | 2.38902e47i | 0.0118674i | ||||||||
\(974\) | −2.46574e49 | −1.20427 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.51274e49 | −0.714236 | ||||||||
\(977\) | 2.43707e49i | 1.13138i | 0.824618 | + | 0.565690i | \(0.191390\pi\) | ||||
−0.824618 | + | 0.565690i | \(0.808610\pi\) | |||||||
\(978\) | 4.32860e48i | 0.197586i | ||||||||
\(979\) | −2.13193e49 | −0.956883 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.72819e49 | 0.749986 | ||||||||
\(982\) | − 1.18062e49i | − 0.503815i | ||||||||
\(983\) | 1.27767e48i | 0.0536148i | 0.999641 | + | 0.0268074i | \(0.00853409\pi\) | ||||
−0.999641 | + | 0.0268074i | \(0.991466\pi\) | |||||||
\(984\) | −4.87607e48 | −0.201210 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.94723e49 | 2.77231 | ||||||||
\(987\) | − 1.18191e49i | − 0.463820i | ||||||||
\(988\) | − 2.34760e49i | − 0.906015i | ||||||||
\(989\) | 8.50838e48 | 0.322930 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.47131e48 | −0.310982 | −0.155491 | − | 0.987837i | \(-0.549696\pi\) | ||||
−0.155491 | + | 0.987837i | \(0.549696\pi\) | |||||||
\(992\) | 2.02497e49i | 0.731100i | ||||||||
\(993\) | 5.04722e49i | 1.79221i | ||||||||
\(994\) | 5.15336e48 | 0.179976 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.25346e49 | 0.761326 | ||||||||
\(997\) | 4.23201e49i | 1.40629i | 0.711045 | + | 0.703147i | \(0.248222\pi\) | ||||
−0.711045 | + | 0.703147i | \(0.751778\pi\) | |||||||
\(998\) | 3.69327e49i | 1.20714i | ||||||||
\(999\) | −1.50840e49 | −0.484936 |
(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 | 25.34.b.c.24.2 | 12 | ||
5.2 | odd | 4 | 5.34.a.b.1.5 | ✓ | 6 | ||
5.3 | odd | 4 | 25.34.a.c.1.2 | 6 | |||
5.4 | even | 2 | inner | 25.34.b.c.24.11 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.34.a.b.1.5 | ✓ | 6 | 5.2 | odd | 4 | ||
25.34.a.c.1.2 | 6 | 5.3 | odd | 4 | |||
25.34.b.c.24.2 | 12 | 1.1 | even | 1 | trivial | ||
25.34.b.c.24.11 | 12 | 5.4 | even | 2 | inner |