Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,8,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
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: | yes |
Analytic conductor: | \(55.2921495107\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 6 x^{17} - 1798 x^{16} + 11087 x^{15} + 1326765 x^{14} - 8403720 x^{13} - 518334228 x^{12} + 3375594921 x^{11} + 115310342333 x^{10} + \cdots + 51\!\cdots\!48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-10.5486\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −9.54862 | −0.843986 | −0.421993 | − | 0.906599i | \(-0.638669\pi\) | ||||
−0.421993 | + | 0.906599i | \(0.638669\pi\) | |||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | −36.8240 | −0.287687 | ||||||||
\(5\) | 248.981 | 0.890781 | 0.445390 | − | 0.895336i | \(-0.353065\pi\) | ||||
0.445390 | + | 0.895336i | \(0.353065\pi\) | |||||||
\(6\) | −257.813 | −0.487276 | ||||||||
\(7\) | −1453.31 | −1.60145 | −0.800726 | − | 0.599031i | \(-0.795553\pi\) | ||||
−0.800726 | + | 0.599031i | \(0.795553\pi\) | |||||||
\(8\) | 1573.84 | 1.08679 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | −2377.42 | −0.751807 | ||||||||
\(11\) | −6465.27 | −1.46458 | −0.732288 | − | 0.680995i | \(-0.761548\pi\) | ||||
−0.732288 | + | 0.680995i | \(0.761548\pi\) | |||||||
\(12\) | −994.247 | −0.166096 | ||||||||
\(13\) | 4142.86 | 0.522996 | 0.261498 | − | 0.965204i | \(-0.415784\pi\) | ||||
0.261498 | + | 0.965204i | \(0.415784\pi\) | |||||||
\(14\) | 13877.1 | 1.35160 | ||||||||
\(15\) | 6722.48 | 0.514293 | ||||||||
\(16\) | −10314.5 | −0.629549 | ||||||||
\(17\) | −25815.2 | −1.27440 | −0.637198 | − | 0.770700i | \(-0.719907\pi\) | ||||
−0.637198 | + | 0.770700i | \(0.719907\pi\) | |||||||
\(18\) | −6960.94 | −0.281329 | ||||||||
\(19\) | 26877.5 | 0.898984 | 0.449492 | − | 0.893284i | \(-0.351605\pi\) | ||||
0.449492 | + | 0.893284i | \(0.351605\pi\) | |||||||
\(20\) | −9168.46 | −0.256266 | ||||||||
\(21\) | −39239.3 | −0.924599 | ||||||||
\(22\) | 61734.4 | 1.23608 | ||||||||
\(23\) | 58835.3 | 1.00830 | 0.504151 | − | 0.863616i | \(-0.331806\pi\) | ||||
0.504151 | + | 0.863616i | \(0.331806\pi\) | |||||||
\(24\) | 42493.7 | 0.627459 | ||||||||
\(25\) | −16133.6 | −0.206510 | ||||||||
\(26\) | −39558.6 | −0.441401 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | 53516.5 | 0.460717 | ||||||||
\(29\) | 13734.2 | 0.104571 | 0.0522856 | − | 0.998632i | \(-0.483349\pi\) | ||||
0.0522856 | + | 0.998632i | \(0.483349\pi\) | |||||||
\(30\) | −64190.4 | −0.434056 | ||||||||
\(31\) | 25833.8 | 0.155748 | 0.0778741 | − | 0.996963i | \(-0.475187\pi\) | ||||
0.0778741 | + | 0.996963i | \(0.475187\pi\) | |||||||
\(32\) | −102962. | −0.555460 | ||||||||
\(33\) | −174562. | −0.845574 | ||||||||
\(34\) | 246499. | 1.07557 | ||||||||
\(35\) | −361845. | −1.42654 | ||||||||
\(36\) | −26844.7 | −0.0958957 | ||||||||
\(37\) | 124281. | 0.403365 | 0.201682 | − | 0.979451i | \(-0.435359\pi\) | ||||
0.201682 | + | 0.979451i | \(0.435359\pi\) | |||||||
\(38\) | −256643. | −0.758730 | ||||||||
\(39\) | 111857. | 0.301952 | ||||||||
\(40\) | 391856. | 0.968092 | ||||||||
\(41\) | −201398. | −0.456365 | −0.228182 | − | 0.973618i | \(-0.573278\pi\) | ||||
−0.228182 | + | 0.973618i | \(0.573278\pi\) | |||||||
\(42\) | 374681. | 0.780349 | ||||||||
\(43\) | 24676.8 | 0.0473314 | 0.0236657 | − | 0.999720i | \(-0.492466\pi\) | ||||
0.0236657 | + | 0.999720i | \(0.492466\pi\) | |||||||
\(44\) | 238077. | 0.421340 | ||||||||
\(45\) | 181507. | 0.296927 | ||||||||
\(46\) | −561796. | −0.850993 | ||||||||
\(47\) | −412000. | −0.578835 | −0.289418 | − | 0.957203i | \(-0.593462\pi\) | ||||
−0.289418 | + | 0.957203i | \(0.593462\pi\) | |||||||
\(48\) | −278492. | −0.363470 | ||||||||
\(49\) | 1.28856e6 | 1.56465 | ||||||||
\(50\) | 154053. | 0.174291 | ||||||||
\(51\) | −697010. | −0.735773 | ||||||||
\(52\) | −152556. | −0.150459 | ||||||||
\(53\) | −43501.3 | −0.0401362 | −0.0200681 | − | 0.999799i | \(-0.506388\pi\) | ||||
−0.0200681 | + | 0.999799i | \(0.506388\pi\) | |||||||
\(54\) | −187945. | −0.162425 | ||||||||
\(55\) | −1.60973e6 | −1.30462 | ||||||||
\(56\) | −2.28727e6 | −1.74044 | ||||||||
\(57\) | 725694. | 0.519029 | ||||||||
\(58\) | −131143. | −0.0882566 | ||||||||
\(59\) | 205379. | 0.130189 | ||||||||
\(60\) | −247548. | −0.147955 | ||||||||
\(61\) | −1.61032e6 | −0.908362 | −0.454181 | − | 0.890909i | \(-0.650068\pi\) | ||||
−0.454181 | + | 0.890909i | \(0.650068\pi\) | |||||||
\(62\) | −246677. | −0.131449 | ||||||||
\(63\) | −1.05946e6 | −0.533817 | ||||||||
\(64\) | 2.30341e6 | 1.09835 | ||||||||
\(65\) | 1.03149e6 | 0.465875 | ||||||||
\(66\) | 1.66683e6 | 0.713653 | ||||||||
\(67\) | 1.37101e6 | 0.556904 | 0.278452 | − | 0.960450i | \(-0.410179\pi\) | ||||
0.278452 | + | 0.960450i | \(0.410179\pi\) | |||||||
\(68\) | 950617. | 0.366627 | ||||||||
\(69\) | 1.58855e6 | 0.582143 | ||||||||
\(70\) | 3.45512e6 | 1.20398 | ||||||||
\(71\) | 2.87276e6 | 0.952568 | 0.476284 | − | 0.879292i | \(-0.341983\pi\) | ||||
0.476284 | + | 0.879292i | \(0.341983\pi\) | |||||||
\(72\) | 1.14733e6 | 0.362263 | ||||||||
\(73\) | 4.37743e6 | 1.31701 | 0.658505 | − | 0.752576i | \(-0.271189\pi\) | ||||
0.658505 | + | 0.752576i | \(0.271189\pi\) | |||||||
\(74\) | −1.18671e6 | −0.340434 | ||||||||
\(75\) | −435606. | −0.119228 | ||||||||
\(76\) | −989737. | −0.258626 | ||||||||
\(77\) | 9.39602e6 | 2.34545 | ||||||||
\(78\) | −1.06808e6 | −0.254843 | ||||||||
\(79\) | −960831. | −0.219256 | −0.109628 | − | 0.993973i | \(-0.534966\pi\) | ||||
−0.109628 | + | 0.993973i | \(0.534966\pi\) | |||||||
\(80\) | −2.56812e6 | −0.560790 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 1.92307e6 | 0.385166 | ||||||||
\(83\) | 6.21351e6 | 1.19279 | 0.596395 | − | 0.802691i | \(-0.296599\pi\) | ||||
0.596395 | + | 0.802691i | \(0.296599\pi\) | |||||||
\(84\) | 1.44494e6 | 0.265995 | ||||||||
\(85\) | −6.42749e6 | −1.13521 | ||||||||
\(86\) | −235630. | −0.0399471 | ||||||||
\(87\) | 370825. | 0.0603742 | ||||||||
\(88\) | −1.01753e7 | −1.59169 | ||||||||
\(89\) | 9.66681e6 | 1.45351 | 0.726755 | − | 0.686896i | \(-0.241027\pi\) | ||||
0.726755 | + | 0.686896i | \(0.241027\pi\) | |||||||
\(90\) | −1.73314e6 | −0.250602 | ||||||||
\(91\) | −6.02084e6 | −0.837553 | ||||||||
\(92\) | −2.16655e6 | −0.290075 | ||||||||
\(93\) | 697514. | 0.0899213 | ||||||||
\(94\) | 3.93403e6 | 0.488529 | ||||||||
\(95\) | 6.69199e6 | 0.800798 | ||||||||
\(96\) | −2.77998e6 | −0.320695 | ||||||||
\(97\) | −1.18859e7 | −1.32231 | −0.661153 | − | 0.750251i | \(-0.729933\pi\) | ||||
−0.661153 | + | 0.750251i | \(0.729933\pi\) | |||||||
\(98\) | −1.23039e7 | −1.32054 | ||||||||
\(99\) | −4.71318e6 | −0.488192 | ||||||||
\(100\) | 594101. | 0.0594101 | ||||||||
\(101\) | 1.70394e7 | 1.64562 | 0.822808 | − | 0.568319i | \(-0.192406\pi\) | ||||
0.822808 | + | 0.568319i | \(0.192406\pi\) | |||||||
\(102\) | 6.65548e6 | 0.620982 | ||||||||
\(103\) | 1.76135e7 | 1.58824 | 0.794118 | − | 0.607764i | \(-0.207933\pi\) | ||||
0.794118 | + | 0.607764i | \(0.207933\pi\) | |||||||
\(104\) | 6.52020e6 | 0.568387 | ||||||||
\(105\) | −9.76983e6 | −0.823615 | ||||||||
\(106\) | 415377. | 0.0338744 | ||||||||
\(107\) | 2.01177e7 | 1.58758 | 0.793789 | − | 0.608193i | \(-0.208105\pi\) | ||||
0.793789 | + | 0.608193i | \(0.208105\pi\) | |||||||
\(108\) | −724806. | −0.0553654 | ||||||||
\(109\) | 1.35078e7 | 0.999063 | 0.499531 | − | 0.866296i | \(-0.333506\pi\) | ||||
0.499531 | + | 0.866296i | \(0.333506\pi\) | |||||||
\(110\) | 1.53707e7 | 1.10108 | ||||||||
\(111\) | 3.35558e6 | 0.232883 | ||||||||
\(112\) | 1.49902e7 | 1.00819 | ||||||||
\(113\) | −477253. | −0.0311153 | −0.0155577 | − | 0.999879i | \(-0.504952\pi\) | ||||
−0.0155577 | + | 0.999879i | \(0.504952\pi\) | |||||||
\(114\) | −6.92937e6 | −0.438053 | ||||||||
\(115\) | 1.46489e7 | 0.898176 | ||||||||
\(116\) | −505749. | −0.0300838 | ||||||||
\(117\) | 3.02014e6 | 0.174332 | ||||||||
\(118\) | −1.96109e6 | −0.109878 | ||||||||
\(119\) | 3.75174e7 | 2.04088 | ||||||||
\(120\) | 1.05801e7 | 0.558928 | ||||||||
\(121\) | 2.23125e7 | 1.14499 | ||||||||
\(122\) | 1.53764e7 | 0.766645 | ||||||||
\(123\) | −5.43775e6 | −0.263482 | ||||||||
\(124\) | −951304. | −0.0448068 | ||||||||
\(125\) | −2.34686e7 | −1.07474 | ||||||||
\(126\) | 1.01164e7 | 0.450535 | ||||||||
\(127\) | 2.32024e7 | 1.00512 | 0.502562 | − | 0.864541i | \(-0.332391\pi\) | ||||
0.502562 | + | 0.864541i | \(0.332391\pi\) | |||||||
\(128\) | −8.81518e6 | −0.371532 | ||||||||
\(129\) | 666274. | 0.0273268 | ||||||||
\(130\) | −9.84932e6 | −0.393192 | ||||||||
\(131\) | −4.19666e6 | −0.163100 | −0.0815501 | − | 0.996669i | \(-0.525987\pi\) | ||||
−0.0815501 | + | 0.996669i | \(0.525987\pi\) | |||||||
\(132\) | 6.42807e6 | 0.243261 | ||||||||
\(133\) | −3.90613e7 | −1.43968 | ||||||||
\(134\) | −1.30913e7 | −0.470019 | ||||||||
\(135\) | 4.90069e6 | 0.171431 | ||||||||
\(136\) | −4.06290e7 | −1.38500 | ||||||||
\(137\) | −2.12221e7 | −0.705126 | −0.352563 | − | 0.935788i | \(-0.614690\pi\) | ||||
−0.352563 | + | 0.935788i | \(0.614690\pi\) | |||||||
\(138\) | −1.51685e7 | −0.491321 | ||||||||
\(139\) | 5.22180e7 | 1.64918 | 0.824591 | − | 0.565729i | \(-0.191405\pi\) | ||||
0.824591 | + | 0.565729i | \(0.191405\pi\) | |||||||
\(140\) | 1.33246e7 | 0.410398 | ||||||||
\(141\) | −1.11240e7 | −0.334191 | ||||||||
\(142\) | −2.74309e7 | −0.803954 | ||||||||
\(143\) | −2.67847e7 | −0.765968 | ||||||||
\(144\) | −7.51929e6 | −0.209850 | ||||||||
\(145\) | 3.41956e6 | 0.0931500 | ||||||||
\(146\) | −4.17984e7 | −1.11154 | ||||||||
\(147\) | 3.47910e7 | 0.903351 | ||||||||
\(148\) | −4.57651e6 | −0.116043 | ||||||||
\(149\) | 3.35373e7 | 0.830569 | 0.415285 | − | 0.909692i | \(-0.363682\pi\) | ||||
0.415285 | + | 0.909692i | \(0.363682\pi\) | |||||||
\(150\) | 4.15943e6 | 0.100627 | ||||||||
\(151\) | −2.21646e7 | −0.523890 | −0.261945 | − | 0.965083i | \(-0.584364\pi\) | ||||
−0.261945 | + | 0.965083i | \(0.584364\pi\) | |||||||
\(152\) | 4.23010e7 | 0.977007 | ||||||||
\(153\) | −1.88193e7 | −0.424798 | ||||||||
\(154\) | −8.97189e7 | −1.97953 | ||||||||
\(155\) | 6.43213e6 | 0.138738 | ||||||||
\(156\) | −4.11902e6 | −0.0868676 | ||||||||
\(157\) | −5.80763e7 | −1.19771 | −0.598853 | − | 0.800859i | \(-0.704377\pi\) | ||||
−0.598853 | + | 0.800859i | \(0.704377\pi\) | |||||||
\(158\) | 9.17461e6 | 0.185049 | ||||||||
\(159\) | −1.17453e6 | −0.0231727 | ||||||||
\(160\) | −2.56356e7 | −0.494793 | ||||||||
\(161\) | −8.55057e7 | −1.61475 | ||||||||
\(162\) | −5.07453e6 | −0.0937763 | ||||||||
\(163\) | −7.64837e7 | −1.38329 | −0.691643 | − | 0.722239i | \(-0.743113\pi\) | ||||
−0.691643 | + | 0.722239i | \(0.743113\pi\) | |||||||
\(164\) | 7.41628e6 | 0.131290 | ||||||||
\(165\) | −4.34627e7 | −0.753221 | ||||||||
\(166\) | −5.93304e7 | −1.00670 | ||||||||
\(167\) | 7.60086e7 | 1.26286 | 0.631430 | − | 0.775433i | \(-0.282468\pi\) | ||||
0.631430 | + | 0.775433i | \(0.282468\pi\) | |||||||
\(168\) | −6.17564e7 | −1.00485 | ||||||||
\(169\) | −4.55852e7 | −0.726475 | ||||||||
\(170\) | 6.13736e7 | 0.958099 | ||||||||
\(171\) | 1.95937e7 | 0.299661 | ||||||||
\(172\) | −908698. | −0.0136166 | ||||||||
\(173\) | −9.21166e7 | −1.35262 | −0.676311 | − | 0.736616i | \(-0.736422\pi\) | ||||
−0.676311 | + | 0.736616i | \(0.736422\pi\) | |||||||
\(174\) | −3.54086e6 | −0.0509550 | ||||||||
\(175\) | 2.34470e7 | 0.330715 | ||||||||
\(176\) | 6.66862e7 | 0.922023 | ||||||||
\(177\) | 5.54523e6 | 0.0751646 | ||||||||
\(178\) | −9.23047e7 | −1.22674 | ||||||||
\(179\) | 5.97291e7 | 0.778396 | 0.389198 | − | 0.921154i | \(-0.372752\pi\) | ||||
0.389198 | + | 0.921154i | \(0.372752\pi\) | |||||||
\(180\) | −6.68381e6 | −0.0854221 | ||||||||
\(181\) | −9.97102e7 | −1.24987 | −0.624934 | − | 0.780677i | \(-0.714874\pi\) | ||||
−0.624934 | + | 0.780677i | \(0.714874\pi\) | |||||||
\(182\) | 5.74907e7 | 0.706883 | ||||||||
\(183\) | −4.34787e7 | −0.524443 | ||||||||
\(184\) | 9.25974e7 | 1.09581 | ||||||||
\(185\) | 3.09435e7 | 0.359309 | ||||||||
\(186\) | −6.66029e6 | −0.0758923 | ||||||||
\(187\) | 1.66902e8 | 1.86645 | ||||||||
\(188\) | 1.51715e7 | 0.166523 | ||||||||
\(189\) | −2.86054e7 | −0.308200 | ||||||||
\(190\) | −6.38993e7 | −0.675862 | ||||||||
\(191\) | −2.03999e6 | −0.0211841 | −0.0105921 | − | 0.999944i | \(-0.503372\pi\) | ||||
−0.0105921 | + | 0.999944i | \(0.503372\pi\) | |||||||
\(192\) | 6.21919e7 | 0.634132 | ||||||||
\(193\) | 1.32752e8 | 1.32920 | 0.664602 | − | 0.747198i | \(-0.268601\pi\) | ||||
0.664602 | + | 0.747198i | \(0.268601\pi\) | |||||||
\(194\) | 1.13494e8 | 1.11601 | ||||||||
\(195\) | 2.78503e7 | 0.268973 | ||||||||
\(196\) | −4.74497e7 | −0.450130 | ||||||||
\(197\) | −1.07186e8 | −0.998867 | −0.499434 | − | 0.866352i | \(-0.666458\pi\) | ||||
−0.499434 | + | 0.866352i | \(0.666458\pi\) | |||||||
\(198\) | 4.50043e7 | 0.412028 | ||||||||
\(199\) | −1.08221e8 | −0.973474 | −0.486737 | − | 0.873549i | \(-0.661813\pi\) | ||||
−0.486737 | + | 0.873549i | \(0.661813\pi\) | |||||||
\(200\) | −2.53916e7 | −0.224433 | ||||||||
\(201\) | 3.70174e7 | 0.321528 | ||||||||
\(202\) | −1.62702e8 | −1.38888 | ||||||||
\(203\) | −1.99601e7 | −0.167466 | ||||||||
\(204\) | 2.56667e7 | 0.211672 | ||||||||
\(205\) | −5.01443e7 | −0.406521 | ||||||||
\(206\) | −1.68184e8 | −1.34045 | ||||||||
\(207\) | 4.28909e7 | 0.336101 | ||||||||
\(208\) | −4.27316e7 | −0.329252 | ||||||||
\(209\) | −1.73771e8 | −1.31663 | ||||||||
\(210\) | 9.32883e7 | 0.695120 | ||||||||
\(211\) | 1.65214e8 | 1.21076 | 0.605380 | − | 0.795937i | \(-0.293021\pi\) | ||||
0.605380 | + | 0.795937i | \(0.293021\pi\) | |||||||
\(212\) | 1.60189e6 | 0.0115467 | ||||||||
\(213\) | 7.75647e7 | 0.549965 | ||||||||
\(214\) | −1.92096e8 | −1.33989 | ||||||||
\(215\) | 6.14406e6 | 0.0421619 | ||||||||
\(216\) | 3.09779e7 | 0.209153 | ||||||||
\(217\) | −3.75445e7 | −0.249423 | ||||||||
\(218\) | −1.28981e8 | −0.843195 | ||||||||
\(219\) | 1.18191e8 | 0.760377 | ||||||||
\(220\) | 5.92765e7 | 0.375321 | ||||||||
\(221\) | −1.06949e8 | −0.666504 | ||||||||
\(222\) | −3.20411e7 | −0.196550 | ||||||||
\(223\) | 1.30090e7 | 0.0785558 | 0.0392779 | − | 0.999228i | \(-0.487494\pi\) | ||||
0.0392779 | + | 0.999228i | \(0.487494\pi\) | |||||||
\(224\) | 1.49635e8 | 0.889542 | ||||||||
\(225\) | −1.17614e7 | −0.0688365 | ||||||||
\(226\) | 4.55711e6 | 0.0262609 | ||||||||
\(227\) | 3.00513e8 | 1.70519 | 0.852595 | − | 0.522572i | \(-0.175027\pi\) | ||||
0.852595 | + | 0.522572i | \(0.175027\pi\) | |||||||
\(228\) | −2.67229e7 | −0.149318 | ||||||||
\(229\) | 4.51247e7 | 0.248308 | 0.124154 | − | 0.992263i | \(-0.460378\pi\) | ||||
0.124154 | + | 0.992263i | \(0.460378\pi\) | |||||||
\(230\) | −1.39876e8 | −0.758048 | ||||||||
\(231\) | 2.53692e8 | 1.35415 | ||||||||
\(232\) | 2.16155e7 | 0.113647 | ||||||||
\(233\) | 2.62782e8 | 1.36097 | 0.680486 | − | 0.732761i | \(-0.261769\pi\) | ||||
0.680486 | + | 0.732761i | \(0.261769\pi\) | |||||||
\(234\) | −2.88382e7 | −0.147134 | ||||||||
\(235\) | −1.02580e8 | −0.515615 | ||||||||
\(236\) | −7.56287e6 | −0.0374537 | ||||||||
\(237\) | −2.59424e7 | −0.126588 | ||||||||
\(238\) | −3.58239e8 | −1.72248 | ||||||||
\(239\) | −3.84804e8 | −1.82325 | −0.911626 | − | 0.411022i | \(-0.865172\pi\) | ||||
−0.911626 | + | 0.411022i | \(0.865172\pi\) | |||||||
\(240\) | −6.93392e7 | −0.323772 | ||||||||
\(241\) | 1.89745e8 | 0.873194 | 0.436597 | − | 0.899657i | \(-0.356184\pi\) | ||||
0.436597 | + | 0.899657i | \(0.356184\pi\) | |||||||
\(242\) | −2.13054e8 | −0.966352 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | 5.92985e7 | 0.261324 | ||||||||
\(245\) | 3.20826e8 | 1.39376 | ||||||||
\(246\) | 5.19230e7 | 0.222375 | ||||||||
\(247\) | 1.11350e8 | 0.470165 | ||||||||
\(248\) | 4.06583e7 | 0.169266 | ||||||||
\(249\) | 1.67765e8 | 0.688657 | ||||||||
\(250\) | 2.24092e8 | 0.907062 | ||||||||
\(251\) | −1.89901e8 | −0.758002 | −0.379001 | − | 0.925396i | \(-0.623732\pi\) | ||||
−0.379001 | + | 0.925396i | \(0.623732\pi\) | |||||||
\(252\) | 3.90135e7 | 0.153572 | ||||||||
\(253\) | −3.80386e8 | −1.47674 | ||||||||
\(254\) | −2.21550e8 | −0.848310 | ||||||||
\(255\) | −1.73542e8 | −0.655412 | ||||||||
\(256\) | −2.10663e8 | −0.784781 | ||||||||
\(257\) | 3.23214e8 | 1.18775 | 0.593874 | − | 0.804558i | \(-0.297598\pi\) | ||||
0.593874 | + | 0.804558i | \(0.297598\pi\) | |||||||
\(258\) | −6.36200e6 | −0.0230635 | ||||||||
\(259\) | −1.80618e8 | −0.645969 | ||||||||
\(260\) | −3.79836e7 | −0.134026 | ||||||||
\(261\) | 1.00123e7 | 0.0348571 | ||||||||
\(262\) | 4.00723e7 | 0.137654 | ||||||||
\(263\) | −9.96217e7 | −0.337683 | −0.168841 | − | 0.985643i | \(-0.554003\pi\) | ||||
−0.168841 | + | 0.985643i | \(0.554003\pi\) | |||||||
\(264\) | −2.74733e8 | −0.918961 | ||||||||
\(265\) | −1.08310e7 | −0.0357526 | ||||||||
\(266\) | 3.72981e8 | 1.21507 | ||||||||
\(267\) | 2.61004e8 | 0.839185 | ||||||||
\(268\) | −5.04861e7 | −0.160214 | ||||||||
\(269\) | 5.17058e8 | 1.61960 | 0.809798 | − | 0.586709i | \(-0.199577\pi\) | ||||
0.809798 | + | 0.586709i | \(0.199577\pi\) | |||||||
\(270\) | −4.67948e7 | −0.144685 | ||||||||
\(271\) | 9.10242e6 | 0.0277821 | 0.0138910 | − | 0.999904i | \(-0.495578\pi\) | ||||
0.0138910 | + | 0.999904i | \(0.495578\pi\) | |||||||
\(272\) | 2.66272e8 | 0.802294 | ||||||||
\(273\) | −1.62563e8 | −0.483561 | ||||||||
\(274\) | 2.02642e8 | 0.595117 | ||||||||
\(275\) | 1.04308e8 | 0.302449 | ||||||||
\(276\) | −5.84968e7 | −0.167475 | ||||||||
\(277\) | 1.04754e8 | 0.296135 | 0.148068 | − | 0.988977i | \(-0.452695\pi\) | ||||
0.148068 | + | 0.988977i | \(0.452695\pi\) | |||||||
\(278\) | −4.98610e8 | −1.39189 | ||||||||
\(279\) | 1.88329e7 | 0.0519161 | ||||||||
\(280\) | −5.69487e8 | −1.55035 | ||||||||
\(281\) | −2.20844e8 | −0.593765 | −0.296882 | − | 0.954914i | \(-0.595947\pi\) | ||||
−0.296882 | + | 0.954914i | \(0.595947\pi\) | |||||||
\(282\) | 1.06219e8 | 0.282052 | ||||||||
\(283\) | 4.56240e8 | 1.19658 | 0.598289 | − | 0.801280i | \(-0.295847\pi\) | ||||
0.598289 | + | 0.801280i | \(0.295847\pi\) | |||||||
\(284\) | −1.05787e8 | −0.274041 | ||||||||
\(285\) | 1.80684e8 | 0.462341 | ||||||||
\(286\) | 2.55757e8 | 0.646466 | ||||||||
\(287\) | 2.92693e8 | 0.730846 | ||||||||
\(288\) | −7.50594e7 | −0.185153 | ||||||||
\(289\) | 2.56086e8 | 0.624084 | ||||||||
\(290\) | −3.26521e7 | −0.0786173 | ||||||||
\(291\) | −3.20920e8 | −0.763434 | ||||||||
\(292\) | −1.61194e8 | −0.378887 | ||||||||
\(293\) | 1.06837e8 | 0.248133 | 0.124067 | − | 0.992274i | \(-0.460406\pi\) | ||||
0.124067 | + | 0.992274i | \(0.460406\pi\) | |||||||
\(294\) | −3.32206e8 | −0.762416 | ||||||||
\(295\) | 5.11354e7 | 0.115970 | ||||||||
\(296\) | 1.95598e8 | 0.438373 | ||||||||
\(297\) | −1.27256e8 | −0.281858 | ||||||||
\(298\) | −3.20235e8 | −0.700989 | ||||||||
\(299\) | 2.43746e8 | 0.527338 | ||||||||
\(300\) | 1.60407e7 | 0.0343005 | ||||||||
\(301\) | −3.58630e7 | −0.0757991 | ||||||||
\(302\) | 2.11641e8 | 0.442156 | ||||||||
\(303\) | 4.60063e8 | 0.950097 | ||||||||
\(304\) | −2.77229e8 | −0.565954 | ||||||||
\(305\) | −4.00940e8 | −0.809151 | ||||||||
\(306\) | 1.79698e8 | 0.358524 | ||||||||
\(307\) | −4.91926e8 | −0.970322 | −0.485161 | − | 0.874425i | \(-0.661239\pi\) | ||||
−0.485161 | + | 0.874425i | \(0.661239\pi\) | |||||||
\(308\) | −3.45998e8 | −0.674756 | ||||||||
\(309\) | 4.75564e8 | 0.916969 | ||||||||
\(310\) | −6.14179e7 | −0.117093 | ||||||||
\(311\) | −34302.1 | −6.46634e−5 0 | −3.23317e−5 | − | 1.00000i | \(-0.500010\pi\) | ||||
−3.23317e−5 | 1.00000i | \(0.500010\pi\) | ||||||||
\(312\) | 1.76045e8 | 0.328158 | ||||||||
\(313\) | −2.14984e8 | −0.396279 | −0.198139 | − | 0.980174i | \(-0.563490\pi\) | ||||
−0.198139 | + | 0.980174i | \(0.563490\pi\) | |||||||
\(314\) | 5.54548e8 | 1.01085 | ||||||||
\(315\) | −2.63785e8 | −0.475514 | ||||||||
\(316\) | 3.53816e7 | 0.0630772 | ||||||||
\(317\) | −4.71181e8 | −0.830769 | −0.415385 | − | 0.909646i | \(-0.636353\pi\) | ||||
−0.415385 | + | 0.909646i | \(0.636353\pi\) | |||||||
\(318\) | 1.12152e7 | 0.0195574 | ||||||||
\(319\) | −8.87956e7 | −0.153152 | ||||||||
\(320\) | 5.73504e8 | 0.978388 | ||||||||
\(321\) | 5.43178e8 | 0.916589 | ||||||||
\(322\) | 8.16461e8 | 1.36282 | ||||||||
\(323\) | −6.93849e8 | −1.14566 | ||||||||
\(324\) | −1.95698e7 | −0.0319652 | ||||||||
\(325\) | −6.68390e7 | −0.108004 | ||||||||
\(326\) | 7.30313e8 | 1.16747 | ||||||||
\(327\) | 3.64711e8 | 0.576809 | ||||||||
\(328\) | −3.16969e8 | −0.495973 | ||||||||
\(329\) | 5.98762e8 | 0.926977 | ||||||||
\(330\) | 4.15008e8 | 0.635708 | ||||||||
\(331\) | 1.20626e9 | 1.82829 | 0.914143 | − | 0.405391i | \(-0.132865\pi\) | ||||
0.914143 | + | 0.405391i | \(0.132865\pi\) | |||||||
\(332\) | −2.28806e8 | −0.343150 | ||||||||
\(333\) | 9.06007e7 | 0.134455 | ||||||||
\(334\) | −7.25777e8 | −1.06584 | ||||||||
\(335\) | 3.41356e8 | 0.496079 | ||||||||
\(336\) | 4.04735e8 | 0.582080 | ||||||||
\(337\) | −5.37145e8 | −0.764517 | −0.382258 | − | 0.924055i | \(-0.624854\pi\) | ||||
−0.382258 | + | 0.924055i | \(0.624854\pi\) | |||||||
\(338\) | 4.35276e8 | 0.613135 | ||||||||
\(339\) | −1.28858e7 | −0.0179644 | ||||||||
\(340\) | 2.36686e8 | 0.326584 | ||||||||
\(341\) | −1.67023e8 | −0.228105 | ||||||||
\(342\) | −1.87093e8 | −0.252910 | ||||||||
\(343\) | −6.75807e8 | −0.904259 | ||||||||
\(344\) | 3.88374e7 | 0.0514394 | ||||||||
\(345\) | 3.95519e8 | 0.518562 | ||||||||
\(346\) | 8.79586e8 | 1.14159 | ||||||||
\(347\) | −1.07234e9 | −1.37778 | −0.688888 | − | 0.724867i | \(-0.741901\pi\) | ||||
−0.688888 | + | 0.724867i | \(0.741901\pi\) | |||||||
\(348\) | −1.36552e7 | −0.0173689 | ||||||||
\(349\) | −6.30212e8 | −0.793592 | −0.396796 | − | 0.917907i | \(-0.629878\pi\) | ||||
−0.396796 | + | 0.917907i | \(0.629878\pi\) | |||||||
\(350\) | −2.23886e8 | −0.279119 | ||||||||
\(351\) | 8.15439e7 | 0.100651 | ||||||||
\(352\) | 6.65678e8 | 0.813513 | ||||||||
\(353\) | −1.30728e9 | −1.58182 | −0.790908 | − | 0.611936i | \(-0.790391\pi\) | ||||
−0.790908 | + | 0.611936i | \(0.790391\pi\) | |||||||
\(354\) | −5.29493e7 | −0.0634379 | ||||||||
\(355\) | 7.15263e8 | 0.848529 | ||||||||
\(356\) | −3.55970e8 | −0.418156 | ||||||||
\(357\) | 1.01297e9 | 1.17830 | ||||||||
\(358\) | −5.70330e8 | −0.656956 | ||||||||
\(359\) | 1.57238e9 | 1.79360 | 0.896802 | − | 0.442432i | \(-0.145884\pi\) | ||||
0.896802 | + | 0.442432i | \(0.145884\pi\) | |||||||
\(360\) | 2.85663e8 | 0.322697 | ||||||||
\(361\) | −1.71470e8 | −0.191828 | ||||||||
\(362\) | 9.52094e8 | 1.05487 | ||||||||
\(363\) | 6.02438e8 | 0.661058 | ||||||||
\(364\) | 2.21711e8 | 0.240953 | ||||||||
\(365\) | 1.08990e9 | 1.17317 | ||||||||
\(366\) | 4.15162e8 | 0.442623 | ||||||||
\(367\) | −1.48548e9 | −1.56868 | −0.784342 | − | 0.620329i | \(-0.786999\pi\) | ||||
−0.784342 | + | 0.620329i | \(0.786999\pi\) | |||||||
\(368\) | −6.06858e8 | −0.634775 | ||||||||
\(369\) | −1.46819e8 | −0.152122 | ||||||||
\(370\) | −2.95468e8 | −0.303252 | ||||||||
\(371\) | 6.32207e7 | 0.0642763 | ||||||||
\(372\) | −2.56852e7 | −0.0258692 | ||||||||
\(373\) | −9.92307e8 | −0.990069 | −0.495034 | − | 0.868873i | \(-0.664845\pi\) | ||||
−0.495034 | + | 0.868873i | \(0.664845\pi\) | |||||||
\(374\) | −1.59368e9 | −1.57526 | ||||||||
\(375\) | −6.33651e8 | −0.620499 | ||||||||
\(376\) | −6.48422e8 | −0.629072 | ||||||||
\(377\) | 5.68990e7 | 0.0546903 | ||||||||
\(378\) | 2.73142e8 | 0.260116 | ||||||||
\(379\) | −1.37321e9 | −1.29569 | −0.647844 | − | 0.761773i | \(-0.724329\pi\) | ||||
−0.647844 | + | 0.761773i | \(0.724329\pi\) | |||||||
\(380\) | −2.46426e8 | −0.230379 | ||||||||
\(381\) | 6.26464e8 | 0.580308 | ||||||||
\(382\) | 1.94790e7 | 0.0178791 | ||||||||
\(383\) | 1.58828e9 | 1.44455 | 0.722275 | − | 0.691606i | \(-0.243097\pi\) | ||||
0.722275 | + | 0.691606i | \(0.243097\pi\) | |||||||
\(384\) | −2.38010e8 | −0.214504 | ||||||||
\(385\) | 2.33943e9 | 2.08928 | ||||||||
\(386\) | −1.26760e9 | −1.12183 | ||||||||
\(387\) | 1.79894e7 | 0.0157771 | ||||||||
\(388\) | 4.37687e8 | 0.380410 | ||||||||
\(389\) | −1.66679e8 | −0.143568 | −0.0717841 | − | 0.997420i | \(-0.522869\pi\) | ||||
−0.0717841 | + | 0.997420i | \(0.522869\pi\) | |||||||
\(390\) | −2.65932e8 | −0.227009 | ||||||||
\(391\) | −1.51884e9 | −1.28497 | ||||||||
\(392\) | 2.02798e9 | 1.70045 | ||||||||
\(393\) | −1.13310e8 | −0.0941659 | ||||||||
\(394\) | 1.02348e9 | 0.843030 | ||||||||
\(395\) | −2.39229e8 | −0.195309 | ||||||||
\(396\) | 1.73558e8 | 0.140447 | ||||||||
\(397\) | −1.07153e9 | −0.859482 | −0.429741 | − | 0.902952i | \(-0.641395\pi\) | ||||
−0.429741 | + | 0.902952i | \(0.641395\pi\) | |||||||
\(398\) | 1.03336e9 | 0.821599 | ||||||||
\(399\) | −1.05466e9 | −0.831200 | ||||||||
\(400\) | 1.66410e8 | 0.130008 | ||||||||
\(401\) | 1.56895e8 | 0.121508 | 0.0607538 | − | 0.998153i | \(-0.480650\pi\) | ||||
0.0607538 | + | 0.998153i | \(0.480650\pi\) | |||||||
\(402\) | −3.53465e8 | −0.271366 | ||||||||
\(403\) | 1.07026e8 | 0.0814557 | ||||||||
\(404\) | −6.27457e8 | −0.473423 | ||||||||
\(405\) | 1.32319e8 | 0.0989756 | ||||||||
\(406\) | 1.90591e8 | 0.141339 | ||||||||
\(407\) | −8.03508e8 | −0.590758 | ||||||||
\(408\) | −1.09698e9 | −0.799630 | ||||||||
\(409\) | −1.06873e9 | −0.772392 | −0.386196 | − | 0.922417i | \(-0.626211\pi\) | ||||
−0.386196 | + | 0.922417i | \(0.626211\pi\) | |||||||
\(410\) | 4.78808e8 | 0.343098 | ||||||||
\(411\) | −5.72997e8 | −0.407105 | ||||||||
\(412\) | −6.48598e8 | −0.456915 | ||||||||
\(413\) | −2.98479e8 | −0.208491 | ||||||||
\(414\) | −4.09549e8 | −0.283664 | ||||||||
\(415\) | 1.54705e9 | 1.06251 | ||||||||
\(416\) | −4.26557e8 | −0.290503 | ||||||||
\(417\) | 1.40989e9 | 0.952156 | ||||||||
\(418\) | 1.65927e9 | 1.11122 | ||||||||
\(419\) | 9.24350e7 | 0.0613885 | 0.0306943 | − | 0.999529i | \(-0.490228\pi\) | ||||
0.0306943 | + | 0.999529i | \(0.490228\pi\) | |||||||
\(420\) | 3.59764e8 | 0.236943 | ||||||||
\(421\) | 8.98575e8 | 0.586904 | 0.293452 | − | 0.955974i | \(-0.405196\pi\) | ||||
0.293452 | + | 0.955974i | \(0.405196\pi\) | |||||||
\(422\) | −1.57756e9 | −1.02186 | ||||||||
\(423\) | −3.00348e8 | −0.192945 | ||||||||
\(424\) | −6.84641e7 | −0.0436197 | ||||||||
\(425\) | 4.16491e8 | 0.263175 | ||||||||
\(426\) | −7.40635e8 | −0.464163 | ||||||||
\(427\) | 2.34029e9 | 1.45470 | ||||||||
\(428\) | −7.40814e8 | −0.456726 | ||||||||
\(429\) | −7.23187e8 | −0.442232 | ||||||||
\(430\) | −5.86672e7 | −0.0355841 | ||||||||
\(431\) | −7.64033e8 | −0.459665 | −0.229833 | − | 0.973230i | \(-0.573818\pi\) | ||||
−0.229833 | + | 0.973230i | \(0.573818\pi\) | |||||||
\(432\) | −2.03021e8 | −0.121157 | ||||||||
\(433\) | 1.90959e8 | 0.113040 | 0.0565199 | − | 0.998401i | \(-0.482000\pi\) | ||||
0.0565199 | + | 0.998401i | \(0.482000\pi\) | |||||||
\(434\) | 3.58498e8 | 0.210510 | ||||||||
\(435\) | 9.23282e7 | 0.0537802 | ||||||||
\(436\) | −4.97412e8 | −0.287417 | ||||||||
\(437\) | 1.58135e9 | 0.906447 | ||||||||
\(438\) | −1.12856e9 | −0.641747 | ||||||||
\(439\) | 2.64998e9 | 1.49492 | 0.747458 | − | 0.664309i | \(-0.231274\pi\) | ||||
0.747458 | + | 0.664309i | \(0.231274\pi\) | |||||||
\(440\) | −2.53345e9 | −1.41785 | ||||||||
\(441\) | 9.39358e8 | 0.521550 | ||||||||
\(442\) | 1.02121e9 | 0.562520 | ||||||||
\(443\) | 3.33143e9 | 1.82061 | 0.910307 | − | 0.413934i | \(-0.135846\pi\) | ||||
0.910307 | + | 0.413934i | \(0.135846\pi\) | |||||||
\(444\) | −1.23566e8 | −0.0669973 | ||||||||
\(445\) | 2.40685e9 | 1.29476 | ||||||||
\(446\) | −1.24218e8 | −0.0663001 | ||||||||
\(447\) | 9.05507e8 | 0.479529 | ||||||||
\(448\) | −3.34755e9 | −1.75895 | ||||||||
\(449\) | −1.02214e8 | −0.0532902 | −0.0266451 | − | 0.999645i | \(-0.508482\pi\) | ||||
−0.0266451 | + | 0.999645i | \(0.508482\pi\) | |||||||
\(450\) | 1.12305e8 | 0.0580971 | ||||||||
\(451\) | 1.30209e9 | 0.668381 | ||||||||
\(452\) | 1.75743e7 | 0.00895148 | ||||||||
\(453\) | −5.98444e8 | −0.302468 | ||||||||
\(454\) | −2.86948e9 | −1.43916 | ||||||||
\(455\) | −1.49907e9 | −0.746076 | ||||||||
\(456\) | 1.14213e9 | 0.564075 | ||||||||
\(457\) | −2.28925e9 | −1.12198 | −0.560992 | − | 0.827821i | \(-0.689580\pi\) | ||||
−0.560992 | + | 0.827821i | \(0.689580\pi\) | |||||||
\(458\) | −4.30879e8 | −0.209568 | ||||||||
\(459\) | −5.08120e8 | −0.245258 | ||||||||
\(460\) | −5.39429e8 | −0.258394 | ||||||||
\(461\) | 6.39371e8 | 0.303948 | 0.151974 | − | 0.988384i | \(-0.451437\pi\) | ||||
0.151974 | + | 0.988384i | \(0.451437\pi\) | |||||||
\(462\) | −2.42241e9 | −1.14288 | ||||||||
\(463\) | −1.36469e9 | −0.638998 | −0.319499 | − | 0.947587i | \(-0.603515\pi\) | ||||
−0.319499 | + | 0.947587i | \(0.603515\pi\) | |||||||
\(464\) | −1.41662e8 | −0.0658327 | ||||||||
\(465\) | 1.73668e8 | 0.0801001 | ||||||||
\(466\) | −2.50920e9 | −1.14864 | ||||||||
\(467\) | 2.57730e9 | 1.17100 | 0.585498 | − | 0.810674i | \(-0.300899\pi\) | ||||
0.585498 | + | 0.810674i | \(0.300899\pi\) | |||||||
\(468\) | −1.11214e8 | −0.0501531 | ||||||||
\(469\) | −1.99250e9 | −0.891855 | ||||||||
\(470\) | 9.79498e8 | 0.435172 | ||||||||
\(471\) | −1.56806e9 | −0.691496 | ||||||||
\(472\) | 3.23234e8 | 0.141488 | ||||||||
\(473\) | −1.59542e8 | −0.0693205 | ||||||||
\(474\) | 2.47714e8 | 0.106838 | ||||||||
\(475\) | −4.33630e8 | −0.185649 | ||||||||
\(476\) | −1.38154e9 | −0.587136 | ||||||||
\(477\) | −3.17124e7 | −0.0133787 | ||||||||
\(478\) | 3.67434e9 | 1.53880 | ||||||||
\(479\) | 2.51029e9 | 1.04364 | 0.521818 | − | 0.853057i | \(-0.325254\pi\) | ||||
0.521818 | + | 0.853057i | \(0.325254\pi\) | |||||||
\(480\) | −6.92161e8 | −0.285669 | ||||||||
\(481\) | 5.14877e8 | 0.210958 | ||||||||
\(482\) | −1.81180e9 | −0.736964 | ||||||||
\(483\) | −2.30865e9 | −0.932275 | ||||||||
\(484\) | −8.21635e8 | −0.329398 | ||||||||
\(485\) | −2.95937e9 | −1.17788 | ||||||||
\(486\) | −1.37012e8 | −0.0541417 | ||||||||
\(487\) | −1.03970e9 | −0.407905 | −0.203952 | − | 0.978981i | \(-0.565379\pi\) | ||||
−0.203952 | + | 0.978981i | \(0.565379\pi\) | |||||||
\(488\) | −2.53439e9 | −0.987199 | ||||||||
\(489\) | −2.06506e9 | −0.798641 | ||||||||
\(490\) | −3.06344e9 | −1.17631 | ||||||||
\(491\) | −4.29594e9 | −1.63785 | −0.818923 | − | 0.573903i | \(-0.805429\pi\) | ||||
−0.818923 | + | 0.573903i | \(0.805429\pi\) | |||||||
\(492\) | 2.00239e8 | 0.0758005 | ||||||||
\(493\) | −3.54552e8 | −0.133265 | ||||||||
\(494\) | −1.06324e9 | −0.396813 | ||||||||
\(495\) | −1.17349e9 | −0.434872 | ||||||||
\(496\) | −2.66464e8 | −0.0980511 | ||||||||
\(497\) | −4.17501e9 | −1.52549 | ||||||||
\(498\) | −1.60192e9 | −0.581217 | ||||||||
\(499\) | −2.36884e9 | −0.853461 | −0.426730 | − | 0.904379i | \(-0.640335\pi\) | ||||
−0.426730 | + | 0.904379i | \(0.640335\pi\) | |||||||
\(500\) | 8.64206e8 | 0.309188 | ||||||||
\(501\) | 2.05223e9 | 0.729112 | ||||||||
\(502\) | 1.81330e9 | 0.639743 | ||||||||
\(503\) | 3.86205e9 | 1.35310 | 0.676551 | − | 0.736396i | \(-0.263474\pi\) | ||||
0.676551 | + | 0.736396i | \(0.263474\pi\) | |||||||
\(504\) | −1.66742e9 | −0.580148 | ||||||||
\(505\) | 4.24247e9 | 1.46588 | ||||||||
\(506\) | 3.63216e9 | 1.24634 | ||||||||
\(507\) | −1.23080e9 | −0.419431 | ||||||||
\(508\) | −8.54403e8 | −0.289161 | ||||||||
\(509\) | −2.82144e8 | −0.0948327 | −0.0474163 | − | 0.998875i | \(-0.515099\pi\) | ||||
−0.0474163 | + | 0.998875i | \(0.515099\pi\) | |||||||
\(510\) | 1.65709e9 | 0.553159 | ||||||||
\(511\) | −6.36175e9 | −2.10913 | ||||||||
\(512\) | 3.13988e9 | 1.03388 | ||||||||
\(513\) | 5.29031e8 | 0.173010 | ||||||||
\(514\) | −3.08625e9 | −1.00244 | ||||||||
\(515\) | 4.38542e9 | 1.41477 | ||||||||
\(516\) | −2.45349e7 | −0.00786157 | ||||||||
\(517\) | 2.66369e9 | 0.847748 | ||||||||
\(518\) | 1.72465e9 | 0.545189 | ||||||||
\(519\) | −2.48715e9 | −0.780936 | ||||||||
\(520\) | 1.62340e9 | 0.506308 | ||||||||
\(521\) | 1.57821e9 | 0.488915 | 0.244457 | − | 0.969660i | \(-0.421390\pi\) | ||||
0.244457 | + | 0.969660i | \(0.421390\pi\) | |||||||
\(522\) | −9.56033e7 | −0.0294189 | ||||||||
\(523\) | −2.13247e9 | −0.651818 | −0.325909 | − | 0.945401i | \(-0.605670\pi\) | ||||
−0.325909 | + | 0.945401i | \(0.605670\pi\) | |||||||
\(524\) | 1.54538e8 | 0.0469218 | ||||||||
\(525\) | 6.33069e8 | 0.190939 | ||||||||
\(526\) | 9.51249e8 | 0.285000 | ||||||||
\(527\) | −6.66906e8 | −0.198485 | ||||||||
\(528\) | 1.80053e9 | 0.532330 | ||||||||
\(529\) | 5.67661e7 | 0.0166722 | ||||||||
\(530\) | 1.03421e8 | 0.0301747 | ||||||||
\(531\) | 1.49721e8 | 0.0433963 | ||||||||
\(532\) | 1.43839e9 | 0.414177 | ||||||||
\(533\) | −8.34364e8 | −0.238677 | ||||||||
\(534\) | −2.49223e9 | −0.708261 | ||||||||
\(535\) | 5.00892e9 | 1.41418 | ||||||||
\(536\) | 2.15776e9 | 0.605237 | ||||||||
\(537\) | 1.61269e9 | 0.449407 | ||||||||
\(538\) | −4.93719e9 | −1.36692 | ||||||||
\(539\) | −8.33086e9 | −2.29155 | ||||||||
\(540\) | −1.80463e8 | −0.0493184 | ||||||||
\(541\) | 1.40969e9 | 0.382766 | 0.191383 | − | 0.981515i | \(-0.438703\pi\) | ||||
0.191383 | + | 0.981515i | \(0.438703\pi\) | |||||||
\(542\) | −8.69155e7 | −0.0234477 | ||||||||
\(543\) | −2.69217e9 | −0.721612 | ||||||||
\(544\) | 2.65799e9 | 0.707875 | ||||||||
\(545\) | 3.36319e9 | 0.889946 | ||||||||
\(546\) | 1.55225e9 | 0.408119 | ||||||||
\(547\) | 2.03003e9 | 0.530331 | 0.265166 | − | 0.964203i | \(-0.414573\pi\) | ||||
0.265166 | + | 0.964203i | \(0.414573\pi\) | |||||||
\(548\) | 7.81482e8 | 0.202856 | ||||||||
\(549\) | −1.17393e9 | −0.302787 | ||||||||
\(550\) | −9.95995e8 | −0.255263 | ||||||||
\(551\) | 3.69143e8 | 0.0940078 | ||||||||
\(552\) | 2.50013e9 | 0.632668 | ||||||||
\(553\) | 1.39638e9 | 0.351129 | ||||||||
\(554\) | −1.00025e9 | −0.249934 | ||||||||
\(555\) | 8.35475e8 | 0.207447 | ||||||||
\(556\) | −1.92287e9 | −0.474448 | ||||||||
\(557\) | −1.08167e9 | −0.265216 | −0.132608 | − | 0.991169i | \(-0.542335\pi\) | ||||
−0.132608 | + | 0.991169i | \(0.542335\pi\) | |||||||
\(558\) | −1.79828e8 | −0.0438165 | ||||||||
\(559\) | 1.02233e8 | 0.0247542 | ||||||||
\(560\) | 3.73227e9 | 0.898079 | ||||||||
\(561\) | 4.50636e9 | 1.07760 | ||||||||
\(562\) | 2.10876e9 | 0.501129 | ||||||||
\(563\) | 3.83004e8 | 0.0904533 | 0.0452266 | − | 0.998977i | \(-0.485599\pi\) | ||||
0.0452266 | + | 0.998977i | \(0.485599\pi\) | |||||||
\(564\) | 4.09630e8 | 0.0961423 | ||||||||
\(565\) | −1.18827e8 | −0.0277169 | ||||||||
\(566\) | −4.35646e9 | −1.00990 | ||||||||
\(567\) | −7.72347e8 | −0.177939 | ||||||||
\(568\) | 4.52127e9 | 1.03524 | ||||||||
\(569\) | 2.51189e9 | 0.571620 | 0.285810 | − | 0.958286i | \(-0.407737\pi\) | ||||
0.285810 | + | 0.958286i | \(0.407737\pi\) | |||||||
\(570\) | −1.72528e9 | −0.390209 | ||||||||
\(571\) | 3.94620e9 | 0.887060 | 0.443530 | − | 0.896259i | \(-0.353726\pi\) | ||||
0.443530 | + | 0.896259i | \(0.353726\pi\) | |||||||
\(572\) | 9.86318e8 | 0.220359 | ||||||||
\(573\) | −5.50796e7 | −0.0122307 | ||||||||
\(574\) | −2.79482e9 | −0.616824 | ||||||||
\(575\) | −9.49223e8 | −0.208224 | ||||||||
\(576\) | 1.67918e9 | 0.366116 | ||||||||
\(577\) | 3.82097e9 | 0.828053 | 0.414027 | − | 0.910265i | \(-0.364122\pi\) | ||||
0.414027 | + | 0.910265i | \(0.364122\pi\) | |||||||
\(578\) | −2.44526e9 | −0.526718 | ||||||||
\(579\) | 3.58431e9 | 0.767416 | ||||||||
\(580\) | −1.25922e8 | −0.0267980 | ||||||||
\(581\) | −9.03014e9 | −1.91020 | ||||||||
\(582\) | 3.06434e9 | 0.644328 | ||||||||
\(583\) | 2.81248e8 | 0.0587826 | ||||||||
\(584\) | 6.88938e9 | 1.43131 | ||||||||
\(585\) | 7.51958e8 | 0.155292 | ||||||||
\(586\) | −1.02014e9 | −0.209421 | ||||||||
\(587\) | −5.26096e9 | −1.07357 | −0.536786 | − | 0.843718i | \(-0.680362\pi\) | ||||
−0.536786 | + | 0.843718i | \(0.680362\pi\) | |||||||
\(588\) | −1.28114e9 | −0.259882 | ||||||||
\(589\) | 6.94350e8 | 0.140015 | ||||||||
\(590\) | −4.88273e8 | −0.0978769 | ||||||||
\(591\) | −2.89403e9 | −0.576696 | ||||||||
\(592\) | −1.28190e9 | −0.253938 | ||||||||
\(593\) | 5.47065e9 | 1.07733 | 0.538664 | − | 0.842521i | \(-0.318929\pi\) | ||||
0.538664 | + | 0.842521i | \(0.318929\pi\) | |||||||
\(594\) | 1.21512e9 | 0.237884 | ||||||||
\(595\) | 9.34111e9 | 1.81798 | ||||||||
\(596\) | −1.23498e9 | −0.238944 | ||||||||
\(597\) | −2.92196e9 | −0.562036 | ||||||||
\(598\) | −2.32744e9 | −0.445066 | ||||||||
\(599\) | −6.15736e9 | −1.17058 | −0.585289 | − | 0.810825i | \(-0.699019\pi\) | ||||
−0.585289 | + | 0.810825i | \(0.699019\pi\) | |||||||
\(600\) | −6.85574e8 | −0.129576 | ||||||||
\(601\) | −7.30212e9 | −1.37211 | −0.686054 | − | 0.727550i | \(-0.740659\pi\) | ||||
−0.686054 | + | 0.727550i | \(0.740659\pi\) | |||||||
\(602\) | 3.42442e8 | 0.0639734 | ||||||||
\(603\) | 9.99469e8 | 0.185635 | ||||||||
\(604\) | 8.16187e8 | 0.150716 | ||||||||
\(605\) | 5.55539e9 | 1.01993 | ||||||||
\(606\) | −4.39296e9 | −0.801869 | ||||||||
\(607\) | −6.94268e9 | −1.25999 | −0.629995 | − | 0.776599i | \(-0.716943\pi\) | ||||
−0.629995 | + | 0.776599i | \(0.716943\pi\) | |||||||
\(608\) | −2.76737e9 | −0.499349 | ||||||||
\(609\) | −5.38922e8 | −0.0966864 | ||||||||
\(610\) | 3.82842e9 | 0.682913 | ||||||||
\(611\) | −1.70686e9 | −0.302728 | ||||||||
\(612\) | 6.93000e8 | 0.122209 | ||||||||
\(613\) | 3.42370e9 | 0.600323 | 0.300161 | − | 0.953888i | \(-0.402960\pi\) | ||||
0.300161 | + | 0.953888i | \(0.402960\pi\) | |||||||
\(614\) | 4.69722e9 | 0.818938 | ||||||||
\(615\) | −1.35390e9 | −0.234705 | ||||||||
\(616\) | 1.47878e10 | 2.54901 | ||||||||
\(617\) | −2.18204e9 | −0.373995 | −0.186997 | − | 0.982360i | \(-0.559876\pi\) | ||||
−0.186997 | + | 0.982360i | \(0.559876\pi\) | |||||||
\(618\) | −4.54098e9 | −0.773909 | ||||||||
\(619\) | 1.11884e10 | 1.89605 | 0.948025 | − | 0.318197i | \(-0.103077\pi\) | ||||
0.948025 | + | 0.318197i | \(0.103077\pi\) | |||||||
\(620\) | −2.36856e8 | −0.0399130 | ||||||||
\(621\) | 1.15806e9 | 0.194048 | ||||||||
\(622\) | 327537. | 5.45751e−5 0 | ||||||||
\(623\) | −1.40488e10 | −2.32773 | ||||||||
\(624\) | −1.15375e9 | −0.190093 | ||||||||
\(625\) | −4.58279e9 | −0.750844 | ||||||||
\(626\) | 2.05280e9 | 0.334454 | ||||||||
\(627\) | −4.69180e9 | −0.760157 | ||||||||
\(628\) | 2.13860e9 | 0.344564 | ||||||||
\(629\) | −3.20833e9 | −0.514046 | ||||||||
\(630\) | 2.51878e9 | 0.401328 | ||||||||
\(631\) | 4.03660e9 | 0.639606 | 0.319803 | − | 0.947484i | \(-0.396383\pi\) | ||||
0.319803 | + | 0.947484i | \(0.396383\pi\) | |||||||
\(632\) | −1.51220e9 | −0.238286 | ||||||||
\(633\) | 4.46077e9 | 0.699032 | ||||||||
\(634\) | 4.49913e9 | 0.701158 | ||||||||
\(635\) | 5.77694e9 | 0.895344 | ||||||||
\(636\) | 4.32510e7 | 0.00666648 | ||||||||
\(637\) | 5.33831e9 | 0.818305 | ||||||||
\(638\) | 8.47875e8 | 0.129259 | ||||||||
\(639\) | 2.09425e9 | 0.317523 | ||||||||
\(640\) | −2.19481e9 | −0.330954 | ||||||||
\(641\) | 2.82614e9 | 0.423830 | 0.211915 | − | 0.977288i | \(-0.432030\pi\) | ||||
0.211915 | + | 0.977288i | \(0.432030\pi\) | |||||||
\(642\) | −5.18660e9 | −0.773589 | ||||||||
\(643\) | 7.92165e9 | 1.17511 | 0.587553 | − | 0.809186i | \(-0.300091\pi\) | ||||
0.587553 | + | 0.809186i | \(0.300091\pi\) | |||||||
\(644\) | 3.14866e9 | 0.464542 | ||||||||
\(645\) | 1.65890e8 | 0.0243422 | ||||||||
\(646\) | 6.62530e9 | 0.966922 | ||||||||
\(647\) | −6.23017e9 | −0.904347 | −0.452173 | − | 0.891930i | \(-0.649351\pi\) | ||||
−0.452173 | + | 0.891930i | \(0.649351\pi\) | |||||||
\(648\) | 8.36403e8 | 0.120754 | ||||||||
\(649\) | −1.32783e9 | −0.190672 | ||||||||
\(650\) | 6.38220e8 | 0.0911536 | ||||||||
\(651\) | −1.01370e9 | −0.144005 | ||||||||
\(652\) | 2.81643e9 | 0.397954 | ||||||||
\(653\) | 8.41425e9 | 1.18255 | 0.591275 | − | 0.806470i | \(-0.298625\pi\) | ||||
0.591275 | + | 0.806470i | \(0.298625\pi\) | |||||||
\(654\) | −3.48249e9 | −0.486819 | ||||||||
\(655\) | −1.04489e9 | −0.145286 | ||||||||
\(656\) | 2.07733e9 | 0.287304 | ||||||||
\(657\) | 3.19115e9 | 0.439004 | ||||||||
\(658\) | −5.71735e9 | −0.782356 | ||||||||
\(659\) | 7.96272e9 | 1.08383 | 0.541917 | − | 0.840432i | \(-0.317699\pi\) | ||||
0.541917 | + | 0.840432i | \(0.317699\pi\) | |||||||
\(660\) | 1.60047e9 | 0.216692 | ||||||||
\(661\) | 1.16395e10 | 1.56758 | 0.783790 | − | 0.621026i | \(-0.213284\pi\) | ||||
0.783790 | + | 0.621026i | \(0.213284\pi\) | |||||||
\(662\) | −1.15181e10 | −1.54305 | ||||||||
\(663\) | −2.88761e9 | −0.384806 | ||||||||
\(664\) | 9.77908e9 | 1.29631 | ||||||||
\(665\) | −9.72551e9 | −1.28244 | ||||||||
\(666\) | −8.65111e8 | −0.113478 | ||||||||
\(667\) | 8.08058e8 | 0.105439 | ||||||||
\(668\) | −2.79894e9 | −0.363308 | ||||||||
\(669\) | 3.51244e8 | 0.0453542 | ||||||||
\(670\) | −3.25948e9 | −0.418684 | ||||||||
\(671\) | 1.04112e10 | 1.33037 | ||||||||
\(672\) | 4.04016e9 | 0.513577 | ||||||||
\(673\) | 6.37828e8 | 0.0806586 | 0.0403293 | − | 0.999186i | \(-0.487159\pi\) | ||||
0.0403293 | + | 0.999186i | \(0.487159\pi\) | |||||||
\(674\) | 5.12899e9 | 0.645242 | ||||||||
\(675\) | −3.17557e8 | −0.0397428 | ||||||||
\(676\) | 1.67863e9 | 0.208998 | ||||||||
\(677\) | −8.92413e9 | −1.10536 | −0.552682 | − | 0.833392i | \(-0.686396\pi\) | ||||
−0.552682 | + | 0.833392i | \(0.686396\pi\) | |||||||
\(678\) | 1.23042e8 | 0.0151617 | ||||||||
\(679\) | 1.72739e10 | 2.11761 | ||||||||
\(680\) | −1.01158e10 | −1.23373 | ||||||||
\(681\) | 8.11386e9 | 0.984492 | ||||||||
\(682\) | 1.59484e9 | 0.192518 | ||||||||
\(683\) | 2.24023e9 | 0.269042 | 0.134521 | − | 0.990911i | \(-0.457050\pi\) | ||||
0.134521 | + | 0.990911i | \(0.457050\pi\) | |||||||
\(684\) | −7.21518e8 | −0.0862087 | ||||||||
\(685\) | −5.28390e9 | −0.628113 | ||||||||
\(686\) | 6.45302e9 | 0.763183 | ||||||||
\(687\) | 1.21837e9 | 0.143361 | ||||||||
\(688\) | −2.54530e8 | −0.0297975 | ||||||||
\(689\) | −1.80220e8 | −0.0209911 | ||||||||
\(690\) | −3.77666e9 | −0.437659 | ||||||||
\(691\) | −1.59406e10 | −1.83794 | −0.918972 | − | 0.394322i | \(-0.870979\pi\) | ||||
−0.918972 | + | 0.394322i | \(0.870979\pi\) | |||||||
\(692\) | 3.39210e9 | 0.389132 | ||||||||
\(693\) | 6.84970e9 | 0.781817 | ||||||||
\(694\) | 1.02394e10 | 1.16282 | ||||||||
\(695\) | 1.30013e10 | 1.46906 | ||||||||
\(696\) | 5.83619e8 | 0.0656141 | ||||||||
\(697\) | 5.19913e9 | 0.581589 | ||||||||
\(698\) | 6.01765e9 | 0.669781 | ||||||||
\(699\) | 7.09511e9 | 0.785758 | ||||||||
\(700\) | −8.63411e8 | −0.0951425 | ||||||||
\(701\) | 1.79817e10 | 1.97160 | 0.985800 | − | 0.167926i | \(-0.0537071\pi\) | ||||
0.985800 | + | 0.167926i | \(0.0537071\pi\) | |||||||
\(702\) | −7.78631e8 | −0.0849477 | ||||||||
\(703\) | 3.34036e9 | 0.362618 | ||||||||
\(704\) | −1.48921e10 | −1.60862 | ||||||||
\(705\) | −2.76966e9 | −0.297691 | ||||||||
\(706\) | 1.24827e10 | 1.33503 | ||||||||
\(707\) | −2.47634e10 | −2.63538 | ||||||||
\(708\) | −2.04197e8 | −0.0216239 | ||||||||
\(709\) | −5.70361e9 | −0.601019 | −0.300510 | − | 0.953779i | \(-0.597157\pi\) | ||||
−0.300510 | + | 0.953779i | \(0.597157\pi\) | |||||||
\(710\) | −6.82977e9 | −0.716147 | ||||||||
\(711\) | −7.00446e8 | −0.0730855 | ||||||||
\(712\) | 1.52140e10 | 1.57966 | ||||||||
\(713\) | 1.51994e9 | 0.157041 | ||||||||
\(714\) | −9.67246e9 | −0.994473 | ||||||||
\(715\) | −6.66887e9 | −0.682309 | ||||||||
\(716\) | −2.19946e9 | −0.223935 | ||||||||
\(717\) | −1.03897e10 | −1.05265 | ||||||||
\(718\) | −1.50140e10 | −1.51378 | ||||||||
\(719\) | 1.38876e10 | 1.39340 | 0.696702 | − | 0.717360i | \(-0.254650\pi\) | ||||
0.696702 | + | 0.717360i | \(0.254650\pi\) | |||||||
\(720\) | −1.87216e9 | −0.186930 | ||||||||
\(721\) | −2.55978e10 | −2.54348 | ||||||||
\(722\) | 1.63730e9 | 0.161900 | ||||||||
\(723\) | 5.12311e9 | 0.504139 | ||||||||
\(724\) | 3.67172e9 | 0.359571 | ||||||||
\(725\) | −2.21582e8 | −0.0215949 | ||||||||
\(726\) | −5.75245e9 | −0.557924 | ||||||||
\(727\) | −7.90006e8 | −0.0762535 | −0.0381268 | − | 0.999273i | \(-0.512139\pi\) | ||||
−0.0381268 | + | 0.999273i | \(0.512139\pi\) | |||||||
\(728\) | −9.47584e9 | −0.910244 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −1.04070e10 | −0.990138 | ||||||||
\(731\) | −6.37037e8 | −0.0603190 | ||||||||
\(732\) | 1.60106e9 | 0.150875 | ||||||||
\(733\) | 5.65590e8 | 0.0530442 | 0.0265221 | − | 0.999648i | \(-0.491557\pi\) | ||||
0.0265221 | + | 0.999648i | \(0.491557\pi\) | |||||||
\(734\) | 1.41843e10 | 1.32395 | ||||||||
\(735\) | 8.66230e9 | 0.804688 | ||||||||
\(736\) | −6.05780e9 | −0.560071 | ||||||||
\(737\) | −8.86397e9 | −0.815628 | ||||||||
\(738\) | 1.40192e9 | 0.128389 | ||||||||
\(739\) | −1.70229e10 | −1.55159 | −0.775796 | − | 0.630984i | \(-0.782651\pi\) | ||||
−0.775796 | + | 0.630984i | \(0.782651\pi\) | |||||||
\(740\) | −1.13946e9 | −0.103369 | ||||||||
\(741\) | 3.00645e9 | 0.271450 | ||||||||
\(742\) | −6.03670e8 | −0.0542483 | ||||||||
\(743\) | 1.64681e7 | 0.00147294 | 0.000736468 | − | 1.00000i | \(-0.499766\pi\) | ||||
0.000736468 | 1.00000i | \(0.499766\pi\) | ||||||||
\(744\) | 1.09778e9 | 0.0977256 | ||||||||
\(745\) | 8.35014e9 | 0.739855 | ||||||||
\(746\) | 9.47516e9 | 0.835604 | ||||||||
\(747\) | 4.52965e9 | 0.397597 | ||||||||
\(748\) | −6.14600e9 | −0.536954 | ||||||||
\(749\) | −2.92372e10 | −2.54243 | ||||||||
\(750\) | 6.05049e9 | 0.523693 | ||||||||
\(751\) | −9.72464e9 | −0.837787 | −0.418893 | − | 0.908035i | \(-0.637582\pi\) | ||||
−0.418893 | + | 0.908035i | \(0.637582\pi\) | |||||||
\(752\) | 4.24959e9 | 0.364405 | ||||||||
\(753\) | −5.12734e9 | −0.437633 | ||||||||
\(754\) | −5.43307e8 | −0.0461578 | ||||||||
\(755\) | −5.51856e9 | −0.466671 | ||||||||
\(756\) | 1.05336e9 | 0.0886651 | ||||||||
\(757\) | 3.21906e9 | 0.269708 | 0.134854 | − | 0.990866i | \(-0.456944\pi\) | ||||
0.134854 | + | 0.990866i | \(0.456944\pi\) | |||||||
\(758\) | 1.31123e10 | 1.09354 | ||||||||
\(759\) | −1.02704e10 | −0.852594 | ||||||||
\(760\) | 1.05321e10 | 0.870299 | ||||||||
\(761\) | −1.87932e10 | −1.54580 | −0.772902 | − | 0.634526i | \(-0.781195\pi\) | ||||
−0.772902 | + | 0.634526i | \(0.781195\pi\) | |||||||
\(762\) | −5.98186e9 | −0.489772 | ||||||||
\(763\) | −1.96310e10 | −1.59995 | ||||||||
\(764\) | 7.51204e7 | 0.00609440 | ||||||||
\(765\) | −4.68564e9 | −0.378402 | ||||||||
\(766\) | −1.51659e10 | −1.21918 | ||||||||
\(767\) | 8.50856e8 | 0.0680883 | ||||||||
\(768\) | −5.68790e9 | −0.453094 | ||||||||
\(769\) | 4.53024e9 | 0.359235 | 0.179617 | − | 0.983737i | \(-0.442514\pi\) | ||||
0.179617 | + | 0.983737i | \(0.442514\pi\) | |||||||
\(770\) | −2.23383e10 | −1.76333 | ||||||||
\(771\) | 8.72679e9 | 0.685747 | ||||||||
\(772\) | −4.88846e9 | −0.382395 | ||||||||
\(773\) | 2.02996e10 | 1.58074 | 0.790369 | − | 0.612631i | \(-0.209889\pi\) | ||||
0.790369 | + | 0.612631i | \(0.209889\pi\) | |||||||
\(774\) | −1.71774e8 | −0.0133157 | ||||||||
\(775\) | −4.16792e8 | −0.0321635 | ||||||||
\(776\) | −1.87066e10 | −1.43707 | ||||||||
\(777\) | −4.87669e9 | −0.372950 | ||||||||
\(778\) | 1.59156e9 | 0.121170 | ||||||||
\(779\) | −5.41309e9 | −0.410265 | ||||||||
\(780\) | −1.02556e9 | −0.0773800 | ||||||||
\(781\) | −1.85732e10 | −1.39511 | ||||||||
\(782\) | 1.45029e10 | 1.08450 | ||||||||
\(783\) | 2.70331e8 | 0.0201247 | ||||||||
\(784\) | −1.32909e10 | −0.985024 | ||||||||
\(785\) | −1.44599e10 | −1.06689 | ||||||||
\(786\) | 1.08195e9 | 0.0794748 | ||||||||
\(787\) | 1.91261e10 | 1.39867 | 0.699333 | − | 0.714796i | \(-0.253480\pi\) | ||||
0.699333 | + | 0.714796i | \(0.253480\pi\) | |||||||
\(788\) | 3.94702e9 | 0.287361 | ||||||||
\(789\) | −2.68979e9 | −0.194961 | ||||||||
\(790\) | 2.28430e9 | 0.164838 | ||||||||
\(791\) | 6.93595e8 | 0.0498297 | ||||||||
\(792\) | −7.41779e9 | −0.530563 | ||||||||
\(793\) | −6.67134e9 | −0.475069 | ||||||||
\(794\) | 1.02316e10 | 0.725391 | ||||||||
\(795\) | −2.92437e8 | −0.0206418 | ||||||||
\(796\) | 3.98511e9 | 0.280056 | ||||||||
\(797\) | 1.30414e10 | 0.912470 | 0.456235 | − | 0.889859i | \(-0.349198\pi\) | ||||
0.456235 | + | 0.889859i | \(0.349198\pi\) | |||||||
\(798\) | 1.00705e10 | 0.701521 | ||||||||
\(799\) | 1.06359e10 | 0.737665 | ||||||||
\(800\) | 1.66114e9 | 0.114708 | ||||||||
\(801\) | 7.04711e9 | 0.484504 | ||||||||
\(802\) | −1.49813e9 | −0.102551 | ||||||||
\(803\) | −2.83013e10 | −1.92886 | ||||||||
\(804\) | −1.36313e9 | −0.0924996 | ||||||||
\(805\) | −2.12893e10 | −1.43839 | ||||||||
\(806\) | −1.02195e9 | −0.0687475 | ||||||||
\(807\) | 1.39606e10 | 0.935074 | ||||||||
\(808\) | 2.68172e10 | 1.78844 | ||||||||
\(809\) | 5.94145e9 | 0.394523 | 0.197262 | − | 0.980351i | \(-0.436795\pi\) | ||||
0.197262 | + | 0.980351i | \(0.436795\pi\) | |||||||
\(810\) | −1.26346e9 | −0.0835341 | ||||||||
\(811\) | 5.51763e9 | 0.363228 | 0.181614 | − | 0.983370i | \(-0.441868\pi\) | ||||
0.181614 | + | 0.983370i | \(0.441868\pi\) | |||||||
\(812\) | 7.35009e8 | 0.0481777 | ||||||||
\(813\) | 2.45765e8 | 0.0160400 | ||||||||
\(814\) | 7.67239e9 | 0.498592 | ||||||||
\(815\) | −1.90430e10 | −1.23221 | ||||||||
\(816\) | 7.18933e9 | 0.463205 | ||||||||
\(817\) | 6.63252e8 | 0.0425502 | ||||||||
\(818\) | 1.02049e10 | 0.651889 | ||||||||
\(819\) | −4.38919e9 | −0.279184 | ||||||||
\(820\) | 1.84651e9 | 0.116951 | ||||||||
\(821\) | 2.25214e10 | 1.42035 | 0.710173 | − | 0.704027i | \(-0.248617\pi\) | ||||
0.710173 | + | 0.704027i | \(0.248617\pi\) | |||||||
\(822\) | 5.47133e9 | 0.343591 | ||||||||
\(823\) | −1.14413e10 | −0.715446 | −0.357723 | − | 0.933828i | \(-0.616447\pi\) | ||||
−0.357723 | + | 0.933828i | \(0.616447\pi\) | |||||||
\(824\) | 2.77208e10 | 1.72608 | ||||||||
\(825\) | 2.81631e9 | 0.174619 | ||||||||
\(826\) | 2.85006e9 | 0.175964 | ||||||||
\(827\) | −9.39865e9 | −0.577825 | −0.288912 | − | 0.957356i | \(-0.593294\pi\) | ||||
−0.288912 | + | 0.957356i | \(0.593294\pi\) | |||||||
\(828\) | −1.57941e9 | −0.0966918 | ||||||||
\(829\) | −1.97222e10 | −1.20230 | −0.601152 | − | 0.799135i | \(-0.705291\pi\) | ||||
−0.601152 | + | 0.799135i | \(0.705291\pi\) | |||||||
\(830\) | −1.47721e10 | −0.896747 | ||||||||
\(831\) | 2.82835e9 | 0.170974 | ||||||||
\(832\) | 9.54268e9 | 0.574432 | ||||||||
\(833\) | −3.32643e10 | −1.99398 | ||||||||
\(834\) | −1.34625e10 | −0.803606 | ||||||||
\(835\) | 1.89247e10 | 1.12493 | ||||||||
\(836\) | 6.39892e9 | 0.378778 | ||||||||
\(837\) | 5.08488e8 | 0.0299738 | ||||||||
\(838\) | −8.82626e8 | −0.0518111 | ||||||||
\(839\) | 1.88016e10 | 1.09908 | 0.549539 | − | 0.835468i | \(-0.314804\pi\) | ||||
0.549539 | + | 0.835468i | \(0.314804\pi\) | |||||||
\(840\) | −1.53761e10 | −0.895097 | ||||||||
\(841\) | −1.70612e10 | −0.989065 | ||||||||
\(842\) | −8.58014e9 | −0.495339 | ||||||||
\(843\) | −5.96280e9 | −0.342810 | ||||||||
\(844\) | −6.08383e9 | −0.348320 | ||||||||
\(845\) | −1.13499e10 | −0.647130 | ||||||||
\(846\) | 2.86791e9 | 0.162843 | ||||||||
\(847\) | −3.24269e10 | −1.83364 | ||||||||
\(848\) | 4.48695e8 | 0.0252677 | ||||||||
\(849\) | 1.23185e10 | 0.690845 | ||||||||
\(850\) | −3.97691e9 | −0.222116 | ||||||||
\(851\) | 7.31209e9 | 0.406713 | ||||||||
\(852\) | −2.85624e9 | −0.158218 | ||||||||
\(853\) | 1.36908e10 | 0.755276 | 0.377638 | − | 0.925953i | \(-0.376736\pi\) | ||||
0.377638 | + | 0.925953i | \(0.376736\pi\) | |||||||
\(854\) | −2.23466e10 | −1.22775 | ||||||||
\(855\) | 4.87846e9 | 0.266933 | ||||||||
\(856\) | 3.16621e10 | 1.72537 | ||||||||
\(857\) | −1.50548e10 | −0.817038 | −0.408519 | − | 0.912750i | \(-0.633955\pi\) | ||||
−0.408519 | + | 0.912750i | \(0.633955\pi\) | |||||||
\(858\) | 6.90543e9 | 0.373237 | ||||||||
\(859\) | −3.48451e10 | −1.87571 | −0.937856 | − | 0.347025i | \(-0.887192\pi\) | ||||
−0.937856 | + | 0.347025i | \(0.887192\pi\) | |||||||
\(860\) | −2.26248e8 | −0.0121294 | ||||||||
\(861\) | 7.90272e9 | 0.421954 | ||||||||
\(862\) | 7.29546e9 | 0.387951 | ||||||||
\(863\) | 2.13694e10 | 1.13176 | 0.565879 | − | 0.824488i | \(-0.308537\pi\) | ||||
0.565879 | + | 0.824488i | \(0.308537\pi\) | |||||||
\(864\) | −2.02660e9 | −0.106898 | ||||||||
\(865\) | −2.29353e10 | −1.20489 | ||||||||
\(866\) | −1.82339e9 | −0.0954041 | ||||||||
\(867\) | 6.91431e9 | 0.360315 | ||||||||
\(868\) | 1.38254e9 | 0.0717559 | ||||||||
\(869\) | 6.21203e9 | 0.321118 | ||||||||
\(870\) | −8.81607e8 | −0.0453897 | ||||||||
\(871\) | 5.67992e9 | 0.291258 | ||||||||
\(872\) | 2.12592e10 | 1.08577 | ||||||||
\(873\) | −8.66484e9 | −0.440769 | ||||||||
\(874\) | −1.50997e10 | −0.765029 | ||||||||
\(875\) | 3.41070e10 | 1.72114 | ||||||||
\(876\) | −4.35225e9 | −0.218751 | ||||||||
\(877\) | 6.17620e9 | 0.309188 | 0.154594 | − | 0.987978i | \(-0.450593\pi\) | ||||
0.154594 | + | 0.987978i | \(0.450593\pi\) | |||||||
\(878\) | −2.53036e10 | −1.26169 | ||||||||
\(879\) | 2.88460e9 | 0.143260 | ||||||||
\(880\) | 1.66036e10 | 0.821320 | ||||||||
\(881\) | 2.32664e10 | 1.14634 | 0.573170 | − | 0.819437i | \(-0.305714\pi\) | ||||
0.573170 | + | 0.819437i | \(0.305714\pi\) | |||||||
\(882\) | −8.96956e9 | −0.440181 | ||||||||
\(883\) | 3.59095e10 | 1.75528 | 0.877640 | − | 0.479320i | \(-0.159117\pi\) | ||||
0.877640 | + | 0.479320i | \(0.159117\pi\) | |||||||
\(884\) | 3.93827e9 | 0.191744 | ||||||||
\(885\) | 1.38066e9 | 0.0669552 | ||||||||
\(886\) | −3.18106e10 | −1.53657 | ||||||||
\(887\) | −4.49012e9 | −0.216035 | −0.108018 | − | 0.994149i | \(-0.534450\pi\) | ||||
−0.108018 | + | 0.994149i | \(0.534450\pi\) | |||||||
\(888\) | 5.28115e9 | 0.253095 | ||||||||
\(889\) | −3.37201e10 | −1.60966 | ||||||||
\(890\) | −2.29821e10 | −1.09276 | ||||||||
\(891\) | −3.43591e9 | −0.162731 | ||||||||
\(892\) | −4.79045e8 | −0.0225995 | ||||||||
\(893\) | −1.10736e10 | −0.520363 | ||||||||
\(894\) | −8.64633e9 | −0.404716 | ||||||||
\(895\) | 1.48714e10 | 0.693380 | ||||||||
\(896\) | 1.28112e10 | 0.594991 | ||||||||
\(897\) | 6.58115e9 | 0.304459 | ||||||||
\(898\) | 9.76000e8 | 0.0449762 | ||||||||
\(899\) | 3.54808e8 | 0.0162868 | ||||||||
\(900\) | 4.33100e8 | 0.0198034 | ||||||||
\(901\) | 1.12299e9 | 0.0511494 | ||||||||
\(902\) | −1.24332e10 | −0.564105 | ||||||||
\(903\) | −9.68301e8 | −0.0437626 | ||||||||
\(904\) | −7.51120e8 | −0.0338158 | ||||||||
\(905\) | −2.48259e10 | −1.11336 | ||||||||
\(906\) | 5.71431e9 | 0.255279 | ||||||||
\(907\) | 4.38937e10 | 1.95333 | 0.976667 | − | 0.214758i | \(-0.0688963\pi\) | ||||
0.976667 | + | 0.214758i | \(0.0688963\pi\) | |||||||
\(908\) | −1.10661e10 | −0.490561 | ||||||||
\(909\) | 1.24217e10 | 0.548539 | ||||||||
\(910\) | 1.43141e10 | 0.629678 | ||||||||
\(911\) | 1.57039e10 | 0.688165 | 0.344082 | − | 0.938939i | \(-0.388190\pi\) | ||||
0.344082 | + | 0.938939i | \(0.388190\pi\) | |||||||
\(912\) | −7.48519e9 | −0.326754 | ||||||||
\(913\) | −4.01720e10 | −1.74693 | ||||||||
\(914\) | 2.18592e10 | 0.946939 | ||||||||
\(915\) | −1.08254e10 | −0.467164 | ||||||||
\(916\) | −1.66167e9 | −0.0714350 | ||||||||
\(917\) | 6.09903e9 | 0.261197 | ||||||||
\(918\) | 4.85185e9 | 0.206994 | ||||||||
\(919\) | −2.38584e10 | −1.01400 | −0.506998 | − | 0.861947i | \(-0.669245\pi\) | ||||
−0.506998 | + | 0.861947i | \(0.669245\pi\) | |||||||
\(920\) | 2.30550e10 | 0.976129 | ||||||||
\(921\) | −1.32820e10 | −0.560216 | ||||||||
\(922\) | −6.10511e9 | −0.256528 | ||||||||
\(923\) | 1.19015e10 | 0.498189 | ||||||||
\(924\) | −9.34196e9 | −0.389570 | ||||||||
\(925\) | −2.00509e9 | −0.0832986 | ||||||||
\(926\) | 1.30309e10 | 0.539305 | ||||||||
\(927\) | 1.28402e10 | 0.529412 | ||||||||
\(928\) | −1.41411e9 | −0.0580850 | ||||||||
\(929\) | 6.67984e9 | 0.273345 | 0.136672 | − | 0.990616i | \(-0.456359\pi\) | ||||
0.136672 | + | 0.990616i | \(0.456359\pi\) | |||||||
\(930\) | −1.65828e9 | −0.0676034 | ||||||||
\(931\) | 3.46332e10 | 1.40659 | ||||||||
\(932\) | −9.67666e9 | −0.391534 | ||||||||
\(933\) | −926156. | −3.73335e−5 0 | ||||||||
\(934\) | −2.46096e10 | −0.988304 | ||||||||
\(935\) | 4.15554e10 | 1.66260 | ||||||||
\(936\) | 4.75322e9 | 0.189462 | ||||||||
\(937\) | 2.07249e10 | 0.823009 | 0.411504 | − | 0.911408i | \(-0.365003\pi\) | ||||
0.411504 | + | 0.911408i | \(0.365003\pi\) | |||||||
\(938\) | 1.90256e10 | 0.752713 | ||||||||
\(939\) | −5.80456e9 | −0.228792 | ||||||||
\(940\) | 3.77741e9 | 0.148336 | ||||||||
\(941\) | 1.64161e10 | 0.642255 | 0.321127 | − | 0.947036i | \(-0.395938\pi\) | ||||
0.321127 | + | 0.947036i | \(0.395938\pi\) | |||||||
\(942\) | 1.49728e10 | 0.583613 | ||||||||
\(943\) | −1.18493e10 | −0.460153 | ||||||||
\(944\) | −2.11839e9 | −0.0819603 | ||||||||
\(945\) | −7.12220e9 | −0.274538 | ||||||||
\(946\) | 1.52341e9 | 0.0585056 | ||||||||
\(947\) | 3.58035e10 | 1.36994 | 0.684968 | − | 0.728573i | \(-0.259816\pi\) | ||||
0.684968 | + | 0.728573i | \(0.259816\pi\) | |||||||
\(948\) | 9.55303e8 | 0.0364177 | ||||||||
\(949\) | 1.81351e10 | 0.688791 | ||||||||
\(950\) | 4.14057e9 | 0.156685 | ||||||||
\(951\) | −1.27219e10 | −0.479645 | ||||||||
\(952\) | 5.90464e10 | 2.21801 | ||||||||
\(953\) | −1.53516e10 | −0.574550 | −0.287275 | − | 0.957848i | \(-0.592749\pi\) | ||||
−0.287275 | + | 0.957848i | \(0.592749\pi\) | |||||||
\(954\) | 3.02810e8 | 0.0112915 | ||||||||
\(955\) | −5.07917e8 | −0.0188704 | ||||||||
\(956\) | 1.41700e10 | 0.524526 | ||||||||
\(957\) | −2.39748e9 | −0.0884226 | ||||||||
\(958\) | −2.39698e10 | −0.880814 | ||||||||
\(959\) | 3.08422e10 | 1.12923 | ||||||||
\(960\) | 1.54846e10 | 0.564873 | ||||||||
\(961\) | −2.68452e10 | −0.975742 | ||||||||
\(962\) | −4.91637e9 | −0.178046 | ||||||||
\(963\) | 1.46658e10 | 0.529193 | ||||||||
\(964\) | −6.98716e9 | −0.251207 | ||||||||
\(965\) | 3.30528e10 | 1.18403 | ||||||||
\(966\) | 2.20444e10 | 0.786827 | ||||||||
\(967\) | −3.79457e10 | −1.34949 | −0.674745 | − | 0.738051i | \(-0.735747\pi\) | ||||
−0.674745 | + | 0.738051i | \(0.735747\pi\) | |||||||
\(968\) | 3.51164e10 | 1.24436 | ||||||||
\(969\) | −1.87339e10 | −0.661448 | ||||||||
\(970\) | 2.82579e10 | 0.994119 | ||||||||
\(971\) | −1.75229e10 | −0.614242 | −0.307121 | − | 0.951670i | \(-0.599366\pi\) | ||||
−0.307121 | + | 0.951670i | \(0.599366\pi\) | |||||||
\(972\) | −5.28383e8 | −0.0184551 | ||||||||
\(973\) | −7.58888e10 | −2.64109 | ||||||||
\(974\) | 9.92774e9 | 0.344266 | ||||||||
\(975\) | −1.80465e9 | −0.0623559 | ||||||||
\(976\) | 1.66097e10 | 0.571858 | ||||||||
\(977\) | −2.92529e10 | −1.00355 | −0.501773 | − | 0.864999i | \(-0.667319\pi\) | ||||
−0.501773 | + | 0.864999i | \(0.667319\pi\) | |||||||
\(978\) | 1.97185e10 | 0.674042 | ||||||||
\(979\) | −6.24985e10 | −2.12878 | ||||||||
\(980\) | −1.18141e10 | −0.400967 | ||||||||
\(981\) | 9.84720e9 | 0.333021 | ||||||||
\(982\) | 4.10203e10 | 1.38232 | ||||||||
\(983\) | −1.43406e10 | −0.481536 | −0.240768 | − | 0.970583i | \(-0.577399\pi\) | ||||
−0.240768 | + | 0.970583i | \(0.577399\pi\) | |||||||
\(984\) | −8.55815e9 | −0.286350 | ||||||||
\(985\) | −2.66873e10 | −0.889772 | ||||||||
\(986\) | 3.38548e9 | 0.112474 | ||||||||
\(987\) | 1.61666e10 | 0.535190 | ||||||||
\(988\) | −4.10034e9 | −0.135260 | ||||||||
\(989\) | 1.45187e9 | 0.0477244 | ||||||||
\(990\) | 1.12052e10 | 0.367026 | ||||||||
\(991\) | −3.77304e10 | −1.23150 | −0.615749 | − | 0.787942i | \(-0.711146\pi\) | ||||
−0.615749 | + | 0.787942i | \(0.711146\pi\) | |||||||
\(992\) | −2.65991e9 | −0.0865118 | ||||||||
\(993\) | 3.25691e10 | 1.05556 | ||||||||
\(994\) | 3.98655e10 | 1.28749 | ||||||||
\(995\) | −2.69449e10 | −0.867152 | ||||||||
\(996\) | −6.17776e9 | −0.198118 | ||||||||
\(997\) | 4.59214e10 | 1.46751 | 0.733757 | − | 0.679412i | \(-0.237765\pi\) | ||||
0.733757 | + | 0.679412i | \(0.237765\pi\) | |||||||
\(998\) | 2.26191e10 | 0.720309 | ||||||||
\(999\) | 2.44622e9 | 0.0776276 |
(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 | 177.8.a.d.1.6 | ✓ | 18 | |
3.2 | odd | 2 | 531.8.a.e.1.13 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.d.1.6 | ✓ | 18 | 1.1 | even | 1 | trivial | |
531.8.a.e.1.13 | 18 | 3.2 | odd | 2 |