Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,65,Mod(2,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 65, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.2");
S:= CuspForms(chi, 65);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 65 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(77.8210007872\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + \cdots + 16\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{190}\cdot 3^{282}\cdot 5^{19}\cdot 7^{8}\cdot 11^{4}\cdot 13^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2.8 | ||
Root | \(-4.99832e8i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.2 |
Dual form | 3.65.b.a.2.13 |
$q$-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 \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.99899e9i | − | 0.698258i | −0.937075 | − | 0.349129i | \(-0.886478\pi\) | ||
0.937075 | − | 0.349129i | \(-0.113522\pi\) | |||||||
\(3\) | −1.38295e15 | − | 1.23335e15i | −0.746321 | − | 0.665587i | ||||
\(4\) | 9.45278e18 | 0.512436 | ||||||||
\(5\) | 5.43489e21i | 0.233427i | 0.993166 | + | 0.116713i | \(0.0372359\pi\) | ||||
−0.993166 | + | 0.116713i | \(0.962764\pi\) | |||||||
\(6\) | −3.69880e24 | + | 4.14745e24i | −0.464751 | + | 0.521124i | ||||
\(7\) | −9.58380e26 | −0.867762 | −0.433881 | − | 0.900970i | \(-0.642856\pi\) | ||||
−0.433881 | + | 0.900970i | \(0.642856\pi\) | |||||||
\(8\) | − | 8.36705e28i | − | 1.05607i | ||||||
\(9\) | 3.91402e29 | + | 3.41130e30i | 0.113989 | + | 0.993482i | ||||
\(10\) | 1.62992e31 | 0.162992 | ||||||||
\(11\) | − | 2.57757e33i | − | 1.22080i | −0.792094 | − | 0.610400i | \(-0.791009\pi\) | ||
0.792094 | − | 0.610400i | \(-0.208991\pi\) | |||||||
\(12\) | −1.30727e34 | − | 1.16585e34i | −0.382442 | − | 0.341071i | ||||
\(13\) | 7.94970e35 | 1.79541 | 0.897704 | − | 0.440599i | \(-0.145234\pi\) | ||||
0.897704 | + | 0.440599i | \(0.145234\pi\) | |||||||
\(14\) | 2.87418e36i | 0.605921i | ||||||||
\(15\) | 6.70309e36 | − | 7.51616e36i | 0.155366 | − | 0.174211i | ||||
\(16\) | −7.65544e37 | −0.224973 | ||||||||
\(17\) | 1.08752e39i | 0.459276i | 0.973276 | + | 0.229638i | \(0.0737542\pi\) | ||||
−0.973276 | + | 0.229638i | \(0.926246\pi\) | |||||||
\(18\) | 1.02305e40 | − | 1.17381e39i | 0.693707 | − | 0.0795936i | ||||
\(19\) | −1.03745e41 | −1.24695 | −0.623477 | − | 0.781842i | \(-0.714281\pi\) | ||||
−0.623477 | + | 0.781842i | \(0.714281\pi\) | |||||||
\(20\) | 5.13748e40i | 0.119616i | ||||||||
\(21\) | 1.32539e42 | + | 1.18201e42i | 0.647629 | + | 0.577571i | ||||
\(22\) | −7.73011e42 | −0.852432 | ||||||||
\(23\) | − | 3.54618e43i | − | 0.942909i | −0.881891 | − | 0.471454i | \(-0.843729\pi\) | ||
0.881891 | − | 0.471454i | \(-0.156271\pi\) | |||||||
\(24\) | −1.03195e44 | + | 1.15712e44i | −0.702906 | + | 0.788167i | ||||
\(25\) | 5.12563e44 | 0.945512 | ||||||||
\(26\) | − | 2.38411e45i | − | 1.25366i | ||||||
\(27\) | 3.66603e45 | − | 5.20039e45i | 0.576176 | − | 0.817326i | ||||
\(28\) | −9.05936e45 | −0.444673 | ||||||||
\(29\) | − | 7.35680e46i | − | 1.17477i | −0.809307 | − | 0.587386i | \(-0.800157\pi\) | ||
0.809307 | − | 0.587386i | \(-0.199843\pi\) | |||||||
\(30\) | −2.25409e46 | − | 2.01025e46i | −0.121644 | − | 0.108485i | ||||
\(31\) | 2.62380e47 | 0.495857 | 0.247928 | − | 0.968778i | \(-0.420250\pi\) | ||||
0.247928 | + | 0.968778i | \(0.420250\pi\) | |||||||
\(32\) | − | 1.31386e48i | − | 0.898981i | ||||||
\(33\) | −3.17903e48 | + | 3.56464e48i | −0.812548 | + | 0.911107i | ||||
\(34\) | 3.26148e48 | 0.320693 | ||||||||
\(35\) | − | 5.20869e48i | − | 0.202559i | ||||||
\(36\) | 3.69984e48 | + | 3.22463e49i | 0.0584120 | + | 0.509096i | ||||
\(37\) | −1.16325e49 | −0.0764220 | −0.0382110 | − | 0.999270i | \(-0.512166\pi\) | ||||
−0.0382110 | + | 0.999270i | \(0.512166\pi\) | |||||||
\(38\) | 3.11130e50i | 0.870695i | ||||||||
\(39\) | −1.09940e51 | − | 9.80472e50i | −1.33995 | − | 1.19500i | ||||
\(40\) | 4.54740e50 | 0.246515 | ||||||||
\(41\) | − | 5.84077e51i | − | 1.43677i | −0.695646 | − | 0.718385i | \(-0.744882\pi\) | ||
0.695646 | − | 0.718385i | \(-0.255118\pi\) | |||||||
\(42\) | 3.54485e51 | − | 3.97483e51i | 0.403293 | − | 0.452212i | ||||
\(43\) | −1.86825e52 | −1.00102 | −0.500511 | − | 0.865730i | \(-0.666854\pi\) | ||||
−0.500511 | + | 0.865730i | \(0.666854\pi\) | |||||||
\(44\) | − | 2.43652e52i | − | 0.625581i | ||||||
\(45\) | −1.85400e52 | + | 2.12722e51i | −0.231905 | + | 0.0266080i | ||||
\(46\) | −1.06350e53 | −0.658393 | ||||||||
\(47\) | 1.99196e53i | 0.619655i | 0.950793 | + | 0.309827i | \(0.100271\pi\) | ||||
−0.950793 | + | 0.309827i | \(0.899729\pi\) | |||||||
\(48\) | 1.05871e53 | + | 9.44180e52i | 0.167902 | + | 0.149739i | ||||
\(49\) | −3.01268e53 | −0.246989 | ||||||||
\(50\) | − | 1.53717e54i | − | 0.660211i | ||||||
\(51\) | 1.34129e54 | − | 1.50399e54i | 0.305688 | − | 0.342767i | ||||
\(52\) | 7.51467e54 | 0.920032 | ||||||||
\(53\) | 1.50061e55i | 0.998710i | 0.866398 | + | 0.499355i | \(0.166430\pi\) | ||||
−0.866398 | + | 0.499355i | \(0.833570\pi\) | |||||||
\(54\) | −1.55959e55 | − | 1.09944e55i | −0.570704 | − | 0.402319i | ||||
\(55\) | 1.40088e55 | 0.284967 | ||||||||
\(56\) | 8.01882e55i | 0.916418i | ||||||||
\(57\) | 1.43473e56 | + | 1.27953e56i | 0.930628 | + | 0.829956i | ||||
\(58\) | −2.20630e56 | −0.820293 | ||||||||
\(59\) | − | 5.11137e56i | − | 1.09970i | −0.835264 | − | 0.549849i | \(-0.814685\pi\) | ||
0.835264 | − | 0.549849i | \(-0.185315\pi\) | |||||||
\(60\) | 6.33628e55 | − | 7.10486e55i | 0.0796149 | − | 0.0892720i | ||||
\(61\) | −5.59245e56 | −0.414045 | −0.207023 | − | 0.978336i | \(-0.566377\pi\) | ||||
−0.207023 | + | 0.978336i | \(0.566377\pi\) | |||||||
\(62\) | − | 7.86876e56i | − | 0.346236i | ||||||
\(63\) | −3.75112e56 | − | 3.26933e57i | −0.0989152 | − | 0.862106i | ||||
\(64\) | −5.35244e57 | −0.852694 | ||||||||
\(65\) | 4.32057e57i | 0.419096i | ||||||||
\(66\) | 1.06903e58 | + | 9.53390e57i | 0.636188 | + | 0.567368i | ||||
\(67\) | 8.34459e57 | 0.306910 | 0.153455 | − | 0.988156i | \(-0.450960\pi\) | ||||
0.153455 | + | 0.988156i | \(0.450960\pi\) | |||||||
\(68\) | 1.02801e58i | 0.235350i | ||||||||
\(69\) | −4.37366e58 | + | 4.90417e58i | −0.627587 | + | 0.703712i | ||||
\(70\) | −1.56208e58 | −0.141438 | ||||||||
\(71\) | 6.80033e58i | 0.391077i | 0.980696 | + | 0.195539i | \(0.0626455\pi\) | ||||
−0.980696 | + | 0.195539i | \(0.937354\pi\) | |||||||
\(72\) | 2.85425e59 | − | 3.27488e58i | 1.04919 | − | 0.120380i | ||||
\(73\) | −3.18733e59 | −0.753522 | −0.376761 | − | 0.926310i | \(-0.622962\pi\) | ||||
−0.376761 | + | 0.926310i | \(0.622962\pi\) | |||||||
\(74\) | 3.48858e58i | 0.0533622i | ||||||||
\(75\) | −7.08848e59 | − | 6.32167e59i | −0.705655 | − | 0.629320i | ||||
\(76\) | −9.80675e59 | −0.638984 | ||||||||
\(77\) | 2.47029e60i | 1.05936i | ||||||||
\(78\) | −2.94043e60 | + | 3.29710e60i | −0.834418 | + | 0.935631i | ||||
\(79\) | −4.25925e59 | −0.0804019 | −0.0402010 | − | 0.999192i | \(-0.512800\pi\) | ||||
−0.0402010 | + | 0.999192i | \(0.512800\pi\) | |||||||
\(80\) | − | 4.16064e59i | − | 0.0525147i | ||||||
\(81\) | −1.14838e61 | + | 2.67038e60i | −0.974013 | + | 0.226492i | ||||
\(82\) | −1.75164e61 | −1.00324 | ||||||||
\(83\) | 2.15064e61i | 0.835735i | 0.908508 | + | 0.417868i | \(0.137222\pi\) | ||||
−0.908508 | + | 0.417868i | \(0.862778\pi\) | |||||||
\(84\) | 1.25286e61 | + | 1.11733e61i | 0.331868 | + | 0.295968i | ||||
\(85\) | −5.91057e60 | −0.107207 | ||||||||
\(86\) | 5.60286e61i | 0.698971i | ||||||||
\(87\) | −9.07348e61 | + | 1.01741e62i | −0.781912 | + | 0.876756i | ||||
\(88\) | −2.15666e62 | −1.28925 | ||||||||
\(89\) | 4.70607e62i | 1.95965i | 0.199860 | + | 0.979825i | \(0.435951\pi\) | ||||
−0.199860 | + | 0.979825i | \(0.564049\pi\) | |||||||
\(90\) | 6.37954e60 | + | 5.56015e61i | 0.0185793 | + | 0.161930i | ||||
\(91\) | −7.61883e62 | −1.55799 | ||||||||
\(92\) | − | 3.35212e62i | − | 0.483180i | ||||||
\(93\) | −3.62857e62 | − | 3.23605e62i | −0.370068 | − | 0.330036i | ||||
\(94\) | 5.97389e62 | 0.432679 | ||||||||
\(95\) | − | 5.63840e62i | − | 0.291072i | ||||||
\(96\) | −1.62045e63 | + | 1.81700e63i | −0.598350 | + | 0.670928i | ||||
\(97\) | −3.65284e63 | −0.968133 | −0.484066 | − | 0.875031i | \(-0.660841\pi\) | ||||
−0.484066 | + | 0.875031i | \(0.660841\pi\) | |||||||
\(98\) | 9.03500e62i | 0.172462i | ||||||||
\(99\) | 8.79287e63 | − | 1.00886e63i | 1.21284 | − | 0.139158i | ||||
\(100\) | 4.84514e63 | 0.484514 | ||||||||
\(101\) | 1.69601e64i | 1.23351i | 0.787154 | + | 0.616756i | \(0.211554\pi\) | ||||
−0.787154 | + | 0.616756i | \(0.788446\pi\) | |||||||
\(102\) | −4.51046e63 | − | 4.02253e63i | −0.239340 | − | 0.213449i | ||||
\(103\) | 3.36268e64 | 1.30586 | 0.652928 | − | 0.757420i | \(-0.273541\pi\) | ||||
0.652928 | + | 0.757420i | \(0.273541\pi\) | |||||||
\(104\) | − | 6.65155e64i | − | 1.89608i | ||||||
\(105\) | −6.42411e63 | + | 7.20334e63i | −0.134820 | + | 0.151174i | ||||
\(106\) | 4.50031e64 | 0.697357 | ||||||||
\(107\) | − | 1.31767e65i | − | 1.51191i | −0.654625 | − | 0.755954i | \(-0.727173\pi\) | ||
0.654625 | − | 0.755954i | \(-0.272827\pi\) | |||||||
\(108\) | 3.46541e64 | − | 4.91581e64i | 0.295253 | − | 0.418827i | ||||
\(109\) | 4.13515e64 | 0.262327 | 0.131164 | − | 0.991361i | \(-0.458129\pi\) | ||||
0.131164 | + | 0.991361i | \(0.458129\pi\) | |||||||
\(110\) | − | 4.20123e64i | − | 0.198980i | ||||||
\(111\) | 1.60871e64 | + | 1.43469e64i | 0.0570353 | + | 0.0508654i | ||||
\(112\) | 7.33682e64 | 0.195223 | ||||||||
\(113\) | 2.74921e65i | 0.550424i | 0.961384 | + | 0.275212i | \(0.0887481\pi\) | ||||
−0.961384 | + | 0.275212i | \(0.911252\pi\) | |||||||
\(114\) | 3.83730e65 | − | 4.30276e65i | 0.579523 | − | 0.649818i | ||||
\(115\) | 1.92731e65 | 0.220100 | ||||||||
\(116\) | − | 6.95422e65i | − | 0.601995i | ||||||
\(117\) | 3.11153e65 | + | 2.71188e66i | 0.204657 | + | 1.78371i | ||||
\(118\) | −1.53290e66 | −0.767872 | ||||||||
\(119\) | − | 1.04226e66i | − | 0.398542i | ||||||
\(120\) | −6.28881e65 | − | 5.60851e65i | −0.183979 | − | 0.164077i | ||||
\(121\) | −2.18594e66 | −0.490350 | ||||||||
\(122\) | 1.67717e66i | 0.289110i | ||||||||
\(123\) | −7.20369e66 | + | 8.07748e66i | −0.956294 | + | 1.07229i | ||||
\(124\) | 2.48022e66 | 0.254095 | ||||||||
\(125\) | 5.73198e66i | 0.454134i | ||||||||
\(126\) | −9.80469e66 | + | 1.12496e66i | −0.601972 | + | 0.0690683i | ||||
\(127\) | −3.53730e67 | −1.68637 | −0.843184 | − | 0.537625i | \(-0.819321\pi\) | ||||
−0.843184 | + | 0.537625i | \(0.819321\pi\) | |||||||
\(128\) | − | 8.18453e66i | − | 0.303581i | ||||||
\(129\) | 2.58369e67 | + | 2.30419e67i | 0.747083 | + | 0.666267i | ||||
\(130\) | 1.29574e67 | 0.292637 | ||||||||
\(131\) | − | 4.79670e67i | − | 0.847737i | −0.905724 | − | 0.423869i | \(-0.860672\pi\) | ||
0.905724 | − | 0.423869i | \(-0.139328\pi\) | |||||||
\(132\) | −3.00507e67 | + | 3.36957e67i | −0.416379 | + | 0.466884i | ||||
\(133\) | 9.94268e67 | 1.08206 | ||||||||
\(134\) | − | 2.50254e67i | − | 0.214302i | ||||||
\(135\) | 2.82635e67 | + | 1.99244e67i | 0.190786 | + | 0.134495i | ||||
\(136\) | 9.09938e67 | 0.485028 | ||||||||
\(137\) | − | 1.79854e68i | − | 0.758338i | −0.925327 | − | 0.379169i | \(-0.876210\pi\) | ||
0.925327 | − | 0.379169i | \(-0.123790\pi\) | |||||||
\(138\) | 1.47076e68 | + | 1.31166e68i | 0.491372 | + | 0.438218i | ||||
\(139\) | −1.00310e68 | −0.265992 | −0.132996 | − | 0.991117i | \(-0.542460\pi\) | ||||
−0.132996 | + | 0.991117i | \(0.542460\pi\) | |||||||
\(140\) | − | 4.92366e67i | − | 0.103798i | ||||||
\(141\) | 2.45678e68 | − | 2.75478e68i | 0.412434 | − | 0.462461i | ||||
\(142\) | 2.03941e68 | 0.273073 | ||||||||
\(143\) | − | 2.04909e69i | − | 2.19183i | ||||||
\(144\) | −2.99635e67 | − | 2.61150e68i | −0.0256444 | − | 0.223507i | ||||
\(145\) | 3.99834e68 | 0.274223 | ||||||||
\(146\) | 9.55880e68i | 0.526153i | ||||||||
\(147\) | 4.16637e68 | + | 3.71567e68i | 0.184333 | + | 0.164393i | ||||
\(148\) | −1.09960e68 | −0.0391614 | ||||||||
\(149\) | 3.08904e69i | 0.886875i | 0.896305 | + | 0.443438i | \(0.146241\pi\) | ||||
−0.896305 | + | 0.443438i | \(0.853759\pi\) | |||||||
\(150\) | −1.89587e69 | + | 2.12583e69i | −0.439428 | + | 0.492729i | ||||
\(151\) | −2.29418e69 | −0.429898 | −0.214949 | − | 0.976625i | \(-0.568958\pi\) | ||||
−0.214949 | + | 0.976625i | \(0.568958\pi\) | |||||||
\(152\) | 8.68037e69i | 1.31687i | ||||||||
\(153\) | −3.70988e69 | + | 4.25659e68i | −0.456282 | + | 0.0523524i | ||||
\(154\) | 7.40839e69 | 0.739708 | ||||||||
\(155\) | 1.42600e69i | 0.115746i | ||||||||
\(156\) | −1.03924e70 | − | 9.26818e69i | −0.686639 | − | 0.612361i | ||||
\(157\) | −3.48146e70 | −1.87487 | −0.937437 | − | 0.348155i | \(-0.886808\pi\) | ||||
−0.937437 | + | 0.348155i | \(0.886808\pi\) | |||||||
\(158\) | 1.27735e69i | 0.0561413i | ||||||||
\(159\) | 1.85077e70 | − | 2.07526e70i | 0.664728 | − | 0.745358i | ||||
\(160\) | 7.14069e69 | 0.209846 | ||||||||
\(161\) | 3.39859e70i | 0.818220i | ||||||||
\(162\) | 8.00846e69 | + | 3.44398e70i | 0.158150 | + | 0.680112i | ||||
\(163\) | −4.50820e70 | −0.731139 | −0.365569 | − | 0.930784i | \(-0.619126\pi\) | ||||
−0.365569 | + | 0.930784i | \(0.619126\pi\) | |||||||
\(164\) | − | 5.52115e70i | − | 0.736252i | ||||||
\(165\) | −1.93734e70 | − | 1.72777e70i | −0.212677 | − | 0.189670i | ||||
\(166\) | 6.44975e70 | 0.583558 | ||||||||
\(167\) | 1.14924e71i | 0.857992i | 0.903306 | + | 0.428996i | \(0.141133\pi\) | ||||
−0.903306 | + | 0.428996i | \(0.858867\pi\) | |||||||
\(168\) | 9.88997e70 | − | 1.10896e71i | 0.609955 | − | 0.683941i | ||||
\(169\) | 4.35923e71 | 2.22349 | ||||||||
\(170\) | 1.77258e70i | 0.0748583i | ||||||||
\(171\) | −4.06059e70 | − | 3.53904e71i | −0.142139 | − | 1.23883i | ||||
\(172\) | −1.76601e71 | −0.512960 | ||||||||
\(173\) | − | 5.86283e71i | − | 1.41460i | −0.706916 | − | 0.707298i | \(-0.749914\pi\) | ||
0.706916 | − | 0.707298i | \(-0.250086\pi\) | |||||||
\(174\) | 3.05120e71 | + | 2.72113e71i | 0.612202 | + | 0.545976i | ||||
\(175\) | −4.91230e71 | −0.820479 | ||||||||
\(176\) | 1.97324e71i | 0.274647i | ||||||||
\(177\) | −6.30409e71 | + | 7.06876e71i | −0.731944 | + | 0.820727i | ||||
\(178\) | 1.41135e72 | 1.36834 | ||||||||
\(179\) | − | 1.19758e72i | − | 0.970525i | −0.874368 | − | 0.485263i | \(-0.838724\pi\) | ||
0.874368 | − | 0.485263i | \(-0.161276\pi\) | |||||||
\(180\) | −1.75255e71 | + | 2.01082e70i | −0.118837 | + | 0.0136349i | ||||
\(181\) | −2.05567e72 | −1.16745 | −0.583726 | − | 0.811951i | \(-0.698406\pi\) | ||||
−0.583726 | + | 0.811951i | \(0.698406\pi\) | |||||||
\(182\) | 2.28488e72i | 1.08788i | ||||||||
\(183\) | 7.73407e71 | + | 6.89743e71i | 0.309010 | + | 0.275583i | ||||
\(184\) | −2.96710e72 | −0.995778 | ||||||||
\(185\) | − | 6.32214e70i | − | 0.0178389i | ||||||
\(186\) | −9.70489e71 | + | 1.08821e72i | −0.230450 | + | 0.258403i | ||||
\(187\) | 2.80317e72 | 0.560684 | ||||||||
\(188\) | 1.88296e72i | 0.317533i | ||||||||
\(189\) | −3.51345e72 | + | 4.98395e72i | −0.499984 | + | 0.709244i | ||||
\(190\) | −1.69095e72 | −0.203243 | ||||||||
\(191\) | − | 7.06194e72i | − | 0.717557i | −0.933423 | − | 0.358778i | \(-0.883193\pi\) | ||
0.933423 | − | 0.358778i | \(-0.116807\pi\) | |||||||
\(192\) | 7.40215e72 | + | 6.60141e72i | 0.636383 | + | 0.567541i | ||||
\(193\) | −1.17299e73 | −0.854002 | −0.427001 | − | 0.904251i | \(-0.640430\pi\) | ||||
−0.427001 | + | 0.904251i | \(0.640430\pi\) | |||||||
\(194\) | 1.09548e73i | 0.676006i | ||||||||
\(195\) | 5.32875e72 | − | 5.97512e72i | 0.278945 | − | 0.312780i | ||||
\(196\) | −2.84782e72 | −0.126566 | ||||||||
\(197\) | − | 2.34063e73i | − | 0.883922i | −0.897034 | − | 0.441961i | \(-0.854283\pi\) | ||
0.897034 | − | 0.441961i | \(-0.145717\pi\) | |||||||
\(198\) | −3.02558e72 | − | 2.63698e73i | −0.0971678 | − | 0.846876i | ||||
\(199\) | 3.83054e73 | 1.04704 | 0.523518 | − | 0.852015i | \(-0.324619\pi\) | ||||
0.523518 | + | 0.852015i | \(0.324619\pi\) | |||||||
\(200\) | − | 4.28864e73i | − | 0.998527i | ||||||
\(201\) | −1.15401e73 | − | 1.02918e73i | −0.229053 | − | 0.204275i | ||||
\(202\) | 5.08632e73 | 0.861310 | ||||||||
\(203\) | 7.05062e73i | 1.01942i | ||||||||
\(204\) | 1.26790e73 | − | 1.42169e73i | 0.156646 | − | 0.175646i | ||||
\(205\) | 3.17439e73 | 0.335380 | ||||||||
\(206\) | − | 1.00847e74i | − | 0.911823i | ||||||
\(207\) | 1.20971e74 | − | 1.38798e73i | 0.936763 | − | 0.107481i | ||||
\(208\) | −6.08584e73 | −0.403919 | ||||||||
\(209\) | 2.67409e74i | 1.52228i | ||||||||
\(210\) | 2.16028e73 | + | 1.92659e73i | 0.105558 | + | 0.0941394i | ||||
\(211\) | −2.11177e74 | −0.886355 | −0.443177 | − | 0.896434i | \(-0.646149\pi\) | ||||
−0.443177 | + | 0.896434i | \(0.646149\pi\) | |||||||
\(212\) | 1.41849e74i | 0.511775i | ||||||||
\(213\) | 8.38715e73 | − | 9.40450e73i | 0.260296 | − | 0.291869i | ||||
\(214\) | −3.95168e74 | −1.05570 | ||||||||
\(215\) | − | 1.01537e74i | − | 0.233665i | ||||||
\(216\) | −4.35119e74 | − | 3.06738e74i | −0.863153 | − | 0.608482i | ||||
\(217\) | −2.51460e74 | −0.430286 | ||||||||
\(218\) | − | 1.24013e74i | − | 0.183172i | ||||||
\(219\) | 4.40791e74 | + | 3.93108e74i | 0.562369 | + | 0.501534i | ||||
\(220\) | 1.32422e74 | 0.146027 | ||||||||
\(221\) | 8.64549e74i | 0.824588i | ||||||||
\(222\) | 4.30263e73 | − | 4.82453e73i | 0.0355172 | − | 0.0398253i | ||||
\(223\) | −1.58196e75 | −1.13094 | −0.565470 | − | 0.824769i | \(-0.691305\pi\) | ||||
−0.565470 | + | 0.824769i | \(0.691305\pi\) | |||||||
\(224\) | 1.25918e75i | 0.780101i | ||||||||
\(225\) | 2.00618e74 | + | 1.74851e75i | 0.107778 | + | 0.939349i | ||||
\(226\) | 8.24486e74 | 0.384338 | ||||||||
\(227\) | − | 3.37965e75i | − | 1.36787i | −0.729544 | − | 0.683933i | \(-0.760268\pi\) | ||
0.729544 | − | 0.683933i | \(-0.239732\pi\) | |||||||
\(228\) | 1.35622e75 | + | 1.20951e75i | 0.476887 | + | 0.425299i | ||||
\(229\) | 3.48419e75 | 1.06504 | 0.532520 | − | 0.846417i | \(-0.321245\pi\) | ||||
0.532520 | + | 0.846417i | \(0.321245\pi\) | |||||||
\(230\) | − | 5.77998e74i | − | 0.153686i | ||||||
\(231\) | 3.04672e75 | − | 3.41628e75i | 0.705098 | − | 0.790624i | ||||
\(232\) | −6.15548e75 | −1.24064 | ||||||||
\(233\) | − | 8.31148e75i | − | 1.45978i | −0.683562 | − | 0.729892i | \(-0.739570\pi\) | ||
0.683562 | − | 0.729892i | \(-0.260430\pi\) | |||||||
\(234\) | 8.13292e75 | − | 9.33145e74i | 1.24549 | − | 0.142903i | ||||
\(235\) | −1.08261e75 | −0.144644 | ||||||||
\(236\) | − | 4.83167e75i | − | 0.563525i | ||||||
\(237\) | 5.89032e74 | + | 5.25313e74i | 0.0600056 | + | 0.0535145i | ||||
\(238\) | −3.12574e75 | −0.278285 | ||||||||
\(239\) | 9.40845e75i | 0.732462i | 0.930524 | + | 0.366231i | \(0.119352\pi\) | ||||
−0.930524 | + | 0.366231i | \(0.880648\pi\) | |||||||
\(240\) | −5.13151e74 | + | 5.75395e74i | −0.0349531 | + | 0.0391928i | ||||
\(241\) | −7.98891e75 | −0.476368 | −0.238184 | − | 0.971220i | \(-0.576552\pi\) | ||||
−0.238184 | + | 0.971220i | \(0.576552\pi\) | |||||||
\(242\) | 6.55562e75i | 0.342391i | ||||||||
\(243\) | 1.91750e76 | + | 1.04705e76i | 0.877676 | + | 0.479254i | ||||
\(244\) | −5.28642e75 | −0.212172 | ||||||||
\(245\) | − | 1.63736e75i | − | 0.0576539i | ||||||
\(246\) | 2.42243e76 | + | 2.16038e76i | 0.748735 | + | 0.667740i | ||||
\(247\) | −8.24738e76 | −2.23879 | ||||||||
\(248\) | − | 2.19535e76i | − | 0.523660i | ||||||
\(249\) | 2.65248e76 | − | 2.97422e76i | 0.556254 | − | 0.623726i | ||||
\(250\) | 1.71902e76 | 0.317103 | ||||||||
\(251\) | 1.02540e77i | 1.66469i | 0.554261 | + | 0.832343i | \(0.313001\pi\) | ||||
−0.554261 | + | 0.832343i | \(0.686999\pi\) | |||||||
\(252\) | −3.54585e75 | − | 3.09042e76i | −0.0506877 | − | 0.441774i | ||||
\(253\) | −9.14051e76 | −1.15110 | ||||||||
\(254\) | 1.06083e77i | 1.17752i | ||||||||
\(255\) | 8.17401e75 | + | 7.28978e75i | 0.0800110 | + | 0.0713557i | ||||
\(256\) | −1.23281e77 | −1.06467 | ||||||||
\(257\) | − | 1.06843e77i | − | 0.814492i | −0.913319 | − | 0.407246i | \(-0.866489\pi\) | ||
0.913319 | − | 0.407246i | \(-0.133511\pi\) | |||||||
\(258\) | 6.91026e76 | − | 7.74846e76i | 0.465226 | − | 0.521657i | ||||
\(259\) | 1.11484e76 | 0.0663161 | ||||||||
\(260\) | 4.08414e76i | 0.214760i | ||||||||
\(261\) | 2.50963e77 | − | 2.87947e76i | 1.16711 | − | 0.133911i | ||||
\(262\) | −1.43853e77 | −0.591939 | ||||||||
\(263\) | − | 2.64211e77i | − | 0.962424i | −0.876604 | − | 0.481212i | \(-0.840197\pi\) | ||
0.876604 | − | 0.481212i | \(-0.159803\pi\) | |||||||
\(264\) | 2.98255e77 | + | 2.65991e77i | 0.962194 | + | 0.858107i | ||||
\(265\) | −8.15563e76 | −0.233125 | ||||||||
\(266\) | − | 2.98180e77i | − | 0.755556i | ||||||
\(267\) | 5.80421e77 | − | 6.50825e77i | 1.30432 | − | 1.46253i | ||||
\(268\) | 7.88796e76 | 0.157272 | ||||||||
\(269\) | 6.70620e77i | 1.18687i | 0.804881 | + | 0.593436i | \(0.202229\pi\) | ||||
−0.804881 | + | 0.593436i | \(0.797771\pi\) | |||||||
\(270\) | 5.97533e76 | − | 8.47621e76i | 0.0939120 | − | 0.133217i | ||||
\(271\) | −4.99455e77 | −0.697395 | −0.348697 | − | 0.937235i | \(-0.613376\pi\) | ||||
−0.348697 | + | 0.937235i | \(0.613376\pi\) | |||||||
\(272\) | − | 8.32548e76i | − | 0.103325i | ||||||
\(273\) | 1.05364e78 | + | 9.39665e77i | 1.16276 | + | 1.03698i | ||||
\(274\) | −5.39382e77 | −0.529515 | ||||||||
\(275\) | − | 1.32117e78i | − | 1.15428i | ||||||
\(276\) | −4.13432e77 | + | 4.63581e77i | −0.321598 | + | 0.360607i | ||||
\(277\) | −1.03981e78 | −0.720445 | −0.360222 | − | 0.932866i | \(-0.617299\pi\) | ||||
−0.360222 | + | 0.932866i | \(0.617299\pi\) | |||||||
\(278\) | 3.00828e77i | 0.185731i | ||||||||
\(279\) | 1.02696e77 | + | 8.95057e77i | 0.0565222 | + | 0.492625i | ||||
\(280\) | −4.35814e77 | −0.213916 | ||||||||
\(281\) | − | 8.94834e77i | − | 0.391868i | −0.980617 | − | 0.195934i | \(-0.937226\pi\) | ||
0.980617 | − | 0.195934i | \(-0.0627739\pi\) | |||||||
\(282\) | −8.26157e77 | − | 7.36786e77i | −0.322917 | − | 0.287985i | ||||
\(283\) | −1.43173e78 | −0.499683 | −0.249841 | − | 0.968287i | \(-0.580378\pi\) | ||||
−0.249841 | + | 0.968287i | \(0.580378\pi\) | |||||||
\(284\) | 6.42820e77i | 0.200402i | ||||||||
\(285\) | −6.95410e77 | + | 7.79761e77i | −0.193734 | + | 0.217233i | ||||
\(286\) | −6.14520e78 | −1.53046 | ||||||||
\(287\) | 5.59768e78i | 1.24677i | ||||||||
\(288\) | 4.48198e78 | − | 5.14248e77i | 0.893121 | − | 0.102474i | ||||
\(289\) | 4.42429e78 | 0.789066 | ||||||||
\(290\) | − | 1.19910e78i | − | 0.191478i | ||||||
\(291\) | 5.05168e78 | + | 4.50521e78i | 0.722537 | + | 0.644376i | ||||
\(292\) | −3.01292e78 | −0.386132 | ||||||||
\(293\) | 2.61705e78i | 0.300641i | 0.988637 | + | 0.150320i | \(0.0480305\pi\) | ||||
−0.988637 | + | 0.150320i | \(0.951970\pi\) | |||||||
\(294\) | 1.11433e78 | − | 1.24949e78i | 0.114789 | − | 0.128712i | ||||
\(295\) | 2.77797e78 | 0.256699 | ||||||||
\(296\) | 9.73298e77i | 0.0807070i | ||||||||
\(297\) | −1.34043e79 | − | 9.44943e78i | −0.997790 | − | 0.703395i | ||||
\(298\) | 9.26401e78 | 0.619268 | ||||||||
\(299\) | − | 2.81910e79i | − | 1.69291i | ||||||
\(300\) | −6.70058e78 | − | 5.97574e78i | −0.361603 | − | 0.322486i | ||||
\(301\) | 1.79049e79 | 0.868648 | ||||||||
\(302\) | 6.88023e78i | 0.300179i | ||||||||
\(303\) | 2.09176e79 | − | 2.34549e79i | 0.821010 | − | 0.920596i | ||||
\(304\) | 7.94211e78 | 0.280531 | ||||||||
\(305\) | − | 3.03943e78i | − | 0.0966491i | ||||||
\(306\) | 1.27655e78 | + | 1.11259e79i | 0.0365555 | + | 0.318603i | ||||
\(307\) | 2.24623e78 | 0.0579463 | 0.0289731 | − | 0.999580i | \(-0.490776\pi\) | ||||
0.0289731 | + | 0.999580i | \(0.490776\pi\) | |||||||
\(308\) | 2.33511e79i | 0.542856i | ||||||||
\(309\) | −4.65042e79 | − | 4.14735e79i | −0.974587 | − | 0.869160i | ||||
\(310\) | 4.27658e78 | 0.0808206 | ||||||||
\(311\) | 3.81659e79i | 0.650643i | 0.945603 | + | 0.325322i | \(0.105473\pi\) | ||||
−0.945603 | + | 0.325322i | \(0.894527\pi\) | |||||||
\(312\) | −8.20366e79 | + | 9.19874e79i | −1.26200 | + | 1.41508i | ||||
\(313\) | 1.21255e80 | 1.68376 | 0.841881 | − | 0.539663i | \(-0.181449\pi\) | ||||
0.841881 | + | 0.539663i | \(0.181449\pi\) | |||||||
\(314\) | 1.04409e80i | 1.30915i | ||||||||
\(315\) | 1.77684e79 | − | 2.03869e78i | 0.201238 | − | 0.0230894i | ||||
\(316\) | −4.02618e78 | −0.0412009 | ||||||||
\(317\) | − | 1.29379e80i | − | 1.19665i | −0.801255 | − | 0.598323i | \(-0.795834\pi\) | ||
0.801255 | − | 0.598323i | \(-0.204166\pi\) | |||||||
\(318\) | −6.22369e79 | − | 5.55044e79i | −0.520452 | − | 0.464151i | ||||
\(319\) | −1.89627e80 | −1.43416 | ||||||||
\(320\) | − | 2.90899e79i | − | 0.199041i | ||||||
\(321\) | −1.62514e80 | + | 1.82227e80i | −1.00631 | + | 1.12837i | ||||
\(322\) | 1.01923e80 | 0.571329 | ||||||||
\(323\) | − | 1.12825e80i | − | 0.572696i | ||||||
\(324\) | −1.08554e80 | + | 2.52425e79i | −0.499119 | + | 0.116063i | ||||
\(325\) | 4.07472e80 | 1.69758 | ||||||||
\(326\) | 1.35201e80i | 0.510523i | ||||||||
\(327\) | −5.71869e79 | − | 5.10007e79i | −0.195780 | − | 0.174601i | ||||
\(328\) | −4.88701e80 | −1.51733 | ||||||||
\(329\) | − | 1.90906e80i | − | 0.537713i | ||||||
\(330\) | −5.18156e79 | + | 5.81008e79i | −0.132439 | + | 0.148503i | ||||
\(331\) | 5.78671e80 | 1.34257 | 0.671283 | − | 0.741201i | \(-0.265743\pi\) | ||||
0.671283 | + | 0.741201i | \(0.265743\pi\) | |||||||
\(332\) | 2.03295e80i | 0.428261i | ||||||||
\(333\) | −4.55299e78 | − | 3.96820e79i | −0.00871126 | − | 0.0759239i | ||||
\(334\) | 3.44656e80 | 0.599100 | ||||||||
\(335\) | 4.53519e79i | 0.0716410i | ||||||||
\(336\) | −1.01464e80 | − | 9.04884e79i | −0.145699 | − | 0.129938i | ||||
\(337\) | 1.19792e81 | 1.56413 | 0.782064 | − | 0.623198i | \(-0.214167\pi\) | ||||
0.782064 | + | 0.623198i | \(0.214167\pi\) | |||||||
\(338\) | − | 1.30733e81i | − | 1.55257i | ||||||
\(339\) | 3.39072e80 | − | 3.80201e80i | 0.366355 | − | 0.410793i | ||||
\(340\) | −5.58713e79 | −0.0549369 | ||||||||
\(341\) | − | 6.76302e80i | − | 0.605341i | ||||||
\(342\) | −1.06136e81 | + | 1.21777e80i | −0.865020 | + | 0.0992496i | ||||
\(343\) | 1.45772e81 | 1.08209 | ||||||||
\(344\) | 1.56317e81i | 1.05715i | ||||||||
\(345\) | −2.66536e80 | − | 2.37703e80i | −0.164265 | − | 0.146496i | ||||
\(346\) | −1.75826e81 | −0.987753 | ||||||||
\(347\) | 1.62754e81i | 0.833657i | 0.908985 | + | 0.416829i | \(0.136859\pi\) | ||||
−0.908985 | + | 0.416829i | \(0.863141\pi\) | |||||||
\(348\) | −8.57696e80 | + | 9.61732e80i | −0.400680 | + | 0.449281i | ||||
\(349\) | −2.46602e81 | −1.05095 | −0.525475 | − | 0.850809i | \(-0.676112\pi\) | ||||
−0.525475 | + | 0.850809i | \(0.676112\pi\) | |||||||
\(350\) | 1.47320e81i | 0.572906i | ||||||||
\(351\) | 2.91438e81 | − | 4.13415e81i | 1.03447 | − | 1.46743i | ||||
\(352\) | −3.38657e81 | −1.09748 | ||||||||
\(353\) | − | 8.47826e80i | − | 0.250909i | −0.992099 | − | 0.125454i | \(-0.959961\pi\) | ||
0.992099 | − | 0.125454i | \(-0.0400389\pi\) | |||||||
\(354\) | 2.11992e81 | + | 1.89059e81i | 0.573079 | + | 0.511085i | ||||
\(355\) | −3.69590e80 | −0.0912879 | ||||||||
\(356\) | 4.44854e81i | 1.00419i | ||||||||
\(357\) | −1.28547e81 | + | 1.44139e81i | −0.265264 | + | 0.297440i | ||||
\(358\) | −3.59153e81 | −0.677677 | ||||||||
\(359\) | − | 5.66175e81i | − | 0.977076i | −0.872543 | − | 0.488538i | \(-0.837530\pi\) | ||
0.872543 | − | 0.488538i | \(-0.162470\pi\) | |||||||
\(360\) | 1.77986e80 | + | 1.55125e81i | 0.0281000 | + | 0.244908i | ||||
\(361\) | 3.84097e81 | 0.554894 | ||||||||
\(362\) | 6.16494e81i | 0.815183i | ||||||||
\(363\) | 3.02304e81 | + | 2.69602e81i | 0.365959 | + | 0.326371i | ||||
\(364\) | −7.20191e81 | −0.798369 | ||||||||
\(365\) | − | 1.73228e81i | − | 0.175892i | ||||||
\(366\) | 2.06853e81 | − | 2.31944e81i | 0.192428 | − | 0.215769i | ||||
\(367\) | 6.79728e80 | 0.0579457 | 0.0289728 | − | 0.999580i | \(-0.490776\pi\) | ||||
0.0289728 | + | 0.999580i | \(0.490776\pi\) | |||||||
\(368\) | 2.71475e81i | 0.212129i | ||||||||
\(369\) | 1.99247e82 | − | 2.28609e81i | 1.42740 | − | 0.163776i | ||||
\(370\) | −1.89601e80 | −0.0124562 | ||||||||
\(371\) | − | 1.43815e82i | − | 0.866642i | ||||||
\(372\) | −3.43001e81 | − | 3.05897e81i | −0.189636 | − | 0.169122i | ||||
\(373\) | −1.36735e82 | −0.693739 | −0.346870 | − | 0.937913i | \(-0.612755\pi\) | ||||
−0.346870 | + | 0.937913i | \(0.612755\pi\) | |||||||
\(374\) | − | 8.40669e81i | − | 0.391502i | ||||||
\(375\) | 7.06951e81 | − | 7.92703e81i | 0.302266 | − | 0.338930i | ||||
\(376\) | 1.66669e82 | 0.654399 | ||||||||
\(377\) | − | 5.84844e82i | − | 2.10919i | ||||||
\(378\) | 1.49468e82 | + | 1.05368e82i | 0.495235 | + | 0.349117i | ||||
\(379\) | −2.20461e82 | −0.671238 | −0.335619 | − | 0.941998i | \(-0.608946\pi\) | ||||
−0.335619 | + | 0.941998i | \(0.608946\pi\) | |||||||
\(380\) | − | 5.32986e81i | − | 0.149156i | ||||||
\(381\) | 4.89189e82 | + | 4.36271e82i | 1.25857 | + | 1.12242i | ||||
\(382\) | −2.11787e82 | −0.501040 | ||||||||
\(383\) | 5.33721e82i | 1.16132i | 0.814145 | + | 0.580662i | \(0.197206\pi\) | ||||
−0.814145 | + | 0.580662i | \(0.802794\pi\) | |||||||
\(384\) | −1.00944e82 | + | 1.13188e82i | −0.202059 | + | 0.226569i | ||||
\(385\) | −1.34257e82 | −0.247283 | ||||||||
\(386\) | 3.51778e82i | 0.596313i | ||||||||
\(387\) | −7.31235e81 | − | 6.37315e82i | −0.114105 | − | 0.994497i | ||||
\(388\) | −3.45295e82 | −0.496106 | ||||||||
\(389\) | 9.21408e82i | 1.21917i | 0.792720 | + | 0.609586i | \(0.208664\pi\) | ||||
−0.792720 | + | 0.609586i | \(0.791336\pi\) | |||||||
\(390\) | −1.79193e82 | − | 1.59809e82i | −0.218401 | − | 0.194775i | ||||
\(391\) | 3.85656e82 | 0.433055 | ||||||||
\(392\) | 2.52072e82i | 0.260838i | ||||||||
\(393\) | −5.91599e82 | + | 6.63359e82i | −0.564243 | + | 0.632684i | ||||
\(394\) | −7.01954e82 | −0.617205 | ||||||||
\(395\) | − | 2.31486e81i | − | 0.0187679i | ||||||
\(396\) | 8.31170e82 | − | 9.53658e81i | 0.621504 | − | 0.0713094i | ||||
\(397\) | −1.08936e83 | −0.751404 | −0.375702 | − | 0.926741i | \(-0.622598\pi\) | ||||
−0.375702 | + | 0.926741i | \(0.622598\pi\) | |||||||
\(398\) | − | 1.14878e83i | − | 0.731101i | ||||||
\(399\) | −1.37502e83 | − | 1.22628e83i | −0.807563 | − | 0.720204i | ||||
\(400\) | −3.92390e82 | −0.212715 | ||||||||
\(401\) | − | 4.18269e82i | − | 0.209332i | −0.994507 | − | 0.104666i | \(-0.966623\pi\) | ||
0.994507 | − | 0.104666i | \(-0.0333773\pi\) | |||||||
\(402\) | −3.08649e82 | + | 3.46088e82i | −0.142637 | + | 0.159938i | ||||
\(403\) | 2.08584e83 | 0.890265 | ||||||||
\(404\) | 1.60320e83i | 0.632097i | ||||||||
\(405\) | −1.45132e82 | − | 6.24131e82i | −0.0528692 | − | 0.227361i | ||||
\(406\) | 2.11448e83 | 0.711819 | ||||||||
\(407\) | 2.99836e82i | 0.0932959i | ||||||||
\(408\) | −1.25840e83 | − | 1.12227e83i | −0.361986 | − | 0.322828i | ||||
\(409\) | 6.88521e83 | 1.83135 | 0.915675 | − | 0.401921i | \(-0.131657\pi\) | ||||
0.915675 | + | 0.401921i | \(0.131657\pi\) | |||||||
\(410\) | − | 9.51999e82i | − | 0.234182i | ||||||
\(411\) | −2.21823e83 | + | 2.48729e83i | −0.504740 | + | 0.565963i | ||||
\(412\) | 3.17867e83 | 0.669167 | ||||||||
\(413\) | 4.89864e83i | 0.954275i | ||||||||
\(414\) | −4.16254e82 | − | 3.62791e83i | −0.0750495 | − | 0.654102i | ||||
\(415\) | −1.16885e83 | −0.195083 | ||||||||
\(416\) | − | 1.04448e84i | − | 1.61404i | ||||||
\(417\) | 1.38723e83 | + | 1.23716e83i | 0.198515 | + | 0.177041i | ||||
\(418\) | 8.01958e83 | 1.06294 | ||||||||
\(419\) | − | 8.54985e83i | − | 1.04981i | −0.851162 | − | 0.524904i | \(-0.824101\pi\) | ||
0.851162 | − | 0.524904i | \(-0.175899\pi\) | |||||||
\(420\) | −6.07257e82 | + | 6.80916e82i | −0.0690868 | + | 0.0774669i | ||||
\(421\) | −1.63418e84 | −1.72295 | −0.861476 | − | 0.507799i | \(-0.830459\pi\) | ||||
−0.861476 | + | 0.507799i | \(0.830459\pi\) | |||||||
\(422\) | 6.33318e83i | 0.618904i | ||||||||
\(423\) | −6.79519e83 | + | 7.79658e82i | −0.615616 | + | 0.0706338i | ||||
\(424\) | 1.25557e84 | 1.05471 | ||||||||
\(425\) | 5.57425e83i | 0.434251i | ||||||||
\(426\) | −2.82040e83 | − | 2.51530e83i | −0.203800 | − | 0.181754i | ||||
\(427\) | 5.35970e83 | 0.359293 | ||||||||
\(428\) | − | 1.24556e84i | − | 0.774756i | ||||||
\(429\) | −2.52723e84 | + | 2.83378e84i | −1.45885 | + | 1.63581i | ||||
\(430\) | −3.04509e83 | −0.163158 | ||||||||
\(431\) | 1.21887e84i | 0.606296i | 0.952944 | + | 0.303148i | \(0.0980376\pi\) | ||||
−0.952944 | + | 0.303148i | \(0.901962\pi\) | |||||||
\(432\) | −2.80651e83 | + | 3.98112e83i | −0.129624 | + | 0.183876i | ||||
\(433\) | −1.17391e84 | −0.503525 | −0.251762 | − | 0.967789i | \(-0.581010\pi\) | ||||
−0.251762 | + | 0.967789i | \(0.581010\pi\) | |||||||
\(434\) | 7.54126e83i | 0.300450i | ||||||||
\(435\) | −5.52949e83 | − | 4.93133e83i | −0.204658 | − | 0.182519i | ||||
\(436\) | 3.90886e83 | 0.134426 | ||||||||
\(437\) | 3.67897e84i | 1.17576i | ||||||||
\(438\) | 1.17893e84 | − | 1.32193e84i | 0.350200 | − | 0.392679i | ||||
\(439\) | 1.38578e84 | 0.382674 | 0.191337 | − | 0.981524i | \(-0.438718\pi\) | ||||
0.191337 | + | 0.981524i | \(0.438718\pi\) | |||||||
\(440\) | − | 1.17212e84i | − | 0.300945i | ||||||
\(441\) | −1.17917e83 | − | 1.02772e84i | −0.0281540 | − | 0.245379i | ||||
\(442\) | 2.59278e84 | 0.575775 | ||||||||
\(443\) | − | 6.60390e84i | − | 1.36421i | −0.731254 | − | 0.682105i | \(-0.761065\pi\) | ||
0.731254 | − | 0.682105i | \(-0.238935\pi\) | |||||||
\(444\) | 1.52068e83 | + | 1.35618e83i | 0.0292269 | + | 0.0260653i | ||||
\(445\) | −2.55770e84 | −0.457434 | ||||||||
\(446\) | 4.74429e84i | 0.789688i | ||||||||
\(447\) | 3.80985e84 | − | 4.27198e84i | 0.590292 | − | 0.661893i | ||||
\(448\) | 5.12968e84 | 0.739935 | ||||||||
\(449\) | − | 2.15053e84i | − | 0.288843i | −0.989516 | − | 0.144422i | \(-0.953868\pi\) | ||
0.989516 | − | 0.144422i | \(-0.0461321\pi\) | |||||||
\(450\) | 5.24377e84 | − | 6.01653e83i | 0.655908 | − | 0.0752568i | ||||
\(451\) | −1.50550e85 | −1.75401 | ||||||||
\(452\) | 2.59877e84i | 0.282057i | ||||||||
\(453\) | 3.17273e84 | + | 2.82952e84i | 0.320841 | + | 0.286134i | ||||
\(454\) | −1.01355e85 | −0.955124 | ||||||||
\(455\) | − | 4.14075e84i | − | 0.363676i | ||||||
\(456\) | 1.07059e85 | − | 1.20045e85i | 0.876492 | − | 0.982808i | ||||
\(457\) | 1.88138e85 | 1.43601 | 0.718005 | − | 0.696038i | \(-0.245055\pi\) | ||||
0.718005 | + | 0.696038i | \(0.245055\pi\) | |||||||
\(458\) | − | 1.04491e85i | − | 0.743672i | ||||||
\(459\) | 5.65555e84 | + | 3.98690e84i | 0.375378 | + | 0.264624i | ||||
\(460\) | 1.82184e84 | 0.112787 | ||||||||
\(461\) | 1.93945e85i | 1.12008i | 0.828467 | + | 0.560039i | \(0.189214\pi\) | ||||
−0.828467 | + | 0.560039i | \(0.810786\pi\) | |||||||
\(462\) | −1.02454e85 | − | 9.13710e84i | −0.552060 | − | 0.492340i | ||||
\(463\) | −5.79816e84 | −0.291540 | −0.145770 | − | 0.989319i | \(-0.546566\pi\) | ||||
−0.145770 | + | 0.989319i | \(0.546566\pi\) | |||||||
\(464\) | 5.63196e84i | 0.264292i | ||||||||
\(465\) | 1.75876e84 | − | 1.97209e84i | 0.0770391 | − | 0.0863837i | ||||
\(466\) | −2.49261e85 | −1.01931 | ||||||||
\(467\) | − | 1.40072e85i | − | 0.534824i | −0.963582 | − | 0.267412i | \(-0.913831\pi\) | ||
0.963582 | − | 0.267412i | \(-0.0861685\pi\) | |||||||
\(468\) | 2.94126e84 | + | 2.56348e85i | 0.104873 | + | 0.914035i | ||||
\(469\) | −7.99729e84 | −0.266325 | ||||||||
\(470\) | 3.24674e84i | 0.100999i | ||||||||
\(471\) | 4.81467e85 | + | 4.29384e85i | 1.39926 | + | 1.24789i | ||||
\(472\) | −4.27671e85 | −1.16136 | ||||||||
\(473\) | 4.81553e85i | 1.22205i | ||||||||
\(474\) | 1.57541e84 | − | 1.76650e84i | 0.0373669 | − | 0.0418994i | ||||
\(475\) | −5.31757e85 | −1.17901 | ||||||||
\(476\) | − | 9.85227e84i | − | 0.204227i | ||||||
\(477\) | −5.11903e85 | + | 5.87341e84i | −0.992200 | + | 0.113842i | ||||
\(478\) | 2.82159e85 | 0.511447 | ||||||||
\(479\) | − | 8.64619e85i | − | 1.46585i | −0.680311 | − | 0.732923i | \(-0.738155\pi\) | ||
0.680311 | − | 0.732923i | \(-0.261845\pi\) | |||||||
\(480\) | −9.87520e84 | − | 8.80694e84i | −0.156612 | − | 0.139671i | ||||
\(481\) | −9.24749e84 | −0.137209 | ||||||||
\(482\) | 2.39587e85i | 0.332627i | ||||||||
\(483\) | 4.19163e85 | − | 4.70006e85i | 0.544596 | − | 0.610655i | ||||
\(484\) | −2.06632e85 | −0.251273 | ||||||||
\(485\) | − | 1.98528e85i | − | 0.225988i | ||||||
\(486\) | 3.14009e85 | − | 5.75057e85i | 0.334643 | − | 0.612844i | ||||
\(487\) | 1.32845e86 | 1.32562 | 0.662810 | − | 0.748788i | \(-0.269364\pi\) | ||||
0.662810 | + | 0.748788i | \(0.269364\pi\) | |||||||
\(488\) | 4.67923e85i | 0.437261i | ||||||||
\(489\) | 6.23460e85 | + | 5.56017e85i | 0.545664 | + | 0.486636i | ||||
\(490\) | −4.91042e84 | −0.0402573 | ||||||||
\(491\) | − | 2.43669e86i | − | 1.87151i | −0.352653 | − | 0.935754i | \(-0.614720\pi\) | ||
0.352653 | − | 0.935754i | \(-0.385280\pi\) | |||||||
\(492\) | −6.80949e85 | + | 7.63546e85i | −0.490040 | + | 0.549480i | ||||
\(493\) | 8.00071e85 | 0.539544 | ||||||||
\(494\) | 2.47339e86i | 1.56325i | ||||||||
\(495\) | 5.48307e84 | + | 4.77882e85i | 0.0324831 | + | 0.283110i | ||||
\(496\) | −2.00863e85 | −0.111554 | ||||||||
\(497\) | − | 6.51730e85i | − | 0.339362i | ||||||
\(498\) | −8.91967e85 | − | 7.95478e85i | −0.435522 | − | 0.388409i | ||||
\(499\) | 1.90498e86 | 0.872316 | 0.436158 | − | 0.899870i | \(-0.356339\pi\) | ||||
0.436158 | + | 0.899870i | \(0.356339\pi\) | |||||||
\(500\) | 5.41831e85i | 0.232715i | ||||||||
\(501\) | 1.41741e86 | − | 1.58934e86i | 0.571068 | − | 0.640337i | ||||
\(502\) | 3.07516e86 | 1.16238 | ||||||||
\(503\) | − | 1.91828e86i | − | 0.680355i | −0.940361 | − | 0.340177i | \(-0.889513\pi\) | ||
0.940361 | − | 0.340177i | \(-0.110487\pi\) | |||||||
\(504\) | −2.73546e86 | + | 3.13858e85i | −0.910444 | + | 0.104461i | ||||
\(505\) | −9.21761e85 | −0.287935 | ||||||||
\(506\) | 2.74123e86i | 0.803766i | ||||||||
\(507\) | −6.02859e86 | − | 5.37644e86i | −1.65944 | − | 1.47993i | ||||
\(508\) | −3.34373e86 | −0.864156 | ||||||||
\(509\) | 1.71294e86i | 0.415692i | 0.978162 | + | 0.207846i | \(0.0666453\pi\) | ||||
−0.978162 | + | 0.207846i | \(0.933355\pi\) | |||||||
\(510\) | 2.18620e85 | − | 2.45138e85i | 0.0498247 | − | 0.0558683i | ||||
\(511\) | 3.05468e86 | 0.653878 | ||||||||
\(512\) | 2.18740e86i | 0.439834i | ||||||||
\(513\) | −3.80331e86 | + | 5.39512e86i | −0.718465 | + | 1.01917i | ||||
\(514\) | −3.20422e86 | −0.568725 | ||||||||
\(515\) | 1.82758e86i | 0.304821i | ||||||||
\(516\) | 2.44230e86 | + | 2.17810e86i | 0.382832 | + | 0.341419i | ||||
\(517\) | 5.13442e86 | 0.756474 | ||||||||
\(518\) | − | 3.34339e85i | − | 0.0463057i | ||||||
\(519\) | −7.23090e86 | + | 8.10799e86i | −0.941536 | + | 1.05574i | ||||
\(520\) | 3.61504e86 | 0.442595 | ||||||||
\(521\) | 2.13564e86i | 0.245879i | 0.992414 | + | 0.122939i | \(0.0392321\pi\) | ||||
−0.992414 | + | 0.122939i | \(0.960768\pi\) | |||||||
\(522\) | −8.63551e85 | − | 7.52636e86i | −0.0935043 | − | 0.814946i | ||||
\(523\) | 1.21201e86 | 0.123439 | 0.0617196 | − | 0.998094i | \(-0.480342\pi\) | ||||
0.0617196 | + | 0.998094i | \(0.480342\pi\) | |||||||
\(524\) | − | 4.53422e86i | − | 0.434411i | ||||||
\(525\) | 6.79346e86 | + | 6.05857e86i | 0.612341 | + | 0.546100i | ||||
\(526\) | −7.92367e86 | −0.672020 | ||||||||
\(527\) | 2.85345e86i | 0.227735i | ||||||||
\(528\) | 2.43369e86 | − | 2.72889e86i | 0.182801 | − | 0.204975i | ||||
\(529\) | 1.56894e86 | 0.110924 | ||||||||
\(530\) | 2.44587e86i | 0.162782i | ||||||||
\(531\) | 1.74364e87 | − | 2.00060e86i | 1.09253 | − | 0.125353i | ||||
\(532\) | 9.39860e86 | 0.554486 | ||||||||
\(533\) | − | 4.64324e87i | − | 2.57959i | ||||||
\(534\) | −1.95182e87 | − | 1.74068e87i | −1.02122 | − | 0.910749i | ||||
\(535\) | 7.16138e86 | 0.352920 | ||||||||
\(536\) | − | 6.98196e86i | − | 0.324119i | ||||||
\(537\) | −1.47703e87 | + | 1.65619e87i | −0.645969 | + | 0.724323i | ||||
\(538\) | 2.01119e87 | 0.828742 | ||||||||
\(539\) | 7.76538e86i | 0.301524i | ||||||||
\(540\) | 2.67169e86 | + | 1.88341e86i | 0.0977654 | + | 0.0689200i | ||||
\(541\) | −1.36669e87 | −0.471366 | −0.235683 | − | 0.971830i | \(-0.575733\pi\) | ||||
−0.235683 | + | 0.971830i | \(0.575733\pi\) | |||||||
\(542\) | 1.49786e87i | 0.486961i | ||||||||
\(543\) | 2.84288e87 | + | 2.53535e87i | 0.871294 | + | 0.777041i | ||||
\(544\) | 1.42886e87 | 0.412880 | ||||||||
\(545\) | 2.24741e86i | 0.0612341i | ||||||||
\(546\) | 2.81805e87 | − | 3.15987e87i | 0.724076 | − | 0.811905i | ||||
\(547\) | −6.25385e87 | −1.51549 | −0.757745 | − | 0.652550i | \(-0.773699\pi\) | ||||
−0.757745 | + | 0.652550i | \(0.773699\pi\) | |||||||
\(548\) | − | 1.70012e87i | − | 0.388600i | ||||||
\(549\) | −2.18890e86 | − | 1.90776e87i | −0.0471965 | − | 0.411346i | ||||
\(550\) | −3.96217e87 | −0.805985 | ||||||||
\(551\) | 7.63229e87i | 1.46489i | ||||||||
\(552\) | 4.10335e87 | + | 3.65946e87i | 0.743169 | + | 0.662776i | ||||
\(553\) | 4.08198e86 | 0.0697697 | ||||||||
\(554\) | 3.11838e87i | 0.503056i | ||||||||
\(555\) | −7.79738e85 | + | 8.74318e85i | −0.0118733 | + | 0.0133136i | ||||
\(556\) | −9.48204e86 | −0.136304 | ||||||||
\(557\) | − | 3.53118e87i | − | 0.479241i | −0.970867 | − | 0.239621i | \(-0.922977\pi\) | ||
0.970867 | − | 0.239621i | \(-0.0770230\pi\) | |||||||
\(558\) | 2.68427e87 | − | 3.07985e86i | 0.343979 | − | 0.0394670i | ||||
\(559\) | −1.48520e88 | −1.79724 | ||||||||
\(560\) | 3.98748e86i | 0.0455703i | ||||||||
\(561\) | −3.87664e87 | − | 3.45728e87i | −0.418450 | − | 0.373184i | ||||
\(562\) | −2.68360e87 | −0.273625 | ||||||||
\(563\) | 5.24759e87i | 0.505466i | 0.967536 | + | 0.252733i | \(0.0813294\pi\) | ||||
−0.967536 | + | 0.252733i | \(0.918671\pi\) | |||||||
\(564\) | 2.32234e87 | − | 2.60403e87i | 0.211346 | − | 0.236982i | ||||
\(565\) | −1.49416e87 | −0.128484 | ||||||||
\(566\) | 4.29374e87i | 0.348907i | ||||||||
\(567\) | 1.10058e88 | − | 2.55924e87i | 0.845211 | − | 0.196541i | ||||
\(568\) | 5.68987e87 | 0.413005 | ||||||||
\(569\) | 1.45481e88i | 0.998195i | 0.866546 | + | 0.499097i | \(0.166335\pi\) | ||||
−0.866546 | + | 0.499097i | \(0.833665\pi\) | |||||||
\(570\) | 2.33850e87 | + | 2.08553e87i | 0.151685 | + | 0.135276i | ||||
\(571\) | −2.03909e88 | −1.25049 | −0.625246 | − | 0.780428i | \(-0.715001\pi\) | ||||
−0.625246 | + | 0.780428i | \(0.715001\pi\) | |||||||
\(572\) | − | 1.93696e88i | − | 1.12317i | ||||||
\(573\) | −8.70981e87 | + | 9.76629e87i | −0.477596 | + | 0.535527i | ||||
\(574\) | 1.67874e88 | 0.870569 | ||||||||
\(575\) | − | 1.81764e88i | − | 0.891531i | ||||||
\(576\) | −2.09496e87 | − | 1.82588e88i | −0.0971976 | − | 0.847136i | ||||
\(577\) | 2.08779e88 | 0.916349 | 0.458175 | − | 0.888862i | \(-0.348503\pi\) | ||||
0.458175 | + | 0.888862i | \(0.348503\pi\) | |||||||
\(578\) | − | 1.32684e88i | − | 0.550971i | ||||||
\(579\) | 1.62218e88 | + | 1.44670e88i | 0.637359 | + | 0.568412i | ||||
\(580\) | 3.77954e87 | 0.140522 | ||||||||
\(581\) | − | 2.06113e88i | − | 0.725219i | ||||||
\(582\) | 1.35111e88 | − | 1.51500e88i | 0.449941 | − | 0.504517i | ||||
\(583\) | 3.86792e88 | 1.21922 | ||||||||
\(584\) | 2.66686e88i | 0.795772i | ||||||||
\(585\) | −1.47388e88 | + | 1.69108e87i | −0.416364 | + | 0.0477723i | ||||
\(586\) | 7.84851e87 | 0.209925 | ||||||||
\(587\) | 1.80571e88i | 0.457329i | 0.973505 | + | 0.228665i | \(0.0734359\pi\) | ||||
−0.973505 | + | 0.228665i | \(0.926564\pi\) | |||||||
\(588\) | 3.93838e87 | + | 3.51234e87i | 0.0944590 | + | 0.0842408i | ||||
\(589\) | −2.72205e88 | −0.618311 | ||||||||
\(590\) | − | 8.33113e87i | − | 0.179242i | ||||||
\(591\) | −2.88681e88 | + | 3.23697e88i | −0.588327 | + | 0.659689i | ||||
\(592\) | 8.90520e86 | 0.0171929 | ||||||||
\(593\) | − | 5.37381e88i | − | 0.982951i | −0.870891 | − | 0.491475i | \(-0.836458\pi\) | ||
0.870891 | − | 0.491475i | \(-0.163542\pi\) | |||||||
\(594\) | −2.83388e88 | + | 4.01996e88i | −0.491151 | + | 0.696715i | ||||
\(595\) | 5.66458e87 | 0.0930303 | ||||||||
\(596\) | 2.92000e88i | 0.454467i | ||||||||
\(597\) | −5.29743e88 | − | 4.72438e88i | −0.781424 | − | 0.696893i | ||||
\(598\) | −8.45447e88 | −1.18208 | ||||||||
\(599\) | 2.09457e88i | 0.277611i | 0.990320 | + | 0.138805i | \(0.0443263\pi\) | ||||
−0.990320 | + | 0.138805i | \(0.955674\pi\) | |||||||
\(600\) | −5.28938e88 | + | 5.93096e88i | −0.664606 | + | 0.745221i | ||||
\(601\) | 1.58629e89 | 1.88973 | 0.944863 | − | 0.327466i | \(-0.106195\pi\) | ||||
0.944863 | + | 0.327466i | \(0.106195\pi\) | |||||||
\(602\) | − | 5.36967e88i | − | 0.606541i | ||||||
\(603\) | 3.26609e87 | + | 2.84659e88i | 0.0349844 | + | 0.304910i | ||||
\(604\) | −2.16864e88 | −0.220295 | ||||||||
\(605\) | − | 1.18803e88i | − | 0.114461i | ||||||
\(606\) | −7.03411e88 | − | 6.27318e88i | −0.642813 | − | 0.573276i | ||||
\(607\) | −6.32225e88 | −0.548067 | −0.274033 | − | 0.961720i | \(-0.588358\pi\) | ||||
−0.274033 | + | 0.961720i | \(0.588358\pi\) | |||||||
\(608\) | 1.36306e89i | 1.12099i | ||||||||
\(609\) | 8.69585e88 | − | 9.75063e88i | 0.678513 | − | 0.760815i | ||||
\(610\) | −9.11525e87 | −0.0674860 | ||||||||
\(611\) | 1.58355e89i | 1.11253i | ||||||||
\(612\) | −3.50686e88 | + | 4.02366e87i | −0.233816 | + | 0.0268272i | ||||
\(613\) | 4.05229e88 | 0.256428 | 0.128214 | − | 0.991747i | \(-0.459076\pi\) | ||||
0.128214 | + | 0.991747i | \(0.459076\pi\) | |||||||
\(614\) | − | 6.73642e87i | − | 0.0404614i | ||||||
\(615\) | −4.39002e88 | − | 3.91512e88i | −0.250301 | − | 0.223225i | ||||
\(616\) | 2.06690e89 | 1.11876 | ||||||||
\(617\) | 1.39471e89i | 0.716737i | 0.933580 | + | 0.358368i | \(0.116667\pi\) | ||||
−0.933580 | + | 0.358368i | \(0.883333\pi\) | |||||||
\(618\) | −1.24379e89 | + | 1.39466e89i | −0.606897 | + | 0.680513i | ||||
\(619\) | 1.68530e89 | 0.780866 | 0.390433 | − | 0.920631i | \(-0.372325\pi\) | ||||
0.390433 | + | 0.920631i | \(0.372325\pi\) | |||||||
\(620\) | 1.34797e88i | 0.0593125i | ||||||||
\(621\) | −1.84415e89 | − | 1.30004e89i | −0.770663 | − | 0.543281i | ||||
\(622\) | 1.14459e89 | 0.454317 | ||||||||
\(623\) | − | 4.51021e89i | − | 1.70051i | ||||||
\(624\) | 8.41640e88 | + | 7.50594e88i | 0.301453 | + | 0.268843i | ||||
\(625\) | 2.46708e89 | 0.839505 | ||||||||
\(626\) | − | 3.63643e89i | − | 1.17570i | ||||||
\(627\) | 3.29807e89 | − | 3.69812e89i | 1.01321 | − | 1.13611i | ||||
\(628\) | −3.29094e89 | −0.960753 | ||||||||
\(629\) | − | 1.26506e88i | − | 0.0350988i | ||||||
\(630\) | −6.11402e87 | − | 5.32874e88i | −0.0161224 | − | 0.140516i | ||||
\(631\) | −9.38495e88 | −0.235230 | −0.117615 | − | 0.993059i | \(-0.537525\pi\) | ||||
−0.117615 | + | 0.993059i | \(0.537525\pi\) | |||||||
\(632\) | 3.56374e88i | 0.0849101i | ||||||||
\(633\) | 2.92046e89 | + | 2.60454e89i | 0.661505 | + | 0.589946i | ||||
\(634\) | −3.88005e89 | −0.835567 | ||||||||
\(635\) | − | 1.92248e89i | − | 0.393643i | ||||||
\(636\) | 1.74949e89 | − | 1.96170e89i | 0.340630 | − | 0.381948i | ||||
\(637\) | −2.39499e89 | −0.443447 | ||||||||
\(638\) | 5.68689e89i | 1.00141i | ||||||||
\(639\) | −2.31980e89 | + | 2.66166e88i | −0.388528 | + | 0.0445785i | ||||
\(640\) | 4.44820e88 | 0.0708639 | ||||||||
\(641\) | 8.60445e89i | 1.30397i | 0.758234 | + | 0.651983i | \(0.226063\pi\) | ||||
−0.758234 | + | 0.651983i | \(0.773937\pi\) | |||||||
\(642\) | 5.46497e89 | + | 4.87379e89i | 0.787892 | + | 0.702661i | ||||
\(643\) | −6.87434e88 | −0.0942931 | −0.0471465 | − | 0.998888i | \(-0.515013\pi\) | ||||
−0.0471465 | + | 0.998888i | \(0.515013\pi\) | |||||||
\(644\) | 3.21261e89i | 0.419286i | ||||||||
\(645\) | −1.25230e89 | + | 1.40420e89i | −0.155524 | + | 0.174389i | ||||
\(646\) | −3.38361e89 | −0.399889 | ||||||||
\(647\) | − | 4.76001e89i | − | 0.535391i | −0.963504 | − | 0.267696i | \(-0.913738\pi\) | ||
0.963504 | − | 0.267696i | \(-0.0862622\pi\) | |||||||
\(648\) | 2.23432e89 | + | 9.60855e89i | 0.239191 | + | 1.02863i | ||||
\(649\) | −1.31749e90 | −1.34251 | ||||||||
\(650\) | − | 1.22201e90i | − | 1.18535i | ||||||
\(651\) | 3.47755e89 | + | 3.10137e89i | 0.321131 | + | 0.286392i | ||||
\(652\) | −4.26150e89 | −0.374662 | ||||||||
\(653\) | − | 3.25186e89i | − | 0.272214i | −0.990694 | − | 0.136107i | \(-0.956541\pi\) | ||
0.990694 | − | 0.136107i | \(-0.0434590\pi\) | |||||||
\(654\) | −1.52951e89 | + | 1.71503e89i | −0.121917 | + | 0.136705i | ||||
\(655\) | 2.60695e89 | 0.197884 | ||||||||
\(656\) | 4.47137e89i | 0.323234i | ||||||||
\(657\) | −1.24753e89 | − | 1.08730e90i | −0.0858932 | − | 0.748611i | ||||
\(658\) | −5.72525e89 | −0.375462 | ||||||||
\(659\) | 9.20777e89i | 0.575203i | 0.957750 | + | 0.287601i | \(0.0928578\pi\) | ||||
−0.957750 | + | 0.287601i | \(0.907142\pi\) | |||||||
\(660\) | −1.83133e89 | − | 1.63322e89i | −0.108983 | − | 0.0971939i | ||||
\(661\) | −4.70156e89 | −0.266560 | −0.133280 | − | 0.991078i | \(-0.542551\pi\) | ||||
−0.133280 | + | 0.991078i | \(0.542551\pi\) | |||||||
\(662\) | − | 1.73543e90i | − | 0.937458i | ||||||
\(663\) | 1.06629e90 | − | 1.19563e90i | 0.548835 | − | 0.615407i | ||||
\(664\) | 1.79945e90 | 0.882595 | ||||||||
\(665\) | 5.40373e89i | 0.252581i | ||||||||
\(666\) | −1.19006e89 | + | 1.36544e88i | −0.0530144 | + | 0.00608270i | ||||
\(667\) | −2.60885e90 | −1.10770 | ||||||||
\(668\) | 1.08635e90i | 0.439666i | ||||||||
\(669\) | 2.18777e90 | + | 1.95110e90i | 0.844044 | + | 0.752739i | ||||
\(670\) | 1.36010e89 | 0.0500239 | ||||||||
\(671\) | 1.44149e90i | 0.505466i | ||||||||
\(672\) | 1.55300e90 | − | 1.74138e90i | 0.519225 | − | 0.582206i | ||||
\(673\) | 9.98599e89 | 0.318353 | 0.159177 | − | 0.987250i | \(-0.449116\pi\) | ||||
0.159177 | + | 0.987250i | \(0.449116\pi\) | |||||||
\(674\) | − | 3.59257e90i | − | 1.09216i | ||||||
\(675\) | 1.87907e90 | − | 2.66553e90i | 0.544781 | − | 0.772791i | ||||
\(676\) | 4.12068e90 | 1.13940 | ||||||||
\(677\) | − | 2.68601e89i | − | 0.0708386i | −0.999373 | − | 0.0354193i | \(-0.988723\pi\) | ||
0.999373 | − | 0.0354193i | \(-0.0112767\pi\) | |||||||
\(678\) | −1.14022e90 | − | 1.01688e90i | −0.286839 | − | 0.255810i | ||||
\(679\) | 3.50081e90 | 0.840109 | ||||||||
\(680\) | 4.94541e89i | 0.113218i | ||||||||
\(681\) | −4.16827e90 | + | 4.67387e90i | −0.910434 | + | 1.02087i | ||||
\(682\) | −2.02823e90 | −0.422684 | ||||||||
\(683\) | 3.11683e90i | 0.619799i | 0.950769 | + | 0.309900i | \(0.100295\pi\) | ||||
−0.950769 | + | 0.309900i | \(0.899705\pi\) | |||||||
\(684\) | −3.83838e89 | − | 3.34538e90i | −0.0728371 | − | 0.634819i | ||||
\(685\) | 9.77488e89 | 0.177016 | ||||||||
\(686\) | − | 4.37170e90i | − | 0.755578i | ||||||
\(687\) | −4.81845e90 | − | 4.29721e90i | −0.794861 | − | 0.708876i | ||||
\(688\) | 1.43022e90 | 0.225203 | ||||||||
\(689\) | 1.19294e91i | 1.79309i | ||||||||
\(690\) | −7.12871e89 | + | 7.99341e89i | −0.102292 | + | 0.114699i | ||||
\(691\) | −9.62439e90 | −1.31849 | −0.659243 | − | 0.751930i | \(-0.729123\pi\) | ||||
−0.659243 | + | 0.751930i | \(0.729123\pi\) | |||||||
\(692\) | − | 5.54201e90i | − | 0.724890i | ||||||
\(693\) | −8.42691e90 | + | 9.66876e89i | −1.05246 | + | 0.120756i | ||||
\(694\) | 4.88097e90 | 0.582108 | ||||||||
\(695\) | − | 5.45171e89i | − | 0.0620896i | ||||||
\(696\) | 8.51270e90 | + | 7.59183e90i | 0.925916 | + | 0.825754i | ||||
\(697\) | 6.35199e90 | 0.659874 | ||||||||
\(698\) | 7.39557e90i | 0.733834i | ||||||||
\(699\) | −1.02509e91 | + | 1.14943e91i | −0.971613 | + | 1.08947i | ||||
\(700\) | −4.64349e90 | −0.420443 | ||||||||
\(701\) | − | 1.12608e91i | − | 0.974074i | −0.873381 | − | 0.487037i | \(-0.838078\pi\) | ||
0.873381 | − | 0.487037i | \(-0.161922\pi\) | |||||||
\(702\) | −1.23983e91 | − | 8.74021e90i | −1.02465 | − | 0.722328i | ||||
\(703\) | 1.20681e90 | 0.0952947 | ||||||||
\(704\) | 1.37963e91i | 1.04097i | ||||||||
\(705\) | 1.49719e90 | + | 1.33523e90i | 0.107951 | + | 0.0962731i | ||||
\(706\) | −2.54262e90 | −0.175199 | ||||||||
\(707\) | − | 1.62542e91i | − | 1.07040i | ||||||
\(708\) | −5.95911e90 | + | 6.68194e90i | −0.375074 | + | 0.420570i | ||||
\(709\) | 1.16613e91 | 0.701562 | 0.350781 | − | 0.936458i | \(-0.385916\pi\) | ||||
0.350781 | + | 0.936458i | \(0.385916\pi\) | |||||||
\(710\) | 1.10840e90i | 0.0637425i | ||||||||
\(711\) | −1.66708e89 | − | 1.45296e90i | −0.00916493 | − | 0.0798779i | ||||
\(712\) | 3.93759e91 | 2.06953 | ||||||||
\(713\) | − | 9.30445e90i | − | 0.467548i | ||||||
\(714\) | 4.32273e90 | + | 3.85512e90i | 0.207690 | + | 0.185223i | ||||
\(715\) | 1.11366e91 | 0.511632 | ||||||||
\(716\) | − | 1.13204e91i | − | 0.497332i | ||||||
\(717\) | 1.16039e91 | − | 1.30114e91i | 0.487517 | − | 0.546652i | ||||
\(718\) | −1.69796e91 | −0.682251 | ||||||||
\(719\) | 1.45383e91i | 0.558714i | 0.960187 | + | 0.279357i | \(0.0901212\pi\) | ||||
−0.960187 | + | 0.279357i | \(0.909879\pi\) | |||||||
\(720\) | 1.41932e90 | − | 1.62848e89i | 0.0521724 | − | 0.00598610i | ||||
\(721\) | −3.22273e91 | −1.13317 | ||||||||
\(722\) | − | 1.15190e91i | − | 0.387459i | ||||||
\(723\) | 1.10482e91 | + | 9.85308e90i | 0.355523 | + | 0.317064i | ||||
\(724\) | −1.94318e91 | −0.598245 | ||||||||
\(725\) | − | 3.77083e91i | − | 1.11076i | ||||||
\(726\) | 8.08535e90 | − | 9.06608e90i | 0.227891 | − | 0.255533i | ||||
\(727\) | 6.46642e91 | 1.74407 | 0.872033 | − | 0.489447i | \(-0.162801\pi\) | ||||
0.872033 | + | 0.489447i | \(0.162801\pi\) | |||||||
\(728\) | 6.37471e91i | 1.64534i | ||||||||
\(729\) | −1.36043e91 | − | 3.81295e91i | −0.336042 | − | 0.941847i | ||||
\(730\) | −5.19510e90 | −0.122818 | ||||||||
\(731\) | − | 2.03176e91i | − | 0.459745i | ||||||
\(732\) | 7.31084e90 | + | 6.51998e90i | 0.158348 | + | 0.141219i | ||||
\(733\) | −2.46440e91 | −0.510956 | −0.255478 | − | 0.966815i | \(-0.582233\pi\) | ||||
−0.255478 | + | 0.966815i | \(0.582233\pi\) | |||||||
\(734\) | − | 2.03850e90i | − | 0.0404610i | ||||||
\(735\) | −2.01943e90 | + | 2.26438e90i | −0.0383736 | + | 0.0430283i | ||||
\(736\) | −4.65919e91 | −0.847657 | ||||||||
\(737\) | − | 2.15087e91i | − | 0.374676i | ||||||
\(738\) | −6.85597e90 | − | 5.97539e91i | −0.114358 | − | 0.996696i | ||||
\(739\) | −2.52022e91 | −0.402548 | −0.201274 | − | 0.979535i | \(-0.564508\pi\) | ||||
−0.201274 | + | 0.979535i | \(0.564508\pi\) | |||||||
\(740\) | − | 5.97618e89i | − | 0.00914131i | ||||||
\(741\) | 1.14057e92 | + | 1.01719e92i | 1.67086 | + | 1.49011i | ||||
\(742\) | −4.31301e91 | −0.605140 | ||||||||
\(743\) | 9.30994e91i | 1.25114i | 0.780170 | + | 0.625568i | \(0.215133\pi\) | ||||
−0.780170 | + | 0.625568i | \(0.784867\pi\) | |||||||
\(744\) | −2.70762e91 | + | 3.03605e91i | −0.348541 | + | 0.390818i | ||||
\(745\) | −1.67886e91 | −0.207020 | ||||||||
\(746\) | 4.10067e91i | 0.484409i | ||||||||
\(747\) | −7.33648e91 | + | 8.41764e90i | −0.830288 | + | 0.0952645i | ||||
\(748\) | 2.64977e91 | 0.287315 | ||||||||
\(749\) | 1.26283e92i | 1.31198i | ||||||||
\(750\) | −2.37731e91 | − | 2.12014e91i | −0.236660 | − | 0.211059i | ||||
\(751\) | 3.91006e91 | 0.372997 | 0.186498 | − | 0.982455i | \(-0.440286\pi\) | ||||
0.186498 | + | 0.982455i | \(0.440286\pi\) | |||||||
\(752\) | − | 1.52494e91i | − | 0.139406i | ||||||
\(753\) | 1.26467e92 | − | 1.41807e92i | 1.10799 | − | 1.24239i | ||||
\(754\) | −1.75394e92 | −1.47276 | ||||||||
\(755\) | − | 1.24686e91i | − | 0.100350i | ||||||
\(756\) | −3.32118e91 | + | 4.71121e91i | −0.256210 | + | 0.363442i | ||||
\(757\) | −1.67304e92 | −1.23720 | −0.618598 | − | 0.785708i | \(-0.712299\pi\) | ||||
−0.618598 | + | 0.785708i | \(0.712299\pi\) | |||||||
\(758\) | 6.61161e91i | 0.468697i | ||||||||
\(759\) | 1.26408e92 | + | 1.12734e92i | 0.859091 | + | 0.766158i | ||||
\(760\) | −4.71768e91 | −0.307393 | ||||||||
\(761\) | − | 2.82054e92i | − | 1.76207i | −0.473053 | − | 0.881034i | \(-0.656848\pi\) | ||
0.473053 | − | 0.881034i | \(-0.343152\pi\) | |||||||
\(762\) | 1.30837e92 | − | 1.46708e92i | 0.783741 | − | 0.878807i | ||||
\(763\) | −3.96305e91 | −0.227638 | ||||||||
\(764\) | − | 6.67549e91i | − | 0.367702i | ||||||
\(765\) | −2.31341e90 | − | 2.01628e91i | −0.0122204 | − | 0.106508i | ||||
\(766\) | 1.60063e92 | 0.810903 | ||||||||
\(767\) | − | 4.06339e92i | − | 1.97441i | ||||||
\(768\) | 1.70490e92 | + | 1.52047e92i | 0.794586 | + | 0.708631i | ||||
\(769\) | 2.99778e92 | 1.34016 | 0.670080 | − | 0.742289i | \(-0.266260\pi\) | ||||
0.670080 | + | 0.742289i | \(0.266260\pi\) | |||||||
\(770\) | 4.02637e91i | 0.172668i | ||||||||
\(771\) | −1.31775e92 | + | 1.47758e92i | −0.542115 | + | 0.607872i | ||||
\(772\) | −1.10880e92 | −0.437621 | ||||||||
\(773\) | − | 1.76960e92i | − | 0.670086i | −0.942203 | − | 0.335043i | \(-0.891249\pi\) | ||
0.942203 | − | 0.335043i | \(-0.108751\pi\) | |||||||
\(774\) | −1.91131e92 | + | 2.19297e91i | −0.694415 | + | 0.0796750i | ||||
\(775\) | 1.34486e92 | 0.468839 | ||||||||
\(776\) | 3.05635e92i | 1.02242i | ||||||||
\(777\) | −1.54176e91 | − | 1.37498e91i | −0.0494931 | − | 0.0441391i | ||||
\(778\) | 2.76330e92 | 0.851296 | ||||||||
\(779\) | 6.05949e92i | 1.79159i | ||||||||
\(780\) | 5.03715e91 | − | 5.64815e91i | 0.142941 | − | 0.160280i | ||||
\(781\) | 1.75283e92 | 0.477427 | ||||||||
\(782\) | − | 1.15658e92i | − | 0.302384i | ||||||
\(783\) | −3.82582e92 | − | 2.69702e92i | −0.960171 | − | 0.676875i | ||||
\(784\) | 2.30634e91 | 0.0555660 | ||||||||
\(785\) | − | 1.89213e92i | − | 0.437646i | ||||||
\(786\) | 1.98941e92 | + | 1.77420e92i | 0.441776 | + | 0.393987i | ||||
\(787\) | −1.62859e92 | −0.347233 | −0.173616 | − | 0.984813i | \(-0.555545\pi\) | ||||
−0.173616 | + | 0.984813i | \(0.555545\pi\) | |||||||
\(788\) | − | 2.21255e92i | − | 0.452954i | ||||||
\(789\) | −3.25863e92 | + | 3.65390e92i | −0.640577 | + | 0.718277i | ||||
\(790\) | −6.94224e90 | −0.0131049 | ||||||||
\(791\) | − | 2.63479e92i | − | 0.477637i | ||||||
\(792\) | −8.44122e91 | − | 7.35703e92i | −0.146960 | − | 1.28085i | ||||
\(793\) | −4.44583e92 | −0.743380 | ||||||||
\(794\) | 3.26697e92i | 0.524673i | ||||||||
\(795\) | 1.12788e92 | + | 1.00587e92i | 0.173986 | + | 0.155165i | ||||
\(796\) | 3.62092e92 | 0.536539 | ||||||||
\(797\) | 8.69252e92i | 1.23731i | 0.785662 | + | 0.618657i | \(0.212323\pi\) | ||||
−0.785662 | + | 0.618657i | \(0.787677\pi\) | |||||||
\(798\) | −3.67760e92 | + | 4.12368e92i | −0.502888 | + | 0.563887i | ||||
\(799\) | −2.16631e92 | −0.284593 | ||||||||
\(800\) | − | 6.73437e92i | − | 0.849997i | ||||||
\(801\) | −1.60538e93 | + | 1.84197e92i | −1.94688 | + | 0.223378i | ||||
\(802\) | −1.25439e92 | −0.146168 | ||||||||
\(803\) | 8.21557e92i | 0.919899i | ||||||||
\(804\) | −1.09086e92 | − | 9.72857e91i | −0.117375 | − | 0.104678i | ||||
\(805\) | −1.84709e92 | −0.190994 | ||||||||
\(806\) | − | 6.25542e92i | − | 0.621635i | ||||||
\(807\) | 8.27107e92 | − | 9.27433e92i | 0.789966 | − | 0.885787i | ||||
\(808\) | 1.41906e93 | 1.30268 | ||||||||
\(809\) | 2.02034e93i | 1.78267i | 0.453345 | + | 0.891335i | \(0.350230\pi\) | ||||
−0.453345 | + | 0.891335i | \(0.649770\pi\) | |||||||
\(810\) | −1.87177e92 | + | 4.35251e91i | −0.158756 | + | 0.0369163i | ||||
\(811\) | 2.79945e92 | 0.228247 | 0.114124 | − | 0.993467i | \(-0.463594\pi\) | ||||
0.114124 | + | 0.993467i | \(0.463594\pi\) | |||||||
\(812\) | 6.66479e92i | 0.522388i | ||||||||
\(813\) | 6.90719e92 | + | 6.16000e92i | 0.520480 | + | 0.464177i | ||||
\(814\) | 8.99206e91 | 0.0651446 | ||||||||
\(815\) | − | 2.45016e92i | − | 0.170667i | ||||||
\(816\) | −1.02682e92 | + | 1.15137e92i | −0.0687716 | + | 0.0771134i | ||||
\(817\) | 1.93821e93 | 1.24823 | ||||||||
\(818\) | − | 2.06487e93i | − | 1.27875i | ||||||
\(819\) | −2.98202e92 | − | 2.59901e93i | −0.177593 | − | 1.54783i | ||||
\(820\) | 3.00068e92 | 0.171861 | ||||||||
\(821\) | − | 2.38579e93i | − | 1.31417i | −0.753818 | − | 0.657084i | \(-0.771790\pi\) | ||
0.753818 | − | 0.657084i | \(-0.228210\pi\) | |||||||
\(822\) | 7.45937e92 | + | 6.65245e92i | 0.395188 | + | 0.352438i | ||||
\(823\) | −1.62406e93 | −0.827573 | −0.413787 | − | 0.910374i | \(-0.635794\pi\) | ||||
−0.413787 | + | 0.910374i | \(0.635794\pi\) | |||||||
\(824\) | − | 2.81358e93i | − | 1.37907i | ||||||
\(825\) | −1.62945e93 | + | 1.82710e93i | −0.768273 | + | 0.861463i | ||||
\(826\) | 1.46910e93 | 0.666330 | ||||||||
\(827\) | 2.04188e93i | 0.890949i | 0.895295 | + | 0.445475i | \(0.146965\pi\) | ||||
−0.895295 | + | 0.445475i | \(0.853035\pi\) | |||||||
\(828\) | 1.14351e93 | − | 1.31203e92i | 0.480031 | − | 0.0550772i | ||||
\(829\) | 1.87901e93 | 0.758899 | 0.379450 | − | 0.925212i | \(-0.376113\pi\) | ||||
0.379450 | + | 0.925212i | \(0.376113\pi\) | |||||||
\(830\) | 3.50537e92i | 0.136218i | ||||||||
\(831\) | 1.43800e93 | + | 1.28244e93i | 0.537683 | + | 0.479518i | ||||
\(832\) | −4.25503e93 | −1.53093 | ||||||||
\(833\) | − | 3.27636e92i | − | 0.113436i | ||||||
\(834\) | 3.71025e92 | − | 4.16029e92i | 0.123620 | − | 0.138615i | ||||
\(835\) | −6.24598e92 | −0.200278 | ||||||||
\(836\) | 2.52776e93i | 0.780071i | ||||||||
\(837\) | 9.61892e92 | − | 1.36448e93i | 0.285701 | − | 0.405276i | ||||
\(838\) | −2.56409e93 | −0.733036 | ||||||||
\(839\) | − | 5.22071e93i | − | 1.43664i | −0.695715 | − | 0.718318i | \(-0.744912\pi\) | ||
0.695715 | − | 0.718318i | \(-0.255088\pi\) | |||||||
\(840\) | 6.02707e92 | + | 5.37509e92i | 0.159650 | + | 0.142380i | ||||
\(841\) | −1.49058e93 | −0.380087 | ||||||||
\(842\) | 4.90090e93i | 1.20306i | ||||||||
\(843\) | −1.10364e93 | + | 1.23751e93i | −0.260822 | + | 0.292460i | ||||
\(844\) | −1.99621e93 | −0.454200 | ||||||||
\(845\) | 2.36919e93i | 0.519022i | ||||||||
\(846\) | 2.33819e92 | + | 2.03787e93i | 0.0493206 | + | 0.429859i | ||||
\(847\) | 2.09496e93 | 0.425507 | ||||||||
\(848\) | − | 1.14878e93i | − | 0.224683i | ||||||
\(849\) | 1.98000e93 | + | 1.76581e93i | 0.372924 | + | 0.332582i | ||||
\(850\) | 1.67171e93 | 0.303219 | ||||||||
\(851\) | 4.12509e92i | 0.0720589i | ||||||||
\(852\) | 7.92819e92 | − | 8.88986e92i | 0.133385 | − | 0.149564i | ||||
\(853\) | −1.01173e94 | −1.63945 | −0.819723 | − | 0.572761i | \(-0.805872\pi\) | ||||
−0.819723 | + | 0.572761i | \(0.805872\pi\) | |||||||
\(854\) | − | 1.60737e93i | − | 0.250879i | ||||||
\(855\) | 1.92343e93 | − | 2.20688e92i | 0.289175 | − | 0.0331790i | ||||
\(856\) | −1.10250e94 | −1.59668 | ||||||||
\(857\) | 4.85540e93i | 0.677390i | 0.940896 | + | 0.338695i | \(0.109985\pi\) | ||||
−0.940896 | + | 0.338695i | \(0.890015\pi\) | |||||||
\(858\) | 8.49849e93 | + | 7.57916e93i | 1.14222 | + | 1.01866i | ||||
\(859\) | 5.54073e92 | 0.0717440 | 0.0358720 | − | 0.999356i | \(-0.488579\pi\) | ||||
0.0358720 | + | 0.999356i | \(0.488579\pi\) | |||||||
\(860\) | − | 9.59807e92i | − | 0.119738i | ||||||
\(861\) | 6.90388e93 | − | 7.74130e93i | 0.829836 | − | 0.930493i | ||||
\(862\) | 3.65538e93 | 0.423351 | ||||||||
\(863\) | − | 3.02266e92i | − | 0.0337321i | −0.999858 | − | 0.0168661i | \(-0.994631\pi\) | ||
0.999858 | − | 0.0168661i | \(-0.00536889\pi\) | |||||||
\(864\) | −6.83259e93 | − | 4.81665e93i | −0.734760 | − | 0.517971i | ||||
\(865\) | 3.18638e93 | 0.330204 | ||||||||
\(866\) | 3.52054e93i | 0.351590i | ||||||||
\(867\) | −6.11857e93 | − | 5.45668e93i | −0.588896 | − | 0.525191i | ||||
\(868\) | −2.37699e93 | −0.220494 | ||||||||
\(869\) | 1.09785e93i | 0.0981546i | ||||||||
\(870\) | −1.47890e93 | + | 1.65829e93i | −0.127445 | + | 0.142904i | ||||
\(871\) | 6.63369e93 | 0.551029 | ||||||||
\(872\) | − | 3.45990e93i | − | 0.277036i | ||||||
\(873\) | −1.42973e93 | − | 1.24609e94i | −0.110356 | − | 0.961822i | ||||
\(874\) | 1.10332e94 | 0.820986 | ||||||||
\(875\) | − | 5.49342e93i | − | 0.394080i | ||||||
\(876\) | 4.16670e93 | + | 3.71597e93i | 0.288178 | + | 0.257004i | ||||
\(877\) | 1.19698e94 | 0.798177 | 0.399088 | − | 0.916912i | \(-0.369327\pi\) | ||||
0.399088 | + | 0.916912i | \(0.369327\pi\) | |||||||
\(878\) | − | 4.15594e93i | − | 0.267205i | ||||||
\(879\) | 3.22772e93 | − | 3.61924e93i | 0.200102 | − | 0.224374i | ||||
\(880\) | −1.07243e93 | −0.0641099 | ||||||||
\(881\) | − | 1.68649e94i | − | 0.972201i | −0.873903 | − | 0.486100i | \(-0.838419\pi\) | ||
0.873903 | − | 0.486100i | \(-0.161581\pi\) | |||||||
\(882\) | −3.08211e93 | + | 3.53632e92i | −0.171338 | + | 0.0196588i | ||||
\(883\) | 7.23402e93 | 0.387826 | 0.193913 | − | 0.981019i | \(-0.437882\pi\) | ||||
0.193913 | + | 0.981019i | \(0.437882\pi\) | |||||||
\(884\) | 8.17239e93i | 0.422549i | ||||||||
\(885\) | −3.84179e93 | − | 3.42620e93i | −0.191579 | − | 0.170855i | ||||
\(886\) | −1.98051e94 | −0.952570 | ||||||||
\(887\) | 2.28568e94i | 1.06037i | 0.847881 | + | 0.530187i | \(0.177878\pi\) | ||||
−0.847881 | + | 0.530187i | \(0.822122\pi\) | |||||||
\(888\) | 1.20041e93 | − | 1.34602e93i | 0.0537175 | − | 0.0602333i | ||||
\(889\) | 3.39007e94 | 1.46337 | ||||||||
\(890\) | 7.67052e93i | 0.319407i | ||||||||
\(891\) | 6.88309e93 | + | 2.96003e94i | 0.276501 | + | 1.18907i | ||||
\(892\) | −1.49539e94 | −0.579534 | ||||||||
\(893\) | − | 2.06655e94i | − | 0.772681i | ||||||
\(894\) | −1.28116e94 | − | 1.14257e94i | −0.462172 | − | 0.412176i | ||||
\(895\) | 6.50870e93 | 0.226546 | ||||||||
\(896\) | 7.84389e93i | 0.263436i | ||||||||
\(897\) | −3.47693e94 | + | 3.89867e94i | −1.12678 | + | 1.26345i | ||||
\(898\) | −6.44942e93 | −0.201687 | ||||||||
\(899\) | − | 1.93028e94i | − | 0.582518i | ||||||
\(900\) | 1.89640e93 | + | 1.65283e94i | 0.0552293 | + | 0.481356i | ||||
\(901\) | −1.63195e94 | −0.458683 | ||||||||
\(902\) | 4.51498e94i | 1.22475i | ||||||||
\(903\) | −2.47615e94 | − | 2.20829e94i | −0.648290 | − | 0.578161i | ||||
\(904\) | 2.30028e94 | 0.581287 | ||||||||
\(905\) | − | 1.11723e94i | − | 0.272514i | ||||||
\(906\) | 8.48570e93 | − | 9.51499e93i | 0.199795 | − | 0.224030i | ||||
\(907\) | −4.18507e94 | −0.951194 | −0.475597 | − | 0.879663i | \(-0.657768\pi\) | ||||
−0.475597 | + | 0.879663i | \(0.657768\pi\) | |||||||
\(908\) | − | 3.19470e94i | − | 0.700944i | ||||||
\(909\) | −5.78559e94 | + | 6.63820e93i | −1.22547 | + | 0.140607i | ||||
\(910\) | −1.24181e94 | −0.253939 | ||||||||
\(911\) | 1.46500e94i | 0.289233i | 0.989488 | + | 0.144617i | \(0.0461949\pi\) | ||||
−0.989488 | + | 0.144617i | \(0.953805\pi\) | |||||||
\(912\) | −1.09835e94 | − | 9.79536e93i | −0.209366 | − | 0.186718i | ||||
\(913\) | 5.54342e94 | 1.02026 | ||||||||
\(914\) | − | 5.64224e94i | − | 1.00271i | ||||||
\(915\) | −3.74867e93 | + | 4.20338e93i | −0.0643284 | + | 0.0721312i | ||||
\(916\) | 3.29352e94 | 0.545765 | ||||||||
\(917\) | 4.59706e94i | 0.735634i | ||||||||
\(918\) | 1.19567e94 | − | 1.69610e94i | 0.184776 | − | 0.262111i | ||||
\(919\) | 7.70259e94 | 1.14958 | 0.574791 | − | 0.818300i | \(-0.305083\pi\) | ||||
0.574791 | + | 0.818300i | \(0.305083\pi\) | |||||||
\(920\) | − | 1.61259e94i | − | 0.232441i | ||||||
\(921\) | −3.10641e93 | − | 2.77037e93i | −0.0432465 | − | 0.0385683i | ||||
\(922\) | 5.81638e94 | 0.782102 | ||||||||
\(923\) | 5.40605e94i | 0.702144i | ||||||||
\(924\) | 2.88000e94 | − | 3.22933e94i | 0.361318 | − | 0.405144i | ||||
\(925\) | −5.96240e93 | −0.0722579 | ||||||||
\(926\) | 1.73886e94i | 0.203570i | ||||||||
\(927\) | 1.31616e94 | + | 1.14711e95i | 0.148853 | + | 1.29734i | ||||
\(928\) | −9.66583e94 | −1.05610 | ||||||||
\(929\) | − | 4.52332e94i | − | 0.477480i | −0.971084 | − | 0.238740i | \(-0.923266\pi\) | ||
0.971084 | − | 0.238740i | \(-0.0767343\pi\) | |||||||
\(930\) | −5.91428e93 | − | 5.27450e93i | −0.0603181 | − | 0.0537931i | ||||
\(931\) | 3.12549e94 | 0.307984 | ||||||||
\(932\) | − | 7.85665e94i | − | 0.748046i | ||||||
\(933\) | 4.70717e94 | − | 5.27814e94i | 0.433060 | − | 0.485589i | ||||
\(934\) | −4.20075e94 | −0.373445 | ||||||||
\(935\) | 1.52349e94i | 0.130878i | ||||||||
\(936\) | 2.26905e95 | − | 2.60343e94i | 1.88372 | − | 0.216132i | ||||
\(937\) | 4.38230e94 | 0.351589 | 0.175795 | − | 0.984427i | \(-0.443751\pi\) | ||||
0.175795 | + | 0.984427i | \(0.443751\pi\) | |||||||
\(938\) | 2.39838e94i | 0.185963i | ||||||||
\(939\) | −1.67689e95 | − | 1.49549e95i | −1.25663 | − | 1.12069i | ||||
\(940\) | −1.02337e94 | −0.0741208 | ||||||||
\(941\) | − | 3.08249e94i | − | 0.215791i | −0.994162 | − | 0.107896i | \(-0.965589\pi\) | ||
0.994162 | − | 0.107896i | \(-0.0344112\pi\) | |||||||
\(942\) | 1.28772e95 | − | 1.44392e95i | 0.871350 | − | 0.977042i | ||||
\(943\) | −2.07124e95 | −1.35474 | ||||||||
\(944\) | 3.91298e94i | 0.247402i | ||||||||
\(945\) | −2.70872e94 | − | 1.90952e94i | −0.165556 | − | 0.116709i | ||||
\(946\) | 1.44417e95 | 0.853303 | ||||||||
\(947\) | 3.76716e93i | 0.0215186i | 0.999942 | + | 0.0107593i | \(0.00342486\pi\) | ||||
−0.999942 | + | 0.0107593i | \(0.996575\pi\) | |||||||
\(948\) | 5.56799e93 | + | 4.96567e93i | 0.0307490 | + | 0.0274227i | ||||
\(949\) | −2.53383e95 | −1.35288 | ||||||||
\(950\) | 1.59474e95i | 0.823253i | ||||||||
\(951\) | −1.59568e95 | + | 1.78924e95i | −0.796472 | + | 0.893082i | ||||
\(952\) | −8.72066e94 | −0.420889 | ||||||||
\(953\) | − | 7.71246e94i | − | 0.359932i | −0.983673 | − | 0.179966i | \(-0.942401\pi\) | ||
0.983673 | − | 0.179966i | \(-0.0575987\pi\) | |||||||
\(954\) | 1.76143e94 | + | 1.53519e95i | 0.0794909 | + | 0.692811i | ||||
\(955\) | 3.83808e94 | 0.167497 | ||||||||
\(956\) | 8.89360e94i | 0.375340i | ||||||||
\(957\) | 2.62244e95 | + | 2.33875e95i | 1.07034 | + | 0.954557i | ||||
\(958\) | −2.59299e95 | −1.02354 | ||||||||
\(959\) | 1.72369e95i | 0.658057i | ||||||||
\(960\) | −3.58779e94 | + | 4.02298e94i | −0.132479 | + | 0.148549i | ||||
\(961\) | −2.11151e95 | −0.754126 | ||||||||
\(962\) | 2.77332e94i | 0.0958070i | ||||||||
\(963\) | 4.49497e95 | − | 5.15738e94i | 1.50205 | − | 0.172341i | ||||
\(964\) | −7.55174e94 | −0.244108 | ||||||||
\(965\) | − | 6.37504e94i | − | 0.199347i | ||||||
\(966\) | −1.40955e95 | − | 1.25707e95i | −0.426394 | − | 0.380269i | ||||
\(967\) | 1.08948e95 | 0.318840 | 0.159420 | − | 0.987211i | \(-0.449038\pi\) | ||||
0.159420 | + | 0.987211i | \(0.449038\pi\) | |||||||
\(968\) | 1.82899e95i | 0.517844i | ||||||||
\(969\) | −1.39152e95 | + | 1.56031e95i | −0.381179 | + | 0.427415i | ||||
\(970\) | −5.95383e94 | −0.157798 | ||||||||
\(971\) | − | 2.76333e95i | − | 0.708626i | −0.935127 | − | 0.354313i | \(-0.884715\pi\) | ||
0.935127 | − | 0.354313i | \(-0.115285\pi\) | |||||||
\(972\) | 1.81257e95 | + | 9.89752e94i | 0.449753 | + | 0.245587i | ||||
\(973\) | 9.61347e94 | 0.230818 | ||||||||
\(974\) | − | 3.98402e95i | − | 0.925624i | ||||||
\(975\) | −5.63512e95 | − | 5.02554e95i | −1.26694 | − | 1.12989i | ||||
\(976\) | 4.28127e94 | 0.0931490 | ||||||||
\(977\) | − | 8.77787e94i | − | 0.184826i | −0.995721 | − | 0.0924130i | \(-0.970542\pi\) | ||
0.995721 | − | 0.0924130i | \(-0.0294580\pi\) | |||||||
\(978\) | 1.66749e95 | − | 1.86975e95i | 0.339798 | − | 0.381014i | ||||
\(979\) | 1.21302e96 | 2.39234 | ||||||||
\(980\) | − | 1.54776e94i | − | 0.0295439i | ||||||
\(981\) | 1.61851e94 | + | 1.41062e95i | 0.0299024 | + | 0.260617i | ||||
\(982\) | −7.30761e95 | −1.30680 | ||||||||
\(983\) | − | 6.99416e95i | − | 1.21066i | −0.795974 | − | 0.605331i | \(-0.793041\pi\) | ||
0.795974 | − | 0.605331i | \(-0.206959\pi\) | |||||||
\(984\) | 6.75847e95 | + | 6.02737e95i | 1.13241 | + | 1.00991i | ||||
\(985\) | 1.27211e95 | 0.206331 | ||||||||
\(986\) | − | 2.39941e95i | − | 0.376741i | ||||||
\(987\) | −2.35453e95 | + | 2.64013e95i | −0.357894 | + | 0.401306i | ||||
\(988\) | −7.79607e95 | −1.14724 | ||||||||
\(989\) | 6.62513e95i | 0.943872i | ||||||||
\(990\) | 1.43317e95 | − | 1.64437e94i | 0.197683 | − | 0.0226816i | ||||
\(991\) | 5.76846e95 | 0.770377 | 0.385188 | − | 0.922838i | \(-0.374136\pi\) | ||||
0.385188 | + | 0.922838i | \(0.374136\pi\) | |||||||
\(992\) | − | 3.44731e95i | − | 0.445766i | ||||||
\(993\) | −8.00271e95 | − | 7.13701e95i | −1.00199 | − | 0.893594i | ||||
\(994\) | −1.95453e95 | −0.236962 | ||||||||
\(995\) | 2.08185e95i | 0.244406i | ||||||||
\(996\) | 2.50733e95 | − | 2.81146e95i | 0.285045 | − | 0.319620i | ||||
\(997\) | 1.60508e96 | 1.76706 | 0.883530 | − | 0.468375i | \(-0.155160\pi\) | ||||
0.883530 | + | 0.468375i | \(0.155160\pi\) | |||||||
\(998\) | − | 5.71304e95i | − | 0.609102i | ||||||
\(999\) | −4.26451e94 | + | 6.04935e94i | −0.0440325 | + | 0.0624616i |
(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 | 3.65.b.a.2.8 | ✓ | 20 | |
3.2 | odd | 2 | inner | 3.65.b.a.2.13 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.65.b.a.2.8 | ✓ | 20 | 1.1 | even | 1 | trivial | |
3.65.b.a.2.13 | yes | 20 | 3.2 | odd | 2 | inner |