Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [45,9,Mod(28,45)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("45.28");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 45.g (of order \(4\), degree \(2\), 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: | \(18.3320374528\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 3006 x^{14} + 3660359 x^{12} + 2360769624 x^{10} + 888292333775 x^{8} + 201214811046486 x^{6} + \cdots + 60\!\cdots\!84 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{14}\cdot 3^{12}\cdot 5^{19} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 37.4 | ||
Root | \(-29.6766i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 45.37 |
Dual form | 45.9.g.b.28.4 |
$q$-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 \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.79807 | − | 3.79807i | −0.237379 | − | 0.237379i | 0.578385 | − | 0.815764i | \(-0.303683\pi\) |
−0.815764 | + | 0.578385i | \(0.803683\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 227.149i | − | 0.887302i | ||||||
\(5\) | −563.744 | − | 269.849i | −0.901990 | − | 0.431758i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1263.51 | − | 1263.51i | −0.526244 | − | 0.526244i | 0.393206 | − | 0.919450i | \(-0.371366\pi\) |
−0.919450 | + | 0.393206i | \(0.871366\pi\) | |||||||
\(8\) | −1835.03 | + | 1835.03i | −0.448006 | + | 0.448006i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1116.23 | + | 3166.04i | 0.111623 | + | 0.316604i | ||||
\(11\) | 2393.22 | 0.163460 | 0.0817301 | − | 0.996654i | \(-0.473955\pi\) | ||||
0.0817301 | + | 0.996654i | \(0.473955\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4601.53 | − | 4601.53i | 0.161113 | − | 0.161113i | −0.621947 | − | 0.783059i | \(-0.713658\pi\) |
0.783059 | + | 0.621947i | \(0.213658\pi\) | |||||||
\(14\) | 9597.80i | 0.249839i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −44211.1 | −0.674608 | ||||||||
\(17\) | 62989.7 | + | 62989.7i | 0.754177 | + | 0.754177i | 0.975256 | − | 0.221079i | \(-0.0709577\pi\) |
−0.221079 | + | 0.975256i | \(0.570958\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 114324.i | − | 0.877248i | −0.898671 | − | 0.438624i | \(-0.855466\pi\) | ||
0.898671 | − | 0.438624i | \(-0.144534\pi\) | |||||||
\(20\) | −61295.9 | + | 128054.i | −0.383100 | + | 0.800337i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −9089.61 | − | 9089.61i | −0.0388020 | − | 0.0388020i | ||||
\(23\) | −264286. | + | 264286.i | −0.944415 | + | 0.944415i | −0.998534 | − | 0.0541198i | \(-0.982765\pi\) |
0.0541198 | + | 0.998534i | \(0.482765\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 244988. | + | 304251.i | 0.627171 | + | 0.778882i | ||||
\(26\) | −34953.9 | −0.0764895 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −287006. | + | 287006.i | −0.466938 | + | 0.466938i | ||||
\(29\) | 1.26150e6i | 1.78359i | 0.452443 | + | 0.891793i | \(0.350553\pi\) | ||||
−0.452443 | + | 0.891793i | \(0.649447\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 462025. | 0.500287 | 0.250143 | − | 0.968209i | \(-0.419522\pi\) | ||||
0.250143 | + | 0.968209i | \(0.419522\pi\) | |||||||
\(32\) | 637685. | + | 637685.i | 0.608144 | + | 0.608144i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 478478.i | − | 0.358052i | ||||||
\(35\) | 371340. | + | 1.05325e6i | 0.247457 | + | 0.701877i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −785681. | − | 785681.i | −0.419218 | − | 0.419218i | 0.465716 | − | 0.884934i | \(-0.345797\pi\) |
−0.884934 | + | 0.465716i | \(0.845797\pi\) | |||||||
\(38\) | −434210. | + | 434210.i | −0.208240 | + | 0.208240i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.52967e6 | − | 539307.i | 0.597527 | − | 0.210667i | ||||
\(41\) | −1.91676e6 | −0.678318 | −0.339159 | − | 0.940729i | \(-0.610142\pi\) | ||||
−0.339159 | + | 0.940729i | \(0.610142\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.06087e6 | + | 3.06087e6i | −0.895306 | + | 0.895306i | −0.995017 | − | 0.0997103i | \(-0.968208\pi\) |
0.0997103 | + | 0.995017i | \(0.468208\pi\) | |||||||
\(44\) | − | 543619.i | − | 0.145039i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.00755e6 | 0.448369 | ||||||||
\(47\) | −1.27822e6 | − | 1.27822e6i | −0.261947 | − | 0.261947i | 0.563898 | − | 0.825844i | \(-0.309301\pi\) |
−0.825844 | + | 0.563898i | \(0.809301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 2.57188e6i | − | 0.446134i | ||||||
\(50\) | 225082. | − | 2.08605e6i | 0.0360131 | − | 0.333767i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.04524e6 | − | 1.04524e6i | −0.142956 | − | 0.142956i | ||||
\(53\) | 5.22439e6 | − | 5.22439e6i | 0.662113 | − | 0.662113i | −0.293765 | − | 0.955878i | \(-0.594908\pi\) |
0.955878 | + | 0.293765i | \(0.0949082\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.34916e6 | − | 645807.i | −0.147439 | − | 0.0705752i | ||||
\(56\) | 4.63717e6 | 0.471521 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.79125e6 | − | 4.79125e6i | 0.423386 | − | 0.423386i | ||||
\(59\) | − | 2.36986e7i | − | 1.95576i | −0.209169 | − | 0.977880i | \(-0.567076\pi\) | ||
0.209169 | − | 0.977880i | \(-0.432924\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.07351e7 | −0.775329 | −0.387665 | − | 0.921801i | \(-0.626718\pi\) | ||||
−0.387665 | + | 0.921801i | \(0.626718\pi\) | |||||||
\(62\) | −1.75480e6 | − | 1.75480e6i | −0.118758 | − | 0.118758i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.47410e6i | 0.385887i | ||||||||
\(65\) | −3.83580e6 | + | 1.35237e6i | −0.214883 | + | 0.0757602i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.21877e7 | + | 2.21877e7i | 1.10107 | + | 1.10107i | 0.994282 | + | 0.106783i | \(0.0340551\pi\) |
0.106783 | + | 0.994282i | \(0.465945\pi\) | |||||||
\(68\) | 1.43081e7 | − | 1.43081e7i | 0.669183 | − | 0.669183i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.58995e6 | − | 5.41070e6i | 0.107870 | − | 0.225352i | ||||
\(71\) | −2.73960e7 | −1.07809 | −0.539043 | − | 0.842278i | \(-0.681214\pi\) | ||||
−0.539043 | + | 0.842278i | \(0.681214\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.75412e6 | − | 4.75412e6i | 0.167409 | − | 0.167409i | −0.618430 | − | 0.785840i | \(-0.712231\pi\) |
0.785840 | + | 0.618430i | \(0.212231\pi\) | |||||||
\(74\) | 5.96814e6i | 0.199027i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.59686e7 | −0.778384 | ||||||||
\(77\) | −3.02386e6 | − | 3.02386e6i | −0.0860200 | − | 0.0860200i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 8.87427e6i | − | 0.227837i | −0.993490 | − | 0.113919i | \(-0.963660\pi\) | ||
0.993490 | − | 0.113919i | \(-0.0363403\pi\) | |||||||
\(80\) | 2.49237e7 | + | 1.19303e7i | 0.608489 | + | 0.291267i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.28000e6 | + | 7.28000e6i | 0.161019 | + | 0.161019i | ||||
\(83\) | −2.53098e7 | + | 2.53098e7i | −0.533305 | + | 0.533305i | −0.921554 | − | 0.388249i | \(-0.873080\pi\) |
0.388249 | + | 0.921554i | \(0.373080\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.85123e7 | − | 5.25077e7i | −0.354638 | − | 1.00588i | ||||
\(86\) | 2.32508e7 | 0.425054 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.39164e6 | + | 4.39164e6i | −0.0732312 | + | 0.0732312i | ||||
\(89\) | 6.89392e7i | 1.09877i | 0.835570 | + | 0.549384i | \(0.185138\pi\) | ||||
−0.835570 | + | 0.549384i | \(0.814862\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.16282e7 | −0.169569 | ||||||||
\(92\) | 6.00324e7 | + | 6.00324e7i | 0.837981 | + | 0.837981i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.70949e6i | 0.124361i | ||||||||
\(95\) | −3.08501e7 | + | 6.44493e7i | −0.378759 | + | 0.791269i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.46963e7 | + | 5.46963e7i | 0.617833 | + | 0.617833i | 0.944975 | − | 0.327142i | \(-0.106086\pi\) |
−0.327142 | + | 0.944975i | \(0.606086\pi\) | |||||||
\(98\) | −9.76815e6 | + | 9.76815e6i | −0.105903 | + | 0.105903i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.91104e7 | − | 5.56490e7i | 0.691104 | − | 0.556490i | ||||
\(101\) | −1.29927e8 | −1.24857 | −0.624287 | − | 0.781195i | \(-0.714611\pi\) | ||||
−0.624287 | + | 0.781195i | \(0.714611\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.27844e8 | + | 1.27844e8i | −1.13588 | + | 1.13588i | −0.146696 | + | 0.989182i | \(0.546864\pi\) |
−0.989182 | + | 0.146696i | \(0.953136\pi\) | |||||||
\(104\) | 1.68879e7i | 0.144359i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.96852e7 | −0.314344 | ||||||||
\(107\) | −3.20088e7 | − | 3.20088e7i | −0.244194 | − | 0.244194i | 0.574389 | − | 0.818583i | \(-0.305240\pi\) |
−0.818583 | + | 0.574389i | \(0.805240\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1.68791e8i | − | 1.19576i | −0.801585 | − | 0.597880i | \(-0.796010\pi\) | ||
0.801585 | − | 0.597880i | \(-0.203990\pi\) | |||||||
\(110\) | 2.67139e6 | + | 7.57703e6i | 0.0182460 | + | 0.0517521i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5.58612e7 | + | 5.58612e7i | 0.355008 | + | 0.355008i | ||||
\(113\) | −4.34518e7 | + | 4.34518e7i | −0.266498 | + | 0.266498i | −0.827687 | − | 0.561189i | \(-0.810344\pi\) |
0.561189 | + | 0.827687i | \(0.310344\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.20307e8 | − | 7.76723e7i | 1.25961 | − | 0.444094i | ||||
\(116\) | 2.86548e8 | 1.58258 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −9.00090e7 | + | 9.00090e7i | −0.464256 | + | 0.464256i | ||||
\(119\) | − | 1.59176e8i | − | 0.793763i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.08631e8 | −0.973281 | ||||||||
\(122\) | 4.07726e7 | + | 4.07726e7i | 0.184047 | + | 0.184047i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 1.04949e8i | − | 0.443906i | ||||||
\(125\) | −5.60090e7 | − | 2.37629e8i | −0.229413 | − | 0.973329i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.83349e8 | + | 2.83349e8i | 1.08920 | + | 1.08920i | 0.995611 | + | 0.0935869i | \(0.0298333\pi\) |
0.0935869 | + | 0.995611i | \(0.470167\pi\) | |||||||
\(128\) | 1.87836e8 | − | 1.87836e8i | 0.699745 | − | 0.699745i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.97050e7 | + | 9.43225e6i | 0.0689927 | + | 0.0330249i | ||||
\(131\) | −1.56673e8 | −0.531997 | −0.265998 | − | 0.963973i | \(-0.585702\pi\) | ||||
−0.265998 | + | 0.963973i | \(0.585702\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.44450e8 | + | 1.44450e8i | −0.461647 | + | 0.461647i | ||||
\(134\) | − | 1.68541e8i | − | 0.522740i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.31176e8 | −0.675752 | ||||||||
\(137\) | −4.29110e8 | − | 4.29110e8i | −1.21811 | − | 1.21811i | −0.968293 | − | 0.249817i | \(-0.919630\pi\) |
−0.249817 | − | 0.968293i | \(-0.580370\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 3.83809e8i | − | 1.02815i | −0.857746 | − | 0.514074i | \(-0.828136\pi\) | ||
0.857746 | − | 0.514074i | \(-0.171864\pi\) | |||||||
\(140\) | 2.39246e8 | − | 8.43496e7i | 0.622777 | − | 0.219569i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.04052e8 | + | 1.04052e8i | 0.255915 | + | 0.255915i | ||||
\(143\) | 1.10125e7 | − | 1.10125e7i | 0.0263355 | − | 0.0263355i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.40413e8 | − | 7.11161e8i | 0.770077 | − | 1.60878i | ||||
\(146\) | −3.61129e7 | −0.0794788 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.78467e8 | + | 1.78467e8i | −0.371973 | + | 0.371973i | ||||
\(149\) | 1.64089e8i | 0.332916i | 0.986049 | + | 0.166458i | \(0.0532330\pi\) | ||||
−0.986049 | + | 0.166458i | \(0.946767\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.72571e8 | −1.29369 | −0.646845 | − | 0.762622i | \(-0.723912\pi\) | ||||
−0.646845 | + | 0.762622i | \(0.723912\pi\) | |||||||
\(152\) | 2.09788e8 | + | 2.09788e8i | 0.393013 | + | 0.393013i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.29697e7i | 0.0408387i | ||||||||
\(155\) | −2.60464e8 | − | 1.24677e8i | −0.451253 | − | 0.216003i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.08820e8 | + | 7.08820e8i | 1.16664 | + | 1.16664i | 0.982992 | + | 0.183649i | \(0.0587911\pi\) |
0.183649 | + | 0.982992i | \(0.441209\pi\) | |||||||
\(158\) | −3.37051e7 | + | 3.37051e7i | −0.0540838 | + | 0.0540838i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.87412e8 | − | 5.31569e8i | −0.285969 | − | 0.811110i | ||||
\(161\) | 6.67857e8 | 0.993985 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.86978e8 | + | 1.86978e8i | −0.264874 | + | 0.264874i | −0.827031 | − | 0.562157i | \(-0.809972\pi\) |
0.562157 | + | 0.827031i | \(0.309972\pi\) | |||||||
\(164\) | 4.35392e8i | 0.601873i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.92256e8 | 0.253191 | ||||||||
\(167\) | 2.92261e8 | + | 2.92261e8i | 0.375756 | + | 0.375756i | 0.869568 | − | 0.493813i | \(-0.164397\pi\) |
−0.493813 | + | 0.869568i | \(0.664397\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.73382e8i | 0.948086i | ||||||||
\(170\) | −1.29117e8 | + | 2.69739e8i | −0.154592 | + | 0.322959i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.95276e8 | + | 6.95276e8i | 0.794407 | + | 0.794407i | ||||
\(173\) | −9.48183e8 | + | 9.48183e8i | −1.05854 | + | 1.05854i | −0.0603642 | + | 0.998176i | \(0.519226\pi\) |
−0.998176 | + | 0.0603642i | \(0.980774\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.48786e7 | − | 6.93970e8i | 0.0798373 | − | 0.739927i | ||||
\(176\) | −1.05807e8 | −0.110272 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.61836e8 | − | 2.61836e8i | 0.260825 | − | 0.260825i | ||||
\(179\) | 8.32961e8i | 0.811358i | 0.914016 | + | 0.405679i | \(0.132965\pi\) | ||||
−0.914016 | + | 0.405679i | \(0.867035\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.03144e9 | −0.961011 | −0.480505 | − | 0.876992i | \(-0.659547\pi\) | ||||
−0.480505 | + | 0.876992i | \(0.659547\pi\) | |||||||
\(182\) | 4.41646e7 | + | 4.41646e7i | 0.0402521 | + | 0.0402521i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 9.69947e8i | − | 0.846207i | ||||||
\(185\) | 2.30908e8 | + | 6.54938e8i | 0.197129 | + | 0.559130i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.50748e8 | + | 1.50748e8i | 0.123278 | + | 0.123278i | ||||
\(188\) | −2.90346e8 | + | 2.90346e8i | −0.232426 | + | 0.232426i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.61954e8 | − | 1.27612e8i | 0.277740 | − | 0.0979213i | ||||
\(191\) | −1.15496e9 | −0.867827 | −0.433913 | − | 0.900955i | \(-0.642868\pi\) | ||||
−0.433913 | + | 0.900955i | \(0.642868\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.80665e8 | + | 7.80665e8i | −0.562646 | + | 0.562646i | −0.930058 | − | 0.367412i | \(-0.880244\pi\) |
0.367412 | + | 0.930058i | \(0.380244\pi\) | |||||||
\(194\) | − | 4.15480e8i | − | 0.293321i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.84200e8 | −0.395856 | ||||||||
\(197\) | 8.77672e8 | + | 8.77672e8i | 0.582730 | + | 0.582730i | 0.935653 | − | 0.352923i | \(-0.114812\pi\) |
−0.352923 | + | 0.935653i | \(0.614812\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.28132e9i | − | 0.817041i | −0.912749 | − | 0.408521i | \(-0.866045\pi\) | ||
0.912749 | − | 0.408521i | \(-0.133955\pi\) | |||||||
\(200\) | −1.00787e9 | − | 1.08748e8i | −0.629920 | − | 0.0679677i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.93472e8 | + | 4.93472e8i | 0.296386 | + | 0.296386i | ||||
\(203\) | 1.59392e9 | − | 1.59392e9i | 0.938602 | − | 0.938602i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.08056e9 | + | 5.17236e8i | 0.611836 | + | 0.292869i | ||||
\(206\) | 9.71120e8 | 0.539267 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.03439e8 | + | 2.03439e8i | −0.108688 | + | 0.108688i | ||||
\(209\) | − | 2.73602e8i | − | 0.143395i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.42670e8 | −0.122429 | −0.0612147 | − | 0.998125i | \(-0.519497\pi\) | ||||
−0.0612147 | + | 0.998125i | \(0.519497\pi\) | |||||||
\(212\) | −1.18672e9 | − | 1.18672e9i | −0.587495 | − | 0.587495i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.43143e8i | 0.115933i | ||||||||
\(215\) | 2.55152e9 | − | 8.99575e8i | 1.19411 | − | 0.421002i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.83775e8 | − | 5.83775e8i | −0.263273 | − | 0.263273i | ||||
\(218\) | −6.41081e8 | + | 6.41081e8i | −0.283849 | + | 0.283849i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.46695e8 | + | 3.06461e8i | −0.0626215 | + | 0.130823i | ||||
\(221\) | 5.79698e8 | 0.243015 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.08119e7 | + | 8.08119e7i | −0.0326780 | + | 0.0326780i | −0.723257 | − | 0.690579i | \(-0.757356\pi\) |
0.690579 | + | 0.723257i | \(0.257356\pi\) | |||||||
\(224\) | − | 1.61145e9i | − | 0.640064i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.30065e8 | 0.126522 | ||||||||
\(227\) | −2.04069e9 | − | 2.04069e9i | −0.768552 | − | 0.768552i | 0.209300 | − | 0.977851i | \(-0.432882\pi\) |
−0.977851 | + | 0.209300i | \(0.932882\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 9.69115e8i | − | 0.352398i | −0.984355 | − | 0.176199i | \(-0.943620\pi\) | ||
0.984355 | − | 0.176199i | \(-0.0563802\pi\) | |||||||
\(230\) | −1.13174e9 | − | 5.41735e8i | −0.404424 | − | 0.193587i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.31489e9 | − | 2.31489e9i | −0.799058 | − | 0.799058i | ||||
\(233\) | 3.48900e9 | − | 3.48900e9i | 1.18380 | − | 1.18380i | 0.205046 | − | 0.978752i | \(-0.434265\pi\) |
0.978752 | − | 0.205046i | \(-0.0657345\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.75661e8 | + | 1.06551e9i | 0.123176 | + | 0.349370i | ||||
\(236\) | −5.38313e9 | −1.73535 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.04562e8 | + | 6.04562e8i | −0.188423 | + | 0.188423i | ||||
\(239\) | − | 3.23778e9i | − | 0.992330i | −0.868228 | − | 0.496165i | \(-0.834741\pi\) | ||
0.868228 | − | 0.496165i | \(-0.165259\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.80806e9 | 1.72172 | 0.860861 | − | 0.508840i | \(-0.169925\pi\) | ||||
0.860861 | + | 0.508840i | \(0.169925\pi\) | |||||||
\(242\) | 7.92396e8 | + | 7.92396e8i | 0.231036 | + | 0.231036i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.43847e9i | 0.687951i | ||||||||
\(245\) | −6.94017e8 | + | 1.44988e9i | −0.192622 | + | 0.402409i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.26065e8 | − | 5.26065e8i | −0.141336 | − | 0.141336i | ||||
\(248\) | −8.47832e8 | + | 8.47832e8i | −0.224132 | + | 0.224132i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.89805e8 | + | 1.11526e9i | −0.176590 | + | 0.285506i | ||||
\(251\) | 4.71877e9 | 1.18887 | 0.594434 | − | 0.804144i | \(-0.297376\pi\) | ||||
0.594434 | + | 0.804144i | \(0.297376\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.32495e8 | + | 6.32495e8i | −0.154374 | + | 0.154374i | ||||
\(254\) | − | 2.15236e9i | − | 0.517106i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.30540e8 | 0.0536767 | ||||||||
\(257\) | 4.32801e9 | + | 4.32801e9i | 0.992100 | + | 0.992100i | 0.999969 | − | 0.00786898i | \(-0.00250480\pi\) |
−0.00786898 | + | 0.999969i | \(0.502505\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.98544e9i | 0.441222i | ||||||||
\(260\) | 3.07189e8 | + | 8.71300e8i | 0.0672222 | + | 0.190667i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.95054e8 | + | 5.95054e8i | 0.126285 | + | 0.126285i | ||||
\(263\) | −2.02736e9 | + | 2.02736e9i | −0.423748 | + | 0.423748i | −0.886492 | − | 0.462744i | \(-0.846865\pi\) |
0.462744 | + | 0.886492i | \(0.346865\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.35501e9 | + | 1.53542e9i | −0.883092 | + | 0.311347i | ||||
\(266\) | 1.09726e9 | 0.219171 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.03992e9 | − | 5.03992e9i | 0.976978 | − | 0.976978i | ||||
\(269\) | 6.96389e9i | 1.32997i | 0.746855 | + | 0.664987i | \(0.231563\pi\) | ||||
−0.746855 | + | 0.664987i | \(0.768437\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.60908e8 | −0.0854548 | −0.0427274 | − | 0.999087i | \(-0.513605\pi\) | ||||
−0.0427274 | + | 0.999087i | \(0.513605\pi\) | |||||||
\(272\) | −2.78484e9 | − | 2.78484e9i | −0.508774 | − | 0.508774i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.25958e9i | 0.578308i | ||||||||
\(275\) | 5.86312e8 | + | 7.28139e8i | 0.102517 | + | 0.127316i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.03729e9 | − | 7.03729e9i | −1.19533 | − | 1.19533i | −0.975550 | − | 0.219776i | \(-0.929467\pi\) |
−0.219776 | − | 0.975550i | \(-0.570533\pi\) | |||||||
\(278\) | −1.45773e9 | + | 1.45773e9i | −0.244061 | + | 0.244061i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.61418e9 | − | 1.25133e9i | −0.425307 | − | 0.203583i | ||||
\(281\) | −6.38779e9 | −1.02453 | −0.512266 | − | 0.858827i | \(-0.671194\pi\) | ||||
−0.512266 | + | 0.858827i | \(0.671194\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.73852e9 | − | 7.73852e9i | 1.20646 | − | 1.20646i | 0.234292 | − | 0.972166i | \(-0.424723\pi\) |
0.972166 | − | 0.234292i | \(-0.0752772\pi\) | |||||||
\(284\) | 6.22298e9i | 0.956589i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.36523e7 | −0.0125030 | ||||||||
\(287\) | 2.42186e9 | + | 2.42186e9i | 0.356961 | + | 0.356961i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.59636e8i | 0.137567i | ||||||||
\(290\) | −3.99395e9 | + | 1.40812e9i | −0.564690 | + | 0.199090i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.07990e9 | − | 1.07990e9i | −0.148542 | − | 0.148542i | ||||
\(293\) | −3.65403e9 | + | 3.65403e9i | −0.495794 | + | 0.495794i | −0.910126 | − | 0.414332i | \(-0.864015\pi\) |
0.414332 | + | 0.910126i | \(0.364015\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.39504e9 | + | 1.33600e10i | −0.844414 | + | 1.76407i | ||||
\(296\) | 2.88350e9 | 0.375624 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.23221e8 | − | 6.23221e8i | 0.0790273 | − | 0.0790273i | ||||
\(299\) | 2.43224e9i | 0.304314i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.73490e9 | 0.942299 | ||||||||
\(302\) | 2.55447e9 | + | 2.55447e9i | 0.307095 | + | 0.307095i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.05438e9i | 0.591798i | ||||||||
\(305\) | 6.05183e9 | + | 2.89685e9i | 0.699339 | + | 0.334754i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.90099e9 | − | 1.90099e9i | −0.214006 | − | 0.214006i | 0.591961 | − | 0.805967i | \(-0.298354\pi\) |
−0.805967 | + | 0.591961i | \(0.798354\pi\) | |||||||
\(308\) | −6.86869e8 | + | 6.86869e8i | −0.0763257 | + | 0.0763257i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5.15728e8 | + | 1.46279e9i | 0.0558436 | + | 0.158393i | ||||
\(311\) | 3.14139e9 | 0.335799 | 0.167900 | − | 0.985804i | \(-0.446302\pi\) | ||||
0.167900 | + | 0.985804i | \(0.446302\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.51498e9 | − | 2.51498e9i | 0.262034 | − | 0.262034i | −0.563846 | − | 0.825880i | \(-0.690679\pi\) |
0.825880 | + | 0.563846i | \(0.190679\pi\) | |||||||
\(314\) | − | 5.38429e9i | − | 0.553872i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.01579e9 | −0.202160 | ||||||||
\(317\) | −8.48738e9 | − | 8.48738e9i | −0.840498 | − | 0.840498i | 0.148426 | − | 0.988924i | \(-0.452579\pi\) |
−0.988924 | + | 0.148426i | \(0.952579\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.01904e9i | 0.291545i | ||||||||
\(320\) | 1.74703e9 | − | 3.64973e9i | 0.166609 | − | 0.348066i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.53656e9 | − | 2.53656e9i | −0.235951 | − | 0.235951i | ||||
\(323\) | 7.20122e9 | − | 7.20122e9i | 0.661601 | − | 0.661601i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.52734e9 | + | 2.72697e8i | 0.226533 | + | 0.0244426i | ||||
\(326\) | 1.42031e9 | 0.125751 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.51733e9 | − | 3.51733e9i | 0.303891 | − | 0.303891i | ||||
\(329\) | 3.23008e9i | 0.275696i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.47303e10 | 1.22716 | 0.613579 | − | 0.789634i | \(-0.289729\pi\) | ||||
0.613579 | + | 0.789634i | \(0.289729\pi\) | |||||||
\(332\) | 5.74909e9 | + | 5.74909e9i | 0.473203 | + | 0.473203i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 2.22006e9i | − | 0.178393i | ||||||
\(335\) | −6.52085e9 | − | 1.84955e10i | −0.517756 | − | 1.46854i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.23187e10 | − | 1.23187e10i | −0.955093 | − | 0.955093i | 0.0439408 | − | 0.999034i | \(-0.486009\pi\) |
−0.999034 | + | 0.0439408i | \(0.986009\pi\) | |||||||
\(338\) | 2.93736e9 | − | 2.93736e9i | 0.225056 | − | 0.225056i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.19271e10 | + | 4.20507e9i | −0.892522 | + | 0.314671i | ||||
\(341\) | 1.10573e9 | 0.0817770 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.05335e10 | + | 1.05335e10i | −0.761020 | + | 0.761020i | ||||
\(344\) | − | 1.12336e10i | − | 0.802205i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.20252e9 | 0.502551 | ||||||||
\(347\) | −1.53260e10 | − | 1.53260e10i | −1.05709 | − | 1.05709i | −0.998269 | − | 0.0588205i | \(-0.981266\pi\) |
−0.0588205 | − | 0.998269i | \(-0.518734\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.75699e9i | 0.185837i | 0.995674 | + | 0.0929187i | \(0.0296197\pi\) | ||||
−0.995674 | + | 0.0929187i | \(0.970380\pi\) | |||||||
\(350\) | −2.92014e9 | + | 2.35135e9i | −0.194595 | + | 0.156691i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.52612e9 | + | 1.52612e9i | 0.0994073 | + | 0.0994073i | ||||
\(353\) | −1.01786e10 | + | 1.01786e10i | −0.655525 | + | 0.655525i | −0.954318 | − | 0.298793i | \(-0.903416\pi\) |
0.298793 | + | 0.954318i | \(0.403416\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.54443e10 | + | 7.39277e9i | 0.972423 | + | 0.465472i | ||||
\(356\) | 1.56595e10 | 0.974940 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.16364e9 | − | 3.16364e9i | 0.192599 | − | 0.192599i | ||||
\(359\) | − | 2.18455e10i | − | 1.31517i | −0.753378 | − | 0.657587i | \(-0.771577\pi\) | ||
0.753378 | − | 0.657587i | \(-0.228423\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.91362e9 | 0.230436 | ||||||||
\(362\) | 3.91746e9 | + | 3.91746e9i | 0.228124 | + | 0.228124i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.64134e9i | 0.150459i | ||||||||
\(365\) | −3.96300e9 | + | 1.39721e9i | −0.223281 | + | 0.0787211i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.57287e10 | − | 1.57287e10i | −0.867020 | − | 0.867020i | 0.125121 | − | 0.992141i | \(-0.460068\pi\) |
−0.992141 | + | 0.125121i | \(0.960068\pi\) | |||||||
\(368\) | 1.16844e10 | − | 1.16844e10i | 0.637109 | − | 0.637109i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.61049e9 | − | 3.36450e9i | 0.0859314 | − | 0.179520i | ||||
\(371\) | −1.32022e10 | −0.696866 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.34880e10 | + | 1.34880e10i | −0.696809 | + | 0.696809i | −0.963721 | − | 0.266912i | \(-0.913997\pi\) |
0.266912 | + | 0.963721i | \(0.413997\pi\) | |||||||
\(374\) | − | 1.14510e9i | − | 0.0585272i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.69114e9 | 0.234707 | ||||||||
\(377\) | 5.80482e9 | + | 5.80482e9i | 0.287358 | + | 0.287358i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.99838e10i | − | 0.968546i | −0.874917 | − | 0.484273i | \(-0.839084\pi\) | ||
0.874917 | − | 0.484273i | \(-0.160916\pi\) | |||||||
\(380\) | 1.46396e10 | + | 7.00759e9i | 0.702095 | + | 0.336073i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.38661e9 | + | 4.38661e9i | 0.206004 | + | 0.206004i | ||||
\(383\) | 1.80028e9 | − | 1.80028e9i | 0.0836653 | − | 0.0836653i | −0.664036 | − | 0.747701i | \(-0.731158\pi\) |
0.747701 | + | 0.664036i | \(0.231158\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.88698e8 | + | 2.52067e9i | 0.0404493 | + | 0.114729i | ||||
\(386\) | 5.93003e9 | 0.267121 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.24242e10 | − | 1.24242e10i | 0.548204 | − | 0.548204i | ||||
\(389\) | 3.97690e10i | 1.73679i | 0.495876 | + | 0.868393i | \(0.334847\pi\) | ||||
−0.495876 | + | 0.868393i | \(0.665153\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.32946e10 | −1.42451 | ||||||||
\(392\) | 4.71948e9 | + | 4.71948e9i | 0.199871 | + | 0.199871i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 6.66691e9i | − | 0.276656i | ||||||
\(395\) | −2.39471e9 | + | 5.00281e9i | −0.0983704 | + | 0.205507i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.14166e10 | + | 2.14166e10i | 0.862162 | + | 0.862162i | 0.991589 | − | 0.129427i | \(-0.0413137\pi\) |
−0.129427 | + | 0.991589i | \(0.541314\pi\) | |||||||
\(398\) | −4.86652e9 | + | 4.86652e9i | −0.193949 | + | 0.193949i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.08312e10 | − | 1.34513e10i | −0.423094 | − | 0.525440i | ||||
\(401\) | −1.76006e10 | −0.680690 | −0.340345 | − | 0.940301i | \(-0.610544\pi\) | ||||
−0.340345 | + | 0.940301i | \(0.610544\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.12603e9 | − | 2.12603e9i | 0.0806025 | − | 0.0806025i | ||||
\(404\) | 2.95129e10i | 1.10786i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.21076e10 | −0.445609 | ||||||||
\(407\) | −1.88031e9 | − | 1.88031e9i | −0.0685254 | − | 0.0685254i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.01202e10i | 0.361655i | 0.983515 | + | 0.180827i | \(0.0578776\pi\) | ||||
−0.983515 | + | 0.180827i | \(0.942122\pi\) | |||||||
\(410\) | −2.13955e9 | − | 6.06855e9i | −0.0757160 | − | 0.214758i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.90397e10 | + | 2.90397e10i | 1.00787 | + | 1.00787i | ||||
\(413\) | −2.99435e10 | + | 2.99435e10i | −1.02921 | + | 1.02921i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.10980e10 | − | 7.43841e9i | 0.711294 | − | 0.250777i | ||||
\(416\) | 5.86866e9 | 0.195959 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.03916e9 | + | 1.03916e9i | −0.0340390 | + | 0.0340390i | ||||
\(419\) | − | 1.92609e10i | − | 0.624913i | −0.949932 | − | 0.312457i | \(-0.898848\pi\) | ||
0.949932 | − | 0.312457i | \(-0.101152\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.32612e9 | 0.169544 | 0.0847720 | − | 0.996400i | \(-0.472984\pi\) | ||||
0.0847720 | + | 0.996400i | \(0.472984\pi\) | |||||||
\(422\) | 9.21676e8 | + | 9.21676e8i | 0.0290622 | + | 0.0290622i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.91739e10i | 0.593262i | ||||||||
\(425\) | −3.73291e9 | + | 3.45964e10i | −0.114417 | + | 1.06041i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.35639e10 | + | 1.35639e10i | 0.408012 | + | 0.408012i | ||||
\(428\) | −7.27078e9 | + | 7.27078e9i | −0.216674 | + | 0.216674i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.31075e10 | − | 6.27420e9i | −0.383394 | − | 0.183520i | ||||
\(431\) | −2.68556e10 | −0.778262 | −0.389131 | − | 0.921182i | \(-0.627225\pi\) | ||||
−0.389131 | + | 0.921182i | \(0.627225\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.08434e10 | + | 1.08434e10i | −0.308472 | + | 0.308472i | −0.844317 | − | 0.535845i | \(-0.819993\pi\) |
0.535845 | + | 0.844317i | \(0.319993\pi\) | |||||||
\(434\) | 4.43443e9i | 0.124991i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.83409e10 | −1.06100 | ||||||||
\(437\) | 3.02142e10 | + | 3.02142e10i | 0.828486 | + | 0.828486i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2.77833e10i | − | 0.748041i | −0.927420 | − | 0.374021i | \(-0.877979\pi\) | ||
0.927420 | − | 0.374021i | \(-0.122021\pi\) | |||||||
\(440\) | 3.66084e9 | − | 1.29068e9i | 0.0976719 | − | 0.0344356i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.20173e9 | − | 2.20173e9i | −0.0576866 | − | 0.0576866i | ||||
\(443\) | 4.95264e10 | − | 4.95264e10i | 1.28594 | − | 1.28594i | 0.348714 | − | 0.937229i | \(-0.386618\pi\) |
0.937229 | − | 0.348714i | \(-0.113382\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.86031e10 | − | 3.88640e10i | 0.474402 | − | 0.991078i | ||||
\(446\) | 6.13858e8 | 0.0155142 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.18010e9 | − | 8.18010e9i | 0.203070 | − | 0.203070i | ||||
\(449\) | 5.42287e9i | 0.133427i | 0.997772 | + | 0.0667136i | \(0.0212514\pi\) | ||||
−0.997772 | + | 0.0667136i | \(0.978749\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.58724e9 | −0.110878 | ||||||||
\(452\) | 9.87005e9 | + | 9.87005e9i | 0.236464 | + | 0.236464i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.55013e10i | 0.364876i | ||||||||
\(455\) | 6.55532e9 | + | 3.13785e9i | 0.152949 | + | 0.0732127i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.55109e10 | + | 1.55109e10i | 0.355609 | + | 0.355609i | 0.862191 | − | 0.506583i | \(-0.169091\pi\) |
−0.506583 | + | 0.862191i | \(0.669091\pi\) | |||||||
\(458\) | −3.68076e9 | + | 3.68076e9i | −0.0836519 | + | 0.0836519i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.76432e10 | − | 5.00425e10i | −0.394046 | − | 1.11766i | ||||
\(461\) | 3.26888e10 | 0.723761 | 0.361881 | − | 0.932224i | \(-0.382135\pi\) | ||||
0.361881 | + | 0.932224i | \(0.382135\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.92199e10 | + | 2.92199e10i | −0.635849 | + | 0.635849i | −0.949529 | − | 0.313680i | \(-0.898438\pi\) |
0.313680 | + | 0.949529i | \(0.398438\pi\) | |||||||
\(464\) | − | 5.57722e10i | − | 1.20322i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.65029e10 | −0.562018 | ||||||||
\(467\) | −4.90240e10 | − | 4.90240e10i | −1.03072 | − | 1.03072i | −0.999513 | − | 0.0312094i | \(-0.990064\pi\) |
−0.0312094 | − | 0.999513i | \(-0.509936\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 5.60689e10i | − | 1.15886i | ||||||
\(470\) | 2.62009e9 | − | 5.47366e9i | 0.0536939 | − | 0.112173i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.34878e10 | + | 4.34878e10i | 0.876192 | + | 0.876192i | ||||
\(473\) | −7.32535e9 | + | 7.32535e9i | −0.146347 | + | 0.146347i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.47831e10 | − | 2.80080e10i | 0.683273 | − | 0.550184i | ||||
\(476\) | −3.61568e10 | −0.704308 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.22973e10 | + | 1.22973e10i | −0.235558 | + | 0.235558i | ||||
\(479\) | − | 7.35533e10i | − | 1.39721i | −0.715510 | − | 0.698603i | \(-0.753805\pi\) | ||
0.715510 | − | 0.698603i | \(-0.246195\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.23068e9 | −0.135082 | ||||||||
\(482\) | −2.20594e10 | − | 2.20594e10i | −0.408701 | − | 0.408701i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.73905e10i | 0.863594i | ||||||||
\(485\) | −1.60750e10 | − | 4.55944e10i | −0.290525 | − | 0.824033i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.47809e10 | + | 2.47809e10i | 0.440556 | + | 0.440556i | 0.892199 | − | 0.451643i | \(-0.149162\pi\) |
−0.451643 | + | 0.892199i | \(0.649162\pi\) | |||||||
\(488\) | 1.96992e10 | − | 1.96992e10i | 0.347352 | − | 0.347352i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 8.14266e9 | − | 2.87081e9i | 0.141248 | − | 0.0497990i | ||||
\(491\) | 2.36469e10 | 0.406864 | 0.203432 | − | 0.979089i | \(-0.434790\pi\) | ||||
0.203432 | + | 0.979089i | \(0.434790\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.94613e10 | + | 7.94613e10i | −1.34514 | + | 1.34514i | ||||
\(494\) | 3.99606e9i | 0.0671003i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.04266e10 | −0.337497 | ||||||||
\(497\) | 3.46152e10 | + | 3.46152e10i | 0.567337 | + | 0.567337i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 8.08962e10i | − | 1.30475i | −0.757898 | − | 0.652373i | \(-0.773773\pi\) | ||
0.757898 | − | 0.652373i | \(-0.226227\pi\) | |||||||
\(500\) | −5.39773e10 | + | 1.27224e10i | −0.863637 | + | 0.203559i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.79222e10 | − | 1.79222e10i | −0.282213 | − | 0.282213i | ||||
\(503\) | 3.19123e10 | − | 3.19123e10i | 0.498525 | − | 0.498525i | −0.412454 | − | 0.910978i | \(-0.635328\pi\) |
0.910978 | + | 0.412454i | \(0.135328\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.32456e10 | + | 3.50607e10i | 1.12620 | + | 0.539082i | ||||
\(506\) | 4.80451e9 | 0.0732904 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.43626e10 | − | 6.43626e10i | 0.966448 | − | 0.966448i | ||||
\(509\) | 4.29973e10i | 0.640576i | 0.947320 | + | 0.320288i | \(0.103780\pi\) | ||||
−0.947320 | + | 0.320288i | \(0.896220\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.20138e10 | −0.176196 | ||||||||
\(512\) | −4.89617e10 | − | 4.89617e10i | −0.712487 | − | 0.712487i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 3.28761e10i | − | 0.471008i | ||||||
\(515\) | 1.06570e11 | − | 3.75727e10i | 1.51497 | − | 0.534126i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.05905e9 | − | 3.05905e9i | −0.0428178 | − | 0.0428178i | ||||
\(518\) | 7.54081e9 | − | 7.54081e9i | 0.104737 | − | 0.104737i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.55719e9 | − | 9.52046e9i | 0.0623280 | − | 0.130210i | ||||
\(521\) | −2.79302e9 | −0.0379073 | −0.0189536 | − | 0.999820i | \(-0.506033\pi\) | ||||
−0.0189536 | + | 0.999820i | \(0.506033\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.03667e10 | + | 8.03667e10i | −1.07416 | + | 1.07416i | −0.0771414 | + | 0.997020i | \(0.524579\pi\) |
−0.997020 | + | 0.0771414i | \(0.975421\pi\) | |||||||
\(524\) | 3.55882e10i | 0.472042i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.54001e10 | 0.201178 | ||||||||
\(527\) | 2.91028e10 | + | 2.91028e10i | 0.377305 | + | 0.377305i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 6.13831e10i | − | 0.783838i | ||||||
\(530\) | 2.23723e10 | + | 1.07090e10i | 0.283535 | + | 0.135720i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.28116e10 | + | 3.28116e10i | 0.409620 | + | 0.409620i | ||||
\(533\) | −8.82006e9 | + | 8.82006e9i | −0.109286 | + | 0.109286i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.40722e9 | + | 2.66823e10i | 0.114828 | + | 0.325693i | ||||
\(536\) | −8.14303e10 | −0.986568 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.64493e10 | − | 2.64493e10i | 0.315708 | − | 0.315708i | ||||
\(539\) | − | 6.15507e9i | − | 0.0729252i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.13690e10 | −0.249457 | −0.124728 | − | 0.992191i | \(-0.539806\pi\) | ||||
−0.124728 | + | 0.992191i | \(0.539806\pi\) | |||||||
\(542\) | 1.75056e9 | + | 1.75056e9i | 0.0202852 | + | 0.0202852i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.03351e10i | 0.917297i | ||||||||
\(545\) | −4.55481e10 | + | 9.51550e10i | −0.516279 | + | 1.07856i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.23893e10 | + | 1.23893e10i | 0.138387 | + | 0.138387i | 0.772907 | − | 0.634520i | \(-0.218802\pi\) |
−0.634520 | + | 0.772907i | \(0.718802\pi\) | |||||||
\(548\) | −9.74721e10 | + | 9.74721e10i | −1.08083 | + | 1.08083i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5.38671e8 | − | 4.99237e9i | 0.00588671 | − | 0.0545577i | ||||
\(551\) | 1.44219e11 | 1.56465 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.12128e10 | + | 1.12128e10i | −0.119898 | + | 0.119898i | ||||
\(554\) | 5.34562e10i | 0.567491i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.71820e10 | −0.912278 | ||||||||
\(557\) | 4.20197e10 | + | 4.20197e10i | 0.436549 | + | 0.436549i | 0.890849 | − | 0.454300i | \(-0.150111\pi\) |
−0.454300 | + | 0.890849i | \(0.650111\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.81694e10i | 0.288490i | ||||||||
\(560\) | −1.64173e10 | − | 4.65655e10i | −0.166936 | − | 0.473491i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.42613e10 | + | 2.42613e10i | 0.243202 | + | 0.243202i | ||||
\(563\) | −5.40384e10 | + | 5.40384e10i | −0.537860 | + | 0.537860i | −0.922900 | − | 0.385040i | \(-0.874188\pi\) |
0.385040 | + | 0.922900i | \(0.374188\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.62211e10 | − | 1.27703e10i | 0.355441 | − | 0.125316i | ||||
\(566\) | −5.87828e10 | −0.572776 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.02726e10 | − | 5.02726e10i | 0.482989 | − | 0.482989i | ||||
\(569\) | 1.43322e11i | 1.36730i | 0.729812 | + | 0.683648i | \(0.239608\pi\) | ||||
−0.729812 | + | 0.683648i | \(0.760392\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.10340e11 | 1.03798 | 0.518990 | − | 0.854780i | \(-0.326308\pi\) | ||||
0.518990 | + | 0.854780i | \(0.326308\pi\) | |||||||
\(572\) | −2.50148e9 | − | 2.50148e9i | −0.0233675 | − | 0.0233675i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 1.83967e10i | − | 0.169470i | ||||||
\(575\) | −1.45156e11 | − | 1.56622e10i | −1.32790 | − | 0.143279i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.29057e11 | − | 1.29057e11i | −1.16434 | − | 1.16434i | −0.983515 | − | 0.180825i | \(-0.942123\pi\) |
−0.180825 | − | 0.983515i | \(-0.557877\pi\) | |||||||
\(578\) | 3.64476e9 | − | 3.64476e9i | 0.0326556 | − | 0.0326556i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.61540e11 | − | 7.73247e10i | −1.42747 | − | 0.683291i | ||||
\(581\) | 6.39583e10 | 0.561297 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.25031e10 | − | 1.25031e10i | 0.108229 | − | 0.108229i | ||||
\(584\) | 1.74479e10i | 0.150001i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.77565e10 | 0.235382 | ||||||||
\(587\) | 3.68418e10 | + | 3.68418e10i | 0.310304 | + | 0.310304i | 0.845027 | − | 0.534723i | \(-0.179584\pi\) |
−0.534723 | + | 0.845027i | \(0.679584\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 5.28205e10i | − | 0.438876i | ||||||
\(590\) | 7.50308e10 | − | 2.64532e10i | 0.619201 | − | 0.218308i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.47358e10 | + | 3.47358e10i | 0.282807 | + | 0.282807i | ||||
\(593\) | −4.73580e10 | + | 4.73580e10i | −0.382979 | + | 0.382979i | −0.872174 | − | 0.489195i | \(-0.837290\pi\) |
0.489195 | + | 0.872174i | \(0.337290\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.29535e10 | + | 8.97346e10i | −0.342713 | + | 0.715966i | ||||
\(596\) | 3.72727e10 | 0.295397 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.23781e9 | − | 9.23781e9i | 0.0722378 | − | 0.0722378i | ||||
\(599\) | − | 1.11240e11i | − | 0.864076i | −0.901855 | − | 0.432038i | \(-0.857795\pi\) | ||
0.901855 | − | 0.432038i | \(-0.142205\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.47420e10 | 0.496236 | 0.248118 | − | 0.968730i | \(-0.420188\pi\) | ||||
0.248118 | + | 0.968730i | \(0.420188\pi\) | |||||||
\(602\) | −2.93777e10 | − | 2.93777e10i | −0.223682 | − | 0.223682i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.52774e11i | 1.14789i | ||||||||
\(605\) | 1.17615e11 | + | 5.62989e10i | 0.877889 | + | 0.420222i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.31206e10 | − | 8.31206e10i | −0.612285 | − | 0.612285i | 0.331256 | − | 0.943541i | \(-0.392528\pi\) |
−0.943541 | + | 0.331256i | \(0.892528\pi\) | |||||||
\(608\) | 7.29026e10 | − | 7.29026e10i | 0.533493 | − | 0.533493i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.19828e10 | − | 3.39877e10i | −0.0865447 | − | 0.245472i | ||||
\(611\) | −1.17635e10 | −0.0844057 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.95760e10 | − | 5.95760e10i | 0.421919 | − | 0.421919i | −0.463945 | − | 0.885864i | \(-0.653566\pi\) |
0.885864 | + | 0.463945i | \(0.153566\pi\) | |||||||
\(614\) | 1.44401e10i | 0.101601i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.10978e10 | 0.0770749 | ||||||||
\(617\) | −1.40069e10 | − | 1.40069e10i | −0.0966502 | − | 0.0966502i | 0.657128 | − | 0.753779i | \(-0.271771\pi\) |
−0.753779 | + | 0.657128i | \(0.771771\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.09904e11i | 1.42974i | 0.699255 | + | 0.714872i | \(0.253515\pi\) | ||||
−0.699255 | + | 0.714872i | \(0.746485\pi\) | |||||||
\(620\) | −2.83203e10 | + | 5.91642e10i | −0.191660 | + | 0.400398i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.19312e10 | − | 1.19312e10i | −0.0797118 | − | 0.0797118i | ||||
\(623\) | 8.71055e10 | − | 8.71055e10i | 0.578220 | − | 0.578220i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.25492e10 | + | 1.49076e11i | −0.213314 | + | 0.976984i | ||||
\(626\) | −1.91041e10 | −0.124403 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.61008e11 | − | 1.61008e11i | 1.03516 | − | 1.03516i | ||||
\(629\) | − | 9.89796e10i | − | 0.632329i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.62984e11 | 1.02808 | 0.514039 | − | 0.857767i | \(-0.328148\pi\) | ||||
0.514039 | + | 0.857767i | \(0.328148\pi\) | |||||||
\(632\) | 1.62846e10 | + | 1.62846e10i | 0.102072 | + | 0.102072i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.44713e10i | 0.399033i | ||||||||
\(635\) | −8.32748e10 | − | 2.36198e11i | −0.512176 | − | 1.45272i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.18346e10 | − | 1.18346e10i | −0.0718778 | − | 0.0718778i | ||||
\(638\) | 1.14665e10 | − | 1.14665e10i | 0.0692068 | − | 0.0692068i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.56579e11 | + | 5.52042e10i | −0.933283 | + | 0.329043i | ||||
\(641\) | −1.17439e11 | −0.695631 | −0.347815 | − | 0.937563i | \(-0.613076\pi\) | ||||
−0.347815 | + | 0.937563i | \(0.613076\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.23655e10 | − | 2.23655e10i | 0.130838 | − | 0.130838i | −0.638655 | − | 0.769493i | \(-0.720509\pi\) |
0.769493 | + | 0.638655i | \(0.220509\pi\) | |||||||
\(644\) | − | 1.51703e11i | − | 0.881965i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.47014e10 | −0.314100 | ||||||||
\(647\) | −1.67021e11 | − | 1.67021e11i | −0.953136 | − | 0.953136i | 0.0458137 | − | 0.998950i | \(-0.485412\pi\) |
−0.998950 | + | 0.0458137i | \(0.985412\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 5.67161e10i | − | 0.319689i | ||||||
\(650\) | −8.56329e9 | − | 1.06347e10i | −0.0479719 | − | 0.0595763i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.24719e10 | + | 4.24719e10i | 0.235023 | + | 0.235023i | ||||
\(653\) | −1.48677e9 | + | 1.48677e9i | −0.00817696 | + | 0.00817696i | −0.711183 | − | 0.703006i | \(-0.751840\pi\) |
0.703006 | + | 0.711183i | \(0.251840\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.83234e10 | + | 4.22780e10i | 0.479855 | + | 0.229694i | ||||
\(656\) | 8.47423e10 | 0.457599 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.22681e10 | − | 1.22681e10i | 0.0654444 | − | 0.0654444i | ||||
\(659\) | − | 3.54544e10i | − | 0.187987i | −0.995573 | − | 0.0939937i | \(-0.970037\pi\) | ||
0.995573 | − | 0.0939937i | \(-0.0299633\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.32084e10 | −0.278724 | −0.139362 | − | 0.990241i | \(-0.544505\pi\) | ||||
−0.139362 | + | 0.990241i | \(0.544505\pi\) | |||||||
\(662\) | −5.59467e10 | − | 5.59467e10i | −0.291302 | − | 0.291302i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 9.28885e10i | − | 0.477848i | ||||||
\(665\) | 1.20412e11 | − | 4.24530e10i | 0.615720 | − | 0.217081i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.33396e11 | − | 3.33396e11i | −1.68445 | − | 1.68445i | ||||
\(668\) | 6.63870e10 | − | 6.63870e10i | 0.333409 | − | 0.333409i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.54805e10 | + | 9.50137e10i | −0.225697 | + | 0.471506i | ||||
\(671\) | −2.56914e10 | −0.126735 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.97227e10 | + | 4.97227e10i | −0.242379 | + | 0.242379i | −0.817834 | − | 0.575455i | \(-0.804825\pi\) |
0.575455 | + | 0.817834i | \(0.304825\pi\) | |||||||
\(674\) | 9.35746e10i | 0.453438i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.75673e11 | 0.841238 | ||||||||
\(677\) | −5.21560e10 | − | 5.21560e10i | −0.248284 | − | 0.248284i | 0.571982 | − | 0.820266i | \(-0.306175\pi\) |
−0.820266 | + | 0.571982i | \(0.806175\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1.38219e11i | − | 0.650262i | ||||||
\(680\) | 1.30324e11 | + | 6.23826e10i | 0.609521 | + | 0.291761i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.19963e9 | − | 4.19963e9i | −0.0194121 | − | 0.0194121i | ||||
\(683\) | 8.03643e10 | − | 8.03643e10i | 0.369301 | − | 0.369301i | −0.497921 | − | 0.867222i | \(-0.665903\pi\) |
0.867222 | + | 0.497921i | \(0.165903\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.26113e11 | + | 3.57703e11i | 0.572794 | + | 1.62465i | ||||
\(686\) | 8.00138e10 | 0.361300 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.35325e11 | − | 1.35325e11i | 0.603981 | − | 0.603981i | ||||
\(689\) | − | 4.80804e10i | − | 0.213349i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.30282e11 | 0.571443 | 0.285722 | − | 0.958313i | \(-0.407767\pi\) | ||||
0.285722 | + | 0.958313i | \(0.407767\pi\) | |||||||
\(692\) | 2.15379e11 | + | 2.15379e11i | 0.939246 | + | 0.939246i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.16418e11i | 0.501862i | ||||||||
\(695\) | −1.03570e11 | + | 2.16370e11i | −0.443911 | + | 0.927379i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.20736e11 | − | 1.20736e11i | −0.511572 | − | 0.511572i | ||||
\(698\) | 1.04712e10 | − | 1.04712e10i | 0.0441139 | − | 0.0441139i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.57635e11 | − | 1.70086e10i | −0.656539 | − | 0.0708398i | ||||
\(701\) | −2.33961e11 | −0.968882 | −0.484441 | − | 0.874824i | \(-0.660977\pi\) | ||||
−0.484441 | + | 0.874824i | \(0.660977\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.98221e10 | + | 8.98221e10i | −0.367758 | + | 0.367758i | ||||
\(704\) | 1.54940e10i | 0.0630771i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.73179e10 | 0.311216 | ||||||||
\(707\) | 1.64165e11 | + | 1.64165e11i | 0.657055 | + | 0.657055i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.64363e10i | 0.104620i | 0.998631 | + | 0.0523102i | \(0.0166584\pi\) | ||||
−0.998631 | + | 0.0523102i | \(0.983342\pi\) | |||||||
\(710\) | −3.05803e10 | − | 8.67367e10i | −0.120340 | − | 0.341326i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.26506e11 | − | 1.26506e11i | −0.492255 | − | 0.492255i | ||||
\(713\) | −1.22107e11 | + | 1.22107e11i | −0.472478 | + | 0.472478i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.17992e9 | + | 3.23651e9i | −0.0351249 | + | 0.0123838i | ||||
\(716\) | 1.89207e11 | 0.719920 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8.29705e10 | + | 8.29705e10i | −0.312195 | + | 0.312195i | ||||
\(719\) | 4.16438e9i | 0.0155824i | 0.999970 | + | 0.00779120i | \(0.00248004\pi\) | ||||
−0.999970 | + | 0.00779120i | \(0.997520\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.23065e11 | 1.19550 | ||||||||
\(722\) | −1.48642e10 | − | 1.48642e10i | −0.0547006 | − | 0.0547006i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.34290e11i | 0.852707i | ||||||||
\(725\) | −3.83811e11 | + | 3.09052e11i | −1.38920 | + | 1.11861i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.08982e11 | − | 1.08982e11i | −0.390137 | − | 0.390137i | 0.484600 | − | 0.874736i | \(-0.338965\pi\) |
−0.874736 | + | 0.484600i | \(0.838965\pi\) | |||||||
\(728\) | 2.13381e10 | − | 2.13381e10i | 0.0759679 | − | 0.0759679i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.03584e10 | + | 9.74503e9i | 0.0716891 | + | 0.0343156i | ||||
\(731\) | −3.85607e11 | −1.35044 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.49618e10 | − | 7.49618e10i | 0.259672 | − | 0.259672i | −0.565249 | − | 0.824920i | \(-0.691220\pi\) |
0.824920 | + | 0.565249i | \(0.191220\pi\) | |||||||
\(734\) | 1.19477e11i | 0.411625i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.37062e11 | −1.14868 | ||||||||
\(737\) | 5.31001e10 | + | 5.31001e10i | 0.179980 | + | 0.179980i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 2.78382e11i | − | 0.933391i | −0.884418 | − | 0.466696i | \(-0.845444\pi\) | ||
0.884418 | − | 0.466696i | \(-0.154556\pi\) | |||||||
\(740\) | 1.48769e11 | − | 5.24506e10i | 0.496118 | − | 0.174913i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.01427e10 | + | 5.01427e10i | 0.165421 | + | 0.165421i | ||||
\(743\) | −3.99433e11 | + | 3.99433e11i | −1.31066 | + | 1.31066i | −0.389723 | + | 0.920932i | \(0.627429\pi\) |
−0.920932 | + | 0.389723i | \(0.872571\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.42792e10 | − | 9.25041e10i | 0.143739 | − | 0.300287i | ||||
\(746\) | 1.02457e11 | 0.330816 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.42424e10 | − | 3.42424e10i | 0.109385 | − | 0.109385i | ||||
\(749\) | 8.08870e10i | 0.257011i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.16261e11 | 0.994228 | 0.497114 | − | 0.867685i | \(-0.334393\pi\) | ||||
0.497114 | + | 0.867685i | \(0.334393\pi\) | |||||||
\(752\) | 5.65113e10 | + | 5.65113e10i | 0.176711 | + | 0.176711i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 4.40942e10i | − | 0.136426i | ||||||
\(755\) | 3.79157e11 | + | 1.81492e11i | 1.16689 | + | 0.558561i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.03260e10 | + | 2.03260e10i | 0.0618968 | + | 0.0618968i | 0.737378 | − | 0.675481i | \(-0.236064\pi\) |
−0.675481 | + | 0.737378i | \(0.736064\pi\) | |||||||
\(758\) | −7.58996e10 | + | 7.58996e10i | −0.229913 | + | 0.229913i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.16556e10 | − | 1.74878e11i | −0.184807 | − | 0.524179i | ||||
\(761\) | 2.39323e11 | 0.713586 | 0.356793 | − | 0.934183i | \(-0.383870\pi\) | ||||
0.356793 | + | 0.934183i | \(0.383870\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.13270e11 | + | 2.13270e11i | −0.629262 | + | 0.629262i | ||||
\(764\) | 2.62348e11i | 0.770025i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.36752e10 | −0.0397208 | ||||||||
\(767\) | −1.09050e11 | − | 1.09050e11i | −0.315097 | − | 0.315097i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.89431e11i | 1.11359i | 0.830650 | + | 0.556795i | \(0.187969\pi\) | ||||
−0.830650 | + | 0.556795i | \(0.812031\pi\) | |||||||
\(770\) | 6.19833e9 | − | 1.29490e10i | 0.0176324 | − | 0.0368361i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.77328e11 | + | 1.77328e11i | 0.499237 | + | 0.499237i | ||||
\(773\) | 2.96297e11 | − | 2.96297e11i | 0.829868 | − | 0.829868i | −0.157630 | − | 0.987498i | \(-0.550385\pi\) |
0.987498 | + | 0.157630i | \(0.0503855\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.13191e11 | + | 1.40572e11i | 0.313765 | + | 0.389664i | ||||
\(776\) | −2.00739e11 | −0.553586 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.51045e11 | − | 1.51045e11i | 0.412277 | − | 0.412277i | ||||
\(779\) | 2.19132e11i | 0.595053i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.55647e10 | −0.176224 | ||||||||
\(782\) | 1.26455e11 | + | 1.26455e11i | 0.338149 | + | 0.338149i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.13705e11i | 0.300966i | ||||||||
\(785\) | −2.08319e11 | − | 5.90867e11i | −0.548592 | − | 1.55600i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.21354e11 | + | 1.21354e11i | 0.316342 | + | 0.316342i | 0.847360 | − | 0.531019i | \(-0.178191\pi\) |
−0.531019 | + | 0.847360i | \(0.678191\pi\) | |||||||
\(788\) | 1.99363e11 | − | 1.99363e11i | 0.517058 | − | 0.517058i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.80963e10 | − | 9.90575e9i | 0.0721341 | − | 0.0254319i | ||||
\(791\) | 1.09804e11 | 0.280486 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.93979e10 | + | 4.93979e10i | −0.124915 | + | 0.124915i | ||||
\(794\) | − | 1.62683e11i | − | 0.409319i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.91050e11 | −0.724963 | ||||||||
\(797\) | −3.88575e10 | − | 3.88575e10i | −0.0963033 | − | 0.0963033i | 0.657314 | − | 0.753617i | \(-0.271693\pi\) |
−0.753617 | + | 0.657314i | \(0.771693\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.61029e11i | − | 0.395108i | ||||||
\(800\) | −3.77907e10 | + | 3.50242e11i | −0.0922624 | + | 0.855082i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.68481e10 | + | 6.68481e10i | 0.161581 | + | 0.161581i | ||||
\(803\) | 1.13777e10 | − | 1.13777e10i | 0.0273647 | − | 0.0273647i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.76500e11 | − | 1.80220e11i | −0.896564 | − | 0.429161i | ||||
\(806\) | −1.61496e10 | −0.0382667 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.38421e11 | − | 2.38421e11i | 0.559369 | − | 0.559369i | ||||
\(809\) | − | 5.38642e11i | − | 1.25749i | −0.777610 | − | 0.628747i | \(-0.783568\pi\) | ||
0.777610 | − | 0.628747i | \(-0.216432\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.26130e11 | −1.21621 | −0.608107 | − | 0.793855i | \(-0.708071\pi\) | ||||
−0.608107 | + | 0.793855i | \(0.708071\pi\) | |||||||
\(812\) | −3.62057e11 | − | 3.62057e11i | −0.832824 | − | 0.832824i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.42831e10i | 0.0325330i | ||||||||
\(815\) | 1.55863e11 | − | 5.49518e10i | 0.353275 | − | 0.124552i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.49931e11 | + | 3.49931e11i | 0.785406 | + | 0.785406i | ||||
\(818\) | 3.84370e10 | − | 3.84370e10i | 0.0858493 | − | 0.0858493i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.17490e11 | − | 2.45449e11i | 0.259863 | − | 0.542883i | ||||
\(821\) | −8.36261e10 | −0.184064 | −0.0920320 | − | 0.995756i | \(-0.529336\pi\) | ||||
−0.0920320 | + | 0.995756i | \(0.529336\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.08310e11 | − | 2.08310e11i | 0.454058 | − | 0.454058i | −0.442641 | − | 0.896699i | \(-0.645958\pi\) |
0.896699 | + | 0.442641i | \(0.145958\pi\) | |||||||
\(824\) | − | 4.69196e11i | − | 1.01776i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.27455e11 | 0.488624 | ||||||||
\(827\) | −6.03123e10 | − | 6.03123e10i | −0.128939 | − | 0.128939i | 0.639692 | − | 0.768631i | \(-0.279062\pi\) |
−0.768631 | + | 0.639692i | \(0.779062\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 7.70491e11i | − | 1.63136i | −0.578504 | − | 0.815680i | \(-0.696363\pi\) | ||
0.578504 | − | 0.815680i | \(-0.303637\pi\) | |||||||
\(830\) | −1.08383e11 | − | 5.18801e10i | −0.228375 | − | 0.109317i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.97908e10 | + | 2.97908e10i | 0.0621711 | + | 0.0621711i | ||||
\(833\) | 1.62002e11 | − | 1.62002e11i | 0.336465 | − | 0.336465i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.58942e10 | − | 2.43627e11i | −0.176692 | − | 0.501163i | ||||
\(836\) | −6.21486e10 | −0.127235 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7.31540e10 | + | 7.31540e10i | −0.148341 | + | 0.148341i | ||||
\(839\) | 2.81465e11i | 0.568037i | 0.958819 | + | 0.284018i | \(0.0916677\pi\) | ||||
−0.958819 | + | 0.284018i | \(0.908332\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.09113e12 | −2.18118 | ||||||||
\(842\) | −2.02290e10 | − | 2.02290e10i | −0.0402462 | − | 0.0402462i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.51223e10i | 0.108632i | ||||||||
\(845\) | 2.08696e11 | − | 4.35989e11i | 0.409343 | − | 0.855163i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.63608e11 | + | 2.63608e11i | 0.512183 | + | 0.512183i | ||||
\(848\) | −2.30976e11 | + | 2.30976e11i | −0.446667 | + | 0.446667i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.45577e11 | − | 1.17222e11i | 0.278880 | − | 0.224560i | ||||
\(851\) | 4.15289e11 | 0.791830 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.95360e11 | + | 3.95360e11i | −0.746787 | + | 0.746787i | −0.973874 | − | 0.227087i | \(-0.927080\pi\) |
0.227087 | + | 0.973874i | \(0.427080\pi\) | |||||||
\(854\) | − | 1.03033e11i | − | 0.193707i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.17474e11 | 0.218800 | ||||||||
\(857\) | −5.29610e11 | − | 5.29610e11i | −0.981822 | − | 0.981822i | 0.0180158 | − | 0.999838i | \(-0.494265\pi\) |
−0.999838 | + | 0.0180158i | \(0.994265\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.68396e11i | 1.04395i | 0.852962 | + | 0.521973i | \(0.174804\pi\) | ||||
−0.852962 | + | 0.521973i | \(0.825196\pi\) | |||||||
\(860\) | −2.04338e11 | − | 5.79576e11i | −0.373556 | − | 1.05954i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.01999e11 | + | 1.01999e11i | 0.184743 | + | 0.184743i | ||||
\(863\) | 2.15388e11 | − | 2.15388e11i | 0.388310 | − | 0.388310i | −0.485774 | − | 0.874084i | \(-0.661462\pi\) |
0.874084 | + | 0.485774i | \(0.161462\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.90397e11 | − | 2.78666e11i | 1.41183 | − | 0.497760i | ||||
\(866\) | 8.23682e10 | 0.146449 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.32604e11 | + | 1.32604e11i | −0.233603 | + | 0.233603i | ||||
\(869\) | − | 2.12381e10i | − | 0.0372423i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.04195e11 | 0.354791 | ||||||||
\(872\) | 3.09738e11 | + | 3.09738e11i | 0.535708 | + | 0.535708i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 2.29511e11i | − | 0.393331i | ||||||
\(875\) | −2.29479e11 | + | 3.71015e11i | −0.391481 | + | 0.632936i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.94884e11 | + | 4.94884e11i | 0.836575 | + | 0.836575i | 0.988406 | − | 0.151832i | \(-0.0485171\pi\) |
−0.151832 | + | 0.988406i | \(0.548517\pi\) | |||||||
\(878\) | −1.05523e11 | + | 1.05523e11i | −0.177569 | + | 0.177569i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.96480e10 | + | 2.85518e10i | 0.0994638 | + | 0.0476106i | ||||
\(881\) | 1.03433e12 | 1.71694 | 0.858469 | − | 0.512865i | \(-0.171416\pi\) | ||||
0.858469 | + | 0.512865i | \(0.171416\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.47773e11 | + | 7.47773e11i | −1.23006 | + | 1.23006i | −0.266123 | + | 0.963939i | \(0.585743\pi\) |
−0.963939 | + | 0.266123i | \(0.914257\pi\) | |||||||
\(884\) | − | 1.31678e11i | − | 0.215628i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.76209e11 | −0.610512 | ||||||||
\(887\) | 6.17384e11 | + | 6.17384e11i | 0.997380 | + | 0.997380i | 0.999997 | − | 0.00261651i | \(-0.000832863\pi\) |
−0.00261651 | + | 0.999997i | \(0.500833\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 7.16030e11i | − | 1.14637i | ||||||
\(890\) | −2.18264e11 | + | 7.69521e10i | −0.347874 | + | 0.122648i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.83564e10 | + | 1.83564e10i | 0.0289953 | + | 0.0289953i | ||||
\(893\) | −1.46131e11 | + | 1.46131e11i | −0.229792 | + | 0.229792i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.24773e11 | − | 4.69576e11i | 0.350310 | − | 0.731836i | ||||
\(896\) | −4.74667e11 | −0.736474 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.05964e10 | − | 2.05964e10i | 0.0316728 | − | 0.0316728i | ||||
\(899\) | 5.82844e11i | 0.892305i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.58165e11 | 0.998702 | ||||||||
\(902\) | 1.74226e10 | + | 1.74226e10i | 0.0263201 | + | 0.0263201i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 1.59471e11i | − | 0.238785i | ||||||
\(905\) | 5.81466e11 | + | 2.78332e11i | 0.866822 | + | 0.414924i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.19603e11 | + | 1.19603e11i | 0.176731 | + | 0.176731i | 0.789929 | − | 0.613198i | \(-0.210117\pi\) |
−0.613198 | + | 0.789929i | \(0.710117\pi\) | |||||||
\(908\) | −4.63541e11 | + | 4.63541e11i | −0.681938 | + | 0.681938i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.29798e10 | − | 3.68153e10i | −0.0189278 | − | 0.0536862i | ||||
\(911\) | −8.32730e11 | −1.20901 | −0.604506 | − | 0.796601i | \(-0.706629\pi\) | ||||
−0.604506 | + | 0.796601i | \(0.706629\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.05718e10 | + | 6.05718e10i | −0.0871741 | + | 0.0871741i | ||||
\(914\) | − | 1.17823e11i | − | 0.168828i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.20134e11 | −0.312683 | ||||||||
\(917\) | 1.97958e11 | + | 1.97958e11i | 0.279960 | + | 0.279960i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1.64422e11i | − | 0.230514i | −0.993336 | − | 0.115257i | \(-0.963231\pi\) | ||
0.993336 | − | 0.115257i | \(-0.0367691\pi\) | |||||||
\(920\) | −2.61739e11 | + | 5.46801e11i | −0.365356 | + | 0.763270i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.24154e11 | − | 1.24154e11i | −0.171806 | − | 0.171806i | ||||
\(923\) | −1.26064e11 | + | 1.26064e11i | −0.173693 | + | 0.173693i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.65613e10 | − | 4.31527e11i | 0.0636001 | − | 0.589442i | ||||
\(926\) | 2.21958e11 | 0.301875 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.04438e11 | + | 8.04438e11i | −1.08468 | + | 1.08468i | ||||
\(929\) | 4.23919e11i | 0.569142i | 0.958655 | + | 0.284571i | \(0.0918511\pi\) | ||||
−0.958655 | + | 0.284571i | \(0.908149\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.94027e11 | −0.391371 | ||||||||
\(932\) | −7.92525e11 | − | 7.92525e11i | −1.05039 | − | 1.05039i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.72393e11i | 0.489344i | ||||||||
\(935\) | −4.43041e10 | − | 1.25662e11i | −0.0579692 | − | 0.164422i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.39851e11 | − | 1.39851e11i | −0.181430 | − | 0.181430i | 0.610549 | − | 0.791979i | \(-0.290949\pi\) |
−0.791979 | + | 0.610549i | \(0.790949\pi\) | |||||||
\(938\) | −2.12953e11 | + | 2.12953e11i | −0.275089 | + | 0.275089i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.42030e11 | − | 8.53312e10i | 0.309997 | − | 0.109294i | ||||
\(941\) | −3.60703e11 | −0.460035 | −0.230018 | − | 0.973186i | \(-0.573878\pi\) | ||||
−0.230018 | + | 0.973186i | \(0.573878\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.06574e11 | − | 5.06574e11i | 0.640614 | − | 0.640614i | ||||
\(944\) | 1.04774e12i | 1.31937i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.56443e10 | 0.0694794 | ||||||||
\(947\) | 6.11835e11 | + | 6.11835e11i | 0.760737 | + | 0.760737i | 0.976456 | − | 0.215718i | \(-0.0692093\pi\) |
−0.215718 | + | 0.976456i | \(0.569209\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 4.37525e10i | − | 0.0539434i | ||||||
\(950\) | −2.38485e11 | − | 2.57323e10i | −0.292797 | − | 0.0315925i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.92094e11 | + | 2.92094e11i | 0.355611 | + | 0.355611i | ||||
\(953\) | 3.04156e11 | − | 3.04156e11i | 0.368744 | − | 0.368744i | −0.498275 | − | 0.867019i | \(-0.666033\pi\) |
0.867019 | + | 0.498275i | \(0.166033\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.51101e11 | + | 3.11664e11i | 0.782771 | + | 0.374691i | ||||
\(956\) | −7.35460e11 | −0.880497 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.79360e11 | + | 2.79360e11i | −0.331667 | + | 0.331667i | ||||
\(959\) | 1.08437e12i | 1.28205i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.39424e11 | −0.749713 | ||||||||
\(962\) | 2.74626e10 | + | 2.74626e10i | 0.0320657 | + | 0.0320657i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 1.31930e12i | − | 1.52769i | ||||||
\(965\) | 6.50756e11 | − | 2.29433e11i | 0.750428 | − | 0.264574i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.65811e11 | + | 6.65811e11i | 0.761457 | + | 0.761457i | 0.976586 | − | 0.215129i | \(-0.0690172\pi\) |
−0.215129 | + | 0.976586i | \(0.569017\pi\) | |||||||
\(968\) | 3.82845e11 | − | 3.82845e11i | 0.436036 | − | 0.436036i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.12117e11 | + | 2.34224e11i | −0.126644 | + | 0.264573i | ||||
\(971\) | 1.11212e12 | 1.25105 | 0.625525 | − | 0.780205i | \(-0.284885\pi\) | ||||
0.625525 | + | 0.780205i | \(0.284885\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.84947e11 | + | 4.84947e11i | −0.541057 | + | 0.541057i | ||||
\(974\) | − | 1.88239e11i | − | 0.209157i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.74610e11 | 0.523043 | ||||||||
\(977\) | 7.14891e10 | + | 7.14891e10i | 0.0784624 | + | 0.0784624i | 0.745249 | − | 0.666786i | \(-0.232331\pi\) |
−0.666786 | + | 0.745249i | \(0.732331\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.64987e11i | 0.179605i | ||||||||
\(980\) | 3.29339e11 | + | 1.57646e11i | 0.357058 | + | 0.170914i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −8.98126e10 | − | 8.98126e10i | −0.0965810 | − | 0.0965810i | ||||
\(983\) | −5.26321e11 | + | 5.26321e11i | −0.563685 | + | 0.563685i | −0.930352 | − | 0.366667i | \(-0.880499\pi\) |
0.366667 | + | 0.930352i | \(0.380499\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.57943e11 | − | 7.31621e11i | −0.274018 | − | 0.777215i | ||||
\(986\) | 6.03598e11 | 0.638617 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.19495e11 | + | 1.19495e11i | −0.125407 | + | 0.125407i | ||||
\(989\) | − | 1.61789e12i | − | 1.69108i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.21186e12 | −1.25649 | −0.628245 | − | 0.778016i | \(-0.716226\pi\) | ||||
−0.628245 | + | 0.778016i | \(0.716226\pi\) | |||||||
\(992\) | 2.94627e11 | + | 2.94627e11i | 0.304246 | + | 0.304246i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 2.62941e11i | − | 0.269348i | ||||||
\(995\) | −3.45761e11 | + | 7.22334e11i | −0.352764 | + | 0.736963i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.69885e11 | − | 5.69885e11i | −0.576775 | − | 0.576775i | 0.357238 | − | 0.934013i | \(-0.383718\pi\) |
−0.934013 | + | 0.357238i | \(0.883718\pi\) | |||||||
\(998\) | −3.07249e11 | + | 3.07249e11i | −0.309720 | + | 0.309720i | ||||
\(999\) | 0 | 0 |
(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 | 45.9.g.b.37.4 | yes | 16 | |
3.2 | odd | 2 | inner | 45.9.g.b.37.5 | yes | 16 | |
5.3 | odd | 4 | inner | 45.9.g.b.28.4 | ✓ | 16 | |
15.8 | even | 4 | inner | 45.9.g.b.28.5 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.9.g.b.28.4 | ✓ | 16 | 5.3 | odd | 4 | inner | |
45.9.g.b.28.5 | yes | 16 | 15.8 | even | 4 | inner | |
45.9.g.b.37.4 | yes | 16 | 1.1 | even | 1 | trivial | |
45.9.g.b.37.5 | yes | 16 | 3.2 | odd | 2 | inner |