Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,10,Mod(9,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.9");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.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: | \(5.15035836164\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{319})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 159x^{2} + 6400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{10}\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 9.1 | ||
Root | \(8.93029 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.9 |
Dual form | 10.10.b.a.9.4 |
$q$-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 \(\left(\mathbb{Z}/10\mathbb{Z}\right)^\times\).
\(n\) | \(7\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 16.0000i | − | 0.707107i | ||||||
\(3\) | − | 254.606i | − | 1.81477i | −0.420296 | − | 0.907387i | \(-0.638074\pi\) | ||
0.420296 | − | 0.907387i | \(-0.361926\pi\) | |||||||
\(4\) | −256.000 | −0.500000 | ||||||||
\(5\) | 69.4228 | + | 1395.82i | 0.0496749 | + | 0.998765i | ||||
\(6\) | −4073.69 | −1.28324 | ||||||||
\(7\) | − | 4788.05i | − | 0.753732i | −0.926268 | − | 0.376866i | \(-0.877002\pi\) | ||
0.926268 | − | 0.376866i | \(-0.122998\pi\) | |||||||
\(8\) | 4096.00i | 0.353553i | ||||||||
\(9\) | −45141.1 | −2.29340 | ||||||||
\(10\) | 22333.1 | − | 1110.77i | 0.706234 | − | 0.0351255i | ||||
\(11\) | 22672.8 | 0.466914 | 0.233457 | − | 0.972367i | \(-0.424996\pi\) | ||||
0.233457 | + | 0.972367i | \(0.424996\pi\) | |||||||
\(12\) | 65179.1i | 0.907387i | ||||||||
\(13\) | − | 131546.i | − | 1.27742i | −0.769447 | − | 0.638711i | \(-0.779468\pi\) | ||
0.769447 | − | 0.638711i | \(-0.220532\pi\) | |||||||
\(14\) | −76608.7 | −0.532969 | ||||||||
\(15\) | 355383. | − | 17675.5i | 1.81253 | − | 0.0901488i | ||||
\(16\) | 65536.0 | 0.250000 | ||||||||
\(17\) | − | 16522.2i | − | 0.0479787i | −0.999712 | − | 0.0239894i | \(-0.992363\pi\) | ||
0.999712 | − | 0.0239894i | \(-0.00763679\pi\) | |||||||
\(18\) | 722257.i | 1.62168i | ||||||||
\(19\) | 173684. | 0.305751 | 0.152876 | − | 0.988245i | \(-0.451147\pi\) | ||||
0.152876 | + | 0.988245i | \(0.451147\pi\) | |||||||
\(20\) | −17772.2 | − | 357329.i | −0.0248375 | − | 0.499383i | ||||
\(21\) | −1.21906e6 | −1.36785 | ||||||||
\(22\) | − | 362764.i | − | 0.330158i | ||||||
\(23\) | − | 2.08964e6i | − | 1.55703i | −0.627626 | − | 0.778515i | \(-0.715973\pi\) | ||
0.627626 | − | 0.778515i | \(-0.284027\pi\) | |||||||
\(24\) | 1.04286e6 | 0.641619 | ||||||||
\(25\) | −1.94349e6 | + | 193803.i | −0.995065 | + | 0.0992272i | ||||
\(26\) | −2.10474e6 | −0.903273 | ||||||||
\(27\) | 6.48177e6i | 2.34724i | ||||||||
\(28\) | 1.22574e6i | 0.376866i | ||||||||
\(29\) | 4.08468e6 | 1.07242 | 0.536212 | − | 0.844083i | \(-0.319855\pi\) | ||||
0.536212 | + | 0.844083i | \(0.319855\pi\) | |||||||
\(30\) | −282807. | − | 5.68613e6i | −0.0637448 | − | 1.28165i | ||||
\(31\) | 2.73719e6 | 0.532325 | 0.266163 | − | 0.963928i | \(-0.414244\pi\) | ||||
0.266163 | + | 0.963928i | \(0.414244\pi\) | |||||||
\(32\) | − | 1.04858e6i | − | 0.176777i | ||||||
\(33\) | − | 5.77261e6i | − | 0.847344i | ||||||
\(34\) | −264356. | −0.0339261 | ||||||||
\(35\) | 6.68324e6 | − | 332400.i | 0.752802 | − | 0.0374416i | ||||
\(36\) | 1.15561e7 | 1.14670 | ||||||||
\(37\) | 1.32992e7i | 1.16659i | 0.812261 | + | 0.583294i | \(0.198236\pi\) | ||||
−0.812261 | + | 0.583294i | \(0.801764\pi\) | |||||||
\(38\) | − | 2.77894e6i | − | 0.216199i | ||||||
\(39\) | −3.34925e7 | −2.31823 | ||||||||
\(40\) | −5.71727e6 | + | 284356.i | −0.353117 | + | 0.0175627i | ||||
\(41\) | 1.49196e7 | 0.824575 | 0.412288 | − | 0.911054i | \(-0.364730\pi\) | ||||
0.412288 | + | 0.911054i | \(0.364730\pi\) | |||||||
\(42\) | 1.95050e7i | 0.967218i | ||||||||
\(43\) | 2.38880e6i | 0.106554i | 0.998580 | + | 0.0532772i | \(0.0169667\pi\) | ||||
−0.998580 | + | 0.0532772i | \(0.983033\pi\) | |||||||
\(44\) | −5.80422e6 | −0.233457 | ||||||||
\(45\) | −3.13382e6 | − | 6.30087e7i | −0.113925 | − | 2.29057i | ||||
\(46\) | −3.34343e7 | −1.10099 | ||||||||
\(47\) | 2.41417e7i | 0.721650i | 0.932634 | + | 0.360825i | \(0.117505\pi\) | ||||
−0.932634 | + | 0.360825i | \(0.882495\pi\) | |||||||
\(48\) | − | 1.66858e7i | − | 0.453693i | ||||||
\(49\) | 1.74282e7 | 0.431888 | ||||||||
\(50\) | 3.10085e6 | + | 3.10958e7i | 0.0701642 | + | 0.703617i | ||||
\(51\) | −4.20666e6 | −0.0870706 | ||||||||
\(52\) | 3.36759e7i | 0.638711i | ||||||||
\(53\) | − | 1.58870e7i | − | 0.276568i | −0.990393 | − | 0.138284i | \(-0.955841\pi\) | ||
0.990393 | − | 0.138284i | \(-0.0441586\pi\) | |||||||
\(54\) | 1.03708e8 | 1.65975 | ||||||||
\(55\) | 1.57401e6 | + | 3.16470e7i | 0.0231939 | + | 0.466338i | ||||
\(56\) | 1.96118e7 | 0.266485 | ||||||||
\(57\) | − | 4.42209e7i | − | 0.554869i | ||||||
\(58\) | − | 6.53548e7i | − | 0.758319i | ||||||
\(59\) | 9.17479e7 | 0.985739 | 0.492870 | − | 0.870103i | \(-0.335948\pi\) | ||||
0.492870 | + | 0.870103i | \(0.335948\pi\) | |||||||
\(60\) | −9.09781e7 | + | 4.52492e6i | −0.906267 | + | 0.0450744i | ||||
\(61\) | −9.24480e7 | −0.854896 | −0.427448 | − | 0.904040i | \(-0.640587\pi\) | ||||
−0.427448 | + | 0.904040i | \(0.640587\pi\) | |||||||
\(62\) | − | 4.37950e7i | − | 0.376411i | ||||||
\(63\) | 2.16137e8i | 1.72861i | ||||||||
\(64\) | −1.67772e7 | −0.125000 | ||||||||
\(65\) | 1.83615e8 | − | 9.13233e6i | 1.27584 | − | 0.0634558i | ||||
\(66\) | −9.23618e7 | −0.599163 | ||||||||
\(67\) | − | 5.16583e7i | − | 0.313187i | −0.987663 | − | 0.156593i | \(-0.949949\pi\) | ||
0.987663 | − | 0.156593i | \(-0.0500512\pi\) | |||||||
\(68\) | 4.22969e6i | 0.0239894i | ||||||||
\(69\) | −5.32035e8 | −2.82566 | ||||||||
\(70\) | −5.31840e6 | − | 1.06932e8i | −0.0264752 | − | 0.532311i | ||||
\(71\) | 1.36557e8 | 0.637751 | 0.318876 | − | 0.947797i | \(-0.396695\pi\) | ||||
0.318876 | + | 0.947797i | \(0.396695\pi\) | |||||||
\(72\) | − | 1.84898e8i | − | 0.810841i | ||||||
\(73\) | − | 2.97223e8i | − | 1.22498i | −0.790478 | − | 0.612491i | \(-0.790168\pi\) | ||
0.790478 | − | 0.612491i | \(-0.209832\pi\) | |||||||
\(74\) | 2.12787e8 | 0.824902 | ||||||||
\(75\) | 4.93434e7 | + | 4.94823e8i | 0.180075 | + | 1.80582i | ||||
\(76\) | −4.44631e7 | −0.152876 | ||||||||
\(77\) | − | 1.08558e8i | − | 0.351928i | ||||||
\(78\) | 5.35880e8i | 1.63924i | ||||||||
\(79\) | −3.08136e8 | −0.890062 | −0.445031 | − | 0.895515i | \(-0.646807\pi\) | ||||
−0.445031 | + | 0.895515i | \(0.646807\pi\) | |||||||
\(80\) | 4.54970e6 | + | 9.14763e7i | 0.0124187 | + | 0.249691i | ||||
\(81\) | 7.61784e8 | 1.96630 | ||||||||
\(82\) | − | 2.38714e8i | − | 0.583063i | ||||||
\(83\) | 6.97423e7i | 0.161304i | 0.996742 | + | 0.0806519i | \(0.0257002\pi\) | ||||
−0.996742 | + | 0.0806519i | \(0.974300\pi\) | |||||||
\(84\) | 3.12080e8 | 0.683927 | ||||||||
\(85\) | 2.30620e7 | − | 1.14702e6i | 0.0479195 | − | 0.00238334i | ||||
\(86\) | 3.82208e7 | 0.0753453 | ||||||||
\(87\) | − | 1.03998e9i | − | 1.94621i | ||||||
\(88\) | 9.28676e7i | 0.165079i | ||||||||
\(89\) | 7.43324e8 | 1.25581 | 0.627904 | − | 0.778291i | \(-0.283913\pi\) | ||||
0.627904 | + | 0.778291i | \(0.283913\pi\) | |||||||
\(90\) | −1.00814e9 | + | 5.01411e7i | −1.61968 | + | 0.0805569i | ||||
\(91\) | −6.29850e8 | −0.962834 | ||||||||
\(92\) | 5.34949e8i | 0.778515i | ||||||||
\(93\) | − | 6.96904e8i | − | 0.966050i | ||||||
\(94\) | 3.86266e8 | 0.510284 | ||||||||
\(95\) | 1.20576e7 | + | 2.42431e8i | 0.0151882 | + | 0.305374i | ||||
\(96\) | −2.66973e8 | −0.320810 | ||||||||
\(97\) | 1.60553e9i | 1.84139i | 0.390284 | + | 0.920694i | \(0.372377\pi\) | ||||
−0.390284 | + | 0.920694i | \(0.627623\pi\) | |||||||
\(98\) | − | 2.78852e8i | − | 0.305391i | ||||||
\(99\) | −1.02347e9 | −1.07082 | ||||||||
\(100\) | 4.97532e8 | − | 4.96136e7i | 0.497532 | − | 0.0496136i | ||||
\(101\) | −1.27833e9 | −1.22236 | −0.611178 | − | 0.791494i | \(-0.709304\pi\) | ||||
−0.611178 | + | 0.791494i | \(0.709304\pi\) | |||||||
\(102\) | 6.73065e7i | 0.0615682i | ||||||||
\(103\) | 1.66282e9i | 1.45572i | 0.685725 | + | 0.727861i | \(0.259485\pi\) | ||||
−0.685725 | + | 0.727861i | \(0.740515\pi\) | |||||||
\(104\) | 5.38814e8 | 0.451637 | ||||||||
\(105\) | −8.46309e7 | − | 1.70159e9i | −0.0679480 | − | 1.36616i | ||||
\(106\) | −2.54193e8 | −0.195563 | ||||||||
\(107\) | − | 1.90635e9i | − | 1.40597i | −0.711207 | − | 0.702983i | \(-0.751851\pi\) | ||
0.711207 | − | 0.702983i | \(-0.248149\pi\) | |||||||
\(108\) | − | 1.65933e9i | − | 1.17362i | ||||||
\(109\) | −6.12845e8 | −0.415845 | −0.207922 | − | 0.978145i | \(-0.566670\pi\) | ||||
−0.207922 | + | 0.978145i | \(0.566670\pi\) | |||||||
\(110\) | 5.06352e8 | − | 2.51841e7i | 0.329751 | − | 0.0164006i | ||||
\(111\) | 3.38605e9 | 2.11709 | ||||||||
\(112\) | − | 3.13789e8i | − | 0.188433i | ||||||
\(113\) | 1.52122e9i | 0.877687i | 0.898564 | + | 0.438843i | \(0.144612\pi\) | ||||
−0.898564 | + | 0.438843i | \(0.855388\pi\) | |||||||
\(114\) | −7.07534e8 | −0.392352 | ||||||||
\(115\) | 2.91676e9 | − | 1.45069e8i | 1.55511 | − | 0.0773454i | ||||
\(116\) | −1.04568e9 | −0.536212 | ||||||||
\(117\) | 5.93815e9i | 2.92964i | ||||||||
\(118\) | − | 1.46797e9i | − | 0.697023i | ||||||
\(119\) | −7.91092e7 | −0.0361631 | ||||||||
\(120\) | 7.23987e7 | + | 1.45565e9i | 0.0318724 | + | 0.640827i | ||||
\(121\) | −1.84389e9 | −0.781991 | ||||||||
\(122\) | 1.47917e9i | 0.604503i | ||||||||
\(123\) | − | 3.79862e9i | − | 1.49642i | ||||||
\(124\) | −7.00720e8 | −0.266163 | ||||||||
\(125\) | −4.05436e8 | − | 2.69930e9i | −0.148535 | − | 0.988907i | ||||
\(126\) | 3.45820e9 | 1.22231 | ||||||||
\(127\) | − | 4.88293e8i | − | 0.166557i | −0.996526 | − | 0.0832787i | \(-0.973461\pi\) | ||
0.996526 | − | 0.0832787i | \(-0.0265392\pi\) | |||||||
\(128\) | 2.68435e8i | 0.0883883i | ||||||||
\(129\) | 6.08202e8 | 0.193372 | ||||||||
\(130\) | −1.46117e8 | − | 2.93784e9i | −0.0448700 | − | 0.902158i | ||||
\(131\) | −4.98938e9 | −1.48022 | −0.740110 | − | 0.672486i | \(-0.765226\pi\) | ||||
−0.740110 | + | 0.672486i | \(0.765226\pi\) | |||||||
\(132\) | 1.47779e9i | 0.423672i | ||||||||
\(133\) | − | 8.31606e8i | − | 0.230455i | ||||||
\(134\) | −8.26533e8 | −0.221457 | ||||||||
\(135\) | −9.04736e9 | + | 4.49983e8i | −2.34434 | + | 0.116599i | ||||
\(136\) | 6.76751e7 | 0.0169630 | ||||||||
\(137\) | − | 1.31314e9i | − | 0.318470i | −0.987241 | − | 0.159235i | \(-0.949097\pi\) | ||
0.987241 | − | 0.159235i | \(-0.0509028\pi\) | |||||||
\(138\) | 8.51256e9i | 1.99804i | ||||||||
\(139\) | 6.81739e9 | 1.54900 | 0.774500 | − | 0.632574i | \(-0.218002\pi\) | ||||
0.774500 | + | 0.632574i | \(0.218002\pi\) | |||||||
\(140\) | −1.71091e9 | + | 8.50943e7i | −0.376401 | + | 0.0187208i | ||||
\(141\) | 6.14660e9 | 1.30963 | ||||||||
\(142\) | − | 2.18491e9i | − | 0.450958i | ||||||
\(143\) | − | 2.98252e9i | − | 0.596446i | ||||||
\(144\) | −2.95837e9 | −0.573351 | ||||||||
\(145\) | 2.83570e8 | + | 5.70146e9i | 0.0532726 | + | 1.07110i | ||||
\(146\) | −4.75557e9 | −0.866193 | ||||||||
\(147\) | − | 4.43733e9i | − | 0.783778i | ||||||
\(148\) | − | 3.40459e9i | − | 0.583294i | ||||||
\(149\) | 3.84585e9 | 0.639226 | 0.319613 | − | 0.947548i | \(-0.396447\pi\) | ||||
0.319613 | + | 0.947548i | \(0.396447\pi\) | |||||||
\(150\) | 7.91716e9 | − | 7.89494e8i | 1.27691 | − | 0.127332i | ||||
\(151\) | 4.08263e9 | 0.639063 | 0.319532 | − | 0.947576i | \(-0.396474\pi\) | ||||
0.319532 | + | 0.947576i | \(0.396474\pi\) | |||||||
\(152\) | 7.11409e8i | 0.108099i | ||||||||
\(153\) | 7.45832e8i | 0.110035i | ||||||||
\(154\) | −1.73693e9 | −0.248851 | ||||||||
\(155\) | 1.90023e8 | + | 3.82061e9i | 0.0264432 | + | 0.531668i | ||||
\(156\) | 8.57408e9 | 1.15912 | ||||||||
\(157\) | − | 4.74150e8i | − | 0.0622826i | −0.999515 | − | 0.0311413i | \(-0.990086\pi\) | ||
0.999515 | − | 0.0311413i | \(-0.00991419\pi\) | |||||||
\(158\) | 4.93017e9i | 0.629369i | ||||||||
\(159\) | −4.04493e9 | −0.501908 | ||||||||
\(160\) | 1.46362e9 | − | 7.27951e7i | 0.176558 | − | 0.00878137i | ||||
\(161\) | −1.00053e10 | −1.17358 | ||||||||
\(162\) | − | 1.21885e10i | − | 1.39038i | ||||||
\(163\) | 5.77882e9i | 0.641203i | 0.947214 | + | 0.320601i | \(0.103885\pi\) | ||||
−0.947214 | + | 0.320601i | \(0.896115\pi\) | |||||||
\(164\) | −3.81942e9 | −0.412288 | ||||||||
\(165\) | 8.05751e9 | − | 4.00751e8i | 0.846298 | − | 0.0420918i | ||||
\(166\) | 1.11588e9 | 0.114059 | ||||||||
\(167\) | 3.79221e9i | 0.377284i | 0.982046 | + | 0.188642i | \(0.0604085\pi\) | ||||
−0.982046 | + | 0.188642i | \(0.939591\pi\) | |||||||
\(168\) | − | 4.99329e9i | − | 0.483609i | ||||||
\(169\) | −6.69997e9 | −0.631805 | ||||||||
\(170\) | −1.83523e7 | − | 3.68992e8i | −0.00168528 | − | 0.0338842i | ||||
\(171\) | −7.84027e9 | −0.701211 | ||||||||
\(172\) | − | 6.11532e8i | − | 0.0532772i | ||||||
\(173\) | 1.42923e9i | 0.121310i | 0.998159 | + | 0.0606548i | \(0.0193189\pi\) | ||||
−0.998159 | + | 0.0606548i | \(0.980681\pi\) | |||||||
\(174\) | −1.66397e10 | −1.37618 | ||||||||
\(175\) | 9.27939e8 | + | 9.30550e9i | 0.0747908 | + | 0.750012i | ||||
\(176\) | 1.48588e9 | 0.116729 | ||||||||
\(177\) | − | 2.33595e10i | − | 1.78889i | ||||||
\(178\) | − | 1.18932e10i | − | 0.887990i | ||||||
\(179\) | 1.24763e10 | 0.908340 | 0.454170 | − | 0.890915i | \(-0.349936\pi\) | ||||
0.454170 | + | 0.890915i | \(0.349936\pi\) | |||||||
\(180\) | 8.02258e8 | + | 1.61302e10i | 0.0569624 | + | 1.14529i | ||||
\(181\) | −1.08573e10 | −0.751913 | −0.375956 | − | 0.926637i | \(-0.622686\pi\) | ||||
−0.375956 | + | 0.926637i | \(0.622686\pi\) | |||||||
\(182\) | 1.00776e10i | 0.680826i | ||||||||
\(183\) | 2.35378e10i | 1.55144i | ||||||||
\(184\) | 8.55918e9 | 0.550493 | ||||||||
\(185\) | −1.85632e10 | + | 9.23268e8i | −1.16515 | + | 0.0579502i | ||||
\(186\) | −1.11505e10 | −0.683100 | ||||||||
\(187\) | − | 3.74605e8i | − | 0.0224020i | ||||||
\(188\) | − | 6.18026e9i | − | 0.360825i | ||||||
\(189\) | 3.10350e10 | 1.76919 | ||||||||
\(190\) | 3.87889e9 | − | 1.92922e8i | 0.215932 | − | 0.0107397i | ||||
\(191\) | 2.91949e10 | 1.58729 | 0.793646 | − | 0.608379i | \(-0.208180\pi\) | ||||
0.793646 | + | 0.608379i | \(0.208180\pi\) | |||||||
\(192\) | 4.27158e9i | 0.226847i | ||||||||
\(193\) | − | 5.33710e8i | − | 0.0276883i | −0.999904 | − | 0.0138442i | \(-0.995593\pi\) | ||
0.999904 | − | 0.0138442i | \(-0.00440688\pi\) | |||||||
\(194\) | 2.56885e10 | 1.30206 | ||||||||
\(195\) | −2.32514e9 | − | 4.67494e10i | −0.115158 | − | 2.31537i | ||||
\(196\) | −4.46163e9 | −0.215944 | ||||||||
\(197\) | − | 2.85727e10i | − | 1.35162i | −0.737077 | − | 0.675809i | \(-0.763795\pi\) | ||
0.737077 | − | 0.675809i | \(-0.236205\pi\) | |||||||
\(198\) | 1.63756e10i | 0.757186i | ||||||||
\(199\) | −2.44466e10 | −1.10504 | −0.552522 | − | 0.833498i | \(-0.686334\pi\) | ||||
−0.552522 | + | 0.833498i | \(0.686334\pi\) | |||||||
\(200\) | −7.93818e8 | − | 7.96052e9i | −0.0350821 | − | 0.351809i | ||||
\(201\) | −1.31525e10 | −0.568363 | ||||||||
\(202\) | 2.04533e10i | 0.864336i | ||||||||
\(203\) | − | 1.95576e10i | − | 0.808321i | ||||||
\(204\) | 1.07690e9 | 0.0435353 | ||||||||
\(205\) | 1.03576e9 | + | 2.08251e10i | 0.0409607 | + | 0.823557i | ||||
\(206\) | 2.66051e10 | 1.02935 | ||||||||
\(207\) | 9.43287e10i | 3.57090i | ||||||||
\(208\) | − | 8.62103e9i | − | 0.319355i | ||||||
\(209\) | 3.93789e9 | 0.142760 | ||||||||
\(210\) | −2.72254e10 | + | 1.35409e9i | −0.966024 | + | 0.0480465i | ||||
\(211\) | 2.94476e10 | 1.02277 | 0.511385 | − | 0.859351i | \(-0.329132\pi\) | ||||
0.511385 | + | 0.859351i | \(0.329132\pi\) | |||||||
\(212\) | 4.06708e9i | 0.138284i | ||||||||
\(213\) | − | 3.47682e10i | − | 1.15737i | ||||||
\(214\) | −3.05015e10 | −0.994168 | ||||||||
\(215\) | −3.33433e9 | + | 1.65837e8i | −0.106423 | + | 0.00529308i | ||||
\(216\) | −2.65493e10 | −0.829873 | ||||||||
\(217\) | − | 1.31058e10i | − | 0.401231i | ||||||
\(218\) | 9.80551e9i | 0.294047i | ||||||||
\(219\) | −7.56747e10 | −2.22307 | ||||||||
\(220\) | −4.02946e8 | − | 8.10164e9i | −0.0115970 | − | 0.233169i | ||||
\(221\) | −2.17344e9 | −0.0612891 | ||||||||
\(222\) | − | 5.41768e10i | − | 1.49701i | ||||||
\(223\) | − | 3.39795e10i | − | 0.920123i | −0.887887 | − | 0.460061i | \(-0.847827\pi\) | ||
0.887887 | − | 0.460061i | \(-0.152173\pi\) | |||||||
\(224\) | −5.02063e9 | −0.133242 | ||||||||
\(225\) | 8.77310e10 | − | 8.74848e9i | 2.28209 | − | 0.227568i | ||||
\(226\) | 2.43395e10 | 0.620618 | ||||||||
\(227\) | 1.56120e10i | 0.390250i | 0.980778 | + | 0.195125i | \(0.0625112\pi\) | ||||
−0.980778 | + | 0.195125i | \(0.937489\pi\) | |||||||
\(228\) | 1.13205e10i | 0.277435i | ||||||||
\(229\) | −5.39130e10 | −1.29549 | −0.647744 | − | 0.761858i | \(-0.724287\pi\) | ||||
−0.647744 | + | 0.761858i | \(0.724287\pi\) | |||||||
\(230\) | −2.32110e9 | − | 4.66682e10i | −0.0546914 | − | 1.09963i | ||||
\(231\) | −2.76395e10 | −0.638670 | ||||||||
\(232\) | 1.67308e10i | 0.379159i | ||||||||
\(233\) | 7.59413e10i | 1.68802i | 0.536330 | + | 0.844008i | \(0.319810\pi\) | ||||
−0.536330 | + | 0.844008i | \(0.680190\pi\) | |||||||
\(234\) | 9.50104e10 | 2.07157 | ||||||||
\(235\) | −3.36973e10 | + | 1.67598e9i | −0.720759 | + | 0.0358479i | ||||
\(236\) | −2.34875e10 | −0.492870 | ||||||||
\(237\) | 7.84532e10i | 1.61526i | ||||||||
\(238\) | 1.26575e9i | 0.0255712i | ||||||||
\(239\) | 6.70401e10 | 1.32906 | 0.664529 | − | 0.747262i | \(-0.268632\pi\) | ||||
0.664529 | + | 0.747262i | \(0.268632\pi\) | |||||||
\(240\) | 2.32904e10 | − | 1.15838e9i | 0.453133 | − | 0.0225372i | ||||
\(241\) | 3.19687e10 | 0.610447 | 0.305223 | − | 0.952281i | \(-0.401269\pi\) | ||||
0.305223 | + | 0.952281i | \(0.401269\pi\) | |||||||
\(242\) | 2.95023e10i | 0.552951i | ||||||||
\(243\) | − | 6.63739e10i | − | 1.22115i | ||||||
\(244\) | 2.36667e10 | 0.427448 | ||||||||
\(245\) | 1.20992e9 | + | 2.43266e10i | 0.0214540 | + | 0.431355i | ||||
\(246\) | −6.07779e10 | −1.05813 | ||||||||
\(247\) | − | 2.28475e10i | − | 0.390573i | ||||||
\(248\) | 1.12115e10i | 0.188205i | ||||||||
\(249\) | 1.77568e10 | 0.292730 | ||||||||
\(250\) | −4.31887e10 | + | 6.48698e9i | −0.699263 | + | 0.105030i | ||||
\(251\) | 7.52832e10 | 1.19720 | 0.598600 | − | 0.801048i | \(-0.295724\pi\) | ||||
0.598600 | + | 0.801048i | \(0.295724\pi\) | |||||||
\(252\) | − | 5.53312e10i | − | 0.864306i | ||||||
\(253\) | − | 4.73780e10i | − | 0.727000i | ||||||
\(254\) | −7.81269e9 | −0.117774 | ||||||||
\(255\) | −2.92038e8 | − | 5.87172e9i | −0.00432522 | − | 0.0869631i | ||||
\(256\) | 4.29497e9 | 0.0625000 | ||||||||
\(257\) | − | 8.40723e10i | − | 1.20214i | −0.799197 | − | 0.601069i | \(-0.794742\pi\) | ||
0.799197 | − | 0.601069i | \(-0.205258\pi\) | |||||||
\(258\) | − | 9.73123e9i | − | 0.136735i | ||||||
\(259\) | 6.36771e10 | 0.879295 | ||||||||
\(260\) | −4.70054e10 | + | 2.33788e9i | −0.637922 | + | 0.0317279i | ||||
\(261\) | −1.84387e11 | −2.45950 | ||||||||
\(262\) | 7.98301e10i | 1.04667i | ||||||||
\(263\) | 1.14528e11i | 1.47608i | 0.674758 | + | 0.738039i | \(0.264248\pi\) | ||||
−0.674758 | + | 0.738039i | \(0.735752\pi\) | |||||||
\(264\) | 2.36446e10 | 0.299581 | ||||||||
\(265\) | 2.21754e10 | − | 1.10292e9i | 0.276226 | − | 0.0137385i | ||||
\(266\) | −1.33057e10 | −0.162956 | ||||||||
\(267\) | − | 1.89255e11i | − | 2.27901i | ||||||
\(268\) | 1.32245e10i | 0.156593i | ||||||||
\(269\) | −9.83288e10 | −1.14497 | −0.572487 | − | 0.819914i | \(-0.694021\pi\) | ||||
−0.572487 | + | 0.819914i | \(0.694021\pi\) | |||||||
\(270\) | 7.19973e9 | + | 1.44758e11i | 0.0824478 | + | 1.65770i | ||||
\(271\) | −2.22694e9 | −0.0250811 | −0.0125406 | − | 0.999921i | \(-0.503992\pi\) | ||||
−0.0125406 | + | 0.999921i | \(0.503992\pi\) | |||||||
\(272\) | − | 1.08280e9i | − | 0.0119947i | ||||||
\(273\) | 1.60364e11i | 1.74733i | ||||||||
\(274\) | −2.10103e10 | −0.225193 | ||||||||
\(275\) | −4.40642e10 | + | 4.39405e9i | −0.464610 | + | 0.0463306i | ||||
\(276\) | 1.36201e11 | 1.41283 | ||||||||
\(277\) | 2.36816e10i | 0.241686i | 0.992672 | + | 0.120843i | \(0.0385598\pi\) | ||||
−0.992672 | + | 0.120843i | \(0.961440\pi\) | |||||||
\(278\) | − | 1.09078e11i | − | 1.09531i | ||||||
\(279\) | −1.23560e11 | −1.22084 | ||||||||
\(280\) | 1.36151e9 | + | 2.73745e10i | 0.0132376 | + | 0.266156i | ||||
\(281\) | 1.30111e9 | 0.0124490 | 0.00622451 | − | 0.999981i | \(-0.498019\pi\) | ||||
0.00622451 | + | 0.999981i | \(0.498019\pi\) | |||||||
\(282\) | − | 9.83456e10i | − | 0.926049i | ||||||
\(283\) | − | 1.62403e11i | − | 1.50507i | −0.658553 | − | 0.752534i | \(-0.728831\pi\) | ||
0.658553 | − | 0.752534i | \(-0.271169\pi\) | |||||||
\(284\) | −3.49586e10 | −0.318876 | ||||||||
\(285\) | 6.17243e10 | − | 3.06994e9i | 0.554184 | − | 0.0275631i | ||||
\(286\) | −4.77203e10 | −0.421751 | ||||||||
\(287\) | − | 7.14358e10i | − | 0.621509i | ||||||
\(288\) | 4.73338e10i | 0.405420i | ||||||||
\(289\) | 1.18315e11 | 0.997698 | ||||||||
\(290\) | 9.12234e10 | − | 4.53712e9i | 0.757382 | − | 0.0376694i | ||||
\(291\) | 4.08777e11 | 3.34170 | ||||||||
\(292\) | 7.60891e10i | 0.612491i | ||||||||
\(293\) | 2.01290e10i | 0.159557i | 0.996813 | + | 0.0797787i | \(0.0254214\pi\) | ||||
−0.996813 | + | 0.0797787i | \(0.974579\pi\) | |||||||
\(294\) | −7.09972e10 | −0.554215 | ||||||||
\(295\) | 6.36940e9 | + | 1.28063e11i | 0.0489665 | + | 0.984522i | ||||
\(296\) | −5.44735e10 | −0.412451 | ||||||||
\(297\) | 1.46960e11i | 1.09596i | ||||||||
\(298\) | − | 6.15336e10i | − | 0.452001i | ||||||
\(299\) | −2.74885e11 | −1.98898 | ||||||||
\(300\) | −1.26319e10 | − | 1.26675e11i | −0.0900375 | − | 0.902909i | ||||
\(301\) | 1.14377e10 | 0.0803135 | ||||||||
\(302\) | − | 6.53221e10i | − | 0.451886i | ||||||
\(303\) | 3.25471e11i | 2.21830i | ||||||||
\(304\) | 1.13825e10 | 0.0764378 | ||||||||
\(305\) | −6.41800e9 | − | 1.29041e11i | −0.0424669 | − | 0.853841i | ||||
\(306\) | 1.19333e10 | 0.0778062 | ||||||||
\(307\) | − | 1.28834e11i | − | 0.827766i | −0.910330 | − | 0.413883i | \(-0.864172\pi\) | ||
0.910330 | − | 0.413883i | \(-0.135828\pi\) | |||||||
\(308\) | 2.77909e10i | 0.175964i | ||||||||
\(309\) | 4.23364e11 | 2.64180 | ||||||||
\(310\) | 6.11298e10 | − | 3.04037e9i | 0.375946 | − | 0.0186982i | ||||
\(311\) | −2.16554e11 | −1.31264 | −0.656320 | − | 0.754483i | \(-0.727888\pi\) | ||||
−0.656320 | + | 0.754483i | \(0.727888\pi\) | |||||||
\(312\) | − | 1.37185e11i | − | 0.819618i | ||||||
\(313\) | − | 2.10212e11i | − | 1.23796i | −0.785405 | − | 0.618982i | \(-0.787545\pi\) | ||
0.785405 | − | 0.618982i | \(-0.212455\pi\) | |||||||
\(314\) | −7.58640e9 | −0.0440405 | ||||||||
\(315\) | −3.01688e11 | + | 1.50049e10i | −1.72648 | + | 0.0858687i | ||||
\(316\) | 7.88828e10 | 0.445031 | ||||||||
\(317\) | 8.70887e10i | 0.484390i | 0.970228 | + | 0.242195i | \(0.0778674\pi\) | ||||
−0.970228 | + | 0.242195i | \(0.922133\pi\) | |||||||
\(318\) | 6.47189e10i | 0.354902i | ||||||||
\(319\) | 9.26109e10 | 0.500730 | ||||||||
\(320\) | −1.16472e9 | − | 2.34179e10i | −0.00620937 | − | 0.124846i | ||||
\(321\) | −4.85367e11 | −2.55151 | ||||||||
\(322\) | 1.60085e11i | 0.829849i | ||||||||
\(323\) | − | 2.86965e9i | − | 0.0146696i | ||||||
\(324\) | −1.95017e11 | −0.983149 | ||||||||
\(325\) | 2.54941e10 | + | 2.55659e11i | 0.126755 | + | 1.27112i | ||||
\(326\) | 9.24612e10 | 0.453399 | ||||||||
\(327\) | 1.56034e11i | 0.754664i | ||||||||
\(328\) | 6.11108e10i | 0.291531i | ||||||||
\(329\) | 1.15591e11 | 0.543931 | ||||||||
\(330\) | −6.41202e9 | − | 1.28920e11i | −0.0297634 | − | 0.598423i | ||||
\(331\) | −1.94118e11 | −0.888873 | −0.444436 | − | 0.895810i | \(-0.646596\pi\) | ||||
−0.444436 | + | 0.895810i | \(0.646596\pi\) | |||||||
\(332\) | − | 1.78540e10i | − | 0.0806519i | ||||||
\(333\) | − | 6.00340e11i | − | 2.67546i | ||||||
\(334\) | 6.06753e10 | 0.266780 | ||||||||
\(335\) | 7.21056e10 | − | 3.58627e9i | 0.312800 | − | 0.0155575i | ||||
\(336\) | −7.98926e10 | −0.341963 | ||||||||
\(337\) | 3.33772e11i | 1.40966i | 0.709375 | + | 0.704831i | \(0.248977\pi\) | ||||
−0.709375 | + | 0.704831i | \(0.751023\pi\) | |||||||
\(338\) | 1.07200e11i | 0.446753i | ||||||||
\(339\) | 3.87312e11 | 1.59280 | ||||||||
\(340\) | −5.90388e9 | + | 2.93637e8i | −0.0239598 | + | 0.00119167i | ||||
\(341\) | 6.20596e10 | 0.248550 | ||||||||
\(342\) | 1.25444e11i | 0.495831i | ||||||||
\(343\) | − | 2.76662e11i | − | 1.07926i | ||||||
\(344\) | −9.78452e9 | −0.0376727 | ||||||||
\(345\) | −3.69354e10 | − | 7.42624e11i | −0.140364 | − | 2.82217i | ||||
\(346\) | 2.28677e10 | 0.0857788 | ||||||||
\(347\) | 1.31507e11i | 0.486930i | 0.969910 | + | 0.243465i | \(0.0782842\pi\) | ||||
−0.969910 | + | 0.243465i | \(0.921716\pi\) | |||||||
\(348\) | 2.66235e11i | 0.973104i | ||||||||
\(349\) | −1.83355e11 | −0.661573 | −0.330786 | − | 0.943706i | \(-0.607314\pi\) | ||||
−0.330786 | + | 0.943706i | \(0.607314\pi\) | |||||||
\(350\) | 1.48888e11 | − | 1.48470e10i | 0.530339 | − | 0.0528851i | ||||
\(351\) | 8.52654e11 | 2.99841 | ||||||||
\(352\) | − | 2.37741e10i | − | 0.0825396i | ||||||
\(353\) | 2.99531e11i | 1.02673i | 0.858171 | + | 0.513365i | \(0.171601\pi\) | ||||
−0.858171 | + | 0.513365i | \(0.828399\pi\) | |||||||
\(354\) | −3.73753e11 | −1.26494 | ||||||||
\(355\) | 9.48017e9 | + | 1.90609e11i | 0.0316803 | + | 0.636964i | ||||
\(356\) | −1.90291e11 | −0.627904 | ||||||||
\(357\) | 2.01417e10i | 0.0656279i | ||||||||
\(358\) | − | 1.99621e11i | − | 0.642294i | ||||||
\(359\) | −6.25349e10 | −0.198700 | −0.0993500 | − | 0.995053i | \(-0.531676\pi\) | ||||
−0.0993500 | + | 0.995053i | \(0.531676\pi\) | |||||||
\(360\) | 2.58084e11 | − | 1.28361e10i | 0.809840 | − | 0.0402785i | ||||
\(361\) | −2.92522e11 | −0.906516 | ||||||||
\(362\) | 1.73716e11i | 0.531683i | ||||||||
\(363\) | 4.69466e11i | 1.41914i | ||||||||
\(364\) | 1.61242e11 | 0.481417 | ||||||||
\(365\) | 4.14869e11 | − | 2.06341e10i | 1.22347 | − | 0.0608509i | ||||
\(366\) | 3.76605e11 | 1.09704 | ||||||||
\(367\) | − | 4.06657e10i | − | 0.117012i | −0.998287 | − | 0.0585061i | \(-0.981366\pi\) | ||
0.998287 | − | 0.0585061i | \(-0.0186337\pi\) | |||||||
\(368\) | − | 1.36947e11i | − | 0.389257i | ||||||
\(369\) | −6.73488e11 | −1.89108 | ||||||||
\(370\) | 1.47723e10 | + | 2.97012e11i | 0.0409770 | + | 0.823884i | ||||
\(371\) | −7.60679e10 | −0.208458 | ||||||||
\(372\) | 1.78407e11i | 0.483025i | ||||||||
\(373\) | − | 3.44510e11i | − | 0.921537i | −0.887520 | − | 0.460768i | \(-0.847574\pi\) | ||
0.887520 | − | 0.460768i | \(-0.152426\pi\) | |||||||
\(374\) | −5.99367e9 | −0.0158406 | ||||||||
\(375\) | −6.87256e11 | + | 1.03226e11i | −1.79464 | + | 0.269557i | ||||
\(376\) | −9.88842e10 | −0.255142 | ||||||||
\(377\) | − | 5.37325e11i | − | 1.36994i | ||||||
\(378\) | − | 4.96560e11i | − | 1.25100i | ||||||
\(379\) | −4.30309e10 | −0.107128 | −0.0535642 | − | 0.998564i | \(-0.517058\pi\) | ||||
−0.0535642 | + | 0.998564i | \(0.517058\pi\) | |||||||
\(380\) | −3.08675e9 | − | 6.20623e10i | −0.00759409 | − | 0.152687i | ||||
\(381\) | −1.24322e11 | −0.302264 | ||||||||
\(382\) | − | 4.67119e11i | − | 1.12239i | ||||||
\(383\) | 2.89909e11i | 0.688441i | 0.938889 | + | 0.344220i | \(0.111857\pi\) | ||||
−0.938889 | + | 0.344220i | \(0.888143\pi\) | |||||||
\(384\) | 6.83452e10 | 0.160405 | ||||||||
\(385\) | 1.51527e11 | − | 7.53642e9i | 0.351494 | − | 0.0174820i | ||||
\(386\) | −8.53935e9 | −0.0195786 | ||||||||
\(387\) | − | 1.07833e11i | − | 0.244372i | ||||||
\(388\) | − | 4.11016e11i | − | 0.920694i | ||||||
\(389\) | 5.10079e11 | 1.12944 | 0.564722 | − | 0.825282i | \(-0.308984\pi\) | ||||
0.564722 | + | 0.825282i | \(0.308984\pi\) | |||||||
\(390\) | −7.47990e11 | + | 3.72023e10i | −1.63721 | + | 0.0814290i | ||||
\(391\) | −3.45256e10 | −0.0747043 | ||||||||
\(392\) | 7.13860e10i | 0.152695i | ||||||||
\(393\) | 1.27033e12i | 2.68626i | ||||||||
\(394\) | −4.57164e11 | −0.955738 | ||||||||
\(395\) | −2.13917e10 | − | 4.30101e11i | −0.0442138 | − | 0.888964i | ||||
\(396\) | 2.62009e11 | 0.535412 | ||||||||
\(397\) | 2.54945e11i | 0.515097i | 0.966265 | + | 0.257549i | \(0.0829148\pi\) | ||||
−0.966265 | + | 0.257549i | \(0.917085\pi\) | |||||||
\(398\) | 3.91145e11i | 0.781384i | ||||||||
\(399\) | −2.11732e11 | −0.418223 | ||||||||
\(400\) | −1.27368e11 | + | 1.27011e10i | −0.248766 | + | 0.0248068i | ||||
\(401\) | 5.09680e11 | 0.984347 | 0.492173 | − | 0.870497i | \(-0.336203\pi\) | ||||
0.492173 | + | 0.870497i | \(0.336203\pi\) | |||||||
\(402\) | 2.10440e11i | 0.401894i | ||||||||
\(403\) | − | 3.60067e11i | − | 0.680003i | ||||||
\(404\) | 3.27253e11 | 0.611178 | ||||||||
\(405\) | 5.28852e10 | + | 1.06331e12i | 0.0976757 | + | 1.96387i | ||||
\(406\) | −3.12922e11 | −0.571569 | ||||||||
\(407\) | 3.01529e11i | 0.544697i | ||||||||
\(408\) | − | 1.72305e10i | − | 0.0307841i | ||||||
\(409\) | 1.06695e12 | 1.88533 | 0.942666 | − | 0.333737i | \(-0.108310\pi\) | ||||
0.942666 | + | 0.333737i | \(0.108310\pi\) | |||||||
\(410\) | 3.33201e11 | − | 1.65722e10i | 0.582343 | − | 0.0289636i | ||||
\(411\) | −3.34333e11 | −0.577952 | ||||||||
\(412\) | − | 4.25682e11i | − | 0.727861i | ||||||
\(413\) | − | 4.39293e11i | − | 0.742983i | ||||||
\(414\) | 1.50926e12 | 2.52501 | ||||||||
\(415\) | −9.73474e10 | + | 4.84171e9i | −0.161105 | + | 0.00801276i | ||||
\(416\) | −1.37936e11 | −0.225818 | ||||||||
\(417\) | − | 1.73575e12i | − | 2.81108i | ||||||
\(418\) | − | 6.30062e10i | − | 0.100946i | ||||||
\(419\) | −4.72157e11 | −0.748383 | −0.374191 | − | 0.927352i | \(-0.622080\pi\) | ||||
−0.374191 | + | 0.927352i | \(0.622080\pi\) | |||||||
\(420\) | 2.16655e10 | + | 4.35607e11i | 0.0339740 | + | 0.683082i | ||||
\(421\) | −4.82741e11 | −0.748936 | −0.374468 | − | 0.927240i | \(-0.622175\pi\) | ||||
−0.374468 | + | 0.927240i | \(0.622175\pi\) | |||||||
\(422\) | − | 4.71161e11i | − | 0.723208i | ||||||
\(423\) | − | 1.08978e12i | − | 1.65503i | ||||||
\(424\) | 6.50733e10 | 0.0977815 | ||||||||
\(425\) | 3.20206e9 | + | 3.21107e10i | 0.00476080 | + | 0.0477420i | ||||
\(426\) | −5.56291e11 | −0.818387 | ||||||||
\(427\) | 4.42645e11i | 0.644363i | ||||||||
\(428\) | 4.88025e11i | 0.702983i | ||||||||
\(429\) | −7.59367e11 | −1.08241 | ||||||||
\(430\) | 2.65339e9 | + | 5.33492e10i | 0.00374278 | + | 0.0752523i | ||||
\(431\) | 1.22570e12 | 1.71095 | 0.855476 | − | 0.517843i | \(-0.173265\pi\) | ||||
0.855476 | + | 0.517843i | \(0.173265\pi\) | |||||||
\(432\) | 4.24789e11i | 0.586809i | ||||||||
\(433\) | 1.24088e12i | 1.69642i | 0.529661 | + | 0.848210i | \(0.322319\pi\) | ||||
−0.529661 | + | 0.848210i | \(0.677681\pi\) | |||||||
\(434\) | −2.09692e11 | −0.283713 | ||||||||
\(435\) | 1.45162e12 | − | 7.21985e10i | 1.94381 | − | 0.0966778i | ||||
\(436\) | 1.56888e11 | 0.207922 | ||||||||
\(437\) | − | 3.62937e11i | − | 0.476064i | ||||||
\(438\) | 1.21080e12i | 1.57194i | ||||||||
\(439\) | −1.20939e12 | −1.55409 | −0.777047 | − | 0.629442i | \(-0.783283\pi\) | ||||
−0.777047 | + | 0.629442i | \(0.783283\pi\) | |||||||
\(440\) | −1.29626e11 | + | 6.44713e9i | −0.164875 | + | 0.00820030i | ||||
\(441\) | −7.86729e11 | −0.990493 | ||||||||
\(442\) | 3.47751e10i | 0.0433379i | ||||||||
\(443\) | 4.45765e10i | 0.0549907i | 0.999622 | + | 0.0274954i | \(0.00875315\pi\) | ||||
−0.999622 | + | 0.0274954i | \(0.991247\pi\) | |||||||
\(444\) | −8.66829e11 | −1.05855 | ||||||||
\(445\) | 5.16037e10 | + | 1.03754e12i | 0.0623822 | + | 1.25426i | ||||
\(446\) | −5.43673e11 | −0.650625 | ||||||||
\(447\) | − | 9.79176e11i | − | 1.16005i | ||||||
\(448\) | 8.03301e10i | 0.0942165i | ||||||||
\(449\) | −7.28323e11 | −0.845698 | −0.422849 | − | 0.906200i | \(-0.638970\pi\) | ||||
−0.422849 | + | 0.906200i | \(0.638970\pi\) | |||||||
\(450\) | −1.39976e11 | − | 1.40370e12i | −0.160915 | − | 1.61368i | ||||
\(451\) | 3.38269e11 | 0.385006 | ||||||||
\(452\) | − | 3.89433e11i | − | 0.438843i | ||||||
\(453\) | − | 1.03946e12i | − | 1.15975i | ||||||
\(454\) | 2.49792e11 | 0.275948 | ||||||||
\(455\) | −4.37260e10 | − | 8.79156e11i | −0.0478287 | − | 0.961645i | ||||
\(456\) | 1.81129e11 | 0.196176 | ||||||||
\(457\) | 1.61869e12i | 1.73596i | 0.496598 | + | 0.867981i | \(0.334582\pi\) | ||||
−0.496598 | + | 0.867981i | \(0.665418\pi\) | |||||||
\(458\) | 8.62607e11i | 0.916049i | ||||||||
\(459\) | 1.07093e11 | 0.112617 | ||||||||
\(460\) | −7.46691e11 | + | 3.71377e10i | −0.777554 | + | 0.0386727i | ||||
\(461\) | −5.26233e11 | −0.542655 | −0.271328 | − | 0.962487i | \(-0.587463\pi\) | ||||
−0.271328 | + | 0.962487i | \(0.587463\pi\) | |||||||
\(462\) | 4.42233e11i | 0.451608i | ||||||||
\(463\) | − | 1.71642e12i | − | 1.73583i | −0.496709 | − | 0.867917i | \(-0.665458\pi\) | ||
0.496709 | − | 0.867917i | \(-0.334542\pi\) | |||||||
\(464\) | 2.67693e11 | 0.268106 | ||||||||
\(465\) | 9.72750e11 | − | 4.83810e10i | 0.964857 | − | 0.0479885i | ||||
\(466\) | 1.21506e12 | 1.19361 | ||||||||
\(467\) | 1.36109e12i | 1.32422i | 0.749405 | + | 0.662112i | \(0.230339\pi\) | ||||
−0.749405 | + | 0.662112i | \(0.769661\pi\) | |||||||
\(468\) | − | 1.52017e12i | − | 1.46482i | ||||||
\(469\) | −2.47342e11 | −0.236059 | ||||||||
\(470\) | 2.68157e10 | + | 5.39157e11i | 0.0253483 | + | 0.509654i | ||||
\(471\) | −1.20721e11 | −0.113029 | ||||||||
\(472\) | 3.75799e11i | 0.348511i | ||||||||
\(473\) | 5.41606e10i | 0.0497518i | ||||||||
\(474\) | 1.25525e12 | 1.14216 | ||||||||
\(475\) | −3.37552e11 | + | 3.36605e10i | −0.304242 | + | 0.0303388i | ||||
\(476\) | 2.02520e10 | 0.0180816 | ||||||||
\(477\) | 7.17158e11i | 0.634282i | ||||||||
\(478\) | − | 1.07264e12i | − | 0.939786i | ||||||
\(479\) | 7.71338e11 | 0.669476 | 0.334738 | − | 0.942311i | \(-0.391352\pi\) | ||||
0.334738 | + | 0.942311i | \(0.391352\pi\) | |||||||
\(480\) | −1.85341e10 | − | 3.72646e11i | −0.0159362 | − | 0.320414i | ||||
\(481\) | 1.74946e12 | 1.49022 | ||||||||
\(482\) | − | 5.11499e11i | − | 0.431651i | ||||||
\(483\) | 2.54741e12i | 2.12979i | ||||||||
\(484\) | 4.72037e11 | 0.390996 | ||||||||
\(485\) | −2.24103e12 | + | 1.11460e11i | −1.83912 | + | 0.0914709i | ||||
\(486\) | −1.06198e12 | −0.863483 | ||||||||
\(487\) | 7.00790e10i | 0.0564557i | 0.999602 | + | 0.0282278i | \(0.00898639\pi\) | ||||
−0.999602 | + | 0.0282278i | \(0.991014\pi\) | |||||||
\(488\) | − | 3.78667e11i | − | 0.302251i | ||||||
\(489\) | 1.47132e12 | 1.16364 | ||||||||
\(490\) | 3.89226e11 | − | 1.93587e10i | 0.305014 | − | 0.0151703i | ||||
\(491\) | −3.27391e11 | −0.254214 | −0.127107 | − | 0.991889i | \(-0.540569\pi\) | ||||
−0.127107 | + | 0.991889i | \(0.540569\pi\) | |||||||
\(492\) | 9.72447e11i | 0.748209i | ||||||||
\(493\) | − | 6.74880e10i | − | 0.0514536i | ||||||
\(494\) | −3.65560e11 | −0.276177 | ||||||||
\(495\) | −7.10524e10 | − | 1.42858e12i | −0.0531931 | − | 1.06950i | ||||
\(496\) | 1.79384e11 | 0.133081 | ||||||||
\(497\) | − | 6.53841e11i | − | 0.480694i | ||||||
\(498\) | − | 2.84108e11i | − | 0.206991i | ||||||
\(499\) | 1.55301e12 | 1.12130 | 0.560649 | − | 0.828054i | \(-0.310552\pi\) | ||||
0.560649 | + | 0.828054i | \(0.310552\pi\) | |||||||
\(500\) | 1.03792e11 | + | 6.91020e11i | 0.0742673 | + | 0.494454i | ||||
\(501\) | 9.65518e11 | 0.684685 | ||||||||
\(502\) | − | 1.20453e12i | − | 0.846548i | ||||||
\(503\) | 3.75654e11i | 0.261657i | 0.991405 | + | 0.130828i | \(0.0417637\pi\) | ||||
−0.991405 | + | 0.130828i | \(0.958236\pi\) | |||||||
\(504\) | −8.85299e11 | −0.611157 | ||||||||
\(505\) | −8.87454e10 | − | 1.78432e12i | −0.0607204 | − | 1.22085i | ||||
\(506\) | −7.58048e11 | −0.514066 | ||||||||
\(507\) | 1.70585e12i | 1.14658i | ||||||||
\(508\) | 1.25003e11i | 0.0832787i | ||||||||
\(509\) | −1.82659e12 | −1.20618 | −0.603090 | − | 0.797673i | \(-0.706064\pi\) | ||||
−0.603090 | + | 0.797673i | \(0.706064\pi\) | |||||||
\(510\) | −9.39476e10 | + | 4.67261e9i | −0.0614922 | + | 0.00305840i | ||||
\(511\) | −1.42312e12 | −0.923308 | ||||||||
\(512\) | − | 6.87195e10i | − | 0.0441942i | ||||||
\(513\) | 1.12578e12i | 0.717670i | ||||||||
\(514\) | −1.34516e12 | −0.850039 | ||||||||
\(515\) | −2.32100e12 | + | 1.15438e11i | −1.45392 | + | 0.0723129i | ||||
\(516\) | −1.55700e11 | −0.0966861 | ||||||||
\(517\) | 5.47358e11i | 0.336949i | ||||||||
\(518\) | − | 1.01883e12i | − | 0.621756i | ||||||
\(519\) | 3.63890e11 | 0.220149 | ||||||||
\(520\) | 3.74060e10 | + | 7.52086e11i | 0.0224350 | + | 0.451079i | ||||
\(521\) | 1.09737e12 | 0.652506 | 0.326253 | − | 0.945283i | \(-0.394214\pi\) | ||||
0.326253 | + | 0.945283i | \(0.394214\pi\) | |||||||
\(522\) | 2.95019e12i | 1.73913i | ||||||||
\(523\) | − | 2.23460e12i | − | 1.30600i | −0.757359 | − | 0.652999i | \(-0.773510\pi\) | ||
0.757359 | − | 0.652999i | \(-0.226490\pi\) | |||||||
\(524\) | 1.27728e12 | 0.740110 | ||||||||
\(525\) | 2.36923e12 | − | 2.36258e11i | 1.36110 | − | 0.135728i | ||||
\(526\) | 1.83244e12 | 1.04375 | ||||||||
\(527\) | − | 4.52245e10i | − | 0.0255403i | ||||||
\(528\) | − | 3.78314e11i | − | 0.211836i | ||||||
\(529\) | −2.56546e12 | −1.42434 | ||||||||
\(530\) | −1.76468e10 | − | 3.54806e11i | −0.00971458 | − | 0.195321i | ||||
\(531\) | −4.14160e12 | −2.26070 | ||||||||
\(532\) | 2.12891e11i | 0.115227i | ||||||||
\(533\) | − | 1.96262e12i | − | 1.05333i | ||||||
\(534\) | −3.02807e12 | −1.61150 | ||||||||
\(535\) | 2.66091e12 | − | 1.32344e11i | 1.40423 | − | 0.0698413i | ||||
\(536\) | 2.11592e11 | 0.110728 | ||||||||
\(537\) | − | 3.17655e12i | − | 1.64843i | ||||||
\(538\) | 1.57326e12i | 0.809619i | ||||||||
\(539\) | 3.95146e11 | 0.201655 | ||||||||
\(540\) | 2.31613e12 | − | 1.15196e11i | 1.17217 | − | 0.0582994i | ||||
\(541\) | −1.87101e11 | −0.0939049 | −0.0469525 | − | 0.998897i | \(-0.514951\pi\) | ||||
−0.0469525 | + | 0.998897i | \(0.514951\pi\) | |||||||
\(542\) | 3.56310e10i | 0.0177350i | ||||||||
\(543\) | 2.76433e12i | 1.36455i | ||||||||
\(544\) | −1.73248e10 | −0.00848152 | ||||||||
\(545\) | −4.25454e10 | − | 8.55419e11i | −0.0206571 | − | 0.415331i | ||||
\(546\) | 2.56582e12 | 1.23555 | ||||||||
\(547\) | − | 1.68930e12i | − | 0.806796i | −0.915025 | − | 0.403398i | \(-0.867829\pi\) | ||
0.915025 | − | 0.403398i | \(-0.132171\pi\) | |||||||
\(548\) | 3.36164e11i | 0.159235i | ||||||||
\(549\) | 4.17320e12 | 1.96062 | ||||||||
\(550\) | 7.03048e10 | + | 7.05027e11i | 0.0327607 | + | 0.328529i | ||||
\(551\) | 7.09442e11 | 0.327895 | ||||||||
\(552\) | − | 2.17922e12i | − | 0.999021i | ||||||
\(553\) | 1.47537e12i | 0.670869i | ||||||||
\(554\) | 3.78906e11 | 0.170898 | ||||||||
\(555\) | 2.35069e11 | + | 4.72631e12i | 0.105166 | + | 2.11448i | ||||
\(556\) | −1.74525e12 | −0.774500 | ||||||||
\(557\) | 1.21557e12i | 0.535094i | 0.963545 | + | 0.267547i | \(0.0862130\pi\) | ||||
−0.963545 | + | 0.267547i | \(0.913787\pi\) | |||||||
\(558\) | 1.97695e12i | 0.863262i | ||||||||
\(559\) | 3.14238e11 | 0.136115 | ||||||||
\(560\) | 4.37993e11 | − | 2.17841e10i | 0.188200 | − | 0.00936040i | ||||
\(561\) | −9.53765e10 | −0.0406545 | ||||||||
\(562\) | − | 2.08177e10i | − | 0.00880279i | ||||||
\(563\) | 1.35075e12i | 0.566615i | 0.959029 | + | 0.283308i | \(0.0914318\pi\) | ||||
−0.959029 | + | 0.283308i | \(0.908568\pi\) | |||||||
\(564\) | −1.57353e12 | −0.654816 | ||||||||
\(565\) | −2.12335e12 | + | 1.05608e11i | −0.876603 | + | 0.0435990i | ||||
\(566\) | −2.59845e12 | −1.06424 | ||||||||
\(567\) | − | 3.64746e12i | − | 1.48206i | ||||||
\(568\) | 5.59337e11i | 0.225479i | ||||||||
\(569\) | 1.96503e12 | 0.785894 | 0.392947 | − | 0.919561i | \(-0.371456\pi\) | ||||
0.392947 | + | 0.919561i | \(0.371456\pi\) | |||||||
\(570\) | −4.91190e10 | − | 9.87588e11i | −0.0194901 | − | 0.391867i | ||||
\(571\) | 4.44321e12 | 1.74918 | 0.874590 | − | 0.484863i | \(-0.161131\pi\) | ||||
0.874590 | + | 0.484863i | \(0.161131\pi\) | |||||||
\(572\) | 7.63525e11i | 0.298223i | ||||||||
\(573\) | − | 7.43319e12i | − | 2.88058i | ||||||
\(574\) | −1.14297e12 | −0.439473 | ||||||||
\(575\) | 4.04980e11 | + | 4.06119e12i | 0.154500 | + | 1.54935i | ||||
\(576\) | 7.57341e11 | 0.286675 | ||||||||
\(577\) | 7.74499e11i | 0.290891i | 0.989366 | + | 0.145445i | \(0.0464615\pi\) | ||||
−0.989366 | + | 0.145445i | \(0.953538\pi\) | |||||||
\(578\) | − | 1.89304e12i | − | 0.705479i | ||||||
\(579\) | −1.35885e11 | −0.0502481 | ||||||||
\(580\) | −7.25939e10 | − | 1.45957e12i | −0.0266363 | − | 0.535550i | ||||
\(581\) | 3.33929e11 | 0.121580 | ||||||||
\(582\) | − | 6.54043e12i | − | 2.36294i | ||||||
\(583\) | − | 3.60203e11i | − | 0.129133i | ||||||
\(584\) | 1.21743e12 | 0.433097 | ||||||||
\(585\) | −8.28857e12 | + | 4.12243e11i | −2.92603 | + | 0.145530i | ||||
\(586\) | 3.22063e11 | 0.112824 | ||||||||
\(587\) | 5.79614e11i | 0.201496i | 0.994912 | + | 0.100748i | \(0.0321237\pi\) | ||||
−0.994912 | + | 0.100748i | \(0.967876\pi\) | |||||||
\(588\) | 1.13596e12i | 0.391889i | ||||||||
\(589\) | 4.75405e11 | 0.162759 | ||||||||
\(590\) | 2.04901e12 | − | 1.01910e11i | 0.696162 | − | 0.0346246i | ||||
\(591\) | −7.27478e12 | −2.45288 | ||||||||
\(592\) | 8.71576e11i | 0.291647i | ||||||||
\(593\) | 3.11892e12i | 1.03576i | 0.855454 | + | 0.517879i | \(0.173278\pi\) | ||||
−0.855454 | + | 0.517879i | \(0.826722\pi\) | |||||||
\(594\) | 2.35135e12 | 0.774959 | ||||||||
\(595\) | −5.49199e9 | − | 1.10422e11i | −0.00179640 | − | 0.0361185i | ||||
\(596\) | −9.84538e11 | −0.319613 | ||||||||
\(597\) | 6.22424e12i | 2.00540i | ||||||||
\(598\) | 4.39816e12i | 1.40642i | ||||||||
\(599\) | 3.65634e12 | 1.16045 | 0.580225 | − | 0.814456i | \(-0.302965\pi\) | ||||
0.580225 | + | 0.814456i | \(0.302965\pi\) | |||||||
\(600\) | −2.02679e12 | + | 2.02111e11i | −0.638453 | + | 0.0636661i | ||||
\(601\) | −5.00312e12 | −1.56425 | −0.782124 | − | 0.623123i | \(-0.785864\pi\) | ||||
−0.782124 | + | 0.623123i | \(0.785864\pi\) | |||||||
\(602\) | − | 1.83003e11i | − | 0.0567902i | ||||||
\(603\) | 2.33191e12i | 0.718264i | ||||||||
\(604\) | −1.04515e12 | −0.319532 | ||||||||
\(605\) | −1.28008e11 | − | 2.57374e12i | −0.0388454 | − | 0.781026i | ||||
\(606\) | 5.20753e12 | 1.56857 | ||||||||
\(607\) | − | 4.66337e12i | − | 1.39428i | −0.716934 | − | 0.697141i | \(-0.754455\pi\) | ||
0.716934 | − | 0.697141i | \(-0.245545\pi\) | |||||||
\(608\) | − | 1.82121e11i | − | 0.0540497i | ||||||
\(609\) | −4.97948e12 | −1.46692 | ||||||||
\(610\) | −2.06465e12 | + | 1.02688e11i | −0.603757 | + | 0.0300286i | ||||
\(611\) | 3.17575e12 | 0.921851 | ||||||||
\(612\) | − | 1.90933e11i | − | 0.0550173i | ||||||
\(613\) | 6.42000e12i | 1.83638i | 0.396139 | + | 0.918190i | \(0.370350\pi\) | ||||
−0.396139 | + | 0.918190i | \(0.629650\pi\) | |||||||
\(614\) | −2.06134e12 | −0.585319 | ||||||||
\(615\) | 5.30218e12 | − | 2.63711e11i | 1.49457 | − | 0.0743345i | ||||
\(616\) | 4.44654e11 | 0.124425 | ||||||||
\(617\) | − | 2.91245e12i | − | 0.809050i | −0.914527 | − | 0.404525i | \(-0.867437\pi\) | ||
0.914527 | − | 0.404525i | \(-0.132563\pi\) | |||||||
\(618\) | − | 6.77382e12i | − | 1.86804i | ||||||
\(619\) | −9.63523e10 | −0.0263787 | −0.0131894 | − | 0.999913i | \(-0.504198\pi\) | ||||
−0.0131894 | + | 0.999913i | \(0.504198\pi\) | |||||||
\(620\) | −4.86460e10 | − | 9.78077e11i | −0.0132216 | − | 0.265834i | ||||
\(621\) | 1.35446e13 | 3.65472 | ||||||||
\(622\) | 3.46487e12i | 0.928176i | ||||||||
\(623\) | − | 3.55907e12i | − | 0.946543i | ||||||
\(624\) | −2.19496e12 | −0.579558 | ||||||||
\(625\) | 3.73958e12 | − | 7.53308e11i | 0.980308 | − | 0.197475i | ||||
\(626\) | −3.36339e12 | −0.875373 | ||||||||
\(627\) | − | 1.00261e12i | − | 0.259076i | ||||||
\(628\) | 1.21382e11i | 0.0311413i | ||||||||
\(629\) | 2.19732e11 | 0.0559714 | ||||||||
\(630\) | 2.40078e11 | + | 4.82701e12i | 0.0607184 | + | 1.22080i | ||||
\(631\) | −5.22061e12 | −1.31096 | −0.655480 | − | 0.755213i | \(-0.727534\pi\) | ||||
−0.655480 | + | 0.755213i | \(0.727534\pi\) | |||||||
\(632\) | − | 1.26212e12i | − | 0.314685i | ||||||
\(633\) | − | 7.49752e12i | − | 1.85610i | ||||||
\(634\) | 1.39342e12 | 0.342515 | ||||||||
\(635\) | 6.81568e11 | − | 3.38987e10i | 0.166352 | − | 0.00827373i | ||||
\(636\) | 1.03550e12 | 0.250954 | ||||||||
\(637\) | − | 2.29262e12i | − | 0.551702i | ||||||
\(638\) | − | 1.48177e12i | − | 0.354070i | ||||||
\(639\) | −6.16433e12 | −1.46262 | ||||||||
\(640\) | −3.74687e11 | + | 1.86356e10i | −0.0882792 | + | 0.00439069i | ||||
\(641\) | 5.72517e12 | 1.33945 | 0.669726 | − | 0.742608i | \(-0.266412\pi\) | ||||
0.669726 | + | 0.742608i | \(0.266412\pi\) | |||||||
\(642\) | 7.76587e12i | 1.80419i | ||||||||
\(643\) | 1.79153e12i | 0.413309i | 0.978414 | + | 0.206654i | \(0.0662575\pi\) | ||||
−0.978414 | + | 0.206654i | \(0.933742\pi\) | |||||||
\(644\) | 2.56136e12 | 0.586792 | ||||||||
\(645\) | 4.22231e10 | + | 8.48938e11i | 0.00960575 | + | 0.193133i | ||||
\(646\) | −4.59143e10 | −0.0103729 | ||||||||
\(647\) | 3.37135e12i | 0.756370i | 0.925730 | + | 0.378185i | \(0.123452\pi\) | ||||
−0.925730 | + | 0.378185i | \(0.876548\pi\) | |||||||
\(648\) | 3.12027e12i | 0.695191i | ||||||||
\(649\) | 2.08018e12 | 0.460256 | ||||||||
\(650\) | 4.09054e12 | − | 4.07906e11i | 0.898815 | − | 0.0896293i | ||||
\(651\) | −3.33681e12 | −0.728143 | ||||||||
\(652\) | − | 1.47938e12i | − | 0.320601i | ||||||
\(653\) | 2.66457e12i | 0.573479i | 0.958009 | + | 0.286739i | \(0.0925714\pi\) | ||||
−0.958009 | + | 0.286739i | \(0.907429\pi\) | |||||||
\(654\) | 2.49654e12 | 0.533628 | ||||||||
\(655\) | −3.46377e11 | − | 6.96427e12i | −0.0735298 | − | 1.47839i | ||||
\(656\) | 9.77772e11 | 0.206144 | ||||||||
\(657\) | 1.34170e13i | 2.80938i | ||||||||
\(658\) | − | 1.84946e12i | − | 0.384617i | ||||||
\(659\) | −3.70933e12 | −0.766146 | −0.383073 | − | 0.923718i | \(-0.625134\pi\) | ||||
−0.383073 | + | 0.923718i | \(0.625134\pi\) | |||||||
\(660\) | −2.06272e12 | + | 1.02592e11i | −0.423149 | + | 0.0210459i | ||||
\(661\) | −5.60206e12 | −1.14141 | −0.570705 | − | 0.821156i | \(-0.693330\pi\) | ||||
−0.570705 | + | 0.821156i | \(0.693330\pi\) | |||||||
\(662\) | 3.10589e12i | 0.628528i | ||||||||
\(663\) | 5.53371e11i | 0.111226i | ||||||||
\(664\) | −2.85664e11 | −0.0570295 | ||||||||
\(665\) | 1.16077e12 | − | 5.77325e10i | 0.230170 | − | 0.0114478i | ||||
\(666\) | −9.60544e12 | −1.89183 | ||||||||
\(667\) | − | 8.53552e12i | − | 1.66980i | ||||||
\(668\) | − | 9.70805e11i | − | 0.188642i | ||||||
\(669\) | −8.65139e12 | −1.66981 | ||||||||
\(670\) | −5.73803e10 | − | 1.15369e12i | −0.0110008 | − | 0.221183i | ||||
\(671\) | −2.09605e12 | −0.399163 | ||||||||
\(672\) | 1.27828e12i | 0.241805i | ||||||||
\(673\) | 1.97705e12i | 0.371493i | 0.982598 | + | 0.185746i | \(0.0594703\pi\) | ||||
−0.982598 | + | 0.185746i | \(0.940530\pi\) | |||||||
\(674\) | 5.34035e12 | 0.996782 | ||||||||
\(675\) | −1.25619e12 | − | 1.25972e13i | −0.232910 | − | 2.33565i | ||||
\(676\) | 1.71519e12 | 0.315902 | ||||||||
\(677\) | − | 1.55123e12i | − | 0.283810i | −0.989880 | − | 0.141905i | \(-0.954677\pi\) | ||
0.989880 | − | 0.141905i | \(-0.0453228\pi\) | |||||||
\(678\) | − | 6.19699e12i | − | 1.12628i | ||||||
\(679\) | 7.68735e12 | 1.38791 | ||||||||
\(680\) | 4.69820e9 | + | 9.44621e10i | 0.000842638 | + | 0.0169421i | ||||
\(681\) | 3.97491e12 | 0.708215 | ||||||||
\(682\) | − | 9.92953e11i | − | 0.175752i | ||||||
\(683\) | − | 6.96146e12i | − | 1.22407i | −0.790830 | − | 0.612036i | \(-0.790351\pi\) | ||
0.790830 | − | 0.612036i | \(-0.209649\pi\) | |||||||
\(684\) | 2.00711e12 | 0.350605 | ||||||||
\(685\) | 1.83291e12 | − | 9.11620e10i | 0.318077 | − | 0.0158200i | ||||
\(686\) | −4.42659e12 | −0.763152 | ||||||||
\(687\) | 1.37265e13i | 2.35102i | ||||||||
\(688\) | 1.56552e11i | 0.0266386i | ||||||||
\(689\) | −2.08988e12 | −0.353293 | ||||||||
\(690\) | −1.18820e13 | + | 5.90966e11i | −1.99557 | + | 0.0992526i | ||||
\(691\) | −8.36212e12 | −1.39529 | −0.697646 | − | 0.716443i | \(-0.745769\pi\) | ||||
−0.697646 | + | 0.716443i | \(0.745769\pi\) | |||||||
\(692\) | − | 3.65883e11i | − | 0.0606548i | ||||||
\(693\) | 4.90043e12i | 0.807114i | ||||||||
\(694\) | 2.10412e12 | 0.344312 | ||||||||
\(695\) | 4.73283e11 | + | 9.51583e12i | 0.0769465 | + | 1.54709i | ||||
\(696\) | 4.25977e12 | 0.688088 | ||||||||
\(697\) | − | 2.46506e11i | − | 0.0395621i | ||||||
\(698\) | 2.93367e12i | 0.467802i | ||||||||
\(699\) | 1.93351e13 | 3.06337 | ||||||||
\(700\) | −2.37552e11 | − | 2.38221e12i | −0.0373954 | − | 0.375006i | ||||
\(701\) | −4.13171e12 | −0.646247 | −0.323123 | − | 0.946357i | \(-0.604733\pi\) | ||||
−0.323123 | + | 0.946357i | \(0.604733\pi\) | |||||||
\(702\) | − | 1.36425e13i | − | 2.12019i | ||||||
\(703\) | 2.30985e12i | 0.356686i | ||||||||
\(704\) | −3.80386e11 | −0.0583643 | ||||||||
\(705\) | 4.26715e11 | + | 8.57953e12i | 0.0650559 | + | 1.30801i | ||||
\(706\) | 4.79250e12 | 0.726007 | ||||||||
\(707\) | 6.12071e12i | 0.921328i | ||||||||
\(708\) | 5.98004e12i | 0.894447i | ||||||||
\(709\) | −4.22719e12 | −0.628266 | −0.314133 | − | 0.949379i | \(-0.601714\pi\) | ||||
−0.314133 | + | 0.949379i | \(0.601714\pi\) | |||||||
\(710\) | 3.04974e12 | − | 1.51683e11i | 0.450401 | − | 0.0224013i | ||||
\(711\) | 1.39096e13 | 2.04127 | ||||||||
\(712\) | 3.04465e12i | 0.443995i | ||||||||
\(713\) | − | 5.71975e12i | − | 0.828846i | ||||||
\(714\) | 3.22267e11 | 0.0464059 | ||||||||
\(715\) | 4.16305e12 | − | 2.07055e11i | 0.595710 | − | 0.0296284i | ||||
\(716\) | −3.19394e12 | −0.454170 | ||||||||
\(717\) | − | 1.70688e13i | − | 2.41194i | ||||||
\(718\) | 1.00056e12i | 0.140502i | ||||||||
\(719\) | −1.34429e13 | −1.87591 | −0.937954 | − | 0.346760i | \(-0.887282\pi\) | ||||
−0.937954 | + | 0.346760i | \(0.887282\pi\) | |||||||
\(720\) | −2.05378e11 | − | 4.12934e12i | −0.0284812 | − | 0.572643i | ||||
\(721\) | 7.96167e12 | 1.09722 | ||||||||
\(722\) | 4.68035e12i | 0.641004i | ||||||||
\(723\) | − | 8.13941e12i | − | 1.10782i | ||||||
\(724\) | 2.77946e12 | 0.375956 | ||||||||
\(725\) | −7.93851e12 | + | 7.91623e11i | −1.06713 | + | 0.106414i | ||||
\(726\) | 7.51145e12 | 1.00348 | ||||||||
\(727\) | 6.20467e12i | 0.823785i | 0.911233 | + | 0.411892i | \(0.135132\pi\) | ||||
−0.911233 | + | 0.411892i | \(0.864868\pi\) | |||||||
\(728\) | − | 2.57987e12i | − | 0.340413i | ||||||
\(729\) | −1.90497e12 | −0.249813 | ||||||||
\(730\) | −3.30145e11 | − | 6.63791e12i | −0.0430281 | − | 0.865124i | ||||
\(731\) | 3.94683e10 | 0.00511235 | ||||||||
\(732\) | − | 6.02568e12i | − | 0.775722i | ||||||
\(733\) | 1.45106e13i | 1.85660i | 0.371831 | + | 0.928300i | \(0.378730\pi\) | ||||
−0.371831 | + | 0.928300i | \(0.621270\pi\) | |||||||
\(734\) | −6.50652e11 | −0.0827401 | ||||||||
\(735\) | 6.19370e12 | − | 3.08052e11i | 0.782811 | − | 0.0389342i | ||||
\(736\) | −2.19115e12 | −0.275247 | ||||||||
\(737\) | − | 1.17124e12i | − | 0.146231i | ||||||
\(738\) | 1.07758e13i | 1.33720i | ||||||||
\(739\) | −8.77240e12 | −1.08198 | −0.540989 | − | 0.841030i | \(-0.681950\pi\) | ||||
−0.540989 | + | 0.841030i | \(0.681950\pi\) | |||||||
\(740\) | 4.75219e12 | − | 2.36357e11i | 0.582574 | − | 0.0289751i | ||||
\(741\) | −5.81710e12 | −0.708802 | ||||||||
\(742\) | 1.21709e12i | 0.147402i | ||||||||
\(743\) | − | 5.03647e12i | − | 0.606285i | −0.952945 | − | 0.303142i | \(-0.901964\pi\) | ||
0.952945 | − | 0.303142i | \(-0.0980358\pi\) | |||||||
\(744\) | 2.85452e12 | 0.341550 | ||||||||
\(745\) | 2.66990e11 | + | 5.36810e12i | 0.0317535 | + | 0.638437i | ||||
\(746\) | −5.51217e12 | −0.651625 | ||||||||
\(747\) | − | 3.14824e12i | − | 0.369935i | ||||||
\(748\) | 9.58988e10i | 0.0112010i | ||||||||
\(749\) | −9.12767e12 | −1.05972 | ||||||||
\(750\) | 1.65162e12 | + | 1.09961e13i | 0.190605 | + | 1.26900i | ||||
\(751\) | 8.65348e12 | 0.992685 | 0.496342 | − | 0.868127i | \(-0.334676\pi\) | ||||
0.496342 | + | 0.868127i | \(0.334676\pi\) | |||||||
\(752\) | 1.58215e12i | 0.180413i | ||||||||
\(753\) | − | 1.91675e13i | − | 2.17265i | ||||||
\(754\) | −8.59720e12 | −0.968692 | ||||||||
\(755\) | 2.83428e11 | + | 5.69860e12i | 0.0317454 | + | 0.638274i | ||||
\(756\) | −7.94496e12 | −0.884594 | ||||||||
\(757\) | − | 4.54387e12i | − | 0.502915i | −0.967868 | − | 0.251457i | \(-0.919090\pi\) | ||
0.967868 | − | 0.251457i | \(-0.0809099\pi\) | |||||||
\(758\) | 6.88495e11i | 0.0757512i | ||||||||
\(759\) | −1.20627e13 | −1.31934 | ||||||||
\(760\) | −9.92997e11 | + | 4.93880e10i | −0.107966 | + | 0.00536983i | ||||
\(761\) | 1.14418e13 | 1.23670 | 0.618351 | − | 0.785902i | \(-0.287801\pi\) | ||||
0.618351 | + | 0.785902i | \(0.287801\pi\) | |||||||
\(762\) | 1.98916e12i | 0.213733i | ||||||||
\(763\) | 2.93433e12i | 0.313435i | ||||||||
\(764\) | −7.47390e12 | −0.793646 | ||||||||
\(765\) | −1.04104e12 | + | 5.17777e10i | −0.109899 | + | 0.00546596i | ||||
\(766\) | 4.63854e12 | 0.486801 | ||||||||
\(767\) | − | 1.20691e13i | − | 1.25920i | ||||||
\(768\) | − | 1.09352e12i | − | 0.113423i | ||||||
\(769\) | 1.80380e13 | 1.86003 | 0.930016 | − | 0.367518i | \(-0.119793\pi\) | ||||
0.930016 | + | 0.367518i | \(0.119793\pi\) | |||||||
\(770\) | −1.20583e11 | − | 2.42444e12i | −0.0123617 | − | 0.248544i | ||||
\(771\) | −2.14053e13 | −2.18161 | ||||||||
\(772\) | 1.36630e11i | 0.0138442i | ||||||||
\(773\) | 3.13678e12i | 0.315992i | 0.987440 | + | 0.157996i | \(0.0505033\pi\) | ||||
−0.987440 | + | 0.157996i | \(0.949497\pi\) | |||||||
\(774\) | −1.72533e12 | −0.172797 | ||||||||
\(775\) | −5.31969e12 | + | 5.30476e11i | −0.529698 | + | 0.0528212i | ||||
\(776\) | −6.57625e12 | −0.651029 | ||||||||
\(777\) | − | 1.62126e13i | − | 1.59572i | ||||||
\(778\) | − | 8.16127e12i | − | 0.798637i | ||||||
\(779\) | 2.59130e12 | 0.252115 | ||||||||
\(780\) | 5.95237e11 | + | 1.19678e13i | 0.0575790 | + | 1.15768i | ||||
\(781\) | 3.09612e12 | 0.297775 | ||||||||
\(782\) | 5.52410e11i | 0.0528239i | ||||||||
\(783\) | 2.64759e13i | 2.51723i | ||||||||
\(784\) | 1.14218e12 | 0.107972 | ||||||||
\(785\) | 6.61826e11 | − | 3.29168e10i | 0.0622058 | − | 0.00309389i | ||||
\(786\) | 2.03252e13 | 1.89948 | ||||||||
\(787\) | 5.28159e12i | 0.490770i | 0.969426 | + | 0.245385i | \(0.0789144\pi\) | ||||
−0.969426 | + | 0.245385i | \(0.921086\pi\) | |||||||
\(788\) | 7.31462e12i | 0.675809i | ||||||||
\(789\) | 2.91594e13 | 2.67875 | ||||||||
\(790\) | −6.88162e12 | + | 3.42267e11i | −0.628592 | + | 0.0312639i | ||||
\(791\) | 7.28368e12 | 0.661541 | ||||||||
\(792\) | − | 4.19214e12i | − | 0.378593i | ||||||
\(793\) | 1.21612e13i | 1.09206i | ||||||||
\(794\) | 4.07912e12 | 0.364229 | ||||||||
\(795\) | −2.80811e11 | − | 5.64598e12i | −0.0249322 | − | 0.501288i | ||||
\(796\) | 6.25833e12 | 0.552522 | ||||||||
\(797\) | − | 1.49680e13i | − | 1.31402i | −0.753881 | − | 0.657011i | \(-0.771821\pi\) | ||
0.753881 | − | 0.657011i | \(-0.228179\pi\) | |||||||
\(798\) | 3.38771e12i | 0.295728i | ||||||||
\(799\) | 3.98874e11 | 0.0346239 | ||||||||
\(800\) | 2.03217e11 | + | 2.03789e12i | 0.0175411 | + | 0.175904i | ||||
\(801\) | −3.35544e13 | −2.88007 | ||||||||
\(802\) | − | 8.15488e12i | − | 0.696038i | ||||||
\(803\) | − | 6.73887e12i | − | 0.571962i | ||||||
\(804\) | 3.36704e12 | 0.284182 | ||||||||
\(805\) | −6.94597e11 | − | 1.39656e13i | −0.0582977 | − | 1.17213i | ||||
\(806\) | −5.76108e12 | −0.480835 | ||||||||
\(807\) | 2.50351e13i | 2.07787i | ||||||||
\(808\) | − | 5.23605e12i | − | 0.432168i | ||||||
\(809\) | 7.67334e12 | 0.629819 | 0.314910 | − | 0.949122i | \(-0.398026\pi\) | ||||
0.314910 | + | 0.949122i | \(0.398026\pi\) | |||||||
\(810\) | 1.70130e13 | − | 8.46163e11i | 1.38867 | − | 0.0690672i | ||||
\(811\) | −1.09542e13 | −0.889175 | −0.444587 | − | 0.895736i | \(-0.646650\pi\) | ||||
−0.444587 | + | 0.895736i | \(0.646650\pi\) | |||||||
\(812\) | 5.00675e12i | 0.404160i | ||||||||
\(813\) | 5.66992e11i | 0.0455165i | ||||||||
\(814\) | 4.82447e12 | 0.385159 | ||||||||
\(815\) | −8.06618e12 | + | 4.01182e11i | −0.640411 | + | 0.0318517i | ||||
\(816\) | −2.75687e11 | −0.0217676 | ||||||||
\(817\) | 4.14896e11i | 0.0325791i | ||||||||
\(818\) | − | 1.70712e13i | − | 1.33313i | ||||||
\(819\) | 2.84321e13 | 2.20817 | ||||||||
\(820\) | −2.65155e11 | − | 5.33122e12i | −0.0204804 | − | 0.411779i | ||||
\(821\) | 9.17326e12 | 0.704660 | 0.352330 | − | 0.935876i | \(-0.385389\pi\) | ||||
0.352330 | + | 0.935876i | \(0.385389\pi\) | |||||||
\(822\) | 5.34933e12i | 0.408673i | ||||||||
\(823\) | − | 9.50868e12i | − | 0.722472i | −0.932475 | − | 0.361236i | \(-0.882355\pi\) | ||
0.932475 | − | 0.361236i | \(-0.117645\pi\) | |||||||
\(824\) | −6.81092e12 | −0.514675 | ||||||||
\(825\) | 1.11875e12 | + | 1.12190e13i | 0.0840796 | + | 0.843162i | ||||
\(826\) | −7.02869e12 | −0.525369 | ||||||||
\(827\) | 9.88575e11i | 0.0734911i | 0.999325 | + | 0.0367456i | \(0.0116991\pi\) | ||||
−0.999325 | + | 0.0367456i | \(0.988301\pi\) | |||||||
\(828\) | − | 2.41482e13i | − | 1.78545i | ||||||
\(829\) | −6.00947e12 | −0.441917 | −0.220959 | − | 0.975283i | \(-0.570919\pi\) | ||||
−0.220959 | + | 0.975283i | \(0.570919\pi\) | |||||||
\(830\) | 7.74673e10 | + | 1.55756e12i | 0.00566587 | + | 0.113918i | ||||
\(831\) | 6.02947e12 | 0.438606 | ||||||||
\(832\) | 2.20698e12i | 0.159678i | ||||||||
\(833\) | − | 2.87953e11i | − | 0.0207214i | ||||||
\(834\) | −2.77719e13 | −1.98774 | ||||||||
\(835\) | −5.29323e12 | + | 2.63266e11i | −0.376818 | + | 0.0187415i | ||||
\(836\) | −1.00810e12 | −0.0713798 | ||||||||
\(837\) | 1.77418e13i | 1.24949i | ||||||||
\(838\) | 7.55452e12i | 0.529186i | ||||||||
\(839\) | −1.12593e13 | −0.784484 | −0.392242 | − | 0.919862i | \(-0.628300\pi\) | ||||
−0.392242 | + | 0.919862i | \(0.628300\pi\) | |||||||
\(840\) | 6.96971e12 | − | 3.46648e11i | 0.483012 | − | 0.0240233i | ||||
\(841\) | 2.17744e12 | 0.150094 | ||||||||
\(842\) | 7.72386e12i | 0.529578i | ||||||||
\(843\) | − | 3.31270e11i | − | 0.0225922i | ||||||
\(844\) | −7.53858e12 | −0.511385 | ||||||||
\(845\) | −4.65131e11 | − | 9.35194e12i | −0.0313849 | − | 0.631025i | ||||
\(846\) | −1.74365e13 | −1.17029 | ||||||||
\(847\) | 8.82865e12i | 0.589412i | ||||||||
\(848\) | − | 1.04117e12i | − | 0.0691419i | ||||||
\(849\) | −4.13488e13 | −2.73136 | ||||||||
\(850\) | 5.13772e11 | − | 5.12330e10i | 0.0337587 | − | 0.00336639i | ||||
\(851\) | 2.77906e13 | 1.81641 | ||||||||
\(852\) | 8.90065e12i | 0.578687i | ||||||||
\(853\) | 1.60111e13i | 1.03550i | 0.855532 | + | 0.517751i | \(0.173231\pi\) | ||||
−0.855532 | + | 0.517751i | \(0.826769\pi\) | |||||||
\(854\) | 7.08233e12 | 0.455633 | ||||||||
\(855\) | −5.44294e11 | − | 1.09436e13i | −0.0348326 | − | 0.700345i | ||||
\(856\) | 7.80839e12 | 0.497084 | ||||||||
\(857\) | 2.37698e13i | 1.50526i | 0.658442 | + | 0.752631i | \(0.271216\pi\) | ||||
−0.658442 | + | 0.752631i | \(0.728784\pi\) | |||||||
\(858\) | 1.21499e13i | 0.765383i | ||||||||
\(859\) | 9.00506e12 | 0.564309 | 0.282155 | − | 0.959369i | \(-0.408951\pi\) | ||||
0.282155 | + | 0.959369i | \(0.408951\pi\) | |||||||
\(860\) | 8.53587e11 | − | 4.24543e10i | 0.0532114 | − | 0.00264654i | ||||
\(861\) | −1.81880e13 | −1.12790 | ||||||||
\(862\) | − | 1.96113e13i | − | 1.20983i | ||||||
\(863\) | 2.23368e13i | 1.37080i | 0.728169 | + | 0.685398i | \(0.240372\pi\) | ||||
−0.728169 | + | 0.685398i | \(0.759628\pi\) | |||||||
\(864\) | 6.79663e12 | 0.414937 | ||||||||
\(865\) | −1.99495e12 | + | 9.92213e10i | −0.121160 | + | 0.00602605i | ||||
\(866\) | 1.98540e13 | 1.19955 | ||||||||
\(867\) | − | 3.01236e13i | − | 1.81060i | ||||||
\(868\) | 3.35508e12i | 0.200615i | ||||||||
\(869\) | −6.98629e12 | −0.415583 | ||||||||
\(870\) | −1.15518e12 | − | 2.32260e13i | −0.0683615 | − | 1.37448i | ||||
\(871\) | −6.79547e12 | −0.400072 | ||||||||
\(872\) | − | 2.51021e12i | − | 0.147023i | ||||||
\(873\) | − | 7.24753e13i | − | 4.22305i | ||||||
\(874\) | −5.80700e12 | −0.336628 | ||||||||
\(875\) | −1.29244e13 | + | 1.94125e12i | −0.745371 | + | 0.111955i | ||||
\(876\) | 1.93727e13 | 1.11153 | ||||||||
\(877\) | − | 5.15128e12i | − | 0.294047i | −0.989133 | − | 0.147023i | \(-0.953031\pi\) | ||
0.989133 | − | 0.147023i | \(-0.0469693\pi\) | |||||||
\(878\) | 1.93503e13i | 1.09891i | ||||||||
\(879\) | 5.12495e12 | 0.289561 | ||||||||
\(880\) | 1.03154e11 | + | 2.07402e12i | 0.00579849 | + | 0.116584i | ||||
\(881\) | 7.13386e12 | 0.398963 | 0.199482 | − | 0.979902i | \(-0.436074\pi\) | ||||
0.199482 | + | 0.979902i | \(0.436074\pi\) | |||||||
\(882\) | 1.25877e13i | 0.700384i | ||||||||
\(883\) | − | 1.68937e13i | − | 0.935192i | −0.883942 | − | 0.467596i | \(-0.845120\pi\) | ||
0.883942 | − | 0.467596i | \(-0.154880\pi\) | |||||||
\(884\) | 5.56401e11 | 0.0306445 | ||||||||
\(885\) | 3.26056e13 | − | 1.62169e12i | 1.78668 | − | 0.0888632i | ||||
\(886\) | 7.13225e11 | 0.0388843 | ||||||||
\(887\) | − | 1.25560e13i | − | 0.681073i | −0.940231 | − | 0.340537i | \(-0.889391\pi\) | ||
0.940231 | − | 0.340537i | \(-0.110609\pi\) | |||||||
\(888\) | 1.38693e13i | 0.748506i | ||||||||
\(889\) | −2.33797e12 | −0.125540 | ||||||||
\(890\) | 1.66007e13 | − | 8.25659e11i | 0.886894 | − | 0.0441109i | ||||
\(891\) | 1.72717e13 | 0.918092 | ||||||||
\(892\) | 8.69876e12i | 0.460061i | ||||||||
\(893\) | 4.19301e12i | 0.220645i | ||||||||
\(894\) | −1.56668e13 | −0.820279 | ||||||||
\(895\) | 8.66143e11 | + | 1.74147e13i | 0.0451218 | + | 0.907219i | ||||
\(896\) | 1.28528e12 | 0.0666211 | ||||||||
\(897\) | 6.99874e13i | 3.60955i | ||||||||
\(898\) | 1.16532e13i | 0.597999i | ||||||||
\(899\) | 1.11805e13 | 0.570879 | ||||||||
\(900\) | −2.24591e13 | + | 2.23961e12i | −1.14104 | + | 0.113784i | ||||
\(901\) | −2.62489e11 | −0.0132694 | ||||||||
\(902\) | − | 5.41230e12i | − | 0.272240i | ||||||
\(903\) | − | 2.91210e12i | − | 0.145751i | ||||||
\(904\) | −6.23092e12 | −0.310309 | ||||||||
\(905\) | −7.53743e11 | − | 1.51548e13i | −0.0373512 | − | 0.750984i | ||||
\(906\) | −1.66314e13 | −0.820071 | ||||||||
\(907\) | 9.91682e11i | 0.0486564i | 0.999704 | + | 0.0243282i | \(0.00774466\pi\) | ||||
−0.999704 | + | 0.0243282i | \(0.992255\pi\) | |||||||
\(908\) | − | 3.99668e12i | − | 0.195125i | ||||||
\(909\) | 5.77053e13 | 2.80335 | ||||||||
\(910\) | −1.40665e13 | + | 6.99616e11i | −0.679986 | + | 0.0338200i | ||||
\(911\) | 4.26457e12 | 0.205136 | 0.102568 | − | 0.994726i | \(-0.467294\pi\) | ||||
0.102568 | + | 0.994726i | \(0.467294\pi\) | |||||||
\(912\) | − | 2.89806e12i | − | 0.138717i | ||||||
\(913\) | 1.58125e12i | 0.0753150i | ||||||||
\(914\) | 2.58990e13 | 1.22751 | ||||||||
\(915\) | −3.28545e13 | + | 1.63406e12i | −1.54953 | + | 0.0770679i | ||||
\(916\) | 1.38017e13 | 0.647744 | ||||||||
\(917\) | 2.38894e13i | 1.11569i | ||||||||
\(918\) | − | 1.71349e12i | − | 0.0796325i | ||||||
\(919\) | −1.87200e13 | −0.865736 | −0.432868 | − | 0.901457i | \(-0.642498\pi\) | ||||
−0.432868 | + | 0.901457i | \(0.642498\pi\) | |||||||
\(920\) | 5.94203e11 | + | 1.19471e13i | 0.0273457 | + | 0.549814i | ||||
\(921\) | −3.28019e13 | −1.50221 | ||||||||
\(922\) | 8.41973e12i | 0.383715i | ||||||||
\(923\) | − | 1.79636e13i | − | 0.814677i | ||||||
\(924\) | 7.07572e12 | 0.319335 | ||||||||
\(925\) | −2.57743e12 | − | 2.58468e13i | −0.115757 | − | 1.16083i | ||||
\(926\) | −2.74627e13 | −1.22742 | ||||||||
\(927\) | − | 7.50616e13i | − | 3.33856i | ||||||
\(928\) | − | 4.28309e12i | − | 0.189580i | ||||||
\(929\) | 2.63022e13 | 1.15857 | 0.579284 | − | 0.815126i | \(-0.303332\pi\) | ||||
0.579284 | + | 0.815126i | \(0.303332\pi\) | |||||||
\(930\) | −7.74097e11 | − | 1.55640e13i | −0.0339330 | − | 0.682257i | ||||
\(931\) | 3.02700e12 | 0.132050 | ||||||||
\(932\) | − | 1.94410e13i | − | 0.844008i | ||||||
\(933\) | 5.51360e13i | 2.38214i | ||||||||
\(934\) | 2.17775e13 | 0.936367 | ||||||||
\(935\) | 5.22880e11 | − | 2.60061e10i | 0.0223743 | − | 0.00111282i | ||||
\(936\) | −2.43227e13 | −1.03579 | ||||||||
\(937\) | − | 2.42588e13i | − | 1.02811i | −0.857757 | − | 0.514056i | \(-0.828142\pi\) | ||
0.857757 | − | 0.514056i | \(-0.171858\pi\) | |||||||
\(938\) | 3.95748e12i | 0.166919i | ||||||||
\(939\) | −5.35212e13 | −2.24662 | ||||||||
\(940\) | 8.62652e12 | − | 4.29051e11i | 0.360380 | − | 0.0179240i | ||||
\(941\) | −6.41319e12 | −0.266637 | −0.133319 | − | 0.991073i | \(-0.542563\pi\) | ||||
−0.133319 | + | 0.991073i | \(0.542563\pi\) | |||||||
\(942\) | 1.93154e12i | 0.0799235i | ||||||||
\(943\) | − | 3.11767e13i | − | 1.28389i | ||||||
\(944\) | 6.01279e12 | 0.246435 | ||||||||
\(945\) | 2.15454e12 | + | 4.33192e13i | 0.0878843 | + | 1.76700i | ||||
\(946\) | 8.66570e11 | 0.0351798 | ||||||||
\(947\) | 1.66444e13i | 0.672500i | 0.941773 | + | 0.336250i | \(0.109159\pi\) | ||||
−0.941773 | + | 0.336250i | \(0.890841\pi\) | |||||||
\(948\) | − | 2.00840e13i | − | 0.807631i | ||||||
\(949\) | −3.90986e13 | −1.56482 | ||||||||
\(950\) | 5.38568e11 | + | 5.40083e12i | 0.0214528 | + | 0.215132i | ||||
\(951\) | 2.21733e13 | 0.879058 | ||||||||
\(952\) | − | 3.24031e11i | − | 0.0127856i | ||||||
\(953\) | 8.34836e12i | 0.327856i | 0.986472 | + | 0.163928i | \(0.0524164\pi\) | ||||
−0.986472 | + | 0.163928i | \(0.947584\pi\) | |||||||
\(954\) | 1.14745e13 | 0.448505 | ||||||||
\(955\) | 2.02679e12 | + | 4.07508e13i | 0.0788487 | + | 1.58533i | ||||
\(956\) | −1.71623e13 | −0.664529 | ||||||||
\(957\) | − | 2.35793e13i | − | 0.908712i | ||||||
\(958\) | − | 1.23414e13i | − | 0.473391i | ||||||
\(959\) | −6.28738e12 | −0.240041 | ||||||||
\(960\) | −5.96234e12 | + | 2.96545e11i | −0.226567 | + | 0.0112686i | ||||
\(961\) | −1.89474e13 | −0.716630 | ||||||||
\(962\) | − | 2.79914e13i | − | 1.05375i | ||||||
\(963\) | 8.60545e13i | 3.22445i | ||||||||
\(964\) | −8.18398e12 | −0.305223 | ||||||||
\(965\) | 7.44961e11 | − | 3.70516e10i | 0.0276542 | − | 0.00137542i | ||||
\(966\) | 4.07585e13 | 1.50599 | ||||||||
\(967\) | 7.78660e12i | 0.286371i | 0.989696 | + | 0.143185i | \(0.0457345\pi\) | ||||
−0.989696 | + | 0.143185i | \(0.954265\pi\) | |||||||
\(968\) | − | 7.55259e12i | − | 0.276476i | ||||||
\(969\) | −7.30628e11 | −0.0266219 | ||||||||
\(970\) | 1.78337e12 | + | 3.58564e13i | 0.0646797 | + | 1.30045i | ||||
\(971\) | −2.49047e13 | −0.899071 | −0.449536 | − | 0.893262i | \(-0.648410\pi\) | ||||
−0.449536 | + | 0.893262i | \(0.648410\pi\) | |||||||
\(972\) | 1.69917e13i | 0.610575i | ||||||||
\(973\) | − | 3.26420e13i | − | 1.16753i | ||||||
\(974\) | 1.12126e12 | 0.0399202 | ||||||||
\(975\) | 6.50922e13 | − | 6.49095e12i | 2.30679 | − | 0.230032i | ||||
\(976\) | −6.05867e12 | −0.213724 | ||||||||
\(977\) | − | 1.85806e13i | − | 0.652429i | −0.945296 | − | 0.326215i | \(-0.894227\pi\) | ||
0.945296 | − | 0.326215i | \(-0.105773\pi\) | |||||||
\(978\) | − | 2.35411e13i | − | 0.822816i | ||||||
\(979\) | 1.68532e13 | 0.586354 | ||||||||
\(980\) | −3.09739e11 | − | 6.22761e12i | −0.0107270 | − | 0.215677i | ||||
\(981\) | 2.76645e13 | 0.953700 | ||||||||
\(982\) | 5.23825e12i | 0.179757i | ||||||||
\(983\) | − | 7.22251e12i | − | 0.246716i | −0.992362 | − | 0.123358i | \(-0.960634\pi\) | ||
0.992362 | − | 0.123358i | \(-0.0393663\pi\) | |||||||
\(984\) | 1.55591e13 | 0.529064 | ||||||||
\(985\) | 3.98823e13 | − | 1.98360e12i | 1.34995 | − | 0.0671415i | ||||
\(986\) | −1.07981e12 | −0.0363832 | ||||||||
\(987\) | − | 2.94302e13i | − | 0.987111i | ||||||
\(988\) | 5.84896e12i | 0.195287i | ||||||||
\(989\) | 4.99174e12 | 0.165908 | ||||||||
\(990\) | −2.28573e13 | + | 1.13684e12i | −0.756251 | + | 0.0376132i | ||||
\(991\) | 2.71238e13 | 0.893344 | 0.446672 | − | 0.894698i | \(-0.352609\pi\) | ||||
0.446672 | + | 0.894698i | \(0.352609\pi\) | |||||||
\(992\) | − | 2.87015e12i | − | 0.0941027i | ||||||
\(993\) | 4.94235e13i | 1.61310i | ||||||||
\(994\) | −1.04615e13 | −0.339902 | ||||||||
\(995\) | −1.69715e12 | − | 3.41230e13i | −0.0548930 | − | 1.10368i | ||||
\(996\) | −4.54573e12 | −0.146365 | ||||||||
\(997\) | 2.34124e13i | 0.750442i | 0.926935 | + | 0.375221i | \(0.122433\pi\) | ||||
−0.926935 | + | 0.375221i | \(0.877567\pi\) | |||||||
\(998\) | − | 2.48481e13i | − | 0.792877i | ||||||
\(999\) | −8.62023e13 | −2.73826 |
(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 | 10.10.b.a.9.1 | ✓ | 4 | |
3.2 | odd | 2 | 90.10.c.b.19.3 | 4 | |||
4.3 | odd | 2 | 80.10.c.a.49.4 | 4 | |||
5.2 | odd | 4 | 50.10.a.i.1.1 | 2 | |||
5.3 | odd | 4 | 50.10.a.h.1.2 | 2 | |||
5.4 | even | 2 | inner | 10.10.b.a.9.4 | yes | 4 | |
15.14 | odd | 2 | 90.10.c.b.19.1 | 4 | |||
20.3 | even | 4 | 400.10.a.m.1.1 | 2 | |||
20.7 | even | 4 | 400.10.a.s.1.2 | 2 | |||
20.19 | odd | 2 | 80.10.c.a.49.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.10.b.a.9.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
10.10.b.a.9.4 | yes | 4 | 5.4 | even | 2 | inner | |
50.10.a.h.1.2 | 2 | 5.3 | odd | 4 | |||
50.10.a.i.1.1 | 2 | 5.2 | odd | 4 | |||
80.10.c.a.49.1 | 4 | 20.19 | odd | 2 | |||
80.10.c.a.49.4 | 4 | 4.3 | odd | 2 | |||
90.10.c.b.19.1 | 4 | 15.14 | odd | 2 | |||
90.10.c.b.19.3 | 4 | 3.2 | odd | 2 | |||
400.10.a.m.1.1 | 2 | 20.3 | even | 4 | |||
400.10.a.s.1.2 | 2 | 20.7 | even | 4 |