Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,9,Mod(23,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("33.23");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.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: | \(13.4434941320\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 23.7 | ||
Character | \(\chi\) | \(=\) | 33.23 |
Dual form | 33.9.b.a.23.20 |
$q$-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 \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).
\(n\) | \(13\) | \(23\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 16.2016i | − | 1.01260i | −0.862358 | − | 0.506299i | \(-0.831013\pi\) | ||
0.862358 | − | 0.506299i | \(-0.168987\pi\) | |||||||
\(3\) | −80.7607 | − | 6.22143i | −0.997046 | − | 0.0768077i | ||||
\(4\) | −6.49112 | −0.0253559 | ||||||||
\(5\) | − | 809.269i | − | 1.29483i | −0.762137 | − | 0.647415i | \(-0.775850\pi\) | ||
0.762137 | − | 0.647415i | \(-0.224150\pi\) | |||||||
\(6\) | −100.797 | + | 1308.45i | −0.0777754 | + | 1.00961i | ||||
\(7\) | −3530.96 | −1.47062 | −0.735310 | − | 0.677731i | \(-0.762963\pi\) | ||||
−0.735310 | + | 0.677731i | \(0.762963\pi\) | |||||||
\(8\) | − | 4042.44i | − | 0.986923i | ||||||
\(9\) | 6483.59 | + | 1004.89i | 0.988201 | + | 0.153162i | ||||
\(10\) | −13111.4 | −1.31114 | ||||||||
\(11\) | 4414.43i | 0.301511i | ||||||||
\(12\) | 524.228 | + | 40.3840i | 0.0252810 | + | 0.00194753i | ||||
\(13\) | −10356.8 | −0.362619 | −0.181309 | − | 0.983426i | \(-0.558034\pi\) | ||||
−0.181309 | + | 0.983426i | \(0.558034\pi\) | |||||||
\(14\) | 57207.1i | 1.48915i | ||||||||
\(15\) | −5034.81 | + | 65357.2i | −0.0994530 | + | 1.29101i | ||||
\(16\) | −67155.6 | −1.02471 | ||||||||
\(17\) | 92534.7i | 1.10792i | 0.832543 | + | 0.553961i | \(0.186884\pi\) | ||||
−0.832543 | + | 0.553961i | \(0.813116\pi\) | |||||||
\(18\) | 16280.9 | − | 105044.i | 0.155091 | − | 1.00065i | ||||
\(19\) | 184504. | 1.41576 | 0.707881 | − | 0.706331i | \(-0.249651\pi\) | ||||
0.707881 | + | 0.706331i | \(0.249651\pi\) | |||||||
\(20\) | 5253.06i | 0.0328317i | ||||||||
\(21\) | 285163. | + | 21967.6i | 1.46628 | + | 0.112955i | ||||
\(22\) | 71520.7 | 0.305310 | ||||||||
\(23\) | 201854.i | 0.721317i | 0.932698 | + | 0.360659i | \(0.117448\pi\) | ||||
−0.932698 | + | 0.360659i | \(0.882552\pi\) | |||||||
\(24\) | −25149.7 | + | 326470.i | −0.0758033 | + | 0.984008i | ||||
\(25\) | −264291. | −0.676586 | ||||||||
\(26\) | 167796.i | 0.367187i | ||||||||
\(27\) | −517367. | − | 121493.i | −0.973518 | − | 0.228611i | ||||
\(28\) | 22919.9 | 0.0372890 | ||||||||
\(29\) | − | 37264.0i | − | 0.0526863i | −0.999653 | − | 0.0263431i | \(-0.991614\pi\) | ||
0.999653 | − | 0.0263431i | \(-0.00838625\pi\) | |||||||
\(30\) | 1.05889e6 | + | 81571.8i | 1.30727 | + | 0.100706i | ||||
\(31\) | −1.26758e6 | −1.37255 | −0.686277 | − | 0.727341i | \(-0.740756\pi\) | ||||
−0.686277 | + | 0.727341i | \(0.740756\pi\) | |||||||
\(32\) | 53162.6i | 0.0506998i | ||||||||
\(33\) | 27464.0 | − | 356512.i | 0.0231584 | − | 0.300621i | ||||
\(34\) | 1.49921e6 | 1.12188 | ||||||||
\(35\) | 2.85750e6i | 1.90420i | ||||||||
\(36\) | −42085.8 | − | 6522.89i | −0.0250568 | − | 0.00388356i | ||||
\(37\) | −2.14855e6 | −1.14640 | −0.573202 | − | 0.819414i | \(-0.694299\pi\) | ||||
−0.573202 | + | 0.819414i | \(0.694299\pi\) | |||||||
\(38\) | − | 2.98925e6i | − | 1.43360i | ||||||
\(39\) | 836419. | + | 64433.8i | 0.361548 | + | 0.0278519i | ||||
\(40\) | −3.27142e6 | −1.27790 | ||||||||
\(41\) | − | 3.61216e6i | − | 1.27830i | −0.769083 | − | 0.639148i | \(-0.779287\pi\) | ||
0.769083 | − | 0.639148i | \(-0.220713\pi\) | |||||||
\(42\) | 355910. | − | 4.62009e6i | 0.114378 | − | 1.48475i | ||||
\(43\) | −2.62505e6 | −0.767827 | −0.383913 | − | 0.923369i | \(-0.625424\pi\) | ||||
−0.383913 | + | 0.923369i | \(0.625424\pi\) | |||||||
\(44\) | − | 28654.6i | − | 0.00764511i | ||||||
\(45\) | 813230. | − | 5.24697e6i | 0.198318 | − | 1.27955i | ||||
\(46\) | 3.27036e6 | 0.730405 | ||||||||
\(47\) | 4.99275e6i | 1.02317i | 0.859233 | + | 0.511585i | \(0.170942\pi\) | ||||
−0.859233 | + | 0.511585i | \(0.829058\pi\) | |||||||
\(48\) | 5.42353e6 | + | 417804.i | 1.02169 | + | 0.0787059i | ||||
\(49\) | 6.70286e6 | 1.16272 | ||||||||
\(50\) | 4.28194e6i | 0.685110i | ||||||||
\(51\) | 575698. | − | 7.47317e6i | 0.0850970 | − | 1.10465i | ||||
\(52\) | 67227.0 | 0.00919454 | ||||||||
\(53\) | − | 1.16999e7i | − | 1.48279i | −0.671069 | − | 0.741395i | \(-0.734165\pi\) | ||
0.671069 | − | 0.741395i | \(-0.265835\pi\) | |||||||
\(54\) | −1.96838e6 | + | 8.38217e6i | −0.231491 | + | 0.985783i | ||||
\(55\) | 3.57246e6 | 0.390406 | ||||||||
\(56\) | 1.42737e7i | 1.45139i | ||||||||
\(57\) | −1.49006e7 | − | 1.14788e6i | −1.41158 | − | 0.108742i | ||||
\(58\) | −603736. | −0.0533500 | ||||||||
\(59\) | − | 417021.i | − | 0.0344152i | −0.999852 | − | 0.0172076i | \(-0.994522\pi\) | ||
0.999852 | − | 0.0172076i | \(-0.00547762\pi\) | |||||||
\(60\) | 32681.6 | − | 424241.i | 0.00252173 | − | 0.0327347i | ||||
\(61\) | 1.53477e7 | 1.10847 | 0.554236 | − | 0.832360i | \(-0.313011\pi\) | ||||
0.554236 | + | 0.832360i | \(0.313011\pi\) | |||||||
\(62\) | 2.05368e7i | 1.38985i | ||||||||
\(63\) | −2.28933e7 | − | 3.54824e6i | −1.45327 | − | 0.225243i | ||||
\(64\) | −1.63305e7 | −0.973375 | ||||||||
\(65\) | 8.38140e6i | 0.469530i | ||||||||
\(66\) | −5.77606e6 | − | 444961.i | −0.304408 | − | 0.0234502i | ||||
\(67\) | −8.02130e6 | −0.398057 | −0.199029 | − | 0.979994i | \(-0.563779\pi\) | ||||
−0.199029 | + | 0.979994i | \(0.563779\pi\) | |||||||
\(68\) | − | 600654.i | − | 0.0280924i | ||||||
\(69\) | 1.25582e6 | − | 1.63019e7i | 0.0554028 | − | 0.719186i | ||||
\(70\) | 4.62959e7 | 1.92819 | ||||||||
\(71\) | 3.66962e7i | 1.44407i | 0.691857 | + | 0.722035i | \(0.256793\pi\) | ||||
−0.691857 | + | 0.722035i | \(0.743207\pi\) | |||||||
\(72\) | 4.06222e6 | − | 2.62095e7i | 0.151159 | − | 0.975279i | ||||
\(73\) | −1.19377e7 | −0.420368 | −0.210184 | − | 0.977662i | \(-0.567406\pi\) | ||||
−0.210184 | + | 0.977662i | \(0.567406\pi\) | |||||||
\(74\) | 3.48099e7i | 1.16085i | ||||||||
\(75\) | 2.13444e7 | + | 1.64427e6i | 0.674587 | + | 0.0519670i | ||||
\(76\) | −1.19764e6 | −0.0358980 | ||||||||
\(77\) | − | 1.55872e7i | − | 0.443409i | ||||||
\(78\) | 1.04393e6 | − | 1.35513e7i | 0.0282028 | − | 0.366103i | ||||
\(79\) | −3.44849e7 | −0.885361 | −0.442681 | − | 0.896679i | \(-0.645972\pi\) | ||||
−0.442681 | + | 0.896679i | \(0.645972\pi\) | |||||||
\(80\) | 5.43469e7i | 1.32683i | ||||||||
\(81\) | 4.10271e7 | + | 1.30306e7i | 0.953083 | + | 0.302709i | ||||
\(82\) | −5.85227e7 | −1.29440 | ||||||||
\(83\) | − | 6.78006e7i | − | 1.42863i | −0.699822 | − | 0.714317i | \(-0.746737\pi\) | ||
0.699822 | − | 0.714317i | \(-0.253263\pi\) | |||||||
\(84\) | −1.85103e6 | − | 142594.i | −0.0371788 | − | 0.00286408i | ||||
\(85\) | 7.48855e7 | 1.43457 | ||||||||
\(86\) | 4.25299e7i | 0.777500i | ||||||||
\(87\) | −231835. | + | 3.00947e6i | −0.00404671 | + | 0.0525306i | ||||
\(88\) | 1.78450e7 | 0.297569 | ||||||||
\(89\) | 3.79929e6i | 0.0605540i | 0.999542 | + | 0.0302770i | \(0.00963894\pi\) | ||||
−0.999542 | + | 0.0302770i | \(0.990361\pi\) | |||||||
\(90\) | −8.50091e7 | − | 1.31756e7i | −1.29567 | − | 0.200817i | ||||
\(91\) | 3.65693e7 | 0.533274 | ||||||||
\(92\) | − | 1.31026e6i | − | 0.0182897i | ||||||
\(93\) | 1.02371e8 | + | 7.88617e6i | 1.36850 | + | 0.105423i | ||||
\(94\) | 8.08904e7 | 1.03606 | ||||||||
\(95\) | − | 1.49313e8i | − | 1.83317i | ||||||
\(96\) | 330747. | − | 4.29345e6i | 0.00389413 | − | 0.0505500i | ||||
\(97\) | −1.09278e8 | −1.23437 | −0.617184 | − | 0.786819i | \(-0.711727\pi\) | ||||
−0.617184 | + | 0.786819i | \(0.711727\pi\) | |||||||
\(98\) | − | 1.08597e8i | − | 1.17737i | ||||||
\(99\) | −4.43603e6 | + | 2.86213e7i | −0.0461800 | + | 0.297954i | ||||
\(100\) | 1.71555e6 | 0.0171555 | ||||||||
\(101\) | − | 1.50287e8i | − | 1.44423i | −0.691773 | − | 0.722115i | \(-0.743170\pi\) | ||
0.691773 | − | 0.722115i | \(-0.256830\pi\) | |||||||
\(102\) | −1.21077e8 | − | 9.32722e6i | −1.11857 | − | 0.0861691i | ||||
\(103\) | −1.26768e8 | −1.12632 | −0.563160 | − | 0.826348i | \(-0.690415\pi\) | ||||
−0.563160 | + | 0.826348i | \(0.690415\pi\) | |||||||
\(104\) | 4.18665e7i | 0.357877i | ||||||||
\(105\) | 1.77777e7 | − | 2.30773e8i | 0.146258 | − | 1.89858i | ||||
\(106\) | −1.89557e8 | −1.50147 | ||||||||
\(107\) | 2.33208e8i | 1.77913i | 0.456809 | + | 0.889565i | \(0.348992\pi\) | ||||
−0.456809 | + | 0.889565i | \(0.651008\pi\) | |||||||
\(108\) | 3.35829e6 | + | 788627.i | 0.0246845 | + | 0.00579664i | ||||
\(109\) | −1.94192e8 | −1.37571 | −0.687853 | − | 0.725850i | \(-0.741447\pi\) | ||||
−0.687853 | + | 0.725850i | \(0.741447\pi\) | |||||||
\(110\) | − | 5.78795e7i | − | 0.395325i | ||||||
\(111\) | 1.73518e8 | + | 1.33670e7i | 1.14302 | + | 0.0880528i | ||||
\(112\) | 2.37124e8 | 1.50696 | ||||||||
\(113\) | 2.70114e8i | 1.65666i | 0.560239 | + | 0.828331i | \(0.310709\pi\) | ||||
−0.560239 | + | 0.828331i | \(0.689291\pi\) | |||||||
\(114\) | −1.85974e7 | + | 2.41414e8i | −0.110112 | + | 1.42936i | ||||
\(115\) | 1.63354e8 | 0.933984 | ||||||||
\(116\) | 241885.i | 0.00133591i | ||||||||
\(117\) | −6.71489e7 | − | 1.04074e7i | −0.358340 | − | 0.0555393i | ||||
\(118\) | −6.75640e6 | −0.0348488 | ||||||||
\(119\) | − | 3.26736e8i | − | 1.62933i | ||||||
\(120\) | 2.64202e8 | + | 2.03529e7i | 1.27412 | + | 0.0981525i | ||||
\(121\) | −1.94872e7 | −0.0909091 | ||||||||
\(122\) | − | 2.48657e8i | − | 1.12244i | ||||||
\(123\) | −2.24728e7 | + | 2.91721e8i | −0.0981831 | + | 1.27452i | ||||
\(124\) | 8.22803e6 | 0.0348024 | ||||||||
\(125\) | − | 1.02238e8i | − | 0.418766i | ||||||
\(126\) | −5.74871e7 | + | 3.70907e8i | −0.228080 | + | 1.47158i | ||||
\(127\) | 1.13356e8 | 0.435743 | 0.217872 | − | 0.975977i | \(-0.430089\pi\) | ||||
0.217872 | + | 0.975977i | \(0.430089\pi\) | |||||||
\(128\) | 2.78190e8i | 1.03634i | ||||||||
\(129\) | 2.12001e8 | + | 1.63315e7i | 0.765558 | + | 0.0589750i | ||||
\(130\) | 1.35792e8 | 0.475445 | ||||||||
\(131\) | 1.15367e8i | 0.391738i | 0.980630 | + | 0.195869i | \(0.0627527\pi\) | ||||
−0.980630 | + | 0.195869i | \(0.937247\pi\) | |||||||
\(132\) | −178272. | + | 2.31417e6i | −0.000587203 | + | 0.00762252i | ||||
\(133\) | −6.51475e8 | −2.08205 | ||||||||
\(134\) | 1.29958e8i | 0.403072i | ||||||||
\(135\) | −9.83206e7 | + | 4.18689e8i | −0.296012 | + | 1.26054i | ||||
\(136\) | 3.74066e8 | 1.09343 | ||||||||
\(137\) | − | 3.94517e8i | − | 1.11991i | −0.828523 | − | 0.559955i | \(-0.810818\pi\) | ||
0.828523 | − | 0.559955i | \(-0.189182\pi\) | |||||||
\(138\) | −2.64116e8 | − | 2.03463e7i | −0.728247 | − | 0.0561007i | ||||
\(139\) | 1.85138e8 | 0.495949 | 0.247975 | − | 0.968767i | \(-0.420235\pi\) | ||||
0.247975 | + | 0.968767i | \(0.420235\pi\) | |||||||
\(140\) | − | 1.85483e7i | − | 0.0482829i | ||||||
\(141\) | 3.10620e7 | − | 4.03218e8i | 0.0785874 | − | 1.02015i | ||||
\(142\) | 5.94537e8 | 1.46226 | ||||||||
\(143\) | − | 4.57191e7i | − | 0.109334i | ||||||
\(144\) | −4.35409e8 | − | 6.74842e7i | −1.01262 | − | 0.156947i | ||||
\(145\) | −3.01566e7 | −0.0682198 | ||||||||
\(146\) | 1.93410e8i | 0.425664i | ||||||||
\(147\) | −5.41328e8 | − | 4.17014e7i | −1.15929 | − | 0.0893061i | ||||
\(148\) | 1.39465e7 | 0.0290682 | ||||||||
\(149\) | − | 2.46239e8i | − | 0.499587i | −0.968299 | − | 0.249794i | \(-0.919637\pi\) | ||
0.968299 | − | 0.249794i | \(-0.0803628\pi\) | |||||||
\(150\) | 2.66398e7 | − | 3.45812e8i | 0.0526218 | − | 0.683086i | ||||
\(151\) | −2.67578e8 | −0.514686 | −0.257343 | − | 0.966320i | \(-0.582847\pi\) | ||||
−0.257343 | + | 0.966320i | \(0.582847\pi\) | |||||||
\(152\) | − | 7.45844e8i | − | 1.39725i | ||||||
\(153\) | −9.29876e7 | + | 5.99957e8i | −0.169691 | + | 1.09485i | ||||
\(154\) | −2.52537e8 | −0.448995 | ||||||||
\(155\) | 1.02581e9i | 1.77722i | ||||||||
\(156\) | −5.42930e6 | − | 418248.i | −0.00916738 | − | 0.000706212i | ||||
\(157\) | 3.28157e8 | 0.540111 | 0.270056 | − | 0.962845i | \(-0.412958\pi\) | ||||
0.270056 | + | 0.962845i | \(0.412958\pi\) | |||||||
\(158\) | 5.58710e8i | 0.896516i | ||||||||
\(159\) | −7.27902e7 | + | 9.44894e8i | −0.113890 | + | 1.47841i | ||||
\(160\) | 4.30228e7 | 0.0656476 | ||||||||
\(161\) | − | 7.12738e8i | − | 1.06078i | ||||||
\(162\) | 2.11117e8 | − | 6.64704e8i | 0.306523 | − | 0.965091i | ||||
\(163\) | 7.69943e8 | 1.09071 | 0.545354 | − | 0.838206i | \(-0.316395\pi\) | ||||
0.545354 | + | 0.838206i | \(0.316395\pi\) | |||||||
\(164\) | 2.34470e7i | 0.0324124i | ||||||||
\(165\) | −2.88514e8 | − | 2.22258e7i | −0.389253 | − | 0.0299862i | ||||
\(166\) | −1.09848e9 | −1.44663 | ||||||||
\(167\) | − | 1.06785e9i | − | 1.37291i | −0.727171 | − | 0.686457i | \(-0.759165\pi\) | ||
0.727171 | − | 0.686457i | \(-0.240835\pi\) | |||||||
\(168\) | 8.88026e7 | − | 1.15275e9i | 0.111478 | − | 1.44710i | ||||
\(169\) | −7.08468e8 | −0.868508 | ||||||||
\(170\) | − | 1.21326e9i | − | 1.45264i | ||||||
\(171\) | 1.19625e9 | + | 1.85407e8i | 1.39906 | + | 0.216841i | ||||
\(172\) | 1.70395e7 | 0.0194690 | ||||||||
\(173\) | 3.17187e8i | 0.354104i | 0.984201 | + | 0.177052i | \(0.0566561\pi\) | ||||
−0.984201 | + | 0.177052i | \(0.943344\pi\) | |||||||
\(174\) | 4.87581e7 | + | 3.75610e6i | 0.0531924 | + | 0.00409770i | ||||
\(175\) | 9.33202e8 | 0.995001 | ||||||||
\(176\) | − | 2.96454e8i | − | 0.308963i | ||||||
\(177\) | −2.59447e6 | + | 3.36789e7i | −0.00264335 | + | 0.0343135i | ||||
\(178\) | 6.15545e7 | 0.0613169 | ||||||||
\(179\) | − | 4.84139e6i | − | 0.00471583i | −0.999997 | − | 0.00235792i | \(-0.999249\pi\) | ||
0.999997 | − | 0.00235792i | \(-0.000750549\pi\) | |||||||
\(180\) | −5.27877e6 | + | 3.40587e7i | −0.00502855 | + | 0.0324443i | ||||
\(181\) | 5.53185e8 | 0.515414 | 0.257707 | − | 0.966223i | \(-0.417033\pi\) | ||||
0.257707 | + | 0.966223i | \(0.417033\pi\) | |||||||
\(182\) | − | 5.92480e8i | − | 0.539993i | ||||||
\(183\) | −1.23949e9 | − | 9.54847e7i | −1.10520 | − | 0.0851392i | ||||
\(184\) | 8.15983e8 | 0.711885 | ||||||||
\(185\) | 1.73875e9i | 1.48440i | ||||||||
\(186\) | 1.27768e8 | − | 1.65857e9i | 0.106751 | − | 1.38574i | ||||
\(187\) | −4.08488e8 | −0.334051 | ||||||||
\(188\) | − | 3.24085e7i | − | 0.0259435i | ||||||
\(189\) | 1.82680e9 | + | 4.28987e8i | 1.43167 | + | 0.336199i | ||||
\(190\) | −2.41911e9 | −1.85627 | ||||||||
\(191\) | 3.13087e8i | 0.235251i | 0.993058 | + | 0.117625i | \(0.0375282\pi\) | ||||
−0.993058 | + | 0.117625i | \(0.962472\pi\) | |||||||
\(192\) | 1.31886e9 | + | 1.01599e8i | 0.970499 | + | 0.0747627i | ||||
\(193\) | 4.83543e8 | 0.348502 | 0.174251 | − | 0.984701i | \(-0.444250\pi\) | ||||
0.174251 | + | 0.984701i | \(0.444250\pi\) | |||||||
\(194\) | 1.77047e9i | 1.24992i | ||||||||
\(195\) | 5.21443e7 | − | 6.76888e8i | 0.0360635 | − | 0.468143i | ||||
\(196\) | −4.35091e7 | −0.0294819 | ||||||||
\(197\) | 8.26672e8i | 0.548868i | 0.961606 | + | 0.274434i | \(0.0884905\pi\) | ||||
−0.961606 | + | 0.274434i | \(0.911509\pi\) | |||||||
\(198\) | 4.63711e8 | + | 7.18707e7i | 0.301708 | + | 0.0467618i | ||||
\(199\) | 1.09074e8 | 0.0695520 | 0.0347760 | − | 0.999395i | \(-0.488928\pi\) | ||||
0.0347760 | + | 0.999395i | \(0.488928\pi\) | |||||||
\(200\) | 1.06838e9i | 0.667738i | ||||||||
\(201\) | 6.47806e8 | + | 4.99039e7i | 0.396881 | + | 0.0305739i | ||||
\(202\) | −2.43489e9 | −1.46243 | ||||||||
\(203\) | 1.31578e8i | 0.0774815i | ||||||||
\(204\) | −3.73693e6 | + | 4.85093e7i | −0.00215771 | + | 0.0280094i | ||||
\(205\) | −2.92321e9 | −1.65518 | ||||||||
\(206\) | 2.05385e9i | 1.14051i | ||||||||
\(207\) | −2.02842e8 | + | 1.30874e9i | −0.110478 | + | 0.712807i | ||||
\(208\) | 6.95514e8 | 0.371580 | ||||||||
\(209\) | 8.14478e8i | 0.426869i | ||||||||
\(210\) | −3.73889e9 | − | 2.88027e8i | −1.92250 | − | 0.148100i | ||||
\(211\) | −2.01418e9 | −1.01617 | −0.508086 | − | 0.861306i | \(-0.669647\pi\) | ||||
−0.508086 | + | 0.861306i | \(0.669647\pi\) | |||||||
\(212\) | 7.59456e7i | 0.0375975i | ||||||||
\(213\) | 2.28303e8 | − | 2.96361e9i | 0.110916 | − | 1.43980i | ||||
\(214\) | 3.77833e9 | 1.80154 | ||||||||
\(215\) | 2.12437e9i | 0.994205i | ||||||||
\(216\) | −4.91128e8 | + | 2.09143e9i | −0.225621 | + | 0.960787i | ||||
\(217\) | 4.47578e9 | 2.01850 | ||||||||
\(218\) | 3.14622e9i | 1.39304i | ||||||||
\(219\) | 9.64099e8 | + | 7.42696e7i | 0.419126 | + | 0.0322875i | ||||
\(220\) | −2.31893e7 | −0.00989912 | ||||||||
\(221\) | − | 9.58359e8i | − | 0.401753i | ||||||
\(222\) | 2.16567e8 | − | 2.81127e9i | 0.0891621 | − | 1.15742i | ||||
\(223\) | −3.24663e9 | −1.31284 | −0.656422 | − | 0.754394i | \(-0.727931\pi\) | ||||
−0.656422 | + | 0.754394i | \(0.727931\pi\) | |||||||
\(224\) | − | 1.87715e8i | − | 0.0745601i | ||||||
\(225\) | −1.71356e9 | − | 2.65585e8i | −0.668603 | − | 0.103627i | ||||
\(226\) | 4.37628e9 | 1.67753 | ||||||||
\(227\) | − | 2.62037e9i | − | 0.986868i | −0.869783 | − | 0.493434i | \(-0.835741\pi\) | ||
0.869783 | − | 0.493434i | \(-0.164259\pi\) | |||||||
\(228\) | 9.67219e7 | + | 7.45100e6i | 0.0357920 | + | 0.00275724i | ||||
\(229\) | −7.80560e8 | −0.283834 | −0.141917 | − | 0.989879i | \(-0.545327\pi\) | ||||
−0.141917 | + | 0.989879i | \(0.545327\pi\) | |||||||
\(230\) | − | 2.64660e9i | − | 0.945751i | ||||||
\(231\) | −9.69744e7 | + | 1.25883e9i | −0.0340572 | + | 0.442099i | ||||
\(232\) | −1.50637e8 | −0.0519973 | ||||||||
\(233\) | 6.51126e8i | 0.220923i | 0.993880 | + | 0.110462i | \(0.0352329\pi\) | ||||
−0.993880 | + | 0.110462i | \(0.964767\pi\) | |||||||
\(234\) | −1.68617e8 | + | 1.08792e9i | −0.0562390 | + | 0.362855i | ||||
\(235\) | 4.04047e9 | 1.32483 | ||||||||
\(236\) | 2.70694e6i | 0.000872630i | ||||||||
\(237\) | 2.78503e9 | + | 2.14545e8i | 0.882746 | + | 0.0680026i | ||||
\(238\) | −5.29364e9 | −1.64986 | ||||||||
\(239\) | − | 3.98094e9i | − | 1.22010i | −0.792365 | − | 0.610048i | \(-0.791150\pi\) | ||
0.792365 | − | 0.610048i | \(-0.208850\pi\) | |||||||
\(240\) | 3.38116e8 | − | 4.38910e9i | 0.101911 | − | 1.32291i | ||||
\(241\) | 3.63924e9 | 1.07880 | 0.539402 | − | 0.842048i | \(-0.318650\pi\) | ||||
0.539402 | + | 0.842048i | \(0.318650\pi\) | |||||||
\(242\) | 3.15723e8i | 0.0920544i | ||||||||
\(243\) | −3.23231e9 | − | 1.30761e9i | −0.927017 | − | 0.375019i | ||||
\(244\) | −9.96239e7 | −0.0281063 | ||||||||
\(245\) | − | 5.42442e9i | − | 1.50553i | ||||||
\(246\) | 4.72634e9 | + | 3.64095e8i | 1.29058 | + | 0.0994201i | ||||
\(247\) | −1.91086e9 | −0.513382 | ||||||||
\(248\) | 5.12412e9i | 1.35460i | ||||||||
\(249\) | −4.21816e8 | + | 5.47562e9i | −0.109730 | + | 1.42441i | ||||
\(250\) | −1.65641e9 | −0.424042 | ||||||||
\(251\) | 3.48706e9i | 0.878546i | 0.898354 | + | 0.439273i | \(0.144764\pi\) | ||||
−0.898354 | + | 0.439273i | \(0.855236\pi\) | |||||||
\(252\) | 1.48603e8 | + | 2.30320e7i | 0.0368490 | + | 0.00571124i | ||||
\(253\) | −8.91071e8 | −0.217485 | ||||||||
\(254\) | − | 1.83655e9i | − | 0.441233i | ||||||
\(255\) | −6.04781e9 | − | 4.65895e8i | −1.43033 | − | 0.110186i | ||||
\(256\) | 3.26501e8 | 0.0760193 | ||||||||
\(257\) | − | 2.29937e9i | − | 0.527079i | −0.964649 | − | 0.263540i | \(-0.915110\pi\) | ||
0.964649 | − | 0.263540i | \(-0.0848900\pi\) | |||||||
\(258\) | 2.64597e8 | − | 3.43474e9i | 0.0597180 | − | 0.775203i | ||||
\(259\) | 7.58643e9 | 1.68593 | ||||||||
\(260\) | − | 5.44047e7i | − | 0.0119054i | ||||||
\(261\) | 3.74464e7 | − | 2.41604e8i | 0.00806952 | − | 0.0520646i | ||||
\(262\) | 1.86912e9 | 0.396673 | ||||||||
\(263\) | − | 5.11934e9i | − | 1.07002i | −0.844846 | − | 0.535009i | \(-0.820308\pi\) | ||
0.844846 | − | 0.535009i | \(-0.179692\pi\) | |||||||
\(264\) | −1.44118e9 | − | 1.11022e8i | −0.296690 | − | 0.0228556i | ||||
\(265\) | −9.46839e9 | −1.91996 | ||||||||
\(266\) | 1.05549e10i | 2.10828i | ||||||||
\(267\) | 2.36370e7 | − | 3.06834e8i | 0.00465101 | − | 0.0603751i | ||||
\(268\) | 5.20672e7 | 0.0100931 | ||||||||
\(269\) | − | 6.95627e9i | − | 1.32852i | −0.747503 | − | 0.664259i | \(-0.768747\pi\) | ||
0.747503 | − | 0.664259i | \(-0.231253\pi\) | |||||||
\(270\) | 6.78343e9 | + | 1.59295e9i | 1.27642 | + | 0.299742i | ||||
\(271\) | 2.84996e9 | 0.528398 | 0.264199 | − | 0.964468i | \(-0.414892\pi\) | ||||
0.264199 | + | 0.964468i | \(0.414892\pi\) | |||||||
\(272\) | − | 6.21422e9i | − | 1.13530i | ||||||
\(273\) | −2.95336e9 | − | 2.27513e8i | −0.531699 | − | 0.0409596i | ||||
\(274\) | −6.39180e9 | −1.13402 | ||||||||
\(275\) | − | 1.16670e9i | − | 0.203998i | ||||||
\(276\) | −8.15169e6 | + | 1.05818e8i | −0.00140479 | + | 0.0182357i | ||||
\(277\) | −4.15240e9 | −0.705310 | −0.352655 | − | 0.935753i | \(-0.614721\pi\) | ||||
−0.352655 | + | 0.935753i | \(0.614721\pi\) | |||||||
\(278\) | − | 2.99953e9i | − | 0.502198i | ||||||
\(279\) | −8.21848e9 | − | 1.27379e9i | −1.35636 | − | 0.210223i | ||||
\(280\) | 1.15512e10 | 1.87930 | ||||||||
\(281\) | − | 5.80307e9i | − | 0.930750i | −0.885114 | − | 0.465375i | \(-0.845920\pi\) | ||
0.885114 | − | 0.465375i | \(-0.154080\pi\) | |||||||
\(282\) | −6.53276e9 | − | 5.03253e8i | −1.03300 | − | 0.0795775i | ||||
\(283\) | 2.54243e9 | 0.396372 | 0.198186 | − | 0.980164i | \(-0.436495\pi\) | ||||
0.198186 | + | 0.980164i | \(0.436495\pi\) | |||||||
\(284\) | − | 2.38200e8i | − | 0.0366157i | ||||||
\(285\) | −9.28940e8 | + | 1.20586e10i | −0.140802 | + | 1.82776i | ||||
\(286\) | −7.40722e8 | −0.110711 | ||||||||
\(287\) | 1.27544e10i | 1.87989i | ||||||||
\(288\) | −5.34227e7 | + | 3.44684e8i | −0.00776526 | + | 0.0501016i | ||||
\(289\) | −1.58692e9 | −0.227490 | ||||||||
\(290\) | 4.88585e8i | 0.0690793i | ||||||||
\(291\) | 8.82535e9 | + | 6.79864e8i | 1.23072 | + | 0.0948091i | ||||
\(292\) | 7.74892e7 | 0.0106588 | ||||||||
\(293\) | − | 8.82254e9i | − | 1.19708i | −0.801093 | − | 0.598540i | \(-0.795748\pi\) | ||
0.801093 | − | 0.598540i | \(-0.204252\pi\) | |||||||
\(294\) | −6.75628e8 | + | 8.77037e9i | −0.0904312 | + | 1.17389i | ||||
\(295\) | −3.37482e8 | −0.0445618 | ||||||||
\(296\) | 8.68537e9i | 1.13141i | ||||||||
\(297\) | 5.36323e8 | − | 2.28388e9i | 0.0689287 | − | 0.293527i | ||||
\(298\) | −3.98946e9 | −0.505882 | ||||||||
\(299\) | − | 2.09055e9i | − | 0.261563i | ||||||
\(300\) | −1.38549e8 | − | 1.06732e7i | −0.0171048 | − | 0.00131767i | ||||
\(301\) | 9.26893e9 | 1.12918 | ||||||||
\(302\) | 4.33518e9i | 0.521170i | ||||||||
\(303\) | −9.35001e8 | + | 1.21373e10i | −0.110928 | + | 1.43996i | ||||
\(304\) | −1.23904e10 | −1.45075 | ||||||||
\(305\) | − | 1.24204e10i | − | 1.43528i | ||||||
\(306\) | 9.72025e9 | + | 1.50655e9i | 1.10864 | + | 0.171829i | ||||
\(307\) | 9.24765e9 | 1.04106 | 0.520532 | − | 0.853842i | \(-0.325734\pi\) | ||||
0.520532 | + | 0.853842i | \(0.325734\pi\) | |||||||
\(308\) | 1.01178e8i | 0.0112430i | ||||||||
\(309\) | 1.02379e10 | + | 7.88680e8i | 1.12299 | + | 0.0865102i | ||||
\(310\) | 1.66198e10 | 1.79961 | ||||||||
\(311\) | 1.50719e9i | 0.161112i | 0.996750 | + | 0.0805559i | \(0.0256696\pi\) | ||||
−0.996750 | + | 0.0805559i | \(0.974330\pi\) | |||||||
\(312\) | 2.60470e8 | − | 3.38117e9i | 0.0274877 | − | 0.356820i | ||||
\(313\) | −1.37492e10 | −1.43251 | −0.716256 | − | 0.697837i | \(-0.754146\pi\) | ||||
−0.716256 | + | 0.697837i | \(0.754146\pi\) | |||||||
\(314\) | − | 5.31666e9i | − | 0.546916i | ||||||
\(315\) | −2.87148e9 | + | 1.85268e10i | −0.291651 | + | 1.88174i | ||||
\(316\) | 2.23846e8 | 0.0224492 | ||||||||
\(317\) | 7.77092e9i | 0.769548i | 0.923011 | + | 0.384774i | \(0.125721\pi\) | ||||
−0.923011 | + | 0.384774i | \(0.874279\pi\) | |||||||
\(318\) | 1.53088e10 | + | 1.17932e9i | 1.49704 | + | 0.115325i | ||||
\(319\) | 1.64499e8 | 0.0158855 | ||||||||
\(320\) | 1.32158e10i | 1.26036i | ||||||||
\(321\) | 1.45088e9 | − | 1.88340e10i | 0.136651 | − | 1.77387i | ||||
\(322\) | −1.15475e10 | −1.07415 | ||||||||
\(323\) | 1.70730e10i | 1.56855i | ||||||||
\(324\) | −2.66312e8 | − | 8.45834e7i | −0.0241663 | − | 0.00767548i | ||||
\(325\) | 2.73720e9 | 0.245343 | ||||||||
\(326\) | − | 1.24743e10i | − | 1.10445i | ||||||
\(327\) | 1.56831e10 | + | 1.20815e9i | 1.37164 | + | 0.105665i | ||||
\(328\) | −1.46019e10 | −1.26158 | ||||||||
\(329\) | − | 1.76292e10i | − | 1.50469i | ||||||
\(330\) | −3.60093e8 | + | 4.67439e9i | −0.0303640 | + | 0.394157i | ||||
\(331\) | −1.82116e10 | −1.51718 | −0.758590 | − | 0.651568i | \(-0.774112\pi\) | ||||
−0.758590 | + | 0.651568i | \(0.774112\pi\) | |||||||
\(332\) | 4.40102e8i | 0.0362244i | ||||||||
\(333\) | −1.39303e10 | − | 2.15906e9i | −1.13288 | − | 0.175585i | ||||
\(334\) | −1.73008e10 | −1.39021 | ||||||||
\(335\) | 6.49139e9i | 0.515416i | ||||||||
\(336\) | −1.91503e10 | − | 1.47525e9i | −1.50251 | − | 0.115746i | ||||
\(337\) | 1.08844e10 | 0.843891 | 0.421946 | − | 0.906621i | \(-0.361347\pi\) | ||||
0.421946 | + | 0.906621i | \(0.361347\pi\) | |||||||
\(338\) | 1.14783e10i | 0.879450i | ||||||||
\(339\) | 1.68050e9 | − | 2.18146e10i | 0.127244 | − | 1.65177i | ||||
\(340\) | −4.86091e8 | −0.0363749 | ||||||||
\(341\) | − | 5.59565e9i | − | 0.413840i | ||||||
\(342\) | 3.00388e9 | − | 1.93811e10i | 0.219573 | − | 1.41668i | ||||
\(343\) | −3.31226e9 | −0.239303 | ||||||||
\(344\) | 1.06116e10i | 0.757786i | ||||||||
\(345\) | −1.31926e10 | − | 1.01630e9i | −0.931225 | − | 0.0717372i | ||||
\(346\) | 5.13893e9 | 0.358565 | ||||||||
\(347\) | − | 2.09393e10i | − | 1.44426i | −0.691759 | − | 0.722129i | \(-0.743164\pi\) | ||
0.691759 | − | 0.722129i | \(-0.256836\pi\) | |||||||
\(348\) | 1.50487e6 | − | 1.95348e7i | 0.000102608 | − | 0.00133196i | ||||
\(349\) | 1.07024e10 | 0.721409 | 0.360704 | − | 0.932680i | \(-0.382536\pi\) | ||||
0.360704 | + | 0.932680i | \(0.382536\pi\) | |||||||
\(350\) | − | 1.51193e10i | − | 1.00754i | ||||||
\(351\) | 5.35825e9 | + | 1.25827e9i | 0.353016 | + | 0.0828985i | ||||
\(352\) | −2.34682e8 | −0.0152866 | ||||||||
\(353\) | − | 2.58306e10i | − | 1.66355i | −0.555115 | − | 0.831774i | \(-0.687326\pi\) | ||
0.555115 | − | 0.831774i | \(-0.312674\pi\) | |||||||
\(354\) | 5.45652e8 | + | 4.20345e7i | 0.0347458 | + | 0.00267666i | ||||
\(355\) | 2.96971e10 | 1.86982 | ||||||||
\(356\) | − | 2.46617e7i | − | 0.00153540i | ||||||
\(357\) | −2.03277e9 | + | 2.63875e10i | −0.125145 | + | 1.62452i | ||||
\(358\) | −7.84382e7 | −0.00477525 | ||||||||
\(359\) | − | 7.97178e8i | − | 0.0479930i | −0.999712 | − | 0.0239965i | \(-0.992361\pi\) | ||
0.999712 | − | 0.0239965i | \(-0.00763905\pi\) | |||||||
\(360\) | −2.12105e10 | − | 3.28743e9i | −1.26282 | − | 0.195725i | ||||
\(361\) | 1.70580e10 | 1.00438 | ||||||||
\(362\) | − | 8.96247e9i | − | 0.521907i | ||||||
\(363\) | 1.57380e9 | + | 1.21238e8i | 0.0906405 | + | 0.00698252i | ||||
\(364\) | −2.37376e8 | −0.0135217 | ||||||||
\(365\) | 9.66083e9i | 0.544306i | ||||||||
\(366\) | −1.54700e9 | + | 2.00817e10i | −0.0862118 | + | 1.11912i | ||||
\(367\) | −1.06670e10 | −0.588002 | −0.294001 | − | 0.955805i | \(-0.594987\pi\) | ||||
−0.294001 | + | 0.955805i | \(0.594987\pi\) | |||||||
\(368\) | − | 1.35556e10i | − | 0.739143i | ||||||
\(369\) | 3.62984e9 | − | 2.34198e10i | 0.195786 | − | 1.26321i | ||||
\(370\) | 2.81705e10 | 1.50310 | ||||||||
\(371\) | 4.13119e10i | 2.18062i | ||||||||
\(372\) | −6.64502e8 | − | 5.11901e7i | −0.0346996 | − | 0.00267309i | ||||
\(373\) | −2.59496e10 | −1.34059 | −0.670295 | − | 0.742095i | \(-0.733832\pi\) | ||||
−0.670295 | + | 0.742095i | \(0.733832\pi\) | |||||||
\(374\) | 6.61815e9i | 0.338259i | ||||||||
\(375\) | −6.36065e8 | + | 8.25680e9i | −0.0321645 | + | 0.417529i | ||||
\(376\) | 2.01829e10 | 1.00979 | ||||||||
\(377\) | 3.85934e8i | 0.0191050i | ||||||||
\(378\) | 6.95027e9 | − | 2.95971e10i | 0.340435 | − | 1.44971i | ||||
\(379\) | −5.70570e9 | −0.276536 | −0.138268 | − | 0.990395i | \(-0.544154\pi\) | ||||
−0.138268 | + | 0.990395i | \(0.544154\pi\) | |||||||
\(380\) | 9.69209e8i | 0.0464818i | ||||||||
\(381\) | −9.15474e9 | − | 7.05238e8i | −0.434456 | − | 0.0334685i | ||||
\(382\) | 5.07250e9 | 0.238215 | ||||||||
\(383\) | 3.38835e10i | 1.57468i | 0.616518 | + | 0.787341i | \(0.288543\pi\) | ||||
−0.616518 | + | 0.787341i | \(0.711457\pi\) | |||||||
\(384\) | 1.73074e9 | − | 2.24668e10i | 0.0795987 | − | 1.03328i | ||||
\(385\) | −1.26142e10 | −0.574139 | ||||||||
\(386\) | − | 7.83416e9i | − | 0.352893i | ||||||
\(387\) | −1.70197e10 | − | 2.63789e9i | −0.758767 | − | 0.117602i | ||||
\(388\) | 7.09335e8 | 0.0312986 | ||||||||
\(389\) | 2.22934e10i | 0.973593i | 0.873515 | + | 0.486797i | \(0.161835\pi\) | ||||
−0.873515 | + | 0.486797i | \(0.838165\pi\) | |||||||
\(390\) | −1.09667e10 | − | 8.44820e8i | −0.474041 | − | 0.0365179i | ||||
\(391\) | −1.86785e10 | −0.799163 | ||||||||
\(392\) | − | 2.70959e10i | − | 1.14752i | ||||||
\(393\) | 7.17746e8 | − | 9.31711e9i | 0.0300885 | − | 0.390581i | ||||
\(394\) | 1.33934e10 | 0.555783 | ||||||||
\(395\) | 2.79076e10i | 1.14639i | ||||||||
\(396\) | 2.87948e7 | − | 1.85785e8i | 0.00117094 | − | 0.00755490i | ||||
\(397\) | 2.90338e10 | 1.16880 | 0.584402 | − | 0.811464i | \(-0.301329\pi\) | ||||
0.584402 | + | 0.811464i | \(0.301329\pi\) | |||||||
\(398\) | − | 1.76717e9i | − | 0.0704283i | ||||||
\(399\) | 5.26136e10 | + | 4.05310e9i | 2.07590 | + | 0.159917i | ||||
\(400\) | 1.77486e10 | 0.693307 | ||||||||
\(401\) | 1.27430e10i | 0.492828i | 0.969165 | + | 0.246414i | \(0.0792523\pi\) | ||||
−0.969165 | + | 0.246414i | \(0.920748\pi\) | |||||||
\(402\) | 8.08522e8 | − | 1.04955e10i | 0.0309590 | − | 0.401881i | ||||
\(403\) | 1.31280e10 | 0.497714 | ||||||||
\(404\) | 9.75532e8i | 0.0366198i | ||||||||
\(405\) | 1.05453e10 | − | 3.32020e10i | 0.391957 | − | 1.23408i | ||||
\(406\) | 2.13176e9 | 0.0784576 | ||||||||
\(407\) | − | 9.48461e9i | − | 0.345654i | ||||||
\(408\) | −3.02098e10 | − | 2.32722e9i | −1.09020 | − | 0.0839842i | ||||
\(409\) | 4.47008e9 | 0.159743 | 0.0798716 | − | 0.996805i | \(-0.474549\pi\) | ||||
0.0798716 | + | 0.996805i | \(0.474549\pi\) | |||||||
\(410\) | 4.73606e10i | 1.67603i | ||||||||
\(411\) | −2.45446e9 | + | 3.18615e10i | −0.0860178 | + | 1.11660i | ||||
\(412\) | 8.22869e8 | 0.0285589 | ||||||||
\(413\) | 1.47248e9i | 0.0506117i | ||||||||
\(414\) | 2.12036e10 | + | 3.28636e9i | 0.721787 | + | 0.111870i | ||||
\(415\) | −5.48689e10 | −1.84984 | ||||||||
\(416\) | − | 5.50592e8i | − | 0.0183847i | ||||||
\(417\) | −1.49519e10 | − | 1.15183e9i | −0.494484 | − | 0.0380928i | ||||
\(418\) | 1.31958e10 | 0.432246 | ||||||||
\(419\) | 3.46876e10i | 1.12543i | 0.826652 | + | 0.562714i | \(0.190243\pi\) | ||||
−0.826652 | + | 0.562714i | \(0.809757\pi\) | |||||||
\(420\) | −1.15397e8 | + | 1.49798e9i | −0.00370850 | + | 0.0481402i | ||||
\(421\) | −4.83823e10 | −1.54013 | −0.770066 | − | 0.637965i | \(-0.779777\pi\) | ||||
−0.770066 | + | 0.637965i | \(0.779777\pi\) | |||||||
\(422\) | 3.26328e10i | 1.02897i | ||||||||
\(423\) | −5.01718e9 | + | 3.23709e10i | −0.156711 | + | 1.01110i | ||||
\(424\) | −4.72962e10 | −1.46340 | ||||||||
\(425\) | − | 2.44561e10i | − | 0.749604i | ||||||
\(426\) | −4.80152e10 | − | 3.69887e9i | −1.45794 | − | 0.112313i | ||||
\(427\) | −5.41921e10 | −1.63014 | ||||||||
\(428\) | − | 1.51378e9i | − | 0.0451115i | ||||||
\(429\) | −2.84438e8 | + | 3.69231e9i | −0.00839767 | + | 0.109011i | ||||
\(430\) | 3.44181e10 | 1.00673 | ||||||||
\(431\) | 9.29263e9i | 0.269296i | 0.990894 | + | 0.134648i | \(0.0429903\pi\) | ||||
−0.990894 | + | 0.134648i | \(0.957010\pi\) | |||||||
\(432\) | 3.47441e10 | + | 8.15894e9i | 0.997576 | + | 0.234260i | ||||
\(433\) | 4.35080e10 | 1.23771 | 0.618854 | − | 0.785506i | \(-0.287597\pi\) | ||||
0.618854 | + | 0.785506i | \(0.287597\pi\) | |||||||
\(434\) | − | 7.25147e10i | − | 2.04393i | ||||||
\(435\) | 2.43547e9 | + | 1.87617e8i | 0.0680183 | + | 0.00523981i | ||||
\(436\) | 1.26053e9 | 0.0348823 | ||||||||
\(437\) | 3.72428e10i | 1.02121i | ||||||||
\(438\) | 1.20329e9 | − | 1.56199e10i | 0.0326943 | − | 0.424407i | ||||
\(439\) | −2.31745e10 | −0.623955 | −0.311977 | − | 0.950090i | \(-0.600991\pi\) | ||||
−0.311977 | + | 0.950090i | \(0.600991\pi\) | |||||||
\(440\) | − | 1.44414e10i | − | 0.385301i | ||||||
\(441\) | 4.34586e10 | + | 6.73567e9i | 1.14900 | + | 0.178085i | ||||
\(442\) | −1.55269e10 | −0.406815 | ||||||||
\(443\) | − | 4.95067e10i | − | 1.28543i | −0.766105 | − | 0.642715i | \(-0.777808\pi\) | ||
0.766105 | − | 0.642715i | \(-0.222192\pi\) | |||||||
\(444\) | −1.12633e9 | − | 8.67670e7i | −0.0289823 | − | 0.00223266i | ||||
\(445\) | 3.07465e9 | 0.0784071 | ||||||||
\(446\) | 5.26005e10i | 1.32938i | ||||||||
\(447\) | −1.53196e9 | + | 1.98864e10i | −0.0383722 | + | 0.498112i | ||||
\(448\) | 5.76624e10 | 1.43146 | ||||||||
\(449\) | − | 1.14956e9i | − | 0.0282844i | −0.999900 | − | 0.0141422i | \(-0.995498\pi\) | ||
0.999900 | − | 0.0141422i | \(-0.00450175\pi\) | |||||||
\(450\) | −4.30289e9 | + | 2.77623e10i | −0.104933 | + | 0.677027i | ||||
\(451\) | 1.59456e10 | 0.385421 | ||||||||
\(452\) | − | 1.75335e9i | − | 0.0420062i | ||||||
\(453\) | 2.16098e10 | + | 1.66471e9i | 0.513165 | + | 0.0395318i | ||||
\(454\) | −4.24541e10 | −0.999301 | ||||||||
\(455\) | − | 2.95944e10i | − | 0.690500i | ||||||
\(456\) | −4.64022e9 | + | 6.02349e10i | −0.107320 | + | 1.39312i | ||||
\(457\) | 4.36306e9 | 0.100029 | 0.0500146 | − | 0.998748i | \(-0.484073\pi\) | ||||
0.0500146 | + | 0.998748i | \(0.484073\pi\) | |||||||
\(458\) | 1.26463e10i | 0.287410i | ||||||||
\(459\) | 1.12423e10 | − | 4.78744e10i | 0.253283 | − | 1.07858i | ||||
\(460\) | −1.06035e9 | −0.0236820 | ||||||||
\(461\) | 4.28851e9i | 0.0949516i | 0.998872 | + | 0.0474758i | \(0.0151177\pi\) | ||||
−0.998872 | + | 0.0474758i | \(0.984882\pi\) | |||||||
\(462\) | 2.03950e10 | + | 1.57114e9i | 0.447668 | + | 0.0344863i | ||||
\(463\) | 7.77760e10 | 1.69247 | 0.846236 | − | 0.532808i | \(-0.178863\pi\) | ||||
0.846236 | + | 0.532808i | \(0.178863\pi\) | |||||||
\(464\) | 2.50249e9i | 0.0539883i | ||||||||
\(465\) | 6.38203e9 | − | 8.28455e10i | 0.136505 | − | 1.77197i | ||||
\(466\) | 1.05493e10 | 0.223707 | ||||||||
\(467\) | − | 4.14374e10i | − | 0.871214i | −0.900137 | − | 0.435607i | \(-0.856534\pi\) | ||
0.900137 | − | 0.435607i | \(-0.143466\pi\) | |||||||
\(468\) | 4.35872e8 | + | 6.75560e7i | 0.00908606 | + | 0.00140825i | ||||
\(469\) | 2.83229e10 | 0.585391 | ||||||||
\(470\) | − | 6.54621e10i | − | 1.34152i | ||||||
\(471\) | −2.65022e10 | − | 2.04161e9i | −0.538516 | − | 0.0414847i | ||||
\(472\) | −1.68578e9 | −0.0339651 | ||||||||
\(473\) | − | 1.15881e10i | − | 0.231508i | ||||||
\(474\) | 3.47597e9 | − | 4.51218e10i | 0.0688593 | − | 0.893867i | ||||
\(475\) | −4.87627e10 | −0.957885 | ||||||||
\(476\) | 2.12088e9i | 0.0413132i | ||||||||
\(477\) | 1.17572e10 | − | 7.58575e10i | 0.227107 | − | 1.46529i | ||||
\(478\) | −6.44975e10 | −1.23547 | ||||||||
\(479\) | − | 8.91322e10i | − | 1.69314i | −0.532278 | − | 0.846570i | \(-0.678664\pi\) | ||
0.532278 | − | 0.846570i | \(-0.321336\pi\) | |||||||
\(480\) | −3.47455e9 | − | 2.67663e8i | −0.0654537 | − | 0.00504224i | ||||
\(481\) | 2.22520e10 | 0.415708 | ||||||||
\(482\) | − | 5.89615e10i | − | 1.09240i | ||||||
\(483\) | −4.43425e9 | + | 5.75613e10i | −0.0814764 | + | 1.05765i | ||||
\(484\) | 1.26494e8 | 0.00230509 | ||||||||
\(485\) | 8.84351e10i | 1.59830i | ||||||||
\(486\) | −2.11854e10 | + | 5.23685e10i | −0.379744 | + | 0.938696i | ||||
\(487\) | −3.32665e10 | −0.591414 | −0.295707 | − | 0.955279i | \(-0.595555\pi\) | ||||
−0.295707 | + | 0.955279i | \(0.595555\pi\) | |||||||
\(488\) | − | 6.20422e10i | − | 1.09398i | ||||||
\(489\) | −6.21812e10 | − | 4.79014e9i | −1.08749 | − | 0.0837748i | ||||
\(490\) | −8.78842e10 | −1.52450 | ||||||||
\(491\) | 6.09248e10i | 1.04826i | 0.851639 | + | 0.524129i | \(0.175609\pi\) | ||||
−0.851639 | + | 0.524129i | \(0.824391\pi\) | |||||||
\(492\) | 1.45874e8 | − | 1.89360e9i | 0.00248953 | − | 0.0323167i | ||||
\(493\) | 3.44821e9 | 0.0583723 | ||||||||
\(494\) | 3.09589e10i | 0.519850i | ||||||||
\(495\) | 2.31624e10 | + | 3.58994e9i | 0.385800 | + | 0.0597953i | ||||
\(496\) | 8.51252e10 | 1.40647 | ||||||||
\(497\) | − | 1.29573e11i | − | 2.12368i | ||||||
\(498\) | 8.87138e10 | + | 6.83409e9i | 1.44236 | + | 0.111113i | ||||
\(499\) | 5.67884e9 | 0.0915920 | 0.0457960 | − | 0.998951i | \(-0.485418\pi\) | ||||
0.0457960 | + | 0.998951i | \(0.485418\pi\) | |||||||
\(500\) | 6.63638e8i | 0.0106182i | ||||||||
\(501\) | −6.64353e9 | + | 8.62401e10i | −0.105450 | + | 1.36886i | ||||
\(502\) | 5.64959e10 | 0.889615 | ||||||||
\(503\) | − | 2.85420e10i | − | 0.445874i | −0.974833 | − | 0.222937i | \(-0.928436\pi\) | ||
0.974833 | − | 0.222937i | \(-0.0715645\pi\) | |||||||
\(504\) | −1.43435e10 | + | 9.25446e10i | −0.222297 | + | 1.43426i | ||||
\(505\) | −1.21623e11 | −1.87003 | ||||||||
\(506\) | 1.44367e10i | 0.220225i | ||||||||
\(507\) | 5.72164e10 | + | 4.40768e9i | 0.865942 | + | 0.0667081i | ||||
\(508\) | −7.35810e8 | −0.0110487 | ||||||||
\(509\) | 7.22096e9i | 0.107578i | 0.998552 | + | 0.0537891i | \(0.0171299\pi\) | ||||
−0.998552 | + | 0.0537891i | \(0.982870\pi\) | |||||||
\(510\) | −7.54823e9 | + | 9.79840e10i | −0.111574 | + | 1.44835i | ||||
\(511\) | 4.21516e10 | 0.618202 | ||||||||
\(512\) | 6.59267e10i | 0.959360i | ||||||||
\(513\) | −9.54561e10 | − | 2.24159e10i | −1.37827 | − | 0.323659i | ||||
\(514\) | −3.72534e10 | −0.533720 | ||||||||
\(515\) | 1.02590e11i | 1.45839i | ||||||||
\(516\) | −1.37612e9 | − | 1.06010e8i | −0.0194115 | − | 0.00149537i | ||||
\(517\) | −2.20401e10 | −0.308497 | ||||||||
\(518\) | − | 1.22912e11i | − | 1.70717i | ||||||
\(519\) | 1.97336e9 | − | 2.56163e10i | 0.0271979 | − | 0.353058i | ||||
\(520\) | 3.38813e10 | 0.463390 | ||||||||
\(521\) | − | 3.82374e10i | − | 0.518964i | −0.965748 | − | 0.259482i | \(-0.916448\pi\) | ||
0.965748 | − | 0.259482i | \(-0.0835518\pi\) | |||||||
\(522\) | −3.91437e9 | − | 6.06690e8i | −0.0527206 | − | 0.00817118i | ||||
\(523\) | 9.92608e10 | 1.32670 | 0.663348 | − | 0.748311i | \(-0.269135\pi\) | ||||
0.663348 | + | 0.748311i | \(0.269135\pi\) | |||||||
\(524\) | − | 7.48860e8i | − | 0.00993289i | ||||||
\(525\) | −7.53661e10 | − | 5.80585e9i | −0.992062 | − | 0.0764238i | ||||
\(526\) | −8.29415e10 | −1.08350 | ||||||||
\(527\) | − | 1.17295e11i | − | 1.52068i | ||||||
\(528\) | −1.84436e9 | + | 2.39418e10i | −0.0237307 | + | 0.308050i | ||||
\(529\) | 3.75659e10 | 0.479701 | ||||||||
\(530\) | 1.53403e11i | 1.94415i | ||||||||
\(531\) | 4.19062e8 | − | 2.70379e9i | 0.00527109 | − | 0.0340091i | ||||
\(532\) | 4.22880e9 | 0.0527923 | ||||||||
\(533\) | 3.74103e10i | 0.463534i | ||||||||
\(534\) | −4.97119e9 | − | 3.82957e8i | −0.0611357 | − | 0.00470961i | ||||
\(535\) | 1.88728e11 | 2.30367 | ||||||||
\(536\) | 3.24256e10i | 0.392852i | ||||||||
\(537\) | −3.01204e7 | + | 3.90995e8i | −0.000362212 | + | 0.00470190i | ||||
\(538\) | −1.12703e11 | −1.34526 | ||||||||
\(539\) | 2.95893e10i | 0.350574i | ||||||||
\(540\) | 6.38211e8 | − | 2.71776e9i | 0.00750567 | − | 0.0319622i | ||||
\(541\) | −6.98199e9 | −0.0815061 | −0.0407530 | − | 0.999169i | \(-0.512976\pi\) | ||||
−0.0407530 | + | 0.999169i | \(0.512976\pi\) | |||||||
\(542\) | − | 4.61738e10i | − | 0.535056i | ||||||
\(543\) | −4.46756e10 | − | 3.44160e9i | −0.513891 | − | 0.0395878i | ||||
\(544\) | −4.91938e9 | −0.0561714 | ||||||||
\(545\) | 1.57154e11i | 1.78131i | ||||||||
\(546\) | −3.68607e9 | + | 4.78491e10i | −0.0414756 | + | 0.538398i | ||||
\(547\) | −9.06813e10 | −1.01290 | −0.506452 | − | 0.862268i | \(-0.669043\pi\) | ||||
−0.506452 | + | 0.862268i | \(0.669043\pi\) | |||||||
\(548\) | 2.56086e9i | 0.0283964i | ||||||||
\(549\) | 9.95083e10 | + | 1.54228e10i | 1.09539 | + | 0.169775i | ||||
\(550\) | −1.89023e10 | −0.206568 | ||||||||
\(551\) | − | 6.87534e9i | − | 0.0745913i | ||||||
\(552\) | −6.58994e10 | − | 5.07658e9i | −0.709782 | − | 0.0546783i | ||||
\(553\) | 1.21765e11 | 1.30203 | ||||||||
\(554\) | 6.72754e10i | 0.714196i | ||||||||
\(555\) | 1.08175e10 | − | 1.40423e11i | 0.114013 | − | 1.48001i | ||||
\(556\) | −1.20176e9 | −0.0125753 | ||||||||
\(557\) | − | 4.46197e10i | − | 0.463560i | −0.972768 | − | 0.231780i | \(-0.925545\pi\) | ||
0.972768 | − | 0.231780i | \(-0.0744549\pi\) | |||||||
\(558\) | −2.06373e10 | + | 1.33152e11i | −0.212871 | + | 1.37345i | ||||
\(559\) | 2.71870e10 | 0.278428 | ||||||||
\(560\) | − | 1.91897e11i | − | 1.95126i | ||||||
\(561\) | 3.29898e10 | + | 2.54138e9i | 0.333064 | + | 0.0256577i | ||||
\(562\) | −9.40190e10 | −0.942476 | ||||||||
\(563\) | 1.65656e10i | 0.164882i | 0.996596 | + | 0.0824412i | \(0.0262717\pi\) | ||||
−0.996596 | + | 0.0824412i | \(0.973728\pi\) | |||||||
\(564\) | −2.01627e8 | + | 2.61734e9i | −0.00199266 | + | 0.0258668i | ||||
\(565\) | 2.18595e11 | 2.14510 | ||||||||
\(566\) | − | 4.11914e10i | − | 0.401366i | ||||||
\(567\) | −1.44865e11 | − | 4.60106e10i | −1.40162 | − | 0.445170i | ||||
\(568\) | 1.48342e11 | 1.42519 | ||||||||
\(569\) | 5.68477e10i | 0.542330i | 0.962533 | + | 0.271165i | \(0.0874089\pi\) | ||||
−0.962533 | + | 0.271165i | \(0.912591\pi\) | |||||||
\(570\) | 1.95369e11 | + | 1.50503e10i | 1.85078 | + | 0.142576i | ||||
\(571\) | −2.85153e9 | −0.0268246 | −0.0134123 | − | 0.999910i | \(-0.504269\pi\) | ||||
−0.0134123 | + | 0.999910i | \(0.504269\pi\) | |||||||
\(572\) | 2.96769e8i | 0.00277226i | ||||||||
\(573\) | 1.94785e9 | − | 2.52851e10i | 0.0180691 | − | 0.234556i | ||||
\(574\) | 2.06641e11 | 1.90357 | ||||||||
\(575\) | − | 5.33483e10i | − | 0.488033i | ||||||
\(576\) | −1.05880e11 | − | 1.64104e10i | −0.961890 | − | 0.149084i | ||||
\(577\) | −4.64151e10 | −0.418751 | −0.209376 | − | 0.977835i | \(-0.567143\pi\) | ||||
−0.209376 | + | 0.977835i | \(0.567143\pi\) | |||||||
\(578\) | 2.57105e10i | 0.230356i | ||||||||
\(579\) | −3.90513e10 | − | 3.00833e9i | −0.347473 | − | 0.0267677i | ||||
\(580\) | 1.95750e8 | 0.00172978 | ||||||||
\(581\) | 2.39401e11i | 2.10098i | ||||||||
\(582\) | 1.10149e10 | − | 1.42985e11i | 0.0960035 | − | 1.24623i | ||||
\(583\) | 5.16485e10 | 0.447078 | ||||||||
\(584\) | 4.82575e10i | 0.414871i | ||||||||
\(585\) | −8.42242e9 | + | 5.43416e10i | −0.0719140 | + | 0.463990i | ||||
\(586\) | −1.42939e11 | −1.21216 | ||||||||
\(587\) | − | 1.64956e11i | − | 1.38937i | −0.719316 | − | 0.694683i | \(-0.755545\pi\) | ||
0.719316 | − | 0.694683i | \(-0.244455\pi\) | |||||||
\(588\) | 3.51383e9 | + | 2.70689e8i | 0.0293948 | + | 0.00226444i | ||||
\(589\) | −2.33873e11 | −1.94321 | ||||||||
\(590\) | 5.46775e9i | 0.0451233i | ||||||||
\(591\) | 5.14308e9 | − | 6.67626e10i | 0.0421573 | − | 0.547247i | ||||
\(592\) | 1.44287e11 | 1.17474 | ||||||||
\(593\) | 1.90986e11i | 1.54448i | 0.635329 | + | 0.772242i | \(0.280865\pi\) | ||||
−0.635329 | + | 0.772242i | \(0.719135\pi\) | |||||||
\(594\) | −3.70025e10 | − | 8.68927e9i | −0.297225 | − | 0.0697971i | ||||
\(595\) | −2.64417e11 | −2.10971 | ||||||||
\(596\) | 1.59837e9i | 0.0126675i | ||||||||
\(597\) | −8.80891e9 | − | 6.78597e8i | −0.0693465 | − | 0.00534213i | ||||
\(598\) | −3.38703e10 | −0.264859 | ||||||||
\(599\) | 7.46362e10i | 0.579752i | 0.957064 | + | 0.289876i | \(0.0936141\pi\) | ||||
−0.957064 | + | 0.289876i | \(0.906386\pi\) | |||||||
\(600\) | 6.64686e9 | − | 8.62833e10i | 0.0512875 | − | 0.665766i | ||||
\(601\) | −1.60386e11 | −1.22933 | −0.614663 | − | 0.788790i | \(-0.710708\pi\) | ||||
−0.614663 | + | 0.788790i | \(0.710708\pi\) | |||||||
\(602\) | − | 1.50171e11i | − | 1.14341i | ||||||
\(603\) | −5.20068e10 | − | 8.06055e9i | −0.393360 | − | 0.0609671i | ||||
\(604\) | 1.73688e9 | 0.0130503 | ||||||||
\(605\) | 1.57704e10i | 0.117712i | ||||||||
\(606\) | 1.96643e11 | + | 1.51485e10i | 1.45811 | + | 0.112326i | ||||
\(607\) | 2.92518e10 | 0.215475 | 0.107738 | − | 0.994179i | \(-0.465639\pi\) | ||||
0.107738 | + | 0.994179i | \(0.465639\pi\) | |||||||
\(608\) | 9.80868e9i | 0.0717788i | ||||||||
\(609\) | 8.18601e8 | − | 1.06263e10i | 0.00595118 | − | 0.0772526i | ||||
\(610\) | −2.01231e11 | −1.45336 | ||||||||
\(611\) | − | 5.17086e10i | − | 0.371021i | ||||||
\(612\) | 6.03594e8 | − | 3.89439e9i | 0.00430268 | − | 0.0277609i | ||||
\(613\) | 6.75531e10 | 0.478413 | 0.239207 | − | 0.970969i | \(-0.423113\pi\) | ||||
0.239207 | + | 0.970969i | \(0.423113\pi\) | |||||||
\(614\) | − | 1.49826e11i | − | 1.05418i | ||||||
\(615\) | 2.36081e11 | + | 1.81865e10i | 1.65029 | + | 0.127130i | ||||
\(616\) | −6.30101e10 | −0.437610 | ||||||||
\(617\) | − | 1.42442e11i | − | 0.982875i | −0.870913 | − | 0.491437i | \(-0.836472\pi\) | ||
0.870913 | − | 0.491437i | \(-0.163528\pi\) | |||||||
\(618\) | 1.27779e10 | − | 1.65870e11i | 0.0876001 | − | 1.13714i | ||||
\(619\) | −2.14085e11 | −1.45823 | −0.729113 | − | 0.684394i | \(-0.760067\pi\) | ||||
−0.729113 | + | 0.684394i | \(0.760067\pi\) | |||||||
\(620\) | − | 6.65869e9i | − | 0.0450632i | ||||||
\(621\) | 2.45239e10 | − | 1.04433e11i | 0.164901 | − | 0.702215i | ||||
\(622\) | 2.44189e10 | 0.163142 | ||||||||
\(623\) | − | 1.34151e10i | − | 0.0890519i | ||||||
\(624\) | −5.61702e10 | − | 4.32709e9i | −0.370483 | − | 0.0285402i | ||||
\(625\) | −1.85977e11 | −1.21882 | ||||||||
\(626\) | 2.22758e11i | 1.45056i | ||||||||
\(627\) | 5.06721e9 | − | 6.57778e10i | 0.0327868 | − | 0.425608i | ||||
\(628\) | −2.13011e9 | −0.0136950 | ||||||||
\(629\) | − | 1.98815e11i | − | 1.27013i | ||||||
\(630\) | 3.00164e11 | + | 4.65225e10i | 1.90544 | + | 0.295325i | ||||
\(631\) | −1.41209e11 | −0.890730 | −0.445365 | − | 0.895349i | \(-0.646926\pi\) | ||||
−0.445365 | + | 0.895349i | \(0.646926\pi\) | |||||||
\(632\) | 1.39403e11i | 0.873784i | ||||||||
\(633\) | 1.62666e11 | + | 1.25310e10i | 1.01317 | + | 0.0780499i | ||||
\(634\) | 1.25901e11 | 0.779243 | ||||||||
\(635\) | − | 9.17358e10i | − | 0.564214i | ||||||
\(636\) | 4.72490e8 | − | 6.13342e9i | 0.00288778 | − | 0.0374865i | ||||
\(637\) | −6.94199e10 | −0.421625 | ||||||||
\(638\) | − | 2.66515e9i | − | 0.0160856i | ||||||
\(639\) | −3.68758e10 | + | 2.37923e11i | −0.221176 | + | 1.42703i | ||||
\(640\) | 2.25130e11 | 1.34188 | ||||||||
\(641\) | − | 4.87337e10i | − | 0.288667i | −0.989529 | − | 0.144334i | \(-0.953896\pi\) | ||
0.989529 | − | 0.144334i | \(-0.0461038\pi\) | |||||||
\(642\) | −3.05141e11 | − | 2.35066e10i | −1.79622 | − | 0.138373i | ||||
\(643\) | 3.24029e11 | 1.89557 | 0.947787 | − | 0.318905i | \(-0.103315\pi\) | ||||
0.947787 | + | 0.318905i | \(0.103315\pi\) | |||||||
\(644\) | 4.62647e9i | 0.0268972i | ||||||||
\(645\) | 1.32166e10 | − | 1.71566e11i | 0.0763627 | − | 0.991268i | ||||
\(646\) | 2.76609e11 | 1.58832 | ||||||||
\(647\) | − | 2.74581e11i | − | 1.56694i | −0.621427 | − | 0.783472i | \(-0.713447\pi\) | ||
0.621427 | − | 0.783472i | \(-0.286553\pi\) | |||||||
\(648\) | 5.26755e10 | − | 1.65849e11i | 0.298751 | − | 0.940620i | ||||
\(649\) | 1.84091e9 | 0.0103766 | ||||||||
\(650\) | − | 4.43470e10i | − | 0.248434i | ||||||
\(651\) | −3.61467e11 | − | 2.78457e10i | −2.01254 | − | 0.155037i | ||||
\(652\) | −4.99779e9 | −0.0276559 | ||||||||
\(653\) | 3.19227e11i | 1.75569i | 0.478949 | + | 0.877843i | \(0.341018\pi\) | ||||
−0.478949 | + | 0.877843i | \(0.658982\pi\) | |||||||
\(654\) | 1.95740e10 | − | 2.54091e11i | 0.106996 | − | 1.38892i | ||||
\(655\) | 9.33628e10 | 0.507234 | ||||||||
\(656\) | 2.42577e11i | 1.30989i | ||||||||
\(657\) | −7.73992e10 | − | 1.19961e10i | −0.415408 | − | 0.0643843i | ||||
\(658\) | −2.85620e11 | −1.52365 | ||||||||
\(659\) | 1.43354e11i | 0.760093i | 0.924967 | + | 0.380047i | \(0.124092\pi\) | ||||
−0.924967 | + | 0.380047i | \(0.875908\pi\) | |||||||
\(660\) | 1.87278e9 | + | 1.44270e8i | 0.00986987 | + | 0.000760329i | ||||
\(661\) | 1.79340e11 | 0.939447 | 0.469724 | − | 0.882814i | \(-0.344354\pi\) | ||||
0.469724 | + | 0.882814i | \(0.344354\pi\) | |||||||
\(662\) | 2.95057e11i | 1.53630i | ||||||||
\(663\) | −5.96236e9 | + | 7.73978e10i | −0.0308578 | + | 0.400566i | ||||
\(664\) | −2.74080e11 | −1.40995 | ||||||||
\(665\) | 5.27218e11i | 2.69590i | ||||||||
\(666\) | −3.49802e10 | + | 2.25693e11i | −0.177797 | + | 1.14715i | ||||
\(667\) | 7.52189e9 | 0.0380035 | ||||||||
\(668\) | 6.93153e9i | 0.0348115i | ||||||||
\(669\) | 2.62200e11 | + | 2.01986e10i | 1.30896 | + | 0.100837i | ||||
\(670\) | 1.05171e11 | 0.521910 | ||||||||
\(671\) | 6.77514e10i | 0.334217i | ||||||||
\(672\) | −1.16785e9 | + | 1.51600e10i | −0.00572679 | + | 0.0743398i | ||||
\(673\) | 3.79005e11 | 1.84750 | 0.923750 | − | 0.382996i | \(-0.125108\pi\) | ||||
0.923750 | + | 0.382996i | \(0.125108\pi\) | |||||||
\(674\) | − | 1.76345e11i | − | 0.854523i | ||||||
\(675\) | 1.36736e11 | + | 3.21096e10i | 0.658669 | + | 0.154675i | ||||
\(676\) | 4.59875e9 | 0.0220218 | ||||||||
\(677\) | − | 1.49714e11i | − | 0.712702i | −0.934352 | − | 0.356351i | \(-0.884021\pi\) | ||
0.934352 | − | 0.356351i | \(-0.115979\pi\) | |||||||
\(678\) | −3.53431e11 | − | 2.72267e10i | −1.67258 | − | 0.128848i | ||||
\(679\) | 3.85855e11 | 1.81529 | ||||||||
\(680\) | − | 3.02720e11i | − | 1.41581i | ||||||
\(681\) | −1.63024e10 | + | 2.11623e11i | −0.0757991 | + | 0.983953i | ||||
\(682\) | −9.06583e10 | −0.419054 | ||||||||
\(683\) | 3.39483e11i | 1.56004i | 0.625756 | + | 0.780019i | \(0.284790\pi\) | ||||
−0.625756 | + | 0.780019i | \(0.715210\pi\) | |||||||
\(684\) | −7.76497e9 | − | 1.20350e9i | −0.0354744 | − | 0.00549820i | ||||
\(685\) | −3.19270e11 | −1.45009 | ||||||||
\(686\) | 5.36638e10i | 0.242318i | ||||||||
\(687\) | 6.30385e10 | + | 4.85619e9i | 0.282995 | + | 0.0218006i | ||||
\(688\) | 1.76287e11 | 0.786802 | ||||||||
\(689\) | 1.21173e11i | 0.537687i | ||||||||
\(690\) | −1.64656e10 | + | 2.13741e11i | −0.0726410 | + | 0.942957i | ||||
\(691\) | 1.70731e11 | 0.748858 | 0.374429 | − | 0.927256i | \(-0.377839\pi\) | ||||
0.374429 | + | 0.927256i | \(0.377839\pi\) | |||||||
\(692\) | − | 2.05890e9i | − | 0.00897864i | ||||||
\(693\) | 1.56634e10 | − | 1.01061e11i | 0.0679132 | − | 0.438177i | ||||
\(694\) | −3.39250e11 | −1.46245 | ||||||||
\(695\) | − | 1.49827e11i | − | 0.642170i | ||||||
\(696\) | 1.21656e10 | + | 9.37180e8i | 0.0518437 | + | 0.00399380i | ||||
\(697\) | 3.34250e11 | 1.41625 | ||||||||
\(698\) | − | 1.73397e11i | − | 0.730497i | ||||||
\(699\) | 4.05093e9 | − | 5.25854e10i | 0.0169686 | − | 0.220271i | ||||
\(700\) | −6.05753e9 | −0.0252292 | ||||||||
\(701\) | 2.14649e10i | 0.0888910i | 0.999012 | + | 0.0444455i | \(0.0141521\pi\) | ||||
−0.999012 | + | 0.0444455i | \(0.985848\pi\) | |||||||
\(702\) | 2.03860e10 | − | 8.68121e10i | 0.0839430 | − | 0.357463i | ||||
\(703\) | −3.96415e11 | −1.62304 | ||||||||
\(704\) | − | 7.20899e10i | − | 0.293483i | ||||||
\(705\) | −3.26312e11 | − | 2.51375e10i | −1.32092 | − | 0.101757i | ||||
\(706\) | −4.18496e11 | −1.68451 | ||||||||
\(707\) | 5.30658e11i | 2.12391i | ||||||||
\(708\) | 1.68410e7 | − | 2.18614e8i | 6.70247e−5 | − | 0.000870052i | ||||
\(709\) | −1.22807e11 | −0.486003 | −0.243001 | − | 0.970026i | \(-0.578132\pi\) | ||||
−0.243001 | + | 0.970026i | \(0.578132\pi\) | |||||||
\(710\) | − | 4.81140e11i | − | 1.89338i | ||||||
\(711\) | −2.23586e11 | − | 3.46537e10i | −0.874915 | − | 0.135603i | ||||
\(712\) | 1.53584e10 | 0.0597621 | ||||||||
\(713\) | − | 2.55867e11i | − | 0.990047i | ||||||
\(714\) | 4.27518e11 | + | 3.29340e10i | 1.64498 | + | 0.126722i | ||||
\(715\) | −3.69991e10 | −0.141569 | ||||||||
\(716\) | 3.14261e7i | 0.000119574i | ||||||||
\(717\) | −2.47671e10 | + | 3.21503e11i | −0.0937128 | + | 1.21649i | ||||
\(718\) | −1.29155e10 | −0.0485976 | ||||||||
\(719\) | 7.18957e10i | 0.269022i | 0.990912 | + | 0.134511i | \(0.0429463\pi\) | ||||
−0.990912 | + | 0.134511i | \(0.957054\pi\) | |||||||
\(720\) | −5.46129e10 | + | 3.52363e11i | −0.203219 | + | 1.31117i | ||||
\(721\) | 4.47614e11 | 1.65639 | ||||||||
\(722\) | − | 2.76367e11i | − | 1.01704i | ||||||
\(723\) | −2.93908e11 | − | 2.26413e10i | −1.07562 | − | 0.0828605i | ||||
\(724\) | −3.59079e9 | −0.0130688 | ||||||||
\(725\) | 9.84856e9i | 0.0356468i | ||||||||
\(726\) | 1.96425e9 | − | 2.54980e10i | 0.00707049 | − | 0.0917825i | ||||
\(727\) | 1.79717e11 | 0.643357 | 0.321678 | − | 0.946849i | \(-0.395753\pi\) | ||||
0.321678 | + | 0.946849i | \(0.395753\pi\) | |||||||
\(728\) | − | 1.47829e11i | − | 0.526301i | ||||||
\(729\) | 2.52908e11 | + | 1.25713e11i | 0.895474 | + | 0.445113i | ||||
\(730\) | 1.56521e11 | 0.551163 | ||||||||
\(731\) | − | 2.42908e11i | − | 0.850692i | ||||||
\(732\) | 8.04570e9 | + | 6.19803e8i | 0.0280233 | + | 0.00215878i | ||||
\(733\) | −3.78788e11 | −1.31214 | −0.656071 | − | 0.754699i | \(-0.727783\pi\) | ||||
−0.656071 | + | 0.754699i | \(0.727783\pi\) | |||||||
\(734\) | 1.72823e11i | 0.595411i | ||||||||
\(735\) | −3.37476e10 | + | 4.38080e11i | −0.115636 | + | 1.50108i | ||||
\(736\) | −1.07311e10 | −0.0365706 | ||||||||
\(737\) | − | 3.54094e10i | − | 0.120019i | ||||||
\(738\) | −3.79437e11 | − | 5.88091e10i | −1.27913 | − | 0.198253i | ||||
\(739\) | −2.12799e11 | −0.713498 | −0.356749 | − | 0.934200i | \(-0.616115\pi\) | ||||
−0.356749 | + | 0.934200i | \(0.616115\pi\) | |||||||
\(740\) | − | 1.12865e10i | − | 0.0376384i | ||||||
\(741\) | 1.54322e11 | + | 1.18883e10i | 0.511866 | + | 0.0394317i | ||||
\(742\) | 6.69319e11 | 2.20809 | ||||||||
\(743\) | − | 4.70898e11i | − | 1.54515i | −0.634920 | − | 0.772577i | \(-0.718967\pi\) | ||
0.634920 | − | 0.772577i | \(-0.281033\pi\) | |||||||
\(744\) | 3.18793e10 | − | 4.13828e11i | 0.104044 | − | 1.35060i | ||||
\(745\) | −1.99274e11 | −0.646881 | ||||||||
\(746\) | 4.20425e11i | 1.35748i | ||||||||
\(747\) | 6.81324e10 | − | 4.39591e11i | 0.218812 | − | 1.41178i | ||||
\(748\) | 2.65154e9 | 0.00847018 | ||||||||
\(749\) | − | 8.23446e11i | − | 2.61642i | ||||||
\(750\) | 1.33773e11 | + | 1.03053e10i | 0.422789 | + | 0.0325697i | ||||
\(751\) | −4.36826e11 | −1.37325 | −0.686624 | − | 0.727013i | \(-0.740908\pi\) | ||||
−0.686624 | + | 0.727013i | \(0.740908\pi\) | |||||||
\(752\) | − | 3.35291e11i | − | 1.04846i | ||||||
\(753\) | 2.16945e10 | − | 2.81618e11i | 0.0674792 | − | 0.875951i | ||||
\(754\) | 6.25274e9 | 0.0193457 | ||||||||
\(755\) | 2.16542e11i | 0.666431i | ||||||||
\(756\) | −1.18580e10 | − | 2.78461e9i | −0.0363015 | − | 0.00852466i | ||||
\(757\) | −2.94690e11 | −0.897392 | −0.448696 | − | 0.893685i | \(-0.648111\pi\) | ||||
−0.448696 | + | 0.893685i | \(0.648111\pi\) | |||||||
\(758\) | 9.24414e10i | 0.280020i | ||||||||
\(759\) | 7.19635e10 | + | 5.54373e9i | 0.216843 | + | 0.0167046i | ||||
\(760\) | −6.03589e11 | −1.80920 | ||||||||
\(761\) | 1.65686e11i | 0.494023i | 0.969012 | + | 0.247012i | \(0.0794486\pi\) | ||||
−0.969012 | + | 0.247012i | \(0.920551\pi\) | |||||||
\(762\) | −1.14260e10 | + | 1.48321e11i | −0.0338901 | + | 0.439930i | ||||
\(763\) | 6.85685e11 | 2.02314 | ||||||||
\(764\) | − | 2.03229e9i | − | 0.00596501i | ||||||
\(765\) | 4.85527e11 | + | 7.52520e10i | 1.41764 | + | 0.219721i | ||||
\(766\) | 5.48965e11 | 1.59452 | ||||||||
\(767\) | 4.31899e9i | 0.0124796i | ||||||||
\(768\) | −2.63684e10 | − | 2.03130e9i | −0.0757948 | − | 0.00583887i | ||||
\(769\) | 3.75635e11 | 1.07414 | 0.537070 | − | 0.843538i | \(-0.319531\pi\) | ||||
0.537070 | + | 0.843538i | \(0.319531\pi\) | |||||||
\(770\) | 2.04370e11i | 0.581372i | ||||||||
\(771\) | −1.43053e10 | + | 1.85699e11i | −0.0404838 | + | 0.525522i | ||||
\(772\) | −3.13874e9 | −0.00883661 | ||||||||
\(773\) | 3.33178e11i | 0.933165i | 0.884478 | + | 0.466583i | \(0.154515\pi\) | ||||
−0.884478 | + | 0.466583i | \(0.845485\pi\) | |||||||
\(774\) | −4.27380e10 | + | 2.75746e11i | −0.119083 | + | 0.768327i | ||||
\(775\) | 3.35011e11 | 0.928651 | ||||||||
\(776\) | 4.41749e11i | 1.21823i | ||||||||
\(777\) | −6.12686e11 | − | 4.71984e10i | −1.68095 | − | 0.129492i | ||||
\(778\) | 3.61188e11 | 0.985859 | ||||||||
\(779\) | − | 6.66457e11i | − | 1.80977i | ||||||
\(780\) | −3.38475e8 | + | 4.39376e9i | −0.000914425 | + | 0.0118702i | ||||
\(781\) | −1.61993e11 | −0.435403 | ||||||||
\(782\) | 3.02621e11i | 0.809231i | ||||||||
\(783\) | −4.52732e9 | + | 1.92792e10i | −0.0120446 | + | 0.0512910i | ||||
\(784\) | −4.50135e11 | −1.19146 | ||||||||
\(785\) | − | 2.65567e11i | − | 0.699353i | ||||||
\(786\) | −1.50952e11 | − | 1.16286e10i | −0.395502 | − | 0.0304676i | ||||
\(787\) | 1.92335e11 | 0.501371 | 0.250686 | − | 0.968069i | \(-0.419344\pi\) | ||||
0.250686 | + | 0.968069i | \(0.419344\pi\) | |||||||
\(788\) | − | 5.36603e9i | − | 0.0139171i | ||||||
\(789\) | −3.18496e10 | + | 4.13442e11i | −0.0821857 | + | 1.06686i | ||||
\(790\) | 4.52147e11 | 1.16084 | ||||||||
\(791\) | − | 9.53762e11i | − | 2.43632i | ||||||
\(792\) | 1.15700e11 | + | 1.79324e10i | 0.294058 | + | 0.0455761i | ||||
\(793\) | −1.58953e11 | −0.401952 | ||||||||
\(794\) | − | 4.70393e11i | − | 1.18353i | ||||||
\(795\) | 7.64674e11 | + | 5.89069e10i | 1.91429 | + | 0.147468i | ||||
\(796\) | −7.08014e8 | −0.00176356 | ||||||||
\(797\) | 1.56629e11i | 0.388186i | 0.980983 | + | 0.194093i | \(0.0621764\pi\) | ||||
−0.980983 | + | 0.194093i | \(0.937824\pi\) | |||||||
\(798\) | 6.56666e10 | − | 8.52423e11i | 0.161932 | − | 2.10205i | ||||
\(799\) | −4.62002e11 | −1.13359 | ||||||||
\(800\) | − | 1.40504e10i | − | 0.0343028i | ||||||
\(801\) | −3.81788e9 | + | 2.46330e10i | −0.00927455 | + | 0.0598395i | ||||
\(802\) | 2.06457e11 | 0.499037 | ||||||||
\(803\) | − | 5.26982e10i | − | 0.126746i | ||||||
\(804\) | −4.20499e9 | − | 3.23932e8i | −0.0100633 | − | 0.000775229i | ||||
\(805\) | −5.76797e11 | −1.37353 | ||||||||
\(806\) | − | 2.12695e11i | − | 0.503984i | ||||||
\(807\) | −4.32779e10 | + | 5.61793e11i | −0.102040 | + | 1.32459i | ||||
\(808\) | −6.07527e11 | −1.42534 | ||||||||
\(809\) | 1.57646e11i | 0.368035i | 0.982923 | + | 0.184017i | \(0.0589102\pi\) | ||||
−0.982923 | + | 0.184017i | \(0.941090\pi\) | |||||||
\(810\) | −5.37924e11 | − | 1.70850e11i | −1.24963 | − | 0.396895i | ||||
\(811\) | 3.97407e11 | 0.918655 | 0.459328 | − | 0.888267i | \(-0.348090\pi\) | ||||
0.459328 | + | 0.888267i | \(0.348090\pi\) | |||||||
\(812\) | − | 8.54086e8i | − | 0.00196462i | ||||||
\(813\) | −2.30165e11 | − | 1.77308e10i | −0.526838 | − | 0.0405851i | ||||
\(814\) | −1.53666e11 | −0.350009 | ||||||||
\(815\) | − | 6.23091e11i | − | 1.41228i | ||||||
\(816\) | −3.86613e10 | + | 5.01865e11i | −0.0872000 | + | 1.13195i | ||||
\(817\) | −4.84331e11 | −1.08706 | ||||||||
\(818\) | − | 7.24224e10i | − | 0.161756i | ||||||
\(819\) | 2.37100e11 | + | 3.67482e10i | 0.526982 | + | 0.0816772i | ||||
\(820\) | 1.89749e10 | 0.0419686 | ||||||||
\(821\) | 2.55006e11i | 0.561277i | 0.959814 | + | 0.280639i | \(0.0905462\pi\) | ||||
−0.959814 | + | 0.280639i | \(0.909454\pi\) | |||||||
\(822\) | 5.16206e11 | + | 3.97661e10i | 1.13067 | + | 0.0871015i | ||||
\(823\) | −8.74091e11 | −1.90527 | −0.952636 | − | 0.304112i | \(-0.901640\pi\) | ||||
−0.952636 | + | 0.304112i | \(0.901640\pi\) | |||||||
\(824\) | 5.12453e11i | 1.11159i | ||||||||
\(825\) | −7.25851e9 | + | 9.42232e10i | −0.0156687 | + | 0.203396i | ||||
\(826\) | 2.38566e10 | 0.0512493 | ||||||||
\(827\) | − | 5.32825e11i | − | 1.13910i | −0.821956 | − | 0.569551i | \(-0.807117\pi\) | ||
0.821956 | − | 0.569551i | \(-0.192883\pi\) | |||||||
\(828\) | 1.31667e9 | − | 8.49519e9i | 0.00280128 | − | 0.0180739i | ||||
\(829\) | −3.51967e11 | −0.745218 | −0.372609 | − | 0.927988i | \(-0.621537\pi\) | ||||
−0.372609 | + | 0.927988i | \(0.621537\pi\) | |||||||
\(830\) | 8.88963e11i | 1.87314i | ||||||||
\(831\) | 3.35351e11 | + | 2.58338e10i | 0.703226 | + | 0.0541733i | ||||
\(832\) | 1.69131e11 | 0.352964 | ||||||||
\(833\) | 6.20248e11i | 1.28821i | ||||||||
\(834\) | −1.86614e10 | + | 2.42245e11i | −0.0385727 | + | 0.500714i | ||||
\(835\) | −8.64176e11 | −1.77769 | ||||||||
\(836\) | − | 5.28688e9i | − | 0.0108237i | ||||||
\(837\) | 6.55806e11 | + | 1.54002e11i | 1.33621 | + | 0.313780i | ||||
\(838\) | 5.61993e11 | 1.13961 | ||||||||
\(839\) | − | 6.14265e11i | − | 1.23968i | −0.784730 | − | 0.619838i | \(-0.787198\pi\) | ||
0.784730 | − | 0.619838i | \(-0.212802\pi\) | |||||||
\(840\) | −9.32887e11 | − | 7.18652e10i | −1.87375 | − | 0.144345i | ||||
\(841\) | 4.98858e11 | 0.997224 | ||||||||
\(842\) | 7.83869e11i | 1.55954i | ||||||||
\(843\) | −3.61034e10 | + | 4.68660e11i | −0.0714888 | + | 0.928000i | ||||
\(844\) | 1.30743e10 | 0.0257660 | ||||||||
\(845\) | 5.73342e11i | 1.12457i | ||||||||
\(846\) | 5.24460e11 | + | 8.12862e10i | 1.02384 | + | 0.158685i | ||||
\(847\) | 6.88084e10 | 0.133693 | ||||||||
\(848\) | 7.85715e11i | 1.51943i | ||||||||
\(849\) | −2.05328e11 | − | 1.58175e10i | −0.395201 | − | 0.0304445i | ||||
\(850\) | −3.96228e11 | −0.759048 | ||||||||
\(851\) | − | 4.33693e11i | − | 0.826922i | ||||||
\(852\) | −1.48194e9 | + | 1.92372e10i | −0.00281237 | + | 0.0365076i | ||||
\(853\) | 4.65175e11 | 0.878658 | 0.439329 | − | 0.898326i | \(-0.355216\pi\) | ||||
0.439329 | + | 0.898326i | \(0.355216\pi\) | |||||||
\(854\) | 8.77998e11i | 1.65068i | ||||||||
\(855\) | 1.50044e11 | − | 9.68084e11i | 0.280772 | − | 1.81154i | ||||
\(856\) | 9.42727e11 | 1.75586 | ||||||||
\(857\) | 6.55429e11i | 1.21507i | 0.794292 | + | 0.607536i | \(0.207842\pi\) | ||||
−0.794292 | + | 0.607536i | \(0.792158\pi\) | |||||||
\(858\) | 5.98213e10 | + | 4.60835e9i | 0.110384 | + | 0.00850347i | ||||
\(859\) | −1.98501e11 | −0.364578 | −0.182289 | − | 0.983245i | \(-0.558351\pi\) | ||||
−0.182289 | + | 0.983245i | \(0.558351\pi\) | |||||||
\(860\) | − | 1.37895e10i | − | 0.0252090i | ||||||
\(861\) | 7.93505e10 | − | 1.03005e12i | 0.144390 | − | 1.87434i | ||||
\(862\) | 1.50555e11 | 0.272688 | ||||||||
\(863\) | − | 5.33299e11i | − | 0.961452i | −0.876871 | − | 0.480726i | \(-0.840373\pi\) | ||
0.876871 | − | 0.480726i | \(-0.159627\pi\) | |||||||
\(864\) | 6.45889e9 | − | 2.75046e10i | 0.0115905 | − | 0.0493571i | ||||
\(865\) | 2.56690e11 | 0.458505 | ||||||||
\(866\) | − | 7.04899e11i | − | 1.25330i | ||||||
\(867\) | 1.28161e11 | + | 9.87288e9i | 0.226818 | + | 0.0174730i | ||||
\(868\) | −2.90528e10 | −0.0511811 | ||||||||
\(869\) | − | 1.52231e11i | − | 0.266947i | ||||||
\(870\) | 3.03969e9 | − | 3.94584e10i | 0.00530582 | − | 0.0688752i | ||||
\(871\) | 8.30746e10 | 0.144343 | ||||||||
\(872\) | 7.85010e11i | 1.35772i | ||||||||
\(873\) | −7.08512e11 | − | 1.09813e11i | −1.21980 | − | 0.189058i | ||||
\(874\) | 6.03392e11 | 1.03408 | ||||||||
\(875\) | 3.60998e11i | 0.615846i | ||||||||
\(876\) | −6.25808e9 | − | 4.82093e8i | −0.0106273 | − | 0.000818681i | ||||
\(877\) | 2.41745e9 | 0.00408656 | 0.00204328 | − | 0.999998i | \(-0.499350\pi\) | ||||
0.00204328 | + | 0.999998i | \(0.499350\pi\) | |||||||
\(878\) | 3.75464e11i | 0.631816i | ||||||||
\(879\) | −5.48888e10 | + | 7.12515e11i | −0.0919450 | + | 1.19354i | ||||
\(880\) | −2.39911e11 | −0.400054 | ||||||||
\(881\) | 2.85057e11i | 0.473182i | 0.971609 | + | 0.236591i | \(0.0760302\pi\) | ||||
−0.971609 | + | 0.236591i | \(0.923970\pi\) | |||||||
\(882\) | 1.09128e11 | − | 7.04098e11i | 0.180328 | − | 1.16348i | ||||
\(883\) | 1.77513e11 | 0.292003 | 0.146001 | − | 0.989284i | \(-0.453360\pi\) | ||||
0.146001 | + | 0.989284i | \(0.453360\pi\) | |||||||
\(884\) | 6.22083e9i | 0.0101868i | ||||||||
\(885\) | 2.72553e10 | + | 2.09962e9i | 0.0444302 | + | 0.00342269i | ||||
\(886\) | −8.02086e11 | −1.30163 | ||||||||
\(887\) | 7.87339e8i | 0.00127194i | 1.00000 | 0.000635971i | \(0.000202436\pi\) | |||||
−1.00000 | 0.000635971i | \(0.999798\pi\) | ||||||||
\(888\) | 5.40354e10 | − | 7.01437e11i | 0.0869013 | − | 1.12807i | ||||
\(889\) | −4.00256e11 | −0.640813 | ||||||||
\(890\) | − | 4.98142e10i | − | 0.0793949i | ||||||
\(891\) | −5.75228e10 | + | 1.81111e11i | −0.0912702 | + | 0.287365i | ||||
\(892\) | 2.10742e10 | 0.0332884 | ||||||||
\(893\) | 9.21180e11i | 1.44857i | ||||||||
\(894\) | 3.22192e11 | + | 2.48201e10i | 0.504387 | + | 0.0388556i | ||||
\(895\) | −3.91799e9 | −0.00610620 | ||||||||
\(896\) | − | 9.82276e11i | − | 1.52406i | ||||||
\(897\) | −1.30062e10 | + | 1.68835e11i | −0.0200901 | + | 0.260791i | ||||
\(898\) | −1.86247e10 | −0.0286408 | ||||||||
\(899\) | 4.72352e10i | 0.0723147i | ||||||||
\(900\) | 1.11229e10 | + | 1.72394e9i | 0.0169531 | + | 0.00262756i | ||||
\(901\) | 1.08265e12 | 1.64281 | ||||||||
\(902\) | − | 2.58344e11i | − | 0.390277i | ||||||
\(903\) | −7.48565e11 | − | 5.76660e10i | −1.12585 | − | 0.0867298i | ||||
\(904\) | 1.09192e12 | 1.63500 | ||||||||
\(905\) | − | 4.47676e11i | − | 0.667374i | ||||||
\(906\) | 2.69710e10 | − | 3.50112e11i | 0.0400299 | − | 0.519630i | ||||
\(907\) | −8.29322e11 | −1.22545 | −0.612723 | − | 0.790298i | \(-0.709926\pi\) | ||||
−0.612723 | + | 0.790298i | \(0.709926\pi\) | |||||||
\(908\) | 1.70091e10i | 0.0250230i | ||||||||
\(909\) | 1.51023e11 | − | 9.74400e11i | 0.221201 | − | 1.42719i | ||||
\(910\) | −4.79476e11 | −0.699199 | ||||||||
\(911\) | − | 5.82338e11i | − | 0.845476i | −0.906252 | − | 0.422738i | \(-0.861069\pi\) | ||
0.906252 | − | 0.422738i | \(-0.138931\pi\) | |||||||
\(912\) | 1.00066e12 | + | 7.70863e10i | 1.44646 | + | 0.111429i | ||||
\(913\) | 2.99301e11 | 0.430749 | ||||||||
\(914\) | − | 7.06885e10i | − | 0.101289i | ||||||
\(915\) | −7.72728e10 | + | 1.00308e12i | −0.110241 | + | 1.43104i | ||||
\(916\) | 5.06671e9 | 0.00719687 | ||||||||
\(917\) | − | 4.07355e11i | − | 0.576098i | ||||||
\(918\) | −7.75641e11 | − | 1.82144e11i | −1.09217 | − | 0.256474i | ||||
\(919\) | 2.71867e11 | 0.381148 | 0.190574 | − | 0.981673i | \(-0.438965\pi\) | ||||
0.190574 | + | 0.981673i | \(0.438965\pi\) | |||||||
\(920\) | − | 6.60350e11i | − | 0.921770i | ||||||
\(921\) | −7.46847e11 | − | 5.75336e10i | −1.03799 | − | 0.0799618i | ||||
\(922\) | 6.94806e10 | 0.0961479 | ||||||||
\(923\) | − | 3.80054e11i | − | 0.523647i | ||||||
\(924\) | 6.29472e8 | − | 8.17122e9i | 0.000863553 | − | 0.0112098i | ||||
\(925\) | 5.67843e11 | 0.775642 | ||||||||
\(926\) | − | 1.26009e12i | − | 1.71380i | ||||||
\(927\) | −8.21914e11 | − | 1.27389e11i | −1.11303 | − | 0.172509i | ||||
\(928\) | 1.98105e9 | 0.00267118 | ||||||||
\(929\) | − | 2.57259e11i | − | 0.345388i | −0.984976 | − | 0.172694i | \(-0.944753\pi\) | ||
0.984976 | − | 0.172694i | \(-0.0552472\pi\) | |||||||
\(930\) | −1.34223e12 | − | 1.03399e11i | −1.79430 | − | 0.138224i | ||||
\(931\) | 1.23670e12 | 1.64614 | ||||||||
\(932\) | − | 4.22654e9i | − | 0.00560172i | ||||||
\(933\) | 9.37689e9 | − | 1.21722e11i | 0.0123746 | − | 0.160636i | ||||
\(934\) | −6.71351e11 | −0.882191 | ||||||||
\(935\) | 3.30577e11i | 0.432539i | ||||||||
\(936\) | −4.20714e10 | + | 2.71445e11i | −0.0548130 | + | 0.353654i | ||||
\(937\) | −2.46466e11 | −0.319742 | −0.159871 | − | 0.987138i | \(-0.551108\pi\) | ||||
−0.159871 | + | 0.987138i | \(0.551108\pi\) | |||||||
\(938\) | − | 4.58875e11i | − | 0.592766i | ||||||
\(939\) | 1.11039e12 | + | 8.55393e10i | 1.42828 | + | 0.110028i | ||||
\(940\) | −2.62272e10 | −0.0335924 | ||||||||
\(941\) | 1.14552e12i | 1.46098i | 0.682922 | + | 0.730492i | \(0.260709\pi\) | ||||
−0.682922 | + | 0.730492i | \(0.739291\pi\) | |||||||
\(942\) | −3.30772e10 | + | 4.29378e11i | −0.0420074 | + | 0.545300i | ||||
\(943\) | 7.29130e11 | 0.922058 | ||||||||
\(944\) | 2.80053e10i | 0.0352657i | ||||||||
\(945\) | 3.47166e11 | − | 1.47837e12i | 0.435321 | − | 1.85378i | ||||
\(946\) | −1.87745e11 | −0.234425 | ||||||||
\(947\) | 9.95921e11i | 1.23830i | 0.785274 | + | 0.619149i | \(0.212522\pi\) | ||||
−0.785274 | + | 0.619149i | \(0.787478\pi\) | |||||||
\(948\) | −1.80779e10 | − | 1.39264e9i | −0.0223829 | − | 0.00172427i | ||||
\(949\) | 1.23636e11 | 0.152433 | ||||||||
\(950\) | 7.90033e11i | 0.969953i | ||||||||
\(951\) | 4.83462e10 | − | 6.27585e11i | 0.0591072 | − | 0.767275i | ||||
\(952\) | −1.32081e12 | −1.60802 | ||||||||
\(953\) | 2.81088e11i | 0.340777i | 0.985377 | + | 0.170389i | \(0.0545023\pi\) | ||||
−0.985377 | + | 0.170389i | \(0.945498\pi\) | |||||||
\(954\) | −1.22901e12 | − | 1.90485e11i | −1.48376 | − | 0.229968i | ||||
\(955\) | 2.53372e11 | 0.304610 | ||||||||
\(956\) | 2.58408e10i | 0.0309367i | ||||||||
\(957\) | −1.32851e10 | − | 1.02342e9i | −0.0158386 | − | 0.00122013i | ||||
\(958\) | −1.44408e12 | −1.71447 | ||||||||
\(959\) | 1.39302e12i | 1.64696i | ||||||||
\(960\) | 8.22210e10 | − | 1.06732e12i | 0.0968050 | − | 1.25663i | ||||
\(961\) | 7.53873e11 | 0.883903 | ||||||||
\(962\) | − | 3.60517e11i | − | 0.420945i | ||||||
\(963\) | −2.34349e11 | + | 1.51202e12i | −0.272494 | + | 1.75814i | ||||
\(964\) | −2.36228e10 | −0.0273541 | ||||||||
\(965\) | − | 3.91316e11i | − | 0.451252i | ||||||
\(966\) | 9.32583e11 | + | 7.18419e10i | 1.07097 | + | 0.0825029i | ||||
\(967\) | −1.59032e12 | −1.81877 | −0.909384 | − | 0.415957i | \(-0.863447\pi\) | ||||
−0.909384 | + | 0.415957i | \(0.863447\pi\) | |||||||
\(968\) | 7.87757e10i | 0.0897203i | ||||||||
\(969\) | 1.06218e11 | − | 1.37883e12i | 0.120477 | − | 1.56392i | ||||
\(970\) | 1.43279e12 | 1.61843 | ||||||||
\(971\) | 1.17604e11i | 0.132296i | 0.997810 | + | 0.0661478i | \(0.0210709\pi\) | ||||
−0.997810 | + | 0.0661478i | \(0.978929\pi\) | |||||||
\(972\) | 2.09813e10 | + | 8.48786e9i | 0.0235054 | + | 0.00950896i | ||||
\(973\) | −6.53716e11 | −0.729353 | ||||||||
\(974\) | 5.38970e11i | 0.598865i | ||||||||
\(975\) | −2.21058e11 | − | 1.70293e10i | −0.244618 | − | 0.0188442i | ||||
\(976\) | −1.03068e12 | −1.13586 | ||||||||
\(977\) | − | 2.45765e11i | − | 0.269738i | −0.990863 | − | 0.134869i | \(-0.956939\pi\) | ||
0.990863 | − | 0.134869i | \(-0.0430613\pi\) | |||||||
\(978\) | −7.76079e10 | + | 1.00743e12i | −0.0848302 | + | 1.10119i | ||||
\(979\) | −1.67717e10 | −0.0182577 | ||||||||
\(980\) | 3.52106e10i | 0.0381741i | ||||||||
\(981\) | −1.25906e12 | − | 1.95143e11i | −1.35947 | − | 0.210706i | ||||
\(982\) | 9.87078e11 | 1.06146 | ||||||||
\(983\) | 3.82073e11i | 0.409197i | 0.978846 | + | 0.204598i | \(0.0655889\pi\) | ||||
−0.978846 | + | 0.204598i | \(0.934411\pi\) | |||||||
\(984\) | 1.17926e12 | + | 9.08449e10i | 1.25785 | + | 0.0968992i | ||||
\(985\) | 6.69000e11 | 0.710691 | ||||||||
\(986\) | − | 5.58665e10i | − | 0.0591077i | ||||||
\(987\) | −1.09679e11 | + | 1.42374e12i | −0.115572 | + | 1.50025i | ||||
\(988\) | 1.24036e10 | 0.0130173 | ||||||||
\(989\) | − | 5.29876e11i | − | 0.553847i | ||||||
\(990\) | 5.81627e10 | − | 3.75267e11i | 0.0605486 | − | 0.390660i | ||||
\(991\) | 6.94513e11 | 0.720089 | 0.360044 | − | 0.932935i | \(-0.382762\pi\) | ||||
0.360044 | + | 0.932935i | \(0.382762\pi\) | |||||||
\(992\) | − | 6.73879e10i | − | 0.0695881i | ||||||
\(993\) | 1.47079e12 | + | 1.13302e11i | 1.51270 | + | 0.116531i | ||||
\(994\) | −2.09928e12 | −2.15043 | ||||||||
\(995\) | − | 8.82704e10i | − | 0.0900581i | ||||||
\(996\) | 2.73806e9 | − | 3.55429e10i | 0.00278231 | − | 0.0361174i | ||||
\(997\) | 5.41235e11 | 0.547778 | 0.273889 | − | 0.961761i | \(-0.411690\pi\) | ||||
0.273889 | + | 0.961761i | \(0.411690\pi\) | |||||||
\(998\) | − | 9.20062e10i | − | 0.0927459i | ||||||
\(999\) | 1.11159e12 | + | 2.61034e11i | 1.11605 | + | 0.262080i |
(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 | 33.9.b.a.23.7 | ✓ | 26 | |
3.2 | odd | 2 | inner | 33.9.b.a.23.20 | yes | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.9.b.a.23.7 | ✓ | 26 | 1.1 | even | 1 | trivial | |
33.9.b.a.23.20 | yes | 26 | 3.2 | odd | 2 | inner |