Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [24,8,Mod(11,24)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(24, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("24.11");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 24 = 2^{3} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 24.f (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: | \(7.49724061162\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 274 x^{18} + 45864 x^{16} - 5031360 x^{14} + 776389632 x^{12} - 102828146688 x^{10} + \cdots + 11\!\cdots\!24 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{52}\cdot 3^{20} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 11.12 | ||
Root | \(-3.79334 + 10.6588i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 24.11 |
Dual form | 24.8.f.c.11.11 |
$q$-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 \(\left(\mathbb{Z}/24\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(13\) | \(17\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.79334 | + | 10.6588i | 0.335287 | + | 0.942116i | ||||
\(3\) | 46.6816 | − | 2.79715i | 0.998210 | − | 0.0598124i | ||||
\(4\) | −99.2212 | + | 80.8651i | −0.775165 | + | 0.631758i | ||||
\(5\) | −395.205 | −1.41393 | −0.706963 | − | 0.707250i | \(-0.749935\pi\) | ||||
−0.706963 | + | 0.707250i | \(0.749935\pi\) | |||||||
\(6\) | 206.894 | + | 486.961i | 0.391037 | + | 0.920375i | ||||
\(7\) | 1395.40i | 1.53764i | 0.639464 | + | 0.768821i | \(0.279156\pi\) | ||||
−0.639464 | + | 0.768821i | \(0.720844\pi\) | |||||||
\(8\) | −1238.31 | − | 750.833i | −0.855093 | − | 0.518475i | ||||
\(9\) | 2171.35 | − | 261.151i | 0.992845 | − | 0.119411i | ||||
\(10\) | −1499.14 | − | 4212.42i | −0.474071 | − | 1.33208i | ||||
\(11\) | 5391.17i | 1.22126i | 0.791915 | + | 0.610631i | \(0.209084\pi\) | ||||
−0.791915 | + | 0.610631i | \(0.790916\pi\) | |||||||
\(12\) | −4405.62 | + | 4052.45i | −0.735991 | + | 0.676992i | ||||
\(13\) | − | 3927.39i | − | 0.495795i | −0.968786 | − | 0.247898i | \(-0.920260\pi\) | ||
0.968786 | − | 0.247898i | \(-0.0797396\pi\) | |||||||
\(14\) | −14873.3 | + | 5293.22i | −1.44864 | + | 0.515551i | ||||
\(15\) | −18448.8 | + | 1105.45i | −1.41140 | + | 0.0845703i | ||||
\(16\) | 3305.68 | − | 16047.1i | 0.201763 | − | 0.979434i | ||||
\(17\) | − | 5903.54i | − | 0.291435i | −0.989326 | − | 0.145717i | \(-0.953451\pi\) | ||
0.989326 | − | 0.145717i | \(-0.0465490\pi\) | |||||||
\(18\) | 11020.2 | + | 22153.4i | 0.445387 | + | 0.895338i | ||||
\(19\) | 14851.3 | 0.496737 | 0.248368 | − | 0.968666i | \(-0.420106\pi\) | ||||
0.248368 | + | 0.968666i | \(0.420106\pi\) | |||||||
\(20\) | 39212.7 | − | 31958.2i | 1.09603 | − | 0.893260i | ||||
\(21\) | 3903.14 | + | 65139.5i | 0.0919700 | + | 1.53489i | ||||
\(22\) | −57463.6 | + | 20450.6i | −1.15057 | + | 0.409473i | ||||
\(23\) | 73616.8 | 1.26162 | 0.630812 | − | 0.775936i | \(-0.282722\pi\) | ||||
0.630812 | + | 0.775936i | \(0.282722\pi\) | |||||||
\(24\) | −59906.4 | − | 31586.4i | −0.884573 | − | 0.466402i | ||||
\(25\) | 78061.6 | 0.999189 | ||||||||
\(26\) | 41861.4 | − | 14897.9i | 0.467097 | − | 0.166234i | ||||
\(27\) | 100632. | − | 18264.5i | 0.983925 | − | 0.178581i | ||||
\(28\) | −112839. | − | 138453.i | −0.971418 | − | 1.19193i | ||||
\(29\) | −26579.4 | −0.202373 | −0.101186 | − | 0.994867i | \(-0.532264\pi\) | ||||
−0.101186 | + | 0.994867i | \(0.532264\pi\) | |||||||
\(30\) | −81765.3 | − | 192449.i | −0.552897 | − | 1.30134i | ||||
\(31\) | 205272.i | 1.23755i | 0.785567 | + | 0.618776i | \(0.212371\pi\) | ||||
−0.785567 | + | 0.618776i | \(0.787629\pi\) | |||||||
\(32\) | 183582. | − | 25637.3i | 0.990389 | − | 0.138308i | ||||
\(33\) | 15079.9 | + | 251669.i | 0.0730466 | + | 1.21908i | ||||
\(34\) | 62924.8 | − | 22394.1i | 0.274565 | − | 0.0977143i | ||||
\(35\) | − | 551468.i | − | 2.17411i | ||||||
\(36\) | −194326. | + | 201498.i | −0.694180 | + | 0.719801i | ||||
\(37\) | − | 172154.i | − | 0.558743i | −0.960183 | − | 0.279371i | \(-0.909874\pi\) | ||
0.960183 | − | 0.279371i | \(-0.0901261\pi\) | |||||||
\(38\) | 56335.9 | + | 158297.i | 0.166549 | + | 0.467984i | ||||
\(39\) | −10985.5 | − | 183337.i | −0.0296547 | − | 0.494907i | ||||
\(40\) | 489384. | + | 296732.i | 1.20904 | + | 0.733086i | ||||
\(41\) | 741464.i | 1.68014i | 0.542476 | + | 0.840072i | \(0.317487\pi\) | ||||
−0.542476 | + | 0.840072i | \(0.682513\pi\) | |||||||
\(42\) | −679505. | + | 288699.i | −1.41521 | + | 0.601275i | ||||
\(43\) | −279102. | −0.535331 | −0.267666 | − | 0.963512i | \(-0.586252\pi\) | ||||
−0.267666 | + | 0.963512i | \(0.586252\pi\) | |||||||
\(44\) | −435958. | − | 534919.i | −0.771543 | − | 0.946680i | ||||
\(45\) | −858128. | + | 103208.i | −1.40381 | + | 0.168838i | ||||
\(46\) | 279254. | + | 784669.i | 0.423006 | + | 1.18860i | ||||
\(47\) | 418307. | 0.587696 | 0.293848 | − | 0.955852i | \(-0.405064\pi\) | ||||
0.293848 | + | 0.955852i | \(0.405064\pi\) | |||||||
\(48\) | 109429. | − | 758349.i | 0.142819 | − | 0.989749i | ||||
\(49\) | −1.12359e6 | −1.36434 | ||||||||
\(50\) | 296114. | + | 832045.i | 0.335015 | + | 0.941352i | ||||
\(51\) | −16513.1 | − | 275587.i | −0.0174314 | − | 0.290913i | ||||
\(52\) | 317589. | + | 389680.i | 0.313223 | + | 0.384323i | ||||
\(53\) | 427120. | 0.394080 | 0.197040 | − | 0.980395i | \(-0.436867\pi\) | ||||
0.197040 | + | 0.980395i | \(0.436867\pi\) | |||||||
\(54\) | 576409. | + | 1.00333e6i | 0.498141 | + | 0.867096i | ||||
\(55\) | − | 2.13062e6i | − | 1.72678i | ||||||
\(56\) | 1.04771e6 | − | 1.72793e6i | 0.797229 | − | 1.31483i | ||||
\(57\) | 693282. | − | 41541.2i | 0.495847 | − | 0.0297110i | ||||
\(58\) | −100825. | − | 283305.i | −0.0678529 | − | 0.190658i | ||||
\(59\) | − | 1.65127e6i | − | 1.04674i | −0.852107 | − | 0.523368i | \(-0.824675\pi\) | ||
0.852107 | − | 0.523368i | \(-0.175325\pi\) | |||||||
\(60\) | 1.74112e6 | − | 1.60155e6i | 1.04064 | − | 0.957217i | ||||
\(61\) | − | 1.02459e6i | − | 0.577957i | −0.957336 | − | 0.288979i | \(-0.906684\pi\) | ||
0.957336 | − | 0.288979i | \(-0.0933156\pi\) | |||||||
\(62\) | −2.18796e6 | + | 778666.i | −1.16592 | + | 0.414935i | ||||
\(63\) | 364410. | + | 3.02990e6i | 0.183611 | + | 1.52664i | ||||
\(64\) | 969653. | + | 1.85952e6i | 0.462367 | + | 0.886689i | ||||
\(65\) | 1.55212e6i | 0.701018i | ||||||||
\(66\) | −2.62529e6 | + | 1.11540e6i | −1.12402 | + | 0.477559i | ||||
\(67\) | −2.38005e6 | −0.966772 | −0.483386 | − | 0.875407i | \(-0.660593\pi\) | ||||
−0.483386 | + | 0.875407i | \(0.660593\pi\) | |||||||
\(68\) | 477391. | + | 585756.i | 0.184116 | + | 0.225910i | ||||
\(69\) | 3.43656e6 | − | 205917.i | 1.25936 | − | 0.0754607i | ||||
\(70\) | 5.87800e6 | − | 2.09190e6i | 2.04827 | − | 0.728952i | ||||
\(71\) | 822295. | 0.272661 | 0.136331 | − | 0.990663i | \(-0.456469\pi\) | ||||
0.136331 | + | 0.990663i | \(0.456469\pi\) | |||||||
\(72\) | −2.88488e6 | − | 1.30694e6i | −0.910886 | − | 0.412659i | ||||
\(73\) | −1.84283e6 | −0.554441 | −0.277220 | − | 0.960806i | \(-0.589413\pi\) | ||||
−0.277220 | + | 0.960806i | \(0.589413\pi\) | |||||||
\(74\) | 1.83496e6 | − | 653040.i | 0.526401 | − | 0.187339i | ||||
\(75\) | 3.64404e6 | − | 218350.i | 0.997400 | − | 0.0597638i | ||||
\(76\) | −1.47356e6 | + | 1.20095e6i | −0.385053 | + | 0.313818i | ||||
\(77\) | −7.52284e6 | −1.87786 | ||||||||
\(78\) | 1.91249e6 | − | 812552.i | 0.456317 | − | 0.193874i | ||||
\(79\) | − | 846282.i | − | 0.193117i | −0.995327 | − | 0.0965584i | \(-0.969217\pi\) | ||
0.995327 | − | 0.0965584i | \(-0.0307835\pi\) | |||||||
\(80\) | −1.30642e6 | + | 6.34187e6i | −0.285277 | + | 1.38485i | ||||
\(81\) | 4.64657e6 | − | 1.13410e6i | 0.971482 | − | 0.237112i | ||||
\(82\) | −7.90313e6 | + | 2.81262e6i | −1.58289 | + | 0.563330i | ||||
\(83\) | 130811.i | 0.0251115i | 0.999921 | + | 0.0125557i | \(0.00399672\pi\) | ||||
−0.999921 | + | 0.0125557i | \(0.996003\pi\) | |||||||
\(84\) | −5.65479e6 | − | 6.14759e6i | −1.04097 | − | 1.13169i | ||||
\(85\) | 2.33311e6i | 0.412068i | ||||||||
\(86\) | −1.05873e6 | − | 2.97489e6i | −0.179490 | − | 0.504344i | ||||
\(87\) | −1.24077e6 | + | 74346.4i | −0.202010 | + | 0.0121044i | ||||
\(88\) | 4.04787e6 | − | 6.67593e6i | 0.633194 | − | 1.04429i | ||||
\(89\) | 4.39906e6i | 0.661447i | 0.943728 | + | 0.330724i | \(0.107293\pi\) | ||||
−0.943728 | + | 0.330724i | \(0.892707\pi\) | |||||||
\(90\) | −4.35525e6 | − | 8.75514e6i | −0.629744 | − | 1.26594i | ||||
\(91\) | 5.48027e6 | 0.762355 | ||||||||
\(92\) | −7.30435e6 | + | 5.95303e6i | −0.977967 | + | 0.797041i | ||||
\(93\) | 574176. | + | 9.58243e6i | 0.0740209 | + | 1.23534i | ||||
\(94\) | 1.58678e6 | + | 4.45866e6i | 0.197047 | + | 0.553677i | ||||
\(95\) | −5.86929e6 | −0.702349 | ||||||||
\(96\) | 8.49821e6 | − | 1.71030e6i | 0.980344 | − | 0.197298i | ||||
\(97\) | 3.64708e6 | 0.405736 | 0.202868 | − | 0.979206i | \(-0.434974\pi\) | ||||
0.202868 | + | 0.979206i | \(0.434974\pi\) | |||||||
\(98\) | −4.26218e6 | − | 1.19762e7i | −0.457446 | − | 1.28537i | ||||
\(99\) | 1.40791e6 | + | 1.17061e7i | 0.145832 | + | 1.21252i | ||||
\(100\) | −7.74536e6 | + | 6.31246e6i | −0.774536 | + | 0.631246i | ||||
\(101\) | 1.50610e7 | 1.45456 | 0.727278 | − | 0.686343i | \(-0.240785\pi\) | ||||
0.727278 | + | 0.686343i | \(0.240785\pi\) | |||||||
\(102\) | 2.87480e6 | − | 1.22141e6i | 0.268229 | − | 0.113962i | ||||
\(103\) | 1.04154e7i | 0.939176i | 0.882886 | + | 0.469588i | \(0.155598\pi\) | ||||
−0.882886 | + | 0.469588i | \(0.844402\pi\) | |||||||
\(104\) | −2.94881e6 | + | 4.86331e6i | −0.257058 | + | 0.423951i | ||||
\(105\) | −1.54254e6 | − | 2.57434e7i | −0.130039 | − | 2.17022i | ||||
\(106\) | 1.62021e6 | + | 4.55260e6i | 0.132130 | + | 0.371269i | ||||
\(107\) | 7.91002e6i | 0.624215i | 0.950047 | + | 0.312108i | \(0.101035\pi\) | ||||
−0.950047 | + | 0.312108i | \(0.898965\pi\) | |||||||
\(108\) | −8.50784e6 | + | 9.94983e6i | −0.649885 | + | 0.760033i | ||||
\(109\) | − | 1.78544e7i | − | 1.32054i | −0.751026 | − | 0.660272i | \(-0.770441\pi\) | ||
0.751026 | − | 0.660272i | \(-0.229559\pi\) | |||||||
\(110\) | 2.27099e7 | − | 8.08215e6i | 1.62682 | − | 0.578965i | ||||
\(111\) | −481541. | − | 8.03645e6i | −0.0334197 | − | 0.557743i | ||||
\(112\) | 2.23920e7 | + | 4.61274e6i | 1.50602 | + | 0.310239i | ||||
\(113\) | − | 1.86836e7i | − | 1.21811i | −0.793130 | − | 0.609053i | \(-0.791550\pi\) | ||
0.793130 | − | 0.609053i | \(-0.208450\pi\) | |||||||
\(114\) | 3.07263e6 | + | 7.23199e6i | 0.194242 | + | 0.457184i | ||||
\(115\) | −2.90937e7 | −1.78384 | ||||||||
\(116\) | 2.63724e6 | − | 2.14934e6i | 0.156872 | − | 0.127851i | ||||
\(117\) | −1.02564e6 | − | 8.52775e6i | −0.0592032 | − | 0.492248i | ||||
\(118\) | 1.76006e7 | − | 6.26384e6i | 0.986147 | − | 0.350957i | ||||
\(119\) | 8.23780e6 | 0.448123 | ||||||||
\(120\) | 2.36753e7 | + | 1.24831e7i | 1.25072 | + | 0.659458i | ||||
\(121\) | −9.57759e6 | −0.491482 | ||||||||
\(122\) | 1.09209e7 | − | 3.88662e6i | 0.544503 | − | 0.193781i | ||||
\(123\) | 2.07398e6 | + | 3.46127e7i | 0.100493 | + | 1.67714i | ||||
\(124\) | −1.65993e7 | − | 2.03673e7i | −0.781834 | − | 0.959308i | ||||
\(125\) | 25049.8 | 0.00114715 | ||||||||
\(126\) | −3.09129e7 | + | 1.53776e7i | −1.37671 | + | 0.684845i | ||||
\(127\) | − | 2.78676e7i | − | 1.20722i | −0.797280 | − | 0.603609i | \(-0.793729\pi\) | ||
0.797280 | − | 0.603609i | \(-0.206271\pi\) | |||||||
\(128\) | −1.61421e7 | + | 1.73892e7i | −0.680338 | + | 0.732898i | ||||
\(129\) | −1.30289e7 | + | 780688.i | −0.534373 | + | 0.0320194i | ||||
\(130\) | −1.65438e7 | + | 5.88773e6i | −0.660440 | + | 0.235042i | ||||
\(131\) | − | 2.92965e7i | − | 1.13859i | −0.822134 | − | 0.569293i | \(-0.807217\pi\) | ||
0.822134 | − | 0.569293i | \(-0.192783\pi\) | |||||||
\(132\) | −2.18475e7 | − | 2.37514e7i | −0.826785 | − | 0.898838i | ||||
\(133\) | 2.07235e7i | 0.763803i | ||||||||
\(134\) | −9.02833e6 | − | 2.53685e7i | −0.324146 | − | 0.910811i | ||||
\(135\) | −3.97701e7 | + | 7.21823e6i | −1.39120 | + | 0.252501i | ||||
\(136\) | −4.43257e6 | + | 7.31040e6i | −0.151102 | + | 0.249204i | ||||
\(137\) | 3.76195e7i | 1.24995i | 0.780646 | + | 0.624973i | \(0.214890\pi\) | ||||
−0.780646 | + | 0.624973i | \(0.785110\pi\) | |||||||
\(138\) | 1.52309e7 | + | 3.58485e7i | 0.493341 | + | 1.16117i | ||||
\(139\) | 4.68128e7 | 1.47847 | 0.739235 | − | 0.673447i | \(-0.235187\pi\) | ||||
0.739235 | + | 0.673447i | \(0.235187\pi\) | |||||||
\(140\) | 4.45945e7 | + | 5.47173e7i | 1.37351 | + | 1.68530i | ||||
\(141\) | 1.95272e7 | − | 1.17007e6i | 0.586643 | − | 0.0351515i | ||||
\(142\) | 3.11924e6 | + | 8.76470e6i | 0.0914198 | + | 0.256879i | ||||
\(143\) | 2.11732e7 | 0.605496 | ||||||||
\(144\) | 2.98709e6 | − | 3.57071e7i | 0.0833642 | − | 0.996519i | ||||
\(145\) | 1.05043e7 | 0.286140 | ||||||||
\(146\) | −6.99048e6 | − | 1.96424e7i | −0.185897 | − | 0.522348i | ||||
\(147\) | −5.24513e7 | + | 3.14286e6i | −1.36190 | + | 0.0816045i | ||||
\(148\) | 1.39213e7 | + | 1.70814e7i | 0.352991 | + | 0.433118i | ||||
\(149\) | −6.47201e7 | −1.60283 | −0.801415 | − | 0.598108i | \(-0.795919\pi\) | ||||
−0.801415 | + | 0.598108i | \(0.795919\pi\) | |||||||
\(150\) | 1.61504e7 | + | 3.80130e7i | 0.390720 | + | 0.919628i | ||||
\(151\) | 1.82260e7i | 0.430796i | 0.976526 | + | 0.215398i | \(0.0691049\pi\) | ||||
−0.976526 | + | 0.215398i | \(0.930895\pi\) | |||||||
\(152\) | −1.83904e7 | − | 1.11508e7i | −0.424756 | − | 0.257546i | ||||
\(153\) | −1.54172e6 | − | 1.28187e7i | −0.0348004 | − | 0.289350i | ||||
\(154\) | −2.85367e7 | − | 8.01846e7i | −0.629623 | − | 1.76917i | ||||
\(155\) | − | 8.11244e7i | − | 1.74981i | ||||||
\(156\) | 1.59156e7 | + | 1.73026e7i | 0.335649 | + | 0.364901i | ||||
\(157\) | 2.67214e7i | 0.551075i | 0.961290 | + | 0.275537i | \(0.0888558\pi\) | ||||
−0.961290 | + | 0.275537i | \(0.911144\pi\) | |||||||
\(158\) | 9.02037e6 | − | 3.21023e6i | 0.181938 | − | 0.0647495i | ||||
\(159\) | 1.99387e7 | − | 1.19472e6i | 0.393374 | − | 0.0235708i | ||||
\(160\) | −7.25526e7 | + | 1.01320e7i | −1.40034 | + | 0.195557i | ||||
\(161\) | 1.02725e8i | 1.93993i | ||||||||
\(162\) | 2.97142e7 | + | 4.52249e7i | 0.549113 | + | 0.835748i | ||||
\(163\) | 3.30452e7 | 0.597656 | 0.298828 | − | 0.954307i | \(-0.403404\pi\) | ||||
0.298828 | + | 0.954307i | \(0.403404\pi\) | |||||||
\(164\) | −5.99585e7 | − | 7.35689e7i | −1.06144 | − | 1.30239i | ||||
\(165\) | −5.95965e6 | − | 9.94607e7i | −0.103283 | − | 1.72368i | ||||
\(166\) | −1.39430e6 | + | 496212.i | −0.0236579 | + | 0.00841956i | ||||
\(167\) | 8.08422e7 | 1.34317 | 0.671584 | − | 0.740928i | \(-0.265614\pi\) | ||||
0.671584 | + | 0.740928i | \(0.265614\pi\) | |||||||
\(168\) | 4.40756e7 | − | 8.35933e7i | 0.717159 | − | 1.36016i | ||||
\(169\) | 4.73241e7 | 0.754187 | ||||||||
\(170\) | −2.48682e7 | + | 8.85027e6i | −0.388215 | + | 0.138161i | ||||
\(171\) | 3.22474e7 | − | 3.87842e6i | 0.493183 | − | 0.0593156i | ||||
\(172\) | 2.76928e7 | − | 2.25696e7i | 0.414970 | − | 0.338200i | ||||
\(173\) | 5.95705e7 | 0.874722 | 0.437361 | − | 0.899286i | \(-0.355913\pi\) | ||||
0.437361 | + | 0.899286i | \(0.355913\pi\) | |||||||
\(174\) | −5.49910e6 | − | 1.29431e7i | −0.0791351 | − | 0.186259i | ||||
\(175\) | 1.08927e8i | 1.53639i | ||||||||
\(176\) | 8.65125e7 | + | 1.78215e7i | 1.19615 | + | 0.246405i | ||||
\(177\) | −4.61886e6 | − | 7.70842e7i | −0.0626077 | − | 1.04486i | ||||
\(178\) | −4.68889e7 | + | 1.66871e7i | −0.623160 | + | 0.221775i | ||||
\(179\) | − | 5.29640e7i | − | 0.690232i | −0.938560 | − | 0.345116i | \(-0.887840\pi\) | ||
0.938560 | − | 0.345116i | \(-0.112160\pi\) | |||||||
\(180\) | 7.67985e7 | − | 7.96330e7i | 0.981520 | − | 1.01775i | ||||
\(181\) | 1.19135e8i | 1.49336i | 0.665182 | + | 0.746681i | \(0.268354\pi\) | ||||
−0.665182 | + | 0.746681i | \(0.731646\pi\) | |||||||
\(182\) | 2.07885e7 | + | 5.84133e7i | 0.255608 | + | 0.718227i | ||||
\(183\) | −2.86593e6 | − | 4.78295e7i | −0.0345690 | − | 0.576922i | ||||
\(184\) | −9.11602e7 | − | 5.52739e7i | −1.07880 | − | 0.654121i | ||||
\(185\) | 6.80362e7i | 0.790021i | ||||||||
\(186\) | −9.99594e7 | + | 4.24694e7i | −1.13901 | + | 0.483928i | ||||
\(187\) | 3.18270e7 | 0.355919 | ||||||||
\(188\) | −4.15049e7 | + | 3.38264e7i | −0.455561 | + | 0.371282i | ||||
\(189\) | 2.54863e7 | + | 1.40421e8i | 0.274594 | + | 1.51292i | ||||
\(190\) | −2.22642e7 | − | 6.25598e7i | −0.235489 | − | 0.661694i | ||||
\(191\) | −1.80634e8 | −1.87578 | −0.937890 | − | 0.346934i | \(-0.887223\pi\) | ||||
−0.937890 | + | 0.346934i | \(0.887223\pi\) | |||||||
\(192\) | 5.04664e7 | + | 8.40932e7i | 0.514574 | + | 0.857446i | ||||
\(193\) | 8.94746e7 | 0.895879 | 0.447939 | − | 0.894064i | \(-0.352158\pi\) | ||||
0.447939 | + | 0.894064i | \(0.352158\pi\) | |||||||
\(194\) | 1.38346e7 | + | 3.88736e7i | 0.136038 | + | 0.382251i | ||||
\(195\) | 4.34151e6 | + | 7.24556e7i | 0.0419295 | + | 0.699763i | ||||
\(196\) | 1.11484e8 | − | 9.08596e7i | 1.05759 | − | 0.861935i | ||||
\(197\) | −1.48244e8 | −1.38148 | −0.690741 | − | 0.723102i | \(-0.742716\pi\) | ||||
−0.690741 | + | 0.723102i | \(0.742716\pi\) | |||||||
\(198\) | −1.19433e8 | + | 5.94120e7i | −1.09344 | + | 0.543934i | ||||
\(199\) | − | 1.18822e8i | − | 1.06884i | −0.845219 | − | 0.534419i | \(-0.820530\pi\) | ||
0.845219 | − | 0.534419i | \(-0.179470\pi\) | |||||||
\(200\) | −9.66642e7 | − | 5.86112e7i | −0.854399 | − | 0.518055i | ||||
\(201\) | −1.11105e8 | + | 6.65735e6i | −0.965041 | + | 0.0578249i | ||||
\(202\) | 5.71316e7 | + | 1.60533e8i | 0.487693 | + | 1.37036i | ||||
\(203\) | − | 3.70888e7i | − | 0.311176i | ||||||
\(204\) | 2.39238e7 | + | 2.60087e7i | 0.197299 | + | 0.214493i | ||||
\(205\) | − | 2.93030e8i | − | 2.37560i | ||||||
\(206\) | −1.11016e8 | + | 3.95093e7i | −0.884813 | + | 0.314894i | ||||
\(207\) | 1.59848e8 | − | 1.92251e7i | 1.25260 | − | 0.150651i | ||||
\(208\) | −6.30230e7 | − | 1.29827e7i | −0.485599 | − | 0.100033i | ||||
\(209\) | 8.00658e7i | 0.606646i | ||||||||
\(210\) | 2.68543e8 | − | 1.14095e8i | 2.00100 | − | 0.850158i | ||||
\(211\) | −1.14249e8 | −0.837270 | −0.418635 | − | 0.908155i | \(-0.637491\pi\) | ||||
−0.418635 | + | 0.908155i | \(0.637491\pi\) | |||||||
\(212\) | −4.23793e7 | + | 3.45391e7i | −0.305477 | + | 0.248963i | ||||
\(213\) | 3.83861e7 | − | 2.30008e6i | 0.272173 | − | 0.0163085i | ||||
\(214\) | −8.43115e7 | + | 3.00054e7i | −0.588083 | + | 0.209291i | ||||
\(215\) | 1.10302e8 | 0.756919 | ||||||||
\(216\) | −1.38327e8 | − | 5.29405e7i | −0.933937 | − | 0.357438i | ||||
\(217\) | −2.86436e8 | −1.90291 | ||||||||
\(218\) | 1.90307e8 | − | 6.77279e7i | 1.24411 | − | 0.442761i | ||||
\(219\) | −8.60263e7 | + | 5.15467e6i | −0.553448 | + | 0.0331624i | ||||
\(220\) | 1.72292e8 | + | 2.11402e8i | 1.09091 | + | 1.33854i | ||||
\(221\) | −2.31855e7 | −0.144492 | ||||||||
\(222\) | 8.38325e7 | − | 3.56176e7i | 0.514253 | − | 0.218489i | ||||
\(223\) | 5.04402e7i | 0.304586i | 0.988335 | + | 0.152293i | \(0.0486657\pi\) | ||||
−0.988335 | + | 0.152293i | \(0.951334\pi\) | |||||||
\(224\) | 3.57742e7 | + | 2.56171e8i | 0.212668 | + | 1.52286i | ||||
\(225\) | 1.69499e8 | − | 2.03859e7i | 0.992039 | − | 0.119314i | ||||
\(226\) | 1.99145e8 | − | 7.08731e7i | 1.14760 | − | 0.408415i | ||||
\(227\) | − | 1.22989e6i | − | 0.00697871i | −0.999994 | − | 0.00348935i | \(-0.998889\pi\) | ||
0.999994 | − | 0.00348935i | \(-0.00111070\pi\) | |||||||
\(228\) | −6.54290e7 | + | 6.01841e7i | −0.365593 | + | 0.336287i | ||||
\(229\) | − | 6.31617e7i | − | 0.347560i | −0.984784 | − | 0.173780i | \(-0.944402\pi\) | ||
0.984784 | − | 0.173780i | \(-0.0555982\pi\) | |||||||
\(230\) | −1.10362e8 | − | 3.10105e8i | −0.598099 | − | 1.68059i | ||||
\(231\) | −3.51178e8 | + | 2.10425e7i | −1.87450 | + | 0.112319i | ||||
\(232\) | 3.29134e7 | + | 1.99566e7i | 0.173047 | + | 0.104925i | ||||
\(233\) | − | 2.38993e8i | − | 1.23777i | −0.785482 | − | 0.618885i | \(-0.787585\pi\) | ||
0.785482 | − | 0.618885i | \(-0.212415\pi\) | |||||||
\(234\) | 8.70052e7 | − | 4.32808e7i | 0.443904 | − | 0.220820i | ||||
\(235\) | −1.65317e8 | −0.830958 | ||||||||
\(236\) | 1.33530e8 | + | 1.63841e8i | 0.661284 | + | 0.811393i | ||||
\(237\) | −2.36717e6 | − | 3.95058e7i | −0.0115508 | − | 0.192771i | ||||
\(238\) | 3.12488e7 | + | 8.78053e7i | 0.150250 | + | 0.422183i | ||||
\(239\) | 1.24523e8 | 0.590007 | 0.295003 | − | 0.955496i | \(-0.404679\pi\) | ||||
0.295003 | + | 0.955496i | \(0.404679\pi\) | |||||||
\(240\) | −4.32466e7 | + | 2.99703e8i | −0.201936 | + | 1.39943i | ||||
\(241\) | 1.12969e8 | 0.519874 | 0.259937 | − | 0.965626i | \(-0.416298\pi\) | ||||
0.259937 | + | 0.965626i | \(0.416298\pi\) | |||||||
\(242\) | −3.63311e7 | − | 1.02086e8i | −0.164787 | − | 0.463033i | ||||
\(243\) | 2.13737e8 | − | 6.59388e7i | 0.955561 | − | 0.294794i | ||||
\(244\) | 8.28535e7 | + | 1.01661e8i | 0.365129 | + | 0.448012i | ||||
\(245\) | 4.44050e8 | 1.92908 | ||||||||
\(246\) | −3.61064e8 | + | 1.53404e8i | −1.54636 | + | 0.656998i | ||||
\(247\) | − | 5.83268e7i | − | 0.246280i | ||||||
\(248\) | 1.54125e8 | − | 2.54189e8i | 0.641640 | − | 1.05822i | ||||
\(249\) | 365899. | + | 6.10649e6i | 0.00150198 | + | 0.0250665i | ||||
\(250\) | 95022.3 | + | 267001.i | 0.000384623 | + | 0.00108075i | ||||
\(251\) | 3.91541e8i | 1.56286i | 0.623995 | + | 0.781429i | \(0.285509\pi\) | ||||
−0.623995 | + | 0.781429i | \(0.714491\pi\) | |||||||
\(252\) | −2.81170e8 | − | 2.71162e8i | −1.10680 | − | 1.06740i | ||||
\(253\) | 3.96881e8i | 1.54077i | ||||||||
\(254\) | 2.97036e8 | − | 1.05711e8i | 1.13734 | − | 0.404765i | ||||
\(255\) | 6.52604e6 | + | 1.08913e8i | 0.0246467 | + | 0.411330i | ||||
\(256\) | −2.46580e8 | − | 1.06093e8i | −0.918584 | − | 0.395226i | ||||
\(257\) | − | 3.55429e8i | − | 1.30613i | −0.757301 | − | 0.653066i | \(-0.773483\pi\) | ||
0.757301 | − | 0.653066i | \(-0.226517\pi\) | |||||||
\(258\) | −5.77443e7 | − | 1.35912e8i | −0.209334 | − | 0.492706i | ||||
\(259\) | 2.40224e8 | 0.859146 | ||||||||
\(260\) | −1.25512e8 | − | 1.54003e8i | −0.442874 | − | 0.543405i | ||||
\(261\) | −5.77132e7 | + | 6.94122e6i | −0.200925 | + | 0.0241654i | ||||
\(262\) | 3.12266e8 | − | 1.11132e8i | 1.07268 | − | 0.381753i | ||||
\(263\) | 9.21831e7 | 0.312468 | 0.156234 | − | 0.987720i | \(-0.450065\pi\) | ||||
0.156234 | + | 0.987720i | \(0.450065\pi\) | |||||||
\(264\) | 1.70288e8 | − | 3.22966e8i | 0.569599 | − | 1.08030i | ||||
\(265\) | −1.68800e8 | −0.557200 | ||||||||
\(266\) | −2.20888e8 | + | 7.86111e7i | −0.719591 | + | 0.256093i | ||||
\(267\) | 1.23048e7 | + | 2.05356e8i | 0.0395627 | + | 0.660263i | ||||
\(268\) | 2.36151e8 | − | 1.92463e8i | 0.749408 | − | 0.610766i | ||||
\(269\) | −2.82781e8 | −0.885762 | −0.442881 | − | 0.896580i | \(-0.646044\pi\) | ||||
−0.442881 | + | 0.896580i | \(0.646044\pi\) | |||||||
\(270\) | −2.27799e8 | − | 3.96522e8i | −0.704335 | − | 1.22601i | ||||
\(271\) | − | 5.09934e8i | − | 1.55640i | −0.628015 | − | 0.778201i | \(-0.716133\pi\) | ||
0.628015 | − | 0.778201i | \(-0.283867\pi\) | |||||||
\(272\) | −9.47345e7 | − | 1.95152e7i | −0.285441 | − | 0.0588007i | ||||
\(273\) | 2.55828e8 | − | 1.53291e7i | 0.760990 | − | 0.0455983i | ||||
\(274\) | −4.00980e8 | + | 1.42704e8i | −1.17759 | + | 0.419091i | ||||
\(275\) | 4.20844e8i | 1.22027i | ||||||||
\(276\) | −3.24327e8 | + | 2.98329e8i | −0.928543 | + | 0.854109i | ||||
\(277\) | − | 4.69811e7i | − | 0.132814i | −0.997793 | − | 0.0664071i | \(-0.978846\pi\) | ||
0.997793 | − | 0.0664071i | \(-0.0211536\pi\) | |||||||
\(278\) | 1.77577e8 | + | 4.98969e8i | 0.495712 | + | 1.39289i | ||||
\(279\) | 5.36069e7 | + | 4.45717e8i | 0.147777 | + | 1.22870i | ||||
\(280\) | −4.14060e8 | + | 6.82886e8i | −1.12722 | + | 1.85907i | ||||
\(281\) | − | 4.69927e8i | − | 1.26345i | −0.775192 | − | 0.631726i | \(-0.782347\pi\) | ||
0.775192 | − | 0.631726i | \(-0.217653\pi\) | |||||||
\(282\) | 8.65450e7 | + | 2.03699e8i | 0.229811 | + | 0.540900i | ||||
\(283\) | −3.07291e8 | −0.805929 | −0.402965 | − | 0.915216i | \(-0.632020\pi\) | ||||
−0.402965 | + | 0.915216i | \(0.632020\pi\) | |||||||
\(284\) | −8.15891e7 | + | 6.64950e7i | −0.211358 | + | 0.172256i | ||||
\(285\) | −2.73988e8 | + | 1.64173e7i | −0.701092 | + | 0.0420092i | ||||
\(286\) | 8.03173e7 | + | 2.25682e8i | 0.203015 | + | 0.570448i | ||||
\(287\) | −1.03464e9 | −2.58346 | ||||||||
\(288\) | 3.91927e8 | − | 1.03610e8i | 0.966788 | − | 0.255581i | ||||
\(289\) | 3.75487e8 | 0.915066 | ||||||||
\(290\) | 3.98463e7 | + | 1.11963e8i | 0.0959390 | + | 0.269577i | ||||
\(291\) | 1.70252e8 | − | 1.02014e7i | 0.405010 | − | 0.0242680i | ||||
\(292\) | 1.82848e8 | − | 1.49021e8i | 0.429783 | − | 0.350273i | ||||
\(293\) | 4.83537e8 | 1.12303 | 0.561517 | − | 0.827465i | \(-0.310218\pi\) | ||||
0.561517 | + | 0.827465i | \(0.310218\pi\) | |||||||
\(294\) | −2.32465e8 | − | 5.47147e8i | −0.533508 | − | 1.25571i | ||||
\(295\) | 6.52591e8i | 1.48001i | ||||||||
\(296\) | −1.29259e8 | + | 2.13180e8i | −0.289694 | + | 0.477777i | ||||
\(297\) | 9.84673e7 | + | 5.42524e8i | 0.218094 | + | 1.20163i | ||||
\(298\) | −2.45505e8 | − | 6.89841e8i | −0.537408 | − | 1.51005i | ||||
\(299\) | − | 2.89122e8i | − | 0.625507i | ||||||
\(300\) | −3.43909e8 | + | 3.16341e8i | −0.735393 | + | 0.676443i | ||||
\(301\) | − | 3.89458e8i | − | 0.823148i | ||||||
\(302\) | −1.94268e8 | + | 6.91374e7i | −0.405860 | + | 0.144440i | ||||
\(303\) | 7.03074e8 | − | 4.21280e7i | 1.45195 | − | 0.0870004i | ||||
\(304\) | 4.90935e7 | − | 2.38319e8i | 0.100223 | − | 0.486521i | ||||
\(305\) | 4.04922e8i | 0.817189i | ||||||||
\(306\) | 1.30784e8 | − | 6.50584e7i | 0.260933 | − | 0.129801i | ||||
\(307\) | 4.04574e8 | 0.798020 | 0.399010 | − | 0.916947i | \(-0.369354\pi\) | ||||
0.399010 | + | 0.916947i | \(0.369354\pi\) | |||||||
\(308\) | 7.46425e8 | − | 6.08335e8i | 1.45566 | − | 1.18636i | ||||
\(309\) | 2.91335e7 | + | 4.86210e8i | 0.0561744 | + | 0.937495i | ||||
\(310\) | 8.64691e8 | − | 3.07732e8i | 1.64852 | − | 0.586688i | ||||
\(311\) | 4.29205e8 | 0.809103 | 0.404551 | − | 0.914515i | \(-0.367428\pi\) | ||||
0.404551 | + | 0.914515i | \(0.367428\pi\) | |||||||
\(312\) | −1.24052e8 | + | 2.35276e8i | −0.231240 | + | 0.438567i | ||||
\(313\) | −7.31946e8 | −1.34919 | −0.674597 | − | 0.738187i | \(-0.735682\pi\) | ||||
−0.674597 | + | 0.738187i | \(0.735682\pi\) | |||||||
\(314\) | −2.84819e8 | + | 1.01363e8i | −0.519176 | + | 0.184768i | ||||
\(315\) | −1.44016e8 | − | 1.19743e9i | −0.259612 | − | 2.15856i | ||||
\(316\) | 6.84346e7 | + | 8.39690e7i | 0.122003 | + | 0.149697i | ||||
\(317\) | −1.09363e8 | −0.192824 | −0.0964120 | − | 0.995342i | \(-0.530737\pi\) | ||||
−0.0964120 | + | 0.995342i | \(0.530737\pi\) | |||||||
\(318\) | 8.83684e7 | + | 2.07991e8i | 0.154100 | + | 0.362701i | ||||
\(319\) | − | 1.43294e8i | − | 0.247150i | ||||||
\(320\) | −3.83211e8 | − | 7.34891e8i | −0.653753 | − | 1.25371i | ||||
\(321\) | 2.21255e7 | + | 3.69253e8i | 0.0373358 | + | 0.623098i | ||||
\(322\) | −1.09493e9 | + | 3.89670e8i | −1.82763 | + | 0.650432i | ||||
\(323\) | − | 8.76752e7i | − | 0.144766i | ||||||
\(324\) | −3.69329e8 | + | 4.88272e8i | −0.603262 | + | 0.797543i | ||||
\(325\) | − | 3.06578e8i | − | 0.495393i | ||||||
\(326\) | 1.25352e8 | + | 3.52223e8i | 0.200386 | + | 0.563061i | ||||
\(327\) | −4.99415e7 | − | 8.33474e8i | −0.0789849 | − | 1.31818i | ||||
\(328\) | 5.56715e8 | − | 9.18159e8i | 0.871113 | − | 1.43668i | ||||
\(329\) | 5.83705e8i | 0.903665i | ||||||||
\(330\) | 1.03753e9 | − | 4.40811e8i | 1.58928 | − | 0.675233i | ||||
\(331\) | −4.72046e8 | −0.715461 | −0.357731 | − | 0.933825i | \(-0.616449\pi\) | ||||
−0.357731 | + | 0.933825i | \(0.616449\pi\) | |||||||
\(332\) | −1.05781e7 | − | 1.29793e7i | −0.0158644 | − | 0.0194656i | ||||
\(333\) | −4.49583e7 | − | 3.73808e8i | −0.0667198 | − | 0.554745i | ||||
\(334\) | 3.06662e8 | + | 8.61683e8i | 0.450347 | + | 1.26542i | ||||
\(335\) | 9.40606e8 | 1.36694 | ||||||||
\(336\) | 1.05820e9 | + | 1.52696e8i | 1.52188 | + | 0.219605i | ||||
\(337\) | 6.25292e8 | 0.889975 | 0.444988 | − | 0.895537i | \(-0.353208\pi\) | ||||
0.444988 | + | 0.895537i | \(0.353208\pi\) | |||||||
\(338\) | 1.79516e8 | + | 5.04420e8i | 0.252869 | + | 0.710532i | ||||
\(339\) | −5.22607e7 | − | 8.72179e8i | −0.0728578 | − | 1.21592i | ||||
\(340\) | −1.88667e8 | − | 2.31494e8i | −0.260327 | − | 0.319421i | ||||
\(341\) | −1.10666e9 | −1.51138 | ||||||||
\(342\) | 1.63665e8 | + | 3.29007e8i | 0.221240 | + | 0.444747i | ||||
\(343\) | − | 4.18692e8i | − | 0.560229i | ||||||
\(344\) | 3.45613e8 | + | 2.09559e8i | 0.457758 | + | 0.277556i | ||||
\(345\) | −1.35814e9 | + | 8.13794e7i | −1.78065 | + | 0.106696i | ||||
\(346\) | 2.25971e8 | + | 6.34952e8i | 0.293283 | + | 0.824089i | ||||
\(347\) | 1.63000e8i | 0.209428i | 0.994502 | + | 0.104714i | \(0.0333927\pi\) | ||||
−0.994502 | + | 0.104714i | \(0.966607\pi\) | |||||||
\(348\) | 1.17098e8 | − | 1.07712e8i | 0.148944 | − | 0.137005i | ||||
\(349\) | 5.70900e8i | 0.718904i | 0.933164 | + | 0.359452i | \(0.117036\pi\) | ||||
−0.933164 | + | 0.359452i | \(0.882964\pi\) | |||||||
\(350\) | −1.16103e9 | + | 4.13197e8i | −1.44746 | + | 0.515133i | ||||
\(351\) | −7.17320e7 | − | 3.95220e8i | −0.0885397 | − | 0.487825i | ||||
\(352\) | 1.38215e8 | + | 9.89724e8i | 0.168910 | + | 1.20953i | ||||
\(353\) | − | 6.12270e8i | − | 0.740852i | −0.928862 | − | 0.370426i | \(-0.879212\pi\) | ||
0.928862 | − | 0.370426i | \(-0.120788\pi\) | |||||||
\(354\) | 8.04106e8 | − | 3.41638e8i | 0.963389 | − | 0.409312i | ||||
\(355\) | −3.24975e8 | −0.385523 | ||||||||
\(356\) | −3.55731e8 | − | 4.36480e8i | −0.417875 | − | 0.512731i | ||||
\(357\) | 3.84554e8 | − | 2.30423e7i | 0.447320 | − | 0.0268033i | ||||
\(358\) | 5.64534e8 | − | 2.00910e8i | 0.650278 | − | 0.231426i | ||||
\(359\) | −8.45852e8 | −0.964859 | −0.482429 | − | 0.875935i | \(-0.660246\pi\) | ||||
−0.482429 | + | 0.875935i | \(0.660246\pi\) | |||||||
\(360\) | 1.14012e9 | + | 5.16507e8i | 1.28793 | + | 0.583469i | ||||
\(361\) | −6.73311e8 | −0.753253 | ||||||||
\(362\) | −1.26984e9 | + | 4.51920e8i | −1.40692 | + | 0.500705i | ||||
\(363\) | −4.47098e8 | + | 2.67899e7i | −0.490602 | + | 0.0293967i | ||||
\(364\) | −5.43759e8 | + | 4.43163e8i | −0.590951 | + | 0.481624i | ||||
\(365\) | 7.28295e8 | 0.783939 | ||||||||
\(366\) | 4.98935e8 | − | 2.11981e8i | 0.531937 | − | 0.226002i | ||||
\(367\) | 1.51065e9i | 1.59526i | 0.603144 | + | 0.797632i | \(0.293914\pi\) | ||||
−0.603144 | + | 0.797632i | \(0.706086\pi\) | |||||||
\(368\) | 2.43354e8 | − | 1.18133e9i | 0.254548 | − | 1.23568i | ||||
\(369\) | 1.93634e8 | + | 1.60998e9i | 0.200627 | + | 1.66812i | ||||
\(370\) | −7.25186e8 | + | 2.58084e8i | −0.744292 | + | 0.264884i | ||||
\(371\) | 5.96003e8i | 0.605954i | ||||||||
\(372\) | −8.31854e8 | − | 9.04349e8i | −0.837813 | − | 0.910827i | ||||
\(373\) | − | 7.49026e8i | − | 0.747336i | −0.927563 | − | 0.373668i | \(-0.878100\pi\) | ||
0.927563 | − | 0.373668i | \(-0.121900\pi\) | |||||||
\(374\) | 1.20731e8 | + | 3.39239e8i | 0.119335 | + | 0.335317i | ||||
\(375\) | 1.16937e6 | − | 70068.0i | 0.00114509 | − | 6.86136e-5i | ||||
\(376\) | −5.17992e8 | − | 3.14078e8i | −0.502534 | − | 0.304706i | ||||
\(377\) | 1.04388e8i | 0.100335i | ||||||||
\(378\) | −1.40005e9 | + | 8.04321e8i | −1.33328 | + | 0.765963i | ||||
\(379\) | 1.35776e9 | 1.28110 | 0.640552 | − | 0.767915i | \(-0.278706\pi\) | ||||
0.640552 | + | 0.767915i | \(0.278706\pi\) | |||||||
\(380\) | 5.82358e8 | − | 4.74621e8i | 0.544437 | − | 0.443715i | ||||
\(381\) | −7.79497e7 | − | 1.30090e9i | −0.0722066 | − | 1.20506i | ||||
\(382\) | −6.85204e8 | − | 1.92534e9i | −0.628924 | − | 1.76720i | ||||
\(383\) | −8.99150e8 | −0.817780 | −0.408890 | − | 0.912584i | \(-0.634084\pi\) | ||||
−0.408890 | + | 0.912584i | \(0.634084\pi\) | |||||||
\(384\) | −7.04899e8 | + | 8.56906e8i | −0.635284 | + | 0.772279i | ||||
\(385\) | 2.97306e9 | 2.65516 | ||||||||
\(386\) | 3.39408e8 | + | 9.53694e8i | 0.300376 | + | 0.844022i | ||||
\(387\) | −6.06028e8 | + | 7.28876e7i | −0.531501 | + | 0.0639242i | ||||
\(388\) | −3.61867e8 | + | 2.94921e8i | −0.314513 | + | 0.256327i | ||||
\(389\) | −4.99376e8 | −0.430134 | −0.215067 | − | 0.976599i | \(-0.568997\pi\) | ||||
−0.215067 | + | 0.976599i | \(0.568997\pi\) | |||||||
\(390\) | −7.55823e8 | + | 3.21124e8i | −0.645199 | + | 0.274124i | ||||
\(391\) | − | 4.34600e8i | − | 0.367681i | ||||||
\(392\) | 1.39135e9 | + | 8.43632e8i | 1.16664 | + | 0.707378i | ||||
\(393\) | −8.19466e7 | − | 1.36761e9i | −0.0681016 | − | 1.13655i | ||||
\(394\) | −5.62340e8 | − | 1.58011e9i | −0.463193 | − | 1.30152i | ||||
\(395\) | 3.34454e8i | 0.273053i | ||||||||
\(396\) | −1.08631e9 | − | 1.04765e9i | −0.879066 | − | 0.847776i | ||||
\(397\) | 2.45172e9i | 1.96655i | 0.182128 | + | 0.983275i | \(0.441702\pi\) | ||||
−0.182128 | + | 0.983275i | \(0.558298\pi\) | |||||||
\(398\) | 1.26651e9 | − | 4.50733e8i | 1.00697 | − | 0.358368i | ||||
\(399\) | 5.79666e7 | + | 9.67405e8i | 0.0456849 | + | 0.762436i | ||||
\(400\) | 2.58047e8 | − | 1.25266e9i | 0.201599 | − | 0.978640i | ||||
\(401\) | − | 1.46965e9i | − | 1.13818i | −0.822276 | − | 0.569088i | \(-0.807296\pi\) | ||
0.822276 | − | 0.569088i | \(-0.192704\pi\) | |||||||
\(402\) | −4.92417e8 | − | 1.15899e9i | −0.378043 | − | 0.889793i | ||||
\(403\) | 8.06183e8 | 0.613572 | ||||||||
\(404\) | −1.49437e9 | + | 1.21791e9i | −1.12752 | + | 0.918928i | ||||
\(405\) | −1.83635e9 | + | 4.48202e8i | −1.37360 | + | 0.335259i | ||||
\(406\) | 3.95323e8 | − | 1.40690e8i | 0.293164 | − | 0.104333i | ||||
\(407\) | 9.28114e8 | 0.682372 | ||||||||
\(408\) | −1.86472e8 | + | 3.53660e8i | −0.135926 | + | 0.257795i | ||||
\(409\) | −2.67821e9 | −1.93559 | −0.967794 | − | 0.251742i | \(-0.918997\pi\) | ||||
−0.967794 | + | 0.251742i | \(0.918997\pi\) | |||||||
\(410\) | 3.12335e9 | − | 1.11156e9i | 2.23809 | − | 0.796507i | ||||
\(411\) | 1.05227e8 | + | 1.75614e9i | 0.0747622 | + | 1.24771i | ||||
\(412\) | −8.42245e8 | − | 1.03343e9i | −0.593333 | − | 0.728017i | ||||
\(413\) | 2.30419e9 | 1.60950 | ||||||||
\(414\) | 8.11275e8 | + | 1.63087e9i | 0.561910 | + | 1.12958i | ||||
\(415\) | − | 5.16973e7i | − | 0.0355058i | ||||||
\(416\) | −1.00688e8 | − | 7.20999e8i | −0.0685724 | − | 0.491030i | ||||
\(417\) | 2.18530e9 | − | 1.30942e8i | 1.47582 | − | 0.0884308i | ||||
\(418\) | −8.53408e8 | + | 3.03717e8i | −0.571531 | + | 0.203400i | ||||
\(419\) | − | 1.25323e9i | − | 0.832301i | −0.909296 | − | 0.416151i | \(-0.863379\pi\) | ||
0.909296 | − | 0.416151i | \(-0.136621\pi\) | |||||||
\(420\) | 2.23480e9 | + | 2.42956e9i | 1.47186 | + | 1.60013i | ||||
\(421\) | 1.03003e9i | 0.672761i | 0.941726 | + | 0.336380i | \(0.109203\pi\) | ||||
−0.941726 | + | 0.336380i | \(0.890797\pi\) | |||||||
\(422\) | −4.33387e8 | − | 1.21776e9i | −0.280726 | − | 0.788805i | ||||
\(423\) | 9.08291e8 | − | 1.09241e8i | 0.583491 | − | 0.0701770i | ||||
\(424\) | −5.28905e8 | − | 3.20695e8i | −0.336975 | − | 0.204321i | ||||
\(425\) | − | 4.60840e8i | − | 0.291198i | ||||||
\(426\) | 1.70128e8 | + | 4.00426e8i | 0.106621 | + | 0.250951i | ||||
\(427\) | 1.42971e9 | 0.888691 | ||||||||
\(428\) | −6.39644e8 | − | 7.84841e8i | −0.394353 | − | 0.483870i | ||||
\(429\) | 9.88402e8 | − | 5.92247e7i | 0.604412 | − | 0.0362161i | ||||
\(430\) | 4.18414e8 | + | 1.17569e9i | 0.253785 | + | 0.713106i | ||||
\(431\) | 9.25332e8 | 0.556708 | 0.278354 | − | 0.960479i | \(-0.410211\pi\) | ||||
0.278354 | + | 0.960479i | \(0.410211\pi\) | |||||||
\(432\) | 3.95642e7 | − | 1.67522e9i | 0.0236107 | − | 0.999721i | ||||
\(433\) | 9.64856e8 | 0.571156 | 0.285578 | − | 0.958355i | \(-0.407814\pi\) | ||||
0.285578 | + | 0.958355i | \(0.407814\pi\) | |||||||
\(434\) | −1.08655e9 | − | 3.05307e9i | −0.638022 | − | 1.79276i | ||||
\(435\) | 4.90357e8 | − | 2.93820e7i | 0.285628 | − | 0.0171147i | ||||
\(436\) | 1.44380e9 | + | 1.77154e9i | 0.834265 | + | 1.02364i | ||||
\(437\) | 1.09330e9 | 0.626695 | ||||||||
\(438\) | −3.81270e8 | − | 8.97387e8i | −0.216807 | − | 0.510294i | ||||
\(439\) | − | 1.03378e9i | − | 0.583181i | −0.956543 | − | 0.291590i | \(-0.905816\pi\) | ||
0.956543 | − | 0.291590i | \(-0.0941844\pi\) | |||||||
\(440\) | −1.59974e9 | + | 2.63836e9i | −0.895291 | + | 1.47655i | ||||
\(441\) | −2.43972e9 | + | 2.93428e8i | −1.35458 | + | 0.162917i | ||||
\(442\) | −8.79505e7 | − | 2.47130e8i | −0.0484463 | − | 0.136128i | ||||
\(443\) | 8.76781e8i | 0.479157i | 0.970877 | + | 0.239579i | \(0.0770093\pi\) | ||||
−0.970877 | + | 0.239579i | \(0.922991\pi\) | |||||||
\(444\) | 6.97647e8 | + | 7.58446e8i | 0.378264 | + | 0.411229i | ||||
\(445\) | − | 1.73853e9i | − | 0.935238i | ||||||
\(446\) | −5.37633e8 | + | 1.91337e8i | −0.286955 | + | 0.102124i | ||||
\(447\) | −3.02124e9 | + | 1.81032e8i | −1.59996 | + | 0.0958691i | ||||
\(448\) | −2.59477e9 | + | 1.35305e9i | −1.36341 | + | 0.710954i | ||||
\(449\) | 1.54847e9i | 0.807310i | 0.914911 | + | 0.403655i | \(0.132260\pi\) | ||||
−0.914911 | + | 0.403655i | \(0.867740\pi\) | |||||||
\(450\) | 8.60257e8 | + | 1.72933e9i | 0.445025 | + | 0.894612i | ||||
\(451\) | −3.99736e9 | −2.05190 | ||||||||
\(452\) | 1.51085e9 | + | 1.85380e9i | 0.769549 | + | 0.944233i | ||||
\(453\) | 5.09808e7 | + | 8.50819e8i | 0.0257669 | + | 0.430025i | ||||
\(454\) | 1.31092e7 | − | 4.66538e6i | 0.00657475 | − | 0.00233987i | ||||
\(455\) | −2.16583e9 | −1.07791 | ||||||||
\(456\) | −8.89686e8 | − | 4.69098e8i | −0.439400 | − | 0.231679i | ||||
\(457\) | 9.48722e8 | 0.464978 | 0.232489 | − | 0.972599i | \(-0.425313\pi\) | ||||
0.232489 | + | 0.972599i | \(0.425313\pi\) | |||||||
\(458\) | 6.73230e8 | − | 2.39594e8i | 0.327442 | − | 0.116532i | ||||
\(459\) | −1.07826e8 | − | 5.94084e8i | −0.0520448 | − | 0.286750i | ||||
\(460\) | 2.88671e9 | − | 2.35267e9i | 1.38277 | − | 1.12696i | ||||
\(461\) | −2.35261e9 | −1.11840 | −0.559199 | − | 0.829033i | \(-0.688891\pi\) | ||||
−0.559199 | + | 0.829033i | \(0.688891\pi\) | |||||||
\(462\) | −1.55643e9 | − | 3.66333e9i | −0.734314 | − | 1.72834i | ||||
\(463\) | − | 8.53974e8i | − | 0.399863i | −0.979810 | − | 0.199931i | \(-0.935928\pi\) | ||
0.979810 | − | 0.199931i | \(-0.0640719\pi\) | |||||||
\(464\) | −8.78628e7 | + | 4.26520e8i | −0.0408312 | + | 0.198211i | ||||
\(465\) | −2.26917e8 | − | 3.78702e9i | −0.104660 | − | 1.74668i | ||||
\(466\) | 2.54739e9 | − | 9.06582e8i | 1.16612 | − | 0.415008i | ||||
\(467\) | 1.92473e9i | 0.874504i | 0.899339 | + | 0.437252i | \(0.144048\pi\) | ||||
−0.899339 | + | 0.437252i | \(0.855952\pi\) | |||||||
\(468\) | 7.91362e8 | + | 7.63194e8i | 0.356874 | + | 0.344171i | ||||
\(469\) | − | 3.32112e9i | − | 1.48655i | ||||||
\(470\) | −6.27102e8 | − | 1.76208e9i | −0.278610 | − | 0.782859i | ||||
\(471\) | 7.47437e7 | + | 1.24740e9i | 0.0329611 | + | 0.550088i | ||||
\(472\) | −1.23983e9 | + | 2.04478e9i | −0.542707 | + | 0.895056i | ||||
\(473\) | − | 1.50469e9i | − | 0.653780i | ||||||
\(474\) | 4.12106e8 | − | 1.75090e8i | 0.177740 | − | 0.0755158i | ||||
\(475\) | 1.15931e9 | 0.496334 | ||||||||
\(476\) | −8.17364e8 | + | 6.66150e8i | −0.347369 | + | 0.283105i | ||||
\(477\) | 9.27428e8 | − | 1.11543e8i | 0.391260 | − | 0.0470573i | ||||
\(478\) | 4.72358e8 | + | 1.32727e9i | 0.197822 | + | 0.555855i | ||||
\(479\) | 2.65564e9 | 1.10406 | 0.552032 | − | 0.833823i | \(-0.313853\pi\) | ||||
0.552032 | + | 0.833823i | \(0.313853\pi\) | |||||||
\(480\) | −3.35853e9 | + | 6.75917e8i | −1.38613 | + | 0.278965i | ||||
\(481\) | −6.76117e8 | −0.277022 | ||||||||
\(482\) | 4.28528e8 | + | 1.20411e9i | 0.174307 | + | 0.489781i | ||||
\(483\) | 2.87337e8 | + | 4.79537e9i | 0.116031 | + | 1.93645i | ||||
\(484\) | 9.50300e8 | − | 7.74493e8i | 0.380980 | − | 0.310498i | ||||
\(485\) | −1.44134e9 | −0.573681 | ||||||||
\(486\) | 1.51361e9 | + | 2.02806e9i | 0.598118 | + | 0.801408i | ||||
\(487\) | 3.63297e9i | 1.42531i | 0.701514 | + | 0.712656i | \(0.252508\pi\) | ||||
−0.701514 | + | 0.712656i | \(0.747492\pi\) | |||||||
\(488\) | −7.69295e8 | + | 1.26876e9i | −0.299656 | + | 0.494207i | ||||
\(489\) | 1.54260e9 | − | 9.24322e7i | 0.596586 | − | 0.0357472i | ||||
\(490\) | 1.68443e9 | + | 4.73305e9i | 0.646795 | + | 1.81742i | ||||
\(491\) | − | 5.81674e8i | − | 0.221766i | −0.993833 | − | 0.110883i | \(-0.964632\pi\) | ||
0.993833 | − | 0.110883i | \(-0.0353678\pi\) | |||||||
\(492\) | −3.00474e9 | − | 3.26660e9i | −1.13744 | − | 1.23657i | ||||
\(493\) | 1.56912e8i | 0.0589784i | ||||||||
\(494\) | 6.21695e8 | − | 2.21253e8i | 0.232024 | − | 0.0825743i | ||||
\(495\) | −5.56412e8 | − | 4.62632e9i | −0.206195 | − | 1.71442i | ||||
\(496\) | 3.29401e9 | + | 6.78563e8i | 1.21210 | + | 0.249692i | ||||
\(497\) | 1.14743e9i | 0.419256i | ||||||||
\(498\) | −6.37001e7 | + | 2.70641e7i | −0.0231120 | + | 0.00981952i | ||||
\(499\) | −4.26487e9 | −1.53658 | −0.768288 | − | 0.640104i | \(-0.778891\pi\) | ||||
−0.768288 | + | 0.640104i | \(0.778891\pi\) | |||||||
\(500\) | −2.48547e6 | + | 2.02565e6i | −0.000889229 | + | 0.000724720i | ||||
\(501\) | 3.77385e9 | − | 2.26128e8i | 1.34076 | − | 0.0803381i | ||||
\(502\) | −4.17337e9 | + | 1.48525e9i | −1.47239 | + | 0.524006i | ||||
\(503\) | −1.91118e9 | −0.669596 | −0.334798 | − | 0.942290i | \(-0.608668\pi\) | ||||
−0.334798 | + | 0.942290i | \(0.608668\pi\) | |||||||
\(504\) | 1.82370e9 | − | 4.02556e9i | 0.634521 | − | 1.40062i | ||||
\(505\) | −5.95219e9 | −2.05663 | ||||||||
\(506\) | −4.23029e9 | + | 1.50551e9i | −1.45159 | + | 0.516601i | ||||
\(507\) | 2.20917e9 | − | 1.32373e8i | 0.752837 | − | 0.0451097i | ||||
\(508\) | 2.25351e9 | + | 2.76505e9i | 0.762671 | + | 0.935794i | ||||
\(509\) | −2.87618e9 | −0.966726 | −0.483363 | − | 0.875420i | \(-0.660585\pi\) | ||||
−0.483363 | + | 0.875420i | \(0.660585\pi\) | |||||||
\(510\) | −1.13613e9 | + | 4.82705e8i | −0.379257 | + | 0.161134i | ||||
\(511\) | − | 2.57148e9i | − | 0.852532i | ||||||
\(512\) | 1.95461e8 | − | 3.03070e9i | 0.0643600 | − | 0.997927i | ||||
\(513\) | 1.49451e9 | − | 2.71252e8i | 0.488752 | − | 0.0887078i | ||||
\(514\) | 3.78845e9 | − | 1.34826e9i | 1.23053 | − | 0.437929i | ||||
\(515\) | − | 4.11623e9i | − | 1.32793i | ||||||
\(516\) | 1.22961e9 | − | 1.13105e9i | 0.393999 | − | 0.362415i | ||||
\(517\) | 2.25516e9i | 0.717731i | ||||||||
\(518\) | 9.11251e8 | + | 2.56051e9i | 0.288061 | + | 0.809416i | ||||
\(519\) | 2.78085e9 | − | 1.66627e8i | 0.873156 | − | 0.0523192i | ||||
\(520\) | 1.16538e9 | − | 1.92200e9i | 0.363461 | − | 0.599435i | ||||
\(521\) | 3.00108e9i | 0.929706i | 0.885388 | + | 0.464853i | \(0.153893\pi\) | ||||
−0.885388 | + | 0.464853i | \(0.846107\pi\) | |||||||
\(522\) | −2.92911e8 | − | 5.88824e8i | −0.0901340 | − | 0.181192i | ||||
\(523\) | −4.84455e8 | −0.148080 | −0.0740402 | − | 0.997255i | \(-0.523589\pi\) | ||||
−0.0740402 | + | 0.997255i | \(0.523589\pi\) | |||||||
\(524\) | 2.36906e9 | + | 2.90683e9i | 0.719312 | + | 0.882593i | ||||
\(525\) | 3.04685e8 | + | 5.08490e9i | 0.0918954 | + | 1.53364i | ||||
\(526\) | 3.49682e8 | + | 9.82564e8i | 0.104767 | + | 0.294382i | ||||
\(527\) | 1.21183e9 | 0.360666 | ||||||||
\(528\) | 4.08839e9 | + | 5.89948e8i | 1.20874 | + | 0.174420i | ||||
\(529\) | 2.01461e9 | 0.591694 | ||||||||
\(530\) | −6.40314e8 | − | 1.79921e9i | −0.186822 | − | 0.524947i | ||||
\(531\) | −4.31232e8 | − | 3.58550e9i | −0.124991 | − | 1.03925i | ||||
\(532\) | −1.67580e9 | − | 2.05621e9i | −0.482539 | − | 0.592074i | ||||
\(533\) | 2.91202e9 | 0.833007 | ||||||||
\(534\) | −2.14217e9 | + | 9.10138e8i | −0.608780 | + | 0.258650i | ||||
\(535\) | − | 3.12607e9i | − | 0.882594i | ||||||
\(536\) | 2.94723e9 | + | 1.78702e9i | 0.826680 | + | 0.501247i | ||||
\(537\) | −1.48148e8 | − | 2.47244e9i | −0.0412844 | − | 0.688996i | ||||
\(538\) | −1.07268e9 | − | 3.01411e9i | −0.296984 | − | 0.834490i | ||||
\(539\) | − | 6.05750e9i | − | 1.66622i | ||||||
\(540\) | 3.36234e9 | − | 3.93222e9i | 0.918889 | − | 1.07463i | ||||
\(541\) | − | 7.15006e9i | − | 1.94142i | −0.240259 | − | 0.970709i | \(-0.577232\pi\) | ||
0.240259 | − | 0.970709i | \(-0.422768\pi\) | |||||||
\(542\) | 5.43530e9 | − | 1.93435e9i | 1.46631 | − | 0.521841i | ||||
\(543\) | 3.33239e8 | + | 5.56143e9i | 0.0893215 | + | 1.49069i | ||||
\(544\) | −1.51351e8 | − | 1.08379e9i | −0.0403077 | − | 0.288634i | ||||
\(545\) | 7.05615e9i | 1.86715i | ||||||||
\(546\) | 1.13383e9 | + | 2.66868e9i | 0.298109 | + | 0.701653i | ||||
\(547\) | 6.19208e9 | 1.61764 | 0.808818 | − | 0.588060i | \(-0.200108\pi\) | ||||
0.808818 | + | 0.588060i | \(0.200108\pi\) | |||||||
\(548\) | −3.04211e9 | − | 3.73265e9i | −0.789664 | − | 0.968915i | ||||
\(549\) | −2.67572e8 | − | 2.22474e9i | −0.0690142 | − | 0.573822i | ||||
\(550\) | −4.48570e9 | + | 1.59640e9i | −1.14964 | + | 0.409141i | ||||
\(551\) | −3.94738e8 | −0.100526 | ||||||||
\(552\) | −4.41012e9 | − | 2.32529e9i | −1.11600 | − | 0.588424i | ||||
\(553\) | 1.18090e9 | 0.296945 | ||||||||
\(554\) | 5.00764e8 | − | 1.78215e8i | 0.125126 | − | 0.0445308i | ||||
\(555\) | 1.90307e8 | + | 3.17604e9i | 0.0472530 | + | 0.788607i | ||||
\(556\) | −4.64482e9 | + | 3.78552e9i | −1.14606 | + | 0.934036i | ||||
\(557\) | −3.28030e9 | −0.804304 | −0.402152 | − | 0.915573i | \(-0.631738\pi\) | ||||
−0.402152 | + | 0.915573i | \(0.631738\pi\) | |||||||
\(558\) | −4.54748e9 | + | 2.26214e9i | −1.10803 | + | 0.551189i | ||||
\(559\) | 1.09614e9i | 0.265415i | ||||||||
\(560\) | −8.84944e9 | − | 1.82298e9i | −2.12940 | − | 0.438655i | ||||
\(561\) | 1.48574e9 | − | 8.90249e7i | 0.355281 | − | 0.0212883i | ||||
\(562\) | 5.00887e9 | − | 1.78259e9i | 1.19032 | − | 0.423619i | ||||
\(563\) | − | 2.76254e9i | − | 0.652422i | −0.945297 | − | 0.326211i | \(-0.894228\pi\) | ||
0.945297 | − | 0.326211i | \(-0.105772\pi\) | |||||||
\(564\) | −1.84290e9 | + | 1.69517e9i | −0.432538 | + | 0.397865i | ||||
\(565\) | 7.38383e9i | 1.72231i | ||||||||
\(566\) | −1.16566e9 | − | 3.27536e9i | −0.270217 | − | 0.759279i | ||||
\(567\) | 1.58252e9 | + | 6.48382e9i | 0.364594 | + | 1.49379i | ||||
\(568\) | −1.01825e9 | − | 6.17406e8i | −0.233151 | − | 0.141368i | ||||
\(569\) | 7.17944e9i | 1.63379i | 0.576783 | + | 0.816897i | \(0.304308\pi\) | ||||
−0.576783 | + | 0.816897i | \(0.695692\pi\) | |||||||
\(570\) | −1.21432e9 | − | 2.85812e9i | −0.274644 | − | 0.646425i | ||||
\(571\) | −4.49621e8 | −0.101069 | −0.0505347 | − | 0.998722i | \(-0.516093\pi\) | ||||
−0.0505347 | + | 0.998722i | \(0.516093\pi\) | |||||||
\(572\) | −2.10083e9 | + | 1.71218e9i | −0.469360 | + | 0.382527i | ||||
\(573\) | −8.43227e9 | + | 5.05259e8i | −1.87242 | + | 0.112195i | ||||
\(574\) | −3.92473e9 | − | 1.10280e10i | −0.866200 | − | 2.43392i | ||||
\(575\) | 5.74665e9 | 1.26060 | ||||||||
\(576\) | 2.59107e9 | + | 3.78445e9i | 0.564938 | + | 0.825133i | ||||
\(577\) | 5.82230e9 | 1.26177 | 0.630883 | − | 0.775878i | \(-0.282693\pi\) | ||||
0.630883 | + | 0.775878i | \(0.282693\pi\) | |||||||
\(578\) | 1.42435e9 | + | 4.00225e9i | 0.306810 | + | 0.862098i | ||||
\(579\) | 4.17682e9 | − | 2.50274e8i | 0.894275 | − | 0.0535846i | ||||
\(580\) | −1.04225e9 | + | 8.49430e8i | −0.221806 | + | 0.180771i | ||||
\(581\) | −1.82534e8 | −0.0386125 | ||||||||
\(582\) | 7.54557e8 | + | 1.77598e9i | 0.158658 | + | 0.373430i | ||||
\(583\) | 2.30268e9i | 0.481275i | ||||||||
\(584\) | 2.28199e9 | + | 1.38366e9i | 0.474098 | + | 0.287464i | ||||
\(585\) | 4.05338e8 | + | 3.37020e9i | 0.0837089 | + | 0.696002i | ||||
\(586\) | 1.83422e9 | + | 5.15393e9i | 0.376538 | + | 1.05803i | ||||
\(587\) | − | 2.29761e9i | − | 0.468859i | −0.972133 | − | 0.234430i | \(-0.924678\pi\) | ||
0.972133 | − | 0.234430i | \(-0.0753222\pi\) | |||||||
\(588\) | 4.95013e9 | − | 4.55331e9i | 1.00414 | − | 0.923649i | ||||
\(589\) | 3.04855e9i | 0.614738i | ||||||||
\(590\) | −6.95585e9 | + | 2.47550e9i | −1.39434 | + | 0.496227i | ||||
\(591\) | −6.92028e9 | + | 4.14660e8i | −1.37901 | + | 0.0826297i | ||||
\(592\) | −2.76257e9 | − | 5.69087e8i | −0.547252 | − | 0.112733i | ||||
\(593\) | 8.62589e8i | 0.169868i | 0.996387 | + | 0.0849341i | \(0.0270680\pi\) | ||||
−0.996387 | + | 0.0849341i | \(0.972932\pi\) | |||||||
\(594\) | −5.40915e9 | + | 3.10752e9i | −1.05895 | + | 0.608361i | ||||
\(595\) | −3.25561e9 | −0.633612 | ||||||||
\(596\) | 6.42161e9 | − | 5.23360e9i | 1.24246 | − | 1.01260i | ||||
\(597\) | −3.32363e8 | − | 5.54682e9i | −0.0639298 | − | 1.06693i | ||||
\(598\) | 3.08170e9 | − | 1.09674e9i | 0.589300 | − | 0.209724i | ||||
\(599\) | −4.12221e8 | −0.0783675 | −0.0391838 | − | 0.999232i | \(-0.512476\pi\) | ||||
−0.0391838 | + | 0.999232i | \(0.512476\pi\) | |||||||
\(600\) | −4.67639e9 | − | 2.46568e9i | −0.883855 | − | 0.466024i | ||||
\(601\) | −5.17314e9 | −0.972060 | −0.486030 | − | 0.873942i | \(-0.661555\pi\) | ||||
−0.486030 | + | 0.873942i | \(0.661555\pi\) | |||||||
\(602\) | 4.15116e9 | − | 1.47735e9i | 0.775501 | − | 0.275991i | ||||
\(603\) | −5.16792e9 | + | 6.21552e8i | −0.959855 | + | 0.115443i | ||||
\(604\) | −1.47385e9 | − | 1.80840e9i | −0.272159 | − | 0.333938i | ||||
\(605\) | 3.78511e9 | 0.694920 | ||||||||
\(606\) | 3.11603e9 | + | 7.33414e9i | 0.568785 | + | 1.33874i | ||||
\(607\) | − | 1.01542e9i | − | 0.184283i | −0.995746 | − | 0.0921415i | \(-0.970629\pi\) | ||
0.995746 | − | 0.0921415i | \(-0.0293712\pi\) | |||||||
\(608\) | 2.72643e9 | − | 3.80746e8i | 0.491963 | − | 0.0687026i | ||||
\(609\) | −1.03743e8 | − | 1.73137e9i | −0.0186122 | − | 0.310619i | ||||
\(610\) | −4.31600e9 | + | 1.53601e9i | −0.769887 | + | 0.273993i | ||||
\(611\) | − | 1.64285e9i | − | 0.291377i | ||||||
\(612\) | 1.18955e9 | + | 1.14721e9i | 0.209775 | + | 0.202308i | ||||
\(613\) | − | 1.48233e9i | − | 0.259917i | −0.991519 | − | 0.129958i | \(-0.958516\pi\) | ||
0.991519 | − | 0.129958i | \(-0.0414843\pi\) | |||||||
\(614\) | 1.53469e9 | + | 4.31228e9i | 0.267566 | + | 0.751827i | ||||
\(615\) | −8.19647e8 | − | 1.36791e10i | −0.142090 | − | 2.37135i | ||||
\(616\) | 9.31558e9 | + | 5.64839e9i | 1.60575 | + | 0.973626i | ||||
\(617\) | − | 1.09684e10i | − | 1.87995i | −0.341247 | − | 0.939974i | \(-0.610849\pi\) | ||
0.341247 | − | 0.939974i | \(-0.389151\pi\) | |||||||
\(618\) | −5.07191e9 | + | 2.15489e9i | −0.864395 | + | 0.367253i | ||||
\(619\) | 4.52266e9 | 0.766438 | 0.383219 | − | 0.923658i | \(-0.374816\pi\) | ||||
0.383219 | + | 0.923658i | \(0.374816\pi\) | |||||||
\(620\) | 6.56013e9 | + | 8.04925e9i | 1.10546 | + | 1.35639i | ||||
\(621\) | 7.40820e9 | − | 1.34458e9i | 1.24134 | − | 0.225302i | ||||
\(622\) | 1.62812e9 | + | 4.57483e9i | 0.271282 | + | 0.762269i | ||||
\(623\) | −6.13845e9 | −1.01707 | ||||||||
\(624\) | −2.97833e9 | − | 4.29768e8i | −0.490713 | − | 0.0708090i | ||||
\(625\) | −6.10846e9 | −1.00081 | ||||||||
\(626\) | −2.77652e9 | − | 7.80169e9i | −0.452367 | − | 1.27110i | ||||
\(627\) | 2.23956e8 | + | 3.73760e9i | 0.0362849 | + | 0.605560i | ||||
\(628\) | −2.16083e9 | − | 2.65133e9i | −0.348146 | − | 0.427174i | ||||
\(629\) | −1.01632e9 | −0.162837 | ||||||||
\(630\) | 1.22169e10 | − | 6.07731e9i | 1.94657 | − | 0.968321i | ||||
\(631\) | − | 5.92517e9i | − | 0.938854i | −0.882971 | − | 0.469427i | \(-0.844461\pi\) | ||
0.882971 | − | 0.469427i | \(-0.155539\pi\) | |||||||
\(632\) | −6.35416e8 | + | 1.04796e9i | −0.100126 | + | 0.165133i | ||||
\(633\) | −5.33335e9 | + | 3.19572e8i | −0.835771 | + | 0.0500791i | ||||
\(634\) | −4.14849e8 | − | 1.16568e9i | −0.0646514 | − | 0.181663i | ||||
\(635\) | 1.10134e10i | 1.70692i | ||||||||
\(636\) | −1.88173e9 | + | 1.73088e9i | −0.290039 | + | 0.266789i | ||||
\(637\) | 4.41279e9i | 0.676434i | ||||||||
\(638\) | 1.52735e9 | − | 5.43563e8i | 0.232844 | − | 0.0828662i | ||||
\(639\) | 1.78549e9 | − | 2.14743e8i | 0.270710 | − | 0.0325586i | ||||
\(640\) | 6.37943e9 | − | 6.87227e9i | 0.961948 | − | 1.03626i | ||||
\(641\) | − | 8.25130e9i | − | 1.23743i | −0.785617 | − | 0.618713i | \(-0.787654\pi\) | ||
0.785617 | − | 0.618713i | \(-0.212346\pi\) | |||||||
\(642\) | −3.85187e9 | + | 1.63653e9i | −0.574512 | + | 0.244091i | ||||
\(643\) | −3.43913e8 | −0.0510164 | −0.0255082 | − | 0.999675i | \(-0.508120\pi\) | ||||
−0.0255082 | + | 0.999675i | \(0.508120\pi\) | |||||||
\(644\) | −8.30685e9 | − | 1.01925e10i | −1.22556 | − | 1.50376i | ||||
\(645\) | 5.14909e9 | − | 3.08531e8i | 0.755564 | − | 0.0452731i | ||||
\(646\) | 9.34514e8 | − | 3.32582e8i | 0.136387 | − | 0.0485383i | ||||
\(647\) | 7.67816e9 | 1.11453 | 0.557265 | − | 0.830334i | \(-0.311851\pi\) | ||||
0.557265 | + | 0.830334i | \(0.311851\pi\) | |||||||
\(648\) | −6.60540e9 | − | 2.08443e9i | −0.953644 | − | 0.300937i | ||||
\(649\) | 8.90231e9 | 1.27834 | ||||||||
\(650\) | 3.26777e9 | − | 1.16296e9i | 0.466718 | − | 0.166099i | ||||
\(651\) | −1.33713e10 | + | 8.01204e8i | −1.89951 | + | 0.113818i | ||||
\(652\) | −3.27878e9 | + | 2.67220e9i | −0.463282 | + | 0.377574i | ||||
\(653\) | 4.81816e8 | 0.0677150 | 0.0338575 | − | 0.999427i | \(-0.489221\pi\) | ||||
0.0338575 | + | 0.999427i | \(0.489221\pi\) | |||||||
\(654\) | 8.69441e9 | − | 3.69397e9i | 1.21540 | − | 0.516382i | ||||
\(655\) | 1.15781e10i | 1.60988i | ||||||||
\(656\) | 1.18983e10 | + | 2.45104e9i | 1.64559 | + | 0.338990i | ||||
\(657\) | −4.00143e9 | + | 4.81257e8i | −0.550474 | + | 0.0662061i | ||||
\(658\) | −6.22161e9 | + | 2.21419e9i | −0.851358 | + | 0.302987i | ||||
\(659\) | 5.69152e9i | 0.774693i | 0.921934 | + | 0.387346i | \(0.126608\pi\) | ||||
−0.921934 | + | 0.387346i | \(0.873392\pi\) | |||||||
\(660\) | 8.63422e9 | + | 9.38668e9i | 1.16901 | + | 1.27089i | ||||
\(661\) | − | 4.21717e9i | − | 0.567957i | −0.958831 | − | 0.283979i | \(-0.908346\pi\) | ||
0.958831 | − | 0.283979i | \(-0.0916545\pi\) | |||||||
\(662\) | −1.79063e9 | − | 5.03145e9i | −0.239885 | − | 0.674047i | ||||
\(663\) | −1.08234e9 | + | 6.48533e7i | −0.144233 | + | 0.00864241i | ||||
\(664\) | 9.82175e7 | − | 1.61985e8i | 0.0130197 | − | 0.0214726i | ||||
\(665\) | − | 8.19000e9i | − | 1.07996i | ||||||
\(666\) | 3.81381e9 | − | 1.89718e9i | 0.500264 | − | 0.248857i | ||||
\(667\) | −1.95669e9 | −0.255318 | ||||||||
\(668\) | −8.02126e9 | + | 6.53731e9i | −1.04118 | + | 0.848558i | ||||
\(669\) | 1.41089e8 | + | 2.35463e9i | 0.0182180 | + | 0.304041i | ||||
\(670\) | 3.56804e9 | + | 1.00258e10i | 0.458319 | + | 1.28782i | ||||
\(671\) | 5.52374e9 | 0.705837 | ||||||||
\(672\) | 2.38655e9 | + | 1.18584e10i | 0.303373 | + | 1.50742i | ||||
\(673\) | 4.64381e9 | 0.587248 | 0.293624 | − | 0.955921i | \(-0.405139\pi\) | ||||
0.293624 | + | 0.955921i | \(0.405139\pi\) | |||||||
\(674\) | 2.37194e9 | + | 6.66487e9i | 0.298397 | + | 0.838460i | ||||
\(675\) | 7.85548e9 | − | 1.42576e9i | 0.983127 | − | 0.178436i | ||||
\(676\) | −4.69555e9 | + | 3.82687e9i | −0.584620 | + | 0.476464i | ||||
\(677\) | −2.53205e9 | −0.313626 | −0.156813 | − | 0.987628i | \(-0.550122\pi\) | ||||
−0.156813 | + | 0.987628i | \(0.550122\pi\) | |||||||
\(678\) | 9.09816e9 | − | 3.86551e9i | 1.12111 | − | 0.476324i | ||||
\(679\) | 5.08913e9i | 0.623877i | ||||||||
\(680\) | 1.75177e9 | − | 2.88910e9i | 0.213647 | − | 0.352356i | ||||
\(681\) | −3.44018e6 | − | 5.74132e7i | −0.000417413 | − | 0.00696621i | ||||
\(682\) | −4.19792e9 | − | 1.17957e10i | −0.506745 | − | 1.42389i | ||||
\(683\) | − | 2.88044e9i | − | 0.345928i | −0.984928 | − | 0.172964i | \(-0.944666\pi\) | ||
0.984928 | − | 0.172964i | \(-0.0553345\pi\) | |||||||
\(684\) | −2.88599e9 | + | 2.99251e9i | −0.344825 | + | 0.357552i | ||||
\(685\) | − | 1.48674e10i | − | 1.76733i | ||||||
\(686\) | 4.46276e9 | − | 1.58824e9i | 0.527800 | − | 0.187837i | ||||
\(687\) | −1.76673e8 | − | 2.94849e9i | −0.0207884 | − | 0.346938i | ||||
\(688\) | −9.22620e8 | + | 4.47876e9i | −0.108010 | + | 0.524322i | ||||
\(689\) | − | 1.67747e9i | − | 0.195383i | ||||||
\(690\) | −6.01930e9 | − | 1.41675e10i | −0.697548 | − | 1.64180i | ||||
\(691\) | 3.73498e9 | 0.430641 | 0.215320 | − | 0.976543i | \(-0.430920\pi\) | ||||
0.215320 | + | 0.976543i | \(0.430920\pi\) | |||||||
\(692\) | −5.91065e9 | + | 4.81717e9i | −0.678054 | + | 0.552613i | ||||
\(693\) | −1.63347e10 | + | 1.96460e9i | −1.86443 | + | 0.224237i | ||||
\(694\) | −1.73739e9 | + | 6.18314e8i | −0.197305 | + | 0.0702184i | ||||
\(695\) | −1.85006e10 | −2.09045 | ||||||||
\(696\) | 1.59227e9 | + | 8.39546e8i | 0.179013 | + | 0.0943870i | ||||
\(697\) | 4.37726e9 | 0.489652 | ||||||||
\(698\) | −6.08512e9 | + | 2.16562e9i | −0.677291 | + | 0.241039i | ||||
\(699\) | −6.68499e8 | − | 1.11566e10i | −0.0740339 | − | 1.23555i | ||||
\(700\) | −8.80840e9 | − | 1.08079e10i | −0.970630 | − | 1.19096i | ||||
\(701\) | 1.55641e10 | 1.70652 | 0.853258 | − | 0.521489i | \(-0.174623\pi\) | ||||
0.853258 | + | 0.521489i | \(0.174623\pi\) | |||||||
\(702\) | 3.94048e9 | − | 2.26378e9i | 0.429902 | − | 0.246976i | ||||
\(703\) | − | 2.55671e9i | − | 0.277548i | ||||||
\(704\) | −1.00250e10 | + | 5.22757e9i | −1.08288 | + | 0.564671i | ||||
\(705\) | −7.71726e9 | + | 4.62415e8i | −0.829471 | + | 0.0497016i | ||||
\(706\) | 6.52607e9 | − | 2.32255e9i | 0.697968 | − | 0.248398i | ||||
\(707\) | 2.10162e10i | 2.23659i | ||||||||
\(708\) | 6.69171e9 | + | 7.27488e9i | 0.708632 | + | 0.770388i | ||||
\(709\) | 9.20870e9i | 0.970369i | 0.874412 | + | 0.485184i | \(0.161247\pi\) | ||||
−0.874412 | + | 0.485184i | \(0.838753\pi\) | |||||||
\(710\) | −1.23274e9 | − | 3.46385e9i | −0.129261 | − | 0.363208i | ||||
\(711\) | −2.21007e8 | − | 1.83758e9i | −0.0230602 | − | 0.191735i | ||||
\(712\) | 3.30296e9 | − | 5.44739e9i | 0.342944 | − | 0.565599i | ||||
\(713\) | 1.51115e10i | 1.56132i | ||||||||
\(714\) | 1.70435e9 | + | 4.01149e9i | 0.175232 | + | 0.412441i | ||||
\(715\) | −8.36776e9 | −0.856127 | ||||||||
\(716\) | 4.28293e9 | + | 5.25515e9i | 0.436060 | + | 0.535044i | ||||
\(717\) | 5.81294e9 | − | 3.48309e8i | 0.588951 | − | 0.0352897i | ||||
\(718\) | −3.20860e9 | − | 9.01579e9i | −0.323505 | − | 0.909009i | ||||
\(719\) | −1.27732e10 | −1.28159 | −0.640795 | − | 0.767712i | \(-0.721395\pi\) | ||||
−0.640795 | + | 0.767712i | \(0.721395\pi\) | |||||||
\(720\) | −1.18051e9 | + | 1.41116e10i | −0.117871 | + | 1.40901i | ||||
\(721\) | −1.45337e10 | −1.44412 | ||||||||
\(722\) | −2.55410e9 | − | 7.17671e9i | −0.252556 | − | 0.709651i | ||||
\(723\) | 5.27356e9 | − | 3.15990e8i | 0.518943 | − | 0.0310949i | ||||
\(724\) | −9.63388e9 | − | 1.18207e10i | −0.943444 | − | 1.15760i | ||||
\(725\) | −2.07483e9 | −0.202208 | ||||||||
\(726\) | −1.98154e9 | − | 4.66391e9i | −0.192188 | − | 0.452348i | ||||
\(727\) | − | 1.86923e8i | − | 0.0180423i | −0.999959 | − | 0.00902115i | \(-0.997128\pi\) | ||
0.999959 | − | 0.00902115i | \(-0.00287156\pi\) | |||||||
\(728\) | −6.78626e9 | − | 4.11477e9i | −0.651884 | − | 0.395262i | ||||
\(729\) | 9.79317e9 | − | 3.67599e9i | 0.936218 | − | 0.351421i | ||||
\(730\) | 2.76267e9 | + | 7.76277e9i | 0.262844 | + | 0.738561i | ||||
\(731\) | 1.64769e9i | 0.156014i | ||||||||
\(732\) | 4.15210e9 | + | 4.51395e9i | 0.391272 | + | 0.425371i | ||||
\(733\) | 1.02749e10i | 0.963635i | 0.876271 | + | 0.481818i | \(0.160023\pi\) | ||||
−0.876271 | + | 0.481818i | \(0.839977\pi\) | |||||||
\(734\) | −1.61018e10 | + | 5.73041e9i | −1.50292 | + | 0.534871i | ||||
\(735\) | 2.07290e10 | − | 1.24207e9i | 1.92563 | − | 0.115383i | ||||
\(736\) | 1.35148e10 | − | 1.88733e9i | 1.24950 | − | 0.174492i | ||||
\(737\) | − | 1.28313e10i | − | 1.18068i | ||||||
\(738\) | −1.64260e10 | + | 8.17110e9i | −1.50430 | + | 0.748313i | ||||
\(739\) | 5.65503e9 | 0.515441 | 0.257721 | − | 0.966219i | \(-0.417029\pi\) | ||||
0.257721 | + | 0.966219i | \(0.417029\pi\) | |||||||
\(740\) | −5.50175e9 | − | 6.75063e9i | −0.499103 | − | 0.612397i | ||||
\(741\) | −1.63149e8 | − | 2.72279e9i | −0.0147306 | − | 0.245839i | ||||
\(742\) | −6.35269e9 | + | 2.26084e9i | −0.570879 | + | 0.203168i | ||||
\(743\) | 4.48489e9 | 0.401136 | 0.200568 | − | 0.979680i | \(-0.435721\pi\) | ||||
0.200568 | + | 0.979680i | \(0.435721\pi\) | |||||||
\(744\) | 6.48379e9 | − | 1.22971e10i | 0.577197 | − | 1.09471i | ||||
\(745\) | 2.55777e10 | 2.26628 | ||||||||
\(746\) | 7.98374e9 | − | 2.84131e9i | 0.704077 | − | 0.250572i | ||||
\(747\) | 3.41615e7 | + | 2.84038e8i | 0.00299858 | + | 0.0249318i | ||||
\(748\) | −3.15792e9 | + | 2.57370e9i | −0.275896 | + | 0.224855i | ||||
\(749\) | −1.10376e10 | −0.959819 | ||||||||
\(750\) | 5.18264e6 | + | 1.21983e7i | 0.000448577 | + | 0.00105581i | ||||
\(751\) | − | 1.25488e10i | − | 1.08109i | −0.841314 | − | 0.540547i | \(-0.818217\pi\) | ||
0.841314 | − | 0.540547i | \(-0.181783\pi\) | |||||||
\(752\) | 1.38279e9 | − | 6.71259e9i | 0.118575 | − | 0.575609i | ||||
\(753\) | 1.09520e9 | + | 1.82778e10i | 0.0934782 | + | 1.56006i | ||||
\(754\) | −1.11265e9 | + | 3.95977e8i | −0.0945275 | + | 0.0336411i | ||||
\(755\) | − | 7.20299e9i | − | 0.609114i | ||||||
\(756\) | −1.38840e10 | − | 1.18718e10i | −1.16866 | − | 0.999290i | ||||
\(757\) | 1.12493e10i | 0.942518i | 0.881995 | + | 0.471259i | \(0.156200\pi\) | ||||
−0.881995 | + | 0.471259i | \(0.843800\pi\) | |||||||
\(758\) | 5.15043e9 | + | 1.44721e10i | 0.429538 | + | 1.20695i | ||||
\(759\) | 1.11014e9 | + | 1.85271e10i | 0.0921573 | + | 1.53801i | ||||
\(760\) | 7.26798e9 | + | 4.40686e9i | 0.600574 | + | 0.364151i | ||||
\(761\) | − | 1.04257e10i | − | 0.857546i | −0.903412 | − | 0.428773i | \(-0.858946\pi\) | ||
0.903412 | − | 0.428773i | \(-0.141054\pi\) | |||||||
\(762\) | 1.35704e10 | − | 5.76562e9i | 1.11109 | − | 0.472067i | ||||
\(763\) | 2.49140e10 | 2.03053 | ||||||||
\(764\) | 1.79227e10 | − | 1.46069e10i | 1.45404 | − | 1.18504i | ||||
\(765\) | 6.09293e8 | + | 5.06600e9i | 0.0492052 | + | 0.409119i | ||||
\(766\) | −3.41078e9 | − | 9.58388e9i | −0.274191 | − | 0.770444i | ||||
\(767\) | −6.48520e9 | −0.518967 | ||||||||
\(768\) | −1.18075e10 | − | 4.26286e9i | −0.940579 | − | 0.339576i | ||||
\(769\) | −1.79503e10 | −1.42341 | −0.711706 | − | 0.702478i | \(-0.752077\pi\) | ||||
−0.711706 | + | 0.702478i | \(0.752077\pi\) | |||||||
\(770\) | 1.12778e10 | + | 3.16893e10i | 0.890241 | + | 2.50147i | ||||
\(771\) | −9.94187e8 | − | 1.65920e10i | −0.0781228 | − | 1.30379i | ||||
\(772\) | −8.87778e9 | + | 7.23537e9i | −0.694454 | + | 0.565979i | ||||
\(773\) | −1.30886e9 | −0.101922 | −0.0509608 | − | 0.998701i | \(-0.516228\pi\) | ||||
−0.0509608 | + | 0.998701i | \(0.516228\pi\) | |||||||
\(774\) | −3.07576e9 | − | 6.18306e9i | −0.238429 | − | 0.479303i | ||||
\(775\) | 1.60239e10i | 1.23655i | ||||||||
\(776\) | −4.51620e9 | − | 2.73834e9i | −0.346942 | − | 0.210364i | ||||
\(777\) | 1.12141e10 | − | 6.71942e8i | 0.857608 | − | 0.0513876i | ||||
\(778\) | −1.89430e9 | − | 5.32276e9i | −0.144218 | − | 0.405236i | ||||
\(779\) | 1.10117e10i | 0.834589i | ||||||||
\(780\) | −6.28990e9 | − | 6.83805e9i | −0.474583 | − | 0.515943i | ||||
\(781\) | 4.43314e9i | 0.332991i | ||||||||
\(782\) | 4.63233e9 | − | 1.64859e9i | 0.346398 | − | 0.123279i | ||||
\(783\) | −2.67473e9 | + | 4.85460e8i | −0.199119 | + | 0.0361399i | ||||
\(784\) | −3.71424e9 | + | 1.80304e10i | −0.275273 | + | 1.33628i | ||||
\(785\) | − | 1.05604e10i | − | 0.779179i | ||||||
\(786\) | 1.42663e10 | − | 6.06126e9i | 1.04793 | − | 0.445229i | ||||
\(787\) | −1.43246e10 | −1.04754 | −0.523770 | − | 0.851860i | \(-0.675475\pi\) | ||||
−0.523770 | + | 0.851860i | \(0.675475\pi\) | |||||||
\(788\) | 1.47089e10 | − | 1.19878e10i | 1.07088 | − | 0.872763i | ||||
\(789\) | 4.30326e9 | − | 2.57850e8i | 0.311909 | − | 0.0186895i | ||||
\(790\) | −3.56489e9 | + | 1.26870e9i | −0.257248 | + | 0.0915511i | ||||
\(791\) | 2.60710e10 | 1.87301 | ||||||||
\(792\) | 7.04592e9 | − | 1.55529e10i | 0.503964 | − | 1.11243i | ||||
\(793\) | −4.02396e9 | −0.286548 | ||||||||
\(794\) | −2.61325e10 | + | 9.30022e9i | −1.85272 | + | 0.659358i | ||||
\(795\) | −7.87985e9 | + | 4.72158e8i | −0.556202 | + | 0.0333274i | ||||
\(796\) | 9.60858e9 | + | 1.17897e10i | 0.675248 | + | 0.828527i | ||||
\(797\) | 9.85671e9 | 0.689649 | 0.344824 | − | 0.938667i | \(-0.387938\pi\) | ||||
0.344824 | + | 0.938667i | \(0.387938\pi\) | |||||||
\(798\) | −1.00915e10 | + | 4.28755e9i | −0.702985 | + | 0.298675i | ||||
\(799\) | − | 2.46949e9i | − | 0.171275i | ||||||
\(800\) | 1.43307e10 | − | 2.00129e9i | 0.989586 | − | 0.138196i | ||||
\(801\) | 1.14882e9 | + | 9.55192e9i | 0.0789838 | + | 0.656715i | ||||
\(802\) | 1.56648e10 | − | 5.57490e9i | 1.07229 | − | 0.381616i | ||||
\(803\) | − | 9.93502e9i | − | 0.677118i | ||||||
\(804\) | 1.04856e10 | − | 9.64503e9i | 0.711535 | − | 0.654497i | ||||
\(805\) | − | 4.05973e10i | − | 2.74291i | ||||||
\(806\) | 3.05812e9 | + | 8.59296e9i | 0.205723 | + | 0.578056i | ||||
\(807\) | −1.32007e10 | + | 7.90980e8i | −0.884176 | + | 0.0529795i | ||||
\(808\) | −1.86502e10 | − | 1.13083e10i | −1.24378 | − | 0.754151i | ||||
\(809\) | 1.39740e10i | 0.927903i | 0.885861 | + | 0.463951i | \(0.153569\pi\) | ||||
−0.885861 | + | 0.463951i | \(0.846431\pi\) | |||||||
\(810\) | −1.17432e10 | − | 1.78731e10i | −0.776405 | − | 1.18169i | ||||
\(811\) | −1.11611e10 | −0.734740 | −0.367370 | − | 0.930075i | \(-0.619742\pi\) | ||||
−0.367370 | + | 0.930075i | \(0.619742\pi\) | |||||||
\(812\) | 2.99919e9 | + | 3.67999e9i | 0.196588 | + | 0.241213i | ||||
\(813\) | −1.42636e9 | − | 2.38046e10i | −0.0930921 | − | 1.55362i | ||||
\(814\) | 3.52065e9 | + | 9.89261e9i | 0.228790 | + | 0.642873i | ||||
\(815\) | −1.30596e10 | −0.845042 | ||||||||
\(816\) | −4.47695e9 | − | 6.46016e8i | −0.288447 | − | 0.0416225i | ||||
\(817\) | −4.14501e9 | −0.265919 | ||||||||
\(818\) | −1.01594e10 | − | 2.85466e10i | −0.648978 | − | 1.82355i | ||||
\(819\) | 1.18996e10 | − | 1.43118e9i | 0.756901 | − | 0.0910333i | ||||
\(820\) | 2.36959e10 | + | 2.90748e10i | 1.50080 | + | 1.84148i | ||||
\(821\) | 2.98833e9 | 0.188464 | 0.0942320 | − | 0.995550i | \(-0.469960\pi\) | ||||
0.0942320 | + | 0.995550i | \(0.469960\pi\) | |||||||
\(822\) | −1.83192e10 | + | 7.78324e9i | −1.15042 | + | 0.488775i | ||||
\(823\) | − | 2.49854e10i | − | 1.56238i | −0.624293 | − | 0.781191i | \(-0.714613\pi\) | ||
0.624293 | − | 0.781191i | \(-0.285387\pi\) | |||||||
\(824\) | 7.82025e9 | − | 1.28975e10i | 0.486940 | − | 0.803083i | ||||
\(825\) | 1.17716e9 | + | 1.96457e10i | 0.0729873 | + | 1.21809i | ||||
\(826\) | 8.74056e9 | + | 2.45599e10i | 0.539646 | + | 1.51634i | ||||
\(827\) | − | 6.85599e9i | − | 0.421503i | −0.977540 | − | 0.210752i | \(-0.932409\pi\) | ||
0.977540 | − | 0.210752i | \(-0.0675911\pi\) | |||||||
\(828\) | −1.43057e10 | + | 1.48337e10i | −0.875794 | + | 0.908118i | ||||
\(829\) | 2.08320e10i | 1.26996i | 0.772529 | + | 0.634979i | \(0.218991\pi\) | ||||
−0.772529 | + | 0.634979i | \(0.781009\pi\) | |||||||
\(830\) | 5.51032e8 | − | 1.96105e8i | 0.0334506 | − | 0.0119046i | ||||
\(831\) | −1.31413e8 | − | 2.19316e9i | −0.00794393 | − | 0.132576i | ||||
\(832\) | 7.30306e9 | − | 3.80821e9i | 0.439616 | − | 0.229239i | ||||
\(833\) | 6.63319e9i | 0.397617i | ||||||||
\(834\) | 9.68527e9 | + | 2.27960e10i | 0.578137 | + | 1.36075i | ||||
\(835\) | −3.19492e10 | −1.89914 | ||||||||
\(836\) | −6.47453e9 | − | 7.94423e9i | −0.383254 | − | 0.470251i | ||||
\(837\) | 3.74920e9 | + | 2.06569e10i | 0.221003 | + | 1.21766i | ||||
\(838\) | 1.33579e10 | − | 4.75391e9i | 0.784124 | − | 0.279060i | ||||
\(839\) | 1.94903e10 | 1.13933 | 0.569667 | − | 0.821876i | \(-0.307072\pi\) | ||||
0.569667 | + | 0.821876i | \(0.307072\pi\) | |||||||
\(840\) | −1.74189e10 | + | 3.30364e10i | −1.01401 | + | 1.92316i | ||||
\(841\) | −1.65434e10 | −0.959045 | ||||||||
\(842\) | −1.09789e10 | + | 3.90723e9i | −0.633818 | + | 0.225568i | ||||
\(843\) | −1.31446e9 | − | 2.19370e10i | −0.0755700 | − | 1.26119i | ||||
\(844\) | 1.13360e10 | − | 9.23879e9i | 0.649022 | − | 0.528952i | ||||
\(845\) | −1.87027e10 | −1.06637 | ||||||||
\(846\) | 4.60984e9 | + | 9.26693e9i | 0.261752 | + | 0.526186i | ||||
\(847\) | − | 1.33646e10i | − | 0.755723i | ||||||
\(848\) | 1.41192e9 | − | 6.85402e9i | 0.0795106 | − | 0.385975i | ||||
\(849\) | −1.43448e10 | + | 8.59537e8i | −0.804486 | + | 0.0482045i | ||||
\(850\) | 4.91202e9 | − | 1.74812e9i | 0.274343 | − | 0.0976350i | ||||
\(851\) | − | 1.26735e10i | − | 0.704923i | ||||||
\(852\) | −3.62272e9 | + | 3.33231e9i | −0.200676 | + | 0.184590i | ||||
\(853\) | − | 7.36557e9i | − | 0.406336i | −0.979144 | − | 0.203168i | \(-0.934876\pi\) | ||
0.979144 | − | 0.203168i | \(-0.0651237\pi\) | |||||||
\(854\) | 5.42338e9 | + | 1.52390e10i | 0.297966 | + | 0.837250i | ||||
\(855\) | −1.27443e10 | + | 1.53277e9i | −0.697324 | + | 0.0838679i | ||||
\(856\) | 5.93910e9 | − | 9.79503e9i | 0.323640 | − | 0.533762i | ||||
\(857\) | 1.02885e10i | 0.558368i | 0.960238 | + | 0.279184i | \(0.0900639\pi\) | ||||
−0.960238 | + | 0.279184i | \(0.909936\pi\) | |||||||
\(858\) | 4.38061e9 | + | 1.03105e10i | 0.236771 | + | 0.557283i | ||||
\(859\) | 2.10847e10 | 1.13499 | 0.567494 | − | 0.823378i | \(-0.307913\pi\) | ||||
0.567494 | + | 0.823378i | \(0.307913\pi\) | |||||||
\(860\) | −1.09443e10 | + | 8.91960e9i | −0.586738 | + | 0.478190i | ||||
\(861\) | −4.82986e10 | + | 2.89403e9i | −2.57883 | + | 0.154523i | ||||
\(862\) | 3.51010e9 | + | 9.86296e9i | 0.186657 | + | 0.524483i | ||||
\(863\) | 1.03713e10 | 0.549282 | 0.274641 | − | 0.961547i | \(-0.411441\pi\) | ||||
0.274641 | + | 0.961547i | \(0.411441\pi\) | |||||||
\(864\) | 1.80060e10 | − | 5.93297e9i | 0.949770 | − | 0.312949i | ||||
\(865\) | −2.35425e10 | −1.23679 | ||||||||
\(866\) | 3.66003e9 | + | 1.02842e10i | 0.191501 | + | 0.538096i | ||||
\(867\) | 1.75283e10 | − | 1.05029e9i | 0.913427 | − | 0.0547322i | ||||
\(868\) | 2.84205e10 | − | 2.31627e10i | 1.47507 | − | 1.20218i | ||||
\(869\) | 4.56245e9 | 0.235846 | ||||||||
\(870\) | 2.17327e9 | + | 5.11518e9i | 0.111891 | + | 0.263356i | ||||
\(871\) | 9.34738e9i | 0.479321i | ||||||||
\(872\) | −1.34057e10 | + | 2.21093e10i | −0.684670 | + | 1.12919i | ||||
\(873\) | 7.91909e9 | − | 9.52437e8i | 0.402833 | − | 0.0484492i | ||||
\(874\) | 4.14727e9 | + | 1.16533e10i | 0.210123 | + | 0.590419i | ||||
\(875\) | 3.49545e7i | 0.00176390i | ||||||||
\(876\) | 8.11880e9 | − | 7.46798e9i | 0.408063 | − | 0.375352i | ||||
\(877\) | − | 1.96006e10i | − | 0.981230i | −0.871376 | − | 0.490615i | \(-0.836772\pi\) | ||
0.871376 | − | 0.490615i | \(-0.163228\pi\) | |||||||
\(878\) | 1.10189e10 | − | 3.92149e9i | 0.549424 | − | 0.195533i | ||||
\(879\) | 2.25723e10 | − | 1.35252e9i | 1.12102 | − | 0.0671713i | ||||
\(880\) | −3.41901e10 | − | 7.04313e9i | −1.69126 | − | 0.348399i | ||||
\(881\) | 2.80833e10i | 1.38367i | 0.722055 | + | 0.691836i | \(0.243198\pi\) | ||||
−0.722055 | + | 0.691836i | \(0.756802\pi\) | |||||||
\(882\) | −1.23823e10 | − | 2.48915e10i | −0.607660 | − | 1.22155i | ||||
\(883\) | −2.34002e10 | −1.14382 | −0.571910 | − | 0.820316i | \(-0.693797\pi\) | ||||
−0.571910 | + | 0.820316i | \(0.693797\pi\) | |||||||
\(884\) | 2.30049e9 | − | 1.87490e9i | 0.112005 | − | 0.0912840i | ||||
\(885\) | 1.82539e9 | + | 3.04640e10i | 0.0885227 | + | 1.47736i | ||||
\(886\) | −9.34546e9 | + | 3.32593e9i | −0.451422 | + | 0.160655i | ||||
\(887\) | −2.34643e10 | −1.12895 | −0.564475 | − | 0.825450i | \(-0.690921\pi\) | ||||
−0.564475 | + | 0.825450i | \(0.690921\pi\) | |||||||
\(888\) | −5.43773e9 | + | 1.03131e10i | −0.260599 | + | 0.494249i | ||||
\(889\) | 3.88864e10 | 1.85627 | ||||||||
\(890\) | 1.85307e10 | − | 6.59483e9i | 0.881103 | − | 0.313573i | ||||
\(891\) | 6.11414e9 | + | 2.50505e10i | 0.289576 | + | 1.18643i | ||||
\(892\) | −4.07885e9 | − | 5.00474e9i | −0.192425 | − | 0.236104i | ||||
\(893\) | 6.21239e9 | 0.291930 | ||||||||
\(894\) | −1.33902e10 | − | 3.15162e10i | −0.626766 | − | 1.47521i | ||||
\(895\) | 2.09316e10i | 0.975937i | ||||||||
\(896\) | −2.42648e10 | − | 2.25247e10i | −1.12694 | − | 1.04612i | ||||
\(897\) | −8.08717e8 | − | 1.34967e10i | −0.0374130 | − | 0.624387i | ||||
\(898\) | −1.65049e10 | + | 5.87386e9i | −0.760579 | + | 0.270680i | ||||
\(899\) | − | 5.45600e9i | − | 0.250447i | ||||||
\(900\) | −1.51694e10 | + | 1.57293e10i | −0.693617 | + | 0.719217i | ||||
\(901\) | − | 2.52152e9i | − | 0.114849i | ||||||
\(902\) | −1.51633e10 | − | 4.26072e10i | −0.687974 | − | 1.93312i | ||||
\(903\) | −1.08937e9 | − | 1.81805e10i | −0.0492344 | − | 0.821674i | ||||
\(904\) | −1.40282e10 | + | 2.31360e10i | −0.631558 | + | 1.04159i | ||||
\(905\) | − | 4.70828e10i | − | 2.11150i | ||||||
\(906\) | −8.87535e9 | + | 3.77084e9i | −0.396494 | + | 0.168457i | ||||
\(907\) | 2.07542e10 | 0.923592 | 0.461796 | − | 0.886986i | \(-0.347205\pi\) | ||||
0.461796 | + | 0.886986i | \(0.347205\pi\) | |||||||
\(908\) | 9.94550e7 | + | 1.22031e8i | 0.00440886 | + | 0.00540965i | ||||
\(909\) | 3.27028e10 | − | 3.93320e9i | 1.44415 | − | 0.173689i | ||||
\(910\) | −8.21572e9 | − | 2.30852e10i | −0.361411 | − | 1.01552i | ||||
\(911\) | 8.39905e9 | 0.368058 | 0.184029 | − | 0.982921i | \(-0.441086\pi\) | ||||
0.184029 | + | 0.982921i | \(0.441086\pi\) | |||||||
\(912\) | 1.62515e9 | − | 1.12625e10i | 0.0709435 | − | 0.491645i | ||||
\(913\) | −7.05227e8 | −0.0306677 | ||||||||
\(914\) | 3.59882e9 | + | 1.01123e10i | 0.155901 | + | 0.438063i | ||||
\(915\) | 1.13263e9 | + | 1.89024e10i | 0.0488780 | + | 0.815726i | ||||
\(916\) | 5.10758e9 | + | 6.26698e9i | 0.219574 | + | 0.269417i | ||||
\(917\) | 4.08803e10 | 1.75074 | ||||||||
\(918\) | 5.92322e9 | − | 3.40286e9i | 0.252702 | − | 0.145176i | ||||
\(919\) | − | 1.77784e10i | − | 0.755594i | −0.925889 | − | 0.377797i | \(-0.876682\pi\) | ||
0.925889 | − | 0.377797i | \(-0.123318\pi\) | |||||||
\(920\) | 3.60269e10 | + | 2.18445e10i | 1.52535 | + | 0.924879i | ||||
\(921\) | 1.88862e10 | − | 1.13165e9i | 0.796591 | − | 0.0477314i | ||||
\(922\) | −8.92425e9 | − | 2.50761e10i | −0.374984 | − | 1.05366i | ||||
\(923\) | − | 3.22947e9i | − | 0.135184i | ||||||
\(924\) | 3.31427e10 | − | 3.04859e10i | 1.38209 | − | 1.27130i | ||||
\(925\) | − | 1.34386e10i | − | 0.558290i | ||||||
\(926\) | 9.10236e9 | − | 3.23941e9i | 0.376717 | − | 0.134069i | ||||
\(927\) | 2.72000e9 | + | 2.26156e10i | 0.112148 | + | 0.932457i | ||||
\(928\) | −4.87950e9 | + | 6.81422e8i | −0.200428 | + | 0.0279897i | ||||
\(929\) | 8.89605e8i | 0.0364034i | 0.999834 | + | 0.0182017i | \(0.00579411\pi\) | ||||
−0.999834 | + | 0.0182017i | \(0.994206\pi\) | |||||||
\(930\) | 3.95044e10 | − | 1.67841e10i | 1.61048 | − | 0.684239i | ||||
\(931\) | −1.66868e10 | −0.677719 | ||||||||
\(932\) | 1.93262e10 | + | 2.37132e10i | 0.781972 | + | 0.959476i | ||||
\(933\) | 2.00360e10 | − | 1.20055e9i | 0.807654 | − | 0.0483944i | ||||
\(934\) | −2.05154e10 | + | 7.30117e9i | −0.823884 | + | 0.293210i | ||||
\(935\) | −1.25782e10 | −0.503243 | ||||||||
\(936\) | −5.13285e9 | + | 1.13300e10i | −0.204594 | + | 0.451613i | ||||
\(937\) | 1.09174e10 | 0.433543 | 0.216772 | − | 0.976222i | \(-0.430447\pi\) | ||||
0.216772 | + | 0.976222i | \(0.430447\pi\) | |||||||
\(938\) | 3.53992e10 | − | 1.25981e10i | 1.40050 | − | 0.498420i | ||||
\(939\) | −3.41685e10 | + | 2.04736e9i | −1.34678 | + | 0.0806984i | ||||
\(940\) | 1.64029e10 | − | 1.33684e10i | 0.644130 | − | 0.524965i | ||||
\(941\) | −1.58749e10 | −0.621080 | −0.310540 | − | 0.950560i | \(-0.600510\pi\) | ||||
−0.310540 | + | 0.950560i | \(0.600510\pi\) | |||||||
\(942\) | −1.30123e10 | + | 5.52849e9i | −0.507195 | + | 0.215491i | ||||
\(943\) | 5.45842e10i | 2.11971i | ||||||||
\(944\) | −2.64981e10 | − | 5.45858e9i | −1.02521 | − | 0.211192i | ||||
\(945\) | −1.00723e10 | − | 5.54952e10i | −0.388256 | − | 2.13916i | ||||
\(946\) | 1.60382e10 | − | 5.70778e9i | 0.615937 | − | 0.219204i | ||||
\(947\) | 3.05808e10i | 1.17010i | 0.810996 | + | 0.585051i | \(0.198926\pi\) | ||||
−0.810996 | + | 0.585051i | \(0.801074\pi\) | |||||||
\(948\) | 3.42951e9 | + | 3.72839e9i | 0.130739 | + | 0.142132i | ||||
\(949\) | 7.23751e9i | 0.274889i | ||||||||
\(950\) | 4.39767e9 | + | 1.23569e10i | 0.166414 | + | 0.467604i | ||||
\(951\) | −5.10522e9 | + | 3.05903e8i | −0.192479 | + | 0.0115333i | ||||
\(952\) | −1.02009e10 | − | 6.18521e9i | −0.383186 | − | 0.232340i | ||||
\(953\) | 5.23582e9i | 0.195956i | 0.995189 | + | 0.0979782i | \(0.0312375\pi\) | ||||
−0.995189 | + | 0.0979782i | \(0.968762\pi\) | |||||||
\(954\) | 4.70696e9 | + | 9.46217e9i | 0.175518 | + | 0.352835i | ||||
\(955\) | 7.13872e10 | 2.65221 | ||||||||
\(956\) | −1.23553e10 | + | 1.00696e10i | −0.457353 | + | 0.372742i | ||||
\(957\) | −4.00814e8 | − | 6.68920e9i | −0.0147826 | − | 0.246707i | ||||
\(958\) | 1.00737e10 | + | 2.83060e10i | 0.370178 | + | 1.04016i | ||||
\(959\) | −5.24943e10 | −1.92197 | ||||||||
\(960\) | −1.99445e10 | − | 3.32340e10i | −0.727570 | − | 1.21237i | ||||
\(961\) | −1.46239e10 | −0.531535 | ||||||||
\(962\) | −2.56474e9 | − | 7.20662e9i | −0.0928819 | − | 0.260987i | ||||
\(963\) | 2.06571e9 | + | 1.71754e10i | 0.0745379 | + | 0.619749i | ||||
\(964\) | −1.12089e10 | + | 9.13521e9i | −0.402988 | + | 0.328435i | ||||
\(965\) | −3.53608e10 | −1.26671 | ||||||||
\(966\) | −5.00230e10 | + | 2.12531e10i | −1.78546 | + | 0.758582i | ||||
\(967\) | − | 2.00071e9i | − | 0.0711526i | −0.999367 | − | 0.0355763i | \(-0.988673\pi\) | ||
0.999367 | − | 0.0355763i | \(-0.0113267\pi\) | |||||||
\(968\) | 1.18600e10 | + | 7.19117e9i | 0.420263 | + | 0.254821i | ||||
\(969\) | −2.45240e8 | − | 4.09282e9i | −0.00865882 | − | 0.144507i | ||||
\(970\) | −5.46750e9 | − | 1.53630e10i | −0.192348 | − | 0.540474i | ||||
\(971\) | 5.74860e9i | 0.201509i | 0.994911 | + | 0.100755i | \(0.0321257\pi\) | ||||
−0.994911 | + | 0.100755i | \(0.967874\pi\) | |||||||
\(972\) | −1.58751e10 | + | 2.38264e10i | −0.554479 | + | 0.832198i | ||||
\(973\) | 6.53225e10i | 2.27336i | ||||||||
\(974\) | −3.87232e10 | + | 1.37811e10i | −1.34281 | + | 0.477889i | ||||
\(975\) | −8.57545e8 | − | 1.43116e10i | −0.0296306 | − | 0.494506i | ||||
\(976\) | −1.64416e10 | − | 3.38696e9i | −0.566071 | − | 0.116610i | ||||
\(977\) | − | 3.65906e10i | − | 1.25527i | −0.778506 | − | 0.627637i | \(-0.784022\pi\) | ||
0.778506 | − | 0.627637i | \(-0.215978\pi\) | |||||||
\(978\) | 6.83683e9 | + | 1.60917e10i | 0.233706 | + | 0.550068i | ||||
\(979\) | −2.37161e10 | −0.807801 | ||||||||
\(980\) | −4.40591e10 | + | 3.59081e10i | −1.49536 | + | 1.21871i | ||||
\(981\) | −4.66270e9 | − | 3.87682e10i | −0.157687 | − | 1.31110i | ||||
\(982\) | 6.19996e9 | − | 2.20649e9i | 0.208929 | − | 0.0743551i | ||||
\(983\) | 5.43661e10 | 1.82554 | 0.912769 | − | 0.408476i | \(-0.133939\pi\) | ||||
0.912769 | + | 0.408476i | \(0.133939\pi\) | |||||||
\(984\) | 2.34201e10 | − | 4.44184e10i | 0.783622 | − | 1.48621i | ||||
\(985\) | 5.85867e10 | 1.95332 | ||||||||
\(986\) | −1.67250e9 | + | 5.95222e8i | −0.0555645 | + | 0.0197747i | ||||
\(987\) | 1.63271e9 | + | 2.72483e10i | 0.0540504 | + | 0.902047i | ||||
\(988\) | 4.71660e9 | + | 5.78725e9i | 0.155589 | + | 0.190907i | ||||
\(989\) | −2.05466e10 | −0.675386 | ||||||||
\(990\) | 4.72005e10 | − | 2.34799e10i | 1.54605 | − | 0.769083i | ||||
\(991\) | − | 4.42393e10i | − | 1.44394i | −0.691922 | − | 0.721972i | \(-0.743236\pi\) | ||
0.691922 | − | 0.721972i | \(-0.256764\pi\) | |||||||
\(992\) | 5.26261e9 | + | 3.76843e10i | 0.171163 | + | 1.22566i | ||||
\(993\) | −2.20359e10 | + | 1.32038e9i | −0.714180 | + | 0.0427934i | ||||
\(994\) | −1.22303e10 | + | 4.35259e9i | −0.394987 | + | 0.140571i | ||||
\(995\) | 4.69591e10i | 1.51126i | ||||||||
\(996\) | −5.30107e8 | − | 5.76305e8i | −0.0170003 | − | 0.0184818i | ||||
\(997\) | 3.33656e10i | 1.06627i | 0.846031 | + | 0.533133i | \(0.178986\pi\) | ||||
−0.846031 | + | 0.533133i | \(0.821014\pi\) | |||||||
\(998\) | −1.61781e10 | − | 4.54585e10i | −0.515194 | − | 1.44763i | ||||
\(999\) | −3.14432e9 | − | 1.73242e10i | −0.0997809 | − | 0.549761i |
(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 | 24.8.f.c.11.12 | yes | 20 | |
3.2 | odd | 2 | inner | 24.8.f.c.11.9 | ✓ | 20 | |
4.3 | odd | 2 | 96.8.f.c.47.3 | 20 | |||
8.3 | odd | 2 | inner | 24.8.f.c.11.10 | yes | 20 | |
8.5 | even | 2 | 96.8.f.c.47.4 | 20 | |||
12.11 | even | 2 | 96.8.f.c.47.2 | 20 | |||
24.5 | odd | 2 | 96.8.f.c.47.1 | 20 | |||
24.11 | even | 2 | inner | 24.8.f.c.11.11 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.8.f.c.11.9 | ✓ | 20 | 3.2 | odd | 2 | inner | |
24.8.f.c.11.10 | yes | 20 | 8.3 | odd | 2 | inner | |
24.8.f.c.11.11 | yes | 20 | 24.11 | even | 2 | inner | |
24.8.f.c.11.12 | yes | 20 | 1.1 | even | 1 | trivial | |
96.8.f.c.47.1 | 20 | 24.5 | odd | 2 | |||
96.8.f.c.47.2 | 20 | 12.11 | even | 2 | |||
96.8.f.c.47.3 | 20 | 4.3 | odd | 2 | |||
96.8.f.c.47.4 | 20 | 8.5 | even | 2 |