Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [32,8,Mod(5,32)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(32, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("32.5");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 32 = 2^{5} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 32.g (of order \(8\), degree \(4\), 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: | \(9.99632081549\) |
Analytic rank: | \(0\) |
Dimension: | \(108\) |
Relative dimension: | \(27\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 13.18 | ||
Character | \(\chi\) | \(=\) | 32.13 |
Dual form | 32.8.g.a.5.18 |
$q$-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 \(\left(\mathbb{Z}/32\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(31\) |
\(\chi(n)\) | \(e\left(\frac{7}{8}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.84536 | − | 9.68668i | 0.516662 | − | 0.856190i | ||||
\(3\) | 3.37541 | − | 8.14896i | 0.0721775 | − | 0.174252i | −0.883673 | − | 0.468104i | \(-0.844937\pi\) |
0.955851 | + | 0.293852i | \(0.0949373\pi\) | |||||||
\(4\) | −59.6635 | − | 113.244i | −0.466121 | − | 0.884721i | ||||
\(5\) | 482.880 | − | 200.015i | 1.72760 | − | 0.715597i | 0.728056 | − | 0.685518i | \(-0.240424\pi\) |
0.999548 | − | 0.0300787i | \(-0.00957578\pi\) | |||||||
\(6\) | −59.2059 | − | 80.3301i | −0.111901 | − | 0.151827i | ||||
\(7\) | −141.209 | + | 141.209i | −0.155603 | + | 0.155603i | −0.780615 | − | 0.625012i | \(-0.785094\pi\) |
0.625012 | + | 0.780615i | \(0.285094\pi\) | |||||||
\(8\) | −1445.72 | − | 84.0120i | −0.998316 | − | 0.0580132i | ||||
\(9\) | 1491.43 | + | 1491.43i | 0.681953 | + | 0.681953i | ||||
\(10\) | 885.122 | − | 5846.66i | 0.279900 | − | 1.84888i | ||||
\(11\) | −2979.30 | − | 7192.67i | −0.674901 | − | 1.62936i | −0.773172 | − | 0.634196i | \(-0.781331\pi\) |
0.0982709 | − | 0.995160i | \(-0.468669\pi\) | |||||||
\(12\) | −1124.21 | + | 103.950i | −0.187808 | + | 0.0173656i | ||||
\(13\) | −2566.69 | − | 1063.16i | −0.324019 | − | 0.134213i | 0.214744 | − | 0.976670i | \(-0.431108\pi\) |
−0.538763 | + | 0.842457i | \(0.681108\pi\) | |||||||
\(14\) | 542.427 | + | 2193.26i | 0.0528315 | + | 0.213620i | ||||
\(15\) | − | 4610.10i | − | 0.352688i | ||||||
\(16\) | −9264.53 | + | 13513.1i | −0.565462 | + | 0.824774i | ||||
\(17\) | 6727.00i | 0.332086i | 0.986119 | + | 0.166043i | \(0.0530990\pi\) | ||||
−0.986119 | + | 0.166043i | \(0.946901\pi\) | |||||||
\(18\) | 23165.0 | − | 5729.06i | 0.936220 | − | 0.231542i | ||||
\(19\) | −19530.1 | − | 8089.62i | −0.653230 | − | 0.270577i | 0.0313567 | − | 0.999508i | \(-0.490017\pi\) |
−0.684587 | + | 0.728932i | \(0.740017\pi\) | |||||||
\(20\) | −51460.9 | − | 42749.7i | −1.43838 | − | 1.19489i | ||||
\(21\) | 674.066 | + | 1627.34i | 0.0158831 | + | 0.0383452i | ||||
\(22\) | −87088.2 | − | 13184.2i | −1.74373 | − | 0.263982i | ||||
\(23\) | 46492.7 | + | 46492.7i | 0.796778 | + | 0.796778i | 0.982586 | − | 0.185808i | \(-0.0594903\pi\) |
−0.185808 | + | 0.982586i | \(0.559490\pi\) | |||||||
\(24\) | −5564.49 | + | 11497.5i | −0.0821649 | + | 0.169771i | ||||
\(25\) | 137924. | − | 137924.i | 1.76543 | − | 1.76543i | ||||
\(26\) | −25301.7 | + | 18648.1i | −0.282320 | + | 0.208079i | ||||
\(27\) | 35009.6 | − | 14501.4i | 0.342305 | − | 0.141787i | ||||
\(28\) | 24416.1 | + | 7566.06i | 0.210195 | + | 0.0651353i | ||||
\(29\) | −55819.4 | + | 134760.i | −0.425003 | + | 1.02605i | 0.555847 | + | 0.831285i | \(0.312394\pi\) |
−0.980850 | + | 0.194764i | \(0.937606\pi\) | |||||||
\(30\) | −44656.6 | − | 26947.7i | −0.301968 | − | 0.182220i | ||||
\(31\) | 184799. | 1.11412 | 0.557062 | − | 0.830471i | \(-0.311928\pi\) | ||||
0.557062 | + | 0.830471i | \(0.311928\pi\) | |||||||
\(32\) | 76742.6 | + | 168731.i | 0.414011 | + | 0.910272i | ||||
\(33\) | −68669.1 | −0.332631 | ||||||||
\(34\) | 65162.3 | + | 39321.8i | 0.284328 | + | 0.171576i | ||||
\(35\) | −39942.9 | + | 96430.6i | −0.157471 | + | 0.380169i | ||||
\(36\) | 79911.9 | − | 257880.i | 0.285465 | − | 0.921210i | ||||
\(37\) | 203734. | − | 84389.5i | 0.661239 | − | 0.273894i | −0.0267210 | − | 0.999643i | \(-0.508507\pi\) |
0.687960 | + | 0.725749i | \(0.258507\pi\) | |||||||
\(38\) | −192522. | + | 141895.i | −0.569164 | + | 0.419492i | ||||
\(39\) | −17327.2 | + | 17327.2i | −0.0467738 | + | 0.0467738i | ||||
\(40\) | −714911. | + | 248598.i | −1.76621 | + | 0.614168i | ||||
\(41\) | 491764. | + | 491764.i | 1.11433 | + | 1.11433i | 0.992558 | + | 0.121770i | \(0.0388569\pi\) |
0.121770 | + | 0.992558i | \(0.461143\pi\) | |||||||
\(42\) | 19703.7 | + | 2982.92i | 0.0410369 | + | 0.00621254i | ||||
\(43\) | −189516. | − | 457531.i | −0.363501 | − | 0.877568i | −0.994783 | − | 0.102015i | \(-0.967471\pi\) |
0.631282 | − | 0.775553i | \(-0.282529\pi\) | |||||||
\(44\) | −636773. | + | 766529.i | −1.12694 | + | 1.35658i | ||||
\(45\) | 1.01849e6 | + | 421873.i | 1.66615 | + | 0.690141i | ||||
\(46\) | 722126. | − | 178593.i | 1.09386 | − | 0.270528i | ||||
\(47\) | 309952.i | 0.435464i | 0.976009 | + | 0.217732i | \(0.0698659\pi\) | ||||
−0.976009 | + | 0.217732i | \(0.930134\pi\) | |||||||
\(48\) | 78846.1 | + | 121108.i | 0.102905 | + | 0.158063i | ||||
\(49\) | 783663.i | 0.951575i | ||||||||
\(50\) | −529810. | − | 2.14224e6i | −0.599412 | − | 2.42367i | ||||
\(51\) | 54818.1 | + | 22706.4i | 0.0578666 | + | 0.0239691i | ||||
\(52\) | 32741.2 | + | 354094.i | 0.0322911 | + | 0.349226i | ||||
\(53\) | −525171. | − | 1.26787e6i | −0.484546 | − | 1.16980i | −0.957428 | − | 0.288672i | \(-0.906786\pi\) |
0.472882 | − | 0.881126i | \(-0.343214\pi\) | |||||||
\(54\) | 64172.7 | − | 423892.i | 0.0554590 | − | 0.366334i | ||||
\(55\) | −2.87729e6 | − | 2.87729e6i | −2.33192 | − | 2.33192i | ||||
\(56\) | 216011. | − | 192284.i | 0.164368 | − | 0.146314i | ||||
\(57\) | −131844. | + | 131844.i | −0.0942970 | + | 0.0942970i | ||||
\(58\) | 979092. | + | 1.32842e6i | 0.658909 | + | 0.894003i | ||||
\(59\) | 797543. | − | 330353.i | 0.505559 | − | 0.209410i | −0.115301 | − | 0.993331i | \(-0.536783\pi\) |
0.620861 | + | 0.783921i | \(0.286783\pi\) | |||||||
\(60\) | −522067. | + | 275055.i | −0.312031 | + | 0.164395i | ||||
\(61\) | 204787. | − | 494400.i | 0.115518 | − | 0.278884i | −0.855537 | − | 0.517742i | \(-0.826773\pi\) |
0.971055 | + | 0.238857i | \(0.0767728\pi\) | |||||||
\(62\) | 1.08022e6 | − | 1.79009e6i | 0.575626 | − | 0.953902i | ||||
\(63\) | −421205. | −0.212228 | ||||||||
\(64\) | 2.08304e6 | + | 242915.i | 0.993269 | + | 0.115831i | ||||
\(65\) | −1.45205e6 | −0.655820 | ||||||||
\(66\) | −401396. | + | 665176.i | −0.171858 | + | 0.284795i | ||||
\(67\) | −1.18118e6 | + | 2.85162e6i | −0.479793 | + | 1.15832i | 0.479913 | + | 0.877316i | \(0.340668\pi\) |
−0.959706 | + | 0.281007i | \(0.909332\pi\) | |||||||
\(68\) | 761795. | − | 401357.i | 0.293803 | − | 0.154792i | ||||
\(69\) | 535799. | − | 221935.i | 0.196350 | − | 0.0813306i | ||||
\(70\) | 700612. | + | 950586.i | 0.244138 | + | 0.331244i | ||||
\(71\) | −2.14178e6 | + | 2.14178e6i | −0.710184 | + | 0.710184i | −0.966574 | − | 0.256389i | \(-0.917467\pi\) |
0.256389 | + | 0.966574i | \(0.417467\pi\) | |||||||
\(72\) | −2.03089e6 | − | 2.28148e6i | −0.641242 | − | 0.720366i | ||||
\(73\) | 1.27197e6 | + | 1.27197e6i | 0.382691 | + | 0.382691i | 0.872071 | − | 0.489380i | \(-0.162777\pi\) |
−0.489380 | + | 0.872071i | \(0.662777\pi\) | |||||||
\(74\) | 373446. | − | 2.46680e6i | 0.107132 | − | 0.707656i | ||||
\(75\) | −658387. | − | 1.58949e6i | −0.180205 | − | 0.435053i | ||||
\(76\) | 249130. | + | 2.69432e6i | 0.0650995 | + | 0.704048i | ||||
\(77\) | 1.43637e6 | + | 594964.i | 0.358549 | + | 0.148516i | ||||
\(78\) | 66559.4 | + | 269127.i | 0.0158810 | + | 0.0642135i | ||||
\(79\) | − | 1.67355e6i | − | 0.381895i | −0.981600 | − | 0.190948i | \(-0.938844\pi\) | ||
0.981600 | − | 0.190948i | \(-0.0611561\pi\) | |||||||
\(80\) | −1.77082e6 | + | 8.37825e6i | −0.386688 | + | 1.82953i | ||||
\(81\) | 4.27858e6i | 0.894545i | ||||||||
\(82\) | 7.63809e6 | − | 1.88902e6i | 1.52981 | − | 0.378345i | ||||
\(83\) | −5.03997e6 | − | 2.08762e6i | −0.967508 | − | 0.400755i | −0.157724 | − | 0.987483i | \(-0.550416\pi\) |
−0.809784 | + | 0.586728i | \(0.800416\pi\) | |||||||
\(84\) | 144070. | − | 173427.i | 0.0265213 | − | 0.0319256i | ||||
\(85\) | 1.34550e6 | + | 3.24833e6i | 0.237640 | + | 0.573713i | ||||
\(86\) | −5.53974e6 | − | 838657.i | −0.939172 | − | 0.142180i | ||||
\(87\) | 909740. | + | 909740.i | 0.148115 | + | 0.148115i | ||||
\(88\) | 3.70295e6 | + | 1.06489e7i | 0.579241 | + | 1.66576i | ||||
\(89\) | 221712. | − | 221712.i | 0.0333368 | − | 0.0333368i | −0.690242 | − | 0.723579i | \(-0.742496\pi\) |
0.723579 | + | 0.690242i | \(0.242496\pi\) | |||||||
\(90\) | 1.00400e7 | − | 7.39979e6i | 1.45173 | − | 1.06997i | ||||
\(91\) | 512565. | − | 212311.i | 0.0713024 | − | 0.0295344i | ||||
\(92\) | 2.49111e6 | − | 8.03895e6i | 0.333531 | − | 1.07632i | ||||
\(93\) | 623772. | − | 1.50592e6i | 0.0804148 | − | 0.194138i | ||||
\(94\) | 3.00241e6 | + | 1.81178e6i | 0.372840 | + | 0.224988i | ||||
\(95\) | −1.10487e7 | −1.32215 | ||||||||
\(96\) | 1.63402e6 | − | 55834.7i | 0.188499 | − | 0.00644102i | ||||
\(97\) | 9.62678e6 | 1.07098 | 0.535488 | − | 0.844543i | \(-0.320128\pi\) | ||||
0.535488 | + | 0.844543i | \(0.320128\pi\) | |||||||
\(98\) | 7.59110e6 | + | 4.58079e6i | 0.814729 | + | 0.491643i | ||||
\(99\) | 6.28395e6 | − | 1.51708e7i | 0.650893 | − | 1.57139i | ||||
\(100\) | −2.38481e7 | − | 7.39007e6i | −2.38481 | − | 0.739007i | ||||
\(101\) | 728195. | − | 301628.i | 0.0703272 | − | 0.0291305i | −0.347243 | − | 0.937775i | \(-0.612882\pi\) |
0.417570 | + | 0.908645i | \(0.362882\pi\) | |||||||
\(102\) | 540381. | − | 398278.i | 0.0504196 | − | 0.0371609i | ||||
\(103\) | 2.11052e6 | − | 2.11052e6i | 0.190309 | − | 0.190309i | −0.605521 | − | 0.795830i | \(-0.707035\pi\) |
0.795830 | + | 0.605521i | \(0.207035\pi\) | |||||||
\(104\) | 3.62138e6 | + | 1.75265e6i | 0.315688 | + | 0.152785i | ||||
\(105\) | 650986. | + | 650986.i | 0.0548793 | + | 0.0548793i | ||||
\(106\) | −1.53513e7 | − | 2.32402e6i | −1.25191 | − | 0.189526i | ||||
\(107\) | 7.11467e6 | + | 1.71763e7i | 0.561450 | + | 1.35546i | 0.908606 | + | 0.417653i | \(0.137147\pi\) |
−0.347156 | + | 0.937807i | \(0.612853\pi\) | |||||||
\(108\) | −3.73100e6 | − | 3.09942e6i | −0.284998 | − | 0.236754i | ||||
\(109\) | −6.39882e6 | − | 2.65048e6i | −0.473268 | − | 0.196034i | 0.133284 | − | 0.991078i | \(-0.457448\pi\) |
−0.606552 | + | 0.795044i | \(0.707448\pi\) | |||||||
\(110\) | −4.46902e7 | + | 1.10526e7i | −3.20138 | + | 0.791753i | ||||
\(111\) | − | 1.94507e6i | − | 0.134991i | ||||||
\(112\) | −599936. | − | 3.21640e6i | −0.0403498 | − | 0.216325i | ||||
\(113\) | − | 6.22894e6i | − | 0.406106i | −0.979168 | − | 0.203053i | \(-0.934914\pi\) | ||
0.979168 | − | 0.203053i | \(-0.0650864\pi\) | |||||||
\(114\) | 506454. | + | 2.04780e6i | 0.0320165 | + | 0.129456i | ||||
\(115\) | 3.17496e7 | + | 1.31511e7i | 1.94669 | + | 0.806345i | ||||
\(116\) | 1.85912e7 | − | 1.71903e6i | 1.10587 | − | 0.102254i | ||||
\(117\) | −2.24241e6 | − | 5.41366e6i | −0.129439 | − | 0.312493i | ||||
\(118\) | 1.46190e6 | − | 9.65658e6i | 0.0819089 | − | 0.541049i | ||||
\(119\) | −949910. | − | 949910.i | −0.0516736 | − | 0.0516736i | ||||
\(120\) | −387304. | + | 6.66489e6i | −0.0204606 | + | 0.352094i | ||||
\(121\) | −2.90788e7 | + | 2.90788e7i | −1.49220 | + | 1.49220i | ||||
\(122\) | −3.59204e6 | − | 4.87366e6i | −0.179094 | − | 0.242994i | ||||
\(123\) | 5.66726e6 | − | 2.34746e6i | 0.274603 | − | 0.113744i | ||||
\(124\) | −1.10258e7 | − | 2.09274e7i | −0.519317 | − | 0.985690i | ||||
\(125\) | 2.33876e7 | − | 5.64627e7i | 1.07103 | − | 2.58569i | ||||
\(126\) | −2.46210e6 | + | 4.08008e6i | −0.109650 | + | 0.181707i | ||||
\(127\) | −1.27770e7 | −0.553499 | −0.276749 | − | 0.960942i | \(-0.589257\pi\) | ||||
−0.276749 | + | 0.960942i | \(0.589257\pi\) | |||||||
\(128\) | 1.45291e7 | − | 1.87578e7i | 0.612357 | − | 0.790581i | ||||
\(129\) | −4.36809e6 | −0.179155 | ||||||||
\(130\) | −8.48775e6 | + | 1.40655e7i | −0.338837 | + | 0.561506i | ||||
\(131\) | 1.82759e6 | − | 4.41219e6i | 0.0710279 | − | 0.171477i | −0.884379 | − | 0.466770i | \(-0.845418\pi\) |
0.955407 | + | 0.295294i | \(0.0954175\pi\) | |||||||
\(132\) | 4.09704e6 | + | 7.77639e6i | 0.155046 | + | 0.294286i | ||||
\(133\) | 3.90013e6 | − | 1.61549e6i | 0.143747 | − | 0.0595420i | ||||
\(134\) | 2.07183e7 | + | 2.81105e7i | 0.743854 | + | 1.00926i | ||||
\(135\) | 1.40049e7 | − | 1.40049e7i | 0.489905 | − | 0.489905i | ||||
\(136\) | 565149. | − | 9.72533e6i | 0.0192654 | − | 0.331527i | ||||
\(137\) | −1.38701e7 | − | 1.38701e7i | −0.460847 | − | 0.460847i | 0.438086 | − | 0.898933i | \(-0.355657\pi\) |
−0.898933 | + | 0.438086i | \(0.855657\pi\) | |||||||
\(138\) | 982122. | − | 6.48740e6i | 0.0318118 | − | 0.210133i | ||||
\(139\) | 1.82575e7 | + | 4.40776e7i | 0.576620 | + | 1.39208i | 0.895828 | + | 0.444400i | \(0.146583\pi\) |
−0.319208 | + | 0.947685i | \(0.603417\pi\) | |||||||
\(140\) | 1.33033e7 | − | 1.23009e6i | 0.409744 | − | 0.0378869i | ||||
\(141\) | 2.52579e6 | + | 1.04622e6i | 0.0758805 | + | 0.0314307i | ||||
\(142\) | 8.22727e6 | + | 3.32662e7i | 0.241127 | + | 0.974977i | ||||
\(143\) | 2.16288e7i | 0.618524i | ||||||||
\(144\) | −3.39713e7 | + | 6.33646e6i | −0.948075 | + | 0.176839i | ||||
\(145\) | 7.62376e7i | 2.07674i | ||||||||
\(146\) | 1.97564e7 | − | 4.88606e6i | 0.525378 | − | 0.129934i | ||||
\(147\) | 6.38604e6 | + | 2.64518e6i | 0.165814 | + | 0.0686823i | ||||
\(148\) | −2.17121e7 | − | 1.80368e7i | −0.550537 | − | 0.457344i | ||||
\(149\) | −8.81187e6 | − | 2.12737e7i | −0.218231 | − | 0.526856i | 0.776412 | − | 0.630225i | \(-0.217038\pi\) |
−0.994643 | + | 0.103370i | \(0.967038\pi\) | |||||||
\(150\) | −1.92454e7 | − | 2.91354e6i | −0.465593 | − | 0.0704858i | ||||
\(151\) | −3.79656e7 | − | 3.79656e7i | −0.897370 | − | 0.897370i | 0.0978329 | − | 0.995203i | \(-0.468809\pi\) |
−0.995203 | + | 0.0978329i | \(0.968809\pi\) | |||||||
\(152\) | 2.75553e7 | + | 1.33360e7i | 0.636433 | + | 0.308017i | ||||
\(153\) | −1.00329e7 | + | 1.00329e7i | −0.226467 | + | 0.226467i | ||||
\(154\) | 1.41593e7 | − | 1.04359e7i | 0.312406 | − | 0.230254i | ||||
\(155\) | 8.92357e7 | − | 3.69627e7i | 1.92477 | − | 0.797264i | ||||
\(156\) | 2.99601e6 | + | 928406.i | 0.0631841 | + | 0.0195795i | ||||
\(157\) | 2.19236e6 | − | 5.29283e6i | 0.0452130 | − | 0.109154i | −0.899660 | − | 0.436592i | \(-0.856185\pi\) |
0.944873 | + | 0.327438i | \(0.106185\pi\) | |||||||
\(158\) | −1.62112e7 | − | 9.78251e6i | −0.326975 | − | 0.197311i | ||||
\(159\) | −1.21045e7 | −0.238813 | ||||||||
\(160\) | 7.08063e7 | + | 6.61273e7i | 1.36663 | + | 1.27632i | ||||
\(161\) | −1.31303e7 | −0.247962 | ||||||||
\(162\) | 4.14453e7 | + | 2.50099e7i | 0.765901 | + | 0.462177i | ||||
\(163\) | −3.32672e7 | + | 8.03142e7i | −0.601673 | + | 1.45257i | 0.270186 | + | 0.962808i | \(0.412915\pi\) |
−0.871859 | + | 0.489758i | \(0.837085\pi\) | |||||||
\(164\) | 2.63491e7 | − | 8.50298e7i | 0.466457 | − | 1.50528i | ||||
\(165\) | −3.31589e7 | + | 1.37349e7i | −0.574655 | + | 0.238030i | ||||
\(166\) | −4.96826e7 | + | 3.66177e7i | −0.842997 | + | 0.621316i | ||||
\(167\) | −4.46578e7 | + | 4.46578e7i | −0.741976 | + | 0.741976i | −0.972958 | − | 0.230982i | \(-0.925806\pi\) |
0.230982 | + | 0.972958i | \(0.425806\pi\) | |||||||
\(168\) | −837792. | − | 2.40930e6i | −0.0136318 | − | 0.0392020i | ||||
\(169\) | −3.89123e7 | − | 3.89123e7i | −0.620131 | − | 0.620131i | ||||
\(170\) | 3.93305e7 | + | 5.95422e6i | 0.613986 | + | 0.0929508i | ||||
\(171\) | −1.70626e7 | − | 4.11928e7i | −0.260951 | − | 0.629992i | ||||
\(172\) | −4.05056e7 | + | 4.87595e7i | −0.606967 | + | 0.730650i | ||||
\(173\) | −7.80431e7 | − | 3.23265e7i | −1.14597 | − | 0.474676i | −0.272790 | − | 0.962074i | \(-0.587946\pi\) |
−0.873180 | + | 0.487397i | \(0.837946\pi\) | |||||||
\(174\) | 1.41301e7 | − | 3.49460e6i | 0.203340 | − | 0.0502892i | ||||
\(175\) | 3.89521e7i | 0.549412i | ||||||||
\(176\) | 1.24797e8 | + | 2.63771e7i | 1.72548 | + | 0.364697i | ||||
\(177\) | − | 7.61422e6i | − | 0.103209i | ||||||
\(178\) | −851665. | − | 3.44363e6i | −0.0113188 | − | 0.0457664i | ||||
\(179\) | −7.54027e7 | − | 3.12328e7i | −0.982656 | − | 0.407029i | −0.167247 | − | 0.985915i | \(-0.553488\pi\) |
−0.815409 | + | 0.578886i | \(0.803488\pi\) | |||||||
\(180\) | −1.29921e7 | − | 1.40509e8i | −0.166045 | − | 1.79576i | ||||
\(181\) | −2.45629e7 | − | 5.93001e7i | −0.307897 | − | 0.743328i | −0.999773 | − | 0.0213120i | \(-0.993216\pi\) |
0.691876 | − | 0.722016i | \(-0.256784\pi\) | |||||||
\(182\) | 939535. | − | 6.20609e6i | 0.0115522 | − | 0.0763076i | ||||
\(183\) | −3.33760e6 | − | 3.33760e6i | −0.0402584 | − | 0.0402584i | ||||
\(184\) | −6.33093e7 | − | 7.11212e7i | −0.749212 | − | 0.841660i | ||||
\(185\) | 8.15000e7 | − | 8.15000e7i | 0.946360 | − | 0.946360i | ||||
\(186\) | −1.09412e7 | − | 1.48449e7i | −0.124672 | − | 0.169154i | ||||
\(187\) | 4.83851e7 | − | 2.00418e7i | 0.541086 | − | 0.224125i | ||||
\(188\) | 3.51003e7 | − | 1.84929e7i | 0.385264 | − | 0.202979i | ||||
\(189\) | −2.89592e6 | + | 6.99138e6i | −0.0312012 | + | 0.0753262i | ||||
\(190\) | −6.45837e7 | + | 1.07025e8i | −0.683102 | + | 1.13201i | ||||
\(191\) | 7.10470e7 | 0.737783 | 0.368892 | − | 0.929472i | \(-0.379737\pi\) | ||||
0.368892 | + | 0.929472i | \(0.379737\pi\) | |||||||
\(192\) | 9.01060e6 | − | 1.61546e7i | 0.0918754 | − | 0.164719i | ||||
\(193\) | −7.65287e7 | −0.766256 | −0.383128 | − | 0.923695i | \(-0.625153\pi\) | ||||
−0.383128 | + | 0.923695i | \(0.625153\pi\) | |||||||
\(194\) | 5.62720e7 | − | 9.32516e7i | 0.553333 | − | 0.916959i | ||||
\(195\) | −4.90126e6 | + | 1.18327e7i | −0.0473354 | + | 0.114278i | ||||
\(196\) | 8.87454e7 | − | 4.67561e7i | 0.841879 | − | 0.443550i | ||||
\(197\) | −6.92775e7 | + | 2.86957e7i | −0.645595 | + | 0.267414i | −0.681363 | − | 0.731946i | \(-0.738612\pi\) |
0.0357677 | + | 0.999360i | \(0.488612\pi\) | |||||||
\(198\) | −1.10223e8 | − | 1.49549e8i | −1.00912 | − | 1.36917i | ||||
\(199\) | 1.11038e8 | − | 1.11038e8i | 0.998821 | − | 0.998821i | −0.00117819 | − | 0.999999i | \(-0.500375\pi\) |
0.999999 | + | 0.00117819i | \(0.000375031\pi\) | |||||||
\(200\) | −2.10986e8 | + | 1.87812e8i | −1.86487 | + | 1.66004i | ||||
\(201\) | 1.92508e7 | + | 1.92508e7i | 0.167210 | + | 0.167210i | ||||
\(202\) | 1.33479e6 | − | 8.81692e6i | 0.0113942 | − | 0.0752640i | ||||
\(203\) | −1.11471e7 | − | 2.69114e7i | −0.0935244 | − | 0.225788i | ||||
\(204\) | −699271. | − | 7.56257e6i | −0.00576687 | − | 0.0623683i | ||||
\(205\) | 3.35823e8 | + | 1.39102e8i | 2.72253 | + | 1.12771i | ||||
\(206\) | −8.10719e6 | − | 3.27807e7i | −0.0646152 | − | 0.261266i | ||||
\(207\) | 1.38681e8i | 1.08673i | ||||||||
\(208\) | 3.81457e7 | − | 2.48343e7i | 0.293916 | − | 0.191350i | ||||
\(209\) | 1.64575e8i | 1.24696i | ||||||||
\(210\) | 1.01111e7 | − | 2.50064e6i | 0.0753412 | − | 0.0186331i | ||||
\(211\) | −1.15722e8 | − | 4.79335e7i | −0.848059 | − | 0.351277i | −0.0840327 | − | 0.996463i | \(-0.526780\pi\) |
−0.764026 | + | 0.645186i | \(0.776780\pi\) | |||||||
\(212\) | −1.12246e8 | + | 1.35118e8i | −0.809087 | + | 0.973955i | ||||
\(213\) | 1.02239e7 | + | 2.46827e7i | 0.0724916 | + | 0.175010i | ||||
\(214\) | 2.07969e8 | + | 3.14843e7i | 1.45061 | + | 0.219607i | ||||
\(215\) | −1.83026e8 | − | 1.83026e8i | −1.25597 | − | 1.25597i | ||||
\(216\) | −5.18322e7 | + | 1.80237e7i | −0.349954 | + | 0.121690i | ||||
\(217\) | −2.60952e7 | + | 2.60952e7i | −0.173361 | + | 0.173361i | ||||
\(218\) | −6.30777e7 | + | 4.64903e7i | −0.412361 | + | 0.303924i | ||||
\(219\) | 1.46587e7 | − | 6.07183e6i | 0.0943064 | − | 0.0390630i | ||||
\(220\) | −1.54167e8 | + | 4.97506e8i | −0.976142 | + | 3.15006i | ||||
\(221\) | 7.15186e6 | − | 1.72661e7i | 0.0445703 | − | 0.107602i | ||||
\(222\) | −1.88413e7 | − | 1.13696e7i | −0.115578 | − | 0.0697447i | ||||
\(223\) | −1.35075e8 | −0.815656 | −0.407828 | − | 0.913059i | \(-0.633714\pi\) | ||||
−0.407828 | + | 0.913059i | \(0.633714\pi\) | |||||||
\(224\) | −3.46630e7 | − | 1.29896e7i | −0.206062 | − | 0.0772197i | ||||
\(225\) | 4.11408e8 | 2.40788 | ||||||||
\(226\) | −6.03378e7 | − | 3.64104e7i | −0.347704 | − | 0.209820i | ||||
\(227\) | 5.51550e6 | − | 1.33156e7i | 0.0312964 | − | 0.0755561i | −0.907459 | − | 0.420141i | \(-0.861980\pi\) |
0.938755 | + | 0.344585i | \(0.111980\pi\) | |||||||
\(228\) | 2.27968e7 | + | 7.06429e6i | 0.127380 | + | 0.0394727i | ||||
\(229\) | 3.43654e7 | − | 1.42346e7i | 0.189102 | − | 0.0783287i | −0.286123 | − | 0.958193i | \(-0.592367\pi\) |
0.475225 | + | 0.879864i | \(0.342367\pi\) | |||||||
\(230\) | 3.12979e8 | − | 2.30675e8i | 1.69616 | − | 1.25013i | ||||
\(231\) | 9.69667e6 | − | 9.69667e6i | 0.0517584 | − | 0.0517584i | ||||
\(232\) | 9.20204e7 | − | 1.90135e8i | 0.483812 | − | 0.999664i | ||||
\(233\) | −2.67221e7 | − | 2.67221e7i | −0.138397 | − | 0.138397i | 0.634514 | − | 0.772911i | \(-0.281200\pi\) |
−0.772911 | + | 0.634514i | \(0.781200\pi\) | |||||||
\(234\) | −6.55481e7 | − | 9.92327e6i | −0.334429 | − | 0.0506290i | ||||
\(235\) | 6.19952e7 | + | 1.49670e8i | 0.311617 | + | 0.752309i | ||||
\(236\) | −8.49949e7 | − | 7.06072e7i | −0.420921 | − | 0.349669i | ||||
\(237\) | −1.36377e7 | − | 5.64892e6i | −0.0665460 | − | 0.0275642i | ||||
\(238\) | −1.47540e7 | + | 3.64891e6i | −0.0709401 | + | 0.0175446i | ||||
\(239\) | − | 4.44632e7i | − | 0.210673i | −0.994437 | − | 0.105336i | \(-0.966408\pi\) | ||
0.994437 | − | 0.105336i | \(-0.0335919\pi\) | |||||||
\(240\) | 6.22968e7 | + | 4.27104e7i | 0.290888 | + | 0.199432i | ||||
\(241\) | 1.75636e7i | 0.0808266i | 0.999183 | + | 0.0404133i | \(0.0128674\pi\) | ||||
−0.999183 | + | 0.0404133i | \(0.987133\pi\) | |||||||
\(242\) | 1.11701e8 | + | 4.51653e8i | 0.506644 | + | 2.04857i | ||||
\(243\) | 1.11432e8 | + | 4.61566e7i | 0.498181 | + | 0.206353i | ||||
\(244\) | −6.82063e7 | + | 6.30668e6i | −0.300580 | + | 0.0277930i | ||||
\(245\) | 1.56745e8 | + | 3.78415e8i | 0.680944 | + | 1.64394i | ||||
\(246\) | 1.03881e7 | − | 6.86187e7i | 0.0444902 | − | 0.293880i | ||||
\(247\) | 4.15270e7 | + | 4.15270e7i | 0.175344 | + | 0.175344i | ||||
\(248\) | −2.67167e8 | − | 1.55253e7i | −1.11225 | − | 0.0646339i | ||||
\(249\) | −3.40239e7 | + | 3.40239e7i | −0.139665 | + | 0.139665i | ||||
\(250\) | −4.10227e8 | − | 5.56593e8i | −1.66048 | − | 2.25293i | ||||
\(251\) | 1.89285e8 | − | 7.84042e7i | 0.755539 | − | 0.312955i | 0.0285400 | − | 0.999593i | \(-0.490914\pi\) |
0.727000 | + | 0.686638i | \(0.240914\pi\) | |||||||
\(252\) | 2.51306e7 | + | 4.76991e7i | 0.0989239 | + | 0.187762i | ||||
\(253\) | 1.95891e8 | − | 4.72923e8i | 0.760488 | − | 1.83598i | ||||
\(254\) | −7.46863e7 | + | 1.23767e8i | −0.285972 | + | 0.473900i | ||||
\(255\) | 3.10122e7 | 0.117123 | ||||||||
\(256\) | −9.67725e7 | − | 2.50385e8i | −0.360506 | − | 0.932757i | ||||
\(257\) | 1.49895e8 | 0.550834 | 0.275417 | − | 0.961325i | \(-0.411184\pi\) | ||||
0.275417 | + | 0.961325i | \(0.411184\pi\) | |||||||
\(258\) | −2.55331e7 | + | 4.23123e7i | −0.0925623 | + | 0.153390i | ||||
\(259\) | −1.68525e7 | + | 4.06856e7i | −0.0602720 | + | 0.145509i | ||||
\(260\) | 8.66343e7 | + | 1.64436e8i | 0.305691 | + | 0.580217i | ||||
\(261\) | −2.84236e8 | + | 1.17734e8i | −0.989548 | + | 0.409884i | ||||
\(262\) | −3.20566e7 | − | 4.34941e7i | −0.110119 | − | 0.149409i | ||||
\(263\) | 2.39703e8 | − | 2.39703e8i | 0.812508 | − | 0.812508i | −0.172501 | − | 0.985009i | \(-0.555185\pi\) |
0.985009 | + | 0.172501i | \(0.0551848\pi\) | |||||||
\(264\) | 9.92761e7 | + | 5.76903e6i | 0.332071 | + | 0.0192970i | ||||
\(265\) | −5.07189e8 | − | 5.07189e8i | −1.67421 | − | 1.67421i | ||||
\(266\) | 7.14897e6 | − | 4.72225e7i | 0.0232894 | − | 0.153838i | ||||
\(267\) | −1.05835e6 | − | 2.55509e6i | −0.00340283 | − | 0.00821516i | ||||
\(268\) | 3.93403e8 | − | 3.63759e7i | 1.24843 | − | 0.115436i | ||||
\(269\) | −2.73966e8 | − | 1.13480e8i | −0.858151 | − | 0.355458i | −0.0901668 | − | 0.995927i | \(-0.528740\pi\) |
−0.767984 | + | 0.640469i | \(0.778740\pi\) | |||||||
\(270\) | −5.37973e7 | − | 2.17525e8i | −0.166336 | − | 0.672567i | ||||
\(271\) | 4.53786e8i | 1.38503i | 0.721405 | + | 0.692513i | \(0.243497\pi\) | ||||
−0.721405 | + | 0.692513i | \(0.756503\pi\) | |||||||
\(272\) | −9.09027e7 | − | 6.23225e7i | −0.273896 | − | 0.187782i | ||||
\(273\) | − | 4.89351e6i | − | 0.0145563i | ||||||
\(274\) | −2.15431e8 | + | 5.32794e7i | −0.632675 | + | 0.156470i | ||||
\(275\) | −1.40296e9 | − | 5.81125e8i | −4.06800 | − | 1.68502i | ||||
\(276\) | −5.71005e7 | − | 4.74347e7i | −0.163478 | − | 0.135805i | ||||
\(277\) | 2.29919e8 | + | 5.55073e8i | 0.649973 | + | 1.56917i | 0.812815 | + | 0.582522i | \(0.197934\pi\) |
−0.162842 | + | 0.986652i | \(0.552066\pi\) | |||||||
\(278\) | 5.33687e8 | + | 8.07944e7i | 1.48981 | + | 0.225541i | ||||
\(279\) | 2.75615e8 | + | 2.75615e8i | 0.759780 | + | 0.759780i | ||||
\(280\) | 6.58474e7 | − | 1.36056e8i | 0.179261 | − | 0.370393i | ||||
\(281\) | 1.77116e8 | − | 1.77116e8i | 0.476196 | − | 0.476196i | −0.427717 | − | 0.903913i | \(-0.640682\pi\) |
0.903913 | + | 0.427717i | \(0.140682\pi\) | |||||||
\(282\) | 2.48985e7 | − | 1.83510e7i | 0.0661152 | − | 0.0487290i | ||||
\(283\) | −3.14752e8 | + | 1.30374e8i | −0.825498 | + | 0.341932i | −0.755119 | − | 0.655588i | \(-0.772421\pi\) |
−0.0703788 | + | 0.997520i | \(0.522421\pi\) | |||||||
\(284\) | 3.70331e8 | + | 1.14758e8i | 0.959347 | + | 0.297283i | ||||
\(285\) | −3.72939e7 | + | 9.00355e7i | −0.0954292 | + | 0.230386i | ||||
\(286\) | 2.09511e8 | + | 1.26428e8i | 0.529574 | + | 0.319568i | ||||
\(287\) | −1.38883e8 | −0.346785 | ||||||||
\(288\) | −1.37195e8 | + | 3.66108e8i | −0.338427 | + | 0.903098i | ||||
\(289\) | 3.65086e8 | 0.889719 | ||||||||
\(290\) | 7.38489e8 | + | 4.45636e8i | 1.77808 | + | 1.07297i | ||||
\(291\) | 3.24943e7 | − | 7.84482e7i | 0.0773004 | − | 0.186620i | ||||
\(292\) | 6.81533e7 | − | 2.19934e8i | 0.160194 | − | 0.516955i | ||||
\(293\) | −7.66018e8 | + | 3.17295e8i | −1.77911 | + | 0.736930i | −0.786209 | + | 0.617961i | \(0.787959\pi\) |
−0.992898 | + | 0.118970i | \(0.962041\pi\) | |||||||
\(294\) | 6.29517e7 | − | 4.63975e7i | 0.144475 | − | 0.106483i | ||||
\(295\) | 3.19042e8 | − | 3.19042e8i | 0.723553 | − | 0.723553i | ||||
\(296\) | −3.01632e8 | + | 1.04887e8i | −0.676015 | + | 0.235072i | ||||
\(297\) | −2.08608e8 | − | 2.08608e8i | −0.462044 | − | 0.462044i | ||||
\(298\) | −2.57580e8 | − | 3.89949e7i | −0.563840 | − | 0.0853593i | ||||
\(299\) | −6.99032e7 | − | 1.68761e8i | −0.151233 | − | 0.365110i | ||||
\(300\) | −1.40719e8 | + | 1.69393e8i | −0.300903 | + | 0.362219i | ||||
\(301\) | 9.13685e7 | + | 3.78461e7i | 0.193114 | + | 0.0799904i | ||||
\(302\) | −5.89684e8 | + | 1.45838e8i | −1.23196 | + | 0.304682i | ||||
\(303\) | − | 6.95215e6i | − | 0.0143572i | ||||||
\(304\) | 2.90253e8 | − | 1.88965e8i | 0.592541 | − | 0.385766i | ||||
\(305\) | − | 2.79696e8i | − | 0.564466i | ||||||
\(306\) | 3.85394e7 | + | 1.55831e8i | 0.0768918 | + | 0.310905i | ||||
\(307\) | 4.86790e8 | + | 2.01635e8i | 0.960190 | + | 0.397724i | 0.807051 | − | 0.590481i | \(-0.201062\pi\) |
0.153138 | + | 0.988205i | \(0.451062\pi\) | |||||||
\(308\) | −1.83227e7 | − | 1.98158e8i | −0.0357323 | − | 0.386442i | ||||
\(309\) | −1.00747e7 | − | 2.43224e7i | −0.0194257 | − | 0.0468978i | ||||
\(310\) | 1.63570e8 | − | 1.08046e9i | 0.311844 | − | 2.05988i | ||||
\(311\) | −6.27067e7 | − | 6.27067e7i | −0.118210 | − | 0.118210i | 0.645528 | − | 0.763737i | \(-0.276638\pi\) |
−0.763737 | + | 0.645528i | \(0.776638\pi\) | |||||||
\(312\) | 2.65059e7 | − | 2.35946e7i | 0.0494086 | − | 0.0439816i | ||||
\(313\) | −4.49748e7 | + | 4.49748e7i | −0.0829018 | + | 0.0829018i | −0.747342 | − | 0.664440i | \(-0.768670\pi\) |
0.664440 | + | 0.747342i | \(0.268670\pi\) | |||||||
\(314\) | −3.84548e7 | − | 5.21752e7i | −0.0700966 | − | 0.0951066i | ||||
\(315\) | −2.03392e8 | + | 8.42476e7i | −0.366645 | + | 0.151869i | ||||
\(316\) | −1.89520e8 | + | 9.98500e7i | −0.337871 | + | 0.178009i | ||||
\(317\) | −2.45055e8 | + | 5.91615e8i | −0.432072 | + | 1.04311i | 0.546547 | + | 0.837429i | \(0.315942\pi\) |
−0.978618 | + | 0.205685i | \(0.934058\pi\) | |||||||
\(318\) | −7.07553e7 | + | 1.17253e8i | −0.123385 | + | 0.204469i | ||||
\(319\) | 1.13559e9 | 1.95863 | ||||||||
\(320\) | 1.05444e9 | − | 2.99340e8i | 1.79886 | − | 0.510670i | ||||
\(321\) | 1.63984e8 | 0.276716 | ||||||||
\(322\) | −7.67515e7 | + | 1.27189e8i | −0.128112 | + | 0.212303i | ||||
\(323\) | 5.44189e7 | − | 1.31379e8i | 0.0898547 | − | 0.216928i | ||||
\(324\) | 4.84525e8 | − | 2.55275e8i | 0.791423 | − | 0.416967i | ||||
\(325\) | −5.00643e8 | + | 2.07373e8i | −0.808977 | + | 0.335089i | ||||
\(326\) | 5.83519e8 | + | 7.91715e8i | 0.932811 | + | 1.26563i | ||||
\(327\) | −4.31972e7 | + | 4.31972e7i | −0.0683186 | + | 0.0683186i | ||||
\(328\) | −6.69637e8 | − | 7.52265e8i | −1.04781 | − | 1.17710i | ||||
\(329\) | −4.37679e7 | − | 4.37679e7i | −0.0677595 | − | 0.0677595i | ||||
\(330\) | −6.07805e7 | + | 4.01485e8i | −0.0931034 | + | 0.614994i | ||||
\(331\) | 1.86901e8 | + | 4.51220e8i | 0.283279 | + | 0.683896i | 0.999908 | − | 0.0135583i | \(-0.00431588\pi\) |
−0.716629 | + | 0.697455i | \(0.754316\pi\) | |||||||
\(332\) | 6.42910e7 | + | 6.95303e8i | 0.0964199 | + | 1.04278i | ||||
\(333\) | 4.29717e8 | + | 1.77995e8i | 0.637716 | + | 0.264151i | ||||
\(334\) | 1.71545e8 | + | 6.93627e8i | 0.251922 | + | 1.01862i | ||||
\(335\) | 1.61324e9i | 2.34446i | ||||||||
\(336\) | −2.82353e7 | − | 5.96780e6i | −0.0406074 | − | 0.00858276i | ||||
\(337\) | − | 2.39548e8i | − | 0.340948i | −0.985362 | − | 0.170474i | \(-0.945470\pi\) | ||
0.985362 | − | 0.170474i | \(-0.0545299\pi\) | |||||||
\(338\) | −6.04388e8 | + | 1.49475e8i | −0.851348 | + | 0.210552i | ||||
\(339\) | −5.07594e7 | − | 2.10252e7i | −0.0707648 | − | 0.0293118i | ||||
\(340\) | 2.87578e8 | − | 3.46178e8i | 0.396807 | − | 0.477664i | ||||
\(341\) | −5.50572e8 | − | 1.32920e9i | −0.751924 | − | 1.81531i | ||||
\(342\) | −4.98759e8 | − | 7.55067e7i | −0.674216 | − | 0.102069i | ||||
\(343\) | −2.26951e8 | − | 2.26951e8i | −0.303671 | − | 0.303671i | ||||
\(344\) | 2.35547e8 | + | 6.77381e8i | 0.311978 | + | 0.897178i | ||||
\(345\) | 2.14336e8 | − | 2.14336e8i | 0.281014 | − | 0.281014i | ||||
\(346\) | −7.69327e8 | + | 5.67018e8i | −0.998492 | + | 0.735920i | ||||
\(347\) | 1.25659e9 | − | 5.20496e8i | 1.61451 | − | 0.668751i | 0.621136 | − | 0.783703i | \(-0.286671\pi\) |
0.993371 | + | 0.114952i | \(0.0366715\pi\) | |||||||
\(348\) | 4.87445e7 | − | 1.57301e8i | 0.0620010 | − | 0.200080i | ||||
\(349\) | 4.16411e8 | − | 1.00530e9i | 0.524364 | − | 1.26593i | −0.410804 | − | 0.911724i | \(-0.634752\pi\) |
0.935168 | − | 0.354203i | \(-0.115248\pi\) | |||||||
\(350\) | 3.77317e8 | + | 2.27689e8i | 0.470400 | + | 0.283860i | ||||
\(351\) | −1.05276e8 | −0.129943 | ||||||||
\(352\) | 9.84991e8 | − | 1.05469e9i | 1.20374 | − | 1.28891i | ||||
\(353\) | −1.52792e9 | −1.84879 | −0.924397 | − | 0.381431i | \(-0.875431\pi\) | ||||
−0.924397 | + | 0.381431i | \(0.875431\pi\) | |||||||
\(354\) | −7.37565e7 | − | 4.45079e7i | −0.0883668 | − | 0.0533243i | ||||
\(355\) | −6.05834e8 | + | 1.46261e9i | −0.718711 | + | 1.73512i | ||||
\(356\) | −3.83357e7 | − | 1.18795e7i | −0.0450327 | − | 0.0139548i | ||||
\(357\) | −1.09471e7 | + | 4.53444e6i | −0.0127339 | + | 0.00527455i | ||||
\(358\) | −7.43298e8 | + | 5.47835e8i | −0.856195 | + | 0.631043i | ||||
\(359\) | 3.13976e8 | − | 3.13976e8i | 0.358150 | − | 0.358150i | −0.504980 | − | 0.863131i | \(-0.668500\pi\) |
0.863131 | + | 0.504980i | \(0.168500\pi\) | |||||||
\(360\) | −1.43701e9 | − | 6.95473e8i | −1.62330 | − | 0.785637i | ||||
\(361\) | −3.16081e8 | − | 3.16081e8i | −0.353609 | − | 0.353609i | ||||
\(362\) | −7.18000e8 | − | 1.08697e8i | −0.795508 | − | 0.120431i | ||||
\(363\) | 1.38809e8 | + | 3.35115e8i | 0.152316 | + | 0.367722i | ||||
\(364\) | −5.46245e7 | − | 4.53778e7i | −0.0593653 | − | 0.0493161i | ||||
\(365\) | 8.68625e8 | + | 3.59796e8i | 0.934991 | + | 0.387286i | ||||
\(366\) | −5.18398e7 | + | 1.28208e7i | −0.0552687 | + | 0.0136688i | ||||
\(367\) | − | 9.29519e8i | − | 0.981583i | −0.871277 | − | 0.490792i | \(-0.836708\pi\) | ||
0.871277 | − | 0.490792i | \(-0.163292\pi\) | |||||||
\(368\) | −1.05899e9 | + | 1.97528e8i | −1.10771 | + | 0.206615i | ||||
\(369\) | 1.46686e9i | 1.51984i | ||||||||
\(370\) | −3.13068e8 | − | 1.26586e9i | −0.321316 | − | 1.29921i | ||||
\(371\) | 2.53193e8 | + | 1.04876e8i | 0.257421 | + | 0.106627i | ||||
\(372\) | −2.07753e8 | + | 1.92098e7i | −0.209241 | + | 0.0193474i | ||||
\(373\) | −6.21107e7 | − | 1.49949e8i | −0.0619706 | − | 0.149610i | 0.889861 | − | 0.456232i | \(-0.150801\pi\) |
−0.951831 | + | 0.306622i | \(0.900801\pi\) | |||||||
\(374\) | 8.86903e7 | − | 5.85843e8i | 0.0876648 | − | 0.579069i | ||||
\(375\) | −3.81169e8 | − | 3.81169e8i | −0.373257 | − | 0.373257i | ||||
\(376\) | 2.60397e7 | − | 4.48103e8i | 0.0252627 | − | 0.434731i | ||||
\(377\) | 2.86542e8 | − | 2.86542e8i | 0.275419 | − | 0.275419i | ||||
\(378\) | 5.07955e7 | + | 6.89190e7i | 0.0483731 | + | 0.0656323i | ||||
\(379\) | 1.24582e9 | − | 5.16034e8i | 1.17549 | − | 0.486902i | 0.292483 | − | 0.956271i | \(-0.405519\pi\) |
0.883002 | + | 0.469369i | \(0.155519\pi\) | |||||||
\(380\) | 6.59206e8 | + | 1.25120e9i | 0.616280 | + | 1.16973i | ||||
\(381\) | −4.31277e7 | + | 1.04119e8i | −0.0399502 | + | 0.0964482i | ||||
\(382\) | 4.15295e8 | − | 6.88209e8i | 0.381184 | − | 0.631682i | ||||
\(383\) | 1.16962e9 | 1.06377 | 0.531887 | − | 0.846815i | \(-0.321483\pi\) | ||||
0.531887 | + | 0.846815i | \(0.321483\pi\) | |||||||
\(384\) | −1.03815e8 | − | 1.81712e8i | −0.0935619 | − | 0.163767i | ||||
\(385\) | 8.12596e8 | 0.725708 | ||||||||
\(386\) | −4.47338e8 | + | 7.41309e8i | −0.395895 | + | 0.656060i | ||||
\(387\) | 3.99726e8 | − | 9.65025e8i | 0.350570 | − | 0.846350i | ||||
\(388\) | −5.74368e8 | − | 1.09018e9i | −0.499205 | − | 0.947515i | ||||
\(389\) | 1.41462e9 | − | 5.85956e8i | 1.21848 | − | 0.504709i | 0.321551 | − | 0.946892i | \(-0.395796\pi\) |
0.896925 | + | 0.442183i | \(0.145796\pi\) | |||||||
\(390\) | 8.59698e7 | + | 1.16643e8i | 0.0733871 | + | 0.0995711i | ||||
\(391\) | −3.12757e8 | + | 3.12757e8i | −0.264599 | + | 0.264599i | ||||
\(392\) | 6.58371e7 | − | 1.13295e9i | 0.0552039 | − | 0.949973i | ||||
\(393\) | −2.97859e7 | − | 2.97859e7i | −0.0247535 | − | 0.0247535i | ||||
\(394\) | −1.26986e8 | + | 8.38805e8i | −0.104597 | + | 0.690914i | ||||
\(395\) | −3.34736e8 | − | 8.08124e8i | −0.273283 | − | 0.659763i | ||||
\(396\) | −2.09293e9 | + | 1.93522e8i | −1.69364 | + | 0.156602i | ||||
\(397\) | −1.21161e9 | − | 5.01866e8i | −0.971844 | − | 0.402551i | −0.160446 | − | 0.987045i | \(-0.551293\pi\) |
−0.811398 | + | 0.584494i | \(0.801293\pi\) | |||||||
\(398\) | −4.26534e8 | − | 1.72465e9i | −0.339128 | − | 1.37123i | ||||
\(399\) | − | 3.72350e7i | − | 0.0293458i | ||||||
\(400\) | 5.85981e8 | + | 3.14158e9i | 0.457798 | + | 2.45436i | ||||
\(401\) | − | 3.11173e8i | − | 0.240989i | −0.992714 | − | 0.120495i | \(-0.961552\pi\) | ||
0.992714 | − | 0.120495i | \(-0.0384480\pi\) | |||||||
\(402\) | 2.99004e8 | − | 7.39483e7i | 0.229554 | − | 0.0567724i | ||||
\(403\) | −4.74321e8 | − | 1.96470e8i | −0.360998 | − | 0.149530i | ||||
\(404\) | −7.76044e7 | − | 6.44677e7i | −0.0585533 | − | 0.0486416i | ||||
\(405\) | 8.55782e8 | + | 2.06604e9i | 0.640134 | + | 1.54542i | ||||
\(406\) | −3.25841e8 | − | 4.93288e7i | −0.241638 | − | 0.0365813i | ||||
\(407\) | −1.21397e9 | − | 1.21397e9i | −0.892542 | − | 0.892542i | ||||
\(408\) | −7.73437e7 | − | 3.74324e7i | −0.0563786 | − | 0.0272858i | ||||
\(409\) | 3.01713e8 | − | 3.01713e8i | 0.218053 | − | 0.218053i | −0.589624 | − | 0.807678i | \(-0.700724\pi\) |
0.807678 | + | 0.589624i | \(0.200724\pi\) | |||||||
\(410\) | 3.31045e9 | − | 2.43991e9i | 2.37216 | − | 1.74836i | ||||
\(411\) | −1.59844e8 | + | 6.62095e7i | −0.113566 | + | 0.0470407i | ||||
\(412\) | −3.64926e8 | − | 1.13083e8i | −0.257078 | − | 0.0796633i | ||||
\(413\) | −6.59712e7 | + | 1.59269e8i | −0.0460818 | + | 0.111251i | ||||
\(414\) | 1.34336e9 | + | 8.10642e8i | 0.930447 | + | 0.561472i | ||||
\(415\) | −2.85126e9 | −1.95825 | ||||||||
\(416\) | −1.75863e7 | − | 5.14670e8i | −0.0119770 | − | 0.350512i | ||||
\(417\) | 4.20813e8 | 0.284193 | ||||||||
\(418\) | 1.59418e9 | + | 9.61999e8i | 1.06763 | + | 0.644255i | ||||
\(419\) | −9.84343e8 | + | 2.37642e9i | −0.653729 | + | 1.57824i | 0.153596 | + | 0.988134i | \(0.450914\pi\) |
−0.807325 | + | 0.590107i | \(0.799086\pi\) | |||||||
\(420\) | 3.48803e7 | − | 1.12560e8i | 0.0229725 | − | 0.0741333i | ||||
\(421\) | −7.05921e8 | + | 2.92402e8i | −0.461072 | + | 0.190982i | −0.601114 | − | 0.799163i | \(-0.705276\pi\) |
0.140042 | + | 0.990146i | \(0.455276\pi\) | |||||||
\(422\) | −1.14075e9 | + | 8.40770e8i | −0.738919 | + | 0.544607i | ||||
\(423\) | −4.62272e8 | + | 4.62272e8i | −0.296966 | + | 0.296966i | ||||
\(424\) | 6.52731e8 | + | 1.87711e9i | 0.415866 | + | 1.19594i | ||||
\(425\) | 9.27815e8 | + | 9.27815e8i | 0.586274 | + | 0.586274i | ||||
\(426\) | 2.98856e8 | + | 4.52435e7i | 0.187296 | + | 0.0283545i | ||||
\(427\) | 4.08958e7 | + | 9.87312e7i | 0.0254203 | + | 0.0613701i | ||||
\(428\) | 1.52063e9 | − | 1.83049e9i | 0.937500 | − | 1.12854i | ||||
\(429\) | 1.76252e8 | + | 7.30060e7i | 0.107779 | + | 0.0446435i | ||||
\(430\) | −2.84277e9 | + | 7.03063e8i | −1.72426 | + | 0.426437i | ||||
\(431\) | − | 1.20805e8i | − | 0.0726799i | −0.999339 | − | 0.0363399i | \(-0.988430\pi\) | ||
0.999339 | − | 0.0363399i | \(-0.0115699\pi\) | |||||||
\(432\) | −1.28388e8 | + | 6.07437e8i | −0.0766178 | + | 0.362500i | ||||
\(433\) | 1.22289e9i | 0.723901i | 0.932197 | + | 0.361950i | \(0.117889\pi\) | ||||
−0.932197 | + | 0.361950i | \(0.882111\pi\) | |||||||
\(434\) | 1.00240e8 | + | 4.05312e8i | 0.0588609 | + | 0.237999i | ||||
\(435\) | 6.21257e8 | + | 2.57333e8i | 0.361875 | + | 0.149894i | ||||
\(436\) | 8.16247e7 | + | 8.82766e8i | 0.0471649 | + | 0.510085i | ||||
\(437\) | −5.31897e8 | − | 1.28411e9i | −0.304890 | − | 0.736069i | ||||
\(438\) | 2.68695e7 | − | 1.77486e8i | 0.0152792 | − | 0.100926i | ||||
\(439\) | 1.78280e9 | + | 1.78280e9i | 1.00572 | + | 1.00572i | 0.999984 | + | 0.00573775i | \(0.00182639\pi\) |
0.00573775 | + | 0.999984i | \(0.498174\pi\) | |||||||
\(440\) | 3.91802e9 | + | 4.40147e9i | 2.19271 | + | 2.46328i | ||||
\(441\) | −1.16878e9 | + | 1.16878e9i | −0.648929 | + | 0.648929i | ||||
\(442\) | −1.25446e8 | − | 1.70204e8i | −0.0691002 | − | 0.0937546i | ||||
\(443\) | −1.28845e9 | + | 5.33695e8i | −0.704135 | + | 0.291662i | −0.705875 | − | 0.708336i | \(-0.749446\pi\) |
0.00174038 | + | 0.999998i | \(0.499446\pi\) | |||||||
\(444\) | −2.20268e8 | + | 1.16050e8i | −0.119429 | + | 0.0629222i | ||||
\(445\) | 6.27143e7 | − | 1.51406e8i | 0.0337370 | − | 0.0814484i | ||||
\(446\) | −7.89560e8 | + | 1.30842e9i | −0.421418 | + | 0.698356i | ||||
\(447\) | −2.03102e8 | −0.107557 | ||||||||
\(448\) | −3.28444e8 | + | 2.59841e8i | −0.172579 | + | 0.136532i | ||||
\(449\) | 9.61826e8 | 0.501458 | 0.250729 | − | 0.968057i | \(-0.419330\pi\) | ||||
0.250729 | + | 0.968057i | \(0.419330\pi\) | |||||||
\(450\) | 2.40483e9 | − | 3.98518e9i | 1.24406 | − | 2.06160i | ||||
\(451\) | 2.07198e9 | − | 5.00221e9i | 1.06358 | − | 2.56770i | ||||
\(452\) | −7.05392e8 | + | 3.71641e8i | −0.359291 | + | 0.189295i | ||||
\(453\) | −4.37530e8 | + | 1.81231e8i | −0.221138 | + | 0.0915985i | ||||
\(454\) | −9.67437e7 | − | 1.31261e8i | −0.0485207 | − | 0.0658326i | ||||
\(455\) | 2.05042e8 | − | 2.05042e8i | 0.102047 | − | 0.102047i | ||||
\(456\) | 2.01685e8 | − | 1.79532e8i | 0.0996087 | − | 0.0886677i | ||||
\(457\) | 4.19740e8 | + | 4.19740e8i | 0.205719 | + | 0.205719i | 0.802445 | − | 0.596726i | \(-0.203532\pi\) |
−0.596726 | + | 0.802445i | \(0.703532\pi\) | |||||||
\(458\) | 6.29919e7 | − | 4.16093e8i | 0.0306377 | − | 0.202377i | ||||
\(459\) | 9.75512e7 | + | 2.35509e8i | 0.0470856 | + | 0.113675i | ||||
\(460\) | −4.05005e8 | − | 4.38011e9i | −0.194003 | − | 2.09813i | ||||
\(461\) | −3.85794e8 | − | 1.59801e8i | −0.183401 | − | 0.0759673i | 0.289093 | − | 0.957301i | \(-0.406646\pi\) |
−0.472494 | + | 0.881334i | \(0.656646\pi\) | |||||||
\(462\) | −3.72480e7 | − | 1.50609e8i | −0.0175734 | − | 0.0710566i | ||||
\(463\) | 4.27790e8i | 0.200308i | 0.994972 | + | 0.100154i | \(0.0319335\pi\) | ||||
−0.994972 | + | 0.100154i | \(0.968067\pi\) | |||||||
\(464\) | −1.30388e9 | − | 2.00278e9i | −0.605935 | − | 0.930723i | ||||
\(465\) | − | 8.51942e8i | − | 0.392939i | ||||||
\(466\) | −4.15049e8 | + | 1.02648e8i | −0.189998 | + | 0.0469895i | ||||
\(467\) | −3.39235e8 | − | 1.40516e8i | −0.154132 | − | 0.0638435i | 0.304284 | − | 0.952581i | \(-0.401583\pi\) |
−0.458416 | + | 0.888738i | \(0.651583\pi\) | |||||||
\(468\) | −4.79276e8 | + | 5.76938e8i | −0.216135 | + | 0.260177i | ||||
\(469\) | −2.35880e8 | − | 5.69466e8i | −0.105581 | − | 0.254896i | ||||
\(470\) | 1.81219e9 | + | 2.74346e8i | 0.805120 | + | 0.121886i | ||||
\(471\) | −3.57309e7 | − | 3.57309e7i | −0.0157569 | − | 0.0157569i | ||||
\(472\) | −1.18077e9 | + | 4.10594e8i | −0.516857 | + | 0.179728i | ||||
\(473\) | −2.72625e9 | + | 2.72625e9i | −1.18454 | + | 1.18454i | ||||
\(474\) | −1.34437e8 | + | 9.90840e7i | −0.0579820 | + | 0.0427346i | ||||
\(475\) | −3.80942e9 | + | 1.57791e9i | −1.63091 | + | 0.675546i | ||||
\(476\) | −5.08969e7 | + | 1.64247e8i | −0.0216305 | + | 0.0698028i | ||||
\(477\) | 1.10769e9 | − | 2.67420e9i | 0.467309 | − | 1.12818i | ||||
\(478\) | −4.30701e8 | − | 2.59904e8i | −0.180376 | − | 0.108847i | ||||
\(479\) | −4.59226e9 | −1.90920 | −0.954602 | − | 0.297883i | \(-0.903719\pi\) | ||||
−0.954602 | + | 0.297883i | \(0.903719\pi\) | |||||||
\(480\) | 7.77869e8 | − | 3.53791e8i | 0.321042 | − | 0.146017i | ||||
\(481\) | −6.12642e8 | −0.251014 | ||||||||
\(482\) | 1.70133e8 | + | 1.02666e8i | 0.0692029 | + | 0.0417600i | ||||
\(483\) | −4.43202e7 | + | 1.06999e8i | −0.0178973 | + | 0.0432079i | ||||
\(484\) | 5.02795e9 | + | 1.55806e9i | 2.01573 | + | 0.624635i | ||||
\(485\) | 4.64858e9 | − | 1.92550e9i | 1.85022 | − | 0.766387i | ||||
\(486\) | 1.09846e9 | − | 8.09603e8i | 0.434069 | − | 0.319923i | ||||
\(487\) | −1.99768e9 | + | 1.99768e9i | −0.783743 | + | 0.783743i | −0.980460 | − | 0.196717i | \(-0.936972\pi\) |
0.196717 | + | 0.980460i | \(0.436972\pi\) | |||||||
\(488\) | −3.37600e8 | + | 6.97558e8i | −0.131502 | + | 0.271713i | ||||
\(489\) | 5.42187e8 | + | 5.42187e8i | 0.209685 | + | 0.209685i | ||||
\(490\) | 4.58182e9 | + | 6.93637e8i | 1.75935 | + | 0.266346i | ||||
\(491\) | 1.00452e8 | + | 2.42512e8i | 0.0382977 | + | 0.0924587i | 0.941871 | − | 0.335975i | \(-0.109066\pi\) |
−0.903573 | + | 0.428433i | \(0.859066\pi\) | |||||||
\(492\) | −6.03965e8 | − | 5.01728e8i | −0.228630 | − | 0.189929i | ||||
\(493\) | −9.06531e8 | − | 3.75497e8i | −0.340736 | − | 0.141138i | ||||
\(494\) | 6.44999e8 | − | 1.59519e8i | 0.240722 | − | 0.0595342i | ||||
\(495\) | − | 8.58256e9i | − | 3.18052i | ||||||
\(496\) | −1.71208e9 | + | 2.49721e9i | −0.629995 | + | 0.918902i | ||||
\(497\) | − | 6.04876e8i | − | 0.221014i | ||||||
\(498\) | 1.30697e8 | + | 5.28461e8i | 0.0474201 | + | 0.191739i | ||||
\(499\) | 4.82771e9 | + | 1.99970e9i | 1.73936 | + | 0.720466i | 0.998826 | + | 0.0484478i | \(0.0154274\pi\) |
0.740534 | + | 0.672019i | \(0.234573\pi\) | |||||||
\(500\) | −7.78946e9 | + | 7.20250e8i | −2.78684 | + | 0.257684i | ||||
\(501\) | 2.13176e8 | + | 5.14653e8i | 0.0757368 | + | 0.182845i | ||||
\(502\) | 3.46960e8 | − | 2.29184e9i | 0.122410 | − | 0.808577i | ||||
\(503\) | −3.60445e9 | − | 3.60445e9i | −1.26285 | − | 1.26285i | −0.949706 | − | 0.313143i | \(-0.898618\pi\) |
−0.313143 | − | 0.949706i | \(-0.601382\pi\) | |||||||
\(504\) | 6.08943e8 | + | 3.53863e7i | 0.211870 | + | 0.0123120i | ||||
\(505\) | 2.91301e8 | − | 2.91301e8i | 0.100652 | − | 0.100652i | ||||
\(506\) | −3.43600e9 | − | 4.66194e9i | −1.17903 | − | 1.59970i | ||||
\(507\) | −4.48440e8 | + | 1.85750e8i | −0.152819 | + | 0.0632995i | ||||
\(508\) | 7.62322e8 | + | 1.44692e9i | 0.257998 | + | 0.489692i | ||||
\(509\) | −1.47847e9 | + | 3.56933e9i | −0.496935 | + | 1.19971i | 0.454191 | + | 0.890904i | \(0.349928\pi\) |
−0.951126 | + | 0.308803i | \(0.900072\pi\) | |||||||
\(510\) | 1.81277e8 | − | 3.00405e8i | 0.0605129 | − | 0.100279i | ||||
\(511\) | −3.59227e8 | −0.119096 | ||||||||
\(512\) | −2.99107e9 | − | 5.26186e8i | −0.984876 | − | 0.173258i | ||||
\(513\) | −8.01050e8 | −0.261968 | ||||||||
\(514\) | 8.76190e8 | − | 1.45198e9i | 0.284595 | − | 0.471619i | ||||
\(515\) | 5.96991e8 | − | 1.44126e9i | 0.192594 | − | 0.464963i | ||||
\(516\) | 2.60616e8 | + | 4.94661e8i | 0.0835077 | + | 0.158502i | ||||
\(517\) | 2.22939e9 | − | 9.23442e8i | 0.709526 | − | 0.293895i | ||||
\(518\) | 2.95599e8 | + | 4.01067e8i | 0.0934434 | + | 0.126783i | ||||
\(519\) | −5.26855e8 | + | 5.26855e8i | −0.165427 | + | 0.165427i | ||||
\(520\) | 2.09925e9 | + | 1.21990e8i | 0.654715 | + | 0.0380462i | ||||
\(521\) | 3.47362e9 | + | 3.47362e9i | 1.07610 | + | 1.07610i | 0.996856 | + | 0.0792399i | \(0.0252493\pi\) |
0.0792399 | + | 0.996856i | \(0.474751\pi\) | |||||||
\(522\) | −5.21006e8 | + | 3.44150e9i | −0.160323 | + | 1.05901i | ||||
\(523\) | 9.15878e8 | + | 2.21113e9i | 0.279951 | + | 0.675861i | 0.999834 | − | 0.0182345i | \(-0.00580453\pi\) |
−0.719883 | + | 0.694096i | \(0.755805\pi\) | |||||||
\(524\) | −6.08696e8 | + | 5.62829e7i | −0.184816 | + | 0.0170890i | ||||
\(525\) | 3.17419e8 | + | 1.31479e8i | 0.0957360 | + | 0.0396552i | ||||
\(526\) | −9.20775e8 | − | 3.72307e9i | −0.275869 | − | 1.11545i | ||||
\(527\) | 1.24314e9i | 0.369985i | ||||||||
\(528\) | 6.36187e8 | − | 9.27933e8i | 0.188090 | − | 0.274346i | ||||
\(529\) | 9.18317e8i | 0.269710i | ||||||||
\(530\) | −7.87767e9 | + | 1.94827e9i | −2.29844 | + | 0.568440i | ||||
\(531\) | 1.68218e9 | + | 6.96781e8i | 0.487575 | + | 0.201960i | ||||
\(532\) | −4.15641e8 | − | 3.45282e8i | −0.119682 | − | 0.0994222i | ||||
\(533\) | −7.39382e8 | − | 1.78503e9i | −0.211506 | − | 0.510622i | ||||
\(534\) | −3.09367e7 | − | 4.68349e6i | −0.00879185 | − | 0.00133099i | ||||
\(535\) | 6.87106e9 | + | 6.87106e9i | 1.93993 | + | 1.93993i | ||||
\(536\) | 1.94722e9 | − | 4.02340e9i | 0.546183 | − | 1.12854i | ||||
\(537\) | −5.09030e8 | + | 5.09030e8i | −0.141851 | + | 0.141851i | ||||
\(538\) | −2.70068e9 | + | 1.99049e9i | −0.747713 | + | 0.551088i | ||||
\(539\) | 5.63663e9 | − | 2.33477e9i | 1.55045 | − | 0.642219i | ||||
\(540\) | −2.42156e9 | − | 7.50393e8i | −0.661784 | − | 0.205074i | ||||
\(541\) | 7.28921e8 | − | 1.75977e9i | 0.197920 | − | 0.477821i | −0.793494 | − | 0.608577i | \(-0.791740\pi\) |
0.991415 | + | 0.130756i | \(0.0417405\pi\) | |||||||
\(542\) | 4.39568e9 | + | 2.65254e9i | 1.18585 | + | 0.715590i | ||||
\(543\) | −5.66144e8 | −0.151750 | ||||||||
\(544\) | −1.13506e9 | + | 5.16248e8i | −0.302288 | + | 0.137487i | ||||
\(545\) | −3.61999e9 | −0.957900 | ||||||||
\(546\) | −4.74018e7 | − | 2.86043e7i | −0.0124629 | − | 0.00752068i | ||||
\(547\) | −1.61743e9 | + | 3.90483e9i | −0.422543 | + | 1.02011i | 0.559051 | + | 0.829133i | \(0.311165\pi\) |
−0.981595 | + | 0.190977i | \(0.938835\pi\) | |||||||
\(548\) | −7.43169e8 | + | 2.39824e9i | −0.192910 | + | 0.622532i | ||||
\(549\) | 1.04279e9 | − | 4.31938e8i | 0.268964 | − | 0.111408i | ||||
\(550\) | −1.38300e10 | + | 1.01931e10i | −3.54448 | + | 2.61239i | ||||
\(551\) | 2.18031e9 | − | 2.18031e9i | 0.555249 | − | 0.555249i | ||||
\(552\) | −7.93258e8 | + | 2.75842e8i | −0.200737 | + | 0.0698028i | ||||
\(553\) | 2.36320e8 | + | 2.36320e8i | 0.0594240 | + | 0.0594240i | ||||
\(554\) | 6.72078e9 | + | 1.01745e9i | 1.67933 | + | 0.254232i | ||||
\(555\) | −3.89044e8 | − | 9.39236e8i | −0.0965992 | − | 0.233211i | ||||
\(556\) | 3.90222e9 | − | 4.69738e9i | 0.962831 | − | 1.15903i | ||||
\(557\) | −1.22526e9 | − | 5.07520e8i | −0.300425 | − | 0.124440i | 0.227379 | − | 0.973806i | \(-0.426984\pi\) |
−0.527804 | + | 0.849366i | \(0.676984\pi\) | |||||||
\(558\) | 4.28086e9 | − | 1.05873e9i | 1.04307 | − | 0.257967i | ||||
\(559\) | 1.37582e9i | 0.333136i | ||||||||
\(560\) | −9.33025e8 | − | 1.43314e9i | −0.224510 | − | 0.344849i | ||||
\(561\) | − | 4.61938e8i | − | 0.110462i | ||||||
\(562\) | −6.80359e8 | − | 2.75097e9i | −0.161682 | − | 0.653746i | ||||
\(563\) | 2.48705e9 | + | 1.03017e9i | 0.587360 | + | 0.243293i | 0.656515 | − | 0.754313i | \(-0.272030\pi\) |
−0.0691543 | + | 0.997606i | \(0.522030\pi\) | |||||||
\(564\) | −3.22195e7 | − | 3.48452e8i | −0.00756209 | − | 0.0817836i | ||||
\(565\) | −1.24588e9 | − | 3.00783e9i | −0.290608 | − | 0.701591i | ||||
\(566\) | −5.76942e8 | + | 3.81099e9i | −0.133744 | + | 0.883446i | ||||
\(567\) | −6.04173e8 | − | 6.04173e8i | −0.139194 | − | 0.139194i | ||||
\(568\) | 3.27634e9 | − | 2.91647e9i | 0.750188 | − | 0.667788i | ||||
\(569\) | 3.42275e9 | − | 3.42275e9i | 0.778901 | − | 0.778901i | −0.200743 | − | 0.979644i | \(-0.564336\pi\) |
0.979644 | + | 0.200743i | \(0.0643356\pi\) | |||||||
\(570\) | 6.54149e8 | + | 8.87544e8i | 0.147950 | + | 0.200737i | ||||
\(571\) | −2.05853e6 | + | 852671.i | −0.000462733 | + | 0.000191670i | −0.382915 | − | 0.923784i | \(-0.625080\pi\) |
0.382452 | + | 0.923975i | \(0.375080\pi\) | |||||||
\(572\) | 2.44934e9 | − | 1.29045e9i | 0.547221 | − | 0.288307i | ||||
\(573\) | 2.39813e8 | − | 5.78959e8i | 0.0532514 | − | 0.128560i | ||||
\(574\) | −8.11818e8 | + | 1.34531e9i | −0.179171 | + | 0.296914i | ||||
\(575\) | 1.28249e10 | 2.81331 | ||||||||
\(576\) | 2.74441e9 | + | 3.46899e9i | 0.598371 | + | 0.756354i | ||||
\(577\) | −3.84842e9 | −0.834002 | −0.417001 | − | 0.908906i | \(-0.636919\pi\) | ||||
−0.417001 | + | 0.908906i | \(0.636919\pi\) | |||||||
\(578\) | 2.13406e9 | − | 3.53647e9i | 0.459684 | − | 0.761768i | ||||
\(579\) | −2.58316e8 | + | 6.23629e8i | −0.0553064 | + | 0.133522i | ||||
\(580\) | 8.63347e9 | − | 4.54860e9i | 1.83733 | − | 0.968010i | ||||
\(581\) | 1.00648e9 | − | 4.16897e8i | 0.212906 | − | 0.0881885i | ||||
\(582\) | −5.69962e8 | − | 7.73320e8i | −0.119844 | − | 0.162603i | ||||
\(583\) | −7.55476e9 | + | 7.55476e9i | −1.57900 | + | 1.57900i | ||||
\(584\) | −1.73205e9 | − | 1.94577e9i | −0.359845 | − | 0.404248i | ||||
\(585\) | −2.16563e9 | − | 2.16563e9i | −0.447238 | − | 0.447238i | ||||
\(586\) | −1.40411e9 | + | 9.27487e9i | −0.288244 | + | 1.90400i | ||||
\(587\) | −1.99675e9 | − | 4.82059e9i | −0.407465 | − | 0.983709i | −0.985802 | − | 0.167911i | \(-0.946298\pi\) |
0.578337 | − | 0.815798i | \(-0.303702\pi\) | |||||||
\(588\) | −8.14617e7 | − | 8.81003e8i | −0.0165247 | − | 0.178713i | ||||
\(589\) | −3.60914e9 | − | 1.49495e9i | −0.727780 | − | 0.301456i | ||||
\(590\) | −1.22554e9 | − | 4.95537e9i | −0.245667 | − | 0.993331i | ||||
\(591\) | 6.61399e8i | 0.131797i | ||||||||
\(592\) | −7.47138e8 | + | 3.53491e9i | −0.148004 | + | 0.700249i | ||||
\(593\) | − | 4.01770e9i | − | 0.791199i | −0.918423 | − | 0.395599i | \(-0.870537\pi\) | ||
0.918423 | − | 0.395599i | \(-0.129463\pi\) | |||||||
\(594\) | −3.24011e9 | + | 8.01331e8i | −0.634318 | + | 0.156877i | ||||
\(595\) | −6.48689e8 | − | 2.68696e8i | −0.126249 | − | 0.0522940i | ||||
\(596\) | −1.88338e9 | + | 2.26716e9i | −0.364398 | + | 0.438652i | ||||
\(597\) | −5.30047e8 | − | 1.27965e9i | −0.101954 | − | 0.246139i | ||||
\(598\) | −2.04334e9 | − | 3.09340e8i | −0.390740 | − | 0.0591538i | ||||
\(599\) | 1.85612e8 | + | 1.85612e8i | 0.0352868 | + | 0.0352868i | 0.724530 | − | 0.689243i | \(-0.242057\pi\) |
−0.689243 | + | 0.724530i | \(0.742057\pi\) | |||||||
\(600\) | 8.18304e8 | + | 2.35326e9i | 0.154663 | + | 0.444775i | ||||
\(601\) | 3.22719e9 | − | 3.22719e9i | 0.606406 | − | 0.606406i | −0.335599 | − | 0.942005i | \(-0.608939\pi\) |
0.942005 | + | 0.335599i | \(0.108939\pi\) | |||||||
\(602\) | 9.00685e8 | − | 6.63833e8i | 0.168262 | − | 0.124014i | ||||
\(603\) | −6.01464e9 | + | 2.49135e9i | −1.11712 | + | 0.462725i | ||||
\(604\) | −2.03423e9 | + | 6.56456e9i | −0.375639 | + | 1.21221i | ||||
\(605\) | −8.22536e9 | + | 1.98578e10i | −1.51012 | + | 3.64575i | ||||
\(606\) | −6.73433e7 | − | 4.06378e7i | −0.0122925 | − | 0.00741782i | ||||
\(607\) | 7.74615e9 | 1.40581 | 0.702903 | − | 0.711285i | \(-0.251887\pi\) | ||||
0.702903 | + | 0.711285i | \(0.251887\pi\) | |||||||
\(608\) | −1.33815e8 | − | 3.91615e9i | −0.0241459 | − | 0.706638i | ||||
\(609\) | −2.56926e8 | −0.0460943 | ||||||||
\(610\) | −2.70933e9 | − | 1.63493e9i | −0.483290 | − | 0.291638i | ||||
\(611\) | 3.29528e8 | − | 7.95551e8i | 0.0584451 | − | 0.141099i | ||||
\(612\) | 1.73476e9 | + | 5.37568e8i | 0.305921 | + | 0.0947989i | ||||
\(613\) | −5.67809e9 | + | 2.35194e9i | −0.995613 | + | 0.412396i | −0.820186 | − | 0.572096i | \(-0.806130\pi\) |
−0.175426 | + | 0.984493i | \(0.556130\pi\) | |||||||
\(614\) | 4.79863e9 | − | 3.53675e9i | 0.836620 | − | 0.616616i | ||||
\(615\) | 2.26708e9 | − | 2.26708e9i | 0.393010 | − | 0.393010i | ||||
\(616\) | −2.02660e9 | − | 9.80821e8i | −0.349330 | − | 0.169066i | ||||
\(617\) | 6.41988e9 | + | 6.41988e9i | 1.10035 | + | 1.10035i | 0.994369 | + | 0.105976i | \(0.0337968\pi\) |
0.105976 | + | 0.994369i | \(0.466203\pi\) | |||||||
\(618\) | −2.94494e8 | − | 4.45831e7i | −0.0501899 | − | 0.00759821i | ||||
\(619\) | −2.53808e9 | − | 6.12746e9i | −0.430118 | − | 1.03840i | −0.979249 | − | 0.202660i | \(-0.935041\pi\) |
0.549131 | − | 0.835736i | \(-0.314959\pi\) | |||||||
\(620\) | −9.50993e9 | − | 7.90011e9i | −1.60253 | − | 1.33126i | ||||
\(621\) | 2.30190e9 | + | 9.53478e8i | 0.385714 | + | 0.159768i | ||||
\(622\) | −9.73963e8 | + | 2.40876e8i | −0.162284 | + | 0.0401354i | ||||
\(623\) | 6.26152e7i | 0.0103746i | ||||||||
\(624\) | −7.36161e7 | − | 3.94673e8i | −0.0121290 | − | 0.0650267i | ||||
\(625\) | − | 1.67040e10i | − | 2.73678i | ||||||
\(626\) | 1.72763e8 | + | 6.98550e8i | 0.0281475 | + | 0.113812i | ||||
\(627\) | 1.34111e9 | + | 5.55507e8i | 0.217285 | + | 0.0900022i | ||||
\(628\) | −7.30187e8 | + | 6.75165e7i | −0.117645 | + | 0.0108781i | ||||
\(629\) | 5.67689e8 | + | 1.37052e9i | 0.0909563 | + | 0.219588i | ||||
\(630\) | −3.72818e8 | + | 2.46265e9i | −0.0594025 | + | 0.392383i | ||||
\(631\) | −6.12180e8 | − | 6.12180e8i | −0.0970011 | − | 0.0970011i | 0.656941 | − | 0.753942i | \(-0.271850\pi\) |
−0.753942 | + | 0.656941i | \(0.771850\pi\) | |||||||
\(632\) | −1.40598e8 | + | 2.41948e9i | −0.0221549 | + | 0.381252i | ||||
\(633\) | −7.81215e8 | + | 7.81215e8i | −0.122422 | + | 0.122422i | ||||
\(634\) | 4.29835e9 | + | 5.83197e9i | 0.669868 | + | 0.908872i | ||||
\(635\) | −6.16977e9 | + | 2.55560e9i | −0.956226 | + | 0.396082i | ||||
\(636\) | 7.22198e8 | + | 1.37077e9i | 0.111316 | + | 0.211283i | ||||
\(637\) | 8.33157e8 | − | 2.01142e9i | 0.127714 | − | 0.308329i | ||||
\(638\) | 6.63792e9 | − | 1.10001e10i | 1.01195 | − | 1.67696i | ||||
\(639\) | −6.38864e9 | −0.968624 | ||||||||
\(640\) | 3.26398e9 | − | 1.19638e10i | 0.492173 | − | 1.80401i | ||||
\(641\) | −8.61409e9 | −1.29183 | −0.645916 | − | 0.763408i | \(-0.723524\pi\) | ||||
−0.645916 | + | 0.763408i | \(0.723524\pi\) | |||||||
\(642\) | 9.58546e8 | − | 1.58846e9i | 0.142968 | − | 0.236921i | ||||
\(643\) | 2.67840e6 | − | 6.46624e6i | 0.000397317 | − | 0.000959209i | −0.923681 | − | 0.383163i | \(-0.874835\pi\) |
0.924078 | + | 0.382204i | \(0.124835\pi\) | |||||||
\(644\) | 7.83402e8 | + | 1.48693e9i | 0.115580 | + | 0.219377i | ||||
\(645\) | −2.10926e9 | + | 8.73685e8i | −0.309508 | + | 0.128202i | ||||
\(646\) | −9.54526e8 | − | 1.29509e9i | −0.139307 | − | 0.189011i | ||||
\(647\) | 1.93862e9 | − | 1.93862e9i | 0.281402 | − | 0.281402i | −0.552266 | − | 0.833668i | \(-0.686237\pi\) |
0.833668 | + | 0.552266i | \(0.186237\pi\) | |||||||
\(648\) | 3.59452e8 | − | 6.18562e9i | 0.0518954 | − | 0.893039i | ||||
\(649\) | −4.75225e9 | − | 4.75225e9i | −0.682405 | − | 0.682405i | ||||
\(650\) | −9.17681e8 | + | 6.06173e9i | −0.131067 | + | 0.865765i | ||||
\(651\) | 1.24567e8 | + | 3.00731e8i | 0.0176957 | + | 0.0427213i | ||||
\(652\) | 1.10800e10 | − | 1.02451e9i | 1.56557 | − | 0.144760i | ||||
\(653\) | 5.01222e9 | + | 2.07613e9i | 0.704424 | + | 0.291782i | 0.705995 | − | 0.708217i | \(-0.250500\pi\) |
−0.00157082 | + | 0.999999i | \(0.500500\pi\) | |||||||
\(654\) | 1.65934e8 | + | 6.70941e8i | 0.0231961 | + | 0.0937912i | ||||
\(655\) | − | 2.49610e9i | − | 0.347071i | ||||||
\(656\) | −1.12012e10 | + | 2.08930e9i | −1.54918 | + | 0.288959i | ||||
\(657\) | 3.79412e9i | 0.521954i | ||||||||
\(658\) | −6.79805e8 | + | 1.68127e8i | −0.0930238 | + | 0.0230063i | ||||
\(659\) | −2.01567e9 | − | 8.34919e8i | −0.274360 | − | 0.113644i | 0.241261 | − | 0.970460i | \(-0.422439\pi\) |
−0.515622 | + | 0.856816i | \(0.672439\pi\) | |||||||
\(660\) | 3.53378e9 | + | 2.93559e9i | 0.478449 | + | 0.397458i | ||||
\(661\) | −2.23091e9 | − | 5.38589e9i | −0.300453 | − | 0.725358i | −0.999943 | − | 0.0107150i | \(-0.996589\pi\) |
0.699490 | − | 0.714643i | \(-0.253411\pi\) | |||||||
\(662\) | 5.46333e9 | + | 8.27089e8i | 0.731904 | + | 0.110802i | ||||
\(663\) | −1.16560e8 | − | 1.16560e8i | −0.0155329 | − | 0.0155329i | ||||
\(664\) | 7.11098e9 | + | 3.44153e9i | 0.942630 | + | 0.456208i | ||||
\(665\) | 1.56017e9 | − | 1.56017e9i | 0.205730 | − | 0.205730i | ||||
\(666\) | 4.23603e9 | − | 3.12209e9i | 0.555647 | − | 0.409529i | ||||
\(667\) | −8.86055e9 | + | 3.67016e9i | −1.15617 | + | 0.478900i | ||||
\(668\) | 7.72168e9 | + | 2.39280e9i | 1.00229 | + | 0.310591i | ||||
\(669\) | −4.55932e8 | + | 1.10072e9i | −0.0588720 | + | 0.142130i | ||||
\(670\) | 1.56270e10 | + | 9.42999e9i | 2.00730 | + | 1.21129i | ||||
\(671\) | −4.16618e9 | −0.532365 | ||||||||
\(672\) | −2.22854e8 | + | 2.38622e8i | −0.0283287 | + | 0.0303332i | ||||
\(673\) | 2.65376e9 | 0.335590 | 0.167795 | − | 0.985822i | \(-0.446335\pi\) | ||||
0.167795 | + | 0.985822i | \(0.446335\pi\) | |||||||
\(674\) | −2.32043e9 | − | 1.40025e9i | −0.291916 | − | 0.176155i | ||||
\(675\) | 2.82856e9 | − | 6.82875e9i | 0.353999 | − | 0.854630i | ||||
\(676\) | −2.08495e9 | + | 6.72824e9i | −0.259587 | + | 0.837700i | ||||
\(677\) | 2.35923e9 | − | 9.77224e8i | 0.292220 | − | 0.121041i | −0.231758 | − | 0.972774i | \(-0.574448\pi\) |
0.523977 | + | 0.851732i | \(0.324448\pi\) | |||||||
\(678\) | −5.00372e8 | + | 3.68790e8i | −0.0616579 | + | 0.0454439i | ||||
\(679\) | −1.35938e9 | + | 1.35938e9i | −0.166647 | + | 0.166647i | ||||
\(680\) | −1.67232e9 | − | 4.80921e9i | −0.203956 | − | 0.586533i | ||||
\(681\) | −8.98911e7 | − | 8.98911e7i | −0.0109069 | − | 0.0109069i | ||||
\(682\) | −1.60938e10 | − | 2.43643e9i | −1.94274 | − | 0.294109i | ||||
\(683\) | 8.73998e8 | + | 2.11002e9i | 0.104963 | + | 0.253404i | 0.967632 | − | 0.252366i | \(-0.0812085\pi\) |
−0.862669 | + | 0.505770i | \(0.831209\pi\) | |||||||
\(684\) | −3.64683e9 | + | 4.38995e9i | −0.435732 | + | 0.524522i | ||||
\(685\) | −9.47181e9 | − | 3.92335e9i | −1.12594 | − | 0.466380i | ||||
\(686\) | −3.52502e9 | + | 8.71792e8i | −0.416895 | + | 0.103105i | ||||
\(687\) | − | 3.28089e8i | − | 0.0386050i | ||||||
\(688\) | 7.93844e9 | + | 1.67786e9i | 0.929342 | + | 0.196425i | ||||
\(689\) | 3.81257e9i | 0.444070i | ||||||||
\(690\) | −8.23333e8 | − | 3.32907e9i | −0.0954121 | − | 0.385791i | ||||
\(691\) | 1.20795e9 | + | 5.00348e8i | 0.139276 | + | 0.0576898i | 0.451233 | − | 0.892406i | \(-0.350984\pi\) |
−0.311957 | + | 0.950096i | \(0.600984\pi\) | |||||||
\(692\) | 9.95535e8 | + | 1.07666e10i | 0.114205 | + | 1.23512i | ||||
\(693\) | 1.25490e9 | + | 3.02959e9i | 0.143233 | + | 0.345794i | ||||
\(694\) | 2.30333e9 | − | 1.52147e10i | 0.261577 | − | 1.72784i | ||||
\(695\) | 1.76324e10 | + | 1.76324e10i | 1.99234 | + | 1.99234i | ||||
\(696\) | −1.23880e9 | − | 1.39165e9i | −0.139273 | − | 0.156458i | ||||
\(697\) | −3.30810e9 | + | 3.30810e9i | −0.370053 | + | 0.370053i | ||||
\(698\) | −7.30399e9 | − | 9.91000e9i | −0.812955 | − | 1.10301i | ||||
\(699\) | −3.07956e8 | + | 1.27559e8i | −0.0341050 | + | 0.0141268i | ||||
\(700\) | 4.41110e9 | − | 2.32402e9i | 0.486076 | − | 0.256092i | ||||
\(701\) | 2.97482e9 | − | 7.18185e9i | 0.326172 | − | 0.787450i | −0.672697 | − | 0.739918i | \(-0.734864\pi\) |
0.998870 | − | 0.0475322i | \(-0.0151357\pi\) | |||||||
\(702\) | −6.15375e8 | + | 1.01977e9i | −0.0671367 | + | 0.111256i | ||||
\(703\) | −4.66162e9 | −0.506050 | ||||||||
\(704\) | −4.45879e9 | − | 1.57063e10i | −0.481629 | − | 1.69656i | ||||
\(705\) | 1.42891e9 | 0.153583 | ||||||||
\(706\) | −8.93123e9 | + | 1.48005e10i | −0.955202 | + | 1.58292i | ||||
\(707\) | −6.02349e7 | + | 1.45420e8i | −0.00641033 | + | 0.0154759i | ||||
\(708\) | −8.62267e8 | + | 4.54291e8i | −0.0913115 | + | 0.0481081i | ||||
\(709\) | 1.49755e10 | − | 6.20304e9i | 1.57804 | − | 0.653646i | 0.589940 | − | 0.807447i | \(-0.299152\pi\) |
0.988102 | + | 0.153801i | \(0.0491515\pi\) | |||||||
\(710\) | 1.06265e10 | + | 1.44180e10i | 1.11426 | + | 1.51182i | ||||
\(711\) | 2.49599e9 | − | 2.49599e9i | 0.260434 | − | 0.260434i | ||||
\(712\) | −3.39158e8 | + | 3.01906e8i | −0.0352146 | + | 0.0313466i | ||||
\(713\) | 8.59181e9 | + | 8.59181e9i | 0.887710 | + | 0.887710i | ||||
\(714\) | −2.00661e7 | + | 1.32547e8i | −0.00206310 | + | 0.0136278i | ||||
\(715\) | 4.32609e9 | + | 1.04441e10i | 0.442613 | + | 1.06856i | ||||
\(716\) | 9.61854e8 | + | 1.04024e10i | 0.0979295 | + | 1.05910i | ||||
\(717\) | −3.62329e8 | − | 1.50082e8i | −0.0367101 | − | 0.0152058i | ||||
\(718\) | −1.20608e9 | − | 4.87668e9i | −0.121602 | − | 0.491687i | ||||
\(719\) | − | 1.36604e10i | − | 1.37061i | −0.728258 | − | 0.685303i | \(-0.759670\pi\) | ||
0.728258 | − | 0.685303i | \(-0.240330\pi\) | |||||||
\(720\) | −1.51366e10 | + | 9.85452e9i | −1.51135 | + | 0.983947i | ||||
\(721\) | 5.96047e8i | 0.0592253i | ||||||||
\(722\) | −4.90939e9 | + | 1.21417e9i | −0.485453 | + | 0.120060i | ||||
\(723\) | 1.43125e8 | + | 5.92843e7i | 0.0140842 | + | 0.00583386i | ||||
\(724\) | −5.24989e9 | + | 6.31966e9i | −0.514121 | + | 0.618884i | ||||
\(725\) | 1.08878e10 | + | 2.62855e10i | 1.06110 | + | 2.56173i | ||||
\(726\) | 4.05754e9 | + | 6.14267e8i | 0.393536 | + | 0.0595771i | ||||
\(727\) | −5.78643e9 | − | 5.78643e9i | −0.558522 | − | 0.558522i | 0.370364 | − | 0.928887i | \(-0.379233\pi\) |
−0.928887 | + | 0.370364i | \(0.879233\pi\) | |||||||
\(728\) | −7.58860e8 | + | 2.63880e8i | −0.0728957 | + | 0.0253482i | ||||
\(729\) | −5.86433e9 | + | 5.86433e9i | −0.560624 | + | 0.560624i | ||||
\(730\) | 8.56266e9 | − | 6.31095e9i | 0.814664 | − | 0.600434i | ||||
\(731\) | 3.07781e9 | − | 1.27487e9i | 0.291428 | − | 0.120713i | ||||
\(732\) | −1.78831e8 | + | 5.77098e8i | −0.0168521 | + | 0.0543827i | ||||
\(733\) | −2.20425e8 | + | 5.32152e8i | −0.0206727 | + | 0.0499082i | −0.933879 | − | 0.357590i | \(-0.883599\pi\) |
0.913206 | + | 0.407498i | \(0.133599\pi\) | |||||||
\(734\) | −9.00396e9 | − | 5.43338e9i | −0.840421 | − | 0.507147i | ||||
\(735\) | 3.61277e9 | 0.335609 | ||||||||
\(736\) | −4.27681e9 | + | 1.14128e10i | −0.395410 | + | 1.05516i | ||||
\(737\) | 2.40299e10 | 2.21113 | ||||||||
\(738\) | 1.42090e10 | + | 8.57434e9i | 1.30127 | + | 0.785242i | ||||
\(739\) | −6.89179e8 | + | 1.66383e9i | −0.0628169 | + | 0.151653i | −0.952171 | − | 0.305566i | \(-0.901154\pi\) |
0.889354 | + | 0.457219i | \(0.151154\pi\) | |||||||
\(740\) | −1.40920e10 | − | 4.36683e9i | −1.27838 | − | 0.396146i | ||||
\(741\) | 4.78572e8 | − | 1.98231e8i | 0.0432100 | − | 0.0178982i | ||||
\(742\) | 2.49591e9 | − | 1.83956e9i | 0.224293 | − | 0.165311i | ||||
\(743\) | −1.04141e10 | + | 1.04141e10i | −0.931454 | + | 0.931454i | −0.997797 | − | 0.0663433i | \(-0.978867\pi\) |
0.0663433 | + | 0.997797i | \(0.478867\pi\) | |||||||
\(744\) | −1.02831e9 | + | 2.12473e9i | −0.0915419 | + | 0.189146i | ||||
\(745\) | −8.51015e9 | − | 8.51015e9i | −0.754033 | − | 0.754033i | ||||
\(746\) | −1.81556e9 | − | 2.74857e8i | −0.160113 | − | 0.0242393i | ||||
\(747\) | −4.40322e9 | − | 1.06303e10i | −0.386499 | − | 0.933091i | ||||
\(748\) | −5.15644e9 | − | 4.28358e9i | −0.450500 | − | 0.374241i | ||||
\(749\) | −3.43010e9 | − | 1.42079e9i | −0.298277 | − | 0.123550i | ||||
\(750\) | −5.92033e9 | + | 1.46419e9i | −0.512427 | + | 0.126731i | ||||
\(751\) | − | 5.21564e9i | − | 0.449332i | −0.974436 | − | 0.224666i | \(-0.927871\pi\) | ||
0.974436 | − | 0.224666i | \(-0.0721291\pi\) | |||||||
\(752\) | −4.18842e9 | − | 2.87156e9i | −0.359160 | − | 0.246238i | ||||
\(753\) | − | 1.80712e9i | − | 0.154243i | ||||||
\(754\) | −1.10070e9 | − | 4.45058e9i | −0.0935123 | − | 0.378109i | ||||
\(755\) | −2.59266e10 | − | 1.07391e10i | −2.19245 | − | 0.908144i | ||||
\(756\) | 9.64514e8 | − | 8.91835e7i | 0.0811862 | − | 0.00750686i | ||||
\(757\) | 1.94976e9 | + | 4.70713e9i | 0.163360 | + | 0.394385i | 0.984270 | − | 0.176672i | \(-0.0565333\pi\) |
−0.820910 | + | 0.571058i | \(0.806533\pi\) | |||||||
\(758\) | 2.28359e9 | − | 1.50842e10i | 0.190448 | − | 1.25800i | ||||
\(759\) | −3.19261e9 | − | 3.19261e9i | −0.265033 | − | 0.265033i | ||||
\(760\) | 1.59733e10 | + | 9.28225e8i | 1.31992 | + | 0.0767018i | ||||
\(761\) | 1.31795e10 | − | 1.31795e10i | 1.08406 | − | 1.08406i | 0.0879329 | − | 0.996126i | \(-0.471974\pi\) |
0.996126 | − | 0.0879329i | \(-0.0280261\pi\) | |||||||
\(762\) | 7.56475e8 | + | 1.02638e9i | 0.0619373 | + | 0.0840360i | ||||
\(763\) | 1.27784e9 | − | 5.29298e8i | 0.104145 | − | 0.0431384i | ||||
\(764\) | −4.23891e9 | − | 8.04566e9i | −0.343897 | − | 0.652732i | ||||
\(765\) | −2.83794e9 | + | 6.85139e9i | −0.229186 | + | 0.553304i | ||||
\(766\) | 6.83685e9 | − | 1.13297e10i | 0.549611 | − | 0.910792i | ||||
\(767\) | −2.39826e9 | −0.191917 | ||||||||
\(768\) | −2.36702e9 | − | 5.65565e7i | −0.188555 | − | 0.00450524i | ||||
\(769\) | 9.47745e9 | 0.751535 | 0.375768 | − | 0.926714i | \(-0.377379\pi\) | ||||
0.375768 | + | 0.926714i | \(0.377379\pi\) | |||||||
\(770\) | 4.74992e9 | − | 7.87136e9i | 0.374946 | − | 0.621344i | ||||
\(771\) | 5.05957e8 | − | 1.22149e9i | 0.0397579 | − | 0.0959840i | ||||
\(772\) | 4.56597e9 | + | 8.66644e9i | 0.357168 | + | 0.677922i | ||||
\(773\) | −1.86730e10 | + | 7.73462e9i | −1.45407 | + | 0.602297i | −0.963164 | − | 0.268914i | \(-0.913335\pi\) |
−0.490909 | + | 0.871211i | \(0.663335\pi\) | |||||||
\(774\) | −7.01134e9 | − | 9.51294e9i | −0.543510 | − | 0.737431i | ||||
\(775\) | 2.54882e10 | − | 2.54882e10i | 1.96691 | − | 1.96691i | ||||
\(776\) | −1.39176e10 | − | 8.08765e8i | −1.06917 | − | 0.0621307i | ||||
\(777\) | 2.74661e8 | + | 2.74661e8i | 0.0210050 | + | 0.0210050i | ||||
\(778\) | 2.59301e9 | − | 1.71281e10i | 0.197413 | − | 1.30401i | ||||
\(779\) | −5.62600e9 | − | 1.35824e10i | −0.426401 | − | 1.02942i | ||||
\(780\) | 1.63241e9 | − | 1.50940e8i | 0.123168 | − | 0.0113887i | ||||
\(781\) | 2.17862e10 | + | 9.02412e9i | 1.63645 | + | 0.677839i | ||||
\(782\) | 1.20140e9 | + | 4.85775e9i | 0.0898386 | + | 0.363255i | ||||
\(783\) | 5.52735e9i | 0.411482i | ||||||||
\(784\) | −1.05897e10 | − | 7.26027e9i | −0.784835 | − | 0.538080i | ||||
\(785\) | − | 2.99431e9i | − | 0.220929i | ||||||
\(786\) | −4.62636e8 | + | 1.14417e8i | −0.0339829 | + | 0.00840450i | ||||
\(787\) | 6.39792e9 | + | 2.65010e9i | 0.467872 | + | 0.193799i | 0.604148 | − | 0.796872i | \(-0.293513\pi\) |
−0.136276 | + | 0.990671i | \(0.543513\pi\) | |||||||
\(788\) | 7.38296e9 | + | 6.13319e9i | 0.537513 | + | 0.446524i | ||||
\(789\) | −1.14423e9 | − | 2.76242e9i | −0.0829363 | − | 0.200226i | ||||
\(790\) | −9.78469e9 | − | 1.48130e9i | −0.706077 | − | 0.106892i | ||||
\(791\) | 8.79580e8 | + | 8.79580e8i | 0.0631914 | + | 0.0631914i | ||||
\(792\) | −1.03593e10 | + | 2.14047e10i | −0.740958 | + | 1.53099i | ||||
\(793\) | −1.05125e9 | + | 1.05125e9i | −0.0748600 | + | 0.0748600i | ||||
\(794\) | −1.19437e10 | + | 8.80290e9i | −0.846774 | + | 0.624100i | ||||
\(795\) | −5.84503e9 | + | 2.42109e9i | −0.412574 | + | 0.170894i | ||||
\(796\) | −1.91994e10 | − | 5.94952e9i | −1.34925 | − | 0.418106i | ||||
\(797\) | 5.86600e9 | − | 1.41618e10i | 0.410429 | − | 0.990863i | −0.574594 | − | 0.818439i | \(-0.694840\pi\) |
0.985023 | − | 0.172425i | \(-0.0551601\pi\) | |||||||
\(798\) | −3.60683e8 | − | 2.17652e8i | −0.0251256 | − | 0.0151618i | ||||
\(799\) | −2.08505e9 | −0.144612 | ||||||||
\(800\) | 3.38568e10 | + | 1.26875e10i | 2.33793 | + | 0.876113i | ||||
\(801\) | 6.61335e8 | 0.0454682 | ||||||||
\(802\) | −3.01424e9 | − | 1.81892e9i | −0.206332 | − | 0.124510i | ||||
\(803\) | 5.35930e9 | − | 1.29385e10i | 0.365261 | − | 0.881819i | ||||
\(804\) | 1.03147e9 | − | 3.32861e9i | 0.0699939 | − | 0.225874i | ||||
\(805\) | −6.34037e9 | + | 2.62627e9i | −0.428380 | + | 0.177441i | ||||
\(806\) | −4.67572e9 | + | 3.44616e9i | −0.314540 | + | 0.231826i | ||||
\(807\) | −1.84949e9 | + | 1.84949e9i | −0.123878 | + | 0.123878i | ||||
\(808\) | −1.07810e9 | + | 3.74892e8i | −0.0718987 | + | 0.0250015i | ||||
\(809\) | −7.75368e9 | − | 7.75368e9i | −0.514859 | − | 0.514859i | 0.401152 | − | 0.916011i | \(-0.368610\pi\) |
−0.916011 | + | 0.401152i | \(0.868610\pi\) | |||||||
\(810\) | 2.50154e10 | + | 3.78707e9i | 1.65390 | + | 0.250383i | ||||
\(811\) | 5.52554e9 | + | 1.33398e10i | 0.363749 | + | 0.878167i | 0.994745 | + | 0.102381i | \(0.0326462\pi\) |
−0.630997 | + | 0.775786i | \(0.717354\pi\) | |||||||
\(812\) | −2.38249e9 | + | 2.86797e9i | −0.156166 | + | 0.187988i | ||||
\(813\) | 3.69788e9 | + | 1.53171e9i | 0.241344 | + | 0.0999678i | ||||
\(814\) | −1.88555e10 | + | 4.66326e9i | −1.22533 | + | 0.303043i | ||||
\(815\) | 4.54361e10i | 2.94001i | ||||||||
\(816\) | −8.14697e8 | + | 5.30398e8i | −0.0524905 | + | 0.0341733i | ||||
\(817\) | 1.04687e10i | 0.671608i | ||||||||
\(818\) | −1.15898e9 | − | 4.68622e9i | −0.0740352 | − | 0.299355i | ||||
\(819\) | 1.08110e9 | + | 4.47807e8i | 0.0687659 | + | 0.0284838i | ||||
\(820\) | −4.28383e9 | − | 4.63294e10i | −0.271321 | − | 2.93432i | ||||
\(821\) | −6.71068e9 | − | 1.62010e10i | −0.423219 | − | 1.02174i | −0.981392 | − | 0.192016i | \(-0.938497\pi\) |
0.558173 | − | 0.829725i | \(-0.311503\pi\) | |||||||
\(822\) | −2.92995e8 | + | 1.93537e9i | −0.0183996 | + | 0.121538i | ||||
\(823\) | −8.66533e9 | − | 8.66533e9i | −0.541858 | − | 0.541858i | 0.382215 | − | 0.924073i | \(-0.375161\pi\) |
−0.924073 | + | 0.382215i | \(0.875161\pi\) | |||||||
\(824\) | −3.22852e9 | + | 2.87391e9i | −0.201029 | + | 0.178948i | ||||
\(825\) | −9.47112e9 | + | 9.47112e9i | −0.587236 | + | 0.587236i | ||||
\(826\) | 1.15716e9 | + | 1.57002e9i | 0.0714435 | + | 0.0969341i | ||||
\(827\) | 1.15482e10 | − | 4.78341e9i | 0.709977 | − | 0.294082i | 0.00168195 | − | 0.999999i | \(-0.499465\pi\) |
0.708295 | + | 0.705916i | \(0.249465\pi\) | |||||||
\(828\) | 1.57049e10 | − | 8.27421e9i | 0.961452 | − | 0.506548i | ||||
\(829\) | 1.18942e9 | − | 2.87150e9i | 0.0725092 | − | 0.175053i | −0.883470 | − | 0.468489i | \(-0.844799\pi\) |
0.955979 | + | 0.293436i | \(0.0947987\pi\) | |||||||
\(830\) | −1.66666e10 | + | 2.76192e10i | −1.01175 | + | 1.67663i | ||||
\(831\) | 5.29934e9 | 0.320345 | ||||||||
\(832\) | −5.08824e9 | − | 2.83808e9i | −0.306292 | − | 0.170841i | ||||
\(833\) | −5.27171e9 | −0.316005 | ||||||||
\(834\) | 2.45980e9 | − | 4.07628e9i | 0.146831 | − | 0.243323i | ||||
\(835\) | −1.26321e10 | + | 3.04966e10i | −0.750885 | + | 1.81280i | ||||
\(836\) | 1.86371e10 | − | 9.81911e9i | 1.10321 | − | 0.581233i | ||||
\(837\) | 6.46973e9 | − | 2.67985e9i | 0.381371 | − | 0.157969i | ||||
\(838\) | 1.72657e10 | + | 2.34260e10i | 1.01352 | + | 1.37513i | ||||
\(839\) | −1.93616e10 | + | 1.93616e10i | −1.13181 | + | 1.13181i | −0.141934 | + | 0.989876i | \(0.545332\pi\) |
−0.989876 | + | 0.141934i | \(0.954668\pi\) | |||||||
\(840\) | −8.86449e8 | − | 9.95831e8i | −0.0516032 | − | 0.0579706i | ||||
\(841\) | −2.84693e9 | − | 2.84693e9i | −0.165041 | − | 0.165041i | ||||
\(842\) | −1.29396e9 | + | 8.54722e9i | −0.0747012 | + | 0.493438i | ||||
\(843\) | −8.45472e8 | − | 2.04115e9i | −0.0486074 | − | 0.117349i | ||||
\(844\) | 1.47617e9 | + | 1.59647e10i | 0.0845158 | + | 0.914033i | ||||
\(845\) | −2.65730e10 | − | 1.10069e10i | −1.51510 | − | 0.627577i | ||||
\(846\) | 1.77574e9 | + | 7.18003e9i | 0.100828 | + | 0.407690i | ||||
\(847\) | − | 8.21235e9i | − | 0.464382i | ||||||
\(848\) | 2.19984e10 | + | 4.64957e9i | 1.23881 | + | 0.261835i | ||||
\(849\) | 3.00497e9i | 0.168524i | ||||||||
\(850\) | 1.44109e10 | − | 3.56404e9i | 0.804866 | − | 0.199056i | ||||
\(851\) | 1.33957e10 | + | 5.54866e9i | 0.745093 | + | 0.308628i | ||||
\(852\) | 2.18518e9 | − | 2.63045e9i | 0.121045 | − | 0.145711i | ||||
\(853\) | −9.64007e9 | − | 2.32732e10i | −0.531812 | − | 1.28391i | −0.930322 | − | 0.366744i | \(-0.880472\pi\) |
0.398509 | − | 0.917164i | \(-0.369528\pi\) | |||||||
\(854\) | 1.19543e9 | + | 1.80975e8i | 0.0656782 | + | 0.00994297i | ||||
\(855\) | −1.64784e10 | − | 1.64784e10i | −0.901641 | − | 0.901641i | ||||
\(856\) | −8.84277e9 | − | 2.54298e10i | −0.481870 | − | 1.38575i | ||||
\(857\) | 2.09744e9 | − | 2.09744e9i | 0.113830 | − | 0.113830i | −0.647897 | − | 0.761728i | \(-0.724351\pi\) |
0.761728 | + | 0.647897i | \(0.224351\pi\) | |||||||
\(858\) | 1.73744e9 | − | 1.28055e9i | 0.0939086 | − | 0.0692136i | ||||
\(859\) | 2.24034e10 | − | 9.27979e9i | 1.20597 | − | 0.499531i | 0.313049 | − | 0.949737i | \(-0.398650\pi\) |
0.892925 | + | 0.450206i | \(0.148650\pi\) | |||||||
\(860\) | −9.80669e9 | + | 3.16467e10i | −0.525748 | + | 1.69662i | ||||
\(861\) | −4.68785e8 | + | 1.13175e9i | −0.0250301 | + | 0.0604280i | ||||
\(862\) | −1.17020e9 | − | 7.06148e8i | −0.0622277 | − | 0.0375509i | ||||
\(863\) | 1.32809e10 | 0.703381 | 0.351691 | − | 0.936116i | \(-0.385607\pi\) | ||||
0.351691 | + | 0.936116i | \(0.385607\pi\) | |||||||
\(864\) | 5.13357e9 | + | 4.79434e9i | 0.270783 | + | 0.252889i | ||||
\(865\) | −4.41512e10 | −2.31946 | ||||||||
\(866\) | 1.18457e10 | + | 7.14822e9i | 0.619796 | + | 0.374012i | ||||
\(867\) | 1.23231e9 | − | 2.97507e9i | 0.0642177 | − | 0.155035i | ||||
\(868\) | 4.51207e9 | + | 1.39820e9i | 0.234184 | + | 0.0725689i | ||||
\(869\) | −1.20373e10 | + | 4.98602e9i | −0.622243 | + | 0.257742i | ||||
\(870\) | 6.12417e9 | − | 4.51371e9i | 0.315304 | − | 0.232389i | ||||
\(871\) | 6.06343e9 | − | 6.06343e9i | 0.310925 | − | 0.310925i | ||||
\(872\) | 9.02820e9 | + | 4.36941e9i | 0.461098 | + | 0.223159i | ||||
\(873\) | 1.43577e10 | + | 1.43577e10i | 0.730355 | + | 0.730355i | ||||
\(874\) | −1.55479e10 | − | 2.35379e9i | −0.787739 | − | 0.119255i | ||||
\(875\) | 4.67048e9 | + | 1.12755e10i | 0.235686 | + | 0.568996i | ||||
\(876\) | −1.56219e9 | − | 1.29775e9i | −0.0785180 | − | 0.0652267i | ||||
\(877\) | 2.34530e10 | + | 9.71455e9i | 1.17409 | + | 0.486322i | 0.882541 | − | 0.470235i | \(-0.155831\pi\) |
0.291544 | + | 0.956557i | \(0.405831\pi\) | |||||||
\(878\) | 2.76906e10 | − | 6.84832e9i | 1.38071 | − | 0.341470i | ||||
\(879\) | 7.31324e9i | 0.363203i | ||||||||
\(880\) | 6.55379e10 | − | 1.22244e10i | 3.24192 | − | 0.604697i | ||||
\(881\) | 2.78778e10i | 1.37354i | 0.726874 | + | 0.686771i | \(0.240973\pi\) | ||||
−0.726874 | + | 0.686771i | \(0.759027\pi\) | |||||||
\(882\) | 4.48965e9 | + | 1.81535e10i | 0.220330 | + | 0.890884i | ||||
\(883\) | 1.24844e9 | + | 5.17119e8i | 0.0610245 | + | 0.0252772i | 0.412987 | − | 0.910737i | \(-0.364486\pi\) |
−0.351962 | + | 0.936014i | \(0.614486\pi\) | |||||||
\(884\) | −2.38199e9 | + | 2.20250e8i | −0.115973 | + | 0.0107234i | ||||
\(885\) | −1.52296e9 | − | 3.67675e9i | −0.0738563 | − | 0.178305i | ||||
\(886\) | −2.36174e9 | + | 1.56005e10i | −0.114081 | + | 0.753563i | ||||
\(887\) | −1.26393e10 | − | 1.26393e10i | −0.608121 | − | 0.608121i | 0.334334 | − | 0.942455i | \(-0.391489\pi\) |
−0.942455 | + | 0.334334i | \(0.891489\pi\) | |||||||
\(888\) | −1.63409e8 | + | 2.81202e9i | −0.00783126 | + | 0.134764i | ||||
\(889\) | 1.80423e9 | − | 1.80423e9i | 0.0861261 | − | 0.0861261i | ||||
\(890\) | −1.10003e9 | − | 1.49251e9i | −0.0523046 | − | 0.0709665i | ||||
\(891\) | 3.07745e10 | − | 1.27472e10i | 1.45753 | − | 0.603730i | ||||
\(892\) | 8.05903e9 | + | 1.52964e10i | 0.380194 | + | 0.721627i | ||||
\(893\) | 2.50740e9 | − | 6.05339e9i | 0.117826 | − | 0.284458i | ||||
\(894\) | −1.18721e9 | + | 1.96739e9i | −0.0555706 | + | 0.0920892i | ||||
\(895\) | −4.26575e10 | −1.98891 | ||||||||
\(896\) | 5.97120e8 | + | 4.70040e9i | 0.0277322 | + | 0.218301i | ||||
\(897\) | −1.61118e9 | −0.0745367 | ||||||||
\(898\) | 5.62222e9 | − | 9.31690e9i | 0.259084 | − | 0.429343i | ||||
\(899\) | −1.03154e10 | + | 2.49035e10i | −0.473507 | + | 1.14315i | ||||
\(900\) | −2.45461e10 | − | 4.65896e10i | −1.12236 | − | 2.13030i | ||||
\(901\) | 8.52899e9 | − | 3.53283e9i | 0.388473 | − | 0.160911i | ||||
\(902\) | −3.63433e10 | − | 4.93104e10i | −1.64893 | − | 2.23725i | ||||
\(903\) | 6.16812e8 | − | 6.16812e8i | 0.0278770 | − | 0.0278770i | ||||
\(904\) | −5.23306e8 | + | 9.00528e9i | −0.0235595 | + | 0.405423i | ||||
\(905\) | −2.37219e10 | − | 2.37219e10i | −1.06385 | − | 1.06385i | ||||
\(906\) | −8.01995e8 | + | 5.29757e9i | −0.0358280 | + | 0.236662i | ||||
\(907\) | 1.43966e10 | + | 3.47564e10i | 0.640668 | + | 1.54671i | 0.825780 | + | 0.563993i | \(0.190735\pi\) |
−0.185111 | + | 0.982718i | \(0.559265\pi\) | |||||||
\(908\) | −1.83699e9 | + | 1.69856e8i | −0.0814340 | + | 0.00752977i | ||||
\(909\) | 1.53591e9 | + | 6.36195e8i | 0.0678254 | + | 0.0280942i | ||||
\(910\) | −7.87631e8 | − | 3.18472e9i | −0.0346480 | − | 0.140096i | ||||
\(911\) | − | 3.22959e10i | − | 1.41525i | −0.706588 | − | 0.707625i | \(-0.749767\pi\) | ||
0.706588 | − | 0.707625i | \(-0.250233\pi\) | |||||||
\(912\) | −5.60149e8 | − | 3.00309e9i | −0.0244524 | − | 0.131095i | ||||
\(913\) | 4.24705e10i | 1.84689i | ||||||||
\(914\) | 6.51943e9 | − | 1.61236e9i | 0.282421 | − | 0.0698473i | ||||
\(915\) | −2.27923e9 | − | 9.44090e8i | −0.0983592 | − | 0.0407417i | ||||
\(916\) | −3.66235e9 | − | 3.04239e9i | −0.157444 | − | 0.130792i | ||||
\(917\) | 3.64968e8 | + | 8.81110e8i | 0.0156301 | + | 0.0377344i | ||||
\(918\) | 2.85153e9 | + | 4.31690e8i | 0.121654 | + | 0.0184172i | ||||
\(919\) | −1.41211e10 | − | 1.41211e10i | −0.600156 | − | 0.600156i | 0.340198 | − | 0.940354i | \(-0.389506\pi\) |
−0.940354 | + | 0.340198i | \(0.889506\pi\) | |||||||
\(920\) | −4.47961e10 | − | 2.16801e10i | −1.89663 | − | 0.917920i | ||||
\(921\) | 3.28623e9 | − | 3.28623e9i | 0.138608 | − | 0.138608i | ||||
\(922\) | −3.80305e9 | + | 2.80297e9i | −0.159799 | + | 0.117777i | ||||
\(923\) | 7.77433e9 | − | 3.22023e9i | 0.325430 | − | 0.134797i | ||||
\(924\) | −1.67663e9 | − | 5.19555e8i | −0.0699174 | − | 0.0216660i | ||||
\(925\) | 1.64605e10 | − | 3.97392e10i | 0.683829 | − | 1.65091i | ||||
\(926\) | 4.14387e9 | + | 2.50059e9i | 0.171501 | + | 0.103491i | ||||
\(927\) | 6.29539e9 | 0.259564 | ||||||||
\(928\) | −2.70220e10 | + | 9.23343e8i | −1.10994 | + | 0.0379267i | ||||
\(929\) | 1.11443e10 | 0.456036 | 0.228018 | − | 0.973657i | \(-0.426776\pi\) | ||||
0.228018 | + | 0.973657i | \(0.426776\pi\) | |||||||
\(930\) | −8.25249e9 | − | 4.97991e9i | −0.336430 | − | 0.203016i | ||||
\(931\) | 6.33953e9 | − | 1.53050e10i | 0.257474 | − | 0.621597i | ||||
\(932\) | −1.43179e9 | + | 4.62047e9i | −0.0579327 | + | 0.186952i | ||||
\(933\) | −7.22655e8 | + | 2.99333e8i | −0.0291303 | + | 0.0120662i | ||||
\(934\) | −3.34409e9 | + | 2.46470e9i | −0.134296 | + | 0.0989805i | ||||
\(935\) | 1.93555e10 | − | 1.93555e10i | 0.774399 | − | 0.774399i | ||||
\(936\) | 2.78708e9 | + | 8.01500e9i | 0.111092 | + | 0.319476i | ||||
\(937\) | −1.54037e10 | − | 1.54037e10i | −0.611699 | − | 0.611699i | 0.331689 | − | 0.943389i | \(-0.392381\pi\) |
−0.943389 | + | 0.331689i | \(0.892381\pi\) | |||||||
\(938\) | −6.89504e9 | − | 1.04383e9i | −0.272789 | − | 0.0412973i | ||||
\(939\) | 2.14689e8 | + | 5.18306e8i | 0.00846215 | + | 0.0204294i | ||||
\(940\) | 1.32504e10 | − | 1.59504e10i | 0.520333 | − | 0.626361i | ||||
\(941\) | −5.70259e9 | − | 2.36209e9i | −0.223104 | − | 0.0924129i | 0.268331 | − | 0.963327i | \(-0.413528\pi\) |
−0.491436 | + | 0.870914i | \(0.663528\pi\) | |||||||
\(942\) | −5.54974e8 | + | 1.37254e8i | −0.0216319 | + | 0.00534991i | ||||
\(943\) | 4.57268e10i | 1.77574i | ||||||||
\(944\) | −2.92476e9 | + | 1.38379e10i | −0.113159 | + | 0.535386i | ||||
\(945\) | 3.95522e9i | 0.152461i | ||||||||
\(946\) | 1.04724e10 | + | 4.23442e10i | 0.402186 | + | 1.62620i | ||||
\(947\) | −7.70336e9 | − | 3.19083e9i | −0.294751 | − | 0.122090i | 0.230408 | − | 0.973094i | \(-0.425994\pi\) |
−0.525159 | + | 0.851004i | \(0.675994\pi\) | |||||||
\(948\) | 1.73965e8 | + | 1.88143e9i | 0.00663184 | + | 0.0717229i | ||||
\(949\) | −1.91245e9 | − | 4.61707e9i | −0.0726371 | − | 0.175362i | ||||
\(950\) | −6.98268e9 | + | 4.61241e10i | −0.264235 | + | 1.74540i | ||||
\(951\) | 3.99388e9 | + | 3.99388e9i | 0.150579 | + | 0.150579i | ||||
\(952\) | 1.29350e9 | + | 1.45310e9i | 0.0485888 | + | 0.0545843i | ||||
\(953\) | −9.56220e9 | + | 9.56220e9i | −0.357876 | + | 0.357876i | −0.863029 | − | 0.505154i | \(-0.831436\pi\) |
0.505154 | + | 0.863029i | \(0.331436\pi\) | |||||||
\(954\) | −1.94293e10 | − | 2.63615e10i | −0.724499 | − | 0.982995i | ||||
\(955\) | 3.43071e10 | − | 1.42105e10i | 1.27460 | − | 0.527955i | ||||
\(956\) | −5.03520e9 | + | 2.65283e9i | −0.186387 | + | 0.0981990i | ||||
\(957\) | 3.83307e9 | − | 9.25385e9i | 0.141369 | − | 0.341296i | ||||
\(958\) | −2.68434e10 | + | 4.44838e10i | −0.986413 | + | 1.63464i | ||||
\(959\) | 3.91715e9 | 0.143418 | ||||||||
\(960\) | 1.11986e9 | − | 9.60300e9i | 0.0408522 | − | 0.350314i | ||||
\(961\) | 6.63809e9 | 0.241274 | ||||||||
\(962\) | −3.58111e9 | + | 5.93446e9i | −0.129690 | + | 0.214916i | ||||
\(963\) | −1.50063e10 | + | 3.62283e10i | −0.541478 | + | 1.30724i | ||||
\(964\) | 1.98898e9 | − | 1.04791e9i | 0.0715089 | − | 0.0376750i | ||||
\(965\) | −3.69542e10 | + | 1.53069e10i | −1.32379 | + | 0.548330i | ||||
\(966\) | 7.77393e8 | + | 1.05476e9i | 0.0277473 | + | 0.0376473i | ||||
\(967\) | −8.35425e9 | + | 8.35425e9i | −0.297108 | + | 0.297108i | −0.839880 | − | 0.542772i | \(-0.817375\pi\) |
0.542772 | + | 0.839880i | \(0.317375\pi\) | |||||||
\(968\) | 4.44826e10 | − | 3.95967e10i | 1.57626 | − | 1.40312i | ||||
\(969\) | −8.86914e8 | − | 8.86914e8i | −0.0313147 | − | 0.0313147i | ||||
\(970\) | 8.52087e9 | − | 5.62846e10i | 0.299766 | − | 1.98010i | ||||
\(971\) | −6.03056e9 | − | 1.45591e10i | −0.211393 | − | 0.510348i | 0.782245 | − | 0.622971i | \(-0.214075\pi\) |
−0.993638 | + | 0.112623i | \(0.964075\pi\) | |||||||
\(972\) | −1.42145e9 | − | 1.53729e10i | −0.0496477 | − | 0.536937i | ||||
\(973\) | −8.80225e9 | − | 3.64601e9i | −0.306336 | − | 0.126889i | ||||
\(974\) | 7.67371e9 | + | 3.10280e10i | 0.266103 | + | 1.07596i | ||||
\(975\) | 4.77968e9i | 0.165152i | ||||||||
\(976\) | 4.78362e9 | + | 7.34770e9i | 0.164696 | + | 0.252975i | ||||
\(977\) | − | 3.52736e10i | − | 1.21009i | −0.796190 | − | 0.605047i | \(-0.793154\pi\) | ||
0.796190 | − | 0.605047i | \(-0.206846\pi\) | |||||||
\(978\) | 8.42126e9 | − | 2.08271e9i | 0.287867 | − | 0.0711940i | ||||
\(979\) | −2.25525e9 | − | 9.34153e8i | −0.0768165 | − | 0.0318184i | ||||
\(980\) | 3.35014e10 | − | 4.03280e10i | 1.13703 | − | 1.36872i | ||||
\(981\) | −5.59039e9 | − | 1.34964e10i | −0.189060 | − | 0.456432i | ||||
\(982\) | 2.93631e9 | + | 4.44526e8i | 0.0989491 | + | 0.0149798i | ||||
\(983\) | 2.10863e10 | + | 2.10863e10i | 0.708050 | + | 0.708050i | 0.966125 | − | 0.258075i | \(-0.0830881\pi\) |
−0.258075 | + | 0.966125i | \(0.583088\pi\) | |||||||
\(984\) | −8.39047e9 | + | 2.91764e9i | −0.280739 | + | 0.0976222i | ||||
\(985\) | −2.77131e10 | + | 2.77131e10i | −0.923971 | + | 0.923971i | ||||
\(986\) | −8.93632e9 | + | 6.58635e9i | −0.296886 | + | 0.218814i | ||||
\(987\) | −5.04398e8 | + | 2.08928e8i | −0.0166979 | + | 0.00691651i | ||||
\(988\) | 2.22505e9 | − | 7.18034e9i | 0.0733990 | − | 0.236862i | ||||
\(989\) | 1.24608e10 | − | 3.00829e10i | 0.409598 | − | 0.988856i | ||||
\(990\) | −8.31365e10 | − | 5.01681e10i | −2.72313 | − | 1.64325i | ||||
\(991\) | 4.10809e10 | 1.34085 | 0.670427 | − | 0.741975i | \(-0.266111\pi\) | ||||
0.670427 | + | 0.741975i | \(0.266111\pi\) | |||||||
\(992\) | 1.41820e10 | + | 3.11814e10i | 0.461260 | + | 1.01416i | ||||
\(993\) | 4.30784e9 | 0.139617 | ||||||||
\(994\) | −5.85924e9 | − | 3.53572e9i | −0.189229 | − | 0.114189i | ||||
\(995\) | 3.14088e10 | − | 7.58276e10i | 1.01081 | − | 2.44032i | ||||
\(996\) | 5.88300e9 | + | 1.82303e9i | 0.188665 | + | 0.0584636i | ||||
\(997\) | 1.05169e10 | − | 4.35626e9i | 0.336090 | − | 0.139213i | −0.208255 | − | 0.978075i | \(-0.566778\pi\) |
0.544345 | + | 0.838861i | \(0.316778\pi\) | |||||||
\(998\) | 4.75902e10 | − | 3.50755e10i | 1.51552 | − | 1.11698i | ||||
\(999\) | 5.90888e9 | − | 5.90888e9i | 0.187511 | − | 0.187511i |
(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 | 32.8.g.a.13.18 | yes | 108 | |
32.5 | even | 8 | inner | 32.8.g.a.5.18 | ✓ | 108 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.8.g.a.5.18 | ✓ | 108 | 32.5 | even | 8 | inner | |
32.8.g.a.13.18 | yes | 108 | 1.1 | even | 1 | trivial |