Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [24,8,Mod(13,24)]
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([0, 1, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("24.13");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 24 = 2^{3} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 24.d (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: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 6 x^{13} - 52 x^{12} + 300 x^{11} - 1005 x^{10} - 23250 x^{9} + 349930 x^{8} + 2867784 x^{7} - 20463993 x^{6} - 78987210 x^{5} + 94608296 x^{4} + \cdots + 3813237677250 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{37}\cdot 3^{16} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 13.1 | ||
Root | \(-4.99225 + 5.30027i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 24.13 |
Dual form | 24.8.d.a.13.2 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −11.2925 | − | 0.691979i | −0.998128 | − | 0.0611629i | ||||
\(3\) | − | 27.0000i | − | 0.577350i | ||||||
\(4\) | 127.042 | + | 15.6284i | 0.992518 | + | 0.122097i | ||||
\(5\) | 124.215i | 0.444406i | 0.975000 | + | 0.222203i | \(0.0713248\pi\) | ||||
−0.975000 | + | 0.222203i | \(0.928675\pi\) | |||||||
\(6\) | −18.6834 | + | 304.898i | −0.0353124 | + | 0.576269i | ||||
\(7\) | 646.373 | 0.712262 | 0.356131 | − | 0.934436i | \(-0.384096\pi\) | ||||
0.356131 | + | 0.934436i | \(0.384096\pi\) | |||||||
\(8\) | −1423.81 | − | 264.394i | −0.983192 | − | 0.182573i | ||||
\(9\) | −729.000 | −0.333333 | ||||||||
\(10\) | 85.9543 | − | 1402.70i | 0.0271811 | − | 0.443574i | ||||
\(11\) | − | 5132.96i | − | 1.16277i | −0.813629 | − | 0.581384i | \(-0.802511\pi\) | ||
0.813629 | − | 0.581384i | \(-0.197489\pi\) | |||||||
\(12\) | 421.966 | − | 3430.14i | 0.0704926 | − | 0.573031i | ||||
\(13\) | − | 13479.3i | − | 1.70163i | −0.525464 | − | 0.850816i | \(-0.676108\pi\) | ||
0.525464 | − | 0.850816i | \(-0.323892\pi\) | |||||||
\(14\) | −7299.18 | − | 447.276i | −0.710929 | − | 0.0435640i | ||||
\(15\) | 3353.81 | 0.256578 | ||||||||
\(16\) | 15895.5 | + | 3970.93i | 0.970185 | + | 0.242366i | ||||
\(17\) | −21363.6 | −1.05464 | −0.527318 | − | 0.849668i | \(-0.676802\pi\) | ||||
−0.527318 | + | 0.849668i | \(0.676802\pi\) | |||||||
\(18\) | 8232.25 | + | 504.453i | 0.332709 | + | 0.0203876i | ||||
\(19\) | − | 12292.3i | − | 0.411145i | −0.978642 | − | 0.205573i | \(-0.934094\pi\) | ||
0.978642 | − | 0.205573i | \(-0.0659057\pi\) | |||||||
\(20\) | −1941.28 | + | 15780.6i | −0.0542605 | + | 0.441081i | ||||
\(21\) | − | 17452.1i | − | 0.411225i | ||||||
\(22\) | −3551.90 | + | 57964.0i | −0.0711182 | + | 1.16059i | ||||
\(23\) | −15142.2 | −0.259503 | −0.129752 | − | 0.991547i | \(-0.541418\pi\) | ||||
−0.129752 | + | 0.991547i | \(0.541418\pi\) | |||||||
\(24\) | −7138.65 | + | 38443.0i | −0.105409 | + | 0.567646i | ||||
\(25\) | 62695.6 | 0.802503 | ||||||||
\(26\) | −9327.39 | + | 152215.i | −0.104077 | + | 1.69845i | ||||
\(27\) | 19683.0i | 0.192450i | ||||||||
\(28\) | 82116.7 | + | 10101.8i | 0.706933 | + | 0.0869648i | ||||
\(29\) | − | 132704.i | − | 1.01039i | −0.863005 | − | 0.505196i | \(-0.831420\pi\) | ||
0.863005 | − | 0.505196i | \(-0.168580\pi\) | |||||||
\(30\) | −37873.0 | − | 2320.77i | −0.256098 | − | 0.0156930i | ||||
\(31\) | 81021.1 | 0.488463 | 0.244232 | − | 0.969717i | \(-0.421464\pi\) | ||||
0.244232 | + | 0.969717i | \(0.421464\pi\) | |||||||
\(32\) | −176753. | − | 55841.2i | −0.953545 | − | 0.301252i | ||||
\(33\) | −138590. | −0.671324 | ||||||||
\(34\) | 241249. | + | 14783.1i | 1.05266 | + | 0.0645046i | ||||
\(35\) | 80289.3i | 0.316533i | ||||||||
\(36\) | −92613.9 | − | 11393.1i | −0.330839 | − | 0.0406989i | ||||
\(37\) | − | 429188.i | − | 1.39297i | −0.717572 | − | 0.696484i | \(-0.754747\pi\) | ||
0.717572 | − | 0.696484i | \(-0.245253\pi\) | |||||||
\(38\) | −8506.01 | + | 138811.i | −0.0251468 | + | 0.410376i | ||||
\(39\) | −363941. | −0.982437 | ||||||||
\(40\) | 32841.8 | − | 176859.i | 0.0811367 | − | 0.436936i | ||||
\(41\) | 314662. | 0.713018 | 0.356509 | − | 0.934292i | \(-0.383967\pi\) | ||||
0.356509 | + | 0.934292i | \(0.383967\pi\) | |||||||
\(42\) | −12076.5 | + | 197078.i | −0.0251517 | + | 0.410455i | ||||
\(43\) | 686180.i | 1.31613i | 0.752962 | + | 0.658064i | \(0.228624\pi\) | ||||
−0.752962 | + | 0.658064i | \(0.771376\pi\) | |||||||
\(44\) | 80219.8 | − | 652103.i | 0.141970 | − | 1.15407i | ||||
\(45\) | − | 90552.9i | − | 0.148135i | ||||||
\(46\) | 170994. | + | 10478.1i | 0.259017 | + | 0.0158719i | ||||
\(47\) | 351245. | 0.493477 | 0.246739 | − | 0.969082i | \(-0.420641\pi\) | ||||
0.246739 | + | 0.969082i | \(0.420641\pi\) | |||||||
\(48\) | 107215. | − | 429179.i | 0.139930 | − | 0.560136i | ||||
\(49\) | −405745. | −0.492683 | ||||||||
\(50\) | −707991. | − | 43384.0i | −0.801001 | − | 0.0490834i | ||||
\(51\) | 576817.i | 0.608895i | ||||||||
\(52\) | 210660. | − | 1.71244e6i | 0.207764 | − | 1.68890i | ||||
\(53\) | − | 602657.i | − | 0.556039i | −0.960575 | − | 0.278019i | \(-0.910322\pi\) | ||
0.960575 | − | 0.278019i | \(-0.0896779\pi\) | |||||||
\(54\) | 13620.2 | − | 222271.i | 0.0117708 | − | 0.192090i | ||||
\(55\) | 637591. | 0.516741 | ||||||||
\(56\) | −920315. | − | 170897.i | −0.700290 | − | 0.130040i | ||||
\(57\) | −331892. | −0.237375 | ||||||||
\(58\) | −91828.1 | + | 1.49856e6i | −0.0617984 | + | 1.00850i | ||||
\(59\) | 2.99946e6i | 1.90134i | 0.310197 | + | 0.950672i | \(0.399605\pi\) | ||||
−0.310197 | + | 0.950672i | \(0.600395\pi\) | |||||||
\(60\) | 426076. | + | 52414.6i | 0.254658 | + | 0.0313273i | ||||
\(61\) | 372829.i | 0.210308i | 0.994456 | + | 0.105154i | \(0.0335335\pi\) | ||||
−0.994456 | + | 0.105154i | \(0.966467\pi\) | |||||||
\(62\) | −914933. | − | 56064.9i | −0.487549 | − | 0.0298758i | ||||
\(63\) | −471206. | −0.237421 | ||||||||
\(64\) | 1.95734e6 | + | 752897.i | 0.933334 | + | 0.359009i | ||||
\(65\) | 1.67433e6 | 0.756215 | ||||||||
\(66\) | 1.56503e6 | + | 95901.2i | 0.670068 | + | 0.0410601i | ||||
\(67\) | 1.57142e6i | 0.638309i | 0.947703 | + | 0.319155i | \(0.103399\pi\) | ||||
−0.947703 | + | 0.319155i | \(0.896601\pi\) | |||||||
\(68\) | −2.71408e6 | − | 333878.i | −1.04675 | − | 0.128768i | ||||
\(69\) | 408840.i | 0.149824i | ||||||||
\(70\) | 55558.5 | − | 906669.i | 0.0193601 | − | 0.315941i | ||||
\(71\) | 3.21138e6 | 1.06485 | 0.532423 | − | 0.846478i | \(-0.321282\pi\) | ||||
0.532423 | + | 0.846478i | \(0.321282\pi\) | |||||||
\(72\) | 1.03796e6 | + | 192744.i | 0.327731 | + | 0.0608578i | ||||
\(73\) | −3.96716e6 | −1.19357 | −0.596787 | − | 0.802400i | \(-0.703556\pi\) | ||||
−0.596787 | + | 0.802400i | \(0.703556\pi\) | |||||||
\(74\) | −296989. | + | 4.84661e6i | −0.0851979 | + | 1.39036i | ||||
\(75\) | − | 1.69278e6i | − | 0.463326i | ||||||
\(76\) | 192109. | − | 1.56164e6i | 0.0501995 | − | 0.408069i | ||||
\(77\) | − | 3.31780e6i | − | 0.828195i | ||||||
\(78\) | 4.10981e6 | + | 251839.i | 0.980598 | + | 0.0600887i | ||||
\(79\) | −5.94163e6 | −1.35585 | −0.677923 | − | 0.735133i | \(-0.737120\pi\) | ||||
−0.677923 | + | 0.735133i | \(0.737120\pi\) | |||||||
\(80\) | −493250. | + | 1.97446e6i | −0.107709 | + | 0.431156i | ||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −3.55332e6 | − | 217739.i | −0.711683 | − | 0.0436102i | ||||
\(83\) | − | 9.26430e6i | − | 1.77844i | −0.457480 | − | 0.889220i | \(-0.651248\pi\) | ||
0.457480 | − | 0.889220i | \(-0.348752\pi\) | |||||||
\(84\) | 272747. | − | 2.21715e6i | 0.0502092 | − | 0.408148i | ||||
\(85\) | − | 2.65368e6i | − | 0.468687i | ||||||
\(86\) | 474822. | − | 7.74870e6i | 0.0804982 | − | 1.31366i | ||||
\(87\) | −3.58300e6 | −0.583350 | ||||||||
\(88\) | −1.35712e6 | + | 7.30838e6i | −0.212290 | + | 1.14322i | ||||
\(89\) | 1.28258e7 | 1.92850 | 0.964250 | − | 0.264993i | \(-0.0853697\pi\) | ||||
0.964250 | + | 0.264993i | \(0.0853697\pi\) | |||||||
\(90\) | −62660.7 | + | 1.02257e6i | −0.00906038 | + | 0.147858i | ||||
\(91\) | − | 8.71265e6i | − | 1.21201i | ||||||
\(92\) | −1.92370e6 | − | 236648.i | −0.257561 | − | 0.0316845i | ||||
\(93\) | − | 2.18757e6i | − | 0.282014i | ||||||
\(94\) | −3.96644e6 | − | 243054.i | −0.492553 | − | 0.0301825i | ||||
\(95\) | 1.52689e6 | 0.182715 | ||||||||
\(96\) | −1.50771e6 | + | 4.77232e6i | −0.173928 | + | 0.550529i | ||||
\(97\) | −1.36350e7 | −1.51690 | −0.758448 | − | 0.651734i | \(-0.774042\pi\) | ||||
−0.758448 | + | 0.651734i | \(0.774042\pi\) | |||||||
\(98\) | 4.58189e6 | + | 280767.i | 0.491760 | + | 0.0301339i | ||||
\(99\) | 3.74192e6i | 0.387589i | ||||||||
\(100\) | 7.96499e6 | + | 979830.i | 0.796499 | + | 0.0979830i | ||||
\(101\) | 1.15744e7i | 1.11782i | 0.829228 | + | 0.558910i | \(0.188780\pi\) | ||||
−0.829228 | + | 0.558910i | \(0.811220\pi\) | |||||||
\(102\) | 399145. | − | 6.51372e6i | 0.0372417 | − | 0.607755i | ||||
\(103\) | 1.54055e7 | 1.38914 | 0.694571 | − | 0.719424i | \(-0.255594\pi\) | ||||
0.694571 | + | 0.719424i | \(0.255594\pi\) | |||||||
\(104\) | −3.56385e6 | + | 1.91920e7i | −0.310673 | + | 1.67303i | ||||
\(105\) | 2.16781e6 | 0.182751 | ||||||||
\(106\) | −417026. | + | 6.80553e6i | −0.0340089 | + | 0.554998i | ||||
\(107\) | − | 3.25844e6i | − | 0.257138i | −0.991701 | − | 0.128569i | \(-0.958962\pi\) | ||
0.991701 | − | 0.128569i | \(-0.0410383\pi\) | |||||||
\(108\) | −307613. | + | 2.50057e6i | −0.0234975 | + | 0.191010i | ||||
\(109\) | 2.19394e7i | 1.62268i | 0.584577 | + | 0.811338i | \(0.301261\pi\) | ||||
−0.584577 | + | 0.811338i | \(0.698739\pi\) | |||||||
\(110\) | −7.20002e6 | − | 441200.i | −0.515774 | − | 0.0316054i | ||||
\(111\) | −1.15881e7 | −0.804230 | ||||||||
\(112\) | 1.02744e7 | + | 2.56670e6i | 0.691026 | + | 0.172628i | ||||
\(113\) | −2.56062e6 | −0.166944 | −0.0834721 | − | 0.996510i | \(-0.526601\pi\) | ||||
−0.0834721 | + | 0.996510i | \(0.526601\pi\) | |||||||
\(114\) | 3.74790e6 | + | 229662.i | 0.236931 | + | 0.0145185i | ||||
\(115\) | − | 1.88090e6i | − | 0.115325i | ||||||
\(116\) | 2.07394e6 | − | 1.68590e7i | 0.123365 | − | 1.00283i | ||||
\(117\) | 9.82641e6i | 0.567211i | ||||||||
\(118\) | 2.07556e6 | − | 3.38715e7i | 0.116292 | − | 1.89778i | ||||
\(119\) | −1.38088e7 | −0.751177 | ||||||||
\(120\) | −4.77521e6 | − | 886729.i | −0.252265 | − | 0.0468443i | ||||
\(121\) | −6.86006e6 | −0.352029 | ||||||||
\(122\) | 257990. | − | 4.21018e6i | 0.0128630 | − | 0.209914i | ||||
\(123\) | − | 8.49586e6i | − | 0.411661i | ||||||
\(124\) | 1.02931e7 | + | 1.26623e6i | 0.484809 | + | 0.0596398i | ||||
\(125\) | 1.74921e7i | 0.801043i | ||||||||
\(126\) | 5.32110e6 | + | 326064.i | 0.236976 | + | 0.0145213i | ||||
\(127\) | 3.97514e7 | 1.72203 | 0.861013 | − | 0.508583i | \(-0.169831\pi\) | ||||
0.861013 | + | 0.508583i | \(0.169831\pi\) | |||||||
\(128\) | −2.15824e7 | − | 9.85655e6i | −0.909629 | − | 0.415423i | ||||
\(129\) | 1.85268e7 | 0.759867 | ||||||||
\(130\) | −1.89075e7 | − | 1.15860e6i | −0.754799 | − | 0.0462523i | ||||
\(131\) | 1.09930e7i | 0.427233i | 0.976918 | + | 0.213617i | \(0.0685243\pi\) | ||||
−0.976918 | + | 0.213617i | \(0.931476\pi\) | |||||||
\(132\) | −1.76068e7 | − | 2.16593e6i | −0.666302 | − | 0.0819665i | ||||
\(133\) | − | 7.94540e6i | − | 0.292843i | ||||||
\(134\) | 1.08739e6 | − | 1.77453e7i | 0.0390408 | − | 0.637114i | ||||
\(135\) | −2.44493e6 | −0.0855260 | ||||||||
\(136\) | 3.04178e7 | + | 5.64841e6i | 1.03691 | + | 0.192548i | ||||
\(137\) | −6.84719e6 | −0.227505 | −0.113752 | − | 0.993509i | \(-0.536287\pi\) | ||||
−0.113752 | + | 0.993509i | \(0.536287\pi\) | |||||||
\(138\) | 282909. | − | 4.61684e6i | 0.00916367 | − | 0.149544i | ||||
\(139\) | 5.55412e6i | 0.175414i | 0.996146 | + | 0.0877068i | \(0.0279539\pi\) | ||||
−0.996146 | + | 0.0877068i | \(0.972046\pi\) | |||||||
\(140\) | −1.25479e6 | + | 1.02001e7i | −0.0386477 | + | 0.314165i | ||||
\(141\) | − | 9.48360e6i | − | 0.284909i | ||||||
\(142\) | −3.62645e7 | − | 2.22220e6i | −1.06285 | − | 0.0651290i | ||||
\(143\) | −6.91886e7 | −1.97860 | ||||||||
\(144\) | −1.15878e7 | − | 2.89481e6i | −0.323395 | − | 0.0807888i | ||||
\(145\) | 1.64838e7 | 0.449024 | ||||||||
\(146\) | 4.47992e7 | + | 2.74519e6i | 1.19134 | + | 0.0730024i | ||||
\(147\) | 1.09551e7i | 0.284451i | ||||||||
\(148\) | 6.70751e6 | − | 5.45250e7i | 0.170077 | − | 1.38255i | ||||
\(149\) | − | 3.66701e7i | − | 0.908154i | −0.890962 | − | 0.454077i | \(-0.849969\pi\) | ||
0.890962 | − | 0.454077i | \(-0.150031\pi\) | |||||||
\(150\) | −1.17137e6 | + | 1.91158e7i | −0.0283383 | + | 0.462458i | ||||
\(151\) | 4.09127e7 | 0.967027 | 0.483513 | − | 0.875337i | \(-0.339360\pi\) | ||||
0.483513 | + | 0.875337i | \(0.339360\pi\) | |||||||
\(152\) | −3.25002e6 | + | 1.75020e7i | −0.0750642 | + | 0.404235i | ||||
\(153\) | 1.55740e7 | 0.351545 | ||||||||
\(154\) | −2.29585e6 | + | 3.74664e7i | −0.0506548 | + | 0.826645i | ||||
\(155\) | 1.00641e7i | 0.217076i | ||||||||
\(156\) | −4.62359e7 | − | 5.68781e6i | −0.975087 | − | 0.119952i | ||||
\(157\) | − | 1.97881e7i | − | 0.408088i | −0.978962 | − | 0.204044i | \(-0.934591\pi\) | ||
0.978962 | − | 0.204044i | \(-0.0654086\pi\) | |||||||
\(158\) | 6.70960e7 | + | 4.11148e6i | 1.35331 | + | 0.0829274i | ||||
\(159\) | −1.62718e7 | −0.321029 | ||||||||
\(160\) | 6.93633e6 | − | 2.19554e7i | 0.133878 | − | 0.423761i | ||||
\(161\) | −9.78752e6 | −0.184834 | ||||||||
\(162\) | −6.00131e6 | − | 367746.i | −0.110903 | − | 0.00679587i | ||||
\(163\) | − | 1.94325e7i | − | 0.351457i | −0.984439 | − | 0.175728i | \(-0.943772\pi\) | ||
0.984439 | − | 0.175728i | \(-0.0562280\pi\) | |||||||
\(164\) | 3.99753e7 | + | 4.91765e6i | 0.707683 | + | 0.0870571i | ||||
\(165\) | − | 1.72150e7i | − | 0.298341i | ||||||
\(166\) | −6.41070e6 | + | 1.04617e8i | −0.108774 | + | 1.77511i | ||||
\(167\) | 1.44338e7 | 0.239813 | 0.119906 | − | 0.992785i | \(-0.461741\pi\) | ||||
0.119906 | + | 0.992785i | \(0.461741\pi\) | |||||||
\(168\) | −4.61423e6 | + | 2.48485e7i | −0.0750787 | + | 0.404313i | ||||
\(169\) | −1.18943e8 | −1.89555 | ||||||||
\(170\) | −1.83629e6 | + | 2.99668e7i | −0.0286662 | + | 0.467809i | ||||
\(171\) | 8.96109e6i | 0.137048i | ||||||||
\(172\) | −1.07239e7 | + | 8.71738e7i | −0.160695 | + | 1.30628i | ||||
\(173\) | − | 5.75803e7i | − | 0.845498i | −0.906247 | − | 0.422749i | \(-0.861065\pi\) | ||
0.906247 | − | 0.422749i | \(-0.138935\pi\) | |||||||
\(174\) | 4.04611e7 | + | 2.47936e6i | 0.582258 | + | 0.0356793i | ||||
\(175\) | 4.05247e7 | 0.571593 | ||||||||
\(176\) | 2.03826e7 | − | 8.15909e7i | 0.281816 | − | 1.12810i | ||||
\(177\) | 8.09854e7 | 1.09774 | ||||||||
\(178\) | −1.44836e8 | − | 8.87519e6i | −1.92489 | − | 0.117953i | ||||
\(179\) | 6.92684e7i | 0.902713i | 0.892344 | + | 0.451357i | \(0.149060\pi\) | ||||
−0.892344 | + | 0.451357i | \(0.850940\pi\) | |||||||
\(180\) | 1.41520e6 | − | 1.15041e7i | 0.0180868 | − | 0.147027i | ||||
\(181\) | − | 8.27698e7i | − | 1.03752i | −0.854920 | − | 0.518761i | \(-0.826394\pi\) | ||
0.854920 | − | 0.518761i | \(-0.173606\pi\) | |||||||
\(182\) | −6.02897e6 | + | 9.83878e7i | −0.0741298 | + | 1.20974i | ||||
\(183\) | 1.00664e7 | 0.121421 | ||||||||
\(184\) | 2.15597e7 | + | 4.00352e6i | 0.255141 | + | 0.0473783i | ||||
\(185\) | 5.33116e7 | 0.619043 | ||||||||
\(186\) | −1.51375e6 | + | 2.47032e7i | −0.0172488 | + | 0.281487i | ||||
\(187\) | 1.09658e8i | 1.22630i | ||||||||
\(188\) | 4.46229e7 | + | 5.48938e6i | 0.489785 | + | 0.0602519i | ||||
\(189\) | 1.27226e7i | 0.137075i | ||||||||
\(190\) | −1.72425e7 | − | 1.05658e6i | −0.182373 | − | 0.0111754i | ||||
\(191\) | −7.12908e7 | −0.740316 | −0.370158 | − | 0.928969i | \(-0.620696\pi\) | ||||
−0.370158 | + | 0.928969i | \(0.620696\pi\) | |||||||
\(192\) | 2.03282e7 | − | 5.28483e7i | 0.207274 | − | 0.538861i | ||||
\(193\) | −8.45423e7 | −0.846493 | −0.423247 | − | 0.906015i | \(-0.639110\pi\) | ||||
−0.423247 | + | 0.906015i | \(0.639110\pi\) | |||||||
\(194\) | 1.53974e8 | + | 9.43516e6i | 1.51406 | + | 0.0927777i | ||||
\(195\) | − | 4.52070e7i | − | 0.436601i | ||||||
\(196\) | −5.15469e7 | − | 6.34114e6i | −0.488997 | − | 0.0601549i | ||||
\(197\) | − | 4.53519e7i | − | 0.422634i | −0.977418 | − | 0.211317i | \(-0.932225\pi\) | ||
0.977418 | − | 0.211317i | \(-0.0677752\pi\) | |||||||
\(198\) | 2.58933e6 | − | 4.22558e7i | 0.0237061 | − | 0.386864i | ||||
\(199\) | 8.78225e7 | 0.789987 | 0.394993 | − | 0.918684i | \(-0.370747\pi\) | ||||
0.394993 | + | 0.918684i | \(0.370747\pi\) | |||||||
\(200\) | −8.92669e7 | − | 1.65764e7i | −0.789015 | − | 0.146516i | ||||
\(201\) | 4.24284e7 | 0.368528 | ||||||||
\(202\) | 8.00921e6 | − | 1.30704e8i | 0.0683691 | − | 1.11573i | ||||
\(203\) | − | 8.57760e7i | − | 0.719664i | ||||||
\(204\) | −9.01471e6 | + | 7.32801e7i | −0.0743440 | + | 0.604339i | ||||
\(205\) | 3.90858e7i | 0.316869i | ||||||||
\(206\) | −1.73967e8 | − | 1.06603e7i | −1.38654 | − | 0.0849639i | ||||
\(207\) | 1.10387e7 | 0.0865010 | ||||||||
\(208\) | 5.35254e7 | − | 2.14260e8i | 0.412418 | − | 1.65090i | ||||
\(209\) | −6.30958e7 | −0.478067 | ||||||||
\(210\) | −2.44801e7 | − | 1.50008e6i | −0.182409 | − | 0.0111776i | ||||
\(211\) | − | 7.44392e7i | − | 0.545523i | −0.962082 | − | 0.272761i | \(-0.912063\pi\) | ||
0.962082 | − | 0.272761i | \(-0.0879369\pi\) | |||||||
\(212\) | 9.41856e6 | − | 7.65630e7i | 0.0678905 | − | 0.551878i | ||||
\(213\) | − | 8.67071e7i | − | 0.614789i | ||||||
\(214\) | −2.25477e6 | + | 3.67960e7i | −0.0157273 | + | 0.256656i | ||||
\(215\) | −8.52339e7 | −0.584895 | ||||||||
\(216\) | 5.20408e6 | − | 2.80249e7i | 0.0351363 | − | 0.189215i | ||||
\(217\) | 5.23698e7 | 0.347914 | ||||||||
\(218\) | 1.51816e7 | − | 2.47751e8i | 0.0992476 | − | 1.61964i | ||||
\(219\) | 1.07113e8i | 0.689110i | ||||||||
\(220\) | 8.10011e7 | + | 9.96452e6i | 0.512875 | + | 0.0630924i | ||||
\(221\) | 2.87966e8i | 1.79460i | ||||||||
\(222\) | 1.30859e8 | + | 8.01869e6i | 0.802725 | + | 0.0491890i | ||||
\(223\) | −8.46115e7 | −0.510931 | −0.255466 | − | 0.966818i | \(-0.582229\pi\) | ||||
−0.255466 | + | 0.966818i | \(0.582229\pi\) | |||||||
\(224\) | −1.14248e8 | − | 3.60942e7i | −0.679174 | − | 0.214570i | ||||
\(225\) | −4.57051e7 | −0.267501 | ||||||||
\(226\) | 2.89159e7 | + | 1.77190e6i | 0.166632 | + | 0.0102108i | ||||
\(227\) | 8.23087e7i | 0.467041i | 0.972352 | + | 0.233521i | \(0.0750247\pi\) | ||||
−0.972352 | + | 0.233521i | \(0.924975\pi\) | |||||||
\(228\) | −4.21643e7 | − | 5.18693e6i | −0.235599 | − | 0.0289827i | ||||
\(229\) | 2.13102e8i | 1.17264i | 0.810081 | + | 0.586318i | \(0.199423\pi\) | ||||
−0.810081 | + | 0.586318i | \(0.800577\pi\) | |||||||
\(230\) | −1.30154e6 | + | 2.12401e7i | −0.00705359 | + | 0.115109i | ||||
\(231\) | −8.95806e7 | −0.478159 | ||||||||
\(232\) | −3.50861e7 | + | 1.88945e8i | −0.184471 | + | 0.993409i | ||||
\(233\) | 1.70596e8 | 0.883536 | 0.441768 | − | 0.897129i | \(-0.354351\pi\) | ||||
0.441768 | + | 0.897129i | \(0.354351\pi\) | |||||||
\(234\) | 6.79967e6 | − | 1.10965e8i | 0.0346922 | − | 0.566149i | ||||
\(235\) | 4.36299e7i | 0.219304i | ||||||||
\(236\) | −4.68767e7 | + | 3.81058e8i | −0.232148 | + | 1.88712i | ||||
\(237\) | 1.60424e8i | 0.782798i | ||||||||
\(238\) | 1.55937e8 | + | 9.55542e6i | 0.749771 | + | 0.0459442i | ||||
\(239\) | 3.87765e8 | 1.83728 | 0.918642 | − | 0.395090i | \(-0.129287\pi\) | ||||
0.918642 | + | 0.395090i | \(0.129287\pi\) | |||||||
\(240\) | 5.33105e7 | + | 1.33178e7i | 0.248928 | + | 0.0621859i | ||||
\(241\) | 1.12927e8 | 0.519683 | 0.259841 | − | 0.965651i | \(-0.416330\pi\) | ||||
0.259841 | + | 0.965651i | \(0.416330\pi\) | |||||||
\(242\) | 7.74674e7 | + | 4.74701e6i | 0.351370 | + | 0.0215311i | ||||
\(243\) | − | 1.43489e7i | − | 0.0641500i | ||||||
\(244\) | −5.82671e6 | + | 4.73650e7i | −0.0256779 | + | 0.208734i | ||||
\(245\) | − | 5.03998e7i | − | 0.218951i | ||||||
\(246\) | −5.87896e6 | + | 9.59398e7i | −0.0251784 | + | 0.410890i | ||||
\(247\) | −1.65692e8 | −0.699618 | ||||||||
\(248\) | −1.15359e8 | − | 2.14215e7i | −0.480253 | − | 0.0891804i | ||||
\(249\) | −2.50136e8 | −1.02678 | ||||||||
\(250\) | 1.21041e7 | − | 1.97530e8i | 0.0489941 | − | 0.799543i | ||||
\(251\) | − | 1.91451e8i | − | 0.764187i | −0.924124 | − | 0.382093i | \(-0.875203\pi\) | ||
0.924124 | − | 0.382093i | \(-0.124797\pi\) | |||||||
\(252\) | −5.98631e7 | − | 7.36418e6i | −0.235644 | − | 0.0289883i | ||||
\(253\) | 7.77244e7i | 0.301742i | ||||||||
\(254\) | −4.48894e8 | − | 2.75071e7i | −1.71880 | − | 0.105324i | ||||
\(255\) | −7.16494e7 | −0.270596 | ||||||||
\(256\) | 2.36899e8 | + | 1.26240e8i | 0.882517 | + | 0.470280i | ||||
\(257\) | 1.62153e8 | 0.595880 | 0.297940 | − | 0.954585i | \(-0.403701\pi\) | ||||
0.297940 | + | 0.954585i | \(0.403701\pi\) | |||||||
\(258\) | −2.09215e8 | − | 1.28202e7i | −0.758444 | − | 0.0464756i | ||||
\(259\) | − | 2.77415e8i | − | 0.992158i | ||||||
\(260\) | 2.12711e8 | + | 2.61671e7i | 0.750557 | + | 0.0923314i | ||||
\(261\) | 9.67409e7i | 0.336797i | ||||||||
\(262\) | 7.60689e6 | − | 1.24138e8i | 0.0261308 | − | 0.426433i | ||||
\(263\) | −8.57486e6 | −0.0290658 | −0.0145329 | − | 0.999894i | \(-0.504626\pi\) | ||||
−0.0145329 | + | 0.999894i | \(0.504626\pi\) | |||||||
\(264\) | 1.97326e8 | + | 3.66424e7i | 0.660041 | + | 0.122566i | ||||
\(265\) | 7.48592e7 | 0.247107 | ||||||||
\(266\) | −5.49805e6 | + | 8.97237e7i | −0.0179111 | + | 0.292295i | ||||
\(267\) | − | 3.46297e8i | − | 1.11342i | ||||||
\(268\) | −2.45588e7 | + | 1.99637e8i | −0.0779354 | + | 0.633534i | ||||
\(269\) | 2.35872e7i | 0.0738828i | 0.999317 | + | 0.0369414i | \(0.0117615\pi\) | ||||
−0.999317 | + | 0.0369414i | \(0.988239\pi\) | |||||||
\(270\) | 2.76094e7 | + | 1.69184e6i | 0.0853658 | + | 0.00523101i | ||||
\(271\) | 2.51796e7 | 0.0768522 | 0.0384261 | − | 0.999261i | \(-0.487766\pi\) | ||||
0.0384261 | + | 0.999261i | \(0.487766\pi\) | |||||||
\(272\) | −3.39585e8 | − | 8.48333e7i | −1.02319 | − | 0.255608i | ||||
\(273\) | −2.35242e8 | −0.699753 | ||||||||
\(274\) | 7.73221e7 | + | 4.73811e6i | 0.227079 | + | 0.0139148i | ||||
\(275\) | − | 3.21814e8i | − | 0.933125i | ||||||
\(276\) | −6.38951e6 | + | 5.19400e7i | −0.0182930 | + | 0.148703i | ||||
\(277\) | − | 3.44675e8i | − | 0.974384i | −0.873295 | − | 0.487192i | \(-0.838021\pi\) | ||
0.873295 | − | 0.487192i | \(-0.161979\pi\) | |||||||
\(278\) | 3.84333e6 | − | 6.27200e7i | 0.0107288 | − | 0.175085i | ||||
\(279\) | −5.90644e7 | −0.162821 | ||||||||
\(280\) | 2.12281e7 | − | 1.14317e8i | 0.0577906 | − | 0.311213i | ||||
\(281\) | −3.37409e8 | −0.907162 | −0.453581 | − | 0.891215i | \(-0.649854\pi\) | ||||
−0.453581 | + | 0.891215i | \(0.649854\pi\) | |||||||
\(282\) | −6.56245e6 | + | 1.07094e8i | −0.0174259 | + | 0.284376i | ||||
\(283\) | − | 3.95114e8i | − | 1.03626i | −0.855301 | − | 0.518131i | \(-0.826628\pi\) | ||
0.855301 | − | 0.518131i | \(-0.173372\pi\) | |||||||
\(284\) | 4.07981e8 | + | 5.01886e7i | 1.05688 | + | 0.130014i | ||||
\(285\) | − | 4.12260e7i | − | 0.105491i | ||||||
\(286\) | 7.81315e8 | + | 4.78771e7i | 1.97490 | + | 0.121017i | ||||
\(287\) | 2.03389e8 | 0.507855 | ||||||||
\(288\) | 1.28853e8 | + | 4.07082e7i | 0.317848 | + | 0.100417i | ||||
\(289\) | 4.60637e7 | 0.112258 | ||||||||
\(290\) | −1.86144e8 | − | 1.14064e7i | −0.448183 | − | 0.0274636i | ||||
\(291\) | 3.68146e8i | 0.875780i | ||||||||
\(292\) | −5.03997e8 | − | 6.20002e7i | −1.18464 | − | 0.145731i | ||||
\(293\) | − | 6.01628e8i | − | 1.39731i | −0.715461 | − | 0.698653i | \(-0.753783\pi\) | ||
0.715461 | − | 0.698653i | \(-0.246217\pi\) | |||||||
\(294\) | 7.58072e6 | − | 1.23711e8i | 0.0173978 | − | 0.283918i | ||||
\(295\) | −3.72578e8 | −0.844969 | ||||||||
\(296\) | −1.13475e8 | + | 6.11083e8i | −0.254319 | + | 1.36956i | ||||
\(297\) | 1.01032e8 | 0.223775 | ||||||||
\(298\) | −2.53749e7 | + | 4.14098e8i | −0.0555453 | + | 0.906454i | ||||
\(299\) | 2.04107e8i | 0.441579i | ||||||||
\(300\) | 2.64554e7 | − | 2.15055e8i | 0.0565705 | − | 0.459859i | ||||
\(301\) | 4.43528e8i | 0.937428i | ||||||||
\(302\) | −4.62007e8 | − | 2.83107e7i | −0.965216 | − | 0.0591461i | ||||
\(303\) | 3.12508e8 | 0.645374 | ||||||||
\(304\) | 4.88119e7 | − | 1.95392e8i | 0.0996478 | − | 0.398887i | ||||
\(305\) | −4.63110e7 | −0.0934620 | ||||||||
\(306\) | −1.75870e8 | − | 1.07769e7i | −0.350887 | − | 0.0215015i | ||||
\(307\) | 5.80663e8i | 1.14535i | 0.819781 | + | 0.572677i | \(0.194095\pi\) | ||||
−0.819781 | + | 0.572677i | \(0.805905\pi\) | |||||||
\(308\) | 5.18519e7 | − | 4.21501e8i | 0.101120 | − | 0.821999i | ||||
\(309\) | − | 4.15950e8i | − | 0.802022i | ||||||
\(310\) | 6.96411e6 | − | 1.13649e8i | 0.0132770 | − | 0.216670i | ||||
\(311\) | 3.05489e8 | 0.575883 | 0.287942 | − | 0.957648i | \(-0.407029\pi\) | ||||
0.287942 | + | 0.957648i | \(0.407029\pi\) | |||||||
\(312\) | 5.18185e8 | + | 9.62240e7i | 0.965925 | + | 0.179367i | ||||
\(313\) | 4.78994e8 | 0.882928 | 0.441464 | − | 0.897279i | \(-0.354459\pi\) | ||||
0.441464 | + | 0.897279i | \(0.354459\pi\) | |||||||
\(314\) | −1.36929e7 | + | 2.23457e8i | −0.0249599 | + | 0.407324i | ||||
\(315\) | − | 5.85309e7i | − | 0.105511i | ||||||
\(316\) | −7.54838e8 | − | 9.28580e7i | −1.34570 | − | 0.165544i | ||||
\(317\) | 8.73052e8i | 1.53933i | 0.638446 | + | 0.769666i | \(0.279577\pi\) | ||||
−0.638446 | + | 0.769666i | \(0.720423\pi\) | |||||||
\(318\) | 1.83749e8 | + | 1.12597e7i | 0.320428 | + | 0.0196351i | ||||
\(319\) | −6.81162e8 | −1.17485 | ||||||||
\(320\) | −9.35213e7 | + | 2.43132e8i | −0.159546 | + | 0.414779i | ||||
\(321\) | −8.79778e7 | −0.148459 | ||||||||
\(322\) | 1.10526e8 | + | 6.77276e6i | 0.184488 | + | 0.0113050i | ||||
\(323\) | 2.62607e8i | 0.433609i | ||||||||
\(324\) | 6.75155e7 | + | 8.30556e6i | 0.110280 | + | 0.0135663i | ||||
\(325\) | − | 8.45092e8i | − | 1.36557i | ||||||
\(326\) | −1.34469e7 | + | 2.19442e8i | −0.0214961 | + | 0.350799i | ||||
\(327\) | 5.92364e8 | 0.936853 | ||||||||
\(328\) | −4.48020e8 | − | 8.31948e7i | −0.701033 | − | 0.130178i | ||||
\(329\) | 2.27035e8 | 0.351485 | ||||||||
\(330\) | −1.19124e7 | + | 1.94400e8i | −0.0182474 | + | 0.297782i | ||||
\(331\) | 9.94404e8i | 1.50718i | 0.657346 | + | 0.753589i | \(0.271679\pi\) | ||||
−0.657346 | + | 0.753589i | \(0.728321\pi\) | |||||||
\(332\) | 1.44786e8 | − | 1.17696e9i | 0.217142 | − | 1.76513i | ||||
\(333\) | 3.12878e8i | 0.464323i | ||||||||
\(334\) | −1.62994e8 | − | 9.98787e6i | −0.239364 | − | 0.0146676i | ||||
\(335\) | −1.95195e8 | −0.283668 | ||||||||
\(336\) | 6.93009e7 | − | 2.77409e8i | 0.0996670 | − | 0.398964i | ||||
\(337\) | 2.60603e8 | 0.370916 | 0.185458 | − | 0.982652i | \(-0.440623\pi\) | ||||
0.185458 | + | 0.982652i | \(0.440623\pi\) | |||||||
\(338\) | 1.34317e9 | + | 8.23060e7i | 1.89200 | + | 0.115937i | ||||
\(339\) | 6.91369e7i | 0.0963853i | ||||||||
\(340\) | 4.14727e7 | − | 3.37130e8i | 0.0572251 | − | 0.465180i | ||||
\(341\) | − | 4.15878e8i | − | 0.567970i | ||||||
\(342\) | 6.20088e6 | − | 1.01193e8i | 0.00838228 | − | 0.136792i | ||||
\(343\) | −7.94578e8 | −1.06318 | ||||||||
\(344\) | 1.81422e8 | − | 9.76992e8i | 0.240290 | − | 1.29401i | ||||
\(345\) | −5.07842e7 | −0.0665827 | ||||||||
\(346\) | −3.98443e7 | + | 6.50227e8i | −0.0517130 | + | 0.843915i | ||||
\(347\) | 1.06575e9i | 1.36931i | 0.728865 | + | 0.684657i | \(0.240048\pi\) | ||||
−0.728865 | + | 0.684657i | \(0.759952\pi\) | |||||||
\(348\) | −4.55192e8 | − | 5.59964e7i | −0.578985 | − | 0.0712251i | ||||
\(349\) | 4.25455e8i | 0.535754i | 0.963453 | + | 0.267877i | \(0.0863220\pi\) | ||||
−0.963453 | + | 0.267877i | \(0.913678\pi\) | |||||||
\(350\) | −4.57626e8 | − | 2.80422e7i | −0.570523 | − | 0.0349602i | ||||
\(351\) | 2.65313e8 | 0.327479 | ||||||||
\(352\) | −2.86630e8 | + | 9.07263e8i | −0.350286 | + | 1.10875i | ||||
\(353\) | −8.81730e8 | −1.06690 | −0.533451 | − | 0.845831i | \(-0.679105\pi\) | ||||
−0.533451 | + | 0.845831i | \(0.679105\pi\) | |||||||
\(354\) | −9.14530e8 | − | 5.60402e7i | −1.09569 | − | 0.0671410i | ||||
\(355\) | 3.98902e8i | 0.473224i | ||||||||
\(356\) | 1.62942e9 | + | 2.00447e8i | 1.91407 | + | 0.235464i | ||||
\(357\) | 3.72838e8i | 0.433692i | ||||||||
\(358\) | 4.79323e7 | − | 7.82216e8i | 0.0552125 | − | 0.901023i | ||||
\(359\) | 2.70320e8 | 0.308353 | 0.154176 | − | 0.988043i | \(-0.450728\pi\) | ||||
0.154176 | + | 0.988043i | \(0.450728\pi\) | |||||||
\(360\) | −2.39417e7 | + | 1.28931e8i | −0.0270456 | + | 0.145645i | ||||
\(361\) | 7.42771e8 | 0.830959 | ||||||||
\(362\) | −5.72750e7 | + | 9.34680e8i | −0.0634578 | + | 1.03558i | ||||
\(363\) | 1.85222e8i | 0.203244i | ||||||||
\(364\) | 1.36165e8 | − | 1.10688e9i | 0.147982 | − | 1.20294i | ||||
\(365\) | − | 4.92781e8i | − | 0.530431i | ||||||
\(366\) | −1.13675e8 | − | 6.96572e6i | −0.121194 | − | 0.00742647i | ||||
\(367\) | 3.82422e8 | 0.403842 | 0.201921 | − | 0.979402i | \(-0.435282\pi\) | ||||
0.201921 | + | 0.979402i | \(0.435282\pi\) | |||||||
\(368\) | −2.40693e8 | − | 6.01288e7i | −0.251766 | − | 0.0628948i | ||||
\(369\) | −2.29388e8 | −0.237673 | ||||||||
\(370\) | −6.02023e8 | − | 3.68905e7i | −0.617884 | − | 0.0378625i | ||||
\(371\) | − | 3.89541e8i | − | 0.396045i | ||||||
\(372\) | 3.41882e7 | − | 2.77914e8i | 0.0344330 | − | 0.279905i | ||||
\(373\) | − | 1.28178e9i | − | 1.27889i | −0.768838 | − | 0.639443i | \(-0.779165\pi\) | ||
0.768838 | − | 0.639443i | \(-0.220835\pi\) | |||||||
\(374\) | 7.58812e7 | − | 1.23832e9i | 0.0750038 | − | 1.22400i | ||||
\(375\) | 4.72286e8 | 0.462483 | ||||||||
\(376\) | −5.00107e8 | − | 9.28671e7i | −0.485183 | − | 0.0900958i | ||||
\(377\) | −1.78875e9 | −1.71931 | ||||||||
\(378\) | 8.80374e6 | − | 1.43670e8i | 0.00838389 | − | 0.136818i | ||||
\(379\) | − | 9.91369e8i | − | 0.935402i | −0.883887 | − | 0.467701i | \(-0.845082\pi\) | ||
0.883887 | − | 0.467701i | \(-0.154918\pi\) | |||||||
\(380\) | 1.93980e8 | + | 2.38628e7i | 0.181348 | + | 0.0223090i | ||||
\(381\) | − | 1.07329e9i | − | 0.994212i | ||||||
\(382\) | 8.05054e8 | + | 4.93317e7i | 0.738930 | + | 0.0452798i | ||||
\(383\) | 2.86442e8 | 0.260520 | 0.130260 | − | 0.991480i | \(-0.458419\pi\) | ||||
0.130260 | + | 0.991480i | \(0.458419\pi\) | |||||||
\(384\) | −2.66127e8 | + | 5.82724e8i | −0.239844 | + | 0.525174i | ||||
\(385\) | 4.12121e8 | 0.368055 | ||||||||
\(386\) | 9.54696e8 | + | 5.85015e7i | 0.844908 | + | 0.0517739i | ||||
\(387\) | − | 5.00225e8i | − | 0.438709i | ||||||
\(388\) | −1.73223e9 | − | 2.13094e8i | −1.50555 | − | 0.185208i | ||||
\(389\) | − | 8.13802e8i | − | 0.700963i | −0.936570 | − | 0.350481i | \(-0.886018\pi\) | ||
0.936570 | − | 0.350481i | \(-0.113982\pi\) | |||||||
\(390\) | −3.12823e7 | + | 5.10502e8i | −0.0267038 | + | 0.435784i | ||||
\(391\) | 3.23492e8 | 0.273681 | ||||||||
\(392\) | 5.77706e8 | + | 1.07277e8i | 0.484402 | + | 0.0899508i | ||||
\(393\) | 2.96810e8 | 0.246663 | ||||||||
\(394\) | −3.13826e7 | + | 5.12138e8i | −0.0258495 | + | 0.421842i | ||||
\(395\) | − | 7.38041e8i | − | 0.602546i | ||||||
\(396\) | −5.84802e7 | + | 4.75383e8i | −0.0473234 | + | 0.384689i | ||||
\(397\) | 1.88070e9i | 1.50853i | 0.656571 | + | 0.754265i | \(0.272006\pi\) | ||||
−0.656571 | + | 0.754265i | \(0.727994\pi\) | |||||||
\(398\) | −9.91737e8 | − | 6.07713e7i | −0.788508 | − | 0.0483178i | ||||
\(399\) | −2.14526e8 | −0.169073 | ||||||||
\(400\) | 9.96578e8 | + | 2.48960e8i | 0.778577 | + | 0.194500i | ||||
\(401\) | 1.34747e9 | 1.04355 | 0.521776 | − | 0.853083i | \(-0.325270\pi\) | ||||
0.521776 | + | 0.853083i | \(0.325270\pi\) | |||||||
\(402\) | −4.79124e8 | − | 2.93596e7i | −0.367838 | − | 0.0225402i | ||||
\(403\) | − | 1.09211e9i | − | 0.831185i | ||||||
\(404\) | −1.80888e8 | + | 1.47043e9i | −0.136482 | + | 1.10946i | ||||
\(405\) | 6.60131e7i | 0.0493784i | ||||||||
\(406\) | −5.93552e7 | + | 9.68627e8i | −0.0440167 | + | 0.718316i | ||||
\(407\) | −2.20300e9 | −1.61970 | ||||||||
\(408\) | 1.52507e8 | − | 8.21280e8i | 0.111168 | − | 0.598660i | ||||
\(409\) | −2.51620e8 | −0.181850 | −0.0909250 | − | 0.995858i | \(-0.528982\pi\) | ||||
−0.0909250 | + | 0.995858i | \(0.528982\pi\) | |||||||
\(410\) | 2.70465e7 | − | 4.41377e8i | 0.0193806 | − | 0.316276i | ||||
\(411\) | 1.84874e8i | 0.131350i | ||||||||
\(412\) | 1.95716e9 | + | 2.40764e8i | 1.37875 | + | 0.169610i | ||||
\(413\) | 1.93877e9i | 1.35426i | ||||||||
\(414\) | −1.24655e8 | − | 7.63854e6i | −0.0863391 | − | 0.00529065i | ||||
\(415\) | 1.15077e9 | 0.790349 | ||||||||
\(416\) | −7.52700e8 | + | 2.38250e9i | −0.512620 | + | 1.62258i | ||||
\(417\) | 1.49961e8 | 0.101275 | ||||||||
\(418\) | 7.12511e8 | + | 4.36610e7i | 0.477172 | + | 0.0292399i | ||||
\(419\) | − | 3.20953e8i | − | 0.213153i | −0.994304 | − | 0.106577i | \(-0.966011\pi\) | ||
0.994304 | − | 0.106577i | \(-0.0339889\pi\) | |||||||
\(420\) | 2.75404e8 | + | 3.38794e7i | 0.181383 | + | 0.0223133i | ||||
\(421\) | − | 1.60605e9i | − | 1.04899i | −0.851414 | − | 0.524494i | \(-0.824254\pi\) | ||
0.851414 | − | 0.524494i | \(-0.175746\pi\) | |||||||
\(422\) | −5.15103e7 | + | 8.40606e8i | −0.0333657 | + | 0.544501i | ||||
\(423\) | −2.56057e8 | −0.164492 | ||||||||
\(424\) | −1.59339e8 | + | 8.58072e8i | −0.101518 | + | 0.546693i | ||||
\(425\) | −1.33940e9 | −0.846349 | ||||||||
\(426\) | −5.99995e7 | + | 9.79143e8i | −0.0376023 | + | 0.613638i | ||||
\(427\) | 2.40986e8i | 0.149794i | ||||||||
\(428\) | 5.09241e7 | − | 4.13959e8i | 0.0313957 | − | 0.255214i | ||||
\(429\) | 1.86809e9i | 1.14235i | ||||||||
\(430\) | 9.62507e8 | + | 5.89801e7i | 0.583800 | + | 0.0357739i | ||||
\(431\) | −1.54536e9 | −0.929735 | −0.464868 | − | 0.885380i | \(-0.653898\pi\) | ||||
−0.464868 | + | 0.885380i | \(0.653898\pi\) | |||||||
\(432\) | −7.81598e7 | + | 3.12871e8i | −0.0466434 | + | 0.186712i | ||||
\(433\) | 1.64675e9 | 0.974811 | 0.487405 | − | 0.873176i | \(-0.337943\pi\) | ||||
0.487405 | + | 0.873176i | \(0.337943\pi\) | |||||||
\(434\) | −5.91387e8 | − | 3.62388e7i | −0.347263 | − | 0.0212794i | ||||
\(435\) | − | 4.45063e8i | − | 0.259244i | ||||||
\(436\) | −3.42877e8 | + | 2.78723e9i | −0.198123 | + | 1.61054i | ||||
\(437\) | 1.86133e8i | 0.106693i | ||||||||
\(438\) | 7.41201e7 | − | 1.20958e9i | 0.0421479 | − | 0.687820i | ||||
\(439\) | 1.90299e9 | 1.07352 | 0.536762 | − | 0.843734i | \(-0.319647\pi\) | ||||
0.536762 | + | 0.843734i | \(0.319647\pi\) | |||||||
\(440\) | −9.07812e8 | − | 1.68576e8i | −0.508056 | − | 0.0943431i | ||||
\(441\) | 2.95788e8 | 0.164228 | ||||||||
\(442\) | 1.99266e8 | − | 3.25186e9i | 0.109763 | − | 1.79124i | ||||
\(443\) | − | 1.07338e9i | − | 0.586598i | −0.956021 | − | 0.293299i | \(-0.905247\pi\) | ||
0.956021 | − | 0.293299i | \(-0.0947531\pi\) | |||||||
\(444\) | −1.47217e9 | − | 1.81103e8i | −0.798213 | − | 0.0981939i | ||||
\(445\) | 1.59316e9i | 0.857037i | ||||||||
\(446\) | 9.55478e8 | + | 5.85494e7i | 0.509975 | + | 0.0312500i | ||||
\(447\) | −9.90091e8 | −0.524323 | ||||||||
\(448\) | 1.26517e9 | + | 4.86652e8i | 0.664778 | + | 0.255709i | ||||
\(449\) | 1.87557e8 | 0.0977850 | 0.0488925 | − | 0.998804i | \(-0.484431\pi\) | ||||
0.0488925 | + | 0.998804i | \(0.484431\pi\) | |||||||
\(450\) | 5.16126e8 | + | 3.16269e7i | 0.267000 | + | 0.0163611i | ||||
\(451\) | − | 1.61514e9i | − | 0.829074i | ||||||
\(452\) | −3.25308e8 | − | 4.00184e7i | −0.165695 | − | 0.0203833i | ||||
\(453\) | − | 1.10464e9i | − | 0.558313i | ||||||
\(454\) | 5.69559e7 | − | 9.29474e8i | 0.0285656 | − | 0.466167i | ||||
\(455\) | 1.08224e9 | 0.538623 | ||||||||
\(456\) | 4.72553e8 | + | 8.77504e7i | 0.233385 | + | 0.0433383i | ||||
\(457\) | −1.01128e9 | −0.495640 | −0.247820 | − | 0.968806i | \(-0.579714\pi\) | ||||
−0.247820 | + | 0.968806i | \(0.579714\pi\) | |||||||
\(458\) | 1.47462e8 | − | 2.40646e9i | 0.0717218 | − | 1.17044i | ||||
\(459\) | − | 4.20499e8i | − | 0.202965i | ||||||
\(460\) | 2.93953e7 | − | 2.38953e8i | 0.0140808 | − | 0.114462i | ||||
\(461\) | 1.15008e9i | 0.546734i | 0.961910 | + | 0.273367i | \(0.0881373\pi\) | ||||
−0.961910 | + | 0.273367i | \(0.911863\pi\) | |||||||
\(462\) | 1.01159e9 | + | 6.19879e7i | 0.477264 | + | 0.0292456i | ||||
\(463\) | −3.01661e9 | −1.41249 | −0.706245 | − | 0.707967i | \(-0.749612\pi\) | ||||
−0.706245 | + | 0.707967i | \(0.749612\pi\) | |||||||
\(464\) | 5.26957e8 | − | 2.10939e9i | 0.244885 | − | 0.980267i | ||||
\(465\) | 2.71729e8 | 0.125329 | ||||||||
\(466\) | −1.92647e9 | − | 1.18049e8i | −0.881882 | − | 0.0540396i | ||||
\(467\) | 1.34443e9i | 0.610843i | 0.952217 | + | 0.305421i | \(0.0987974\pi\) | ||||
−0.952217 | + | 0.305421i | \(0.901203\pi\) | |||||||
\(468\) | −1.53571e8 | + | 1.24837e9i | −0.0692545 | + | 0.562967i | ||||
\(469\) | 1.01572e9i | 0.454643i | ||||||||
\(470\) | 3.01910e7 | − | 4.92692e8i | 0.0134133 | − | 0.218894i | ||||
\(471\) | −5.34277e8 | −0.235610 | ||||||||
\(472\) | 7.93040e8 | − | 4.27067e9i | 0.347135 | − | 1.86939i | ||||
\(473\) | 3.52213e9 | 1.53035 | ||||||||
\(474\) | 1.11010e8 | − | 1.81159e9i | 0.0478782 | − | 0.781333i | ||||
\(475\) | − | 7.70673e8i | − | 0.329946i | ||||||
\(476\) | −1.75431e9 | − | 2.15810e8i | −0.745557 | − | 0.0917163i | ||||
\(477\) | 4.39337e8i | 0.185346i | ||||||||
\(478\) | −4.37885e9 | − | 2.68325e8i | −1.83384 | − | 0.112374i | ||||
\(479\) | 3.13761e9 | 1.30444 | 0.652220 | − | 0.758030i | \(-0.273838\pi\) | ||||
0.652220 | + | 0.758030i | \(0.273838\pi\) | |||||||
\(480\) | −5.92795e8 | − | 1.87281e8i | −0.244658 | − | 0.0772946i | ||||
\(481\) | −5.78515e9 | −2.37032 | ||||||||
\(482\) | −1.27523e9 | − | 7.81431e7i | −0.518710 | − | 0.0317853i | ||||
\(483\) | 2.64263e8i | 0.106714i | ||||||||
\(484\) | −8.71518e8 | − | 1.07212e8i | −0.349396 | − | 0.0429816i | ||||
\(485\) | − | 1.69368e9i | − | 0.674117i | ||||||
\(486\) | −9.92914e6 | + | 1.62035e8i | −0.00392360 | + | 0.0640299i | ||||
\(487\) | 3.33575e9 | 1.30871 | 0.654354 | − | 0.756189i | \(-0.272941\pi\) | ||||
0.654354 | + | 0.756189i | \(0.272941\pi\) | |||||||
\(488\) | 9.85739e7 | − | 5.30839e8i | 0.0383966 | − | 0.206773i | ||||
\(489\) | −5.24677e8 | −0.202914 | ||||||||
\(490\) | −3.48756e7 | + | 5.69141e8i | −0.0133917 | + | 0.218541i | ||||
\(491\) | − | 2.38332e9i | − | 0.908649i | −0.890836 | − | 0.454325i | \(-0.849881\pi\) | ||
0.890836 | − | 0.454325i | \(-0.150119\pi\) | |||||||
\(492\) | 1.32777e8 | − | 1.07933e9i | 0.0502624 | − | 0.408581i | ||||
\(493\) | 2.83502e9i | 1.06560i | ||||||||
\(494\) | 1.87108e9 | + | 1.14655e8i | 0.698308 | + | 0.0427906i | ||||
\(495\) | −4.64804e8 | −0.172247 | ||||||||
\(496\) | 1.28787e9 | + | 3.21729e8i | 0.473900 | + | 0.118387i | ||||
\(497\) | 2.07575e9 | 0.758450 | ||||||||
\(498\) | 2.82467e9 | + | 1.73089e8i | 1.02486 | + | 0.0628010i | ||||
\(499\) | 3.49696e9i | 1.25991i | 0.776633 | + | 0.629954i | \(0.216926\pi\) | ||||
−0.776633 | + | 0.629954i | \(0.783074\pi\) | |||||||
\(500\) | −2.73373e8 | + | 2.22223e9i | −0.0978047 | + | 0.795050i | ||||
\(501\) | − | 3.89712e8i | − | 0.138456i | ||||||
\(502\) | −1.32480e8 | + | 2.16196e9i | −0.0467398 | + | 0.762756i | ||||
\(503\) | 1.55596e9 | 0.545142 | 0.272571 | − | 0.962136i | \(-0.412126\pi\) | ||||
0.272571 | + | 0.962136i | \(0.412126\pi\) | |||||||
\(504\) | 6.70909e8 | + | 1.24584e8i | 0.233430 | + | 0.0433467i | ||||
\(505\) | −1.43771e9 | −0.496766 | ||||||||
\(506\) | 5.37836e7 | − | 8.77705e8i | 0.0184554 | − | 0.301177i | ||||
\(507\) | 3.21146e9i | 1.09440i | ||||||||
\(508\) | 5.05011e9 | + | 6.21250e8i | 1.70914 | + | 0.210254i | ||||
\(509\) | 3.55919e9i | 1.19630i | 0.801385 | + | 0.598149i | \(0.204097\pi\) | ||||
−0.801385 | + | 0.598149i | \(0.795903\pi\) | |||||||
\(510\) | 8.09103e8 | + | 4.95799e7i | 0.270090 | + | 0.0165504i | ||||
\(511\) | −2.56426e9 | −0.850137 | ||||||||
\(512\) | −2.58783e9 | − | 1.58950e9i | −0.852101 | − | 0.523377i | ||||
\(513\) | 2.41949e8 | 0.0791250 | ||||||||
\(514\) | −1.83112e9 | − | 1.12206e8i | −0.594764 | − | 0.0364457i | ||||
\(515\) | 1.91360e9i | 0.617343i | ||||||||
\(516\) | 2.35369e9 | + | 2.89545e8i | 0.754182 | + | 0.0927772i | ||||
\(517\) | − | 1.80292e9i | − | 0.573799i | ||||||
\(518\) | −1.91965e8 | + | 3.13272e9i | −0.0606832 | + | 0.990301i | ||||
\(519\) | −1.55467e9 | −0.488148 | ||||||||
\(520\) | −2.38394e9 | − | 4.42685e8i | −0.743505 | − | 0.138065i | ||||
\(521\) | 4.88706e9 | 1.51396 | 0.756982 | − | 0.653436i | \(-0.226673\pi\) | ||||
0.756982 | + | 0.653436i | \(0.226673\pi\) | |||||||
\(522\) | 6.69427e7 | − | 1.09245e9i | 0.0205995 | − | 0.336167i | ||||
\(523\) | 2.25480e9i | 0.689212i | 0.938747 | + | 0.344606i | \(0.111987\pi\) | ||||
−0.938747 | + | 0.344606i | \(0.888013\pi\) | |||||||
\(524\) | −1.71802e8 | + | 1.39657e9i | −0.0521638 | + | 0.424037i | ||||
\(525\) | − | 1.09417e9i | − | 0.330009i | ||||||
\(526\) | 9.68318e7 | + | 5.93362e6i | 0.0290113 | + | 0.00177775i | ||||
\(527\) | −1.73090e9 | −0.515151 | ||||||||
\(528\) | −2.20295e9 | − | 5.50330e8i | −0.651309 | − | 0.162706i | ||||
\(529\) | −3.17554e9 | −0.932658 | ||||||||
\(530\) | −8.45350e8 | − | 5.18010e7i | −0.246644 | − | 0.0151138i | ||||
\(531\) | − | 2.18661e9i | − | 0.633781i | ||||||
\(532\) | 1.24174e8 | − | 1.00940e9i | 0.0357552 | − | 0.290652i | ||||
\(533\) | − | 4.24142e9i | − | 1.21329i | ||||||
\(534\) | −2.39630e8 | + | 3.91057e9i | −0.0681000 | + | 1.11134i | ||||
\(535\) | 4.04747e8 | 0.114274 | ||||||||
\(536\) | 4.15475e8 | − | 2.23741e9i | 0.116538 | − | 0.627581i | ||||
\(537\) | 1.87025e9 | 0.521182 | ||||||||
\(538\) | 1.63218e7 | − | 2.66359e8i | 0.00451888 | − | 0.0737445i | ||||
\(539\) | 2.08267e9i | 0.572876i | ||||||||
\(540\) | −3.10609e8 | − | 3.82103e7i | −0.0848861 | − | 0.0104424i | ||||
\(541\) | − | 6.18666e9i | − | 1.67983i | −0.542718 | − | 0.839915i | \(-0.682605\pi\) | ||
0.542718 | − | 0.839915i | \(-0.317395\pi\) | |||||||
\(542\) | −2.84341e8 | − | 1.74238e7i | −0.0767084 | − | 0.00470050i | ||||
\(543\) | −2.23479e9 | −0.599013 | ||||||||
\(544\) | 3.77607e9 | + | 1.19297e9i | 1.00564 | + | 0.317711i | ||||
\(545\) | −2.72521e9 | −0.721127 | ||||||||
\(546\) | 2.65647e9 | + | 1.62782e8i | 0.698443 | + | 0.0427989i | ||||
\(547\) | 1.78927e9i | 0.467433i | 0.972305 | + | 0.233717i | \(0.0750888\pi\) | ||||
−0.972305 | + | 0.233717i | \(0.924911\pi\) | |||||||
\(548\) | −8.69883e8 | − | 1.07010e8i | −0.225803 | − | 0.0277776i | ||||
\(549\) | − | 2.71792e8i | − | 0.0701025i | ||||||
\(550\) | −2.22688e8 | + | 3.63409e9i | −0.0570726 | + | 0.931378i | ||||
\(551\) | −1.63123e9 | −0.415418 | ||||||||
\(552\) | 1.08095e8 | − | 5.82113e8i | 0.0273539 | − | 0.147306i | ||||
\(553\) | −3.84050e9 | −0.965718 | ||||||||
\(554\) | −2.38508e8 | + | 3.89225e9i | −0.0595961 | + | 0.972560i | ||||
\(555\) | − | 1.43941e9i | − | 0.357405i | ||||||
\(556\) | −8.68018e7 | + | 7.05608e8i | −0.0214174 | + | 0.174101i | ||||
\(557\) | − | 3.18701e9i | − | 0.781430i | −0.920512 | − | 0.390715i | \(-0.872228\pi\) | ||
0.920512 | − | 0.390715i | \(-0.127772\pi\) | |||||||
\(558\) | 6.66986e8 | + | 4.08713e7i | 0.162516 | + | 0.00995861i | ||||
\(559\) | 9.24922e9 | 2.23957 | ||||||||
\(560\) | −3.18823e8 | + | 1.27624e9i | −0.0767171 | + | 0.307096i | ||||
\(561\) | 2.96077e9 | 0.708003 | ||||||||
\(562\) | 3.81020e9 | + | 2.33480e8i | 0.905464 | + | 0.0554846i | ||||
\(563\) | − | 1.15604e9i | − | 0.273020i | −0.990639 | − | 0.136510i | \(-0.956411\pi\) | ||
0.990639 | − | 0.136510i | \(-0.0435886\pi\) | |||||||
\(564\) | 1.48213e8 | − | 1.20482e9i | 0.0347865 | − | 0.282778i | ||||
\(565\) | − | 3.18069e8i | − | 0.0741910i | ||||||
\(566\) | −2.73410e8 | + | 4.46183e9i | −0.0633807 | + | 1.03432i | ||||
\(567\) | 3.43509e8 | 0.0791402 | ||||||||
\(568\) | −4.57240e9 | − | 8.49070e8i | −1.04695 | − | 0.194413i | ||||
\(569\) | 5.86706e8 | 0.133514 | 0.0667571 | − | 0.997769i | \(-0.478735\pi\) | ||||
0.0667571 | + | 0.997769i | \(0.478735\pi\) | |||||||
\(570\) | −2.85276e7 | + | 4.65546e8i | −0.00645212 | + | 0.105293i | ||||
\(571\) | − | 5.83720e9i | − | 1.31213i | −0.754702 | − | 0.656067i | \(-0.772219\pi\) | ||
0.754702 | − | 0.656067i | \(-0.227781\pi\) | |||||||
\(572\) | −8.78989e9 | − | 1.08131e9i | −1.96380 | − | 0.241581i | ||||
\(573\) | 1.92485e9i | 0.427421i | ||||||||
\(574\) | −2.29677e9 | − | 1.40741e8i | −0.506905 | − | 0.0310619i | ||||
\(575\) | −9.49351e8 | −0.208252 | ||||||||
\(576\) | −1.42690e9 | − | 5.48862e8i | −0.311111 | − | 0.119670i | ||||
\(577\) | 5.04159e9 | 1.09258 | 0.546289 | − | 0.837597i | \(-0.316040\pi\) | ||||
0.546289 | + | 0.837597i | \(0.316040\pi\) | |||||||
\(578\) | −5.20175e8 | − | 3.18751e7i | −0.112047 | − | 0.00686600i | ||||
\(579\) | 2.28264e9i | 0.488723i | ||||||||
\(580\) | 2.09414e9 | + | 2.57615e8i | 0.445665 | + | 0.0548244i | ||||
\(581\) | − | 5.98819e9i | − | 1.26672i | ||||||
\(582\) | 2.54749e8 | − | 4.15730e9i | 0.0535652 | − | 0.874140i | ||||
\(583\) | −3.09341e9 | −0.646544 | ||||||||
\(584\) | 5.64849e9 | + | 1.04889e9i | 1.17351 | + | 0.217915i | ||||
\(585\) | −1.22059e9 | −0.252072 | ||||||||
\(586\) | −4.16314e8 | + | 6.79390e9i | −0.0854632 | + | 1.39469i | ||||
\(587\) | 5.71937e9i | 1.16712i | 0.812071 | + | 0.583559i | \(0.198340\pi\) | ||||
−0.812071 | + | 0.583559i | \(0.801660\pi\) | |||||||
\(588\) | −1.71211e8 | + | 1.39177e9i | −0.0347305 | + | 0.282322i | ||||
\(589\) | − | 9.95935e8i | − | 0.200830i | ||||||
\(590\) | 4.20735e9 | + | 2.57816e8i | 0.843387 | + | 0.0516807i | ||||
\(591\) | −1.22450e9 | −0.244008 | ||||||||
\(592\) | 1.70427e9 | − | 6.82215e9i | 0.337609 | − | 1.35144i | ||||
\(593\) | 2.07985e9 | 0.409581 | 0.204791 | − | 0.978806i | \(-0.434349\pi\) | ||||
0.204791 | + | 0.978806i | \(0.434349\pi\) | |||||||
\(594\) | −1.14091e9 | − | 6.99120e7i | −0.223356 | − | 0.0136867i | ||||
\(595\) | − | 1.71527e9i | − | 0.333828i | ||||||
\(596\) | 5.73093e8 | − | 4.65865e9i | 0.110883 | − | 0.901360i | ||||
\(597\) | − | 2.37121e9i | − | 0.456099i | ||||||
\(598\) | 1.41237e8 | − | 2.30488e9i | 0.0270082 | − | 0.440752i | ||||
\(599\) | −6.32006e9 | −1.20151 | −0.600755 | − | 0.799433i | \(-0.705133\pi\) | ||||
−0.600755 | + | 0.799433i | \(0.705133\pi\) | |||||||
\(600\) | −4.47562e8 | + | 2.41021e9i | −0.0845909 | + | 0.455538i | ||||
\(601\) | −3.92467e9 | −0.737466 | −0.368733 | − | 0.929535i | \(-0.620208\pi\) | ||||
−0.368733 | + | 0.929535i | \(0.620208\pi\) | |||||||
\(602\) | 3.06912e8 | − | 5.00855e9i | 0.0573358 | − | 0.935673i | ||||
\(603\) | − | 1.14557e9i | − | 0.212770i | ||||||
\(604\) | 5.19764e9 | + | 6.39398e8i | 0.959791 | + | 0.118071i | ||||
\(605\) | − | 8.52123e8i | − | 0.156444i | ||||||
\(606\) | −3.52900e9 | − | 2.16249e8i | −0.644166 | − | 0.0394729i | ||||
\(607\) | −3.19677e8 | −0.0580164 | −0.0290082 | − | 0.999579i | \(-0.509235\pi\) | ||||
−0.0290082 | + | 0.999579i | \(0.509235\pi\) | |||||||
\(608\) | −6.86417e8 | + | 2.17270e9i | −0.123858 | + | 0.392046i | ||||
\(609\) | −2.31595e9 | −0.415498 | ||||||||
\(610\) | 5.22968e8 | + | 3.20462e7i | 0.0932870 | + | 0.00571640i | ||||
\(611\) | − | 4.73453e9i | − | 0.839716i | ||||||
\(612\) | 1.97856e9 | + | 2.43397e8i | 0.348915 | + | 0.0429225i | ||||
\(613\) | 1.39750e9i | 0.245043i | 0.992466 | + | 0.122521i | \(0.0390980\pi\) | ||||
−0.992466 | + | 0.122521i | \(0.960902\pi\) | |||||||
\(614\) | 4.01806e8 | − | 6.55715e9i | 0.0700531 | − | 1.14321i | ||||
\(615\) | 1.05532e9 | 0.182945 | ||||||||
\(616\) | −8.77208e8 | + | 4.72393e9i | −0.151206 | + | 0.814275i | ||||
\(617\) | −5.55555e9 | −0.952202 | −0.476101 | − | 0.879391i | \(-0.657950\pi\) | ||||
−0.476101 | + | 0.879391i | \(0.657950\pi\) | |||||||
\(618\) | −2.87828e8 | + | 4.69712e9i | −0.0490539 | + | 0.800520i | ||||
\(619\) | 1.48636e9i | 0.251887i | 0.992037 | + | 0.125944i | \(0.0401959\pi\) | ||||
−0.992037 | + | 0.125944i | \(0.959804\pi\) | |||||||
\(620\) | −1.57285e8 | + | 1.27856e9i | −0.0265043 | + | 0.215452i | ||||
\(621\) | − | 2.98045e8i | − | 0.0499414i | ||||||
\(622\) | −3.44974e9 | − | 2.11392e8i | −0.574805 | − | 0.0352227i | ||||
\(623\) | 8.29025e9 | 1.37360 | ||||||||
\(624\) | −5.78503e9 | − | 1.44518e9i | −0.953146 | − | 0.238110i | ||||
\(625\) | 2.72531e9 | 0.446515 | ||||||||
\(626\) | −5.40906e9 | − | 3.31454e8i | −0.881275 | − | 0.0540024i | ||||
\(627\) | 1.70359e9i | 0.276012i | ||||||||
\(628\) | 3.09255e8 | − | 2.51392e9i | 0.0498263 | − | 0.405035i | ||||
\(629\) | 9.16898e9i | 1.46907i | ||||||||
\(630\) | −4.05022e7 | + | 6.60962e8i | −0.00645336 | + | 0.105314i | ||||
\(631\) | 7.72780e9 | 1.22448 | 0.612242 | − | 0.790670i | \(-0.290268\pi\) | ||||
0.612242 | + | 0.790670i | \(0.290268\pi\) | |||||||
\(632\) | 8.45977e9 | + | 1.57093e9i | 1.33306 | + | 0.247541i | ||||
\(633\) | −2.00986e9 | −0.314958 | ||||||||
\(634\) | 6.04133e8 | − | 9.85896e9i | 0.0941500 | − | 1.53645i | ||||
\(635\) | 4.93773e9i | 0.765278i | ||||||||
\(636\) | −2.06720e9 | − | 2.54301e8i | −0.318627 | − | 0.0391966i | ||||
\(637\) | 5.46916e9i | 0.838365i | ||||||||
\(638\) | 7.69204e9 | + | 4.71349e8i | 1.17265 | + | 0.0718572i | ||||
\(639\) | −2.34109e9 | −0.354949 | ||||||||
\(640\) | 1.22433e9 | − | 2.68086e9i | 0.184616 | − | 0.404244i | ||||
\(641\) | −6.28895e9 | −0.943137 | −0.471569 | − | 0.881829i | \(-0.656312\pi\) | ||||
−0.471569 | + | 0.881829i | \(0.656312\pi\) | |||||||
\(642\) | 9.93491e8 | + | 6.08787e7i | 0.148181 | + | 0.00908015i | ||||
\(643\) | 7.19728e9i | 1.06765i | 0.845594 | + | 0.533826i | \(0.179246\pi\) | ||||
−0.845594 | + | 0.533826i | \(0.820754\pi\) | |||||||
\(644\) | −1.24343e9 | − | 1.52963e8i | −0.183451 | − | 0.0225676i | ||||
\(645\) | 2.30132e9i | 0.337689i | ||||||||
\(646\) | 1.81719e8 | − | 2.96550e9i | 0.0265208 | − | 0.432797i | ||||
\(647\) | −8.28399e9 | −1.20247 | −0.601235 | − | 0.799072i | \(-0.705325\pi\) | ||||
−0.601235 | + | 0.799072i | \(0.705325\pi\) | |||||||
\(648\) | −7.56673e8 | − | 1.40510e8i | −0.109244 | − | 0.0202859i | ||||
\(649\) | 1.53961e10 | 2.21082 | ||||||||
\(650\) | −5.84786e8 | + | 9.54323e9i | −0.0835219 | + | 1.36301i | ||||
\(651\) | − | 1.41398e9i | − | 0.200868i | ||||||
\(652\) | 3.03698e8 | − | 2.46875e9i | 0.0429117 | − | 0.348827i | ||||
\(653\) | 9.71933e9i | 1.36597i | 0.730434 | + | 0.682983i | \(0.239318\pi\) | ||||
−0.730434 | + | 0.682983i | \(0.760682\pi\) | |||||||
\(654\) | −6.68929e9 | − | 4.09903e8i | −0.935099 | − | 0.0573006i | ||||
\(655\) | −1.36549e9 | −0.189865 | ||||||||
\(656\) | 5.00171e9 | + | 1.24950e9i | 0.691759 | + | 0.172812i | ||||
\(657\) | 2.89206e9 | 0.397858 | ||||||||
\(658\) | −2.56380e9 | − | 1.57103e8i | −0.350827 | − | 0.0214978i | ||||
\(659\) | − | 9.81337e9i | − | 1.33573i | −0.744282 | − | 0.667866i | \(-0.767208\pi\) | ||
0.744282 | − | 0.667866i | \(-0.232792\pi\) | |||||||
\(660\) | 2.69042e8 | − | 2.18703e9i | 0.0364264 | − | 0.296108i | ||||
\(661\) | 4.59313e9i | 0.618591i | 0.950966 | + | 0.309295i | \(0.100093\pi\) | ||||
−0.950966 | + | 0.309295i | \(0.899907\pi\) | |||||||
\(662\) | 6.88106e8 | − | 1.12293e10i | 0.0921833 | − | 1.50436i | ||||
\(663\) | 7.77508e9 | 1.03611 | ||||||||
\(664\) | −2.44943e9 | + | 1.31906e10i | −0.324696 | + | 1.74855i | ||||
\(665\) | 9.86940e8 | 0.130141 | ||||||||
\(666\) | 2.16505e8 | − | 3.53318e9i | 0.0283993 | − | 0.463453i | ||||
\(667\) | 2.00943e9i | 0.262200i | ||||||||
\(668\) | 1.83370e9 | + | 2.25576e8i | 0.238019 | + | 0.0292803i | ||||
\(669\) | 2.28451e9i | 0.294986i | ||||||||
\(670\) | 2.20424e9 | + | 1.35071e8i | 0.283137 | + | 0.0173500i | ||||
\(671\) | 1.91371e9 | 0.244539 | ||||||||
\(672\) | −9.74544e8 | + | 3.08470e9i | −0.123882 | + | 0.392121i | ||||
\(673\) | −7.01118e8 | −0.0886622 | −0.0443311 | − | 0.999017i | \(-0.514116\pi\) | ||||
−0.0443311 | + | 0.999017i | \(0.514116\pi\) | |||||||
\(674\) | −2.94287e9 | − | 1.80332e8i | −0.370221 | − | 0.0226863i | ||||
\(675\) | 1.23404e9i | 0.154442i | ||||||||
\(676\) | −1.51108e10 | − | 1.85889e9i | −1.88137 | − | 0.231440i | ||||
\(677\) | 1.33165e10i | 1.64941i | 0.565560 | + | 0.824707i | \(0.308660\pi\) | ||||
−0.565560 | + | 0.824707i | \(0.691340\pi\) | |||||||
\(678\) | 4.78412e7 | − | 7.80730e8i | 0.00589520 | − | 0.0962048i | ||||
\(679\) | −8.81332e9 | −1.08043 | ||||||||
\(680\) | −7.01619e8 | + | 3.77835e9i | −0.0855697 | + | 0.460809i | ||||
\(681\) | 2.22234e9 | 0.269647 | ||||||||
\(682\) | −2.87778e8 | + | 4.69631e9i | −0.0347386 | + | 0.566906i | ||||
\(683\) | − | 2.68818e9i | − | 0.322839i | −0.986886 | − | 0.161419i | \(-0.948393\pi\) | ||
0.986886 | − | 0.161419i | \(-0.0516072\pi\) | |||||||
\(684\) | −1.40047e8 | + | 1.13844e9i | −0.0167332 | + | 0.136023i | ||||
\(685\) | − | 8.50525e8i | − | 0.101104i | ||||||
\(686\) | 8.97280e9 | + | 5.49831e8i | 1.06119 | + | 0.0650272i | ||||
\(687\) | 5.75376e9 | 0.677022 | ||||||||
\(688\) | −2.72477e9 | + | 1.09072e10i | −0.318985 | + | 1.27689i | ||||
\(689\) | −8.12340e9 | −0.946173 | ||||||||
\(690\) | 5.73482e8 | + | 3.51416e7i | 0.0664581 | + | 0.00407239i | ||||
\(691\) | − | 1.41484e10i | − | 1.63131i | −0.578541 | − | 0.815653i | \(-0.696378\pi\) | ||
0.578541 | − | 0.815653i | \(-0.303622\pi\) | |||||||
\(692\) | 8.99886e8 | − | 7.31513e9i | 0.103232 | − | 0.839172i | ||||
\(693\) | 2.41868e9i | 0.276065i | ||||||||
\(694\) | 7.37478e8 | − | 1.20350e10i | 0.0837512 | − | 1.36675i | ||||
\(695\) | −6.89906e8 | −0.0779548 | ||||||||
\(696\) | 5.10152e9 | + | 9.47325e8i | 0.573545 | + | 0.106504i | ||||
\(697\) | −6.72230e9 | −0.751974 | ||||||||
\(698\) | 2.94406e8 | − | 4.80447e9i | 0.0327682 | − | 0.534751i | ||||
\(699\) | − | 4.60610e9i | − | 0.510110i | ||||||
\(700\) | 5.14835e9 | + | 6.33335e8i | 0.567316 | + | 0.0697896i | ||||
\(701\) | − | 1.53529e10i | − | 1.68337i | −0.539972 | − | 0.841683i | \(-0.681565\pi\) | ||
0.539972 | − | 0.841683i | \(-0.318435\pi\) | |||||||
\(702\) | −2.99605e9 | − | 1.83591e8i | −0.326866 | − | 0.0200296i | ||||
\(703\) | −5.27570e9 | −0.572712 | ||||||||
\(704\) | 3.86459e9 | − | 1.00470e10i | 0.417445 | − | 1.08525i | ||||
\(705\) | 1.17801e9 | 0.126615 | ||||||||
\(706\) | 9.95696e9 | + | 6.10139e8i | 1.06490 | + | 0.0652547i | ||||
\(707\) | 7.48135e9i | 0.796181i | ||||||||
\(708\) | 1.02886e10 | + | 1.26567e9i | 1.08953 | + | 0.134031i | ||||
\(709\) | − | 5.59636e8i | − | 0.0589717i | −0.999565 | − | 0.0294859i | \(-0.990613\pi\) | ||
0.999565 | − | 0.0294859i | \(-0.00938700\pi\) | |||||||
\(710\) | 2.76032e8 | − | 4.50461e9i | 0.0289437 | − | 0.472338i | ||||
\(711\) | 4.33145e9 | 0.451949 | ||||||||
\(712\) | −1.82616e10 | − | 3.39107e9i | −1.89609 | − | 0.352093i | ||||
\(713\) | −1.22684e9 | −0.126758 | ||||||||
\(714\) | 2.57996e8 | − | 4.21029e9i | 0.0265259 | − | 0.432880i | ||||
\(715\) | − | 8.59428e9i | − | 0.879303i | ||||||
\(716\) | −1.08255e9 | + | 8.80002e9i | −0.110218 | + | 0.895959i | ||||
\(717\) | − | 1.04697e10i | − | 1.06076i | ||||||
\(718\) | −3.05260e9 | − | 1.87056e8i | −0.307776 | − | 0.0188598i | ||||
\(719\) | −7.25097e9 | −0.727520 | −0.363760 | − | 0.931493i | \(-0.618507\pi\) | ||||
−0.363760 | + | 0.931493i | \(0.618507\pi\) | |||||||
\(720\) | 3.59579e8 | − | 1.43938e9i | 0.0359030 | − | 0.143719i | ||||
\(721\) | 9.95772e9 | 0.989433 | ||||||||
\(722\) | −8.38776e9 | − | 5.13982e8i | −0.829404 | − | 0.0508239i | ||||
\(723\) | − | 3.04903e9i | − | 0.300039i | ||||||
\(724\) | 1.29356e9 | − | 1.05153e10i | 0.126678 | − | 1.02976i | ||||
\(725\) | − | 8.31993e9i | − | 0.810843i | ||||||
\(726\) | 1.28169e8 | − | 2.09162e9i | 0.0124310 | − | 0.202864i | ||||
\(727\) | −3.30176e9 | −0.318695 | −0.159347 | − | 0.987223i | \(-0.550939\pi\) | ||||
−0.159347 | + | 0.987223i | \(0.550939\pi\) | |||||||
\(728\) | −2.30358e9 | + | 1.24052e10i | −0.221280 | + | 1.19164i | ||||
\(729\) | −3.87420e8 | −0.0370370 | ||||||||
\(730\) | −3.40994e8 | + | 5.56475e9i | −0.0324427 | + | 0.529438i | ||||
\(731\) | − | 1.46592e10i | − | 1.38804i | ||||||
\(732\) | 1.27886e9 | + | 1.57321e8i | 0.120513 | + | 0.0148251i | ||||
\(733\) | 1.17975e9i | 0.110644i | 0.998469 | + | 0.0553218i | \(0.0176185\pi\) | ||||
−0.998469 | + | 0.0553218i | \(0.982382\pi\) | |||||||
\(734\) | −4.31851e9 | − | 2.64628e8i | −0.403086 | − | 0.0247001i | ||||
\(735\) | −1.36079e9 | −0.126412 | ||||||||
\(736\) | 2.67643e9 | + | 8.45560e8i | 0.247448 | + | 0.0781758i | ||||
\(737\) | 8.06604e9 | 0.742206 | ||||||||
\(738\) | 2.59037e9 | + | 1.58732e8i | 0.237228 | + | 0.0145367i | ||||
\(739\) | − | 4.28180e9i | − | 0.390275i | −0.980776 | − | 0.195138i | \(-0.937485\pi\) | ||
0.980776 | − | 0.195138i | \(-0.0625153\pi\) | |||||||
\(740\) | 6.77283e9 | + | 8.33174e8i | 0.614412 | + | 0.0755831i | ||||
\(741\) | 4.47367e9i | 0.403925i | ||||||||
\(742\) | −2.69554e8 | + | 4.39890e9i | −0.0242233 | + | 0.395304i | ||||
\(743\) | −2.30686e9 | −0.206329 | −0.103165 | − | 0.994664i | \(-0.532897\pi\) | ||||
−0.103165 | + | 0.994664i | \(0.532897\pi\) | |||||||
\(744\) | −5.78381e8 | + | 3.11469e9i | −0.0514883 | + | 0.277274i | ||||
\(745\) | 4.55498e9 | 0.403589 | ||||||||
\(746\) | −8.86964e8 | + | 1.44745e10i | −0.0782204 | + | 1.27649i | ||||
\(747\) | 6.75367e9i | 0.592813i | ||||||||
\(748\) | −1.71378e9 | + | 1.39312e10i | −0.149727 | + | 1.21712i | ||||
\(749\) | − | 2.10616e9i | − | 0.183149i | ||||||
\(750\) | −5.33330e9 | − | 3.26812e8i | −0.461617 | − | 0.0282868i | ||||
\(751\) | −1.92214e10 | −1.65594 | −0.827972 | − | 0.560770i | \(-0.810505\pi\) | ||||
−0.827972 | + | 0.560770i | \(0.810505\pi\) | |||||||
\(752\) | 5.58321e9 | + | 1.39477e9i | 0.478764 | + | 0.119602i | ||||
\(753\) | −5.16917e9 | −0.441203 | ||||||||
\(754\) | 2.01995e10 | + | 1.23778e9i | 1.71610 | + | 0.105158i | ||||
\(755\) | 5.08198e9i | 0.429752i | ||||||||
\(756\) | −1.98833e8 | + | 1.61630e9i | −0.0167364 | + | 0.136049i | ||||
\(757\) | − | 1.11993e9i | − | 0.0938329i | −0.998899 | − | 0.0469164i | \(-0.985061\pi\) | ||
0.998899 | − | 0.0469164i | \(-0.0149395\pi\) | |||||||
\(758\) | −6.86007e8 | + | 1.11951e10i | −0.0572119 | + | 0.933651i | ||||
\(759\) | 2.09856e9 | 0.174211 | ||||||||
\(760\) | −2.17401e9 | − | 4.03701e8i | −0.179644 | − | 0.0333590i | ||||
\(761\) | −1.10491e10 | −0.908826 | −0.454413 | − | 0.890791i | \(-0.650151\pi\) | ||||
−0.454413 | + | 0.890791i | \(0.650151\pi\) | |||||||
\(762\) | −7.42693e8 | + | 1.21201e10i | −0.0608088 | + | 0.992350i | ||||
\(763\) | 1.41810e10i | 1.15577i | ||||||||
\(764\) | −9.05695e9 | − | 1.11416e9i | −0.734777 | − | 0.0903901i | ||||
\(765\) | 1.93453e9i | 0.156229i | ||||||||
\(766\) | −3.23465e9 | − | 1.98212e8i | −0.260032 | − | 0.0159341i | ||||
\(767\) | 4.04306e10 | 3.23539 | ||||||||
\(768\) | 3.40848e9 | − | 6.39627e9i | 0.271517 | − | 0.509521i | ||||
\(769\) | −3.08275e9 | −0.244453 | −0.122227 | − | 0.992502i | \(-0.539003\pi\) | ||||
−0.122227 | + | 0.992502i | \(0.539003\pi\) | |||||||
\(770\) | −4.65389e9 | − | 2.85179e8i | −0.367366 | − | 0.0225113i | ||||
\(771\) | − | 4.37813e9i | − | 0.344031i | ||||||
\(772\) | −1.07405e10 | − | 1.32126e9i | −0.840160 | − | 0.103354i | ||||
\(773\) | 1.61813e10i | 1.26004i | 0.776577 | + | 0.630022i | \(0.216954\pi\) | ||||
−0.776577 | + | 0.630022i | \(0.783046\pi\) | |||||||
\(774\) | −3.46145e8 | + | 5.64880e9i | −0.0268327 | + | 0.437888i | ||||
\(775\) | 5.07966e9 | 0.391994 | ||||||||
\(776\) | 1.94138e10 | + | 3.60503e9i | 1.49140 | + | 0.276945i | ||||
\(777\) | −7.49021e9 | −0.572823 | ||||||||
\(778\) | −5.63133e8 | + | 9.18988e9i | −0.0428729 | + | 0.699650i | ||||
\(779\) | − | 3.86791e9i | − | 0.293154i | ||||||
\(780\) | 7.06512e8 | − | 5.74321e9i | 0.0533075 | − | 0.433335i | ||||
\(781\) | − | 1.64838e10i | − | 1.23817i | ||||||
\(782\) | −3.65304e9 | − | 2.23850e8i | −0.273169 | − | 0.0167391i | ||||
\(783\) | 2.61201e9 | 0.194450 | ||||||||
\(784\) | −6.44953e9 | − | 1.61119e9i | −0.477993 | − | 0.119410i | ||||
\(785\) | 2.45798e9 | 0.181357 | ||||||||
\(786\) | −3.35173e9 | − | 2.05386e8i | −0.246201 | − | 0.0150866i | ||||
\(787\) | 1.76252e10i | 1.28891i | 0.764644 | + | 0.644453i | \(0.222915\pi\) | ||||
−0.764644 | + | 0.644453i | \(0.777085\pi\) | |||||||
\(788\) | 7.08777e8 | − | 5.76162e9i | 0.0516022 | − | 0.419472i | ||||
\(789\) | 2.31521e8i | 0.0167811i | ||||||||
\(790\) | −5.10708e8 | + | 8.33434e9i | −0.0368535 | + | 0.601418i | ||||
\(791\) | −1.65512e9 | −0.118908 | ||||||||
\(792\) | 9.89344e8 | − | 5.32781e9i | 0.0707635 | − | 0.381075i | ||||
\(793\) | 5.02547e9 | 0.357866 | ||||||||
\(794\) | 1.30141e9 | − | 2.12379e10i | 0.0922660 | − | 1.50571i | ||||
\(795\) | − | 2.02120e9i | − | 0.142667i | ||||||
\(796\) | 1.11572e10 | + | 1.37252e9i | 0.784076 | + | 0.0964548i | ||||
\(797\) | − | 1.78726e10i | − | 1.25050i | −0.780423 | − | 0.625251i | \(-0.784996\pi\) | ||
0.780423 | − | 0.625251i | \(-0.215004\pi\) | |||||||
\(798\) | 2.42254e9 | + | 1.48447e8i | 0.168757 | + | 0.0103410i | ||||
\(799\) | −7.50384e9 | −0.520439 | ||||||||
\(800\) | −1.10816e10 | − | 3.50100e9i | −0.765223 | − | 0.241756i | ||||
\(801\) | −9.35002e9 | −0.642834 | ||||||||
\(802\) | −1.52163e10 | − | 9.32421e8i | −1.04160 | − | 0.0638266i | ||||
\(803\) | 2.03632e10i | 1.38785i | ||||||||
\(804\) | 5.39020e9 | + | 6.63087e8i | 0.365771 | + | 0.0449961i | ||||
\(805\) | − | 1.21576e9i | − | 0.0821414i | ||||||
\(806\) | −7.55715e8 | + | 1.23326e10i | −0.0508376 | + | 0.829629i | ||||
\(807\) | 6.36854e8 | 0.0426562 | ||||||||
\(808\) | 3.06020e9 | − | 1.64797e10i | 0.204084 | − | 1.09903i | ||||
\(809\) | 6.25322e9 | 0.415225 | 0.207613 | − | 0.978211i | \(-0.433431\pi\) | ||||
0.207613 | + | 0.978211i | \(0.433431\pi\) | |||||||
\(810\) | 4.56796e7 | − | 7.45454e8i | 0.00302013 | − | 0.0492860i | ||||
\(811\) | 5.32870e9i | 0.350791i | 0.984498 | + | 0.175395i | \(0.0561204\pi\) | ||||
−0.984498 | + | 0.175395i | \(0.943880\pi\) | |||||||
\(812\) | 1.34054e9 | − | 1.08972e10i | 0.0878685 | − | 0.714279i | ||||
\(813\) | − | 6.79850e8i | − | 0.0443707i | ||||||
\(814\) | 2.48774e10 | + | 1.52443e9i | 1.61667 | + | 0.0990654i | ||||
\(815\) | 2.41381e9 | 0.156189 | ||||||||
\(816\) | −2.29050e9 | + | 9.16879e9i | −0.147576 | + | 0.590740i | ||||
\(817\) | 8.43472e9 | 0.541120 | ||||||||
\(818\) | 2.84142e9 | + | 1.74116e8i | 0.181509 | + | 0.0111225i | ||||
\(819\) | 6.35152e9i | 0.404003i | ||||||||
\(820\) | −6.10847e8 | + | 4.96555e9i | −0.0386887 | + | 0.314498i | ||||
\(821\) | − | 9.82164e9i | − | 0.619417i | −0.950832 | − | 0.309708i | \(-0.899769\pi\) | ||
0.950832 | − | 0.309708i | \(-0.100231\pi\) | |||||||
\(822\) | 1.27929e8 | − | 2.08770e9i | 0.00803374 | − | 0.131104i | ||||
\(823\) | −9.91646e9 | −0.620093 | −0.310047 | − | 0.950721i | \(-0.600345\pi\) | ||||
−0.310047 | + | 0.950721i | \(0.600345\pi\) | |||||||
\(824\) | −2.19346e10 | − | 4.07314e9i | −1.36579 | − | 0.253620i | ||||
\(825\) | −8.68897e9 | −0.538740 | ||||||||
\(826\) | 1.34159e9 | − | 2.18936e10i | 0.0828301 | − | 1.35172i | ||||
\(827\) | 6.85015e9i | 0.421144i | 0.977578 | + | 0.210572i | \(0.0675327\pi\) | ||||
−0.977578 | + | 0.210572i | \(0.932467\pi\) | |||||||
\(828\) | 1.40238e9 | + | 1.72517e8i | 0.0858538 | + | 0.0105615i | ||||
\(829\) | 1.40904e9i | 0.0858978i | 0.999077 | + | 0.0429489i | \(0.0136753\pi\) | ||||
−0.999077 | + | 0.0429489i | \(0.986325\pi\) | |||||||
\(830\) | −1.29951e10 | − | 7.96306e8i | −0.788870 | − | 0.0483400i | ||||
\(831\) | −9.30622e9 | −0.562561 | ||||||||
\(832\) | 1.01485e10 | − | 2.63836e10i | 0.610902 | − | 1.58819i | ||||
\(833\) | 8.66817e9 | 0.519601 | ||||||||
\(834\) | −1.69344e9 | − | 1.03770e8i | −0.101085 | − | 0.00619427i | ||||
\(835\) | 1.79289e9i | 0.106574i | ||||||||
\(836\) | −8.01584e9 | − | 9.86085e8i | −0.474490 | − | 0.0583704i | ||||
\(837\) | 1.59474e9i | 0.0940048i | ||||||||
\(838\) | −2.22092e8 | + | 3.62437e9i | −0.0130371 | + | 0.212754i | ||||
\(839\) | 3.05412e9 | 0.178533 | 0.0892667 | − | 0.996008i | \(-0.471548\pi\) | ||||
0.0892667 | + | 0.996008i | \(0.471548\pi\) | |||||||
\(840\) | −3.08656e9 | − | 5.73157e8i | −0.179679 | − | 0.0333654i | ||||
\(841\) | −3.60372e8 | −0.0208913 | ||||||||
\(842\) | −1.11135e9 | + | 1.81363e10i | −0.0641591 | + | 1.04702i | ||||
\(843\) | 9.11005e9i | 0.523750i | ||||||||
\(844\) | 1.16336e9 | − | 9.45692e9i | 0.0666065 | − | 0.541441i | ||||
\(845\) | − | 1.47745e10i | − | 0.842394i | ||||||
\(846\) | 2.89153e9 | + | 1.77186e8i | 0.164184 | + | 0.0100608i | ||||
\(847\) | −4.43415e9 | −0.250737 | ||||||||
\(848\) | 2.39311e9 | − | 9.57955e9i | 0.134765 | − | 0.539460i | ||||
\(849\) | −1.06681e10 | −0.598286 | ||||||||
\(850\) | 1.51252e10 | + | 9.26837e8i | 0.844765 | + | 0.0517651i | ||||
\(851\) | 6.49886e9i | 0.361479i | ||||||||
\(852\) | 1.35509e9 | − | 1.10155e10i | 0.0750637 | − | 0.610190i | ||||
\(853\) | 1.95266e10i | 1.07722i | 0.842555 | + | 0.538610i | \(0.181051\pi\) | ||||
−0.842555 | + | 0.538610i | \(0.818949\pi\) | |||||||
\(854\) | 1.66757e8 | − | 2.72134e9i | 0.00916184 | − | 0.149514i | ||||
\(855\) | −1.11310e9 | −0.0609052 | ||||||||
\(856\) | −8.61512e8 | + | 4.63941e9i | −0.0469465 | + | 0.252816i | ||||
\(857\) | −8.87348e9 | −0.481572 | −0.240786 | − | 0.970578i | \(-0.577405\pi\) | ||||
−0.240786 | + | 0.970578i | \(0.577405\pi\) | |||||||
\(858\) | 1.29268e9 | − | 2.10955e10i | 0.0698692 | − | 1.14021i | ||||
\(859\) | − | 2.58119e9i | − | 0.138945i | −0.997584 | − | 0.0694727i | \(-0.977868\pi\) | ||
0.997584 | − | 0.0694727i | \(-0.0221317\pi\) | |||||||
\(860\) | −1.08283e10 | − | 1.33207e9i | −0.580519 | − | 0.0714138i | ||||
\(861\) | − | 5.49149e9i | − | 0.293210i | ||||||
\(862\) | 1.74510e10 | + | 1.06936e9i | 0.927994 | + | 0.0568653i | ||||
\(863\) | 8.06781e9 | 0.427285 | 0.213643 | − | 0.976912i | \(-0.431467\pi\) | ||||
0.213643 | + | 0.976912i | \(0.431467\pi\) | |||||||
\(864\) | 1.09912e9 | − | 3.47902e9i | 0.0579760 | − | 0.183510i | ||||
\(865\) | 7.15235e9 | 0.375744 | ||||||||
\(866\) | −1.85960e10 | − | 1.13952e9i | −0.972986 | − | 0.0596222i | ||||
\(867\) | − | 1.24372e9i | − | 0.0648120i | ||||||
\(868\) | 6.65318e9 | + | 8.18455e8i | 0.345311 | + | 0.0424791i | ||||
\(869\) | 3.04981e10i | 1.57653i | ||||||||
\(870\) | −3.07974e8 | + | 5.02588e9i | −0.0158561 | + | 0.258759i | ||||
\(871\) | 2.11817e10 | 1.08617 | ||||||||
\(872\) | 5.80066e9 | − | 3.12376e10i | 0.296258 | − | 1.59540i | ||||
\(873\) | 9.93995e9 | 0.505632 | ||||||||
\(874\) | 1.28800e8 | − | 2.10191e9i | 0.00652568 | − | 0.106494i | ||||
\(875\) | 1.13064e10i | 0.570553i | ||||||||
\(876\) | −1.67401e9 | + | 1.36079e10i | −0.0841381 | + | 0.683954i | ||||
\(877\) | − | 2.78406e10i | − | 1.39373i | −0.717200 | − | 0.696867i | \(-0.754577\pi\) | ||
0.717200 | − | 0.696867i | \(-0.245423\pi\) | |||||||
\(878\) | −2.14896e10 | − | 1.31683e9i | −1.07151 | − | 0.0656598i | ||||
\(879\) | −1.62440e10 | −0.806735 | ||||||||
\(880\) | 1.01348e10 | + | 2.53183e9i | 0.501334 | + | 0.125241i | ||||
\(881\) | 8.64505e9 | 0.425943 | 0.212972 | − | 0.977058i | \(-0.431686\pi\) | ||||
0.212972 | + | 0.977058i | \(0.431686\pi\) | |||||||
\(882\) | −3.34020e9 | − | 2.04679e8i | −0.163920 | − | 0.0100446i | ||||
\(883\) | − | 2.55194e10i | − | 1.24741i | −0.781661 | − | 0.623704i | \(-0.785627\pi\) | ||
0.781661 | − | 0.623704i | \(-0.214373\pi\) | |||||||
\(884\) | −4.50044e9 | + | 3.65839e10i | −0.219115 | + | 1.78118i | ||||
\(885\) | 1.00596e10i | 0.487843i | ||||||||
\(886\) | −7.42756e8 | + | 1.21212e10i | −0.0358780 | + | 0.585500i | ||||
\(887\) | −2.64691e10 | −1.27352 | −0.636761 | − | 0.771061i | \(-0.719726\pi\) | ||||
−0.636761 | + | 0.771061i | \(0.719726\pi\) | |||||||
\(888\) | 1.64993e10 | + | 3.06382e9i | 0.790713 | + | 0.146831i | ||||
\(889\) | 2.56942e10 | 1.22653 | ||||||||
\(890\) | 1.10243e9 | − | 1.79908e10i | 0.0524188 | − | 0.855433i | ||||
\(891\) | − | 2.72786e9i | − | 0.129196i | ||||||
\(892\) | −1.07492e10 | − | 1.32234e9i | −0.507109 | − | 0.0623830i | ||||
\(893\) | − | 4.31760e9i | − | 0.202891i | ||||||
\(894\) | 1.11806e10 | + | 6.85122e8i | 0.523341 | + | 0.0320691i | ||||
\(895\) | −8.60420e9 | −0.401171 | ||||||||
\(896\) | −1.39502e10 | − | 6.37101e9i | −0.647894 | − | 0.295890i | ||||
\(897\) | 5.51088e9 | 0.254946 | ||||||||
\(898\) | −2.11800e9 | − | 1.29786e8i | −0.0976019 | − | 0.00598081i | ||||
\(899\) | − | 1.07518e10i | − | 0.493539i | ||||||
\(900\) | −5.80648e9 | − | 7.14296e8i | −0.265500 | − | 0.0326610i | ||||
\(901\) | 1.28749e10i | 0.586418i | ||||||||
\(902\) | −1.11765e9 | + | 1.82391e10i | −0.0507085 | + | 0.827522i | ||||
\(903\) | 1.19752e10 | 0.541224 | ||||||||
\(904\) | 3.64585e9 | + | 6.77015e8i | 0.164138 | + | 0.0304796i | ||||
\(905\) | 1.02813e10 | 0.461081 | ||||||||
\(906\) | −7.64389e8 | + | 1.24742e10i | −0.0341480 | + | 0.557268i | ||||
\(907\) | 2.81900e10i | 1.25450i | 0.778819 | + | 0.627249i | \(0.215819\pi\) | ||||
−0.778819 | + | 0.627249i | \(0.784181\pi\) | |||||||
\(908\) | −1.28635e9 | + | 1.04567e10i | −0.0570242 | + | 0.463547i | ||||
\(909\) | − | 8.43771e9i | − | 0.372607i | ||||||
\(910\) | −1.22213e10 | − | 7.48890e8i | −0.537615 | − | 0.0329437i | ||||
\(911\) | 1.11448e10 | 0.488381 | 0.244190 | − | 0.969727i | \(-0.421478\pi\) | ||||
0.244190 | + | 0.969727i | \(0.421478\pi\) | |||||||
\(912\) | −5.27559e9 | − | 1.31792e9i | −0.230298 | − | 0.0575317i | ||||
\(913\) | −4.75532e10 | −2.06791 | ||||||||
\(914\) | 1.14199e10 | + | 6.99787e8i | 0.494712 | + | 0.0303147i | ||||
\(915\) | 1.25040e9i | 0.0539603i | ||||||||
\(916\) | −3.33044e9 | + | 2.70730e10i | −0.143175 | + | 1.16386i | ||||
\(917\) | 7.10554e9i | 0.304302i | ||||||||
\(918\) | −2.90977e8 | + | 4.74850e9i | −0.0124139 | + | 0.202585i | ||||
\(919\) | 3.43901e10 | 1.46160 | 0.730801 | − | 0.682591i | \(-0.239147\pi\) | ||||
0.730801 | + | 0.682591i | \(0.239147\pi\) | |||||||
\(920\) | −4.97298e8 | + | 2.67805e9i | −0.0210552 | + | 0.113386i | ||||
\(921\) | 1.56779e10 | 0.661270 | ||||||||
\(922\) | 7.95833e8 | − | 1.29873e10i | 0.0334398 | − | 0.545710i | ||||
\(923\) | − | 4.32871e10i | − | 1.81198i | ||||||
\(924\) | −1.13805e10 | − | 1.40000e9i | −0.474581 | − | 0.0583816i | ||||
\(925\) | − | 2.69082e10i | − | 1.11786i | ||||||
\(926\) | 3.40651e10 | + | 2.08743e9i | 1.40985 | + | 0.0863919i | ||||
\(927\) | −1.12306e10 | −0.463047 | ||||||||
\(928\) | −7.41033e9 | + | 2.34557e10i | −0.304382 | + | 0.963453i | ||||
\(929\) | −2.08357e10 | −0.852617 | −0.426308 | − | 0.904578i | \(-0.640186\pi\) | ||||
−0.426308 | + | 0.904578i | \(0.640186\pi\) | |||||||
\(930\) | −3.06851e9 | − | 1.88031e8i | −0.125094 | − | 0.00766547i | ||||
\(931\) | 4.98754e9i | 0.202564i | ||||||||
\(932\) | 2.16730e10 | + | 2.66615e9i | 0.876926 | + | 0.107877i | ||||
\(933\) | − | 8.24821e9i | − | 0.332486i | ||||||
\(934\) | 9.30318e8 | − | 1.51820e10i | 0.0373609 | − | 0.609699i | ||||
\(935\) | −1.36212e10 | −0.544974 | ||||||||
\(936\) | 2.59805e9 | − | 1.39910e10i | 0.103558 | − | 0.557677i | ||||
\(937\) | −3.36470e10 | −1.33616 | −0.668079 | − | 0.744090i | \(-0.732883\pi\) | ||||
−0.668079 | + | 0.744090i | \(0.732883\pi\) | |||||||
\(938\) | 7.02860e8 | − | 1.14701e10i | 0.0278073 | − | 0.453792i | ||||
\(939\) | − | 1.29328e10i | − | 0.509759i | ||||||
\(940\) | −6.81865e8 | + | 5.54285e9i | −0.0267763 | + | 0.217663i | ||||
\(941\) | 1.90133e10i | 0.743865i | 0.928260 | + | 0.371932i | \(0.121305\pi\) | ||||
−0.928260 | + | 0.371932i | \(0.878695\pi\) | |||||||
\(942\) | 6.03334e9 | + | 3.69709e8i | 0.235169 | + | 0.0144106i | ||||
\(943\) | −4.76468e9 | −0.185030 | ||||||||
\(944\) | −1.19106e10 | + | 4.76779e10i | −0.460822 | + | 1.84466i | ||||
\(945\) | −1.58033e9 | −0.0609169 | ||||||||
\(946\) | −3.97737e10 | − | 2.43724e9i | −1.52749 | − | 0.0936007i | ||||
\(947\) | − | 3.29218e10i | − | 1.25968i | −0.776727 | − | 0.629838i | \(-0.783121\pi\) | ||
0.776727 | − | 0.629838i | \(-0.216879\pi\) | |||||||
\(948\) | −2.50717e9 | + | 2.03806e10i | −0.0955771 | + | 0.776942i | ||||
\(949\) | 5.34745e10i | 2.03102i | ||||||||
\(950\) | −5.33289e8 | + | 8.70284e9i | −0.0201804 | + | 0.329328i | ||||
\(951\) | 2.35724e10 | 0.888734 | ||||||||
\(952\) | 1.96612e10 | + | 3.65098e9i | 0.738552 | + | 0.137145i | ||||
\(953\) | 2.39320e10 | 0.895684 | 0.447842 | − | 0.894113i | \(-0.352193\pi\) | ||||
0.447842 | + | 0.894113i | \(0.352193\pi\) | |||||||
\(954\) | 3.04012e8 | − | 4.96123e9i | 0.0113363 | − | 0.184999i | ||||
\(955\) | − | 8.85541e9i | − | 0.329001i | ||||||
\(956\) | 4.92626e10 | + | 6.06014e9i | 1.82354 | + | 0.224326i | ||||
\(957\) | 1.83914e10i | 0.678301i | ||||||||
\(958\) | −3.54315e10 | − | 2.17116e9i | −1.30200 | − | 0.0797833i | ||||
\(959\) | −4.42584e9 | −0.162043 | ||||||||
\(960\) | 6.56456e9 | + | 2.52508e9i | 0.239473 | + | 0.0921139i | ||||
\(961\) | −2.09482e10 | −0.761403 | ||||||||
\(962\) | 6.53289e10 | + | 4.00320e9i | 2.36588 | + | 0.144975i | ||||
\(963\) | 2.37540e9i | 0.0857126i | ||||||||
\(964\) | 1.43465e10 | + | 1.76487e9i | 0.515795 | + | 0.0634516i | ||||
\(965\) | − | 1.05014e10i | − | 0.376187i | ||||||
\(966\) | 1.82864e8 | − | 2.98420e9i | 0.00652694 | − | 0.106514i | ||||
\(967\) | 1.73835e9 | 0.0618221 | 0.0309110 | − | 0.999522i | \(-0.490159\pi\) | ||||
0.0309110 | + | 0.999522i | \(0.490159\pi\) | |||||||
\(968\) | 9.76745e9 | + | 1.81376e9i | 0.346113 | + | 0.0642712i | ||||
\(969\) | 7.09040e9 | 0.250344 | ||||||||
\(970\) | −1.17199e9 | + | 1.91259e10i | −0.0412309 | + | 0.672855i | ||||
\(971\) | 2.13641e10i | 0.748889i | 0.927249 | + | 0.374444i | \(0.122167\pi\) | ||||
−0.927249 | + | 0.374444i | \(0.877833\pi\) | |||||||
\(972\) | 2.24250e8 | − | 1.82292e9i | 0.00783251 | − | 0.0636701i | ||||
\(973\) | 3.59003e9i | 0.124940i | ||||||||
\(974\) | −3.76691e10 | − | 2.30827e9i | −1.30626 | − | 0.0800443i | ||||
\(975\) | −2.28175e10 | −0.788409 | ||||||||
\(976\) | −1.48048e9 | + | 5.92630e9i | −0.0509715 | + | 0.204037i | ||||
\(977\) | 2.02894e10 | 0.696045 | 0.348023 | − | 0.937486i | \(-0.386853\pi\) | ||||
0.348023 | + | 0.937486i | \(0.386853\pi\) | |||||||
\(978\) | 5.92493e9 | + | 3.63065e8i | 0.202534 | + | 0.0124108i | ||||
\(979\) | − | 6.58343e10i | − | 2.24240i | ||||||
\(980\) | 7.87667e8 | − | 6.40290e9i | 0.0267332 | − | 0.217313i | ||||
\(981\) | − | 1.59938e10i | − | 0.540892i | ||||||
\(982\) | −1.64920e9 | + | 2.69137e10i | −0.0555756 | + | 0.906948i | ||||
\(983\) | 2.41614e9 | 0.0811306 | 0.0405653 | − | 0.999177i | \(-0.487084\pi\) | ||||
0.0405653 | + | 0.999177i | \(0.487084\pi\) | |||||||
\(984\) | −2.24626e9 | + | 1.20965e10i | −0.0751583 | + | 0.404742i | ||||
\(985\) | 5.63340e9 | 0.187821 | ||||||||
\(986\) | 1.96178e9 | − | 3.20146e10i | 0.0651749 | − | 1.06360i | ||||
\(987\) | − | 6.12994e9i | − | 0.202930i | ||||||
\(988\) | −2.10498e10 | − | 2.58949e9i | −0.694384 | − | 0.0854211i | ||||
\(989\) | − | 1.03903e10i | − | 0.341539i | ||||||
\(990\) | 5.24881e9 | + | 3.21634e8i | 0.171925 | + | 0.0105351i | ||||
\(991\) | −9.02687e9 | −0.294631 | −0.147316 | − | 0.989090i | \(-0.547063\pi\) | ||||
−0.147316 | + | 0.989090i | \(0.547063\pi\) | |||||||
\(992\) | −1.43207e10 | − | 4.52431e9i | −0.465772 | − | 0.147151i | ||||
\(993\) | 2.68489e10 | 0.870170 | ||||||||
\(994\) | −2.34404e10 | − | 1.43637e9i | −0.757030 | − | 0.0463889i | ||||
\(995\) | 1.09089e10i | 0.351075i | ||||||||
\(996\) | −3.17779e10 | − | 3.90922e9i | −1.01910 | − | 0.125367i | ||||
\(997\) | − | 3.77389e9i | − | 0.120602i | −0.998180 | − | 0.0603012i | \(-0.980794\pi\) | ||
0.998180 | − | 0.0603012i | \(-0.0192061\pi\) | |||||||
\(998\) | 2.41982e9 | − | 3.94895e10i | 0.0770595 | − | 1.25755i | ||||
\(999\) | 8.44770e9 | 0.268077 |
(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.d.a.13.1 | ✓ | 14 | |
3.2 | odd | 2 | 72.8.d.d.37.14 | 14 | |||
4.3 | odd | 2 | 96.8.d.a.49.12 | 14 | |||
8.3 | odd | 2 | 96.8.d.a.49.3 | 14 | |||
8.5 | even | 2 | inner | 24.8.d.a.13.2 | yes | 14 | |
12.11 | even | 2 | 288.8.d.d.145.5 | 14 | |||
24.5 | odd | 2 | 72.8.d.d.37.13 | 14 | |||
24.11 | even | 2 | 288.8.d.d.145.10 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.8.d.a.13.1 | ✓ | 14 | 1.1 | even | 1 | trivial | |
24.8.d.a.13.2 | yes | 14 | 8.5 | even | 2 | inner | |
72.8.d.d.37.13 | 14 | 24.5 | odd | 2 | |||
72.8.d.d.37.14 | 14 | 3.2 | odd | 2 | |||
96.8.d.a.49.3 | 14 | 8.3 | odd | 2 | |||
96.8.d.a.49.12 | 14 | 4.3 | odd | 2 | |||
288.8.d.d.145.5 | 14 | 12.11 | even | 2 | |||
288.8.d.d.145.10 | 14 | 24.11 | even | 2 |