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: | \( x^{14} - 6 x^{13} - 52 x^{12} + 300 x^{11} - 1005 x^{10} - 23250 x^{9} + 349930 x^{8} + \cdots + 3813237677250 \) |
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 | 13.8 | ||
Root | \(-5.80663 + 4.20354i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 24.13 |
Dual form | 24.8.d.a.13.7 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.60309 | + | 11.0102i | −0.230083 | + | 0.973171i | ||||
\(3\) | 27.0000i | 0.577350i | ||||||||
\(4\) | −114.448 | − | 57.3210i | −0.894123 | − | 0.447821i | ||||
\(5\) | − | 468.400i | − | 1.67580i | −0.545824 | − | 0.837900i | \(-0.683783\pi\) | ||
0.545824 | − | 0.837900i | \(-0.316217\pi\) | |||||||
\(6\) | −297.275 | − | 70.2836i | −0.561861 | − | 0.132839i | ||||
\(7\) | 81.2421 | 0.0895237 | 0.0447618 | − | 0.998998i | \(-0.485747\pi\) | ||||
0.0447618 | + | 0.998998i | \(0.485747\pi\) | |||||||
\(8\) | 929.033 | − | 1110.88i | 0.641529 | − | 0.767099i | ||||
\(9\) | −729.000 | −0.333333 | ||||||||
\(10\) | 5157.17 | + | 1219.29i | 1.63084 | + | 0.385574i | ||||
\(11\) | 3394.58i | 0.768974i | 0.923130 | + | 0.384487i | \(0.125622\pi\) | ||||
−0.923130 | + | 0.384487i | \(0.874378\pi\) | |||||||
\(12\) | 1547.67 | − | 3090.09i | 0.258549 | − | 0.516222i | ||||
\(13\) | − | 14492.5i | − | 1.82954i | −0.403975 | − | 0.914770i | \(-0.632372\pi\) | ||
0.403975 | − | 0.914770i | \(-0.367628\pi\) | |||||||
\(14\) | −211.481 | + | 894.489i | −0.0205979 | + | 0.0871218i | ||||
\(15\) | 12646.8 | 0.967524 | ||||||||
\(16\) | 9812.60 | + | 13120.5i | 0.598913 | + | 0.800814i | ||||
\(17\) | 5178.19 | 0.255627 | 0.127814 | − | 0.991798i | \(-0.459204\pi\) | ||||
0.127814 | + | 0.991798i | \(0.459204\pi\) | |||||||
\(18\) | 1897.66 | − | 8026.42i | 0.0766944 | − | 0.324390i | ||||
\(19\) | − | 46067.9i | − | 1.54085i | −0.637529 | − | 0.770426i | \(-0.720044\pi\) | ||
0.637529 | − | 0.770426i | \(-0.279956\pi\) | |||||||
\(20\) | −26849.2 | + | 53607.4i | −0.750458 | + | 1.49837i | ||||
\(21\) | 2193.54i | 0.0516865i | ||||||||
\(22\) | −37374.9 | − | 8836.41i | −0.748343 | − | 0.176928i | ||||
\(23\) | −67535.4 | −1.15740 | −0.578701 | − | 0.815540i | \(-0.696440\pi\) | ||||
−0.578701 | + | 0.815540i | \(0.696440\pi\) | |||||||
\(24\) | 29993.7 | + | 25083.9i | 0.442885 | + | 0.370387i | ||||
\(25\) | −141274. | −1.80831 | ||||||||
\(26\) | 159565. | + | 37725.4i | 1.78046 | + | 0.420947i | ||||
\(27\) | − | 19683.0i | − | 0.192450i | ||||||
\(28\) | −9297.97 | − | 4656.88i | −0.0800452 | − | 0.0400905i | ||||
\(29\) | − | 25387.3i | − | 0.193296i | −0.995319 | − | 0.0966480i | \(-0.969188\pi\) | ||
0.995319 | − | 0.0966480i | \(-0.0308121\pi\) | |||||||
\(30\) | −32920.8 | + | 139244.i | −0.222611 | + | 0.941566i | ||||
\(31\) | 123808. | 0.746419 | 0.373210 | − | 0.927747i | \(-0.378257\pi\) | ||||
0.373210 | + | 0.927747i | \(0.378257\pi\) | |||||||
\(32\) | −170002. | + | 73884.4i | −0.917129 | + | 0.398591i | ||||
\(33\) | −91653.7 | −0.443967 | ||||||||
\(34\) | −13479.3 | + | 57012.8i | −0.0588155 | + | 0.248769i | ||||
\(35\) | − | 38053.8i | − | 0.150024i | ||||||
\(36\) | 83432.4 | + | 41787.0i | 0.298041 | + | 0.149274i | ||||
\(37\) | − | 104623.i | − | 0.339562i | −0.985482 | − | 0.169781i | \(-0.945694\pi\) | ||
0.985482 | − | 0.169781i | \(-0.0543061\pi\) | |||||||
\(38\) | 507216. | + | 119919.i | 1.49951 | + | 0.354524i | ||||
\(39\) | 391298. | 1.05629 | ||||||||
\(40\) | −520336. | − | 435159.i | −1.28550 | − | 1.07507i | ||||
\(41\) | −160655. | −0.364042 | −0.182021 | − | 0.983295i | \(-0.558264\pi\) | ||||
−0.182021 | + | 0.983295i | \(0.558264\pi\) | |||||||
\(42\) | −24151.2 | − | 5709.98i | −0.0502998 | − | 0.0118922i | ||||
\(43\) | − | 378823.i | − | 0.726603i | −0.931672 | − | 0.363301i | \(-0.881650\pi\) | ||
0.931672 | − | 0.363301i | \(-0.118350\pi\) | |||||||
\(44\) | 194581. | − | 388502.i | 0.344362 | − | 0.687558i | ||||
\(45\) | 341464.i | 0.558600i | ||||||||
\(46\) | 175801. | − | 743577.i | 0.266299 | − | 1.12635i | ||||
\(47\) | 683674. | 0.960520 | 0.480260 | − | 0.877126i | \(-0.340542\pi\) | ||||
0.480260 | + | 0.877126i | \(0.340542\pi\) | |||||||
\(48\) | −354254. | + | 264940.i | −0.462350 | + | 0.345783i | ||||
\(49\) | −816943. | −0.991986 | ||||||||
\(50\) | 367749. | − | 1.55545e6i | 0.416061 | − | 1.75979i | ||||
\(51\) | 139811.i | 0.147586i | ||||||||
\(52\) | −830726. | + | 1.65864e6i | −0.819306 | + | 1.63583i | ||||
\(53\) | 1.74261e6i | 1.60781i | 0.594757 | + | 0.803906i | \(0.297248\pi\) | ||||
−0.594757 | + | 0.803906i | \(0.702752\pi\) | |||||||
\(54\) | 216713. | + | 51236.7i | 0.187287 | + | 0.0442795i | ||||
\(55\) | 1.59002e6 | 1.28865 | ||||||||
\(56\) | 75476.6 | − | 90250.0i | 0.0574320 | − | 0.0686735i | ||||
\(57\) | 1.24383e6 | 0.889611 | ||||||||
\(58\) | 279518. | + | 66085.5i | 0.188110 | + | 0.0444742i | ||||
\(59\) | 1.48196e6i | 0.939406i | 0.882824 | + | 0.469703i | \(0.155639\pi\) | ||||
−0.882824 | + | 0.469703i | \(0.844361\pi\) | |||||||
\(60\) | −1.44740e6 | − | 724928.i | −0.865086 | − | 0.433277i | ||||
\(61\) | − | 444587.i | − | 0.250785i | −0.992107 | − | 0.125393i | \(-0.959981\pi\) | ||
0.992107 | − | 0.125393i | \(-0.0400191\pi\) | |||||||
\(62\) | −322284. | + | 1.36315e6i | −0.171739 | + | 0.726393i | ||||
\(63\) | −59225.5 | −0.0298412 | ||||||||
\(64\) | −370947. | − | 2.06408e6i | −0.176881 | − | 0.984232i | ||||
\(65\) | −6.78830e6 | −3.06594 | ||||||||
\(66\) | 238583. | − | 1.00912e6i | 0.102149 | − | 0.432056i | ||||
\(67\) | 2.48180e6i | 1.00810i | 0.863674 | + | 0.504051i | \(0.168158\pi\) | ||||
−0.863674 | + | 0.504051i | \(0.831842\pi\) | |||||||
\(68\) | −592632. | − | 296819.i | −0.228562 | − | 0.114475i | ||||
\(69\) | − | 1.82346e6i | − | 0.668226i | ||||||
\(70\) | 418979. | + | 99057.7i | 0.145999 | + | 0.0345180i | ||||
\(71\) | −510618. | −0.169313 | −0.0846567 | − | 0.996410i | \(-0.526979\pi\) | ||||
−0.0846567 | + | 0.996410i | \(0.526979\pi\) | |||||||
\(72\) | −677265. | + | 809830.i | −0.213843 | + | 0.255700i | ||||
\(73\) | 4.80319e6 | 1.44511 | 0.722553 | − | 0.691315i | \(-0.242968\pi\) | ||||
0.722553 | + | 0.691315i | \(0.242968\pi\) | |||||||
\(74\) | 1.15191e6 | + | 272342.i | 0.330452 | + | 0.0781276i | ||||
\(75\) | − | 3.81440e6i | − | 1.04403i | ||||||
\(76\) | −2.64066e6 | + | 5.27237e6i | −0.690025 | + | 1.37771i | ||||
\(77\) | 275783.i | 0.0688414i | ||||||||
\(78\) | −1.01859e6 | + | 4.30826e6i | −0.243034 | + | 1.02795i | ||||
\(79\) | 1.57434e6 | 0.359255 | 0.179627 | − | 0.983735i | \(-0.442511\pi\) | ||||
0.179627 | + | 0.983735i | \(0.442511\pi\) | |||||||
\(80\) | 6.14566e6 | − | 4.59622e6i | 1.34200 | − | 1.00366i | ||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 418201. | − | 1.76884e6i | 0.0837600 | − | 0.354275i | ||||
\(83\) | − | 7.91066e6i | − | 1.51859i | −0.650749 | − | 0.759293i | \(-0.725545\pi\) | ||
0.650749 | − | 0.759293i | \(-0.274455\pi\) | |||||||
\(84\) | 125736. | − | 251045.i | 0.0231463 | − | 0.0462141i | ||||
\(85\) | − | 2.42547e6i | − | 0.428380i | ||||||
\(86\) | 4.17091e6 | + | 986113.i | 0.707109 | + | 0.167179i | ||||
\(87\) | 685456. | 0.111600 | ||||||||
\(88\) | 3.77096e6 | + | 3.15368e6i | 0.589879 | + | 0.493319i | ||||
\(89\) | 6.35526e6 | 0.955583 | 0.477791 | − | 0.878473i | \(-0.341437\pi\) | ||||
0.477791 | + | 0.878473i | \(0.341437\pi\) | |||||||
\(90\) | −3.75958e6 | − | 888863.i | −0.543613 | − | 0.128525i | ||||
\(91\) | − | 1.17740e6i | − | 0.163787i | ||||||
\(92\) | 7.72928e6 | + | 3.87120e6i | 1.03486 | + | 0.518308i | ||||
\(93\) | 3.34282e6i | 0.430945i | ||||||||
\(94\) | −1.77967e6 | + | 7.52737e6i | −0.221000 | + | 0.934750i | ||||
\(95\) | −2.15782e7 | −2.58216 | ||||||||
\(96\) | −1.99488e6 | − | 4.59007e6i | −0.230127 | − | 0.529505i | ||||
\(97\) | −3.68231e6 | −0.409656 | −0.204828 | − | 0.978798i | \(-0.565664\pi\) | ||||
−0.204828 | + | 0.978798i | \(0.565664\pi\) | |||||||
\(98\) | 2.12658e6 | − | 8.99468e6i | 0.228239 | − | 0.965371i | ||||
\(99\) | − | 2.47465e6i | − | 0.256325i | ||||||
\(100\) | 1.61685e7 | + | 8.09797e6i | 1.61685 | + | 0.809797i | ||||
\(101\) | − | 1.61014e6i | − | 0.155503i | −0.996973 | − | 0.0777514i | \(-0.975226\pi\) | ||
0.996973 | − | 0.0777514i | \(-0.0247740\pi\) | |||||||
\(102\) | −1.53934e6 | − | 363942.i | −0.143627 | − | 0.0339571i | ||||
\(103\) | 392152. | 0.0353609 | 0.0176805 | − | 0.999844i | \(-0.494372\pi\) | ||||
0.0176805 | + | 0.999844i | \(0.494372\pi\) | |||||||
\(104\) | −1.60994e7 | − | 1.34640e7i | −1.40344 | − | 1.17370i | ||||
\(105\) | 1.02745e6 | 0.0866163 | ||||||||
\(106\) | −1.91865e7 | − | 4.53618e6i | −1.56468 | − | 0.369930i | ||||
\(107\) | 1.62922e7i | 1.28569i | 0.765998 | + | 0.642843i | \(0.222245\pi\) | ||||
−0.765998 | + | 0.642843i | \(0.777755\pi\) | |||||||
\(108\) | −1.12825e6 | + | 2.25268e6i | −0.0861831 | + | 0.172074i | ||||
\(109\) | − | 2.39639e7i | − | 1.77241i | −0.463294 | − | 0.886205i | \(-0.653333\pi\) | ||
0.463294 | − | 0.886205i | \(-0.346667\pi\) | |||||||
\(110\) | −4.13898e6 | + | 1.75064e7i | −0.296496 | + | 1.25407i | ||||
\(111\) | 2.82481e6 | 0.196046 | ||||||||
\(112\) | 797195. | + | 1.06594e6i | 0.0536169 | + | 0.0716918i | ||||
\(113\) | 1.91168e7 | 1.24635 | 0.623176 | − | 0.782081i | \(-0.285842\pi\) | ||||
0.623176 | + | 0.782081i | \(0.285842\pi\) | |||||||
\(114\) | −3.23782e6 | + | 1.36948e7i | −0.204685 | + | 0.865744i | ||||
\(115\) | 3.16336e7i | 1.93957i | ||||||||
\(116\) | −1.45522e6 | + | 2.90552e6i | −0.0865620 | + | 0.172831i | ||||
\(117\) | 1.05650e7i | 0.609847i | ||||||||
\(118\) | −1.63166e7 | − | 3.85767e6i | −0.914203 | − | 0.216142i | ||||
\(119\) | 420687. | 0.0228847 | ||||||||
\(120\) | 1.17493e7 | − | 1.40491e7i | 0.620694 | − | 0.742186i | ||||
\(121\) | 7.96400e6 | 0.408679 | ||||||||
\(122\) | 4.89498e6 | + | 1.15730e6i | 0.244057 | + | 0.0577015i | ||||
\(123\) | − | 4.33770e6i | − | 0.210180i | ||||||
\(124\) | −1.41696e7 | − | 7.09680e6i | −0.667391 | − | 0.334262i | ||||
\(125\) | 2.95790e7i | 1.35456i | ||||||||
\(126\) | 154169. | − | 652083.i | 0.00686596 | − | 0.0290406i | ||||
\(127\) | −1.67337e7 | −0.724901 | −0.362451 | − | 0.932003i | \(-0.618060\pi\) | ||||
−0.362451 | + | 0.932003i | \(0.618060\pi\) | |||||||
\(128\) | 2.36915e7 | + | 1.28881e6i | 0.998524 | + | 0.0543195i | ||||
\(129\) | 1.02282e7 | 0.419504 | ||||||||
\(130\) | 1.76706e7 | − | 7.47403e7i | 0.705422 | − | 2.98369i | ||||
\(131\) | − | 2.21897e7i | − | 0.862386i | −0.902260 | − | 0.431193i | \(-0.858093\pi\) | ||
0.902260 | − | 0.431193i | \(-0.141907\pi\) | |||||||
\(132\) | 1.04896e7 | + | 5.25368e6i | 0.396962 | + | 0.198818i | ||||
\(133\) | − | 3.74265e6i | − | 0.137943i | ||||||
\(134\) | −2.73250e7 | − | 6.46035e6i | −0.981056 | − | 0.231947i | ||||
\(135\) | −9.21953e6 | −0.322508 | ||||||||
\(136\) | 4.81071e6 | − | 5.75234e6i | 0.163992 | − | 0.196091i | ||||
\(137\) | −582593. | −0.0193572 | −0.00967862 | − | 0.999953i | \(-0.503081\pi\) | ||||
−0.00967862 | + | 0.999953i | \(0.503081\pi\) | |||||||
\(138\) | 2.00766e7 | + | 4.74663e6i | 0.650298 | + | 0.153748i | ||||
\(139\) | 3.81869e6i | 0.120604i | 0.998180 | + | 0.0603021i | \(0.0192064\pi\) | ||||
−0.998180 | + | 0.0603021i | \(0.980794\pi\) | |||||||
\(140\) | −2.18128e6 | + | 4.35518e6i | −0.0671837 | + | 0.134140i | ||||
\(141\) | 1.84592e7i | 0.554557i | ||||||||
\(142\) | 1.32919e6 | − | 5.62199e6i | 0.0389562 | − | 0.164771i | ||||
\(143\) | 4.91960e7 | 1.40687 | ||||||||
\(144\) | −7.15338e6 | − | 9.56487e6i | −0.199638 | − | 0.266938i | ||||
\(145\) | −1.18914e7 | −0.323926 | ||||||||
\(146\) | −1.25032e7 | + | 5.28840e7i | −0.332495 | + | 1.40634i | ||||
\(147\) | − | 2.20575e7i | − | 0.572723i | ||||||
\(148\) | −5.99707e6 | + | 1.19738e7i | −0.152063 | + | 0.303611i | ||||
\(149\) | 8.12196e6i | 0.201145i | 0.994930 | + | 0.100572i | \(0.0320674\pi\) | ||||
−0.994930 | + | 0.100572i | \(0.967933\pi\) | |||||||
\(150\) | 4.19972e7 | + | 9.92924e6i | 1.01602 | + | 0.240213i | ||||
\(151\) | 2.00853e7 | 0.474744 | 0.237372 | − | 0.971419i | \(-0.423714\pi\) | ||||
0.237372 | + | 0.971419i | \(0.423714\pi\) | |||||||
\(152\) | −5.11758e7 | − | 4.27986e7i | −1.18199 | − | 0.988501i | ||||
\(153\) | −3.77490e6 | −0.0852090 | ||||||||
\(154\) | −3.03641e6 | − | 717888.i | −0.0669944 | − | 0.0158392i | ||||
\(155\) | − | 5.79917e7i | − | 1.25085i | ||||||
\(156\) | −4.47832e7 | − | 2.24296e7i | −0.944450 | − | 0.473026i | ||||
\(157\) | − | 7.13959e7i | − | 1.47239i | −0.676767 | − | 0.736197i | \(-0.736620\pi\) | ||
0.676767 | − | 0.736197i | \(-0.263380\pi\) | |||||||
\(158\) | −4.09815e6 | + | 1.73337e7i | −0.0826585 | + | 0.349616i | ||||
\(159\) | −4.70505e7 | −0.928270 | ||||||||
\(160\) | 3.46075e7 | + | 7.96292e7i | 0.667959 | + | 1.53692i | ||||
\(161\) | −5.48672e6 | −0.103615 | ||||||||
\(162\) | −1.38339e6 | + | 5.85126e6i | −0.0255648 | + | 0.108130i | ||||
\(163\) | 7.14988e7i | 1.29313i | 0.762859 | + | 0.646565i | \(0.223795\pi\) | ||||
−0.762859 | + | 0.646565i | \(0.776205\pi\) | |||||||
\(164\) | 1.83867e7 | + | 9.20893e6i | 0.325499 | + | 0.163026i | ||||
\(165\) | 4.29306e7i | 0.744001i | ||||||||
\(166\) | 8.70978e7 | + | 2.05922e7i | 1.47784 | + | 0.349401i | ||||
\(167\) | 7.80714e7 | 1.29713 | 0.648566 | − | 0.761158i | \(-0.275369\pi\) | ||||
0.648566 | + | 0.761158i | \(0.275369\pi\) | |||||||
\(168\) | 2.43675e6 | + | 2.03787e6i | 0.0396487 | + | 0.0331584i | ||||
\(169\) | −1.47284e8 | −2.34722 | ||||||||
\(170\) | 2.67048e7 | + | 6.31372e6i | 0.416887 | + | 0.0985630i | ||||
\(171\) | 3.35835e7i | 0.513617i | ||||||||
\(172\) | −2.17145e7 | + | 4.33555e7i | −0.325388 | + | 0.649673i | ||||
\(173\) | − | 4.84863e7i | − | 0.711963i | −0.934493 | − | 0.355981i | \(-0.884147\pi\) | ||
0.934493 | − | 0.355981i | \(-0.115853\pi\) | |||||||
\(174\) | −1.78431e6 | + | 7.54699e6i | −0.0256772 | + | 0.108605i | ||||
\(175\) | −1.14774e7 | −0.161886 | ||||||||
\(176\) | −4.45387e7 | + | 3.33096e7i | −0.615805 | + | 0.460549i | ||||
\(177\) | −4.00128e7 | −0.542366 | ||||||||
\(178\) | −1.65433e7 | + | 6.99725e7i | −0.219864 | + | 0.929946i | ||||
\(179\) | − | 7.56733e7i | − | 0.986182i | −0.869978 | − | 0.493091i | \(-0.835867\pi\) | ||
0.869978 | − | 0.493091i | \(-0.164133\pi\) | |||||||
\(180\) | 1.95731e7 | − | 3.90798e7i | 0.250153 | − | 0.499457i | ||||
\(181\) | − | 2.01200e7i | − | 0.252204i | −0.992017 | − | 0.126102i | \(-0.959753\pi\) | ||
0.992017 | − | 0.126102i | \(-0.0402467\pi\) | |||||||
\(182\) | 1.29634e7 | + | 3.06489e6i | 0.159393 | + | 0.0376847i | ||||
\(183\) | 1.20038e7 | 0.144791 | ||||||||
\(184\) | −6.27426e7 | + | 7.50236e7i | −0.742507 | + | 0.887842i | ||||
\(185\) | −4.90053e7 | −0.569038 | ||||||||
\(186\) | −3.68050e7 | − | 8.70167e6i | −0.419383 | − | 0.0991533i | ||||
\(187\) | 1.75778e7i | 0.196571i | ||||||||
\(188\) | −7.82450e7 | − | 3.91889e7i | −0.858824 | − | 0.430141i | ||||
\(189\) | − | 1.59909e6i | − | 0.0172288i | ||||||
\(190\) | 5.61702e7 | − | 2.37580e8i | 0.594112 | − | 2.51288i | ||||
\(191\) | −3.28127e7 | −0.340741 | −0.170371 | − | 0.985380i | \(-0.554496\pi\) | ||||
−0.170371 | + | 0.985380i | \(0.554496\pi\) | |||||||
\(192\) | 5.57303e7 | − | 1.00156e7i | 0.568247 | − | 0.102123i | ||||
\(193\) | 9.98286e7 | 0.999550 | 0.499775 | − | 0.866155i | \(-0.333416\pi\) | ||||
0.499775 | + | 0.866155i | \(0.333416\pi\) | |||||||
\(194\) | 9.58541e6 | − | 4.05429e7i | 0.0942551 | − | 0.398666i | ||||
\(195\) | − | 1.83284e8i | − | 1.77012i | ||||||
\(196\) | 9.34973e7 | + | 4.68280e7i | 0.886957 | + | 0.444232i | ||||
\(197\) | 8.59728e7i | 0.801179i | 0.916258 | + | 0.400589i | \(0.131195\pi\) | ||||
−0.916258 | + | 0.400589i | \(0.868805\pi\) | |||||||
\(198\) | 2.72463e7 | + | 6.44175e6i | 0.249448 | + | 0.0589760i | ||||
\(199\) | 1.62250e8 | 1.45948 | 0.729741 | − | 0.683724i | \(-0.239641\pi\) | ||||
0.729741 | + | 0.683724i | \(0.239641\pi\) | |||||||
\(200\) | −1.31248e8 | + | 1.56938e8i | −1.16008 | + | 1.38715i | ||||
\(201\) | −6.70085e7 | −0.582028 | ||||||||
\(202\) | 1.77279e7 | + | 4.19134e6i | 0.151331 | + | 0.0357786i | ||||
\(203\) | − | 2.06251e6i | − | 0.0173046i | ||||||
\(204\) | 8.01412e6 | − | 1.60011e7i | 0.0660922 | − | 0.131960i | ||||
\(205\) | 7.52511e7i | 0.610062i | ||||||||
\(206\) | −1.02081e6 | + | 4.31766e6i | −0.00813596 | + | 0.0344122i | ||||
\(207\) | 4.92333e7 | 0.385801 | ||||||||
\(208\) | 1.90150e8 | − | 1.42209e8i | 1.46512 | − | 1.09574i | ||||
\(209\) | 1.56381e8 | 1.18488 | ||||||||
\(210\) | −2.67456e6 | + | 1.13124e7i | −0.0199289 | + | 0.0842924i | ||||
\(211\) | 2.14780e8i | 1.57400i | 0.616953 | + | 0.787000i | \(0.288367\pi\) | ||||
−0.616953 | + | 0.787000i | \(0.711633\pi\) | |||||||
\(212\) | 9.98883e7 | − | 1.99438e8i | 0.720011 | − | 1.43758i | ||||
\(213\) | − | 1.37867e7i | − | 0.0977532i | ||||||
\(214\) | −1.79379e8 | − | 4.24100e7i | −1.25119 | − | 0.295815i | ||||
\(215\) | −1.77441e8 | −1.21764 | ||||||||
\(216\) | −2.18654e7 | − | 1.82862e7i | −0.147628 | − | 0.123462i | ||||
\(217\) | 1.00584e7 | 0.0668222 | ||||||||
\(218\) | 2.63846e8 | + | 6.23802e7i | 1.72486 | + | 0.407802i | ||||
\(219\) | 1.29686e8i | 0.834333i | ||||||||
\(220\) | −1.81975e8 | − | 9.11418e7i | −1.15221 | − | 0.577083i | ||||
\(221\) | − | 7.50450e7i | − | 0.467680i | ||||||
\(222\) | −7.35325e6 | + | 3.11016e7i | −0.0451070 | + | 0.190787i | ||||
\(223\) | 1.26786e8 | 0.765603 | 0.382802 | − | 0.923831i | \(-0.374959\pi\) | ||||
0.382802 | + | 0.923831i | \(0.374959\pi\) | |||||||
\(224\) | −1.38114e7 | + | 6.00252e6i | −0.0821047 | + | 0.0356833i | ||||
\(225\) | 1.02989e8 | 0.602769 | ||||||||
\(226\) | −4.97629e7 | + | 2.10479e8i | −0.286765 | + | 1.21291i | ||||
\(227\) | 1.99430e8i | 1.13162i | 0.824536 | + | 0.565810i | \(0.191436\pi\) | ||||
−0.824536 | + | 0.565810i | \(0.808564\pi\) | |||||||
\(228\) | −1.42354e8 | − | 7.12978e7i | −0.795422 | − | 0.398386i | ||||
\(229\) | − | 3.66567e7i | − | 0.201711i | −0.994901 | − | 0.100856i | \(-0.967842\pi\) | ||
0.994901 | − | 0.100856i | \(-0.0321580\pi\) | |||||||
\(230\) | −3.48292e8 | − | 8.23453e7i | −1.88754 | − | 0.446264i | ||||
\(231\) | −7.44613e6 | −0.0397456 | ||||||||
\(232\) | −2.82022e7 | − | 2.35856e7i | −0.148277 | − | 0.124005i | ||||
\(233\) | 9.86007e7 | 0.510663 | 0.255331 | − | 0.966854i | \(-0.417815\pi\) | ||||
0.255331 | + | 0.966854i | \(0.417815\pi\) | |||||||
\(234\) | −1.16323e8 | − | 2.75018e7i | −0.593485 | − | 0.140316i | ||||
\(235\) | − | 3.20233e8i | − | 1.60964i | ||||||
\(236\) | 8.49473e7 | − | 1.69607e8i | 0.420685 | − | 0.839945i | ||||
\(237\) | 4.25071e7i | 0.207416i | ||||||||
\(238\) | −1.09509e6 | + | 4.63183e6i | −0.00526538 | + | 0.0222707i | ||||
\(239\) | −1.07872e8 | −0.511110 | −0.255555 | − | 0.966795i | \(-0.582258\pi\) | ||||
−0.255555 | + | 0.966795i | \(0.582258\pi\) | |||||||
\(240\) | 1.24098e8 | + | 1.65933e8i | 0.579463 | + | 0.774806i | ||||
\(241\) | −9.47834e7 | −0.436187 | −0.218093 | − | 0.975928i | \(-0.569984\pi\) | ||||
−0.218093 | + | 0.975928i | \(0.569984\pi\) | |||||||
\(242\) | −2.07310e7 | + | 8.76850e7i | −0.0940302 | + | 0.397715i | ||||
\(243\) | 1.43489e7i | 0.0641500i | ||||||||
\(244\) | −2.54842e7 | + | 5.08820e7i | −0.112307 | + | 0.224233i | ||||
\(245\) | 3.82656e8i | 1.66237i | ||||||||
\(246\) | 4.77588e7 | + | 1.12914e7i | 0.204541 | + | 0.0483589i | ||||
\(247\) | −6.67640e8 | −2.81905 | ||||||||
\(248\) | 1.15022e8 | − | 1.37536e8i | 0.478849 | − | 0.572577i | ||||
\(249\) | 2.13588e8 | 0.876756 | ||||||||
\(250\) | −3.25670e8 | − | 7.69969e7i | −1.31822 | − | 0.311662i | ||||
\(251\) | 1.76729e8i | 0.705422i | 0.935732 | + | 0.352711i | \(0.114740\pi\) | ||||
−0.935732 | + | 0.352711i | \(0.885260\pi\) | |||||||
\(252\) | 6.77822e6 | + | 3.39487e6i | 0.0266817 | + | 0.0133635i | ||||
\(253\) | − | 2.29254e8i | − | 0.890012i | ||||||
\(254\) | 4.35594e7 | − | 1.84241e8i | 0.166788 | − | 0.705453i | ||||
\(255\) | 6.54876e7 | 0.247325 | ||||||||
\(256\) | −7.58614e7 | + | 2.57493e8i | −0.282606 | + | 0.959236i | ||||
\(257\) | −4.65413e8 | −1.71030 | −0.855151 | − | 0.518380i | \(-0.826535\pi\) | ||||
−0.855151 | + | 0.518380i | \(0.826535\pi\) | |||||||
\(258\) | −2.66250e7 | + | 1.12615e8i | −0.0965209 | + | 0.408249i | ||||
\(259\) | − | 8.49975e6i | − | 0.0303988i | ||||||
\(260\) | 7.76906e8 | + | 3.89112e8i | 2.74133 | + | 1.37299i | ||||
\(261\) | 1.85073e7i | 0.0644320i | ||||||||
\(262\) | 2.44312e8 | + | 5.77619e7i | 0.839249 | + | 0.198421i | ||||
\(263\) | 1.23925e8 | 0.420061 | 0.210031 | − | 0.977695i | \(-0.432644\pi\) | ||||
0.210031 | + | 0.977695i | \(0.432644\pi\) | |||||||
\(264\) | −8.51493e7 | + | 1.01816e8i | −0.284818 | + | 0.340567i | ||||
\(265\) | 8.16240e8 | 2.69437 | ||||||||
\(266\) | 4.12072e7 | + | 9.74248e6i | 0.134242 | + | 0.0317383i | ||||
\(267\) | 1.71592e8i | 0.551706i | ||||||||
\(268\) | 1.42259e8 | − | 2.84036e8i | 0.451449 | − | 0.901368i | ||||
\(269\) | − | 4.78420e8i | − | 1.49857i | −0.662250 | − | 0.749283i | \(-0.730398\pi\) | ||
0.662250 | − | 0.749283i | \(-0.269602\pi\) | |||||||
\(270\) | 2.39993e7 | − | 1.01509e8i | 0.0742037 | − | 0.313855i | ||||
\(271\) | −1.18688e8 | −0.362255 | −0.181128 | − | 0.983460i | \(-0.557975\pi\) | ||||
−0.181128 | + | 0.983460i | \(0.557975\pi\) | |||||||
\(272\) | 5.08115e7 | + | 6.79406e7i | 0.153098 | + | 0.204710i | ||||
\(273\) | 3.17898e7 | 0.0945625 | ||||||||
\(274\) | 1.51655e6 | − | 6.41445e6i | 0.00445378 | − | 0.0188379i | ||||
\(275\) | − | 4.79566e8i | − | 1.39054i | ||||||
\(276\) | −1.04522e8 | + | 2.08691e8i | −0.299245 | + | 0.597477i | ||||
\(277\) | 1.89410e8i | 0.535455i | 0.963495 | + | 0.267728i | \(0.0862727\pi\) | ||||
−0.963495 | + | 0.267728i | \(0.913727\pi\) | |||||||
\(278\) | −4.20444e7 | − | 9.94041e6i | −0.117369 | − | 0.0277490i | ||||
\(279\) | −9.02560e7 | −0.248806 | ||||||||
\(280\) | −4.22731e7 | − | 3.53533e7i | −0.115083 | − | 0.0962446i | ||||
\(281\) | 9.40783e6 | 0.0252940 | 0.0126470 | − | 0.999920i | \(-0.495974\pi\) | ||||
0.0126470 | + | 0.999920i | \(0.495974\pi\) | |||||||
\(282\) | −2.03239e8 | − | 4.80510e7i | −0.539678 | − | 0.127594i | ||||
\(283\) | − | 5.76835e8i | − | 1.51286i | −0.654075 | − | 0.756430i | \(-0.726942\pi\) | ||
0.654075 | − | 0.756430i | \(-0.273058\pi\) | |||||||
\(284\) | 5.84391e7 | + | 2.92691e7i | 0.151387 | + | 0.0758221i | ||||
\(285\) | − | 5.82612e8i | − | 1.49081i | ||||||
\(286\) | −1.28062e8 | + | 5.41656e8i | −0.323697 | + | 1.36912i | ||||
\(287\) | −1.30520e7 | −0.0325904 | ||||||||
\(288\) | 1.23932e8 | − | 5.38617e7i | 0.305710 | − | 0.132864i | ||||
\(289\) | −3.83525e8 | −0.934655 | ||||||||
\(290\) | 3.09545e7 | − | 1.30926e8i | 0.0745299 | − | 0.315235i | ||||
\(291\) | − | 9.94225e7i | − | 0.236515i | ||||||
\(292\) | −5.49715e8 | − | 2.75324e8i | −1.29210 | − | 0.647149i | ||||
\(293\) | − | 2.91338e8i | − | 0.676643i | −0.941031 | − | 0.338322i | \(-0.890141\pi\) | ||
0.941031 | − | 0.338322i | \(-0.109859\pi\) | |||||||
\(294\) | 2.42856e8 | + | 5.74176e7i | 0.557357 | + | 0.131774i | ||||
\(295\) | 6.94149e8 | 1.57426 | ||||||||
\(296\) | −1.16223e8 | − | 9.71978e7i | −0.260478 | − | 0.217839i | ||||
\(297\) | 6.68155e7 | 0.147989 | ||||||||
\(298\) | −8.94241e7 | − | 2.11422e7i | −0.195748 | − | 0.0462800i | ||||
\(299\) | 9.78758e8i | 2.11751i | ||||||||
\(300\) | −2.18645e8 | + | 4.36549e8i | −0.467537 | + | 0.933488i | ||||
\(301\) | − | 3.07764e7i | − | 0.0650481i | ||||||
\(302\) | −5.22840e7 | + | 2.21143e8i | −0.109231 | + | 0.462007i | ||||
\(303\) | 4.34737e7 | 0.0897796 | ||||||||
\(304\) | 6.04436e8 | − | 4.52046e8i | 1.23394 | − | 0.922837i | ||||
\(305\) | −2.08245e8 | −0.420266 | ||||||||
\(306\) | 9.82642e6 | − | 4.15623e7i | 0.0196052 | − | 0.0829229i | ||||
\(307\) | 2.68815e8i | 0.530236i | 0.964216 | + | 0.265118i | \(0.0854108\pi\) | ||||
−0.964216 | + | 0.265118i | \(0.914589\pi\) | |||||||
\(308\) | 1.58082e7 | − | 3.15627e7i | 0.0308286 | − | 0.0615527i | ||||
\(309\) | 1.05881e7i | 0.0204156i | ||||||||
\(310\) | 6.38499e8 | + | 1.50958e8i | 1.21729 | + | 0.287800i | ||||
\(311\) | −8.66482e8 | −1.63342 | −0.816711 | − | 0.577047i | \(-0.804205\pi\) | ||||
−0.816711 | + | 0.577047i | \(0.804205\pi\) | |||||||
\(312\) | 3.63529e8 | − | 4.34684e8i | 0.677638 | − | 0.810275i | ||||
\(313\) | −4.30400e8 | −0.793353 | −0.396677 | − | 0.917958i | \(-0.629837\pi\) | ||||
−0.396677 | + | 0.917958i | \(0.629837\pi\) | |||||||
\(314\) | 7.86081e8 | + | 1.85850e8i | 1.43289 | + | 0.338773i | ||||
\(315\) | 2.77412e7i | 0.0500079i | ||||||||
\(316\) | −1.80179e8 | − | 9.02426e7i | −0.321218 | − | 0.160882i | ||||
\(317\) | 3.18718e8i | 0.561953i | 0.959715 | + | 0.280976i | \(0.0906583\pi\) | ||||
−0.959715 | + | 0.280976i | \(0.909342\pi\) | |||||||
\(318\) | 1.22477e8 | − | 5.18034e8i | 0.213579 | − | 0.903366i | ||||
\(319\) | 8.61791e7 | 0.148640 | ||||||||
\(320\) | −9.66818e8 | + | 1.73752e8i | −1.64938 | + | 0.296418i | ||||
\(321\) | −4.39888e8 | −0.742292 | ||||||||
\(322\) | 1.42824e7 | − | 6.04097e7i | 0.0238400 | − | 0.100835i | ||||
\(323\) | − | 2.38548e8i | − | 0.393883i | ||||||
\(324\) | −6.08223e7 | − | 3.04628e7i | −0.0993470 | − | 0.0497579i | ||||
\(325\) | 2.04741e9i | 3.30837i | ||||||||
\(326\) | −7.87214e8 | − | 1.86118e8i | −1.25844 | − | 0.297527i | ||||
\(327\) | 6.47024e8 | 1.02330 | ||||||||
\(328\) | −1.49254e8 | + | 1.78469e8i | −0.233544 | + | 0.279256i | ||||
\(329\) | 5.55431e7 | 0.0859893 | ||||||||
\(330\) | −4.72673e8 | − | 1.11752e8i | −0.724040 | − | 0.171182i | ||||
\(331\) | − | 1.06114e9i | − | 1.60832i | −0.594411 | − | 0.804161i | \(-0.702615\pi\) | ||
0.594411 | − | 0.804161i | \(-0.297385\pi\) | |||||||
\(332\) | −4.53447e8 | + | 9.05358e8i | −0.680054 | + | 1.35780i | ||||
\(333\) | 7.62699e7i | 0.113187i | ||||||||
\(334\) | −2.03227e8 | + | 8.59579e8i | −0.298448 | + | 1.26233i | ||||
\(335\) | 1.16247e9 | 1.68938 | ||||||||
\(336\) | −2.87804e7 | + | 2.15243e7i | −0.0413913 | + | 0.0309557i | ||||
\(337\) | 6.46738e8 | 0.920499 | 0.460250 | − | 0.887790i | \(-0.347760\pi\) | ||||
0.460250 | + | 0.887790i | \(0.347760\pi\) | |||||||
\(338\) | 3.83395e8 | − | 1.62163e9i | 0.540055 | − | 2.28424i | ||||
\(339\) | 5.16154e8i | 0.719582i | ||||||||
\(340\) | −1.39030e8 | + | 2.77589e8i | −0.191837 | + | 0.383024i | ||||
\(341\) | 4.20276e8i | 0.573977i | ||||||||
\(342\) | −3.69760e8 | − | 8.74210e7i | −0.499837 | − | 0.118175i | ||||
\(343\) | −1.33276e8 | −0.178330 | ||||||||
\(344\) | −4.20826e8 | − | 3.51939e8i | −0.557376 | − | 0.466137i | ||||
\(345\) | −8.54108e8 | −1.11981 | ||||||||
\(346\) | 5.33842e8 | + | 1.26214e8i | 0.692862 | + | 0.163811i | ||||
\(347\) | − | 5.65479e7i | − | 0.0726546i | −0.999340 | − | 0.0363273i | \(-0.988434\pi\) | ||
0.999340 | − | 0.0363273i | \(-0.0115659\pi\) | |||||||
\(348\) | −7.84490e7 | − | 3.92911e7i | −0.0997838 | − | 0.0499766i | ||||
\(349\) | − | 2.17863e8i | − | 0.274343i | −0.990547 | − | 0.137172i | \(-0.956199\pi\) | ||
0.990547 | − | 0.137172i | \(-0.0438012\pi\) | |||||||
\(350\) | 2.98767e7 | − | 1.26368e8i | 0.0372473 | − | 0.157543i | ||||
\(351\) | −2.85256e8 | −0.352095 | ||||||||
\(352\) | −2.50806e8 | − | 5.77087e8i | −0.306506 | − | 0.705248i | ||||
\(353\) | 7.33462e8 | 0.887496 | 0.443748 | − | 0.896152i | \(-0.353649\pi\) | ||||
0.443748 | + | 0.896152i | \(0.353649\pi\) | |||||||
\(354\) | 1.04157e8 | − | 4.40548e8i | 0.124789 | − | 0.527815i | ||||
\(355\) | 2.39173e8i | 0.283736i | ||||||||
\(356\) | −7.27346e8 | − | 3.64290e8i | −0.854409 | − | 0.427930i | ||||
\(357\) | 1.13585e7i | 0.0132125i | ||||||||
\(358\) | 8.33176e8 | + | 1.96985e8i | 0.959724 | + | 0.226904i | ||||
\(359\) | 1.21920e9 | 1.39073 | 0.695366 | − | 0.718656i | \(-0.255242\pi\) | ||||
0.695366 | + | 0.718656i | \(0.255242\pi\) | |||||||
\(360\) | 3.79325e8 | + | 3.17231e8i | 0.428502 | + | 0.358358i | ||||
\(361\) | −1.22838e9 | −1.37422 | ||||||||
\(362\) | 2.21524e8 | + | 5.23742e7i | 0.245438 | + | 0.0580279i | ||||
\(363\) | 2.15028e8i | 0.235951i | ||||||||
\(364\) | −6.74899e7 | + | 1.34751e8i | −0.0733473 | + | 0.146446i | ||||
\(365\) | − | 2.24982e9i | − | 2.42171i | ||||||
\(366\) | −3.12472e7 | + | 1.32164e8i | −0.0333140 | + | 0.140906i | ||||
\(367\) | 6.80496e8 | 0.718612 | 0.359306 | − | 0.933220i | \(-0.383013\pi\) | ||||
0.359306 | + | 0.933220i | \(0.383013\pi\) | |||||||
\(368\) | −6.62698e8 | − | 8.86101e8i | −0.693183 | − | 0.926863i | ||||
\(369\) | 1.17118e8 | 0.121347 | ||||||||
\(370\) | 1.27565e8 | − | 5.39556e8i | 0.130926 | − | 0.553772i | ||||
\(371\) | 1.41573e8i | 0.143937i | ||||||||
\(372\) | 1.91614e8 | − | 3.82578e8i | 0.192986 | − | 0.385318i | ||||
\(373\) | 7.23854e8i | 0.722221i | 0.932523 | + | 0.361110i | \(0.117602\pi\) | ||||
−0.932523 | + | 0.361110i | \(0.882398\pi\) | |||||||
\(374\) | −1.93534e8 | − | 4.57566e7i | −0.191297 | − | 0.0452276i | ||||
\(375\) | −7.98633e8 | −0.782056 | ||||||||
\(376\) | 6.35156e8 | − | 7.59478e8i | 0.616201 | − | 0.736814i | ||||
\(377\) | −3.67925e8 | −0.353643 | ||||||||
\(378\) | 1.76062e7 | + | 4.16258e6i | 0.0167666 | + | 0.00396407i | ||||
\(379\) | 8.60978e8i | 0.812372i | 0.913790 | + | 0.406186i | \(0.133141\pi\) | ||||
−0.913790 | + | 0.406186i | \(0.866859\pi\) | |||||||
\(380\) | 2.46958e9 | + | 1.23689e9i | 2.30877 | + | 1.15634i | ||||
\(381\) | − | 4.51810e8i | − | 0.418522i | ||||||
\(382\) | 8.54145e7 | − | 3.61273e8i | 0.0783988 | − | 0.331599i | ||||
\(383\) | 1.03603e8 | 0.0942269 | 0.0471135 | − | 0.998890i | \(-0.484998\pi\) | ||||
0.0471135 | + | 0.998890i | \(0.484998\pi\) | |||||||
\(384\) | −3.47980e7 | + | 6.39671e8i | −0.0313614 | + | 0.576498i | ||||
\(385\) | 1.29177e8 | 0.115364 | ||||||||
\(386\) | −2.59863e8 | + | 1.09913e9i | −0.229980 | + | 0.972733i | ||||
\(387\) | 2.76162e8i | 0.242201i | ||||||||
\(388\) | 4.21433e8 | + | 2.11074e8i | 0.366283 | + | 0.183453i | ||||
\(389\) | 2.23948e8i | 0.192896i | 0.995338 | + | 0.0964481i | \(0.0307482\pi\) | ||||
−0.995338 | + | 0.0964481i | \(0.969252\pi\) | |||||||
\(390\) | 2.01799e9 | + | 4.77106e8i | 1.72263 | + | 0.407276i | ||||
\(391\) | −3.49711e8 | −0.295863 | ||||||||
\(392\) | −7.58967e8 | + | 9.07524e8i | −0.636387 | + | 0.760951i | ||||
\(393\) | 5.99122e8 | 0.497899 | ||||||||
\(394\) | −9.46576e8 | − | 2.23795e8i | −0.779684 | − | 0.184338i | ||||
\(395\) | − | 7.37420e8i | − | 0.602039i | ||||||
\(396\) | −1.41849e8 | + | 2.83218e8i | −0.114787 | + | 0.229186i | ||||
\(397\) | − | 1.14346e9i | − | 0.917179i | −0.888648 | − | 0.458589i | \(-0.848355\pi\) | ||
0.888648 | − | 0.458589i | \(-0.151645\pi\) | |||||||
\(398\) | −4.22352e8 | + | 1.78640e9i | −0.335802 | + | 1.42033i | ||||
\(399\) | 1.01052e8 | 0.0796412 | ||||||||
\(400\) | −1.38626e9 | − | 1.85359e9i | −1.08302 | − | 1.44812i | ||||
\(401\) | 3.48918e8 | 0.270220 | 0.135110 | − | 0.990831i | \(-0.456861\pi\) | ||||
0.135110 | + | 0.990831i | \(0.456861\pi\) | |||||||
\(402\) | 1.74430e8 | − | 7.37775e8i | 0.133915 | − | 0.566413i | ||||
\(403\) | − | 1.79429e9i | − | 1.36560i | ||||||
\(404\) | −9.22947e7 | + | 1.84277e8i | −0.0696373 | + | 0.139039i | ||||
\(405\) | − | 2.48927e8i | − | 0.186200i | ||||||
\(406\) | 2.27086e7 | + | 5.36892e6i | 0.0168403 | + | 0.00398149i | ||||
\(407\) | 3.55150e8 | 0.261115 | ||||||||
\(408\) | 1.55313e8 | + | 1.29889e8i | 0.113213 | + | 0.0946809i | ||||
\(409\) | 1.29700e8 | 0.0937368 | 0.0468684 | − | 0.998901i | \(-0.485076\pi\) | ||||
0.0468684 | + | 0.998901i | \(0.485076\pi\) | |||||||
\(410\) | −8.28527e8 | − | 1.95886e8i | −0.593695 | − | 0.140365i | ||||
\(411\) | − | 1.57300e7i | − | 0.0111759i | ||||||
\(412\) | −4.48809e7 | − | 2.24785e7i | −0.0316170 | − | 0.0158354i | ||||
\(413\) | 1.20397e8i | 0.0840991i | ||||||||
\(414\) | −1.28159e8 | + | 5.42067e8i | −0.0887662 | + | 0.375450i | ||||
\(415\) | −3.70536e9 | −2.54485 | ||||||||
\(416\) | 1.07077e9 | + | 2.46376e9i | 0.729239 | + | 1.67792i | ||||
\(417\) | −1.03105e8 | −0.0696309 | ||||||||
\(418\) | −4.07075e8 | + | 1.72178e9i | −0.272620 | + | 1.15309i | ||||
\(419\) | 1.23819e8i | 0.0822312i | 0.999154 | + | 0.0411156i | \(0.0130912\pi\) | ||||
−0.999154 | + | 0.0411156i | \(0.986909\pi\) | |||||||
\(420\) | −1.17590e8 | − | 5.88947e7i | −0.0774456 | − | 0.0387886i | ||||
\(421\) | − | 2.72698e7i | − | 0.0178112i | −0.999960 | − | 0.00890562i | \(-0.997165\pi\) | ||
0.999960 | − | 0.00890562i | \(-0.00283478\pi\) | |||||||
\(422\) | −2.36476e9 | − | 5.59092e8i | −1.53177 | − | 0.362151i | ||||
\(423\) | −4.98398e8 | −0.320173 | ||||||||
\(424\) | 1.93583e9 | + | 1.61894e9i | 1.23335 | + | 1.03146i | ||||
\(425\) | −7.31543e8 | −0.462252 | ||||||||
\(426\) | 1.51794e8 | + | 3.58880e7i | 0.0951306 | + | 0.0224914i | ||||
\(427\) | − | 3.61192e7i | − | 0.0224512i | ||||||
\(428\) | 9.33883e8 | − | 1.86460e9i | 0.575757 | − | 1.14956i | ||||
\(429\) | 1.32829e9i | 0.812256i | ||||||||
\(430\) | 4.61896e8 | − | 1.95366e9i | 0.280159 | − | 1.18497i | ||||
\(431\) | −1.06503e9 | −0.640754 | −0.320377 | − | 0.947290i | \(-0.603810\pi\) | ||||
−0.320377 | + | 0.947290i | \(0.603810\pi\) | |||||||
\(432\) | 2.58251e8 | − | 1.93141e8i | 0.154117 | − | 0.115261i | ||||
\(433\) | 7.41521e8 | 0.438951 | 0.219475 | − | 0.975618i | \(-0.429565\pi\) | ||||
0.219475 | + | 0.975618i | \(0.429565\pi\) | |||||||
\(434\) | −2.61830e7 | + | 1.10745e8i | −0.0153747 | + | 0.0650294i | ||||
\(435\) | − | 3.21068e8i | − | 0.187019i | ||||||
\(436\) | −1.37363e9 | + | 2.74261e9i | −0.793721 | + | 1.58475i | ||||
\(437\) | 3.11122e9i | 1.78338i | ||||||||
\(438\) | −1.42787e9 | − | 3.37585e8i | −0.811949 | − | 0.191966i | ||||
\(439\) | −1.10708e9 | −0.624531 | −0.312265 | − | 0.949995i | \(-0.601088\pi\) | ||||
−0.312265 | + | 0.949995i | \(0.601088\pi\) | |||||||
\(440\) | 1.47718e9 | − | 1.76632e9i | 0.826704 | − | 0.988520i | ||||
\(441\) | 5.95551e8 | 0.330662 | ||||||||
\(442\) | 8.26258e8 | + | 1.95349e8i | 0.455133 | + | 0.107605i | ||||
\(443\) | − | 1.11670e9i | − | 0.610272i | −0.952309 | − | 0.305136i | \(-0.901298\pi\) | ||
0.952309 | − | 0.305136i | \(-0.0987019\pi\) | |||||||
\(444\) | −3.23293e8 | − | 1.61921e8i | −0.175290 | − | 0.0877936i | ||||
\(445\) | − | 2.97681e9i | − | 1.60137i | ||||||
\(446\) | −3.30036e8 | + | 1.39593e9i | −0.176153 | + | 0.745063i | ||||
\(447\) | −2.19293e8 | −0.116131 | ||||||||
\(448\) | −3.01365e7 | − | 1.67690e8i | −0.0158351 | − | 0.0881121i | ||||
\(449\) | 1.94185e9 | 1.01240 | 0.506201 | − | 0.862416i | \(-0.331050\pi\) | ||||
0.506201 | + | 0.862416i | \(0.331050\pi\) | |||||||
\(450\) | −2.68089e8 | + | 1.13392e9i | −0.138687 | + | 0.586597i | ||||
\(451\) | − | 5.45358e8i | − | 0.279939i | ||||||
\(452\) | −2.18788e9 | − | 1.09580e9i | −1.11439 | − | 0.558142i | ||||
\(453\) | 5.42304e8i | 0.274094i | ||||||||
\(454\) | −2.19576e9 | − | 5.19136e8i | −1.10126 | − | 0.260367i | ||||
\(455\) | −5.51495e8 | −0.274475 | ||||||||
\(456\) | 1.15556e9 | − | 1.38175e9i | 0.570711 | − | 0.682420i | ||||
\(457\) | 1.89332e9 | 0.927936 | 0.463968 | − | 0.885852i | \(-0.346425\pi\) | ||||
0.463968 | + | 0.885852i | \(0.346425\pi\) | |||||||
\(458\) | 4.03597e8 | + | 9.54210e7i | 0.196299 | + | 0.0464103i | ||||
\(459\) | − | 1.01922e8i | − | 0.0491954i | ||||||
\(460\) | 1.81327e9 | − | 3.62040e9i | 0.868581 | − | 1.73422i | ||||
\(461\) | − | 2.70468e9i | − | 1.28577i | −0.765964 | − | 0.642883i | \(-0.777738\pi\) | ||
0.765964 | − | 0.642883i | \(-0.222262\pi\) | |||||||
\(462\) | 1.93830e7 | − | 8.19832e7i | 0.00914479 | − | 0.0386792i | ||||
\(463\) | 3.19942e9 | 1.49809 | 0.749046 | − | 0.662518i | \(-0.230512\pi\) | ||||
0.749046 | + | 0.662518i | \(0.230512\pi\) | |||||||
\(464\) | 3.33095e8 | − | 2.49115e8i | 0.154794 | − | 0.115768i | ||||
\(465\) | 1.56578e9 | 0.722178 | ||||||||
\(466\) | −2.56667e8 | + | 1.08561e9i | −0.117495 | + | 0.496962i | ||||
\(467\) | 4.00868e9i | 1.82134i | 0.413130 | + | 0.910672i | \(0.364435\pi\) | ||||
−0.413130 | + | 0.910672i | \(0.635565\pi\) | |||||||
\(468\) | 6.05599e8 | − | 1.20915e9i | 0.273102 | − | 0.545278i | ||||
\(469\) | 2.01626e8i | 0.0902490i | ||||||||
\(470\) | 3.52582e9 | + | 8.33597e8i | 1.56645 | + | 0.370351i | ||||
\(471\) | 1.92769e9 | 0.850087 | ||||||||
\(472\) | 1.64627e9 | + | 1.37679e9i | 0.720617 | + | 0.602656i | ||||
\(473\) | 1.28595e9 | 0.558739 | ||||||||
\(474\) | −4.68010e8 | − | 1.10650e8i | −0.201851 | − | 0.0477229i | ||||
\(475\) | 6.50820e9i | 2.78633i | ||||||||
\(476\) | −4.81467e7 | − | 2.41142e7i | −0.0204617 | − | 0.0102482i | ||||
\(477\) | − | 1.27036e9i | − | 0.535937i | ||||||
\(478\) | 2.80800e8 | − | 1.18768e9i | 0.117598 | − | 0.497398i | ||||
\(479\) | −2.36136e9 | −0.981721 | −0.490860 | − | 0.871238i | \(-0.663317\pi\) | ||||
−0.490860 | + | 0.871238i | \(0.663317\pi\) | |||||||
\(480\) | −2.14999e9 | + | 9.34402e8i | −0.887344 | + | 0.385646i | ||||
\(481\) | −1.51624e9 | −0.621243 | ||||||||
\(482\) | 2.46730e8 | − | 1.04358e9i | 0.100359 | − | 0.424484i | ||||
\(483\) | − | 1.48141e8i | − | 0.0598220i | ||||||
\(484\) | −9.11462e8 | − | 4.56505e8i | −0.365409 | − | 0.183015i | ||||
\(485\) | 1.72480e9i | 0.686502i | ||||||||
\(486\) | −1.57984e8 | − | 3.73516e7i | −0.0624289 | − | 0.0147598i | ||||
\(487\) | 2.82968e9 | 1.11016 | 0.555080 | − | 0.831797i | \(-0.312688\pi\) | ||||
0.555080 | + | 0.831797i | \(0.312688\pi\) | |||||||
\(488\) | −4.93882e8 | − | 4.13036e8i | −0.192377 | − | 0.160886i | ||||
\(489\) | −1.93047e9 | −0.746588 | ||||||||
\(490\) | −4.21311e9 | − | 9.96091e8i | −1.61777 | − | 0.382483i | ||||
\(491\) | − | 3.04210e9i | − | 1.15981i | −0.814682 | − | 0.579907i | \(-0.803089\pi\) | ||
0.814682 | − | 0.579907i | \(-0.196911\pi\) | |||||||
\(492\) | −2.48641e8 | + | 4.96440e8i | −0.0941229 | + | 0.187927i | ||||
\(493\) | − | 1.31460e8i | − | 0.0494117i | ||||||
\(494\) | 1.73793e9 | − | 7.35083e9i | 0.648616 | − | 2.74342i | ||||
\(495\) | −1.15913e9 | −0.429549 | ||||||||
\(496\) | 1.21488e9 | + | 1.62443e9i | 0.447040 | + | 0.597743i | ||||
\(497\) | −4.14836e7 | −0.0151576 | ||||||||
\(498\) | −5.55990e8 | + | 2.35164e9i | −0.201727 | + | 0.853234i | ||||
\(499\) | − | 6.92433e8i | − | 0.249474i | −0.992190 | − | 0.124737i | \(-0.960191\pi\) | ||
0.992190 | − | 0.124737i | \(-0.0398088\pi\) | |||||||
\(500\) | 1.69550e9 | − | 3.38525e9i | 0.606600 | − | 1.21114i | ||||
\(501\) | 2.10793e9i | 0.748900i | ||||||||
\(502\) | −1.94581e9 | − | 4.60042e8i | −0.686496 | − | 0.162306i | ||||
\(503\) | −3.40321e9 | −1.19234 | −0.596171 | − | 0.802858i | \(-0.703312\pi\) | ||||
−0.596171 | + | 0.802858i | \(0.703312\pi\) | |||||||
\(504\) | −5.50224e7 | + | 6.57923e7i | −0.0191440 | + | 0.0228912i | ||||
\(505\) | −7.54189e8 | −0.260592 | ||||||||
\(506\) | 2.52413e9 | + | 5.96771e8i | 0.866134 | + | 0.204777i | ||||
\(507\) | − | 3.97668e9i | − | 1.35517i | ||||||
\(508\) | 1.91514e9 | + | 9.59193e8i | 0.648151 | + | 0.324626i | ||||
\(509\) | 2.36640e8i | 0.0795383i | 0.999209 | + | 0.0397691i | \(0.0126623\pi\) | ||||
−0.999209 | + | 0.0397691i | \(0.987338\pi\) | |||||||
\(510\) | −1.70470e8 | + | 7.21030e8i | −0.0569054 | + | 0.240690i | ||||
\(511\) | 3.90221e8 | 0.129371 | ||||||||
\(512\) | −2.63757e9 | − | 1.50553e9i | −0.868478 | − | 0.495728i | ||||
\(513\) | −9.06755e8 | −0.296537 | ||||||||
\(514\) | 1.21151e9 | − | 5.12428e9i | 0.393512 | − | 1.66442i | ||||
\(515\) | − | 1.83684e8i | − | 0.0592579i | ||||||
\(516\) | −1.17060e9 | − | 5.86293e8i | −0.375089 | − | 0.187863i | ||||
\(517\) | 2.32079e9i | 0.738615i | ||||||||
\(518\) | 9.35837e7 | + | 2.21257e7i | 0.0295833 | + | 0.00699427i | ||||
\(519\) | 1.30913e9 | 0.411052 | ||||||||
\(520\) | −6.30655e9 | + | 7.54097e9i | −1.96689 | + | 2.35188i | ||||
\(521\) | −2.10503e8 | −0.0652119 | −0.0326059 | − | 0.999468i | \(-0.510381\pi\) | ||||
−0.0326059 | + | 0.999468i | \(0.510381\pi\) | |||||||
\(522\) | −2.03769e8 | − | 4.81763e7i | −0.0627034 | − | 0.0148247i | ||||
\(523\) | 4.88451e9i | 1.49302i | 0.665376 | + | 0.746509i | \(0.268271\pi\) | ||||
−0.665376 | + | 0.746509i | \(0.731729\pi\) | |||||||
\(524\) | −1.27194e9 | + | 2.53956e9i | −0.386194 | + | 0.771080i | ||||
\(525\) | − | 3.09889e8i | − | 0.0934650i | ||||||
\(526\) | −3.22588e8 | + | 1.36443e9i | −0.0966491 | + | 0.408792i | ||||
\(527\) | 6.41101e8 | 0.190805 | ||||||||
\(528\) | −8.99360e8 | − | 1.20254e9i | −0.265898 | − | 0.355535i | ||||
\(529\) | 1.15621e9 | 0.339579 | ||||||||
\(530\) | −2.12475e9 | + | 8.98694e9i | −0.619930 | + | 2.62208i | ||||
\(531\) | − | 1.08035e9i | − | 0.313135i | ||||||
\(532\) | −2.14533e8 | + | 4.28338e8i | −0.0617736 | + | 0.123338i | ||||
\(533\) | 2.32830e9i | 0.666030i | ||||||||
\(534\) | −1.88926e9 | − | 4.46670e8i | −0.536904 | − | 0.126938i | ||||
\(535\) | 7.63125e9 | 2.15455 | ||||||||
\(536\) | 2.75697e9 | + | 2.30567e9i | 0.773314 | + | 0.646727i | ||||
\(537\) | 2.04318e9 | 0.569373 | ||||||||
\(538\) | 5.26748e9 | + | 1.24537e9i | 1.45836 | + | 0.344795i | ||||
\(539\) | − | 2.77318e9i | − | 0.762811i | ||||||
\(540\) | 1.05515e9 | + | 5.28473e8i | 0.288362 | + | 0.144426i | ||||
\(541\) | − | 3.13607e9i | − | 0.851521i | −0.904836 | − | 0.425760i | \(-0.860007\pi\) | ||
0.904836 | − | 0.425760i | \(-0.139993\pi\) | |||||||
\(542\) | 3.08957e8 | − | 1.30678e9i | 0.0833489 | − | 0.352536i | ||||
\(543\) | 5.43239e8 | 0.145610 | ||||||||
\(544\) | −8.80305e8 | + | 3.82587e8i | −0.234443 | + | 0.101891i | ||||
\(545\) | −1.12247e10 | −2.97020 | ||||||||
\(546\) | −8.27520e7 | + | 3.50012e8i | −0.0217573 | + | 0.0920255i | ||||
\(547\) | − | 2.24354e9i | − | 0.586110i | −0.956096 | − | 0.293055i | \(-0.905328\pi\) | ||
0.956096 | − | 0.293055i | \(-0.0946719\pi\) | |||||||
\(548\) | 6.66765e7 | + | 3.33949e7i | 0.0173078 | + | 0.00866858i | ||||
\(549\) | 3.24104e8i | 0.0835951i | ||||||||
\(550\) | 5.28010e9 | + | 1.24836e9i | 1.35323 | + | 0.319940i | ||||
\(551\) | −1.16954e9 | −0.297841 | ||||||||
\(552\) | −2.02564e9 | − | 1.69405e9i | −0.512596 | − | 0.428686i | ||||
\(553\) | 1.27902e8 | 0.0321618 | ||||||||
\(554\) | −2.08543e9 | − | 4.93051e8i | −0.521089 | − | 0.123199i | ||||
\(555\) | − | 1.32314e9i | − | 0.328535i | ||||||
\(556\) | 2.18891e8 | − | 4.37041e8i | 0.0540091 | − | 0.107835i | ||||
\(557\) | 4.59390e9i | 1.12639i | 0.826324 | + | 0.563195i | \(0.190428\pi\) | ||||
−0.826324 | + | 0.563195i | \(0.809572\pi\) | |||||||
\(558\) | 2.34945e8 | − | 9.93735e8i | 0.0572462 | − | 0.242131i | ||||
\(559\) | −5.49010e9 | −1.32935 | ||||||||
\(560\) | 4.99286e8 | − | 3.73407e8i | 0.120141 | − | 0.0898512i | ||||
\(561\) | −4.74600e8 | −0.113490 | ||||||||
\(562\) | −2.44895e7 | + | 1.03582e8i | −0.00581973 | + | 0.0246154i | ||||
\(563\) | − | 9.25935e7i | − | 0.0218676i | −0.999940 | − | 0.0109338i | \(-0.996520\pi\) | ||
0.999940 | − | 0.0109338i | \(-0.00348040\pi\) | |||||||
\(564\) | 1.05810e9 | − | 2.11261e9i | 0.248342 | − | 0.495842i | ||||
\(565\) | − | 8.95432e9i | − | 2.08864i | ||||||
\(566\) | 6.35105e9 | + | 1.50156e9i | 1.47227 | + | 0.348084i | ||||
\(567\) | 4.31754e7 | 0.00994707 | ||||||||
\(568\) | −4.74381e8 | + | 5.67234e8i | −0.108619 | + | 0.129880i | ||||
\(569\) | −1.80174e9 | −0.410013 | −0.205007 | − | 0.978761i | \(-0.565722\pi\) | ||||
−0.205007 | + | 0.978761i | \(0.565722\pi\) | |||||||
\(570\) | 6.41466e9 | + | 1.51659e9i | 1.45081 | + | 0.343011i | ||||
\(571\) | − | 4.05799e9i | − | 0.912188i | −0.889932 | − | 0.456094i | \(-0.849248\pi\) | ||
0.889932 | − | 0.456094i | \(-0.150752\pi\) | |||||||
\(572\) | −5.63037e9 | − | 2.81997e9i | −1.25791 | − | 0.630025i | ||||
\(573\) | − | 8.85942e8i | − | 0.196727i | ||||||
\(574\) | 3.39755e7 | − | 1.43704e8i | 0.00749850 | − | 0.0317160i | ||||
\(575\) | 9.54099e9 | 2.09294 | ||||||||
\(576\) | 2.70421e8 | + | 1.50472e9i | 0.0589605 | + | 0.328077i | ||||
\(577\) | −7.82764e9 | −1.69635 | −0.848175 | − | 0.529716i | \(-0.822298\pi\) | ||||
−0.848175 | + | 0.529716i | \(0.822298\pi\) | |||||||
\(578\) | 9.98352e8 | − | 4.22268e9i | 0.215048 | − | 0.909579i | ||||
\(579\) | 2.69537e9i | 0.577090i | ||||||||
\(580\) | 1.36095e9 | + | 6.81628e8i | 0.289629 | + | 0.145061i | ||||
\(581\) | − | 6.42679e8i | − | 0.135949i | ||||||
\(582\) | 1.09466e9 | + | 2.58806e8i | 0.230170 | + | 0.0544182i | ||||
\(583\) | −5.91543e9 | −1.23637 | ||||||||
\(584\) | 4.46232e9 | − | 5.33576e9i | 0.927078 | − | 1.10854i | ||||
\(585\) | 4.94867e9 | 1.02198 | ||||||||
\(586\) | 3.20768e9 | + | 7.58379e8i | 0.658490 | + | 0.155684i | ||||
\(587\) | 1.45350e9i | 0.296607i | 0.988942 | + | 0.148304i | \(0.0473813\pi\) | ||||
−0.988942 | + | 0.148304i | \(0.952619\pi\) | |||||||
\(588\) | −1.26436e9 | + | 2.52443e9i | −0.256477 | + | 0.512085i | ||||
\(589\) | − | 5.70358e9i | − | 1.15012i | ||||||
\(590\) | −1.80694e9 | + | 7.64270e9i | −0.362210 | + | 1.53202i | ||||
\(591\) | −2.32127e9 | −0.462561 | ||||||||
\(592\) | 1.37270e9 | − | 1.02662e9i | 0.271926 | − | 0.203368i | ||||
\(593\) | 8.26005e8 | 0.162664 | 0.0813320 | − | 0.996687i | \(-0.474083\pi\) | ||||
0.0813320 | + | 0.996687i | \(0.474083\pi\) | |||||||
\(594\) | −1.73927e8 | + | 7.35650e8i | −0.0340498 | + | 0.144019i | ||||
\(595\) | − | 1.97050e8i | − | 0.0383501i | ||||||
\(596\) | 4.65559e8 | − | 9.29540e8i | 0.0900768 | − | 0.179848i | ||||
\(597\) | 4.38075e9i | 0.842632i | ||||||||
\(598\) | −1.07763e10 | − | 2.54780e9i | −2.06070 | − | 0.487204i | ||||
\(599\) | 3.81768e9 | 0.725780 | 0.362890 | − | 0.931832i | \(-0.381790\pi\) | ||||
0.362890 | + | 0.931832i | \(0.381790\pi\) | |||||||
\(600\) | −4.23733e9 | − | 3.54370e9i | −0.800871 | − | 0.669773i | ||||
\(601\) | 1.48375e9 | 0.278805 | 0.139402 | − | 0.990236i | \(-0.455482\pi\) | ||||
0.139402 | + | 0.990236i | \(0.455482\pi\) | |||||||
\(602\) | 3.38853e8 | + | 8.01138e7i | 0.0633030 | + | 0.0149665i | ||||
\(603\) | − | 1.80923e9i | − | 0.336034i | ||||||
\(604\) | −2.29872e9 | − | 1.15131e9i | −0.424480 | − | 0.212600i | ||||
\(605\) | − | 3.73034e9i | − | 0.684864i | ||||||
\(606\) | −1.13166e8 | + | 4.78653e8i | −0.0206568 | + | 0.0873709i | ||||
\(607\) | 1.01217e10 | 1.83693 | 0.918463 | − | 0.395506i | \(-0.129431\pi\) | ||||
0.918463 | + | 0.395506i | \(0.129431\pi\) | |||||||
\(608\) | 3.40370e9 | + | 7.83166e9i | 0.614170 | + | 1.41316i | ||||
\(609\) | 5.56879e7 | 0.00999080 | ||||||||
\(610\) | 5.42081e8 | − | 2.29281e9i | 0.0966962 | − | 0.408991i | ||||
\(611\) | − | 9.90815e9i | − | 1.75731i | ||||||
\(612\) | 4.32029e8 | + | 2.16381e8i | 0.0761874 | + | 0.0381584i | ||||
\(613\) | 8.24178e9i | 1.44514i | 0.691299 | + | 0.722569i | \(0.257039\pi\) | ||||
−0.691299 | + | 0.722569i | \(0.742961\pi\) | |||||||
\(614\) | −2.95970e9 | − | 6.99750e8i | −0.516010 | − | 0.121998i | ||||
\(615\) | −2.03178e9 | −0.352220 | ||||||||
\(616\) | 3.06361e8 | + | 2.56211e8i | 0.0528081 | + | 0.0441637i | ||||
\(617\) | 8.98164e9 | 1.53942 | 0.769710 | − | 0.638393i | \(-0.220401\pi\) | ||||
0.769710 | + | 0.638393i | \(0.220401\pi\) | |||||||
\(618\) | −1.16577e8 | − | 2.75618e7i | −0.0198679 | − | 0.00469730i | ||||
\(619\) | 3.83653e9i | 0.650162i | 0.945686 | + | 0.325081i | \(0.105392\pi\) | ||||
−0.945686 | + | 0.325081i | \(0.894608\pi\) | |||||||
\(620\) | −3.32415e9 | + | 6.63702e9i | −0.560156 | + | 1.11841i | ||||
\(621\) | 1.32930e9i | 0.222742i | ||||||||
\(622\) | 2.25554e9 | − | 9.54012e9i | 0.375823 | − | 1.58960i | ||||
\(623\) | 5.16315e8 | 0.0855473 | ||||||||
\(624\) | 3.83965e9 | + | 5.13404e9i | 0.632623 | + | 0.845888i | ||||
\(625\) | 2.81779e9 | 0.461666 | ||||||||
\(626\) | 1.12037e9 | − | 4.73877e9i | 0.182537 | − | 0.772068i | ||||
\(627\) | 4.22229e9i | 0.684088i | ||||||||
\(628\) | −4.09248e9 | + | 8.17110e9i | −0.659369 | + | 1.31650i | ||||
\(629\) | − | 5.41756e8i | − | 0.0868013i | ||||||
\(630\) | −3.05436e8 | − | 7.22131e7i | −0.0486663 | − | 0.0115060i | ||||
\(631\) | −5.55269e9 | −0.879834 | −0.439917 | − | 0.898039i | \(-0.644992\pi\) | ||||
−0.439917 | + | 0.898039i | \(0.644992\pi\) | |||||||
\(632\) | 1.46261e9 | − | 1.74890e9i | 0.230472 | − | 0.275584i | ||||
\(633\) | −5.79906e9 | −0.908750 | ||||||||
\(634\) | −3.50914e9 | − | 8.29654e8i | −0.546876 | − | 0.129296i | ||||
\(635\) | 7.83807e9i | 1.21479i | ||||||||
\(636\) | 5.38483e9 | + | 2.69698e9i | 0.829988 | + | 0.415699i | ||||
\(637\) | 1.18396e10i | 1.81488i | ||||||||
\(638\) | −2.24332e8 | + | 9.48847e8i | −0.0341995 | + | 0.144652i | ||||
\(639\) | 3.72240e8 | 0.0564378 | ||||||||
\(640\) | 6.03681e8 | − | 1.10971e10i | 0.0910286 | − | 1.67333i | ||||
\(641\) | 7.35378e9 | 1.10283 | 0.551413 | − | 0.834232i | \(-0.314089\pi\) | ||||
0.551413 | + | 0.834232i | \(0.314089\pi\) | |||||||
\(642\) | 1.14507e9 | − | 4.84324e9i | 0.170789 | − | 0.722377i | ||||
\(643\) | 4.34387e9i | 0.644375i | 0.946676 | + | 0.322187i | \(0.104418\pi\) | ||||
−0.946676 | + | 0.322187i | \(0.895582\pi\) | |||||||
\(644\) | 6.27943e8 | + | 3.14504e8i | 0.0926444 | + | 0.0464009i | ||||
\(645\) | − | 4.79091e9i | − | 0.703005i | ||||||
\(646\) | 2.62646e9 | + | 6.20964e8i | 0.383316 | + | 0.0906260i | ||||
\(647\) | −9.96133e9 | −1.44595 | −0.722973 | − | 0.690876i | \(-0.757225\pi\) | ||||
−0.722973 | + | 0.690876i | \(0.757225\pi\) | |||||||
\(648\) | 4.93726e8 | − | 5.90366e8i | 0.0712810 | − | 0.0852332i | ||||
\(649\) | −5.03062e9 | −0.722379 | ||||||||
\(650\) | −2.25424e10 | − | 5.32961e9i | −3.21961 | − | 0.761200i | ||||
\(651\) | 2.71577e8i | 0.0385798i | ||||||||
\(652\) | 4.09838e9 | − | 8.18288e9i | 0.579090 | − | 1.15622i | ||||
\(653\) | 2.99451e9i | 0.420852i | 0.977610 | + | 0.210426i | \(0.0674850\pi\) | ||||
−0.977610 | + | 0.210426i | \(0.932515\pi\) | |||||||
\(654\) | −1.68427e9 | + | 7.12385e9i | −0.235444 | + | 0.995847i | ||||
\(655\) | −1.03937e10 | −1.44519 | ||||||||
\(656\) | −1.57645e9 | − | 2.10788e9i | −0.218030 | − | 0.291530i | ||||
\(657\) | −3.50153e9 | −0.481702 | ||||||||
\(658\) | −1.44584e8 | + | 6.11539e8i | −0.0197847 | + | 0.0836823i | ||||
\(659\) | 7.84192e9i | 1.06739i | 0.845677 | + | 0.533695i | \(0.179197\pi\) | ||||
−0.845677 | + | 0.533695i | \(0.820803\pi\) | |||||||
\(660\) | 2.46083e9 | − | 4.91331e9i | 0.333179 | − | 0.665228i | ||||
\(661\) | − | 5.55066e9i | − | 0.747549i | −0.927520 | − | 0.373775i | \(-0.878063\pi\) | ||
0.927520 | − | 0.373775i | \(-0.121937\pi\) | |||||||
\(662\) | 1.16833e10 | + | 2.76224e9i | 1.56517 | + | 0.370048i | ||||
\(663\) | 2.02621e9 | 0.270015 | ||||||||
\(664\) | −8.78778e9 | − | 7.34927e9i | −1.16491 | − | 0.974217i | ||||
\(665\) | −1.75306e9 | −0.231164 | ||||||||
\(666\) | −8.39744e8 | − | 1.98538e8i | −0.110151 | − | 0.0260425i | ||||
\(667\) | 1.71454e9i | 0.223721i | ||||||||
\(668\) | −8.93510e9 | − | 4.47513e9i | −1.15980 | − | 0.580883i | ||||
\(669\) | 3.42322e9i | 0.442021i | ||||||||
\(670\) | −3.02603e9 | + | 1.27990e10i | −0.388697 | + | 1.64405i | ||||
\(671\) | 1.50919e9 | 0.192847 | ||||||||
\(672\) | −1.62068e8 | − | 3.72906e8i | −0.0206018 | − | 0.0474032i | ||||
\(673\) | 9.93043e9 | 1.25578 | 0.627892 | − | 0.778300i | \(-0.283918\pi\) | ||||
0.627892 | + | 0.778300i | \(0.283918\pi\) | |||||||
\(674\) | −1.68352e9 | + | 7.12069e9i | −0.211791 | + | 0.895803i | ||||
\(675\) | 2.78070e9i | 0.348009i | ||||||||
\(676\) | 1.68564e10 | + | 8.44250e9i | 2.09870 | + | 1.05113i | ||||
\(677\) | − | 8.68747e9i | − | 1.07605i | −0.842929 | − | 0.538026i | \(-0.819170\pi\) | ||
0.842929 | − | 0.538026i | \(-0.180830\pi\) | |||||||
\(678\) | −5.68294e9 | − | 1.34360e9i | −0.700276 | − | 0.165564i | ||||
\(679\) | −2.99159e8 | −0.0366739 | ||||||||
\(680\) | −2.69440e9 | − | 2.25334e9i | −0.328610 | − | 0.274818i | ||||
\(681\) | −5.38461e9 | −0.653341 | ||||||||
\(682\) | −4.62731e9 | − | 1.09402e9i | −0.558578 | − | 0.132062i | ||||
\(683\) | − | 9.19143e8i | − | 0.110385i | −0.998476 | − | 0.0551925i | \(-0.982423\pi\) | ||
0.998476 | − | 0.0551925i | \(-0.0175773\pi\) | |||||||
\(684\) | 1.92504e9 | − | 3.84356e9i | 0.230008 | − | 0.459237i | ||||
\(685\) | 2.72887e8i | 0.0324389i | ||||||||
\(686\) | 3.46931e8 | − | 1.46740e9i | 0.0410307 | − | 0.173545i | ||||
\(687\) | 9.89732e8 | 0.116458 | ||||||||
\(688\) | 4.97036e9 | − | 3.71724e9i | 0.581874 | − | 0.435172i | ||||
\(689\) | 2.52548e10 | 2.94156 | ||||||||
\(690\) | 2.22332e9 | − | 9.40387e9i | 0.257650 | − | 1.08977i | ||||
\(691\) | − | 2.66387e9i | − | 0.307142i | −0.988138 | − | 0.153571i | \(-0.950923\pi\) | ||
0.988138 | − | 0.153571i | \(-0.0490774\pi\) | |||||||
\(692\) | −2.77928e9 | + | 5.54915e9i | −0.318832 | + | 0.636583i | ||||
\(693\) | − | 2.01046e8i | − | 0.0229471i | ||||||
\(694\) | 6.22602e8 | + | 1.47199e8i | 0.0707054 | + | 0.0167166i | ||||
\(695\) | 1.78868e9 | 0.202109 | ||||||||
\(696\) | 6.36812e8 | − | 7.61458e8i | 0.0715943 | − | 0.0856079i | ||||
\(697\) | −8.31904e8 | −0.0930590 | ||||||||
\(698\) | 2.39871e9 | + | 5.67118e8i | 0.266983 | + | 0.0631218i | ||||
\(699\) | 2.66222e9i | 0.294831i | ||||||||
\(700\) | 1.31356e9 | + | 6.57896e8i | 0.144746 | + | 0.0724960i | ||||
\(701\) | − | 9.10026e9i | − | 0.997794i | −0.866661 | − | 0.498897i | \(-0.833739\pi\) | ||
0.866661 | − | 0.498897i | \(-0.166261\pi\) | |||||||
\(702\) | 7.42549e8 | − | 3.14072e9i | 0.0810112 | − | 0.342649i | ||||
\(703\) | −4.81974e9 | −0.523215 | ||||||||
\(704\) | 7.00670e9 | − | 1.25921e9i | 0.756849 | − | 0.136017i | ||||
\(705\) | 8.64630e9 | 0.929326 | ||||||||
\(706\) | −1.90927e9 | + | 8.07555e9i | −0.204198 | + | 0.863685i | ||||
\(707\) | − | 1.30811e8i | − | 0.0139212i | ||||||
\(708\) | 4.57938e9 | + | 2.29358e9i | 0.484942 | + | 0.242883i | ||||
\(709\) | 4.42773e9i | 0.466573i | 0.972408 | + | 0.233286i | \(0.0749480\pi\) | ||||
−0.972408 | + | 0.233286i | \(0.925052\pi\) | |||||||
\(710\) | −2.63334e9 | − | 6.22591e8i | −0.276123 | − | 0.0652828i | ||||
\(711\) | −1.14769e9 | −0.119752 | ||||||||
\(712\) | 5.90425e9 | − | 7.05992e9i | 0.613034 | − | 0.733027i | ||||
\(713\) | −8.36142e9 | −0.863907 | ||||||||
\(714\) | −1.25060e8 | − | 2.95674e7i | −0.0128580 | − | 0.00303997i | ||||
\(715\) | − | 2.30434e10i | − | 2.35763i | ||||||
\(716\) | −4.33767e9 | + | 8.66065e9i | −0.441633 | + | 0.881769i | ||||
\(717\) | − | 2.91253e9i | − | 0.295090i | ||||||
\(718\) | −3.17369e9 | + | 1.34236e10i | −0.319984 | + | 1.35342i | ||||
\(719\) | −2.91984e9 | −0.292960 | −0.146480 | − | 0.989214i | \(-0.546794\pi\) | ||||
−0.146480 | + | 0.989214i | \(0.546794\pi\) | |||||||
\(720\) | −4.48019e9 | + | 3.35065e9i | −0.447335 | + | 0.334553i | ||||
\(721\) | 3.18592e7 | 0.00316564 | ||||||||
\(722\) | 3.19759e9 | − | 1.35247e10i | 0.316186 | − | 1.33736i | ||||
\(723\) | − | 2.55915e9i | − | 0.251833i | ||||||
\(724\) | −1.15330e9 | + | 2.30269e9i | −0.112942 | + | 0.225502i | ||||
\(725\) | 3.58656e9i | 0.349539i | ||||||||
\(726\) | −2.36749e9 | − | 5.59738e8i | −0.229621 | − | 0.0542884i | ||||
\(727\) | 1.29199e10 | 1.24706 | 0.623530 | − | 0.781799i | \(-0.285698\pi\) | ||||
0.623530 | + | 0.781799i | \(0.285698\pi\) | |||||||
\(728\) | −1.30795e9 | − | 1.09385e9i | −0.125641 | − | 0.105074i | ||||
\(729\) | −3.87420e8 | −0.0370370 | ||||||||
\(730\) | 2.47709e10 | + | 5.85649e9i | 2.35674 | + | 0.557195i | ||||
\(731\) | − | 1.96162e9i | − | 0.185739i | ||||||
\(732\) | −1.37381e9 | − | 6.88073e8i | −0.129461 | − | 0.0648404i | ||||
\(733\) | 1.48967e10i | 1.39710i | 0.715563 | + | 0.698548i | \(0.246170\pi\) | ||||
−0.715563 | + | 0.698548i | \(0.753830\pi\) | |||||||
\(734\) | −1.77140e9 | + | 7.49238e9i | −0.165341 | + | 0.699333i | ||||
\(735\) | −1.03317e10 | −0.959770 | ||||||||
\(736\) | 1.14812e10 | − | 4.98981e9i | 1.06149 | − | 0.461330i | ||||
\(737\) | −8.42466e9 | −0.775204 | ||||||||
\(738\) | −3.04869e8 | + | 1.28949e9i | −0.0279200 | + | 0.118092i | ||||
\(739\) | − | 3.02167e9i | − | 0.275418i | −0.990473 | − | 0.137709i | \(-0.956026\pi\) | ||
0.990473 | − | 0.137709i | \(-0.0439738\pi\) | |||||||
\(740\) | 5.60854e9 | + | 2.80903e9i | 0.508791 | + | 0.254827i | ||||
\(741\) | − | 1.80263e10i | − | 1.62758i | ||||||
\(742\) | −1.55875e9 | − | 3.68529e8i | −0.140075 | − | 0.0331175i | ||||
\(743\) | −1.52499e10 | −1.36397 | −0.681985 | − | 0.731366i | \(-0.738883\pi\) | ||||
−0.681985 | + | 0.731366i | \(0.738883\pi\) | |||||||
\(744\) | 3.71346e9 | + | 3.10559e9i | 0.330578 | + | 0.276464i | ||||
\(745\) | 3.80433e9 | 0.337078 | ||||||||
\(746\) | −7.96976e9 | − | 1.88426e9i | −0.702844 | − | 0.166171i | ||||
\(747\) | 5.76687e9i | 0.506196i | ||||||||
\(748\) | 1.00758e9 | − | 2.01174e9i | 0.0880284 | − | 0.175758i | ||||
\(749\) | 1.32361e9i | 0.115099i | ||||||||
\(750\) | 2.07892e9 | − | 8.79309e9i | 0.179938 | − | 0.761074i | ||||
\(751\) | −1.30306e9 | −0.112260 | −0.0561298 | − | 0.998423i | \(-0.517876\pi\) | ||||
−0.0561298 | + | 0.998423i | \(0.517876\pi\) | |||||||
\(752\) | 6.70862e9 | + | 8.97017e9i | 0.575268 | + | 0.769198i | ||||
\(753\) | −4.77168e9 | −0.407276 | ||||||||
\(754\) | 9.57745e8 | − | 4.05092e9i | 0.0813673 | − | 0.344155i | ||||
\(755\) | − | 9.40797e9i | − | 0.795576i | ||||||
\(756\) | −9.16614e7 | + | 1.83012e8i | −0.00771543 | + | 0.0154047i | ||||
\(757\) | 3.51770e9i | 0.294729i | 0.989082 | + | 0.147364i | \(0.0470790\pi\) | ||||
−0.989082 | + | 0.147364i | \(0.952921\pi\) | |||||||
\(758\) | −9.47952e9 | − | 2.24121e9i | −0.790576 | − | 0.186913i | ||||
\(759\) | 6.18987e9 | 0.513849 | ||||||||
\(760\) | −2.00469e10 | + | 2.39708e10i | −1.65653 | + | 1.98077i | ||||
\(761\) | −1.23448e10 | −1.01541 | −0.507703 | − | 0.861532i | \(-0.669505\pi\) | ||||
−0.507703 | + | 0.861532i | \(0.669505\pi\) | |||||||
\(762\) | 4.97451e9 | + | 1.17610e9i | 0.407294 | + | 0.0962949i | ||||
\(763\) | − | 1.94687e9i | − | 0.158673i | ||||||
\(764\) | 3.75534e9 | + | 1.88086e9i | 0.304665 | + | 0.152591i | ||||
\(765\) | 1.76817e9i | 0.142793i | ||||||||
\(766\) | −2.69687e8 | + | 1.14068e9i | −0.0216800 | + | 0.0916989i | ||||
\(767\) | 2.14773e10 | 1.71868 | ||||||||
\(768\) | −6.95231e9 | − | 2.04826e9i | −0.553815 | − | 0.163162i | ||||
\(769\) | 1.18155e10 | 0.936940 | 0.468470 | − | 0.883479i | \(-0.344805\pi\) | ||||
0.468470 | + | 0.883479i | \(0.344805\pi\) | |||||||
\(770\) | −3.36259e8 | + | 1.42226e9i | −0.0265434 | + | 0.112269i | ||||
\(771\) | − | 1.25662e10i | − | 0.987443i | ||||||
\(772\) | −1.14252e10 | − | 5.72228e9i | −0.893721 | − | 0.447619i | ||||
\(773\) | − | 1.62582e10i | − | 1.26603i | −0.774138 | − | 0.633017i | \(-0.781816\pi\) | ||
0.774138 | − | 0.633017i | \(-0.218184\pi\) | |||||||
\(774\) | −3.04059e9 | − | 7.18876e8i | −0.235703 | − | 0.0557264i | ||||
\(775\) | −1.74908e10 | −1.34975 | ||||||||
\(776\) | −3.42099e9 | + | 4.09060e9i | −0.262806 | + | 0.314247i | ||||
\(777\) | 2.29493e8 | 0.0175508 | ||||||||
\(778\) | −2.46571e9 | − | 5.82958e8i | −0.187721 | − | 0.0443822i | ||||
\(779\) | 7.40106e9i | 0.560935i | ||||||||
\(780\) | −1.05060e10 | + | 2.09765e10i | −0.792698 | + | 1.58271i | ||||
\(781\) | − | 1.73333e9i | − | 0.130198i | ||||||
\(782\) | 9.10331e8 | − | 3.85038e9i | 0.0680732 | − | 0.287925i | ||||
\(783\) | −4.99698e8 | −0.0371998 | ||||||||
\(784\) | −8.01633e9 | − | 1.07187e10i | −0.594113 | − | 0.794396i | ||||
\(785\) | −3.34418e10 | −2.46744 | ||||||||
\(786\) | −1.55957e9 | + | 6.59644e9i | −0.114558 | + | 0.484541i | ||||
\(787\) | 1.80876e10i | 1.32273i | 0.750066 | + | 0.661363i | \(0.230022\pi\) | ||||
−0.750066 | + | 0.661363i | \(0.769978\pi\) | |||||||
\(788\) | 4.92805e9 | − | 9.83940e9i | 0.358784 | − | 0.716353i | ||||
\(789\) | 3.34597e9i | 0.242523i | ||||||||
\(790\) | 8.11912e9 | + | 1.91957e9i | 0.585887 | + | 0.138519i | ||||
\(791\) | 1.55309e9 | 0.111578 | ||||||||
\(792\) | −2.74903e9 | − | 2.29903e9i | −0.196626 | − | 0.164440i | ||||
\(793\) | −6.44318e9 | −0.458822 | ||||||||
\(794\) | 1.25897e10 | + | 2.97653e9i | 0.892572 | + | 0.211027i | ||||
\(795\) | 2.20385e10i | 1.55560i | ||||||||
\(796\) | −1.85691e10 | − | 9.30033e9i | −1.30496 | − | 0.653586i | ||||
\(797\) | 8.07805e9i | 0.565201i | 0.959238 | + | 0.282600i | \(0.0911970\pi\) | ||||
−0.959238 | + | 0.282600i | \(0.908803\pi\) | |||||||
\(798\) | −2.63047e8 | + | 1.11260e9i | −0.0183241 | + | 0.0775046i | ||||
\(799\) | 3.54019e9 | 0.245535 | ||||||||
\(800\) | 2.40169e10 | − | 1.04379e10i | 1.65845 | − | 0.720775i | ||||
\(801\) | −4.63299e9 | −0.318528 | ||||||||
\(802\) | −9.08267e8 | + | 3.84165e9i | −0.0621732 | + | 0.262971i | ||||
\(803\) | 1.63048e10i | 1.11125i | ||||||||
\(804\) | 7.66898e9 | + | 3.84100e9i | 0.520405 | + | 0.260644i | ||||
\(805\) | 2.56998e9i | 0.173638i | ||||||||
\(806\) | 1.97554e10 | + | 4.67070e9i | 1.32897 | + | 0.314203i | ||||
\(807\) | 1.29173e10 | 0.865198 | ||||||||
\(808\) | −1.78867e9 | − | 1.49587e9i | −0.119286 | − | 0.0997595i | ||||
\(809\) | 6.18309e9 | 0.410568 | 0.205284 | − | 0.978702i | \(-0.434188\pi\) | ||||
0.205284 | + | 0.978702i | \(0.434188\pi\) | |||||||
\(810\) | 2.74073e9 | + | 6.47981e8i | 0.181204 | + | 0.0428415i | ||||
\(811\) | − | 3.48351e9i | − | 0.229321i | −0.993405 | − | 0.114660i | \(-0.963422\pi\) | ||
0.993405 | − | 0.114660i | \(-0.0365780\pi\) | |||||||
\(812\) | −1.18225e8 | + | 2.36050e8i | −0.00774934 | + | 0.0154724i | ||||
\(813\) | − | 3.20458e9i | − | 0.209148i | ||||||
\(814\) | −9.24488e8 | + | 3.91026e9i | −0.0600781 | + | 0.254109i | ||||
\(815\) | 3.34901e10 | 2.16703 | ||||||||
\(816\) | −1.83440e9 | + | 1.37191e9i | −0.118189 | + | 0.0883914i | ||||
\(817\) | −1.74516e10 | −1.11959 | ||||||||
\(818\) | −3.37623e8 | + | 1.42802e9i | −0.0215673 | + | 0.0912219i | ||||
\(819\) | 8.58326e8i | 0.0545957i | ||||||||
\(820\) | 4.31347e9 | − | 8.61232e9i | 0.273198 | − | 0.545471i | ||||
\(821\) | − | 2.22317e10i | − | 1.40208i | −0.713123 | − | 0.701039i | \(-0.752720\pi\) | ||
0.713123 | − | 0.701039i | \(-0.247280\pi\) | |||||||
\(822\) | 1.73190e8 | + | 4.09467e7i | 0.0108761 | + | 0.00257139i | ||||
\(823\) | 2.30533e10 | 1.44156 | 0.720781 | − | 0.693163i | \(-0.243783\pi\) | ||||
0.720781 | + | 0.693163i | \(0.243783\pi\) | |||||||
\(824\) | 3.64322e8 | − | 4.35632e8i | 0.0226851 | − | 0.0271253i | ||||
\(825\) | 1.29483e10 | 0.802829 | ||||||||
\(826\) | −1.32559e9 | − | 3.13405e8i | −0.0818428 | − | 0.0193498i | ||||
\(827\) | 3.93422e9i | 0.241874i | 0.992660 | + | 0.120937i | \(0.0385899\pi\) | ||||
−0.992660 | + | 0.120937i | \(0.961410\pi\) | |||||||
\(828\) | −5.63464e9 | − | 2.82211e9i | −0.344953 | − | 0.172769i | ||||
\(829\) | 2.39962e10i | 1.46286i | 0.681917 | + | 0.731430i | \(0.261147\pi\) | ||||
−0.681917 | + | 0.731430i | \(0.738853\pi\) | |||||||
\(830\) | 9.64540e9 | − | 4.07966e10i | 0.585527 | − | 2.47657i | ||||
\(831\) | −5.11406e9 | −0.309145 | ||||||||
\(832\) | −2.99138e10 | + | 5.37596e9i | −1.80069 | + | 0.323612i | ||||
\(833\) | −4.23028e9 | −0.253578 | ||||||||
\(834\) | 2.68391e8 | − | 1.13520e9i | 0.0160209 | − | 0.0677628i | ||||
\(835\) | − | 3.65687e10i | − | 2.17373i | ||||||
\(836\) | −1.78975e10 | − | 8.96393e9i | −1.05942 | − | 0.530612i | ||||
\(837\) | − | 2.43691e9i | − | 0.143648i | ||||||
\(838\) | −1.36326e9 | − | 3.22311e8i | −0.0800250 | − | 0.0189200i | ||||
\(839\) | −2.16432e10 | −1.26518 | −0.632592 | − | 0.774485i | \(-0.718009\pi\) | ||||
−0.632592 | + | 0.774485i | \(0.718009\pi\) | |||||||
\(840\) | 9.54538e8 | − | 1.14137e9i | 0.0555668 | − | 0.0664432i | ||||
\(841\) | 1.66054e10 | 0.962637 | ||||||||
\(842\) | 3.00245e8 | + | 7.09858e7i | 0.0173334 | + | 0.00409807i | ||||
\(843\) | 2.54012e8i | 0.0146035i | ||||||||
\(844\) | 1.23114e10 | − | 2.45811e10i | 0.704870 | − | 1.40735i | ||||
\(845\) | 6.89881e10i | 3.93347i | ||||||||
\(846\) | 1.29738e9 | − | 5.48745e9i | 0.0736665 | − | 0.311583i | ||||
\(847\) | 6.47012e8 | 0.0365864 | ||||||||
\(848\) | −2.28640e10 | + | 1.70995e10i | −1.28756 | + | 0.962940i | ||||
\(849\) | 1.55745e10 | 0.873450 | ||||||||
\(850\) | 1.90428e9 | − | 8.05442e9i | 0.106356 | − | 0.449850i | ||||
\(851\) | 7.06573e9i | 0.393010i | ||||||||
\(852\) | −7.90267e8 | + | 1.57785e9i | −0.0437759 | + | 0.0874034i | ||||
\(853\) | − | 2.96549e10i | − | 1.63597i | −0.575239 | − | 0.817985i | \(-0.695091\pi\) | ||
0.575239 | − | 0.817985i | \(-0.304909\pi\) | |||||||
\(854\) | 3.97678e8 | + | 9.40216e7i | 0.0218489 | + | 0.00516565i | ||||
\(855\) | 1.57305e10 | 0.860720 | ||||||||
\(856\) | 1.80986e10 | + | 1.51359e10i | 0.986249 | + | 0.824805i | ||||
\(857\) | 1.12112e10 | 0.608442 | 0.304221 | − | 0.952602i | \(-0.401604\pi\) | ||||
0.304221 | + | 0.952602i | \(0.401604\pi\) | |||||||
\(858\) | −1.46247e10 | − | 3.45767e9i | −0.790464 | − | 0.186887i | ||||
\(859\) | − | 3.49012e10i | − | 1.87873i | −0.342917 | − | 0.939366i | \(-0.611415\pi\) | ||
0.342917 | − | 0.939366i | \(-0.388585\pi\) | |||||||
\(860\) | 2.03077e10 | + | 1.01711e10i | 1.08872 | + | 0.545285i | ||||
\(861\) | − | 3.52403e8i | − | 0.0188161i | ||||||
\(862\) | 2.77237e9 | − | 1.17262e10i | 0.147427 | − | 0.623563i | ||||
\(863\) | −1.84338e10 | −0.976286 | −0.488143 | − | 0.872764i | \(-0.662326\pi\) | ||||
−0.488143 | + | 0.872764i | \(0.662326\pi\) | |||||||
\(864\) | 1.45427e9 | + | 3.34616e9i | 0.0767089 | + | 0.176502i | ||||
\(865\) | −2.27110e10 | −1.19311 | ||||||||
\(866\) | −1.93025e9 | + | 8.16427e9i | −0.100995 | + | 0.427174i | ||||
\(867\) | − | 1.03552e10i | − | 0.539623i | ||||||
\(868\) | −1.15116e9 | − | 5.76559e8i | −0.0597473 | − | 0.0299243i | ||||
\(869\) | 5.34421e9i | 0.276258i | ||||||||
\(870\) | 3.53501e9 | + | 8.35770e8i | 0.182001 | + | 0.0430298i | ||||
\(871\) | 3.59675e10 | 1.84436 | ||||||||
\(872\) | −2.66209e10 | − | 2.22632e10i | −1.35961 | − | 1.13705i | ||||
\(873\) | 2.68441e9 | 0.136552 | ||||||||
\(874\) | −3.42550e10 | − | 8.09879e9i | −1.73554 | − | 0.410327i | ||||
\(875\) | 2.40306e9i | 0.121265i | ||||||||
\(876\) | 7.43375e9 | − | 1.48423e10i | 0.373631 | − | 0.745997i | ||||
\(877\) | − | 5.90107e9i | − | 0.295415i | −0.989031 | − | 0.147707i | \(-0.952811\pi\) | ||
0.989031 | − | 0.147707i | \(-0.0471894\pi\) | |||||||
\(878\) | 2.88184e9 | − | 1.21892e10i | 0.143694 | − | 0.607775i | ||||
\(879\) | 7.86611e9 | 0.390660 | ||||||||
\(880\) | 1.56022e10 | + | 2.08619e10i | 0.771788 | + | 1.03197i | ||||
\(881\) | 4.16251e9 | 0.205088 | 0.102544 | − | 0.994728i | \(-0.467302\pi\) | ||||
0.102544 | + | 0.994728i | \(0.467302\pi\) | |||||||
\(882\) | −1.55028e9 | + | 6.55712e9i | −0.0760797 | + | 0.321790i | ||||
\(883\) | 3.49741e10i | 1.70956i | 0.518990 | + | 0.854780i | \(0.326308\pi\) | ||||
−0.518990 | + | 0.854780i | \(0.673692\pi\) | |||||||
\(884\) | −4.30166e9 | + | 8.58873e9i | −0.209437 | + | 0.418164i | ||||
\(885\) | 1.87420e10i | 0.908898i | ||||||||
\(886\) | 1.22951e10 | + | 2.90687e9i | 0.593899 | + | 0.140413i | ||||
\(887\) | −9.16854e9 | −0.441131 | −0.220566 | − | 0.975372i | \(-0.570790\pi\) | ||||
−0.220566 | + | 0.975372i | \(0.570790\pi\) | |||||||
\(888\) | 2.62434e9 | − | 3.13802e9i | 0.125769 | − | 0.150387i | ||||
\(889\) | −1.35948e9 | −0.0648958 | ||||||||
\(890\) | 3.27752e10 | + | 7.74891e9i | 1.55840 | + | 0.368448i | ||||
\(891\) | 1.80402e9i | 0.0854416i | ||||||||
\(892\) | −1.45104e10 | − | 7.26750e9i | −0.684544 | − | 0.342853i | ||||
\(893\) | − | 3.14954e10i | − | 1.48002i | ||||||
\(894\) | 5.70840e8 | − | 2.41445e9i | 0.0267198 | − | 0.113015i | ||||
\(895\) | −3.54454e10 | −1.65264 | ||||||||
\(896\) | 1.92475e9 | + | 1.04706e8i | 0.0893915 | + | 0.00486288i | ||||
\(897\) | −2.64265e10 | −1.22255 | ||||||||
\(898\) | −5.05481e9 | + | 2.13801e10i | −0.232937 | + | 0.985239i | ||||
\(899\) | − | 3.14315e9i | − | 0.144280i | ||||||
\(900\) | −1.17868e10 | − | 5.90342e9i | −0.538950 | − | 0.269932i | ||||
\(901\) | 9.02358e9i | 0.411000i | ||||||||
\(902\) | 6.00448e9 | + | 1.41962e9i | 0.272429 | + | 0.0644093i | ||||
\(903\) | 8.30962e8 | 0.0375556 | ||||||||
\(904\) | 1.77601e10 | − | 2.12364e10i | 0.799571 | − | 0.956075i | ||||
\(905\) | −9.42420e9 | −0.422644 | ||||||||
\(906\) | −5.97086e9 | − | 1.41167e9i | −0.266740 | − | 0.0630643i | ||||
\(907\) | 6.50089e9i | 0.289299i | 0.989483 | + | 0.144650i | \(0.0462055\pi\) | ||||
−0.989483 | + | 0.144650i | \(0.953794\pi\) | |||||||
\(908\) | 1.14315e10 | − | 2.28243e10i | 0.506763 | − | 1.01181i | ||||
\(909\) | 1.17379e9i | 0.0518342i | ||||||||
\(910\) | 1.43559e9 | − | 6.07206e9i | 0.0631520 | − | 0.267111i | ||||
\(911\) | −2.88490e10 | −1.26420 | −0.632100 | − | 0.774887i | \(-0.717807\pi\) | ||||
−0.632100 | + | 0.774887i | \(0.717807\pi\) | |||||||
\(912\) | 1.22052e10 | + | 1.63198e10i | 0.532800 | + | 0.712413i | ||||
\(913\) | 2.68534e10 | 1.16775 | ||||||||
\(914\) | −4.92850e9 | + | 2.08458e10i | −0.213503 | + | 0.903041i | ||||
\(915\) | − | 5.62261e9i | − | 0.242641i | ||||||
\(916\) | −2.10120e9 | + | 4.19528e9i | −0.0903304 | + | 0.180355i | ||||
\(917\) | − | 1.80274e9i | − | 0.0772040i | ||||||
\(918\) | 1.12218e9 | + | 2.65313e8i | 0.0478756 | + | 0.0113190i | ||||
\(919\) | −2.06389e10 | −0.877167 | −0.438584 | − | 0.898690i | \(-0.644520\pi\) | ||||
−0.438584 | + | 0.898690i | \(0.644520\pi\) | |||||||
\(920\) | 3.51411e10 | + | 2.93887e10i | 1.48785 | + | 1.24429i | ||||
\(921\) | −7.25800e9 | −0.306132 | ||||||||
\(922\) | 2.97790e10 | + | 7.04053e9i | 1.25127 | + | 0.295833i | ||||
\(923\) | 7.40013e9i | 0.309766i | ||||||||
\(924\) | 8.52193e8 | + | 4.26820e8i | 0.0355375 | + | 0.0177989i | ||||
\(925\) | 1.47804e10i | 0.614033i | ||||||||
\(926\) | −8.32841e9 | + | 3.52262e10i | −0.344686 | + | 1.45790i | ||||
\(927\) | −2.85878e8 | −0.0117870 | ||||||||
\(928\) | 1.87572e9 | + | 4.31590e9i | 0.0770461 | + | 0.177277i | ||||
\(929\) | 2.08036e10 | 0.851301 | 0.425651 | − | 0.904888i | \(-0.360045\pi\) | ||||
0.425651 | + | 0.904888i | \(0.360045\pi\) | |||||||
\(930\) | −4.07586e9 | + | 1.72395e10i | −0.166161 | + | 0.702803i | ||||
\(931\) | 3.76348e10i | 1.52850i | ||||||||
\(932\) | −1.12846e10 | − | 5.65190e9i | −0.456596 | − | 0.228685i | ||||
\(933\) | − | 2.33950e10i | − | 0.943057i | ||||||
\(934\) | −4.41362e10 | − | 1.04350e10i | −1.77248 | − | 0.419061i | ||||
\(935\) | 8.23344e9 | 0.329413 | ||||||||
\(936\) | 1.17365e10 | + | 9.81527e9i | 0.467813 | + | 0.391234i | ||||
\(937\) | −1.01845e10 | −0.404437 | −0.202219 | − | 0.979340i | \(-0.564815\pi\) | ||||
−0.202219 | + | 0.979340i | \(0.564815\pi\) | |||||||
\(938\) | −2.21994e9 | − | 5.24852e8i | −0.0878277 | − | 0.0207648i | ||||
\(939\) | − | 1.16208e10i | − | 0.458043i | ||||||
\(940\) | −1.83561e10 | + | 3.66500e10i | −0.720830 | + | 1.43922i | ||||
\(941\) | − | 1.22264e10i | − | 0.478340i | −0.970978 | − | 0.239170i | \(-0.923125\pi\) | ||
0.970978 | − | 0.239170i | \(-0.0768753\pi\) | |||||||
\(942\) | −5.01795e9 | + | 2.12242e10i | −0.195591 | + | 0.827280i | ||||
\(943\) | 1.08499e10 | 0.421343 | ||||||||
\(944\) | −1.94441e10 | + | 1.45418e10i | −0.752289 | + | 0.562623i | ||||
\(945\) | −7.49013e8 | −0.0288721 | ||||||||
\(946\) | −3.34744e9 | + | 1.41585e10i | −0.128556 | + | 0.543748i | ||||
\(947\) | − | 1.46789e10i | − | 0.561654i | −0.959758 | − | 0.280827i | \(-0.909391\pi\) | ||
0.959758 | − | 0.280827i | \(-0.0906087\pi\) | |||||||
\(948\) | 2.43655e9 | − | 4.86484e9i | 0.0928851 | − | 0.185455i | ||||
\(949\) | − | 6.96103e10i | − | 2.64388i | ||||||
\(950\) | −7.16564e10 | − | 1.69415e10i | −2.71158 | − | 0.641088i | ||||
\(951\) | −8.60540e9 | −0.324444 | ||||||||
\(952\) | 3.90832e8 | − | 4.67332e8i | 0.0146812 | − | 0.0175548i | ||||
\(953\) | 3.02381e10 | 1.13170 | 0.565848 | − | 0.824510i | \(-0.308549\pi\) | ||||
0.565848 | + | 0.824510i | \(0.308549\pi\) | |||||||
\(954\) | 1.39869e10 | + | 3.30688e9i | 0.521558 | + | 0.123310i | ||||
\(955\) | 1.53695e10i | 0.571014i | ||||||||
\(956\) | 1.23457e10 | + | 6.18331e9i | 0.456996 | + | 0.228886i | ||||
\(957\) | 2.32684e9i | 0.0858171i | ||||||||
\(958\) | 6.14684e9 | − | 2.59990e10i | 0.225877 | − | 0.955382i | ||||
\(959\) | −4.73311e7 | −0.00173293 | ||||||||
\(960\) | −4.69130e9 | − | 2.61041e10i | −0.171137 | − | 0.952268i | ||||
\(961\) | −1.21842e10 | −0.442858 | ||||||||
\(962\) | 3.94693e9 | − | 1.66941e10i | 0.142938 | − | 0.604575i | ||||
\(963\) | − | 1.18770e10i | − | 0.428562i | ||||||
\(964\) | 1.08477e10 | + | 5.43308e9i | 0.390005 | + | 0.195333i | ||||
\(965\) | − | 4.67598e10i | − | 1.67505i | ||||||
\(966\) | 1.63106e9 | + | 3.85626e8i | 0.0582171 | + | 0.0137641i | ||||
\(967\) | 5.85290e9 | 0.208151 | 0.104075 | − | 0.994569i | \(-0.466812\pi\) | ||||
0.104075 | + | 0.994569i | \(0.466812\pi\) | |||||||
\(968\) | 7.39882e9 | − | 8.84703e9i | 0.262179 | − | 0.313497i | ||||
\(969\) | 6.44081e9 | 0.227409 | ||||||||
\(970\) | −1.89903e10 | − | 4.48981e9i | −0.668084 | − | 0.157953i | ||||
\(971\) | − | 3.40526e10i | − | 1.19367i | −0.802366 | − | 0.596833i | \(-0.796426\pi\) | ||
0.802366 | − | 0.596833i | \(-0.203574\pi\) | |||||||
\(972\) | 8.22494e8 | − | 1.64220e9i | 0.0287277 | − | 0.0573580i | ||||
\(973\) | 3.10238e8i | 0.0107969i | ||||||||
\(974\) | −7.36592e9 | + | 3.11552e10i | −0.255429 | + | 1.08038i | ||||
\(975\) | −5.52802e10 | −1.91009 | ||||||||
\(976\) | 5.83322e9 | − | 4.36255e9i | 0.200832 | − | 0.150199i | ||||
\(977\) | −1.22080e10 | −0.418807 | −0.209404 | − | 0.977829i | \(-0.567152\pi\) | ||||
−0.209404 | + | 0.977829i | \(0.567152\pi\) | |||||||
\(978\) | 5.02519e9 | − | 2.12548e10i | 0.171777 | − | 0.726558i | ||||
\(979\) | 2.15734e10i | 0.734818i | ||||||||
\(980\) | 2.19343e10 | − | 4.37942e10i | 0.744443 | − | 1.48636i | ||||
\(981\) | 1.74697e10i | 0.590803i | ||||||||
\(982\) | 3.34941e10 | + | 7.91888e9i | 1.12870 | + | 0.266854i | ||||
\(983\) | −2.99405e10 | −1.00536 | −0.502680 | − | 0.864473i | \(-0.667652\pi\) | ||||
−0.502680 | + | 0.864473i | \(0.667652\pi\) | |||||||
\(984\) | −4.81865e9 | − | 4.02986e9i | −0.161229 | − | 0.134836i | ||||
\(985\) | 4.02697e10 | 1.34262 | ||||||||
\(986\) | 1.44740e9 | + | 3.42203e8i | 0.0480860 | + | 0.0113688i | ||||
\(987\) | 1.49966e9i | 0.0496459i | ||||||||
\(988\) | 7.64099e10 | + | 3.82698e10i | 2.52058 | + | 1.26243i | ||||
\(989\) | 2.55840e10i | 0.840971i | ||||||||
\(990\) | 3.01732e9 | − | 1.27622e10i | 0.0988320 | − | 0.418025i | ||||
\(991\) | −2.04298e10 | −0.666815 | −0.333408 | − | 0.942783i | \(-0.608199\pi\) | ||||
−0.333408 | + | 0.942783i | \(0.608199\pi\) | |||||||
\(992\) | −2.10477e10 | + | 9.14748e9i | −0.684562 | + | 0.297516i | ||||
\(993\) | 2.86507e10 | 0.928565 | ||||||||
\(994\) | 1.07986e8 | − | 4.56742e8i | 0.00348750 | − | 0.0147509i | ||||
\(995\) | − | 7.59979e10i | − | 2.44580i | ||||||
\(996\) | −2.44447e10 | − | 1.22431e10i | −0.783928 | − | 0.392630i | ||||
\(997\) | 2.36775e10i | 0.756664i | 0.925670 | + | 0.378332i | \(0.123502\pi\) | ||||
−0.925670 | + | 0.378332i | \(0.876498\pi\) | |||||||
\(998\) | 7.62381e9 | + | 1.80247e9i | 0.242781 | + | 0.0573999i | ||||
\(999\) | −2.05929e9 | −0.0653488 |
(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.13.8 | yes | 14 | |
3.2 | odd | 2 | 72.8.d.d.37.7 | 14 | |||
4.3 | odd | 2 | 96.8.d.a.49.1 | 14 | |||
8.3 | odd | 2 | 96.8.d.a.49.14 | 14 | |||
8.5 | even | 2 | inner | 24.8.d.a.13.7 | ✓ | 14 | |
12.11 | even | 2 | 288.8.d.d.145.14 | 14 | |||
24.5 | odd | 2 | 72.8.d.d.37.8 | 14 | |||
24.11 | even | 2 | 288.8.d.d.145.1 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.8.d.a.13.7 | ✓ | 14 | 8.5 | even | 2 | inner | |
24.8.d.a.13.8 | yes | 14 | 1.1 | even | 1 | trivial | |
72.8.d.d.37.7 | 14 | 3.2 | odd | 2 | |||
72.8.d.d.37.8 | 14 | 24.5 | odd | 2 | |||
96.8.d.a.49.1 | 14 | 4.3 | odd | 2 | |||
96.8.d.a.49.14 | 14 | 8.3 | odd | 2 | |||
288.8.d.d.145.1 | 14 | 24.11 | even | 2 | |||
288.8.d.d.145.14 | 14 | 12.11 | even | 2 |