Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [37,8,Mod(36,37)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(37, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("37.36");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 37 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 37.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.5582459429\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 1702 x^{18} + 1194509 x^{16} + 450999516 x^{14} + 100204783492 x^{12} + 13461378480848 x^{10} + \cdots + 13\!\cdots\!96 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{19}\cdot 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 36.10 | ||
Root | \(-0.118026i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 37.36 |
Dual form | 37.8.b.a.36.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/37\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 0.118026i | − | 0.0104321i | −0.999986 | − | 0.00521606i | \(-0.998340\pi\) | ||
0.999986 | − | 0.00521606i | \(-0.00166033\pi\) | |||||||
\(3\) | −7.03331 | −0.150396 | −0.0751979 | − | 0.997169i | \(-0.523959\pi\) | ||||
−0.0751979 | + | 0.997169i | \(0.523959\pi\) | |||||||
\(4\) | 127.986 | 0.999891 | ||||||||
\(5\) | 225.549i | 0.806949i | 0.914991 | + | 0.403475i | \(0.132198\pi\) | ||||
−0.914991 | + | 0.403475i | \(0.867802\pi\) | |||||||
\(6\) | 0.830113i | 0.00156895i | ||||||||
\(7\) | 6.20125 | 0.00683339 | 0.00341669 | − | 0.999994i | \(-0.498912\pi\) | ||||
0.00341669 | + | 0.999994i | \(0.498912\pi\) | |||||||
\(8\) | − | 30.2130i | − | 0.0208631i | ||||||
\(9\) | −2137.53 | −0.977381 | ||||||||
\(10\) | 26.6207 | 0.00841819 | ||||||||
\(11\) | 5456.67 | 1.23610 | 0.618049 | − | 0.786139i | \(-0.287923\pi\) | ||||
0.618049 | + | 0.786139i | \(0.287923\pi\) | |||||||
\(12\) | −900.166 | −0.150379 | ||||||||
\(13\) | 9336.83i | 1.17869i | 0.807883 | + | 0.589343i | \(0.200613\pi\) | ||||
−0.807883 | + | 0.589343i | \(0.799387\pi\) | |||||||
\(14\) | − | 0.731908i | − | 7.12867e-5i | ||||||
\(15\) | − | 1586.36i | − | 0.121362i | ||||||
\(16\) | 16378.7 | 0.999674 | ||||||||
\(17\) | 24263.8i | 1.19781i | 0.800821 | + | 0.598904i | \(0.204397\pi\) | ||||
−0.800821 | + | 0.598904i | \(0.795603\pi\) | |||||||
\(18\) | 252.284i | 0.0101962i | ||||||||
\(19\) | 36170.0i | 1.20979i | 0.796304 | + | 0.604897i | \(0.206786\pi\) | ||||
−0.796304 | + | 0.604897i | \(0.793214\pi\) | |||||||
\(20\) | 28867.2i | 0.806862i | ||||||||
\(21\) | −43.6153 | −0.00102771 | ||||||||
\(22\) | − | 644.028i | − | 0.0128951i | ||||||
\(23\) | − | 60783.9i | − | 1.04170i | −0.853650 | − | 0.520848i | \(-0.825616\pi\) | ||
0.853650 | − | 0.520848i | \(-0.174384\pi\) | |||||||
\(24\) | 212.497i | 0.00313772i | ||||||||
\(25\) | 27252.5 | 0.348833 | ||||||||
\(26\) | 1101.99 | 0.0122962 | ||||||||
\(27\) | 30415.8 | 0.297390 | ||||||||
\(28\) | 793.674 | 0.00683265 | ||||||||
\(29\) | 238742.i | 1.81776i | 0.417057 | + | 0.908880i | \(0.363061\pi\) | ||||
−0.417057 | + | 0.908880i | \(0.636939\pi\) | |||||||
\(30\) | −187.231 | −0.00126606 | ||||||||
\(31\) | − | 166706.i | − | 1.00505i | −0.864564 | − | 0.502523i | \(-0.832405\pi\) | ||
0.864564 | − | 0.502523i | \(-0.167595\pi\) | |||||||
\(32\) | − | 5800.37i | − | 0.0312918i | ||||||
\(33\) | −38378.5 | −0.185904 | ||||||||
\(34\) | 2863.75 | 0.0124957 | ||||||||
\(35\) | 1398.69i | 0.00551420i | ||||||||
\(36\) | −273574. | −0.977275 | ||||||||
\(37\) | 123926. | − | 282089.i | 0.402213 | − | 0.915546i | ||||
\(38\) | 4269.00 | 0.0126207 | ||||||||
\(39\) | − | 65668.9i | − | 0.177269i | ||||||
\(40\) | 6814.52 | 0.0168355 | ||||||||
\(41\) | −415672. | −0.941905 | −0.470952 | − | 0.882159i | \(-0.656090\pi\) | ||||
−0.470952 | + | 0.882159i | \(0.656090\pi\) | |||||||
\(42\) | 5.14774i | 1.07212e-5i | ||||||||
\(43\) | − | 900886.i | − | 1.72795i | −0.503538 | − | 0.863973i | \(-0.667969\pi\) | ||
0.503538 | − | 0.863973i | \(-0.332031\pi\) | |||||||
\(44\) | 698378. | 1.23596 | ||||||||
\(45\) | − | 482119.i | − | 0.788697i | ||||||
\(46\) | −7174.07 | −0.0108671 | ||||||||
\(47\) | −585683. | −0.822849 | −0.411425 | − | 0.911444i | \(-0.634969\pi\) | ||||
−0.411425 | + | 0.911444i | \(0.634969\pi\) | |||||||
\(48\) | −115196. | −0.150347 | ||||||||
\(49\) | −823505. | −0.999953 | ||||||||
\(50\) | − | 3216.51i | − | 0.00363906i | ||||||
\(51\) | − | 170655.i | − | 0.180145i | ||||||
\(52\) | 1.19498e6i | 1.17856i | ||||||||
\(53\) | 1.40140e6 | 1.29299 | 0.646496 | − | 0.762917i | \(-0.276234\pi\) | ||||
0.646496 | + | 0.762917i | \(0.276234\pi\) | |||||||
\(54\) | − | 3589.85i | − | 0.00310240i | ||||||
\(55\) | 1.23075e6i | 0.997469i | ||||||||
\(56\) | − | 187.358i | − | 0.000142566i | ||||||
\(57\) | − | 254395.i | − | 0.181948i | ||||||
\(58\) | 28177.8 | 0.0189631 | ||||||||
\(59\) | 1.03209e6i | 0.654240i | 0.944983 | + | 0.327120i | \(0.106078\pi\) | ||||
−0.944983 | + | 0.327120i | \(0.893922\pi\) | |||||||
\(60\) | − | 203032.i | − | 0.121349i | ||||||
\(61\) | − | 944290.i | − | 0.532661i | −0.963882 | − | 0.266330i | \(-0.914189\pi\) | ||
0.963882 | − | 0.266330i | \(-0.0858112\pi\) | |||||||
\(62\) | −19675.7 | −0.0104848 | ||||||||
\(63\) | −13255.4 | −0.00667883 | ||||||||
\(64\) | 2.09578e6 | 0.999347 | ||||||||
\(65\) | −2.10592e6 | −0.951140 | ||||||||
\(66\) | 4529.65i | 0.00193937i | ||||||||
\(67\) | 1.87144e6 | 0.760177 | 0.380089 | − | 0.924950i | \(-0.375894\pi\) | ||||
0.380089 | + | 0.924950i | \(0.375894\pi\) | |||||||
\(68\) | 3.10542e6i | 1.19768i | ||||||||
\(69\) | 427512.i | 0.156667i | ||||||||
\(70\) | 165.081 | 5.75248e−5 | ||||||||
\(71\) | 3.16808e6 | 1.05049 | 0.525244 | − | 0.850951i | \(-0.323974\pi\) | ||||
0.525244 | + | 0.850951i | \(0.323974\pi\) | |||||||
\(72\) | 64581.2i | 0.0203912i | ||||||||
\(73\) | −5.00057e6 | −1.50449 | −0.752246 | − | 0.658883i | \(-0.771029\pi\) | ||||
−0.752246 | + | 0.658883i | \(0.771029\pi\) | |||||||
\(74\) | −33293.8 | − | 14626.5i | −0.00955108 | − | 0.00419593i | ||||
\(75\) | −191676. | −0.0524629 | ||||||||
\(76\) | 4.62926e6i | 1.20966i | ||||||||
\(77\) | 33838.2 | 0.00844675 | ||||||||
\(78\) | −7750.63 | −0.00184929 | ||||||||
\(79\) | − | 4.38910e6i | − | 1.00157i | −0.865572 | − | 0.500784i | \(-0.833045\pi\) | ||
0.865572 | − | 0.500784i | \(-0.166955\pi\) | |||||||
\(80\) | 3.69419e6i | 0.806686i | ||||||||
\(81\) | 4.46086e6 | 0.932655 | ||||||||
\(82\) | 49060.0i | 0.00982606i | ||||||||
\(83\) | 3.16473e6 | 0.607524 | 0.303762 | − | 0.952748i | \(-0.401757\pi\) | ||||
0.303762 | + | 0.952748i | \(0.401757\pi\) | |||||||
\(84\) | −5582.16 | −0.00102760 | ||||||||
\(85\) | −5.47267e6 | −0.966570 | ||||||||
\(86\) | −106328. | −0.0180261 | ||||||||
\(87\) | − | 1.67915e6i | − | 0.273383i | ||||||
\(88\) | − | 164862.i | − | 0.0257888i | ||||||
\(89\) | − | 9.98897e6i | − | 1.50195i | −0.660331 | − | 0.750975i | \(-0.729584\pi\) | ||
0.660331 | − | 0.750975i | \(-0.270416\pi\) | |||||||
\(90\) | −56902.5 | −0.00822778 | ||||||||
\(91\) | 57900.1i | 0.00805442i | ||||||||
\(92\) | − | 7.77949e6i | − | 1.04158i | ||||||
\(93\) | 1.17250e6i | 0.151155i | ||||||||
\(94\) | 69125.8i | 0.00858406i | ||||||||
\(95\) | −8.15812e6 | −0.976242 | ||||||||
\(96\) | 40795.8i | 0.00470615i | ||||||||
\(97\) | − | 3.91455e6i | − | 0.435493i | −0.976005 | − | 0.217746i | \(-0.930129\pi\) | ||
0.976005 | − | 0.217746i | \(-0.0698706\pi\) | |||||||
\(98\) | 97194.9i | 0.0104316i | ||||||||
\(99\) | −1.16638e7 | −1.20814 | ||||||||
\(100\) | 3.48795e6 | 0.348795 | ||||||||
\(101\) | 3.54427e6 | 0.342296 | 0.171148 | − | 0.985245i | \(-0.445252\pi\) | ||||
0.171148 | + | 0.985245i | \(0.445252\pi\) | |||||||
\(102\) | −20141.7 | −0.00187929 | ||||||||
\(103\) | − | 1.12121e7i | − | 1.01102i | −0.862822 | − | 0.505508i | \(-0.831305\pi\) | ||
0.862822 | − | 0.505508i | \(-0.168695\pi\) | |||||||
\(104\) | 282094. | 0.0245910 | ||||||||
\(105\) | − | 9837.41i | − | 0.000829312i | ||||||
\(106\) | − | 165401.i | − | 0.0134886i | ||||||
\(107\) | −3.13013e6 | −0.247012 | −0.123506 | − | 0.992344i | \(-0.539414\pi\) | ||||
−0.123506 | + | 0.992344i | \(0.539414\pi\) | |||||||
\(108\) | 3.89280e6 | 0.297357 | ||||||||
\(109\) | 1.32545e7i | 0.980329i | 0.871630 | + | 0.490164i | \(0.163063\pi\) | ||||
−0.871630 | + | 0.490164i | \(0.836937\pi\) | |||||||
\(110\) | 145260. | 0.0104057 | ||||||||
\(111\) | −871609. | + | 1.98402e6i | −0.0604911 | + | 0.137694i | ||||
\(112\) | 101568. | 0.00683116 | ||||||||
\(113\) | − | 6.10937e6i | − | 0.398310i | −0.979968 | − | 0.199155i | \(-0.936180\pi\) | ||
0.979968 | − | 0.199155i | \(-0.0638198\pi\) | |||||||
\(114\) | −30025.2 | −0.00189810 | ||||||||
\(115\) | 1.37098e7 | 0.840596 | ||||||||
\(116\) | 3.05557e7i | 1.81756i | ||||||||
\(117\) | − | 1.99578e7i | − | 1.15202i | ||||||
\(118\) | 121814. | 0.00682510 | ||||||||
\(119\) | 150466.i | 0.00818508i | ||||||||
\(120\) | −47928.6 | −0.00253198 | ||||||||
\(121\) | 1.02881e7 | 0.527941 | ||||||||
\(122\) | −111451. | −0.00555678 | ||||||||
\(123\) | 2.92355e6 | 0.141658 | ||||||||
\(124\) | − | 2.13361e7i | − | 1.00494i | ||||||
\(125\) | 2.37678e7i | 1.08844i | ||||||||
\(126\) | 1564.48i | 6.96743e-5i | ||||||||
\(127\) | −2.86639e7 | −1.24171 | −0.620857 | − | 0.783924i | \(-0.713215\pi\) | ||||
−0.620857 | + | 0.783924i | \(0.713215\pi\) | |||||||
\(128\) | − | 989804.i | − | 0.0417171i | ||||||
\(129\) | 6.33621e6i | 0.259876i | ||||||||
\(130\) | 248553.i | 0.00992240i | ||||||||
\(131\) | 4.10992e7i | 1.59729i | 0.601801 | + | 0.798646i | \(0.294450\pi\) | ||||
−0.601801 | + | 0.798646i | \(0.705550\pi\) | |||||||
\(132\) | −4.91191e6 | −0.185884 | ||||||||
\(133\) | 224299.i | 0.00826699i | ||||||||
\(134\) | − | 220879.i | − | 0.00793025i | ||||||
\(135\) | 6.86026e6i | 0.239978i | ||||||||
\(136\) | 733081. | 0.0249900 | ||||||||
\(137\) | 3.56466e7 | 1.18439 | 0.592196 | − | 0.805794i | \(-0.298261\pi\) | ||||
0.592196 | + | 0.805794i | \(0.298261\pi\) | |||||||
\(138\) | 50457.5 | 0.00163436 | ||||||||
\(139\) | 5.45504e7 | 1.72285 | 0.861423 | − | 0.507888i | \(-0.169574\pi\) | ||||
0.861423 | + | 0.507888i | \(0.169574\pi\) | |||||||
\(140\) | 179013.i | 0.00551360i | ||||||||
\(141\) | 4.11929e6 | 0.123753 | ||||||||
\(142\) | − | 373915.i | − | 0.0109588i | ||||||
\(143\) | 5.09480e7i | 1.45697i | ||||||||
\(144\) | −3.50099e7 | −0.977062 | ||||||||
\(145\) | −5.38482e7 | −1.46684 | ||||||||
\(146\) | 590197.i | 0.0156950i | ||||||||
\(147\) | 5.79197e6 | 0.150389 | ||||||||
\(148\) | 1.58608e7 | − | 3.61035e7i | 0.402169 | − | 0.915447i | ||||
\(149\) | 5.12903e7 | 1.27023 | 0.635116 | − | 0.772417i | \(-0.280952\pi\) | ||||
0.635116 | + | 0.772417i | \(0.280952\pi\) | |||||||
\(150\) | 22622.7i | 0.000547299i | ||||||||
\(151\) | −3.41108e7 | −0.806254 | −0.403127 | − | 0.915144i | \(-0.632077\pi\) | ||||
−0.403127 | + | 0.915144i | \(0.632077\pi\) | |||||||
\(152\) | 1.09280e6 | 0.0252400 | ||||||||
\(153\) | − | 5.18646e7i | − | 1.17071i | ||||||
\(154\) | − | 3993.78i | − | 8.81174e-5i | ||||||
\(155\) | 3.76005e7 | 0.811022 | ||||||||
\(156\) | − | 8.40470e6i | − | 0.177250i | ||||||
\(157\) | −5.30635e7 | −1.09433 | −0.547164 | − | 0.837026i | \(-0.684292\pi\) | ||||
−0.547164 | + | 0.837026i | \(0.684292\pi\) | |||||||
\(158\) | −518027. | −0.0104485 | ||||||||
\(159\) | −9.85647e6 | −0.194461 | ||||||||
\(160\) | 1.30827e6 | 0.0252509 | ||||||||
\(161\) | − | 376936.i | − | 0.00711831i | ||||||
\(162\) | − | 526497.i | − | 0.00972956i | ||||||
\(163\) | − | 2.70879e7i | − | 0.489913i | −0.969534 | − | 0.244957i | \(-0.921226\pi\) | ||
0.969534 | − | 0.244957i | \(-0.0787737\pi\) | |||||||
\(164\) | −5.32002e7 | −0.941802 | ||||||||
\(165\) | − | 8.65623e6i | − | 0.150015i | ||||||
\(166\) | − | 373520.i | − | 0.00633776i | ||||||
\(167\) | 2.58701e7i | 0.429824i | 0.976633 | + | 0.214912i | \(0.0689464\pi\) | ||||
−0.976633 | + | 0.214912i | \(0.931054\pi\) | |||||||
\(168\) | 1317.75i | 2.14413e-5i | ||||||||
\(169\) | −2.44280e7 | −0.389299 | ||||||||
\(170\) | 645917.i | 0.0100834i | ||||||||
\(171\) | − | 7.73146e7i | − | 1.18243i | ||||||
\(172\) | − | 1.15301e8i | − | 1.72776i | ||||||
\(173\) | −7.44012e7 | −1.09249 | −0.546246 | − | 0.837625i | \(-0.683944\pi\) | ||||
−0.546246 | + | 0.837625i | \(0.683944\pi\) | |||||||
\(174\) | −198183. | −0.00285197 | ||||||||
\(175\) | 169000. | 0.00238371 | ||||||||
\(176\) | 8.93729e7 | 1.23570 | ||||||||
\(177\) | − | 7.25904e6i | − | 0.0983949i | ||||||
\(178\) | −1.17896e6 | −0.0156685 | ||||||||
\(179\) | 1.02302e8i | 1.33321i | 0.745409 | + | 0.666607i | \(0.232254\pi\) | ||||
−0.745409 | + | 0.666607i | \(0.767746\pi\) | |||||||
\(180\) | − | 6.17045e7i | − | 0.788611i | ||||||
\(181\) | 6.03017e7 | 0.755883 | 0.377941 | − | 0.925830i | \(-0.376632\pi\) | ||||
0.377941 | + | 0.925830i | \(0.376632\pi\) | |||||||
\(182\) | 6833.71 | 8.40246e−5 | ||||||||
\(183\) | 6.64148e6i | 0.0801099i | ||||||||
\(184\) | −1.83646e6 | −0.0217330 | ||||||||
\(185\) | 6.36250e7 | + | 2.79514e7i | 0.738799 | + | 0.324565i | ||||
\(186\) | 138385. | 0.00157686 | ||||||||
\(187\) | 1.32399e8i | 1.48061i | ||||||||
\(188\) | −7.49593e7 | −0.822760 | ||||||||
\(189\) | 188616. | 0.00203218 | ||||||||
\(190\) | 962869.i | 0.0101843i | ||||||||
\(191\) | − | 4.31250e7i | − | 0.447829i | −0.974609 | − | 0.223915i | \(-0.928116\pi\) | ||
0.974609 | − | 0.223915i | \(-0.0718837\pi\) | |||||||
\(192\) | −1.47403e7 | −0.150298 | ||||||||
\(193\) | − | 3.69409e7i | − | 0.369877i | −0.982750 | − | 0.184938i | \(-0.940791\pi\) | ||
0.982750 | − | 0.184938i | \(-0.0592085\pi\) | |||||||
\(194\) | −462019. | −0.00454311 | ||||||||
\(195\) | 1.48116e7 | 0.143047 | ||||||||
\(196\) | −1.05397e8 | −0.999844 | ||||||||
\(197\) | 4.25981e7 | 0.396971 | 0.198485 | − | 0.980104i | \(-0.436398\pi\) | ||||
0.198485 | + | 0.980104i | \(0.436398\pi\) | |||||||
\(198\) | 1.37663e6i | 0.0126035i | ||||||||
\(199\) | − | 8.23772e7i | − | 0.741006i | −0.928831 | − | 0.370503i | \(-0.879185\pi\) | ||
0.928831 | − | 0.370503i | \(-0.120815\pi\) | |||||||
\(200\) | − | 823381.i | − | 0.00727773i | ||||||
\(201\) | −1.31624e7 | −0.114327 | ||||||||
\(202\) | − | 418315.i | − | 0.00357087i | ||||||
\(203\) | 1.48050e6i | 0.0124215i | ||||||||
\(204\) | − | 2.18414e7i | − | 0.180126i | ||||||
\(205\) | − | 9.37544e7i | − | 0.760070i | ||||||
\(206\) | −1.32332e6 | −0.0105470 | ||||||||
\(207\) | 1.29927e8i | 1.01813i | ||||||||
\(208\) | 1.52925e8i | 1.17830i | ||||||||
\(209\) | 1.97368e8i | 1.49542i | ||||||||
\(210\) | −1161.07 | −8.65148e−6 | ||||||||
\(211\) | −4.55502e7 | −0.333812 | −0.166906 | − | 0.985973i | \(-0.553378\pi\) | ||||
−0.166906 | + | 0.985973i | \(0.553378\pi\) | |||||||
\(212\) | 1.79359e8 | 1.29285 | ||||||||
\(213\) | −2.22821e7 | −0.157989 | ||||||||
\(214\) | 369436.i | 0.00257686i | ||||||||
\(215\) | 2.03194e8 | 1.39437 | ||||||||
\(216\) | − | 918952.i | − | 0.00620447i | ||||||
\(217\) | − | 1.03379e6i | − | 0.00686788i | ||||||
\(218\) | 1.56438e6 | 0.0102269 | ||||||||
\(219\) | 3.51706e7 | 0.226269 | ||||||||
\(220\) | 1.57519e8i | 0.997361i | ||||||||
\(221\) | −2.26547e8 | −1.41184 | ||||||||
\(222\) | 234166. | + | 102872.i | 0.00143644 | + | 0.000631050i | ||||
\(223\) | 2.06659e8 | 1.24792 | 0.623960 | − | 0.781456i | \(-0.285523\pi\) | ||||
0.623960 | + | 0.781456i | \(0.285523\pi\) | |||||||
\(224\) | − | 35969.5i | − | 0.000213829i | ||||||
\(225\) | −5.82532e7 | −0.340942 | ||||||||
\(226\) | −721064. | −0.00415522 | ||||||||
\(227\) | 5.65625e7i | 0.320951i | 0.987040 | + | 0.160475i | \(0.0513027\pi\) | ||||
−0.987040 | + | 0.160475i | \(0.948697\pi\) | |||||||
\(228\) | − | 3.25590e7i | − | 0.181928i | ||||||
\(229\) | 1.45433e8 | 0.800276 | 0.400138 | − | 0.916455i | \(-0.368962\pi\) | ||||
0.400138 | + | 0.916455i | \(0.368962\pi\) | |||||||
\(230\) | − | 1.61811e6i | − | 0.00876919i | ||||||
\(231\) | −237995. | −0.00127035 | ||||||||
\(232\) | 7.21312e6 | 0.0379241 | ||||||||
\(233\) | −1.53386e8 | −0.794401 | −0.397200 | − | 0.917732i | \(-0.630018\pi\) | ||||
−0.397200 | + | 0.917732i | \(0.630018\pi\) | |||||||
\(234\) | −2.35554e6 | −0.0120181 | ||||||||
\(235\) | − | 1.32100e8i | − | 0.663998i | ||||||
\(236\) | 1.32094e8i | 0.654169i | ||||||||
\(237\) | 3.08699e7i | 0.150632i | ||||||||
\(238\) | 17758.8 | 8.53877e−5 | ||||||||
\(239\) | 8.98230e7i | 0.425594i | 0.977096 | + | 0.212797i | \(0.0682572\pi\) | ||||
−0.977096 | + | 0.212797i | \(0.931743\pi\) | |||||||
\(240\) | − | 2.59824e7i | − | 0.121322i | ||||||
\(241\) | − | 2.90622e7i | − | 0.133742i | −0.997762 | − | 0.0668711i | \(-0.978698\pi\) | ||
0.997762 | − | 0.0668711i | \(-0.0213016\pi\) | |||||||
\(242\) | − | 1.21426e6i | − | 0.00550754i | ||||||
\(243\) | −9.78940e7 | −0.437657 | ||||||||
\(244\) | − | 1.20856e8i | − | 0.532603i | ||||||
\(245\) | − | 1.85741e8i | − | 0.806912i | ||||||
\(246\) | − | 345055.i | − | 0.00147780i | ||||||
\(247\) | −3.37713e8 | −1.42597 | ||||||||
\(248\) | −5.03670e6 | −0.0209684 | ||||||||
\(249\) | −2.22585e7 | −0.0913690 | ||||||||
\(250\) | 2.80522e6 | 0.0113547 | ||||||||
\(251\) | 1.97276e7i | 0.0787437i | 0.999225 | + | 0.0393718i | \(0.0125357\pi\) | ||||
−0.999225 | + | 0.0393718i | \(0.987464\pi\) | |||||||
\(252\) | −1.69650e6 | −0.00667810 | ||||||||
\(253\) | − | 3.31677e8i | − | 1.28764i | ||||||
\(254\) | 3.38308e6i | 0.0129537i | ||||||||
\(255\) | 3.84910e7 | 0.145368 | ||||||||
\(256\) | 2.68143e8 | 0.998912 | ||||||||
\(257\) | − | 4.16128e8i | − | 1.52919i | −0.644511 | − | 0.764595i | \(-0.722939\pi\) | ||
0.644511 | − | 0.764595i | \(-0.277061\pi\) | |||||||
\(258\) | 747837. | 0.00271105 | ||||||||
\(259\) | 768496. | − | 1.74931e6i | 0.00274848 | − | 0.00625628i | ||||
\(260\) | −2.69528e8 | −0.951036 | ||||||||
\(261\) | − | 5.10320e8i | − | 1.77664i | ||||||
\(262\) | 4.85078e6 | 0.0166631 | ||||||||
\(263\) | 1.77175e8 | 0.600563 | 0.300281 | − | 0.953851i | \(-0.402919\pi\) | ||||
0.300281 | + | 0.953851i | \(0.402919\pi\) | |||||||
\(264\) | 1.15953e6i | 0.00387853i | ||||||||
\(265\) | 3.16084e8i | 1.04338i | ||||||||
\(266\) | 26473.1 | 8.62422e−5 | ||||||||
\(267\) | 7.02555e7i | 0.225887i | ||||||||
\(268\) | 2.39519e8 | 0.760094 | ||||||||
\(269\) | −2.79188e8 | −0.874508 | −0.437254 | − | 0.899338i | \(-0.644049\pi\) | ||||
−0.437254 | + | 0.899338i | \(0.644049\pi\) | |||||||
\(270\) | 809688. | 0.00250348 | ||||||||
\(271\) | −3.00313e8 | −0.916605 | −0.458302 | − | 0.888796i | \(-0.651542\pi\) | ||||
−0.458302 | + | 0.888796i | \(0.651542\pi\) | |||||||
\(272\) | 3.97408e8i | 1.19742i | ||||||||
\(273\) | − | 407229.i | − | 0.00121135i | ||||||
\(274\) | − | 4.20722e6i | − | 0.0123557i | ||||||
\(275\) | 1.48708e8 | 0.431192 | ||||||||
\(276\) | 5.47156e7i | 0.156650i | ||||||||
\(277\) | 2.31585e7i | 0.0654682i | 0.999464 | + | 0.0327341i | \(0.0104215\pi\) | ||||
−0.999464 | + | 0.0327341i | \(0.989579\pi\) | |||||||
\(278\) | − | 6.43836e6i | − | 0.0179729i | ||||||
\(279\) | 3.56340e8i | 0.982314i | ||||||||
\(280\) | 42258.5 | 0.000115043 | ||||||||
\(281\) | − | 3.91160e8i | − | 1.05168i | −0.850585 | − | 0.525838i | \(-0.823752\pi\) | ||
0.850585 | − | 0.525838i | \(-0.176248\pi\) | |||||||
\(282\) | − | 486183.i | − | 0.00129101i | ||||||
\(283\) | − | 2.84253e8i | − | 0.745508i | −0.927930 | − | 0.372754i | \(-0.878413\pi\) | ||
0.927930 | − | 0.372754i | \(-0.121587\pi\) | |||||||
\(284\) | 4.05470e8 | 1.05037 | ||||||||
\(285\) | 5.73786e7 | 0.146823 | ||||||||
\(286\) | 6.01319e6 | 0.0151993 | ||||||||
\(287\) | −2.57768e6 | −0.00643640 | ||||||||
\(288\) | 1.23985e7i | 0.0305840i | ||||||||
\(289\) | −1.78391e8 | −0.434742 | ||||||||
\(290\) | 6.35548e6i | 0.0153023i | ||||||||
\(291\) | 2.75323e7i | 0.0654963i | ||||||||
\(292\) | −6.40004e8 | −1.50433 | ||||||||
\(293\) | −2.97152e8 | −0.690147 | −0.345074 | − | 0.938576i | \(-0.612146\pi\) | ||||
−0.345074 | + | 0.938576i | \(0.612146\pi\) | |||||||
\(294\) | − | 683602.i | − | 0.00156887i | ||||||
\(295\) | −2.32788e8 | −0.527938 | ||||||||
\(296\) | −8.52275e6 | − | 3.74417e6i | −0.0191011 | − | 0.00839140i | ||||
\(297\) | 1.65969e8 | 0.367603 | ||||||||
\(298\) | − | 6.05358e6i | − | 0.0132512i | ||||||
\(299\) | 5.67529e8 | 1.22783 | ||||||||
\(300\) | −2.45318e7 | −0.0524572 | ||||||||
\(301\) | − | 5.58662e6i | − | 0.0118077i | ||||||
\(302\) | 4.02595e6i | 0.00841094i | ||||||||
\(303\) | −2.49279e7 | −0.0514798 | ||||||||
\(304\) | 5.92416e8i | 1.20940i | ||||||||
\(305\) | 2.12984e8 | 0.429830 | ||||||||
\(306\) | −6.12136e6 | −0.0122130 | ||||||||
\(307\) | 9.19105e8 | 1.81293 | 0.906465 | − | 0.422281i | \(-0.138771\pi\) | ||||
0.906465 | + | 0.422281i | \(0.138771\pi\) | |||||||
\(308\) | 4.33082e6 | 0.00844583 | ||||||||
\(309\) | 7.88584e7i | 0.152052i | ||||||||
\(310\) | − | 4.43783e6i | − | 0.00846067i | ||||||
\(311\) | 5.11798e8i | 0.964800i | 0.875951 | + | 0.482400i | \(0.160235\pi\) | ||||
−0.875951 | + | 0.482400i | \(0.839765\pi\) | |||||||
\(312\) | −1.98405e6 | −0.00369839 | ||||||||
\(313\) | − | 6.11738e8i | − | 1.12761i | −0.825906 | − | 0.563807i | \(-0.809336\pi\) | ||
0.825906 | − | 0.563807i | \(-0.190664\pi\) | |||||||
\(314\) | 6.26287e6i | 0.0114161i | ||||||||
\(315\) | − | 2.98974e6i | − | 0.00538948i | ||||||
\(316\) | − | 5.61744e8i | − | 1.00146i | ||||||
\(317\) | 2.59966e7 | 0.0458362 | 0.0229181 | − | 0.999737i | \(-0.492704\pi\) | ||||
0.0229181 | + | 0.999737i | \(0.492704\pi\) | |||||||
\(318\) | 1.16332e6i | 0.00202863i | ||||||||
\(319\) | 1.30274e9i | 2.24693i | ||||||||
\(320\) | 4.72702e8i | 0.806423i | ||||||||
\(321\) | 2.20152e7 | 0.0371496 | ||||||||
\(322\) | −44488.2 | −7.42591e−5 | ||||||||
\(323\) | −8.77621e8 | −1.44910 | ||||||||
\(324\) | 5.70928e8 | 0.932553 | ||||||||
\(325\) | 2.54452e8i | 0.411164i | ||||||||
\(326\) | −3.19708e6 | −0.00511083 | ||||||||
\(327\) | − | 9.32233e7i | − | 0.147437i | ||||||
\(328\) | 1.25587e7i | 0.0196510i | ||||||||
\(329\) | −3.63197e6 | −0.00562285 | ||||||||
\(330\) | −1.02166e6 | −0.00156498 | ||||||||
\(331\) | 2.55538e8i | 0.387308i | 0.981070 | + | 0.193654i | \(0.0620340\pi\) | ||||
−0.981070 | + | 0.193654i | \(0.937966\pi\) | |||||||
\(332\) | 4.05041e8 | 0.607458 | ||||||||
\(333\) | −2.64896e8 | + | 6.02975e8i | −0.393115 | + | 0.894838i | ||||
\(334\) | 3.05334e6 | 0.00448397 | ||||||||
\(335\) | 4.22102e8i | 0.613424i | ||||||||
\(336\) | −714360. | −0.00102738 | ||||||||
\(337\) | 6.22166e8 | 0.885526 | 0.442763 | − | 0.896639i | \(-0.353998\pi\) | ||||
0.442763 | + | 0.896639i | \(0.353998\pi\) | |||||||
\(338\) | 2.88313e6i | 0.00406121i | ||||||||
\(339\) | 4.29691e7i | 0.0599042i | ||||||||
\(340\) | −7.00426e8 | −0.966465 | ||||||||
\(341\) | − | 9.09662e8i | − | 1.24234i | ||||||
\(342\) | −9.12512e6 | −0.0123352 | ||||||||
\(343\) | −1.02138e7 | −0.0136665 | ||||||||
\(344\) | −2.72185e7 | −0.0360503 | ||||||||
\(345\) | −9.64250e7 | −0.126422 | ||||||||
\(346\) | 8.78126e6i | 0.0113970i | ||||||||
\(347\) | − | 1.00916e9i | − | 1.29660i | −0.761383 | − | 0.648302i | \(-0.775479\pi\) | ||
0.761383 | − | 0.648302i | \(-0.224521\pi\) | |||||||
\(348\) | − | 2.14908e8i | − | 0.273354i | ||||||
\(349\) | 2.43348e8 | 0.306435 | 0.153218 | − | 0.988192i | \(-0.451036\pi\) | ||||
0.153218 | + | 0.988192i | \(0.451036\pi\) | |||||||
\(350\) | − | 19946.4i | − | 2.48671e-5i | ||||||
\(351\) | 2.83987e8i | 0.350529i | ||||||||
\(352\) | − | 3.16507e7i | − | 0.0386798i | ||||||
\(353\) | − | 6.70861e8i | − | 0.811748i | −0.913929 | − | 0.405874i | \(-0.866967\pi\) | ||
0.913929 | − | 0.405874i | \(-0.133033\pi\) | |||||||
\(354\) | −856754. | −0.00102647 | ||||||||
\(355\) | 7.14557e8i | 0.847691i | ||||||||
\(356\) | − | 1.27845e9i | − | 1.50179i | ||||||
\(357\) | − | 1.05827e6i | − | 0.00123100i | ||||||
\(358\) | 1.20743e7 | 0.0139082 | ||||||||
\(359\) | −9.91138e8 | −1.13059 | −0.565293 | − | 0.824890i | \(-0.691237\pi\) | ||||
−0.565293 | + | 0.824890i | \(0.691237\pi\) | |||||||
\(360\) | −1.45662e7 | −0.0164547 | ||||||||
\(361\) | −4.14398e8 | −0.463599 | ||||||||
\(362\) | − | 7.11716e6i | − | 0.00788545i | ||||||
\(363\) | −7.23592e7 | −0.0794000 | ||||||||
\(364\) | 7.41040e6i | 0.00805354i | ||||||||
\(365\) | − | 1.12788e9i | − | 1.21405i | ||||||
\(366\) | 783867. | 0.000835716 | ||||||||
\(367\) | 2.69313e8 | 0.284397 | 0.142199 | − | 0.989838i | \(-0.454583\pi\) | ||||
0.142199 | + | 0.989838i | \(0.454583\pi\) | |||||||
\(368\) | − | 9.95558e8i | − | 1.04136i | ||||||
\(369\) | 8.88512e8 | 0.920600 | ||||||||
\(370\) | 3.29899e6 | − | 7.50940e6i | 0.00338590 | − | 0.00770724i | ||||
\(371\) | 8.69042e6 | 0.00883552 | ||||||||
\(372\) | 1.50063e8i | 0.151138i | ||||||||
\(373\) | 4.97436e8 | 0.496313 | 0.248157 | − | 0.968720i | \(-0.420175\pi\) | ||||
0.248157 | + | 0.968720i | \(0.420175\pi\) | |||||||
\(374\) | 1.56266e7 | 0.0154459 | ||||||||
\(375\) | − | 1.67167e8i | − | 0.163697i | ||||||
\(376\) | 1.76952e7i | 0.0171672i | ||||||||
\(377\) | −2.22910e9 | −2.14257 | ||||||||
\(378\) | − | 22261.6i | − | 2.11999e-5i | ||||||
\(379\) | 4.95355e8 | 0.467390 | 0.233695 | − | 0.972310i | \(-0.424918\pi\) | ||||
0.233695 | + | 0.972310i | \(0.424918\pi\) | |||||||
\(380\) | −1.04413e9 | −0.976136 | ||||||||
\(381\) | 2.01602e8 | 0.186749 | ||||||||
\(382\) | −5.08987e6 | −0.00467180 | ||||||||
\(383\) | 2.85654e7i | 0.0259803i | 0.999916 | + | 0.0129901i | \(0.00413501\pi\) | ||||
−0.999916 | + | 0.0129901i | \(0.995865\pi\) | |||||||
\(384\) | 6.96160e6i | 0.00627408i | ||||||||
\(385\) | 7.63218e6i | 0.00681610i | ||||||||
\(386\) | −4.35998e6 | −0.00385860 | ||||||||
\(387\) | 1.92567e9i | 1.68886i | ||||||||
\(388\) | − | 5.01008e8i | − | 0.435446i | ||||||
\(389\) | − | 6.56407e7i | − | 0.0565392i | −0.999600 | − | 0.0282696i | \(-0.991000\pi\) | ||
0.999600 | − | 0.0282696i | \(-0.00899970\pi\) | |||||||
\(390\) | − | 1.74815e6i | − | 0.00149229i | ||||||
\(391\) | 1.47485e9 | 1.24775 | ||||||||
\(392\) | 2.48805e7i | 0.0208621i | ||||||||
\(393\) | − | 2.89064e8i | − | 0.240226i | ||||||
\(394\) | − | 5.02768e6i | − | 0.00414124i | ||||||
\(395\) | 9.89958e8 | 0.808215 | ||||||||
\(396\) | −1.49280e9 | −1.20801 | ||||||||
\(397\) | −1.87721e9 | −1.50573 | −0.752864 | − | 0.658176i | \(-0.771328\pi\) | ||||
−0.752864 | + | 0.658176i | \(0.771328\pi\) | |||||||
\(398\) | −9.72265e6 | −0.00773026 | ||||||||
\(399\) | − | 1.57757e6i | − | 0.00124332i | ||||||
\(400\) | 4.46360e8 | 0.348719 | ||||||||
\(401\) | 1.98076e8i | 0.153401i | 0.997054 | + | 0.0767003i | \(0.0244384\pi\) | ||||
−0.997054 | + | 0.0767003i | \(0.975562\pi\) | |||||||
\(402\) | 1.55351e6i | 0.00119268i | ||||||||
\(403\) | 1.55651e9 | 1.18463 | ||||||||
\(404\) | 4.53617e8 | 0.342259 | ||||||||
\(405\) | 1.00614e9i | 0.752605i | ||||||||
\(406\) | 174738. | 0.000129582 | ||||||||
\(407\) | 6.76223e8 | − | 1.53927e9i | 0.497175 | − | 1.13171i | ||||
\(408\) | −5.15599e6 | −0.00375838 | ||||||||
\(409\) | − | 3.48048e8i | − | 0.251540i | −0.992059 | − | 0.125770i | \(-0.959860\pi\) | ||
0.992059 | − | 0.125770i | \(-0.0401402\pi\) | |||||||
\(410\) | −1.10655e7 | −0.00792913 | ||||||||
\(411\) | −2.50713e8 | −0.178128 | ||||||||
\(412\) | − | 1.43500e9i | − | 1.01091i | ||||||
\(413\) | 6.40027e6i | 0.00447068i | ||||||||
\(414\) | 1.53348e7 | 0.0106213 | ||||||||
\(415\) | 7.13803e8i | 0.490241i | ||||||||
\(416\) | 5.41571e7 | 0.0368832 | ||||||||
\(417\) | −3.83670e8 | −0.259109 | ||||||||
\(418\) | 2.32945e7 | 0.0156004 | ||||||||
\(419\) | −2.10303e8 | −0.139668 | −0.0698339 | − | 0.997559i | \(-0.522247\pi\) | ||||
−0.0698339 | + | 0.997559i | \(0.522247\pi\) | |||||||
\(420\) | − | 1.25905e6i | − | 0.000829222i | ||||||
\(421\) | 2.42616e9i | 1.58465i | 0.610102 | + | 0.792323i | \(0.291128\pi\) | ||||
−0.610102 | + | 0.792323i | \(0.708872\pi\) | |||||||
\(422\) | 5.37610e6i | 0.00348236i | ||||||||
\(423\) | 1.25192e9 | 0.804237 | ||||||||
\(424\) | − | 4.23404e7i | − | 0.0269758i | ||||||
\(425\) | 6.61249e8i | 0.417834i | ||||||||
\(426\) | 2.62986e6i | 0.00164816i | ||||||||
\(427\) | − | 5.85578e6i | − | 0.00363988i | ||||||
\(428\) | −4.00613e8 | −0.246985 | ||||||||
\(429\) | − | 3.58333e8i | − | 0.219122i | ||||||
\(430\) | − | 2.39822e7i | − | 0.0145462i | ||||||
\(431\) | 5.19659e8i | 0.312643i | 0.987706 | + | 0.156321i | \(0.0499635\pi\) | ||||
−0.987706 | + | 0.156321i | \(0.950036\pi\) | |||||||
\(432\) | 4.98170e8 | 0.297293 | ||||||||
\(433\) | −2.71549e9 | −1.60746 | −0.803730 | − | 0.594995i | \(-0.797154\pi\) | ||||
−0.803730 | + | 0.594995i | \(0.797154\pi\) | |||||||
\(434\) | −122014. | −7.16465e−5 | ||||||||
\(435\) | 3.78731e8 | 0.220607 | ||||||||
\(436\) | 1.69640e9i | 0.980222i | ||||||||
\(437\) | 2.19855e9 | 1.26024 | ||||||||
\(438\) | − | 4.15104e6i | − | 0.00236047i | ||||||
\(439\) | 2.25261e9i | 1.27075i | 0.772205 | + | 0.635374i | \(0.219154\pi\) | ||||
−0.772205 | + | 0.635374i | \(0.780846\pi\) | |||||||
\(440\) | 3.71846e7 | 0.0208103 | ||||||||
\(441\) | 1.76027e9 | 0.977335 | ||||||||
\(442\) | 2.67384e7i | 0.0147285i | ||||||||
\(443\) | −1.57118e9 | −0.858645 | −0.429322 | − | 0.903151i | \(-0.641248\pi\) | ||||
−0.429322 | + | 0.903151i | \(0.641248\pi\) | |||||||
\(444\) | −1.11554e8 | + | 2.53927e8i | −0.0604845 | + | 0.137679i | ||||
\(445\) | 2.25300e9 | 1.21200 | ||||||||
\(446\) | − | 2.43911e7i | − | 0.0130185i | ||||||
\(447\) | −3.60741e8 | −0.191038 | ||||||||
\(448\) | 1.29965e7 | 0.00682893 | ||||||||
\(449\) | 2.88058e9i | 1.50182i | 0.660405 | + | 0.750909i | \(0.270385\pi\) | ||||
−0.660405 | + | 0.750909i | \(0.729615\pi\) | |||||||
\(450\) | 6.87539e6i | 0.00355675i | ||||||||
\(451\) | −2.26818e9 | −1.16429 | ||||||||
\(452\) | − | 7.81914e8i | − | 0.398267i | ||||||
\(453\) | 2.39912e8 | 0.121257 | ||||||||
\(454\) | 6.67584e6 | 0.00334819 | ||||||||
\(455\) | −1.30593e7 | −0.00649951 | ||||||||
\(456\) | −7.68603e6 | −0.00379599 | ||||||||
\(457\) | − | 1.17420e9i | − | 0.575486i | −0.957708 | − | 0.287743i | \(-0.907095\pi\) | ||
0.957708 | − | 0.287743i | \(-0.0929049\pi\) | |||||||
\(458\) | − | 1.71649e7i | − | 0.00834857i | ||||||
\(459\) | 7.38002e8i | 0.356216i | ||||||||
\(460\) | 1.75466e9 | 0.840504 | ||||||||
\(461\) | − | 3.28279e9i | − | 1.56059i | −0.625409 | − | 0.780297i | \(-0.715068\pi\) | ||
0.625409 | − | 0.780297i | \(-0.284932\pi\) | |||||||
\(462\) | 28089.5i | 1.32525e-5i | ||||||||
\(463\) | − | 6.93602e8i | − | 0.324771i | −0.986727 | − | 0.162385i | \(-0.948081\pi\) | ||
0.986727 | − | 0.162385i | \(-0.0519188\pi\) | |||||||
\(464\) | 3.91028e9i | 1.81717i | ||||||||
\(465\) | −2.64456e8 | −0.121974 | ||||||||
\(466\) | 1.81035e7i | 0.00828728i | ||||||||
\(467\) | 8.58502e8i | 0.390061i | 0.980797 | + | 0.195030i | \(0.0624805\pi\) | ||||
−0.980797 | + | 0.195030i | \(0.937519\pi\) | |||||||
\(468\) | − | 2.55432e9i | − | 1.15190i | ||||||
\(469\) | 1.16053e7 | 0.00519459 | ||||||||
\(470\) | −1.55913e7 | −0.00692690 | ||||||||
\(471\) | 3.73212e8 | 0.164582 | ||||||||
\(472\) | 3.11826e7 | 0.0136495 | ||||||||
\(473\) | − | 4.91584e9i | − | 2.13591i | ||||||
\(474\) | 3.64345e6 | 0.00157141 | ||||||||
\(475\) | 9.85725e8i | 0.422015i | ||||||||
\(476\) | 1.92575e7i | 0.00818419i | ||||||||
\(477\) | −2.99553e9 | −1.26375 | ||||||||
\(478\) | 1.06014e7 | 0.00443984 | ||||||||
\(479\) | 1.00841e9i | 0.419240i | 0.977783 | + | 0.209620i | \(0.0672227\pi\) | ||||
−0.977783 | + | 0.209620i | \(0.932777\pi\) | |||||||
\(480\) | −9.20146e6 | −0.00379763 | ||||||||
\(481\) | 2.63382e9 | + | 1.15708e9i | 1.07914 | + | 0.474082i | ||||
\(482\) | −3.43009e6 | −0.00139521 | ||||||||
\(483\) | 2.65111e6i | 0.00107056i | ||||||||
\(484\) | 1.31673e9 | 0.527883 | ||||||||
\(485\) | 8.82924e8 | 0.351421 | ||||||||
\(486\) | 1.15540e7i | 0.00456569i | ||||||||
\(487\) | − | 4.51679e9i | − | 1.77206i | −0.463629 | − | 0.886030i | \(-0.653453\pi\) | ||
0.463629 | − | 0.886030i | \(-0.346547\pi\) | |||||||
\(488\) | −2.85298e7 | −0.0111130 | ||||||||
\(489\) | 1.90518e8i | 0.0736809i | ||||||||
\(490\) | −2.19222e7 | −0.00841780 | ||||||||
\(491\) | −4.14586e9 | −1.58063 | −0.790313 | − | 0.612704i | \(-0.790082\pi\) | ||||
−0.790313 | + | 0.612704i | \(0.790082\pi\) | |||||||
\(492\) | 3.74174e8 | 0.141643 | ||||||||
\(493\) | −5.79279e9 | −2.17733 | ||||||||
\(494\) | 3.98589e7i | 0.0148758i | ||||||||
\(495\) | − | 2.63076e9i | − | 0.974908i | ||||||
\(496\) | − | 2.73043e9i | − | 1.00472i | ||||||
\(497\) | 1.96460e7 | 0.00717840 | ||||||||
\(498\) | 2.62708e6i | 0.000953172i | ||||||||
\(499\) | − | 1.81428e9i | − | 0.653661i | −0.945083 | − | 0.326831i | \(-0.894019\pi\) | ||
0.945083 | − | 0.326831i | \(-0.105981\pi\) | |||||||
\(500\) | 3.04195e9i | 1.08832i | ||||||||
\(501\) | − | 1.81952e8i | − | 0.0646436i | ||||||
\(502\) | 2.32837e6 | 0.000821463 | ||||||||
\(503\) | − | 1.73846e9i | − | 0.609085i | −0.952499 | − | 0.304542i | \(-0.901496\pi\) | ||
0.952499 | − | 0.304542i | \(-0.0985035\pi\) | |||||||
\(504\) | 400485.i | 0.000139341i | ||||||||
\(505\) | 7.99406e8i | 0.276215i | ||||||||
\(506\) | −3.91465e7 | −0.0134328 | ||||||||
\(507\) | 1.71809e8 | 0.0585490 | ||||||||
\(508\) | −3.66858e9 | −1.24158 | ||||||||
\(509\) | 4.32091e9 | 1.45232 | 0.726160 | − | 0.687525i | \(-0.241303\pi\) | ||||
0.726160 | + | 0.687525i | \(0.241303\pi\) | |||||||
\(510\) | − | 4.54294e6i | − | 0.00151650i | ||||||
\(511\) | −3.10098e7 | −0.0102808 | ||||||||
\(512\) | − | 1.58343e8i | − | 0.0521379i | ||||||
\(513\) | 1.10014e9i | 0.359780i | ||||||||
\(514\) | −4.91139e7 | −0.0159527 | ||||||||
\(515\) | 2.52889e9 | 0.815839 | ||||||||
\(516\) | 8.10947e8i | 0.259847i | ||||||||
\(517\) | −3.19588e9 | −1.01712 | ||||||||
\(518\) | −206463. | − | 90702.4i | −6.52663e−5 | − | 2.86724e-5i | ||||
\(519\) | 5.23287e8 | 0.164306 | ||||||||
\(520\) | 6.36260e7i | 0.0198437i | ||||||||
\(521\) | 3.09896e9 | 0.960030 | 0.480015 | − | 0.877260i | \(-0.340631\pi\) | ||||
0.480015 | + | 0.877260i | \(0.340631\pi\) | |||||||
\(522\) | −6.02309e7 | −0.0185342 | ||||||||
\(523\) | − | 1.42280e9i | − | 0.434898i | −0.976072 | − | 0.217449i | \(-0.930226\pi\) | ||
0.976072 | − | 0.217449i | \(-0.0697737\pi\) | |||||||
\(524\) | 5.26013e9i | 1.59712i | ||||||||
\(525\) | −1.18863e6 | −0.000358500 | ||||||||
\(526\) | − | 2.09113e7i | − | 0.00626514i | ||||||
\(527\) | 4.04492e9 | 1.20385 | ||||||||
\(528\) | −6.28587e8 | −0.185843 | ||||||||
\(529\) | −2.89853e8 | −0.0851300 | ||||||||
\(530\) | 3.73061e7 | 0.0108847 | ||||||||
\(531\) | − | 2.20613e9i | − | 0.639442i | ||||||
\(532\) | 2.87072e7i | 0.00826609i | ||||||||
\(533\) | − | 3.88106e9i | − | 1.11021i | ||||||
\(534\) | 8.29197e6 | 0.00235648 | ||||||||
\(535\) | − | 7.05998e8i | − | 0.199326i | ||||||
\(536\) | − | 5.65419e7i | − | 0.0158596i | ||||||
\(537\) | − | 7.19524e8i | − | 0.200510i | ||||||
\(538\) | 3.29514e7i | 0.00912297i | ||||||||
\(539\) | −4.49359e9 | −1.23604 | ||||||||
\(540\) | 8.78017e8i | 0.239952i | ||||||||
\(541\) | − | 3.02485e9i | − | 0.821323i | −0.911788 | − | 0.410661i | \(-0.865298\pi\) | ||
0.911788 | − | 0.410661i | \(-0.134702\pi\) | |||||||
\(542\) | 3.54448e7i | 0.00956213i | ||||||||
\(543\) | −4.24121e8 | −0.113682 | ||||||||
\(544\) | 1.40739e8 | 0.0374815 | ||||||||
\(545\) | −2.98955e9 | −0.791076 | ||||||||
\(546\) | −48063.6 | −1.26369e−5 | ||||||||
\(547\) | 2.82964e9i | 0.739223i | 0.929186 | + | 0.369611i | \(0.120509\pi\) | ||||
−0.929186 | + | 0.369611i | \(0.879491\pi\) | |||||||
\(548\) | 4.56226e9 | 1.18426 | ||||||||
\(549\) | 2.01845e9i | 0.520613i | ||||||||
\(550\) | − | 1.75514e7i | − | 0.00449824i | ||||||
\(551\) | −8.63532e9 | −2.19911 | ||||||||
\(552\) | 1.29164e7 | 0.00326855 | ||||||||
\(553\) | − | 2.72179e7i | − | 0.00684411i | ||||||
\(554\) | 2.73330e6 | 0.000682972 | ||||||||
\(555\) | −4.47494e8 | − | 1.96591e8i | −0.111112 | − | 0.0488133i | ||||
\(556\) | 6.98170e9 | 1.72266 | ||||||||
\(557\) | 5.54519e9i | 1.35964i | 0.733380 | + | 0.679819i | \(0.237942\pi\) | ||||
−0.733380 | + | 0.679819i | \(0.762058\pi\) | |||||||
\(558\) | 4.20574e7 | 0.0102476 | ||||||||
\(559\) | 8.41142e9 | 2.03671 | ||||||||
\(560\) | 2.29086e7i | 0.00551240i | ||||||||
\(561\) | − | 9.31206e8i | − | 0.222677i | ||||||
\(562\) | −4.61670e7 | −0.0109712 | ||||||||
\(563\) | 1.10986e9i | 0.262113i | 0.991375 | + | 0.131057i | \(0.0418370\pi\) | ||||
−0.991375 | + | 0.131057i | \(0.958163\pi\) | |||||||
\(564\) | 5.27212e8 | 0.123740 | ||||||||
\(565\) | 1.37796e9 | 0.321416 | ||||||||
\(566\) | −3.35492e7 | −0.00777723 | ||||||||
\(567\) | 2.76629e7 | 0.00637319 | ||||||||
\(568\) | − | 9.57170e7i | − | 0.0219164i | ||||||
\(569\) | 6.13313e9i | 1.39569i | 0.716248 | + | 0.697845i | \(0.245858\pi\) | ||||
−0.716248 | + | 0.697845i | \(0.754142\pi\) | |||||||
\(570\) | − | 6.77216e6i | − | 0.00153167i | ||||||
\(571\) | −5.69940e9 | −1.28116 | −0.640579 | − | 0.767892i | \(-0.721306\pi\) | ||||
−0.640579 | + | 0.767892i | \(0.721306\pi\) | |||||||
\(572\) | 6.52064e9i | 1.45681i | ||||||||
\(573\) | 3.03312e8i | 0.0673516i | ||||||||
\(574\) | 304234.i | 6.71453e-5i | ||||||||
\(575\) | − | 1.65652e9i | − | 0.363377i | ||||||
\(576\) | −4.47980e9 | −0.976743 | ||||||||
\(577\) | 5.45080e9i | 1.18126i | 0.806943 | + | 0.590629i | \(0.201120\pi\) | ||||
−0.806943 | + | 0.590629i | \(0.798880\pi\) | |||||||
\(578\) | 2.10548e7i | 0.00453528i | ||||||||
\(579\) | 2.59817e8i | 0.0556279i | ||||||||
\(580\) | −6.89182e9 | −1.46668 | ||||||||
\(581\) | 1.96253e7 | 0.00415145 | ||||||||
\(582\) | 3.24952e6 | 0.000683265 | ||||||||
\(583\) | 7.64696e9 | 1.59827 | ||||||||
\(584\) | 1.51082e8i | 0.0313883i | ||||||||
\(585\) | 4.50146e9 | 0.929626 | ||||||||
\(586\) | 3.50716e7i | 0.00719969i | ||||||||
\(587\) | − | 3.59960e9i | − | 0.734549i | −0.930113 | − | 0.367274i | \(-0.880291\pi\) | ||
0.930113 | − | 0.367274i | \(-0.119709\pi\) | |||||||
\(588\) | 7.41291e8 | 0.150372 | ||||||||
\(589\) | 6.02977e9 | 1.21590 | ||||||||
\(590\) | 2.74750e7i | 0.00550751i | ||||||||
\(591\) | −2.99606e8 | −0.0597027 | ||||||||
\(592\) | 2.02974e9 | − | 4.62024e9i | 0.402082 | − | 0.915247i | ||||
\(593\) | 3.95945e9 | 0.779729 | 0.389865 | − | 0.920872i | \(-0.372522\pi\) | ||||
0.389865 | + | 0.920872i | \(0.372522\pi\) | |||||||
\(594\) | − | 1.95886e7i | − | 0.00383488i | ||||||
\(595\) | −3.39374e7 | −0.00660495 | ||||||||
\(596\) | 6.56444e9 | 1.27009 | ||||||||
\(597\) | 5.79385e8i | 0.111444i | ||||||||
\(598\) | − | 6.69831e7i | − | 0.0128089i | ||||||
\(599\) | −6.41846e9 | −1.22022 | −0.610108 | − | 0.792318i | \(-0.708874\pi\) | ||||
−0.610108 | + | 0.792318i | \(0.708874\pi\) | |||||||
\(600\) | 5.79109e6i | 0.00109454i | ||||||||
\(601\) | 8.93587e8 | 0.167910 | 0.0839550 | − | 0.996470i | \(-0.473245\pi\) | ||||
0.0839550 | + | 0.996470i | \(0.473245\pi\) | |||||||
\(602\) | −659366. | −0.000123180 | ||||||||
\(603\) | −4.00027e9 | −0.742983 | ||||||||
\(604\) | −4.36570e9 | −0.806167 | ||||||||
\(605\) | 2.32047e9i | 0.426021i | ||||||||
\(606\) | 2.94214e6i | 0.000537043i | ||||||||
\(607\) | 1.01241e10i | 1.83737i | 0.394987 | + | 0.918687i | \(0.370749\pi\) | ||||
−0.394987 | + | 0.918687i | \(0.629251\pi\) | |||||||
\(608\) | 2.09799e8 | 0.0378566 | ||||||||
\(609\) | − | 1.04128e7i | − | 0.00186814i | ||||||
\(610\) | − | 2.51376e7i | − | 0.00448404i | ||||||
\(611\) | − | 5.46843e9i | − | 0.969880i | ||||||
\(612\) | − | 6.63794e9i | − | 1.17059i | ||||||
\(613\) | −4.29861e9 | −0.753730 | −0.376865 | − | 0.926268i | \(-0.622998\pi\) | ||||
−0.376865 | + | 0.926268i | \(0.622998\pi\) | |||||||
\(614\) | − | 1.08478e8i | − | 0.0189127i | ||||||
\(615\) | 6.59404e8i | 0.114311i | ||||||||
\(616\) | − | 1.02235e6i | − | 0.000176225i | ||||||
\(617\) | −2.19805e9 | −0.376738 | −0.188369 | − | 0.982098i | \(-0.560320\pi\) | ||||
−0.188369 | + | 0.982098i | \(0.560320\pi\) | |||||||
\(618\) | 9.30734e6 | 0.00158623 | ||||||||
\(619\) | −3.19748e9 | −0.541865 | −0.270932 | − | 0.962598i | \(-0.587332\pi\) | ||||
−0.270932 | + | 0.962598i | \(0.587332\pi\) | |||||||
\(620\) | 4.81234e9 | 0.810934 | ||||||||
\(621\) | − | 1.84879e9i | − | 0.309790i | ||||||
\(622\) | 6.04054e7 | 0.0100649 | ||||||||
\(623\) | − | 6.19441e7i | − | 0.0102634i | ||||||
\(624\) | − | 1.07557e9i | − | 0.177211i | ||||||
\(625\) | −3.23171e9 | −0.529483 | ||||||||
\(626\) | −7.22010e7 | −0.0117634 | ||||||||
\(627\) | − | 1.38815e9i | − | 0.224905i | ||||||
\(628\) | −6.79139e9 | −1.09421 | ||||||||
\(629\) | 6.84454e9 | + | 3.00691e9i | 1.09665 | + | 0.481773i | ||||
\(630\) | −352867. | −5.62236e−5 | ||||||||
\(631\) | − | 1.01591e10i | − | 1.60972i | −0.593463 | − | 0.804861i | \(-0.702240\pi\) | ||
0.593463 | − | 0.804861i | \(-0.297760\pi\) | |||||||
\(632\) | −1.32608e8 | −0.0208958 | ||||||||
\(633\) | 3.20369e8 | 0.0502039 | ||||||||
\(634\) | − | 3.06827e6i | − | 0.000478169i | ||||||
\(635\) | − | 6.46511e9i | − | 1.00200i | ||||||
\(636\) | −1.26149e9 | −0.194439 | ||||||||
\(637\) | − | 7.68893e9i | − | 1.17863i | ||||||
\(638\) | 1.53757e8 | 0.0234402 | ||||||||
\(639\) | −6.77187e9 | −1.02673 | ||||||||
\(640\) | 2.23249e8 | 0.0336636 | ||||||||
\(641\) | −5.17854e8 | −0.0776612 | −0.0388306 | − | 0.999246i | \(-0.512363\pi\) | ||||
−0.0388306 | + | 0.999246i | \(0.512363\pi\) | |||||||
\(642\) | − | 2.59836e6i | − | 0.000387549i | ||||||
\(643\) | − | 9.35982e9i | − | 1.38845i | −0.719760 | − | 0.694223i | \(-0.755748\pi\) | ||
0.719760 | − | 0.694223i | \(-0.244252\pi\) | |||||||
\(644\) | − | 4.82426e7i | − | 0.00711754i | ||||||
\(645\) | −1.42913e9 | −0.209707 | ||||||||
\(646\) | 1.03582e8i | 0.0151172i | ||||||||
\(647\) | 9.45516e9i | 1.37247i | 0.727378 | + | 0.686237i | \(0.240739\pi\) | ||||
−0.727378 | + | 0.686237i | \(0.759261\pi\) | |||||||
\(648\) | − | 1.34776e8i | − | 0.0194581i | ||||||
\(649\) | 5.63179e9i | 0.808705i | ||||||||
\(650\) | 3.00320e7 | 0.00428931 | ||||||||
\(651\) | 7.27096e6i | 0.00103290i | ||||||||
\(652\) | − | 3.46688e9i | − | 0.489860i | ||||||
\(653\) | 3.04622e9i | 0.428120i | 0.976820 | + | 0.214060i | \(0.0686689\pi\) | ||||
−0.976820 | + | 0.214060i | \(0.931331\pi\) | |||||||
\(654\) | −1.10028e7 | −0.00153808 | ||||||||
\(655\) | −9.26990e9 | −1.28893 | ||||||||
\(656\) | −6.80814e9 | −0.941597 | ||||||||
\(657\) | 1.06889e10 | 1.47046 | ||||||||
\(658\) | 428666.i | 5.86582e-5i | ||||||||
\(659\) | 1.28087e10 | 1.74343 | 0.871717 | − | 0.490009i | \(-0.163006\pi\) | ||||
0.871717 | + | 0.490009i | \(0.163006\pi\) | |||||||
\(660\) | − | 1.10788e9i | − | 0.149999i | ||||||
\(661\) | 2.58361e9i | 0.347954i | 0.984750 | + | 0.173977i | \(0.0556619\pi\) | ||||
−0.984750 | + | 0.173977i | \(0.944338\pi\) | |||||||
\(662\) | 3.01601e7 | 0.00404045 | ||||||||
\(663\) | 1.59337e9 | 0.212334 | ||||||||
\(664\) | − | 9.56160e7i | − | 0.0126748i | ||||||
\(665\) | −5.05905e7 | −0.00667104 | ||||||||
\(666\) | 7.11666e7 | + | 3.12645e7i | 0.00933505 | + | 0.00410102i | ||||
\(667\) | 1.45117e10 | 1.89355 | ||||||||
\(668\) | 3.31101e9i | 0.429777i | ||||||||
\(669\) | −1.45350e9 | −0.187682 | ||||||||
\(670\) | 4.98190e7 | 0.00639931 | ||||||||
\(671\) | − | 5.15268e9i | − | 0.658422i | ||||||
\(672\) | 252985.i | 3.21590e-5i | ||||||||
\(673\) | −6.95576e9 | −0.879613 | −0.439807 | − | 0.898092i | \(-0.644953\pi\) | ||||
−0.439807 | + | 0.898092i | \(0.644953\pi\) | |||||||
\(674\) | − | 7.34317e7i | − | 0.00923791i | ||||||
\(675\) | 8.28908e8 | 0.103739 | ||||||||
\(676\) | −3.12644e9 | −0.389257 | ||||||||
\(677\) | −8.39759e9 | −1.04015 | −0.520073 | − | 0.854122i | \(-0.674095\pi\) | ||||
−0.520073 | + | 0.854122i | \(0.674095\pi\) | |||||||
\(678\) | 5.07147e6 | 0.000624927 | ||||||||
\(679\) | − | 2.42751e7i | − | 0.00297589i | ||||||
\(680\) | 1.65346e8i | 0.0201656i | ||||||||
\(681\) | − | 3.97822e8i | − | 0.0482696i | ||||||
\(682\) | −1.07364e8 | −0.0129602 | ||||||||
\(683\) | − | 8.58541e9i | − | 1.03107i | −0.856868 | − | 0.515535i | \(-0.827593\pi\) | ||
0.856868 | − | 0.515535i | \(-0.172407\pi\) | |||||||
\(684\) | − | 9.89519e9i | − | 1.18230i | ||||||
\(685\) | 8.04005e9i | 0.955745i | ||||||||
\(686\) | 1.20549e6i | 0.000142570i | ||||||||
\(687\) | −1.02288e9 | −0.120358 | ||||||||
\(688\) | − | 1.47553e10i | − | 1.72738i | ||||||
\(689\) | 1.30846e10i | 1.52403i | ||||||||
\(690\) | 1.13806e7i | 0.00131885i | ||||||||
\(691\) | −2.69314e9 | −0.310517 | −0.155258 | − | 0.987874i | \(-0.549621\pi\) | ||||
−0.155258 | + | 0.987874i | \(0.549621\pi\) | |||||||
\(692\) | −9.52231e9 | −1.09237 | ||||||||
\(693\) | −7.23302e7 | −0.00825569 | ||||||||
\(694\) | −1.19107e8 | −0.0135263 | ||||||||
\(695\) | 1.23038e10i | 1.39025i | ||||||||
\(696\) | −5.07321e7 | −0.00570362 | ||||||||
\(697\) | − | 1.00858e10i | − | 1.12822i | ||||||
\(698\) | − | 2.87214e7i | − | 0.00319677i | ||||||
\(699\) | 1.07881e9 | 0.119474 | ||||||||
\(700\) | 2.16296e7 | 0.00238345 | ||||||||
\(701\) | − | 4.84603e9i | − | 0.531341i | −0.964064 | − | 0.265670i | \(-0.914407\pi\) | ||
0.964064 | − | 0.265670i | \(-0.0855933\pi\) | |||||||
\(702\) | 3.35178e7 | 0.00365676 | ||||||||
\(703\) | 1.02032e10 | + | 4.48240e9i | 1.10762 | + | 0.486594i | ||||
\(704\) | 1.14360e10 | 1.23529 | ||||||||
\(705\) | 9.29103e8i | 0.0998624i | ||||||||
\(706\) | −7.91790e7 | −0.00846825 | ||||||||
\(707\) | 2.19789e7 | 0.00233904 | ||||||||
\(708\) | − | 9.29056e8i | − | 0.0983842i | ||||||
\(709\) | 1.60424e10i | 1.69047i | 0.534398 | + | 0.845233i | \(0.320538\pi\) | ||||
−0.534398 | + | 0.845233i | \(0.679462\pi\) | |||||||
\(710\) | 8.43363e7 | 0.00884321 | ||||||||
\(711\) | 9.38184e9i | 0.978914i | ||||||||
\(712\) | −3.01796e8 | −0.0313353 | ||||||||
\(713\) | −1.01331e10 | −1.04695 | ||||||||
\(714\) | −124904. | −1.28420e−5 | ||||||||
\(715\) | −1.14913e10 | −1.17570 | ||||||||
\(716\) | 1.30933e10i | 1.33307i | ||||||||
\(717\) | − | 6.31753e8i | − | 0.0640075i | ||||||
\(718\) | 1.16980e8i | 0.0117944i | ||||||||
\(719\) | 8.33955e9 | 0.836742 | 0.418371 | − | 0.908276i | \(-0.362601\pi\) | ||||
0.418371 | + | 0.908276i | \(0.362601\pi\) | |||||||
\(720\) | − | 7.89646e9i | − | 0.788440i | ||||||
\(721\) | − | 6.95292e7i | − | 0.00690866i | ||||||
\(722\) | 4.89097e7i | 0.00483632i | ||||||||
\(723\) | 2.04403e8i | 0.0201142i | ||||||||
\(724\) | 7.71777e9 | 0.755800 | ||||||||
\(725\) | 6.50634e9i | 0.634094i | ||||||||
\(726\) | 8.54026e6i | 0.000828310i | ||||||||
\(727\) | − | 4.49456e9i | − | 0.433828i | −0.976191 | − | 0.216914i | \(-0.930401\pi\) | ||
0.976191 | − | 0.216914i | \(-0.0695991\pi\) | |||||||
\(728\) | 1.74933e6 | 0.000168040 | ||||||||
\(729\) | −9.06738e9 | −0.866833 | ||||||||
\(730\) | −1.33118e8 | −0.0126651 | ||||||||
\(731\) | 2.18589e10 | 2.06975 | ||||||||
\(732\) | 8.50018e8i | 0.0801012i | ||||||||
\(733\) | 1.73912e10 | 1.63104 | 0.815522 | − | 0.578727i | \(-0.196450\pi\) | ||||
0.815522 | + | 0.578727i | \(0.196450\pi\) | |||||||
\(734\) | − | 3.17859e7i | − | 0.00296687i | ||||||
\(735\) | 1.30637e9i | 0.121356i | ||||||||
\(736\) | −3.52569e8 | −0.0325965 | ||||||||
\(737\) | 1.02118e10 | 0.939654 | ||||||||
\(738\) | − | 1.04867e8i | − | 0.00960380i | ||||||
\(739\) | −1.46686e10 | −1.33701 | −0.668503 | − | 0.743710i | \(-0.733065\pi\) | ||||
−0.668503 | + | 0.743710i | \(0.733065\pi\) | |||||||
\(740\) | 8.14311e9 | + | 3.57739e9i | 0.738719 | + | 0.324530i | ||||
\(741\) | 2.37524e9 | 0.214459 | ||||||||
\(742\) | − | 1.02569e6i | − | 9.21732e-5i | ||||||
\(743\) | −8.50015e9 | −0.760266 | −0.380133 | − | 0.924932i | \(-0.624122\pi\) | ||||
−0.380133 | + | 0.924932i | \(0.624122\pi\) | |||||||
\(744\) | 3.54247e7 | 0.00315356 | ||||||||
\(745\) | 1.15685e10i | 1.02501i | ||||||||
\(746\) | − | 5.87103e7i | − | 0.00517760i | ||||||
\(747\) | −6.76471e9 | −0.593782 | ||||||||
\(748\) | 1.69453e10i | 1.48045i | ||||||||
\(749\) | −1.94107e7 | −0.00168793 | ||||||||
\(750\) | −1.97300e7 | −0.00170770 | ||||||||
\(751\) | 7.86967e9 | 0.677980 | 0.338990 | − | 0.940790i | \(-0.389915\pi\) | ||||
0.338990 | + | 0.940790i | \(0.389915\pi\) | |||||||
\(752\) | −9.59270e9 | −0.822580 | ||||||||
\(753\) | − | 1.38750e8i | − | 0.0118427i | ||||||
\(754\) | 2.63091e8i | 0.0223515i | ||||||||
\(755\) | − | 7.69366e9i | − | 0.650607i | ||||||
\(756\) | 2.41402e7 | 0.00203196 | ||||||||
\(757\) | 1.50730e10i | 1.26289i | 0.775422 | + | 0.631444i | \(0.217537\pi\) | ||||
−0.775422 | + | 0.631444i | \(0.782463\pi\) | |||||||
\(758\) | − | 5.84647e7i | − | 0.00487586i | ||||||
\(759\) | 2.33279e9i | 0.193655i | ||||||||
\(760\) | 2.46481e8i | 0.0203674i | ||||||||
\(761\) | −2.18794e9 | −0.179966 | −0.0899828 | − | 0.995943i | \(-0.528681\pi\) | ||||
−0.0899828 | + | 0.995943i | \(0.528681\pi\) | |||||||
\(762\) | − | 2.37943e7i | − | 0.00194818i | ||||||
\(763\) | 8.21947e7i | 0.00669897i | ||||||||
\(764\) | − | 5.51940e9i | − | 0.447780i | ||||||
\(765\) | 1.16980e10 | 0.944707 | ||||||||
\(766\) | 3.37145e6 | 0.000271029 | ||||||||
\(767\) | −9.63648e9 | −0.771143 | ||||||||
\(768\) | −1.88594e9 | −0.150232 | ||||||||
\(769\) | − | 1.90029e10i | − | 1.50687i | −0.657521 | − | 0.753436i | \(-0.728395\pi\) | ||
0.657521 | − | 0.753436i | \(-0.271605\pi\) | |||||||
\(770\) | 900794. | 7.11063e−5 | ||||||||
\(771\) | 2.92676e9i | 0.229984i | ||||||||
\(772\) | − | 4.72792e9i | − | 0.369836i | ||||||
\(773\) | −1.35216e10 | −1.05293 | −0.526466 | − | 0.850196i | \(-0.676483\pi\) | ||||
−0.526466 | + | 0.850196i | \(0.676483\pi\) | |||||||
\(774\) | 2.27279e8 | 0.0176184 | ||||||||
\(775\) | − | 4.54317e9i | − | 0.350593i | ||||||
\(776\) | −1.18270e8 | −0.00908573 | ||||||||
\(777\) | −5.40507e6 | + | 1.23034e7i | −0.000413359 | + | 0.000940919i | ||||
\(778\) | −7.74731e6 | −0.000589824 | ||||||||
\(779\) | − | 1.50349e10i | − | 1.13951i | ||||||
\(780\) | 1.89567e9 | 0.143032 | ||||||||
\(781\) | 1.72871e10 | 1.29851 | ||||||||
\(782\) | − | 1.74070e8i | − | 0.0130167i | ||||||
\(783\) | 7.26154e9i | 0.540583i | ||||||||
\(784\) | −1.34879e10 | −0.999627 | ||||||||
\(785\) | − | 1.19684e10i | − | 0.883067i | ||||||
\(786\) | −3.41170e7 | −0.00250606 | ||||||||
\(787\) | −2.36053e10 | −1.72623 | −0.863113 | − | 0.505011i | \(-0.831488\pi\) | ||||
−0.863113 | + | 0.505011i | \(0.831488\pi\) | |||||||
\(788\) | 5.45196e9 | 0.396928 | ||||||||
\(789\) | −1.24613e9 | −0.0903221 | ||||||||
\(790\) | − | 1.16841e8i | − | 0.00843139i | ||||||
\(791\) | − | 3.78857e7i | − | 0.00272181i | ||||||
\(792\) | 3.52398e8i | 0.0252055i | ||||||||
\(793\) | 8.81668e9 | 0.627840 | ||||||||
\(794\) | 2.21560e8i | 0.0157079i | ||||||||
\(795\) | − | 2.22312e9i | − | 0.156920i | ||||||
\(796\) | − | 1.05431e10i | − | 0.740925i | ||||||
\(797\) | − | 1.78368e10i | − | 1.24799i | −0.781426 | − | 0.623997i | \(-0.785508\pi\) | ||
0.781426 | − | 0.623997i | \(-0.214492\pi\) | |||||||
\(798\) | −186194. | −1.29705e−5 | ||||||||
\(799\) | − | 1.42109e10i | − | 0.985615i | ||||||
\(800\) | − | 1.58075e8i | − | 0.0109156i | ||||||
\(801\) | 2.13517e10i | 1.46798i | ||||||||
\(802\) | 2.33781e7 | 0.00160029 | ||||||||
\(803\) | −2.72865e10 | −1.85970 | ||||||||
\(804\) | −1.68461e9 | −0.114315 | ||||||||
\(805\) | 8.50176e7 | 0.00574412 | ||||||||
\(806\) | − | 1.83708e8i | − | 0.0123582i | ||||||
\(807\) | 1.96362e9 | 0.131522 | ||||||||
\(808\) | − | 1.07083e8i | − | 0.00714135i | ||||||
\(809\) | − | 9.57799e9i | − | 0.635996i | −0.948091 | − | 0.317998i | \(-0.896989\pi\) | ||
0.948091 | − | 0.317998i | \(-0.103011\pi\) | |||||||
\(810\) | 1.18751e8 | 0.00785127 | ||||||||
\(811\) | 2.97576e9 | 0.195896 | 0.0979479 | − | 0.995192i | \(-0.468772\pi\) | ||||
0.0979479 | + | 0.995192i | \(0.468772\pi\) | |||||||
\(812\) | 1.89484e8i | 0.0124201i | ||||||||
\(813\) | 2.11220e9 | 0.137853 | ||||||||
\(814\) | −1.81673e8 | − | 7.98118e7i | −0.0118061 | − | 0.00518659i | ||||
\(815\) | 6.10966e9 | 0.395335 | ||||||||
\(816\) | − | 2.79509e9i | − | 0.180086i | ||||||
\(817\) | 3.25851e10 | 2.09046 | ||||||||
\(818\) | −4.10787e7 | −0.00262410 | ||||||||
\(819\) | − | 1.23763e8i | − | 0.00787223i | ||||||
\(820\) | − | 1.19993e10i | − | 0.759987i | ||||||
\(821\) | −2.20177e10 | −1.38858 | −0.694291 | − | 0.719695i | \(-0.744282\pi\) | ||||
−0.694291 | + | 0.719695i | \(0.744282\pi\) | |||||||
\(822\) | 2.95907e7i | 0.00185825i | ||||||||
\(823\) | 2.92011e10 | 1.82600 | 0.912998 | − | 0.407964i | \(-0.133761\pi\) | ||||
0.912998 | + | 0.407964i | \(0.133761\pi\) | |||||||
\(824\) | −3.38752e8 | −0.0210929 | ||||||||
\(825\) | −1.04591e9 | −0.0648494 | ||||||||
\(826\) | 755398. | 4.66386e−5 | ||||||||
\(827\) | − | 2.73175e10i | − | 1.67947i | −0.543000 | − | 0.839733i | \(-0.682712\pi\) | ||
0.543000 | − | 0.839733i | \(-0.317288\pi\) | |||||||
\(828\) | 1.66289e10i | 1.01802i | ||||||||
\(829\) | 1.46616e10i | 0.893797i | 0.894585 | + | 0.446899i | \(0.147472\pi\) | ||||
−0.894585 | + | 0.446899i | \(0.852528\pi\) | |||||||
\(830\) | 8.42472e7 | 0.00511425 | ||||||||
\(831\) | − | 1.62881e8i | − | 0.00984614i | ||||||
\(832\) | 1.95680e10i | 1.17792i | ||||||||
\(833\) | − | 1.99813e10i | − | 1.19775i | ||||||
\(834\) | 4.52830e7i | 0.00270305i | ||||||||
\(835\) | −5.83498e9 | −0.346846 | ||||||||
\(836\) | 2.52603e10i | 1.49526i | ||||||||
\(837\) | − | 5.07051e9i | − | 0.298891i | ||||||
\(838\) | 2.48212e7i | 0.00145703i | ||||||||
\(839\) | −1.93520e10 | −1.13125 | −0.565625 | − | 0.824662i | \(-0.691365\pi\) | ||||
−0.565625 | + | 0.824662i | \(0.691365\pi\) | |||||||
\(840\) | −297217. | −1.73020e−5 | ||||||||
\(841\) | −3.97481e10 | −2.30425 | ||||||||
\(842\) | 2.86350e8 | 0.0165312 | ||||||||
\(843\) | 2.75115e9i | 0.158168i | ||||||||
\(844\) | −5.82979e9 | −0.333776 | ||||||||
\(845\) | − | 5.50971e9i | − | 0.314145i | ||||||
\(846\) | − | 1.47759e8i | − | 0.00838989i | ||||||
\(847\) | 6.37989e7 | 0.00360762 | ||||||||
\(848\) | 2.29530e10 | 1.29257 | ||||||||
\(849\) | 1.99924e9i | 0.112121i | ||||||||
\(850\) | 7.80445e7 | 0.00435889 | ||||||||
\(851\) | −1.71465e10 | − | 7.53269e9i | −0.953721 | − | 0.418983i | ||||
\(852\) | −2.85179e9 | −0.157972 | ||||||||
\(853\) | 1.74995e10i | 0.965395i | 0.875787 | + | 0.482698i | \(0.160343\pi\) | ||||
−0.875787 | + | 0.482698i | \(0.839657\pi\) | |||||||
\(854\) | −691133. | −3.79716e−5 | ||||||||
\(855\) | 1.74382e10 | 0.954160 | ||||||||
\(856\) | 9.45705e7i | 0.00515344i | ||||||||
\(857\) | 9.96612e8i | 0.0540870i | 0.999634 | + | 0.0270435i | \(0.00860927\pi\) | ||||
−0.999634 | + | 0.0270435i | \(0.991391\pi\) | |||||||
\(858\) | −4.22926e7 | −0.00228591 | ||||||||
\(859\) | − | 1.88375e10i | − | 1.01402i | −0.861939 | − | 0.507012i | \(-0.830750\pi\) | ||
0.861939 | − | 0.507012i | \(-0.169250\pi\) | |||||||
\(860\) | 2.60060e10 | 1.39421 | ||||||||
\(861\) | 1.81297e7 | 0.000968008 | ||||||||
\(862\) | 6.13333e7 | 0.00326152 | ||||||||
\(863\) | −6.43540e9 | −0.340830 | −0.170415 | − | 0.985372i | \(-0.554511\pi\) | ||||
−0.170415 | + | 0.985372i | \(0.554511\pi\) | |||||||
\(864\) | − | 1.76423e8i | − | 0.00930586i | ||||||
\(865\) | − | 1.67811e10i | − | 0.881586i | ||||||
\(866\) | 3.20498e8i | 0.0167692i | ||||||||
\(867\) | 1.25468e9 | 0.0653833 | ||||||||
\(868\) | − | 1.32310e8i | − | 0.00686713i | ||||||
\(869\) | − | 2.39499e10i | − | 1.23804i | ||||||
\(870\) | − | 4.47001e7i | − | 0.00230139i | ||||||
\(871\) | 1.74734e10i | 0.896010i | ||||||||
\(872\) | 4.00459e8 | 0.0204527 | ||||||||
\(873\) | 8.36748e9i | 0.425643i | ||||||||
\(874\) | − | 2.59486e8i | − | 0.0131469i | ||||||
\(875\) | 1.47390e8i | 0.00743773i | ||||||||
\(876\) | 4.50135e9 | 0.226244 | ||||||||
\(877\) | −1.06279e10 | −0.532043 | −0.266022 | − | 0.963967i | \(-0.585709\pi\) | ||||
−0.266022 | + | 0.963967i | \(0.585709\pi\) | |||||||
\(878\) | 2.65866e8 | 0.0132566 | ||||||||
\(879\) | 2.08996e9 | 0.103795 | ||||||||
\(880\) | 2.01580e10i | 0.997144i | ||||||||
\(881\) | 1.01389e10 | 0.499545 | 0.249772 | − | 0.968305i | \(-0.419644\pi\) | ||||
0.249772 | + | 0.968305i | \(0.419644\pi\) | |||||||
\(882\) | − | 2.07757e8i | − | 0.0101957i | ||||||
\(883\) | 1.95154e10i | 0.953925i | 0.878924 | + | 0.476963i | \(0.158262\pi\) | ||||
−0.878924 | + | 0.476963i | \(0.841738\pi\) | |||||||
\(884\) | −2.89948e10 | −1.41168 | ||||||||
\(885\) | 1.63727e9 | 0.0793997 | ||||||||
\(886\) | 1.85440e8i | 0.00895748i | ||||||||
\(887\) | 1.09529e9 | 0.0526983 | 0.0263492 | − | 0.999653i | \(-0.491612\pi\) | ||||
0.0263492 | + | 0.999653i | \(0.491612\pi\) | |||||||
\(888\) | 5.99432e7 | + | 2.63339e7i | 0.00287273 | + | 0.00126203i | ||||
\(889\) | −1.77752e8 | −0.00848512 | ||||||||
\(890\) | − | 2.65913e8i | − | 0.0126437i | ||||||
\(891\) | 2.43414e10 | 1.15285 | ||||||||
\(892\) | 2.64495e10 | 1.24778 | ||||||||
\(893\) | − | 2.11842e10i | − | 0.995477i | ||||||
\(894\) | 4.25767e7i | 0.00199293i | ||||||||
\(895\) | −2.30742e10 | −1.07584 | ||||||||
\(896\) | − | 6.13802e6i | − | 0.000285069i | ||||||
\(897\) | −3.99161e9 | −0.184661 | ||||||||
\(898\) | 3.39983e8 | 0.0156671 | ||||||||
\(899\) | 3.97999e10 | 1.82693 | ||||||||
\(900\) | −7.45560e9 | −0.340905 | ||||||||
\(901\) | 3.40032e10i | 1.54876i | ||||||||
\(902\) | 2.67704e8i | 0.0121460i | ||||||||
\(903\) | 3.92925e7i | 0.00177583i | ||||||||
\(904\) | −1.84582e8 | −0.00830999 | ||||||||
\(905\) | 1.36010e10i | 0.609959i | ||||||||
\(906\) | − | 2.83158e7i | − | 0.00126497i | ||||||
\(907\) | 4.29573e10i | 1.91166i | 0.293912 | + | 0.955832i | \(0.405043\pi\) | ||||
−0.293912 | + | 0.955832i | \(0.594957\pi\) | |||||||
\(908\) | 7.23921e9i | 0.320916i | ||||||||
\(909\) | −7.57598e9 | −0.334553 | ||||||||
\(910\) | 1.54134e6i | 6.78036e-5i | ||||||||
\(911\) | − | 1.95080e10i | − | 0.854865i | −0.904047 | − | 0.427432i | \(-0.859418\pi\) | ||
0.904047 | − | 0.427432i | \(-0.140582\pi\) | |||||||
\(912\) | − | 4.16665e9i | − | 0.181888i | ||||||
\(913\) | 1.72689e10 | 0.750960 | ||||||||
\(914\) | −1.38586e8 | −0.00600353 | ||||||||
\(915\) | −1.49798e9 | −0.0646447 | ||||||||
\(916\) | 1.86134e10 | 0.800189 | ||||||||
\(917\) | 2.54867e8i | 0.0109149i | ||||||||
\(918\) | 8.71033e7 | 0.00371608 | ||||||||
\(919\) | 2.58034e10i | 1.09666i | 0.836261 | + | 0.548331i | \(0.184737\pi\) | ||||
−0.836261 | + | 0.548331i | \(0.815263\pi\) | |||||||
\(920\) | − | 4.14213e8i | − | 0.0175374i | ||||||
\(921\) | −6.46436e9 | −0.272657 | ||||||||
\(922\) | −3.87454e8 | −0.0162803 | ||||||||
\(923\) | 2.95798e10i | 1.23820i | ||||||||
\(924\) | −3.04600e7 | −0.00127022 | ||||||||
\(925\) | 3.37730e9 | − | 7.68765e9i | 0.140305 | − | 0.319372i | ||||
\(926\) | −8.18630e7 | −0.00338805 | ||||||||
\(927\) | 2.39663e10i | 0.988148i | ||||||||
\(928\) | 1.38479e9 | 0.0568810 | ||||||||
\(929\) | 5.62679e9 | 0.230253 | 0.115127 | − | 0.993351i | \(-0.463273\pi\) | ||||
0.115127 | + | 0.993351i | \(0.463273\pi\) | |||||||
\(930\) | 3.12127e7i | 0.00127245i | ||||||||
\(931\) | − | 2.97862e10i | − | 1.20974i | ||||||
\(932\) | −1.96313e10 | −0.794314 | ||||||||
\(933\) | − | 3.59964e9i | − | 0.145102i | ||||||
\(934\) | 1.01325e8 | 0.00406916 | ||||||||
\(935\) | −2.98626e10 | −1.19478 | ||||||||
\(936\) | −6.02984e8 | −0.0240348 | ||||||||
\(937\) | −1.67508e10 | −0.665192 | −0.332596 | − | 0.943069i | \(-0.607925\pi\) | ||||
−0.332596 | + | 0.943069i | \(0.607925\pi\) | |||||||
\(938\) | − | 1.36972e6i | − | 5.41905e-5i | ||||||
\(939\) | 4.30255e9i | 0.169588i | ||||||||
\(940\) | − | 1.69070e10i | − | 0.663925i | ||||||
\(941\) | 2.95555e10 | 1.15631 | 0.578155 | − | 0.815927i | \(-0.303773\pi\) | ||||
0.578155 | + | 0.815927i | \(0.303773\pi\) | |||||||
\(942\) | − | 4.40487e7i | − | 0.00171694i | ||||||
\(943\) | 2.52661e10i | 0.981178i | ||||||||
\(944\) | 1.69043e10i | 0.654026i | ||||||||
\(945\) | 4.25422e7i | 0.00163987i | ||||||||
\(946\) | −5.80196e8 | −0.0222821 | ||||||||
\(947\) | − | 2.90619e10i | − | 1.11199i | −0.831187 | − | 0.555993i | \(-0.812338\pi\) | ||
0.831187 | − | 0.555993i | \(-0.187662\pi\) | |||||||
\(948\) | 3.95092e9i | 0.150615i | ||||||||
\(949\) | − | 4.66895e10i | − | 1.77332i | ||||||
\(950\) | 1.16341e8 | 0.00440251 | ||||||||
\(951\) | −1.82842e8 | −0.00689357 | ||||||||
\(952\) | 4.54602e6 | 0.000170766 | ||||||||
\(953\) | −2.54602e10 | −0.952878 | −0.476439 | − | 0.879208i | \(-0.658073\pi\) | ||||
−0.476439 | + | 0.879208i | \(0.658073\pi\) | |||||||
\(954\) | 3.53551e8i | 0.0131835i | ||||||||
\(955\) | 9.72681e9 | 0.361375 | ||||||||
\(956\) | 1.14961e10i | 0.425547i | ||||||||
\(957\) | − | 9.16257e9i | − | 0.337929i | ||||||
\(958\) | 1.19018e8 | 0.00437356 | ||||||||
\(959\) | 2.21053e8 | 0.00809342 | ||||||||
\(960\) | − | 3.32466e9i | − | 0.121283i | ||||||
\(961\) | −2.78397e8 | −0.0101189 | ||||||||
\(962\) | 1.36565e8 | − | 3.10859e8i | 0.00494568 | − | 0.0112577i | ||||
\(963\) | 6.69075e9 | 0.241425 | ||||||||
\(964\) | − | 3.71955e9i | − | 0.133728i | ||||||
\(965\) | 8.33199e9 | 0.298472 | ||||||||
\(966\) | 312900. | 1.11682e−5 | ||||||||
\(967\) | 1.24502e10i | 0.442777i | 0.975186 | + | 0.221389i | \(0.0710589\pi\) | ||||
−0.975186 | + | 0.221389i | \(0.928941\pi\) | |||||||
\(968\) | − | 3.10833e8i | − | 0.0110145i | ||||||
\(969\) | 6.17258e9 | 0.217938 | ||||||||
\(970\) | − | 1.04208e8i | − | 0.00366606i | ||||||
\(971\) | 1.50921e10 | 0.529032 | 0.264516 | − | 0.964381i | \(-0.414788\pi\) | ||||
0.264516 | + | 0.964381i | \(0.414788\pi\) | |||||||
\(972\) | −1.25291e10 | −0.437609 | ||||||||
\(973\) | 3.38281e8 | 0.0117729 | ||||||||
\(974\) | −5.33098e8 | −0.0184863 | ||||||||
\(975\) | − | 1.78964e9i | − | 0.0618373i | ||||||
\(976\) | − | 1.54662e10i | − | 0.532487i | ||||||
\(977\) | − | 1.37763e10i | − | 0.472610i | −0.971679 | − | 0.236305i | \(-0.924064\pi\) | ||
0.971679 | − | 0.236305i | \(-0.0759365\pi\) | |||||||
\(978\) | 2.24860e7 | 0.000768647 | ||||||||
\(979\) | − | 5.45065e10i | − | 1.85656i | ||||||
\(980\) | − | 2.37722e10i | − | 0.806824i | ||||||
\(981\) | − | 2.83320e10i | − | 0.958155i | ||||||
\(982\) | 4.89318e8i | 0.0164893i | ||||||||
\(983\) | 2.51612e10 | 0.844880 | 0.422440 | − | 0.906391i | \(-0.361174\pi\) | ||||
0.422440 | + | 0.906391i | \(0.361174\pi\) | |||||||
\(984\) | − | 8.83292e7i | − | 0.00295543i | ||||||
\(985\) | 9.60797e9i | 0.320335i | ||||||||
\(986\) | 6.83699e8i | 0.0227141i | ||||||||
\(987\) | 2.55448e7 | 0.000845653 | ||||||||
\(988\) | −4.32226e10 | −1.42581 | ||||||||
\(989\) | −5.47593e10 | −1.79999 | ||||||||
\(990\) | −3.10498e8 | −0.0101703 | ||||||||
\(991\) | − | 9.62789e9i | − | 0.314248i | −0.987579 | − | 0.157124i | \(-0.949778\pi\) | ||
0.987579 | − | 0.157124i | \(-0.0502223\pi\) | |||||||
\(992\) | −9.66958e8 | −0.0314497 | ||||||||
\(993\) | − | 1.79728e9i | − | 0.0582495i | ||||||
\(994\) | − | 2.31874e6i | − | 7.48859e-5i | ||||||
\(995\) | 1.85801e10 | 0.597954 | ||||||||
\(996\) | −2.84878e9 | −0.0913591 | ||||||||
\(997\) | − | 1.20386e10i | − | 0.384718i | −0.981325 | − | 0.192359i | \(-0.938386\pi\) | ||
0.981325 | − | 0.192359i | \(-0.0616139\pi\) | |||||||
\(998\) | −2.14132e8 | −0.00681907 | ||||||||
\(999\) | 3.76930e9 | − | 8.57996e9i | 0.119614 | − | 0.272274i |
(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 | 37.8.b.a.36.10 | ✓ | 20 | |
37.36 | even | 2 | inner | 37.8.b.a.36.11 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
37.8.b.a.36.10 | ✓ | 20 | 1.1 | even | 1 | trivial | |
37.8.b.a.36.11 | yes | 20 | 37.36 | even | 2 | inner |