Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,6,Mod(139,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("230.139");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.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: | \(36.8882785570\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 139.15 | ||
Character | \(\chi\) | \(=\) | 230.139 |
Dual form | 230.6.b.a.139.12 |
$q$-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 \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000i | 0.707107i | ||||||||
\(3\) | − | 19.5707i | − | 1.25546i | −0.778430 | − | 0.627732i | \(-0.783983\pi\) | ||
0.778430 | − | 0.627732i | \(-0.216017\pi\) | |||||||
\(4\) | −16.0000 | −0.500000 | ||||||||
\(5\) | 11.6274 | − | 54.6791i | 0.207997 | − | 0.978129i | ||||
\(6\) | 78.2830 | 0.887747 | ||||||||
\(7\) | 53.5462i | 0.413032i | 0.978443 | + | 0.206516i | \(0.0662126\pi\) | ||||
−0.978443 | + | 0.206516i | \(0.933787\pi\) | |||||||
\(8\) | − | 64.0000i | − | 0.353553i | ||||||
\(9\) | −140.014 | −0.576188 | ||||||||
\(10\) | 218.716 | + | 46.5095i | 0.691642 | + | 0.147076i | ||||
\(11\) | −780.443 | −1.94473 | −0.972365 | − | 0.233464i | \(-0.924994\pi\) | ||||
−0.972365 | + | 0.233464i | \(0.924994\pi\) | |||||||
\(12\) | 313.132i | 0.627732i | ||||||||
\(13\) | 672.602i | 1.10382i | 0.833903 | + | 0.551912i | \(0.186101\pi\) | ||||
−0.833903 | + | 0.551912i | \(0.813899\pi\) | |||||||
\(14\) | −214.185 | −0.292058 | ||||||||
\(15\) | −1070.11 | − | 227.556i | −1.22801 | − | 0.261133i | ||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 1468.88i | 1.23271i | 0.787467 | + | 0.616357i | \(0.211392\pi\) | ||||
−0.787467 | + | 0.616357i | \(0.788608\pi\) | |||||||
\(18\) | − | 560.055i | − | 0.407427i | ||||||
\(19\) | 644.576 | 0.409628 | 0.204814 | − | 0.978801i | \(-0.434341\pi\) | ||||
0.204814 | + | 0.978801i | \(0.434341\pi\) | |||||||
\(20\) | −186.038 | + | 874.866i | −0.103998 | + | 0.489065i | ||||
\(21\) | 1047.94 | 0.518547 | ||||||||
\(22\) | − | 3121.77i | − | 1.37513i | ||||||
\(23\) | 529.000i | 0.208514i | ||||||||
\(24\) | −1252.53 | −0.443873 | ||||||||
\(25\) | −2854.61 | − | 1271.55i | −0.913475 | − | 0.406896i | ||||
\(26\) | −2690.41 | −0.780521 | ||||||||
\(27\) | − | 2015.52i | − | 0.532080i | ||||||
\(28\) | − | 856.740i | − | 0.206516i | ||||||
\(29\) | 1678.02 | 0.370511 | 0.185256 | − | 0.982690i | \(-0.440689\pi\) | ||||
0.185256 | + | 0.982690i | \(0.440689\pi\) | |||||||
\(30\) | 910.226 | − | 4280.44i | 0.184649 | − | 0.868331i | ||||
\(31\) | 8393.89 | 1.56877 | 0.784384 | − | 0.620275i | \(-0.212979\pi\) | ||||
0.784384 | + | 0.620275i | \(0.212979\pi\) | |||||||
\(32\) | 1024.00i | 0.176777i | ||||||||
\(33\) | 15273.8i | 2.44154i | ||||||||
\(34\) | −5875.50 | −0.871661 | ||||||||
\(35\) | 2927.86 | + | 622.602i | 0.403999 | + | 0.0859094i | ||||
\(36\) | 2240.22 | 0.288094 | ||||||||
\(37\) | − | 1726.62i | − | 0.207345i | −0.994611 | − | 0.103672i | \(-0.966941\pi\) | ||
0.994611 | − | 0.103672i | \(-0.0330593\pi\) | |||||||
\(38\) | 2578.30i | 0.289651i | ||||||||
\(39\) | 13163.3 | 1.38581 | ||||||||
\(40\) | −3499.46 | − | 744.152i | −0.345821 | − | 0.0735380i | ||||
\(41\) | −3755.78 | −0.348932 | −0.174466 | − | 0.984663i | \(-0.555820\pi\) | ||||
−0.174466 | + | 0.984663i | \(0.555820\pi\) | |||||||
\(42\) | 4191.76i | 0.366668i | ||||||||
\(43\) | − | 5020.95i | − | 0.414109i | −0.978329 | − | 0.207054i | \(-0.933612\pi\) | ||
0.978329 | − | 0.207054i | \(-0.0663877\pi\) | |||||||
\(44\) | 12487.1 | 0.972365 | ||||||||
\(45\) | −1627.99 | + | 7655.83i | −0.119845 | + | 0.563587i | ||||
\(46\) | −2116.00 | −0.147442 | ||||||||
\(47\) | 22479.4i | 1.48436i | 0.670199 | + | 0.742181i | \(0.266209\pi\) | ||||
−0.670199 | + | 0.742181i | \(0.733791\pi\) | |||||||
\(48\) | − | 5010.11i | − | 0.313866i | ||||||
\(49\) | 13939.8 | 0.829405 | ||||||||
\(50\) | 5086.20 | − | 11418.4i | 0.287719 | − | 0.645924i | ||||
\(51\) | 28747.0 | 1.54763 | ||||||||
\(52\) | − | 10761.6i | − | 0.551912i | ||||||
\(53\) | 35954.8i | 1.75819i | 0.476643 | + | 0.879097i | \(0.341853\pi\) | ||||
−0.476643 | + | 0.879097i | \(0.658147\pi\) | |||||||
\(54\) | 8062.06 | 0.376237 | ||||||||
\(55\) | −9074.51 | + | 42673.9i | −0.404498 | + | 1.90220i | ||||
\(56\) | 3426.96 | 0.146029 | ||||||||
\(57\) | − | 12614.8i | − | 0.514273i | ||||||
\(58\) | 6712.07i | 0.261991i | ||||||||
\(59\) | 15530.7 | 0.580846 | 0.290423 | − | 0.956898i | \(-0.406204\pi\) | ||||
0.290423 | + | 0.956898i | \(0.406204\pi\) | |||||||
\(60\) | 17121.8 | + | 3640.90i | 0.614003 | + | 0.130566i | ||||
\(61\) | −44622.7 | −1.53544 | −0.767718 | − | 0.640788i | \(-0.778608\pi\) | ||||
−0.767718 | + | 0.640788i | \(0.778608\pi\) | |||||||
\(62\) | 33575.5i | 1.10929i | ||||||||
\(63\) | − | 7497.21i | − | 0.237984i | ||||||
\(64\) | −4096.00 | −0.125000 | ||||||||
\(65\) | 36777.3 | + | 7820.60i | 1.07968 | + | 0.229592i | ||||
\(66\) | −61095.4 | −1.72643 | ||||||||
\(67\) | − | 65599.9i | − | 1.78532i | −0.450730 | − | 0.892660i | \(-0.648836\pi\) | ||
0.450730 | − | 0.892660i | \(-0.351164\pi\) | |||||||
\(68\) | − | 23502.0i | − | 0.616357i | ||||||
\(69\) | 10352.9 | 0.261782 | ||||||||
\(70\) | −2490.41 | + | 11711.4i | −0.0607471 | + | 0.285670i | ||||
\(71\) | 28123.0 | 0.662087 | 0.331044 | − | 0.943615i | \(-0.392599\pi\) | ||||
0.331044 | + | 0.943615i | \(0.392599\pi\) | |||||||
\(72\) | 8960.88i | 0.203713i | ||||||||
\(73\) | 40306.9i | 0.885262i | 0.896704 | + | 0.442631i | \(0.145955\pi\) | ||||
−0.896704 | + | 0.442631i | \(0.854045\pi\) | |||||||
\(74\) | 6906.49 | 0.146615 | ||||||||
\(75\) | −24885.2 | + | 55866.8i | −0.510843 | + | 1.14683i | ||||
\(76\) | −10313.2 | −0.204814 | ||||||||
\(77\) | − | 41789.8i | − | 0.803236i | ||||||
\(78\) | 52653.2i | 0.979915i | ||||||||
\(79\) | −58608.1 | −1.05655 | −0.528275 | − | 0.849073i | \(-0.677161\pi\) | ||||
−0.528275 | + | 0.849073i | \(0.677161\pi\) | |||||||
\(80\) | 2976.61 | − | 13997.8i | 0.0519992 | − | 0.244532i | ||||
\(81\) | −73468.5 | −1.24420 | ||||||||
\(82\) | − | 15023.1i | − | 0.246732i | ||||||
\(83\) | 102900.i | 1.63954i | 0.572696 | + | 0.819768i | \(0.305898\pi\) | ||||
−0.572696 | + | 0.819768i | \(0.694102\pi\) | |||||||
\(84\) | −16767.0 | −0.259273 | ||||||||
\(85\) | 80316.8 | + | 17079.2i | 1.20575 | + | 0.256401i | ||||
\(86\) | 20083.8 | 0.292819 | ||||||||
\(87\) | − | 32840.0i | − | 0.465163i | ||||||
\(88\) | 49948.4i | 0.687566i | ||||||||
\(89\) | 126371. | 1.69111 | 0.845555 | − | 0.533888i | \(-0.179270\pi\) | ||||
0.845555 | + | 0.533888i | \(0.179270\pi\) | |||||||
\(90\) | −30623.3 | − | 6511.97i | −0.398516 | − | 0.0847435i | ||||
\(91\) | −36015.3 | −0.455914 | ||||||||
\(92\) | − | 8464.00i | − | 0.104257i | ||||||
\(93\) | − | 164275.i | − | 1.96953i | ||||||
\(94\) | −89917.6 | −1.04960 | ||||||||
\(95\) | 7494.73 | − | 35244.8i | 0.0852014 | − | 0.400670i | ||||
\(96\) | 20040.4 | 0.221937 | ||||||||
\(97\) | 38113.0i | 0.411286i | 0.978627 | + | 0.205643i | \(0.0659286\pi\) | ||||
−0.978627 | + | 0.205643i | \(0.934071\pi\) | |||||||
\(98\) | 55759.2i | 0.586478i | ||||||||
\(99\) | 109273. | 1.12053 | ||||||||
\(100\) | 45673.7 | + | 20344.8i | 0.456737 | + | 0.203448i | ||||
\(101\) | −146414. | −1.42817 | −0.714085 | − | 0.700059i | \(-0.753157\pi\) | ||||
−0.714085 | + | 0.700059i | \(0.753157\pi\) | |||||||
\(102\) | 114988.i | 1.09434i | ||||||||
\(103\) | 209304.i | 1.94395i | 0.235090 | + | 0.971974i | \(0.424461\pi\) | ||||
−0.235090 | + | 0.971974i | \(0.575539\pi\) | |||||||
\(104\) | 43046.5 | 0.390260 | ||||||||
\(105\) | 12184.8 | − | 57300.4i | 0.107856 | − | 0.507206i | ||||
\(106\) | −143819. | −1.24323 | ||||||||
\(107\) | 62158.7i | 0.524859i | 0.964951 | + | 0.262429i | \(0.0845237\pi\) | ||||
−0.964951 | + | 0.262429i | \(0.915476\pi\) | |||||||
\(108\) | 32248.3i | 0.266040i | ||||||||
\(109\) | −147391. | −1.18824 | −0.594120 | − | 0.804377i | \(-0.702500\pi\) | ||||
−0.594120 | + | 0.804377i | \(0.702500\pi\) | |||||||
\(110\) | −170696. | − | 36298.0i | −1.34506 | − | 0.286023i | ||||
\(111\) | −33791.3 | −0.260314 | ||||||||
\(112\) | 13707.8i | 0.103258i | ||||||||
\(113\) | 36497.6i | 0.268886i | 0.990921 | + | 0.134443i | \(0.0429246\pi\) | ||||
−0.990921 | + | 0.134443i | \(0.957075\pi\) | |||||||
\(114\) | 50459.3 | 0.363646 | ||||||||
\(115\) | 28925.2 | + | 6150.88i | 0.203954 | + | 0.0433704i | ||||
\(116\) | −26848.3 | −0.185256 | ||||||||
\(117\) | − | 94173.5i | − | 0.636010i | ||||||
\(118\) | 62122.8i | 0.410720i | ||||||||
\(119\) | −78652.7 | −0.509151 | ||||||||
\(120\) | −14563.6 | + | 68487.1i | −0.0923243 | + | 0.434166i | ||||
\(121\) | 448040. | 2.78198 | ||||||||
\(122\) | − | 178491.i | − | 1.08572i | ||||||
\(123\) | 73503.5i | 0.438071i | ||||||||
\(124\) | −134302. | −0.784384 | ||||||||
\(125\) | −102719. | + | 141303.i | −0.587997 | + | 0.808863i | ||||
\(126\) | 29988.8 | 0.168280 | ||||||||
\(127\) | − | 134203.i | − | 0.738335i | −0.929363 | − | 0.369167i | \(-0.879643\pi\) | ||
0.929363 | − | 0.369167i | \(-0.120357\pi\) | |||||||
\(128\) | − | 16384.0i | − | 0.0883883i | ||||||
\(129\) | −98263.6 | −0.519898 | ||||||||
\(130\) | −31282.4 | + | 147109.i | −0.162346 | + | 0.763450i | ||||
\(131\) | 56217.3 | 0.286215 | 0.143107 | − | 0.989707i | \(-0.454291\pi\) | ||||
0.143107 | + | 0.989707i | \(0.454291\pi\) | |||||||
\(132\) | − | 244382.i | − | 1.22077i | ||||||
\(133\) | 34514.6i | 0.169190i | ||||||||
\(134\) | 262400. | 1.26241 | ||||||||
\(135\) | −110207. | − | 23435.2i | −0.520443 | − | 0.110671i | ||||
\(136\) | 94008.0 | 0.435830 | ||||||||
\(137\) | 36226.1i | 0.164900i | 0.996595 | + | 0.0824500i | \(0.0262745\pi\) | ||||
−0.996595 | + | 0.0824500i | \(0.973726\pi\) | |||||||
\(138\) | 41411.7i | 0.185108i | ||||||||
\(139\) | −8168.50 | −0.0358596 | −0.0179298 | − | 0.999839i | \(-0.505708\pi\) | ||||
−0.0179298 | + | 0.999839i | \(0.505708\pi\) | |||||||
\(140\) | −46845.7 | − | 9961.64i | −0.201999 | − | 0.0429547i | ||||
\(141\) | 439938. | 1.86356 | ||||||||
\(142\) | 112492.i | 0.468166i | ||||||||
\(143\) | − | 524927.i | − | 2.14664i | ||||||
\(144\) | −35843.5 | −0.144047 | ||||||||
\(145\) | 19510.9 | − | 91752.5i | 0.0770652 | − | 0.362408i | ||||
\(146\) | −161227. | −0.625975 | ||||||||
\(147\) | − | 272812.i | − | 1.04129i | ||||||
\(148\) | 27626.0i | 0.103672i | ||||||||
\(149\) | −194349. | −0.717162 | −0.358581 | − | 0.933499i | \(-0.616739\pi\) | ||||
−0.358581 | + | 0.933499i | \(0.616739\pi\) | |||||||
\(150\) | −223467. | − | 99540.6i | −0.810934 | − | 0.361220i | ||||
\(151\) | 307204. | 1.09644 | 0.548219 | − | 0.836335i | \(-0.315306\pi\) | ||||
0.548219 | + | 0.836335i | \(0.315306\pi\) | |||||||
\(152\) | − | 41252.9i | − | 0.144825i | ||||||
\(153\) | − | 205663.i | − | 0.710276i | ||||||
\(154\) | 167159. | 0.567974 | ||||||||
\(155\) | 97598.9 | − | 458970.i | 0.326299 | − | 1.53446i | ||||
\(156\) | −210613. | −0.692905 | ||||||||
\(157\) | − | 60613.2i | − | 0.196254i | −0.995174 | − | 0.0981269i | \(-0.968715\pi\) | ||
0.995174 | − | 0.0981269i | \(-0.0312851\pi\) | |||||||
\(158\) | − | 234433.i | − | 0.747094i | ||||||
\(159\) | 703661. | 2.20735 | ||||||||
\(160\) | 55991.4 | + | 11906.4i | 0.172910 | + | 0.0367690i | ||||
\(161\) | −28326.0 | −0.0861231 | ||||||||
\(162\) | − | 293874.i | − | 0.879779i | ||||||
\(163\) | 295.269i | 0.000870459i | 1.00000 | 0.000435230i | \(0.000138538\pi\) | |||||
−1.00000 | 0.000435230i | \(0.999861\pi\) | ||||||||
\(164\) | 60092.5 | 0.174466 | ||||||||
\(165\) | 835160. | + | 177595.i | 2.38814 | + | 0.507832i | ||||
\(166\) | −411601. | −1.15933 | ||||||||
\(167\) | − | 437607.i | − | 1.21421i | −0.794623 | − | 0.607104i | \(-0.792331\pi\) | ||
0.794623 | − | 0.607104i | \(-0.207669\pi\) | |||||||
\(168\) | − | 67068.1i | − | 0.183334i | ||||||
\(169\) | −81099.9 | −0.218426 | ||||||||
\(170\) | −68316.7 | + | 321267.i | −0.181303 | + | 0.852597i | ||||
\(171\) | −90249.5 | −0.236023 | ||||||||
\(172\) | 80335.1i | 0.207054i | ||||||||
\(173\) | 427168.i | 1.08513i | 0.840012 | + | 0.542567i | \(0.182548\pi\) | ||||
−0.840012 | + | 0.542567i | \(0.817452\pi\) | |||||||
\(174\) | 131360. | 0.328920 | ||||||||
\(175\) | 68086.7 | − | 152853.i | 0.168061 | − | 0.377294i | ||||
\(176\) | −199793. | −0.486183 | ||||||||
\(177\) | − | 303947.i | − | 0.729230i | ||||||
\(178\) | 505483.i | 1.19580i | ||||||||
\(179\) | −20401.9 | −0.0475925 | −0.0237962 | − | 0.999717i | \(-0.507575\pi\) | ||||
−0.0237962 | + | 0.999717i | \(0.507575\pi\) | |||||||
\(180\) | 26047.9 | − | 122493.i | 0.0599227 | − | 0.281793i | ||||
\(181\) | −271233. | −0.615384 | −0.307692 | − | 0.951486i | \(-0.599557\pi\) | ||||
−0.307692 | + | 0.951486i | \(0.599557\pi\) | |||||||
\(182\) | − | 144061.i | − | 0.322380i | ||||||
\(183\) | 873300.i | 1.92768i | ||||||||
\(184\) | 33856.0 | 0.0737210 | ||||||||
\(185\) | −94410.2 | − | 20076.1i | −0.202810 | − | 0.0431271i | ||||
\(186\) | 657098. | 1.39267 | ||||||||
\(187\) | − | 1.14637e6i | − | 2.39730i | ||||||
\(188\) | − | 359670.i | − | 0.742181i | ||||||
\(189\) | 107923. | 0.219766 | ||||||||
\(190\) | 140979. | + | 29978.9i | 0.283316 | + | 0.0602465i | ||||
\(191\) | 730775. | 1.44944 | 0.724720 | − | 0.689044i | \(-0.241969\pi\) | ||||
0.724720 | + | 0.689044i | \(0.241969\pi\) | |||||||
\(192\) | 80161.7i | 0.156933i | ||||||||
\(193\) | 114401.i | 0.221074i | 0.993872 | + | 0.110537i | \(0.0352571\pi\) | ||||
−0.993872 | + | 0.110537i | \(0.964743\pi\) | |||||||
\(194\) | −152452. | −0.290823 | ||||||||
\(195\) | 153055. | − | 719758.i | 0.288244 | − | 1.35550i | ||||
\(196\) | −223037. | −0.414702 | ||||||||
\(197\) | 803909.i | 1.47585i | 0.674885 | + | 0.737923i | \(0.264193\pi\) | ||||
−0.674885 | + | 0.737923i | \(0.735807\pi\) | |||||||
\(198\) | 437091.i | 0.792335i | ||||||||
\(199\) | −752458. | −1.34694 | −0.673472 | − | 0.739213i | \(-0.735198\pi\) | ||||
−0.673472 | + | 0.739213i | \(0.735198\pi\) | |||||||
\(200\) | −81379.2 | + | 182695.i | −0.143859 | + | 0.322962i | ||||
\(201\) | −1.28384e6 | −2.24141 | ||||||||
\(202\) | − | 585657.i | − | 1.00987i | ||||||
\(203\) | 89851.5i | 0.153033i | ||||||||
\(204\) | −459951. | −0.773814 | ||||||||
\(205\) | −43669.9 | + | 205363.i | −0.0725768 | + | 0.341301i | ||||
\(206\) | −837216. | −1.37458 | ||||||||
\(207\) | − | 74067.3i | − | 0.120144i | ||||||
\(208\) | 172186.i | 0.275956i | ||||||||
\(209\) | −503055. | −0.796617 | ||||||||
\(210\) | 229201. | + | 48739.2i | 0.358649 | + | 0.0762658i | ||||
\(211\) | −1.25423e6 | −1.93942 | −0.969710 | − | 0.244257i | \(-0.921456\pi\) | ||||
−0.969710 | + | 0.244257i | \(0.921456\pi\) | |||||||
\(212\) | − | 575276.i | − | 0.879097i | ||||||
\(213\) | − | 550387.i | − | 0.831226i | ||||||
\(214\) | −248635. | −0.371131 | ||||||||
\(215\) | −274541. | − | 58380.5i | −0.405052 | − | 0.0861333i | ||||
\(216\) | −128993. | −0.188119 | ||||||||
\(217\) | 449461.i | 0.647952i | ||||||||
\(218\) | − | 589563.i | − | 0.840212i | ||||||
\(219\) | 788835. | 1.11141 | ||||||||
\(220\) | 145192. | − | 682783.i | 0.202249 | − | 0.951099i | ||||
\(221\) | −987968. | −1.36070 | ||||||||
\(222\) | − | 135165.i | − | 0.184070i | ||||||
\(223\) | − | 90970.3i | − | 0.122500i | −0.998122 | − | 0.0612502i | \(-0.980491\pi\) | ||
0.998122 | − | 0.0612502i | \(-0.0195087\pi\) | |||||||
\(224\) | −54831.3 | −0.0730144 | ||||||||
\(225\) | 399684. | + | 178034.i | 0.526333 | + | 0.234449i | ||||
\(226\) | −145991. | −0.190131 | ||||||||
\(227\) | 1.07836e6i | 1.38899i | 0.719495 | + | 0.694497i | \(0.244373\pi\) | ||||
−0.719495 | + | 0.694497i | \(0.755627\pi\) | |||||||
\(228\) | 201837.i | 0.257137i | ||||||||
\(229\) | −580885. | −0.731984 | −0.365992 | − | 0.930618i | \(-0.619270\pi\) | ||||
−0.365992 | + | 0.930618i | \(0.619270\pi\) | |||||||
\(230\) | −24603.5 | + | 115701.i | −0.0306675 | + | 0.144217i | ||||
\(231\) | −817857. | −1.00843 | ||||||||
\(232\) | − | 107393.i | − | 0.130996i | ||||||
\(233\) | 248758.i | 0.300184i | 0.988672 | + | 0.150092i | \(0.0479570\pi\) | ||||
−0.988672 | + | 0.150092i | \(0.952043\pi\) | |||||||
\(234\) | 376694. | 0.449727 | ||||||||
\(235\) | 1.22915e6 | + | 261377.i | 1.45190 | + | 0.308743i | ||||
\(236\) | −248491. | −0.290423 | ||||||||
\(237\) | 1.14700e6i | 1.32646i | ||||||||
\(238\) | − | 314611.i | − | 0.360024i | ||||||
\(239\) | −1.04225e6 | −1.18026 | −0.590129 | − | 0.807309i | \(-0.700923\pi\) | ||||
−0.590129 | + | 0.807309i | \(0.700923\pi\) | |||||||
\(240\) | −273948. | − | 58254.4i | −0.307001 | − | 0.0652831i | ||||
\(241\) | 214720. | 0.238139 | 0.119069 | − | 0.992886i | \(-0.462009\pi\) | ||||
0.119069 | + | 0.992886i | \(0.462009\pi\) | |||||||
\(242\) | 1.79216e6i | 1.96716i | ||||||||
\(243\) | 948062.i | 1.02996i | ||||||||
\(244\) | 713964. | 0.767718 | ||||||||
\(245\) | 162083. | − | 762216.i | 0.172514 | − | 0.811265i | ||||
\(246\) | −294014. | −0.309763 | ||||||||
\(247\) | 433543.i | 0.452157i | ||||||||
\(248\) | − | 537209.i | − | 0.554643i | ||||||
\(249\) | 2.01383e6 | 2.05838 | ||||||||
\(250\) | −565210. | − | 410875.i | −0.571953 | − | 0.415776i | ||||
\(251\) | 771736. | 0.773187 | 0.386593 | − | 0.922250i | \(-0.373652\pi\) | ||||
0.386593 | + | 0.922250i | \(0.373652\pi\) | |||||||
\(252\) | 119955.i | 0.118992i | ||||||||
\(253\) | − | 412854.i | − | 0.405504i | ||||||
\(254\) | 536813. | 0.522082 | ||||||||
\(255\) | 334252. | − | 1.57186e6i | 0.321902 | − | 1.51378i | ||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 1.40812e6i | 1.32987i | 0.746903 | + | 0.664933i | \(0.231540\pi\) | ||||
−0.746903 | + | 0.664933i | \(0.768460\pi\) | |||||||
\(258\) | − | 393054.i | − | 0.367624i | ||||||
\(259\) | 92454.1 | 0.0856400 | ||||||||
\(260\) | −588436. | − | 125130.i | −0.539841 | − | 0.114796i | ||||
\(261\) | −234946. | −0.213484 | ||||||||
\(262\) | 224869.i | 0.202384i | ||||||||
\(263\) | 243557.i | 0.217126i | 0.994090 | + | 0.108563i | \(0.0346249\pi\) | ||||
−0.994090 | + | 0.108563i | \(0.965375\pi\) | |||||||
\(264\) | 977526. | 0.863214 | ||||||||
\(265\) | 1.96597e6 | + | 418060.i | 1.71974 | + | 0.365699i | ||||
\(266\) | −138058. | −0.119635 | ||||||||
\(267\) | − | 2.47317e6i | − | 2.12313i | ||||||
\(268\) | 1.04960e6i | 0.892660i | ||||||||
\(269\) | −826330. | −0.696263 | −0.348131 | − | 0.937446i | \(-0.613184\pi\) | ||||
−0.348131 | + | 0.937446i | \(0.613184\pi\) | |||||||
\(270\) | 93740.7 | − | 440826.i | 0.0782562 | − | 0.368009i | ||||
\(271\) | −882227. | −0.729721 | −0.364861 | − | 0.931062i | \(-0.618883\pi\) | ||||
−0.364861 | + | 0.931062i | \(0.618883\pi\) | |||||||
\(272\) | 376032.i | 0.308179i | ||||||||
\(273\) | 704846.i | 0.572384i | ||||||||
\(274\) | −144904. | −0.116602 | ||||||||
\(275\) | 2.22786e6 | + | 992372.i | 1.77646 | + | 0.791303i | ||||
\(276\) | −165647. | −0.130891 | ||||||||
\(277\) | 190943.i | 0.149522i | 0.997201 | + | 0.0747610i | \(0.0238194\pi\) | ||||
−0.997201 | + | 0.0747610i | \(0.976181\pi\) | |||||||
\(278\) | − | 32674.0i | − | 0.0253566i | ||||||
\(279\) | −1.17526e6 | −0.903906 | ||||||||
\(280\) | 39846.6 | − | 187383.i | 0.0303736 | − | 0.142835i | ||||
\(281\) | −1.26870e6 | −0.958500 | −0.479250 | − | 0.877678i | \(-0.659091\pi\) | ||||
−0.479250 | + | 0.877678i | \(0.659091\pi\) | |||||||
\(282\) | 1.75975e6i | 1.31774i | ||||||||
\(283\) | − | 2.40747e6i | − | 1.78688i | −0.449183 | − | 0.893440i | \(-0.648285\pi\) | ||
0.449183 | − | 0.893440i | \(-0.351715\pi\) | |||||||
\(284\) | −449967. | −0.331044 | ||||||||
\(285\) | −689767. | − | 146677.i | −0.503026 | − | 0.106967i | ||||
\(286\) | 2.09971e6 | 1.51790 | ||||||||
\(287\) | − | 201108.i | − | 0.144120i | ||||||
\(288\) | − | 143374.i | − | 0.101857i | ||||||
\(289\) | −737737. | −0.519585 | ||||||||
\(290\) | 367010. | + | 78043.8i | 0.256261 | + | 0.0544933i | ||||
\(291\) | 745900. | 0.516355 | ||||||||
\(292\) | − | 644910.i | − | 0.442631i | ||||||
\(293\) | 125712.i | 0.0855477i | 0.999085 | + | 0.0427739i | \(0.0136195\pi\) | ||||
−0.999085 | + | 0.0427739i | \(0.986381\pi\) | |||||||
\(294\) | 1.09125e6 | 0.736301 | ||||||||
\(295\) | 180581. | − | 849204.i | 0.120814 | − | 0.568142i | ||||
\(296\) | −110504. | −0.0733075 | ||||||||
\(297\) | 1.57300e6i | 1.03475i | ||||||||
\(298\) | − | 777397.i | − | 0.507110i | ||||||
\(299\) | −355806. | −0.230163 | ||||||||
\(300\) | 398163. | − | 893869.i | 0.255421 | − | 0.573417i | ||||
\(301\) | 268853. | 0.171040 | ||||||||
\(302\) | 1.22881e6i | 0.775298i | ||||||||
\(303\) | 2.86543e6i | 1.79301i | ||||||||
\(304\) | 165011. | 0.102407 | ||||||||
\(305\) | −518845. | + | 2.43993e6i | −0.319366 | + | 1.50185i | ||||
\(306\) | 822651. | 0.502241 | ||||||||
\(307\) | 756024.i | 0.457815i | 0.973448 | + | 0.228907i | \(0.0735153\pi\) | ||||
−0.973448 | + | 0.228907i | \(0.926485\pi\) | |||||||
\(308\) | 668636.i | 0.401618i | ||||||||
\(309\) | 4.09623e6 | 2.44055 | ||||||||
\(310\) | 1.83588e6 | + | 390396.i | 1.08503 | + | 0.230728i | ||||
\(311\) | 307652. | 0.180368 | 0.0901838 | − | 0.995925i | \(-0.471255\pi\) | ||||
0.0901838 | + | 0.995925i | \(0.471255\pi\) | |||||||
\(312\) | − | 842452.i | − | 0.489958i | ||||||
\(313\) | − | 1.89986e6i | − | 1.09613i | −0.836437 | − | 0.548063i | \(-0.815366\pi\) | ||
0.836437 | − | 0.548063i | \(-0.184634\pi\) | |||||||
\(314\) | 242453. | 0.138772 | ||||||||
\(315\) | −409941. | − | 87172.9i | −0.232779 | − | 0.0495000i | ||||
\(316\) | 937730. | 0.528275 | ||||||||
\(317\) | − | 382866.i | − | 0.213993i | −0.994259 | − | 0.106996i | \(-0.965877\pi\) | ||
0.994259 | − | 0.106996i | \(-0.0341233\pi\) | |||||||
\(318\) | 2.81465e6i | 1.56083i | ||||||||
\(319\) | −1.30960e6 | −0.720545 | ||||||||
\(320\) | −47625.8 | + | 223966.i | −0.0259996 | + | 0.122266i | ||||
\(321\) | 1.21649e6 | 0.658941 | ||||||||
\(322\) | − | 113304.i | − | 0.0608983i | ||||||
\(323\) | 946801.i | 0.504955i | ||||||||
\(324\) | 1.17550e6 | 0.622098 | ||||||||
\(325\) | 855246. | − | 1.92001e6i | 0.449141 | − | 1.00831i | ||||
\(326\) | −1181.07 | −0.000615508 | ||||||||
\(327\) | 2.88455e6i | 1.49179i | ||||||||
\(328\) | 240370.i | 0.123366i | ||||||||
\(329\) | −1.20369e6 | −0.613089 | ||||||||
\(330\) | −710379. | + | 3.34064e6i | −0.359092 | + | 1.68867i | ||||
\(331\) | 102208. | 0.0512761 | 0.0256381 | − | 0.999671i | \(-0.491838\pi\) | ||||
0.0256381 | + | 0.999671i | \(0.491838\pi\) | |||||||
\(332\) | − | 1.64640e6i | − | 0.819768i | ||||||
\(333\) | 241751.i | 0.119470i | ||||||||
\(334\) | 1.75043e6 | 0.858574 | ||||||||
\(335\) | −3.58694e6 | − | 762755.i | −1.74627 | − | 0.371341i | ||||
\(336\) | 268272. | 0.129637 | ||||||||
\(337\) | 934385.i | 0.448178i | 0.974569 | + | 0.224089i | \(0.0719407\pi\) | ||||
−0.974569 | + | 0.224089i | \(0.928059\pi\) | |||||||
\(338\) | − | 324400.i | − | 0.154450i | ||||||
\(339\) | 714286. | 0.337577 | ||||||||
\(340\) | −1.28507e6 | − | 273267.i | −0.602877 | − | 0.128200i | ||||
\(341\) | −6.55095e6 | −3.05083 | ||||||||
\(342\) | − | 360998.i | − | 0.166894i | ||||||
\(343\) | 1.64638e6i | 0.755603i | ||||||||
\(344\) | −321341. | −0.146410 | ||||||||
\(345\) | 120377. | − | 566088.i | 0.0544499 | − | 0.256057i | ||||
\(346\) | −1.70867e6 | −0.767306 | ||||||||
\(347\) | 469939.i | 0.209517i | 0.994498 | + | 0.104758i | \(0.0334069\pi\) | ||||
−0.994498 | + | 0.104758i | \(0.966593\pi\) | |||||||
\(348\) | 525441.i | 0.232582i | ||||||||
\(349\) | −1.93259e6 | −0.849328 | −0.424664 | − | 0.905351i | \(-0.639608\pi\) | ||||
−0.424664 | + | 0.905351i | \(0.639608\pi\) | |||||||
\(350\) | 611414. | + | 272347.i | 0.266787 | + | 0.118837i | ||||
\(351\) | 1.35564e6 | 0.587322 | ||||||||
\(352\) | − | 799174.i | − | 0.343783i | ||||||
\(353\) | − | 1.47738e6i | − | 0.631040i | −0.948919 | − | 0.315520i | \(-0.897821\pi\) | ||
0.948919 | − | 0.315520i | \(-0.102179\pi\) | |||||||
\(354\) | 1.21579e6 | 0.515644 | ||||||||
\(355\) | 326996. | − | 1.53774e6i | 0.137712 | − | 0.647607i | ||||
\(356\) | −2.02193e6 | −0.845555 | ||||||||
\(357\) | 1.53929e6i | 0.639220i | ||||||||
\(358\) | − | 81607.7i | − | 0.0336530i | ||||||
\(359\) | 2.81086e6 | 1.15107 | 0.575537 | − | 0.817776i | \(-0.304793\pi\) | ||||
0.575537 | + | 0.817776i | \(0.304793\pi\) | |||||||
\(360\) | 489973. | + | 104192.i | 0.199258 | + | 0.0423718i | ||||
\(361\) | −2.06062e6 | −0.832205 | ||||||||
\(362\) | − | 1.08493e6i | − | 0.435142i | ||||||
\(363\) | − | 8.76848e6i | − | 3.49267i | ||||||
\(364\) | 576244. | 0.227957 | ||||||||
\(365\) | 2.20394e6 | + | 468663.i | 0.865901 | + | 0.184132i | ||||
\(366\) | −3.49320e6 | −1.36308 | ||||||||
\(367\) | 1.24139e6i | 0.481107i | 0.970636 | + | 0.240553i | \(0.0773289\pi\) | ||||
−0.970636 | + | 0.240553i | \(0.922671\pi\) | |||||||
\(368\) | 135424.i | 0.0521286i | ||||||||
\(369\) | 525861. | 0.201051 | ||||||||
\(370\) | 80304.4 | − | 377641.i | 0.0304954 | − | 0.143408i | ||||
\(371\) | −1.92524e6 | −0.726190 | ||||||||
\(372\) | 2.62839e6i | 0.984766i | ||||||||
\(373\) | − | 3.43064e6i | − | 1.27674i | −0.769729 | − | 0.638371i | \(-0.779609\pi\) | ||
0.769729 | − | 0.638371i | \(-0.220391\pi\) | |||||||
\(374\) | 4.58549e6 | 1.69515 | ||||||||
\(375\) | 2.76540e6 | + | 2.01028e6i | 1.01550 | + | 0.738208i | ||||
\(376\) | 1.43868e6 | 0.524802 | ||||||||
\(377\) | 1.12864e6i | 0.408979i | ||||||||
\(378\) | 431693.i | 0.155398i | ||||||||
\(379\) | −1.99082e6 | −0.711925 | −0.355963 | − | 0.934500i | \(-0.615847\pi\) | ||||
−0.355963 | + | 0.934500i | \(0.615847\pi\) | |||||||
\(380\) | −119916. | + | 563917.i | −0.0426007 | + | 0.200335i | ||||
\(381\) | −2.62645e6 | −0.926952 | ||||||||
\(382\) | 2.92310e6i | 1.02491i | ||||||||
\(383\) | 1.44737e6i | 0.504177i | 0.967704 | + | 0.252089i | \(0.0811174\pi\) | ||||
−0.967704 | + | 0.252089i | \(0.918883\pi\) | |||||||
\(384\) | −320647. | −0.110968 | ||||||||
\(385\) | −2.28503e6 | − | 485906.i | −0.785669 | − | 0.167071i | ||||
\(386\) | −457605. | −0.156323 | ||||||||
\(387\) | 703002.i | 0.238605i | ||||||||
\(388\) | − | 609809.i | − | 0.205643i | ||||||
\(389\) | −555267. | −0.186049 | −0.0930246 | − | 0.995664i | \(-0.529654\pi\) | ||||
−0.0930246 | + | 0.995664i | \(0.529654\pi\) | |||||||
\(390\) | 2.87903e6 | + | 612219.i | 0.958484 | + | 0.203819i | ||||
\(391\) | −777035. | −0.257039 | ||||||||
\(392\) | − | 892147.i | − | 0.293239i | ||||||
\(393\) | − | 1.10021e6i | − | 0.359332i | ||||||
\(394\) | −3.21563e6 | −1.04358 | ||||||||
\(395\) | −681459. | + | 3.20464e6i | −0.219759 | + | 1.03344i | ||||
\(396\) | −1.74836e6 | −0.560266 | ||||||||
\(397\) | 1.58334e6i | 0.504195i | 0.967702 | + | 0.252097i | \(0.0811203\pi\) | ||||
−0.967702 | + | 0.252097i | \(0.918880\pi\) | |||||||
\(398\) | − | 3.00983e6i | − | 0.952433i | ||||||
\(399\) | 675476. | 0.212411 | ||||||||
\(400\) | −730780. | − | 325517.i | −0.228369 | − | 0.101724i | ||||
\(401\) | −4.49011e6 | −1.39443 | −0.697213 | − | 0.716864i | \(-0.745577\pi\) | ||||
−0.697213 | + | 0.716864i | \(0.745577\pi\) | |||||||
\(402\) | − | 5.13536e6i | − | 1.58491i | ||||||
\(403\) | 5.64574e6i | 1.73164i | ||||||||
\(404\) | 2.34263e6 | 0.714085 | ||||||||
\(405\) | −854246. | + | 4.01719e6i | −0.258789 | + | 1.21698i | ||||
\(406\) | −359406. | −0.108211 | ||||||||
\(407\) | 1.34753e6i | 0.403230i | ||||||||
\(408\) | − | 1.83981e6i | − | 0.547169i | ||||||
\(409\) | 3.30151e6 | 0.975897 | 0.487949 | − | 0.872872i | \(-0.337745\pi\) | ||||
0.487949 | + | 0.872872i | \(0.337745\pi\) | |||||||
\(410\) | −821451. | − | 174680.i | −0.241336 | − | 0.0513195i | ||||
\(411\) | 708972. | 0.207026 | ||||||||
\(412\) | − | 3.34886e6i | − | 0.971974i | ||||||
\(413\) | 831610.i | 0.239908i | ||||||||
\(414\) | 296269. | 0.0849543 | ||||||||
\(415\) | 5.62649e6 | + | 1.19646e6i | 1.60368 | + | 0.341018i | ||||
\(416\) | −688744. | −0.195130 | ||||||||
\(417\) | 159864.i | 0.0450204i | ||||||||
\(418\) | − | 2.01222e6i | − | 0.563293i | ||||||
\(419\) | −1.20798e6 | −0.336145 | −0.168072 | − | 0.985775i | \(-0.553754\pi\) | ||||
−0.168072 | + | 0.985775i | \(0.553754\pi\) | |||||||
\(420\) | −194957. | + | 916806.i | −0.0539281 | + | 0.253603i | ||||
\(421\) | −3.15446e6 | −0.867401 | −0.433701 | − | 0.901057i | \(-0.642792\pi\) | ||||
−0.433701 | + | 0.901057i | \(0.642792\pi\) | |||||||
\(422\) | − | 5.01693e6i | − | 1.37138i | ||||||
\(423\) | − | 3.14743e6i | − | 0.855273i | ||||||
\(424\) | 2.30110e6 | 0.621615 | ||||||||
\(425\) | 1.86775e6 | − | 4.19306e6i | 0.501586 | − | 1.12605i | ||||
\(426\) | 2.20155e6 | 0.587766 | ||||||||
\(427\) | − | 2.38938e6i | − | 0.634184i | ||||||
\(428\) | − | 994539.i | − | 0.262429i | ||||||
\(429\) | −1.02732e7 | −2.69503 | ||||||||
\(430\) | 233522. | − | 1.09816e6i | 0.0609055 | − | 0.286415i | ||||
\(431\) | 3.27599e6 | 0.849473 | 0.424737 | − | 0.905317i | \(-0.360367\pi\) | ||||
0.424737 | + | 0.905317i | \(0.360367\pi\) | |||||||
\(432\) | − | 515972.i | − | 0.133020i | ||||||
\(433\) | 1.75726e6i | 0.450418i | 0.974310 | + | 0.225209i | \(0.0723065\pi\) | ||||
−0.974310 | + | 0.225209i | \(0.927693\pi\) | |||||||
\(434\) | −1.79784e6 | −0.458171 | ||||||||
\(435\) | −1.79566e6 | − | 381844.i | −0.454990 | − | 0.0967525i | ||||
\(436\) | 2.35825e6 | 0.594120 | ||||||||
\(437\) | 340981.i | 0.0854134i | ||||||||
\(438\) | 3.15534e6i | 0.785889i | ||||||||
\(439\) | 2.81340e6 | 0.696739 | 0.348369 | − | 0.937357i | \(-0.386736\pi\) | ||||
0.348369 | + | 0.937357i | \(0.386736\pi\) | |||||||
\(440\) | 2.73113e6 | + | 580769.i | 0.672529 | + | 0.143012i | ||||
\(441\) | −1.95176e6 | −0.477893 | ||||||||
\(442\) | − | 3.95187e6i | − | 0.962159i | ||||||
\(443\) | 1.90766e6i | 0.461839i | 0.972973 | + | 0.230919i | \(0.0741734\pi\) | ||||
−0.972973 | + | 0.230919i | \(0.925827\pi\) | |||||||
\(444\) | 540660. | 0.130157 | ||||||||
\(445\) | 1.46936e6 | − | 6.90984e6i | 0.351746 | − | 1.65412i | ||||
\(446\) | 363881. | 0.0866208 | ||||||||
\(447\) | 3.80356e6i | 0.900371i | ||||||||
\(448\) | − | 219325.i | − | 0.0516290i | ||||||
\(449\) | 3.31733e6 | 0.776555 | 0.388278 | − | 0.921542i | \(-0.373070\pi\) | ||||
0.388278 | + | 0.921542i | \(0.373070\pi\) | |||||||
\(450\) | −712138. | + | 1.59874e6i | −0.165780 | + | 0.372174i | ||||
\(451\) | 2.93118e6 | 0.678579 | ||||||||
\(452\) | − | 583962.i | − | 0.134443i | ||||||
\(453\) | − | 6.01220e6i | − | 1.37654i | ||||||
\(454\) | −4.31345e6 | −0.982167 | ||||||||
\(455\) | −418763. | + | 1.96928e6i | −0.0948288 | + | 0.445943i | ||||
\(456\) | −807349. | −0.181823 | ||||||||
\(457\) | − | 5.76386e6i | − | 1.29099i | −0.763765 | − | 0.645495i | \(-0.776651\pi\) | ||
0.763765 | − | 0.645495i | \(-0.223349\pi\) | |||||||
\(458\) | − | 2.32354e6i | − | 0.517591i | ||||||
\(459\) | 2.96054e6 | 0.655903 | ||||||||
\(460\) | −462804. | − | 98414.2i | −0.101977 | − | 0.0216852i | ||||
\(461\) | −727884. | −0.159518 | −0.0797591 | − | 0.996814i | \(-0.525415\pi\) | ||||
−0.0797591 | + | 0.996814i | \(0.525415\pi\) | |||||||
\(462\) | − | 3.27143e6i | − | 0.713070i | ||||||
\(463\) | − | 7.57732e6i | − | 1.64272i | −0.570412 | − | 0.821359i | \(-0.693216\pi\) | ||
0.570412 | − | 0.821359i | \(-0.306784\pi\) | |||||||
\(464\) | 429572. | 0.0926278 | ||||||||
\(465\) | −8.98238e6 | − | 1.91008e6i | −1.92646 | − | 0.409656i | ||||
\(466\) | −995033. | −0.212262 | ||||||||
\(467\) | − | 6.84806e6i | − | 1.45303i | −0.687149 | − | 0.726517i | \(-0.741138\pi\) | ||
0.687149 | − | 0.726517i | \(-0.258862\pi\) | |||||||
\(468\) | 1.50678e6i | 0.318005i | ||||||||
\(469\) | 3.51263e6 | 0.737395 | ||||||||
\(470\) | −1.04551e6 | + | 4.91661e6i | −0.218314 | + | 1.02665i | ||||
\(471\) | −1.18624e6 | −0.246389 | ||||||||
\(472\) | − | 993964.i | − | 0.205360i | ||||||
\(473\) | 3.91856e6i | 0.805330i | ||||||||
\(474\) | −4.58802e6 | −0.937949 | ||||||||
\(475\) | −1.84001e6 | − | 819610.i | −0.374185 | − | 0.166676i | ||||
\(476\) | 1.25844e6 | 0.254575 | ||||||||
\(477\) | − | 5.03416e6i | − | 1.01305i | ||||||
\(478\) | − | 4.16900e6i | − | 0.834569i | ||||||
\(479\) | 9.44682e6 | 1.88125 | 0.940626 | − | 0.339446i | \(-0.110239\pi\) | ||||
0.940626 | + | 0.339446i | \(0.110239\pi\) | |||||||
\(480\) | 233018. | − | 1.09579e6i | 0.0461621 | − | 0.217083i | ||||
\(481\) | 1.16133e6 | 0.228872 | ||||||||
\(482\) | 858880.i | 0.168390i | ||||||||
\(483\) | 554360.i | 0.108124i | ||||||||
\(484\) | −7.16865e6 | −1.39099 | ||||||||
\(485\) | 2.08399e6 | + | 443155.i | 0.402291 | + | 0.0855463i | ||||
\(486\) | −3.79225e6 | −0.728293 | ||||||||
\(487\) | 9.32525e6i | 1.78171i | 0.454284 | + | 0.890857i | \(0.349895\pi\) | ||||
−0.454284 | + | 0.890857i | \(0.650105\pi\) | |||||||
\(488\) | 2.85585e6i | 0.542858i | ||||||||
\(489\) | 5778.63 | 0.00109283 | ||||||||
\(490\) | 3.04886e6 | + | 648334.i | 0.573651 | + | 0.121986i | ||||
\(491\) | 1.36714e6 | 0.255923 | 0.127961 | − | 0.991779i | \(-0.459157\pi\) | ||||
0.127961 | + | 0.991779i | \(0.459157\pi\) | |||||||
\(492\) | − | 1.17606e6i | − | 0.219036i | ||||||
\(493\) | 2.46480e6i | 0.456735i | ||||||||
\(494\) | −1.73417e6 | −0.319723 | ||||||||
\(495\) | 1.27056e6 | − | 5.97494e6i | 0.233067 | − | 1.09602i | ||||
\(496\) | 2.14883e6 | 0.392192 | ||||||||
\(497\) | 1.50588e6i | 0.273463i | ||||||||
\(498\) | 8.05533e6i | 1.45549i | ||||||||
\(499\) | −1.48585e6 | −0.267130 | −0.133565 | − | 0.991040i | \(-0.542643\pi\) | ||||
−0.133565 | + | 0.991040i | \(0.542643\pi\) | |||||||
\(500\) | 1.64350e6 | − | 2.26084e6i | 0.293998 | − | 0.404432i | ||||
\(501\) | −8.56429e6 | −1.52439 | ||||||||
\(502\) | 3.08694e6i | 0.546725i | ||||||||
\(503\) | 4.47115e6i | 0.787950i | 0.919121 | + | 0.393975i | \(0.128900\pi\) | ||||
−0.919121 | + | 0.393975i | \(0.871100\pi\) | |||||||
\(504\) | −479821. | −0.0841401 | ||||||||
\(505\) | −1.70241e6 | + | 8.00579e6i | −0.297055 | + | 1.39693i | ||||
\(506\) | 1.65142e6 | 0.286735 | ||||||||
\(507\) | 1.58719e6i | 0.274225i | ||||||||
\(508\) | 2.14725e6i | 0.369167i | ||||||||
\(509\) | −2.69478e6 | −0.461029 | −0.230515 | − | 0.973069i | \(-0.574041\pi\) | ||||
−0.230515 | + | 0.973069i | \(0.574041\pi\) | |||||||
\(510\) | 6.28743e6 | + | 1.33701e6i | 1.07040 | + | 0.227619i | ||||
\(511\) | −2.15828e6 | −0.365642 | ||||||||
\(512\) | 262144.i | 0.0441942i | ||||||||
\(513\) | − | 1.29915e6i | − | 0.217955i | ||||||
\(514\) | −5.63249e6 | −0.940357 | ||||||||
\(515\) | 1.14446e7 | + | 2.43366e6i | 1.90143 | + | 0.404335i | ||||
\(516\) | 1.57222e6 | 0.259949 | ||||||||
\(517\) | − | 1.75439e7i | − | 2.88669i | ||||||
\(518\) | 369816.i | 0.0605567i | ||||||||
\(519\) | 8.36000e6 | 1.36235 | ||||||||
\(520\) | 500518. | − | 2.35374e6i | 0.0811730 | − | 0.381725i | ||||
\(521\) | 7.16127e6 | 1.15583 | 0.577917 | − | 0.816095i | \(-0.303866\pi\) | ||||
0.577917 | + | 0.816095i | \(0.303866\pi\) | |||||||
\(522\) | − | 939782.i | − | 0.150956i | ||||||
\(523\) | − | 6.27593e6i | − | 1.00328i | −0.865075 | − | 0.501642i | \(-0.832729\pi\) | ||
0.865075 | − | 0.501642i | \(-0.167271\pi\) | |||||||
\(524\) | −899477. | −0.143107 | ||||||||
\(525\) | −2.99146e6 | − | 1.33251e6i | −0.473679 | − | 0.210994i | ||||
\(526\) | −974228. | −0.153531 | ||||||||
\(527\) | 1.23296e7i | 1.93384i | ||||||||
\(528\) | 3.91010e6i | 0.610385i | ||||||||
\(529\) | −279841. | −0.0434783 | ||||||||
\(530\) | −1.67224e6 | + | 7.86390e6i | −0.258588 | + | 1.21604i | ||||
\(531\) | −2.17451e6 | −0.334677 | ||||||||
\(532\) | − | 552234.i | − | 0.0845948i | ||||||
\(533\) | − | 2.52615e6i | − | 0.385159i | ||||||
\(534\) | 9.89268e6 | 1.50128 | ||||||||
\(535\) | 3.39878e6 | + | 722743.i | 0.513380 | + | 0.109169i | ||||
\(536\) | −4.19839e6 | −0.631206 | ||||||||
\(537\) | 399281.i | 0.0597506i | ||||||||
\(538\) | − | 3.30532e6i | − | 0.492332i | ||||||
\(539\) | −1.08792e7 | −1.61297 | ||||||||
\(540\) | 1.76331e6 | + | 374963.i | 0.260222 | + | 0.0553355i | ||||
\(541\) | 4.63215e6 | 0.680440 | 0.340220 | − | 0.940346i | \(-0.389499\pi\) | ||||
0.340220 | + | 0.940346i | \(0.389499\pi\) | |||||||
\(542\) | − | 3.52891e6i | − | 0.515991i | ||||||
\(543\) | 5.30823e6i | 0.772592i | ||||||||
\(544\) | −1.50413e6 | −0.217915 | ||||||||
\(545\) | −1.71377e6 | + | 8.05920e6i | −0.247150 | + | 1.16225i | ||||
\(546\) | −2.81938e6 | −0.404736 | ||||||||
\(547\) | − | 1.21288e7i | − | 1.73321i | −0.498996 | − | 0.866604i | \(-0.666298\pi\) | ||
0.498996 | − | 0.866604i | \(-0.333702\pi\) | |||||||
\(548\) | − | 579618.i | − | 0.0824500i | ||||||
\(549\) | 6.24780e6 | 0.884700 | ||||||||
\(550\) | −3.96949e6 | + | 8.91144e6i | −0.559536 | + | 1.25615i | ||||
\(551\) | 1.08161e6 | 0.151772 | ||||||||
\(552\) | − | 662587.i | − | 0.0925540i | ||||||
\(553\) | − | 3.13824e6i | − | 0.436389i | ||||||
\(554\) | −763773. | −0.105728 | ||||||||
\(555\) | −392904. | + | 1.84768e6i | −0.0541445 | + | 0.254621i | ||||
\(556\) | 130696. | 0.0179298 | ||||||||
\(557\) | − | 3.23067e6i | − | 0.441220i | −0.975362 | − | 0.220610i | \(-0.929195\pi\) | ||
0.975362 | − | 0.220610i | \(-0.0708048\pi\) | |||||||
\(558\) | − | 4.70104e6i | − | 0.639158i | ||||||
\(559\) | 3.37710e6 | 0.457103 | ||||||||
\(560\) | 749532. | + | 159386.i | 0.101000 | + | 0.0214773i | ||||
\(561\) | −2.24354e7 | −3.00972 | ||||||||
\(562\) | − | 5.07479e6i | − | 0.677762i | ||||||
\(563\) | 1.05981e7i | 1.40914i | 0.709632 | + | 0.704572i | \(0.248861\pi\) | ||||
−0.709632 | + | 0.704572i | \(0.751139\pi\) | |||||||
\(564\) | −7.03902e6 | −0.931782 | ||||||||
\(565\) | 1.99566e6 | + | 424372.i | 0.263006 | + | 0.0559275i | ||||
\(566\) | 9.62989e6 | 1.26351 | ||||||||
\(567\) | − | 3.93396e6i | − | 0.513893i | ||||||
\(568\) | − | 1.79987e6i | − | 0.234083i | ||||||
\(569\) | 861625. | 0.111567 | 0.0557837 | − | 0.998443i | \(-0.482234\pi\) | ||||
0.0557837 | + | 0.998443i | \(0.482234\pi\) | |||||||
\(570\) | 586709. | − | 2.75907e6i | 0.0756373 | − | 0.355693i | ||||
\(571\) | 2.42311e6 | 0.311016 | 0.155508 | − | 0.987835i | \(-0.450299\pi\) | ||||
0.155508 | + | 0.987835i | \(0.450299\pi\) | |||||||
\(572\) | 8.39884e6i | 1.07332i | ||||||||
\(573\) | − | 1.43018e7i | − | 1.81972i | ||||||
\(574\) | 804432. | 0.101908 | ||||||||
\(575\) | 672650. | − | 1.51009e6i | 0.0848436 | − | 0.190473i | ||||
\(576\) | 573496. | 0.0720236 | ||||||||
\(577\) | 1.06364e7i | 1.33001i | 0.746838 | + | 0.665006i | \(0.231571\pi\) | ||||
−0.746838 | + | 0.665006i | \(0.768429\pi\) | |||||||
\(578\) | − | 2.95095e6i | − | 0.367402i | ||||||
\(579\) | 2.23892e6 | 0.277550 | ||||||||
\(580\) | −312175. | + | 1.46804e6i | −0.0385326 | + | 0.181204i | ||||
\(581\) | −5.50992e6 | −0.677181 | ||||||||
\(582\) | 2.98360e6i | 0.365118i | ||||||||
\(583\) | − | 2.80606e7i | − | 3.41921i | ||||||
\(584\) | 2.57964e6 | 0.312987 | ||||||||
\(585\) | −5.14932e6 | − | 1.09499e6i | −0.622100 | − | 0.132288i | ||||
\(586\) | −502849. | −0.0604914 | ||||||||
\(587\) | − | 1.21123e7i | − | 1.45088i | −0.688287 | − | 0.725439i | \(-0.741637\pi\) | ||
0.688287 | − | 0.725439i | \(-0.258363\pi\) | |||||||
\(588\) | 4.36500e6i | 0.520644i | ||||||||
\(589\) | 5.41050e6 | 0.642612 | ||||||||
\(590\) | 3.39682e6 | + | 722325.i | 0.401737 | + | 0.0854285i | ||||
\(591\) | 1.57331e7 | 1.85287 | ||||||||
\(592\) | − | 442015.i | − | 0.0518362i | ||||||
\(593\) | − | 588269.i | − | 0.0686972i | −0.999410 | − | 0.0343486i | \(-0.989064\pi\) | ||
0.999410 | − | 0.0343486i | \(-0.0109357\pi\) | |||||||
\(594\) | −6.29198e6 | −0.731680 | ||||||||
\(595\) | −914525. | + | 4.30066e6i | −0.105902 | + | 0.498015i | ||||
\(596\) | 3.10959e6 | 0.358581 | ||||||||
\(597\) | 1.47262e7i | 1.69104i | ||||||||
\(598\) | − | 1.42322e6i | − | 0.162750i | ||||||
\(599\) | 2.11966e6 | 0.241379 | 0.120690 | − | 0.992690i | \(-0.461489\pi\) | ||||
0.120690 | + | 0.992690i | \(0.461489\pi\) | |||||||
\(600\) | 3.57547e6 | + | 1.59265e6i | 0.405467 | + | 0.180610i | ||||
\(601\) | 1.05488e7 | 1.19129 | 0.595645 | − | 0.803248i | \(-0.296897\pi\) | ||||
0.595645 | + | 0.803248i | \(0.296897\pi\) | |||||||
\(602\) | 1.07541e6i | 0.120944i | ||||||||
\(603\) | 9.18489e6i | 1.02868i | ||||||||
\(604\) | −4.91526e6 | −0.548219 | ||||||||
\(605\) | 5.20954e6 | − | 2.44984e7i | 0.578643 | − | 2.72113i | ||||
\(606\) | −1.14617e7 | −1.26785 | ||||||||
\(607\) | 5.38842e6i | 0.593595i | 0.954940 | + | 0.296797i | \(0.0959186\pi\) | ||||
−0.954940 | + | 0.296797i | \(0.904081\pi\) | |||||||
\(608\) | 660046.i | 0.0724127i | ||||||||
\(609\) | 1.75846e6 | 0.192127 | ||||||||
\(610\) | −9.75972e6 | − | 2.07538e6i | −1.06197 | − | 0.225826i | ||||
\(611\) | −1.51197e7 | −1.63847 | ||||||||
\(612\) | 3.29060e6i | 0.355138i | ||||||||
\(613\) | 1.09383e7i | 1.17571i | 0.808968 | + | 0.587853i | \(0.200027\pi\) | ||||
−0.808968 | + | 0.587853i | \(0.799973\pi\) | |||||||
\(614\) | −3.02410e6 | −0.323724 | ||||||||
\(615\) | 4.01910e6 | + | 854653.i | 0.428491 | + | 0.0911175i | ||||
\(616\) | −2.67455e6 | −0.283987 | ||||||||
\(617\) | − | 1.36733e6i | − | 0.144597i | −0.997383 | − | 0.0722984i | \(-0.976967\pi\) | ||
0.997383 | − | 0.0722984i | \(-0.0230334\pi\) | |||||||
\(618\) | 1.63849e7i | 1.72573i | ||||||||
\(619\) | 1.32601e7 | 1.39097 | 0.695487 | − | 0.718539i | \(-0.255189\pi\) | ||||
0.695487 | + | 0.718539i | \(0.255189\pi\) | |||||||
\(620\) | −1.56158e6 | + | 7.34352e6i | −0.163150 | + | 0.767229i | ||||
\(621\) | 1.06621e6 | 0.110946 | ||||||||
\(622\) | 1.23061e6i | 0.127539i | ||||||||
\(623\) | 6.76668e6i | 0.698483i | ||||||||
\(624\) | 3.36981e6 | 0.346452 | ||||||||
\(625\) | 6.53195e6 | + | 7.25955e6i | 0.668872 | + | 0.743378i | ||||
\(626\) | 7.59943e6 | 0.775077 | ||||||||
\(627\) | 9.84515e6i | 1.00012i | ||||||||
\(628\) | 969811.i | 0.0981269i | ||||||||
\(629\) | 2.53619e6 | 0.255597 | ||||||||
\(630\) | 348692. | − | 1.63976e6i | 0.0350018 | − | 0.164600i | ||||
\(631\) | −1.18972e7 | −1.18952 | −0.594759 | − | 0.803904i | \(-0.702752\pi\) | ||||
−0.594759 | + | 0.803904i | \(0.702752\pi\) | |||||||
\(632\) | 3.75092e6i | 0.373547i | ||||||||
\(633\) | 2.45463e7i | 2.43487i | ||||||||
\(634\) | 1.53147e6 | 0.151316 | ||||||||
\(635\) | −7.33811e6 | − | 1.56043e6i | −0.722187 | − | 0.153571i | ||||
\(636\) | −1.12586e7 | −1.10367 | ||||||||
\(637\) | 9.37593e6i | 0.915516i | ||||||||
\(638\) | − | 5.23839e6i | − | 0.509502i | ||||||
\(639\) | −3.93760e6 | −0.381487 | ||||||||
\(640\) | −895862. | − | 190503.i | −0.0864552 | − | 0.0183845i | ||||
\(641\) | 5.59030e6 | 0.537390 | 0.268695 | − | 0.963225i | \(-0.413408\pi\) | ||||
0.268695 | + | 0.963225i | \(0.413408\pi\) | |||||||
\(642\) | 4.86597e6i | 0.465942i | ||||||||
\(643\) | − | 6.57079e6i | − | 0.626744i | −0.949631 | − | 0.313372i | \(-0.898541\pi\) | ||
0.949631 | − | 0.313372i | \(-0.101459\pi\) | |||||||
\(644\) | 453215. | 0.0430616 | ||||||||
\(645\) | −1.14255e6 | + | 5.37297e6i | −0.108137 | + | 0.508528i | ||||
\(646\) | −3.78721e6 | −0.357057 | ||||||||
\(647\) | 1.89036e6i | 0.177535i | 0.996052 | + | 0.0887675i | \(0.0282928\pi\) | ||||
−0.996052 | + | 0.0887675i | \(0.971707\pi\) | |||||||
\(648\) | 4.70198e6i | 0.439889i | ||||||||
\(649\) | −1.21208e7 | −1.12959 | ||||||||
\(650\) | 7.68006e6 | + | 3.42098e6i | 0.712986 | + | 0.317591i | ||||
\(651\) | 8.79628e6 | 0.813480 | ||||||||
\(652\) | − | 4724.30i | − | 0.000435230i | ||||||
\(653\) | − | 5.78907e6i | − | 0.531283i | −0.964072 | − | 0.265642i | \(-0.914416\pi\) | ||
0.964072 | − | 0.265642i | \(-0.0855838\pi\) | |||||||
\(654\) | −1.15382e7 | −1.05486 | ||||||||
\(655\) | 653660. | − | 3.07391e6i | 0.0595318 | − | 0.279955i | ||||
\(656\) | −961481. | −0.0872330 | ||||||||
\(657\) | − | 5.64352e6i | − | 0.510078i | ||||||
\(658\) | − | 4.81475e6i | − | 0.433520i | ||||||
\(659\) | 9.61079e6 | 0.862076 | 0.431038 | − | 0.902334i | \(-0.358148\pi\) | ||||
0.431038 | + | 0.902334i | \(0.358148\pi\) | |||||||
\(660\) | −1.33626e7 | − | 2.84152e6i | −1.19407 | − | 0.253916i | ||||
\(661\) | 2.38311e6 | 0.212149 | 0.106074 | − | 0.994358i | \(-0.466172\pi\) | ||||
0.106074 | + | 0.994358i | \(0.466172\pi\) | |||||||
\(662\) | 408832.i | 0.0362577i | ||||||||
\(663\) | 1.93353e7i | 1.70831i | ||||||||
\(664\) | 6.58561e6 | 0.579663 | ||||||||
\(665\) | 1.88723e6 | + | 401314.i | 0.165489 | + | 0.0351909i | ||||
\(666\) | −967004. | −0.0844778 | ||||||||
\(667\) | 887671.i | 0.0772569i | ||||||||
\(668\) | 7.00171e6i | 0.607104i | ||||||||
\(669\) | −1.78036e6 | −0.153795 | ||||||||
\(670\) | 3.05102e6 | − | 1.43478e7i | 0.262578 | − | 1.23480i | ||||
\(671\) | 3.48255e7 | 2.98601 | ||||||||
\(672\) | 1.07309e6i | 0.0916670i | ||||||||
\(673\) | 2.50943e6i | 0.213568i | 0.994282 | + | 0.106784i | \(0.0340554\pi\) | ||||
−0.994282 | + | 0.106784i | \(0.965945\pi\) | |||||||
\(674\) | −3.73754e6 | −0.316910 | ||||||||
\(675\) | −2.56283e6 | + | 5.75351e6i | −0.216501 | + | 0.486041i | ||||
\(676\) | 1.29760e6 | 0.109213 | ||||||||
\(677\) | 1.40322e7i | 1.17667i | 0.808618 | + | 0.588334i | \(0.200216\pi\) | ||||
−0.808618 | + | 0.588334i | \(0.799784\pi\) | |||||||
\(678\) | 2.85714e6i | 0.238703i | ||||||||
\(679\) | −2.04081e6 | −0.169874 | ||||||||
\(680\) | 1.09307e6 | − | 5.14027e6i | 0.0906514 | − | 0.426299i | ||||
\(681\) | 2.11044e7 | 1.74383 | ||||||||
\(682\) | − | 2.62038e7i | − | 2.15726i | ||||||
\(683\) | − | 8.92764e6i | − | 0.732293i | −0.930557 | − | 0.366147i | \(-0.880677\pi\) | ||
0.930557 | − | 0.366147i | \(-0.119323\pi\) | |||||||
\(684\) | 1.44399e6 | 0.118012 | ||||||||
\(685\) | 1.98081e6 | + | 421215.i | 0.161293 | + | 0.0342987i | ||||
\(686\) | −6.58550e6 | −0.534292 | ||||||||
\(687\) | 1.13683e7i | 0.918979i | ||||||||
\(688\) | − | 1.28536e6i | − | 0.103527i | ||||||
\(689\) | −2.41832e7 | −1.94074 | ||||||||
\(690\) | 2.26435e6 | + | 481509.i | 0.181060 | + | 0.0385019i | ||||
\(691\) | −2.95681e6 | −0.235574 | −0.117787 | − | 0.993039i | \(-0.537580\pi\) | ||||
−0.117787 | + | 0.993039i | \(0.537580\pi\) | |||||||
\(692\) | − | 6.83469e6i | − | 0.542567i | ||||||
\(693\) | 5.85114e6i | 0.462815i | ||||||||
\(694\) | −1.87976e6 | −0.148151 | ||||||||
\(695\) | −94978.3 | + | 446646.i | −0.00745868 | + | 0.0350753i | ||||
\(696\) | −2.10176e6 | −0.164460 | ||||||||
\(697\) | − | 5.51678e6i | − | 0.430134i | ||||||
\(698\) | − | 7.73035e6i | − | 0.600565i | ||||||
\(699\) | 4.86838e6 | 0.376870 | ||||||||
\(700\) | −1.08939e6 | + | 2.44566e6i | −0.0840305 | + | 0.188647i | ||||
\(701\) | −1.61483e7 | −1.24117 | −0.620586 | − | 0.784138i | \(-0.713105\pi\) | ||||
−0.620586 | + | 0.784138i | \(0.713105\pi\) | |||||||
\(702\) | 5.42256e6i | 0.415300i | ||||||||
\(703\) | − | 1.11294e6i | − | 0.0849343i | ||||||
\(704\) | 3.19669e6 | 0.243091 | ||||||||
\(705\) | 5.11533e6 | − | 2.40554e7i | 0.387615 | − | 1.82281i | ||||
\(706\) | 5.90954e6 | 0.446213 | ||||||||
\(707\) | − | 7.83993e6i | − | 0.589880i | ||||||
\(708\) | 4.86315e6i | 0.364615i | ||||||||
\(709\) | 2.50051e7 | 1.86815 | 0.934077 | − | 0.357071i | \(-0.116224\pi\) | ||||
0.934077 | + | 0.357071i | \(0.116224\pi\) | |||||||
\(710\) | 6.15095e6 | + | 1.30799e6i | 0.457927 | + | 0.0973771i | ||||
\(711\) | 8.20595e6 | 0.608772 | ||||||||
\(712\) | − | 8.08773e6i | − | 0.597898i | ||||||
\(713\) | 4.44037e6i | 0.327111i | ||||||||
\(714\) | −6.15717e6 | −0.451997 | ||||||||
\(715\) | −2.87025e7 | − | 6.10353e6i | −2.09969 | − | 0.446494i | ||||
\(716\) | 326431. | 0.0237962 | ||||||||
\(717\) | 2.03976e7i | 1.48177i | ||||||||
\(718\) | 1.12434e7i | 0.813932i | ||||||||
\(719\) | 8.14571e6 | 0.587634 | 0.293817 | − | 0.955862i | \(-0.405074\pi\) | ||||
0.293817 | + | 0.955862i | \(0.405074\pi\) | |||||||
\(720\) | −416766. | + | 1.95989e6i | −0.0299614 | + | 0.140897i | ||||
\(721\) | −1.12074e7 | −0.802912 | ||||||||
\(722\) | − | 8.24248e6i | − | 0.588458i | ||||||
\(723\) | − | 4.20223e6i | − | 0.298975i | ||||||
\(724\) | 4.33973e6 | 0.307692 | ||||||||
\(725\) | −4.79008e6 | − | 2.13368e6i | −0.338453 | − | 0.150759i | ||||
\(726\) | 3.50739e7 | 2.46969 | ||||||||
\(727\) | 1.19636e7i | 0.839513i | 0.907637 | + | 0.419757i | \(0.137885\pi\) | ||||
−0.907637 | + | 0.419757i | \(0.862115\pi\) | |||||||
\(728\) | 2.30498e6i | 0.161190i | ||||||||
\(729\) | 701432. | 0.0488840 | ||||||||
\(730\) | −1.87465e6 | + | 8.81577e6i | −0.130201 | + | 0.612284i | ||||
\(731\) | 7.37514e6 | 0.510478 | ||||||||
\(732\) | − | 1.39728e7i | − | 0.963841i | ||||||
\(733\) | 2.10035e7i | 1.44388i | 0.691953 | + | 0.721942i | \(0.256750\pi\) | ||||
−0.691953 | + | 0.721942i | \(0.743250\pi\) | |||||||
\(734\) | −4.96554e6 | −0.340194 | ||||||||
\(735\) | −1.49171e7 | − | 3.17209e6i | −1.01851 | − | 0.216585i | ||||
\(736\) | −541696. | −0.0368605 | ||||||||
\(737\) | 5.11970e7i | 3.47197i | ||||||||
\(738\) | 2.10345e6i | 0.142164i | ||||||||
\(739\) | −1.94336e6 | −0.130901 | −0.0654504 | − | 0.997856i | \(-0.520848\pi\) | ||||
−0.0654504 | + | 0.997856i | \(0.520848\pi\) | |||||||
\(740\) | 1.51056e6 | + | 321218.i | 0.101405 | + | 0.0215635i | ||||
\(741\) | 8.48475e6 | 0.567667 | ||||||||
\(742\) | − | 7.70097e6i | − | 0.513494i | ||||||
\(743\) | − | 2.01868e7i | − | 1.34152i | −0.741676 | − | 0.670759i | \(-0.765969\pi\) | ||
0.741676 | − | 0.670759i | \(-0.234031\pi\) | |||||||
\(744\) | −1.05136e7 | −0.696335 | ||||||||
\(745\) | −2.25977e6 | + | 1.06268e7i | −0.149168 | + | 0.701477i | ||||
\(746\) | 1.37226e7 | 0.902793 | ||||||||
\(747\) | − | 1.44074e7i | − | 0.944682i | ||||||
\(748\) | 1.83420e7i | 1.19865i | ||||||||
\(749\) | −3.32836e6 | −0.216784 | ||||||||
\(750\) | −8.04113e6 | + | 1.10616e7i | −0.521992 | + | 0.718066i | ||||
\(751\) | 9.14175e6 | 0.591465 | 0.295733 | − | 0.955271i | \(-0.404436\pi\) | ||||
0.295733 | + | 0.955271i | \(0.404436\pi\) | |||||||
\(752\) | 5.75473e6i | 0.371091i | ||||||||
\(753\) | − | 1.51034e7i | − | 0.970707i | ||||||
\(754\) | −4.51455e6 | −0.289192 | ||||||||
\(755\) | 3.57197e6 | − | 1.67976e7i | 0.228056 | − | 1.07246i | ||||
\(756\) | −1.72677e6 | −0.109883 | ||||||||
\(757\) | − | 5.63495e6i | − | 0.357397i | −0.983904 | − | 0.178698i | \(-0.942811\pi\) | ||
0.983904 | − | 0.178698i | \(-0.0571886\pi\) | |||||||
\(758\) | − | 7.96329e6i | − | 0.503407i | ||||||
\(759\) | −8.07986e6 | −0.509096 | ||||||||
\(760\) | −2.25567e6 | − | 479663.i | −0.141658 | − | 0.0301233i | ||||
\(761\) | 1.12069e7 | 0.701493 | 0.350746 | − | 0.936471i | \(-0.385928\pi\) | ||||
0.350746 | + | 0.936471i | \(0.385928\pi\) | |||||||
\(762\) | − | 1.05058e7i | − | 0.655454i | ||||||
\(763\) | − | 7.89222e6i | − | 0.490781i | ||||||
\(764\) | −1.16924e7 | −0.724720 | ||||||||
\(765\) | −1.12455e7 | − | 2.39132e6i | −0.694742 | − | 0.147735i | ||||
\(766\) | −5.78949e6 | −0.356507 | ||||||||
\(767\) | 1.04460e7i | 0.641151i | ||||||||
\(768\) | − | 1.28259e6i | − | 0.0784665i | ||||||
\(769\) | −2.71072e7 | −1.65298 | −0.826491 | − | 0.562949i | \(-0.809667\pi\) | ||||
−0.826491 | + | 0.562949i | \(0.809667\pi\) | |||||||
\(770\) | 1.94362e6 | − | 9.14011e6i | 0.118137 | − | 0.555552i | ||||
\(771\) | 2.75580e7 | 1.66960 | ||||||||
\(772\) | − | 1.83042e6i | − | 0.110537i | ||||||
\(773\) | 2.01774e7i | 1.21455i | 0.794492 | + | 0.607275i | \(0.207737\pi\) | ||||
−0.794492 | + | 0.607275i | \(0.792263\pi\) | |||||||
\(774\) | −2.81201e6 | −0.168719 | ||||||||
\(775\) | −2.39613e7 | − | 1.06732e7i | −1.43303 | − | 0.638325i | ||||
\(776\) | 2.43923e6 | 0.145412 | ||||||||
\(777\) | − | 1.80940e6i | − | 0.107518i | ||||||
\(778\) | − | 2.22107e6i | − | 0.131557i | ||||||
\(779\) | −2.42089e6 | −0.142932 | ||||||||
\(780\) | −2.44888e6 | + | 1.15161e7i | −0.144122 | + | 0.677751i | ||||
\(781\) | −2.19484e7 | −1.28758 | ||||||||
\(782\) | − | 3.10814e6i | − | 0.181754i | ||||||
\(783\) | − | 3.38207e6i | − | 0.197142i | ||||||
\(784\) | 3.56859e6 | 0.207351 | ||||||||
\(785\) | −3.31427e6 | − | 704773.i | −0.191962 | − | 0.0408202i | ||||
\(786\) | 4.40086e6 | 0.254086 | ||||||||
\(787\) | 6.49867e6i | 0.374014i | 0.982359 | + | 0.187007i | \(0.0598787\pi\) | ||||
−0.982359 | + | 0.187007i | \(0.940121\pi\) | |||||||
\(788\) | − | 1.28625e7i | − | 0.737923i | ||||||
\(789\) | 4.76659e6 | 0.272594 | ||||||||
\(790\) | −1.28186e7 | − | 2.72584e6i | −0.730754 | − | 0.155393i | ||||
\(791\) | −1.95431e6 | −0.111059 | ||||||||
\(792\) | − | 6.99346e6i | − | 0.396168i | ||||||
\(793\) | − | 3.00133e7i | − | 1.69485i | ||||||
\(794\) | −6.33337e6 | −0.356520 | ||||||||
\(795\) | 8.18174e6 | − | 3.84756e7i | 0.459122 | − | 2.15907i | ||||
\(796\) | 1.20393e7 | 0.673472 | ||||||||
\(797\) | 1.37055e6i | 0.0764272i | 0.999270 | + | 0.0382136i | \(0.0121667\pi\) | ||||
−0.999270 | + | 0.0382136i | \(0.987833\pi\) | |||||||
\(798\) | 2.70190e6i | 0.150198i | ||||||||
\(799\) | −3.30194e7 | −1.82980 | ||||||||
\(800\) | 1.30207e6 | − | 2.92312e6i | 0.0719297 | − | 0.161481i | ||||
\(801\) | −1.76937e7 | −0.974398 | ||||||||
\(802\) | − | 1.79604e7i | − | 0.986009i | ||||||
\(803\) | − | 3.14572e7i | − | 1.72160i | ||||||
\(804\) | 2.05414e7 | 1.12070 | ||||||||
\(805\) | −329357. | + | 1.54884e6i | −0.0179133 | + | 0.0842396i | ||||
\(806\) | −2.25830e7 | −1.22446 | ||||||||
\(807\) | 1.61719e7i | 0.874132i | ||||||||
\(808\) | 9.37051e6i | 0.504934i | ||||||||
\(809\) | −5.75863e6 | −0.309348 | −0.154674 | − | 0.987966i | \(-0.549433\pi\) | ||||
−0.154674 | + | 0.987966i | \(0.549433\pi\) | |||||||
\(810\) | −1.60688e7 | − | 3.41698e6i | −0.860538 | − | 0.182991i | ||||
\(811\) | 2.12716e7 | 1.13566 | 0.567829 | − | 0.823147i | \(-0.307784\pi\) | ||||
0.567829 | + | 0.823147i | \(0.307784\pi\) | |||||||
\(812\) | − | 1.43762e6i | − | 0.0765165i | ||||||
\(813\) | 1.72658e7i | 0.916138i | ||||||||
\(814\) | −5.39012e6 | −0.285127 | ||||||||
\(815\) | 16145.0 | + | 3433.20i | 0.000851422 | + | 0.000181053i | ||||
\(816\) | 7.35922e6 | 0.386907 | ||||||||
\(817\) | − | 3.23638e6i | − | 0.169631i | ||||||
\(818\) | 1.32060e7i | 0.690063i | ||||||||
\(819\) | 5.04264e6 | 0.262693 | ||||||||
\(820\) | 698719. | − | 3.28581e6i | 0.0362884 | − | 0.170650i | ||||
\(821\) | −2.14080e6 | −0.110846 | −0.0554229 | − | 0.998463i | \(-0.517651\pi\) | ||||
−0.0554229 | + | 0.998463i | \(0.517651\pi\) | |||||||
\(822\) | 2.83589e6i | 0.146389i | ||||||||
\(823\) | − | 2.73634e7i | − | 1.40822i | −0.710092 | − | 0.704109i | \(-0.751347\pi\) | ||
0.710092 | − | 0.704109i | \(-0.248653\pi\) | |||||||
\(824\) | 1.33955e7 | 0.687289 | ||||||||
\(825\) | 1.94215e7 | − | 4.36008e7i | 0.993452 | − | 2.23028i | ||||
\(826\) | −3.32644e6 | −0.169640 | ||||||||
\(827\) | − | 1.03201e7i | − | 0.524709i | −0.964972 | − | 0.262354i | \(-0.915501\pi\) | ||
0.964972 | − | 0.262354i | \(-0.0844990\pi\) | |||||||
\(828\) | 1.18508e6i | 0.0600718i | ||||||||
\(829\) | 1.77400e7 | 0.896534 | 0.448267 | − | 0.893900i | \(-0.352041\pi\) | ||||
0.448267 | + | 0.893900i | \(0.352041\pi\) | |||||||
\(830\) | −4.78584e6 | + | 2.25060e7i | −0.241136 | + | 1.13397i | ||||
\(831\) | 3.73690e6 | 0.187719 | ||||||||
\(832\) | − | 2.75498e6i | − | 0.137978i | ||||||
\(833\) | 2.04758e7i | 1.02242i | ||||||||
\(834\) | −639454. | −0.0318342 | ||||||||
\(835\) | −2.39279e7 | − | 5.08822e6i | −1.18765 | − | 0.252551i | ||||
\(836\) | 8.04888e6 | 0.398308 | ||||||||
\(837\) | − | 1.69180e7i | − | 0.834710i | ||||||
\(838\) | − | 4.83194e6i | − | 0.237690i | ||||||
\(839\) | −1.66701e7 | −0.817587 | −0.408793 | − | 0.912627i | \(-0.634050\pi\) | ||||
−0.408793 | + | 0.912627i | \(0.634050\pi\) | |||||||
\(840\) | −3.66722e6 | − | 779826.i | −0.179324 | − | 0.0381329i | ||||
\(841\) | −1.76954e7 | −0.862721 | ||||||||
\(842\) | − | 1.26178e7i | − | 0.613345i | ||||||
\(843\) | 2.48293e7i | 1.20336i | ||||||||
\(844\) | 2.00677e7 | 0.969710 | ||||||||
\(845\) | −942980. | + | 4.43447e6i | −0.0454319 | + | 0.213649i | ||||
\(846\) | 1.25897e7 | 0.604769 | ||||||||
\(847\) | 2.39909e7i | 1.14905i | ||||||||
\(848\) | 9.20442e6i | 0.439548i | ||||||||
\(849\) | −4.71160e7 | −2.24336 | ||||||||
\(850\) | 1.67722e7 | + | 7.47099e6i | 0.796240 | + | 0.354675i | ||||
\(851\) | 913383. | 0.0432344 | ||||||||
\(852\) | 8.80619e6i | 0.415613i | ||||||||
\(853\) | 1.87430e7i | 0.881995i | 0.897508 | + | 0.440998i | \(0.145375\pi\) | ||||
−0.897508 | + | 0.440998i | \(0.854625\pi\) | |||||||
\(854\) | 9.55751e6 | 0.448436 | ||||||||
\(855\) | −1.04937e6 | + | 4.93476e6i | −0.0490921 | + | 0.230861i | ||||
\(856\) | 3.97816e6 | 0.185566 | ||||||||
\(857\) | − | 2.38821e7i | − | 1.11076i | −0.831597 | − | 0.555380i | \(-0.812573\pi\) | ||
0.831597 | − | 0.555380i | \(-0.187427\pi\) | |||||||
\(858\) | − | 4.10929e7i | − | 1.90567i | ||||||
\(859\) | 1.33765e7 | 0.618529 | 0.309265 | − | 0.950976i | \(-0.399917\pi\) | ||||
0.309265 | + | 0.950976i | \(0.399917\pi\) | |||||||
\(860\) | 4.39265e6 | + | 934087.i | 0.202526 | + | 0.0430667i | ||||
\(861\) | −3.93583e6 | −0.180938 | ||||||||
\(862\) | 1.31040e7i | 0.600668i | ||||||||
\(863\) | 1.81344e6i | 0.0828850i | 0.999141 | + | 0.0414425i | \(0.0131953\pi\) | ||||
−0.999141 | + | 0.0414425i | \(0.986805\pi\) | |||||||
\(864\) | 2.06389e6 | 0.0940593 | ||||||||
\(865\) | 2.33572e7 | + | 4.96685e6i | 1.06140 | + | 0.225705i | ||||
\(866\) | −7.02903e6 | −0.318494 | ||||||||
\(867\) | 1.44381e7i | 0.652320i | ||||||||
\(868\) | − | 7.19137e6i | − | 0.323976i | ||||||
\(869\) | 4.57403e7 | 2.05471 | ||||||||
\(870\) | 1.52737e6 | − | 7.18265e6i | 0.0684144 | − | 0.321726i | ||||
\(871\) | 4.41226e7 | 1.97068 | ||||||||
\(872\) | 9.43301e6i | 0.420106i | ||||||||
\(873\) | − | 5.33635e6i | − | 0.236978i | ||||||
\(874\) | −1.36392e6 | −0.0603964 | ||||||||
\(875\) | −7.56622e6 | − | 5.50020e6i | −0.334086 | − | 0.242861i | ||||
\(876\) | −1.26214e7 | −0.555707 | ||||||||
\(877\) | − | 9.61599e6i | − | 0.422177i | −0.977467 | − | 0.211089i | \(-0.932299\pi\) | ||
0.977467 | − | 0.211089i | \(-0.0677009\pi\) | |||||||
\(878\) | 1.12536e7i | 0.492669i | ||||||||
\(879\) | 2.46028e6 | 0.107402 | ||||||||
\(880\) | −2.32307e6 | + | 1.09245e7i | −0.101125 | + | 0.475550i | ||||
\(881\) | −3.25972e7 | −1.41495 | −0.707473 | − | 0.706740i | \(-0.750165\pi\) | ||||
−0.707473 | + | 0.706740i | \(0.750165\pi\) | |||||||
\(882\) | − | 7.80706e6i | − | 0.337922i | ||||||
\(883\) | − | 3.13913e7i | − | 1.35490i | −0.735569 | − | 0.677450i | \(-0.763085\pi\) | ||
0.735569 | − | 0.677450i | \(-0.236915\pi\) | |||||||
\(884\) | 1.58075e7 | 0.680349 | ||||||||
\(885\) | −1.66196e7 | − | 3.53411e6i | −0.713282 | − | 0.151678i | ||||
\(886\) | −7.63062e6 | −0.326569 | ||||||||
\(887\) | 2.47183e7i | 1.05490i | 0.849588 | + | 0.527448i | \(0.176851\pi\) | ||||
−0.849588 | + | 0.527448i | \(0.823149\pi\) | |||||||
\(888\) | 2.16264e6i | 0.0920348i | ||||||||
\(889\) | 7.18607e6 | 0.304956 | ||||||||
\(890\) | 2.76394e7 | + | 5.87745e6i | 1.16964 | + | 0.248722i | ||||
\(891\) | 5.73380e7 | 2.41963 | ||||||||
\(892\) | 1.45552e6i | 0.0612502i | ||||||||
\(893\) | 1.44897e7i | 0.608037i | ||||||||
\(894\) | −1.52142e7 | −0.636658 | ||||||||
\(895\) | −237221. | + | 1.11556e6i | −0.00989909 | + | 0.0465516i | ||||
\(896\) | 877301. | 0.0365072 | ||||||||
\(897\) | 6.96339e6i | 0.288961i | ||||||||
\(898\) | 1.32693e7i | 0.549107i | ||||||||
\(899\) | 1.40851e7 | 0.581246 | ||||||||
\(900\) | −6.39495e6 | − | 2.84855e6i | −0.263167 | − | 0.117224i | ||||
\(901\) | −5.28131e7 | −2.16735 | ||||||||
\(902\) | 1.17247e7i | 0.479828i | ||||||||
\(903\) | − | 5.26165e6i | − | 0.214735i | ||||||
\(904\) | 2.33585e6 | 0.0950657 | ||||||||
\(905\) | −3.15373e6 | + | 1.48308e7i | −0.127998 | + | 0.601925i | ||||
\(906\) | 2.40488e7 | 0.973359 | ||||||||
\(907\) | − | 4.82951e7i | − | 1.94933i | −0.223673 | − | 0.974664i | \(-0.571805\pi\) | ||
0.223673 | − | 0.974664i | \(-0.428195\pi\) | |||||||
\(908\) | − | 1.72538e7i | − | 0.694497i | ||||||
\(909\) | 2.05000e7 | 0.822895 | ||||||||
\(910\) | −7.87713e6 | − | 1.67505e6i | −0.315330 | − | 0.0670541i | ||||
\(911\) | −1.21362e7 | −0.484492 | −0.242246 | − | 0.970215i | \(-0.577884\pi\) | ||||
−0.242246 | + | 0.970215i | \(0.577884\pi\) | |||||||
\(912\) | − | 3.22939e6i | − | 0.128568i | ||||||
\(913\) | − | 8.03077e7i | − | 3.18846i | ||||||
\(914\) | 2.30554e7 | 0.912867 | ||||||||
\(915\) | 4.77512e7 | + | 1.01542e7i | 1.88552 | + | 0.400952i | ||||
\(916\) | 9.29416e6 | 0.365992 | ||||||||
\(917\) | 3.01023e6i | 0.118216i | ||||||||
\(918\) | 1.18422e7i | 0.463793i | ||||||||
\(919\) | 2.48523e7 | 0.970684 | 0.485342 | − | 0.874324i | \(-0.338695\pi\) | ||||
0.485342 | + | 0.874324i | \(0.338695\pi\) | |||||||
\(920\) | 393657. | − | 1.85122e6i | 0.0153337 | − | 0.0721087i | ||||
\(921\) | 1.47960e7 | 0.574770 | ||||||||
\(922\) | − | 2.91154e6i | − | 0.112796i | ||||||
\(923\) | 1.89155e7i | 0.730827i | ||||||||
\(924\) | 1.30857e7 | 0.504217 | ||||||||
\(925\) | −2.19549e6 | + | 4.92883e6i | −0.0843677 | + | 0.189404i | ||||
\(926\) | 3.03093e7 | 1.16158 | ||||||||
\(927\) | − | 2.93054e7i | − | 1.12008i | ||||||
\(928\) | 1.71829e6i | 0.0654978i | ||||||||
\(929\) | −2.82241e7 | −1.07295 | −0.536477 | − | 0.843915i | \(-0.680245\pi\) | ||||
−0.536477 | + | 0.843915i | \(0.680245\pi\) | |||||||
\(930\) | 7.64033e6 | − | 3.59295e7i | 0.289671 | − | 1.36221i | ||||
\(931\) | 8.98526e6 | 0.339748 | ||||||||
\(932\) | − | 3.98013e6i | − | 0.150092i | ||||||
\(933\) | − | 6.02097e6i | − | 0.226445i | ||||||
\(934\) | 2.73923e7 | 1.02745 | ||||||||
\(935\) | −6.26827e7 | − | 1.33293e7i | −2.34487 | − | 0.498631i | ||||
\(936\) | −6.02710e6 | −0.224864 | ||||||||
\(937\) | − | 1.78987e7i | − | 0.665999i | −0.942927 | − | 0.333000i | \(-0.891939\pi\) | ||
0.942927 | − | 0.333000i | \(-0.108061\pi\) | |||||||
\(938\) | 1.40505e7i | 0.521417i | ||||||||
\(939\) | −3.71816e7 | −1.37614 | ||||||||
\(940\) | −1.96665e7 | − | 4.18202e6i | −0.725950 | − | 0.154371i | ||||
\(941\) | −1.57831e7 | −0.581057 | −0.290528 | − | 0.956866i | \(-0.593831\pi\) | ||||
−0.290528 | + | 0.956866i | \(0.593831\pi\) | |||||||
\(942\) | − | 4.74498e6i | − | 0.174224i | ||||||
\(943\) | − | 1.98681e6i | − | 0.0727574i | ||||||
\(944\) | 3.97586e6 | 0.145211 | ||||||||
\(945\) | 1.25487e6 | − | 5.90115e6i | 0.0457107 | − | 0.214960i | ||||
\(946\) | −1.56743e7 | −0.569454 | ||||||||
\(947\) | 2.94240e7i | 1.06617i | 0.846062 | + | 0.533085i | \(0.178967\pi\) | ||||
−0.846062 | + | 0.533085i | \(0.821033\pi\) | |||||||
\(948\) | − | 1.83521e7i | − | 0.663230i | ||||||
\(949\) | −2.71105e7 | −0.977173 | ||||||||
\(950\) | 3.27844e6 | − | 7.36004e6i | 0.117858 | − | 0.264589i | ||||
\(951\) | −7.49298e6 | −0.268660 | ||||||||
\(952\) | 5.03377e6i | 0.180012i | ||||||||
\(953\) | 3.16123e7i | 1.12752i | 0.825939 | + | 0.563760i | \(0.190646\pi\) | ||||
−0.825939 | + | 0.563760i | \(0.809354\pi\) | |||||||
\(954\) | 2.01367e7 | 0.716335 | ||||||||
\(955\) | 8.49700e6 | − | 3.99581e7i | 0.301479 | − | 1.41774i | ||||
\(956\) | 1.66760e7 | 0.590129 | ||||||||
\(957\) | 2.56298e7i | 0.904617i | ||||||||
\(958\) | 3.77873e7i | 1.33025i | ||||||||
\(959\) | −1.93977e6 | −0.0681089 | ||||||||
\(960\) | 4.38317e6 | + | 932071.i | 0.153501 | + | 0.0326416i | ||||
\(961\) | 4.18282e7 | 1.46103 | ||||||||
\(962\) | 4.64532e6i | 0.161837i | ||||||||
\(963\) | − | 8.70308e6i | − | 0.302418i | ||||||
\(964\) | −3.43552e6 | −0.119069 | ||||||||
\(965\) | 6.25536e6 | + | 1.33019e6i | 0.216239 | + | 0.0459827i | ||||
\(966\) | −2.21744e6 | −0.0764555 | ||||||||
\(967\) | − | 4.06367e7i | − | 1.39750i | −0.715366 | − | 0.698750i | \(-0.753740\pi\) | ||
0.715366 | − | 0.698750i | \(-0.246260\pi\) | |||||||
\(968\) | − | 2.86746e7i | − | 0.983578i | ||||||
\(969\) | 1.85296e7 | 0.633952 | ||||||||
\(970\) | −1.77262e6 | + | 8.33595e6i | −0.0604904 | + | 0.284463i | ||||
\(971\) | −5.45379e7 | −1.85631 | −0.928154 | − | 0.372197i | \(-0.878605\pi\) | ||||
−0.928154 | + | 0.372197i | \(0.878605\pi\) | |||||||
\(972\) | − | 1.51690e7i | − | 0.514981i | ||||||
\(973\) | − | 437392.i | − | 0.0148112i | ||||||
\(974\) | −3.73010e7 | −1.25986 | ||||||||
\(975\) | −3.75761e7 | − | 1.67378e7i | −1.26590 | − | 0.563880i | ||||
\(976\) | −1.14234e7 | −0.383859 | ||||||||
\(977\) | 1.04362e7i | 0.349788i | 0.984587 | + | 0.174894i | \(0.0559583\pi\) | ||||
−0.984587 | + | 0.174894i | \(0.944042\pi\) | |||||||
\(978\) | 23114.5i | 0.000772747i | ||||||||
\(979\) | −9.86253e7 | −3.28875 | ||||||||
\(980\) | −2.59333e6 | + | 1.21955e7i | −0.0862568 | + | 0.405633i | ||||
\(981\) | 2.06367e7 | 0.684650 | ||||||||
\(982\) | 5.46855e6i | 0.180965i | ||||||||
\(983\) | − | 2.08178e6i | − | 0.0687150i | −0.999410 | − | 0.0343575i | \(-0.989062\pi\) | ||
0.999410 | − | 0.0343575i | \(-0.0109385\pi\) | |||||||
\(984\) | 4.70422e6 | 0.154882 | ||||||||
\(985\) | 4.39570e7 | + | 9.34735e6i | 1.44357 | + | 0.306972i | ||||
\(986\) | −9.85919e6 | −0.322960 | ||||||||
\(987\) | 2.35570e7i | 0.769711i | ||||||||
\(988\) | − | 6.93668e6i | − | 0.226079i | ||||||
\(989\) | 2.65608e6 | 0.0863476 | ||||||||
\(990\) | 2.38998e7 | + | 5.08223e6i | 0.775007 | + | 0.164803i | ||||
\(991\) | −4.04409e7 | −1.30809 | −0.654044 | − | 0.756457i | \(-0.726929\pi\) | ||||
−0.654044 | + | 0.756457i | \(0.726929\pi\) | |||||||
\(992\) | 8.59534e6i | 0.277322i | ||||||||
\(993\) | − | 2.00029e6i | − | 0.0643753i | ||||||
\(994\) | −6.02351e6 | −0.193368 | ||||||||
\(995\) | −8.74912e6 | + | 4.11437e7i | −0.280160 | + | 1.31749i | ||||
\(996\) | −3.22213e7 | −1.02919 | ||||||||
\(997\) | 6.40147e6i | 0.203959i | 0.994787 | + | 0.101979i | \(0.0325175\pi\) | ||||
−0.994787 | + | 0.101979i | \(0.967482\pi\) | |||||||
\(998\) | − | 5.94340e6i | − | 0.188890i | ||||||
\(999\) | −3.48004e6 | −0.110324 |
(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 | 230.6.b.a.139.15 | yes | 26 | |
5.4 | even | 2 | inner | 230.6.b.a.139.12 | ✓ | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.6.b.a.139.12 | ✓ | 26 | 5.4 | even | 2 | inner | |
230.6.b.a.139.15 | yes | 26 | 1.1 | even | 1 | trivial |