Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,6,Mod(35,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.35");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.h (of order \(6\), degree \(2\), not 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: | \(17.3214525398\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 71.18 | ||
Character | \(\chi\) | \(=\) | 108.71 |
Dual form | 108.6.h.a.35.18 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.90579 | + | 5.32616i | 0.336899 | + | 0.941541i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −24.7359 | + | 20.3011i | −0.772997 | + | 0.634409i | ||||
\(5\) | 51.8636 | + | 29.9435i | 0.927765 | + | 0.535645i | 0.886104 | − | 0.463486i | \(-0.153402\pi\) |
0.0416611 | + | 0.999132i | \(0.486735\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −33.8827 | + | 19.5622i | −0.261356 | + | 0.150894i | −0.624953 | − | 0.780662i | \(-0.714882\pi\) |
0.363597 | + | 0.931556i | \(0.381549\pi\) | |||||||
\(8\) | −155.268 | − | 93.0578i | −0.857744 | − | 0.514076i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −60.6425 | + | 333.300i | −0.191768 | + | 1.05399i | ||||
\(11\) | 108.537 | + | 187.992i | 0.270456 | + | 0.468443i | 0.968979 | − | 0.247144i | \(-0.0794922\pi\) |
−0.698523 | + | 0.715588i | \(0.746159\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −532.156 | + | 921.721i | −0.873334 | + | 1.51266i | −0.0148071 | + | 0.999890i | \(0.504713\pi\) |
−0.858527 | + | 0.512769i | \(0.828620\pi\) | |||||||
\(14\) | −168.765 | − | 143.183i | −0.230124 | − | 0.195241i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 199.731 | − | 1004.33i | 0.195050 | − | 0.980793i | ||||
\(17\) | 315.283i | 0.264593i | 0.991210 | + | 0.132297i | \(0.0422351\pi\) | ||||
−0.991210 | + | 0.132297i | \(0.957765\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1889.72i | − | 1.20092i | −0.799655 | − | 0.600460i | \(-0.794984\pi\) | ||
0.799655 | − | 0.600460i | \(-0.205016\pi\) | |||||||
\(20\) | −1890.78 | + | 312.209i | −1.05698 | + | 0.174530i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −794.425 | + | 936.359i | −0.349942 | + | 0.412464i | ||||
\(23\) | −1200.19 | + | 2078.79i | −0.473074 | + | 0.819389i | −0.999525 | − | 0.0308168i | \(-0.990189\pi\) |
0.526451 | + | 0.850206i | \(0.323522\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 230.725 | + | 399.628i | 0.0738321 | + | 0.127881i | ||||
\(26\) | −5923.41 | − | 1077.74i | −1.71846 | − | 0.312665i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 440.986 | − | 1171.75i | 0.106299 | − | 0.282448i | ||||
\(29\) | −5185.33 | + | 2993.75i | −1.14494 | + | 0.661030i | −0.947648 | − | 0.319315i | \(-0.896547\pi\) |
−0.197289 | + | 0.980345i | \(0.563214\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6949.56 | − | 4012.33i | −1.29883 | − | 0.749881i | −0.318629 | − | 0.947879i | \(-0.603222\pi\) |
−0.980202 | + | 0.197999i | \(0.936556\pi\) | |||||||
\(32\) | 5729.88 | − | 850.247i | 0.989169 | − | 0.146781i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1679.25 | + | 600.864i | −0.249125 | + | 0.0891413i | ||||
\(35\) | −2343.04 | −0.323303 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5243.91 | 0.629725 | 0.314862 | − | 0.949137i | \(-0.398042\pi\) | ||||
0.314862 | + | 0.949137i | \(0.398042\pi\) | |||||||
\(38\) | 10065.0 | − | 3601.42i | 1.13072 | − | 0.404590i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5266.31 | − | 9475.59i | −0.520423 | − | 0.936389i | ||||
\(41\) | 7589.92 | + | 4382.04i | 0.705144 | + | 0.407115i | 0.809260 | − | 0.587450i | \(-0.199868\pi\) |
−0.104117 | + | 0.994565i | \(0.533202\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8780.43 | − | 5069.38i | 0.724176 | − | 0.418103i | −0.0921115 | − | 0.995749i | \(-0.529362\pi\) |
0.816288 | + | 0.577645i | \(0.196028\pi\) | |||||||
\(44\) | −6501.20 | − | 2446.73i | −0.506247 | − | 0.190526i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −13359.2 | − | 2430.66i | −0.930866 | − | 0.169367i | ||||
\(47\) | −7272.14 | − | 12595.7i | −0.480195 | − | 0.831721i | 0.519547 | − | 0.854442i | \(-0.326101\pi\) |
−0.999742 | + | 0.0227202i | \(0.992767\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7638.14 | + | 13229.6i | −0.454462 | + | 0.787151i | ||||
\(50\) | −1688.77 | + | 1990.49i | −0.0955311 | + | 0.112599i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5548.58 | − | 33603.0i | −0.284560 | − | 1.72333i | ||||
\(53\) | 19631.3i | 0.959974i | 0.877276 | + | 0.479987i | \(0.159359\pi\) | ||||
−0.877276 | + | 0.479987i | \(0.840641\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12999.9i | 0.579474i | ||||||||
\(56\) | 7081.33 | + | 115.661i | 0.301748 | + | 0.00492851i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −25827.4 | − | 21912.4i | −1.00812 | − | 0.855304i | ||||
\(59\) | −909.551 | + | 1575.39i | −0.0340171 | + | 0.0589193i | −0.882533 | − | 0.470251i | \(-0.844163\pi\) |
0.848516 | + | 0.529170i | \(0.177497\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 24421.5 | + | 42299.3i | 0.840327 | + | 1.45549i | 0.889619 | + | 0.456704i | \(0.150970\pi\) |
−0.0492921 | + | 0.998784i | \(0.515697\pi\) | |||||||
\(62\) | 8125.89 | − | 44661.1i | 0.268467 | − | 1.47554i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 15448.5 | + | 28897.8i | 0.471451 | + | 0.881892i | ||||
\(65\) | −55199.1 | + | 31869.2i | −1.62050 | + | 0.935595i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 37065.9 | + | 21400.0i | 1.00876 | + | 0.582407i | 0.910828 | − | 0.412786i | \(-0.135444\pi\) |
0.0979310 | + | 0.995193i | \(0.468778\pi\) | |||||||
\(68\) | −6400.60 | − | 7798.82i | −0.167860 | − | 0.204530i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4465.35 | − | 12479.4i | −0.108921 | − | 0.304403i | ||||
\(71\) | 29409.1 | 0.692365 | 0.346183 | − | 0.938167i | \(-0.387478\pi\) | ||||
0.346183 | + | 0.938167i | \(0.387478\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 38022.9 | 0.835099 | 0.417550 | − | 0.908654i | \(-0.362889\pi\) | ||||
0.417550 | + | 0.908654i | \(0.362889\pi\) | |||||||
\(74\) | 9993.79 | + | 27929.9i | 0.212154 | + | 0.592911i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 38363.5 | + | 46744.1i | 0.761875 | + | 0.928309i | ||||
\(77\) | −7355.06 | − | 4246.45i | −0.141371 | − | 0.0816205i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12858.2 | + | 7423.70i | −0.231800 | + | 0.133830i | −0.611402 | − | 0.791320i | \(-0.709394\pi\) |
0.379602 | + | 0.925150i | \(0.376061\pi\) | |||||||
\(80\) | 40432.0 | − | 46107.7i | 0.706318 | − | 0.805468i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8874.65 | + | 48776.4i | −0.145753 | + | 0.801078i | ||||
\(83\) | 60168.3 | + | 104215.i | 0.958677 | + | 1.66048i | 0.725719 | + | 0.687991i | \(0.241507\pi\) |
0.232959 | + | 0.972487i | \(0.425159\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9440.69 | + | 16351.7i | −0.141728 | + | 0.245480i | ||||
\(86\) | 43734.0 | + | 37104.8i | 0.637636 | + | 0.540983i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 641.721 | − | 39289.4i | 0.00883364 | − | 0.540840i | ||||
\(89\) | − | 35496.5i | − | 0.475019i | −0.971385 | − | 0.237509i | \(-0.923669\pi\) | ||
0.971385 | − | 0.237509i | \(-0.0763311\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 41640.5i | − | 0.527124i | ||||||
\(92\) | −12513.9 | − | 75785.8i | −0.154142 | − | 0.933508i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 53227.6 | − | 62737.3i | 0.621322 | − | 0.732329i | ||||
\(95\) | 56584.9 | − | 98008.0i | 0.643268 | − | 1.11417i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1491.62 | + | 2583.55i | 0.0160964 | + | 0.0278797i | 0.873961 | − | 0.485995i | \(-0.161543\pi\) |
−0.857865 | + | 0.513875i | \(0.828209\pi\) | |||||||
\(98\) | −85019.9 | − | 15469.0i | −0.894243 | − | 0.162704i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −13820.1 | − | 5201.19i | −0.138201 | − | 0.0520119i | ||||
\(101\) | −45537.2 | + | 26290.9i | −0.444184 | + | 0.256450i | −0.705371 | − | 0.708838i | \(-0.749220\pi\) |
0.261187 | + | 0.965288i | \(0.415886\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10418.1 | + | 6014.90i | 0.0967600 | + | 0.0558644i | 0.547599 | − | 0.836741i | \(-0.315542\pi\) |
−0.450839 | + | 0.892605i | \(0.648875\pi\) | |||||||
\(104\) | 168400. | − | 93592.8i | 1.52672 | − | 0.848514i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −104559. | + | 37413.2i | −0.903855 | + | 0.323415i | ||||
\(107\) | −89559.8 | −0.756229 | −0.378115 | − | 0.925759i | \(-0.623428\pi\) | ||||
−0.378115 | + | 0.925759i | \(0.623428\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −29876.1 | −0.240856 | −0.120428 | − | 0.992722i | \(-0.538427\pi\) | ||||
−0.120428 | + | 0.992722i | \(0.538427\pi\) | |||||||
\(110\) | −69239.6 | + | 24775.1i | −0.545598 | + | 0.195225i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 12879.5 | + | 37936.7i | 0.0970184 | + | 0.285769i | ||||
\(113\) | 214387. | + | 123776.i | 1.57943 | + | 0.911886i | 0.994938 | + | 0.100490i | \(0.0320409\pi\) |
0.584496 | + | 0.811397i | \(0.301292\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −124492. | + | 71875.6i | −0.877804 | + | 0.506800i | ||||
\(116\) | 67487.5 | − | 179321.i | 0.465670 | − | 1.23733i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10124.2 | − | 1842.05i | −0.0669352 | − | 0.0121786i | ||||
\(119\) | −6167.64 | − | 10682.7i | −0.0399256 | − | 0.0691531i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 56964.9 | − | 98666.1i | 0.353707 | − | 0.612639i | ||||
\(122\) | −178751. | + | 210687.i | −1.08730 | + | 1.28155i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 253358. | − | 41835.0i | 1.47972 | − | 0.244335i | ||||
\(125\) | − | 159512.i | − | 0.913100i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 265961.i | − | 1.46322i | −0.681724 | − | 0.731610i | \(-0.738769\pi\) | ||
0.681724 | − | 0.731610i | \(-0.261231\pi\) | |||||||
\(128\) | −124473. | + | 137354.i | −0.671506 | + | 0.740999i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −274938. | − | 233263.i | −1.42685 | − | 1.21056i | ||||
\(131\) | −37162.9 | + | 64368.0i | −0.189204 | + | 0.327712i | −0.944985 | − | 0.327113i | \(-0.893924\pi\) |
0.755781 | + | 0.654825i | \(0.227258\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 36967.1 | + | 64029.0i | 0.181212 | + | 0.313868i | ||||
\(134\) | −43339.9 | + | 238203.i | −0.208510 | + | 1.14600i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 29339.6 | − | 48953.5i | 0.136021 | − | 0.226953i | ||||
\(137\) | −20104.8 | + | 11607.5i | −0.0915163 | + | 0.0528370i | −0.545060 | − | 0.838397i | \(-0.683493\pi\) |
0.453543 | + | 0.891234i | \(0.350160\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 287391. | + | 165925.i | 1.26164 | + | 0.728410i | 0.973392 | − | 0.229145i | \(-0.0735930\pi\) |
0.288251 | + | 0.957555i | \(0.406926\pi\) | |||||||
\(140\) | 57957.3 | − | 47566.3i | 0.249912 | − | 0.205106i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 56047.5 | + | 156637.i | 0.233257 | + | 0.651890i | ||||
\(143\) | −231035. | −0.944794 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −358574. | −1.41631 | ||||||||
\(146\) | 72463.7 | + | 202516.i | 0.281345 | + | 0.786280i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −129713. | + | 106457.i | −0.486776 | + | 0.399503i | ||||
\(149\) | −287800. | − | 166162.i | −1.06200 | − | 0.613147i | −0.136017 | − | 0.990707i | \(-0.543430\pi\) |
−0.925985 | + | 0.377559i | \(0.876763\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −300515. | + | 173503.i | −1.07257 | + | 0.619247i | −0.928882 | − | 0.370377i | \(-0.879229\pi\) |
−0.143685 | + | 0.989623i | \(0.545895\pi\) | |||||||
\(152\) | −175853. | + | 293414.i | −0.617365 | + | 1.03008i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 8600.04 | − | 47267.1i | 0.0292212 | − | 0.160604i | ||||
\(155\) | −240286. | − | 416188.i | −0.803340 | − | 1.39143i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 72572.9 | − | 125700.i | 0.234977 | − | 0.406992i | −0.724289 | − | 0.689497i | \(-0.757832\pi\) |
0.959266 | + | 0.282504i | \(0.0911651\pi\) | |||||||
\(158\) | −64044.9 | − | 54336.9i | −0.204099 | − | 0.173162i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 322632. | + | 127476.i | 0.996339 | + | 0.393665i | ||||
\(161\) | − | 93913.2i | − | 0.285537i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 240037.i | − | 0.707635i | −0.935314 | − | 0.353818i | \(-0.884883\pi\) | ||
0.935314 | − | 0.353818i | \(-0.115117\pi\) | |||||||
\(164\) | −276704. | + | 45689.8i | −0.803352 | + | 0.132651i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −440395. | + | 519077.i | −1.24043 | + | 1.46205i | ||||
\(167\) | −144730. | + | 250679.i | −0.401575 | + | 0.695548i | −0.993916 | − | 0.110139i | \(-0.964870\pi\) |
0.592341 | + | 0.805687i | \(0.298204\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −380733. | − | 659449.i | −1.02542 | − | 1.77609i | ||||
\(170\) | −105084. | − | 19119.6i | −0.278878 | − | 0.0507406i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −114278. | + | 303648.i | −0.294538 | + | 0.782617i | ||||
\(173\) | 490809. | − | 283369.i | 1.24680 | − | 0.719841i | 0.276332 | − | 0.961062i | \(-0.410881\pi\) |
0.970470 | + | 0.241221i | \(0.0775479\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15635.2 | − | 9026.99i | −0.0385930 | − | 0.0222817i | ||||
\(176\) | 210485. | − | 71459.5i | 0.512199 | − | 0.173891i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 189060. | − | 67649.0i | 0.447250 | − | 0.160034i | ||||
\(179\) | 440866. | 1.02843 | 0.514214 | − | 0.857662i | \(-0.328084\pi\) | ||||
0.514214 | + | 0.857662i | \(0.328084\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 103852. | 0.235623 | 0.117812 | − | 0.993036i | \(-0.462412\pi\) | ||||
0.117812 | + | 0.993036i | \(0.462412\pi\) | |||||||
\(182\) | 221784. | − | 79358.2i | 0.496309 | − | 0.177588i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 379798. | − | 211083.i | 0.827005 | − | 0.459630i | ||||
\(185\) | 271968. | + | 157021.i | 0.584237 | + | 0.337309i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −59270.7 | + | 34220.0i | −0.123947 | + | 0.0715608i | ||||
\(188\) | 435590. | + | 163934.i | 0.898841 | + | 0.338279i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 629845. | + | 114598.i | 1.26576 | + | 0.230299i | ||||
\(191\) | 215522. | + | 373294.i | 0.427472 | + | 0.740403i | 0.996648 | − | 0.0818131i | \(-0.0260711\pi\) |
−0.569176 | + | 0.822216i | \(0.692738\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20745.9 | − | 35932.9i | 0.0400903 | − | 0.0694384i | −0.845284 | − | 0.534317i | \(-0.820569\pi\) |
0.885374 | + | 0.464879i | \(0.153902\pi\) | |||||||
\(194\) | −10917.7 | + | 12868.3i | −0.0208270 | + | 0.0245480i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −79639.9 | − | 482310.i | −0.148078 | − | 0.896781i | ||||
\(197\) | − | 353610.i | − | 0.649170i | −0.945856 | − | 0.324585i | \(-0.894775\pi\) | ||
0.945856 | − | 0.324585i | \(-0.105225\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 167614.i | 0.300038i | 0.988683 | + | 0.150019i | \(0.0479336\pi\) | ||||
−0.988683 | + | 0.150019i | \(0.952066\pi\) | |||||||
\(200\) | 1364.15 | − | 83520.3i | 0.00241150 | − | 0.147644i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −226814. | − | 192434.i | −0.391104 | − | 0.331820i | ||||
\(203\) | 117129. | − | 202873.i | 0.199491 | − | 0.345529i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 262427. | + | 454537.i | 0.436138 | + | 0.755414i | ||||
\(206\) | −12181.6 | + | 66951.7i | −0.0200002 | + | 0.109924i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 819426. | + | 718558.i | 1.31326 | + | 1.15160i | ||||
\(209\) | 355253. | − | 205105.i | 0.562563 | − | 0.324796i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 60893.8 | + | 35157.0i | 0.0941601 | + | 0.0543633i | 0.546341 | − | 0.837563i | \(-0.316020\pi\) |
−0.452181 | + | 0.891926i | \(0.649354\pi\) | |||||||
\(212\) | −398537. | − | 485598.i | −0.609016 | − | 0.742058i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −170682. | − | 477010.i | −0.254773 | − | 0.712021i | ||||
\(215\) | 607180. | 0.895821 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 313960. | 0.452611 | ||||||||
\(218\) | −56937.7 | − | 159125.i | −0.0811444 | − | 0.226776i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −263913. | − | 321565.i | −0.367624 | − | 0.447932i | ||||
\(221\) | −290603. | − | 167780.i | −0.400239 | − | 0.231078i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −439612. | + | 253810.i | −0.591980 | + | 0.341780i | −0.765880 | − | 0.642983i | \(-0.777696\pi\) |
0.173900 | + | 0.984763i | \(0.444363\pi\) | |||||||
\(224\) | −177511. | + | 140898.i | −0.236377 | + | 0.187622i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −250675. | + | 1.37775e6i | −0.326468 | + | 1.79432i | ||||
\(227\) | 54791.0 | + | 94900.8i | 0.0705739 | + | 0.122238i | 0.899153 | − | 0.437634i | \(-0.144184\pi\) |
−0.828579 | + | 0.559872i | \(0.810850\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 180234. | − | 312174.i | 0.227116 | − | 0.393376i | −0.729836 | − | 0.683622i | \(-0.760404\pi\) |
0.956952 | + | 0.290246i | \(0.0937370\pi\) | |||||||
\(230\) | −620077. | − | 526085.i | −0.772905 | − | 0.655747i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.08371e6 | + | 17700.4i | 1.32188 | + | 0.0215906i | ||||
\(233\) | 938716.i | 1.13278i | 0.824138 | + | 0.566389i | \(0.191660\pi\) | ||||
−0.824138 | + | 0.566389i | \(0.808340\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 871012.i | − | 1.02886i | ||||||
\(236\) | −9483.52 | − | 57433.5i | −0.0110838 | − | 0.0671252i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 45143.3 | − | 53208.7i | 0.0516596 | − | 0.0608892i | ||||
\(239\) | 163017. | − | 282354.i | 0.184603 | − | 0.319742i | −0.758840 | − | 0.651278i | \(-0.774233\pi\) |
0.943443 | + | 0.331536i | \(0.107567\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 37903.3 | + | 65650.4i | 0.0420373 | + | 0.0728107i | 0.886279 | − | 0.463153i | \(-0.153282\pi\) |
−0.844241 | + | 0.535963i | \(0.819949\pi\) | |||||||
\(242\) | 634074. | + | 115367.i | 0.695988 | + | 0.126632i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.46281e6 | − | 550529.i | −1.57295 | − | 0.591978i | ||||
\(245\) | −792284. | + | 457425.i | −0.843268 | + | 0.486861i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.74180e6 | + | 1.00563e6i | 1.81658 | + | 1.04880i | ||||
\(248\) | 705668. | + | 1.26970e6i | 0.728569 | + | 1.31090i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 849586. | − | 303996.i | 0.859720 | − | 0.307623i | ||||
\(251\) | −971568. | −0.973394 | −0.486697 | − | 0.873571i | \(-0.661798\pi\) | ||||
−0.486697 | + | 0.873571i | \(0.661798\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −521060. | −0.511783 | ||||||||
\(254\) | 1.41655e6 | − | 506867.i | 1.37768 | − | 0.492958i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −968791. | − | 401193.i | −0.923911 | − | 0.382608i | ||||
\(257\) | −1.19547e6 | − | 690206.i | −1.12903 | − | 0.651848i | −0.185342 | − | 0.982674i | \(-0.559339\pi\) |
−0.943692 | + | 0.330826i | \(0.892673\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −177678. | + | 102582.i | −0.164583 | + | 0.0950218i | ||||
\(260\) | 718420. | − | 1.90892e6i | 0.659091 | − | 1.75127i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −413659. | − | 75263.4i | −0.372297 | − | 0.0677377i | ||||
\(263\) | 240670. | + | 416853.i | 0.214552 | + | 0.371615i | 0.953134 | − | 0.302549i | \(-0.0978374\pi\) |
−0.738582 | + | 0.674164i | \(0.764504\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −587830. | + | 1.01815e6i | −0.514206 | + | 0.890631i | ||||
\(266\) | −270577. | + | 318919.i | −0.234470 | + | 0.276360i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.35130e6 | + | 223129.i | −1.14925 | + | 0.189767i | ||||
\(269\) | 1.12150e6i | 0.944969i | 0.881339 | + | 0.472484i | \(0.156643\pi\) | ||||
−0.881339 | + | 0.472484i | \(0.843357\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 873330.i | 0.722362i | 0.932496 | + | 0.361181i | \(0.117626\pi\) | ||||
−0.932496 | + | 0.361181i | \(0.882374\pi\) | |||||||
\(272\) | 316649. | + | 62972.0i | 0.259511 | + | 0.0516090i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −100139. | − | 84959.9i | −0.0805800 | − | 0.0683656i | ||||
\(275\) | −50084.5 | + | 86748.9i | −0.0399367 | + | 0.0691723i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 900195. | + | 1.55918e6i | 0.704915 | + | 1.22095i | 0.966722 | + | 0.255829i | \(0.0823483\pi\) |
−0.261807 | + | 0.965120i | \(0.584318\pi\) | |||||||
\(278\) | −336037. | + | 1.84691e6i | −0.260781 | + | 1.43329i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 363800. | + | 218038.i | 0.277311 | + | 0.166203i | ||||
\(281\) | 236453. | − | 136516.i | 0.178640 | − | 0.103138i | −0.408014 | − | 0.912976i | \(-0.633778\pi\) |
0.586654 | + | 0.809838i | \(0.300445\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −644438. | − | 372067.i | −0.478316 | − | 0.276156i | 0.241398 | − | 0.970426i | \(-0.422394\pi\) |
−0.719715 | + | 0.694270i | \(0.755727\pi\) | |||||||
\(284\) | −727460. | + | 597036.i | −0.535196 | + | 0.439243i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −440304. | − | 1.23053e6i | −0.318301 | − | 0.889562i | ||||
\(287\) | −342889. | −0.245725 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.32045e6 | 0.929990 | ||||||||
\(290\) | −683367. | − | 1.90982e6i | −0.477154 | − | 1.33351i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −940531. | + | 771906.i | −0.645530 | + | 0.529795i | ||||
\(293\) | 330601. | + | 190873.i | 0.224976 | + | 0.129890i | 0.608252 | − | 0.793744i | \(-0.291871\pi\) |
−0.383276 | + | 0.923634i | \(0.625204\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −94345.2 | + | 54470.2i | −0.0631197 | + | 0.0364422i | ||||
\(296\) | −814213. | − | 487986.i | −0.540143 | − | 0.323727i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 336515. | − | 1.84954e6i | 0.219515 | − | 1.20649i | ||||
\(299\) | −1.27737e6 | − | 2.21248e6i | −0.826304 | − | 1.43120i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −198336. | + | 343529.i | −0.126179 | + | 0.218548i | ||||
\(302\) | −1.49682e6 | − | 1.26993e6i | −0.944393 | − | 0.801241i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.89791e6 | − | 377437.i | −1.17785 | − | 0.234240i | ||||
\(305\) | 2.92506e6i | 1.80047i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 3.21986e6i | − | 1.94980i | −0.222640 | − | 0.974901i | \(-0.571467\pi\) | ||
0.222640 | − | 0.974901i | \(-0.428533\pi\) | |||||||
\(308\) | 268142. | − | 44276.0i | 0.161060 | − | 0.0265945i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.75875e6 | − | 2.07297e6i | 1.03944 | − | 1.22515i | ||||
\(311\) | −775835. | + | 1.34378e6i | −0.454850 | + | 0.787823i | −0.998680 | − | 0.0513724i | \(-0.983640\pi\) |
0.543830 | + | 0.839196i | \(0.316974\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 263995. | + | 457253.i | 0.152312 | + | 0.263813i | 0.932077 | − | 0.362260i | \(-0.117995\pi\) |
−0.779765 | + | 0.626073i | \(0.784661\pi\) | |||||||
\(314\) | 807807. | + | 146977.i | 0.462364 | + | 0.0841250i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 167351. | − | 444668.i | 0.0942779 | − | 0.250506i | ||||
\(317\) | −764737. | + | 441521.i | −0.427429 | + | 0.246776i | −0.698251 | − | 0.715853i | \(-0.746038\pi\) |
0.270822 | + | 0.962630i | \(0.412705\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.12560e6 | − | 649867.i | −0.619310 | − | 0.357559i | ||||
\(320\) | −64086.6 | + | 1.96133e6i | −0.0349858 | + | 1.07072i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 500197. | − | 178979.i | 0.268844 | − | 0.0961972i | ||||
\(323\) | 595799. | 0.317756 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −491127. | −0.257920 | ||||||||
\(326\) | 1.27848e6 | − | 457461.i | 0.666267 | − | 0.238402i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −770691. | − | 1.38669e6i | −0.395545 | − | 0.711698i | ||||
\(329\) | 492799. | + | 284518.i | 0.251004 | + | 0.144917i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 128289. | − | 74067.9i | 0.0643607 | − | 0.0371587i | −0.467474 | − | 0.884007i | \(-0.654836\pi\) |
0.531835 | + | 0.846848i | \(0.321503\pi\) | |||||||
\(332\) | −3.60399e6 | − | 1.35636e6i | −1.79448 | − | 0.675352i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.61098e6 | − | 293111.i | −0.790177 | − | 0.143769i | ||||
\(335\) | 1.28158e6 | + | 2.21976e6i | 0.623928 | + | 1.08067i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 191733. | − | 332092.i | 0.0919651 | − | 0.159288i | −0.816373 | − | 0.577525i | \(-0.804019\pi\) |
0.908338 | + | 0.418237i | \(0.137352\pi\) | |||||||
\(338\) | 2.78673e6 | − | 3.28462e6i | 1.32679 | − | 1.56384i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −98434.3 | − | 596132.i | −0.0461795 | − | 0.279669i | ||||
\(341\) | − | 1.74195e6i | − | 0.811239i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.25524e6i | − | 0.576091i | ||||||
\(344\) | −1.83507e6 | − | 29972.5i | −0.836095 | − | 0.0136561i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.44465e6 | + | 2.07409e6i | 1.09781 | + | 0.931400i | ||||
\(347\) | 602848. | − | 1.04416e6i | 0.268772 | − | 0.465527i | −0.699773 | − | 0.714365i | \(-0.746716\pi\) |
0.968545 | + | 0.248839i | \(0.0800489\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −145755. | − | 252456.i | −0.0640562 | − | 0.110949i | 0.832219 | − | 0.554447i | \(-0.187070\pi\) |
−0.896275 | + | 0.443499i | \(0.853737\pi\) | |||||||
\(350\) | 18281.7 | − | 100479.i | 0.00797714 | − | 0.0438435i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 781744. | + | 984887.i | 0.336285 | + | 0.423672i | ||||
\(353\) | 162770. | − | 93975.5i | 0.0695246 | − | 0.0401400i | −0.464835 | − | 0.885397i | \(-0.653886\pi\) |
0.534359 | + | 0.845257i | \(0.320553\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.52526e6 | + | 880610.i | 0.642352 | + | 0.370862i | ||||
\(356\) | 720618. | + | 878039.i | 0.301356 | + | 0.367188i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 840199. | + | 2.34812e6i | 0.346477 | + | 0.968307i | ||||
\(359\) | 1.70884e6 | 0.699786 | 0.349893 | − | 0.936790i | \(-0.386218\pi\) | ||||
0.349893 | + | 0.936790i | \(0.386218\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.09496e6 | −0.442211 | ||||||||
\(362\) | 197920. | + | 553132.i | 0.0793814 | + | 0.221849i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 845348. | + | 1.03002e6i | 0.334412 | + | 0.407466i | ||||
\(365\) | 1.97201e6 | + | 1.13854e6i | 0.774776 | + | 0.447317i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.26612e6 | + | 1.88569e6i | −1.26581 | + | 0.730813i | −0.974191 | − | 0.225723i | \(-0.927526\pi\) |
−0.291614 | + | 0.956536i | \(0.594192\pi\) | |||||||
\(368\) | 1.84808e6 | + | 1.62059e6i | 0.711378 | + | 0.623810i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −318004. | + | 1.74779e6i | −0.120761 | + | 0.663722i | ||||
\(371\) | −384031. | − | 665162.i | −0.144855 | − | 0.250895i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.13464e6 | − | 1.96526e6i | 0.422267 | − | 0.731388i | −0.573894 | − | 0.818930i | \(-0.694568\pi\) |
0.996161 | + | 0.0875420i | \(0.0279012\pi\) | |||||||
\(374\) | −295218. | − | 250469.i | −0.109135 | − | 0.0925923i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −42996.2 | + | 2.63244e6i | −0.0156841 | + | 0.960261i | ||||
\(377\) | − | 6.37257e6i | − | 2.30920i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.07165e6i | 1.45604i | 0.685557 | + | 0.728019i | \(0.259559\pi\) | ||||
−0.685557 | + | 0.728019i | \(0.740441\pi\) | |||||||
\(380\) | 589989. | + | 3.57305e6i | 0.209597 | + | 1.26935i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.57749e6 | + | 1.85932e6i | −0.553104 | + | 0.651923i | ||||
\(383\) | −1.22056e6 | + | 2.11407e6i | −0.425170 | + | 0.736415i | −0.996436 | − | 0.0843491i | \(-0.973119\pi\) |
0.571267 | + | 0.820765i | \(0.306452\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −254307. | − | 440473.i | −0.0874393 | − | 0.151449i | ||||
\(386\) | 230922. | + | 42015.2i | 0.0788854 | + | 0.0143529i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −89345.5 | − | 33625.2i | −0.0301296 | − | 0.0113393i | ||||
\(389\) | −924047. | + | 533499.i | −0.309614 | + | 0.178756i | −0.646754 | − | 0.762699i | \(-0.723874\pi\) |
0.337140 | + | 0.941455i | \(0.390540\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −655407. | − | 378399.i | −0.216805 | − | 0.125172i | ||||
\(392\) | 2.41708e6 | − | 1.34336e6i | 0.794468 | − | 0.441546i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.88338e6 | − | 673906.i | 0.611220 | − | 0.218705i | ||||
\(395\) | −889166. | −0.286741 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.64187e6 | −0.841271 | −0.420635 | − | 0.907230i | \(-0.638193\pi\) | ||||
−0.420635 | + | 0.907230i | \(0.638193\pi\) | |||||||
\(398\) | −892737. | + | 319437.i | −0.282498 | + | 0.101083i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 447442. | − | 151907.i | 0.139826 | − | 0.0474708i | ||||
\(401\) | −2.41745e6 | − | 1.39571e6i | −0.750751 | − | 0.433446i | 0.0752142 | − | 0.997167i | \(-0.476036\pi\) |
−0.825965 | + | 0.563721i | \(0.809369\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.39649e6 | − | 4.27037e6i | 2.26863 | − | 1.30979i | ||||
\(404\) | 592671. | − | 1.57479e6i | 0.180659 | − | 0.480030i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.30376e6 | + | 237213.i | 0.392538 | + | 0.0714205i | ||||
\(407\) | 569159. | + | 985812.i | 0.170313 | + | 0.294990i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −502887. | + | 871025.i | −0.148649 | + | 0.257468i | −0.930728 | − | 0.365711i | \(-0.880826\pi\) |
0.782079 | + | 0.623179i | \(0.214159\pi\) | |||||||
\(410\) | −1.92081e6 | + | 2.26398e6i | −0.564318 | + | 0.665141i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −379811. | + | 62715.0i | −0.110236 | + | 0.0182024i | ||||
\(413\) | − | 71171.2i | − | 0.0205319i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.20660e6i | 2.05404i | ||||||||
\(416\) | −2.26550e6 | + | 5.73381e6i | −0.641845 | + | 1.62446i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.76946e6 | + | 1.50124e6i | 0.495336 | + | 0.420253i | ||||
\(419\) | 2.85052e6 | − | 4.93724e6i | 0.793210 | − | 1.37388i | −0.130759 | − | 0.991414i | \(-0.541741\pi\) |
0.923969 | − | 0.382466i | \(-0.124925\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.95835e6 | − | 5.12400e6i | −0.813474 | − | 1.40898i | −0.910419 | − | 0.413688i | \(-0.864240\pi\) |
0.0969446 | − | 0.995290i | \(-0.469093\pi\) | |||||||
\(422\) | −71201.1 | + | 391332.i | −0.0194628 | + | 0.106971i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.82685e6 | − | 3.04812e6i | 0.493500 | − | 0.823412i | ||||
\(425\) | −125996. | + | 72743.8i | −0.0338364 | + | 0.0195355i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.65493e6 | − | 955477.i | −0.439249 | − | 0.253601i | ||||
\(428\) | 2.21534e6 | − | 1.81816e6i | 0.584563 | − | 0.479759i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.15716e6 | + | 3.23394e6i | 0.301802 | + | 0.843452i | ||||
\(431\) | 516224. | 0.133858 | 0.0669291 | − | 0.997758i | \(-0.478680\pi\) | ||||
0.0669291 | + | 0.997758i | \(0.478680\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.50137e6 | 1.66642 | 0.833212 | − | 0.552954i | \(-0.186499\pi\) | ||||
0.833212 | + | 0.552954i | \(0.186499\pi\) | |||||||
\(434\) | 598342. | + | 1.67220e6i | 0.152484 | + | 0.426151i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 739014. | − | 606518.i | 0.186181 | − | 0.152801i | ||||
\(437\) | 3.92833e6 | + | 2.26802e6i | 0.984021 | + | 0.568125i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 762498. | − | 440228.i | 0.188833 | − | 0.109023i | −0.402603 | − | 0.915375i | \(-0.631895\pi\) |
0.591436 | + | 0.806352i | \(0.298561\pi\) | |||||||
\(440\) | 1.20974e6 | − | 2.01848e6i | 0.297894 | − | 0.497041i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 339793. | − | 1.86755e6i | 0.0827292 | − | 0.454692i | ||||
\(443\) | −372571. | − | 645312.i | −0.0901985 | − | 0.156228i | 0.817396 | − | 0.576076i | \(-0.195417\pi\) |
−0.907595 | + | 0.419848i | \(0.862083\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.06289e6 | − | 1.84098e6i | 0.254442 | − | 0.440706i | ||||
\(446\) | −2.18964e6 | − | 1.85773e6i | −0.521238 | − | 0.442228i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.08874e6 | − | 676931.i | −0.256289 | − | 0.159349i | ||||
\(449\) | − | 3.80614e6i | − | 0.890983i | −0.895286 | − | 0.445492i | \(-0.853029\pi\) | ||
0.895286 | − | 0.445492i | \(-0.146971\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.90246e6i | 0.440427i | ||||||||
\(452\) | −7.81584e6 | + | 1.29056e6i | −1.79941 | + | 0.297121i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −401036. | + | 472686.i | −0.0913154 | + | 0.107630i | ||||
\(455\) | 1.24686e6 | − | 2.15963e6i | 0.282352 | − | 0.489047i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.54711e6 | − | 2.67967e6i | −0.346521 | − | 0.600192i | 0.639108 | − | 0.769117i | \(-0.279304\pi\) |
−0.985629 | + | 0.168925i | \(0.945970\pi\) | |||||||
\(458\) | 2.00618e6 | + | 365015.i | 0.446895 | + | 0.0813106i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.62028e6 | − | 4.30524e6i | 0.357021 | − | 0.948642i | ||||
\(461\) | 6.16631e6 | − | 3.56012e6i | 1.35137 | − | 0.780212i | 0.362926 | − | 0.931818i | \(-0.381778\pi\) |
0.988441 | + | 0.151606i | \(0.0484445\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.12079e6 | − | 2.37914e6i | −0.893363 | − | 0.515784i | −0.0183222 | − | 0.999832i | \(-0.505832\pi\) |
−0.875041 | + | 0.484049i | \(0.839166\pi\) | |||||||
\(464\) | 1.97105e6 | + | 5.80575e6i | 0.425014 | + | 1.25188i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.99975e6 | + | 1.78900e6i | −1.06656 | + | 0.381632i | ||||
\(467\) | −7.37952e6 | −1.56580 | −0.782900 | − | 0.622148i | \(-0.786260\pi\) | ||||
−0.782900 | + | 0.622148i | \(0.786260\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.67452e6 | −0.351528 | ||||||||
\(470\) | 4.63915e6 | − | 1.65997e6i | 0.968710 | − | 0.346621i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 287826. | − | 159967.i | 0.0594670 | − | 0.0330503i | ||||
\(473\) | 1.90600e6 | + | 1.10043e6i | 0.391716 | + | 0.226157i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 755186. | − | 436007.i | 0.153575 | − | 0.0886665i | ||||
\(476\) | 369432. | + | 139036.i | 0.0747338 | + | 0.0281260i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.81454e6 | + | 330148.i | 0.363243 | + | 0.0660904i | ||||
\(479\) | −553793. | − | 959197.i | −0.110283 | − | 0.191016i | 0.805601 | − | 0.592458i | \(-0.201842\pi\) |
−0.915884 | + | 0.401442i | \(0.868509\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.79058e6 | + | 4.83342e6i | −0.549960 | + | 0.952559i | ||||
\(482\) | −277429. | + | 326995.i | −0.0543919 | + | 0.0641097i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 593950. | + | 3.59705e6i | 0.115249 | + | 0.697963i | ||||
\(485\) | 178657.i | 0.0344878i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 763869.i | 0.145948i | 0.997334 | + | 0.0729738i | \(0.0232489\pi\) | ||||
−0.997334 | + | 0.0729738i | \(0.976751\pi\) | |||||||
\(488\) | 144391. | − | 8.84036e6i | 0.0274468 | − | 1.68043i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.94625e6 | − | 3.34807e6i | −0.742496 | − | 0.629948i | ||||
\(491\) | −3.47276e6 | + | 6.01500e6i | −0.650087 | + | 1.12598i | 0.333015 | + | 0.942922i | \(0.391934\pi\) |
−0.983101 | + | 0.183061i | \(0.941399\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −943881. | − | 1.63485e6i | −0.174904 | − | 0.302943i | ||||
\(494\) | −2.03663e6 | + | 1.11936e7i | −0.375486 | + | 2.06373i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.41775e6 | + | 6.17828e6i | −0.988815 | + | 1.12762i | ||||
\(497\) | −996459. | + | 575306.i | −0.180954 | + | 0.104474i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.34730e6 | − | 3.08727e6i | −0.961354 | − | 0.555038i | −0.0647647 | − | 0.997901i | \(-0.520630\pi\) |
−0.896590 | + | 0.442862i | \(0.853963\pi\) | |||||||
\(500\) | 3.23827e6 | + | 3.94567e6i | 0.579279 | + | 0.705824i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.85161e6 | − | 5.17472e6i | −0.327936 | − | 0.916490i | ||||
\(503\) | 3.43627e6 | 0.605574 | 0.302787 | − | 0.953058i | \(-0.402083\pi\) | ||||
0.302787 | + | 0.953058i | \(0.402083\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.14897e6 | −0.549465 | ||||||||
\(506\) | −993031. | − | 2.77525e6i | −0.172420 | − | 0.481865i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.39931e6 | + | 6.57880e6i | 0.928280 | + | 1.13106i | ||||
\(509\) | −2.45696e6 | − | 1.41853e6i | −0.420343 | − | 0.242685i | 0.274881 | − | 0.961478i | \(-0.411362\pi\) |
−0.695224 | + | 0.718793i | \(0.744695\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.28832e6 | + | 743811.i | −0.218259 | + | 0.126012i | ||||
\(512\) | 290506. | − | 5.92452e6i | 0.0489756 | − | 0.998800i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.39783e6 | − | 7.68266e6i | 0.233370 | − | 1.28264i | ||||
\(515\) | 360214. | + | 623909.i | 0.0598470 | + | 0.103658i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.57859e6 | − | 2.73420e6i | 0.259743 | − | 0.449888i | ||||
\(518\) | −884987. | − | 750840.i | −0.144915 | − | 0.122948i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.15363e7 | + | 188425.i | 1.87094 | + | 0.0305584i | ||||
\(521\) | 1.84176e6i | 0.297261i | 0.988893 | + | 0.148631i | \(0.0474866\pi\) | ||||
−0.988893 | + | 0.148631i | \(0.952513\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 1.03954e7i | − | 1.66183i | −0.556398 | − | 0.830916i | \(-0.687817\pi\) | ||
0.556398 | − | 0.830916i | \(-0.312183\pi\) | |||||||
\(524\) | −387483. | − | 2.34665e6i | −0.0616487 | − | 0.373353i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.76156e6 | + | 2.07628e6i | −0.277608 | + | 0.327207i | ||||
\(527\) | 1.26502e6 | − | 2.19108e6i | 0.198413 | − | 0.343662i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 337272. | + | 584172.i | 0.0524012 | + | 0.0907615i | ||||
\(530\) | −6.54312e6 | − | 1.19049e6i | −1.01180 | − | 0.184093i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.21427e6 | − | 833342.i | −0.339197 | − | 0.127657i | ||||
\(533\) | −8.07804e6 | + | 4.66386e6i | −1.23165 | + | 0.711094i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.64490e6 | − | 2.68173e6i | −0.701603 | − | 0.405071i | ||||
\(536\) | −3.76372e6 | − | 6.77201e6i | −0.565856 | − | 1.01814i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.97327e6 | + | 2.13734e6i | −0.889726 | + | 0.318359i | ||||
\(539\) | −3.31609e6 | −0.491648 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 330411. | 0.0485357 | 0.0242679 | − | 0.999705i | \(-0.492275\pi\) | ||||
0.0242679 | + | 0.999705i | \(0.492275\pi\) | |||||||
\(542\) | −4.65149e6 | + | 1.66438e6i | −0.680133 | + | 0.243364i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 268069. | + | 1.80654e6i | 0.0388373 | + | 0.261727i | ||||
\(545\) | −1.54949e6 | − | 894596.i | −0.223458 | − | 0.129014i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.06834e7 | − | 6.16808e6i | 1.52666 | − | 0.881417i | 0.527160 | − | 0.849766i | \(-0.323257\pi\) |
0.999499 | − | 0.0316507i | \(-0.0100764\pi\) | |||||||
\(548\) | 261666. | − | 695272.i | 0.0372216 | − | 0.0989017i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −557489. | − | 101433.i | −0.0785832 | − | 0.0142979i | ||||
\(551\) | 5.65737e6 | + | 9.79885e6i | 0.793845 | + | 1.37498i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 290448. | − | 503070.i | 0.0403883 | − | 0.0699545i | ||||
\(554\) | −6.58887e6 | + | 7.76606e6i | −0.912088 | + | 1.07504i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.04774e7 | + | 1.73004e6i | −1.43736 | + | 0.237339i | ||||
\(557\) | 5.94173e6i | 0.811474i | 0.913990 | + | 0.405737i | \(0.132985\pi\) | ||||
−0.913990 | + | 0.405737i | \(0.867015\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.07908e7i | 1.46058i | ||||||||
\(560\) | −467979. | + | 2.35319e6i | −0.0630603 | + | 0.317094i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.17774e6 | + | 999214.i | 0.157292 | + | 0.133450i | ||||
\(563\) | 66573.9 | − | 115309.i | 0.00885182 | − | 0.0153318i | −0.861566 | − | 0.507646i | \(-0.830516\pi\) |
0.870417 | + | 0.492315i | \(0.163849\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.41258e6 | + | 1.28390e7i | 0.976896 | + | 1.69203i | ||||
\(566\) | 753521. | − | 4.14146e6i | 0.0988676 | − | 0.543391i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.56629e6 | − | 2.73674e6i | −0.593872 | − | 0.355929i | ||||
\(569\) | −3.70587e6 | + | 2.13959e6i | −0.479854 | + | 0.277044i | −0.720356 | − | 0.693605i | \(-0.756021\pi\) |
0.240501 | + | 0.970649i | \(0.422688\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 525371. | + | 303323.i | 0.0674335 | + | 0.0389328i | 0.533338 | − | 0.845902i | \(-0.320938\pi\) |
−0.465904 | + | 0.884835i | \(0.654271\pi\) | |||||||
\(572\) | 5.71485e6 | − | 4.69025e6i | 0.730323 | − | 0.599386i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −653476. | − | 1.82628e6i | −0.0827846 | − | 0.231360i | ||||
\(575\) | −1.10765e6 | −0.139712 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −496600. | −0.0620965 | −0.0310483 | − | 0.999518i | \(-0.509885\pi\) | ||||
−0.0310483 | + | 0.999518i | \(0.509885\pi\) | |||||||
\(578\) | 2.51651e6 | + | 7.03294e6i | 0.313313 | + | 0.875624i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8.86965e6 | − | 7.27944e6i | 1.09480 | − | 0.898520i | ||||
\(581\) | −4.07733e6 | − | 2.35405e6i | −0.501113 | − | 0.289318i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.69053e6 | + | 2.13073e6i | −0.449694 | + | 0.259631i | ||||
\(584\) | −5.90375e6 | − | 3.53833e6i | −0.716302 | − | 0.429305i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −386561. | + | 2.12460e6i | −0.0465023 | + | 0.255583i | ||||
\(587\) | −7.37488e6 | − | 1.27737e7i | −0.883405 | − | 1.53010i | −0.847531 | − | 0.530746i | \(-0.821912\pi\) |
−0.0358744 | − | 0.999356i | \(-0.511422\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.58219e6 | + | 1.31327e7i | −0.900547 | + | 1.55979i | ||||
\(590\) | −469919. | − | 398689.i | −0.0555768 | − | 0.0471524i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.04737e6 | − | 5.26663e6i | 0.122828 | − | 0.617630i | ||||
\(593\) | 1.01532e7i | 1.18568i | 0.805322 | + | 0.592838i | \(0.201992\pi\) | ||||
−0.805322 | + | 0.592838i | \(0.798008\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 738722.i | − | 0.0855438i | ||||||
\(596\) | 1.04923e7 | − | 1.73250e6i | 1.20991 | − | 0.199783i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.34959e6 | − | 1.10200e7i | 1.06915 | − | 1.26017i | ||||
\(599\) | −5.29325e6 | + | 9.16817e6i | −0.602775 | + | 1.04404i | 0.389624 | + | 0.920974i | \(0.372605\pi\) |
−0.992399 | + | 0.123062i | \(0.960728\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.67071e6 | + | 1.15540e7i | 0.753331 | + | 1.30481i | 0.946200 | + | 0.323583i | \(0.104887\pi\) |
−0.192869 | + | 0.981224i | \(0.561779\pi\) | |||||||
\(602\) | −2.20768e6 | − | 401677.i | −0.248281 | − | 0.0451737i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.91123e6 | − | 1.03925e7i | 0.436235 | − | 1.15912i | ||||
\(605\) | 5.90881e6 | − | 3.41146e6i | 0.656314 | − | 0.378923i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.57795e6 | + | 3.79778e6i | 0.724635 | + | 0.418368i | 0.816456 | − | 0.577408i | \(-0.195936\pi\) |
−0.0918216 | + | 0.995775i | \(0.529269\pi\) | |||||||
\(608\) | −1.60673e6 | − | 1.08279e7i | −0.176273 | − | 1.18791i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.55793e7 | + | 5.57456e6i | −1.69521 | + | 0.606577i | ||||
\(611\) | 1.54796e7 | 1.67748 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.15773e7 | 1.24438 | 0.622192 | − | 0.782865i | \(-0.286242\pi\) | ||||
0.622192 | + | 0.782865i | \(0.286242\pi\) | |||||||
\(614\) | 1.71495e7 | − | 6.13637e6i | 1.83582 | − | 0.656887i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 746844. | + | 1.34378e6i | 0.0793009 | + | 0.142685i | ||||
\(617\) | 4.79775e6 | + | 2.76998e6i | 0.507370 | + | 0.292930i | 0.731752 | − | 0.681571i | \(-0.238703\pi\) |
−0.224382 | + | 0.974501i | \(0.572036\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 399838. | − | 230847.i | 0.0419428 | − | 0.0242157i | −0.478882 | − | 0.877879i | \(-0.658958\pi\) |
0.520825 | + | 0.853664i | \(0.325624\pi\) | |||||||
\(620\) | 1.43928e7 | + | 5.41672e6i | 1.50371 | + | 0.565923i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −8.63579e6 | − | 1.57124e6i | −0.895006 | − | 0.162842i | ||||
\(623\) | 694390. | + | 1.20272e6i | 0.0716776 | + | 0.124149i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.49736e6 | − | 9.52171e6i | 0.562930 | − | 0.975023i | ||||
\(626\) | −1.93228e6 | + | 2.27751e6i | −0.197076 | + | 0.232287i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 756689. | + | 4.58262e6i | 0.0765629 | + | 0.463676i | ||||
\(629\) | 1.65332e6i | 0.166621i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.33405e7i | 1.33383i | 0.745136 | + | 0.666913i | \(0.232385\pi\) | ||||
−0.745136 | + | 0.666913i | \(0.767615\pi\) | |||||||
\(632\) | 2.68731e6 | + | 43892.3i | 0.267624 | + | 0.00437115i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.80904e6 | − | 3.23166e6i | −0.376350 | − | 0.319303i | ||||
\(635\) | 7.96382e6 | − | 1.37937e7i | 0.783767 | − | 1.35752i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.12936e6 | − | 1.40805e7i | −0.793794 | − | 1.37489i | ||||
\(638\) | 1.31613e6 | − | 7.23365e6i | 0.128011 | − | 0.703567i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.05685e7 | + | 3.39655e6i | −1.01991 | + | 0.327784i | ||||
\(641\) | 2.31892e6 | − | 1.33883e6i | 0.222915 | − | 0.128700i | −0.384384 | − | 0.923173i | \(-0.625586\pi\) |
0.607299 | + | 0.794473i | \(0.292253\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.46328e7 | + | 8.44826e6i | 1.39573 | + | 0.805824i | 0.993942 | − | 0.109910i | \(-0.0350563\pi\) |
0.401786 | + | 0.915734i | \(0.368390\pi\) | |||||||
\(644\) | 1.90654e6 | + | 2.32303e6i | 0.181147 | + | 0.220719i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.13547e6 | + | 3.17332e6i | 0.107052 | + | 0.299180i | ||||
\(647\) | 7.65712e6 | 0.719126 | 0.359563 | − | 0.933121i | \(-0.382926\pi\) | ||||
0.359563 | + | 0.933121i | \(0.382926\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −394880. | −0.0368005 | ||||||||
\(650\) | −935986. | − | 2.61582e6i | −0.0868932 | − | 0.242842i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.87302e6 | + | 5.93754e6i | 0.448930 | + | 0.547000i | ||||
\(653\) | −957462. | − | 552791.i | −0.0878696 | − | 0.0507315i | 0.455421 | − | 0.890276i | \(-0.349489\pi\) |
−0.543291 | + | 0.839544i | \(0.682822\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.85480e6 | + | 2.22557e6i | −0.351074 | + | 0.202693i | ||||
\(656\) | 5.91697e6 | − | 6.74757e6i | 0.536834 | − | 0.612192i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −576214. | + | 3.16696e6i | −0.0518823 | + | 0.285153i | ||||
\(659\) | −7.66650e6 | − | 1.32788e7i | −0.687675 | − | 1.19109i | −0.972588 | − | 0.232535i | \(-0.925298\pi\) |
0.284912 | − | 0.958554i | \(-0.408035\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.77496e6 | − | 6.53842e6i | 0.336054 | − | 0.582062i | −0.647633 | − | 0.761952i | \(-0.724241\pi\) |
0.983687 | + | 0.179890i | \(0.0575743\pi\) | |||||||
\(662\) | 638990. | + | 542131.i | 0.0566695 | + | 0.0480795i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 355742. | − | 2.17803e7i | 0.0313123 | − | 1.91710i | ||||
\(665\) | 4.42770e6i | 0.388261i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1.43723e7i | − | 1.25087i | ||||||
\(668\) | −1.50904e6 | − | 9.13895e6i | −0.130846 | − | 0.792420i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −9.38039e6 | + | 1.10563e7i | −0.807298 | + | 0.951532i | ||||
\(671\) | −5.30128e6 | + | 9.18209e6i | −0.454543 | + | 0.787291i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.45359e6 | + | 2.51769e6i | 0.123710 | + | 0.214271i | 0.921228 | − | 0.389023i | \(-0.127188\pi\) |
−0.797518 | + | 0.603295i | \(0.793854\pi\) | |||||||
\(674\) | 2.13418e6 | + | 388304.i | 0.180959 | + | 0.0329248i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.28053e7 | + | 8.58278e6i | 1.91942 | + | 0.722372i | ||||
\(677\) | −8.20582e6 | + | 4.73763e6i | −0.688098 | + | 0.397274i | −0.802899 | − | 0.596115i | \(-0.796710\pi\) |
0.114801 | + | 0.993389i | \(0.463377\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −101080. | − | 58358.6i | −0.00841377 | − | 0.00485769i | ||||
\(680\) | 2.98750e6 | − | 1.66038e6i | 0.247762 | − | 0.137700i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9.27788e6 | − | 3.31979e6i | 0.763814 | − | 0.273306i | ||||
\(683\) | −6.62953e6 | −0.543789 | −0.271895 | − | 0.962327i | \(-0.587650\pi\) | ||||
−0.271895 | + | 0.962327i | \(0.587650\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.39028e6 | −0.113208 | ||||||||
\(686\) | 6.68560e6 | − | 2.39222e6i | 0.542413 | − | 0.194085i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.33762e6 | − | 9.83098e6i | −0.268822 | − | 0.791819i | ||||
\(689\) | −1.80946e7 | − | 1.04469e7i | −1.45211 | − | 0.838378i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.59285e6 | + | 3.80638e6i | −0.525264 | + | 0.303261i | −0.739086 | − | 0.673611i | \(-0.764742\pi\) |
0.213822 | + | 0.976873i | \(0.431409\pi\) | |||||||
\(692\) | −6.38792e6 | + | 1.69733e7i | −0.507101 | + | 1.34742i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.71028e6 | + | 1.22091e6i | 0.528861 | + | 0.0962240i | ||||
\(695\) | 9.93677e6 | + | 1.72110e7i | 0.780339 | + | 1.35159i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.38159e6 | + | 2.39298e6i | −0.107720 | + | 0.186576i | ||||
\(698\) | 1.06684e6 | − | 1.25744e6i | 0.0828821 | − | 0.0976900i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 570009. | − | 94120.8i | 0.0439680 | − | 0.00726007i | ||||
\(701\) | − | 3.35628e6i | − | 0.257966i | −0.991647 | − | 0.128983i | \(-0.958829\pi\) | ||
0.991647 | − | 0.128983i | \(-0.0411713\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 9.90954e6i | − | 0.756249i | ||||||
\(704\) | −3.75582e6 | + | 6.04068e6i | −0.285610 | + | 0.459361i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 810734. | + | 687842.i | 0.0612163 | + | 0.0519370i | ||||
\(707\) | 1.02862e6 | − | 1.78162e6i | 0.0773936 | − | 0.134050i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.57561e6 | + | 6.19313e6i | 0.267137 | + | 0.462695i | 0.968121 | − | 0.250482i | \(-0.0805890\pi\) |
−0.700984 | + | 0.713177i | \(0.747256\pi\) | |||||||
\(710\) | −1.78344e6 | + | 9.80204e6i | −0.132774 | + | 0.729744i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.30323e6 | + | 5.51149e6i | −0.244196 | + | 0.407445i | ||||
\(713\) | 1.66815e7 | − | 9.63109e6i | 1.22889 | − | 0.709499i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.19823e7 | − | 6.91798e6i | −0.876547 | − | 0.506074i | ||||
\(716\) | −1.09052e7 | + | 8.95006e6i | −0.794972 | + | 0.652444i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.25669e6 | + | 9.10155e6i | 0.235758 | + | 0.658877i | ||||
\(719\) | 1.05572e7 | 0.761603 | 0.380801 | − | 0.924657i | \(-0.375648\pi\) | ||||
0.380801 | + | 0.924657i | \(0.375648\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −470659. | −0.0337185 | ||||||||
\(722\) | −2.08676e6 | − | 5.83191e6i | −0.148981 | − | 0.416359i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.56887e6 | + | 2.10831e6i | −0.182136 | + | 0.149482i | ||||
\(725\) | −2.39278e6 | − | 1.38147e6i | −0.169066 | − | 0.0976104i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 457178. | − | 263952.i | 0.0320811 | − | 0.0185220i | −0.483874 | − | 0.875138i | \(-0.660771\pi\) |
0.515955 | + | 0.856616i | \(0.327437\pi\) | |||||||
\(728\) | −3.87498e6 | + | 6.46546e6i | −0.270982 | + | 0.452138i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.30580e6 | + | 1.26730e7i | −0.160146 | + | 0.880184i | ||||
\(731\) | 1.59829e6 | + | 2.76832e6i | 0.110627 | + | 0.191612i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.01725e7 | + | 1.76192e7i | −0.699304 | + | 1.21123i | 0.269404 | + | 0.963027i | \(0.413173\pi\) |
−0.968708 | + | 0.248202i | \(0.920160\pi\) | |||||||
\(734\) | −1.62681e7 | − | 1.38021e7i | −1.11454 | − | 0.945596i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.10945e6 | + | 1.29316e7i | −0.347680 | + | 0.879953i | ||||
\(737\) | 9.29078e6i | 0.630062i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.56621e6i | 0.307570i | 0.988104 | + | 0.153785i | \(0.0491464\pi\) | ||||
−0.988104 | + | 0.153785i | \(0.950854\pi\) | |||||||
\(740\) | −9.91508e6 | + | 1.63719e6i | −0.665605 | + | 0.109906i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.81087e6 | − | 3.31307e6i | 0.187427 | − | 0.220913i | ||||
\(743\) | −8.52924e6 | + | 1.47731e7i | −0.566811 | + | 0.981745i | 0.430068 | + | 0.902797i | \(0.358490\pi\) |
−0.996879 | + | 0.0789485i | \(0.974844\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.95091e6 | − | 1.72355e7i | −0.656859 | − | 1.13771i | ||||
\(746\) | 1.26297e7 | + | 2.29791e6i | 0.830893 | + | 0.151177i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 771413. | − | 2.04972e6i | 0.0504119 | − | 0.133949i | ||||
\(749\) | 3.03453e6 | − | 1.75199e6i | 0.197645 | − | 0.114111i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.42935e6 | + | 2.55729e6i | 0.286576 | + | 0.165455i | 0.636397 | − | 0.771362i | \(-0.280424\pi\) |
−0.349821 | + | 0.936817i | \(0.613757\pi\) | |||||||
\(752\) | −1.41027e7 | + | 4.78788e6i | −0.909409 | + | 0.308744i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.39413e7 | − | 1.21448e7i | 2.17421 | − | 0.777968i | ||||
\(755\) | −2.07811e7 | −1.32679 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.36558e6 | 0.403736 | 0.201868 | − | 0.979413i | \(-0.435299\pi\) | ||||
0.201868 | + | 0.979413i | \(0.435299\pi\) | |||||||
\(758\) | −2.16863e7 | + | 7.75972e6i | −1.37092 | + | 0.490539i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.79062e7 | + | 9.95187e6i | −1.12453 | + | 0.624986i | ||||
\(761\) | 9.28199e6 | + | 5.35896e6i | 0.581005 | + | 0.335443i | 0.761533 | − | 0.648127i | \(-0.224447\pi\) |
−0.180528 | + | 0.983570i | \(0.557781\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.01228e6 | − | 584443.i | 0.0629494 | − | 0.0363438i | ||||
\(764\) | −1.29094e7 | − | 4.85845e6i | −0.800153 | − | 0.301137i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.35860e7 | − | 2.47192e6i | −0.836605 | − | 0.152217i | ||||
\(767\) | −968045. | − | 1.67670e6i | −0.0594165 | − | 0.102912i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.59857e6 | − | 1.31611e7i | 0.463358 | − | 0.802559i | −0.535768 | − | 0.844365i | \(-0.679978\pi\) |
0.999126 | + | 0.0418063i | \(0.0133112\pi\) | |||||||
\(770\) | 1.86137e6 | − | 2.19393e6i | 0.113137 | − | 0.133351i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 216309. | + | 1.31000e6i | 0.0130627 | + | 0.0791093i | ||||
\(773\) | − | 2.52966e7i | − | 1.52270i | −0.648342 | − | 0.761349i | \(-0.724537\pi\) | ||
0.648342 | − | 0.761349i | \(-0.275463\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 3.70298e6i | − | 0.221461i | ||||||
\(776\) | 8819.11 | − | 539951.i | 0.000525739 | − | 0.0321884i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.60254e6 | − | 3.90488e6i | −0.272614 | − | 0.231291i | ||||
\(779\) | 8.28085e6 | − | 1.43429e7i | 0.488913 | − | 0.846822i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.19197e6 | + | 5.52866e6i | 0.187254 | + | 0.324334i | ||||
\(782\) | 766345. | − | 4.21195e6i | 0.0448134 | − | 0.246301i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.17614e7 | + | 1.03136e7i | 0.683390 | + | 0.599267i | ||||
\(785\) | 7.52780e6 | − | 4.34617e6i | 0.436007 | − | 0.251729i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.86663e7 | − | 1.07770e7i | −1.07429 | − | 0.620240i | −0.144938 | − | 0.989441i | \(-0.546298\pi\) |
−0.929350 | + | 0.369201i | \(0.879631\pi\) | |||||||
\(788\) | 7.17866e6 | + | 8.74686e6i | 0.411840 | + | 0.501807i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.69456e6 | − | 4.73584e6i | −0.0966029 | − | 0.269978i | ||||
\(791\) | −9.68533e6 | −0.550393 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.19842e7 | −2.93554 | ||||||||
\(794\) | −5.03486e6 | − | 1.40710e7i | −0.283424 | − | 0.792091i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.40274e6 | − | 4.14608e6i | −0.190347 | − | 0.231929i | ||||
\(797\) | 2.02403e7 | + | 1.16857e7i | 1.12868 | + | 0.651643i | 0.943602 | − | 0.331081i | \(-0.107413\pi\) |
0.185077 | + | 0.982724i | \(0.440747\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.97122e6 | − | 2.29278e6i | 0.220068 | − | 0.127056i | ||||
\(800\) | 1.66181e6 | + | 2.09365e6i | 0.0918029 | + | 0.115659i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.82664e6 | − | 1.55356e7i | 0.155180 | − | 0.852890i | ||||
\(803\) | 4.12690e6 | + | 7.14799e6i | 0.225858 | + | 0.391197i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.81209e6 | − | 4.87068e6i | 0.152946 | − | 0.264911i | ||||
\(806\) | 3.68408e7 | + | 3.12565e7i | 1.99752 | + | 1.69474i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.51707e6 | + | 155444.i | 0.512832 | + | 0.00837617i | ||||
\(809\) | 1.04327e7i | 0.560434i | 0.959937 | + | 0.280217i | \(0.0904064\pi\) | ||||
−0.959937 | + | 0.280217i | \(0.909594\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2.11443e7i | − | 1.12886i | −0.825480 | − | 0.564431i | \(-0.809096\pi\) | ||
0.825480 | − | 0.564431i | \(-0.190904\pi\) | |||||||
\(812\) | 1.22126e6 | + | 7.39609e6i | 0.0650005 | + | 0.393652i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.16589e6 | + | 4.91018e6i | −0.220367 | + | 0.259739i | ||||
\(815\) | 7.18755e6 | − | 1.24492e7i | 0.379042 | − | 0.656519i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.57973e6 | − | 1.65926e7i | −0.502109 | − | 0.869679i | ||||
\(818\) | −5.59761e6 | − | 1.01846e6i | −0.292496 | − | 0.0532183i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.57190e7 | − | 5.91584e6i | −0.816375 | − | 0.307243i | ||||
\(821\) | −1.20134e7 | + | 6.93595e6i | −0.622027 | + | 0.359127i | −0.777658 | − | 0.628688i | \(-0.783592\pi\) |
0.155631 | + | 0.987815i | \(0.450259\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.96052e6 | + | 3.44131e6i | 0.306750 | + | 0.177102i | 0.645471 | − | 0.763785i | \(-0.276661\pi\) |
−0.338721 | + | 0.940887i | \(0.609994\pi\) | |||||||
\(824\) | −1.05787e6 | − | 1.90341e6i | −0.0542768 | − | 0.0976594i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 379069. | − | 135637.i | 0.0193316 | − | 0.00691719i | ||||
\(827\) | −2.50557e7 | −1.27392 | −0.636962 | − | 0.770895i | \(-0.719809\pi\) | ||||
−0.636962 | + | 0.770895i | \(0.719809\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.56223e6 | 0.432714 | 0.216357 | − | 0.976314i | \(-0.430583\pi\) | ||||
0.216357 | + | 0.976314i | \(0.430583\pi\) | |||||||
\(830\) | −3.83835e7 | + | 1.37343e7i | −1.93397 | + | 0.692007i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.48568e7 | − | 1.13895e6i | −1.74574 | − | 0.0570421i | ||||
\(833\) | −4.17109e6 | − | 2.40818e6i | −0.208275 | − | 0.120248i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.50124e7 | + | 8.66743e6i | −0.745134 | + | 0.430204i | ||||
\(836\) | −4.62364e6 | + | 1.22855e7i | −0.228806 | + | 0.607962i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.17290e7 | + | 5.77295e6i | 1.56080 | + | 0.283980i | ||||
\(839\) | −1.86706e7 | − | 3.23384e7i | −0.915701 | − | 1.58604i | −0.805872 | − | 0.592090i | \(-0.798303\pi\) |
−0.109828 | − | 0.993951i | \(-0.535030\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.66955e6 | − | 1.32841e7i | 0.373921 | − | 0.647650i | ||||
\(842\) | 2.16533e7 | − | 2.55219e7i | 1.05255 | − | 1.24060i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.21999e6 | + | 366569.i | −0.107274 | + | 0.0177133i | ||||
\(845\) | − | 4.56019e7i | − | 2.19706i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.45743e6i | 0.213489i | ||||||||
\(848\) | 1.97164e7 | + | 3.92099e6i | 0.941536 | + | 0.187243i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −627567. | − | 532440.i | −0.0297929 | − | 0.0252769i | ||||
\(851\) | −6.29367e6 | + | 1.09010e7i | −0.297907 | + | 0.515989i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.88097e6 | − | 1.53823e7i | −0.417915 | − | 0.723850i | 0.577815 | − | 0.816168i | \(-0.303906\pi\) |
−0.995730 | + | 0.0923182i | \(0.970572\pi\) | |||||||
\(854\) | 1.93506e6 | − | 1.06354e7i | 0.0907925 | − | 0.499009i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.39058e7 | + | 8.33423e6i | 0.648652 | + | 0.388760i | ||||
\(857\) | 2.38271e7 | − | 1.37566e7i | 1.10820 | − | 0.639822i | 0.169840 | − | 0.985472i | \(-0.445675\pi\) |
0.938363 | + | 0.345650i | \(0.112342\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.17405e7 | + | 1.83254e7i | 1.46768 | + | 0.847365i | 0.999345 | − | 0.0361865i | \(-0.0115210\pi\) |
0.468334 | + | 0.883551i | \(0.344854\pi\) | |||||||
\(860\) | −1.50192e7 | + | 1.23264e7i | −0.692467 | + | 0.568317i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 983815. | + | 2.74949e6i | 0.0450968 | + | 0.126033i | ||||
\(863\) | −5.86388e6 | −0.268015 | −0.134007 | − | 0.990980i | \(-0.542785\pi\) | ||||
−0.134007 | + | 0.990980i | \(0.542785\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.39402e7 | 1.54232 | ||||||||
\(866\) | 1.23903e7 | + | 3.46273e7i | 0.561417 | + | 1.56901i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.76608e6 | + | 6.37373e6i | −0.349867 | + | 0.287140i | ||||
\(869\) | −2.79119e6 | − | 1.61149e6i | −0.125383 | − | 0.0723901i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.94497e7 | + | 2.27763e7i | −1.76197 | + | 1.01727i | ||||
\(872\) | 4.63882e6 | + | 2.78021e6i | 0.206593 | + | 0.123819i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.59327e6 | + | 2.52453e7i | −0.203396 | + | 1.11790i | ||||
\(875\) | 3.12040e6 | + | 5.40470e6i | 0.137781 | + | 0.238644i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.52615e7 | − | 2.64338e7i | 0.670038 | − | 1.16054i | −0.307855 | − | 0.951433i | \(-0.599611\pi\) |
0.977893 | − | 0.209106i | \(-0.0670555\pi\) | |||||||
\(878\) | 3.79789e6 | + | 3.22220e6i | 0.166267 | + | 0.141064i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.30562e7 | + | 2.59649e6i | 0.568344 | + | 0.113026i | ||||
\(881\) | 940107.i | 0.0408073i | 0.999792 | + | 0.0204036i | \(0.00649513\pi\) | ||||
−0.999792 | + | 0.0204036i | \(0.993505\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.57094e6i | 0.0678045i | 0.999425 | + | 0.0339022i | \(0.0107935\pi\) | ||||
−0.999425 | + | 0.0339022i | \(0.989207\pi\) | |||||||
\(884\) | 1.05945e7 | − | 1.74937e6i | 0.455982 | − | 0.0752926i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.72699e6 | − | 3.21420e6i | 0.116708 | − | 0.137559i | ||||
\(887\) | 1.53981e7 | − | 2.66703e7i | 0.657140 | − | 1.13820i | −0.324213 | − | 0.945984i | \(-0.605099\pi\) |
0.981353 | − | 0.192216i | \(-0.0615673\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.20279e6 | + | 9.01150e6i | 0.220791 | + | 0.382422i | ||||
\(890\) | 1.18310e7 | + | 2.15260e6i | 0.500664 | + | 0.0910936i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.72158e6 | − | 1.52028e7i | 0.240771 | − | 0.639753i | ||||
\(893\) | −2.38024e7 | + | 1.37423e7i | −0.998832 | + | 0.576676i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.28649e7 | + | 1.32011e7i | 0.954140 | + | 0.550873i | ||||
\(896\) | 1.53052e6 | − | 7.08890e6i | 0.0636899 | − | 0.294991i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.02721e7 | − | 7.25372e6i | 0.838897 | − | 0.300172i | ||||
\(899\) | 4.80477e7 | 1.98277 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.18943e6 | −0.254003 | ||||||||
\(902\) | −1.01328e7 | + | 3.62569e6i | −0.414680 | + | 0.148379i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.17691e7 | − | 3.91688e7i | −0.885971 | − | 1.59412i | ||||
\(905\) | 5.38614e6 | + | 3.10969e6i | 0.218603 | + | 0.126211i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.63670e7 | − | 9.44950e6i | 0.660619 | − | 0.381409i | −0.131894 | − | 0.991264i | \(-0.542106\pi\) |
0.792513 | + | 0.609855i | \(0.208772\pi\) | |||||||
\(908\) | −3.28189e6 | − | 1.23514e6i | −0.132102 | − | 0.0497166i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.38788e7 | + | 2.52519e6i | 0.555582 | + | 0.101086i | ||||
\(911\) | 2.19197e7 | + | 3.79660e7i | 0.875060 | + | 1.51565i | 0.856699 | + | 0.515817i | \(0.172511\pi\) |
0.0183608 | + | 0.999831i | \(0.494155\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.30610e7 | + | 2.26223e7i | −0.518560 | + | 0.898172i | ||||
\(914\) | 1.13239e7 | − | 1.33470e7i | 0.448362 | − | 0.528468i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.87923e6 | + | 1.13809e7i | 0.0740015 | + | 0.448163i | ||||
\(917\) | − | 2.90795e6i | − | 0.114199i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 3.62995e7i | − | 1.41779i | −0.705313 | − | 0.708896i | \(-0.749194\pi\) | ||
0.705313 | − | 0.708896i | \(-0.250806\pi\) | |||||||
\(920\) | 2.60183e7 | + | 424961.i | 1.01347 | + | 0.0165531i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.07135e7 | + | 2.60579e7i | 1.18988 | + | 1.00951i | ||||
\(923\) | −1.56502e7 | + | 2.71069e7i | −0.604666 | + | 1.04731i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.20990e6 | + | 2.09561e6i | 0.0464939 | + | 0.0805298i | ||||
\(926\) | 4.81831e6 | − | 2.64821e7i | 0.184658 | − | 1.01491i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.71659e7 | + | 2.15627e7i | −1.03551 | + | 0.821926i | ||||
\(929\) | −3.32057e7 | + | 1.91713e7i | −1.26233 | + | 0.728807i | −0.973525 | − | 0.228581i | \(-0.926591\pi\) |
−0.288805 | + | 0.957388i | \(0.593258\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.50004e7 | + | 1.44340e7i | 0.945306 | + | 0.545773i | ||||
\(932\) | −1.90570e7 | − | 2.32200e7i | −0.718644 | − | 0.875634i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.40638e7 | − | 3.93045e7i | −0.527517 | − | 1.47426i | ||||
\(935\) | −4.09866e6 | −0.153325 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −102797. | −0.00382500 | −0.00191250 | − | 0.999998i | \(-0.500609\pi\) | ||||
−0.00191250 | + | 0.999998i | \(0.500609\pi\) | |||||||
\(938\) | −3.19129e6 | − | 8.91878e6i | −0.118429 | − | 0.330977i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.76825e7 | + | 2.15453e7i | 0.652716 | + | 0.795303i | ||||
\(941\) | 1.82125e7 | + | 1.05150e7i | 0.670496 | + | 0.387111i | 0.796265 | − | 0.604948i | \(-0.206806\pi\) |
−0.125768 | + | 0.992060i | \(0.540140\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.82187e7 | + | 1.05185e7i | −0.667171 | + | 0.385191i | ||||
\(944\) | 1.40055e6 | + | 1.22815e6i | 0.0511526 | + | 0.0448559i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.22863e6 | + | 1.22489e7i | −0.0809673 | + | 0.445008i | ||||
\(947\) | −7.49577e6 | − | 1.29831e7i | −0.271607 | − | 0.470438i | 0.697666 | − | 0.716423i | \(-0.254222\pi\) |
−0.969274 | + | 0.245985i | \(0.920889\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.02341e7 | + | 3.50465e7i | −0.729321 | + | 1.26322i | ||||
\(950\) | 3.76147e6 | + | 3.19130e6i | 0.135222 | + | 0.114725i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −36465.9 | + | 2.23262e6i | −0.00130405 | + | 0.0798405i | ||||
\(953\) | 716587.i | 0.0255586i | 0.999918 | + | 0.0127793i | \(0.00406788\pi\) | ||||
−0.999918 | + | 0.0127793i | \(0.995932\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.58139e7i | 0.915893i | ||||||||
\(956\) | 1.69972e6 | + | 1.02937e7i | 0.0601495 | + | 0.364273i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.05342e6 | − | 4.77762e6i | 0.142695 | − | 0.168189i | ||||
\(959\) | 454137. | − | 786589.i | 0.0159456 | − | 0.0276186i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.78830e7 | + | 3.09742e7i | 0.624642 | + | 1.08191i | ||||
\(962\) | −3.10618e7 | − | 5.65156e6i | −1.08215 | − | 0.196893i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.27035e6 | − | 854445.i | −0.0786864 | − | 0.0296136i | ||||
\(965\) | 2.15192e6 | − | 1.24241e6i | 0.0743887 | − | 0.0429483i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.27307e6 | − | 4.19911e6i | −0.250122 | − | 0.144408i | 0.369698 | − | 0.929152i | \(-0.379461\pi\) |
−0.619820 | + | 0.784744i | \(0.712794\pi\) | |||||||
\(968\) | −1.80265e7 | + | 1.00187e7i | −0.618333 | + | 0.343655i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −951554. | + | 340482.i | −0.0324716 | + | 0.0116189i | ||||
\(971\) | 1.84209e7 | 0.626992 | 0.313496 | − | 0.949590i | \(-0.398500\pi\) | ||||
0.313496 | + | 0.949590i | \(0.398500\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.29835e7 | −0.439651 | ||||||||
\(974\) | −4.06849e6 | + | 1.45578e6i | −0.137416 | + | 0.0491696i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.73603e7 | − | 1.60788e7i | 1.59144 | − | 0.540293i | ||||
\(977\) | −1.70913e6 | − | 986767.i | −0.0572848 | − | 0.0330734i | 0.471084 | − | 0.882088i | \(-0.343863\pi\) |
−0.528369 | + | 0.849015i | \(0.677196\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.67306e6 | − | 3.85269e6i | 0.222519 | − | 0.128472i | ||||
\(980\) | 1.03116e7 | − | 2.73991e7i | 0.342975 | − | 0.911319i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.86552e7 | − | 7.03314e6i | −1.27917 | − | 0.232740i | ||||
\(983\) | −1.64275e7 | − | 2.84533e7i | −0.542236 | − | 0.939181i | −0.998775 | − | 0.0494775i | \(-0.984244\pi\) |
0.456539 | − | 0.889703i | \(-0.349089\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.05883e7 | − | 1.83395e7i | 0.347725 | − | 0.602278i | ||||
\(986\) | 6.90863e6 | − | 8.14294e6i | 0.226308 | − | 0.266741i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.35003e7 | + | 1.04853e7i | −2.06959 | + | 0.341734i | ||||
\(989\) | 2.43368e7i | 0.791176i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.19722e7i | − | 0.387250i | −0.981076 | − | 0.193625i | \(-0.937976\pi\) | ||
0.981076 | − | 0.193625i | \(-0.0620244\pi\) | |||||||
\(992\) | −4.32316e7 | − | 1.70813e7i | −1.39483 | − | 0.551115i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.96321e6 | − | 4.21088e6i | −0.159330 | − | 0.135178i | ||||
\(995\) | −5.01894e6 | + | 8.69306e6i | −0.160714 | + | 0.278365i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.60260e7 | + | 2.77579e7i | 0.510608 | + | 0.884400i | 0.999924 | + | 0.0122932i | \(0.00391315\pi\) |
−0.489316 | + | 0.872107i | \(0.662754\pi\) | |||||||
\(998\) | 6.25243e6 | − | 3.43643e7i | 0.198711 | − | 1.09215i | ||||
\(999\) | 0 | 0 |
(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 | 108.6.h.a.71.18 | 56 | ||
3.2 | odd | 2 | 36.6.h.a.23.11 | yes | 56 | ||
4.3 | odd | 2 | inner | 108.6.h.a.71.9 | 56 | ||
9.2 | odd | 6 | inner | 108.6.h.a.35.9 | 56 | ||
9.7 | even | 3 | 36.6.h.a.11.20 | yes | 56 | ||
12.11 | even | 2 | 36.6.h.a.23.20 | yes | 56 | ||
36.7 | odd | 6 | 36.6.h.a.11.11 | ✓ | 56 | ||
36.11 | even | 6 | inner | 108.6.h.a.35.18 | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.6.h.a.11.11 | ✓ | 56 | 36.7 | odd | 6 | ||
36.6.h.a.11.20 | yes | 56 | 9.7 | even | 3 | ||
36.6.h.a.23.11 | yes | 56 | 3.2 | odd | 2 | ||
36.6.h.a.23.20 | yes | 56 | 12.11 | even | 2 | ||
108.6.h.a.35.9 | 56 | 9.2 | odd | 6 | inner | ||
108.6.h.a.35.18 | 56 | 36.11 | even | 6 | inner | ||
108.6.h.a.71.9 | 56 | 4.3 | odd | 2 | inner | ||
108.6.h.a.71.18 | 56 | 1.1 | even | 1 | trivial |