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 | 35.9 | ||
Character | \(\chi\) | \(=\) | 108.35 |
Dual form | 108.6.h.a.71.9 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.65969 | + | 4.31354i | −0.646948 | + | 0.762534i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.21330 | − | 31.5725i | −0.162916 | − | 0.986640i | ||||
\(5\) | 51.8636 | − | 29.9435i | 0.927765 | − | 0.535645i | 0.0416611 | − | 0.999132i | \(-0.486735\pi\) |
0.886104 | + | 0.463486i | \(0.153402\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 33.8827 | + | 19.5622i | 0.261356 | + | 0.150894i | 0.624953 | − | 0.780662i | \(-0.285118\pi\) |
−0.363597 | + | 0.931556i | \(0.618451\pi\) | |||||||
\(8\) | 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 | \(-0.920508\pi\) |
0.698523 | + | 0.715588i | \(0.253841\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −532.156 | − | 921.721i | −0.873334 | − | 1.51266i | −0.858527 | − | 0.512769i | \(-0.828620\pi\) |
−0.0148071 | − | 0.999890i | \(-0.504713\pi\) | |||||||
\(14\) | −208.383 | + | 74.5629i | −0.284146 | + | 0.101672i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −969.643 | + | 329.194i | −0.946917 | + | 0.321478i | ||||
\(17\) | − | 315.283i | − | 0.264593i | −0.991210 | − | 0.132297i | \(-0.957765\pi\) | ||
0.991210 | − | 0.132297i | \(-0.0422351\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1889.72i | − | 1.20092i | −0.799655 | − | 0.600460i | \(-0.794984\pi\) | ||
0.799655 | − | 0.600460i | \(-0.205016\pi\) | |||||||
\(20\) | −1215.77 | − | 1481.36i | −0.679637 | − | 0.828105i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −413.698 | − | 1156.17i | −0.182233 | − | 0.509291i | ||||
\(23\) | 1200.19 | + | 2078.79i | 0.473074 | + | 0.819389i | 0.999525 | − | 0.0308168i | \(-0.00981084\pi\) |
−0.526451 | + | 0.850206i | \(0.676478\pi\) | |||||||
\(24\) | 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 | −0.197289 | − | 0.980345i | \(-0.563214\pi\) |
−0.947648 | + | 0.319315i | \(0.896547\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6949.56 | − | 4012.33i | 1.29883 | − | 0.749881i | 0.318629 | − | 0.947879i | \(-0.396778\pi\) |
0.980202 | + | 0.197999i | \(0.0634442\pi\) | |||||||
\(32\) | 2128.60 | − | 5387.34i | 0.367468 | − | 0.930036i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1359.99 | + | 1153.84i | 0.201761 | + | 0.171178i | ||||
\(35\) | 2343.04 | 0.323303 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5243.91 | 0.629725 | 0.314862 | − | 0.949137i | \(-0.398042\pi\) | ||||
0.314862 | + | 0.949137i | \(0.398042\pi\) | |||||||
\(38\) | 8151.40 | + | 6915.81i | 0.915743 | + | 0.776934i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 10839.3 | + | 177.040i | 1.07115 | + | 0.0174953i | ||||
\(41\) | 7589.92 | − | 4382.04i | 0.705144 | − | 0.407115i | −0.104117 | − | 0.994565i | \(-0.533202\pi\) |
0.809260 | + | 0.587450i | \(0.199868\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8780.43 | − | 5069.38i | −0.724176 | − | 0.418103i | 0.0921115 | − | 0.995749i | \(-0.470638\pi\) |
−0.816288 | + | 0.577645i | \(0.803972\pi\) | |||||||
\(44\) | 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 | \(-0.673899\pi\) |
0.999742 | + | 0.0227202i | \(0.00723270\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7638.14 | − | 13229.6i | −0.454462 | − | 0.787151i | ||||
\(50\) | 879.429 | + | 2457.76i | 0.0497480 | + | 0.139032i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −26326.7 | + | 21606.7i | −1.35017 | + | 1.10810i | ||||
\(53\) | − | 19631.3i | − | 0.959974i | −0.877276 | − | 0.479987i | \(-0.840641\pi\) | ||
0.877276 | − | 0.479987i | \(-0.159359\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12999.9i | 0.579474i | ||||||||
\(56\) | 3440.50 | + | 6190.44i | 0.146606 | + | 0.263786i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 31890.4 | − | 11410.9i | 1.24477 | − | 0.445401i | ||||
\(59\) | 909.551 | + | 1575.39i | 0.0340171 | + | 0.0589193i | 0.882533 | − | 0.470251i | \(-0.155837\pi\) |
−0.848516 | + | 0.529170i | \(0.822503\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 24421.5 | − | 42299.3i | 0.840327 | − | 1.45549i | −0.0492921 | − | 0.998784i | \(-0.515697\pi\) |
0.889619 | − | 0.456704i | \(-0.150970\pi\) | |||||||
\(62\) | −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 | \(-0.864556\pi\) |
−0.0979310 | + | 0.995193i | \(0.531222\pi\) | |||||||
\(68\) | −9954.28 | + | 1643.67i | −0.261058 | + | 0.0431064i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −8574.81 | + | 10106.8i | −0.209160 | + | 0.246530i | ||||
\(71\) | −29409.1 | −0.692365 | −0.346183 | − | 0.938167i | \(-0.612522\pi\) | ||||
−0.346183 | + | 0.938167i | \(0.612522\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 38022.9 | 0.835099 | 0.417550 | − | 0.908654i | \(-0.362889\pi\) | ||||
0.417550 | + | 0.908654i | \(0.362889\pi\) | |||||||
\(74\) | −19191.1 | + | 22619.8i | −0.407399 | + | 0.480186i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −59663.3 | + | 9851.70i | −1.18488 | + | 0.195649i | ||||
\(77\) | −7355.06 | + | 4246.45i | −0.141371 | + | 0.0816205i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12858.2 | + | 7423.70i | 0.231800 | + | 0.133830i | 0.611402 | − | 0.791320i | \(-0.290606\pi\) |
−0.379602 | + | 0.925150i | \(0.623939\pi\) | |||||||
\(80\) | −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 | −0.232959 | + | 0.972487i | \(0.574841\pi\) |
−0.725719 | + | 0.687991i | \(0.758493\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9440.69 | − | 16351.7i | −0.141728 | − | 0.245480i | ||||
\(86\) | 54000.6 | − | 19322.4i | 0.787323 | − | 0.281718i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −34346.5 | + | 19089.0i | −0.472798 | + | 0.262770i | ||||
\(89\) | 35496.5i | 0.475019i | 0.971385 | + | 0.237509i | \(0.0763311\pi\) | ||||
−0.971385 | + | 0.237509i | \(0.923669\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 41640.5i | − | 0.527124i | ||||||
\(92\) | 59375.5 | − | 48730.2i | 0.731371 | − | 0.600245i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 27718.3 | + | 77465.1i | 0.323555 | + | 0.904245i | ||||
\(95\) | −56584.9 | − | 98008.0i | −0.643268 | − | 1.11417i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1491.62 | − | 2583.55i | 0.0160964 | − | 0.0278797i | −0.857865 | − | 0.513875i | \(-0.828209\pi\) |
0.873961 | + | 0.485995i | \(0.161543\pi\) | |||||||
\(98\) | 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 | 0.261187 | − | 0.965288i | \(-0.415886\pi\) |
−0.705371 | + | 0.708838i | \(0.749220\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10418.1 | + | 6014.90i | −0.0967600 | + | 0.0558644i | −0.547599 | − | 0.836741i | \(-0.684458\pi\) |
0.450839 | + | 0.892605i | \(0.351125\pi\) | |||||||
\(104\) | 3146.35 | − | 192635.i | 0.0285248 | − | 1.74644i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 84680.5 | + | 71844.5i | 0.732013 | + | 0.621054i | ||||
\(107\) | 89559.8 | 0.756229 | 0.378115 | − | 0.925759i | \(-0.376572\pi\) | ||||
0.378115 | + | 0.925759i | \(0.376572\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −29876.1 | −0.240856 | −0.120428 | − | 0.992722i | \(-0.538427\pi\) | ||||
−0.120428 | + | 0.992722i | \(0.538427\pi\) | |||||||
\(110\) | −56075.7 | − | 47575.7i | −0.441869 | − | 0.374890i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −39293.9 | − | 7814.37i | −0.295992 | − | 0.0588639i | ||||
\(113\) | 214387. | − | 123776.i | 1.57943 | − | 0.911886i | 0.584496 | − | 0.811397i | \(-0.301292\pi\) |
0.994938 | − | 0.100490i | \(-0.0320409\pi\) | |||||||
\(114\) | 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 | ||||
\(122\) | 93084.6 | + | 260146.i | 0.566211 | + | 1.58240i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −162909. | − | 198497.i | −0.951462 | − | 1.15931i | ||||
\(125\) | 159512.i | 0.913100i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 265961.i | − | 1.46322i | −0.681724 | − | 0.731610i | \(-0.738769\pi\) | ||
0.681724 | − | 0.731610i | \(-0.261231\pi\) | |||||||
\(128\) | −181189. | − | 39119.4i | −0.977477 | − | 0.211041i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 339481. | − | 121472.i | 1.76180 | − | 0.630403i | ||||
\(131\) | 37162.9 | + | 64368.0i | 0.189204 | + | 0.327712i | 0.944985 | − | 0.327113i | \(-0.106076\pi\) |
−0.755781 | + | 0.654825i | \(0.772742\pi\) | |||||||
\(132\) | 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 | 0.453543 | − | 0.891234i | \(-0.350160\pi\) |
−0.545060 | + | 0.838397i | \(0.683493\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −287391. | + | 165925.i | −1.26164 | + | 0.728410i | −0.973392 | − | 0.229145i | \(-0.926407\pi\) |
−0.288251 | + | 0.957555i | \(0.593074\pi\) | |||||||
\(140\) | −12215.0 | − | 73975.6i | −0.0526712 | − | 0.318984i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 107628. | − | 126857.i | 0.447924 | − | 0.527952i | ||||
\(143\) | 231035. | 0.944794 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −358574. | −1.41631 | ||||||||
\(146\) | −139152. | + | 164013.i | −0.540266 | + | 0.636791i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −27338.1 | − | 165563.i | −0.102592 | − | 0.621312i | ||||
\(149\) | −287800. | + | 166162.i | −1.06200 | + | 0.613147i | −0.925985 | − | 0.377559i | \(-0.876763\pi\) |
−0.136017 | + | 0.990707i | \(0.543430\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 300515. | + | 173503.i | 1.07257 | + | 0.619247i | 0.928882 | − | 0.370377i | \(-0.120771\pi\) |
0.143685 | + | 0.989623i | \(0.454105\pi\) | |||||||
\(152\) | 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 | 0.959266 | − | 0.282504i | \(-0.0911651\pi\) |
−0.724289 | + | 0.689497i | \(0.757832\pi\) | |||||||
\(158\) | −79079.6 | + | 28296.0i | −0.252012 | + | 0.0901743i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −50918.7 | − | 343145.i | −0.157245 | − | 1.05969i | ||||
\(161\) | 93913.2i | 0.285537i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 240037.i | − | 0.707635i | −0.935314 | − | 0.353818i | \(-0.884883\pi\) | ||
0.935314 | − | 0.353818i | \(-0.115117\pi\) | |||||||
\(164\) | −177920. | − | 216788.i | −0.516555 | − | 0.629397i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −229336. | − | 640932.i | −0.645956 | − | 1.80527i | ||||
\(167\) | 144730. | + | 250679.i | 0.401575 | + | 0.695548i | 0.993916 | − | 0.110139i | \(-0.0351296\pi\) |
−0.592341 | + | 0.805687i | \(0.701796\pi\) | |||||||
\(168\) | 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 | 0.970470 | − | 0.241221i | \(-0.0775479\pi\) |
0.276332 | + | 0.961062i | \(0.410881\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15635.2 | − | 9026.99i | 0.0385930 | − | 0.0222817i | ||||
\(176\) | 43356.5 | − | 218015.i | 0.105505 | − | 0.530523i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −153116. | − | 129906.i | −0.362218 | − | 0.307313i | ||||
\(179\) | −440866. | −1.02843 | −0.514214 | − | 0.857662i | \(-0.671916\pi\) | ||||
−0.514214 | + | 0.857662i | \(0.671916\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 103852. | 0.235623 | 0.117812 | − | 0.993036i | \(-0.462412\pi\) | ||||
0.117812 | + | 0.993036i | \(0.462412\pi\) | |||||||
\(182\) | 179618. | + | 152392.i | 0.401950 | + | 0.341022i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7096.05 | + | 434456.i | −0.0154516 | + | 0.946023i | ||||
\(185\) | 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 | \(-0.973929\pi\) |
0.569176 | + | 0.822216i | \(0.307262\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20745.9 | + | 35932.9i | 0.0400903 | + | 0.0694384i | 0.885374 | − | 0.464879i | \(-0.153902\pi\) |
−0.845284 | + | 0.534317i | \(0.820569\pi\) | |||||||
\(194\) | 5685.42 | + | 15889.2i | 0.0108457 | + | 0.0303107i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −377873. | + | 310125.i | −0.702596 | + | 0.576630i | ||||
\(197\) | 353610.i | 0.649170i | 0.945856 | + | 0.324585i | \(0.105225\pi\) | ||||
−0.945856 | + | 0.324585i | \(0.894775\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 167614.i | 0.300038i | 0.988683 | + | 0.150019i | \(0.0479336\pi\) | ||||
−0.988683 | + | 0.150019i | \(0.952066\pi\) | |||||||
\(200\) | 73012.8 | − | 40578.8i | 0.129070 | − | 0.0717338i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 280059. | − | 100210.i | 0.482916 | − | 0.172796i | ||||
\(203\) | −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 | \(-0.683980\pi\) |
0.452181 | + | 0.891926i | \(0.350646\pi\) | |||||||
\(212\) | −619809. | + | 102344.i | −0.947149 | + | 0.156395i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −327761. | + | 386320.i | −0.489241 | + | 0.576651i | ||||
\(215\) | −607180. | −0.895821 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 313960. | 0.452611 | ||||||||
\(218\) | 109337. | − | 128872.i | 0.155822 | − | 0.183661i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 410440. | − | 67772.5i | 0.571732 | − | 0.0944054i | ||||
\(221\) | −290603. | + | 167780.i | −0.400239 | + | 0.231078i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 439612. | + | 253810.i | 0.591980 | + | 0.341780i | 0.765880 | − | 0.642983i | \(-0.222304\pi\) |
−0.173900 | + | 0.984763i | \(0.555637\pi\) | |||||||
\(224\) | 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 | \(-0.855816\pi\) |
0.828579 | + | 0.559872i | \(0.189150\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 180234. | + | 312174.i | 0.227116 | + | 0.393376i | 0.956952 | − | 0.290246i | \(-0.0937370\pi\) |
−0.729836 | + | 0.683622i | \(0.760404\pi\) | |||||||
\(230\) | −765642. | + | 273960.i | −0.954346 | + | 0.341482i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −526526. | − | 947371.i | −0.642244 | − | 1.15558i | ||||
\(233\) | − | 938716.i | − | 1.13278i | −0.824138 | − | 0.566389i | \(-0.808340\pi\) | ||
0.824138 | − | 0.566389i | \(-0.191660\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 871012.i | − | 1.02886i | ||||||
\(236\) | 44997.1 | − | 36929.7i | 0.0525902 | − | 0.0431615i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 23508.5 | + | 65699.6i | 0.0269018 | + | 0.0751831i | ||||
\(239\) | −163017. | − | 282354.i | −0.184603 | − | 0.319742i | 0.758840 | − | 0.651278i | \(-0.225767\pi\) |
−0.943443 | + | 0.331536i | \(0.892433\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 37903.3 | − | 65650.4i | 0.0420373 | − | 0.0728107i | −0.844241 | − | 0.535963i | \(-0.819949\pi\) |
0.886279 | + | 0.463153i | \(0.153282\pi\) | |||||||
\(242\) | −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 | ||||
\(248\) | 1.45242e6 | + | 23722.7i | 1.49956 | + | 0.0244926i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −688062. | − | 583765.i | −0.696269 | − | 0.590728i | ||||
\(251\) | 971568. | 0.973394 | 0.486697 | − | 0.873571i | \(-0.338202\pi\) | ||||
0.486697 | + | 0.873571i | \(0.338202\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −521060. | −0.511783 | ||||||||
\(254\) | 1.14724e6 | + | 973337.i | 1.11575 | + | 0.946627i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 831839. | − | 638401.i | 0.793303 | − | 0.608826i | ||||
\(257\) | −1.19547e6 | + | 690206.i | −1.12903 | + | 0.651848i | −0.943692 | − | 0.330826i | \(-0.892673\pi\) |
−0.185342 | + | 0.982674i | \(0.559339\pi\) | |||||||
\(258\) | 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 | \(-0.902163\pi\) |
0.738582 | + | 0.674164i | \(0.235496\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −587830. | − | 1.01815e6i | −0.514206 | − | 0.890631i | ||||
\(266\) | 140903. | + | 393786.i | 0.122100 | + | 0.341237i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 868887. | + | 1.05870e6i | 0.738969 | + | 0.900399i | ||||
\(269\) | − | 1.12150e6i | − | 0.944969i | −0.881339 | − | 0.472484i | \(-0.843357\pi\) | ||
0.881339 | − | 0.472484i | \(-0.156643\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 873330.i | 0.722362i | 0.932496 | + | 0.361181i | \(0.117626\pi\) | ||||
−0.932496 | + | 0.361181i | \(0.882374\pi\) | |||||||
\(272\) | 103789. | + | 305712.i | 0.0850610 | + | 0.250548i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 123647. | − | 44243.0i | 0.0994963 | − | 0.0356015i | ||||
\(275\) | 50084.5 | + | 86748.9i | 0.0399367 | + | 0.0691723i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 900195. | − | 1.55918e6i | 0.704915 | − | 1.22095i | −0.261807 | − | 0.965120i | \(-0.584318\pi\) |
0.966722 | − | 0.255829i | \(-0.0823483\pi\) | |||||||
\(278\) | 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 | 0.586654 | − | 0.809838i | \(-0.300445\pi\) |
−0.408014 | + | 0.912976i | \(0.633778\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 644438. | − | 372067.i | 0.478316 | − | 0.276156i | −0.241398 | − | 0.970426i | \(-0.577606\pi\) |
0.719715 | + | 0.694270i | \(0.244273\pi\) | |||||||
\(284\) | 153318. | + | 928517.i | 0.112797 | + | 0.683115i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −845516. | + | 996578.i | −0.611233 | + | 0.720437i | ||||
\(287\) | 342889. | 0.245725 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.32045e6 | 0.929990 | ||||||||
\(290\) | 1.31227e6 | − | 1.54672e6i | 0.916280 | − | 1.07998i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −198225. | − | 1.20048e6i | −0.136051 | − | 0.823942i | ||||
\(293\) | 330601. | − | 190873.i | 0.224976 | − | 0.129890i | −0.383276 | − | 0.923634i | \(-0.625204\pi\) |
0.608252 | + | 0.793744i | \(0.291871\pi\) | |||||||
\(294\) | 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 | ||||
\(302\) | −1.84820e6 | + | 661319.i | −1.16609 | + | 0.417248i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 622085. | + | 1.83236e6i | 0.386070 | + | 1.13717i | ||||
\(305\) | − | 2.92506e6i | − | 1.80047i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 3.21986e6i | − | 1.94980i | −0.222640 | − | 0.974901i | \(-0.571467\pi\) | ||
0.222640 | − | 0.974901i | \(-0.428533\pi\) | |||||||
\(308\) | 172415. | + | 210080.i | 0.103562 | + | 0.126185i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 915871. | + | 2.55960e6i | 0.541290 | + | 1.51276i | ||||
\(311\) | 775835. | + | 1.34378e6i | 0.454850 | + | 0.787823i | 0.998680 | − | 0.0513724i | \(-0.0163596\pi\) |
−0.543830 | + | 0.839196i | \(0.683026\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 263995. | − | 457253.i | 0.152312 | − | 0.263813i | −0.779765 | − | 0.626073i | \(-0.784661\pi\) |
0.932077 | + | 0.362260i | \(0.117995\pi\) | |||||||
\(314\) | −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 | 0.270822 | − | 0.962630i | \(-0.412705\pi\) |
−0.698251 | + | 0.715853i | \(0.746038\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.12560e6 | − | 649867.i | 0.619310 | − | 0.357559i | ||||
\(320\) | 1.66652e6 | + | 1.03617e6i | 0.909777 | + | 0.565658i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −405099. | − | 343693.i | −0.217731 | − | 0.184727i | ||||
\(323\) | −595799. | −0.317756 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −491127. | −0.257920 | ||||||||
\(326\) | 1.03541e6 | + | 878462.i | 0.539596 | + | 0.457803i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.58626e6 | + | 25908.6i | 0.814121 | + | 0.0132972i | ||||
\(329\) | 492799. | − | 284518.i | 0.251004 | − | 0.144917i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −128289. | − | 74067.9i | −0.0643607 | − | 0.0371587i | 0.467474 | − | 0.884007i | \(-0.345164\pi\) |
−0.531835 | + | 0.846848i | \(0.678497\pi\) | |||||||
\(332\) | 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 | 0.908338 | − | 0.418237i | \(-0.137352\pi\) |
−0.816373 | + | 0.577525i | \(0.804019\pi\) | |||||||
\(338\) | −1.45120e6 | − | 4.05569e6i | −0.690930 | − | 1.93096i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −467048. | + | 383312.i | −0.219111 | + | 0.179827i | ||||
\(341\) | 1.74195e6i | 0.811239i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.25524e6i | − | 0.576091i | ||||||
\(344\) | −891577. | − | 1.60420e6i | −0.406221 | − | 0.730908i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.01853e6 | + | 1.08008e6i | −1.35552 | + | 0.485028i | ||||
\(347\) | −602848. | − | 1.04416e6i | −0.268772 | − | 0.465527i | 0.699773 | − | 0.714365i | \(-0.253284\pi\) |
−0.968545 | + | 0.248839i | \(0.919951\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −145755. | + | 252456.i | −0.0640562 | + | 0.110949i | −0.896275 | − | 0.443499i | \(-0.853737\pi\) |
0.832219 | + | 0.554447i | \(0.187070\pi\) | |||||||
\(350\) | −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 | 0.534359 | − | 0.845257i | \(-0.320553\pi\) |
−0.464835 | + | 0.885397i | \(0.653886\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.52526e6 | + | 880610.i | −0.642352 | + | 0.370862i | ||||
\(356\) | 1.12071e6 | − | 185054.i | 0.468673 | − | 0.0773880i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.61343e6 | − | 1.90169e6i | 0.665340 | − | 0.784211i | ||||
\(359\) | −1.70884e6 | −0.699786 | −0.349893 | − | 0.936790i | \(-0.613782\pi\) | ||||
−0.349893 | + | 0.936790i | \(0.613782\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.09496e6 | −0.442211 | ||||||||
\(362\) | −380066. | + | 447970.i | −0.152436 | + | 0.179671i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.31470e6 | + | 217085.i | −0.520082 | + | 0.0858768i | ||||
\(365\) | 1.97201e6 | − | 1.13854e6i | 0.774776 | − | 0.447317i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.26612e6 | + | 1.88569e6i | 1.26581 | + | 0.730813i | 0.974191 | − | 0.225723i | \(-0.0724745\pi\) |
0.291614 | + | 0.956536i | \(0.405808\pi\) | |||||||
\(368\) | −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 | 0.996161 | − | 0.0875420i | \(-0.0279012\pi\) |
−0.573894 | + | 0.818930i | \(0.694568\pi\) | |||||||
\(374\) | −364522. | + | 130432.i | −0.134755 | + | 0.0482176i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.30126e6 | − | 1.27899e6i | 0.839453 | − | 0.466548i | ||||
\(377\) | 6.37257e6i | 2.30920i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.07165e6i | 1.45604i | 0.685557 | + | 0.728019i | \(0.259559\pi\) | ||||
−0.685557 | + | 0.728019i | \(0.740441\pi\) | |||||||
\(380\) | −2.79936e6 | + | 2.29747e6i | −0.994489 | + | 0.816190i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −821478. | − | 2.29580e6i | −0.288030 | − | 0.804964i | ||||
\(383\) | 1.22056e6 | + | 2.11407e6i | 0.425170 | + | 0.736415i | 0.996436 | − | 0.0843491i | \(-0.0268811\pi\) |
−0.571267 | + | 0.820765i | \(0.693548\pi\) | |||||||
\(384\) | 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 | 0.337140 | − | 0.941455i | \(-0.390540\pi\) |
−0.646754 | + | 0.762699i | \(0.723874\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 655407. | − | 378399.i | 0.216805 | − | 0.125172i | ||||
\(392\) | 45160.2 | − | 2.76493e6i | 0.0148436 | − | 0.908803i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.52531e6 | − | 1.29410e6i | −0.495014 | − | 0.419980i | ||||
\(395\) | 889166. | 0.286741 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.64187e6 | −0.841271 | −0.420635 | − | 0.907230i | \(-0.638193\pi\) | ||||
−0.420635 | + | 0.907230i | \(0.638193\pi\) | |||||||
\(398\) | −723009. | − | 613415.i | −0.228789 | − | 0.194109i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −92166.1 | + | 463450.i | −0.0288019 | + | 0.144828i | ||||
\(401\) | −2.41745e6 | + | 1.39571e6i | −0.750751 | + | 0.433446i | −0.825965 | − | 0.563721i | \(-0.809369\pi\) |
0.0752142 | + | 0.997167i | \(0.476036\pi\) | |||||||
\(402\) | 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 | 0.782079 | − | 0.623179i | \(-0.214159\pi\) |
−0.930728 | + | 0.365711i | \(0.880826\pi\) | |||||||
\(410\) | 1.00026e6 | + | 2.79546e6i | 0.293870 | + | 0.821284i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 244218. | + | 297568.i | 0.0708818 | + | 0.0863661i | ||||
\(413\) | 71171.2i | 0.0205319i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.20660e6i | 2.05404i | ||||||||
\(416\) | −6.09838e6 | + | 904928.i | −1.72775 | + | 0.256378i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.18485e6 | + | 781775.i | −0.611618 | + | 0.218847i | ||||
\(419\) | −2.85052e6 | − | 4.93724e6i | −0.793210 | − | 1.37388i | −0.923969 | − | 0.382466i | \(-0.875075\pi\) |
0.130759 | − | 0.991414i | \(-0.458259\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.95835e6 | + | 5.12400e6i | −0.813474 | + | 1.40898i | 0.0969446 | + | 0.995290i | \(0.469093\pi\) |
−0.910419 | + | 0.413688i | \(0.864240\pi\) | |||||||
\(422\) | 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 | ||||
\(428\) | −466902. | − | 2.82762e6i | −0.123202 | − | 0.746126i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.22209e6 | − | 2.61910e6i | 0.579550 | − | 0.683094i | ||||
\(431\) | −516224. | −0.133858 | −0.0669291 | − | 0.997758i | \(-0.521320\pi\) | ||||
−0.0669291 | + | 0.997758i | \(0.521320\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.50137e6 | 1.66642 | 0.833212 | − | 0.552954i | \(-0.186499\pi\) | ||||
0.833212 | + | 0.552954i | \(0.186499\pi\) | |||||||
\(434\) | −1.14900e6 | + | 1.35428e6i | −0.292816 | + | 0.345131i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 155753. | + | 943264.i | 0.0392393 | + | 0.237639i | ||||
\(437\) | 3.92833e6 | − | 2.26802e6i | 0.984021 | − | 0.568125i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −762498. | − | 440228.i | −0.188833 | − | 0.109023i | 0.402603 | − | 0.915375i | \(-0.368105\pi\) |
−0.591436 | + | 0.806352i | \(0.701439\pi\) | |||||||
\(440\) | −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 | \(-0.804583\pi\) |
0.907595 | + | 0.419848i | \(0.137917\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.06289e6 | + | 1.84098e6i | 0.254442 | + | 0.440706i | ||||
\(446\) | −2.70366e6 | + | 967418.i | −0.643599 | + | 0.230291i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −41868.0 | + | 1.28134e6i | −0.00985570 | + | 0.301627i | ||||
\(449\) | 3.80614e6i | 0.890983i | 0.895286 | + | 0.445492i | \(0.146971\pi\) | ||||
−0.895286 | + | 0.445492i | \(0.853029\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.90246e6i | 0.440427i | ||||||||
\(452\) | −5.02558e6 | − | 6.12343e6i | −1.15702 | − | 1.40977i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −208840. | − | 583651.i | −0.0475527 | − | 0.132896i | ||||
\(455\) | −1.24686e6 | − | 2.15963e6i | −0.282352 | − | 0.489047i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.54711e6 | + | 2.67967e6i | −0.346521 | + | 0.600192i | −0.985629 | − | 0.168925i | \(-0.945970\pi\) |
0.639108 | + | 0.769117i | \(0.279304\pi\) | |||||||
\(458\) | −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 | 0.988441 | − | 0.151606i | \(-0.0484445\pi\) |
0.362926 | + | 0.931818i | \(0.381778\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.12079e6 | − | 2.37914e6i | 0.893363 | − | 0.515784i | 0.0183222 | − | 0.999832i | \(-0.494168\pi\) |
0.875041 | + | 0.484049i | \(0.160834\pi\) | |||||||
\(464\) | 6.01345e6 | + | 1.19589e6i | 1.29667 | + | 0.257868i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.04919e6 | + | 3.43541e6i | 0.863781 | + | 0.732848i | ||||
\(467\) | 7.37952e6 | 1.56580 | 0.782900 | − | 0.622148i | \(-0.213740\pi\) | ||||
0.782900 | + | 0.622148i | \(0.213740\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.67452e6 | −0.351528 | ||||||||
\(470\) | 3.75715e6 | + | 3.18764e6i | 0.784538 | + | 0.665617i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5377.68 | + | 329249.i | −0.00111107 | + | 0.0680251i | ||||
\(473\) | 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 | \(-0.798158\pi\) |
0.915884 | + | 0.401442i | \(0.131491\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.79058e6 | − | 4.83342e6i | −0.549960 | − | 0.952559i | ||||
\(482\) | 144472. | + | 403758.i | 0.0283247 | + | 0.0791596i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.81816e6 | − | 2.31290e6i | 0.546829 | − | 0.448790i | ||||
\(485\) | − | 178657.i | − | 0.0344878i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 763869.i | 0.145948i | 0.997334 | + | 0.0729738i | \(0.0232489\pi\) | ||||
−0.997334 | + | 0.0729738i | \(0.976751\pi\) | |||||||
\(488\) | 7.72817e6 | − | 4.29513e6i | 1.46902 | − | 0.816445i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.87264e6 | − | 1.74351e6i | 0.916799 | − | 0.328046i | ||||
\(491\) | 3.47276e6 | + | 6.01500e6i | 0.650087 | + | 1.12598i | 0.983101 | + | 0.183061i | \(0.0586007\pi\) |
−0.333015 | + | 0.942922i | \(0.608066\pi\) | |||||||
\(492\) | 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 | \(-0.479370\pi\) |
0.896590 | + | 0.442862i | \(0.146037\pi\) | |||||||
\(500\) | 5.03619e6 | − | 831584.i | 0.900901 | − | 0.148758i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.55564e6 | + | 4.19090e6i | −0.629736 | + | 0.742246i | ||||
\(503\) | −3.43627e6 | −0.605574 | −0.302787 | − | 0.953058i | \(-0.597917\pi\) | ||||
−0.302787 | + | 0.953058i | \(0.597917\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.14897e6 | −0.549465 | ||||||||
\(506\) | 1.90692e6 | − | 2.24761e6i | 0.331097 | − | 0.390252i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.39706e6 | + | 1.38654e6i | −1.44367 | + | 0.238381i | ||||
\(509\) | −2.45696e6 | + | 1.41853e6i | −0.420343 | + | 0.242685i | −0.695224 | − | 0.718793i | \(-0.744695\pi\) |
0.274881 | + | 0.961478i | \(0.411362\pi\) | |||||||
\(510\) | 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 | ||||
\(518\) | −1.09274e6 | + | 391001.i | −0.178934 | + | 0.0640256i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.60499e6 | − | 1.00850e7i | −0.909006 | − | 1.63556i | ||||
\(521\) | − | 1.84176e6i | − | 0.297261i | −0.988893 | − | 0.148631i | \(-0.952513\pi\) | ||
0.988893 | − | 0.148631i | \(-0.0474866\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 1.03954e7i | − | 1.66183i | −0.556398 | − | 0.830916i | \(-0.687817\pi\) | ||
0.556398 | − | 0.830916i | \(-0.312183\pi\) | |||||||
\(524\) | 1.83852e6 | − | 1.50889e6i | 0.292509 | − | 0.240066i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −917335. | − | 2.56370e6i | −0.144565 | − | 0.404019i | ||||
\(527\) | −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 | ||||
\(536\) | −7.74660e6 | − | 126527.i | −1.16466 | − | 0.0190226i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.83762e6 | + | 4.10433e6i | 0.720570 | + | 0.611346i | ||||
\(539\) | 3.31609e6 | 0.491648 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 330411. | 0.0485357 | 0.0242679 | − | 0.999705i | \(-0.492275\pi\) | ||||
0.0242679 | + | 0.999705i | \(0.492275\pi\) | |||||||
\(542\) | −3.76715e6 | − | 3.19612e6i | −0.550826 | − | 0.467331i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.69854e6 | − | 671113.i | −0.246081 | − | 0.0972296i | ||||
\(545\) | −1.54949e6 | + | 894596.i | −0.223458 | + | 0.129014i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.06834e7 | − | 6.16808e6i | −1.52666 | − | 0.881417i | −0.999499 | − | 0.0316507i | \(-0.989924\pi\) |
−0.527160 | − | 0.849766i | \(-0.676743\pi\) | |||||||
\(548\) | −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 | ||||
\(554\) | 3.43117e6 | + | 9.58916e6i | 0.474971 | + | 1.32741i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.73693e6 | + | 8.20863e6i | 0.924220 | + | 1.12612i | ||||
\(557\) | − | 5.94173e6i | − | 0.811474i | −0.913990 | − | 0.405737i | \(-0.867015\pi\) | ||
0.913990 | − | 0.405737i | \(-0.132985\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.07908e7i | 1.46058i | ||||||||
\(560\) | −2.27191e6 | + | 771315.i | −0.306141 | + | 0.103935i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.45421e6 | + | 520343.i | −0.194217 | + | 0.0694942i | ||||
\(563\) | −66573.9 | − | 115309.i | −0.00885182 | − | 0.0153318i | 0.861566 | − | 0.507646i | \(-0.169484\pi\) |
−0.870417 | + | 0.492315i | \(0.836151\pi\) | |||||||
\(564\) | 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 | 0.240501 | − | 0.970649i | \(-0.422688\pi\) |
−0.720356 | + | 0.693605i | \(0.756021\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −525371. | + | 303323.i | −0.0674335 | + | 0.0389328i | −0.533338 | − | 0.845902i | \(-0.679062\pi\) |
0.465904 | + | 0.884835i | \(0.345729\pi\) | |||||||
\(572\) | −1.20445e6 | − | 7.29434e6i | −0.153922 | − | 0.932171i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.25487e6 | + | 1.47907e6i | −0.158971 | + | 0.187374i | ||||
\(575\) | 1.10765e6 | 0.139712 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −496600. | −0.0620965 | −0.0310483 | − | 0.999518i | \(-0.509885\pi\) | ||||
−0.0310483 | + | 0.999518i | \(0.509885\pi\) | |||||||
\(578\) | −4.83245e6 | + | 5.69583e6i | −0.601656 | + | 0.709149i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.86935e6 | + | 1.13211e7i | 0.230739 | + | 1.39739i | ||||
\(581\) | −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 | 0.0358744 | − | 0.999356i | \(-0.488578\pi\) |
0.847531 | − | 0.530746i | \(-0.178088\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.58219e6 | − | 1.31327e7i | −0.900547 | − | 1.55979i | ||||
\(590\) | −580234. | + | 207618.i | −0.0686236 | + | 0.0245547i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.08472e6 | + | 1.72626e6i | −0.596297 | + | 0.202443i | ||||
\(593\) | − | 1.01532e7i | − | 1.18568i | −0.805322 | − | 0.592838i | \(-0.798008\pi\) | ||
0.805322 | − | 0.592838i | \(-0.201992\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 738722.i | − | 0.0855438i | ||||||
\(596\) | 6.74652e6 | + | 8.22032e6i | 0.777973 | + | 0.947923i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.86881e6 | + | 1.36070e7i | 0.556763 | + | 1.55600i | ||||
\(599\) | 5.29325e6 | + | 9.16817e6i | 0.602775 | + | 1.04404i | 0.992399 | + | 0.123062i | \(0.0392715\pi\) |
−0.389624 | + | 0.920974i | \(0.627395\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.67071e6 | − | 1.15540e7i | 0.753331 | − | 1.30481i | −0.192869 | − | 0.981224i | \(-0.561779\pi\) |
0.946200 | − | 0.323583i | \(-0.104887\pi\) | |||||||
\(602\) | 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 | \(-0.804064\pi\) |
0.0918216 | + | 0.995775i | \(0.470731\pi\) | |||||||
\(608\) | −1.01806e7 | − | 4.02247e6i | −1.11690 | − | 0.441300i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.26174e7 | + | 1.07048e7i | 1.37292 | + | 1.16481i | ||||
\(611\) | −1.54796e7 | −1.67748 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.15773e7 | 1.24438 | 0.622192 | − | 0.782865i | \(-0.286242\pi\) | ||||
0.622192 | + | 0.782865i | \(0.286242\pi\) | |||||||
\(614\) | 1.38890e7 | + | 1.17837e7i | 1.48679 | + | 1.26142i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.53717e6 | − | 25106.9i | −0.163219 | − | 0.00266589i | ||||
\(617\) | 4.79775e6 | − | 2.76998e6i | 0.507370 | − | 0.292930i | −0.224382 | − | 0.974501i | \(-0.572036\pi\) |
0.731752 | + | 0.681571i | \(0.238703\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −399838. | − | 230847.i | −0.0419428 | − | 0.0242157i | 0.478882 | − | 0.877879i | \(-0.341042\pi\) |
−0.520825 | + | 0.853664i | \(0.674376\pi\) | |||||||
\(620\) | −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 | ||||
\(626\) | 1.00624e6 | + | 2.81216e6i | 0.102628 | + | 0.286816i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.59032e6 | − | 2.94662e6i | 0.363273 | − | 0.298143i | ||||
\(629\) | − | 1.65332e6i | − | 0.166621i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.33405e7i | 1.33383i | 0.745136 | + | 0.666913i | \(0.232385\pi\) | ||||
−0.745136 | + | 0.666913i | \(0.767615\pi\) | |||||||
\(632\) | 1.30564e6 | + | 2.34922e6i | 0.130026 | + | 0.233955i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.70322e6 | − | 1.68289e6i | 0.464700 | − | 0.166278i | ||||
\(635\) | −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 | 0.607299 | − | 0.794473i | \(-0.292253\pi\) |
−0.384384 | + | 0.923173i | \(0.625586\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.46328e7 | + | 8.44826e6i | −1.39573 | + | 0.805824i | −0.993942 | − | 0.109910i | \(-0.964944\pi\) |
−0.401786 | + | 0.915734i | \(0.631610\pi\) | |||||||
\(644\) | 2.96507e6 | − | 489598.i | 0.281722 | − | 0.0465184i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.18044e6 | − | 2.57000e6i | 0.205571 | − | 0.242299i | ||||
\(647\) | −7.65712e6 | −0.719126 | −0.359563 | − | 0.933121i | \(-0.617074\pi\) | ||||
−0.359563 | + | 0.933121i | \(0.617074\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −394880. | −0.0368005 | ||||||||
\(650\) | 1.79737e6 | − | 2.11850e6i | 0.166861 | − | 0.196673i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.57857e6 | + | 1.25139e6i | −0.698181 | + | 0.115285i | ||||
\(653\) | −957462. | + | 552791.i | −0.0878696 | + | 0.0507315i | −0.543291 | − | 0.839544i | \(-0.682822\pi\) |
0.455421 | + | 0.890276i | \(0.349489\pi\) | |||||||
\(654\) | 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 | −0.284912 | − | 0.958554i | \(-0.591965\pi\) |
0.972588 | − | 0.232535i | \(-0.0747021\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.77496e6 | + | 6.53842e6i | 0.336054 | + | 0.582062i | 0.983687 | − | 0.179890i | \(-0.0575743\pi\) |
−0.647633 | + | 0.761952i | \(0.724241\pi\) | |||||||
\(662\) | 788995. | − | 282316.i | 0.0699728 | − | 0.0250375i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.90402e7 | + | 1.05821e7i | −1.67591 | + | 0.931432i | ||||
\(665\) | − | 4.42770e6i | − | 0.388261i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1.43723e7i | − | 1.25087i | ||||||
\(668\) | 7.16005e6 | − | 5.87634e6i | 0.620833 | − | 0.509526i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.88485e6 | − | 1.36518e7i | −0.420402 | − | 1.17491i | ||||
\(671\) | 5.30128e6 | + | 9.18209e6i | 0.454543 | + | 0.787291i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.45359e6 | − | 2.51769e6i | 0.123710 | − | 0.214271i | −0.797518 | − | 0.603295i | \(-0.793854\pi\) |
0.921228 | + | 0.389023i | \(0.127188\pi\) | |||||||
\(674\) | −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 | 0.114801 | − | 0.993389i | \(-0.463377\pi\) |
−0.802899 | + | 0.596115i | \(0.796710\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 101080. | − | 58358.6i | 0.00841377 | − | 0.00485769i | ||||
\(680\) | 55817.6 | − | 3.41744e6i | 0.00462913 | − | 0.283419i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.51396e6 | − | 6.37499e6i | −0.618597 | − | 0.524830i | ||||
\(683\) | 6.62953e6 | 0.543789 | 0.271895 | − | 0.962327i | \(-0.412350\pi\) | ||||
0.271895 | + | 0.962327i | \(0.412350\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.39028e6 | −0.113208 | ||||||||
\(686\) | 5.41453e6 | + | 4.59379e6i | 0.439289 | + | 0.372701i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.01827e7 | + | 2.02503e6i | 0.820146 | + | 0.163102i | ||||
\(689\) | −1.80946e7 | + | 1.04469e7i | −1.45211 | + | 0.838378i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.59285e6 | + | 3.80638e6i | 0.525264 | + | 0.303261i | 0.739086 | − | 0.673611i | \(-0.235258\pi\) |
−0.213822 | + | 0.976873i | \(0.568591\pi\) | |||||||
\(692\) | 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 | ||||
\(698\) | −555559. | − | 1.55263e6i | −0.0431610 | − | 0.120623i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −366515. | − | 446582.i | −0.0282714 | − | 0.0344473i | ||||
\(701\) | 3.35628e6i | 0.257966i | 0.991647 | + | 0.128983i | \(0.0411713\pi\) | ||||
−0.991647 | + | 0.128983i | \(0.958829\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 9.90954e6i | − | 0.756249i | ||||||
\(704\) | −7.10929e6 | − | 232297.i | −0.540623 | − | 0.0176649i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.00106e6 | + | 358195.i | −0.0755869 | + | 0.0270463i | ||||
\(707\) | −1.02862e6 | − | 1.78162e6i | −0.0773936 | − | 0.134050i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.57561e6 | − | 6.19313e6i | 0.267137 | − | 0.462695i | −0.700984 | − | 0.713177i | \(-0.747256\pi\) |
0.968121 | + | 0.250482i | \(0.0805890\pi\) | |||||||
\(710\) | 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 | ||||
\(716\) | 2.29837e6 | + | 1.39192e7i | 0.167547 | + | 1.01469i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.25383e6 | − | 7.37116e6i | 0.452725 | − | 0.533611i | ||||
\(719\) | −1.05572e7 | −0.761603 | −0.380801 | − | 0.924657i | \(-0.624352\pi\) | ||||
−0.380801 | + | 0.924657i | \(0.624352\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −470659. | −0.0337185 | ||||||||
\(722\) | 4.00721e6 | − | 4.72314e6i | 0.286087 | − | 0.337200i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −541412. | − | 3.27887e6i | −0.0383868 | − | 0.232475i | ||||
\(725\) | −2.39278e6 | + | 1.38147e6i | −0.169066 | + | 0.0976104i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −457178. | − | 263952.i | −0.0320811 | − | 0.0185220i | 0.483874 | − | 0.875138i | \(-0.339229\pi\) |
−0.515955 | + | 0.856616i | \(0.672563\pi\) | |||||||
\(728\) | 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 | −0.968708 | − | 0.248202i | \(-0.920160\pi\) |
0.269404 | − | 0.963027i | \(-0.413173\pi\) | |||||||
\(734\) | −2.00870e7 | + | 7.18748e6i | −1.37618 | + | 0.492421i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.37539e7 | − | 2.04091e6i | 0.935901 | − | 0.138877i | ||||
\(737\) | − | 9.29078e6i | − | 0.630062i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.56621e6i | 0.307570i | 0.988104 | + | 0.153785i | \(0.0491464\pi\) | ||||
−0.988104 | + | 0.153785i | \(0.950854\pi\) | |||||||
\(740\) | −6.37539e6 | − | 7.76811e6i | −0.427984 | − | 0.521478i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.46377e6 | + | 4.09082e6i | 0.0976028 | + | 0.272773i | ||||
\(743\) | 8.52924e6 | + | 1.47731e7i | 0.566811 | + | 0.981745i | 0.996879 | + | 0.0789485i | \(0.0251563\pi\) |
−0.430068 | + | 0.902797i | \(0.641510\pi\) | |||||||
\(744\) | 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 | \(-0.719576\pi\) |
0.349821 | + | 0.936817i | \(0.386243\pi\) | |||||||
\(752\) | −2.90495e6 | + | 1.46073e7i | −0.187324 | + | 0.941943i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.74884e7 | − | 2.33217e7i | −1.76084 | − | 1.49393i | ||||
\(755\) | 2.07811e7 | 1.32679 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.36558e6 | 0.403736 | 0.201868 | − | 0.979413i | \(-0.435299\pi\) | ||||
0.201868 | + | 0.979413i | \(0.435299\pi\) | |||||||
\(758\) | −1.75633e7 | − | 1.49010e7i | −1.11028 | − | 0.941981i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 334556. | − | 2.04832e7i | 0.0210104 | − | 1.28636i | ||||
\(761\) | 9.28199e6 | − | 5.35896e6i | 0.581005 | − | 0.335443i | −0.180528 | − | 0.983570i | \(-0.557781\pi\) |
0.761533 | + | 0.648127i | \(0.224447\pi\) | |||||||
\(762\) | 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 | 0.999126 | − | 0.0418063i | \(-0.0133112\pi\) |
−0.535768 | + | 0.844365i | \(0.679978\pi\) | |||||||
\(770\) | −969312. | − | 2.70896e6i | −0.0589165 | − | 0.164655i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.02634e6 | − | 842329.i | 0.0619794 | − | 0.0508673i | ||||
\(773\) | 2.52966e7i | 1.52270i | 0.648342 | + | 0.761349i | \(0.275463\pi\) | ||||
−0.648342 | + | 0.761349i | \(0.724537\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 3.70298e6i | − | 0.221461i | ||||||
\(776\) | 472020. | − | 262338.i | 0.0281389 | − | 0.0156389i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.68300e6 | − | 2.03348e6i | 0.336611 | − | 0.120445i | ||||
\(779\) | −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 | \(-0.453702\pi\) |
0.929350 | + | 0.369201i | \(0.120369\pi\) | |||||||
\(788\) | 1.11643e7 | − | 1.84347e6i | 0.640497 | − | 0.105760i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3.25407e6 | + | 3.83545e6i | −0.185507 | + | 0.218650i | ||||
\(791\) | 9.68533e6 | 0.550393 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.19842e7 | −2.93554 | ||||||||
\(794\) | 9.66845e6 | − | 1.13958e7i | 0.544259 | − | 0.641497i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.29198e6 | − | 873821.i | 0.296030 | − | 0.0488810i | ||||
\(797\) | 2.02403e7 | − | 1.16857e7i | 1.12868 | − | 0.651643i | 0.185077 | − | 0.982724i | \(-0.440747\pi\) |
0.943602 | + | 0.331081i | \(0.107413\pi\) | |||||||
\(798\) | 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 | ||||
\(806\) | 4.54893e7 | − | 1.62769e7i | 2.46645 | − | 0.882537i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.62392e6 | − | 8.31975e6i | −0.249162 | − | 0.448313i | ||||
\(809\) | − | 1.04327e7i | − | 0.560434i | −0.959937 | − | 0.280217i | \(-0.909594\pi\) | ||
0.959937 | − | 0.280217i | \(-0.0904064\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2.11443e7i | − | 1.12886i | −0.825480 | − | 0.564431i | \(-0.809096\pi\) | ||
0.825480 | − | 0.564431i | \(-0.190904\pi\) | |||||||
\(812\) | −5.79458e6 | + | 4.75569e6i | −0.308412 | + | 0.253118i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.16940e6 | − | 6.06286e6i | −0.114757 | − | 0.320713i | ||||
\(815\) | −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 | 0.155631 | − | 0.987815i | \(-0.450259\pi\) |
−0.777658 | + | 0.628688i | \(0.783592\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.96052e6 | + | 3.44131e6i | −0.306750 | + | 0.177102i | −0.645471 | − | 0.763785i | \(-0.723339\pi\) |
0.338721 | + | 0.940887i | \(0.390006\pi\) | |||||||
\(824\) | −2.17734e6 | − | 35562.8i | −0.111714 | − | 0.00182464i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −307000. | − | 260465.i | −0.0156563 | − | 0.0132831i | ||||
\(827\) | 2.50557e7 | 1.27392 | 0.636962 | − | 0.770895i | \(-0.280191\pi\) | ||||
0.636962 | + | 0.770895i | \(0.280191\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.56223e6 | 0.432714 | 0.216357 | − | 0.976314i | \(-0.430583\pi\) | ||||
0.216357 | + | 0.976314i | \(0.430583\pi\) | |||||||
\(830\) | −3.10860e7 | − | 2.63739e7i | −1.56628 | − | 1.32886i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.84147e7 | − | 2.96174e7i | 0.922268 | − | 1.48333i | ||||
\(833\) | −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 | 0.109828 | − | 0.993951i | \(-0.464970\pi\) |
0.805872 | − | 0.592090i | \(-0.201697\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.66955e6 | + | 1.32841e7i | 0.373921 | + | 0.647650i | ||||
\(842\) | −1.12760e7 | − | 3.15132e7i | −0.548118 | − | 1.53184i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.42745e6 | + | 1.73928e6i | 0.0689772 | + | 0.0840454i | ||||
\(845\) | 4.56019e7i | 2.19706i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.45743e6i | 0.213489i | ||||||||
\(848\) | 6.46250e6 | + | 1.90354e7i | 0.308611 | + | 0.909016i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 774890. | − | 277269.i | 0.0367869 | − | 0.0131630i | ||||
\(851\) | 6.29367e6 | + | 1.09010e7i | 0.297907 | + | 0.515989i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.88097e6 | + | 1.53823e7i | −0.417915 | + | 0.723850i | −0.995730 | − | 0.0923182i | \(-0.970572\pi\) |
0.577815 | + | 0.816168i | \(0.303906\pi\) | |||||||
\(854\) | −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 | 0.938363 | − | 0.345650i | \(-0.112342\pi\) |
0.169840 | + | 0.985472i | \(0.445675\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.17405e7 | + | 1.83254e7i | −1.46768 | + | 0.847365i | −0.999345 | − | 0.0361865i | \(-0.988479\pi\) |
−0.468334 | + | 0.883551i | \(0.655146\pi\) | |||||||
\(860\) | 3.16541e6 | + | 1.91702e7i | 0.145943 | + | 0.883853i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.88922e6 | − | 2.22675e6i | 0.0865993 | − | 0.102071i | ||||
\(863\) | 5.86388e6 | 0.268015 | 0.134007 | − | 0.990980i | \(-0.457215\pi\) | ||||
0.134007 | + | 0.990980i | \(0.457215\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.39402e7 | 1.54232 | ||||||||
\(866\) | −2.37930e7 | + | 2.80440e7i | −1.07809 | + | 1.27070i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.63677e6 | − | 9.91249e6i | −0.0737374 | − | 0.446564i | ||||
\(869\) | −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 | 0.977893 | + | 0.209106i | \(0.0670555\pi\) |
−0.307855 | + | 0.951433i | \(0.599611\pi\) | |||||||
\(878\) | 4.68945e6 | − | 1.67797e6i | 0.205298 | − | 0.0734593i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.27949e6 | − | 1.26053e7i | −0.186288 | − | 0.548714i | ||||
\(881\) | − | 940107.i | − | 0.0408073i | −0.999792 | − | 0.0204036i | \(-0.993505\pi\) | ||
0.999792 | − | 0.0204036i | \(-0.00649513\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.57094e6i | 0.0678045i | 0.999425 | + | 0.0339022i | \(0.0107935\pi\) | ||||
−0.999425 | + | 0.0339022i | \(0.989207\pi\) | |||||||
\(884\) | 6.81223e6 | + | 8.30038e6i | 0.293196 | + | 0.357246i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.42008e6 | + | 3.96874e6i | 0.0607757 | + | 0.169851i | ||||
\(887\) | −1.53981e7 | − | 2.66703e7i | −0.657140 | − | 1.13820i | −0.981353 | − | 0.192216i | \(-0.938433\pi\) |
0.324213 | − | 0.945984i | \(-0.394901\pi\) | |||||||
\(888\) | 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 | ||||
\(896\) | −5.37391e6 | − | 4.86993e6i | −0.223625 | − | 0.202653i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.64180e7 | − | 1.39293e7i | −0.679405 | − | 0.576420i | ||||
\(899\) | −4.80477e7 | −1.98277 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.18943e6 | −0.254003 | ||||||||
\(902\) | −8.20633e6 | − | 6.96241e6i | −0.335840 | − | 0.284933i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.48058e7 | + | 731821.i | 1.82353 | + | 0.0297840i | ||||
\(905\) | 5.38614e6 | − | 3.10969e6i | 0.218603 | − | 0.126211i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.63670e7 | − | 9.44950e6i | −0.660619 | − | 0.381409i | 0.131894 | − | 0.991264i | \(-0.457894\pi\) |
−0.792513 | + | 0.609855i | \(0.791228\pi\) | |||||||
\(908\) | 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 | −0.0183608 | + | 0.999831i | \(0.505845\pi\) |
−0.856699 | + | 0.515817i | \(0.827489\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.30610e7 | − | 2.26223e7i | −0.518560 | − | 0.898172i | ||||
\(914\) | −5.89692e6 | − | 1.64803e7i | −0.233486 | − | 0.652527i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.91650e6 | − | 7.31789e6i | 0.351120 | − | 0.288169i | ||||
\(917\) | 2.90795e6i | 0.114199i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 3.62995e7i | − | 1.41779i | −0.705313 | − | 0.708896i | \(-0.749194\pi\) | ||
0.705313 | − | 0.708896i | \(-0.250806\pi\) | |||||||
\(920\) | 1.26411e7 | + | 2.27450e7i | 0.492397 | + | 0.885963i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.79236e7 | + | 1.35697e7i | −1.46920 | + | 0.525706i | ||||
\(923\) | 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 | −0.288805 | − | 0.957388i | \(-0.593258\pi\) |
−0.973525 | + | 0.228581i | \(0.926591\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.50004e7 | + | 1.44340e7i | −0.945306 | + | 0.545773i | ||||
\(932\) | −2.96376e7 | + | 4.89381e6i | −1.11764 | + | 0.184547i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.70068e7 | + | 3.18319e7i | −1.01299 | + | 1.19397i | ||||
\(935\) | 4.09866e6 | 0.153325 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −102797. | −0.00382500 | −0.00191250 | − | 0.999998i | \(-0.500609\pi\) | ||||
−0.00191250 | + | 0.999998i | \(0.500609\pi\) | |||||||
\(938\) | 6.12824e6 | − | 7.22313e6i | 0.227420 | − | 0.268052i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.75000e7 | + | 4.54085e6i | −1.01511 | + | 0.167617i | ||||
\(941\) | 1.82125e7 | − | 1.05150e7i | 0.670496 | − | 0.387111i | −0.125768 | − | 0.992060i | \(-0.540140\pi\) |
0.796265 | + | 0.604948i | \(0.206806\pi\) | |||||||
\(942\) | 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 | \(-0.745778\pi\) |
0.969274 | + | 0.245985i | \(0.0791115\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.02341e7 | − | 3.50465e7i | −0.729321 | − | 1.26322i | ||||
\(950\) | 4.64449e6 | − | 1.66188e6i | 0.166966 | − | 0.0597434i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.95174e6 | − | 1.08473e6i | 0.0697959 | − | 0.0387909i | ||||
\(953\) | − | 716587.i | − | 0.0255586i | −0.999918 | − | 0.0127793i | \(-0.995932\pi\) | ||
0.999918 | − | 0.0127793i | \(-0.00406788\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.58139e7i | 0.915893i | ||||||||
\(956\) | −8.06476e6 | + | 6.61886e6i | −0.285395 | + | 0.234228i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.11083e6 | + | 5.89917e6i | 0.0743085 | + | 0.207672i | ||||
\(959\) | −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 | \(-0.620539\pi\) |
0.619820 | + | 0.784744i | \(0.287206\pi\) | |||||||
\(968\) | −336802. | + | 2.06207e7i | −0.0115528 | + | 0.707320i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 770643. | + | 653829.i | 0.0262981 | + | 0.0223118i | ||||
\(971\) | −1.84209e7 | −0.626992 | −0.313496 | − | 0.949590i | \(-0.601500\pi\) | ||||
−0.313496 | + | 0.949590i | \(0.601500\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.29835e7 | −0.439651 | ||||||||
\(974\) | −3.29498e6 | − | 2.79553e6i | −0.111290 | − | 0.0944205i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.75549e6 | + | 4.90546e7i | −0.327812 | + | 1.64837i | ||||
\(977\) | −1.70913e6 | + | 986767.i | −0.0572848 | + | 0.0330734i | −0.528369 | − | 0.849015i | \(-0.677196\pi\) |
0.471084 | + | 0.882088i | \(0.343863\pi\) | |||||||
\(978\) | 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 | −0.456539 | − | 0.889703i | \(-0.650911\pi\) |
0.998775 | − | 0.0494775i | \(-0.0157556\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.05883e7 | + | 1.83395e7i | 0.347725 | + | 0.602278i | ||||
\(986\) | −3.59768e6 | − | 1.00545e7i | −0.117850 | − | 0.329359i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.08307e7 | + | 4.97502e7i | 1.33074 | + | 1.62145i | ||||
\(989\) | − | 2.43368e7i | − | 0.791176i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.19722e7i | − | 0.387250i | −0.981076 | − | 0.193625i | \(-0.937976\pi\) | ||
0.981076 | − | 0.193625i | \(-0.0620244\pi\) | |||||||
\(992\) | −6.82294e6 | − | 4.59803e7i | −0.220137 | − | 1.48352i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.12834e6 | − | 2.19282e6i | 0.196733 | − | 0.0703944i | ||||
\(995\) | 5.01894e6 | + | 8.69306e6i | 0.160714 | + | 0.278365i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.60260e7 | − | 2.77579e7i | 0.510608 | − | 0.884400i | −0.489316 | − | 0.872107i | \(-0.662754\pi\) |
0.999924 | − | 0.0122932i | \(-0.00391315\pi\) | |||||||
\(998\) | −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.35.9 | 56 | ||
3.2 | odd | 2 | 36.6.h.a.11.20 | yes | 56 | ||
4.3 | odd | 2 | inner | 108.6.h.a.35.18 | 56 | ||
9.4 | even | 3 | 36.6.h.a.23.11 | yes | 56 | ||
9.5 | odd | 6 | inner | 108.6.h.a.71.18 | 56 | ||
12.11 | even | 2 | 36.6.h.a.11.11 | ✓ | 56 | ||
36.23 | even | 6 | inner | 108.6.h.a.71.9 | 56 | ||
36.31 | odd | 6 | 36.6.h.a.23.20 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.6.h.a.11.11 | ✓ | 56 | 12.11 | even | 2 | ||
36.6.h.a.11.20 | yes | 56 | 3.2 | odd | 2 | ||
36.6.h.a.23.11 | yes | 56 | 9.4 | even | 3 | ||
36.6.h.a.23.20 | yes | 56 | 36.31 | odd | 6 | ||
108.6.h.a.35.9 | 56 | 1.1 | even | 1 | trivial | ||
108.6.h.a.35.18 | 56 | 4.3 | odd | 2 | inner | ||
108.6.h.a.71.9 | 56 | 36.23 | even | 6 | inner | ||
108.6.h.a.71.18 | 56 | 9.5 | odd | 6 | inner |