Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,6,Mod(67,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.67");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.e (of order \(3\), 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: | \(23.5764215125\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-83})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - x^{3} - 20x^{2} - 21x + 441 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 79.2 | ||
Root | \(-3.69493 + 2.71062i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.79 |
Dual form | 147.6.e.l.67.2 |
$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.69493 | − | 8.13186i | 0.829955 | − | 1.43752i | −0.0681181 | − | 0.997677i | \(-0.521699\pi\) |
0.898073 | − | 0.439847i | \(-0.144967\pi\) | |||||||
\(3\) | −4.50000 | − | 7.79423i | −0.288675 | − | 0.500000i | ||||
\(4\) | −28.0848 | − | 48.6443i | −0.877650 | − | 1.52013i | ||||
\(5\) | −35.8645 | + | 62.1192i | −0.641564 | + | 1.11122i | 0.343519 | + | 0.939146i | \(0.388381\pi\) |
−0.985084 | + | 0.172076i | \(0.944952\pi\) | |||||||
\(6\) | −84.5088 | −0.958349 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −226.949 | −1.25373 | ||||||||
\(9\) | −40.5000 | + | 70.1481i | −0.166667 | + | 0.288675i | ||||
\(10\) | 336.763 | + | 583.291i | 1.06494 | + | 1.84453i | ||||
\(11\) | 280.305 | + | 485.503i | 0.698472 | + | 1.20979i | 0.968996 | + | 0.247076i | \(0.0794698\pi\) |
−0.270524 | + | 0.962713i | \(0.587197\pi\) | |||||||
\(12\) | −252.763 | + | 437.799i | −0.506711 | + | 0.877650i | ||||
\(13\) | −533.509 | −0.875555 | −0.437777 | − | 0.899083i | \(-0.644234\pi\) | ||||
−0.437777 | + | 0.899083i | \(0.644234\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 645.562 | 0.740815 | ||||||||
\(16\) | −166.798 | + | 288.903i | −0.162889 | + | 0.282132i | ||||
\(17\) | 502.850 | + | 870.962i | 0.422004 | + | 0.730932i | 0.996135 | − | 0.0878311i | \(-0.0279936\pi\) |
−0.574132 | + | 0.818763i | \(0.694660\pi\) | |||||||
\(18\) | 380.290 | + | 658.681i | 0.276652 | + | 0.479175i | ||||
\(19\) | 684.263 | − | 1185.18i | 0.434850 | − | 0.753182i | −0.562434 | − | 0.826842i | \(-0.690135\pi\) |
0.997283 | + | 0.0736606i | \(0.0234682\pi\) | |||||||
\(20\) | 4028.99 | 2.25228 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5264.05 | 2.31880 | ||||||||
\(23\) | −1614.04 | + | 2795.60i | −0.636201 | + | 1.10193i | 0.350058 | + | 0.936728i | \(0.386162\pi\) |
−0.986259 | + | 0.165205i | \(0.947171\pi\) | |||||||
\(24\) | 1021.27 | + | 1768.90i | 0.361921 | + | 0.626865i | ||||
\(25\) | −1010.03 | − | 1749.42i | −0.323209 | − | 0.559815i | ||||
\(26\) | −2504.79 | + | 4338.42i | −0.726671 | + | 1.25863i | ||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −753.456 | −0.166365 | −0.0831827 | − | 0.996534i | \(-0.526508\pi\) | ||||
−0.0831827 | + | 0.996534i | \(0.526508\pi\) | |||||||
\(30\) | 3030.87 | − | 5249.62i | 0.614843 | − | 1.06494i | ||||
\(31\) | 4103.21 | + | 7106.97i | 0.766866 | + | 1.32825i | 0.939254 | + | 0.343222i | \(0.111518\pi\) |
−0.172389 | + | 0.985029i | \(0.555148\pi\) | |||||||
\(32\) | −2064.97 | − | 3576.64i | −0.356484 | − | 0.617448i | ||||
\(33\) | 2522.75 | − | 4369.52i | 0.403263 | − | 0.698472i | ||||
\(34\) | 9443.39 | 1.40098 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4549.74 | 0.585100 | ||||||||
\(37\) | 1404.33 | − | 2432.37i | 0.168642 | − | 0.292096i | −0.769301 | − | 0.638887i | \(-0.779395\pi\) |
0.937943 | + | 0.346791i | \(0.112729\pi\) | |||||||
\(38\) | −6425.14 | − | 11128.7i | −0.721811 | − | 1.25021i | ||||
\(39\) | 2400.79 | + | 4158.29i | 0.252751 | + | 0.437777i | ||||
\(40\) | 8139.43 | − | 14097.9i | 0.804348 | − | 1.39317i | ||||
\(41\) | −245.827 | −0.0228387 | −0.0114193 | − | 0.999935i | \(-0.503635\pi\) | ||||
−0.0114193 | + | 0.999935i | \(0.503635\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −17504.5 | −1.44371 | −0.721853 | − | 0.692047i | \(-0.756709\pi\) | ||||
−0.721853 | + | 0.692047i | \(0.756709\pi\) | |||||||
\(44\) | 15744.6 | − | 27270.5i | 1.22603 | − | 2.12354i | ||||
\(45\) | −2905.03 | − | 5031.65i | −0.213855 | − | 0.370407i | ||||
\(46\) | 15155.6 | + | 26250.3i | 1.05604 | + | 1.82911i | ||||
\(47\) | −8172.74 | + | 14155.6i | −0.539663 | + | 0.934725i | 0.459258 | + | 0.888303i | \(0.348115\pi\) |
−0.998922 | + | 0.0464219i | \(0.985218\pi\) | |||||||
\(48\) | 3002.37 | 0.188088 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −18968.1 | −1.07300 | ||||||||
\(51\) | 4525.65 | − | 7838.66i | 0.243644 | − | 0.422004i | ||||
\(52\) | 14983.5 | + | 25952.2i | 0.768430 | + | 1.33096i | ||||
\(53\) | 14820.8 | + | 25670.4i | 0.724741 | + | 1.25529i | 0.959081 | + | 0.283133i | \(0.0913739\pi\) |
−0.234340 | + | 0.972155i | \(0.575293\pi\) | |||||||
\(54\) | 3422.61 | − | 5928.13i | 0.159725 | − | 0.276652i | ||||
\(55\) | −40212.0 | −1.79246 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12316.7 | −0.502121 | ||||||||
\(58\) | −3537.43 | + | 6127.00i | −0.138076 | + | 0.239154i | ||||
\(59\) | −5178.05 | − | 8968.65i | −0.193659 | − | 0.335426i | 0.752801 | − | 0.658248i | \(-0.228702\pi\) |
−0.946460 | + | 0.322821i | \(0.895369\pi\) | |||||||
\(60\) | −18130.5 | − | 31402.9i | −0.650176 | − | 1.12614i | ||||
\(61\) | 477.089 | − | 826.343i | 0.0164163 | − | 0.0284339i | −0.857701 | − | 0.514150i | \(-0.828108\pi\) |
0.874117 | + | 0.485716i | \(0.161441\pi\) | |||||||
\(62\) | 77057.2 | 2.54586 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −49454.8 | −1.50924 | ||||||||
\(65\) | 19134.0 | − | 33141.1i | 0.561725 | − | 0.972935i | ||||
\(66\) | −23688.2 | − | 41029.2i | −0.669380 | − | 1.15940i | ||||
\(67\) | 9907.60 | + | 17160.5i | 0.269638 | + | 0.467027i | 0.968768 | − | 0.247967i | \(-0.0797626\pi\) |
−0.699130 | + | 0.714994i | \(0.746429\pi\) | |||||||
\(68\) | 28244.9 | − | 48921.6i | 0.740743 | − | 1.28300i | ||||
\(69\) | 29052.7 | 0.734622 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 62125.4 | 1.46259 | 0.731296 | − | 0.682060i | \(-0.238916\pi\) | ||||
0.731296 | + | 0.682060i | \(0.238916\pi\) | |||||||
\(72\) | 9191.45 | − | 15920.1i | 0.208955 | − | 0.361921i | ||||
\(73\) | 13554.8 | + | 23477.6i | 0.297705 | + | 0.515641i | 0.975611 | − | 0.219509i | \(-0.0704454\pi\) |
−0.677905 | + | 0.735149i | \(0.737112\pi\) | |||||||
\(74\) | −13186.5 | − | 22839.7i | −0.279930 | − | 0.484853i | ||||
\(75\) | −9090.27 | + | 15744.8i | −0.186605 | + | 0.323209i | ||||
\(76\) | −76869.6 | −1.52658 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 45086.2 | 0.839087 | ||||||||
\(79\) | −22343.7 | + | 38700.4i | −0.402798 | + | 0.697666i | −0.994062 | − | 0.108812i | \(-0.965295\pi\) |
0.591265 | + | 0.806477i | \(0.298629\pi\) | |||||||
\(80\) | −11964.3 | − | 20722.8i | −0.209008 | − | 0.362012i | ||||
\(81\) | −3280.50 | − | 5681.99i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −1154.14 | + | 1999.03i | −0.0189551 | + | 0.0328311i | ||||
\(83\) | −15606.6 | −0.248665 | −0.124332 | − | 0.992241i | \(-0.539679\pi\) | ||||
−0.124332 | + | 0.992241i | \(0.539679\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −72137.9 | −1.08297 | ||||||||
\(86\) | −82182.5 | + | 142344.i | −1.19821 | + | 2.07536i | ||||
\(87\) | 3390.55 | + | 5872.61i | 0.0480255 | + | 0.0831827i | ||||
\(88\) | −63615.0 | − | 110184.i | −0.875696 | − | 1.51675i | ||||
\(89\) | 6817.66 | − | 11808.5i | 0.0912347 | − | 0.158023i | −0.816796 | − | 0.576926i | \(-0.804252\pi\) |
0.908031 | + | 0.418903i | \(0.137585\pi\) | |||||||
\(90\) | −54555.6 | −0.709959 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 181320. | 2.23345 | ||||||||
\(93\) | 36928.9 | − | 63962.7i | 0.442750 | − | 0.766866i | ||||
\(94\) | 76740.9 | + | 132919.i | 0.895793 | + | 1.55156i | ||||
\(95\) | 49081.6 | + | 85011.8i | 0.557968 | + | 0.966429i | ||||
\(96\) | −18584.8 | + | 32189.8i | −0.205816 | + | 0.356484i | ||||
\(97\) | 12919.5 | 0.139417 | 0.0697086 | − | 0.997567i | \(-0.477793\pi\) | ||||
0.0697086 | + | 0.997567i | \(0.477793\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −45409.4 | −0.465648 | ||||||||
\(100\) | −56733.0 | + | 98264.4i | −0.567330 | + | 0.982644i | ||||
\(101\) | 12571.5 | + | 21774.4i | 0.122626 | + | 0.212394i | 0.920802 | − | 0.390029i | \(-0.127535\pi\) |
−0.798177 | + | 0.602424i | \(0.794202\pi\) | |||||||
\(102\) | −42495.3 | − | 73604.0i | −0.404427 | − | 0.700488i | ||||
\(103\) | −80376.6 | + | 139216.i | −0.746511 | + | 1.29300i | 0.202974 | + | 0.979184i | \(0.434939\pi\) |
−0.949485 | + | 0.313811i | \(0.898394\pi\) | |||||||
\(104\) | 121079. | 1.09771 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 278331. | 2.40601 | ||||||||
\(107\) | 47187.8 | − | 81731.6i | 0.398446 | − | 0.690129i | −0.595088 | − | 0.803661i | \(-0.702883\pi\) |
0.993534 | + | 0.113531i | \(0.0362162\pi\) | |||||||
\(108\) | −20473.8 | − | 35461.7i | −0.168904 | − | 0.292550i | ||||
\(109\) | 41696.7 | + | 72220.9i | 0.336152 | + | 0.582233i | 0.983705 | − | 0.179788i | \(-0.0575410\pi\) |
−0.647553 | + | 0.762020i | \(0.724208\pi\) | |||||||
\(110\) | −188793. | + | 326999.i | −1.48766 | + | 2.57670i | ||||
\(111\) | −25278.0 | −0.194731 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −179254. | −1.32060 | −0.660301 | − | 0.751001i | \(-0.729571\pi\) | ||||
−0.660301 | + | 0.751001i | \(0.729571\pi\) | |||||||
\(114\) | −57826.3 | + | 100158.i | −0.416738 | + | 0.721811i | ||||
\(115\) | −115774. | − | 200526.i | −0.816328 | − | 1.41392i | ||||
\(116\) | 21160.7 | + | 36651.3i | 0.146011 | + | 0.252898i | ||||
\(117\) | 21607.1 | − | 37424.6i | 0.145926 | − | 0.252751i | ||||
\(118\) | −97242.5 | −0.642911 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −146510. | −0.928781 | ||||||||
\(121\) | −76616.4 | + | 132703.i | −0.475727 | + | 0.823984i | ||||
\(122\) | −4479.80 | − | 7759.25i | −0.0272496 | − | 0.0471976i | ||||
\(123\) | 1106.22 | + | 1916.04i | 0.00659295 | + | 0.0114193i | ||||
\(124\) | 230476. | − | 399195.i | 1.34608 | − | 2.33148i | ||||
\(125\) | −79256.4 | −0.453690 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −143674. | −0.790440 | −0.395220 | − | 0.918586i | \(-0.629332\pi\) | ||||
−0.395220 | + | 0.918586i | \(0.629332\pi\) | |||||||
\(128\) | −166108. | + | 287707.i | −0.896117 | + | 1.55212i | ||||
\(129\) | 78770.2 | + | 136434.i | 0.416762 | + | 0.721853i | ||||
\(130\) | −179666. | − | 311191.i | −0.932412 | − | 1.61498i | ||||
\(131\) | 26144.9 | − | 45284.3i | 0.133110 | − | 0.230553i | −0.791764 | − | 0.610827i | \(-0.790837\pi\) |
0.924874 | + | 0.380274i | \(0.124170\pi\) | |||||||
\(132\) | −283403. | −1.41570 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 186062. | 0.895150 | ||||||||
\(135\) | −26145.2 | + | 45284.9i | −0.123469 | + | 0.213855i | ||||
\(136\) | −114122. | − | 197664.i | −0.529079 | − | 0.916391i | ||||
\(137\) | −4705.05 | − | 8149.39i | −0.0214172 | − | 0.0370957i | 0.855118 | − | 0.518433i | \(-0.173484\pi\) |
−0.876535 | + | 0.481337i | \(0.840151\pi\) | |||||||
\(138\) | 136401. | − | 236253.i | 0.609703 | − | 1.05604i | ||||
\(139\) | −183094. | −0.803781 | −0.401890 | − | 0.915688i | \(-0.631647\pi\) | ||||
−0.401890 | + | 0.915688i | \(0.631647\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 147109. | 0.623150 | ||||||||
\(142\) | 291674. | − | 505195.i | 1.21389 | − | 2.10251i | ||||
\(143\) | −149545. | − | 259020.i | −0.611551 | − | 1.05924i | ||||
\(144\) | −13510.7 | − | 23401.2i | −0.0542964 | − | 0.0940441i | ||||
\(145\) | 27022.3 | − | 46804.1i | 0.106734 | − | 0.184869i | ||||
\(146\) | 254556. | 0.988328 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −157762. | −0.592034 | ||||||||
\(149\) | 83500.8 | − | 144628.i | 0.308123 | − | 0.533685i | −0.669828 | − | 0.742516i | \(-0.733632\pi\) |
0.977952 | + | 0.208830i | \(0.0669657\pi\) | |||||||
\(150\) | 85356.4 | + | 147842.i | 0.309748 | + | 0.536499i | ||||
\(151\) | −188132. | − | 325855.i | −0.671461 | − | 1.16300i | −0.977490 | − | 0.210982i | \(-0.932334\pi\) |
0.306029 | − | 0.952022i | \(-0.401000\pi\) | |||||||
\(152\) | −155293. | + | 268976.i | −0.545184 | + | 0.944286i | ||||
\(153\) | −81461.7 | −0.281336 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −588639. | −1.96797 | ||||||||
\(156\) | 134851. | − | 233569.i | 0.443654 | − | 0.768430i | ||||
\(157\) | 19537.5 | + | 33840.0i | 0.0632587 | + | 0.109567i | 0.895920 | − | 0.444215i | \(-0.146517\pi\) |
−0.832662 | + | 0.553782i | \(0.813184\pi\) | |||||||
\(158\) | 209804. | + | 363391.i | 0.668608 | + | 1.15806i | ||||
\(159\) | 133387. | − | 231034.i | 0.418429 | − | 0.724741i | ||||
\(160\) | 296237. | 0.914829 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −61606.9 | −0.184434 | ||||||||
\(163\) | 238959. | − | 413890.i | 0.704458 | − | 1.22016i | −0.262428 | − | 0.964951i | \(-0.584523\pi\) |
0.966887 | − | 0.255206i | \(-0.0821433\pi\) | |||||||
\(164\) | 6904.01 | + | 11958.1i | 0.0200444 | + | 0.0347178i | ||||
\(165\) | 180954. | + | 313422.i | 0.517439 | + | 0.896230i | ||||
\(166\) | −73272.1 | + | 126911.i | −0.206381 | + | 0.357462i | ||||
\(167\) | −39793.4 | −0.110413 | −0.0552064 | − | 0.998475i | \(-0.517582\pi\) | ||||
−0.0552064 | + | 0.998475i | \(0.517582\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −86661.4 | −0.233404 | ||||||||
\(170\) | −338683. | + | 586616.i | −0.898816 | + | 1.55680i | ||||
\(171\) | 55425.3 | + | 95999.5i | 0.144950 | + | 0.251061i | ||||
\(172\) | 491610. | + | 851494.i | 1.26707 | + | 2.19463i | ||||
\(173\) | 24169.1 | − | 41862.1i | 0.0613968 | − | 0.106342i | −0.833693 | − | 0.552228i | \(-0.813778\pi\) |
0.895090 | + | 0.445886i | \(0.147111\pi\) | |||||||
\(174\) | 63673.7 | 0.159436 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −187018. | −0.455094 | ||||||||
\(177\) | −46602.5 | + | 80717.9i | −0.111809 | + | 0.193659i | ||||
\(178\) | −64016.9 | − | 110881.i | −0.151441 | − | 0.262304i | ||||
\(179\) | 71455.3 | + | 123764.i | 0.166687 | + | 0.288711i | 0.937253 | − | 0.348650i | \(-0.113360\pi\) |
−0.770566 | + | 0.637360i | \(0.780026\pi\) | |||||||
\(180\) | −163174. | + | 282626.i | −0.375379 | + | 0.650176i | ||||
\(181\) | 77245.3 | 0.175257 | 0.0876285 | − | 0.996153i | \(-0.472071\pi\) | ||||
0.0876285 | + | 0.996153i | \(0.472071\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8587.61 | −0.0189559 | ||||||||
\(184\) | 366305. | − | 634459.i | 0.797625 | − | 1.38153i | ||||
\(185\) | 100731. | + | 174472.i | 0.216389 | + | 0.374797i | ||||
\(186\) | −346757. | − | 600601.i | −0.734925 | − | 1.27293i | ||||
\(187\) | −281903. | + | 488270.i | −0.589516 | + | 1.02107i | ||||
\(188\) | 918119. | 1.89454 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 921739. | 1.85235 | ||||||||
\(191\) | −136027. | + | 235606.i | −0.269800 | + | 0.467307i | −0.968810 | − | 0.247805i | \(-0.920291\pi\) |
0.699010 | + | 0.715112i | \(0.253624\pi\) | |||||||
\(192\) | 222546. | + | 385462.i | 0.435680 | + | 0.754620i | ||||
\(193\) | 8016.89 | + | 13885.7i | 0.0154922 | + | 0.0268333i | 0.873668 | − | 0.486523i | \(-0.161735\pi\) |
−0.858175 | + | 0.513357i | \(0.828402\pi\) | |||||||
\(194\) | 60656.2 | − | 105060.i | 0.115710 | − | 0.200415i | ||||
\(195\) | −344413. | −0.648624 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.03228e6 | 1.89510 | 0.947552 | − | 0.319603i | \(-0.103549\pi\) | ||||
0.947552 | + | 0.319603i | \(0.103549\pi\) | |||||||
\(198\) | −213194. | + | 369263.i | −0.386467 | + | 0.669380i | ||||
\(199\) | −440868. | − | 763606.i | −0.789180 | − | 1.36690i | −0.926470 | − | 0.376369i | \(-0.877173\pi\) |
0.137290 | − | 0.990531i | \(-0.456161\pi\) | |||||||
\(200\) | 229226. | + | 397030.i | 0.405217 | + | 0.701857i | ||||
\(201\) | 89168.4 | − | 154444.i | 0.155676 | − | 0.269638i | ||||
\(202\) | 236089. | 0.407096 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −508408. | −0.855337 | ||||||||
\(205\) | 8816.49 | − | 15270.6i | 0.0146525 | − | 0.0253788i | ||||
\(206\) | 754725. | + | 1.30722e6i | 1.23914 | + | 2.14626i | ||||
\(207\) | −130737. | − | 226443.i | −0.212067 | − | 0.367311i | ||||
\(208\) | 88988.4 | − | 154132.i | 0.142618 | − | 0.247022i | ||||
\(209\) | 767210. | 1.21492 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −372813. | −0.576480 | −0.288240 | − | 0.957558i | \(-0.593070\pi\) | ||||
−0.288240 | + | 0.957558i | \(0.593070\pi\) | |||||||
\(212\) | 832480. | − | 1.44190e6i | 1.27214 | − | 2.20341i | ||||
\(213\) | −279564. | − | 484219.i | −0.422214 | − | 0.731296i | ||||
\(214\) | −443087. | − | 767449.i | −0.661385 | − | 1.14555i | ||||
\(215\) | 627791. | − | 1.08737e6i | 0.926230 | − | 1.60428i | ||||
\(216\) | −165446. | −0.241280 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 783054. | 1.11596 | ||||||||
\(219\) | 121993. | − | 211299.i | 0.171880 | − | 0.297705i | ||||
\(220\) | 1.12935e6 | + | 1.95609e6i | 1.57315 | + | 2.72478i | ||||
\(221\) | −268275. | − | 464666.i | −0.369487 | − | 0.639971i | ||||
\(222\) | −118678. | + | 205557.i | −0.161618 | + | 0.279930i | ||||
\(223\) | 1.08205e6 | 1.45708 | 0.728541 | − | 0.685002i | \(-0.240199\pi\) | ||||
0.728541 | + | 0.685002i | \(0.240199\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 163625. | 0.215473 | ||||||||
\(226\) | −841584. | + | 1.45767e6i | −1.09604 | + | 1.89840i | ||||
\(227\) | 276524. | + | 478954.i | 0.356179 | + | 0.616921i | 0.987319 | − | 0.158748i | \(-0.0507459\pi\) |
−0.631140 | + | 0.775669i | \(0.717413\pi\) | |||||||
\(228\) | 345913. | + | 599139.i | 0.440687 | + | 0.763292i | ||||
\(229\) | 261512. | − | 452952.i | 0.329536 | − | 0.570773i | −0.652884 | − | 0.757458i | \(-0.726441\pi\) |
0.982420 | + | 0.186685i | \(0.0597743\pi\) | |||||||
\(230\) | −2.17420e6 | −2.71006 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 170996. | 0.208577 | ||||||||
\(233\) | 182090. | − | 315390.i | 0.219734 | − | 0.380590i | −0.734993 | − | 0.678075i | \(-0.762814\pi\) |
0.954727 | + | 0.297485i | \(0.0961477\pi\) | |||||||
\(234\) | −202888. | − | 351412.i | −0.242224 | − | 0.419544i | ||||
\(235\) | −586223. | − | 1.01537e6i | −0.692458 | − | 1.19937i | ||||
\(236\) | −290849. | + | 503766.i | −0.339929 | + | 0.588774i | ||||
\(237\) | 402186. | 0.465111 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 371841. | 0.421078 | 0.210539 | − | 0.977585i | \(-0.432478\pi\) | ||||
0.210539 | + | 0.977585i | \(0.432478\pi\) | |||||||
\(240\) | −107679. | + | 186505.i | −0.120671 | + | 0.209008i | ||||
\(241\) | −855737. | − | 1.48218e6i | −0.949069 | − | 1.64384i | −0.747391 | − | 0.664384i | \(-0.768694\pi\) |
−0.201678 | − | 0.979452i | \(-0.564640\pi\) | |||||||
\(242\) | 719417. | + | 1.24607e6i | 0.789664 | + | 1.36774i | ||||
\(243\) | −29524.5 | + | 51137.9i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −53595.8 | −0.0576310 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 20774.6 | 0.0218874 | ||||||||
\(247\) | −365060. | + | 632303.i | −0.380735 | + | 0.659452i | ||||
\(248\) | −931221. | − | 1.61292e6i | −0.961443 | − | 1.66527i | ||||
\(249\) | 70229.9 | + | 121642.i | 0.0717833 | + | 0.124332i | ||||
\(250\) | −372103. | + | 644502.i | −0.376542 | + | 0.652190i | ||||
\(251\) | −58134.1 | −0.0582434 | −0.0291217 | − | 0.999576i | \(-0.509271\pi\) | ||||
−0.0291217 | + | 0.999576i | \(0.509271\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.80969e6 | −1.77748 | ||||||||
\(254\) | −674540. | + | 1.16834e6i | −0.656030 | + | 1.13628i | ||||
\(255\) | 324621. | + | 562260.i | 0.312627 | + | 0.541485i | ||||
\(256\) | 768453. | + | 1.33100e6i | 0.732853 | + | 1.26934i | ||||
\(257\) | −155920. | + | 270061.i | −0.147254 | + | 0.255052i | −0.930212 | − | 0.367023i | \(-0.880377\pi\) |
0.782957 | + | 0.622075i | \(0.213710\pi\) | |||||||
\(258\) | 1.47928e6 | 1.38357 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.14950e6 | −1.97199 | ||||||||
\(261\) | 30515.0 | − | 52853.5i | 0.0277276 | − | 0.0480255i | ||||
\(262\) | −245497. | − | 425214.i | −0.220950 | − | 0.382696i | ||||
\(263\) | −431983. | − | 748216.i | −0.385103 | − | 0.667018i | 0.606681 | − | 0.794946i | \(-0.292501\pi\) |
−0.991783 | + | 0.127928i | \(0.959167\pi\) | |||||||
\(264\) | −572535. | + | 991660.i | −0.505583 | + | 0.875696i | ||||
\(265\) | −2.12617e6 | −1.85987 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −122718. | −0.105349 | ||||||||
\(268\) | 556506. | − | 963896.i | 0.473296 | − | 0.819773i | ||||
\(269\) | −560346. | − | 970548.i | −0.472145 | − | 0.817779i | 0.527347 | − | 0.849650i | \(-0.323187\pi\) |
−0.999492 | + | 0.0318707i | \(0.989854\pi\) | |||||||
\(270\) | 245500. | + | 425219.i | 0.204948 | + | 0.354980i | ||||
\(271\) | 570058. | − | 987369.i | 0.471515 | − | 0.816688i | −0.527954 | − | 0.849273i | \(-0.677041\pi\) |
0.999469 | + | 0.0325848i | \(0.0103739\pi\) | |||||||
\(272\) | −335498. | −0.274959 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −88359.6 | −0.0711013 | ||||||||
\(275\) | 566233. | − | 980744.i | 0.451506 | − | 0.782031i | ||||
\(276\) | −815940. | − | 1.41325e6i | −0.644741 | − | 1.11672i | ||||
\(277\) | 994005. | + | 1.72167e6i | 0.778375 | + | 1.34819i | 0.932878 | + | 0.360193i | \(0.117289\pi\) |
−0.154502 | + | 0.987992i | \(0.549377\pi\) | |||||||
\(278\) | −859615. | + | 1.48890e6i | −0.667102 | + | 1.15545i | ||||
\(279\) | −664720. | −0.511244 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 532321. | 0.402168 | 0.201084 | − | 0.979574i | \(-0.435554\pi\) | ||||
0.201084 | + | 0.979574i | \(0.435554\pi\) | |||||||
\(282\) | 690668. | − | 1.19627e6i | 0.517186 | − | 0.895793i | ||||
\(283\) | 1.31237e6 | + | 2.27308e6i | 0.974067 | + | 1.68713i | 0.682980 | + | 0.730437i | \(0.260684\pi\) |
0.291087 | + | 0.956697i | \(0.405983\pi\) | |||||||
\(284\) | −1.74478e6 | − | 3.02205e6i | −1.28364 | − | 2.22334i | ||||
\(285\) | 441734. | − | 765106.i | 0.322143 | − | 0.557968i | ||||
\(286\) | −2.80842e6 | −2.03024 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 334526. | 0.237656 | ||||||||
\(289\) | 204212. | − | 353705.i | 0.143826 | − | 0.249113i | ||||
\(290\) | −253736. | − | 439484.i | −0.177169 | − | 0.306866i | ||||
\(291\) | −58137.7 | − | 100697.i | −0.0402463 | − | 0.0697086i | ||||
\(292\) | 761369. | − | 1.31873e6i | 0.522562 | − | 0.905104i | ||||
\(293\) | −609962. | −0.415082 | −0.207541 | − | 0.978226i | \(-0.566546\pi\) | ||||
−0.207541 | + | 0.978226i | \(0.566546\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 742834. | 0.496978 | ||||||||
\(296\) | −318712. | + | 552026.i | −0.211431 | + | 0.366210i | ||||
\(297\) | 204342. | + | 353931.i | 0.134421 | + | 0.232824i | ||||
\(298\) | −784061. | − | 1.35803e6i | −0.511457 | − | 0.885870i | ||||
\(299\) | 861104. | − | 1.49148e6i | 0.557029 | − | 0.964802i | ||||
\(300\) | 1.02119e6 | 0.655096 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3.53307e6 | −2.22913 | ||||||||
\(303\) | 113143. | − | 195970.i | 0.0707981 | − | 0.122626i | ||||
\(304\) | 228268. | + | 395372.i | 0.141665 | + | 0.245370i | ||||
\(305\) | 34221.2 | + | 59272.8i | 0.0210642 | + | 0.0364843i | ||||
\(306\) | −382457. | + | 662436.i | −0.233496 | + | 0.404427i | ||||
\(307\) | 1.34843e6 | 0.816551 | 0.408275 | − | 0.912859i | \(-0.366130\pi\) | ||||
0.408275 | + | 0.912859i | \(0.366130\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.44678e6 | 0.861997 | ||||||||
\(310\) | −2.76362e6 | + | 4.78673e6i | −1.63333 | + | 2.82901i | ||||
\(311\) | −1.66530e6 | − | 2.88439e6i | −0.976320 | − | 1.69104i | −0.675507 | − | 0.737353i | \(-0.736075\pi\) |
−0.300813 | − | 0.953683i | \(-0.597258\pi\) | |||||||
\(312\) | −544858. | − | 943721.i | −0.316881 | − | 0.548854i | ||||
\(313\) | −1.41835e6 | + | 2.45666e6i | −0.818320 | + | 1.41737i | 0.0885991 | + | 0.996067i | \(0.471761\pi\) |
−0.906919 | + | 0.421305i | \(0.861572\pi\) | |||||||
\(314\) | 366909. | 0.210007 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.51007e6 | 1.41406 | ||||||||
\(317\) | 544195. | − | 942574.i | 0.304163 | − | 0.526826i | −0.672912 | − | 0.739723i | \(-0.734957\pi\) |
0.977075 | + | 0.212897i | \(0.0682899\pi\) | |||||||
\(318\) | −1.25249e6 | − | 2.16938e6i | −0.694555 | − | 1.20300i | ||||
\(319\) | −211198. | − | 365805.i | −0.116202 | − | 0.201267i | ||||
\(320\) | 1.77367e6 | − | 3.07209e6i | 0.968274 | − | 1.67710i | ||||
\(321\) | −849380. | −0.460086 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.37633e6 | 0.734033 | ||||||||
\(324\) | −184264. | + | 319155.i | −0.0975167 | + | 0.168904i | ||||
\(325\) | 538860. | + | 933332.i | 0.282988 | + | 0.490149i | ||||
\(326\) | −2.24380e6 | − | 3.88637e6i | −1.16934 | − | 2.02535i | ||||
\(327\) | 375271. | − | 649988.i | 0.194078 | − | 0.336152i | ||||
\(328\) | 55790.4 | 0.0286335 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 3.39827e6 | 1.71780 | ||||||||
\(331\) | −652773. | + | 1.13064e6i | −0.327485 | + | 0.567221i | −0.982012 | − | 0.188817i | \(-0.939535\pi\) |
0.654527 | + | 0.756039i | \(0.272868\pi\) | |||||||
\(332\) | 438309. | + | 759174.i | 0.218241 | + | 0.378004i | ||||
\(333\) | 113751. | + | 197022.i | 0.0562140 | + | 0.0973654i | ||||
\(334\) | −186827. | + | 323594.i | −0.0916376 | + | 0.158721i | ||||
\(335\) | −1.42133e6 | −0.691961 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.17016e6 | −1.52057 | −0.760285 | − | 0.649590i | \(-0.774941\pi\) | ||||
−0.760285 | + | 0.649590i | \(0.774941\pi\) | |||||||
\(338\) | −406869. | + | 704718.i | −0.193715 | + | 0.335524i | ||||
\(339\) | 806641. | + | 1.39714e6i | 0.381225 | + | 0.660301i | ||||
\(340\) | 2.02598e6 | + | 3.50910e6i | 0.950469 | + | 1.64626i | ||||
\(341\) | −2.30030e6 | + | 3.98424e6i | −1.07127 | + | 1.85549i | ||||
\(342\) | 1.04087e6 | 0.481207 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.97263e6 | 1.81002 | ||||||||
\(345\) | −1.04196e6 | + | 1.80473e6i | −0.471307 | + | 0.816328i | ||||
\(346\) | −226945. | − | 393080.i | −0.101913 | − | 0.176519i | ||||
\(347\) | 857958. | + | 1.48603e6i | 0.382510 | + | 0.662526i | 0.991420 | − | 0.130713i | \(-0.0417265\pi\) |
−0.608911 | + | 0.793239i | \(0.708393\pi\) | |||||||
\(348\) | 190446. | − | 329862.i | 0.0842992 | − | 0.146011i | ||||
\(349\) | 2.95822e6 | 1.30007 | 0.650034 | − | 0.759905i | \(-0.274755\pi\) | ||||
0.650034 | + | 0.759905i | \(0.274755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −388928. | −0.168501 | ||||||||
\(352\) | 1.15765e6 | − | 2.00510e6i | 0.497988 | − | 0.862541i | ||||
\(353\) | 1.88490e6 | + | 3.26474e6i | 0.805103 | + | 1.39448i | 0.916222 | + | 0.400672i | \(0.131223\pi\) |
−0.111119 | + | 0.993807i | \(0.535443\pi\) | |||||||
\(354\) | 437591. | + | 757930.i | 0.185592 | + | 0.321456i | ||||
\(355\) | −2.22810e6 | + | 3.85918e6i | −0.938347 | + | 1.62526i | ||||
\(356\) | −765890. | −0.320289 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.34191e6 | 0.553371 | ||||||||
\(359\) | −964935. | + | 1.67132e6i | −0.395150 | + | 0.684420i | −0.993120 | − | 0.117099i | \(-0.962641\pi\) |
0.597970 | + | 0.801518i | \(0.295974\pi\) | |||||||
\(360\) | 659294. | + | 1.14193e6i | 0.268116 | + | 0.464391i | ||||
\(361\) | 301617. | + | 522416.i | 0.121811 | + | 0.210984i | ||||
\(362\) | 362662. | − | 628148.i | 0.145455 | − | 0.251936i | ||||
\(363\) | 1.37909e6 | 0.549323 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.94455e6 | −0.763988 | ||||||||
\(366\) | −40318.2 | + | 69833.2i | −0.0157325 | + | 0.0272496i | ||||
\(367\) | 1.18371e6 | + | 2.05025e6i | 0.458754 | + | 0.794586i | 0.998895 | − | 0.0469885i | \(-0.0149624\pi\) |
−0.540141 | + | 0.841575i | \(0.681629\pi\) | |||||||
\(368\) | −538438. | − | 932603.i | −0.207260 | − | 0.358986i | ||||
\(369\) | 9956.01 | − | 17244.3i | 0.00380644 | − | 0.00659295i | ||||
\(370\) | 1.89171e6 | 0.718373 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −4.14856e6 | −1.55432 | ||||||||
\(373\) | −1.76914e6 | + | 3.06425e6i | −0.658402 | + | 1.14039i | 0.322627 | + | 0.946526i | \(0.395434\pi\) |
−0.981029 | + | 0.193860i | \(0.937899\pi\) | |||||||
\(374\) | 2.64703e6 | + | 4.58479e6i | 0.978543 | + | 1.69489i | ||||
\(375\) | 356654. | + | 617742.i | 0.130969 | + | 0.226845i | ||||
\(376\) | 1.85480e6 | − | 3.21260e6i | 0.676592 | − | 1.17189i | ||||
\(377\) | 401975. | 0.145662 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.79847e6 | 0.643139 | 0.321569 | − | 0.946886i | \(-0.395790\pi\) | ||||
0.321569 | + | 0.946886i | \(0.395790\pi\) | |||||||
\(380\) | 2.75689e6 | − | 4.77508e6i | 0.979401 | − | 1.69637i | ||||
\(381\) | 646533. | + | 1.11983e6i | 0.228180 | + | 0.395220i | ||||
\(382\) | 1.27728e6 | + | 2.21231e6i | 0.447843 | + | 0.775687i | ||||
\(383\) | 1.30407e6 | − | 2.25872e6i | 0.454261 | − | 0.786802i | −0.544385 | − | 0.838836i | \(-0.683237\pi\) |
0.998645 | + | 0.0520333i | \(0.0165702\pi\) | |||||||
\(384\) | 2.98994e6 | 1.03475 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 150555. | 0.0514313 | ||||||||
\(387\) | 708932. | − | 1.22791e6i | 0.240618 | − | 0.416762i | ||||
\(388\) | −362841. | − | 628460.i | −0.122359 | − | 0.211933i | ||||
\(389\) | 1.41498e6 | + | 2.45081e6i | 0.474106 | + | 0.821175i | 0.999560 | − | 0.0296466i | \(-0.00943818\pi\) |
−0.525455 | + | 0.850821i | \(0.676105\pi\) | |||||||
\(390\) | −1.61700e6 | + | 2.80072e6i | −0.538328 | + | 0.932412i | ||||
\(391\) | −3.24648e6 | −1.07392 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −470609. | −0.153702 | ||||||||
\(394\) | 4.84650e6 | − | 8.39438e6i | 1.57285 | − | 2.72426i | ||||
\(395\) | −1.60269e6 | − | 2.77594e6i | −0.516841 | − | 0.895195i | ||||
\(396\) | 1.27531e6 | + | 2.20891e6i | 0.408676 | + | 0.707848i | ||||
\(397\) | −1.21531e6 | + | 2.10498e6i | −0.387000 | + | 0.670303i | −0.992044 | − | 0.125888i | \(-0.959822\pi\) |
0.605045 | + | 0.796191i | \(0.293155\pi\) | |||||||
\(398\) | −8.27939e6 | −2.61993 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 673885. | 0.210589 | ||||||||
\(401\) | 1.21592e6 | − | 2.10604e6i | 0.377611 | − | 0.654041i | −0.613103 | − | 0.790003i | \(-0.710079\pi\) |
0.990714 | + | 0.135962i | \(0.0434124\pi\) | |||||||
\(402\) | −837279. | − | 1.45021e6i | −0.258408 | − | 0.447575i | ||||
\(403\) | −2.18910e6 | − | 3.79163e6i | −0.671433 | − | 1.16296i | ||||
\(404\) | 706134. | − | 1.22306e6i | 0.215245 | − | 0.372816i | ||||
\(405\) | 470614. | 0.142570 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.57457e6 | 0.471167 | ||||||||
\(408\) | −1.02709e6 | + | 1.77898e6i | −0.305464 | + | 0.529079i | ||||
\(409\) | −2.38733e6 | − | 4.13497e6i | −0.705674 | − | 1.22226i | −0.966448 | − | 0.256863i | \(-0.917311\pi\) |
0.260774 | − | 0.965400i | \(-0.416022\pi\) | |||||||
\(410\) | −82785.6 | − | 143389.i | −0.0243218 | − | 0.0421266i | ||||
\(411\) | −42345.5 | + | 73344.5i | −0.0123652 | + | 0.0214172i | ||||
\(412\) | 9.02944e6 | 2.62070 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.45521e6 | −0.704024 | ||||||||
\(415\) | 559725. | − | 969472.i | 0.159534 | − | 0.276322i | ||||
\(416\) | 1.10168e6 | + | 1.90817e6i | 0.312121 | + | 0.540609i | ||||
\(417\) | 823924. | + | 1.42708e6i | 0.232032 | + | 0.401890i | ||||
\(418\) | 3.60200e6 | − | 6.23884e6i | 1.00833 | − | 1.74648i | ||||
\(419\) | 457181. | 0.127219 | 0.0636097 | − | 0.997975i | \(-0.479739\pi\) | ||||
0.0636097 | + | 0.997975i | \(0.479739\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.82396e6 | −0.501545 | −0.250773 | − | 0.968046i | \(-0.580685\pi\) | ||||
−0.250773 | + | 0.968046i | \(0.580685\pi\) | |||||||
\(422\) | −1.75033e6 | + | 3.03166e6i | −0.478453 | + | 0.828704i | ||||
\(423\) | −661992. | − | 1.14660e6i | −0.179888 | − | 0.311575i | ||||
\(424\) | −3.36358e6 | − | 5.82589e6i | −0.908629 | − | 1.57379i | ||||
\(425\) | 1.01579e6 | − | 1.75939e6i | 0.272791 | − | 0.472488i | ||||
\(426\) | −5.25014e6 | −1.40167 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5.30104e6 | −1.39879 | ||||||||
\(429\) | −1.34591e6 | + | 2.33118e6i | −0.353079 | + | 0.611551i | ||||
\(430\) | −5.89487e6 | − | 1.02102e7i | −1.53746 | − | 2.66295i | ||||
\(431\) | 1.69124e6 | + | 2.92932e6i | 0.438544 | + | 0.759580i | 0.997577 | − | 0.0695651i | \(-0.0221612\pi\) |
−0.559034 | + | 0.829145i | \(0.688828\pi\) | |||||||
\(432\) | −121596. | + | 210611.i | −0.0313480 | + | 0.0542964i | ||||
\(433\) | 285266. | 0.0731190 | 0.0365595 | − | 0.999331i | \(-0.488360\pi\) | ||||
0.0365595 | + | 0.999331i | \(0.488360\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −486402. | −0.123246 | ||||||||
\(436\) | 2.34209e6 | − | 4.05662e6i | 0.590048 | − | 1.02199i | ||||
\(437\) | 2.20886e6 | + | 3.82585e6i | 0.553304 | + | 0.958351i | ||||
\(438\) | −1.14550e6 | − | 1.98407e6i | −0.285306 | − | 0.494164i | ||||
\(439\) | 2.17610e6 | − | 3.76911e6i | 0.538911 | − | 0.933421i | −0.460052 | − | 0.887892i | \(-0.652169\pi\) |
0.998963 | − | 0.0455294i | \(-0.0144975\pi\) | |||||||
\(440\) | 9.12610e6 | 2.24726 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.03813e6 | −1.22663 | ||||||||
\(443\) | 2.55280e6 | − | 4.42158e6i | 0.618027 | − | 1.07045i | −0.371819 | − | 0.928305i | \(-0.621266\pi\) |
0.989845 | − | 0.142148i | \(-0.0454010\pi\) | |||||||
\(444\) | 709927. | + | 1.22963e6i | 0.170906 | + | 0.296017i | ||||
\(445\) | 489024. | + | 847015.i | 0.117066 | + | 0.202764i | ||||
\(446\) | 5.08014e6 | − | 8.79906e6i | 1.20931 | − | 2.09459i | ||||
\(447\) | −1.50301e6 | −0.355790 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.04163e6 | 0.712016 | 0.356008 | − | 0.934483i | \(-0.384138\pi\) | ||||
0.356008 | + | 0.934483i | \(0.384138\pi\) | |||||||
\(450\) | 768208. | − | 1.33057e6i | 0.178833 | − | 0.309748i | ||||
\(451\) | −68906.7 | − | 119350.i | −0.0159522 | − | 0.0276300i | ||||
\(452\) | 5.03430e6 | + | 8.71966e6i | 1.15903 | + | 2.00749i | ||||
\(453\) | −1.69319e6 | + | 2.93269e6i | −0.387668 | + | 0.671461i | ||||
\(454\) | 5.19305e6 | 1.18245 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.79528e6 | 0.629524 | ||||||||
\(457\) | 872162. | − | 1.51063e6i | 0.195347 | − | 0.338351i | −0.751667 | − | 0.659542i | \(-0.770750\pi\) |
0.947014 | + | 0.321192i | \(0.104083\pi\) | |||||||
\(458\) | −2.45556e6 | − | 4.25316e6i | −0.547000 | − | 0.947432i | ||||
\(459\) | 366578. | + | 634931.i | 0.0812147 | + | 0.140668i | ||||
\(460\) | −6.50295e6 | + | 1.12634e7i | −1.43290 | + | 2.48186i | ||||
\(461\) | 6.85701e6 | 1.50273 | 0.751367 | − | 0.659884i | \(-0.229395\pi\) | ||||
0.751367 | + | 0.659884i | \(0.229395\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.13844e6 | 1.11398 | 0.556992 | − | 0.830518i | \(-0.311955\pi\) | ||||
0.556992 | + | 0.830518i | \(0.311955\pi\) | |||||||
\(464\) | 125675. | − | 217676.i | 0.0270991 | − | 0.0469370i | ||||
\(465\) | 2.64887e6 | + | 4.58798e6i | 0.568105 | + | 0.983987i | ||||
\(466\) | −1.70980e6 | − | 2.96147e6i | −0.364738 | − | 0.631746i | ||||
\(467\) | −2.29085e6 | + | 3.96788e6i | −0.486077 | + | 0.841910i | −0.999872 | − | 0.0160029i | \(-0.994906\pi\) |
0.513795 | + | 0.857913i | \(0.328239\pi\) | |||||||
\(468\) | −2.42733e6 | −0.512287 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.10091e7 | −2.29883 | ||||||||
\(471\) | 175838. | − | 304560.i | 0.0365224 | − | 0.0632587i | ||||
\(472\) | 1.17516e6 | + | 2.03543e6i | 0.242795 | + | 0.420534i | ||||
\(473\) | −4.90660e6 | − | 8.49848e6i | −1.00839 | − | 1.74658i | ||||
\(474\) | 1.88824e6 | − | 3.27052e6i | 0.386021 | − | 0.668608i | ||||
\(475\) | −2.76450e6 | −0.562190 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.40097e6 | −0.483161 | ||||||||
\(478\) | 1.74577e6 | − | 3.02376e6i | 0.349476 | − | 0.605310i | ||||
\(479\) | −144261. | − | 249868.i | −0.0287284 | − | 0.0497590i | 0.851304 | − | 0.524673i | \(-0.175812\pi\) |
−0.880032 | + | 0.474914i | \(0.842479\pi\) | |||||||
\(480\) | −1.33307e6 | − | 2.30894e6i | −0.264088 | − | 0.457414i | ||||
\(481\) | −749223. | + | 1.29769e6i | −0.147655 | + | 0.255746i | ||||
\(482\) | −1.60705e7 | −3.15074 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.60702e6 | 1.67009 | ||||||||
\(485\) | −463352. | + | 802549.i | −0.0894451 | + | 0.154923i | ||||
\(486\) | 277231. | + | 480178.i | 0.0532416 | + | 0.0922172i | ||||
\(487\) | 3.90842e6 | + | 6.76959e6i | 0.746757 | + | 1.29342i | 0.949369 | + | 0.314162i | \(0.101723\pi\) |
−0.202613 | + | 0.979259i | \(0.564943\pi\) | |||||||
\(488\) | −108275. | + | 187538.i | −0.0205816 | + | 0.0356484i | ||||
\(489\) | −4.30127e6 | −0.813438 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.14467e6 | 0.588669 | 0.294335 | − | 0.955702i | \(-0.404902\pi\) | ||||
0.294335 | + | 0.955702i | \(0.404902\pi\) | |||||||
\(492\) | 62136.1 | − | 107623.i | 0.0115726 | − | 0.0200444i | ||||
\(493\) | −378875. | − | 656232.i | −0.0702068 | − | 0.121602i | ||||
\(494\) | 3.42787e6 | + | 5.93724e6i | 0.631985 | + | 1.09463i | ||||
\(495\) | 1.62859e6 | − | 2.82080e6i | 0.298743 | − | 0.517439i | ||||
\(496\) | −2.73763e6 | −0.499656 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.31890e6 | 0.238308 | ||||||||
\(499\) | −3.36281e6 | + | 5.82456e6i | −0.604577 | + | 1.04716i | 0.387541 | + | 0.921852i | \(0.373324\pi\) |
−0.992118 | + | 0.125305i | \(0.960009\pi\) | |||||||
\(500\) | 2.22590e6 | + | 3.85537e6i | 0.398181 | + | 0.689670i | ||||
\(501\) | 179070. | + | 310159.i | 0.0318734 | + | 0.0552064i | ||||
\(502\) | −272936. | + | 472738.i | −0.0483394 | + | 0.0837262i | ||||
\(503\) | 9.45056e6 | 1.66547 | 0.832737 | − | 0.553669i | \(-0.186773\pi\) | ||||
0.832737 | + | 0.553669i | \(0.186773\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.80348e6 | −0.314690 | ||||||||
\(506\) | −8.49639e6 | + | 1.47162e7i | −1.47522 | + | 2.55516i | ||||
\(507\) | 389976. | + | 675458.i | 0.0673780 | + | 0.116702i | ||||
\(508\) | 4.03506e6 | + | 6.98892e6i | 0.693730 | + | 1.20158i | ||||
\(509\) | −4.41851e6 | + | 7.65308e6i | −0.755930 | + | 1.30931i | 0.188981 | + | 0.981981i | \(0.439481\pi\) |
−0.944911 | + | 0.327328i | \(0.893852\pi\) | |||||||
\(510\) | 6.09629e6 | 1.03786 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 3.80044e6 | 0.640707 | ||||||||
\(513\) | 498828. | − | 863995.i | 0.0836869 | − | 0.144950i | ||||
\(514\) | 1.46406e6 | + | 2.53583e6i | 0.244429 | + | 0.423363i | ||||
\(515\) | −5.76534e6 | − | 9.98585e6i | −0.957870 | − | 1.65908i | ||||
\(516\) | 4.42449e6 | − | 7.66345e6i | 0.731542 | − | 1.26707i | ||||
\(517\) | −9.16344e6 | −1.50776 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −435044. | −0.0708949 | ||||||||
\(520\) | −4.34246e6 | + | 7.52136e6i | −0.704251 | + | 1.21980i | ||||
\(521\) | 347492. | + | 601874.i | 0.0560855 | + | 0.0971430i | 0.892705 | − | 0.450641i | \(-0.148805\pi\) |
−0.836619 | + | 0.547784i | \(0.815471\pi\) | |||||||
\(522\) | −286531. | − | 496287.i | −0.0460252 | − | 0.0797181i | ||||
\(523\) | 1.79105e6 | − | 3.10219e6i | 0.286321 | − | 0.495923i | −0.686607 | − | 0.727028i | \(-0.740901\pi\) |
0.972929 | + | 0.231105i | \(0.0742342\pi\) | |||||||
\(524\) | −2.93710e6 | −0.467294 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.11252e6 | −1.27847 | ||||||||
\(527\) | −4.12660e6 | + | 7.14748e6i | −0.647240 | + | 1.12105i | ||||
\(528\) | 841580. | + | 1.45766e6i | 0.131374 | + | 0.227547i | ||||
\(529\) | −1.99208e6 | − | 3.45038e6i | −0.309504 | − | 0.536077i | ||||
\(530\) | −9.98222e6 | + | 1.72897e7i | −1.54361 | + | 2.67361i | ||||
\(531\) | 838845. | 0.129106 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 131151. | 0.0199965 | ||||||||
\(534\) | −576152. | + | 997925.i | −0.0874347 | + | 0.151441i | ||||
\(535\) | 3.38473e6 | + | 5.86253e6i | 0.511258 | + | 0.885525i | ||||
\(536\) | −2.24852e6 | − | 3.89456e6i | −0.338053 | − | 0.585526i | ||||
\(537\) | 643098. | − | 1.11388e6i | 0.0962368 | − | 0.166687i | ||||
\(538\) | −1.05231e7 | −1.56744 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.93714e6 | 0.433451 | ||||||||
\(541\) | 2.58423e6 | − | 4.47602e6i | 0.379610 | − | 0.657504i | −0.611395 | − | 0.791325i | \(-0.709391\pi\) |
0.991005 | + | 0.133821i | \(0.0427248\pi\) | |||||||
\(542\) | −5.35277e6 | − | 9.27126e6i | −0.782673 | − | 1.35563i | ||||
\(543\) | −347604. | − | 602068.i | −0.0505924 | − | 0.0876285i | ||||
\(544\) | 2.07675e6 | − | 3.59703e6i | 0.300875 | − | 0.521131i | ||||
\(545\) | −5.98174e6 | −0.862653 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.47489e6 | 1.21106 | 0.605530 | − | 0.795822i | \(-0.292961\pi\) | ||||
0.605530 | + | 0.795822i | \(0.292961\pi\) | |||||||
\(548\) | −264281. | + | 457748.i | −0.0375936 | + | 0.0651141i | ||||
\(549\) | 38644.2 | + | 66933.8i | 0.00547210 | + | 0.00947795i | ||||
\(550\) | −5.31685e6 | − | 9.20906e6i | −0.749459 | − | 1.29810i | ||||
\(551\) | −515562. | + | 892980.i | −0.0723439 | + | 0.125303i | ||||
\(552\) | −6.59349e6 | −0.921018 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.86671e7 | 2.58407 | ||||||||
\(555\) | 906583. | − | 1.57025e6i | 0.124932 | − | 0.216389i | ||||
\(556\) | 5.14217e6 | + | 8.90649e6i | 0.705438 | + | 1.22186i | ||||
\(557\) | 5.21063e6 | + | 9.02508e6i | 0.711627 | + | 1.23257i | 0.964246 | + | 0.265009i | \(0.0853748\pi\) |
−0.252619 | + | 0.967566i | \(0.581292\pi\) | |||||||
\(558\) | −3.12082e6 | + | 5.40541e6i | −0.424309 | + | 0.734925i | ||||
\(559\) | 9.33880e6 | 1.26404 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.07425e6 | 0.680714 | ||||||||
\(562\) | 2.49921e6 | − | 4.32876e6i | 0.333781 | − | 0.578126i | ||||
\(563\) | −3.62039e6 | − | 6.27069e6i | −0.481375 | − | 0.833767i | 0.518396 | − | 0.855141i | \(-0.326529\pi\) |
−0.999772 | + | 0.0213739i | \(0.993196\pi\) | |||||||
\(564\) | −4.13154e6 | − | 7.15603e6i | −0.546907 | − | 0.947271i | ||||
\(565\) | 6.42885e6 | − | 1.11351e7i | 0.847251 | − | 1.46748i | ||||
\(566\) | 2.46459e7 | 3.23373 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.40993e7 | −1.83369 | ||||||||
\(569\) | −458268. | + | 793743.i | −0.0593388 | + | 0.102778i | −0.894169 | − | 0.447730i | \(-0.852233\pi\) |
0.834830 | + | 0.550508i | \(0.185566\pi\) | |||||||
\(570\) | −4.14782e6 | − | 7.18424e6i | −0.534728 | − | 0.926177i | ||||
\(571\) | −5.03538e6 | − | 8.72154e6i | −0.646312 | − | 1.11944i | −0.983997 | − | 0.178186i | \(-0.942977\pi\) |
0.337685 | − | 0.941259i | \(-0.390356\pi\) | |||||||
\(572\) | −8.39990e6 | + | 1.45490e7i | −1.07345 | + | 1.85928i | ||||
\(573\) | 2.44849e6 | 0.311538 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.52091e6 | 0.822505 | ||||||||
\(576\) | 2.00292e6 | − | 3.46916e6i | 0.251540 | − | 0.435680i | ||||
\(577\) | 5.84987e6 | + | 1.01323e7i | 0.731488 | + | 1.26697i | 0.956247 | + | 0.292560i | \(0.0945070\pi\) |
−0.224760 | + | 0.974414i | \(0.572160\pi\) | |||||||
\(578\) | −1.91752e6 | − | 3.32125e6i | −0.238738 | − | 0.413506i | ||||
\(579\) | 72152.0 | − | 124971.i | 0.00894442 | − | 0.0154922i | ||||
\(580\) | −3.03567e6 | −0.374701 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1.09181e6 | −0.133610 | ||||||||
\(583\) | −8.30871e6 | + | 1.43911e7i | −1.01242 | + | 1.75357i | ||||
\(584\) | −3.07626e6 | − | 5.32823e6i | −0.373242 | − | 0.646474i | ||||
\(585\) | 1.54986e6 | + | 2.68443e6i | 0.187242 | + | 0.324312i | ||||
\(586\) | −2.86373e6 | + | 4.96013e6i | −0.344499 | + | 0.596690i | ||||
\(587\) | 6.92367e6 | 0.829357 | 0.414678 | − | 0.909968i | \(-0.363894\pi\) | ||||
0.414678 | + | 0.909968i | \(0.363894\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.12307e7 | 1.33389 | ||||||||
\(590\) | 3.48756e6 | − | 6.04062e6i | 0.412469 | − | 0.714417i | ||||
\(591\) | −4.64527e6 | − | 8.04584e6i | −0.547069 | − | 0.947552i | ||||
\(592\) | 468481. | + | 811432.i | 0.0549398 | + | 0.0951586i | ||||
\(593\) | 7.88850e6 | − | 1.36633e7i | 0.921208 | − | 1.59558i | 0.123660 | − | 0.992325i | \(-0.460537\pi\) |
0.797548 | − | 0.603255i | \(-0.206130\pi\) | |||||||
\(594\) | 3.83750e6 | 0.446254 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.38041e6 | −1.08170 | ||||||||
\(597\) | −3.96781e6 | + | 6.87245e6i | −0.455633 | + | 0.789180i | ||||
\(598\) | −8.08565e6 | − | 1.40048e7i | −0.924618 | − | 1.60148i | ||||
\(599\) | −7.13541e6 | − | 1.23589e7i | −0.812553 | − | 1.40738i | −0.911072 | − | 0.412248i | \(-0.864744\pi\) |
0.0985183 | − | 0.995135i | \(-0.468590\pi\) | |||||||
\(600\) | 2.06303e6 | − | 3.57327e6i | 0.233952 | − | 0.405217i | ||||
\(601\) | −7.63222e6 | −0.861916 | −0.430958 | − | 0.902372i | \(-0.641824\pi\) | ||||
−0.430958 | + | 0.902372i | \(0.641824\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.60503e6 | −0.179759 | ||||||||
\(604\) | −1.05673e7 | + | 1.83031e7i | −1.17862 | + | 2.04142i | ||||
\(605\) | −5.49562e6 | − | 9.51869e6i | −0.610419 | − | 1.05728i | ||||
\(606\) | −1.06240e6 | − | 1.84013e6i | −0.117518 | − | 0.203548i | ||||
\(607\) | −1.78017e6 | + | 3.08335e6i | −0.196106 | + | 0.339665i | −0.947262 | − | 0.320459i | \(-0.896163\pi\) |
0.751157 | + | 0.660124i | \(0.229496\pi\) | |||||||
\(608\) | −5.65194e6 | −0.620067 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 642664. | 0.0699294 | ||||||||
\(611\) | 4.36023e6 | − | 7.55214e6i | 0.472505 | − | 0.818402i | ||||
\(612\) | 2.28784e6 | + | 3.96265e6i | 0.246914 | + | 0.427668i | ||||
\(613\) | 6.86420e6 | + | 1.18891e7i | 0.737800 | + | 1.27791i | 0.953484 | + | 0.301445i | \(0.0974688\pi\) |
−0.215683 | + | 0.976463i | \(0.569198\pi\) | |||||||
\(614\) | 6.33080e6 | − | 1.09653e7i | 0.677700 | − | 1.17381i | ||||
\(615\) | −158697. | −0.0169192 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.51173e6 | −0.688626 | −0.344313 | − | 0.938855i | \(-0.611888\pi\) | ||||
−0.344313 | + | 0.938855i | \(0.611888\pi\) | |||||||
\(618\) | 6.79253e6 | − | 1.17650e7i | 0.715419 | − | 1.23914i | ||||
\(619\) | 4.42555e6 | + | 7.66527e6i | 0.464238 | + | 0.804083i | 0.999167 | − | 0.0408136i | \(-0.0129950\pi\) |
−0.534929 | + | 0.844897i | \(0.679662\pi\) | |||||||
\(620\) | 1.65318e7 | + | 2.86339e7i | 1.72719 | + | 2.99159i | ||||
\(621\) | −1.17663e6 | + | 2.03799e6i | −0.122437 | + | 0.212067i | ||||
\(622\) | −3.12739e7 | −3.24121 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.60179e6 | −0.164681 | ||||||||
\(625\) | 5.99884e6 | − | 1.03903e7i | 0.614281 | − | 1.06397i | ||||
\(626\) | 1.33181e7 | + | 2.30677e7i | 1.35834 | + | 2.35271i | ||||
\(627\) | −3.45244e6 | − | 5.97981e6i | −0.350718 | − | 0.607461i | ||||
\(628\) | 1.09741e6 | − | 1.90078e6i | 0.111038 | − | 0.192323i | ||||
\(629\) | 2.82467e6 | 0.284670 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.89663e6 | −0.689546 | −0.344773 | − | 0.938686i | \(-0.612044\pi\) | ||||
−0.344773 | + | 0.938686i | \(0.612044\pi\) | |||||||
\(632\) | 5.07088e6 | − | 8.78303e6i | 0.504999 | − | 0.874685i | ||||
\(633\) | 1.67766e6 | + | 2.90579e6i | 0.166416 | + | 0.288240i | ||||
\(634\) | −5.10992e6 | − | 8.85064e6i | −0.504883 | − | 0.874483i | ||||
\(635\) | 5.15280e6 | − | 8.92492e6i | 0.507118 | − | 0.878355i | ||||
\(636\) | −1.49846e7 | −1.46894 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −3.96623e6 | −0.385768 | ||||||||
\(639\) | −2.51608e6 | + | 4.35797e6i | −0.243765 | + | 0.422214i | ||||
\(640\) | −1.19147e7 | − | 2.06369e7i | −1.14983 | − | 1.99157i | ||||
\(641\) | 8.33473e6 | + | 1.44362e7i | 0.801210 | + | 1.38774i | 0.918820 | + | 0.394677i | \(0.129144\pi\) |
−0.117610 | + | 0.993060i | \(0.537523\pi\) | |||||||
\(642\) | −3.98778e6 | + | 6.90704e6i | −0.381851 | + | 0.661385i | ||||
\(643\) | 1.28697e7 | 1.22756 | 0.613779 | − | 0.789478i | \(-0.289649\pi\) | ||||
0.613779 | + | 0.789478i | \(0.289649\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.13002e7 | −1.06952 | ||||||||
\(646\) | 6.46177e6 | − | 1.11921e7i | 0.609214 | − | 1.05519i | ||||
\(647\) | −5.73656e6 | − | 9.93601e6i | −0.538754 | − | 0.933150i | −0.998971 | − | 0.0453435i | \(-0.985562\pi\) |
0.460217 | − | 0.887806i | \(-0.347772\pi\) | |||||||
\(648\) | 744507. | + | 1.28952e6i | 0.0696517 | + | 0.120640i | ||||
\(649\) | 2.90287e6 | − | 5.02792e6i | 0.270530 | − | 0.468572i | ||||
\(650\) | 1.01196e7 | 0.939467 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.68445e7 | −2.47307 | ||||||||
\(653\) | 6.59005e6 | − | 1.14143e7i | 0.604791 | − | 1.04753i | −0.387293 | − | 0.921957i | \(-0.626590\pi\) |
0.992084 | − | 0.125573i | \(-0.0400768\pi\) | |||||||
\(654\) | −3.52374e6 | − | 6.10330e6i | −0.322151 | − | 0.557982i | ||||
\(655\) | 1.87535e6 | + | 3.24820e6i | 0.170797 | + | 0.295829i | ||||
\(656\) | 41003.6 | − | 71020.4i | 0.00372017 | − | 0.00644352i | ||||
\(657\) | −2.19588e6 | −0.198470 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.13068e7 | −1.01421 | −0.507104 | − | 0.861885i | \(-0.669284\pi\) | ||||
−0.507104 | + | 0.861885i | \(0.669284\pi\) | |||||||
\(660\) | 1.01641e7 | − | 1.76048e7i | 0.908260 | − | 1.57315i | ||||
\(661\) | 1.10160e6 | + | 1.90802e6i | 0.0980661 | + | 0.169856i | 0.910884 | − | 0.412662i | \(-0.135401\pi\) |
−0.812818 | + | 0.582518i | \(0.802068\pi\) | |||||||
\(662\) | 6.12945e6 | + | 1.06165e7i | 0.543596 | + | 0.941536i | ||||
\(663\) | −2.41447e6 | + | 4.18199e6i | −0.213324 | + | 0.369487i | ||||
\(664\) | 3.54192e6 | 0.311758 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.13621e6 | 0.186620 | ||||||||
\(667\) | 1.21611e6 | − | 2.10636e6i | 0.105842 | − | 0.183323i | ||||
\(668\) | 1.11759e6 | + | 1.93572e6i | 0.0969038 | + | 0.167842i | ||||
\(669\) | −4.86921e6 | − | 8.43372e6i | −0.420623 | − | 0.728541i | ||||
\(670\) | −6.67303e6 | + | 1.15580e7i | −0.574296 | + | 0.994710i | ||||
\(671\) | 534922. | 0.0458653 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.89787e7 | −1.61521 | −0.807606 | − | 0.589723i | \(-0.799237\pi\) | ||||
−0.807606 | + | 0.589723i | \(0.799237\pi\) | |||||||
\(674\) | −1.48837e7 | + | 2.57793e7i | −1.26200 | + | 2.18586i | ||||
\(675\) | −736312. | − | 1.27533e6i | −0.0622017 | − | 0.107736i | ||||
\(676\) | 2.43387e6 | + | 4.21558e6i | 0.204847 | + | 0.354806i | ||||
\(677\) | −9.82377e6 | + | 1.70153e7i | −0.823771 | + | 1.42681i | 0.0790842 | + | 0.996868i | \(0.474800\pi\) |
−0.902855 | + | 0.429945i | \(0.858533\pi\) | |||||||
\(678\) | 1.51485e7 | 1.26560 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.63717e7 | 1.35775 | ||||||||
\(681\) | 2.48872e6 | − | 4.31059e6i | 0.205640 | − | 0.356179i | ||||
\(682\) | 2.15995e7 | + | 3.74115e7i | 1.77821 | + | 3.07995i | ||||
\(683\) | −8.13523e6 | − | 1.40906e7i | −0.667295 | − | 1.15579i | −0.978658 | − | 0.205498i | \(-0.934119\pi\) |
0.311363 | − | 0.950291i | \(-0.399215\pi\) | |||||||
\(684\) | 3.11322e6 | − | 5.39225e6i | 0.254431 | − | 0.440687i | ||||
\(685\) | 674978. | 0.0549621 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.70722e6 | −0.380515 | ||||||||
\(688\) | 2.91972e6 | − | 5.05711e6i | 0.235164 | − | 0.407316i | ||||
\(689\) | −7.90704e6 | − | 1.36954e7i | −0.634550 | − | 1.09907i | ||||
\(690\) | 9.78388e6 | + | 1.69462e7i | 0.782327 | + | 1.35503i | ||||
\(691\) | 9.72335e6 | − | 1.68413e7i | 0.774677 | − | 1.34178i | −0.160299 | − | 0.987069i | \(-0.551246\pi\) |
0.934976 | − | 0.354712i | \(-0.115421\pi\) | |||||||
\(692\) | −2.71514e6 | −0.215539 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.61122e7 | 1.26986 | ||||||||
\(695\) | 6.56659e6 | − | 1.13737e7i | 0.515677 | − | 0.893179i | ||||
\(696\) | −769484. | − | 1.33278e6i | −0.0602111 | − | 0.104289i | ||||
\(697\) | −123614. | − | 214106.i | −0.00963800 | − | 0.0166935i | ||||
\(698\) | 1.38886e7 | − | 2.40558e7i | 1.07900 | − | 1.86888i | ||||
\(699\) | −3.27763e6 | −0.253727 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.49625e7 | 1.15003 | 0.575014 | − | 0.818144i | \(-0.304997\pi\) | ||||
0.575014 | + | 0.818144i | \(0.304997\pi\) | |||||||
\(702\) | −1.82599e6 | + | 3.16271e6i | −0.139848 | + | 0.242224i | ||||
\(703\) | −1.92187e6 | − | 3.32877e6i | −0.146668 | − | 0.254036i | ||||
\(704\) | −1.38624e7 | − | 2.40104e7i | −1.05416 | − | 1.82586i | ||||
\(705\) | −5.27601e6 | + | 9.13831e6i | −0.399791 | + | 0.692458i | ||||
\(706\) | 3.53979e7 | 2.67280 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 5.23529e6 | 0.392516 | ||||||||
\(709\) | −793193. | + | 1.37385e6i | −0.0592603 | + | 0.102642i | −0.894134 | − | 0.447800i | \(-0.852208\pi\) |
0.834873 | + | 0.550442i | \(0.185541\pi\) | |||||||
\(710\) | 2.09215e7 | + | 3.62372e7i | 1.55757 | + | 2.69779i | ||||
\(711\) | −1.80984e6 | − | 3.13473e6i | −0.134266 | − | 0.232555i | ||||
\(712\) | −1.54726e6 | + | 2.67994e6i | −0.114384 | + | 0.198118i | ||||
\(713\) | −2.64910e7 | −1.95152 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.14535e7 | 1.56940 | ||||||||
\(716\) | 4.01362e6 | − | 6.95179e6i | 0.292586 | − | 0.506774i | ||||
\(717\) | −1.67329e6 | − | 2.89822e6i | −0.121555 | − | 0.210539i | ||||
\(718\) | 9.06061e6 | + | 1.56934e7i | 0.655913 | + | 1.13607i | ||||
\(719\) | −9.08376e6 | + | 1.57335e7i | −0.655305 | + | 1.13502i | 0.326512 | + | 0.945193i | \(0.394127\pi\) |
−0.981817 | + | 0.189829i | \(0.939207\pi\) | |||||||
\(720\) | 1.93822e6 | 0.139338 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 5.66429e6 | 0.404392 | ||||||||
\(723\) | −7.70164e6 | + | 1.33396e7i | −0.547945 | + | 0.949069i | ||||
\(724\) | −2.16942e6 | − | 3.75754e6i | −0.153814 | − | 0.266414i | ||||
\(725\) | 761013. | + | 1.31811e6i | 0.0537709 | + | 0.0931339i | ||||
\(726\) | 6.47476e6 | − | 1.12146e7i | 0.455913 | − | 0.789664i | ||||
\(727\) | −1.26903e7 | −0.890506 | −0.445253 | − | 0.895405i | \(-0.646886\pi\) | ||||
−0.445253 | + | 0.895405i | \(0.646886\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −9.12953e6 | + | 1.58128e7i | −0.634076 | + | 1.09825i | ||||
\(731\) | −8.80214e6 | − | 1.52458e7i | −0.609249 | − | 1.05525i | ||||
\(732\) | 241181. | + | 417738.i | 0.0166366 | + | 0.0288155i | ||||
\(733\) | −1.55701e6 | + | 2.69681e6i | −0.107036 | + | 0.185392i | −0.914568 | − | 0.404432i | \(-0.867469\pi\) |
0.807532 | + | 0.589824i | \(0.200803\pi\) | |||||||
\(734\) | 2.22298e7 | 1.52298 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.33318e7 | 0.907182 | ||||||||
\(737\) | −5.55430e6 | + | 9.62033e6i | −0.376670 | + | 0.652411i | ||||
\(738\) | −93485.6 | − | 161922.i | −0.00631835 | − | 0.0109437i | ||||
\(739\) | −4.54950e6 | − | 7.87996e6i | −0.306445 | − | 0.530778i | 0.671137 | − | 0.741333i | \(-0.265806\pi\) |
−0.977582 | + | 0.210555i | \(0.932473\pi\) | |||||||
\(740\) | 5.65804e6 | − | 9.80002e6i | 0.379828 | − | 0.657881i | ||||
\(741\) | 6.57109e6 | 0.439634 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.79218e6 | −0.584285 | −0.292142 | − | 0.956375i | \(-0.594368\pi\) | ||||
−0.292142 | + | 0.956375i | \(0.594368\pi\) | |||||||
\(744\) | −8.38098e6 | + | 1.45163e7i | −0.555089 | + | 0.961443i | ||||
\(745\) | 5.98943e6 | + | 1.03740e7i | 0.395362 | + | 0.684787i | ||||
\(746\) | 1.66120e7 | + | 2.87729e7i | 1.09289 | + | 1.89294i | ||||
\(747\) | 632069. | − | 1.09478e6i | 0.0414441 | − | 0.0717833i | ||||
\(748\) | 3.16687e7 | 2.06955 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 6.69786e6 | 0.434793 | ||||||||
\(751\) | 1.40459e7 | − | 2.43282e7i | 0.908759 | − | 1.57402i | 0.0929698 | − | 0.995669i | \(-0.470364\pi\) |
0.815790 | − | 0.578349i | \(-0.196303\pi\) | |||||||
\(752\) | −2.72640e6 | − | 4.72226e6i | −0.175811 | − | 0.304513i | ||||
\(753\) | 261603. | + | 453110.i | 0.0168134 | + | 0.0291217i | ||||
\(754\) | 1.88725e6 | − | 3.26881e6i | 0.120893 | − | 0.209393i | ||||
\(755\) | 2.69891e7 | 1.72314 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.18815e6 | −0.265634 | −0.132817 | − | 0.991141i | \(-0.542402\pi\) | ||||
−0.132817 | + | 0.991141i | \(0.542402\pi\) | |||||||
\(758\) | 8.44369e6 | − | 1.46249e7i | 0.533776 | − | 0.924527i | ||||
\(759\) | 8.14362e6 | + | 1.41052e7i | 0.513113 | + | 0.888738i | ||||
\(760\) | −1.11390e7 | − | 1.92934e7i | −0.699541 | − | 1.21164i | ||||
\(761\) | −196591. | + | 340506.i | −0.0123056 | + | 0.0213139i | −0.872113 | − | 0.489305i | \(-0.837250\pi\) |
0.859807 | + | 0.510619i | \(0.170584\pi\) | |||||||
\(762\) | 1.21417e7 | 0.757518 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.52812e7 | 0.947159 | ||||||||
\(765\) | 2.92159e6 | − | 5.06034e6i | 0.180495 | − | 0.312627i | ||||
\(766\) | −1.22451e7 | − | 2.12091e7i | −0.754031 | − | 1.30602i | ||||
\(767\) | 2.76254e6 | + | 4.78486e6i | 0.169559 | + | 0.293684i | ||||
\(768\) | 6.91607e6 | − | 1.19790e7i | 0.423113 | − | 0.732853i | ||||
\(769\) | −1.57517e7 | −0.960530 | −0.480265 | − | 0.877124i | \(-0.659459\pi\) | ||||
−0.480265 | + | 0.877124i | \(0.659459\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.80655e6 | 0.170035 | ||||||||
\(772\) | 450306. | − | 779952.i | 0.0271934 | − | 0.0471004i | ||||
\(773\) | 1.44236e6 | + | 2.49824e6i | 0.0868210 | + | 0.150378i | 0.906166 | − | 0.422923i | \(-0.138996\pi\) |
−0.819345 | + | 0.573301i | \(0.805663\pi\) | |||||||
\(774\) | −6.65678e6 | − | 1.15299e7i | −0.399403 | − | 0.691787i | ||||
\(775\) | 8.28873e6 | − | 1.43565e7i | 0.495717 | − | 0.858606i | ||||
\(776\) | −2.93207e6 | −0.174791 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.65729e7 | 1.57394 | ||||||||
\(779\) | −168211. | + | 291349.i | −0.00993139 | + | 0.0172017i | ||||
\(780\) | 9.67276e6 | + | 1.67537e7i | 0.569265 | + | 0.985995i | ||||
\(781\) | 1.74141e7 | + | 3.01620e7i | 1.02158 | + | 1.76943i | ||||
\(782\) | −1.52420e7 | + | 2.63999e7i | −0.891303 | + | 1.54378i | ||||
\(783\) | −549269. | −0.0320170 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.80281e6 | −0.162338 | ||||||||
\(786\) | −2.20948e6 | + | 3.82693e6i | −0.127565 | + | 0.220950i | ||||
\(787\) | −1.48933e7 | − | 2.57960e7i | −0.857145 | − | 1.48462i | −0.874641 | − | 0.484771i | \(-0.838903\pi\) |
0.0174963 | − | 0.999847i | \(-0.494430\pi\) | |||||||
\(788\) | −2.89914e7 | − | 5.02146e7i | −1.66324 | − | 2.88081i | ||||
\(789\) | −3.88784e6 | + | 6.73394e6i | −0.222339 | + | 0.385103i | ||||
\(790\) | −3.00981e7 | −1.71582 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.03056e7 | 0.583797 | ||||||||
\(793\) | −254531. | + | 440861.i | −0.0143734 | + | 0.0248954i | ||||
\(794\) | 1.14116e7 | + | 1.97655e7i | 0.642385 | + | 1.11264i | ||||
\(795\) | 9.56776e6 | + | 1.65718e7i | 0.536899 | + | 0.929936i | ||||
\(796\) | −2.47634e7 | + | 4.28914e7i | −1.38525 | + | 2.39932i | ||||
\(797\) | −8.11321e6 | −0.452425 | −0.226213 | − | 0.974078i | \(-0.572634\pi\) | ||||
−0.226213 | + | 0.974078i | \(0.572634\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.64387e7 | −0.910960 | ||||||||
\(800\) | −4.17137e6 | + | 7.22503e6i | −0.230438 | + | 0.399130i | ||||
\(801\) | 552230. | + | 956491.i | 0.0304116 | + | 0.0526744i | ||||
\(802\) | −1.14173e7 | − | 1.97754e7i | −0.626800 | − | 1.08565i | ||||
\(803\) | −7.59897e6 | + | 1.31618e7i | −0.415878 | + | 0.720321i | ||||
\(804\) | −1.00171e7 | −0.546515 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.11107e7 | −2.22904 | ||||||||
\(807\) | −5.04311e6 | + | 8.73493e6i | −0.272593 | + | 0.472145i | ||||
\(808\) | −2.85308e6 | − | 4.94169e6i | −0.153740 | − | 0.266285i | ||||
\(809\) | −55798.5 | − | 96645.8i | −0.00299744 | − | 0.00519173i | 0.864523 | − | 0.502594i | \(-0.167621\pi\) |
−0.867520 | + | 0.497402i | \(0.834287\pi\) | |||||||
\(810\) | 2.20950e6 | − | 3.82697e6i | 0.118327 | − | 0.204948i | ||||
\(811\) | 209250. | 0.0111716 | 0.00558578 | − | 0.999984i | \(-0.498222\pi\) | ||||
0.00558578 | + | 0.999984i | \(0.498222\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.02610e7 | −0.544459 | ||||||||
\(814\) | 7.39248e6 | − | 1.28042e7i | 0.391047 | − | 0.677314i | ||||
\(815\) | 1.71403e7 | + | 2.96879e7i | 0.903910 | + | 1.56562i | ||||
\(816\) | 1.50974e6 | + | 2.61495e6i | 0.0793739 | + | 0.137480i | ||||
\(817\) | −1.19777e7 | + | 2.07460e7i | −0.627795 | + | 1.08737i | ||||
\(818\) | −4.48334e7 | −2.34271 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −990437. | −0.0514390 | ||||||||
\(821\) | −3.42307e6 | + | 5.92893e6i | −0.177238 | + | 0.306986i | −0.940934 | − | 0.338591i | \(-0.890050\pi\) |
0.763695 | + | 0.645577i | \(0.223383\pi\) | |||||||
\(822\) | 397618. | + | 688695.i | 0.0205252 | + | 0.0355506i | ||||
\(823\) | 2.80605e6 | + | 4.86022e6i | 0.144409 | + | 0.250125i | 0.929152 | − | 0.369697i | \(-0.120538\pi\) |
−0.784743 | + | 0.619821i | \(0.787205\pi\) | |||||||
\(824\) | 1.82414e7 | − | 3.15950e7i | 0.935923 | − | 1.62107i | ||||
\(825\) | −1.01922e7 | −0.521354 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.15868e7 | −1.09755 | −0.548776 | − | 0.835969i | \(-0.684906\pi\) | ||||
−0.548776 | + | 0.835969i | \(0.684906\pi\) | |||||||
\(828\) | −7.34346e6 | + | 1.27192e7i | −0.372241 | + | 0.644741i | ||||
\(829\) | 9.62135e6 | + | 1.66647e7i | 0.486239 | + | 0.842190i | 0.999875 | − | 0.0158177i | \(-0.00503515\pi\) |
−0.513636 | + | 0.858008i | \(0.671702\pi\) | |||||||
\(830\) | −5.25574e6 | − | 9.10321e6i | −0.264813 | − | 0.458669i | ||||
\(831\) | 8.94604e6 | − | 1.54950e7i | 0.449395 | − | 0.778375i | ||||
\(832\) | 2.63846e7 | 1.32142 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.54731e7 | 0.770303 | ||||||||
\(835\) | 1.42717e6 | − | 2.47193e6i | 0.0708369 | − | 0.122693i | ||||
\(836\) | −2.15469e7 | − | 3.73204e7i | −1.06628 | − | 1.84684i | ||||
\(837\) | 2.99124e6 | + | 5.18098e6i | 0.147583 | + | 0.255622i | ||||
\(838\) | 2.14644e6 | − | 3.71774e6i | 0.105586 | − | 0.182881i | ||||
\(839\) | −2.47678e7 | −1.21474 | −0.607369 | − | 0.794420i | \(-0.707775\pi\) | ||||
−0.607369 | + | 0.794420i | \(0.707775\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.99435e7 | −0.972323 | ||||||||
\(842\) | −8.56337e6 | + | 1.48322e7i | −0.416260 | + | 0.720983i | ||||
\(843\) | −2.39544e6 | − | 4.14903e6i | −0.116096 | − | 0.201084i | ||||
\(844\) | 1.04704e7 | + | 1.81352e7i | 0.505948 | + | 0.876328i | ||||
\(845\) | 3.10807e6 | − | 5.38333e6i | 0.149744 | − | 0.259364i | ||||
\(846\) | −1.24320e7 | −0.597195 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −9.88836e6 | −0.472210 | ||||||||
\(849\) | 1.18113e7 | − | 2.04578e7i | 0.562378 | − | 0.974067i | ||||
\(850\) | −9.53811e6 | − | 1.65205e7i | −0.452809 | − | 0.784288i | ||||
\(851\) | 4.53329e6 | + | 7.85190e6i | 0.214580 | + | 0.371664i | ||||
\(852\) | −1.57030e7 | + | 2.71984e7i | −0.741112 | + | 1.28364i | ||||
\(853\) | 2.91267e7 | 1.37062 | 0.685312 | − | 0.728250i | \(-0.259666\pi\) | ||||
0.685312 | + | 0.728250i | \(0.259666\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.95121e6 | −0.371979 | ||||||||
\(856\) | −1.07092e7 | + | 1.85489e7i | −0.499544 | + | 0.865236i | ||||
\(857\) | −1.61293e6 | − | 2.79367e6i | −0.0750175 | − | 0.129934i | 0.826076 | − | 0.563558i | \(-0.190568\pi\) |
−0.901094 | + | 0.433624i | \(0.857235\pi\) | |||||||
\(858\) | 1.26379e7 | + | 2.18895e7i | 0.586079 | + | 1.01512i | ||||
\(859\) | 1.32335e7 | − | 2.29212e7i | 0.611918 | − | 1.05987i | −0.378999 | − | 0.925397i | \(-0.623732\pi\) |
0.990917 | − | 0.134476i | \(-0.0429350\pi\) | |||||||
\(860\) | −7.05255e7 | −3.25162 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.17611e7 | 1.45589 | ||||||||
\(863\) | −7.92552e6 | + | 1.37274e7i | −0.362243 | + | 0.627424i | −0.988330 | − | 0.152330i | \(-0.951322\pi\) |
0.626086 | + | 0.779754i | \(0.284656\pi\) | |||||||
\(864\) | −1.50537e6 | − | 2.60737e6i | −0.0686053 | − | 0.118828i | ||||
\(865\) | 1.73363e6 | + | 3.00273e6i | 0.0787799 | + | 0.136451i | ||||
\(866\) | 1.33930e6 | − | 2.31974e6i | 0.0606854 | − | 0.105110i | ||||
\(867\) | −3.67582e6 | −0.166076 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.50522e7 | −1.12537 | ||||||||
\(870\) | −2.28363e6 | + | 3.95536e6i | −0.102289 | + | 0.177169i | ||||
\(871\) | −5.28579e6 | − | 9.15526e6i | −0.236083 | − | 0.408908i | ||||
\(872\) | −9.46305e6 | − | 1.63905e7i | −0.421444 | − | 0.729962i | ||||
\(873\) | −523240. | + | 906277.i | −0.0232362 | + | 0.0402463i | ||||
\(874\) | 4.14817e7 | 1.83687 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.37046e7 | −0.603403 | ||||||||
\(877\) | 7.45659e6 | − | 1.29152e7i | 0.327372 | − | 0.567024i | −0.654618 | − | 0.755960i | \(-0.727170\pi\) |
0.981989 | + | 0.188936i | \(0.0605037\pi\) | |||||||
\(878\) | −2.04333e7 | − | 3.53915e7i | −0.894544 | − | 1.54940i | ||||
\(879\) | 2.74483e6 | + | 4.75419e6i | 0.119824 | + | 0.207541i | ||||
\(880\) | 6.70730e6 | − | 1.16174e7i | 0.291972 | − | 0.505711i | ||||
\(881\) | 3.70679e7 | 1.60901 | 0.804504 | − | 0.593947i | \(-0.202431\pi\) | ||||
0.804504 | + | 0.593947i | \(0.202431\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.50440e7 | 0.649325 | 0.324663 | − | 0.945830i | \(-0.394749\pi\) | ||||
0.324663 | + | 0.945830i | \(0.394749\pi\) | |||||||
\(884\) | −1.50689e7 | + | 2.61001e7i | −0.648561 | + | 1.12334i | ||||
\(885\) | −3.34275e6 | − | 5.78982e6i | −0.143465 | − | 0.248489i | ||||
\(886\) | −2.39704e7 | − | 4.15180e7i | −1.02587 | − | 1.77686i | ||||
\(887\) | 8.90504e6 | − | 1.54240e7i | 0.380038 | − | 0.658245i | −0.611030 | − | 0.791608i | \(-0.709244\pi\) |
0.991067 | + | 0.133363i | \(0.0425777\pi\) | |||||||
\(888\) | 5.73682e6 | 0.244140 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 9.18375e6 | 0.388638 | ||||||||
\(891\) | 1.83908e6 | − | 3.18538e6i | 0.0776080 | − | 0.134421i | ||||
\(892\) | −3.03891e7 | − | 5.26354e7i | −1.27881 | − | 2.21496i | ||||
\(893\) | 1.11846e7 | + | 1.93723e7i | 0.469345 | + | 0.812929i | ||||
\(894\) | −7.05655e6 | + | 1.22223e7i | −0.295290 | + | 0.511457i | ||||
\(895\) | −1.02508e7 | −0.427762 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.54999e7 | −0.643202 | ||||||||
\(898\) | 1.42802e7 | − | 2.47341e7i | 0.590941 | − | 1.02354i | ||||
\(899\) | −3.09159e6 | − | 5.35479e6i | −0.127580 | − | 0.220975i | ||||
\(900\) | −4.59537e6 | − | 7.95941e6i | −0.189110 | − | 0.327548i | ||||
\(901\) | −1.49053e7 | + | 2.58168e7i | −0.611687 | + | 1.05947i | ||||
\(902\) | −1.29405e6 | −0.0529583 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.06815e7 | 1.65568 | ||||||||
\(905\) | −2.77037e6 | + | 4.79842e6i | −0.112439 | + | 0.194750i | ||||
\(906\) | 1.58988e7 | + | 2.75376e7i | 0.643494 | + | 1.11456i | ||||
\(907\) | 584680. | + | 1.01270e6i | 0.0235993 | + | 0.0408753i | 0.877584 | − | 0.479423i | \(-0.159154\pi\) |
−0.853985 | + | 0.520298i | \(0.825821\pi\) | |||||||
\(908\) | 1.55323e7 | − | 2.69027e7i | 0.625202 | − | 1.08288i | ||||
\(909\) | −2.03658e6 | −0.0817506 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.74389e7 | 1.09539 | 0.547697 | − | 0.836677i | \(-0.315505\pi\) | ||||
0.547697 | + | 0.836677i | \(0.315505\pi\) | |||||||
\(912\) | 2.05441e6 | − | 3.55835e6i | 0.0817901 | − | 0.141665i | ||||
\(913\) | −4.37462e6 | − | 7.57707e6i | −0.173685 | − | 0.300832i | ||||
\(914\) | −8.18948e6 | − | 1.41846e7i | −0.324258 | − | 0.561632i | ||||
\(915\) | 307991. | − | 533455.i | 0.0121614 | − | 0.0210642i | ||||
\(916\) | −2.93781e7 | −1.15687 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 6.88423e6 | 0.269618 | ||||||||
\(919\) | −5.51091e6 | + | 9.54518e6i | −0.215246 | + | 0.372817i | −0.953349 | − | 0.301872i | \(-0.902389\pi\) |
0.738103 | + | 0.674688i | \(0.235722\pi\) | |||||||
\(920\) | 2.62747e7 | + | 4.55092e7i | 1.02345 | + | 1.77268i | ||||
\(921\) | −6.06794e6 | − | 1.05100e7i | −0.235718 | − | 0.408275i | ||||
\(922\) | 3.21932e7 | − | 5.57602e7i | 1.24720 | − | 2.16022i | ||||
\(923\) | −3.31444e7 | −1.28058 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.67367e6 | −0.218027 | ||||||||
\(926\) | 2.41246e7 | − | 4.17851e7i | 0.924557 | − | 1.60138i | ||||
\(927\) | −6.51050e6 | − | 1.12765e7i | −0.248837 | − | 0.430998i | ||||
\(928\) | 1.55587e6 | + | 2.69484e6i | 0.0593065 | + | 0.102722i | ||||
\(929\) | 2.12526e6 | − | 3.68105e6i | 0.0807927 | − | 0.139937i | −0.822798 | − | 0.568334i | \(-0.807588\pi\) |
0.903591 | + | 0.428397i | \(0.140921\pi\) | |||||||
\(930\) | 4.97452e7 | 1.88601 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.04559e7 | −0.771398 | ||||||||
\(933\) | −1.49877e7 | + | 2.59595e7i | −0.563679 | + | 0.976320i | ||||
\(934\) | 2.15108e7 | + | 3.72578e7i | 0.806844 | + | 1.39749i | ||||
\(935\) | −2.02206e7 | − | 3.50232e7i | −0.756425 | − | 1.31017i | ||||
\(936\) | −4.90372e6 | + | 8.49349e6i | −0.182951 | + | 0.316881i | ||||
\(937\) | −3.75738e7 | −1.39809 | −0.699046 | − | 0.715077i | \(-0.746392\pi\) | ||||
−0.699046 | + | 0.715077i | \(0.746392\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.55303e7 | 0.944915 | ||||||||
\(940\) | −3.29279e7 | + | 5.70328e7i | −1.21547 | + | 2.10526i | ||||
\(941\) | 3.43521e6 | + | 5.94997e6i | 0.126468 | + | 0.219049i | 0.922306 | − | 0.386461i | \(-0.126303\pi\) |
−0.795838 | + | 0.605510i | \(0.792969\pi\) | |||||||
\(942\) | −1.65109e6 | − | 2.85977e6i | −0.0606239 | − | 0.105004i | ||||
\(943\) | 396775. | − | 687235.i | 0.0145300 | − | 0.0251667i | ||||
\(944\) | 3.45476e6 | 0.126179 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.21446e7 | −3.34767 | ||||||||
\(947\) | 1.15462e7 | − | 1.99985e7i | 0.418372 | − | 0.724641i | −0.577404 | − | 0.816459i | \(-0.695934\pi\) |
0.995776 | + | 0.0918172i | \(0.0292676\pi\) | |||||||
\(948\) | −1.12953e7 | − | 1.95641e7i | −0.408204 | − | 0.707031i | ||||
\(949\) | −7.23161e6 | − | 1.25255e7i | −0.260657 | − | 0.451471i | ||||
\(950\) | −1.29792e7 | + | 2.24806e7i | −0.466592 | + | 0.808162i | ||||
\(951\) | −9.79551e6 | −0.351217 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.95399e7 | −1.05360 | −0.526802 | − | 0.849988i | \(-0.676609\pi\) | ||||
−0.526802 | + | 0.849988i | \(0.676609\pi\) | |||||||
\(954\) | −1.12724e7 | + | 1.95244e7i | −0.401002 | + | 0.694555i | ||||
\(955\) | −9.75709e6 | − | 1.68998e7i | −0.346188 | − | 0.599615i | ||||
\(956\) | −1.04431e7 | − | 1.80880e7i | −0.369559 | − | 0.640096i | ||||
\(957\) | −1.90078e6 | + | 3.29224e6i | −0.0670890 | + | 0.116202i | ||||
\(958\) | −2.70919e6 | −0.0953730 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.19261e7 | −1.11807 | ||||||||
\(961\) | −1.93581e7 | + | 3.35292e7i | −0.676166 | + | 1.17115i | ||||
\(962\) | 7.03511e6 | + | 1.21852e7i | 0.245094 | + | 0.424516i | ||||
\(963\) | 3.82221e6 | + | 6.62026e6i | 0.132815 | + | 0.230043i | ||||
\(964\) | −4.80664e7 | + | 8.32535e7i | −1.66590 | + | 2.88543i | ||||
\(965\) | −1.15009e6 | −0.0397569 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.49151e7 | 0.512931 | 0.256466 | − | 0.966553i | \(-0.417442\pi\) | ||||
0.256466 | + | 0.966553i | \(0.417442\pi\) | |||||||
\(968\) | 1.73880e7 | − | 3.01170e7i | 0.596434 | − | 1.03305i | ||||
\(969\) | −6.19347e6 | − | 1.07274e7i | −0.211897 | − | 0.367016i | ||||
\(970\) | 4.35081e6 | + | 7.53582e6i | 0.148471 | + | 0.257159i | ||||
\(971\) | 7.74150e6 | − | 1.34087e7i | 0.263498 | − | 0.456391i | −0.703671 | − | 0.710526i | \(-0.748457\pi\) |
0.967169 | + | 0.254134i | \(0.0817905\pi\) | |||||||
\(972\) | 3.31676e6 | 0.112603 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 7.33992e7 | 2.47910 | ||||||||
\(975\) | 4.84974e6 | − | 8.39999e6i | 0.163383 | − | 0.282988i | ||||
\(976\) | 159155. | + | 275665.i | 0.00534807 | + | 0.00926313i | ||||
\(977\) | 1.41714e7 | + | 2.45455e7i | 0.474980 | + | 0.822690i | 0.999589 | − | 0.0286531i | \(-0.00912183\pi\) |
−0.524609 | + | 0.851343i | \(0.675788\pi\) | |||||||
\(978\) | −2.01942e7 | + | 3.49773e7i | −0.675117 | + | 1.16934i | ||||
\(979\) | 7.64410e6 | 0.254900 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.75487e6 | −0.224101 | ||||||||
\(982\) | 1.47640e7 | − | 2.55720e7i | 0.488569 | − | 0.846226i | ||||
\(983\) | 1.28497e7 | + | 2.22563e7i | 0.424139 | + | 0.734630i | 0.996340 | − | 0.0854834i | \(-0.0272434\pi\) |
−0.572201 | + | 0.820114i | \(0.693910\pi\) | |||||||
\(984\) | −251057. | − | 434843.i | −0.00826578 | − | 0.0143168i | ||||
\(985\) | −3.70223e7 | + | 6.41245e7i | −1.21583 | + | 2.10588i | ||||
\(986\) | −7.11518e6 | −0.233074 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.10106e7 | 1.33661 | ||||||||
\(989\) | 2.82530e7 | − | 4.89355e7i | 0.918487 | − | 1.59087i | ||||
\(990\) | −1.52922e7 | − | 2.64869e7i | −0.495887 | − | 0.858901i | ||||
\(991\) | −2.23202e7 | − | 3.86598e7i | −0.721962 | − | 1.25048i | −0.960212 | − | 0.279271i | \(-0.909907\pi\) |
0.238250 | − | 0.971204i | \(-0.423426\pi\) | |||||||
\(992\) | 1.69460e7 | − | 2.93514e7i | 0.546750 | − | 0.947000i | ||||
\(993\) | 1.17499e7 | 0.378148 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.32461e7 | 2.02524 | ||||||||
\(996\) | 3.94479e6 | − | 6.83257e6i | 0.126001 | − | 0.218241i | ||||
\(997\) | 1.15277e7 | + | 1.99665e7i | 0.367286 | + | 0.636158i | 0.989140 | − | 0.146975i | \(-0.0469537\pi\) |
−0.621854 | + | 0.783133i | \(0.713620\pi\) | |||||||
\(998\) | 3.15764e7 | + | 5.46919e7i | 1.00354 | + | 1.73819i | ||||
\(999\) | 1.02376e6 | − | 1.77320e6i | 0.0324551 | − | 0.0562140i |
(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 | 147.6.e.l.79.2 | 4 | ||
7.2 | even | 3 | 147.6.a.k.1.1 | 2 | |||
7.3 | odd | 6 | 21.6.e.b.4.2 | ✓ | 4 | ||
7.4 | even | 3 | inner | 147.6.e.l.67.2 | 4 | ||
7.5 | odd | 6 | 147.6.a.i.1.1 | 2 | |||
7.6 | odd | 2 | 21.6.e.b.16.2 | yes | 4 | ||
21.2 | odd | 6 | 441.6.a.s.1.2 | 2 | |||
21.5 | even | 6 | 441.6.a.t.1.2 | 2 | |||
21.17 | even | 6 | 63.6.e.c.46.1 | 4 | |||
21.20 | even | 2 | 63.6.e.c.37.1 | 4 | |||
28.3 | even | 6 | 336.6.q.e.193.2 | 4 | |||
28.27 | even | 2 | 336.6.q.e.289.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.6.e.b.4.2 | ✓ | 4 | 7.3 | odd | 6 | ||
21.6.e.b.16.2 | yes | 4 | 7.6 | odd | 2 | ||
63.6.e.c.37.1 | 4 | 21.20 | even | 2 | |||
63.6.e.c.46.1 | 4 | 21.17 | even | 6 | |||
147.6.a.i.1.1 | 2 | 7.5 | odd | 6 | |||
147.6.a.k.1.1 | 2 | 7.2 | even | 3 | |||
147.6.e.l.67.2 | 4 | 7.4 | even | 3 | inner | ||
147.6.e.l.79.2 | 4 | 1.1 | even | 1 | trivial | ||
336.6.q.e.193.2 | 4 | 28.3 | even | 6 | |||
336.6.q.e.289.2 | 4 | 28.27 | even | 2 | |||
441.6.a.s.1.2 | 2 | 21.2 | odd | 6 | |||
441.6.a.t.1.2 | 2 | 21.5 | even | 6 |