Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,6,Mod(6,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.6");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.c (of order \(3\), degree \(2\), 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: | \(6.89650425196\) |
Analytic rank: | \(0\) |
Dimension: | \(34\) |
Relative dimension: | \(17\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 36.1 | ||
Character | \(\chi\) | \(=\) | 43.36 |
Dual form | 43.6.c.a.6.1 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −10.9797 | −1.94096 | −0.970482 | − | 0.241175i | \(-0.922467\pi\) | ||||
−0.970482 | + | 0.241175i | \(0.922467\pi\) | |||||||
\(3\) | 8.65096 | + | 14.9839i | 0.554959 | + | 0.961218i | 0.997907 | + | 0.0646700i | \(0.0205995\pi\) |
−0.442947 | + | 0.896548i | \(0.646067\pi\) | |||||||
\(4\) | 88.5548 | 2.76734 | ||||||||
\(5\) | −5.02316 | − | 8.70037i | −0.0898571 | − | 0.155637i | 0.817594 | − | 0.575796i | \(-0.195308\pi\) |
−0.907451 | + | 0.420159i | \(0.861974\pi\) | |||||||
\(6\) | −94.9853 | − | 164.519i | −1.07716 | − | 1.86569i | ||||
\(7\) | 36.4175 | − | 63.0770i | 0.280909 | − | 0.486549i | −0.690700 | − | 0.723141i | \(-0.742697\pi\) |
0.971609 | + | 0.236593i | \(0.0760308\pi\) | |||||||
\(8\) | −620.957 | −3.43034 | ||||||||
\(9\) | −28.1782 | + | 48.8060i | −0.115959 | + | 0.200848i | ||||
\(10\) | 55.1531 | + | 95.5279i | 0.174409 | + | 0.302086i | ||||
\(11\) | 500.662 | 1.24757 | 0.623783 | − | 0.781598i | \(-0.285595\pi\) | ||||
0.623783 | + | 0.781598i | \(0.285595\pi\) | |||||||
\(12\) | 766.084 | + | 1326.90i | 1.53576 | + | 2.66001i | ||||
\(13\) | 376.594 | − | 652.280i | 0.618037 | − | 1.07047i | −0.371806 | − | 0.928310i | \(-0.621261\pi\) |
0.989843 | − | 0.142162i | \(-0.0454053\pi\) | |||||||
\(14\) | −399.855 | + | 692.570i | −0.545234 | + | 0.944373i | ||||
\(15\) | 86.9104 | − | 150.533i | 0.0997340 | − | 0.172744i | ||||
\(16\) | 3984.20 | 3.89082 | ||||||||
\(17\) | −829.023 | + | 1435.91i | −0.695736 | + | 1.20505i | 0.274196 | + | 0.961674i | \(0.411588\pi\) |
−0.969932 | + | 0.243376i | \(0.921745\pi\) | |||||||
\(18\) | 309.389 | − | 535.877i | 0.225073 | − | 0.389838i | ||||
\(19\) | 1131.01 | + | 1958.96i | 0.718755 | + | 1.24492i | 0.961493 | + | 0.274829i | \(0.0886211\pi\) |
−0.242738 | + | 0.970092i | \(0.578046\pi\) | |||||||
\(20\) | −444.825 | − | 770.460i | −0.248665 | − | 0.430700i | ||||
\(21\) | 1260.19 | 0.623572 | ||||||||
\(22\) | −5497.15 | −2.42148 | ||||||||
\(23\) | 20.0997 | + | 34.8138i | 0.00792265 | + | 0.0137224i | 0.869960 | − | 0.493123i | \(-0.164145\pi\) |
−0.862037 | + | 0.506846i | \(0.830811\pi\) | |||||||
\(24\) | −5371.88 | − | 9304.36i | −1.90370 | − | 3.29730i | ||||
\(25\) | 1512.04 | − | 2618.92i | 0.483851 | − | 0.838055i | ||||
\(26\) | −4134.90 | + | 7161.86i | −1.19959 | + | 2.07775i | ||||
\(27\) | 3229.29 | 0.852507 | ||||||||
\(28\) | 3224.95 | − | 5585.78i | 0.777370 | − | 1.34644i | ||||
\(29\) | −638.786 | + | 1106.41i | −0.141046 | + | 0.244299i | −0.927891 | − | 0.372852i | \(-0.878380\pi\) |
0.786845 | + | 0.617151i | \(0.211713\pi\) | |||||||
\(30\) | −954.254 | + | 1652.82i | −0.193580 | + | 0.335291i | ||||
\(31\) | 2826.10 | + | 4894.95i | 0.528182 | + | 0.914838i | 0.999460 | + | 0.0328537i | \(0.0104595\pi\) |
−0.471278 | + | 0.881985i | \(0.656207\pi\) | |||||||
\(32\) | −23874.9 | −4.12160 | ||||||||
\(33\) | 4331.21 | + | 7501.88i | 0.692348 | + | 1.19918i | ||||
\(34\) | 9102.46 | − | 15765.9i | 1.35040 | − | 2.33896i | ||||
\(35\) | −731.725 | −0.100967 | ||||||||
\(36\) | −2495.31 | + | 4322.01i | −0.320899 | + | 0.555813i | ||||
\(37\) | 1526.84 | + | 2644.57i | 0.183354 | + | 0.317578i | 0.943021 | − | 0.332734i | \(-0.107971\pi\) |
−0.759667 | + | 0.650313i | \(0.774638\pi\) | |||||||
\(38\) | −12418.2 | − | 21508.9i | −1.39508 | − | 2.41634i | ||||
\(39\) | 13031.6 | 1.37194 | ||||||||
\(40\) | 3119.17 | + | 5402.56i | 0.308240 | + | 0.533888i | ||||
\(41\) | −2618.84 | −0.243304 | −0.121652 | − | 0.992573i | \(-0.538819\pi\) | ||||
−0.121652 | + | 0.992573i | \(0.538819\pi\) | |||||||
\(42\) | −13836.5 | −1.21033 | ||||||||
\(43\) | −12059.1 | − | 1259.13i | −0.994593 | − | 0.103848i | ||||
\(44\) | 44336.1 | 3.45243 | ||||||||
\(45\) | 566.174 | 0.0416791 | ||||||||
\(46\) | −220.690 | − | 382.246i | −0.0153776 | − | 0.0266347i | ||||
\(47\) | 21065.7 | 1.39101 | 0.695506 | − | 0.718520i | \(-0.255180\pi\) | ||||
0.695506 | + | 0.718520i | \(0.255180\pi\) | |||||||
\(48\) | 34467.2 | + | 59698.9i | 2.15925 | + | 3.73993i | ||||
\(49\) | 5751.03 | + | 9961.07i | 0.342180 | + | 0.592674i | ||||
\(50\) | −16601.8 | + | 28755.1i | −0.939138 | + | 1.62663i | ||||
\(51\) | −28687.4 | −1.54442 | ||||||||
\(52\) | 33349.2 | − | 57762.5i | 1.71032 | − | 2.96236i | ||||
\(53\) | −17059.7 | − | 29548.2i | −0.834221 | − | 1.44491i | −0.894663 | − | 0.446741i | \(-0.852585\pi\) |
0.0604429 | − | 0.998172i | \(-0.480749\pi\) | |||||||
\(54\) | −35456.8 | −1.65469 | ||||||||
\(55\) | −2514.91 | − | 4355.95i | −0.112103 | − | 0.194167i | ||||
\(56\) | −22613.7 | + | 39168.2i | −0.963612 | + | 1.66903i | ||||
\(57\) | −19568.6 | + | 33893.8i | −0.797760 | + | 1.38176i | ||||
\(58\) | 7013.71 | − | 12148.1i | 0.273765 | − | 0.474175i | ||||
\(59\) | 17442.8 | 0.652358 | 0.326179 | − | 0.945308i | \(-0.394239\pi\) | ||||
0.326179 | + | 0.945308i | \(0.394239\pi\) | |||||||
\(60\) | 7696.33 | − | 13330.4i | 0.275998 | − | 0.478042i | ||||
\(61\) | 448.086 | − | 776.108i | 0.0154183 | − | 0.0267053i | −0.858213 | − | 0.513293i | \(-0.828425\pi\) |
0.873632 | + | 0.486588i | \(0.161759\pi\) | |||||||
\(62\) | −31029.9 | − | 53745.3i | −1.02518 | − | 1.77567i | ||||
\(63\) | 2052.36 | + | 3554.79i | 0.0651481 | + | 0.112840i | ||||
\(64\) | 134646. | 4.10906 | ||||||||
\(65\) | −7566.77 | −0.222140 | ||||||||
\(66\) | −47555.6 | − | 82368.7i | −1.34382 | − | 2.32757i | ||||
\(67\) | −20575.5 | − | 35637.9i | −0.559970 | − | 0.969896i | −0.997498 | − | 0.0706912i | \(-0.977480\pi\) |
0.437529 | − | 0.899204i | \(-0.355854\pi\) | |||||||
\(68\) | −73414.0 | + | 127157.i | −1.92534 | + | 3.33478i | ||||
\(69\) | −347.764 | + | 602.345i | −0.00879350 | + | 0.0152308i | ||||
\(70\) | 8034.16 | 0.195972 | ||||||||
\(71\) | 10965.4 | − | 18992.6i | 0.258153 | − | 0.447135i | −0.707594 | − | 0.706619i | \(-0.750219\pi\) |
0.965747 | + | 0.259485i | \(0.0835527\pi\) | |||||||
\(72\) | 17497.4 | − | 30306.4i | 0.397780 | − | 0.688975i | ||||
\(73\) | −19444.9 | + | 33679.6i | −0.427070 | + | 0.739707i | −0.996611 | − | 0.0822557i | \(-0.973788\pi\) |
0.569541 | + | 0.821963i | \(0.307121\pi\) | |||||||
\(74\) | −16764.3 | − | 29036.7i | −0.355883 | − | 0.616408i | ||||
\(75\) | 52322.2 | 1.07407 | ||||||||
\(76\) | 100156. | + | 173475.i | 1.98904 | + | 3.44512i | ||||
\(77\) | 18232.9 | − | 31580.3i | 0.350452 | − | 0.607001i | ||||
\(78\) | −143084. | −2.66289 | ||||||||
\(79\) | 45994.2 | − | 79664.2i | 0.829154 | − | 1.43614i | −0.0695491 | − | 0.997579i | \(-0.522156\pi\) |
0.898703 | − | 0.438558i | \(-0.144511\pi\) | |||||||
\(80\) | −20013.3 | − | 34664.0i | −0.349618 | − | 0.605556i | ||||
\(81\) | 34783.8 | + | 60247.3i | 0.589066 | + | 1.02029i | ||||
\(82\) | 28754.2 | 0.472244 | ||||||||
\(83\) | 39178.2 | + | 67858.7i | 0.624237 | + | 1.08121i | 0.988688 | + | 0.149988i | \(0.0479235\pi\) |
−0.364450 | + | 0.931223i | \(0.618743\pi\) | |||||||
\(84\) | 111596. | 1.72563 | ||||||||
\(85\) | 16657.3 | 0.250067 | ||||||||
\(86\) | 132406. | + | 13824.9i | 1.93047 | + | 0.201566i | ||||
\(87\) | −22104.4 | −0.313099 | ||||||||
\(88\) | −310890. | −4.27957 | ||||||||
\(89\) | −28420.5 | − | 49225.7i | −0.380326 | − | 0.658744i | 0.610783 | − | 0.791798i | \(-0.290855\pi\) |
−0.991109 | + | 0.133054i | \(0.957522\pi\) | |||||||
\(90\) | −6216.44 | −0.0808976 | ||||||||
\(91\) | −27429.2 | − | 47508.8i | −0.347224 | − | 0.601410i | ||||
\(92\) | 1779.93 | + | 3082.93i | 0.0219247 | + | 0.0379746i | ||||
\(93\) | −48897.0 | + | 84692.1i | −0.586239 | + | 1.01540i | ||||
\(94\) | −231296. | −2.69990 | ||||||||
\(95\) | 11362.5 | − | 19680.4i | 0.129170 | − | 0.223730i | ||||
\(96\) | −206541. | − | 357739.i | −2.28732 | − | 3.96176i | ||||
\(97\) | −331.126 | −0.00357325 | −0.00178663 | − | 0.999998i | \(-0.500569\pi\) | ||||
−0.00178663 | + | 0.999998i | \(0.500569\pi\) | |||||||
\(98\) | −63144.8 | − | 109370.i | −0.664159 | − | 1.15036i | ||||
\(99\) | −14107.7 | + | 24435.3i | −0.144667 | + | 0.250571i | ||||
\(100\) | 133898. | − | 231918.i | 1.33898 | − | 2.31918i | ||||
\(101\) | 37817.0 | − | 65501.0i | 0.368879 | − | 0.638917i | −0.620511 | − | 0.784197i | \(-0.713075\pi\) |
0.989391 | + | 0.145280i | \(0.0464083\pi\) | |||||||
\(102\) | 314980. | 2.99766 | ||||||||
\(103\) | −47711.9 | + | 82639.4i | −0.443132 | + | 0.767528i | −0.997920 | − | 0.0644642i | \(-0.979466\pi\) |
0.554788 | + | 0.831992i | \(0.312800\pi\) | |||||||
\(104\) | −233849. | + | 405038.i | −2.12008 | + | 3.67208i | ||||
\(105\) | −6330.12 | − | 10964.1i | −0.0560324 | − | 0.0970509i | ||||
\(106\) | 187311. | + | 324432.i | 1.61919 | + | 2.80452i | ||||
\(107\) | −67921.9 | −0.573522 | −0.286761 | − | 0.958002i | \(-0.592579\pi\) | ||||
−0.286761 | + | 0.958002i | \(0.592579\pi\) | |||||||
\(108\) | 285969. | 2.35918 | ||||||||
\(109\) | 30174.0 | + | 52263.0i | 0.243258 | + | 0.421335i | 0.961640 | − | 0.274313i | \(-0.0884505\pi\) |
−0.718382 | + | 0.695648i | \(0.755117\pi\) | |||||||
\(110\) | 27613.1 | + | 47827.2i | 0.217587 | + | 0.376872i | ||||
\(111\) | −26417.3 | + | 45756.1i | −0.203508 | + | 0.352486i | ||||
\(112\) | 145095. | − | 251312.i | 1.09297 | − | 1.89307i | ||||
\(113\) | −49345.3 | −0.363538 | −0.181769 | − | 0.983341i | \(-0.558182\pi\) | ||||
−0.181769 | + | 0.983341i | \(0.558182\pi\) | |||||||
\(114\) | 214858. | − | 372145.i | 1.54842 | − | 2.68195i | ||||
\(115\) | 201.928 | − | 349.750i | 0.00142381 | − | 0.00246612i | ||||
\(116\) | −56567.6 | + | 97977.9i | −0.390322 | + | 0.676057i | ||||
\(117\) | 21223.4 | + | 36760.1i | 0.143335 | + | 0.248263i | ||||
\(118\) | −191517. | −1.26620 | ||||||||
\(119\) | 60382.0 | + | 104585.i | 0.390877 | + | 0.677019i | ||||
\(120\) | −53967.6 | + | 93474.7i | −0.342121 | + | 0.592572i | ||||
\(121\) | 89611.9 | 0.556419 | ||||||||
\(122\) | −4919.87 | + | 8521.47i | −0.0299264 | + | 0.0518340i | ||||
\(123\) | −22655.5 | − | 39240.4i | −0.135024 | − | 0.233868i | ||||
\(124\) | 250265. | + | 433472.i | 1.46166 | + | 2.53167i | ||||
\(125\) | −61775.6 | −0.353624 | ||||||||
\(126\) | −22534.4 | − | 39030.7i | −0.126450 | − | 0.219018i | ||||
\(127\) | −122729. | −0.675206 | −0.337603 | − | 0.941289i | \(-0.609616\pi\) | ||||
−0.337603 | + | 0.941289i | \(0.609616\pi\) | |||||||
\(128\) | −714379. | −3.85393 | ||||||||
\(129\) | −85456.5 | − | 191586.i | −0.452138 | − | 1.01365i | ||||
\(130\) | 83081.2 | 0.431166 | ||||||||
\(131\) | −134688. | −0.685727 | −0.342863 | − | 0.939385i | \(-0.611397\pi\) | ||||
−0.342863 | + | 0.939385i | \(0.611397\pi\) | |||||||
\(132\) | 383549. | + | 664327.i | 1.91596 | + | 3.31854i | ||||
\(133\) | 164754. | 0.807619 | ||||||||
\(134\) | 225914. | + | 391295.i | 1.08688 | + | 1.88253i | ||||
\(135\) | −16221.3 | − | 28096.1i | −0.0766038 | − | 0.132682i | ||||
\(136\) | 514788. | − | 891639.i | 2.38661 | − | 4.13373i | ||||
\(137\) | 282687. | 1.28678 | 0.643391 | − | 0.765538i | \(-0.277527\pi\) | ||||
0.643391 | + | 0.765538i | \(0.277527\pi\) | |||||||
\(138\) | 3818.36 | − | 6613.59i | 0.0170679 | − | 0.0295624i | ||||
\(139\) | −208305. | − | 360795.i | −0.914457 | − | 1.58389i | −0.807694 | − | 0.589602i | \(-0.799285\pi\) |
−0.106764 | − | 0.994284i | \(-0.534049\pi\) | |||||||
\(140\) | −64797.8 | −0.279409 | ||||||||
\(141\) | 182238. | + | 315646.i | 0.771955 | + | 1.33707i | ||||
\(142\) | −120397. | + | 208534.i | −0.501066 | + | 0.867872i | ||||
\(143\) | 188546. | − | 326572.i | 0.771042 | − | 1.33548i | ||||
\(144\) | −112267. | + | 194453.i | −0.451178 | + | 0.781462i | ||||
\(145\) | 12834.9 | 0.0506959 | ||||||||
\(146\) | 213500. | − | 369793.i | 0.828927 | − | 1.43574i | ||||
\(147\) | −99503.8 | + | 172346.i | −0.379792 | + | 0.657820i | ||||
\(148\) | 135209. | + | 234189.i | 0.507402 | + | 0.878846i | ||||
\(149\) | 49843.7 | + | 86331.8i | 0.183927 | + | 0.318570i | 0.943214 | − | 0.332185i | \(-0.107786\pi\) |
−0.759288 | + | 0.650755i | \(0.774452\pi\) | |||||||
\(150\) | −574485. | −2.08473 | ||||||||
\(151\) | −538696. | −1.92265 | −0.961327 | − | 0.275409i | \(-0.911187\pi\) | ||||
−0.961327 | + | 0.275409i | \(0.911187\pi\) | |||||||
\(152\) | −702307. | − | 1.21643e6i | −2.46557 | − | 4.27050i | ||||
\(153\) | −46720.7 | − | 80922.6i | −0.161354 | − | 0.279474i | ||||
\(154\) | −200193. | + | 346744.i | −0.680215 | + | 1.17817i | ||||
\(155\) | 28392.0 | − | 49176.3i | 0.0949218 | − | 0.164409i | ||||
\(156\) | 1.15401e6 | 3.79663 | ||||||||
\(157\) | 24542.7 | − | 42509.2i | 0.0794645 | − | 0.137637i | −0.823555 | − | 0.567237i | \(-0.808012\pi\) |
0.903019 | + | 0.429601i | \(0.141346\pi\) | |||||||
\(158\) | −505004. | + | 874693.i | −1.60936 | + | 2.78749i | ||||
\(159\) | 295165. | − | 511241.i | 0.925917 | − | 1.60373i | ||||
\(160\) | 119927. | + | 207720.i | 0.370355 | + | 0.641474i | ||||
\(161\) | 2927.93 | 0.00890218 | ||||||||
\(162\) | −381917. | − | 661500.i | −1.14336 | − | 1.98035i | ||||
\(163\) | −267536. | + | 463386.i | −0.788703 | + | 1.36607i | 0.138059 | + | 0.990424i | \(0.455914\pi\) |
−0.926762 | + | 0.375649i | \(0.877420\pi\) | |||||||
\(164\) | −231911. | −0.673305 | ||||||||
\(165\) | 43512.7 | − | 75366.3i | 0.124425 | − | 0.215510i | ||||
\(166\) | −430167. | − | 745071.i | −1.21162 | − | 2.09859i | ||||
\(167\) | −2529.34 | − | 4380.94i | −0.00701803 | − | 0.0121556i | 0.862495 | − | 0.506065i | \(-0.168901\pi\) |
−0.869513 | + | 0.493910i | \(0.835567\pi\) | |||||||
\(168\) | −782522. | −2.13906 | ||||||||
\(169\) | −97999.3 | − | 169740.i | −0.263941 | − | 0.457159i | ||||
\(170\) | −182893. | −0.485371 | ||||||||
\(171\) | −127479. | −0.333386 | ||||||||
\(172\) | −1.06790e6 | − | 111502.i | −2.75238 | − | 0.287384i | ||||
\(173\) | −313445. | −0.796244 | −0.398122 | − | 0.917332i | \(-0.630338\pi\) | ||||
−0.398122 | + | 0.917332i | \(0.630338\pi\) | |||||||
\(174\) | 242701. | 0.607713 | ||||||||
\(175\) | −110129. | − | 190749.i | −0.271836 | − | 0.470834i | ||||
\(176\) | 1.99474e6 | 4.85405 | ||||||||
\(177\) | 150897. | + | 261361.i | 0.362032 | + | 0.627058i | ||||
\(178\) | 312050. | + | 540486.i | 0.738199 | + | 1.27860i | ||||
\(179\) | 108557. | − | 188026.i | 0.253236 | − | 0.438617i | −0.711179 | − | 0.703011i | \(-0.751839\pi\) |
0.964415 | + | 0.264394i | \(0.0851719\pi\) | |||||||
\(180\) | 50137.4 | 0.115340 | ||||||||
\(181\) | −192913. | + | 334134.i | −0.437687 | + | 0.758097i | −0.997511 | − | 0.0705153i | \(-0.977536\pi\) |
0.559823 | + | 0.828612i | \(0.310869\pi\) | |||||||
\(182\) | 301166. | + | 521635.i | 0.673950 | + | 1.16732i | ||||
\(183\) | 15505.5 | 0.0342261 | ||||||||
\(184\) | −12481.1 | − | 21617.9i | −0.0271774 | − | 0.0470726i | ||||
\(185\) | 15339.2 | − | 26568.2i | 0.0329513 | − | 0.0570733i | ||||
\(186\) | 536877. | − | 929898.i | 1.13787 | − | 1.97085i | ||||
\(187\) | −415061. | + | 718906.i | −0.867976 | + | 1.50338i | ||||
\(188\) | 1.86547e6 | 3.84940 | ||||||||
\(189\) | 117603. | − | 203694.i | 0.239477 | − | 0.414786i | ||||
\(190\) | −124757. | + | 216085.i | −0.250715 | + | 0.434251i | ||||
\(191\) | −146123. | − | 253092.i | −0.289824 | − | 0.501991i | 0.683943 | − | 0.729535i | \(-0.260264\pi\) |
−0.973768 | + | 0.227545i | \(0.926930\pi\) | |||||||
\(192\) | 1.16481e6 | + | 2.01752e6i | 2.28036 | + | 3.94970i | ||||
\(193\) | 159495. | 0.308216 | 0.154108 | − | 0.988054i | \(-0.450750\pi\) | ||||
0.154108 | + | 0.988054i | \(0.450750\pi\) | |||||||
\(194\) | 3635.68 | 0.00693555 | ||||||||
\(195\) | −65459.8 | − | 113380.i | −0.123279 | − | 0.213525i | ||||
\(196\) | 509281. | + | 882100.i | 0.946929 | + | 1.64013i | ||||
\(197\) | 335011. | − | 580255.i | 0.615025 | − | 1.06525i | −0.375355 | − | 0.926881i | \(-0.622479\pi\) |
0.990380 | − | 0.138374i | \(-0.0441875\pi\) | |||||||
\(198\) | 154899. | − | 268294.i | 0.280793 | − | 0.486348i | ||||
\(199\) | −209704. | −0.375383 | −0.187692 | − | 0.982228i | \(-0.560101\pi\) | ||||
−0.187692 | + | 0.982228i | \(0.560101\pi\) | |||||||
\(200\) | −938910. | + | 1.62624e6i | −1.65977 | + | 2.87481i | ||||
\(201\) | 355996. | − | 616604.i | 0.621520 | − | 1.07651i | ||||
\(202\) | −415221. | + | 719185.i | −0.715981 | + | 1.24012i | ||||
\(203\) | 46526.0 | + | 80585.5i | 0.0792421 | + | 0.137251i | ||||
\(204\) | −2.54041e6 | −4.27393 | ||||||||
\(205\) | 13154.9 | + | 22784.9i | 0.0218626 | + | 0.0378671i | ||||
\(206\) | 523864. | − | 907360.i | 0.860104 | − | 1.48974i | ||||
\(207\) | −2265.49 | −0.00367483 | ||||||||
\(208\) | 1.50043e6 | − | 2.59881e6i | 2.40467 | − | 4.16502i | ||||
\(209\) | 566252. | + | 980778.i | 0.896694 | + | 1.55312i | ||||
\(210\) | 69503.1 | + | 120383.i | 0.108757 | + | 0.188372i | ||||
\(211\) | 12638.9 | 0.0195435 | 0.00977177 | − | 0.999952i | \(-0.496890\pi\) | ||||
0.00977177 | + | 0.999952i | \(0.496890\pi\) | |||||||
\(212\) | −1.51072e6 | − | 2.61664e6i | −2.30857 | − | 3.99856i | ||||
\(213\) | 379444. | 0.573058 | ||||||||
\(214\) | 745765. | 1.11319 | ||||||||
\(215\) | 49620.2 | + | 111244.i | 0.0732086 | + | 0.164127i | ||||
\(216\) | −2.00525e6 | −2.92439 | ||||||||
\(217\) | 411679. | 0.593484 | ||||||||
\(218\) | −331303. | − | 573834.i | −0.472155 | − | 0.817796i | ||||
\(219\) | −672869. | −0.948026 | ||||||||
\(220\) | −222707. | − | 385740.i | −0.310226 | − | 0.537327i | ||||
\(221\) | 624410. | + | 1.08151e6i | 0.859982 | + | 1.48953i | ||||
\(222\) | 290055. | − | 502391.i | 0.395001 | − | 0.684162i | ||||
\(223\) | −280171. | −0.377278 | −0.188639 | − | 0.982047i | \(-0.560408\pi\) | ||||
−0.188639 | + | 0.982047i | \(0.560408\pi\) | |||||||
\(224\) | −869464. | + | 1.50596e6i | −1.15780 | + | 2.00536i | ||||
\(225\) | 85212.7 | + | 147593.i | 0.112214 | + | 0.194361i | ||||
\(226\) | 541798. | 0.705613 | ||||||||
\(227\) | −259056. | − | 448698.i | −0.333679 | − | 0.577950i | 0.649551 | − | 0.760318i | \(-0.274957\pi\) |
−0.983230 | + | 0.182369i | \(0.941624\pi\) | |||||||
\(228\) | −1.73289e6 | + | 3.00146e6i | −2.20767 | + | 3.82380i | ||||
\(229\) | 109788. | − | 190158.i | 0.138346 | − | 0.239622i | −0.788525 | − | 0.615003i | \(-0.789155\pi\) |
0.926871 | + | 0.375381i | \(0.122488\pi\) | |||||||
\(230\) | −2217.12 | + | 3840.17i | −0.00276357 | + | 0.00478664i | ||||
\(231\) | 630928. | 0.777947 | ||||||||
\(232\) | 396659. | − | 687033.i | 0.483835 | − | 0.838027i | ||||
\(233\) | −466639. | + | 808242.i | −0.563107 | + | 0.975330i | 0.434116 | + | 0.900857i | \(0.357061\pi\) |
−0.997223 | + | 0.0744733i | \(0.976272\pi\) | |||||||
\(234\) | −233028. | − | 403616.i | −0.278207 | − | 0.481869i | ||||
\(235\) | −105816. | − | 183279.i | −0.124992 | − | 0.216493i | ||||
\(236\) | 1.54464e6 | 1.80529 | ||||||||
\(237\) | 1.59157e6 | 1.84059 | ||||||||
\(238\) | −662979. | − | 1.14831e6i | −0.758678 | − | 1.31407i | ||||
\(239\) | −373296. | − | 646567.i | −0.422725 | − | 0.732181i | 0.573480 | − | 0.819220i | \(-0.305593\pi\) |
−0.996205 | + | 0.0870383i | \(0.972260\pi\) | |||||||
\(240\) | 346268. | − | 599754.i | 0.388047 | − | 0.672118i | ||||
\(241\) | −563630. | + | 976236.i | −0.625103 | + | 1.08271i | 0.363418 | + | 0.931626i | \(0.381610\pi\) |
−0.988521 | + | 0.151084i | \(0.951724\pi\) | |||||||
\(242\) | −983916. | −1.07999 | ||||||||
\(243\) | −209467. | + | 362807.i | −0.227562 | + | 0.394149i | ||||
\(244\) | 39680.2 | − | 68728.1i | 0.0426677 | − | 0.0739026i | ||||
\(245\) | 57776.7 | − | 100072.i | 0.0614947 | − | 0.106512i | ||||
\(246\) | 248751. | + | 430850.i | 0.262076 | + | 0.453929i | ||||
\(247\) | 1.70372e6 | 1.77687 | ||||||||
\(248\) | −1.75489e6 | − | 3.03956e6i | −1.81184 | − | 3.13820i | ||||
\(249\) | −677859. | + | 1.17409e6i | −0.692853 | + | 1.20006i | ||||
\(250\) | 678280. | 0.686371 | ||||||||
\(251\) | −440706. | + | 763326.i | −0.441535 | + | 0.764761i | −0.997804 | − | 0.0662417i | \(-0.978899\pi\) |
0.556269 | + | 0.831002i | \(0.312232\pi\) | |||||||
\(252\) | 181746. | + | 314794.i | 0.180287 | + | 0.312266i | ||||
\(253\) | 10063.2 | + | 17429.9i | 0.00988403 | + | 0.0171196i | ||||
\(254\) | 1.34753e6 | 1.31055 | ||||||||
\(255\) | 144101. | + | 249591.i | 0.138777 | + | 0.240369i | ||||
\(256\) | 3.53504e6 | 3.37127 | ||||||||
\(257\) | 585552. | 0.553009 | 0.276505 | − | 0.961013i | \(-0.410824\pi\) | ||||
0.276505 | + | 0.961013i | \(0.410824\pi\) | |||||||
\(258\) | 938290. | + | 2.10356e6i | 0.877583 | + | 1.96746i | ||||
\(259\) | 222416. | 0.206023 | ||||||||
\(260\) | −670074. | −0.614737 | ||||||||
\(261\) | −35999.6 | − | 62353.2i | −0.0327112 | − | 0.0566575i | ||||
\(262\) | 1.47884e6 | 1.33097 | ||||||||
\(263\) | 21088.5 | + | 36526.4i | 0.0187999 | + | 0.0325625i | 0.875272 | − | 0.483630i | \(-0.160682\pi\) |
−0.856472 | + | 0.516193i | \(0.827349\pi\) | |||||||
\(264\) | −2.68950e6 | − | 4.65835e6i | −2.37499 | − | 4.11360i | ||||
\(265\) | −171387. | + | 296851.i | −0.149921 | + | 0.259671i | ||||
\(266\) | −1.80896e6 | −1.56756 | ||||||||
\(267\) | 491729. | − | 851699.i | 0.422131 | − | 0.731152i | ||||
\(268\) | −1.82206e6 | − | 3.15591e6i | −1.54962 | − | 2.68403i | ||||
\(269\) | 124175. | 0.104629 | 0.0523147 | − | 0.998631i | \(-0.483340\pi\) | ||||
0.0523147 | + | 0.998631i | \(0.483340\pi\) | |||||||
\(270\) | 178105. | + | 308488.i | 0.148685 | + | 0.257530i | ||||
\(271\) | 23151.5 | − | 40099.6i | 0.0191495 | − | 0.0331678i | −0.856292 | − | 0.516492i | \(-0.827237\pi\) |
0.875441 | + | 0.483324i | \(0.160571\pi\) | |||||||
\(272\) | −3.30300e6 | + | 5.72096e6i | −2.70698 | + | 4.68863i | ||||
\(273\) | 474578. | − | 821994.i | 0.385391 | − | 0.667517i | ||||
\(274\) | −3.10383e6 | −2.49760 | ||||||||
\(275\) | 757019. | − | 1.31120e6i | 0.603636 | − | 1.04553i | ||||
\(276\) | −30796.2 | + | 53340.5i | −0.0243346 | + | 0.0421487i | ||||
\(277\) | 558590. | + | 967507.i | 0.437415 | + | 0.757626i | 0.997489 | − | 0.0708170i | \(-0.0225606\pi\) |
−0.560074 | + | 0.828443i | \(0.689227\pi\) | |||||||
\(278\) | 2.28714e6 | + | 3.96144e6i | 1.77493 | + | 3.07427i | ||||
\(279\) | −318537. | −0.244991 | ||||||||
\(280\) | 454370. | 0.346350 | ||||||||
\(281\) | −493131. | − | 854128.i | −0.372560 | − | 0.645293i | 0.617399 | − | 0.786651i | \(-0.288187\pi\) |
−0.989959 | + | 0.141358i | \(0.954853\pi\) | |||||||
\(282\) | −2.00093e6 | − | 3.46571e6i | −1.49834 | − | 2.59520i | ||||
\(283\) | −204863. | + | 354834.i | −0.152054 | + | 0.263365i | −0.931982 | − | 0.362503i | \(-0.881922\pi\) |
0.779928 | + | 0.625869i | \(0.215255\pi\) | |||||||
\(284\) | 971037. | − | 1.68188e6i | 0.714397 | − | 1.23737i | ||||
\(285\) | 393185. | 0.286737 | ||||||||
\(286\) | −2.07019e6 | + | 3.58568e6i | −1.49656 | + | 2.59213i | ||||
\(287\) | −95371.7 | + | 165189.i | −0.0683463 | + | 0.118379i | ||||
\(288\) | 672750. | − | 1.16524e6i | 0.477939 | − | 0.827814i | ||||
\(289\) | −664631. | − | 1.15117e6i | −0.468097 | − | 0.810768i | ||||
\(290\) | −140924. | −0.0983988 | ||||||||
\(291\) | −2864.56 | − | 4961.56i | −0.00198301 | − | 0.00343467i | ||||
\(292\) | −1.72194e6 | + | 2.98249e6i | −1.18185 | + | 2.04702i | ||||
\(293\) | −224494. | −0.152769 | −0.0763844 | − | 0.997078i | \(-0.524338\pi\) | ||||
−0.0763844 | + | 0.997078i | \(0.524338\pi\) | |||||||
\(294\) | 1.09253e6 | − | 1.89231e6i | 0.737163 | − | 1.27680i | ||||
\(295\) | −87617.9 | − | 151759.i | −0.0586189 | − | 0.101531i | ||||
\(296\) | −948105. | − | 1.64217e6i | −0.628966 | − | 1.08940i | ||||
\(297\) | 1.61679e6 | 1.06356 | ||||||||
\(298\) | −547271. | − | 947901.i | −0.356995 | − | 0.618333i | ||||
\(299\) | 30277.7 | 0.0195860 | ||||||||
\(300\) | 4.63339e6 | 2.97232 | ||||||||
\(301\) | −518587. | + | 714801.i | −0.329917 | + | 0.454746i | ||||
\(302\) | 5.91474e6 | 3.73180 | ||||||||
\(303\) | 1.30861e6 | 0.818852 | ||||||||
\(304\) | 4.50616e6 | + | 7.80489e6i | 2.79655 | + | 4.84376i | ||||
\(305\) | −9003.24 | −0.00554178 | ||||||||
\(306\) | 512981. | + | 888510.i | 0.313183 | + | 0.542449i | ||||
\(307\) | −936168. | − | 1.62149e6i | −0.566902 | − | 0.981903i | −0.996870 | − | 0.0790590i | \(-0.974808\pi\) |
0.429968 | − | 0.902844i | \(-0.358525\pi\) | |||||||
\(308\) | 1.61461e6 | − | 2.79659e6i | 0.969820 | − | 1.67978i | ||||
\(309\) | −1.65101e6 | −0.983682 | ||||||||
\(310\) | −311736. | + | 539943.i | −0.184240 | + | 0.319113i | ||||
\(311\) | −166912. | − | 289099.i | −0.0978555 | − | 0.169491i | 0.812941 | − | 0.582346i | \(-0.197865\pi\) |
−0.910797 | + | 0.412855i | \(0.864532\pi\) | |||||||
\(312\) | −8.09206e6 | −4.70623 | ||||||||
\(313\) | −1.50992e6 | − | 2.61526e6i | −0.871151 | − | 1.50888i | −0.860807 | − | 0.508931i | \(-0.830041\pi\) |
−0.0103440 | − | 0.999946i | \(-0.503293\pi\) | |||||||
\(314\) | −269473. | + | 466740.i | −0.154238 | + | 0.267148i | ||||
\(315\) | 20618.7 | − | 35712.6i | 0.0117080 | − | 0.0202789i | ||||
\(316\) | 4.07301e6 | − | 7.05465e6i | 2.29455 | − | 3.97427i | ||||
\(317\) | −2.97812e6 | −1.66454 | −0.832269 | − | 0.554371i | \(-0.812959\pi\) | ||||
−0.832269 | + | 0.554371i | \(0.812959\pi\) | |||||||
\(318\) | −3.24084e6 | + | 5.61329e6i | −1.79717 | + | 3.11279i | ||||
\(319\) | −319816. | + | 553938.i | −0.175964 | + | 0.304779i | ||||
\(320\) | −676347. | − | 1.17147e6i | −0.369228 | − | 0.639522i | ||||
\(321\) | −587589. | − | 1.01773e6i | −0.318282 | − | 0.551280i | ||||
\(322\) | −32147.9 | −0.0172788 | ||||||||
\(323\) | −3.75052e6 | −2.00025 | ||||||||
\(324\) | 3.08027e6 | + | 5.33519e6i | 1.63015 | + | 2.82349i | ||||
\(325\) | −1.13885e6 | − | 1.97254e6i | −0.598077 | − | 1.03590i | ||||
\(326\) | 2.93748e6 | − | 5.08786e6i | 1.53084 | − | 2.65150i | ||||
\(327\) | −522069. | + | 904250.i | −0.269997 | + | 0.467648i | ||||
\(328\) | 1.62619e6 | 0.834615 | ||||||||
\(329\) | 767161. | − | 1.32876e6i | 0.390748 | − | 0.676795i | ||||
\(330\) | −477759. | + | 827503.i | −0.241504 | + | 0.418297i | ||||
\(331\) | −906110. | + | 1.56943e6i | −0.454581 | + | 0.787357i | −0.998664 | − | 0.0516745i | \(-0.983544\pi\) |
0.544083 | + | 0.839031i | \(0.316877\pi\) | |||||||
\(332\) | 3.46942e6 | + | 6.00922e6i | 1.72748 | + | 2.99208i | ||||
\(333\) | −172094. | −0.0850465 | ||||||||
\(334\) | 27771.5 | + | 48101.6i | 0.0136217 | + | 0.0235936i | ||||
\(335\) | −206709. | + | 358030.i | −0.100634 | + | 0.174304i | ||||
\(336\) | 5.02084e6 | 2.42621 | ||||||||
\(337\) | −486844. | + | 843239.i | −0.233515 | + | 0.404460i | −0.958840 | − | 0.283946i | \(-0.908356\pi\) |
0.725325 | + | 0.688407i | \(0.241690\pi\) | |||||||
\(338\) | 1.07601e6 | + | 1.86370e6i | 0.512299 | + | 0.887328i | ||||
\(339\) | −426884. | − | 739384.i | −0.201749 | − | 0.349439i | ||||
\(340\) | 1.47508e6 | 0.692020 | ||||||||
\(341\) | 1.41492e6 | + | 2.45072e6i | 0.658942 | + | 1.14132i | ||||
\(342\) | 1.39968e6 | 0.647090 | ||||||||
\(343\) | 2.06189e6 | 0.946304 | ||||||||
\(344\) | 7.48822e6 | + | 781867.i | 3.41179 | + | 0.356235i | ||||
\(345\) | 6987.50 | 0.00316063 | ||||||||
\(346\) | 3.44155e6 | 1.54548 | ||||||||
\(347\) | −1.60766e6 | − | 2.78454e6i | −0.716753 | − | 1.24145i | −0.962280 | − | 0.272062i | \(-0.912294\pi\) |
0.245527 | − | 0.969390i | \(-0.421039\pi\) | |||||||
\(348\) | −1.95745e6 | −0.866450 | ||||||||
\(349\) | 746288. | + | 1.29261e6i | 0.327977 | + | 0.568072i | 0.982110 | − | 0.188307i | \(-0.0603000\pi\) |
−0.654134 | + | 0.756379i | \(0.726967\pi\) | |||||||
\(350\) | 1.20919e6 | + | 2.09438e6i | 0.527624 | + | 0.913872i | ||||
\(351\) | 1.21613e6 | − | 2.10640e6i | 0.526881 | − | 0.912586i | ||||
\(352\) | −1.19533e7 | −5.14197 | ||||||||
\(353\) | −1.81167e6 | + | 3.13790e6i | −0.773822 | + | 1.34030i | 0.161631 | + | 0.986851i | \(0.448324\pi\) |
−0.935454 | + | 0.353449i | \(0.885009\pi\) | |||||||
\(354\) | −1.65681e6 | − | 2.86968e6i | −0.702691 | − | 1.21710i | ||||
\(355\) | −220323. | −0.0927876 | ||||||||
\(356\) | −2.51677e6 | − | 4.35917e6i | −1.05249 | − | 1.82297i | ||||
\(357\) | −1.04472e6 | + | 1.80952e6i | −0.433841 | + | 0.751435i | ||||
\(358\) | −1.19193e6 | + | 2.06448e6i | −0.491521 | + | 0.851339i | ||||
\(359\) | 551097. | − | 954528.i | 0.225679 | − | 0.390888i | −0.730844 | − | 0.682545i | \(-0.760873\pi\) |
0.956523 | + | 0.291657i | \(0.0942065\pi\) | |||||||
\(360\) | −351570. | −0.142973 | ||||||||
\(361\) | −1.32030e6 | + | 2.28683e6i | −0.533218 | + | 0.923560i | ||||
\(362\) | 2.11813e6 | − | 3.66871e6i | 0.849535 | − | 1.47144i | ||||
\(363\) | 775229. | + | 1.34274e6i | 0.308790 | + | 0.534840i | ||||
\(364\) | −2.42899e6 | − | 4.20714e6i | −0.960888 | − | 1.66431i | ||||
\(365\) | 390700. | 0.153501 | ||||||||
\(366\) | −170246. | −0.0664317 | ||||||||
\(367\) | −1.06747e6 | − | 1.84891e6i | −0.413704 | − | 0.716557i | 0.581587 | − | 0.813484i | \(-0.302432\pi\) |
−0.995291 | + | 0.0969272i | \(0.969099\pi\) | |||||||
\(368\) | 80081.4 | + | 138705.i | 0.0308256 | + | 0.0533916i | ||||
\(369\) | 73794.1 | − | 127815.i | 0.0282134 | − | 0.0488671i | ||||
\(370\) | −168420. | + | 291712.i | −0.0639572 | + | 0.110777i | ||||
\(371\) | −2.48508e6 | −0.937360 | ||||||||
\(372\) | −4.33006e6 | + | 7.49989e6i | −1.62232 | + | 2.80994i | ||||
\(373\) | 2.18818e6 | − | 3.79004e6i | 0.814350 | − | 1.41050i | −0.0954433 | − | 0.995435i | \(-0.530427\pi\) |
0.909794 | − | 0.415061i | \(-0.136240\pi\) | |||||||
\(374\) | 4.55726e6 | − | 7.89341e6i | 1.68471 | − | 2.91800i | ||||
\(375\) | −534418. | − | 925639.i | −0.196247 | − | 0.339910i | ||||
\(376\) | −1.30809e7 | −4.77164 | ||||||||
\(377\) | 481126. | + | 833334.i | 0.174343 | + | 0.301971i | ||||
\(378\) | −1.29125e6 | + | 2.23651e6i | −0.464816 | + | 0.805085i | ||||
\(379\) | 147627. | 0.0527918 | 0.0263959 | − | 0.999652i | \(-0.491597\pi\) | ||||
0.0263959 | + | 0.999652i | \(0.491597\pi\) | |||||||
\(380\) | 1.00620e6 | − | 1.74279e6i | 0.357458 | − | 0.619136i | ||||
\(381\) | −1.06172e6 | − | 1.83895e6i | −0.374712 | − | 0.649020i | ||||
\(382\) | 1.60439e6 | + | 2.77889e6i | 0.562539 | + | 0.974345i | ||||
\(383\) | 4.70208e6 | 1.63792 | 0.818961 | − | 0.573850i | \(-0.194551\pi\) | ||||
0.818961 | + | 0.573850i | \(0.194551\pi\) | |||||||
\(384\) | −6.18006e6 | − | 1.07042e7i | −2.13877 | − | 3.70446i | ||||
\(385\) | −366347. | −0.125962 | ||||||||
\(386\) | −1.75122e6 | −0.598236 | ||||||||
\(387\) | 401258. | − | 553079.i | 0.136190 | − | 0.187720i | ||||
\(388\) | −29322.8 | −0.00988840 | ||||||||
\(389\) | 1.57266e6 | 0.526941 | 0.263471 | − | 0.964667i | \(-0.415133\pi\) | ||||
0.263471 | + | 0.964667i | \(0.415133\pi\) | |||||||
\(390\) | 718732. | + | 1.24488e6i | 0.239279 | + | 0.414444i | ||||
\(391\) | −66652.6 | −0.0220483 | ||||||||
\(392\) | −3.57114e6 | − | 6.18540e6i | −1.17379 | − | 2.03307i | ||||
\(393\) | −1.16518e6 | − | 2.01815e6i | −0.380550 | − | 0.659133i | ||||
\(394\) | −3.67833e6 | + | 6.37105e6i | −1.19374 | + | 2.06762i | ||||
\(395\) | −924145. | −0.298021 | ||||||||
\(396\) | −1.24931e6 | + | 2.16387e6i | −0.400343 | + | 0.693414i | ||||
\(397\) | 2.57403e6 | + | 4.45835e6i | 0.819666 | + | 1.41970i | 0.905928 | + | 0.423431i | \(0.139174\pi\) |
−0.0862623 | + | 0.996272i | \(0.527492\pi\) | |||||||
\(398\) | 2.30250e6 | 0.728605 | ||||||||
\(399\) | 1.42528e6 | + | 2.46866e6i | 0.448196 | + | 0.776298i | ||||
\(400\) | 6.02425e6 | − | 1.04343e7i | 1.88258 | − | 3.26072i | ||||
\(401\) | 567285. | − | 982566.i | 0.176173 | − | 0.305141i | −0.764393 | − | 0.644750i | \(-0.776961\pi\) |
0.940567 | + | 0.339609i | \(0.110295\pi\) | |||||||
\(402\) | −3.90875e6 | + | 6.77015e6i | −1.20635 | + | 2.08946i | ||||
\(403\) | 4.25717e6 | 1.30575 | ||||||||
\(404\) | 3.34888e6 | − | 5.80043e6i | 1.02081 | − | 1.76810i | ||||
\(405\) | 349449. | − | 605264.i | 0.105864 | − | 0.183361i | ||||
\(406\) | −510844. | − | 884808.i | −0.153806 | − | 0.266400i | ||||
\(407\) | 764433. | + | 1.32404e6i | 0.228746 | + | 0.396200i | ||||
\(408\) | 1.78136e7 | 5.29788 | ||||||||
\(409\) | −2.05089e6 | −0.606224 | −0.303112 | − | 0.952955i | \(-0.598026\pi\) | ||||
−0.303112 | + | 0.952955i | \(0.598026\pi\) | |||||||
\(410\) | −144437. | − | 250172.i | −0.0424345 | − | 0.0734987i | ||||
\(411\) | 2.44552e6 | + | 4.23576e6i | 0.714111 | + | 1.23688i | ||||
\(412\) | −4.22512e6 | + | 7.31812e6i | −1.22630 | + | 2.12401i | ||||
\(413\) | 635223. | − | 1.10024e6i | 0.183253 | − | 0.317404i | ||||
\(414\) | 24874.5 | 0.00713270 | ||||||||
\(415\) | 393597. | − | 681731.i | 0.112184 | − | 0.194309i | ||||
\(416\) | −8.99113e6 | + | 1.55731e7i | −2.54731 | + | 4.41206i | ||||
\(417\) | 3.60408e6 | − | 6.24245e6i | 1.01497 | − | 1.75798i | ||||
\(418\) | −6.21731e6 | − | 1.07687e7i | −1.74045 | − | 3.01455i | ||||
\(419\) | 2.20325e6 | 0.613096 | 0.306548 | − | 0.951855i | \(-0.400826\pi\) | ||||
0.306548 | + | 0.951855i | \(0.400826\pi\) | |||||||
\(420\) | −560563. | − | 970923.i | −0.155060 | − | 0.268573i | ||||
\(421\) | −1.61280e6 | + | 2.79345e6i | −0.443481 | + | 0.768131i | −0.997945 | − | 0.0640765i | \(-0.979590\pi\) |
0.554464 | + | 0.832207i | \(0.312923\pi\) | |||||||
\(422\) | −138772. | −0.0379333 | ||||||||
\(423\) | −593592. | + | 1.02813e6i | −0.161301 | + | 0.279382i | ||||
\(424\) | 1.05933e7 | + | 1.83482e7i | 2.86166 | + | 4.95654i | ||||
\(425\) | 2.50703e6 | + | 4.34230e6i | 0.673266 | + | 1.16613i | ||||
\(426\) | −4.16620e6 | −1.11228 | ||||||||
\(427\) | −32636.4 | − | 56527.9i | −0.00866228 | − | 0.0150035i | ||||
\(428\) | −6.01481e6 | −1.58713 | ||||||||
\(429\) | 6.52443e6 | 1.71159 | ||||||||
\(430\) | −544817. | − | 1.22143e6i | −0.142095 | − | 0.318565i | ||||
\(431\) | −2.60589e6 | −0.675713 | −0.337857 | − | 0.941198i | \(-0.609702\pi\) | ||||
−0.337857 | + | 0.941198i | \(0.609702\pi\) | |||||||
\(432\) | 1.28662e7 | 3.31695 | ||||||||
\(433\) | −493922. | − | 855498.i | −0.126601 | − | 0.219280i | 0.795756 | − | 0.605617i | \(-0.207074\pi\) |
−0.922358 | + | 0.386337i | \(0.873740\pi\) | |||||||
\(434\) | −4.52013e6 | −1.15193 | ||||||||
\(435\) | 111034. | + | 192317.i | 0.0281341 | + | 0.0487298i | ||||
\(436\) | 2.67206e6 | + | 4.62814e6i | 0.673177 | + | 1.16598i | ||||
\(437\) | −45465.8 | + | 78749.2i | −0.0113889 | + | 0.0197261i | ||||
\(438\) | 7.38793e6 | 1.84008 | ||||||||
\(439\) | −1.34500e6 | + | 2.32962e6i | −0.333091 | + | 0.576930i | −0.983116 | − | 0.182982i | \(-0.941425\pi\) |
0.650026 | + | 0.759912i | \(0.274758\pi\) | |||||||
\(440\) | 1.56165e6 | + | 2.70486e6i | 0.384550 | + | 0.666060i | ||||
\(441\) | −648213. | −0.158716 | ||||||||
\(442\) | −6.85586e6 | − | 1.18747e7i | −1.66919 | − | 2.89113i | ||||
\(443\) | −3.25280e6 | + | 5.63402e6i | −0.787496 | + | 1.36398i | 0.140001 | + | 0.990151i | \(0.455289\pi\) |
−0.927497 | + | 0.373831i | \(0.878044\pi\) | |||||||
\(444\) | −2.33938e6 | + | 4.05193e6i | −0.563175 | + | 0.975448i | ||||
\(445\) | −285521. | + | 494537.i | −0.0683500 | + | 0.118386i | ||||
\(446\) | 3.07621e6 | 0.732282 | ||||||||
\(447\) | −862391. | + | 1.49371e6i | −0.204144 | + | 0.353587i | ||||
\(448\) | 4.90346e6 | − | 8.49305e6i | 1.15427 | − | 1.99926i | ||||
\(449\) | −3.36046e6 | − | 5.82048e6i | −0.786651 | − | 1.36252i | −0.928008 | − | 0.372561i | \(-0.878480\pi\) |
0.141356 | − | 0.989959i | \(-0.454854\pi\) | |||||||
\(450\) | −935614. | − | 1.62053e6i | −0.217804 | − | 0.377247i | ||||
\(451\) | −1.31116e6 | −0.303538 | ||||||||
\(452\) | −4.36976e6 | −1.00603 | ||||||||
\(453\) | −4.66024e6 | − | 8.07176e6i | −1.06699 | − | 1.84809i | ||||
\(454\) | 2.84437e6 | + | 4.92659e6i | 0.647659 | + | 1.12178i | ||||
\(455\) | −275563. | + | 477289.i | −0.0624012 | + | 0.108082i | ||||
\(456\) | 1.21513e7 | − | 2.10466e7i | 2.73658 | − | 4.73990i | ||||
\(457\) | 4.09315e6 | 0.916785 | 0.458393 | − | 0.888750i | \(-0.348425\pi\) | ||||
0.458393 | + | 0.888750i | \(0.348425\pi\) | |||||||
\(458\) | −1.20544e6 | + | 2.08789e6i | −0.268524 | + | 0.465097i | ||||
\(459\) | −2.67716e6 | + | 4.63698e6i | −0.593120 | + | 1.02731i | ||||
\(460\) | 17881.7 | − | 30972.1i | 0.00394017 | − | 0.00682458i | ||||
\(461\) | 1.23734e6 | + | 2.14314e6i | 0.271168 | + | 0.469676i | 0.969161 | − | 0.246428i | \(-0.0792568\pi\) |
−0.697993 | + | 0.716104i | \(0.745924\pi\) | |||||||
\(462\) | −6.92743e6 | −1.50997 | ||||||||
\(463\) | −190639. | − | 330196.i | −0.0413294 | − | 0.0715846i | 0.844621 | − | 0.535365i | \(-0.179826\pi\) |
−0.885950 | + | 0.463780i | \(0.846493\pi\) | |||||||
\(464\) | −2.54505e6 | + | 4.40816e6i | −0.548784 | + | 0.950522i | ||||
\(465\) | 982470. | 0.210711 | ||||||||
\(466\) | 5.12358e6 | − | 8.87429e6i | 1.09297 | − | 1.89308i | ||||
\(467\) | −84316.9 | − | 146041.i | −0.0178905 | − | 0.0309873i | 0.856942 | − | 0.515414i | \(-0.172362\pi\) |
−0.874832 | + | 0.484426i | \(0.839028\pi\) | |||||||
\(468\) | 1.87944e6 | + | 3.25528e6i | 0.396655 | + | 0.687027i | ||||
\(469\) | −2.99724e6 | −0.629202 | ||||||||
\(470\) | 1.16184e6 | + | 2.01236e6i | 0.242605 | + | 0.420205i | ||||
\(471\) | 849272. | 0.176398 | ||||||||
\(472\) | −1.08312e7 | −2.23781 | ||||||||
\(473\) | −6.03756e6 | − | 630400.i | −1.24082 | − | 0.129558i | ||||
\(474\) | −1.74751e7 | −3.57251 | ||||||||
\(475\) | 6.84049e6 | 1.39108 | ||||||||
\(476\) | 5.34712e6 | + | 9.26147e6i | 1.08169 | + | 1.87354i | ||||
\(477\) | 1.92284e6 | 0.386943 | ||||||||
\(478\) | 4.09869e6 | + | 7.09914e6i | 0.820494 | + | 1.42114i | ||||
\(479\) | 2.90428e6 | + | 5.03036e6i | 0.578362 | + | 1.00175i | 0.995667 | + | 0.0929866i | \(0.0296414\pi\) |
−0.417305 | + | 0.908767i | \(0.637025\pi\) | |||||||
\(480\) | −2.07497e6 | + | 3.59396e6i | −0.411064 | + | 0.711984i | ||||
\(481\) | 2.30000e6 | 0.453278 | ||||||||
\(482\) | 6.18851e6 | − | 1.07188e7i | 1.21330 | − | 2.10150i | ||||
\(483\) | 25329.4 | + | 43871.8i | 0.00494035 | + | 0.00855693i | ||||
\(484\) | 7.93556e6 | 1.53980 | ||||||||
\(485\) | 1663.30 | + | 2880.92i | 0.000321082 | + | 0.000556130i | ||||
\(486\) | 2.29989e6 | − | 3.98353e6i | 0.441689 | − | 0.765028i | ||||
\(487\) | 4.77091e6 | − | 8.26346e6i | 0.911546 | − | 1.57884i | 0.0996661 | − | 0.995021i | \(-0.468223\pi\) |
0.811880 | − | 0.583824i | \(-0.198444\pi\) | |||||||
\(488\) | −278242. | + | 481930.i | −0.0528900 | + | 0.0916082i | ||||
\(489\) | −9.25778e6 | −1.75079 | ||||||||
\(490\) | −634373. | + | 1.09877e6i | −0.119359 | + | 0.206736i | ||||
\(491\) | −704101. | + | 1.21954e6i | −0.131805 | + | 0.228293i | −0.924372 | − | 0.381491i | \(-0.875411\pi\) |
0.792567 | + | 0.609784i | \(0.208744\pi\) | |||||||
\(492\) | −2.00625e6 | − | 3.47493e6i | −0.373657 | − | 0.647192i | ||||
\(493\) | −1.05914e6 | − | 1.83448e6i | −0.196261 | − | 0.339935i | ||||
\(494\) | −1.87064e7 | −3.44884 | ||||||||
\(495\) | 283462. | 0.0519974 | ||||||||
\(496\) | 1.12598e7 | + | 1.95025e7i | 2.05506 | + | 3.55947i | ||||
\(497\) | −798664. | − | 1.38333e6i | −0.145035 | − | 0.251208i | ||||
\(498\) | 7.44272e6 | − | 1.28912e7i | 1.34480 | − | 2.32926i | ||||
\(499\) | −2.03319e6 | + | 3.52159e6i | −0.365533 | + | 0.633122i | −0.988862 | − | 0.148838i | \(-0.952447\pi\) |
0.623328 | + | 0.781960i | \(0.285780\pi\) | |||||||
\(500\) | −5.47052e6 | −0.978597 | ||||||||
\(501\) | 43762.4 | − | 75798.7i | 0.00778945 | − | 0.0134917i | ||||
\(502\) | 4.83884e6 | − | 8.38112e6i | 0.857003 | − | 1.48437i | ||||
\(503\) | −351293. | + | 608457.i | −0.0619083 | + | 0.107228i | −0.895318 | − | 0.445427i | \(-0.853052\pi\) |
0.833410 | + | 0.552655i | \(0.186385\pi\) | |||||||
\(504\) | −1.27443e6 | − | 2.20737e6i | −0.223480 | − | 0.387079i | ||||
\(505\) | −759845. | −0.132586 | ||||||||
\(506\) | −110491. | − | 191376.i | −0.0191845 | − | 0.0332286i | ||||
\(507\) | 1.69558e6 | − | 2.93682e6i | 0.292953 | − | 0.507409i | ||||
\(508\) | −1.08682e7 | −1.86852 | ||||||||
\(509\) | −4.42953e6 | + | 7.67218e6i | −0.757815 | + | 1.31257i | 0.186147 | + | 0.982522i | \(0.440400\pi\) |
−0.943962 | + | 0.330053i | \(0.892933\pi\) | |||||||
\(510\) | −1.58220e6 | − | 2.74045e6i | −0.269361 | − | 0.466547i | ||||
\(511\) | 1.41627e6 | + | 2.45306e6i | 0.239936 | + | 0.415581i | ||||
\(512\) | −1.59537e7 | −2.68959 | ||||||||
\(513\) | 3.65235e6 | + | 6.32606e6i | 0.612744 | + | 1.06130i | ||||
\(514\) | −6.42921e6 | −1.07337 | ||||||||
\(515\) | 958658. | 0.159274 | ||||||||
\(516\) | −7.56758e6 | − | 1.69658e7i | −1.25122 | − | 2.80512i | ||||
\(517\) | 1.05468e7 | 1.73538 | ||||||||
\(518\) | −2.44207e6 | −0.399883 | ||||||||
\(519\) | −2.71160e6 | − | 4.69663e6i | −0.441883 | − | 0.765364i | ||||
\(520\) | 4.69864e6 | 0.762016 | ||||||||
\(521\) | −3.79348e6 | − | 6.57049e6i | −0.612270 | − | 1.06048i | −0.990857 | − | 0.134917i | \(-0.956923\pi\) |
0.378587 | − | 0.925566i | \(-0.376410\pi\) | |||||||
\(522\) | 395267. | + | 684622.i | 0.0634913 | + | 0.109970i | ||||
\(523\) | 5.16090e6 | − | 8.93895e6i | 0.825033 | − | 1.42900i | −0.0768605 | − | 0.997042i | \(-0.524490\pi\) |
0.901894 | − | 0.431958i | \(-0.142177\pi\) | |||||||
\(524\) | −1.19273e7 | −1.89764 | ||||||||
\(525\) | 1.90545e6 | − | 3.30033e6i | 0.301716 | − | 0.522588i | ||||
\(526\) | −231547. | − | 401050.i | −0.0364900 | − | 0.0632026i | ||||
\(527\) | −9.37162e6 | −1.46990 | ||||||||
\(528\) | 1.72564e7 | + | 2.98890e7i | 2.69380 | + | 4.66580i | ||||
\(529\) | 3.21736e6 | − | 5.57264e6i | 0.499874 | − | 0.865808i | ||||
\(530\) | 1.88179e6 | − | 3.25935e6i | 0.290992 | − | 0.504012i | ||||
\(531\) | −491505. | + | 851312.i | −0.0756470 | + | 0.131025i | ||||
\(532\) | 1.45897e7 | 2.23495 | ||||||||
\(533\) | −986239. | + | 1.70822e6i | −0.150371 | + | 0.260450i | ||||
\(534\) | −5.39905e6 | + | 9.35144e6i | −0.819341 | + | 1.41914i | ||||
\(535\) | 341183. | + | 590946.i | 0.0515350 | + | 0.0892613i | ||||
\(536\) | 1.27765e7 | + | 2.21296e7i | 1.92088 | + | 3.32707i | ||||
\(537\) | 3.75648e6 | 0.562142 | ||||||||
\(538\) | −1.36341e6 | −0.203082 | ||||||||
\(539\) | 2.87932e6 | + | 4.98713e6i | 0.426892 | + | 0.739399i | ||||
\(540\) | −1.43647e6 | − | 2.48804e6i | −0.211989 | − | 0.367175i | ||||
\(541\) | −1.59418e6 | + | 2.76121e6i | −0.234178 | + | 0.405607i | −0.959033 | − | 0.283293i | \(-0.908573\pi\) |
0.724856 | + | 0.688901i | \(0.241906\pi\) | |||||||
\(542\) | −254198. | + | 440284.i | −0.0371684 | + | 0.0643776i | ||||
\(543\) | −6.67551e6 | −0.971594 | ||||||||
\(544\) | 1.97928e7 | − | 3.42822e7i | 2.86755 | − | 4.96674i | ||||
\(545\) | 303138. | − | 525051.i | 0.0437169 | − | 0.0757199i | ||||
\(546\) | −5.21075e6 | + | 9.02529e6i | −0.748029 | + | 1.29563i | ||||
\(547\) | 4.90549e6 | + | 8.49655e6i | 0.700993 | + | 1.21416i | 0.968118 | + | 0.250494i | \(0.0805929\pi\) |
−0.267125 | + | 0.963662i | \(0.586074\pi\) | |||||||
\(548\) | 2.50333e7 | 3.56096 | ||||||||
\(549\) | 25252.5 | + | 43738.6i | 0.00357580 | + | 0.00619346i | ||||
\(550\) | −8.31188e6 | + | 1.43966e7i | −1.17164 | + | 2.02933i | ||||
\(551\) | −2.88988e6 | −0.405510 | ||||||||
\(552\) | 215947. | − | 374030.i | 0.0301647 | − | 0.0522468i | ||||
\(553\) | −3.34999e6 | − | 5.80235e6i | −0.465833 | − | 0.806847i | ||||
\(554\) | −6.13318e6 | − | 1.06230e7i | −0.849007 | − | 1.47052i | ||||
\(555\) | 530794. | 0.0731465 | ||||||||
\(556\) | −1.84464e7 | − | 3.19502e7i | −2.53061 | − | 4.38315i | ||||
\(557\) | −4.05122e6 | −0.553283 | −0.276642 | − | 0.960973i | \(-0.589222\pi\) | ||||
−0.276642 | + | 0.960973i | \(0.589222\pi\) | |||||||
\(558\) | 3.49746e6 | 0.475518 | ||||||||
\(559\) | −5.36271e6 | + | 7.39176e6i | −0.725863 | + | 1.00050i | ||||
\(560\) | −2.91534e6 | −0.392843 | ||||||||
\(561\) | −1.43627e7 | −1.92677 | ||||||||
\(562\) | 5.41445e6 | + | 9.37810e6i | 0.723125 | + | 1.25249i | ||||
\(563\) | 966125. | 0.128458 | 0.0642292 | − | 0.997935i | \(-0.479541\pi\) | ||||
0.0642292 | + | 0.997935i | \(0.479541\pi\) | |||||||
\(564\) | 1.61381e7 | + | 2.79520e7i | 2.13626 | + | 3.70011i | ||||
\(565\) | 247869. | + | 429322.i | 0.0326664 | + | 0.0565799i | ||||
\(566\) | 2.24935e6 | − | 3.89598e6i | 0.295131 | − | 0.511183i | ||||
\(567\) | 5.06696e6 | 0.661896 | ||||||||
\(568\) | −6.80903e6 | + | 1.17936e7i | −0.885553 | + | 1.53382i | ||||
\(569\) | −1.79077e6 | − | 3.10170e6i | −0.231877 | − | 0.401624i | 0.726483 | − | 0.687184i | \(-0.241154\pi\) |
−0.958361 | + | 0.285561i | \(0.907820\pi\) | |||||||
\(570\) | −4.31707e6 | −0.556547 | ||||||||
\(571\) | 1.70131e6 | + | 2.94676e6i | 0.218371 | + | 0.378229i | 0.954310 | − | 0.298819i | \(-0.0965925\pi\) |
−0.735939 | + | 0.677047i | \(0.763259\pi\) | |||||||
\(572\) | 1.66967e7 | − | 2.89195e7i | 2.13373 | − | 3.69574i | ||||
\(573\) | 2.52821e6 | − | 4.37898e6i | 0.321681 | − | 0.557169i | ||||
\(574\) | 1.04716e6 | − | 1.81373e6i | 0.132658 | − | 0.229770i | ||||
\(575\) | 121566. | 0.0153335 | ||||||||
\(576\) | −3.79406e6 | + | 6.57151e6i | −0.476484 | + | 0.825295i | ||||
\(577\) | 1.39626e6 | − | 2.41840e6i | 0.174594 | − | 0.302405i | −0.765427 | − | 0.643523i | \(-0.777472\pi\) |
0.940021 | + | 0.341118i | \(0.110806\pi\) | |||||||
\(578\) | 7.29748e6 | + | 1.26396e7i | 0.908559 | + | 1.57367i | ||||
\(579\) | 1.37979e6 | + | 2.38986e6i | 0.171047 | + | 0.296263i | ||||
\(580\) | 1.13659e6 | 0.140293 | ||||||||
\(581\) | 5.70710e6 | 0.701415 | ||||||||
\(582\) | 31452.1 | + | 54476.6i | 0.00384895 | + | 0.00666657i | ||||
\(583\) | −8.54113e6 | − | 1.47937e7i | −1.04074 | − | 1.80262i | ||||
\(584\) | 1.20745e7 | − | 2.09136e7i | 1.46499 | − | 2.53745i | ||||
\(585\) | 213218. | − | 369304.i | 0.0257593 | − | 0.0446163i | ||||
\(586\) | 2.46488e6 | 0.296519 | ||||||||
\(587\) | 4.37350e6 | − | 7.57513e6i | 0.523883 | − | 0.907392i | −0.475731 | − | 0.879591i | \(-0.657816\pi\) |
0.999613 | − | 0.0278007i | \(-0.00885039\pi\) | |||||||
\(588\) | −8.81154e6 | + | 1.52620e7i | −1.05101 | + | 1.82041i | ||||
\(589\) | −6.39268e6 | + | 1.10724e7i | −0.759267 | + | 1.31509i | ||||
\(590\) | 962023. | + | 1.66627e6i | 0.113777 | + | 0.197068i | ||||
\(591\) | 1.15926e7 | 1.36526 | ||||||||
\(592\) | 6.08325e6 | + | 1.05365e7i | 0.713397 | + | 1.23564i | ||||
\(593\) | −3.70637e6 | + | 6.41962e6i | −0.432824 | + | 0.749674i | −0.997115 | − | 0.0759023i | \(-0.975816\pi\) |
0.564291 | + | 0.825576i | \(0.309150\pi\) | |||||||
\(594\) | −1.77519e7 | −2.06433 | ||||||||
\(595\) | 606617. | − | 1.05069e6i | 0.0702461 | − | 0.121670i | ||||
\(596\) | 4.41390e6 | + | 7.64510e6i | 0.508987 | + | 0.881591i | ||||
\(597\) | −1.81414e6 | − | 3.14219e6i | −0.208322 | − | 0.360825i | ||||
\(598\) | −332442. | −0.0380157 | ||||||||
\(599\) | 5.05365e6 | + | 8.75318e6i | 0.575491 | + | 0.996779i | 0.995988 | + | 0.0894854i | \(0.0285223\pi\) |
−0.420497 | + | 0.907294i | \(0.638144\pi\) | |||||||
\(600\) | −3.24899e7 | −3.68443 | ||||||||
\(601\) | −4.17965e6 | −0.472013 | −0.236006 | − | 0.971752i | \(-0.575839\pi\) | ||||
−0.236006 | + | 0.971752i | \(0.575839\pi\) | |||||||
\(602\) | 5.69395e6 | − | 7.84833e6i | 0.640357 | − | 0.882645i | ||||
\(603\) | 2.31912e6 | 0.259735 | ||||||||
\(604\) | −4.77041e7 | −5.32063 | ||||||||
\(605\) | −450135. | − | 779657.i | −0.0499982 | − | 0.0865994i | ||||
\(606\) | −1.43683e7 | −1.58936 | ||||||||
\(607\) | 2.91717e6 | + | 5.05268e6i | 0.321358 | + | 0.556609i | 0.980769 | − | 0.195174i | \(-0.0625272\pi\) |
−0.659410 | + | 0.751783i | \(0.729194\pi\) | |||||||
\(608\) | −2.70026e7 | − | 4.67699e7i | −2.96242 | − | 5.13107i | ||||
\(609\) | −804990. | + | 1.39428e6i | −0.0879523 | + | 0.152338i | ||||
\(610\) | 98853.3 | 0.0107564 | ||||||||
\(611\) | 7.93321e6 | − | 1.37407e7i | 0.859698 | − | 1.48904i | ||||
\(612\) | −4.13734e6 | − | 7.16609e6i | −0.446522 | − | 0.773399i | ||||
\(613\) | 1.63198e7 | 1.75414 | 0.877070 | − | 0.480362i | \(-0.159495\pi\) | ||||
0.877070 | + | 0.480362i | \(0.159495\pi\) | |||||||
\(614\) | 1.02789e7 | + | 1.78036e7i | 1.10034 | + | 1.90584i | ||||
\(615\) | −227604. | + | 394222.i | −0.0242657 | + | 0.0420294i | ||||
\(616\) | −1.13219e7 | + | 1.96100e7i | −1.20217 | + | 2.08222i | ||||
\(617\) | −2.65640e6 | + | 4.60101e6i | −0.280918 | + | 0.486565i | −0.971611 | − | 0.236583i | \(-0.923972\pi\) |
0.690693 | + | 0.723148i | \(0.257306\pi\) | |||||||
\(618\) | 1.81277e7 | 1.90929 | ||||||||
\(619\) | 7.23199e6 | − | 1.25262e7i | 0.758632 | − | 1.31399i | −0.184917 | − | 0.982754i | \(-0.559202\pi\) |
0.943548 | − | 0.331234i | \(-0.107465\pi\) | |||||||
\(620\) | 2.51424e6 | − | 4.35480e6i | 0.262681 | − | 0.454976i | ||||
\(621\) | 64907.9 | + | 112424.i | 0.00675412 | + | 0.0116985i | ||||
\(622\) | 1.83265e6 | + | 3.17424e6i | 0.189934 | + | 0.328975i | ||||
\(623\) | −4.14001e6 | −0.427348 | ||||||||
\(624\) | 5.19205e7 | 5.33798 | ||||||||
\(625\) | −4.41480e6 | − | 7.64666e6i | −0.452076 | − | 0.783018i | ||||
\(626\) | 1.65786e7 | + | 2.87149e7i | 1.69087 | + | 2.92868i | ||||
\(627\) | −9.79725e6 | + | 1.69693e7i | −0.995257 | + | 1.72384i | ||||
\(628\) | 2.17337e6 | − | 3.76440e6i | 0.219905 | − | 0.380887i | ||||
\(629\) | −5.06315e6 | −0.510264 | ||||||||
\(630\) | −226388. | + | 392115.i | −0.0227249 | + | 0.0393606i | ||||
\(631\) | 3.93843e6 | − | 6.82156e6i | 0.393776 | − | 0.682040i | −0.599168 | − | 0.800623i | \(-0.704502\pi\) |
0.992944 | + | 0.118583i | \(0.0378352\pi\) | |||||||
\(632\) | −2.85604e7 | + | 4.94681e7i | −2.84428 | + | 4.92643i | ||||
\(633\) | 109339. | + | 189380.i | 0.0108459 | + | 0.0187856i | ||||
\(634\) | 3.26990e7 | 3.23081 | ||||||||
\(635\) | 616486. | + | 1.06778e6i | 0.0606721 | + | 0.105087i | ||||
\(636\) | 2.61383e7 | − | 4.52728e7i | 2.56232 | − | 4.43808i | ||||
\(637\) | 8.66320e6 | 0.845921 | ||||||||
\(638\) | 3.51150e6 | − | 6.08210e6i | 0.341540 | − | 0.591564i | ||||
\(639\) | 617968. | + | 1.07035e6i | 0.0598706 | + | 0.103699i | ||||
\(640\) | 3.58844e6 | + | 6.21536e6i | 0.346303 | + | 0.599814i | ||||
\(641\) | −1.62760e7 | −1.56460 | −0.782301 | − | 0.622901i | \(-0.785954\pi\) | ||||
−0.782301 | + | 0.622901i | \(0.785954\pi\) | |||||||
\(642\) | 6.45158e6 | + | 1.11745e7i | 0.617773 | + | 1.07001i | ||||
\(643\) | 1.26517e7 | 1.20676 | 0.603382 | − | 0.797452i | \(-0.293819\pi\) | ||||
0.603382 | + | 0.797452i | \(0.293819\pi\) | |||||||
\(644\) | 259282. | 0.0246353 | ||||||||
\(645\) | −1.23761e6 | + | 1.70587e6i | −0.117134 | + | 0.161453i | ||||
\(646\) | 4.11798e7 | 3.88242 | ||||||||
\(647\) | 1.68252e7 | 1.58015 | 0.790075 | − | 0.613010i | \(-0.210041\pi\) | ||||
0.790075 | + | 0.613010i | \(0.210041\pi\) | |||||||
\(648\) | −2.15992e7 | − | 3.74110e7i | −2.02070 | − | 3.49995i | ||||
\(649\) | 8.73295e6 | 0.813859 | ||||||||
\(650\) | 1.25042e7 | + | 2.16580e7i | 1.16084 | + | 2.01064i | ||||
\(651\) | 3.56142e6 | + | 6.16856e6i | 0.329360 | + | 0.570468i | ||||
\(652\) | −2.36916e7 | + | 4.10351e7i | −2.18261 | + | 3.78039i | ||||
\(653\) | −1.56294e7 | −1.43436 | −0.717180 | − | 0.696888i | \(-0.754567\pi\) | ||||
−0.717180 | + | 0.696888i | \(0.754567\pi\) | |||||||
\(654\) | 5.73218e6 | − | 9.92843e6i | 0.524054 | − | 0.907687i | ||||
\(655\) | 676560. | + | 1.17184e6i | 0.0616174 | + | 0.106724i | ||||
\(656\) | −1.04340e7 | −0.946653 | ||||||||
\(657\) | −1.09584e6 | − | 1.89806e6i | −0.0990456 | − | 0.171552i | ||||
\(658\) | −8.42323e6 | + | 1.45895e7i | −0.758427 | + | 1.31363i | ||||
\(659\) | −457666. | + | 792700.i | −0.0410520 | + | 0.0711042i | −0.885821 | − | 0.464026i | \(-0.846404\pi\) |
0.844769 | + | 0.535131i | \(0.179738\pi\) | |||||||
\(660\) | 3.85326e6 | − | 6.67405e6i | 0.344325 | − | 0.596389i | ||||
\(661\) | −8.73256e6 | −0.777389 | −0.388694 | − | 0.921367i | \(-0.627074\pi\) | ||||
−0.388694 | + | 0.921367i | \(0.627074\pi\) | |||||||
\(662\) | 9.94885e6 | − | 1.72319e7i | 0.882324 | − | 1.52823i | ||||
\(663\) | −1.08035e7 | + | 1.87122e7i | −0.954510 | + | 1.65326i | ||||
\(664\) | −2.43280e7 | − | 4.21374e7i | −2.14135 | − | 3.70892i | ||||
\(665\) | −827586. | − | 1.43342e6i | −0.0725703 | − | 0.125695i | ||||
\(666\) | 1.88955e6 | 0.165072 | ||||||||
\(667\) | −51357.7 | −0.00446983 | ||||||||
\(668\) | −223985. | − | 387953.i | −0.0194213 | − | 0.0336386i | ||||
\(669\) | −2.42375e6 | − | 4.19806e6i | −0.209374 | − | 0.362646i | ||||
\(670\) | 2.26961e6 | − | 3.93108e6i | 0.195328 | − | 0.338318i | ||||
\(671\) | 224340. | − | 388568.i | 0.0192354 | − | 0.0333166i | ||||
\(672\) | −3.00868e7 | −2.57012 | ||||||||
\(673\) | −3.97823e6 | + | 6.89050e6i | −0.338573 | + | 0.586426i | −0.984165 | − | 0.177257i | \(-0.943278\pi\) |
0.645591 | + | 0.763683i | \(0.276611\pi\) | |||||||
\(674\) | 5.34542e6 | − | 9.25855e6i | 0.453244 | − | 0.785042i | ||||
\(675\) | 4.88281e6 | − | 8.45727e6i | 0.412487 | − | 0.714448i | ||||
\(676\) | −8.67831e6 | − | 1.50313e7i | −0.730413 | − | 1.26511i | ||||
\(677\) | 7.91314e6 | 0.663555 | 0.331778 | − | 0.943358i | \(-0.392352\pi\) | ||||
0.331778 | + | 0.943358i | \(0.392352\pi\) | |||||||
\(678\) | 4.68708e6 | + | 8.11825e6i | 0.391586 | + | 0.678248i | ||||
\(679\) | −12058.8 | + | 20886.4i | −0.00100376 | + | 0.00173856i | ||||
\(680\) | −1.03435e7 | −0.857815 | ||||||||
\(681\) | 4.48217e6 | − | 7.76334e6i | 0.370357 | − | 0.641477i | ||||
\(682\) | −1.55355e7 | − | 2.69083e7i | −1.27898 | − | 2.21526i | ||||
\(683\) | −6.47217e6 | − | 1.12101e7i | −0.530882 | − | 0.919515i | −0.999351 | − | 0.0360349i | \(-0.988527\pi\) |
0.468468 | − | 0.883480i | \(-0.344806\pi\) | |||||||
\(684\) | −1.12888e7 | −0.922591 | ||||||||
\(685\) | −1.41998e6 | − | 2.45948e6i | −0.115626 | − | 0.200271i | ||||
\(686\) | −2.26391e7 | −1.83674 | ||||||||
\(687\) | 3.79908e6 | 0.307105 | ||||||||
\(688\) | −4.80461e7 | − | 5.01663e6i | −3.86978 | − | 0.404056i | ||||
\(689\) | −2.56983e7 | −2.06232 | ||||||||
\(690\) | −76721.0 | −0.00613467 | ||||||||
\(691\) | −1.25765e6 | − | 2.17831e6i | −0.100199 | − | 0.173550i | 0.811568 | − | 0.584259i | \(-0.198615\pi\) |
−0.911767 | + | 0.410709i | \(0.865281\pi\) | |||||||
\(692\) | −2.77571e7 | −2.20348 | ||||||||
\(693\) | 1.02754e6 | + | 1.77975e6i | 0.0812765 | + | 0.140775i | ||||
\(694\) | 1.76516e7 | + | 3.05736e7i | 1.39119 | + | 2.40961i | ||||
\(695\) | −2.09270e6 | + | 3.62467e6i | −0.164341 | + | 0.284647i | ||||
\(696\) | 1.37259e7 | 1.07403 | ||||||||
\(697\) | 2.17108e6 | − | 3.76042e6i | 0.169275 | − | 0.293194i | ||||
\(698\) | −8.19405e6 | − | 1.41925e7i | −0.636590 | − | 1.10261i | ||||
\(699\) | −1.61475e7 | −1.25001 | ||||||||
\(700\) | −9.75247e6 | − | 1.68918e7i | −0.752263 | − | 1.30296i | ||||
\(701\) | −9.67939e6 | + | 1.67652e7i | −0.743966 | + | 1.28859i | 0.206711 | + | 0.978402i | \(0.433724\pi\) |
−0.950676 | + | 0.310184i | \(0.899609\pi\) | |||||||
\(702\) | −1.33528e7 | + | 2.31278e7i | −1.02266 | + | 1.77129i | ||||
\(703\) | −3.45374e6 | + | 5.98205e6i | −0.263573 | + | 0.456522i | ||||
\(704\) | 6.74120e7 | 5.12632 | ||||||||
\(705\) | 1.83083e6 | − | 3.17108e6i | 0.138731 | − | 0.240290i | ||||
\(706\) | 1.98916e7 | − | 3.44533e7i | 1.50196 | − | 2.60147i | ||||
\(707\) | −2.75441e6 | − | 4.77077e6i | −0.207243 | − | 0.358955i | ||||
\(708\) | 1.33626e7 | + | 2.31448e7i | 1.00186 | + | 1.73528i | ||||
\(709\) | 2.02872e7 | 1.51568 | 0.757838 | − | 0.652442i | \(-0.226256\pi\) | ||||
0.757838 | + | 0.652442i | \(0.226256\pi\) | |||||||
\(710\) | 2.41910e6 | 0.180097 | ||||||||
\(711\) | 2.59206e6 | + | 4.48958e6i | 0.192296 | + | 0.333067i | ||||
\(712\) | 1.76479e7 | + | 3.05671e7i | 1.30465 | + | 2.25972i | ||||
\(713\) | −113608. | + | 196775.i | −0.00836921 | + | 0.0144959i | ||||
\(714\) | 1.14708e7 | − | 1.98680e7i | 0.842070 | − | 1.45851i | ||||
\(715\) | −3.78840e6 | −0.277134 | ||||||||
\(716\) | 9.61324e6 | − | 1.66506e7i | 0.700789 | − | 1.21380i | ||||
\(717\) | 6.45873e6 | − | 1.11868e7i | 0.469190 | − | 0.812662i | ||||
\(718\) | −6.05090e6 | + | 1.04805e7i | −0.438035 | + | 0.758699i | ||||
\(719\) | 2.06802e6 | + | 3.58192e6i | 0.149188 | + | 0.258401i | 0.930927 | − | 0.365204i | \(-0.119001\pi\) |
−0.781740 | + | 0.623605i | \(0.785667\pi\) | |||||||
\(720\) | 2.25575e6 | 0.162166 | ||||||||
\(721\) | 3.47510e6 | + | 6.01905e6i | 0.248960 | + | 0.431211i | ||||
\(722\) | 1.44966e7 | − | 2.51088e7i | 1.03496 | − | 1.79260i | ||||
\(723\) | −1.95038e7 | −1.38763 | ||||||||
\(724\) | −1.70833e7 | + | 2.95892e7i | −1.21123 | + | 2.09791i | ||||
\(725\) | 1.93173e6 | + | 3.34586e6i | 0.136490 | + | 0.236408i | ||||
\(726\) | −8.51181e6 | − | 1.47429e7i | −0.599350 | − | 1.03810i | ||||
\(727\) | −2.55897e7 | −1.79568 | −0.897841 | − | 0.440319i | \(-0.854865\pi\) | ||||
−0.897841 | + | 0.440319i | \(0.854865\pi\) | |||||||
\(728\) | 1.70324e7 | + | 2.95010e7i | 1.19110 | + | 2.06304i | ||||
\(729\) | 9.65656e6 | 0.672982 | ||||||||
\(730\) | −4.28979e6 | −0.297940 | ||||||||
\(731\) | 1.18053e7 | − | 1.62720e7i | 0.817117 | − | 1.12628i | ||||
\(732\) | 1.37309e6 | 0.0947153 | ||||||||
\(733\) | −4.15702e6 | −0.285774 | −0.142887 | − | 0.989739i | \(-0.545638\pi\) | ||||
−0.142887 | + | 0.989739i | \(0.545638\pi\) | |||||||
\(734\) | 1.17205e7 | + | 2.03006e7i | 0.802985 | + | 1.39081i | ||||
\(735\) | 1.99929e6 | 0.136508 | ||||||||
\(736\) | −479879. | − | 831174.i | −0.0326540 | − | 0.0565584i | ||||
\(737\) | −1.03014e7 | − | 1.78426e7i | −0.698599 | − | 1.21001i | ||||
\(738\) | −810240. | + | 1.40338e6i | −0.0547612 | + | 0.0948492i | ||||
\(739\) | 2.19214e6 | 0.147658 | 0.0738290 | − | 0.997271i | \(-0.476478\pi\) | ||||
0.0738290 | + | 0.997271i | \(0.476478\pi\) | |||||||
\(740\) | 1.35836e6 | − | 2.35274e6i | 0.0911873 | − | 0.157941i | ||||
\(741\) | 1.47388e7 | + | 2.55284e7i | 0.986091 | + | 1.70796i | ||||
\(742\) | 2.72856e7 | 1.81938 | ||||||||
\(743\) | −9.13301e6 | − | 1.58188e7i | −0.606935 | − | 1.05124i | −0.991743 | − | 0.128245i | \(-0.959066\pi\) |
0.384808 | − | 0.922997i | \(-0.374268\pi\) | |||||||
\(744\) | 3.03630e7 | − | 5.25902e7i | 2.01100 | − | 3.48315i | ||||
\(745\) | 500746. | − | 867318.i | 0.0330542 | − | 0.0572516i | ||||
\(746\) | −2.40257e7 | + | 4.16137e7i | −1.58062 | + | 2.73772i | ||||
\(747\) | −4.41588e6 | −0.289545 | ||||||||
\(748\) | −3.67556e7 | + | 6.36626e7i | −2.40198 | + | 4.16036i | ||||
\(749\) | −2.47355e6 | + | 4.28431e6i | −0.161108 | + | 0.279046i | ||||
\(750\) | 5.86777e6 | + | 1.01633e7i | 0.380908 | + | 0.659752i | ||||
\(751\) | −1.14127e7 | − | 1.97674e7i | −0.738395 | − | 1.27894i | −0.953218 | − | 0.302285i | \(-0.902250\pi\) |
0.214822 | − | 0.976653i | \(-0.431083\pi\) | |||||||
\(752\) | 8.39299e7 | 5.41218 | ||||||||
\(753\) | −1.52501e7 | −0.980135 | ||||||||
\(754\) | −5.28264e6 | − | 9.14980e6i | −0.338394 | − | 0.586115i | ||||
\(755\) | 2.70596e6 | + | 4.68686e6i | 0.172764 | + | 0.299236i | ||||
\(756\) | 1.04143e7 | − | 1.80381e7i | 0.662714 | − | 1.14785i | ||||
\(757\) | 2.80633e6 | − | 4.86071e6i | 0.177992 | − | 0.308290i | −0.763201 | − | 0.646161i | \(-0.776373\pi\) |
0.941193 | + | 0.337871i | \(0.109707\pi\) | |||||||
\(758\) | −1.62090e6 | −0.102467 | ||||||||
\(759\) | −174112. | + | 301571.i | −0.0109705 | + | 0.0190014i | ||||
\(760\) | −7.05560e6 | + | 1.22207e7i | −0.443098 | + | 0.767469i | ||||
\(761\) | 2.35036e6 | − | 4.07094e6i | 0.147120 | − | 0.254820i | −0.783042 | − | 0.621969i | \(-0.786333\pi\) |
0.930162 | + | 0.367149i | \(0.119666\pi\) | |||||||
\(762\) | 1.16574e7 | + | 2.01912e7i | 0.727302 | + | 1.25972i | ||||
\(763\) | 4.39546e6 | 0.273333 | ||||||||
\(764\) | −1.29399e7 | − | 2.24125e7i | −0.802042 | − | 1.38918i | ||||
\(765\) | −469371. | + | 812975.i | −0.0289977 | + | 0.0502254i | ||||
\(766\) | −5.16276e7 | −3.17914 | ||||||||
\(767\) | 6.56884e6 | − | 1.13776e7i | 0.403181 | − | 0.698331i | ||||
\(768\) | 3.05814e7 | + | 5.29686e7i | 1.87092 | + | 3.24053i | ||||
\(769\) | −5.12371e6 | − | 8.87453e6i | −0.312442 | − | 0.541165i | 0.666449 | − | 0.745551i | \(-0.267814\pi\) |
−0.978890 | + | 0.204386i | \(0.934480\pi\) | |||||||
\(770\) | 4.02240e6 | 0.244488 | ||||||||
\(771\) | 5.06558e6 | + | 8.77385e6i | 0.306898 | + | 0.531562i | ||||
\(772\) | 1.41241e7 | 0.852937 | ||||||||
\(773\) | 2.01869e7 | 1.21512 | 0.607562 | − | 0.794272i | \(-0.292147\pi\) | ||||
0.607562 | + | 0.794272i | \(0.292147\pi\) | |||||||
\(774\) | −4.40571e6 | + | 6.07266e6i | −0.264340 | + | 0.364357i | ||||
\(775\) | 1.70927e7 | 1.02225 | ||||||||
\(776\) | 205615. | 0.0122575 | ||||||||
\(777\) | 1.92411e6 | + | 3.33265e6i | 0.114334 | + | 0.198033i | ||||
\(778\) | −1.72675e7 | −1.02277 | ||||||||
\(779\) | −2.96192e6 | − | 5.13020e6i | −0.174876 | − | 0.302894i | ||||
\(780\) | −5.79678e6 | − | 1.00403e7i | −0.341154 | − | 0.590896i | ||||
\(781\) | 5.48995e6 | − | 9.50887e6i | 0.322063 | − | 0.557830i | ||||
\(782\) | 731828. | 0.0427949 | ||||||||
\(783\) | −2.06283e6 | + | 3.57292e6i | −0.120243 | + | 0.208266i | ||||
\(784\) | 2.29132e7 | + | 3.96869e7i | 1.33136 | + | 2.30599i | ||||
\(785\) | −493128. | −0.0285618 | ||||||||
\(786\) | 1.27934e7 | + | 2.21588e7i | 0.738634 | + | 1.27935i | ||||
\(787\) | 1.42806e7 | − | 2.47348e7i | 0.821884 | − | 1.42354i | −0.0823943 | − | 0.996600i | \(-0.526257\pi\) |
0.904278 | − | 0.426944i | \(-0.140410\pi\) | |||||||
\(788\) | 2.96668e7 | − | 5.13844e7i | 1.70198 | − | 2.94792i | ||||
\(789\) | −364872. | + | 631976.i | −0.0208664 | + | 0.0361417i | ||||
\(790\) | 1.01469e7 | 0.578448 | ||||||||
\(791\) | −1.79703e6 | + | 3.11255e6i | −0.102121 | + | 0.176879i | ||||
\(792\) | 8.76031e6 | − | 1.51733e7i | 0.496257 | − | 0.859542i | ||||
\(793\) | −337493. | − | 584555.i | −0.0190582 | − | 0.0330098i | ||||
\(794\) | −2.82622e7 | − | 4.89515e7i | −1.59094 | − | 2.75559i | ||||
\(795\) | −5.93065e6 | −0.332801 | ||||||||
\(796\) | −1.85703e7 | −1.03881 | ||||||||
\(797\) | 1.65647e7 | + | 2.86909e7i | 0.923715 | + | 1.59992i | 0.793614 | + | 0.608421i | \(0.208197\pi\) |
0.130101 | + | 0.991501i | \(0.458470\pi\) | |||||||
\(798\) | −1.56492e7 | − | 2.71052e7i | −0.869931 | − | 1.50676i | ||||
\(799\) | −1.74639e7 | + | 3.02484e7i | −0.967777 | + | 1.67624i | ||||
\(800\) | −3.60997e7 | + | 6.25264e7i | −1.99424 | + | 3.45413i | ||||
\(801\) | 3.20335e6 | 0.176410 | ||||||||
\(802\) | −6.22864e6 | + | 1.07883e7i | −0.341946 | + | 0.592268i | ||||
\(803\) | −9.73534e6 | + | 1.68621e7i | −0.532798 | + | 0.922833i | ||||
\(804\) | 3.15252e7 | − | 5.46032e7i | 1.71996 | − | 2.97905i | ||||
\(805\) | −14707.5 | − | 25474.1i | −0.000799924 | − | 0.00138551i | ||||
\(806\) | −4.67427e7 | −2.53440 | ||||||||
\(807\) | 1.07423e6 | + | 1.86063e6i | 0.0580651 | + | 0.100572i | ||||
\(808\) | −2.34828e7 | + | 4.06734e7i | −1.26538 | + | 2.19170i | ||||
\(809\) | 2.47179e7 | 1.32782 | 0.663912 | − | 0.747811i | \(-0.268895\pi\) | ||||
0.663912 | + | 0.747811i | \(0.268895\pi\) | |||||||
\(810\) | −3.83686e6 | + | 6.64564e6i | −0.205477 | + | 0.355897i | ||||
\(811\) | −9.71928e6 | − | 1.68343e7i | −0.518898 | − | 0.898758i | −0.999759 | − | 0.0219609i | \(-0.993009\pi\) |
0.480861 | − | 0.876797i | \(-0.340324\pi\) | |||||||
\(812\) | 4.12010e6 | + | 7.13623e6i | 0.219290 | + | 0.379821i | ||||
\(813\) | 801132. | 0.0425087 | ||||||||
\(814\) | −8.39328e6 | − | 1.45376e7i | −0.443987 | − | 0.769009i | ||||
\(815\) | 5.37551e6 | 0.283482 | ||||||||
\(816\) | −1.14296e8 | −6.00906 | ||||||||
\(817\) | −1.11724e7 | − | 2.50475e7i | −0.585586 | − | 1.31283i | ||||
\(818\) | 2.25182e7 | 1.17666 | ||||||||
\(819\) | 3.09162e6 | 0.161056 | ||||||||
\(820\) | 1.16493e6 | + | 2.01771e6i | 0.0605012 | + | 0.104791i | ||||
\(821\) | 3.17753e7 | 1.64525 | 0.822626 | − | 0.568583i | \(-0.192508\pi\) | ||||
0.822626 | + | 0.568583i | \(0.192508\pi\) | |||||||
\(822\) | −2.68511e7 | − | 4.65075e7i | −1.38606 | − | 2.40073i | ||||
\(823\) | 1.03903e7 | + | 1.79965e7i | 0.534720 | + | 0.926163i | 0.999177 | + | 0.0405668i | \(0.0129164\pi\) |
−0.464457 | + | 0.885596i | \(0.653750\pi\) | |||||||
\(824\) | 2.96271e7 | − | 5.13156e7i | 1.52009 | − | 2.63288i | ||||
\(825\) | 2.61958e7 | 1.33997 | ||||||||
\(826\) | −6.97459e6 | + | 1.20803e7i | −0.355687 | + | 0.616069i | ||||
\(827\) | 1.19335e7 | + | 2.06694e7i | 0.606742 | + | 1.05091i | 0.991774 | + | 0.128005i | \(0.0408573\pi\) |
−0.385031 | + | 0.922903i | \(0.625809\pi\) | |||||||
\(828\) | −200620. | −0.0101695 | ||||||||
\(829\) | −543558. | − | 941470.i | −0.0274701 | − | 0.0475795i | 0.851964 | − | 0.523601i | \(-0.175412\pi\) |
−0.879434 | + | 0.476022i | \(0.842078\pi\) | |||||||
\(830\) | −4.32160e6 | + | 7.48523e6i | −0.217746 | + | 0.377146i | ||||
\(831\) | −9.66468e6 | + | 1.67397e7i | −0.485495 | + | 0.840903i | ||||
\(832\) | 5.07067e7 | − | 8.78266e7i | 2.53955 | − | 4.39863i | ||||
\(833\) | −1.90709e7 | −0.952269 | ||||||||
\(834\) | −3.95719e7 | + | 6.85405e7i | −1.97003 | + | 3.41218i | ||||
\(835\) | −25410.5 | + | 44012.4i | −0.00126124 | + | 0.00218453i | ||||
\(836\) | 5.01444e7 | + | 8.68526e7i | 2.48146 | + | 4.29801i | ||||
\(837\) | 9.12632e6 | + | 1.58072e7i | 0.450279 | + | 0.779906i | ||||
\(838\) | −2.41911e7 | −1.19000 | ||||||||
\(839\) | −1.63778e7 | −0.803250 | −0.401625 | − | 0.915804i | \(-0.631555\pi\) | ||||
−0.401625 | + | 0.915804i | \(0.631555\pi\) | |||||||
\(840\) | 3.93074e6 | + | 6.80824e6i | 0.192210 | + | 0.332917i | ||||
\(841\) | 9.43948e6 | + | 1.63497e7i | 0.460212 | + | 0.797111i | ||||
\(842\) | 1.77081e7 | − | 3.06713e7i | 0.860780 | − | 1.49091i | ||||
\(843\) | 8.53211e6 | − | 1.47780e7i | 0.413511 | − | 0.716223i | ||||
\(844\) | 1.11924e6 | 0.0540836 | ||||||||
\(845\) | −984533. | + | 1.70526e6i | −0.0474339 | + | 0.0821579i | ||||
\(846\) | 6.51749e6 | − | 1.12886e7i | 0.313079 | − | 0.542269i | ||||
\(847\) | 3.26344e6 | − | 5.65245e6i | 0.156303 | − | 0.270725i | ||||
\(848\) | −6.79691e7 | − | 1.17726e8i | −3.24580 | − | 5.62190i | ||||
\(849\) | −7.08906e6 | −0.337535 | ||||||||
\(850\) | −2.75265e7 | − | 4.76773e7i | −1.30678 | − | 2.26342i | ||||
\(851\) | −61378.3 | + | 106310.i | −0.00290530 | + | 0.00503213i | ||||
\(852\) | 3.36016e7 | 1.58585 | ||||||||
\(853\) | −1.26391e7 | + | 2.18915e7i | −0.594761 | + | 1.03016i | 0.398820 | + | 0.917029i | \(0.369420\pi\) |
−0.993581 | + | 0.113126i | \(0.963913\pi\) | |||||||
\(854\) | 358339. | + | 620662.i | 0.0168132 | + | 0.0291213i | ||||
\(855\) | 640346. | + | 1.10911e6i | 0.0299571 | + | 0.0518872i | ||||
\(856\) | 4.21766e7 | 1.96738 | ||||||||
\(857\) | 5.73535e6 | + | 9.93392e6i | 0.266752 | + | 0.462028i | 0.968021 | − | 0.250868i | \(-0.0807161\pi\) |
−0.701269 | + | 0.712897i | \(0.747383\pi\) | |||||||
\(858\) | −7.16366e7 | −3.32213 | ||||||||
\(859\) | −1.05011e7 | −0.485570 | −0.242785 | − | 0.970080i | \(-0.578061\pi\) | ||||
−0.242785 | + | 0.970080i | \(0.578061\pi\) | |||||||
\(860\) | 4.39410e6 | + | 9.85118e6i | 0.202593 | + | 0.454195i | ||||
\(861\) | −3.30023e6 | −0.151718 | ||||||||
\(862\) | 2.86120e7 | 1.31153 | ||||||||
\(863\) | −5.85029e6 | − | 1.01330e7i | −0.267393 | − | 0.463139i | 0.700795 | − | 0.713363i | \(-0.252829\pi\) |
−0.968188 | + | 0.250224i | \(0.919496\pi\) | |||||||
\(864\) | −7.70990e7 | −3.51370 | ||||||||
\(865\) | 1.57449e6 | + | 2.72709e6i | 0.0715482 | + | 0.123925i | ||||
\(866\) | 5.42313e6 | + | 9.39314e6i | 0.245729 | + | 0.425614i | ||||
\(867\) | 1.14994e7 | − | 1.99175e7i | 0.519549 | − | 0.899886i | ||||
\(868\) | 3.64561e7 | 1.64237 | ||||||||
\(869\) | 2.30276e7 | − | 3.98849e7i | 1.03442 | − | 1.79167i | ||||
\(870\) | −1.21913e6 | − | 2.11159e6i | −0.0546073 | − | 0.0945827i | ||||
\(871\) | −3.09945e7 | −1.38433 | ||||||||
\(872\) | −1.87368e7 | − | 3.24531e7i | −0.834457 | − | 1.44532i | ||||
\(873\) | 9330.51 | − | 16160.9i | 0.000414352 | − | 0.000717680i | ||||
\(874\) | 499203. | − | 864646.i | 0.0221054 | − | 0.0382877i | ||||
\(875\) | −2.24971e6 | + | 3.89662e6i | −0.0993362 | + | 0.172055i | ||||
\(876\) | −5.95858e7 | −2.62351 | ||||||||
\(877\) | −419021. | + | 725766.i | −0.0183966 | + | 0.0318638i | −0.875077 | − | 0.483983i | \(-0.839189\pi\) |
0.856681 | + | 0.515847i | \(0.172523\pi\) | |||||||
\(878\) | 1.47678e7 | − | 2.55786e7i | 0.646517 | − | 1.11980i | ||||
\(879\) | −1.94208e6 | − | 3.36379e6i | −0.0847805 | − | 0.146844i | ||||
\(880\) | −1.00199e7 | − | 1.73550e7i | −0.436171 | − | 0.755470i | ||||
\(881\) | −3.69163e7 | −1.60243 | −0.801213 | − | 0.598379i | \(-0.795812\pi\) | ||||
−0.801213 | + | 0.598379i | \(0.795812\pi\) | |||||||
\(882\) | 7.11721e6 | 0.308062 | ||||||||
\(883\) | 1.24749e7 | + | 2.16072e7i | 0.538438 | + | 0.932602i | 0.998988 | + | 0.0449681i | \(0.0143186\pi\) |
−0.460551 | + | 0.887633i | \(0.652348\pi\) | |||||||
\(884\) | 5.52945e7 | + | 9.57729e7i | 2.37986 | + | 4.12204i | ||||
\(885\) | 1.51596e6 | − | 2.62572e6i | 0.0650623 | − | 0.112691i | ||||
\(886\) | 3.57149e7 | − | 6.18601e7i | 1.52850 | − | 2.64744i | ||||
\(887\) | 1.02677e7 | 0.438191 | 0.219096 | − | 0.975703i | \(-0.429689\pi\) | ||||
0.219096 | + | 0.975703i | \(0.429689\pi\) | |||||||
\(888\) | 1.64040e7 | − | 2.84126e7i | 0.698101 | − | 1.20915i | ||||
\(889\) | −4.46947e6 | + | 7.74136e6i | −0.189671 | + | 0.328521i | ||||
\(890\) | 3.13495e6 | − | 5.42990e6i | 0.132665 | − | 0.229782i | ||||
\(891\) | 1.74149e7 | + | 3.01635e7i | 0.734899 | + | 1.27288i | ||||
\(892\) | −2.48105e7 | −1.04406 | ||||||||
\(893\) | 2.38254e7 | + | 4.12668e7i | 0.999797 | + | 1.73170i | ||||
\(894\) | 9.46884e6 | − | 1.64005e7i | 0.396235 | − | 0.686299i | ||||
\(895\) | −2.18120e6 | −0.0910201 | ||||||||
\(896\) | −2.60159e7 | + | 4.50609e7i | −1.08260 | + | 1.87512i | ||||
\(897\) | 261931. | + | 453679.i | 0.0108694 | + | 0.0188264i | ||||
\(898\) | 3.68969e7 | + | 6.39074e7i | 1.52686 | + | 2.64460i | ||||
\(899\) | −7.22110e6 | −0.297992 | ||||||||
\(900\) | 7.54600e6 | + | 1.30701e7i | 0.310535 | + | 0.537862i | ||||
\(901\) | 5.65714e7 | 2.32159 | ||||||||
\(902\) | 1.43961e7 | 0.589156 | ||||||||
\(903\) | −1.51968e7 | − | 1.58674e6i | −0.620200 | − | 0.0647570i | ||||
\(904\) | 3.06413e7 | 1.24706 | ||||||||
\(905\) | 3.87612e6 | 0.157317 | ||||||||
\(906\) | 5.11682e7 | + | 8.86259e7i | 2.07100 | + | 3.58707i | ||||
\(907\) | 1.41953e7 | 0.572962 | 0.286481 | − | 0.958086i | \(-0.407514\pi\) | ||||
0.286481 | + | 0.958086i | \(0.407514\pi\) | |||||||
\(908\) | −2.29407e7 | − | 3.97344e7i | −0.923403 | − | 1.59938i | ||||
\(909\) | 2.13123e6 | + | 3.69140e6i | 0.0855501 | + | 0.148177i | ||||
\(910\) | 3.02561e6 | − | 5.24052e6i | 0.121118 | − | 0.209783i | ||||
\(911\) | −1.46693e7 | −0.585615 | −0.292808 | − | 0.956171i | \(-0.594590\pi\) | ||||
−0.292808 | + | 0.956171i | \(0.594590\pi\) | |||||||
\(912\) | −7.79651e7 | + | 1.35040e8i | −3.10394 | + | 5.37618i | ||||
\(913\) | 1.96151e7 | + | 3.39743e7i | 0.778777 | + | 1.34888i | ||||
\(914\) | −4.49418e7 | −1.77945 | ||||||||
\(915\) | −77886.6 | − | 134904.i | −0.00307546 | − | 0.00532685i | ||||
\(916\) | 9.72224e6 | − | 1.68394e7i | 0.382849 | − | 0.663114i | ||||
\(917\) | −4.90501e6 | + | 8.49573e6i | −0.192627 | + | 0.333639i | ||||
\(918\) | 2.93945e7 | − | 5.09128e7i | 1.15122 | − | 1.99398i | ||||
\(919\) | −4.28459e7 | −1.67348 | −0.836739 | − | 0.547601i | \(-0.815541\pi\) | ||||
−0.836739 | + | 0.547601i | \(0.815541\pi\) | |||||||
\(920\) | −125389. | + | 217180.i | −0.00488416 | + | 0.00845961i | ||||
\(921\) | 1.61975e7 | − | 2.80549e7i | 0.629215 | − | 1.08983i | ||||
\(922\) | −1.35857e7 | − | 2.35312e7i | −0.526327 | − | 0.911625i | ||||
\(923\) | −8.25899e6 | − | 1.43050e7i | −0.319097 | − | 0.552692i | ||||
\(924\) | 5.58717e7 | 2.15284 | ||||||||
\(925\) | 9.23457e6 | 0.354864 | ||||||||
\(926\) | 2.09317e6 | + | 3.62547e6i | 0.0802188 | + | 0.138943i | ||||
\(927\) | −2.68887e6 | − | 4.65725e6i | −0.102771 | − | 0.178004i | ||||
\(928\) | 1.52509e7 | − | 2.64154e7i | 0.581335 | − | 1.00690i | ||||
\(929\) | 8.68346e6 | − | 1.50402e7i | 0.330106 | − | 0.571761i | −0.652426 | − | 0.757852i | \(-0.726249\pi\) |
0.982532 | + | 0.186092i | \(0.0595821\pi\) | |||||||
\(930\) | −1.07873e7 | −0.408982 | ||||||||
\(931\) | −1.30089e7 | + | 2.25321e7i | −0.491888 | + | 0.851975i | ||||
\(932\) | −4.13231e7 | + | 7.15737e7i | −1.55831 | + | 2.69907i | ||||
\(933\) | 2.88789e6 | − | 5.00197e6i | 0.108612 | − | 0.188121i | ||||
\(934\) | 925778. | + | 1.60350e6i | 0.0347248 | + | 0.0601451i | ||||
\(935\) | 8.33967e6 | 0.311975 | ||||||||
\(936\) | −1.31789e7 | − | 2.28264e7i | −0.491686 | − | 0.851625i | ||||
\(937\) | −7.81450e6 | + | 1.35351e7i | −0.290772 | + | 0.503632i | −0.973992 | − | 0.226580i | \(-0.927245\pi\) |
0.683221 | + | 0.730212i | \(0.260579\pi\) | |||||||
\(938\) | 3.29090e7 | 1.22126 | ||||||||
\(939\) | 2.61245e7 | − | 4.52490e7i | 0.966907 | − | 1.67473i | ||||
\(940\) | −9.37055e6 | − | 1.62303e7i | −0.345896 | − | 0.599109i | ||||
\(941\) | 1.02564e6 | + | 1.77647e6i | 0.0377592 | + | 0.0654009i | 0.884287 | − | 0.466943i | \(-0.154645\pi\) |
−0.846528 | + | 0.532344i | \(0.821311\pi\) | |||||||
\(942\) | −9.32479e6 | −0.342383 | ||||||||
\(943\) | −52638.0 | − | 91171.7i | −0.00192761 | − | 0.00333873i | ||||
\(944\) | 6.94955e7 | 2.53821 | ||||||||
\(945\) | −2.36296e6 | −0.0860748 | ||||||||
\(946\) | 6.62909e7 | + | 6.92163e6i | 2.40839 | + | 0.251467i | ||||
\(947\) | −3.01915e7 | −1.09398 | −0.546991 | − | 0.837138i | \(-0.684227\pi\) | ||||
−0.546991 | + | 0.837138i | \(0.684227\pi\) | |||||||
\(948\) | 1.40942e8 | 5.09352 | ||||||||
\(949\) | 1.46457e7 | + | 2.53671e7i | 0.527891 | + | 0.914333i | ||||
\(950\) | −7.51068e7 | −2.70004 | ||||||||
\(951\) | −2.57636e7 | − | 4.46238e7i | −0.923751 | − | 1.59998i | ||||
\(952\) | −3.74946e7 | − | 6.49426e7i | −1.34084 | − | 2.32240i | ||||
\(953\) | 6.69422e6 | − | 1.15947e7i | 0.238763 | − | 0.413550i | −0.721596 | − | 0.692314i | \(-0.756591\pi\) |
0.960360 | + | 0.278764i | \(0.0899246\pi\) | |||||||
\(954\) | −2.11123e7 | −0.751042 | ||||||||
\(955\) | −1.46800e6 | + | 2.54265e6i | −0.0520855 | + | 0.0902148i | ||||
\(956\) | −3.30571e7 | − | 5.72566e7i | −1.16982 | − | 2.02619i | ||||
\(957\) | −1.10669e7 | −0.390611 | ||||||||
\(958\) | −3.18883e7 | − | 5.52321e7i | −1.12258 | − | 1.94437i | ||||
\(959\) | 1.02948e7 | − | 1.78311e7i | 0.361468 | − | 0.626082i | ||||
\(960\) | 1.17021e7 | − | 2.02686e7i | 0.409813 | − | 0.709817i | ||||
\(961\) | −1.65914e6 | + | 2.87372e6i | −0.0579529 | + | 0.100377i | ||||
\(962\) | −2.52534e7 | −0.879796 | ||||||||
\(963\) | 1.91391e6 | − | 3.31500e6i | 0.0665053 | − | 0.115191i | ||||
\(964\) | −4.99121e7 | + | 8.64504e7i | −1.72987 | + | 2.99622i | ||||
\(965\) | −801172. | − | 1.38767e6i | −0.0276954 | − | 0.0479698i | ||||
\(966\) | −278111. | − | 481702.i | −0.00958903 | − | 0.0166087i | ||||
\(967\) | 8.15640e6 | 0.280500 | 0.140250 | − | 0.990116i | \(-0.455209\pi\) | ||||
0.140250 | + | 0.990116i | \(0.455209\pi\) | |||||||
\(968\) | −5.56452e7 | −1.90871 | ||||||||
\(969\) | −3.24456e7 | − | 5.61974e7i | −1.11006 | − | 1.92268i | ||||
\(970\) | −18262.6 | − | 31631.8i | −0.000623208 | − | 0.00107943i | ||||
\(971\) | −1.58889e7 | + | 2.75204e7i | −0.540812 | + | 0.936714i | 0.458046 | + | 0.888929i | \(0.348550\pi\) |
−0.998858 | + | 0.0477851i | \(0.984784\pi\) | |||||||
\(972\) | −1.85493e7 | + | 3.21283e7i | −0.629741 | + | 1.09074i | ||||
\(973\) | −3.03439e7 | −1.02752 | ||||||||
\(974\) | −5.23834e7 | + | 9.07307e7i | −1.76928 | + | 3.06448i | ||||
\(975\) | 1.97042e7 | − | 3.41287e7i | 0.663816 | − | 1.14976i | ||||
\(976\) | 1.78526e6 | − | 3.09217e6i | 0.0599899 | − | 0.103906i | ||||
\(977\) | 2.49221e7 | + | 4.31663e7i | 0.835311 | + | 1.44680i | 0.893777 | + | 0.448511i | \(0.148046\pi\) |
−0.0584663 | + | 0.998289i | \(0.518621\pi\) | |||||||
\(978\) | 1.01648e8 | 3.39822 | ||||||||
\(979\) | −1.42291e7 | − | 2.46455e7i | −0.474482 | − | 0.821827i | ||||
\(980\) | 5.11640e6 | − | 8.86187e6i | 0.170176 | − | 0.294754i | ||||
\(981\) | −3.40100e6 | −0.112832 | ||||||||
\(982\) | 7.73085e6 | − | 1.33902e7i | 0.255828 | − | 0.443108i | ||||
\(983\) | 6.95688e6 | + | 1.20497e7i | 0.229631 | + | 0.397733i | 0.957699 | − | 0.287773i | \(-0.0929147\pi\) |
−0.728068 | + | 0.685505i | \(0.759581\pi\) | |||||||
\(984\) | 1.40681e7 | + | 2.43666e7i | 0.463177 | + | 0.802247i | ||||
\(985\) | −6.73125e6 | −0.221057 | ||||||||
\(986\) | 1.16291e7 | + | 2.01421e7i | 0.380936 | + | 0.659801i | ||||
\(987\) | 2.65467e7 | 0.867396 | ||||||||
\(988\) | 1.50873e8 | 4.91720 | ||||||||
\(989\) | −198551. | − | 445132.i | −0.00645476 | − | 0.0144710i | ||||
\(990\) | −3.11234e6 | −0.100925 | ||||||||
\(991\) | −4.44803e7 | −1.43874 | −0.719372 | − | 0.694625i | \(-0.755570\pi\) | ||||
−0.719372 | + | 0.694625i | \(0.755570\pi\) | |||||||
\(992\) | −6.74729e7 | − | 1.16866e8i | −2.17696 | − | 3.77060i | ||||
\(993\) | −3.13549e7 | −1.00909 | ||||||||
\(994\) | 8.76913e6 | + | 1.51886e7i | 0.281508 | + | 0.487586i | ||||
\(995\) | 1.05338e6 | + | 1.82451e6i | 0.0337308 | + | 0.0584235i | ||||
\(996\) | −6.00277e7 | + | 1.03971e8i | −1.91736 | + | 3.32096i | ||||
\(997\) | −3.38451e7 | −1.07835 | −0.539173 | − | 0.842195i | \(-0.681263\pi\) | ||||
−0.539173 | + | 0.842195i | \(0.681263\pi\) | |||||||
\(998\) | 2.23239e7 | − | 3.86662e7i | 0.709487 | − | 1.22887i | ||||
\(999\) | 4.93062e6 | + | 8.54009e6i | 0.156311 | + | 0.270738i |
(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 | 43.6.c.a.36.1 | yes | 34 | |
43.6 | even | 3 | inner | 43.6.c.a.6.1 | ✓ | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.6.c.a.6.1 | ✓ | 34 | 43.6 | even | 3 | inner | |
43.6.c.a.36.1 | yes | 34 | 1.1 | even | 1 | trivial |