Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,7,Mod(31,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.31");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.8032450172\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 31.8 | ||
Character | \(\chi\) | \(=\) | 60.31 |
Dual form | 60.7.c.a.31.7 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.08457 | + | 7.38143i | −0.385571 | + | 0.922678i | ||||
\(3\) | − | 15.5885i | − | 0.577350i | ||||||
\(4\) | −44.9709 | − | 45.5370i | −0.702670 | − | 0.711516i | ||||
\(5\) | 55.9017 | 0.447214 | ||||||||
\(6\) | 115.065 | + | 48.0836i | 0.532709 | + | 0.222609i | ||||
\(7\) | 200.003i | 0.583099i | 0.956556 | + | 0.291549i | \(0.0941708\pi\) | ||||
−0.956556 | + | 0.291549i | \(0.905829\pi\) | |||||||
\(8\) | 474.844 | − | 191.487i | 0.927429 | − | 0.373999i | ||||
\(9\) | −243.000 | −0.333333 | ||||||||
\(10\) | −172.433 | + | 412.634i | −0.172433 | + | 0.412634i | ||||
\(11\) | − | 76.4809i | − | 0.0574613i | −0.999587 | − | 0.0287306i | \(-0.990853\pi\) | ||
0.999587 | − | 0.0287306i | \(-0.00914650\pi\) | |||||||
\(12\) | −709.852 | + | 701.027i | −0.410794 | + | 0.405687i | ||||
\(13\) | −2210.14 | −1.00598 | −0.502991 | − | 0.864292i | \(-0.667767\pi\) | ||||
−0.502991 | + | 0.864292i | \(0.667767\pi\) | |||||||
\(14\) | −1476.31 | − | 616.922i | −0.538013 | − | 0.224826i | ||||
\(15\) | − | 871.421i | − | 0.258199i | ||||||
\(16\) | −51.2371 | + | 4095.68i | −0.0125091 | + | 0.999922i | ||||
\(17\) | −7764.25 | −1.58035 | −0.790174 | − | 0.612883i | \(-0.790010\pi\) | ||||
−0.790174 | + | 0.612883i | \(0.790010\pi\) | |||||||
\(18\) | 749.550 | − | 1793.69i | 0.128524 | − | 0.307559i | ||||
\(19\) | − | 3205.95i | − | 0.467408i | −0.972308 | − | 0.233704i | \(-0.924915\pi\) | ||
0.972308 | − | 0.233704i | \(-0.0750846\pi\) | |||||||
\(20\) | −2513.95 | − | 2545.60i | −0.314244 | − | 0.318199i | ||||
\(21\) | 3117.74 | 0.336652 | ||||||||
\(22\) | 564.538 | + | 235.911i | 0.0530182 | + | 0.0221554i | ||||
\(23\) | − | 12464.7i | − | 1.02447i | −0.858845 | − | 0.512235i | \(-0.828818\pi\) | ||
0.858845 | − | 0.512235i | \(-0.171182\pi\) | |||||||
\(24\) | −2984.99 | − | 7402.08i | −0.215928 | − | 0.535451i | ||||
\(25\) | 3125.00 | 0.200000 | ||||||||
\(26\) | 6817.33 | − | 16314.0i | 0.387877 | − | 0.928198i | ||||
\(27\) | 3788.00i | 0.192450i | ||||||||
\(28\) | 9107.53 | − | 8994.31i | 0.414884 | − | 0.409726i | ||||
\(29\) | −36699.1 | −1.50474 | −0.752369 | − | 0.658742i | \(-0.771089\pi\) | ||||
−0.752369 | + | 0.658742i | \(0.771089\pi\) | |||||||
\(30\) | 6432.33 | + | 2687.96i | 0.238234 | + | 0.0995540i | ||||
\(31\) | − | 13711.2i | − | 0.460247i | −0.973161 | − | 0.230124i | \(-0.926087\pi\) | ||
0.973161 | − | 0.230124i | \(-0.0739130\pi\) | |||||||
\(32\) | −30073.9 | − | 13011.6i | −0.917783 | − | 0.397083i | ||||
\(33\) | −1192.22 | −0.0331753 | ||||||||
\(34\) | 23949.3 | − | 57311.2i | 0.609336 | − | 1.45815i | ||||
\(35\) | 11180.5i | 0.260770i | ||||||||
\(36\) | 10927.9 | + | 11065.5i | 0.234223 | + | 0.237172i | ||||
\(37\) | −44039.1 | −0.869427 | −0.434713 | − | 0.900569i | \(-0.643150\pi\) | ||||
−0.434713 | + | 0.900569i | \(0.643150\pi\) | |||||||
\(38\) | 23664.5 | + | 9888.97i | 0.431267 | + | 0.180219i | ||||
\(39\) | 34452.7i | 0.580804i | ||||||||
\(40\) | 26544.6 | − | 10704.5i | 0.414759 | − | 0.167257i | ||||
\(41\) | −75533.6 | −1.09594 | −0.547972 | − | 0.836497i | \(-0.684600\pi\) | ||||
−0.547972 | + | 0.836497i | \(0.684600\pi\) | |||||||
\(42\) | −9616.87 | + | 23013.3i | −0.129803 | + | 0.310622i | ||||
\(43\) | 22258.6i | 0.279957i | 0.990155 | + | 0.139979i | \(0.0447034\pi\) | ||||
−0.990155 | + | 0.139979i | \(0.955297\pi\) | |||||||
\(44\) | −3482.71 | + | 3439.42i | −0.0408846 | + | 0.0403763i | ||||
\(45\) | −13584.1 | −0.149071 | ||||||||
\(46\) | 92007.5 | + | 38448.3i | 0.945257 | + | 0.395006i | ||||
\(47\) | 176111.i | 1.69627i | 0.529783 | + | 0.848133i | \(0.322273\pi\) | ||||
−0.529783 | + | 0.848133i | \(0.677727\pi\) | |||||||
\(48\) | 63845.3 | + | 798.708i | 0.577305 | + | 0.00722211i | ||||
\(49\) | 77647.8 | 0.659996 | ||||||||
\(50\) | −9639.27 | + | 23067.0i | −0.0771142 | + | 0.184536i | ||||
\(51\) | 121033.i | 0.912414i | ||||||||
\(52\) | 99392.1 | + | 100643.i | 0.706873 | + | 0.715772i | ||||
\(53\) | −75090.0 | −0.504376 | −0.252188 | − | 0.967678i | \(-0.581150\pi\) | ||||
−0.252188 | + | 0.967678i | \(0.581150\pi\) | |||||||
\(54\) | −27960.8 | − | 11684.3i | −0.177570 | − | 0.0742031i | ||||
\(55\) | − | 4275.41i | − | 0.0256975i | ||||||
\(56\) | 38298.0 | + | 94970.1i | 0.218078 | + | 0.540783i | ||||
\(57\) | −49975.8 | −0.269858 | ||||||||
\(58\) | 113201. | − | 270891.i | 0.580183 | − | 1.38839i | ||||
\(59\) | − | 176642.i | − | 0.860080i | −0.902810 | − | 0.430040i | \(-0.858499\pi\) | ||
0.902810 | − | 0.430040i | \(-0.141501\pi\) | |||||||
\(60\) | −39681.9 | + | 39188.6i | −0.183713 | + | 0.181429i | ||||
\(61\) | −32696.9 | −0.144051 | −0.0720255 | − | 0.997403i | \(-0.522946\pi\) | ||||
−0.0720255 | + | 0.997403i | \(0.522946\pi\) | |||||||
\(62\) | 101208. | + | 42293.2i | 0.424660 | + | 0.177458i | ||||
\(63\) | − | 48600.7i | − | 0.194366i | ||||||
\(64\) | 188809. | − | 181853.i | 0.720250 | − | 0.693715i | ||||
\(65\) | −123551. | −0.449889 | ||||||||
\(66\) | 3677.48 | − | 8800.28i | 0.0127914 | − | 0.0306101i | ||||
\(67\) | 309523.i | 1.02913i | 0.857453 | + | 0.514563i | \(0.172046\pi\) | ||||
−0.857453 | + | 0.514563i | \(0.827954\pi\) | |||||||
\(68\) | 349165. | + | 353560.i | 1.11046 | + | 1.12444i | ||||
\(69\) | −194306. | −0.591478 | ||||||||
\(70\) | −82528.0 | − | 34487.0i | −0.240607 | − | 0.100545i | ||||
\(71\) | − | 377693.i | − | 1.05527i | −0.849471 | − | 0.527635i | \(-0.823079\pi\) | ||
0.849471 | − | 0.527635i | \(-0.176921\pi\) | |||||||
\(72\) | −115387. | + | 46531.4i | −0.309143 | + | 0.124666i | ||||
\(73\) | 423700. | 1.08915 | 0.544577 | − | 0.838711i | \(-0.316690\pi\) | ||||
0.544577 | + | 0.838711i | \(0.316690\pi\) | |||||||
\(74\) | 135841. | − | 325071.i | 0.335226 | − | 0.802201i | ||||
\(75\) | − | 48713.9i | − | 0.115470i | ||||||
\(76\) | −145989. | + | 144174.i | −0.332568 | + | 0.328434i | ||||
\(77\) | 15296.4 | 0.0335056 | ||||||||
\(78\) | −254310. | − | 106272.i | −0.535895 | − | 0.223941i | ||||
\(79\) | − | 643249.i | − | 1.30466i | −0.757934 | − | 0.652331i | \(-0.773791\pi\) | ||
0.757934 | − | 0.652331i | \(-0.226209\pi\) | |||||||
\(80\) | −2864.24 | + | 228955.i | −0.00559422 | + | 0.447179i | ||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | 232988. | − | 557546.i | 0.422564 | − | 1.01120i | ||||
\(83\) | 824425.i | 1.44184i | 0.693019 | + | 0.720919i | \(0.256280\pi\) | ||||
−0.693019 | + | 0.720919i | \(0.743720\pi\) | |||||||
\(84\) | −140207. | − | 141972.i | −0.236556 | − | 0.239533i | ||||
\(85\) | −434035. | −0.706753 | ||||||||
\(86\) | −164300. | − | 68658.0i | −0.258310 | − | 0.107943i | ||||
\(87\) | 572082.i | 0.868761i | ||||||||
\(88\) | −14645.1 | − | 36316.5i | −0.0214904 | − | 0.0532912i | ||||
\(89\) | −539925. | −0.765885 | −0.382942 | − | 0.923772i | \(-0.625089\pi\) | ||||
−0.382942 | + | 0.923772i | \(0.625089\pi\) | |||||||
\(90\) | 41901.1 | − | 100270.i | 0.0574775 | − | 0.137545i | ||||
\(91\) | − | 442035.i | − | 0.586587i | ||||||
\(92\) | −567607. | + | 560550.i | −0.728927 | + | 0.719865i | ||||
\(93\) | −213737. | −0.265724 | ||||||||
\(94\) | −1.29995e6 | − | 543227.i | −1.56511 | − | 0.654031i | ||||
\(95\) | − | 179218.i | − | 0.209031i | ||||||
\(96\) | −202831. | + | 468806.i | −0.229256 | + | 0.529882i | ||||
\(97\) | 1.03950e6 | 1.13896 | 0.569481 | − | 0.822005i | \(-0.307144\pi\) | ||||
0.569481 | + | 0.822005i | \(0.307144\pi\) | |||||||
\(98\) | −239510. | + | 573152.i | −0.254475 | + | 0.608964i | ||||
\(99\) | 18584.9i | 0.0191538i | ||||||||
\(100\) | −140534. | − | 142303.i | −0.140534 | − | 0.142303i | ||||
\(101\) | 1.03704e6 | 1.00654 | 0.503269 | − | 0.864130i | \(-0.332130\pi\) | ||||
0.503269 | + | 0.864130i | \(0.332130\pi\) | |||||||
\(102\) | −893393. | − | 373333.i | −0.841864 | − | 0.351800i | ||||
\(103\) | 147507.i | 0.134989i | 0.997720 | + | 0.0674947i | \(0.0215006\pi\) | ||||
−0.997720 | + | 0.0674947i | \(0.978499\pi\) | |||||||
\(104\) | −1.04947e6 | + | 423214.i | −0.932977 | + | 0.376236i | ||||
\(105\) | 174287. | 0.150555 | ||||||||
\(106\) | 231620. | − | 554271.i | 0.194473 | − | 0.465377i | ||||
\(107\) | − | 2.37593e6i | − | 1.93947i | −0.244159 | − | 0.969735i | \(-0.578512\pi\) | ||
0.244159 | − | 0.969735i | \(-0.421488\pi\) | |||||||
\(108\) | 172494. | − | 170350.i | 0.136931 | − | 0.135229i | ||||
\(109\) | 220507. | 0.170272 | 0.0851361 | − | 0.996369i | \(-0.472867\pi\) | ||||
0.0851361 | + | 0.996369i | \(0.472867\pi\) | |||||||
\(110\) | 31558.7 | + | 13187.8i | 0.0237105 | + | 0.00990819i | ||||
\(111\) | 686501.i | 0.501964i | ||||||||
\(112\) | −819148. | − | 10247.6i | −0.583053 | − | 0.00729402i | ||||
\(113\) | −6962.21 | −0.00482516 | −0.00241258 | − | 0.999997i | \(-0.500768\pi\) | ||||
−0.00241258 | + | 0.999997i | \(0.500768\pi\) | |||||||
\(114\) | 154154. | − | 368893.i | 0.104049 | − | 0.248992i | ||||
\(115\) | − | 696800.i | − | 0.458157i | ||||||
\(116\) | 1.65039e6 | + | 1.67116e6i | 1.05733 | + | 1.07064i | ||||
\(117\) | 537065. | 0.335327 | ||||||||
\(118\) | 1.30387e6 | + | 544865.i | 0.793577 | + | 0.331622i | ||||
\(119\) | − | 1.55287e6i | − | 0.921499i | ||||||
\(120\) | −166866. | − | 413789.i | −0.0965661 | − | 0.239461i | ||||
\(121\) | 1.76571e6 | 0.996698 | ||||||||
\(122\) | 100856. | − | 241349.i | 0.0555419 | − | 0.132913i | ||||
\(123\) | 1.17745e6i | 0.632744i | ||||||||
\(124\) | −624368. | + | 616606.i | −0.327473 | + | 0.323402i | ||||
\(125\) | 174693. | 0.0894427 | ||||||||
\(126\) | 358742. | + | 149912.i | 0.179338 | + | 0.0749420i | ||||
\(127\) | 1.62503e6i | 0.793324i | 0.917965 | + | 0.396662i | \(0.129832\pi\) | ||||
−0.917965 | + | 0.396662i | \(0.870168\pi\) | |||||||
\(128\) | 759941. | + | 1.95462e6i | 0.362368 | + | 0.932035i | ||||
\(129\) | 346977. | 0.161633 | ||||||||
\(130\) | 381100. | − | 911980.i | 0.173464 | − | 0.415103i | ||||
\(131\) | − | 2.19004e6i | − | 0.974178i | −0.873352 | − | 0.487089i | \(-0.838059\pi\) | ||
0.873352 | − | 0.487089i | \(-0.161941\pi\) | |||||||
\(132\) | 53615.2 | + | 54290.1i | 0.0233113 | + | 0.0236047i | ||||
\(133\) | 641199. | 0.272545 | ||||||||
\(134\) | −2.28472e6 | − | 954744.i | −0.949552 | − | 0.396801i | ||||
\(135\) | 211755.i | 0.0860663i | ||||||||
\(136\) | −3.68680e6 | + | 1.48676e6i | −1.46566 | + | 0.591048i | ||||
\(137\) | 645148. | 0.250898 | 0.125449 | − | 0.992100i | \(-0.459963\pi\) | ||||
0.125449 | + | 0.992100i | \(0.459963\pi\) | |||||||
\(138\) | 599350. | − | 1.43426e6i | 0.228057 | − | 0.545744i | ||||
\(139\) | 1.82992e6i | 0.681376i | 0.940176 | + | 0.340688i | \(0.110660\pi\) | ||||
−0.940176 | + | 0.340688i | \(0.889340\pi\) | |||||||
\(140\) | 509127. | − | 502797.i | 0.185542 | − | 0.183235i | ||||
\(141\) | 2.74531e6 | 0.979340 | ||||||||
\(142\) | 2.78791e6 | + | 1.16502e6i | 0.973675 | + | 0.406881i | ||||
\(143\) | 169034.i | 0.0578050i | ||||||||
\(144\) | 12450.6 | − | 995250.i | 0.00416969 | − | 0.333307i | ||||
\(145\) | −2.05154e6 | −0.672939 | ||||||||
\(146\) | −1.30693e6 | + | 3.12751e6i | −0.419946 | + | 1.00494i | ||||
\(147\) | − | 1.21041e6i | − | 0.381049i | ||||||
\(148\) | 1.98048e6 | + | 2.00541e6i | 0.610920 | + | 0.618611i | ||||
\(149\) | −5.15717e6 | −1.55902 | −0.779511 | − | 0.626388i | \(-0.784532\pi\) | ||||
−0.779511 | + | 0.626388i | \(0.784532\pi\) | |||||||
\(150\) | 359578. | + | 150261.i | 0.106542 | + | 0.0445219i | ||||
\(151\) | 4.15675e6i | 1.20732i | 0.797241 | + | 0.603662i | \(0.206292\pi\) | ||||
−0.797241 | + | 0.603662i | \(0.793708\pi\) | |||||||
\(152\) | −613899. | − | 1.52233e6i | −0.174810 | − | 0.433488i | ||||
\(153\) | 1.88671e6 | 0.526782 | ||||||||
\(154\) | −47182.8 | + | 112909.i | −0.0129188 | + | 0.0309149i | ||||
\(155\) | − | 766480.i | − | 0.205829i | ||||||
\(156\) | 1.56887e6 | − | 1.54937e6i | 0.413251 | − | 0.408114i | ||||
\(157\) | 2.10057e6 | 0.542798 | 0.271399 | − | 0.962467i | \(-0.412514\pi\) | ||||
0.271399 | + | 0.962467i | \(0.412514\pi\) | |||||||
\(158\) | 4.74810e6 | + | 1.98415e6i | 1.20378 | + | 0.503040i | ||||
\(159\) | 1.17054e6i | 0.291202i | ||||||||
\(160\) | −1.68118e6 | − | 727371.i | −0.410445 | − | 0.177581i | ||||
\(161\) | 2.49298e6 | 0.597368 | ||||||||
\(162\) | −182141. | + | 435866.i | −0.0428412 | + | 0.102520i | ||||
\(163\) | 7.38999e6i | 1.70640i | 0.521583 | + | 0.853200i | \(0.325342\pi\) | ||||
−0.521583 | + | 0.853200i | \(0.674658\pi\) | |||||||
\(164\) | 3.39681e6 | + | 3.43957e6i | 0.770088 | + | 0.779782i | ||||
\(165\) | −66647.1 | −0.0148364 | ||||||||
\(166\) | −6.08543e6 | − | 2.54299e6i | −1.33035 | − | 0.555931i | ||||
\(167\) | − | 5.20318e6i | − | 1.11717i | −0.829447 | − | 0.558585i | \(-0.811344\pi\) | ||
0.829447 | − | 0.558585i | \(-0.188656\pi\) | |||||||
\(168\) | 1.48044e6 | − | 597007.i | 0.312221 | − | 0.125908i | ||||
\(169\) | 57919.0 | 0.0119994 | ||||||||
\(170\) | 1.33881e6 | − | 3.20379e6i | 0.272503 | − | 0.652105i | ||||
\(171\) | 779046.i | 0.155803i | ||||||||
\(172\) | 1.01359e6 | − | 1.00099e6i | 0.199194 | − | 0.196718i | ||||
\(173\) | −7.71907e6 | −1.49083 | −0.745413 | − | 0.666603i | \(-0.767747\pi\) | ||||
−0.745413 | + | 0.666603i | \(0.767747\pi\) | |||||||
\(174\) | −4.22278e6 | − | 1.76462e6i | −0.801587 | − | 0.334969i | ||||
\(175\) | 625009.i | 0.116620i | ||||||||
\(176\) | 313241. | + | 3918.66i | 0.0574568 | + | 0.000718787i | ||||
\(177\) | −2.75358e6 | −0.496567 | ||||||||
\(178\) | 1.66543e6 | − | 3.98542e6i | 0.295303 | − | 0.706665i | ||||
\(179\) | − | 5.62557e6i | − | 0.980860i | −0.871481 | − | 0.490430i | \(-0.836840\pi\) | ||
0.871481 | − | 0.490430i | \(-0.163160\pi\) | |||||||
\(180\) | 610890. | + | 618580.i | 0.104748 | + | 0.106066i | ||||
\(181\) | −8.06911e6 | −1.36079 | −0.680393 | − | 0.732848i | \(-0.738191\pi\) | ||||
−0.680393 | + | 0.732848i | \(0.738191\pi\) | |||||||
\(182\) | 3.26285e6 | + | 1.36349e6i | 0.541231 | + | 0.226171i | ||||
\(183\) | 509694.i | 0.0831679i | ||||||||
\(184\) | −2.38684e6 | − | 5.91880e6i | −0.383151 | − | 0.950124i | ||||
\(185\) | −2.46186e6 | −0.388819 | ||||||||
\(186\) | 659285. | − | 1.57768e6i | 0.102455 | − | 0.245178i | ||||
\(187\) | 593817.i | 0.0908087i | ||||||||
\(188\) | 8.01959e6 | − | 7.91989e6i | 1.20692 | − | 1.19192i | ||||
\(189\) | −757610. | −0.112217 | ||||||||
\(190\) | 1.32288e6 | + | 552810.i | 0.192868 | + | 0.0805963i | ||||
\(191\) | 4.37551e6i | 0.627955i | 0.949430 | + | 0.313978i | \(0.101662\pi\) | ||||
−0.949430 | + | 0.313978i | \(0.898338\pi\) | |||||||
\(192\) | −2.83481e6 | − | 2.94324e6i | −0.400516 | − | 0.415836i | ||||
\(193\) | −1.27283e7 | −1.77052 | −0.885259 | − | 0.465099i | \(-0.846019\pi\) | ||||
−0.885259 | + | 0.465099i | \(0.846019\pi\) | |||||||
\(194\) | −3.20640e6 | + | 7.67299e6i | −0.439150 | + | 1.05089i | ||||
\(195\) | 1.92596e6i | 0.259743i | ||||||||
\(196\) | −3.49189e6 | − | 3.53585e6i | −0.463759 | − | 0.469597i | ||||
\(197\) | 1.95623e6 | 0.255872 | 0.127936 | − | 0.991782i | \(-0.459165\pi\) | ||||
0.127936 | + | 0.991782i | \(0.459165\pi\) | |||||||
\(198\) | −137183. | − | 57326.3i | −0.0176727 | − | 0.00738513i | ||||
\(199\) | − | 4.27520e6i | − | 0.542497i | −0.962509 | − | 0.271248i | \(-0.912564\pi\) | ||
0.962509 | − | 0.271248i | \(-0.0874365\pi\) | |||||||
\(200\) | 1.48389e6 | − | 598398.i | 0.185486 | − | 0.0747998i | ||||
\(201\) | 4.82498e6 | 0.594166 | ||||||||
\(202\) | −3.19881e6 | + | 7.65482e6i | −0.388092 | + | 0.928711i | ||||
\(203\) | − | 7.33992e6i | − | 0.877411i | ||||||
\(204\) | 5.51146e6 | − | 5.44295e6i | 0.649197 | − | 0.641126i | ||||
\(205\) | −4.22246e6 | −0.490121 | ||||||||
\(206\) | −1.08881e6 | − | 454994.i | −0.124552 | − | 0.0520480i | ||||
\(207\) | 3.02893e6i | 0.341490i | ||||||||
\(208\) | 113241. | − | 9.05203e6i | 0.0125839 | − | 1.00590i | ||||
\(209\) | −245194. | −0.0268578 | ||||||||
\(210\) | −537599. | + | 1.28648e6i | −0.0580498 | + | 0.138914i | ||||
\(211\) | − | 1.28034e7i | − | 1.36294i | −0.731846 | − | 0.681470i | \(-0.761341\pi\) | ||
0.731846 | − | 0.681470i | \(-0.238659\pi\) | |||||||
\(212\) | 3.37686e6 | + | 3.41937e6i | 0.354410 | + | 0.358871i | ||||
\(213\) | −5.88765e6 | −0.609260 | ||||||||
\(214\) | 1.75378e7 | + | 7.32873e6i | 1.78951 | + | 0.747803i | ||||
\(215\) | 1.24429e6i | 0.125201i | ||||||||
\(216\) | 725353. | + | 1.79871e6i | 0.0719761 | + | 0.178484i | ||||
\(217\) | 2.74228e6 | 0.268369 | ||||||||
\(218\) | −680170. | + | 1.62766e6i | −0.0656520 | + | 0.157106i | ||||
\(219\) | − | 6.60482e6i | − | 0.628824i | ||||||
\(220\) | −194690. | + | 192269.i | −0.0182841 | + | 0.0180568i | ||||
\(221\) | 1.71601e7 | 1.58980 | ||||||||
\(222\) | −5.06736e6 | − | 2.11756e6i | −0.463151 | − | 0.193543i | ||||
\(223\) | 1.08749e7i | 0.980643i | 0.871542 | + | 0.490321i | \(0.163121\pi\) | ||||
−0.871542 | + | 0.490321i | \(0.836879\pi\) | |||||||
\(224\) | 2.60236e6 | − | 6.01487e6i | 0.231538 | − | 0.535158i | ||||
\(225\) | −759375. | −0.0666667 | ||||||||
\(226\) | 21475.4 | − | 51391.0i | 0.00186044 | − | 0.00445207i | ||||
\(227\) | − | 2.18048e6i | − | 0.186412i | −0.995647 | − | 0.0932059i | \(-0.970289\pi\) | ||
0.995647 | − | 0.0932059i | \(-0.0297115\pi\) | |||||||
\(228\) | 2.24746e6 | + | 2.27575e6i | 0.189621 | + | 0.192008i | ||||
\(229\) | 4.73117e6 | 0.393969 | 0.196985 | − | 0.980407i | \(-0.436885\pi\) | ||||
0.196985 | + | 0.980407i | \(0.436885\pi\) | |||||||
\(230\) | 5.14338e6 | + | 2.14933e6i | 0.422732 | + | 0.176652i | ||||
\(231\) | − | 238447.i | − | 0.0193445i | ||||||
\(232\) | −1.74263e7 | + | 7.02741e6i | −1.39554 | + | 0.562770i | ||||
\(233\) | −1.55698e7 | −1.23088 | −0.615440 | − | 0.788183i | \(-0.711022\pi\) | ||||
−0.615440 | + | 0.788183i | \(0.711022\pi\) | |||||||
\(234\) | −1.65661e6 | + | 3.96430e6i | −0.129292 | + | 0.309399i | ||||
\(235\) | 9.84493e6i | 0.758593i | ||||||||
\(236\) | −8.04376e6 | + | 7.94377e6i | −0.611960 | + | 0.604353i | ||||
\(237\) | −1.00273e7 | −0.753247 | ||||||||
\(238\) | 1.14624e7 | + | 4.78994e6i | 0.850247 | + | 0.355303i | ||||
\(239\) | 2.29769e7i | 1.68306i | 0.540214 | + | 0.841528i | \(0.318343\pi\) | ||||
−0.540214 | + | 0.841528i | \(0.681657\pi\) | |||||||
\(240\) | 3.56906e6 | + | 44649.1i | 0.258179 | + | 0.00322983i | ||||
\(241\) | 2.43938e7 | 1.74272 | 0.871362 | − | 0.490642i | \(-0.163238\pi\) | ||||
0.871362 | + | 0.490642i | \(0.163238\pi\) | |||||||
\(242\) | −5.44646e6 | + | 1.30335e7i | −0.384298 | + | 0.919632i | ||||
\(243\) | − | 920483.i | − | 0.0641500i | ||||||
\(244\) | 1.47041e6 | + | 1.48892e6i | 0.101220 | + | 0.102495i | ||||
\(245\) | 4.34065e6 | 0.295159 | ||||||||
\(246\) | −8.69127e6 | − | 3.63193e6i | −0.583819 | − | 0.243968i | ||||
\(247\) | 7.08561e6i | 0.470204i | ||||||||
\(248\) | −2.62553e6 | − | 6.51069e6i | −0.172132 | − | 0.426846i | ||||
\(249\) | 1.28515e7 | 0.832446 | ||||||||
\(250\) | −538852. | + | 1.28948e6i | −0.0344865 | + | 0.0825268i | ||||
\(251\) | − | 7.13591e6i | − | 0.451261i | −0.974213 | − | 0.225631i | \(-0.927556\pi\) | ||
0.974213 | − | 0.225631i | \(-0.0724442\pi\) | |||||||
\(252\) | −2.21313e6 | + | 2.18562e6i | −0.138295 | + | 0.136575i | ||||
\(253\) | −953315. | −0.0588674 | ||||||||
\(254\) | −1.19951e7 | − | 5.01252e6i | −0.731983 | − | 0.305883i | ||||
\(255\) | 6.76593e6i | 0.408044i | ||||||||
\(256\) | −1.67720e7 | − | 419702.i | −0.999687 | − | 0.0250162i | ||||
\(257\) | 4.16162e6 | 0.245168 | 0.122584 | − | 0.992458i | \(-0.460882\pi\) | ||||
0.122584 | + | 0.992458i | \(0.460882\pi\) | |||||||
\(258\) | −1.07027e6 | + | 2.56118e6i | −0.0623211 | + | 0.149136i | ||||
\(259\) | − | 8.80794e6i | − | 0.506962i | ||||||
\(260\) | 5.55619e6 | + | 5.62613e6i | 0.316123 | + | 0.320103i | ||||
\(261\) | 8.91787e6 | 0.501579 | ||||||||
\(262\) | 1.61656e7 | + | 6.75533e6i | 0.898853 | + | 0.375615i | ||||
\(263\) | 1.42161e7i | 0.781474i | 0.920502 | + | 0.390737i | \(0.127780\pi\) | ||||
−0.920502 | + | 0.390737i | \(0.872220\pi\) | |||||||
\(264\) | −566118. | + | 228295.i | −0.0307677 | + | 0.0124075i | ||||
\(265\) | −4.19766e6 | −0.225564 | ||||||||
\(266\) | −1.97782e6 | + | 4.73297e6i | −0.105085 | + | 0.251471i | ||||
\(267\) | 8.41660e6i | 0.442184i | ||||||||
\(268\) | 1.40947e7 | − | 1.39195e7i | 0.732239 | − | 0.723136i | ||||
\(269\) | 2.27308e7 | 1.16777 | 0.583887 | − | 0.811835i | \(-0.301531\pi\) | ||||
0.583887 | + | 0.811835i | \(0.301531\pi\) | |||||||
\(270\) | −1.56306e6 | − | 653174.i | −0.0794115 | − | 0.0331847i | ||||
\(271\) | − | 1.88317e7i | − | 0.946196i | −0.881010 | − | 0.473098i | \(-0.843136\pi\) | ||
0.881010 | − | 0.473098i | \(-0.156864\pi\) | |||||||
\(272\) | 397818. | − | 3.17999e7i | 0.0197687 | − | 1.58022i | ||||
\(273\) | −6.89064e6 | −0.338666 | ||||||||
\(274\) | −1.99000e6 | + | 4.76211e6i | −0.0967391 | + | 0.231498i | ||||
\(275\) | − | 239003.i | − | 0.0114923i | ||||||
\(276\) | 8.73811e6 | + | 8.84811e6i | 0.415614 | + | 0.420846i | ||||
\(277\) | 3.49012e7 | 1.64211 | 0.821053 | − | 0.570852i | \(-0.193387\pi\) | ||||
0.821053 | + | 0.570852i | \(0.193387\pi\) | |||||||
\(278\) | −1.35074e7 | − | 5.64450e6i | −0.628691 | − | 0.262719i | ||||
\(279\) | 3.33183e6i | 0.153416i | ||||||||
\(280\) | 2.14093e6 | + | 5.30899e6i | 0.0975276 | + | 0.241845i | ||||
\(281\) | −2.31838e6 | −0.104488 | −0.0522440 | − | 0.998634i | \(-0.516637\pi\) | ||||
−0.0522440 | + | 0.998634i | \(0.516637\pi\) | |||||||
\(282\) | −8.46808e6 | + | 2.02643e7i | −0.377605 | + | 0.903615i | ||||
\(283\) | − | 4.22387e7i | − | 1.86359i | −0.362982 | − | 0.931796i | \(-0.618241\pi\) | ||
0.362982 | − | 0.931796i | \(-0.381759\pi\) | |||||||
\(284\) | −1.71990e7 | + | 1.69852e7i | −0.750841 | + | 0.741507i | ||||
\(285\) | −2.79373e6 | −0.120684 | ||||||||
\(286\) | −1.24771e6 | − | 521396.i | −0.0533354 | − | 0.0222879i | ||||
\(287\) | − | 1.51069e7i | − | 0.639044i | ||||||
\(288\) | 7.30796e6 | + | 3.16182e6i | 0.305928 | + | 0.132361i | ||||
\(289\) | 3.61460e7 | 1.49750 | ||||||||
\(290\) | 6.32811e6 | − | 1.51433e7i | 0.259466 | − | 0.620906i | ||||
\(291\) | − | 1.62042e7i | − | 0.657580i | ||||||
\(292\) | −1.90542e7 | − | 1.92940e7i | −0.765316 | − | 0.774950i | ||||
\(293\) | −3.90188e7 | −1.55121 | −0.775606 | − | 0.631217i | \(-0.782556\pi\) | ||||
−0.775606 | + | 0.631217i | \(0.782556\pi\) | |||||||
\(294\) | 8.93455e6 | + | 3.73359e6i | 0.351585 | + | 0.146921i | ||||
\(295\) | − | 9.87461e6i | − | 0.384639i | ||||||
\(296\) | −2.09117e7 | + | 8.43293e6i | −0.806332 | + | 0.325165i | ||||
\(297\) | 289709. | 0.0110584 | ||||||||
\(298\) | 1.59076e7 | − | 3.80672e7i | 0.601113 | − | 1.43848i | ||||
\(299\) | 2.75488e7i | 1.03060i | ||||||||
\(300\) | −2.21829e6 | + | 2.19071e6i | −0.0821588 | + | 0.0811374i | ||||
\(301\) | −4.45178e6 | −0.163243 | ||||||||
\(302\) | −3.06828e7 | − | 1.28218e7i | −1.11397 | − | 0.465509i | ||||
\(303\) | − | 1.61658e7i | − | 0.581125i | ||||||
\(304\) | 1.31305e7 | + | 164264.i | 0.467371 | + | 0.00584684i | ||||
\(305\) | −1.82781e6 | −0.0644216 | ||||||||
\(306\) | −5.81969e6 | + | 1.39266e7i | −0.203112 | + | 0.486051i | ||||
\(307\) | − | 1.55131e7i | − | 0.536146i | −0.963399 | − | 0.268073i | \(-0.913613\pi\) | ||
0.963399 | − | 0.268073i | \(-0.0863868\pi\) | |||||||
\(308\) | −687893. | − | 696553.i | −0.0235434 | − | 0.0238398i | ||||
\(309\) | 2.29940e6 | 0.0779362 | ||||||||
\(310\) | 5.65772e6 | + | 2.36426e6i | 0.189914 | + | 0.0793616i | ||||
\(311\) | − | 7.03395e6i | − | 0.233840i | −0.993141 | − | 0.116920i | \(-0.962698\pi\) | ||
0.993141 | − | 0.116920i | \(-0.0373021\pi\) | |||||||
\(312\) | 6.59726e6 | + | 1.63597e7i | 0.217220 | + | 0.538654i | ||||
\(313\) | −2.40261e7 | −0.783519 | −0.391759 | − | 0.920068i | \(-0.628133\pi\) | ||||
−0.391759 | + | 0.920068i | \(0.628133\pi\) | |||||||
\(314\) | −6.47935e6 | + | 1.55052e7i | −0.209287 | + | 0.500828i | ||||
\(315\) | − | 2.71686e6i | − | 0.0869232i | ||||||
\(316\) | −2.92916e7 | + | 2.89275e7i | −0.928287 | + | 0.916747i | ||||
\(317\) | 5.56316e7 | 1.74640 | 0.873200 | − | 0.487362i | \(-0.162041\pi\) | ||||
0.873200 | + | 0.487362i | \(0.162041\pi\) | |||||||
\(318\) | −8.64023e6 | − | 3.61060e6i | −0.268685 | − | 0.112279i | ||||
\(319\) | 2.80678e6i | 0.0864641i | ||||||||
\(320\) | 1.05548e7 | − | 1.01659e7i | 0.322105 | − | 0.310239i | ||||
\(321\) | −3.70372e7 | −1.11975 | ||||||||
\(322\) | −7.68977e6 | + | 1.84018e7i | −0.230328 | + | 0.551178i | ||||
\(323\) | 2.48918e7i | 0.738667i | ||||||||
\(324\) | −2.65549e6 | − | 2.68891e6i | −0.0780745 | − | 0.0790573i | ||||
\(325\) | −6.90669e6 | −0.201196 | ||||||||
\(326\) | −5.45487e7 | − | 2.27949e7i | −1.57446 | − | 0.657938i | ||||
\(327\) | − | 3.43737e6i | − | 0.0983067i | ||||||
\(328\) | −3.58666e7 | + | 1.44637e7i | −1.01641 | + | 0.409882i | ||||
\(329\) | −3.52228e7 | −0.989091 | ||||||||
\(330\) | 205577. | − | 491951.i | 0.00572050 | − | 0.0136893i | ||||
\(331\) | − | 5.14649e6i | − | 0.141915i | −0.997479 | − | 0.0709573i | \(-0.977395\pi\) | ||
0.997479 | − | 0.0709573i | \(-0.0226054\pi\) | |||||||
\(332\) | 3.75418e7 | − | 3.70751e7i | 1.02589 | − | 1.01314i | ||||
\(333\) | 1.07015e7 | 0.289809 | ||||||||
\(334\) | 3.84069e7 | + | 1.60496e7i | 1.03079 | + | 0.430749i | ||||
\(335\) | 1.73029e7i | 0.460239i | ||||||||
\(336\) | −159744. | + | 1.27693e7i | −0.00421121 | + | 0.336626i | ||||
\(337\) | −6.46645e7 | −1.68957 | −0.844784 | − | 0.535107i | \(-0.820271\pi\) | ||||
−0.844784 | + | 0.535107i | \(0.820271\pi\) | |||||||
\(338\) | −178655. | + | 427525.i | −0.00462663 | + | 0.0110716i | ||||
\(339\) | 108530.i | 0.00278581i | ||||||||
\(340\) | 1.95189e7 | + | 1.97646e7i | 0.496614 | + | 0.502866i | ||||
\(341\) | −1.04865e6 | −0.0264464 | ||||||||
\(342\) | −5.75047e6 | − | 2.40302e6i | −0.143756 | − | 0.0600729i | ||||
\(343\) | 3.90599e7i | 0.967942i | ||||||||
\(344\) | 4.26223e6 | + | 1.05693e7i | 0.104704 | + | 0.259641i | ||||
\(345\) | −1.08620e7 | −0.264517 | ||||||||
\(346\) | 2.38100e7 | − | 5.69777e7i | 0.574819 | − | 1.37555i | ||||
\(347\) | − | 1.93865e7i | − | 0.463994i | −0.972717 | − | 0.231997i | \(-0.925474\pi\) | ||
0.972717 | − | 0.231997i | \(-0.0745259\pi\) | |||||||
\(348\) | 2.60509e7 | − | 2.57270e7i | 0.618137 | − | 0.610452i | ||||
\(349\) | −2.55563e7 | −0.601205 | −0.300602 | − | 0.953750i | \(-0.597188\pi\) | ||||
−0.300602 | + | 0.953750i | \(0.597188\pi\) | |||||||
\(350\) | −4.61346e6 | − | 1.92788e6i | −0.107603 | − | 0.0449652i | ||||
\(351\) | − | 8.37201e6i | − | 0.193601i | ||||||
\(352\) | −995139. | + | 2.30008e6i | −0.0228169 | + | 0.0527370i | ||||
\(353\) | −4.60766e6 | −0.104751 | −0.0523753 | − | 0.998627i | \(-0.516679\pi\) | ||||
−0.0523753 | + | 0.998627i | \(0.516679\pi\) | |||||||
\(354\) | 8.49361e6 | − | 2.03254e7i | 0.191462 | − | 0.458172i | ||||
\(355\) | − | 2.11137e7i | − | 0.471931i | ||||||
\(356\) | 2.42809e7 | + | 2.45866e7i | 0.538164 | + | 0.544939i | ||||
\(357\) | −2.42069e7 | −0.532027 | ||||||||
\(358\) | 4.15247e7 | + | 1.73524e7i | 0.905018 | + | 0.378191i | ||||
\(359\) | 8.33832e7i | 1.80217i | 0.433646 | + | 0.901083i | \(0.357227\pi\) | ||||
−0.433646 | + | 0.901083i | \(0.642773\pi\) | |||||||
\(360\) | −6.45033e6 | + | 2.60119e6i | −0.138253 | + | 0.0557525i | ||||
\(361\) | 3.67678e7 | 0.781530 | ||||||||
\(362\) | 2.48897e7 | − | 5.95615e7i | 0.524679 | − | 1.25557i | ||||
\(363\) | − | 2.75247e7i | − | 0.575444i | ||||||
\(364\) | −2.01289e7 | + | 1.98787e7i | −0.417366 | + | 0.412177i | ||||
\(365\) | 2.36855e7 | 0.487085 | ||||||||
\(366\) | −3.76227e6 | − | 1.57218e6i | −0.0767372 | − | 0.0320671i | ||||
\(367\) | 2.81067e7i | 0.568606i | 0.958734 | + | 0.284303i | \(0.0917622\pi\) | ||||
−0.958734 | + | 0.284303i | \(0.908238\pi\) | |||||||
\(368\) | 5.10516e7 | + | 638657.i | 1.02439 | + | 0.0128152i | ||||
\(369\) | 1.83547e7 | 0.365315 | ||||||||
\(370\) | 7.59377e6 | − | 1.81720e7i | 0.149917 | − | 0.358755i | ||||
\(371\) | − | 1.50182e7i | − | 0.294101i | ||||||
\(372\) | 9.61193e6 | + | 9.73293e6i | 0.186716 | + | 0.189067i | ||||
\(373\) | −3.04923e7 | −0.587576 | −0.293788 | − | 0.955871i | \(-0.594916\pi\) | ||||
−0.293788 | + | 0.955871i | \(0.594916\pi\) | |||||||
\(374\) | −4.38321e6 | − | 1.83167e6i | −0.0837872 | − | 0.0350132i | ||||
\(375\) | − | 2.72319e6i | − | 0.0516398i | ||||||
\(376\) | 3.37231e7 | + | 8.36254e7i | 0.634402 | + | 1.57317i | ||||
\(377\) | 8.11101e7 | 1.51374 | ||||||||
\(378\) | 2.33690e6 | − | 5.59224e6i | 0.0432678 | − | 0.103541i | ||||
\(379\) | − | 8.15538e7i | − | 1.49805i | −0.662541 | − | 0.749026i | \(-0.730522\pi\) | ||
0.662541 | − | 0.749026i | \(-0.269478\pi\) | |||||||
\(380\) | −8.16105e6 | + | 8.05960e6i | −0.148729 | + | 0.146880i | ||||
\(381\) | 2.53317e7 | 0.458026 | ||||||||
\(382\) | −3.22975e7 | − | 1.34966e7i | −0.579400 | − | 0.242121i | ||||
\(383\) | 9.61974e7i | 1.71225i | 0.516769 | + | 0.856125i | \(0.327135\pi\) | ||||
−0.516769 | + | 0.856125i | \(0.672865\pi\) | |||||||
\(384\) | 3.04695e7 | − | 1.18463e7i | 0.538111 | − | 0.209213i | ||||
\(385\) | 855095. | 0.0149842 | ||||||||
\(386\) | 3.92614e7 | − | 9.39534e7i | 0.682660 | − | 1.63362i | ||||
\(387\) | − | 5.40883e6i | − | 0.0933191i | ||||||
\(388\) | −4.67472e7 | − | 4.73357e7i | −0.800314 | − | 0.810389i | ||||
\(389\) | −3.31294e7 | −0.562814 | −0.281407 | − | 0.959589i | \(-0.590801\pi\) | ||||
−0.281407 | + | 0.959589i | \(0.590801\pi\) | |||||||
\(390\) | −1.42164e7 | − | 5.94077e6i | −0.239660 | − | 0.100149i | ||||
\(391\) | 9.67793e7i | 1.61902i | ||||||||
\(392\) | 3.68706e7 | − | 1.48686e7i | 0.612099 | − | 0.246838i | ||||
\(393\) | −3.41393e7 | −0.562442 | ||||||||
\(394\) | −6.03413e6 | + | 1.44398e7i | −0.0986566 | + | 0.236087i | ||||
\(395\) | − | 3.59587e7i | − | 0.583463i | ||||||
\(396\) | 846299. | − | 835778.i | 0.0136282 | − | 0.0134588i | ||||
\(397\) | −8.50731e7 | −1.35963 | −0.679815 | − | 0.733384i | \(-0.737940\pi\) | ||||
−0.679815 | + | 0.733384i | \(0.737940\pi\) | |||||||
\(398\) | 3.15571e7 | + | 1.31871e7i | 0.500550 | + | 0.209171i | ||||
\(399\) | − | 9.99531e6i | − | 0.157354i | ||||||
\(400\) | −160116. | + | 1.27990e7i | −0.00250181 | + | 0.199984i | ||||
\(401\) | 1.16975e7 | 0.181409 | 0.0907047 | − | 0.995878i | \(-0.471088\pi\) | ||||
0.0907047 | + | 0.995878i | \(0.471088\pi\) | |||||||
\(402\) | −1.48830e7 | + | 3.56153e7i | −0.229093 | + | 0.548224i | ||||
\(403\) | 3.03037e7i | 0.463000i | ||||||||
\(404\) | −4.66365e7 | − | 4.72236e7i | −0.707265 | − | 0.716168i | ||||
\(405\) | 3.30094e6 | 0.0496904 | ||||||||
\(406\) | 5.41791e7 | + | 2.26405e7i | 0.809568 | + | 0.338304i | ||||
\(407\) | 3.36815e6i | 0.0499583i | ||||||||
\(408\) | 2.31762e7 | + | 5.74716e7i | 0.341242 | + | 0.846199i | ||||
\(409\) | −6.19837e7 | −0.905958 | −0.452979 | − | 0.891521i | \(-0.649639\pi\) | ||||
−0.452979 | + | 0.891521i | \(0.649639\pi\) | |||||||
\(410\) | 1.30244e7 | − | 3.11677e7i | 0.188976 | − | 0.452224i | ||||
\(411\) | − | 1.00569e7i | − | 0.144856i | ||||||
\(412\) | 6.71701e6 | − | 6.63351e6i | 0.0960471 | − | 0.0948531i | ||||
\(413\) | 3.53290e7 | 0.501512 | ||||||||
\(414\) | −2.23578e7 | − | 9.34294e6i | −0.315086 | − | 0.131669i | ||||
\(415\) | 4.60867e7i | 0.644810i | ||||||||
\(416\) | 6.64676e7 | + | 2.87575e7i | 0.923273 | + | 0.399458i | ||||
\(417\) | 2.85256e7 | 0.393393 | ||||||||
\(418\) | 756317. | − | 1.80988e6i | 0.0103556 | − | 0.0247811i | ||||
\(419\) | 4.21622e7i | 0.573167i | 0.958055 | + | 0.286584i | \(0.0925197\pi\) | ||||
−0.958055 | + | 0.286584i | \(0.907480\pi\) | |||||||
\(420\) | −7.83783e6 | − | 7.93650e6i | −0.105791 | − | 0.107123i | ||||
\(421\) | 1.11714e7 | 0.149714 | 0.0748568 | − | 0.997194i | \(-0.476150\pi\) | ||||
0.0748568 | + | 0.997194i | \(0.476150\pi\) | |||||||
\(422\) | 9.45071e7 | + | 3.94928e7i | 1.25756 | + | 0.525510i | ||||
\(423\) | − | 4.27951e7i | − | 0.565422i | ||||||
\(424\) | −3.56560e7 | + | 1.43788e7i | −0.467773 | + | 0.188636i | ||||
\(425\) | −2.42633e7 | −0.316069 | ||||||||
\(426\) | 1.81608e7 | − | 4.34592e7i | 0.234913 | − | 0.562151i | ||||
\(427\) | − | 6.53947e6i | − | 0.0839960i | ||||||
\(428\) | −1.08193e8 | + | 1.06848e8i | −1.37996 | + | 1.36281i | ||||
\(429\) | 2.63497e6 | 0.0333737 | ||||||||
\(430\) | −9.18465e6 | − | 3.83810e6i | −0.115520 | − | 0.0482737i | ||||
\(431\) | 4.14547e7i | 0.517776i | 0.965907 | + | 0.258888i | \(0.0833561\pi\) | ||||
−0.965907 | + | 0.258888i | \(0.916644\pi\) | |||||||
\(432\) | −1.55144e7 | − | 194086.i | −0.192435 | − | 0.00240737i | ||||
\(433\) | 1.02877e8 | 1.26722 | 0.633612 | − | 0.773651i | \(-0.281571\pi\) | ||||
0.633612 | + | 0.773651i | \(0.281571\pi\) | |||||||
\(434\) | −8.45876e6 | + | 2.02420e7i | −0.103475 | + | 0.247619i | ||||
\(435\) | 3.19803e7i | 0.388522i | ||||||||
\(436\) | −9.91642e6 | − | 1.00412e7i | −0.119645 | − | 0.121151i | ||||
\(437\) | −3.99613e7 | −0.478846 | ||||||||
\(438\) | 4.87530e7 | + | 2.03730e7i | 0.580202 | + | 0.242456i | ||||
\(439\) | − | 1.17242e8i | − | 1.38576i | −0.721052 | − | 0.692881i | \(-0.756341\pi\) | ||
0.721052 | − | 0.692881i | \(-0.243659\pi\) | |||||||
\(440\) | −818688. | − | 2.03015e6i | −0.00961082 | − | 0.0238326i | ||||
\(441\) | −1.88684e7 | −0.219999 | ||||||||
\(442\) | −5.29314e7 | + | 1.26666e8i | −0.612981 | + | 1.46687i | ||||
\(443\) | − | 1.14320e8i | − | 1.31495i | −0.753475 | − | 0.657477i | \(-0.771624\pi\) | ||
0.753475 | − | 0.657477i | \(-0.228376\pi\) | |||||||
\(444\) | 3.12612e7 | − | 3.08726e7i | 0.357155 | − | 0.352715i | ||||
\(445\) | −3.01827e7 | −0.342514 | ||||||||
\(446\) | −8.02723e7 | − | 3.35444e7i | −0.904818 | − | 0.378107i | ||||
\(447\) | 8.03923e7i | 0.900102i | ||||||||
\(448\) | 3.63712e7 | + | 3.77624e7i | 0.404504 | + | 0.419977i | ||||
\(449\) | 7.55165e6 | 0.0834262 | 0.0417131 | − | 0.999130i | \(-0.486718\pi\) | ||||
0.0417131 | + | 0.999130i | \(0.486718\pi\) | |||||||
\(450\) | 2.34234e6 | − | 5.60527e6i | 0.0257047 | − | 0.0615119i | ||||
\(451\) | 5.77688e6i | 0.0629743i | ||||||||
\(452\) | 313097. | + | 317038.i | 0.00339049 | + | 0.00343318i | ||||
\(453\) | 6.47974e7 | 0.697048 | ||||||||
\(454\) | 1.60950e7 | + | 6.72582e6i | 0.171998 | + | 0.0718750i | ||||
\(455\) | − | 2.47105e7i | − | 0.262330i | ||||||
\(456\) | −2.37307e7 | + | 9.56974e6i | −0.250274 | + | 0.100927i | ||||
\(457\) | −7.56188e7 | −0.792285 | −0.396142 | − | 0.918189i | \(-0.629651\pi\) | ||||
−0.396142 | + | 0.918189i | \(0.629651\pi\) | |||||||
\(458\) | −1.45936e7 | + | 3.49228e7i | −0.151903 | + | 0.363507i | ||||
\(459\) | − | 2.94109e7i | − | 0.304138i | ||||||
\(460\) | −3.17302e7 | + | 3.13357e7i | −0.325986 | + | 0.321933i | ||||
\(461\) | −1.40082e8 | −1.42981 | −0.714905 | − | 0.699222i | \(-0.753530\pi\) | ||||
−0.714905 | + | 0.699222i | \(0.753530\pi\) | |||||||
\(462\) | 1.76008e6 | + | 735507.i | 0.0178487 | + | 0.00745866i | ||||
\(463\) | 8.24447e7i | 0.830653i | 0.909672 | + | 0.415327i | \(0.136333\pi\) | ||||
−0.909672 | + | 0.415327i | \(0.863667\pi\) | |||||||
\(464\) | 1.88035e6 | − | 1.50308e8i | 0.0188229 | − | 1.50462i | ||||
\(465\) | −1.19482e7 | −0.118835 | ||||||||
\(466\) | 4.80262e7 | − | 1.14928e8i | 0.474592 | − | 1.13571i | ||||
\(467\) | − | 1.71631e8i | − | 1.68518i | −0.538556 | − | 0.842589i | \(-0.681030\pi\) | ||
0.538556 | − | 0.842589i | \(-0.318970\pi\) | |||||||
\(468\) | −2.41523e7 | − | 2.44563e7i | −0.235624 | − | 0.238591i | ||||
\(469\) | −6.19055e7 | −0.600082 | ||||||||
\(470\) | −7.26696e7 | − | 3.03673e7i | −0.699937 | − | 0.292491i | ||||
\(471\) | − | 3.27447e7i | − | 0.313385i | ||||||
\(472\) | −3.38248e7 | − | 8.38775e7i | −0.321669 | − | 0.797663i | ||||
\(473\) | 1.70236e6 | 0.0160867 | ||||||||
\(474\) | 3.09298e7 | − | 7.40155e7i | 0.290430 | − | 0.695005i | ||||
\(475\) | − | 1.00186e7i | − | 0.0934816i | ||||||
\(476\) | −7.07131e7 | + | 6.98340e7i | −0.655661 | + | 0.647510i | ||||
\(477\) | 1.82469e7 | 0.168125 | ||||||||
\(478\) | −1.69603e8 | − | 7.08739e7i | −1.55292 | − | 0.648937i | ||||
\(479\) | − | 1.12033e8i | − | 1.01939i | −0.860355 | − | 0.509694i | \(-0.829758\pi\) | ||
0.860355 | − | 0.509694i | \(-0.170242\pi\) | |||||||
\(480\) | −1.13386e7 | + | 2.62070e7i | −0.102526 | + | 0.236971i | ||||
\(481\) | 9.73326e7 | 0.874627 | ||||||||
\(482\) | −7.52443e7 | + | 1.80061e8i | −0.671943 | + | 1.60797i | ||||
\(483\) | − | 3.88618e7i | − | 0.344890i | ||||||
\(484\) | −7.94056e7 | − | 8.04052e7i | −0.700350 | − | 0.709166i | ||||
\(485\) | 5.81098e7 | 0.509359 | ||||||||
\(486\) | 6.79448e6 | + | 2.83929e6i | 0.0591898 | + | 0.0247344i | ||||
\(487\) | 1.66667e8i | 1.44299i | 0.692419 | + | 0.721496i | \(0.256545\pi\) | ||||
−0.692419 | + | 0.721496i | \(0.743455\pi\) | |||||||
\(488\) | −1.55259e7 | + | 6.26104e6i | −0.133597 | + | 0.0538749i | ||||
\(489\) | 1.15199e8 | 0.985191 | ||||||||
\(490\) | −1.33890e7 | + | 3.20402e7i | −0.113805 | + | 0.272337i | ||||
\(491\) | 1.44837e7i | 0.122358i | 0.998127 | + | 0.0611792i | \(0.0194861\pi\) | ||||
−0.998127 | + | 0.0611792i | \(0.980514\pi\) | |||||||
\(492\) | 5.36176e7 | − | 5.29511e7i | 0.450207 | − | 0.444610i | ||||
\(493\) | 2.84940e8 | 2.37801 | ||||||||
\(494\) | −5.23019e7 | − | 2.18560e7i | −0.433847 | − | 0.181297i | ||||
\(495\) | 1.03893e6i | 0.00856582i | ||||||||
\(496\) | 5.61568e7 | + | 702524.i | 0.460211 | + | 0.00575726i | ||||
\(497\) | 7.55396e7 | 0.615327 | ||||||||
\(498\) | −3.96413e7 | + | 9.48625e7i | −0.320967 | + | 0.768080i | ||||
\(499\) | − | 1.82797e8i | − | 1.47118i | −0.677425 | − | 0.735592i | \(-0.736904\pi\) | ||
0.677425 | − | 0.735592i | \(-0.263096\pi\) | |||||||
\(500\) | −7.85609e6 | − | 7.95499e6i | −0.0628487 | − | 0.0636399i | ||||
\(501\) | −8.11096e7 | −0.644999 | ||||||||
\(502\) | 5.26732e7 | + | 2.20112e7i | 0.416369 | + | 0.173993i | ||||
\(503\) | − | 1.85820e8i | − | 1.46012i | −0.683382 | − | 0.730061i | \(-0.739491\pi\) | ||
0.683382 | − | 0.730061i | \(-0.260509\pi\) | |||||||
\(504\) | −9.30642e6 | − | 2.30777e7i | −0.0726928 | − | 0.180261i | ||||
\(505\) | 5.79722e7 | 0.450138 | ||||||||
\(506\) | 2.94056e6 | − | 7.03682e6i | 0.0226975 | − | 0.0543156i | ||||
\(507\) | − | 902867.i | − | 0.00692788i | ||||||
\(508\) | 7.39991e7 | − | 7.30792e7i | 0.564463 | − | 0.557446i | ||||
\(509\) | −4.52912e7 | −0.343447 | −0.171724 | − | 0.985145i | \(-0.554934\pi\) | ||||
−0.171724 | + | 0.985145i | \(0.554934\pi\) | |||||||
\(510\) | −4.99422e7 | − | 2.08700e7i | −0.376493 | − | 0.157330i | ||||
\(511\) | 8.47412e7i | 0.635085i | ||||||||
\(512\) | 5.48322e7 | − | 1.22506e8i | 0.408532 | − | 0.912744i | ||||
\(513\) | 1.21441e7 | 0.0899527 | ||||||||
\(514\) | −1.28368e7 | + | 3.07187e7i | −0.0945296 | + | 0.226211i | ||||
\(515\) | 8.24587e6i | 0.0603691i | ||||||||
\(516\) | −1.56039e7 | − | 1.58003e7i | −0.113575 | − | 0.115005i | ||||
\(517\) | 1.34692e7 | 0.0974696 | ||||||||
\(518\) | 6.50152e7 | + | 2.71687e7i | 0.467762 | + | 0.195470i | ||||
\(519\) | 1.20328e8i | 0.860728i | ||||||||
\(520\) | −5.86673e7 | + | 2.36584e7i | −0.417240 | + | 0.168258i | ||||
\(521\) | 1.08623e7 | 0.0768086 | 0.0384043 | − | 0.999262i | \(-0.487773\pi\) | ||||
0.0384043 | + | 0.999262i | \(0.487773\pi\) | |||||||
\(522\) | −2.75078e7 | + | 6.58266e7i | −0.193394 | + | 0.462796i | ||||
\(523\) | 8.35512e7i | 0.584047i | 0.956411 | + | 0.292023i | \(0.0943285\pi\) | ||||
−0.956411 | + | 0.292023i | \(0.905671\pi\) | |||||||
\(524\) | −9.97279e7 | + | 9.84881e7i | −0.693143 | + | 0.684526i | ||||
\(525\) | 9.74293e6 | 0.0673305 | ||||||||
\(526\) | −1.04935e8 | − | 4.38507e7i | −0.721049 | − | 0.301314i | ||||
\(527\) | 1.06457e8i | 0.727350i | ||||||||
\(528\) | 61085.9 | − | 4.88295e6i | 0.000414992 | − | 0.0331727i | ||||
\(529\) | −7.33375e6 | −0.0495403 | ||||||||
\(530\) | 1.29480e7 | − | 3.09847e7i | 0.0869708 | − | 0.208123i | ||||
\(531\) | 4.29241e7i | 0.286693i | ||||||||
\(532\) | −2.88353e7 | − | 2.91983e7i | −0.191509 | − | 0.193920i | ||||
\(533\) | 1.66940e8 | 1.10250 | ||||||||
\(534\) | −6.21265e7 | − | 2.59616e7i | −0.407993 | − | 0.170493i | ||||
\(535\) | − | 1.32819e8i | − | 0.867358i | ||||||
\(536\) | 5.92697e7 | + | 1.46975e8i | 0.384892 | + | 0.954441i | ||||
\(537\) | −8.76939e7 | −0.566300 | ||||||||
\(538\) | −7.01148e7 | + | 1.67786e8i | −0.450259 | + | 1.07748i | ||||
\(539\) | − | 5.93858e6i | − | 0.0379242i | ||||||
\(540\) | 9.64270e6 | − | 9.52283e6i | 0.0612375 | − | 0.0604762i | ||||
\(541\) | −6.89690e7 | −0.435574 | −0.217787 | − | 0.975996i | \(-0.569884\pi\) | ||||
−0.217787 | + | 0.975996i | \(0.569884\pi\) | |||||||
\(542\) | 1.39005e8 | + | 5.80876e7i | 0.873034 | + | 0.364826i | ||||
\(543\) | 1.25785e8i | 0.785650i | ||||||||
\(544\) | 2.33501e8 | + | 1.01025e8i | 1.45042 | + | 0.627528i | ||||
\(545\) | 1.23267e7 | 0.0761480 | ||||||||
\(546\) | 2.12546e7 | − | 5.08628e7i | 0.130580 | − | 0.312480i | ||||
\(547\) | − | 1.06248e8i | − | 0.649170i | −0.945857 | − | 0.324585i | \(-0.894775\pi\) | ||
0.945857 | − | 0.324585i | \(-0.105225\pi\) | |||||||
\(548\) | −2.90129e7 | − | 2.93781e7i | −0.176299 | − | 0.178518i | ||||
\(549\) | 7.94534e6 | 0.0480170 | ||||||||
\(550\) | 1.76418e6 | + | 737220.i | 0.0106036 | + | 0.00443108i | ||||
\(551\) | 1.17655e8i | 0.703326i | ||||||||
\(552\) | −9.22650e7 | + | 3.72072e7i | −0.548554 | + | 0.221212i | ||||
\(553\) | 1.28652e8 | 0.760747 | ||||||||
\(554\) | −1.07655e8 | + | 2.57621e8i | −0.633148 | + | 1.51513i | ||||
\(555\) | 3.83766e7i | 0.224485i | ||||||||
\(556\) | 8.33289e7 | − | 8.22930e7i | 0.484810 | − | 0.478783i | ||||
\(557\) | −1.14599e8 | −0.663154 | −0.331577 | − | 0.943428i | \(-0.607581\pi\) | ||||
−0.331577 | + | 0.943428i | \(0.607581\pi\) | |||||||
\(558\) | −2.45936e7 | − | 1.02772e7i | −0.141553 | − | 0.0591526i | ||||
\(559\) | − | 4.91946e7i | − | 0.281632i | ||||||
\(560\) | −4.57918e7 | − | 572857.i | −0.260749 | − | 0.00326199i | ||||
\(561\) | 9.25669e6 | 0.0524284 | ||||||||
\(562\) | 7.15121e6 | − | 1.71130e7i | 0.0402875 | − | 0.0964088i | ||||
\(563\) | − | 1.15455e8i | − | 0.646975i | −0.946232 | − | 0.323488i | \(-0.895145\pi\) | ||
0.946232 | − | 0.323488i | \(-0.104855\pi\) | |||||||
\(564\) | −1.23459e8 | − | 1.25013e8i | −0.688153 | − | 0.696816i | ||||
\(565\) | −389199. | −0.00215788 | ||||||||
\(566\) | 3.11782e8 | + | 1.30288e8i | 1.71950 | + | 0.718547i | ||||
\(567\) | 1.18100e7i | 0.0647888i | ||||||||
\(568\) | −7.23234e7 | − | 1.79345e8i | −0.394670 | − | 0.978688i | ||||
\(569\) | −2.08398e8 | −1.13125 | −0.565624 | − | 0.824663i | \(-0.691365\pi\) | ||||
−0.565624 | + | 0.824663i | \(0.691365\pi\) | |||||||
\(570\) | 8.61746e6 | − | 2.06217e7i | 0.0465323 | − | 0.111353i | ||||
\(571\) | 1.99293e8i | 1.07049i | 0.844696 | + | 0.535246i | \(0.179781\pi\) | ||||
−0.844696 | + | 0.535246i | \(0.820219\pi\) | |||||||
\(572\) | 7.69729e6 | − | 7.60160e6i | 0.0411291 | − | 0.0406178i | ||||
\(573\) | 6.82074e7 | 0.362550 | ||||||||
\(574\) | 1.11511e8 | + | 4.65984e7i | 0.589632 | + | 0.246397i | ||||
\(575\) | − | 3.89523e7i | − | 0.204894i | ||||||
\(576\) | −4.58806e7 | + | 4.41903e7i | −0.240083 | + | 0.231238i | ||||
\(577\) | 2.29061e8 | 1.19240 | 0.596201 | − | 0.802835i | \(-0.296676\pi\) | ||||
0.596201 | + | 0.802835i | \(0.296676\pi\) | |||||||
\(578\) | −1.11495e8 | + | 2.66809e8i | −0.577391 | + | 1.38171i | ||||
\(579\) | 1.98415e8i | 1.02221i | ||||||||
\(580\) | 9.22596e7 | + | 9.34210e7i | 0.472854 | + | 0.478807i | ||||
\(581\) | −1.64887e8 | −0.840735 | ||||||||
\(582\) | 1.19610e8 | + | 4.99829e7i | 0.606734 | + | 0.253544i | ||||
\(583\) | 5.74295e6i | 0.0289821i | ||||||||
\(584\) | 2.01191e8 | − | 8.11331e7i | 1.01011 | − | 0.407343i | ||||
\(585\) | 3.00228e7 | 0.149963 | ||||||||
\(586\) | 1.20356e8 | − | 2.88015e8i | 0.598103 | − | 1.43127i | ||||
\(587\) | 1.44645e8i | 0.715137i | 0.933887 | + | 0.357569i | \(0.116394\pi\) | ||||
−0.933887 | + | 0.357569i | \(0.883606\pi\) | |||||||
\(588\) | −5.51184e7 | + | 5.44332e7i | −0.271122 | + | 0.267752i | ||||
\(589\) | −4.39575e7 | −0.215123 | ||||||||
\(590\) | 7.28887e7 | + | 3.04589e7i | 0.354898 | + | 0.148306i | ||||
\(591\) | − | 3.04947e7i | − | 0.147728i | ||||||
\(592\) | 2.25644e6 | − | 1.80370e8i | 0.0108757 | − | 0.869359i | ||||
\(593\) | 7.73515e7 | 0.370941 | 0.185471 | − | 0.982650i | \(-0.440619\pi\) | ||||
0.185471 | + | 0.982650i | \(0.440619\pi\) | |||||||
\(594\) | −893628. | + | 2.13847e6i | −0.00426381 | + | 0.0102034i | ||||
\(595\) | − | 8.68082e7i | − | 0.412107i | ||||||
\(596\) | 2.31922e8 | + | 2.34842e8i | 1.09548 | + | 1.10927i | ||||
\(597\) | −6.66438e7 | −0.313211 | ||||||||
\(598\) | −2.03350e8 | − | 8.49762e7i | −0.950911 | − | 0.397369i | ||||
\(599\) | 2.61293e8i | 1.21576i | 0.794029 | + | 0.607880i | \(0.207980\pi\) | ||||
−0.794029 | + | 0.607880i | \(0.792020\pi\) | |||||||
\(600\) | −9.32810e6 | − | 2.31315e7i | −0.0431857 | − | 0.107090i | ||||
\(601\) | −1.90411e8 | −0.877141 | −0.438570 | − | 0.898697i | \(-0.644515\pi\) | ||||
−0.438570 | + | 0.898697i | \(0.644515\pi\) | |||||||
\(602\) | 1.37318e7 | − | 3.28605e7i | 0.0629417 | − | 0.150621i | ||||
\(603\) | − | 7.52141e7i | − | 0.343042i | ||||||
\(604\) | 1.89286e8 | − | 1.86933e8i | 0.859029 | − | 0.848350i | ||||
\(605\) | 9.87063e7 | 0.445737 | ||||||||
\(606\) | 1.19327e8 | + | 4.98645e7i | 0.536192 | + | 0.224065i | ||||
\(607\) | − | 8.66310e7i | − | 0.387354i | −0.981065 | − | 0.193677i | \(-0.937959\pi\) | ||
0.981065 | − | 0.193677i | \(-0.0620413\pi\) | |||||||
\(608\) | −4.17145e7 | + | 9.64155e7i | −0.185599 | + | 0.428979i | ||||
\(609\) | −1.14418e8 | −0.506573 | ||||||||
\(610\) | 5.63800e6 | − | 1.34918e7i | 0.0248391 | − | 0.0594404i | ||||
\(611\) | − | 3.89231e8i | − | 1.70641i | ||||||
\(612\) | −8.48471e7 | − | 8.59152e7i | −0.370154 | − | 0.374814i | ||||
\(613\) | −3.14018e7 | −0.136324 | −0.0681620 | − | 0.997674i | \(-0.521713\pi\) | ||||
−0.0681620 | + | 0.997674i | \(0.521713\pi\) | |||||||
\(614\) | 1.14509e8 | + | 4.78511e7i | 0.494690 | + | 0.206722i | ||||
\(615\) | 6.58216e7i | 0.282972i | ||||||||
\(616\) | 7.26340e6 | − | 2.92907e6i | 0.0310741 | − | 0.0125311i | ||||
\(617\) | −2.78014e8 | −1.18362 | −0.591808 | − | 0.806079i | \(-0.701585\pi\) | ||||
−0.591808 | + | 0.806079i | \(0.701585\pi\) | |||||||
\(618\) | −7.09266e6 | + | 1.69729e7i | −0.0300499 | + | 0.0719100i | ||||
\(619\) | − | 6.69159e7i | − | 0.282135i | −0.990000 | − | 0.141068i | \(-0.954947\pi\) | ||
0.990000 | − | 0.141068i | \(-0.0450535\pi\) | |||||||
\(620\) | −3.49032e7 | + | 3.44693e7i | −0.146450 | + | 0.144630i | ||||
\(621\) | 4.72164e7 | 0.197159 | ||||||||
\(622\) | 5.19206e7 | + | 2.16967e7i | 0.215759 | + | 0.0901618i | ||||
\(623\) | − | 1.07987e8i | − | 0.446586i | ||||||
\(624\) | −1.41107e8 | − | 1.76526e6i | −0.580758 | − | 0.00726531i | ||||
\(625\) | 9.76562e6 | 0.0400000 | ||||||||
\(626\) | 7.41100e7 | − | 1.77347e8i | 0.302102 | − | 0.722936i | ||||
\(627\) | 3.82220e6i | 0.0155064i | ||||||||
\(628\) | −9.44646e7 | − | 9.56537e7i | −0.381408 | − | 0.386210i | ||||
\(629\) | 3.41930e8 | 1.37400 | ||||||||
\(630\) | 2.00543e7 | + | 8.38034e6i | 0.0802022 | + | 0.0335151i | ||||
\(631\) | − | 5.44695e7i | − | 0.216803i | −0.994107 | − | 0.108401i | \(-0.965427\pi\) | ||
0.994107 | − | 0.108401i | \(-0.0345732\pi\) | |||||||
\(632\) | −1.23174e8 | − | 3.05443e8i | −0.487942 | − | 1.20998i | ||||
\(633\) | −1.99585e8 | −0.786894 | ||||||||
\(634\) | −1.71599e8 | + | 4.10640e8i | −0.673361 | + | 1.61136i | ||||
\(635\) | 9.08421e7i | 0.354786i | ||||||||
\(636\) | 5.33028e7 | − | 5.26401e7i | 0.207195 | − | 0.204619i | ||||
\(637\) | −1.71613e8 | −0.663944 | ||||||||
\(638\) | −2.07180e7 | − | 8.65769e6i | −0.0797786 | − | 0.0333380i | ||||
\(639\) | 9.17793e7i | 0.351757i | ||||||||
\(640\) | 4.24820e7 | + | 1.09267e8i | 0.162056 | + | 0.416819i | ||||
\(641\) | −2.54657e8 | −0.966899 | −0.483450 | − | 0.875372i | \(-0.660616\pi\) | ||||
−0.483450 | + | 0.875372i | \(0.660616\pi\) | |||||||
\(642\) | 1.14244e8 | − | 2.73387e8i | 0.431744 | − | 1.03317i | ||||
\(643\) | 2.69874e8i | 1.01514i | 0.861610 | + | 0.507572i | \(0.169457\pi\) | ||||
−0.861610 | + | 0.507572i | \(0.830543\pi\) | |||||||
\(644\) | −1.12112e8 | − | 1.13523e8i | −0.419753 | − | 0.425036i | ||||
\(645\) | 1.93966e7 | 0.0722847 | ||||||||
\(646\) | −1.83737e8 | − | 7.67804e7i | −0.681552 | − | 0.284808i | ||||
\(647\) | − | 4.58078e8i | − | 1.69132i | −0.533719 | − | 0.845662i | \(-0.679206\pi\) | ||
0.533719 | − | 0.845662i | \(-0.320794\pi\) | |||||||
\(648\) | 2.80390e7 | − | 1.13071e7i | 0.103048 | − | 0.0415554i | ||||
\(649\) | −1.35098e7 | −0.0494213 | ||||||||
\(650\) | 2.13042e7 | − | 5.09812e7i | 0.0775755 | − | 0.185640i | ||||
\(651\) | − | 4.27480e7i | − | 0.154943i | ||||||
\(652\) | 3.36518e8 | − | 3.32335e8i | 1.21413 | − | 1.19904i | ||||
\(653\) | −2.94949e8 | −1.05927 | −0.529636 | − | 0.848225i | \(-0.677671\pi\) | ||||
−0.529636 | + | 0.848225i | \(0.677671\pi\) | |||||||
\(654\) | 2.53727e7 | + | 1.06028e7i | 0.0907054 | + | 0.0379042i | ||||
\(655\) | − | 1.22427e8i | − | 0.435666i | ||||||
\(656\) | 3.87012e6 | − | 3.09361e8i | 0.0137092 | − | 1.09586i | ||||
\(657\) | −1.02959e8 | −0.363051 | ||||||||
\(658\) | 1.08647e8 | − | 2.59994e8i | 0.381365 | − | 0.912613i | ||||
\(659\) | 2.78956e8i | 0.974720i | 0.873201 | + | 0.487360i | \(0.162040\pi\) | ||||
−0.873201 | + | 0.487360i | \(0.837960\pi\) | |||||||
\(660\) | 2.99718e6 | + | 3.03491e6i | 0.0104251 | + | 0.0105564i | ||||
\(661\) | −3.82952e8 | −1.32599 | −0.662995 | − | 0.748624i | \(-0.730715\pi\) | ||||
−0.662995 | + | 0.748624i | \(0.730715\pi\) | |||||||
\(662\) | 3.79884e7 | + | 1.58747e7i | 0.130942 | + | 0.0547182i | ||||
\(663\) | − | 2.67499e8i | − | 0.917872i | ||||||
\(664\) | 1.57867e8 | + | 3.91473e8i | 0.539246 | + | 1.33720i | ||||
\(665\) | 3.58441e7 | 0.121886 | ||||||||
\(666\) | −3.30095e7 | + | 7.89923e7i | −0.111742 | + | 0.267400i | ||||
\(667\) | 4.57444e8i | 1.54156i | ||||||||
\(668\) | −2.36937e8 | + | 2.33992e8i | −0.794885 | + | 0.785003i | ||||
\(669\) | 1.69523e8 | 0.566174 | ||||||||
\(670\) | −1.27720e8 | − | 5.33718e7i | −0.424652 | − | 0.177455i | ||||
\(671\) | 2.50069e6i | 0.00827736i | ||||||||
\(672\) | −9.37625e7 | − | 4.05667e7i | −0.308974 | − | 0.133679i | ||||
\(673\) | −1.79065e8 | −0.587443 | −0.293722 | − | 0.955891i | \(-0.594894\pi\) | ||||
−0.293722 | + | 0.955891i | \(0.594894\pi\) | |||||||
\(674\) | 1.99462e8 | − | 4.77316e8i | 0.651449 | − | 1.55893i | ||||
\(675\) | 1.18375e7i | 0.0384900i | ||||||||
\(676\) | −2.60467e6 | − | 2.63746e6i | −0.00843164 | − | 0.00853778i | ||||
\(677\) | −2.03295e8 | −0.655179 | −0.327589 | − | 0.944820i | \(-0.606236\pi\) | ||||
−0.327589 | + | 0.944820i | \(0.606236\pi\) | |||||||
\(678\) | −801106. | − | 334768.i | −0.00257040 | − | 0.00107413i | ||||
\(679\) | 2.07903e8i | 0.664127i | ||||||||
\(680\) | −2.06099e8 | + | 8.31122e7i | −0.655463 | + | 0.264325i | ||||
\(681\) | −3.39902e7 | −0.107625 | ||||||||
\(682\) | 3.23462e6 | − | 7.74051e6i | 0.0101969 | − | 0.0244015i | ||||
\(683\) | − | 2.12975e8i | − | 0.668446i | −0.942494 | − | 0.334223i | \(-0.891526\pi\) | ||
0.942494 | − | 0.334223i | \(-0.108474\pi\) | |||||||
\(684\) | 3.54754e7 | − | 3.50344e7i | 0.110856 | − | 0.109478i | ||||
\(685\) | 3.60649e7 | 0.112205 | ||||||||
\(686\) | −2.88318e8 | − | 1.20483e8i | −0.893099 | − | 0.373210i | ||||
\(687\) | − | 7.37517e7i | − | 0.227458i | ||||||
\(688\) | −9.11639e7 | − | 1.14046e6i | −0.279935 | − | 0.00350200i | ||||
\(689\) | 1.65960e8 | 0.507393 | ||||||||
\(690\) | 3.35047e7 | − | 8.01773e7i | 0.101990 | − | 0.244064i | ||||
\(691\) | − | 3.42495e7i | − | 0.103805i | −0.998652 | − | 0.0519027i | \(-0.983471\pi\) | ||
0.998652 | − | 0.0519027i | \(-0.0165286\pi\) | |||||||
\(692\) | 3.47134e8 | + | 3.51503e8i | 1.04756 | + | 1.06075i | ||||
\(693\) | −3.71703e6 | −0.0111685 | ||||||||
\(694\) | 1.43100e8 | + | 5.97991e7i | 0.428117 | + | 0.178902i | ||||
\(695\) | 1.02295e8i | 0.304721i | ||||||||
\(696\) | 1.09546e8 | + | 2.71649e8i | 0.324916 | + | 0.805714i | ||||
\(697\) | 5.86461e8 | 1.73197 | ||||||||
\(698\) | 7.88303e7 | − | 1.88642e8i | 0.231807 | − | 0.554719i | ||||
\(699\) | 2.42710e8i | 0.710649i | ||||||||
\(700\) | 2.84610e7 | − | 2.81072e7i | 0.0829768 | − | 0.0819452i | ||||
\(701\) | 1.80432e7 | 0.0523794 | 0.0261897 | − | 0.999657i | \(-0.491663\pi\) | ||||
0.0261897 | + | 0.999657i | \(0.491663\pi\) | |||||||
\(702\) | 6.17974e7 | + | 2.58240e7i | 0.178632 | + | 0.0746470i | ||||
\(703\) | 1.41187e8i | 0.406377i | ||||||||
\(704\) | −1.39083e7 | − | 1.44403e7i | −0.0398617 | − | 0.0413865i | ||||
\(705\) | 1.53467e8 | 0.437974 | ||||||||
\(706\) | 1.42126e7 | − | 3.40111e7i | 0.0403887 | − | 0.0966510i | ||||
\(707\) | 2.07411e8i | 0.586911i | ||||||||
\(708\) | 1.23831e8 | + | 1.25390e8i | 0.348923 | + | 0.353316i | ||||
\(709\) | −3.29774e8 | −0.925289 | −0.462645 | − | 0.886544i | \(-0.653099\pi\) | ||||
−0.462645 | + | 0.886544i | \(0.653099\pi\) | |||||||
\(710\) | 1.55849e8 | + | 6.51265e7i | 0.435440 | + | 0.181963i | ||||
\(711\) | 1.56310e8i | 0.434887i | ||||||||
\(712\) | −2.56380e8 | + | 1.03389e8i | −0.710304 | + | 0.286440i | ||||
\(713\) | −1.70907e8 | −0.471510 | ||||||||
\(714\) | 7.46677e7 | − | 1.78681e8i | 0.205134 | − | 0.490890i | ||||
\(715\) | 9.44927e6i | 0.0258512i | ||||||||
\(716\) | −2.56171e8 | + | 2.52987e8i | −0.697897 | + | 0.689221i | ||||
\(717\) | 3.58175e8 | 0.971713 | ||||||||
\(718\) | −6.15487e8 | − | 2.57201e8i | −1.66282 | − | 0.694863i | ||||
\(719\) | − | 4.14856e7i | − | 0.111612i | −0.998442 | − | 0.0558060i | \(-0.982227\pi\) | ||
0.998442 | − | 0.0558060i | \(-0.0177728\pi\) | |||||||
\(720\) | 696011. | − | 5.56362e7i | 0.00186474 | − | 0.149060i | ||||
\(721\) | −2.95018e7 | −0.0787122 | ||||||||
\(722\) | −1.13413e8 | + | 2.71399e8i | −0.301335 | + | 0.721101i | ||||
\(723\) | − | 3.80262e8i | − | 1.00616i | ||||||
\(724\) | 3.62875e8 | + | 3.67443e8i | 0.956184 | + | 0.968220i | ||||
\(725\) | −1.14685e8 | −0.300948 | ||||||||
\(726\) | 2.03172e8 | + | 8.49018e7i | 0.530950 | + | 0.221874i | ||||
\(727\) | − | 1.30895e8i | − | 0.340660i | −0.985387 | − | 0.170330i | \(-0.945517\pi\) | ||
0.985387 | − | 0.170330i | \(-0.0544833\pi\) | |||||||
\(728\) | −8.46441e7 | − | 2.09897e8i | −0.219383 | − | 0.544018i | ||||
\(729\) | −1.43489e7 | −0.0370370 | ||||||||
\(730\) | −7.30596e7 | + | 1.74833e8i | −0.187806 | + | 0.449422i | ||||
\(731\) | − | 1.72821e8i | − | 0.442430i | ||||||
\(732\) | 2.32099e7 | − | 2.29214e7i | 0.0591753 | − | 0.0584396i | ||||
\(733\) | 5.25156e8 | 1.33345 | 0.666725 | − | 0.745304i | \(-0.267696\pi\) | ||||
0.666725 | + | 0.745304i | \(0.267696\pi\) | |||||||
\(734\) | −2.07467e8 | − | 8.66969e7i | −0.524640 | − | 0.219238i | ||||
\(735\) | − | 6.76640e7i | − | 0.170410i | ||||||
\(736\) | −1.62186e8 | + | 3.74863e8i | −0.406799 | + | 0.940242i | ||||
\(737\) | 2.36726e7 | 0.0591348 | ||||||||
\(738\) | −5.66162e7 | + | 1.35484e8i | −0.140855 | + | 0.337068i | ||||
\(739\) | − | 2.54601e8i | − | 0.630850i | −0.948951 | − | 0.315425i | \(-0.897853\pi\) | ||
0.948951 | − | 0.315425i | \(-0.102147\pi\) | |||||||
\(740\) | 1.10712e8 | + | 1.12106e8i | 0.273212 | + | 0.276651i | ||||
\(741\) | 1.10454e8 | 0.271472 | ||||||||
\(742\) | 1.10856e8 | + | 4.63247e7i | 0.271361 | + | 0.113397i | ||||
\(743\) | − | 8.88222e7i | − | 0.216548i | −0.994121 | − | 0.108274i | \(-0.965468\pi\) | ||
0.994121 | − | 0.108274i | \(-0.0345324\pi\) | |||||||
\(744\) | −1.01492e8 | + | 4.09279e7i | −0.246440 | + | 0.0993804i | ||||
\(745\) | −2.88294e8 | −0.697216 | ||||||||
\(746\) | 9.40556e7 | − | 2.25077e8i | 0.226552 | − | 0.542144i | ||||
\(747\) | − | 2.00335e8i | − | 0.480613i | ||||||
\(748\) | 2.70406e7 | − | 2.67045e7i | 0.0646118 | − | 0.0638086i | ||||
\(749\) | 4.75194e8 | 1.13090 | ||||||||
\(750\) | 2.01010e7 | + | 8.39987e6i | 0.0476469 | + | 0.0199108i | ||||
\(751\) | − | 8.81576e7i | − | 0.208133i | −0.994570 | − | 0.104066i | \(-0.966815\pi\) | ||
0.994570 | − | 0.104066i | \(-0.0331854\pi\) | |||||||
\(752\) | −7.21296e8 | − | 9.02345e6i | −1.69613 | − | 0.0212187i | ||||
\(753\) | −1.11238e8 | −0.260536 | ||||||||
\(754\) | −2.50190e8 | + | 5.98708e8i | −0.583654 | + | 1.39669i | ||||
\(755\) | 2.32370e8i | 0.539931i | ||||||||
\(756\) | 3.40704e7 | + | 3.44993e7i | 0.0788518 | + | 0.0798445i | ||||
\(757\) | −2.37075e8 | −0.546511 | −0.273255 | − | 0.961942i | \(-0.588100\pi\) | ||||
−0.273255 | + | 0.961942i | \(0.588100\pi\) | |||||||
\(758\) | 6.01984e8 | + | 2.51558e8i | 1.38222 | + | 0.577605i | ||||
\(759\) | 1.48607e7i | 0.0339871i | ||||||||
\(760\) | −3.43180e7 | − | 8.51006e7i | −0.0781774 | − | 0.193862i | ||||
\(761\) | 4.57746e8 | 1.03865 | 0.519327 | − | 0.854576i | \(-0.326183\pi\) | ||||
0.519327 | + | 0.854576i | \(0.326183\pi\) | |||||||
\(762\) | −7.81375e7 | + | 1.86984e8i | −0.176602 | + | 0.422611i | ||||
\(763\) | 4.41021e7i | 0.0992855i | ||||||||
\(764\) | 1.99248e8 | − | 1.96771e8i | 0.446800 | − | 0.441245i | ||||
\(765\) | 1.05470e8 | 0.235584 | ||||||||
\(766\) | −7.10074e8 | − | 2.96727e8i | −1.57986 | − | 0.660194i | ||||
\(767\) | 3.90405e8i | 0.865225i | ||||||||
\(768\) | −6.54250e6 | + | 2.61449e8i | −0.0144431 | + | 0.577170i | ||||
\(769\) | 3.39638e8 | 0.746857 | 0.373428 | − | 0.927659i | \(-0.378182\pi\) | ||||
0.373428 | + | 0.927659i | \(0.378182\pi\) | |||||||
\(770\) | −2.63760e6 | + | 6.31182e6i | −0.00577745 | + | 0.0138256i | ||||
\(771\) | − | 6.48733e7i | − | 0.141548i | ||||||
\(772\) | 5.72405e8 | + | 5.79611e8i | 1.24409 | + | 1.25975i | ||||
\(773\) | 5.73031e8 | 1.24062 | 0.620311 | − | 0.784356i | \(-0.287006\pi\) | ||||
0.620311 | + | 0.784356i | \(0.287006\pi\) | |||||||
\(774\) | 3.99249e7 | + | 1.66839e7i | 0.0861035 | + | 0.0359811i | ||||
\(775\) | − | 4.28476e7i | − | 0.0920494i | ||||||
\(776\) | 4.93600e8 | − | 1.99051e8i | 1.05631 | − | 0.425970i | ||||
\(777\) | −1.37302e8 | −0.292694 | ||||||||
\(778\) | 1.02190e8 | − | 2.44542e8i | 0.217005 | − | 0.519296i | ||||
\(779\) | 2.42157e8i | 0.512253i | ||||||||
\(780\) | 8.77027e7 | − | 8.66124e7i | 0.184811 | − | 0.182514i | ||||
\(781\) | −2.88863e7 | −0.0606371 | ||||||||
\(782\) | −7.14369e8 | − | 2.98522e8i | −1.49383 | − | 0.624247i | ||||
\(783\) | − | 1.39016e8i | − | 0.289587i | ||||||
\(784\) | −3.97845e6 | + | 3.18021e8i | −0.00825593 | + | 0.659944i | ||||
\(785\) | 1.17426e8 | 0.242747 | ||||||||
\(786\) | 1.05305e8 | − | 2.51997e8i | 0.216861 | − | 0.518953i | ||||
\(787\) | − | 3.28483e8i | − | 0.673890i | −0.941524 | − | 0.336945i | \(-0.890606\pi\) | ||
0.941524 | − | 0.336945i | \(-0.109394\pi\) | |||||||
\(788\) | −8.79736e7 | − | 8.90810e7i | −0.179793 | − | 0.182057i | ||||
\(789\) | 2.21608e8 | 0.451184 | ||||||||
\(790\) | 2.65427e8 | + | 1.10917e8i | 0.538348 | + | 0.224966i | ||||
\(791\) | − | 1.39246e6i | − | 0.00281354i | ||||||
\(792\) | 3.55877e6 | + | 8.82491e6i | 0.00716348 | + | 0.0177637i | ||||
\(793\) | 7.22647e7 | 0.144913 | ||||||||
\(794\) | 2.62414e8 | − | 6.27961e8i | 0.524234 | − | 1.25450i | ||||
\(795\) | 6.54350e7i | 0.130229i | ||||||||
\(796\) | −1.94680e8 | + | 1.92260e8i | −0.385995 | + | 0.381196i | ||||
\(797\) | 2.52036e8 | 0.497838 | 0.248919 | − | 0.968524i | \(-0.419925\pi\) | ||||
0.248919 | + | 0.968524i | \(0.419925\pi\) | |||||||
\(798\) | 7.37796e7 | + | 3.08312e7i | 0.145187 | + | 0.0606711i | ||||
\(799\) | − | 1.36737e9i | − | 2.68069i | ||||||
\(800\) | −9.39810e7 | − | 4.06613e7i | −0.183557 | − | 0.0794165i | ||||
\(801\) | 1.31202e8 | 0.255295 | ||||||||
\(802\) | −3.60817e7 | + | 8.63442e7i | −0.0699462 | + | 0.167382i | ||||
\(803\) | − | 3.24049e7i | − | 0.0625842i | ||||||
\(804\) | −2.16984e8 | − | 2.19715e8i | −0.417503 | − | 0.422758i | ||||
\(805\) | 1.39362e8 | 0.267151 | ||||||||
\(806\) | −2.23685e8 | − | 9.34739e7i | −0.427200 | − | 0.178519i | ||||
\(807\) | − | 3.54339e8i | − | 0.674214i | ||||||
\(808\) | 4.92431e8 | − | 1.98580e8i | 0.933493 | − | 0.376444i | ||||
\(809\) | 5.91008e8 | 1.11622 | 0.558108 | − | 0.829769i | \(-0.311528\pi\) | ||||
0.558108 | + | 0.829769i | \(0.311528\pi\) | |||||||
\(810\) | −1.01820e7 | + | 2.43656e7i | −0.0191592 | + | 0.0458482i | ||||
\(811\) | 8.19467e8i | 1.53628i | 0.640285 | + | 0.768138i | \(0.278816\pi\) | ||||
−0.640285 | + | 0.768138i | \(0.721184\pi\) | |||||||
\(812\) | −3.34238e8 | + | 3.30083e8i | −0.624292 | + | 0.616531i | ||||
\(813\) | −2.93557e8 | −0.546286 | ||||||||
\(814\) | −2.48617e7 | − | 1.03893e7i | −0.0460955 | − | 0.0192625i | ||||
\(815\) | 4.13113e8i | 0.763126i | ||||||||
\(816\) | −4.95711e8 | − | 6.20136e6i | −0.912343 | − | 0.0114134i | ||||
\(817\) | 7.13598e7 | 0.130854 | ||||||||
\(818\) | 1.91193e8 | − | 4.57528e8i | 0.349311 | − | 0.835907i | ||||
\(819\) | 1.07414e8i | 0.195529i | ||||||||
\(820\) | 1.89888e8 | + | 1.92278e8i | 0.344394 | + | 0.348729i | ||||
\(821\) | 8.40553e8 | 1.51892 | 0.759461 | − | 0.650553i | \(-0.225463\pi\) | ||||
0.759461 | + | 0.650553i | \(0.225463\pi\) | |||||||
\(822\) | 7.42340e7 | + | 3.10211e7i | 0.133656 | + | 0.0558523i | ||||
\(823\) | 7.57436e8i | 1.35877i | 0.733781 | + | 0.679386i | \(0.237754\pi\) | ||||
−0.733781 | + | 0.679386i | \(0.762246\pi\) | |||||||
\(824\) | 2.82457e7 | + | 7.00426e7i | 0.0504859 | + | 0.125193i | ||||
\(825\) | −3.72569e6 | −0.00663505 | ||||||||
\(826\) | −1.08975e8 | + | 2.60778e8i | −0.193368 | + | 0.462734i | ||||
\(827\) | 9.32243e8i | 1.64821i | 0.566437 | + | 0.824105i | \(0.308321\pi\) | ||||
−0.566437 | + | 0.824105i | \(0.691679\pi\) | |||||||
\(828\) | 1.37928e8 | − | 1.36214e8i | 0.242976 | − | 0.239955i | ||||
\(829\) | −4.80613e8 | −0.843590 | −0.421795 | − | 0.906691i | \(-0.638600\pi\) | ||||
−0.421795 | + | 0.906691i | \(0.638600\pi\) | |||||||
\(830\) | −3.40186e8 | − | 1.42158e8i | −0.594952 | − | 0.248620i | ||||
\(831\) | − | 5.44056e8i | − | 0.948070i | ||||||
\(832\) | −4.17295e8 | + | 4.01921e8i | −0.724558 | + | 0.697865i | ||||
\(833\) | −6.02877e8 | −1.04302 | ||||||||
\(834\) | −8.79891e7 | + | 2.10560e8i | −0.151681 | + | 0.362975i | ||||
\(835\) | − | 2.90867e8i | − | 0.499614i | ||||||
\(836\) | 1.10266e7 | + | 1.11654e7i | 0.0188722 | + | 0.0191098i | ||||
\(837\) | 5.19380e7 | 0.0885746 | ||||||||
\(838\) | −3.11217e8 | − | 1.30052e8i | −0.528849 | − | 0.220997i | ||||
\(839\) | − | 8.26539e8i | − | 1.39952i | −0.714380 | − | 0.699758i | \(-0.753291\pi\) | ||
0.714380 | − | 0.699758i | \(-0.246709\pi\) | |||||||
\(840\) | 8.27590e7 | − | 3.33737e7i | 0.139630 | − | 0.0563076i | ||||
\(841\) | 7.51997e8 | 1.26424 | ||||||||
\(842\) | −3.44589e7 | + | 8.24609e7i | −0.0577252 | + | 0.138138i | ||||
\(843\) | 3.61400e7i | 0.0603262i | ||||||||
\(844\) | −5.83027e8 | + | 5.75779e8i | −0.969753 | + | 0.957698i | ||||
\(845\) | 3.23777e6 | 0.00536631 | ||||||||
\(846\) | 3.15889e8 | + | 1.32004e8i | 0.521703 | + | 0.218010i | ||||
\(847\) | 3.53147e8i | 0.581174i | ||||||||
\(848\) | 3.84740e6 | − | 3.07545e8i | 0.00630927 | − | 0.504337i | ||||
\(849\) | −6.58436e8 | −1.07595 | ||||||||
\(850\) | 7.48417e7 | − | 1.79098e8i | 0.121867 | − | 0.291630i | ||||
\(851\) | 5.48935e8i | 0.890702i | ||||||||
\(852\) | 2.64773e8 | + | 2.68106e8i | 0.428109 | + | 0.433498i | ||||
\(853\) | −1.07837e9 | −1.73749 | −0.868744 | − | 0.495261i | \(-0.835072\pi\) | ||||
−0.868744 | + | 0.495261i | \(0.835072\pi\) | |||||||
\(854\) | 4.82706e7 | + | 2.01714e7i | 0.0775013 | + | 0.0323864i | ||||
\(855\) | 4.35500e7i | 0.0696770i | ||||||||
\(856\) | −4.54962e8 | − | 1.12820e9i | −0.725360 | − | 1.79872i | ||||
\(857\) | −8.51626e8 | −1.35303 | −0.676514 | − | 0.736430i | \(-0.736510\pi\) | ||||
−0.676514 | + | 0.736430i | \(0.736510\pi\) | |||||||
\(858\) | −8.12776e6 | + | 1.94499e7i | −0.0128679 | + | 0.0307932i | ||||
\(859\) | 3.73382e8i | 0.589079i | 0.955639 | + | 0.294539i | \(0.0951662\pi\) | ||||
−0.955639 | + | 0.294539i | \(0.904834\pi\) | |||||||
\(860\) | 5.66613e7 | − | 5.59569e7i | 0.0890823 | − | 0.0879748i | ||||
\(861\) | −2.35494e8 | −0.368952 | ||||||||
\(862\) | −3.05995e8 | − | 1.27870e8i | −0.477741 | − | 0.199640i | ||||
\(863\) | − | 3.38704e8i | − | 0.526973i | −0.964663 | − | 0.263486i | \(-0.915128\pi\) | ||
0.964663 | − | 0.263486i | \(-0.0848724\pi\) | |||||||
\(864\) | 4.92879e7 | − | 1.13920e8i | 0.0764186 | − | 0.176627i | ||||
\(865\) | −4.31509e8 | −0.666717 | ||||||||
\(866\) | −3.17330e8 | + | 7.59377e8i | −0.488605 | + | 1.16924i | ||||
\(867\) | − | 5.63460e8i | − | 0.864581i | ||||||
\(868\) | −1.23323e8 | − | 1.24875e8i | −0.188575 | − | 0.190949i | ||||
\(869\) | −4.91963e7 | −0.0749675 | ||||||||
\(870\) | −2.36060e8 | − | 9.86455e7i | −0.358480 | − | 0.149803i | ||||
\(871\) | − | 6.84089e8i | − | 1.03528i | ||||||
\(872\) | 1.04707e8 | − | 4.22244e7i | 0.157915 | − | 0.0636816i | ||||
\(873\) | −2.52598e8 | −0.379654 | ||||||||
\(874\) | 1.23263e8 | − | 2.94972e8i | 0.184629 | − | 0.441820i | ||||
\(875\) | 3.49391e7i | 0.0521539i | ||||||||
\(876\) | −3.00764e8 | + | 2.97025e8i | −0.447418 | + | 0.441856i | ||||
\(877\) | −4.66212e8 | −0.691169 | −0.345585 | − | 0.938388i | \(-0.612319\pi\) | ||||
−0.345585 | + | 0.938388i | \(0.612319\pi\) | |||||||
\(878\) | 8.65412e8 | + | 3.61640e8i | 1.27861 | + | 0.534310i | ||||
\(879\) | 6.08243e8i | 0.895593i | ||||||||
\(880\) | 1.75107e7 | + | 219060.i | 0.0256954 | + | 0.000321451i | ||||
\(881\) | 2.98435e8 | 0.436438 | 0.218219 | − | 0.975900i | \(-0.429975\pi\) | ||||
0.218219 | + | 0.975900i | \(0.429975\pi\) | |||||||
\(882\) | 5.82009e7 | − | 1.39276e8i | 0.0848250 | − | 0.202988i | ||||
\(883\) | 2.08263e8i | 0.302504i | 0.988495 | + | 0.151252i | \(0.0483305\pi\) | ||||
−0.988495 | + | 0.151252i | \(0.951670\pi\) | |||||||
\(884\) | −7.71704e8 | − | 7.81419e8i | −1.11711 | − | 1.13117i | ||||
\(885\) | −1.53930e8 | −0.222072 | ||||||||
\(886\) | 8.43844e8 | + | 3.52627e8i | 1.21328 | + | 0.507008i | ||||
\(887\) | − | 2.38652e8i | − | 0.341975i | −0.985273 | − | 0.170987i | \(-0.945304\pi\) | ||
0.985273 | − | 0.170987i | \(-0.0546958\pi\) | |||||||
\(888\) | 1.31456e8 | + | 3.25981e8i | 0.187734 | + | 0.465536i | ||||
\(889\) | −3.25011e8 | −0.462587 | ||||||||
\(890\) | 9.31006e7 | − | 2.22792e8i | 0.132063 | − | 0.316030i | ||||
\(891\) | − | 4.51612e6i | − | 0.00638458i | ||||||
\(892\) | 4.95211e8 | − | 4.89054e8i | 0.697743 | − | 0.689069i | ||||
\(893\) | 5.64605e8 | 0.792848 | ||||||||
\(894\) | −5.93409e8 | − | 2.47975e8i | −0.830504 | − | 0.347053i | ||||
\(895\) | − | 3.14479e8i | − | 0.438654i | ||||||
\(896\) | −3.90929e8 | + | 1.51990e8i | −0.543469 | + | 0.211297i | ||||
\(897\) | 4.29444e8 | 0.595017 | ||||||||
\(898\) | −2.32936e7 | + | 5.57419e7i | −0.0321667 | + | 0.0769756i | ||||
\(899\) | 5.03189e8i | 0.692551i | ||||||||
\(900\) | 3.41498e7 | + | 3.45797e7i | 0.0468447 | + | 0.0474344i | ||||
\(901\) | 5.83017e8 | 0.797089 | ||||||||
\(902\) | −4.26416e7 | − | 1.78192e7i | −0.0581051 | − | 0.0242811i | ||||
\(903\) | 6.93963e7i | 0.0942483i | ||||||||
\(904\) | −3.30596e6 | + | 1.33317e6i | −0.00447499 | + | 0.00180460i | ||||
\(905\) | −4.51077e8 | −0.608562 | ||||||||
\(906\) | −1.99872e8 | + | 4.78297e8i | −0.268762 | + | 0.643151i | ||||
\(907\) | − | 1.00884e9i | − | 1.35207i | −0.736868 | − | 0.676037i | \(-0.763696\pi\) | ||
0.736868 | − | 0.676037i | \(-0.236304\pi\) | |||||||
\(908\) | −9.92923e7 | + | 9.80579e7i | −0.132635 | + | 0.130986i | ||||
\(909\) | −2.52000e8 | −0.335513 | ||||||||
\(910\) | 1.82399e8 | + | 7.62212e7i | 0.242046 | + | 0.101147i | ||||
\(911\) | 2.93975e8i | 0.388825i | 0.980920 | + | 0.194413i | \(0.0622801\pi\) | ||||
−0.980920 | + | 0.194413i | \(0.937720\pi\) | |||||||
\(912\) | 2.56062e6 | − | 2.04685e8i | 0.00337567 | − | 0.269837i | ||||
\(913\) | 6.30528e7 | 0.0828499 | ||||||||
\(914\) | 2.33251e8 | − | 5.58175e8i | 0.305482 | − | 0.731024i | ||||
\(915\) | 2.84927e7i | 0.0371938i | ||||||||
\(916\) | −2.12765e8 | − | 2.15443e8i | −0.276831 | − | 0.280315i | ||||
\(917\) | 4.38014e8 | 0.568042 | ||||||||
\(918\) | 2.17095e8 | + | 9.07200e7i | 0.280621 | + | 0.117267i | ||||
\(919\) | − | 1.43188e9i | − | 1.84484i | −0.386183 | − | 0.922422i | \(-0.626207\pi\) | ||
0.386183 | − | 0.922422i | \(-0.373793\pi\) | |||||||
\(920\) | −1.33428e8 | − | 3.30871e8i | −0.171350 | − | 0.424908i | ||||
\(921\) | −2.41825e8 | −0.309544 | ||||||||
\(922\) | 4.32091e8 | − | 1.03400e9i | 0.551293 | − | 1.31925i | ||||
\(923\) | 8.34754e8i | 1.06158i | ||||||||
\(924\) | −1.08582e7 | + | 1.07232e7i | −0.0137639 | + | 0.0135928i | ||||
\(925\) | −1.37622e8 | −0.173885 | ||||||||
\(926\) | −6.08559e8 | − | 2.54306e8i | −0.766426 | − | 0.320276i | ||||
\(927\) | − | 3.58441e7i | − | 0.0449965i | ||||||
\(928\) | 1.10368e9 | + | 4.77513e8i | 1.38102 | + | 0.597505i | ||||
\(929\) | −8.11875e8 | −1.01261 | −0.506305 | − | 0.862355i | \(-0.668989\pi\) | ||||
−0.506305 | + | 0.862355i | \(0.668989\pi\) | |||||||
\(930\) | 3.68552e7 | − | 8.81951e7i | 0.0458194 | − | 0.109647i | ||||
\(931\) | − | 2.48935e8i | − | 0.308487i | ||||||
\(932\) | 7.00189e8 | + | 7.09003e8i | 0.864903 | + | 0.875791i | ||||
\(933\) | −1.09648e8 | −0.135007 | ||||||||
\(934\) | 1.26688e9 | + | 5.29408e8i | 1.55488 | + | 0.649756i | ||||
\(935\) | 3.31954e7i | 0.0406109i | ||||||||
\(936\) | 2.55022e8 | − | 1.02841e8i | 0.310992 | − | 0.125412i | ||||
\(937\) | 1.58918e9 | 1.93176 | 0.965882 | − | 0.258983i | \(-0.0833874\pi\) | ||||
0.965882 | + | 0.258983i | \(0.0833874\pi\) | |||||||
\(938\) | 1.90952e8 | − | 4.56951e8i | 0.231374 | − | 0.553682i | ||||
\(939\) | 3.74529e8i | 0.452365i | ||||||||
\(940\) | 4.48309e8 | − | 4.42735e8i | 0.539751 | − | 0.533041i | ||||
\(941\) | −7.80199e8 | −0.936346 | −0.468173 | − | 0.883637i | \(-0.655088\pi\) | ||||
−0.468173 | + | 0.883637i | \(0.655088\pi\) | |||||||
\(942\) | 2.41702e8 | + | 1.01003e8i | 0.289153 | + | 0.120832i | ||||
\(943\) | 9.41506e8i | 1.12276i | ||||||||
\(944\) | 7.23471e8 | + | 9.05065e6i | 0.860013 | + | 0.0107588i | ||||
\(945\) | −4.23517e7 | −0.0501852 | ||||||||
\(946\) | −5.25103e6 | + | 1.25658e7i | −0.00620256 | + | 0.0148428i | ||||
\(947\) | 5.58843e7i | 0.0658021i | 0.999459 | + | 0.0329010i | \(0.0104746\pi\) | ||||
−0.999459 | + | 0.0329010i | \(0.989525\pi\) | |||||||
\(948\) | 4.50935e8 | + | 4.56612e8i | 0.529284 | + | 0.535947i | ||||
\(949\) | −9.36436e8 | −1.09567 | ||||||||
\(950\) | 7.39515e7 | + | 3.09030e7i | 0.0862534 | + | 0.0360438i | ||||
\(951\) | − | 8.67211e8i | − | 1.00828i | ||||||
\(952\) | −2.97355e8 | − | 7.37371e8i | −0.344639 | − | 0.854625i | ||||
\(953\) | −1.65002e9 | −1.90639 | −0.953195 | − | 0.302356i | \(-0.902227\pi\) | ||||
−0.953195 | + | 0.302356i | \(0.902227\pi\) | |||||||
\(954\) | −5.62837e7 | + | 1.34688e8i | −0.0648242 | + | 0.155126i | ||||
\(955\) | 2.44598e8i | 0.280830i | ||||||||
\(956\) | 1.04630e9 | − | 1.03329e9i | 1.19752 | − | 1.18263i | ||||
\(957\) | 4.37533e7 | 0.0499201 | ||||||||
\(958\) | 8.26964e8 | + | 3.45574e8i | 0.940568 | + | 0.393047i | ||||
\(959\) | 1.29031e8i | 0.146298i | ||||||||
\(960\) | −1.58471e8 | − | 1.64532e8i | −0.179116 | − | 0.185968i | ||||
\(961\) | 6.99506e8 | 0.788173 | ||||||||
\(962\) | −3.00229e8 | + | 7.18453e8i | −0.337231 | + | 0.807000i | ||||
\(963\) | 5.77352e8i | 0.646490i | ||||||||
\(964\) | −1.09701e9 | − | 1.11082e9i | −1.22456 | − | 1.23997i | ||||
\(965\) | −7.11536e8 | −0.791799 | ||||||||
\(966\) | 2.86855e8 | + | 1.19872e8i | 0.318223 | + | 0.132980i | ||||
\(967\) | − | 1.07504e9i | − | 1.18890i | −0.804134 | − | 0.594448i | \(-0.797371\pi\) | ||
0.804134 | − | 0.594448i | \(-0.202629\pi\) | |||||||
\(968\) | 8.38437e8 | − | 3.38112e8i | 0.924367 | − | 0.372764i | ||||
\(969\) | 3.88025e8 | 0.426469 | ||||||||
\(970\) | −1.79243e8 | + | 4.28933e8i | −0.196394 | + | 0.469974i | ||||
\(971\) | − | 4.45105e8i | − | 0.486188i | −0.970003 | − | 0.243094i | \(-0.921838\pi\) | ||
0.970003 | − | 0.243094i | \(-0.0781624\pi\) | |||||||
\(972\) | −4.19160e7 | + | 4.13949e7i | −0.0456438 | + | 0.0450763i | ||||
\(973\) | −3.65989e8 | −0.397310 | ||||||||
\(974\) | −1.23024e9 | − | 5.14097e8i | −1.33142 | − | 0.556375i | ||||
\(975\) | 1.07665e8i | 0.116161i | ||||||||
\(976\) | 1.67529e6 | − | 1.33916e8i | 0.00180194 | − | 0.144040i | ||||
\(977\) | 1.61942e8 | 0.173650 | 0.0868250 | − | 0.996224i | \(-0.472328\pi\) | ||||
0.0868250 | + | 0.996224i | \(0.472328\pi\) | |||||||
\(978\) | −3.55338e8 | + | 8.50330e8i | −0.379861 | + | 0.909014i | ||||
\(979\) | 4.12940e7i | 0.0440087i | ||||||||
\(980\) | −1.95203e8 | − | 1.97660e8i | −0.207399 | − | 0.210010i | ||||
\(981\) | −5.35833e7 | −0.0567574 | ||||||||
\(982\) | −1.06910e8 | − | 4.46758e7i | −0.112897 | − | 0.0471778i | ||||
\(983\) | 3.67236e8i | 0.386621i | 0.981138 | + | 0.193310i | \(0.0619224\pi\) | ||||
−0.981138 | + | 0.193310i | \(0.938078\pi\) | |||||||
\(984\) | 2.25467e8 | + | 5.59106e8i | 0.236645 | + | 0.586825i | ||||
\(985\) | 1.09357e8 | 0.114429 | ||||||||
\(986\) | −8.78918e8 | + | 2.10327e9i | −0.916891 | + | 2.19414i | ||||
\(987\) | 5.49069e8i | 0.571052i | ||||||||
\(988\) | 3.22657e8 | − | 3.18646e8i | 0.334557 | − | 0.330398i | ||||
\(989\) | 2.77447e8 | 0.286808 | ||||||||
\(990\) | −7.66875e6 | − | 3.20464e6i | −0.00790349 | − | 0.00330273i | ||||
\(991\) | 1.66636e9i | 1.71218i | 0.516830 | + | 0.856088i | \(0.327112\pi\) | ||||
−0.516830 | + | 0.856088i | \(0.672888\pi\) | |||||||
\(992\) | −1.78405e8 | + | 4.12350e8i | −0.182756 | + | 0.422407i | ||||
\(993\) | −8.02259e7 | −0.0819345 | ||||||||
\(994\) | −2.33007e8 | + | 5.57590e8i | −0.237252 | + | 0.567748i | ||||
\(995\) | − | 2.38991e8i | − | 0.242612i | ||||||
\(996\) | −5.77944e8 | − | 5.85219e8i | −0.584935 | − | 0.592298i | ||||
\(997\) | 2.88083e8 | 0.290691 | 0.145346 | − | 0.989381i | \(-0.453571\pi\) | ||||
0.145346 | + | 0.989381i | \(0.453571\pi\) | |||||||
\(998\) | 1.34930e9 | + | 5.63849e8i | 1.35743 | + | 0.567245i | ||||
\(999\) | − | 1.66820e8i | − | 0.167321i |
(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 | 60.7.c.a.31.8 | yes | 24 | |
3.2 | odd | 2 | 180.7.c.b.91.17 | 24 | |||
4.3 | odd | 2 | inner | 60.7.c.a.31.7 | ✓ | 24 | |
12.11 | even | 2 | 180.7.c.b.91.18 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.7.c.a.31.7 | ✓ | 24 | 4.3 | odd | 2 | inner | |
60.7.c.a.31.8 | yes | 24 | 1.1 | even | 1 | trivial | |
180.7.c.b.91.17 | 24 | 3.2 | odd | 2 | |||
180.7.c.b.91.18 | 24 | 12.11 | even | 2 |