Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [354,7,Mod(235,354)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(354, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("354.235");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 354 = 2 \cdot 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 354.d (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: | \(81.4391456014\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 235.3 | ||
Character | \(\chi\) | \(=\) | 354.235 |
Dual form | 354.7.d.a.235.4 |
$q$-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 \(\left(\mathbb{Z}/354\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 5.65685i | − | 0.707107i | ||||||
\(3\) | 15.5885 | 0.577350 | ||||||||
\(4\) | −32.0000 | −0.500000 | ||||||||
\(5\) | 117.083 | 0.936667 | 0.468334 | − | 0.883552i | \(-0.344855\pi\) | ||||
0.468334 | + | 0.883552i | \(0.344855\pi\) | |||||||
\(6\) | − | 88.1816i | − | 0.408248i | ||||||
\(7\) | 626.230 | 1.82574 | 0.912872 | − | 0.408246i | \(-0.133859\pi\) | ||||
0.912872 | + | 0.408246i | \(0.133859\pi\) | |||||||
\(8\) | 181.019i | 0.353553i | ||||||||
\(9\) | 243.000 | 0.333333 | ||||||||
\(10\) | − | 662.324i | − | 0.662324i | ||||||
\(11\) | − | 2448.22i | − | 1.83938i | −0.392641 | − | 0.919692i | \(-0.628439\pi\) | ||
0.392641 | − | 0.919692i | \(-0.371561\pi\) | |||||||
\(12\) | −498.831 | −0.288675 | ||||||||
\(13\) | 657.581i | 0.299308i | 0.988738 | + | 0.149654i | \(0.0478160\pi\) | ||||
−0.988738 | + | 0.149654i | \(0.952184\pi\) | |||||||
\(14\) | − | 3542.49i | − | 1.29100i | ||||||
\(15\) | 1825.15 | 0.540785 | ||||||||
\(16\) | 1024.00 | 0.250000 | ||||||||
\(17\) | 8454.02 | 1.72074 | 0.860372 | − | 0.509666i | \(-0.170231\pi\) | ||||
0.860372 | + | 0.509666i | \(0.170231\pi\) | |||||||
\(18\) | − | 1374.62i | − | 0.235702i | ||||||
\(19\) | −5380.68 | −0.784469 | −0.392235 | − | 0.919865i | \(-0.628298\pi\) | ||||
−0.392235 | + | 0.919865i | \(0.628298\pi\) | |||||||
\(20\) | −3746.67 | −0.468334 | ||||||||
\(21\) | 9761.96 | 1.05409 | ||||||||
\(22\) | −13849.2 | −1.30064 | ||||||||
\(23\) | − | 19941.2i | − | 1.63896i | −0.573109 | − | 0.819479i | \(-0.694263\pi\) | ||
0.573109 | − | 0.819479i | \(-0.305737\pi\) | |||||||
\(24\) | 2821.81i | 0.204124i | ||||||||
\(25\) | −1916.48 | −0.122655 | ||||||||
\(26\) | 3719.84 | 0.211643 | ||||||||
\(27\) | 3788.00 | 0.192450 | ||||||||
\(28\) | −20039.4 | −0.912872 | ||||||||
\(29\) | −23410.8 | −0.959891 | −0.479945 | − | 0.877298i | \(-0.659344\pi\) | ||||
−0.479945 | + | 0.877298i | \(0.659344\pi\) | |||||||
\(30\) | − | 10324.6i | − | 0.382393i | ||||||
\(31\) | 1133.12i | 0.0380356i | 0.999819 | + | 0.0190178i | \(0.00605391\pi\) | ||||
−0.999819 | + | 0.0190178i | \(0.993946\pi\) | |||||||
\(32\) | − | 5792.62i | − | 0.176777i | ||||||
\(33\) | − | 38164.0i | − | 1.06197i | ||||||
\(34\) | − | 47823.1i | − | 1.21675i | ||||||
\(35\) | 73321.2 | 1.71011 | ||||||||
\(36\) | −7776.00 | −0.166667 | ||||||||
\(37\) | − | 14477.3i | − | 0.285814i | −0.989736 | − | 0.142907i | \(-0.954355\pi\) | ||
0.989736 | − | 0.142907i | \(-0.0456450\pi\) | |||||||
\(38\) | 30437.7i | 0.554704i | ||||||||
\(39\) | 10250.7i | 0.172806i | ||||||||
\(40\) | 21194.4i | 0.331162i | ||||||||
\(41\) | −14137.9 | −0.205131 | −0.102566 | − | 0.994726i | \(-0.532705\pi\) | ||||
−0.102566 | + | 0.994726i | \(0.532705\pi\) | |||||||
\(42\) | − | 55222.0i | − | 0.745357i | ||||||
\(43\) | 115979.i | 1.45873i | 0.684126 | + | 0.729364i | \(0.260184\pi\) | ||||
−0.684126 | + | 0.729364i | \(0.739816\pi\) | |||||||
\(44\) | 78343.0i | 0.919692i | ||||||||
\(45\) | 28451.3 | 0.312222 | ||||||||
\(46\) | −112805. | −1.15892 | ||||||||
\(47\) | 80048.2i | 0.771006i | 0.922707 | + | 0.385503i | \(0.125972\pi\) | ||||
−0.922707 | + | 0.385503i | \(0.874028\pi\) | |||||||
\(48\) | 15962.6 | 0.144338 | ||||||||
\(49\) | 274515. | 2.33334 | ||||||||
\(50\) | 10841.2i | 0.0867299i | ||||||||
\(51\) | 131785. | 0.993472 | ||||||||
\(52\) | − | 21042.6i | − | 0.149654i | ||||||
\(53\) | 198626. | 1.33416 | 0.667082 | − | 0.744984i | \(-0.267543\pi\) | ||||
0.667082 | + | 0.744984i | \(0.267543\pi\) | |||||||
\(54\) | − | 21428.1i | − | 0.136083i | ||||||
\(55\) | − | 286646.i | − | 1.72289i | ||||||
\(56\) | 113360.i | 0.645498i | ||||||||
\(57\) | −83876.4 | −0.452914 | ||||||||
\(58\) | 132431.i | 0.678745i | ||||||||
\(59\) | −204279. | − | 21232.5i | −0.994642 | − | 0.103382i | ||||
\(60\) | −58404.8 | −0.270393 | ||||||||
\(61\) | − | 110067.i | − | 0.484915i | −0.970162 | − | 0.242458i | \(-0.922046\pi\) | ||
0.970162 | − | 0.242458i | \(-0.0779536\pi\) | |||||||
\(62\) | 6409.88 | 0.0268952 | ||||||||
\(63\) | 152174. | 0.608581 | ||||||||
\(64\) | −32768.0 | −0.125000 | ||||||||
\(65\) | 76991.8i | 0.280352i | ||||||||
\(66\) | −215888. | −0.750925 | ||||||||
\(67\) | 290250.i | 0.965046i | 0.875883 | + | 0.482523i | \(0.160279\pi\) | ||||
−0.875883 | + | 0.482523i | \(0.839721\pi\) | |||||||
\(68\) | −270529. | −0.860372 | ||||||||
\(69\) | − | 310853.i | − | 0.946253i | ||||||
\(70\) | − | 414767.i | − | 1.20923i | ||||||
\(71\) | 243917. | 0.681502 | 0.340751 | − | 0.940154i | \(-0.389319\pi\) | ||||
0.340751 | + | 0.940154i | \(0.389319\pi\) | |||||||
\(72\) | 43987.7i | 0.117851i | ||||||||
\(73\) | − | 444431.i | − | 1.14245i | −0.820795 | − | 0.571223i | \(-0.806469\pi\) | ||
0.820795 | − | 0.571223i | \(-0.193531\pi\) | |||||||
\(74\) | −81896.2 | −0.202101 | ||||||||
\(75\) | −29874.9 | −0.0708147 | ||||||||
\(76\) | 172182. | 0.392235 | ||||||||
\(77\) | − | 1.53315e6i | − | 3.35824i | ||||||
\(78\) | 57986.5 | 0.122192 | ||||||||
\(79\) | −376135. | −0.762890 | −0.381445 | − | 0.924392i | \(-0.624573\pi\) | ||||
−0.381445 | + | 0.924392i | \(0.624573\pi\) | |||||||
\(80\) | 119893. | 0.234167 | ||||||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | 79975.8i | 0.145050i | ||||||||
\(83\) | 266953.i | 0.466875i | 0.972372 | + | 0.233438i | \(0.0749975\pi\) | ||||
−0.972372 | + | 0.233438i | \(0.925002\pi\) | |||||||
\(84\) | −312383. | −0.527047 | ||||||||
\(85\) | 989825. | 1.61176 | ||||||||
\(86\) | 656077. | 1.03148 | ||||||||
\(87\) | −364938. | −0.554193 | ||||||||
\(88\) | 443175. | 0.650320 | ||||||||
\(89\) | 117162.i | 0.166195i | 0.996541 | + | 0.0830974i | \(0.0264813\pi\) | ||||
−0.996541 | + | 0.0830974i | \(0.973519\pi\) | |||||||
\(90\) | − | 160945.i | − | 0.220775i | ||||||
\(91\) | 411797.i | 0.546461i | ||||||||
\(92\) | 638119.i | 0.819479i | ||||||||
\(93\) | 17663.6i | 0.0219599i | ||||||||
\(94\) | 452821. | 0.545184 | ||||||||
\(95\) | −629988. | −0.734787 | ||||||||
\(96\) | − | 90298.0i | − | 0.102062i | ||||||
\(97\) | 1.21239e6i | 1.32840i | 0.747555 | + | 0.664199i | \(0.231227\pi\) | ||||
−0.747555 | + | 0.664199i | \(0.768773\pi\) | |||||||
\(98\) | − | 1.55289e6i | − | 1.64992i | ||||||
\(99\) | − | 594917.i | − | 0.613128i | ||||||
\(100\) | 61327.3 | 0.0613273 | ||||||||
\(101\) | − | 383864.i | − | 0.372575i | −0.982495 | − | 0.186287i | \(-0.940354\pi\) | ||
0.982495 | − | 0.186287i | \(-0.0596456\pi\) | |||||||
\(102\) | − | 745489.i | − | 0.702491i | ||||||
\(103\) | 773923.i | 0.708250i | 0.935198 | + | 0.354125i | \(0.115221\pi\) | ||||
−0.935198 | + | 0.354125i | \(0.884779\pi\) | |||||||
\(104\) | −119035. | −0.105822 | ||||||||
\(105\) | 1.14296e6 | 0.987335 | ||||||||
\(106\) | − | 1.12360e6i | − | 0.943397i | ||||||
\(107\) | 686959. | 0.560763 | 0.280382 | − | 0.959889i | \(-0.409539\pi\) | ||||
0.280382 | + | 0.959889i | \(0.409539\pi\) | |||||||
\(108\) | −121216. | −0.0962250 | ||||||||
\(109\) | 257809.i | 0.199076i | 0.995034 | + | 0.0995380i | \(0.0317365\pi\) | ||||
−0.995034 | + | 0.0995380i | \(0.968264\pi\) | |||||||
\(110\) | −1.62151e6 | −1.21827 | ||||||||
\(111\) | − | 225679.i | − | 0.165015i | ||||||
\(112\) | 641260. | 0.456436 | ||||||||
\(113\) | − | 1.56285e6i | − | 1.08313i | −0.840659 | − | 0.541565i | \(-0.817832\pi\) | ||
0.840659 | − | 0.541565i | \(-0.182168\pi\) | |||||||
\(114\) | 474477.i | 0.320258i | ||||||||
\(115\) | − | 2.33478e6i | − | 1.53516i | ||||||
\(116\) | 749145. | 0.479945 | ||||||||
\(117\) | 159792.i | 0.0997695i | ||||||||
\(118\) | −120109. | + | 1.15557e6i | −0.0731021 | + | 0.703318i | ||||
\(119\) | 5.29416e6 | 3.14164 | ||||||||
\(120\) | 330387.i | 0.191196i | ||||||||
\(121\) | −4.22222e6 | −2.38333 | ||||||||
\(122\) | −622631. | −0.342887 | ||||||||
\(123\) | −220387. | −0.118433 | ||||||||
\(124\) | − | 36259.8i | − | 0.0190178i | ||||||
\(125\) | −2.05382e6 | −1.05155 | ||||||||
\(126\) | − | 860826.i | − | 0.430332i | ||||||
\(127\) | 1.20126e6 | 0.586443 | 0.293221 | − | 0.956045i | \(-0.405273\pi\) | ||||
0.293221 | + | 0.956045i | \(0.405273\pi\) | |||||||
\(128\) | 185364.i | 0.0883883i | ||||||||
\(129\) | 1.80793e6i | 0.842197i | ||||||||
\(130\) | 435531. | 0.198239 | ||||||||
\(131\) | − | 2.92321e6i | − | 1.30031i | −0.759804 | − | 0.650153i | \(-0.774705\pi\) | ||
0.759804 | − | 0.650153i | \(-0.225295\pi\) | |||||||
\(132\) | 1.22125e6i | 0.530984i | ||||||||
\(133\) | −3.36954e6 | −1.43224 | ||||||||
\(134\) | 1.64190e6 | 0.682390 | ||||||||
\(135\) | 443511. | 0.180262 | ||||||||
\(136\) | 1.53034e6i | 0.608375i | ||||||||
\(137\) | −1.14141e6 | −0.443893 | −0.221946 | − | 0.975059i | \(-0.571241\pi\) | ||||
−0.221946 | + | 0.975059i | \(0.571241\pi\) | |||||||
\(138\) | −1.75845e6 | −0.669102 | ||||||||
\(139\) | −4.56066e6 | −1.69818 | −0.849088 | − | 0.528251i | \(-0.822848\pi\) | ||||
−0.849088 | + | 0.528251i | \(0.822848\pi\) | |||||||
\(140\) | −2.34628e6 | −0.855057 | ||||||||
\(141\) | 1.24783e6i | 0.445141i | ||||||||
\(142\) | − | 1.37980e6i | − | 0.481895i | ||||||
\(143\) | 1.60990e6 | 0.550543 | ||||||||
\(144\) | 248832. | 0.0833333 | ||||||||
\(145\) | −2.74101e6 | −0.899098 | ||||||||
\(146\) | −2.51408e6 | −0.807832 | ||||||||
\(147\) | 4.27927e6 | 1.34715 | ||||||||
\(148\) | 463275.i | 0.142907i | ||||||||
\(149\) | − | 2.82142e6i | − | 0.852920i | −0.904506 | − | 0.426460i | \(-0.859760\pi\) | ||
0.904506 | − | 0.426460i | \(-0.140240\pi\) | |||||||
\(150\) | 168998.i | 0.0500735i | ||||||||
\(151\) | 1.74960e6i | 0.508169i | 0.967182 | + | 0.254085i | \(0.0817742\pi\) | ||||
−0.967182 | + | 0.254085i | \(0.918226\pi\) | |||||||
\(152\) | − | 974006.i | − | 0.277352i | ||||||
\(153\) | 2.05433e6 | 0.573582 | ||||||||
\(154\) | −8.67280e6 | −2.37464 | ||||||||
\(155\) | 132669.i | 0.0356267i | ||||||||
\(156\) | − | 328021.i | − | 0.0864029i | ||||||
\(157\) | − | 5.81803e6i | − | 1.50341i | −0.659500 | − | 0.751704i | \(-0.729232\pi\) | ||
0.659500 | − | 0.751704i | \(-0.270768\pi\) | |||||||
\(158\) | 2.12774e6i | 0.539445i | ||||||||
\(159\) | 3.09628e6 | 0.770280 | ||||||||
\(160\) | − | 678219.i | − | 0.165581i | ||||||
\(161\) | − | 1.24878e7i | − | 2.99232i | ||||||
\(162\) | − | 334032.i | − | 0.0785674i | ||||||
\(163\) | 5.84246e6 | 1.34907 | 0.674533 | − | 0.738245i | \(-0.264345\pi\) | ||||
0.674533 | + | 0.738245i | \(0.264345\pi\) | |||||||
\(164\) | 452411. | 0.102566 | ||||||||
\(165\) | − | 4.46837e6i | − | 0.994711i | ||||||
\(166\) | 1.51012e6 | 0.330131 | ||||||||
\(167\) | −5.89974e6 | −1.26673 | −0.633364 | − | 0.773854i | \(-0.718326\pi\) | ||||
−0.633364 | + | 0.773854i | \(0.718326\pi\) | |||||||
\(168\) | 1.76710e6i | 0.372678i | ||||||||
\(169\) | 4.39440e6 | 0.910414 | ||||||||
\(170\) | − | 5.59930e6i | − | 1.13969i | ||||||
\(171\) | −1.30750e6 | −0.261490 | ||||||||
\(172\) | − | 3.71133e6i | − | 0.729364i | ||||||
\(173\) | 8.33462e6i | 1.60971i | 0.593472 | + | 0.804855i | \(0.297757\pi\) | ||||
−0.593472 | + | 0.804855i | \(0.702243\pi\) | |||||||
\(174\) | 2.06440e6i | 0.391874i | ||||||||
\(175\) | −1.20016e6 | −0.223936 | ||||||||
\(176\) | − | 2.50698e6i | − | 0.459846i | ||||||
\(177\) | −3.18439e6 | − | 330982.i | −0.574257 | − | 0.0596876i | ||||
\(178\) | 662770. | 0.117518 | ||||||||
\(179\) | 1.07999e7i | 1.88305i | 0.336943 | + | 0.941525i | \(0.390607\pi\) | ||||
−0.336943 | + | 0.941525i | \(0.609393\pi\) | |||||||
\(180\) | −910440. | −0.156111 | ||||||||
\(181\) | −659045. | −0.111142 | −0.0555712 | − | 0.998455i | \(-0.517698\pi\) | ||||
−0.0555712 | + | 0.998455i | \(0.517698\pi\) | |||||||
\(182\) | 2.32947e6 | 0.386406 | ||||||||
\(183\) | − | 1.71577e6i | − | 0.279966i | ||||||
\(184\) | 3.60974e6 | 0.579459 | ||||||||
\(185\) | − | 1.69506e6i | − | 0.267712i | ||||||
\(186\) | 99920.2 | 0.0155280 | ||||||||
\(187\) | − | 2.06973e7i | − | 3.16511i | ||||||
\(188\) | − | 2.56154e6i | − | 0.385503i | ||||||
\(189\) | 2.37216e6 | 0.351365 | ||||||||
\(190\) | 3.56375e6i | 0.519573i | ||||||||
\(191\) | − | 5.50856e6i | − | 0.790566i | −0.918559 | − | 0.395283i | \(-0.870646\pi\) | ||
0.918559 | − | 0.395283i | \(-0.129354\pi\) | |||||||
\(192\) | −510803. | −0.0721688 | ||||||||
\(193\) | −888897. | −0.123646 | −0.0618229 | − | 0.998087i | \(-0.519691\pi\) | ||||
−0.0618229 | + | 0.998087i | \(0.519691\pi\) | |||||||
\(194\) | 6.85834e6 | 0.939320 | ||||||||
\(195\) | 1.20018e6i | 0.161862i | ||||||||
\(196\) | −8.78449e6 | −1.16667 | ||||||||
\(197\) | 7.16430e6 | 0.937077 | 0.468538 | − | 0.883443i | \(-0.344781\pi\) | ||||
0.468538 | + | 0.883443i | \(0.344781\pi\) | |||||||
\(198\) | −3.36536e6 | −0.433547 | ||||||||
\(199\) | 6.98402e6 | 0.886229 | 0.443115 | − | 0.896465i | \(-0.353873\pi\) | ||||
0.443115 | + | 0.896465i | \(0.353873\pi\) | |||||||
\(200\) | − | 346920.i | − | 0.0433650i | ||||||
\(201\) | 4.52455e6i | 0.557169i | ||||||||
\(202\) | −2.17146e6 | −0.263450 | ||||||||
\(203\) | −1.46605e7 | −1.75251 | ||||||||
\(204\) | −4.21712e6 | −0.496736 | ||||||||
\(205\) | −1.65531e6 | −0.192140 | ||||||||
\(206\) | 4.37797e6 | 0.500808 | ||||||||
\(207\) | − | 4.84571e6i | − | 0.546319i | ||||||
\(208\) | 673363.i | 0.0748271i | ||||||||
\(209\) | 1.31731e7i | 1.44294i | ||||||||
\(210\) | − | 6.46558e6i | − | 0.698151i | ||||||
\(211\) | − | 6.62052e6i | − | 0.704765i | −0.935856 | − | 0.352383i | \(-0.885372\pi\) | ||
0.935856 | − | 0.352383i | \(-0.114628\pi\) | |||||||
\(212\) | −6.35605e6 | −0.667082 | ||||||||
\(213\) | 3.80229e6 | 0.393465 | ||||||||
\(214\) | − | 3.88603e6i | − | 0.396519i | ||||||
\(215\) | 1.35792e7i | 1.36634i | ||||||||
\(216\) | 685700.i | 0.0680414i | ||||||||
\(217\) | 709593.i | 0.0694432i | ||||||||
\(218\) | 1.45839e6 | 0.140768 | ||||||||
\(219\) | − | 6.92799e6i | − | 0.659592i | ||||||
\(220\) | 9.17267e6i | 0.861445i | ||||||||
\(221\) | 5.55920e6i | 0.515033i | ||||||||
\(222\) | −1.27663e6 | −0.116683 | ||||||||
\(223\) | −2.04661e6 | −0.184553 | −0.0922763 | − | 0.995733i | \(-0.529414\pi\) | ||||
−0.0922763 | + | 0.995733i | \(0.529414\pi\) | |||||||
\(224\) | − | 3.62751e6i | − | 0.322749i | ||||||
\(225\) | −465704. | −0.0408849 | ||||||||
\(226\) | −8.84079e6 | −0.765889 | ||||||||
\(227\) | 1.70364e7i | 1.45646i | 0.685330 | + | 0.728232i | \(0.259658\pi\) | ||||
−0.685330 | + | 0.728232i | \(0.740342\pi\) | |||||||
\(228\) | 2.68405e6 | 0.226457 | ||||||||
\(229\) | − | 1.03402e7i | − | 0.861038i | −0.902582 | − | 0.430519i | \(-0.858331\pi\) | ||
0.902582 | − | 0.430519i | \(-0.141669\pi\) | |||||||
\(230\) | −1.32075e7 | −1.08552 | ||||||||
\(231\) | − | 2.38994e7i | − | 1.93888i | ||||||
\(232\) | − | 4.23780e6i | − | 0.339373i | ||||||
\(233\) | − | 5.05020e6i | − | 0.399246i | −0.979873 | − | 0.199623i | \(-0.936028\pi\) | ||
0.979873 | − | 0.199623i | \(-0.0639717\pi\) | |||||||
\(234\) | 903921. | 0.0705477 | ||||||||
\(235\) | 9.37231e6i | 0.722176i | ||||||||
\(236\) | 6.53691e6 | + | 679439.i | 0.497321 | + | 0.0516910i | ||||
\(237\) | −5.86336e6 | −0.440455 | ||||||||
\(238\) | − | 2.99483e7i | − | 2.22147i | ||||||
\(239\) | −6.29929e6 | −0.461422 | −0.230711 | − | 0.973022i | \(-0.574105\pi\) | ||||
−0.230711 | + | 0.973022i | \(0.574105\pi\) | |||||||
\(240\) | 1.86895e6 | 0.135196 | ||||||||
\(241\) | 7.61877e6 | 0.544294 | 0.272147 | − | 0.962256i | \(-0.412266\pi\) | ||||
0.272147 | + | 0.962256i | \(0.412266\pi\) | |||||||
\(242\) | 2.38845e7i | 1.68527i | ||||||||
\(243\) | 920483. | 0.0641500 | ||||||||
\(244\) | 3.52213e6i | 0.242458i | ||||||||
\(245\) | 3.21412e7 | 2.18556 | ||||||||
\(246\) | 1.24670e6i | 0.0837445i | ||||||||
\(247\) | − | 3.53823e6i | − | 0.234798i | ||||||
\(248\) | −205116. | −0.0134476 | ||||||||
\(249\) | 4.16139e6i | 0.269551i | ||||||||
\(250\) | 1.16181e7i | 0.743561i | ||||||||
\(251\) | 1.50591e7 | 0.952308 | 0.476154 | − | 0.879362i | \(-0.342030\pi\) | ||||
0.476154 | + | 0.879362i | \(0.342030\pi\) | |||||||
\(252\) | −4.86957e6 | −0.304291 | ||||||||
\(253\) | −4.88205e7 | −3.01467 | ||||||||
\(254\) | − | 6.79535e6i | − | 0.414678i | ||||||
\(255\) | 1.54298e7 | 0.930553 | ||||||||
\(256\) | 1.04858e6 | 0.0625000 | ||||||||
\(257\) | 2.56607e7 | 1.51171 | 0.755857 | − | 0.654737i | \(-0.227221\pi\) | ||||
0.755857 | + | 0.654737i | \(0.227221\pi\) | |||||||
\(258\) | 1.02272e7 | 0.595523 | ||||||||
\(259\) | − | 9.06614e6i | − | 0.521823i | ||||||
\(260\) | − | 2.46374e6i | − | 0.140176i | ||||||
\(261\) | −5.68882e6 | −0.319964 | ||||||||
\(262\) | −1.65361e7 | −0.919455 | ||||||||
\(263\) | −1.21340e7 | −0.667016 | −0.333508 | − | 0.942747i | \(-0.608232\pi\) | ||||
−0.333508 | + | 0.942747i | \(0.608232\pi\) | |||||||
\(264\) | 6.90842e6 | 0.375463 | ||||||||
\(265\) | 2.32559e7 | 1.24967 | ||||||||
\(266\) | 1.90610e7i | 1.01275i | ||||||||
\(267\) | 1.82638e6i | 0.0959526i | ||||||||
\(268\) | − | 9.28800e6i | − | 0.482523i | ||||||
\(269\) | 2.64537e7i | 1.35903i | 0.733662 | + | 0.679515i | \(0.237810\pi\) | ||||
−0.733662 | + | 0.679515i | \(0.762190\pi\) | |||||||
\(270\) | − | 2.50888e6i | − | 0.127464i | ||||||
\(271\) | 2.61362e7 | 1.31321 | 0.656605 | − | 0.754235i | \(-0.271992\pi\) | ||||
0.656605 | + | 0.754235i | \(0.271992\pi\) | |||||||
\(272\) | 8.65691e6 | 0.430186 | ||||||||
\(273\) | 6.41928e6i | 0.315499i | ||||||||
\(274\) | 6.45676e6i | 0.313880i | ||||||||
\(275\) | 4.69196e6i | 0.225609i | ||||||||
\(276\) | 9.94728e6i | 0.473127i | ||||||||
\(277\) | −8.31876e6 | −0.391398 | −0.195699 | − | 0.980664i | \(-0.562698\pi\) | ||||
−0.195699 | + | 0.980664i | \(0.562698\pi\) | |||||||
\(278\) | 2.57990e7i | 1.20079i | ||||||||
\(279\) | 275348.i | 0.0126785i | ||||||||
\(280\) | 1.32725e7i | 0.604617i | ||||||||
\(281\) | 4.36527e7 | 1.96740 | 0.983699 | − | 0.179820i | \(-0.0575516\pi\) | ||||
0.983699 | + | 0.179820i | \(0.0575516\pi\) | |||||||
\(282\) | 7.05878e6 | 0.314762 | ||||||||
\(283\) | − | 9.41605e6i | − | 0.415441i | −0.978188 | − | 0.207721i | \(-0.933396\pi\) | ||
0.978188 | − | 0.207721i | \(-0.0666045\pi\) | |||||||
\(284\) | −7.80535e6 | −0.340751 | ||||||||
\(285\) | −9.82054e6 | −0.424229 | ||||||||
\(286\) | − | 9.10698e6i | − | 0.389293i | ||||||
\(287\) | −8.85355e6 | −0.374517 | ||||||||
\(288\) | − | 1.40761e6i | − | 0.0589256i | ||||||
\(289\) | 4.73329e7 | 1.96096 | ||||||||
\(290\) | 1.55055e7i | 0.635758i | ||||||||
\(291\) | 1.88993e7i | 0.766951i | ||||||||
\(292\) | 1.42218e7i | 0.571223i | ||||||||
\(293\) | −6.42985e6 | −0.255622 | −0.127811 | − | 0.991799i | \(-0.540795\pi\) | ||||
−0.127811 | + | 0.991799i | \(0.540795\pi\) | |||||||
\(294\) | − | 2.42072e7i | − | 0.952582i | ||||||
\(295\) | −2.39176e7 | − | 2.48597e6i | −0.931648 | − | 0.0968345i | ||||
\(296\) | 2.62068e6 | 0.101050 | ||||||||
\(297\) | − | 9.27384e6i | − | 0.353990i | ||||||
\(298\) | −1.59603e7 | −0.603106 | ||||||||
\(299\) | 1.31130e7 | 0.490554 | ||||||||
\(300\) | 955998. | 0.0354073 | ||||||||
\(301\) | 7.26296e7i | 2.66326i | ||||||||
\(302\) | 9.89724e6 | 0.359330 | ||||||||
\(303\) | − | 5.98385e6i | − | 0.215106i | ||||||
\(304\) | −5.50981e6 | −0.196117 | ||||||||
\(305\) | − | 1.28870e7i | − | 0.454204i | ||||||
\(306\) | − | 1.16210e7i | − | 0.405583i | ||||||
\(307\) | 3.68285e6 | 0.127283 | 0.0636413 | − | 0.997973i | \(-0.479729\pi\) | ||||
0.0636413 | + | 0.997973i | \(0.479729\pi\) | |||||||
\(308\) | 4.90608e7i | 1.67912i | ||||||||
\(309\) | 1.20643e7i | 0.408908i | ||||||||
\(310\) | 750491. | 0.0251919 | ||||||||
\(311\) | 3.63411e7 | 1.20814 | 0.604070 | − | 0.796932i | \(-0.293545\pi\) | ||||
0.604070 | + | 0.796932i | \(0.293545\pi\) | |||||||
\(312\) | −1.85557e6 | −0.0610961 | ||||||||
\(313\) | − | 7.68297e6i | − | 0.250551i | −0.992122 | − | 0.125276i | \(-0.960019\pi\) | ||
0.992122 | − | 0.125276i | \(-0.0399815\pi\) | |||||||
\(314\) | −3.29118e7 | −1.06307 | ||||||||
\(315\) | 1.78170e7 | 0.570038 | ||||||||
\(316\) | 1.20363e7 | 0.381445 | ||||||||
\(317\) | −3.06323e7 | −0.961618 | −0.480809 | − | 0.876825i | \(-0.659657\pi\) | ||||
−0.480809 | + | 0.876825i | \(0.659657\pi\) | |||||||
\(318\) | − | 1.75152e7i | − | 0.544670i | ||||||
\(319\) | 5.73147e7i | 1.76561i | ||||||||
\(320\) | −3.83659e6 | −0.117083 | ||||||||
\(321\) | 1.07086e7 | 0.323757 | ||||||||
\(322\) | −7.06416e7 | −2.11589 | ||||||||
\(323\) | −4.54883e7 | −1.34987 | ||||||||
\(324\) | −1.88957e6 | −0.0555556 | ||||||||
\(325\) | − | 1.26024e6i | − | 0.0367116i | ||||||
\(326\) | − | 3.30499e7i | − | 0.953933i | ||||||
\(327\) | 4.01885e6i | 0.114937i | ||||||||
\(328\) | − | 2.55923e6i | − | 0.0725249i | ||||||
\(329\) | 5.01286e7i | 1.40766i | ||||||||
\(330\) | −2.52769e7 | −0.703367 | ||||||||
\(331\) | −1.10379e6 | −0.0304370 | −0.0152185 | − | 0.999884i | \(-0.504844\pi\) | ||||
−0.0152185 | + | 0.999884i | \(0.504844\pi\) | |||||||
\(332\) | − | 8.54251e6i | − | 0.233438i | ||||||
\(333\) | − | 3.51799e6i | − | 0.0952713i | ||||||
\(334\) | 3.33740e7i | 0.895712i | ||||||||
\(335\) | 3.39835e7i | 0.903927i | ||||||||
\(336\) | 9.99625e6 | 0.263523 | ||||||||
\(337\) | 3.31881e7i | 0.867146i | 0.901118 | + | 0.433573i | \(0.142747\pi\) | ||||
−0.901118 | + | 0.433573i | \(0.857253\pi\) | |||||||
\(338\) | − | 2.48585e7i | − | 0.643760i | ||||||
\(339\) | − | 2.43624e7i | − | 0.625346i | ||||||
\(340\) | −3.16744e7 | −0.805882 | ||||||||
\(341\) | 2.77412e6 | 0.0699620 | ||||||||
\(342\) | 7.39636e6i | 0.184901i | ||||||||
\(343\) | 9.82344e7 | 2.43434 | ||||||||
\(344\) | −2.09945e7 | −0.515738 | ||||||||
\(345\) | − | 3.63957e7i | − | 0.886324i | ||||||
\(346\) | 4.71477e7 | 1.13824 | ||||||||
\(347\) | 4.06627e7i | 0.973213i | 0.873621 | + | 0.486606i | \(0.161765\pi\) | ||||
−0.873621 | + | 0.486606i | \(0.838235\pi\) | |||||||
\(348\) | 1.16780e7 | 0.277097 | ||||||||
\(349\) | 4.39822e7i | 1.03467i | 0.855784 | + | 0.517334i | \(0.173075\pi\) | ||||
−0.855784 | + | 0.517334i | \(0.826925\pi\) | |||||||
\(350\) | 6.78911e6i | 0.158347i | ||||||||
\(351\) | 2.49091e6i | 0.0576019i | ||||||||
\(352\) | −1.41816e7 | −0.325160 | ||||||||
\(353\) | − | 3.03736e7i | − | 0.690513i | −0.938508 | − | 0.345256i | \(-0.887792\pi\) | ||
0.938508 | − | 0.345256i | \(-0.112208\pi\) | |||||||
\(354\) | −1.87231e6 | + | 1.80136e7i | −0.0422055 | + | 0.406061i | ||||
\(355\) | 2.85586e7 | 0.638341 | ||||||||
\(356\) | − | 3.74919e6i | − | 0.0830974i | ||||||
\(357\) | 8.25278e7 | 1.81383 | ||||||||
\(358\) | 6.10936e7 | 1.33152 | ||||||||
\(359\) | 5.67589e7 | 1.22673 | 0.613367 | − | 0.789798i | \(-0.289815\pi\) | ||||
0.613367 | + | 0.789798i | \(0.289815\pi\) | |||||||
\(360\) | 5.15023e6i | 0.110387i | ||||||||
\(361\) | −1.80942e7 | −0.384608 | ||||||||
\(362\) | 3.72812e6i | 0.0785895i | ||||||||
\(363\) | −6.58179e7 | −1.37602 | ||||||||
\(364\) | − | 1.31775e7i | − | 0.273230i | ||||||
\(365\) | − | 5.20355e7i | − | 1.07009i | ||||||
\(366\) | −9.70585e6 | −0.197966 | ||||||||
\(367\) | 8.31785e7i | 1.68272i | 0.540472 | + | 0.841362i | \(0.318246\pi\) | ||||
−0.540472 | + | 0.841362i | \(0.681754\pi\) | |||||||
\(368\) | − | 2.04198e7i | − | 0.409740i | ||||||
\(369\) | −3.43550e6 | −0.0683771 | ||||||||
\(370\) | −9.58868e6 | −0.189301 | ||||||||
\(371\) | 1.24386e8 | 2.43584 | ||||||||
\(372\) | − | 565234.i | − | 0.0109799i | ||||||
\(373\) | −5.94682e7 | −1.14593 | −0.572965 | − | 0.819580i | \(-0.694207\pi\) | ||||
−0.572965 | + | 0.819580i | \(0.694207\pi\) | |||||||
\(374\) | −1.17082e8 | −2.23807 | ||||||||
\(375\) | −3.20158e7 | −0.607115 | ||||||||
\(376\) | −1.44903e7 | −0.272592 | ||||||||
\(377\) | − | 1.53945e7i | − | 0.287303i | ||||||
\(378\) | − | 1.34189e7i | − | 0.248452i | ||||||
\(379\) | −6.93731e7 | −1.27430 | −0.637152 | − | 0.770738i | \(-0.719888\pi\) | ||||
−0.637152 | + | 0.770738i | \(0.719888\pi\) | |||||||
\(380\) | 2.01596e7 | 0.367393 | ||||||||
\(381\) | 1.87258e7 | 0.338583 | ||||||||
\(382\) | −3.11611e7 | −0.559015 | ||||||||
\(383\) | −8.52075e7 | −1.51664 | −0.758318 | − | 0.651885i | \(-0.773979\pi\) | ||||
−0.758318 | + | 0.651885i | \(0.773979\pi\) | |||||||
\(384\) | 2.88954e6i | 0.0510310i | ||||||||
\(385\) | − | 1.79506e8i | − | 3.14556i | ||||||
\(386\) | 5.02836e6i | 0.0874308i | ||||||||
\(387\) | 2.81829e7i | 0.486243i | ||||||||
\(388\) | − | 3.87966e7i | − | 0.664199i | ||||||
\(389\) | 7.08718e7 | 1.20399 | 0.601997 | − | 0.798498i | \(-0.294372\pi\) | ||||
0.601997 | + | 0.798498i | \(0.294372\pi\) | |||||||
\(390\) | 6.78926e6 | 0.114453 | ||||||||
\(391\) | − | 1.68583e8i | − | 2.82023i | ||||||
\(392\) | 4.96926e7i | 0.824961i | ||||||||
\(393\) | − | 4.55683e7i | − | 0.750732i | ||||||
\(394\) | − | 4.05274e7i | − | 0.662613i | ||||||
\(395\) | −4.40391e7 | −0.714574 | ||||||||
\(396\) | 1.90374e7i | 0.306564i | ||||||||
\(397\) | − | 7.51278e7i | − | 1.20069i | −0.799743 | − | 0.600343i | \(-0.795031\pi\) | ||
0.799743 | − | 0.600343i | \(-0.204969\pi\) | |||||||
\(398\) | − | 3.95076e7i | − | 0.626659i | ||||||
\(399\) | −5.25260e7 | −0.826904 | ||||||||
\(400\) | −1.96247e6 | −0.0306637 | ||||||||
\(401\) | − | 960104.i | − | 0.0148897i | −0.999972 | − | 0.00744484i | \(-0.997630\pi\) | ||
0.999972 | − | 0.00744484i | \(-0.00236979\pi\) | |||||||
\(402\) | 2.55947e7 | 0.393978 | ||||||||
\(403\) | −745116. | −0.0113844 | ||||||||
\(404\) | 1.22837e7i | 0.186287i | ||||||||
\(405\) | 6.91366e6 | 0.104074 | ||||||||
\(406\) | 8.29325e7i | 1.23922i | ||||||||
\(407\) | −3.54437e7 | −0.525721 | ||||||||
\(408\) | 2.38557e7i | 0.351246i | ||||||||
\(409\) | 3.48161e7i | 0.508874i | 0.967089 | + | 0.254437i | \(0.0818901\pi\) | ||||
−0.967089 | + | 0.254437i | \(0.918110\pi\) | |||||||
\(410\) | 9.36384e6i | 0.135863i | ||||||||
\(411\) | −1.77927e7 | −0.256282 | ||||||||
\(412\) | − | 2.47656e7i | − | 0.354125i | ||||||
\(413\) | −1.27925e8 | − | 1.32964e7i | −1.81596 | − | 0.188749i | ||||
\(414\) | −2.74115e7 | −0.386306 | ||||||||
\(415\) | 3.12558e7i | 0.437307i | ||||||||
\(416\) | 3.80911e6 | 0.0529108 | ||||||||
\(417\) | −7.10936e7 | −0.980443 | ||||||||
\(418\) | 7.45182e7 | 1.02031 | ||||||||
\(419\) | 9.15956e7i | 1.24518i | 0.782548 | + | 0.622590i | \(0.213920\pi\) | ||||
−0.782548 | + | 0.622590i | \(0.786080\pi\) | |||||||
\(420\) | −3.65748e7 | −0.493667 | ||||||||
\(421\) | 4.43807e7i | 0.594768i | 0.954758 | + | 0.297384i | \(0.0961142\pi\) | ||||
−0.954758 | + | 0.297384i | \(0.903886\pi\) | |||||||
\(422\) | −3.74513e7 | −0.498344 | ||||||||
\(423\) | 1.94517e7i | 0.257002i | ||||||||
\(424\) | 3.59552e7i | 0.471698i | ||||||||
\(425\) | −1.62019e7 | −0.211057 | ||||||||
\(426\) | − | 2.15090e7i | − | 0.278222i | ||||||
\(427\) | − | 6.89270e7i | − | 0.885331i | ||||||
\(428\) | −2.19827e7 | −0.280382 | ||||||||
\(429\) | 2.50959e7 | 0.317856 | ||||||||
\(430\) | 7.68157e7 | 0.966150 | ||||||||
\(431\) | 9.58430e7i | 1.19709i | 0.801087 | + | 0.598547i | \(0.204255\pi\) | ||||
−0.801087 | + | 0.598547i | \(0.795745\pi\) | |||||||
\(432\) | 3.87891e6 | 0.0481125 | ||||||||
\(433\) | −9.97571e7 | −1.22880 | −0.614399 | − | 0.788996i | \(-0.710601\pi\) | ||||
−0.614399 | + | 0.788996i | \(0.710601\pi\) | |||||||
\(434\) | 4.01406e6 | 0.0491038 | ||||||||
\(435\) | −4.27282e7 | −0.519095 | ||||||||
\(436\) | − | 8.24990e6i | − | 0.0995380i | ||||||
\(437\) | 1.07297e8i | 1.28571i | ||||||||
\(438\) | −3.91907e7 | −0.466402 | ||||||||
\(439\) | 1.30887e8 | 1.54704 | 0.773521 | − | 0.633771i | \(-0.218494\pi\) | ||||
0.773521 | + | 0.633771i | \(0.218494\pi\) | |||||||
\(440\) | 5.18884e7 | 0.609134 | ||||||||
\(441\) | 6.67072e7 | 0.777780 | ||||||||
\(442\) | 3.14476e7 | 0.364184 | ||||||||
\(443\) | 4.38917e7i | 0.504861i | 0.967615 | + | 0.252430i | \(0.0812299\pi\) | ||||
−0.967615 | + | 0.252430i | \(0.918770\pi\) | |||||||
\(444\) | 7.22174e6i | 0.0825074i | ||||||||
\(445\) | 1.37178e7i | 0.155669i | ||||||||
\(446\) | 1.15774e7i | 0.130498i | ||||||||
\(447\) | − | 4.39815e7i | − | 0.492434i | ||||||
\(448\) | −2.05203e7 | −0.228218 | ||||||||
\(449\) | 8.97272e7 | 0.991254 | 0.495627 | − | 0.868535i | \(-0.334938\pi\) | ||||
0.495627 | + | 0.868535i | \(0.334938\pi\) | |||||||
\(450\) | 2.63442e6i | 0.0289100i | ||||||||
\(451\) | 3.46126e7i | 0.377315i | ||||||||
\(452\) | 5.00111e7i | 0.541565i | ||||||||
\(453\) | 2.72736e7i | 0.293392i | ||||||||
\(454\) | 9.63724e7 | 1.02988 | ||||||||
\(455\) | 4.82146e7i | 0.511852i | ||||||||
\(456\) | − | 1.51833e7i | − | 0.160129i | ||||||
\(457\) | − | 1.77370e8i | − | 1.85837i | −0.369617 | − | 0.929184i | \(-0.620511\pi\) | ||
0.369617 | − | 0.929184i | \(-0.379489\pi\) | |||||||
\(458\) | −5.84930e7 | −0.608846 | ||||||||
\(459\) | 3.20238e7 | 0.331157 | ||||||||
\(460\) | 7.47131e7i | 0.767579i | ||||||||
\(461\) | 6.89053e7 | 0.703315 | 0.351657 | − | 0.936129i | \(-0.385618\pi\) | ||||
0.351657 | + | 0.936129i | \(0.385618\pi\) | |||||||
\(462\) | −1.35196e8 | −1.37100 | ||||||||
\(463\) | 3.42086e7i | 0.344661i | 0.985039 | + | 0.172331i | \(0.0551297\pi\) | ||||
−0.985039 | + | 0.172331i | \(0.944870\pi\) | |||||||
\(464\) | −2.39726e7 | −0.239973 | ||||||||
\(465\) | 2.06811e6i | 0.0205691i | ||||||||
\(466\) | −2.85682e7 | −0.282310 | ||||||||
\(467\) | 1.04701e8i | 1.02802i | 0.857785 | + | 0.514009i | \(0.171840\pi\) | ||||
−0.857785 | + | 0.514009i | \(0.828160\pi\) | |||||||
\(468\) | − | 5.11335e6i | − | 0.0498847i | ||||||
\(469\) | 1.81763e8i | 1.76193i | ||||||||
\(470\) | 5.30178e7 | 0.510656 | ||||||||
\(471\) | − | 9.06941e7i | − | 0.867993i | ||||||
\(472\) | 3.84349e6 | − | 3.69784e7i | 0.0365510 | − | 0.351659i | ||||
\(473\) | 2.83942e8 | 2.68316 | ||||||||
\(474\) | 3.31682e7i | 0.311449i | ||||||||
\(475\) | 1.03120e7 | 0.0962188 | ||||||||
\(476\) | −1.69413e8 | −1.57082 | ||||||||
\(477\) | 4.82662e7 | 0.444722 | ||||||||
\(478\) | 3.56342e7i | 0.326275i | ||||||||
\(479\) | −1.39074e8 | −1.26543 | −0.632716 | − | 0.774384i | \(-0.718060\pi\) | ||||
−0.632716 | + | 0.774384i | \(0.718060\pi\) | |||||||
\(480\) | − | 1.05724e7i | − | 0.0955982i | ||||||
\(481\) | 9.52001e6 | 0.0855465 | ||||||||
\(482\) | − | 4.30983e7i | − | 0.384874i | ||||||
\(483\) | − | 1.94665e8i | − | 1.72762i | ||||||
\(484\) | 1.35111e8 | 1.19167 | ||||||||
\(485\) | 1.41951e8i | 1.24427i | ||||||||
\(486\) | − | 5.20704e6i | − | 0.0453609i | ||||||
\(487\) | −5.17092e7 | −0.447694 | −0.223847 | − | 0.974624i | \(-0.571862\pi\) | ||||
−0.223847 | + | 0.974624i | \(0.571862\pi\) | |||||||
\(488\) | 1.99242e7 | 0.171443 | ||||||||
\(489\) | 9.10750e7 | 0.778883 | ||||||||
\(490\) | − | 1.81818e8i | − | 1.54543i | ||||||
\(491\) | 7.53699e7 | 0.636727 | 0.318363 | − | 0.947969i | \(-0.396867\pi\) | ||||
0.318363 | + | 0.947969i | \(0.396867\pi\) | |||||||
\(492\) | 7.05240e6 | 0.0592163 | ||||||||
\(493\) | −1.97915e8 | −1.65173 | ||||||||
\(494\) | −2.00152e7 | −0.166027 | ||||||||
\(495\) | − | 6.96549e7i | − | 0.574297i | ||||||
\(496\) | 1.16031e6i | 0.00950889i | ||||||||
\(497\) | 1.52748e8 | 1.24425 | ||||||||
\(498\) | 2.35404e7 | 0.190601 | ||||||||
\(499\) | −7.37094e7 | −0.593227 | −0.296614 | − | 0.954998i | \(-0.595857\pi\) | ||||
−0.296614 | + | 0.954998i | \(0.595857\pi\) | |||||||
\(500\) | 6.57221e7 | 0.525777 | ||||||||
\(501\) | −9.19678e7 | −0.731346 | ||||||||
\(502\) | − | 8.51871e7i | − | 0.673384i | ||||||
\(503\) | 1.64385e8i | 1.29169i | 0.763468 | + | 0.645846i | \(0.223495\pi\) | ||||
−0.763468 | + | 0.645846i | \(0.776505\pi\) | |||||||
\(504\) | 2.75464e7i | 0.215166i | ||||||||
\(505\) | − | 4.49441e7i | − | 0.348979i | ||||||
\(506\) | 2.76170e8i | 2.13170i | ||||||||
\(507\) | 6.85019e7 | 0.525628 | ||||||||
\(508\) | −3.84403e7 | −0.293221 | ||||||||
\(509\) | 1.35583e8i | 1.02814i | 0.857748 | + | 0.514070i | \(0.171863\pi\) | ||||
−0.857748 | + | 0.514070i | \(0.828137\pi\) | |||||||
\(510\) | − | 8.72844e7i | − | 0.658000i | ||||||
\(511\) | − | 2.78316e8i | − | 2.08581i | ||||||
\(512\) | − | 5.93164e6i | − | 0.0441942i | ||||||
\(513\) | −2.03820e7 | −0.150971 | ||||||||
\(514\) | − | 1.45159e8i | − | 1.06894i | ||||||
\(515\) | 9.06136e7i | 0.663394i | ||||||||
\(516\) | − | 5.78539e7i | − | 0.421098i | ||||||
\(517\) | 1.95975e8 | 1.41818 | ||||||||
\(518\) | −5.12858e7 | −0.368985 | ||||||||
\(519\) | 1.29924e8i | 0.929366i | ||||||||
\(520\) | −1.39370e7 | −0.0991195 | ||||||||
\(521\) | −2.24967e8 | −1.59076 | −0.795380 | − | 0.606111i | \(-0.792729\pi\) | ||||
−0.795380 | + | 0.606111i | \(0.792729\pi\) | |||||||
\(522\) | 3.21808e7i | 0.226248i | ||||||||
\(523\) | −5.55339e7 | −0.388198 | −0.194099 | − | 0.980982i | \(-0.562178\pi\) | ||||
−0.194099 | + | 0.980982i | \(0.562178\pi\) | |||||||
\(524\) | 9.35426e7i | 0.650153i | ||||||||
\(525\) | −1.87086e7 | −0.129289 | ||||||||
\(526\) | 6.86401e7i | 0.471651i | ||||||||
\(527\) | 9.57940e6i | 0.0654495i | ||||||||
\(528\) | − | 3.90799e7i | − | 0.265492i | ||||||
\(529\) | −2.49616e8 | −1.68618 | ||||||||
\(530\) | − | 1.31555e8i | − | 0.883649i | ||||||
\(531\) | −4.96397e7 | − | 5.15949e6i | −0.331547 | − | 0.0344606i | ||||
\(532\) | 1.07825e8 | 0.716120 | ||||||||
\(533\) | − | 9.29678e6i | − | 0.0613975i | ||||||
\(534\) | 1.03316e7 | 0.0678488 | ||||||||
\(535\) | 8.04315e7 | 0.525248 | ||||||||
\(536\) | −5.25409e7 | −0.341195 | ||||||||
\(537\) | 1.68354e8i | 1.08718i | ||||||||
\(538\) | 1.49644e8 | 0.960979 | ||||||||
\(539\) | − | 6.72074e8i | − | 4.29191i | ||||||
\(540\) | −1.41924e7 | −0.0901308 | ||||||||
\(541\) | − | 1.73413e8i | − | 1.09519i | −0.836744 | − | 0.547595i | \(-0.815543\pi\) | ||
0.836744 | − | 0.547595i | \(-0.184457\pi\) | |||||||
\(542\) | − | 1.47849e8i | − | 0.928580i | ||||||
\(543\) | −1.02735e7 | −0.0641681 | ||||||||
\(544\) | − | 4.89709e7i | − | 0.304188i | ||||||
\(545\) | 3.01852e7i | 0.186468i | ||||||||
\(546\) | 3.63129e7 | 0.223092 | ||||||||
\(547\) | 3.13410e6 | 0.0191492 | 0.00957460 | − | 0.999954i | \(-0.496952\pi\) | ||||
0.00957460 | + | 0.999954i | \(0.496952\pi\) | |||||||
\(548\) | 3.65250e7 | 0.221946 | ||||||||
\(549\) | − | 2.67462e7i | − | 0.161638i | ||||||
\(550\) | 2.65417e7 | 0.159530 | ||||||||
\(551\) | 1.25966e8 | 0.753005 | ||||||||
\(552\) | 5.62703e7 | 0.334551 | ||||||||
\(553\) | −2.35547e8 | −1.39284 | ||||||||
\(554\) | 4.70580e7i | 0.276761i | ||||||||
\(555\) | − | 2.64233e7i | − | 0.154564i | ||||||
\(556\) | 1.45941e8 | 0.849088 | ||||||||
\(557\) | −2.51736e8 | −1.45673 | −0.728365 | − | 0.685190i | \(-0.759719\pi\) | ||||
−0.728365 | + | 0.685190i | \(0.759719\pi\) | |||||||
\(558\) | 1.55760e6 | 0.00896507 | ||||||||
\(559\) | −7.62656e7 | −0.436609 | ||||||||
\(560\) | 7.50809e7 | 0.427529 | ||||||||
\(561\) | − | 3.22639e8i | − | 1.82738i | ||||||
\(562\) | − | 2.46937e8i | − | 1.39116i | ||||||
\(563\) | 5.42737e7i | 0.304134i | 0.988370 | + | 0.152067i | \(0.0485929\pi\) | ||||
−0.988370 | + | 0.152067i | \(0.951407\pi\) | |||||||
\(564\) | − | 3.99305e7i | − | 0.222570i | ||||||
\(565\) | − | 1.82983e8i | − | 1.01453i | ||||||
\(566\) | −5.32652e7 | −0.293761 | ||||||||
\(567\) | 3.69783e7 | 0.202860 | ||||||||
\(568\) | 4.41537e7i | 0.240947i | ||||||||
\(569\) | − | 2.86608e8i | − | 1.55579i | −0.628394 | − | 0.777895i | \(-0.716287\pi\) | ||
0.628394 | − | 0.777895i | \(-0.283713\pi\) | |||||||
\(570\) | 5.55533e7i | 0.299975i | ||||||||
\(571\) | 2.63425e7i | 0.141498i | 0.997494 | + | 0.0707489i | \(0.0225389\pi\) | ||||
−0.997494 | + | 0.0707489i | \(0.977461\pi\) | |||||||
\(572\) | −5.15169e7 | −0.275272 | ||||||||
\(573\) | − | 8.58700e7i | − | 0.456434i | ||||||
\(574\) | 5.00833e7i | 0.264824i | ||||||||
\(575\) | 3.82169e7i | 0.201026i | ||||||||
\(576\) | −7.96262e6 | −0.0416667 | ||||||||
\(577\) | −2.41063e7 | −0.125488 | −0.0627441 | − | 0.998030i | \(-0.519985\pi\) | ||||
−0.0627441 | + | 0.998030i | \(0.519985\pi\) | |||||||
\(578\) | − | 2.67755e8i | − | 1.38661i | ||||||
\(579\) | −1.38565e7 | −0.0713870 | ||||||||
\(580\) | 8.77124e7 | 0.449549 | ||||||||
\(581\) | 1.67174e8i | 0.852395i | ||||||||
\(582\) | 1.06911e8 | 0.542317 | ||||||||
\(583\) | − | 4.86281e8i | − | 2.45404i | ||||||
\(584\) | 8.04506e7 | 0.403916 | ||||||||
\(585\) | 1.87090e7i | 0.0934508i | ||||||||
\(586\) | 3.63727e7i | 0.180752i | ||||||||
\(587\) | − | 2.49986e8i | − | 1.23595i | −0.786198 | − | 0.617975i | \(-0.787953\pi\) | ||
0.786198 | − | 0.617975i | \(-0.212047\pi\) | |||||||
\(588\) | −1.36937e8 | −0.673577 | ||||||||
\(589\) | − | 6.09694e6i | − | 0.0298377i | ||||||
\(590\) | −1.40628e7 | + | 1.35299e8i | −0.0684723 | + | 0.658775i | ||||
\(591\) | 1.11680e8 | 0.541022 | ||||||||
\(592\) | − | 1.48248e7i | − | 0.0714535i | ||||||
\(593\) | 3.33338e8 | 1.59853 | 0.799265 | − | 0.600979i | \(-0.205223\pi\) | ||||
0.799265 | + | 0.600979i | \(0.205223\pi\) | |||||||
\(594\) | −5.24608e7 | −0.250308 | ||||||||
\(595\) | 6.19858e8 | 2.94267 | ||||||||
\(596\) | 9.02853e7i | 0.426460i | ||||||||
\(597\) | 1.08870e8 | 0.511665 | ||||||||
\(598\) | − | 7.41781e7i | − | 0.346874i | ||||||
\(599\) | −3.13374e8 | −1.45808 | −0.729042 | − | 0.684469i | \(-0.760034\pi\) | ||||
−0.729042 | + | 0.684469i | \(0.760034\pi\) | |||||||
\(600\) | − | 5.40794e6i | − | 0.0250368i | ||||||
\(601\) | − | 2.12094e8i | − | 0.977024i | −0.872557 | − | 0.488512i | \(-0.837540\pi\) | ||
0.872557 | − | 0.488512i | \(-0.162460\pi\) | |||||||
\(602\) | 4.10855e8 | 1.88321 | ||||||||
\(603\) | 7.05308e7i | 0.321682i | ||||||||
\(604\) | − | 5.59873e7i | − | 0.254085i | ||||||
\(605\) | −4.94352e8 | −2.23239 | ||||||||
\(606\) | −3.38498e7 | −0.152103 | ||||||||
\(607\) | 9.55577e7 | 0.427267 | 0.213634 | − | 0.976914i | \(-0.431470\pi\) | ||||
0.213634 | + | 0.976914i | \(0.431470\pi\) | |||||||
\(608\) | 3.11682e7i | 0.138676i | ||||||||
\(609\) | −2.28535e8 | −1.01181 | ||||||||
\(610\) | −7.28997e7 | −0.321171 | ||||||||
\(611\) | −5.26381e7 | −0.230769 | ||||||||
\(612\) | −6.57384e7 | −0.286791 | ||||||||
\(613\) | 1.90882e8i | 0.828675i | 0.910123 | + | 0.414337i | \(0.135987\pi\) | ||||
−0.910123 | + | 0.414337i | \(0.864013\pi\) | |||||||
\(614\) | − | 2.08334e7i | − | 0.0900024i | ||||||
\(615\) | −2.58037e7 | −0.110932 | ||||||||
\(616\) | 2.77530e8 | 1.18732 | ||||||||
\(617\) | 3.86424e8 | 1.64516 | 0.822580 | − | 0.568649i | \(-0.192534\pi\) | ||||
0.822580 | + | 0.568649i | \(0.192534\pi\) | |||||||
\(618\) | 6.82458e7 | 0.289142 | ||||||||
\(619\) | −2.65985e8 | −1.12146 | −0.560731 | − | 0.827998i | \(-0.689480\pi\) | ||||
−0.560731 | + | 0.827998i | \(0.689480\pi\) | |||||||
\(620\) | − | 4.24542e6i | − | 0.0178133i | ||||||
\(621\) | − | 7.55372e7i | − | 0.315418i | ||||||
\(622\) | − | 2.05576e8i | − | 0.854283i | ||||||
\(623\) | 7.33705e7i | 0.303429i | ||||||||
\(624\) | 1.04967e7i | 0.0432015i | ||||||||
\(625\) | −2.10523e8 | −0.862301 | ||||||||
\(626\) | −4.34615e7 | −0.177166 | ||||||||
\(627\) | 2.05348e8i | 0.833082i | ||||||||
\(628\) | 1.86177e8i | 0.751704i | ||||||||
\(629\) | − | 1.22392e8i | − | 0.491813i | ||||||
\(630\) | − | 1.00788e8i | − | 0.403078i | ||||||
\(631\) | 8.22936e7 | 0.327550 | 0.163775 | − | 0.986498i | \(-0.447633\pi\) | ||||
0.163775 | + | 0.986498i | \(0.447633\pi\) | |||||||
\(632\) | − | 6.80876e7i | − | 0.269722i | ||||||
\(633\) | − | 1.03204e8i | − | 0.406896i | ||||||
\(634\) | 1.73283e8i | 0.679966i | ||||||||
\(635\) | 1.40648e8 | 0.549302 | ||||||||
\(636\) | −9.90809e7 | −0.385140 | ||||||||
\(637\) | 1.80516e8i | 0.698389i | ||||||||
\(638\) | 3.24221e8 | 1.24847 | ||||||||
\(639\) | 5.92718e7 | 0.227167 | ||||||||
\(640\) | 2.17030e7i | 0.0827905i | ||||||||
\(641\) | 2.91404e7 | 0.110642 | 0.0553212 | − | 0.998469i | \(-0.482382\pi\) | ||||
0.0553212 | + | 0.998469i | \(0.482382\pi\) | |||||||
\(642\) | − | 6.05772e7i | − | 0.228931i | ||||||
\(643\) | 1.42475e7 | 0.0535927 | 0.0267964 | − | 0.999641i | \(-0.491469\pi\) | ||||
0.0267964 | + | 0.999641i | \(0.491469\pi\) | |||||||
\(644\) | 3.99609e8i | 1.49616i | ||||||||
\(645\) | 2.11679e8i | 0.788858i | ||||||||
\(646\) | 2.57321e8i | 0.954503i | ||||||||
\(647\) | −2.31261e8 | −0.853865 | −0.426932 | − | 0.904284i | \(-0.640406\pi\) | ||||
−0.426932 | + | 0.904284i | \(0.640406\pi\) | |||||||
\(648\) | 1.06890e7i | 0.0392837i | ||||||||
\(649\) | −5.19818e7 | + | 5.00119e8i | −0.190159 | + | 1.82953i | ||||
\(650\) | −7.12899e6 | −0.0259590 | ||||||||
\(651\) | 1.10615e7i | 0.0400931i | ||||||||
\(652\) | −1.86959e8 | −0.674533 | ||||||||
\(653\) | −4.35499e8 | −1.56404 | −0.782019 | − | 0.623254i | \(-0.785810\pi\) | ||||
−0.782019 | + | 0.623254i | \(0.785810\pi\) | |||||||
\(654\) | 2.27340e7 | 0.0812724 | ||||||||
\(655\) | − | 3.42259e8i | − | 1.21795i | ||||||
\(656\) | −1.44772e7 | −0.0512828 | ||||||||
\(657\) | − | 1.07997e8i | − | 0.380815i | ||||||
\(658\) | 2.83570e8 | 0.995366 | ||||||||
\(659\) | 3.04274e8i | 1.06319i | 0.847000 | + | 0.531593i | \(0.178406\pi\) | ||||
−0.847000 | + | 0.531593i | \(0.821594\pi\) | |||||||
\(660\) | 1.42988e8i | 0.497356i | ||||||||
\(661\) | −2.55140e8 | −0.883435 | −0.441718 | − | 0.897154i | \(-0.645631\pi\) | ||||
−0.441718 | + | 0.897154i | \(0.645631\pi\) | |||||||
\(662\) | 6.24397e6i | 0.0215222i | ||||||||
\(663\) | 8.66593e7i | 0.297355i | ||||||||
\(664\) | −4.83237e7 | −0.165065 | ||||||||
\(665\) | −3.94517e8 | −1.34153 | ||||||||
\(666\) | −1.99008e7 | −0.0673670 | ||||||||
\(667\) | 4.66839e8i | 1.57322i | ||||||||
\(668\) | 1.88792e8 | 0.633364 | ||||||||
\(669\) | −3.19035e7 | −0.106552 | ||||||||
\(670\) | 1.92239e8 | 0.639173 | ||||||||
\(671\) | −2.69467e8 | −0.891945 | ||||||||
\(672\) | − | 5.65473e7i | − | 0.186339i | ||||||
\(673\) | 2.80257e8i | 0.919415i | 0.888071 | + | 0.459707i | \(0.152046\pi\) | ||||
−0.888071 | + | 0.459707i | \(0.847954\pi\) | |||||||
\(674\) | 1.87740e8 | 0.613165 | ||||||||
\(675\) | −7.25961e6 | −0.0236049 | ||||||||
\(676\) | −1.40621e8 | −0.455207 | ||||||||
\(677\) | 2.54527e8 | 0.820291 | 0.410145 | − | 0.912020i | \(-0.365478\pi\) | ||||
0.410145 | + | 0.912020i | \(0.365478\pi\) | |||||||
\(678\) | −1.37814e8 | −0.442186 | ||||||||
\(679\) | 7.59238e8i | 2.42532i | ||||||||
\(680\) | 1.79177e8i | 0.569845i | ||||||||
\(681\) | 2.65571e8i | 0.840890i | ||||||||
\(682\) | − | 1.56928e7i | − | 0.0494706i | ||||||
\(683\) | − | 5.66274e8i | − | 1.77732i | −0.458571 | − | 0.888658i | \(-0.651639\pi\) | ||
0.458571 | − | 0.888658i | \(-0.348361\pi\) | |||||||
\(684\) | 4.18401e7 | 0.130745 | ||||||||
\(685\) | −1.33640e8 | −0.415780 | ||||||||
\(686\) | − | 5.55697e8i | − | 1.72134i | ||||||
\(687\) | − | 1.61188e8i | − | 0.497120i | ||||||
\(688\) | 1.18763e8i | 0.364682i | ||||||||
\(689\) | 1.30613e8i | 0.399327i | ||||||||
\(690\) | −2.05885e8 | −0.626726 | ||||||||
\(691\) | − | 3.34577e8i | − | 1.01406i | −0.861930 | − | 0.507028i | \(-0.830744\pi\) | ||
0.861930 | − | 0.507028i | \(-0.169256\pi\) | |||||||
\(692\) | − | 2.66708e8i | − | 0.804855i | ||||||
\(693\) | − | 3.72555e8i | − | 1.11941i | ||||||
\(694\) | 2.30023e8 | 0.688165 | ||||||||
\(695\) | −5.33977e8 | −1.59063 | ||||||||
\(696\) | − | 6.60608e7i | − | 0.195937i | ||||||
\(697\) | −1.19522e8 | −0.352979 | ||||||||
\(698\) | 2.48801e8 | 0.731621 | ||||||||
\(699\) | − | 7.87248e7i | − | 0.230505i | ||||||
\(700\) | 3.84050e7 | 0.111968 | ||||||||
\(701\) | − | 2.17724e8i | − | 0.632050i | −0.948751 | − | 0.316025i | \(-0.897652\pi\) | ||
0.948751 | − | 0.316025i | \(-0.102348\pi\) | |||||||
\(702\) | 1.40907e7 | 0.0407307 | ||||||||
\(703\) | 7.78978e7i | 0.224212i | ||||||||
\(704\) | 8.02233e7i | 0.229923i | ||||||||
\(705\) | 1.46100e8i | 0.416949i | ||||||||
\(706\) | −1.71819e8 | −0.488266 | ||||||||
\(707\) | − | 2.40387e8i | − | 0.680226i | ||||||
\(708\) | 1.01900e8 | + | 1.05914e7i | 0.287128 | + | 0.0298438i | ||||
\(709\) | 1.59760e8 | 0.448259 | 0.224129 | − | 0.974559i | \(-0.428046\pi\) | ||||
0.224129 | + | 0.974559i | \(0.428046\pi\) | |||||||
\(710\) | − | 1.61552e8i | − | 0.451375i | ||||||
\(711\) | −9.14007e7 | −0.254297 | ||||||||
\(712\) | −2.12086e7 | −0.0587588 | ||||||||
\(713\) | 2.25957e7 | 0.0623387 | ||||||||
\(714\) | − | 4.66848e8i | − | 1.28257i | ||||||
\(715\) | 1.88493e8 | 0.515676 | ||||||||
\(716\) | − | 3.45598e8i | − | 0.941525i | ||||||
\(717\) | −9.81963e7 | −0.266402 | ||||||||
\(718\) | − | 3.21077e8i | − | 0.867432i | ||||||
\(719\) | 3.73546e8i | 1.00498i | 0.864583 | + | 0.502490i | \(0.167582\pi\) | ||||
−0.864583 | + | 0.502490i | \(0.832418\pi\) | |||||||
\(720\) | 2.91341e7 | 0.0780556 | ||||||||
\(721\) | 4.84654e8i | 1.29308i | ||||||||
\(722\) | 1.02356e8i | 0.271959i | ||||||||
\(723\) | 1.18765e8 | 0.314248 | ||||||||
\(724\) | 2.10895e7 | 0.0555712 | ||||||||
\(725\) | 4.48663e7 | 0.117735 | ||||||||
\(726\) | 3.72322e8i | 0.972991i | ||||||||
\(727\) | −2.65165e8 | −0.690101 | −0.345050 | − | 0.938584i | \(-0.612138\pi\) | ||||
−0.345050 | + | 0.938584i | \(0.612138\pi\) | |||||||
\(728\) | −7.45432e7 | −0.193203 | ||||||||
\(729\) | 1.43489e7 | 0.0370370 | ||||||||
\(730\) | −2.94357e8 | −0.756669 | ||||||||
\(731\) | 9.80489e8i | 2.51010i | ||||||||
\(732\) | 5.49046e7i | 0.139983i | ||||||||
\(733\) | −1.23734e8 | −0.314178 | −0.157089 | − | 0.987584i | \(-0.550211\pi\) | ||||
−0.157089 | + | 0.987584i | \(0.550211\pi\) | |||||||
\(734\) | 4.70529e8 | 1.18987 | ||||||||
\(735\) | 5.01031e8 | 1.26184 | ||||||||
\(736\) | −1.15512e8 | −0.289730 | ||||||||
\(737\) | 7.10596e8 | 1.77509 | ||||||||
\(738\) | 1.94341e7i | 0.0483499i | ||||||||
\(739\) | − | 2.34627e8i | − | 0.581358i | −0.956821 | − | 0.290679i | \(-0.906119\pi\) | ||
0.956821 | − | 0.290679i | \(-0.0938812\pi\) | |||||||
\(740\) | 5.42418e7i | 0.133856i | ||||||||
\(741\) | − | 5.51555e7i | − | 0.135561i | ||||||
\(742\) | − | 7.03633e8i | − | 1.72240i | ||||||
\(743\) | −4.76649e8 | −1.16207 | −0.581034 | − | 0.813879i | \(-0.697352\pi\) | ||||
−0.581034 | + | 0.813879i | \(0.697352\pi\) | |||||||
\(744\) | −3.19745e6 | −0.00776398 | ||||||||
\(745\) | − | 3.30341e8i | − | 0.798903i | ||||||
\(746\) | 3.36403e8i | 0.810296i | ||||||||
\(747\) | 6.48697e7i | 0.155625i | ||||||||
\(748\) | 6.62313e8i | 1.58255i | ||||||||
\(749\) | 4.30194e8 | 1.02381 | ||||||||
\(750\) | 1.81109e8i | 0.429295i | ||||||||
\(751\) | 1.25753e8i | 0.296891i | 0.988921 | + | 0.148446i | \(0.0474270\pi\) | ||||
−0.988921 | + | 0.148446i | \(0.952573\pi\) | |||||||
\(752\) | 8.19693e7i | 0.192752i | ||||||||
\(753\) | 2.34748e8 | 0.549815 | ||||||||
\(754\) | −8.70843e7 | −0.203154 | ||||||||
\(755\) | 2.04849e8i | 0.475985i | ||||||||
\(756\) | −7.59090e7 | −0.175682 | ||||||||
\(757\) | −3.64141e8 | −0.839426 | −0.419713 | − | 0.907657i | \(-0.637869\pi\) | ||||
−0.419713 | + | 0.907657i | \(0.637869\pi\) | |||||||
\(758\) | 3.92433e8i | 0.901070i | ||||||||
\(759\) | −7.61036e8 | −1.74052 | ||||||||
\(760\) | − | 1.14040e8i | − | 0.259786i | ||||||
\(761\) | 7.02172e8 | 1.59327 | 0.796635 | − | 0.604460i | \(-0.206611\pi\) | ||||
0.796635 | + | 0.604460i | \(0.206611\pi\) | |||||||
\(762\) | − | 1.05929e8i | − | 0.239414i | ||||||
\(763\) | 1.61448e8i | 0.363462i | ||||||||
\(764\) | 1.76274e8i | 0.395283i | ||||||||
\(765\) | 2.40528e8 | 0.537255 | ||||||||
\(766\) | 4.82006e8i | 1.07242i | ||||||||
\(767\) | 1.39621e7 | − | 1.34330e8i | 0.0309431 | − | 0.297705i | ||||
\(768\) | 1.63457e7 | 0.0360844 | ||||||||
\(769\) | 2.75560e8i | 0.605950i | 0.952998 | + | 0.302975i | \(0.0979799\pi\) | ||||
−0.952998 | + | 0.302975i | \(0.902020\pi\) | |||||||
\(770\) | −1.01544e9 | −2.22424 | ||||||||
\(771\) | 4.00011e8 | 0.872788 | ||||||||
\(772\) | 2.84447e7 | 0.0618229 | ||||||||
\(773\) | 2.31760e8i | 0.501764i | 0.968018 | + | 0.250882i | \(0.0807206\pi\) | ||||
−0.968018 | + | 0.250882i | \(0.919279\pi\) | |||||||
\(774\) | 1.59427e8 | 0.343825 | ||||||||
\(775\) | − | 2.17160e6i | − | 0.00466524i | ||||||
\(776\) | −2.19467e8 | −0.469660 | ||||||||
\(777\) | − | 1.41327e8i | − | 0.301275i | ||||||
\(778\) | − | 4.00911e8i | − | 0.851352i | ||||||
\(779\) | 7.60712e7 | 0.160919 | ||||||||
\(780\) | − | 3.84059e7i | − | 0.0809308i | ||||||
\(781\) | − | 5.97162e8i | − | 1.25354i | ||||||
\(782\) | −9.53651e8 | −1.99420 | ||||||||
\(783\) | −8.86799e7 | −0.184731 | ||||||||
\(784\) | 2.81104e8 | 0.583335 | ||||||||
\(785\) | − | 6.81195e8i | − | 1.40819i | ||||||
\(786\) | −2.57773e8 | −0.530848 | ||||||||
\(787\) | −8.95649e8 | −1.83744 | −0.918721 | − | 0.394908i | \(-0.870776\pi\) | ||||
−0.918721 | + | 0.394908i | \(0.870776\pi\) | |||||||
\(788\) | −2.29258e8 | −0.468538 | ||||||||
\(789\) | −1.89150e8 | −0.385102 | ||||||||
\(790\) | 2.49123e8i | 0.505280i | ||||||||
\(791\) | − | 9.78701e8i | − | 1.97752i | ||||||
\(792\) | 1.07692e8 | 0.216773 | ||||||||
\(793\) | 7.23776e7 | 0.145139 | ||||||||
\(794\) | −4.24987e8 | −0.849013 | ||||||||
\(795\) | 3.62523e8 | 0.721496 | ||||||||
\(796\) | −2.23489e8 | −0.443115 | ||||||||
\(797\) | 4.47371e8i | 0.883676i | 0.897095 | + | 0.441838i | \(0.145673\pi\) | ||||
−0.897095 | + | 0.441838i | \(0.854327\pi\) | |||||||
\(798\) | 2.97132e8i | 0.584710i | ||||||||
\(799\) | 6.76729e8i | 1.32670i | ||||||||
\(800\) | 1.11014e7i | 0.0216825i | ||||||||
\(801\) | 2.84704e7i | 0.0553983i | ||||||||
\(802\) | −5.43117e6 | −0.0105286 | ||||||||
\(803\) | −1.08806e9 | −2.10140 | ||||||||
\(804\) | − | 1.44786e8i | − | 0.278585i | ||||||
\(805\) | − | 1.46211e9i | − | 2.80281i | ||||||
\(806\) | 4.21501e6i | 0.00804996i | ||||||||
\(807\) | 4.12372e8i | 0.784636i | ||||||||
\(808\) | 6.94868e7 | 0.131725 | ||||||||
\(809\) | 9.23404e8i | 1.74400i | 0.489507 | + | 0.872000i | \(0.337177\pi\) | ||||
−0.489507 | + | 0.872000i | \(0.662823\pi\) | |||||||
\(810\) | − | 3.91096e7i | − | 0.0735915i | ||||||
\(811\) | 8.16530e8i | 1.53077i | 0.643574 | + | 0.765384i | \(0.277451\pi\) | ||||
−0.643574 | + | 0.765384i | \(0.722549\pi\) | |||||||
\(812\) | 4.69137e8 | 0.876257 | ||||||||
\(813\) | 4.07423e8 | 0.758182 | ||||||||
\(814\) | 2.00500e8i | 0.371741i | ||||||||
\(815\) | 6.84055e8 | 1.26363 | ||||||||
\(816\) | 1.34948e8 | 0.248368 | ||||||||
\(817\) | − | 6.24046e8i | − | 1.14433i | ||||||
\(818\) | 1.96949e8 | 0.359828 | ||||||||
\(819\) | 1.00067e8i | 0.182154i | ||||||||
\(820\) | 5.29699e7 | 0.0960699 | ||||||||
\(821\) | 7.87168e8i | 1.42245i | 0.702963 | + | 0.711227i | \(0.251860\pi\) | ||||
−0.702963 | + | 0.711227i | \(0.748140\pi\) | |||||||
\(822\) | 1.00651e8i | 0.181218i | ||||||||
\(823\) | − | 1.71767e8i | − | 0.308135i | −0.988060 | − | 0.154067i | \(-0.950763\pi\) | ||
0.988060 | − | 0.154067i | \(-0.0492373\pi\) | |||||||
\(824\) | −1.40095e8 | −0.250404 | ||||||||
\(825\) | 7.31404e7i | 0.130255i | ||||||||
\(826\) | −7.52159e7 | + | 7.23655e8i | −0.133466 | + | 1.28408i | ||||
\(827\) | 5.05093e8 | 0.893008 | 0.446504 | − | 0.894782i | \(-0.352669\pi\) | ||||
0.446504 | + | 0.894782i | \(0.352669\pi\) | |||||||
\(828\) | 1.55063e8i | 0.273160i | ||||||||
\(829\) | 2.75561e8 | 0.483676 | 0.241838 | − | 0.970317i | \(-0.422250\pi\) | ||||
0.241838 | + | 0.970317i | \(0.422250\pi\) | |||||||
\(830\) | 1.76810e8 | 0.309223 | ||||||||
\(831\) | −1.29677e8 | −0.225974 | ||||||||
\(832\) | − | 2.15476e7i | − | 0.0374136i | ||||||
\(833\) | 2.32076e9 | 4.01508 | ||||||||
\(834\) | 4.02166e8i | 0.693278i | ||||||||
\(835\) | −6.90761e8 | −1.18650 | ||||||||
\(836\) | − | 4.21538e8i | − | 0.721470i | ||||||
\(837\) | 4.29224e6i | 0.00731995i | ||||||||
\(838\) | 5.18143e8 | 0.880476 | ||||||||
\(839\) | − | 1.13829e8i | − | 0.192738i | −0.995346 | − | 0.0963691i | \(-0.969277\pi\) | ||
0.995346 | − | 0.0963691i | \(-0.0307229\pi\) | |||||||
\(840\) | 2.06899e8i | 0.349076i | ||||||||
\(841\) | −4.67589e7 | −0.0786097 | ||||||||
\(842\) | 2.51055e8 | 0.420565 | ||||||||
\(843\) | 6.80479e8 | 1.13588 | ||||||||
\(844\) | 2.11857e8i | 0.352383i | ||||||||
\(845\) | 5.14511e8 | 0.852755 | ||||||||
\(846\) | 1.10035e8 | 0.181728 | ||||||||
\(847\) | −2.64408e9 | −4.35135 | ||||||||
\(848\) | 2.03393e8 | 0.333541 | ||||||||
\(849\) | − | 1.46782e8i | − | 0.239855i | ||||||
\(850\) | 9.16520e7i | 0.149240i | ||||||||
\(851\) | −2.88695e8 | −0.468437 | ||||||||
\(852\) | −1.21673e8 | −0.196733 | ||||||||
\(853\) | 9.67947e7 | 0.155957 | 0.0779784 | − | 0.996955i | \(-0.475153\pi\) | ||||
0.0779784 | + | 0.996955i | \(0.475153\pi\) | |||||||
\(854\) | −3.89910e8 | −0.626024 | ||||||||
\(855\) | −1.53087e8 | −0.244929 | ||||||||
\(856\) | 1.24353e8i | 0.198260i | ||||||||
\(857\) | 2.81411e8i | 0.447094i | 0.974693 | + | 0.223547i | \(0.0717636\pi\) | ||||
−0.974693 | + | 0.223547i | \(0.928236\pi\) | |||||||
\(858\) | − | 1.41964e8i | − | 0.224758i | ||||||
\(859\) | 8.67660e8i | 1.36890i | 0.729062 | + | 0.684448i | \(0.239957\pi\) | ||||
−0.729062 | + | 0.684448i | \(0.760043\pi\) | |||||||
\(860\) | − | 4.34535e8i | − | 0.683171i | ||||||
\(861\) | −1.38013e8 | −0.216228 | ||||||||
\(862\) | 5.42170e8 | 0.846474 | ||||||||
\(863\) | 8.73813e8i | 1.35952i | 0.733434 | + | 0.679761i | \(0.237916\pi\) | ||||
−0.733434 | + | 0.679761i | \(0.762084\pi\) | |||||||
\(864\) | − | 2.19424e7i | − | 0.0340207i | ||||||
\(865\) | 9.75846e8i | 1.50776i | ||||||||
\(866\) | 5.64312e8i | 0.868891i | ||||||||
\(867\) | 7.37846e8 | 1.13216 | ||||||||
\(868\) | − | 2.27070e7i | − | 0.0347216i | ||||||
\(869\) | 9.20860e8i | 1.40325i | ||||||||
\(870\) | 2.41707e8i | 0.367055i | ||||||||
\(871\) | −1.90863e8 | −0.288846 | ||||||||
\(872\) | −4.66685e7 | −0.0703840 | ||||||||
\(873\) | 2.94612e8i | 0.442800i | ||||||||
\(874\) | 6.06964e8 | 0.909136 | ||||||||
\(875\) | −1.28616e9 | −1.91987 | ||||||||
\(876\) | 2.21696e8i | 0.329796i | ||||||||
\(877\) | −1.93143e8 | −0.286338 | −0.143169 | − | 0.989698i | \(-0.545729\pi\) | ||||
−0.143169 | + | 0.989698i | \(0.545729\pi\) | |||||||
\(878\) | − | 7.40407e8i | − | 1.09392i | ||||||
\(879\) | −1.00231e8 | −0.147583 | ||||||||
\(880\) | − | 2.93525e8i | − | 0.430723i | ||||||
\(881\) | 3.49813e8i | 0.511573i | 0.966733 | + | 0.255787i | \(0.0823345\pi\) | ||||
−0.966733 | + | 0.255787i | \(0.917666\pi\) | |||||||
\(882\) | − | 3.77353e8i | − | 0.549974i | ||||||
\(883\) | −9.17352e7 | −0.133246 | −0.0666230 | − | 0.997778i | \(-0.521222\pi\) | ||||
−0.0666230 | + | 0.997778i | \(0.521222\pi\) | |||||||
\(884\) | − | 1.77894e8i | − | 0.257517i | ||||||
\(885\) | −3.72839e8 | − | 3.87524e7i | −0.537887 | − | 0.0559074i | ||||
\(886\) | 2.48289e8 | 0.356990 | ||||||||
\(887\) | − | 1.35679e9i | − | 1.94420i | −0.234572 | − | 0.972099i | \(-0.575369\pi\) | ||
0.234572 | − | 0.972099i | \(-0.424631\pi\) | |||||||
\(888\) | 4.08523e7 | 0.0583415 | ||||||||
\(889\) | 7.52265e8 | 1.07069 | ||||||||
\(890\) | 7.75993e7 | 0.110075 | ||||||||
\(891\) | − | 1.44565e8i | − | 0.204376i | ||||||
\(892\) | 6.54915e7 | 0.0922763 | ||||||||
\(893\) | − | 4.30713e8i | − | 0.604831i | ||||||
\(894\) | −2.48797e8 | −0.348203 | ||||||||
\(895\) | 1.26449e9i | 1.76379i | ||||||||
\(896\) | 1.16080e8i | 0.161374i | ||||||||
\(897\) | 2.04411e8 | 0.283222 | ||||||||
\(898\) | − | 5.07574e8i | − | 0.700923i | ||||||
\(899\) | − | 2.65272e7i | − | 0.0365100i | ||||||
\(900\) | 1.49025e7 | 0.0204424 | ||||||||
\(901\) | 1.67919e9 | 2.29576 | ||||||||
\(902\) | 1.95798e8 | 0.266802 | ||||||||
\(903\) | 1.13218e9i | 1.53764i | ||||||||
\(904\) | 2.82905e8 | 0.382945 | ||||||||
\(905\) | −7.71633e7 | −0.104103 | ||||||||
\(906\) | 1.54283e8 | 0.207459 | ||||||||
\(907\) | 5.48952e8 | 0.735720 | 0.367860 | − | 0.929881i | \(-0.380091\pi\) | ||||
0.367860 | + | 0.929881i | \(0.380091\pi\) | |||||||
\(908\) | − | 5.45165e8i | − | 0.728232i | ||||||
\(909\) | − | 9.32790e7i | − | 0.124192i | ||||||
\(910\) | 2.72743e8 | 0.361934 | ||||||||
\(911\) | −3.30400e8 | −0.437004 | −0.218502 | − | 0.975837i | \(-0.570117\pi\) | ||||
−0.218502 | + | 0.975837i | \(0.570117\pi\) | |||||||
\(912\) | −8.58895e7 | −0.113228 | ||||||||
\(913\) | 6.53560e8 | 0.858763 | ||||||||
\(914\) | −1.00336e9 | −1.31406 | ||||||||
\(915\) | − | 2.00888e8i | − | 0.262235i | ||||||
\(916\) | 3.30886e8i | 0.430519i | ||||||||
\(917\) | − | 1.83060e9i | − | 2.37402i | ||||||
\(918\) | − | 1.81154e8i | − | 0.234164i | ||||||
\(919\) | − | 3.72892e8i | − | 0.480437i | −0.970719 | − | 0.240218i | \(-0.922781\pi\) | ||
0.970719 | − | 0.240218i | \(-0.0772191\pi\) | |||||||
\(920\) | 4.22641e8 | 0.542761 | ||||||||
\(921\) | 5.74100e7 | 0.0734867 | ||||||||
\(922\) | − | 3.89787e8i | − | 0.497319i | ||||||
\(923\) | 1.60395e8i | 0.203979i | ||||||||
\(924\) | 7.64782e8i | 0.969441i | ||||||||
\(925\) | 2.77455e7i | 0.0350564i | ||||||||
\(926\) | 1.93513e8 | 0.243712 | ||||||||
\(927\) | 1.88063e8i | 0.236083i | ||||||||
\(928\) | 1.35610e8i | 0.169686i | ||||||||
\(929\) | − | 3.42159e8i | − | 0.426758i | −0.976970 | − | 0.213379i | \(-0.931553\pi\) | ||
0.976970 | − | 0.213379i | \(-0.0684468\pi\) | |||||||
\(930\) | 1.16990e7 | 0.0145445 | ||||||||
\(931\) | −1.47708e9 | −1.83043 | ||||||||
\(932\) | 1.61606e8i | 0.199623i | ||||||||
\(933\) | 5.66502e8 | 0.697520 | ||||||||
\(934\) | 5.92279e8 | 0.726919 | ||||||||
\(935\) | − | 2.42331e9i | − | 2.96465i | ||||||
\(936\) | −2.89255e7 | −0.0352738 | ||||||||
\(937\) | 1.02496e9i | 1.24591i | 0.782258 | + | 0.622955i | \(0.214068\pi\) | ||||
−0.782258 | + | 0.622955i | \(0.785932\pi\) | |||||||
\(938\) | 1.02821e9 | 1.24587 | ||||||||
\(939\) | − | 1.19766e8i | − | 0.144656i | ||||||
\(940\) | − | 2.99914e8i | − | 0.361088i | ||||||
\(941\) | − | 1.46817e9i | − | 1.76201i | −0.473110 | − | 0.881004i | \(-0.656869\pi\) | ||
0.473110 | − | 0.881004i | \(-0.343131\pi\) | |||||||
\(942\) | −5.13043e8 | −0.613764 | ||||||||
\(943\) | 2.81926e8i | 0.336202i | ||||||||
\(944\) | −2.09181e8 | − | 2.17421e7i | −0.248660 | − | 0.0258455i | ||||
\(945\) | 2.77740e8 | 0.329112 | ||||||||
\(946\) | − | 1.60622e9i | − | 1.89728i | ||||||
\(947\) | −3.59648e8 | −0.423475 | −0.211737 | − | 0.977327i | \(-0.567912\pi\) | ||||
−0.211737 | + | 0.977327i | \(0.567912\pi\) | |||||||
\(948\) | 1.87627e8 | 0.220227 | ||||||||
\(949\) | 2.92249e8 | 0.341944 | ||||||||
\(950\) | − | 5.83332e7i | − | 0.0680370i | ||||||
\(951\) | −4.77511e8 | −0.555190 | ||||||||
\(952\) | 9.58346e8i | 1.11074i | ||||||||
\(953\) | 3.38000e8 | 0.390515 | 0.195258 | − | 0.980752i | \(-0.437446\pi\) | ||||
0.195258 | + | 0.980752i | \(0.437446\pi\) | |||||||
\(954\) | − | 2.73035e8i | − | 0.314466i | ||||||
\(955\) | − | 6.44961e8i | − | 0.740497i | ||||||
\(956\) | 2.01577e8 | 0.230711 | ||||||||
\(957\) | 8.93448e8i | 1.01937i | ||||||||
\(958\) | 7.86720e8i | 0.894796i | ||||||||
\(959\) | −7.14782e8 | −0.810435 | ||||||||
\(960\) | −5.98065e7 | −0.0675981 | ||||||||
\(961\) | 8.86220e8 | 0.998553 | ||||||||
\(962\) | − | 5.38533e7i | − | 0.0604905i | ||||||
\(963\) | 1.66931e8 | 0.186921 | ||||||||
\(964\) | −2.43801e8 | −0.272147 | ||||||||
\(965\) | −1.04075e8 | −0.115815 | ||||||||
\(966\) | −1.10119e9 | −1.22161 | ||||||||
\(967\) | 1.15571e8i | 0.127812i | 0.997956 | + | 0.0639058i | \(0.0203557\pi\) | ||||
−0.997956 | + | 0.0639058i | \(0.979644\pi\) | |||||||
\(968\) | − | 7.64303e8i | − | 0.842635i | ||||||
\(969\) | −7.09093e8 | −0.779349 | ||||||||
\(970\) | 8.02997e8 | 0.879830 | ||||||||
\(971\) | 2.55114e8 | 0.278661 | 0.139330 | − | 0.990246i | \(-0.455505\pi\) | ||||
0.139330 | + | 0.990246i | \(0.455505\pi\) | |||||||
\(972\) | −2.94555e7 | −0.0320750 | ||||||||
\(973\) | −2.85602e9 | −3.10044 | ||||||||
\(974\) | 2.92511e8i | 0.316567i | ||||||||
\(975\) | − | 1.96452e7i | − | 0.0211954i | ||||||
\(976\) | − | 1.12708e8i | − | 0.121229i | ||||||
\(977\) | − | 3.75608e8i | − | 0.402764i | −0.979513 | − | 0.201382i | \(-0.935457\pi\) | ||
0.979513 | − | 0.201382i | \(-0.0645433\pi\) | |||||||
\(978\) | − | 5.15198e8i | − | 0.550754i | ||||||
\(979\) | 2.86839e8 | 0.305696 | ||||||||
\(980\) | −1.02852e9 | −1.09278 | ||||||||
\(981\) | 6.26476e7i | 0.0663587i | ||||||||
\(982\) | − | 4.26356e8i | − | 0.450234i | ||||||
\(983\) | 1.76441e9i | 1.85755i | 0.370648 | + | 0.928773i | \(0.379136\pi\) | ||||
−0.370648 | + | 0.928773i | \(0.620864\pi\) | |||||||
\(984\) | − | 3.98944e7i | − | 0.0418723i | ||||||
\(985\) | 8.38821e8 | 0.877729 | ||||||||
\(986\) | 1.11958e9i | 1.16795i | ||||||||
\(987\) | 7.81427e8i | 0.812713i | ||||||||
\(988\) | 1.13223e8i | 0.117399i | ||||||||
\(989\) | 2.31276e9 | 2.39079 | ||||||||
\(990\) | −3.94028e8 | −0.406089 | ||||||||
\(991\) | − | 5.99599e8i | − | 0.616083i | −0.951373 | − | 0.308042i | \(-0.900326\pi\) | ||
0.951373 | − | 0.308042i | \(-0.0996736\pi\) | |||||||
\(992\) | 6.56372e6 | 0.00672380 | ||||||||
\(993\) | −1.72064e7 | −0.0175728 | ||||||||
\(994\) | − | 8.64074e8i | − | 0.879816i | ||||||
\(995\) | 8.17712e8 | 0.830102 | ||||||||
\(996\) | − | 1.33164e8i | − | 0.134775i | ||||||
\(997\) | 3.34106e8 | 0.337131 | 0.168566 | − | 0.985690i | \(-0.446087\pi\) | ||||
0.168566 | + | 0.985690i | \(0.446087\pi\) | |||||||
\(998\) | 4.16963e8i | 0.419475i | ||||||||
\(999\) | − | 5.48401e7i | − | 0.0550049i |
(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 | 354.7.d.a.235.3 | ✓ | 60 | |
59.58 | odd | 2 | inner | 354.7.d.a.235.4 | yes | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
354.7.d.a.235.3 | ✓ | 60 | 1.1 | even | 1 | trivial | |
354.7.d.a.235.4 | yes | 60 | 59.58 | odd | 2 | inner |