Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,7,Mod(19,60)]
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, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.19");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.f (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: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 19.34 | ||
Character | \(\chi\) | \(=\) | 60.19 |
Dual form | 60.7.f.a.19.33 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 7.65640 | + | 2.31937i | 0.957050 | + | 0.289921i | ||||
\(3\) | 15.5885 | 0.577350 | ||||||||
\(4\) | 53.2410 | + | 35.5161i | 0.831891 | + | 0.554939i | ||||
\(5\) | 87.3911 | − | 89.3745i | 0.699129 | − | 0.714996i | ||||
\(6\) | 119.352 | + | 36.1554i | 0.552553 | + | 0.167386i | ||||
\(7\) | 36.3122 | 0.105866 | 0.0529332 | − | 0.998598i | \(-0.483143\pi\) | ||||
0.0529332 | + | 0.998598i | \(0.483143\pi\) | |||||||
\(8\) | 325.260 | + | 395.411i | 0.635273 | + | 0.772288i | ||||
\(9\) | 243.000 | 0.333333 | ||||||||
\(10\) | 876.394 | − | 481.595i | 0.876394 | − | 0.481595i | ||||
\(11\) | − | 995.783i | − | 0.748146i | −0.927399 | − | 0.374073i | \(-0.877961\pi\) | ||
0.927399 | − | 0.374073i | \(-0.122039\pi\) | |||||||
\(12\) | 829.945 | + | 553.641i | 0.480293 | + | 0.320394i | ||||
\(13\) | 105.943i | 0.0482218i | 0.999709 | + | 0.0241109i | \(0.00767548\pi\) | ||||
−0.999709 | + | 0.0241109i | \(0.992325\pi\) | |||||||
\(14\) | 278.021 | + | 84.2215i | 0.101320 | + | 0.0306930i | ||||
\(15\) | 1362.29 | − | 1393.21i | 0.403642 | − | 0.412803i | ||||
\(16\) | 1573.21 | + | 3781.83i | 0.384085 | + | 0.923298i | ||||
\(17\) | − | 1286.27i | − | 0.261809i | −0.991395 | − | 0.130905i | \(-0.958212\pi\) | ||
0.991395 | − | 0.130905i | \(-0.0417881\pi\) | |||||||
\(18\) | 1860.51 | + | 563.607i | 0.319017 | + | 0.0966405i | ||||
\(19\) | 9085.22i | 1.32457i | 0.749253 | + | 0.662284i | \(0.230413\pi\) | ||||
−0.749253 | + | 0.662284i | \(0.769587\pi\) | |||||||
\(20\) | 7827.02 | − | 1654.60i | 0.978378 | − | 0.206825i | ||||
\(21\) | 566.051 | 0.0611221 | ||||||||
\(22\) | 2309.59 | − | 7624.12i | 0.216904 | − | 0.716014i | ||||
\(23\) | 1331.63 | 0.109446 | 0.0547231 | − | 0.998502i | \(-0.482572\pi\) | ||||
0.0547231 | + | 0.998502i | \(0.482572\pi\) | |||||||
\(24\) | 5070.30 | + | 6163.85i | 0.366775 | + | 0.445880i | ||||
\(25\) | −350.602 | − | 15621.1i | −0.0224386 | − | 0.999748i | ||||
\(26\) | −245.722 | + | 811.144i | −0.0139805 | + | 0.0461507i | ||||
\(27\) | 3788.00 | 0.192450 | ||||||||
\(28\) | 1933.30 | + | 1289.67i | 0.0880694 | + | 0.0587494i | ||||
\(29\) | −14223.4 | −0.583188 | −0.291594 | − | 0.956542i | \(-0.594186\pi\) | ||||
−0.291594 | + | 0.956542i | \(0.594186\pi\) | |||||||
\(30\) | 13661.6 | − | 7507.32i | 0.505986 | − | 0.278049i | ||||
\(31\) | 40502.0i | 1.35954i | 0.733426 | + | 0.679769i | \(0.237920\pi\) | ||||
−0.733426 | + | 0.679769i | \(0.762080\pi\) | |||||||
\(32\) | 3273.70 | + | 32604.1i | 0.0999054 | + | 0.994997i | ||||
\(33\) | − | 15522.7i | − | 0.431943i | ||||||
\(34\) | 2983.33 | − | 9848.19i | 0.0759041 | − | 0.250565i | ||||
\(35\) | 3173.36 | − | 3245.39i | 0.0740143 | − | 0.0756941i | ||||
\(36\) | 12937.6 | + | 8630.41i | 0.277297 | + | 0.184980i | ||||
\(37\) | − | 71359.6i | − | 1.40879i | −0.709807 | − | 0.704396i | \(-0.751218\pi\) | ||
0.709807 | − | 0.704396i | \(-0.248782\pi\) | |||||||
\(38\) | −21072.0 | + | 69560.1i | −0.384021 | + | 1.26768i | ||||
\(39\) | 1651.49i | 0.0278409i | ||||||||
\(40\) | 63764.5 | + | 5485.49i | 0.996320 | + | 0.0857107i | ||||
\(41\) | −68453.6 | −0.993218 | −0.496609 | − | 0.867974i | \(-0.665422\pi\) | ||||
−0.496609 | + | 0.867974i | \(0.665422\pi\) | |||||||
\(42\) | 4333.92 | + | 1312.88i | 0.0584969 | + | 0.0177206i | ||||
\(43\) | 6391.48 | 0.0803889 | 0.0401945 | − | 0.999192i | \(-0.487202\pi\) | ||||
0.0401945 | + | 0.999192i | \(0.487202\pi\) | |||||||
\(44\) | 35366.3 | − | 53016.5i | 0.415176 | − | 0.622376i | ||||
\(45\) | 21236.0 | − | 21718.0i | 0.233043 | − | 0.238332i | ||||
\(46\) | 10195.5 | + | 3088.55i | 0.104746 | + | 0.0317308i | ||||
\(47\) | −56471.4 | −0.543920 | −0.271960 | − | 0.962309i | \(-0.587672\pi\) | ||||
−0.271960 | + | 0.962309i | \(0.587672\pi\) | |||||||
\(48\) | 24524.0 | + | 58952.8i | 0.221752 | + | 0.533066i | ||||
\(49\) | −116330. | −0.988792 | ||||||||
\(50\) | 33546.7 | − | 120414.i | 0.268374 | − | 0.963315i | ||||
\(51\) | − | 20050.9i | − | 0.151156i | ||||||
\(52\) | −3762.69 | + | 5640.53i | −0.0267601 | + | 0.0401153i | ||||
\(53\) | − | 62845.9i | − | 0.422133i | −0.977472 | − | 0.211066i | \(-0.932306\pi\) | ||
0.977472 | − | 0.211066i | \(-0.0676936\pi\) | |||||||
\(54\) | 29002.4 | + | 8785.77i | 0.184184 | + | 0.0557954i | ||||
\(55\) | −88997.6 | − | 87022.5i | −0.534922 | − | 0.523051i | ||||
\(56\) | 11810.9 | + | 14358.3i | 0.0672541 | + | 0.0817594i | ||||
\(57\) | 141624.i | 0.764740i | ||||||||
\(58\) | −108900. | − | 32989.3i | −0.558141 | − | 0.169079i | ||||
\(59\) | − | 132995.i | − | 0.647561i | −0.946132 | − | 0.323780i | \(-0.895046\pi\) | ||
0.946132 | − | 0.323780i | \(-0.104954\pi\) | |||||||
\(60\) | 122011. | − | 25792.7i | 0.564867 | − | 0.119411i | ||||
\(61\) | −387193. | −1.70584 | −0.852920 | − | 0.522042i | \(-0.825171\pi\) | ||||
−0.852920 | + | 0.522042i | \(0.825171\pi\) | |||||||
\(62\) | −93939.2 | + | 310100.i | −0.394159 | + | 1.30115i | ||||
\(63\) | 8823.87 | 0.0352888 | ||||||||
\(64\) | −50556.2 | + | 257223.i | −0.192857 | + | 0.981227i | ||||
\(65\) | 9468.63 | + | 9258.50i | 0.0344784 | + | 0.0337132i | ||||
\(66\) | 36003.0 | − | 118848.i | 0.125229 | − | 0.413391i | ||||
\(67\) | −476348. | −1.58380 | −0.791899 | − | 0.610653i | \(-0.790907\pi\) | ||||
−0.791899 | + | 0.610653i | \(0.790907\pi\) | |||||||
\(68\) | 45683.2 | − | 68482.2i | 0.145288 | − | 0.217797i | ||||
\(69\) | 20758.1 | 0.0631888 | ||||||||
\(70\) | 31823.8 | − | 17487.8i | 0.0927808 | − | 0.0509848i | ||||
\(71\) | 483101.i | 1.34978i | 0.737919 | + | 0.674889i | \(0.235809\pi\) | ||||
−0.737919 | + | 0.674889i | \(0.764191\pi\) | |||||||
\(72\) | 79038.1 | + | 96084.9i | 0.211758 | + | 0.257429i | ||||
\(73\) | − | 654838.i | − | 1.68331i | −0.540012 | − | 0.841657i | \(-0.681580\pi\) | ||
0.540012 | − | 0.841657i | \(-0.318420\pi\) | |||||||
\(74\) | 165509. | − | 546358.i | 0.408439 | − | 1.34829i | ||||
\(75\) | −5465.35 | − | 243508.i | −0.0129549 | − | 0.577205i | ||||
\(76\) | −322671. | + | 483706.i | −0.735055 | + | 1.10190i | ||||
\(77\) | − | 36159.1i | − | 0.0792036i | ||||||
\(78\) | −3830.42 | + | 12644.5i | −0.00807166 | + | 0.0266451i | ||||
\(79\) | 80187.9i | 0.162640i | 0.996688 | + | 0.0813200i | \(0.0259136\pi\) | ||||
−0.996688 | + | 0.0813200i | \(0.974086\pi\) | |||||||
\(80\) | 475484. | + | 189893.i | 0.928679 | + | 0.370884i | ||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | −524108. | − | 158769.i | −0.950559 | − | 0.287955i | ||||
\(83\) | 1.03615e6 | 1.81213 | 0.906066 | − | 0.423137i | \(-0.139071\pi\) | ||||
0.906066 | + | 0.423137i | \(0.139071\pi\) | |||||||
\(84\) | 30137.2 | + | 20103.9i | 0.0508469 | + | 0.0339190i | ||||
\(85\) | −114960. | − | 112408.i | −0.187192 | − | 0.183038i | ||||
\(86\) | 48935.8 | + | 14824.2i | 0.0769362 | + | 0.0233065i | ||||
\(87\) | −221721. | −0.336704 | ||||||||
\(88\) | 393744. | − | 323888.i | 0.577784 | − | 0.475277i | ||||
\(89\) | 1.20220e6 | 1.70532 | 0.852662 | − | 0.522463i | \(-0.174987\pi\) | ||||
0.852662 | + | 0.522463i | \(0.174987\pi\) | |||||||
\(90\) | 212964. | − | 117028.i | 0.292131 | − | 0.160532i | ||||
\(91\) | 3847.03i | 0.00510507i | ||||||||
\(92\) | 70897.4 | + | 47294.4i | 0.0910473 | + | 0.0607360i | ||||
\(93\) | 631363.i | 0.784929i | ||||||||
\(94\) | −432368. | − | 130978.i | −0.520559 | − | 0.157694i | ||||
\(95\) | 811987. | + | 793967.i | 0.947061 | + | 0.926044i | ||||
\(96\) | 51031.9 | + | 508247.i | 0.0576804 | + | 0.574462i | ||||
\(97\) | 1.45683e6i | 1.59622i | 0.602511 | + | 0.798111i | \(0.294167\pi\) | ||||
−0.602511 | + | 0.798111i | \(0.705833\pi\) | |||||||
\(98\) | −890673. | − | 269814.i | −0.946324 | − | 0.286672i | ||||
\(99\) | − | 241975.i | − | 0.249382i | ||||||
\(100\) | 536133. | − | 844134.i | 0.536133 | − | 0.844134i | ||||
\(101\) | 796216. | 0.772800 | 0.386400 | − | 0.922331i | \(-0.373718\pi\) | ||||
0.386400 | + | 0.922331i | \(0.373718\pi\) | |||||||
\(102\) | 46505.6 | − | 153518.i | 0.0438232 | − | 0.144664i | ||||
\(103\) | 747900. | 0.684435 | 0.342217 | − | 0.939621i | \(-0.388822\pi\) | ||||
0.342217 | + | 0.939621i | \(0.388822\pi\) | |||||||
\(104\) | −41891.2 | + | 34459.1i | −0.0372411 | + | 0.0306340i | ||||
\(105\) | 49467.8 | − | 50590.6i | 0.0427322 | − | 0.0437020i | ||||
\(106\) | 145763. | − | 481173.i | 0.122385 | − | 0.404002i | ||||
\(107\) | 75240.9 | 0.0614190 | 0.0307095 | − | 0.999528i | \(-0.490223\pi\) | ||||
0.0307095 | + | 0.999528i | \(0.490223\pi\) | |||||||
\(108\) | 201677. | + | 134535.i | 0.160098 | + | 0.106798i | ||||
\(109\) | 905540. | 0.699243 | 0.349622 | − | 0.936891i | \(-0.386310\pi\) | ||||
0.349622 | + | 0.936891i | \(0.386310\pi\) | |||||||
\(110\) | −479564. | − | 872698.i | −0.360303 | − | 0.655671i | ||||
\(111\) | − | 1.11239e6i | − | 0.813367i | ||||||
\(112\) | 57126.9 | + | 137326.i | 0.0406618 | + | 0.0977463i | ||||
\(113\) | 799166.i | 0.553862i | 0.960890 | + | 0.276931i | \(0.0893173\pi\) | ||||
−0.960890 | + | 0.276931i | \(0.910683\pi\) | |||||||
\(114\) | −328480. | + | 1.08433e6i | −0.221715 | + | 0.731895i | ||||
\(115\) | 116373. | − | 119014.i | 0.0765170 | − | 0.0782536i | ||||
\(116\) | −757267. | − | 505159.i | −0.485149 | − | 0.323634i | ||||
\(117\) | 25744.2i | 0.0160739i | ||||||||
\(118\) | 308466. | − | 1.01827e6i | 0.187742 | − | 0.619748i | ||||
\(119\) | − | 46707.2i | − | 0.0277168i | ||||||
\(120\) | 993990. | + | 85510.3i | 0.575226 | + | 0.0494851i | ||||
\(121\) | 779977. | 0.440277 | ||||||||
\(122\) | −2.96451e6 | − | 898045.i | −1.63258 | − | 0.494560i | ||||
\(123\) | −1.06709e6 | −0.573434 | ||||||||
\(124\) | −1.43847e6 | + | 2.15637e6i | −0.754460 | + | 1.13099i | ||||
\(125\) | −1.42676e6 | − | 1.33381e6i | −0.730503 | − | 0.682909i | ||||
\(126\) | 67559.1 | + | 20465.8i | 0.0337732 | + | 0.0102310i | ||||
\(127\) | −3.25779e6 | −1.59042 | −0.795209 | − | 0.606335i | \(-0.792639\pi\) | ||||
−0.795209 | + | 0.606335i | \(0.792639\pi\) | |||||||
\(128\) | −983674. | + | 1.85214e6i | −0.469052 | + | 0.883170i | ||||
\(129\) | 99633.3 | 0.0464126 | ||||||||
\(130\) | 51021.7 | + | 92848.0i | 0.0232234 | + | 0.0422613i | ||||
\(131\) | 208824.i | 0.0928893i | 0.998921 | + | 0.0464446i | \(0.0147891\pi\) | ||||
−0.998921 | + | 0.0464446i | \(0.985211\pi\) | |||||||
\(132\) | 551306. | − | 826446.i | 0.239702 | − | 0.359329i | ||||
\(133\) | 329904.i | 0.140227i | ||||||||
\(134\) | −3.64711e6 | − | 1.10483e6i | −1.51577 | − | 0.459177i | ||||
\(135\) | 331037. | − | 338550.i | 0.134547 | − | 0.137601i | ||||
\(136\) | 508605. | − | 418371.i | 0.202192 | − | 0.166320i | ||||
\(137\) | 2.47104e6i | 0.960987i | 0.876998 | + | 0.480493i | \(0.159542\pi\) | ||||
−0.876998 | + | 0.480493i | \(0.840458\pi\) | |||||||
\(138\) | 158932. | + | 48145.7i | 0.0604749 | + | 0.0183198i | ||||
\(139\) | − | 1.93989e6i | − | 0.722327i | −0.932503 | − | 0.361163i | \(-0.882380\pi\) | ||
0.932503 | − | 0.361163i | \(-0.117620\pi\) | |||||||
\(140\) | 284217. | − | 60082.2i | 0.103577 | − | 0.0218959i | ||||
\(141\) | −880303. | −0.314033 | ||||||||
\(142\) | −1.12049e6 | + | 3.69881e6i | −0.391330 | + | 1.29181i | ||||
\(143\) | 105496. | 0.0360770 | ||||||||
\(144\) | 382291. | + | 918984.i | 0.128028 | + | 0.307766i | ||||
\(145\) | −1.24300e6 | + | 1.27121e6i | −0.407724 | + | 0.416977i | ||||
\(146\) | 1.51881e6 | − | 5.01370e6i | 0.488029 | − | 1.61102i | ||||
\(147\) | −1.81341e6 | −0.570879 | ||||||||
\(148\) | 2.53441e6 | − | 3.79926e6i | 0.781794 | − | 1.17196i | ||||
\(149\) | 502061. | 0.151774 | 0.0758870 | − | 0.997116i | \(-0.475821\pi\) | ||||
0.0758870 | + | 0.997116i | \(0.475821\pi\) | |||||||
\(150\) | 522941. | − | 1.87707e6i | 0.154946 | − | 0.556170i | ||||
\(151\) | − | 3.91206e6i | − | 1.13625i | −0.822941 | − | 0.568127i | \(-0.807668\pi\) | ||
0.822941 | − | 0.568127i | \(-0.192332\pi\) | |||||||
\(152\) | −3.59240e6 | + | 2.95505e6i | −1.02295 | + | 0.841463i | ||||
\(153\) | − | 312563.i | − | 0.0872697i | ||||||
\(154\) | 83866.3 | − | 276848.i | 0.0229628 | − | 0.0758019i | ||||
\(155\) | 3.61984e6 | + | 3.53951e6i | 0.972064 | + | 0.950492i | ||||
\(156\) | −58654.5 | + | 87927.1i | −0.0154500 | + | 0.0231606i | ||||
\(157\) | 1.57181e6i | 0.406163i | 0.979162 | + | 0.203081i | \(0.0650956\pi\) | ||||
−0.979162 | + | 0.203081i | \(0.934904\pi\) | |||||||
\(158\) | −185986. | + | 613951.i | −0.0471528 | + | 0.155655i | ||||
\(159\) | − | 979670.i | − | 0.243719i | ||||||
\(160\) | 3.20006e6 | + | 2.55672e6i | 0.781266 | + | 0.624199i | ||||
\(161\) | 48354.5 | 0.0115867 | ||||||||
\(162\) | 452103. | + | 136957.i | 0.106339 | + | 0.0322135i | ||||
\(163\) | 3.02276e6 | 0.697977 | 0.348989 | − | 0.937127i | \(-0.386525\pi\) | ||||
0.348989 | + | 0.937127i | \(0.386525\pi\) | |||||||
\(164\) | −3.64454e6 | − | 2.43120e6i | −0.826249 | − | 0.551175i | ||||
\(165\) | −1.38734e6 | − | 1.35655e6i | −0.308837 | − | 0.301983i | ||||
\(166\) | 7.93321e6 | + | 2.40323e6i | 1.73430 | + | 0.525376i | ||||
\(167\) | 1.71951e6 | 0.369194 | 0.184597 | − | 0.982814i | \(-0.440902\pi\) | ||||
0.184597 | + | 0.982814i | \(0.440902\pi\) | |||||||
\(168\) | 184114. | + | 223823.i | 0.0388292 | + | 0.0472038i | ||||
\(169\) | 4.81559e6 | 0.997675 | ||||||||
\(170\) | −619460. | − | 1.12728e6i | −0.126086 | − | 0.229448i | ||||
\(171\) | 2.20771e6i | 0.441523i | ||||||||
\(172\) | 340289. | + | 227000.i | 0.0668748 | + | 0.0446109i | ||||
\(173\) | − | 6.03741e6i | − | 1.16604i | −0.812459 | − | 0.583019i | \(-0.801871\pi\) | ||
0.812459 | − | 0.583019i | \(-0.198129\pi\) | |||||||
\(174\) | −1.69758e6 | − | 514252.i | −0.322243 | − | 0.0976177i | ||||
\(175\) | −12731.2 | − | 567235.i | −0.00237549 | − | 0.105840i | ||||
\(176\) | 3.76588e6 | − | 1.56658e6i | 0.690762 | − | 0.287352i | ||||
\(177\) | − | 2.07319e6i | − | 0.373869i | ||||||
\(178\) | 9.20453e6 | + | 2.78835e6i | 1.63208 | + | 0.494410i | ||||
\(179\) | 1.11888e7i | 1.95086i | 0.220311 | + | 0.975430i | \(0.429293\pi\) | ||||
−0.220311 | + | 0.975430i | \(0.570707\pi\) | |||||||
\(180\) | 1.90197e6 | − | 402068.i | 0.326126 | − | 0.0689417i | ||||
\(181\) | −5.54253e6 | −0.934700 | −0.467350 | − | 0.884072i | \(-0.654791\pi\) | ||||
−0.467350 | + | 0.884072i | \(0.654791\pi\) | |||||||
\(182\) | −8922.70 | + | 29454.4i | −0.00148007 | + | 0.00488581i | ||||
\(183\) | −6.03575e6 | −0.984867 | ||||||||
\(184\) | 433126. | + | 526542.i | 0.0695282 | + | 0.0845239i | ||||
\(185\) | −6.37773e6 | − | 6.23619e6i | −1.00728 | − | 0.984927i | ||||
\(186\) | −1.46437e6 | + | 4.83397e6i | −0.227568 | + | 0.751217i | ||||
\(187\) | −1.28084e6 | −0.195872 | ||||||||
\(188\) | −3.00660e6 | − | 2.00565e6i | −0.452483 | − | 0.301843i | ||||
\(189\) | 137550. | 0.0203740 | ||||||||
\(190\) | 4.37539e6 | + | 7.96223e6i | 0.637905 | + | 1.16084i | ||||
\(191\) | 4.62646e6i | 0.663970i | 0.943285 | + | 0.331985i | \(0.107718\pi\) | ||||
−0.943285 | + | 0.331985i | \(0.892282\pi\) | |||||||
\(192\) | −788093. | + | 4.00971e6i | −0.111346 | + | 0.566512i | ||||
\(193\) | − | 7.66995e6i | − | 1.06689i | −0.845834 | − | 0.533446i | \(-0.820897\pi\) | ||
0.845834 | − | 0.533446i | \(-0.179103\pi\) | |||||||
\(194\) | −3.37893e6 | + | 1.11541e7i | −0.462779 | + | 1.52766i | ||||
\(195\) | 147601. | + | 144326.i | 0.0199061 | + | 0.0194643i | ||||
\(196\) | −6.19355e6 | − | 4.13160e6i | −0.822567 | − | 0.548719i | ||||
\(197\) | − | 1.07837e7i | − | 1.41049i | −0.708963 | − | 0.705246i | \(-0.750837\pi\) | ||
0.708963 | − | 0.705246i | \(-0.249163\pi\) | |||||||
\(198\) | 561231. | − | 1.85266e6i | 0.0723012 | − | 0.238671i | ||||
\(199\) | − | 9.05284e6i | − | 1.14875i | −0.818592 | − | 0.574375i | \(-0.805245\pi\) | ||
0.818592 | − | 0.574375i | \(-0.194755\pi\) | |||||||
\(200\) | 6.06271e6 | − | 5.21954e6i | 0.757839 | − | 0.652442i | ||||
\(201\) | −7.42552e6 | −0.914406 | ||||||||
\(202\) | 6.09615e6 | + | 1.84672e6i | 0.739608 | + | 0.224051i | ||||
\(203\) | −516482. | −0.0617401 | ||||||||
\(204\) | 712131. | − | 1.06753e6i | 0.0838821 | − | 0.125745i | ||||
\(205\) | −5.98223e6 | + | 6.11800e6i | −0.694387 | + | 0.710147i | ||||
\(206\) | 5.72623e6 | + | 1.73466e6i | 0.655038 | + | 0.198432i | ||||
\(207\) | 323587. | 0.0364821 | ||||||||
\(208\) | −400659. | + | 166671.i | −0.0445231 | + | 0.0185213i | ||||
\(209\) | 9.04690e6 | 0.990971 | ||||||||
\(210\) | 496084. | − | 272607.i | 0.0535670 | − | 0.0294361i | ||||
\(211\) | 1.08423e7i | 1.15418i | 0.816680 | + | 0.577090i | \(0.195812\pi\) | ||||
−0.816680 | + | 0.577090i | \(0.804188\pi\) | |||||||
\(212\) | 2.23204e6 | − | 3.34598e6i | 0.234258 | − | 0.351169i | ||||
\(213\) | 7.53079e6i | 0.779295i | ||||||||
\(214\) | 576075. | + | 174512.i | 0.0587811 | + | 0.0178067i | ||||
\(215\) | 558558. | − | 571235.i | 0.0562022 | − | 0.0574777i | ||||
\(216\) | 1.23208e6 | + | 1.49782e6i | 0.122258 | + | 0.148627i | ||||
\(217\) | 1.47072e6i | 0.143929i | ||||||||
\(218\) | 6.93318e6 | + | 2.10028e6i | 0.669211 | + | 0.202726i | ||||
\(219\) | − | 1.02079e7i | − | 0.971862i | ||||||
\(220\) | −1.64762e6 | − | 7.79402e6i | −0.154735 | − | 0.731970i | ||||
\(221\) | 136271. | 0.0126249 | ||||||||
\(222\) | 2.58004e6 | − | 8.51688e6i | 0.235813 | − | 0.778433i | ||||
\(223\) | −6.18382e6 | −0.557625 | −0.278813 | − | 0.960345i | \(-0.589941\pi\) | ||||
−0.278813 | + | 0.960345i | \(0.589941\pi\) | |||||||
\(224\) | 118875. | + | 1.18393e6i | 0.0105766 | + | 0.105337i | ||||
\(225\) | −85196.4 | − | 3.79592e6i | −0.00747952 | − | 0.333249i | ||||
\(226\) | −1.85356e6 | + | 6.11874e6i | −0.160576 | + | 0.530074i | ||||
\(227\) | 1.17330e7 | 1.00307 | 0.501534 | − | 0.865138i | \(-0.332769\pi\) | ||||
0.501534 | + | 0.865138i | \(0.332769\pi\) | |||||||
\(228\) | −5.02995e6 | + | 7.54023e6i | −0.424384 | + | 0.636180i | ||||
\(229\) | 1.95291e7 | 1.62621 | 0.813105 | − | 0.582116i | \(-0.197775\pi\) | ||||
0.813105 | + | 0.582116i | \(0.197775\pi\) | |||||||
\(230\) | 1.16703e6 | − | 641307.i | 0.0959180 | − | 0.0527087i | ||||
\(231\) | − | 563664.i | − | 0.0457282i | ||||||
\(232\) | −4.62629e6 | − | 5.62409e6i | −0.370484 | − | 0.450389i | ||||
\(233\) | 2.06220e7i | 1.63029i | 0.579260 | + | 0.815143i | \(0.303342\pi\) | ||||
−0.579260 | + | 0.815143i | \(0.696658\pi\) | |||||||
\(234\) | −59710.4 | + | 197108.i | −0.00466018 | + | 0.0153836i | ||||
\(235\) | −4.93510e6 | + | 5.04711e6i | −0.380270 | + | 0.388901i | ||||
\(236\) | 4.72348e6 | − | 7.08081e6i | 0.359357 | − | 0.538700i | ||||
\(237\) | 1.25001e6i | 0.0939003i | ||||||||
\(238\) | 108331. | − | 357609.i | 0.00803570 | − | 0.0265264i | ||||
\(239\) | − | 1.82892e7i | − | 1.33968i | −0.742506 | − | 0.669840i | \(-0.766363\pi\) | ||
0.742506 | − | 0.669840i | \(-0.233637\pi\) | |||||||
\(240\) | 7.41206e6 | + | 2.96013e6i | 0.536173 | + | 0.214130i | ||||
\(241\) | −1.88580e7 | −1.34724 | −0.673620 | − | 0.739078i | \(-0.735262\pi\) | ||||
−0.673620 | + | 0.739078i | \(0.735262\pi\) | |||||||
\(242\) | 5.97182e6 | + | 1.80906e6i | 0.421367 | + | 0.127646i | ||||
\(243\) | 920483. | 0.0641500 | ||||||||
\(244\) | −2.06146e7 | − | 1.37516e7i | −1.41907 | − | 0.946637i | ||||
\(245\) | −1.01662e7 | + | 1.03970e7i | −0.691293 | + | 0.706983i | ||||
\(246\) | −8.17004e6 | − | 2.47497e6i | −0.548806 | − | 0.166251i | ||||
\(247\) | −962517. | −0.0638731 | ||||||||
\(248\) | −1.60149e7 | + | 1.31737e7i | −1.04995 | + | 0.863678i | ||||
\(249\) | 1.61520e7 | 1.04623 | ||||||||
\(250\) | −7.83029e6 | − | 1.35214e7i | −0.501139 | − | 0.865367i | ||||
\(251\) | − | 1.05499e7i | − | 0.667154i | −0.942723 | − | 0.333577i | \(-0.891744\pi\) | ||
0.942723 | − | 0.333577i | \(-0.108256\pi\) | |||||||
\(252\) | 469792. | + | 313389.i | 0.0293565 | + | 0.0195831i | ||||
\(253\) | − | 1.32602e6i | − | 0.0818818i | ||||||
\(254\) | −2.49429e7 | − | 7.55602e6i | −1.52211 | − | 0.461096i | ||||
\(255\) | −1.79204e6 | − | 1.75227e6i | −0.108076 | − | 0.105677i | ||||
\(256\) | −1.18272e7 | + | 1.18992e7i | −0.704957 | + | 0.709250i | ||||
\(257\) | 343840.i | 0.0202562i | 0.999949 | + | 0.0101281i | \(0.00322393\pi\) | ||||
−0.999949 | + | 0.0101281i | \(0.996776\pi\) | |||||||
\(258\) | 762833. | + | 231087.i | 0.0444192 | + | 0.0134560i | ||||
\(259\) | − | 2.59122e6i | − | 0.149144i | ||||||
\(260\) | 175294. | + | 829220.i | 0.00997348 | + | 0.0471791i | ||||
\(261\) | −3.45628e6 | −0.194396 | ||||||||
\(262\) | −484339. | + | 1.59884e6i | −0.0269306 | + | 0.0888997i | ||||
\(263\) | −1.68620e7 | −0.926920 | −0.463460 | − | 0.886118i | \(-0.653392\pi\) | ||||
−0.463460 | + | 0.886118i | \(0.653392\pi\) | |||||||
\(264\) | 6.13786e6 | − | 5.04892e6i | 0.333584 | − | 0.274401i | ||||
\(265\) | −5.61682e6 | − | 5.49217e6i | −0.301823 | − | 0.295125i | ||||
\(266\) | −765171. | + | 2.52588e6i | −0.0406549 | + | 0.134205i | ||||
\(267\) | 1.87405e7 | 0.984569 | ||||||||
\(268\) | −2.53612e7 | − | 1.69180e7i | −1.31755 | − | 0.878911i | ||||
\(269\) | 2.06767e7 | 1.06224 | 0.531121 | − | 0.847296i | \(-0.321771\pi\) | ||||
0.531121 | + | 0.847296i | \(0.321771\pi\) | |||||||
\(270\) | 3.31978e6 | − | 1.82428e6i | 0.168662 | − | 0.0926830i | ||||
\(271\) | 1.38151e7i | 0.694138i | 0.937840 | + | 0.347069i | \(0.112823\pi\) | ||||
−0.937840 | + | 0.347069i | \(0.887177\pi\) | |||||||
\(272\) | 4.86444e6 | − | 2.02358e6i | 0.241728 | − | 0.100557i | ||||
\(273\) | 59969.3i | 0.00294741i | ||||||||
\(274\) | −5.73125e6 | + | 1.89193e7i | −0.278611 | + | 0.919713i | ||||
\(275\) | −1.55552e7 | + | 349124.i | −0.747958 | + | 0.0167873i | ||||
\(276\) | 1.10518e6 | + | 737246.i | 0.0525662 | + | 0.0350659i | ||||
\(277\) | 2.13872e6i | 0.100627i | 0.998733 | + | 0.0503134i | \(0.0160220\pi\) | ||||
−0.998733 | + | 0.0503134i | \(0.983978\pi\) | |||||||
\(278\) | 4.49934e6 | − | 1.48526e7i | 0.209418 | − | 0.691303i | ||||
\(279\) | 9.84198e6i | 0.453179i | ||||||||
\(280\) | 2.31543e6 | + | 199190.i | 0.105477 | + | 0.00907389i | ||||
\(281\) | 1.43930e7 | 0.648685 | 0.324342 | − | 0.945940i | \(-0.394857\pi\) | ||||
0.324342 | + | 0.945940i | \(0.394857\pi\) | |||||||
\(282\) | −6.73995e6 | − | 2.04175e6i | −0.300545 | − | 0.0910448i | ||||
\(283\) | 2.56055e7 | 1.12973 | 0.564865 | − | 0.825183i | \(-0.308928\pi\) | ||||
0.564865 | + | 0.825183i | \(0.308928\pi\) | |||||||
\(284\) | −1.71578e7 | + | 2.57208e7i | −0.749045 | + | 1.12287i | ||||
\(285\) | 1.26576e7 | + | 1.23767e7i | 0.546786 | + | 0.534652i | ||||
\(286\) | 807724. | + | 244686.i | 0.0345275 | + | 0.0104595i | ||||
\(287\) | −2.48570e6 | −0.105148 | ||||||||
\(288\) | 795509. | + | 7.92279e6i | 0.0333018 | + | 0.331666i | ||||
\(289\) | 2.24831e7 | 0.931456 | ||||||||
\(290\) | −1.24653e7 | + | 6.84991e6i | −0.511103 | + | 0.280861i | ||||
\(291\) | 2.27097e7i | 0.921579i | ||||||||
\(292\) | 2.32573e7 | − | 3.48643e7i | 0.934137 | − | 1.40033i | ||||
\(293\) | 8.11800e6i | 0.322735i | 0.986894 | + | 0.161367i | \(0.0515904\pi\) | ||||
−0.986894 | + | 0.161367i | \(0.948410\pi\) | |||||||
\(294\) | −1.38842e7 | − | 4.20598e6i | −0.546360 | − | 0.165510i | ||||
\(295\) | −1.18864e7 | − | 1.16226e7i | −0.463003 | − | 0.452728i | ||||
\(296\) | 2.82164e7 | − | 2.32104e7i | 1.08799 | − | 0.894968i | ||||
\(297\) | − | 3.77202e6i | − | 0.143981i | ||||||
\(298\) | 3.84398e6 | + | 1.16447e6i | 0.145255 | + | 0.0440026i | ||||
\(299\) | 141077.i | 0.00527769i | ||||||||
\(300\) | 8.35748e6 | − | 1.31587e7i | 0.309536 | − | 0.487361i | ||||
\(301\) | 232089. | 0.00851049 | ||||||||
\(302\) | 9.07353e6 | − | 2.99523e7i | 0.329424 | − | 1.08745i | ||||
\(303\) | 1.24118e7 | 0.446176 | ||||||||
\(304\) | −3.43587e7 | + | 1.42930e7i | −1.22297 | + | 0.508748i | ||||
\(305\) | −3.38372e7 | + | 3.46052e7i | −1.19260 | + | 1.21967i | ||||
\(306\) | 724950. | − | 2.39311e6i | 0.0253014 | − | 0.0835215i | ||||
\(307\) | 2.07910e7 | 0.718555 | 0.359277 | − | 0.933231i | \(-0.383023\pi\) | ||||
0.359277 | + | 0.933231i | \(0.383023\pi\) | |||||||
\(308\) | 1.28423e6 | − | 1.92515e6i | 0.0439532 | − | 0.0658888i | ||||
\(309\) | 1.16586e7 | 0.395159 | ||||||||
\(310\) | 1.95055e7 | + | 3.54957e7i | 0.654746 | + | 1.19149i | ||||
\(311\) | − | 5.61955e7i | − | 1.86819i | −0.357026 | − | 0.934094i | \(-0.616209\pi\) | ||
0.357026 | − | 0.934094i | \(-0.383791\pi\) | |||||||
\(312\) | −653019. | + | 537164.i | −0.0215012 | + | 0.0176865i | ||||
\(313\) | − | 6.05170e6i | − | 0.197353i | −0.995120 | − | 0.0986766i | \(-0.968539\pi\) | ||
0.995120 | − | 0.0986766i | \(-0.0314609\pi\) | |||||||
\(314\) | −3.64560e6 | + | 1.20344e7i | −0.117755 | + | 0.388718i | ||||
\(315\) | 771127. | − | 788629.i | 0.0246714 | − | 0.0252314i | ||||
\(316\) | −2.84796e6 | + | 4.26929e6i | −0.0902553 | + | 0.135299i | ||||
\(317\) | 8.06566e6i | 0.253199i | 0.991954 | + | 0.126600i | \(0.0404063\pi\) | ||||
−0.991954 | + | 0.126600i | \(0.959594\pi\) | |||||||
\(318\) | 2.27222e6 | − | 7.50075e6i | 0.0706592 | − | 0.233251i | ||||
\(319\) | 1.41634e7i | 0.436310i | ||||||||
\(320\) | 1.85710e7 | + | 2.69974e7i | 0.566742 | + | 0.823895i | ||||
\(321\) | 1.17289e6 | 0.0354603 | ||||||||
\(322\) | 370221. | + | 112152.i | 0.0110890 | + | 0.00335923i | ||||
\(323\) | 1.16860e7 | 0.346784 | ||||||||
\(324\) | 3.14383e6 | + | 2.09719e6i | 0.0924323 | + | 0.0616599i | ||||
\(325\) | 1.65495e6 | − | 37144.0i | 0.0482096 | − | 0.00108203i | ||||
\(326\) | 2.31435e7 | + | 7.01091e6i | 0.667999 | + | 0.202359i | ||||
\(327\) | 1.41160e7 | 0.403708 | ||||||||
\(328\) | −2.22652e7 | − | 2.70673e7i | −0.630964 | − | 0.767050i | ||||
\(329\) | −2.05060e6 | −0.0575829 | ||||||||
\(330\) | −7.47566e6 | − | 1.36040e7i | −0.208021 | − | 0.378552i | ||||
\(331\) | 6.79995e6i | 0.187509i | 0.995595 | + | 0.0937545i | \(0.0298869\pi\) | ||||
−0.995595 | + | 0.0937545i | \(0.970113\pi\) | |||||||
\(332\) | 5.51659e7 | + | 3.68001e7i | 1.50750 | + | 1.00562i | ||||
\(333\) | − | 1.73404e7i | − | 0.469598i | ||||||
\(334\) | 1.31652e7 | + | 3.98817e6i | 0.353337 | + | 0.107037i | ||||
\(335\) | −4.16285e7 | + | 4.25733e7i | −1.10728 | + | 1.13241i | ||||
\(336\) | 890520. | + | 2.14071e6i | 0.0234761 | + | 0.0564338i | ||||
\(337\) | − | 4.63328e7i | − | 1.21059i | −0.796000 | − | 0.605297i | \(-0.793054\pi\) | ||
0.796000 | − | 0.605297i | \(-0.206946\pi\) | |||||||
\(338\) | 3.68701e7 | + | 1.11691e7i | 0.954825 | + | 0.289247i | ||||
\(339\) | 1.24578e7i | 0.319772i | ||||||||
\(340\) | −2.12826e6 | − | 1.00677e7i | −0.0541487 | − | 0.256148i | ||||
\(341\) | 4.03312e7 | 1.01713 | ||||||||
\(342\) | −5.12049e6 | + | 1.69031e7i | −0.128007 | + | 0.422560i | ||||
\(343\) | −8.49631e6 | −0.210546 | ||||||||
\(344\) | 2.07889e6 | + | 2.52726e6i | 0.0510689 | + | 0.0620834i | ||||
\(345\) | 1.81407e6 | − | 1.85524e6i | 0.0441771 | − | 0.0451797i | ||||
\(346\) | 1.40030e7 | − | 4.62249e7i | 0.338059 | − | 1.11596i | ||||
\(347\) | 6.18772e6 | 0.148096 | 0.0740478 | − | 0.997255i | \(-0.476408\pi\) | ||||
0.0740478 | + | 0.997255i | \(0.476408\pi\) | |||||||
\(348\) | −1.18046e7 | − | 7.87465e6i | −0.280101 | − | 0.186850i | ||||
\(349\) | −9.57198e6 | −0.225178 | −0.112589 | − | 0.993642i | \(-0.535914\pi\) | ||||
−0.112589 | + | 0.993642i | \(0.535914\pi\) | |||||||
\(350\) | 1.21816e6 | − | 4.37251e6i | 0.0284118 | − | 0.101983i | ||||
\(351\) | 401313.i | 0.00928029i | ||||||||
\(352\) | 3.24666e7 | − | 3.25989e6i | 0.744403 | − | 0.0747439i | ||||
\(353\) | − | 4.38759e7i | − | 0.997474i | −0.866753 | − | 0.498737i | \(-0.833797\pi\) | ||
0.866753 | − | 0.498737i | \(-0.166203\pi\) | |||||||
\(354\) | 4.80850e6 | − | 1.58732e7i | 0.108393 | − | 0.357812i | ||||
\(355\) | 4.31769e7 | + | 4.22187e7i | 0.965086 | + | 0.943669i | ||||
\(356\) | 6.40064e7 | + | 4.26975e7i | 1.41864 | + | 0.946351i | ||||
\(357\) | − | 728094.i | − | 0.0160023i | ||||||
\(358\) | −2.59511e7 | + | 8.56663e7i | −0.565596 | + | 1.86707i | ||||
\(359\) | − | 6.69337e7i | − | 1.44664i | −0.690511 | − | 0.723322i | \(-0.742614\pi\) | ||
0.690511 | − | 0.723322i | \(-0.257386\pi\) | |||||||
\(360\) | 1.54948e7 | + | 1.33297e6i | 0.332107 | + | 0.0285702i | ||||
\(361\) | −3.54953e7 | −0.754482 | ||||||||
\(362\) | −4.24359e7 | − | 1.28552e7i | −0.894555 | − | 0.270990i | ||||
\(363\) | 1.21586e7 | 0.254194 | ||||||||
\(364\) | −136632. | + | 204820.i | −0.00283300 | + | 0.00424686i | ||||
\(365\) | −5.85258e7 | − | 5.72270e7i | −1.20356 | − | 1.17685i | ||||
\(366\) | −4.62121e7 | − | 1.39991e7i | −0.942568 | − | 0.285534i | ||||
\(367\) | −5.48058e7 | −1.10874 | −0.554369 | − | 0.832271i | \(-0.687040\pi\) | ||||
−0.554369 | + | 0.832271i | \(0.687040\pi\) | |||||||
\(368\) | 2.09494e6 | + | 5.03600e6i | 0.0420367 | + | 0.101051i | ||||
\(369\) | −1.66342e7 | −0.331073 | ||||||||
\(370\) | −3.43664e7 | − | 6.25391e7i | −0.678467 | − | 1.23466i | ||||
\(371\) | − | 2.28207e6i | − | 0.0446897i | ||||||
\(372\) | −2.24236e7 | + | 3.36144e7i | −0.435588 | + | 0.652976i | ||||
\(373\) | 3.78565e7i | 0.729482i | 0.931109 | + | 0.364741i | \(0.118842\pi\) | ||||
−0.931109 | + | 0.364741i | \(0.881158\pi\) | |||||||
\(374\) | −9.80666e6 | − | 2.97075e6i | −0.187459 | − | 0.0567874i | ||||
\(375\) | −2.22411e7 | − | 2.07920e7i | −0.421756 | − | 0.394278i | ||||
\(376\) | −1.83679e7 | − | 2.23294e7i | −0.345538 | − | 0.420063i | ||||
\(377\) | − | 1.50687e6i | − | 0.0281224i | ||||||
\(378\) | 1.05314e6 | + | 319031.i | 0.0194990 | + | 0.00590687i | ||||
\(379\) | 3.60927e7i | 0.662982i | 0.943458 | + | 0.331491i | \(0.107552\pi\) | ||||
−0.943458 | + | 0.331491i | \(0.892448\pi\) | |||||||
\(380\) | 1.50324e7 | + | 7.11102e7i | 0.273954 | + | 1.29593i | ||||
\(381\) | −5.07839e7 | −0.918229 | ||||||||
\(382\) | −1.07305e7 | + | 3.54220e7i | −0.192499 | + | 0.635453i | ||||
\(383\) | −5.97603e7 | −1.06369 | −0.531847 | − | 0.846841i | \(-0.678502\pi\) | ||||
−0.531847 | + | 0.846841i | \(0.678502\pi\) | |||||||
\(384\) | −1.53340e7 | + | 2.88720e7i | −0.270807 | + | 0.509899i | ||||
\(385\) | −3.23170e6 | − | 3.15998e6i | −0.0566303 | − | 0.0553735i | ||||
\(386\) | 1.77895e7 | − | 5.87243e7i | 0.309315 | − | 1.02107i | ||||
\(387\) | 1.55313e6 | 0.0267963 | ||||||||
\(388\) | −5.17409e7 | + | 7.75630e7i | −0.885806 | + | 1.32788i | ||||
\(389\) | −6.96398e7 | −1.18306 | −0.591532 | − | 0.806281i | \(-0.701477\pi\) | ||||
−0.591532 | + | 0.806281i | \(0.701477\pi\) | |||||||
\(390\) | 795350. | + | 1.44736e6i | 0.0134080 | + | 0.0243996i | ||||
\(391\) | − | 1.71284e6i | − | 0.0286540i | ||||||
\(392\) | −3.78376e7 | − | 4.59984e7i | −0.628153 | − | 0.763632i | ||||
\(393\) | 3.25524e6i | 0.0536297i | ||||||||
\(394\) | 2.50115e7 | − | 8.25646e7i | 0.408932 | − | 1.34991i | ||||
\(395\) | 7.16675e6 | + | 7.00770e6i | 0.116287 | + | 0.113706i | ||||
\(396\) | 8.59402e6 | − | 1.28830e7i | 0.138392 | − | 0.207459i | ||||
\(397\) | 2.84760e7i | 0.455101i | 0.973766 | + | 0.227551i | \(0.0730717\pi\) | ||||
−0.973766 | + | 0.227551i | \(0.926928\pi\) | |||||||
\(398\) | 2.09969e7 | − | 6.93122e7i | 0.333047 | − | 1.09941i | ||||
\(399\) | 5.14270e6i | 0.0809603i | ||||||||
\(400\) | 5.85246e7 | − | 2.59012e7i | 0.914447 | − | 0.404706i | ||||
\(401\) | −1.00700e6 | −0.0156170 | −0.00780848 | − | 0.999970i | \(-0.502486\pi\) | ||||
−0.00780848 | + | 0.999970i | \(0.502486\pi\) | |||||||
\(402\) | −5.68528e7 | − | 1.72226e7i | −0.875132 | − | 0.265106i | ||||
\(403\) | −4.29091e6 | −0.0655593 | ||||||||
\(404\) | 4.23914e7 | + | 2.82785e7i | 0.642885 | + | 0.428857i | ||||
\(405\) | 5.16036e6 | − | 5.27747e6i | 0.0776809 | − | 0.0794440i | ||||
\(406\) | −3.95440e6 | − | 1.19791e6i | −0.0590884 | − | 0.0178998i | ||||
\(407\) | −7.10587e7 | −1.05398 | ||||||||
\(408\) | 7.92837e6 | − | 6.52176e6i | 0.116736 | − | 0.0960251i | ||||
\(409\) | 3.61611e7 | 0.528532 | 0.264266 | − | 0.964450i | \(-0.414870\pi\) | ||||
0.264266 | + | 0.964450i | \(0.414870\pi\) | |||||||
\(410\) | −5.99923e7 | + | 3.29669e7i | −0.870450 | + | 0.478329i | ||||
\(411\) | 3.85196e7i | 0.554826i | ||||||||
\(412\) | 3.98190e7 | + | 2.65625e7i | 0.569375 | + | 0.379819i | ||||
\(413\) | − | 4.82936e6i | − | 0.0685550i | ||||||
\(414\) | 2.47751e6 | + | 750517.i | 0.0349152 | + | 0.0105769i | ||||
\(415\) | 9.05505e7 | − | 9.26057e7i | 1.26691 | − | 1.29567i | ||||
\(416\) | −3.45418e6 | + | 346826.i | −0.0479805 | + | 0.00481762i | ||||
\(417\) | − | 3.02400e7i | − | 0.417036i | ||||||
\(418\) | 6.92667e7 | + | 2.09831e7i | 0.948409 | + | 0.287304i | ||||
\(419\) | 7.71961e7i | 1.04943i | 0.851278 | + | 0.524715i | \(0.175828\pi\) | ||||
−0.851278 | + | 0.524715i | \(0.824172\pi\) | |||||||
\(420\) | 4.43050e6 | − | 936589.i | 0.0598005 | − | 0.0126416i | ||||
\(421\) | 1.80523e6 | 0.0241928 | 0.0120964 | − | 0.999927i | \(-0.496150\pi\) | ||||
0.0120964 | + | 0.999927i | \(0.496150\pi\) | |||||||
\(422\) | −2.51473e7 | + | 8.30130e7i | −0.334622 | + | 1.10461i | ||||
\(423\) | −1.37226e7 | −0.181307 | ||||||||
\(424\) | 2.48500e7 | − | 2.04412e7i | 0.326008 | − | 0.268170i | ||||
\(425\) | −2.00929e7 | + | 450969.i | −0.261743 | + | 0.00587462i | ||||
\(426\) | −1.74667e7 | + | 5.76588e7i | −0.225934 | + | 0.745825i | ||||
\(427\) | −1.40598e7 | −0.180591 | ||||||||
\(428\) | 4.00590e6 | + | 2.67226e6i | 0.0510939 | + | 0.0340838i | ||||
\(429\) | 1.64453e6 | 0.0208290 | ||||||||
\(430\) | 5.60145e6 | − | 3.07810e6i | 0.0704523 | − | 0.0387149i | ||||
\(431\) | − | 8.38390e7i | − | 1.04716i | −0.851976 | − | 0.523581i | \(-0.824596\pi\) | ||
0.851976 | − | 0.523581i | \(-0.175404\pi\) | |||||||
\(432\) | 5.95933e6 | + | 1.43255e7i | 0.0739173 | + | 0.177689i | ||||
\(433\) | 3.21731e7i | 0.396305i | 0.980171 | + | 0.198153i | \(0.0634942\pi\) | ||||
−0.980171 | + | 0.198153i | \(0.936506\pi\) | |||||||
\(434\) | −3.41114e6 | + | 1.12604e7i | −0.0417283 | + | 0.137748i | ||||
\(435\) | −1.93764e7 | + | 1.98162e7i | −0.235399 | + | 0.240742i | ||||
\(436\) | 4.82119e7 | + | 3.21613e7i | 0.581694 | + | 0.388037i | ||||
\(437\) | 1.20982e7i | 0.144969i | ||||||||
\(438\) | 2.36760e7 | − | 7.81559e7i | 0.281764 | − | 0.930121i | ||||
\(439\) | − | 1.14441e8i | − | 1.35266i | −0.736597 | − | 0.676332i | \(-0.763569\pi\) | ||
0.736597 | − | 0.676332i | \(-0.236431\pi\) | |||||||
\(440\) | 5.46235e6 | − | 6.34956e7i | 0.0641242 | − | 0.745393i | ||||
\(441\) | −2.82683e7 | −0.329597 | ||||||||
\(442\) | 1.04335e6 | + | 316064.i | 0.0120827 | + | 0.00366023i | ||||
\(443\) | 3.67575e7 | 0.422799 | 0.211400 | − | 0.977400i | \(-0.432198\pi\) | ||||
0.211400 | + | 0.977400i | \(0.432198\pi\) | |||||||
\(444\) | 3.95076e7 | − | 5.92246e7i | 0.451369 | − | 0.676633i | ||||
\(445\) | 1.05062e8 | − | 1.07446e8i | 1.19224 | − | 1.21930i | ||||
\(446\) | −4.73459e7 | − | 1.43426e7i | −0.533676 | − | 0.161668i | ||||
\(447\) | 7.82636e6 | 0.0876268 | ||||||||
\(448\) | −1.83581e6 | + | 9.34033e6i | −0.0204170 | + | 0.103879i | ||||
\(449\) | 4.64770e6 | 0.0513451 | 0.0256725 | − | 0.999670i | \(-0.491827\pi\) | ||||
0.0256725 | + | 0.999670i | \(0.491827\pi\) | |||||||
\(450\) | 8.15185e6 | − | 2.92607e7i | 0.0894579 | − | 0.321105i | ||||
\(451\) | 6.81649e7i | 0.743072i | ||||||||
\(452\) | −2.83832e7 | + | 4.25484e7i | −0.307360 | + | 0.460753i | ||||
\(453\) | − | 6.09830e7i | − | 0.656016i | ||||||
\(454\) | 8.98323e7 | + | 2.72131e7i | 0.959987 | + | 0.290811i | ||||
\(455\) | 343827. | + | 336196.i | 0.00365011 | + | 0.00356910i | ||||
\(456\) | −5.59999e7 | + | 4.60647e7i | −0.590599 | + | 0.485819i | ||||
\(457\) | 1.37829e8i | 1.44408i | 0.691851 | + | 0.722040i | \(0.256795\pi\) | ||||
−0.691851 | + | 0.722040i | \(0.743205\pi\) | |||||||
\(458\) | 1.49523e8 | + | 4.52954e7i | 1.55637 | + | 0.471474i | ||||
\(459\) | − | 4.87238e6i | − | 0.0503852i | ||||||
\(460\) | 1.04227e7 | − | 2.20332e6i | 0.107080 | − | 0.0226362i | ||||
\(461\) | 6.11454e7 | 0.624110 | 0.312055 | − | 0.950064i | \(-0.398983\pi\) | ||||
0.312055 | + | 0.950064i | \(0.398983\pi\) | |||||||
\(462\) | 1.30735e6 | − | 4.31564e6i | 0.0132576 | − | 0.0437642i | ||||
\(463\) | 8.92817e6 | 0.0899538 | 0.0449769 | − | 0.998988i | \(-0.485679\pi\) | ||||
0.0449769 | + | 0.998988i | \(0.485679\pi\) | |||||||
\(464\) | −2.23764e7 | − | 5.37904e7i | −0.223994 | − | 0.538456i | ||||
\(465\) | 5.64278e7 | + | 5.51755e7i | 0.561221 | + | 0.548767i | ||||
\(466\) | −4.78302e7 | + | 1.57891e8i | −0.472655 | + | 1.56027i | ||||
\(467\) | 9.31715e7 | 0.914814 | 0.457407 | − | 0.889258i | \(-0.348778\pi\) | ||||
0.457407 | + | 0.889258i | \(0.348778\pi\) | |||||||
\(468\) | −914334. | + | 1.37065e6i | −0.00892005 | + | 0.0133718i | ||||
\(469\) | −1.72972e7 | −0.167671 | ||||||||
\(470\) | −4.94912e7 | + | 2.71964e7i | −0.476689 | + | 0.261949i | ||||
\(471\) | 2.45020e7i | 0.234498i | ||||||||
\(472\) | 5.25879e7 | − | 4.32580e7i | 0.500103 | − | 0.411378i | ||||
\(473\) | − | 6.36453e6i | − | 0.0601427i | ||||||
\(474\) | −2.89923e6 | + | 9.57055e6i | −0.0272237 | + | 0.0898673i | ||||
\(475\) | 1.41921e8 | − | 3.18530e6i | 1.32424 | − | 0.0297214i | ||||
\(476\) | 1.65886e6 | − | 2.48674e6i | 0.0153811 | − | 0.0230574i | ||||
\(477\) | − | 1.52715e7i | − | 0.140711i | ||||||
\(478\) | 4.24195e7 | − | 1.40030e8i | 0.388402 | − | 1.28214i | ||||
\(479\) | 7.79984e7i | 0.709707i | 0.934922 | + | 0.354854i | \(0.115469\pi\) | ||||
−0.934922 | + | 0.354854i | \(0.884531\pi\) | |||||||
\(480\) | 4.98841e7 | + | 3.98553e7i | 0.451064 | + | 0.360381i | ||||
\(481\) | 7.56007e6 | 0.0679345 | ||||||||
\(482\) | −1.44385e8 | − | 4.37388e7i | −1.28938 | − | 0.390594i | ||||
\(483\) | 753772. | 0.00668958 | ||||||||
\(484\) | 4.15268e7 | + | 2.77018e7i | 0.366262 | + | 0.244327i | ||||
\(485\) | 1.30203e8 | + | 1.27314e8i | 1.14129 | + | 1.11596i | ||||
\(486\) | 7.04759e6 | + | 2.13494e6i | 0.0613948 | + | 0.0185985i | ||||
\(487\) | −1.84100e8 | −1.59392 | −0.796962 | − | 0.604030i | \(-0.793561\pi\) | ||||
−0.796962 | + | 0.604030i | \(0.793561\pi\) | |||||||
\(488\) | −1.25938e8 | − | 1.53101e8i | −1.08367 | − | 1.31740i | ||||
\(489\) | 4.71202e7 | 0.402977 | ||||||||
\(490\) | −1.01951e8 | + | 5.60241e7i | −0.866572 | + | 0.476197i | ||||
\(491\) | 1.36182e8i | 1.15047i | 0.817987 | + | 0.575236i | \(0.195090\pi\) | ||||
−0.817987 | + | 0.575236i | \(0.804910\pi\) | |||||||
\(492\) | −5.68127e7 | − | 3.78987e7i | −0.477035 | − | 0.318221i | ||||
\(493\) | 1.82951e7i | 0.152684i | ||||||||
\(494\) | −7.36942e6 | − | 2.23244e6i | −0.0611297 | − | 0.0185182i | ||||
\(495\) | −2.16264e7 | − | 2.11465e7i | −0.178307 | − | 0.174350i | ||||
\(496\) | −1.53171e8 | + | 6.37183e7i | −1.25526 | + | 0.522179i | ||||
\(497\) | 1.75424e7i | 0.142896i | ||||||||
\(498\) | 1.23666e8 | + | 3.74626e7i | 1.00130 | + | 0.303326i | ||||
\(499\) | 5.25199e7i | 0.422690i | 0.977412 | + | 0.211345i | \(0.0677844\pi\) | ||||
−0.977412 | + | 0.211345i | \(0.932216\pi\) | |||||||
\(500\) | −2.85908e7 | − | 1.21686e8i | −0.228726 | − | 0.973491i | ||||
\(501\) | 2.68044e7 | 0.213154 | ||||||||
\(502\) | 2.44691e7 | − | 8.07741e7i | 0.193422 | − | 0.638500i | ||||
\(503\) | 7.30908e7 | 0.574326 | 0.287163 | − | 0.957882i | \(-0.407288\pi\) | ||||
0.287163 | + | 0.957882i | \(0.407288\pi\) | |||||||
\(504\) | 2.87005e6 | + | 3.48906e6i | 0.0224180 | + | 0.0272531i | ||||
\(505\) | 6.95822e7 | − | 7.11614e7i | 0.540286 | − | 0.552549i | ||||
\(506\) | 3.07552e6 | − | 1.01525e7i | 0.0237393 | − | 0.0783650i | ||||
\(507\) | 7.50675e7 | 0.576008 | ||||||||
\(508\) | −1.73448e8 | − | 1.15704e8i | −1.32305 | − | 0.882585i | ||||
\(509\) | −1.93773e8 | −1.46940 | −0.734699 | − | 0.678393i | \(-0.762677\pi\) | ||||
−0.734699 | + | 0.678393i | \(0.762677\pi\) | |||||||
\(510\) | −9.65643e6 | − | 1.75725e7i | −0.0727957 | − | 0.132472i | ||||
\(511\) | − | 2.37786e7i | − | 0.178207i | ||||||
\(512\) | −1.18153e8 | + | 6.36737e7i | −0.880306 | + | 0.474406i | ||||
\(513\) | 3.44148e7i | 0.254913i | ||||||||
\(514\) | −797494. | + | 2.63258e6i | −0.00587270 | + | 0.0193862i | ||||
\(515\) | 6.53598e7 | − | 6.68432e7i | 0.478508 | − | 0.489368i | ||||
\(516\) | 5.30458e6 | + | 3.53859e6i | 0.0386102 | + | 0.0257561i | ||||
\(517\) | 5.62333e7i | 0.406932i | ||||||||
\(518\) | 6.01001e6 | − | 1.98395e7i | 0.0432400 | − | 0.142738i | ||||
\(519\) | − | 9.41139e7i | − | 0.673212i | ||||||
\(520\) | −581150. | + | 6.75542e6i | −0.00413312 | + | 0.0480443i | ||||
\(521\) | 2.38564e8 | 1.68691 | 0.843453 | − | 0.537203i | \(-0.180519\pi\) | ||||
0.843453 | + | 0.537203i | \(0.180519\pi\) | |||||||
\(522\) | −2.64627e7 | − | 8.01640e6i | −0.186047 | − | 0.0563596i | ||||
\(523\) | 4.75494e7 | 0.332384 | 0.166192 | − | 0.986093i | \(-0.446853\pi\) | ||||
0.166192 | + | 0.986093i | \(0.446853\pi\) | |||||||
\(524\) | −7.41660e6 | + | 1.11180e7i | −0.0515479 | + | 0.0772738i | ||||
\(525\) | −198459. | − | 8.84233e6i | −0.00137149 | − | 0.0611067i | ||||
\(526\) | −1.29102e8 | − | 3.91093e7i | −0.887109 | − | 0.268734i | ||||
\(527\) | 5.20964e7 | 0.355939 | ||||||||
\(528\) | 5.87042e7 | − | 2.44206e7i | 0.398811 | − | 0.165903i | ||||
\(529\) | −1.46263e8 | −0.988022 | ||||||||
\(530\) | −3.02663e7 | − | 5.50777e7i | −0.203297 | − | 0.369955i | ||||
\(531\) | − | 3.23179e7i | − | 0.215854i | ||||||
\(532\) | −1.17169e7 | + | 1.75644e7i | −0.0778177 | + | 0.116654i | ||||
\(533\) | − | 7.25219e6i | − | 0.0478947i | ||||||
\(534\) | 1.43484e8 | + | 4.34661e7i | 0.942282 | + | 0.285448i | ||||
\(535\) | 6.57539e6 | − | 6.72462e6i | 0.0429398 | − | 0.0439144i | ||||
\(536\) | −1.54937e8 | − | 1.88353e8i | −1.00614 | − | 1.22315i | ||||
\(537\) | 1.74417e8i | 1.12633i | ||||||||
\(538\) | 1.58309e8 | + | 4.79568e7i | 1.01662 | + | 0.307967i | ||||
\(539\) | 1.15840e8i | 0.739761i | ||||||||
\(540\) | 2.96487e7 | − | 6.26762e6i | 0.188289 | − | 0.0398035i | ||||
\(541\) | 7.93945e6 | 0.0501417 | 0.0250708 | − | 0.999686i | \(-0.492019\pi\) | ||||
0.0250708 | + | 0.999686i | \(0.492019\pi\) | |||||||
\(542\) | −3.20423e7 | + | 1.05774e8i | −0.201246 | + | 0.664325i | ||||
\(543\) | −8.63995e7 | −0.539649 | ||||||||
\(544\) | 4.19376e7 | − | 4.21086e6i | 0.260499 | − | 0.0261561i | ||||
\(545\) | 7.91361e7 | − | 8.09322e7i | 0.488861 | − | 0.499956i | ||||
\(546\) | −139091. | + | 459149.i | −0.000854519 | + | 0.00282082i | ||||
\(547\) | −2.71214e8 | −1.65711 | −0.828554 | − | 0.559909i | \(-0.810836\pi\) | ||||
−0.828554 | + | 0.559909i | \(0.810836\pi\) | |||||||
\(548\) | −8.77616e7 | + | 1.31561e8i | −0.533289 | + | 0.799436i | ||||
\(549\) | −9.40880e7 | −0.568613 | ||||||||
\(550\) | −1.19907e8 | − | 3.34052e7i | −0.720701 | − | 0.200783i | ||||
\(551\) | − | 1.29222e8i | − | 0.772473i | ||||||
\(552\) | 6.75177e6 | + | 8.20798e6i | 0.0401421 | + | 0.0487999i | ||||
\(553\) | 2.91180e6i | 0.0172181i | ||||||||
\(554\) | −4.96048e6 | + | 1.63749e7i | −0.0291739 | + | 0.0963049i | ||||
\(555\) | −9.94189e7 | − | 9.72126e7i | −0.581554 | − | 0.568648i | ||||
\(556\) | 6.88975e7 | − | 1.03282e8i | 0.400847 | − | 0.600897i | ||||
\(557\) | 2.95321e7i | 0.170895i | 0.996343 | + | 0.0854474i | \(0.0272320\pi\) | ||||
−0.996343 | + | 0.0854474i | \(0.972768\pi\) | |||||||
\(558\) | −2.28272e7 | + | 7.53542e7i | −0.131386 | + | 0.433715i | ||||
\(559\) | 677134.i | 0.00387650i | ||||||||
\(560\) | 1.72659e7 | + | 6.89542e6i | 0.0983160 | + | 0.0392642i | ||||
\(561\) | −1.99664e7 | −0.113087 | ||||||||
\(562\) | 1.10199e8 | + | 3.33828e7i | 0.620824 | + | 0.188068i | ||||
\(563\) | 3.69382e7 | 0.206991 | 0.103495 | − | 0.994630i | \(-0.466997\pi\) | ||||
0.103495 | + | 0.994630i | \(0.466997\pi\) | |||||||
\(564\) | −4.68682e7 | − | 3.12649e7i | −0.261241 | − | 0.174269i | ||||
\(565\) | 7.14250e7 | + | 6.98399e7i | 0.396009 | + | 0.387221i | ||||
\(566\) | 1.96046e8 | + | 5.93888e7i | 1.08121 | + | 0.327533i | ||||
\(567\) | 2.14420e6 | 0.0117629 | ||||||||
\(568\) | −1.91023e8 | + | 1.57133e8i | −1.04242 | + | 0.857478i | ||||
\(569\) | −4.40705e7 | −0.239227 | −0.119614 | − | 0.992821i | \(-0.538166\pi\) | ||||
−0.119614 | + | 0.992821i | \(0.538166\pi\) | |||||||
\(570\) | 6.82056e7 | + | 1.24119e8i | 0.368295 | + | 0.670214i | ||||
\(571\) | − | 1.86429e8i | − | 1.00139i | −0.865623 | − | 0.500697i | \(-0.833077\pi\) | ||
0.865623 | − | 0.500697i | \(-0.166923\pi\) | |||||||
\(572\) | 5.61674e6 | + | 3.74682e6i | 0.0300121 | + | 0.0200205i | ||||
\(573\) | 7.21193e7i | 0.383343i | ||||||||
\(574\) | −1.90315e7 | − | 5.76526e6i | −0.100632 | − | 0.0304848i | ||||
\(575\) | −466873. | − | 2.08015e7i | −0.00245581 | − | 0.109419i | ||||
\(576\) | −1.22852e7 | + | 6.25051e7i | −0.0642855 | + | 0.327076i | ||||
\(577\) | − | 9.75841e7i | − | 0.507986i | −0.967206 | − | 0.253993i | \(-0.918256\pi\) | ||
0.967206 | − | 0.253993i | \(-0.0817440\pi\) | |||||||
\(578\) | 1.72140e8 | + | 5.21466e7i | 0.891450 | + | 0.270049i | ||||
\(579\) | − | 1.19563e8i | − | 0.615971i | ||||||
\(580\) | −1.11327e8 | + | 2.35340e7i | −0.570579 | + | 0.120618i | ||||
\(581\) | 3.76250e7 | 0.191844 | ||||||||
\(582\) | −5.26723e7 | + | 1.73875e8i | −0.267186 | + | 0.881998i | ||||
\(583\) | −6.25808e7 | −0.315817 | ||||||||
\(584\) | 2.58930e8 | − | 2.12992e8i | 1.30000 | − | 1.06936i | ||||
\(585\) | 2.30088e6 | + | 2.24981e6i | 0.0114928 | + | 0.0112377i | ||||
\(586\) | −1.88287e7 | + | 6.21547e7i | −0.0935678 | + | 0.308874i | ||||
\(587\) | 2.62750e8 | 1.29906 | 0.649529 | − | 0.760337i | \(-0.274966\pi\) | ||||
0.649529 | + | 0.760337i | \(0.274966\pi\) | |||||||
\(588\) | −9.65479e7 | − | 6.44053e7i | −0.474910 | − | 0.316803i | ||||
\(589\) | −3.67969e8 | −1.80080 | ||||||||
\(590\) | −6.40499e7 | − | 1.16556e8i | −0.311862 | − | 0.567518i | ||||
\(591\) | − | 1.68102e8i | − | 0.814347i | ||||||
\(592\) | 2.69870e8 | − | 1.12264e8i | 1.30074 | − | 0.541097i | ||||
\(593\) | 1.29038e8i | 0.618806i | 0.950931 | + | 0.309403i | \(0.100129\pi\) | ||||
−0.950931 | + | 0.309403i | \(0.899871\pi\) | |||||||
\(594\) | 8.74872e6 | − | 2.88801e7i | 0.0417431 | − | 0.137797i | ||||
\(595\) | −4.17444e6 | − | 4.08180e6i | −0.0198174 | − | 0.0193776i | ||||
\(596\) | 2.67302e7 | + | 1.78312e7i | 0.126260 | + | 0.0842254i | ||||
\(597\) | − | 1.41120e8i | − | 0.663231i | ||||||
\(598\) | −327211. | + | 1.08015e6i | −0.00153012 | + | 0.00505102i | ||||
\(599\) | 3.16683e8i | 1.47348i | 0.676176 | + | 0.736740i | \(0.263636\pi\) | ||||
−0.676176 | + | 0.736740i | \(0.736364\pi\) | |||||||
\(600\) | 9.45083e7 | − | 8.13645e7i | 0.437538 | − | 0.376688i | ||||
\(601\) | −6.91171e7 | −0.318392 | −0.159196 | − | 0.987247i | \(-0.550890\pi\) | ||||
−0.159196 | + | 0.987247i | \(0.550890\pi\) | |||||||
\(602\) | 1.77697e6 | + | 538300.i | 0.00814497 | + | 0.00246737i | ||||
\(603\) | −1.15752e8 | −0.527932 | ||||||||
\(604\) | 1.38941e8 | − | 2.08282e8i | 0.630551 | − | 0.945239i | ||||
\(605\) | 6.81631e7 | − | 6.97101e7i | 0.307810 | − | 0.314796i | ||||
\(606\) | 9.50296e7 | + | 2.87875e7i | 0.427013 | + | 0.129356i | ||||
\(607\) | −3.08877e8 | −1.38108 | −0.690542 | − | 0.723292i | \(-0.742628\pi\) | ||||
−0.690542 | + | 0.723292i | \(0.742628\pi\) | |||||||
\(608\) | −2.96215e8 | + | 2.97423e7i | −1.31794 | + | 0.132332i | ||||
\(609\) | −8.05116e6 | −0.0356457 | ||||||||
\(610\) | −3.39334e8 | + | 1.86470e8i | −1.49499 | + | 0.821524i | ||||
\(611\) | − | 5.98277e6i | − | 0.0262288i | ||||||
\(612\) | 1.11010e7 | − | 1.66412e7i | 0.0484294 | − | 0.0725989i | ||||
\(613\) | − | 2.65213e8i | − | 1.15137i | −0.817673 | − | 0.575683i | \(-0.804736\pi\) | ||
0.817673 | − | 0.575683i | \(-0.195264\pi\) | |||||||
\(614\) | 1.59184e8 | + | 4.82220e7i | 0.687693 | + | 0.208324i | ||||
\(615\) | −9.32537e7 | + | 9.53702e7i | −0.400904 | + | 0.410003i | ||||
\(616\) | 1.42977e7 | − | 1.17611e7i | 0.0611680 | − | 0.0503159i | ||||
\(617\) | − | 3.68044e8i | − | 1.56691i | −0.621449 | − | 0.783455i | \(-0.713456\pi\) | ||
0.621449 | − | 0.783455i | \(-0.286544\pi\) | |||||||
\(618\) | 8.92630e7 | + | 2.70407e7i | 0.378187 | + | 0.114565i | ||||
\(619\) | 9.59461e7i | 0.404534i | 0.979330 | + | 0.202267i | \(0.0648309\pi\) | ||||
−0.979330 | + | 0.202267i | \(0.935169\pi\) | |||||||
\(620\) | 6.70146e7 | + | 3.17010e8i | 0.281187 | + | 1.33014i | ||||
\(621\) | 5.04421e6 | 0.0210629 | ||||||||
\(622\) | 1.30338e8 | − | 4.30256e8i | 0.541628 | − | 1.78795i | ||||
\(623\) | 4.36546e7 | 0.180537 | ||||||||
\(624\) | −6.24566e6 | + | 2.59815e6i | −0.0257054 | + | 0.0106933i | ||||
\(625\) | −2.43895e8 | + | 1.09536e7i | −0.998993 | + | 0.0448658i | ||||
\(626\) | 1.40361e7 | − | 4.63342e7i | 0.0572169 | − | 0.188877i | ||||
\(627\) | 1.41027e8 | 0.572137 | ||||||||
\(628\) | −5.58244e7 | + | 8.36846e7i | −0.225396 | + | 0.337883i | ||||
\(629\) | −9.17876e7 | −0.368835 | ||||||||
\(630\) | 7.73318e6 | − | 4.24953e6i | 0.0309269 | − | 0.0169949i | ||||
\(631\) | 2.46173e8i | 0.979832i | 0.871770 | + | 0.489916i | \(0.162973\pi\) | ||||
−0.871770 | + | 0.489916i | \(0.837027\pi\) | |||||||
\(632\) | −3.17072e7 | + | 2.60819e7i | −0.125605 | + | 0.103321i | ||||
\(633\) | 1.69015e8i | 0.666367i | ||||||||
\(634\) | −1.87073e7 | + | 6.17539e7i | −0.0734078 | + | 0.242324i | ||||
\(635\) | −2.84701e8 | + | 2.91163e8i | −1.11191 | + | 1.13714i | ||||
\(636\) | 3.47941e7 | − | 5.21587e7i | 0.135249 | − | 0.202747i | ||||
\(637\) | − | 1.23244e7i | − | 0.0476813i | ||||||
\(638\) | −3.28502e7 | + | 1.08441e8i | −0.126496 | + | 0.417571i | ||||
\(639\) | 1.17393e8i | 0.449926i | ||||||||
\(640\) | 7.95700e7 | + | 2.49776e8i | 0.303536 | + | 0.952820i | ||||
\(641\) | −1.40284e8 | −0.532641 | −0.266321 | − | 0.963884i | \(-0.585808\pi\) | ||||
−0.266321 | + | 0.963884i | \(0.585808\pi\) | |||||||
\(642\) | 8.98012e6 | + | 2.72037e6i | 0.0339373 | + | 0.0102807i | ||||
\(643\) | 1.91656e8 | 0.720924 | 0.360462 | − | 0.932774i | \(-0.382619\pi\) | ||||
0.360462 | + | 0.932774i | \(0.382619\pi\) | |||||||
\(644\) | 2.57444e6 | + | 1.71736e6i | 0.00963886 | + | 0.00642990i | ||||
\(645\) | 8.70706e6 | − | 8.90468e6i | 0.0324483 | − | 0.0331848i | ||||
\(646\) | 8.94729e7 | + | 2.71042e7i | 0.331890 | + | 0.100540i | ||||
\(647\) | 4.33268e8 | 1.59972 | 0.799860 | − | 0.600187i | \(-0.204907\pi\) | ||||
0.799860 | + | 0.600187i | \(0.204907\pi\) | |||||||
\(648\) | 1.92063e7 | + | 2.33486e7i | 0.0705859 | + | 0.0858097i | ||||
\(649\) | −1.32435e8 | −0.484470 | ||||||||
\(650\) | 1.27571e7 | + | 3.55405e6i | 0.0464528 | + | 0.0129415i | ||||
\(651\) | 2.29262e7i | 0.0830977i | ||||||||
\(652\) | 1.60935e8 | + | 1.07357e8i | 0.580641 | + | 0.387335i | ||||
\(653\) | − | 1.61233e8i | − | 0.579048i | −0.957171 | − | 0.289524i | \(-0.906503\pi\) | ||
0.957171 | − | 0.289524i | \(-0.0934969\pi\) | |||||||
\(654\) | 1.08078e8 | + | 3.27402e7i | 0.386369 | + | 0.117044i | ||||
\(655\) | 1.86635e7 | + | 1.82493e7i | 0.0664155 | + | 0.0649415i | ||||
\(656\) | −1.07692e8 | − | 2.58879e8i | −0.381480 | − | 0.917035i | ||||
\(657\) | − | 1.59126e8i | − | 0.561105i | ||||||
\(658\) | −1.57002e7 | − | 4.75611e6i | −0.0551098 | − | 0.0166945i | ||||
\(659\) | − | 2.39459e8i | − | 0.836711i | −0.908283 | − | 0.418356i | \(-0.862607\pi\) | ||
0.908283 | − | 0.418356i | \(-0.137393\pi\) | |||||||
\(660\) | −2.56839e7 | − | 1.21497e8i | −0.0893366 | − | 0.422603i | ||||
\(661\) | 3.06751e8 | 1.06214 | 0.531071 | − | 0.847328i | \(-0.321790\pi\) | ||||
0.531071 | + | 0.847328i | \(0.321790\pi\) | |||||||
\(662\) | −1.57716e7 | + | 5.20632e7i | −0.0543629 | + | 0.179456i | ||||
\(663\) | 2.12426e6 | 0.00728899 | ||||||||
\(664\) | 3.37019e8 | + | 4.09707e8i | 1.15120 | + | 1.39949i | ||||
\(665\) | 2.94850e7 | + | 2.88307e7i | 0.100262 | + | 0.0980370i | ||||
\(666\) | 4.02188e7 | − | 1.32765e8i | 0.136146 | − | 0.449429i | ||||
\(667\) | −1.89403e7 | −0.0638277 | ||||||||
\(668\) | 9.15483e7 | + | 6.10701e7i | 0.307129 | + | 0.204880i | ||||
\(669\) | −9.63963e7 | −0.321945 | ||||||||
\(670\) | −4.17468e8 | + | 2.29407e8i | −1.38803 | + | 0.762749i | ||||
\(671\) | 3.85560e8i | 1.27622i | ||||||||
\(672\) | 1.85308e6 | + | 1.84556e7i | 0.00610642 | + | 0.0608163i | ||||
\(673\) | − | 4.75380e8i | − | 1.55954i | −0.626068 | − | 0.779769i | \(-0.715337\pi\) | ||
0.626068 | − | 0.779769i | \(-0.284663\pi\) | |||||||
\(674\) | 1.07463e8 | − | 3.54742e8i | 0.350977 | − | 1.15860i | ||||
\(675\) | −1.32808e6 | − | 5.91725e7i | −0.00431830 | − | 0.192402i | ||||
\(676\) | 2.56387e8 | + | 1.71031e8i | 0.829957 | + | 0.553649i | ||||
\(677\) | − | 1.03793e8i | − | 0.334505i | −0.985914 | − | 0.167252i | \(-0.946511\pi\) | ||
0.985914 | − | 0.167252i | \(-0.0534895\pi\) | |||||||
\(678\) | −2.88942e7 | + | 9.53816e7i | −0.0927089 | + | 0.306038i | ||||
\(679\) | 5.29007e7i | 0.168986i | ||||||||
\(680\) | 7.05581e6 | − | 8.20182e7i | 0.0224399 | − | 0.260846i | ||||
\(681\) | 1.82899e8 | 0.579122 | ||||||||
\(682\) | 3.08792e8 | + | 9.35430e7i | 0.973448 | + | 0.294889i | ||||
\(683\) | −1.94870e8 | −0.611621 | −0.305810 | − | 0.952092i | \(-0.598927\pi\) | ||||
−0.305810 | + | 0.952092i | \(0.598927\pi\) | |||||||
\(684\) | −7.84091e7 | + | 1.17541e8i | −0.245018 | + | 0.367299i | ||||
\(685\) | 2.20848e8 | + | 2.15947e8i | 0.687102 | + | 0.671853i | ||||
\(686\) | −6.50512e7 | − | 1.97061e7i | −0.201504 | − | 0.0610419i | ||||
\(687\) | 3.04429e8 | 0.938893 | ||||||||
\(688\) | 1.00552e7 | + | 2.41715e7i | 0.0308762 | + | 0.0742229i | ||||
\(689\) | 6.65810e6 | 0.0203560 | ||||||||
\(690\) | 1.81923e7 | − | 9.99699e6i | 0.0553783 | − | 0.0304314i | ||||
\(691\) | − | 4.76743e8i | − | 1.44494i | −0.691402 | − | 0.722471i | \(-0.743006\pi\) | ||
0.691402 | − | 0.722471i | \(-0.256994\pi\) | |||||||
\(692\) | 2.14425e8 | − | 3.21438e8i | 0.647079 | − | 0.970016i | ||||
\(693\) | − | 8.78666e6i | − | 0.0264012i | ||||||
\(694\) | 4.73757e7 | + | 1.43516e7i | 0.141735 | + | 0.0429361i | ||||
\(695\) | −1.73377e8 | − | 1.69529e8i | −0.516461 | − | 0.504999i | ||||
\(696\) | −7.21168e7 | − | 8.76708e7i | −0.213899 | − | 0.260032i | ||||
\(697\) | 8.80496e7i | 0.260033i | ||||||||
\(698\) | −7.32869e7 | − | 2.22010e7i | −0.215506 | − | 0.0652838i | ||||
\(699\) | 3.21466e8i | 0.941246i | ||||||||
\(700\) | 1.94682e7 | − | 3.06524e7i | 0.0567585 | − | 0.0893655i | ||||
\(701\) | −1.50161e8 | −0.435915 | −0.217958 | − | 0.975958i | \(-0.569939\pi\) | ||||
−0.217958 | + | 0.975958i | \(0.569939\pi\) | |||||||
\(702\) | −930793. | + | 3.07261e6i | −0.00269055 | + | 0.00888170i | ||||
\(703\) | 6.48317e8 | 1.86604 | ||||||||
\(704\) | 2.56138e8 | + | 5.03430e7i | 0.734101 | + | 0.144285i | ||||
\(705\) | −7.69306e7 | + | 7.86766e7i | −0.219549 | + | 0.224532i | ||||
\(706\) | 1.01764e8 | − | 3.35931e8i | 0.289189 | − | 0.954633i | ||||
\(707\) | 2.89124e7 | 0.0818136 | ||||||||
\(708\) | 7.36317e7 | − | 1.10379e8i | 0.207475 | − | 0.311019i | ||||
\(709\) | 2.76865e8 | 0.776836 | 0.388418 | − | 0.921483i | \(-0.373022\pi\) | ||||
0.388418 | + | 0.921483i | \(0.373022\pi\) | |||||||
\(710\) | 2.32659e8 | + | 4.23386e8i | 0.650046 | + | 1.18294i | ||||
\(711\) | 1.94857e7i | 0.0542133i | ||||||||
\(712\) | 3.91027e8 | + | 4.75364e8i | 1.08335 | + | 1.31700i | ||||
\(713\) | 5.39337e7i | 0.148796i | ||||||||
\(714\) | 1.68872e6 | − | 5.57458e6i | 0.00463941 | − | 0.0153150i | ||||
\(715\) | 9.21945e6 | − | 9.42870e6i | 0.0252224 | − | 0.0257949i | ||||
\(716\) | −3.97384e8 | + | 5.95705e8i | −1.08261 | + | 1.62290i | ||||
\(717\) | − | 2.85100e8i | − | 0.773465i | ||||||
\(718\) | 1.55244e8 | − | 5.12472e8i | 0.419413 | − | 1.38451i | ||||
\(719\) | − | 4.05407e8i | − | 1.09070i | −0.838209 | − | 0.545349i | \(-0.816397\pi\) | ||
0.838209 | − | 0.545349i | \(-0.183603\pi\) | |||||||
\(720\) | 1.15543e8 | + | 4.61439e7i | 0.309560 | + | 0.123628i | ||||
\(721\) | 2.71579e7 | 0.0724587 | ||||||||
\(722\) | −2.71766e8 | − | 8.23267e7i | −0.722077 | − | 0.218740i | ||||
\(723\) | −2.93967e8 | −0.777829 | ||||||||
\(724\) | −2.95090e8 | − | 1.96849e8i | −0.777569 | − | 0.518702i | ||||
\(725\) | 4.98675e6 | + | 2.22184e8i | 0.0130859 | + | 0.583042i | ||||
\(726\) | 9.30915e7 | + | 2.82004e7i | 0.243276 | + | 0.0736963i | ||||
\(727\) | −2.43401e8 | −0.633460 | −0.316730 | − | 0.948516i | \(-0.602585\pi\) | ||||
−0.316730 | + | 0.948516i | \(0.602585\pi\) | |||||||
\(728\) | −1.52116e6 | + | 1.25129e6i | −0.00394258 | + | 0.00324311i | ||||
\(729\) | 1.43489e7 | 0.0370370 | ||||||||
\(730\) | −3.15367e8 | − | 5.73896e8i | −0.810676 | − | 1.47525i | ||||
\(731\) | − | 8.22116e6i | − | 0.0210465i | ||||||
\(732\) | −3.21349e8 | − | 2.14366e8i | −0.819302 | − | 0.546541i | ||||
\(733\) | 6.38589e8i | 1.62147i | 0.585411 | + | 0.810737i | \(0.300933\pi\) | ||||
−0.585411 | + | 0.810737i | \(0.699067\pi\) | |||||||
\(734\) | −4.19616e8 | − | 1.27115e8i | −1.06112 | − | 0.321447i | ||||
\(735\) | −1.58476e8 | + | 1.62073e8i | −0.399118 | + | 0.408177i | ||||
\(736\) | 4.35936e6 | + | 4.34166e7i | 0.0109343 | + | 0.108899i | ||||
\(737\) | 4.74339e8i | 1.18491i | ||||||||
\(738\) | −1.27358e8 | − | 3.85809e7i | −0.316853 | − | 0.0959850i | ||||
\(739\) | 1.88890e7i | 0.0468031i | 0.999726 | + | 0.0234016i | \(0.00744963\pi\) | ||||
−0.999726 | + | 0.0234016i | \(0.992550\pi\) | |||||||
\(740\) | −1.18072e8 | − | 5.58533e8i | −0.291374 | − | 1.37833i | ||||
\(741\) | −1.50042e7 | −0.0368771 | ||||||||
\(742\) | 5.29298e6 | − | 1.74725e7i | 0.0129565 | − | 0.0427703i | ||||
\(743\) | −5.63528e8 | −1.37388 | −0.686940 | − | 0.726714i | \(-0.741047\pi\) | ||||
−0.686940 | + | 0.726714i | \(0.741047\pi\) | |||||||
\(744\) | −2.49648e8 | + | 2.05357e8i | −0.606191 | + | 0.498644i | ||||
\(745\) | 4.38756e7 | − | 4.48714e7i | 0.106110 | − | 0.108518i | ||||
\(746\) | −8.78034e7 | + | 2.89845e8i | −0.211492 | + | 0.698151i | ||||
\(747\) | 2.51785e8 | 0.604044 | ||||||||
\(748\) | −6.81934e7 | − | 4.54906e7i | −0.162944 | − | 0.108697i | ||||
\(749\) | 2.73216e6 | 0.00650222 | ||||||||
\(750\) | −1.22062e8 | − | 2.10777e8i | −0.289333 | − | 0.499620i | ||||
\(751\) | − | 1.95339e8i | − | 0.461178i | −0.973051 | − | 0.230589i | \(-0.925935\pi\) | ||
0.973051 | − | 0.230589i | \(-0.0740652\pi\) | |||||||
\(752\) | −8.88417e7 | − | 2.13565e8i | −0.208912 | − | 0.502200i | ||||
\(753\) | − | 1.64456e8i | − | 0.385182i | ||||||
\(754\) | 3.49500e6 | − | 1.15372e7i | 0.00815328 | − | 0.0269145i | ||||
\(755\) | −3.49639e8 | − | 3.41879e8i | −0.812416 | − | 0.794387i | ||||
\(756\) | 7.32333e6 | + | 4.88526e6i | 0.0169490 | + | 0.0113063i | ||||
\(757\) | 6.04178e8i | 1.39276i | 0.717671 | + | 0.696382i | \(0.245208\pi\) | ||||
−0.717671 | + | 0.696382i | \(0.754792\pi\) | |||||||
\(758\) | −8.37123e7 | + | 2.76340e8i | −0.192213 | + | 0.634507i | ||||
\(759\) | − | 2.06705e7i | − | 0.0472745i | ||||||
\(760\) | −4.98368e7 | + | 5.79314e8i | −0.113530 | + | 1.31969i | ||||
\(761\) | −6.11654e8 | −1.38788 | −0.693940 | − | 0.720033i | \(-0.744127\pi\) | ||||
−0.693940 | + | 0.720033i | \(0.744127\pi\) | |||||||
\(762\) | −3.88822e8 | − | 1.17787e8i | −0.878791 | − | 0.266214i | ||||
\(763\) | 3.28822e7 | 0.0740264 | ||||||||
\(764\) | −1.64314e8 | + | 2.46317e8i | −0.368463 | + | 0.552351i | ||||
\(765\) | −2.79352e7 | − | 2.73152e7i | −0.0623975 | − | 0.0610127i | ||||
\(766\) | −4.57549e8 | − | 1.38606e8i | −1.01801 | − | 0.308388i | ||||
\(767\) | 1.40900e7 | 0.0312265 | ||||||||
\(768\) | −1.84368e8 | + | 1.85491e8i | −0.407007 | + | 0.409486i | ||||
\(769\) | 1.56867e8 | 0.344948 | 0.172474 | − | 0.985014i | \(-0.444824\pi\) | ||||
0.172474 | + | 0.985014i | \(0.444824\pi\) | |||||||
\(770\) | −1.74140e7 | − | 3.16896e7i | −0.0381441 | − | 0.0694136i | ||||
\(771\) | 5.35994e6i | 0.0116949i | ||||||||
\(772\) | 2.72407e8 | − | 4.08356e8i | 0.592060 | − | 0.887539i | ||||
\(773\) | 6.26937e8i | 1.35733i | 0.734448 | + | 0.678665i | \(0.237441\pi\) | ||||
−0.734448 | + | 0.678665i | \(0.762559\pi\) | |||||||
\(774\) | 1.18914e7 | + | 3.60229e6i | 0.0256454 | + | 0.00776882i | ||||
\(775\) | 6.32684e8 | − | 1.42001e7i | 1.35920 | − | 0.0305061i | ||||
\(776\) | −5.76046e8 | + | 4.73848e8i | −1.23274 | + | 1.01404i | ||||
\(777\) | − | 4.03932e7i | − | 0.0861083i | ||||||
\(778\) | −5.33190e8 | − | 1.61520e8i | −1.13225 | − | 0.342996i | ||||
\(779\) | − | 6.21915e8i | − | 1.31558i | ||||||
\(780\) | 2.73256e6 | + | 1.29263e7i | 0.00575819 | + | 0.0272389i | ||||
\(781\) | 4.81063e8 | 1.00983 | ||||||||
\(782\) | 3.97270e6 | − | 1.31142e7i | 0.00830741 | − | 0.0274233i | ||||
\(783\) | −5.38781e7 | −0.112235 | ||||||||
\(784\) | −1.83013e8 | − | 4.39942e8i | −0.379781 | − | 0.912949i | ||||
\(785\) | 1.40479e8 | + | 1.37362e8i | 0.290405 | + | 0.283960i | ||||
\(786\) | −7.55011e6 | + | 2.49234e7i | −0.0155484 | + | 0.0513263i | ||||
\(787\) | −4.20122e8 | −0.861888 | −0.430944 | − | 0.902379i | \(-0.641819\pi\) | ||||
−0.430944 | + | 0.902379i | \(0.641819\pi\) | |||||||
\(788\) | 3.82996e8 | − | 5.74137e8i | 0.782736 | − | 1.17337i | ||||
\(789\) | −2.62853e8 | −0.535157 | ||||||||
\(790\) | 3.86181e7 | + | 7.02762e7i | 0.0783266 | + | 0.142537i | ||||
\(791\) | 2.90195e7i | 0.0586354i | ||||||||
\(792\) | 9.56797e7 | − | 7.87048e7i | 0.192595 | − | 0.158426i | ||||
\(793\) | − | 4.10205e7i | − | 0.0822587i | ||||||
\(794\) | −6.60465e7 | + | 2.18024e8i | −0.131944 | + | 0.435555i | ||||
\(795\) | −8.75575e7 | − | 8.56144e7i | −0.174258 | − | 0.170391i | ||||
\(796\) | 3.21522e8 | − | 4.81983e8i | 0.637487 | − | 0.955635i | ||||
\(797\) | − | 8.14269e8i | − | 1.60840i | −0.594362 | − | 0.804198i | \(-0.702595\pi\) | ||
0.594362 | − | 0.804198i | \(-0.297405\pi\) | |||||||
\(798\) | −1.19278e7 | + | 3.93746e7i | −0.0234721 | + | 0.0774831i | ||||
\(799\) | 7.26374e7i | 0.142403i | ||||||||
\(800\) | 5.08162e8 | − | 6.25697e7i | 0.992505 | − | 0.122207i | ||||
\(801\) | 2.92135e8 | 0.568441 | ||||||||
\(802\) | −7.71000e6 | − | 2.33561e6i | −0.0149462 | − | 0.00452769i | ||||
\(803\) | −6.52077e8 | −1.25937 | ||||||||
\(804\) | −3.95343e8 | − | 2.63726e8i | −0.760686 | − | 0.507439i | ||||
\(805\) | 4.22575e6 | − | 4.32166e6i | 0.00810058 | − | 0.00828443i | ||||
\(806\) | −3.28530e7 | − | 9.95222e6i | −0.0627436 | − | 0.0190071i | ||||
\(807\) | 3.22317e8 | 0.613286 | ||||||||
\(808\) | 2.58977e8 | + | 3.14833e8i | 0.490939 | + | 0.596824i | ||||
\(809\) | 1.00451e9 | 1.89719 | 0.948594 | − | 0.316496i | \(-0.102506\pi\) | ||||
0.948594 | + | 0.316496i | \(0.102506\pi\) | |||||||
\(810\) | 5.17502e7 | − | 2.84377e7i | 0.0973771 | − | 0.0535105i | ||||
\(811\) | 9.40317e8i | 1.76283i | 0.472338 | + | 0.881417i | \(0.343410\pi\) | ||||
−0.472338 | + | 0.881417i | \(0.656590\pi\) | |||||||
\(812\) | −2.74981e7 | − | 1.83434e7i | −0.0513610 | − | 0.0342620i | ||||
\(813\) | 2.15356e8i | 0.400761i | ||||||||
\(814\) | −5.44054e8 | − | 1.64811e8i | −1.00872 | − | 0.305572i | ||||
\(815\) | 2.64162e8 | − | 2.70158e8i | 0.487976 | − | 0.499051i | ||||
\(816\) | 7.58292e7 | − | 3.15444e7i | 0.139562 | − | 0.0580567i | ||||
\(817\) | 5.80680e7i | 0.106481i | ||||||||
\(818\) | 2.76864e8 | + | 8.38710e7i | 0.505832 | + | 0.153233i | ||||
\(819\) | 934829.i | 0.00170169i | ||||||||
\(820\) | −5.35788e8 | + | 1.13263e8i | −0.971742 | + | 0.205422i | ||||
\(821\) | −5.07811e8 | −0.917640 | −0.458820 | − | 0.888529i | \(-0.651728\pi\) | ||||
−0.458820 | + | 0.888529i | \(0.651728\pi\) | |||||||
\(822\) | −8.93414e7 | + | 2.94922e8i | −0.160856 | + | 0.530997i | ||||
\(823\) | 3.22556e8 | 0.578637 | 0.289318 | − | 0.957233i | \(-0.406571\pi\) | ||||
0.289318 | + | 0.957233i | \(0.406571\pi\) | |||||||
\(824\) | 2.43262e8 | + | 2.95728e8i | 0.434803 | + | 0.528580i | ||||
\(825\) | −2.42481e8 | + | 5.44230e6i | −0.431834 | + | 0.00969217i | ||||
\(826\) | 1.12011e7 | − | 3.69755e7i | 0.0198756 | − | 0.0656106i | ||||
\(827\) | 4.20915e8 | 0.744180 | 0.372090 | − | 0.928197i | \(-0.378641\pi\) | ||||
0.372090 | + | 0.928197i | \(0.378641\pi\) | |||||||
\(828\) | 1.72281e7 | + | 1.14925e7i | 0.0303491 | + | 0.0202453i | ||||
\(829\) | 7.22698e8 | 1.26851 | 0.634254 | − | 0.773125i | \(-0.281307\pi\) | ||||
0.634254 | + | 0.773125i | \(0.281307\pi\) | |||||||
\(830\) | 9.08079e8 | − | 4.99006e8i | 1.58814 | − | 0.872713i | ||||
\(831\) | 3.33393e7i | 0.0580969i | ||||||||
\(832\) | −2.72510e7 | − | 5.35609e6i | −0.0473165 | − | 0.00929989i | ||||
\(833\) | 1.49632e8i | 0.258875i | ||||||||
\(834\) | 7.01377e7 | − | 2.31529e8i | 0.120908 | − | 0.399124i | ||||
\(835\) | 1.50269e8 | − | 1.53680e8i | 0.258114 | − | 0.263972i | ||||
\(836\) | 4.81666e8 | + | 3.21311e8i | 0.824380 | + | 0.549929i | ||||
\(837\) | 1.53421e8i | 0.261643i | ||||||||
\(838\) | −1.79047e8 | + | 5.91045e8i | −0.304252 | + | 1.00436i | ||||
\(839\) | 3.57997e8i | 0.606168i | 0.952964 | + | 0.303084i | \(0.0980163\pi\) | ||||
−0.952964 | + | 0.303084i | \(0.901984\pi\) | |||||||
\(840\) | 3.60940e7 | + | 3.10507e6i | 0.0608971 | + | 0.00523882i | ||||
\(841\) | −3.92519e8 | −0.659891 | ||||||||
\(842\) | 1.38216e7 | + | 4.18699e6i | 0.0231537 | + | 0.00701401i | ||||
\(843\) | 2.24365e8 | 0.374518 | ||||||||
\(844\) | −3.85076e8 | + | 5.77255e8i | −0.640500 | + | 0.960153i | ||||
\(845\) | 4.20839e8 | − | 4.30391e8i | 0.697503 | − | 0.713333i | ||||
\(846\) | −1.05065e8 | − | 3.18277e7i | −0.173520 | − | 0.0525647i | ||||
\(847\) | 2.83227e7 | 0.0466106 | ||||||||
\(848\) | 2.37672e8 | − | 9.88700e7i | 0.389754 | − | 0.162135i | ||||
\(849\) | 3.99151e8 | 0.652250 | ||||||||
\(850\) | −1.54885e8 | − | 4.31501e7i | −0.252205 | − | 0.0702627i | ||||
\(851\) | − | 9.50247e7i | − | 0.154187i | ||||||
\(852\) | −2.67464e8 | + | 4.00947e8i | −0.432461 | + | 0.648289i | ||||
\(853\) | − | 1.53019e8i | − | 0.246546i | −0.992373 | − | 0.123273i | \(-0.960661\pi\) | ||
0.992373 | − | 0.123273i | \(-0.0393390\pi\) | |||||||
\(854\) | −1.07648e8 | − | 3.26100e7i | −0.172835 | − | 0.0523573i | ||||
\(855\) | 1.97313e8 | + | 1.92934e8i | 0.315687 | + | 0.308681i | ||||
\(856\) | 2.44728e7 | + | 2.97511e7i | 0.0390178 | + | 0.0474332i | ||||
\(857\) | 2.61817e8i | 0.415963i | 0.978133 | + | 0.207982i | \(0.0666894\pi\) | ||||
−0.978133 | + | 0.207982i | \(0.933311\pi\) | |||||||
\(858\) | 1.25912e7 | + | 3.81427e6i | 0.0199344 | + | 0.00603879i | ||||
\(859\) | − | 6.48325e7i | − | 0.102285i | −0.998691 | − | 0.0511426i | \(-0.983714\pi\) | ||
0.998691 | − | 0.0511426i | \(-0.0162863\pi\) | |||||||
\(860\) | 5.00263e7 | − | 1.05753e7i | 0.0786507 | − | 0.0166264i | ||||
\(861\) | −3.87482e7 | −0.0607075 | ||||||||
\(862\) | 1.94454e8 | − | 6.41905e8i | 0.303595 | − | 1.00219i | ||||
\(863\) | 3.46397e8 | 0.538942 | 0.269471 | − | 0.963008i | \(-0.413151\pi\) | ||||
0.269471 | + | 0.963008i | \(0.413151\pi\) | |||||||
\(864\) | 1.24008e7 | + | 1.23504e8i | 0.0192268 | + | 0.191487i | ||||
\(865\) | −5.39591e8 | − | 5.27616e8i | −0.833712 | − | 0.815210i | ||||
\(866\) | −7.46215e7 | + | 2.46331e8i | −0.114897 | + | 0.379284i | ||||
\(867\) | 3.50477e8 | 0.537776 | ||||||||
\(868\) | −5.22341e7 | + | 7.83025e7i | −0.0798721 | + | 0.119734i | ||||
\(869\) | 7.98497e7 | 0.121679 | ||||||||
\(870\) | −1.94315e8 | + | 1.06779e8i | −0.295085 | + | 0.162155i | ||||
\(871\) | − | 5.04658e7i | − | 0.0763735i | ||||||
\(872\) | 2.94536e8 | + | 3.58061e8i | 0.444210 | + | 0.540017i | ||||
\(873\) | 3.54009e8i | 0.532074i | ||||||||
\(874\) | −2.80601e7 | + | 9.26284e7i | −0.0420296 | + | 0.138743i | ||||
\(875\) | −5.18090e7 | − | 4.84335e7i | −0.0773358 | − | 0.0722972i | ||||
\(876\) | 3.62545e8 | − | 5.43480e8i | 0.539324 | − | 0.808484i | ||||
\(877\) | 3.86932e8i | 0.573635i | 0.957985 | + | 0.286817i | \(0.0925973\pi\) | ||||
−0.957985 | + | 0.286817i | \(0.907403\pi\) | |||||||
\(878\) | 2.65432e8 | − | 8.76210e8i | 0.392166 | − | 1.29457i | ||||
\(879\) | 1.26547e8i | 0.186331i | ||||||||
\(880\) | 1.89092e8 | − | 4.73479e8i | 0.277476 | − | 0.694788i | ||||
\(881\) | −7.55475e7 | −0.110482 | −0.0552411 | − | 0.998473i | \(-0.517593\pi\) | ||||
−0.0552411 | + | 0.998473i | \(0.517593\pi\) | |||||||
\(882\) | −2.16433e8 | − | 6.55647e7i | −0.315441 | − | 0.0955574i | ||||
\(883\) | −1.09819e8 | −0.159513 | −0.0797563 | − | 0.996814i | \(-0.525414\pi\) | ||||
−0.0797563 | + | 0.996814i | \(0.525414\pi\) | |||||||
\(884\) | 7.25523e6 | + | 4.83983e6i | 0.0105025 | + | 0.00700605i | ||||
\(885\) | −1.85291e8 | − | 1.81179e8i | −0.267315 | − | 0.261383i | ||||
\(886\) | 2.81430e8 | + | 8.52542e7i | 0.404640 | + | 0.122579i | ||||
\(887\) | −4.08975e8 | −0.586038 | −0.293019 | − | 0.956107i | \(-0.594660\pi\) | ||||
−0.293019 | + | 0.956107i | \(0.594660\pi\) | |||||||
\(888\) | 4.39850e8 | − | 3.61814e8i | 0.628153 | − | 0.516710i | ||||
\(889\) | −1.18297e8 | −0.168372 | ||||||||
\(890\) | 1.05360e9 | − | 5.78974e8i | 1.49454 | − | 0.821275i | ||||
\(891\) | − | 5.88000e7i | − | 0.0831274i | ||||||
\(892\) | −3.29233e8 | − | 2.19625e8i | −0.463884 | − | 0.309448i | ||||
\(893\) | − | 5.13055e8i | − | 0.720460i | ||||||
\(894\) | 5.99217e7 | + | 1.81522e7i | 0.0838633 | + | 0.0254049i | ||||
\(895\) | 9.99997e8 | + | 9.77805e8i | 1.39486 | + | 1.36390i | ||||
\(896\) | −3.57194e7 | + | 6.72554e7i | −0.0496569 | + | 0.0934982i | ||||
\(897\) | 2.19918e6i | 0.00304708i | ||||||||
\(898\) | 3.55846e7 | + | 1.07797e7i | 0.0491398 | + | 0.0148860i | ||||
\(899\) | − | 5.76075e8i | − | 0.792867i | ||||||
\(900\) | 1.30280e8 | − | 2.05124e8i | 0.178711 | − | 0.281378i | ||||
\(901\) | −8.08367e7 | −0.110518 | ||||||||
\(902\) | −1.58100e8 | + | 5.21898e8i | −0.215433 | + | 0.711158i | ||||
\(903\) | 3.61791e6 | 0.00491353 | ||||||||
\(904\) | −3.15999e8 | + | 2.59936e8i | −0.427741 | + | 0.351854i | ||||
\(905\) | −4.84368e8 | + | 4.95361e8i | −0.653476 | + | 0.668307i | ||||
\(906\) | 1.41442e8 | − | 4.66911e8i | 0.190193 | − | 0.627840i | ||||
\(907\) | −1.19298e9 | −1.59886 | −0.799429 | − | 0.600761i | \(-0.794864\pi\) | ||||
−0.799429 | + | 0.600761i | \(0.794864\pi\) | |||||||
\(908\) | 6.24675e8 | + | 4.16709e8i | 0.834443 | + | 0.556641i | ||||
\(909\) | 1.93481e8 | 0.257600 | ||||||||
\(910\) | 1.85271e6 | + | 3.37152e6i | 0.00245858 | + | 0.00447405i | ||||
\(911\) | 6.51943e8i | 0.862292i | 0.902282 | + | 0.431146i | \(0.141891\pi\) | ||||
−0.902282 | + | 0.431146i | \(0.858109\pi\) | |||||||
\(912\) | −5.35599e8 | + | 2.22806e8i | −0.706083 | + | 0.293726i | ||||
\(913\) | − | 1.03178e9i | − | 1.35574i | ||||||
\(914\) | −3.19676e8 | + | 1.05527e9i | −0.418670 | + | 1.38206i | ||||
\(915\) | −5.27470e8 | + | 5.39442e8i | −0.688549 | + | 0.704176i | ||||
\(916\) | 1.03975e9 | + | 6.93599e8i | 1.35283 | + | 0.902448i | ||||
\(917\) | 7.58284e6i | 0.00983386i | ||||||||
\(918\) | 1.13009e7 | − | 3.73049e7i | 0.0146077 | − | 0.0482212i | ||||
\(919\) | 5.07991e7i | 0.0654500i | 0.999464 | + | 0.0327250i | \(0.0104185\pi\) | ||||
−0.999464 | + | 0.0327250i | \(0.989581\pi\) | |||||||
\(920\) | 8.49108e7 | + | 7.30465e6i | 0.109043 | + | 0.00938071i | ||||
\(921\) | 3.24099e8 | 0.414858 | ||||||||
\(922\) | 4.68154e8 | + | 1.41819e8i | 0.597305 | + | 0.180943i | ||||
\(923\) | −5.11813e7 | −0.0650887 | ||||||||
\(924\) | 2.00192e7 | − | 3.00101e7i | 0.0253764 | − | 0.0380409i | ||||
\(925\) | −1.11471e9 | + | 2.50188e7i | −1.40844 | + | 0.0316113i | ||||
\(926\) | 6.83577e7 | + | 2.07077e7i | 0.0860903 | + | 0.0260795i | ||||
\(927\) | 1.81740e8 | 0.228145 | ||||||||
\(928\) | −4.65631e7 | − | 4.63740e8i | −0.0582637 | − | 0.580271i | ||||
\(929\) | 5.44046e8 | 0.678560 | 0.339280 | − | 0.940685i | \(-0.389817\pi\) | ||||
0.339280 | + | 0.940685i | \(0.389817\pi\) | |||||||
\(930\) | 3.04061e8 | + | 5.53323e8i | 0.378018 | + | 0.687907i | ||||
\(931\) | − | 1.05689e9i | − | 1.30972i | ||||||
\(932\) | −7.32414e8 | + | 1.09794e9i | −0.904709 | + | 1.35622i | ||||
\(933\) | − | 8.76002e8i | − | 1.07860i | ||||||
\(934\) | 7.13359e8 | + | 2.16099e8i | 0.875523 | + | 0.265224i | ||||
\(935\) | −1.11934e8 | + | 1.14475e8i | −0.136939 | + | 0.140047i | ||||
\(936\) | −1.01796e7 | + | 8.37356e6i | −0.0124137 | + | 0.0102113i | ||||
\(937\) | − | 1.23031e9i | − | 1.49553i | −0.663963 | − | 0.747765i | \(-0.731127\pi\) | ||
0.663963 | − | 0.747765i | \(-0.268873\pi\) | |||||||
\(938\) | −1.32435e8 | − | 4.01187e7i | −0.160470 | − | 0.0486114i | ||||
\(939\) | − | 9.43366e7i | − | 0.113942i | ||||||
\(940\) | −4.42003e8 | + | 9.34377e7i | −0.532160 | + | 0.112496i | ||||
\(941\) | −1.04638e9 | −1.25580 | −0.627901 | − | 0.778293i | \(-0.716086\pi\) | ||||
−0.627901 | + | 0.778293i | \(0.716086\pi\) | |||||||
\(942\) | −5.68293e7 | + | 1.87597e8i | −0.0679860 | + | 0.224427i | ||||
\(943\) | −9.11549e7 | −0.108704 | ||||||||
\(944\) | 5.02965e8 | − | 2.09230e8i | 0.597891 | − | 0.248719i | ||||
\(945\) | 1.20207e7 | − | 1.22935e7i | 0.0142441 | − | 0.0145673i | ||||
\(946\) | 1.47617e7 | − | 4.87294e7i | 0.0174367 | − | 0.0575596i | ||||
\(947\) | −1.05258e9 | −1.23938 | −0.619692 | − | 0.784845i | \(-0.712743\pi\) | ||||
−0.619692 | + | 0.784845i | \(0.712743\pi\) | |||||||
\(948\) | −4.43953e7 | + | 6.65516e7i | −0.0521089 | + | 0.0781148i | ||||
\(949\) | 6.93757e7 | 0.0811725 | ||||||||
\(950\) | 1.09399e9 | + | 3.04779e8i | 1.27598 | + | 0.355479i | ||||
\(951\) | 1.25731e8i | 0.146185i | ||||||||
\(952\) | 1.84686e7 | − | 1.51920e7i | 0.0214054 | − | 0.0176077i | ||||
\(953\) | 1.26282e8i | 0.145902i | 0.997336 | + | 0.0729512i | \(0.0232417\pi\) | ||||
−0.997336 | + | 0.0729512i | \(0.976758\pi\) | |||||||
\(954\) | 3.54204e7 | − | 1.16925e8i | 0.0407951 | − | 0.134667i | ||||
\(955\) | 4.13487e8 | + | 4.04311e8i | 0.474736 | + | 0.464200i | ||||
\(956\) | 6.49561e8 | − | 9.73736e8i | 0.743441 | − | 1.11447i | ||||
\(957\) | 2.20786e8i | 0.251904i | ||||||||
\(958\) | −1.80907e8 | + | 5.97187e8i | −0.205759 | + | 0.679225i | ||||
\(959\) | 8.97288e7i | 0.101736i | ||||||||
\(960\) | 2.89493e8 | + | 4.20848e8i | 0.327209 | + | 0.475676i | ||||
\(961\) | −7.52907e8 | −0.848343 | ||||||||
\(962\) | 5.78829e7 | + | 1.75346e7i | 0.0650168 | + | 0.0196957i | ||||
\(963\) | 1.82835e7 | 0.0204730 | ||||||||
\(964\) | −1.00402e9 | − | 6.69763e8i | −1.12076 | − | 0.747636i | ||||
\(965\) | −6.85498e8 | − | 6.70285e8i | −0.762824 | − | 0.745895i | ||||
\(966\) | 5.77118e6 | + | 1.74828e6i | 0.00640226 | + | 0.00193945i | ||||
\(967\) | −1.32116e9 | −1.46108 | −0.730542 | − | 0.682868i | \(-0.760732\pi\) | ||||
−0.730542 | + | 0.682868i | \(0.760732\pi\) | |||||||
\(968\) | 2.53695e8 | + | 3.08412e8i | 0.279696 | + | 0.340020i | ||||
\(969\) | 1.82167e8 | 0.200216 | ||||||||
\(970\) | 7.01601e8 | + | 1.27676e9i | 0.768732 | + | 1.39892i | ||||
\(971\) | − | 6.03829e8i | − | 0.659563i | −0.944057 | − | 0.329781i | \(-0.893025\pi\) | ||
0.944057 | − | 0.329781i | \(-0.106975\pi\) | |||||||
\(972\) | 4.90075e7 | + | 3.26920e7i | 0.0533658 | + | 0.0355994i | ||||
\(973\) | − | 7.04419e7i | − | 0.0764702i | ||||||
\(974\) | −1.40955e9 | − | 4.26997e8i | −1.52547 | − | 0.462113i | ||||
\(975\) | 2.57981e7 | − | 579017.i | 0.0278339 | − | 0.000624709i | ||||
\(976\) | −6.09138e8 | − | 1.46430e9i | −0.655188 | − | 1.57500i | ||||
\(977\) | 9.72123e8i | 1.04241i | 0.853432 | + | 0.521204i | \(0.174517\pi\) | ||||
−0.853432 | + | 0.521204i | \(0.825483\pi\) | |||||||
\(978\) | 3.60771e8 | + | 1.09289e8i | 0.385670 | + | 0.116832i | ||||
\(979\) | − | 1.19713e9i | − | 1.27583i | ||||||
\(980\) | −9.10521e8 | + | 1.92480e8i | −0.967413 | + | 0.204507i | ||||
\(981\) | 2.20046e8 | 0.233081 | ||||||||
\(982\) | −3.15858e8 | + | 1.04267e9i | −0.333547 | + | 1.10106i | ||||
\(983\) | 5.59576e8 | 0.589112 | 0.294556 | − | 0.955634i | \(-0.404828\pi\) | ||||
0.294556 | + | 0.955634i | \(0.404828\pi\) | |||||||
\(984\) | −3.47080e8 | − | 4.21938e8i | −0.364287 | − | 0.442856i | ||||
\(985\) | −9.63791e8 | − | 9.42402e8i | −1.00850 | − | 0.986115i | ||||
\(986\) | −4.24331e7 | + | 1.40075e8i | −0.0442664 | + | 0.146126i | ||||
\(987\) | −3.19657e7 | −0.0332455 | ||||||||
\(988\) | −5.12454e7 | − | 3.41849e7i | −0.0531354 | − | 0.0354457i | ||||
\(989\) | 8.51110e6 | 0.00879826 | ||||||||
\(990\) | −1.16534e8 | − | 2.12066e8i | −0.120101 | − | 0.218557i | ||||
\(991\) | 1.32095e9i | 1.35727i | 0.734477 | + | 0.678634i | \(0.237428\pi\) | ||||
−0.734477 | + | 0.678634i | \(0.762572\pi\) | |||||||
\(992\) | −1.32053e9 | + | 1.32591e8i | −1.35274 | + | 0.135825i | ||||
\(993\) | 1.06001e8i | 0.108258i | ||||||||
\(994\) | −4.06875e7 | + | 1.34312e8i | −0.0414287 | + | 0.136759i | ||||
\(995\) | −8.09093e8 | − | 7.91138e8i | −0.821352 | − | 0.803124i | ||||
\(996\) | 8.59951e8 | + | 5.73657e8i | 0.870353 | + | 0.580596i | ||||
\(997\) | 8.80146e8i | 0.888115i | 0.895998 | + | 0.444058i | \(0.146461\pi\) | ||||
−0.895998 | + | 0.444058i | \(0.853539\pi\) | |||||||
\(998\) | −1.21813e8 | + | 4.02113e8i | −0.122547 | + | 0.404536i | ||||
\(999\) | − | 2.70310e8i | − | 0.271122i |
(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.f.a.19.34 | yes | 36 | |
3.2 | odd | 2 | 180.7.f.g.19.3 | 36 | |||
4.3 | odd | 2 | inner | 60.7.f.a.19.4 | yes | 36 | |
5.4 | even | 2 | inner | 60.7.f.a.19.3 | ✓ | 36 | |
12.11 | even | 2 | 180.7.f.g.19.33 | 36 | |||
15.14 | odd | 2 | 180.7.f.g.19.34 | 36 | |||
20.19 | odd | 2 | inner | 60.7.f.a.19.33 | yes | 36 | |
60.59 | even | 2 | 180.7.f.g.19.4 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.7.f.a.19.3 | ✓ | 36 | 5.4 | even | 2 | inner | |
60.7.f.a.19.4 | yes | 36 | 4.3 | odd | 2 | inner | |
60.7.f.a.19.33 | yes | 36 | 20.19 | odd | 2 | inner | |
60.7.f.a.19.34 | yes | 36 | 1.1 | even | 1 | trivial | |
180.7.f.g.19.3 | 36 | 3.2 | odd | 2 | |||
180.7.f.g.19.4 | 36 | 60.59 | even | 2 | |||
180.7.f.g.19.33 | 36 | 12.11 | even | 2 | |||
180.7.f.g.19.34 | 36 | 15.14 | odd | 2 |