Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,7,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, 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("177.58");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(40.7195728007\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.6 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.7.c.a.58.55 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 13.7128i | − | 1.71409i | −0.515238 | − | 0.857047i | \(-0.672296\pi\) | ||
0.515238 | − | 0.857047i | \(-0.327704\pi\) | |||||||
\(3\) | −15.5885 | −0.577350 | ||||||||
\(4\) | −124.040 | −1.93812 | ||||||||
\(5\) | 78.2520 | 0.626016 | 0.313008 | − | 0.949751i | \(-0.398663\pi\) | ||||
0.313008 | + | 0.949751i | \(0.398663\pi\) | |||||||
\(6\) | 213.761i | 0.989633i | ||||||||
\(7\) | 452.461 | 1.31913 | 0.659564 | − | 0.751648i | \(-0.270741\pi\) | ||||
0.659564 | + | 0.751648i | \(0.270741\pi\) | |||||||
\(8\) | 823.310i | 1.60803i | ||||||||
\(9\) | 243.000 | 0.333333 | ||||||||
\(10\) | − | 1073.05i | − | 1.07305i | ||||||
\(11\) | − | 259.004i | − | 0.194594i | −0.995255 | − | 0.0972969i | \(-0.968980\pi\) | ||
0.995255 | − | 0.0972969i | \(-0.0310196\pi\) | |||||||
\(12\) | 1933.59 | 1.11897 | ||||||||
\(13\) | 652.587i | 0.297036i | 0.988910 | + | 0.148518i | \(0.0474502\pi\) | ||||
−0.988910 | + | 0.148518i | \(0.952550\pi\) | |||||||
\(14\) | − | 6204.49i | − | 2.26111i | ||||||
\(15\) | −1219.83 | −0.361430 | ||||||||
\(16\) | 3351.31 | 0.818190 | ||||||||
\(17\) | −3110.24 | −0.633064 | −0.316532 | − | 0.948582i | \(-0.602518\pi\) | ||||
−0.316532 | + | 0.948582i | \(0.602518\pi\) | |||||||
\(18\) | − | 3332.20i | − | 0.571365i | ||||||
\(19\) | −10605.2 | −1.54618 | −0.773088 | − | 0.634299i | \(-0.781289\pi\) | ||||
−0.773088 | + | 0.634299i | \(0.781289\pi\) | |||||||
\(20\) | −9706.35 | −1.21329 | ||||||||
\(21\) | −7053.17 | −0.761599 | ||||||||
\(22\) | −3551.66 | −0.333552 | ||||||||
\(23\) | − | 1836.91i | − | 0.150975i | −0.997147 | − | 0.0754875i | \(-0.975949\pi\) | ||
0.997147 | − | 0.0754875i | \(-0.0240513\pi\) | |||||||
\(24\) | − | 12834.1i | − | 0.928395i | ||||||
\(25\) | −9501.63 | −0.608104 | ||||||||
\(26\) | 8948.77 | 0.509147 | ||||||||
\(27\) | −3788.00 | −0.192450 | ||||||||
\(28\) | −56123.1 | −2.55663 | ||||||||
\(29\) | −3215.28 | −0.131833 | −0.0659165 | − | 0.997825i | \(-0.520997\pi\) | ||||
−0.0659165 | + | 0.997825i | \(0.520997\pi\) | |||||||
\(30\) | 16727.2i | 0.619526i | ||||||||
\(31\) | − | 49794.1i | − | 1.67145i | −0.549151 | − | 0.835723i | \(-0.685049\pi\) | ||
0.549151 | − | 0.835723i | \(-0.314951\pi\) | |||||||
\(32\) | 6736.18i | 0.205572i | ||||||||
\(33\) | 4037.48i | 0.112349i | ||||||||
\(34\) | 42650.0i | 1.08513i | ||||||||
\(35\) | 35406.0 | 0.825795 | ||||||||
\(36\) | −30141.6 | −0.646040 | ||||||||
\(37\) | 3989.90i | 0.0787693i | 0.999224 | + | 0.0393847i | \(0.0125398\pi\) | ||||
−0.999224 | + | 0.0393847i | \(0.987460\pi\) | |||||||
\(38\) | 145427.i | 2.65029i | ||||||||
\(39\) | − | 10172.8i | − | 0.171494i | ||||||
\(40\) | 64425.6i | 1.00665i | ||||||||
\(41\) | −48864.4 | −0.708991 | −0.354495 | − | 0.935058i | \(-0.615347\pi\) | ||||
−0.354495 | + | 0.935058i | \(0.615347\pi\) | |||||||
\(42\) | 96718.4i | 1.30545i | ||||||||
\(43\) | 40700.9i | 0.511916i | 0.966688 | + | 0.255958i | \(0.0823909\pi\) | ||||
−0.966688 | + | 0.255958i | \(0.917609\pi\) | |||||||
\(44\) | 32126.8i | 0.377146i | ||||||||
\(45\) | 19015.2 | 0.208672 | ||||||||
\(46\) | −25189.1 | −0.258785 | ||||||||
\(47\) | − | 14800.9i | − | 0.142559i | −0.997456 | − | 0.0712794i | \(-0.977292\pi\) | ||
0.997456 | − | 0.0712794i | \(-0.0227082\pi\) | |||||||
\(48\) | −52241.7 | −0.472382 | ||||||||
\(49\) | 87071.9 | 0.740099 | ||||||||
\(50\) | 130293.i | 1.04235i | ||||||||
\(51\) | 48483.9 | 0.365499 | ||||||||
\(52\) | − | 80946.7i | − | 0.575691i | ||||||
\(53\) | −246352. | −1.65474 | −0.827368 | − | 0.561660i | \(-0.810163\pi\) | ||||
−0.827368 | + | 0.561660i | \(0.810163\pi\) | |||||||
\(54\) | 51943.9i | 0.329878i | ||||||||
\(55\) | − | 20267.6i | − | 0.121819i | ||||||
\(56\) | 372515.i | 2.12119i | ||||||||
\(57\) | 165319. | 0.892685 | ||||||||
\(58\) | 44090.3i | 0.225974i | ||||||||
\(59\) | −47272.8 | + | 199865.i | −0.230173 | + | 0.973150i | ||||
\(60\) | 151307. | 0.700496 | ||||||||
\(61\) | − | 253372.i | − | 1.11627i | −0.829751 | − | 0.558134i | \(-0.811517\pi\) | ||
0.829751 | − | 0.558134i | \(-0.188483\pi\) | |||||||
\(62\) | −682814. | −2.86502 | ||||||||
\(63\) | 109948. | 0.439709 | ||||||||
\(64\) | 306855. | 1.17056 | ||||||||
\(65\) | 51066.3i | 0.185949i | ||||||||
\(66\) | 55365.0 | 0.192576 | ||||||||
\(67\) | − | 475304.i | − | 1.58033i | −0.612895 | − | 0.790164i | \(-0.709995\pi\) | ||
0.612895 | − | 0.790164i | \(-0.290005\pi\) | |||||||
\(68\) | 385793. | 1.22695 | ||||||||
\(69\) | 28634.6i | 0.0871654i | ||||||||
\(70\) | − | 485513.i | − | 1.41549i | ||||||
\(71\) | 75588.7 | 0.211194 | 0.105597 | − | 0.994409i | \(-0.466325\pi\) | ||||
0.105597 | + | 0.994409i | \(0.466325\pi\) | |||||||
\(72\) | 200064.i | 0.536009i | ||||||||
\(73\) | 284785.i | 0.732064i | 0.930602 | + | 0.366032i | \(0.119284\pi\) | ||||
−0.930602 | + | 0.366032i | \(0.880716\pi\) | |||||||
\(74\) | 54712.6 | 0.135018 | ||||||||
\(75\) | 148116. | 0.351089 | ||||||||
\(76\) | 1.31547e6 | 2.99667 | ||||||||
\(77\) | − | 117189.i | − | 0.256694i | ||||||
\(78\) | −139498. | −0.293956 | ||||||||
\(79\) | −530314. | −1.07560 | −0.537801 | − | 0.843072i | \(-0.680745\pi\) | ||||
−0.537801 | + | 0.843072i | \(0.680745\pi\) | |||||||
\(80\) | 262246. | 0.512200 | ||||||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | 670065.i | 1.21528i | ||||||||
\(83\) | 947140.i | 1.65646i | 0.560391 | + | 0.828228i | \(0.310651\pi\) | ||||
−0.560391 | + | 0.828228i | \(0.689349\pi\) | |||||||
\(84\) | 874873. | 1.47607 | ||||||||
\(85\) | −243383. | −0.396308 | ||||||||
\(86\) | 558121. | 0.877472 | ||||||||
\(87\) | 50121.2 | 0.0761138 | ||||||||
\(88\) | 213241. | 0.312912 | ||||||||
\(89\) | − | 985993.i | − | 1.39863i | −0.714812 | − | 0.699317i | \(-0.753488\pi\) | ||
0.714812 | − | 0.699317i | \(-0.246512\pi\) | |||||||
\(90\) | − | 260751.i | − | 0.357684i | ||||||
\(91\) | 295270.i | 0.391828i | ||||||||
\(92\) | 227850.i | 0.292608i | ||||||||
\(93\) | 776213.i | 0.965010i | ||||||||
\(94\) | −202961. | −0.244359 | ||||||||
\(95\) | −829879. | −0.967930 | ||||||||
\(96\) | − | 105007.i | − | 0.118687i | ||||||
\(97\) | 310962.i | 0.340716i | 0.985382 | + | 0.170358i | \(0.0544924\pi\) | ||||
−0.985382 | + | 0.170358i | \(0.945508\pi\) | |||||||
\(98\) | − | 1.19400e6i | − | 1.26860i | ||||||
\(99\) | − | 62938.1i | − | 0.0648646i | ||||||
\(100\) | 1.17858e6 | 1.17858 | ||||||||
\(101\) | 526681.i | 0.511191i | 0.966784 | + | 0.255596i | \(0.0822716\pi\) | ||||
−0.966784 | + | 0.255596i | \(0.917728\pi\) | |||||||
\(102\) | − | 664847.i | − | 0.626501i | ||||||
\(103\) | 362144.i | 0.331413i | 0.986175 | + | 0.165706i | \(0.0529904\pi\) | ||||
−0.986175 | + | 0.165706i | \(0.947010\pi\) | |||||||
\(104\) | −537282. | −0.477641 | ||||||||
\(105\) | −551924. | −0.476773 | ||||||||
\(106\) | 3.37817e6i | 2.83638i | ||||||||
\(107\) | 81885.6 | 0.0668431 | 0.0334215 | − | 0.999441i | \(-0.489360\pi\) | ||||
0.0334215 | + | 0.999441i | \(0.489360\pi\) | |||||||
\(108\) | 469862. | 0.372991 | ||||||||
\(109\) | 659312.i | 0.509110i | 0.967058 | + | 0.254555i | \(0.0819290\pi\) | ||||
−0.967058 | + | 0.254555i | \(0.918071\pi\) | |||||||
\(110\) | −277925. | −0.208809 | ||||||||
\(111\) | − | 62196.4i | − | 0.0454775i | ||||||
\(112\) | 1.51633e6 | 1.07930 | ||||||||
\(113\) | 760603.i | 0.527136i | 0.964641 | + | 0.263568i | \(0.0848993\pi\) | ||||
−0.964641 | + | 0.263568i | \(0.915101\pi\) | |||||||
\(114\) | − | 2.26698e6i | − | 1.53015i | ||||||
\(115\) | − | 143742.i | − | 0.0945127i | ||||||
\(116\) | 398822. | 0.255508 | ||||||||
\(117\) | 158579.i | 0.0990119i | ||||||||
\(118\) | 2.74069e6 | + | 648240.i | 1.66807 | + | 0.394539i | ||||
\(119\) | −1.40726e6 | −0.835092 | ||||||||
\(120\) | − | 1.00430e6i | − | 0.581190i | ||||||
\(121\) | 1.70448e6 | 0.962133 | ||||||||
\(122\) | −3.47442e6 | −1.91339 | ||||||||
\(123\) | 761720. | 0.409336 | ||||||||
\(124\) | 6.17644e6i | 3.23946i | ||||||||
\(125\) | −1.96621e6 | −1.00670 | ||||||||
\(126\) | − | 1.50769e6i | − | 0.753703i | ||||||
\(127\) | 609001. | 0.297308 | 0.148654 | − | 0.988889i | \(-0.452506\pi\) | ||||
0.148654 | + | 0.988889i | \(0.452506\pi\) | |||||||
\(128\) | − | 3.77672e6i | − | 1.80088i | ||||||
\(129\) | − | 634464.i | − | 0.295555i | ||||||
\(130\) | 700259. | 0.318734 | ||||||||
\(131\) | − | 354986.i | − | 0.157905i | −0.996878 | − | 0.0789527i | \(-0.974842\pi\) | ||
0.996878 | − | 0.0789527i | \(-0.0251576\pi\) | |||||||
\(132\) | − | 500808.i | − | 0.217745i | ||||||
\(133\) | −4.79845e6 | −2.03960 | ||||||||
\(134\) | −6.51773e6 | −2.70883 | ||||||||
\(135\) | −296418. | −0.120477 | ||||||||
\(136\) | − | 2.56069e6i | − | 1.01798i | ||||||
\(137\) | −3.51364e6 | −1.36646 | −0.683229 | − | 0.730205i | \(-0.739425\pi\) | ||||
−0.683229 | + | 0.730205i | \(0.739425\pi\) | |||||||
\(138\) | 392660. | 0.149410 | ||||||||
\(139\) | −3.04917e6 | −1.13537 | −0.567685 | − | 0.823246i | \(-0.692161\pi\) | ||||
−0.567685 | + | 0.823246i | \(0.692161\pi\) | |||||||
\(140\) | −4.39175e6 | −1.60049 | ||||||||
\(141\) | 230723.i | 0.0823064i | ||||||||
\(142\) | − | 1.03653e6i | − | 0.362006i | ||||||
\(143\) | 169023. | 0.0578013 | ||||||||
\(144\) | 814367. | 0.272730 | ||||||||
\(145\) | −251602. | −0.0825296 | ||||||||
\(146\) | 3.90519e6 | 1.25483 | ||||||||
\(147\) | −1.35732e6 | −0.427296 | ||||||||
\(148\) | − | 494906.i | − | 0.152664i | ||||||
\(149\) | 1.71211e6i | 0.517574i | 0.965934 | + | 0.258787i | \(0.0833227\pi\) | ||||
−0.965934 | + | 0.258787i | \(0.916677\pi\) | |||||||
\(150\) | − | 2.03107e6i | − | 0.601800i | ||||||
\(151\) | − | 2.86817e6i | − | 0.833057i | −0.909123 | − | 0.416528i | \(-0.863247\pi\) | ||
0.909123 | − | 0.416528i | \(-0.136753\pi\) | |||||||
\(152\) | − | 8.73138e6i | − | 2.48629i | ||||||
\(153\) | −755789. | −0.211021 | ||||||||
\(154\) | −1.60699e6 | −0.439998 | ||||||||
\(155\) | − | 3.89648e6i | − | 1.04635i | ||||||
\(156\) | 1.26183e6i | 0.332375i | ||||||||
\(157\) | − | 22056.5i | − | 0.00569952i | −0.999996 | − | 0.00284976i | \(-0.999093\pi\) | ||
0.999996 | − | 0.00284976i | \(-0.000907108\pi\) | |||||||
\(158\) | 7.27206e6i | 1.84368i | ||||||||
\(159\) | 3.84025e6 | 0.955363 | ||||||||
\(160\) | 527120.i | 0.128691i | ||||||||
\(161\) | − | 831131.i | − | 0.199155i | ||||||
\(162\) | − | 809725.i | − | 0.190455i | ||||||
\(163\) | −3.33224e6 | −0.769438 | −0.384719 | − | 0.923034i | \(-0.625702\pi\) | ||||
−0.384719 | + | 0.923034i | \(0.625702\pi\) | |||||||
\(164\) | 6.06112e6 | 1.37411 | ||||||||
\(165\) | 315941.i | 0.0703321i | ||||||||
\(166\) | 1.29879e7 | 2.83932 | ||||||||
\(167\) | −1.78430e6 | −0.383106 | −0.191553 | − | 0.981482i | \(-0.561352\pi\) | ||||
−0.191553 | + | 0.981482i | \(0.561352\pi\) | |||||||
\(168\) | − | 5.80694e6i | − | 1.22467i | ||||||
\(169\) | 4.40094e6 | 0.911770 | ||||||||
\(170\) | 3.33745e6i | 0.679309i | ||||||||
\(171\) | −2.57707e6 | −0.515392 | ||||||||
\(172\) | − | 5.04853e6i | − | 0.992155i | ||||||
\(173\) | − | 3.85930e6i | − | 0.745367i | −0.927959 | − | 0.372684i | \(-0.878438\pi\) | ||
0.927959 | − | 0.372684i | \(-0.121562\pi\) | |||||||
\(174\) | − | 687300.i | − | 0.130466i | ||||||
\(175\) | −4.29911e6 | −0.802167 | ||||||||
\(176\) | − | 868003.i | − | 0.159215i | ||||||
\(177\) | 736910. | − | 3.11558e6i | 0.132891 | − | 0.561848i | ||||
\(178\) | −1.35207e7 | −2.39739 | ||||||||
\(179\) | − | 686308.i | − | 0.119663i | −0.998208 | − | 0.0598315i | \(-0.980944\pi\) | ||
0.998208 | − | 0.0598315i | \(-0.0190563\pi\) | |||||||
\(180\) | −2.35864e6 | −0.404431 | ||||||||
\(181\) | 3.82235e6 | 0.644606 | 0.322303 | − | 0.946637i | \(-0.395543\pi\) | ||||
0.322303 | + | 0.946637i | \(0.395543\pi\) | |||||||
\(182\) | 4.04897e6 | 0.671630 | ||||||||
\(183\) | 3.94967e6i | 0.644478i | ||||||||
\(184\) | 1.51235e6 | 0.242772 | ||||||||
\(185\) | 312218.i | 0.0493109i | ||||||||
\(186\) | 1.06440e7 | 1.65412 | ||||||||
\(187\) | 805566.i | 0.123190i | ||||||||
\(188\) | 1.83590e6i | 0.276296i | ||||||||
\(189\) | −1.71392e6 | −0.253866 | ||||||||
\(190\) | 1.13799e7i | 1.65912i | ||||||||
\(191\) | 1.30564e6i | 0.187380i | 0.995601 | + | 0.0936899i | \(0.0298662\pi\) | ||||
−0.995601 | + | 0.0936899i | \(0.970134\pi\) | |||||||
\(192\) | −4.78340e6 | −0.675823 | ||||||||
\(193\) | 2.12355e6 | 0.295386 | 0.147693 | − | 0.989033i | \(-0.452815\pi\) | ||||
0.147693 | + | 0.989033i | \(0.452815\pi\) | |||||||
\(194\) | 4.26415e6 | 0.584019 | ||||||||
\(195\) | − | 796044.i | − | 0.107358i | ||||||
\(196\) | −1.08004e7 | −1.43440 | ||||||||
\(197\) | −1.97152e6 | −0.257872 | −0.128936 | − | 0.991653i | \(-0.541156\pi\) | ||||
−0.128936 | + | 0.991653i | \(0.541156\pi\) | |||||||
\(198\) | −863054. | −0.111184 | ||||||||
\(199\) | 1.10320e7 | 1.39990 | 0.699949 | − | 0.714193i | \(-0.253206\pi\) | ||||
0.699949 | + | 0.714193i | \(0.253206\pi\) | |||||||
\(200\) | − | 7.82278e6i | − | 0.977848i | ||||||
\(201\) | 7.40926e6i | 0.912403i | ||||||||
\(202\) | 7.22225e6 | 0.876231 | ||||||||
\(203\) | −1.45479e6 | −0.173905 | ||||||||
\(204\) | −6.01392e6 | −0.708382 | ||||||||
\(205\) | −3.82373e6 | −0.443840 | ||||||||
\(206\) | 4.96599e6 | 0.568073 | ||||||||
\(207\) | − | 446370.i | − | 0.0503250i | ||||||
\(208\) | 2.18702e6i | 0.243032i | ||||||||
\(209\) | 2.74680e6i | 0.300876i | ||||||||
\(210\) | 7.56840e6i | 0.817234i | ||||||||
\(211\) | − | 1.15651e7i | − | 1.23112i | −0.788089 | − | 0.615561i | \(-0.788929\pi\) | ||
0.788089 | − | 0.615561i | \(-0.211071\pi\) | |||||||
\(212\) | 3.05575e7 | 3.20708 | ||||||||
\(213\) | −1.17831e6 | −0.121933 | ||||||||
\(214\) | − | 1.12288e6i | − | 0.114575i | ||||||
\(215\) | 3.18493e6i | 0.320467i | ||||||||
\(216\) | − | 3.11869e6i | − | 0.309465i | ||||||
\(217\) | − | 2.25299e7i | − | 2.20485i | ||||||
\(218\) | 9.04098e6 | 0.872662 | ||||||||
\(219\) | − | 4.43937e6i | − | 0.422658i | ||||||
\(220\) | 2.51399e6i | 0.236100i | ||||||||
\(221\) | − | 2.02970e6i | − | 0.188042i | ||||||
\(222\) | −852885. | −0.0779527 | ||||||||
\(223\) | −966458. | −0.0871502 | −0.0435751 | − | 0.999050i | \(-0.513875\pi\) | ||||
−0.0435751 | + | 0.999050i | \(0.513875\pi\) | |||||||
\(224\) | 3.04786e6i | 0.271176i | ||||||||
\(225\) | −2.30890e6 | −0.202701 | ||||||||
\(226\) | 1.04300e7 | 0.903561 | ||||||||
\(227\) | − | 1.11687e6i | − | 0.0954824i | −0.998860 | − | 0.0477412i | \(-0.984798\pi\) | ||
0.998860 | − | 0.0477412i | \(-0.0152023\pi\) | |||||||
\(228\) | −2.05061e7 | −1.73013 | ||||||||
\(229\) | 8.34569e6i | 0.694953i | 0.937689 | + | 0.347477i | \(0.112961\pi\) | ||||
−0.937689 | + | 0.347477i | \(0.887039\pi\) | |||||||
\(230\) | −1.97110e6 | −0.162004 | ||||||||
\(231\) | 1.82680e6i | 0.148202i | ||||||||
\(232\) | − | 2.64717e6i | − | 0.211991i | ||||||
\(233\) | − | 1.74749e7i | − | 1.38148i | −0.723101 | − | 0.690742i | \(-0.757284\pi\) | ||
0.723101 | − | 0.690742i | \(-0.242716\pi\) | |||||||
\(234\) | 2.17455e6 | 0.169716 | ||||||||
\(235\) | − | 1.15820e6i | − | 0.0892441i | ||||||
\(236\) | 5.86370e6 | − | 2.47911e7i | 0.446104 | − | 1.88608i | ||||
\(237\) | 8.26677e6 | 0.620999 | ||||||||
\(238\) | 1.92974e7i | 1.43143i | ||||||||
\(239\) | −1.75221e7 | −1.28349 | −0.641744 | − | 0.766919i | \(-0.721789\pi\) | ||||
−0.641744 | + | 0.766919i | \(0.721789\pi\) | |||||||
\(240\) | −4.08802e6 | −0.295719 | ||||||||
\(241\) | −424356. | −0.0303165 | −0.0151583 | − | 0.999885i | \(-0.504825\pi\) | ||||
−0.0151583 | + | 0.999885i | \(0.504825\pi\) | |||||||
\(242\) | − | 2.33731e7i | − | 1.64919i | ||||||
\(243\) | −920483. | −0.0641500 | ||||||||
\(244\) | 3.14281e7i | 2.16346i | ||||||||
\(245\) | 6.81355e6 | 0.463313 | ||||||||
\(246\) | − | 1.04453e7i | − | 0.701641i | ||||||
\(247\) | − | 6.92083e6i | − | 0.459269i | ||||||
\(248\) | 4.09959e7 | 2.68773 | ||||||||
\(249\) | − | 1.47645e7i | − | 0.956355i | ||||||
\(250\) | 2.69621e7i | 1.72558i | ||||||||
\(251\) | −1.87344e6 | −0.118473 | −0.0592364 | − | 0.998244i | \(-0.518867\pi\) | ||||
−0.0592364 | + | 0.998244i | \(0.518867\pi\) | |||||||
\(252\) | −1.36379e7 | −0.852210 | ||||||||
\(253\) | −475768. | −0.0293788 | ||||||||
\(254\) | − | 8.35108e6i | − | 0.509614i | ||||||
\(255\) | 3.79396e6 | 0.228808 | ||||||||
\(256\) | −3.21504e7 | −1.91632 | ||||||||
\(257\) | 3.56173e6 | 0.209827 | 0.104914 | − | 0.994481i | \(-0.466543\pi\) | ||||
0.104914 | + | 0.994481i | \(0.466543\pi\) | |||||||
\(258\) | −8.70025e6 | −0.506609 | ||||||||
\(259\) | 1.80528e6i | 0.103907i | ||||||||
\(260\) | − | 6.33424e6i | − | 0.360392i | ||||||
\(261\) | −781312. | −0.0439443 | ||||||||
\(262\) | −4.86783e6 | −0.270665 | ||||||||
\(263\) | −1.09649e6 | −0.0602748 | −0.0301374 | − | 0.999546i | \(-0.509594\pi\) | ||||
−0.0301374 | + | 0.999546i | \(0.509594\pi\) | |||||||
\(264\) | −3.32410e6 | −0.180660 | ||||||||
\(265\) | −1.92776e7 | −1.03589 | ||||||||
\(266\) | 6.57999e7i | 3.49607i | ||||||||
\(267\) | 1.53701e7i | 0.807501i | ||||||||
\(268\) | 5.89566e7i | 3.06287i | ||||||||
\(269\) | − | 1.29997e7i | − | 0.667848i | −0.942600 | − | 0.333924i | \(-0.891627\pi\) | ||
0.942600 | − | 0.333924i | \(-0.108373\pi\) | |||||||
\(270\) | 4.06471e6i | 0.206509i | ||||||||
\(271\) | 4.49647e6 | 0.225925 | 0.112962 | − | 0.993599i | \(-0.463966\pi\) | ||||
0.112962 | + | 0.993599i | \(0.463966\pi\) | |||||||
\(272\) | −1.04234e7 | −0.517966 | ||||||||
\(273\) | − | 4.60281e6i | − | 0.226222i | ||||||
\(274\) | 4.81817e7i | 2.34224i | ||||||||
\(275\) | 2.46096e6i | 0.118333i | ||||||||
\(276\) | − | 3.55183e6i | − | 0.168937i | ||||||
\(277\) | 9.37091e6 | 0.440902 | 0.220451 | − | 0.975398i | \(-0.429247\pi\) | ||||
0.220451 | + | 0.975398i | \(0.429247\pi\) | |||||||
\(278\) | 4.18126e7i | 1.94613i | ||||||||
\(279\) | − | 1.21000e7i | − | 0.557149i | ||||||
\(280\) | 2.91501e7i | 1.32790i | ||||||||
\(281\) | −2.71429e7 | −1.22331 | −0.611657 | − | 0.791123i | \(-0.709497\pi\) | ||||
−0.611657 | + | 0.791123i | \(0.709497\pi\) | |||||||
\(282\) | 3.16385e6 | 0.141081 | ||||||||
\(283\) | 2.60309e7i | 1.14850i | 0.818681 | + | 0.574249i | \(0.194706\pi\) | ||||
−0.818681 | + | 0.574249i | \(0.805294\pi\) | |||||||
\(284\) | −9.37599e6 | −0.409319 | ||||||||
\(285\) | 1.29365e7 | 0.558835 | ||||||||
\(286\) | − | 2.31777e6i | − | 0.0990769i | ||||||
\(287\) | −2.21092e7 | −0.935250 | ||||||||
\(288\) | 1.63689e6i | 0.0685240i | ||||||||
\(289\) | −1.44640e7 | −0.599231 | ||||||||
\(290\) | 3.45015e6i | 0.141464i | ||||||||
\(291\) | − | 4.84742e6i | − | 0.196712i | ||||||
\(292\) | − | 3.53247e7i | − | 1.41883i | ||||||
\(293\) | −2.55220e7 | −1.01464 | −0.507319 | − | 0.861758i | \(-0.669363\pi\) | ||||
−0.507319 | + | 0.861758i | \(0.669363\pi\) | |||||||
\(294\) | 1.86125e7i | 0.732426i | ||||||||
\(295\) | −3.69919e6 | + | 1.56398e7i | −0.144092 | + | 0.609207i | ||||
\(296\) | −3.28493e6 | −0.126663 | ||||||||
\(297\) | 981107.i | 0.0374496i | ||||||||
\(298\) | 2.34777e7 | 0.887170 | ||||||||
\(299\) | 1.19875e6 | 0.0448449 | ||||||||
\(300\) | −1.83722e7 | −0.680453 | ||||||||
\(301\) | 1.84156e7i | 0.675283i | ||||||||
\(302\) | −3.93306e7 | −1.42794 | ||||||||
\(303\) | − | 8.21015e6i | − | 0.295137i | ||||||
\(304\) | −3.55413e7 | −1.26506 | ||||||||
\(305\) | − | 1.98268e7i | − | 0.698802i | ||||||
\(306\) | 1.03639e7i | 0.361710i | ||||||||
\(307\) | 4.11042e7 | 1.42060 | 0.710299 | − | 0.703900i | \(-0.248560\pi\) | ||||
0.710299 | + | 0.703900i | \(0.248560\pi\) | |||||||
\(308\) | 1.45361e7i | 0.497504i | ||||||||
\(309\) | − | 5.64526e6i | − | 0.191341i | ||||||
\(310\) | −5.34315e7 | −1.79355 | ||||||||
\(311\) | 4.47374e7 | 1.48727 | 0.743634 | − | 0.668587i | \(-0.233101\pi\) | ||||
0.743634 | + | 0.668587i | \(0.233101\pi\) | |||||||
\(312\) | 8.37539e6 | 0.275766 | ||||||||
\(313\) | − | 3.06210e7i | − | 0.998589i | −0.866432 | − | 0.499295i | \(-0.833593\pi\) | ||
0.866432 | − | 0.499295i | \(-0.166407\pi\) | |||||||
\(314\) | −302456. | −0.00976952 | ||||||||
\(315\) | 8.60365e6 | 0.275265 | ||||||||
\(316\) | 6.57800e7 | 2.08465 | ||||||||
\(317\) | 5.80961e7 | 1.82377 | 0.911883 | − | 0.410450i | \(-0.134629\pi\) | ||||
0.911883 | + | 0.410450i | \(0.134629\pi\) | |||||||
\(318\) | − | 5.26604e7i | − | 1.63758i | ||||||
\(319\) | 832770.i | 0.0256539i | ||||||||
\(320\) | 2.40120e7 | 0.732789 | ||||||||
\(321\) | −1.27647e6 | −0.0385919 | ||||||||
\(322\) | −1.13971e7 | −0.341371 | ||||||||
\(323\) | 3.29848e7 | 0.978827 | ||||||||
\(324\) | −7.32442e6 | −0.215347 | ||||||||
\(325\) | − | 6.20064e6i | − | 0.180629i | ||||||
\(326\) | 4.56942e7i | 1.31889i | ||||||||
\(327\) | − | 1.02777e7i | − | 0.293935i | ||||||
\(328\) | − | 4.02305e7i | − | 1.14008i | ||||||
\(329\) | − | 6.69682e6i | − | 0.188053i | ||||||
\(330\) | 4.33242e6 | 0.120556 | ||||||||
\(331\) | 3.32831e7 | 0.917783 | 0.458891 | − | 0.888492i | \(-0.348247\pi\) | ||||
0.458891 | + | 0.888492i | \(0.348247\pi\) | |||||||
\(332\) | − | 1.17483e8i | − | 3.21041i | ||||||
\(333\) | 969547.i | 0.0262564i | ||||||||
\(334\) | 2.44677e7i | 0.656680i | ||||||||
\(335\) | − | 3.71935e7i | − | 0.989310i | ||||||
\(336\) | −2.36373e7 | −0.623133 | ||||||||
\(337\) | − | 1.87279e7i | − | 0.489326i | −0.969608 | − | 0.244663i | \(-0.921323\pi\) | ||
0.969608 | − | 0.244663i | \(-0.0786773\pi\) | |||||||
\(338\) | − | 6.03490e7i | − | 1.56286i | ||||||
\(339\) | − | 1.18566e7i | − | 0.304342i | ||||||
\(340\) | 3.01891e7 | 0.768092 | ||||||||
\(341\) | −1.28969e7 | −0.325253 | ||||||||
\(342\) | 3.53387e7i | 0.883430i | ||||||||
\(343\) | −1.38350e7 | −0.342843 | ||||||||
\(344\) | −3.35094e7 | −0.823174 | ||||||||
\(345\) | 2.24072e6i | 0.0545669i | ||||||||
\(346\) | −5.29216e7 | −1.27763 | ||||||||
\(347\) | 2.98270e7i | 0.713874i | 0.934128 | + | 0.356937i | \(0.116179\pi\) | ||||
−0.934128 | + | 0.356937i | \(0.883821\pi\) | |||||||
\(348\) | −6.21702e6 | −0.147518 | ||||||||
\(349\) | − | 7.76118e7i | − | 1.82579i | −0.408190 | − | 0.912897i | \(-0.633840\pi\) | ||
0.408190 | − | 0.912897i | \(-0.366160\pi\) | |||||||
\(350\) | 5.89527e7i | 1.37499i | ||||||||
\(351\) | − | 2.47200e6i | − | 0.0571645i | ||||||
\(352\) | 1.74470e6 | 0.0400030 | ||||||||
\(353\) | − | 6.61940e7i | − | 1.50485i | −0.658676 | − | 0.752427i | \(-0.728883\pi\) | ||
0.658676 | − | 0.752427i | \(-0.271117\pi\) | |||||||
\(354\) | −4.27232e7 | − | 1.01051e7i | −0.963061 | − | 0.227787i | ||||
\(355\) | 5.91496e6 | 0.132211 | ||||||||
\(356\) | 1.22302e8i | 2.71072i | ||||||||
\(357\) | 2.19371e7 | 0.482140 | ||||||||
\(358\) | −9.41118e6 | −0.205114 | ||||||||
\(359\) | 5.98796e7 | 1.29418 | 0.647091 | − | 0.762413i | \(-0.275985\pi\) | ||||
0.647091 | + | 0.762413i | \(0.275985\pi\) | |||||||
\(360\) | 1.56554e7i | 0.335550i | ||||||||
\(361\) | 6.54247e7 | 1.39066 | ||||||||
\(362\) | − | 5.24149e7i | − | 1.10492i | ||||||
\(363\) | −2.65702e7 | −0.555488 | ||||||||
\(364\) | − | 3.66252e7i | − | 0.759410i | ||||||
\(365\) | 2.22850e7i | 0.458284i | ||||||||
\(366\) | 5.41609e7 | 1.10470 | ||||||||
\(367\) | 6.54533e7i | 1.32414i | 0.749443 | + | 0.662069i | \(0.230322\pi\) | ||||
−0.749443 | + | 0.662069i | \(0.769678\pi\) | |||||||
\(368\) | − | 6.15605e6i | − | 0.123526i | ||||||
\(369\) | −1.18740e7 | −0.236330 | ||||||||
\(370\) | 4.28137e6 | 0.0845235 | ||||||||
\(371\) | −1.11465e8 | −2.18281 | ||||||||
\(372\) | − | 9.62812e7i | − | 1.87031i | ||||||
\(373\) | 6.29630e7 | 1.21327 | 0.606637 | − | 0.794979i | \(-0.292518\pi\) | ||||
0.606637 | + | 0.794979i | \(0.292518\pi\) | |||||||
\(374\) | 1.10465e7 | 0.211160 | ||||||||
\(375\) | 3.06502e7 | 0.581218 | ||||||||
\(376\) | 1.21857e7 | 0.229238 | ||||||||
\(377\) | − | 2.09825e6i | − | 0.0391591i | ||||||
\(378\) | 2.35026e7i | 0.435151i | ||||||||
\(379\) | −2.82722e7 | −0.519328 | −0.259664 | − | 0.965699i | \(-0.583612\pi\) | ||||
−0.259664 | + | 0.965699i | \(0.583612\pi\) | |||||||
\(380\) | 1.02938e8 | 1.87597 | ||||||||
\(381\) | −9.49338e6 | −0.171651 | ||||||||
\(382\) | 1.79039e7 | 0.321187 | ||||||||
\(383\) | −1.86237e7 | −0.331489 | −0.165744 | − | 0.986169i | \(-0.553003\pi\) | ||||
−0.165744 | + | 0.986169i | \(0.553003\pi\) | |||||||
\(384\) | 5.88732e7i | 1.03974i | ||||||||
\(385\) | − | 9.17030e6i | − | 0.160695i | ||||||
\(386\) | − | 2.91197e7i | − | 0.506320i | ||||||
\(387\) | 9.89032e6i | 0.170639i | ||||||||
\(388\) | − | 3.85716e7i | − | 0.660348i | ||||||
\(389\) | −4.03075e7 | −0.684758 | −0.342379 | − | 0.939562i | \(-0.611233\pi\) | ||||
−0.342379 | + | 0.939562i | \(0.611233\pi\) | |||||||
\(390\) | −1.09160e7 | −0.184021 | ||||||||
\(391\) | 5.71324e6i | 0.0955767i | ||||||||
\(392\) | 7.16871e7i | 1.19010i | ||||||||
\(393\) | 5.53368e6i | 0.0911667i | ||||||||
\(394\) | 2.70350e7i | 0.442016i | ||||||||
\(395\) | −4.14981e7 | −0.673344 | ||||||||
\(396\) | 7.80682e6i | 0.125715i | ||||||||
\(397\) | − | 6.55839e7i | − | 1.04816i | −0.851671 | − | 0.524078i | \(-0.824410\pi\) | ||
0.851671 | − | 0.524078i | \(-0.175590\pi\) | |||||||
\(398\) | − | 1.51280e8i | − | 2.39956i | ||||||
\(399\) | 7.48004e7 | 1.17757 | ||||||||
\(400\) | −3.18429e7 | −0.497545 | ||||||||
\(401\) | 1.24598e8i | 1.93232i | 0.257950 | + | 0.966158i | \(0.416953\pi\) | ||||
−0.257950 | + | 0.966158i | \(0.583047\pi\) | |||||||
\(402\) | 1.01601e8 | 1.56394 | ||||||||
\(403\) | 3.24950e7 | 0.496479 | ||||||||
\(404\) | − | 6.53294e7i | − | 0.990751i | ||||||
\(405\) | 4.62070e6 | 0.0695573 | ||||||||
\(406\) | 1.99491e7i | 0.298089i | ||||||||
\(407\) | 1.03340e6 | 0.0153280 | ||||||||
\(408\) | 3.99172e7i | 0.587733i | ||||||||
\(409\) | − | 1.03807e8i | − | 1.51725i | −0.651526 | − | 0.758626i | \(-0.725871\pi\) | ||
0.651526 | − | 0.758626i | \(-0.274129\pi\) | |||||||
\(410\) | 5.24339e7i | 0.760783i | ||||||||
\(411\) | 5.47723e7 | 0.788924 | ||||||||
\(412\) | − | 4.49202e7i | − | 0.642318i | ||||||
\(413\) | −2.13891e7 | + | 9.04309e7i | −0.303628 | + | 1.28371i | ||||
\(414\) | −6.12096e6 | −0.0862618 | ||||||||
\(415\) | 7.41156e7i | 1.03697i | ||||||||
\(416\) | −4.39595e6 | −0.0610622 | ||||||||
\(417\) | 4.75319e7 | 0.655507 | ||||||||
\(418\) | 3.76662e7 | 0.515730 | ||||||||
\(419\) | 9.05965e7i | 1.23160i | 0.787903 | + | 0.615799i | \(0.211167\pi\) | ||||
−0.787903 | + | 0.615799i | \(0.788833\pi\) | |||||||
\(420\) | 6.84605e7 | 0.924043 | ||||||||
\(421\) | 2.63419e7i | 0.353022i | 0.984299 | + | 0.176511i | \(0.0564811\pi\) | ||||
−0.984299 | + | 0.176511i | \(0.943519\pi\) | |||||||
\(422\) | −1.58589e8 | −2.11026 | ||||||||
\(423\) | − | 3.59662e6i | − | 0.0475196i | ||||||
\(424\) | − | 2.02824e8i | − | 2.66086i | ||||||
\(425\) | 2.95523e7 | 0.384968 | ||||||||
\(426\) | 1.61579e7i | 0.209005i | ||||||||
\(427\) | − | 1.14641e8i | − | 1.47250i | ||||||
\(428\) | −1.01571e7 | −0.129550 | ||||||||
\(429\) | −2.63481e6 | −0.0333716 | ||||||||
\(430\) | 4.36741e7 | 0.549312 | ||||||||
\(431\) | − | 4.56261e7i | − | 0.569877i | −0.958546 | − | 0.284939i | \(-0.908027\pi\) | ||
0.958546 | − | 0.284939i | \(-0.0919732\pi\) | |||||||
\(432\) | −1.26947e7 | −0.157461 | ||||||||
\(433\) | −1.22197e8 | −1.50521 | −0.752604 | − | 0.658473i | \(-0.771202\pi\) | ||||
−0.752604 | + | 0.658473i | \(0.771202\pi\) | |||||||
\(434\) | −3.08947e8 | −3.77932 | ||||||||
\(435\) | 3.92208e6 | 0.0476485 | ||||||||
\(436\) | − | 8.17808e7i | − | 0.986716i | ||||||
\(437\) | 1.94808e7i | 0.233434i | ||||||||
\(438\) | −6.08760e7 | −0.724475 | ||||||||
\(439\) | 5.78606e7 | 0.683895 | 0.341947 | − | 0.939719i | \(-0.388914\pi\) | ||||
0.341947 | + | 0.939719i | \(0.388914\pi\) | |||||||
\(440\) | 1.66865e7 | 0.195888 | ||||||||
\(441\) | 2.11585e7 | 0.246700 | ||||||||
\(442\) | −2.78328e7 | −0.322323 | ||||||||
\(443\) | 1.17033e8i | 1.34616i | 0.739570 | + | 0.673079i | \(0.235029\pi\) | ||||
−0.739570 | + | 0.673079i | \(0.764971\pi\) | |||||||
\(444\) | 7.71483e6i | 0.0881409i | ||||||||
\(445\) | − | 7.71559e7i | − | 0.875567i | ||||||
\(446\) | 1.32528e7i | 0.149384i | ||||||||
\(447\) | − | 2.66891e7i | − | 0.298821i | ||||||
\(448\) | 1.38840e8 | 1.54412 | ||||||||
\(449\) | −1.21901e8 | −1.34669 | −0.673344 | − | 0.739329i | \(-0.735143\pi\) | ||||
−0.673344 | + | 0.739329i | \(0.735143\pi\) | |||||||
\(450\) | 3.16613e7i | 0.347449i | ||||||||
\(451\) | 1.26561e7i | 0.137965i | ||||||||
\(452\) | − | 9.43450e7i | − | 1.02165i | ||||||
\(453\) | 4.47104e7i | 0.480966i | ||||||||
\(454\) | −1.53153e7 | −0.163666 | ||||||||
\(455\) | 2.31055e7i | 0.245291i | ||||||||
\(456\) | 1.36109e8i | 1.43546i | ||||||||
\(457\) | − | 1.76454e8i | − | 1.84877i | −0.381462 | − | 0.924385i | \(-0.624579\pi\) | ||
0.381462 | − | 0.924385i | \(-0.375421\pi\) | |||||||
\(458\) | 1.14442e8 | 1.19122 | ||||||||
\(459\) | 1.17816e7 | 0.121833 | ||||||||
\(460\) | 1.78297e7i | 0.183177i | ||||||||
\(461\) | −1.42578e8 | −1.45530 | −0.727648 | − | 0.685951i | \(-0.759386\pi\) | ||||
−0.727648 | + | 0.685951i | \(0.759386\pi\) | |||||||
\(462\) | 2.50505e7 | 0.254033 | ||||||||
\(463\) | 1.45074e8i | 1.46166i | 0.682558 | + | 0.730832i | \(0.260868\pi\) | ||||
−0.682558 | + | 0.730832i | \(0.739132\pi\) | |||||||
\(464\) | −1.07754e7 | −0.107864 | ||||||||
\(465\) | 6.07402e7i | 0.604112i | ||||||||
\(466\) | −2.39628e8 | −2.36799 | ||||||||
\(467\) | − | 1.48028e8i | − | 1.45342i | −0.686942 | − | 0.726712i | \(-0.741048\pi\) | ||
0.686942 | − | 0.726712i | \(-0.258952\pi\) | |||||||
\(468\) | − | 1.96701e7i | − | 0.191897i | ||||||
\(469\) | − | 2.15057e8i | − | 2.08465i | ||||||
\(470\) | −1.58821e7 | −0.152973 | ||||||||
\(471\) | 343827.i | 0.00329062i | ||||||||
\(472\) | −1.64550e8 | − | 3.89201e7i | −1.56485 | − | 0.370125i | ||||
\(473\) | 1.05417e7 | 0.0996157 | ||||||||
\(474\) | − | 1.13360e8i | − | 1.06445i | ||||||
\(475\) | 1.00767e8 | 0.940235 | ||||||||
\(476\) | 1.74556e8 | 1.61851 | ||||||||
\(477\) | −5.98636e7 | −0.551579 | ||||||||
\(478\) | 2.40276e8i | 2.20002i | ||||||||
\(479\) | −1.49506e8 | −1.36036 | −0.680178 | − | 0.733047i | \(-0.738098\pi\) | ||||
−0.680178 | + | 0.733047i | \(0.738098\pi\) | |||||||
\(480\) | − | 8.21698e6i | − | 0.0743000i | ||||||
\(481\) | −2.60376e6 | −0.0233973 | ||||||||
\(482\) | 5.81910e6i | 0.0519654i | ||||||||
\(483\) | 1.29560e7i | 0.114982i | ||||||||
\(484\) | −2.11423e8 | −1.86473 | ||||||||
\(485\) | 2.43334e7i | 0.213293i | ||||||||
\(486\) | 1.26224e7i | 0.109959i | ||||||||
\(487\) | −1.09033e8 | −0.943996 | −0.471998 | − | 0.881600i | \(-0.656467\pi\) | ||||
−0.471998 | + | 0.881600i | \(0.656467\pi\) | |||||||
\(488\) | 2.08603e8 | 1.79499 | ||||||||
\(489\) | 5.19445e7 | 0.444235 | ||||||||
\(490\) | − | 9.34325e7i | − | 0.794163i | ||||||
\(491\) | −1.57201e8 | −1.32804 | −0.664019 | − | 0.747715i | \(-0.731151\pi\) | ||||
−0.664019 | + | 0.747715i | \(0.731151\pi\) | |||||||
\(492\) | −9.44835e7 | −0.793343 | ||||||||
\(493\) | 1.00003e7 | 0.0834587 | ||||||||
\(494\) | −9.49037e7 | −0.787231 | ||||||||
\(495\) | − | 4.92503e6i | − | 0.0406063i | ||||||
\(496\) | − | 1.66875e8i | − | 1.36756i | ||||||
\(497\) | 3.42009e7 | 0.278592 | ||||||||
\(498\) | −2.02461e8 | −1.63928 | ||||||||
\(499\) | 6.89738e7 | 0.555114 | 0.277557 | − | 0.960709i | \(-0.410475\pi\) | ||||
0.277557 | + | 0.960709i | \(0.410475\pi\) | |||||||
\(500\) | 2.43888e8 | 1.95110 | ||||||||
\(501\) | 2.78145e7 | 0.221186 | ||||||||
\(502\) | 2.56900e7i | 0.203073i | ||||||||
\(503\) | − | 1.36368e8i | − | 1.07154i | −0.844363 | − | 0.535771i | \(-0.820021\pi\) | ||
0.844363 | − | 0.535771i | \(-0.179979\pi\) | |||||||
\(504\) | 9.05213e7i | 0.707064i | ||||||||
\(505\) | 4.12138e7i | 0.320014i | ||||||||
\(506\) | 6.52409e6i | 0.0503580i | ||||||||
\(507\) | −6.86038e7 | −0.526411 | ||||||||
\(508\) | −7.55402e7 | −0.576219 | ||||||||
\(509\) | 2.13696e7i | 0.162047i | 0.996712 | + | 0.0810237i | \(0.0258190\pi\) | ||||
−0.996712 | + | 0.0810237i | \(0.974181\pi\) | |||||||
\(510\) | − | 5.20256e7i | − | 0.392199i | ||||||
\(511\) | 1.28854e8i | 0.965687i | ||||||||
\(512\) | 1.99161e8i | 1.48387i | ||||||||
\(513\) | 4.01725e7 | 0.297562 | ||||||||
\(514\) | − | 4.88412e7i | − | 0.359664i | ||||||
\(515\) | 2.83385e7i | 0.207470i | ||||||||
\(516\) | 7.86987e7i | 0.572821i | ||||||||
\(517\) | −3.83349e6 | −0.0277411 | ||||||||
\(518\) | 2.47553e7 | 0.178106 | ||||||||
\(519\) | 6.01605e7i | 0.430338i | ||||||||
\(520\) | −4.20434e7 | −0.299011 | ||||||||
\(521\) | −2.25805e8 | −1.59669 | −0.798345 | − | 0.602200i | \(-0.794291\pi\) | ||||
−0.798345 | + | 0.602200i | \(0.794291\pi\) | |||||||
\(522\) | 1.07139e7i | 0.0753248i | ||||||||
\(523\) | 3.75262e7 | 0.262319 | 0.131160 | − | 0.991361i | \(-0.458130\pi\) | ||||
0.131160 | + | 0.991361i | \(0.458130\pi\) | |||||||
\(524\) | 4.40323e7i | 0.306040i | ||||||||
\(525\) | 6.70166e7 | 0.463131 | ||||||||
\(526\) | 1.50358e7i | 0.103317i | ||||||||
\(527\) | 1.54872e8i | 1.05813i | ||||||||
\(528\) | 1.35308e7i | 0.0919227i | ||||||||
\(529\) | 1.44662e8 | 0.977207 | ||||||||
\(530\) | 2.64348e8i | 1.77562i | ||||||||
\(531\) | −1.14873e7 | + | 4.85671e7i | −0.0767244 | + | 0.324383i | ||||
\(532\) | 5.95198e8 | 3.95300 | ||||||||
\(533\) | − | 3.18883e7i | − | 0.210596i | ||||||
\(534\) | 2.10767e8 | 1.38413 | ||||||||
\(535\) | 6.40771e6 | 0.0418448 | ||||||||
\(536\) | 3.91323e8 | 2.54121 | ||||||||
\(537\) | 1.06985e7i | 0.0690875i | ||||||||
\(538\) | −1.78262e8 | −1.14476 | ||||||||
\(539\) | − | 2.25520e7i | − | 0.144019i | ||||||
\(540\) | 3.67676e7 | 0.233499 | ||||||||
\(541\) | − | 1.13661e8i | − | 0.717825i | −0.933371 | − | 0.358913i | \(-0.883148\pi\) | ||
0.933371 | − | 0.358913i | \(-0.116852\pi\) | |||||||
\(542\) | − | 6.16590e7i | − | 0.387257i | ||||||
\(543\) | −5.95845e7 | −0.372163 | ||||||||
\(544\) | − | 2.09511e7i | − | 0.130140i | ||||||
\(545\) | 5.15925e7i | 0.318711i | ||||||||
\(546\) | −6.31172e7 | −0.387766 | ||||||||
\(547\) | −1.35059e8 | −0.825203 | −0.412601 | − | 0.910912i | \(-0.635380\pi\) | ||||
−0.412601 | + | 0.910912i | \(0.635380\pi\) | |||||||
\(548\) | 4.35831e8 | 2.64836 | ||||||||
\(549\) | − | 6.15693e7i | − | 0.372089i | ||||||
\(550\) | 3.37466e7 | 0.202834 | ||||||||
\(551\) | 3.40987e7 | 0.203837 | ||||||||
\(552\) | −2.35752e7 | −0.140164 | ||||||||
\(553\) | −2.39946e8 | −1.41886 | ||||||||
\(554\) | − | 1.28501e8i | − | 0.755748i | ||||||
\(555\) | − | 4.86700e6i | − | 0.0284696i | ||||||
\(556\) | 3.78218e8 | 2.20048 | ||||||||
\(557\) | 8.63421e7 | 0.499640 | 0.249820 | − | 0.968292i | \(-0.419629\pi\) | ||||
0.249820 | + | 0.968292i | \(0.419629\pi\) | |||||||
\(558\) | −1.65924e8 | −0.955006 | ||||||||
\(559\) | −2.65609e7 | −0.152057 | ||||||||
\(560\) | 1.18656e8 | 0.675657 | ||||||||
\(561\) | − | 1.25575e7i | − | 0.0711239i | ||||||
\(562\) | 3.72204e8i | 2.09687i | ||||||||
\(563\) | 1.55337e8i | 0.870461i | 0.900319 | + | 0.435231i | \(0.143333\pi\) | ||||
−0.900319 | + | 0.435231i | \(0.856667\pi\) | |||||||
\(564\) | − | 2.86188e7i | − | 0.159520i | ||||||
\(565\) | 5.95187e7i | 0.329996i | ||||||||
\(566\) | 3.56956e8 | 1.96864 | ||||||||
\(567\) | 2.67174e7 | 0.146570 | ||||||||
\(568\) | 6.22329e7i | 0.339606i | ||||||||
\(569\) | − | 3.58071e7i | − | 0.194371i | −0.995266 | − | 0.0971856i | \(-0.969016\pi\) | ||
0.995266 | − | 0.0971856i | \(-0.0309840\pi\) | |||||||
\(570\) | − | 1.77396e8i | − | 0.957896i | ||||||
\(571\) | − | 4.23278e7i | − | 0.227362i | −0.993517 | − | 0.113681i | \(-0.963736\pi\) | ||
0.993517 | − | 0.113681i | \(-0.0362642\pi\) | |||||||
\(572\) | −2.09656e7 | −0.112026 | ||||||||
\(573\) | − | 2.03529e7i | − | 0.108184i | ||||||
\(574\) | 3.03178e8i | 1.60311i | ||||||||
\(575\) | 1.74537e7i | 0.0918085i | ||||||||
\(576\) | 7.45658e7 | 0.390187 | ||||||||
\(577\) | −1.16324e8 | −0.605541 | −0.302770 | − | 0.953064i | \(-0.597912\pi\) | ||||
−0.302770 | + | 0.953064i | \(0.597912\pi\) | |||||||
\(578\) | 1.98341e8i | 1.02714i | ||||||||
\(579\) | −3.31029e7 | −0.170541 | ||||||||
\(580\) | 3.12086e7 | 0.159952 | ||||||||
\(581\) | 4.28544e8i | 2.18508i | ||||||||
\(582\) | −6.64715e7 | −0.337183 | ||||||||
\(583\) | 6.38063e7i | 0.322002i | ||||||||
\(584\) | −2.34467e8 | −1.17718 | ||||||||
\(585\) | 1.24091e7i | 0.0619830i | ||||||||
\(586\) | 3.49977e8i | 1.73919i | ||||||||
\(587\) | − | 2.56920e8i | − | 1.27024i | −0.772415 | − | 0.635118i | \(-0.780951\pi\) | ||
0.772415 | − | 0.635118i | \(-0.219049\pi\) | |||||||
\(588\) | 1.68361e8 | 0.828151 | ||||||||
\(589\) | 5.28077e8i | 2.58435i | ||||||||
\(590\) | 2.14465e8 | + | 5.07261e7i | 1.04424 | + | 0.246988i | ||||
\(591\) | 3.07330e7 | 0.148882 | ||||||||
\(592\) | 1.33714e7i | 0.0644483i | ||||||||
\(593\) | 2.20865e7 | 0.105916 | 0.0529581 | − | 0.998597i | \(-0.483135\pi\) | ||||
0.0529581 | + | 0.998597i | \(0.483135\pi\) | |||||||
\(594\) | 1.34537e7 | 0.0641922 | ||||||||
\(595\) | −1.10121e8 | −0.522781 | ||||||||
\(596\) | − | 2.12369e8i | − | 1.00312i | ||||||
\(597\) | −1.71972e8 | −0.808231 | ||||||||
\(598\) | − | 1.64381e7i | − | 0.0768685i | ||||||
\(599\) | −3.37760e8 | −1.57155 | −0.785773 | − | 0.618515i | \(-0.787735\pi\) | ||||
−0.785773 | + | 0.618515i | \(0.787735\pi\) | |||||||
\(600\) | 1.21945e8i | 0.564561i | ||||||||
\(601\) | − | 1.94838e8i | − | 0.897533i | −0.893649 | − | 0.448766i | \(-0.851864\pi\) | ||
0.893649 | − | 0.448766i | \(-0.148136\pi\) | |||||||
\(602\) | 2.52528e8 | 1.15750 | ||||||||
\(603\) | − | 1.15499e8i | − | 0.526776i | ||||||
\(604\) | 3.55767e8i | 1.61456i | ||||||||
\(605\) | 1.33379e8 | 0.602311 | ||||||||
\(606\) | −1.12584e8 | −0.505892 | ||||||||
\(607\) | 1.31760e7 | 0.0589138 | 0.0294569 | − | 0.999566i | \(-0.490622\pi\) | ||||
0.0294569 | + | 0.999566i | \(0.490622\pi\) | |||||||
\(608\) | − | 7.14387e7i | − | 0.317850i | ||||||
\(609\) | 2.26779e7 | 0.100404 | ||||||||
\(610\) | −2.71881e8 | −1.19781 | ||||||||
\(611\) | 9.65887e6 | 0.0423451 | ||||||||
\(612\) | 9.37478e7 | 0.408984 | ||||||||
\(613\) | 9.33914e7i | 0.405439i | 0.979237 | + | 0.202719i | \(0.0649779\pi\) | ||||
−0.979237 | + | 0.202719i | \(0.935022\pi\) | |||||||
\(614\) | − | 5.63652e8i | − | 2.43504i | ||||||
\(615\) | 5.96061e7 | 0.256251 | ||||||||
\(616\) | 9.64831e7 | 0.412771 | ||||||||
\(617\) | 2.34906e8 | 1.00009 | 0.500045 | − | 0.866000i | \(-0.333317\pi\) | ||||
0.500045 | + | 0.866000i | \(0.333317\pi\) | |||||||
\(618\) | −7.74121e7 | −0.327977 | ||||||||
\(619\) | 3.69057e8 | 1.55604 | 0.778020 | − | 0.628239i | \(-0.216224\pi\) | ||||
0.778020 | + | 0.628239i | \(0.216224\pi\) | |||||||
\(620\) | 4.83319e8i | 2.02796i | ||||||||
\(621\) | 6.95821e6i | 0.0290551i | ||||||||
\(622\) | − | 6.13472e8i | − | 2.54932i | ||||||
\(623\) | − | 4.46123e8i | − | 1.84498i | ||||||
\(624\) | − | 3.40923e7i | − | 0.140314i | ||||||
\(625\) | −5.39683e6 | −0.0221054 | ||||||||
\(626\) | −4.19899e8 | −1.71168 | ||||||||
\(627\) | − | 4.28183e7i | − | 0.173711i | ||||||
\(628\) | 2.73589e6i | 0.0110464i | ||||||||
\(629\) | − | 1.24096e7i | − | 0.0498660i | ||||||
\(630\) | − | 1.17980e8i | − | 0.471830i | ||||||
\(631\) | −2.90620e7 | −0.115675 | −0.0578373 | − | 0.998326i | \(-0.518420\pi\) | ||||
−0.0578373 | + | 0.998326i | \(0.518420\pi\) | |||||||
\(632\) | − | 4.36613e8i | − | 1.72960i | ||||||
\(633\) | 1.80282e8i | 0.710789i | ||||||||
\(634\) | − | 7.96657e8i | − | 3.12611i | ||||||
\(635\) | 4.76555e7 | 0.186120 | ||||||||
\(636\) | −4.76344e8 | −1.85161 | ||||||||
\(637\) | 5.68220e7i | 0.219836i | ||||||||
\(638\) | 1.14196e7 | 0.0439732 | ||||||||
\(639\) | 1.83680e7 | 0.0703980 | ||||||||
\(640\) | − | 2.95535e8i | − | 1.12738i | ||||||
\(641\) | 5.18494e8 | 1.96865 | 0.984327 | − | 0.176353i | \(-0.0564301\pi\) | ||||
0.984327 | + | 0.176353i | \(0.0564301\pi\) | |||||||
\(642\) | 1.75039e7i | 0.0661501i | ||||||||
\(643\) | −1.94176e8 | −0.730403 | −0.365202 | − | 0.930928i | \(-0.619000\pi\) | ||||
−0.365202 | + | 0.930928i | \(0.619000\pi\) | |||||||
\(644\) | 1.03093e8i | 0.385987i | ||||||||
\(645\) | − | 4.96481e7i | − | 0.185022i | ||||||
\(646\) | − | 4.52312e8i | − | 1.67780i | ||||||
\(647\) | 5.09645e8 | 1.88172 | 0.940859 | − | 0.338798i | \(-0.110020\pi\) | ||||
0.940859 | + | 0.338798i | \(0.110020\pi\) | |||||||
\(648\) | 4.86156e7i | 0.178670i | ||||||||
\(649\) | 5.17658e7 | + | 1.22439e7i | 0.189369 | + | 0.0447903i | ||||
\(650\) | −8.50279e7 | −0.309614 | ||||||||
\(651\) | 3.51206e8i | 1.27297i | ||||||||
\(652\) | 4.13330e8 | 1.49126 | ||||||||
\(653\) | 1.15463e8 | 0.414672 | 0.207336 | − | 0.978270i | \(-0.433521\pi\) | ||||
0.207336 | + | 0.978270i | \(0.433521\pi\) | |||||||
\(654\) | −1.40935e8 | −0.503832 | ||||||||
\(655\) | − | 2.77783e7i | − | 0.0988513i | ||||||
\(656\) | −1.63759e8 | −0.580089 | ||||||||
\(657\) | 6.92029e7i | 0.244021i | ||||||||
\(658\) | −9.18319e7 | −0.322341 | ||||||||
\(659\) | 2.63375e8i | 0.920277i | 0.887847 | + | 0.460139i | \(0.152200\pi\) | ||||
−0.887847 | + | 0.460139i | \(0.847800\pi\) | |||||||
\(660\) | − | 3.91892e7i | − | 0.136312i | ||||||
\(661\) | −3.64442e7 | −0.126190 | −0.0630948 | − | 0.998008i | \(-0.520097\pi\) | ||||
−0.0630948 | + | 0.998008i | \(0.520097\pi\) | |||||||
\(662\) | − | 4.56403e8i | − | 1.57317i | ||||||
\(663\) | 3.16400e7i | 0.108566i | ||||||||
\(664\) | −7.79790e8 | −2.66363 | ||||||||
\(665\) | −3.75488e8 | −1.27682 | ||||||||
\(666\) | 1.32952e7 | 0.0450060 | ||||||||
\(667\) | 5.90618e6i | 0.0199035i | ||||||||
\(668\) | 2.21324e8 | 0.742505 | ||||||||
\(669\) | 1.50656e7 | 0.0503162 | ||||||||
\(670\) | −5.10025e8 | −1.69577 | ||||||||
\(671\) | −6.56244e7 | −0.217219 | ||||||||
\(672\) | − | 4.75114e7i | − | 0.156563i | ||||||
\(673\) | − | 3.87285e8i | − | 1.27053i | −0.772293 | − | 0.635266i | \(-0.780890\pi\) | ||
0.772293 | − | 0.635266i | \(-0.219110\pi\) | |||||||
\(674\) | −2.56811e8 | −0.838751 | ||||||||
\(675\) | 3.59921e7 | 0.117030 | ||||||||
\(676\) | −5.45891e8 | −1.76712 | ||||||||
\(677\) | −6.45220e7 | −0.207942 | −0.103971 | − | 0.994580i | \(-0.533155\pi\) | ||||
−0.103971 | + | 0.994580i | \(0.533155\pi\) | |||||||
\(678\) | −1.62587e8 | −0.521671 | ||||||||
\(679\) | 1.40698e8i | 0.449448i | ||||||||
\(680\) | − | 2.00379e8i | − | 0.637274i | ||||||
\(681\) | 1.74102e7i | 0.0551268i | ||||||||
\(682\) | 1.76852e8i | 0.557515i | ||||||||
\(683\) | 2.66210e8i | 0.835531i | 0.908555 | + | 0.417765i | \(0.137187\pi\) | ||||
−0.908555 | + | 0.417765i | \(0.862813\pi\) | |||||||
\(684\) | 3.19659e8 | 0.998891 | ||||||||
\(685\) | −2.74950e8 | −0.855424 | ||||||||
\(686\) | 1.89715e8i | 0.587666i | ||||||||
\(687\) | − | 1.30096e8i | − | 0.401231i | ||||||
\(688\) | 1.36401e8i | 0.418844i | ||||||||
\(689\) | − | 1.60766e8i | − | 0.491516i | ||||||
\(690\) | 3.07264e7 | 0.0935329 | ||||||||
\(691\) | − | 2.91925e6i | − | 0.00884785i | −0.999990 | − | 0.00442392i | \(-0.998592\pi\) | ||
0.999990 | − | 0.00442392i | \(-0.00140818\pi\) | |||||||
\(692\) | 4.78706e8i | 1.44461i | ||||||||
\(693\) | − | 2.84770e7i | − | 0.0855647i | ||||||
\(694\) | 4.09011e8 | 1.22365 | ||||||||
\(695\) | −2.38604e8 | −0.710760 | ||||||||
\(696\) | 4.12653e7i | 0.122393i | ||||||||
\(697\) | 1.51980e8 | 0.448836 | ||||||||
\(698\) | −1.06427e9 | −3.12958 | ||||||||
\(699\) | 2.72406e8i | 0.797600i | ||||||||
\(700\) | 5.33261e8 | 1.55470 | ||||||||
\(701\) | 5.60034e8i | 1.62577i | 0.582421 | + | 0.812887i | \(0.302105\pi\) | ||||
−0.582421 | + | 0.812887i | \(0.697895\pi\) | |||||||
\(702\) | −3.38979e7 | −0.0979854 | ||||||||
\(703\) | − | 4.23138e7i | − | 0.121791i | ||||||
\(704\) | − | 7.94768e7i | − | 0.227784i | ||||||
\(705\) | 1.80545e7i | 0.0515251i | ||||||||
\(706\) | −9.07702e8 | −2.57946 | ||||||||
\(707\) | 2.38303e8i | 0.674327i | ||||||||
\(708\) | −9.14060e7 | + | 3.86456e8i | −0.257558 | + | 1.08893i | ||||
\(709\) | −1.51717e7 | −0.0425692 | −0.0212846 | − | 0.999773i | \(-0.506776\pi\) | ||||
−0.0212846 | + | 0.999773i | \(0.506776\pi\) | |||||||
\(710\) | − | 8.11104e7i | − | 0.226622i | ||||||
\(711\) | −1.28866e8 | −0.358534 | ||||||||
\(712\) | 8.11778e8 | 2.24904 | ||||||||
\(713\) | −9.14673e7 | −0.252347 | ||||||||
\(714\) | − | 3.00817e8i | − | 0.826434i | ||||||
\(715\) | 1.32264e7 | 0.0361845 | ||||||||
\(716\) | 8.51294e7i | 0.231921i | ||||||||
\(717\) | 2.73142e8 | 0.741023 | ||||||||
\(718\) | − | 8.21114e8i | − | 2.21835i | ||||||
\(719\) | 3.86036e8i | 1.03858i | 0.854597 | + | 0.519292i | \(0.173804\pi\) | ||||
−0.854597 | + | 0.519292i | \(0.826196\pi\) | |||||||
\(720\) | 6.37259e7 | 0.170733 | ||||||||
\(721\) | 1.63856e8i | 0.437176i | ||||||||
\(722\) | − | 8.97153e8i | − | 2.38372i | ||||||
\(723\) | 6.61506e6 | 0.0175033 | ||||||||
\(724\) | −4.74123e8 | −1.24932 | ||||||||
\(725\) | 3.05503e7 | 0.0801682 | ||||||||
\(726\) | 3.64350e8i | 0.952159i | ||||||||
\(727\) | 3.33880e8 | 0.868935 | 0.434468 | − | 0.900687i | \(-0.356937\pi\) | ||||
0.434468 | + | 0.900687i | \(0.356937\pi\) | |||||||
\(728\) | −2.43099e8 | −0.630070 | ||||||||
\(729\) | 1.43489e7 | 0.0370370 | ||||||||
\(730\) | 3.05589e8 | 0.785542 | ||||||||
\(731\) | − | 1.26590e8i | − | 0.324075i | ||||||
\(732\) | − | 4.89916e8i | − | 1.24908i | ||||||
\(733\) | −7.33257e8 | −1.86185 | −0.930924 | − | 0.365214i | \(-0.880996\pi\) | ||||
−0.930924 | + | 0.365214i | \(0.880996\pi\) | |||||||
\(734\) | 8.97545e8 | 2.26970 | ||||||||
\(735\) | −1.06213e8 | −0.267494 | ||||||||
\(736\) | 1.23738e7 | 0.0310362 | ||||||||
\(737\) | −1.23106e8 | −0.307522 | ||||||||
\(738\) | 1.62826e8i | 0.405092i | ||||||||
\(739\) | − | 8.14134e7i | − | 0.201726i | −0.994900 | − | 0.100863i | \(-0.967840\pi\) | ||
0.994900 | − | 0.100863i | \(-0.0321604\pi\) | |||||||
\(740\) | − | 3.87274e7i | − | 0.0955704i | ||||||
\(741\) | 1.07885e8i | 0.265159i | ||||||||
\(742\) | 1.52849e9i | 3.74154i | ||||||||
\(743\) | 3.99055e8 | 0.972895 | 0.486448 | − | 0.873710i | \(-0.338292\pi\) | ||||
0.486448 | + | 0.873710i | \(0.338292\pi\) | |||||||
\(744\) | −6.39063e8 | −1.55176 | ||||||||
\(745\) | 1.33976e8i | 0.324009i | ||||||||
\(746\) | − | 8.63397e8i | − | 2.07967i | ||||||
\(747\) | 2.30155e8i | 0.552152i | ||||||||
\(748\) | − | 9.99222e7i | − | 0.238758i | ||||||
\(749\) | 3.70500e7 | 0.0881746 | ||||||||
\(750\) | − | 4.20298e8i | − | 0.996262i | ||||||
\(751\) | − | 6.73928e8i | − | 1.59109i | −0.605897 | − | 0.795543i | \(-0.707186\pi\) | ||
0.605897 | − | 0.795543i | \(-0.292814\pi\) | |||||||
\(752\) | − | 4.96023e7i | − | 0.116640i | ||||||
\(753\) | 2.92040e7 | 0.0684003 | ||||||||
\(754\) | −2.87728e7 | −0.0671224 | ||||||||
\(755\) | − | 2.24440e8i | − | 0.521507i | ||||||
\(756\) | 2.12594e8 | 0.492023 | ||||||||
\(757\) | 6.32443e8 | 1.45792 | 0.728960 | − | 0.684556i | \(-0.240004\pi\) | ||||
0.728960 | + | 0.684556i | \(0.240004\pi\) | |||||||
\(758\) | 3.87689e8i | 0.890177i | ||||||||
\(759\) | 7.41649e6 | 0.0169619 | ||||||||
\(760\) | − | 6.83248e8i | − | 1.55646i | ||||||
\(761\) | −3.07136e8 | −0.696909 | −0.348454 | − | 0.937326i | \(-0.613293\pi\) | ||||
−0.348454 | + | 0.937326i | \(0.613293\pi\) | |||||||
\(762\) | 1.30180e8i | 0.294226i | ||||||||
\(763\) | 2.98313e8i | 0.671581i | ||||||||
\(764\) | − | 1.61951e8i | − | 0.363164i | ||||||
\(765\) | −5.91420e7 | −0.132103 | ||||||||
\(766\) | 2.55382e8i | 0.568203i | ||||||||
\(767\) | −1.30429e8 | − | 3.08496e7i | −0.289060 | − | 0.0683697i | ||||
\(768\) | 5.01176e8 | 1.10639 | ||||||||
\(769\) | − | 4.77329e8i | − | 1.04964i | −0.851214 | − | 0.524818i | \(-0.824133\pi\) | ||
0.851214 | − | 0.524818i | \(-0.175867\pi\) | |||||||
\(770\) | −1.25750e8 | −0.275446 | ||||||||
\(771\) | −5.55219e7 | −0.121144 | ||||||||
\(772\) | −2.63404e8 | −0.572494 | ||||||||
\(773\) | 2.57272e8i | 0.556999i | 0.960436 | + | 0.278500i | \(0.0898371\pi\) | ||||
−0.960436 | + | 0.278500i | \(0.910163\pi\) | |||||||
\(774\) | 1.35624e8 | 0.292491 | ||||||||
\(775\) | 4.73125e8i | 1.01641i | ||||||||
\(776\) | −2.56018e8 | −0.547880 | ||||||||
\(777\) | − | 2.81415e7i | − | 0.0599906i | ||||||
\(778\) | 5.52727e8i | 1.17374i | ||||||||
\(779\) | 5.18217e8 | 1.09622 | ||||||||
\(780\) | 9.87411e7i | 0.208072i | ||||||||
\(781\) | − | 1.95778e7i | − | 0.0410970i | ||||||
\(782\) | 7.83443e7 | 0.163828 | ||||||||
\(783\) | 1.21794e7 | 0.0253713 | ||||||||
\(784\) | 2.91804e8 | 0.605541 | ||||||||
\(785\) | − | 1.72597e6i | − | 0.00356799i | ||||||
\(786\) | 7.58820e7 | 0.156268 | ||||||||
\(787\) | −3.50470e8 | −0.718996 | −0.359498 | − | 0.933146i | \(-0.617052\pi\) | ||||
−0.359498 | + | 0.933146i | \(0.617052\pi\) | |||||||
\(788\) | 2.44547e8 | 0.499786 | ||||||||
\(789\) | 1.70925e7 | 0.0347997 | ||||||||
\(790\) | 5.69054e8i | 1.15418i | ||||||||
\(791\) | 3.44143e8i | 0.695360i | ||||||||
\(792\) | 5.18175e7 | 0.104304 | ||||||||
\(793\) | 1.65347e8 | 0.331572 | ||||||||
\(794\) | −8.99336e8 | −1.79664 | ||||||||
\(795\) | 3.00507e8 | 0.598072 | ||||||||
\(796\) | −1.36841e9 | −2.71317 | ||||||||
\(797\) | − | 2.47372e8i | − | 0.488626i | −0.969696 | − | 0.244313i | \(-0.921438\pi\) | ||
0.969696 | − | 0.244313i | \(-0.0785624\pi\) | |||||||
\(798\) | − | 1.02572e9i | − | 2.01846i | ||||||
\(799\) | 4.60343e7i | 0.0902488i | ||||||||
\(800\) | − | 6.40047e7i | − | 0.125009i | ||||||
\(801\) | − | 2.39596e8i | − | 0.466211i | ||||||
\(802\) | 1.70858e9 | 3.31217 | ||||||||
\(803\) | 7.37607e7 | 0.142455 | ||||||||
\(804\) | − | 9.19042e8i | − | 1.76835i | ||||||
\(805\) | − | 6.50376e7i | − | 0.124674i | ||||||
\(806\) | − | 4.45596e8i | − | 0.851012i | ||||||
\(807\) | 2.02646e8i | 0.385582i | ||||||||
\(808\) | −4.33622e8 | −0.822010 | ||||||||
\(809\) | − | 9.95238e8i | − | 1.87967i | −0.341629 | − | 0.939835i | \(-0.610979\pi\) | ||
0.341629 | − | 0.939835i | \(-0.389021\pi\) | |||||||
\(810\) | − | 6.33626e7i | − | 0.119228i | ||||||
\(811\) | − | 9.52402e8i | − | 1.78549i | −0.450560 | − | 0.892746i | \(-0.648776\pi\) | ||
0.450560 | − | 0.892746i | \(-0.351224\pi\) | |||||||
\(812\) | 1.80451e8 | 0.337048 | ||||||||
\(813\) | −7.00931e7 | −0.130438 | ||||||||
\(814\) | − | 1.41708e7i | − | 0.0262737i | ||||||
\(815\) | −2.60754e8 | −0.481680 | ||||||||
\(816\) | 1.62484e8 | 0.299048 | ||||||||
\(817\) | − | 4.31642e8i | − | 0.791512i | ||||||
\(818\) | −1.42348e9 | −2.60071 | ||||||||
\(819\) | 7.17507e7i | 0.130609i | ||||||||
\(820\) | 4.74295e8 | 0.860214 | ||||||||
\(821\) | − | 5.46045e7i | − | 0.0986731i | −0.998782 | − | 0.0493366i | \(-0.984289\pi\) | ||
0.998782 | − | 0.0493366i | \(-0.0157107\pi\) | |||||||
\(822\) | − | 7.51079e8i | − | 1.35229i | ||||||
\(823\) | 9.80986e8i | 1.75980i | 0.475159 | + | 0.879900i | \(0.342391\pi\) | ||||
−0.475159 | + | 0.879900i | \(0.657609\pi\) | |||||||
\(824\) | −2.98156e8 | −0.532921 | ||||||||
\(825\) | − | 3.83626e7i | − | 0.0683198i | ||||||
\(826\) | 1.24006e9 | + | 2.93303e8i | 2.20040 | + | 0.520447i | ||||
\(827\) | 9.25388e8 | 1.63609 | 0.818045 | − | 0.575154i | \(-0.195058\pi\) | ||||
0.818045 | + | 0.575154i | \(0.195058\pi\) | |||||||
\(828\) | 5.53676e7i | 0.0975359i | ||||||||
\(829\) | 7.87859e8 | 1.38288 | 0.691440 | − | 0.722433i | \(-0.256976\pi\) | ||||
0.691440 | + | 0.722433i | \(0.256976\pi\) | |||||||
\(830\) | 1.01633e9 | 1.77746 | ||||||||
\(831\) | −1.46078e8 | −0.254555 | ||||||||
\(832\) | 2.00250e8i | 0.347698i | ||||||||
\(833\) | −2.70814e8 | −0.468529 | ||||||||
\(834\) | − | 6.51793e8i | − | 1.12360i | ||||||
\(835\) | −1.39625e8 | −0.239830 | ||||||||
\(836\) | − | 3.40712e8i | − | 0.583134i | ||||||
\(837\) | 1.88620e8i | 0.321670i | ||||||||
\(838\) | 1.24233e9 | 2.11108 | ||||||||
\(839\) | − | 6.31753e7i | − | 0.106970i | −0.998569 | − | 0.0534849i | \(-0.982967\pi\) | ||
0.998569 | − | 0.0534849i | \(-0.0170329\pi\) | |||||||
\(840\) | − | 4.54405e8i | − | 0.766664i | ||||||
\(841\) | −5.84485e8 | −0.982620 | ||||||||
\(842\) | 3.61221e8 | 0.605113 | ||||||||
\(843\) | 4.23116e8 | 0.706280 | ||||||||
\(844\) | 1.43453e9i | 2.38606i | ||||||||
\(845\) | 3.44382e8 | 0.570782 | ||||||||
\(846\) | −4.93195e7 | −0.0814531 | ||||||||
\(847\) | 7.71210e8 | 1.26918 | ||||||||
\(848\) | −8.25602e8 | −1.35389 | ||||||||
\(849\) | − | 4.05782e8i | − | 0.663086i | ||||||
\(850\) | − | 4.05244e8i | − | 0.659872i | ||||||
\(851\) | 7.32910e6 | 0.0118922 | ||||||||
\(852\) | 1.46157e8 | 0.236321 | ||||||||
\(853\) | 6.77396e8 | 1.09143 | 0.545714 | − | 0.837971i | \(-0.316258\pi\) | ||||
0.545714 | + | 0.837971i | \(0.316258\pi\) | |||||||
\(854\) | −1.57204e9 | −2.52401 | ||||||||
\(855\) | −2.01661e8 | −0.322643 | ||||||||
\(856\) | 6.74172e7i | 0.107485i | ||||||||
\(857\) | − | 3.55653e8i | − | 0.565046i | −0.959261 | − | 0.282523i | \(-0.908829\pi\) | ||
0.959261 | − | 0.282523i | \(-0.0911713\pi\) | |||||||
\(858\) | 3.61305e7i | 0.0572021i | ||||||||
\(859\) | − | 6.92963e8i | − | 1.09328i | −0.837368 | − | 0.546639i | \(-0.815907\pi\) | ||
0.837368 | − | 0.546639i | \(-0.184093\pi\) | |||||||
\(860\) | − | 3.95057e8i | − | 0.621105i | ||||||
\(861\) | 3.44648e8 | 0.539967 | ||||||||
\(862\) | −6.25659e8 | −0.976824 | ||||||||
\(863\) | 7.24024e8i | 1.12647i | 0.826296 | + | 0.563236i | \(0.190444\pi\) | ||||
−0.826296 | + | 0.563236i | \(0.809556\pi\) | |||||||
\(864\) | − | 2.55166e7i | − | 0.0395623i | ||||||
\(865\) | − | 3.01998e8i | − | 0.466612i | ||||||
\(866\) | 1.67566e9i | 2.58007i | ||||||||
\(867\) | 2.25471e8 | 0.345966 | ||||||||
\(868\) | 2.79460e9i | 4.27327i | ||||||||
\(869\) | 1.37354e8i | 0.209306i | ||||||||
\(870\) | − | 5.37826e7i | − | 0.0816740i | ||||||
\(871\) | 3.10178e8 | 0.469414 | ||||||||
\(872\) | −5.42818e8 | −0.818662 | ||||||||
\(873\) | 7.55638e7i | 0.113572i | ||||||||
\(874\) | 2.67136e8 | 0.400127 | ||||||||
\(875\) | −8.89632e8 | −1.32796 | ||||||||
\(876\) | 5.50658e8i | 0.819161i | ||||||||
\(877\) | 3.22550e8 | 0.478187 | 0.239094 | − | 0.970997i | \(-0.423150\pi\) | ||||
0.239094 | + | 0.970997i | \(0.423150\pi\) | |||||||
\(878\) | − | 7.93428e8i | − | 1.17226i | ||||||
\(879\) | 3.97848e8 | 0.585802 | ||||||||
\(880\) | − | 6.79230e7i | − | 0.0996709i | ||||||
\(881\) | − | 1.25113e9i | − | 1.82967i | −0.403825 | − | 0.914836i | \(-0.632319\pi\) | ||
0.403825 | − | 0.914836i | \(-0.367681\pi\) | |||||||
\(882\) | − | 2.90141e8i | − | 0.422866i | ||||||
\(883\) | 8.60311e6 | 0.0124961 | 0.00624803 | − | 0.999980i | \(-0.498011\pi\) | ||||
0.00624803 | + | 0.999980i | \(0.498011\pi\) | |||||||
\(884\) | 2.51764e8i | 0.364449i | ||||||||
\(885\) | 5.76646e7 | − | 2.43800e8i | 0.0831917 | − | 0.351726i | ||||
\(886\) | 1.60484e9 | 2.30744 | ||||||||
\(887\) | 1.02492e9i | 1.46865i | 0.678798 | + | 0.734325i | \(0.262501\pi\) | ||||
−0.678798 | + | 0.734325i | \(0.737499\pi\) | |||||||
\(888\) | 5.12069e7 | 0.0731290 | ||||||||
\(889\) | 2.75549e8 | 0.392187 | ||||||||
\(890\) | −1.05802e9 | −1.50080 | ||||||||
\(891\) | − | 1.52939e7i | − | 0.0216215i | ||||||
\(892\) | 1.19879e8 | 0.168908 | ||||||||
\(893\) | 1.56967e8i | 0.220421i | ||||||||
\(894\) | −3.65981e8 | −0.512208 | ||||||||
\(895\) | − | 5.37050e7i | − | 0.0749110i | ||||||
\(896\) | − | 1.70882e9i | − | 2.37559i | ||||||
\(897\) | −1.86866e7 | −0.0258912 | ||||||||
\(898\) | 1.67159e9i | 2.30835i | ||||||||
\(899\) | 1.60102e8i | 0.220352i | ||||||||
\(900\) | 2.86395e8 | 0.392860 | ||||||||
\(901\) | 7.66215e8 | 1.04755 | ||||||||
\(902\) | 1.73550e8 | 0.236485 | ||||||||
\(903\) | − | 2.87070e8i | − | 0.389875i | ||||||
\(904\) | −6.26212e8 | −0.847649 | ||||||||
\(905\) | 2.99106e8 | 0.403534 | ||||||||
\(906\) | 6.13103e8 | 0.824420 | ||||||||
\(907\) | −5.61846e8 | −0.753001 | −0.376500 | − | 0.926416i | \(-0.622873\pi\) | ||||
−0.376500 | + | 0.926416i | \(0.622873\pi\) | |||||||
\(908\) | 1.38536e8i | 0.185056i | ||||||||
\(909\) | 1.27984e8i | 0.170397i | ||||||||
\(910\) | 3.16840e8 | 0.420451 | ||||||||
\(911\) | 1.18732e9 | 1.57041 | 0.785206 | − | 0.619234i | \(-0.212557\pi\) | ||||
0.785206 | + | 0.619234i | \(0.212557\pi\) | |||||||
\(912\) | 5.54034e8 | 0.730386 | ||||||||
\(913\) | 2.45313e8 | 0.322336 | ||||||||
\(914\) | −2.41967e9 | −3.16896 | ||||||||
\(915\) | 3.09070e8i | 0.403453i | ||||||||
\(916\) | − | 1.03520e9i | − | 1.34690i | ||||||
\(917\) | − | 1.60617e8i | − | 0.208297i | ||||||
\(918\) | − | 1.61558e8i | − | 0.208834i | ||||||
\(919\) | 1.48969e9i | 1.91932i | 0.281156 | + | 0.959662i | \(0.409282\pi\) | ||||
−0.281156 | + | 0.959662i | \(0.590718\pi\) | |||||||
\(920\) | 1.18344e8 | 0.151979 | ||||||||
\(921\) | −6.40751e8 | −0.820183 | ||||||||
\(922\) | 1.95514e9i | 2.49451i | ||||||||
\(923\) | 4.93282e7i | 0.0627321i | ||||||||
\(924\) | − | 2.26596e8i | − | 0.287234i | ||||||
\(925\) | − | 3.79106e7i | − | 0.0479000i | ||||||
\(926\) | 1.98937e9 | 2.50543 | ||||||||
\(927\) | 8.80009e7i | 0.110471i | ||||||||
\(928\) | − | 2.16587e7i | − | 0.0271012i | ||||||
\(929\) | 1.12410e9i | 1.40203i | 0.713146 | + | 0.701015i | \(0.247270\pi\) | ||||
−0.713146 | + | 0.701015i | \(0.752730\pi\) | |||||||
\(930\) | 8.32915e8 | 1.03550 | ||||||||
\(931\) | −9.23416e8 | −1.14432 | ||||||||
\(932\) | 2.16758e9i | 2.67748i | ||||||||
\(933\) | −6.97386e8 | −0.858674 | ||||||||
\(934\) | −2.02987e9 | −2.49131 | ||||||||
\(935\) | 6.30371e7i | 0.0771191i | ||||||||
\(936\) | −1.30559e8 | −0.159214 | ||||||||
\(937\) | − | 1.12266e9i | − | 1.36468i | −0.731037 | − | 0.682338i | \(-0.760963\pi\) | ||
0.731037 | − | 0.682338i | \(-0.239037\pi\) | |||||||
\(938\) | −2.94902e9 | −3.57330 | ||||||||
\(939\) | 4.77335e8i | 0.576536i | ||||||||
\(940\) | 1.43663e8i | 0.172966i | ||||||||
\(941\) | 8.62986e7i | 0.103570i | 0.998658 | + | 0.0517851i | \(0.0164911\pi\) | ||||
−0.998658 | + | 0.0517851i | \(0.983509\pi\) | |||||||
\(942\) | 4.71482e6 | 0.00564043 | ||||||||
\(943\) | 8.97595e7i | 0.107040i | ||||||||
\(944\) | −1.58426e8 | + | 6.69807e8i | −0.188326 | + | 0.796221i | ||||
\(945\) | −1.34118e8 | −0.158924 | ||||||||
\(946\) | − | 1.44556e8i | − | 0.170751i | ||||||
\(947\) | 1.15823e9 | 1.36378 | 0.681889 | − | 0.731456i | \(-0.261159\pi\) | ||||
0.681889 | + | 0.731456i | \(0.261159\pi\) | |||||||
\(948\) | −1.02541e9 | −1.20357 | ||||||||
\(949\) | −1.85847e8 | −0.217449 | ||||||||
\(950\) | − | 1.38179e9i | − | 1.61165i | ||||||
\(951\) | −9.05628e8 | −1.05295 | ||||||||
\(952\) | − | 1.15861e9i | − | 1.34285i | ||||||
\(953\) | 1.05961e9 | 1.22424 | 0.612120 | − | 0.790765i | \(-0.290317\pi\) | ||||
0.612120 | + | 0.790765i | \(0.290317\pi\) | |||||||
\(954\) | 8.20895e8i | 0.945458i | ||||||||
\(955\) | 1.02169e8i | 0.117303i | ||||||||
\(956\) | 2.17343e9 | 2.48756 | ||||||||
\(957\) | − | 1.29816e7i | − | 0.0148113i | ||||||
\(958\) | 2.05014e9i | 2.33178i | ||||||||
\(959\) | −1.58979e9 | −1.80253 | ||||||||
\(960\) | −3.74311e8 | −0.423076 | ||||||||
\(961\) | −1.59194e9 | −1.79373 | ||||||||
\(962\) | 3.57047e7i | 0.0401052i | ||||||||
\(963\) | 1.98982e7 | 0.0222810 | ||||||||
\(964\) | 5.26370e7 | 0.0587571 | ||||||||
\(965\) | 1.66172e8 | 0.184917 | ||||||||
\(966\) | 1.77663e8 | 0.197091 | ||||||||
\(967\) | 2.94496e7i | 0.0325687i | 0.999867 | + | 0.0162843i | \(0.00518370\pi\) | ||||
−0.999867 | + | 0.0162843i | \(0.994816\pi\) | |||||||
\(968\) | 1.40331e9i | 1.54714i | ||||||||
\(969\) | −5.14182e8 | −0.565126 | ||||||||
\(970\) | 3.33678e8 | 0.365605 | ||||||||
\(971\) | 1.96774e8 | 0.214936 | 0.107468 | − | 0.994209i | \(-0.465726\pi\) | ||||
0.107468 | + | 0.994209i | \(0.465726\pi\) | |||||||
\(972\) | 1.14176e8 | 0.124330 | ||||||||
\(973\) | −1.37963e9 | −1.49770 | ||||||||
\(974\) | 1.49514e9i | 1.61810i | ||||||||
\(975\) | 9.66584e7i | 0.104286i | ||||||||
\(976\) | − | 8.49126e8i | − | 0.913319i | ||||||
\(977\) | − | 3.80962e8i | − | 0.408506i | −0.978918 | − | 0.204253i | \(-0.934524\pi\) | ||
0.978918 | − | 0.204253i | \(-0.0654765\pi\) | |||||||
\(978\) | − | 7.12302e8i | − | 0.761461i | ||||||
\(979\) | −2.55377e8 | −0.272165 | ||||||||
\(980\) | −8.45150e8 | −0.897957 | ||||||||
\(981\) | 1.60213e8i | 0.169703i | ||||||||
\(982\) | 2.15566e9i | 2.27638i | ||||||||
\(983\) | − | 3.93998e8i | − | 0.414795i | −0.978257 | − | 0.207398i | \(-0.933501\pi\) | ||
0.978257 | − | 0.207398i | \(-0.0664994\pi\) | |||||||
\(984\) | 6.27131e8i | 0.658223i | ||||||||
\(985\) | −1.54276e8 | −0.161432 | ||||||||
\(986\) | − | 1.37131e8i | − | 0.143056i | ||||||
\(987\) | 1.04393e8i | 0.108573i | ||||||||
\(988\) | 8.58458e8i | 0.890119i | ||||||||
\(989\) | 7.47640e7 | 0.0772865 | ||||||||
\(990\) | −6.75357e7 | −0.0696030 | ||||||||
\(991\) | − | 1.18032e9i | − | 1.21277i | −0.795172 | − | 0.606384i | \(-0.792619\pi\) | ||
0.795172 | − | 0.606384i | \(-0.207381\pi\) | |||||||
\(992\) | 3.35422e8 | 0.343602 | ||||||||
\(993\) | −5.18832e8 | −0.529882 | ||||||||
\(994\) | − | 4.68989e8i | − | 0.477533i | ||||||
\(995\) | 8.63278e8 | 0.876358 | ||||||||
\(996\) | 1.83138e9i | 1.85353i | ||||||||
\(997\) | −1.14829e9 | −1.15868 | −0.579342 | − | 0.815085i | \(-0.696690\pi\) | ||||
−0.579342 | + | 0.815085i | \(0.696690\pi\) | |||||||
\(998\) | − | 9.45821e8i | − | 0.951518i | ||||||
\(999\) | − | 1.51137e7i | − | 0.0151592i |
(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 | 177.7.c.a.58.6 | ✓ | 60 | |
59.58 | odd | 2 | inner | 177.7.c.a.58.55 | yes | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.7.c.a.58.6 | ✓ | 60 | 1.1 | even | 1 | trivial | |
177.7.c.a.58.55 | yes | 60 | 59.58 | odd | 2 | inner |