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 | 19.15 | ||
Character | \(\chi\) | \(=\) | 60.19 |
Dual form | 60.7.f.a.19.16 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.63894 | − | 7.83032i | −0.204867 | − | 0.978790i | ||||
\(3\) | −15.5885 | −0.577350 | ||||||||
\(4\) | −58.6278 | + | 25.6668i | −0.916059 | + | 0.401044i | ||||
\(5\) | −44.2074 | + | 116.922i | −0.353659 | + | 0.935374i | ||||
\(6\) | 25.5485 | + | 122.063i | 0.118280 | + | 0.565105i | ||||
\(7\) | 42.6864 | 0.124450 | 0.0622250 | − | 0.998062i | \(-0.480180\pi\) | ||||
0.0622250 | + | 0.998062i | \(0.480180\pi\) | |||||||
\(8\) | 297.066 | + | 417.008i | 0.580208 | + | 0.814469i | ||||
\(9\) | 243.000 | 0.333333 | ||||||||
\(10\) | 987.988 | + | 154.531i | 0.987988 | + | 0.154531i | ||||
\(11\) | − | 1842.57i | − | 1.38435i | −0.721729 | − | 0.692176i | \(-0.756652\pi\) | ||
0.721729 | − | 0.692176i | \(-0.243348\pi\) | |||||||
\(12\) | 913.917 | − | 400.106i | 0.528887 | − | 0.231543i | ||||
\(13\) | 887.003i | 0.403734i | 0.979413 | + | 0.201867i | \(0.0647008\pi\) | ||||
−0.979413 | + | 0.201867i | \(0.935299\pi\) | |||||||
\(14\) | −69.9602 | − | 334.248i | −0.0254957 | − | 0.121810i | ||||
\(15\) | 689.125 | − | 1822.63i | 0.204185 | − | 0.540039i | ||||
\(16\) | 2778.43 | − | 3009.57i | 0.678328 | − | 0.734759i | ||||
\(17\) | 798.396i | 0.162507i | 0.996693 | + | 0.0812534i | \(0.0258923\pi\) | ||||
−0.996693 | + | 0.0812534i | \(0.974108\pi\) | |||||||
\(18\) | −398.262 | − | 1902.77i | −0.0682890 | − | 0.326263i | ||||
\(19\) | − | 2308.89i | − | 0.336622i | −0.985734 | − | 0.168311i | \(-0.946169\pi\) | ||
0.985734 | − | 0.168311i | \(-0.0538314\pi\) | |||||||
\(20\) | −409.225 | − | 7989.53i | −0.0511532 | − | 0.998691i | ||||
\(21\) | −665.414 | −0.0718512 | ||||||||
\(22\) | −14427.9 | + | 3019.86i | −1.35499 | + | 0.283608i | ||||
\(23\) | 7162.68 | 0.588697 | 0.294348 | − | 0.955698i | \(-0.404897\pi\) | ||||
0.294348 | + | 0.955698i | \(0.404897\pi\) | |||||||
\(24\) | −4630.81 | − | 6500.51i | −0.334983 | − | 0.470234i | ||||
\(25\) | −11716.4 | − | 10337.6i | −0.749850 | − | 0.661608i | ||||
\(26\) | 6945.51 | − | 1453.74i | 0.395170 | − | 0.0827117i | ||||
\(27\) | −3788.00 | −0.192450 | ||||||||
\(28\) | −2502.61 | + | 1095.62i | −0.114004 | + | 0.0499099i | ||||
\(29\) | 37170.9 | 1.52408 | 0.762042 | − | 0.647527i | \(-0.224197\pi\) | ||||
0.762042 | + | 0.647527i | \(0.224197\pi\) | |||||||
\(30\) | −15401.2 | − | 2408.89i | −0.570415 | − | 0.0892183i | ||||
\(31\) | − | 47643.5i | − | 1.59926i | −0.600494 | − | 0.799629i | \(-0.705029\pi\) | ||
0.600494 | − | 0.799629i | \(-0.294971\pi\) | |||||||
\(32\) | −28119.6 | − | 16823.5i | −0.858142 | − | 0.513413i | ||||
\(33\) | 28722.9i | 0.799256i | ||||||||
\(34\) | 6251.69 | − | 1308.52i | 0.159060 | − | 0.0332923i | ||||
\(35\) | −1887.05 | + | 4990.96i | −0.0440129 | + | 0.116407i | ||||
\(36\) | −14246.5 | + | 6237.03i | −0.305353 | + | 0.133681i | ||||
\(37\) | − | 30635.5i | − | 0.604812i | −0.953179 | − | 0.302406i | \(-0.902210\pi\) | ||
0.953179 | − | 0.302406i | \(-0.0977899\pi\) | |||||||
\(38\) | −18079.4 | + | 3784.13i | −0.329483 | + | 0.0689629i | ||||
\(39\) | − | 13827.0i | − | 0.233096i | ||||||
\(40\) | −61889.8 | + | 16298.7i | −0.967029 | + | 0.254667i | ||||
\(41\) | 51219.0 | 0.743156 | 0.371578 | − | 0.928402i | \(-0.378817\pi\) | ||||
0.371578 | + | 0.928402i | \(0.378817\pi\) | |||||||
\(42\) | 1090.57 | + | 5210.41i | 0.0147200 | + | 0.0703273i | ||||
\(43\) | 135337. | 1.70220 | 0.851099 | − | 0.525005i | \(-0.175937\pi\) | ||||
0.851099 | + | 0.525005i | \(0.175937\pi\) | |||||||
\(44\) | 47292.9 | + | 108026.i | 0.555185 | + | 1.26815i | ||||
\(45\) | −10742.4 | + | 28412.0i | −0.117886 | + | 0.311791i | ||||
\(46\) | −11739.2 | − | 56086.0i | −0.120605 | − | 0.576211i | ||||
\(47\) | 157494. | 1.51694 | 0.758471 | − | 0.651706i | \(-0.225947\pi\) | ||||
0.758471 | + | 0.651706i | \(0.225947\pi\) | |||||||
\(48\) | −43311.5 | + | 46914.6i | −0.391633 | + | 0.424213i | ||||
\(49\) | −115827. | −0.984512 | ||||||||
\(50\) | −61744.4 | + | 108686.i | −0.493955 | + | 0.869487i | ||||
\(51\) | − | 12445.8i | − | 0.0938233i | ||||||
\(52\) | −22766.5 | − | 52003.0i | −0.161915 | − | 0.369844i | ||||
\(53\) | 140651.i | 0.944743i | 0.881400 | + | 0.472372i | \(0.156602\pi\) | ||||
−0.881400 | + | 0.472372i | \(0.843398\pi\) | |||||||
\(54\) | 6208.28 | + | 29661.2i | 0.0394267 | + | 0.188368i | ||||
\(55\) | 215437. | + | 81455.3i | 1.29489 | + | 0.489589i | ||||
\(56\) | 12680.7 | + | 17800.5i | 0.0722068 | + | 0.101361i | ||||
\(57\) | 35992.1i | 0.194349i | ||||||||
\(58\) | −60920.8 | − | 291060.i | −0.312235 | − | 1.49176i | ||||
\(59\) | 150330.i | 0.731965i | 0.930622 | + | 0.365983i | \(0.119267\pi\) | ||||
−0.930622 | + | 0.365983i | \(0.880733\pi\) | |||||||
\(60\) | 6379.19 | + | 124544.i | 0.0295333 | + | 0.576594i | ||||
\(61\) | 39704.1 | 0.174923 | 0.0874613 | − | 0.996168i | \(-0.472125\pi\) | ||||
0.0874613 | + | 0.996168i | \(0.472125\pi\) | |||||||
\(62\) | −373064. | + | 78084.7i | −1.56534 | + | 0.327635i | ||||
\(63\) | 10372.8 | 0.0414833 | ||||||||
\(64\) | −85647.2 | + | 247758.i | −0.326718 | + | 0.945122i | ||||
\(65\) | −103710. | − | 39212.1i | −0.377642 | − | 0.142784i | ||||
\(66\) | 224909. | − | 47074.9i | 0.782303 | − | 0.163741i | ||||
\(67\) | −188483. | −0.626683 | −0.313342 | − | 0.949640i | \(-0.601448\pi\) | ||||
−0.313342 | + | 0.949640i | \(0.601448\pi\) | |||||||
\(68\) | −20492.3 | − | 46808.2i | −0.0651723 | − | 0.148866i | ||||
\(69\) | −111655. | −0.339884 | ||||||||
\(70\) | 42173.6 | + | 6596.35i | 0.122955 | + | 0.0192313i | ||||
\(71\) | − | 300445.i | − | 0.839440i | −0.907654 | − | 0.419720i | \(-0.862128\pi\) | ||
0.907654 | − | 0.419720i | \(-0.137872\pi\) | |||||||
\(72\) | 72187.1 | + | 101333.i | 0.193403 | + | 0.271490i | ||||
\(73\) | − | 137469.i | − | 0.353376i | −0.984267 | − | 0.176688i | \(-0.943462\pi\) | ||
0.984267 | − | 0.176688i | \(-0.0565383\pi\) | |||||||
\(74\) | −239886. | + | 50209.7i | −0.591984 | + | 0.123906i | ||||
\(75\) | 182641. | + | 161148.i | 0.432926 | + | 0.381979i | ||||
\(76\) | 59261.9 | + | 135365.i | 0.135000 | + | 0.308366i | ||||
\(77\) | − | 78652.7i | − | 0.172283i | ||||||
\(78\) | −108270. | + | 22661.6i | −0.228152 | + | 0.0477536i | ||||
\(79\) | − | 392225.i | − | 0.795526i | −0.917488 | − | 0.397763i | \(-0.869787\pi\) | ||
0.917488 | − | 0.397763i | \(-0.130213\pi\) | |||||||
\(80\) | 229057. | + | 457905.i | 0.447378 | + | 0.894345i | ||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | −83944.7 | − | 401061.i | −0.152248 | − | 0.727393i | ||||
\(83\) | −261510. | −0.457356 | −0.228678 | − | 0.973502i | \(-0.573440\pi\) | ||||
−0.228678 | + | 0.973502i | \(0.573440\pi\) | |||||||
\(84\) | 39011.8 | − | 17079.1i | 0.0658200 | − | 0.0288155i | ||||
\(85\) | −93349.8 | − | 35295.0i | −0.152005 | − | 0.0574720i | ||||
\(86\) | −221808. | − | 1.05973e6i | −0.348724 | − | 1.66609i | ||||
\(87\) | −579437. | −0.879931 | ||||||||
\(88\) | 768367. | − | 547366.i | 1.12751 | − | 0.803211i | ||||
\(89\) | 944102. | 1.33921 | 0.669605 | − | 0.742717i | \(-0.266463\pi\) | ||||
0.669605 | + | 0.742717i | \(0.266463\pi\) | |||||||
\(90\) | 240081. | + | 37550.9i | 0.329329 | + | 0.0515102i | ||||
\(91\) | 37862.9i | 0.0502446i | ||||||||
\(92\) | −419932. | + | 183843.i | −0.539281 | + | 0.236093i | ||||
\(93\) | 742689.i | 0.923332i | ||||||||
\(94\) | −258122. | − | 1.23322e6i | −0.310772 | − | 1.48477i | ||||
\(95\) | 269960. | + | 102070.i | 0.314868 | + | 0.119050i | ||||
\(96\) | 438341. | + | 262253.i | 0.495448 | + | 0.296419i | ||||
\(97\) | − | 1.18506e6i | − | 1.29845i | −0.760596 | − | 0.649225i | \(-0.775093\pi\) | ||
0.760596 | − | 0.649225i | \(-0.224907\pi\) | |||||||
\(98\) | 189833. | + | 906961.i | 0.201694 | + | 0.963631i | ||||
\(99\) | − | 447745.i | − | 0.461451i | ||||||
\(100\) | 952241. | + | 305349.i | 0.952241 | + | 0.305349i | ||||
\(101\) | 713405. | 0.692424 | 0.346212 | − | 0.938156i | \(-0.387468\pi\) | ||||
0.346212 | + | 0.938156i | \(0.387468\pi\) | |||||||
\(102\) | −97454.2 | + | 20397.8i | −0.0918333 | + | 0.0192213i | ||||
\(103\) | 261895. | 0.239671 | 0.119836 | − | 0.992794i | \(-0.461763\pi\) | ||||
0.119836 | + | 0.992794i | \(0.461763\pi\) | |||||||
\(104\) | −369887. | + | 263499.i | −0.328828 | + | 0.234249i | ||||
\(105\) | 29416.2 | − | 77801.4i | 0.0254109 | − | 0.0672078i | ||||
\(106\) | 1.10134e6 | − | 230517.i | 0.924705 | − | 0.193547i | ||||
\(107\) | −2.24212e6 | −1.83024 | −0.915118 | − | 0.403185i | \(-0.867903\pi\) | ||||
−0.915118 | + | 0.403185i | \(0.867903\pi\) | |||||||
\(108\) | 222082. | − | 97225.7i | 0.176296 | − | 0.0771809i | ||||
\(109\) | −1.25787e6 | −0.971307 | −0.485654 | − | 0.874151i | \(-0.661418\pi\) | ||||
−0.485654 | + | 0.874151i | \(0.661418\pi\) | |||||||
\(110\) | 284734. | − | 1.82044e6i | 0.213925 | − | 1.36772i | ||||
\(111\) | 477561.i | 0.349188i | ||||||||
\(112\) | 118601. | − | 128468.i | 0.0844179 | − | 0.0914408i | ||||
\(113\) | 687372.i | 0.476383i | 0.971218 | + | 0.238192i | \(0.0765546\pi\) | ||||
−0.971218 | + | 0.238192i | \(0.923445\pi\) | |||||||
\(114\) | 281830. | − | 58988.7i | 0.190227 | − | 0.0398157i | ||||
\(115\) | −316643. | + | 837473.i | −0.208198 | + | 0.550652i | ||||
\(116\) | −2.17925e6 | + | 954058.i | −1.39615 | + | 0.611224i | ||||
\(117\) | 215542.i | 0.134578i | ||||||||
\(118\) | 1.17713e6 | − | 246382.i | 0.716440 | − | 0.149956i | ||||
\(119\) | 34080.6i | 0.0202240i | ||||||||
\(120\) | 964767. | − | 254071.i | 0.558314 | − | 0.147032i | ||||
\(121\) | −1.62351e6 | −0.916430 | ||||||||
\(122\) | −65072.5 | − | 310896.i | −0.0358359 | − | 0.171212i | ||||
\(123\) | −798426. | −0.429061 | ||||||||
\(124\) | 1.22286e6 | + | 2.79323e6i | 0.641372 | + | 1.46502i | ||||
\(125\) | 1.72664e6 | − | 912905.i | 0.884042 | − | 0.467407i | ||||
\(126\) | −17000.3 | − | 81222.2i | −0.00849857 | − | 0.0406035i | ||||
\(127\) | −3.19336e6 | −1.55897 | −0.779484 | − | 0.626422i | \(-0.784519\pi\) | ||||
−0.779484 | + | 0.626422i | \(0.784519\pi\) | |||||||
\(128\) | 2.08039e6 | + | 264585.i | 0.992009 | + | 0.126164i | ||||
\(129\) | −2.10969e6 | −0.982764 | ||||||||
\(130\) | −137069. | + | 876348.i | −0.0623892 | + | 0.398884i | ||||
\(131\) | 3.71407e6i | 1.65210i | 0.563596 | + | 0.826051i | \(0.309418\pi\) | ||||
−0.563596 | + | 0.826051i | \(0.690582\pi\) | |||||||
\(132\) | −737224. | − | 1.68396e6i | −0.320536 | − | 0.732165i | ||||
\(133\) | − | 98558.2i | − | 0.0418927i | ||||||
\(134\) | 308912. | + | 1.47588e6i | 0.128387 | + | 0.613391i | ||||
\(135\) | 167457. | − | 442899.i | 0.0680617 | − | 0.180013i | ||||
\(136\) | −332937. | + | 237176.i | −0.132357 | + | 0.0942876i | ||||
\(137\) | − | 4.29631e6i | − | 1.67084i | −0.549614 | − | 0.835419i | \(-0.685225\pi\) | ||
0.549614 | − | 0.835419i | \(-0.314775\pi\) | |||||||
\(138\) | 182996. | + | 874295.i | 0.0696311 | + | 0.332675i | ||||
\(139\) | − | 2.19309e6i | − | 0.816605i | −0.912847 | − | 0.408302i | \(-0.866121\pi\) | ||
0.912847 | − | 0.408302i | \(-0.133879\pi\) | |||||||
\(140\) | −17468.3 | − | 341044.i | −0.00636601 | − | 0.124287i | ||||
\(141\) | −2.45508e6 | −0.875807 | ||||||||
\(142\) | −2.35258e6 | + | 492410.i | −0.821636 | + | 0.171974i | ||||
\(143\) | 1.63437e6 | 0.558909 | ||||||||
\(144\) | 675159. | − | 731326.i | 0.226109 | − | 0.244920i | ||||
\(145\) | −1.64323e6 | + | 4.34609e6i | −0.539007 | + | 1.42559i | ||||
\(146\) | −1.07643e6 | + | 225303.i | −0.345881 | + | 0.0723951i | ||||
\(147\) | 1.80556e6 | 0.568408 | ||||||||
\(148\) | 786316. | + | 1.79609e6i | 0.242556 | + | 0.554044i | ||||
\(149\) | 6.37636e6 | 1.92759 | 0.963793 | − | 0.266651i | \(-0.0859170\pi\) | ||||
0.963793 | + | 0.266651i | \(0.0859170\pi\) | |||||||
\(150\) | 962500. | − | 1.69425e6i | 0.285185 | − | 0.501999i | ||||
\(151\) | 2.84487e6i | 0.826289i | 0.910665 | + | 0.413145i | \(0.135570\pi\) | ||||
−0.910665 | + | 0.413145i | \(0.864430\pi\) | |||||||
\(152\) | 962827. | − | 685895.i | 0.274168 | − | 0.195311i | ||||
\(153\) | 194010.i | 0.0541689i | ||||||||
\(154\) | −615876. | + | 128907.i | −0.168628 | + | 0.0352950i | ||||
\(155\) | 5.57056e6 | + | 2.10620e6i | 1.49591 | + | 0.565593i | ||||
\(156\) | 354895. | + | 810646.i | 0.0934815 | + | 0.213529i | ||||
\(157\) | 6.80838e6i | 1.75932i | 0.475604 | + | 0.879660i | \(0.342230\pi\) | ||||
−0.475604 | + | 0.879660i | \(0.657770\pi\) | |||||||
\(158\) | −3.07125e6 | + | 642832.i | −0.778653 | + | 0.162977i | ||||
\(159\) | − | 2.19252e6i | − | 0.545448i | ||||||
\(160\) | 3.21013e6 | − | 2.54407e6i | 0.783723 | − | 0.621111i | ||||
\(161\) | 305748. | 0.0732633 | ||||||||
\(162\) | −96777.6 | − | 462372.i | −0.0227630 | − | 0.108754i | ||||
\(163\) | 3.53027e6 | 0.815164 | 0.407582 | − | 0.913169i | \(-0.366372\pi\) | ||||
0.407582 | + | 0.913169i | \(0.366372\pi\) | |||||||
\(164\) | −3.00286e6 | + | 1.31463e6i | −0.680774 | + | 0.298038i | ||||
\(165\) | −3.35833e6 | − | 1.26976e6i | −0.747603 | − | 0.282664i | ||||
\(166\) | 428599. | + | 2.04771e6i | 0.0936972 | + | 0.447656i | ||||
\(167\) | −558205. | −0.119852 | −0.0599258 | − | 0.998203i | \(-0.519086\pi\) | ||||
−0.0599258 | + | 0.998203i | \(0.519086\pi\) | |||||||
\(168\) | −197672. | − | 277483.i | −0.0416886 | − | 0.0585206i | ||||
\(169\) | 4.04004e6 | 0.836999 | ||||||||
\(170\) | −123377. | + | 788805.i | −0.0251123 | + | 0.160555i | ||||
\(171\) | − | 561061.i | − | 0.112207i | ||||||
\(172\) | −7.93449e6 | + | 3.47366e6i | −1.55931 | + | 0.682656i | ||||
\(173\) | − | 4.94875e6i | − | 0.955778i | −0.878420 | − | 0.477889i | \(-0.841402\pi\) | ||
0.878420 | − | 0.477889i | \(-0.158598\pi\) | |||||||
\(174\) | 949661. | + | 4.53718e6i | 0.180269 | + | 0.861267i | ||||
\(175\) | −500131. | − | 441275.i | −0.0933189 | − | 0.0823371i | ||||
\(176\) | −5.54536e6 | − | 5.11946e6i | −1.01717 | − | 0.939045i | ||||
\(177\) | − | 2.34342e6i | − | 0.422600i | ||||||
\(178\) | −1.54732e6 | − | 7.39262e6i | −0.274360 | − | 1.31081i | ||||
\(179\) | − | 8.92645e6i | − | 1.55639i | −0.628020 | − | 0.778197i | \(-0.716135\pi\) | ||
0.628020 | − | 0.778197i | \(-0.283865\pi\) | |||||||
\(180\) | −99441.8 | − | 1.94145e6i | −0.0170511 | − | 0.332897i | ||||
\(181\) | 489115. | 0.0824850 | 0.0412425 | − | 0.999149i | \(-0.486868\pi\) | ||||
0.0412425 | + | 0.999149i | \(0.486868\pi\) | |||||||
\(182\) | 296479. | − | 62054.9i | 0.0491789 | − | 0.0102935i | ||||
\(183\) | −618925. | −0.100992 | ||||||||
\(184\) | 2.12779e6 | + | 2.98689e6i | 0.341566 | + | 0.479475i | ||||
\(185\) | 3.58196e6 | + | 1.35432e6i | 0.565726 | + | 0.213897i | ||||
\(186\) | 5.81549e6 | − | 1.21722e6i | 0.903748 | − | 0.189160i | ||||
\(187\) | 1.47110e6 | 0.224966 | ||||||||
\(188\) | −9.23350e6 | + | 4.04235e6i | −1.38961 | + | 0.608360i | ||||
\(189\) | −161696. | −0.0239504 | ||||||||
\(190\) | 356795. | − | 2.28116e6i | 0.0520185 | − | 0.332579i | ||||
\(191\) | − | 6.73881e6i | − | 0.967126i | −0.875310 | − | 0.483563i | \(-0.839342\pi\) | ||
0.875310 | − | 0.483563i | \(-0.160658\pi\) | |||||||
\(192\) | 1.33511e6 | − | 3.86217e6i | 0.188631 | − | 0.545666i | ||||
\(193\) | − | 4.71075e6i | − | 0.655267i | −0.944805 | − | 0.327634i | \(-0.893749\pi\) | ||
0.944805 | − | 0.327634i | \(-0.106251\pi\) | |||||||
\(194\) | −9.27940e6 | + | 1.94224e6i | −1.27091 | + | 0.266010i | ||||
\(195\) | 1.61668e6 | + | 611256.i | 0.218032 | + | 0.0824364i | ||||
\(196\) | 6.79067e6 | − | 2.97290e6i | 0.901871 | − | 0.394832i | ||||
\(197\) | 1.51577e6i | 0.198260i | 0.995075 | + | 0.0991299i | \(0.0316059\pi\) | ||||
−0.995075 | + | 0.0991299i | \(0.968394\pi\) | |||||||
\(198\) | −3.50599e6 | + | 733826.i | −0.451663 | + | 0.0945360i | ||||
\(199\) | − | 1.23590e7i | − | 1.56828i | −0.620586 | − | 0.784139i | \(-0.713105\pi\) | ||
0.620586 | − | 0.784139i | \(-0.286895\pi\) | |||||||
\(200\) | 830317. | − | 7.95679e6i | 0.103790 | − | 0.994599i | ||||
\(201\) | 2.93816e6 | 0.361816 | ||||||||
\(202\) | −1.16923e6 | − | 5.58619e6i | −0.141855 | − | 0.677738i | ||||
\(203\) | 1.58669e6 | 0.189672 | ||||||||
\(204\) | 319443. | + | 729667.i | 0.0376272 | + | 0.0859477i | ||||
\(205\) | −2.26426e6 | + | 5.98862e6i | −0.262824 | + | 0.695129i | ||||
\(206\) | −429230. | − | 2.05072e6i | −0.0491007 | − | 0.234588i | ||||
\(207\) | 1.74053e6 | 0.196232 | ||||||||
\(208\) | 2.66950e6 | + | 2.46448e6i | 0.296647 | + | 0.273864i | ||||
\(209\) | −4.25430e6 | −0.466004 | ||||||||
\(210\) | −657421. | − | 102827.i | −0.0709882 | − | 0.0111032i | ||||
\(211\) | 989173.i | 0.105299i | 0.998613 | + | 0.0526496i | \(0.0167666\pi\) | ||||
−0.998613 | + | 0.0526496i | \(0.983233\pi\) | |||||||
\(212\) | −3.61005e6 | − | 8.24603e6i | −0.378883 | − | 0.865440i | ||||
\(213\) | 4.68347e6i | 0.484651i | ||||||||
\(214\) | 3.67469e6 | + | 1.75565e7i | 0.374955 | + | 1.79142i | ||||
\(215\) | −5.98288e6 | + | 1.58238e7i | −0.601998 | + | 1.59219i | ||||
\(216\) | −1.12529e6 | − | 1.57962e6i | −0.111661 | − | 0.156745i | ||||
\(217\) | − | 2.03373e6i | − | 0.199028i | ||||||
\(218\) | 2.06157e6 | + | 9.84953e6i | 0.198989 | + | 0.950706i | ||||
\(219\) | 2.14293e6i | 0.204022i | ||||||||
\(220\) | −1.47213e7 | + | 754027.i | −1.38254 | + | 0.0708140i | ||||
\(221\) | −708179. | −0.0656094 | ||||||||
\(222\) | 3.73945e6 | − | 782692.i | 0.341782 | − | 0.0715372i | ||||
\(223\) | 6.80020e6 | 0.613207 | 0.306604 | − | 0.951837i | \(-0.400807\pi\) | ||||
0.306604 | + | 0.951837i | \(0.400807\pi\) | |||||||
\(224\) | −1.20032e6 | − | 718134.i | −0.106796 | − | 0.0638942i | ||||
\(225\) | −2.84709e6 | − | 2.51204e6i | −0.249950 | − | 0.220536i | ||||
\(226\) | 5.38234e6 | − | 1.12656e6i | 0.466279 | − | 0.0975953i | ||||
\(227\) | 1.40557e7 | 1.20164 | 0.600821 | − | 0.799384i | \(-0.294840\pi\) | ||||
0.600821 | + | 0.799384i | \(0.294840\pi\) | |||||||
\(228\) | −923801. | − | 2.11014e6i | −0.0779424 | − | 0.178035i | ||||
\(229\) | −1.18694e7 | −0.988375 | −0.494188 | − | 0.869355i | \(-0.664534\pi\) | ||||
−0.494188 | + | 0.869355i | \(0.664534\pi\) | |||||||
\(230\) | 7.07664e6 | + | 1.10685e6i | 0.581625 | + | 0.0909717i | ||||
\(231\) | 1.22607e6i | 0.0994674i | ||||||||
\(232\) | 1.10422e7 | + | 1.55006e7i | 0.884286 | + | 1.24132i | ||||
\(233\) | 1.00854e7i | 0.797310i | 0.917101 | + | 0.398655i | \(0.130523\pi\) | ||||
−0.917101 | + | 0.398655i | \(0.869477\pi\) | |||||||
\(234\) | 1.68776e6 | − | 353259.i | 0.131723 | − | 0.0275706i | ||||
\(235\) | −6.96238e6 | + | 1.84144e7i | −0.536481 | + | 1.41891i | ||||
\(236\) | −3.85850e6 | − | 8.81353e6i | −0.293550 | − | 0.670523i | ||||
\(237\) | 6.11419e6i | 0.459297i | ||||||||
\(238\) | 266862. | − | 55855.9i | 0.0197950 | − | 0.00414322i | ||||
\(239\) | − | 1.83092e7i | − | 1.34114i | −0.741845 | − | 0.670571i | \(-0.766049\pi\) | ||
0.741845 | − | 0.670571i | \(-0.233951\pi\) | |||||||
\(240\) | −3.57065e6 | − | 7.13803e6i | −0.258294 | − | 0.516350i | ||||
\(241\) | 9.34514e6 | 0.667629 | 0.333814 | − | 0.942639i | \(-0.391664\pi\) | ||||
0.333814 | + | 0.942639i | \(0.391664\pi\) | |||||||
\(242\) | 2.66083e6 | + | 1.27126e7i | 0.187746 | + | 0.896992i | ||||
\(243\) | −920483. | −0.0641500 | ||||||||
\(244\) | −2.32776e6 | + | 1.01908e6i | −0.160239 | + | 0.0701515i | ||||
\(245\) | 5.12041e6 | − | 1.35427e7i | 0.348182 | − | 0.920887i | ||||
\(246\) | 1.30857e6 | + | 6.25193e6i | 0.0879005 | + | 0.419961i | ||||
\(247\) | 2.04799e6 | 0.135906 | ||||||||
\(248\) | 1.98677e7 | − | 1.41533e7i | 1.30255 | − | 0.927902i | ||||
\(249\) | 4.07654e6 | 0.264055 | ||||||||
\(250\) | −9.97819e6 | − | 1.20240e7i | −0.638604 | − | 0.769535i | ||||
\(251\) | 1.63531e7i | 1.03414i | 0.855943 | + | 0.517070i | \(0.172977\pi\) | ||||
−0.855943 | + | 0.517070i | \(0.827023\pi\) | |||||||
\(252\) | −608133. | + | 266236.i | −0.0380012 | + | 0.0166366i | ||||
\(253\) | − | 1.31977e7i | − | 0.814964i | ||||||
\(254\) | 5.23372e6 | + | 2.50051e7i | 0.319381 | + | 1.52590i | ||||
\(255\) | 1.45518e6 | + | 550194.i | 0.0877599 | + | 0.0331815i | ||||
\(256\) | −1.33785e6 | − | 1.67238e7i | −0.0797420 | − | 0.996816i | ||||
\(257\) | 1.43214e7i | 0.843694i | 0.906667 | + | 0.421847i | \(0.138618\pi\) | ||||
−0.906667 | + | 0.421847i | \(0.861382\pi\) | |||||||
\(258\) | 3.45765e6 | + | 1.65195e7i | 0.201336 | + | 0.961920i | ||||
\(259\) | − | 1.30772e6i | − | 0.0752689i | ||||||
\(260\) | 7.08673e6 | − | 362984.i | 0.403205 | − | 0.0206523i | ||||
\(261\) | 9.03253e6 | 0.508028 | ||||||||
\(262\) | 2.90824e7 | − | 6.08713e6i | 1.61706 | − | 0.338461i | ||||
\(263\) | −2.73591e7 | −1.50396 | −0.751978 | − | 0.659188i | \(-0.770900\pi\) | ||||
−0.751978 | + | 0.659188i | \(0.770900\pi\) | |||||||
\(264\) | −1.19777e7 | + | 8.53259e6i | −0.650969 | + | 0.463734i | ||||
\(265\) | −1.64451e7 | − | 6.21779e6i | −0.883688 | − | 0.334117i | ||||
\(266\) | −771742. | + | 161531.i | −0.0410041 | + | 0.00858243i | ||||
\(267\) | −1.47171e7 | −0.773194 | ||||||||
\(268\) | 1.10503e7 | − | 4.83776e6i | 0.574079 | − | 0.251327i | ||||
\(269\) | 1.18794e7 | 0.610294 | 0.305147 | − | 0.952305i | \(-0.401294\pi\) | ||||
0.305147 | + | 0.952305i | \(0.401294\pi\) | |||||||
\(270\) | −3.74249e6 | − | 585361.i | −0.190138 | − | 0.0297394i | ||||
\(271\) | 8.03680e6i | 0.403809i | 0.979405 | + | 0.201904i | \(0.0647130\pi\) | ||||
−0.979405 | + | 0.201904i | \(0.935287\pi\) | |||||||
\(272\) | 2.40283e6 | + | 2.21829e6i | 0.119403 | + | 0.110233i | ||||
\(273\) | − | 590224.i | − | 0.0290088i | ||||||
\(274\) | −3.36415e7 | + | 7.04138e6i | −1.63540 | + | 0.342300i | ||||
\(275\) | −1.90478e7 | + | 2.15883e7i | −0.915897 | + | 1.03806i | ||||
\(276\) | 6.54609e6 | − | 2.86583e6i | 0.311354 | − | 0.136308i | ||||
\(277\) | − | 2.36287e7i | − | 1.11173i | −0.831271 | − | 0.555867i | \(-0.812386\pi\) | ||
0.831271 | − | 0.555867i | \(-0.187614\pi\) | |||||||
\(278\) | −1.71726e7 | + | 3.59433e6i | −0.799285 | + | 0.167295i | ||||
\(279\) | − | 1.15774e7i | − | 0.533086i | ||||||
\(280\) | −2.64185e6 | + | 695732.i | −0.120347 | + | 0.0316933i | ||||
\(281\) | −4.00913e7 | −1.80689 | −0.903444 | − | 0.428707i | \(-0.858969\pi\) | ||||
−0.903444 | + | 0.428707i | \(0.858969\pi\) | |||||||
\(282\) | 4.02372e6 | + | 1.92241e7i | 0.179424 | + | 0.857231i | ||||
\(283\) | −2.00039e7 | −0.882584 | −0.441292 | − | 0.897364i | \(-0.645480\pi\) | ||||
−0.441292 | + | 0.897364i | \(0.645480\pi\) | |||||||
\(284\) | 7.71146e6 | + | 1.76144e7i | 0.336652 | + | 0.768977i | ||||
\(285\) | −4.20826e6 | − | 1.59112e6i | −0.181789 | − | 0.0687333i | ||||
\(286\) | −2.67862e6 | − | 1.27976e7i | −0.114502 | − | 0.547055i | ||||
\(287\) | 2.18635e6 | 0.0924857 | ||||||||
\(288\) | −6.83306e6 | − | 4.08811e6i | −0.286047 | − | 0.171138i | ||||
\(289\) | 2.35001e7 | 0.973592 | ||||||||
\(290\) | 3.67244e7 | + | 5.74404e6i | 1.50578 | + | 0.235518i | ||||
\(291\) | 1.84733e7i | 0.749661i | ||||||||
\(292\) | 3.52839e6 | + | 8.05952e6i | 0.141719 | + | 0.323713i | ||||
\(293\) | 1.18746e6i | 0.0472080i | 0.999721 | + | 0.0236040i | \(0.00751408\pi\) | ||||
−0.999721 | + | 0.0236040i | \(0.992486\pi\) | |||||||
\(294\) | −2.95920e6 | − | 1.41381e7i | −0.116448 | − | 0.556352i | ||||
\(295\) | −1.75769e7 | − | 6.64571e6i | −0.684661 | − | 0.258866i | ||||
\(296\) | 1.27753e7 | − | 9.10079e6i | 0.492600 | − | 0.350917i | ||||
\(297\) | 6.97965e6i | 0.266419i | ||||||||
\(298\) | −1.04504e7 | − | 4.99289e7i | −0.394899 | − | 1.88670i | ||||
\(299\) | 6.35331e6i | 0.237677i | ||||||||
\(300\) | −1.48440e7 | − | 4.75992e6i | −0.549776 | − | 0.176293i | ||||
\(301\) | 5.77703e6 | 0.211839 | ||||||||
\(302\) | 2.22763e7 | − | 4.66257e6i | 0.808764 | − | 0.169279i | ||||
\(303\) | −1.11209e7 | −0.399771 | ||||||||
\(304\) | −6.94878e6 | − | 6.41510e6i | −0.247336 | − | 0.228340i | ||||
\(305\) | −1.75521e6 | + | 4.64227e6i | −0.0618630 | + | 0.163618i | ||||
\(306\) | 1.51916e6 | − | 317970.i | 0.0530200 | − | 0.0110974i | ||||
\(307\) | 3.06814e7 | 1.06038 | 0.530188 | − | 0.847880i | \(-0.322121\pi\) | ||||
0.530188 | + | 0.847880i | \(0.322121\pi\) | |||||||
\(308\) | 2.01876e6 | + | 4.61123e6i | 0.0690928 | + | 0.157821i | ||||
\(309\) | −4.08254e6 | −0.138374 | ||||||||
\(310\) | 7.36238e6 | − | 4.70712e7i | 0.247134 | − | 1.58005i | ||||
\(311\) | − | 3.32935e7i | − | 1.10682i | −0.832908 | − | 0.553412i | \(-0.813326\pi\) | ||
0.832908 | − | 0.553412i | \(-0.186674\pi\) | |||||||
\(312\) | 5.76597e6 | − | 4.10754e6i | 0.189849 | − | 0.135244i | ||||
\(313\) | 1.22049e7i | 0.398018i | 0.979998 | + | 0.199009i | \(0.0637722\pi\) | ||||
−0.979998 | + | 0.199009i | \(0.936228\pi\) | |||||||
\(314\) | 5.33118e7 | − | 1.11585e7i | 1.72200 | − | 0.360427i | ||||
\(315\) | −458554. | + | 1.21280e6i | −0.0146710 | + | 0.0388024i | ||||
\(316\) | 1.00672e7 | + | 2.29953e7i | 0.319041 | + | 0.728749i | ||||
\(317\) | 1.63806e7i | 0.514225i | 0.966382 | + | 0.257112i | \(0.0827710\pi\) | ||||
−0.966382 | + | 0.257112i | \(0.917229\pi\) | |||||||
\(318\) | −1.71682e7 | + | 3.59341e6i | −0.533879 | + | 0.111744i | ||||
\(319\) | − | 6.84901e7i | − | 2.10987i | ||||||
\(320\) | −2.51821e7 | − | 2.09668e7i | −0.768496 | − | 0.639855i | ||||
\(321\) | 3.49512e7 | 1.05669 | ||||||||
\(322\) | −501102. | − | 2.39411e6i | −0.0150092 | − | 0.0717094i | ||||
\(323\) | 1.84341e6 | 0.0547034 | ||||||||
\(324\) | −3.46191e6 | + | 1.51560e6i | −0.101784 | + | 0.0445604i | ||||
\(325\) | 9.16949e6 | − | 1.03925e7i | 0.267113 | − | 0.302740i | ||||
\(326\) | −5.78588e6 | − | 2.76431e7i | −0.167000 | − | 0.797874i | ||||
\(327\) | 1.96083e7 | 0.560785 | ||||||||
\(328\) | 1.52154e7 | + | 2.13587e7i | 0.431185 | + | 0.605277i | ||||
\(329\) | 6.72282e6 | 0.188784 | ||||||||
\(330\) | −4.43856e6 | + | 2.83778e7i | −0.123510 | + | 0.789655i | ||||
\(331\) | 4.78385e7i | 1.31915i | 0.751639 | + | 0.659574i | \(0.229263\pi\) | ||||
−0.751639 | + | 0.659574i | \(0.770737\pi\) | |||||||
\(332\) | 1.53318e7 | − | 6.71213e6i | 0.418965 | − | 0.183420i | ||||
\(333\) | − | 7.44444e6i | − | 0.201604i | ||||||
\(334\) | 914862. | + | 4.37092e6i | 0.0245537 | + | 0.117310i | ||||
\(335\) | 8.33235e6 | − | 2.20378e7i | 0.221632 | − | 0.586183i | ||||
\(336\) | −1.84881e6 | + | 2.00261e6i | −0.0487387 | + | 0.0527934i | ||||
\(337\) | − | 6.77117e6i | − | 0.176919i | −0.996080 | − | 0.0884593i | \(-0.971806\pi\) | ||
0.996080 | − | 0.0884593i | \(-0.0281943\pi\) | |||||||
\(338\) | −6.62136e6 | − | 3.16348e7i | −0.171474 | − | 0.819246i | ||||
\(339\) | − | 1.07151e7i | − | 0.275040i | ||||||
\(340\) | 6.37880e6 | − | 326724.i | 0.162294 | − | 0.00831274i | ||||
\(341\) | −8.77866e7 | −2.21394 | ||||||||
\(342\) | −4.39329e6 | + | 919544.i | −0.109828 | + | 0.0229876i | ||||
\(343\) | −9.96623e6 | −0.246973 | ||||||||
\(344\) | 4.02040e7 | + | 5.64365e7i | 0.987628 | + | 1.38639i | ||||
\(345\) | 4.93598e6 | − | 1.30549e7i | 0.120203 | − | 0.317919i | ||||
\(346\) | −3.87503e7 | + | 8.11069e6i | −0.935506 | + | 0.195808i | ||||
\(347\) | 1.75962e6 | 0.0421145 | 0.0210572 | − | 0.999778i | \(-0.493297\pi\) | ||||
0.0210572 | + | 0.999778i | \(0.493297\pi\) | |||||||
\(348\) | 3.39711e7 | − | 1.48723e7i | 0.806069 | − | 0.352891i | ||||
\(349\) | 8.41394e6 | 0.197935 | 0.0989677 | − | 0.995091i | \(-0.468446\pi\) | ||||
0.0989677 | + | 0.995091i | \(0.468446\pi\) | |||||||
\(350\) | −2.63564e6 | + | 4.63941e6i | −0.0614727 | + | 0.108208i | ||||
\(351\) | − | 3.35996e6i | − | 0.0776985i | ||||||
\(352\) | −3.09985e7 | + | 5.18124e7i | −0.710744 | + | 1.18797i | ||||
\(353\) | 4.18620e6i | 0.0951691i | 0.998867 | + | 0.0475846i | \(0.0151524\pi\) | ||||
−0.998867 | + | 0.0475846i | \(0.984848\pi\) | |||||||
\(354\) | −1.83497e7 | + | 3.84071e6i | −0.413637 | + | 0.0865769i | ||||
\(355\) | 3.51286e7 | + | 1.32819e7i | 0.785191 | + | 0.296876i | ||||
\(356\) | −5.53506e7 | + | 2.42321e7i | −1.22680 | + | 0.537082i | ||||
\(357\) | − | 531264.i | − | 0.0116763i | ||||||
\(358\) | −6.98969e7 | + | 1.46299e7i | −1.52338 | + | 0.318854i | ||||
\(359\) | − | 3.66938e7i | − | 0.793065i | −0.918021 | − | 0.396532i | \(-0.870213\pi\) | ||
0.918021 | − | 0.396532i | \(-0.129787\pi\) | |||||||
\(360\) | −1.50392e7 | + | 3.96058e6i | −0.322343 | + | 0.0848890i | ||||
\(361\) | 4.17149e7 | 0.886685 | ||||||||
\(362\) | −801628. | − | 3.82992e6i | −0.0168985 | − | 0.0807354i | ||||
\(363\) | 2.53080e7 | 0.529101 | ||||||||
\(364\) | −971819. | − | 2.21982e6i | −0.0201503 | − | 0.0460271i | ||||
\(365\) | 1.60731e7 | + | 6.07716e6i | 0.330539 | + | 0.124975i | ||||
\(366\) | 1.01438e6 | + | 4.84638e6i | 0.0206898 | + | 0.0988495i | ||||
\(367\) | 9.45536e6 | 0.191285 | 0.0956423 | − | 0.995416i | \(-0.469509\pi\) | ||||
0.0956423 | + | 0.995416i | \(0.469509\pi\) | |||||||
\(368\) | 1.99010e7 | − | 2.15566e7i | 0.399330 | − | 0.432550i | ||||
\(369\) | 1.24462e7 | 0.247719 | ||||||||
\(370\) | 4.73413e6 | − | 3.02676e7i | 0.0934620 | − | 0.597547i | ||||
\(371\) | 6.00386e6i | 0.117573i | ||||||||
\(372\) | −1.90624e7 | − | 4.35422e7i | −0.370297 | − | 0.845827i | ||||
\(373\) | 5.35560e7i | 1.03200i | 0.856587 | + | 0.516002i | \(0.172580\pi\) | ||||
−0.856587 | + | 0.516002i | \(0.827420\pi\) | |||||||
\(374\) | −2.41104e6 | − | 1.15192e7i | −0.0460882 | − | 0.220195i | ||||
\(375\) | −2.69157e7 | + | 1.42308e7i | −0.510402 | + | 0.269858i | ||||
\(376\) | 4.67860e7 | + | 6.56760e7i | 0.880142 | + | 1.23550i | ||||
\(377\) | 3.29707e7i | 0.615324i | ||||||||
\(378\) | 265009. | + | 1.26613e6i | 0.00490665 | + | 0.0234424i | ||||
\(379\) | 5.05485e7i | 0.928518i | 0.885699 | + | 0.464259i | \(0.153679\pi\) | ||||
−0.885699 | + | 0.464259i | \(0.846321\pi\) | |||||||
\(380\) | −1.84470e7 | + | 944858.i | −0.336182 | + | 0.0172193i | ||||
\(381\) | 4.97796e7 | 0.900071 | ||||||||
\(382\) | −5.27670e7 | + | 1.10445e7i | −0.946613 | + | 0.198132i | ||||
\(383\) | 7.44208e7 | 1.32464 | 0.662320 | − | 0.749221i | \(-0.269572\pi\) | ||||
0.662320 | + | 0.749221i | \(0.269572\pi\) | |||||||
\(384\) | −3.24301e7 | − | 4.12447e6i | −0.572737 | − | 0.0728408i | ||||
\(385\) | 9.19621e6 | + | 3.47703e6i | 0.161149 | + | 0.0609293i | ||||
\(386\) | −3.68867e7 | + | 7.72063e6i | −0.641369 | + | 0.134243i | ||||
\(387\) | 3.28868e7 | 0.567399 | ||||||||
\(388\) | 3.04167e7 | + | 6.94775e7i | 0.520735 | + | 1.18946i | ||||
\(389\) | −3.91704e7 | −0.665441 | −0.332721 | − | 0.943025i | \(-0.607967\pi\) | ||||
−0.332721 | + | 0.943025i | \(0.607967\pi\) | |||||||
\(390\) | 2.13670e6 | − | 1.36609e7i | 0.0360204 | − | 0.230296i | ||||
\(391\) | 5.71865e6i | 0.0956672i | ||||||||
\(392\) | −3.44083e7 | − | 4.83007e7i | −0.571222 | − | 0.801854i | ||||
\(393\) | − | 5.78967e7i | − | 0.953841i | ||||||
\(394\) | 1.18690e7 | − | 2.48425e6i | 0.194055 | − | 0.0406169i | ||||
\(395\) | 4.58597e7 | + | 1.73393e7i | 0.744114 | + | 0.281345i | ||||
\(396\) | 1.14922e7 | + | 2.62503e7i | 0.185062 | + | 0.422716i | ||||
\(397\) | − | 6.48990e7i | − | 1.03721i | −0.855014 | − | 0.518604i | \(-0.826452\pi\) | ||
0.855014 | − | 0.518604i | \(-0.173548\pi\) | |||||||
\(398\) | −9.67746e7 | + | 2.02556e7i | −1.53501 | + | 0.321288i | ||||
\(399\) | 1.53637e6i | 0.0241867i | ||||||||
\(400\) | −6.36651e7 | + | 6.53904e6i | −0.994767 | + | 0.102172i | ||||
\(401\) | −9.69420e7 | −1.50341 | −0.751707 | − | 0.659497i | \(-0.770769\pi\) | ||||
−0.751707 | + | 0.659497i | \(0.770769\pi\) | |||||||
\(402\) | −4.81546e6 | − | 2.30067e7i | −0.0741241 | − | 0.354142i | ||||
\(403\) | 4.22599e7 | 0.645674 | ||||||||
\(404\) | −4.18254e7 | + | 1.83108e7i | −0.634301 | + | 0.277692i | ||||
\(405\) | −2.61040e6 | + | 6.90411e6i | −0.0392955 | + | 0.103930i | ||||
\(406\) | −2.60048e6 | − | 1.24243e7i | −0.0388576 | − | 0.185649i | ||||
\(407\) | −5.64482e7 | −0.837273 | ||||||||
\(408\) | 5.18998e6 | − | 3.69721e6i | 0.0764161 | − | 0.0544370i | ||||
\(409\) | −3.78803e7 | −0.553660 | −0.276830 | − | 0.960919i | \(-0.589284\pi\) | ||||
−0.276830 | + | 0.960919i | \(0.589284\pi\) | |||||||
\(410\) | 5.06038e7 | + | 7.91491e6i | 0.734229 | + | 0.114840i | ||||
\(411\) | 6.69729e7i | 0.964658i | ||||||||
\(412\) | −1.53543e7 | + | 6.72201e6i | −0.219553 | + | 0.0961186i | ||||
\(413\) | 6.41705e6i | 0.0910931i | ||||||||
\(414\) | −2.85262e6 | − | 1.36289e7i | −0.0402015 | − | 0.192070i | ||||
\(415\) | 1.15607e7 | − | 3.05763e7i | 0.161748 | − | 0.427799i | ||||
\(416\) | 1.49225e7 | − | 2.49421e7i | 0.207282 | − | 0.346461i | ||||
\(417\) | 3.41869e7i | 0.471467i | ||||||||
\(418\) | 6.97253e6 | + | 3.33125e7i | 0.0954688 | + | 0.456120i | ||||
\(419\) | 5.92341e7i | 0.805248i | 0.915365 | + | 0.402624i | \(0.131902\pi\) | ||||
−0.915365 | + | 0.402624i | \(0.868098\pi\) | |||||||
\(420\) | 272304. | + | 5.31635e6i | 0.00367542 | + | 0.0717572i | ||||
\(421\) | 7.02355e7 | 0.941262 | 0.470631 | − | 0.882330i | \(-0.344026\pi\) | ||||
0.470631 | + | 0.882330i | \(0.344026\pi\) | |||||||
\(422\) | 7.74554e6 | − | 1.62119e6i | 0.103066 | − | 0.0215723i | ||||
\(423\) | 3.82709e7 | 0.505648 | ||||||||
\(424\) | −5.86524e7 | + | 4.17825e7i | −0.769464 | + | 0.548147i | ||||
\(425\) | 8.25351e6 | − | 9.35433e6i | 0.107516 | − | 0.121856i | ||||
\(426\) | 3.66731e7 | − | 7.67592e6i | 0.474372 | − | 0.0992891i | ||||
\(427\) | 1.69482e6 | 0.0217691 | ||||||||
\(428\) | 1.31450e8 | − | 5.75480e7i | 1.67660 | − | 0.734005i | ||||
\(429\) | −2.54772e7 | −0.322686 | ||||||||
\(430\) | 1.33711e8 | + | 2.09137e7i | 1.68175 | + | 0.263042i | ||||
\(431\) | − | 9.18112e7i | − | 1.14674i | −0.819298 | − | 0.573368i | \(-0.805636\pi\) | ||
0.819298 | − | 0.573368i | \(-0.194364\pi\) | |||||||
\(432\) | −1.05247e7 | + | 1.14002e7i | −0.130544 | + | 0.141404i | ||||
\(433\) | 1.07675e8i | 1.32632i | 0.748476 | + | 0.663162i | \(0.230786\pi\) | ||||
−0.748476 | + | 0.663162i | \(0.769214\pi\) | |||||||
\(434\) | −1.59247e7 | + | 3.33315e6i | −0.194806 | + | 0.0407742i | ||||
\(435\) | 2.56154e7 | − | 6.77488e7i | 0.311196 | − | 0.823065i | ||||
\(436\) | 7.37462e7 | − | 3.22855e7i | 0.889775 | − | 0.389537i | ||||
\(437\) | − | 1.65379e7i | − | 0.198169i | ||||||
\(438\) | 1.67799e7 | − | 3.51213e6i | 0.199694 | − | 0.0417973i | ||||
\(439\) | − | 6.90483e6i | − | 0.0816130i | −0.999167 | − | 0.0408065i | \(-0.987007\pi\) | ||
0.999167 | − | 0.0408065i | \(-0.0129927\pi\) | |||||||
\(440\) | 3.00315e7 | + | 1.14036e8i | 0.352549 | + | 1.33871i | ||||
\(441\) | −2.81459e7 | −0.328171 | ||||||||
\(442\) | 1.16066e6 | + | 5.54527e6i | 0.0134412 | + | 0.0642178i | ||||
\(443\) | 5.25821e7 | 0.604821 | 0.302410 | − | 0.953178i | \(-0.402209\pi\) | ||||
0.302410 | + | 0.953178i | \(0.402209\pi\) | |||||||
\(444\) | −1.22575e7 | − | 2.79983e7i | −0.140040 | − | 0.319877i | ||||
\(445\) | −4.17363e7 | + | 1.10386e8i | −0.473624 | + | 1.25266i | ||||
\(446\) | −1.11451e7 | − | 5.32477e7i | −0.125626 | − | 0.600201i | ||||
\(447\) | −9.93976e7 | −1.11289 | ||||||||
\(448\) | −3.65597e6 | + | 1.05759e7i | −0.0406601 | + | 0.117620i | ||||
\(449\) | 9.75225e7 | 1.07737 | 0.538686 | − | 0.842506i | \(-0.318921\pi\) | ||||
0.538686 | + | 0.842506i | \(0.318921\pi\) | |||||||
\(450\) | −1.50039e7 | + | 2.64107e7i | −0.164652 | + | 0.289829i | ||||
\(451\) | − | 9.43747e7i | − | 1.02879i | ||||||
\(452\) | −1.76426e7 | − | 4.02991e7i | −0.191050 | − | 0.436395i | ||||
\(453\) | − | 4.43472e7i | − | 0.477058i | ||||||
\(454\) | −2.30364e7 | − | 1.10061e8i | −0.246177 | − | 1.17615i | ||||
\(455\) | −4.42700e6 | − | 1.67382e6i | −0.0469975 | − | 0.0177695i | ||||
\(456\) | −1.50090e7 | + | 1.06920e7i | −0.158291 | + | 0.112763i | ||||
\(457\) | − | 3.78570e7i | − | 0.396641i | −0.980137 | − | 0.198320i | \(-0.936451\pi\) | ||
0.980137 | − | 0.198320i | \(-0.0635486\pi\) | |||||||
\(458\) | 1.94532e7 | + | 9.29411e7i | 0.202485 | + | 0.967411i | ||||
\(459\) | − | 3.02432e6i | − | 0.0312744i | ||||||
\(460\) | −2.93115e6 | − | 5.72264e7i | −0.0301137 | − | 0.587926i | ||||
\(461\) | 7.34284e7 | 0.749483 | 0.374741 | − | 0.927129i | \(-0.377732\pi\) | ||||
0.374741 | + | 0.927129i | \(0.377732\pi\) | |||||||
\(462\) | 9.60055e6 | − | 2.00946e6i | 0.0973577 | − | 0.0203776i | ||||
\(463\) | −1.84010e8 | −1.85395 | −0.926977 | − | 0.375118i | \(-0.877602\pi\) | ||||
−0.926977 | + | 0.375118i | \(0.877602\pi\) | |||||||
\(464\) | 1.03277e8 | − | 1.11869e8i | 1.03383 | − | 1.11984i | ||||
\(465\) | −8.68365e7 | − | 3.28323e7i | −0.863661 | − | 0.326545i | ||||
\(466\) | 7.89722e7 | − | 1.65294e7i | 0.780398 | − | 0.163342i | ||||
\(467\) | −9.86693e7 | −0.968794 | −0.484397 | − | 0.874848i | \(-0.660961\pi\) | ||||
−0.484397 | + | 0.874848i | \(0.660961\pi\) | |||||||
\(468\) | −5.53226e6 | − | 1.26367e7i | −0.0539716 | − | 0.123281i | ||||
\(469\) | −8.04566e6 | −0.0779907 | ||||||||
\(470\) | 1.55602e8 | + | 2.43376e7i | 1.49872 | + | 0.234414i | ||||
\(471\) | − | 1.06132e8i | − | 1.01574i | ||||||
\(472\) | −6.26889e7 | + | 4.46581e7i | −0.596163 | + | 0.424692i | ||||
\(473\) | − | 2.49368e8i | − | 2.35644i | ||||||
\(474\) | 4.78760e7 | − | 1.00208e7i | 0.449555 | − | 0.0940948i | ||||
\(475\) | −2.38685e7 | + | 2.70519e7i | −0.222712 | + | 0.252416i | ||||
\(476\) | −874739. | − | 1.99807e6i | −0.00811069 | − | 0.0185263i | ||||
\(477\) | 3.41781e7i | 0.314914i | ||||||||
\(478\) | −1.43367e8 | + | 3.00076e7i | −1.31270 | + | 0.274756i | ||||
\(479\) | 8.02038e7i | 0.729774i | 0.931052 | + | 0.364887i | \(0.118892\pi\) | ||||
−0.931052 | + | 0.364887i | \(0.881108\pi\) | |||||||
\(480\) | −5.00410e7 | + | 3.96581e7i | −0.452483 | + | 0.358598i | ||||
\(481\) | 2.71738e7 | 0.244183 | ||||||||
\(482\) | −1.53161e7 | − | 7.31755e7i | −0.136775 | − | 0.653468i | ||||
\(483\) | −4.76615e6 | −0.0422986 | ||||||||
\(484\) | 9.51828e7 | − | 4.16703e7i | 0.839504 | − | 0.367528i | ||||
\(485\) | 1.38559e8 | + | 5.23885e7i | 1.21454 | + | 0.459209i | ||||
\(486\) | 1.50861e6 | + | 7.20767e6i | 0.0131422 | + | 0.0627894i | ||||
\(487\) | −1.13713e8 | −0.984516 | −0.492258 | − | 0.870449i | \(-0.663828\pi\) | ||||
−0.492258 | + | 0.870449i | \(0.663828\pi\) | |||||||
\(488\) | 1.17947e7 | + | 1.65569e7i | 0.101491 | + | 0.142469i | ||||
\(489\) | −5.50314e7 | −0.470635 | ||||||||
\(490\) | −1.14436e8 | − | 1.78988e7i | −0.972686 | − | 0.152137i | ||||
\(491\) | 9.37372e6i | 0.0791895i | 0.999216 | + | 0.0395947i | \(0.0126067\pi\) | ||||
−0.999216 | + | 0.0395947i | \(0.987393\pi\) | |||||||
\(492\) | 4.68099e7 | − | 2.04930e7i | 0.393045 | − | 0.172072i | ||||
\(493\) | 2.96771e7i | 0.247674i | ||||||||
\(494\) | −3.35653e6 | − | 1.60364e7i | −0.0278426 | − | 0.133023i | ||||
\(495\) | 5.23512e7 | + | 1.97936e7i | 0.431629 | + | 0.163196i | ||||
\(496\) | −1.43387e8 | − | 1.32374e8i | −1.17507 | − | 1.08482i | ||||
\(497\) | − | 1.28249e7i | − | 0.104468i | ||||||
\(498\) | −6.68120e6 | − | 3.19206e7i | −0.0540961 | − | 0.258454i | ||||
\(499\) | 1.95311e8i | 1.57190i | 0.618289 | + | 0.785951i | \(0.287826\pi\) | ||||
−0.618289 | + | 0.785951i | \(0.712174\pi\) | |||||||
\(500\) | −7.77980e7 | + | 9.78390e7i | −0.622384 | + | 0.782712i | ||||
\(501\) | 8.70155e6 | 0.0691964 | ||||||||
\(502\) | 1.28050e8 | − | 2.68017e7i | 1.01220 | − | 0.211861i | ||||
\(503\) | −1.57813e8 | −1.24005 | −0.620024 | − | 0.784583i | \(-0.712877\pi\) | ||||
−0.620024 | + | 0.784583i | \(0.712877\pi\) | |||||||
\(504\) | 3.08140e6 | + | 4.32553e6i | 0.0240689 | + | 0.0337869i | ||||
\(505\) | −3.15378e7 | + | 8.34126e7i | −0.244882 | + | 0.647676i | ||||
\(506\) | −1.03343e8 | + | 2.16303e7i | −0.797678 | + | 0.166959i | ||||
\(507\) | −6.29779e7 | −0.483242 | ||||||||
\(508\) | 1.87220e8 | − | 8.19634e7i | 1.42811 | − | 0.625214i | ||||
\(509\) | −7.46265e7 | −0.565900 | −0.282950 | − | 0.959135i | \(-0.591313\pi\) | ||||
−0.282950 | + | 0.959135i | \(0.591313\pi\) | |||||||
\(510\) | 1.92325e6 | − | 1.22963e7i | 0.0144986 | − | 0.0926963i | ||||
\(511\) | − | 5.86806e6i | − | 0.0439776i | ||||||
\(512\) | −1.28760e8 | + | 3.78850e7i | −0.959336 | + | 0.282265i | ||||
\(513\) | 8.74608e6i | 0.0647830i | ||||||||
\(514\) | 1.12141e8 | − | 2.34718e7i | 0.825799 | − | 0.172845i | ||||
\(515\) | −1.15777e7 | + | 3.06213e7i | −0.0847619 | + | 0.224182i | ||||
\(516\) | 1.23686e8 | − | 5.41490e7i | 0.900270 | − | 0.394131i | ||||
\(517\) | − | 2.90193e8i | − | 2.09998i | ||||||
\(518\) | −1.02399e7 | + | 2.14327e6i | −0.0736724 | + | 0.0154201i | ||||
\(519\) | 7.71434e7i | 0.551819i | ||||||||
\(520\) | −1.44570e7 | − | 5.48964e7i | −0.102818 | − | 0.390422i | ||||
\(521\) | 1.33012e8 | 0.940543 | 0.470272 | − | 0.882522i | \(-0.344156\pi\) | ||||
0.470272 | + | 0.882522i | \(0.344156\pi\) | |||||||
\(522\) | −1.48037e7 | − | 7.07276e7i | −0.104078 | − | 0.497253i | ||||
\(523\) | 8.07772e7 | 0.564656 | 0.282328 | − | 0.959318i | \(-0.408893\pi\) | ||||
0.282328 | + | 0.959318i | \(0.408893\pi\) | |||||||
\(524\) | −9.53284e7 | − | 2.17748e8i | −0.662565 | − | 1.51342i | ||||
\(525\) | 7.79627e6 | + | 6.87880e6i | 0.0538777 | + | 0.0475373i | ||||
\(526\) | 4.48399e7 | + | 2.14231e8i | 0.308111 | + | 1.47206i | ||||
\(527\) | 3.80384e7 | 0.259890 | ||||||||
\(528\) | 8.64435e7 | + | 7.98045e7i | 0.587261 | + | 0.542158i | ||||
\(529\) | −9.67320e7 | −0.653436 | ||||||||
\(530\) | −2.17348e7 | + | 1.38961e8i | −0.145992 | + | 0.933395i | ||||
\(531\) | 3.65303e7i | 0.243988i | ||||||||
\(532\) | 2.52967e6 | + | 5.77825e6i | 0.0168008 | + | 0.0383762i | ||||
\(533\) | 4.54314e7i | 0.300037i | ||||||||
\(534\) | 2.41204e7 | + | 1.15240e8i | 0.158402 | + | 0.756794i | ||||
\(535\) | 9.91182e7 | − | 2.62153e8i | 0.647280 | − | 1.71196i | ||||
\(536\) | −5.59920e7 | − | 7.85989e7i | −0.363606 | − | 0.510414i | ||||
\(537\) | 1.39150e8i | 0.898584i | ||||||||
\(538\) | −1.94696e7 | − | 9.30198e7i | −0.125029 | − | 0.597349i | ||||
\(539\) | 2.13419e8i | 1.36291i | ||||||||
\(540\) | 1.55014e6 | + | 3.02643e7i | 0.00984443 | + | 0.192198i | ||||
\(541\) | −1.30546e8 | −0.824465 | −0.412232 | − | 0.911079i | \(-0.635251\pi\) | ||||
−0.412232 | + | 0.911079i | \(0.635251\pi\) | |||||||
\(542\) | 6.29307e7 | − | 1.31718e7i | 0.395244 | − | 0.0827271i | ||||
\(543\) | −7.62454e6 | −0.0476227 | ||||||||
\(544\) | 1.34318e7 | − | 2.24506e7i | 0.0834330 | − | 0.139454i | ||||
\(545\) | 5.56072e7 | − | 1.47073e8i | 0.343512 | − | 0.908536i | ||||
\(546\) | −4.62164e6 | + | 967340.i | −0.0283935 | + | 0.00594294i | ||||
\(547\) | −9.69022e7 | −0.592068 | −0.296034 | − | 0.955177i | \(-0.595664\pi\) | ||||
−0.296034 | + | 0.955177i | \(0.595664\pi\) | |||||||
\(548\) | 1.10273e8 | + | 2.51883e8i | 0.670079 | + | 1.53059i | ||||
\(549\) | 9.64809e6 | 0.0583075 | ||||||||
\(550\) | 2.00262e8 | + | 1.13768e8i | 1.20368 | + | 0.683808i | ||||
\(551\) | − | 8.58237e7i | − | 0.513041i | ||||||
\(552\) | −3.31690e7 | − | 4.65610e7i | −0.197203 | − | 0.276825i | ||||
\(553\) | − | 1.67427e7i | − | 0.0990032i | ||||||
\(554\) | −1.85021e8 | + | 3.87260e7i | −1.08815 | + | 0.227758i | ||||
\(555\) | −5.58373e7 | − | 2.11117e7i | −0.326622 | − | 0.123494i | ||||
\(556\) | 5.62896e7 | + | 1.28576e8i | 0.327494 | + | 0.748058i | ||||
\(557\) | 3.21040e8i | 1.85778i | 0.370356 | + | 0.928890i | \(0.379236\pi\) | ||||
−0.370356 | + | 0.928890i | \(0.620764\pi\) | |||||||
\(558\) | −9.06545e7 | + | 1.89746e7i | −0.521779 | + | 0.109212i | ||||
\(559\) | 1.20044e8i | 0.687234i | ||||||||
\(560\) | 9.77763e6 | + | 1.95463e7i | 0.0556762 | + | 0.111301i | ||||
\(561\) | −2.29322e7 | −0.129884 | ||||||||
\(562\) | 6.57071e7 | + | 3.13928e8i | 0.370172 | + | 1.76856i | ||||
\(563\) | 1.10496e8 | 0.619186 | 0.309593 | − | 0.950869i | \(-0.399807\pi\) | ||||
0.309593 | + | 0.950869i | \(0.399807\pi\) | |||||||
\(564\) | 1.43936e8 | − | 6.30141e7i | 0.802291 | − | 0.351237i | ||||
\(565\) | −8.03688e7 | − | 3.03869e7i | −0.445597 | − | 0.168477i | ||||
\(566\) | 3.27852e7 | + | 1.56637e8i | 0.180812 | + | 0.863864i | ||||
\(567\) | 2.52059e6 | 0.0138278 | ||||||||
\(568\) | 1.25288e8 | − | 8.92521e7i | 0.683698 | − | 0.487050i | ||||
\(569\) | 1.78862e8 | 0.970913 | 0.485457 | − | 0.874261i | \(-0.338653\pi\) | ||||
0.485457 | + | 0.874261i | \(0.338653\pi\) | |||||||
\(570\) | −5.56188e6 | + | 3.55598e7i | −0.0300329 | + | 0.192015i | ||||
\(571\) | 4.65669e6i | 0.0250132i | 0.999922 | + | 0.0125066i | \(0.00398108\pi\) | ||||
−0.999922 | + | 0.0125066i | \(0.996019\pi\) | |||||||
\(572\) | −9.58192e7 | + | 4.19489e7i | −0.511994 | + | 0.224147i | ||||
\(573\) | 1.05048e8i | 0.558371i | ||||||||
\(574\) | −3.58329e6 | − | 1.71198e7i | −0.0189473 | − | 0.0905241i | ||||
\(575\) | −8.39208e7 | − | 7.40450e7i | −0.441435 | − | 0.389486i | ||||
\(576\) | −2.08123e7 | + | 6.02052e7i | −0.108906 | + | 0.315041i | ||||
\(577\) | − | 1.91916e8i | − | 0.999041i | −0.866302 | − | 0.499521i | \(-0.833510\pi\) | ||
0.866302 | − | 0.499521i | \(-0.166490\pi\) | |||||||
\(578\) | −3.85152e7 | − | 1.84014e8i | −0.199457 | − | 0.952942i | ||||
\(579\) | 7.34334e7i | 0.378319i | ||||||||
\(580\) | −1.52113e7 | − | 2.96978e8i | −0.0779618 | − | 1.52209i | ||||
\(581\) | −1.11629e7 | −0.0569180 | ||||||||
\(582\) | 1.44652e8 | − | 3.02765e7i | 0.733760 | − | 0.153581i | ||||
\(583\) | 2.59159e8 | 1.30786 | ||||||||
\(584\) | 5.73258e7 | − | 4.08375e7i | 0.287814 | − | 0.205031i | ||||
\(585\) | −2.52015e7 | − | 9.52853e6i | −0.125881 | − | 0.0475947i | ||||
\(586\) | 9.29818e6 | − | 1.94617e6i | 0.0462067 | − | 0.00967136i | ||||
\(587\) | 8.23978e7 | 0.407382 | 0.203691 | − | 0.979035i | \(-0.434706\pi\) | ||||
0.203691 | + | 0.979035i | \(0.434706\pi\) | |||||||
\(588\) | −1.05856e8 | + | 4.63430e7i | −0.520696 | + | 0.227957i | ||||
\(589\) | −1.10004e8 | −0.538346 | ||||||||
\(590\) | −2.32306e7 | + | 1.48525e8i | −0.113111 | + | 0.723173i | ||||
\(591\) | − | 2.36285e7i | − | 0.114465i | ||||||
\(592\) | −9.21999e7 | − | 8.51188e7i | −0.444391 | − | 0.410261i | ||||
\(593\) | 3.25768e8i | 1.56223i | 0.624388 | + | 0.781114i | \(0.285348\pi\) | ||||
−0.624388 | + | 0.781114i | \(0.714652\pi\) | |||||||
\(594\) | 5.46529e7 | − | 1.14392e7i | 0.260768 | − | 0.0545804i | ||||
\(595\) | −3.98476e6 | − | 1.50661e6i | −0.0189170 | − | 0.00715239i | ||||
\(596\) | −3.73832e8 | + | 1.63661e8i | −1.76578 | + | 0.773046i | ||||
\(597\) | 1.92657e8i | 0.905445i | ||||||||
\(598\) | 4.97484e7 | − | 1.04127e7i | 0.232635 | − | 0.0486921i | ||||
\(599\) | 2.65951e7i | 0.123743i | 0.998084 | + | 0.0618716i | \(0.0197069\pi\) | ||||
−0.998084 | + | 0.0618716i | \(0.980293\pi\) | |||||||
\(600\) | −1.29434e7 | + | 1.24034e8i | −0.0599230 | + | 0.574232i | ||||
\(601\) | −2.51378e8 | −1.15799 | −0.578994 | − | 0.815332i | \(-0.696555\pi\) | ||||
−0.578994 | + | 0.815332i | \(0.696555\pi\) | |||||||
\(602\) | −9.46818e6 | − | 4.52360e7i | −0.0433987 | − | 0.207345i | ||||
\(603\) | −4.58014e7 | −0.208894 | ||||||||
\(604\) | −7.30188e7 | − | 1.66789e8i | −0.331378 | − | 0.756930i | ||||
\(605\) | 7.17712e7 | − | 1.89824e8i | 0.324104 | − | 0.857205i | ||||
\(606\) | 1.82264e7 | + | 8.70801e7i | 0.0819000 | + | 0.391292i | ||||
\(607\) | 4.32296e8 | 1.93293 | 0.966463 | − | 0.256805i | \(-0.0826697\pi\) | ||||
0.966463 | + | 0.256805i | \(0.0826697\pi\) | |||||||
\(608\) | −3.88437e7 | + | 6.49251e7i | −0.172826 | + | 0.288870i | ||||
\(609\) | −2.47341e7 | −0.109507 | ||||||||
\(610\) | 3.92272e7 | + | 6.13550e6i | 0.172821 | + | 0.0270309i | ||||
\(611\) | 1.39697e8i | 0.612441i | ||||||||
\(612\) | −4.97962e6 | − | 1.13744e7i | −0.0217241 | − | 0.0496219i | ||||
\(613\) | − | 8.56795e7i | − | 0.371959i | −0.982554 | − | 0.185980i | \(-0.940454\pi\) | ||
0.982554 | − | 0.185980i | \(-0.0595458\pi\) | |||||||
\(614\) | −5.02849e7 | − | 2.40245e8i | −0.217236 | − | 1.03789i | ||||
\(615\) | 3.52963e7 | − | 9.33533e7i | 0.151741 | − | 0.401333i | ||||
\(616\) | 3.27988e7 | − | 2.33651e7i | 0.140319 | − | 0.0999597i | ||||
\(617\) | − | 2.77104e8i | − | 1.17974i | −0.807497 | − | 0.589871i | \(-0.799179\pi\) | ||
0.807497 | − | 0.589871i | \(-0.200821\pi\) | |||||||
\(618\) | 6.69103e6 | + | 3.19676e7i | 0.0283483 | + | 0.135439i | ||||
\(619\) | 1.95819e6i | 0.00825625i | 0.999991 | + | 0.00412813i | \(0.00131403\pi\) | ||||
−0.999991 | + | 0.00412813i | \(0.998686\pi\) | |||||||
\(620\) | −3.80649e8 | + | 1.94969e7i | −1.59716 | + | 0.0818072i | ||||
\(621\) | −2.71322e7 | −0.113295 | ||||||||
\(622\) | −2.60699e8 | + | 5.45660e7i | −1.08335 | + | 0.226752i | ||||
\(623\) | 4.03003e7 | 0.166665 | ||||||||
\(624\) | −4.16134e7 | − | 3.84174e7i | −0.171269 | − | 0.158115i | ||||
\(625\) | 3.04080e7 | + | 2.42240e8i | 0.124551 | + | 0.992213i | ||||
\(626\) | 9.55685e7 | − | 2.00031e7i | 0.389576 | − | 0.0815407i | ||||
\(627\) | 6.63180e7 | 0.269047 | ||||||||
\(628\) | −1.74749e8 | − | 3.99160e8i | −0.705564 | − | 1.61164i | ||||
\(629\) | 2.44593e7 | 0.0982860 | ||||||||
\(630\) | 1.02482e7 | + | 1.60291e6i | 0.0409850 | + | 0.00641045i | ||||
\(631\) | − | 7.22111e6i | − | 0.0287419i | −0.999897 | − | 0.0143710i | \(-0.995425\pi\) | ||
0.999897 | − | 0.0143710i | \(-0.00457458\pi\) | |||||||
\(632\) | 1.63561e8 | − | 1.16517e8i | 0.647931 | − | 0.461570i | ||||
\(633\) | − | 1.54197e7i | − | 0.0607945i | ||||||
\(634\) | 1.28266e8 | − | 2.68468e7i | 0.503318 | − | 0.105348i | ||||
\(635\) | 1.41170e8 | − | 3.73374e8i | 0.551343 | − | 1.45822i | ||||
\(636\) | 5.62751e7 | + | 1.28543e8i | 0.218748 | + | 0.499662i | ||||
\(637\) | − | 1.02739e8i | − | 0.397481i | ||||||
\(638\) | −5.36299e8 | + | 1.12251e8i | −2.06512 | + | 0.432243i | ||||
\(639\) | − | 7.30081e7i | − | 0.279813i | ||||||
\(640\) | −1.22905e8 | + | 2.31547e8i | −0.468844 | + | 0.883281i | ||||
\(641\) | 1.00144e8 | 0.380232 | 0.190116 | − | 0.981762i | \(-0.439114\pi\) | ||||
0.190116 | + | 0.981762i | \(0.439114\pi\) | |||||||
\(642\) | −5.72828e7 | − | 2.73679e8i | −0.216480 | − | 1.03428i | ||||
\(643\) | −2.09841e8 | −0.789328 | −0.394664 | − | 0.918825i | \(-0.629139\pi\) | ||||
−0.394664 | + | 0.918825i | \(0.629139\pi\) | |||||||
\(644\) | −1.79254e7 | + | 7.84758e6i | −0.0671135 | + | 0.0293818i | ||||
\(645\) | 9.32639e7 | − | 2.46669e8i | 0.347564 | − | 0.919253i | ||||
\(646\) | −3.02123e6 | − | 1.44345e7i | −0.0112069 | − | 0.0535431i | ||||
\(647\) | 1.00473e8 | 0.370967 | 0.185484 | − | 0.982647i | \(-0.440615\pi\) | ||||
0.185484 | + | 0.982647i | \(0.440615\pi\) | |||||||
\(648\) | 1.75415e7 | + | 2.46239e7i | 0.0644675 | + | 0.0904965i | ||||
\(649\) | 2.76994e8 | 1.01330 | ||||||||
\(650\) | −9.64047e7 | − | 5.47674e7i | −0.351041 | − | 0.199426i | ||||
\(651\) | 3.17027e7i | 0.114909i | ||||||||
\(652\) | −2.06972e8 | + | 9.06106e7i | −0.746738 | + | 0.326916i | ||||
\(653\) | − | 2.46927e8i | − | 0.886808i | −0.896322 | − | 0.443404i | \(-0.853771\pi\) | ||
0.896322 | − | 0.443404i | \(-0.146229\pi\) | |||||||
\(654\) | −3.21367e7 | − | 1.53539e8i | −0.114886 | − | 0.548890i | ||||
\(655\) | −4.34256e8 | − | 1.64190e8i | −1.54533 | − | 0.584281i | ||||
\(656\) | 1.42309e8 | − | 1.54147e8i | 0.504103 | − | 0.546040i | ||||
\(657\) | − | 3.34050e7i | − | 0.117792i | ||||||
\(658\) | −1.10183e7 | − | 5.26419e7i | −0.0386755 | − | 0.184779i | ||||
\(659\) | − | 1.58874e8i | − | 0.555133i | −0.960706 | − | 0.277566i | \(-0.910472\pi\) | ||
0.960706 | − | 0.277566i | \(-0.0895279\pi\) | |||||||
\(660\) | 2.29482e8 | − | 1.17541e7i | 0.798209 | − | 0.0408845i | ||||
\(661\) | 3.01264e8 | 1.04314 | 0.521571 | − | 0.853208i | \(-0.325346\pi\) | ||||
0.521571 | + | 0.853208i | \(0.325346\pi\) | |||||||
\(662\) | 3.74591e8 | − | 7.84043e7i | 1.29117 | − | 0.270250i | ||||
\(663\) | 1.10394e7 | 0.0378796 | ||||||||
\(664\) | −7.76859e7 | − | 1.09052e8i | −0.265362 | − | 0.372502i | ||||
\(665\) | 1.15236e7 | + | 4.35700e6i | 0.0391853 | + | 0.0148157i | ||||
\(666\) | −5.82923e7 | + | 1.22010e7i | −0.197328 | + | 0.0413020i | ||||
\(667\) | 2.66243e8 | 0.897224 | ||||||||
\(668\) | 3.27263e7 | − | 1.43273e7i | 0.109791 | − | 0.0480658i | ||||
\(669\) | −1.06005e8 | −0.354035 | ||||||||
\(670\) | −1.86219e8 | − | 2.91264e7i | −0.619155 | − | 0.0968418i | ||||
\(671\) | − | 7.31576e7i | − | 0.242154i | ||||||
\(672\) | 1.87112e7 | + | 1.11946e7i | 0.0616586 | + | 0.0368893i | ||||
\(673\) | 4.48612e8i | 1.47172i | 0.677133 | + | 0.735861i | \(0.263222\pi\) | ||||
−0.677133 | + | 0.735861i | \(0.736778\pi\) | |||||||
\(674\) | −5.30204e7 | + | 1.10975e7i | −0.173166 | + | 0.0362448i | ||||
\(675\) | 4.43817e7 | + | 3.91588e7i | 0.144309 | + | 0.127326i | ||||
\(676\) | −2.36858e8 | + | 1.03695e8i | −0.766741 | + | 0.335673i | ||||
\(677\) | 3.71161e8i | 1.19618i | 0.801429 | + | 0.598089i | \(0.204073\pi\) | ||||
−0.801429 | + | 0.598089i | \(0.795927\pi\) | |||||||
\(678\) | −8.39024e7 | + | 1.75613e7i | −0.269206 | + | 0.0563467i | ||||
\(679\) | − | 5.05859e7i | − | 0.161592i | ||||||
\(680\) | −1.30128e7 | − | 4.94126e7i | −0.0413851 | − | 0.157149i | ||||
\(681\) | −2.19107e8 | −0.693768 | ||||||||
\(682\) | 1.43877e8 | + | 6.87397e8i | 0.453563 | + | 2.16698i | ||||
\(683\) | −1.22266e8 | −0.383745 | −0.191872 | − | 0.981420i | \(-0.561456\pi\) | ||||
−0.191872 | + | 0.981420i | \(0.561456\pi\) | |||||||
\(684\) | 1.44006e7 | + | 3.28938e7i | 0.0450001 | + | 0.102789i | ||||
\(685\) | 5.02333e8 | + | 1.89929e8i | 1.56286 | + | 0.590907i | ||||
\(686\) | 1.63340e7 | + | 7.80388e7i | 0.0505965 | + | 0.241734i | ||||
\(687\) | 1.85025e8 | 0.570639 | ||||||||
\(688\) | 3.76024e8 | − | 4.07306e8i | 1.15465 | − | 1.25071i | ||||
\(689\) | −1.24757e8 | −0.381424 | ||||||||
\(690\) | −1.10314e8 | − | 1.72541e7i | −0.335802 | − | 0.0525225i | ||||
\(691\) | − | 4.44528e8i | − | 1.34730i | −0.739049 | − | 0.673652i | \(-0.764725\pi\) | ||
0.739049 | − | 0.673652i | \(-0.235275\pi\) | |||||||
\(692\) | 1.27019e8 | + | 2.90134e8i | 0.383309 | + | 0.875549i | ||||
\(693\) | − | 1.91126e7i | − | 0.0574275i | ||||||
\(694\) | −2.88391e6 | − | 1.37784e7i | −0.00862787 | − | 0.0412212i | ||||
\(695\) | 2.56420e8 | + | 9.69508e7i | 0.763831 | + | 0.288800i | ||||
\(696\) | −1.72131e8 | − | 2.41630e8i | −0.510543 | − | 0.716676i | ||||
\(697\) | 4.08930e7i | 0.120768i | ||||||||
\(698\) | −1.37899e7 | − | 6.58839e7i | −0.0405504 | − | 0.193737i | ||||
\(699\) | − | 1.57216e8i | − | 0.460327i | ||||||
\(700\) | 4.06477e7 | + | 1.30342e7i | 0.118506 | + | 0.0380007i | ||||
\(701\) | 3.22331e8 | 0.935724 | 0.467862 | − | 0.883801i | \(-0.345024\pi\) | ||||
0.467862 | + | 0.883801i | \(0.345024\pi\) | |||||||
\(702\) | −2.63096e7 | + | 5.50676e6i | −0.0760505 | + | 0.0159179i | ||||
\(703\) | −7.07342e7 | −0.203593 | ||||||||
\(704\) | 4.56512e8 | + | 1.57811e8i | 1.30838 | + | 0.452293i | ||||
\(705\) | 1.08533e8 | − | 2.87052e8i | 0.309737 | − | 0.819208i | ||||
\(706\) | 3.27793e7 | − | 6.86092e6i | 0.0931506 | − | 0.0194970i | ||||
\(707\) | 3.04527e7 | 0.0861722 | ||||||||
\(708\) | 6.01480e7 | + | 1.37389e8i | 0.169481 | + | 0.387127i | ||||
\(709\) | −6.64544e8 | −1.86460 | −0.932299 | − | 0.361689i | \(-0.882200\pi\) | ||||
−0.932299 | + | 0.361689i | \(0.882200\pi\) | |||||||
\(710\) | 4.64280e7 | − | 2.96836e8i | 0.129719 | − | 0.829357i | ||||
\(711\) | − | 9.53107e7i | − | 0.265175i | ||||||
\(712\) | 2.80461e8 | + | 3.93698e8i | 0.777020 | + | 1.09075i | ||||
\(713\) | − | 3.41255e8i | − | 0.941479i | ||||||
\(714\) | −4.15997e6 | + | 870708.i | −0.0114287 | + | 0.00239209i | ||||
\(715\) | −7.22511e7 | + | 1.91093e8i | −0.197663 | + | 0.522789i | ||||
\(716\) | 2.29113e8 | + | 5.23338e8i | 0.624182 | + | 1.42575i | ||||
\(717\) | 2.85412e8i | 0.774309i | ||||||||
\(718\) | −2.87324e8 | + | 6.01387e7i | −0.776244 | + | 0.162473i | ||||
\(719\) | 5.57077e8i | 1.49875i | 0.662148 | + | 0.749373i | \(0.269645\pi\) | ||||
−0.662148 | + | 0.749373i | \(0.730355\pi\) | |||||||
\(720\) | 5.56610e7 | + | 1.11271e8i | 0.149126 | + | 0.298115i | ||||
\(721\) | 1.11793e7 | 0.0298271 | ||||||||
\(722\) | −6.83681e7 | − | 3.26641e8i | −0.181653 | − | 0.867879i | ||||
\(723\) | −1.45676e8 | −0.385456 | ||||||||
\(724\) | −2.86757e7 | + | 1.25540e7i | −0.0755611 | + | 0.0330801i | ||||
\(725\) | −4.35510e8 | − | 3.84259e8i | −1.14284 | − | 1.00835i | ||||
\(726\) | −4.14783e7 | − | 1.98170e8i | −0.108395 | − | 0.517879i | ||||
\(727\) | 7.39877e7 | 0.192556 | 0.0962779 | − | 0.995354i | \(-0.469306\pi\) | ||||
0.0962779 | + | 0.995354i | \(0.469306\pi\) | |||||||
\(728\) | −1.57891e7 | + | 1.12478e7i | −0.0409227 | + | 0.0291523i | ||||
\(729\) | 1.43489e7 | 0.0370370 | ||||||||
\(730\) | 2.12432e7 | − | 1.35818e8i | 0.0546074 | − | 0.349131i | ||||
\(731\) | 1.08052e8i | 0.276619i | ||||||||
\(732\) | 3.62862e7 | − | 1.58858e7i | 0.0925142 | − | 0.0405020i | ||||
\(733\) | − | 3.30711e8i | − | 0.839725i | −0.907588 | − | 0.419862i | \(-0.862078\pi\) | ||
0.907588 | − | 0.419862i | \(-0.137922\pi\) | |||||||
\(734\) | −1.54967e7 | − | 7.40385e7i | −0.0391879 | − | 0.187227i | ||||
\(735\) | −7.98192e7 | + | 2.11110e8i | −0.201023 | + | 0.531675i | ||||
\(736\) | −2.01412e8 | − | 1.20501e8i | −0.505185 | − | 0.302244i | ||||
\(737\) | 3.47294e8i | 0.867550i | ||||||||
\(738\) | −2.03986e7 | − | 9.74579e7i | −0.0507494 | − | 0.242464i | ||||
\(739\) | 3.13996e7i | 0.0778020i | 0.999243 | + | 0.0389010i | \(0.0123857\pi\) | ||||
−0.999243 | + | 0.0389010i | \(0.987614\pi\) | |||||||
\(740\) | −2.44764e8 | + | 1.25368e7i | −0.604020 | + | 0.0309381i | ||||
\(741\) | −3.19251e7 | −0.0784652 | ||||||||
\(742\) | 4.70121e7 | − | 9.83994e6i | 0.115080 | − | 0.0240869i | ||||
\(743\) | −1.07991e8 | −0.263283 | −0.131642 | − | 0.991297i | \(-0.542025\pi\) | ||||
−0.131642 | + | 0.991297i | \(0.542025\pi\) | |||||||
\(744\) | −3.09707e8 | + | 2.20628e8i | −0.752025 | + | 0.535725i | ||||
\(745\) | −2.81882e8 | + | 7.45535e8i | −0.681709 | + | 1.80301i | ||||
\(746\) | 4.19361e8 | − | 8.77749e7i | 1.01012 | − | 0.211424i | ||||
\(747\) | −6.35470e7 | −0.152452 | ||||||||
\(748\) | −8.62474e7 | + | 3.77584e7i | −0.206083 | + | 0.0902214i | ||||
\(749\) | −9.57079e7 | −0.227773 | ||||||||
\(750\) | 1.55545e8 | + | 1.87435e8i | 0.368698 | + | 0.444291i | ||||
\(751\) | 7.98972e8i | 1.88631i | 0.332360 | + | 0.943153i | \(0.392155\pi\) | ||||
−0.332360 | + | 0.943153i | \(0.607845\pi\) | |||||||
\(752\) | 4.37585e8 | − | 4.73988e8i | 1.02898 | − | 1.11459i | ||||
\(753\) | − | 2.54920e8i | − | 0.597061i | ||||||
\(754\) | 2.58171e8 | − | 5.40369e7i | 0.602273 | − | 0.126060i | ||||
\(755\) | −3.32628e8 | − | 1.25764e8i | −0.772890 | − | 0.292225i | ||||
\(756\) | 9.47986e6 | − | 4.15021e6i | 0.0219400 | − | 0.00960516i | ||||
\(757\) | − | 5.82545e8i | − | 1.34290i | −0.741052 | − | 0.671448i | \(-0.765673\pi\) | ||
0.741052 | − | 0.671448i | \(-0.234327\pi\) | |||||||
\(758\) | 3.95811e8 | − | 8.28458e7i | 0.908824 | − | 0.190223i | ||||
\(759\) | 2.05732e8i | 0.470519i | ||||||||
\(760\) | 3.76319e7 | + | 1.42897e8i | 0.0857267 | + | 0.325524i | ||||
\(761\) | −1.80005e8 | −0.408443 | −0.204221 | − | 0.978925i | \(-0.565466\pi\) | ||||
−0.204221 | + | 0.978925i | \(0.565466\pi\) | |||||||
\(762\) | −8.15856e7 | − | 3.89790e8i | −0.184395 | − | 0.880980i | ||||
\(763\) | −5.36939e7 | −0.120879 | ||||||||
\(764\) | 1.72964e8 | + | 3.95081e8i | 0.387860 | + | 0.885945i | ||||
\(765\) | −2.26840e7 | − | 8.57668e6i | −0.0506682 | − | 0.0191573i | ||||
\(766\) | −1.21971e8 | − | 5.82739e8i | −0.271375 | − | 1.29654i | ||||
\(767\) | −1.33343e8 | −0.295519 | ||||||||
\(768\) | 2.08550e7 | + | 2.60698e8i | 0.0460391 | + | 0.575512i | ||||
\(769\) | 8.51283e8 | 1.87195 | 0.935976 | − | 0.352063i | \(-0.114520\pi\) | ||||
0.935976 | + | 0.352063i | \(0.114520\pi\) | |||||||
\(770\) | 1.21542e7 | − | 7.77079e7i | 0.0266229 | − | 0.170213i | ||||
\(771\) | − | 2.23248e8i | − | 0.487107i | ||||||
\(772\) | 1.20910e8 | + | 2.76181e8i | 0.262791 | + | 0.600263i | ||||
\(773\) | 4.28461e8i | 0.927626i | 0.885933 | + | 0.463813i | \(0.153519\pi\) | ||||
−0.885933 | + | 0.463813i | \(0.846481\pi\) | |||||||
\(774\) | −5.38994e7 | − | 2.57514e8i | −0.116241 | − | 0.555365i | ||||
\(775\) | −4.92520e8 | + | 5.58211e8i | −1.05808 | + | 1.19920i | ||||
\(776\) | 4.94180e8 | − | 3.52042e8i | 1.05755 | − | 0.753371i | ||||
\(777\) | 2.03853e7i | 0.0434565i | ||||||||
\(778\) | 6.41979e7 | + | 3.06717e8i | 0.136327 | + | 0.651327i | ||||
\(779\) | − | 1.18259e8i | − | 0.250163i | ||||||
\(780\) | −1.10471e8 | + | 5.65836e6i | −0.232790 | + | 0.0119236i | ||||
\(781\) | −5.53592e8 | −1.16208 | ||||||||
\(782\) | 4.47788e7 | − | 9.37250e6i | 0.0936381 | − | 0.0195991i | ||||
\(783\) | −1.40803e8 | −0.293310 | ||||||||
\(784\) | −3.21817e8 | + | 3.48589e8i | −0.667822 | + | 0.723379i | ||||
\(785\) | −7.96048e8 | − | 3.00981e8i | −1.64562 | − | 0.622199i | ||||
\(786\) | −4.53350e8 | + | 9.48890e7i | −0.933610 | + | 0.195411i | ||||
\(787\) | −3.33224e8 | −0.683615 | −0.341808 | − | 0.939770i | \(-0.611039\pi\) | ||||
−0.341808 | + | 0.939770i | \(0.611039\pi\) | |||||||
\(788\) | −3.89049e7 | − | 8.88662e7i | −0.0795108 | − | 0.181618i | ||||
\(789\) | 4.26487e8 | 0.868309 | ||||||||
\(790\) | 6.06108e7 | − | 3.87514e8i | 0.122933 | − | 0.785970i | ||||
\(791\) | 2.93414e7i | 0.0592859i | ||||||||
\(792\) | 1.86713e8 | − | 1.33010e8i | 0.375837 | − | 0.267737i | ||||
\(793\) | 3.52176e7i | 0.0706221i | ||||||||
\(794\) | −5.08179e8 | + | 1.06365e8i | −1.01521 | + | 0.212490i | ||||
\(795\) | 2.56354e8 | + | 9.69258e7i | 0.510198 | + | 0.192903i | ||||
\(796\) | 3.17215e8 | + | 7.24578e8i | 0.628947 | + | 1.43663i | ||||
\(797\) | − | 2.03165e7i | − | 0.0401305i | −0.999799 | − | 0.0200653i | \(-0.993613\pi\) | ||
0.999799 | − | 0.0200653i | \(-0.00638740\pi\) | |||||||
\(798\) | 1.20303e7 | − | 2.51801e6i | 0.0236737 | − | 0.00495507i | ||||
\(799\) | 1.25742e8i | 0.246513i | ||||||||
\(800\) | 1.55546e8 | + | 4.87801e8i | 0.303800 | + | 0.952736i | ||||
\(801\) | 2.29417e8 | 0.446404 | ||||||||
\(802\) | 1.58882e8 | + | 7.59086e8i | 0.308000 | + | 1.47153i | ||||
\(803\) | −2.53297e8 | −0.489197 | ||||||||
\(804\) | −1.72258e8 | + | 7.54132e7i | −0.331445 | + | 0.145104i | ||||
\(805\) | −1.35163e7 | + | 3.57487e7i | −0.0259103 | + | 0.0685286i | ||||
\(806\) | −6.92613e7 | − | 3.30909e8i | −0.132277 | − | 0.631979i | ||||
\(807\) | −1.85182e8 | −0.352353 | ||||||||
\(808\) | 2.11929e8 | + | 2.97496e8i | 0.401750 | + | 0.563958i | ||||
\(809\) | −4.55083e8 | −0.859499 | −0.429749 | − | 0.902948i | \(-0.641398\pi\) | ||||
−0.429749 | + | 0.902948i | \(0.641398\pi\) | |||||||
\(810\) | 5.83397e7 | + | 9.12488e6i | 0.109776 | + | 0.0171701i | ||||
\(811\) | − | 5.22513e8i | − | 0.979567i | −0.871844 | − | 0.489784i | \(-0.837076\pi\) | ||
0.871844 | − | 0.489784i | \(-0.162924\pi\) | |||||||
\(812\) | −9.30241e7 | + | 4.07252e7i | −0.173751 | + | 0.0760669i | ||||
\(813\) | − | 1.25281e8i | − | 0.233139i | ||||||
\(814\) | 9.25150e7 | + | 4.42007e8i | 0.171530 | + | 0.819514i | ||||
\(815\) | −1.56064e8 | + | 4.12765e8i | −0.288290 | + | 0.762483i | ||||
\(816\) | −3.74564e7 | − | 3.45797e7i | −0.0689375 | − | 0.0636430i | ||||
\(817\) | − | 3.12478e8i | − | 0.572998i | ||||||
\(818\) | 6.20834e7 | + | 2.96615e8i | 0.113427 | + | 0.541917i | ||||
\(819\) | 9.20068e6i | 0.0167482i | ||||||||
\(820\) | −2.09601e7 | − | 4.09216e8i | −0.0380148 | − | 0.742183i | ||||
\(821\) | 5.58769e7 | 0.100972 | 0.0504862 | − | 0.998725i | \(-0.483923\pi\) | ||||
0.0504862 | + | 0.998725i | \(0.483923\pi\) | |||||||
\(822\) | 5.24419e8 | − | 1.09764e8i | 0.944198 | − | 0.197627i | ||||
\(823\) | −6.67182e7 | −0.119686 | −0.0598432 | − | 0.998208i | \(-0.519060\pi\) | ||||
−0.0598432 | + | 0.998208i | \(0.519060\pi\) | |||||||
\(824\) | 7.78002e7 | + | 1.09212e8i | 0.139059 | + | 0.195205i | ||||
\(825\) | 2.96926e8 | − | 3.36529e8i | 0.528794 | − | 0.599322i | ||||
\(826\) | 5.02476e7 | − | 1.05171e7i | 0.0891610 | − | 0.0186620i | ||||
\(827\) | −3.12256e8 | −0.552070 | −0.276035 | − | 0.961148i | \(-0.589021\pi\) | ||||
−0.276035 | + | 0.961148i | \(0.589021\pi\) | |||||||
\(828\) | −1.02043e8 | + | 4.46738e7i | −0.179760 | + | 0.0786977i | ||||
\(829\) | 5.05526e8 | 0.887319 | 0.443660 | − | 0.896195i | \(-0.353680\pi\) | ||||
0.443660 | + | 0.896195i | \(0.353680\pi\) | |||||||
\(830\) | −2.58369e8 | − | 4.04114e7i | −0.451863 | − | 0.0706756i | ||||
\(831\) | 3.68336e8i | 0.641860i | ||||||||
\(832\) | −2.19762e8 | − | 7.59693e7i | −0.381577 | − | 0.131907i | ||||
\(833\) | − | 9.24757e7i | − | 0.159990i | ||||||
\(834\) | 2.67694e8 | − | 5.60301e7i | 0.461467 | − | 0.0965881i | ||||
\(835\) | 2.46768e7 | − | 6.52663e7i | 0.0423867 | − | 0.112106i | ||||
\(836\) | 2.49420e8 | − | 1.09194e8i | 0.426887 | − | 0.186888i | ||||
\(837\) | 1.80473e8i | 0.307777i | ||||||||
\(838\) | 4.63822e8 | − | 9.70809e7i | 0.788169 | − | 0.164969i | ||||
\(839\) | − | 9.40483e8i | − | 1.59245i | −0.605003 | − | 0.796223i | \(-0.706828\pi\) | ||
0.605003 | − | 0.796223i | \(-0.293172\pi\) | |||||||
\(840\) | 4.11824e7 | − | 1.08454e7i | 0.0694822 | − | 0.0182981i | ||||
\(841\) | 7.86853e8 | 1.32283 | ||||||||
\(842\) | −1.15112e8 | − | 5.49966e8i | −0.192834 | − | 0.921298i | ||||
\(843\) | 6.24961e8 | 1.04321 | ||||||||
\(844\) | −2.53889e7 | − | 5.79930e7i | −0.0422295 | − | 0.0964602i | ||||
\(845\) | −1.78599e8 | + | 4.72368e8i | −0.296013 | + | 0.782908i | ||||
\(846\) | −6.27236e7 | − | 2.99674e8i | −0.103591 | − | 0.494923i | ||||
\(847\) | −6.93018e7 | −0.114050 | ||||||||
\(848\) | 4.23298e8 | + | 3.90788e8i | 0.694159 | + | 0.640846i | ||||
\(849\) | 3.11830e8 | 0.509560 | ||||||||
\(850\) | −8.67744e7 | − | 4.92964e7i | −0.141298 | − | 0.0802710i | ||||
\(851\) | − | 2.19432e8i | − | 0.356051i | ||||||
\(852\) | −1.20210e8 | − | 2.74582e8i | −0.194366 | − | 0.443969i | ||||
\(853\) | 3.83843e7i | 0.0618453i | 0.999522 | + | 0.0309226i | \(0.00984455\pi\) | ||||
−0.999522 | + | 0.0309226i | \(0.990155\pi\) | |||||||
\(854\) | −2.77771e6 | − | 1.32710e7i | −0.00445977 | − | 0.0213074i | ||||
\(855\) | 6.56003e7 | + | 2.48031e7i | 0.104956 | + | 0.0396832i | ||||
\(856\) | −6.66058e8 | − | 9.34981e8i | −1.06192 | − | 1.49067i | ||||
\(857\) | 7.80244e8i | 1.23962i | 0.784753 | + | 0.619809i | \(0.212790\pi\) | ||||
−0.784753 | + | 0.619809i | \(0.787210\pi\) | |||||||
\(858\) | 4.17556e7 | + | 1.99495e8i | 0.0661078 | + | 0.315842i | ||||
\(859\) | − | 5.41399e8i | − | 0.854157i | −0.904214 | − | 0.427079i | \(-0.859543\pi\) | ||
0.904214 | − | 0.427079i | \(-0.140457\pi\) | |||||||
\(860\) | −5.53832e7 | − | 1.08128e9i | −0.0870728 | − | 1.69997i | ||||
\(861\) | −3.40819e7 | −0.0533967 | ||||||||
\(862\) | −7.18911e8 | + | 1.50473e8i | −1.12241 | + | 0.234929i | ||||
\(863\) | 1.87897e8 | 0.292339 | 0.146170 | − | 0.989260i | \(-0.453305\pi\) | ||||
0.146170 | + | 0.989260i | \(0.453305\pi\) | |||||||
\(864\) | 1.06517e8 | + | 6.37274e7i | 0.165149 | + | 0.0988063i | ||||
\(865\) | 5.78617e8 | + | 2.18771e8i | 0.894011 | + | 0.338020i | ||||
\(866\) | 8.43126e8 | − | 1.76472e8i | 1.29819 | − | 0.271720i | ||||
\(867\) | −3.66331e8 | −0.562103 | ||||||||
\(868\) | 5.21993e7 | + | 1.19233e8i | 0.0798188 | + | 0.182321i | ||||
\(869\) | −7.22703e8 | −1.10129 | ||||||||
\(870\) | −5.72477e8 | − | 8.95408e7i | −0.869361 | − | 0.135976i | ||||
\(871\) | − | 1.67185e8i | − | 0.253013i | ||||||
\(872\) | −3.73671e8 | − | 5.24542e8i | −0.563560 | − | 0.791099i | ||||
\(873\) | − | 2.87970e8i | − | 0.432817i | ||||||
\(874\) | −1.29497e8 | + | 2.71045e7i | −0.193965 | + | 0.0405982i | ||||
\(875\) | 7.37042e7 | − | 3.89686e7i | 0.110019 | − | 0.0581688i | ||||
\(876\) | −5.50022e7 | − | 1.25635e8i | −0.0818216 | − | 0.186896i | ||||
\(877\) | − | 9.77817e8i | − | 1.44964i | −0.688941 | − | 0.724818i | \(-0.741924\pi\) | ||
0.688941 | − | 0.724818i | \(-0.258076\pi\) | |||||||
\(878\) | −5.40670e7 | + | 1.13166e7i | −0.0798820 | + | 0.0167198i | ||||
\(879\) | − | 1.85106e7i | − | 0.0272555i | ||||||
\(880\) | 8.43722e8 | − | 4.22055e8i | 1.23809 | − | 0.619328i | ||||
\(881\) | −1.01906e8 | −0.149029 | −0.0745147 | − | 0.997220i | \(-0.523741\pi\) | ||||
−0.0745147 | + | 0.997220i | \(0.523741\pi\) | |||||||
\(882\) | 4.61294e7 | + | 2.20392e8i | 0.0672314 | + | 0.321210i | ||||
\(883\) | 3.87166e8 | 0.562361 | 0.281180 | − | 0.959655i | \(-0.409274\pi\) | ||||
0.281180 | + | 0.959655i | \(0.409274\pi\) | |||||||
\(884\) | 4.15189e7 | − | 1.81767e7i | 0.0601021 | − | 0.0263122i | ||||
\(885\) | 2.73997e8 | + | 1.03596e8i | 0.395289 | + | 0.149456i | ||||
\(886\) | −8.61787e7 | − | 4.11735e8i | −0.123908 | − | 0.591992i | ||||
\(887\) | 6.78239e8 | 0.971878 | 0.485939 | − | 0.873993i | \(-0.338478\pi\) | ||||
0.485939 | + | 0.873993i | \(0.338478\pi\) | |||||||
\(888\) | −1.99147e8 | + | 1.41867e8i | −0.284403 | + | 0.202602i | ||||
\(889\) | −1.36313e8 | −0.194014 | ||||||||
\(890\) | 9.32762e8 | + | 1.45893e8i | 1.32312 | + | 0.206949i | ||||
\(891\) | − | 1.08802e8i | − | 0.153817i | ||||||
\(892\) | −3.98681e8 | + | 1.74539e8i | −0.561734 | + | 0.245923i | ||||
\(893\) | − | 3.63636e8i | − | 0.510637i | ||||||
\(894\) | 1.62906e8 | + | 7.78315e8i | 0.227995 | + | 1.08929i | ||||
\(895\) | 1.04370e9 | + | 3.94615e8i | 1.45581 | + | 0.550433i | ||||
\(896\) | 8.88045e7 | + | 1.12942e7i | 0.123456 | + | 0.0157011i | ||||
\(897\) | − | 9.90383e7i | − | 0.137223i | ||||||
\(898\) | −1.59833e8 | − | 7.63633e8i | −0.220718 | − | 1.05452i | ||||
\(899\) | − | 1.77095e9i | − | 2.43741i | ||||||
\(900\) | 2.31394e8 | + | 7.41998e7i | 0.317414 | + | 0.101783i | ||||
\(901\) | −1.12295e8 | −0.153527 | ||||||||
\(902\) | −7.38984e8 | + | 1.54674e8i | −1.00697 | + | 0.210765i | ||||
\(903\) | −9.00550e7 | −0.122305 | ||||||||
\(904\) | −2.86640e8 | + | 2.04195e8i | −0.387999 | + | 0.276401i | ||||
\(905\) | −2.16225e7 | + | 5.71881e7i | −0.0291716 | + | 0.0771543i | ||||
\(906\) | −3.47253e8 | + | 7.26822e7i | −0.466940 | + | 0.0977336i | ||||
\(907\) | −3.95120e8 | −0.529551 | −0.264775 | − | 0.964310i | \(-0.585298\pi\) | ||||
−0.264775 | + | 0.964310i | \(0.585298\pi\) | |||||||
\(908\) | −8.24055e8 | + | 3.60765e8i | −1.10077 | + | 0.481911i | ||||
\(909\) | 1.73357e8 | 0.230808 | ||||||||
\(910\) | −5.85098e6 | + | 3.74081e7i | −0.00776434 | + | 0.0496411i | ||||
\(911\) | 1.40048e9i | 1.85234i | 0.377107 | + | 0.926170i | \(0.376919\pi\) | ||||
−0.377107 | + | 0.926170i | \(0.623081\pi\) | |||||||
\(912\) | 1.08321e8 | + | 1.00002e8i | 0.142800 | + | 0.131832i | ||||
\(913\) | 4.81852e8i | 0.633142i | ||||||||
\(914\) | −2.96432e8 | + | 6.20452e7i | −0.388228 | + | 0.0812586i | ||||
\(915\) | 2.73611e7 | − | 7.23659e7i | 0.0357166 | − | 0.0944649i | ||||
\(916\) | 6.95876e8 | − | 3.04649e8i | 0.905410 | − | 0.396381i | ||||
\(917\) | 1.58540e8i | 0.205604i | ||||||||
\(918\) | −2.36814e7 | + | 4.95667e6i | −0.0306111 | + | 0.00640710i | ||||
\(919\) | − | 1.65383e8i | − | 0.213081i | −0.994308 | − | 0.106540i | \(-0.966023\pi\) | ||
0.994308 | − | 0.106540i | \(-0.0339774\pi\) | |||||||
\(920\) | −4.43297e8 | + | 1.16742e8i | −0.569287 | + | 0.149922i | ||||
\(921\) | −4.78276e8 | −0.612208 | ||||||||
\(922\) | −1.20345e8 | − | 5.74968e8i | −0.153544 | − | 0.733586i | ||||
\(923\) | 2.66495e8 | 0.338910 | ||||||||
\(924\) | −3.14694e7 | − | 7.18820e7i | −0.0398908 | − | 0.0911180i | ||||
\(925\) | −3.16699e8 | + | 3.58939e8i | −0.400148 | + | 0.453519i | ||||
\(926\) | 3.01581e8 | + | 1.44086e9i | 0.379814 | + | 1.81463i | ||||
\(927\) | 6.36405e7 | 0.0798904 | ||||||||
\(928\) | −1.04523e9 | − | 6.25345e8i | −1.30788 | − | 0.782485i | ||||
\(929\) | −7.21234e8 | −0.899557 | −0.449779 | − | 0.893140i | \(-0.648497\pi\) | ||||
−0.449779 | + | 0.893140i | \(0.648497\pi\) | |||||||
\(930\) | −1.14768e8 | + | 7.33768e8i | −0.142683 | + | 0.912241i | ||||
\(931\) | 2.67432e8i | 0.331409i | ||||||||
\(932\) | −2.58861e8 | − | 5.91287e8i | −0.319756 | − | 0.730383i | ||||
\(933\) | 5.18995e8i | 0.639025i | ||||||||
\(934\) | 1.61713e8 | + | 7.72612e8i | 0.198474 | + | 0.948246i | ||||
\(935\) | −6.50336e7 | + | 1.72004e8i | −0.0795615 | + | 0.210428i | ||||
\(936\) | −8.98826e7 | + | 6.40302e7i | −0.109609 | + | 0.0780831i | ||||
\(937\) | − | 6.16936e8i | − | 0.749931i | −0.927039 | − | 0.374966i | \(-0.877654\pi\) | ||
0.927039 | − | 0.374966i | \(-0.122346\pi\) | |||||||
\(938\) | 1.31863e7 | + | 6.30001e7i | 0.0159777 | + | 0.0763365i | ||||
\(939\) | − | 1.90256e8i | − | 0.229796i | ||||||
\(940\) | −6.44504e7 | − | 1.25830e9i | −0.0775964 | − | 1.51496i | ||||
\(941\) | 1.02280e9 | 1.22750 | 0.613748 | − | 0.789502i | \(-0.289661\pi\) | ||||
0.613748 | + | 0.789502i | \(0.289661\pi\) | |||||||
\(942\) | −8.31048e8 | + | 1.73944e8i | −0.994199 | + | 0.208092i | ||||
\(943\) | 3.66865e8 | 0.437493 | ||||||||
\(944\) | 4.52430e8 | + | 4.17682e8i | 0.537818 | + | 0.496513i | ||||
\(945\) | 7.14815e6 | − | 1.89058e7i | 0.00847028 | − | 0.0224026i | ||||
\(946\) | −1.95263e9 | + | 4.08698e8i | −2.30646 | + | 0.482757i | ||||
\(947\) | −1.01174e9 | −1.19130 | −0.595648 | − | 0.803246i | \(-0.703105\pi\) | ||||
−0.595648 | + | 0.803246i | \(0.703105\pi\) | |||||||
\(948\) | −1.56932e8 | − | 3.58461e8i | −0.184198 | − | 0.420743i | ||||
\(949\) | 1.21936e8 | 0.142670 | ||||||||
\(950\) | 2.50944e8 | + | 1.42561e8i | 0.292689 | + | 0.166276i | ||||
\(951\) | − | 2.55349e8i | − | 0.296888i | ||||||
\(952\) | −1.42119e7 | + | 1.01242e7i | −0.0164718 | + | 0.0117341i | ||||
\(953\) | − | 2.58951e8i | − | 0.299184i | −0.988748 | − | 0.149592i | \(-0.952204\pi\) | ||
0.988748 | − | 0.149592i | \(-0.0477961\pi\) | |||||||
\(954\) | 2.67625e8 | − | 5.60157e7i | 0.308235 | − | 0.0645156i | ||||
\(955\) | 7.87914e8 | + | 2.97905e8i | 0.904625 | + | 0.342033i | ||||
\(956\) | 4.69937e8 | + | 1.07343e9i | 0.537856 | + | 1.22857i | ||||
\(957\) | 1.06765e9i | 1.21813i | ||||||||
\(958\) | 6.28022e8 | − | 1.31449e8i | 0.714296 | − | 0.149507i | ||||
\(959\) | − | 1.83394e8i | − | 0.207936i | ||||||
\(960\) | 3.92550e8 | + | 3.26839e8i | 0.443691 | + | 0.369420i | ||||
\(961\) | −1.38240e9 | −1.55763 | ||||||||
\(962\) | −4.45361e7 | − | 2.12780e8i | −0.0500250 | − | 0.239004i | ||||
\(963\) | −5.44835e8 | −0.610079 | ||||||||
\(964\) | −5.47885e8 | + | 2.39860e8i | −0.611587 | + | 0.267748i | ||||
\(965\) | 5.50790e8 | + | 2.08250e8i | 0.612920 | + | 0.231741i | ||||
\(966\) | 7.81141e6 | + | 3.73204e7i | 0.00866559 | + | 0.0414014i | ||||
\(967\) | 6.55319e8 | 0.724725 | 0.362362 | − | 0.932037i | \(-0.381970\pi\) | ||||
0.362362 | + | 0.932037i | \(0.381970\pi\) | |||||||
\(968\) | −4.82290e8 | − | 6.77017e8i | −0.531720 | − | 0.746403i | ||||
\(969\) | −2.87359e7 | −0.0315830 | ||||||||
\(970\) | 1.83128e8 | − | 1.17083e9i | 0.200650 | − | 1.28285i | ||||
\(971\) | 3.60583e8i | 0.393865i | 0.980417 | + | 0.196933i | \(0.0630980\pi\) | ||||
−0.980417 | + | 0.196933i | \(0.936902\pi\) | |||||||
\(972\) | 5.39659e7 | − | 2.36258e7i | 0.0587652 | − | 0.0257270i | ||||
\(973\) | − | 9.36150e7i | − | 0.101626i | ||||||
\(974\) | 1.86368e8 | + | 8.90408e8i | 0.201695 | + | 0.963634i | ||||
\(975\) | −1.42938e8 | + | 1.62003e8i | −0.154218 | + | 0.174787i | ||||
\(976\) | 1.10315e8 | − | 1.19492e8i | 0.118655 | − | 0.128526i | ||||
\(977\) | 2.40742e8i | 0.258147i | 0.991635 | + | 0.129074i | \(0.0412003\pi\) | ||||
−0.991635 | + | 0.129074i | \(0.958800\pi\) | |||||||
\(978\) | 9.01930e7 | + | 4.30914e8i | 0.0964176 | + | 0.460653i | ||||
\(979\) | − | 1.73958e9i | − | 1.85394i | ||||||
\(980\) | 4.73993e7 | + | 9.25402e8i | 0.0503609 | + | 0.983223i | ||||
\(981\) | −3.05663e8 | −0.323769 | ||||||||
\(982\) | 7.33992e7 | − | 1.53629e7i | 0.0775098 | − | 0.0162233i | ||||
\(983\) | 9.35058e8 | 0.984415 | 0.492207 | − | 0.870478i | \(-0.336190\pi\) | ||||
0.492207 | + | 0.870478i | \(0.336190\pi\) | |||||||
\(984\) | −2.37185e8 | − | 3.32950e8i | −0.248945 | − | 0.349457i | ||||
\(985\) | −1.77227e8 | − | 6.70082e7i | −0.185447 | − | 0.0701164i | ||||
\(986\) | 2.32381e8 | − | 4.86389e7i | 0.242421 | − | 0.0507403i | ||||
\(987\) | −1.04798e8 | −0.108994 | ||||||||
\(988\) | −1.20069e8 | + | 5.25654e7i | −0.124498 | + | 0.0545041i | ||||
\(989\) | 9.69372e8 | 1.00208 | ||||||||
\(990\) | 6.91903e7 | − | 4.42367e8i | 0.0713083 | − | 0.455908i | ||||
\(991\) | 5.34695e7i | 0.0549396i | 0.999623 | + | 0.0274698i | \(0.00874500\pi\) | ||||
−0.999623 | + | 0.0274698i | \(0.991255\pi\) | |||||||
\(992\) | −8.01531e8 | + | 1.33972e9i | −0.821080 | + | 1.37239i | ||||
\(993\) | − | 7.45729e8i | − | 0.761611i | ||||||
\(994\) | −1.00423e8 | + | 2.10192e7i | −0.102253 | + | 0.0214021i | ||||
\(995\) | 1.44503e9 | + | 5.46358e8i | 1.46693 | + | 0.554636i | ||||
\(996\) | −2.38999e8 | + | 1.04632e8i | −0.241890 | + | 0.105897i | ||||
\(997\) | − | 1.60576e9i | − | 1.62030i | −0.586222 | − | 0.810150i | \(-0.699386\pi\) | ||
0.586222 | − | 0.810150i | \(-0.300614\pi\) | |||||||
\(998\) | 1.52935e9 | − | 3.20102e8i | 1.53856 | − | 0.322031i | ||||
\(999\) | 1.16047e8i | 0.116396i |
(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.19.15 | ✓ | 36 | |
3.2 | odd | 2 | 180.7.f.g.19.22 | 36 | |||
4.3 | odd | 2 | inner | 60.7.f.a.19.21 | yes | 36 | |
5.4 | even | 2 | inner | 60.7.f.a.19.22 | yes | 36 | |
12.11 | even | 2 | 180.7.f.g.19.16 | 36 | |||
15.14 | odd | 2 | 180.7.f.g.19.15 | 36 | |||
20.19 | odd | 2 | inner | 60.7.f.a.19.16 | yes | 36 | |
60.59 | even | 2 | 180.7.f.g.19.21 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.7.f.a.19.15 | ✓ | 36 | 1.1 | even | 1 | trivial | |
60.7.f.a.19.16 | yes | 36 | 20.19 | odd | 2 | inner | |
60.7.f.a.19.21 | yes | 36 | 4.3 | odd | 2 | inner | |
60.7.f.a.19.22 | yes | 36 | 5.4 | even | 2 | inner | |
180.7.f.g.19.15 | 36 | 15.14 | odd | 2 | |||
180.7.f.g.19.16 | 36 | 12.11 | even | 2 | |||
180.7.f.g.19.21 | 36 | 60.59 | even | 2 | |||
180.7.f.g.19.22 | 36 | 3.2 | odd | 2 |