Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(100,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.100");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.j (of order \(3\), degree \(2\), 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: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 11 x^{14} - 4 x^{13} + 87 x^{12} - 35 x^{11} + 326 x^{10} - 205 x^{9} + 895 x^{8} - 481 x^{7} + 1005 x^{6} - 544 x^{5} + 811 x^{4} - 312 x^{3} + 195 x^{2} + 13 x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 172.2 | ||
Root | \(-1.02737 + 1.77946i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.172 |
Dual form | 273.2.j.b.100.2 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.02737 | + | 1.77946i | −0.726461 | + | 1.25827i | 0.231909 | + | 0.972738i | \(0.425503\pi\) |
−0.958370 | + | 0.285530i | \(0.907830\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.11098 | − | 1.92428i | −0.555491 | − | 0.962139i | ||||
\(5\) | −0.274662 | − | 0.475728i | −0.122833 | − | 0.212752i | 0.798051 | − | 0.602590i | \(-0.205864\pi\) |
−0.920884 | + | 0.389838i | \(0.872531\pi\) | |||||||
\(6\) | 1.02737 | − | 1.77946i | 0.419422 | − | 0.726461i | ||||
\(7\) | −0.839752 | − | 2.50895i | −0.317397 | − | 0.948293i | ||||
\(8\) | 0.456078 | 0.161248 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.12872 | 0.356932 | ||||||||
\(11\) | 4.69824 | 1.41657 | 0.708287 | − | 0.705925i | \(-0.249468\pi\) | ||||
0.708287 | + | 0.705925i | \(0.249468\pi\) | |||||||
\(12\) | 1.11098 | + | 1.92428i | 0.320713 | + | 0.555491i | ||||
\(13\) | −0.663964 | − | 3.54389i | −0.184150 | − | 0.982898i | ||||
\(14\) | 5.32730 | + | 1.08331i | 1.42378 | + | 0.289528i | ||||
\(15\) | 0.274662 | + | 0.475728i | 0.0709174 | + | 0.122833i | ||||
\(16\) | 1.75340 | − | 3.03698i | 0.438351 | − | 0.759245i | ||||
\(17\) | 0.301806 | + | 0.522743i | 0.0731987 | + | 0.126784i | 0.900302 | − | 0.435267i | \(-0.143346\pi\) |
−0.827103 | + | 0.562051i | \(0.810013\pi\) | |||||||
\(18\) | −1.02737 | + | 1.77946i | −0.242154 | + | 0.419422i | ||||
\(19\) | 0.561110 | 0.128727 | 0.0643637 | − | 0.997927i | \(-0.479498\pi\) | ||||
0.0643637 | + | 0.997927i | \(0.479498\pi\) | |||||||
\(20\) | −0.610289 | + | 1.05705i | −0.136465 | + | 0.236364i | ||||
\(21\) | 0.839752 | + | 2.50895i | 0.183249 | + | 0.547497i | ||||
\(22\) | −4.82684 | + | 8.36033i | −1.02909 | + | 1.78243i | ||||
\(23\) | −0.188350 | + | 0.326231i | −0.0392736 | + | 0.0680239i | −0.884994 | − | 0.465602i | \(-0.845838\pi\) |
0.845720 | + | 0.533626i | \(0.179171\pi\) | |||||||
\(24\) | −0.456078 | −0.0930966 | ||||||||
\(25\) | 2.34912 | − | 4.06880i | 0.469824 | − | 0.813760i | ||||
\(26\) | 6.98834 | + | 2.45939i | 1.37053 | + | 0.482327i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −3.89496 | + | 4.40331i | −0.736078 | + | 0.832148i | ||||
\(29\) | 2.09200 | + | 3.62344i | 0.388474 | + | 0.672856i | 0.992244 | − | 0.124302i | \(-0.0396691\pi\) |
−0.603771 | + | 0.797158i | \(0.706336\pi\) | |||||||
\(30\) | −1.12872 | −0.206075 | ||||||||
\(31\) | −0.577330 | + | 0.999965i | −0.103691 | + | 0.179599i | −0.913203 | − | 0.407505i | \(-0.866399\pi\) |
0.809511 | + | 0.587104i | \(0.199732\pi\) | |||||||
\(32\) | 4.05887 | + | 7.03016i | 0.717513 | + | 1.24277i | ||||
\(33\) | −4.69824 | −0.817859 | ||||||||
\(34\) | −1.24027 | −0.212704 | ||||||||
\(35\) | −0.962929 | + | 1.08861i | −0.162765 | + | 0.184008i | ||||
\(36\) | −1.11098 | − | 1.92428i | −0.185164 | − | 0.320713i | ||||
\(37\) | 4.40116 | − | 7.62304i | 0.723547 | − | 1.25322i | −0.236023 | − | 0.971748i | \(-0.575844\pi\) |
0.959569 | − | 0.281472i | \(-0.0908227\pi\) | |||||||
\(38\) | −0.576468 | + | 0.998472i | −0.0935154 | + | 0.161973i | ||||
\(39\) | 0.663964 | + | 3.54389i | 0.106319 | + | 0.567476i | ||||
\(40\) | −0.125267 | − | 0.216969i | −0.0198065 | − | 0.0343059i | ||||
\(41\) | −3.96001 | − | 6.85894i | −0.618450 | − | 1.07119i | −0.989769 | − | 0.142681i | \(-0.954428\pi\) |
0.371319 | − | 0.928506i | \(-0.378906\pi\) | |||||||
\(42\) | −5.32730 | − | 1.08331i | −0.822021 | − | 0.167159i | ||||
\(43\) | −0.747200 | + | 1.29419i | −0.113947 | + | 0.197362i | −0.917358 | − | 0.398062i | \(-0.869683\pi\) |
0.803411 | + | 0.595424i | \(0.203016\pi\) | |||||||
\(44\) | −5.21966 | − | 9.04072i | −0.786894 | − | 1.36294i | ||||
\(45\) | −0.274662 | − | 0.475728i | −0.0409442 | − | 0.0709174i | ||||
\(46\) | −0.387010 | − | 0.670321i | −0.0570615 | − | 0.0988334i | ||||
\(47\) | −1.09885 | − | 1.90326i | −0.160283 | − | 0.277619i | 0.774687 | − | 0.632345i | \(-0.217907\pi\) |
−0.934970 | + | 0.354726i | \(0.884574\pi\) | |||||||
\(48\) | −1.75340 | + | 3.03698i | −0.253082 | + | 0.438351i | ||||
\(49\) | −5.58963 | + | 4.21379i | −0.798519 | + | 0.601970i | ||||
\(50\) | 4.82684 | + | 8.36033i | 0.682618 | + | 1.18233i | ||||
\(51\) | −0.301806 | − | 0.522743i | −0.0422613 | − | 0.0731987i | ||||
\(52\) | −6.08177 | + | 5.21485i | −0.843390 | + | 0.723169i | ||||
\(53\) | 4.52338 | − | 7.83473i | 0.621334 | − | 1.07618i | −0.367903 | − | 0.929864i | \(-0.619924\pi\) |
0.989238 | − | 0.146318i | \(-0.0467424\pi\) | |||||||
\(54\) | 1.02737 | − | 1.77946i | 0.139807 | − | 0.242154i | ||||
\(55\) | −1.29043 | − | 2.23509i | −0.174001 | − | 0.301379i | ||||
\(56\) | −0.382993 | − | 1.14428i | −0.0511796 | − | 0.152910i | ||||
\(57\) | −0.561110 | −0.0743208 | ||||||||
\(58\) | −8.59702 | −1.12884 | ||||||||
\(59\) | −4.26827 | − | 7.39286i | −0.555681 | − | 0.962468i | −0.997850 | − | 0.0655364i | \(-0.979124\pi\) |
0.442169 | − | 0.896932i | \(-0.354209\pi\) | |||||||
\(60\) | 0.610289 | − | 1.05705i | 0.0787879 | − | 0.136465i | ||||
\(61\) | 7.42424 | 0.950576 | 0.475288 | − | 0.879830i | \(-0.342344\pi\) | ||||
0.475288 | + | 0.879830i | \(0.342344\pi\) | |||||||
\(62\) | −1.18626 | − | 2.05467i | −0.150656 | − | 0.260943i | ||||
\(63\) | −0.839752 | − | 2.50895i | −0.105799 | − | 0.316098i | ||||
\(64\) | −9.66624 | −1.20828 | ||||||||
\(65\) | −1.50356 | + | 1.28924i | −0.186494 | + | 0.159910i | ||||
\(66\) | 4.82684 | − | 8.36033i | 0.594143 | − | 1.02909i | ||||
\(67\) | −9.59873 | −1.17267 | −0.586336 | − | 0.810068i | \(-0.699430\pi\) | ||||
−0.586336 | + | 0.810068i | \(0.699430\pi\) | |||||||
\(68\) | 0.670602 | − | 1.16152i | 0.0813224 | − | 0.140855i | ||||
\(69\) | 0.188350 | − | 0.326231i | 0.0226746 | − | 0.0392736i | ||||
\(70\) | −0.947844 | − | 2.83190i | −0.113289 | − | 0.338476i | ||||
\(71\) | 2.88877 | − | 5.00350i | 0.342834 | − | 0.593806i | −0.642124 | − | 0.766601i | \(-0.721947\pi\) |
0.984958 | + | 0.172795i | \(0.0552799\pi\) | |||||||
\(72\) | 0.456078 | 0.0537494 | ||||||||
\(73\) | 7.24668 | − | 12.5516i | 0.848160 | − | 1.46906i | −0.0346892 | − | 0.999398i | \(-0.511044\pi\) |
0.882849 | − | 0.469657i | \(-0.155623\pi\) | |||||||
\(74\) | 9.04325 | + | 15.6634i | 1.05126 | + | 1.82083i | ||||
\(75\) | −2.34912 | + | 4.06880i | −0.271253 | + | 0.469824i | ||||
\(76\) | −0.623383 | − | 1.07973i | −0.0715069 | − | 0.123854i | ||||
\(77\) | −3.94536 | − | 11.7876i | −0.449616 | − | 1.34333i | ||||
\(78\) | −6.98834 | − | 2.45939i | −0.791274 | − | 0.278471i | ||||
\(79\) | 7.31102 | + | 12.6631i | 0.822554 | + | 1.42471i | 0.903774 | + | 0.428009i | \(0.140785\pi\) |
−0.0812206 | + | 0.996696i | \(0.525882\pi\) | |||||||
\(80\) | −1.92637 | −0.215375 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 16.2736 | 1.79712 | ||||||||
\(83\) | −14.8750 | −1.63274 | −0.816371 | − | 0.577528i | \(-0.804017\pi\) | ||||
−0.816371 | + | 0.577528i | \(0.804017\pi\) | |||||||
\(84\) | 3.89496 | − | 4.40331i | 0.424975 | − | 0.480441i | ||||
\(85\) | 0.165789 | − | 0.287155i | 0.0179824 | − | 0.0311464i | ||||
\(86\) | −1.53530 | − | 2.65922i | −0.165556 | − | 0.286751i | ||||
\(87\) | −2.09200 | − | 3.62344i | −0.224285 | − | 0.388474i | ||||
\(88\) | 2.14277 | 0.228420 | ||||||||
\(89\) | −4.59177 | + | 7.95317i | −0.486726 | + | 0.843035i | −0.999884 | − | 0.0152600i | \(-0.995142\pi\) |
0.513157 | + | 0.858295i | \(0.328476\pi\) | |||||||
\(90\) | 1.12872 | 0.118977 | ||||||||
\(91\) | −8.33387 | + | 4.64184i | −0.873627 | + | 0.486597i | ||||
\(92\) | 0.837013 | 0.0872646 | ||||||||
\(93\) | 0.577330 | − | 0.999965i | 0.0598663 | − | 0.103691i | ||||
\(94\) | 4.51569 | 0.465758 | ||||||||
\(95\) | −0.154115 | − | 0.266936i | −0.0158119 | − | 0.0273870i | ||||
\(96\) | −4.05887 | − | 7.03016i | −0.414256 | − | 0.717513i | ||||
\(97\) | 3.15034 | − | 5.45655i | 0.319869 | − | 0.554029i | −0.660592 | − | 0.750745i | \(-0.729695\pi\) |
0.980460 | + | 0.196717i | \(0.0630279\pi\) | |||||||
\(98\) | −1.75564 | − | 14.2756i | −0.177346 | − | 1.44206i | ||||
\(99\) | 4.69824 | 0.472191 | ||||||||
\(100\) | −10.4393 | −1.04393 | ||||||||
\(101\) | 4.44387 | 0.442182 | 0.221091 | − | 0.975253i | \(-0.429038\pi\) | ||||
0.221091 | + | 0.975253i | \(0.429038\pi\) | |||||||
\(102\) | 1.24027 | 0.122805 | ||||||||
\(103\) | 8.31431 | + | 14.4008i | 0.819234 | + | 1.41895i | 0.906248 | + | 0.422747i | \(0.138934\pi\) |
−0.0870141 | + | 0.996207i | \(0.527733\pi\) | |||||||
\(104\) | −0.302820 | − | 1.61629i | −0.0296939 | − | 0.158490i | ||||
\(105\) | 0.962929 | − | 1.08861i | 0.0939723 | − | 0.106237i | ||||
\(106\) | 9.29438 | + | 16.0983i | 0.902750 | + | 1.56361i | ||||
\(107\) | −8.93605 | + | 15.4777i | −0.863881 | + | 1.49629i | 0.00427332 | + | 0.999991i | \(0.498640\pi\) |
−0.868154 | + | 0.496295i | \(0.834694\pi\) | |||||||
\(108\) | 1.11098 | + | 1.92428i | 0.106904 | + | 0.185164i | ||||
\(109\) | −5.07774 | + | 8.79490i | −0.486359 | + | 0.842399i | −0.999877 | − | 0.0156799i | \(-0.995009\pi\) |
0.513518 | + | 0.858079i | \(0.328342\pi\) | |||||||
\(110\) | 5.30299 | 0.505621 | ||||||||
\(111\) | −4.40116 | + | 7.62304i | −0.417740 | + | 0.723547i | ||||
\(112\) | −9.09205 | − | 1.84888i | −0.859118 | − | 0.174703i | ||||
\(113\) | −3.74505 | + | 6.48662i | −0.352305 | + | 0.610210i | −0.986653 | − | 0.162838i | \(-0.947935\pi\) |
0.634348 | + | 0.773048i | \(0.281269\pi\) | |||||||
\(114\) | 0.576468 | − | 0.998472i | 0.0539912 | − | 0.0935154i | ||||
\(115\) | 0.206930 | 0.0192963 | ||||||||
\(116\) | 4.64834 | − | 8.05116i | 0.431587 | − | 0.747531i | ||||
\(117\) | −0.663964 | − | 3.54389i | −0.0613835 | − | 0.327633i | ||||
\(118\) | 17.5404 | 1.61472 | ||||||||
\(119\) | 1.05809 | − | 1.19619i | 0.0969952 | − | 0.109655i | ||||
\(120\) | 0.125267 | + | 0.216969i | 0.0114353 | + | 0.0198065i | ||||
\(121\) | 11.0735 | 1.00668 | ||||||||
\(122\) | −7.62745 | + | 13.2111i | −0.690557 | + | 1.19608i | ||||
\(123\) | 3.96001 | + | 6.85894i | 0.357062 | + | 0.618450i | ||||
\(124\) | 2.56561 | 0.230399 | ||||||||
\(125\) | −5.32748 | −0.476504 | ||||||||
\(126\) | 5.32730 | + | 1.08331i | 0.474594 | + | 0.0965094i | ||||
\(127\) | 2.36612 | + | 4.09824i | 0.209959 | + | 0.363660i | 0.951702 | − | 0.307025i | \(-0.0993335\pi\) |
−0.741742 | + | 0.670685i | \(0.766000\pi\) | |||||||
\(128\) | 1.81308 | − | 3.14034i | 0.160255 | − | 0.277570i | ||||
\(129\) | 0.747200 | − | 1.29419i | 0.0657873 | − | 0.113947i | ||||
\(130\) | −0.749428 | − | 4.00005i | −0.0657292 | − | 0.350828i | ||||
\(131\) | −1.78705 | − | 3.09527i | −0.156136 | − | 0.270435i | 0.777336 | − | 0.629085i | \(-0.216570\pi\) |
−0.933472 | + | 0.358650i | \(0.883237\pi\) | |||||||
\(132\) | 5.21966 | + | 9.04072i | 0.454313 | + | 0.786894i | ||||
\(133\) | −0.471193 | − | 1.40779i | −0.0408576 | − | 0.122071i | ||||
\(134\) | 9.86145 | − | 17.0805i | 0.851900 | − | 1.47553i | ||||
\(135\) | 0.274662 | + | 0.475728i | 0.0236391 | + | 0.0409442i | ||||
\(136\) | 0.137647 | + | 0.238412i | 0.0118031 | + | 0.0204437i | ||||
\(137\) | 9.62880 | + | 16.6776i | 0.822644 | + | 1.42486i | 0.903707 | + | 0.428152i | \(0.140835\pi\) |
−0.0810628 | + | 0.996709i | \(0.525831\pi\) | |||||||
\(138\) | 0.387010 | + | 0.670321i | 0.0329445 | + | 0.0570615i | ||||
\(139\) | −4.83155 | + | 8.36849i | −0.409807 | + | 0.709806i | −0.994868 | − | 0.101183i | \(-0.967737\pi\) |
0.585061 | + | 0.810989i | \(0.301070\pi\) | |||||||
\(140\) | 3.16458 | + | 0.643521i | 0.267456 | + | 0.0543875i | ||||
\(141\) | 1.09885 | + | 1.90326i | 0.0925395 | + | 0.160283i | ||||
\(142\) | 5.93568 | + | 10.2809i | 0.498111 | + | 0.862753i | ||||
\(143\) | −3.11946 | − | 16.6501i | −0.260863 | − | 1.39235i | ||||
\(144\) | 1.75340 | − | 3.03698i | 0.146117 | − | 0.253082i | ||||
\(145\) | 1.14918 | − | 1.99044i | 0.0954344 | − | 0.165297i | ||||
\(146\) | 14.8901 | + | 25.7903i | 1.23231 | + | 2.13442i | ||||
\(147\) | 5.58963 | − | 4.21379i | 0.461025 | − | 0.347547i | ||||
\(148\) | −19.5584 | −1.60769 | ||||||||
\(149\) | 7.12496 | 0.583699 | 0.291850 | − | 0.956464i | \(-0.405729\pi\) | ||||
0.291850 | + | 0.956464i | \(0.405729\pi\) | |||||||
\(150\) | −4.82684 | − | 8.36033i | −0.394110 | − | 0.682618i | ||||
\(151\) | 9.82744 | − | 17.0216i | 0.799746 | − | 1.38520i | −0.120036 | − | 0.992770i | \(-0.538301\pi\) |
0.919781 | − | 0.392431i | \(-0.128366\pi\) | |||||||
\(152\) | 0.255910 | 0.0207570 | ||||||||
\(153\) | 0.301806 | + | 0.522743i | 0.0243996 | + | 0.0422613i | ||||
\(154\) | 25.0290 | + | 5.08968i | 2.01689 | + | 0.410138i | ||||
\(155\) | 0.634282 | 0.0509468 | ||||||||
\(156\) | 6.08177 | − | 5.21485i | 0.486932 | − | 0.417522i | ||||
\(157\) | 2.60509 | − | 4.51215i | 0.207909 | − | 0.360109i | −0.743147 | − | 0.669129i | \(-0.766668\pi\) |
0.951056 | + | 0.309020i | \(0.100001\pi\) | |||||||
\(158\) | −30.0445 | −2.39021 | ||||||||
\(159\) | −4.52338 | + | 7.83473i | −0.358727 | + | 0.621334i | ||||
\(160\) | 2.22963 | − | 3.86184i | 0.176268 | − | 0.305305i | ||||
\(161\) | 0.976664 | + | 0.198606i | 0.0769719 | + | 0.0156523i | ||||
\(162\) | −1.02737 | + | 1.77946i | −0.0807179 | + | 0.139807i | ||||
\(163\) | −4.17379 | −0.326917 | −0.163458 | − | 0.986550i | \(-0.552265\pi\) | ||||
−0.163458 | + | 0.986550i | \(0.552265\pi\) | |||||||
\(164\) | −8.79901 | + | 15.2403i | −0.687087 | + | 1.19007i | ||||
\(165\) | 1.29043 | + | 2.23509i | 0.100460 | + | 0.174001i | ||||
\(166\) | 15.2821 | − | 26.4694i | 1.18612 | − | 2.05442i | ||||
\(167\) | −2.52335 | − | 4.37058i | −0.195263 | − | 0.338205i | 0.751724 | − | 0.659478i | \(-0.229223\pi\) |
−0.946987 | + | 0.321273i | \(0.895889\pi\) | |||||||
\(168\) | 0.382993 | + | 1.14428i | 0.0295485 | + | 0.0882829i | ||||
\(169\) | −12.1183 | + | 4.70603i | −0.932177 | + | 0.362002i | ||||
\(170\) | 0.340654 | + | 0.590030i | 0.0261270 | + | 0.0452532i | ||||
\(171\) | 0.561110 | 0.0429091 | ||||||||
\(172\) | 3.32050 | 0.253186 | ||||||||
\(173\) | 2.73897 | 0.208240 | 0.104120 | − | 0.994565i | \(-0.466797\pi\) | ||||
0.104120 | + | 0.994565i | \(0.466797\pi\) | |||||||
\(174\) | 8.59702 | 0.651738 | ||||||||
\(175\) | −12.1811 | − | 2.47704i | −0.920803 | − | 0.187247i | ||||
\(176\) | 8.23791 | − | 14.2685i | 0.620956 | − | 1.07553i | ||||
\(177\) | 4.26827 | + | 7.39286i | 0.320823 | + | 0.555681i | ||||
\(178\) | −9.43489 | − | 16.3417i | −0.707175 | − | 1.22486i | ||||
\(179\) | −12.6956 | −0.948917 | −0.474459 | − | 0.880278i | \(-0.657356\pi\) | ||||
−0.474459 | + | 0.880278i | \(0.657356\pi\) | |||||||
\(180\) | −0.610289 | + | 1.05705i | −0.0454882 | + | 0.0787879i | ||||
\(181\) | 7.95691 | 0.591432 | 0.295716 | − | 0.955276i | \(-0.404442\pi\) | ||||
0.295716 | + | 0.955276i | \(0.404442\pi\) | |||||||
\(182\) | 0.302011 | − | 19.5987i | 0.0223866 | − | 1.45275i | ||||
\(183\) | −7.42424 | −0.548816 | ||||||||
\(184\) | −0.0859023 | + | 0.148787i | −0.00633280 | + | 0.0109687i | ||||
\(185\) | −4.83533 | −0.355500 | ||||||||
\(186\) | 1.18626 | + | 2.05467i | 0.0869811 | + | 0.150656i | ||||
\(187\) | 1.41796 | + | 2.45597i | 0.103691 | + | 0.179599i | ||||
\(188\) | −2.44160 | + | 4.22897i | −0.178072 | + | 0.308429i | ||||
\(189\) | 0.839752 | + | 2.50895i | 0.0610830 | + | 0.182499i | ||||
\(190\) | 0.633335 | 0.0459469 | ||||||||
\(191\) | 3.07979 | 0.222846 | 0.111423 | − | 0.993773i | \(-0.464459\pi\) | ||||
0.111423 | + | 0.993773i | \(0.464459\pi\) | |||||||
\(192\) | 9.66624 | 0.697601 | ||||||||
\(193\) | −3.39175 | −0.244143 | −0.122072 | − | 0.992521i | \(-0.538954\pi\) | ||||
−0.122072 | + | 0.992521i | \(0.538954\pi\) | |||||||
\(194\) | 6.47314 | + | 11.2118i | 0.464744 | + | 0.804961i | ||||
\(195\) | 1.50356 | − | 1.28924i | 0.107672 | − | 0.0923242i | ||||
\(196\) | 14.3185 | + | 6.07456i | 1.02275 | + | 0.433897i | ||||
\(197\) | 2.06163 | + | 3.57085i | 0.146885 | + | 0.254413i | 0.930075 | − | 0.367370i | \(-0.119742\pi\) |
−0.783189 | + | 0.621783i | \(0.786409\pi\) | |||||||
\(198\) | −4.82684 | + | 8.36033i | −0.343028 | + | 0.594143i | ||||
\(199\) | 0.574142 | + | 0.994443i | 0.0406998 | + | 0.0704942i | 0.885658 | − | 0.464339i | \(-0.153708\pi\) |
−0.844958 | + | 0.534833i | \(0.820375\pi\) | |||||||
\(200\) | 1.07138 | − | 1.85569i | 0.0757583 | − | 0.131217i | ||||
\(201\) | 9.59873 | 0.677042 | ||||||||
\(202\) | −4.56551 | + | 7.90769i | −0.321228 | + | 0.556383i | ||||
\(203\) | 7.33427 | − | 8.29150i | 0.514765 | − | 0.581949i | ||||
\(204\) | −0.670602 | + | 1.16152i | −0.0469515 | + | 0.0813224i | ||||
\(205\) | −2.17533 | + | 3.76778i | −0.151932 | + | 0.263153i | ||||
\(206\) | −34.1675 | −2.38056 | ||||||||
\(207\) | −0.188350 | + | 0.326231i | −0.0130912 | + | 0.0226746i | ||||
\(208\) | −11.9269 | − | 4.19742i | −0.826983 | − | 0.291039i | ||||
\(209\) | 2.63623 | 0.182352 | ||||||||
\(210\) | 0.947844 | + | 2.83190i | 0.0654074 | + | 0.195419i | ||||
\(211\) | −2.28300 | − | 3.95427i | −0.157168 | − | 0.272223i | 0.776678 | − | 0.629898i | \(-0.216903\pi\) |
−0.933846 | + | 0.357674i | \(0.883570\pi\) | |||||||
\(212\) | −20.1016 | −1.38058 | ||||||||
\(213\) | −2.88877 | + | 5.00350i | −0.197935 | + | 0.342834i | ||||
\(214\) | −18.3613 | − | 31.8027i | −1.25515 | − | 2.17399i | ||||
\(215\) | 0.820910 | 0.0559856 | ||||||||
\(216\) | −0.456078 | −0.0310322 | ||||||||
\(217\) | 2.99367 | + | 0.608768i | 0.203224 | + | 0.0413258i | ||||
\(218\) | −10.4334 | − | 18.0713i | −0.706642 | − | 1.22394i | ||||
\(219\) | −7.24668 | + | 12.5516i | −0.489685 | + | 0.848160i | ||||
\(220\) | −2.86729 | + | 4.96628i | −0.193312 | + | 0.334827i | ||||
\(221\) | 1.65216 | − | 1.41665i | 0.111136 | − | 0.0952941i | ||||
\(222\) | −9.04325 | − | 15.6634i | −0.606943 | − | 1.05126i | ||||
\(223\) | 8.42312 | + | 14.5893i | 0.564054 | + | 0.976970i | 0.997137 | + | 0.0756163i | \(0.0240924\pi\) |
−0.433083 | + | 0.901354i | \(0.642574\pi\) | |||||||
\(224\) | 14.2299 | − | 16.0871i | 0.950773 | − | 1.07486i | ||||
\(225\) | 2.34912 | − | 4.06880i | 0.156608 | − | 0.271253i | ||||
\(226\) | −7.69512 | − | 13.3283i | −0.511872 | − | 0.886588i | ||||
\(227\) | 14.2365 | + | 24.6583i | 0.944909 | + | 1.63663i | 0.755933 | + | 0.654649i | \(0.227184\pi\) |
0.188976 | + | 0.981982i | \(0.439483\pi\) | |||||||
\(228\) | 0.623383 | + | 1.07973i | 0.0412845 | + | 0.0715069i | ||||
\(229\) | −13.1373 | − | 22.7545i | −0.868137 | − | 1.50366i | −0.863899 | − | 0.503666i | \(-0.831984\pi\) |
−0.00423787 | − | 0.999991i | \(-0.501349\pi\) | |||||||
\(230\) | −0.212594 | + | 0.368223i | −0.0140180 | + | 0.0242799i | ||||
\(231\) | 3.94536 | + | 11.7876i | 0.259586 | + | 0.775570i | ||||
\(232\) | 0.954114 | + | 1.65257i | 0.0626406 | + | 0.108497i | ||||
\(233\) | −11.0974 | − | 19.2212i | −0.727014 | − | 1.25922i | −0.958140 | − | 0.286301i | \(-0.907574\pi\) |
0.231126 | − | 0.972924i | \(-0.425759\pi\) | |||||||
\(234\) | 6.98834 | + | 2.45939i | 0.456842 | + | 0.160776i | ||||
\(235\) | −0.603622 | + | 1.04550i | −0.0393760 | + | 0.0682012i | ||||
\(236\) | −9.48394 | + | 16.4267i | −0.617352 | + | 1.06928i | ||||
\(237\) | −7.31102 | − | 12.6631i | −0.474902 | − | 0.822554i | ||||
\(238\) | 1.04152 | + | 3.11176i | 0.0675115 | + | 0.201706i | ||||
\(239\) | 27.3213 | 1.76727 | 0.883633 | − | 0.468180i | \(-0.155090\pi\) | ||||
0.883633 | + | 0.468180i | \(0.155090\pi\) | |||||||
\(240\) | 1.92637 | 0.124347 | ||||||||
\(241\) | 11.8915 | + | 20.5967i | 0.766001 | + | 1.32675i | 0.939716 | + | 0.341957i | \(0.111090\pi\) |
−0.173715 | + | 0.984796i | \(0.555577\pi\) | |||||||
\(242\) | −11.3766 | + | 19.7048i | −0.731314 | + | 1.26667i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −8.24820 | − | 14.2863i | −0.528037 | − | 0.914586i | ||||
\(245\) | 3.53988 | + | 1.50178i | 0.226154 | + | 0.0959452i | ||||
\(246\) | −16.2736 | −1.03757 | ||||||||
\(247\) | −0.372557 | − | 1.98851i | −0.0237052 | − | 0.126526i | ||||
\(248\) | −0.263308 | + | 0.456062i | −0.0167201 | + | 0.0289600i | ||||
\(249\) | 14.8750 | 0.942664 | ||||||||
\(250\) | 5.47329 | − | 9.48002i | 0.346161 | − | 0.599569i | ||||
\(251\) | 4.16795 | − | 7.21910i | 0.263079 | − | 0.455666i | −0.703980 | − | 0.710220i | \(-0.748595\pi\) |
0.967058 | + | 0.254554i | \(0.0819288\pi\) | |||||||
\(252\) | −3.89496 | + | 4.40331i | −0.245359 | + | 0.277383i | ||||
\(253\) | −0.884913 | + | 1.53271i | −0.0556340 | + | 0.0963609i | ||||
\(254\) | −9.72354 | −0.610109 | ||||||||
\(255\) | −0.165789 | + | 0.287155i | −0.0103821 | + | 0.0179824i | ||||
\(256\) | −5.94083 | − | 10.2898i | −0.371302 | − | 0.643114i | ||||
\(257\) | 6.88712 | − | 11.9288i | 0.429607 | − | 0.744101i | −0.567231 | − | 0.823558i | \(-0.691985\pi\) |
0.996838 | + | 0.0794576i | \(0.0253188\pi\) | |||||||
\(258\) | 1.53530 | + | 2.65922i | 0.0955838 | + | 0.165556i | ||||
\(259\) | −22.8217 | − | 4.64082i | −1.41807 | − | 0.288367i | ||||
\(260\) | 4.15128 | + | 1.46095i | 0.257452 | + | 0.0906044i | ||||
\(261\) | 2.09200 | + | 3.62344i | 0.129491 | + | 0.224285i | ||||
\(262\) | 7.34387 | 0.453706 | ||||||||
\(263\) | −9.04564 | −0.557778 | −0.278889 | − | 0.960323i | \(-0.589966\pi\) | ||||
−0.278889 | + | 0.960323i | \(0.589966\pi\) | |||||||
\(264\) | −2.14277 | −0.131878 | ||||||||
\(265\) | −4.96960 | −0.305280 | ||||||||
\(266\) | 2.98920 | + | 0.607859i | 0.183280 | + | 0.0372702i | ||||
\(267\) | 4.59177 | − | 7.95317i | 0.281012 | − | 0.486726i | ||||
\(268\) | 10.6640 | + | 18.4706i | 0.651408 | + | 1.12827i | ||||
\(269\) | −1.14428 | − | 1.98196i | −0.0697681 | − | 0.120842i | 0.829031 | − | 0.559203i | \(-0.188893\pi\) |
−0.898799 | + | 0.438361i | \(0.855559\pi\) | |||||||
\(270\) | −1.12872 | −0.0686916 | ||||||||
\(271\) | −1.99057 | + | 3.44778i | −0.120919 | + | 0.209437i | −0.920130 | − | 0.391612i | \(-0.871917\pi\) |
0.799211 | + | 0.601050i | \(0.205251\pi\) | |||||||
\(272\) | 2.11675 | 0.128347 | ||||||||
\(273\) | 8.33387 | − | 4.64184i | 0.504389 | − | 0.280937i | ||||
\(274\) | −39.5694 | −2.39047 | ||||||||
\(275\) | 11.0367 | − | 19.1162i | 0.665541 | − | 1.15275i | ||||
\(276\) | −0.837013 | −0.0503822 | ||||||||
\(277\) | 4.19999 | + | 7.27460i | 0.252353 | + | 0.437089i | 0.964173 | − | 0.265273i | \(-0.0854622\pi\) |
−0.711820 | + | 0.702362i | \(0.752129\pi\) | |||||||
\(278\) | −9.92758 | − | 17.1951i | −0.595417 | − | 1.03129i | ||||
\(279\) | −0.577330 | + | 0.999965i | −0.0345638 | + | 0.0598663i | ||||
\(280\) | −0.439171 | + | 0.496490i | −0.0262455 | + | 0.0296709i | ||||
\(281\) | −12.9559 | −0.772884 | −0.386442 | − | 0.922314i | \(-0.626296\pi\) | ||||
−0.386442 | + | 0.922314i | \(0.626296\pi\) | |||||||
\(282\) | −4.51569 | −0.268905 | ||||||||
\(283\) | 25.6051 | 1.52207 | 0.761033 | − | 0.648713i | \(-0.224692\pi\) | ||||
0.761033 | + | 0.648713i | \(0.224692\pi\) | |||||||
\(284\) | −12.8375 | −0.761765 | ||||||||
\(285\) | 0.154115 | + | 0.266936i | 0.00912901 | + | 0.0158119i | ||||
\(286\) | 32.8329 | + | 11.5548i | 1.94145 | + | 0.683251i | ||||
\(287\) | −13.8833 | + | 15.6953i | −0.819505 | + | 0.926463i | ||||
\(288\) | 4.05887 | + | 7.03016i | 0.239171 | + | 0.414256i | ||||
\(289\) | 8.31783 | − | 14.4069i | 0.489284 | − | 0.847465i | ||||
\(290\) | 2.36127 | + | 4.08985i | 0.138659 | + | 0.240164i | ||||
\(291\) | −3.15034 | + | 5.45655i | −0.184676 | + | 0.319869i | ||||
\(292\) | −32.2037 | −1.88458 | ||||||||
\(293\) | −12.3943 | + | 21.4675i | −0.724081 | + | 1.25415i | 0.235270 | + | 0.971930i | \(0.424403\pi\) |
−0.959351 | + | 0.282215i | \(0.908931\pi\) | |||||||
\(294\) | 1.75564 | + | 14.2756i | 0.102391 | + | 0.832572i | ||||
\(295\) | −2.34466 | + | 4.06107i | −0.136511 | + | 0.236445i | ||||
\(296\) | 2.00728 | − | 3.47670i | 0.116671 | − | 0.202079i | ||||
\(297\) | −4.69824 | −0.272620 | ||||||||
\(298\) | −7.31997 | + | 12.6786i | −0.424035 | + | 0.734450i | ||||
\(299\) | 1.28118 | + | 0.450885i | 0.0740928 | + | 0.0260753i | ||||
\(300\) | 10.4393 | 0.602715 | ||||||||
\(301\) | 3.87451 | + | 0.787888i | 0.223323 | + | 0.0454131i | ||||
\(302\) | 20.1929 | + | 34.9751i | 1.16197 | + | 2.01259i | ||||
\(303\) | −4.44387 | −0.255294 | ||||||||
\(304\) | 0.983851 | − | 1.70408i | 0.0564277 | − | 0.0977357i | ||||
\(305\) | −2.03916 | − | 3.53192i | −0.116762 | − | 0.202237i | ||||
\(306\) | −1.24027 | −0.0709013 | ||||||||
\(307\) | −25.2086 | −1.43873 | −0.719365 | − | 0.694632i | \(-0.755567\pi\) | ||||
−0.719365 | + | 0.694632i | \(0.755567\pi\) | |||||||
\(308\) | −18.2995 | + | 20.6878i | −1.04271 | + | 1.17880i | ||||
\(309\) | −8.31431 | − | 14.4008i | −0.472985 | − | 0.819234i | ||||
\(310\) | −0.651643 | + | 1.12868i | −0.0370108 | + | 0.0641046i | ||||
\(311\) | −2.06640 | + | 3.57911i | −0.117175 | + | 0.202953i | −0.918647 | − | 0.395079i | \(-0.870717\pi\) |
0.801472 | + | 0.598032i | \(0.204050\pi\) | |||||||
\(312\) | 0.302820 | + | 1.61629i | 0.0171438 | + | 0.0915045i | ||||
\(313\) | 15.0691 | + | 26.1005i | 0.851758 | + | 1.47529i | 0.879620 | + | 0.475676i | \(0.157797\pi\) |
−0.0278626 | + | 0.999612i | \(0.508870\pi\) | |||||||
\(314\) | 5.35279 | + | 9.27131i | 0.302076 | + | 0.523210i | ||||
\(315\) | −0.962929 | + | 1.08861i | −0.0542549 | + | 0.0613360i | ||||
\(316\) | 16.2448 | − | 28.1369i | 0.913843 | − | 1.58282i | ||||
\(317\) | −5.76330 | − | 9.98233i | −0.323699 | − | 0.560663i | 0.657549 | − | 0.753412i | \(-0.271593\pi\) |
−0.981248 | + | 0.192748i | \(0.938260\pi\) | |||||||
\(318\) | −9.29438 | − | 16.0983i | −0.521203 | − | 0.902750i | ||||
\(319\) | 9.82870 | + | 17.0238i | 0.550302 | + | 0.953150i | ||||
\(320\) | 2.65495 | + | 4.59850i | 0.148416 | + | 0.257064i | ||||
\(321\) | 8.93605 | − | 15.4777i | 0.498762 | − | 0.863881i | ||||
\(322\) | −1.35681 | + | 1.53389i | −0.0756119 | + | 0.0854804i | ||||
\(323\) | 0.169346 | + | 0.293316i | 0.00942268 | + | 0.0163206i | ||||
\(324\) | −1.11098 | − | 1.92428i | −0.0617212 | − | 0.106904i | ||||
\(325\) | −15.9791 | − | 5.62349i | −0.886361 | − | 0.311935i | ||||
\(326\) | 4.28803 | − | 7.42709i | 0.237492 | − | 0.411348i | ||||
\(327\) | 5.07774 | − | 8.79490i | 0.280800 | − | 0.486359i | ||||
\(328\) | −1.80608 | − | 3.12822i | −0.0997239 | − | 0.172727i | ||||
\(329\) | −3.85241 | + | 4.35521i | −0.212390 | + | 0.240110i | ||||
\(330\) | −5.30299 | −0.291920 | ||||||||
\(331\) | −1.13539 | −0.0624067 | −0.0312033 | − | 0.999513i | \(-0.509934\pi\) | ||||
−0.0312033 | + | 0.999513i | \(0.509934\pi\) | |||||||
\(332\) | 16.5258 | + | 28.6236i | 0.906973 | + | 1.57092i | ||||
\(333\) | 4.40116 | − | 7.62304i | 0.241182 | − | 0.417740i | ||||
\(334\) | 10.3697 | 0.567404 | ||||||||
\(335\) | 2.63640 | + | 4.56639i | 0.144042 | + | 0.249488i | ||||
\(336\) | 9.09205 | + | 1.84888i | 0.496012 | + | 0.100865i | ||||
\(337\) | 23.3181 | 1.27022 | 0.635110 | − | 0.772421i | \(-0.280955\pi\) | ||||
0.635110 | + | 0.772421i | \(0.280955\pi\) | |||||||
\(338\) | 4.07581 | − | 26.3989i | 0.221695 | − | 1.43591i | ||||
\(339\) | 3.74505 | − | 6.48662i | 0.203403 | − | 0.352305i | ||||
\(340\) | −0.736755 | −0.0399562 | ||||||||
\(341\) | −2.71244 | + | 4.69808i | −0.146887 | + | 0.254415i | ||||
\(342\) | −0.576468 | + | 0.998472i | −0.0311718 | + | 0.0539912i | ||||
\(343\) | 15.2661 | + | 10.4856i | 0.824291 | + | 0.566167i | ||||
\(344\) | −0.340782 | + | 0.590252i | −0.0183737 | + | 0.0318242i | ||||
\(345\) | −0.206930 | −0.0111407 | ||||||||
\(346\) | −2.81394 | + | 4.87389i | −0.151279 | + | 0.262022i | ||||
\(347\) | −1.26911 | − | 2.19816i | −0.0681294 | − | 0.118004i | 0.829948 | − | 0.557840i | \(-0.188370\pi\) |
−0.898078 | + | 0.439836i | \(0.855036\pi\) | |||||||
\(348\) | −4.64834 | + | 8.05116i | −0.249177 | + | 0.431587i | ||||
\(349\) | −5.34353 | − | 9.25527i | −0.286033 | − | 0.495423i | 0.686826 | − | 0.726822i | \(-0.259003\pi\) |
−0.972859 | + | 0.231398i | \(0.925670\pi\) | |||||||
\(350\) | 16.9223 | − | 19.1309i | 0.904534 | − | 1.02259i | ||||
\(351\) | 0.663964 | + | 3.54389i | 0.0354398 | + | 0.189159i | ||||
\(352\) | 19.0695 | + | 33.0294i | 1.01641 | + | 1.76047i | ||||
\(353\) | 22.2407 | 1.18375 | 0.591875 | − | 0.806030i | \(-0.298388\pi\) | ||||
0.591875 | + | 0.806030i | \(0.298388\pi\) | |||||||
\(354\) | −17.5404 | −0.932261 | ||||||||
\(355\) | −3.17374 | −0.168445 | ||||||||
\(356\) | 20.4055 | 1.08149 | ||||||||
\(357\) | −1.05809 | + | 1.19619i | −0.0560002 | + | 0.0633091i | ||||
\(358\) | 13.0431 | − | 22.5914i | 0.689351 | − | 1.19399i | ||||
\(359\) | 8.38142 | + | 14.5170i | 0.442354 | + | 0.766180i | 0.997864 | − | 0.0653300i | \(-0.0208100\pi\) |
−0.555509 | + | 0.831510i | \(0.687477\pi\) | |||||||
\(360\) | −0.125267 | − | 0.216969i | −0.00660217 | − | 0.0114353i | ||||
\(361\) | −18.6852 | −0.983429 | ||||||||
\(362\) | −8.17470 | + | 14.1590i | −0.429653 | + | 0.744180i | ||||
\(363\) | −11.0735 | −0.581208 | ||||||||
\(364\) | 18.1910 | + | 10.8797i | 0.953465 | + | 0.570250i | ||||
\(365\) | −7.96155 | −0.416726 | ||||||||
\(366\) | 7.62745 | − | 13.2111i | 0.398693 | − | 0.690557i | ||||
\(367\) | −4.68194 | −0.244395 | −0.122198 | − | 0.992506i | \(-0.538994\pi\) | ||||
−0.122198 | + | 0.992506i | \(0.538994\pi\) | |||||||
\(368\) | 0.660506 | + | 1.14403i | 0.0344312 | + | 0.0596366i | ||||
\(369\) | −3.96001 | − | 6.85894i | −0.206150 | − | 0.357062i | ||||
\(370\) | 4.96767 | − | 8.60426i | 0.258257 | − | 0.447314i | ||||
\(371\) | −23.4554 | − | 4.76970i | −1.21775 | − | 0.247630i | ||||
\(372\) | −2.56561 | −0.133021 | ||||||||
\(373\) | −6.76172 | −0.350109 | −0.175054 | − | 0.984559i | \(-0.556010\pi\) | ||||
−0.175054 | + | 0.984559i | \(0.556010\pi\) | |||||||
\(374\) | −5.82707 | −0.301311 | ||||||||
\(375\) | 5.32748 | 0.275110 | ||||||||
\(376\) | −0.501160 | − | 0.868034i | −0.0258453 | − | 0.0447655i | ||||
\(377\) | 11.4521 | − | 9.81963i | 0.589811 | − | 0.505737i | ||||
\(378\) | −5.32730 | − | 1.08331i | −0.274007 | − | 0.0557197i | ||||
\(379\) | 9.62497 | + | 16.6709i | 0.494402 | + | 0.856329i | 0.999979 | − | 0.00645256i | \(-0.00205393\pi\) |
−0.505578 | + | 0.862781i | \(0.668721\pi\) | |||||||
\(380\) | −0.342439 | + | 0.593122i | −0.0175667 | + | 0.0304265i | ||||
\(381\) | −2.36612 | − | 4.09824i | −0.121220 | − | 0.209959i | ||||
\(382\) | −3.16408 | + | 5.48036i | −0.161889 | + | 0.280399i | ||||
\(383\) | 13.4851 | 0.689055 | 0.344528 | − | 0.938776i | \(-0.388039\pi\) | ||||
0.344528 | + | 0.938776i | \(0.388039\pi\) | |||||||
\(384\) | −1.81308 | + | 3.14034i | −0.0925233 | + | 0.160255i | ||||
\(385\) | −4.52408 | + | 5.11454i | −0.230568 | + | 0.260661i | ||||
\(386\) | 3.48458 | − | 6.03547i | 0.177361 | − | 0.307198i | ||||
\(387\) | −0.747200 | + | 1.29419i | −0.0379823 | + | 0.0657873i | ||||
\(388\) | −13.9999 | −0.710737 | ||||||||
\(389\) | 16.4229 | − | 28.4453i | 0.832675 | − | 1.44224i | −0.0632336 | − | 0.997999i | \(-0.520141\pi\) |
0.895909 | − | 0.444238i | \(-0.146525\pi\) | |||||||
\(390\) | 0.749428 | + | 4.00005i | 0.0379488 | + | 0.202551i | ||||
\(391\) | −0.227380 | −0.0114991 | ||||||||
\(392\) | −2.54931 | + | 1.92182i | −0.128760 | + | 0.0970665i | ||||
\(393\) | 1.78705 | + | 3.09527i | 0.0901449 | + | 0.156136i | ||||
\(394\) | −8.47225 | −0.426826 | ||||||||
\(395\) | 4.01612 | − | 6.95612i | 0.202073 | − | 0.350000i | ||||
\(396\) | −5.21966 | − | 9.04072i | −0.262298 | − | 0.454313i | ||||
\(397\) | −26.6109 | −1.33556 | −0.667781 | − | 0.744358i | \(-0.732756\pi\) | ||||
−0.667781 | + | 0.744358i | \(0.732756\pi\) | |||||||
\(398\) | −2.35943 | −0.118267 | ||||||||
\(399\) | 0.471193 | + | 1.40779i | 0.0235892 | + | 0.0704779i | ||||
\(400\) | −8.23791 | − | 14.2685i | −0.411895 | − | 0.713424i | ||||
\(401\) | 11.5558 | − | 20.0153i | 0.577071 | − | 0.999517i | −0.418742 | − | 0.908105i | \(-0.637529\pi\) |
0.995813 | − | 0.0914115i | \(-0.0291379\pi\) | |||||||
\(402\) | −9.86145 | + | 17.0805i | −0.491845 | + | 0.851900i | ||||
\(403\) | 3.92709 | + | 1.38205i | 0.195622 | + | 0.0688450i | ||||
\(404\) | −4.93706 | − | 8.55124i | −0.245628 | − | 0.425440i | ||||
\(405\) | −0.274662 | − | 0.475728i | −0.0136481 | − | 0.0236391i | ||||
\(406\) | 7.21937 | + | 21.5695i | 0.358291 | + | 1.07047i | ||||
\(407\) | 20.6777 | − | 35.8149i | 1.02496 | − | 1.77528i | ||||
\(408\) | −0.137647 | − | 0.238412i | −0.00681455 | − | 0.0118031i | ||||
\(409\) | 3.62073 | + | 6.27129i | 0.179034 | + | 0.310096i | 0.941550 | − | 0.336874i | \(-0.109370\pi\) |
−0.762516 | + | 0.646969i | \(0.776036\pi\) | |||||||
\(410\) | −4.46974 | − | 7.74182i | −0.220745 | − | 0.382341i | ||||
\(411\) | −9.62880 | − | 16.6776i | −0.474954 | − | 0.822644i | ||||
\(412\) | 18.4741 | − | 31.9981i | 0.910154 | − | 1.57643i | ||||
\(413\) | −14.9640 | + | 16.9170i | −0.736330 | + | 0.832433i | ||||
\(414\) | −0.387010 | − | 0.670321i | −0.0190205 | − | 0.0329445i | ||||
\(415\) | 4.08559 | + | 7.07645i | 0.200554 | + | 0.347369i | ||||
\(416\) | 22.2192 | − | 19.0520i | 1.08939 | − | 0.934099i | ||||
\(417\) | 4.83155 | − | 8.36849i | 0.236602 | − | 0.409807i | ||||
\(418\) | −2.70839 | + | 4.69106i | −0.132471 | + | 0.229447i | ||||
\(419\) | −17.5550 | − | 30.4062i | −0.857618 | − | 1.48544i | −0.874194 | − | 0.485576i | \(-0.838610\pi\) |
0.0165759 | − | 0.999863i | \(-0.494723\pi\) | |||||||
\(420\) | −3.16458 | − | 0.643521i | −0.154416 | − | 0.0314006i | ||||
\(421\) | 25.2731 | 1.23174 | 0.615868 | − | 0.787849i | \(-0.288805\pi\) | ||||
0.615868 | + | 0.787849i | \(0.288805\pi\) | |||||||
\(422\) | 9.38195 | 0.456706 | ||||||||
\(423\) | −1.09885 | − | 1.90326i | −0.0534277 | − | 0.0925395i | ||||
\(424\) | 2.06302 | − | 3.57325i | 0.100189 | − | 0.173532i | ||||
\(425\) | 2.83592 | 0.137562 | ||||||||
\(426\) | −5.93568 | − | 10.2809i | −0.287584 | − | 0.498111i | ||||
\(427\) | −6.23452 | − | 18.6270i | −0.301710 | − | 0.901425i | ||||
\(428\) | 39.7112 | 1.91951 | ||||||||
\(429\) | 3.11946 | + | 16.6501i | 0.150609 | + | 0.803872i | ||||
\(430\) | −0.843379 | + | 1.46077i | −0.0406713 | + | 0.0704448i | ||||
\(431\) | 17.5693 | 0.846285 | 0.423142 | − | 0.906063i | \(-0.360927\pi\) | ||||
0.423142 | + | 0.906063i | \(0.360927\pi\) | |||||||
\(432\) | −1.75340 | + | 3.03698i | −0.0843606 | + | 0.146117i | ||||
\(433\) | −3.02011 | + | 5.23098i | −0.145137 | + | 0.251385i | −0.929424 | − | 0.369013i | \(-0.879696\pi\) |
0.784287 | + | 0.620398i | \(0.213029\pi\) | |||||||
\(434\) | −4.15889 | + | 4.70169i | −0.199633 | + | 0.225688i | ||||
\(435\) | −1.14918 | + | 1.99044i | −0.0550991 | + | 0.0954344i | ||||
\(436\) | 22.5651 | 1.08067 | ||||||||
\(437\) | −0.105685 | + | 0.183052i | −0.00505559 | + | 0.00875654i | ||||
\(438\) | −14.8901 | − | 25.7903i | −0.711474 | − | 1.23231i | ||||
\(439\) | −12.4282 | + | 21.5262i | −0.593164 | + | 1.02739i | 0.400639 | + | 0.916236i | \(0.368788\pi\) |
−0.993803 | + | 0.111155i | \(0.964545\pi\) | |||||||
\(440\) | −0.588537 | − | 1.01938i | −0.0280574 | − | 0.0485968i | ||||
\(441\) | −5.58963 | + | 4.21379i | −0.266173 | + | 0.200657i | ||||
\(442\) | 0.823492 | + | 4.39537i | 0.0391695 | + | 0.209066i | ||||
\(443\) | 15.8094 | + | 27.3826i | 0.751126 | + | 1.30099i | 0.947278 | + | 0.320414i | \(0.103822\pi\) |
−0.196152 | + | 0.980574i | \(0.562845\pi\) | |||||||
\(444\) | 19.5584 | 0.928203 | ||||||||
\(445\) | 5.04473 | 0.239143 | ||||||||
\(446\) | −34.6147 | −1.63905 | ||||||||
\(447\) | −7.12496 | −0.336999 | ||||||||
\(448\) | 8.11725 | + | 24.2521i | 0.383504 | + | 1.14580i | ||||
\(449\) | −2.63384 | + | 4.56194i | −0.124298 | + | 0.215291i | −0.921459 | − | 0.388477i | \(-0.873001\pi\) |
0.797160 | + | 0.603768i | \(0.206335\pi\) | |||||||
\(450\) | 4.82684 | + | 8.36033i | 0.227539 | + | 0.394110i | ||||
\(451\) | −18.6051 | − | 32.2250i | −0.876080 | − | 1.51742i | ||||
\(452\) | 16.6427 | 0.782809 | ||||||||
\(453\) | −9.82744 | + | 17.0216i | −0.461733 | + | 0.799746i | ||||
\(454\) | −58.5046 | −2.74576 | ||||||||
\(455\) | 4.49725 | + | 2.68972i | 0.210834 | + | 0.126096i | ||||
\(456\) | −0.255910 | −0.0119841 | ||||||||
\(457\) | 9.24474 | − | 16.0124i | 0.432451 | − | 0.749027i | −0.564633 | − | 0.825342i | \(-0.690982\pi\) |
0.997084 | + | 0.0763154i | \(0.0243156\pi\) | |||||||
\(458\) | 53.9875 | 2.52267 | ||||||||
\(459\) | −0.301806 | − | 0.522743i | −0.0140871 | − | 0.0243996i | ||||
\(460\) | −0.229895 | − | 0.398191i | −0.0107189 | − | 0.0185657i | ||||
\(461\) | 4.79101 | − | 8.29827i | 0.223140 | − | 0.386489i | −0.732620 | − | 0.680638i | \(-0.761703\pi\) |
0.955760 | + | 0.294149i | \(0.0950361\pi\) | |||||||
\(462\) | −25.0290 | − | 5.08968i | −1.16445 | − | 0.236793i | ||||
\(463\) | 2.22178 | 0.103255 | 0.0516275 | − | 0.998666i | \(-0.483559\pi\) | ||||
0.0516275 | + | 0.998666i | \(0.483559\pi\) | |||||||
\(464\) | 14.6724 | 0.681151 | ||||||||
\(465\) | −0.634282 | −0.0294141 | ||||||||
\(466\) | 45.6045 | 2.11259 | ||||||||
\(467\) | 6.76331 | + | 11.7144i | 0.312969 | + | 0.542078i | 0.979004 | − | 0.203843i | \(-0.0653431\pi\) |
−0.666035 | + | 0.745921i | \(0.732010\pi\) | |||||||
\(468\) | −6.08177 | + | 5.21485i | −0.281130 | + | 0.241056i | ||||
\(469\) | 8.06055 | + | 24.0827i | 0.372202 | + | 1.11204i | ||||
\(470\) | −1.24029 | − | 2.14824i | −0.0572102 | − | 0.0990910i | ||||
\(471\) | −2.60509 | + | 4.51215i | −0.120036 | + | 0.207909i | ||||
\(472\) | −1.94667 | − | 3.37172i | −0.0896025 | − | 0.155196i | ||||
\(473\) | −3.51053 | + | 6.08041i | −0.161414 | + | 0.279578i | ||||
\(474\) | 30.0445 | 1.37999 | ||||||||
\(475\) | 1.31812 | − | 2.28304i | 0.0604793 | − | 0.104753i | ||||
\(476\) | −3.47732 | − | 0.707119i | −0.159383 | − | 0.0324107i | ||||
\(477\) | 4.52338 | − | 7.83473i | 0.207111 | − | 0.358727i | ||||
\(478\) | −28.0691 | + | 48.6171i | −1.28385 | + | 2.22369i | ||||
\(479\) | −14.5871 | −0.666501 | −0.333251 | − | 0.942838i | \(-0.608146\pi\) | ||||
−0.333251 | + | 0.942838i | \(0.608146\pi\) | |||||||
\(480\) | −2.22963 | + | 3.86184i | −0.101768 | + | 0.176268i | ||||
\(481\) | −29.9374 | − | 10.5358i | −1.36503 | − | 0.480392i | ||||
\(482\) | −48.8681 | −2.22588 | ||||||||
\(483\) | −0.976664 | − | 0.198606i | −0.0444398 | − | 0.00903689i | ||||
\(484\) | −12.3024 | − | 21.3085i | −0.559202 | − | 0.968567i | ||||
\(485\) | −3.46111 | −0.157161 | ||||||||
\(486\) | 1.02737 | − | 1.77946i | 0.0466025 | − | 0.0807179i | ||||
\(487\) | 0.750628 | + | 1.30013i | 0.0340142 | + | 0.0589143i | 0.882531 | − | 0.470254i | \(-0.155838\pi\) |
−0.848517 | + | 0.529168i | \(0.822504\pi\) | |||||||
\(488\) | 3.38604 | 0.153279 | ||||||||
\(489\) | 4.17379 | 0.188745 | ||||||||
\(490\) | −6.30912 | + | 4.75618i | −0.285017 | + | 0.214862i | ||||
\(491\) | 14.1980 | + | 24.5917i | 0.640748 | + | 1.10981i | 0.985266 | + | 0.171028i | \(0.0547089\pi\) |
−0.344518 | + | 0.938780i | \(0.611958\pi\) | |||||||
\(492\) | 8.79901 | − | 15.2403i | 0.396690 | − | 0.687087i | ||||
\(493\) | −1.26275 | + | 2.18715i | −0.0568715 | + | 0.0985044i | ||||
\(494\) | 3.92123 | + | 1.37999i | 0.176424 | + | 0.0620886i | ||||
\(495\) | −1.29043 | − | 2.23509i | −0.0580004 | − | 0.100460i | ||||
\(496\) | 2.02458 | + | 3.50668i | 0.0909064 | + | 0.157455i | ||||
\(497\) | −14.9794 | − | 3.04607i | −0.671916 | − | 0.136635i | ||||
\(498\) | −15.2821 | + | 26.4694i | −0.684808 | + | 1.18612i | ||||
\(499\) | −10.5569 | − | 18.2851i | −0.472593 | − | 0.818554i | 0.526915 | − | 0.849918i | \(-0.323348\pi\) |
−0.999508 | + | 0.0313633i | \(0.990015\pi\) | |||||||
\(500\) | 5.91873 | + | 10.2515i | 0.264694 | + | 0.458463i | ||||
\(501\) | 2.52335 | + | 4.37058i | 0.112735 | + | 0.195263i | ||||
\(502\) | 8.56406 | + | 14.8334i | 0.382233 | + | 0.662046i | ||||
\(503\) | 14.2618 | − | 24.7022i | 0.635903 | − | 1.10142i | −0.350420 | − | 0.936593i | \(-0.613961\pi\) |
0.986323 | − | 0.164824i | \(-0.0527056\pi\) | |||||||
\(504\) | −0.382993 | − | 1.14428i | −0.0170599 | − | 0.0509701i | ||||
\(505\) | −1.22056 | − | 2.11408i | −0.0543143 | − | 0.0940752i | ||||
\(506\) | −1.81827 | − | 3.14933i | −0.0808318 | − | 0.140005i | ||||
\(507\) | 12.1183 | − | 4.70603i | 0.538193 | − | 0.209002i | ||||
\(508\) | 5.25744 | − | 9.10615i | 0.233261 | − | 0.404020i | ||||
\(509\) | −17.1295 | + | 29.6691i | −0.759250 | + | 1.31506i | 0.183984 | + | 0.982929i | \(0.441100\pi\) |
−0.943234 | + | 0.332130i | \(0.892233\pi\) | |||||||
\(510\) | −0.340654 | − | 0.590030i | −0.0150844 | − | 0.0261270i | ||||
\(511\) | −37.5768 | − | 7.64129i | −1.66230 | − | 0.338031i | ||||
\(512\) | 31.6661 | 1.39946 | ||||||||
\(513\) | −0.561110 | −0.0247736 | ||||||||
\(514\) | 14.1513 | + | 24.5107i | 0.624185 | + | 1.08112i | ||||
\(515\) | 4.56725 | − | 7.91071i | 0.201257 | − | 0.348587i | ||||
\(516\) | −3.32050 | −0.146177 | ||||||||
\(517\) | −5.16264 | − | 8.94196i | −0.227053 | − | 0.393267i | ||||
\(518\) | 31.7045 | − | 35.8424i | 1.39302 | − | 1.57482i | ||||
\(519\) | −2.73897 | −0.120228 | ||||||||
\(520\) | −0.685743 | + | 0.587994i | −0.0300718 | + | 0.0257852i | ||||
\(521\) | −17.2434 | + | 29.8665i | −0.755448 | + | 1.30847i | 0.189703 | + | 0.981841i | \(0.439247\pi\) |
−0.945151 | + | 0.326633i | \(0.894086\pi\) | |||||||
\(522\) | −8.59702 | −0.376281 | ||||||||
\(523\) | −15.6948 | + | 27.1842i | −0.686285 | + | 1.18868i | 0.286746 | + | 0.958007i | \(0.407427\pi\) |
−0.973031 | + | 0.230674i | \(0.925907\pi\) | |||||||
\(524\) | −3.97077 | + | 6.87757i | −0.173464 | + | 0.300448i | ||||
\(525\) | 12.1811 | + | 2.47704i | 0.531626 | + | 0.108107i | ||||
\(526\) | 9.29323 | − | 16.0963i | 0.405204 | − | 0.701834i | ||||
\(527\) | −0.696966 | −0.0303603 | ||||||||
\(528\) | −8.23791 | + | 14.2685i | −0.358509 | + | 0.620956i | ||||
\(529\) | 11.4290 | + | 19.7957i | 0.496915 | + | 0.860682i | ||||
\(530\) | 5.10562 | − | 8.84320i | 0.221774 | − | 0.384124i | ||||
\(531\) | −4.26827 | − | 7.39286i | −0.185227 | − | 0.320823i | ||||
\(532\) | −2.18550 | + | 2.47074i | −0.0947534 | + | 0.107120i | ||||
\(533\) | −21.6780 | + | 18.5879i | −0.938980 | + | 0.805133i | ||||
\(534\) | 9.43489 | + | 16.3417i | 0.408288 | + | 0.707175i | ||||
\(535\) | 9.81757 | 0.424451 | ||||||||
\(536\) | −4.37777 | −0.189091 | ||||||||
\(537\) | 12.6956 | 0.547858 | ||||||||
\(538\) | 4.70241 | 0.202735 | ||||||||
\(539\) | −26.2615 | + | 19.7974i | −1.13116 | + | 0.852734i | ||||
\(540\) | 0.610289 | − | 1.05705i | 0.0262626 | − | 0.0454882i | ||||
\(541\) | −4.55013 | − | 7.88106i | −0.195626 | − | 0.338833i | 0.751480 | − | 0.659756i | \(-0.229340\pi\) |
−0.947105 | + | 0.320923i | \(0.896007\pi\) | |||||||
\(542\) | −4.09012 | − | 7.08429i | −0.175685 | − | 0.304296i | ||||
\(543\) | −7.95691 | −0.341464 | ||||||||
\(544\) | −2.44998 | + | 4.24349i | −0.105042 | + | 0.181938i | ||||
\(545\) | 5.57865 | 0.238963 | ||||||||
\(546\) | −0.302011 | + | 19.5987i | −0.0129249 | + | 0.838745i | ||||
\(547\) | −35.9950 | −1.53903 | −0.769517 | − | 0.638626i | \(-0.779503\pi\) | ||||
−0.769517 | + | 0.638626i | \(0.779503\pi\) | |||||||
\(548\) | 21.3948 | − | 37.0570i | 0.913943 | − | 1.58299i | ||||
\(549\) | 7.42424 | 0.316859 | ||||||||
\(550\) | 22.6777 | + | 39.2789i | 0.966979 | + | 1.67486i | ||||
\(551\) | 1.17384 | + | 2.03315i | 0.0500072 | + | 0.0866150i | ||||
\(552\) | 0.0859023 | − | 0.148787i | 0.00365624 | − | 0.00633280i | ||||
\(553\) | 25.6315 | − | 28.9768i | 1.08996 | − | 1.23222i | ||||
\(554\) | −17.2598 | −0.733299 | ||||||||
\(555\) | 4.83533 | 0.205248 | ||||||||
\(556\) | 21.4710 | 0.910575 | ||||||||
\(557\) | −15.9142 | −0.674304 | −0.337152 | − | 0.941450i | \(-0.609464\pi\) | ||||
−0.337152 | + | 0.941450i | \(0.609464\pi\) | |||||||
\(558\) | −1.18626 | − | 2.05467i | −0.0502185 | − | 0.0869811i | ||||
\(559\) | 5.08257 | + | 1.78870i | 0.214970 | + | 0.0756540i | ||||
\(560\) | 1.61767 | + | 4.83316i | 0.0683592 | + | 0.204238i | ||||
\(561\) | −1.41796 | − | 2.45597i | −0.0598662 | − | 0.103691i | ||||
\(562\) | 13.3105 | − | 23.0545i | 0.561470 | − | 0.972495i | ||||
\(563\) | 12.6124 | + | 21.8453i | 0.531548 | + | 0.920668i | 0.999322 | + | 0.0368201i | \(0.0117228\pi\) |
−0.467774 | + | 0.883848i | \(0.654944\pi\) | |||||||
\(564\) | 2.44160 | − | 4.22897i | 0.102810 | − | 0.178072i | ||||
\(565\) | 4.11449 | 0.173098 | ||||||||
\(566\) | −26.3059 | + | 45.5632i | −1.10572 | + | 1.91517i | ||||
\(567\) | −0.839752 | − | 2.50895i | −0.0352663 | − | 0.105366i | ||||
\(568\) | 1.31751 | − | 2.28199i | 0.0552813 | − | 0.0957501i | ||||
\(569\) | −17.0842 | + | 29.5908i | −0.716208 | + | 1.24051i | 0.246283 | + | 0.969198i | \(0.420791\pi\) |
−0.962492 | + | 0.271311i | \(0.912543\pi\) | |||||||
\(570\) | −0.633335 | −0.0265275 | ||||||||
\(571\) | −7.15867 | + | 12.3992i | −0.299581 | + | 0.518889i | −0.976040 | − | 0.217591i | \(-0.930180\pi\) |
0.676459 | + | 0.736480i | \(0.263514\pi\) | |||||||
\(572\) | −28.5737 | + | 24.5006i | −1.19472 | + | 1.02442i | ||||
\(573\) | −3.07979 | −0.128660 | ||||||||
\(574\) | −13.6658 | − | 40.8296i | −0.570399 | − | 1.70420i | ||||
\(575\) | 0.884913 | + | 1.53271i | 0.0369034 | + | 0.0639186i | ||||
\(576\) | −9.66624 | −0.402760 | ||||||||
\(577\) | 5.34662 | − | 9.26061i | 0.222583 | − | 0.385524i | −0.733009 | − | 0.680219i | \(-0.761885\pi\) |
0.955591 | + | 0.294695i | \(0.0952180\pi\) | |||||||
\(578\) | 17.0910 | + | 29.6025i | 0.710891 | + | 1.23130i | ||||
\(579\) | 3.39175 | 0.140956 | ||||||||
\(580\) | −5.10688 | −0.212052 | ||||||||
\(581\) | 12.4913 | + | 37.3205i | 0.518226 | + | 1.54832i | ||||
\(582\) | −6.47314 | − | 11.2118i | −0.268320 | − | 0.464744i | ||||
\(583\) | 21.2519 | − | 36.8095i | 0.880166 | − | 1.52449i | ||||
\(584\) | 3.30505 | − | 5.72452i | 0.136764 | − | 0.236882i | ||||
\(585\) | −1.50356 | + | 1.28924i | −0.0621647 | + | 0.0533034i | ||||
\(586\) | −25.4670 | − | 44.1102i | −1.05203 | − | 1.82217i | ||||
\(587\) | −21.3592 | − | 36.9951i | −0.881587 | − | 1.52695i | −0.849576 | − | 0.527465i | \(-0.823142\pi\) |
−0.0320103 | − | 0.999488i | \(-0.510191\pi\) | |||||||
\(588\) | −14.3185 | − | 6.07456i | −0.590484 | − | 0.250511i | ||||
\(589\) | −0.323945 | + | 0.561090i | −0.0133479 | + | 0.0231193i | ||||
\(590\) | −4.81767 | − | 8.34446i | −0.198341 | − | 0.343536i | ||||
\(591\) | −2.06163 | − | 3.57085i | −0.0848042 | − | 0.146885i | ||||
\(592\) | −15.4340 | − | 26.7325i | −0.634334 | − | 1.09870i | ||||
\(593\) | 14.0922 | + | 24.4084i | 0.578697 | + | 1.00233i | 0.995629 | + | 0.0933948i | \(0.0297719\pi\) |
−0.416932 | + | 0.908938i | \(0.636895\pi\) | |||||||
\(594\) | 4.82684 | − | 8.36033i | 0.198048 | − | 0.343028i | ||||
\(595\) | −0.859679 | − | 0.174817i | −0.0352434 | − | 0.00716680i | ||||
\(596\) | −7.91570 | − | 13.7104i | −0.324240 | − | 0.561599i | ||||
\(597\) | −0.574142 | − | 0.994443i | −0.0234981 | − | 0.0406998i | ||||
\(598\) | −2.11858 | + | 1.81659i | −0.0866353 | + | 0.0742859i | ||||
\(599\) | 15.7857 | − | 27.3417i | 0.644987 | − | 1.11715i | −0.339317 | − | 0.940672i | \(-0.610196\pi\) |
0.984304 | − | 0.176479i | \(-0.0564707\pi\) | |||||||
\(600\) | −1.07138 | + | 1.85569i | −0.0437391 | + | 0.0757583i | ||||
\(601\) | 16.0445 | + | 27.7899i | 0.654469 | + | 1.13357i | 0.982027 | + | 0.188742i | \(0.0604409\pi\) |
−0.327558 | + | 0.944831i | \(0.606226\pi\) | |||||||
\(602\) | −5.38258 | + | 6.08508i | −0.219377 | + | 0.248009i | ||||
\(603\) | −9.59873 | −0.390890 | ||||||||
\(604\) | −43.6724 | −1.77701 | ||||||||
\(605\) | −3.04147 | − | 5.26797i | −0.123653 | − | 0.214174i | ||||
\(606\) | 4.56551 | − | 7.90769i | 0.185461 | − | 0.321228i | ||||
\(607\) | −18.6665 | −0.757649 | −0.378825 | − | 0.925468i | \(-0.623672\pi\) | ||||
−0.378825 | + | 0.925468i | \(0.623672\pi\) | |||||||
\(608\) | 2.27747 | + | 3.94469i | 0.0923636 | + | 0.159978i | ||||
\(609\) | −7.33427 | + | 8.29150i | −0.297199 | + | 0.335988i | ||||
\(610\) | 8.37988 | 0.339291 | ||||||||
\(611\) | −6.01534 | + | 5.15788i | −0.243354 | + | 0.208666i | ||||
\(612\) | 0.670602 | − | 1.16152i | 0.0271075 | − | 0.0469515i | ||||
\(613\) | 17.9314 | 0.724241 | 0.362121 | − | 0.932131i | \(-0.382053\pi\) | ||||
0.362121 | + | 0.932131i | \(0.382053\pi\) | |||||||
\(614\) | 25.8986 | − | 44.8576i | 1.04518 | − | 1.81031i | ||||
\(615\) | 2.17533 | − | 3.76778i | 0.0877177 | − | 0.151932i | ||||
\(616\) | −1.79939 | − | 5.37609i | −0.0724997 | − | 0.216609i | ||||
\(617\) | −15.8059 | + | 27.3765i | −0.636320 | + | 1.10214i | 0.349914 | + | 0.936782i | \(0.386211\pi\) |
−0.986234 | + | 0.165356i | \(0.947123\pi\) | |||||||
\(618\) | 34.1675 | 1.37442 | ||||||||
\(619\) | 16.3184 | − | 28.2644i | 0.655894 | − | 1.13604i | −0.325775 | − | 0.945447i | \(-0.605625\pi\) |
0.981669 | − | 0.190594i | \(-0.0610413\pi\) | |||||||
\(620\) | −0.704676 | − | 1.22053i | −0.0283005 | − | 0.0490178i | ||||
\(621\) | 0.188350 | − | 0.326231i | 0.00755821 | − | 0.0130912i | ||||
\(622\) | −4.24592 | − | 7.35415i | −0.170246 | − | 0.294875i | ||||
\(623\) | 23.8100 | + | 4.84180i | 0.953929 | + | 0.193983i | ||||
\(624\) | 11.9269 | + | 4.19742i | 0.477459 | + | 0.168031i | ||||
\(625\) | −10.2824 | − | 17.8096i | −0.411294 | − | 0.712382i | ||||
\(626\) | −61.9264 | −2.47508 | ||||||||
\(627\) | −2.63623 | −0.105281 | ||||||||
\(628\) | −11.5768 | −0.461966 | ||||||||
\(629\) | 5.31319 | 0.211851 | ||||||||
\(630\) | −0.947844 | − | 2.83190i | −0.0377630 | − | 0.112825i | ||||
\(631\) | 12.7985 | − | 22.1676i | 0.509500 | − | 0.882480i | −0.490440 | − | 0.871475i | \(-0.663164\pi\) |
0.999939 | − | 0.0110045i | \(-0.00350290\pi\) | |||||||
\(632\) | 3.33440 | + | 5.77535i | 0.132635 | + | 0.229731i | ||||
\(633\) | 2.28300 | + | 3.95427i | 0.0907411 | + | 0.157168i | ||||
\(634\) | 23.6842 | 0.940619 | ||||||||
\(635\) | 1.29977 | − | 2.25126i | 0.0515797 | − | 0.0893387i | ||||
\(636\) | 20.1016 | 0.797080 | ||||||||
\(637\) | 18.6445 | + | 17.0112i | 0.738722 | + | 0.674010i | ||||
\(638\) | −40.3909 | −1.59909 | ||||||||
\(639\) | 2.88877 | − | 5.00350i | 0.114278 | − | 0.197935i | ||||
\(640\) | −1.99193 | −0.0787381 | ||||||||
\(641\) | −21.6208 | − | 37.4483i | −0.853969 | − | 1.47912i | −0.877598 | − | 0.479397i | \(-0.840855\pi\) |
0.0236292 | − | 0.999721i | \(-0.492478\pi\) | |||||||
\(642\) | 18.3613 | + | 31.8027i | 0.724662 | + | 1.25515i | ||||
\(643\) | 2.25709 | − | 3.90939i | 0.0890108 | − | 0.154171i | −0.818082 | − | 0.575101i | \(-0.804963\pi\) |
0.907093 | + | 0.420930i | \(0.138296\pi\) | |||||||
\(644\) | −0.702883 | − | 2.10002i | −0.0276975 | − | 0.0827524i | ||||
\(645\) | −0.820910 | −0.0323233 | ||||||||
\(646\) | −0.695926 | −0.0273808 | ||||||||
\(647\) | −11.4404 | −0.449769 | −0.224884 | − | 0.974385i | \(-0.572200\pi\) | ||||
−0.224884 | + | 0.974385i | \(0.572200\pi\) | |||||||
\(648\) | 0.456078 | 0.0179165 | ||||||||
\(649\) | −20.0534 | − | 34.7334i | −0.787163 | − | 1.36341i | ||||
\(650\) | 26.4232 | − | 22.6567i | 1.03640 | − | 0.888670i | ||||
\(651\) | −2.99367 | − | 0.608768i | −0.117331 | − | 0.0238595i | ||||
\(652\) | 4.63701 | + | 8.03153i | 0.181599 | + | 0.314539i | ||||
\(653\) | 10.8757 | − | 18.8373i | 0.425600 | − | 0.737162i | −0.570876 | − | 0.821036i | \(-0.693396\pi\) |
0.996476 | + | 0.0838748i | \(0.0267296\pi\) | |||||||
\(654\) | 10.4334 | + | 18.0713i | 0.407980 | + | 0.706642i | ||||
\(655\) | −0.981671 | + | 1.70030i | −0.0383571 | + | 0.0664364i | ||||
\(656\) | −27.7740 | −1.08439 | ||||||||
\(657\) | 7.24668 | − | 12.5516i | 0.282720 | − | 0.489685i | ||||
\(658\) | −3.79206 | − | 11.3296i | −0.147830 | − | 0.441675i | ||||
\(659\) | 3.28320 | − | 5.68668i | 0.127895 | − | 0.221521i | −0.794966 | − | 0.606655i | \(-0.792511\pi\) |
0.922861 | + | 0.385133i | \(0.125844\pi\) | |||||||
\(660\) | 2.86729 | − | 4.96628i | 0.111609 | − | 0.193312i | ||||
\(661\) | −46.1554 | −1.79524 | −0.897619 | − | 0.440772i | \(-0.854705\pi\) | ||||
−0.897619 | + | 0.440772i | \(0.854705\pi\) | |||||||
\(662\) | 1.16647 | − | 2.02038i | 0.0453360 | − | 0.0785243i | ||||
\(663\) | −1.65216 | + | 1.41665i | −0.0641644 | + | 0.0550181i | ||||
\(664\) | −6.78416 | −0.263276 | ||||||||
\(665\) | −0.540309 | + | 0.610828i | −0.0209523 | + | 0.0236869i | ||||
\(666\) | 9.04325 | + | 15.6634i | 0.350419 | + | 0.606943i | ||||
\(667\) | −1.57611 | −0.0610271 | ||||||||
\(668\) | −5.60680 | + | 9.71127i | −0.216934 | + | 0.375740i | ||||
\(669\) | −8.42312 | − | 14.5893i | −0.325657 | − | 0.564054i | ||||
\(670\) | −10.8343 | −0.418564 | ||||||||
\(671\) | 34.8809 | 1.34656 | ||||||||
\(672\) | −14.2299 | + | 16.0871i | −0.548929 | + | 0.620573i | ||||
\(673\) | −5.50174 | − | 9.52930i | −0.212077 | − | 0.367327i | 0.740288 | − | 0.672290i | \(-0.234689\pi\) |
−0.952364 | + | 0.304963i | \(0.901356\pi\) | |||||||
\(674\) | −23.9564 | + | 41.4937i | −0.922766 | + | 1.59828i | ||||
\(675\) | −2.34912 | + | 4.06880i | −0.0904177 | + | 0.156608i | ||||
\(676\) | 22.5189 | + | 18.0907i | 0.866112 | + | 0.695795i | ||||
\(677\) | −11.0575 | − | 19.1522i | −0.424976 | − | 0.736080i | 0.571442 | − | 0.820642i | \(-0.306384\pi\) |
−0.996418 | + | 0.0845623i | \(0.973051\pi\) | |||||||
\(678\) | 7.69512 | + | 13.3283i | 0.295529 | + | 0.511872i | ||||
\(679\) | −16.3357 | − | 3.32189i | −0.626907 | − | 0.127482i | ||||
\(680\) | 0.0756129 | − | 0.130965i | 0.00289962 | − | 0.00502229i | ||||
\(681\) | −14.2365 | − | 24.6583i | −0.545544 | − | 0.944909i | ||||
\(682\) | −5.57336 | − | 9.65334i | −0.213415 | − | 0.369645i | ||||
\(683\) | 4.23809 | + | 7.34059i | 0.162166 | + | 0.280880i | 0.935645 | − | 0.352942i | \(-0.114819\pi\) |
−0.773479 | + | 0.633822i | \(0.781485\pi\) | |||||||
\(684\) | −0.623383 | − | 1.07973i | −0.0238356 | − | 0.0412845i | ||||
\(685\) | 5.28933 | − | 9.16139i | 0.202095 | − | 0.350039i | ||||
\(686\) | −34.3425 | + | 16.3928i | −1.31120 | + | 0.625880i | ||||
\(687\) | 13.1373 | + | 22.7545i | 0.501219 | + | 0.868137i | ||||
\(688\) | 2.62028 | + | 4.53847i | 0.0998974 | + | 0.173027i | ||||
\(689\) | −30.7688 | − | 10.8284i | −1.17220 | − | 0.412529i | ||||
\(690\) | 0.212594 | − | 0.368223i | 0.00809331 | − | 0.0140180i | ||||
\(691\) | −0.959714 | + | 1.66227i | −0.0365092 | + | 0.0632359i | −0.883703 | − | 0.468049i | \(-0.844957\pi\) |
0.847193 | + | 0.531285i | \(0.178291\pi\) | |||||||
\(692\) | −3.04295 | − | 5.27055i | −0.115676 | − | 0.200356i | ||||
\(693\) | −3.94536 | − | 11.7876i | −0.149872 | − | 0.447776i | ||||
\(694\) | 5.21539 | 0.197973 | ||||||||
\(695\) | 5.30817 | 0.201350 | ||||||||
\(696\) | −0.954114 | − | 1.65257i | −0.0361656 | − | 0.0626406i | ||||
\(697\) | 2.39031 | − | 4.14014i | 0.0905395 | − | 0.156819i | ||||
\(698\) | 21.9592 | 0.831166 | ||||||||
\(699\) | 11.0974 | + | 19.2212i | 0.419742 | + | 0.727014i | ||||
\(700\) | 8.76645 | + | 26.1917i | 0.331341 | + | 0.989954i | ||||
\(701\) | −18.1080 | −0.683929 | −0.341965 | − | 0.939713i | \(-0.611092\pi\) | ||||
−0.341965 | + | 0.939713i | \(0.611092\pi\) | |||||||
\(702\) | −6.98834 | − | 2.45939i | −0.263758 | − | 0.0928238i | ||||
\(703\) | 2.46953 | − | 4.27736i | 0.0931403 | − | 0.161324i | ||||
\(704\) | −45.4143 | −1.71162 | ||||||||
\(705\) | 0.603622 | − | 1.04550i | 0.0227337 | − | 0.0393760i | ||||
\(706\) | −22.8494 | + | 39.5763i | −0.859948 | + | 1.48947i | ||||
\(707\) | −3.73175 | − | 11.1494i | −0.140347 | − | 0.419318i | ||||
\(708\) | 9.48394 | − | 16.4267i | 0.356428 | − | 0.617352i | ||||
\(709\) | −28.3768 | −1.06571 | −0.532857 | − | 0.846205i | \(-0.678882\pi\) | ||||
−0.532857 | + | 0.846205i | \(0.678882\pi\) | |||||||
\(710\) | 3.26061 | − | 5.64754i | 0.122368 | − | 0.211948i | ||||
\(711\) | 7.31102 | + | 12.6631i | 0.274185 | + | 0.474902i | ||||
\(712\) | −2.09421 | + | 3.62727i | −0.0784837 | + | 0.135938i | ||||
\(713\) | −0.217480 | − | 0.376686i | −0.00814468 | − | 0.0141070i | ||||
\(714\) | −1.04152 | − | 3.11176i | −0.0389778 | − | 0.116455i | ||||
\(715\) | −7.06411 | + | 6.05715i | −0.264183 | + | 0.226525i | ||||
\(716\) | 14.1046 | + | 24.4299i | 0.527115 | + | 0.912990i | ||||
\(717\) | −27.3213 | −1.02033 | ||||||||
\(718\) | −34.4433 | −1.28541 | ||||||||
\(719\) | 44.3482 | 1.65391 | 0.826955 | − | 0.562269i | \(-0.190071\pi\) | ||||
0.826955 | + | 0.562269i | \(0.190071\pi\) | |||||||
\(720\) | −1.92637 | −0.0717916 | ||||||||
\(721\) | 29.1489 | − | 32.9533i | 1.08556 | − | 1.22724i | ||||
\(722\) | 19.1966 | − | 33.2495i | 0.714423 | − | 1.23742i | ||||
\(723\) | −11.8915 | − | 20.5967i | −0.442251 | − | 0.766001i | ||||
\(724\) | −8.83998 | − | 15.3113i | −0.328535 | − | 0.569040i | ||||
\(725\) | 19.6574 | 0.730058 | ||||||||
\(726\) | 11.3766 | − | 19.7048i | 0.422225 | − | 0.731314i | ||||
\(727\) | 24.1298 | 0.894924 | 0.447462 | − | 0.894303i | \(-0.352328\pi\) | ||||
0.447462 | + | 0.894303i | \(0.352328\pi\) | |||||||
\(728\) | −3.80090 | + | 2.11704i | −0.140871 | + | 0.0784628i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 8.17946 | − | 14.1672i | 0.302735 | − | 0.524353i | ||||
\(731\) | −0.902038 | −0.0333631 | ||||||||
\(732\) | 8.24820 | + | 14.2863i | 0.304862 | + | 0.528037i | ||||
\(733\) | 16.7734 | + | 29.0524i | 0.619540 | + | 1.07308i | 0.989570 | + | 0.144055i | \(0.0460143\pi\) |
−0.370029 | + | 0.929020i | \(0.620652\pi\) | |||||||
\(734\) | 4.81009 | − | 8.33132i | 0.177544 | − | 0.307515i | ||||
\(735\) | −3.53988 | − | 1.50178i | −0.130570 | − | 0.0553940i | ||||
\(736\) | −3.05795 | −0.112717 | ||||||||
\(737\) | −45.0972 | −1.66118 | ||||||||
\(738\) | 16.2736 | 0.599040 | ||||||||
\(739\) | −16.8221 | −0.618811 | −0.309405 | − | 0.950930i | \(-0.600130\pi\) | ||||
−0.309405 | + | 0.950930i | \(0.600130\pi\) | |||||||
\(740\) | 5.37196 | + | 9.30451i | 0.197477 | + | 0.342041i | ||||
\(741\) | 0.372557 | + | 1.98851i | 0.0136862 | + | 0.0730498i | ||||
\(742\) | 32.5849 | − | 36.8377i | 1.19623 | − | 1.35236i | ||||
\(743\) | −16.5645 | − | 28.6906i | −0.607694 | − | 1.05256i | −0.991620 | − | 0.129192i | \(-0.958761\pi\) |
0.383926 | − | 0.923364i | \(-0.374572\pi\) | |||||||
\(744\) | 0.263308 | − | 0.456062i | 0.00965333 | − | 0.0167201i | ||||
\(745\) | −1.95695 | − | 3.38954i | −0.0716972 | − | 0.124183i | ||||
\(746\) | 6.94680 | − | 12.0322i | 0.254340 | − | 0.440530i | ||||
\(747\) | −14.8750 | −0.544247 | ||||||||
\(748\) | 3.15065 | − | 5.45709i | 0.115199 | − | 0.199531i | ||||
\(749\) | 46.3368 | + | 9.42265i | 1.69311 | + | 0.344296i | ||||
\(750\) | −5.47329 | + | 9.48002i | −0.199856 | + | 0.346161i | ||||
\(751\) | 14.8975 | − | 25.8032i | 0.543616 | − | 0.941571i | −0.455076 | − | 0.890453i | \(-0.650388\pi\) |
0.998693 | − | 0.0511187i | \(-0.0162787\pi\) | |||||||
\(752\) | −7.70687 | −0.281041 | ||||||||
\(753\) | −4.16795 | + | 7.21910i | −0.151889 | + | 0.263079i | ||||
\(754\) | 5.70811 | + | 30.4669i | 0.207877 | + | 1.10954i | ||||
\(755\) | −10.7969 | −0.392939 | ||||||||
\(756\) | 3.89496 | − | 4.40331i | 0.141658 | − | 0.160147i | ||||
\(757\) | −11.0742 | − | 19.1810i | −0.402498 | − | 0.697147i | 0.591529 | − | 0.806284i | \(-0.298525\pi\) |
−0.994027 | + | 0.109137i | \(0.965191\pi\) | |||||||
\(758\) | −39.5537 | −1.43665 | ||||||||
\(759\) | 0.884913 | − | 1.53271i | 0.0321203 | − | 0.0556340i | ||||
\(760\) | −0.0702887 | − | 0.121744i | −0.00254964 | − | 0.00441611i | ||||
\(761\) | 42.8934 | 1.55489 | 0.777443 | − | 0.628954i | \(-0.216517\pi\) | ||||
0.777443 | + | 0.628954i | \(0.216517\pi\) | |||||||
\(762\) | 9.72354 | 0.352247 | ||||||||
\(763\) | 26.3300 | + | 5.35424i | 0.953210 | + | 0.193837i | ||||
\(764\) | −3.42159 | − | 5.92637i | −0.123789 | − | 0.214408i | ||||
\(765\) | 0.165789 | − | 0.287155i | 0.00599412 | − | 0.0103821i | ||||
\(766\) | −13.8542 | + | 23.9961i | −0.500572 | + | 0.867016i | ||||
\(767\) | −23.3655 | + | 20.0349i | −0.843679 | + | 0.723417i | ||||
\(768\) | 5.94083 | + | 10.2898i | 0.214371 | + | 0.371302i | ||||
\(769\) | 25.5865 | + | 44.3171i | 0.922671 | + | 1.59811i | 0.795264 | + | 0.606263i | \(0.207332\pi\) |
0.127407 | + | 0.991850i | \(0.459334\pi\) | |||||||
\(770\) | −4.45320 | − | 13.3049i | −0.160482 | − | 0.479477i | ||||
\(771\) | −6.88712 | + | 11.9288i | −0.248034 | + | 0.429607i | ||||
\(772\) | 3.76817 | + | 6.52666i | 0.135619 | + | 0.234900i | ||||
\(773\) | 18.1625 | + | 31.4583i | 0.653259 | + | 1.13148i | 0.982327 | + | 0.187171i | \(0.0599319\pi\) |
−0.329069 | + | 0.944306i | \(0.606735\pi\) | |||||||
\(774\) | −1.53530 | − | 2.65922i | −0.0551853 | − | 0.0955838i | ||||
\(775\) | 2.71244 | + | 4.69808i | 0.0974336 | + | 0.168760i | ||||
\(776\) | 1.43680 | − | 2.48862i | 0.0515782 | − | 0.0893361i | ||||
\(777\) | 22.8217 | + | 4.64082i | 0.818723 | + | 0.166489i | ||||
\(778\) | 33.7449 | + | 58.4478i | 1.20981 | + | 2.09546i | ||||
\(779\) | −2.22200 | − | 3.84862i | −0.0796115 | − | 0.137891i | ||||
\(780\) | −4.15128 | − | 1.46095i | −0.148640 | − | 0.0523105i | ||||
\(781\) | 13.5721 | − | 23.5076i | 0.485650 | − | 0.841170i | ||||
\(782\) | 0.233604 | − | 0.404614i | 0.00835366 | − | 0.0144690i | ||||
\(783\) | −2.09200 | − | 3.62344i | −0.0747618 | − | 0.129491i | ||||
\(784\) | 2.99632 | + | 24.3641i | 0.107012 | + | 0.870146i | ||||
\(785\) | −2.86208 | −0.102152 | ||||||||
\(786\) | −7.34387 | −0.261947 | ||||||||
\(787\) | 27.1974 | + | 47.1072i | 0.969482 | + | 1.67919i | 0.697058 | + | 0.717015i | \(0.254492\pi\) |
0.272424 | + | 0.962177i | \(0.412175\pi\) | |||||||
\(788\) | 4.58087 | − | 7.93431i | 0.163187 | − | 0.282648i | ||||
\(789\) | 9.04564 | 0.322033 | ||||||||
\(790\) | 8.25208 | + | 14.2930i | 0.293596 | + | 0.508523i | ||||
\(791\) | 19.4195 | + | 3.94898i | 0.690478 | + | 0.140410i | ||||
\(792\) | 2.14277 | 0.0761399 | ||||||||
\(793\) | −4.92943 | − | 26.3107i | −0.175049 | − | 0.934320i | ||||
\(794\) | 27.3392 | − | 47.3529i | 0.970233 | − | 1.68049i | ||||
\(795\) | 4.96960 | 0.176254 | ||||||||
\(796\) | 1.27572 | − | 2.20962i | 0.0452168 | − | 0.0783178i | ||||
\(797\) | 15.9900 | − | 27.6955i | 0.566396 | − | 0.981026i | −0.430522 | − | 0.902580i | \(-0.641671\pi\) |
0.996918 | − | 0.0784465i | \(-0.0249960\pi\) | |||||||
\(798\) | −2.98920 | − | 0.607859i | −0.105817 | − | 0.0215180i | ||||
\(799\) | 0.663276 | − | 1.14883i | 0.0234650 | − | 0.0406426i | ||||
\(800\) | 38.1391 | 1.34842 | ||||||||
\(801\) | −4.59177 | + | 7.95317i | −0.162242 | + | 0.281012i | ||||
\(802\) | 23.7443 | + | 41.1263i | 0.838440 | + | 1.45222i | ||||
\(803\) | 34.0467 | − | 58.9705i | 1.20148 | − | 2.08103i | ||||
\(804\) | −10.6640 | − | 18.4706i | −0.376091 | − | 0.651408i | ||||
\(805\) | −0.173770 | − | 0.519176i | −0.00612458 | − | 0.0182986i | ||||
\(806\) | −6.49388 | + | 5.56821i | −0.228737 | + | 0.196132i | ||||
\(807\) | 1.14428 | + | 1.98196i | 0.0402806 | + | 0.0697681i | ||||
\(808\) | 2.02675 | 0.0713010 | ||||||||
\(809\) | −0.0847866 | −0.00298094 | −0.00149047 | − | 0.999999i | \(-0.500474\pi\) | ||||
−0.00149047 | + | 0.999999i | \(0.500474\pi\) | |||||||
\(810\) | 1.12872 | 0.0396591 | ||||||||
\(811\) | 2.81654 | 0.0989019 | 0.0494510 | − | 0.998777i | \(-0.484253\pi\) | ||||
0.0494510 | + | 0.998777i | \(0.484253\pi\) | |||||||
\(812\) | −24.1034 | − | 4.90146i | −0.845863 | − | 0.172007i | ||||
\(813\) | 1.99057 | − | 3.44778i | 0.0698125 | − | 0.120919i | ||||
\(814\) | 42.4874 | + | 73.5903i | 1.48918 | + | 2.57934i | ||||
\(815\) | 1.14638 | + | 1.98559i | 0.0401560 | + | 0.0695522i | ||||
\(816\) | −2.11675 | −0.0741010 | ||||||||
\(817\) | −0.419261 | + | 0.726182i | −0.0146681 | + | 0.0254059i | ||||
\(818\) | −14.8793 | −0.520244 | ||||||||
\(819\) | −8.33387 | + | 4.64184i | −0.291209 | + | 0.162199i | ||||
\(820\) | 9.66701 | 0.337586 | ||||||||
\(821\) | −8.35156 | + | 14.4653i | −0.291471 | + | 0.504843i | −0.974158 | − | 0.225868i | \(-0.927478\pi\) |
0.682687 | + | 0.730711i | \(0.260811\pi\) | |||||||
\(822\) | 39.5694 | 1.38014 | ||||||||
\(823\) | 13.1869 | + | 22.8405i | 0.459668 | + | 0.796168i | 0.998943 | − | 0.0459612i | \(-0.0146351\pi\) |
−0.539275 | + | 0.842130i | \(0.681302\pi\) | |||||||
\(824\) | 3.79198 | + | 6.56790i | 0.132100 | + | 0.228804i | ||||
\(825\) | −11.0367 | + | 19.1162i | −0.384250 | + | 0.665541i | ||||
\(826\) | −14.7296 | − | 44.0079i | −0.512507 | − | 1.53123i | ||||
\(827\) | −36.8372 | −1.28095 | −0.640477 | − | 0.767977i | \(-0.721263\pi\) | ||||
−0.640477 | + | 0.767977i | \(0.721263\pi\) | |||||||
\(828\) | 0.837013 | 0.0290882 | ||||||||
\(829\) | 24.8055 | 0.861530 | 0.430765 | − | 0.902464i | \(-0.358244\pi\) | ||||
0.430765 | + | 0.902464i | \(0.358244\pi\) | |||||||
\(830\) | −16.7897 | −0.582778 | ||||||||
\(831\) | −4.19999 | − | 7.27460i | −0.145696 | − | 0.252353i | ||||
\(832\) | 6.41803 | + | 34.2561i | 0.222505 | + | 1.18762i | ||||
\(833\) | −3.88971 | − | 1.65020i | −0.134771 | − | 0.0571759i | ||||
\(834\) | 9.92758 | + | 17.1951i | 0.343764 | + | 0.595417i | ||||
\(835\) | −1.38614 | + | 2.40086i | −0.0479693 | + | 0.0830853i | ||||
\(836\) | −2.92880 | − | 5.07284i | −0.101295 | − | 0.175448i | ||||
\(837\) | 0.577330 | − | 0.999965i | 0.0199554 | − | 0.0345638i | ||||
\(838\) | 72.1420 | 2.49211 | ||||||||
\(839\) | −11.4460 | + | 19.8250i | −0.395159 | + | 0.684435i | −0.993121 | − | 0.117089i | \(-0.962644\pi\) |
0.597963 | + | 0.801524i | \(0.295977\pi\) | |||||||
\(840\) | 0.439171 | − | 0.496490i | 0.0151529 | − | 0.0171305i | ||||
\(841\) | 5.74711 | − | 9.95429i | 0.198176 | − | 0.343251i | ||||
\(842\) | −25.9649 | + | 44.9725i | −0.894808 | + | 1.54985i | ||||
\(843\) | 12.9559 | 0.446225 | ||||||||
\(844\) | −5.07274 | + | 8.78625i | −0.174611 | + | 0.302435i | ||||
\(845\) | 5.56723 | + | 4.47245i | 0.191518 | + | 0.153857i | ||||
\(846\) | 4.51569 | 0.155253 | ||||||||
\(847\) | −9.29899 | − | 27.7828i | −0.319517 | − | 0.954628i | ||||
\(848\) | −15.8626 | − | 27.4749i | −0.544724 | − | 0.943490i | ||||
\(849\) | −25.6051 | −0.878765 | ||||||||
\(850\) | −2.91354 | + | 5.04639i | −0.0999335 | + | 0.173090i | ||||
\(851\) | 1.65792 | + | 2.87159i | 0.0568326 | + | 0.0984370i | ||||
\(852\) | 12.8375 | 0.439805 | ||||||||
\(853\) | 0.727097 | 0.0248953 | 0.0124477 | − | 0.999923i | \(-0.496038\pi\) | ||||
0.0124477 | + | 0.999923i | \(0.496038\pi\) | |||||||
\(854\) | 39.5512 | + | 8.04279i | 1.35341 | + | 0.275219i | ||||
\(855\) | −0.154115 | − | 0.266936i | −0.00527064 | − | 0.00912901i | ||||
\(856\) | −4.07554 | + | 7.05904i | −0.139299 | + | 0.241273i | ||||
\(857\) | 6.16106 | − | 10.6713i | 0.210458 | − | 0.364524i | −0.741400 | − | 0.671063i | \(-0.765838\pi\) |
0.951858 | + | 0.306540i | \(0.0991712\pi\) | |||||||
\(858\) | −32.8329 | − | 11.5548i | −1.12090 | − | 0.394475i | ||||
\(859\) | −17.1581 | − | 29.7187i | −0.585427 | − | 1.01399i | −0.994822 | − | 0.101632i | \(-0.967594\pi\) |
0.409395 | − | 0.912357i | \(-0.365740\pi\) | |||||||
\(860\) | −0.912016 | − | 1.57966i | −0.0310995 | − | 0.0538659i | ||||
\(861\) | 13.8833 | − | 15.6953i | 0.473141 | − | 0.534894i | ||||
\(862\) | −18.0502 | + | 31.2639i | −0.614793 | + | 1.06485i | ||||
\(863\) | 17.8997 | + | 31.0032i | 0.609313 | + | 1.05536i | 0.991354 | + | 0.131216i | \(0.0418881\pi\) |
−0.382041 | + | 0.924146i | \(0.624779\pi\) | |||||||
\(864\) | −4.05887 | − | 7.03016i | −0.138085 | − | 0.239171i | ||||
\(865\) | −0.752292 | − | 1.30301i | −0.0255787 | − | 0.0443036i | ||||
\(866\) | −6.20554 | − | 10.7483i | −0.210873 | − | 0.365242i | ||||
\(867\) | −8.31783 | + | 14.4069i | −0.282488 | + | 0.489284i | ||||
\(868\) | −2.15448 | − | 6.43699i | −0.0731278 | − | 0.218486i | ||||
\(869\) | 34.3489 | + | 59.4941i | 1.16521 | + | 2.01820i | ||||
\(870\) | −2.36127 | − | 4.08985i | −0.0800547 | − | 0.138659i | ||||
\(871\) | 6.37321 | + | 34.0168i | 0.215948 | + | 1.15262i | ||||
\(872\) | −2.31585 | + | 4.01117i | −0.0784245 | + | 0.135835i | ||||
\(873\) | 3.15034 | − | 5.45655i | 0.106623 | − | 0.184676i | ||||
\(874\) | −0.217155 | − | 0.376124i | −0.00734538 | − | 0.0127226i | ||||
\(875\) | 4.47376 | + | 13.3664i | 0.151241 | + | 0.451865i | ||||
\(876\) | 32.2037 | 1.08806 | ||||||||
\(877\) | 29.8080 | 1.00654 | 0.503272 | − | 0.864128i | \(-0.332129\pi\) | ||||
0.503272 | + | 0.864128i | \(0.332129\pi\) | |||||||
\(878\) | −25.5367 | − | 44.2308i | −0.861821 | − | 1.49272i | ||||
\(879\) | 12.3943 | − | 21.4675i | 0.418048 | − | 0.724081i | ||||
\(880\) | −9.05056 | −0.305094 | ||||||||
\(881\) | 11.3524 | + | 19.6629i | 0.382470 | + | 0.662458i | 0.991415 | − | 0.130755i | \(-0.0417400\pi\) |
−0.608944 | + | 0.793213i | \(0.708407\pi\) | |||||||
\(882\) | −1.75564 | − | 14.2756i | −0.0591153 | − | 0.480686i | ||||
\(883\) | 51.4418 | 1.73115 | 0.865577 | − | 0.500776i | \(-0.166952\pi\) | ||||
0.865577 | + | 0.500776i | \(0.166952\pi\) | |||||||
\(884\) | −4.56154 | − | 1.60533i | −0.153421 | − | 0.0539932i | ||||
\(885\) | 2.34466 | − | 4.06107i | 0.0788149 | − | 0.136511i | ||||
\(886\) | −64.9683 | −2.18265 | ||||||||
\(887\) | −7.40385 | + | 12.8238i | −0.248597 | + | 0.430583i | −0.963137 | − | 0.269012i | \(-0.913303\pi\) |
0.714540 | + | 0.699595i | \(0.246636\pi\) | |||||||
\(888\) | −2.00728 | + | 3.47670i | −0.0673598 | + | 0.116671i | ||||
\(889\) | 8.29532 | − | 9.37799i | 0.278216 | − | 0.314528i | ||||
\(890\) | −5.18281 | + | 8.97689i | −0.173728 | + | 0.300906i | ||||
\(891\) | 4.69824 | 0.157397 | ||||||||
\(892\) | 18.7159 | − | 32.4169i | 0.626654 | − | 1.08540i | ||||
\(893\) | −0.616573 | − | 1.06794i | −0.0206328 | − | 0.0357371i | ||||
\(894\) | 7.31997 | − | 12.6786i | 0.244817 | − | 0.424035i | ||||
\(895\) | 3.48701 | + | 6.03968i | 0.116558 | + | 0.201884i | ||||
\(896\) | −9.40150 | − | 1.91181i | −0.314082 | − | 0.0638690i | ||||
\(897\) | −1.28118 | − | 0.450885i | −0.0427775 | − | 0.0150546i | ||||
\(898\) | −5.41186 | − | 9.37361i | −0.180596 | − | 0.312801i | ||||
\(899\) | −4.83108 | −0.161126 | ||||||||
\(900\) | −10.4393 | −0.347978 | ||||||||
\(901\) | 5.46073 | 0.181923 | ||||||||
\(902\) | 76.4574 | 2.54575 | ||||||||
\(903\) | −3.87451 | − | 0.787888i | −0.128936 | − | 0.0262193i | ||||
\(904\) | −1.70804 | + | 2.95841i | −0.0568085 | + | 0.0983952i | ||||
\(905\) | −2.18546 | − | 3.78533i | −0.0726471 | − | 0.125829i | ||||
\(906\) | −20.1929 | − | 34.9751i | −0.670863 | − | 1.16197i | ||||
\(907\) | −2.22350 | −0.0738303 | −0.0369151 | − | 0.999318i | \(-0.511753\pi\) | ||||
−0.0369151 | + | 0.999318i | \(0.511753\pi\) | |||||||
\(908\) | 31.6330 | − | 54.7899i | 1.04978 | − | 1.81827i | ||||
\(909\) | 4.44387 | 0.147394 | ||||||||
\(910\) | −9.40659 | + | 5.23933i | −0.311825 | + | 0.173682i | ||||
\(911\) | −29.3786 | −0.973355 | −0.486678 | − | 0.873582i | \(-0.661791\pi\) | ||||
−0.486678 | + | 0.873582i | \(0.661791\pi\) | |||||||
\(912\) | −0.983851 | + | 1.70408i | −0.0325786 | + | 0.0564277i | ||||
\(913\) | −69.8863 | −2.31290 | ||||||||
\(914\) | 18.9956 | + | 32.9013i | 0.628317 | + | 1.08828i | ||||
\(915\) | 2.03916 | + | 3.53192i | 0.0674124 | + | 0.116762i | ||||
\(916\) | −29.1906 | + | 50.5596i | −0.964484 | + | 1.67054i | ||||
\(917\) | −6.26518 | + | 7.08288i | −0.206895 | + | 0.233897i | ||||
\(918\) | 1.24027 | 0.0409349 | ||||||||
\(919\) | −21.6911 | −0.715522 | −0.357761 | − | 0.933813i | \(-0.616460\pi\) | ||||
−0.357761 | + | 0.933813i | \(0.616460\pi\) | |||||||
\(920\) | 0.0943763 | 0.00311149 | ||||||||
\(921\) | 25.2086 | 0.830651 | ||||||||
\(922\) | 9.84429 | + | 17.0508i | 0.324204 | + | 0.561538i | ||||
\(923\) | −19.6499 | − | 6.91534i | −0.646784 | − | 0.227621i | ||||
\(924\) | 18.2995 | − | 20.6878i | 0.602008 | − | 0.680580i | ||||
\(925\) | −20.6777 | − | 35.8149i | −0.679880 | − | 1.17759i | ||||
\(926\) | −2.28259 | + | 3.95357i | −0.0750107 | + | 0.129922i | ||||
\(927\) | 8.31431 | + | 14.4008i | 0.273078 | + | 0.472985i | ||||
\(928\) | −16.9823 | + | 29.4141i | −0.557470 | + | 0.965566i | ||||
\(929\) | −31.1231 | −1.02111 | −0.510557 | − | 0.859844i | \(-0.670561\pi\) | ||||
−0.510557 | + | 0.859844i | \(0.670561\pi\) | |||||||
\(930\) | 0.651643 | − | 1.12868i | 0.0213682 | − | 0.0370108i | ||||
\(931\) | −3.13640 | + | 2.36440i | −0.102791 | + | 0.0774900i | ||||
\(932\) | −24.6580 | + | 42.7089i | −0.807699 | + | 1.39898i | ||||
\(933\) | 2.06640 | − | 3.57911i | 0.0676510 | − | 0.117175i | ||||
\(934\) | −27.7937 | −0.909439 | ||||||||
\(935\) | 0.778918 | − | 1.34913i | 0.0254733 | − | 0.0441211i | ||||
\(936\) | −0.302820 | − | 1.61629i | −0.00989797 | − | 0.0528301i | ||||
\(937\) | 13.1250 | 0.428777 | 0.214388 | − | 0.976749i | \(-0.431224\pi\) | ||||
0.214388 | + | 0.976749i | \(0.431224\pi\) | |||||||
\(938\) | −51.1354 | − | 10.3984i | −1.66963 | − | 0.339521i | ||||
\(939\) | −15.0691 | − | 26.1005i | −0.491763 | − | 0.851758i | ||||
\(940\) | 2.68245 | 0.0874920 | ||||||||
\(941\) | −23.5806 | + | 40.8428i | −0.768705 | + | 1.33144i | 0.169560 | + | 0.985520i | \(0.445765\pi\) |
−0.938265 | + | 0.345917i | \(0.887568\pi\) | |||||||
\(942\) | −5.35279 | − | 9.27131i | −0.174403 | − | 0.302076i | ||||
\(943\) | 2.98347 | 0.0971551 | ||||||||
\(944\) | −29.9360 | −0.974333 | ||||||||
\(945\) | 0.962929 | − | 1.08861i | 0.0313241 | − | 0.0354124i | ||||
\(946\) | −7.21323 | − | 12.4937i | −0.234522 | − | 0.406204i | ||||
\(947\) | −2.15742 | + | 3.73676i | −0.0701068 | + | 0.121429i | −0.898948 | − | 0.438055i | \(-0.855667\pi\) |
0.828841 | + | 0.559484i | \(0.189001\pi\) | |||||||
\(948\) | −16.2448 | + | 28.1369i | −0.527607 | + | 0.913843i | ||||
\(949\) | −49.2931 | − | 17.3476i | −1.60012 | − | 0.563127i | ||||
\(950\) | 2.70839 | + | 4.69106i | 0.0878716 | + | 0.152198i | ||||
\(951\) | 5.76330 | + | 9.98233i | 0.186888 | + | 0.323699i | ||||
\(952\) | 0.482573 | − | 0.545556i | 0.0156403 | − | 0.0176816i | ||||
\(953\) | −5.09812 | + | 8.83020i | −0.165144 | + | 0.286038i | −0.936707 | − | 0.350116i | \(-0.886142\pi\) |
0.771562 | + | 0.636154i | \(0.219476\pi\) | |||||||
\(954\) | 9.29438 | + | 16.0983i | 0.300917 | + | 0.521203i | ||||
\(955\) | −0.845901 | − | 1.46514i | −0.0273727 | − | 0.0474109i | ||||
\(956\) | −30.3534 | − | 52.5737i | −0.981700 | − | 1.70035i | ||||
\(957\) | −9.82870 | − | 17.0238i | −0.317717 | − | 0.550302i | ||||
\(958\) | 14.9864 | − | 25.9571i | 0.484187 | − | 0.838637i | ||||
\(959\) | 33.7573 | − | 38.1632i | 1.09008 | − | 1.23235i | ||||
\(960\) | −2.65495 | − | 4.59850i | −0.0856881 | − | 0.148416i | ||||
\(961\) | 14.8334 | + | 25.6922i | 0.478496 | + | 0.828780i | ||||
\(962\) | 49.5049 | − | 42.4482i | 1.59610 | − | 1.36858i | ||||
\(963\) | −8.93605 | + | 15.4777i | −0.287960 | + | 0.498762i | ||||
\(964\) | 26.4226 | − | 45.7652i | 0.851013 | − | 1.47400i | ||||
\(965\) | 0.931584 | + | 1.61355i | 0.0299887 | + | 0.0519420i | ||||
\(966\) | 1.35681 | − | 1.53389i | 0.0436546 | − | 0.0493521i | ||||
\(967\) | 14.3246 | 0.460649 | 0.230324 | − | 0.973114i | \(-0.426021\pi\) | ||||
0.230324 | + | 0.973114i | \(0.426021\pi\) | |||||||
\(968\) | 5.05038 | 0.162325 | ||||||||
\(969\) | −0.169346 | − | 0.293316i | −0.00544018 | − | 0.00942268i | ||||
\(970\) | 3.55585 | − | 6.15891i | 0.114171 | − | 0.197751i | ||||
\(971\) | −17.0859 | −0.548312 | −0.274156 | − | 0.961685i | \(-0.588398\pi\) | ||||
−0.274156 | + | 0.961685i | \(0.588398\pi\) | |||||||
\(972\) | 1.11098 | + | 1.92428i | 0.0356348 | + | 0.0617212i | ||||
\(973\) | 25.0534 | + | 5.09464i | 0.803175 | + | 0.163327i | ||||
\(974\) | −3.08469 | −0.0988400 | ||||||||
\(975\) | 15.9791 | + | 5.62349i | 0.511741 | + | 0.180096i | ||||
\(976\) | 13.0177 | − | 22.5473i | 0.416686 | − | 0.721721i | ||||
\(977\) | −50.0570 | −1.60147 | −0.800733 | − | 0.599021i | \(-0.795557\pi\) | ||||
−0.800733 | + | 0.599021i | \(0.795557\pi\) | |||||||
\(978\) | −4.28803 | + | 7.42709i | −0.137116 | + | 0.237492i | ||||
\(979\) | −21.5732 | + | 37.3659i | −0.689484 | + | 1.19422i | ||||
\(980\) | −1.04290 | − | 8.48016i | −0.0333142 | − | 0.270889i | ||||
\(981\) | −5.07774 | + | 8.79490i | −0.162120 | + | 0.280800i | ||||
\(982\) | −58.3465 | −1.86191 | ||||||||
\(983\) | 20.6067 | − | 35.6919i | 0.657252 | − | 1.13839i | −0.324072 | − | 0.946032i | \(-0.605052\pi\) |
0.981324 | − | 0.192362i | \(-0.0616147\pi\) | |||||||
\(984\) | 1.80608 | + | 3.12822i | 0.0575756 | + | 0.0997239i | ||||
\(985\) | 1.13250 | − | 1.96155i | 0.0360846 | − | 0.0625003i | ||||
\(986\) | −2.59463 | − | 4.49403i | −0.0826299 | − | 0.143119i | ||||
\(987\) | 3.85241 | − | 4.35521i | 0.122624 | − | 0.138628i | ||||
\(988\) | −3.41254 | + | 2.92610i | −0.108567 | + | 0.0930917i | ||||
\(989\) | −0.281470 | − | 0.487520i | −0.00895022 | − | 0.0155022i | ||||
\(990\) | 5.30299 | 0.168540 | ||||||||
\(991\) | 10.0248 | 0.318449 | 0.159225 | − | 0.987242i | \(-0.449101\pi\) | ||||
0.159225 | + | 0.987242i | \(0.449101\pi\) | |||||||
\(992\) | −9.37322 | −0.297600 | ||||||||
\(993\) | 1.13539 | 0.0360305 | ||||||||
\(994\) | 20.8097 | − | 23.5257i | 0.660044 | − | 0.746190i | ||||
\(995\) | 0.315390 | − | 0.546271i | 0.00999853 | − | 0.0173180i | ||||
\(996\) | −16.5258 | − | 28.6236i | −0.523641 | − | 0.906973i | ||||
\(997\) | 21.9259 | + | 37.9768i | 0.694401 | + | 1.20274i | 0.970382 | + | 0.241574i | \(0.0776638\pi\) |
−0.275982 | + | 0.961163i | \(0.589003\pi\) | |||||||
\(998\) | 43.3835 | 1.37328 | ||||||||
\(999\) | −4.40116 | + | 7.62304i | −0.139247 | + | 0.241182i |
(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 | 273.2.j.b.172.2 | yes | 16 | |
3.2 | odd | 2 | 819.2.n.e.172.7 | 16 | |||
7.2 | even | 3 | 273.2.l.b.16.7 | yes | 16 | ||
13.9 | even | 3 | 273.2.l.b.256.7 | yes | 16 | ||
21.2 | odd | 6 | 819.2.s.e.289.2 | 16 | |||
39.35 | odd | 6 | 819.2.s.e.802.2 | 16 | |||
91.9 | even | 3 | inner | 273.2.j.b.100.2 | ✓ | 16 | |
273.191 | odd | 6 | 819.2.n.e.100.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.j.b.100.2 | ✓ | 16 | 91.9 | even | 3 | inner | |
273.2.j.b.172.2 | yes | 16 | 1.1 | even | 1 | trivial | |
273.2.l.b.16.7 | yes | 16 | 7.2 | even | 3 | ||
273.2.l.b.256.7 | yes | 16 | 13.9 | even | 3 | ||
819.2.n.e.100.7 | 16 | 273.191 | odd | 6 | |||
819.2.n.e.172.7 | 16 | 3.2 | odd | 2 | |||
819.2.s.e.289.2 | 16 | 21.2 | odd | 6 | |||
819.2.s.e.802.2 | 16 | 39.35 | odd | 6 |