Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [61,2,Mod(13,61)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(61, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("61.13");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 61.c (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: | \(0.487087452330\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.310217769.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 4x^{6} - 2x^{5} + 15x^{4} - 4x^{3} + 5x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 13.3 | ||
Root | \(-0.198169 + 0.343239i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 61.13 |
Dual form | 61.2.c.a.47.3 |
$q$-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 \(\left(\mathbb{Z}/61\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.198169 | − | 0.343239i | 0.140127 | − | 0.242707i | −0.787417 | − | 0.616420i | \(-0.788582\pi\) |
0.927544 | + | 0.373713i | \(0.121916\pi\) | |||||||
\(3\) | −0.716159 | −0.413474 | −0.206737 | − | 0.978397i | \(-0.566285\pi\) | ||||
−0.206737 | + | 0.978397i | \(0.566285\pi\) | |||||||
\(4\) | 0.921458 | + | 1.59601i | 0.460729 | + | 0.798006i | ||||
\(5\) | 1.82493 | − | 3.16087i | 0.816132 | − | 1.41358i | −0.0923805 | − | 0.995724i | \(-0.529448\pi\) |
0.908512 | − | 0.417858i | \(-0.137219\pi\) | |||||||
\(6\) | −0.141921 | + | 0.245814i | −0.0579389 | + | 0.100353i | ||||
\(7\) | −1.26155 | + | 2.18506i | −0.476820 | + | 0.825877i | −0.999647 | − | 0.0265620i | \(-0.991544\pi\) |
0.522827 | + | 0.852439i | \(0.324877\pi\) | |||||||
\(8\) | 1.52310 | 0.538496 | ||||||||
\(9\) | −2.48712 | −0.829039 | ||||||||
\(10\) | −0.723289 | − | 1.25277i | −0.228724 | − | 0.396161i | ||||
\(11\) | −4.36601 | −1.31640 | −0.658201 | − | 0.752842i | \(-0.728682\pi\) | ||||
−0.658201 | + | 0.752842i | \(0.728682\pi\) | |||||||
\(12\) | −0.659910 | − | 1.14300i | −0.190500 | − | 0.329955i | ||||
\(13\) | 0.443751 | − | 0.768600i | 0.123074 | − | 0.213171i | −0.797904 | − | 0.602784i | \(-0.794058\pi\) |
0.920979 | + | 0.389613i | \(0.127391\pi\) | |||||||
\(14\) | 0.500000 | + | 0.866025i | 0.133631 | + | 0.231455i | ||||
\(15\) | −1.30694 | + | 2.26368i | −0.337450 | + | 0.584480i | ||||
\(16\) | −1.54109 | + | 2.66924i | −0.385271 | + | 0.667309i | ||||
\(17\) | 2.14475 | + | 3.71481i | 0.520177 | + | 0.900974i | 0.999725 | + | 0.0234578i | \(0.00746752\pi\) |
−0.479547 | + | 0.877516i | \(0.659199\pi\) | |||||||
\(18\) | −0.492870 | + | 0.853676i | −0.116171 | + | 0.201213i | ||||
\(19\) | −2.69014 | − | 4.65945i | −0.617159 | − | 1.06895i | −0.990002 | − | 0.141057i | \(-0.954950\pi\) |
0.372842 | − | 0.927895i | \(-0.378383\pi\) | |||||||
\(20\) | 6.72637 | 1.50406 | ||||||||
\(21\) | 0.903468 | − | 1.56485i | 0.197153 | − | 0.341479i | ||||
\(22\) | −0.865209 | + | 1.49859i | −0.184463 | + | 0.319500i | ||||
\(23\) | 4.92509 | 1.02695 | 0.513476 | − | 0.858104i | \(-0.328358\pi\) | ||||
0.513476 | + | 0.858104i | \(0.328358\pi\) | |||||||
\(24\) | −1.09078 | −0.222654 | ||||||||
\(25\) | −4.16071 | − | 7.20656i | −0.832142 | − | 1.44131i | ||||
\(26\) | −0.175876 | − | 0.304626i | −0.0344921 | − | 0.0597420i | ||||
\(27\) | 3.92965 | 0.756261 | ||||||||
\(28\) | −4.64985 | −0.878740 | ||||||||
\(29\) | −3.71413 | − | 6.43307i | −0.689698 | − | 1.19459i | −0.971936 | − | 0.235247i | \(-0.924410\pi\) |
0.282238 | − | 0.959344i | \(-0.408923\pi\) | |||||||
\(30\) | 0.517989 | + | 0.897184i | 0.0945715 | + | 0.163803i | ||||
\(31\) | 3.66502 | + | 6.34799i | 0.658256 | + | 1.14013i | 0.981067 | + | 0.193670i | \(0.0620390\pi\) |
−0.322810 | + | 0.946464i | \(0.604628\pi\) | |||||||
\(32\) | 2.13389 | + | 3.69600i | 0.377221 | + | 0.653367i | ||||
\(33\) | 3.12676 | 0.544299 | ||||||||
\(34\) | 1.70009 | 0.291563 | ||||||||
\(35\) | 4.60446 | + | 7.97516i | 0.778296 | + | 1.34805i | ||||
\(36\) | −2.29177 | − | 3.96947i | −0.381962 | − | 0.661578i | ||||
\(37\) | 5.30716 | 0.872492 | 0.436246 | − | 0.899827i | \(-0.356308\pi\) | ||||
0.436246 | + | 0.899827i | \(0.356308\pi\) | |||||||
\(38\) | −2.13241 | −0.345922 | ||||||||
\(39\) | −0.317796 | + | 0.550440i | −0.0508882 | + | 0.0881409i | ||||
\(40\) | 2.77954 | − | 4.81430i | 0.439483 | − | 0.761208i | ||||
\(41\) | 0.964021 | 0.150555 | 0.0752774 | − | 0.997163i | \(-0.476016\pi\) | ||||
0.0752774 | + | 0.997163i | \(0.476016\pi\) | |||||||
\(42\) | −0.358079 | − | 0.620212i | −0.0552528 | − | 0.0957007i | ||||
\(43\) | −0.230419 | + | 0.399097i | −0.0351385 | + | 0.0608617i | −0.883060 | − | 0.469260i | \(-0.844521\pi\) |
0.847921 | + | 0.530122i | \(0.177854\pi\) | |||||||
\(44\) | −4.02310 | − | 6.96821i | −0.606504 | − | 1.05050i | ||||
\(45\) | −4.53880 | + | 7.86144i | −0.676605 | + | 1.17191i | ||||
\(46\) | 0.976001 | − | 1.69048i | 0.143903 | − | 0.249248i | ||||
\(47\) | −2.23755 | − | 3.87555i | −0.326380 | − | 0.565307i | 0.655411 | − | 0.755273i | \(-0.272496\pi\) |
−0.981791 | + | 0.189966i | \(0.939162\pi\) | |||||||
\(48\) | 1.10366 | − | 1.91160i | 0.159300 | − | 0.275915i | ||||
\(49\) | 0.316994 | + | 0.549050i | 0.0452849 | + | 0.0784358i | ||||
\(50\) | −3.29810 | −0.466422 | ||||||||
\(51\) | −1.53598 | − | 2.66039i | −0.215080 | − | 0.372530i | ||||
\(52\) | 1.63559 | 0.226816 | ||||||||
\(53\) | −0.555027 | −0.0762388 | −0.0381194 | − | 0.999273i | \(-0.512137\pi\) | ||||
−0.0381194 | + | 0.999273i | \(0.512137\pi\) | |||||||
\(54\) | 0.778735 | − | 1.34881i | 0.105972 | − | 0.183550i | ||||
\(55\) | −7.96765 | + | 13.8004i | −1.07436 | + | 1.86084i | ||||
\(56\) | −1.92146 | + | 3.32806i | −0.256766 | + | 0.444731i | ||||
\(57\) | 1.92656 | + | 3.33691i | 0.255180 | + | 0.441984i | ||||
\(58\) | −2.94411 | −0.386581 | ||||||||
\(59\) | 1.91715 | − | 3.32061i | 0.249592 | − | 0.432306i | −0.713821 | − | 0.700329i | \(-0.753037\pi\) |
0.963413 | + | 0.268022i | \(0.0863701\pi\) | |||||||
\(60\) | −4.81715 | −0.621891 | ||||||||
\(61\) | −1.48882 | + | 7.66703i | −0.190624 | + | 0.981663i | ||||
\(62\) | 2.90517 | 0.368958 | ||||||||
\(63\) | 3.13762 | − | 5.43451i | 0.395303 | − | 0.684684i | ||||
\(64\) | −4.47286 | −0.559107 | ||||||||
\(65\) | −1.61963 | − | 2.80528i | −0.200890 | − | 0.347952i | ||||
\(66\) | 0.619627 | − | 1.07323i | 0.0762708 | − | 0.132105i | ||||
\(67\) | 1.15586 | − | 2.00201i | 0.141211 | − | 0.244585i | −0.786742 | − | 0.617282i | \(-0.788234\pi\) |
0.927953 | + | 0.372697i | \(0.121567\pi\) | |||||||
\(68\) | −3.95259 | + | 6.84608i | −0.479322 | + | 0.830209i | ||||
\(69\) | −3.52714 | −0.424618 | ||||||||
\(70\) | 3.64985 | 0.436241 | ||||||||
\(71\) | −1.47600 | − | 2.55651i | −0.175169 | − | 0.303402i | 0.765051 | − | 0.643970i | \(-0.222714\pi\) |
−0.940220 | + | 0.340568i | \(0.889381\pi\) | |||||||
\(72\) | −3.78812 | −0.446434 | ||||||||
\(73\) | −5.96254 | − | 10.3274i | −0.697863 | − | 1.20873i | −0.969206 | − | 0.246251i | \(-0.920801\pi\) |
0.271343 | − | 0.962483i | \(-0.412532\pi\) | |||||||
\(74\) | 1.05172 | − | 1.82163i | 0.122260 | − | 0.211760i | ||||
\(75\) | 2.97973 | + | 5.16104i | 0.344070 | + | 0.595946i | ||||
\(76\) | 4.95769 | − | 8.58698i | 0.568686 | − | 0.984994i | ||||
\(77\) | 5.50793 | − | 9.54002i | 0.627687 | − | 1.08719i | ||||
\(78\) | 0.125955 | + | 0.218160i | 0.0142616 | + | 0.0247018i | ||||
\(79\) | −1.20903 | + | 2.09410i | −0.136026 | + | 0.235605i | −0.925989 | − | 0.377550i | \(-0.876767\pi\) |
0.789963 | + | 0.613155i | \(0.210100\pi\) | |||||||
\(80\) | 5.62473 | + | 9.74232i | 0.628864 | + | 1.08922i | ||||
\(81\) | 4.64710 | 0.516344 | ||||||||
\(82\) | 0.191039 | − | 0.330890i | 0.0210968 | − | 0.0365407i | ||||
\(83\) | 0.751592 | − | 1.30180i | 0.0824979 | − | 0.142891i | −0.821824 | − | 0.569741i | \(-0.807044\pi\) |
0.904322 | + | 0.426850i | \(0.140377\pi\) | |||||||
\(84\) | 3.33003 | 0.363336 | ||||||||
\(85\) | 15.6560 | 1.69813 | ||||||||
\(86\) | 0.0913237 | + | 0.158177i | 0.00984769 | + | 0.0170567i | ||||
\(87\) | 2.65991 | + | 4.60710i | 0.285172 | + | 0.493933i | ||||
\(88\) | −6.64985 | −0.708877 | ||||||||
\(89\) | 3.10048 | 0.328650 | 0.164325 | − | 0.986406i | \(-0.447455\pi\) | ||||
0.164325 | + | 0.986406i | \(0.447455\pi\) | |||||||
\(90\) | 1.79890 | + | 3.11579i | 0.189621 | + | 0.328433i | ||||
\(91\) | 1.11963 | + | 1.93925i | 0.117369 | + | 0.203289i | ||||
\(92\) | 4.53826 | + | 7.86050i | 0.473146 | + | 0.819513i | ||||
\(93\) | −2.62473 | − | 4.54617i | −0.272172 | − | 0.471416i | ||||
\(94\) | −1.77365 | −0.182938 | ||||||||
\(95\) | −19.6372 | −2.01473 | ||||||||
\(96\) | −1.52820 | − | 2.64692i | −0.155971 | − | 0.270150i | ||||
\(97\) | 9.54529 | + | 16.5329i | 0.969177 | + | 1.67866i | 0.697947 | + | 0.716149i | \(0.254097\pi\) |
0.271230 | + | 0.962515i | \(0.412570\pi\) | |||||||
\(98\) | 0.251274 | 0.0253825 | ||||||||
\(99\) | 10.8588 | 1.09135 | ||||||||
\(100\) | 7.66784 | − | 13.2811i | 0.766784 | − | 1.32811i | ||||
\(101\) | 0.796725 | − | 1.37997i | 0.0792771 | − | 0.137312i | −0.823661 | − | 0.567082i | \(-0.808072\pi\) |
0.902938 | + | 0.429770i | \(0.141405\pi\) | |||||||
\(102\) | −1.21754 | −0.120554 | ||||||||
\(103\) | −5.51021 | − | 9.54397i | −0.542937 | − | 0.940395i | −0.998734 | − | 0.0503109i | \(-0.983979\pi\) |
0.455796 | − | 0.890084i | \(-0.349355\pi\) | |||||||
\(104\) | 0.675876 | − | 1.17065i | 0.0662751 | − | 0.114792i | ||||
\(105\) | −3.29753 | − | 5.71148i | −0.321806 | − | 0.557384i | ||||
\(106\) | −0.109989 | + | 0.190507i | −0.0106831 | + | 0.0185037i | ||||
\(107\) | −3.76235 | + | 6.51658i | −0.363720 | + | 0.629982i | −0.988570 | − | 0.150763i | \(-0.951827\pi\) |
0.624850 | + | 0.780745i | \(0.285160\pi\) | |||||||
\(108\) | 3.62100 | + | 6.27176i | 0.348431 | + | 0.603501i | ||||
\(109\) | −0.285547 | + | 0.494582i | −0.0273505 | + | 0.0473724i | −0.879377 | − | 0.476127i | \(-0.842040\pi\) |
0.852026 | + | 0.523499i | \(0.175374\pi\) | |||||||
\(110\) | 3.15789 | + | 5.46962i | 0.301093 | + | 0.521508i | ||||
\(111\) | −3.80077 | −0.360753 | ||||||||
\(112\) | −3.88830 | − | 6.73474i | −0.367410 | − | 0.636373i | ||||
\(113\) | −14.5333 | −1.36718 | −0.683589 | − | 0.729867i | \(-0.739582\pi\) | ||||
−0.683589 | + | 0.729867i | \(0.739582\pi\) | |||||||
\(114\) | 1.52714 | 0.143030 | ||||||||
\(115\) | 8.98792 | − | 15.5675i | 0.838128 | − | 1.45168i | ||||
\(116\) | 6.84484 | − | 11.8556i | 0.635527 | − | 1.10077i | ||||
\(117\) | −1.10366 | + | 1.91160i | −0.102034 | + | 0.176727i | ||||
\(118\) | −0.759842 | − | 1.31608i | −0.0699491 | − | 0.121155i | ||||
\(119\) | −10.8228 | −0.992125 | ||||||||
\(120\) | −1.99059 | + | 3.44780i | −0.181715 | + | 0.314740i | ||||
\(121\) | 8.06206 | 0.732914 | ||||||||
\(122\) | 2.33659 | + | 2.03039i | 0.211545 | + | 0.183823i | ||||
\(123\) | −0.690392 | −0.0622506 | ||||||||
\(124\) | −6.75432 | + | 11.6988i | −0.606556 | + | 1.05058i | ||||
\(125\) | −12.1227 | −1.08429 | ||||||||
\(126\) | −1.24356 | − | 2.15391i | −0.110785 | − | 0.191885i | ||||
\(127\) | −8.66662 | + | 15.0110i | −0.769038 | + | 1.33201i | 0.169047 | + | 0.985608i | \(0.445931\pi\) |
−0.938085 | + | 0.346405i | \(0.887402\pi\) | |||||||
\(128\) | −5.15416 | + | 8.92726i | −0.455567 | + | 0.789066i | ||||
\(129\) | 0.165016 | − | 0.285817i | 0.0145289 | − | 0.0251647i | ||||
\(130\) | −1.28384 | −0.112600 | ||||||||
\(131\) | −1.53055 | −0.133725 | −0.0668626 | − | 0.997762i | \(-0.521299\pi\) | ||||
−0.0668626 | + | 0.997762i | \(0.521299\pi\) | |||||||
\(132\) | 2.88117 | + | 4.99034i | 0.250774 | + | 0.434353i | ||||
\(133\) | 13.5749 | 1.17710 | ||||||||
\(134\) | −0.458113 | − | 0.793475i | −0.0395749 | − | 0.0685458i | ||||
\(135\) | 7.17132 | − | 12.4211i | 0.617209 | − | 1.06904i | ||||
\(136\) | 3.26665 | + | 5.65801i | 0.280113 | + | 0.485170i | ||||
\(137\) | 6.57764 | − | 11.3928i | 0.561966 | − | 0.973353i | −0.435359 | − | 0.900257i | \(-0.643379\pi\) |
0.997325 | − | 0.0730961i | \(-0.0232880\pi\) | |||||||
\(138\) | −0.698971 | + | 1.21065i | −0.0595004 | + | 0.103058i | ||||
\(139\) | 0.602859 | + | 1.04418i | 0.0511339 | + | 0.0885665i | 0.890459 | − | 0.455063i | \(-0.150383\pi\) |
−0.839326 | + | 0.543629i | \(0.817050\pi\) | |||||||
\(140\) | −8.48564 | + | 14.6976i | −0.717167 | + | 1.24217i | ||||
\(141\) | 1.60244 | + | 2.77551i | 0.134950 | + | 0.233740i | ||||
\(142\) | −1.16999 | −0.0981835 | ||||||||
\(143\) | −1.93742 | + | 3.35572i | −0.162015 | + | 0.280619i | ||||
\(144\) | 3.83286 | − | 6.63871i | 0.319405 | − | 0.553225i | ||||
\(145\) | −27.1121 | −2.25154 | ||||||||
\(146\) | −4.72637 | −0.391157 | ||||||||
\(147\) | −0.227018 | − | 0.393207i | −0.0187241 | − | 0.0324312i | ||||
\(148\) | 4.89033 | + | 8.47030i | 0.401983 | + | 0.696254i | ||||
\(149\) | −19.1768 | −1.57102 | −0.785512 | − | 0.618846i | \(-0.787600\pi\) | ||||
−0.785512 | + | 0.618846i | \(0.787600\pi\) | |||||||
\(150\) | 2.36196 | 0.192854 | ||||||||
\(151\) | −10.2515 | − | 17.7561i | −0.834254 | − | 1.44497i | −0.894636 | − | 0.446796i | \(-0.852565\pi\) |
0.0603815 | − | 0.998175i | \(-0.480768\pi\) | |||||||
\(152\) | −4.09733 | − | 7.09679i | −0.332338 | − | 0.575626i | ||||
\(153\) | −5.33423 | − | 9.23917i | −0.431247 | − | 0.746942i | ||||
\(154\) | −2.18301 | − | 3.78108i | −0.175912 | − | 0.304688i | ||||
\(155\) | 26.7535 | 2.14890 | ||||||||
\(156\) | −1.17134 | −0.0937826 | ||||||||
\(157\) | 2.37835 | + | 4.11942i | 0.189813 | + | 0.328766i | 0.945188 | − | 0.326527i | \(-0.105879\pi\) |
−0.755375 | + | 0.655293i | \(0.772545\pi\) | |||||||
\(158\) | 0.479185 | + | 0.829972i | 0.0381219 | + | 0.0660290i | ||||
\(159\) | 0.397487 | 0.0315228 | ||||||||
\(160\) | 15.5767 | 1.23145 | ||||||||
\(161\) | −6.21323 | + | 10.7616i | −0.489671 | + | 0.848135i | ||||
\(162\) | 0.920912 | − | 1.59507i | 0.0723537 | − | 0.125320i | ||||
\(163\) | 14.1426 | 1.10774 | 0.553868 | − | 0.832605i | \(-0.313151\pi\) | ||||
0.553868 | + | 0.832605i | \(0.313151\pi\) | |||||||
\(164\) | 0.888305 | + | 1.53859i | 0.0693650 | + | 0.120144i | ||||
\(165\) | 5.70610 | − | 9.88326i | 0.444219 | − | 0.769411i | ||||
\(166\) | −0.297885 | − | 0.515952i | −0.0231204 | − | 0.0400456i | ||||
\(167\) | −0.521748 | + | 0.903694i | −0.0403741 | + | 0.0699299i | −0.885506 | − | 0.464627i | \(-0.846188\pi\) |
0.845132 | + | 0.534557i | \(0.179522\pi\) | |||||||
\(168\) | 1.37607 | − | 2.38342i | 0.106166 | − | 0.183885i | ||||
\(169\) | 6.10617 | + | 10.5762i | 0.469705 | + | 0.813554i | ||||
\(170\) | 3.10254 | − | 5.37376i | 0.237954 | − | 0.412149i | ||||
\(171\) | 6.69068 | + | 11.5886i | 0.511649 | + | 0.886202i | ||||
\(172\) | −0.849284 | −0.0647573 | ||||||||
\(173\) | 8.36884 | + | 14.4953i | 0.636271 | + | 1.10205i | 0.986244 | + | 0.165294i | \(0.0528573\pi\) |
−0.349973 | + | 0.936760i | \(0.613809\pi\) | |||||||
\(174\) | 2.10845 | 0.159841 | ||||||||
\(175\) | 20.9957 | 1.58713 | ||||||||
\(176\) | 6.72839 | − | 11.6539i | 0.507172 | − | 0.878447i | ||||
\(177\) | −1.37299 | + | 2.37808i | −0.103200 | + | 0.178748i | ||||
\(178\) | 0.614419 | − | 1.06421i | 0.0460527 | − | 0.0797656i | ||||
\(179\) | −3.69467 | − | 6.39935i | −0.276152 | − | 0.478310i | 0.694273 | − | 0.719712i | \(-0.255726\pi\) |
−0.970425 | + | 0.241402i | \(0.922393\pi\) | |||||||
\(180\) | −16.7293 | −1.24693 | ||||||||
\(181\) | −10.1720 | + | 17.6185i | −0.756082 | + | 1.30957i | 0.188752 | + | 0.982025i | \(0.439556\pi\) |
−0.944835 | + | 0.327548i | \(0.893778\pi\) | |||||||
\(182\) | 0.887503 | 0.0657861 | ||||||||
\(183\) | 1.06623 | − | 5.49081i | 0.0788182 | − | 0.405893i | ||||
\(184\) | 7.50138 | 0.553009 | ||||||||
\(185\) | 9.68518 | − | 16.7752i | 0.712069 | − | 1.23334i | ||||
\(186\) | −2.08057 | −0.152554 | ||||||||
\(187\) | −9.36399 | − | 16.2189i | −0.684763 | − | 1.18604i | ||||
\(188\) | 4.12361 | − | 7.14231i | 0.300745 | − | 0.520906i | ||||
\(189\) | −4.95744 | + | 8.58653i | −0.360600 | + | 0.624578i | ||||
\(190\) | −3.89149 | + | 6.74026i | −0.282318 | + | 0.488990i | ||||
\(191\) | −24.7981 | −1.79433 | −0.897165 | − | 0.441696i | \(-0.854377\pi\) | ||||
−0.897165 | + | 0.441696i | \(0.854377\pi\) | |||||||
\(192\) | 3.20328 | 0.231176 | ||||||||
\(193\) | 4.84792 | + | 8.39684i | 0.348961 | + | 0.604418i | 0.986065 | − | 0.166360i | \(-0.0532013\pi\) |
−0.637104 | + | 0.770778i | \(0.719868\pi\) | |||||||
\(194\) | 7.56633 | 0.543231 | ||||||||
\(195\) | 1.15991 | + | 2.00902i | 0.0830629 | + | 0.143869i | ||||
\(196\) | −0.584194 | + | 1.01185i | −0.0417281 | + | 0.0722752i | ||||
\(197\) | −2.16864 | − | 3.75620i | −0.154510 | − | 0.267618i | 0.778371 | − | 0.627805i | \(-0.216046\pi\) |
−0.932880 | + | 0.360186i | \(0.882713\pi\) | |||||||
\(198\) | 2.15188 | − | 3.72716i | 0.152927 | − | 0.264878i | ||||
\(199\) | 5.94398 | − | 10.2953i | 0.421358 | − | 0.729813i | −0.574715 | − | 0.818354i | \(-0.694887\pi\) |
0.996073 | + | 0.0885410i | \(0.0282204\pi\) | |||||||
\(200\) | −6.33716 | − | 10.9763i | −0.448105 | − | 0.776141i | ||||
\(201\) | −0.827781 | + | 1.43376i | −0.0583872 | + | 0.101130i | ||||
\(202\) | −0.315773 | − | 0.546934i | −0.0222177 | − | 0.0384822i | ||||
\(203\) | 18.7422 | 1.31545 | ||||||||
\(204\) | 2.83068 | − | 4.90288i | 0.198187 | − | 0.343270i | ||||
\(205\) | 1.75927 | − | 3.04714i | 0.122873 | − | 0.212822i | ||||
\(206\) | −4.36782 | −0.304320 | ||||||||
\(207\) | −12.2493 | −0.851383 | ||||||||
\(208\) | 1.36772 | + | 2.36896i | 0.0948341 | + | 0.164258i | ||||
\(209\) | 11.7452 | + | 20.3432i | 0.812430 | + | 1.40717i | ||||
\(210\) | −2.61387 | −0.180374 | ||||||||
\(211\) | 5.73093 | 0.394534 | 0.197267 | − | 0.980350i | \(-0.436793\pi\) | ||||
0.197267 | + | 0.980350i | \(0.436793\pi\) | |||||||
\(212\) | −0.511434 | − | 0.885830i | −0.0351254 | − | 0.0608390i | ||||
\(213\) | 1.05705 | + | 1.83087i | 0.0724279 | + | 0.125449i | ||||
\(214\) | 1.49116 | + | 2.58277i | 0.101934 | + | 0.176555i | ||||
\(215\) | 0.840994 | + | 1.45664i | 0.0573553 | + | 0.0993423i | ||||
\(216\) | 5.98523 | 0.407243 | ||||||||
\(217\) | −18.4944 | −1.25548 | ||||||||
\(218\) | 0.113173 | + | 0.196022i | 0.00766507 | + | 0.0132763i | ||||
\(219\) | 4.27013 | + | 7.39608i | 0.288548 | + | 0.499781i | ||||
\(220\) | −29.3674 | −1.97995 | ||||||||
\(221\) | 3.80694 | 0.256082 | ||||||||
\(222\) | −0.753196 | + | 1.30457i | −0.0505512 | + | 0.0875573i | ||||
\(223\) | 6.40969 | − | 11.1019i | 0.429225 | − | 0.743439i | −0.567580 | − | 0.823318i | \(-0.692120\pi\) |
0.996805 | + | 0.0798792i | \(0.0254534\pi\) | |||||||
\(224\) | −10.7680 | −0.719467 | ||||||||
\(225\) | 10.3482 | + | 17.9236i | 0.689878 | + | 1.19490i | ||||
\(226\) | −2.88005 | + | 4.98840i | −0.191578 | + | 0.331824i | ||||
\(227\) | 7.61465 | + | 13.1890i | 0.505402 | + | 0.875382i | 0.999980 | + | 0.00624882i | \(0.00198907\pi\) |
−0.494579 | + | 0.869133i | \(0.664678\pi\) | |||||||
\(228\) | −3.55050 | + | 6.14964i | −0.235137 | + | 0.407270i | ||||
\(229\) | 7.66151 | − | 13.2701i | 0.506287 | − | 0.876915i | −0.493686 | − | 0.869640i | \(-0.664351\pi\) |
0.999974 | − | 0.00727501i | \(-0.00231573\pi\) | |||||||
\(230\) | −3.56226 | − | 6.17001i | −0.234888 | − | 0.406839i | ||||
\(231\) | −3.94455 | + | 6.83217i | −0.259533 | + | 0.449524i | ||||
\(232\) | −5.65698 | − | 9.79818i | −0.371399 | − | 0.643282i | ||||
\(233\) | −10.8456 | −0.710520 | −0.355260 | − | 0.934768i | \(-0.615608\pi\) | ||||
−0.355260 | + | 0.934768i | \(0.615608\pi\) | |||||||
\(234\) | 0.437424 | + | 0.757640i | 0.0285953 | + | 0.0495285i | ||||
\(235\) | −16.3334 | −1.06548 | ||||||||
\(236\) | 7.06631 | 0.459977 | ||||||||
\(237\) | 0.865857 | − | 1.49971i | 0.0562434 | − | 0.0974165i | ||||
\(238\) | −2.14475 | + | 3.71481i | −0.139023 | + | 0.240795i | ||||
\(239\) | 3.56428 | − | 6.17352i | 0.230554 | − | 0.399332i | −0.727417 | − | 0.686196i | \(-0.759279\pi\) |
0.957971 | + | 0.286864i | \(0.0926127\pi\) | |||||||
\(240\) | −4.02820 | − | 6.97705i | −0.260019 | − | 0.450367i | ||||
\(241\) | 1.81086 | 0.116648 | 0.0583239 | − | 0.998298i | \(-0.481424\pi\) | ||||
0.0583239 | + | 0.998298i | \(0.481424\pi\) | |||||||
\(242\) | 1.59765 | − | 2.76721i | 0.102701 | − | 0.177883i | ||||
\(243\) | −15.1170 | −0.969756 | ||||||||
\(244\) | −13.6086 | + | 4.68867i | −0.871199 | + | 0.300161i | ||||
\(245\) | 2.31397 | 0.147834 | ||||||||
\(246\) | −0.136814 | + | 0.236970i | −0.00872297 | + | 0.0151086i | ||||
\(247\) | −4.77501 | −0.303826 | ||||||||
\(248\) | 5.58217 | + | 9.66860i | 0.354468 | + | 0.613957i | ||||
\(249\) | −0.538259 | + | 0.932292i | −0.0341108 | + | 0.0590816i | ||||
\(250\) | −2.40235 | + | 4.16099i | −0.151938 | + | 0.263164i | ||||
\(251\) | 5.13155 | − | 8.88810i | 0.323900 | − | 0.561012i | −0.657389 | − | 0.753551i | \(-0.728339\pi\) |
0.981289 | + | 0.192540i | \(0.0616724\pi\) | |||||||
\(252\) | 11.5647 | 0.728509 | ||||||||
\(253\) | −21.5030 | −1.35188 | ||||||||
\(254\) | 3.43492 | + | 5.94945i | 0.215526 | + | 0.373302i | ||||
\(255\) | −11.2122 | −0.702135 | ||||||||
\(256\) | −2.43007 | − | 4.20900i | −0.151879 | − | 0.263062i | ||||
\(257\) | 15.1940 | − | 26.3168i | 0.947777 | − | 1.64160i | 0.197684 | − | 0.980266i | \(-0.436658\pi\) |
0.750093 | − | 0.661332i | \(-0.230009\pi\) | |||||||
\(258\) | −0.0654023 | − | 0.113280i | −0.00407177 | − | 0.00705251i | ||||
\(259\) | −6.69524 | + | 11.5965i | −0.416022 | + | 0.720571i | ||||
\(260\) | 2.98484 | − | 5.16989i | 0.185112 | − | 0.320623i | ||||
\(261\) | 9.23749 | + | 15.9998i | 0.571786 | + | 0.990363i | ||||
\(262\) | −0.303309 | + | 0.525346i | −0.0187385 | + | 0.0324560i | ||||
\(263\) | 3.29177 | + | 5.70152i | 0.202979 | + | 0.351571i | 0.949487 | − | 0.313806i | \(-0.101604\pi\) |
−0.746508 | + | 0.665377i | \(0.768271\pi\) | |||||||
\(264\) | 4.76235 | 0.293102 | ||||||||
\(265\) | −1.01288 | + | 1.75437i | −0.0622209 | + | 0.107770i | ||||
\(266\) | 2.69014 | − | 4.65945i | 0.164943 | − | 0.285689i | ||||
\(267\) | −2.22043 | −0.135888 | ||||||||
\(268\) | 4.26031 | 0.260240 | ||||||||
\(269\) | −3.01654 | − | 5.22480i | −0.183922 | − | 0.318562i | 0.759291 | − | 0.650751i | \(-0.225546\pi\) |
−0.943213 | + | 0.332190i | \(0.892213\pi\) | |||||||
\(270\) | −2.84227 | − | 4.92295i | −0.172975 | − | 0.299601i | ||||
\(271\) | 26.7289 | 1.62366 | 0.811831 | − | 0.583892i | \(-0.198471\pi\) | ||||
0.811831 | + | 0.583892i | \(0.198471\pi\) | |||||||
\(272\) | −13.2209 | −0.801638 | ||||||||
\(273\) | −0.801831 | − | 1.38881i | −0.0485290 | − | 0.0840547i | ||||
\(274\) | −2.60697 | − | 4.51541i | −0.157493 | − | 0.272786i | ||||
\(275\) | 18.1657 | + | 31.4639i | 1.09543 | + | 1.89735i | ||||
\(276\) | −3.25011 | − | 5.62936i | −0.195634 | − | 0.338848i | ||||
\(277\) | −12.7372 | −0.765305 | −0.382653 | − | 0.923892i | \(-0.624989\pi\) | ||||
−0.382653 | + | 0.923892i | \(0.624989\pi\) | |||||||
\(278\) | 0.477873 | 0.0286609 | ||||||||
\(279\) | −9.11532 | − | 15.7882i | −0.545720 | − | 0.945215i | ||||
\(280\) | 7.01304 | + | 12.1469i | 0.419109 | + | 0.725918i | ||||
\(281\) | 3.70819 | 0.221212 | 0.110606 | − | 0.993864i | \(-0.464721\pi\) | ||||
0.110606 | + | 0.993864i | \(0.464721\pi\) | |||||||
\(282\) | 1.27022 | 0.0756403 | ||||||||
\(283\) | 9.62294 | − | 16.6674i | 0.572024 | − | 0.990775i | −0.424334 | − | 0.905506i | \(-0.639492\pi\) |
0.996358 | − | 0.0852692i | \(-0.0271750\pi\) | |||||||
\(284\) | 2.72014 | − | 4.71143i | 0.161411 | − | 0.279572i | ||||
\(285\) | 14.0633 | 0.833041 | ||||||||
\(286\) | 0.767876 | + | 1.33000i | 0.0454054 | + | 0.0786445i | ||||
\(287\) | −1.21616 | + | 2.10645i | −0.0717876 | + | 0.124340i | ||||
\(288\) | −5.30723 | − | 9.19238i | −0.312731 | − | 0.541666i | ||||
\(289\) | −0.699875 | + | 1.21222i | −0.0411691 | + | 0.0713070i | ||||
\(290\) | −5.37278 | + | 9.30593i | −0.315501 | + | 0.546463i | ||||
\(291\) | −6.83594 | − | 11.8402i | −0.400730 | − | 0.694085i | ||||
\(292\) | 10.9885 | − | 19.0326i | 0.643051 | − | 1.11380i | ||||
\(293\) | 6.29665 | + | 10.9061i | 0.367854 | + | 0.637142i | 0.989230 | − | 0.146371i | \(-0.0467592\pi\) |
−0.621376 | + | 0.783513i | \(0.713426\pi\) | |||||||
\(294\) | −0.179952 | −0.0104950 | ||||||||
\(295\) | −6.99733 | − | 12.1197i | −0.407400 | − | 0.705638i | ||||
\(296\) | 8.08332 | 0.469833 | ||||||||
\(297\) | −17.1569 | −0.995543 | ||||||||
\(298\) | −3.80025 | + | 6.58223i | −0.220143 | + | 0.381298i | ||||
\(299\) | 2.18551 | − | 3.78542i | 0.126392 | − | 0.218917i | ||||
\(300\) | −5.49139 | + | 9.51137i | −0.317046 | + | 0.549139i | ||||
\(301\) | −0.581368 | − | 1.00696i | −0.0335095 | − | 0.0580401i | ||||
\(302\) | −8.12612 | −0.467606 | ||||||||
\(303\) | −0.570581 | + | 0.988276i | −0.0327790 | + | 0.0567750i | ||||
\(304\) | 16.5829 | 0.951095 | ||||||||
\(305\) | 21.5175 | + | 18.6977i | 1.23209 | + | 1.07063i | ||||
\(306\) | −4.22833 | −0.241717 | ||||||||
\(307\) | 1.40671 | − | 2.43650i | 0.0802854 | − | 0.139058i | −0.823087 | − | 0.567915i | \(-0.807750\pi\) |
0.903373 | + | 0.428857i | \(0.141083\pi\) | |||||||
\(308\) | 20.3013 | 1.15677 | ||||||||
\(309\) | 3.94619 | + | 6.83500i | 0.224491 | + | 0.388829i | ||||
\(310\) | 5.30173 | − | 9.18286i | 0.301118 | − | 0.521552i | ||||
\(311\) | −6.33026 | + | 10.9643i | −0.358956 | + | 0.621730i | −0.987787 | − | 0.155812i | \(-0.950201\pi\) |
0.628831 | + | 0.777542i | \(0.283534\pi\) | |||||||
\(312\) | −0.484034 | + | 0.838372i | −0.0274030 | + | 0.0474635i | ||||
\(313\) | 12.1666 | 0.687696 | 0.343848 | − | 0.939025i | \(-0.388270\pi\) | ||||
0.343848 | + | 0.939025i | \(0.388270\pi\) | |||||||
\(314\) | 1.88526 | 0.106392 | ||||||||
\(315\) | −11.4518 | − | 19.8352i | −0.645238 | − | 1.11758i | ||||
\(316\) | −4.45628 | −0.250685 | ||||||||
\(317\) | −2.58818 | − | 4.48286i | −0.145367 | − | 0.251782i | 0.784143 | − | 0.620580i | \(-0.213103\pi\) |
−0.929510 | + | 0.368798i | \(0.879770\pi\) | |||||||
\(318\) | 0.0787698 | − | 0.136433i | 0.00441719 | − | 0.00765080i | ||||
\(319\) | 16.2160 | + | 28.0869i | 0.907919 | + | 1.57256i | ||||
\(320\) | −8.16263 | + | 14.1381i | −0.456305 | + | 0.790344i | ||||
\(321\) | 2.69444 | − | 4.66691i | 0.150389 | − | 0.260481i | ||||
\(322\) | 2.46254 | + | 4.26525i | 0.137232 | + | 0.237693i | ||||
\(323\) | 11.5393 | − | 19.9867i | 0.642065 | − | 1.11209i | ||||
\(324\) | 4.28211 | + | 7.41683i | 0.237895 | + | 0.412046i | ||||
\(325\) | −7.38529 | −0.409662 | ||||||||
\(326\) | 2.80263 | − | 4.85430i | 0.155223 | − | 0.268855i | ||||
\(327\) | 0.204497 | − | 0.354199i | 0.0113087 | − | 0.0195873i | ||||
\(328\) | 1.46830 | 0.0810731 | ||||||||
\(329\) | 11.2911 | 0.622498 | ||||||||
\(330\) | −2.26155 | − | 3.91712i | −0.124494 | − | 0.215630i | ||||
\(331\) | −6.74603 | − | 11.6845i | −0.370795 | − | 0.642236i | 0.618893 | − | 0.785475i | \(-0.287581\pi\) |
−0.989688 | + | 0.143239i | \(0.954248\pi\) | |||||||
\(332\) | 2.77024 | 0.152037 | ||||||||
\(333\) | −13.1995 | −0.723330 | ||||||||
\(334\) | 0.206789 | + | 0.358169i | 0.0113150 | + | 0.0195981i | ||||
\(335\) | −4.21873 | − | 7.30705i | −0.230494 | − | 0.399227i | ||||
\(336\) | 2.78464 | + | 4.82314i | 0.151915 | + | 0.263124i | ||||
\(337\) | 13.8008 | + | 23.9038i | 0.751779 | + | 1.30212i | 0.946960 | + | 0.321353i | \(0.104138\pi\) |
−0.195180 | + | 0.980767i | \(0.562529\pi\) | |||||||
\(338\) | 4.84022 | 0.263273 | ||||||||
\(339\) | 10.4082 | 0.565293 | ||||||||
\(340\) | 14.4264 | + | 24.9872i | 0.782379 | + | 1.35512i | ||||
\(341\) | −16.0015 | − | 27.7154i | −0.866530 | − | 1.50087i | ||||
\(342\) | 5.30355 | 0.286783 | ||||||||
\(343\) | −19.2613 | −1.04001 | ||||||||
\(344\) | −0.350949 | + | 0.607862i | −0.0189219 | + | 0.0327737i | ||||
\(345\) | −6.43678 | + | 11.1488i | −0.346544 | + | 0.600232i | ||||
\(346\) | 6.63379 | 0.356635 | ||||||||
\(347\) | −16.6106 | − | 28.7704i | −0.891703 | − | 1.54448i | −0.837833 | − | 0.545927i | \(-0.816178\pi\) |
−0.0538704 | − | 0.998548i | \(-0.517156\pi\) | |||||||
\(348\) | −4.90199 | + | 8.49050i | −0.262774 | + | 0.455138i | ||||
\(349\) | −7.89906 | − | 13.6816i | −0.422827 | − | 0.732358i | 0.573388 | − | 0.819284i | \(-0.305629\pi\) |
−0.996215 | + | 0.0869261i | \(0.972296\pi\) | |||||||
\(350\) | 4.16071 | − | 7.20656i | 0.222399 | − | 0.385207i | ||||
\(351\) | 1.74379 | − | 3.02033i | 0.0930764 | − | 0.161213i | ||||
\(352\) | −9.31657 | − | 16.1368i | −0.496575 | − | 0.860093i | ||||
\(353\) | 8.04577 | − | 13.9357i | 0.428233 | − | 0.741722i | −0.568483 | − | 0.822695i | \(-0.692470\pi\) |
0.996716 | + | 0.0809733i | \(0.0258028\pi\) | |||||||
\(354\) | 0.544167 | + | 0.942526i | 0.0289222 | + | 0.0500947i | ||||
\(355\) | −10.7744 | −0.571844 | ||||||||
\(356\) | 2.85696 | + | 4.94840i | 0.151419 | + | 0.262265i | ||||
\(357\) | 7.75084 | 0.410218 | ||||||||
\(358\) | −2.92868 | −0.154785 | ||||||||
\(359\) | −12.7646 | + | 22.1090i | −0.673691 | + | 1.16687i | 0.303158 | + | 0.952940i | \(0.401959\pi\) |
−0.976850 | + | 0.213927i | \(0.931374\pi\) | |||||||
\(360\) | −6.91303 | + | 11.9737i | −0.364349 | + | 0.631071i | ||||
\(361\) | −4.97366 | + | 8.61463i | −0.261772 | + | 0.453402i | ||||
\(362\) | 4.03157 | + | 6.98289i | 0.211895 | + | 0.367013i | ||||
\(363\) | −5.77371 | −0.303041 | ||||||||
\(364\) | −2.06338 | + | 3.57388i | −0.108150 | + | 0.187322i | ||||
\(365\) | −43.5248 | −2.27819 | ||||||||
\(366\) | −1.67337 | − | 1.45408i | −0.0874683 | − | 0.0760062i | ||||
\(367\) | 4.77673 | 0.249343 | 0.124672 | − | 0.992198i | \(-0.460212\pi\) | ||||
0.124672 | + | 0.992198i | \(0.460212\pi\) | |||||||
\(368\) | −7.58998 | + | 13.1462i | −0.395655 | + | 0.685294i | ||||
\(369\) | −2.39763 | −0.124816 | ||||||||
\(370\) | −3.83861 | − | 6.64867i | −0.199560 | − | 0.345648i | ||||
\(371\) | 0.700193 | − | 1.21277i | 0.0363522 | − | 0.0629639i | ||||
\(372\) | 4.83716 | − | 8.37821i | 0.250795 | − | 0.434390i | ||||
\(373\) | −12.0480 | + | 20.8678i | −0.623822 | + | 1.08049i | 0.364945 | + | 0.931029i | \(0.381088\pi\) |
−0.988767 | + | 0.149463i | \(0.952246\pi\) | |||||||
\(374\) | −7.42262 | −0.383814 | ||||||||
\(375\) | 8.68178 | 0.448325 | ||||||||
\(376\) | −3.40800 | − | 5.90283i | −0.175754 | − | 0.304415i | ||||
\(377\) | −6.59261 | −0.339537 | ||||||||
\(378\) | 1.96482 | + | 3.40317i | 0.101060 | + | 0.175040i | ||||
\(379\) | −2.84484 | + | 4.92740i | −0.146130 | + | 0.253104i | −0.929794 | − | 0.368081i | \(-0.880015\pi\) |
0.783664 | + | 0.621185i | \(0.213348\pi\) | |||||||
\(380\) | −18.0949 | − | 31.3412i | −0.928246 | − | 1.60777i | ||||
\(381\) | 6.20668 | − | 10.7503i | 0.317978 | − | 0.550753i | ||||
\(382\) | −4.91423 | + | 8.51169i | −0.251434 | + | 0.435496i | ||||
\(383\) | 9.23399 | + | 15.9937i | 0.471835 | + | 0.817241i | 0.999481 | − | 0.0322228i | \(-0.0102586\pi\) |
−0.527646 | + | 0.849464i | \(0.676925\pi\) | |||||||
\(384\) | 3.69119 | − | 6.39334i | 0.188365 | − | 0.326259i | ||||
\(385\) | −20.1031 | − | 34.8197i | −1.02455 | − | 1.77457i | ||||
\(386\) | 3.84284 | 0.195595 | ||||||||
\(387\) | 0.573078 | − | 0.992600i | 0.0291312 | − | 0.0504567i | ||||
\(388\) | −17.5912 | + | 30.4688i | −0.893056 | + | 1.54682i | ||||
\(389\) | 24.7174 | 1.25322 | 0.626610 | − | 0.779333i | \(-0.284442\pi\) | ||||
0.626610 | + | 0.779333i | \(0.284442\pi\) | |||||||
\(390\) | 0.919434 | 0.0465574 | ||||||||
\(391\) | 10.5631 | + | 18.2958i | 0.534197 | + | 0.925256i | ||||
\(392\) | 0.482813 | + | 0.836256i | 0.0243857 | + | 0.0422373i | ||||
\(393\) | 1.09612 | 0.0552919 | ||||||||
\(394\) | −1.71903 | −0.0866037 | ||||||||
\(395\) | 4.41278 | + | 7.64315i | 0.222031 | + | 0.384569i | ||||
\(396\) | 10.0059 | + | 17.3307i | 0.502816 | + | 0.870903i | ||||
\(397\) | −3.37064 | − | 5.83813i | −0.169168 | − | 0.293007i | 0.768960 | − | 0.639297i | \(-0.220775\pi\) |
−0.938128 | + | 0.346290i | \(0.887441\pi\) | |||||||
\(398\) | −2.35583 | − | 4.08041i | −0.118087 | − | 0.204533i | ||||
\(399\) | −9.72181 | −0.486699 | ||||||||
\(400\) | 25.6480 | 1.28240 | ||||||||
\(401\) | 6.28327 | + | 10.8829i | 0.313771 | + | 0.543468i | 0.979176 | − | 0.203015i | \(-0.0650741\pi\) |
−0.665404 | + | 0.746483i | \(0.731741\pi\) | |||||||
\(402\) | 0.328082 | + | 0.568254i | 0.0163632 | + | 0.0283419i | ||||
\(403\) | 6.50542 | 0.324058 | ||||||||
\(404\) | 2.93659 | 0.146101 | ||||||||
\(405\) | 8.48061 | − | 14.6889i | 0.421405 | − | 0.729895i | ||||
\(406\) | 3.71413 | − | 6.43307i | 0.184329 | − | 0.319268i | ||||
\(407\) | −23.1711 | −1.14855 | ||||||||
\(408\) | −2.33944 | − | 4.05203i | −0.115820 | − | 0.200606i | ||||
\(409\) | 1.94953 | − | 3.37669i | 0.0963982 | − | 0.166967i | −0.813793 | − | 0.581155i | \(-0.802601\pi\) |
0.910191 | + | 0.414188i | \(0.135934\pi\) | |||||||
\(410\) | −0.697265 | − | 1.20770i | −0.0344355 | − | 0.0596440i | ||||
\(411\) | −4.71063 | + | 8.15906i | −0.232358 | + | 0.402457i | ||||
\(412\) | 10.1549 | − | 17.5887i | 0.500294 | − | 0.866534i | ||||
\(413\) | 4.83716 | + | 8.37821i | 0.238021 | + | 0.412265i | ||||
\(414\) | −2.42743 | + | 4.20443i | −0.119302 | + | 0.206636i | ||||
\(415\) | −2.74320 | − | 4.75136i | −0.134658 | − | 0.233235i | ||||
\(416\) | 3.78766 | 0.185705 | ||||||||
\(417\) | −0.431743 | − | 0.747801i | −0.0211425 | − | 0.0366200i | ||||
\(418\) | 9.31012 | 0.455373 | ||||||||
\(419\) | 18.9331 | 0.924940 | 0.462470 | − | 0.886635i | \(-0.346963\pi\) | ||||
0.462470 | + | 0.886635i | \(0.346963\pi\) | |||||||
\(420\) | 6.07706 | − | 10.5258i | 0.296530 | − | 0.513606i | ||||
\(421\) | −12.9581 | + | 22.4442i | −0.631541 | + | 1.09386i | 0.355696 | + | 0.934602i | \(0.384244\pi\) |
−0.987237 | + | 0.159259i | \(0.949089\pi\) | |||||||
\(422\) | 1.13569 | − | 1.96708i | 0.0552847 | − | 0.0957560i | ||||
\(423\) | 5.56504 | + | 9.63894i | 0.270582 | + | 0.468661i | ||||
\(424\) | −0.845359 | −0.0410543 | ||||||||
\(425\) | 17.8473 | − | 30.9125i | 0.865723 | − | 1.49948i | ||||
\(426\) | 0.837900 | 0.0405964 | ||||||||
\(427\) | −14.8747 | − | 12.9255i | −0.719839 | − | 0.625509i | ||||
\(428\) | −13.8674 | −0.670305 | ||||||||
\(429\) | 1.38750 | − | 2.40323i | 0.0669893 | − | 0.116029i | ||||
\(430\) | 0.666636 | 0.0321481 | ||||||||
\(431\) | 12.9904 | + | 22.5001i | 0.625727 | + | 1.08379i | 0.988400 | + | 0.151874i | \(0.0485309\pi\) |
−0.362673 | + | 0.931916i | \(0.618136\pi\) | |||||||
\(432\) | −6.05592 | + | 10.4892i | −0.291366 | + | 0.504660i | ||||
\(433\) | 11.2528 | − | 19.4905i | 0.540777 | − | 0.936653i | −0.458083 | − | 0.888910i | \(-0.651464\pi\) |
0.998860 | − | 0.0477435i | \(-0.0152030\pi\) | |||||||
\(434\) | −3.66502 | + | 6.34799i | −0.175926 | + | 0.304713i | ||||
\(435\) | 19.4166 | 0.930953 | ||||||||
\(436\) | −1.05248 | −0.0504046 | ||||||||
\(437\) | −13.2491 | − | 22.9482i | −0.633793 | − | 1.09776i | ||||
\(438\) | 3.38483 | 0.161734 | ||||||||
\(439\) | 0.480952 | + | 0.833033i | 0.0229546 | + | 0.0397585i | 0.877275 | − | 0.479989i | \(-0.159359\pi\) |
−0.854320 | + | 0.519748i | \(0.826026\pi\) | |||||||
\(440\) | −12.1355 | + | 21.0193i | −0.578537 | + | 1.00206i | ||||
\(441\) | −0.788402 | − | 1.36555i | −0.0375429 | − | 0.0650263i | ||||
\(442\) | 0.754418 | − | 1.30669i | 0.0358840 | − | 0.0621529i | ||||
\(443\) | −3.43492 | + | 5.94945i | −0.163198 | + | 0.282667i | −0.936014 | − | 0.351963i | \(-0.885514\pi\) |
0.772816 | + | 0.634630i | \(0.218848\pi\) | |||||||
\(444\) | −3.50225 | − | 6.06608i | −0.166209 | − | 0.287883i | ||||
\(445\) | 5.65814 | − | 9.80019i | 0.268222 | − | 0.464574i | ||||
\(446\) | −2.54041 | − | 4.40012i | −0.120292 | − | 0.208352i | ||||
\(447\) | 13.7336 | 0.649578 | ||||||||
\(448\) | 5.64272 | − | 9.77348i | 0.266594 | − | 0.461754i | ||||
\(449\) | −5.34079 | + | 9.25052i | −0.252047 | + | 0.436559i | −0.964089 | − | 0.265578i | \(-0.914437\pi\) |
0.712042 | + | 0.702137i | \(0.247771\pi\) | |||||||
\(450\) | 8.20276 | 0.386682 | ||||||||
\(451\) | −4.20893 | −0.198191 | ||||||||
\(452\) | −13.3918 | − | 23.1953i | −0.629899 | − | 1.09102i | ||||
\(453\) | 7.34169 | + | 12.7162i | 0.344943 | + | 0.597459i | ||||
\(454\) | 6.03596 | 0.283281 | ||||||||
\(455\) | 8.17295 | 0.383154 | ||||||||
\(456\) | 2.93434 | + | 5.08243i | 0.137413 | + | 0.238006i | ||||
\(457\) | −3.49945 | − | 6.06123i | −0.163698 | − | 0.283533i | 0.772494 | − | 0.635022i | \(-0.219009\pi\) |
−0.936192 | + | 0.351489i | \(0.885675\pi\) | |||||||
\(458\) | −3.03655 | − | 5.25946i | −0.141889 | − | 0.245759i | ||||
\(459\) | 8.42810 | + | 14.5979i | 0.393390 | + | 0.681371i | ||||
\(460\) | 33.1280 | 1.54460 | ||||||||
\(461\) | 5.77526 | 0.268981 | 0.134490 | − | 0.990915i | \(-0.457060\pi\) | ||||
0.134490 | + | 0.990915i | \(0.457060\pi\) | |||||||
\(462\) | 1.56338 | + | 2.70785i | 0.0727350 | + | 0.125981i | ||||
\(463\) | −5.60187 | − | 9.70272i | −0.260341 | − | 0.450923i | 0.705992 | − | 0.708220i | \(-0.250502\pi\) |
−0.966332 | + | 0.257297i | \(0.917168\pi\) | |||||||
\(464\) | 22.8952 | 1.06288 | ||||||||
\(465\) | −19.1598 | −0.888514 | ||||||||
\(466\) | −2.14927 | + | 3.72264i | −0.0995629 | + | 0.172448i | ||||
\(467\) | −17.0665 | + | 29.5600i | −0.789742 | + | 1.36787i | 0.136383 | + | 0.990656i | \(0.456452\pi\) |
−0.926125 | + | 0.377217i | \(0.876881\pi\) | |||||||
\(468\) | −4.06791 | −0.188039 | ||||||||
\(469\) | 2.91635 | + | 5.05127i | 0.134665 | + | 0.233246i | ||||
\(470\) | −3.23679 | + | 5.60628i | −0.149302 | + | 0.258598i | ||||
\(471\) | −1.70328 | − | 2.95016i | −0.0784828 | − | 0.135936i | ||||
\(472\) | 2.92001 | − | 5.05760i | 0.134404 | − | 0.232795i | ||||
\(473\) | 1.00601 | − | 1.74246i | 0.0462564 | − | 0.0801184i | ||||
\(474\) | −0.343172 | − | 0.594392i | −0.0157624 | − | 0.0273013i | ||||
\(475\) | −22.3858 | + | 38.7733i | −1.02713 | + | 1.77904i | ||||
\(476\) | −9.97276 | − | 17.2733i | −0.457100 | − | 0.791721i | ||||
\(477\) | 1.38042 | 0.0632049 | ||||||||
\(478\) | −1.41266 | − | 2.44680i | −0.0646137 | − | 0.111914i | ||||
\(479\) | −21.6236 | −0.988006 | −0.494003 | − | 0.869460i | \(-0.664467\pi\) | ||||
−0.494003 | + | 0.869460i | \(0.664467\pi\) | |||||||
\(480\) | −11.1554 | −0.509173 | ||||||||
\(481\) | 2.35506 | − | 4.07909i | 0.107382 | − | 0.185990i | ||||
\(482\) | 0.358857 | − | 0.621559i | 0.0163455 | − | 0.0283112i | ||||
\(483\) | 4.44966 | − | 7.70704i | 0.202467 | − | 0.350682i | ||||
\(484\) | 7.42884 | + | 12.8671i | 0.337675 | + | 0.584870i | ||||
\(485\) | 69.6778 | 3.16391 | ||||||||
\(486\) | −2.99572 | + | 5.18875i | −0.135889 | + | 0.235366i | ||||
\(487\) | 43.4768 | 1.97012 | 0.985062 | − | 0.172202i | \(-0.0550883\pi\) | ||||
0.985062 | + | 0.172202i | \(0.0550883\pi\) | |||||||
\(488\) | −2.26762 | + | 11.6776i | −0.102650 | + | 0.528621i | ||||
\(489\) | −10.1284 | −0.458020 | ||||||||
\(490\) | 0.458557 | − | 0.794244i | 0.0207155 | − | 0.0358803i | ||||
\(491\) | −12.6884 | −0.572619 | −0.286309 | − | 0.958137i | \(-0.592428\pi\) | ||||
−0.286309 | + | 0.958137i | \(0.592428\pi\) | |||||||
\(492\) | −0.636167 | − | 1.10187i | −0.0286806 | − | 0.0496763i | ||||
\(493\) | 15.9318 | − | 27.5946i | 0.717530 | − | 1.24280i | ||||
\(494\) | −0.946259 | + | 1.63897i | −0.0425742 | + | 0.0737407i | ||||
\(495\) | 19.8165 | − | 34.3231i | 0.890684 | − | 1.54271i | ||||
\(496\) | −22.5924 | −1.01443 | ||||||||
\(497\) | 7.44818 | 0.334097 | ||||||||
\(498\) | 0.213333 | + | 0.369503i | 0.00955967 | + | 0.0165578i | ||||
\(499\) | 8.93711 | 0.400080 | 0.200040 | − | 0.979788i | \(-0.435893\pi\) | ||||
0.200040 | + | 0.979788i | \(0.435893\pi\) | |||||||
\(500\) | −11.1706 | − | 19.3480i | −0.499563 | − | 0.865268i | ||||
\(501\) | 0.373654 | − | 0.647188i | 0.0166936 | − | 0.0289142i | ||||
\(502\) | −2.03383 | − | 3.52270i | −0.0907742 | − | 0.157226i | ||||
\(503\) | −0.305015 | + | 0.528301i | −0.0135999 | + | 0.0235558i | −0.872745 | − | 0.488176i | \(-0.837662\pi\) |
0.859145 | + | 0.511732i | \(0.170996\pi\) | |||||||
\(504\) | 4.77889 | − | 8.27728i | 0.212869 | − | 0.368699i | ||||
\(505\) | −2.90793 | − | 5.03668i | −0.129401 | − | 0.224129i | ||||
\(506\) | −4.26123 | + | 7.38067i | −0.189435 | + | 0.328111i | ||||
\(507\) | −4.37299 | − | 7.57423i | −0.194211 | − | 0.336384i | ||||
\(508\) | −31.9437 | −1.41727 | ||||||||
\(509\) | −10.1083 | + | 17.5081i | −0.448043 | + | 0.776034i | −0.998259 | − | 0.0589890i | \(-0.981212\pi\) |
0.550215 | + | 0.835023i | \(0.314546\pi\) | |||||||
\(510\) | −2.22191 | + | 3.84846i | −0.0983879 | + | 0.170413i | ||||
\(511\) | 30.0881 | 1.33102 | ||||||||
\(512\) | −22.5429 | −0.996264 | ||||||||
\(513\) | −10.5713 | − | 18.3100i | −0.466733 | − | 0.808406i | ||||
\(514\) | −6.02198 | − | 10.4304i | −0.265618 | − | 0.460064i | ||||
\(515\) | −40.2229 | −1.77243 | ||||||||
\(516\) | 0.608222 | 0.0267755 | ||||||||
\(517\) | 9.76916 | + | 16.9207i | 0.429647 | + | 0.744171i | ||||
\(518\) | 2.65358 | + | 4.59614i | 0.116592 | + | 0.201943i | ||||
\(519\) | −5.99342 | − | 10.3809i | −0.263082 | − | 0.455671i | ||||
\(520\) | −2.46685 | − | 4.27270i | −0.108178 | − | 0.187370i | ||||
\(521\) | −35.3195 | −1.54738 | −0.773688 | − | 0.633567i | \(-0.781590\pi\) | ||||
−0.773688 | + | 0.633567i | \(0.781590\pi\) | |||||||
\(522\) | 7.32234 | 0.320490 | ||||||||
\(523\) | −9.79155 | − | 16.9595i | −0.428154 | − | 0.741585i | 0.568555 | − | 0.822645i | \(-0.307503\pi\) |
−0.996709 | + | 0.0810602i | \(0.974169\pi\) | |||||||
\(524\) | −1.41034 | − | 2.44278i | −0.0616111 | − | 0.106714i | ||||
\(525\) | −15.0363 | −0.656237 | ||||||||
\(526\) | 2.60931 | 0.113771 | ||||||||
\(527\) | −15.7211 | + | 27.2297i | −0.684820 | + | 1.18614i | ||||
\(528\) | −4.81860 | + | 8.34606i | −0.209703 | + | 0.363216i | ||||
\(529\) | 1.25647 | 0.0546292 | ||||||||
\(530\) | 0.401445 | + | 0.695323i | 0.0174376 | + | 0.0302029i | ||||
\(531\) | −4.76819 | + | 8.25874i | −0.206922 | + | 0.358399i | ||||
\(532\) | 12.5087 | + | 21.6658i | 0.542322 | + | 0.939330i | ||||
\(533\) | 0.427786 | − | 0.740947i | 0.0185295 | − | 0.0320940i | ||||
\(534\) | −0.440022 | + | 0.762140i | −0.0190416 | + | 0.0329810i | ||||
\(535\) | 13.7320 | + | 23.7846i | 0.593687 | + | 1.02830i | ||||
\(536\) | 1.76049 | − | 3.04926i | 0.0760416 | − | 0.131708i | ||||
\(537\) | 2.64597 | + | 4.58295i | 0.114182 | + | 0.197769i | ||||
\(538\) | −2.39114 | −0.103089 | ||||||||
\(539\) | −1.38400 | − | 2.39716i | −0.0596131 | − | 0.103253i | ||||
\(540\) | 26.4323 | 1.13746 | ||||||||
\(541\) | −14.7092 | −0.632396 | −0.316198 | − | 0.948693i | \(-0.602406\pi\) | ||||
−0.316198 | + | 0.948693i | \(0.602406\pi\) | |||||||
\(542\) | 5.29684 | − | 9.17439i | 0.227519 | − | 0.394074i | ||||
\(543\) | 7.28480 | − | 12.6176i | 0.312621 | − | 0.541475i | ||||
\(544\) | −9.15329 | + | 15.8540i | −0.392444 | + | 0.679733i | ||||
\(545\) | 1.04221 | + | 1.80515i | 0.0446432 | + | 0.0773242i | ||||
\(546\) | −0.635593 | −0.0272009 | ||||||||
\(547\) | −6.47999 | + | 11.2237i | −0.277064 | + | 0.479889i | −0.970654 | − | 0.240481i | \(-0.922695\pi\) |
0.693590 | + | 0.720370i | \(0.256028\pi\) | |||||||
\(548\) | 24.2441 | 1.03566 | ||||||||
\(549\) | 3.70288 | − | 19.0688i | 0.158035 | − | 0.813837i | ||||
\(550\) | 14.3995 | 0.613999 | ||||||||
\(551\) | −19.9831 | + | 34.6117i | −0.851307 | + | 1.47451i | ||||
\(552\) | −5.37218 | −0.228655 | ||||||||
\(553\) | −3.05050 | − | 5.28361i | −0.129720 | − | 0.224682i | ||||
\(554\) | −2.52413 | + | 4.37191i | −0.107240 | + | 0.185745i | ||||
\(555\) | −6.93613 | + | 12.0137i | −0.294422 | + | 0.509954i | ||||
\(556\) | −1.11102 | + | 1.92434i | −0.0471177 | + | 0.0816103i | ||||
\(557\) | 26.5978 | 1.12699 | 0.563493 | − | 0.826121i | \(-0.309457\pi\) | ||||
0.563493 | + | 0.826121i | \(0.309457\pi\) | |||||||
\(558\) | −7.22551 | −0.305880 | ||||||||
\(559\) | 0.204497 | + | 0.354199i | 0.00864930 | + | 0.0149810i | ||||
\(560\) | −28.3835 | −1.19942 | ||||||||
\(561\) | 6.70610 | + | 11.6153i | 0.283132 | + | 0.490399i | ||||
\(562\) | 0.734849 | − | 1.27280i | 0.0309977 | − | 0.0536896i | ||||
\(563\) | 12.5730 | + | 21.7772i | 0.529891 | + | 0.917798i | 0.999392 | + | 0.0348658i | \(0.0111004\pi\) |
−0.469501 | + | 0.882932i | \(0.655566\pi\) | |||||||
\(564\) | −2.95316 | + | 5.11503i | −0.124351 | + | 0.215381i | ||||
\(565\) | −26.5222 | + | 45.9378i | −1.11580 | + | 1.93262i | ||||
\(566\) | −3.81394 | − | 6.60594i | −0.160312 | − | 0.277668i | ||||
\(567\) | −5.86254 | + | 10.1542i | −0.246203 | + | 0.426437i | ||||
\(568\) | −2.24809 | − | 3.89381i | −0.0943278 | − | 0.163380i | ||||
\(569\) | −27.3135 | −1.14504 | −0.572520 | − | 0.819891i | \(-0.694034\pi\) | ||||
−0.572520 | + | 0.819891i | \(0.694034\pi\) | |||||||
\(570\) | 2.78692 | − | 4.82709i | 0.116731 | − | 0.202185i | ||||
\(571\) | 22.9754 | − | 39.7945i | 0.961490 | − | 1.66535i | 0.242725 | − | 0.970095i | \(-0.421959\pi\) |
0.718764 | − | 0.695254i | \(-0.244708\pi\) | |||||||
\(572\) | −7.14102 | −0.298581 | ||||||||
\(573\) | 17.7594 | 0.741909 | ||||||||
\(574\) | 0.482011 | + | 0.834867i | 0.0201187 | + | 0.0348467i | ||||
\(575\) | −20.4919 | − | 35.4930i | −0.854570 | − | 1.48016i | ||||
\(576\) | 11.1245 | 0.463522 | ||||||||
\(577\) | 29.2224 | 1.21654 | 0.608272 | − | 0.793728i | \(-0.291863\pi\) | ||||
0.608272 | + | 0.793728i | \(0.291863\pi\) | |||||||
\(578\) | 0.277387 | + | 0.480449i | 0.0115378 | + | 0.0199841i | ||||
\(579\) | −3.47188 | − | 6.01347i | −0.144286 | − | 0.249911i | ||||
\(580\) | −24.9826 | − | 43.2712i | −1.03735 | − | 1.79674i | ||||
\(581\) | 1.89634 | + | 3.28455i | 0.0786734 | + | 0.136266i | ||||
\(582\) | −5.41869 | −0.224612 | ||||||||
\(583\) | 2.42325 | 0.100361 | ||||||||
\(584\) | −9.08152 | − | 15.7297i | −0.375796 | − | 0.650898i | ||||
\(585\) | 4.02820 | + | 6.97705i | 0.166546 | + | 0.288466i | ||||
\(586\) | 4.99121 | 0.206185 | ||||||||
\(587\) | −1.54502 | −0.0637697 | −0.0318849 | − | 0.999492i | \(-0.510151\pi\) | ||||
−0.0318849 | + | 0.999492i | \(0.510151\pi\) | |||||||
\(588\) | 0.418376 | − | 0.724648i | 0.0172535 | − | 0.0298840i | ||||
\(589\) | 19.7188 | − | 34.1539i | 0.812498 | − | 1.40729i | ||||
\(590\) | −5.54662 | −0.228351 | ||||||||
\(591\) | 1.55309 | + | 2.69004i | 0.0638857 | + | 0.110653i | ||||
\(592\) | −8.17879 | + | 14.1661i | −0.336146 | + | 0.582222i | ||||
\(593\) | −1.44160 | − | 2.49692i | −0.0591993 | − | 0.102536i | 0.834907 | − | 0.550391i | \(-0.185521\pi\) |
−0.894106 | + | 0.447855i | \(0.852188\pi\) | |||||||
\(594\) | −3.39997 | + | 5.88891i | −0.139502 | + | 0.241625i | ||||
\(595\) | −19.7508 | + | 34.2094i | −0.809704 | + | 1.40245i | ||||
\(596\) | −17.6706 | − | 30.6064i | −0.723816 | − | 1.25369i | ||||
\(597\) | −4.25683 | + | 7.37305i | −0.174221 | + | 0.301759i | ||||
\(598\) | −0.866203 | − | 1.50031i | −0.0354217 | − | 0.0613522i | ||||
\(599\) | 25.0351 | 1.02291 | 0.511454 | − | 0.859311i | \(-0.329107\pi\) | ||||
0.511454 | + | 0.859311i | \(0.329107\pi\) | |||||||
\(600\) | 4.53841 | + | 7.86076i | 0.185280 | + | 0.320914i | ||||
\(601\) | −0.684105 | −0.0279052 | −0.0139526 | − | 0.999903i | \(-0.504441\pi\) | ||||
−0.0139526 | + | 0.999903i | \(0.504441\pi\) | |||||||
\(602\) | −0.460837 | −0.0187823 | ||||||||
\(603\) | −2.87477 | + | 4.97924i | −0.117069 | + | 0.202770i | ||||
\(604\) | 18.8926 | − | 32.7230i | 0.768730 | − | 1.33148i | ||||
\(605\) | 14.7127 | − | 25.4831i | 0.598155 | − | 1.03603i | ||||
\(606\) | 0.226143 | + | 0.391692i | 0.00918645 | + | 0.0159114i | ||||
\(607\) | −0.503559 | −0.0204388 | −0.0102194 | − | 0.999948i | \(-0.503253\pi\) | ||||
−0.0102194 | + | 0.999948i | \(0.503253\pi\) | |||||||
\(608\) | 11.4809 | − | 19.8855i | 0.465612 | − | 0.806463i | ||||
\(609\) | −13.4224 | −0.543904 | ||||||||
\(610\) | 10.6819 | − | 3.68032i | 0.432497 | − | 0.149012i | ||||
\(611\) | −3.97166 | −0.160676 | ||||||||
\(612\) | 9.83055 | − | 17.0270i | 0.397376 | − | 0.688276i | ||||
\(613\) | 23.4050 | 0.945319 | 0.472659 | − | 0.881245i | \(-0.343294\pi\) | ||||
0.472659 | + | 0.881245i | \(0.343294\pi\) | |||||||
\(614\) | −0.557535 | − | 0.965679i | −0.0225003 | − | 0.0389716i | ||||
\(615\) | −1.25991 | + | 2.18224i | −0.0508047 | + | 0.0879963i | ||||
\(616\) | 8.38911 | − | 14.5304i | 0.338007 | − | 0.585445i | ||||
\(617\) | −6.43742 | + | 11.1499i | −0.259161 | + | 0.448880i | −0.966017 | − | 0.258477i | \(-0.916779\pi\) |
0.706856 | + | 0.707357i | \(0.250113\pi\) | |||||||
\(618\) | 3.12805 | 0.125829 | ||||||||
\(619\) | 22.2499 | 0.894299 | 0.447149 | − | 0.894459i | \(-0.352439\pi\) | ||||
0.447149 | + | 0.894459i | \(0.352439\pi\) | |||||||
\(620\) | 24.6523 | + | 42.6990i | 0.990059 | + | 1.71483i | ||||
\(621\) | 19.3538 | 0.776643 | ||||||||
\(622\) | 2.50893 | + | 4.34559i | 0.100599 | + | 0.174242i | ||||
\(623\) | −3.91140 | + | 6.77474i | −0.156707 | + | 0.271424i | ||||
\(624\) | −0.979503 | − | 1.69655i | −0.0392115 | − | 0.0679163i | ||||
\(625\) | −1.31949 | + | 2.28543i | −0.0527796 | + | 0.0914170i | ||||
\(626\) | 2.41104 | − | 4.17605i | 0.0963646 | − | 0.166908i | ||||
\(627\) | −8.41140 | − | 14.5690i | −0.335919 | − | 0.581829i | ||||
\(628\) | −4.38310 | + | 7.59175i | −0.174905 | + | 0.302944i | ||||
\(629\) | 11.3825 | + | 19.7151i | 0.453851 | + | 0.786093i | ||||
\(630\) | −9.07761 | −0.361661 | ||||||||
\(631\) | 0.756926 | − | 1.31103i | 0.0301327 | − | 0.0521914i | −0.850566 | − | 0.525869i | \(-0.823740\pi\) |
0.880699 | + | 0.473677i | \(0.157074\pi\) | |||||||
\(632\) | −1.84147 | + | 3.18951i | −0.0732496 | + | 0.126872i | ||||
\(633\) | −4.10426 | −0.163130 | ||||||||
\(634\) | −2.05159 | −0.0814791 | ||||||||
\(635\) | 31.6319 | + | 54.7880i | 1.25527 | + | 2.17420i | ||||
\(636\) | 0.366268 | + | 0.634395i | 0.0145235 | + | 0.0251554i | ||||
\(637\) | 0.562667 | 0.0222937 | ||||||||
\(638\) | 12.8540 | 0.508895 | ||||||||
\(639\) | 3.67099 | + | 6.35833i | 0.145222 | + | 0.251532i | ||||
\(640\) | 18.8119 | + | 32.5832i | 0.743606 | + | 1.28796i | ||||
\(641\) | −11.3234 | − | 19.6127i | −0.447246 | − | 0.774654i | 0.550959 | − | 0.834532i | \(-0.314262\pi\) |
−0.998206 | + | 0.0598786i | \(0.980929\pi\) | |||||||
\(642\) | −1.06791 | − | 1.84967i | −0.0421471 | − | 0.0730008i | ||||
\(643\) | −46.7934 | −1.84535 | −0.922675 | − | 0.385579i | \(-0.874002\pi\) | ||||
−0.922675 | + | 0.385579i | \(0.874002\pi\) | |||||||
\(644\) | −22.9009 | −0.902423 | ||||||||
\(645\) | −0.602285 | − | 1.04319i | −0.0237149 | − | 0.0410755i | ||||
\(646\) | −4.57348 | − | 7.92149i | −0.179941 | − | 0.311667i | ||||
\(647\) | 14.1047 | 0.554514 | 0.277257 | − | 0.960796i | \(-0.410575\pi\) | ||||
0.277257 | + | 0.960796i | \(0.410575\pi\) | |||||||
\(648\) | 7.07798 | 0.278049 | ||||||||
\(649\) | −8.37032 | + | 14.4978i | −0.328564 | + | 0.569089i | ||||
\(650\) | −1.46354 | + | 2.53492i | −0.0574046 | + | 0.0994278i | ||||
\(651\) | 13.2449 | 0.519109 | ||||||||
\(652\) | 13.0318 | + | 22.5718i | 0.510366 | + | 0.883980i | ||||
\(653\) | 13.6009 | − | 23.5574i | 0.532244 | − | 0.921873i | −0.467047 | − | 0.884232i | \(-0.654682\pi\) |
0.999291 | − | 0.0376412i | \(-0.0119844\pi\) | |||||||
\(654\) | −0.0810501 | − | 0.140383i | −0.00316931 | − | 0.00548940i | ||||
\(655\) | −2.79315 | + | 4.83788i | −0.109137 | + | 0.189032i | ||||
\(656\) | −1.48564 | + | 2.57320i | −0.0580044 | + | 0.100467i | ||||
\(657\) | 14.8295 | + | 25.6855i | 0.578555 | + | 1.00209i | ||||
\(658\) | 2.23755 | − | 3.87555i | 0.0872287 | − | 0.151085i | ||||
\(659\) | −7.33662 | − | 12.7074i | −0.285794 | − | 0.495010i | 0.687007 | − | 0.726650i | \(-0.258924\pi\) |
−0.972801 | + | 0.231641i | \(0.925591\pi\) | |||||||
\(660\) | 21.0317 | 0.818659 | ||||||||
\(661\) | −5.65695 | − | 9.79813i | −0.220030 | − | 0.381103i | 0.734787 | − | 0.678298i | \(-0.237282\pi\) |
−0.954817 | + | 0.297195i | \(0.903949\pi\) | |||||||
\(662\) | −5.34742 | −0.207833 | ||||||||
\(663\) | −2.72637 | −0.105883 | ||||||||
\(664\) | 1.14475 | − | 1.98276i | 0.0444248 | − | 0.0769460i | ||||
\(665\) | 24.7733 | − | 42.9085i | 0.960666 | − | 1.66392i | ||||
\(666\) | −2.61574 | + | 4.53060i | −0.101358 | + | 0.175557i | ||||
\(667\) | −18.2924 | − | 31.6834i | −0.708286 | − | 1.22679i | ||||
\(668\) | −1.92307 | −0.0744060 | ||||||||
\(669\) | −4.59036 | + | 7.95073i | −0.177474 | + | 0.307393i | ||||
\(670\) | −3.34409 | −0.129193 | ||||||||
\(671\) | 6.50022 | − | 33.4744i | 0.250938 | − | 1.29226i | ||||
\(672\) | 7.71160 | 0.297481 | ||||||||
\(673\) | 12.0184 | − | 20.8165i | 0.463277 | − | 0.802419i | −0.535845 | − | 0.844316i | \(-0.680007\pi\) |
0.999122 | + | 0.0418976i | \(0.0133403\pi\) | |||||||
\(674\) | 10.9396 | 0.421378 | ||||||||
\(675\) | −16.3501 | − | 28.3193i | −0.629317 | − | 1.09001i | ||||
\(676\) | −11.2532 | + | 19.4910i | −0.432814 | + | 0.749655i | ||||
\(677\) | 10.7838 | − | 18.6780i | 0.414453 | − | 0.717854i | −0.580918 | − | 0.813962i | \(-0.697306\pi\) |
0.995371 | + | 0.0961083i | \(0.0306395\pi\) | |||||||
\(678\) | 2.06258 | − | 3.57249i | 0.0792128 | − | 0.137201i | ||||
\(679\) | −48.1673 | −1.84849 | ||||||||
\(680\) | 23.8456 | 0.914437 | ||||||||
\(681\) | −5.45330 | − | 9.44539i | −0.208971 | − | 0.361948i | ||||
\(682\) | −12.6840 | −0.485696 | ||||||||
\(683\) | 22.7142 | + | 39.3421i | 0.869134 | + | 1.50538i | 0.862883 | + | 0.505404i | \(0.168657\pi\) |
0.00625155 | + | 0.999980i | \(0.498010\pi\) | |||||||
\(684\) | −12.3304 | + | 21.3568i | −0.471463 | + | 0.816598i | ||||
\(685\) | −24.0074 | − | 41.5821i | −0.917276 | − | 1.58877i | ||||
\(686\) | −3.81699 | + | 6.61123i | −0.145734 | + | 0.252418i | ||||
\(687\) | −5.48686 | + | 9.50352i | −0.209337 | + | 0.362582i | ||||
\(688\) | −0.710189 | − | 1.23008i | −0.0270757 | − | 0.0468965i | ||||
\(689\) | −0.246294 | + | 0.426594i | −0.00938305 | + | 0.0162519i | ||||
\(690\) | 2.55114 | + | 4.41871i | 0.0971203 | + | 0.168217i | ||||
\(691\) | −4.01839 | −0.152867 | −0.0764333 | − | 0.997075i | \(-0.524353\pi\) | ||||
−0.0764333 | + | 0.997075i | \(0.524353\pi\) | |||||||
\(692\) | −15.4231 | + | 26.7135i | −0.586297 | + | 1.01550i | ||||
\(693\) | −13.6989 | + | 23.7271i | −0.520377 | + | 0.901319i | ||||
\(694\) | −13.1668 | −0.499806 | ||||||||
\(695\) | 4.40070 | 0.166928 | ||||||||
\(696\) | 4.05130 | + | 7.01705i | 0.153564 | + | 0.265981i | ||||
\(697\) | 2.06758 | + | 3.58116i | 0.0783152 | + | 0.135646i | ||||
\(698\) | −6.26141 | −0.236998 | ||||||||
\(699\) | 7.76718 | 0.293782 | ||||||||
\(700\) | 19.3467 | + | 33.5095i | 0.731236 | + | 1.26654i | ||||
\(701\) | −17.8368 | − | 30.8943i | −0.673687 | − | 1.16686i | −0.976851 | − | 0.213921i | \(-0.931376\pi\) |
0.303164 | − | 0.952938i | \(-0.401957\pi\) | |||||||
\(702\) | −0.691130 | − | 1.19707i | −0.0260850 | − | 0.0451806i | ||||
\(703\) | −14.2770 | − | 24.7285i | −0.538467 | − | 0.932652i | ||||
\(704\) | 19.5285 | 0.736010 | ||||||||
\(705\) | 11.6973 | 0.440547 | ||||||||
\(706\) | −3.18885 | − | 5.52325i | −0.120014 | − | 0.207870i | ||||
\(707\) | 2.01021 | + | 3.48179i | 0.0756018 | + | 0.130946i | ||||
\(708\) | −5.06060 | −0.190189 | ||||||||
\(709\) | −21.7635 | −0.817345 | −0.408673 | − | 0.912681i | \(-0.634008\pi\) | ||||
−0.408673 | + | 0.912681i | \(0.634008\pi\) | |||||||
\(710\) | −2.13515 | + | 3.69819i | −0.0801307 | + | 0.138790i | ||||
\(711\) | 3.00700 | − | 5.20827i | 0.112771 | − | 0.195325i | ||||
\(712\) | 4.72232 | 0.176977 | ||||||||
\(713\) | 18.0505 | + | 31.2644i | 0.675997 | + | 1.17086i | ||||
\(714\) | 1.53598 | − | 2.66039i | 0.0574826 | − | 0.0995627i | ||||
\(715\) | 7.07131 | + | 12.2479i | 0.264452 | + | 0.458044i | ||||
\(716\) | 6.80896 | − | 11.7935i | 0.254463 | − | 0.440743i | ||||
\(717\) | −2.55259 | + | 4.42122i | −0.0953283 | + | 0.165113i | ||||
\(718\) | 5.05911 | + | 8.76264i | 0.188804 | + | 0.327019i | ||||
\(719\) | 9.09666 | − | 15.7559i | 0.339248 | − | 0.587595i | −0.645043 | − | 0.764146i | \(-0.723161\pi\) |
0.984291 | + | 0.176551i | \(0.0564941\pi\) | |||||||
\(720\) | −13.9894 | − | 24.2303i | −0.521353 | − | 0.903010i | ||||
\(721\) | 27.8056 | 1.03553 | ||||||||
\(722\) | 1.97125 | + | 3.41431i | 0.0733624 | + | 0.127067i | ||||
\(723\) | −1.29686 | −0.0482309 | ||||||||
\(724\) | −37.4924 | −1.39340 | ||||||||
\(725\) | −30.9069 | + | 53.5323i | −1.14785 | + | 1.98814i | ||||
\(726\) | −1.14417 | + | 1.98176i | −0.0424642 | + | 0.0735502i | ||||
\(727\) | 14.5942 | − | 25.2779i | 0.541268 | − | 0.937504i | −0.457563 | − | 0.889177i | \(-0.651278\pi\) |
0.998832 | − | 0.0483269i | \(-0.0153889\pi\) | |||||||
\(728\) | 1.70530 | + | 2.95366i | 0.0632026 | + | 0.109470i | ||||
\(729\) | −3.11513 | −0.115375 | ||||||||
\(730\) | −8.62528 | + | 14.9394i | −0.319236 | + | 0.552933i | ||||
\(731\) | −1.97676 | −0.0731130 | ||||||||
\(732\) | 9.74589 | − | 3.35783i | 0.360219 | − | 0.124109i | ||||
\(733\) | −44.9718 | −1.66107 | −0.830536 | − | 0.556964i | \(-0.811966\pi\) | ||||
−0.830536 | + | 0.556964i | \(0.811966\pi\) | |||||||
\(734\) | 0.946602 | − | 1.63956i | 0.0349397 | − | 0.0605173i | ||||
\(735\) | −1.65717 | −0.0611255 | ||||||||
\(736\) | 10.5096 | + | 18.2031i | 0.387388 | + | 0.670976i | ||||
\(737\) | −5.04651 | + | 8.74081i | −0.185891 | + | 0.321972i | ||||
\(738\) | −0.475137 | + | 0.822962i | −0.0174900 | + | 0.0302936i | ||||
\(739\) | 26.1675 | − | 45.3234i | 0.962586 | − | 1.66725i | 0.246622 | − | 0.969112i | \(-0.420679\pi\) |
0.715964 | − | 0.698137i | \(-0.245987\pi\) | |||||||
\(740\) | 35.6980 | 1.31228 | ||||||||
\(741\) | 3.41966 | 0.125624 | ||||||||
\(742\) | −0.277513 | − | 0.480667i | −0.0101878 | − | 0.0176459i | ||||
\(743\) | 7.44457 | 0.273115 | 0.136557 | − | 0.990632i | \(-0.456396\pi\) | ||||
0.136557 | + | 0.990632i | \(0.456396\pi\) | |||||||
\(744\) | −3.99772 | − | 6.92425i | −0.146564 | − | 0.253855i | ||||
\(745\) | −34.9962 | + | 60.6153i | −1.28216 | + | 2.22077i | ||||
\(746\) | 4.77509 | + | 8.27070i | 0.174829 | + | 0.302812i | ||||
\(747\) | −1.86930 | + | 3.23772i | −0.0683940 | + | 0.118462i | ||||
\(748\) | 17.2570 | − | 29.8901i | 0.630980 | − | 1.09289i | ||||
\(749\) | −9.49277 | − | 16.4420i | −0.346858 | − | 0.600776i | ||||
\(750\) | 1.72046 | − | 2.97993i | 0.0628224 | − | 0.108812i | ||||
\(751\) | 18.9022 | + | 32.7395i | 0.689750 | + | 1.19468i | 0.971919 | + | 0.235317i | \(0.0756129\pi\) |
−0.282169 | + | 0.959365i | \(0.591054\pi\) | |||||||
\(752\) | 13.7930 | 0.502979 | ||||||||
\(753\) | −3.67500 | + | 6.36529i | −0.133924 | + | 0.231964i | ||||
\(754\) | −1.30645 | + | 2.26284i | −0.0475782 | + | 0.0824079i | ||||
\(755\) | −74.8329 | −2.72345 | ||||||||
\(756\) | −18.2723 | −0.664556 | ||||||||
\(757\) | 16.3204 | + | 28.2678i | 0.593176 | + | 1.02741i | 0.993802 | + | 0.111169i | \(0.0354594\pi\) |
−0.400626 | + | 0.916242i | \(0.631207\pi\) | |||||||
\(758\) | 1.12752 | + | 1.95292i | 0.0409533 | + | 0.0709332i | ||||
\(759\) | 15.3995 | 0.558968 | ||||||||
\(760\) | −29.9093 | −1.08493 | ||||||||
\(761\) | −18.6822 | − | 32.3585i | −0.677228 | − | 1.17299i | −0.975812 | − | 0.218610i | \(-0.929848\pi\) |
0.298584 | − | 0.954383i | \(-0.403486\pi\) | |||||||
\(762\) | −2.45994 | − | 4.26075i | −0.0891144 | − | 0.154351i | ||||
\(763\) | −0.720463 | − | 1.24788i | −0.0260825 | − | 0.0451762i | ||||
\(764\) | −22.8504 | − | 39.5781i | −0.826699 | − | 1.43189i | ||||
\(765\) | −38.9383 | −1.40782 | ||||||||
\(766\) | 7.31957 | 0.264467 | ||||||||
\(767\) | −1.70148 | − | 2.94705i | −0.0614369 | − | 0.106412i | ||||
\(768\) | 1.74031 | + | 3.01431i | 0.0627981 | + | 0.108770i | ||||
\(769\) | −8.84174 | −0.318841 | −0.159421 | − | 0.987211i | \(-0.550963\pi\) | ||||
−0.159421 | + | 0.987211i | \(0.550963\pi\) | |||||||
\(770\) | −15.9353 | −0.574268 | ||||||||
\(771\) | −10.8813 | + | 18.8470i | −0.391882 | + | 0.678759i | ||||
\(772\) | −8.93431 | + | 15.4747i | −0.321553 | + | 0.556946i | ||||
\(773\) | −35.5776 | −1.27964 | −0.639819 | − | 0.768525i | \(-0.720991\pi\) | ||||
−0.639819 | + | 0.768525i | \(0.720991\pi\) | |||||||
\(774\) | −0.227133 | − | 0.393406i | −0.00816412 | − | 0.0141407i | ||||
\(775\) | 30.4982 | − | 52.8244i | 1.09553 | − | 1.89751i | ||||
\(776\) | 14.5384 | + | 25.1812i | 0.521898 | + | 0.903953i | ||||
\(777\) | 4.79486 | − | 8.30493i | 0.172014 | − | 0.297938i | ||||
\(778\) | 4.89822 | − | 8.48397i | 0.175610 | − | 0.304165i | ||||
\(779\) | −2.59335 | − | 4.49181i | −0.0929163 | − | 0.160936i | ||||
\(780\) | −2.13762 | + | 3.70246i | −0.0765390 | + | 0.132569i | ||||
\(781\) | 6.44424 | + | 11.1617i | 0.230593 | + | 0.399399i | ||||
\(782\) | 8.37310 | 0.299421 | ||||||||
\(783\) | −14.5952 | − | 25.2797i | −0.521591 | − | 0.903422i | ||||
\(784\) | −1.95406 | −0.0697879 | ||||||||
\(785\) | 17.3612 | 0.619649 | ||||||||
\(786\) | 0.217217 | − | 0.376231i | 0.00774789 | − | 0.0134197i | ||||
\(787\) | −5.27494 | + | 9.13647i | −0.188031 | + | 0.325680i | −0.944594 | − | 0.328241i | \(-0.893544\pi\) |
0.756562 | + | 0.653922i | \(0.226877\pi\) | |||||||
\(788\) | 3.99663 | − | 6.92236i | 0.142374 | − | 0.246599i | ||||
\(789\) | −2.35743 | − | 4.08319i | −0.0839268 | − | 0.145365i | ||||
\(790\) | 3.49791 | 0.124450 | ||||||||
\(791\) | 18.3345 | − | 31.7562i | 0.651898 | − | 1.12912i | ||||
\(792\) | 16.5390 | 0.587686 | ||||||||
\(793\) | 5.23221 | + | 4.54657i | 0.185801 | + | 0.161453i | ||||
\(794\) | −2.67183 | −0.0948198 | ||||||||
\(795\) | 0.725385 | − | 1.25640i | 0.0257268 | − | 0.0445601i | ||||
\(796\) | 21.9085 | 0.776526 | ||||||||
\(797\) | −1.54938 | − | 2.68360i | −0.0548817 | − | 0.0950579i | 0.837279 | − | 0.546775i | \(-0.184145\pi\) |
−0.892161 | + | 0.451717i | \(0.850811\pi\) | |||||||
\(798\) | −1.92656 | + | 3.33691i | −0.0681996 | + | 0.118125i | ||||
\(799\) | 9.59795 | − | 16.6241i | 0.339551 | − | 0.588120i | ||||
\(800\) | 17.7570 | − | 30.7560i | 0.627804 | − | 1.08739i | ||||
\(801\) | −7.71125 | −0.272464 | ||||||||
\(802\) | 4.98060 | 0.175871 | ||||||||
\(803\) | 26.0325 | + | 45.0897i | 0.918668 | + | 1.59118i | ||||
\(804\) | −3.05106 | −0.107603 | ||||||||
\(805\) | 22.6774 | + | 39.2784i | 0.799273 | + | 1.38438i | ||||
\(806\) | 1.28918 | − | 2.23292i | 0.0454093 | − | 0.0786511i | ||||
\(807\) | 2.16032 | + | 3.74179i | 0.0760469 | + | 0.131717i | ||||
\(808\) | 1.21349 | − | 2.10182i | 0.0426903 | − | 0.0739419i | ||||
\(809\) | −10.1630 | + | 17.6028i | −0.357312 | + | 0.618882i | −0.987511 | − | 0.157551i | \(-0.949640\pi\) |
0.630199 | + | 0.776434i | \(0.282973\pi\) | |||||||
\(810\) | −3.36119 | − | 5.82176i | −0.118100 | − | 0.204556i | ||||
\(811\) | 1.67725 | − | 2.90509i | 0.0588963 | − | 0.102011i | −0.835074 | − | 0.550138i | \(-0.814575\pi\) |
0.893970 | + | 0.448126i | \(0.147909\pi\) | |||||||
\(812\) | 17.2702 | + | 29.9128i | 0.606065 | + | 1.04973i | ||||
\(813\) | −19.1421 | −0.671343 | ||||||||
\(814\) | −4.59181 | + | 7.95324i | −0.160943 | + | 0.278761i | ||||
\(815\) | 25.8092 | − | 44.7029i | 0.904058 | − | 1.56587i | ||||
\(816\) | 9.46830 | 0.331457 | ||||||||
\(817\) | 2.47943 | 0.0867442 | ||||||||
\(818\) | −0.772675 | − | 1.33831i | −0.0270160 | − | 0.0467930i | ||||
\(819\) | −2.78464 | − | 4.82314i | −0.0973033 | − | 0.168534i | ||||
\(820\) | 6.48436 | 0.226444 | ||||||||
\(821\) | −8.33953 | −0.291052 | −0.145526 | − | 0.989354i | \(-0.546487\pi\) | ||||
−0.145526 | + | 0.989354i | \(0.546487\pi\) | |||||||
\(822\) | 1.86701 | + | 3.23375i | 0.0651193 | + | 0.112790i | ||||
\(823\) | 8.64872 | + | 14.9800i | 0.301475 | + | 0.522171i | 0.976470 | − | 0.215652i | \(-0.0691875\pi\) |
−0.674995 | + | 0.737822i | \(0.735854\pi\) | |||||||
\(824\) | −8.39258 | − | 14.5364i | −0.292369 | − | 0.506399i | ||||
\(825\) | −13.0095 | − | 22.5332i | −0.452934 | − | 0.784505i | ||||
\(826\) | 3.83431 | 0.133413 | ||||||||
\(827\) | 42.9127 | 1.49222 | 0.746111 | − | 0.665822i | \(-0.231919\pi\) | ||||
0.746111 | + | 0.665822i | \(0.231919\pi\) | |||||||
\(828\) | −11.2872 | − | 19.5500i | −0.392257 | − | 0.679408i | ||||
\(829\) | −0.435747 | − | 0.754735i | −0.0151341 | − | 0.0262130i | 0.858359 | − | 0.513049i | \(-0.171484\pi\) |
−0.873493 | + | 0.486836i | \(0.838151\pi\) | |||||||
\(830\) | −2.17447 | −0.0754770 | ||||||||
\(831\) | 9.12187 | 0.316434 | ||||||||
\(832\) | −1.98484 | + | 3.43784i | −0.0688118 | + | 0.119186i | ||||
\(833\) | −1.35974 | + | 2.35515i | −0.0471124 | + | 0.0816010i | ||||
\(834\) | −0.342233 | −0.0118506 | ||||||||
\(835\) | 1.90430 | + | 3.29835i | 0.0659011 | + | 0.114144i | ||||
\(836\) | −21.6453 | + | 37.4908i | −0.748620 | + | 1.29665i | ||||
\(837\) | 14.4022 | + | 24.9454i | 0.497813 | + | 0.862238i | ||||
\(838\) | 3.75195 | − | 6.49857i | 0.129609 | − | 0.224489i | ||||
\(839\) | 14.3433 | − | 24.8433i | 0.495185 | − | 0.857686i | −0.504799 | − | 0.863237i | \(-0.668434\pi\) |
0.999985 | + | 0.00555070i | \(0.00176685\pi\) | |||||||
\(840\) | −5.02245 | − | 8.69914i | −0.173291 | − | 0.300149i | ||||
\(841\) | −13.0896 | + | 22.6718i | −0.451365 | + | 0.781788i | ||||
\(842\) | 5.13581 | + | 8.89548i | 0.176992 | + | 0.306559i | ||||
\(843\) | −2.65565 | −0.0914654 | ||||||||
\(844\) | 5.28081 | + | 9.14663i | 0.181773 | + | 0.314840i | ||||
\(845\) | 44.5732 | 1.53337 | ||||||||
\(846\) | 4.41128 | 0.151663 | ||||||||
\(847\) | −10.1707 | + | 17.6161i | −0.349468 | + | 0.605297i | ||||
\(848\) | 0.855344 | − | 1.48150i | 0.0293726 | − | 0.0508749i | ||||
\(849\) | −6.89155 | + | 11.9365i | −0.236517 | + | 0.409660i | ||||
\(850\) | −7.07359 | − | 12.2518i | −0.242622 | − | 0.420234i | ||||
\(851\) | 26.1382 | 0.896007 | ||||||||
\(852\) | −1.94806 | + | 3.37413i | −0.0667393 | + | 0.115596i | ||||
\(853\) | −18.8522 | −0.645487 | −0.322744 | − | 0.946486i | \(-0.604605\pi\) | ||||
−0.322744 | + | 0.946486i | \(0.604605\pi\) | |||||||
\(854\) | −7.38426 | + | 2.54416i | −0.252684 | + | 0.0870593i | ||||
\(855\) | 48.8400 | 1.67029 | ||||||||
\(856\) | −5.73042 | + | 9.92538i | −0.195862 | + | 0.339242i | ||||
\(857\) | 13.3248 | 0.455167 | 0.227583 | − | 0.973759i | \(-0.426918\pi\) | ||||
0.227583 | + | 0.973759i | \(0.426918\pi\) | |||||||
\(858\) | −0.549921 | − | 0.952491i | −0.0187740 | − | 0.0325175i | ||||
\(859\) | −17.6435 | + | 30.5595i | −0.601990 | + | 1.04268i | 0.390529 | + | 0.920591i | \(0.372292\pi\) |
−0.992519 | + | 0.122087i | \(0.961041\pi\) | |||||||
\(860\) | −1.54988 | + | 2.68447i | −0.0528505 | + | 0.0915397i | ||||
\(861\) | 0.870963 | − | 1.50855i | 0.0296823 | − | 0.0514113i | ||||
\(862\) | 10.2972 | 0.350724 | ||||||||
\(863\) | −30.9955 | −1.05510 | −0.527549 | − | 0.849524i | \(-0.676889\pi\) | ||||
−0.527549 | + | 0.849524i | \(0.676889\pi\) | |||||||
\(864\) | 8.38542 | + | 14.5240i | 0.285278 | + | 0.494116i | ||||
\(865\) | 61.0900 | 2.07712 | ||||||||
\(866\) | −4.45993 | − | 7.72483i | −0.151555 | − | 0.262500i | ||||
\(867\) | 0.501222 | − | 0.868141i | 0.0170224 | − | 0.0294836i | ||||
\(868\) | −17.0418 | − | 29.5172i | −0.578436 | − | 1.00188i | ||||
\(869\) | 5.27863 | − | 9.14286i | 0.179065 | − | 0.310150i | ||||
\(870\) | 3.84777 | − | 6.66453i | 0.130451 | − | 0.225949i | ||||
\(871\) | −1.02583 | − | 1.77679i | −0.0347590 | − | 0.0602043i | ||||
\(872\) | −0.434916 | + | 0.753296i | −0.0147281 | + | 0.0255098i | ||||
\(873\) | −23.7402 | − | 41.1193i | −0.803486 | − | 1.39168i | ||||
\(874\) | −10.5023 | −0.355245 | ||||||||
\(875\) | 15.2934 | − | 26.4889i | 0.517011 | − | 0.895488i | ||||
\(876\) | −7.86948 | + | 13.6303i | −0.265885 | + | 0.460527i | ||||
\(877\) | 54.4698 | 1.83932 | 0.919658 | − | 0.392721i | \(-0.128466\pi\) | ||||
0.919658 | + | 0.392721i | \(0.128466\pi\) | |||||||
\(878\) | 0.381240 | 0.0128662 | ||||||||
\(879\) | −4.50940 | − | 7.81051i | −0.152098 | − | 0.263442i | ||||
\(880\) | −24.5576 | − | 42.5351i | −0.827838 | − | 1.43386i | ||||
\(881\) | 13.7004 | 0.461579 | 0.230790 | − | 0.973004i | \(-0.425869\pi\) | ||||
0.230790 | + | 0.973004i | \(0.425869\pi\) | |||||||
\(882\) | −0.624948 | −0.0210431 | ||||||||
\(883\) | 0.553452 | + | 0.958606i | 0.0186251 | + | 0.0322597i | 0.875188 | − | 0.483783i | \(-0.160738\pi\) |
−0.856563 | + | 0.516043i | \(0.827404\pi\) | |||||||
\(884\) | 3.50793 | + | 6.07592i | 0.117985 | + | 0.204355i | ||||
\(885\) | 5.01120 | + | 8.67965i | 0.168450 | + | 0.291763i | ||||
\(886\) | 1.36139 | + | 2.35800i | 0.0457368 | + | 0.0792184i | ||||
\(887\) | −11.5750 | −0.388650 | −0.194325 | − | 0.980937i | \(-0.562252\pi\) | ||||
−0.194325 | + | 0.980937i | \(0.562252\pi\) | |||||||
\(888\) | −5.78894 | −0.194264 | ||||||||
\(889\) | −21.8667 | − | 37.8743i | −0.733386 | − | 1.27026i | ||||
\(890\) | −2.24254 | − | 3.88419i | −0.0751701 | − | 0.130198i | ||||
\(891\) | −20.2893 | −0.679717 | ||||||||
\(892\) | 23.6251 | 0.791025 | ||||||||
\(893\) | −12.0386 | + | 20.8515i | −0.402857 | + | 0.697769i | ||||
\(894\) | 2.72158 | − | 4.71392i | 0.0910233 | − | 0.157657i | ||||
\(895\) | −26.9700 | −0.901507 | ||||||||
\(896\) | −13.0044 | − | 22.5243i | −0.434448 | − | 0.752485i | ||||
\(897\) | −1.56517 | + | 2.71096i | −0.0522597 | + | 0.0905164i | ||||
\(898\) | 2.11676 | + | 3.66634i | 0.0706372 | + | 0.122347i | ||||
\(899\) | 27.2247 | − | 47.1546i | 0.907996 | − | 1.57269i | ||||
\(900\) | −19.0708 | + | 33.0316i | −0.635694 | + | 1.10105i | ||||
\(901\) | −1.19039 | − | 2.06182i | −0.0396577 | − | 0.0686892i | ||||
\(902\) | −0.834080 | + | 1.44467i | −0.0277718 | + | 0.0481022i | ||||
\(903\) | 0.416352 | + | 0.721142i | 0.0138553 | + | 0.0239981i | ||||
\(904\) | −22.1356 | −0.736220 | ||||||||
\(905\) | 37.1265 | + | 64.3049i | 1.23413 | + | 2.13757i | ||||
\(906\) | 5.81959 | 0.193343 | ||||||||
\(907\) | −44.8586 | −1.48951 | −0.744753 | − | 0.667340i | \(-0.767433\pi\) | ||||
−0.744753 | + | 0.667340i | \(0.767433\pi\) | |||||||
\(908\) | −14.0332 | + | 24.3061i | −0.465707 | + | 0.806627i | ||||
\(909\) | −1.98155 | + | 3.43214i | −0.0657238 | + | 0.113837i | ||||
\(910\) | 1.61963 | − | 2.80528i | 0.0536901 | − | 0.0929940i | ||||
\(911\) | 4.60716 | + | 7.97984i | 0.152642 | + | 0.264384i | 0.932198 | − | 0.361949i | \(-0.117888\pi\) |
−0.779556 | + | 0.626333i | \(0.784555\pi\) | |||||||
\(912\) | −11.8760 | −0.393254 | ||||||||
\(913\) | −3.28146 | + | 5.68365i | −0.108600 | + | 0.188102i | ||||
\(914\) | −2.77394 | −0.0917537 | ||||||||
\(915\) | −15.4099 | − | 13.3905i | −0.509436 | − | 0.442678i | ||||
\(916\) | 28.2391 | 0.933045 | ||||||||
\(917\) | 1.93087 | − | 3.34436i | 0.0637629 | − | 0.110441i | ||||
\(918\) | 6.68076 | 0.220498 | ||||||||
\(919\) | 12.9221 | + | 22.3818i | 0.426262 | + | 0.738308i | 0.996537 | − | 0.0831458i | \(-0.0264967\pi\) |
−0.570275 | + | 0.821454i | \(0.693163\pi\) | |||||||
\(920\) | 13.6895 | − | 23.7108i | 0.451328 | − | 0.781723i | ||||
\(921\) | −1.00743 | + | 1.74492i | −0.0331960 | + | 0.0574971i | ||||
\(922\) | 1.14448 | − | 1.98229i | 0.0376914 | − | 0.0652834i | ||||
\(923\) | −2.61991 | −0.0862354 | ||||||||
\(924\) | −14.5390 | −0.478297 | ||||||||
\(925\) | −22.0816 | − | 38.2464i | −0.726038 | − | 1.25753i | ||||
\(926\) | −4.44047 | −0.145923 | ||||||||
\(927\) | 13.7045 | + | 23.7370i | 0.450116 | + | 0.779624i | ||||
\(928\) | 15.8511 | − | 27.4549i | 0.520337 | − | 0.901251i | ||||
\(929\) | 12.1935 | + | 21.1198i | 0.400057 | + | 0.692920i | 0.993732 | − | 0.111785i | \(-0.0356569\pi\) |
−0.593675 | + | 0.804705i | \(0.702324\pi\) | |||||||
\(930\) | −3.79688 | + | 6.57639i | −0.124505 | + | 0.215648i | ||||
\(931\) | 1.70552 | − | 2.95404i | 0.0558960 | − | 0.0968147i | ||||
\(932\) | −9.99377 | − | 17.3097i | −0.327357 | − | 0.566999i | ||||
\(933\) | 4.53347 | − | 7.85220i | 0.148419 | − | 0.257070i | ||||
\(934\) | 6.76410 | + | 11.7158i | 0.221328 | + | 0.383351i | ||||
\(935\) | −68.3543 | −2.23543 | ||||||||
\(936\) | −1.68098 | + | 2.91155i | −0.0549446 | + | 0.0951669i | ||||
\(937\) | 7.91847 | − | 13.7152i | 0.258685 | − | 0.448056i | −0.707205 | − | 0.707009i | \(-0.750044\pi\) |
0.965890 | + | 0.258953i | \(0.0833775\pi\) | |||||||
\(938\) | 2.31173 | 0.0754805 | ||||||||
\(939\) | −8.71320 | −0.284345 | ||||||||
\(940\) | −15.0506 | − | 26.0684i | −0.490896 | − | 0.850257i | ||||
\(941\) | −5.21809 | − | 9.03800i | −0.170105 | − | 0.294630i | 0.768351 | − | 0.640028i | \(-0.221077\pi\) |
−0.938456 | + | 0.345398i | \(0.887744\pi\) | |||||||
\(942\) | −1.35015 | −0.0439902 | ||||||||
\(943\) | 4.74789 | 0.154612 | ||||||||
\(944\) | 5.90899 | + | 10.2347i | 0.192321 | + | 0.333110i | ||||
\(945\) | 18.0939 | + | 31.3396i | 0.588595 | + | 1.01948i | ||||
\(946\) | −0.398720 | − | 0.690604i | −0.0129635 | − | 0.0224535i | ||||
\(947\) | 16.1386 | + | 27.9529i | 0.524435 | + | 0.908348i | 0.999595 | + | 0.0284490i | \(0.00905682\pi\) |
−0.475160 | + | 0.879899i | \(0.657610\pi\) | |||||||
\(948\) | 3.19140 | 0.103652 | ||||||||
\(949\) | −10.5835 | −0.343556 | ||||||||
\(950\) | 8.87234 | + | 15.3673i | 0.287857 | + | 0.498582i | ||||
\(951\) | 1.85355 | + | 3.21044i | 0.0601054 | + | 0.104106i | ||||
\(952\) | −16.4842 | −0.534255 | ||||||||
\(953\) | −40.4644 | −1.31077 | −0.655385 | − | 0.755295i | \(-0.727493\pi\) | ||||
−0.655385 | + | 0.755295i | \(0.727493\pi\) | |||||||
\(954\) | 0.273556 | − | 0.473813i | 0.00885671 | − | 0.0153403i | ||||
\(955\) | −45.2548 | + | 78.3835i | −1.46441 | + | 2.53643i | ||||
\(956\) | 13.1373 | 0.424892 | ||||||||
\(957\) | −11.6132 | − | 20.1146i | −0.375401 | − | 0.650214i | ||||
\(958\) | −4.28513 | + | 7.42206i | −0.138446 | + | 0.239796i | ||||
\(959\) | 16.5960 | + | 28.7451i | 0.535913 | + | 0.928229i | ||||
\(960\) | 5.84574 | − | 10.1251i | 0.188670 | − | 0.326787i | ||||
\(961\) | −11.3647 | + | 19.6842i | −0.366603 | + | 0.634975i | ||||
\(962\) | −0.933402 | − | 1.61670i | −0.0300941 | − | 0.0521245i | ||||
\(963\) | 9.35740 | − | 16.2075i | 0.301538 | − | 0.522279i | ||||
\(964\) | 1.66863 | + | 2.89016i | 0.0537430 | + | 0.0930857i | ||||
\(965\) | 35.3884 | 1.13919 | ||||||||
\(966\) | −1.76357 | − | 3.05460i | −0.0567420 | − | 0.0982800i | ||||
\(967\) | 7.76447 | 0.249688 | 0.124844 | − | 0.992176i | \(-0.460157\pi\) | ||||
0.124844 | + | 0.992176i | \(0.460157\pi\) | |||||||
\(968\) | 12.2793 | 0.394671 | ||||||||
\(969\) | −8.26398 | + | 14.3136i | −0.265477 | + | 0.459820i | ||||
\(970\) | 13.8080 | − | 23.9161i | 0.443348 | − | 0.767901i | ||||
\(971\) | 12.5352 | − | 21.7116i | 0.402274 | − | 0.696759i | −0.591726 | − | 0.806139i | \(-0.701553\pi\) |
0.994000 | + | 0.109380i | \(0.0348866\pi\) | |||||||
\(972\) | −13.9297 | − | 24.1269i | −0.446795 | − | 0.773871i | ||||
\(973\) | −3.04214 | −0.0975266 | ||||||||
\(974\) | 8.61577 | − | 14.9230i | 0.276067 | − | 0.478162i | ||||
\(975\) | 5.28904 | 0.169385 | ||||||||
\(976\) | −18.1707 | − | 15.7896i | −0.581631 | − | 0.505412i | ||||
\(977\) | −36.2003 | −1.15815 | −0.579075 | − | 0.815274i | \(-0.696586\pi\) | ||||
−0.579075 | + | 0.815274i | \(0.696586\pi\) | |||||||
\(978\) | −2.00713 | + | 3.47645i | −0.0641809 | + | 0.111165i | ||||
\(979\) | −13.5367 | −0.432635 | ||||||||
\(980\) | 2.13222 | + | 3.69312i | 0.0681113 | + | 0.117972i | ||||
\(981\) | 0.710189 | − | 1.23008i | 0.0226746 | − | 0.0392735i | ||||
\(982\) | −2.51445 | + | 4.35515i | −0.0802392 | + | 0.138978i | ||||
\(983\) | −16.8261 | + | 29.1437i | −0.536670 | + | 0.929539i | 0.462411 | + | 0.886666i | \(0.346985\pi\) |
−0.999081 | + | 0.0428733i | \(0.986349\pi\) | |||||||
\(984\) | −1.05153 | −0.0335217 | ||||||||
\(985\) | −15.8305 | −0.504401 | ||||||||
\(986\) | −6.31437 | − | 10.9368i | −0.201090 | − | 0.348299i | ||||
\(987\) | −8.08622 | −0.257387 | ||||||||
\(988\) | −4.39997 | − | 7.62097i | −0.139982 | − | 0.242455i | ||||
\(989\) | −1.13483 | + | 1.96559i | −0.0360855 | + | 0.0625020i | ||||
\(990\) | −7.85403 | − | 13.6036i | −0.249618 | − | 0.432350i | ||||
\(991\) | −15.4271 | + | 26.7205i | −0.490057 | + | 0.848804i | −0.999935 | − | 0.0114434i | \(-0.996357\pi\) |
0.509878 | + | 0.860247i | \(0.329691\pi\) | |||||||
\(992\) | −15.6415 | + | 27.0918i | −0.496617 | + | 0.860166i | ||||
\(993\) | 4.83123 | + | 8.36793i | 0.153314 | + | 0.265548i | ||||
\(994\) | 1.47600 | − | 2.55651i | 0.0468159 | − | 0.0810875i | ||||
\(995\) | −21.6946 | − | 37.5762i | −0.687767 | − | 1.19125i | ||||
\(996\) | −1.98393 | −0.0628633 | ||||||||
\(997\) | −5.14169 | + | 8.90567i | −0.162839 | + | 0.282046i | −0.935886 | − | 0.352304i | \(-0.885398\pi\) |
0.773047 | + | 0.634349i | \(0.218732\pi\) | |||||||
\(998\) | 1.77106 | − | 3.06757i | 0.0560619 | − | 0.0971021i | ||||
\(999\) | 20.8553 | 0.659832 |
(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 | 61.2.c.a.13.3 | ✓ | 8 | |
3.2 | odd | 2 | 549.2.e.g.379.2 | 8 | |||
4.3 | odd | 2 | 976.2.i.g.257.3 | 8 | |||
61.13 | even | 3 | 3721.2.a.e.1.2 | 4 | |||
61.47 | even | 3 | inner | 61.2.c.a.47.3 | yes | 8 | |
61.48 | even | 6 | 3721.2.a.d.1.3 | 4 | |||
183.47 | odd | 6 | 549.2.e.g.352.2 | 8 | |||
244.47 | odd | 6 | 976.2.i.g.657.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
61.2.c.a.13.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
61.2.c.a.47.3 | yes | 8 | 61.47 | even | 3 | inner | |
549.2.e.g.352.2 | 8 | 183.47 | odd | 6 | |||
549.2.e.g.379.2 | 8 | 3.2 | odd | 2 | |||
976.2.i.g.257.3 | 8 | 4.3 | odd | 2 | |||
976.2.i.g.657.3 | 8 | 244.47 | odd | 6 | |||
3721.2.a.d.1.3 | 4 | 61.48 | even | 6 | |||
3721.2.a.e.1.2 | 4 | 61.13 | even | 3 |