Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [171,2,Mod(106,171)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(171, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("171.106");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 171 = 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 171.g (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: | \(1.36544187456\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 121.4 | ||
Character | \(\chi\) | \(=\) | 171.121 |
Dual form | 171.2.g.c.106.4 |
$q$-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 \(\left(\mathbb{Z}/171\mathbb{Z}\right)^\times\).
\(n\) | \(20\) | \(154\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.888985 | + | 1.53977i | −0.628607 | + | 1.08878i | 0.359224 | + | 0.933251i | \(0.383041\pi\) |
−0.987831 | + | 0.155529i | \(0.950292\pi\) | |||||||
\(3\) | 1.15573 | + | 1.29008i | 0.667258 | + | 0.744827i | ||||
\(4\) | −0.580589 | − | 1.00561i | −0.290295 | − | 0.502805i | ||||
\(5\) | −1.27957 | −0.572242 | −0.286121 | − | 0.958194i | \(-0.592366\pi\) | ||||
−0.286121 | + | 0.958194i | \(0.592366\pi\) | |||||||
\(6\) | −3.01384 | + | 0.632688i | −1.23040 | + | 0.258294i | ||||
\(7\) | 0.657761 | + | 1.13928i | 0.248610 | + | 0.430606i | 0.963140 | − | 0.268999i | \(-0.0866928\pi\) |
−0.714530 | + | 0.699605i | \(0.753359\pi\) | |||||||
\(8\) | −1.49140 | −0.527290 | ||||||||
\(9\) | −0.328599 | + | 2.98195i | −0.109533 | + | 0.993983i | ||||
\(10\) | 1.13752 | − | 1.97024i | 0.359715 | − | 0.623045i | ||||
\(11\) | −0.130095 | − | 0.225331i | −0.0392251 | − | 0.0679398i | 0.845746 | − | 0.533585i | \(-0.179156\pi\) |
−0.884971 | + | 0.465645i | \(0.845822\pi\) | |||||||
\(12\) | 0.626313 | − | 1.91121i | 0.180801 | − | 0.551720i | ||||
\(13\) | 0.933961 | + | 1.61767i | 0.259034 | + | 0.448660i | 0.965983 | − | 0.258604i | \(-0.0832625\pi\) |
−0.706949 | + | 0.707264i | \(0.749929\pi\) | |||||||
\(14\) | −2.33896 | −0.625113 | ||||||||
\(15\) | −1.47883 | − | 1.65075i | −0.381833 | − | 0.426221i | ||||
\(16\) | 2.48701 | − | 4.30763i | 0.621753 | − | 1.07691i | ||||
\(17\) | −0.0508308 | − | 0.0880415i | −0.0123283 | − | 0.0213532i | 0.859795 | − | 0.510639i | \(-0.170591\pi\) |
−0.872124 | + | 0.489285i | \(0.837258\pi\) | |||||||
\(18\) | −4.29939 | − | 3.15688i | −1.01338 | − | 0.744083i | ||||
\(19\) | 3.11089 | − | 3.05326i | 0.713687 | − | 0.700465i | ||||
\(20\) | 0.742905 | + | 1.28675i | 0.166119 | + | 0.287726i | ||||
\(21\) | −0.709563 | + | 2.16525i | −0.154839 | + | 0.472497i | ||||
\(22\) | 0.462610 | 0.0986287 | ||||||||
\(23\) | 0.611950 | + | 1.05993i | 0.127600 | + | 0.221010i | 0.922746 | − | 0.385408i | \(-0.125939\pi\) |
−0.795146 | + | 0.606418i | \(0.792606\pi\) | |||||||
\(24\) | −1.72365 | − | 1.92402i | −0.351838 | − | 0.392739i | ||||
\(25\) | −3.36270 | −0.672540 | ||||||||
\(26\) | −3.32111 | −0.651323 | ||||||||
\(27\) | −4.22672 | + | 3.02240i | −0.813432 | + | 0.581660i | ||||
\(28\) | 0.763778 | − | 1.32290i | 0.144340 | − | 0.250005i | ||||
\(29\) | 6.52642 | 1.21193 | 0.605963 | − | 0.795493i | \(-0.292788\pi\) | ||||
0.605963 | + | 0.795493i | \(0.292788\pi\) | |||||||
\(30\) | 3.85642 | − | 0.809570i | 0.704084 | − | 0.147806i | ||||
\(31\) | −0.617667 | + | 1.06983i | −0.110936 | + | 0.192147i | −0.916148 | − | 0.400840i | \(-0.868718\pi\) |
0.805212 | + | 0.592987i | \(0.202052\pi\) | |||||||
\(32\) | 2.93043 | + | 5.07566i | 0.518032 | + | 0.897258i | ||||
\(33\) | 0.140340 | − | 0.428253i | 0.0244301 | − | 0.0745493i | ||||
\(34\) | 0.180751 | 0.0309986 | ||||||||
\(35\) | −0.841652 | − | 1.45778i | −0.142265 | − | 0.246411i | ||||
\(36\) | 3.18946 | − | 1.40084i | 0.531576 | − | 0.233474i | ||||
\(37\) | 8.59418 | 1.41287 | 0.706437 | − | 0.707776i | \(-0.250301\pi\) | ||||
0.706437 | + | 0.707776i | \(0.250301\pi\) | |||||||
\(38\) | 1.93577 | + | 7.50434i | 0.314023 | + | 1.21737i | ||||
\(39\) | −1.00751 | + | 3.07446i | −0.161331 | + | 0.492308i | ||||
\(40\) | 1.90835 | 0.301737 | ||||||||
\(41\) | 8.21490 | 1.28295 | 0.641476 | − | 0.767143i | \(-0.278322\pi\) | ||||
0.641476 | + | 0.767143i | \(0.278322\pi\) | |||||||
\(42\) | −2.70319 | − | 3.01744i | −0.417112 | − | 0.465601i | ||||
\(43\) | −1.53770 | + | 2.66338i | −0.234498 | + | 0.406162i | −0.959127 | − | 0.282977i | \(-0.908678\pi\) |
0.724629 | + | 0.689139i | \(0.242011\pi\) | |||||||
\(44\) | −0.151063 | + | 0.261649i | −0.0227736 | + | 0.0394451i | ||||
\(45\) | 0.420466 | − | 3.81562i | 0.0626794 | − | 0.568799i | ||||
\(46\) | −2.17606 | −0.320842 | ||||||||
\(47\) | 1.58093 | 0.230602 | 0.115301 | − | 0.993331i | \(-0.463217\pi\) | ||||
0.115301 | + | 0.993331i | \(0.463217\pi\) | |||||||
\(48\) | 8.43148 | − | 1.77000i | 1.21698 | − | 0.255477i | ||||
\(49\) | 2.63470 | − | 4.56344i | 0.376386 | − | 0.651919i | ||||
\(50\) | 2.98939 | − | 5.17777i | 0.422763 | − | 0.732248i | ||||
\(51\) | 0.0548339 | − | 0.167327i | 0.00767828 | − | 0.0234305i | ||||
\(52\) | 1.08449 | − | 1.87840i | 0.150392 | − | 0.260487i | ||||
\(53\) | −2.59998 | + | 4.50330i | −0.357135 | + | 0.618575i | −0.987481 | − | 0.157739i | \(-0.949580\pi\) |
0.630346 | + | 0.776314i | \(0.282913\pi\) | |||||||
\(54\) | −0.896298 | − | 9.19502i | −0.121971 | − | 1.25128i | ||||
\(55\) | 0.166466 | + | 0.288327i | 0.0224462 | + | 0.0388780i | ||||
\(56\) | −0.980985 | − | 1.69912i | −0.131090 | − | 0.227054i | ||||
\(57\) | 7.53427 | + | 0.484562i | 0.997938 | + | 0.0641818i | ||||
\(58\) | −5.80189 | + | 10.0492i | −0.761826 | + | 1.31952i | ||||
\(59\) | 8.02123 | 1.04428 | 0.522138 | − | 0.852861i | \(-0.325135\pi\) | ||||
0.522138 | + | 0.852861i | \(0.325135\pi\) | |||||||
\(60\) | −0.801412 | + | 2.44553i | −0.103462 | + | 0.315717i | ||||
\(61\) | −14.1310 | −1.80928 | −0.904642 | − | 0.426171i | \(-0.859862\pi\) | ||||
−0.904642 | + | 0.426171i | \(0.859862\pi\) | |||||||
\(62\) | −1.09819 | − | 1.90213i | −0.139471 | − | 0.241570i | ||||
\(63\) | −3.61340 | + | 1.58705i | −0.455246 | + | 0.199949i | ||||
\(64\) | −0.472395 | −0.0590494 | ||||||||
\(65\) | −1.19507 | − | 2.06992i | −0.148230 | − | 0.256742i | ||||
\(66\) | 0.534649 | + | 0.596802i | 0.0658108 | + | 0.0734613i | ||||
\(67\) | 0.390956 | + | 0.677156i | 0.0477629 | + | 0.0827277i | 0.888918 | − | 0.458065i | \(-0.151457\pi\) |
−0.841156 | + | 0.540793i | \(0.818124\pi\) | |||||||
\(68\) | −0.0590236 | + | 0.102232i | −0.00715766 | + | 0.0123974i | ||||
\(69\) | −0.660144 | + | 2.01445i | −0.0794720 | + | 0.242511i | ||||
\(70\) | 2.99287 | 0.357716 | ||||||||
\(71\) | −8.19574 | − | 14.1954i | −0.972656 | − | 1.68469i | −0.687463 | − | 0.726219i | \(-0.741276\pi\) |
−0.285193 | − | 0.958470i | \(-0.592058\pi\) | |||||||
\(72\) | 0.490073 | − | 4.44728i | 0.0577556 | − | 0.524117i | ||||
\(73\) | −0.397074 | − | 0.687753i | −0.0464740 | − | 0.0804954i | 0.841853 | − | 0.539707i | \(-0.181465\pi\) |
−0.888327 | + | 0.459212i | \(0.848132\pi\) | |||||||
\(74\) | −7.64010 | + | 13.2330i | −0.888143 | + | 1.53831i | ||||
\(75\) | −3.88635 | − | 4.33814i | −0.448758 | − | 0.500925i | ||||
\(76\) | −4.87653 | − | 1.35565i | −0.559377 | − | 0.155504i | ||||
\(77\) | 0.171143 | − | 0.296428i | 0.0195035 | − | 0.0337811i | ||||
\(78\) | −3.83829 | − | 4.28449i | −0.434601 | − | 0.485123i | ||||
\(79\) | −5.82382 | + | 10.0871i | −0.655230 | + | 1.13489i | 0.326606 | + | 0.945161i | \(0.394095\pi\) |
−0.981836 | + | 0.189732i | \(0.939238\pi\) | |||||||
\(80\) | −3.18231 | + | 5.51192i | −0.355793 | + | 0.616251i | ||||
\(81\) | −8.78405 | − | 1.95973i | −0.976005 | − | 0.217748i | ||||
\(82\) | −7.30292 | + | 12.6490i | −0.806473 | + | 1.39685i | ||||
\(83\) | −3.03265 | − | 5.25271i | −0.332877 | − | 0.576560i | 0.650198 | − | 0.759765i | \(-0.274686\pi\) |
−0.983075 | + | 0.183205i | \(0.941353\pi\) | |||||||
\(84\) | 2.58936 | − | 0.543579i | 0.282523 | − | 0.0593093i | ||||
\(85\) | 0.0650416 | + | 0.112655i | 0.00705475 | + | 0.0122192i | ||||
\(86\) | −2.73399 | − | 4.73542i | −0.294814 | − | 0.510633i | ||||
\(87\) | 7.54275 | + | 8.41959i | 0.808668 | + | 0.902675i | ||||
\(88\) | 0.194023 | + | 0.336058i | 0.0206830 | + | 0.0358240i | ||||
\(89\) | 5.75551 | − | 9.96883i | 0.610082 | − | 1.05669i | −0.381144 | − | 0.924516i | \(-0.624470\pi\) |
0.991226 | − | 0.132178i | \(-0.0421970\pi\) | |||||||
\(90\) | 5.50137 | + | 4.03945i | 0.579896 | + | 0.425795i | ||||
\(91\) | −1.22865 | + | 2.12808i | −0.128797 | + | 0.223083i | ||||
\(92\) | 0.710583 | − | 1.23077i | 0.0740834 | − | 0.128316i | ||||
\(93\) | −2.09402 | + | 0.439592i | −0.217140 | + | 0.0455836i | ||||
\(94\) | −1.40542 | + | 2.43426i | −0.144958 | + | 0.251075i | ||||
\(95\) | −3.98060 | + | 3.90686i | −0.408401 | + | 0.400835i | ||||
\(96\) | −3.16122 | + | 9.64654i | −0.322640 | + | 0.984546i | ||||
\(97\) | 5.83968 | − | 10.1146i | 0.592930 | − | 1.02698i | −0.400906 | − | 0.916119i | \(-0.631304\pi\) |
0.993835 | − | 0.110865i | \(-0.0353622\pi\) | |||||||
\(98\) | 4.68442 | + | 8.11365i | 0.473198 | + | 0.819603i | ||||
\(99\) | 0.714674 | − | 0.313893i | 0.0718275 | − | 0.0315474i | ||||
\(100\) | 1.95235 | + | 3.38156i | 0.195235 | + | 0.338156i | ||||
\(101\) | −13.7351 | −1.36670 | −0.683349 | − | 0.730092i | \(-0.739477\pi\) | ||||
−0.683349 | + | 0.730092i | \(0.739477\pi\) | |||||||
\(102\) | 0.208899 | + | 0.233183i | 0.0206840 | + | 0.0230886i | ||||
\(103\) | −3.88901 | + | 6.73596i | −0.383195 | + | 0.663714i | −0.991517 | − | 0.129977i | \(-0.958510\pi\) |
0.608322 | + | 0.793691i | \(0.291843\pi\) | |||||||
\(104\) | −1.39291 | − | 2.41259i | −0.136586 | − | 0.236574i | ||||
\(105\) | 0.907936 | − | 2.77059i | 0.0886055 | − | 0.270382i | ||||
\(106\) | −4.62269 | − | 8.00673i | −0.448995 | − | 0.777682i | ||||
\(107\) | 2.71691 | 0.262654 | 0.131327 | − | 0.991339i | \(-0.458076\pi\) | ||||
0.131327 | + | 0.991339i | \(0.458076\pi\) | |||||||
\(108\) | 5.49334 | + | 2.49566i | 0.528596 | + | 0.240145i | ||||
\(109\) | −9.03891 | − | 15.6558i | −0.865770 | − | 1.49956i | −0.866280 | − | 0.499559i | \(-0.833496\pi\) |
0.000509715 | − | 1.00000i | \(-0.499838\pi\) | |||||||
\(110\) | −0.591942 | −0.0564394 | ||||||||
\(111\) | 9.93251 | + | 11.0872i | 0.942752 | + | 1.05235i | ||||
\(112\) | 6.54344 | 0.618297 | ||||||||
\(113\) | 5.83591 | − | 10.1081i | 0.548997 | − | 0.950890i | −0.449347 | − | 0.893357i | \(-0.648343\pi\) |
0.998344 | − | 0.0575326i | \(-0.0183233\pi\) | |||||||
\(114\) | −7.44397 | + | 11.1703i | −0.697191 | + | 1.04619i | ||||
\(115\) | −0.783034 | − | 1.35625i | −0.0730183 | − | 0.126471i | ||||
\(116\) | −3.78917 | − | 6.56304i | −0.351816 | − | 0.609363i | ||||
\(117\) | −5.13070 | + | 2.25346i | −0.474333 | + | 0.208332i | ||||
\(118\) | −7.13075 | + | 12.3508i | −0.656439 | + | 1.13699i | ||||
\(119\) | 0.0668690 | − | 0.115820i | 0.00612987 | − | 0.0106172i | ||||
\(120\) | 2.20553 | + | 2.46192i | 0.201337 | + | 0.224742i | ||||
\(121\) | 5.46615 | − | 9.46765i | 0.496923 | − | 0.860696i | ||||
\(122\) | 12.5622 | − | 21.7584i | 1.13733 | − | 1.96991i | ||||
\(123\) | 9.49417 | + | 10.5979i | 0.856060 | + | 0.955577i | ||||
\(124\) | 1.43444 | 0.128817 | ||||||||
\(125\) | 10.7007 | 0.957097 | ||||||||
\(126\) | 0.768580 | − | 6.97466i | 0.0684706 | − | 0.621352i | ||||
\(127\) | 2.39063 | − | 4.14069i | 0.212134 | − | 0.367427i | −0.740248 | − | 0.672334i | \(-0.765292\pi\) |
0.952382 | + | 0.304907i | \(0.0986253\pi\) | |||||||
\(128\) | −5.44091 | + | 9.42393i | −0.480913 | + | 0.832966i | ||||
\(129\) | −5.21313 | + | 1.09438i | −0.458991 | + | 0.0963548i | ||||
\(130\) | 4.24959 | 0.372714 | ||||||||
\(131\) | −11.5587 | −1.00989 | −0.504945 | − | 0.863151i | \(-0.668487\pi\) | ||||
−0.504945 | + | 0.863151i | \(0.668487\pi\) | |||||||
\(132\) | −0.512135 | + | 0.107511i | −0.0445757 | + | 0.00935766i | ||||
\(133\) | 5.52472 | + | 1.53585i | 0.479054 | + | 0.133175i | ||||
\(134\) | −1.39022 | −0.120096 | ||||||||
\(135\) | 5.40838 | − | 3.86737i | 0.465480 | − | 0.332850i | ||||
\(136\) | 0.0758090 | + | 0.131305i | 0.00650057 | + | 0.0112593i | ||||
\(137\) | 11.8095 | 1.00895 | 0.504476 | − | 0.863426i | \(-0.331686\pi\) | ||||
0.504476 | + | 0.863426i | \(0.331686\pi\) | |||||||
\(138\) | −2.51493 | − | 2.80728i | −0.214085 | − | 0.238972i | ||||
\(139\) | 2.61207 | + | 4.52424i | 0.221553 | + | 0.383741i | 0.955280 | − | 0.295704i | \(-0.0955542\pi\) |
−0.733727 | + | 0.679445i | \(0.762221\pi\) | |||||||
\(140\) | −0.977308 | + | 1.69275i | −0.0825976 | + | 0.143063i | ||||
\(141\) | 1.82712 | + | 2.03952i | 0.153871 | + | 0.171759i | ||||
\(142\) | 29.1436 | 2.44568 | ||||||||
\(143\) | 0.243007 | − | 0.420900i | 0.0203213 | − | 0.0351974i | ||||
\(144\) | 12.0279 | + | 8.83162i | 1.00233 | + | 0.735969i | ||||
\(145\) | −8.35102 | −0.693515 | ||||||||
\(146\) | 1.41197 | 0.116856 | ||||||||
\(147\) | 8.93217 | − | 1.87511i | 0.736713 | − | 0.154656i | ||||
\(148\) | −4.98969 | − | 8.64239i | −0.410150 | − | 0.710400i | ||||
\(149\) | −13.2345 | −1.08422 | −0.542108 | − | 0.840309i | \(-0.682374\pi\) | ||||
−0.542108 | + | 0.840309i | \(0.682374\pi\) | |||||||
\(150\) | 10.1346 | − | 2.12754i | 0.827490 | − | 0.173713i | ||||
\(151\) | 7.38449 | + | 12.7903i | 0.600942 | + | 1.04086i | 0.992679 | + | 0.120784i | \(0.0385409\pi\) |
−0.391737 | + | 0.920077i | \(0.628126\pi\) | |||||||
\(152\) | −4.63958 | + | 4.55363i | −0.376320 | + | 0.369348i | ||||
\(153\) | 0.279238 | − | 0.122644i | 0.0225751 | − | 0.00991521i | ||||
\(154\) | 0.304287 | + | 0.527040i | 0.0245201 | + | 0.0424701i | ||||
\(155\) | 0.790349 | − | 1.36892i | 0.0634824 | − | 0.109955i | ||||
\(156\) | 3.67666 | − | 0.771832i | 0.294368 | − | 0.0617960i | ||||
\(157\) | −0.0780549 | −0.00622946 | −0.00311473 | − | 0.999995i | \(-0.500991\pi\) | ||||
−0.00311473 | + | 0.999995i | \(0.500991\pi\) | |||||||
\(158\) | −10.3546 | − | 17.9346i | −0.823765 | − | 1.42680i | ||||
\(159\) | −8.81446 | + | 1.85040i | −0.699032 | + | 0.146746i | ||||
\(160\) | −3.74969 | − | 6.49466i | −0.296439 | − | 0.513448i | ||||
\(161\) | −0.805034 | + | 1.39436i | −0.0634456 | + | 0.109891i | ||||
\(162\) | 10.8264 | − | 11.7832i | 0.850604 | − | 0.925777i | ||||
\(163\) | −19.5891 | −1.53434 | −0.767170 | − | 0.641444i | \(-0.778336\pi\) | ||||
−0.767170 | + | 0.641444i | \(0.778336\pi\) | |||||||
\(164\) | −4.76948 | − | 8.26099i | −0.372434 | − | 0.645075i | ||||
\(165\) | −0.179576 | + | 0.547980i | −0.0139799 | + | 0.0426602i | ||||
\(166\) | 10.7839 | 0.836996 | ||||||||
\(167\) | 11.6324 | + | 20.1479i | 0.900140 | + | 1.55909i | 0.827311 | + | 0.561744i | \(0.189869\pi\) |
0.0728285 | + | 0.997344i | \(0.476797\pi\) | |||||||
\(168\) | 1.05824 | − | 3.22926i | 0.0816451 | − | 0.249143i | ||||
\(169\) | 4.75544 | − | 8.23666i | 0.365803 | − | 0.633589i | ||||
\(170\) | −0.231284 | −0.0177387 | ||||||||
\(171\) | 8.08242 | + | 10.2798i | 0.618078 | + | 0.786117i | ||||
\(172\) | 3.57110 | 0.272294 | ||||||||
\(173\) | 2.86145 | − | 4.95618i | 0.217552 | − | 0.376811i | −0.736507 | − | 0.676430i | \(-0.763526\pi\) |
0.954059 | + | 0.299619i | \(0.0968595\pi\) | |||||||
\(174\) | −19.6696 | + | 4.12919i | −1.49115 | + | 0.313033i | ||||
\(175\) | −2.21185 | − | 3.83104i | −0.167200 | − | 0.289599i | ||||
\(176\) | −1.29419 | −0.0975532 | ||||||||
\(177\) | 9.27034 | + | 10.3480i | 0.696801 | + | 0.777804i | ||||
\(178\) | 10.2331 | + | 17.7243i | 0.767005 | + | 1.32849i | ||||
\(179\) | −7.56033 | −0.565085 | −0.282543 | − | 0.959255i | \(-0.591178\pi\) | ||||
−0.282543 | + | 0.959255i | \(0.591178\pi\) | |||||||
\(180\) | −4.08114 | + | 1.79248i | −0.304190 | + | 0.133604i | ||||
\(181\) | −4.37626 | + | 7.57990i | −0.325285 | + | 0.563410i | −0.981570 | − | 0.191103i | \(-0.938793\pi\) |
0.656285 | + | 0.754513i | \(0.272127\pi\) | |||||||
\(182\) | −2.18450 | − | 3.78366i | −0.161926 | − | 0.280463i | ||||
\(183\) | −16.3315 | − | 18.2300i | −1.20726 | − | 1.34760i | ||||
\(184\) | −0.912663 | − | 1.58078i | −0.0672824 | − | 0.116536i | ||||
\(185\) | −10.9969 | −0.808505 | ||||||||
\(186\) | 1.18468 | − | 3.61509i | 0.0868651 | − | 0.265071i | ||||
\(187\) | −0.0132256 | + | 0.0229075i | −0.000967154 | + | 0.00167516i | ||||
\(188\) | −0.917870 | − | 1.58980i | −0.0669425 | − | 0.115948i | ||||
\(189\) | −6.22351 | − | 2.82738i | −0.452694 | − | 0.205662i | ||||
\(190\) | −2.47696 | − | 9.60234i | −0.179697 | − | 0.696627i | ||||
\(191\) | 1.36408 | + | 2.36265i | 0.0987011 | + | 0.170955i | 0.911147 | − | 0.412081i | \(-0.135198\pi\) |
−0.812446 | + | 0.583036i | \(0.801865\pi\) | |||||||
\(192\) | −0.545959 | − | 0.609426i | −0.0394012 | − | 0.0439816i | ||||
\(193\) | −24.5813 | −1.76940 | −0.884699 | − | 0.466164i | \(-0.845636\pi\) | ||||
−0.884699 | + | 0.466164i | \(0.845636\pi\) | |||||||
\(194\) | 10.3828 | + | 17.9835i | 0.745440 | + | 1.29114i | ||||
\(195\) | 1.28919 | − | 3.93399i | 0.0923205 | − | 0.281719i | ||||
\(196\) | −6.11871 | −0.437051 | ||||||||
\(197\) | 4.62417 | 0.329458 | 0.164729 | − | 0.986339i | \(-0.447325\pi\) | ||||
0.164729 | + | 0.986339i | \(0.447325\pi\) | |||||||
\(198\) | −0.152013 | + | 1.37948i | −0.0108031 | + | 0.0980352i | ||||
\(199\) | 3.26083 | − | 5.64792i | 0.231154 | − | 0.400370i | −0.726994 | − | 0.686644i | \(-0.759083\pi\) |
0.958148 | + | 0.286273i | \(0.0924165\pi\) | |||||||
\(200\) | 5.01513 | 0.354623 | ||||||||
\(201\) | −0.421745 | + | 1.28697i | −0.0297476 | + | 0.0907758i | ||||
\(202\) | 12.2103 | − | 21.1489i | 0.859116 | − | 1.48803i | ||||
\(203\) | 4.29283 | + | 7.43540i | 0.301297 | + | 0.521862i | ||||
\(204\) | −0.200102 | + | 0.0420069i | −0.0140099 | + | 0.00294107i | ||||
\(205\) | −10.5115 | −0.734158 | ||||||||
\(206\) | −6.91454 | − | 11.9763i | −0.481759 | − | 0.834431i | ||||
\(207\) | −3.36174 | + | 1.47651i | −0.233657 | + | 0.102625i | ||||
\(208\) | 9.29108 | 0.644220 | ||||||||
\(209\) | −1.09270 | − | 0.303766i | −0.0755839 | − | 0.0210120i | ||||
\(210\) | 3.45893 | + | 3.86103i | 0.238689 | + | 0.266436i | ||||
\(211\) | 5.21704 | 0.359156 | 0.179578 | − | 0.983744i | \(-0.442527\pi\) | ||||
0.179578 | + | 0.983744i | \(0.442527\pi\) | |||||||
\(212\) | 6.03808 | 0.414697 | ||||||||
\(213\) | 8.84120 | − | 26.9792i | 0.605789 | − | 1.84858i | ||||
\(214\) | −2.41530 | + | 4.18341i | −0.165106 | + | 0.285972i | ||||
\(215\) | 1.96760 | − | 3.40799i | 0.134189 | − | 0.232423i | ||||
\(216\) | 6.30372 | − | 4.50760i | 0.428914 | − | 0.306703i | ||||
\(217\) | −1.62511 | −0.110320 | ||||||||
\(218\) | 32.1418 | 2.17692 | ||||||||
\(219\) | 0.428346 | − | 1.30711i | 0.0289449 | − | 0.0883263i | ||||
\(220\) | 0.193296 | − | 0.334799i | 0.0130320 | − | 0.0225721i | ||||
\(221\) | 0.0949478 | − | 0.164454i | 0.00638688 | − | 0.0110624i | ||||
\(222\) | −25.9015 | + | 5.43744i | −1.73839 | + | 0.364937i | ||||
\(223\) | −2.46764 | + | 4.27407i | −0.165245 | + | 0.286213i | −0.936742 | − | 0.350020i | \(-0.886175\pi\) |
0.771497 | + | 0.636233i | \(0.219508\pi\) | |||||||
\(224\) | −3.85505 | + | 6.67714i | −0.257576 | + | 0.446135i | ||||
\(225\) | 1.10498 | − | 10.0274i | 0.0736653 | − | 0.668493i | ||||
\(226\) | 10.3761 | + | 17.9719i | 0.690207 | + | 1.19547i | ||||
\(227\) | −7.33746 | − | 12.7089i | −0.487004 | − | 0.843516i | 0.512884 | − | 0.858458i | \(-0.328577\pi\) |
−0.999888 | + | 0.0149416i | \(0.995244\pi\) | |||||||
\(228\) | −3.88703 | − | 7.85787i | −0.257425 | − | 0.520400i | ||||
\(229\) | 0.589497 | − | 1.02104i | 0.0389551 | − | 0.0674722i | −0.845891 | − | 0.533357i | \(-0.820930\pi\) |
0.884846 | + | 0.465884i | \(0.154264\pi\) | |||||||
\(230\) | 2.78442 | 0.183599 | ||||||||
\(231\) | 0.580209 | − | 0.121802i | 0.0381749 | − | 0.00801397i | ||||
\(232\) | −9.73351 | −0.639036 | ||||||||
\(233\) | 10.8188 | + | 18.7387i | 0.708761 | + | 1.22761i | 0.965317 | + | 0.261081i | \(0.0840790\pi\) |
−0.256555 | + | 0.966530i | \(0.582588\pi\) | |||||||
\(234\) | 1.09131 | − | 9.90338i | 0.0713414 | − | 0.647404i | ||||
\(235\) | −2.02291 | −0.131960 | ||||||||
\(236\) | −4.65704 | − | 8.06623i | −0.303147 | − | 0.525067i | ||||
\(237\) | −19.7439 | + | 4.14479i | −1.28251 | + | 0.269233i | ||||
\(238\) | 0.118891 | + | 0.205925i | 0.00770656 | + | 0.0133482i | ||||
\(239\) | −8.89153 | + | 15.4006i | −0.575145 | + | 0.996180i | 0.420881 | + | 0.907116i | \(0.361721\pi\) |
−0.996026 | + | 0.0890644i | \(0.971612\pi\) | |||||||
\(240\) | −10.7887 | + | 2.26484i | −0.696406 | + | 0.146195i | ||||
\(241\) | −2.65337 | −0.170919 | −0.0854594 | − | 0.996342i | \(-0.527236\pi\) | ||||
−0.0854594 | + | 0.996342i | \(0.527236\pi\) | |||||||
\(242\) | 9.71865 | + | 16.8332i | 0.624739 | + | 1.08208i | ||||
\(243\) | −7.62374 | − | 13.5970i | −0.489063 | − | 0.872249i | ||||
\(244\) | 8.20429 | + | 14.2102i | 0.525226 | + | 0.909717i | ||||
\(245\) | −3.37129 | + | 5.83924i | −0.215384 | + | 0.373055i | ||||
\(246\) | −24.7584 | + | 5.19747i | −1.57854 | + | 0.331379i | ||||
\(247\) | 7.84460 | + | 2.18076i | 0.499140 | + | 0.138759i | ||||
\(248\) | 0.921189 | − | 1.59555i | 0.0584956 | − | 0.101317i | ||||
\(249\) | 3.27149 | − | 9.98305i | 0.207322 | − | 0.632650i | ||||
\(250\) | −9.51273 | + | 16.4765i | −0.601638 | + | 1.04207i | ||||
\(251\) | 3.23211 | − | 5.59818i | 0.204009 | − | 0.353354i | −0.745807 | − | 0.666162i | \(-0.767936\pi\) |
0.949817 | + | 0.312807i | \(0.101269\pi\) | |||||||
\(252\) | 3.69385 | + | 2.71225i | 0.232691 | + | 0.170856i | ||||
\(253\) | 0.159223 | − | 0.275783i | 0.0100103 | − | 0.0173383i | ||||
\(254\) | 4.25047 | + | 7.36203i | 0.266698 | + | 0.461935i | ||||
\(255\) | −0.0701639 | + | 0.214107i | −0.00439383 | + | 0.0134079i | ||||
\(256\) | −10.1462 | − | 17.5737i | −0.634136 | − | 1.09836i | ||||
\(257\) | 8.36616 | + | 14.4906i | 0.521867 | + | 0.903899i | 0.999676 | + | 0.0254362i | \(0.00809745\pi\) |
−0.477810 | + | 0.878463i | \(0.658569\pi\) | |||||||
\(258\) | 2.94931 | − | 8.99990i | 0.183616 | − | 0.560309i | ||||
\(259\) | 5.65292 | + | 9.79114i | 0.351255 | + | 0.608392i | ||||
\(260\) | −1.38769 | + | 2.40355i | −0.0860608 | + | 0.149062i | ||||
\(261\) | −2.14458 | + | 19.4615i | −0.132746 | + | 1.20463i | ||||
\(262\) | 10.2755 | − | 17.7978i | 0.634825 | − | 1.09955i | ||||
\(263\) | −10.4792 | + | 18.1506i | −0.646178 | + | 1.11921i | 0.337851 | + | 0.941200i | \(0.390300\pi\) |
−0.984028 | + | 0.178013i | \(0.943033\pi\) | |||||||
\(264\) | −0.209304 | + | 0.638697i | −0.0128818 | + | 0.0393091i | ||||
\(265\) | 3.32686 | − | 5.76229i | 0.204367 | − | 0.353974i | ||||
\(266\) | −7.27624 | + | 7.14144i | −0.446135 | + | 0.437870i | ||||
\(267\) | 19.5123 | − | 4.09618i | 1.19414 | − | 0.250682i | ||||
\(268\) | 0.453970 | − | 0.786298i | 0.0277306 | − | 0.0480308i | ||||
\(269\) | 8.04348 | + | 13.9317i | 0.490420 | + | 0.849432i | 0.999939 | − | 0.0110273i | \(-0.00351018\pi\) |
−0.509520 | + | 0.860459i | \(0.670177\pi\) | |||||||
\(270\) | 1.14688 | + | 11.7657i | 0.0697967 | + | 0.716037i | ||||
\(271\) | 13.0212 | + | 22.5533i | 0.790979 | + | 1.37002i | 0.925362 | + | 0.379086i | \(0.123761\pi\) |
−0.134383 | + | 0.990929i | \(0.542905\pi\) | |||||||
\(272\) | −0.505667 | −0.0306605 | ||||||||
\(273\) | −4.16536 | + | 0.874424i | −0.252099 | + | 0.0529225i | ||||
\(274\) | −10.4984 | + | 18.1838i | −0.634234 | + | 1.09853i | ||||
\(275\) | 0.437470 | + | 0.757720i | 0.0263804 | + | 0.0456922i | ||||
\(276\) | 2.40902 | − | 0.505720i | 0.145006 | − | 0.0304408i | ||||
\(277\) | −7.36125 | − | 12.7501i | −0.442295 | − | 0.766077i | 0.555564 | − | 0.831473i | \(-0.312502\pi\) |
−0.997859 | + | 0.0653962i | \(0.979169\pi\) | |||||||
\(278\) | −9.28836 | −0.557079 | ||||||||
\(279\) | −2.98722 | − | 2.19340i | −0.178840 | − | 0.131315i | ||||
\(280\) | 1.25524 | + | 2.17414i | 0.0750149 | + | 0.129930i | ||||
\(281\) | 17.7201 | 1.05709 | 0.528545 | − | 0.848905i | \(-0.322738\pi\) | ||||
0.528545 | + | 0.848905i | \(0.322738\pi\) | |||||||
\(282\) | −4.76467 | + | 1.00023i | −0.283732 | + | 0.0595631i | ||||
\(283\) | −13.7058 | −0.814723 | −0.407361 | − | 0.913267i | \(-0.633551\pi\) | ||||
−0.407361 | + | 0.913267i | \(0.633551\pi\) | |||||||
\(284\) | −9.51672 | + | 16.4834i | −0.564713 | + | 0.978112i | ||||
\(285\) | −9.64063 | − | 0.620032i | −0.571062 | − | 0.0367275i | ||||
\(286\) | 0.432059 | + | 0.748348i | 0.0255482 | + | 0.0442508i | ||||
\(287\) | 5.40344 | + | 9.35904i | 0.318955 | + | 0.552447i | ||||
\(288\) | −16.0983 | + | 7.07054i | −0.948601 | + | 0.416636i | ||||
\(289\) | 8.49483 | − | 14.7135i | 0.499696 | − | 0.865499i | ||||
\(290\) | 7.42393 | − | 12.8586i | 0.435948 | − | 0.755085i | ||||
\(291\) | 19.7977 | − | 4.15608i | 1.16056 | − | 0.243634i | ||||
\(292\) | −0.461074 | + | 0.798604i | −0.0269823 | + | 0.0467347i | ||||
\(293\) | 14.2271 | − | 24.6420i | 0.831153 | − | 1.43960i | −0.0659708 | − | 0.997822i | \(-0.521014\pi\) |
0.897124 | − | 0.441778i | \(-0.145652\pi\) | |||||||
\(294\) | −5.05334 | + | 15.4204i | −0.294717 | + | 0.899337i | ||||
\(295\) | −10.2637 | −0.597578 | ||||||||
\(296\) | −12.8174 | −0.744994 | ||||||||
\(297\) | 1.23091 | + | 0.559212i | 0.0714248 | + | 0.0324487i | ||||
\(298\) | 11.7653 | − | 20.3781i | 0.681546 | − | 1.18047i | ||||
\(299\) | −1.14307 | + | 1.97986i | −0.0661057 | + | 0.114498i | ||||
\(300\) | −2.10610 | + | 6.42683i | −0.121596 | + | 0.371053i | ||||
\(301\) | −4.04577 | −0.233194 | ||||||||
\(302\) | −26.2588 | −1.51103 | ||||||||
\(303\) | −15.8740 | − | 17.7194i | −0.911940 | − | 1.01795i | ||||
\(304\) | −5.41548 | − | 20.9940i | −0.310599 | − | 1.20409i | ||||
\(305\) | 18.0816 | 1.03535 | ||||||||
\(306\) | −0.0593947 | + | 0.538991i | −0.00339537 | + | 0.0308121i | ||||
\(307\) | −4.96283 | − | 8.59587i | −0.283244 | − | 0.490592i | 0.688938 | − | 0.724820i | \(-0.258077\pi\) |
−0.972182 | + | 0.234228i | \(0.924744\pi\) | |||||||
\(308\) | −0.397454 | −0.0226471 | ||||||||
\(309\) | −13.1845 | + | 2.76780i | −0.750042 | + | 0.157454i | ||||
\(310\) | 1.40522 | + | 2.43391i | 0.0798110 | + | 0.138237i | ||||
\(311\) | −5.07553 | + | 8.79108i | −0.287807 | + | 0.498496i | −0.973286 | − | 0.229596i | \(-0.926260\pi\) |
0.685479 | + | 0.728092i | \(0.259593\pi\) | |||||||
\(312\) | 1.50261 | − | 4.58525i | 0.0850683 | − | 0.259589i | ||||
\(313\) | 25.9255 | 1.46540 | 0.732699 | − | 0.680552i | \(-0.238260\pi\) | ||||
0.732699 | + | 0.680552i | \(0.238260\pi\) | |||||||
\(314\) | 0.0693896 | − | 0.120186i | 0.00391588 | − | 0.00678251i | ||||
\(315\) | 4.62361 | − | 2.03074i | 0.260511 | − | 0.114419i | ||||
\(316\) | 13.5250 | 0.760839 | ||||||||
\(317\) | −24.3048 | −1.36509 | −0.682546 | − | 0.730843i | \(-0.739127\pi\) | ||||
−0.682546 | + | 0.730843i | \(0.739127\pi\) | |||||||
\(318\) | 4.98674 | − | 15.2172i | 0.279643 | − | 0.853338i | ||||
\(319\) | −0.849054 | − | 1.47060i | −0.0475379 | − | 0.0823381i | ||||
\(320\) | 0.604463 | 0.0337905 | ||||||||
\(321\) | 3.14000 | + | 3.50503i | 0.175258 | + | 0.195632i | ||||
\(322\) | −1.43133 | − | 2.47913i | −0.0797647 | − | 0.138157i | ||||
\(323\) | −0.426942 | − | 0.118688i | −0.0237557 | − | 0.00660397i | ||||
\(324\) | 3.12919 | + | 9.97112i | 0.173844 | + | 0.553951i | ||||
\(325\) | −3.14063 | − | 5.43973i | −0.174211 | − | 0.301742i | ||||
\(326\) | 17.4145 | − | 30.1627i | 0.964498 | − | 1.67056i | ||||
\(327\) | 9.75076 | − | 29.7547i | 0.539218 | − | 1.64544i | ||||
\(328\) | −12.2517 | −0.676487 | ||||||||
\(329\) | 1.03987 | + | 1.80111i | 0.0573301 | + | 0.0992986i | ||||
\(330\) | −0.684122 | − | 0.763651i | −0.0376597 | − | 0.0420376i | ||||
\(331\) | −4.85091 | − | 8.40202i | −0.266630 | − | 0.461817i | 0.701359 | − | 0.712808i | \(-0.252577\pi\) |
−0.967989 | + | 0.250991i | \(0.919244\pi\) | |||||||
\(332\) | −3.52145 | + | 6.09933i | −0.193265 | + | 0.334744i | ||||
\(333\) | −2.82404 | + | 25.6274i | −0.154756 | + | 1.40437i | ||||
\(334\) | −41.3640 | −2.26334 | ||||||||
\(335\) | −0.500256 | − | 0.866469i | −0.0273319 | − | 0.0473402i | ||||
\(336\) | 7.56241 | + | 8.44154i | 0.412563 | + | 0.460524i | ||||
\(337\) | 33.7366 | 1.83775 | 0.918876 | − | 0.394546i | \(-0.129098\pi\) | ||||
0.918876 | + | 0.394546i | \(0.129098\pi\) | |||||||
\(338\) | 8.45502 | + | 14.6445i | 0.459893 | + | 0.796557i | ||||
\(339\) | 19.7849 | − | 4.15340i | 1.07457 | − | 0.225582i | ||||
\(340\) | 0.0755249 | − | 0.130813i | 0.00409591 | − | 0.00709432i | ||||
\(341\) | 0.321421 | 0.0174059 | ||||||||
\(342\) | −23.0137 | + | 3.30645i | −1.24444 | + | 0.178792i | ||||
\(343\) | 16.1407 | 0.871514 | ||||||||
\(344\) | 2.29333 | − | 3.97217i | 0.123648 | − | 0.214165i | ||||
\(345\) | 0.844701 | − | 2.57763i | 0.0454772 | − | 0.138775i | ||||
\(346\) | 5.08757 | + | 8.81193i | 0.273510 | + | 0.473732i | ||||
\(347\) | −29.2979 | −1.57279 | −0.786396 | − | 0.617723i | \(-0.788055\pi\) | ||||
−0.786396 | + | 0.617723i | \(0.788055\pi\) | |||||||
\(348\) | 4.08758 | − | 12.4734i | 0.219118 | − | 0.668644i | ||||
\(349\) | −1.69824 | − | 2.94144i | −0.0909049 | − | 0.157452i | 0.816987 | − | 0.576656i | \(-0.195643\pi\) |
−0.907892 | + | 0.419204i | \(0.862309\pi\) | |||||||
\(350\) | 7.86521 | 0.420413 | ||||||||
\(351\) | −8.83681 | − | 4.01462i | −0.471674 | − | 0.214285i | ||||
\(352\) | 0.762468 | − | 1.32063i | 0.0406397 | − | 0.0703900i | ||||
\(353\) | −3.31809 | − | 5.74710i | −0.176604 | − | 0.305887i | 0.764111 | − | 0.645085i | \(-0.223178\pi\) |
−0.940715 | + | 0.339197i | \(0.889845\pi\) | |||||||
\(354\) | −24.1747 | + | 5.07494i | −1.28487 | + | 0.269730i | ||||
\(355\) | 10.4870 | + | 18.1641i | 0.556594 | + | 0.964049i | ||||
\(356\) | −13.3663 | −0.708414 | ||||||||
\(357\) | 0.226700 | − | 0.0475905i | 0.0119982 | − | 0.00251875i | ||||
\(358\) | 6.72102 | − | 11.6411i | 0.355217 | − | 0.615254i | ||||
\(359\) | −18.5021 | − | 32.0466i | −0.976505 | − | 1.69136i | −0.674876 | − | 0.737931i | \(-0.735803\pi\) |
−0.301629 | − | 0.953425i | \(-0.597530\pi\) | |||||||
\(360\) | −0.627083 | + | 5.69061i | −0.0330502 | + | 0.299922i | ||||
\(361\) | 0.355254 | − | 18.9967i | 0.0186976 | − | 0.999825i | ||||
\(362\) | −7.78086 | − | 13.4768i | −0.408953 | − | 0.708327i | ||||
\(363\) | 18.5314 | − | 3.89024i | 0.972645 | − | 0.204185i | ||||
\(364\) | 2.85335 | 0.149556 | ||||||||
\(365\) | 0.508085 | + | 0.880029i | 0.0265944 | + | 0.0460628i | ||||
\(366\) | 42.5885 | − | 8.94050i | 2.22614 | − | 0.467327i | ||||
\(367\) | 14.7101 | 0.767859 | 0.383929 | − | 0.923363i | \(-0.374571\pi\) | ||||
0.383929 | + | 0.923363i | \(0.374571\pi\) | |||||||
\(368\) | 6.08771 | 0.317344 | ||||||||
\(369\) | −2.69941 | + | 24.4964i | −0.140526 | + | 1.27523i | ||||
\(370\) | 9.77605 | − | 16.9326i | 0.508233 | − | 0.880285i | ||||
\(371\) | −6.84066 | −0.355149 | ||||||||
\(372\) | 1.65782 | + | 1.85054i | 0.0859541 | + | 0.0959462i | ||||
\(373\) | −0.728793 | + | 1.26231i | −0.0377355 | + | 0.0653598i | −0.884276 | − | 0.466964i | \(-0.845348\pi\) |
0.846541 | + | 0.532324i | \(0.178681\pi\) | |||||||
\(374\) | −0.0235148 | − | 0.0407288i | −0.00121592 | − | 0.00210604i | ||||
\(375\) | 12.3670 | + | 13.8047i | 0.638631 | + | 0.712871i | ||||
\(376\) | −2.35780 | −0.121594 | ||||||||
\(377\) | 6.09542 | + | 10.5576i | 0.313930 | + | 0.543743i | ||||
\(378\) | 9.88612 | − | 7.06926i | 0.508487 | − | 0.363604i | ||||
\(379\) | 30.8963 | 1.58704 | 0.793519 | − | 0.608546i | \(-0.208247\pi\) | ||||
0.793519 | + | 0.608546i | \(0.208247\pi\) | |||||||
\(380\) | 6.23987 | + | 1.73465i | 0.320099 | + | 0.0889859i | ||||
\(381\) | 8.10473 | − | 1.70141i | 0.415218 | − | 0.0871656i | ||||
\(382\) | −4.85058 | −0.248177 | ||||||||
\(383\) | 18.4547 | 0.942990 | 0.471495 | − | 0.881869i | \(-0.343715\pi\) | ||||
0.471495 | + | 0.881869i | \(0.343715\pi\) | |||||||
\(384\) | −18.4458 | + | 3.87228i | −0.941308 | + | 0.197606i | ||||
\(385\) | −0.218989 | + | 0.379300i | −0.0111607 | + | 0.0193309i | ||||
\(386\) | 21.8524 | − | 37.8494i | 1.11226 | − | 1.92648i | ||||
\(387\) | −7.43679 | − | 5.46054i | −0.378033 | − | 0.277575i | ||||
\(388\) | −13.5618 | −0.688497 | ||||||||
\(389\) | −0.838973 | −0.0425376 | −0.0212688 | − | 0.999774i | \(-0.506771\pi\) | ||||
−0.0212688 | + | 0.999774i | \(0.506771\pi\) | |||||||
\(390\) | 4.91136 | + | 5.48230i | 0.248696 | + | 0.277607i | ||||
\(391\) | 0.0622118 | − | 0.107754i | 0.00314618 | − | 0.00544935i | ||||
\(392\) | −3.92939 | + | 6.80591i | −0.198464 | + | 0.343750i | ||||
\(393\) | −13.3587 | − | 14.9117i | −0.673858 | − | 0.752193i | ||||
\(394\) | −4.11081 | + | 7.12014i | −0.207100 | + | 0.358707i | ||||
\(395\) | 7.45199 | − | 12.9072i | 0.374950 | − | 0.649433i | ||||
\(396\) | −0.730586 | − | 0.536441i | −0.0367133 | − | 0.0269572i | ||||
\(397\) | 10.4063 | + | 18.0243i | 0.522279 | + | 0.904613i | 0.999664 | + | 0.0259191i | \(0.00825123\pi\) |
−0.477385 | + | 0.878694i | \(0.658415\pi\) | |||||||
\(398\) | 5.79766 | + | 10.0418i | 0.290610 | + | 0.503352i | ||||
\(399\) | 4.40370 | + | 8.90234i | 0.220461 | + | 0.445674i | ||||
\(400\) | −8.36307 | + | 14.4853i | −0.418153 | + | 0.724263i | ||||
\(401\) | −34.0303 | −1.69939 | −0.849697 | − | 0.527271i | \(-0.823215\pi\) | ||||
−0.849697 | + | 0.527271i | \(0.823215\pi\) | |||||||
\(402\) | −1.60671 | − | 1.79349i | −0.0801353 | − | 0.0894510i | ||||
\(403\) | −2.30751 | −0.114945 | ||||||||
\(404\) | 7.97447 | + | 13.8122i | 0.396745 | + | 0.687182i | ||||
\(405\) | 11.2398 | + | 2.50762i | 0.558511 | + | 0.124604i | ||||
\(406\) | −15.2650 | −0.757591 | ||||||||
\(407\) | −1.11806 | − | 1.93653i | −0.0554201 | − | 0.0959904i | ||||
\(408\) | −0.0817793 | + | 0.249552i | −0.00404868 | + | 0.0123547i | ||||
\(409\) | 15.7351 | + | 27.2540i | 0.778051 | + | 1.34762i | 0.933064 | + | 0.359711i | \(0.117125\pi\) |
−0.155013 | + | 0.987912i | \(0.549542\pi\) | |||||||
\(410\) | 9.34461 | − | 16.1853i | 0.461497 | − | 0.799337i | ||||
\(411\) | 13.6485 | + | 15.2351i | 0.673231 | + | 0.751494i | ||||
\(412\) | 9.03166 | 0.444958 | ||||||||
\(413\) | 5.27605 | + | 9.13839i | 0.259618 | + | 0.449671i | ||||
\(414\) | 0.715051 | − | 6.48890i | 0.0351428 | − | 0.318912i | ||||
\(415\) | 3.88050 | + | 6.72122i | 0.190486 | + | 0.329932i | ||||
\(416\) | −5.47381 | + | 9.48092i | −0.268376 | + | 0.464841i | ||||
\(417\) | −2.81778 | + | 8.59854i | −0.137987 | + | 0.421072i | ||||
\(418\) | 1.43913 | − | 1.41247i | 0.0703900 | − | 0.0690859i | ||||
\(419\) | 9.72553 | − | 16.8451i | 0.475123 | − | 0.822938i | −0.524471 | − | 0.851428i | \(-0.675737\pi\) |
0.999594 | + | 0.0284908i | \(0.00907012\pi\) | |||||||
\(420\) | −3.31327 | + | 0.695547i | −0.161671 | + | 0.0339392i | ||||
\(421\) | 9.96050 | − | 17.2521i | 0.485445 | − | 0.840815i | −0.514415 | − | 0.857541i | \(-0.671991\pi\) |
0.999860 | + | 0.0167261i | \(0.00532433\pi\) | |||||||
\(422\) | −4.63787 | + | 8.03303i | −0.225768 | + | 0.391042i | ||||
\(423\) | −0.519492 | + | 4.71425i | −0.0252586 | + | 0.229215i | ||||
\(424\) | 3.87761 | − | 6.71622i | 0.188313 | − | 0.326168i | ||||
\(425\) | 0.170928 | + | 0.296057i | 0.00829125 | + | 0.0143609i | ||||
\(426\) | 33.6820 | + | 37.5975i | 1.63190 | + | 1.82160i | ||||
\(427\) | −9.29480 | − | 16.0991i | −0.449807 | − | 0.779088i | ||||
\(428\) | −1.57741 | − | 2.73215i | −0.0762470 | − | 0.132064i | ||||
\(429\) | 0.823843 | − | 0.172947i | 0.0397755 | − | 0.00834997i | ||||
\(430\) | 3.49834 | + | 6.05930i | 0.168705 | + | 0.292205i | ||||
\(431\) | 1.45784 | − | 2.52505i | 0.0702215 | − | 0.121627i | −0.828777 | − | 0.559579i | \(-0.810963\pi\) |
0.898998 | + | 0.437952i | \(0.144296\pi\) | |||||||
\(432\) | 2.50747 | + | 25.7239i | 0.120641 | + | 1.23764i | ||||
\(433\) | −16.0100 | + | 27.7302i | −0.769393 | + | 1.33263i | 0.168500 | + | 0.985702i | \(0.446108\pi\) |
−0.937893 | + | 0.346926i | \(0.887226\pi\) | |||||||
\(434\) | 1.44470 | − | 2.50229i | 0.0693478 | − | 0.120114i | ||||
\(435\) | −9.65149 | − | 10.7735i | −0.462753 | − | 0.516548i | ||||
\(436\) | −10.4958 | + | 18.1792i | −0.502657 | + | 0.870627i | ||||
\(437\) | 5.13994 | + | 1.42888i | 0.245877 | + | 0.0683526i | ||||
\(438\) | 1.63185 | + | 1.82155i | 0.0779729 | + | 0.0870372i | ||||
\(439\) | −5.64478 | + | 9.77704i | −0.269411 | + | 0.466633i | −0.968710 | − | 0.248196i | \(-0.920162\pi\) |
0.699299 | + | 0.714829i | \(0.253496\pi\) | |||||||
\(440\) | −0.248267 | − | 0.430011i | −0.0118357 | − | 0.0205000i | ||||
\(441\) | 12.7422 | + | 9.35608i | 0.606770 | + | 0.445528i | ||||
\(442\) | 0.168814 | + | 0.292395i | 0.00802968 | + | 0.0139078i | ||||
\(443\) | −38.4359 | −1.82614 | −0.913071 | − | 0.407800i | \(-0.866296\pi\) | ||||
−0.913071 | + | 0.407800i | \(0.866296\pi\) | |||||||
\(444\) | 5.38265 | − | 16.4253i | 0.255449 | − | 0.779511i | ||||
\(445\) | −7.36458 | + | 12.7558i | −0.349115 | + | 0.604684i | ||||
\(446\) | −4.38738 | − | 7.59917i | −0.207749 | − | 0.359831i | ||||
\(447\) | −15.2955 | − | 17.0736i | −0.723452 | − | 0.807553i | ||||
\(448\) | −0.310723 | − | 0.538188i | −0.0146803 | − | 0.0254270i | ||||
\(449\) | −0.523696 | −0.0247147 | −0.0123574 | − | 0.999924i | \(-0.503934\pi\) | ||||
−0.0123574 | + | 0.999924i | \(0.503934\pi\) | |||||||
\(450\) | 14.4575 | + | 10.6156i | 0.681535 | + | 0.500425i | ||||
\(451\) | −1.06872 | − | 1.85107i | −0.0503239 | − | 0.0871635i | ||||
\(452\) | −13.5531 | −0.637483 | ||||||||
\(453\) | −7.96605 | + | 24.3087i | −0.374278 | + | 1.14212i | ||||
\(454\) | 26.0916 | 1.22454 | ||||||||
\(455\) | 1.57214 | − | 2.72303i | 0.0737030 | − | 0.127657i | ||||
\(456\) | −11.2366 | − | 0.722676i | −0.526202 | − | 0.0338424i | ||||
\(457\) | −10.7106 | − | 18.5513i | −0.501022 | − | 0.867795i | −0.999999 | − | 0.00118016i | \(-0.999624\pi\) |
0.498978 | − | 0.866615i | \(-0.333709\pi\) | |||||||
\(458\) | 1.04811 | + | 1.81538i | 0.0489749 | + | 0.0848270i | ||||
\(459\) | 0.480943 | + | 0.218496i | 0.0224485 | + | 0.0101985i | ||||
\(460\) | −0.909242 | + | 1.57485i | −0.0423936 | + | 0.0734279i | ||||
\(461\) | 0.504860 | − | 0.874443i | 0.0235137 | − | 0.0407269i | −0.854029 | − | 0.520225i | \(-0.825848\pi\) |
0.877543 | + | 0.479498i | \(0.159181\pi\) | |||||||
\(462\) | −0.328250 | + | 1.00167i | −0.0152716 | + | 0.0466017i | ||||
\(463\) | 5.44085 | − | 9.42382i | 0.252858 | − | 0.437962i | −0.711454 | − | 0.702733i | \(-0.751963\pi\) |
0.964311 | + | 0.264771i | \(0.0852963\pi\) | |||||||
\(464\) | 16.2313 | − | 28.1134i | 0.753518 | − | 1.30513i | ||||
\(465\) | 2.67945 | − | 0.562489i | 0.124256 | − | 0.0260848i | ||||
\(466\) | −38.4709 | −1.78213 | ||||||||
\(467\) | −0.227947 | −0.0105481 | −0.00527407 | − | 0.999986i | \(-0.501679\pi\) | ||||
−0.00527407 | + | 0.999986i | \(0.501679\pi\) | |||||||
\(468\) | 5.24493 | + | 3.85115i | 0.242447 | + | 0.178019i | ||||
\(469\) | −0.514311 | + | 0.890813i | −0.0237487 | + | 0.0411339i | ||||
\(470\) | 1.79834 | − | 3.11481i | 0.0829511 | − | 0.143676i | ||||
\(471\) | −0.0902100 | − | 0.100697i | −0.00415666 | − | 0.00463986i | ||||
\(472\) | −11.9629 | −0.550635 | ||||||||
\(473\) | 0.800190 | 0.0367928 | ||||||||
\(474\) | 11.1700 | − | 34.0857i | 0.513057 | − | 1.56561i | ||||
\(475\) | −10.4610 | + | 10.2672i | −0.479983 | + | 0.471090i | ||||
\(476\) | −0.155294 | −0.00711787 | ||||||||
\(477\) | −12.5742 | − | 9.23279i | −0.575735 | − | 0.422740i | ||||
\(478\) | −15.8089 | − | 27.3818i | −0.723081 | − | 1.25241i | ||||
\(479\) | −13.6303 | −0.622786 | −0.311393 | − | 0.950281i | \(-0.600796\pi\) | ||||
−0.311393 | + | 0.950281i | \(0.600796\pi\) | |||||||
\(480\) | 4.04500 | − | 12.3434i | 0.184628 | − | 0.563398i | ||||
\(481\) | 8.02662 | + | 13.9025i | 0.365983 | + | 0.633900i | ||||
\(482\) | 2.35881 | − | 4.08558i | 0.107441 | − | 0.186093i | ||||
\(483\) | −2.72923 | + | 0.572940i | −0.124184 | + | 0.0260697i | ||||
\(484\) | −12.6944 | −0.577016 | ||||||||
\(485\) | −7.47229 | + | 12.9424i | −0.339299 | + | 0.587683i | ||||
\(486\) | 27.7136 | + | 0.348760i | 1.25712 | + | 0.0158201i | ||||
\(487\) | −18.8745 | −0.855286 | −0.427643 | − | 0.903948i | \(-0.640656\pi\) | ||||
−0.427643 | + | 0.903948i | \(0.640656\pi\) | |||||||
\(488\) | 21.0749 | 0.954017 | ||||||||
\(489\) | −22.6397 | − | 25.2715i | −1.02380 | − | 1.14282i | ||||
\(490\) | −5.99405 | − | 10.3820i | −0.270783 | − | 0.469011i | ||||
\(491\) | −0.829442 | −0.0374322 | −0.0187161 | − | 0.999825i | \(-0.505958\pi\) | ||||
−0.0187161 | + | 0.999825i | \(0.505958\pi\) | |||||||
\(492\) | 5.14510 | − | 15.7004i | 0.231959 | − | 0.707830i | ||||
\(493\) | −0.331743 | − | 0.574596i | −0.0149410 | − | 0.0258785i | ||||
\(494\) | −10.3316 | + | 10.1402i | −0.464841 | + | 0.456229i | ||||
\(495\) | −0.914477 | + | 0.401648i | −0.0411027 | + | 0.0180527i | ||||
\(496\) | 3.07229 | + | 5.32136i | 0.137950 | + | 0.238936i | ||||
\(497\) | 10.7817 | − | 18.6744i | 0.483625 | − | 0.837663i | ||||
\(498\) | 12.4633 | + | 13.9121i | 0.558492 | + | 0.623417i | ||||
\(499\) | 1.50254 | 0.0672629 | 0.0336314 | − | 0.999434i | \(-0.489293\pi\) | ||||
0.0336314 | + | 0.999434i | \(0.489293\pi\) | |||||||
\(500\) | −6.21269 | − | 10.7607i | −0.277840 | − | 0.481233i | ||||
\(501\) | −12.5485 | + | 38.2920i | −0.560624 | + | 1.71076i | ||||
\(502\) | 5.74660 | + | 9.95340i | 0.256483 | + | 0.444242i | ||||
\(503\) | −4.60299 | + | 7.97262i | −0.205237 | + | 0.355481i | −0.950208 | − | 0.311615i | \(-0.899130\pi\) |
0.744971 | + | 0.667097i | \(0.232463\pi\) | |||||||
\(504\) | 5.38903 | − | 2.36692i | 0.240046 | − | 0.105431i | ||||
\(505\) | 17.5751 | 0.782081 | ||||||||
\(506\) | 0.283094 | + | 0.490333i | 0.0125851 | + | 0.0217980i | ||||
\(507\) | 16.1219 | − | 3.38443i | 0.715999 | − | 0.150308i | ||||
\(508\) | −5.55190 | −0.246326 | ||||||||
\(509\) | −1.22085 | − | 2.11458i | −0.0541133 | − | 0.0937271i | 0.837700 | − | 0.546131i | \(-0.183900\pi\) |
−0.891813 | + | 0.452404i | \(0.850567\pi\) | |||||||
\(510\) | −0.267301 | − | 0.298374i | −0.0118363 | − | 0.0132122i | ||||
\(511\) | 0.522360 | − | 0.904754i | 0.0231078 | − | 0.0400240i | ||||
\(512\) | 14.3155 | 0.632664 | ||||||||
\(513\) | −3.92069 | + | 22.3076i | −0.173103 | + | 0.984904i | ||||
\(514\) | −29.7496 | −1.31220 | ||||||||
\(515\) | 4.97626 | − | 8.61914i | 0.219280 | − | 0.379805i | ||||
\(516\) | 4.12721 | + | 4.60699i | 0.181690 | + | 0.202812i | ||||
\(517\) | −0.205671 | − | 0.356232i | −0.00904538 | − | 0.0156671i | ||||
\(518\) | −20.1014 | −0.883206 | ||||||||
\(519\) | 9.70090 | − | 2.03649i | 0.425822 | − | 0.0893918i | ||||
\(520\) | 1.78233 | + | 3.08708i | 0.0781602 | + | 0.135377i | ||||
\(521\) | 4.12120 | 0.180553 | 0.0902764 | − | 0.995917i | \(-0.471225\pi\) | ||||
0.0902764 | + | 0.995917i | \(0.471225\pi\) | |||||||
\(522\) | −28.0596 | − | 20.6031i | −1.22814 | − | 0.901773i | ||||
\(523\) | −15.9501 | + | 27.6263i | −0.697448 | + | 1.20802i | 0.271900 | + | 0.962325i | \(0.412348\pi\) |
−0.969348 | + | 0.245690i | \(0.920985\pi\) | |||||||
\(524\) | 6.71087 | + | 11.6236i | 0.293166 | + | 0.507778i | ||||
\(525\) | 2.38605 | − | 7.28109i | 0.104136 | − | 0.317773i | ||||
\(526\) | −18.6318 | − | 32.2712i | −0.812384 | − | 1.40709i | ||||
\(527\) | 0.125586 | 0.00547061 | ||||||||
\(528\) | −1.49573 | − | 1.66960i | −0.0650932 | − | 0.0726602i | ||||
\(529\) | 10.7510 | − | 18.6213i | 0.467436 | − | 0.809623i | ||||
\(530\) | 5.91505 | + | 10.2452i | 0.256934 | + | 0.445022i | ||||
\(531\) | −2.63577 | + | 23.9189i | −0.114383 | + | 1.03799i | ||||
\(532\) | −1.66313 | − | 6.44741i | −0.0721059 | − | 0.279531i | ||||
\(533\) | 7.67239 | + | 13.2890i | 0.332328 | + | 0.575609i | ||||
\(534\) | −11.0390 | + | 33.6859i | −0.477705 | + | 1.45773i | ||||
\(535\) | −3.47648 | −0.150301 | ||||||||
\(536\) | −0.583072 | − | 1.00991i | −0.0251849 | − | 0.0436215i | ||||
\(537\) | −8.73766 | − | 9.75341i | −0.377058 | − | 0.420891i | ||||
\(538\) | −28.6021 | −1.23313 | ||||||||
\(539\) | −1.37104 | −0.0590550 | ||||||||
\(540\) | −7.02911 | − | 3.19337i | −0.302485 | − | 0.137421i | ||||
\(541\) | −7.44884 | + | 12.9018i | −0.320251 | + | 0.554690i | −0.980540 | − | 0.196321i | \(-0.937100\pi\) |
0.660289 | + | 0.751012i | \(0.270434\pi\) | |||||||
\(542\) | −46.3024 | −1.98886 | ||||||||
\(543\) | −14.8364 | + | 3.11457i | −0.636691 | + | 0.133659i | ||||
\(544\) | 0.297912 | − | 0.515999i | 0.0127729 | − | 0.0221233i | ||||
\(545\) | 11.5659 | + | 20.0328i | 0.495430 | + | 0.858110i | ||||
\(546\) | 2.35653 | − | 7.19104i | 0.100850 | − | 0.307748i | ||||
\(547\) | −7.85484 | −0.335849 | −0.167924 | − | 0.985800i | \(-0.553706\pi\) | ||||
−0.167924 | + | 0.985800i | \(0.553706\pi\) | |||||||
\(548\) | −6.85645 | − | 11.8757i | −0.292893 | − | 0.507306i | ||||
\(549\) | 4.64342 | − | 42.1378i | 0.198177 | − | 1.79840i | ||||
\(550\) | −1.55562 | −0.0663317 | ||||||||
\(551\) | 20.3030 | − | 19.9268i | 0.864936 | − | 0.848912i | ||||
\(552\) | 0.984539 | − | 3.00435i | 0.0419048 | − | 0.127874i | ||||
\(553\) | −15.3227 | −0.651588 | ||||||||
\(554\) | 26.1762 | 1.11212 | ||||||||
\(555\) | −12.7093 | − | 14.1868i | −0.539482 | − | 0.602196i | ||||
\(556\) | 3.03308 | − | 5.25344i | 0.128631 | − | 0.222796i | ||||
\(557\) | −12.9954 | + | 22.5087i | −0.550632 | + | 0.953722i | 0.447597 | + | 0.894235i | \(0.352280\pi\) |
−0.998229 | + | 0.0594871i | \(0.981053\pi\) | |||||||
\(558\) | 6.03291 | − | 2.64972i | 0.255394 | − | 0.112172i | ||||
\(559\) | −5.74462 | −0.242972 | ||||||||
\(560\) | −8.37279 | −0.353815 | ||||||||
\(561\) | −0.0448376 | + | 0.00941265i | −0.00189305 | + | 0.000397402i | ||||
\(562\) | −15.7529 | + | 27.2848i | −0.664494 | + | 1.15094i | ||||
\(563\) | 0.182015 | − | 0.315259i | 0.00767101 | − | 0.0132866i | −0.862164 | − | 0.506629i | \(-0.830892\pi\) |
0.869835 | + | 0.493342i | \(0.164225\pi\) | |||||||
\(564\) | 0.990156 | − | 3.02149i | 0.0416931 | − | 0.127228i | ||||
\(565\) | −7.46747 | + | 12.9340i | −0.314159 | + | 0.544139i | ||||
\(566\) | 12.1842 | − | 21.1037i | 0.512141 | − | 0.887054i | ||||
\(567\) | −3.54513 | − | 11.2965i | −0.148881 | − | 0.474408i | ||||
\(568\) | 12.2231 | + | 21.1711i | 0.512871 | + | 0.888319i | ||||
\(569\) | −6.09470 | − | 10.5563i | −0.255503 | − | 0.442544i | 0.709529 | − | 0.704676i | \(-0.248908\pi\) |
−0.965032 | + | 0.262132i | \(0.915574\pi\) | |||||||
\(570\) | 9.52508 | − | 14.2931i | 0.398962 | − | 0.598673i | ||||
\(571\) | −0.379660 | + | 0.657591i | −0.0158883 | + | 0.0275193i | −0.873860 | − | 0.486177i | \(-0.838391\pi\) |
0.857972 | + | 0.513697i | \(0.171724\pi\) | |||||||
\(572\) | −0.564349 | −0.0235966 | ||||||||
\(573\) | −1.47150 | + | 4.49034i | −0.0614730 | + | 0.187587i | ||||
\(574\) | −19.2143 | −0.801990 | ||||||||
\(575\) | −2.05780 | − | 3.56422i | −0.0858163 | − | 0.148638i | ||||
\(576\) | 0.155229 | − | 1.40866i | 0.00646786 | − | 0.0586941i | ||||
\(577\) | −10.8385 | −0.451212 | −0.225606 | − | 0.974219i | \(-0.572436\pi\) | ||||
−0.225606 | + | 0.974219i | \(0.572436\pi\) | |||||||
\(578\) | 15.1036 | + | 26.1601i | 0.628225 | + | 1.08812i | ||||
\(579\) | −28.4092 | − | 31.7117i | −1.18064 | − | 1.31789i | ||||
\(580\) | 4.84851 | + | 8.39787i | 0.201324 | + | 0.348703i | ||||
\(581\) | 3.98952 | − | 6.91006i | 0.165513 | − | 0.286678i | ||||
\(582\) | −11.2005 | + | 34.1786i | −0.464274 | + | 1.41675i | ||||
\(583\) | 1.35298 | 0.0560345 | ||||||||
\(584\) | 0.592197 | + | 1.02571i | 0.0245053 | + | 0.0424444i | ||||
\(585\) | 6.56510 | − | 2.88346i | 0.271433 | − | 0.119216i | ||||
\(586\) | 25.2953 | + | 43.8127i | 1.04494 | + | 1.80989i | ||||
\(587\) | 6.63595 | − | 11.4938i | 0.273895 | − | 0.474400i | −0.695961 | − | 0.718080i | \(-0.745021\pi\) |
0.969856 | + | 0.243680i | \(0.0783546\pi\) | |||||||
\(588\) | −7.07155 | − | 7.89361i | −0.291626 | − | 0.325527i | ||||
\(589\) | 1.34497 | + | 5.21402i | 0.0554187 | + | 0.214840i | ||||
\(590\) | 9.12431 | − | 15.8038i | 0.375642 | − | 0.650631i | ||||
\(591\) | 5.34426 | + | 5.96553i | 0.219834 | + | 0.245389i | ||||
\(592\) | 21.3738 | − | 37.0205i | 0.878458 | − | 1.52153i | ||||
\(593\) | −0.533785 | + | 0.924543i | −0.0219199 | + | 0.0379664i | −0.876777 | − | 0.480897i | \(-0.840311\pi\) |
0.854857 | + | 0.518863i | \(0.173645\pi\) | |||||||
\(594\) | −1.95532 | + | 1.39819i | −0.0802277 | + | 0.0573684i | ||||
\(595\) | −0.0855636 | + | 0.148201i | −0.00350777 | + | 0.00607563i | ||||
\(596\) | 7.68383 | + | 13.3088i | 0.314742 | + | 0.545149i | ||||
\(597\) | 11.0549 | − | 2.32072i | 0.452446 | − | 0.0949808i | ||||
\(598\) | −2.03235 | − | 3.52014i | −0.0831091 | − | 0.143949i | ||||
\(599\) | −6.67115 | − | 11.5548i | −0.272576 | − | 0.472115i | 0.696945 | − | 0.717125i | \(-0.254542\pi\) |
−0.969521 | + | 0.245010i | \(0.921209\pi\) | |||||||
\(600\) | 5.79611 | + | 6.46990i | 0.236625 | + | 0.264133i | ||||
\(601\) | 22.5595 | + | 39.0742i | 0.920220 | + | 1.59387i | 0.799074 | + | 0.601233i | \(0.205324\pi\) |
0.121147 | + | 0.992635i | \(0.461343\pi\) | |||||||
\(602\) | 3.59663 | − | 6.22955i | 0.146588 | − | 0.253897i | ||||
\(603\) | −2.14771 | + | 0.943298i | −0.0874616 | + | 0.0384141i | ||||
\(604\) | 8.57471 | − | 14.8518i | 0.348900 | − | 0.604313i | ||||
\(605\) | −6.99433 | + | 12.1145i | −0.284360 | + | 0.492526i | ||||
\(606\) | 41.3955 | − | 8.69006i | 1.68158 | − | 0.353010i | ||||
\(607\) | 12.5161 | − | 21.6785i | 0.508012 | − | 0.879903i | −0.491944 | − | 0.870627i | \(-0.663714\pi\) |
0.999957 | − | 0.00927687i | \(-0.00295296\pi\) | |||||||
\(608\) | 24.6135 | + | 6.84244i | 0.998210 | + | 0.277498i | ||||
\(609\) | −4.63091 | + | 14.1314i | −0.187654 | + | 0.572631i | ||||
\(610\) | −16.0743 | + | 27.8414i | −0.650827 | + | 1.12727i | ||||
\(611\) | 1.47652 | + | 2.55742i | 0.0597338 | + | 0.103462i | ||||
\(612\) | −0.285455 | − | 0.209599i | −0.0115388 | − | 0.00847252i | ||||
\(613\) | 10.4697 | + | 18.1341i | 0.422869 | + | 0.732430i | 0.996219 | − | 0.0868805i | \(-0.0276898\pi\) |
−0.573350 | + | 0.819310i | \(0.694357\pi\) | |||||||
\(614\) | 17.6475 | 0.712196 | ||||||||
\(615\) | −12.1485 | − | 13.5607i | −0.489873 | − | 0.546821i | ||||
\(616\) | −0.255242 | + | 0.442092i | −0.0102840 | + | 0.0178124i | ||||
\(617\) | 9.25883 | + | 16.0368i | 0.372746 | + | 0.645616i | 0.989987 | − | 0.141159i | \(-0.0450828\pi\) |
−0.617241 | + | 0.786774i | \(0.711750\pi\) | |||||||
\(618\) | 7.45909 | − | 22.7616i | 0.300049 | − | 0.915607i | ||||
\(619\) | 13.2353 | + | 22.9241i | 0.531970 | + | 0.921398i | 0.999303 | + | 0.0373175i | \(0.0118813\pi\) |
−0.467334 | + | 0.884081i | \(0.654785\pi\) | |||||||
\(620\) | −1.83547 | −0.0737144 | ||||||||
\(621\) | −5.79006 | − | 2.63046i | −0.232347 | − | 0.105557i | ||||
\(622\) | −9.02415 | − | 15.6303i | −0.361835 | − | 0.626717i | ||||
\(623\) | 15.1430 | 0.606691 | ||||||||
\(624\) | 10.7379 | + | 11.9862i | 0.429861 | + | 0.479832i | ||||
\(625\) | 3.12123 | 0.124849 | ||||||||
\(626\) | −23.0474 | + | 39.9193i | −0.921160 | + | 1.59550i | ||||
\(627\) | −0.870983 | − | 1.76074i | −0.0347837 | − | 0.0703173i | ||||
\(628\) | 0.0453178 | + | 0.0784927i | 0.00180838 | + | 0.00313220i | ||||
\(629\) | −0.436849 | − | 0.756644i | −0.0174183 | − | 0.0301694i | ||||
\(630\) | −0.983453 | + | 8.92457i | −0.0391817 | + | 0.355563i | ||||
\(631\) | 7.09305 | − | 12.2855i | 0.282370 | − | 0.489079i | −0.689598 | − | 0.724192i | \(-0.742213\pi\) |
0.971968 | + | 0.235113i | \(0.0755462\pi\) | |||||||
\(632\) | 8.68564 | − | 15.0440i | 0.345496 | − | 0.598417i | ||||
\(633\) | 6.02947 | + | 6.73039i | 0.239650 | + | 0.267509i | ||||
\(634\) | 21.6066 | − | 37.4237i | 0.858107 | − | 1.48628i | ||||
\(635\) | −3.05898 | + | 5.29831i | −0.121392 | + | 0.210257i | ||||
\(636\) | 6.97836 | + | 7.78959i | 0.276710 | + | 0.308877i | ||||
\(637\) | 9.84282 | 0.389987 | ||||||||
\(638\) | 3.01919 | 0.119531 | ||||||||
\(639\) | 45.0232 | − | 19.7747i | 1.78109 | − | 0.782274i | ||||
\(640\) | 6.96203 | − | 12.0586i | 0.275198 | − | 0.476658i | ||||
\(641\) | 8.29318 | − | 14.3642i | 0.327561 | − | 0.567352i | −0.654466 | − | 0.756091i | \(-0.727107\pi\) |
0.982027 | + | 0.188739i | \(0.0604400\pi\) | |||||||
\(642\) | −8.18834 | + | 1.71896i | −0.323168 | + | 0.0678419i | ||||
\(643\) | −22.0545 | −0.869745 | −0.434872 | − | 0.900492i | \(-0.643207\pi\) | ||||
−0.434872 | + | 0.900492i | \(0.643207\pi\) | |||||||
\(644\) | 1.86958 | 0.0736716 | ||||||||
\(645\) | 6.67058 | − | 1.40034i | 0.262654 | − | 0.0551382i | ||||
\(646\) | 0.562297 | − | 0.551880i | 0.0221233 | − | 0.0217134i | ||||
\(647\) | −20.3310 | −0.799292 | −0.399646 | − | 0.916669i | \(-0.630867\pi\) | ||||
−0.399646 | + | 0.916669i | \(0.630867\pi\) | |||||||
\(648\) | 13.1005 | + | 2.92274i | 0.514637 | + | 0.114816i | ||||
\(649\) | −1.04352 | − | 1.80743i | −0.0409618 | − | 0.0709479i | ||||
\(650\) | 11.1679 | 0.438040 | ||||||||
\(651\) | −1.87818 | − | 2.09652i | −0.0736117 | − | 0.0821690i | ||||
\(652\) | 11.3732 | + | 19.6990i | 0.445411 | + | 0.771474i | ||||
\(653\) | 10.5732 | − | 18.3133i | 0.413761 | − | 0.716655i | −0.581537 | − | 0.813520i | \(-0.697548\pi\) |
0.995297 | + | 0.0968655i | \(0.0308817\pi\) | |||||||
\(654\) | 37.1471 | + | 41.4654i | 1.45257 | + | 1.62143i | ||||
\(655\) | 14.7902 | 0.577901 | ||||||||
\(656\) | 20.4305 | − | 35.3867i | 0.797679 | − | 1.38162i | ||||
\(657\) | 2.18132 | − | 0.958060i | 0.0851015 | − | 0.0373775i | ||||
\(658\) | −3.69773 | −0.144152 | ||||||||
\(659\) | −31.4873 | −1.22657 | −0.613286 | − | 0.789861i | \(-0.710153\pi\) | ||||
−0.613286 | + | 0.789861i | \(0.710153\pi\) | |||||||
\(660\) | 0.655314 | − | 0.137568i | 0.0255081 | − | 0.00535484i | ||||
\(661\) | −1.49130 | − | 2.58300i | −0.0580047 | − | 0.100467i | 0.835565 | − | 0.549392i | \(-0.185140\pi\) |
−0.893570 | + | 0.448925i | \(0.851807\pi\) | |||||||
\(662\) | 17.2495 | 0.670423 | ||||||||
\(663\) | 0.321893 | − | 0.0675741i | 0.0125013 | − | 0.00262436i | ||||
\(664\) | 4.52290 | + | 7.83389i | 0.175523 | + | 0.304014i | ||||
\(665\) | −7.06927 | − | 1.96522i | −0.274135 | − | 0.0762082i | ||||
\(666\) | −36.9497 | − | 27.1307i | −1.43177 | − | 1.05130i | ||||
\(667\) | 3.99385 | + | 6.91754i | 0.154642 | + | 0.267848i | ||||
\(668\) | 13.5073 | − | 23.3953i | 0.522611 | − | 0.905190i | ||||
\(669\) | −8.36579 | + | 1.75621i | −0.323440 | + | 0.0678990i | ||||
\(670\) | 1.77888 | 0.0687241 | ||||||||
\(671\) | 1.83837 | + | 3.18414i | 0.0709693 | + | 0.122922i | ||||
\(672\) | −13.0694 | + | 2.74363i | −0.504163 | + | 0.105838i | ||||
\(673\) | −22.7026 | − | 39.3221i | −0.875122 | − | 1.51576i | −0.856633 | − | 0.515927i | \(-0.827448\pi\) |
−0.0184895 | − | 0.999829i | \(-0.505886\pi\) | |||||||
\(674\) | −29.9914 | + | 51.9466i | −1.15522 | + | 2.00091i | ||||
\(675\) | 14.2132 | − | 10.1634i | 0.547065 | − | 0.391190i | ||||
\(676\) | −11.0438 | −0.424762 | ||||||||
\(677\) | 17.5918 | + | 30.4700i | 0.676109 | + | 1.17106i | 0.976143 | + | 0.217127i | \(0.0696686\pi\) |
−0.300034 | + | 0.953928i | \(0.596998\pi\) | |||||||
\(678\) | −11.1932 | + | 34.1565i | −0.429874 | + | 1.31177i | ||||
\(679\) | 15.3645 | 0.589634 | ||||||||
\(680\) | −0.0970030 | − | 0.168014i | −0.00371990 | − | 0.00644305i | ||||
\(681\) | 7.91532 | − | 24.1538i | 0.303316 | − | 0.925577i | ||||
\(682\) | −0.285739 | + | 0.494914i | −0.0109415 | + | 0.0189512i | ||||
\(683\) | 13.9565 | 0.534031 | 0.267015 | − | 0.963692i | \(-0.413963\pi\) | ||||
0.267015 | + | 0.963692i | \(0.413963\pi\) | |||||||
\(684\) | 5.64491 | − | 14.0961i | 0.215839 | − | 0.538978i | ||||
\(685\) | −15.1111 | −0.577364 | ||||||||
\(686\) | −14.3488 | + | 24.8529i | −0.547840 | + | 0.948887i | ||||
\(687\) | 1.99852 | − | 0.419543i | 0.0762481 | − | 0.0160066i | ||||
\(688\) | 7.64858 | + | 13.2477i | 0.291599 | + | 0.505065i | ||||
\(689\) | −9.71311 | −0.370040 | ||||||||
\(690\) | 3.21803 | + | 3.59212i | 0.122508 | + | 0.136750i | ||||
\(691\) | 5.37036 | + | 9.30173i | 0.204298 | + | 0.353854i | 0.949909 | − | 0.312527i | \(-0.101176\pi\) |
−0.745611 | + | 0.666382i | \(0.767842\pi\) | |||||||
\(692\) | −6.64531 | −0.252617 | ||||||||
\(693\) | 0.827695 | + | 0.607745i | 0.0314415 | + | 0.0230863i | ||||
\(694\) | 26.0454 | − | 45.1119i | 0.988668 | − | 1.71242i | ||||
\(695\) | −3.34233 | − | 5.78908i | −0.126782 | − | 0.219592i | ||||
\(696\) | −11.2493 | − | 12.5570i | −0.426402 | − | 0.475971i | ||||
\(697\) | −0.417570 | − | 0.723252i | −0.0158166 | − | 0.0273951i | ||||
\(698\) | 6.03885 | 0.228574 | ||||||||
\(699\) | −11.6708 | + | 35.6138i | −0.441430 | + | 1.34704i | ||||
\(700\) | −2.56835 | + | 4.44852i | −0.0970747 | + | 0.168138i | ||||
\(701\) | −13.3387 | − | 23.1033i | −0.503795 | − | 0.872599i | −0.999990 | − | 0.00438802i | \(-0.998603\pi\) |
0.496195 | − | 0.868211i | \(-0.334730\pi\) | |||||||
\(702\) | 14.0374 | − | 10.0377i | 0.529807 | − | 0.378849i | ||||
\(703\) | 26.7355 | − | 26.2402i | 1.00835 | − | 0.989669i | ||||
\(704\) | 0.0614562 | + | 0.106445i | 0.00231622 | + | 0.00401181i | ||||
\(705\) | −2.33793 | − | 2.60971i | −0.0880515 | − | 0.0982874i | ||||
\(706\) | 11.7989 | 0.444059 | ||||||||
\(707\) | −9.03444 | − | 15.6481i | −0.339775 | − | 0.588508i | ||||
\(708\) | 5.02380 | − | 15.3303i | 0.188806 | − | 0.576147i | ||||
\(709\) | 23.1688 | 0.870123 | 0.435061 | − | 0.900401i | \(-0.356727\pi\) | ||||
0.435061 | + | 0.900401i | \(0.356727\pi\) | |||||||
\(710\) | −37.2913 | −1.39952 | ||||||||
\(711\) | −28.1657 | − | 20.6810i | −1.05629 | − | 0.775596i | ||||
\(712\) | −8.58376 | + | 14.8675i | −0.321690 | + | 0.557184i | ||||
\(713\) | −1.51193 | −0.0566221 | ||||||||
\(714\) | −0.128254 | + | 0.391372i | −0.00479980 | + | 0.0146467i | ||||
\(715\) | −0.310945 | + | 0.538572i | −0.0116287 | + | 0.0201414i | ||||
\(716\) | 4.38944 | + | 7.60274i | 0.164041 | + | 0.284128i | ||||
\(717\) | −30.1441 | + | 6.32807i | −1.12575 | + | 0.236326i | ||||
\(718\) | 65.7925 | 2.45535 | ||||||||
\(719\) | −7.72298 | − | 13.3766i | −0.288019 | − | 0.498863i | 0.685318 | − | 0.728244i | \(-0.259663\pi\) |
−0.973337 | + | 0.229381i | \(0.926330\pi\) | |||||||
\(720\) | −15.3906 | − | 11.3007i | −0.573572 | − | 0.421152i | ||||
\(721\) | −10.2322 | −0.381065 | ||||||||
\(722\) | 28.9347 | + | 17.4348i | 1.07684 | + | 0.648855i | ||||
\(723\) | −3.06657 | − | 3.42305i | −0.114047 | − | 0.127305i | ||||
\(724\) | 10.1632 | 0.377714 | ||||||||
\(725\) | −21.9464 | −0.815068 | ||||||||
\(726\) | −10.4840 | + | 31.9924i | −0.389099 | + | 1.18735i | ||||
\(727\) | 18.5288 | − | 32.0927i | 0.687193 | − | 1.19025i | −0.285549 | − | 0.958364i | \(-0.592176\pi\) |
0.972742 | − | 0.231890i | \(-0.0744909\pi\) | |||||||
\(728\) | 1.83240 | − | 3.17381i | 0.0679134 | − | 0.117629i | ||||
\(729\) | 8.73025 | − | 25.5496i | 0.323343 | − | 0.946282i | ||||
\(730\) | −1.80672 | −0.0668697 | ||||||||
\(731\) | 0.312651 | 0.0115638 | ||||||||
\(732\) | −8.85041 | + | 27.0073i | −0.327121 | + | 0.998218i | ||||
\(733\) | 18.8660 | − | 32.6769i | 0.696832 | − | 1.20695i | −0.272727 | − | 0.962091i | \(-0.587926\pi\) |
0.969559 | − | 0.244857i | \(-0.0787409\pi\) | |||||||
\(734\) | −13.0770 | + | 22.6501i | −0.482682 | + | 0.836029i | ||||
\(735\) | −11.4294 | + | 2.39934i | −0.421578 | + | 0.0885008i | ||||
\(736\) | −3.58656 | + | 6.21210i | −0.132202 | + | 0.228981i | ||||
\(737\) | 0.101723 | − | 0.176189i | 0.00374700 | − | 0.00649000i | ||||
\(738\) | −35.3191 | − | 25.9334i | −1.30011 | − | 0.954622i | ||||
\(739\) | 2.29341 | + | 3.97230i | 0.0843643 | + | 0.146123i | 0.905120 | − | 0.425156i | \(-0.139781\pi\) |
−0.820756 | + | 0.571279i | \(0.806447\pi\) | |||||||
\(740\) | 6.38466 | + | 11.0586i | 0.234705 | + | 0.406521i | ||||
\(741\) | 6.25285 | + | 12.6405i | 0.229704 | + | 0.464360i | ||||
\(742\) | 6.08125 | − | 10.5330i | 0.223250 | − | 0.386680i | ||||
\(743\) | −5.67781 | −0.208299 | −0.104149 | − | 0.994562i | \(-0.533212\pi\) | ||||
−0.104149 | + | 0.994562i | \(0.533212\pi\) | |||||||
\(744\) | 3.12302 | − | 0.655608i | 0.114495 | − | 0.0240357i | ||||
\(745\) | 16.9345 | 0.620434 | ||||||||
\(746\) | −1.29577 | − | 2.24434i | −0.0474416 | − | 0.0821713i | ||||
\(747\) | 16.6598 | − | 7.31718i | 0.609552 | − | 0.267722i | ||||
\(748\) | 0.0307146 | 0.00112304 | ||||||||
\(749\) | 1.78708 | + | 3.09531i | 0.0652985 | + | 0.113100i | ||||
\(750\) | −32.2501 | + | 6.77019i | −1.17761 | + | 0.247212i | ||||
\(751\) | −24.9720 | − | 43.2529i | −0.911243 | − | 1.57832i | −0.812311 | − | 0.583225i | \(-0.801791\pi\) |
−0.0989320 | − | 0.995094i | \(-0.531543\pi\) | |||||||
\(752\) | 3.93179 | − | 6.81005i | 0.143377 | − | 0.248337i | ||||
\(753\) | 10.9575 | − | 2.30029i | 0.399314 | − | 0.0838271i | ||||
\(754\) | −21.6750 | −0.789355 | ||||||||
\(755\) | −9.44898 | − | 16.3661i | −0.343884 | − | 0.595624i | ||||
\(756\) | 0.770061 | + | 7.89997i | 0.0280069 | + | 0.287319i | ||||
\(757\) | −10.2071 | − | 17.6792i | −0.370984 | − | 0.642563i | 0.618733 | − | 0.785601i | \(-0.287646\pi\) |
−0.989717 | + | 0.143038i | \(0.954313\pi\) | |||||||
\(758\) | −27.4664 | + | 47.5731i | −0.997623 | + | 1.72793i | ||||
\(759\) | 0.539799 | − | 0.113319i | 0.0195935 | − | 0.00411321i | ||||
\(760\) | 5.93667 | − | 5.82669i | 0.215346 | − | 0.211356i | ||||
\(761\) | 5.85476 | − | 10.1407i | 0.212235 | − | 0.367601i | −0.740179 | − | 0.672410i | \(-0.765259\pi\) |
0.952414 | + | 0.304809i | \(0.0985925\pi\) | |||||||
\(762\) | −4.58521 | + | 13.9919i | −0.166105 | + | 0.506874i | ||||
\(763\) | 11.8909 | − | 20.5956i | 0.430479 | − | 0.745611i | ||||
\(764\) | 1.58394 | − | 2.74346i | 0.0573048 | − | 0.0992548i | ||||
\(765\) | −0.357305 | + | 0.156932i | −0.0129184 | + | 0.00567390i | ||||
\(766\) | −16.4059 | + | 28.4159i | −0.592770 | + | 1.02671i | ||||
\(767\) | 7.49151 | + | 12.9757i | 0.270503 | + | 0.468525i | ||||
\(768\) | 10.9452 | − | 33.3997i | 0.394952 | − | 1.20521i | ||||
\(769\) | −22.3655 | − | 38.7381i | −0.806520 | − | 1.39693i | −0.915260 | − | 0.402863i | \(-0.868015\pi\) |
0.108741 | − | 0.994070i | \(-0.465318\pi\) | |||||||
\(770\) | −0.389356 | − | 0.674385i | −0.0140314 | − | 0.0243031i | ||||
\(771\) | −9.02503 | + | 27.5402i | −0.325029 | + | 0.991834i | ||||
\(772\) | 14.2716 | + | 24.7191i | 0.513646 | + | 0.889662i | ||||
\(773\) | −1.53754 | + | 2.66310i | −0.0553014 | + | 0.0957849i | −0.892351 | − | 0.451342i | \(-0.850945\pi\) |
0.837049 | + | 0.547127i | \(0.184279\pi\) | |||||||
\(774\) | 15.0192 | − | 6.59658i | 0.539853 | − | 0.237109i | ||||
\(775\) | 2.07703 | − | 3.59752i | 0.0746091 | − | 0.129227i | ||||
\(776\) | −8.70930 | + | 15.0850i | −0.312646 | + | 0.541518i | ||||
\(777\) | −6.09811 | + | 18.6086i | −0.218768 | + | 0.667579i | ||||
\(778\) | 0.745834 | − | 1.29182i | 0.0267395 | − | 0.0463141i | ||||
\(779\) | 25.5556 | − | 25.0822i | 0.915626 | − | 0.898663i | ||||
\(780\) | −4.70455 | + | 0.987614i | −0.168450 | + | 0.0353622i | ||||
\(781\) | −2.13245 | + | 3.69351i | −0.0763050 | + | 0.132164i | ||||
\(782\) | 0.110611 | + | 0.191583i | 0.00395543 | + | 0.00685101i | ||||
\(783\) | −27.5853 | + | 19.7254i | −0.985819 | + | 0.704929i | ||||
\(784\) | −13.1051 | − | 22.6986i | −0.468038 | − | 0.810665i | ||||
\(785\) | 0.0998768 | 0.00356475 | ||||||||
\(786\) | 34.8362 | − | 7.31307i | 1.24257 | − | 0.260849i | ||||
\(787\) | −20.1946 | + | 34.9780i | −0.719859 | + | 1.24683i | 0.241197 | + | 0.970476i | \(0.422460\pi\) |
−0.961055 | + | 0.276356i | \(0.910873\pi\) | |||||||
\(788\) | −2.68474 | − | 4.65011i | −0.0956399 | − | 0.165653i | ||||
\(789\) | −35.5268 | + | 7.45804i | −1.26479 | + | 0.265513i | ||||
\(790\) | 13.2494 | + | 22.9486i | 0.471393 | + | 0.816476i | ||||
\(791\) | 15.3545 | 0.545945 | ||||||||
\(792\) | −1.06587 | + | 0.468140i | −0.0378739 | + | 0.0166346i | ||||
\(793\) | −13.1978 | − | 22.8592i | −0.468666 | − | 0.811754i | ||||
\(794\) | −37.0043 | −1.31323 | ||||||||
\(795\) | 11.2787 | − | 2.36772i | 0.400015 | − | 0.0839742i | ||||
\(796\) | −7.57281 | −0.268411 | ||||||||
\(797\) | −22.3467 | + | 38.7056i | −0.791561 | + | 1.37102i | 0.133440 | + | 0.991057i | \(0.457398\pi\) |
−0.925000 | + | 0.379966i | \(0.875936\pi\) | |||||||
\(798\) | −17.6223 | − | 1.13337i | −0.623824 | − | 0.0401209i | ||||
\(799\) | −0.0803598 | − | 0.139187i | −0.00284292 | − | 0.00492409i | ||||
\(800\) | −9.85415 | − | 17.0679i | −0.348397 | − | 0.603441i | ||||
\(801\) | 27.8353 | + | 20.4384i | 0.983512 | + | 0.722154i | ||||
\(802\) | 30.2525 | − | 52.3988i | 1.06825 | − | 1.85027i | ||||
\(803\) | −0.103315 | + | 0.178946i | −0.00364589 | + | 0.00631487i | ||||
\(804\) | 1.53905 | − | 0.323089i | 0.0542781 | − | 0.0113945i | ||||
\(805\) | 1.03010 | − | 1.78418i | 0.0363062 | − | 0.0628842i | ||||
\(806\) | 2.05134 | − | 3.55302i | 0.0722554 | − | 0.125150i | ||||
\(807\) | −8.67694 | + | 26.4779i | −0.305443 | + | 0.932068i | ||||
\(808\) | 20.4846 | 0.720645 | ||||||||
\(809\) | 27.4216 | 0.964091 | 0.482046 | − | 0.876146i | \(-0.339894\pi\) | ||||
0.482046 | + | 0.876146i | \(0.339894\pi\) | |||||||
\(810\) | −13.8532 | + | 15.0775i | −0.486751 | + | 0.529768i | ||||
\(811\) | −11.3213 | + | 19.6090i | −0.397543 | + | 0.688565i | −0.993422 | − | 0.114509i | \(-0.963470\pi\) |
0.595879 | + | 0.803074i | \(0.296804\pi\) | |||||||
\(812\) | 4.98474 | − | 8.63382i | 0.174930 | − | 0.302988i | ||||
\(813\) | −14.0466 | + | 42.8637i | −0.492637 | + | 1.50330i | ||||
\(814\) | 3.97575 | 0.139350 | ||||||||
\(815\) | 25.0657 | 0.878013 | ||||||||
\(816\) | −0.584412 | − | 0.652349i | −0.0204585 | − | 0.0228368i | ||||
\(817\) | 3.34836 | + | 12.9805i | 0.117144 | + | 0.454130i | ||||
\(818\) | −55.9531 | −1.95635 | ||||||||
\(819\) | −5.94209 | − | 4.36304i | −0.207633 | − | 0.152457i | ||||
\(820\) | 6.10289 | + | 10.5705i | 0.213122 | + | 0.369138i | ||||
\(821\) | 4.76813 | 0.166409 | 0.0832044 | − | 0.996533i | \(-0.473485\pi\) | ||||
0.0832044 | + | 0.996533i | \(0.473485\pi\) | |||||||
\(822\) | −35.5919 | + | 7.47171i | −1.24141 | + | 0.260606i | ||||
\(823\) | −11.3428 | − | 19.6464i | −0.395386 | − | 0.684829i | 0.597764 | − | 0.801672i | \(-0.296056\pi\) |
−0.993150 | + | 0.116843i | \(0.962723\pi\) | |||||||
\(824\) | 5.80007 | − | 10.0460i | 0.202055 | − | 0.349969i | ||||
\(825\) | −0.471922 | + | 1.44009i | −0.0164302 | + | 0.0501373i | ||||
\(826\) | −18.7613 | −0.652790 | ||||||||
\(827\) | 18.3589 | − | 31.7985i | 0.638400 | − | 1.10574i | −0.347384 | − | 0.937723i | \(-0.612930\pi\) |
0.985784 | − | 0.168018i | \(-0.0537367\pi\) | |||||||
\(828\) | 3.43659 | + | 2.52335i | 0.119430 | + | 0.0876925i | ||||
\(829\) | −4.14173 | −0.143848 | −0.0719242 | − | 0.997410i | \(-0.522914\pi\) | ||||
−0.0719242 | + | 0.997410i | \(0.522914\pi\) | |||||||
\(830\) | −13.7988 | −0.478964 | ||||||||
\(831\) | 7.94099 | − | 24.2322i | 0.275470 | − | 0.840604i | ||||
\(832\) | −0.441199 | − | 0.764178i | −0.0152958 | − | 0.0264931i | ||||
\(833\) | −0.535695 | −0.0185607 | ||||||||
\(834\) | −10.7348 | − | 11.9827i | −0.371715 | − | 0.414927i | ||||
\(835\) | −14.8844 | − | 25.7806i | −0.515098 | − | 0.892175i | ||||
\(836\) | 0.328941 | + | 1.27520i | 0.0113767 | + | 0.0441036i | ||||
\(837\) | −0.622749 | − | 6.38871i | −0.0215253 | − | 0.220826i | ||||
\(838\) | 17.2917 | + | 29.9501i | 0.597332 | + | 1.03461i | ||||
\(839\) | −25.9853 | + | 45.0079i | −0.897112 | + | 1.55384i | −0.0659441 | + | 0.997823i | \(0.521006\pi\) |
−0.831168 | + | 0.556021i | \(0.812327\pi\) | |||||||
\(840\) | −1.35410 | + | 4.13206i | −0.0467207 | + | 0.142570i | ||||
\(841\) | 13.5942 | 0.468766 | ||||||||
\(842\) | 17.7095 | + | 30.6737i | 0.610308 | + | 1.05709i | ||||
\(843\) | 20.4795 | + | 22.8602i | 0.705352 | + | 0.787348i | ||||
\(844\) | −3.02896 | − | 5.24631i | −0.104261 | − | 0.180585i | ||||
\(845\) | −6.08492 | + | 10.5394i | −0.209328 | + | 0.362566i | ||||
\(846\) | −6.79703 | − | 4.99079i | −0.233687 | − | 0.171587i | ||||
\(847\) | 14.3817 | 0.494161 | ||||||||
\(848\) | 12.9324 | + | 22.3995i | 0.444099 | + | 0.769202i | ||||
\(849\) | −15.8401 | − | 17.6815i | −0.543630 | − | 0.606827i | ||||
\(850\) | −0.607811 | −0.0208478 | ||||||||
\(851\) | 5.25921 | + | 9.10922i | 0.180283 | + | 0.312260i | ||||
\(852\) | −32.2636 | + | 6.77302i | −1.10533 | + | 0.232040i | ||||
\(853\) | −11.8152 | + | 20.4645i | −0.404544 | + | 0.700690i | −0.994268 | − | 0.106914i | \(-0.965903\pi\) |
0.589725 | + | 0.807604i | \(0.299236\pi\) | |||||||
\(854\) | 33.0518 | 1.13101 | ||||||||
\(855\) | −10.3420 | − | 13.1537i | −0.353690 | − | 0.449849i | ||||
\(856\) | −4.05200 | −0.138495 | ||||||||
\(857\) | −22.2493 | + | 38.5369i | −0.760021 | + | 1.31640i | 0.182818 | + | 0.983147i | \(0.441478\pi\) |
−0.942839 | + | 0.333249i | \(0.891855\pi\) | |||||||
\(858\) | −0.466086 | + | 1.42227i | −0.0159119 | + | 0.0485556i | ||||
\(859\) | 21.3956 | + | 37.0582i | 0.730008 | + | 1.26441i | 0.956879 | + | 0.290486i | \(0.0938169\pi\) |
−0.226872 | + | 0.973925i | \(0.572850\pi\) | |||||||
\(860\) | −4.56948 | −0.155818 | ||||||||
\(861\) | −5.82899 | + | 17.7873i | −0.198651 | + | 0.606191i | ||||
\(862\) | 2.59199 | + | 4.48946i | 0.0882836 | + | 0.152912i | ||||
\(863\) | −36.9884 | −1.25910 | −0.629550 | − | 0.776960i | \(-0.716761\pi\) | ||||
−0.629550 | + | 0.776960i | \(0.716761\pi\) | |||||||
\(864\) | −27.7267 | − | 12.5964i | −0.943283 | − | 0.428539i | ||||
\(865\) | −3.66143 | + | 6.34178i | −0.124492 | + | 0.215627i | ||||
\(866\) | −28.4653 | − | 49.3034i | −0.967292 | − | 1.67540i | ||||
\(867\) | 28.7992 | − | 6.04575i | 0.978073 | − | 0.205324i | ||||
\(868\) | 0.943521 | + | 1.63423i | 0.0320252 | + | 0.0554693i | ||||
\(869\) | 3.03059 | 0.102806 | ||||||||
\(870\) | 25.1687 | − | 5.28359i | 0.853297 | − | 0.179131i | ||||
\(871\) | −0.730275 | + | 1.26487i | −0.0247444 | + | 0.0428586i | ||||
\(872\) | 13.4806 | + | 23.3491i | 0.456512 | + | 0.790702i | ||||
\(873\) | 28.2424 | + | 20.7373i | 0.955860 | + | 0.701851i | ||||
\(874\) | −6.76947 | + | 6.64406i | −0.228981 | + | 0.224739i | ||||
\(875\) | 7.03848 | + | 12.1910i | 0.237944 | + | 0.412131i | ||||
\(876\) | −1.56314 | + | 0.328145i | −0.0528134 | + | 0.0110870i | ||||
\(877\) | −20.8501 | −0.704058 | −0.352029 | − | 0.935989i | \(-0.614508\pi\) | ||||
−0.352029 | + | 0.935989i | \(0.614508\pi\) | |||||||
\(878\) | −10.0362 | − | 17.3833i | −0.338707 | − | 0.586658i | ||||
\(879\) | 48.2326 | − | 10.1254i | 1.62685 | − | 0.341520i | ||||
\(880\) | 1.65601 | 0.0558240 | ||||||||
\(881\) | −14.9759 | −0.504550 | −0.252275 | − | 0.967656i | \(-0.581179\pi\) | ||||
−0.252275 | + | 0.967656i | \(0.581179\pi\) | |||||||
\(882\) | −25.7338 | + | 11.3026i | −0.866502 | + | 0.380577i | ||||
\(883\) | −12.7234 | + | 22.0375i | −0.428176 | + | 0.741622i | −0.996711 | − | 0.0810366i | \(-0.974177\pi\) |
0.568535 | + | 0.822659i | \(0.307510\pi\) | |||||||
\(884\) | −0.220503 | −0.00741631 | ||||||||
\(885\) | −11.8621 | − | 13.2410i | −0.398739 | − | 0.445092i | ||||
\(886\) | 34.1689 | − | 59.1823i | 1.14793 | − | 1.98827i | ||||
\(887\) | 18.1281 | + | 31.3988i | 0.608681 | + | 1.05427i | 0.991458 | + | 0.130426i | \(0.0416346\pi\) |
−0.382777 | + | 0.923841i | \(0.625032\pi\) | |||||||
\(888\) | −14.8133 | − | 16.5354i | −0.497103 | − | 0.554891i | ||||
\(889\) | 6.28986 | 0.210955 | ||||||||
\(890\) | −13.0940 | − | 22.6795i | −0.438912 | − | 0.760218i | ||||
\(891\) | 0.701171 | + | 2.23427i | 0.0234901 | + | 0.0748508i | ||||
\(892\) | 5.73073 | 0.191879 | ||||||||
\(893\) | 4.91809 | − | 4.82698i | 0.164578 | − | 0.161529i | ||||
\(894\) | 39.8868 | − | 8.37334i | 1.33401 | − | 0.280046i | ||||
\(895\) | 9.67398 | 0.323365 | ||||||||
\(896\) | −14.3153 | −0.478240 | ||||||||
\(897\) | −3.87526 | + | 0.813523i | −0.129391 | + | 0.0271627i | ||||
\(898\) | 0.465558 | − | 0.806370i | 0.0155359 | − | 0.0269089i | ||||
\(899\) | −4.03116 | + | 6.98217i | −0.134447 | + | 0.232868i | ||||
\(900\) | −10.7252 | + | 4.71062i | −0.357506 | + | 0.157021i | ||||
\(901\) | 0.528636 | 0.0176114 | ||||||||
\(902\) | 3.80029 | 0.126536 | ||||||||
\(903\) | −4.67580 | − | 5.21936i | −0.155601 | − | 0.173689i | ||||
\(904\) | −8.70368 | + | 15.0752i | −0.289480 | + | 0.501394i | ||||
\(905\) | 5.59973 | − | 9.69903i | 0.186141 | − | 0.322407i | ||||
\(906\) | −30.3480 | − | 33.8759i | −1.00824 | − | 1.12545i | ||||
\(907\) | −17.2593 | + | 29.8940i | −0.573087 | + | 0.992615i | 0.423160 | + | 0.906055i | \(0.360921\pi\) |
−0.996247 | + | 0.0865602i | \(0.972413\pi\) | |||||||
\(908\) | −8.52010 | + | 14.7572i | −0.282749 | + | 0.489736i | ||||
\(909\) | 4.51336 | − | 40.9575i | 0.149699 | − | 1.35847i | ||||
\(910\) | 2.79522 | + | 4.84146i | 0.0926606 | + | 0.160493i | ||||
\(911\) | 12.7760 | + | 22.1287i | 0.423289 | + | 0.733158i | 0.996259 | − | 0.0864183i | \(-0.0275422\pi\) |
−0.572970 | + | 0.819576i | \(0.694209\pi\) | |||||||
\(912\) | 20.8251 | − | 31.2497i | 0.689589 | − | 1.03478i | ||||
\(913\) | −0.789065 | + | 1.36670i | −0.0261142 | + | 0.0452312i | ||||
\(914\) | 38.0863 | 1.25978 | ||||||||
\(915\) | 20.8973 | + | 23.3266i | 0.690844 | + | 0.771155i | ||||
\(916\) | −1.36902 | −0.0452338 | ||||||||
\(917\) | −7.60288 | − | 13.1686i | −0.251069 | − | 0.434865i | ||||
\(918\) | −0.763984 | + | 0.546301i | −0.0252152 | + | 0.0180306i | ||||
\(919\) | 35.7063 | 1.17784 | 0.588920 | − | 0.808191i | \(-0.299553\pi\) | ||||
0.588920 | + | 0.808191i | \(0.299553\pi\) | |||||||
\(920\) | 1.16782 | + | 2.02272i | 0.0385018 | + | 0.0666870i | ||||
\(921\) | 5.35367 | − | 16.3369i | 0.176410 | − | 0.538319i | ||||
\(922\) | 0.897626 | + | 1.55473i | 0.0295618 | + | 0.0512025i | ||||
\(923\) | 15.3090 | − | 26.5160i | 0.503902 | − | 0.872784i | ||||
\(924\) | −0.459348 | − | 0.512747i | −0.0151114 | − | 0.0168681i | ||||
\(925\) | −28.8996 | −0.950214 | ||||||||
\(926\) | 9.67366 | + | 16.7553i | 0.317896 | + | 0.550612i | ||||
\(927\) | −18.8084 | − | 13.8103i | −0.617748 | − | 0.453588i | ||||
\(928\) | 19.1252 | + | 33.1259i | 0.627817 | + | 1.08741i | ||||
\(929\) | 25.8611 | − | 44.7927i | 0.848475 | − | 1.46960i | −0.0340937 | − | 0.999419i | \(-0.510854\pi\) |
0.882569 | − | 0.470183i | \(-0.155812\pi\) | |||||||
\(930\) | −1.51588 | + | 4.62577i | −0.0497078 | + | 0.151685i | ||||
\(931\) | −5.73708 | − | 22.2408i | −0.188025 | − | 0.728911i | ||||
\(932\) | 12.5625 | − | 21.7589i | 0.411499 | − | 0.712737i | ||||
\(933\) | −17.2071 | + | 3.61224i | −0.563335 | + | 0.118260i | ||||
\(934\) | 0.202642 | − | 0.350986i | 0.00663064 | − | 0.0114846i | ||||
\(935\) | 0.0169231 | − | 0.0293117i | 0.000553446 | − | 0.000958597i | ||||
\(936\) | 7.65193 | − | 3.36081i | 0.250111 | − | 0.109851i | ||||
\(937\) | −15.7019 | + | 27.1965i | −0.512959 | + | 0.888470i | 0.486929 | + | 0.873442i | \(0.338117\pi\) |
−0.999887 | + | 0.0150285i | \(0.995216\pi\) | |||||||
\(938\) | −0.914430 | − | 1.58384i | −0.0298572 | − | 0.0517142i | ||||
\(939\) | 29.9628 | + | 33.4460i | 0.977799 | + | 1.09147i | ||||
\(940\) | 1.17448 | + | 2.03426i | 0.0383073 | + | 0.0663502i | ||||
\(941\) | 4.39317 | + | 7.60920i | 0.143213 | + | 0.248053i | 0.928705 | − | 0.370819i | \(-0.120923\pi\) |
−0.785492 | + | 0.618872i | \(0.787590\pi\) | |||||||
\(942\) | 0.235245 | − | 0.0493844i | 0.00766470 | − | 0.00160903i | ||||
\(943\) | 5.02711 | + | 8.70721i | 0.163705 | + | 0.283546i | ||||
\(944\) | 19.9489 | − | 34.5525i | 0.649281 | − | 1.12459i | ||||
\(945\) | 7.96343 | + | 3.61783i | 0.259050 | + | 0.117688i | ||||
\(946\) | −0.711357 | + | 1.23211i | −0.0231282 | + | 0.0400592i | ||||
\(947\) | −9.14726 | + | 15.8435i | −0.297246 | + | 0.514845i | −0.975505 | − | 0.219978i | \(-0.929402\pi\) |
0.678259 | + | 0.734823i | \(0.262735\pi\) | |||||||
\(948\) | 15.6312 | + | 17.4483i | 0.507676 | + | 0.566693i | ||||
\(949\) | 0.741703 | − | 1.28467i | 0.0240767 | − | 0.0417021i | ||||
\(950\) | −6.50941 | − | 25.2348i | −0.211193 | − | 0.818726i | ||||
\(951\) | −28.0896 | − | 31.3550i | −0.910869 | − | 1.01676i | ||||
\(952\) | −0.0997284 | + | 0.172735i | −0.00323222 | + | 0.00559836i | ||||
\(953\) | 1.15491 | + | 2.00037i | 0.0374113 | + | 0.0647983i | 0.884125 | − | 0.467251i | \(-0.154756\pi\) |
−0.846713 | + | 0.532049i | \(0.821422\pi\) | |||||||
\(954\) | 25.3947 | − | 11.1536i | 0.822183 | − | 0.361111i | ||||
\(955\) | −1.74543 | − | 3.02318i | −0.0564809 | − | 0.0978278i | ||||
\(956\) | 20.6493 | 0.667846 | ||||||||
\(957\) | 0.915921 | − | 2.79496i | 0.0296075 | − | 0.0903482i | ||||
\(958\) | 12.1172 | − | 20.9876i | 0.391488 | − | 0.678077i | ||||
\(959\) | 7.76781 | + | 13.4542i | 0.250836 | + | 0.434460i | ||||
\(960\) | 0.698593 | + | 0.779804i | 0.0225470 | + | 0.0251681i | ||||
\(961\) | 14.7370 | + | 25.5252i | 0.475386 | + | 0.823393i | ||||
\(962\) | −28.5422 | −0.920237 | ||||||||
\(963\) | −0.892775 | + | 8.10170i | −0.0287693 | + | 0.261074i | ||||
\(964\) | 1.54052 | + | 2.66826i | 0.0496168 | + | 0.0859388i | ||||
\(965\) | 31.4535 | 1.01252 | ||||||||
\(966\) | 1.54405 | − | 4.71172i | 0.0496790 | − | 0.151597i | ||||
\(967\) | −44.0535 | −1.41667 | −0.708333 | − | 0.705878i | \(-0.750553\pi\) | ||||
−0.708333 | + | 0.705878i | \(0.750553\pi\) | |||||||
\(968\) | −8.15222 | + | 14.1201i | −0.262022 | + | 0.453836i | ||||
\(969\) | −0.340311 | − | 0.687959i | −0.0109324 | − | 0.0221004i | ||||
\(970\) | −13.2855 | − | 23.0112i | −0.426572 | − | 0.738844i | ||||
\(971\) | 6.62462 | + | 11.4742i | 0.212594 | + | 0.368224i | 0.952526 | − | 0.304458i | \(-0.0984755\pi\) |
−0.739932 | + | 0.672682i | \(0.765142\pi\) | |||||||
\(972\) | −9.24703 | + | 15.5608i | −0.296599 | + | 0.499112i | ||||
\(973\) | −3.43623 | + | 5.95173i | −0.110161 | + | 0.190804i | ||||
\(974\) | 16.7792 | − | 29.0624i | 0.537639 | − | 0.931218i | ||||
\(975\) | 3.38797 | − | 10.3385i | 0.108502 | − | 0.331096i | ||||
\(976\) | −35.1439 | + | 60.8710i | −1.12493 | + | 1.94843i | ||||
\(977\) | −3.80938 | + | 6.59803i | −0.121873 | + | 0.211090i | −0.920506 | − | 0.390728i | \(-0.872223\pi\) |
0.798633 | + | 0.601818i | \(0.205557\pi\) | |||||||
\(978\) | 59.0386 | − | 12.3938i | 1.88785 | − | 0.396311i | ||||
\(979\) | −2.99505 | −0.0957221 | ||||||||
\(980\) | 7.82933 | 0.250099 | ||||||||
\(981\) | 49.6551 | − | 21.8091i | 1.58537 | − | 0.696310i | ||||
\(982\) | 0.737362 | − | 1.27715i | 0.0235302 | − | 0.0407554i | ||||
\(983\) | 22.5126 | − | 38.9930i | 0.718042 | − | 1.24368i | −0.243733 | − | 0.969842i | \(-0.578372\pi\) |
0.961775 | − | 0.273842i | \(-0.0882946\pi\) | |||||||
\(984\) | −14.1596 | − | 15.8056i | −0.451392 | − | 0.503866i | ||||
\(985\) | −5.91695 | −0.188530 | ||||||||
\(986\) | 1.17966 | 0.0375680 | ||||||||
\(987\) | −1.12177 | + | 3.42311i | −0.0357063 | + | 0.108959i | ||||
\(988\) | −2.36149 | − | 9.15473i | −0.0751291 | − | 0.291251i | ||||
\(989\) | −3.76400 | −0.119688 | ||||||||
\(990\) | 0.194512 | − | 1.76514i | 0.00618198 | − | 0.0560998i | ||||
\(991\) | −9.93366 | − | 17.2056i | −0.315553 | − | 0.546554i | 0.664002 | − | 0.747731i | \(-0.268857\pi\) |
−0.979555 | + | 0.201177i | \(0.935523\pi\) | |||||||
\(992\) | −7.24013 | −0.229874 | ||||||||
\(993\) | 5.23294 | − | 15.9685i | 0.166062 | − | 0.506744i | ||||
\(994\) | 19.1695 | + | 33.2026i | 0.608020 | + | 1.05312i | ||||
\(995\) | −4.17246 | + | 7.22692i | −0.132276 | + | 0.229109i | ||||
\(996\) | −11.9384 | + | 2.50621i | −0.378284 | + | 0.0794122i | ||||
\(997\) | −37.2092 | −1.17843 | −0.589214 | − | 0.807977i | \(-0.700563\pi\) | ||||
−0.589214 | + | 0.807977i | \(0.700563\pi\) | |||||||
\(998\) | −1.33573 | + | 2.31356i | −0.0422819 | + | 0.0732345i | ||||
\(999\) | −36.3252 | + | 25.9750i | −1.14928 | + | 0.821813i |
(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 | 171.2.g.c.121.4 | yes | 32 | |
3.2 | odd | 2 | 513.2.g.c.64.13 | 32 | |||
9.2 | odd | 6 | 513.2.h.c.235.4 | 32 | |||
9.7 | even | 3 | 171.2.h.c.7.13 | yes | 32 | ||
19.11 | even | 3 | 171.2.h.c.49.13 | yes | 32 | ||
57.11 | odd | 6 | 513.2.h.c.334.4 | 32 | |||
171.11 | odd | 6 | 513.2.g.c.505.13 | 32 | |||
171.106 | even | 3 | inner | 171.2.g.c.106.4 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
171.2.g.c.106.4 | ✓ | 32 | 171.106 | even | 3 | inner | |
171.2.g.c.121.4 | yes | 32 | 1.1 | even | 1 | trivial | |
171.2.h.c.7.13 | yes | 32 | 9.7 | even | 3 | ||
171.2.h.c.49.13 | yes | 32 | 19.11 | even | 3 | ||
513.2.g.c.64.13 | 32 | 3.2 | odd | 2 | |||
513.2.g.c.505.13 | 32 | 171.11 | odd | 6 | |||
513.2.h.c.235.4 | 32 | 9.2 | odd | 6 | |||
513.2.h.c.334.4 | 32 | 57.11 | odd | 6 |