Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [228,2,Mod(191,228)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(228, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("228.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 228 = 2^{2} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 228.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.82058916609\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 191.25 | ||
Character | \(\chi\) | \(=\) | 228.191 |
Dual form | 228.2.c.a.191.26 |
$q$-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 \(\left(\mathbb{Z}/228\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(97\) | \(115\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.791500 | − | 1.17198i | 0.559675 | − | 0.828712i | ||||
\(3\) | −1.69893 | + | 0.337110i | −0.980877 | + | 0.194631i | ||||
\(4\) | −0.747055 | − | 1.85524i | −0.373527 | − | 0.927619i | ||||
\(5\) | 0.951020i | 0.425309i | 0.977127 | + | 0.212654i | \(0.0682109\pi\) | ||||
−0.977127 | + | 0.212654i | \(0.931789\pi\) | |||||||
\(6\) | −0.949617 | + | 2.25793i | −0.387679 | + | 0.921794i | ||||
\(7\) | − | 4.82396i | − | 1.82328i | −0.410985 | − | 0.911642i | \(-0.634815\pi\) | ||
0.410985 | − | 0.911642i | \(-0.365185\pi\) | |||||||
\(8\) | −2.76559 | − | 0.592892i | −0.977783 | − | 0.209619i | ||||
\(9\) | 2.77271 | − | 1.14545i | 0.924238 | − | 0.381818i | ||||
\(10\) | 1.11457 | + | 0.752732i | 0.352459 | + | 0.238035i | ||||
\(11\) | −3.58981 | −1.08237 | −0.541184 | − | 0.840904i | \(-0.682024\pi\) | ||||
−0.541184 | + | 0.840904i | \(0.682024\pi\) | |||||||
\(12\) | 1.89461 | + | 2.90008i | 0.546927 | + | 0.837180i | ||||
\(13\) | −2.89059 | −0.801705 | −0.400852 | − | 0.916143i | \(-0.631286\pi\) | ||||
−0.400852 | + | 0.916143i | \(0.631286\pi\) | |||||||
\(14\) | −5.65356 | − | 3.81816i | −1.51098 | − | 1.02045i | ||||
\(15\) | −0.320599 | − | 1.61571i | −0.0827782 | − | 0.417176i | ||||
\(16\) | −2.88382 | + | 2.77193i | −0.720955 | + | 0.692982i | ||||
\(17\) | − | 3.29763i | − | 0.799793i | −0.916560 | − | 0.399897i | \(-0.869046\pi\) | ||
0.916560 | − | 0.399897i | \(-0.130954\pi\) | |||||||
\(18\) | 0.852160 | − | 4.15618i | 0.200856 | − | 0.979621i | ||||
\(19\) | − | 1.00000i | − | 0.229416i | ||||||
\(20\) | 1.76437 | − | 0.710464i | 0.394525 | − | 0.158865i | ||||
\(21\) | 1.62621 | + | 8.19556i | 0.354867 | + | 1.78842i | ||||
\(22\) | −2.84134 | + | 4.20717i | −0.605775 | + | 0.896972i | ||||
\(23\) | 8.68428 | 1.81080 | 0.905399 | − | 0.424562i | \(-0.139572\pi\) | ||||
0.905399 | + | 0.424562i | \(0.139572\pi\) | |||||||
\(24\) | 4.89841 | + | 0.0749715i | 0.999883 | + | 0.0153035i | ||||
\(25\) | 4.09556 | 0.819112 | ||||||||
\(26\) | −2.28790 | + | 3.38770i | −0.448694 | + | 0.664382i | ||||
\(27\) | −4.32450 | + | 2.88075i | −0.832250 | + | 0.554401i | ||||
\(28\) | −8.94959 | + | 3.60376i | −1.69131 | + | 0.681047i | ||||
\(29\) | − | 5.48837i | − | 1.01916i | −0.860422 | − | 0.509582i | \(-0.829800\pi\) | ||
0.860422 | − | 0.509582i | \(-0.170200\pi\) | |||||||
\(30\) | −2.14733 | − | 0.903104i | −0.392047 | − | 0.164884i | ||||
\(31\) | 6.59046i | 1.18368i | 0.806055 | + | 0.591841i | \(0.201599\pi\) | ||||
−0.806055 | + | 0.591841i | \(0.798401\pi\) | |||||||
\(32\) | 0.966091 | + | 5.57375i | 0.170782 | + | 0.985309i | ||||
\(33\) | 6.09883 | − | 1.21016i | 1.06167 | − | 0.210662i | ||||
\(34\) | −3.86474 | − | 2.61008i | −0.662798 | − | 0.447624i | ||||
\(35\) | 4.58768 | 0.775459 | ||||||||
\(36\) | −4.19646 | − | 4.28833i | −0.699409 | − | 0.714721i | ||||
\(37\) | 8.68838 | 1.42836 | 0.714180 | − | 0.699962i | \(-0.246800\pi\) | ||||
0.714180 | + | 0.699962i | \(0.246800\pi\) | |||||||
\(38\) | −1.17198 | − | 0.791500i | −0.190120 | − | 0.128398i | ||||
\(39\) | 4.91090 | − | 0.974447i | 0.786374 | − | 0.156036i | ||||
\(40\) | 0.563852 | − | 2.63013i | 0.0891528 | − | 0.415860i | ||||
\(41\) | 0.964782i | 0.150674i | 0.997158 | + | 0.0753368i | \(0.0240032\pi\) | ||||
−0.997158 | + | 0.0753368i | \(0.975997\pi\) | |||||||
\(42\) | 10.8921 | + | 4.58091i | 1.68069 | + | 0.706850i | ||||
\(43\) | − | 3.20516i | − | 0.488783i | −0.969677 | − | 0.244391i | \(-0.921412\pi\) | ||
0.969677 | − | 0.244391i | \(-0.0785882\pi\) | |||||||
\(44\) | 2.68179 | + | 6.65996i | 0.404294 | + | 1.00403i | ||||
\(45\) | 1.08935 | + | 2.63690i | 0.162390 | + | 0.393087i | ||||
\(46\) | 6.87361 | − | 10.1778i | 1.01346 | − | 1.50063i | ||||
\(47\) | 0.581952 | 0.0848864 | 0.0424432 | − | 0.999099i | \(-0.486486\pi\) | ||||
0.0424432 | + | 0.999099i | \(0.486486\pi\) | |||||||
\(48\) | 3.96495 | − | 5.68147i | 0.572292 | − | 0.820050i | ||||
\(49\) | −16.2706 | −2.32437 | ||||||||
\(50\) | 3.24164 | − | 4.79990i | 0.458437 | − | 0.678808i | ||||
\(51\) | 1.11167 | + | 5.60244i | 0.155664 | + | 0.784498i | ||||
\(52\) | 2.15943 | + | 5.36273i | 0.299459 | + | 0.743677i | ||||
\(53\) | − | 1.07053i | − | 0.147049i | −0.997293 | − | 0.0735245i | \(-0.976575\pi\) | ||
0.997293 | − | 0.0735245i | \(-0.0234247\pi\) | |||||||
\(54\) | −0.0466684 | + | 7.34832i | −0.00635076 | + | 0.999980i | ||||
\(55\) | − | 3.41398i | − | 0.460341i | ||||||
\(56\) | −2.86008 | + | 13.3411i | −0.382195 | + | 1.78278i | ||||
\(57\) | 0.337110 | + | 1.69893i | 0.0446514 | + | 0.225029i | ||||
\(58\) | −6.43224 | − | 4.34405i | −0.844594 | − | 0.570401i | ||||
\(59\) | 4.73171 | 0.616016 | 0.308008 | − | 0.951384i | \(-0.400338\pi\) | ||||
0.308008 | + | 0.951384i | \(0.400338\pi\) | |||||||
\(60\) | −2.75803 | + | 1.80181i | −0.356060 | + | 0.232613i | ||||
\(61\) | −5.55370 | −0.711079 | −0.355540 | − | 0.934661i | \(-0.615703\pi\) | ||||
−0.355540 | + | 0.934661i | \(0.615703\pi\) | |||||||
\(62\) | 7.72386 | + | 5.21635i | 0.980931 | + | 0.662477i | ||||
\(63\) | −5.52561 | − | 13.3754i | −0.696162 | − | 1.68515i | ||||
\(64\) | 7.29696 | + | 3.27939i | 0.912120 | + | 0.409923i | ||||
\(65\) | − | 2.74901i | − | 0.340972i | ||||||
\(66\) | 3.40894 | − | 8.10553i | 0.419612 | − | 0.997721i | ||||
\(67\) | − | 2.99264i | − | 0.365609i | −0.983149 | − | 0.182805i | \(-0.941482\pi\) | ||
0.983149 | − | 0.182805i | \(-0.0585176\pi\) | |||||||
\(68\) | −6.11789 | + | 2.46351i | −0.741903 | + | 0.298745i | ||||
\(69\) | −14.7540 | + | 2.92756i | −1.77617 | + | 0.352437i | ||||
\(70\) | 3.63115 | − | 5.37665i | 0.434005 | − | 0.642632i | ||||
\(71\) | −4.79797 | −0.569415 | −0.284707 | − | 0.958614i | \(-0.591896\pi\) | ||||
−0.284707 | + | 0.958614i | \(0.591896\pi\) | |||||||
\(72\) | −8.34731 | + | 1.52393i | −0.983740 | + | 0.179597i | ||||
\(73\) | −1.18991 | −0.139269 | −0.0696344 | − | 0.997573i | \(-0.522183\pi\) | ||||
−0.0696344 | + | 0.997573i | \(0.522183\pi\) | |||||||
\(74\) | 6.87685 | − | 10.1826i | 0.799418 | − | 1.18370i | ||||
\(75\) | −6.95806 | + | 1.38066i | −0.803448 | + | 0.159424i | ||||
\(76\) | −1.85524 | + | 0.747055i | −0.212810 | + | 0.0856931i | ||||
\(77\) | 17.3171i | 1.97347i | ||||||||
\(78\) | 2.74495 | − | 6.52673i | 0.310804 | − | 0.739007i | ||||
\(79\) | 0.0661975i | 0.00744780i | 0.999993 | + | 0.00372390i | \(0.00118536\pi\) | ||||
−0.999993 | + | 0.00372390i | \(0.998815\pi\) | |||||||
\(80\) | −2.63616 | − | 2.74257i | −0.294732 | − | 0.306628i | ||||
\(81\) | 6.37588 | − | 6.35202i | 0.708431 | − | 0.705780i | ||||
\(82\) | 1.13070 | + | 0.763625i | 0.124865 | + | 0.0843283i | ||||
\(83\) | 8.75808 | 0.961324 | 0.480662 | − | 0.876906i | \(-0.340396\pi\) | ||||
0.480662 | + | 0.876906i | \(0.340396\pi\) | |||||||
\(84\) | 13.9898 | − | 9.13953i | 1.52642 | − | 0.997204i | ||||
\(85\) | 3.13611 | 0.340159 | ||||||||
\(86\) | −3.75637 | − | 2.53689i | −0.405060 | − | 0.273560i | ||||
\(87\) | 1.85019 | + | 9.32434i | 0.198361 | + | 0.999675i | ||||
\(88\) | 9.92794 | + | 2.12837i | 1.05832 | + | 0.226885i | ||||
\(89\) | − | 6.42337i | − | 0.680876i | −0.940267 | − | 0.340438i | \(-0.889425\pi\) | ||
0.940267 | − | 0.340438i | \(-0.110575\pi\) | |||||||
\(90\) | 3.95261 | + | 0.810421i | 0.416641 | + | 0.0854259i | ||||
\(91\) | 13.9441i | 1.46174i | ||||||||
\(92\) | −6.48763 | − | 16.1114i | −0.676382 | − | 1.67973i | ||||
\(93\) | −2.22171 | − | 11.1967i | −0.230381 | − | 1.16105i | ||||
\(94\) | 0.460615 | − | 0.682033i | 0.0475088 | − | 0.0703463i | ||||
\(95\) | 0.951020 | 0.0975726 | ||||||||
\(96\) | −3.52029 | − | 9.14372i | −0.359288 | − | 0.933227i | ||||
\(97\) | −0.00303833 | −0.000308495 | −0.000154248 | − | 1.00000i | \(-0.500049\pi\) | ||||
−0.000154248 | 1.00000i | \(0.500049\pi\) | ||||||||
\(98\) | −12.8782 | + | 19.0687i | −1.30089 | + | 1.92623i | ||||
\(99\) | −9.95352 | + | 4.11196i | −1.00037 | + | 0.413267i | ||||
\(100\) | −3.05961 | − | 7.59824i | −0.305961 | − | 0.759824i | ||||
\(101\) | − | 8.03074i | − | 0.799089i | −0.916714 | − | 0.399544i | \(-0.869168\pi\) | ||
0.916714 | − | 0.399544i | \(-0.130832\pi\) | |||||||
\(102\) | 7.44581 | + | 3.13149i | 0.737245 | + | 0.310063i | ||||
\(103\) | 10.1386i | 0.998989i | 0.866317 | + | 0.499495i | \(0.166481\pi\) | ||||
−0.866317 | + | 0.499495i | \(0.833519\pi\) | |||||||
\(104\) | 7.99418 | + | 1.71381i | 0.783894 | + | 0.168052i | ||||
\(105\) | −7.79414 | + | 1.54655i | −0.760630 | + | 0.150928i | ||||
\(106\) | −1.25464 | − | 0.847327i | −0.121861 | − | 0.0822997i | ||||
\(107\) | −0.769003 | −0.0743423 | −0.0371711 | − | 0.999309i | \(-0.511835\pi\) | ||||
−0.0371711 | + | 0.999309i | \(0.511835\pi\) | |||||||
\(108\) | 8.57512 | + | 5.87089i | 0.825141 | + | 0.564927i | ||||
\(109\) | 2.74345 | 0.262775 | 0.131388 | − | 0.991331i | \(-0.458057\pi\) | ||||
0.131388 | + | 0.991331i | \(0.458057\pi\) | |||||||
\(110\) | −4.00110 | − | 2.70217i | −0.381490 | − | 0.257642i | ||||
\(111\) | −14.7609 | + | 2.92894i | −1.40105 | + | 0.278003i | ||||
\(112\) | 13.3717 | + | 13.9114i | 1.26350 | + | 1.31451i | ||||
\(113\) | 5.53855i | 0.521023i | 0.965471 | + | 0.260512i | \(0.0838912\pi\) | ||||
−0.965471 | + | 0.260512i | \(0.916109\pi\) | |||||||
\(114\) | 2.25793 | + | 0.949617i | 0.211474 | + | 0.0889398i | ||||
\(115\) | 8.25892i | 0.770148i | ||||||||
\(116\) | −10.1822 | + | 4.10011i | −0.945396 | + | 0.380686i | ||||
\(117\) | −8.01477 | + | 3.31103i | −0.740966 | + | 0.306105i | ||||
\(118\) | 3.74515 | − | 5.54545i | 0.344769 | − | 0.510500i | ||||
\(119\) | −15.9076 | −1.45825 | ||||||||
\(120\) | −0.0712993 | + | 4.65848i | −0.00650871 | + | 0.425259i | ||||
\(121\) | 1.88674 | 0.171522 | ||||||||
\(122\) | −4.39576 | + | 6.50881i | −0.397973 | + | 0.589280i | ||||
\(123\) | −0.325238 | − | 1.63910i | −0.0293257 | − | 0.147792i | ||||
\(124\) | 12.2269 | − | 4.92343i | 1.09801 | − | 0.442137i | ||||
\(125\) | 8.65006i | 0.773685i | ||||||||
\(126\) | −20.0492 | − | 4.11079i | −1.78613 | − | 0.366218i | ||||
\(127\) | − | 10.8027i | − | 0.958584i | −0.877655 | − | 0.479292i | \(-0.840893\pi\) | ||
0.877655 | − | 0.479292i | \(-0.159107\pi\) | |||||||
\(128\) | 9.61891 | − | 5.95622i | 0.850199 | − | 0.526461i | ||||
\(129\) | 1.08049 | + | 5.44534i | 0.0951322 | + | 0.479436i | ||||
\(130\) | −3.22177 | − | 2.17584i | −0.282568 | − | 0.190834i | ||||
\(131\) | 0.348602 | 0.0304575 | 0.0152287 | − | 0.999884i | \(-0.495152\pi\) | ||||
0.0152287 | + | 0.999884i | \(0.495152\pi\) | |||||||
\(132\) | −6.80130 | − | 10.4107i | −0.591977 | − | 0.906137i | ||||
\(133\) | −4.82396 | −0.418290 | ||||||||
\(134\) | −3.50730 | − | 2.36868i | −0.302985 | − | 0.204622i | ||||
\(135\) | −2.73965 | − | 4.11268i | −0.235792 | − | 0.353963i | ||||
\(136\) | −1.95514 | + | 9.11989i | −0.167652 | + | 0.782024i | ||||
\(137\) | − | 17.5754i | − | 1.50157i | −0.660548 | − | 0.750784i | \(-0.729676\pi\) | ||
0.660548 | − | 0.750784i | \(-0.270324\pi\) | |||||||
\(138\) | −8.24674 | + | 19.6085i | −0.702009 | + | 1.66918i | ||||
\(139\) | − | 9.25489i | − | 0.784989i | −0.919754 | − | 0.392495i | \(-0.871612\pi\) | ||
0.919754 | − | 0.392495i | \(-0.128388\pi\) | |||||||
\(140\) | −3.42725 | − | 8.51124i | −0.289655 | − | 0.719331i | ||||
\(141\) | −0.988694 | + | 0.196182i | −0.0832630 | + | 0.0165215i | ||||
\(142\) | −3.79760 | + | 5.62311i | −0.318687 | + | 0.471881i | ||||
\(143\) | 10.3767 | 0.867740 | ||||||||
\(144\) | −4.82089 | + | 10.9890i | −0.401741 | + | 0.915753i | ||||
\(145\) | 5.21955 | 0.433460 | ||||||||
\(146\) | −0.941816 | + | 1.39455i | −0.0779452 | + | 0.115414i | ||||
\(147\) | 27.6425 | − | 5.48497i | 2.27992 | − | 0.452393i | ||||
\(148\) | −6.49070 | − | 16.1190i | −0.533532 | − | 1.32497i | ||||
\(149\) | − | 0.276738i | − | 0.0226712i | −0.999936 | − | 0.0113356i | \(-0.996392\pi\) | ||
0.999936 | − | 0.0113356i | \(-0.00360831\pi\) | |||||||
\(150\) | −3.88921 | + | 9.24747i | −0.317553 | + | 0.755053i | ||||
\(151\) | 13.7785i | 1.12128i | 0.828060 | + | 0.560640i | \(0.189445\pi\) | ||||
−0.828060 | + | 0.560640i | \(0.810555\pi\) | |||||||
\(152\) | −0.592892 | + | 2.76559i | −0.0480899 | + | 0.224319i | ||||
\(153\) | −3.77728 | − | 9.14339i | −0.305375 | − | 0.739199i | ||||
\(154\) | 20.2952 | + | 13.7065i | 1.63544 | + | 1.10450i | ||||
\(155\) | −6.26766 | −0.503430 | ||||||||
\(156\) | −5.47654 | − | 8.38293i | −0.438474 | − | 0.671171i | ||||
\(157\) | 8.94060 | 0.713538 | 0.356769 | − | 0.934193i | \(-0.383878\pi\) | ||||
0.356769 | + | 0.934193i | \(0.383878\pi\) | |||||||
\(158\) | 0.0775818 | + | 0.0523953i | 0.00617208 | + | 0.00416835i | ||||
\(159\) | 0.360888 | + | 1.81876i | 0.0286203 | + | 0.144237i | ||||
\(160\) | −5.30074 | + | 0.918771i | −0.419061 | + | 0.0726353i | ||||
\(161\) | − | 41.8926i | − | 3.30160i | ||||||
\(162\) | −2.39791 | − | 12.5000i | −0.188398 | − | 0.982093i | ||||
\(163\) | − | 14.0725i | − | 1.10224i | −0.834425 | − | 0.551122i | \(-0.814200\pi\) | ||
0.834425 | − | 0.551122i | \(-0.185800\pi\) | |||||||
\(164\) | 1.78990 | − | 0.720745i | 0.139768 | − | 0.0562807i | ||||
\(165\) | 1.15089 | + | 5.80011i | 0.0895965 | + | 0.451538i | ||||
\(166\) | 6.93202 | − | 10.2643i | 0.538029 | − | 0.796661i | ||||
\(167\) | 5.11581 | 0.395873 | 0.197937 | − | 0.980215i | \(-0.436576\pi\) | ||||
0.197937 | + | 0.980215i | \(0.436576\pi\) | |||||||
\(168\) | 0.361659 | − | 23.6297i | 0.0279026 | − | 1.82307i | ||||
\(169\) | −4.64450 | −0.357269 | ||||||||
\(170\) | 2.48223 | − | 3.67545i | 0.190379 | − | 0.281894i | ||||
\(171\) | −1.14545 | − | 2.77271i | −0.0875949 | − | 0.212035i | ||||
\(172\) | −5.94634 | + | 2.39443i | −0.453404 | + | 0.182574i | ||||
\(173\) | 15.6615i | 1.19073i | 0.803457 | + | 0.595363i | \(0.202992\pi\) | ||||
−0.803457 | + | 0.595363i | \(0.797008\pi\) | |||||||
\(174\) | 12.3923 | + | 5.21185i | 0.939460 | + | 0.395109i | ||||
\(175\) | − | 19.7568i | − | 1.49347i | ||||||
\(176\) | 10.3524 | − | 9.95070i | 0.780339 | − | 0.750062i | ||||
\(177\) | −8.03883 | + | 1.59511i | −0.604235 | + | 0.119896i | ||||
\(178\) | −7.52803 | − | 5.08410i | −0.564250 | − | 0.381069i | ||||
\(179\) | 14.3431 | 1.07205 | 0.536026 | − | 0.844202i | \(-0.319925\pi\) | ||||
0.536026 | + | 0.844202i | \(0.319925\pi\) | |||||||
\(180\) | 4.07828 | − | 3.99091i | 0.303977 | − | 0.297465i | ||||
\(181\) | 3.60378 | 0.267867 | 0.133933 | − | 0.990990i | \(-0.457239\pi\) | ||||
0.133933 | + | 0.990990i | \(0.457239\pi\) | |||||||
\(182\) | 16.3421 | + | 11.0367i | 1.21136 | + | 0.818097i | ||||
\(183\) | 9.43535 | − | 1.87221i | 0.697481 | − | 0.138398i | ||||
\(184\) | −24.0171 | − | 5.14884i | −1.77057 | − | 0.379577i | ||||
\(185\) | 8.26282i | 0.607495i | ||||||||
\(186\) | −14.8808 | − | 6.25841i | −1.09111 | − | 0.458889i | ||||
\(187\) | 11.8379i | 0.865671i | ||||||||
\(188\) | −0.434750 | − | 1.07966i | −0.0317074 | − | 0.0787422i | ||||
\(189\) | 13.8966 | + | 20.8612i | 1.01083 | + | 1.51743i | ||||
\(190\) | 0.752732 | − | 1.11457i | 0.0546089 | − | 0.0808596i | ||||
\(191\) | −12.9210 | −0.934933 | −0.467467 | − | 0.884011i | \(-0.654833\pi\) | ||||
−0.467467 | + | 0.884011i | \(0.654833\pi\) | |||||||
\(192\) | −13.5025 | − | 3.11156i | −0.974461 | − | 0.224558i | ||||
\(193\) | −10.4423 | −0.751654 | −0.375827 | − | 0.926690i | \(-0.622641\pi\) | ||||
−0.375827 | + | 0.926690i | \(0.622641\pi\) | |||||||
\(194\) | −0.00240484 | + | 0.00356085i | −0.000172657 | + | 0.000255654i | ||||
\(195\) | 0.926718 | + | 4.67036i | 0.0663637 | + | 0.334452i | ||||
\(196\) | 12.1550 | + | 30.1858i | 0.868214 | + | 2.15613i | ||||
\(197\) | 17.5579i | 1.25095i | 0.780244 | + | 0.625475i | \(0.215095\pi\) | ||||
−0.780244 | + | 0.625475i | \(0.784905\pi\) | |||||||
\(198\) | −3.05910 | + | 14.9199i | −0.217400 | + | 1.06031i | ||||
\(199\) | 23.4265i | 1.66066i | 0.557269 | + | 0.830332i | \(0.311849\pi\) | ||||
−0.557269 | + | 0.830332i | \(0.688151\pi\) | |||||||
\(200\) | −11.3266 | − | 2.42822i | −0.800914 | − | 0.171701i | ||||
\(201\) | 1.00885 | + | 5.08428i | 0.0711588 | + | 0.358618i | ||||
\(202\) | −9.41184 | − | 6.35633i | −0.662214 | − | 0.447230i | ||||
\(203\) | −26.4757 | −1.85823 | ||||||||
\(204\) | 9.56338 | − | 6.24773i | 0.669571 | − | 0.437429i | ||||
\(205\) | −0.917527 | −0.0640829 | ||||||||
\(206\) | 11.8822 | + | 8.02473i | 0.827874 | + | 0.559109i | ||||
\(207\) | 24.0790 | − | 9.94743i | 1.67361 | − | 0.691394i | ||||
\(208\) | 8.33593 | − | 8.01250i | 0.577993 | − | 0.555567i | ||||
\(209\) | 3.58981i | 0.248312i | ||||||||
\(210\) | −4.35654 | + | 10.3586i | −0.300630 | + | 0.714814i | ||||
\(211\) | − | 10.8969i | − | 0.750174i | −0.926990 | − | 0.375087i | \(-0.877613\pi\) | ||
0.926990 | − | 0.375087i | \(-0.122387\pi\) | |||||||
\(212\) | −1.98609 | + | 0.799747i | −0.136405 | + | 0.0549268i | ||||
\(213\) | 8.15141 | − | 1.61745i | 0.558525 | − | 0.110826i | ||||
\(214\) | −0.608666 | + | 0.901253i | −0.0416075 | + | 0.0616084i | ||||
\(215\) | 3.04817 | 0.207884 | ||||||||
\(216\) | 13.6678 | − | 5.40302i | 0.929973 | − | 0.367629i | ||||
\(217\) | 31.7921 | 2.15819 | ||||||||
\(218\) | 2.17144 | − | 3.21526i | 0.147069 | − | 0.217765i | ||||
\(219\) | 2.02158 | − | 0.401132i | 0.136605 | − | 0.0271060i | ||||
\(220\) | −6.33375 | + | 2.55043i | −0.427021 | + | 0.171950i | ||||
\(221\) | 9.53209i | 0.641198i | ||||||||
\(222\) | −8.25063 | + | 19.6177i | −0.553746 | + | 1.31665i | ||||
\(223\) | 13.9272i | 0.932635i | 0.884617 | + | 0.466318i | \(0.154420\pi\) | ||||
−0.884617 | + | 0.466318i | \(0.845580\pi\) | |||||||
\(224\) | 26.8875 | − | 4.66038i | 1.79650 | − | 0.311385i | ||||
\(225\) | 11.3558 | − | 4.69127i | 0.757054 | − | 0.312751i | ||||
\(226\) | 6.49105 | + | 4.38377i | 0.431778 | + | 0.291604i | ||||
\(227\) | −7.19414 | −0.477492 | −0.238746 | − | 0.971082i | \(-0.576736\pi\) | ||||
−0.238746 | + | 0.971082i | \(0.576736\pi\) | |||||||
\(228\) | 2.90008 | − | 1.89461i | 0.192062 | − | 0.125474i | ||||
\(229\) | 3.92778 | 0.259555 | 0.129777 | − | 0.991543i | \(-0.458574\pi\) | ||||
0.129777 | + | 0.991543i | \(0.458574\pi\) | |||||||
\(230\) | 9.67926 | + | 6.53694i | 0.638231 | + | 0.431033i | ||||
\(231\) | −5.83777 | − | 29.4205i | −0.384097 | − | 1.93573i | ||||
\(232\) | −3.25401 | + | 15.1786i | −0.213636 | + | 0.996522i | ||||
\(233\) | 13.7058i | 0.897898i | 0.893557 | + | 0.448949i | \(0.148201\pi\) | ||||
−0.893557 | + | 0.448949i | \(0.851799\pi\) | |||||||
\(234\) | −2.46324 | + | 12.0138i | −0.161027 | + | 0.785367i | ||||
\(235\) | 0.553447i | 0.0361029i | ||||||||
\(236\) | −3.53484 | − | 8.77844i | −0.230099 | − | 0.571428i | ||||
\(237\) | −0.0223159 | − | 0.112465i | −0.00144957 | − | 0.00730537i | ||||
\(238\) | −12.5909 | + | 18.6434i | −0.816146 | + | 1.20847i | ||||
\(239\) | −9.08397 | −0.587593 | −0.293797 | − | 0.955868i | \(-0.594919\pi\) | ||||
−0.293797 | + | 0.955868i | \(0.594919\pi\) | |||||||
\(240\) | 5.40319 | + | 3.77075i | 0.348775 | + | 0.243401i | ||||
\(241\) | 25.2962 | 1.62947 | 0.814737 | − | 0.579831i | \(-0.196881\pi\) | ||||
0.814737 | + | 0.579831i | \(0.196881\pi\) | |||||||
\(242\) | 1.49336 | − | 2.21122i | 0.0959967 | − | 0.142142i | ||||
\(243\) | −8.69082 | + | 12.9410i | −0.557517 | + | 0.830166i | ||||
\(244\) | 4.14892 | + | 10.3034i | 0.265607 | + | 0.659611i | ||||
\(245\) | − | 15.4736i | − | 0.988574i | ||||||
\(246\) | −2.17841 | − | 0.916173i | −0.138890 | − | 0.0584131i | ||||
\(247\) | 2.89059i | 0.183924i | ||||||||
\(248\) | 3.90743 | − | 18.2265i | 0.248122 | − | 1.15738i | ||||
\(249\) | −14.8793 | + | 2.95244i | −0.942940 | + | 0.187103i | ||||
\(250\) | 10.1377 | + | 6.84652i | 0.641162 | + | 0.433012i | ||||
\(251\) | 25.4643 | 1.60729 | 0.803645 | − | 0.595109i | \(-0.202891\pi\) | ||||
0.803645 | + | 0.595109i | \(0.202891\pi\) | |||||||
\(252\) | −20.6867 | + | 20.2435i | −1.30314 | + | 1.27522i | ||||
\(253\) | −31.1749 | −1.95995 | ||||||||
\(254\) | −12.6605 | − | 8.55034i | −0.794390 | − | 0.536496i | ||||
\(255\) | −5.32803 | + | 1.05722i | −0.333654 | + | 0.0662054i | ||||
\(256\) | 0.632818 | − | 15.9875i | 0.0395511 | − | 0.999218i | ||||
\(257\) | − | 8.31052i | − | 0.518396i | −0.965824 | − | 0.259198i | \(-0.916542\pi\) | ||
0.965824 | − | 0.259198i | \(-0.0834582\pi\) | |||||||
\(258\) | 7.23702 | + | 3.04368i | 0.450557 | + | 0.189491i | ||||
\(259\) | − | 41.9124i | − | 2.60431i | ||||||
\(260\) | −5.10006 | + | 2.05366i | −0.316292 | + | 0.127362i | ||||
\(261\) | −6.28667 | − | 15.2177i | −0.389135 | − | 0.941950i | ||||
\(262\) | 0.275918 | − | 0.408553i | 0.0170463 | − | 0.0252405i | ||||
\(263\) | 27.9744 | 1.72498 | 0.862489 | − | 0.506076i | \(-0.168905\pi\) | ||||
0.862489 | + | 0.506076i | \(0.168905\pi\) | |||||||
\(264\) | −17.5844 | − | 0.269133i | −1.08224 | − | 0.0165640i | ||||
\(265\) | 1.01810 | 0.0625412 | ||||||||
\(266\) | −3.81816 | + | 5.65356i | −0.234107 | + | 0.346642i | ||||
\(267\) | 2.16538 | + | 10.9128i | 0.132519 | + | 0.667855i | ||||
\(268\) | −5.55206 | + | 2.23567i | −0.339146 | + | 0.136565i | ||||
\(269\) | 23.2667i | 1.41860i | 0.704908 | + | 0.709299i | \(0.250988\pi\) | ||||
−0.704908 | + | 0.709299i | \(0.749012\pi\) | |||||||
\(270\) | −6.98840 | − | 0.0443826i | −0.425300 | − | 0.00270104i | ||||
\(271\) | − | 3.59338i | − | 0.218283i | −0.994026 | − | 0.109141i | \(-0.965190\pi\) | ||
0.994026 | − | 0.109141i | \(-0.0348101\pi\) | |||||||
\(272\) | 9.14080 | + | 9.50977i | 0.554242 | + | 0.576614i | ||||
\(273\) | −4.70069 | − | 23.6900i | −0.284499 | − | 1.43378i | ||||
\(274\) | −20.5979 | − | 13.9109i | −1.24437 | − | 0.840390i | ||||
\(275\) | −14.7023 | −0.886582 | ||||||||
\(276\) | 16.4533 | + | 25.1851i | 0.990375 | + | 1.51596i | ||||
\(277\) | 27.7637 | 1.66816 | 0.834078 | − | 0.551646i | \(-0.186000\pi\) | ||||
0.834078 | + | 0.551646i | \(0.186000\pi\) | |||||||
\(278\) | −10.8465 | − | 7.32525i | −0.650530 | − | 0.439339i | ||||
\(279\) | 7.54906 | + | 18.2735i | 0.451950 | + | 1.09400i | ||||
\(280\) | −12.6876 | − | 2.72000i | −0.758231 | − | 0.162551i | ||||
\(281\) | 30.6548i | 1.82871i | 0.404911 | + | 0.914356i | \(0.367303\pi\) | ||||
−0.404911 | + | 0.914356i | \(0.632697\pi\) | |||||||
\(282\) | −0.552631 | + | 1.31400i | −0.0329087 | + | 0.0782478i | ||||
\(283\) | − | 15.0302i | − | 0.893452i | −0.894671 | − | 0.446726i | \(-0.852590\pi\) | ||
0.894671 | − | 0.446726i | \(-0.147410\pi\) | |||||||
\(284\) | 3.58435 | + | 8.90138i | 0.212692 | + | 0.528200i | ||||
\(285\) | −1.61571 | + | 0.320599i | −0.0957066 | + | 0.0189906i | ||||
\(286\) | 8.21313 | − | 12.1612i | 0.485653 | − | 0.719107i | ||||
\(287\) | 4.65407 | 0.274721 | ||||||||
\(288\) | 9.06316 | + | 14.3478i | 0.534052 | + | 0.845452i | ||||
\(289\) | 6.12563 | 0.360331 | ||||||||
\(290\) | 4.13127 | − | 6.11718i | 0.242597 | − | 0.359213i | ||||
\(291\) | 0.00516190 | − | 0.00102425i | 0.000302596 | − | 6.00427e-5i | ||||
\(292\) | 0.888930 | + | 2.20757i | 0.0520207 | + | 0.129188i | ||||
\(293\) | − | 5.81594i | − | 0.339771i | −0.985464 | − | 0.169885i | \(-0.945660\pi\) | ||
0.985464 | − | 0.169885i | \(-0.0543397\pi\) | |||||||
\(294\) | 15.4508 | − | 36.7377i | 0.901109 | − | 2.14259i | ||||
\(295\) | 4.49995i | 0.261997i | ||||||||
\(296\) | −24.0285 | − | 5.15127i | −1.39663 | − | 0.299411i | ||||
\(297\) | 15.5241 | − | 10.3414i | 0.900801 | − | 0.600066i | ||||
\(298\) | −0.324330 | − | 0.219038i | −0.0187879 | − | 0.0126885i | ||||
\(299\) | −25.1027 | −1.45173 | ||||||||
\(300\) | 7.75950 | + | 11.8774i | 0.447995 | + | 0.685744i | ||||
\(301\) | −15.4616 | −0.891190 | ||||||||
\(302\) | 16.1481 | + | 10.9057i | 0.929217 | + | 0.627552i | ||||
\(303\) | 2.70725 | + | 13.6437i | 0.155527 | + | 0.783807i | ||||
\(304\) | 2.77193 | + | 2.88382i | 0.158981 | + | 0.165398i | ||||
\(305\) | − | 5.28168i | − | 0.302428i | ||||||
\(306\) | −13.7055 | − | 2.81011i | −0.783494 | − | 0.160643i | ||||
\(307\) | − | 19.3942i | − | 1.10688i | −0.832888 | − | 0.553442i | \(-0.813314\pi\) | ||
0.832888 | − | 0.553442i | \(-0.186686\pi\) | |||||||
\(308\) | 32.1273 | − | 12.9368i | 1.83062 | − | 0.737144i | ||||
\(309\) | −3.41784 | − | 17.2248i | −0.194434 | − | 0.979885i | ||||
\(310\) | −4.96085 | + | 7.34554i | −0.281757 | + | 0.417199i | ||||
\(311\) | −30.8338 | −1.74843 | −0.874213 | − | 0.485542i | \(-0.838622\pi\) | ||||
−0.874213 | + | 0.485542i | \(0.838622\pi\) | |||||||
\(312\) | −14.1593 | − | 0.216712i | −0.801611 | − | 0.0122689i | ||||
\(313\) | 4.21670 | 0.238342 | 0.119171 | − | 0.992874i | \(-0.461976\pi\) | ||||
0.119171 | + | 0.992874i | \(0.461976\pi\) | |||||||
\(314\) | 7.07649 | − | 10.4782i | 0.399349 | − | 0.591317i | ||||
\(315\) | 12.7203 | − | 5.25497i | 0.716709 | − | 0.296084i | ||||
\(316\) | 0.122812 | − | 0.0494531i | 0.00690872 | − | 0.00278196i | ||||
\(317\) | 11.1792i | 0.627885i | 0.949442 | + | 0.313942i | \(0.101650\pi\) | ||||
−0.949442 | + | 0.313942i | \(0.898350\pi\) | |||||||
\(318\) | 2.41718 | + | 1.01660i | 0.135549 | + | 0.0570079i | ||||
\(319\) | 19.7022i | 1.10311i | ||||||||
\(320\) | −3.11876 | + | 6.93955i | −0.174344 | + | 0.387933i | ||||
\(321\) | 1.30648 | − | 0.259239i | 0.0729206 | − | 0.0144693i | ||||
\(322\) | −49.0971 | − | 33.1580i | −2.73607 | − | 1.84782i | ||||
\(323\) | −3.29763 | −0.183485 | ||||||||
\(324\) | −16.5476 | − | 7.08346i | −0.919314 | − | 0.393526i | ||||
\(325\) | −11.8386 | −0.656686 | ||||||||
\(326\) | −16.4926 | − | 11.1384i | −0.913443 | − | 0.616899i | ||||
\(327\) | −4.66093 | + | 0.924846i | −0.257750 | + | 0.0511441i | ||||
\(328\) | 0.572011 | − | 2.66819i | 0.0315840 | − | 0.147326i | ||||
\(329\) | − | 2.80731i | − | 0.154772i | ||||||
\(330\) | 7.70852 | + | 3.24197i | 0.424340 | + | 0.178465i | ||||
\(331\) | − | 9.21698i | − | 0.506611i | −0.967386 | − | 0.253306i | \(-0.918482\pi\) | ||
0.967386 | − | 0.253306i | \(-0.0815178\pi\) | |||||||
\(332\) | −6.54276 | − | 16.2483i | −0.359081 | − | 0.891742i | ||||
\(333\) | 24.0904 | − | 9.95213i | 1.32015 | − | 0.545373i | ||||
\(334\) | 4.04916 | − | 5.99560i | 0.221560 | − | 0.328065i | ||||
\(335\) | 2.84606 | 0.155497 | ||||||||
\(336\) | −27.4072 | − | 19.1268i | −1.49518 | − | 1.04345i | ||||
\(337\) | −21.7976 | −1.18739 | −0.593696 | − | 0.804690i | \(-0.702332\pi\) | ||||
−0.593696 | + | 0.804690i | \(0.702332\pi\) | |||||||
\(338\) | −3.67612 | + | 5.44324i | −0.199955 | + | 0.296073i | ||||
\(339\) | −1.86710 | − | 9.40960i | −0.101407 | − | 0.511059i | ||||
\(340\) | −2.34285 | − | 5.81824i | −0.127059 | − | 0.315538i | ||||
\(341\) | − | 23.6585i | − | 1.28118i | ||||||
\(342\) | −4.15618 | − | 0.852160i | −0.224740 | − | 0.0460796i | ||||
\(343\) | 44.7208i | 2.41470i | ||||||||
\(344\) | −1.90031 | + | 8.86416i | −0.102458 | + | 0.477924i | ||||
\(345\) | −2.78417 | − | 14.0313i | −0.149895 | − | 0.755421i | ||||
\(346\) | 18.3550 | + | 12.3961i | 0.986768 | + | 0.666419i | ||||
\(347\) | 20.9139 | 1.12271 | 0.561357 | − | 0.827574i | \(-0.310279\pi\) | ||||
0.561357 | + | 0.827574i | \(0.310279\pi\) | |||||||
\(348\) | 15.9167 | − | 10.3983i | 0.853224 | − | 0.557409i | ||||
\(349\) | −25.3462 | −1.35675 | −0.678376 | − | 0.734715i | \(-0.737316\pi\) | ||||
−0.678376 | + | 0.734715i | \(0.737316\pi\) | |||||||
\(350\) | −23.1545 | − | 15.6375i | −1.23766 | − | 0.835861i | ||||
\(351\) | 12.5003 | − | 8.32707i | 0.667219 | − | 0.444466i | ||||
\(352\) | −3.46808 | − | 20.0087i | −0.184849 | − | 1.06647i | ||||
\(353\) | 11.4825i | 0.611151i | 0.952168 | + | 0.305575i | \(0.0988488\pi\) | ||||
−0.952168 | + | 0.305575i | \(0.901151\pi\) | |||||||
\(354\) | −4.49331 | + | 10.6838i | −0.238817 | + | 0.567840i | ||||
\(355\) | − | 4.56297i | − | 0.242177i | ||||||
\(356\) | −11.9169 | + | 4.79861i | −0.631593 | + | 0.254326i | ||||
\(357\) | 27.0259 | − | 5.36263i | 1.43036 | − | 0.283820i | ||||
\(358\) | 11.3525 | − | 16.8097i | 0.600001 | − | 0.888422i | ||||
\(359\) | −18.4842 | −0.975557 | −0.487779 | − | 0.872967i | \(-0.662193\pi\) | ||||
−0.487779 | + | 0.872967i | \(0.662193\pi\) | |||||||
\(360\) | −1.44929 | − | 7.93846i | −0.0763843 | − | 0.418394i | ||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 2.85239 | − | 4.22354i | 0.149918 | − | 0.221984i | ||||
\(363\) | −3.20544 | + | 0.636041i | −0.168242 | + | 0.0333835i | ||||
\(364\) | 25.8696 | − | 10.4170i | 1.35593 | − | 0.545998i | ||||
\(365\) | − | 1.13163i | − | 0.0592322i | ||||||
\(366\) | 5.27389 | − | 12.5399i | 0.275671 | − | 0.655469i | ||||
\(367\) | − | 10.4391i | − | 0.544915i | −0.962168 | − | 0.272458i | \(-0.912164\pi\) | ||
0.962168 | − | 0.272458i | \(-0.0878364\pi\) | |||||||
\(368\) | −25.0439 | + | 24.0722i | −1.30550 | + | 1.25485i | ||||
\(369\) | 1.10511 | + | 2.67506i | 0.0575298 | + | 0.139258i | ||||
\(370\) | 9.68383 | + | 6.54002i | 0.503438 | + | 0.340000i | ||||
\(371\) | −5.16420 | −0.268112 | ||||||||
\(372\) | −19.1128 | + | 12.4864i | −0.990954 | + | 0.647388i | ||||
\(373\) | 1.43539 | 0.0743216 | 0.0371608 | − | 0.999309i | \(-0.488169\pi\) | ||||
0.0371608 | + | 0.999309i | \(0.488169\pi\) | |||||||
\(374\) | 13.8737 | + | 9.36968i | 0.717392 | + | 0.484495i | ||||
\(375\) | −2.91602 | − | 14.6958i | −0.150583 | − | 0.758889i | ||||
\(376\) | −1.60944 | − | 0.345034i | −0.0830004 | − | 0.0177938i | ||||
\(377\) | 15.8646i | 0.817069i | ||||||||
\(378\) | 35.4480 | + | 0.225126i | 1.82325 | + | 0.0115792i | ||||
\(379\) | 32.2908i | 1.65867i | 0.558754 | + | 0.829334i | \(0.311280\pi\) | ||||
−0.558754 | + | 0.829334i | \(0.688720\pi\) | |||||||
\(380\) | −0.710464 | − | 1.76437i | −0.0364460 | − | 0.0905102i | ||||
\(381\) | 3.64170 | + | 18.3530i | 0.186570 | + | 0.940253i | ||||
\(382\) | −10.2270 | + | 15.1431i | −0.523259 | + | 0.774791i | ||||
\(383\) | 10.1823 | 0.520292 | 0.260146 | − | 0.965569i | \(-0.416229\pi\) | ||||
0.260146 | + | 0.965569i | \(0.416229\pi\) | |||||||
\(384\) | −14.3339 | + | 13.3618i | −0.731475 | + | 0.681868i | ||||
\(385\) | −16.4689 | −0.839333 | ||||||||
\(386\) | −8.26509 | + | 12.2381i | −0.420682 | + | 0.622905i | ||||
\(387\) | −3.67136 | − | 8.88700i | −0.186626 | − | 0.451752i | ||||
\(388\) | 0.00226980 | + | 0.00563682i | 0.000115231 | + | 0.000286166i | ||||
\(389\) | 28.7081i | 1.45556i | 0.685812 | + | 0.727779i | \(0.259447\pi\) | ||||
−0.685812 | + | 0.727779i | \(0.740553\pi\) | |||||||
\(390\) | 6.20705 | + | 2.61050i | 0.314306 | + | 0.132188i | ||||
\(391\) | − | 28.6376i | − | 1.44826i | ||||||
\(392\) | 44.9977 | + | 9.64668i | 2.27273 | + | 0.487231i | ||||
\(393\) | −0.592249 | + | 0.117517i | −0.0298750 | + | 0.00592796i | ||||
\(394\) | 20.5775 | + | 13.8971i | 1.03668 | + | 0.700125i | ||||
\(395\) | −0.0629551 | −0.00316762 | ||||||||
\(396\) | 15.0645 | + | 15.3943i | 0.757019 | + | 0.773592i | ||||
\(397\) | −12.3366 | −0.619155 | −0.309577 | − | 0.950874i | \(-0.600188\pi\) | ||||
−0.309577 | + | 0.950874i | \(0.600188\pi\) | |||||||
\(398\) | 27.4553 | + | 18.5421i | 1.37621 | + | 0.929432i | ||||
\(399\) | 8.19556 | − | 1.62621i | 0.410291 | − | 0.0814121i | ||||
\(400\) | −11.8109 | + | 11.3526i | −0.590543 | + | 0.567630i | ||||
\(401\) | − | 19.0493i | − | 0.951278i | −0.879640 | − | 0.475639i | \(-0.842217\pi\) | ||
0.879640 | − | 0.475639i | \(-0.157783\pi\) | |||||||
\(402\) | 6.75716 | + | 2.84186i | 0.337016 | + | 0.141739i | ||||
\(403\) | − | 19.0503i | − | 0.948963i | ||||||
\(404\) | −14.8989 | + | 5.99940i | −0.741250 | + | 0.298481i | ||||
\(405\) | 6.04090 | + | 6.06358i | 0.300175 | + | 0.301302i | ||||
\(406\) | −20.9555 | + | 31.0288i | −1.04000 | + | 1.53993i | ||||
\(407\) | −31.1896 | −1.54601 | ||||||||
\(408\) | 0.247228 | − | 16.1531i | 0.0122396 | − | 0.799699i | ||||
\(409\) | −33.8235 | −1.67246 | −0.836231 | − | 0.548377i | \(-0.815246\pi\) | ||||
−0.836231 | + | 0.548377i | \(0.815246\pi\) | |||||||
\(410\) | −0.726223 | + | 1.07532i | −0.0358656 | + | 0.0531062i | ||||
\(411\) | 5.92485 | + | 29.8593i | 0.292251 | + | 1.47285i | ||||
\(412\) | 18.8096 | − | 7.57411i | 0.926681 | − | 0.373150i | ||||
\(413\) | − | 22.8255i | − | 1.12317i | ||||||
\(414\) | 7.40040 | − | 36.0934i | 0.363710 | − | 1.77389i | ||||
\(415\) | 8.32910i | 0.408860i | ||||||||
\(416\) | −2.79257 | − | 16.1114i | −0.136917 | − | 0.789927i | ||||
\(417\) | 3.11992 | + | 15.7234i | 0.152783 | + | 0.769978i | ||||
\(418\) | 4.20717 | + | 2.84134i | 0.205780 | + | 0.138974i | ||||
\(419\) | −13.9089 | −0.679496 | −0.339748 | − | 0.940516i | \(-0.610342\pi\) | ||||
−0.339748 | + | 0.940516i | \(0.610342\pi\) | |||||||
\(420\) | 8.69187 | + | 13.3046i | 0.424120 | + | 0.649199i | ||||
\(421\) | −6.16578 | −0.300502 | −0.150251 | − | 0.988648i | \(-0.548008\pi\) | ||||
−0.150251 | + | 0.988648i | \(0.548008\pi\) | |||||||
\(422\) | −12.7709 | − | 8.62490i | −0.621678 | − | 0.419854i | ||||
\(423\) | 1.61358 | − | 0.666598i | 0.0784552 | − | 0.0324111i | ||||
\(424\) | −0.634710 | + | 2.96065i | −0.0308242 | + | 0.143782i | ||||
\(425\) | − | 13.5057i | − | 0.655120i | ||||||
\(426\) | 4.55624 | − | 10.8335i | 0.220750 | − | 0.524883i | ||||
\(427\) | 26.7908i | 1.29650i | ||||||||
\(428\) | 0.574487 | + | 1.42668i | 0.0277689 | + | 0.0689613i | ||||
\(429\) | −17.6292 | + | 3.49808i | −0.851146 | + | 0.168889i | ||||
\(430\) | 2.41263 | − | 3.57239i | 0.116347 | − | 0.172276i | ||||
\(431\) | 14.8379 | 0.714718 | 0.357359 | − | 0.933967i | \(-0.383677\pi\) | ||||
0.357359 | + | 0.933967i | \(0.383677\pi\) | |||||||
\(432\) | 4.48582 | − | 20.2948i | 0.215824 | − | 0.976432i | ||||
\(433\) | 15.1202 | 0.726633 | 0.363316 | − | 0.931666i | \(-0.381644\pi\) | ||||
0.363316 | + | 0.931666i | \(0.381644\pi\) | |||||||
\(434\) | 25.1634 | − | 37.2596i | 1.20788 | − | 1.78852i | ||||
\(435\) | −8.86763 | + | 1.75956i | −0.425171 | + | 0.0843646i | ||||
\(436\) | −2.04951 | − | 5.08976i | −0.0981537 | − | 0.243755i | ||||
\(437\) | − | 8.68428i | − | 0.415425i | ||||||
\(438\) | 1.12996 | − | 2.68673i | 0.0539916 | − | 0.128377i | ||||
\(439\) | 26.6310i | 1.27103i | 0.772090 | + | 0.635514i | \(0.219212\pi\) | ||||
−0.772090 | + | 0.635514i | \(0.780788\pi\) | |||||||
\(440\) | −2.02412 | + | 9.44167i | −0.0964962 | + | 0.450114i | ||||
\(441\) | −45.1136 | + | 18.6372i | −2.14827 | + | 0.887484i | ||||
\(442\) | 11.1714 | + | 7.54465i | 0.531368 | + | 0.358863i | ||||
\(443\) | 9.37347 | 0.445347 | 0.222673 | − | 0.974893i | \(-0.428522\pi\) | ||||
0.222673 | + | 0.974893i | \(0.428522\pi\) | |||||||
\(444\) | 16.4611 | + | 25.1970i | 0.781210 | + | 1.19580i | ||||
\(445\) | 6.10875 | 0.289583 | ||||||||
\(446\) | 16.3224 | + | 11.0234i | 0.772886 | + | 0.521973i | ||||
\(447\) | 0.0932911 | + | 0.470157i | 0.00441252 | + | 0.0222377i | ||||
\(448\) | 15.8196 | − | 35.2002i | 0.747407 | − | 1.66305i | ||||
\(449\) | − | 38.8101i | − | 1.83156i | −0.401681 | − | 0.915780i | \(-0.631574\pi\) | ||
0.401681 | − | 0.915780i | \(-0.368426\pi\) | |||||||
\(450\) | 3.49008 | − | 17.0219i | 0.164524 | − | 0.802419i | ||||
\(451\) | − | 3.46339i | − | 0.163084i | ||||||
\(452\) | 10.2753 | − | 4.13760i | 0.483311 | − | 0.194616i | ||||
\(453\) | −4.64488 | − | 23.4087i | −0.218235 | − | 1.09984i | ||||
\(454\) | −5.69417 | + | 8.43136i | −0.267240 | + | 0.395703i | ||||
\(455\) | −13.2611 | −0.621689 | ||||||||
\(456\) | 0.0749715 | − | 4.89841i | 0.00351086 | − | 0.229389i | ||||
\(457\) | 23.2367 | 1.08697 | 0.543483 | − | 0.839420i | \(-0.317105\pi\) | ||||
0.543483 | + | 0.839420i | \(0.317105\pi\) | |||||||
\(458\) | 3.10884 | − | 4.60326i | 0.145266 | − | 0.215096i | ||||
\(459\) | 9.49966 | + | 14.2606i | 0.443406 | + | 0.665628i | ||||
\(460\) | 15.3223 | − | 6.16987i | 0.714404 | − | 0.287672i | ||||
\(461\) | 16.9358i | 0.788778i | 0.918944 | + | 0.394389i | \(0.129044\pi\) | ||||
−0.918944 | + | 0.394389i | \(0.870956\pi\) | |||||||
\(462\) | −39.1007 | − | 16.4446i | −1.81913 | − | 0.765072i | ||||
\(463\) | − | 20.9617i | − | 0.974172i | −0.873354 | − | 0.487086i | \(-0.838060\pi\) | ||
0.873354 | − | 0.487086i | \(-0.161940\pi\) | |||||||
\(464\) | 15.2134 | + | 15.8275i | 0.706263 | + | 0.734771i | ||||
\(465\) | 10.6483 | − | 2.11289i | 0.493803 | − | 0.0979830i | ||||
\(466\) | 16.0629 | + | 10.8482i | 0.744099 | + | 0.502531i | ||||
\(467\) | 2.88133 | 0.133332 | 0.0666660 | − | 0.997775i | \(-0.478764\pi\) | ||||
0.0666660 | + | 0.997775i | \(0.478764\pi\) | |||||||
\(468\) | 12.1302 | + | 12.3958i | 0.560720 | + | 0.572996i | ||||
\(469\) | −14.4364 | −0.666610 | ||||||||
\(470\) | 0.648627 | + | 0.438054i | 0.0299189 | + | 0.0202059i | ||||
\(471\) | −15.1894 | + | 3.01397i | −0.699892 | + | 0.138876i | ||||
\(472\) | −13.0860 | − | 2.80539i | −0.602330 | − | 0.129128i | ||||
\(473\) | 11.5059i | 0.529043i | ||||||||
\(474\) | −0.149469 | − | 0.0628622i | −0.00686534 | − | 0.00288736i | ||||
\(475\) | − | 4.09556i | − | 0.187917i | ||||||
\(476\) | 11.8839 | + | 29.5124i | 0.544696 | + | 1.35270i | ||||
\(477\) | −1.22624 | − | 2.96828i | −0.0561459 | − | 0.135908i | ||||
\(478\) | −7.18996 | + | 10.6462i | −0.328861 | + | 0.486946i | ||||
\(479\) | −6.68550 | −0.305468 | −0.152734 | − | 0.988267i | \(-0.548808\pi\) | ||||
−0.152734 | + | 0.988267i | \(0.548808\pi\) | |||||||
\(480\) | 8.69586 | − | 3.34786i | 0.396910 | − | 0.152808i | ||||
\(481\) | −25.1145 | −1.14512 | ||||||||
\(482\) | 20.0220 | − | 29.6466i | 0.911976 | − | 1.35036i | ||||
\(483\) | 14.1224 | + | 71.1725i | 0.642593 | + | 3.23846i | ||||
\(484\) | −1.40950 | − | 3.50036i | −0.0640682 | − | 0.159107i | ||||
\(485\) | − | 0.00288951i | − | 0.000131206i | ||||||
\(486\) | 8.28775 | + | 20.4282i | 0.375940 | + | 0.926644i | ||||
\(487\) | − | 16.3608i | − | 0.741381i | −0.928757 | − | 0.370690i | \(-0.879121\pi\) | ||
0.928757 | − | 0.370690i | \(-0.120879\pi\) | |||||||
\(488\) | 15.3593 | + | 3.29274i | 0.695281 | + | 0.149056i | ||||
\(489\) | 4.74399 | + | 23.9082i | 0.214531 | + | 1.08117i | ||||
\(490\) | −18.1347 | − | 12.2474i | −0.819243 | − | 0.553280i | ||||
\(491\) | −5.14652 | −0.232259 | −0.116130 | − | 0.993234i | \(-0.537049\pi\) | ||||
−0.116130 | + | 0.993234i | \(0.537049\pi\) | |||||||
\(492\) | −2.79794 | + | 1.82789i | −0.126141 | + | 0.0824076i | ||||
\(493\) | −18.0986 | −0.815121 | ||||||||
\(494\) | 3.38770 | + | 2.28790i | 0.152420 | + | 0.102938i | ||||
\(495\) | −3.91055 | − | 9.46599i | −0.175766 | − | 0.425465i | ||||
\(496\) | −18.2683 | − | 19.0057i | −0.820270 | − | 0.853381i | ||||
\(497\) | 23.1452i | 1.03820i | ||||||||
\(498\) | −8.31682 | + | 19.7751i | −0.372685 | + | 0.886143i | ||||
\(499\) | 29.0105i | 1.29869i | 0.760494 | + | 0.649345i | \(0.224957\pi\) | ||||
−0.760494 | + | 0.649345i | \(0.775043\pi\) | |||||||
\(500\) | 16.0479 | − | 6.46207i | 0.717685 | − | 0.288992i | ||||
\(501\) | −8.69139 | + | 1.72459i | −0.388303 | + | 0.0770491i | ||||
\(502\) | 20.1550 | − | 29.8435i | 0.899560 | − | 1.33198i | ||||
\(503\) | 16.4421 | 0.733118 | 0.366559 | − | 0.930395i | \(-0.380536\pi\) | ||||
0.366559 | + | 0.930395i | \(0.380536\pi\) | |||||||
\(504\) | 7.35138 | + | 40.2671i | 0.327457 | + | 1.79364i | ||||
\(505\) | 7.63739 | 0.339860 | ||||||||
\(506\) | −24.6750 | + | 36.5363i | −1.09694 | + | 1.62423i | ||||
\(507\) | 7.89067 | − | 1.56571i | 0.350437 | − | 0.0695356i | ||||
\(508\) | −20.0416 | + | 8.07020i | −0.889201 | + | 0.358057i | ||||
\(509\) | − | 36.4370i | − | 1.61504i | −0.589839 | − | 0.807521i | \(-0.700809\pi\) | ||
0.589839 | − | 0.807521i | \(-0.299191\pi\) | |||||||
\(510\) | −2.97810 | + | 7.08111i | −0.131873 | + | 0.313557i | ||||
\(511\) | 5.74009i | 0.253926i | ||||||||
\(512\) | −18.2361 | − | 13.3957i | −0.805928 | − | 0.592014i | ||||
\(513\) | 2.88075 | + | 4.32450i | 0.127188 | + | 0.190931i | ||||
\(514\) | −9.73973 | − | 6.57778i | −0.429601 | − | 0.290133i | ||||
\(515\) | −9.64204 | −0.424879 | ||||||||
\(516\) | 9.29522 | − | 6.07254i | 0.409199 | − | 0.267329i | ||||
\(517\) | −2.08910 | −0.0918783 | ||||||||
\(518\) | −49.1203 | − | 33.1737i | −2.15822 | − | 1.45757i | ||||
\(519\) | −5.27967 | − | 26.6078i | −0.231752 | − | 1.16795i | ||||
\(520\) | −1.62986 | + | 7.60262i | −0.0714742 | + | 0.333397i | ||||
\(521\) | 41.4186i | 1.81458i | 0.420504 | + | 0.907291i | \(0.361853\pi\) | ||||
−0.420504 | + | 0.907291i | \(0.638147\pi\) | |||||||
\(522\) | −22.8106 | − | 4.67697i | −0.998395 | − | 0.204705i | ||||
\(523\) | − | 24.6573i | − | 1.07819i | −0.842245 | − | 0.539095i | \(-0.818766\pi\) | ||
0.842245 | − | 0.539095i | \(-0.181234\pi\) | |||||||
\(524\) | −0.260425 | − | 0.646739i | −0.0113767 | − | 0.0282529i | ||||
\(525\) | 6.66023 | + | 33.5654i | 0.290676 | + | 1.46491i | ||||
\(526\) | 22.1418 | − | 32.7854i | 0.965427 | − | 1.42951i | ||||
\(527\) | 21.7329 | 0.946700 | ||||||||
\(528\) | −14.2334 | + | 20.3954i | −0.619431 | + | 0.887597i | ||||
\(529\) | 52.4167 | 2.27899 | ||||||||
\(530\) | 0.805825 | − | 1.19319i | 0.0350028 | − | 0.0518287i | ||||
\(531\) | 13.1197 | − | 5.41995i | 0.569345 | − | 0.235206i | ||||
\(532\) | 3.60376 | + | 8.94959i | 0.156243 | + | 0.388014i | ||||
\(533\) | − | 2.78879i | − | 0.120796i | ||||||
\(534\) | 14.5035 | + | 6.09974i | 0.627627 | + | 0.263961i | ||||
\(535\) | − | 0.731337i | − | 0.0316184i | ||||||
\(536\) | −1.77431 | + | 8.27641i | −0.0766386 | + | 0.357487i | ||||
\(537\) | −24.3678 | + | 4.83520i | −1.05155 | + | 0.208654i | ||||
\(538\) | 27.2681 | + | 18.4156i | 1.17561 | + | 0.793954i | ||||
\(539\) | 58.4082 | 2.51582 | ||||||||
\(540\) | −5.58333 | + | 8.15511i | −0.240268 | + | 0.350940i | ||||
\(541\) | 32.7039 | 1.40605 | 0.703026 | − | 0.711164i | \(-0.251832\pi\) | ||||
0.703026 | + | 0.711164i | \(0.251832\pi\) | |||||||
\(542\) | −4.21136 | − | 2.84416i | −0.180893 | − | 0.122167i | ||||
\(543\) | −6.12256 | + | 1.21487i | −0.262744 | + | 0.0521351i | ||||
\(544\) | 18.3802 | − | 3.18581i | 0.788043 | − | 0.136591i | ||||
\(545\) | 2.60908i | 0.111761i | ||||||||
\(546\) | −31.4847 | − | 13.2415i | −1.34742 | − | 0.566685i | ||||
\(547\) | 1.87569i | 0.0801986i | 0.999196 | + | 0.0400993i | \(0.0127674\pi\) | ||||
−0.999196 | + | 0.0400993i | \(0.987233\pi\) | |||||||
\(548\) | −32.6066 | + | 13.1298i | −1.39288 | + | 0.560877i | ||||
\(549\) | −15.3988 | + | 6.36151i | −0.657206 | + | 0.271502i | ||||
\(550\) | −11.6369 | + | 17.2307i | −0.496198 | + | 0.734721i | ||||
\(551\) | −5.48837 | −0.233812 | ||||||||
\(552\) | 42.5391 | + | 0.651073i | 1.81059 | + | 0.0277115i | ||||
\(553\) | 0.319334 | 0.0135795 | ||||||||
\(554\) | 21.9749 | − | 32.5383i | 0.933626 | − | 1.38242i | ||||
\(555\) | −2.78548 | − | 14.0379i | −0.118237 | − | 0.595877i | ||||
\(556\) | −17.1700 | + | 6.91391i | −0.728171 | + | 0.293215i | ||||
\(557\) | 1.47483i | 0.0624906i | 0.999512 | + | 0.0312453i | \(0.00994731\pi\) | ||||
−0.999512 | + | 0.0312453i | \(0.990053\pi\) | |||||||
\(558\) | 27.3911 | + | 5.61613i | 1.15956 | + | 0.237750i | ||||
\(559\) | 9.26481i | 0.391860i | ||||||||
\(560\) | −13.2300 | + | 12.7167i | −0.559071 | + | 0.537379i | ||||
\(561\) | −3.99067 | − | 20.1117i | −0.168486 | − | 0.849116i | ||||
\(562\) | 35.9267 | + | 24.2633i | 1.51548 | + | 1.02349i | ||||
\(563\) | −21.3747 | −0.900836 | −0.450418 | − | 0.892818i | \(-0.648725\pi\) | ||||
−0.450418 | + | 0.892818i | \(0.648725\pi\) | |||||||
\(564\) | 1.10257 | + | 1.68770i | 0.0464267 | + | 0.0710652i | ||||
\(565\) | −5.26727 | −0.221596 | ||||||||
\(566\) | −17.6150 | − | 11.8964i | −0.740415 | − | 0.500043i | ||||
\(567\) | −30.6419 | − | 30.7570i | −1.28684 | − | 1.29167i | ||||
\(568\) | 13.2692 | + | 2.84468i | 0.556764 | + | 0.119360i | ||||
\(569\) | 0.0254956i | 0.00106883i | 1.00000 | 0.000534416i | \(0.000170110\pi\) | |||||
−1.00000 | 0.000534416i | \(0.999830\pi\) | ||||||||
\(570\) | −0.903104 | + | 2.14733i | −0.0378269 | + | 0.0899418i | ||||
\(571\) | − | 26.7349i | − | 1.11882i | −0.828891 | − | 0.559411i | \(-0.811027\pi\) | ||
0.828891 | − | 0.559411i | \(-0.188973\pi\) | |||||||
\(572\) | −7.75194 | − | 19.2512i | −0.324125 | − | 0.804933i | ||||
\(573\) | 21.9519 | − | 4.35582i | 0.917054 | − | 0.181967i | ||||
\(574\) | 3.68370 | − | 5.45446i | 0.153754 | − | 0.227665i | ||||
\(575\) | 35.5670 | 1.48325 | ||||||||
\(576\) | 23.9888 | + | 0.734481i | 0.999532 | + | 0.0306034i | ||||
\(577\) | −2.13654 | −0.0889455 | −0.0444727 | − | 0.999011i | \(-0.514161\pi\) | ||||
−0.0444727 | + | 0.999011i | \(0.514161\pi\) | |||||||
\(578\) | 4.84844 | − | 7.17909i | 0.201668 | − | 0.298611i | ||||
\(579\) | 17.7407 | − | 3.52021i | 0.737280 | − | 0.146295i | ||||
\(580\) | −3.89929 | − | 9.68350i | −0.161909 | − | 0.402086i | ||||
\(581\) | − | 42.2486i | − | 1.75277i | ||||||
\(582\) | 0.00288525 | − | 0.00686032i | 0.000119597 | − | 0.000284369i | ||||
\(583\) | 3.84301i | 0.159161i | ||||||||
\(584\) | 3.29081 | + | 0.705489i | 0.136175 | + | 0.0291933i | ||||
\(585\) | −3.14886 | − | 7.62221i | −0.130189 | − | 0.315139i | ||||
\(586\) | −6.81614 | − | 4.60331i | −0.281572 | − | 0.190161i | ||||
\(587\) | 18.0251 | 0.743977 | 0.371988 | − | 0.928237i | \(-0.378676\pi\) | ||||
0.371988 | + | 0.928237i | \(0.378676\pi\) | |||||||
\(588\) | −30.8264 | − | 47.1859i | −1.27126 | − | 1.94591i | ||||
\(589\) | 6.59046 | 0.271555 | ||||||||
\(590\) | 5.27383 | + | 3.56171i | 0.217120 | + | 0.146633i | ||||
\(591\) | −5.91896 | − | 29.8296i | −0.243473 | − | 1.22703i | ||||
\(592\) | −25.0557 | + | 24.0836i | −1.02978 | + | 0.989829i | ||||
\(593\) | − | 19.2807i | − | 0.791764i | −0.918301 | − | 0.395882i | \(-0.870439\pi\) | ||
0.918301 | − | 0.395882i | \(-0.129561\pi\) | |||||||
\(594\) | 0.167531 | − | 26.3791i | 0.00687387 | − | 1.08235i | ||||
\(595\) | − | 15.1285i | − | 0.620207i | ||||||
\(596\) | −0.513414 | + | 0.206738i | −0.0210303 | + | 0.00846832i | ||||
\(597\) | −7.89733 | − | 39.8000i | −0.323216 | − | 1.62891i | ||||
\(598\) | −19.8688 | + | 29.4197i | −0.812495 | + | 1.20306i | ||||
\(599\) | 9.53524 | 0.389599 | 0.194800 | − | 0.980843i | \(-0.437594\pi\) | ||||
0.194800 | + | 0.980843i | \(0.437594\pi\) | |||||||
\(600\) | 20.0617 | + | 0.307050i | 0.819016 | + | 0.0125353i | ||||
\(601\) | −22.8706 | −0.932913 | −0.466456 | − | 0.884544i | \(-0.654470\pi\) | ||||
−0.466456 | + | 0.884544i | \(0.654470\pi\) | |||||||
\(602\) | −12.2378 | + | 18.1206i | −0.498777 | + | 0.738540i | ||||
\(603\) | −3.42793 | − | 8.29773i | −0.139596 | − | 0.337910i | ||||
\(604\) | 25.5624 | − | 10.2933i | 1.04012 | − | 0.418828i | ||||
\(605\) | 1.79433i | 0.0729499i | ||||||||
\(606\) | 18.1328 | + | 7.62613i | 0.736595 | + | 0.309790i | ||||
\(607\) | 18.0821i | 0.733929i | 0.930235 | + | 0.366964i | \(0.119603\pi\) | ||||
−0.930235 | + | 0.366964i | \(0.880397\pi\) | |||||||
\(608\) | 5.57375 | − | 0.966091i | 0.226045 | − | 0.0391802i | ||||
\(609\) | 44.9802 | − | 8.92522i | 1.82269 | − | 0.361668i | ||||
\(610\) | −6.19000 | − | 4.18045i | −0.250626 | − | 0.169262i | ||||
\(611\) | −1.68218 | −0.0680538 | ||||||||
\(612\) | −14.1413 | + | 13.8384i | −0.571629 | + | 0.559383i | ||||
\(613\) | 7.45343 | 0.301041 | 0.150521 | − | 0.988607i | \(-0.451905\pi\) | ||||
0.150521 | + | 0.988607i | \(0.451905\pi\) | |||||||
\(614\) | −22.7295 | − | 15.3505i | −0.917288 | − | 0.619496i | ||||
\(615\) | 1.55881 | − | 0.309308i | 0.0628574 | − | 0.0124725i | ||||
\(616\) | 10.2672 | − | 47.8920i | 0.413676 | − | 1.92962i | ||||
\(617\) | 28.7715i | 1.15830i | 0.815222 | + | 0.579148i | \(0.196615\pi\) | ||||
−0.815222 | + | 0.579148i | \(0.803385\pi\) | |||||||
\(618\) | −22.8923 | − | 9.62782i | −0.920862 | − | 0.387288i | ||||
\(619\) | 31.2226i | 1.25494i | 0.778640 | + | 0.627471i | \(0.215910\pi\) | ||||
−0.778640 | + | 0.627471i | \(0.784090\pi\) | |||||||
\(620\) | 4.68228 | + | 11.6280i | 0.188045 | + | 0.466992i | ||||
\(621\) | −37.5551 | + | 25.0173i | −1.50704 | + | 1.00391i | ||||
\(622\) | −24.4050 | + | 36.1365i | −0.978551 | + | 1.44894i | ||||
\(623\) | −30.9861 | −1.24143 | ||||||||
\(624\) | −11.4610 | + | 16.4228i | −0.458809 | + | 0.657438i | ||||
\(625\) | 12.2514 | 0.490057 | ||||||||
\(626\) | 3.33752 | − | 4.94188i | 0.133394 | − | 0.197517i | ||||
\(627\) | −1.21016 | − | 6.09883i | −0.0483292 | − | 0.243564i | ||||
\(628\) | −6.67912 | − | 16.5869i | −0.266526 | − | 0.661891i | ||||
\(629\) | − | 28.6511i | − | 1.14239i | ||||||
\(630\) | 3.90944 | − | 19.0672i | 0.155756 | − | 0.759656i | ||||
\(631\) | 8.36561i | 0.333030i | 0.986039 | + | 0.166515i | \(0.0532514\pi\) | ||||
−0.986039 | + | 0.166515i | \(0.946749\pi\) | |||||||
\(632\) | 0.0392479 | − | 0.183075i | 0.00156120 | − | 0.00728233i | ||||
\(633\) | 3.67346 | + | 18.5131i | 0.146007 | + | 0.735828i | ||||
\(634\) | 13.1017 | + | 8.84832i | 0.520336 | + | 0.351412i | ||||
\(635\) | 10.2736 | 0.407694 | ||||||||
\(636\) | 3.10463 | − | 2.02824i | 0.123106 | − | 0.0804251i | ||||
\(637\) | 47.0315 | 1.86346 | ||||||||
\(638\) | 23.0905 | + | 15.5943i | 0.914162 | + | 0.617384i | ||||
\(639\) | −13.3034 | + | 5.49585i | −0.526274 | + | 0.217412i | ||||
\(640\) | 5.66449 | + | 9.14777i | 0.223908 | + | 0.361597i | ||||
\(641\) | − | 14.0482i | − | 0.554869i | −0.960745 | − | 0.277434i | \(-0.910516\pi\) | ||
0.960745 | − | 0.277434i | \(-0.0894841\pi\) | |||||||
\(642\) | 0.730258 | − | 1.73635i | 0.0288210 | − | 0.0685283i | ||||
\(643\) | 32.7422i | 1.29123i | 0.763665 | + | 0.645613i | \(0.223398\pi\) | ||||
−0.763665 | + | 0.645613i | \(0.776602\pi\) | |||||||
\(644\) | −77.7207 | + | 31.2961i | −3.06263 | + | 1.23324i | ||||
\(645\) | −5.17863 | + | 1.02757i | −0.203908 | + | 0.0404606i | ||||
\(646\) | −2.61008 | + | 3.86474i | −0.102692 | + | 0.152056i | ||||
\(647\) | 38.1801 | 1.50101 | 0.750507 | − | 0.660863i | \(-0.229810\pi\) | ||||
0.750507 | + | 0.660863i | \(0.229810\pi\) | |||||||
\(648\) | −21.3991 | + | 13.7869i | −0.840637 | + | 0.541600i | ||||
\(649\) | −16.9859 | −0.666756 | ||||||||
\(650\) | −9.37024 | + | 13.8745i | −0.367531 | + | 0.544204i | ||||
\(651\) | −54.0125 | + | 10.7174i | −2.11692 | + | 0.420050i | ||||
\(652\) | −26.1079 | + | 10.5129i | −1.02246 | + | 0.411718i | ||||
\(653\) | 42.6331i | 1.66836i | 0.551492 | + | 0.834180i | \(0.314059\pi\) | ||||
−0.551492 | + | 0.834180i | \(0.685941\pi\) | |||||||
\(654\) | −2.60523 | + | 6.19451i | −0.101873 | + | 0.242225i | ||||
\(655\) | 0.331527i | 0.0129538i | ||||||||
\(656\) | −2.67431 | − | 2.78226i | −0.104414 | − | 0.108629i | ||||
\(657\) | −3.29929 | + | 1.36299i | −0.128717 | + | 0.0531752i | ||||
\(658\) | −3.29010 | − | 2.22199i | −0.128261 | − | 0.0866220i | ||||
\(659\) | 2.38481 | 0.0928990 | 0.0464495 | − | 0.998921i | \(-0.485209\pi\) | ||||
0.0464495 | + | 0.998921i | \(0.485209\pi\) | |||||||
\(660\) | 9.90081 | − | 6.46817i | 0.385388 | − | 0.251773i | ||||
\(661\) | 50.3186 | 1.95717 | 0.978584 | − | 0.205848i | \(-0.0659953\pi\) | ||||
0.978584 | + | 0.205848i | \(0.0659953\pi\) | |||||||
\(662\) | −10.8021 | − | 7.29524i | −0.419835 | − | 0.283538i | ||||
\(663\) | −3.21337 | − | 16.1943i | −0.124797 | − | 0.628936i | ||||
\(664\) | −24.2212 | − | 5.19259i | −0.939966 | − | 0.201512i | ||||
\(665\) | − | 4.58768i | − | 0.177903i | ||||||
\(666\) | 7.40389 | − | 36.1105i | 0.286895 | − | 1.39925i | ||||
\(667\) | − | 47.6625i | − | 1.84550i | ||||||
\(668\) | −3.82179 | − | 9.49104i | −0.147869 | − | 0.367220i | ||||
\(669\) | −4.69501 | − | 23.6613i | −0.181520 | − | 0.914800i | ||||
\(670\) | 2.25266 | − | 3.33551i | 0.0870277 | − | 0.128862i | ||||
\(671\) | 19.9368 | 0.769650 | ||||||||
\(672\) | −44.1089 | + | 16.9817i | −1.70154 | + | 0.655084i | ||||
\(673\) | −33.4419 | −1.28909 | −0.644546 | − | 0.764566i | \(-0.722954\pi\) | ||||
−0.644546 | + | 0.764566i | \(0.722954\pi\) | |||||||
\(674\) | −17.2528 | + | 25.5463i | −0.664554 | + | 0.984006i | ||||
\(675\) | −17.7112 | + | 11.7983i | −0.681706 | + | 0.454117i | ||||
\(676\) | 3.46970 | + | 8.61666i | 0.133450 | + | 0.331410i | ||||
\(677\) | − | 16.8038i | − | 0.645821i | −0.946430 | − | 0.322910i | \(-0.895339\pi\) | ||
0.946430 | − | 0.322910i | \(-0.104661\pi\) | |||||||
\(678\) | −12.5056 | − | 5.25950i | −0.480276 | − | 0.201990i | ||||
\(679\) | 0.0146568i | 0.000562475i | ||||||||
\(680\) | −8.67320 | − | 1.85937i | −0.332602 | − | 0.0713037i | ||||
\(681\) | 12.2223 | − | 2.42522i | 0.468361 | − | 0.0929347i | ||||
\(682\) | −27.7272 | − | 18.7257i | −1.06173 | − | 0.717045i | ||||
\(683\) | −37.0755 | −1.41866 | −0.709328 | − | 0.704879i | \(-0.751001\pi\) | ||||
−0.709328 | + | 0.704879i | \(0.751001\pi\) | |||||||
\(684\) | −4.28833 | + | 4.19646i | −0.163968 | + | 0.160456i | ||||
\(685\) | 16.7146 | 0.638630 | ||||||||
\(686\) | 52.4117 | + | 35.3965i | 2.00109 | + | 1.35145i | ||||
\(687\) | −6.67302 | + | 1.32410i | −0.254591 | + | 0.0505174i | ||||
\(688\) | 8.88448 | + | 9.24311i | 0.338718 | + | 0.352390i | ||||
\(689\) | 3.09447i | 0.117890i | ||||||||
\(690\) | −18.6480 | − | 7.84281i | −0.709918 | − | 0.298571i | ||||
\(691\) | 25.6654i | 0.976360i | 0.872743 | + | 0.488180i | \(0.162339\pi\) | ||||
−0.872743 | + | 0.488180i | \(0.837661\pi\) | |||||||
\(692\) | 29.0559 | − | 11.7000i | 1.10454 | − | 0.444768i | ||||
\(693\) | 19.8359 | + | 48.0153i | 0.753504 | + | 1.82395i | ||||
\(694\) | 16.5533 | − | 24.5105i | 0.628356 | − | 0.930407i | ||||
\(695\) | 8.80158 | 0.333863 | ||||||||
\(696\) | 0.411471 | − | 26.8843i | 0.0155968 | − | 1.01905i | ||||
\(697\) | 3.18150 | 0.120508 | ||||||||
\(698\) | −20.0615 | + | 29.7052i | −0.759340 | + | 1.12436i | ||||
\(699\) | −4.62037 | − | 23.2852i | −0.174759 | − | 0.880727i | ||||
\(700\) | −36.6536 | + | 14.7594i | −1.38538 | + | 0.557854i | ||||
\(701\) | − | 24.9520i | − | 0.942423i | −0.882020 | − | 0.471212i | \(-0.843817\pi\) | ||
0.882020 | − | 0.471212i | \(-0.156183\pi\) | |||||||
\(702\) | 0.134899 | − | 21.2410i | 0.00509144 | − | 0.801689i | ||||
\(703\) | − | 8.68838i | − | 0.327688i | ||||||
\(704\) | −26.1947 | − | 11.7724i | −0.987250 | − | 0.443688i | ||||
\(705\) | −0.186573 | − | 0.940267i | −0.00702674 | − | 0.0354125i | ||||
\(706\) | 13.4572 | + | 9.08839i | 0.506468 | + | 0.342046i | ||||
\(707\) | −38.7400 | −1.45697 | ||||||||
\(708\) | 8.96475 | + | 13.7223i | 0.336916 | + | 0.515716i | ||||
\(709\) | 15.8658 | 0.595853 | 0.297927 | − | 0.954589i | \(-0.403705\pi\) | ||||
0.297927 | + | 0.954589i | \(0.403705\pi\) | |||||||
\(710\) | −5.34769 | − | 3.61159i | −0.200695 | − | 0.135541i | ||||
\(711\) | 0.0758261 | + | 0.183547i | 0.00284370 | + | 0.00688354i | ||||
\(712\) | −3.80836 | + | 17.7644i | −0.142724 | + | 0.665749i | ||||
\(713\) | 57.2334i | 2.14341i | ||||||||
\(714\) | 15.1062 | − | 35.9182i | 0.565334 | − | 1.34421i | ||||
\(715\) | 9.86841i | 0.369058i | ||||||||
\(716\) | −10.7151 | − | 26.6098i | −0.400441 | − | 0.994456i | ||||
\(717\) | 15.4330 | − | 3.06230i | 0.576356 | − | 0.114364i | ||||
\(718\) | −14.6302 | + | 21.6630i | −0.545995 | + | 0.808456i | ||||
\(719\) | 3.57702 | 0.133400 | 0.0667001 | − | 0.997773i | \(-0.478753\pi\) | ||||
0.0667001 | + | 0.997773i | \(0.478753\pi\) | |||||||
\(720\) | −10.4508 | − | 4.58476i | −0.389478 | − | 0.170864i | ||||
\(721\) | 48.9083 | 1.82144 | ||||||||
\(722\) | −0.791500 | + | 1.17198i | −0.0294566 | + | 0.0436164i | ||||
\(723\) | −42.9765 | + | 8.52762i | −1.59831 | + | 0.317146i | ||||
\(724\) | −2.69222 | − | 6.68587i | −0.100056 | − | 0.248478i | ||||
\(725\) | − | 22.4780i | − | 0.834810i | ||||||
\(726\) | −1.79168 | + | 4.26013i | −0.0664956 | + | 0.158108i | ||||
\(727\) | − | 32.1506i | − | 1.19240i | −0.802836 | − | 0.596199i | \(-0.796677\pi\) | ||
0.802836 | − | 0.596199i | \(-0.203323\pi\) | |||||||
\(728\) | 8.26732 | − | 38.5636i | 0.306407 | − | 1.42926i | ||||
\(729\) | 10.4025 | − | 24.9156i | 0.385279 | − | 0.922800i | ||||
\(730\) | −1.32624 | − | 0.895686i | −0.0490865 | − | 0.0331508i | ||||
\(731\) | −10.5694 | −0.390925 | ||||||||
\(732\) | −10.5221 | − | 16.1062i | −0.388909 | − | 0.595301i | ||||
\(733\) | −6.40001 | −0.236390 | −0.118195 | − | 0.992990i | \(-0.537711\pi\) | ||||
−0.118195 | + | 0.992990i | \(0.537711\pi\) | |||||||
\(734\) | −12.2343 | − | 8.26253i | −0.451578 | − | 0.304975i | ||||
\(735\) | 5.21632 | + | 26.2886i | 0.192407 | + | 0.969669i | ||||
\(736\) | 8.38980 | + | 48.4040i | 0.309252 | + | 1.78419i | ||||
\(737\) | 10.7430i | 0.395724i | ||||||||
\(738\) | 4.00981 | + | 0.822149i | 0.147603 | + | 0.0302637i | ||||
\(739\) | − | 39.6512i | − | 1.45859i | −0.684197 | − | 0.729297i | \(-0.739847\pi\) | ||
0.684197 | − | 0.729297i | \(-0.260153\pi\) | |||||||
\(740\) | 15.3295 | − | 6.17278i | 0.563524 | − | 0.226916i | ||||
\(741\) | −0.974447 | − | 4.91090i | −0.0357972 | − | 0.180406i | ||||
\(742\) | −4.08747 | + | 6.05232i | −0.150056 | + | 0.222188i | ||||
\(743\) | −22.7258 | −0.833728 | −0.416864 | − | 0.908969i | \(-0.636871\pi\) | ||||
−0.416864 | + | 0.908969i | \(0.636871\pi\) | |||||||
\(744\) | −0.494096 | + | 32.2827i | −0.0181145 | + | 1.18354i | ||||
\(745\) | 0.263183 | 0.00964227 | ||||||||
\(746\) | 1.13611 | − | 1.68224i | 0.0415960 | − | 0.0615912i | ||||
\(747\) | 24.2836 | − | 10.0320i | 0.888492 | − | 0.367050i | ||||
\(748\) | 21.9621 | − | 8.84354i | 0.803013 | − | 0.323352i | ||||
\(749\) | 3.70964i | 0.135547i | ||||||||
\(750\) | −19.5312 | − | 8.21424i | −0.713178 | − | 0.299942i | ||||
\(751\) | − | 18.9665i | − | 0.692097i | −0.938217 | − | 0.346049i | \(-0.887523\pi\) | ||
0.938217 | − | 0.346049i | \(-0.112477\pi\) | |||||||
\(752\) | −1.67824 | + | 1.61313i | −0.0611992 | + | 0.0588247i | ||||
\(753\) | −43.2619 | + | 8.58427i | −1.57655 | + | 0.312828i | ||||
\(754\) | 18.5929 | + | 12.5568i | 0.677115 | + | 0.457293i | ||||
\(755\) | −13.1036 | −0.476890 | ||||||||
\(756\) | 28.3209 | − | 41.3660i | 1.03002 | − | 1.50447i | ||||
\(757\) | −24.1900 | −0.879202 | −0.439601 | − | 0.898193i | \(-0.644880\pi\) | ||||
−0.439601 | + | 0.898193i | \(0.644880\pi\) | |||||||
\(758\) | 37.8440 | + | 25.5582i | 1.37456 | + | 0.928315i | ||||
\(759\) | 52.9640 | − | 10.5094i | 1.92247 | − | 0.381467i | ||||
\(760\) | −2.63013 | − | 0.563852i | −0.0954048 | − | 0.0204530i | ||||
\(761\) | − | 7.33058i | − | 0.265733i | −0.991134 | − | 0.132867i | \(-0.957582\pi\) | ||
0.991134 | − | 0.132867i | \(-0.0424182\pi\) | |||||||
\(762\) | 24.3917 | + | 10.2584i | 0.883617 | + | 0.371623i | ||||
\(763\) | − | 13.2343i | − | 0.479114i | ||||||
\(764\) | 9.65272 | + | 23.9716i | 0.349223 | + | 0.867262i | ||||
\(765\) | 8.69554 | − | 3.59227i | 0.314388 | − | 0.129879i | ||||
\(766\) | 8.05930 | − | 11.9334i | 0.291195 | − | 0.431172i | ||||
\(767\) | −13.6774 | −0.493863 | ||||||||
\(768\) | 4.31443 | + | 27.3749i | 0.155684 | + | 0.987807i | ||||
\(769\) | −40.7632 | −1.46996 | −0.734979 | − | 0.678090i | \(-0.762808\pi\) | ||||
−0.734979 | + | 0.678090i | \(0.762808\pi\) | |||||||
\(770\) | −13.0351 | + | 19.3012i | −0.469754 | + | 0.695565i | ||||
\(771\) | 2.80156 | + | 14.1190i | 0.100896 | + | 0.508483i | ||||
\(772\) | 7.80098 | + | 19.3730i | 0.280763 | + | 0.697249i | ||||
\(773\) | − | 40.1989i | − | 1.44585i | −0.690925 | − | 0.722927i | \(-0.742796\pi\) | ||
0.690925 | − | 0.722927i | \(-0.257204\pi\) | |||||||
\(774\) | −13.3212 | − | 2.73131i | −0.478822 | − | 0.0981750i | ||||
\(775\) | 26.9916i | 0.969568i | ||||||||
\(776\) | 0.00840276 | + | 0.00180140i | 0.000301642 | + | 6.46664e-5i | ||||
\(777\) | 14.1291 | + | 71.2061i | 0.506878 | + | 2.55450i | ||||
\(778\) | 33.6452 | + | 22.7225i | 1.20624 | + | 0.814639i | ||||
\(779\) | 0.964782 | 0.0345669 | ||||||||
\(780\) | 7.97233 | − | 5.20830i | 0.285455 | − | 0.186487i | ||||
\(781\) | 17.2238 | 0.616317 | ||||||||
\(782\) | −33.5625 | − | 22.6666i | −1.20019 | − | 0.810557i | ||||
\(783\) | 15.8106 | + | 23.7344i | 0.565026 | + | 0.848199i | ||||
\(784\) | 46.9213 | − | 45.1008i | 1.67576 | − | 1.61074i | ||||
\(785\) | 8.50269i | 0.303474i | ||||||||
\(786\) | −0.331038 | + | 0.787117i | −0.0118077 | + | 0.0280755i | ||||
\(787\) | − | 30.1104i | − | 1.07332i | −0.843799 | − | 0.536660i | \(-0.819686\pi\) | ||
0.843799 | − | 0.536660i | \(-0.180314\pi\) | |||||||
\(788\) | 32.5741 | − | 13.1167i | 1.16040 | − | 0.467264i | ||||
\(789\) | −47.5266 | + | 9.43047i | −1.69199 | + | 0.335734i | ||||
\(790\) | −0.0498290 | + | 0.0737819i | −0.00177284 | + | 0.00262504i | ||||
\(791\) | 26.7177 | 0.949973 | ||||||||
\(792\) | 29.9653 | − | 5.47063i | 1.06477 | − | 0.194390i | ||||
\(793\) | 16.0535 | 0.570076 | ||||||||
\(794\) | −9.76440 | + | 14.4582i | −0.346526 | + | 0.513101i | ||||
\(795\) | −1.72967 | + | 0.343211i | −0.0613452 | + | 0.0121725i | ||||
\(796\) | 43.4618 | − | 17.5009i | 1.54046 | − | 0.620303i | ||||
\(797\) | − | 29.1120i | − | 1.03120i | −0.856829 | − | 0.515600i | \(-0.827569\pi\) | ||
0.856829 | − | 0.515600i | \(-0.172431\pi\) | |||||||
\(798\) | 4.58091 | − | 10.8921i | 0.162162 | − | 0.385577i | ||||
\(799\) | − | 1.91906i | − | 0.0678915i | ||||||
\(800\) | 3.95668 | + | 22.8276i | 0.139890 | + | 0.807079i | ||||
\(801\) | −7.35766 | − | 17.8102i | −0.259970 | − | 0.629291i | ||||
\(802\) | −22.3254 | − | 15.0776i | −0.788336 | − | 0.532407i | ||||
\(803\) | 4.27156 | 0.150740 | ||||||||
\(804\) | 8.67889 | − | 5.66989i | 0.306081 | − | 0.199962i | ||||
\(805\) | 39.8407 | 1.40420 | ||||||||
\(806\) | −22.3265 | − | 15.0783i | −0.786417 | − | 0.531111i | ||||
\(807\) | −7.84346 | − | 39.5285i | −0.276103 | − | 1.39147i | ||||
\(808\) | −4.76136 | + | 22.2097i | −0.167504 | + | 0.781336i | ||||
\(809\) | − | 17.5960i | − | 0.618644i | −0.950957 | − | 0.309322i | \(-0.899898\pi\) | ||
0.950957 | − | 0.309322i | \(-0.100102\pi\) | |||||||
\(810\) | 11.8877 | − | 2.28046i | 0.417693 | − | 0.0801272i | ||||
\(811\) | 12.1077i | 0.425159i | 0.977144 | + | 0.212579i | \(0.0681864\pi\) | ||||
−0.977144 | + | 0.212579i | \(0.931814\pi\) | |||||||
\(812\) | 19.7788 | + | 49.1186i | 0.694098 | + | 1.72373i | ||||
\(813\) | 1.21137 | + | 6.10490i | 0.0424845 | + | 0.214108i | ||||
\(814\) | −24.6866 | + | 36.5535i | −0.865265 | + | 1.28120i | ||||
\(815\) | 13.3832 | 0.468794 | ||||||||
\(816\) | −18.7354 | − | 13.0750i | −0.655870 | − | 0.457715i | ||||
\(817\) | −3.20516 | −0.112134 | ||||||||
\(818\) | −26.7713 | + | 39.6403i | −0.936036 | + | 1.38599i | ||||
\(819\) | 15.9723 | + | 38.6629i | 0.558116 | + | 1.35099i | ||||
\(820\) | 0.685443 | + | 1.70223i | 0.0239367 | + | 0.0594445i | ||||
\(821\) | 48.6819i | 1.69901i | 0.527580 | + | 0.849506i | \(0.323100\pi\) | ||||
−0.527580 | + | 0.849506i | \(0.676900\pi\) | |||||||
\(822\) | 39.6839 | + | 16.6899i | 1.38414 | + | 0.582127i | ||||
\(823\) | 6.40201i | 0.223160i | 0.993755 | + | 0.111580i | \(0.0355911\pi\) | ||||
−0.993755 | + | 0.111580i | \(0.964409\pi\) | |||||||
\(824\) | 6.01111 | − | 28.0393i | 0.209407 | − | 0.976795i | ||||
\(825\) | 24.9781 | − | 4.95630i | 0.869627 | − | 0.172556i | ||||
\(826\) | −26.7510 | − | 18.0664i | −0.930786 | − | 0.628611i | ||||
\(827\) | −41.1870 | −1.43221 | −0.716107 | − | 0.697991i | \(-0.754078\pi\) | ||||
−0.716107 | + | 0.697991i | \(0.754078\pi\) | |||||||
\(828\) | −36.4432 | − | 37.2410i | −1.26649 | − | 1.29422i | ||||
\(829\) | −4.94586 | −0.171777 | −0.0858883 | − | 0.996305i | \(-0.527373\pi\) | ||||
−0.0858883 | + | 0.996305i | \(0.527373\pi\) | |||||||
\(830\) | 9.76151 | + | 6.59249i | 0.338827 | + | 0.228829i | ||||
\(831\) | −47.1685 | + | 9.35942i | −1.63626 | + | 0.324675i | ||||
\(832\) | −21.0925 | − | 9.47936i | −0.731251 | − | 0.328638i | ||||
\(833\) | 53.6543i | 1.85901i | ||||||||
\(834\) | 20.8968 | + | 8.78860i | 0.723599 | + | 0.304324i | ||||
\(835\) | 4.86523i | 0.168368i | ||||||||
\(836\) | 6.65996 | − | 2.68179i | 0.230339 | − | 0.0927515i | ||||
\(837\) | −18.9855 | − | 28.5004i | −0.656234 | − | 0.985119i | ||||
\(838\) | −11.0089 | + | 16.3009i | −0.380297 | + | 0.563107i | ||||
\(839\) | 47.4963 | 1.63975 | 0.819877 | − | 0.572540i | \(-0.194042\pi\) | ||||
0.819877 | + | 0.572540i | \(0.194042\pi\) | |||||||
\(840\) | 22.4723 | + | 0.343945i | 0.775368 | + | 0.0118672i | ||||
\(841\) | −1.12219 | −0.0386962 | ||||||||
\(842\) | −4.88021 | + | 7.22614i | −0.168183 | + | 0.249029i | ||||
\(843\) | −10.3341 | − | 52.0803i | −0.355924 | − | 1.79374i | ||||
\(844\) | −20.2164 | + | 8.14059i | −0.695876 | + | 0.280210i | ||||
\(845\) | − | 4.41701i | − | 0.151950i | ||||||
\(846\) | 0.495916 | − | 2.41869i | 0.0170499 | − | 0.0831564i | ||||
\(847\) | − | 9.10157i | − | 0.312734i | ||||||
\(848\) | 2.96744 | + | 3.08722i | 0.101902 | + | 0.106016i | ||||
\(849\) | 5.06684 | + | 25.5352i | 0.173893 | + | 0.876367i | ||||
\(850\) | −15.8283 | − | 10.6897i | −0.542906 | − | 0.366655i | ||||
\(851\) | 75.4523 | 2.58647 | ||||||||
\(852\) | −9.09030 | − | 13.9145i | −0.311429 | − | 0.476703i | ||||
\(853\) | −37.4489 | −1.28222 | −0.641112 | − | 0.767447i | \(-0.721527\pi\) | ||||
−0.641112 | + | 0.767447i | \(0.721527\pi\) | |||||||
\(854\) | 31.3982 | + | 21.2050i | 1.07442 | + | 0.725618i | ||||
\(855\) | 2.63690 | − | 1.08935i | 0.0901802 | − | 0.0372549i | ||||
\(856\) | 2.12675 | + | 0.455935i | 0.0726906 | + | 0.0155835i | ||||
\(857\) | − | 47.8228i | − | 1.63359i | −0.576925 | − | 0.816797i | \(-0.695747\pi\) | ||
0.576925 | − | 0.816797i | \(-0.304253\pi\) | |||||||
\(858\) | −9.85385 | + | 23.4297i | −0.336405 | + | 0.799878i | ||||
\(859\) | − | 16.5196i | − | 0.563643i | −0.959467 | − | 0.281821i | \(-0.909061\pi\) | ||
0.959467 | − | 0.281821i | \(-0.0909386\pi\) | |||||||
\(860\) | −2.27715 | − | 5.65509i | −0.0776502 | − | 0.192837i | ||||
\(861\) | −7.90693 | + | 1.56893i | −0.269467 | + | 0.0534691i | ||||
\(862\) | 11.7442 | − | 17.3897i | 0.400010 | − | 0.592296i | ||||
\(863\) | −11.3696 | −0.387026 | −0.193513 | − | 0.981098i | \(-0.561988\pi\) | ||||
−0.193513 | + | 0.981098i | \(0.561988\pi\) | |||||||
\(864\) | −20.2344 | − | 21.3206i | −0.688390 | − | 0.725341i | ||||
\(865\) | −14.8944 | −0.506426 | ||||||||
\(866\) | 11.9677 | − | 17.7206i | 0.406678 | − | 0.602169i | ||||
\(867\) | −10.4070 | + | 2.06501i | −0.353440 | + | 0.0701315i | ||||
\(868\) | −23.7504 | − | 58.9819i | −0.806142 | − | 2.00198i | ||||
\(869\) | − | 0.237636i | − | 0.00806126i | ||||||
\(870\) | −4.95657 | + | 11.7853i | −0.168043 | + | 0.399561i | ||||
\(871\) | 8.65049i | 0.293111i | ||||||||
\(872\) | −7.58726 | − | 1.62657i | −0.256937 | − | 0.0550826i | ||||
\(873\) | −0.00842441 | + | 0.00348026i | −0.000285123 | + | 0.000117789i | ||||
\(874\) | −10.1778 | − | 6.87361i | −0.344268 | − | 0.232503i | ||||
\(875\) | 41.7275 | 1.41065 | ||||||||
\(876\) | −2.25442 | − | 3.45084i | −0.0761699 | − | 0.116593i | ||||
\(877\) | 3.22713 | 0.108973 | 0.0544863 | − | 0.998515i | \(-0.482648\pi\) | ||||
0.0544863 | + | 0.998515i | \(0.482648\pi\) | |||||||
\(878\) | 31.2109 | + | 21.0784i | 1.05332 | + | 0.711362i | ||||
\(879\) | 1.96061 | + | 9.88086i | 0.0661298 | + | 0.333273i | ||||
\(880\) | 9.46331 | + | 9.84530i | 0.319008 | + | 0.331885i | ||||
\(881\) | 0.717838i | 0.0241846i | 0.999927 | + | 0.0120923i | \(0.00384919\pi\) | ||||
−0.999927 | + | 0.0120923i | \(0.996151\pi\) | |||||||
\(882\) | −13.8651 | + | 67.6234i | −0.466863 | + | 2.27700i | ||||
\(883\) | 16.5693i | 0.557601i | 0.960349 | + | 0.278801i | \(0.0899369\pi\) | ||||
−0.960349 | + | 0.278801i | \(0.910063\pi\) | |||||||
\(884\) | 17.6843 | − | 7.12099i | 0.594787 | − | 0.239505i | ||||
\(885\) | −1.51698 | − | 7.64509i | −0.0509927 | − | 0.256987i | ||||
\(886\) | 7.41910 | − | 10.9855i | 0.249250 | − | 0.369064i | ||||
\(887\) | 6.02979 | 0.202461 | 0.101230 | − | 0.994863i | \(-0.467722\pi\) | ||||
0.101230 | + | 0.994863i | \(0.467722\pi\) | |||||||
\(888\) | 42.5592 | + | 0.651381i | 1.42819 | + | 0.0218589i | ||||
\(889\) | −52.1117 | −1.74777 | ||||||||
\(890\) | 4.83508 | − | 7.15931i | 0.162072 | − | 0.239981i | ||||
\(891\) | −22.8882 | + | 22.8026i | −0.766783 | + | 0.763915i | ||||
\(892\) | 25.8383 | − | 10.4044i | 0.865130 | − | 0.348365i | ||||
\(893\) | − | 0.581952i | − | 0.0194743i | ||||||
\(894\) | 0.624853 | + | 0.262795i | 0.0208982 | + | 0.00878917i | ||||
\(895\) | 13.6405i | 0.455953i | ||||||||
\(896\) | −28.7326 | − | 46.4012i | −0.959888 | − | 1.55016i | ||||
\(897\) | 42.6476 | − | 8.46237i | 1.42396 | − | 0.282550i | ||||
\(898\) | −45.4844 | − | 30.7182i | −1.51784 | − | 1.02508i | ||||
\(899\) | 36.1709 | 1.20637 | ||||||||
\(900\) | −17.1868 | − | 17.5631i | −0.572895 | − | 0.585437i | ||||
\(901\) | −3.53022 | −0.117609 | ||||||||
\(902\) | −4.05900 | − | 2.74127i | −0.135150 | − | 0.0912743i | ||||
\(903\) | 26.2681 | − | 5.21226i | 0.874147 | − | 0.173453i | ||||
\(904\) | 3.28376 | − | 15.3174i | 0.109216 | − | 0.509448i | ||||
\(905\) | 3.42726i | 0.113926i | ||||||||
\(906\) | −31.1108 | − | 13.0843i | −1.03359 | − | 0.434697i | ||||
\(907\) | 31.4118i | 1.04301i | 0.853248 | + | 0.521506i | \(0.174629\pi\) | ||||
−0.853248 | + | 0.521506i | \(0.825371\pi\) | |||||||
\(908\) | 5.37442 | + | 13.3469i | 0.178356 | + | 0.442931i | ||||
\(909\) | −9.19883 | − | 22.2669i | −0.305106 | − | 0.738548i | ||||
\(910\) | −10.4962 | + | 15.5417i | −0.347944 | + | 0.515201i | ||||
\(911\) | 11.8765 | 0.393487 | 0.196743 | − | 0.980455i | \(-0.436963\pi\) | ||||
0.196743 | + | 0.980455i | \(0.436963\pi\) | |||||||
\(912\) | −5.68147 | − | 3.96495i | −0.188132 | − | 0.131293i | ||||
\(913\) | −31.4398 | −1.04051 | ||||||||
\(914\) | 18.3918 | − | 27.2328i | 0.608348 | − | 0.900781i | ||||
\(915\) | 1.78051 | + | 8.97320i | 0.0588618 | + | 0.296645i | ||||
\(916\) | −2.93427 | − | 7.28697i | −0.0969509 | − | 0.240768i | ||||
\(917\) | − | 1.68164i | − | 0.0555327i | ||||||
\(918\) | 24.2321 | + | 0.153895i | 0.799777 | + | 0.00507930i | ||||
\(919\) | − | 3.14393i | − | 0.103709i | −0.998655 | − | 0.0518543i | \(-0.983487\pi\) | ||
0.998655 | − | 0.0518543i | \(-0.0165131\pi\) | |||||||
\(920\) | 4.89664 | − | 22.8408i | 0.161438 | − | 0.753038i | ||||
\(921\) | 6.53798 | + | 32.9493i | 0.215434 | + | 1.08572i | ||||
\(922\) | 19.8483 | + | 13.4047i | 0.653669 | + | 0.441459i | ||||
\(923\) | 13.8690 | 0.456502 | ||||||||
\(924\) | −50.2209 | + | 32.8092i | −1.65215 | + | 1.07934i | ||||
\(925\) | 35.5838 | 1.16999 | ||||||||
\(926\) | −24.5666 | − | 16.5912i | −0.807308 | − | 0.545220i | ||||
\(927\) | 11.6133 | + | 28.1115i | 0.381432 | + | 0.923303i | ||||
\(928\) | 30.5908 | − | 5.30226i | 1.00419 | − | 0.174055i | ||||
\(929\) | 18.0736i | 0.592974i | 0.955037 | + | 0.296487i | \(0.0958152\pi\) | ||||
−0.955037 | + | 0.296487i | \(0.904185\pi\) | |||||||
\(930\) | 5.95187 | − | 14.1519i | 0.195170 | − | 0.464059i | ||||
\(931\) | 16.2706i | 0.533246i | ||||||||
\(932\) | 25.4276 | − | 10.2390i | 0.832907 | − | 0.335389i | ||||
\(933\) | 52.3845 | − | 10.3944i | 1.71499 | − | 0.340298i | ||||
\(934\) | 2.28057 | − | 3.37685i | 0.0746227 | − | 0.110494i | ||||
\(935\) | −11.2581 | −0.368178 | ||||||||
\(936\) | 24.1286 | − | 4.40506i | 0.788669 | − | 0.143984i | ||||
\(937\) | −7.96670 | −0.260261 | −0.130130 | − | 0.991497i | \(-0.541540\pi\) | ||||
−0.130130 | + | 0.991497i | \(0.541540\pi\) | |||||||
\(938\) | −11.4264 | + | 16.9191i | −0.373085 | + | 0.552427i | ||||
\(939\) | −7.16388 | + | 1.42149i | −0.233784 | + | 0.0463887i | ||||
\(940\) | 1.02678 | − | 0.413455i | 0.0334898 | − | 0.0134854i | ||||
\(941\) | 15.0985i | 0.492197i | 0.969245 | + | 0.246099i | \(0.0791487\pi\) | ||||
−0.969245 | + | 0.246099i | \(0.920851\pi\) | |||||||
\(942\) | −8.49015 | + | 20.1872i | −0.276624 | + | 0.657735i | ||||
\(943\) | 8.37844i | 0.272840i | ||||||||
\(944\) | −13.6454 | + | 13.1160i | −0.444119 | + | 0.426888i | ||||
\(945\) | −19.8394 | + | 13.2160i | −0.645376 | + | 0.429915i | ||||
\(946\) | 13.4847 | + | 9.10695i | 0.438425 | + | 0.296092i | ||||
\(947\) | 6.70111 | 0.217757 | 0.108878 | − | 0.994055i | \(-0.465274\pi\) | ||||
0.108878 | + | 0.994055i | \(0.465274\pi\) | |||||||
\(948\) | −0.191978 | + | 0.125419i | −0.00623515 | + | 0.00407341i | ||||
\(949\) | 3.43955 | 0.111652 | ||||||||
\(950\) | −4.79990 | − | 3.24164i | −0.155729 | − | 0.105173i | ||||
\(951\) | −3.76862 | − | 18.9926i | −0.122206 | − | 0.615878i | ||||
\(952\) | 43.9940 | + | 9.43150i | 1.42585 | + | 0.305677i | ||||
\(953\) | − | 34.0038i | − | 1.10149i | −0.834673 | − | 0.550746i | \(-0.814343\pi\) | ||
0.834673 | − | 0.550746i | \(-0.185657\pi\) | |||||||
\(954\) | −4.44933 | − | 0.912266i | −0.144052 | − | 0.0295357i | ||||
\(955\) | − | 12.2882i | − | 0.397636i | ||||||
\(956\) | 6.78622 | + | 16.8529i | 0.219482 | + | 0.545063i | ||||
\(957\) | −6.64182 | − | 33.4726i | −0.214699 | − | 1.08202i | ||||
\(958\) | −5.29157 | + | 7.83524i | −0.170963 | + | 0.253145i | ||||
\(959\) | −84.7830 | −2.73778 | ||||||||
\(960\) | 2.95916 | − | 12.8412i | 0.0955064 | − | 0.414447i | ||||
\(961\) | −12.4342 | −0.401102 | ||||||||
\(962\) | −19.8782 | + | 29.4336i | −0.640897 | + | 0.948978i | ||||
\(963\) | −2.13222 | + | 0.880856i | −0.0687100 | + | 0.0283852i | ||||
\(964\) | −18.8977 | − | 46.9305i | −0.608653 | − | 1.51153i | ||||
\(965\) | − | 9.93084i | − | 0.319685i | ||||||
\(966\) | 94.5904 | + | 39.7819i | 3.04339 | + | 1.27996i | ||||
\(967\) | 15.4605i | 0.497177i | 0.968609 | + | 0.248589i | \(0.0799667\pi\) | ||||
−0.968609 | + | 0.248589i | \(0.920033\pi\) | |||||||
\(968\) | −5.21796 | − | 1.11863i | −0.167711 | − | 0.0359543i | ||||
\(969\) | 5.60244 | − | 1.11167i | 0.179976 | − | 0.0357118i | ||||
\(970\) | −0.00338643 | − | 0.00228705i | −0.000108732 | − | 7.34326e-5i | ||||
\(971\) | 14.5494 | 0.466911 | 0.233456 | − | 0.972367i | \(-0.424997\pi\) | ||||
0.233456 | + | 0.972367i | \(0.424997\pi\) | |||||||
\(972\) | 30.5012 | + | 6.45591i | 0.978325 | + | 0.207073i | ||||
\(973\) | −44.6452 | −1.43126 | ||||||||
\(974\) | −19.1745 | − | 12.9496i | −0.614391 | − | 0.414932i | ||||
\(975\) | 20.1129 | − | 3.99091i | 0.644128 | − | 0.127811i | ||||
\(976\) | 16.0159 | − | 15.3945i | 0.512656 | − | 0.492765i | ||||
\(977\) | 30.4691i | 0.974794i | 0.873180 | + | 0.487397i | \(0.162054\pi\) | ||||
−0.873180 | + | 0.487397i | \(0.837946\pi\) | |||||||
\(978\) | 31.7747 | + | 13.3635i | 1.01604 | + | 0.427317i | ||||
\(979\) | 23.0587i | 0.736959i | ||||||||
\(980\) | −28.7073 | + | 11.5596i | −0.917020 | + | 0.369259i | ||||
\(981\) | 7.60681 | − | 3.14249i | 0.242867 | − | 0.100332i | ||||
\(982\) | −4.07347 | + | 6.03159i | −0.129990 | + | 0.192476i | ||||
\(983\) | −3.64757 | −0.116339 | −0.0581696 | − | 0.998307i | \(-0.518526\pi\) | ||||
−0.0581696 | + | 0.998307i | \(0.518526\pi\) | |||||||
\(984\) | −0.0723311 | + | 4.72589i | −0.00230583 | + | 0.150656i | ||||
\(985\) | −16.6979 | −0.532040 | ||||||||
\(986\) | −14.3251 | + | 21.2111i | −0.456203 | + | 0.675500i | ||||
\(987\) | 0.946373 | + | 4.76942i | 0.0301234 | + | 0.151812i | ||||
\(988\) | 5.36273 | − | 2.15943i | 0.170611 | − | 0.0687005i | ||||
\(989\) | − | 27.8345i | − | 0.885087i | ||||||
\(990\) | −14.1891 | − | 2.90926i | −0.450960 | − | 0.0924623i | ||||
\(991\) | 44.4264i | 1.41125i | 0.708584 | + | 0.705626i | \(0.249334\pi\) | ||||
−0.708584 | + | 0.705626i | \(0.750666\pi\) | |||||||
\(992\) | −36.7336 | + | 6.36698i | −1.16629 | + | 0.202152i | ||||
\(993\) | 3.10714 | + | 15.6590i | 0.0986021 | + | 0.496923i | ||||
\(994\) | 27.1256 | + | 18.3194i | 0.860373 | + | 0.581057i | ||||
\(995\) | −22.2791 | −0.706295 | ||||||||
\(996\) | 16.5932 | + | 25.3991i | 0.525774 | + | 0.804801i | ||||
\(997\) | −44.7668 | −1.41778 | −0.708889 | − | 0.705320i | \(-0.750803\pi\) | ||||
−0.708889 | + | 0.705320i | \(0.750803\pi\) | |||||||
\(998\) | 33.9996 | + | 22.9618i | 1.07624 | + | 0.726844i | ||||
\(999\) | −37.5729 | + | 25.0291i | −1.18875 | + | 0.791885i |
(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 | 228.2.c.a.191.25 | yes | 36 | |
3.2 | odd | 2 | inner | 228.2.c.a.191.12 | yes | 36 | |
4.3 | odd | 2 | inner | 228.2.c.a.191.11 | ✓ | 36 | |
12.11 | even | 2 | inner | 228.2.c.a.191.26 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
228.2.c.a.191.11 | ✓ | 36 | 4.3 | odd | 2 | inner | |
228.2.c.a.191.12 | yes | 36 | 3.2 | odd | 2 | inner | |
228.2.c.a.191.25 | yes | 36 | 1.1 | even | 1 | trivial | |
228.2.c.a.191.26 | yes | 36 | 12.11 | even | 2 | inner |