Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,2,Mod(46,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.46");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.h (of order \(5\), degree \(4\), 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: | \(1.79663404548\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 16.0.1130304400000000000000.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 5x^{14} + 5x^{12} - 10x^{10} + 205x^{8} - 700x^{6} + 1250x^{4} - 1250x^{2} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 91.4 | ||
Root | \(1.13937 - 0.289499i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.91 |
Dual form | 225.2.h.e.136.4 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.64259 | + | 1.19341i | 1.16149 | + | 0.843869i | 0.989965 | − | 0.141311i | \(-0.0451317\pi\) |
0.171521 | + | 0.985180i | \(0.445132\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.655837 | + | 2.01846i | 0.327919 | + | 1.00923i | ||||
\(5\) | 2.23130 | + | 0.145994i | 0.997866 | + | 0.0652906i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.504300 | −0.190607 | −0.0953037 | − | 0.995448i | \(-0.530382\pi\) | ||||
−0.0953037 | + | 0.995448i | \(0.530382\pi\) | |||||||
\(8\) | −0.0767537 | + | 0.236224i | −0.0271365 | + | 0.0835177i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.49087 | + | 2.90266i | 1.10391 | + | 0.917903i | ||||
\(11\) | −2.78196 | − | 2.02121i | −0.838792 | − | 0.609418i | 0.0832413 | − | 0.996529i | \(-0.473473\pi\) |
−0.922033 | + | 0.387112i | \(0.873473\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.99517 | + | 2.90266i | −1.10806 | + | 0.805054i | −0.982357 | − | 0.187014i | \(-0.940119\pi\) |
−0.125705 | + | 0.992068i | \(0.540119\pi\) | |||||||
\(14\) | −0.828357 | − | 0.601837i | −0.221388 | − | 0.160848i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.02602 | − | 2.19853i | 0.756505 | − | 0.549633i | ||||
\(17\) | 0.363841 | − | 1.11979i | 0.0882443 | − | 0.271588i | −0.897190 | − | 0.441645i | \(-0.854395\pi\) |
0.985434 | + | 0.170057i | \(0.0543951\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.83504 | + | 5.64767i | −0.420987 | + | 1.29566i | 0.485799 | + | 0.874071i | \(0.338529\pi\) |
−0.906785 | + | 0.421593i | \(0.861471\pi\) | |||||||
\(20\) | 1.16868 | + | 4.59953i | 0.261326 | + | 1.02849i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.15748 | − | 6.64004i | −0.459976 | − | 1.41566i | ||||
\(23\) | −2.40939 | − | 1.75052i | −0.502392 | − | 0.365009i | 0.307538 | − | 0.951536i | \(-0.400495\pi\) |
−0.809930 | + | 0.586527i | \(0.800495\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.95737 | + | 0.651513i | 0.991474 | + | 0.130303i | ||||
\(26\) | −10.0265 | −1.96636 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.330738 | − | 1.01791i | −0.0625037 | − | 0.192367i | ||||
\(29\) | −1.55064 | − | 4.77239i | −0.287947 | − | 0.886211i | −0.985500 | − | 0.169677i | \(-0.945728\pi\) |
0.697552 | − | 0.716534i | \(-0.254272\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.10061 | − | 3.38734i | 0.197676 | − | 0.608383i | −0.802259 | − | 0.596976i | \(-0.796369\pi\) |
0.999935 | − | 0.0114076i | \(-0.00363122\pi\) | |||||||
\(32\) | 8.09103 | 1.43031 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.93401 | − | 1.40514i | 0.331680 | − | 0.240979i | ||||
\(35\) | −1.12524 | − | 0.0736248i | −0.190201 | − | 0.0124449i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.21435 | − | 0.882274i | 0.199637 | − | 0.145045i | −0.483475 | − | 0.875358i | \(-0.660626\pi\) |
0.683113 | + | 0.730313i | \(0.260626\pi\) | |||||||
\(38\) | −9.75420 | + | 7.08684i | −1.58234 | + | 1.14964i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.205748 | + | 0.515879i | −0.0325316 | + | 0.0815677i | ||||
\(41\) | 7.10690 | − | 5.16346i | 1.10991 | − | 0.806397i | 0.127261 | − | 0.991869i | \(-0.459381\pi\) |
0.982650 | + | 0.185472i | \(0.0593814\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.2500 | −1.56311 | −0.781554 | − | 0.623838i | \(-0.785573\pi\) | ||||
−0.781554 | + | 0.623838i | \(0.785573\pi\) | |||||||
\(44\) | 2.25522 | − | 6.94085i | 0.339987 | − | 1.04637i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.86854 | − | 5.75078i | −0.275501 | − | 0.847906i | ||||
\(47\) | −0.881597 | − | 2.71328i | −0.128594 | − | 0.395772i | 0.865945 | − | 0.500140i | \(-0.166718\pi\) |
−0.994539 | + | 0.104368i | \(0.966718\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.74568 | −0.963669 | ||||||||
\(50\) | 7.36541 | + | 6.98635i | 1.04163 | + | 0.988020i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −8.47909 | − | 6.16042i | −1.17584 | − | 0.854297i | ||||
\(53\) | 4.09875 | + | 12.6147i | 0.563007 | + | 1.73276i | 0.673800 | + | 0.738914i | \(0.264661\pi\) |
−0.110793 | + | 0.993844i | \(0.535339\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.91229 | − | 4.91607i | −0.797213 | − | 0.662883i | ||||
\(56\) | 0.0387069 | − | 0.119127i | 0.00517242 | − | 0.0159191i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.14835 | − | 9.68964i | 0.413399 | − | 1.27231i | ||||
\(59\) | 7.68621 | − | 5.58436i | 1.00066 | − | 0.727022i | 0.0384302 | − | 0.999261i | \(-0.487764\pi\) |
0.962230 | + | 0.272239i | \(0.0877643\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.86106 | + | 4.98485i | 0.878469 | + | 0.638245i | 0.932846 | − | 0.360276i | \(-0.117317\pi\) |
−0.0543773 | + | 0.998520i | \(0.517317\pi\) | |||||||
\(62\) | 5.85034 | − | 4.25052i | 0.742994 | − | 0.539817i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.23820 | + | 5.25886i | 0.904775 | + | 0.657357i | ||||
\(65\) | −9.33819 | + | 5.89343i | −1.15826 | + | 0.730990i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.99836 | + | 9.22800i | −0.366308 | + | 1.12738i | 0.582850 | + | 0.812579i | \(0.301937\pi\) |
−0.949158 | + | 0.314800i | \(0.898063\pi\) | |||||||
\(68\) | 2.49886 | 0.303032 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.76045 | − | 1.46381i | −0.210414 | − | 0.174959i | ||||
\(71\) | 4.23839 | + | 13.0444i | 0.503004 | + | 1.54809i | 0.804100 | + | 0.594494i | \(0.202647\pi\) |
−0.301096 | + | 0.953594i | \(0.597353\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.0633 | + | 7.31141i | 1.17782 | + | 0.855736i | 0.991924 | − | 0.126833i | \(-0.0404813\pi\) |
0.185896 | + | 0.982569i | \(0.440481\pi\) | |||||||
\(74\) | 3.04759 | 0.354275 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −12.6031 | −1.44567 | ||||||||
\(77\) | 1.40294 | + | 1.01930i | 0.159880 | + | 0.116159i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.54026 | − | 13.9735i | −0.510819 | − | 1.57214i | −0.790763 | − | 0.612123i | \(-0.790316\pi\) |
0.279943 | − | 0.960016i | \(-0.409684\pi\) | |||||||
\(80\) | 7.07292 | − | 4.46380i | 0.790777 | − | 0.499068i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 17.8359 | 1.96964 | ||||||||
\(83\) | 0.110065 | − | 0.338746i | 0.0120812 | − | 0.0371823i | −0.944834 | − | 0.327549i | \(-0.893777\pi\) |
0.956915 | + | 0.290367i | \(0.0937773\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.975319 | − | 2.44546i | 0.105788 | − | 0.265247i | ||||
\(86\) | −16.8365 | − | 12.2324i | −1.81553 | − | 1.31906i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.690983 | − | 0.502029i | 0.0736590 | − | 0.0535164i | ||||
\(89\) | −5.26703 | − | 3.82672i | −0.558304 | − | 0.405632i | 0.272534 | − | 0.962146i | \(-0.412138\pi\) |
−0.830838 | + | 0.556515i | \(0.812138\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.01476 | − | 1.46381i | 0.211205 | − | 0.153449i | ||||
\(92\) | 1.95319 | − | 6.01131i | 0.203634 | − | 0.626722i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.78995 | − | 5.50891i | 0.184620 | − | 0.568201i | ||||
\(95\) | −4.91904 | + | 12.3337i | −0.504683 | + | 1.26541i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.39322 | + | 10.4433i | 0.344530 | + | 1.06035i | 0.961835 | + | 0.273629i | \(0.0882242\pi\) |
−0.617306 | + | 0.786723i | \(0.711776\pi\) | |||||||
\(98\) | −11.0804 | − | 8.05038i | −1.11929 | − | 0.813211i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.93618 | + | 10.4335i | 0.193618 | + | 1.04335i | ||||
\(101\) | −8.10395 | −0.806373 | −0.403187 | − | 0.915118i | \(-0.632097\pi\) | ||||
−0.403187 | + | 0.915118i | \(0.632097\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.66863 | + | 5.13553i | 0.164415 | + | 0.506019i | 0.998993 | − | 0.0448722i | \(-0.0142881\pi\) |
−0.834577 | + | 0.550891i | \(0.814288\pi\) | |||||||
\(104\) | −0.379033 | − | 1.16654i | −0.0371673 | − | 0.114389i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.32192 | + | 25.6122i | −0.808296 | + | 2.48768i | ||||
\(107\) | −10.6007 | −1.02481 | −0.512403 | − | 0.858745i | \(-0.671245\pi\) | ||||
−0.512403 | + | 0.858745i | \(0.671245\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.26426 | − | 1.64508i | 0.216876 | − | 0.157570i | −0.474043 | − | 0.880502i | \(-0.657206\pi\) |
0.690920 | + | 0.722932i | \(0.257206\pi\) | |||||||
\(110\) | −3.84457 | − | 15.1309i | −0.366565 | − | 1.44267i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.52602 | + | 1.10872i | −0.144195 | + | 0.104764i | ||||
\(113\) | −5.77531 | + | 4.19601i | −0.543296 | + | 0.394728i | −0.825308 | − | 0.564683i | \(-0.808998\pi\) |
0.282012 | + | 0.959411i | \(0.408998\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.12049 | − | 4.25769i | −0.477488 | − | 0.397032i | ||||
\(116\) | 8.61591 | − | 6.25982i | 0.799967 | − | 0.581210i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 19.2897 | 1.77576 | ||||||||
\(119\) | −0.183485 | + | 0.564708i | −0.0168200 | + | 0.0517667i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.254807 | + | 0.784215i | 0.0231643 | + | 0.0712923i | ||||
\(122\) | 5.32093 | + | 16.3761i | 0.481734 | + | 1.48263i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.55902 | 0.678820 | ||||||||
\(125\) | 10.9663 | + | 2.17747i | 0.980851 | + | 0.194759i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.66227 | + | 2.66079i | 0.324974 | + | 0.236107i | 0.738295 | − | 0.674478i | \(-0.235631\pi\) |
−0.413321 | + | 0.910585i | \(0.635631\pi\) | |||||||
\(128\) | 0.612881 | + | 1.88625i | 0.0541715 | + | 0.166723i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −22.3721 | − | 1.46381i | −1.96216 | − | 0.128385i | ||||
\(131\) | 2.99410 | − | 9.21489i | 0.261596 | − | 0.805109i | −0.730863 | − | 0.682525i | \(-0.760882\pi\) |
0.992458 | − | 0.122584i | \(-0.0391180\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.925409 | − | 2.84812i | 0.0802431 | − | 0.246963i | ||||
\(134\) | −15.9379 | + | 11.5795i | −1.37682 | + | 1.00032i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.236594 | + | 0.171896i | 0.0202878 | + | 0.0147399i | ||||
\(137\) | 3.22362 | − | 2.34210i | 0.275412 | − | 0.200099i | −0.441502 | − | 0.897260i | \(-0.645554\pi\) |
0.716914 | + | 0.697162i | \(0.245554\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.01391 | − | 2.91628i | −0.340456 | − | 0.247356i | 0.404398 | − | 0.914583i | \(-0.367481\pi\) |
−0.744854 | + | 0.667227i | \(0.767481\pi\) | |||||||
\(140\) | −0.589367 | − | 2.31954i | −0.0498106 | − | 0.196037i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.60542 | + | 26.4848i | −0.722151 | + | 2.22255i | ||||
\(143\) | 16.9813 | 1.42005 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.76321 | − | 10.8750i | −0.229472 | − | 0.903120i | ||||
\(146\) | 7.80435 | + | 24.0193i | 0.645892 | + | 1.98785i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.57725 | + | 1.87248i | 0.211849 | + | 0.153917i | ||||
\(149\) | −5.62123 | −0.460509 | −0.230254 | − | 0.973130i | \(-0.573956\pi\) | ||||
−0.230254 | + | 0.973130i | \(0.573956\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.35414 | −0.191577 | −0.0957886 | − | 0.995402i | \(-0.530537\pi\) | ||||
−0.0957886 | + | 0.995402i | \(0.530537\pi\) | |||||||
\(152\) | −1.19327 | − | 0.866959i | −0.0967867 | − | 0.0703196i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.08802 | + | 3.34857i | 0.0876748 | + | 0.269835i | ||||
\(155\) | 2.95032 | − | 7.39747i | 0.236976 | − | 0.594179i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.7688 | 1.65753 | 0.828767 | − | 0.559594i | \(-0.189043\pi\) | ||||
0.828767 | + | 0.559594i | \(0.189043\pi\) | |||||||
\(158\) | 9.21833 | − | 28.3711i | 0.733371 | − | 2.25708i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 18.0535 | + | 1.18124i | 1.42725 | + | 0.0933855i | ||||
\(161\) | 1.21505 | + | 0.882787i | 0.0957595 | + | 0.0695734i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.65797 | − | 4.11075i | 0.443166 | − | 0.321979i | −0.343725 | − | 0.939070i | \(-0.611689\pi\) |
0.786892 | + | 0.617091i | \(0.211689\pi\) | |||||||
\(164\) | 15.0832 | + | 10.9586i | 1.17780 | + | 0.855722i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.585056 | − | 0.425068i | 0.0454092 | − | 0.0329917i | ||||
\(167\) | −4.59910 | + | 14.1546i | −0.355889 | + | 1.09531i | 0.599603 | + | 0.800297i | \(0.295325\pi\) |
−0.955492 | + | 0.295016i | \(0.904675\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.51874 | − | 10.8296i | 0.270672 | − | 0.833043i | ||||
\(170\) | 4.52049 | − | 2.85293i | 0.346706 | − | 0.218810i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.72232 | − | 20.6892i | −0.512572 | − | 1.57753i | ||||
\(173\) | −1.26528 | − | 0.919283i | −0.0961978 | − | 0.0698918i | 0.538647 | − | 0.842532i | \(-0.318936\pi\) |
−0.634844 | + | 0.772640i | \(0.718936\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.50000 | − | 0.328558i | −0.188982 | − | 0.0248366i | ||||
\(176\) | −12.8620 | −0.969506 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.08472 | − | 12.5715i | −0.306162 | − | 0.942271i | ||||
\(179\) | 3.69979 | + | 11.3868i | 0.276535 | + | 0.851089i | 0.988809 | + | 0.149187i | \(0.0476655\pi\) |
−0.712274 | + | 0.701902i | \(0.752334\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.257789 | + | 0.793394i | −0.0191613 | + | 0.0589725i | −0.960180 | − | 0.279382i | \(-0.909870\pi\) |
0.941019 | + | 0.338355i | \(0.109870\pi\) | |||||||
\(182\) | 5.05636 | 0.374803 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.598444 | − | 0.434795i | 0.0441179 | − | 0.0320535i | ||||
\(185\) | 2.83837 | − | 1.79133i | 0.208681 | − | 0.131701i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.27551 | + | 2.37980i | −0.239529 | + | 0.174028i | ||||
\(188\) | 4.89845 | − | 3.55893i | 0.357256 | − | 0.259562i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −22.7992 | + | 14.3888i | −1.65403 | + | 1.04387i | ||||
\(191\) | 21.4128 | − | 15.5573i | 1.54938 | − | 1.12569i | 0.605287 | − | 0.796007i | \(-0.293058\pi\) |
0.944092 | − | 0.329683i | \(-0.106942\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.97684 | −0.286259 | −0.143130 | − | 0.989704i | \(-0.545717\pi\) | ||||
−0.143130 | + | 0.989704i | \(0.545717\pi\) | |||||||
\(194\) | −6.88944 | + | 21.2035i | −0.494633 | + | 1.52232i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.42407 | − | 13.6159i | −0.316005 | − | 0.972563i | ||||
\(197\) | −7.21923 | − | 22.2185i | −0.514349 | − | 1.58300i | −0.784464 | − | 0.620174i | \(-0.787062\pi\) |
0.270115 | − | 0.962828i | \(-0.412938\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.43506 | −0.314393 | −0.157197 | − | 0.987567i | \(-0.550246\pi\) | ||||
−0.157197 | + | 0.987567i | \(0.550246\pi\) | |||||||
\(200\) | −0.534399 | + | 1.12104i | −0.0377877 | + | 0.0792697i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −13.3115 | − | 9.67135i | −0.936592 | − | 0.680474i | ||||
\(203\) | 0.781989 | + | 2.40671i | 0.0548849 | + | 0.168918i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.6114 | − | 10.4837i | 1.16019 | − | 0.732210i | ||||
\(206\) | −3.38792 | + | 10.4269i | −0.236047 | + | 0.726479i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.70788 | + | 17.5670i | −0.395770 | + | 1.21806i | ||||
\(209\) | 16.5201 | − | 12.0026i | 1.14272 | − | 0.830235i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.09234 | + | 3.69980i | 0.350571 | + | 0.254705i | 0.749109 | − | 0.662447i | \(-0.230482\pi\) |
−0.398538 | + | 0.917152i | \(0.630482\pi\) | |||||||
\(212\) | −22.7741 | + | 16.5463i | −1.56413 | + | 1.13641i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −17.4126 | − | 12.6510i | −1.19030 | − | 0.864803i | ||||
\(215\) | −22.8708 | − | 1.49644i | −1.55977 | − | 0.102056i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.555038 | + | 1.70823i | −0.0376784 | + | 0.115962i | ||||
\(218\) | 5.68250 | 0.384868 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.04539 | − | 15.1578i | 0.407580 | − | 1.02194i | ||||
\(221\) | 1.79676 | + | 5.52985i | 0.120863 | + | 0.371978i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.7640 | − | 14.3594i | −1.32350 | − | 0.961577i | −0.999882 | − | 0.0153877i | \(-0.995102\pi\) |
−0.323615 | − | 0.946189i | \(-0.604898\pi\) | |||||||
\(224\) | −4.08030 | −0.272627 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.4940 | −0.964129 | ||||||||
\(227\) | −10.8784 | − | 7.90360i | −0.722023 | − | 0.524581i | 0.165007 | − | 0.986292i | \(-0.447235\pi\) |
−0.887030 | + | 0.461712i | \(0.847235\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.68153 | + | 14.4083i | 0.309364 | + | 0.952126i | 0.978012 | + | 0.208547i | \(0.0668733\pi\) |
−0.668648 | + | 0.743579i | \(0.733127\pi\) | |||||||
\(230\) | −3.32969 | − | 13.1045i | −0.219553 | − | 0.864085i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.24637 | 0.0818281 | ||||||||
\(233\) | −0.986111 | + | 3.03494i | −0.0646023 | + | 0.198825i | −0.978148 | − | 0.207911i | \(-0.933333\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.57098 | − | 6.18283i | −0.102480 | − | 0.403324i | ||||
\(236\) | 16.3127 | + | 11.8519i | 1.06187 | + | 0.771491i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.975319 | + | 0.708611i | −0.0632206 | + | 0.0459324i | ||||
\(239\) | −18.2944 | − | 13.2917i | −1.18337 | − | 0.859767i | −0.190820 | − | 0.981625i | \(-0.561115\pi\) |
−0.992548 | + | 0.121858i | \(0.961115\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.5019 | − | 11.2628i | 0.998567 | − | 0.725501i | 0.0367866 | − | 0.999323i | \(-0.488288\pi\) |
0.961780 | + | 0.273822i | \(0.0882878\pi\) | |||||||
\(242\) | −0.517348 | + | 1.59223i | −0.0332564 | + | 0.102353i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.56198 | + | 17.1180i | −0.356069 | + | 1.09587i | ||||
\(245\) | −15.0516 | − | 0.984831i | −0.961613 | − | 0.0629185i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.06198 | − | 27.8899i | −0.576600 | − | 1.77459i | ||||
\(248\) | 0.715693 | + | 0.519981i | 0.0454465 | + | 0.0330188i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 15.4144 | + | 16.6639i | 0.974895 | + | 1.05392i | ||||
\(251\) | 21.1160 | 1.33283 | 0.666414 | − | 0.745582i | \(-0.267828\pi\) | ||||
0.666414 | + | 0.745582i | \(0.267828\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.16464 | + | 9.73975i | 0.198959 | + | 0.612333i | ||||
\(254\) | 2.84018 | + | 8.74119i | 0.178209 | + | 0.548471i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.28513 | − | 13.1883i | 0.267820 | − | 0.824267i | ||||
\(257\) | −18.4143 | −1.14865 | −0.574325 | − | 0.818627i | \(-0.694735\pi\) | ||||
−0.574325 | + | 0.818627i | \(0.694735\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.612394 | + | 0.444931i | −0.0380523 | + | 0.0276466i | ||||
\(260\) | −18.0200 | − | 14.9836i | −1.11755 | − | 0.929245i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 15.9152 | − | 11.5631i | 0.983246 | − | 0.714370i | ||||
\(263\) | 0.481568 | − | 0.349879i | 0.0296947 | − | 0.0215745i | −0.572839 | − | 0.819668i | \(-0.694158\pi\) |
0.602534 | + | 0.798093i | \(0.294158\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.30387 | + | 28.7455i | 0.448673 | + | 1.76582i | ||||
\(266\) | 4.91904 | − | 3.57389i | 0.301606 | − | 0.219129i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −20.5928 | −1.25790 | ||||||||
\(269\) | 2.41478 | − | 7.43193i | 0.147232 | − | 0.453133i | −0.850059 | − | 0.526687i | \(-0.823434\pi\) |
0.997291 | + | 0.0735538i | \(0.0234341\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.51138 | − | 20.0400i | −0.395538 | − | 1.21734i | −0.928542 | − | 0.371228i | \(-0.878937\pi\) |
0.533003 | − | 0.846113i | \(-0.321063\pi\) | |||||||
\(272\) | −1.36090 | − | 4.18841i | −0.0825166 | − | 0.253960i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.09017 | 0.488745 | ||||||||
\(275\) | −12.4743 | − | 11.8324i | −0.752232 | − | 0.713519i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.1304 | − | 11.7194i | −0.969184 | − | 0.704153i | −0.0139182 | − | 0.999903i | \(-0.504430\pi\) |
−0.955265 | + | 0.295750i | \(0.904430\pi\) | |||||||
\(278\) | −3.11289 | − | 9.58050i | −0.186699 | − | 0.574600i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.103758 | − | 0.260158i | 0.00620075 | − | 0.0155474i | ||||
\(281\) | −3.17758 | + | 9.77960i | −0.189559 | + | 0.583402i | −0.999997 | − | 0.00242215i | \(-0.999229\pi\) |
0.810438 | + | 0.585824i | \(0.199229\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.98891 | + | 9.19891i | −0.177672 | + | 0.546819i | −0.999745 | − | 0.0225631i | \(-0.992817\pi\) |
0.822073 | + | 0.569382i | \(0.192817\pi\) | |||||||
\(284\) | −23.5499 | + | 17.1100i | −1.39743 | + | 1.01529i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 27.8933 | + | 20.2657i | 1.64937 | + | 1.19833i | ||||
\(287\) | −3.58400 | + | 2.60393i | −0.211557 | + | 0.153705i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.6317 | + | 9.17750i | 0.743044 | + | 0.539853i | ||||
\(290\) | 8.43954 | − | 21.1608i | 0.495587 | − | 1.24261i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.15791 | + | 25.1075i | −0.477405 | + | 1.46930i | ||||
\(293\) | 11.0903 | 0.647900 | 0.323950 | − | 0.946074i | \(-0.394989\pi\) | ||||
0.323950 | + | 0.946074i | \(0.394989\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.9655 | − | 11.3382i | 1.04599 | − | 0.660137i | ||||
\(296\) | 0.115208 | + | 0.354575i | 0.00669636 | + | 0.0206093i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.23337 | − | 6.70844i | −0.534875 | − | 0.388609i | ||||
\(299\) | 14.7071 | 0.850533 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.16906 | 0.297940 | ||||||||
\(302\) | −3.86689 | − | 2.80946i | −0.222514 | − | 0.161666i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.86372 | + | 21.1243i | 0.393661 | + | 1.21156i | ||||
\(305\) | 14.5813 | + | 12.1244i | 0.834923 | + | 0.694239i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.14760 | 0.122570 | 0.0612850 | − | 0.998120i | \(-0.480480\pi\) | ||||
0.0612850 | + | 0.998120i | \(0.480480\pi\) | |||||||
\(308\) | −1.13731 | + | 3.50027i | −0.0648040 | + | 0.199446i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 13.6744 | − | 8.63006i | 0.776654 | − | 0.490154i | ||||
\(311\) | 8.93231 | + | 6.48970i | 0.506505 | + | 0.367997i | 0.811496 | − | 0.584358i | \(-0.198654\pi\) |
−0.304991 | + | 0.952355i | \(0.598654\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.40884 | − | 6.83592i | 0.531819 | − | 0.386389i | −0.289219 | − | 0.957263i | \(-0.593396\pi\) |
0.821038 | + | 0.570874i | \(0.193396\pi\) | |||||||
\(314\) | 34.1147 | + | 24.7858i | 1.92520 | + | 1.39874i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 25.2272 | − | 18.3287i | 1.41914 | − | 1.03107i | ||||
\(317\) | 3.25520 | − | 10.0185i | 0.182830 | − | 0.562694i | −0.817074 | − | 0.576533i | \(-0.804405\pi\) |
0.999904 | + | 0.0138389i | \(0.00440520\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.33218 | + | 16.4108i | −0.298545 | + | 0.918826i | ||||
\(320\) | 15.3828 | + | 12.7908i | 0.859925 | + | 0.715028i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.942305 | + | 2.90012i | 0.0525126 | + | 0.161617i | ||||
\(323\) | 5.65652 | + | 4.10970i | 0.314737 | + | 0.228670i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −21.6967 | + | 11.7867i | −1.20352 | + | 0.653807i | ||||
\(326\) | 14.1995 | 0.786440 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.674251 | + | 2.07513i | 0.0372293 | + | 0.114580i | ||||
\(329\) | 0.444589 | + | 1.36830i | 0.0245110 | + | 0.0754370i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.22593 | + | 22.2391i | −0.397173 | + | 1.22237i | 0.530083 | + | 0.847945i | \(0.322161\pi\) |
−0.927256 | + | 0.374427i | \(0.877839\pi\) | |||||||
\(332\) | 0.755931 | 0.0414871 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −24.4467 | + | 17.7615i | −1.33766 | + | 0.971868i | ||||
\(335\) | −8.03746 | + | 20.1527i | −0.439133 | + | 1.10106i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.37793 | + | 2.45421i | −0.184008 | + | 0.133689i | −0.675976 | − | 0.736924i | \(-0.736278\pi\) |
0.491968 | + | 0.870613i | \(0.336278\pi\) | |||||||
\(338\) | 18.7040 | − | 13.5892i | 1.01736 | − | 0.739157i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.57571 | + | 0.364820i | 0.302385 | + | 0.0197851i | ||||
\(341\) | −9.90837 | + | 7.19885i | −0.536568 | + | 0.389840i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.93194 | 0.374290 | ||||||||
\(344\) | 0.786724 | − | 2.42129i | 0.0424173 | − | 0.130547i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.981261 | − | 3.02001i | −0.0527529 | − | 0.162357i | ||||
\(347\) | 2.58175 | + | 7.94582i | 0.138596 | + | 0.426554i | 0.996132 | − | 0.0878696i | \(-0.0280059\pi\) |
−0.857536 | + | 0.514424i | \(0.828006\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.84117 | 0.473257 | 0.236628 | − | 0.971600i | \(-0.423958\pi\) | ||||
0.236628 | + | 0.971600i | \(0.423958\pi\) | |||||||
\(350\) | −3.71437 | − | 3.52321i | −0.198541 | − | 0.188324i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −22.5089 | − | 16.3537i | −1.19973 | − | 0.871653i | ||||
\(353\) | 2.87823 | + | 8.85828i | 0.153193 | + | 0.471479i | 0.997973 | − | 0.0636341i | \(-0.0202691\pi\) |
−0.844781 | + | 0.535113i | \(0.820269\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.55269 | + | 29.7247i | 0.400855 | + | 1.57763i | ||||
\(356\) | 4.26977 | − | 13.1410i | 0.226297 | − | 0.696471i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.51188 | + | 23.1192i | −0.397015 | + | 1.22189i | ||||
\(359\) | 5.70869 | − | 4.14761i | 0.301293 | − | 0.218902i | −0.426858 | − | 0.904319i | \(-0.640380\pi\) |
0.728152 | + | 0.685416i | \(0.240380\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.1574 | − | 9.55944i | −0.692497 | − | 0.503128i | ||||
\(362\) | −1.37029 | + | 0.995572i | −0.0720207 | + | 0.0523261i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.27600 | + | 3.10670i | 0.224123 | + | 0.162835i | ||||
\(365\) | 21.3868 | + | 17.7831i | 1.11944 | + | 0.930811i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.03134 | − | 3.17412i | 0.0538353 | − | 0.165688i | −0.920524 | − | 0.390686i | \(-0.872238\pi\) |
0.974359 | + | 0.224998i | \(0.0722377\pi\) | |||||||
\(368\) | −11.1394 | −0.580683 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.80008 | + | 0.444931i | 0.353519 | + | 0.0231308i | ||||
\(371\) | −2.06700 | − | 6.36157i | −0.107313 | − | 0.330276i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.6425 | − | 9.91184i | −0.706381 | − | 0.513216i | 0.175623 | − | 0.984457i | \(-0.443806\pi\) |
−0.882004 | + | 0.471242i | \(0.843806\pi\) | |||||||
\(374\) | −8.22041 | −0.425067 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.708606 | 0.0365436 | ||||||||
\(377\) | 20.0477 | + | 14.5655i | 1.03251 | + | 0.750163i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.605237 | − | 1.86273i | −0.0310889 | − | 0.0956819i | 0.934308 | − | 0.356467i | \(-0.116019\pi\) |
−0.965397 | + | 0.260785i | \(0.916019\pi\) | |||||||
\(380\) | −28.1212 | − | 1.83998i | −1.44259 | − | 0.0943887i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 53.7388 | 2.74952 | ||||||||
\(383\) | 4.58432 | − | 14.1091i | 0.234248 | − | 0.720940i | −0.762973 | − | 0.646431i | \(-0.776261\pi\) |
0.997220 | − | 0.0745092i | \(-0.0237390\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.98156 | + | 2.47917i | 0.151955 | + | 0.126350i | ||||
\(386\) | −6.53231 | − | 4.74600i | −0.332486 | − | 0.241565i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −18.8539 | + | 13.6982i | −0.957162 | + | 0.695419i | ||||
\(389\) | −24.1901 | − | 17.5751i | −1.22649 | − | 0.891094i | −0.229863 | − | 0.973223i | \(-0.573828\pi\) |
−0.996622 | + | 0.0821294i | \(0.973828\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.83684 | + | 2.06109i | −0.143465 | + | 0.104234i | ||||
\(392\) | 0.517756 | − | 1.59349i | 0.0261506 | − | 0.0804834i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 14.6576 | − | 45.1114i | 0.738438 | − | 2.27268i | ||||
\(395\) | −8.09062 | − | 31.8418i | −0.407083 | − | 1.60214i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.858602 | + | 2.64251i | 0.0430920 | + | 0.132624i | 0.970288 | − | 0.241953i | \(-0.0777880\pi\) |
−0.927196 | + | 0.374577i | \(0.877788\pi\) | |||||||
\(398\) | −7.28499 | − | 5.29285i | −0.365163 | − | 0.265307i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.4335 | − | 8.92745i | 0.821674 | − | 0.446373i | ||||
\(401\) | −8.54941 | −0.426937 | −0.213469 | − | 0.976950i | \(-0.568476\pi\) | ||||
−0.213469 | + | 0.976950i | \(0.568476\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.43516 | + | 16.7277i | 0.270745 | + | 0.833266i | ||||
\(404\) | −5.31487 | − | 16.3575i | −0.264425 | − | 0.813816i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.58771 | + | 4.88648i | −0.0787969 | + | 0.242512i | ||||
\(407\) | −5.16152 | −0.255847 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.03563 | + | 3.65860i | −0.248996 | + | 0.180906i | −0.705282 | − | 0.708927i | \(-0.749180\pi\) |
0.456286 | + | 0.889833i | \(0.349180\pi\) | |||||||
\(410\) | 39.7971 | + | 2.60393i | 1.96544 | + | 0.128599i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.27150 | + | 6.73614i | −0.456774 | + | 0.331866i | ||||
\(413\) | −3.87615 | + | 2.81619i | −0.190733 | + | 0.138576i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.295044 | − | 0.739775i | 0.0144831 | − | 0.0363141i | ||||
\(416\) | −32.3251 | + | 23.4855i | −1.58487 | + | 1.15147i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 41.4598 | 2.02786 | ||||||||
\(419\) | −11.5879 | + | 35.6639i | −0.566106 | + | 1.74229i | 0.0985382 | + | 0.995133i | \(0.468583\pi\) |
−0.664644 | + | 0.747160i | \(0.731417\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.92653 | + | 9.00692i | 0.142630 | + | 0.438970i | 0.996699 | − | 0.0811902i | \(-0.0258721\pi\) |
−0.854069 | + | 0.520161i | \(0.825872\pi\) | |||||||
\(422\) | 3.94924 | + | 12.1545i | 0.192246 | + | 0.591672i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.29448 | −0.159994 | ||||||||
\(425\) | 2.53325 | − | 5.31415i | 0.122881 | − | 0.257774i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.46003 | − | 2.51386i | −0.167443 | − | 0.121654i | ||||
\(428\) | −6.95232 | − | 21.3970i | −0.336053 | − | 1.03427i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −35.7814 | − | 29.7523i | −1.72553 | − | 1.43478i | ||||
\(431\) | 3.05401 | − | 9.39927i | 0.147106 | − | 0.452747i | −0.850170 | − | 0.526509i | \(-0.823501\pi\) |
0.997276 | + | 0.0737623i | \(0.0235006\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.50377 | − | 23.0942i | 0.360608 | − | 1.10984i | −0.592077 | − | 0.805881i | \(-0.701692\pi\) |
0.952686 | − | 0.303957i | \(-0.0983080\pi\) | |||||||
\(434\) | −2.95032 | + | 2.14354i | −0.141620 | + | 0.102893i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.80551 | + | 3.49141i | 0.230142 | + | 0.167208i | ||||
\(437\) | 14.3077 | − | 10.3951i | 0.684429 | − | 0.497267i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.42111 | + | 1.03250i | 0.0678258 | + | 0.0492784i | 0.621182 | − | 0.783667i | \(-0.286653\pi\) |
−0.553356 | + | 0.832945i | \(0.686653\pi\) | |||||||
\(440\) | 1.61508 | − | 1.01930i | 0.0769960 | − | 0.0485930i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.64805 | + | 11.2276i | −0.173520 | + | 0.534040i | ||||
\(443\) | −37.3529 | −1.77469 | −0.887346 | − | 0.461105i | \(-0.847453\pi\) | ||||
−0.887346 | + | 0.461105i | \(0.847453\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.1936 | − | 9.30751i | −0.530629 | − | 0.441218i | ||||
\(446\) | −15.3275 | − | 47.1732i | −0.725779 | − | 2.23372i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.65022 | − | 2.65204i | −0.172457 | − | 0.125297i | ||||
\(449\) | −12.9452 | −0.610923 | −0.305461 | − | 0.952204i | \(-0.598811\pi\) | ||||
−0.305461 | + | 0.952204i | \(0.598811\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −30.2075 | −1.42242 | ||||||||
\(452\) | −12.2571 | − | 8.90534i | −0.576528 | − | 0.418872i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8.43646 | − | 25.9648i | −0.395943 | − | 1.21859i | ||||
\(455\) | 4.70925 | − | 2.97206i | 0.220773 | − | 0.139332i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.2891 | −1.04264 | −0.521320 | − | 0.853361i | \(-0.674560\pi\) | ||||
−0.521320 | + | 0.853361i | \(0.674560\pi\) | |||||||
\(458\) | −9.50516 | + | 29.2539i | −0.444147 | + | 1.36694i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.23577 | − | 13.1279i | 0.244119 | − | 0.612089i | ||||
\(461\) | −0.434539 | − | 0.315711i | −0.0202385 | − | 0.0147041i | 0.577620 | − | 0.816306i | \(-0.303982\pi\) |
−0.597859 | + | 0.801602i | \(0.703982\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.0822 | − | 13.1375i | 0.840349 | − | 0.610550i | −0.0821189 | − | 0.996623i | \(-0.526169\pi\) |
0.922468 | + | 0.386073i | \(0.126169\pi\) | |||||||
\(464\) | −15.1845 | − | 11.0322i | −0.704925 | − | 0.512158i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.24171 | + | 3.80832i | −0.242817 | + | 0.176417i | ||||
\(467\) | −11.5807 | + | 35.6417i | −0.535890 | + | 1.64930i | 0.205827 | + | 0.978588i | \(0.434012\pi\) |
−0.741717 | + | 0.670712i | \(0.765988\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.51207 | − | 4.65367i | 0.0698209 | − | 0.214887i | ||||
\(470\) | 4.79819 | − | 12.0307i | 0.221324 | − | 0.554934i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.729213 | + | 2.24429i | 0.0335647 | + | 0.103302i | ||||
\(473\) | 28.5150 | + | 20.7174i | 1.31112 | + | 0.952585i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.7765 | + | 26.8020i | −0.586226 | + | 1.22976i | ||||
\(476\) | −1.26018 | −0.0577601 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −14.1878 | − | 43.6656i | −0.648935 | − | 1.99722i | ||||
\(479\) | 5.75361 | + | 17.7078i | 0.262889 | + | 0.809089i | 0.992172 | + | 0.124877i | \(0.0398538\pi\) |
−0.729283 | + | 0.684212i | \(0.760146\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.29058 | + | 7.04968i | −0.104441 | + | 0.321438i | ||||
\(482\) | 38.9045 | 1.77205 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.41579 | + | 1.02864i | −0.0643543 | + | 0.0467561i | ||||
\(485\) | 6.04663 | + | 23.7974i | 0.274563 | + | 1.08058i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.44904 | − | 1.05279i | 0.0656622 | − | 0.0477064i | −0.554470 | − | 0.832204i | \(-0.687079\pi\) |
0.620132 | + | 0.784497i | \(0.287079\pi\) | |||||||
\(488\) | −1.70415 | + | 1.23814i | −0.0771433 | + | 0.0560479i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −23.5483 | − | 19.5804i | −1.06381 | − | 0.884555i | ||||
\(491\) | −22.0663 | + | 16.0321i | −0.995839 | + | 0.723519i | −0.961192 | − | 0.275880i | \(-0.911031\pi\) |
−0.0346469 | + | 0.999400i | \(0.511031\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.90825 | −0.266094 | ||||||||
\(494\) | 18.3990 | − | 56.6264i | 0.827811 | − | 2.54774i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.11669 | − | 12.6699i | −0.184845 | − | 0.568894i | ||||
\(497\) | −2.13742 | − | 6.57829i | −0.0958763 | − | 0.295077i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.5722 | 0.473275 | 0.236637 | − | 0.971598i | \(-0.423955\pi\) | ||||
0.236637 | + | 0.971598i | \(0.423955\pi\) | |||||||
\(500\) | 2.79695 | + | 23.5630i | 0.125083 | + | 1.05377i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 34.6849 | + | 25.2000i | 1.54806 | + | 1.12473i | ||||
\(503\) | −8.37251 | − | 25.7679i | −0.373312 | − | 1.14894i | −0.944610 | − | 0.328194i | \(-0.893560\pi\) |
0.571299 | − | 0.820742i | \(-0.306440\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.0823 | − | 1.18313i | −0.804653 | − | 0.0526486i | ||||
\(506\) | −6.42533 | + | 19.7751i | −0.285641 | + | 0.879112i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.96885 | + | 9.13719i | −0.131721 | + | 0.405397i | ||||
\(509\) | 22.7355 | − | 16.5183i | 1.00773 | − | 0.732161i | 0.0440004 | − | 0.999032i | \(-0.485990\pi\) |
0.963732 | + | 0.266871i | \(0.0859897\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.07492 | − | 3.68714i | −0.224501 | − | 0.163110i | ||||
\(512\) | 25.9868 | − | 18.8805i | 1.14847 | − | 0.834410i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −30.2471 | − | 21.9758i | −1.33414 | − | 0.969311i | ||||
\(515\) | 2.97346 | + | 11.7025i | 0.131026 | + | 0.515674i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.03154 | + | 9.33011i | −0.133327 | + | 0.410338i | ||||
\(518\) | −1.53690 | −0.0675274 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.675427 | − | 2.65824i | −0.0296194 | − | 0.116572i | ||||
\(521\) | −10.2133 | − | 31.4332i | −0.447452 | − | 1.37711i | −0.879772 | − | 0.475395i | \(-0.842305\pi\) |
0.432321 | − | 0.901720i | \(-0.357695\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.9601 | + | 23.9469i | 1.44125 | + | 1.04713i | 0.987780 | + | 0.155852i | \(0.0498122\pi\) |
0.453465 | + | 0.891274i | \(0.350188\pi\) | |||||||
\(524\) | 20.5635 | 0.898321 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.20857 | 0.0526961 | ||||||||
\(527\) | −3.39265 | − | 2.46490i | −0.147786 | − | 0.107373i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.36657 | − | 13.4389i | −0.189851 | − | 0.584301i | ||||
\(530\) | −22.3079 | + | 55.9335i | −0.968993 | + | 2.42960i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.35572 | 0.275555 | ||||||||
\(533\) | −13.4055 | + | 41.2579i | −0.580656 | + | 1.78708i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −23.6533 | − | 1.54764i | −1.02262 | − | 0.0669102i | ||||
\(536\) | −1.94974 | − | 1.41657i | −0.0842158 | − | 0.0611863i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 12.8359 | − | 9.32579i | 0.553393 | − | 0.402063i | ||||
\(539\) | 18.7662 | + | 13.6344i | 0.808317 | + | 0.587277i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −36.5725 | + | 26.5715i | −1.57238 | + | 1.14240i | −0.647538 | + | 0.762033i | \(0.724201\pi\) |
−0.924837 | + | 0.380364i | \(0.875799\pi\) | |||||||
\(542\) | 13.2204 | − | 40.6882i | 0.567865 | − | 1.74771i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.94385 | − | 9.06022i | 0.126216 | − | 0.388454i | ||||
\(545\) | 5.29240 | − | 3.34009i | 0.226702 | − | 0.143074i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.753668 | + | 2.31955i | 0.0322245 | + | 0.0991768i | 0.965875 | − | 0.259008i | \(-0.0833957\pi\) |
−0.933651 | + | 0.358185i | \(0.883396\pi\) | |||||||
\(548\) | 6.84159 | + | 4.97071i | 0.292258 | + | 0.212338i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.36936 | − | 34.3228i | −0.271590 | − | 1.46353i | ||||
\(551\) | 29.7984 | 1.26945 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.28965 | + | 7.04682i | 0.0973659 | + | 0.299661i | ||||
\(554\) | −12.5096 | − | 38.5005i | −0.531480 | − | 1.63573i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.25392 | − | 10.0145i | 0.137997 | − | 0.424710i | ||||
\(557\) | −7.91914 | −0.335545 | −0.167772 | − | 0.985826i | \(-0.553657\pi\) | ||||
−0.167772 | + | 0.985826i | \(0.553657\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 40.9505 | − | 29.7523i | 1.73202 | − | 1.25839i | ||||
\(560\) | −3.56687 | + | 2.25109i | −0.150728 | + | 0.0951260i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16.8906 | + | 12.2717i | −0.712485 | + | 0.517651i | ||||
\(563\) | 19.4577 | − | 14.1369i | 0.820045 | − | 0.595797i | −0.0966805 | − | 0.995315i | \(-0.530822\pi\) |
0.916725 | + | 0.399518i | \(0.130822\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.4990 | + | 8.51939i | −0.567909 | + | 0.358413i | ||||
\(566\) | −15.8876 | + | 11.5430i | −0.667807 | + | 0.485190i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.40671 | −0.142942 | ||||||||
\(569\) | 4.52263 | − | 13.9192i | 0.189598 | − | 0.583524i | −0.810399 | − | 0.585879i | \(-0.800749\pi\) |
0.999997 | + | 0.00235460i | \(0.000749494\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.53259 | + | 20.1052i | 0.273380 | + | 0.841378i | 0.989643 | + | 0.143548i | \(0.0458511\pi\) |
−0.716263 | + | 0.697830i | \(0.754149\pi\) | |||||||
\(572\) | 11.1370 | + | 34.2761i | 0.465660 | + | 1.43315i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.99461 | −0.375428 | ||||||||
\(575\) | −10.8037 | − | 10.2477i | −0.450547 | − | 0.427360i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.19476 | + | 2.32113i | 0.132999 | + | 0.0966298i | 0.652296 | − | 0.757964i | \(-0.273806\pi\) |
−0.519296 | + | 0.854594i | \(0.673806\pi\) | |||||||
\(578\) | 9.79625 | + | 30.1497i | 0.407470 | + | 1.25406i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 20.1385 | − | 12.7096i | 0.836207 | − | 0.527739i | ||||
\(581\) | −0.0555059 | + | 0.170830i | −0.00230277 | + | 0.00708721i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.0943 | − | 43.3779i | 0.583728 | − | 1.79653i | ||||
\(584\) | −2.49952 | + | 1.81601i | −0.103431 | + | 0.0751471i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.2168 | + | 13.2353i | 0.752528 | + | 0.546743i | ||||
\(587\) | 16.4014 | − | 11.9164i | 0.676960 | − | 0.491840i | −0.195388 | − | 0.980726i | \(-0.562596\pi\) |
0.872348 | + | 0.488886i | \(0.162596\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.1109 | + | 12.4318i | 0.705041 | + | 0.512243i | ||||
\(590\) | 43.0411 | + | 2.81619i | 1.77198 | + | 0.115941i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.73493 | − | 5.33956i | 0.0713051 | − | 0.219455i | ||||
\(593\) | −30.2561 | −1.24247 | −0.621234 | − | 0.783625i | \(-0.713368\pi\) | ||||
−0.621234 | + | 0.783625i | \(0.713368\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.491853 | + | 1.23324i | −0.0201640 | + | 0.0505580i | ||||
\(596\) | −3.68661 | − | 11.3462i | −0.151009 | − | 0.464759i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 24.1577 | + | 17.5516i | 0.987883 | + | 0.717739i | ||||
\(599\) | 1.02686 | 0.0419563 | 0.0209781 | − | 0.999780i | \(-0.493322\pi\) | ||||
0.0209781 | + | 0.999780i | \(0.493322\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.9840 | −0.692791 | −0.346396 | − | 0.938089i | \(-0.612594\pi\) | ||||
−0.346396 | + | 0.938089i | \(0.612594\pi\) | |||||||
\(602\) | 8.49065 | + | 6.16882i | 0.346053 | + | 0.251422i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.54393 | − | 4.75173i | −0.0628217 | − | 0.193345i | ||||
\(605\) | 0.454059 | + | 1.78702i | 0.0184601 | + | 0.0726526i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.7660 | 0.436977 | 0.218488 | − | 0.975840i | \(-0.429887\pi\) | ||||
0.218488 | + | 0.975840i | \(0.429887\pi\) | |||||||
\(608\) | −14.8473 | + | 45.6954i | −0.602139 | + | 1.85319i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.48175 | + | 37.3168i | 0.383905 | + | 1.51091i | ||||
\(611\) | 11.3979 | + | 8.28103i | 0.461108 | + | 0.335015i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.08204 | − | 2.96577i | 0.164872 | − | 0.119786i | −0.502290 | − | 0.864699i | \(-0.667509\pi\) |
0.667162 | + | 0.744913i | \(0.267509\pi\) | |||||||
\(614\) | 3.52763 | + | 2.56297i | 0.142363 | + | 0.103433i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.348462 | + | 0.253173i | −0.0140400 | + | 0.0102006i | ||||
\(617\) | 9.60737 | − | 29.5684i | 0.386778 | − | 1.19038i | −0.548404 | − | 0.836213i | \(-0.684764\pi\) |
0.935182 | − | 0.354167i | \(-0.115236\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.7533 | + | 33.0951i | −0.432210 | + | 1.33021i | 0.463708 | + | 0.885988i | \(0.346519\pi\) |
−0.895919 | + | 0.444218i | \(0.853481\pi\) | |||||||
\(620\) | 16.8664 | + | 1.10357i | 0.677372 | + | 0.0443206i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.92724 | + | 21.3198i | 0.277757 | + | 0.854848i | ||||
\(623\) | 2.65616 | + | 1.92981i | 0.106417 | + | 0.0773163i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.1511 | + | 6.45958i | 0.966042 | + | 0.258383i | ||||
\(626\) | 23.6129 | 0.943763 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.6210 | + | 41.9211i | 0.543536 | + | 1.67283i | ||||
\(629\) | −0.546130 | − | 1.68082i | −0.0217756 | − | 0.0670186i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.86250 | + | 8.80987i | −0.113954 | + | 0.350715i | −0.991727 | − | 0.128361i | \(-0.959028\pi\) |
0.877773 | + | 0.479076i | \(0.159028\pi\) | |||||||
\(632\) | 3.64935 | 0.145163 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 17.3031 | − | 12.5715i | 0.687195 | − | 0.499277i | ||||
\(635\) | 7.78315 | + | 6.47169i | 0.308865 | + | 0.256821i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.9502 | − | 19.5804i | 1.06780 | − | 0.775806i | ||||
\(638\) | −28.3434 | + | 20.5927i | −1.12213 | + | 0.815272i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.09214 | + | 4.29827i | 0.0431705 | + | 0.169904i | ||||
\(641\) | −35.3179 | + | 25.6600i | −1.39497 | + | 1.01351i | −0.399674 | + | 0.916657i | \(0.630877\pi\) |
−0.995299 | + | 0.0968498i | \(0.969123\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.4133 | −1.39656 | −0.698281 | − | 0.715824i | \(-0.746051\pi\) | ||||
−0.698281 | + | 0.715824i | \(0.746051\pi\) | |||||||
\(644\) | −0.984994 | + | 3.03150i | −0.0388142 | + | 0.119458i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.38678 | + | 13.5011i | 0.172595 | + | 0.531194i | ||||
\(647\) | −10.2984 | − | 31.6951i | −0.404870 | − | 1.24606i | −0.921004 | − | 0.389554i | \(-0.872629\pi\) |
0.516134 | − | 0.856508i | \(-0.327371\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −32.6699 | −1.28240 | ||||||||
\(650\) | −49.7051 | − | 6.53240i | −1.94960 | − | 0.256222i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.0081 | + | 8.72439i | 0.470273 | + | 0.341674i | ||||
\(653\) | −5.78030 | − | 17.7899i | −0.226201 | − | 0.696174i | −0.998168 | − | 0.0605113i | \(-0.980727\pi\) |
0.771967 | − | 0.635663i | \(-0.219273\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.02604 | − | 20.1240i | 0.313603 | − | 0.786311i | ||||
\(656\) | 10.1536 | − | 31.2495i | 0.396430 | − | 1.22009i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.902672 | + | 2.77814i | −0.0351898 | + | 0.108303i | ||||
\(659\) | 20.9712 | − | 15.2365i | 0.816921 | − | 0.593528i | −0.0989077 | − | 0.995097i | \(-0.531535\pi\) |
0.915829 | + | 0.401569i | \(0.131535\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.6395 | − | 13.5424i | −0.724992 | − | 0.526738i | 0.162983 | − | 0.986629i | \(-0.447888\pi\) |
−0.887975 | + | 0.459891i | \(0.847888\pi\) | |||||||
\(662\) | −38.4097 | + | 27.9063i | −1.49283 | + | 1.08461i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.0715720 | + | 0.0520001i | 0.00277753 | + | 0.00201800i | ||||
\(665\) | 2.48067 | − | 6.21989i | 0.0961963 | − | 0.241197i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.61807 | + | 14.2130i | −0.178813 | + | 0.550328i | ||||
\(668\) | −31.5867 | −1.22213 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −37.2527 | + | 23.5106i | −1.43920 | + | 0.908292i | ||||
\(671\) | −9.01174 | − | 27.7353i | −0.347894 | − | 1.07071i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.97293 | + | 3.61304i | 0.191692 | + | 0.139273i | 0.679492 | − | 0.733683i | \(-0.262200\pi\) |
−0.487800 | + | 0.872956i | \(0.662200\pi\) | |||||||
\(674\) | −8.47744 | −0.326539 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 24.1668 | 0.929491 | ||||||||
\(677\) | 28.7547 | + | 20.8915i | 1.10513 | + | 0.802925i | 0.981890 | − | 0.189452i | \(-0.0606711\pi\) |
0.123241 | + | 0.992377i | \(0.460671\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.71120 | − | 5.26653i | −0.0656698 | − | 0.202111i | ||||
\(680\) | 0.502816 | + | 0.418091i | 0.0192821 | + | 0.0160331i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −24.8666 | −0.952191 | ||||||||
\(683\) | 5.23883 | − | 16.1235i | 0.200458 | − | 0.616947i | −0.799411 | − | 0.600784i | \(-0.794855\pi\) |
0.999869 | − | 0.0161627i | \(-0.00514496\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.53478 | − | 4.75528i | 0.287889 | − | 0.181690i | ||||
\(686\) | 11.3863 | + | 8.27266i | 0.434732 | + | 0.315852i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −31.0167 | + | 22.5349i | −1.18250 | + | 0.859136i | ||||
\(689\) | −52.9914 | − | 38.5005i | −2.01881 | − | 1.46675i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.9241 | − | 9.38990i | 0.491656 | − | 0.357209i | −0.314165 | − | 0.949368i | \(-0.601725\pi\) |
0.805821 | + | 0.592160i | \(0.201725\pi\) | |||||||
\(692\) | 1.02571 | − | 3.15683i | 0.0389918 | − | 0.120004i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.24187 | + | 16.1328i | −0.198979 | + | 0.612394i | ||||
\(695\) | −8.53047 | − | 7.09309i | −0.323579 | − | 0.269056i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.19620 | − | 9.83689i | −0.121065 | − | 0.372599i | ||||
\(698\) | 14.5224 | + | 10.5512i | 0.549681 | + | 0.399367i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.976413 | − | 5.26163i | −0.0369049 | − | 0.198871i | ||||
\(701\) | −19.5403 | −0.738026 | −0.369013 | − | 0.929424i | \(-0.620304\pi\) | ||||
−0.369013 | + | 0.929424i | \(0.620304\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.75442 | + | 8.47723i | 0.103885 | + | 0.319725i | ||||
\(704\) | −9.50710 | − | 29.2598i | −0.358312 | − | 1.10277i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.84382 | + | 17.9854i | −0.219935 | + | 0.676891i | ||||
\(707\) | 4.08682 | 0.153701 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.6571 | − | 7.74285i | 0.400236 | − | 0.290789i | −0.369401 | − | 0.929270i | \(-0.620437\pi\) |
0.769637 | + | 0.638481i | \(0.220437\pi\) | |||||||
\(710\) | −23.0679 | + | 57.8390i | −0.865722 | + | 2.17066i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.30823 | − | 0.950482i | 0.0490278 | − | 0.0356208i | ||||
\(713\) | −8.58141 | + | 6.23476i | −0.321376 | + | 0.233493i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 37.8903 | + | 2.47917i | 1.41702 | + | 0.0927157i | ||||
\(716\) | −20.5573 | + | 14.9358i | −0.768263 | + | 0.558175i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14.3268 | 0.534673 | ||||||||
\(719\) | 2.58348 | − | 7.95114i | 0.0963476 | − | 0.296527i | −0.891255 | − | 0.453503i | \(-0.850174\pi\) |
0.987603 | + | 0.156975i | \(0.0501743\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.841492 | − | 2.58984i | −0.0313388 | − | 0.0964509i | ||||
\(722\) | −10.2039 | − | 31.4045i | −0.379751 | − | 1.16875i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.77050 | −0.0658002 | ||||||||
\(725\) | −4.57784 | − | 24.6688i | −0.170017 | − | 0.916175i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.213756 | + | 0.155303i | 0.00792778 | + | 0.00575987i | 0.591742 | − | 0.806127i | \(-0.298440\pi\) |
−0.583814 | + | 0.811887i | \(0.698440\pi\) | |||||||
\(728\) | 0.191146 | + | 0.588288i | 0.00708436 | + | 0.0218034i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 13.9071 | + | 54.7336i | 0.514726 | + | 2.02578i | ||||
\(731\) | −3.72936 | + | 11.4778i | −0.137935 | + | 0.424522i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.55648 | − | 17.1011i | 0.205233 | − | 0.631643i | −0.794470 | − | 0.607303i | \(-0.792251\pi\) |
0.999704 | − | 0.0243402i | \(-0.00774850\pi\) | |||||||
\(734\) | 5.48210 | − | 3.98298i | 0.202348 | − | 0.147014i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −19.4944 | − | 14.1635i | −0.718574 | − | 0.522074i | ||||
\(737\) | 26.9930 | − | 19.6116i | 0.994301 | − | 0.722402i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.3496 | + | 22.0502i | 1.11643 | + | 0.811132i | 0.983664 | − | 0.180016i | \(-0.0576150\pi\) |
0.132763 | + | 0.991148i | \(0.457615\pi\) | |||||||
\(740\) | 5.47724 | + | 4.55432i | 0.201347 | + | 0.167420i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.19674 | − | 12.9162i | 0.154067 | − | 0.474170i | ||||
\(743\) | 18.6523 | 0.684285 | 0.342142 | − | 0.939648i | \(-0.388847\pi\) | ||||
0.342142 | + | 0.939648i | \(0.388847\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.5426 | − | 0.820667i | −0.459526 | − | 0.0300669i | ||||
\(746\) | −10.5801 | − | 32.5622i | −0.387365 | − | 1.19219i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.95173 | − | 5.05073i | −0.254180 | − | 0.184673i | ||||
\(749\) | 5.34592 | 0.195336 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 51.3728 | 1.87462 | 0.937310 | − | 0.348496i | \(-0.113307\pi\) | ||||
0.937310 | + | 0.348496i | \(0.113307\pi\) | |||||||
\(752\) | −8.63296 | − | 6.27221i | −0.314812 | − | 0.228724i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 15.5475 | + | 47.8504i | 0.566208 | + | 1.74261i | ||||
\(755\) | −5.25278 | − | 0.343691i | −0.191168 | − | 0.0125082i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.8427 | −1.23003 | −0.615016 | − | 0.788514i | \(-0.710851\pi\) | ||||
−0.615016 | + | 0.788514i | \(0.710851\pi\) | |||||||
\(758\) | 1.22884 | − | 3.78199i | 0.0446336 | − | 0.137368i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.53596 | − | 2.10865i | −0.0919889 | − | 0.0764888i | ||||
\(761\) | −8.76122 | − | 6.36540i | −0.317594 | − | 0.230746i | 0.417554 | − | 0.908652i | \(-0.362887\pi\) |
−0.735148 | + | 0.677906i | \(0.762887\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.14186 | + | 0.829613i | −0.0413382 | + | 0.0300340i | ||||
\(764\) | 45.4452 | + | 33.0179i | 1.64415 | + | 1.19454i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.3681 | − | 17.7044i | 0.880455 | − | 0.639688i | ||||
\(767\) | −14.4982 | + | 44.6210i | −0.523501 | + | 1.61117i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.2290 | + | 31.4815i | −0.368866 | + | 1.13525i | 0.578658 | + | 0.815570i | \(0.303577\pi\) |
−0.947524 | + | 0.319683i | \(0.896423\pi\) | |||||||
\(770\) | 1.93881 | + | 7.63049i | 0.0698700 | + | 0.274984i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.60816 | − | 8.02708i | −0.0938696 | − | 0.288901i | ||||
\(773\) | −8.15139 | − | 5.92233i | −0.293185 | − | 0.213011i | 0.431463 | − | 0.902131i | \(-0.357998\pi\) |
−0.724648 | + | 0.689119i | \(0.757998\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.66304 | − | 16.0752i | 0.275264 | − | 0.577439i | ||||
\(776\) | −2.72739 | −0.0979075 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −18.7600 | − | 57.7374i | −0.672579 | − | 2.06999i | ||||
\(779\) | 16.1201 | + | 49.6125i | 0.577562 | + | 1.77755i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.5745 | − | 44.8557i | 0.521516 | − | 1.60506i | ||||
\(782\) | −7.11950 | −0.254593 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −20.4126 | + | 14.8306i | −0.729021 | + | 0.529664i | ||||
\(785\) | 46.3415 | + | 3.03213i | 1.65400 | + | 0.108221i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.26393 | + | 3.82447i | −0.187639 | + | 0.136328i | −0.677639 | − | 0.735395i | \(-0.736997\pi\) |
0.490000 | + | 0.871722i | \(0.336997\pi\) | |||||||
\(788\) | 40.1125 | − | 29.1434i | 1.42895 | − | 1.03819i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 24.7108 | − | 61.9585i | 0.879172 | − | 2.20439i | ||||
\(791\) | 2.91249 | − | 2.11605i | 0.103556 | − | 0.0752380i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −41.8805 | −1.48722 | ||||||||
\(794\) | −1.74327 | + | 5.36522i | −0.0618662 | + | 0.190405i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.90868 | − | 8.95199i | −0.103095 | − | 0.317295i | ||||
\(797\) | 5.20336 | + | 16.0143i | 0.184312 | + | 0.567255i | 0.999936 | − | 0.0113279i | \(-0.00360587\pi\) |
−0.815623 | + | 0.578583i | \(0.803606\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.35905 | −0.118835 | ||||||||
\(800\) | 40.1102 | + | 5.27141i | 1.41811 | + | 0.186372i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −14.0432 | − | 10.2030i | −0.495882 | − | 0.360279i | ||||
\(803\) | −13.2178 | − | 40.6801i | −0.466445 | − | 1.43557i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.58226 | + | 2.14715i | 0.0910127 | + | 0.0756771i | ||||
\(806\) | −11.0353 | + | 33.9631i | −0.388702 | + | 1.19630i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.622008 | − | 1.91435i | 0.0218822 | − | 0.0673464i | ||||
\(809\) | −33.7304 | + | 24.5065i | −1.18590 | + | 0.861604i | −0.992824 | − | 0.119581i | \(-0.961845\pi\) |
−0.193072 | + | 0.981185i | \(0.561845\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.0451 | + | 20.3760i | 0.984797 | + | 0.715497i | 0.958776 | − | 0.284164i | \(-0.0917162\pi\) |
0.0260215 | + | 0.999661i | \(0.491716\pi\) | |||||||
\(812\) | −4.34500 | + | 3.15683i | −0.152480 | + | 0.110783i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.47826 | − | 6.15982i | −0.297163 | − | 0.215902i | ||||
\(815\) | 13.2248 | − | 8.34628i | 0.463243 | − | 0.292358i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.8091 | − | 57.8885i | 0.658047 | − | 2.02526i | ||||
\(818\) | −12.6377 | −0.441867 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 32.0552 | + | 26.6539i | 1.11942 | + | 0.930795i | ||||
\(821\) | −8.05430 | − | 24.7886i | −0.281097 | − | 0.865128i | −0.987541 | − | 0.157359i | \(-0.949702\pi\) |
0.706444 | − | 0.707769i | \(-0.250298\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.0510 | + | 7.30244i | 0.350354 | + | 0.254547i | 0.749018 | − | 0.662550i | \(-0.230526\pi\) |
−0.398663 | + | 0.917097i | \(0.630526\pi\) | |||||||
\(824\) | −1.34121 | −0.0467232 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.72781 | −0.338474 | ||||||||
\(827\) | 25.5860 | + | 18.5893i | 0.889713 | + | 0.646414i | 0.935803 | − | 0.352523i | \(-0.114676\pi\) |
−0.0460905 | + | 0.998937i | \(0.514676\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.1998 | − | 37.5471i | −0.423716 | − | 1.30406i | −0.904218 | − | 0.427070i | \(-0.859546\pi\) |
0.480502 | − | 0.876993i | \(-0.340454\pi\) | |||||||
\(830\) | 1.36749 | − | 0.863039i | 0.0474663 | − | 0.0299565i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −44.1826 | −1.53176 | ||||||||
\(833\) | −2.45435 | + | 7.55373i | −0.0850383 | + | 0.261721i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.3284 | + | 30.9116i | −0.426643 | + | 1.06974i | ||||
\(836\) | 35.0612 | + | 25.4734i | 1.21262 | + | 0.881018i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −61.5958 | + | 44.7520i | −2.12779 | + | 1.54593i | ||||
\(839\) | 15.3954 | + | 11.1854i | 0.531509 | + | 0.386164i | 0.820922 | − | 0.571041i | \(-0.193460\pi\) |
−0.289413 | + | 0.957204i | \(0.593460\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.09027 | − | 2.24522i | 0.106561 | − | 0.0774212i | ||||
\(842\) | −5.94188 | + | 18.2872i | −0.204771 | + | 0.630219i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.12815 | + | 12.7051i | −0.142097 | + | 0.437329i | ||||
\(845\) | 9.43241 | − | 23.6503i | 0.324485 | − | 0.813594i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.128499 | − | 0.395479i | −0.00441528 | − | 0.0135888i | ||||
\(848\) | 40.1367 | + | 29.1610i | 1.37830 | + | 1.00139i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 10.5031 | − | 5.70576i | 0.360252 | − | 0.195706i | ||||
\(851\) | −4.47027 | −0.153239 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.92882 | + | 27.4801i | 0.305717 | + | 0.940900i | 0.979409 | + | 0.201887i | \(0.0647075\pi\) |
−0.673692 | + | 0.739012i | \(0.735292\pi\) | |||||||
\(854\) | −2.68334 | − | 8.25848i | −0.0918221 | − | 0.282599i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.813642 | − | 2.50413i | 0.0278097 | − | 0.0855894i | ||||
\(857\) | 54.7084 | 1.86880 | 0.934401 | − | 0.356222i | \(-0.115935\pi\) | ||||
0.934401 | + | 0.356222i | \(0.115935\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.0341 | + | 10.1963i | −0.478836 | + | 0.347895i | −0.800875 | − | 0.598832i | \(-0.795632\pi\) |
0.322039 | + | 0.946726i | \(0.395632\pi\) | |||||||
\(860\) | −11.9790 | − | 47.1451i | −0.408480 | − | 1.60763i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.2337 | − | 11.7945i | 0.552921 | − | 0.401721i | ||||
\(863\) | 25.6542 | − | 18.6388i | 0.873278 | − | 0.634473i | −0.0581867 | − | 0.998306i | \(-0.518532\pi\) |
0.931464 | + | 0.363832i | \(0.118532\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.68902 | − | 2.23592i | −0.0914293 | − | 0.0760235i | ||||
\(866\) | 39.8866 | − | 28.9793i | 1.35540 | − | 0.984756i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.81201 | −0.129388 | ||||||||
\(869\) | −15.6125 | + | 48.0504i | −0.529619 | + | 1.63000i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.8068 | − | 45.5707i | −0.501710 | − | 1.54410i | ||||
\(872\) | 0.214816 | + | 0.661137i | 0.00727460 | + | 0.0223889i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 35.9073 | 1.21458 | ||||||||
\(875\) | −5.53027 | − | 1.09810i | −0.186957 | − | 0.0371224i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.0784 | − | 18.9470i | −0.880603 | − | 0.639796i | 0.0528077 | − | 0.998605i | \(-0.483183\pi\) |
−0.933411 | + | 0.358809i | \(0.883183\pi\) | |||||||
\(878\) | 1.10211 | + | 3.39194i | 0.0371943 | + | 0.114472i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −28.6988 | − | 1.87777i | −0.967438 | − | 0.0632997i | ||||
\(881\) | −11.5043 | + | 35.4065i | −0.387589 | + | 1.19288i | 0.546996 | + | 0.837135i | \(0.315771\pi\) |
−0.934585 | + | 0.355740i | \(0.884229\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.68169 | − | 5.17572i | 0.0565935 | − | 0.174177i | −0.918764 | − | 0.394807i | \(-0.870811\pi\) |
0.975358 | + | 0.220630i | \(0.0708114\pi\) | |||||||
\(884\) | −9.98340 | + | 7.25336i | −0.335778 | + | 0.243957i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −61.3556 | − | 44.5774i | −2.06128 | − | 1.49761i | ||||
\(887\) | −38.4937 | + | 27.9673i | −1.29249 | + | 0.939052i | −0.999853 | − | 0.0171708i | \(-0.994534\pi\) |
−0.292641 | + | 0.956222i | \(0.594534\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.84688 | − | 1.34184i | −0.0619424 | − | 0.0450038i | ||||
\(890\) | −7.27886 | − | 28.6470i | −0.243988 | − | 0.960250i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 16.0219 | − | 49.3103i | 0.536452 | − | 1.65103i | ||||
\(893\) | 16.9414 | 0.566924 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.59293 | + | 25.9475i | 0.220377 | + | 0.867328i | ||||
\(896\) | −0.309076 | − | 0.951237i | −0.0103255 | − | 0.0317786i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −21.2637 | − | 15.4490i | −0.709579 | − | 0.515539i | ||||
\(899\) | −17.8723 | −0.596076 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.6170 | 0.520279 | ||||||||
\(902\) | −49.6186 | − | 36.0500i | −1.65212 | − | 1.20033i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.547920 | − | 1.68633i | −0.0182236 | − | 0.0560863i | ||||
\(905\) | −0.691035 | + | 1.73266i | −0.0229708 | + | 0.0575956i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.0436 | 0.698742 | 0.349371 | − | 0.936985i | \(-0.386395\pi\) | ||||
0.349371 | + | 0.936985i | \(0.386395\pi\) | |||||||
\(908\) | 8.81866 | − | 27.1410i | 0.292657 | − | 0.900707i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 11.2822 | + | 0.738200i | 0.374003 | + | 0.0244711i | ||||
\(911\) | 3.57453 | + | 2.59705i | 0.118430 | + | 0.0860441i | 0.645423 | − | 0.763825i | \(-0.276681\pi\) |
−0.526994 | + | 0.849869i | \(0.676681\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.990875 | + | 0.719913i | −0.0327932 | + | 0.0238256i | ||||
\(914\) | −36.6118 | − | 26.6001i | −1.21101 | − | 0.879852i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −26.0122 | + | 18.8990i | −0.859467 | + | 0.624439i | ||||
\(917\) | −1.50992 | + | 4.64706i | −0.0498620 | + | 0.153460i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.5305 | − | 41.6425i | 0.446329 | − | 1.37366i | −0.434690 | − | 0.900580i | \(-0.643142\pi\) |
0.881019 | − | 0.473081i | \(-0.156858\pi\) | |||||||
\(920\) | 1.39878 | − | 0.882787i | 0.0461165 | − | 0.0291046i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.336996 | − | 1.03717i | −0.0110984 | − | 0.0341573i | ||||
\(923\) | −54.7967 | − | 39.8121i | −1.80365 | − | 1.31043i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.59478 | − | 3.58260i | 0.216835 | − | 0.117795i | ||||
\(926\) | 45.3800 | 1.49128 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −12.5463 | − | 38.6135i | −0.411853 | − | 1.26755i | ||||
\(929\) | 0.921674 | + | 2.83662i | 0.0302391 | + | 0.0930665i | 0.965037 | − | 0.262114i | \(-0.0844195\pi\) |
−0.934798 | + | 0.355180i | \(0.884420\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.3786 | − | 38.0974i | 0.405692 | − | 1.24859i | ||||
\(932\) | −6.77263 | −0.221845 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −61.5575 | + | 44.7242i | −2.01422 | + | 1.46342i | ||||
\(935\) | −7.65608 | + | 4.83183i | −0.250381 | + | 0.158018i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.5941 | + | 14.9625i | −0.672780 | + | 0.488803i | −0.870955 | − | 0.491363i | \(-0.836499\pi\) |
0.198175 | + | 0.980167i | \(0.436499\pi\) | |||||||
\(938\) | 8.03746 | − | 5.83956i | 0.262432 | − | 0.190668i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 11.4495 | − | 7.22589i | 0.373441 | − | 0.235683i | ||||
\(941\) | −14.1636 | + | 10.2904i | −0.461719 | + | 0.335458i | −0.794205 | − | 0.607650i | \(-0.792112\pi\) |
0.332486 | + | 0.943108i | \(0.392112\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −26.1620 | −0.851952 | ||||||||
\(944\) | 10.9812 | − | 33.7968i | 0.357409 | − | 1.09999i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.1141 | + | 68.0603i | 0.718992 | + | 2.21283i | ||||
\(947\) | 8.48958 | + | 26.1282i | 0.275874 | + | 0.849054i | 0.988987 | + | 0.148004i | \(0.0472849\pi\) |
−0.713112 | + | 0.701050i | \(0.752715\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −61.4272 | −1.99401 | ||||||||
\(950\) | −52.9724 | + | 28.7771i | −1.71865 | + | 0.933653i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.119314 | − | 0.0866869i | −0.00386700 | − | 0.00280954i | ||||
\(953\) | 8.11556 | + | 24.9771i | 0.262889 | + | 0.809088i | 0.992172 | + | 0.124877i | \(0.0398535\pi\) |
−0.729284 | + | 0.684212i | \(0.760146\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 50.0497 | − | 31.5869i | 1.61957 | − | 1.02213i | ||||
\(956\) | 14.8305 | − | 45.6437i | 0.479654 | − | 1.47622i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −11.6819 | + | 35.9531i | −0.377424 | + | 1.16159i | ||||
\(959\) | −1.62567 | + | 1.18112i | −0.0524956 | + | 0.0381403i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.8168 | + | 10.7651i | 0.477962 | + | 0.347260i | ||||
\(962\) | −12.1757 | + | 8.84613i | −0.392559 | + | 0.285211i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 32.9003 | + | 23.9034i | 1.05965 | + | 0.769878i | ||||
\(965\) | −8.87350 | − | 0.580595i | −0.285648 | − | 0.0186900i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.99684 | − | 15.3787i | 0.160688 | − | 0.494545i | −0.838005 | − | 0.545662i | \(-0.816278\pi\) |
0.998693 | + | 0.0511170i | \(0.0162781\pi\) | |||||||
\(968\) | −0.204808 | −0.00658276 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −18.4680 | + | 46.3055i | −0.592971 | + | 1.48678i | ||||
\(971\) | 13.8119 | + | 42.5085i | 0.443244 | + | 1.36416i | 0.884398 | + | 0.466733i | \(0.154569\pi\) |
−0.441155 | + | 0.897431i | \(0.645431\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.02421 | + | 1.47068i | 0.0648933 | + | 0.0471478i | ||||
\(974\) | 3.63658 | 0.116524 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 31.7211 | 1.01537 | ||||||||
\(977\) | −18.0949 | − | 13.1467i | −0.578907 | − | 0.420600i | 0.259423 | − | 0.965764i | \(-0.416468\pi\) |
−0.838330 | + | 0.545164i | \(0.816468\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.91804 | + | 21.2915i | 0.221102 | + | 0.680481i | ||||
\(980\) | −7.88357 | − | 31.0270i | −0.251831 | − | 0.991120i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −55.3788 | −1.76721 | ||||||||
\(983\) | 1.51247 | − | 4.65491i | 0.0482404 | − | 0.148469i | −0.924035 | − | 0.382308i | \(-0.875129\pi\) |
0.972275 | + | 0.233840i | \(0.0751292\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.8645 | − | 50.6300i | −0.409896 | − | 1.61321i | ||||
\(986\) | −9.70483 | − | 7.05097i | −0.309065 | − | 0.224549i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 50.3515 | − | 36.5825i | 1.60189 | − | 1.16384i | ||||
\(989\) | 24.6962 | + | 17.9428i | 0.785292 | + | 0.570548i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.8113 | − | 7.85485i | 0.343431 | − | 0.249518i | −0.402677 | − | 0.915342i | \(-0.631920\pi\) |
0.746108 | + | 0.665825i | \(0.231920\pi\) | |||||||
\(992\) | 8.90508 | − | 27.4070i | 0.282737 | − | 0.870174i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.33971 | − | 13.3563i | 0.137647 | − | 0.423635i | ||||
\(995\) | −9.89593 | − | 0.647493i | −0.313722 | − | 0.0205269i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.4967 | + | 41.5386i | 0.427445 | + | 1.31554i | 0.900633 | + | 0.434580i | \(0.143103\pi\) |
−0.473188 | + | 0.880961i | \(0.656897\pi\) | |||||||
\(998\) | 17.3657 | + | 12.6169i | 0.549702 | + | 0.399382i | ||||
\(999\) | 0 | 0 |
(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 | 225.2.h.e.91.4 | yes | 16 | |
3.2 | odd | 2 | inner | 225.2.h.e.91.1 | ✓ | 16 | |
25.6 | even | 5 | 5625.2.a.w.1.2 | 8 | |||
25.11 | even | 5 | inner | 225.2.h.e.136.4 | yes | 16 | |
25.19 | even | 10 | 5625.2.a.v.1.7 | 8 | |||
75.11 | odd | 10 | inner | 225.2.h.e.136.1 | yes | 16 | |
75.44 | odd | 10 | 5625.2.a.v.1.2 | 8 | |||
75.56 | odd | 10 | 5625.2.a.w.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.2.h.e.91.1 | ✓ | 16 | 3.2 | odd | 2 | inner | |
225.2.h.e.91.4 | yes | 16 | 1.1 | even | 1 | trivial | |
225.2.h.e.136.1 | yes | 16 | 75.11 | odd | 10 | inner | |
225.2.h.e.136.4 | yes | 16 | 25.11 | even | 5 | inner | |
5625.2.a.v.1.2 | 8 | 75.44 | odd | 10 | |||
5625.2.a.v.1.7 | 8 | 25.19 | even | 10 | |||
5625.2.a.w.1.2 | 8 | 25.6 | even | 5 | |||
5625.2.a.w.1.7 | 8 | 75.56 | odd | 10 |