Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(165,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.x (of order \(12\), degree \(4\), not 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: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 165.7 | ||
Character | \(\chi\) | \(=\) | 784.165 |
Dual form | 784.2.x.o.765.7 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0582062 | − | 1.41302i | 0.0411580 | − | 0.999153i | ||||
\(3\) | 0.523249 | + | 1.95279i | 0.302098 | + | 1.12744i | 0.935415 | + | 0.353552i | \(0.115026\pi\) |
−0.633317 | + | 0.773893i | \(0.718307\pi\) | |||||||
\(4\) | −1.99322 | − | 0.164492i | −0.996612 | − | 0.0822462i | ||||
\(5\) | 0.256983 | − | 0.959072i | 0.114926 | − | 0.428910i | −0.884355 | − | 0.466814i | \(-0.845402\pi\) |
0.999281 | + | 0.0379045i | \(0.0120683\pi\) | |||||||
\(6\) | 2.78978 | − | 0.625694i | 1.13892 | − | 0.255439i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.348448 | + | 2.80688i | −0.123195 | + | 0.992382i | ||||
\(9\) | −0.941530 | + | 0.543593i | −0.313843 | + | 0.181198i | ||||
\(10\) | −1.34023 | − | 0.418944i | −0.423816 | − | 0.132482i | ||||
\(11\) | 1.88773 | − | 0.505816i | 0.569172 | − | 0.152509i | 0.0372551 | − | 0.999306i | \(-0.488139\pi\) |
0.531917 | + | 0.846797i | \(0.321472\pi\) | |||||||
\(12\) | −0.721733 | − | 3.97842i | −0.208346 | − | 1.14847i | ||||
\(13\) | 2.10314 | − | 2.10314i | 0.583307 | − | 0.583307i | −0.352504 | − | 0.935810i | \(-0.614670\pi\) |
0.935810 | + | 0.352504i | \(0.114670\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.00733 | 0.518291 | ||||||||
\(16\) | 3.94588 | + | 0.655741i | 0.986471 | + | 0.163935i | ||||
\(17\) | −2.83885 | + | 4.91704i | −0.688523 | + | 1.19256i | 0.283792 | + | 0.958886i | \(0.408407\pi\) |
−0.972316 | + | 0.233672i | \(0.924926\pi\) | |||||||
\(18\) | 0.713302 | + | 1.36204i | 0.168127 | + | 0.321035i | ||||
\(19\) | −0.616573 | − | 0.165210i | −0.141451 | − | 0.0379018i | 0.187399 | − | 0.982284i | \(-0.439994\pi\) |
−0.328850 | + | 0.944382i | \(0.606661\pi\) | |||||||
\(20\) | −0.669984 | + | 1.86937i | −0.149813 | + | 0.418005i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.604848 | − | 2.69683i | −0.128954 | − | 0.574967i | ||||
\(23\) | 5.92691 | − | 3.42190i | 1.23585 | − | 0.713516i | 0.267604 | − | 0.963529i | \(-0.413768\pi\) |
0.968243 | + | 0.250013i | \(0.0804348\pi\) | |||||||
\(24\) | −5.66358 | + | 0.788251i | −1.15607 | + | 0.160901i | ||||
\(25\) | 3.47635 | + | 2.00707i | 0.695270 | + | 0.401414i | ||||
\(26\) | −2.84936 | − | 3.09419i | −0.558805 | − | 0.606820i | ||||
\(27\) | 2.73445 | + | 2.73445i | 0.526245 | + | 0.526245i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.207295 | + | 0.207295i | −0.0384937 | + | 0.0384937i | −0.726092 | − | 0.687598i | \(-0.758665\pi\) |
0.687598 | + | 0.726092i | \(0.258665\pi\) | |||||||
\(30\) | 0.116839 | − | 2.83639i | 0.0213318 | − | 0.517852i | ||||
\(31\) | 3.94693 | − | 6.83628i | 0.708889 | − | 1.22783i | −0.256381 | − | 0.966576i | \(-0.582530\pi\) |
0.965270 | − | 0.261255i | \(-0.0841365\pi\) | |||||||
\(32\) | 1.15625 | − | 5.53743i | 0.204397 | − | 0.978888i | ||||
\(33\) | 1.97551 | + | 3.42168i | 0.343891 | + | 0.595637i | ||||
\(34\) | 6.78261 | + | 4.29755i | 1.16321 | + | 0.737023i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.96610 | − | 0.928627i | 0.327683 | − | 0.154771i | ||||
\(37\) | −2.57374 | + | 9.60533i | −0.423120 | + | 1.57911i | 0.344873 | + | 0.938649i | \(0.387922\pi\) |
−0.767994 | + | 0.640457i | \(0.778745\pi\) | |||||||
\(38\) | −0.269333 | + | 0.861610i | −0.0436916 | + | 0.139772i | ||||
\(39\) | 5.20747 | + | 3.00653i | 0.833862 | + | 0.481430i | ||||
\(40\) | 2.60246 | + | 1.05551i | 0.411484 | + | 0.166890i | ||||
\(41\) | − | 2.40202i | − | 0.375132i | −0.982252 | − | 0.187566i | \(-0.939940\pi\) | ||
0.982252 | − | 0.187566i | \(-0.0600599\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.65586 | + | 3.65586i | 0.557514 | + | 0.557514i | 0.928599 | − | 0.371085i | \(-0.121014\pi\) |
−0.371085 | + | 0.928599i | \(0.621014\pi\) | |||||||
\(44\) | −3.84587 | + | 0.697687i | −0.579787 | + | 0.105180i | ||||
\(45\) | 0.279388 | + | 1.04269i | 0.0416486 | + | 0.155435i | ||||
\(46\) | −4.49022 | − | 8.57399i | −0.662047 | − | 1.26417i | ||||
\(47\) | 0.144593 | + | 0.250442i | 0.0210910 | + | 0.0365307i | 0.876378 | − | 0.481623i | \(-0.159953\pi\) |
−0.855287 | + | 0.518154i | \(0.826619\pi\) | |||||||
\(48\) | 0.784155 | + | 8.04861i | 0.113183 | + | 1.16172i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.03837 | − | 4.79531i | 0.429690 | − | 0.678159i | ||||
\(51\) | −11.0874 | − | 2.97086i | −1.55254 | − | 0.416003i | ||||
\(52\) | −4.53798 | + | 3.84608i | −0.629305 | + | 0.533356i | ||||
\(53\) | 7.62740 | − | 2.04376i | 1.04770 | − | 0.280732i | 0.306402 | − | 0.951902i | \(-0.400875\pi\) |
0.741303 | + | 0.671171i | \(0.234208\pi\) | |||||||
\(54\) | 4.02298 | − | 3.70466i | 0.547459 | − | 0.504140i | ||||
\(55\) | − | 1.94045i | − | 0.261651i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.29048i | − | 0.170929i | ||||||
\(58\) | 0.280845 | + | 0.304976i | 0.0368767 | + | 0.0400454i | ||||
\(59\) | 13.4543 | − | 3.60507i | 1.75160 | − | 0.469340i | 0.766634 | − | 0.642084i | \(-0.221930\pi\) |
0.984967 | + | 0.172744i | \(0.0552633\pi\) | |||||||
\(60\) | −4.00107 | − | 0.330191i | −0.516535 | − | 0.0426275i | ||||
\(61\) | −3.61701 | − | 0.969174i | −0.463110 | − | 0.124090i | 0.0197171 | − | 0.999806i | \(-0.493723\pi\) |
−0.482827 | + | 0.875716i | \(0.660390\pi\) | |||||||
\(62\) | −9.43003 | − | 5.97498i | −1.19761 | − | 0.758823i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.75717 | − | 1.95611i | −0.969646 | − | 0.244513i | ||||
\(65\) | −1.47659 | − | 2.55754i | −0.183149 | − | 0.317223i | ||||
\(66\) | 4.94987 | − | 2.59226i | 0.609286 | − | 0.319085i | ||||
\(67\) | −2.69202 | − | 10.0468i | −0.328883 | − | 1.22741i | −0.910350 | − | 0.413838i | \(-0.864188\pi\) |
0.581467 | − | 0.813570i | \(-0.302479\pi\) | |||||||
\(68\) | 6.46729 | − | 9.33379i | 0.784274 | − | 1.13189i | ||||
\(69\) | 9.78352 | + | 9.78352i | 1.17780 | + | 1.17780i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.5947i | 1.37603i | 0.725695 | + | 0.688017i | \(0.241518\pi\) | ||||
−0.725695 | + | 0.688017i | \(0.758482\pi\) | |||||||
\(72\) | −1.19773 | − | 2.83218i | −0.141153 | − | 0.333775i | ||||
\(73\) | −0.310772 | − | 0.179424i | −0.0363731 | − | 0.0210000i | 0.481703 | − | 0.876334i | \(-0.340018\pi\) |
−0.518076 | + | 0.855334i | \(0.673352\pi\) | |||||||
\(74\) | 13.4227 | + | 4.19582i | 1.56035 | + | 0.487755i | ||||
\(75\) | −2.10040 | + | 7.83878i | −0.242533 | + | 0.905145i | ||||
\(76\) | 1.20179 | + | 0.430722i | 0.137855 | + | 0.0494073i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.55138 | − | 7.18323i | 0.515342 | − | 0.813341i | ||||
\(79\) | −3.84953 | − | 6.66758i | −0.433106 | − | 0.750161i | 0.564033 | − | 0.825752i | \(-0.309249\pi\) |
−0.997139 | + | 0.0755910i | \(0.975916\pi\) | |||||||
\(80\) | 1.64293 | − | 3.61587i | 0.183685 | − | 0.404267i | ||||
\(81\) | −5.53979 | + | 9.59520i | −0.615532 | + | 1.06613i | ||||
\(82\) | −3.39409 | − | 0.139812i | −0.374814 | − | 0.0154397i | ||||
\(83\) | 0.424001 | − | 0.424001i | 0.0465402 | − | 0.0465402i | −0.683454 | − | 0.729994i | \(-0.739523\pi\) |
0.729994 | + | 0.683454i | \(0.239523\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.98626 | + | 3.98626i | 0.432371 | + | 0.432371i | ||||
\(86\) | 5.37858 | − | 4.95300i | 0.579988 | − | 0.534095i | ||||
\(87\) | −0.513270 | − | 0.296337i | −0.0550283 | − | 0.0317706i | ||||
\(88\) | 0.761988 | + | 5.47488i | 0.0812282 | + | 0.583625i | ||||
\(89\) | −15.2323 | + | 8.79437i | −1.61462 | + | 0.932201i | −0.626340 | + | 0.779550i | \(0.715448\pi\) |
−0.988280 | + | 0.152652i | \(0.951219\pi\) | |||||||
\(90\) | 1.48960 | − | 0.334088i | 0.157017 | − | 0.0352160i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −12.3765 | + | 5.84569i | −1.29034 | + | 0.609455i | ||||
\(93\) | 15.4150 | + | 4.13045i | 1.59847 | + | 0.428308i | ||||
\(94\) | 0.362294 | − | 0.189734i | 0.0373678 | − | 0.0195696i | ||||
\(95\) | −0.316897 | + | 0.548881i | −0.0325129 | + | 0.0563140i | ||||
\(96\) | 11.4184 | − | 0.639544i | 1.16539 | − | 0.0652732i | ||||
\(97\) | −12.2678 | −1.24560 | −0.622802 | − | 0.782379i | \(-0.714006\pi\) | ||||
−0.622802 | + | 0.782379i | \(0.714006\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.50240 | + | 1.50240i | −0.150997 | + | 0.150997i | ||||
\(100\) | −6.59899 | − | 4.57237i | −0.659899 | − | 0.457237i | ||||
\(101\) | −1.16857 | + | 0.313118i | −0.116277 | + | 0.0311564i | −0.316488 | − | 0.948596i | \(-0.602504\pi\) |
0.200211 | + | 0.979753i | \(0.435837\pi\) | |||||||
\(102\) | −4.84322 | + | 15.4937i | −0.479550 | + | 1.53411i | ||||
\(103\) | 5.06181 | − | 2.92244i | 0.498755 | − | 0.287956i | −0.229444 | − | 0.973322i | \(-0.573691\pi\) |
0.728199 | + | 0.685365i | \(0.240357\pi\) | |||||||
\(104\) | 5.17043 | + | 6.63611i | 0.507003 | + | 0.650724i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.44390 | − | 10.8966i | −0.237372 | − | 1.05837i | ||||
\(107\) | −0.971295 | + | 3.62492i | −0.0938987 | + | 0.350435i | −0.996850 | − | 0.0793079i | \(-0.974729\pi\) |
0.902952 | + | 0.429742i | \(0.141396\pi\) | |||||||
\(108\) | −5.00058 | − | 5.90017i | −0.481181 | − | 0.567744i | ||||
\(109\) | −2.59283 | − | 9.67656i | −0.248348 | − | 0.926846i | −0.971671 | − | 0.236337i | \(-0.924053\pi\) |
0.723323 | − | 0.690509i | \(-0.242614\pi\) | |||||||
\(110\) | −2.74189 | − | 0.112946i | −0.261429 | − | 0.0107690i | ||||
\(111\) | −20.1039 | −1.90818 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.07461 | 0.477379 | 0.238689 | − | 0.971096i | \(-0.423282\pi\) | ||||
0.238689 | + | 0.971096i | \(0.423282\pi\) | |||||||
\(114\) | −1.82347 | − | 0.0751142i | −0.170784 | − | 0.00703509i | ||||
\(115\) | −1.75874 | − | 6.56370i | −0.164003 | − | 0.612069i | ||||
\(116\) | 0.447283 | − | 0.379086i | 0.0415292 | − | 0.0351973i | ||||
\(117\) | −0.836919 | + | 3.12342i | −0.0773732 | + | 0.288761i | ||||
\(118\) | −4.31089 | − | 19.2210i | −0.396850 | − | 1.76943i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.699452 | + | 5.63435i | −0.0638509 | + | 0.514343i | ||||
\(121\) | −6.21861 | + | 3.59031i | −0.565328 | + | 0.326392i | ||||
\(122\) | −1.57999 | + | 5.05447i | −0.143046 | + | 0.457611i | ||||
\(123\) | 4.69064 | − | 1.25685i | 0.422941 | − | 0.113327i | ||||
\(124\) | −8.99162 | + | 12.9770i | −0.807472 | + | 1.16537i | ||||
\(125\) | 6.32873 | − | 6.32873i | 0.566059 | − | 0.566059i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.1710 | −0.991270 | −0.495635 | − | 0.868531i | \(-0.665065\pi\) | ||||
−0.495635 | + | 0.868531i | \(0.665065\pi\) | |||||||
\(128\) | −3.21552 | + | 10.8471i | −0.284215 | + | 0.958761i | ||||
\(129\) | −5.22621 | + | 9.05207i | −0.460142 | + | 0.796990i | ||||
\(130\) | −3.69978 | + | 1.93758i | −0.324492 | + | 0.169937i | ||||
\(131\) | −12.1789 | − | 3.26332i | −1.06407 | − | 0.285118i | −0.316017 | − | 0.948753i | \(-0.602346\pi\) |
−0.748056 | + | 0.663636i | \(0.769012\pi\) | |||||||
\(132\) | −3.37478 | − | 7.14512i | −0.293737 | − | 0.621903i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −14.3529 | + | 3.21909i | −1.23990 | + | 0.278087i | ||||
\(135\) | 3.32524 | − | 1.91983i | 0.286191 | − | 0.165233i | ||||
\(136\) | −12.8124 | − | 9.68166i | −1.09865 | − | 0.830196i | ||||
\(137\) | −14.0325 | − | 8.10166i | −1.19888 | − | 0.692172i | −0.238572 | − | 0.971125i | \(-0.576679\pi\) |
−0.960305 | + | 0.278953i | \(0.910013\pi\) | |||||||
\(138\) | 14.3937 | − | 13.2548i | 1.22527 | − | 1.12832i | ||||
\(139\) | −10.5018 | − | 10.5018i | −0.890748 | − | 0.890748i | 0.103846 | − | 0.994593i | \(-0.466885\pi\) |
−0.994593 | + | 0.103846i | \(0.966885\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.413403 | + | 0.413403i | −0.0348148 | + | 0.0348148i | ||||
\(142\) | 16.3834 | + | 0.674881i | 1.37487 | + | 0.0566348i | ||||
\(143\) | 2.90636 | − | 5.03397i | 0.243042 | − | 0.420961i | ||||
\(144\) | −4.07162 | + | 1.52755i | −0.339302 | + | 0.127296i | ||||
\(145\) | 0.145539 | + | 0.252082i | 0.0120864 | + | 0.0209342i | ||||
\(146\) | −0.271618 | + | 0.428682i | −0.0224793 | + | 0.0354780i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.71005 | − | 18.7222i | 0.551562 | − | 1.53896i | ||||
\(149\) | 2.57749 | − | 9.61931i | 0.211156 | − | 0.788045i | −0.776328 | − | 0.630329i | \(-0.782920\pi\) |
0.987484 | − | 0.157716i | \(-0.0504132\pi\) | |||||||
\(150\) | 10.9541 | + | 3.42416i | 0.894395 | + | 0.279581i | ||||
\(151\) | −8.97638 | − | 5.18252i | −0.730487 | − | 0.421747i | 0.0881130 | − | 0.996110i | \(-0.471916\pi\) |
−0.818600 | + | 0.574363i | \(0.805250\pi\) | |||||||
\(152\) | 0.678569 | − | 1.67308i | 0.0550392 | − | 0.135705i | ||||
\(153\) | − | 6.17272i | − | 0.499035i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.54219 | − | 5.54219i | −0.445159 | − | 0.445159i | ||||
\(156\) | −9.88509 | − | 6.84928i | −0.791441 | − | 0.548381i | ||||
\(157\) | 1.06781 | + | 3.98512i | 0.0852205 | + | 0.318047i | 0.995356 | − | 0.0962637i | \(-0.0306892\pi\) |
−0.910135 | + | 0.414311i | \(0.864023\pi\) | |||||||
\(158\) | −9.64546 | + | 5.05135i | −0.767351 | + | 0.401864i | ||||
\(159\) | 7.98206 | + | 13.8253i | 0.633019 | + | 1.09642i | ||||
\(160\) | −5.01366 | − | 2.53195i | −0.396364 | − | 0.200168i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 13.2357 | + | 8.38631i | 1.03990 | + | 0.658891i | ||||
\(163\) | −7.98280 | − | 2.13899i | −0.625261 | − | 0.167538i | −0.0677429 | − | 0.997703i | \(-0.521580\pi\) |
−0.557518 | + | 0.830165i | \(0.688246\pi\) | |||||||
\(164\) | −0.395114 | + | 4.78776i | −0.0308532 | + | 0.373861i | ||||
\(165\) | 3.78930 | − | 1.01534i | 0.294997 | − | 0.0790442i | ||||
\(166\) | −0.574440 | − | 0.623799i | −0.0445852 | − | 0.0484162i | ||||
\(167\) | 8.92669i | 0.690768i | 0.938462 | + | 0.345384i | \(0.112251\pi\) | ||||
−0.938462 | + | 0.345384i | \(0.887749\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.15359i | 0.319507i | ||||||||
\(170\) | 5.86467 | − | 5.40062i | 0.449800 | − | 0.414209i | ||||
\(171\) | 0.670329 | − | 0.179614i | 0.0512613 | − | 0.0137354i | ||||
\(172\) | −6.68559 | − | 7.88832i | −0.509772 | − | 0.601478i | ||||
\(173\) | 5.26383 | + | 1.41044i | 0.400202 | + | 0.107234i | 0.453305 | − | 0.891355i | \(-0.350245\pi\) |
−0.0531037 | + | 0.998589i | \(0.516911\pi\) | |||||||
\(174\) | −0.448604 | + | 0.708010i | −0.0340086 | + | 0.0536741i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.78045 | − | 0.758029i | 0.586473 | − | 0.0571386i | ||||
\(177\) | 14.0799 | + | 24.3871i | 1.05831 | + | 1.83305i | ||||
\(178\) | 11.5400 | + | 22.0354i | 0.864957 | + | 1.65162i | ||||
\(179\) | 2.52526 | + | 9.42440i | 0.188747 | + | 0.704413i | 0.993797 | + | 0.111207i | \(0.0354715\pi\) |
−0.805050 | + | 0.593206i | \(0.797862\pi\) | |||||||
\(180\) | −0.385368 | − | 2.12427i | −0.0287236 | − | 0.158334i | ||||
\(181\) | 8.42976 | + | 8.42976i | 0.626579 | + | 0.626579i | 0.947206 | − | 0.320627i | \(-0.103894\pi\) |
−0.320627 | + | 0.947206i | \(0.603894\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 7.57038i | − | 0.559619i | ||||||
\(184\) | 7.53966 | + | 17.8285i | 0.555831 | + | 1.31433i | ||||
\(185\) | 8.55080 | + | 4.93680i | 0.628667 | + | 0.362961i | ||||
\(186\) | 6.73364 | − | 21.5413i | 0.493734 | − | 1.57948i | ||||
\(187\) | −2.87187 | + | 10.7180i | −0.210012 | + | 0.783776i | ||||
\(188\) | −0.247010 | − | 0.522971i | −0.0180150 | − | 0.0381416i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.757132 | + | 0.479728i | 0.0549282 | + | 0.0348032i | ||||
\(191\) | 2.46522 | + | 4.26989i | 0.178377 | + | 0.308958i | 0.941325 | − | 0.337502i | \(-0.109582\pi\) |
−0.762948 | + | 0.646460i | \(0.776249\pi\) | |||||||
\(192\) | −0.239061 | − | 16.1717i | −0.0172527 | − | 1.16709i | ||||
\(193\) | −10.9543 | + | 18.9735i | −0.788510 | + | 1.36574i | 0.138370 | + | 0.990381i | \(0.455814\pi\) |
−0.926880 | + | 0.375358i | \(0.877520\pi\) | |||||||
\(194\) | −0.714061 | + | 17.3346i | −0.0512666 | + | 1.24455i | ||||
\(195\) | 4.22171 | − | 4.22171i | 0.302323 | − | 0.302323i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.61984 | + | 7.61984i | 0.542891 | + | 0.542891i | 0.924375 | − | 0.381484i | \(-0.124587\pi\) |
−0.381484 | + | 0.924375i | \(0.624587\pi\) | |||||||
\(198\) | 2.03546 | + | 2.21036i | 0.144654 | + | 0.157083i | ||||
\(199\) | −3.09710 | − | 1.78811i | −0.219547 | − | 0.126756i | 0.386193 | − | 0.922418i | \(-0.373790\pi\) |
−0.605741 | + | 0.795662i | \(0.707123\pi\) | |||||||
\(200\) | −6.84494 | + | 9.05834i | −0.484010 | + | 0.640521i | ||||
\(201\) | 18.2106 | − | 10.5139i | 1.28448 | − | 0.741595i | ||||
\(202\) | 0.374422 | + | 1.66944i | 0.0263443 | + | 0.117461i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 21.6110 | + | 7.74537i | 1.51307 | + | 0.542285i | ||||
\(205\) | −2.30371 | − | 0.617276i | −0.160898 | − | 0.0431125i | ||||
\(206\) | −3.83482 | − | 7.32252i | −0.267185 | − | 0.510184i | ||||
\(207\) | −3.72024 | + | 6.44365i | −0.258575 | + | 0.447865i | ||||
\(208\) | 9.67787 | − | 6.91964i | 0.671040 | − | 0.479791i | ||||
\(209\) | −1.24749 | −0.0862906 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.33737 | − | 7.33737i | 0.505126 | − | 0.505126i | −0.407901 | − | 0.913026i | \(-0.633739\pi\) |
0.913026 | + | 0.407901i | \(0.133739\pi\) | |||||||
\(212\) | −15.5393 | + | 2.81901i | −1.06724 | + | 0.193611i | ||||
\(213\) | −22.6420 | + | 6.06690i | −1.55140 | + | 0.415697i | ||||
\(214\) | 5.06554 | + | 1.58345i | 0.346273 | + | 0.108242i | ||||
\(215\) | 4.44573 | − | 2.56674i | 0.303196 | − | 0.175050i | ||||
\(216\) | −8.62809 | + | 6.72246i | −0.587067 | + | 0.457406i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −13.8240 | + | 3.10047i | −0.936283 | + | 0.209990i | ||||
\(219\) | 0.187767 | − | 0.700757i | 0.0126881 | − | 0.0473528i | ||||
\(220\) | −0.319190 | + | 3.86776i | −0.0215198 | + | 0.260764i | ||||
\(221\) | 4.37072 | + | 16.3117i | 0.294006 | + | 1.09725i | ||||
\(222\) | −1.17017 | + | 28.4071i | −0.0785368 | + | 1.90656i | ||||
\(223\) | −4.26037 | −0.285295 | −0.142648 | − | 0.989774i | \(-0.545562\pi\) | ||||
−0.142648 | + | 0.989774i | \(0.545562\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.36411 | −0.290941 | ||||||||
\(226\) | 0.295373 | − | 7.17049i | 0.0196479 | − | 0.476974i | ||||
\(227\) | −1.25223 | − | 4.67340i | −0.0831136 | − | 0.310184i | 0.911837 | − | 0.410553i | \(-0.134664\pi\) |
−0.994950 | + | 0.100369i | \(0.967998\pi\) | |||||||
\(228\) | −0.212275 | + | 2.57222i | −0.0140583 | + | 0.170350i | ||||
\(229\) | 5.07737 | − | 18.9490i | 0.335522 | − | 1.25218i | −0.567781 | − | 0.823180i | \(-0.692198\pi\) |
0.903302 | − | 0.429005i | \(-0.141136\pi\) | |||||||
\(230\) | −9.37698 | + | 2.10308i | −0.618300 | + | 0.138673i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.509620 | − | 0.654083i | −0.0334582 | − | 0.0429427i | ||||
\(233\) | −4.38681 | + | 2.53273i | −0.287390 | + | 0.165925i | −0.636764 | − | 0.771059i | \(-0.719727\pi\) |
0.349374 | + | 0.936983i | \(0.386394\pi\) | |||||||
\(234\) | 4.36473 | + | 1.36438i | 0.285331 | + | 0.0891924i | ||||
\(235\) | 0.277349 | − | 0.0743155i | 0.0180923 | − | 0.00484781i | ||||
\(236\) | −27.4104 | + | 4.97258i | −1.78427 | + | 0.323687i | ||||
\(237\) | 11.0061 | − | 11.0061i | 0.714925 | − | 0.714925i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.32494 | −0.603181 | −0.301590 | − | 0.953438i | \(-0.597517\pi\) | ||||
−0.301590 | + | 0.953438i | \(0.597517\pi\) | |||||||
\(240\) | 7.92071 | + | 1.31629i | 0.511279 | + | 0.0849662i | ||||
\(241\) | 12.8663 | − | 22.2850i | 0.828789 | − | 1.43550i | −0.0702006 | − | 0.997533i | \(-0.522364\pi\) |
0.898989 | − | 0.437971i | \(-0.144303\pi\) | |||||||
\(242\) | 4.71121 | + | 8.99596i | 0.302848 | + | 0.578282i | ||||
\(243\) | −10.4301 | − | 2.79475i | −0.669093 | − | 0.179283i | ||||
\(244\) | 7.05008 | + | 2.52675i | 0.451335 | + | 0.161759i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.50293 | − | 6.70110i | −0.0958232 | − | 0.427247i | ||||
\(247\) | −1.64420 | + | 0.949280i | −0.104618 | + | 0.0604012i | ||||
\(248\) | 17.8133 | + | 13.4606i | 1.13115 | + | 0.854752i | ||||
\(249\) | 1.04984 | + | 0.606128i | 0.0665312 | + | 0.0384118i | ||||
\(250\) | −8.57422 | − | 9.31097i | −0.542282 | − | 0.588877i | ||||
\(251\) | 3.64372 | + | 3.64372i | 0.229990 | + | 0.229990i | 0.812688 | − | 0.582699i | \(-0.198003\pi\) |
−0.582699 | + | 0.812688i | \(0.698003\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.45755 | − | 9.45755i | 0.594591 | − | 0.594591i | ||||
\(254\) | −0.650224 | + | 15.7849i | −0.0407987 | + | 0.990430i | ||||
\(255\) | −5.69853 | + | 9.87014i | −0.356856 | + | 0.618092i | ||||
\(256\) | 15.1400 | + | 5.17495i | 0.946251 | + | 0.323435i | ||||
\(257\) | −1.87774 | − | 3.25234i | −0.117130 | − | 0.202875i | 0.801499 | − | 0.597996i | \(-0.204036\pi\) |
−0.918629 | + | 0.395121i | \(0.870703\pi\) | |||||||
\(258\) | 12.4865 | + | 7.91160i | 0.777376 | + | 0.492555i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.52249 | + | 5.34063i | 0.156438 | + | 0.331212i | ||||
\(261\) | 0.0824903 | − | 0.307858i | 0.00510602 | − | 0.0190559i | ||||
\(262\) | −5.32001 | + | 17.0190i | −0.328671 | + | 1.05144i | ||||
\(263\) | 16.3252 | + | 9.42534i | 1.00665 | + | 0.581191i | 0.910210 | − | 0.414147i | \(-0.135920\pi\) |
0.0964430 | + | 0.995339i | \(0.469253\pi\) | |||||||
\(264\) | −10.2926 | + | 4.35273i | −0.633466 | + | 0.267892i | ||||
\(265\) | − | 7.84044i | − | 0.481634i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −25.1439 | − | 25.1439i | −1.53878 | − | 1.53878i | ||||
\(268\) | 3.71319 | + | 20.4683i | 0.226819 | + | 1.25030i | ||||
\(269\) | 4.43839 | + | 16.5643i | 0.270614 | + | 1.00994i | 0.958724 | + | 0.284338i | \(0.0917737\pi\) |
−0.688111 | + | 0.725606i | \(0.741560\pi\) | |||||||
\(270\) | −2.51920 | − | 4.81036i | −0.153313 | − | 0.292749i | ||||
\(271\) | 2.65608 | + | 4.60046i | 0.161345 | + | 0.279458i | 0.935351 | − | 0.353720i | \(-0.115083\pi\) |
−0.774006 | + | 0.633178i | \(0.781750\pi\) | |||||||
\(272\) | −14.4261 | + | 17.5405i | −0.874711 | + | 1.06355i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.2646 | + | 19.3566i | −0.740929 | + | 1.16937i | ||||
\(275\) | 7.57761 | + | 2.03042i | 0.456947 | + | 0.122439i | ||||
\(276\) | −17.8914 | − | 21.1101i | −1.07694 | − | 1.27068i | ||||
\(277\) | 14.6832 | − | 3.93434i | 0.882226 | − | 0.236392i | 0.210859 | − | 0.977517i | \(-0.432374\pi\) |
0.671367 | + | 0.741125i | \(0.265707\pi\) | |||||||
\(278\) | −15.4504 | + | 14.2279i | −0.926654 | + | 0.853331i | ||||
\(279\) | 8.58208i | 0.513795i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 3.15786i | − | 0.188382i | −0.995554 | − | 0.0941910i | \(-0.969974\pi\) | ||
0.995554 | − | 0.0941910i | \(-0.0300264\pi\) | |||||||
\(282\) | 0.560082 | + | 0.608207i | 0.0333524 | + | 0.0362182i | ||||
\(283\) | −13.6357 | + | 3.65368i | −0.810559 | + | 0.217189i | −0.640215 | − | 0.768196i | \(-0.721155\pi\) |
−0.170344 | + | 0.985385i | \(0.554488\pi\) | |||||||
\(284\) | 1.90723 | − | 23.1108i | 0.113174 | − | 1.37137i | ||||
\(285\) | −1.23767 | − | 0.331632i | −0.0733131 | − | 0.0196442i | ||||
\(286\) | −6.94390 | − | 4.39974i | −0.410602 | − | 0.260162i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.92146 | + | 5.84218i | 0.113223 | + | 0.344254i | ||||
\(289\) | −7.61819 | − | 13.1951i | −0.448129 | − | 0.776182i | ||||
\(290\) | 0.364666 | − | 0.190977i | 0.0214140 | − | 0.0112145i | ||||
\(291\) | −6.41911 | − | 23.9564i | −0.376295 | − | 1.40435i | ||||
\(292\) | 0.589925 | + | 0.408753i | 0.0345227 | + | 0.0239204i | ||||
\(293\) | 10.9335 | + | 10.9335i | 0.638743 | + | 0.638743i | 0.950245 | − | 0.311502i | \(-0.100832\pi\) |
−0.311502 | + | 0.950245i | \(0.600832\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 13.8301i | − | 0.805219i | ||||||
\(296\) | −26.0642 | − | 10.5711i | −1.51495 | − | 0.614435i | ||||
\(297\) | 6.54503 | + | 3.77878i | 0.379781 | + | 0.219267i | ||||
\(298\) | −13.4422 | − | 4.20193i | −0.778686 | − | 0.243411i | ||||
\(299\) | 5.26839 | − | 19.6619i | 0.304679 | − | 1.13708i | ||||
\(300\) | 5.47598 | − | 15.2789i | 0.316156 | − | 0.882131i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −7.84545 | + | 12.3821i | −0.451455 | + | 0.712510i | ||||
\(303\) | −1.22291 | − | 2.11814i | −0.0702543 | − | 0.121684i | ||||
\(304\) | −2.32459 | − | 1.05621i | −0.133324 | − | 0.0605779i | ||||
\(305\) | −1.85902 | + | 3.21991i | −0.106447 | + | 0.184371i | ||||
\(306\) | −8.72215 | − | 0.359291i | −0.498612 | − | 0.0205393i | ||||
\(307\) | 14.7735 | − | 14.7735i | 0.843170 | − | 0.843170i | −0.146100 | − | 0.989270i | \(-0.546672\pi\) |
0.989270 | + | 0.146100i | \(0.0466721\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.35550 | + | 8.35550i | 0.475328 | + | 0.475328i | ||||
\(310\) | −8.15379 | + | 7.50861i | −0.463104 | + | 0.426460i | ||||
\(311\) | −7.56549 | − | 4.36794i | −0.429000 | − | 0.247683i | 0.269921 | − | 0.962883i | \(-0.413002\pi\) |
−0.698920 | + | 0.715199i | \(0.746336\pi\) | |||||||
\(312\) | −10.2535 | + | 13.5691i | −0.580491 | + | 0.768200i | ||||
\(313\) | 3.56615 | − | 2.05892i | 0.201571 | − | 0.116377i | −0.395817 | − | 0.918329i | \(-0.629539\pi\) |
0.597388 | + | 0.801952i | \(0.296205\pi\) | |||||||
\(314\) | 5.69319 | − | 1.27687i | 0.321285 | − | 0.0720581i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.57621 | + | 13.9232i | 0.369940 | + | 0.783241i | ||||
\(317\) | −23.5962 | − | 6.32257i | −1.32529 | − | 0.355111i | −0.474335 | − | 0.880345i | \(-0.657311\pi\) |
−0.850958 | + | 0.525234i | \(0.823978\pi\) | |||||||
\(318\) | 20.0000 | − | 10.4741i | 1.12155 | − | 0.587356i | ||||
\(319\) | −0.286463 | + | 0.496169i | −0.0160389 | + | 0.0277801i | ||||
\(320\) | −3.86950 | + | 6.93700i | −0.216312 | + | 0.387790i | ||||
\(321\) | −7.58695 | −0.423462 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.56271 | − | 2.56271i | 0.142593 | − | 0.142593i | ||||
\(324\) | 12.6204 | − | 18.2141i | 0.701133 | − | 1.01190i | ||||
\(325\) | 11.5324 | − | 3.09010i | 0.639703 | − | 0.171408i | ||||
\(326\) | −3.48707 | + | 11.1553i | −0.193131 | + | 0.617836i | ||||
\(327\) | 17.5396 | − | 10.1265i | 0.969943 | − | 0.559997i | ||||
\(328\) | 6.74218 | + | 0.836979i | 0.372274 | + | 0.0462144i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.21413 | − | 5.41344i | −0.0668357 | − | 0.298000i | ||||
\(331\) | 1.89039 | − | 7.05503i | 0.103905 | − | 0.387780i | −0.894313 | − | 0.447441i | \(-0.852335\pi\) |
0.998219 | + | 0.0596615i | \(0.0190021\pi\) | |||||||
\(332\) | −0.914874 | + | 0.775384i | −0.0502102 | + | 0.0425547i | ||||
\(333\) | −2.79813 | − | 10.4428i | −0.153337 | − | 0.572260i | ||||
\(334\) | 12.6135 | + | 0.519588i | 0.690182 | + | 0.0284306i | ||||
\(335\) | −10.3274 | −0.564245 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.53985 | −0.519669 | −0.259834 | − | 0.965653i | \(-0.583668\pi\) | ||||
−0.259834 | + | 0.965653i | \(0.583668\pi\) | |||||||
\(338\) | 5.86908 | + | 0.241765i | 0.319236 | + | 0.0131503i | ||||
\(339\) | 2.65528 | + | 9.90965i | 0.144215 | + | 0.538218i | ||||
\(340\) | −7.28980 | − | 8.60122i | −0.395345 | − | 0.466467i | ||||
\(341\) | 3.99283 | − | 14.9015i | 0.216224 | − | 0.806959i | ||||
\(342\) | −0.214780 | − | 0.957639i | −0.0116140 | − | 0.0517832i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −11.5355 | + | 8.98769i | −0.621950 | + | 0.484584i | ||||
\(345\) | 11.8973 | − | 6.86890i | 0.640528 | − | 0.369809i | ||||
\(346\) | 2.29936 | − | 7.35578i | 0.123614 | − | 0.395449i | ||||
\(347\) | −8.82567 | + | 2.36483i | −0.473787 | + | 0.126951i | −0.487808 | − | 0.872951i | \(-0.662203\pi\) |
0.0140212 | + | 0.999902i | \(0.495537\pi\) | |||||||
\(348\) | 0.974317 | + | 0.675094i | 0.0522289 | + | 0.0361889i | ||||
\(349\) | −24.4862 | + | 24.4862i | −1.31072 | + | 1.31072i | −0.389831 | + | 0.920887i | \(0.627467\pi\) |
−0.920887 | + | 0.389831i | \(0.872533\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.5019 | 0.613925 | ||||||||
\(352\) | −0.618236 | − | 11.0380i | −0.0329521 | − | 0.588328i | ||||
\(353\) | −13.0352 | + | 22.5776i | −0.693793 | + | 1.20168i | 0.276793 | + | 0.960930i | \(0.410728\pi\) |
−0.970586 | + | 0.240755i | \(0.922605\pi\) | |||||||
\(354\) | 35.2789 | − | 18.4756i | 1.87505 | − | 0.981969i | ||||
\(355\) | 11.1201 | + | 2.97963i | 0.590194 | + | 0.158142i | ||||
\(356\) | 31.8080 | − | 15.0236i | 1.68582 | − | 0.796247i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.4638 | − | 3.01967i | 0.711584 | − | 0.159595i | ||||
\(359\) | 3.01740 | − | 1.74210i | 0.159252 | − | 0.0919443i | −0.418256 | − | 0.908329i | \(-0.637358\pi\) |
0.577508 | + | 0.816385i | \(0.304025\pi\) | |||||||
\(360\) | −3.02406 | + | 0.420885i | −0.159382 | + | 0.0221826i | ||||
\(361\) | −16.1016 | − | 9.29627i | −0.847453 | − | 0.489277i | ||||
\(362\) | 12.4020 | − | 11.4207i | 0.651837 | − | 0.600259i | ||||
\(363\) | −10.2650 | − | 10.2650i | −0.538773 | − | 0.538773i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.251944 | + | 0.251944i | −0.0131873 | + | 0.0131873i | ||||
\(366\) | −10.6971 | − | 0.440643i | −0.559144 | − | 0.0230328i | ||||
\(367\) | 12.2280 | − | 21.1796i | 0.638298 | − | 1.10556i | −0.347508 | − | 0.937677i | \(-0.612972\pi\) |
0.985806 | − | 0.167888i | \(-0.0536946\pi\) | |||||||
\(368\) | 25.6308 | − | 9.61592i | 1.33610 | − | 0.501264i | ||||
\(369\) | 1.30572 | + | 2.26157i | 0.0679730 | + | 0.117733i | ||||
\(370\) | 7.47349 | − | 11.7951i | 0.388528 | − | 0.613196i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −30.0462 | − | 10.7686i | −1.55782 | − | 0.558324i | ||||
\(373\) | 9.51200 | − | 35.4993i | 0.492513 | − | 1.83808i | −0.0510246 | − | 0.998697i | \(-0.516249\pi\) |
0.543537 | − | 0.839385i | \(-0.317085\pi\) | |||||||
\(374\) | 14.9775 | + | 4.68185i | 0.774469 | + | 0.242093i | ||||
\(375\) | 15.6702 | + | 9.04719i | 0.809206 | + | 0.467195i | ||||
\(376\) | −0.753343 | + | 0.318588i | −0.0388507 | + | 0.0164299i | ||||
\(377\) | 0.871940i | 0.0449072i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.5183 | + | 18.5183i | 0.951222 | + | 0.951222i | 0.998864 | − | 0.0476420i | \(-0.0151707\pi\) |
−0.0476420 | + | 0.998864i | \(0.515171\pi\) | |||||||
\(380\) | 0.721933 | − | 1.04192i | 0.0370344 | − | 0.0534492i | ||||
\(381\) | −5.84524 | − | 21.8147i | −0.299461 | − | 1.11760i | ||||
\(382\) | 6.17690 | − | 3.23486i | 0.316038 | − | 0.165510i | ||||
\(383\) | −7.89785 | − | 13.6795i | −0.403562 | − | 0.698989i | 0.590591 | − | 0.806971i | \(-0.298895\pi\) |
−0.994153 | + | 0.107982i | \(0.965561\pi\) | |||||||
\(384\) | −22.8647 | − | 0.603494i | −1.16681 | − | 0.0307969i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 26.1722 | + | 16.5830i | 1.33213 | + | 0.844053i | ||||
\(387\) | −5.42940 | − | 1.45480i | −0.275992 | − | 0.0739519i | ||||
\(388\) | 24.4524 | + | 2.01796i | 1.24138 | + | 0.102446i | ||||
\(389\) | −5.50707 | + | 1.47562i | −0.279220 | + | 0.0748167i | −0.395711 | − | 0.918375i | \(-0.629502\pi\) |
0.116492 | + | 0.993192i | \(0.462835\pi\) | |||||||
\(390\) | −5.71961 | − | 6.21107i | −0.289624 | − | 0.314510i | ||||
\(391\) | 38.8572i | 1.96509i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 25.4903i | − | 1.28582i | ||||||
\(394\) | 11.2105 | − | 10.3234i | 0.564776 | − | 0.520087i | ||||
\(395\) | −7.38395 | + | 1.97852i | −0.371527 | + | 0.0995503i | ||||
\(396\) | 3.24175 | − | 2.74748i | 0.162904 | − | 0.138066i | ||||
\(397\) | 0.971927 | + | 0.260427i | 0.0487796 | + | 0.0130705i | 0.283126 | − | 0.959083i | \(-0.408628\pi\) |
−0.234347 | + | 0.972153i | \(0.575295\pi\) | |||||||
\(398\) | −2.70690 | + | 4.27216i | −0.135684 | + | 0.214144i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 12.4012 | + | 10.1993i | 0.620058 | + | 0.509963i | ||||
\(401\) | 8.70318 | + | 15.0744i | 0.434616 | + | 0.752777i | 0.997264 | − | 0.0739192i | \(-0.0235507\pi\) |
−0.562648 | + | 0.826697i | \(0.690217\pi\) | |||||||
\(402\) | −13.7964 | − | 26.3439i | −0.688100 | − | 1.31391i | ||||
\(403\) | −6.07671 | − | 22.6786i | −0.302703 | − | 1.12970i | ||||
\(404\) | 2.38073 | − | 0.431893i | 0.118446 | − | 0.0214875i | ||||
\(405\) | 7.77886 | + | 7.77886i | 0.386535 | + | 0.386535i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.4341i | 0.963313i | ||||||||
\(408\) | 12.2022 | − | 30.0858i | 0.604100 | − | 1.48947i | ||||
\(409\) | −33.0605 | − | 19.0875i | −1.63474 | − | 0.943815i | −0.982605 | − | 0.185709i | \(-0.940542\pi\) |
−0.652131 | − | 0.758106i | \(-0.726125\pi\) | |||||||
\(410\) | −1.00631 | + | 3.21924i | −0.0496982 | + | 0.158987i | ||||
\(411\) | 8.47837 | − | 31.6417i | 0.418207 | − | 1.56077i | ||||
\(412\) | −10.5700 | + | 4.99245i | −0.520749 | + | 0.245960i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 8.88843 | + | 5.63182i | 0.436843 | + | 0.276789i | ||||
\(415\) | −0.297687 | − | 0.515608i | −0.0146129 | − | 0.0253102i | ||||
\(416\) | −9.21424 | − | 14.0777i | −0.451765 | − | 0.690218i | ||||
\(417\) | 15.0127 | − | 26.0028i | 0.735176 | − | 1.27336i | ||||
\(418\) | −0.0726116 | + | 1.76272i | −0.00355155 | + | 0.0862175i | ||||
\(419\) | 27.0004 | − | 27.0004i | 1.31905 | − | 1.31905i | 0.404529 | − | 0.914525i | \(-0.367435\pi\) |
0.914525 | − | 0.404529i | \(-0.132565\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.1472 | − | 19.1472i | −0.933175 | − | 0.933175i | 0.0647277 | − | 0.997903i | \(-0.479382\pi\) |
−0.997903 | + | 0.0647277i | \(0.979382\pi\) | |||||||
\(422\) | −9.94074 | − | 10.7949i | −0.483908 | − | 0.525488i | ||||
\(423\) | −0.272276 | − | 0.157199i | −0.0132385 | − | 0.00764327i | ||||
\(424\) | 3.07883 | + | 22.1214i | 0.149521 | + | 1.07431i | ||||
\(425\) | −19.7377 | + | 11.3956i | −0.957419 | + | 0.552766i | ||||
\(426\) | 7.25471 | + | 32.3466i | 0.351492 | + | 1.56720i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2.53228 | − | 7.06551i | 0.122402 | − | 0.341524i | ||||
\(429\) | 11.3510 | + | 3.04150i | 0.548033 | + | 0.146845i | ||||
\(430\) | −3.36808 | − | 6.43128i | −0.162423 | − | 0.310144i | ||||
\(431\) | −0.628555 | + | 1.08869i | −0.0302764 | + | 0.0524403i | −0.880767 | − | 0.473551i | \(-0.842972\pi\) |
0.850490 | + | 0.525991i | \(0.176305\pi\) | |||||||
\(432\) | 8.99674 | + | 12.5829i | 0.432856 | + | 0.605396i | ||||
\(433\) | 9.16885 | 0.440627 | 0.220313 | − | 0.975429i | \(-0.429292\pi\) | ||||
0.220313 | + | 0.975429i | \(0.429292\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.416110 | + | 0.416110i | −0.0199509 | + | 0.0199509i | ||||
\(436\) | 3.57636 | + | 19.7141i | 0.171277 | + | 0.944132i | ||||
\(437\) | −4.21971 | + | 1.13067i | −0.201856 | + | 0.0540871i | ||||
\(438\) | −0.979251 | − | 0.306106i | −0.0467904 | − | 0.0146263i | ||||
\(439\) | −6.89864 | + | 3.98293i | −0.329254 | + | 0.190095i | −0.655510 | − | 0.755187i | \(-0.727546\pi\) |
0.326256 | + | 0.945282i | \(0.394213\pi\) | |||||||
\(440\) | 5.44663 | + | 0.676148i | 0.259658 | + | 0.0322341i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 23.3032 | − | 5.22645i | 1.10842 | − | 0.248597i | ||||
\(443\) | 6.47610 | − | 24.1691i | 0.307689 | − | 1.14831i | −0.622918 | − | 0.782288i | \(-0.714053\pi\) |
0.930606 | − | 0.366022i | \(-0.119281\pi\) | |||||||
\(444\) | 40.0716 | + | 3.30694i | 1.90171 | + | 0.156941i | ||||
\(445\) | 4.52000 | + | 16.8689i | 0.214269 | + | 0.799661i | ||||
\(446\) | −0.247980 | + | 6.01996i | −0.0117422 | + | 0.285053i | ||||
\(447\) | 20.1332 | 0.952267 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.33038 | −0.393135 | −0.196567 | − | 0.980490i | \(-0.562979\pi\) | ||||
−0.196567 | + | 0.980490i | \(0.562979\pi\) | |||||||
\(450\) | −0.254018 | + | 6.16656i | −0.0119745 | + | 0.290694i | ||||
\(451\) | −1.21498 | − | 4.53436i | −0.0572111 | − | 0.213515i | ||||
\(452\) | −10.1148 | − | 0.834734i | −0.475761 | − | 0.0392626i | ||||
\(453\) | 5.42349 | − | 20.2407i | 0.254818 | − | 0.950993i | ||||
\(454\) | −6.67647 | + | 1.49740i | −0.313342 | + | 0.0702766i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.62224 | + | 0.449667i | 0.169627 | + | 0.0210576i | ||||
\(457\) | 12.5338 | − | 7.23641i | 0.586308 | − | 0.338505i | −0.177328 | − | 0.984152i | \(-0.556745\pi\) |
0.763636 | + | 0.645647i | \(0.223412\pi\) | |||||||
\(458\) | −26.4797 | − | 8.27734i | −1.23731 | − | 0.386775i | ||||
\(459\) | −21.2081 | + | 5.68270i | −0.989910 | + | 0.265246i | ||||
\(460\) | 2.42588 | + | 13.3722i | 0.113107 | + | 0.623483i | ||||
\(461\) | 4.23021 | − | 4.23021i | 0.197020 | − | 0.197020i | −0.601701 | − | 0.798721i | \(-0.705510\pi\) |
0.798721 | + | 0.601701i | \(0.205510\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.1987 | −1.17108 | −0.585542 | − | 0.810642i | \(-0.699118\pi\) | ||||
−0.585542 | + | 0.810642i | \(0.699118\pi\) | |||||||
\(464\) | −0.953892 | + | 0.682029i | −0.0442833 | + | 0.0316624i | ||||
\(465\) | 7.92280 | − | 13.7227i | 0.367411 | − | 0.636374i | ||||
\(466\) | 3.32344 | + | 6.34605i | 0.153956 | + | 0.293975i | ||||
\(467\) | 14.8411 | + | 3.97667i | 0.686766 | + | 0.184018i | 0.585295 | − | 0.810820i | \(-0.300979\pi\) |
0.101470 | + | 0.994839i | \(0.467645\pi\) | |||||||
\(468\) | 2.18195 | − | 6.08802i | 0.100860 | − | 0.281419i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.0888655 | − | 0.396224i | −0.00409906 | − | 0.0182765i | ||||
\(471\) | −7.22338 | + | 4.17042i | −0.332836 | + | 0.192163i | ||||
\(472\) | 5.43087 | + | 39.0208i | 0.249976 | + | 1.79608i | ||||
\(473\) | 8.75047 | + | 5.05209i | 0.402347 | + | 0.232295i | ||||
\(474\) | −14.9112 | − | 16.1925i | −0.684894 | − | 0.743744i | ||||
\(475\) | −1.81183 | − | 1.81183i | −0.0831326 | − | 0.0831326i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.07046 | + | 6.07046i | −0.277947 | + | 0.277947i | ||||
\(478\) | −0.542770 | + | 13.1763i | −0.0248257 | + | 0.602669i | ||||
\(479\) | −10.4147 | + | 18.0387i | −0.475859 | + | 0.824211i | −0.999618 | − | 0.0276553i | \(-0.991196\pi\) |
0.523759 | + | 0.851867i | \(0.324529\pi\) | |||||||
\(480\) | 2.32097 | − | 11.1155i | 0.105937 | − | 0.507349i | ||||
\(481\) | 14.7884 | + | 25.6143i | 0.674294 | + | 1.16791i | ||||
\(482\) | −30.7402 | − | 19.4773i | −1.40018 | − | 0.887169i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 12.9857 | − | 6.13339i | 0.590257 | − | 0.278790i | ||||
\(485\) | −3.15261 | + | 11.7657i | −0.143152 | + | 0.534252i | ||||
\(486\) | −4.55612 | + | 14.5753i | −0.206670 | + | 0.661147i | ||||
\(487\) | 0.192631 | + | 0.111216i | 0.00872895 | + | 0.00503966i | 0.504358 | − | 0.863495i | \(-0.331729\pi\) |
−0.495629 | + | 0.868534i | \(0.665062\pi\) | |||||||
\(488\) | 3.98070 | − | 9.81480i | 0.180198 | − | 0.444295i | ||||
\(489\) | − | 16.7080i | − | 0.755561i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.1586 | + | 18.1586i | 0.819486 | + | 0.819486i | 0.986033 | − | 0.166547i | \(-0.0532618\pi\) |
−0.166547 | + | 0.986033i | \(0.553262\pi\) | |||||||
\(492\) | −9.55624 | + | 1.73361i | −0.430828 | + | 0.0781574i | ||||
\(493\) | −0.430797 | − | 1.60776i | −0.0194021 | − | 0.0724097i | ||||
\(494\) | 1.24564 | + | 2.37853i | 0.0560442 | + | 0.107015i | ||||
\(495\) | 1.05482 | + | 1.82700i | 0.0474105 | + | 0.0821173i | ||||
\(496\) | 20.0569 | − | 24.3870i | 0.900583 | − | 1.09501i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.917575 | − | 1.44816i | 0.0411175 | − | 0.0648938i | ||||
\(499\) | −3.39149 | − | 0.908747i | −0.151824 | − | 0.0406811i | 0.182107 | − | 0.983279i | \(-0.441708\pi\) |
−0.333930 | + | 0.942598i | \(0.608375\pi\) | |||||||
\(500\) | −13.6556 | + | 11.5736i | −0.610697 | + | 0.517585i | ||||
\(501\) | −17.4320 | + | 4.67088i | −0.778802 | + | 0.208680i | ||||
\(502\) | 5.36072 | − | 4.93654i | 0.239261 | − | 0.220329i | ||||
\(503\) | 7.65278i | 0.341220i | 0.985339 | + | 0.170610i | \(0.0545739\pi\) | ||||
−0.985339 | + | 0.170610i | \(0.945426\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.20121i | 0.0534532i | ||||||||
\(506\) | −12.8132 | − | 13.9142i | −0.569615 | − | 0.618560i | ||||
\(507\) | −8.11109 | + | 2.17336i | −0.360226 | + | 0.0965223i | ||||
\(508\) | 22.2664 | + | 1.83755i | 0.987912 | + | 0.0815282i | ||||
\(509\) | −30.8730 | − | 8.27238i | −1.36842 | − | 0.366667i | −0.501519 | − | 0.865147i | \(-0.667225\pi\) |
−0.866901 | + | 0.498480i | \(0.833892\pi\) | |||||||
\(510\) | 13.6150 | + | 8.62661i | 0.602881 | + | 0.381993i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 8.19353 | − | 21.0918i | 0.362106 | − | 0.932137i | ||||
\(513\) | −1.23423 | − | 2.13775i | −0.0544925 | − | 0.0943838i | ||||
\(514\) | −4.70490 | + | 2.46397i | −0.207524 | + | 0.108681i | ||||
\(515\) | −1.50203 | − | 5.60566i | −0.0661874 | − | 0.247015i | ||||
\(516\) | 11.9060 | − | 17.1831i | 0.524133 | − | 0.756445i | ||||
\(517\) | 0.399629 | + | 0.399629i | 0.0175757 | + | 0.0175757i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.0172i | 0.483600i | ||||||||
\(520\) | 7.69321 | − | 3.25345i | 0.337370 | − | 0.142673i | ||||
\(521\) | 2.39816 | + | 1.38458i | 0.105065 | + | 0.0606595i | 0.551612 | − | 0.834101i | \(-0.314013\pi\) |
−0.446547 | + | 0.894760i | \(0.647346\pi\) | |||||||
\(522\) | −0.430207 | − | 0.134479i | −0.0188296 | − | 0.00588600i | ||||
\(523\) | −5.72293 | + | 21.3583i | −0.250246 | + | 0.933932i | 0.720427 | + | 0.693530i | \(0.243946\pi\) |
−0.970674 | + | 0.240401i | \(0.922721\pi\) | |||||||
\(524\) | 23.7384 | + | 8.50786i | 1.03702 | + | 0.371668i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14.2684 | − | 22.5191i | 0.622131 | − | 0.981879i | ||||
\(527\) | 22.4095 | + | 38.8144i | 0.976173 | + | 1.69078i | ||||
\(528\) | 5.55138 | + | 14.7970i | 0.241593 | + | 0.643955i | ||||
\(529\) | 11.9189 | − | 20.6441i | 0.518211 | − | 0.897568i | ||||
\(530\) | −11.0787 | − | 0.456362i | −0.481226 | − | 0.0198231i | ||||
\(531\) | −10.7079 | + | 10.7079i | −0.464685 | + | 0.464685i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.05178 | − | 5.05178i | −0.218817 | − | 0.218817i | ||||
\(534\) | −36.9922 | + | 34.0651i | −1.60081 | + | 1.47414i | ||||
\(535\) | 3.22696 | + | 1.86308i | 0.139513 | + | 0.0805481i | ||||
\(536\) | 29.1381 | − | 4.05541i | 1.25857 | − | 0.175167i | ||||
\(537\) | −17.0826 | + | 9.86262i | −0.737167 | + | 0.425603i | ||||
\(538\) | 23.6640 | − | 5.30737i | 1.02023 | − | 0.228817i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −6.94375 | + | 3.27967i | −0.298811 | + | 0.141135i | ||||
\(541\) | −32.2635 | − | 8.64497i | −1.38711 | − | 0.371676i | −0.513414 | − | 0.858141i | \(-0.671619\pi\) |
−0.873700 | + | 0.486465i | \(0.838286\pi\) | |||||||
\(542\) | 6.65512 | − | 3.48530i | 0.285862 | − | 0.149706i | ||||
\(543\) | −12.0507 | + | 20.8724i | −0.517145 | + | 0.895721i | ||||
\(544\) | 23.9453 | + | 21.4053i | 1.02665 | + | 0.917743i | ||||
\(545\) | −9.94683 | −0.426075 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.45137 | − | 3.45137i | 0.147570 | − | 0.147570i | −0.629462 | − | 0.777032i | \(-0.716724\pi\) |
0.777032 | + | 0.629462i | \(0.216724\pi\) | |||||||
\(548\) | 26.6372 | + | 18.4567i | 1.13789 | + | 0.788430i | ||||
\(549\) | 3.93236 | − | 1.05367i | 0.167829 | − | 0.0449696i | ||||
\(550\) | 3.31007 | − | 10.5891i | 0.141142 | − | 0.451521i | ||||
\(551\) | 0.162059 | − | 0.0935651i | 0.00690396 | − | 0.00398601i | ||||
\(552\) | −30.8702 | + | 24.0521i | −1.31392 | + | 1.02373i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −4.70464 | − | 20.9765i | −0.199881 | − | 0.891208i | ||||
\(555\) | −5.16636 | + | 19.2811i | −0.219300 | + | 0.818437i | ||||
\(556\) | 19.2049 | + | 22.6598i | 0.814469 | + | 0.960990i | ||||
\(557\) | −5.70879 | − | 21.3055i | −0.241889 | − | 0.902742i | −0.974922 | − | 0.222549i | \(-0.928562\pi\) |
0.733032 | − | 0.680194i | \(-0.238104\pi\) | |||||||
\(558\) | 12.1266 | + | 0.499530i | 0.513360 | + | 0.0211468i | ||||
\(559\) | 15.3776 | 0.650403 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −22.4327 | −0.947109 | ||||||||
\(562\) | −4.46210 | − | 0.183807i | −0.188222 | − | 0.00775342i | ||||
\(563\) | 7.14593 | + | 26.6690i | 0.301165 | + | 1.12396i | 0.936196 | + | 0.351477i | \(0.114321\pi\) |
−0.635031 | + | 0.772486i | \(0.719013\pi\) | |||||||
\(564\) | 0.892006 | − | 0.756002i | 0.0375602 | − | 0.0318334i | ||||
\(565\) | 1.30408 | − | 4.86691i | 0.0548633 | − | 0.204752i | ||||
\(566\) | 4.36902 | + | 19.4801i | 0.183644 | + | 0.818811i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −32.5448 | − | 4.04014i | −1.36555 | − | 0.169521i | ||||
\(569\) | −30.3657 | + | 17.5317i | −1.27300 | + | 0.734965i | −0.975551 | − | 0.219773i | \(-0.929468\pi\) |
−0.297446 | + | 0.954739i | \(0.596135\pi\) | |||||||
\(570\) | −0.540641 | + | 1.72954i | −0.0226450 | + | 0.0724424i | ||||
\(571\) | 1.24755 | − | 0.334280i | 0.0522083 | − | 0.0139892i | −0.232620 | − | 0.972568i | \(-0.574730\pi\) |
0.284829 | + | 0.958578i | \(0.408063\pi\) | |||||||
\(572\) | −6.62108 | + | 9.55575i | −0.276841 | + | 0.399546i | ||||
\(573\) | −7.04827 | + | 7.04827i | −0.294446 | + | 0.294446i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 27.4720 | 1.14566 | ||||||||
\(576\) | 8.36693 | − | 2.37501i | 0.348622 | − | 0.0989586i | ||||
\(577\) | 7.66470 | − | 13.2757i | 0.319086 | − | 0.552673i | −0.661212 | − | 0.750199i | \(-0.729958\pi\) |
0.980298 | + | 0.197527i | \(0.0632909\pi\) | |||||||
\(578\) | −19.0883 | + | 9.99658i | −0.793968 | + | 0.415803i | ||||
\(579\) | −42.7830 | − | 11.4637i | −1.77800 | − | 0.476414i | ||||
\(580\) | −0.248627 | − | 0.526395i | −0.0103237 | − | 0.0218574i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −34.2244 | + | 7.67588i | −1.41865 | + | 0.318176i | ||||
\(583\) | 13.3647 | − | 7.71612i | 0.553510 | − | 0.319569i | ||||
\(584\) | 0.611911 | − | 0.809780i | 0.0253211 | − | 0.0335090i | ||||
\(585\) | 2.78051 | + | 1.60533i | 0.114960 | + | 0.0663722i | ||||
\(586\) | 16.0856 | − | 14.8128i | 0.664491 | − | 0.611913i | ||||
\(587\) | 27.8270 | + | 27.8270i | 1.14854 | + | 1.14854i | 0.986840 | + | 0.161702i | \(0.0516982\pi\) |
0.161702 | + | 0.986840i | \(0.448302\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.56299 | + | 3.56299i | −0.146810 | + | 0.146810i | ||||
\(590\) | −19.5421 | − | 0.804997i | −0.804536 | − | 0.0331412i | ||||
\(591\) | −10.8929 | + | 18.8670i | −0.448074 | + | 0.776087i | ||||
\(592\) | −16.4543 | + | 36.2138i | −0.676267 | + | 1.48838i | ||||
\(593\) | 8.89810 | + | 15.4120i | 0.365401 | + | 0.632894i | 0.988840 | − | 0.148978i | \(-0.0475984\pi\) |
−0.623439 | + | 0.781872i | \(0.714265\pi\) | |||||||
\(594\) | 5.72043 | − | 9.02828i | 0.234712 | − | 0.370435i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.71981 | + | 18.7495i | −0.275254 | + | 0.768008i | ||||
\(597\) | 1.87125 | − | 6.98361i | 0.0765853 | − | 0.285820i | ||||
\(598\) | −27.4759 | − | 8.58875i | −1.12357 | − | 0.351220i | ||||
\(599\) | 16.6221 | + | 9.59676i | 0.679159 | + | 0.392113i | 0.799538 | − | 0.600615i | \(-0.205078\pi\) |
−0.120379 | + | 0.992728i | \(0.538411\pi\) | |||||||
\(600\) | −21.2707 | − | 8.62697i | −0.868371 | − | 0.352195i | ||||
\(601\) | 26.9530i | 1.09944i | 0.835351 | + | 0.549718i | \(0.185265\pi\) | ||||
−0.835351 | + | 0.549718i | \(0.814735\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.99597 | + | 7.99597i | 0.325621 | + | 0.325621i | ||||
\(604\) | 17.0395 | + | 11.8065i | 0.693325 | + | 0.480398i | ||||
\(605\) | 1.84530 | + | 6.88674i | 0.0750219 | + | 0.279986i | ||||
\(606\) | −3.06415 | + | 1.60470i | −0.124472 | + | 0.0651865i | ||||
\(607\) | −14.7276 | − | 25.5089i | −0.597773 | − | 1.03537i | −0.993149 | − | 0.116854i | \(-0.962719\pi\) |
0.395376 | − | 0.918519i | \(-0.370614\pi\) | |||||||
\(608\) | −1.62775 | + | 3.22320i | −0.0660140 | + | 0.130718i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.44157 | + | 2.81424i | 0.179834 | + | 0.113945i | ||||
\(611\) | 0.830813 | + | 0.222616i | 0.0336111 | + | 0.00900607i | ||||
\(612\) | −1.01537 | + | 12.3036i | −0.0410437 | + | 0.497344i | ||||
\(613\) | 24.1091 | − | 6.46001i | 0.973756 | − | 0.260917i | 0.263343 | − | 0.964702i | \(-0.415175\pi\) |
0.710413 | + | 0.703785i | \(0.248508\pi\) | |||||||
\(614\) | −20.0153 | − | 21.7351i | −0.807752 | − | 0.877159i | ||||
\(615\) | − | 4.82165i | − | 0.194428i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.8407i | 0.436431i | 0.975901 | + | 0.218216i | \(0.0700236\pi\) | ||||
−0.975901 | + | 0.218216i | \(0.929976\pi\) | |||||||
\(618\) | 12.2928 | − | 11.3201i | 0.494489 | − | 0.455362i | ||||
\(619\) | 19.3962 | − | 5.19721i | 0.779601 | − | 0.208893i | 0.152992 | − | 0.988227i | \(-0.451109\pi\) |
0.626609 | + | 0.779334i | \(0.284442\pi\) | |||||||
\(620\) | 10.1352 | + | 11.9585i | 0.407038 | + | 0.480264i | ||||
\(621\) | 25.5639 | + | 6.84982i | 1.02584 | + | 0.274874i | ||||
\(622\) | −6.61232 | + | 10.4359i | −0.265130 | + | 0.418442i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 18.5766 | + | 15.2782i | 0.743657 | + | 0.611616i | ||||
\(625\) | 5.59202 | + | 9.68566i | 0.223681 | + | 0.387426i | ||||
\(626\) | −2.70171 | − | 5.15887i | −0.107982 | − | 0.206190i | ||||
\(627\) | −0.652747 | − | 2.43609i | −0.0260682 | − | 0.0972879i | ||||
\(628\) | −1.47286 | − | 8.11889i | −0.0587736 | − | 0.323979i | ||||
\(629\) | −39.9233 | − | 39.9233i | −1.59185 | − | 1.59185i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 5.71697i | − | 0.227589i | −0.993504 | − | 0.113794i | \(-0.963699\pi\) | ||
0.993504 | − | 0.113794i | \(-0.0363005\pi\) | |||||||
\(632\) | 20.0565 | − | 8.48186i | 0.797803 | − | 0.337390i | ||||
\(633\) | 18.1676 | + | 10.4891i | 0.722099 | + | 0.416904i | ||||
\(634\) | −10.3073 | + | 32.9737i | −0.409357 | + | 1.30955i | ||||
\(635\) | −2.87076 | + | 10.7138i | −0.113923 | + | 0.425166i | ||||
\(636\) | −13.6359 | − | 28.8700i | −0.540698 | − | 1.14477i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.684421 | + | 0.433657i | 0.0270965 | + | 0.0171687i | ||||
\(639\) | −6.30277 | − | 10.9167i | −0.249334 | − | 0.431859i | ||||
\(640\) | 9.57685 | + | 5.87144i | 0.378558 | + | 0.232089i | ||||
\(641\) | −14.8475 | + | 25.7166i | −0.586441 | + | 1.01575i | 0.408253 | + | 0.912869i | \(0.366138\pi\) |
−0.994694 | + | 0.102877i | \(0.967195\pi\) | |||||||
\(642\) | −0.441607 | + | 10.7205i | −0.0174289 | + | 0.423103i | ||||
\(643\) | −3.53512 | + | 3.53512i | −0.139412 | + | 0.139412i | −0.773368 | − | 0.633957i | \(-0.781430\pi\) |
0.633957 | + | 0.773368i | \(0.281430\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.33854 | + | 7.33854i | 0.288955 | + | 0.288955i | ||||
\(646\) | −3.47198 | − | 3.77031i | −0.136603 | − | 0.148341i | ||||
\(647\) | 12.7788 | + | 7.37782i | 0.502385 | + | 0.290052i | 0.729698 | − | 0.683770i | \(-0.239661\pi\) |
−0.227313 | + | 0.973822i | \(0.572994\pi\) | |||||||
\(648\) | −25.0023 | − | 18.8930i | −0.982182 | − | 0.742186i | ||||
\(649\) | 23.5746 | − | 13.6108i | 0.925384 | − | 0.534270i | ||||
\(650\) | −3.69510 | − | 16.4753i | −0.144934 | − | 0.646216i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 15.5597 | + | 5.57659i | 0.609364 | + | 0.218396i | ||||
\(653\) | 9.56710 | + | 2.56350i | 0.374390 | + | 0.100317i | 0.441107 | − | 0.897455i | \(-0.354586\pi\) |
−0.0667174 | + | 0.997772i | \(0.521253\pi\) | |||||||
\(654\) | −13.2880 | − | 25.3732i | −0.519601 | − | 0.992169i | ||||
\(655\) | −6.25952 | + | 10.8418i | −0.244580 | + | 0.423624i | ||||
\(656\) | 1.57510 | − | 9.47808i | 0.0614973 | − | 0.370057i | ||||
\(657\) | 0.390135 | 0.0152206 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.68205 | − | 5.68205i | 0.221341 | − | 0.221341i | −0.587722 | − | 0.809063i | \(-0.699975\pi\) |
0.809063 | + | 0.587722i | \(0.199975\pi\) | |||||||
\(660\) | −7.71995 | + | 1.40049i | −0.300498 | + | 0.0545140i | ||||
\(661\) | −9.26542 | + | 2.48266i | −0.360383 | + | 0.0965643i | −0.434467 | − | 0.900688i | \(-0.643063\pi\) |
0.0740843 | + | 0.997252i | \(0.476397\pi\) | |||||||
\(662\) | −9.85883 | − | 3.08180i | −0.383174 | − | 0.119777i | ||||
\(663\) | −29.5665 | + | 17.0702i | −1.14827 | + | 0.662952i | ||||
\(664\) | 1.04238 | + | 1.33786i | 0.0404521 | + | 0.0519192i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −14.9187 | + | 3.34597i | −0.578086 | + | 0.129654i | ||||
\(667\) | −0.519275 | + | 1.93796i | −0.0201064 | + | 0.0750381i | ||||
\(668\) | 1.46837 | − | 17.7929i | 0.0568130 | − | 0.688427i | ||||
\(669\) | −2.22923 | − | 8.31961i | −0.0861871 | − | 0.321655i | ||||
\(670\) | −0.601117 | + | 14.5927i | −0.0232232 | + | 0.563767i | ||||
\(671\) | −7.31815 | −0.282514 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.24280 | 0.125001 | 0.0625004 | − | 0.998045i | \(-0.480093\pi\) | ||||
0.0625004 | + | 0.998045i | \(0.480093\pi\) | |||||||
\(674\) | −0.555278 | + | 13.4800i | −0.0213885 | + | 0.519228i | ||||
\(675\) | 4.01767 | + | 14.9941i | 0.154640 | + | 0.577125i | ||||
\(676\) | 0.683234 | − | 8.27903i | 0.0262782 | − | 0.318424i | ||||
\(677\) | −8.67832 | + | 32.3879i | −0.333535 | + | 1.24477i | 0.571914 | + | 0.820314i | \(0.306201\pi\) |
−0.905449 | + | 0.424455i | \(0.860466\pi\) | |||||||
\(678\) | 14.1570 | − | 3.17515i | 0.543698 | − | 0.121941i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −12.5780 | + | 9.79995i | −0.482343 | + | 0.375811i | ||||
\(681\) | 8.47094 | − | 4.89070i | 0.324607 | − | 0.187412i | ||||
\(682\) | −20.8236 | − | 6.50929i | −0.797376 | − | 0.249254i | ||||
\(683\) | −17.9673 | + | 4.81432i | −0.687499 | + | 0.184215i | −0.585624 | − | 0.810583i | \(-0.699151\pi\) |
−0.101874 | + | 0.994797i | \(0.532484\pi\) | |||||||
\(684\) | −1.36566 | + | 0.247747i | −0.0522173 | + | 0.00947284i | ||||
\(685\) | −11.3762 | + | 11.3762i | −0.434662 | + | 0.434662i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 39.6602 | 1.51313 | ||||||||
\(688\) | 12.0283 | + | 16.8229i | 0.458575 | + | 0.641367i | ||||
\(689\) | 11.7432 | − | 20.3398i | 0.447380 | − | 0.774886i | ||||
\(690\) | −9.01337 | − | 17.2109i | −0.343133 | − | 0.655206i | ||||
\(691\) | 20.9303 | + | 5.60826i | 0.796227 | + | 0.213348i | 0.633927 | − | 0.773393i | \(-0.281442\pi\) |
0.162300 | + | 0.986741i | \(0.448109\pi\) | |||||||
\(692\) | −10.2600 | − | 3.67718i | −0.390026 | − | 0.139786i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.82783 | + | 12.6085i | 0.107343 | + | 0.478611i | ||||
\(695\) | −12.7707 | + | 7.37317i | −0.484421 | + | 0.279680i | ||||
\(696\) | 1.01063 | − | 1.33743i | 0.0383078 | − | 0.0506952i | ||||
\(697\) | 11.8108 | + | 6.81898i | 0.447367 | + | 0.258287i | ||||
\(698\) | 33.1742 | + | 36.0247i | 1.25566 | + | 1.36355i | ||||
\(699\) | −7.24128 | − | 7.24128i | −0.273891 | − | 0.273891i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.96023 | − | 4.96023i | 0.187345 | − | 0.187345i | −0.607202 | − | 0.794547i | \(-0.707708\pi\) |
0.794547 | + | 0.607202i | \(0.207708\pi\) | |||||||
\(702\) | 0.669481 | − | 16.2523i | 0.0252679 | − | 0.613405i | ||||
\(703\) | 3.17380 | − | 5.49718i | 0.119702 | − | 0.207330i | ||||
\(704\) | −15.6329 | + | 0.231096i | −0.589186 | + | 0.00870976i | ||||
\(705\) | 0.290246 | + | 0.502720i | 0.0109313 | + | 0.0189335i | ||||
\(706\) | 31.1438 | + | 19.7331i | 1.17211 | + | 0.742664i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −24.0529 | − | 50.9250i | −0.903963 | − | 1.91388i | ||||
\(709\) | −3.74523 | + | 13.9774i | −0.140655 | + | 0.524932i | 0.859255 | + | 0.511547i | \(0.170927\pi\) |
−0.999910 | + | 0.0133851i | \(0.995739\pi\) | |||||||
\(710\) | 4.85752 | − | 15.5395i | 0.182299 | − | 0.583185i | ||||
\(711\) | 7.24889 | + | 4.18515i | 0.271855 | + | 0.156955i | ||||
\(712\) | −19.3771 | − | 45.8196i | −0.726187 | − | 1.71716i | ||||
\(713\) | − | 54.0240i | − | 2.02321i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.08105 | − | 4.08105i | −0.152623 | − | 0.152623i | ||||
\(716\) | −3.48317 | − | 19.2003i | −0.130172 | − | 0.717550i | ||||
\(717\) | −4.87927 | − | 18.2097i | −0.182220 | − | 0.680053i | ||||
\(718\) | −2.28598 | − | 4.36503i | −0.0853119 | − | 0.162902i | ||||
\(719\) | 16.5646 | + | 28.6908i | 0.617756 | + | 1.06998i | 0.989894 | + | 0.141808i | \(0.0452914\pi\) |
−0.372138 | + | 0.928177i | \(0.621375\pi\) | |||||||
\(720\) | 0.418698 | + | 4.29753i | 0.0156039 | + | 0.160160i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −14.0730 | + | 22.2107i | −0.523742 | + | 0.826598i | ||||
\(723\) | 50.2502 | + | 13.4645i | 1.86883 | + | 0.500751i | ||||
\(724\) | −15.4158 | − | 18.1890i | −0.572922 | − | 0.675990i | ||||
\(725\) | −1.13668 | + | 0.304573i | −0.0422154 | + | 0.0113116i | ||||
\(726\) | −15.1021 | + | 13.9071i | −0.560492 | + | 0.516142i | ||||
\(727\) | − | 23.5496i | − | 0.873406i | −0.899606 | − | 0.436703i | \(-0.856146\pi\) | ||
0.899606 | − | 0.436703i | \(-0.143854\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 11.4085i | 0.422538i | ||||||||
\(730\) | 0.341336 | + | 0.370665i | 0.0126334 | + | 0.0137189i | ||||
\(731\) | −28.3545 | + | 7.59756i | −1.04873 | + | 0.281006i | ||||
\(732\) | −1.24527 | + | 15.0895i | −0.0460265 | + | 0.557723i | ||||
\(733\) | 1.72774 | + | 0.462947i | 0.0638156 | + | 0.0170993i | 0.290586 | − | 0.956849i | \(-0.406150\pi\) |
−0.226770 | + | 0.973948i | \(0.572817\pi\) | |||||||
\(734\) | −29.2153 | − | 18.5112i | −1.07836 | − | 0.683260i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12.0956 | − | 36.7764i | −0.445849 | − | 1.35560i | ||||
\(737\) | −10.1636 | − | 17.6039i | −0.374382 | − | 0.648448i | ||||
\(738\) | 3.27163 | − | 1.71336i | 0.120431 | − | 0.0630698i | ||||
\(739\) | 6.06175 | + | 22.6228i | 0.222985 | + | 0.832192i | 0.983202 | + | 0.182522i | \(0.0584261\pi\) |
−0.760217 | + | 0.649670i | \(0.774907\pi\) | |||||||
\(740\) | −16.2316 | − | 11.2467i | −0.596685 | − | 0.413437i | ||||
\(741\) | −2.71407 | − | 2.71407i | −0.0997039 | − | 0.0997039i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 13.9219i | − | 0.510747i | −0.966843 | − | 0.255373i | \(-0.917802\pi\) | ||
0.966843 | − | 0.255373i | \(-0.0821984\pi\) | |||||||
\(744\) | −16.9650 | + | 41.8290i | −0.621968 | + | 1.53352i | ||||
\(745\) | −8.56324 | − | 4.94399i | −0.313733 | − | 0.181134i | ||||
\(746\) | −49.6073 | − | 15.5069i | −1.81625 | − | 0.567747i | ||||
\(747\) | −0.168726 | + | 0.629693i | −0.00617336 | + | 0.0230393i | ||||
\(748\) | 7.48732 | − | 20.8909i | 0.273763 | − | 0.763848i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 13.6959 | − | 21.6156i | 0.500104 | − | 0.789291i | ||||
\(751\) | 4.53854 | + | 7.86098i | 0.165614 | + | 0.286851i | 0.936873 | − | 0.349670i | \(-0.113706\pi\) |
−0.771259 | + | 0.636521i | \(0.780373\pi\) | |||||||
\(752\) | 0.406321 | + | 1.08303i | 0.0148170 | + | 0.0394940i | ||||
\(753\) | −5.20885 | + | 9.02200i | −0.189821 | + | 0.328780i | ||||
\(754\) | 1.23207 | + | 0.0507523i | 0.0448692 | + | 0.00184829i | ||||
\(755\) | −7.27718 | + | 7.27718i | −0.264844 | + | 0.264844i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.14043 | − | 1.14043i | −0.0414496 | − | 0.0414496i | 0.686078 | − | 0.727528i | \(-0.259331\pi\) |
−0.727528 | + | 0.686078i | \(0.759331\pi\) | |||||||
\(758\) | 27.2446 | − | 25.0888i | 0.989567 | − | 0.911266i | ||||
\(759\) | 23.4173 | + | 13.5200i | 0.849994 | + | 0.490744i | ||||
\(760\) | −1.43022 | − | 1.08075i | −0.0518796 | − | 0.0392029i | ||||
\(761\) | −7.60476 | + | 4.39061i | −0.275672 | + | 0.159159i | −0.631463 | − | 0.775406i | \(-0.717545\pi\) |
0.355790 | + | 0.934566i | \(0.384212\pi\) | |||||||
\(762\) | −31.1648 | + | 6.98966i | −1.12898 | + | 0.253209i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −4.21137 | − | 8.91635i | −0.152362 | − | 0.322582i | ||||
\(765\) | −5.92008 | − | 1.58628i | −0.214041 | − | 0.0573521i | ||||
\(766\) | −19.7890 | + | 10.3636i | −0.715007 | + | 0.374451i | ||||
\(767\) | 20.7143 | − | 35.8783i | 0.747951 | − | 1.29549i | ||||
\(768\) | −2.18361 | + | 32.2731i | −0.0787944 | + | 1.16455i | ||||
\(769\) | −29.8204 | −1.07535 | −0.537676 | − | 0.843152i | \(-0.680697\pi\) | ||||
−0.537676 | + | 0.843152i | \(0.680697\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.36862 | − | 5.36862i | 0.193346 | − | 0.193346i | ||||
\(772\) | 24.9554 | − | 36.0164i | 0.898165 | − | 1.29626i | ||||
\(773\) | 44.5476 | − | 11.9365i | 1.60227 | − | 0.429326i | 0.656540 | − | 0.754291i | \(-0.272019\pi\) |
0.945726 | + | 0.324965i | \(0.105352\pi\) | |||||||
\(774\) | −2.37169 | + | 7.58715i | −0.0852485 | + | 0.272715i | ||||
\(775\) | 27.4418 | − | 15.8435i | 0.985738 | − | 0.569116i | ||||
\(776\) | 4.27469 | − | 34.4342i | 0.153452 | − | 1.23612i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.76452 | + | 7.86746i | 0.0632611 | + | 0.282062i | ||||
\(779\) | −0.396838 | + | 1.48102i | −0.0142182 | + | 0.0530630i | ||||
\(780\) | −9.10925 | + | 7.72037i | −0.326163 | + | 0.276434i | ||||
\(781\) | 5.86476 | + | 21.8876i | 0.209858 | + | 0.783199i | ||||
\(782\) | 54.9057 | + | 2.26173i | 1.96343 | + | 0.0808792i | ||||
\(783\) | −1.13367 | −0.0405142 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.09643 | 0.146208 | ||||||||
\(786\) | −36.0182 | − | 1.48370i | −1.28473 | − | 0.0529217i | ||||
\(787\) | −6.78154 | − | 25.3091i | −0.241736 | − | 0.902170i | −0.974996 | − | 0.222222i | \(-0.928669\pi\) |
0.733260 | − | 0.679948i | \(-0.237998\pi\) | |||||||
\(788\) | −13.9347 | − | 16.4415i | −0.496401 | − | 0.585703i | ||||
\(789\) | −9.86360 | + | 36.8115i | −0.351153 | + | 1.31052i | ||||
\(790\) | 2.36589 | + | 10.5488i | 0.0841746 | + | 0.375309i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −3.69354 | − | 4.74056i | −0.131244 | − | 0.168448i | ||||
\(793\) | −9.64539 | + | 5.56877i | −0.342518 | + | 0.197753i | ||||
\(794\) | 0.424560 | − | 1.35819i | 0.0150671 | − | 0.0482003i | ||||
\(795\) | 15.3107 | − | 4.10250i | 0.543016 | − | 0.145501i | ||||
\(796\) | 5.87908 | + | 4.07355i | 0.208378 | + | 0.144383i | ||||
\(797\) | 16.7419 | − | 16.7419i | 0.593028 | − | 0.593028i | −0.345420 | − | 0.938448i | \(-0.612264\pi\) |
0.938448 | + | 0.345420i | \(0.112264\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.64191 | −0.0580866 | ||||||||
\(800\) | 15.1335 | − | 16.9294i | 0.535051 | − | 0.598543i | ||||
\(801\) | 9.56111 | − | 16.5603i | 0.337825 | − | 0.585130i | ||||
\(802\) | 21.8069 | − | 11.4203i | 0.770027 | − | 0.403265i | ||||
\(803\) | −0.677409 | − | 0.181511i | −0.0239053 | − | 0.00640540i | ||||
\(804\) | −38.0274 | + | 17.9611i | −1.34112 | + | 0.633439i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −32.3989 | + | 7.26645i | −1.14120 | + | 0.255950i | ||||
\(807\) | −30.0243 | + | 17.3345i | −1.05690 | + | 0.610204i | ||||
\(808\) | −0.471698 | − | 3.38915i | −0.0165943 | − | 0.119230i | ||||
\(809\) | −30.7720 | − | 17.7662i | −1.08189 | − | 0.624628i | −0.150482 | − | 0.988613i | \(-0.548083\pi\) |
−0.931405 | + | 0.363985i | \(0.881416\pi\) | |||||||
\(810\) | 11.4444 | − | 10.5389i | 0.402116 | − | 0.370298i | ||||
\(811\) | −29.5602 | − | 29.5602i | −1.03800 | − | 1.03800i | −0.999249 | − | 0.0387507i | \(-0.987662\pi\) |
−0.0387507 | − | 0.999249i | \(-0.512338\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.59395 | + | 7.59395i | −0.266331 | + | 0.266331i | ||||
\(814\) | 27.4607 | + | 1.13119i | 0.962497 | + | 0.0396480i | ||||
\(815\) | −4.10288 | + | 7.10640i | −0.143718 | + | 0.248926i | ||||
\(816\) | −41.8014 | − | 18.9931i | −1.46334 | − | 0.664892i | ||||
\(817\) | −1.65012 | − | 2.85809i | −0.0577304 | − | 0.0999920i | ||||
\(818\) | −28.8952 | + | 45.6040i | −1.01030 | + | 1.59451i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.49027 | + | 1.60931i | 0.156807 | + | 0.0561996i | ||||
\(821\) | 2.04620 | − | 7.63653i | 0.0714129 | − | 0.266517i | −0.920983 | − | 0.389602i | \(-0.872612\pi\) |
0.992396 | + | 0.123086i | \(0.0392791\pi\) | |||||||
\(822\) | −44.2167 | − | 13.8218i | −1.54224 | − | 0.482091i | ||||
\(823\) | −43.2107 | − | 24.9477i | −1.50623 | − | 0.869623i | −0.999974 | − | 0.00724096i | \(-0.997695\pi\) |
−0.506258 | − | 0.862382i | \(-0.668972\pi\) | |||||||
\(824\) | 6.43916 | + | 15.2262i | 0.224319 | + | 0.530431i | ||||
\(825\) | 15.8599i | 0.552171i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.11672 | − | 8.11672i | −0.282246 | − | 0.282246i | 0.551758 | − | 0.834004i | \(-0.313957\pi\) |
−0.834004 | + | 0.551758i | \(0.813957\pi\) | |||||||
\(828\) | 8.47521 | − | 12.2317i | 0.294534 | − | 0.425080i | ||||
\(829\) | 1.84091 | + | 6.87035i | 0.0639373 | + | 0.238617i | 0.990498 | − | 0.137528i | \(-0.0439159\pi\) |
−0.926561 | + | 0.376146i | \(0.877249\pi\) | |||||||
\(830\) | −0.745890 | + | 0.390624i | −0.0258902 | + | 0.0135588i | ||||
\(831\) | 15.3659 | + | 26.6145i | 0.533037 | + | 0.923248i | ||||
\(832\) | −20.4284 | + | 12.2005i | −0.708227 | + | 0.422975i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −35.8685 | − | 22.7267i | −1.24202 | − | 0.786962i | ||||
\(835\) | 8.56133 | + | 2.29400i | 0.296277 | + | 0.0793872i | ||||
\(836\) | 2.48652 | + | 0.205202i | 0.0859982 | + | 0.00709708i | ||||
\(837\) | 29.4861 | − | 7.90079i | 1.01919 | − | 0.273091i | ||||
\(838\) | −36.5803 | − | 39.7235i | −1.26365 | − | 1.37223i | ||||
\(839\) | 3.57060i | 0.123271i | 0.998099 | + | 0.0616354i | \(0.0196316\pi\) | ||||
−0.998099 | + | 0.0616354i | \(0.980368\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.9141i | 0.997036i | ||||||||
\(842\) | −28.1697 | + | 25.9407i | −0.970792 | + | 0.893977i | ||||
\(843\) | 6.16664 | − | 1.65235i | 0.212390 | − | 0.0569098i | ||||
\(844\) | −15.8320 | + | 13.4181i | −0.544959 | + | 0.461870i | ||||
\(845\) | 3.98359 | + | 1.06740i | 0.137040 | + | 0.0367197i | ||||
\(846\) | −0.237973 | + | 0.375581i | −0.00818167 | + | 0.0129127i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 31.4370 | − | 3.06283i | 1.07955 | − | 0.105178i | ||||
\(849\) | −14.2697 | − | 24.7159i | −0.489736 | − | 0.848248i | ||||
\(850\) | 14.9532 | + | 28.5530i | 0.512892 | + | 0.979358i | ||||
\(851\) | 17.6142 | + | 65.7370i | 0.603806 | + | 2.25344i | ||||
\(852\) | 46.1285 | − | 8.36825i | 1.58034 | − | 0.286691i | ||||
\(853\) | −13.8958 | − | 13.8958i | −0.475784 | − | 0.475784i | 0.427996 | − | 0.903780i | \(-0.359220\pi\) |
−0.903780 | + | 0.427996i | \(0.859220\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 0.689051i | − | 0.0235650i | ||||||
\(856\) | −9.83628 | − | 3.98941i | −0.336197 | − | 0.136355i | ||||
\(857\) | 34.8241 | + | 20.1057i | 1.18957 | + | 0.686798i | 0.958209 | − | 0.286070i | \(-0.0923490\pi\) |
0.231360 | + | 0.972868i | \(0.425682\pi\) | |||||||
\(858\) | 4.95839 | − | 15.8622i | 0.169277 | − | 0.541525i | ||||
\(859\) | −6.71022 | + | 25.0429i | −0.228950 | + | 0.854452i | 0.751834 | + | 0.659353i | \(0.229170\pi\) |
−0.980784 | + | 0.195099i | \(0.937497\pi\) | |||||||
\(860\) | −9.28354 | + | 4.38480i | −0.316566 | + | 0.149521i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.50175 | + | 0.951526i | 0.0511497 | + | 0.0324091i | ||||
\(863\) | −8.22908 | − | 14.2532i | −0.280121 | − | 0.485184i | 0.691293 | − | 0.722574i | \(-0.257041\pi\) |
−0.971414 | + | 0.237390i | \(0.923708\pi\) | |||||||
\(864\) | 18.3035 | − | 11.9801i | 0.622698 | − | 0.407572i | ||||
\(865\) | 2.70543 | − | 4.68593i | 0.0919872 | − | 0.159327i | ||||
\(866\) | 0.533684 | − | 12.9557i | 0.0181353 | − | 0.440253i | ||||
\(867\) | 21.7811 | − | 21.7811i | 0.739724 | − | 0.739724i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.6394 | − | 10.6394i | −0.360918 | − | 0.360918i | ||||
\(870\) | 0.563749 | + | 0.612189i | 0.0191129 | + | 0.0207552i | ||||
\(871\) | −26.7915 | − | 15.4681i | −0.907795 | − | 0.524116i | ||||
\(872\) | 28.0644 | − | 3.90598i | 0.950381 | − | 0.132273i | ||||
\(873\) | 11.5505 | − | 6.66868i | 0.390925 | − | 0.225700i | ||||
\(874\) | 1.35204 | + | 6.02832i | 0.0457333 | + | 0.203911i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.489531 | + | 1.36588i | −0.0165397 | + | 0.0461488i | ||||
\(877\) | −22.0521 | − | 5.90884i | −0.744646 | − | 0.199527i | −0.133504 | − | 0.991048i | \(-0.542623\pi\) |
−0.611142 | + | 0.791521i | \(0.709290\pi\) | |||||||
\(878\) | 5.22640 | + | 9.97971i | 0.176382 | + | 0.336799i | ||||
\(879\) | −15.6299 | + | 27.0718i | −0.527185 | + | 0.913111i | ||||
\(880\) | 1.27243 | − | 7.65681i | 0.0428938 | − | 0.258111i | ||||
\(881\) | −5.29761 | −0.178481 | −0.0892405 | − | 0.996010i | \(-0.528444\pi\) | ||||
−0.0892405 | + | 0.996010i | \(0.528444\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30.7426 | + | 30.7426i | −1.03457 | + | 1.03457i | −0.0351900 | + | 0.999381i | \(0.511204\pi\) |
−0.999381 | + | 0.0351900i | \(0.988796\pi\) | |||||||
\(884\) | −6.02866 | − | 33.2319i | −0.202766 | − | 1.11771i | ||||
\(885\) | 27.0073 | − | 7.23658i | 0.907840 | − | 0.243255i | ||||
\(886\) | −33.7744 | − | 10.5576i | −1.13467 | − | 0.354690i | ||||
\(887\) | 5.04199 | − | 2.91100i | 0.169294 | − | 0.0977417i | −0.412959 | − | 0.910750i | \(-0.635505\pi\) |
0.582253 | + | 0.813008i | \(0.302171\pi\) | |||||||
\(888\) | 7.00518 | − | 56.4293i | 0.235078 | − | 1.89364i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 24.0991 | − | 5.40496i | 0.807802 | − | 0.181175i | ||||
\(891\) | −5.60423 | + | 20.9153i | −0.187749 | + | 0.700688i | ||||
\(892\) | 8.49186 | + | 0.700798i | 0.284329 | + | 0.0234645i | ||||
\(893\) | −0.0477763 | − | 0.178304i | −0.00159877 | − | 0.00596671i | ||||
\(894\) | 1.17188 | − | 28.4485i | 0.0391934 | − | 0.951460i | ||||
\(895\) | 9.68763 | 0.323822 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 41.1522 | 1.37403 | ||||||||
\(898\) | −0.484880 | + | 11.7710i | −0.0161806 | + | 0.392802i | ||||
\(899\) | 0.598947 | + | 2.23530i | 0.0199760 | + | 0.0745514i | ||||
\(900\) | 8.69866 | + | 0.717864i | 0.289955 | + | 0.0239288i | ||||
\(901\) | −11.6039 | + | 43.3062i | −0.386581 | + | 1.44274i | ||||
\(902\) | −6.47784 | + | 1.45285i | −0.215688 | + | 0.0483748i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.76824 | + | 14.2438i | −0.0588107 | + | 0.473742i | ||||
\(905\) | 10.2510 | − | 5.91844i | 0.340756 | − | 0.196736i | ||||
\(906\) | −28.2848 | − | 8.84161i | −0.939700 | − | 0.293743i | ||||
\(907\) | 20.3319 | − | 5.44791i | 0.675108 | − | 0.180895i | 0.0950536 | − | 0.995472i | \(-0.469698\pi\) |
0.580055 | + | 0.814577i | \(0.303031\pi\) | |||||||
\(908\) | 1.72724 | + | 9.52111i | 0.0573205 | + | 0.315969i | ||||
\(909\) | 0.930037 | − | 0.930037i | 0.0308474 | − | 0.0308474i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.3231 | −1.53475 | −0.767376 | − | 0.641197i | \(-0.778438\pi\) | ||||
−0.767376 | + | 0.641197i | \(0.778438\pi\) | |||||||
\(912\) | 0.846223 | − | 5.09210i | 0.0280212 | − | 0.168616i | ||||
\(913\) | 0.585933 | − | 1.01487i | 0.0193916 | − | 0.0335872i | ||||
\(914\) | −9.49561 | − | 18.1317i | −0.314087 | − | 0.599743i | ||||
\(915\) | −7.26054 | − | 1.94546i | −0.240026 | − | 0.0643148i | ||||
\(916\) | −13.2373 | + | 36.9344i | −0.437373 | + | 1.22035i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 6.79529 | + | 30.2982i | 0.224278 | + | 0.999988i | ||||
\(919\) | −12.8775 | + | 7.43484i | −0.424790 | + | 0.245253i | −0.697125 | − | 0.716950i | \(-0.745538\pi\) |
0.272335 | + | 0.962203i | \(0.412204\pi\) | |||||||
\(920\) | 19.0364 | − | 2.64946i | 0.627610 | − | 0.0873501i | ||||
\(921\) | 36.5799 | + | 21.1194i | 1.20535 | + | 0.695908i | ||||
\(922\) | −5.73112 | − | 6.22357i | −0.188744 | − | 0.204962i | ||||
\(923\) | 24.3852 | + | 24.3852i | 0.802649 | + | 0.802649i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28.2258 | + | 28.2258i | −0.928058 | + | 0.928058i | ||||
\(926\) | −1.46672 | + | 35.6062i | −0.0481995 | + | 1.17009i | ||||
\(927\) | −3.17723 | + | 5.50313i | −0.104354 | + | 0.180746i | ||||
\(928\) | 0.908195 | + | 1.38756i | 0.0298130 | + | 0.0455490i | ||||
\(929\) | −25.8504 | − | 44.7742i | −0.848124 | − | 1.46899i | −0.882881 | − | 0.469598i | \(-0.844399\pi\) |
0.0347569 | − | 0.999396i | \(-0.488934\pi\) | |||||||
\(930\) | −18.9292 | − | 11.9938i | −0.620713 | − | 0.393291i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 9.16052 | − | 4.32670i | 0.300063 | − | 0.141726i | ||||
\(933\) | 4.57104 | − | 17.0593i | 0.149649 | − | 0.558498i | ||||
\(934\) | 6.48294 | − | 20.7393i | 0.212128 | − | 0.678610i | ||||
\(935\) | 9.54129 | + | 5.50867i | 0.312034 | + | 0.180153i | ||||
\(936\) | −8.47546 | − | 3.43748i | −0.277029 | − | 0.112358i | ||||
\(937\) | 50.1408i | 1.63803i | 0.573773 | + | 0.819014i | \(0.305479\pi\) | ||||
−0.573773 | + | 0.819014i | \(0.694521\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.88663 | + | 5.88663i | 0.192103 | + | 0.192103i | ||||
\(940\) | −0.565044 | + | 0.102506i | −0.0184297 | + | 0.00334337i | ||||
\(941\) | −11.6055 | − | 43.3123i | −0.378328 | − | 1.41194i | −0.848421 | − | 0.529322i | \(-0.822446\pi\) |
0.470093 | − | 0.882617i | \(-0.344220\pi\) | |||||||
\(942\) | 5.47243 | + | 10.4495i | 0.178301 | + | 0.340463i | ||||
\(943\) | −8.21947 | − | 14.2365i | −0.267663 | − | 0.463606i | ||||
\(944\) | 55.4531 | − | 5.40265i | 1.80485 | − | 0.175841i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.64801 | − | 12.0705i | 0.248658 | − | 0.392445i | ||||
\(947\) | −1.59414 | − | 0.427149i | −0.0518027 | − | 0.0138805i | 0.232825 | − | 0.972519i | \(-0.425203\pi\) |
−0.284627 | + | 0.958638i | \(0.591870\pi\) | |||||||
\(948\) | −23.7481 | + | 20.1273i | −0.771303 | + | 0.653703i | ||||
\(949\) | −1.03095 | + | 0.276243i | −0.0334661 | + | 0.00896723i | ||||
\(950\) | −2.66561 | + | 2.45469i | −0.0864837 | + | 0.0796406i | ||||
\(951\) | − | 49.3867i | − | 1.60147i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 40.9510i | − | 1.32653i | −0.748384 | − | 0.663266i | \(-0.769170\pi\) | ||
0.748384 | − | 0.663266i | \(-0.230830\pi\) | |||||||
\(954\) | 8.22431 | + | 8.93099i | 0.266272 | + | 0.289151i | ||||
\(955\) | 4.72865 | − | 1.26704i | 0.153015 | − | 0.0410003i | ||||
\(956\) | 18.5867 | + | 1.53388i | 0.601137 | + | 0.0496093i | ||||
\(957\) | −1.11881 | − | 0.299783i | −0.0361659 | − | 0.00969062i | ||||
\(958\) | 24.8828 | + | 15.7661i | 0.803927 | + | 0.509378i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −15.5712 | − | 3.92656i | −0.502559 | − | 0.126729i | ||||
\(961\) | −15.6564 | − | 27.1177i | −0.505046 | − | 0.874766i | ||||
\(962\) | 37.0542 | − | 19.4054i | 1.19468 | − | 0.625654i | ||||
\(963\) | −1.05598 | − | 3.94096i | −0.0340284 | − | 0.126996i | ||||
\(964\) | −29.3111 | + | 42.3026i | −0.944045 | + | 1.36248i | ||||
\(965\) | 15.3818 | + | 15.3818i | 0.495159 | + | 0.495159i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.6315i | 0.470518i | 0.971933 | + | 0.235259i | \(0.0755938\pi\) | ||||
−0.971933 | + | 0.235259i | \(0.924406\pi\) | |||||||
\(968\) | −7.91072 | − | 18.7059i | −0.254260 | − | 0.601231i | ||||
\(969\) | 6.34536 | + | 3.66350i | 0.203842 | + | 0.117688i | ||||
\(970\) | 16.4416 | + | 5.13952i | 0.527908 | + | 0.165020i | ||||
\(971\) | −6.32211 | + | 23.5944i | −0.202886 | + | 0.757181i | 0.787197 | + | 0.616701i | \(0.211531\pi\) |
−0.990084 | + | 0.140480i | \(0.955135\pi\) | |||||||
\(972\) | 20.3299 | + | 7.28623i | 0.652081 | + | 0.233706i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.168362 | − | 0.265717i | 0.00539466 | − | 0.00851413i | ||||
\(975\) | 12.0686 | + | 20.9035i | 0.386506 | + | 0.669448i | ||||
\(976\) | −13.6368 | − | 6.19607i | −0.436502 | − | 0.198331i | ||||
\(977\) | 2.85781 | − | 4.94988i | 0.0914295 | − | 0.158361i | −0.816683 | − | 0.577086i | \(-0.804190\pi\) |
0.908113 | + | 0.418725i | \(0.137523\pi\) | |||||||
\(978\) | −23.6086 | − | 0.972507i | −0.754920 | − | 0.0310974i | ||||
\(979\) | −24.3061 | + | 24.3061i | −0.776827 | + | 0.776827i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.70133 | + | 7.70133i | 0.245885 | + | 0.245885i | ||||
\(982\) | 26.7153 | − | 24.6014i | 0.852520 | − | 0.785063i | ||||
\(983\) | 18.6714 | + | 10.7799i | 0.595525 | + | 0.343827i | 0.767279 | − | 0.641313i | \(-0.221610\pi\) |
−0.171754 | + | 0.985140i | \(0.554943\pi\) | |||||||
\(984\) | 1.89339 | + | 13.6040i | 0.0603591 | + | 0.433680i | ||||
\(985\) | 9.26615 | − | 5.34981i | 0.295244 | − | 0.170459i | ||||
\(986\) | −2.29686 | + | 0.515141i | −0.0731469 | + | 0.0164054i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.43341 | − | 1.62167i | 0.109231 | − | 0.0515921i | ||||
\(989\) | 34.1780 | + | 9.15796i | 1.08680 | + | 0.291206i | ||||
\(990\) | 2.64297 | − | 1.38413i | 0.0839991 | − | 0.0439905i | ||||
\(991\) | 17.3811 | − | 30.1049i | 0.552128 | − | 0.956314i | −0.445993 | − | 0.895037i | \(-0.647149\pi\) |
0.998121 | − | 0.0612772i | \(-0.0195174\pi\) | |||||||
\(992\) | −33.2918 | − | 29.7602i | −1.05701 | − | 0.944888i | ||||
\(993\) | 14.7661 | 0.468590 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.51082 | + | 2.51082i | −0.0795985 | + | 0.0795985i | ||||
\(996\) | −1.99287 | − | 1.38084i | −0.0631465 | − | 0.0437536i | ||||
\(997\) | 4.95586 | − | 1.32792i | 0.156954 | − | 0.0420556i | −0.179487 | − | 0.983760i | \(-0.557444\pi\) |
0.336440 | + | 0.941705i | \(0.390777\pi\) | |||||||
\(998\) | −1.48148 | + | 4.73933i | −0.0468954 | + | 0.150021i | ||||
\(999\) | −33.3031 | + | 19.2275i | −1.05366 | + | 0.608332i |
(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 | 784.2.x.o.165.7 | 48 | ||
7.2 | even | 3 | inner | 784.2.x.o.373.3 | 48 | ||
7.3 | odd | 6 | 784.2.m.j.197.10 | 24 | |||
7.4 | even | 3 | 784.2.m.k.197.10 | 24 | |||
7.5 | odd | 6 | 112.2.w.c.37.3 | ✓ | 48 | ||
7.6 | odd | 2 | 112.2.w.c.53.7 | yes | 48 | ||
16.13 | even | 4 | inner | 784.2.x.o.557.3 | 48 | ||
28.19 | even | 6 | 448.2.ba.c.177.3 | 48 | |||
28.27 | even | 2 | 448.2.ba.c.305.10 | 48 | |||
56.5 | odd | 6 | 896.2.ba.f.737.3 | 48 | |||
56.13 | odd | 2 | 896.2.ba.f.865.10 | 48 | |||
56.19 | even | 6 | 896.2.ba.e.737.10 | 48 | |||
56.27 | even | 2 | 896.2.ba.e.865.3 | 48 | |||
112.5 | odd | 12 | 896.2.ba.f.289.10 | 48 | |||
112.13 | odd | 4 | 112.2.w.c.109.3 | yes | 48 | ||
112.19 | even | 12 | 448.2.ba.c.401.10 | 48 | |||
112.27 | even | 4 | 896.2.ba.e.417.10 | 48 | |||
112.45 | odd | 12 | 784.2.m.j.589.10 | 24 | |||
112.61 | odd | 12 | 112.2.w.c.93.7 | yes | 48 | ||
112.69 | odd | 4 | 896.2.ba.f.417.3 | 48 | |||
112.75 | even | 12 | 896.2.ba.e.289.3 | 48 | |||
112.83 | even | 4 | 448.2.ba.c.81.3 | 48 | |||
112.93 | even | 12 | inner | 784.2.x.o.765.7 | 48 | ||
112.109 | even | 12 | 784.2.m.k.589.10 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.w.c.37.3 | ✓ | 48 | 7.5 | odd | 6 | ||
112.2.w.c.53.7 | yes | 48 | 7.6 | odd | 2 | ||
112.2.w.c.93.7 | yes | 48 | 112.61 | odd | 12 | ||
112.2.w.c.109.3 | yes | 48 | 112.13 | odd | 4 | ||
448.2.ba.c.81.3 | 48 | 112.83 | even | 4 | |||
448.2.ba.c.177.3 | 48 | 28.19 | even | 6 | |||
448.2.ba.c.305.10 | 48 | 28.27 | even | 2 | |||
448.2.ba.c.401.10 | 48 | 112.19 | even | 12 | |||
784.2.m.j.197.10 | 24 | 7.3 | odd | 6 | |||
784.2.m.j.589.10 | 24 | 112.45 | odd | 12 | |||
784.2.m.k.197.10 | 24 | 7.4 | even | 3 | |||
784.2.m.k.589.10 | 24 | 112.109 | even | 12 | |||
784.2.x.o.165.7 | 48 | 1.1 | even | 1 | trivial | ||
784.2.x.o.373.3 | 48 | 7.2 | even | 3 | inner | ||
784.2.x.o.557.3 | 48 | 16.13 | even | 4 | inner | ||
784.2.x.o.765.7 | 48 | 112.93 | even | 12 | inner | ||
896.2.ba.e.289.3 | 48 | 112.75 | even | 12 | |||
896.2.ba.e.417.10 | 48 | 112.27 | even | 4 | |||
896.2.ba.e.737.10 | 48 | 56.19 | even | 6 | |||
896.2.ba.e.865.3 | 48 | 56.27 | even | 2 | |||
896.2.ba.f.289.10 | 48 | 112.5 | odd | 12 | |||
896.2.ba.f.417.3 | 48 | 112.69 | odd | 4 | |||
896.2.ba.f.737.3 | 48 | 56.5 | odd | 6 | |||
896.2.ba.f.865.10 | 48 | 56.13 | odd | 2 |