Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(41,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.41");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.bl (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 41.2 | ||
Character | \(\chi\) | \(=\) | 315.41 |
Dual form | 315.2.bl.j.146.2 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.21303 | + | 1.27769i | −1.56485 | + | 0.903466i | −0.568096 | + | 0.822963i | \(0.692320\pi\) |
−0.996754 | + | 0.0805039i | \(0.974347\pi\) | |||||||
\(3\) | 0.920618 | − | 1.46713i | 0.531519 | − | 0.847046i | ||||
\(4\) | 2.26501 | − | 3.92311i | 1.13250 | − | 1.96155i | ||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | −0.162815 | + | 4.42307i | −0.0664691 | + | 1.80571i | ||||
\(7\) | 1.04917 | + | 2.42884i | 0.396549 | + | 0.918014i | ||||
\(8\) | 6.46517i | 2.28578i | ||||||||
\(9\) | −1.30493 | − | 2.70133i | −0.434975 | − | 0.900442i | ||||
\(10\) | − | 2.55539i | − | 0.808085i | ||||||
\(11\) | −3.67950 | + | 2.12436i | −1.10941 | + | 0.640518i | −0.938676 | − | 0.344799i | \(-0.887947\pi\) |
−0.170733 | + | 0.985317i | \(0.554614\pi\) | |||||||
\(12\) | −3.67049 | − | 6.93474i | −1.05958 | − | 2.00189i | ||||
\(13\) | 3.06147 | + | 1.76754i | 0.849098 | + | 0.490227i | 0.860346 | − | 0.509710i | \(-0.170247\pi\) |
−0.0112486 | + | 0.999937i | \(0.503581\pi\) | |||||||
\(14\) | −5.42516 | − | 4.03457i | −1.44993 | − | 1.07828i | ||||
\(15\) | 0.810261 | + | 1.53084i | 0.209208 | + | 0.395262i | ||||
\(16\) | −3.73050 | − | 6.46141i | −0.932625 | − | 1.61535i | ||||
\(17\) | 7.46750 | 1.81113 | 0.905567 | − | 0.424202i | \(-0.139445\pi\) | ||||
0.905567 | + | 0.424202i | \(0.139445\pi\) | |||||||
\(18\) | 6.33931 | + | 4.31083i | 1.49419 | + | 1.01607i | ||||
\(19\) | − | 0.474051i | − | 0.108755i | −0.998520 | − | 0.0543774i | \(-0.982683\pi\) | ||
0.998520 | − | 0.0543774i | \(-0.0173174\pi\) | |||||||
\(20\) | 2.26501 | + | 3.92311i | 0.506471 | + | 0.877233i | ||||
\(21\) | 4.52930 | + | 0.696763i | 0.988373 | + | 0.152046i | ||||
\(22\) | 5.42856 | − | 9.40254i | 1.15737 | − | 2.00463i | ||||
\(23\) | 3.79725 | + | 2.19235i | 0.791782 | + | 0.457136i | 0.840590 | − | 0.541673i | \(-0.182209\pi\) |
−0.0488075 | + | 0.998808i | \(0.515542\pi\) | |||||||
\(24\) | 9.48523 | + | 5.95195i | 1.93616 | + | 1.21494i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −9.03349 | −1.77161 | ||||||||
\(27\) | −5.16453 | − | 0.572396i | −0.993914 | − | 0.110158i | ||||
\(28\) | 11.9050 | + | 1.38532i | 2.24983 | + | 0.261802i | ||||
\(29\) | 3.03806 | − | 1.75402i | 0.564154 | − | 0.325714i | −0.190657 | − | 0.981657i | \(-0.561062\pi\) |
0.754811 | + | 0.655942i | \(0.227729\pi\) | |||||||
\(30\) | −3.74908 | − | 2.35254i | −0.684486 | − | 0.429512i | ||||
\(31\) | 6.18566 | + | 3.57129i | 1.11098 | + | 0.641423i | 0.939082 | − | 0.343693i | \(-0.111678\pi\) |
0.171894 | + | 0.985115i | \(0.445011\pi\) | |||||||
\(32\) | 5.31342 | + | 3.06771i | 0.939289 | + | 0.542299i | ||||
\(33\) | −0.270705 | + | 7.35401i | −0.0471237 | + | 1.28017i | ||||
\(34\) | −16.5258 | + | 9.54118i | −2.83415 | + | 1.63630i | ||||
\(35\) | −2.62802 | − | 0.305810i | −0.444216 | − | 0.0516914i | ||||
\(36\) | −13.5533 | − | 0.999159i | −2.25888 | − | 0.166527i | ||||
\(37\) | −6.01728 | −0.989235 | −0.494617 | − | 0.869111i | \(-0.664692\pi\) | ||||
−0.494617 | + | 0.869111i | \(0.664692\pi\) | |||||||
\(38\) | 0.605693 | + | 1.04909i | 0.0982564 | + | 0.170185i | ||||
\(39\) | 5.41164 | − | 2.86433i | 0.866556 | − | 0.458660i | ||||
\(40\) | −5.59900 | − | 3.23258i | −0.885280 | − | 0.511117i | ||||
\(41\) | 0.648068 | − | 1.12249i | 0.101211 | − | 0.175303i | −0.810973 | − | 0.585084i | \(-0.801062\pi\) |
0.912184 | + | 0.409781i | \(0.134395\pi\) | |||||||
\(42\) | −10.9137 | + | 4.24510i | −1.68402 | + | 0.655033i | ||||
\(43\) | 0.406148 | + | 0.703468i | 0.0619369 | + | 0.107278i | 0.895331 | − | 0.445401i | \(-0.146939\pi\) |
−0.833394 | + | 0.552679i | \(0.813606\pi\) | |||||||
\(44\) | 19.2467i | 2.90156i | ||||||||
\(45\) | 2.99188 | + | 0.220564i | 0.446003 | + | 0.0328798i | ||||
\(46\) | −11.2046 | −1.65203 | ||||||||
\(47\) | 6.34775 | + | 10.9946i | 0.925915 | + | 1.60373i | 0.790084 | + | 0.612999i | \(0.210037\pi\) |
0.135831 | + | 0.990732i | \(0.456630\pi\) | |||||||
\(48\) | −12.9141 | − | 0.475374i | −1.86399 | − | 0.0686143i | ||||
\(49\) | −4.79849 | + | 5.09652i | −0.685498 | + | 0.728075i | ||||
\(50\) | 2.21303 | + | 1.27769i | 0.312970 | + | 0.180693i | ||||
\(51\) | 6.87471 | − | 10.9558i | 0.962652 | − | 1.53412i | ||||
\(52\) | 13.8685 | − | 8.00697i | 1.92321 | − | 1.11037i | ||||
\(53\) | − | 2.09014i | − | 0.287102i | −0.989643 | − | 0.143551i | \(-0.954148\pi\) | ||
0.989643 | − | 0.143551i | \(-0.0458522\pi\) | |||||||
\(54\) | 12.1606 | − | 5.33196i | 1.65485 | − | 0.725588i | ||||
\(55\) | − | 4.24872i | − | 0.572897i | ||||||
\(56\) | −15.7028 | + | 6.78306i | −2.09838 | + | 0.906425i | ||||
\(57\) | −0.695494 | − | 0.436420i | −0.0921204 | − | 0.0578053i | ||||
\(58\) | −4.48222 | + | 7.76342i | −0.588544 | + | 1.01939i | ||||
\(59\) | 2.03206 | − | 3.51963i | 0.264552 | − | 0.458217i | −0.702894 | − | 0.711294i | \(-0.748109\pi\) |
0.967446 | + | 0.253077i | \(0.0814427\pi\) | |||||||
\(60\) | 7.84090 | + | 0.288628i | 1.01226 | + | 0.0372617i | ||||
\(61\) | 2.27474 | − | 1.31332i | 0.291251 | − | 0.168154i | −0.347255 | − | 0.937771i | \(-0.612886\pi\) |
0.638506 | + | 0.769617i | \(0.279553\pi\) | |||||||
\(62\) | −18.2521 | −2.31802 | ||||||||
\(63\) | 5.19199 | − | 6.00360i | 0.654129 | − | 0.756383i | ||||
\(64\) | −0.756369 | −0.0945462 | ||||||||
\(65\) | −3.06147 | + | 1.76754i | −0.379728 | + | 0.219236i | ||||
\(66\) | −8.79710 | − | 16.6205i | −1.08285 | − | 2.04585i | ||||
\(67\) | −3.57579 | + | 6.19345i | −0.436853 | + | 0.756651i | −0.997445 | − | 0.0714412i | \(-0.977240\pi\) |
0.560592 | + | 0.828092i | \(0.310574\pi\) | |||||||
\(68\) | 16.9139 | − | 29.2958i | 2.05112 | − | 3.55264i | ||||
\(69\) | 6.71227 | − | 3.55274i | 0.808062 | − | 0.427700i | ||||
\(70\) | 6.20662 | − | 2.68104i | 0.741833 | − | 0.320445i | ||||
\(71\) | − | 11.1585i | − | 1.32427i | −0.749383 | − | 0.662137i | \(-0.769650\pi\) | ||
0.749383 | − | 0.662137i | \(-0.230350\pi\) | |||||||
\(72\) | 17.4645 | − | 8.43657i | 2.05822 | − | 0.994259i | ||||
\(73\) | − | 1.75510i | − | 0.205419i | −0.994711 | − | 0.102709i | \(-0.967249\pi\) | ||
0.994711 | − | 0.102709i | \(-0.0327511\pi\) | |||||||
\(74\) | 13.3164 | − | 7.68825i | 1.54800 | − | 0.893740i | ||||
\(75\) | −1.73088 | − | 0.0637145i | −0.199865 | − | 0.00735712i | ||||
\(76\) | −1.85975 | − | 1.07373i | −0.213328 | − | 0.123165i | ||||
\(77\) | −9.02013 | − | 6.70808i | −1.02794 | − | 0.764457i | ||||
\(78\) | −8.31639 | + | 13.2533i | −0.941646 | + | 1.50064i | ||||
\(79\) | 0.917777 | + | 1.58964i | 0.103258 | + | 0.178848i | 0.913025 | − | 0.407903i | \(-0.133740\pi\) |
−0.809767 | + | 0.586751i | \(0.800407\pi\) | |||||||
\(80\) | 7.46100 | 0.834165 | ||||||||
\(81\) | −5.59434 | + | 7.05006i | −0.621593 | + | 0.783341i | ||||
\(82\) | 3.31213i | 0.365764i | ||||||||
\(83\) | −2.79791 | − | 4.84613i | −0.307111 | − | 0.531931i | 0.670618 | − | 0.741803i | \(-0.266029\pi\) |
−0.977729 | + | 0.209871i | \(0.932696\pi\) | |||||||
\(84\) | 12.9924 | − | 16.1907i | 1.41758 | − | 1.76655i | ||||
\(85\) | −3.73375 | + | 6.46704i | −0.404982 | + | 0.701449i | ||||
\(86\) | −1.79764 | − | 1.03787i | −0.193844 | − | 0.111916i | ||||
\(87\) | 0.223514 | − | 6.07201i | 0.0239632 | − | 0.650987i | ||||
\(88\) | −13.7343 | − | 23.7886i | −1.46409 | − | 2.53587i | ||||
\(89\) | −14.3932 | −1.52568 | −0.762840 | − | 0.646587i | \(-0.776196\pi\) | ||||
−0.762840 | + | 0.646587i | \(0.776196\pi\) | |||||||
\(90\) | −6.90294 | + | 3.33459i | −0.727634 | + | 0.351497i | ||||
\(91\) | −1.08106 | + | 9.29024i | −0.113326 | + | 0.973882i | ||||
\(92\) | 17.2016 | − | 9.93135i | 1.79339 | − | 1.03542i | ||||
\(93\) | 10.9342 | − | 5.78735i | 1.13382 | − | 0.600121i | ||||
\(94\) | −28.0955 | − | 16.2210i | −2.89783 | − | 1.67307i | ||||
\(95\) | 0.410541 | + | 0.237026i | 0.0421206 | + | 0.0243183i | ||||
\(96\) | 9.39235 | − | 4.97128i | 0.958602 | − | 0.507379i | ||||
\(97\) | 7.56815 | − | 4.36947i | 0.768429 | − | 0.443653i | −0.0638848 | − | 0.997957i | \(-0.520349\pi\) |
0.832314 | + | 0.554304i | \(0.187016\pi\) | |||||||
\(98\) | 4.10740 | − | 17.4098i | 0.414911 | − | 1.75865i | ||||
\(99\) | 10.5401 | + | 7.16739i | 1.05932 | + | 0.720350i | ||||
\(100\) | −4.53001 | −0.453001 | ||||||||
\(101\) | −4.67664 | − | 8.10018i | −0.465343 | − | 0.805999i | 0.533874 | − | 0.845564i | \(-0.320736\pi\) |
−0.999217 | + | 0.0395658i | \(0.987403\pi\) | |||||||
\(102\) | −1.21582 | + | 33.0293i | −0.120385 | + | 3.27038i | ||||
\(103\) | −0.668174 | − | 0.385771i | −0.0658372 | − | 0.0380111i | 0.466720 | − | 0.884405i | \(-0.345436\pi\) |
−0.532557 | + | 0.846394i | \(0.678769\pi\) | |||||||
\(104\) | −11.4274 | + | 19.7929i | −1.12055 | + | 1.94085i | ||||
\(105\) | −2.86806 | + | 3.57410i | −0.279894 | + | 0.348797i | ||||
\(106\) | 2.67056 | + | 4.62554i | 0.259387 | + | 0.449272i | ||||
\(107\) | 13.4458i | 1.29985i | 0.759997 | + | 0.649927i | \(0.225200\pi\) | ||||
−0.759997 | + | 0.649927i | \(0.774800\pi\) | |||||||
\(108\) | −13.9433 | + | 18.9645i | −1.34169 | + | 1.82486i | ||||
\(109\) | −4.75379 | −0.455330 | −0.227665 | − | 0.973740i | \(-0.573109\pi\) | ||||
−0.227665 | + | 0.973740i | \(0.573109\pi\) | |||||||
\(110\) | 5.42856 | + | 9.40254i | 0.517593 | + | 0.896497i | ||||
\(111\) | −5.53961 | + | 8.82812i | −0.525797 | + | 0.837928i | ||||
\(112\) | 11.7798 | − | 15.8399i | 1.11308 | − | 1.49673i | ||||
\(113\) | −9.15660 | − | 5.28657i | −0.861381 | − | 0.497318i | 0.00309376 | − | 0.999995i | \(-0.499015\pi\) |
−0.864474 | + | 0.502677i | \(0.832349\pi\) | |||||||
\(114\) | 2.09676 | + | 0.0771829i | 0.196380 | + | 0.00722884i | ||||
\(115\) | −3.79725 | + | 2.19235i | −0.354096 | + | 0.204437i | ||||
\(116\) | − | 15.8915i | − | 1.47549i | ||||||
\(117\) | 0.779711 | − | 10.5765i | 0.0720843 | − | 0.977800i | ||||
\(118\) | 10.3854i | 0.956054i | ||||||||
\(119\) | 7.83467 | + | 18.1373i | 0.718203 | + | 1.66265i | ||||
\(120\) | −9.89715 | + | 5.23847i | −0.903482 | + | 0.478205i | ||||
\(121\) | 3.52579 | − | 6.10685i | 0.320527 | − | 0.555169i | ||||
\(122\) | −3.35605 | + | 5.81285i | −0.303843 | + | 0.526271i | ||||
\(123\) | −1.05021 | − | 1.98418i | −0.0946941 | − | 0.178907i | ||||
\(124\) | 28.0211 | − | 16.1780i | 2.51637 | − | 1.45283i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −3.81927 | + | 19.9199i | −0.340248 | + | 1.77461i | ||||
\(127\) | −11.2674 | −0.999820 | −0.499910 | − | 0.866077i | \(-0.666634\pi\) | ||||
−0.499910 | + | 0.866077i | \(0.666634\pi\) | |||||||
\(128\) | −8.95297 | + | 5.16900i | −0.791339 | + | 0.456880i | ||||
\(129\) | 1.40598 | + | 0.0517550i | 0.123790 | + | 0.00455678i | ||||
\(130\) | 4.51675 | − | 7.82324i | 0.396145 | − | 0.686143i | ||||
\(131\) | 7.79640 | − | 13.5038i | 0.681174 | − | 1.17983i | −0.293448 | − | 0.955975i | \(-0.594803\pi\) |
0.974623 | − | 0.223854i | \(-0.0718638\pi\) | |||||||
\(132\) | 28.2374 | + | 17.7189i | 2.45775 | + | 1.54223i | ||||
\(133\) | 1.15139 | − | 0.497360i | 0.0998384 | − | 0.0431266i | ||||
\(134\) | − | 18.2751i | − | 1.57873i | ||||||
\(135\) | 3.07797 | − | 4.18642i | 0.264910 | − | 0.360309i | ||||
\(136\) | 48.2787i | 4.13986i | ||||||||
\(137\) | 3.25657 | − | 1.88018i | 0.278227 | − | 0.160635i | −0.354393 | − | 0.935096i | \(-0.615313\pi\) |
0.632621 | + | 0.774462i | \(0.281979\pi\) | |||||||
\(138\) | −10.3151 | + | 16.4386i | −0.878083 | + | 1.39934i | ||||
\(139\) | −4.71277 | − | 2.72092i | −0.399732 | − | 0.230786i | 0.286636 | − | 0.958040i | \(-0.407463\pi\) |
−0.686368 | + | 0.727254i | \(0.740796\pi\) | |||||||
\(140\) | −7.15221 | + | 9.61733i | −0.604472 | + | 0.812813i | ||||
\(141\) | 21.9744 | + | 0.808888i | 1.85058 | + | 0.0681207i | ||||
\(142\) | 14.2572 | + | 24.6942i | 1.19644 | + | 2.07229i | ||||
\(143\) | −15.0195 | −1.25600 | ||||||||
\(144\) | −12.5864 | + | 18.5090i | −1.04886 | + | 1.54241i | ||||
\(145\) | 3.50805i | 0.291328i | ||||||||
\(146\) | 2.24248 | + | 3.88409i | 0.185589 | + | 0.321449i | ||||
\(147\) | 3.05968 | + | 11.7319i | 0.252358 | + | 0.967634i | ||||
\(148\) | −13.6292 | + | 23.6064i | −1.12031 | + | 1.94044i | ||||
\(149\) | −6.68258 | − | 3.85819i | −0.547458 | − | 0.316075i | 0.200638 | − | 0.979665i | \(-0.435698\pi\) |
−0.748096 | + | 0.663590i | \(0.769032\pi\) | |||||||
\(150\) | 3.91190 | − | 2.07053i | 0.319405 | − | 0.169058i | ||||
\(151\) | −0.605580 | − | 1.04889i | −0.0492814 | − | 0.0853578i | 0.840332 | − | 0.542071i | \(-0.182360\pi\) |
−0.889614 | + | 0.456714i | \(0.849026\pi\) | |||||||
\(152\) | 3.06482 | 0.248590 | ||||||||
\(153\) | −9.74454 | − | 20.1722i | −0.787799 | − | 1.63082i | ||||
\(154\) | 28.5327 | + | 3.32022i | 2.29923 | + | 0.267551i | ||||
\(155\) | −6.18566 | + | 3.57129i | −0.496844 | + | 0.286853i | ||||
\(156\) | 1.02032 | − | 27.7182i | 0.0816910 | − | 2.21923i | ||||
\(157\) | −15.1908 | − | 8.77042i | −1.21236 | − | 0.699956i | −0.249086 | − | 0.968481i | \(-0.580130\pi\) |
−0.963273 | + | 0.268526i | \(0.913464\pi\) | |||||||
\(158\) | −4.06214 | − | 2.34528i | −0.323167 | − | 0.186580i | ||||
\(159\) | −3.06650 | − | 1.92422i | −0.243189 | − | 0.152600i | ||||
\(160\) | −5.31342 | + | 3.06771i | −0.420063 | + | 0.242523i | ||||
\(161\) | −1.34088 | + | 11.5230i | −0.105676 | + | 0.908143i | ||||
\(162\) | 3.37261 | − | 22.7499i | 0.264977 | − | 1.78740i | ||||
\(163\) | 6.32828 | 0.495669 | 0.247835 | − | 0.968802i | \(-0.420281\pi\) | ||||
0.247835 | + | 0.968802i | \(0.420281\pi\) | |||||||
\(164\) | −2.93576 | − | 5.08488i | −0.229244 | − | 0.397062i | ||||
\(165\) | −6.23341 | − | 3.91144i | −0.485270 | − | 0.304505i | ||||
\(166\) | 12.3837 | + | 7.14975i | 0.961164 | + | 0.554929i | ||||
\(167\) | −0.976158 | + | 1.69076i | −0.0755374 | + | 0.130835i | −0.901320 | − | 0.433154i | \(-0.857401\pi\) |
0.825782 | + | 0.563989i | \(0.190734\pi\) | |||||||
\(168\) | −4.50469 | + | 29.2827i | −0.347545 | + | 2.25921i | ||||
\(169\) | −0.251619 | − | 0.435817i | −0.0193553 | − | 0.0335244i | ||||
\(170\) | − | 19.0824i | − | 1.46355i | ||||||
\(171\) | −1.28057 | + | 0.618602i | −0.0979275 | + | 0.0473057i | ||||
\(172\) | 3.67971 | 0.280575 | ||||||||
\(173\) | 2.81618 | + | 4.87777i | 0.214110 | + | 0.370850i | 0.952997 | − | 0.302980i | \(-0.0979815\pi\) |
−0.738887 | + | 0.673830i | \(0.764648\pi\) | |||||||
\(174\) | 7.26353 | + | 13.7231i | 0.550647 | + | 1.04035i | ||||
\(175\) | 1.57885 | − | 2.12303i | 0.119350 | − | 0.160486i | ||||
\(176\) | 27.4527 | + | 15.8498i | 2.06933 | + | 1.19473i | ||||
\(177\) | −3.29300 | − | 6.22152i | −0.247517 | − | 0.467638i | ||||
\(178\) | 31.8527 | − | 18.3902i | 2.38746 | − | 1.37840i | ||||
\(179\) | 8.09586i | 0.605113i | 0.953131 | + | 0.302557i | \(0.0978401\pi\) | ||||
−0.953131 | + | 0.302557i | \(0.902160\pi\) | |||||||
\(180\) | 7.64193 | − | 11.2379i | 0.569596 | − | 0.837623i | ||||
\(181\) | − | 13.8016i | − | 1.02587i | −0.858429 | − | 0.512933i | \(-0.828559\pi\) | ||
0.858429 | − | 0.512933i | \(-0.171441\pi\) | |||||||
\(182\) | −9.47767 | − | 21.9409i | −0.702532 | − | 1.62637i | ||||
\(183\) | 0.167355 | − | 4.54640i | 0.0123713 | − | 0.336080i | ||||
\(184\) | −14.1739 | + | 24.5499i | −1.04491 | + | 1.80984i | ||||
\(185\) | 3.00864 | − | 5.21112i | 0.221200 | − | 0.383129i | ||||
\(186\) | −16.8032 | + | 26.7781i | −1.23207 | + | 1.96347i | ||||
\(187\) | −27.4766 | + | 15.8636i | −2.00929 | + | 1.16006i | ||||
\(188\) | 57.5108 | 4.19441 | ||||||||
\(189\) | −4.02821 | − | 13.1443i | −0.293009 | − | 0.956110i | ||||
\(190\) | −1.21139 | −0.0878832 | ||||||||
\(191\) | −0.566372 | + | 0.326995i | −0.0409813 | + | 0.0236605i | −0.520351 | − | 0.853953i | \(-0.674199\pi\) |
0.479369 | + | 0.877613i | \(0.340865\pi\) | |||||||
\(192\) | −0.696327 | + | 1.10969i | −0.0502531 | + | 0.0800850i | ||||
\(193\) | 7.14304 | − | 12.3721i | 0.514167 | − | 0.890564i | −0.485698 | − | 0.874127i | \(-0.661434\pi\) |
0.999865 | − | 0.0164367i | \(-0.00523222\pi\) | |||||||
\(194\) | −11.1657 | + | 19.3396i | −0.801651 | + | 1.38850i | ||||
\(195\) | −0.225236 | + | 6.11879i | −0.0161295 | + | 0.438175i | ||||
\(196\) | 9.12560 | + | 30.3686i | 0.651828 | + | 2.16919i | ||||
\(197\) | − | 3.36821i | − | 0.239975i | −0.992775 | − | 0.119988i | \(-0.961715\pi\) | ||
0.992775 | − | 0.119988i | \(-0.0382855\pi\) | |||||||
\(198\) | −32.4832 | − | 2.39469i | −2.30848 | − | 0.170183i | ||||
\(199\) | − | 5.86209i | − | 0.415552i | −0.978176 | − | 0.207776i | \(-0.933377\pi\) | ||
0.978176 | − | 0.207776i | \(-0.0666226\pi\) | |||||||
\(200\) | 5.59900 | − | 3.23258i | 0.395909 | − | 0.228578i | ||||
\(201\) | 5.79465 | + | 10.9479i | 0.408723 | + | 0.772209i | ||||
\(202\) | 20.6991 | + | 11.9506i | 1.45639 | + | 0.840844i | ||||
\(203\) | 7.44768 | + | 5.53868i | 0.522725 | + | 0.388739i | ||||
\(204\) | −27.4094 | − | 51.7851i | −1.91904 | − | 3.62568i | ||||
\(205\) | 0.648068 | + | 1.12249i | 0.0452630 | + | 0.0783979i | ||||
\(206\) | 1.97159 | 0.137367 | ||||||||
\(207\) | 0.967106 | − | 13.1185i | 0.0672185 | − | 0.911797i | ||||
\(208\) | − | 26.3752i | − | 1.82879i | ||||||
\(209\) | 1.00705 | + | 1.74427i | 0.0696594 | + | 0.120654i | ||||
\(210\) | 1.78050 | − | 11.5741i | 0.122866 | − | 0.798690i | ||||
\(211\) | −10.7413 | + | 18.6045i | −0.739463 | + | 1.28079i | 0.213274 | + | 0.976992i | \(0.431587\pi\) |
−0.952737 | + | 0.303796i | \(0.901746\pi\) | |||||||
\(212\) | −8.19983 | − | 4.73417i | −0.563166 | − | 0.325144i | ||||
\(213\) | −16.3710 | − | 10.2727i | −1.12172 | − | 0.703876i | ||||
\(214\) | −17.1796 | − | 29.7560i | −1.17437 | − | 2.03408i | ||||
\(215\) | −0.812295 | −0.0553981 | ||||||||
\(216\) | 3.70064 | − | 33.3896i | 0.251797 | − | 2.27187i | ||||
\(217\) | −2.18427 | + | 18.7708i | −0.148278 | + | 1.27425i | ||||
\(218\) | 10.5203 | − | 6.07389i | 0.712523 | − | 0.411376i | ||||
\(219\) | −2.57495 | − | 1.61577i | −0.173999 | − | 0.109184i | ||||
\(220\) | −16.6682 | − | 9.62337i | −1.12377 | − | 0.648808i | ||||
\(221\) | 22.8615 | + | 13.1991i | 1.53783 | + | 0.887867i | ||||
\(222\) | 0.979706 | − | 26.6148i | 0.0657536 | − | 1.78627i | ||||
\(223\) | −6.87624 | + | 3.97000i | −0.460467 | + | 0.265851i | −0.712241 | − | 0.701935i | \(-0.752320\pi\) |
0.251773 | + | 0.967786i | \(0.418986\pi\) | |||||||
\(224\) | −1.87627 | + | 16.1240i | −0.125364 | + | 1.07733i | ||||
\(225\) | −1.68695 | + | 2.48076i | −0.112464 | + | 0.165384i | ||||
\(226\) | 27.0185 | 1.79724 | ||||||||
\(227\) | −1.52350 | − | 2.63878i | −0.101118 | − | 0.175142i | 0.811027 | − | 0.585008i | \(-0.198909\pi\) |
−0.912146 | + | 0.409866i | \(0.865575\pi\) | |||||||
\(228\) | −3.28742 | + | 1.74000i | −0.217715 | + | 0.115234i | ||||
\(229\) | 20.4678 | + | 11.8171i | 1.35255 | + | 0.780896i | 0.988606 | − | 0.150524i | \(-0.0480962\pi\) |
0.363945 | + | 0.931420i | \(0.381430\pi\) | |||||||
\(230\) | 5.60230 | − | 9.70346i | 0.369404 | − | 0.639827i | ||||
\(231\) | −18.1457 | + | 7.05811i | −1.19390 | + | 0.464389i | ||||
\(232\) | 11.3401 | + | 19.6416i | 0.744512 | + | 1.28953i | ||||
\(233\) | 8.34677i | 0.546815i | 0.961898 | + | 0.273408i | \(0.0881508\pi\) | ||||
−0.961898 | + | 0.273408i | \(0.911849\pi\) | |||||||
\(234\) | 11.7880 | + | 24.4024i | 0.770609 | + | 1.59524i | ||||
\(235\) | −12.6955 | −0.828163 | ||||||||
\(236\) | −9.20525 | − | 15.9440i | −0.599211 | − | 1.03786i | ||||
\(237\) | 3.17712 | + | 0.116951i | 0.206376 | + | 0.00759681i | ||||
\(238\) | −40.5124 | − | 30.1282i | −2.62603 | − | 1.95292i | ||||
\(239\) | 20.4410 | + | 11.8016i | 1.32222 | + | 0.763381i | 0.984082 | − | 0.177717i | \(-0.0568711\pi\) |
0.338134 | + | 0.941098i | \(0.390204\pi\) | |||||||
\(240\) | 6.86873 | − | 10.9462i | 0.443374 | − | 0.706576i | ||||
\(241\) | 17.4442 | − | 10.0714i | 1.12368 | − | 0.648758i | 0.181343 | − | 0.983420i | \(-0.441956\pi\) |
0.942338 | + | 0.334662i | \(0.108622\pi\) | |||||||
\(242\) | 18.0196i | 1.15834i | ||||||||
\(243\) | 5.19310 | + | 14.6980i | 0.333138 | + | 0.942878i | ||||
\(244\) | − | 11.8987i | − | 0.761739i | ||||||
\(245\) | −2.01447 | − | 6.70387i | −0.128700 | − | 0.428295i | ||||
\(246\) | 4.85932 | + | 3.04921i | 0.309819 | + | 0.194410i | ||||
\(247\) | 0.837904 | − | 1.45129i | 0.0533145 | − | 0.0923435i | ||||
\(248\) | −23.0890 | + | 39.9913i | −1.46615 | + | 2.53945i | ||||
\(249\) | −9.68569 | − | 0.356535i | −0.613806 | − | 0.0225945i | ||||
\(250\) | −2.21303 | + | 1.27769i | −0.139964 | + | 0.0808085i | ||||
\(251\) | −26.8096 | −1.69221 | −0.846104 | − | 0.533018i | \(-0.821058\pi\) | ||||
−0.846104 | + | 0.533018i | \(0.821058\pi\) | |||||||
\(252\) | −11.7929 | − | 33.9669i | −0.742882 | − | 2.13972i | ||||
\(253\) | −18.6293 | −1.17121 | ||||||||
\(254\) | 24.9351 | − | 14.3963i | 1.56457 | − | 0.903304i | ||||
\(255\) | 6.05062 | + | 11.4316i | 0.378905 | + | 0.715872i | ||||
\(256\) | 13.9652 | − | 24.1884i | 0.872824 | − | 1.51178i | ||||
\(257\) | 9.42879 | − | 16.3311i | 0.588152 | − | 1.01871i | −0.406323 | − | 0.913730i | \(-0.633189\pi\) |
0.994474 | − | 0.104979i | \(-0.0334775\pi\) | |||||||
\(258\) | −3.17762 | + | 1.68188i | −0.197830 | + | 0.104709i | ||||
\(259\) | −6.31315 | − | 14.6150i | −0.392280 | − | 0.908131i | ||||
\(260\) | 16.0139i | 0.993143i | ||||||||
\(261\) | −8.70264 | − | 5.91792i | −0.538680 | − | 0.366310i | ||||
\(262\) | 39.8457i | 2.46167i | ||||||||
\(263\) | 23.7292 | − | 13.7000i | 1.46320 | − | 0.844781i | 0.464046 | − | 0.885811i | \(-0.346397\pi\) |
0.999158 | + | 0.0410303i | \(0.0130640\pi\) | |||||||
\(264\) | −47.5449 | − | 1.75015i | −2.92619 | − | 0.107715i | ||||
\(265\) | 1.81011 | + | 1.04507i | 0.111194 | + | 0.0641980i | ||||
\(266\) | −1.91259 | + | 2.57180i | −0.117269 | + | 0.157687i | ||||
\(267\) | −13.2507 | + | 21.1167i | −0.810928 | + | 1.29232i | ||||
\(268\) | 16.1984 | + | 28.0564i | 0.989474 | + | 1.71382i | ||||
\(269\) | 21.8704 | 1.33346 | 0.666731 | − | 0.745299i | \(-0.267693\pi\) | ||||
0.666731 | + | 0.745299i | \(0.267693\pi\) | |||||||
\(270\) | −1.46270 | + | 13.1974i | −0.0890168 | + | 0.803167i | ||||
\(271\) | − | 22.2347i | − | 1.35066i | −0.737514 | − | 0.675331i | \(-0.764001\pi\) | ||
0.737514 | − | 0.675331i | \(-0.235999\pi\) | |||||||
\(272\) | −27.8575 | − | 48.2506i | −1.68911 | − | 2.92562i | ||||
\(273\) | 12.6347 | + | 10.1388i | 0.764688 | + | 0.613629i | ||||
\(274\) | −4.80459 | + | 8.32180i | −0.290256 | + | 0.502738i | ||||
\(275\) | 3.67950 | + | 2.12436i | 0.221882 | + | 0.128104i | ||||
\(276\) | 1.26554 | − | 34.3799i | 0.0761767 | − | 2.06943i | ||||
\(277\) | 1.79176 | + | 3.10342i | 0.107657 | + | 0.186467i | 0.914820 | − | 0.403861i | \(-0.132332\pi\) |
−0.807164 | + | 0.590327i | \(0.798999\pi\) | |||||||
\(278\) | 13.9060 | 0.834028 | ||||||||
\(279\) | 1.57540 | − | 21.3698i | 0.0943166 | − | 1.27937i | ||||
\(280\) | 1.97712 | − | 16.9906i | 0.118155 | − | 1.01538i | ||||
\(281\) | −7.90601 | + | 4.56453i | −0.471633 | + | 0.272297i | −0.716923 | − | 0.697152i | \(-0.754450\pi\) |
0.245290 | + | 0.969450i | \(0.421117\pi\) | |||||||
\(282\) | −49.6635 | + | 26.2864i | −2.95742 | + | 1.56533i | ||||
\(283\) | 14.3529 | + | 8.28664i | 0.853190 | + | 0.492589i | 0.861726 | − | 0.507374i | \(-0.169384\pi\) |
−0.00853598 | + | 0.999964i | \(0.502717\pi\) | |||||||
\(284\) | −43.7761 | − | 25.2741i | −2.59763 | − | 1.49974i | ||||
\(285\) | 0.725698 | − | 0.384105i | 0.0429866 | − | 0.0227524i | ||||
\(286\) | 33.2387 | − | 19.1904i | 1.96545 | − | 1.13475i | ||||
\(287\) | 3.40627 | + | 0.396372i | 0.201066 | + | 0.0233971i | ||||
\(288\) | 1.35325 | − | 18.3564i | 0.0797412 | − | 1.08166i | ||||
\(289\) | 38.7636 | 2.28021 | ||||||||
\(290\) | −4.48222 | − | 7.76342i | −0.263205 | − | 0.455884i | ||||
\(291\) | 0.556798 | − | 15.1261i | 0.0326401 | − | 0.886705i | ||||
\(292\) | −6.88544 | − | 3.97531i | −0.402940 | − | 0.232637i | ||||
\(293\) | 11.7759 | − | 20.3965i | 0.687956 | − | 1.19157i | −0.284543 | − | 0.958663i | \(-0.591842\pi\) |
0.972498 | − | 0.232911i | \(-0.0748249\pi\) | |||||||
\(294\) | −21.7610 | − | 22.0538i | −1.26913 | − | 1.28621i | ||||
\(295\) | 2.03206 | + | 3.51963i | 0.118311 | + | 0.204921i | ||||
\(296\) | − | 38.9027i | − | 2.26118i | ||||||
\(297\) | 20.2188 | − | 8.86518i | 1.17322 | − | 0.514410i | ||||
\(298\) | 19.7183 | 1.14225 | ||||||||
\(299\) | 7.75011 | + | 13.4236i | 0.448200 | + | 0.776306i | ||||
\(300\) | −4.17041 | + | 6.64611i | −0.240779 | + | 0.383713i | ||||
\(301\) | −1.28249 | + | 1.72452i | −0.0739216 | + | 0.0993999i | ||||
\(302\) | 2.68033 | + | 1.54749i | 0.154236 | + | 0.0890481i | ||||
\(303\) | −16.1894 | − | 0.595940i | −0.930057 | − | 0.0342359i | ||||
\(304\) | −3.06304 | + | 1.76845i | −0.175677 | + | 0.101427i | ||||
\(305\) | 2.62665i | 0.150401i | ||||||||
\(306\) | 47.3388 | + | 32.1911i | 2.70618 | + | 1.84024i | ||||
\(307\) | − | 12.6259i | − | 0.720598i | −0.932837 | − | 0.360299i | \(-0.882675\pi\) | ||
0.932837 | − | 0.360299i | \(-0.117325\pi\) | |||||||
\(308\) | −46.7472 | + | 20.1931i | −2.66367 | + | 1.15061i | ||||
\(309\) | −1.18111 | + | 0.625150i | −0.0671909 | + | 0.0355635i | ||||
\(310\) | 9.12604 | − | 15.8068i | 0.518324 | − | 0.897764i | ||||
\(311\) | −4.20710 | + | 7.28691i | −0.238563 | + | 0.413203i | −0.960302 | − | 0.278962i | \(-0.910010\pi\) |
0.721739 | + | 0.692165i | \(0.243343\pi\) | |||||||
\(312\) | 18.5184 | + | 34.9872i | 1.04840 | + | 1.98076i | ||||
\(313\) | −16.2566 | + | 9.38575i | −0.918877 | + | 0.530514i | −0.883277 | − | 0.468852i | \(-0.844668\pi\) |
−0.0356003 | + | 0.999366i | \(0.511334\pi\) | |||||||
\(314\) | 44.8237 | 2.52955 | ||||||||
\(315\) | 2.60328 | + | 7.49820i | 0.146678 | + | 0.422476i | ||||
\(316\) | 8.31509 | 0.467760 | ||||||||
\(317\) | −24.4557 | + | 14.1195i | −1.37357 | + | 0.793030i | −0.991375 | − | 0.131053i | \(-0.958164\pi\) |
−0.382192 | + | 0.924083i | \(0.624831\pi\) | |||||||
\(318\) | 9.24481 | + | 0.340306i | 0.518423 | + | 0.0190834i | ||||
\(319\) | −7.45235 | + | 12.9079i | −0.417252 | + | 0.722701i | ||||
\(320\) | 0.378185 | − | 0.655035i | 0.0211412 | − | 0.0366176i | ||||
\(321\) | 19.7267 | + | 12.3784i | 1.10104 | + | 0.690897i | ||||
\(322\) | −11.7555 | − | 27.2141i | −0.655109 | − | 1.51658i | ||||
\(323\) | − | 3.53998i | − | 0.196970i | ||||||
\(324\) | 14.9870 | + | 37.9156i | 0.832608 | + | 2.10642i | ||||
\(325\) | − | 3.53508i | − | 0.196091i | ||||||
\(326\) | −14.0047 | + | 8.08561i | −0.775648 | + | 0.447821i | ||||
\(327\) | −4.37642 | + | 6.97441i | −0.242017 | + | 0.385686i | ||||
\(328\) | 7.25707 | + | 4.18987i | 0.400704 | + | 0.231347i | ||||
\(329\) | −20.0443 | + | 26.9529i | −1.10508 | + | 1.48596i | ||||
\(330\) | 18.7924 | + | 0.691757i | 1.03449 | + | 0.0380799i | ||||
\(331\) | −12.7702 | − | 22.1187i | −0.701916 | − | 1.21575i | −0.967793 | − | 0.251747i | \(-0.918995\pi\) |
0.265877 | − | 0.964007i | \(-0.414338\pi\) | |||||||
\(332\) | −25.3492 | −1.39122 | ||||||||
\(333\) | 7.85211 | + | 16.2546i | 0.430293 | + | 0.890749i | ||||
\(334\) | − | 4.98893i | − | 0.272982i | ||||||
\(335\) | −3.57579 | − | 6.19345i | −0.195366 | − | 0.338385i | ||||
\(336\) | −12.3945 | − | 31.8649i | −0.676173 | − | 1.73837i | ||||
\(337\) | 9.08840 | − | 15.7416i | 0.495077 | − | 0.857498i | −0.504907 | − | 0.863174i | \(-0.668473\pi\) |
0.999984 | + | 0.00567555i | \(0.00180659\pi\) | |||||||
\(338\) | 1.11368 | + | 0.642985i | 0.0605764 | + | 0.0349738i | ||||
\(339\) | −16.1858 | + | 8.56700i | −0.879092 | + | 0.465295i | ||||
\(340\) | 16.9139 | + | 29.2958i | 0.917287 | + | 1.58879i | ||||
\(341\) | −30.3468 | −1.64337 | ||||||||
\(342\) | 2.04355 | − | 3.00516i | 0.110503 | − | 0.162500i | ||||
\(343\) | −17.4130 | − | 6.30762i | −0.940216 | − | 0.340579i | ||||
\(344\) | −4.54804 | + | 2.62581i | −0.245214 | + | 0.141574i | ||||
\(345\) | −0.279369 | + | 7.58937i | −0.0150407 | + | 0.408598i | ||||
\(346\) | −12.4646 | − | 7.19644i | −0.670101 | − | 0.386883i | ||||
\(347\) | −1.12031 | − | 0.646813i | −0.0601415 | − | 0.0347227i | 0.469628 | − | 0.882865i | \(-0.344388\pi\) |
−0.529769 | + | 0.848142i | \(0.677721\pi\) | |||||||
\(348\) | −23.3149 | − | 14.6300i | −1.24981 | − | 0.784251i | ||||
\(349\) | −20.3812 | + | 11.7671i | −1.09098 | + | 0.629879i | −0.933838 | − | 0.357697i | \(-0.883562\pi\) |
−0.157145 | + | 0.987576i | \(0.550229\pi\) | |||||||
\(350\) | −0.781464 | + | 6.71561i | −0.0417710 | + | 0.358964i | ||||
\(351\) | −14.7993 | − | 10.8809i | −0.789928 | − | 0.580778i | ||||
\(352\) | −26.0676 | −1.38941 | ||||||||
\(353\) | 16.0281 | + | 27.7615i | 0.853091 | + | 1.47760i | 0.878404 | + | 0.477918i | \(0.158608\pi\) |
−0.0253130 | + | 0.999680i | \(0.508058\pi\) | |||||||
\(354\) | 15.2367 | + | 9.56099i | 0.809822 | + | 0.508161i | ||||
\(355\) | 9.66357 | + | 5.57926i | 0.512889 | + | 0.296117i | ||||
\(356\) | −32.6008 | + | 56.4662i | −1.72784 | + | 2.99270i | ||||
\(357\) | 33.8225 | + | 5.20308i | 1.79008 | + | 0.275376i | ||||
\(358\) | −10.3440 | − | 17.9164i | −0.546700 | − | 0.946911i | ||||
\(359\) | 26.4174i | 1.39426i | 0.716946 | + | 0.697128i | \(0.245539\pi\) | ||||
−0.716946 | + | 0.697128i | \(0.754461\pi\) | |||||||
\(360\) | −1.42599 | + | 19.3430i | −0.0751560 | + | 1.01947i | ||||
\(361\) | 18.7753 | 0.988172 | ||||||||
\(362\) | 17.6343 | + | 30.5434i | 0.926836 | + | 1.60533i | ||||
\(363\) | −5.71363 | − | 10.7949i | −0.299888 | − | 0.566584i | ||||
\(364\) | 33.9980 | + | 25.2836i | 1.78198 | + | 1.32522i | ||||
\(365\) | 1.51996 | + | 0.877549i | 0.0795583 | + | 0.0459330i | ||||
\(366\) | 5.43855 | + | 10.2752i | 0.284278 | + | 0.537092i | ||||
\(367\) | −29.7815 | + | 17.1943i | −1.55458 | + | 0.897537i | −0.556821 | + | 0.830633i | \(0.687979\pi\) |
−0.997759 | + | 0.0669043i | \(0.978688\pi\) | |||||||
\(368\) | − | 32.7142i | − | 1.70534i | ||||||
\(369\) | −3.87788 | − | 0.285881i | −0.201875 | − | 0.0148824i | ||||
\(370\) | 15.3765i | 0.799386i | ||||||||
\(371\) | 5.07660 | − | 2.19291i | 0.263564 | − | 0.113850i | ||||
\(372\) | 2.06155 | − | 56.0043i | 0.106886 | − | 2.90369i | ||||
\(373\) | 16.3414 | − | 28.3041i | 0.846124 | − | 1.46553i | −0.0385184 | − | 0.999258i | \(-0.512264\pi\) |
0.884642 | − | 0.466271i | \(-0.154403\pi\) | |||||||
\(374\) | 40.5378 | − | 70.2135i | 2.09616 | − | 3.63065i | ||||
\(375\) | 0.920618 | − | 1.46713i | 0.0475405 | − | 0.0757621i | ||||
\(376\) | −71.0821 | + | 41.0393i | −3.66578 | + | 2.11644i | ||||
\(377\) | 12.4012 | 0.638695 | ||||||||
\(378\) | 25.7090 | + | 23.9420i | 1.32233 | + | 1.23144i | ||||
\(379\) | −20.0049 | −1.02758 | −0.513792 | − | 0.857915i | \(-0.671760\pi\) | ||||
−0.513792 | + | 0.857915i | \(0.671760\pi\) | |||||||
\(380\) | 1.85975 | − | 1.07373i | 0.0954034 | − | 0.0550812i | ||||
\(381\) | −10.3730 | + | 16.5307i | −0.531423 | + | 0.846894i | ||||
\(382\) | 0.835600 | − | 1.44730i | 0.0427530 | − | 0.0740504i | ||||
\(383\) | −7.12122 | + | 12.3343i | −0.363878 | + | 0.630254i | −0.988595 | − | 0.150596i | \(-0.951881\pi\) |
0.624718 | + | 0.780851i | \(0.285214\pi\) | |||||||
\(384\) | −0.658681 | + | 17.8938i | −0.0336132 | + | 0.913141i | ||||
\(385\) | 10.3194 | − | 4.45762i | 0.525927 | − | 0.227182i | ||||
\(386\) | 36.5065i | 1.85813i | ||||||||
\(387\) | 1.37031 | − | 2.01511i | 0.0696565 | − | 0.102434i | ||||
\(388\) | − | 39.5875i | − | 2.00975i | ||||||
\(389\) | −2.04713 | + | 1.18191i | −0.103793 | + | 0.0599251i | −0.550998 | − | 0.834506i | \(-0.685753\pi\) |
0.447205 | + | 0.894432i | \(0.352420\pi\) | |||||||
\(390\) | −7.31949 | − | 13.8289i | −0.370637 | − | 0.700251i | ||||
\(391\) | 28.3560 | + | 16.3713i | 1.43402 | + | 0.827934i | ||||
\(392\) | −32.9499 | − | 31.0230i | −1.66422 | − | 1.56690i | ||||
\(393\) | −12.6342 | − | 23.8701i | −0.637313 | − | 1.20409i | ||||
\(394\) | 4.30355 | + | 7.45396i | 0.216809 | + | 0.375525i | ||||
\(395\) | −1.83555 | −0.0923568 | ||||||||
\(396\) | 51.9917 | − | 25.1156i | 2.61268 | − | 1.26211i | ||||
\(397\) | − | 15.4381i | − | 0.774818i | −0.921908 | − | 0.387409i | \(-0.873370\pi\) | ||
0.921908 | − | 0.387409i | \(-0.126630\pi\) | |||||||
\(398\) | 7.48996 | + | 12.9730i | 0.375438 | + | 0.650277i | ||||
\(399\) | 0.330302 | − | 2.14712i | 0.0165358 | − | 0.107490i | ||||
\(400\) | −3.73050 | + | 6.46141i | −0.186525 | + | 0.323071i | ||||
\(401\) | −15.0901 | − | 8.71225i | −0.753562 | − | 0.435069i | 0.0734175 | − | 0.997301i | \(-0.476609\pi\) |
−0.826979 | + | 0.562232i | \(0.809943\pi\) | |||||||
\(402\) | −26.8119 | − | 16.8244i | −1.33725 | − | 0.839123i | ||||
\(403\) | 12.6248 | + | 21.8668i | 0.628885 | + | 1.08926i | ||||
\(404\) | −42.3705 | −2.10801 | ||||||||
\(405\) | −3.30837 | − | 8.36987i | −0.164394 | − | 0.415902i | ||||
\(406\) | −23.5587 | − | 2.74141i | −1.16920 | − | 0.136054i | ||||
\(407\) | 22.1406 | − | 12.7829i | 1.09747 | − | 0.633623i | ||||
\(408\) | 70.8309 | + | 44.4462i | 3.50665 | + | 2.20041i | ||||
\(409\) | 1.65618 | + | 0.956195i | 0.0818927 | + | 0.0472808i | 0.540387 | − | 0.841416i | \(-0.318278\pi\) |
−0.458494 | + | 0.888697i | \(0.651611\pi\) | |||||||
\(410\) | −2.86839 | − | 1.65607i | −0.141660 | − | 0.0817873i | ||||
\(411\) | 0.239590 | − | 6.50873i | 0.0118181 | − | 0.321052i | ||||
\(412\) | −3.02684 | + | 1.74755i | −0.149122 | + | 0.0860954i | ||||
\(413\) | 10.6806 | + | 1.24285i | 0.525557 | + | 0.0611566i | ||||
\(414\) | 14.6212 | + | 30.2673i | 0.718591 | + | 1.48755i | ||||
\(415\) | 5.59582 | 0.274688 | ||||||||
\(416\) | 10.8446 | + | 18.7833i | 0.531699 | + | 0.920929i | ||||
\(417\) | −8.33060 | + | 4.40931i | −0.407951 | + | 0.215925i | ||||
\(418\) | −4.45729 | − | 2.57342i | −0.218013 | − | 0.125870i | ||||
\(419\) | 5.98450 | − | 10.3655i | 0.292362 | − | 0.506385i | −0.682006 | − | 0.731347i | \(-0.738892\pi\) |
0.974368 | + | 0.224961i | \(0.0722255\pi\) | |||||||
\(420\) | 7.52541 | + | 19.3471i | 0.367202 | + | 0.944041i | ||||
\(421\) | −17.3379 | − | 30.0302i | −0.845000 | − | 1.46358i | −0.885622 | − | 0.464408i | \(-0.846267\pi\) |
0.0406220 | − | 0.999175i | \(-0.487066\pi\) | |||||||
\(422\) | − | 54.8965i | − | 2.67232i | ||||||
\(423\) | 21.4167 | − | 31.4945i | 1.04132 | − | 1.53132i | ||||
\(424\) | 13.5131 | 0.656253 | ||||||||
\(425\) | −3.73375 | − | 6.46704i | −0.181113 | − | 0.313698i | ||||
\(426\) | 49.3549 | + | 1.81678i | 2.39125 | + | 0.0880233i | ||||
\(427\) | 5.57643 | + | 4.14708i | 0.269863 | + | 0.200691i | ||||
\(428\) | 52.7493 | + | 30.4548i | 2.54973 | + | 1.47209i | ||||
\(429\) | −13.8272 | + | 22.0356i | −0.667586 | + | 1.06389i | ||||
\(430\) | 1.79764 | − | 1.03787i | 0.0866897 | − | 0.0500503i | ||||
\(431\) | − | 33.2887i | − | 1.60346i | −0.597687 | − | 0.801729i | \(-0.703913\pi\) | ||
0.597687 | − | 0.801729i | \(-0.296087\pi\) | |||||||
\(432\) | 15.5678 | + | 35.5055i | 0.749005 | + | 1.70826i | ||||
\(433\) | − | 1.40309i | − | 0.0674283i | −0.999432 | − | 0.0337142i | \(-0.989266\pi\) | ||
0.999432 | − | 0.0337142i | \(-0.0107336\pi\) | |||||||
\(434\) | −19.1495 | − | 44.3313i | −0.919206 | − | 2.12797i | ||||
\(435\) | 5.14676 | + | 3.22957i | 0.246768 | + | 0.154846i | ||||
\(436\) | −10.7674 | + | 18.6496i | −0.515663 | + | 0.893154i | ||||
\(437\) | 1.03928 | − | 1.80009i | 0.0497157 | − | 0.0861101i | ||||
\(438\) | 7.76292 | + | 0.285757i | 0.370926 | + | 0.0136540i | ||||
\(439\) | 7.50463 | − | 4.33280i | 0.358177 | − | 0.206793i | −0.310104 | − | 0.950703i | \(-0.600364\pi\) |
0.668281 | + | 0.743909i | \(0.267031\pi\) | |||||||
\(440\) | 27.4687 | 1.30952 | ||||||||
\(441\) | 20.0290 | + | 6.31169i | 0.953764 | + | 0.300557i | ||||
\(442\) | −67.4576 | −3.20863 | ||||||||
\(443\) | 1.22623 | − | 0.707967i | 0.0582601 | − | 0.0336365i | −0.470587 | − | 0.882354i | \(-0.655958\pi\) |
0.528847 | + | 0.848717i | \(0.322624\pi\) | |||||||
\(444\) | 22.0864 | + | 41.7282i | 1.04817 | + | 1.98033i | ||||
\(445\) | 7.19662 | − | 12.4649i | 0.341152 | − | 0.590893i | ||||
\(446\) | 10.1449 | − | 17.5715i | 0.480375 | − | 0.832033i | ||||
\(447\) | −11.8126 | + | 6.25228i | −0.558714 | + | 0.295723i | ||||
\(448\) | −0.793560 | − | 1.83710i | −0.0374922 | − | 0.0867947i | ||||
\(449\) | 7.67349i | 0.362134i | 0.983471 | + | 0.181067i | \(0.0579551\pi\) | ||||
−0.983471 | + | 0.181067i | \(0.942045\pi\) | |||||||
\(450\) | 0.563627 | − | 7.64542i | 0.0265697 | − | 0.360409i | ||||
\(451\) | 5.50691i | 0.259310i | ||||||||
\(452\) | −41.4795 | + | 23.9482i | −1.95103 | + | 1.12643i | ||||
\(453\) | −2.09637 | − | 0.0771684i | −0.0984960 | − | 0.00362569i | ||||
\(454\) | 6.74310 | + | 3.89313i | 0.316470 | + | 0.182714i | ||||
\(455\) | −7.50506 | − | 5.58135i | −0.351842 | − | 0.261658i | ||||
\(456\) | 2.82153 | − | 4.49649i | 0.132130 | − | 0.210567i | ||||
\(457\) | −5.32319 | − | 9.22004i | −0.249008 | − | 0.431295i | 0.714243 | − | 0.699898i | \(-0.246771\pi\) |
−0.963251 | + | 0.268603i | \(0.913438\pi\) | |||||||
\(458\) | −60.3946 | −2.82205 | ||||||||
\(459\) | −38.5661 | − | 4.27437i | −1.80011 | − | 0.199510i | ||||
\(460\) | 19.8627i | 0.926104i | ||||||||
\(461\) | −6.44303 | − | 11.1597i | −0.300082 | − | 0.519757i | 0.676072 | − | 0.736835i | \(-0.263681\pi\) |
−0.976154 | + | 0.217078i | \(0.930347\pi\) | |||||||
\(462\) | 31.1389 | − | 38.8045i | 1.44871 | − | 1.80535i | ||||
\(463\) | 6.82413 | − | 11.8197i | 0.317144 | − | 0.549310i | −0.662747 | − | 0.748844i | \(-0.730609\pi\) |
0.979891 | + | 0.199534i | \(0.0639427\pi\) | |||||||
\(464\) | −22.6670 | − | 13.0868i | −1.05229 | − | 0.607538i | ||||
\(465\) | −0.455086 | + | 12.3629i | −0.0211041 | + | 0.573318i | ||||
\(466\) | −10.6646 | − | 18.4717i | −0.494029 | − | 0.855683i | ||||
\(467\) | 19.9617 | 0.923719 | 0.461859 | − | 0.886953i | \(-0.347182\pi\) | ||||
0.461859 | + | 0.886953i | \(0.347182\pi\) | |||||||
\(468\) | −39.7268 | − | 27.0148i | −1.83637 | − | 1.24876i | ||||
\(469\) | −18.7945 | − | 2.18703i | −0.867849 | − | 0.100988i | ||||
\(470\) | 28.0955 | − | 16.2210i | 1.29595 | − | 0.748218i | ||||
\(471\) | −26.8523 | + | 14.2127i | −1.23729 | + | 0.654885i | ||||
\(472\) | 22.7550 | + | 13.1376i | 1.04738 | + | 0.604707i | ||||
\(473\) | −2.98884 | − | 1.72561i | −0.137427 | − | 0.0793434i | ||||
\(474\) | −7.18050 | + | 3.80057i | −0.329811 | + | 0.174566i | ||||
\(475\) | −0.410541 | + | 0.237026i | −0.0188369 | + | 0.0108755i | ||||
\(476\) | 88.9003 | + | 10.3449i | 4.07474 | + | 0.474158i | ||||
\(477\) | −5.64614 | + | 2.72747i | −0.258519 | + | 0.124882i | ||||
\(478\) | −60.3153 | −2.75876 | ||||||||
\(479\) | −12.7288 | − | 22.0469i | −0.581594 | − | 1.00735i | −0.995291 | − | 0.0969357i | \(-0.969096\pi\) |
0.413697 | − | 0.910415i | \(-0.364237\pi\) | |||||||
\(480\) | −0.390915 | + | 10.6197i | −0.0178427 | + | 0.484719i | ||||
\(481\) | −18.4217 | − | 10.6358i | −0.839957 | − | 0.484949i | ||||
\(482\) | −25.7364 | + | 44.5768i | −1.17226 | + | 2.03042i | ||||
\(483\) | 15.6713 | + | 12.5756i | 0.713071 | + | 0.572208i | ||||
\(484\) | −15.9719 | − | 27.6641i | −0.725995 | − | 1.25746i | ||||
\(485\) | 8.73895i | 0.396815i | ||||||||
\(486\) | −30.2721 | − | 25.8920i | −1.37317 | − | 1.17448i | ||||
\(487\) | 11.3891 | 0.516088 | 0.258044 | − | 0.966133i | \(-0.416922\pi\) | ||||
0.258044 | + | 0.966133i | \(0.416922\pi\) | |||||||
\(488\) | 8.49085 | + | 14.7066i | 0.384363 | + | 0.665736i | ||||
\(489\) | 5.82593 | − | 9.28440i | 0.263458 | − | 0.419855i | ||||
\(490\) | 13.0236 | + | 12.2620i | 0.588346 | + | 0.553941i | ||||
\(491\) | 17.8295 | + | 10.2939i | 0.804636 | + | 0.464557i | 0.845090 | − | 0.534625i | \(-0.179547\pi\) |
−0.0404536 | + | 0.999181i | \(0.512880\pi\) | |||||||
\(492\) | −10.1629 | − | 0.374101i | −0.458178 | − | 0.0168658i | ||||
\(493\) | 22.6867 | − | 13.0982i | 1.02176 | − | 0.589912i | ||||
\(494\) | 4.28234i | 0.192672i | ||||||||
\(495\) | −11.4772 | + | 5.54426i | −0.515860 | + | 0.249196i | ||||
\(496\) | − | 53.2908i | − | 2.39283i | ||||||
\(497\) | 27.1022 | − | 11.7072i | 1.21570 | − | 0.525139i | ||||
\(498\) | 21.8903 | − | 11.5863i | 0.980927 | − | 0.519196i | ||||
\(499\) | −4.00243 | + | 6.93242i | −0.179173 | + | 0.310338i | −0.941598 | − | 0.336740i | \(-0.890676\pi\) |
0.762424 | + | 0.647078i | \(0.224009\pi\) | |||||||
\(500\) | 2.26501 | − | 3.92311i | 0.101294 | − | 0.175447i | ||||
\(501\) | 1.58189 | + | 2.98869i | 0.0706734 | + | 0.133525i | ||||
\(502\) | 59.3305 | − | 34.2545i | 2.64805 | − | 1.52885i | ||||
\(503\) | 1.54015 | 0.0686721 | 0.0343360 | − | 0.999410i | \(-0.489068\pi\) | ||||
0.0343360 | + | 0.999410i | \(0.489068\pi\) | |||||||
\(504\) | 38.8143 | + | 33.5671i | 1.72893 | + | 1.49520i | ||||
\(505\) | 9.35329 | 0.416216 | ||||||||
\(506\) | 41.2272 | − | 23.8026i | 1.83277 | − | 1.05815i | ||||
\(507\) | −0.871045 | − | 0.0320636i | −0.0386845 | − | 0.00142399i | ||||
\(508\) | −25.5207 | + | 44.2032i | −1.13230 | + | 1.96120i | ||||
\(509\) | 3.03402 | − | 5.25508i | 0.134481 | − | 0.232927i | −0.790918 | − | 0.611922i | \(-0.790397\pi\) |
0.925399 | + | 0.378994i | \(0.123730\pi\) | |||||||
\(510\) | −27.9963 | − | 17.5676i | −1.23970 | − | 0.777905i | ||||
\(511\) | 4.26284 | − | 1.84140i | 0.188577 | − | 0.0814585i | ||||
\(512\) | 50.6969i | 2.24051i | ||||||||
\(513\) | −0.271345 | + | 2.44825i | −0.0119802 | + | 0.108093i | ||||
\(514\) | 48.1885i | 2.12550i | ||||||||
\(515\) | 0.668174 | − | 0.385771i | 0.0294433 | − | 0.0169991i | ||||
\(516\) | 3.38760 | − | 5.39860i | 0.149131 | − | 0.237660i | ||||
\(517\) | −46.7130 | − | 26.9698i | −2.05444 | − | 1.18613i | ||||
\(518\) | 32.6447 | + | 24.2772i | 1.43433 | + | 1.06668i | ||||
\(519\) | 9.74893 | + | 0.358863i | 0.427931 | + | 0.0157523i | ||||
\(520\) | −11.4274 | − | 19.7929i | −0.501126 | − | 0.867976i | ||||
\(521\) | 7.79260 | 0.341400 | 0.170700 | − | 0.985323i | \(-0.445397\pi\) | ||||
0.170700 | + | 0.985323i | \(0.445397\pi\) | |||||||
\(522\) | 26.8205 | + | 1.97723i | 1.17390 | + | 0.0865411i | ||||
\(523\) | 9.16498i | 0.400757i | 0.979719 | + | 0.200378i | \(0.0642171\pi\) | ||||
−0.979719 | + | 0.200378i | \(0.935783\pi\) | |||||||
\(524\) | −35.3178 | − | 61.1722i | −1.54286 | − | 2.67232i | ||||
\(525\) | −1.66123 | − | 4.27087i | −0.0725022 | − | 0.186396i | ||||
\(526\) | −35.0089 | + | 60.6373i | −1.52646 | + | 2.64391i | ||||
\(527\) | 46.1914 | + | 26.6686i | 2.01213 | + | 1.16170i | ||||
\(528\) | 48.5272 | − | 25.6850i | 2.11187 | − | 1.11780i | ||||
\(529\) | −1.88724 | − | 3.26880i | −0.0820541 | − | 0.142122i | ||||
\(530\) | −5.34111 | −0.232003 | ||||||||
\(531\) | −12.1594 | − | 0.896399i | −0.527671 | − | 0.0389004i | ||||
\(532\) | 0.656715 | − | 5.64356i | 0.0284722 | − | 0.244679i | ||||
\(533\) | 3.96808 | − | 2.29097i | 0.171876 | − | 0.0992329i | ||||
\(534\) | 2.34344 | − | 63.6623i | 0.101411 | − | 2.75494i | ||||
\(535\) | −11.6444 | − | 6.72289i | −0.503431 | − | 0.290656i | ||||
\(536\) | −40.0417 | − | 23.1181i | −1.72954 | − | 0.998550i | ||||
\(537\) | 11.8777 | + | 7.45319i | 0.512559 | + | 0.321629i | ||||
\(538\) | −48.3999 | + | 27.9437i | −2.08667 | + | 1.20474i | ||||
\(539\) | 6.82917 | − | 28.9463i | 0.294153 | − | 1.24681i | ||||
\(540\) | −9.45212 | − | 21.5575i | −0.406755 | − | 0.927686i | ||||
\(541\) | 11.5112 | 0.494907 | 0.247453 | − | 0.968900i | \(-0.420406\pi\) | ||||
0.247453 | + | 0.968900i | \(0.420406\pi\) | |||||||
\(542\) | 28.4092 | + | 49.2061i | 1.22028 | + | 2.11358i | ||||
\(543\) | −20.2487 | − | 12.7060i | −0.868956 | − | 0.545267i | ||||
\(544\) | 39.6780 | + | 22.9081i | 1.70118 | + | 0.982176i | ||||
\(545\) | 2.37689 | − | 4.11690i | 0.101815 | − | 0.176349i | ||||
\(546\) | −40.9154 | − | 6.29421i | −1.75102 | − | 0.269367i | ||||
\(547\) | 14.7106 | + | 25.4795i | 0.628980 | + | 1.08943i | 0.987757 | + | 0.156002i | \(0.0498607\pi\) |
−0.358776 | + | 0.933424i | \(0.616806\pi\) | |||||||
\(548\) | − | 17.0345i | − | 0.727677i | ||||||
\(549\) | −6.51608 | − | 4.43103i | −0.278100 | − | 0.189112i | ||||
\(550\) | −10.8571 | −0.462949 | ||||||||
\(551\) | −0.831498 | − | 1.44020i | −0.0354230 | − | 0.0613544i | ||||
\(552\) | 22.9691 | + | 43.3960i | 0.977629 | + | 1.84705i | ||||
\(553\) | −2.89806 | + | 3.89693i | −0.123238 | + | 0.165714i | ||||
\(554\) | −7.93045 | − | 4.57865i | −0.336933 | − | 0.194528i | ||||
\(555\) | −4.87557 | − | 9.21151i | −0.206956 | − | 0.391007i | ||||
\(556\) | −21.3489 | + | 12.3258i | −0.905396 | + | 0.522731i | ||||
\(557\) | 2.45245i | 0.103914i | 0.998649 | + | 0.0519568i | \(0.0165458\pi\) | ||||
−0.998649 | + | 0.0519568i | \(0.983454\pi\) | |||||||
\(558\) | 23.8176 | + | 49.3048i | 1.00828 | + | 2.08724i | ||||
\(559\) | 2.87153i | 0.121453i | ||||||||
\(560\) | 7.82785 | + | 18.1215i | 0.330787 | + | 0.765775i | ||||
\(561\) | −2.02149 | + | 54.9161i | −0.0853473 | + | 2.31856i | ||||
\(562\) | 11.6642 | − | 20.2029i | 0.492023 | − | 0.852209i | ||||
\(563\) | −12.4793 | + | 21.6148i | −0.525939 | + | 0.910953i | 0.473604 | + | 0.880738i | \(0.342953\pi\) |
−0.999543 | + | 0.0302157i | \(0.990381\pi\) | |||||||
\(564\) | 52.9455 | − | 84.3757i | 2.22941 | − | 3.55286i | ||||
\(565\) | 9.15660 | − | 5.28657i | 0.385221 | − | 0.222408i | ||||
\(566\) | −42.3512 | −1.78015 | ||||||||
\(567\) | −22.9929 | − | 6.19101i | −0.965609 | − | 0.259998i | ||||
\(568\) | 72.1418 | 3.02700 | ||||||||
\(569\) | −11.6289 | + | 6.71395i | −0.487509 | + | 0.281463i | −0.723540 | − | 0.690282i | \(-0.757486\pi\) |
0.236032 | + | 0.971745i | \(0.424153\pi\) | |||||||
\(570\) | −1.11522 | + | 1.77726i | −0.0467116 | + | 0.0744411i | ||||
\(571\) | 1.77883 | − | 3.08102i | 0.0744416 | − | 0.128937i | −0.826402 | − | 0.563081i | \(-0.809616\pi\) |
0.900843 | + | 0.434144i | \(0.142949\pi\) | |||||||
\(572\) | −34.0193 | + | 58.9232i | −1.42242 | + | 2.46370i | ||||
\(573\) | −0.0416687 | + | 1.13198i | −0.00174073 | + | 0.0472890i | ||||
\(574\) | −8.04462 | + | 3.47499i | −0.335776 | + | 0.145043i | ||||
\(575\) | − | 4.38469i | − | 0.182854i | ||||||
\(576\) | 0.987006 | + | 2.04320i | 0.0411253 | + | 0.0851334i | ||||
\(577\) | − | 12.8669i | − | 0.535656i | −0.963467 | − | 0.267828i | \(-0.913694\pi\) | ||
0.963467 | − | 0.267828i | \(-0.0863059\pi\) | |||||||
\(578\) | −85.7850 | + | 49.5280i | −3.56819 | + | 2.06009i | ||||
\(579\) | −11.5754 | − | 21.8697i | −0.481059 | − | 0.908875i | ||||
\(580\) | 13.7625 | + | 7.94576i | 0.571455 | + | 0.329930i | ||||
\(581\) | 8.83496 | − | 11.8801i | 0.366536 | − | 0.492869i | ||||
\(582\) | 18.0943 | + | 34.1859i | 0.750031 | + | 1.41705i | ||||
\(583\) | 4.44020 | + | 7.69065i | 0.183894 | + | 0.318514i | ||||
\(584\) | 11.3470 | 0.469542 | ||||||||
\(585\) | 8.76968 | + | 5.96351i | 0.362582 | + | 0.246561i | ||||
\(586\) | 60.1840i | 2.48618i | ||||||||
\(587\) | 11.5624 | + | 20.0267i | 0.477233 | + | 0.826591i | 0.999660 | − | 0.0260930i | \(-0.00830660\pi\) |
−0.522427 | + | 0.852684i | \(0.674973\pi\) | |||||||
\(588\) | 52.9558 | + | 14.5695i | 2.18386 | + | 0.600835i | ||||
\(589\) | 1.69298 | − | 2.93232i | 0.0697578 | − | 0.120824i | ||||
\(590\) | −8.99402 | − | 5.19270i | −0.370278 | − | 0.213780i | ||||
\(591\) | −4.94160 | − | 3.10083i | −0.203270 | − | 0.127551i | ||||
\(592\) | 22.4475 | + | 38.8801i | 0.922585 | + | 1.59796i | ||||
\(593\) | 8.68451 | 0.356630 | 0.178315 | − | 0.983973i | \(-0.442935\pi\) | ||||
0.178315 | + | 0.983973i | \(0.442935\pi\) | |||||||
\(594\) | −33.4179 | + | 45.4524i | −1.37115 | + | 1.86494i | ||||
\(595\) | −19.6247 | − | 2.28364i | −0.804535 | − | 0.0936200i | ||||
\(596\) | −30.2722 | + | 17.4776i | −1.24000 | + | 0.715912i | ||||
\(597\) | −8.60043 | − | 5.39674i | −0.351992 | − | 0.220874i | ||||
\(598\) | −34.3025 | − | 19.8045i | −1.40273 | − | 0.809868i | ||||
\(599\) | −18.0483 | − | 10.4202i | −0.737435 | − | 0.425758i | 0.0837008 | − | 0.996491i | \(-0.473326\pi\) |
−0.821136 | + | 0.570732i | \(0.806659\pi\) | |||||||
\(600\) | 0.411925 | − | 11.1904i | 0.0168168 | − | 0.456847i | ||||
\(601\) | −2.85200 | + | 1.64660i | −0.116335 | + | 0.0671663i | −0.557039 | − | 0.830487i | \(-0.688062\pi\) |
0.440703 | + | 0.897653i | \(0.354729\pi\) | |||||||
\(602\) | 0.634780 | − | 5.45506i | 0.0258717 | − | 0.222332i | ||||
\(603\) | 21.3967 | + | 1.57738i | 0.871340 | + | 0.0642360i | ||||
\(604\) | −5.48657 | −0.223245 | ||||||||
\(605\) | 3.52579 | + | 6.10685i | 0.143344 | + | 0.248279i | ||||
\(606\) | 36.5891 | − | 19.3663i | 1.48633 | − | 0.786701i | ||||
\(607\) | 19.4942 | + | 11.2550i | 0.791244 | + | 0.456825i | 0.840400 | − | 0.541966i | \(-0.182320\pi\) |
−0.0491565 | + | 0.998791i | \(0.515653\pi\) | |||||||
\(608\) | 1.45425 | − | 2.51884i | 0.0589776 | − | 0.102152i | ||||
\(609\) | 14.9824 | − | 5.82769i | 0.607118 | − | 0.236150i | ||||
\(610\) | −3.35605 | − | 5.81285i | −0.135883 | − | 0.235355i | ||||
\(611\) | 44.8796i | 1.81563i | ||||||||
\(612\) | −101.209 | − | 7.46122i | −4.09113 | − | 0.301602i | ||||
\(613\) | 11.2370 | 0.453858 | 0.226929 | − | 0.973911i | \(-0.427132\pi\) | ||||
0.226929 | + | 0.973911i | \(0.427132\pi\) | |||||||
\(614\) | 16.1320 | + | 27.9415i | 0.651036 | + | 1.12763i | ||||
\(615\) | 2.24345 | + | 0.0825827i | 0.0904648 | + | 0.00333006i | ||||
\(616\) | 43.3689 | − | 58.3167i | 1.74738 | − | 2.34965i | ||||
\(617\) | −35.1572 | − | 20.2980i | −1.41538 | − | 0.817167i | −0.419488 | − | 0.907761i | \(-0.637790\pi\) |
−0.995888 | + | 0.0905937i | \(0.971124\pi\) | |||||||
\(618\) | 1.81508 | − | 2.89257i | 0.0730132 | − | 0.116356i | ||||
\(619\) | −10.5155 | + | 6.07113i | −0.422654 | + | 0.244019i | −0.696212 | − | 0.717836i | \(-0.745133\pi\) |
0.273558 | + | 0.961855i | \(0.411799\pi\) | |||||||
\(620\) | 32.3560i | 1.29945i | ||||||||
\(621\) | −18.3561 | − | 13.4960i | −0.736606 | − | 0.541574i | ||||
\(622\) | − | 21.5016i | − | 0.862134i | ||||||
\(623\) | −15.1009 | − | 34.9588i | −0.605007 | − | 1.40059i | ||||
\(624\) | −38.6958 | − | 24.2815i | −1.54907 | − | 0.972037i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 23.9842 | − | 41.5419i | 0.958603 | − | 1.66035i | ||||
\(627\) | 3.48618 | + | 0.128328i | 0.139225 | + | 0.00512493i | ||||
\(628\) | −68.8146 | + | 39.7301i | −2.74600 | + | 1.58540i | ||||
\(629\) | −44.9340 | −1.79164 | ||||||||
\(630\) | −15.3415 | − | 13.2676i | −0.611222 | − | 0.528592i | ||||
\(631\) | 22.4079 | 0.892046 | 0.446023 | − | 0.895022i | \(-0.352840\pi\) | ||||
0.446023 | + | 0.895022i | \(0.352840\pi\) | |||||||
\(632\) | −10.2773 | + | 5.93358i | −0.408808 | + | 0.236025i | ||||
\(633\) | 17.4066 | + | 32.8865i | 0.691848 | + | 1.30712i | ||||
\(634\) | 36.0808 | − | 62.4938i | 1.43295 | − | 2.48194i | ||||
\(635\) | 5.63370 | − | 9.75786i | 0.223567 | − | 0.387229i | ||||
\(636\) | −14.4945 | + | 7.67183i | −0.574746 | + | 0.304208i | ||||
\(637\) | −23.6987 | + | 7.12132i | −0.938976 | + | 0.282157i | ||||
\(638\) | − | 38.0873i | − | 1.50789i | ||||||
\(639\) | −30.1428 | + | 14.5611i | −1.19243 | + | 0.576026i | ||||
\(640\) | − | 10.3380i | − | 0.408645i | ||||||
\(641\) | −19.0012 | + | 10.9703i | −0.750502 | + | 0.433302i | −0.825875 | − | 0.563853i | \(-0.809318\pi\) |
0.0753736 | + | 0.997155i | \(0.475985\pi\) | |||||||
\(642\) | −59.4716 | − | 2.18918i | −2.34716 | − | 0.0864001i | ||||
\(643\) | 1.23157 | + | 0.711050i | 0.0485686 | + | 0.0280411i | 0.524088 | − | 0.851664i | \(-0.324406\pi\) |
−0.475519 | + | 0.879705i | \(0.657740\pi\) | |||||||
\(644\) | 42.1690 | + | 31.3602i | 1.66169 | + | 1.23577i | ||||
\(645\) | −0.747813 | + | 1.19174i | −0.0294451 | + | 0.0469247i | ||||
\(646\) | 4.52301 | + | 7.83409i | 0.177956 | + | 0.308228i | ||||
\(647\) | 1.82171 | 0.0716186 | 0.0358093 | − | 0.999359i | \(-0.488599\pi\) | ||||
0.0358093 | + | 0.999359i | \(0.488599\pi\) | |||||||
\(648\) | −45.5799 | − | 36.1683i | −1.79055 | − | 1.42083i | ||||
\(649\) | 17.2673i | 0.677800i | ||||||||
\(650\) | 4.51675 | + | 7.82324i | 0.177161 | + | 0.306853i | ||||
\(651\) | 25.5283 | + | 20.4854i | 1.00053 | + | 0.802885i | ||||
\(652\) | 14.3336 | − | 24.8265i | 0.561347 | − | 0.972282i | ||||
\(653\) | −4.13529 | − | 2.38751i | −0.161827 | − | 0.0934306i | 0.416900 | − | 0.908953i | \(-0.363117\pi\) |
−0.578726 | + | 0.815522i | \(0.696450\pi\) | |||||||
\(654\) | 0.773990 | − | 21.0263i | 0.0302654 | − | 0.822194i | ||||
\(655\) | 7.79640 | + | 13.5038i | 0.304630 | + | 0.527635i | ||||
\(656\) | −9.67047 | −0.377568 | ||||||||
\(657\) | −4.74109 | + | 2.29027i | −0.184968 | + | 0.0893521i | ||||
\(658\) | 9.92108 | − | 85.2580i | 0.386764 | − | 3.32370i | ||||
\(659\) | 6.24797 | − | 3.60727i | 0.243386 | − | 0.140519i | −0.373346 | − | 0.927692i | \(-0.621789\pi\) |
0.616732 | + | 0.787173i | \(0.288456\pi\) | |||||||
\(660\) | −29.4637 | + | 15.5949i | −1.14687 | + | 0.607030i | ||||
\(661\) | 39.7860 | + | 22.9705i | 1.54750 | + | 0.893448i | 0.998332 | + | 0.0577339i | \(0.0183875\pi\) |
0.549165 | + | 0.835714i | \(0.314946\pi\) | |||||||
\(662\) | 56.5219 | + | 32.6329i | 2.19679 | + | 1.26832i | ||||
\(663\) | 40.4114 | − | 21.3894i | 1.56945 | − | 0.830696i | ||||
\(664\) | 31.3310 | − | 18.0890i | 1.21588 | − | 0.701988i | ||||
\(665\) | −0.144970 | + | 1.24582i | −0.00562169 | + | 0.0483107i | ||||
\(666\) | −38.1454 | − | 25.9394i | −1.47811 | − | 1.00513i | ||||
\(667\) | 15.3817 | 0.595582 | ||||||||
\(668\) | 4.42201 | + | 7.65915i | 0.171093 | + | 0.296341i | ||||
\(669\) | −0.505893 | + | 13.7432i | −0.0195590 | + | 0.531342i | ||||
\(670\) | 15.8267 | + | 9.13754i | 0.611438 | + | 0.353014i | ||||
\(671\) | −5.57993 | + | 9.66473i | −0.215411 | + | 0.373103i | ||||
\(672\) | 21.9286 | + | 17.5967i | 0.845914 | + | 0.678809i | ||||
\(673\) | −3.92869 | − | 6.80469i | −0.151440 | − | 0.262302i | 0.780317 | − | 0.625384i | \(-0.215058\pi\) |
−0.931757 | + | 0.363082i | \(0.881724\pi\) | |||||||
\(674\) | 46.4488i | 1.78914i | ||||||||
\(675\) | 2.08655 | + | 4.75881i | 0.0803115 | + | 0.183167i | ||||
\(676\) | −2.27968 | −0.0876799 | ||||||||
\(677\) | −7.33822 | − | 12.7102i | −0.282031 | − | 0.488491i | 0.689854 | − | 0.723948i | \(-0.257675\pi\) |
−0.971885 | + | 0.235457i | \(0.924341\pi\) | |||||||
\(678\) | 24.8737 | − | 39.6395i | 0.955268 | − | 1.52235i | ||||
\(679\) | 18.5530 | + | 13.7975i | 0.711999 | + | 0.529498i | ||||
\(680\) | −41.8105 | − | 24.1393i | −1.60336 | − | 0.925701i | ||||
\(681\) | −5.27398 | − | 0.194138i | −0.202100 | − | 0.00743939i | ||||
\(682\) | 67.1584 | − | 38.7739i | 2.57163 | − | 1.48473i | ||||
\(683\) | 35.8729i | 1.37264i | 0.727300 | + | 0.686319i | \(0.240775\pi\) | ||||
−0.727300 | + | 0.686319i | \(0.759225\pi\) | |||||||
\(684\) | −0.473653 | + | 6.42494i | −0.0181106 | + | 0.245664i | ||||
\(685\) | 3.76036i | 0.143676i | ||||||||
\(686\) | 46.5948 | − | 8.28959i | 1.77900 | − | 0.316498i | ||||
\(687\) | 36.1802 | − | 19.1499i | 1.38036 | − | 0.730613i | ||||
\(688\) | 3.03027 | − | 5.24858i | 0.115528 | − | 0.200100i | ||||
\(689\) | 3.69440 | − | 6.39888i | 0.140745 | − | 0.243778i | ||||
\(690\) | −9.07864 | − | 17.1525i | −0.345618 | − | 0.652983i | ||||
\(691\) | 27.2999 | − | 15.7616i | 1.03854 | − | 0.599600i | 0.119119 | − | 0.992880i | \(-0.461993\pi\) |
0.919419 | + | 0.393280i | \(0.128660\pi\) | |||||||
\(692\) | 25.5147 | 0.969922 | ||||||||
\(693\) | −6.35011 | + | 33.1199i | −0.241221 | + | 1.25812i | ||||
\(694\) | 3.30572 | 0.125483 | ||||||||
\(695\) | 4.71277 | − | 2.72092i | 0.178766 | − | 0.103210i | ||||
\(696\) | 39.2566 | + | 1.44505i | 1.48802 | + | 0.0547746i | ||||
\(697\) | 4.83945 | − | 8.38217i | 0.183307 | − | 0.317497i | ||||
\(698\) | 30.0695 | − | 52.0820i | 1.13815 | − | 1.97133i | ||||
\(699\) | 12.2458 | + | 7.68418i | 0.463178 | + | 0.290643i | ||||
\(700\) | −4.75275 | − | 11.0027i | −0.179637 | − | 0.415861i | ||||
\(701\) | − | 26.3154i | − | 0.993918i | −0.867774 | − | 0.496959i | \(-0.834450\pi\) | ||
0.867774 | − | 0.496959i | \(-0.165550\pi\) | |||||||
\(702\) | 46.6537 | + | 5.17074i | 1.76083 | + | 0.195157i | ||||
\(703\) | 2.85250i | 0.107584i | ||||||||
\(704\) | 2.78306 | − | 1.60680i | 0.104890 | − | 0.0605585i | ||||
\(705\) | −11.6877 | + | 18.6259i | −0.440184 | + | 0.701493i | ||||
\(706\) | −70.9415 | − | 40.9581i | −2.66992 | − | 1.54148i | ||||
\(707\) | 14.7674 | − | 19.8573i | 0.555386 | − | 0.746809i | ||||
\(708\) | −31.8664 | − | 1.17302i | −1.19761 | − | 0.0440847i | ||||
\(709\) | −14.9552 | − | 25.9032i | −0.561655 | − | 0.972816i | −0.997352 | − | 0.0727223i | \(-0.976831\pi\) |
0.435697 | − | 0.900094i | \(-0.356502\pi\) | |||||||
\(710\) | −28.5144 | −1.07013 | ||||||||
\(711\) | 3.09650 | − | 4.55357i | 0.116128 | − | 0.170772i | ||||
\(712\) | − | 93.0547i | − | 3.48737i | ||||||
\(713\) | 15.6590 | + | 27.1222i | 0.586434 | + | 1.01573i | ||||
\(714\) | −81.4983 | + | 31.7003i | −3.05000 | + | 1.18635i | ||||
\(715\) | 7.50977 | − | 13.0073i | 0.280849 | − | 0.486445i | ||||
\(716\) | 31.7609 | + | 18.3372i | 1.18696 | + | 0.685293i | ||||
\(717\) | 36.1327 | − | 19.1247i | 1.34940 | − | 0.714226i | ||||
\(718\) | −33.7534 | − | 58.4625i | −1.25966 | − | 2.18180i | ||||
\(719\) | −5.15995 | −0.192434 | −0.0962168 | − | 0.995360i | \(-0.530674\pi\) | ||||
−0.0962168 | + | 0.995360i | \(0.530674\pi\) | |||||||
\(720\) | −9.73605 | − | 20.1546i | −0.362841 | − | 0.751117i | ||||
\(721\) | 0.235945 | − | 2.02762i | 0.00878706 | − | 0.0755127i | ||||
\(722\) | −41.5503 | + | 23.9891i | −1.54634 | + | 0.892781i | ||||
\(723\) | 1.28339 | − | 34.8648i | 0.0477299 | − | 1.29664i | ||||
\(724\) | −54.1452 | − | 31.2608i | −2.01229 | − | 1.16180i | ||||
\(725\) | −3.03806 | − | 1.75402i | −0.112831 | − | 0.0651428i | ||||
\(726\) | 26.4370 | + | 16.5891i | 0.981168 | + | 0.615680i | ||||
\(727\) | −18.9436 | + | 10.9371i | −0.702581 | + | 0.405635i | −0.808308 | − | 0.588760i | \(-0.799616\pi\) |
0.105727 | + | 0.994395i | \(0.466283\pi\) | |||||||
\(728\) | −60.0630 | − | 6.98925i | −2.22608 | − | 0.259039i | ||||
\(729\) | 26.3447 | + | 5.91231i | 0.975731 | + | 0.218975i | ||||
\(730\) | −4.48496 | −0.165996 | ||||||||
\(731\) | 3.03291 | + | 5.25315i | 0.112176 | + | 0.194295i | ||||
\(732\) | −17.4570 | − | 10.9542i | −0.645228 | − | 0.404878i | ||||
\(733\) | −29.8581 | − | 17.2386i | −1.10284 | − | 0.636722i | −0.165871 | − | 0.986147i | \(-0.553044\pi\) |
−0.936964 | + | 0.349425i | \(0.886377\pi\) | |||||||
\(734\) | 43.9382 | − | 76.1032i | 1.62179 | − | 2.80902i | ||||
\(735\) | −11.6900 | − | 3.21621i | −0.431192 | − | 0.118632i | ||||
\(736\) | 13.4509 | + | 23.2977i | 0.495808 | + | 0.858765i | ||||
\(737\) | − | 30.3850i | − | 1.11925i | ||||||
\(738\) | 8.94715 | − | 4.32209i | 0.329349 | − | 0.159098i | ||||
\(739\) | 9.11445 | 0.335280 | 0.167640 | − | 0.985848i | \(-0.446385\pi\) | ||||
0.167640 | + | 0.985848i | \(0.446385\pi\) | |||||||
\(740\) | −13.6292 | − | 23.6064i | −0.501019 | − | 0.867790i | ||||
\(741\) | −1.35784 | − | 2.56540i | −0.0498815 | − | 0.0942422i | ||||
\(742\) | −8.43281 | + | 11.3393i | −0.309578 | + | 0.416279i | ||||
\(743\) | −44.7080 | − | 25.8122i | −1.64018 | − | 0.946956i | −0.980769 | − | 0.195170i | \(-0.937474\pi\) |
−0.659407 | − | 0.751786i | \(-0.729193\pi\) | |||||||
\(744\) | 37.4162 | + | 70.6912i | 1.37175 | + | 2.59167i | ||||
\(745\) | 6.68258 | − | 3.85819i | 0.244831 | − | 0.141353i | ||||
\(746\) | 83.5171i | 3.05778i | ||||||||
\(747\) | −9.43990 | + | 13.8819i | −0.345388 | + | 0.507913i | ||||
\(748\) | 143.725i | 5.25511i | ||||||||
\(749\) | −32.6576 | + | 14.1069i | −1.19328 | + | 0.515455i | ||||
\(750\) | −0.162815 | + | 4.42307i | −0.00594518 | + | 0.161508i | ||||
\(751\) | 1.41105 | − | 2.44401i | 0.0514900 | − | 0.0891833i | −0.839132 | − | 0.543928i | \(-0.816936\pi\) |
0.890622 | + | 0.454745i | \(0.150270\pi\) | |||||||
\(752\) | 47.3605 | − | 82.0309i | 1.72706 | − | 2.99136i | ||||
\(753\) | −24.6814 | + | 39.3331i | −0.899441 | + | 1.43338i | ||||
\(754\) | −27.4443 | + | 15.8450i | −0.999462 | + | 0.577040i | ||||
\(755\) | 1.21116 | 0.0440786 | ||||||||
\(756\) | −60.6906 | − | 13.9689i | −2.20729 | − | 0.508044i | ||||
\(757\) | 14.7361 | 0.535592 | 0.267796 | − | 0.963476i | \(-0.413705\pi\) | ||||
0.267796 | + | 0.963476i | \(0.413705\pi\) | |||||||
\(758\) | 44.2715 | − | 25.5602i | 1.60801 | − | 0.928388i | ||||
\(759\) | −17.1505 | + | 27.3316i | −0.622523 | + | 0.992073i | ||||
\(760\) | −1.53241 | + | 2.65421i | −0.0555864 | + | 0.0962785i | ||||
\(761\) | 2.10497 | − | 3.64591i | 0.0763050 | − | 0.132164i | −0.825348 | − | 0.564624i | \(-0.809021\pi\) |
0.901653 | + | 0.432460i | \(0.142354\pi\) | |||||||
\(762\) | 1.83451 | − | 49.8365i | 0.0664572 | − | 1.80539i | ||||
\(763\) | −4.98753 | − | 11.5462i | −0.180561 | − | 0.417999i | ||||
\(764\) | 2.96259i | 0.107183i | ||||||||
\(765\) | 22.3419 | + | 1.64706i | 0.807772 | + | 0.0595497i | ||||
\(766\) | − | 36.3950i | − | 1.31500i | ||||||
\(767\) | 12.4422 | − | 7.18348i | 0.449260 | − | 0.259381i | ||||
\(768\) | −22.6309 | − | 42.7570i | −0.816622 | − | 1.54286i | ||||
\(769\) | 24.9362 | + | 14.3969i | 0.899221 | + | 0.519165i | 0.876947 | − | 0.480586i | \(-0.159576\pi\) |
0.0222736 | + | 0.999752i | \(0.492910\pi\) | |||||||
\(770\) | −17.1418 | + | 23.0499i | −0.617746 | + | 0.830662i | ||||
\(771\) | −15.2796 | − | 28.8680i | −0.550280 | − | 1.03965i | ||||
\(772\) | −32.3581 | − | 56.0458i | −1.16459 | − | 2.01713i | ||||
\(773\) | −23.0284 | −0.828275 | −0.414137 | − | 0.910214i | \(-0.635917\pi\) | ||||
−0.414137 | + | 0.910214i | \(0.635917\pi\) | |||||||
\(774\) | −0.457832 | + | 6.21034i | −0.0164564 | + | 0.223226i | ||||
\(775\) | − | 7.14258i | − | 0.256569i | ||||||
\(776\) | 28.2494 | + | 48.9294i | 1.01409 | + | 1.75646i | ||||
\(777\) | −27.2540 | − | 4.19262i | −0.977733 | − | 0.150409i | ||||
\(778\) | 3.02024 | − | 5.23120i | 0.108281 | − | 0.187548i | ||||
\(779\) | −0.532116 | − | 0.307218i | −0.0190650 | − | 0.0110072i | ||||
\(780\) | 23.4945 | + | 14.7427i | 0.841238 | + | 0.527874i | ||||
\(781\) | 23.7047 | + | 41.0578i | 0.848221 | + | 1.46916i | ||||
\(782\) | −83.6703 | −2.99204 | ||||||||
\(783\) | −16.6941 | + | 7.31974i | −0.596600 | + | 0.261586i | ||||
\(784\) | 50.8315 | + | 11.9924i | 1.81541 | + | 0.428301i | ||||
\(785\) | 15.1908 | − | 8.77042i | 0.542183 | − | 0.313030i | ||||
\(786\) | 58.4587 | + | 36.6826i | 2.08515 | + | 1.30843i | ||||
\(787\) | −5.85487 | − | 3.38031i | −0.208704 | − | 0.120495i | 0.392005 | − | 0.919963i | \(-0.371782\pi\) |
−0.600709 | + | 0.799468i | \(0.705115\pi\) | |||||||
\(788\) | −13.2139 | − | 7.62902i | −0.470724 | − | 0.271773i | ||||
\(789\) | 1.74578 | − | 47.4262i | 0.0621516 | − | 1.68842i | ||||
\(790\) | 4.06214 | − | 2.34528i | 0.144524 | − | 0.0834412i | ||||
\(791\) | 3.23337 | − | 27.7864i | 0.114965 | − | 0.987970i | ||||
\(792\) | −46.3384 | + | 68.1433i | −1.64656 | + | 2.42137i | ||||
\(793\) | 9.28539 | 0.329734 | ||||||||
\(794\) | 19.7252 | + | 34.1651i | 0.700022 | + | 1.21247i | ||||
\(795\) | 3.19967 | − | 1.69356i | 0.113481 | − | 0.0600642i | ||||
\(796\) | −22.9976 | − | 13.2777i | −0.815128 | − | 0.470615i | ||||
\(797\) | 3.18883 | − | 5.52322i | 0.112954 | − | 0.195642i | −0.804006 | − | 0.594621i | \(-0.797302\pi\) |
0.916960 | + | 0.398979i | \(0.130635\pi\) | |||||||
\(798\) | 2.01239 | + | 5.17367i | 0.0712380 | + | 0.183146i | ||||
\(799\) | 47.4018 | + | 82.1024i | 1.67696 | + | 2.90457i | ||||
\(800\) | − | 6.13541i | − | 0.216920i | ||||||
\(801\) | 18.7821 | + | 38.8808i | 0.663633 | + | 1.37379i | ||||
\(802\) | 44.5264 | 1.57228 | ||||||||
\(803\) | 3.72846 | + | 6.45787i | 0.131574 | + | 0.227893i | ||||
\(804\) | 56.0749 | + | 2.06415i | 1.97761 | + | 0.0727968i | ||||
\(805\) | −9.30881 | − | 6.92276i | −0.328092 | − | 0.243995i | ||||
\(806\) | −55.8781 | − | 32.2612i | −1.96822 | − | 1.13635i | ||||
\(807\) | 20.1343 | − | 32.0867i | 0.708760 | − | 1.12950i | ||||
\(808\) | 52.3691 | − | 30.2353i | 1.84234 | − | 1.06367i | ||||
\(809\) | − | 24.8244i | − | 0.872781i | −0.899757 | − | 0.436390i | \(-0.856257\pi\) | ||
0.899757 | − | 0.436390i | \(-0.143743\pi\) | |||||||
\(810\) | 18.0157 | + | 14.2957i | 0.633006 | + | 0.502300i | ||||
\(811\) | − | 52.6052i | − | 1.84722i | −0.383336 | − | 0.923609i | \(-0.625225\pi\) | ||
0.383336 | − | 0.923609i | \(-0.374775\pi\) | |||||||
\(812\) | 38.5979 | − | 16.6729i | 1.35452 | − | 0.585104i | ||||
\(813\) | −32.6212 | − | 20.4697i | −1.14407 | − | 0.717903i | ||||
\(814\) | −32.6652 | + | 56.5777i | −1.14491 | + | 1.98305i | ||||
\(815\) | −3.16414 | + | 5.48045i | −0.110835 | + | 0.191972i | ||||
\(816\) | −96.4359 | − | 3.54985i | −3.37593 | − | 0.124270i | ||||
\(817\) | 0.333480 | − | 0.192535i | 0.0116670 | − | 0.00673594i | ||||
\(818\) | −4.88690 | −0.170866 | ||||||||
\(819\) | 26.5067 | − | 9.20278i | 0.926219 | − | 0.321571i | ||||
\(820\) | 5.87151 | 0.205042 | ||||||||
\(821\) | −23.1200 | + | 13.3483i | −0.806892 | + | 0.465859i | −0.845875 | − | 0.533380i | \(-0.820921\pi\) |
0.0389833 | + | 0.999240i | \(0.487588\pi\) | |||||||
\(822\) | 7.78595 | + | 14.7101i | 0.271566 | + | 0.513075i | ||||
\(823\) | −20.6957 | + | 35.8460i | −0.721406 | + | 1.24951i | 0.239030 | + | 0.971012i | \(0.423171\pi\) |
−0.960436 | + | 0.278500i | \(0.910163\pi\) | |||||||
\(824\) | 2.49407 | − | 4.31986i | 0.0868852 | − | 0.150489i | ||||
\(825\) | 6.50411 | − | 3.44257i | 0.226444 | − | 0.119855i | ||||
\(826\) | −25.2244 | + | 10.8960i | −0.877670 | + | 0.379122i | ||||
\(827\) | − | 27.3917i | − | 0.952502i | −0.879309 | − | 0.476251i | \(-0.841995\pi\) | ||
0.879309 | − | 0.476251i | \(-0.158005\pi\) | |||||||
\(828\) | −49.2747 | − | 33.5075i | −1.71241 | − | 1.16447i | ||||
\(829\) | 19.1296i | 0.664398i | 0.943209 | + | 0.332199i | \(0.107790\pi\) | ||||
−0.943209 | + | 0.332199i | \(0.892210\pi\) | |||||||
\(830\) | −12.3837 | + | 7.14975i | −0.429846 | + | 0.248172i | ||||
\(831\) | 6.20264 | + | 0.228322i | 0.215167 | + | 0.00792042i | ||||
\(832\) | −2.31560 | − | 1.33691i | −0.0802790 | − | 0.0463491i | ||||
\(833\) | −35.8327 | + | 38.0583i | −1.24153 | + | 1.31864i | ||||
\(834\) | 12.8021 | − | 20.4019i | 0.443302 | − | 0.706461i | ||||
\(835\) | −0.976158 | − | 1.69076i | −0.0337814 | − | 0.0585110i | ||||
\(836\) | 9.12395 | 0.315558 | ||||||||
\(837\) | −29.9018 | − | 21.9847i | −1.03356 | − | 0.759902i | ||||
\(838\) | 30.5854i | 1.05656i | ||||||||
\(839\) | 9.71201 | + | 16.8217i | 0.335296 | + | 0.580749i | 0.983542 | − | 0.180682i | \(-0.0578304\pi\) |
−0.648246 | + | 0.761431i | \(0.724497\pi\) | |||||||
\(840\) | −23.1072 | − | 18.5425i | −0.797274 | − | 0.639777i | ||||
\(841\) | −8.34680 | + | 14.4571i | −0.287821 | + | 0.498520i | ||||
\(842\) | 76.7388 | + | 44.3052i | 2.64460 | + | 1.52686i | ||||
\(843\) | −0.581654 | + | 15.8013i | −0.0200332 | + | 0.544226i | ||||
\(844\) | 48.6584 | + | 84.2787i | 1.67489 | + | 2.90099i | ||||
\(845\) | 0.503239 | 0.0173119 | ||||||||
\(846\) | −7.15553 | + | 97.0624i | −0.246012 | + | 3.33708i | ||||
\(847\) | 18.5317 | + | 2.15645i | 0.636757 | + | 0.0740964i | ||||
\(848\) | −13.5052 | + | 7.79725i | −0.463772 | + | 0.267759i | ||||
\(849\) | 25.3711 | − | 13.4287i | 0.870733 | − | 0.460871i | ||||
\(850\) | 16.5258 | + | 9.54118i | 0.566831 | + | 0.327260i | ||||
\(851\) | −22.8491 | − | 13.1920i | −0.783258 | − | 0.452214i | ||||
\(852\) | −77.3814 | + | 40.9573i | −2.65104 | + | 1.40317i | ||||
\(853\) | 33.1978 | − | 19.1667i | 1.13667 | − | 0.656257i | 0.191066 | − | 0.981577i | \(-0.438805\pi\) |
0.945604 | + | 0.325320i | \(0.105472\pi\) | |||||||
\(854\) | −17.6395 | − | 2.05263i | −0.603612 | − | 0.0702395i | ||||
\(855\) | 0.104559 | − | 1.41831i | 0.00357584 | − | 0.0485050i | ||||
\(856\) | −86.9293 | −2.97118 | ||||||||
\(857\) | 10.1058 | + | 17.5038i | 0.345208 | + | 0.597918i | 0.985392 | − | 0.170304i | \(-0.0544750\pi\) |
−0.640183 | + | 0.768222i | \(0.721142\pi\) | |||||||
\(858\) | 2.44541 | − | 66.4324i | 0.0834850 | − | 2.26797i | ||||
\(859\) | −18.2808 | − | 10.5544i | −0.623732 | − | 0.360112i | 0.154589 | − | 0.987979i | \(-0.450595\pi\) |
−0.778320 | + | 0.627867i | \(0.783928\pi\) | |||||||
\(860\) | −1.83985 | + | 3.18672i | −0.0627385 | + | 0.108666i | ||||
\(861\) | 3.71740 | − | 4.63252i | 0.126689 | − | 0.157876i | ||||
\(862\) | 42.5328 | + | 73.6689i | 1.44867 | + | 2.50917i | ||||
\(863\) | 28.8274i | 0.981295i | 0.871358 | + | 0.490648i | \(0.163240\pi\) | ||||
−0.871358 | + | 0.490648i | \(0.836760\pi\) | |||||||
\(864\) | −25.6854 | − | 18.8846i | −0.873834 | − | 0.642468i | ||||
\(865\) | −5.63236 | −0.191506 | ||||||||
\(866\) | 1.79272 | + | 3.10509i | 0.0609192 | + | 0.105515i | ||||
\(867\) | 35.6864 | − | 56.8711i | 1.21197 | − | 1.93144i | ||||
\(868\) | 68.6926 | + | 51.0852i | 2.33158 | + | 1.73394i | ||||
\(869\) | −6.75391 | − | 3.89937i | −0.229111 | − | 0.132277i | ||||
\(870\) | −15.5163 | − | 0.571165i | −0.526053 | − | 0.0193643i | ||||
\(871\) | −21.8943 | + | 12.6407i | −0.741861 | + | 0.428314i | ||||
\(872\) | − | 30.7340i | − | 1.04079i | ||||||
\(873\) | −21.6793 | − | 14.7422i | −0.733732 | − | 0.498948i | ||||
\(874\) | 5.31155i | 0.179666i | ||||||||
\(875\) | 1.04917 | + | 2.42884i | 0.0354684 | + | 0.0821096i | ||||
\(876\) | −12.1711 | + | 6.44207i | −0.411225 | + | 0.217657i | ||||
\(877\) | 1.70318 | − | 2.94999i | 0.0575123 | − | 0.0996142i | −0.835836 | − | 0.548979i | \(-0.815017\pi\) |
0.893348 | + | 0.449365i | \(0.148350\pi\) | |||||||
\(878\) | −11.0720 | + | 19.1773i | −0.373662 | + | 0.647201i | ||||
\(879\) | −19.0831 | − | 36.0541i | −0.643657 | − | 1.21607i | ||||
\(880\) | −27.4527 | + | 15.8498i | −0.925431 | + | 0.534298i | ||||
\(881\) | 13.9772 | 0.470904 | 0.235452 | − | 0.971886i | \(-0.424343\pi\) | ||||
0.235452 | + | 0.971886i | \(0.424343\pi\) | |||||||
\(882\) | −52.3893 | + | 11.6230i | −1.76404 | + | 0.391367i | ||||
\(883\) | −35.5207 | −1.19537 | −0.597684 | − | 0.801732i | \(-0.703912\pi\) | ||||
−0.597684 | + | 0.801732i | \(0.703912\pi\) | |||||||
\(884\) | 103.563 | − | 59.7921i | 3.48320 | − | 2.01102i | ||||
\(885\) | 7.03449 | + | 0.258943i | 0.236462 | + | 0.00870429i | ||||
\(886\) | −1.80913 | + | 3.13351i | −0.0607789 | + | 0.105272i | ||||
\(887\) | 21.5923 | − | 37.3989i | 0.724997 | − | 1.25573i | −0.233978 | − | 0.972242i | \(-0.575174\pi\) |
0.958975 | − | 0.283490i | \(-0.0914922\pi\) | |||||||
\(888\) | −57.0753 | − | 35.8145i | −1.91532 | − | 1.20186i | ||||
\(889\) | −11.8214 | − | 27.3667i | −0.396478 | − | 0.917849i | ||||
\(890\) | 36.7803i | 1.23288i | ||||||||
\(891\) | 5.60747 | − | 37.8251i | 0.187857 | − | 1.26719i | ||||
\(892\) | 35.9683i | 1.20431i | ||||||||
\(893\) | 5.21202 | − | 3.00916i | 0.174414 | − | 0.100698i | ||||
\(894\) | 18.1531 | − | 28.9293i | 0.607129 | − | 0.967541i | ||||
\(895\) | −7.01122 | − | 4.04793i | −0.234359 | − | 0.135307i | ||||
\(896\) | −21.9478 | − | 16.3221i | −0.733226 | − | 0.545285i | ||||
\(897\) | 26.8290 | + | 0.987589i | 0.895794 | + | 0.0329746i | ||||
\(898\) | −9.80437 | − | 16.9817i | −0.327176 | − | 0.566686i | ||||
\(899\) | 25.0565 | 0.835682 | ||||||||
\(900\) | 5.91133 | + | 12.2370i | 0.197044 | + | 0.407902i | ||||
\(901\) | − | 15.6081i | − | 0.519981i | ||||||
\(902\) | −7.03615 | − | 12.1870i | −0.234278 | − | 0.405782i | ||||
\(903\) | 1.34941 | + | 3.46921i | 0.0449056 | + | 0.115448i | ||||
\(904\) | 34.1785 | − | 59.1990i | 1.13676 | − | 1.96893i | ||||
\(905\) | 11.9526 | + | 6.90081i | 0.397316 | + | 0.229391i | ||||
\(906\) | 4.73793 | − | 2.50774i | 0.157407 | − | 0.0833142i | ||||
\(907\) | 3.24606 | + | 5.62234i | 0.107784 | + | 0.186687i | 0.914872 | − | 0.403744i | \(-0.132291\pi\) |
−0.807088 | + | 0.590431i | \(0.798958\pi\) | |||||||
\(908\) | −13.8029 | −0.458067 | ||||||||
\(909\) | −15.7786 | + | 23.2033i | −0.523342 | + | 0.769604i | ||||
\(910\) | 23.7402 | + | 2.76254i | 0.786980 | + | 0.0915772i | ||||
\(911\) | 27.1552 | − | 15.6781i | 0.899691 | − | 0.519437i | 0.0225913 | − | 0.999745i | \(-0.492808\pi\) |
0.877100 | + | 0.480308i | \(0.159475\pi\) | |||||||
\(912\) | −0.225352 | + | 6.12194i | −0.00746214 | + | 0.202718i | ||||
\(913\) | 20.5898 | + | 11.8875i | 0.681423 | + | 0.393420i | ||||
\(914\) | 23.5608 | + | 13.6028i | 0.779321 | + | 0.449941i | ||||
\(915\) | 3.85362 | + | 2.41814i | 0.127397 | + | 0.0799411i | ||||
\(916\) | 92.7195 | − | 53.5316i | 3.06354 | − | 1.76873i | ||||
\(917\) | 40.9781 | + | 4.76844i | 1.35322 | + | 0.157468i | ||||
\(918\) | 90.8094 | − | 39.8164i | 2.99716 | − | 1.31414i | ||||
\(919\) | −29.6866 | −0.979269 | −0.489635 | − | 0.871928i | \(-0.662870\pi\) | ||||
−0.489635 | + | 0.871928i | \(0.662870\pi\) | |||||||
\(920\) | −14.1739 | − | 24.5499i | −0.467299 | − | 0.809386i | ||||
\(921\) | −18.5238 | − | 11.6236i | −0.610380 | − | 0.383011i | ||||
\(922\) | 28.5173 | + | 16.4644i | 0.939166 | + | 0.542228i | ||||
\(923\) | 19.7231 | − | 34.1614i | 0.649194 | − | 1.12444i | ||||
\(924\) | −13.4104 | + | 87.1742i | −0.441171 | + | 2.86782i | ||||
\(925\) | 3.00864 | + | 5.21112i | 0.0989235 | + | 0.171340i | ||||
\(926\) | 34.8766i | 1.14612i | ||||||||
\(927\) | −0.170174 | + | 2.30836i | −0.00558926 | + | 0.0758165i | ||||
\(928\) | 21.5233 | 0.706538 | ||||||||
\(929\) | 17.0653 | + | 29.5579i | 0.559894 | + | 0.969765i | 0.997505 | + | 0.0706002i | \(0.0224915\pi\) |
−0.437611 | + | 0.899165i | \(0.644175\pi\) | |||||||
\(930\) | −14.7889 | − | 27.9410i | −0.484948 | − | 0.916223i | ||||
\(931\) | 2.41601 | + | 2.27473i | 0.0791816 | + | 0.0745512i | ||||
\(932\) | 32.7453 | + | 18.9055i | 1.07261 | + | 0.619270i | ||||
\(933\) | 6.81770 | + | 12.8808i | 0.223201 | + | 0.421699i | ||||
\(934\) | −44.1760 | + | 25.5050i | −1.44548 | + | 0.834549i | ||||
\(935\) | − | 31.7273i | − | 1.03759i | ||||||
\(936\) | 68.3790 | + | 5.04097i | 2.23504 | + | 0.164769i | ||||
\(937\) | 54.1542i | 1.76914i | 0.466407 | + | 0.884570i | \(0.345548\pi\) | ||||
−0.466407 | + | 0.884570i | \(0.654452\pi\) | |||||||
\(938\) | 44.3872 | − | 19.1737i | 1.44929 | − | 0.626042i | ||||
\(939\) | −1.19602 | + | 32.4912i | −0.0390305 | + | 1.06031i | ||||
\(940\) | −28.7554 | + | 49.8058i | −0.937898 | + | 1.62449i | ||||
\(941\) | −18.8053 | + | 32.5717i | −0.613035 | + | 1.06181i | 0.377691 | + | 0.925932i | \(0.376718\pi\) |
−0.990726 | + | 0.135876i | \(0.956615\pi\) | |||||||
\(942\) | 41.2655 | − | 65.7620i | 1.34450 | − | 2.14264i | ||||
\(943\) | 4.92176 | − | 2.84158i | 0.160274 | − | 0.0925345i | ||||
\(944\) | −30.3224 | −0.986909 | ||||||||
\(945\) | 13.3974 | + | 3.08363i | 0.435819 | + | 0.100311i | ||||
\(946\) | 8.81919 | 0.286737 | ||||||||
\(947\) | −34.9044 | + | 20.1521i | −1.13424 | + | 0.654854i | −0.944998 | − | 0.327076i | \(-0.893937\pi\) |
−0.189243 | + | 0.981930i | \(0.560603\pi\) | |||||||
\(948\) | 7.65501 | − | 12.1993i | 0.248623 | − | 0.396215i | ||||
\(949\) | 3.10220 | − | 5.37317i | 0.100702 | − | 0.174420i | ||||
\(950\) | 0.605693 | − | 1.04909i | 0.0196513 | − | 0.0340370i | ||||
\(951\) | −1.79923 | + | 48.8783i | −0.0583442 | + | 1.58499i | ||||
\(952\) | −117.261 | + | 50.6525i | −3.80045 | + | 1.64166i | ||||
\(953\) | − | 52.4874i | − | 1.70023i | −0.526595 | − | 0.850117i | \(-0.676531\pi\) | ||
0.526595 | − | 0.850117i | \(-0.323469\pi\) | |||||||
\(954\) | 9.01021 | − | 13.2500i | 0.291716 | − | 0.428986i | ||||
\(955\) | − | 0.653990i | − | 0.0211626i | ||||||
\(956\) | 92.5978 | − | 53.4614i | 2.99483 | − | 1.72906i | ||||
\(957\) | 12.0767 | + | 22.8167i | 0.390384 | + | 0.737561i | ||||
\(958\) | 56.3385 | + | 32.5271i | 1.82021 | + | 1.05090i | ||||
\(959\) | 7.98334 | + | 5.93704i | 0.257796 | + | 0.191717i | ||||
\(960\) | −0.612857 | − | 1.15788i | −0.0197799 | − | 0.0373705i | ||||
\(961\) | 10.0082 | + | 17.3348i | 0.322846 | + | 0.559186i | ||||
\(962\) | 54.3571 | 1.75254 | ||||||||
\(963\) | 36.3215 | − | 17.5458i | 1.17044 | − | 0.565404i | ||||
\(964\) | − | 91.2474i | − | 2.93888i | ||||||
\(965\) | 7.14304 | + | 12.3721i | 0.229943 | + | 0.398272i | ||||
\(966\) | −50.7489 | − | 7.80695i | −1.63282 | − | 0.251184i | ||||
\(967\) | −27.2636 | + | 47.2220i | −0.876740 | + | 1.51856i | −0.0218418 | + | 0.999761i | \(0.506953\pi\) |
−0.854898 | + | 0.518796i | \(0.826380\pi\) | |||||||
\(968\) | 39.4819 | + | 22.7949i | 1.26899 | + | 0.732654i | ||||
\(969\) | −5.19360 | − | 3.25897i | −0.166842 | − | 0.104693i | ||||
\(970\) | −11.1657 | − | 19.3396i | −0.358509 | − | 0.620956i | ||||
\(971\) | −3.64784 | −0.117065 | −0.0585324 | − | 0.998286i | \(-0.518642\pi\) | ||||
−0.0585324 | + | 0.998286i | \(0.518642\pi\) | |||||||
\(972\) | 69.4243 | + | 12.9180i | 2.22679 | + | 0.414346i | ||||
\(973\) | 1.66417 | − | 14.3013i | 0.0533509 | − | 0.458477i | ||||
\(974\) | −25.2044 | + | 14.5517i | −0.807600 | + | 0.466268i | ||||
\(975\) | −5.18641 | − | 3.25445i | −0.166098 | − | 0.104226i | ||||
\(976\) | −16.9718 | − | 9.79870i | −0.543255 | − | 0.313649i | ||||
\(977\) | −20.5740 | − | 11.8784i | −0.658222 | − | 0.380025i | 0.133377 | − | 0.991065i | \(-0.457418\pi\) |
−0.791599 | + | 0.611041i | \(0.790751\pi\) | |||||||
\(978\) | −1.03034 | + | 27.9904i | −0.0329467 | + | 0.895035i | ||||
\(979\) | 52.9599 | − | 30.5764i | 1.69260 | − | 0.977225i | ||||
\(980\) | −30.8628 | − | 7.28132i | −0.985876 | − | 0.232593i | ||||
\(981\) | 6.20334 | + | 12.8415i | 0.198057 | + | 0.409999i | ||||
\(982\) | −52.6098 | −1.67885 | ||||||||
\(983\) | −30.9587 | − | 53.6221i | −0.987430 | − | 1.71028i | −0.630595 | − | 0.776112i | \(-0.717189\pi\) |
−0.356835 | − | 0.934167i | \(-0.616144\pi\) | |||||||
\(984\) | 12.8281 | − | 6.78977i | 0.408943 | − | 0.216450i | ||||
\(985\) | 2.91696 | + | 1.68411i | 0.0929420 | + | 0.0536601i | ||||
\(986\) | −33.4709 | + | 57.9734i | −1.06593 | + | 1.84625i | ||||
\(987\) | 21.0902 | + | 54.2208i | 0.671308 | + | 1.72587i | ||||
\(988\) | −3.79572 | − | 6.57437i | −0.120758 | − | 0.209159i | ||||
\(989\) | 3.56166i | 0.113254i | ||||||||
\(990\) | 18.3155 | − | 26.9339i | 0.582104 | − | 0.856017i | ||||
\(991\) | −13.7346 | −0.436295 | −0.218147 | − | 0.975916i | \(-0.570001\pi\) | ||||
−0.218147 | + | 0.975916i | \(0.570001\pi\) | |||||||
\(992\) | 21.9113 | + | 37.9515i | 0.695686 | + | 1.20496i | ||||
\(993\) | −44.2075 | − | 1.62730i | −1.40288 | − | 0.0516408i | ||||
\(994\) | −45.0199 | + | 60.5368i | −1.42794 | + | 1.92011i | ||||
\(995\) | 5.07672 | + | 2.93104i | 0.160943 | + | 0.0929204i | ||||
\(996\) | −23.3369 | + | 37.1905i | −0.739458 | + | 1.17842i | ||||
\(997\) | −41.3771 | + | 23.8891i | −1.31043 | + | 0.756575i | −0.982167 | − | 0.188012i | \(-0.939796\pi\) |
−0.328260 | + | 0.944587i | \(0.606462\pi\) | |||||||
\(998\) | − | 20.4555i | − | 0.647509i | ||||||
\(999\) | 31.0764 | + | 3.44427i | 0.983214 | + | 0.108972i |
(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 | 315.2.bl.j.41.2 | yes | 24 | |
3.2 | odd | 2 | 945.2.bl.j.881.11 | 24 | |||
7.6 | odd | 2 | 315.2.bl.i.41.2 | ✓ | 24 | ||
9.2 | odd | 6 | 315.2.bl.i.146.2 | yes | 24 | ||
9.7 | even | 3 | 945.2.bl.i.251.11 | 24 | |||
21.20 | even | 2 | 945.2.bl.i.881.11 | 24 | |||
63.20 | even | 6 | inner | 315.2.bl.j.146.2 | yes | 24 | |
63.34 | odd | 6 | 945.2.bl.j.251.11 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.bl.i.41.2 | ✓ | 24 | 7.6 | odd | 2 | ||
315.2.bl.i.146.2 | yes | 24 | 9.2 | odd | 6 | ||
315.2.bl.j.41.2 | yes | 24 | 1.1 | even | 1 | trivial | |
315.2.bl.j.146.2 | yes | 24 | 63.20 | even | 6 | inner | |
945.2.bl.i.251.11 | 24 | 9.7 | even | 3 | |||
945.2.bl.i.881.11 | 24 | 21.20 | even | 2 | |||
945.2.bl.j.251.11 | 24 | 63.34 | odd | 6 | |||
945.2.bl.j.881.11 | 24 | 3.2 | odd | 2 |