Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(49,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.q (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: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 49 x^{16} - 8 x^{15} + 72 x^{13} + 2145 x^{12} - 648 x^{11} + 32 x^{10} - 7056 x^{9} + \cdots + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 349.3 | ||
Root | \(2.34324 + 0.627868i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.349 |
Dual form | 570.2.q.c.49.3 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0.384547 | − | 2.20275i | 0.171975 | − | 0.985101i | ||||
\(6\) | −0.500000 | + | 0.866025i | −0.204124 | + | 0.353553i | ||||
\(7\) | − | 2.51805i | − | 0.951732i | −0.879518 | − | 0.475866i | \(-0.842135\pi\) | ||
0.879518 | − | 0.475866i | \(-0.157865\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0.768349 | + | 2.09991i | 0.242973 | + | 0.664051i | ||||
\(11\) | 2.88497 | 0.869851 | 0.434925 | − | 0.900467i | \(-0.356775\pi\) | ||||
0.434925 | + | 0.900467i | \(0.356775\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | −4.03244 | − | 2.32813i | −1.11840 | − | 0.645707i | −0.177406 | − | 0.984138i | \(-0.556770\pi\) |
−0.940991 | + | 0.338431i | \(0.890104\pi\) | |||||||
\(14\) | 1.25902 | + | 2.18069i | 0.336488 | + | 0.582814i | ||||
\(15\) | −0.768349 | − | 2.09991i | −0.198387 | − | 0.542195i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −6.31158 | + | 3.64399i | −1.53078 | + | 0.883798i | −0.531457 | + | 0.847085i | \(0.678355\pi\) |
−0.999326 | + | 0.0367122i | \(0.988312\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 4.11420 | − | 1.43993i | 0.943861 | − | 0.330342i | ||||
\(20\) | −1.71537 | − | 1.43440i | −0.383568 | − | 0.320743i | ||||
\(21\) | −1.25902 | − | 2.18069i | −0.274741 | − | 0.475866i | ||||
\(22\) | −2.49846 | + | 1.44248i | −0.532673 | + | 0.307539i | ||||
\(23\) | 1.48237 | + | 0.855848i | 0.309096 | + | 0.178457i | 0.646522 | − | 0.762895i | \(-0.276223\pi\) |
−0.337426 | + | 0.941352i | \(0.609556\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | −4.70425 | − | 1.69412i | −0.940849 | − | 0.338825i | ||||
\(26\) | 4.65626 | 0.913167 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −2.18069 | − | 1.25902i | −0.412112 | − | 0.237933i | ||||
\(29\) | 2.20959 | − | 3.82712i | 0.410310 | − | 0.710678i | −0.584613 | − | 0.811312i | \(-0.698754\pi\) |
0.994923 | + | 0.100634i | \(0.0320872\pi\) | |||||||
\(30\) | 1.71537 | + | 1.43440i | 0.313182 | + | 0.261885i | ||||
\(31\) | −9.22060 | −1.65607 | −0.828035 | − | 0.560677i | \(-0.810541\pi\) | ||||
−0.828035 | + | 0.560677i | \(0.810541\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 2.49846 | − | 1.44248i | 0.434925 | − | 0.251104i | ||||
\(34\) | 3.64399 | − | 6.31158i | 0.624939 | − | 1.08243i | ||||
\(35\) | −5.54663 | − | 0.968307i | −0.937552 | − | 0.163674i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | − | 3.26480i | − | 0.536730i | −0.963317 | − | 0.268365i | \(-0.913517\pi\) | ||
0.963317 | − | 0.268365i | \(-0.0864834\pi\) | |||||||
\(38\) | −2.84303 | + | 3.30411i | −0.461201 | + | 0.535998i | ||||
\(39\) | −4.65626 | −0.745598 | ||||||||
\(40\) | 2.20275 | + | 0.384547i | 0.348286 | + | 0.0608022i | ||||
\(41\) | 4.48368 | + | 7.76596i | 0.700233 | + | 1.21284i | 0.968384 | + | 0.249463i | \(0.0802540\pi\) |
−0.268151 | + | 0.963377i | \(0.586413\pi\) | |||||||
\(42\) | 2.18069 | + | 1.25902i | 0.336488 | + | 0.194271i | ||||
\(43\) | 5.84894 | − | 3.37689i | 0.891955 | − | 0.514971i | 0.0173738 | − | 0.999849i | \(-0.494469\pi\) |
0.874582 | + | 0.484878i | \(0.161136\pi\) | |||||||
\(44\) | 1.44248 | − | 2.49846i | 0.217463 | − | 0.376656i | ||||
\(45\) | −1.71537 | − | 1.43440i | −0.255712 | − | 0.213828i | ||||
\(46\) | −1.71170 | −0.252376 | ||||||||
\(47\) | −3.98083 | − | 2.29833i | −0.580664 | − | 0.335246i | 0.180733 | − | 0.983532i | \(-0.442153\pi\) |
−0.761397 | + | 0.648286i | \(0.775486\pi\) | |||||||
\(48\) | −0.866025 | − | 0.500000i | −0.125000 | − | 0.0721688i | ||||
\(49\) | 0.659446 | 0.0942065 | ||||||||
\(50\) | 4.92106 | − | 0.884968i | 0.695943 | − | 0.125153i | ||||
\(51\) | −3.64399 | + | 6.31158i | −0.510261 | + | 0.883798i | ||||
\(52\) | −4.03244 | + | 2.32813i | −0.559198 | + | 0.322853i | ||||
\(53\) | 9.38113 | + | 5.41620i | 1.28860 | + | 0.743972i | 0.978404 | − | 0.206701i | \(-0.0662729\pi\) |
0.310193 | + | 0.950673i | \(0.399606\pi\) | |||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | 1.10941 | − | 6.35487i | 0.149592 | − | 0.856891i | ||||
\(56\) | 2.51805 | 0.336488 | ||||||||
\(57\) | 2.84303 | − | 3.30411i | 0.376569 | − | 0.437640i | ||||
\(58\) | 4.41917i | 0.580266i | ||||||||
\(59\) | 4.73274 | + | 8.19734i | 0.616150 | + | 1.06720i | 0.990182 | + | 0.139787i | \(0.0446418\pi\) |
−0.374032 | + | 0.927416i | \(0.622025\pi\) | |||||||
\(60\) | −2.20275 | − | 0.384547i | −0.284374 | − | 0.0496448i | ||||
\(61\) | 7.50173 | − | 12.9934i | 0.960498 | − | 1.66363i | 0.239244 | − | 0.970959i | \(-0.423100\pi\) |
0.721254 | − | 0.692671i | \(-0.243566\pi\) | |||||||
\(62\) | 7.98528 | − | 4.61030i | 1.01413 | − | 0.585509i | ||||
\(63\) | −2.18069 | − | 1.25902i | −0.274741 | − | 0.158622i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −6.67896 | + | 7.98719i | −0.828422 | + | 0.990689i | ||||
\(66\) | −1.44248 | + | 2.49846i | −0.177558 | + | 0.307539i | ||||
\(67\) | −9.23107 | − | 5.32956i | −1.12776 | − | 0.651110i | −0.184386 | − | 0.982854i | \(-0.559030\pi\) |
−0.943369 | + | 0.331744i | \(0.892363\pi\) | |||||||
\(68\) | 7.28798i | 0.883798i | ||||||||
\(69\) | 1.71170 | 0.206064 | ||||||||
\(70\) | 5.28768 | − | 1.93474i | 0.631999 | − | 0.231246i | ||||
\(71\) | −5.38040 | − | 9.31912i | −0.638536 | − | 1.10598i | −0.985754 | − | 0.168192i | \(-0.946207\pi\) |
0.347218 | − | 0.937784i | \(-0.387126\pi\) | |||||||
\(72\) | 0.866025 | + | 0.500000i | 0.102062 | + | 0.0589256i | ||||
\(73\) | 12.2689 | − | 7.08348i | 1.43597 | − | 0.829059i | 0.438405 | − | 0.898777i | \(-0.355543\pi\) |
0.997567 | + | 0.0697187i | \(0.0222102\pi\) | |||||||
\(74\) | 1.63240 | + | 2.82740i | 0.189763 | + | 0.328679i | ||||
\(75\) | −4.92106 | + | 0.884968i | −0.568235 | + | 0.102187i | ||||
\(76\) | 0.810083 | − | 4.28296i | 0.0929229 | − | 0.491289i | ||||
\(77\) | − | 7.26448i | − | 0.827865i | ||||||
\(78\) | 4.03244 | − | 2.32813i | 0.456584 | − | 0.263609i | ||||
\(79\) | 4.11998 | + | 7.13601i | 0.463533 | + | 0.802864i | 0.999134 | − | 0.0416079i | \(-0.0132480\pi\) |
−0.535601 | + | 0.844471i | \(0.679915\pi\) | |||||||
\(80\) | −2.09991 | + | 0.768349i | −0.234778 | + | 0.0859041i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −7.76596 | − | 4.48368i | −0.857607 | − | 0.495140i | ||||
\(83\) | − | 7.14523i | − | 0.784291i | −0.919903 | − | 0.392146i | \(-0.871733\pi\) | ||
0.919903 | − | 0.392146i | \(-0.128267\pi\) | |||||||
\(84\) | −2.51805 | −0.274741 | ||||||||
\(85\) | 5.59972 | + | 15.3041i | 0.607375 | + | 1.65997i | ||||
\(86\) | −3.37689 | + | 5.84894i | −0.364139 | + | 0.630708i | ||||
\(87\) | − | 4.41917i | − | 0.473785i | ||||||
\(88\) | 2.88497i | 0.307539i | ||||||||
\(89\) | 2.37111 | − | 4.10688i | 0.251337 | − | 0.435328i | −0.712557 | − | 0.701614i | \(-0.752463\pi\) |
0.963894 | + | 0.266286i | \(0.0857964\pi\) | |||||||
\(90\) | 2.20275 | + | 0.384547i | 0.232191 | + | 0.0405348i | ||||
\(91\) | −5.86233 | + | 10.1539i | −0.614540 | + | 1.06441i | ||||
\(92\) | 1.48237 | − | 0.855848i | 0.154548 | − | 0.0892284i | ||||
\(93\) | −7.98528 | + | 4.61030i | −0.828035 | + | 0.478066i | ||||
\(94\) | 4.59667 | 0.474110 | ||||||||
\(95\) | −1.58971 | − | 9.61628i | −0.163100 | − | 0.986609i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 1.98898 | − | 1.14834i | 0.201950 | − | 0.116596i | −0.395615 | − | 0.918417i | \(-0.629468\pi\) |
0.597565 | + | 0.801821i | \(0.296135\pi\) | |||||||
\(98\) | −0.571097 | + | 0.329723i | −0.0576895 | + | 0.0333070i | ||||
\(99\) | 1.44248 | − | 2.49846i | 0.144975 | − | 0.251104i | ||||
\(100\) | −3.81928 | + | 3.22694i | −0.381928 | + | 0.322694i | ||||
\(101\) | 1.68398 | − | 2.91673i | 0.167562 | − | 0.290226i | −0.770000 | − | 0.638044i | \(-0.779744\pi\) |
0.937562 | + | 0.347818i | \(0.113077\pi\) | |||||||
\(102\) | − | 7.28798i | − | 0.721618i | ||||||
\(103\) | 10.9873i | 1.08261i | 0.840826 | + | 0.541305i | \(0.182070\pi\) | ||||
−0.840826 | + | 0.541305i | \(0.817930\pi\) | |||||||
\(104\) | 2.32813 | − | 4.03244i | 0.228292 | − | 0.395413i | ||||
\(105\) | −5.28768 | + | 1.93474i | −0.516025 | + | 0.188811i | ||||
\(106\) | −10.8324 | −1.05214 | ||||||||
\(107\) | 3.35775i | 0.324605i | 0.986741 | + | 0.162303i | \(0.0518921\pi\) | ||||
−0.986741 | + | 0.162303i | \(0.948108\pi\) | |||||||
\(108\) | −0.866025 | − | 0.500000i | −0.0833333 | − | 0.0481125i | ||||
\(109\) | 2.11647 | + | 3.66583i | 0.202721 | + | 0.351122i | 0.949404 | − | 0.314057i | \(-0.101688\pi\) |
−0.746683 | + | 0.665180i | \(0.768355\pi\) | |||||||
\(110\) | 2.21666 | + | 6.05819i | 0.211351 | + | 0.577625i | ||||
\(111\) | −1.63240 | − | 2.82740i | −0.154941 | − | 0.268365i | ||||
\(112\) | −2.18069 | + | 1.25902i | −0.206056 | + | 0.118966i | ||||
\(113\) | 18.7982i | 1.76839i | 0.467118 | + | 0.884195i | \(0.345292\pi\) | ||||
−0.467118 | + | 0.884195i | \(0.654708\pi\) | |||||||
\(114\) | −0.810083 | + | 4.28296i | −0.0758712 | + | 0.401136i | ||||
\(115\) | 2.45527 | − | 2.93619i | 0.228955 | − | 0.273801i | ||||
\(116\) | −2.20959 | − | 3.82712i | −0.205155 | − | 0.355339i | ||||
\(117\) | −4.03244 | + | 2.32813i | −0.372799 | + | 0.215236i | ||||
\(118\) | −8.19734 | − | 4.73274i | −0.754626 | − | 0.435684i | ||||
\(119\) | 9.17574 | + | 15.8928i | 0.841138 | + | 1.45689i | ||||
\(120\) | 2.09991 | − | 0.768349i | 0.191695 | − | 0.0701404i | ||||
\(121\) | −2.67696 | −0.243360 | ||||||||
\(122\) | 15.0035i | 1.35835i | ||||||||
\(123\) | 7.76596 | + | 4.48368i | 0.700233 | + | 0.404280i | ||||
\(124\) | −4.61030 | + | 7.98528i | −0.414017 | + | 0.717099i | ||||
\(125\) | −5.54074 | + | 9.71083i | −0.495579 | + | 0.868563i | ||||
\(126\) | 2.51805 | 0.224325 | ||||||||
\(127\) | 13.6465 | + | 7.87880i | 1.21093 | + | 0.699131i | 0.962962 | − | 0.269637i | \(-0.0869038\pi\) |
0.247968 | + | 0.968768i | \(0.420237\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 3.37689 | − | 5.84894i | 0.297318 | − | 0.514971i | ||||
\(130\) | 1.79055 | − | 10.2566i | 0.157042 | − | 0.899562i | ||||
\(131\) | 3.28357 | + | 5.68732i | 0.286887 | + | 0.496903i | 0.973065 | − | 0.230531i | \(-0.0740462\pi\) |
−0.686178 | + | 0.727434i | \(0.740713\pi\) | |||||||
\(132\) | − | 2.88497i | − | 0.251104i | ||||||
\(133\) | −3.62581 | − | 10.3597i | −0.314397 | − | 0.898303i | ||||
\(134\) | 10.6591 | 0.920808 | ||||||||
\(135\) | −2.20275 | − | 0.384547i | −0.189583 | − | 0.0330965i | ||||
\(136\) | −3.64399 | − | 6.31158i | −0.312470 | − | 0.541213i | ||||
\(137\) | 12.5023 | + | 7.21818i | 1.06814 | + | 0.616691i | 0.927673 | − | 0.373394i | \(-0.121806\pi\) |
0.140467 | + | 0.990085i | \(0.455139\pi\) | |||||||
\(138\) | −1.48237 | + | 0.855848i | −0.126188 | + | 0.0728547i | ||||
\(139\) | −3.09728 | + | 5.36464i | −0.262708 | + | 0.455023i | −0.966960 | − | 0.254926i | \(-0.917949\pi\) |
0.704253 | + | 0.709949i | \(0.251282\pi\) | |||||||
\(140\) | −3.61190 | + | 4.31937i | −0.305261 | + | 0.365054i | ||||
\(141\) | −4.59667 | −0.387109 | ||||||||
\(142\) | 9.31912 | + | 5.38040i | 0.782043 | + | 0.451513i | ||||
\(143\) | −11.6335 | − | 6.71658i | −0.972838 | − | 0.561668i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | −7.58051 | − | 6.33888i | −0.629527 | − | 0.526416i | ||||
\(146\) | −7.08348 | + | 12.2689i | −0.586233 | + | 1.01539i | ||||
\(147\) | 0.571097 | − | 0.329723i | 0.0471033 | − | 0.0271951i | ||||
\(148\) | −2.82740 | − | 1.63240i | −0.232411 | − | 0.134183i | ||||
\(149\) | −5.99475 | − | 10.3832i | −0.491109 | − | 0.850626i | 0.508838 | − | 0.860862i | \(-0.330075\pi\) |
−0.999948 | + | 0.0102357i | \(0.996742\pi\) | |||||||
\(150\) | 3.81928 | − | 3.22694i | 0.311843 | − | 0.263478i | ||||
\(151\) | −5.51534 | −0.448832 | −0.224416 | − | 0.974493i | \(-0.572047\pi\) | ||||
−0.224416 | + | 0.974493i | \(0.572047\pi\) | |||||||
\(152\) | 1.43993 | + | 4.11420i | 0.116794 | + | 0.333705i | ||||
\(153\) | 7.28798i | 0.589198i | ||||||||
\(154\) | 3.63224 | + | 6.29123i | 0.292694 | + | 0.506961i | ||||
\(155\) | −3.54576 | + | 20.3107i | −0.284802 | + | 1.63140i | ||||
\(156\) | −2.32813 | + | 4.03244i | −0.186399 | + | 0.322853i | ||||
\(157\) | −10.6341 | + | 6.13962i | −0.848696 | + | 0.489995i | −0.860211 | − | 0.509939i | \(-0.829668\pi\) |
0.0115149 | + | 0.999934i | \(0.496335\pi\) | |||||||
\(158\) | −7.13601 | − | 4.11998i | −0.567710 | − | 0.327768i | ||||
\(159\) | 10.8324 | 0.859065 | ||||||||
\(160\) | 1.43440 | − | 1.71537i | 0.113400 | − | 0.135612i | ||||
\(161\) | 2.15507 | − | 3.73268i | 0.169843 | − | 0.294177i | ||||
\(162\) | 0.866025 | + | 0.500000i | 0.0680414 | + | 0.0392837i | ||||
\(163\) | 3.45801i | 0.270852i | 0.990787 | + | 0.135426i | \(0.0432403\pi\) | ||||
−0.990787 | + | 0.135426i | \(0.956760\pi\) | |||||||
\(164\) | 8.96736 | 0.700233 | ||||||||
\(165\) | −2.21666 | − | 6.05819i | −0.172567 | − | 0.471629i | ||||
\(166\) | 3.57262 | + | 6.18795i | 0.277289 | + | 0.480278i | ||||
\(167\) | −5.37144 | − | 3.10120i | −0.415654 | − | 0.239978i | 0.277562 | − | 0.960708i | \(-0.410474\pi\) |
−0.693216 | + | 0.720730i | \(0.743807\pi\) | |||||||
\(168\) | 2.18069 | − | 1.25902i | 0.168244 | − | 0.0971357i | ||||
\(169\) | 4.34036 | + | 7.51773i | 0.333874 | + | 0.578287i | ||||
\(170\) | −12.5016 | − | 10.4539i | −0.958826 | − | 0.801779i | ||||
\(171\) | 0.810083 | − | 4.28296i | 0.0619486 | − | 0.327526i | ||||
\(172\) | − | 6.75378i | − | 0.514971i | ||||||
\(173\) | 12.4712 | − | 7.20026i | 0.948169 | − | 0.547425i | 0.0556571 | − | 0.998450i | \(-0.482275\pi\) |
0.892512 | + | 0.451025i | \(0.148941\pi\) | |||||||
\(174\) | 2.20959 | + | 3.82712i | 0.167508 | + | 0.290133i | ||||
\(175\) | −4.26588 | + | 11.8455i | −0.322471 | + | 0.895436i | ||||
\(176\) | −1.44248 | − | 2.49846i | −0.108731 | − | 0.188328i | ||||
\(177\) | 8.19734 | + | 4.73274i | 0.616150 | + | 0.355734i | ||||
\(178\) | 4.74222i | 0.355444i | ||||||||
\(179\) | −1.94176 | −0.145134 | −0.0725670 | − | 0.997364i | \(-0.523119\pi\) | ||||
−0.0725670 | + | 0.997364i | \(0.523119\pi\) | |||||||
\(180\) | −2.09991 | + | 0.768349i | −0.156518 | + | 0.0572694i | ||||
\(181\) | −8.81480 | + | 15.2677i | −0.655199 | + | 1.13484i | 0.326645 | + | 0.945147i | \(0.394082\pi\) |
−0.981844 | + | 0.189691i | \(0.939251\pi\) | |||||||
\(182\) | − | 11.7247i | − | 0.869090i | ||||||
\(183\) | − | 15.0035i | − | 1.10909i | ||||||
\(184\) | −0.855848 | + | 1.48237i | −0.0630940 | + | 0.109282i | ||||
\(185\) | −7.19156 | − | 1.25547i | −0.528734 | − | 0.0923040i | ||||
\(186\) | 4.61030 | − | 7.98528i | 0.338044 | − | 0.585509i | ||||
\(187\) | −18.2087 | + | 10.5128i | −1.33155 | + | 0.768772i | ||||
\(188\) | −3.98083 | + | 2.29833i | −0.290332 | + | 0.167623i | ||||
\(189\) | −2.51805 | −0.183161 | ||||||||
\(190\) | 6.18487 | + | 7.53309i | 0.448697 | + | 0.546508i | ||||
\(191\) | −4.61377 | −0.333840 | −0.166920 | − | 0.985970i | \(-0.553382\pi\) | ||||
−0.166920 | + | 0.985970i | \(0.553382\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | 21.7202 | − | 12.5401i | 1.56345 | − | 0.902659i | 0.566547 | − | 0.824030i | \(-0.308279\pi\) |
0.996904 | − | 0.0786292i | \(-0.0250543\pi\) | |||||||
\(194\) | −1.14834 | + | 1.98898i | −0.0824458 | + | 0.142800i | ||||
\(195\) | −1.79055 | + | 10.2566i | −0.128224 | + | 0.734489i | ||||
\(196\) | 0.329723 | − | 0.571097i | 0.0235516 | − | 0.0407926i | ||||
\(197\) | 3.62439i | 0.258227i | 0.991630 | + | 0.129113i | \(0.0412131\pi\) | ||||
−0.991630 | + | 0.129113i | \(0.958787\pi\) | |||||||
\(198\) | 2.88497i | 0.205026i | ||||||||
\(199\) | 0.298493 | − | 0.517005i | 0.0211596 | − | 0.0366495i | −0.855252 | − | 0.518213i | \(-0.826598\pi\) |
0.876411 | + | 0.481563i | \(0.159931\pi\) | |||||||
\(200\) | 1.69412 | − | 4.70425i | 0.119793 | − | 0.332641i | ||||
\(201\) | −10.6591 | −0.751837 | ||||||||
\(202\) | 3.36795i | 0.236968i | ||||||||
\(203\) | −9.63686 | − | 5.56384i | −0.676375 | − | 0.390505i | ||||
\(204\) | 3.64399 | + | 6.31158i | 0.255130 | + | 0.441899i | ||||
\(205\) | 18.8307 | − | 6.89006i | 1.31519 | − | 0.481223i | ||||
\(206\) | −5.49365 | − | 9.51527i | −0.382760 | − | 0.662961i | ||||
\(207\) | 1.48237 | − | 0.855848i | 0.103032 | − | 0.0594856i | ||||
\(208\) | 4.65626i | 0.322853i | ||||||||
\(209\) | 11.8693 | − | 4.15415i | 0.821018 | − | 0.287349i | ||||
\(210\) | 3.61190 | − | 4.31937i | 0.249244 | − | 0.298065i | ||||
\(211\) | 11.4644 | + | 19.8569i | 0.789242 | + | 1.36701i | 0.926432 | + | 0.376462i | \(0.122859\pi\) |
−0.137191 | + | 0.990545i | \(0.543807\pi\) | |||||||
\(212\) | 9.38113 | − | 5.41620i | 0.644299 | − | 0.371986i | ||||
\(213\) | −9.31912 | − | 5.38040i | −0.638536 | − | 0.368659i | ||||
\(214\) | −1.67887 | − | 2.90789i | −0.114765 | − | 0.198779i | ||||
\(215\) | −5.18926 | − | 14.1824i | −0.353905 | − | 0.967228i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 23.2179i | 1.57613i | ||||||||
\(218\) | −3.66583 | − | 2.11647i | −0.248281 | − | 0.143345i | ||||
\(219\) | 7.08348 | − | 12.2689i | 0.478657 | − | 0.829059i | ||||
\(220\) | −4.94878 | − | 4.13821i | −0.333647 | − | 0.278998i | ||||
\(221\) | 33.9347 | 2.28270 | ||||||||
\(222\) | 2.82740 | + | 1.63240i | 0.189763 | + | 0.109560i | ||||
\(223\) | 9.74016 | − | 5.62349i | 0.652250 | − | 0.376576i | −0.137068 | − | 0.990562i | \(-0.543768\pi\) |
0.789318 | + | 0.613985i | \(0.210435\pi\) | |||||||
\(224\) | 1.25902 | − | 2.18069i | 0.0841220 | − | 0.145704i | ||||
\(225\) | −3.81928 | + | 3.22694i | −0.254619 | + | 0.215129i | ||||
\(226\) | −9.39912 | − | 16.2798i | −0.625220 | − | 1.08291i | ||||
\(227\) | − | 8.82814i | − | 0.585944i | −0.956121 | − | 0.292972i | \(-0.905356\pi\) | ||
0.956121 | − | 0.292972i | \(-0.0946443\pi\) | |||||||
\(228\) | −1.43993 | − | 4.11420i | −0.0953616 | − | 0.272469i | ||||
\(229\) | 22.2817 | 1.47241 | 0.736207 | − | 0.676756i | \(-0.236615\pi\) | ||||
0.736207 | + | 0.676756i | \(0.236615\pi\) | |||||||
\(230\) | −0.658228 | + | 3.77045i | −0.0434023 | + | 0.248616i | ||||
\(231\) | −3.63224 | − | 6.29123i | −0.238984 | − | 0.413932i | ||||
\(232\) | 3.82712 | + | 2.20959i | 0.251263 | + | 0.145066i | ||||
\(233\) | −5.35318 | + | 3.09066i | −0.350699 | + | 0.202476i | −0.664993 | − | 0.746850i | \(-0.731565\pi\) |
0.314294 | + | 0.949326i | \(0.398232\pi\) | |||||||
\(234\) | 2.32813 | − | 4.03244i | 0.152195 | − | 0.263609i | ||||
\(235\) | −6.59348 | + | 7.88497i | −0.430111 | + | 0.514359i | ||||
\(236\) | 9.46547 | 0.616150 | ||||||||
\(237\) | 7.13601 | + | 4.11998i | 0.463533 | + | 0.267621i | ||||
\(238\) | −15.8928 | − | 9.17574i | −1.03018 | − | 0.594775i | ||||
\(239\) | −18.1898 | −1.17660 | −0.588299 | − | 0.808644i | \(-0.700202\pi\) | ||||
−0.588299 | + | 0.808644i | \(0.700202\pi\) | |||||||
\(240\) | −1.43440 | + | 1.71537i | −0.0925904 | + | 0.110726i | ||||
\(241\) | −1.24768 | + | 2.16104i | −0.0803699 | + | 0.139205i | −0.903409 | − | 0.428780i | \(-0.858943\pi\) |
0.823039 | + | 0.567985i | \(0.192277\pi\) | |||||||
\(242\) | 2.31831 | − | 1.33848i | 0.149027 | − | 0.0860407i | ||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | −7.50173 | − | 12.9934i | −0.480249 | − | 0.831815i | ||||
\(245\) | 0.253588 | − | 1.45260i | 0.0162011 | − | 0.0928030i | ||||
\(246\) | −8.96736 | −0.571738 | ||||||||
\(247\) | −19.9426 | − | 3.77195i | −1.26892 | − | 0.240004i | ||||
\(248\) | − | 9.22060i | − | 0.585509i | ||||||
\(249\) | −3.57262 | − | 6.18795i | −0.226405 | − | 0.392146i | ||||
\(250\) | −0.0569884 | − | 11.1802i | −0.00360426 | − | 0.707098i | ||||
\(251\) | 10.6317 | − | 18.4147i | 0.671069 | − | 1.16232i | −0.306533 | − | 0.951860i | \(-0.599169\pi\) |
0.977601 | − | 0.210465i | \(-0.0674977\pi\) | |||||||
\(252\) | −2.18069 | + | 1.25902i | −0.137371 | + | 0.0793110i | ||||
\(253\) | 4.27660 | + | 2.46910i | 0.268867 | + | 0.155231i | ||||
\(254\) | −15.7576 | −0.988720 | ||||||||
\(255\) | 12.5016 | + | 10.4539i | 0.782878 | + | 0.654649i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −5.03779 | − | 2.90857i | −0.314249 | − | 0.181432i | 0.334577 | − | 0.942368i | \(-0.391406\pi\) |
−0.648826 | + | 0.760937i | \(0.724740\pi\) | |||||||
\(258\) | 6.75378i | 0.420472i | ||||||||
\(259\) | −8.22092 | −0.510823 | ||||||||
\(260\) | 3.57763 | + | 9.77774i | 0.221875 | + | 0.606390i | ||||
\(261\) | −2.20959 | − | 3.82712i | −0.136770 | − | 0.236893i | ||||
\(262\) | −5.68732 | − | 3.28357i | −0.351364 | − | 0.202860i | ||||
\(263\) | 14.9606 | − | 8.63749i | 0.922508 | − | 0.532610i | 0.0380737 | − | 0.999275i | \(-0.487878\pi\) |
0.884434 | + | 0.466665i | \(0.154544\pi\) | |||||||
\(264\) | 1.44248 | + | 2.49846i | 0.0887788 | + | 0.153769i | ||||
\(265\) | 15.5380 | − | 18.5815i | 0.954494 | − | 1.14145i | ||||
\(266\) | 8.31991 | + | 7.15889i | 0.510126 | + | 0.438940i | ||||
\(267\) | − | 4.74222i | − | 0.290219i | ||||||
\(268\) | −9.23107 | + | 5.32956i | −0.563878 | + | 0.325555i | ||||
\(269\) | −4.82743 | − | 8.36136i | −0.294334 | − | 0.509801i | 0.680496 | − | 0.732752i | \(-0.261764\pi\) |
−0.974830 | + | 0.222951i | \(0.928431\pi\) | |||||||
\(270\) | 2.09991 | − | 0.768349i | 0.127797 | − | 0.0467602i | ||||
\(271\) | −3.21818 | − | 5.57406i | −0.195491 | − | 0.338600i | 0.751571 | − | 0.659653i | \(-0.229297\pi\) |
−0.947061 | + | 0.321053i | \(0.895963\pi\) | |||||||
\(272\) | 6.31158 | + | 3.64399i | 0.382696 | + | 0.220949i | ||||
\(273\) | 11.7247i | 0.709609i | ||||||||
\(274\) | −14.4364 | −0.872133 | ||||||||
\(275\) | −13.5716 | − | 4.88750i | −0.818399 | − | 0.294727i | ||||
\(276\) | 0.855848 | − | 1.48237i | 0.0515160 | − | 0.0892284i | ||||
\(277\) | 11.1309i | 0.668791i | 0.942433 | + | 0.334396i | \(0.108532\pi\) | ||||
−0.942433 | + | 0.334396i | \(0.891468\pi\) | |||||||
\(278\) | − | 6.19455i | − | 0.371525i | ||||||
\(279\) | −4.61030 | + | 7.98528i | −0.276012 | + | 0.478066i | ||||
\(280\) | 0.968307 | − | 5.54663i | 0.0578674 | − | 0.331475i | ||||
\(281\) | −2.84358 | + | 4.92523i | −0.169634 | + | 0.293815i | −0.938291 | − | 0.345846i | \(-0.887592\pi\) |
0.768657 | + | 0.639661i | \(0.220925\pi\) | |||||||
\(282\) | 3.98083 | − | 2.29833i | 0.237055 | − | 0.136864i | ||||
\(283\) | −6.24466 | + | 3.60536i | −0.371207 | + | 0.214316i | −0.673985 | − | 0.738745i | \(-0.735419\pi\) |
0.302779 | + | 0.953061i | \(0.402086\pi\) | |||||||
\(284\) | −10.7608 | −0.638536 | ||||||||
\(285\) | −6.18487 | − | 7.53309i | −0.366360 | − | 0.446222i | ||||
\(286\) | 13.4332 | 0.794319 | ||||||||
\(287\) | 19.5550 | − | 11.2901i | 1.15430 | − | 0.666434i | ||||
\(288\) | 0.866025 | − | 0.500000i | 0.0510310 | − | 0.0294628i | ||||
\(289\) | 18.0573 | − | 31.2762i | 1.06220 | − | 1.83978i | ||||
\(290\) | 9.73435 | + | 1.69938i | 0.571621 | + | 0.0997910i | ||||
\(291\) | 1.14834 | − | 1.98898i | 0.0673167 | − | 0.116596i | ||||
\(292\) | − | 14.1670i | − | 0.829059i | ||||||
\(293\) | − | 9.26719i | − | 0.541395i | −0.962664 | − | 0.270697i | \(-0.912746\pi\) | ||
0.962664 | − | 0.270697i | \(-0.0872543\pi\) | |||||||
\(294\) | −0.329723 | + | 0.571097i | −0.0192298 | + | 0.0333070i | ||||
\(295\) | 19.8767 | − | 7.27279i | 1.15727 | − | 0.423438i | ||||
\(296\) | 3.26480 | 0.189763 | ||||||||
\(297\) | − | 2.88497i | − | 0.167403i | ||||||
\(298\) | 10.3832 | + | 5.99475i | 0.601484 | + | 0.347267i | ||||
\(299\) | −3.98505 | − | 6.90231i | −0.230461 | − | 0.399171i | ||||
\(300\) | −1.69412 | + | 4.70425i | −0.0978103 | + | 0.271600i | ||||
\(301\) | −8.50316 | − | 14.7279i | −0.490114 | − | 0.848902i | ||||
\(302\) | 4.77643 | − | 2.75767i | 0.274852 | − | 0.158686i | ||||
\(303\) | − | 3.36795i | − | 0.193484i | ||||||
\(304\) | −3.30411 | − | 2.84303i | −0.189504 | − | 0.163059i | ||||
\(305\) | −25.7364 | − | 21.5210i | −1.47366 | − | 1.23229i | ||||
\(306\) | −3.64399 | − | 6.31158i | −0.208313 | − | 0.360809i | ||||
\(307\) | −8.89602 | + | 5.13612i | −0.507722 | + | 0.293134i | −0.731897 | − | 0.681415i | \(-0.761365\pi\) |
0.224175 | + | 0.974549i | \(0.428031\pi\) | |||||||
\(308\) | −6.29123 | − | 3.63224i | −0.358476 | − | 0.206966i | ||||
\(309\) | 5.49365 | + | 9.51527i | 0.312523 | + | 0.541305i | ||||
\(310\) | −7.08464 | − | 19.3625i | −0.402381 | − | 1.09971i | ||||
\(311\) | −11.4317 | −0.648232 | −0.324116 | − | 0.946017i | \(-0.605067\pi\) | ||||
−0.324116 | + | 0.946017i | \(0.605067\pi\) | |||||||
\(312\) | − | 4.65626i | − | 0.263609i | ||||||
\(313\) | −3.42825 | − | 1.97930i | −0.193776 | − | 0.111877i | 0.399973 | − | 0.916527i | \(-0.369019\pi\) |
−0.593749 | + | 0.804650i | \(0.702353\pi\) | |||||||
\(314\) | 6.13962 | − | 10.6341i | 0.346479 | − | 0.600118i | ||||
\(315\) | −3.61190 | + | 4.31937i | −0.203507 | + | 0.243369i | ||||
\(316\) | 8.23995 | 0.463533 | ||||||||
\(317\) | 19.0052 | + | 10.9727i | 1.06744 | + | 0.616286i | 0.927480 | − | 0.373872i | \(-0.121970\pi\) |
0.139958 | + | 0.990157i | \(0.455303\pi\) | |||||||
\(318\) | −9.38113 | + | 5.41620i | −0.526068 | + | 0.303725i | ||||
\(319\) | 6.37459 | − | 11.0411i | 0.356908 | − | 0.618184i | ||||
\(320\) | −0.384547 | + | 2.20275i | −0.0214968 | + | 0.123138i | ||||
\(321\) | 1.67887 | + | 2.90789i | 0.0937055 | + | 0.162303i | ||||
\(322\) | 4.31013i | 0.240194i | ||||||||
\(323\) | −20.7200 | + | 24.0803i | −1.15289 | + | 1.33986i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 15.0254 | + | 17.7835i | 0.833461 | + | 0.986453i | ||||
\(326\) | −1.72900 | − | 2.99472i | −0.0957606 | − | 0.165862i | ||||
\(327\) | 3.66583 | + | 2.11647i | 0.202721 | + | 0.117041i | ||||
\(328\) | −7.76596 | + | 4.48368i | −0.428803 | + | 0.247570i | ||||
\(329\) | −5.78731 | + | 10.0239i | −0.319065 | + | 0.552636i | ||||
\(330\) | 4.94878 | + | 4.13821i | 0.272421 | + | 0.227801i | ||||
\(331\) | 7.44789 | 0.409373 | 0.204687 | − | 0.978828i | \(-0.434382\pi\) | ||||
0.204687 | + | 0.978828i | \(0.434382\pi\) | |||||||
\(332\) | −6.18795 | − | 3.57262i | −0.339608 | − | 0.196073i | ||||
\(333\) | −2.82740 | − | 1.63240i | −0.154941 | − | 0.0894551i | ||||
\(334\) | 6.20240 | 0.339380 | ||||||||
\(335\) | −15.2895 | + | 18.2843i | −0.835354 | + | 0.998979i | ||||
\(336\) | −1.25902 | + | 2.18069i | −0.0686853 | + | 0.118966i | ||||
\(337\) | 4.04725 | − | 2.33668i | 0.220468 | − | 0.127287i | −0.385699 | − | 0.922625i | \(-0.626040\pi\) |
0.606167 | + | 0.795338i | \(0.292706\pi\) | |||||||
\(338\) | −7.51773 | − | 4.34036i | −0.408911 | − | 0.236085i | ||||
\(339\) | 9.39912 | + | 16.2798i | 0.510490 | + | 0.884195i | ||||
\(340\) | 16.0536 | + | 2.80257i | 0.870630 | + | 0.151991i | ||||
\(341\) | −26.6011 | −1.44053 | ||||||||
\(342\) | 1.43993 | + | 4.11420i | 0.0778624 | + | 0.222470i | ||||
\(343\) | − | 19.2868i | − | 1.04139i | ||||||
\(344\) | 3.37689 | + | 5.84894i | 0.182070 | + | 0.315354i | ||||
\(345\) | 0.658228 | − | 3.77045i | 0.0354378 | − | 0.202994i | ||||
\(346\) | −7.20026 | + | 12.4712i | −0.387088 | + | 0.670456i | ||||
\(347\) | 11.8564 | − | 6.84531i | 0.636486 | − | 0.367475i | −0.146774 | − | 0.989170i | \(-0.546889\pi\) |
0.783260 | + | 0.621695i | \(0.213556\pi\) | |||||||
\(348\) | −3.82712 | − | 2.20959i | −0.205155 | − | 0.118446i | ||||
\(349\) | 34.7901 | 1.86227 | 0.931137 | − | 0.364671i | \(-0.118818\pi\) | ||||
0.931137 | + | 0.364671i | \(0.118818\pi\) | |||||||
\(350\) | −2.22839 | − | 12.3915i | −0.119113 | − | 0.662351i | ||||
\(351\) | −2.32813 | + | 4.03244i | −0.124266 | + | 0.215236i | ||||
\(352\) | 2.49846 | + | 1.44248i | 0.133168 | + | 0.0768847i | ||||
\(353\) | 3.05876i | 0.162802i | 0.996681 | + | 0.0814008i | \(0.0259394\pi\) | ||||
−0.996681 | + | 0.0814008i | \(0.974061\pi\) | |||||||
\(354\) | −9.46547 | −0.503084 | ||||||||
\(355\) | −22.5967 | + | 8.26805i | −1.19931 | + | 0.438823i | ||||
\(356\) | −2.37111 | − | 4.10688i | −0.125668 | − | 0.217664i | ||||
\(357\) | 15.8928 | + | 9.17574i | 0.841138 | + | 0.485631i | ||||
\(358\) | 1.68161 | − | 0.970880i | 0.0888760 | − | 0.0513126i | ||||
\(359\) | 8.49408 | + | 14.7122i | 0.448300 | + | 0.776479i | 0.998276 | − | 0.0587020i | \(-0.0186962\pi\) |
−0.549975 | + | 0.835181i | \(0.685363\pi\) | |||||||
\(360\) | 1.43440 | − | 1.71537i | 0.0755997 | − | 0.0904078i | ||||
\(361\) | 14.8532 | − | 11.8483i | 0.781748 | − | 0.623595i | ||||
\(362\) | − | 17.6296i | − | 0.926592i | ||||||
\(363\) | −2.31831 | + | 1.33848i | −0.121680 | + | 0.0702519i | ||||
\(364\) | 5.86233 | + | 10.1539i | 0.307270 | + | 0.532207i | ||||
\(365\) | −10.8852 | − | 29.7494i | −0.569756 | − | 1.55715i | ||||
\(366\) | 7.50173 | + | 12.9934i | 0.392121 | + | 0.679174i | ||||
\(367\) | 4.66821 | + | 2.69519i | 0.243679 | + | 0.140688i | 0.616866 | − | 0.787068i | \(-0.288402\pi\) |
−0.373188 | + | 0.927756i | \(0.621735\pi\) | |||||||
\(368\) | − | 1.71170i | − | 0.0892284i | ||||||
\(369\) | 8.96736 | 0.466822 | ||||||||
\(370\) | 6.85581 | − | 2.50851i | 0.356416 | − | 0.130411i | ||||
\(371\) | 13.6382 | − | 23.6221i | 0.708062 | − | 1.22640i | ||||
\(372\) | 9.22060i | 0.478066i | ||||||||
\(373\) | − | 3.85586i | − | 0.199649i | −0.995005 | − | 0.0998244i | \(-0.968172\pi\) | ||
0.995005 | − | 0.0998244i | \(-0.0318281\pi\) | |||||||
\(374\) | 10.5128 | − | 18.2087i | 0.543604 | − | 0.941550i | ||||
\(375\) | 0.0569884 | + | 11.1802i | 0.00294287 | + | 0.577343i | ||||
\(376\) | 2.29833 | − | 3.98083i | 0.118527 | − | 0.205296i | ||||
\(377\) | −17.8200 | + | 10.2884i | −0.917779 | + | 0.529880i | ||||
\(378\) | 2.18069 | − | 1.25902i | 0.112163 | − | 0.0647571i | ||||
\(379\) | −13.6566 | −0.701495 | −0.350747 | − | 0.936470i | \(-0.614072\pi\) | ||||
−0.350747 | + | 0.936470i | \(0.614072\pi\) | |||||||
\(380\) | −9.12280 | − | 3.43141i | −0.467990 | − | 0.176028i | ||||
\(381\) | 15.7576 | 0.807287 | ||||||||
\(382\) | 3.99564 | − | 2.30688i | 0.204435 | − | 0.118030i | ||||
\(383\) | −6.30771 | + | 3.64176i | −0.322309 | + | 0.186085i | −0.652421 | − | 0.757857i | \(-0.726247\pi\) |
0.330112 | + | 0.943942i | \(0.392913\pi\) | |||||||
\(384\) | 0.500000 | − | 0.866025i | 0.0255155 | − | 0.0441942i | ||||
\(385\) | −16.0019 | − | 2.79354i | −0.815531 | − | 0.142372i | ||||
\(386\) | −12.5401 | + | 21.7202i | −0.638276 | + | 1.10553i | ||||
\(387\) | − | 6.75378i | − | 0.343314i | ||||||
\(388\) | − | 2.29667i | − | 0.116596i | ||||||
\(389\) | −9.81327 | + | 16.9971i | −0.497553 | + | 0.861786i | −0.999996 | − | 0.00282365i | \(-0.999101\pi\) |
0.502443 | + | 0.864610i | \(0.332435\pi\) | |||||||
\(390\) | −3.57763 | − | 9.77774i | −0.181160 | − | 0.495115i | ||||
\(391\) | −12.4748 | −0.630879 | ||||||||
\(392\) | 0.659446i | 0.0333070i | ||||||||
\(393\) | 5.68732 | + | 3.28357i | 0.286887 | + | 0.165634i | ||||
\(394\) | −1.81219 | − | 3.13881i | −0.0912969 | − | 0.158131i | ||||
\(395\) | 17.3032 | − | 6.33116i | 0.870618 | − | 0.318555i | ||||
\(396\) | −1.44248 | − | 2.49846i | −0.0724876 | − | 0.125552i | ||||
\(397\) | −10.0280 | + | 5.78964i | −0.503288 | + | 0.290574i | −0.730071 | − | 0.683372i | \(-0.760513\pi\) |
0.226782 | + | 0.973946i | \(0.427179\pi\) | |||||||
\(398\) | 0.596986i | 0.0299242i | ||||||||
\(399\) | −8.31991 | − | 7.15889i | −0.416516 | − | 0.358393i | ||||
\(400\) | 0.884968 | + | 4.92106i | 0.0442484 | + | 0.246053i | ||||
\(401\) | 0.738065 | + | 1.27837i | 0.0368572 | + | 0.0638386i | 0.883866 | − | 0.467741i | \(-0.154932\pi\) |
−0.847008 | + | 0.531580i | \(0.821599\pi\) | |||||||
\(402\) | 9.23107 | − | 5.32956i | 0.460404 | − | 0.265814i | ||||
\(403\) | 37.1815 | + | 21.4667i | 1.85214 | + | 1.06933i | ||||
\(404\) | −1.68398 | − | 2.91673i | −0.0837810 | − | 0.145113i | ||||
\(405\) | −2.09991 | + | 0.768349i | −0.104346 | + | 0.0381796i | ||||
\(406\) | 11.1277 | 0.552258 | ||||||||
\(407\) | − | 9.41885i | − | 0.466875i | ||||||
\(408\) | −6.31158 | − | 3.64399i | −0.312470 | − | 0.180404i | ||||
\(409\) | 0.325761 | − | 0.564235i | 0.0161078 | − | 0.0278996i | −0.857859 | − | 0.513885i | \(-0.828206\pi\) |
0.873967 | + | 0.485985i | \(0.161539\pi\) | |||||||
\(410\) | −12.8628 | + | 15.3823i | −0.635249 | + | 0.759678i | ||||
\(411\) | 14.4364 | 0.712093 | ||||||||
\(412\) | 9.51527 | + | 5.49365i | 0.468784 | + | 0.270653i | ||||
\(413\) | 20.6413 | − | 11.9172i | 1.01569 | − | 0.586409i | ||||
\(414\) | −0.855848 | + | 1.48237i | −0.0420627 | + | 0.0728547i | ||||
\(415\) | −15.7392 | − | 2.74768i | −0.772606 | − | 0.134878i | ||||
\(416\) | −2.32813 | − | 4.03244i | −0.114146 | − | 0.197706i | ||||
\(417\) | 6.19455i | 0.303349i | ||||||||
\(418\) | −8.20206 | + | 9.53226i | −0.401176 | + | 0.466238i | ||||
\(419\) | −25.9557 | −1.26802 | −0.634010 | − | 0.773325i | \(-0.718592\pi\) | ||||
−0.634010 | + | 0.773325i | \(0.718592\pi\) | |||||||
\(420\) | −0.968307 | + | 5.54663i | −0.0472485 | + | 0.270648i | ||||
\(421\) | 14.9470 | + | 25.8890i | 0.728473 | + | 1.26175i | 0.957528 | + | 0.288339i | \(0.0931032\pi\) |
−0.229055 | + | 0.973414i | \(0.573564\pi\) | |||||||
\(422\) | −19.8569 | − | 11.4644i | −0.966620 | − | 0.558078i | ||||
\(423\) | −3.98083 | + | 2.29833i | −0.193555 | + | 0.111749i | ||||
\(424\) | −5.41620 | + | 9.38113i | −0.263034 | + | 0.455588i | ||||
\(425\) | 35.8646 | − | 6.44963i | 1.73969 | − | 0.312853i | ||||
\(426\) | 10.7608 | 0.521362 | ||||||||
\(427\) | −32.7179 | − | 18.8897i | −1.58333 | − | 0.914136i | ||||
\(428\) | 2.90789 | + | 1.67887i | 0.140558 | + | 0.0811514i | ||||
\(429\) | −13.4332 | −0.648559 | ||||||||
\(430\) | 11.5852 | + | 9.68765i | 0.558688 | + | 0.467180i | ||||
\(431\) | −13.7123 | + | 23.7503i | −0.660496 | + | 1.14401i | 0.319989 | + | 0.947421i | \(0.396321\pi\) |
−0.980485 | + | 0.196592i | \(0.937013\pi\) | |||||||
\(432\) | −0.866025 | + | 0.500000i | −0.0416667 | + | 0.0240563i | ||||
\(433\) | −9.75555 | − | 5.63237i | −0.468822 | − | 0.270674i | 0.246925 | − | 0.969035i | \(-0.420580\pi\) |
−0.715746 | + | 0.698360i | \(0.753913\pi\) | |||||||
\(434\) | −11.6089 | − | 20.1073i | −0.557247 | − | 0.965181i | ||||
\(435\) | −9.73435 | − | 1.69938i | −0.466726 | − | 0.0814790i | ||||
\(436\) | 4.23293 | 0.202721 | ||||||||
\(437\) | 7.33113 | + | 1.38662i | 0.350696 | + | 0.0663308i | ||||
\(438\) | 14.1670i | 0.676924i | ||||||||
\(439\) | −7.89796 | − | 13.6797i | −0.376949 | − | 0.652895i | 0.613668 | − | 0.789564i | \(-0.289693\pi\) |
−0.990617 | + | 0.136670i | \(0.956360\pi\) | |||||||
\(440\) | 6.35487 | + | 1.10941i | 0.302957 | + | 0.0528889i | ||||
\(441\) | 0.329723 | − | 0.571097i | 0.0157011 | − | 0.0271951i | ||||
\(442\) | −29.3883 | + | 16.9674i | −1.39786 | + | 0.807055i | ||||
\(443\) | −6.09413 | − | 3.51845i | −0.289541 | − | 0.167167i | 0.348194 | − | 0.937423i | \(-0.386795\pi\) |
−0.637735 | + | 0.770256i | \(0.720128\pi\) | |||||||
\(444\) | −3.26480 | −0.154941 | ||||||||
\(445\) | −8.13464 | − | 6.80226i | −0.385619 | − | 0.322458i | ||||
\(446\) | −5.62349 | + | 9.74016i | −0.266280 | + | 0.461210i | ||||
\(447\) | −10.3832 | − | 5.99475i | −0.491109 | − | 0.283542i | ||||
\(448\) | 2.51805i | 0.118966i | ||||||||
\(449\) | −16.3890 | −0.773444 | −0.386722 | − | 0.922196i | \(-0.626393\pi\) | ||||
−0.386722 | + | 0.922196i | \(0.626393\pi\) | |||||||
\(450\) | 1.69412 | − | 4.70425i | 0.0798618 | − | 0.221760i | ||||
\(451\) | 12.9353 | + | 22.4046i | 0.609098 | + | 1.05499i | ||||
\(452\) | 16.2798 | + | 9.39912i | 0.765735 | + | 0.442097i | ||||
\(453\) | −4.77643 | + | 2.75767i | −0.224416 | + | 0.129567i | ||||
\(454\) | 4.41407 | + | 7.64539i | 0.207163 | + | 0.358816i | ||||
\(455\) | 20.1121 | + | 16.8179i | 0.942870 | + | 0.788436i | ||||
\(456\) | 3.30411 | + | 2.84303i | 0.154729 | + | 0.133137i | ||||
\(457\) | 11.5975i | 0.542508i | 0.962508 | + | 0.271254i | \(0.0874383\pi\) | ||||
−0.962508 | + | 0.271254i | \(0.912562\pi\) | |||||||
\(458\) | −19.2965 | + | 11.1408i | −0.901666 | + | 0.520577i | ||||
\(459\) | 3.64399 | + | 6.31158i | 0.170087 | + | 0.294599i | ||||
\(460\) | −1.31518 | − | 3.59442i | −0.0613206 | − | 0.167591i | ||||
\(461\) | 2.39232 | + | 4.14363i | 0.111422 | + | 0.192988i | 0.916344 | − | 0.400393i | \(-0.131126\pi\) |
−0.804922 | + | 0.593381i | \(0.797793\pi\) | |||||||
\(462\) | 6.29123 | + | 3.63224i | 0.292694 | + | 0.168987i | ||||
\(463\) | 12.1559i | 0.564934i | 0.959277 | + | 0.282467i | \(0.0911527\pi\) | ||||
−0.959277 | + | 0.282467i | \(0.908847\pi\) | |||||||
\(464\) | −4.41917 | −0.205155 | ||||||||
\(465\) | 7.08464 | + | 19.3625i | 0.328542 | + | 0.897913i | ||||
\(466\) | 3.09066 | − | 5.35318i | 0.143172 | − | 0.247981i | ||||
\(467\) | 1.60463i | 0.0742533i | 0.999311 | + | 0.0371266i | \(0.0118205\pi\) | ||||
−0.999311 | + | 0.0371266i | \(0.988180\pi\) | |||||||
\(468\) | 4.65626i | 0.215236i | ||||||||
\(469\) | −13.4201 | + | 23.2443i | −0.619682 | + | 1.07332i | ||||
\(470\) | 1.76763 | − | 10.1253i | 0.0815349 | − | 0.467046i | ||||
\(471\) | −6.13962 | + | 10.6341i | −0.282899 | + | 0.489995i | ||||
\(472\) | −8.19734 | + | 4.73274i | −0.377313 | + | 0.217842i | ||||
\(473\) | 16.8740 | − | 9.74222i | 0.775868 | − | 0.447948i | ||||
\(474\) | −8.23995 | −0.378473 | ||||||||
\(475\) | −21.7936 | − | 0.196179i | −0.999959 | − | 0.00900132i | ||||
\(476\) | 18.3515 | 0.841138 | ||||||||
\(477\) | 9.38113 | − | 5.41620i | 0.429532 | − | 0.247991i | ||||
\(478\) | 15.7528 | − | 9.09488i | 0.720516 | − | 0.415990i | ||||
\(479\) | −17.2940 | + | 29.9541i | −0.790184 | + | 1.36864i | 0.135669 | + | 0.990754i | \(0.456682\pi\) |
−0.925853 | + | 0.377884i | \(0.876652\pi\) | |||||||
\(480\) | 0.384547 | − | 2.20275i | 0.0175521 | − | 0.100541i | ||||
\(481\) | −7.60088 | + | 13.1651i | −0.346570 | + | 0.600277i | ||||
\(482\) | − | 2.49535i | − | 0.113660i | ||||||
\(483\) | − | 4.31013i | − | 0.196118i | ||||||
\(484\) | −1.33848 | + | 2.31831i | −0.0608399 | + | 0.105378i | ||||
\(485\) | −1.76465 | − | 4.82282i | −0.0801286 | − | 0.218993i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | − | 24.3737i | − | 1.10448i | −0.833687 | − | 0.552238i | \(-0.813774\pi\) | ||
0.833687 | − | 0.552238i | \(-0.186226\pi\) | |||||||
\(488\) | 12.9934 | + | 7.50173i | 0.588182 | + | 0.339587i | ||||
\(489\) | 1.72900 | + | 2.99472i | 0.0781882 | + | 0.135426i | ||||
\(490\) | 0.506685 | + | 1.38478i | 0.0228897 | + | 0.0625579i | ||||
\(491\) | 5.45453 | + | 9.44752i | 0.246159 | + | 0.426360i | 0.962457 | − | 0.271434i | \(-0.0874980\pi\) |
−0.716298 | + | 0.697795i | \(0.754165\pi\) | |||||||
\(492\) | 7.76596 | − | 4.48368i | 0.350117 | − | 0.202140i | ||||
\(493\) | 32.2069i | 1.45052i | ||||||||
\(494\) | 19.1568 | − | 6.70468i | 0.861903 | − | 0.301658i | ||||
\(495\) | −4.94878 | − | 4.13821i | −0.222431 | − | 0.185999i | ||||
\(496\) | 4.61030 | + | 7.98528i | 0.207009 | + | 0.358549i | ||||
\(497\) | −23.4660 | + | 13.5481i | −1.05259 | + | 0.607715i | ||||
\(498\) | 6.18795 | + | 3.57262i | 0.277289 | + | 0.160093i | ||||
\(499\) | −5.54788 | − | 9.60920i | −0.248357 | − | 0.430167i | 0.714713 | − | 0.699418i | \(-0.246557\pi\) |
−0.963070 | + | 0.269251i | \(0.913224\pi\) | |||||||
\(500\) | 5.63945 | + | 9.65384i | 0.252204 | + | 0.431733i | ||||
\(501\) | −6.20240 | −0.277103 | ||||||||
\(502\) | 21.2635i | 0.949034i | ||||||||
\(503\) | 17.0870 | + | 9.86519i | 0.761872 | + | 0.439867i | 0.829967 | − | 0.557812i | \(-0.188359\pi\) |
−0.0680955 | + | 0.997679i | \(0.521692\pi\) | |||||||
\(504\) | 1.25902 | − | 2.18069i | 0.0560813 | − | 0.0971357i | ||||
\(505\) | −5.77728 | − | 4.83101i | −0.257085 | − | 0.214977i | ||||
\(506\) | −4.93819 | −0.219529 | ||||||||
\(507\) | 7.51773 | + | 4.34036i | 0.333874 | + | 0.192762i | ||||
\(508\) | 13.6465 | − | 7.87880i | 0.605465 | − | 0.349565i | ||||
\(509\) | −16.6873 | + | 28.9033i | −0.739653 | + | 1.28112i | 0.212999 | + | 0.977052i | \(0.431677\pi\) |
−0.952652 | + | 0.304064i | \(0.901656\pi\) | |||||||
\(510\) | −16.0536 | − | 2.80257i | −0.710867 | − | 0.124100i | ||||
\(511\) | −17.8365 | − | 30.8938i | −0.789042 | − | 1.36666i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −1.43993 | − | 4.11420i | −0.0635744 | − | 0.181646i | ||||
\(514\) | 5.81714 | 0.256583 | ||||||||
\(515\) | 24.2023 | + | 4.22513i | 1.06648 | + | 0.186181i | ||||
\(516\) | −3.37689 | − | 5.84894i | −0.148659 | − | 0.257485i | ||||
\(517\) | −11.4846 | − | 6.63062i | −0.505091 | − | 0.291614i | ||||
\(518\) | 7.11953 | − | 4.11046i | 0.312814 | − | 0.180603i | ||||
\(519\) | 7.20026 | − | 12.4712i | 0.316056 | − | 0.547425i | ||||
\(520\) | −7.98719 | − | 6.67896i | −0.350261 | − | 0.292892i | ||||
\(521\) | −32.4955 | −1.42366 | −0.711828 | − | 0.702354i | \(-0.752132\pi\) | ||||
−0.711828 | + | 0.702354i | \(0.752132\pi\) | |||||||
\(522\) | 3.82712 | + | 2.20959i | 0.167508 | + | 0.0967110i | ||||
\(523\) | −8.12396 | − | 4.69037i | −0.355236 | − | 0.205096i | 0.311753 | − | 0.950163i | \(-0.399084\pi\) |
−0.666989 | + | 0.745068i | \(0.732417\pi\) | |||||||
\(524\) | 6.56715 | 0.286887 | ||||||||
\(525\) | 2.22839 | + | 12.3915i | 0.0972550 | + | 0.540807i | ||||
\(526\) | −8.63749 | + | 14.9606i | −0.376612 | + | 0.652312i | ||||
\(527\) | 58.1966 | − | 33.5998i | 2.53508 | − | 1.46363i | ||||
\(528\) | −2.49846 | − | 1.44248i | −0.108731 | − | 0.0627761i | ||||
\(529\) | −10.0350 | − | 17.3812i | −0.436306 | − | 0.755705i | ||||
\(530\) | −4.16557 | + | 23.8611i | −0.180941 | + | 1.03646i | ||||
\(531\) | 9.46547 | 0.410767 | ||||||||
\(532\) | −10.7847 | − | 2.03983i | −0.467576 | − | 0.0884376i | ||||
\(533\) | − | 41.7543i | − | 1.80858i | ||||||
\(534\) | 2.37111 | + | 4.10688i | 0.102608 | + | 0.177722i | ||||
\(535\) | 7.39629 | + | 1.29121i | 0.319769 | + | 0.0558239i | ||||
\(536\) | 5.32956 | − | 9.23107i | 0.230202 | − | 0.398722i | ||||
\(537\) | −1.68161 | + | 0.970880i | −0.0725670 | + | 0.0418966i | ||||
\(538\) | 8.36136 | + | 4.82743i | 0.360484 | + | 0.208125i | ||||
\(539\) | 1.90248 | 0.0819456 | ||||||||
\(540\) | −1.43440 | + | 1.71537i | −0.0617269 | + | 0.0738176i | ||||
\(541\) | 18.8739 | − | 32.6906i | 0.811453 | − | 1.40548i | −0.100394 | − | 0.994948i | \(-0.532010\pi\) |
0.911847 | − | 0.410530i | \(-0.134656\pi\) | |||||||
\(542\) | 5.57406 | + | 3.21818i | 0.239426 | + | 0.138233i | ||||
\(543\) | 17.6296i | 0.756559i | ||||||||
\(544\) | −7.28798 | −0.312470 | ||||||||
\(545\) | 8.88879 | − | 3.25237i | 0.380754 | − | 0.139316i | ||||
\(546\) | −5.86233 | − | 10.1539i | −0.250885 | − | 0.434545i | ||||
\(547\) | 5.07734 | + | 2.93141i | 0.217092 | + | 0.125338i | 0.604603 | − | 0.796527i | \(-0.293332\pi\) |
−0.387511 | + | 0.921865i | \(0.626665\pi\) | |||||||
\(548\) | 12.5023 | − | 7.21818i | 0.534070 | − | 0.308345i | ||||
\(549\) | −7.50173 | − | 12.9934i | −0.320166 | − | 0.554544i | ||||
\(550\) | 14.1971 | − | 2.55311i | 0.605366 | − | 0.108865i | ||||
\(551\) | 3.57990 | − | 18.9272i | 0.152509 | − | 0.806324i | ||||
\(552\) | 1.71170i | 0.0728547i | ||||||||
\(553\) | 17.9688 | − | 10.3743i | 0.764111 | − | 0.441160i | ||||
\(554\) | −5.56545 | − | 9.63965i | −0.236453 | − | 0.409549i | ||||
\(555\) | −6.85581 | + | 2.50851i | −0.291013 | + | 0.106480i | ||||
\(556\) | 3.09728 | + | 5.36464i | 0.131354 | + | 0.227511i | ||||
\(557\) | −18.3570 | − | 10.5984i | −0.777809 | − | 0.449068i | 0.0578442 | − | 0.998326i | \(-0.481577\pi\) |
−0.835653 | + | 0.549257i | \(0.814911\pi\) | |||||||
\(558\) | − | 9.22060i | − | 0.390339i | ||||||
\(559\) | −31.4473 | −1.33008 | ||||||||
\(560\) | 1.93474 | + | 5.28768i | 0.0817576 | + | 0.223445i | ||||
\(561\) | −10.5128 | + | 18.2087i | −0.443851 | + | 0.768772i | ||||
\(562\) | − | 5.68717i | − | 0.239899i | ||||||
\(563\) | − | 26.4882i | − | 1.11634i | −0.829725 | − | 0.558172i | \(-0.811503\pi\) | ||
0.829725 | − | 0.558172i | \(-0.188497\pi\) | |||||||
\(564\) | −2.29833 | + | 3.98083i | −0.0967773 | + | 0.167623i | ||||
\(565\) | 41.4079 | + | 7.22881i | 1.74204 | + | 0.304118i | ||||
\(566\) | 3.60536 | − | 6.24466i | 0.151544 | − | 0.262483i | ||||
\(567\) | −2.18069 | + | 1.25902i | −0.0915804 | + | 0.0528740i | ||||
\(568\) | 9.31912 | − | 5.38040i | 0.391022 | − | 0.225757i | ||||
\(569\) | −21.8861 | −0.917514 | −0.458757 | − | 0.888562i | \(-0.651705\pi\) | ||||
−0.458757 | + | 0.888562i | \(0.651705\pi\) | |||||||
\(570\) | 9.12280 | + | 3.43141i | 0.382112 | + | 0.143726i | ||||
\(571\) | −14.0325 | −0.587242 | −0.293621 | − | 0.955922i | \(-0.594860\pi\) | ||||
−0.293621 | + | 0.955922i | \(0.594860\pi\) | |||||||
\(572\) | −11.6335 | + | 6.71658i | −0.486419 | + | 0.280834i | ||||
\(573\) | −3.99564 | + | 2.30688i | −0.166920 | + | 0.0963714i | ||||
\(574\) | −11.2901 | + | 19.5550i | −0.471240 | + | 0.816212i | ||||
\(575\) | −5.52353 | − | 6.53745i | −0.230347 | − | 0.272630i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 27.9608i | 1.16402i | 0.813180 | + | 0.582012i | \(0.197734\pi\) | ||||
−0.813180 | + | 0.582012i | \(0.802266\pi\) | |||||||
\(578\) | 36.1147i | 1.50217i | ||||||||
\(579\) | 12.5401 | − | 21.7202i | 0.521150 | − | 0.902659i | ||||
\(580\) | −9.27989 | + | 3.39547i | −0.385326 | + | 0.140989i | ||||
\(581\) | −17.9920 | −0.746435 | ||||||||
\(582\) | 2.29667i | 0.0952002i | ||||||||
\(583\) | 27.0643 | + | 15.6256i | 1.12089 | + | 0.647145i | ||||
\(584\) | 7.08348 | + | 12.2689i | 0.293117 | + | 0.507693i | ||||
\(585\) | 3.57763 | + | 9.77774i | 0.147917 | + | 0.404260i | ||||
\(586\) | 4.63359 | + | 8.02562i | 0.191412 | + | 0.331535i | ||||
\(587\) | −9.03637 | + | 5.21715i | −0.372971 | + | 0.215335i | −0.674756 | − | 0.738041i | \(-0.735751\pi\) |
0.301785 | + | 0.953376i | \(0.402418\pi\) | |||||||
\(588\) | − | 0.659446i | − | 0.0271951i | ||||||
\(589\) | −37.9354 | + | 13.2770i | −1.56310 | + | 0.547070i | ||||
\(590\) | −13.5773 | + | 16.2368i | −0.558969 | + | 0.668457i | ||||
\(591\) | 1.81219 | + | 3.13881i | 0.0745436 | + | 0.129113i | ||||
\(592\) | −2.82740 | + | 1.63240i | −0.116206 | + | 0.0670913i | ||||
\(593\) | −4.77660 | − | 2.75777i | −0.196152 | − | 0.113248i | 0.398708 | − | 0.917078i | \(-0.369459\pi\) |
−0.594859 | + | 0.803830i | \(0.702792\pi\) | |||||||
\(594\) | 1.44248 | + | 2.49846i | 0.0591858 | + | 0.102513i | ||||
\(595\) | 38.5365 | − | 14.1003i | 1.57984 | − | 0.578058i | ||||
\(596\) | −11.9895 | −0.491109 | ||||||||
\(597\) | − | 0.596986i | − | 0.0244330i | ||||||
\(598\) | 6.90231 | + | 3.98505i | 0.282256 | + | 0.162961i | ||||
\(599\) | 22.5946 | − | 39.1349i | 0.923189 | − | 1.59901i | 0.128741 | − | 0.991678i | \(-0.458907\pi\) |
0.794448 | − | 0.607332i | \(-0.207760\pi\) | |||||||
\(600\) | −0.884968 | − | 4.92106i | −0.0361287 | − | 0.200901i | ||||
\(601\) | −10.2025 | −0.416167 | −0.208083 | − | 0.978111i | \(-0.566723\pi\) | ||||
−0.208083 | + | 0.978111i | \(0.566723\pi\) | |||||||
\(602\) | 14.7279 | + | 8.50316i | 0.600265 | + | 0.346563i | ||||
\(603\) | −9.23107 | + | 5.32956i | −0.375918 | + | 0.217037i | ||||
\(604\) | −2.75767 | + | 4.77643i | −0.112208 | + | 0.194350i | ||||
\(605\) | −1.02942 | + | 5.89668i | −0.0418517 | + | 0.239734i | ||||
\(606\) | 1.68398 | + | 2.91673i | 0.0684069 | + | 0.118484i | ||||
\(607\) | 6.78955i | 0.275579i | 0.990462 | + | 0.137790i | \(0.0439998\pi\) | ||||
−0.990462 | + | 0.137790i | \(0.956000\pi\) | |||||||
\(608\) | 4.28296 | + | 0.810083i | 0.173697 | + | 0.0328532i | ||||
\(609\) | −11.1277 | −0.450916 | ||||||||
\(610\) | 33.0489 | + | 5.76953i | 1.33811 | + | 0.233602i | ||||
\(611\) | 10.7016 | + | 18.5358i | 0.432942 | + | 0.749877i | ||||
\(612\) | 6.31158 | + | 3.64399i | 0.255130 | + | 0.147300i | ||||
\(613\) | 20.8847 | − | 12.0578i | 0.843524 | − | 0.487009i | −0.0149366 | − | 0.999888i | \(-0.504755\pi\) |
0.858460 | + | 0.512880i | \(0.171421\pi\) | |||||||
\(614\) | 5.13612 | − | 8.89602i | 0.207277 | − | 0.359014i | ||||
\(615\) | 12.8628 | − | 15.3823i | 0.518679 | − | 0.620275i | ||||
\(616\) | 7.26448 | 0.292694 | ||||||||
\(617\) | 33.6188 | + | 19.4098i | 1.35344 | + | 0.781410i | 0.988730 | − | 0.149711i | \(-0.0478343\pi\) |
0.364712 | + | 0.931121i | \(0.381168\pi\) | |||||||
\(618\) | −9.51527 | − | 5.49365i | −0.382760 | − | 0.220987i | ||||
\(619\) | −43.0532 | −1.73046 | −0.865228 | − | 0.501379i | \(-0.832826\pi\) | ||||
−0.865228 | + | 0.501379i | \(0.832826\pi\) | |||||||
\(620\) | 15.8167 | + | 13.2261i | 0.635215 | + | 0.531172i | ||||
\(621\) | 0.855848 | − | 1.48237i | 0.0343440 | − | 0.0594856i | ||||
\(622\) | 9.90014 | − | 5.71585i | 0.396959 | − | 0.229185i | ||||
\(623\) | −10.3413 | − | 5.97056i | −0.414316 | − | 0.239205i | ||||
\(624\) | 2.32813 | + | 4.03244i | 0.0931997 | + | 0.161427i | ||||
\(625\) | 19.2599 | + | 15.9392i | 0.770395 | + | 0.637567i | ||||
\(626\) | 3.95860 | 0.158217 | ||||||||
\(627\) | 8.20206 | − | 9.53226i | 0.327559 | − | 0.380682i | ||||
\(628\) | 12.2792i | 0.489995i | ||||||||
\(629\) | 11.8969 | + | 20.6061i | 0.474361 | + | 0.821617i | ||||
\(630\) | 0.968307 | − | 5.54663i | 0.0385783 | − | 0.220983i | ||||
\(631\) | 20.9642 | − | 36.3110i | 0.834571 | − | 1.44552i | −0.0598078 | − | 0.998210i | \(-0.519049\pi\) |
0.894379 | − | 0.447310i | \(-0.147618\pi\) | |||||||
\(632\) | −7.13601 | + | 4.11998i | −0.283855 | + | 0.163884i | ||||
\(633\) | 19.8569 | + | 11.4644i | 0.789242 | + | 0.455669i | ||||
\(634\) | −21.9453 | −0.871560 | ||||||||
\(635\) | 22.6028 | − | 27.0301i | 0.896964 | − | 1.07266i | ||||
\(636\) | 5.41620 | − | 9.38113i | 0.214766 | − | 0.371986i | ||||
\(637\) | −2.65917 | − | 1.53527i | −0.105360 | − | 0.0608298i | ||||
\(638\) | 12.7492i | 0.504745i | ||||||||
\(639\) | −10.7608 | −0.425691 | ||||||||
\(640\) | −0.768349 | − | 2.09991i | −0.0303717 | − | 0.0830064i | ||||
\(641\) | 0.126170 | + | 0.218532i | 0.00498340 | + | 0.00863150i | 0.868506 | − | 0.495678i | \(-0.165080\pi\) |
−0.863523 | + | 0.504310i | \(0.831747\pi\) | |||||||
\(642\) | −2.90789 | − | 1.67887i | −0.114765 | − | 0.0662598i | ||||
\(643\) | −35.9135 | + | 20.7347i | −1.41629 | + | 0.817696i | −0.995971 | − | 0.0896801i | \(-0.971416\pi\) |
−0.420320 | + | 0.907376i | \(0.638082\pi\) | |||||||
\(644\) | −2.15507 | − | 3.73268i | −0.0849215 | − | 0.147088i | ||||
\(645\) | −11.5852 | − | 9.68765i | −0.456167 | − | 0.381451i | ||||
\(646\) | 5.90387 | − | 31.2142i | 0.232285 | − | 1.22810i | ||||
\(647\) | 11.3601i | 0.446612i | 0.974748 | + | 0.223306i | \(0.0716848\pi\) | ||||
−0.974748 | + | 0.223306i | \(0.928315\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | 13.6538 | + | 23.6491i | 0.535958 | + | 0.928307i | ||||
\(650\) | −21.9042 | − | 7.88828i | −0.859153 | − | 0.309404i | ||||
\(651\) | 11.6089 | + | 20.1073i | 0.454991 | + | 0.788067i | ||||
\(652\) | 2.99472 | + | 1.72900i | 0.117282 | + | 0.0677130i | ||||
\(653\) | 14.1285i | 0.552889i | 0.961030 | + | 0.276444i | \(0.0891562\pi\) | ||||
−0.961030 | + | 0.276444i | \(0.910844\pi\) | |||||||
\(654\) | −4.23293 | −0.165521 | ||||||||
\(655\) | 13.7904 | − | 5.04586i | 0.538837 | − | 0.197158i | ||||
\(656\) | 4.48368 | − | 7.76596i | 0.175058 | − | 0.303210i | ||||
\(657\) | − | 14.1670i | − | 0.552706i | ||||||
\(658\) | − | 11.5746i | − | 0.451225i | ||||||
\(659\) | −14.6536 | + | 25.3808i | −0.570823 | + | 0.988695i | 0.425658 | + | 0.904884i | \(0.360043\pi\) |
−0.996482 | + | 0.0838112i | \(0.973291\pi\) | |||||||
\(660\) | −6.35487 | − | 1.10941i | −0.247363 | − | 0.0431836i | ||||
\(661\) | 0.0305882 | − | 0.0529803i | 0.00118974 | − | 0.00206070i | −0.865430 | − | 0.501030i | \(-0.832955\pi\) |
0.866620 | + | 0.498969i | \(0.166288\pi\) | |||||||
\(662\) | −6.45007 | + | 3.72395i | −0.250689 | + | 0.144735i | ||||
\(663\) | 29.3883 | − | 16.9674i | 1.14135 | − | 0.658958i | ||||
\(664\) | 7.14523 | 0.277289 | ||||||||
\(665\) | −24.2142 | + | 4.00295i | −0.938988 | + | 0.155228i | ||||
\(666\) | 3.26480 | 0.126509 | ||||||||
\(667\) | 6.55086 | − | 3.78214i | 0.253650 | − | 0.146445i | ||||
\(668\) | −5.37144 | + | 3.10120i | −0.207827 | + | 0.119989i | ||||
\(669\) | 5.62349 | − | 9.74016i | 0.217417 | − | 0.376576i | ||||
\(670\) | 4.09894 | − | 23.4794i | 0.158356 | − | 0.907089i | ||||
\(671\) | 21.6422 | − | 37.4855i | 0.835489 | − | 1.44711i | ||||
\(672\) | − | 2.51805i | − | 0.0971357i | ||||||
\(673\) | − | 29.7678i | − | 1.14747i | −0.819042 | − | 0.573733i | \(-0.805495\pi\) | ||
0.819042 | − | 0.573733i | \(-0.194505\pi\) | |||||||
\(674\) | −2.33668 | + | 4.04725i | −0.0900055 | + | 0.155894i | ||||
\(675\) | −1.69412 | + | 4.70425i | −0.0652069 | + | 0.181067i | ||||
\(676\) | 8.68073 | 0.333874 | ||||||||
\(677\) | 14.3460i | 0.551360i | 0.961249 | + | 0.275680i | \(0.0889031\pi\) | ||||
−0.961249 | + | 0.275680i | \(0.911097\pi\) | |||||||
\(678\) | −16.2798 | − | 9.39912i | −0.625220 | − | 0.360971i | ||||
\(679\) | −2.89157 | − | 5.00834i | −0.110968 | − | 0.192202i | ||||
\(680\) | −15.3041 | + | 5.59972i | −0.586887 | + | 0.214739i | ||||
\(681\) | −4.41407 | − | 7.64539i | −0.169148 | − | 0.292972i | ||||
\(682\) | 23.0373 | − | 13.3006i | 0.882143 | − | 0.509305i | ||||
\(683\) | 39.5539i | 1.51349i | 0.653712 | + | 0.756744i | \(0.273211\pi\) | ||||
−0.653712 | + | 0.756744i | \(0.726789\pi\) | |||||||
\(684\) | −3.30411 | − | 2.84303i | −0.126336 | − | 0.108706i | ||||
\(685\) | 20.7076 | − | 24.7637i | 0.791196 | − | 0.946171i | ||||
\(686\) | 9.64342 | + | 16.7029i | 0.368187 | + | 0.637719i | ||||
\(687\) | 19.2965 | − | 11.1408i | 0.736207 | − | 0.425049i | ||||
\(688\) | −5.84894 | − | 3.37689i | −0.222989 | − | 0.128743i | ||||
\(689\) | −25.2192 | − | 43.6810i | −0.960775 | − | 1.66411i | ||||
\(690\) | 1.31518 | + | 3.59442i | 0.0500681 | + | 0.136837i | ||||
\(691\) | −32.4212 | −1.23336 | −0.616681 | − | 0.787213i | \(-0.711523\pi\) | ||||
−0.616681 | + | 0.787213i | \(0.711523\pi\) | |||||||
\(692\) | − | 14.4005i | − | 0.547425i | ||||||
\(693\) | −6.29123 | − | 3.63224i | −0.238984 | − | 0.137977i | ||||
\(694\) | −6.84531 | + | 11.8564i | −0.259844 | + | 0.450064i | ||||
\(695\) | 10.6259 | + | 8.88550i | 0.403065 | + | 0.337046i | ||||
\(696\) | 4.41917 | 0.167508 | ||||||||
\(697\) | −56.5982 | − | 32.6770i | −2.14381 | − | 1.23773i | ||||
\(698\) | −30.1291 | + | 17.3951i | −1.14040 | + | 0.658413i | ||||
\(699\) | −3.09066 | + | 5.35318i | −0.116900 | + | 0.202476i | ||||
\(700\) | 8.12557 | + | 9.61712i | 0.307118 | + | 0.363493i | ||||
\(701\) | 10.1662 | + | 17.6084i | 0.383972 | + | 0.665059i | 0.991626 | − | 0.129143i | \(-0.0412226\pi\) |
−0.607654 | + | 0.794202i | \(0.707889\pi\) | |||||||
\(702\) | − | 4.65626i | − | 0.175739i | ||||||
\(703\) | −4.70108 | − | 13.4320i | −0.177305 | − | 0.506599i | ||||
\(704\) | −2.88497 | −0.108731 | ||||||||
\(705\) | −1.76763 | + | 10.1253i | −0.0665730 | + | 0.381342i | ||||
\(706\) | −1.52938 | − | 2.64897i | −0.0575590 | − | 0.0996952i | ||||
\(707\) | −7.34447 | − | 4.24033i | −0.276217 | − | 0.159474i | ||||
\(708\) | 8.19734 | − | 4.73274i | 0.308075 | − | 0.177867i | ||||
\(709\) | 20.1591 | − | 34.9165i | 0.757089 | − | 1.31132i | −0.187240 | − | 0.982314i | \(-0.559954\pi\) |
0.944329 | − | 0.329003i | \(-0.106712\pi\) | |||||||
\(710\) | 15.4353 | − | 18.4587i | 0.579278 | − | 0.692743i | ||||
\(711\) | 8.23995 | 0.309022 | ||||||||
\(712\) | 4.10688 | + | 2.37111i | 0.153912 | + | 0.0888610i | ||||
\(713\) | −13.6684 | − | 7.89144i | −0.511885 | − | 0.295537i | ||||
\(714\) | −18.3515 | −0.686787 | ||||||||
\(715\) | −19.2686 | + | 23.0428i | −0.720604 | + | 0.861752i | ||||
\(716\) | −0.970880 | + | 1.68161i | −0.0362835 | + | 0.0628448i | ||||
\(717\) | −15.7528 | + | 9.09488i | −0.588299 | + | 0.339655i | ||||
\(718\) | −14.7122 | − | 8.49408i | −0.549054 | − | 0.316996i | ||||
\(719\) | −14.5708 | − | 25.2374i | −0.543401 | − | 0.941198i | −0.998706 | − | 0.0508623i | \(-0.983803\pi\) |
0.455305 | − | 0.890336i | \(-0.349530\pi\) | |||||||
\(720\) | −0.384547 | + | 2.20275i | −0.0143312 | + | 0.0820918i | ||||
\(721\) | 27.6665 | 1.03035 | ||||||||
\(722\) | −6.93911 | + | 17.6875i | −0.258247 | + | 0.658262i | ||||
\(723\) | 2.49535i | 0.0928031i | ||||||||
\(724\) | 8.81480 | + | 15.2677i | 0.327600 | + | 0.567419i | ||||
\(725\) | −16.8781 | + | 14.2604i | −0.626835 | + | 0.529618i | ||||
\(726\) | 1.33848 | − | 2.31831i | 0.0496756 | − | 0.0860407i | ||||
\(727\) | −15.6863 | + | 9.05647i | −0.581771 | + | 0.335886i | −0.761837 | − | 0.647769i | \(-0.775702\pi\) |
0.180066 | + | 0.983655i | \(0.442369\pi\) | |||||||
\(728\) | −10.1539 | − | 5.86233i | −0.376327 | − | 0.217273i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 24.3015 | + | 20.3212i | 0.899440 | + | 0.752120i | ||||
\(731\) | −24.6107 | + | 42.6270i | −0.910260 | + | 1.57662i | ||||
\(732\) | −12.9934 | − | 7.50173i | −0.480249 | − | 0.277272i | ||||
\(733\) | − | 8.31171i | − | 0.307000i | −0.988149 | − | 0.153500i | \(-0.950946\pi\) | ||
0.988149 | − | 0.153500i | \(-0.0490545\pi\) | |||||||
\(734\) | −5.39039 | −0.198963 | ||||||||
\(735\) | −0.506685 | − | 1.38478i | −0.0186893 | − | 0.0510784i | ||||
\(736\) | 0.855848 | + | 1.48237i | 0.0315470 | + | 0.0546410i | ||||
\(737\) | −26.6314 | − | 15.3756i | −0.980979 | − | 0.566368i | ||||
\(738\) | −7.76596 | + | 4.48368i | −0.285869 | + | 0.165047i | ||||
\(739\) | 7.63311 | + | 13.2209i | 0.280788 | + | 0.486340i | 0.971579 | − | 0.236715i | \(-0.0760708\pi\) |
−0.690791 | + | 0.723055i | \(0.742737\pi\) | |||||||
\(740\) | −4.68305 | + | 5.60034i | −0.172152 | + | 0.205872i | ||||
\(741\) | −19.1568 | + | 6.70468i | −0.703741 | + | 0.246303i | ||||
\(742\) | 27.2765i | 1.00135i | ||||||||
\(743\) | −29.0049 | + | 16.7460i | −1.06409 | + | 0.614351i | −0.926560 | − | 0.376147i | \(-0.877249\pi\) |
−0.137528 | + | 0.990498i | \(0.543916\pi\) | |||||||
\(744\) | −4.61030 | − | 7.98528i | −0.169022 | − | 0.292754i | ||||
\(745\) | −25.1769 | + | 9.21213i | −0.922412 | + | 0.337506i | ||||
\(746\) | 1.92793 | + | 3.33927i | 0.0705865 | + | 0.122259i | ||||
\(747\) | −6.18795 | − | 3.57262i | −0.226405 | − | 0.130715i | ||||
\(748\) | 21.0256i | 0.768772i | ||||||||
\(749\) | 8.45496 | 0.308937 | ||||||||
\(750\) | −5.63945 | − | 9.65384i | −0.205924 | − | 0.352508i | ||||
\(751\) | −10.0737 | + | 17.4481i | −0.367594 | + | 0.636691i | −0.989189 | − | 0.146648i | \(-0.953152\pi\) |
0.621595 | + | 0.783339i | \(0.286485\pi\) | |||||||
\(752\) | 4.59667i | 0.167623i | ||||||||
\(753\) | − | 21.2635i | − | 0.774883i | ||||||
\(754\) | 10.2884 | − | 17.8200i | 0.374682 | − | 0.648968i | ||||
\(755\) | −2.12091 | + | 12.1489i | −0.0771878 | + | 0.442145i | ||||
\(756\) | −1.25902 | + | 2.18069i | −0.0457902 | + | 0.0793110i | ||||
\(757\) | −26.9406 | + | 15.5542i | −0.979174 | + | 0.565327i | −0.902021 | − | 0.431693i | \(-0.857917\pi\) |
−0.0771537 | + | 0.997019i | \(0.524583\pi\) | |||||||
\(758\) | 11.8270 | − | 6.82832i | 0.429576 | − | 0.248016i | ||||
\(759\) | 4.93819 | 0.179245 | ||||||||
\(760\) | 9.61628 | − | 1.58971i | 0.348819 | − | 0.0576647i | ||||
\(761\) | 2.73496 | 0.0991421 | 0.0495710 | − | 0.998771i | \(-0.484215\pi\) | ||||
0.0495710 | + | 0.998771i | \(0.484215\pi\) | |||||||
\(762\) | −13.6465 | + | 7.87880i | −0.494360 | + | 0.285419i | ||||
\(763\) | 9.23072 | − | 5.32936i | 0.334174 | − | 0.192936i | ||||
\(764\) | −2.30688 | + | 3.99564i | −0.0834601 | + | 0.144557i | ||||
\(765\) | 16.0536 | + | 2.80257i | 0.580420 | + | 0.101327i | ||||
\(766\) | 3.64176 | − | 6.30771i | 0.131582 | − | 0.227907i | ||||
\(767\) | − | 44.0737i | − | 1.59141i | ||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | 11.3522 | − | 19.6626i | 0.409371 | − | 0.709052i | −0.585448 | − | 0.810710i | \(-0.699081\pi\) |
0.994819 | + | 0.101658i | \(0.0324147\pi\) | |||||||
\(770\) | 15.2548 | − | 5.58166i | 0.549744 | − | 0.201149i | ||||
\(771\) | −5.81714 | −0.209499 | ||||||||
\(772\) | − | 25.0803i | − | 0.902659i | ||||||
\(773\) | 11.9910 | + | 6.92302i | 0.431287 | + | 0.249004i | 0.699895 | − | 0.714246i | \(-0.253230\pi\) |
−0.268608 | + | 0.963250i | \(0.586563\pi\) | |||||||
\(774\) | 3.37689 | + | 5.84894i | 0.121380 | + | 0.210236i | ||||
\(775\) | 43.3760 | + | 15.6209i | 1.55811 | + | 0.561118i | ||||
\(776\) | 1.14834 | + | 1.98898i | 0.0412229 | + | 0.0714002i | ||||
\(777\) | −7.11953 | + | 4.11046i | −0.255412 | + | 0.147462i | ||||
\(778\) | − | 19.6265i | − | 0.703646i | ||||||
\(779\) | 29.6292 | + | 25.4945i | 1.06158 | + | 0.913435i | ||||
\(780\) | 7.98719 | + | 6.67896i | 0.285987 | + | 0.239145i | ||||
\(781\) | −15.5223 | − | 26.8854i | −0.555431 | − | 0.962034i | ||||
\(782\) | 10.8035 | − | 6.23741i | 0.386333 | − | 0.223049i | ||||
\(783\) | −3.82712 | − | 2.20959i | −0.136770 | − | 0.0789642i | ||||
\(784\) | −0.329723 | − | 0.571097i | −0.0117758 | − | 0.0203963i | ||||
\(785\) | 9.43474 | + | 25.7853i | 0.336740 | + | 0.920318i | ||||
\(786\) | −6.56715 | −0.234242 | ||||||||
\(787\) | − | 0.272719i | − | 0.00972137i | −0.999988 | − | 0.00486069i | \(-0.998453\pi\) | ||
0.999988 | − | 0.00486069i | \(-0.00154721\pi\) | |||||||
\(788\) | 3.13881 | + | 1.81219i | 0.111815 | + | 0.0645567i | ||||
\(789\) | 8.63749 | − | 14.9606i | 0.307503 | − | 0.532610i | ||||
\(790\) | −11.8194 | + | 14.1345i | −0.420516 | + | 0.502884i | ||||
\(791\) | 47.3348 | 1.68303 | ||||||||
\(792\) | 2.49846 | + | 1.44248i | 0.0887788 | + | 0.0512564i | ||||
\(793\) | −60.5005 | + | 34.9300i | −2.14843 | + | 1.24040i | ||||
\(794\) | 5.78964 | − | 10.0280i | 0.205467 | − | 0.355879i | ||||
\(795\) | 4.16557 | − | 23.8611i | 0.147737 | − | 0.846266i | ||||
\(796\) | −0.298493 | − | 0.517005i | −0.0105798 | − | 0.0183248i | ||||
\(797\) | 2.18853i | 0.0775216i | 0.999249 | + | 0.0387608i | \(0.0123410\pi\) | ||||
−0.999249 | + | 0.0387608i | \(0.987659\pi\) | |||||||
\(798\) | 10.7847 | + | 2.03983i | 0.381774 | + | 0.0722090i | ||||
\(799\) | 33.5004 | 1.18516 | ||||||||
\(800\) | −3.22694 | − | 3.81928i | −0.114089 | − | 0.135032i | ||||
\(801\) | −2.37111 | − | 4.10688i | −0.0837790 | − | 0.145109i | ||||
\(802\) | −1.27837 | − | 0.738065i | −0.0451407 | − | 0.0260620i | ||||
\(803\) | 35.3955 | − | 20.4356i | 1.24908 | − | 0.721157i | ||||
\(804\) | −5.32956 | + | 9.23107i | −0.187959 | + | 0.325555i | ||||
\(805\) | −7.39346 | − | 6.18247i | −0.260585 | − | 0.217903i | ||||
\(806\) | −42.9335 | −1.51227 | ||||||||
\(807\) | −8.36136 | − | 4.82743i | −0.294334 | − | 0.169934i | ||||
\(808\) | 2.91673 | + | 1.68398i | 0.102610 | + | 0.0592421i | ||||
\(809\) | 8.89531 | 0.312743 | 0.156371 | − | 0.987698i | \(-0.450020\pi\) | ||||
0.156371 | + | 0.987698i | \(0.450020\pi\) | |||||||
\(810\) | 1.43440 | − | 1.71537i | 0.0503998 | − | 0.0602719i | ||||
\(811\) | 6.06868 | − | 10.5113i | 0.213100 | − | 0.369101i | −0.739583 | − | 0.673065i | \(-0.764977\pi\) |
0.952683 | + | 0.303965i | \(0.0983106\pi\) | |||||||
\(812\) | −9.63686 | + | 5.56384i | −0.338187 | + | 0.195253i | ||||
\(813\) | −5.57406 | − | 3.21818i | −0.195491 | − | 0.112867i | ||||
\(814\) | 4.70943 | + | 8.15697i | 0.165065 | + | 0.285902i | ||||
\(815\) | 7.61714 | + | 1.32977i | 0.266817 | + | 0.0465797i | ||||
\(816\) | 7.28798 | 0.255130 | ||||||||
\(817\) | 19.2012 | − | 22.3152i | 0.671765 | − | 0.780711i | ||||
\(818\) | 0.651522i | 0.0227799i | ||||||||
\(819\) | 5.86233 | + | 10.1539i | 0.204847 | + | 0.354805i | ||||
\(820\) | 3.44837 | − | 19.7529i | 0.120422 | − | 0.689801i | ||||
\(821\) | 21.4432 | − | 37.1408i | 0.748374 | − | 1.29622i | −0.200228 | − | 0.979749i | \(-0.564168\pi\) |
0.948602 | − | 0.316472i | \(-0.102498\pi\) | |||||||
\(822\) | −12.5023 | + | 7.21818i | −0.436066 | + | 0.251763i | ||||
\(823\) | −27.1468 | − | 15.6732i | −0.946278 | − | 0.546334i | −0.0543553 | − | 0.998522i | \(-0.517310\pi\) |
−0.891923 | + | 0.452188i | \(0.850644\pi\) | |||||||
\(824\) | −10.9873 | −0.382760 | ||||||||
\(825\) | −14.1971 | + | 2.55311i | −0.494280 | + | 0.0888877i | ||||
\(826\) | −11.9172 | + | 20.6413i | −0.414654 | + | 0.718202i | ||||
\(827\) | 28.4166 | + | 16.4063i | 0.988143 | + | 0.570505i | 0.904719 | − | 0.426009i | \(-0.140081\pi\) |
0.0834244 | + | 0.996514i | \(0.473414\pi\) | |||||||
\(828\) | − | 1.71170i | − | 0.0594856i | ||||||
\(829\) | −51.8181 | −1.79972 | −0.899858 | − | 0.436182i | \(-0.856330\pi\) | ||||
−0.899858 | + | 0.436182i | \(0.856330\pi\) | |||||||
\(830\) | 15.0044 | − | 5.49003i | 0.520809 | − | 0.190562i | ||||
\(831\) | 5.56545 | + | 9.63965i | 0.193063 | + | 0.334396i | ||||
\(832\) | 4.03244 | + | 2.32813i | 0.139800 | + | 0.0807133i | ||||
\(833\) | −4.16214 | + | 2.40301i | −0.144210 | + | 0.0832595i | ||||
\(834\) | −3.09728 | − | 5.36464i | −0.107250 | − | 0.185762i | ||||
\(835\) | −8.89675 | + | 10.6394i | −0.307885 | + | 0.368192i | ||||
\(836\) | 2.33706 | − | 12.3562i | 0.0808290 | − | 0.427348i | ||||
\(837\) | 9.22060i | 0.318711i | ||||||||
\(838\) | 22.4783 | − | 12.9779i | 0.776500 | − | 0.448313i | ||||
\(839\) | 0.433475 | + | 0.750801i | 0.0149652 | + | 0.0259205i | 0.873411 | − | 0.486984i | \(-0.161903\pi\) |
−0.858446 | + | 0.512904i | \(0.828570\pi\) | |||||||
\(840\) | −1.93474 | − | 5.28768i | −0.0667548 | − | 0.182442i | ||||
\(841\) | 4.73545 | + | 8.20204i | 0.163291 | + | 0.282829i | ||||
\(842\) | −25.8890 | − | 14.9470i | −0.892194 | − | 0.515109i | ||||
\(843\) | 5.68717i | 0.195876i | ||||||||
\(844\) | 22.9288 | 0.789242 | ||||||||
\(845\) | 18.2288 | − | 6.66983i | 0.627089 | − | 0.229449i | ||||
\(846\) | 2.29833 | − | 3.98083i | 0.0790183 | − | 0.136864i | ||||
\(847\) | 6.74070i | 0.231613i | ||||||||
\(848\) | − | 10.8324i | − | 0.371986i | ||||||
\(849\) | −3.60536 | + | 6.24466i | −0.123736 | + | 0.214316i | ||||
\(850\) | −27.8348 | + | 23.5178i | −0.954727 | + | 0.806656i | ||||
\(851\) | 2.79418 | − | 4.83966i | 0.0957831 | − | 0.165901i | ||||
\(852\) | −9.31912 | + | 5.38040i | −0.319268 | + | 0.184329i | ||||
\(853\) | −1.05924 | + | 0.611551i | −0.0362676 | + | 0.0209391i | −0.518024 | − | 0.855366i | \(-0.673332\pi\) |
0.481757 | + | 0.876305i | \(0.339999\pi\) | |||||||
\(854\) | 37.7794 | 1.29278 | ||||||||
\(855\) | −9.12280 | − | 3.43141i | −0.311993 | − | 0.117352i | ||||
\(856\) | −3.35775 | −0.114765 | ||||||||
\(857\) | 14.7442 | − | 8.51258i | 0.503653 | − | 0.290784i | −0.226568 | − | 0.973995i | \(-0.572751\pi\) |
0.730221 | + | 0.683211i | \(0.239417\pi\) | |||||||
\(858\) | 11.6335 | − | 6.71658i | 0.397160 | − | 0.229300i | ||||
\(859\) | −4.21282 | + | 7.29683i | −0.143740 | + | 0.248964i | −0.928902 | − | 0.370326i | \(-0.879246\pi\) |
0.785162 | + | 0.619290i | \(0.212579\pi\) | |||||||
\(860\) | −14.8769 | − | 2.59715i | −0.507298 | − | 0.0885619i | ||||
\(861\) | 11.2901 | − | 19.5550i | 0.384766 | − | 0.666434i | ||||
\(862\) | − | 27.4245i | − | 0.934083i | ||||||
\(863\) | 6.06986i | 0.206620i | 0.994649 | + | 0.103310i | \(0.0329434\pi\) | ||||
−0.994649 | + | 0.103310i | \(0.967057\pi\) | |||||||
\(864\) | 0.500000 | − | 0.866025i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | −11.0646 | − | 30.2398i | −0.376209 | − | 1.02819i | ||||
\(866\) | 11.2647 | 0.382791 | ||||||||
\(867\) | − | 36.1147i | − | 1.22652i | ||||||
\(868\) | 20.1073 | + | 11.6089i | 0.682486 | + | 0.394033i | ||||
\(869\) | 11.8860 | + | 20.5872i | 0.403205 | + | 0.698371i | ||||
\(870\) | 9.27989 | − | 3.39547i | 0.314618 | − | 0.115117i | ||||
\(871\) | 24.8158 | + | 42.9822i | 0.840852 | + | 1.45640i | ||||
\(872\) | −3.66583 | + | 2.11647i | −0.124141 | + | 0.0716726i | ||||
\(873\) | − | 2.29667i | − | 0.0777307i | ||||||
\(874\) | −7.04226 | + | 2.46472i | −0.238208 | + | 0.0833705i | ||||
\(875\) | 24.4523 | + | 13.9518i | 0.826639 | + | 0.471659i | ||||
\(876\) | −7.08348 | − | 12.2689i | −0.239329 | − | 0.414529i | ||||
\(877\) | 29.4618 | − | 17.0098i | 0.994855 | − | 0.574380i | 0.0881333 | − | 0.996109i | \(-0.471910\pi\) |
0.906722 | + | 0.421729i | \(0.138577\pi\) | |||||||
\(878\) | 13.6797 | + | 7.89796i | 0.461666 | + | 0.266543i | ||||
\(879\) | −4.63359 | − | 8.02562i | −0.156287 | − | 0.270697i | ||||
\(880\) | −6.05819 | + | 2.21666i | −0.204221 | + | 0.0747237i | ||||
\(881\) | 37.8182 | 1.27413 | 0.637064 | − | 0.770811i | \(-0.280149\pi\) | ||||
0.637064 | + | 0.770811i | \(0.280149\pi\) | |||||||
\(882\) | 0.659446i | 0.0222047i | ||||||||
\(883\) | 39.0605 | + | 22.5516i | 1.31449 | + | 0.758921i | 0.982836 | − | 0.184480i | \(-0.0590602\pi\) |
0.331653 | + | 0.943401i | \(0.392394\pi\) | |||||||
\(884\) | 16.9674 | − | 29.3883i | 0.570674 | − | 0.988436i | ||||
\(885\) | 13.5773 | − | 16.2368i | 0.456397 | − | 0.545793i | ||||
\(886\) | 7.03690 | 0.236409 | ||||||||
\(887\) | −37.0666 | − | 21.4004i | −1.24457 | − | 0.718555i | −0.274552 | − | 0.961572i | \(-0.588529\pi\) |
−0.970022 | + | 0.243017i | \(0.921863\pi\) | |||||||
\(888\) | 2.82740 | − | 1.63240i | 0.0948814 | − | 0.0547798i | ||||
\(889\) | 19.8392 | − | 34.3625i | 0.665385 | − | 1.15248i | ||||
\(890\) | 10.4459 | + | 1.82361i | 0.350149 | + | 0.0611274i | ||||
\(891\) | −1.44248 | − | 2.49846i | −0.0483250 | − | 0.0837014i | ||||
\(892\) | − | 11.2470i | − | 0.376576i | ||||||
\(893\) | −19.6873 | − | 3.72368i | −0.658812 | − | 0.124608i | ||||
\(894\) | 11.9895 | 0.400989 | ||||||||
\(895\) | −0.746698 | + | 4.27722i | −0.0249594 | + | 0.142972i | ||||
\(896\) | −1.25902 | − | 2.18069i | −0.0420610 | − | 0.0728518i | ||||
\(897\) | −6.90231 | − | 3.98505i | −0.230461 | − | 0.133057i | ||||
\(898\) | 14.1933 | − | 8.19449i | 0.473635 | − | 0.273454i | ||||
\(899\) | −20.3737 | + | 35.2883i | −0.679502 | + | 1.17693i | ||||
\(900\) | 0.884968 | + | 4.92106i | 0.0294989 | + | 0.164035i | ||||
\(901\) | −78.9463 | −2.63008 | ||||||||
\(902\) | −22.4046 | − | 12.9353i | −0.745990 | − | 0.430698i | ||||
\(903\) | −14.7279 | − | 8.50316i | −0.490114 | − | 0.282967i | ||||
\(904\) | −18.7982 | −0.625220 | ||||||||
\(905\) | 30.2412 | + | 25.2880i | 1.00525 | + | 0.840601i | ||||
\(906\) | 2.75767 | − | 4.77643i | 0.0916175 | − | 0.158686i | ||||
\(907\) | −26.2663 | + | 15.1648i | −0.872157 | + | 0.503540i | −0.868065 | − | 0.496451i | \(-0.834636\pi\) |
−0.00409285 | + | 0.999992i | \(0.501303\pi\) | |||||||
\(908\) | −7.64539 | − | 4.41407i | −0.253721 | − | 0.146486i | ||||
\(909\) | −1.68398 | − | 2.91673i | −0.0558540 | − | 0.0967419i | ||||
\(910\) | −25.8266 | − | 4.50869i | −0.856142 | − | 0.149462i | ||||
\(911\) | 35.4194 | 1.17350 | 0.586748 | − | 0.809770i | \(-0.300408\pi\) | ||||
0.586748 | + | 0.809770i | \(0.300408\pi\) | |||||||
\(912\) | −4.28296 | − | 0.810083i | −0.141823 | − | 0.0268245i | ||||
\(913\) | − | 20.6138i | − | 0.682216i | ||||||
\(914\) | −5.79875 | − | 10.0437i | −0.191805 | − | 0.332217i | ||||
\(915\) | −33.0489 | − | 5.76953i | −1.09256 | − | 0.190735i | ||||
\(916\) | 11.1408 | − | 19.2965i | 0.368104 | − | 0.637574i | ||||
\(917\) | 14.3209 | − | 8.26819i | 0.472918 | − | 0.273040i | ||||
\(918\) | −6.31158 | − | 3.64399i | −0.208313 | − | 0.120270i | ||||
\(919\) | −17.0531 | −0.562531 | −0.281265 | − | 0.959630i | \(-0.590754\pi\) | ||||
−0.281265 | + | 0.959630i | \(0.590754\pi\) | |||||||
\(920\) | 2.93619 | + | 2.45527i | 0.0968033 | + | 0.0809477i | ||||
\(921\) | −5.13612 | + | 8.89602i | −0.169241 | + | 0.293134i | ||||
\(922\) | −4.14363 | − | 2.39232i | −0.136463 | − | 0.0787870i | ||||
\(923\) | 50.1050i | 1.64923i | ||||||||
\(924\) | −7.26448 | −0.238984 | ||||||||
\(925\) | −5.53098 | + | 15.3584i | −0.181858 | + | 0.504982i | ||||
\(926\) | −6.07796 | − | 10.5273i | −0.199734 | − | 0.345950i | ||||
\(927\) | 9.51527 | + | 5.49365i | 0.312523 | + | 0.180435i | ||||
\(928\) | 3.82712 | − | 2.20959i | 0.125631 | − | 0.0725332i | ||||
\(929\) | −16.0271 | − | 27.7598i | −0.525834 | − | 0.910771i | −0.999547 | − | 0.0300916i | \(-0.990420\pi\) |
0.473714 | − | 0.880679i | \(-0.342913\pi\) | |||||||
\(930\) | −15.8167 | − | 13.2261i | −0.518651 | − | 0.433700i | ||||
\(931\) | 2.71309 | − | 0.949555i | 0.0889179 | − | 0.0311204i | ||||
\(932\) | 6.18132i | 0.202476i | ||||||||
\(933\) | −9.90014 | + | 5.71585i | −0.324116 | + | 0.187128i | ||||
\(934\) | −0.802313 | − | 1.38965i | −0.0262525 | − | 0.0454706i | ||||
\(935\) | 16.1550 | + | 44.1520i | 0.528325 | + | 1.44392i | ||||
\(936\) | −2.32813 | − | 4.03244i | −0.0760973 | − | 0.131804i | ||||
\(937\) | 22.9312 | + | 13.2393i | 0.749128 | + | 0.432509i | 0.825379 | − | 0.564579i | \(-0.190962\pi\) |
−0.0762506 | + | 0.997089i | \(0.524295\pi\) | |||||||
\(938\) | − | 26.8402i | − | 0.876362i | ||||||
\(939\) | −3.95860 | −0.129184 | ||||||||
\(940\) | 3.53184 | + | 9.65260i | 0.115196 | + | 0.314833i | ||||
\(941\) | −7.18502 | + | 12.4448i | −0.234225 | + | 0.405689i | −0.959047 | − | 0.283247i | \(-0.908589\pi\) |
0.724822 | + | 0.688936i | \(0.241922\pi\) | |||||||
\(942\) | − | 12.2792i | − | 0.400079i | ||||||
\(943\) | 15.3494i | 0.499845i | ||||||||
\(944\) | 4.73274 | − | 8.19734i | 0.154037 | − | 0.266801i | ||||
\(945\) | −0.968307 | + | 5.54663i | −0.0314990 | + | 0.180432i | ||||
\(946\) | −9.74222 | + | 16.8740i | −0.316747 | + | 0.548622i | ||||
\(947\) | −39.4692 | + | 22.7875i | −1.28258 | + | 0.740495i | −0.977318 | − | 0.211775i | \(-0.932076\pi\) |
−0.305257 | + | 0.952270i | \(0.598742\pi\) | |||||||
\(948\) | 7.13601 | − | 4.11998i | 0.231767 | − | 0.133811i | ||||
\(949\) | −65.9650 | −2.14132 | ||||||||
\(950\) | 18.9719 | − | 10.7269i | 0.615530 | − | 0.348027i | ||||
\(951\) | 21.9453 | 0.711625 | ||||||||
\(952\) | −15.8928 | + | 9.17574i | −0.515090 | + | 0.297387i | ||||
\(953\) | −46.7123 | + | 26.9694i | −1.51316 | + | 0.873623i | −0.513278 | + | 0.858222i | \(0.671569\pi\) |
−0.999881 | + | 0.0154010i | \(0.995098\pi\) | |||||||
\(954\) | −5.41620 | + | 9.38113i | −0.175356 | + | 0.303725i | ||||
\(955\) | −1.77421 | + | 10.1630i | −0.0574121 | + | 0.328867i | ||||
\(956\) | −9.09488 | + | 15.7528i | −0.294149 | + | 0.509482i | ||||
\(957\) | − | 12.7492i | − | 0.412122i | ||||||
\(958\) | − | 34.5880i | − | 1.11749i | ||||||
\(959\) | 18.1757 | − | 31.4813i | 0.586924 | − | 1.01658i | ||||
\(960\) | 0.768349 | + | 2.09991i | 0.0247984 | + | 0.0677744i | ||||
\(961\) | 54.0195 | 1.74257 | ||||||||
\(962\) | − | 15.2018i | − | 0.490124i | ||||||
\(963\) | 2.90789 | + | 1.67887i | 0.0937055 | + | 0.0541009i | ||||
\(964\) | 1.24768 | + | 2.16104i | 0.0401849 | + | 0.0696023i | ||||
\(965\) | −19.2704 | − | 52.6664i | −0.620336 | − | 1.69539i | ||||
\(966\) | 2.15507 | + | 3.73268i | 0.0693381 | + | 0.120097i | ||||
\(967\) | 19.5534 | − | 11.2892i | 0.628795 | − | 0.363035i | −0.151490 | − | 0.988459i | \(-0.548407\pi\) |
0.780285 | + | 0.625424i | \(0.215074\pi\) | |||||||
\(968\) | − | 2.67696i | − | 0.0860407i | ||||||
\(969\) | −5.90387 | + | 31.2142i | −0.189660 | + | 1.00274i | ||||
\(970\) | 3.93964 | + | 3.29436i | 0.126494 | + | 0.105776i | ||||
\(971\) | −29.4664 | − | 51.0372i | −0.945621 | − | 1.63786i | −0.754504 | − | 0.656296i | \(-0.772122\pi\) |
−0.191117 | − | 0.981567i | \(-0.561211\pi\) | |||||||
\(972\) | −0.866025 | + | 0.500000i | −0.0277778 | + | 0.0160375i | ||||
\(973\) | 13.5084 | + | 7.79909i | 0.433060 | + | 0.250027i | ||||
\(974\) | 12.1868 | + | 21.1082i | 0.390491 | + | 0.676350i | ||||
\(975\) | 21.9042 | + | 7.88828i | 0.701495 | + | 0.252627i | ||||
\(976\) | −15.0035 | −0.480249 | ||||||||
\(977\) | − | 1.86548i | − | 0.0596821i | −0.999555 | − | 0.0298411i | \(-0.990500\pi\) | ||
0.999555 | − | 0.0298411i | \(-0.00950012\pi\) | |||||||
\(978\) | −2.99472 | − | 1.72900i | −0.0957606 | − | 0.0552874i | ||||
\(979\) | 6.84057 | − | 11.8482i | 0.218626 | − | 0.378671i | ||||
\(980\) | −1.13119 | − | 0.945912i | −0.0361346 | − | 0.0302160i | ||||
\(981\) | 4.23293 | 0.135147 | ||||||||
\(982\) | −9.44752 | − | 5.45453i | −0.301482 | − | 0.174061i | ||||
\(983\) | 38.1239 | − | 22.0109i | 1.21597 | − | 0.702038i | 0.251913 | − | 0.967750i | \(-0.418940\pi\) |
0.964052 | + | 0.265712i | \(0.0856071\pi\) | |||||||
\(984\) | −4.48368 | + | 7.76596i | −0.142934 | + | 0.247570i | ||||
\(985\) | 7.98363 | + | 1.39375i | 0.254380 | + | 0.0444085i | ||||
\(986\) | −16.1034 | − | 27.8920i | −0.512838 | − | 0.888261i | ||||
\(987\) | 11.5746i | 0.368424i | ||||||||
\(988\) | −13.2379 | + | 15.3848i | −0.421154 | + | 0.489456i | ||||
\(989\) | 11.5604 | 0.367600 | ||||||||
\(990\) | 6.35487 | + | 1.10941i | 0.201971 | + | 0.0352592i | ||||
\(991\) | 16.2964 | + | 28.2263i | 0.517674 | + | 0.896637i | 0.999789 | + | 0.0205293i | \(0.00653513\pi\) |
−0.482116 | + | 0.876108i | \(0.660132\pi\) | |||||||
\(992\) | −7.98528 | − | 4.61030i | −0.253533 | − | 0.146377i | ||||
\(993\) | 6.45007 | − | 3.72395i | 0.204687 | − | 0.118176i | ||||
\(994\) | 13.5481 | − | 23.4660i | 0.429719 | − | 0.744296i | ||||
\(995\) | −1.02405 | − | 0.856319i | −0.0324646 | − | 0.0271471i | ||||
\(996\) | −7.14523 | −0.226405 | ||||||||
\(997\) | −16.4589 | − | 9.50256i | −0.521259 | − | 0.300949i | 0.216190 | − | 0.976351i | \(-0.430637\pi\) |
−0.737450 | + | 0.675402i | \(0.763970\pi\) | |||||||
\(998\) | 9.60920 | + | 5.54788i | 0.304174 | + | 0.175615i | ||||
\(999\) | −3.26480 | −0.103294 |
(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 | 570.2.q.c.349.3 | yes | 20 | |
3.2 | odd | 2 | 1710.2.t.c.919.8 | 20 | |||
5.4 | even | 2 | inner | 570.2.q.c.349.6 | yes | 20 | |
15.14 | odd | 2 | 1710.2.t.c.919.5 | 20 | |||
19.11 | even | 3 | inner | 570.2.q.c.49.6 | yes | 20 | |
57.11 | odd | 6 | 1710.2.t.c.1189.5 | 20 | |||
95.49 | even | 6 | inner | 570.2.q.c.49.3 | ✓ | 20 | |
285.239 | odd | 6 | 1710.2.t.c.1189.8 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.q.c.49.3 | ✓ | 20 | 95.49 | even | 6 | inner | |
570.2.q.c.49.6 | yes | 20 | 19.11 | even | 3 | inner | |
570.2.q.c.349.3 | yes | 20 | 1.1 | even | 1 | trivial | |
570.2.q.c.349.6 | yes | 20 | 5.4 | even | 2 | inner | |
1710.2.t.c.919.5 | 20 | 15.14 | odd | 2 | |||
1710.2.t.c.919.8 | 20 | 3.2 | odd | 2 | |||
1710.2.t.c.1189.5 | 20 | 57.11 | odd | 6 | |||
1710.2.t.c.1189.8 | 20 | 285.239 | odd | 6 |