Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,3,Mod(31,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.o (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: | \(5.72208555157\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.3317760000.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 61.4 | ||
Root | \(1.72286 + 0.178197i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.61 |
Dual form | 210.3.o.a.31.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 1.22474i | 0.353553 | − | 0.612372i | ||||
\(3\) | 1.50000 | − | 0.866025i | 0.500000 | − | 0.288675i | ||||
\(4\) | −1.00000 | − | 1.73205i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.93649 | + | 1.11803i | 0.387298 | + | 0.223607i | ||||
\(6\) | − | 2.44949i | − | 0.408248i | ||||||
\(7\) | 5.10237 | − | 4.79227i | 0.728910 | − | 0.684610i | ||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.166667 | − | 0.288675i | ||||
\(10\) | 2.73861 | − | 1.58114i | 0.273861 | − | 0.158114i | ||||
\(11\) | 0.919414 | + | 1.59247i | 0.0835831 | + | 0.144770i | 0.904787 | − | 0.425865i | \(-0.140030\pi\) |
−0.821203 | + | 0.570635i | \(0.806697\pi\) | |||||||
\(12\) | −3.00000 | − | 1.73205i | −0.250000 | − | 0.144338i | ||||
\(13\) | − | 5.40765i | − | 0.415973i | −0.978132 | − | 0.207986i | \(-0.933309\pi\) | ||
0.978132 | − | 0.207986i | \(-0.0666910\pi\) | |||||||
\(14\) | −2.26139 | − | 9.63774i | −0.161528 | − | 0.688410i | ||||
\(15\) | 3.87298 | 0.258199 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.125000 | + | 0.216506i | ||||
\(17\) | 8.71093 | − | 5.02926i | 0.512408 | − | 0.295839i | −0.221415 | − | 0.975180i | \(-0.571068\pi\) |
0.733823 | + | 0.679341i | \(0.237734\pi\) | |||||||
\(18\) | −2.12132 | − | 3.67423i | −0.117851 | − | 0.204124i | ||||
\(19\) | −7.96084 | − | 4.59619i | −0.418992 | − | 0.241905i | 0.275654 | − | 0.961257i | \(-0.411106\pi\) |
−0.694646 | + | 0.719352i | \(0.744439\pi\) | |||||||
\(20\) | − | 4.47214i | − | 0.223607i | ||||||
\(21\) | 3.50333 | − | 11.6072i | 0.166825 | − | 0.552723i | ||||
\(22\) | 2.60049 | 0.118204 | ||||||||
\(23\) | 0.460644 | − | 0.797858i | 0.0200280 | − | 0.0346895i | −0.855838 | − | 0.517244i | \(-0.826958\pi\) |
0.875866 | + | 0.482555i | \(0.160291\pi\) | |||||||
\(24\) | −4.24264 | + | 2.44949i | −0.176777 | + | 0.102062i | ||||
\(25\) | 2.50000 | + | 4.33013i | 0.100000 | + | 0.173205i | ||||
\(26\) | −6.62299 | − | 3.82378i | −0.254730 | − | 0.147069i | ||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | −13.4028 | − | 4.04529i | −0.478672 | − | 0.144475i | ||||
\(29\) | 12.5573 | 0.433012 | 0.216506 | − | 0.976281i | \(-0.430534\pi\) | ||||
0.216506 | + | 0.976281i | \(0.430534\pi\) | |||||||
\(30\) | 2.73861 | − | 4.74342i | 0.0912871 | − | 0.158114i | ||||
\(31\) | −36.1874 | + | 20.8928i | −1.16733 | + | 0.673961i | −0.953051 | − | 0.302811i | \(-0.902075\pi\) |
−0.214284 | + | 0.976771i | \(0.568742\pi\) | |||||||
\(32\) | 2.82843 | + | 4.89898i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 2.75824 | + | 1.59247i | 0.0835831 | + | 0.0482567i | ||||
\(34\) | − | 14.2249i | − | 0.418379i | ||||||
\(35\) | 15.2386 | − | 3.57557i | 0.435389 | − | 0.102159i | ||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | −3.64194 | + | 6.30803i | −0.0984308 | + | 0.170487i | −0.911035 | − | 0.412328i | \(-0.864716\pi\) |
0.812604 | + | 0.582816i | \(0.198049\pi\) | |||||||
\(38\) | −11.2583 | + | 6.50000i | −0.296272 | + | 0.171053i | ||||
\(39\) | −4.68316 | − | 8.11147i | −0.120081 | − | 0.207986i | ||||
\(40\) | −5.47723 | − | 3.16228i | −0.136931 | − | 0.0790569i | ||||
\(41\) | 52.3877i | 1.27775i | 0.769311 | + | 0.638875i | \(0.220600\pi\) | ||||
−0.769311 | + | 0.638875i | \(0.779400\pi\) | |||||||
\(42\) | −11.7386 | − | 12.4982i | −0.279491 | − | 0.297576i | ||||
\(43\) | −8.12312 | −0.188910 | −0.0944549 | − | 0.995529i | \(-0.530111\pi\) | ||||
−0.0944549 | + | 0.995529i | \(0.530111\pi\) | |||||||
\(44\) | 1.83883 | − | 3.18494i | 0.0417915 | − | 0.0723850i | ||||
\(45\) | 5.80948 | − | 3.35410i | 0.129099 | − | 0.0745356i | ||||
\(46\) | −0.651449 | − | 1.12834i | −0.0141619 | − | 0.0245292i | ||||
\(47\) | 29.4117 | + | 16.9809i | 0.625781 | + | 0.361295i | 0.779116 | − | 0.626879i | \(-0.215668\pi\) |
−0.153335 | + | 0.988174i | \(0.549001\pi\) | |||||||
\(48\) | 6.92820i | 0.144338i | ||||||||
\(49\) | 3.06832 | − | 48.9038i | 0.0626188 | − | 0.998038i | ||||
\(50\) | 7.07107 | 0.141421 | ||||||||
\(51\) | 8.71093 | − | 15.0878i | 0.170803 | − | 0.295839i | ||||
\(52\) | −9.36632 | + | 5.40765i | −0.180122 | + | 0.103993i | ||||
\(53\) | 52.0396 | + | 90.1353i | 0.981880 | + | 1.70067i | 0.655055 | + | 0.755582i | \(0.272646\pi\) |
0.326825 | + | 0.945085i | \(0.394021\pi\) | |||||||
\(54\) | −6.36396 | − | 3.67423i | −0.117851 | − | 0.0680414i | ||||
\(55\) | 4.11174i | 0.0747590i | ||||||||
\(56\) | −14.4317 | + | 13.5546i | −0.257709 | + | 0.242046i | ||||
\(57\) | −15.9217 | −0.279328 | ||||||||
\(58\) | 8.87938 | − | 15.3795i | 0.153093 | − | 0.265164i | ||||
\(59\) | 12.5918 | − | 7.26989i | 0.213421 | − | 0.123218i | −0.389479 | − | 0.921035i | \(-0.627345\pi\) |
0.602900 | + | 0.797817i | \(0.294012\pi\) | |||||||
\(60\) | −3.87298 | − | 6.70820i | −0.0645497 | − | 0.111803i | ||||
\(61\) | 20.5913 | + | 11.8884i | 0.337562 | + | 0.194892i | 0.659194 | − | 0.751973i | \(-0.270898\pi\) |
−0.321631 | + | 0.946865i | \(0.604231\pi\) | |||||||
\(62\) | 59.0937i | 0.953125i | ||||||||
\(63\) | −4.79713 | − | 20.4447i | −0.0761449 | − | 0.324520i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 6.04593 | − | 10.4719i | 0.0930144 | − | 0.161106i | ||||
\(66\) | 3.90074 | − | 2.25209i | 0.0591021 | − | 0.0341226i | ||||
\(67\) | 7.46339 | + | 12.9270i | 0.111394 | + | 0.192940i | 0.916332 | − | 0.400418i | \(-0.131135\pi\) |
−0.804939 | + | 0.593358i | \(0.797802\pi\) | |||||||
\(68\) | −17.4219 | − | 10.0585i | −0.256204 | − | 0.147919i | ||||
\(69\) | − | 1.59572i | − | 0.0231263i | ||||||
\(70\) | 6.39617 | − | 21.1917i | 0.0913738 | − | 0.302739i | ||||
\(71\) | −17.9620 | −0.252987 | −0.126493 | − | 0.991967i | \(-0.540372\pi\) | ||||
−0.126493 | + | 0.991967i | \(0.540372\pi\) | |||||||
\(72\) | −4.24264 | + | 7.34847i | −0.0589256 | + | 0.102062i | ||||
\(73\) | −107.705 | + | 62.1833i | −1.47541 | + | 0.851826i | −0.999615 | − | 0.0277318i | \(-0.991172\pi\) |
−0.475791 | + | 0.879558i | \(0.657838\pi\) | |||||||
\(74\) | 5.15048 | + | 8.92090i | 0.0696011 | + | 0.120553i | ||||
\(75\) | 7.50000 | + | 4.33013i | 0.100000 | + | 0.0577350i | ||||
\(76\) | 18.3848i | 0.241905i | ||||||||
\(77\) | 12.3227 | + | 3.71930i | 0.160036 | + | 0.0483026i | ||||
\(78\) | −13.2460 | −0.169820 | ||||||||
\(79\) | 40.4683 | − | 70.0931i | 0.512257 | − | 0.887254i | −0.487642 | − | 0.873043i | \(-0.662143\pi\) |
0.999899 | − | 0.0142110i | \(-0.00452366\pi\) | |||||||
\(80\) | −7.74597 | + | 4.47214i | −0.0968246 | + | 0.0559017i | ||||
\(81\) | −4.50000 | − | 7.79423i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 64.1616 | + | 37.0437i | 0.782459 | + | 0.451753i | ||||
\(83\) | 154.716i | 1.86405i | 0.362395 | + | 0.932025i | \(0.381959\pi\) | ||||
−0.362395 | + | 0.932025i | \(0.618041\pi\) | |||||||
\(84\) | −23.6076 | + | 5.53924i | −0.281042 | + | 0.0659434i | ||||
\(85\) | 22.4915 | 0.264606 | ||||||||
\(86\) | −5.74391 | + | 9.94875i | −0.0667897 | + | 0.115683i | ||||
\(87\) | 18.8360 | − | 10.8750i | 0.216506 | − | 0.125000i | ||||
\(88\) | −2.60049 | − | 4.50419i | −0.0295511 | − | 0.0511840i | ||||
\(89\) | 58.9956 | + | 34.0611i | 0.662872 | + | 0.382709i | 0.793371 | − | 0.608739i | \(-0.208324\pi\) |
−0.130498 | + | 0.991449i | \(0.541658\pi\) | |||||||
\(90\) | − | 9.48683i | − | 0.105409i | ||||||
\(91\) | −25.9149 | − | 27.5918i | −0.284779 | − | 0.303207i | ||||
\(92\) | −1.84258 | −0.0200280 | ||||||||
\(93\) | −36.1874 | + | 62.6784i | −0.389111 | + | 0.673961i | ||||
\(94\) | 41.5944 | − | 24.0146i | 0.442494 | − | 0.255474i | ||||
\(95\) | −10.2774 | − | 17.8010i | −0.108183 | − | 0.187379i | ||||
\(96\) | 8.48528 | + | 4.89898i | 0.0883883 | + | 0.0510310i | ||||
\(97\) | 88.1736i | 0.909006i | 0.890745 | + | 0.454503i | \(0.150183\pi\) | ||||
−0.890745 | + | 0.454503i | \(0.849817\pi\) | |||||||
\(98\) | −57.7251 | − | 38.3381i | −0.589032 | − | 0.391206i | ||||
\(99\) | 5.51648 | 0.0557220 | ||||||||
\(100\) | 5.00000 | − | 8.66025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | −96.4537 | + | 55.6876i | −0.954987 | + | 0.551362i | −0.894627 | − | 0.446814i | \(-0.852558\pi\) |
−0.0603607 | + | 0.998177i | \(0.519225\pi\) | |||||||
\(102\) | −12.3191 | − | 21.3373i | −0.120776 | − | 0.209190i | ||||
\(103\) | −40.6847 | − | 23.4893i | −0.394997 | − | 0.228051i | 0.289326 | − | 0.957231i | \(-0.406569\pi\) |
−0.684323 | + | 0.729179i | \(0.739902\pi\) | |||||||
\(104\) | 15.2951i | 0.147069i | ||||||||
\(105\) | 19.7614 | − | 18.5604i | 0.188204 | − | 0.176765i | ||||
\(106\) | 147.190 | 1.38859 | ||||||||
\(107\) | 92.8409 | − | 160.805i | 0.867672 | − | 1.50285i | 0.00330196 | − | 0.999995i | \(-0.498949\pi\) |
0.864370 | − | 0.502857i | \(-0.167718\pi\) | |||||||
\(108\) | −9.00000 | + | 5.19615i | −0.0833333 | + | 0.0481125i | ||||
\(109\) | −43.1448 | − | 74.7290i | −0.395824 | − | 0.685587i | 0.597382 | − | 0.801957i | \(-0.296208\pi\) |
−0.993206 | + | 0.116369i | \(0.962874\pi\) | |||||||
\(110\) | 5.03584 | + | 2.90744i | 0.0457803 | + | 0.0264313i | ||||
\(111\) | 12.6161i | 0.113658i | ||||||||
\(112\) | 6.39617 | + | 27.2597i | 0.0571087 | + | 0.243390i | ||||
\(113\) | −85.8206 | −0.759474 | −0.379737 | − | 0.925094i | \(-0.623986\pi\) | ||||
−0.379737 | + | 0.925094i | \(0.623986\pi\) | |||||||
\(114\) | −11.2583 | + | 19.5000i | −0.0987572 | + | 0.171053i | ||||
\(115\) | 1.78407 | − | 1.03003i | 0.0155136 | − | 0.00895679i | ||||
\(116\) | −12.5573 | − | 21.7500i | −0.108253 | − | 0.187500i | ||||
\(117\) | −14.0495 | − | 8.11147i | −0.120081 | − | 0.0693288i | ||||
\(118\) | − | 20.5624i | − | 0.174257i | ||||||
\(119\) | 20.3448 | − | 67.4062i | 0.170965 | − | 0.566439i | ||||
\(120\) | −10.9545 | −0.0912871 | ||||||||
\(121\) | 58.8094 | − | 101.861i | 0.486028 | − | 0.841825i | ||||
\(122\) | 29.1205 | − | 16.8127i | 0.238693 | − | 0.137809i | ||||
\(123\) | 45.3691 | + | 78.5816i | 0.368855 | + | 0.638875i | ||||
\(124\) | 72.3747 | + | 41.7856i | 0.583667 | + | 0.336980i | ||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | −28.4317 | − | 8.58136i | −0.225648 | − | 0.0681060i | ||||
\(127\) | −131.740 | −1.03733 | −0.518663 | − | 0.854979i | \(-0.673570\pi\) | ||||
−0.518663 | + | 0.854979i | \(0.673570\pi\) | |||||||
\(128\) | 5.65685 | − | 9.79796i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −12.1847 | + | 7.03483i | −0.0944549 | + | 0.0545336i | ||||
\(130\) | −8.55024 | − | 14.8095i | −0.0657711 | − | 0.113919i | ||||
\(131\) | −102.856 | − | 59.3839i | −0.785160 | − | 0.453312i | 0.0530960 | − | 0.998589i | \(-0.483091\pi\) |
−0.838256 | + | 0.545277i | \(0.816424\pi\) | |||||||
\(132\) | − | 6.36988i | − | 0.0482567i | ||||||
\(133\) | −62.6453 | + | 14.6990i | −0.471017 | + | 0.110519i | ||||
\(134\) | 21.1096 | 0.157535 | ||||||||
\(135\) | 5.80948 | − | 10.0623i | 0.0430331 | − | 0.0745356i | ||||
\(136\) | −24.6382 | + | 14.2249i | −0.181163 | + | 0.104595i | ||||
\(137\) | −40.5765 | − | 70.2805i | −0.296179 | − | 0.512997i | 0.679080 | − | 0.734065i | \(-0.262379\pi\) |
−0.975258 | + | 0.221068i | \(0.929046\pi\) | |||||||
\(138\) | −1.95435 | − | 1.12834i | −0.0141619 | − | 0.00817639i | ||||
\(139\) | − | 248.311i | − | 1.78641i | −0.449646 | − | 0.893207i | \(-0.648450\pi\) | ||
0.449646 | − | 0.893207i | \(-0.351550\pi\) | |||||||
\(140\) | −21.4317 | − | 22.8185i | −0.153083 | − | 0.162989i | ||||
\(141\) | 58.8234 | 0.417187 | ||||||||
\(142\) | −12.7011 | + | 21.9989i | −0.0894442 | + | 0.154922i | ||||
\(143\) | 8.61152 | − | 4.97186i | 0.0602204 | − | 0.0347683i | ||||
\(144\) | 6.00000 | + | 10.3923i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | 24.3172 | + | 14.0395i | 0.167705 | + | 0.0968244i | ||||
\(146\) | 175.881i | 1.20466i | ||||||||
\(147\) | −37.7495 | − | 76.0130i | −0.256799 | − | 0.517095i | ||||
\(148\) | 14.5678 | 0.0984308 | ||||||||
\(149\) | 75.0048 | − | 129.912i | 0.503388 | − | 0.871894i | −0.496604 | − | 0.867977i | \(-0.665420\pi\) |
0.999992 | − | 0.00391672i | \(-0.00124673\pi\) | |||||||
\(150\) | 10.6066 | − | 6.12372i | 0.0707107 | − | 0.0408248i | ||||
\(151\) | −91.5149 | − | 158.509i | −0.606059 | − | 1.04973i | −0.991883 | − | 0.127153i | \(-0.959416\pi\) |
0.385824 | − | 0.922572i | \(-0.373917\pi\) | |||||||
\(152\) | 22.5167 | + | 13.0000i | 0.148136 | + | 0.0855263i | ||||
\(153\) | − | 30.1755i | − | 0.197226i | ||||||
\(154\) | 13.2687 | − | 12.4623i | 0.0861603 | − | 0.0809238i | ||||
\(155\) | −93.4354 | −0.602809 | ||||||||
\(156\) | −9.36632 | + | 16.2229i | −0.0600405 | + | 0.103993i | ||||
\(157\) | −255.724 | + | 147.643i | −1.62882 | + | 0.940398i | −0.644371 | + | 0.764713i | \(0.722881\pi\) |
−0.984446 | + | 0.175685i | \(0.943786\pi\) | |||||||
\(158\) | −57.2308 | − | 99.1266i | −0.362220 | − | 0.627384i | ||||
\(159\) | 156.119 | + | 90.1353i | 0.981880 | + | 0.566889i | ||||
\(160\) | 12.6491i | 0.0790569i | ||||||||
\(161\) | −1.47318 | − | 6.27850i | −0.00915017 | − | 0.0389969i | ||||
\(162\) | −12.7279 | −0.0785674 | ||||||||
\(163\) | 59.1631 | − | 102.473i | 0.362964 | − | 0.628671i | −0.625484 | − | 0.780237i | \(-0.715098\pi\) |
0.988447 | + | 0.151566i | \(0.0484316\pi\) | |||||||
\(164\) | 90.7382 | − | 52.3877i | 0.553282 | − | 0.319437i | ||||
\(165\) | 3.56087 | + | 6.16761i | 0.0215811 | + | 0.0373795i | ||||
\(166\) | 189.488 | + | 109.401i | 1.14149 | + | 0.659041i | ||||
\(167\) | − | 205.186i | − | 1.22866i | −0.789050 | − | 0.614329i | \(-0.789427\pi\) | ||
0.789050 | − | 0.614329i | \(-0.210573\pi\) | |||||||
\(168\) | −9.90890 | + | 32.8301i | −0.0589816 | + | 0.195417i | ||||
\(169\) | 139.757 | 0.826967 | ||||||||
\(170\) | 15.9039 | − | 27.5464i | 0.0935524 | − | 0.162038i | ||||
\(171\) | −23.8825 | + | 13.7886i | −0.139664 | + | 0.0806350i | ||||
\(172\) | 8.12312 | + | 14.0697i | 0.0472274 | + | 0.0818003i | ||||
\(173\) | 97.4572 | + | 56.2670i | 0.563337 | + | 0.325242i | 0.754484 | − | 0.656319i | \(-0.227887\pi\) |
−0.191147 | + | 0.981561i | \(0.561221\pi\) | |||||||
\(174\) | − | 30.7591i | − | 0.176776i | ||||||
\(175\) | 33.5071 | + | 10.1132i | 0.191469 | + | 0.0577899i | ||||
\(176\) | −7.35531 | −0.0417915 | ||||||||
\(177\) | 12.5918 | − | 21.8097i | 0.0711402 | − | 0.123218i | ||||
\(178\) | 83.4324 | − | 48.1697i | 0.468721 | − | 0.270616i | ||||
\(179\) | 22.2349 | + | 38.5120i | 0.124217 | + | 0.215151i | 0.921427 | − | 0.388552i | \(-0.127025\pi\) |
−0.797209 | + | 0.603703i | \(0.793691\pi\) | |||||||
\(180\) | −11.6190 | − | 6.70820i | −0.0645497 | − | 0.0372678i | ||||
\(181\) | 9.24555i | 0.0510804i | 0.999674 | + | 0.0255402i | \(0.00813058\pi\) | ||||
−0.999674 | + | 0.0255402i | \(0.991869\pi\) | |||||||
\(182\) | −52.1175 | + | 12.2288i | −0.286360 | + | 0.0671911i | ||||
\(183\) | 41.1826 | 0.225041 | ||||||||
\(184\) | −1.30290 | + | 2.25668i | −0.00708096 | + | 0.0122646i | ||||
\(185\) | −14.1052 | + | 8.14363i | −0.0762442 | + | 0.0440196i | ||||
\(186\) | 51.1767 | + | 88.6406i | 0.275143 | + | 0.476562i | ||||
\(187\) | 16.0179 | + | 9.24793i | 0.0856572 | + | 0.0494542i | ||||
\(188\) | − | 67.9234i | − | 0.361295i | ||||||
\(189\) | −24.9014 | − | 26.5127i | −0.131753 | − | 0.140279i | ||||
\(190\) | −29.0689 | −0.152994 | ||||||||
\(191\) | 68.4044 | − | 118.480i | 0.358138 | − | 0.620314i | −0.629511 | − | 0.776991i | \(-0.716745\pi\) |
0.987650 | + | 0.156677i | \(0.0500783\pi\) | |||||||
\(192\) | 12.0000 | − | 6.92820i | 0.0625000 | − | 0.0360844i | ||||
\(193\) | 182.937 | + | 316.856i | 0.947860 | + | 1.64174i | 0.749921 | + | 0.661527i | \(0.230091\pi\) |
0.197939 | + | 0.980214i | \(0.436575\pi\) | |||||||
\(194\) | 107.990 | + | 62.3481i | 0.556650 | + | 0.321382i | ||||
\(195\) | − | 20.9437i | − | 0.107404i | ||||||
\(196\) | −87.7723 | + | 43.5893i | −0.447818 | + | 0.222395i | ||||
\(197\) | −194.925 | −0.989468 | −0.494734 | − | 0.869045i | \(-0.664734\pi\) | ||||
−0.494734 | + | 0.869045i | \(0.664734\pi\) | |||||||
\(198\) | 3.90074 | − | 6.75628i | 0.0197007 | − | 0.0341226i | ||||
\(199\) | −210.301 | + | 121.418i | −1.05679 | + | 0.610138i | −0.924543 | − | 0.381078i | \(-0.875553\pi\) |
−0.132248 | + | 0.991217i | \(0.542219\pi\) | |||||||
\(200\) | −7.07107 | − | 12.2474i | −0.0353553 | − | 0.0612372i | ||||
\(201\) | 22.3902 | + | 12.9270i | 0.111394 | + | 0.0643133i | ||||
\(202\) | 157.508i | 0.779744i | ||||||||
\(203\) | 64.0722 | − | 60.1782i | 0.315627 | − | 0.296444i | ||||
\(204\) | −34.8437 | −0.170803 | ||||||||
\(205\) | −58.5713 | + | 101.448i | −0.285714 | + | 0.494870i | ||||
\(206\) | −57.5368 | + | 33.2189i | −0.279305 | + | 0.161257i | ||||
\(207\) | −1.38193 | − | 2.39358i | −0.00667600 | − | 0.0115632i | ||||
\(208\) | 18.7326 | + | 10.8153i | 0.0900608 | + | 0.0519966i | ||||
\(209\) | − | 16.9032i | − | 0.0808766i | ||||||
\(210\) | −8.75832 | − | 37.3268i | −0.0417063 | − | 0.177747i | ||||
\(211\) | 185.930 | 0.881184 | 0.440592 | − | 0.897707i | \(-0.354769\pi\) | ||||
0.440592 | + | 0.897707i | \(0.354769\pi\) | |||||||
\(212\) | 104.079 | − | 180.271i | 0.490940 | − | 0.850333i | ||||
\(213\) | −26.9431 | + | 15.5556i | −0.126493 | + | 0.0730309i | ||||
\(214\) | −131.297 | − | 227.413i | −0.613537 | − | 1.06268i | ||||
\(215\) | −15.7304 | − | 9.08192i | −0.0731644 | − | 0.0422415i | ||||
\(216\) | 14.6969i | 0.0680414i | ||||||||
\(217\) | −84.5174 | + | 280.022i | −0.389481 | + | 1.29043i | ||||
\(218\) | −122.032 | −0.559780 | ||||||||
\(219\) | −107.705 | + | 186.550i | −0.491802 | + | 0.851826i | ||||
\(220\) | 7.12175 | − | 4.11174i | 0.0323716 | − | 0.0186897i | ||||
\(221\) | −27.1965 | − | 47.1056i | −0.123061 | − | 0.213148i | ||||
\(222\) | 15.4514 | + | 8.92090i | 0.0696011 | + | 0.0401842i | ||||
\(223\) | − | 53.6348i | − | 0.240515i | −0.992743 | − | 0.120257i | \(-0.961628\pi\) | ||
0.992743 | − | 0.120257i | \(-0.0383720\pi\) | |||||||
\(224\) | 37.9089 | + | 11.4418i | 0.169236 | + | 0.0510795i | ||||
\(225\) | 15.0000 | 0.0666667 | ||||||||
\(226\) | −60.6843 | + | 105.108i | −0.268515 | + | 0.465081i | ||||
\(227\) | 146.392 | − | 84.5195i | 0.644899 | − | 0.372333i | −0.141600 | − | 0.989924i | \(-0.545225\pi\) |
0.786499 | + | 0.617591i | \(0.211891\pi\) | |||||||
\(228\) | 15.9217 | + | 27.5772i | 0.0698319 | + | 0.120952i | ||||
\(229\) | 247.698 | + | 143.009i | 1.08165 | + | 0.624492i | 0.931342 | − | 0.364147i | \(-0.118639\pi\) |
0.150310 | + | 0.988639i | \(0.451973\pi\) | |||||||
\(230\) | − | 2.91337i | − | 0.0126668i | ||||||
\(231\) | 21.7051 | − | 5.09286i | 0.0939615 | − | 0.0220470i | ||||
\(232\) | −35.5175 | −0.153093 | ||||||||
\(233\) | 90.9194 | − | 157.477i | 0.390212 | − | 0.675867i | −0.602265 | − | 0.798296i | \(-0.705735\pi\) |
0.992477 | + | 0.122429i | \(0.0390684\pi\) | |||||||
\(234\) | −19.8690 | + | 11.4714i | −0.0849101 | + | 0.0490229i | ||||
\(235\) | 37.9703 | + | 65.7666i | 0.161576 | + | 0.279858i | ||||
\(236\) | −25.1836 | − | 14.5398i | −0.106710 | − | 0.0616092i | ||||
\(237\) | − | 140.186i | − | 0.591503i | ||||||
\(238\) | −68.1695 | − | 72.5806i | −0.286426 | − | 0.304961i | ||||
\(239\) | −382.489 | −1.60037 | −0.800185 | − | 0.599753i | \(-0.795266\pi\) | ||||
−0.800185 | + | 0.599753i | \(0.795266\pi\) | |||||||
\(240\) | −7.74597 | + | 13.4164i | −0.0322749 | + | 0.0559017i | ||||
\(241\) | −180.324 | + | 104.110i | −0.748230 | + | 0.431991i | −0.825054 | − | 0.565054i | \(-0.808855\pi\) |
0.0768238 | + | 0.997045i | \(0.475522\pi\) | |||||||
\(242\) | −83.1690 | − | 144.053i | −0.343674 | − | 0.595260i | ||||
\(243\) | −13.5000 | − | 7.79423i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | − | 47.5536i | − | 0.194892i | ||||||
\(245\) | 60.6179 | − | 91.2714i | 0.247420 | − | 0.372536i | ||||
\(246\) | 128.323 | 0.521639 | ||||||||
\(247\) | −24.8546 | + | 43.0494i | −0.100626 | + | 0.174289i | ||||
\(248\) | 102.353 | − | 59.0937i | 0.412715 | − | 0.238281i | ||||
\(249\) | 133.988 | + | 232.074i | 0.538105 | + | 0.932025i | ||||
\(250\) | 13.6931 | + | 7.90569i | 0.0547723 | + | 0.0316228i | ||||
\(251\) | − | 43.4959i | − | 0.173291i | −0.996239 | − | 0.0866453i | \(-0.972385\pi\) | ||
0.996239 | − | 0.0866453i | \(-0.0276147\pi\) | |||||||
\(252\) | −30.6142 | + | 28.7536i | −0.121485 | + | 0.114102i | ||||
\(253\) | 1.69409 | 0.00669600 | ||||||||
\(254\) | −93.1545 | + | 161.348i | −0.366750 | + | 0.635229i | ||||
\(255\) | 33.7373 | − | 19.4782i | 0.132303 | − | 0.0763852i | ||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 3.68915 | + | 2.12993i | 0.0143547 | + | 0.00828766i | 0.507160 | − | 0.861852i | \(-0.330695\pi\) |
−0.492806 | + | 0.870139i | \(0.664029\pi\) | |||||||
\(258\) | 19.8975i | 0.0771221i | ||||||||
\(259\) | 11.6472 | + | 49.6390i | 0.0449700 | + | 0.191656i | ||||
\(260\) | −24.1837 | −0.0930144 | ||||||||
\(261\) | 18.8360 | − | 32.6249i | 0.0721686 | − | 0.125000i | ||||
\(262\) | −145.460 | + | 83.9815i | −0.555192 | + | 0.320540i | ||||
\(263\) | 209.187 | + | 362.323i | 0.795388 | + | 1.37765i | 0.922592 | + | 0.385776i | \(0.126066\pi\) |
−0.127204 | + | 0.991877i | \(0.540600\pi\) | |||||||
\(264\) | −7.80148 | − | 4.50419i | −0.0295511 | − | 0.0170613i | ||||
\(265\) | 232.728i | 0.878220i | ||||||||
\(266\) | −26.2944 | + | 87.1183i | −0.0988511 | + | 0.327512i | ||||
\(267\) | 117.991 | 0.441915 | ||||||||
\(268\) | 14.9268 | − | 25.8539i | 0.0556969 | − | 0.0964699i | ||||
\(269\) | −319.086 | + | 184.224i | −1.18619 | + | 0.684848i | −0.957439 | − | 0.288636i | \(-0.906798\pi\) |
−0.228753 | + | 0.973484i | \(0.573465\pi\) | |||||||
\(270\) | −8.21584 | − | 14.2302i | −0.0304290 | − | 0.0527046i | ||||
\(271\) | −191.411 | − | 110.511i | −0.706312 | − | 0.407790i | 0.103382 | − | 0.994642i | \(-0.467034\pi\) |
−0.809694 | + | 0.586852i | \(0.800367\pi\) | |||||||
\(272\) | 40.2341i | 0.147919i | ||||||||
\(273\) | −62.7676 | − | 18.9448i | −0.229918 | − | 0.0693947i | ||||
\(274\) | −114.768 | −0.418860 | ||||||||
\(275\) | −4.59707 | + | 7.96235i | −0.0167166 | + | 0.0289540i | ||||
\(276\) | −2.76386 | + | 1.59572i | −0.0100140 | + | 0.00578158i | ||||
\(277\) | 198.427 | + | 343.686i | 0.716343 | + | 1.24074i | 0.962439 | + | 0.271497i | \(0.0875187\pi\) |
−0.246096 | + | 0.969245i | \(0.579148\pi\) | |||||||
\(278\) | −304.118 | − | 175.583i | −1.09395 | − | 0.631593i | ||||
\(279\) | 125.357i | 0.449307i | ||||||||
\(280\) | −43.1013 | + | 10.1132i | −0.153933 | + | 0.0361187i | ||||
\(281\) | −114.244 | −0.406562 | −0.203281 | − | 0.979120i | \(-0.565161\pi\) | ||||
−0.203281 | + | 0.979120i | \(0.565161\pi\) | |||||||
\(282\) | 41.5944 | − | 72.0437i | 0.147498 | − | 0.255474i | ||||
\(283\) | 391.819 | − | 226.217i | 1.38452 | − | 0.799353i | 0.391829 | − | 0.920038i | \(-0.371843\pi\) |
0.992691 | + | 0.120685i | \(0.0385092\pi\) | |||||||
\(284\) | 17.9620 | + | 31.1112i | 0.0632466 | + | 0.109546i | ||||
\(285\) | −30.8322 | − | 17.8010i | −0.108183 | − | 0.0624596i | ||||
\(286\) | − | 14.0626i | − | 0.0491698i | ||||||
\(287\) | 251.056 | + | 267.302i | 0.874760 | + | 0.931364i | ||||
\(288\) | 16.9706 | 0.0589256 | ||||||||
\(289\) | −93.9131 | + | 162.662i | −0.324959 | + | 0.562845i | ||||
\(290\) | 34.3897 | − | 19.8549i | 0.118585 | − | 0.0684652i | ||||
\(291\) | 76.3606 | + | 132.260i | 0.262407 | + | 0.454503i | ||||
\(292\) | 215.409 | + | 124.367i | 0.737703 | + | 0.425913i | ||||
\(293\) | 119.134i | 0.406600i | 0.979116 | + | 0.203300i | \(0.0651667\pi\) | ||||
−0.979116 | + | 0.203300i | \(0.934833\pi\) | |||||||
\(294\) | −119.789 | − | 7.51583i | −0.407447 | − | 0.0255640i | ||||
\(295\) | 32.5119 | 0.110210 | ||||||||
\(296\) | 10.3010 | − | 17.8418i | 0.0348006 | − | 0.0602763i | ||||
\(297\) | 8.27472 | − | 4.77741i | 0.0278610 | − | 0.0160856i | ||||
\(298\) | −106.073 | − | 183.724i | −0.355949 | − | 0.616522i | ||||
\(299\) | −4.31454 | − | 2.49100i | −0.0144299 | − | 0.00833110i | ||||
\(300\) | − | 17.3205i | − | 0.0577350i | ||||||
\(301\) | −41.4471 | + | 38.9282i | −0.137698 | + | 0.129329i | ||||
\(302\) | −258.843 | −0.857097 | ||||||||
\(303\) | −96.4537 | + | 167.063i | −0.318329 | + | 0.551362i | ||||
\(304\) | 31.8434 | − | 18.3848i | 0.104748 | − | 0.0604762i | ||||
\(305\) | 26.5833 | + | 46.0435i | 0.0871582 | + | 0.150962i | ||||
\(306\) | −36.9573 | − | 21.3373i | −0.120776 | − | 0.0697298i | ||||
\(307\) | − | 272.643i | − | 0.888087i | −0.896005 | − | 0.444043i | \(-0.853544\pi\) | ||
0.896005 | − | 0.444043i | \(-0.146456\pi\) | |||||||
\(308\) | −5.88072 | − | 25.0629i | −0.0190933 | − | 0.0813731i | ||||
\(309\) | −81.3693 | −0.263331 | ||||||||
\(310\) | −66.0688 | + | 114.435i | −0.213125 | + | 0.369144i | ||||
\(311\) | 65.4476 | − | 37.7862i | 0.210443 | − | 0.121499i | −0.391074 | − | 0.920359i | \(-0.627897\pi\) |
0.601517 | + | 0.798860i | \(0.294563\pi\) | |||||||
\(312\) | 13.2460 | + | 22.9427i | 0.0424551 | + | 0.0735343i | ||||
\(313\) | −55.1057 | − | 31.8153i | −0.176057 | − | 0.101646i | 0.409382 | − | 0.912363i | \(-0.365744\pi\) |
−0.585439 | + | 0.810717i | \(0.699078\pi\) | |||||||
\(314\) | 417.596i | 1.32992i | ||||||||
\(315\) | 13.5683 | − | 44.9544i | 0.0430740 | − | 0.142712i | ||||
\(316\) | −161.873 | −0.512257 | ||||||||
\(317\) | −7.72605 | + | 13.3819i | −0.0243724 | + | 0.0422142i | −0.877954 | − | 0.478744i | \(-0.841092\pi\) |
0.853582 | + | 0.520959i | \(0.174425\pi\) | |||||||
\(318\) | 220.786 | − | 127.471i | 0.694294 | − | 0.400851i | ||||
\(319\) | 11.5454 | + | 19.9972i | 0.0361924 | + | 0.0626872i | ||||
\(320\) | 15.4919 | + | 8.94427i | 0.0484123 | + | 0.0279508i | ||||
\(321\) | − | 321.610i | − | 1.00190i | ||||||
\(322\) | −8.73125 | − | 2.63530i | −0.0271157 | − | 0.00818416i | ||||
\(323\) | −92.4617 | −0.286259 | ||||||||
\(324\) | −9.00000 | + | 15.5885i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | 23.4158 | − | 13.5191i | 0.0720486 | − | 0.0415973i | ||||
\(326\) | −83.6692 | − | 144.919i | −0.256654 | − | 0.444538i | ||||
\(327\) | −129.434 | − | 74.7290i | −0.395824 | − | 0.228529i | ||||
\(328\) | − | 148.175i | − | 0.451753i | ||||||
\(329\) | 231.446 | − | 54.3062i | 0.703484 | − | 0.165064i | ||||
\(330\) | 10.0717 | 0.0305202 | ||||||||
\(331\) | 186.540 | − | 323.096i | 0.563564 | − | 0.976121i | −0.433618 | − | 0.901097i | \(-0.642763\pi\) |
0.997182 | − | 0.0750241i | \(-0.0239034\pi\) | |||||||
\(332\) | 267.976 | − | 154.716i | 0.807157 | − | 0.466012i | ||||
\(333\) | 10.9258 | + | 18.9241i | 0.0328103 | + | 0.0568291i | ||||
\(334\) | −251.301 | − | 145.088i | −0.752397 | − | 0.434397i | ||||
\(335\) | 33.3773i | 0.0996337i | ||||||||
\(336\) | 33.2018 | + | 35.3502i | 0.0988149 | + | 0.105209i | ||||
\(337\) | 642.919 | 1.90777 | 0.953885 | − | 0.300171i | \(-0.0970437\pi\) | ||||
0.953885 | + | 0.300171i | \(0.0970437\pi\) | |||||||
\(338\) | 98.8234 | − | 171.167i | 0.292377 | − | 0.506412i | ||||
\(339\) | −128.731 | + | 74.3228i | −0.379737 | + | 0.219241i | ||||
\(340\) | −22.4915 | − | 38.9565i | −0.0661515 | − | 0.114578i | ||||
\(341\) | −66.5423 | − | 38.4182i | −0.195139 | − | 0.112663i | ||||
\(342\) | 39.0000i | 0.114035i | ||||||||
\(343\) | −218.705 | − | 264.230i | −0.637623 | − | 0.770349i | ||||
\(344\) | 22.9757 | 0.0667897 | ||||||||
\(345\) | 1.78407 | − | 3.09009i | 0.00517120 | − | 0.00895679i | ||||
\(346\) | 137.825 | − | 79.5735i | 0.398339 | − | 0.229981i | ||||
\(347\) | −72.0043 | − | 124.715i | −0.207505 | − | 0.359409i | 0.743423 | − | 0.668822i | \(-0.233201\pi\) |
−0.950928 | + | 0.309412i | \(0.899868\pi\) | |||||||
\(348\) | −37.6720 | − | 21.7500i | −0.108253 | − | 0.0624999i | ||||
\(349\) | − | 566.507i | − | 1.62323i | −0.584194 | − | 0.811614i | \(-0.698589\pi\) | ||
0.584194 | − | 0.811614i | \(-0.301411\pi\) | |||||||
\(350\) | 36.0792 | − | 33.8865i | 0.103083 | − | 0.0968184i | ||||
\(351\) | −28.0990 | −0.0800540 | ||||||||
\(352\) | −5.20099 | + | 9.00838i | −0.0147755 | + | 0.0255920i | ||||
\(353\) | 441.814 | − | 255.082i | 1.25160 | − | 0.722611i | 0.280172 | − | 0.959950i | \(-0.409609\pi\) |
0.971427 | + | 0.237339i | \(0.0762753\pi\) | |||||||
\(354\) | −17.8075 | − | 30.8435i | −0.0503037 | − | 0.0871286i | ||||
\(355\) | −34.7833 | − | 20.0822i | −0.0979813 | − | 0.0565695i | ||||
\(356\) | − | 136.245i | − | 0.382709i | ||||||
\(357\) | −27.8583 | − | 118.728i | −0.0780344 | − | 0.332573i | ||||
\(358\) | 62.8898 | 0.175670 | ||||||||
\(359\) | −333.931 | + | 578.386i | −0.930171 | + | 1.61110i | −0.147145 | + | 0.989115i | \(0.547008\pi\) |
−0.783026 | + | 0.621989i | \(0.786325\pi\) | |||||||
\(360\) | −16.4317 | + | 9.48683i | −0.0456435 | + | 0.0263523i | ||||
\(361\) | −138.250 | − | 239.456i | −0.382964 | − | 0.663313i | ||||
\(362\) | 11.3234 | + | 6.53759i | 0.0312802 | + | 0.0180596i | ||||
\(363\) | − | 203.722i | − | 0.561217i | ||||||
\(364\) | −21.8755 | + | 72.4777i | −0.0600976 | + | 0.199115i | ||||
\(365\) | −278.092 | −0.761897 | ||||||||
\(366\) | 29.1205 | − | 50.4382i | 0.0795642 | − | 0.137809i | ||||
\(367\) | −30.2216 | + | 17.4485i | −0.0823478 | + | 0.0475435i | −0.540608 | − | 0.841274i | \(-0.681806\pi\) |
0.458261 | + | 0.888818i | \(0.348473\pi\) | |||||||
\(368\) | 1.84258 | + | 3.19143i | 0.00500700 | + | 0.00867237i | ||||
\(369\) | 136.107 | + | 78.5816i | 0.368855 | + | 0.212958i | ||||
\(370\) | 23.0337i | 0.0622531i | ||||||||
\(371\) | 697.478 | + | 210.516i | 1.87999 | + | 0.567427i | ||||
\(372\) | 144.749 | 0.389111 | ||||||||
\(373\) | 204.012 | − | 353.360i | 0.546950 | − | 0.947345i | −0.451532 | − | 0.892255i | \(-0.649122\pi\) |
0.998481 | − | 0.0550895i | \(-0.0175444\pi\) | |||||||
\(374\) | 22.6527 | − | 13.0786i | 0.0605688 | − | 0.0349694i | ||||
\(375\) | 9.68246 | + | 16.7705i | 0.0258199 | + | 0.0447214i | ||||
\(376\) | −83.1888 | − | 48.0291i | −0.221247 | − | 0.127737i | ||||
\(377\) | − | 67.9057i | − | 0.180121i | ||||||
\(378\) | −50.0792 | + | 11.7505i | −0.132485 | + | 0.0310860i | ||||
\(379\) | −10.4706 | −0.0276268 | −0.0138134 | − | 0.999905i | \(-0.504397\pi\) | ||||
−0.0138134 | + | 0.999905i | \(0.504397\pi\) | |||||||
\(380\) | −20.5548 | + | 35.6020i | −0.0540916 | + | 0.0936893i | ||||
\(381\) | −197.610 | + | 114.090i | −0.518663 | + | 0.299450i | ||||
\(382\) | −96.7385 | − | 167.556i | −0.253242 | − | 0.438628i | ||||
\(383\) | −199.672 | − | 115.281i | −0.521337 | − | 0.300994i | 0.216145 | − | 0.976361i | \(-0.430652\pi\) |
−0.737481 | + | 0.675367i | \(0.763985\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 19.7046 | + | 20.9796i | 0.0511807 | + | 0.0544925i | ||||
\(386\) | 517.424 | 1.34048 | ||||||||
\(387\) | −12.1847 | + | 21.1045i | −0.0314850 | + | 0.0545336i | ||||
\(388\) | 152.721 | − | 88.1736i | 0.393611 | − | 0.227251i | ||||
\(389\) | −338.107 | − | 585.619i | −0.869170 | − | 1.50545i | −0.862846 | − | 0.505466i | \(-0.831321\pi\) |
−0.00632331 | − | 0.999980i | \(-0.502013\pi\) | |||||||
\(390\) | −25.6507 | − | 14.8095i | −0.0657711 | − | 0.0379730i | ||||
\(391\) | − | 9.26678i | − | 0.0237002i | ||||||
\(392\) | −8.67853 | + | 138.321i | −0.0221391 | + | 0.352860i | ||||
\(393\) | −205.712 | −0.523440 | ||||||||
\(394\) | −137.833 | + | 238.734i | −0.349830 | + | 0.605923i | ||||
\(395\) | 156.733 | − | 90.4898i | 0.396792 | − | 0.229088i | ||||
\(396\) | −5.51648 | − | 9.55483i | −0.0139305 | − | 0.0241283i | ||||
\(397\) | −141.641 | − | 81.7764i | −0.356778 | − | 0.205986i | 0.310889 | − | 0.950446i | \(-0.399373\pi\) |
−0.667666 | + | 0.744461i | \(0.732707\pi\) | |||||||
\(398\) | 343.421i | 0.862866i | ||||||||
\(399\) | −81.2383 | + | 76.3010i | −0.203605 | + | 0.191230i | ||||
\(400\) | −20.0000 | −0.0500000 | ||||||||
\(401\) | 149.624 | − | 259.156i | 0.373127 | − | 0.646274i | −0.616918 | − | 0.787027i | \(-0.711619\pi\) |
0.990045 | + | 0.140753i | \(0.0449524\pi\) | |||||||
\(402\) | 31.6645 | − | 18.2815i | 0.0787674 | − | 0.0454764i | ||||
\(403\) | 112.981 | + | 195.689i | 0.280349 | + | 0.485579i | ||||
\(404\) | 192.907 | + | 111.375i | 0.477494 | + | 0.275681i | ||||
\(405\) | − | 20.1246i | − | 0.0496904i | ||||||
\(406\) | −28.3970 | − | 121.024i | −0.0699434 | − | 0.298090i | ||||
\(407\) | −13.3938 | −0.0329086 | ||||||||
\(408\) | −24.6382 | + | 42.6747i | −0.0603878 | + | 0.104595i | ||||
\(409\) | 403.264 | − | 232.825i | 0.985976 | − | 0.569253i | 0.0819067 | − | 0.996640i | \(-0.473899\pi\) |
0.904069 | + | 0.427387i | \(0.140566\pi\) | |||||||
\(410\) | 82.8323 | + | 143.470i | 0.202030 | + | 0.349926i | ||||
\(411\) | −121.729 | − | 70.2805i | −0.296179 | − | 0.170999i | ||||
\(412\) | 93.9572i | 0.228051i | ||||||||
\(413\) | 29.4088 | − | 97.4370i | 0.0712078 | − | 0.235925i | ||||
\(414\) | −3.90869 | −0.00944129 | ||||||||
\(415\) | −172.978 | + | 299.606i | −0.416814 | + | 0.721943i | ||||
\(416\) | 26.4920 | − | 15.2951i | 0.0636826 | − | 0.0367672i | ||||
\(417\) | −215.044 | − | 372.467i | −0.515693 | − | 0.893207i | ||||
\(418\) | −20.7021 | − | 11.9524i | −0.0495266 | − | 0.0285942i | ||||
\(419\) | 575.882i | 1.37442i | 0.726458 | + | 0.687211i | \(0.241165\pi\) | ||||
−0.726458 | + | 0.687211i | \(0.758835\pi\) | |||||||
\(420\) | −51.9089 | − | 15.6674i | −0.123593 | − | 0.0373032i | ||||
\(421\) | 571.149 | 1.35665 | 0.678324 | − | 0.734763i | \(-0.262706\pi\) | ||||
0.678324 | + | 0.734763i | \(0.262706\pi\) | |||||||
\(422\) | 131.472 | − | 227.717i | 0.311546 | − | 0.539613i | ||||
\(423\) | 88.2351 | − | 50.9426i | 0.208594 | − | 0.120432i | ||||
\(424\) | −147.190 | − | 254.941i | −0.347147 | − | 0.601276i | ||||
\(425\) | 43.5546 | + | 25.1463i | 0.102482 | + | 0.0591677i | ||||
\(426\) | 43.9978i | 0.103281i | ||||||||
\(427\) | 162.037 | − | 38.0201i | 0.379477 | − | 0.0890400i | ||||
\(428\) | −371.363 | −0.867672 | ||||||||
\(429\) | 8.61152 | − | 14.9156i | 0.0200735 | − | 0.0347683i | ||||
\(430\) | −22.2461 | + | 12.8438i | −0.0517351 | + | 0.0298693i | ||||
\(431\) | 13.5697 | + | 23.5034i | 0.0314842 | + | 0.0545322i | 0.881338 | − | 0.472486i | \(-0.156643\pi\) |
−0.849854 | + | 0.527018i | \(0.823310\pi\) | |||||||
\(432\) | 18.0000 | + | 10.3923i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | − | 363.408i | − | 0.839279i | −0.907691 | − | 0.419640i | \(-0.862156\pi\) | ||
0.907691 | − | 0.419640i | \(-0.137844\pi\) | |||||||
\(434\) | 283.193 | + | 301.518i | 0.652518 | + | 0.694742i | ||||
\(435\) | 48.6344 | 0.111803 | ||||||||
\(436\) | −86.2897 | + | 149.458i | −0.197912 | + | 0.342794i | ||||
\(437\) | −7.33422 | + | 4.23441i | −0.0167831 | + | 0.00968974i | ||||
\(438\) | 152.317 | + | 263.822i | 0.347757 | + | 0.602332i | ||||
\(439\) | −403.057 | − | 232.705i | −0.918124 | − | 0.530079i | −0.0350882 | − | 0.999384i | \(-0.511171\pi\) |
−0.883036 | + | 0.469305i | \(0.844505\pi\) | |||||||
\(440\) | − | 11.6298i | − | 0.0264313i | ||||||
\(441\) | −122.453 | − | 81.3275i | −0.277672 | − | 0.184416i | ||||
\(442\) | −76.9232 | −0.174034 | ||||||||
\(443\) | −243.968 | + | 422.565i | −0.550718 | + | 0.953871i | 0.447505 | + | 0.894281i | \(0.352313\pi\) |
−0.998223 | + | 0.0595896i | \(0.981021\pi\) | |||||||
\(444\) | 21.8516 | − | 12.6161i | 0.0492154 | − | 0.0284145i | ||||
\(445\) | 76.1630 | + | 131.918i | 0.171153 | + | 0.296445i | ||||
\(446\) | −65.6889 | − | 37.9255i | −0.147285 | − | 0.0850348i | ||||
\(447\) | − | 259.824i | − | 0.581263i | ||||||
\(448\) | 40.8189 | − | 38.3381i | 0.0911137 | − | 0.0855762i | ||||
\(449\) | −285.837 | −0.636609 | −0.318304 | − | 0.947989i | \(-0.603113\pi\) | ||||
−0.318304 | + | 0.947989i | \(0.603113\pi\) | |||||||
\(450\) | 10.6066 | − | 18.3712i | 0.0235702 | − | 0.0408248i | ||||
\(451\) | −83.4260 | + | 48.1660i | −0.184980 | + | 0.106798i | ||||
\(452\) | 85.8206 | + | 148.646i | 0.189869 | + | 0.328862i | ||||
\(453\) | −274.545 | − | 158.509i | −0.606059 | − | 0.349908i | ||||
\(454\) | − | 239.057i | − | 0.526558i | ||||||
\(455\) | −19.3354 | − | 82.4050i | −0.0424954 | − | 0.181110i | ||||
\(456\) | 45.0333 | 0.0987572 | ||||||||
\(457\) | −211.624 | + | 366.543i | −0.463071 | + | 0.802063i | −0.999112 | − | 0.0421292i | \(-0.986586\pi\) |
0.536041 | + | 0.844192i | \(0.319919\pi\) | |||||||
\(458\) | 350.298 | − | 202.245i | 0.764843 | − | 0.441583i | ||||
\(459\) | −26.1328 | − | 45.2633i | −0.0569342 | − | 0.0986129i | ||||
\(460\) | −3.56813 | − | 2.06006i | −0.00775681 | − | 0.00447839i | ||||
\(461\) | 471.748i | 1.02331i | 0.859190 | + | 0.511657i | \(0.170968\pi\) | ||||
−0.859190 | + | 0.511657i | \(0.829032\pi\) | |||||||
\(462\) | 9.11038 | − | 30.1844i | 0.0197194 | − | 0.0653342i | ||||
\(463\) | −194.019 | −0.419046 | −0.209523 | − | 0.977804i | \(-0.567191\pi\) | ||||
−0.209523 | + | 0.977804i | \(0.567191\pi\) | |||||||
\(464\) | −25.1147 | + | 43.4999i | −0.0541265 | + | 0.0937498i | ||||
\(465\) | −140.153 | + | 80.9174i | −0.301404 | + | 0.174016i | ||||
\(466\) | −128.579 | − | 222.706i | −0.275921 | − | 0.477910i | ||||
\(467\) | −9.80955 | − | 5.66354i | −0.0210055 | − | 0.0121275i | 0.489461 | − | 0.872025i | \(-0.337194\pi\) |
−0.510466 | + | 0.859898i | \(0.670527\pi\) | |||||||
\(468\) | 32.4459i | 0.0693288i | ||||||||
\(469\) | 100.030 | + | 30.1916i | 0.213285 | + | 0.0643744i | ||||
\(470\) | 107.396 | 0.228503 | ||||||||
\(471\) | −255.724 | + | 442.928i | −0.542939 | + | 0.940398i | ||||
\(472\) | −35.6150 | + | 20.5624i | −0.0754556 | + | 0.0435643i | ||||
\(473\) | −7.46851 | − | 12.9358i | −0.0157897 | − | 0.0273485i | ||||
\(474\) | −171.692 | − | 99.1266i | −0.362220 | − | 0.209128i | ||||
\(475\) | − | 45.9619i | − | 0.0967619i | ||||||
\(476\) | −137.096 | + | 32.1680i | −0.288016 | + | 0.0675798i | ||||
\(477\) | 312.238 | 0.654587 | ||||||||
\(478\) | −270.460 | + | 468.451i | −0.565816 | + | 0.980023i | ||||
\(479\) | −547.932 | + | 316.349i | −1.14391 | + | 0.660435i | −0.947395 | − | 0.320066i | \(-0.896295\pi\) |
−0.196512 | + | 0.980501i | \(0.562962\pi\) | |||||||
\(480\) | 10.9545 | + | 18.9737i | 0.0228218 | + | 0.0395285i | ||||
\(481\) | 34.1116 | + | 19.6943i | 0.0709181 | + | 0.0409446i | ||||
\(482\) | 294.467i | 0.610927i | ||||||||
\(483\) | −7.64710 | − | 8.14193i | −0.0158325 | − | 0.0168570i | ||||
\(484\) | −235.237 | −0.486028 | ||||||||
\(485\) | −98.5811 | + | 170.747i | −0.203260 | + | 0.352056i | ||||
\(486\) | −19.0919 | + | 11.0227i | −0.0392837 | + | 0.0226805i | ||||
\(487\) | 31.5102 | + | 54.5773i | 0.0647027 | + | 0.112068i | 0.896562 | − | 0.442918i | \(-0.146057\pi\) |
−0.831859 | + | 0.554986i | \(0.812723\pi\) | |||||||
\(488\) | −58.2410 | − | 33.6254i | −0.119346 | − | 0.0689046i | ||||
\(489\) | − | 204.947i | − | 0.419114i | ||||||
\(490\) | −68.9208 | − | 138.780i | −0.140655 | − | 0.283225i | ||||
\(491\) | 261.092 | 0.531756 | 0.265878 | − | 0.964007i | \(-0.414338\pi\) | ||||
0.265878 | + | 0.964007i | \(0.414338\pi\) | |||||||
\(492\) | 90.7382 | − | 157.163i | 0.184427 | − | 0.319437i | ||||
\(493\) | 109.386 | − | 63.1541i | 0.221879 | − | 0.128102i | ||||
\(494\) | 35.1497 | + | 60.8811i | 0.0711532 | + | 0.123241i | ||||
\(495\) | 10.6826 | + | 6.16761i | 0.0215811 | + | 0.0124598i | ||||
\(496\) | − | 167.142i | − | 0.336980i | ||||||
\(497\) | −91.6490 | + | 86.0789i | −0.184404 | + | 0.173197i | ||||
\(498\) | 378.976 | 0.760995 | ||||||||
\(499\) | −219.481 | + | 380.153i | −0.439843 | + | 0.761830i | −0.997677 | − | 0.0681226i | \(-0.978299\pi\) |
0.557834 | + | 0.829952i | \(0.311632\pi\) | |||||||
\(500\) | 19.3649 | − | 11.1803i | 0.0387298 | − | 0.0223607i | ||||
\(501\) | −177.696 | − | 307.779i | −0.354683 | − | 0.614329i | ||||
\(502\) | −53.2714 | − | 30.7563i | −0.106118 | − | 0.0612675i | ||||
\(503\) | 702.372i | 1.39637i | 0.715919 | + | 0.698183i | \(0.246008\pi\) | ||||
−0.715919 | + | 0.698183i | \(0.753992\pi\) | |||||||
\(504\) | 13.5683 | + | 57.8265i | 0.0269213 | + | 0.114735i | ||||
\(505\) | −249.042 | −0.493153 | ||||||||
\(506\) | 1.19790 | − | 2.07483i | 0.00236739 | − | 0.00410045i | ||||
\(507\) | 209.636 | − | 121.033i | 0.413483 | − | 0.238725i | ||||
\(508\) | 131.740 | + | 228.181i | 0.259331 | + | 0.449175i | ||||
\(509\) | −103.188 | − | 59.5758i | −0.202727 | − | 0.117045i | 0.395200 | − | 0.918595i | \(-0.370675\pi\) |
−0.597927 | + | 0.801551i | \(0.704009\pi\) | |||||||
\(510\) | − | 55.0928i | − | 0.108025i | ||||||
\(511\) | −251.550 | + | 833.432i | −0.492270 | + | 1.63098i | ||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | −23.8825 | + | 41.3657i | −0.0465546 | + | 0.0806350i | ||||
\(514\) | 5.21724 | − | 3.01217i | 0.0101503 | − | 0.00586026i | ||||
\(515\) | −52.5237 | − | 90.9736i | −0.101988 | − | 0.176648i | ||||
\(516\) | 24.3694 | + | 14.0697i | 0.0472274 | + | 0.0272668i | ||||
\(517\) | 62.4497i | 0.120792i | ||||||||
\(518\) | 69.0310 | + | 20.8352i | 0.133264 | + | 0.0402224i | ||||
\(519\) | 194.914 | 0.375558 | ||||||||
\(520\) | −17.1005 | + | 29.6189i | −0.0328855 | + | 0.0569594i | ||||
\(521\) | −391.422 | + | 225.988i | −0.751291 | + | 0.433758i | −0.826160 | − | 0.563435i | \(-0.809479\pi\) |
0.0748694 | + | 0.997193i | \(0.476146\pi\) | |||||||
\(522\) | −26.6381 | − | 46.1386i | −0.0510309 | − | 0.0883882i | ||||
\(523\) | −775.007 | − | 447.451i | −1.48185 | − | 0.855546i | −0.482062 | − | 0.876137i | \(-0.660112\pi\) |
−0.999788 | + | 0.0205911i | \(0.993445\pi\) | |||||||
\(524\) | 237.536i | 0.453312i | ||||||||
\(525\) | 59.0189 | − | 13.8481i | 0.112417 | − | 0.0263774i | ||||
\(526\) | 591.670 | 1.12485 | ||||||||
\(527\) | −210.150 | + | 363.991i | −0.398767 | + | 0.690685i | ||||
\(528\) | −11.0330 | + | 6.36988i | −0.0208958 | + | 0.0120642i | ||||
\(529\) | 264.076 | + | 457.392i | 0.499198 | + | 0.864636i | ||||
\(530\) | 285.033 | + | 164.564i | 0.537798 | + | 0.310498i | ||||
\(531\) | − | 43.6193i | − | 0.0821457i | ||||||
\(532\) | 88.1048 | + | 93.8059i | 0.165610 | + | 0.176327i | ||||
\(533\) | 283.294 | 0.531509 | ||||||||
\(534\) | 83.4324 | − | 144.509i | 0.156240 | − | 0.270616i | ||||
\(535\) | 359.571 | − | 207.598i | 0.672096 | − | 0.388035i | ||||
\(536\) | −21.1096 | − | 36.5630i | −0.0393837 | − | 0.0682145i | ||||
\(537\) | 66.7047 | + | 38.5120i | 0.124217 | + | 0.0717169i | ||||
\(538\) | 521.065i | 0.968522i | ||||||||
\(539\) | 80.6990 | − | 40.0766i | 0.149720 | − | 0.0743537i | ||||
\(540\) | −23.2379 | −0.0430331 | ||||||||
\(541\) | 158.262 | − | 274.119i | 0.292537 | − | 0.506689i | −0.681872 | − | 0.731472i | \(-0.738834\pi\) |
0.974409 | + | 0.224783i | \(0.0721672\pi\) | |||||||
\(542\) | −270.695 | + | 156.286i | −0.499438 | + | 0.288351i | ||||
\(543\) | 8.00688 | + | 13.8683i | 0.0147456 | + | 0.0255402i | ||||
\(544\) | 49.2765 | + | 28.4498i | 0.0905817 | + | 0.0522974i | ||||
\(545\) | − | 192.950i | − | 0.354036i | ||||||
\(546\) | −67.5859 | + | 63.4783i | −0.123784 | + | 0.116261i | ||||
\(547\) | 796.193 | 1.45556 | 0.727782 | − | 0.685809i | \(-0.240551\pi\) | ||||
0.727782 | + | 0.685809i | \(0.240551\pi\) | |||||||
\(548\) | −81.1530 | + | 140.561i | −0.148089 | + | 0.256498i | ||||
\(549\) | 61.7739 | − | 35.6652i | 0.112521 | − | 0.0649639i | ||||
\(550\) | 6.50124 | + | 11.2605i | 0.0118204 | + | 0.0204736i | ||||
\(551\) | −99.9670 | − | 57.7160i | −0.181428 | − | 0.104748i | ||||
\(552\) | 4.51337i | 0.00817639i | ||||||||
\(553\) | −129.421 | − | 551.576i | −0.234034 | − | 0.997424i | ||||
\(554\) | 561.236 | 1.01306 | ||||||||
\(555\) | −14.1052 | + | 24.4309i | −0.0254147 | + | 0.0440196i | ||||
\(556\) | −430.088 | + | 248.311i | −0.773540 | + | 0.446603i | ||||
\(557\) | −155.976 | − | 270.159i | −0.280029 | − | 0.485025i | 0.691363 | − | 0.722508i | \(-0.257011\pi\) |
−0.971392 | + | 0.237484i | \(0.923677\pi\) | |||||||
\(558\) | 153.530 | + | 88.6406i | 0.275143 | + | 0.158854i | ||||
\(559\) | 43.9270i | 0.0785813i | ||||||||
\(560\) | −18.0911 | + | 59.9392i | −0.0323055 | + | 0.107034i | ||||
\(561\) | 32.0358 | 0.0571048 | ||||||||
\(562\) | −80.7827 | + | 139.920i | −0.143741 | + | 0.248968i | ||||
\(563\) | 534.350 | − | 308.507i | 0.949112 | − | 0.547970i | 0.0563071 | − | 0.998413i | \(-0.482067\pi\) |
0.892805 | + | 0.450443i | \(0.148734\pi\) | |||||||
\(564\) | −58.8234 | − | 101.885i | −0.104297 | − | 0.180647i | ||||
\(565\) | −166.191 | − | 95.9504i | −0.294143 | − | 0.169824i | ||||
\(566\) | − | 639.838i | − | 1.13046i | ||||||
\(567\) | −60.3127 | − | 18.2038i | −0.106372 | − | 0.0321055i | ||||
\(568\) | 50.8043 | 0.0894442 | ||||||||
\(569\) | 391.495 | − | 678.089i | 0.688041 | − | 1.19172i | −0.284430 | − | 0.958697i | \(-0.591804\pi\) |
0.972471 | − | 0.233025i | \(-0.0748623\pi\) | |||||||
\(570\) | −43.6033 | + | 25.1744i | −0.0764970 | + | 0.0441656i | ||||
\(571\) | −1.06600 | − | 1.84636i | −0.00186689 | − | 0.00323355i | 0.865090 | − | 0.501616i | \(-0.167261\pi\) |
−0.866957 | + | 0.498382i | \(0.833928\pi\) | |||||||
\(572\) | −17.2230 | − | 9.94373i | −0.0301102 | − | 0.0173841i | ||||
\(573\) | − | 236.960i | − | 0.413543i | ||||||
\(574\) | 504.900 | − | 118.469i | 0.879616 | − | 0.206392i | ||||
\(575\) | 4.60644 | 0.00801120 | ||||||||
\(576\) | 12.0000 | − | 20.7846i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | −828.056 | + | 478.079i | −1.43511 | + | 0.828559i | −0.997504 | − | 0.0706096i | \(-0.977506\pi\) |
−0.437602 | + | 0.899169i | \(0.644172\pi\) | |||||||
\(578\) | 132.813 | + | 230.039i | 0.229781 | + | 0.397992i | ||||
\(579\) | 548.811 | + | 316.856i | 0.947860 | + | 0.547247i | ||||
\(580\) | − | 56.1581i | − | 0.0968244i | ||||||
\(581\) | 741.441 | + | 789.419i | 1.27615 | + | 1.35872i | ||||
\(582\) | 215.980 | 0.371100 | ||||||||
\(583\) | −95.6919 | + | 165.743i | −0.164137 | + | 0.284294i | ||||
\(584\) | 304.635 | − | 175.881i | 0.521635 | − | 0.301166i | ||||
\(585\) | −18.1378 | − | 31.4156i | −0.0310048 | − | 0.0537019i | ||||
\(586\) | 145.909 | + | 84.2403i | 0.248991 | + | 0.143755i | ||||
\(587\) | − | 628.961i | − | 1.07148i | −0.844382 | − | 0.535742i | \(-0.820032\pi\) | ||
0.844382 | − | 0.535742i | \(-0.179968\pi\) | |||||||
\(588\) | −93.9089 | + | 141.397i | −0.159709 | + | 0.240471i | ||||
\(589\) | 384.109 | 0.652138 | ||||||||
\(590\) | 22.9894 | − | 39.8188i | 0.0389651 | − | 0.0674895i | ||||
\(591\) | −292.388 | + | 168.810i | −0.494734 | + | 0.285635i | ||||
\(592\) | −14.5678 | − | 25.2321i | −0.0246077 | − | 0.0426218i | ||||
\(593\) | −417.691 | − | 241.154i | −0.704370 | − | 0.406668i | 0.104603 | − | 0.994514i | \(-0.466643\pi\) |
−0.808973 | + | 0.587846i | \(0.799976\pi\) | |||||||
\(594\) | − | 13.5126i | − | 0.0227484i | ||||||
\(595\) | 114.760 | − | 107.785i | 0.192874 | − | 0.181152i | ||||
\(596\) | −300.019 | −0.503388 | ||||||||
\(597\) | −210.301 | + | 364.253i | −0.352263 | + | 0.610138i | ||||
\(598\) | −6.10168 | + | 3.52280i | −0.0102035 | + | 0.00589098i | ||||
\(599\) | −181.233 | − | 313.904i | −0.302559 | − | 0.524047i | 0.674156 | − | 0.738589i | \(-0.264508\pi\) |
−0.976715 | + | 0.214542i | \(0.931174\pi\) | |||||||
\(600\) | −21.2132 | − | 12.2474i | −0.0353553 | − | 0.0204124i | ||||
\(601\) | 545.450i | 0.907570i | 0.891111 | + | 0.453785i | \(0.149927\pi\) | ||||
−0.891111 | + | 0.453785i | \(0.850073\pi\) | |||||||
\(602\) | 18.3695 | + | 78.2886i | 0.0305142 | + | 0.130047i | ||||
\(603\) | 44.7803 | 0.0742626 | ||||||||
\(604\) | −183.030 | + | 317.017i | −0.303030 | + | 0.524863i | ||||
\(605\) | 227.768 | − | 131.502i | 0.376475 | − | 0.217358i | ||||
\(606\) | 136.406 | + | 236.262i | 0.225093 | + | 0.389872i | ||||
\(607\) | −554.426 | − | 320.098i | −0.913388 | − | 0.527345i | −0.0318683 | − | 0.999492i | \(-0.510146\pi\) |
−0.881520 | + | 0.472147i | \(0.843479\pi\) | |||||||
\(608\) | − | 52.0000i | − | 0.0855263i | ||||||
\(609\) | 43.9925 | − | 145.755i | 0.0722372 | − | 0.239336i | ||||
\(610\) | 75.1888 | 0.123260 | ||||||||
\(611\) | 91.8265 | − | 159.048i | 0.150289 | − | 0.260308i | ||||
\(612\) | −52.2656 | + | 30.1755i | −0.0854013 | + | 0.0493064i | ||||
\(613\) | 198.272 | + | 343.417i | 0.323445 | + | 0.560223i | 0.981196 | − | 0.193012i | \(-0.0618256\pi\) |
−0.657751 | + | 0.753235i | \(0.728492\pi\) | |||||||
\(614\) | −333.918 | − | 192.787i | −0.543840 | − | 0.313986i | ||||
\(615\) | 202.897i | 0.329914i | ||||||||
\(616\) | −34.8540 | − | 10.5198i | −0.0565811 | − | 0.0170775i | ||||
\(617\) | −421.502 | −0.683148 | −0.341574 | − | 0.939855i | \(-0.610960\pi\) | ||||
−0.341574 | + | 0.939855i | \(0.610960\pi\) | |||||||
\(618\) | −57.5368 | + | 99.6566i | −0.0931016 | + | 0.161257i | ||||
\(619\) | 629.261 | − | 363.304i | 1.01658 | − | 0.586921i | 0.103467 | − | 0.994633i | \(-0.467006\pi\) |
0.913111 | + | 0.407712i | \(0.133673\pi\) | |||||||
\(620\) | 93.4354 | + | 161.835i | 0.150702 | + | 0.261024i | ||||
\(621\) | −4.14579 | − | 2.39358i | −0.00667600 | − | 0.00385439i | ||||
\(622\) | − | 106.876i | − | 0.171826i | ||||||
\(623\) | 464.248 | − | 108.930i | 0.745181 | − | 0.174848i | ||||
\(624\) | 37.4653 | 0.0600405 | ||||||||
\(625\) | −12.5000 | + | 21.6506i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −77.9313 | + | 44.9936i | −0.124491 | + | 0.0718748i | ||||
\(627\) | −14.6386 | − | 25.3548i | −0.0233471 | − | 0.0404383i | ||||
\(628\) | 511.449 | + | 295.285i | 0.814409 | + | 0.470199i | ||||
\(629\) | 73.2650i | 0.116479i | ||||||||
\(630\) | −45.4635 | − | 48.4053i | −0.0721642 | − | 0.0768338i | ||||
\(631\) | −537.550 | −0.851901 | −0.425950 | − | 0.904746i | \(-0.640060\pi\) | ||||
−0.425950 | + | 0.904746i | \(0.640060\pi\) | |||||||
\(632\) | −114.462 | + | 198.253i | −0.181110 | + | 0.313692i | ||||
\(633\) | 278.895 | − | 161.020i | 0.440592 | − | 0.254376i | ||||
\(634\) | 10.9263 | + | 18.9249i | 0.0172339 | + | 0.0298500i | ||||
\(635\) | −255.114 | − | 147.290i | −0.401754 | − | 0.231953i | ||||
\(636\) | − | 360.541i | − | 0.566889i | ||||||
\(637\) | −264.455 | − | 16.5924i | −0.415157 | − | 0.0260477i | ||||
\(638\) | 32.6553 | 0.0511838 | ||||||||
\(639\) | −26.9431 | + | 46.6668i | −0.0421644 | + | 0.0730309i | ||||
\(640\) | 21.9089 | − | 12.6491i | 0.0342327 | − | 0.0197642i | ||||
\(641\) | −488.924 | − | 846.841i | −0.762752 | − | 1.32112i | −0.941427 | − | 0.337217i | \(-0.890514\pi\) |
0.178675 | − | 0.983908i | \(-0.442819\pi\) | |||||||
\(642\) | −393.890 | − | 227.413i | −0.613537 | − | 0.354225i | ||||
\(643\) | 276.520i | 0.430047i | 0.976609 | + | 0.215023i | \(0.0689828\pi\) | ||||
−0.976609 | + | 0.215023i | \(0.931017\pi\) | |||||||
\(644\) | −9.40150 | + | 8.83011i | −0.0145986 | + | 0.0137114i | ||||
\(645\) | −31.4607 | −0.0487763 | ||||||||
\(646\) | −65.3803 | + | 113.242i | −0.101208 | + | 0.175297i | ||||
\(647\) | −210.206 | + | 121.362i | −0.324893 | + | 0.187577i | −0.653571 | − | 0.756865i | \(-0.726730\pi\) |
0.328679 | + | 0.944442i | \(0.393397\pi\) | |||||||
\(648\) | 12.7279 | + | 22.0454i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | 23.1542 | + | 13.3681i | 0.0356767 | + | 0.0205980i | ||||
\(650\) | − | 38.2378i | − | 0.0588275i | ||||||
\(651\) | 115.730 | + | 493.228i | 0.177773 | + | 0.757646i | ||||
\(652\) | −236.652 | −0.362964 | ||||||||
\(653\) | 26.6109 | − | 46.0914i | 0.0407518 | − | 0.0705841i | −0.844930 | − | 0.534877i | \(-0.820358\pi\) |
0.885682 | + | 0.464293i | \(0.153691\pi\) | |||||||
\(654\) | −183.048 | + | 105.683i | −0.279890 | + | 0.161595i | ||||
\(655\) | −132.786 | − | 229.993i | −0.202727 | − | 0.351134i | ||||
\(656\) | −181.476 | − | 104.775i | −0.276641 | − | 0.159719i | ||||
\(657\) | 373.100i | 0.567884i | ||||||||
\(658\) | 97.1459 | − | 321.863i | 0.147638 | − | 0.489153i | ||||
\(659\) | 640.732 | 0.972279 | 0.486139 | − | 0.873881i | \(-0.338405\pi\) | ||||
0.486139 | + | 0.873881i | \(0.338405\pi\) | |||||||
\(660\) | 7.12175 | − | 12.3352i | 0.0107905 | − | 0.0186897i | ||||
\(661\) | 10.4335 | − | 6.02380i | 0.0157845 | − | 0.00911317i | −0.492087 | − | 0.870546i | \(-0.663766\pi\) |
0.507871 | + | 0.861433i | \(0.330432\pi\) | |||||||
\(662\) | −263.807 | − | 456.927i | −0.398500 | − | 0.690222i | ||||
\(663\) | −81.5894 | − | 47.1056i | −0.123061 | − | 0.0710492i | ||||
\(664\) | − | 437.603i | − | 0.659041i | ||||||
\(665\) | −137.746 | − | 41.5751i | −0.207137 | − | 0.0625189i | ||||
\(666\) | 30.9029 | 0.0464007 | ||||||||
\(667\) | 5.78446 | − | 10.0190i | 0.00867236 | − | 0.0150210i | ||||
\(668\) | −355.393 | + | 205.186i | −0.532025 | + | 0.307165i | ||||
\(669\) | −46.4491 | − | 80.4522i | −0.0694306 | − | 0.120257i | ||||
\(670\) | 40.8787 | + | 23.6013i | 0.0610129 | + | 0.0352258i | ||||
\(671\) | 43.7214i | 0.0651586i | ||||||||
\(672\) | 66.7723 | − | 15.6674i | 0.0993635 | − | 0.0233145i | ||||
\(673\) | −952.008 | −1.41457 | −0.707286 | − | 0.706927i | \(-0.750081\pi\) | ||||
−0.707286 | + | 0.706927i | \(0.750081\pi\) | |||||||
\(674\) | 454.612 | − | 787.412i | 0.674499 | − | 1.16827i | ||||
\(675\) | 22.5000 | − | 12.9904i | 0.0333333 | − | 0.0192450i | ||||
\(676\) | −139.757 | − | 242.067i | −0.206742 | − | 0.358087i | ||||
\(677\) | 18.2965 | + | 10.5635i | 0.0270259 | + | 0.0156034i | 0.513452 | − | 0.858118i | \(-0.328366\pi\) |
−0.486426 | + | 0.873722i | \(0.661700\pi\) | |||||||
\(678\) | 210.217i | 0.310054i | ||||||||
\(679\) | 422.551 | + | 449.894i | 0.622314 | + | 0.662583i | ||||
\(680\) | −63.6156 | −0.0935524 | ||||||||
\(681\) | 146.392 | − | 253.559i | 0.214966 | − | 0.372333i | ||||
\(682\) | −94.1050 | + | 54.3316i | −0.137984 | + | 0.0796651i | ||||
\(683\) | 196.448 | + | 340.259i | 0.287626 | + | 0.498182i | 0.973243 | − | 0.229780i | \(-0.0738007\pi\) |
−0.685617 | + | 0.727963i | \(0.740467\pi\) | |||||||
\(684\) | 47.7650 | + | 27.5772i | 0.0698319 | + | 0.0403175i | ||||
\(685\) | − | 181.464i | − | 0.264910i | ||||||
\(686\) | −478.261 | + | 81.0188i | −0.697174 | + | 0.118103i | ||||
\(687\) | 495.397 | 0.721101 | ||||||||
\(688\) | 16.2462 | − | 28.1393i | 0.0236137 | − | 0.0409002i | ||||
\(689\) | 487.420 | − | 281.412i | 0.707431 | − | 0.408436i | ||||
\(690\) | −2.52305 | − | 4.37005i | −0.00365659 | − | 0.00633341i | ||||
\(691\) | 230.954 | + | 133.342i | 0.334232 | + | 0.192969i | 0.657718 | − | 0.753264i | \(-0.271522\pi\) |
−0.323486 | + | 0.946233i | \(0.604855\pi\) | |||||||
\(692\) | − | 225.068i | − | 0.325242i | ||||||
\(693\) | 28.1471 | − | 26.4365i | 0.0406163 | − | 0.0381479i | ||||
\(694\) | −203.659 | −0.293457 | ||||||||
\(695\) | 277.621 | − | 480.853i | 0.399454 | − | 0.691875i | ||||
\(696\) | −53.2763 | + | 30.7591i | −0.0765464 | + | 0.0441941i | ||||
\(697\) | 263.471 | + | 456.346i | 0.378008 | + | 0.654729i | ||||
\(698\) | −693.826 | − | 400.581i | −0.994020 | − | 0.573898i | ||||
\(699\) | − | 314.954i | − | 0.450578i | ||||||
\(700\) | −15.9904 | − | 68.1491i | −0.0228435 | − | 0.0973559i | ||||
\(701\) | 207.973 | 0.296680 | 0.148340 | − | 0.988936i | \(-0.452607\pi\) | ||||
0.148340 | + | 0.988936i | \(0.452607\pi\) | |||||||
\(702\) | −19.8690 | + | 34.4141i | −0.0283034 | + | 0.0490229i | ||||
\(703\) | 57.9858 | − | 33.4781i | 0.0824834 | − | 0.0476218i | ||||
\(704\) | 7.35531 | + | 12.7398i | 0.0104479 | + | 0.0180963i | ||||
\(705\) | 113.911 | + | 65.7666i | 0.161576 | + | 0.0932859i | ||||
\(706\) | − | 721.480i | − | 1.02193i | ||||||
\(707\) | −225.273 | + | 746.371i | −0.318632 | + | 1.05569i | ||||
\(708\) | −50.3673 | −0.0711402 | ||||||||
\(709\) | 447.714 | − | 775.463i | 0.631472 | − | 1.09374i | −0.355779 | − | 0.934570i | \(-0.615784\pi\) |
0.987251 | − | 0.159172i | \(-0.0508823\pi\) | |||||||
\(710\) | −49.1911 | + | 28.4005i | −0.0692832 | + | 0.0400007i | ||||
\(711\) | −121.405 | − | 210.279i | −0.170752 | − | 0.295751i | ||||
\(712\) | −166.865 | − | 96.3395i | −0.234361 | − | 0.135308i | ||||
\(713\) | 38.4965i | 0.0539923i | ||||||||
\(714\) | −165.111 | − | 49.8344i | −0.231248 | − | 0.0697961i | ||||
\(715\) | 22.2349 | 0.0310977 | ||||||||
\(716\) | 44.4698 | − | 77.0240i | 0.0621087 | − | 0.107575i | ||||
\(717\) | −573.733 | + | 331.245i | −0.800185 | + | 0.461987i | ||||
\(718\) | 472.250 | + | 817.962i | 0.657730 | + | 1.13922i | ||||
\(719\) | −327.729 | − | 189.215i | −0.455813 | − | 0.263163i | 0.254469 | − | 0.967081i | \(-0.418099\pi\) |
−0.710282 | + | 0.703917i | \(0.751433\pi\) | |||||||
\(720\) | 26.8328i | 0.0372678i | ||||||||
\(721\) | −320.155 | + | 75.1207i | −0.444043 | + | 0.104190i | ||||
\(722\) | −391.030 | −0.541593 | ||||||||
\(723\) | −180.324 | + | 312.329i | −0.249410 | + | 0.431991i | ||||
\(724\) | 16.0138 | − | 9.24555i | 0.0221185 | − | 0.0127701i | ||||
\(725\) | 31.3934 | + | 54.3749i | 0.0433012 | + | 0.0749998i | ||||
\(726\) | −249.507 | − | 144.053i | −0.343674 | − | 0.198420i | ||||
\(727\) | − | 456.052i | − | 0.627307i | −0.949538 | − | 0.313653i | \(-0.898447\pi\) | ||
0.949538 | − | 0.313653i | \(-0.101553\pi\) | |||||||
\(728\) | 73.2984 | + | 78.0414i | 0.100685 | + | 0.107200i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | −196.641 | + | 340.592i | −0.269371 | + | 0.466565i | ||||
\(731\) | −70.7599 | + | 40.8533i | −0.0967988 | + | 0.0558868i | ||||
\(732\) | −41.1826 | − | 71.3303i | −0.0562604 | − | 0.0974458i | ||||
\(733\) | 658.892 | + | 380.412i | 0.898898 | + | 0.518979i | 0.876842 | − | 0.480778i | \(-0.159646\pi\) |
0.0220553 | + | 0.999757i | \(0.492979\pi\) | |||||||
\(734\) | 49.3517i | 0.0672367i | ||||||||
\(735\) | 11.8836 | − | 189.404i | 0.0161681 | − | 0.257692i | ||||
\(736\) | 5.21159 | 0.00708096 | ||||||||
\(737\) | −13.7239 | + | 23.7705i | −0.0186213 | + | 0.0322530i | ||||
\(738\) | 192.485 | − | 111.131i | 0.260820 | − | 0.150584i | ||||
\(739\) | 14.0833 | + | 24.3930i | 0.0190573 | + | 0.0330081i | 0.875397 | − | 0.483405i | \(-0.160600\pi\) |
−0.856340 | + | 0.516413i | \(0.827267\pi\) | |||||||
\(740\) | 28.2104 | + | 16.2873i | 0.0381221 | + | 0.0220098i | ||||
\(741\) | 86.0988i | 0.116193i | ||||||||
\(742\) | 751.019 | − | 705.376i | 1.01216 | − | 0.950641i | ||||
\(743\) | −1077.90 | −1.45073 | −0.725367 | − | 0.688362i | \(-0.758330\pi\) | ||||
−0.725367 | + | 0.688362i | \(0.758330\pi\) | |||||||
\(744\) | 102.353 | − | 177.281i | 0.137572 | − | 0.238281i | ||||
\(745\) | 290.492 | − | 167.716i | 0.389923 | − | 0.225122i | ||||
\(746\) | −288.517 | − | 499.726i | −0.386752 | − | 0.669874i | ||||
\(747\) | 401.964 | + | 232.074i | 0.538105 | + | 0.310675i | ||||
\(748\) | − | 36.9917i | − | 0.0494542i | ||||||
\(749\) | −296.913 | − | 1265.41i | −0.396412 | − | 1.68946i | ||||
\(750\) | 27.3861 | 0.0365148 | ||||||||
\(751\) | −90.0583 | + | 155.986i | −0.119918 | + | 0.207704i | −0.919735 | − | 0.392540i | \(-0.871596\pi\) |
0.799817 | + | 0.600244i | \(0.204930\pi\) | |||||||
\(752\) | −117.647 | + | 67.9234i | −0.156445 | + | 0.0903237i | ||||
\(753\) | −37.6686 | − | 65.2439i | −0.0500247 | − | 0.0866453i | ||||
\(754\) | −83.1671 | − | 48.0166i | −0.110301 | − | 0.0636824i | ||||
\(755\) | − | 409.267i | − | 0.542076i | ||||||
\(756\) | −21.0200 | + | 69.6431i | −0.0278042 | + | 0.0921205i | ||||
\(757\) | 219.675 | 0.290192 | 0.145096 | − | 0.989418i | \(-0.453651\pi\) | ||||
0.145096 | + | 0.989418i | \(0.453651\pi\) | |||||||
\(758\) | −7.40380 | + | 12.8238i | −0.00976755 | + | 0.0169179i | ||||
\(759\) | 2.54113 | − | 1.46712i | 0.00334800 | − | 0.00193297i | ||||
\(760\) | 29.0689 | + | 50.3488i | 0.0382485 | + | 0.0662484i | ||||
\(761\) | 1113.97 | + | 643.150i | 1.46382 | + | 0.845138i | 0.999185 | − | 0.0403636i | \(-0.0128516\pi\) |
0.464637 | + | 0.885501i | \(0.346185\pi\) | |||||||
\(762\) | 322.697i | 0.423486i | ||||||||
\(763\) | −578.262 | − | 174.533i | −0.757880 | − | 0.228746i | ||||
\(764\) | −273.618 | −0.358138 | ||||||||
\(765\) | 33.7373 | − | 58.4347i | 0.0441010 | − | 0.0763852i | ||||
\(766\) | −282.379 | + | 163.031i | −0.368641 | + | 0.212835i | ||||
\(767\) | −39.3130 | − | 68.0921i | −0.0512555 | − | 0.0887772i | ||||
\(768\) | −24.0000 | − | 13.8564i | −0.0312500 | − | 0.0180422i | ||||
\(769\) | 365.543i | 0.475348i | 0.971345 | + | 0.237674i | \(0.0763850\pi\) | ||||
−0.971345 | + | 0.237674i | \(0.923615\pi\) | |||||||
\(770\) | 39.6279 | − | 9.29824i | 0.0514648 | − | 0.0120756i | ||||
\(771\) | 7.37829 | 0.00956977 | ||||||||
\(772\) | 365.874 | − | 633.712i | 0.473930 | − | 0.820871i | ||||
\(773\) | 267.183 | − | 154.258i | 0.345645 | − | 0.199558i | −0.317121 | − | 0.948385i | \(-0.602716\pi\) |
0.662765 | + | 0.748827i | \(0.269383\pi\) | |||||||
\(774\) | 17.2317 | + | 29.8462i | 0.0222632 | + | 0.0385610i | ||||
\(775\) | −180.937 | − | 104.464i | −0.233467 | − | 0.134792i | ||||
\(776\) | − | 249.393i | − | 0.321382i | ||||||
\(777\) | 60.4595 | + | 64.3717i | 0.0778115 | + | 0.0828465i | ||||
\(778\) | −956.311 | −1.22919 | ||||||||
\(779\) | 240.784 | − | 417.050i | 0.309094 | − | 0.535366i | ||||
\(780\) | −36.2756 | + | 20.9437i | −0.0465072 | + | 0.0268509i | ||||
\(781\) | −16.5145 | − | 28.6040i | −0.0211454 | − | 0.0366249i | ||||
\(782\) | −11.3494 | − | 6.55261i | −0.0145134 | − | 0.00837929i | ||||
\(783\) | − | 65.2499i | − | 0.0833332i | ||||||
\(784\) | 163.271 | + | 108.437i | 0.208254 | + | 0.138312i | ||||
\(785\) | −660.277 | −0.841118 | ||||||||
\(786\) | −145.460 | + | 251.945i | −0.185064 | + | 0.320540i | ||||
\(787\) | 1232.85 | − | 711.787i | 1.56652 | − | 0.904431i | 0.569950 | − | 0.821679i | \(-0.306963\pi\) |
0.996570 | − | 0.0827517i | \(-0.0263708\pi\) | |||||||
\(788\) | 194.925 | + | 337.620i | 0.247367 | + | 0.428452i | ||||
\(789\) | 627.561 | + | 362.323i | 0.795388 | + | 0.459218i | ||||
\(790\) | − | 255.944i | − | 0.323980i | ||||||
\(791\) | −437.888 | + | 411.275i | −0.553588 | + | 0.519944i | ||||
\(792\) | −15.6030 | −0.0197007 | ||||||||
\(793\) | 64.2882 | − | 111.350i | 0.0810696 | − | 0.140417i | ||||
\(794\) | −200.310 | + | 115.649i | −0.252280 | + | 0.145654i | ||||
\(795\) | 201.549 | + | 349.093i | 0.253520 | + | 0.439110i | ||||
\(796\) | 420.603 | + | 242.835i | 0.528395 | + | 0.305069i | ||||
\(797\) | 475.713i | 0.596880i | 0.954428 | + | 0.298440i | \(0.0964663\pi\) | ||||
−0.954428 | + | 0.298440i | \(0.903534\pi\) | |||||||
\(798\) | 36.0051 | + | 153.449i | 0.0451191 | + | 0.192292i | ||||
\(799\) | 341.604 | 0.427540 | ||||||||
\(800\) | −14.1421 | + | 24.4949i | −0.0176777 | + | 0.0306186i | ||||
\(801\) | 176.987 | − | 102.183i | 0.220957 | − | 0.127570i | ||||
\(802\) | −211.600 | − | 366.502i | −0.263840 | − | 0.456985i | ||||
\(803\) | −198.050 | − | 114.344i | −0.246638 | − | 0.142397i | ||||
\(804\) | − | 51.7079i | − | 0.0643133i | ||||||
\(805\) | 4.16678 | − | 13.8053i | 0.00517612 | − | 0.0171495i | ||||
\(806\) | 319.558 | 0.396474 | ||||||||
\(807\) | −319.086 | + | 552.672i | −0.395397 | + | 0.684848i | ||||
\(808\) | 272.812 | − | 157.508i | 0.337639 | − | 0.194936i | ||||
\(809\) | −363.710 | − | 629.965i | −0.449580 | − | 0.778696i | 0.548779 | − | 0.835968i | \(-0.315093\pi\) |
−0.998359 | + | 0.0572722i | \(0.981760\pi\) | |||||||
\(810\) | −24.6475 | − | 14.2302i | −0.0304290 | − | 0.0175682i | ||||
\(811\) | 673.804i | 0.830831i | 0.909632 | + | 0.415415i | \(0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(812\) | −168.304 | − | 50.7981i | −0.207271 | − | 0.0625593i | ||||
\(813\) | −382.821 | −0.470875 | ||||||||
\(814\) | −9.47085 | + | 16.4040i | −0.0116349 | + | 0.0201523i | ||||
\(815\) | 229.138 | − | 132.293i | 0.281150 | − | 0.162322i | ||||
\(816\) | 34.8437 | + | 60.3511i | 0.0427006 | + | 0.0739597i | ||||
\(817\) | 64.6668 | + | 37.3354i | 0.0791516 | + | 0.0456982i | ||||
\(818\) | − | 658.527i | − | 0.805046i | ||||||
\(819\) | −110.558 | + | 25.9412i | −0.134991 | + | 0.0316742i | ||||
\(820\) | 234.285 | 0.285714 | ||||||||
\(821\) | 445.465 | − | 771.568i | 0.542588 | − | 0.939790i | −0.456166 | − | 0.889895i | \(-0.650778\pi\) |
0.998754 | − | 0.0498958i | \(-0.0158889\pi\) | |||||||
\(822\) | −172.151 | + | 99.3917i | −0.209430 | + | 0.120914i | ||||
\(823\) | 495.873 | + | 858.877i | 0.602519 | + | 1.04359i | 0.992438 | + | 0.122744i | \(0.0391696\pi\) |
−0.389919 | + | 0.920849i | \(0.627497\pi\) | |||||||
\(824\) | 115.074 | + | 66.4378i | 0.139652 | + | 0.0806283i | ||||
\(825\) | 15.9247i | 0.0193027i | ||||||||
\(826\) | −98.5403 | − | 104.917i | −0.119298 | − | 0.127018i | ||||
\(827\) | 1264.47 | 1.52899 | 0.764493 | − | 0.644632i | \(-0.222989\pi\) | ||||
0.764493 | + | 0.644632i | \(0.222989\pi\) | |||||||
\(828\) | −2.76386 | + | 4.78715i | −0.00333800 | + | 0.00578158i | ||||
\(829\) | −78.3145 | + | 45.2149i | −0.0944686 | + | 0.0545415i | −0.546490 | − | 0.837466i | \(-0.684036\pi\) |
0.452021 | + | 0.892007i | \(0.350703\pi\) | |||||||
\(830\) | 244.628 | + | 423.708i | 0.294732 | + | 0.510491i | ||||
\(831\) | 595.281 | + | 343.686i | 0.716343 | + | 0.413581i | ||||
\(832\) | − | 43.2612i | − | 0.0519966i | ||||||
\(833\) | −219.222 | − | 441.429i | −0.263172 | − | 0.529927i | ||||
\(834\) | −608.236 | −0.729300 | ||||||||
\(835\) | 229.405 | − | 397.341i | 0.274736 | − | 0.475858i | ||||
\(836\) | −29.2772 | + | 16.9032i | −0.0350206 | + | 0.0202191i | ||||
\(837\) | 108.562 | + | 188.035i | 0.129704 | + | 0.224654i | ||||
\(838\) | 705.309 | + | 407.210i | 0.841658 | + | 0.485931i | ||||
\(839\) | − | 148.508i | − | 0.177006i | −0.996076 | − | 0.0885032i | \(-0.971792\pi\) | ||
0.996076 | − | 0.0885032i | \(-0.0282083\pi\) | |||||||
\(840\) | −55.8936 | + | 52.4967i | −0.0665401 | + | 0.0624960i | ||||
\(841\) | −683.313 | −0.812501 | ||||||||
\(842\) | 403.863 | − | 699.512i | 0.479648 | − | 0.830774i | ||||
\(843\) | −171.366 | + | 98.9382i | −0.203281 | + | 0.117364i | ||||
\(844\) | −185.930 | − | 322.040i | −0.220296 | − | 0.381564i | ||||
\(845\) | 270.639 | + | 156.253i | 0.320283 | + | 0.184915i | ||||
\(846\) | − | 144.087i | − | 0.170316i | ||||||
\(847\) | −188.077 | − | 801.562i | −0.222051 | − | 0.946354i | ||||
\(848\) | −416.317 | −0.490940 | ||||||||
\(849\) | 391.819 | − | 678.650i | 0.461507 | − | 0.799353i | ||||
\(850\) | 61.5956 | − | 35.5622i | 0.0724654 | − | 0.0418379i | ||||
\(851\) | 3.35527 | + | 5.81151i | 0.00394274 | + | 0.00682903i | ||||
\(852\) | 53.8861 | + | 31.1112i | 0.0632466 | + | 0.0365155i | ||||
\(853\) | 642.996i | 0.753805i | 0.926253 | + | 0.376902i | \(0.123011\pi\) | ||||
−0.926253 | + | 0.376902i | \(0.876989\pi\) | |||||||
\(854\) | 68.0124 | − | 225.338i | 0.0796398 | − | 0.263862i | ||||
\(855\) | −61.6644 | −0.0721221 | ||||||||
\(856\) | −262.594 | + | 454.826i | −0.306768 | + | 0.531338i | ||||
\(857\) | −109.679 | + | 63.3232i | −0.127980 | + | 0.0738894i | −0.562623 | − | 0.826713i | \(-0.690208\pi\) |
0.434643 | + | 0.900603i | \(0.356875\pi\) | |||||||
\(858\) | −12.1785 | − | 21.0938i | −0.0141941 | − | 0.0245849i | ||||
\(859\) | −435.756 | − | 251.584i | −0.507283 | − | 0.292880i | 0.224433 | − | 0.974489i | \(-0.427947\pi\) |
−0.731716 | + | 0.681610i | \(0.761280\pi\) | |||||||
\(860\) | 36.3277i | 0.0422415i | ||||||||
\(861\) | 608.074 | + | 183.531i | 0.706242 | + | 0.213161i | ||||
\(862\) | 38.3809 | 0.0445254 | ||||||||
\(863\) | −633.889 | + | 1097.93i | −0.734518 | + | 1.27222i | 0.220417 | + | 0.975406i | \(0.429258\pi\) |
−0.954935 | + | 0.296816i | \(0.904075\pi\) | |||||||
\(864\) | 25.4558 | − | 14.6969i | 0.0294628 | − | 0.0170103i | ||||
\(865\) | 125.817 | + | 217.921i | 0.145453 | + | 0.251932i | ||||
\(866\) | −445.082 | − | 256.968i | −0.513951 | − | 0.296730i | ||||
\(867\) | 325.325i | 0.375230i | ||||||||
\(868\) | 569.530 | − | 133.634i | 0.656141 | − | 0.153956i | ||||
\(869\) | 148.828 | 0.171264 | ||||||||
\(870\) | 34.3897 | − | 59.5647i | 0.0395284 | − | 0.0684652i | ||||
\(871\) | 69.9045 | − | 40.3594i | 0.0802577 | − | 0.0463368i | ||||
\(872\) | 122.032 | + | 211.366i | 0.139945 | + | 0.242392i | ||||
\(873\) | 229.082 | + | 132.260i | 0.262407 | + | 0.151501i | ||||
\(874\) | 11.9767i | 0.0137034i | ||||||||
\(875\) | 53.5792 | + | 57.0462i | 0.0612334 | + | 0.0651957i | ||||
\(876\) | 430.819 | 0.491802 | ||||||||
\(877\) | 164.850 | − | 285.529i | 0.187971 | − | 0.325575i | −0.756603 | − | 0.653875i | \(-0.773142\pi\) |
0.944574 | + | 0.328300i | \(0.106476\pi\) | |||||||
\(878\) | −570.008 | + | 329.094i | −0.649212 | + | 0.374823i | ||||
\(879\) | 103.173 | + | 178.701i | 0.117375 | + | 0.203300i | ||||
\(880\) | −14.2435 | − | 8.22348i | −0.0161858 | − | 0.00934487i | ||||
\(881\) | 583.618i | 0.662449i | 0.943552 | + | 0.331224i | \(0.107462\pi\) | ||||
−0.943552 | + | 0.331224i | \(0.892538\pi\) | |||||||
\(882\) | −186.193 | + | 92.4670i | −0.211103 | + | 0.104838i | ||||
\(883\) | −1172.36 | −1.32770 | −0.663849 | − | 0.747867i | \(-0.731078\pi\) | ||||
−0.663849 | + | 0.747867i | \(0.731078\pi\) | |||||||
\(884\) | −54.3929 | + | 94.2113i | −0.0615304 | + | 0.106574i | ||||
\(885\) | 48.7679 | − | 28.1562i | 0.0551050 | − | 0.0318149i | ||||
\(886\) | 345.023 | + | 597.597i | 0.389416 | + | 0.674489i | ||||
\(887\) | 1274.64 | + | 735.915i | 1.43703 | + | 0.829667i | 0.997642 | − | 0.0686323i | \(-0.0218635\pi\) |
0.439384 | + | 0.898299i | \(0.355197\pi\) | |||||||
\(888\) | − | 35.6836i | − | 0.0401842i | ||||||
\(889\) | −672.188 | + | 631.335i | −0.756117 | + | 0.710163i | ||||
\(890\) | 215.422 | 0.242047 | ||||||||
\(891\) | 8.27472 | − | 14.3322i | 0.00928701 | − | 0.0160856i | ||||
\(892\) | −92.8982 | + | 53.6348i | −0.104146 | + | 0.0601287i | ||||
\(893\) | −156.095 | − | 270.364i | −0.174798 | − | 0.302759i | ||||
\(894\) | −318.219 | − | 183.724i | −0.355949 | − | 0.205507i | ||||
\(895\) | 99.4375i | 0.111103i | ||||||||
\(896\) | −18.0911 | − | 77.1020i | −0.0201910 | − | 0.0860513i | ||||
\(897\) | −8.62907 | −0.00961993 | ||||||||
\(898\) | −202.118 | + | 350.078i | −0.225075 | + | 0.389842i | ||||
\(899\) | −454.417 | + | 262.358i | −0.505470 | + | 0.291833i | ||||
\(900\) | −15.0000 | − | 25.9808i | −0.0166667 | − | 0.0288675i | ||||
\(901\) | 906.627 | + | 523.442i | 1.00625 | + | 0.580956i | ||||
\(902\) | 136.234i | 0.151035i | ||||||||
\(903\) | −28.4579 | + | 94.2865i | −0.0315149 | + | 0.104415i | ||||
\(904\) | 242.737 | 0.268515 | ||||||||
\(905\) | −10.3368 | + | 17.9039i | −0.0114219 | + | 0.0197833i | ||||
\(906\) | −388.265 | + | 224.165i | −0.428549 | + | 0.247423i | ||||
\(907\) | −498.599 | − | 863.598i | −0.549723 | − | 0.952148i | −0.998293 | − | 0.0584006i | \(-0.981400\pi\) |
0.448570 | − | 0.893748i | \(-0.351933\pi\) | |||||||
\(908\) | −292.784 | − | 169.039i | −0.322449 | − | 0.186166i | ||||
\(909\) | 334.126i | 0.367575i | ||||||||
\(910\) | −114.597 | − | 34.5882i | −0.125931 | − | 0.0380090i | ||||
\(911\) | −758.955 | −0.833101 | −0.416550 | − | 0.909113i | \(-0.636761\pi\) | ||||
−0.416550 | + | 0.909113i | \(0.636761\pi\) | |||||||
\(912\) | 31.8434 | − | 55.1543i | 0.0349160 | − | 0.0604762i | ||||
\(913\) | −246.381 | + | 142.248i | −0.269859 | + | 0.155803i | ||||
\(914\) | 299.281 | + | 518.370i | 0.327441 | + | 0.567144i | ||||
\(915\) | 79.7498 | + | 46.0435i | 0.0871582 | + | 0.0503208i | ||||
\(916\) | − | 572.035i | − | 0.624492i | ||||||
\(917\) | −809.393 | + | 189.915i | −0.882653 | + | 0.207104i | ||||
\(918\) | −73.9147 | −0.0805171 | ||||||||
\(919\) | −703.781 | + | 1218.99i | −0.765812 | + | 1.32643i | 0.174004 | + | 0.984745i | \(0.444329\pi\) |
−0.939816 | + | 0.341681i | \(0.889004\pi\) | |||||||
\(920\) | −5.04610 | + | 2.91337i | −0.00548489 | + | 0.00316670i | ||||
\(921\) | −236.115 | − | 408.964i | −0.256369 | − | 0.444043i | ||||
\(922\) | 577.771 | + | 333.576i | 0.626649 | + | 0.361796i | ||||
\(923\) | 97.1324i | 0.105236i | ||||||||
\(924\) | −30.5262 | − | 32.5015i | −0.0330370 | − | 0.0351748i | ||||
\(925\) | −36.4194 | −0.0393723 | ||||||||
\(926\) | −137.192 | + | 237.623i | −0.148155 | + | 0.256613i | ||||
\(927\) | −122.054 | + | 70.4679i | −0.131666 | + | 0.0760171i | ||||
\(928\) | 35.5175 | + | 61.5182i | 0.0382732 | + | 0.0662911i | ||||
\(929\) | 314.575 | + | 181.620i | 0.338617 | + | 0.195500i | 0.659660 | − | 0.751564i | \(-0.270700\pi\) |
−0.321044 | + | 0.947064i | \(0.604034\pi\) | |||||||
\(930\) | 228.869i | 0.246096i | ||||||||
\(931\) | −249.198 | + | 375.213i | −0.267667 | + | 0.403021i | ||||
\(932\) | −363.677 | −0.390212 | ||||||||
\(933\) | 65.4476 | − | 113.359i | 0.0701475 | − | 0.121499i | ||||
\(934\) | −13.8728 | + | 8.00946i | −0.0148531 | + | 0.00857544i | ||||
\(935\) | 20.6790 | + | 35.8171i | 0.0221166 | + | 0.0383071i | ||||
\(936\) | 39.7379 | + | 22.9427i | 0.0424551 | + | 0.0245114i | ||||
\(937\) | 401.784i | 0.428798i | 0.976746 | + | 0.214399i | \(0.0687793\pi\) | ||||
−0.976746 | + | 0.214399i | \(0.931221\pi\) | |||||||
\(938\) | 107.709 | − | 101.163i | 0.114829 | − | 0.107850i | ||||
\(939\) | −110.211 | −0.117371 | ||||||||
\(940\) | 75.9407 | − | 131.533i | 0.0807880 | − | 0.139929i | ||||
\(941\) | −731.276 | + | 422.202i | −0.777126 | + | 0.448674i | −0.835411 | − | 0.549626i | \(-0.814770\pi\) |
0.0582845 | + | 0.998300i | \(0.481437\pi\) | |||||||
\(942\) | 361.649 | + | 626.394i | 0.383916 | + | 0.664962i | ||||
\(943\) | 41.7980 | + | 24.1321i | 0.0443245 | + | 0.0255908i | ||||
\(944\) | 58.1591i | 0.0616092i | ||||||||
\(945\) | −18.5792 | − | 79.1822i | −0.0196605 | − | 0.0837906i | ||||
\(946\) | −21.1241 | −0.0223299 | ||||||||
\(947\) | −144.083 | + | 249.560i | −0.152147 | + | 0.263527i | −0.932017 | − | 0.362415i | \(-0.881952\pi\) |
0.779869 | + | 0.625942i | \(0.215285\pi\) | |||||||
\(948\) | −242.810 | + | 140.186i | −0.256128 | + | 0.147876i | ||||
\(949\) | 336.266 | + | 582.429i | 0.354337 | + | 0.613729i | ||||
\(950\) | −56.2916 | − | 32.5000i | −0.0592543 | − | 0.0342105i | ||||
\(951\) | 26.7638i | 0.0281428i | ||||||||
\(952\) | −57.5438 | + | 190.654i | −0.0604452 | + | 0.200266i | ||||
\(953\) | 293.080 | 0.307534 | 0.153767 | − | 0.988107i | \(-0.450859\pi\) | ||||
0.153767 | + | 0.988107i | \(0.450859\pi\) | |||||||
\(954\) | 220.786 | − | 382.412i | 0.231431 | − | 0.400851i | ||||
\(955\) | 264.929 | − | 152.957i | 0.277413 | − | 0.160164i | ||||
\(956\) | 382.489 | + | 662.490i | 0.400093 | + | 0.692981i | ||||
\(957\) | 34.6362 | + | 19.9972i | 0.0361924 | + | 0.0208957i | ||||
\(958\) | 894.769i | 0.933997i | ||||||||
\(959\) | −543.839 | − | 164.144i | −0.567090 | − | 0.171161i | ||||
\(960\) | 30.9839 | 0.0322749 | ||||||||
\(961\) | 392.517 | − | 679.859i | 0.408446 | − | 0.707450i | ||||
\(962\) | 48.2411 | − | 27.8520i | 0.0501466 | − | 0.0289522i | ||||
\(963\) | −278.523 | − | 482.415i | −0.289224 | − | 0.500950i | ||||
\(964\) | 360.647 | + | 208.220i | 0.374115 | + | 0.215995i | ||||
\(965\) | 818.119i | 0.847792i | ||||||||
\(966\) | −15.3791 | + | 3.60853i | −0.0159204 | + | 0.00373554i | ||||
\(967\) | 68.4003 | 0.0707345 | 0.0353673 | − | 0.999374i | \(-0.488740\pi\) | ||||
0.0353673 | + | 0.999374i | \(0.488740\pi\) | |||||||
\(968\) | −166.338 | + | 288.106i | −0.171837 | + | 0.297630i | ||||
\(969\) | −138.693 | + | 80.0742i | −0.143130 | + | 0.0826359i | ||||
\(970\) | 139.415 | + | 241.473i | 0.143726 | + | 0.248942i | ||||
\(971\) | 253.215 | + | 146.194i | 0.260777 | + | 0.150560i | 0.624689 | − | 0.780874i | \(-0.285226\pi\) |
−0.363912 | + | 0.931433i | \(0.618559\pi\) | |||||||
\(972\) | 31.1769i | 0.0320750i | ||||||||
\(973\) | −1189.98 | − | 1266.98i | −1.22300 | − | 1.30213i | ||||
\(974\) | 89.1243 | 0.0915034 | ||||||||
\(975\) | 23.4158 | − | 40.5574i | 0.0240162 | − | 0.0415973i | ||||
\(976\) | −82.3652 | + | 47.5536i | −0.0843906 | + | 0.0487229i | ||||
\(977\) | 538.697 | + | 933.051i | 0.551379 | + | 0.955016i | 0.998175 | + | 0.0603807i | \(0.0192315\pi\) |
−0.446796 | + | 0.894636i | \(0.647435\pi\) | |||||||
\(978\) | −251.008 | − | 144.919i | −0.256654 | − | 0.148179i | ||||
\(979\) | 125.265i | 0.127952i | ||||||||
\(980\) | −218.705 | − | 13.7220i | −0.223168 | − | 0.0140020i | ||||
\(981\) | −258.869 | −0.263883 | ||||||||
\(982\) | 184.620 | − | 319.771i | 0.188004 | − | 0.325632i | ||||
\(983\) | 1354.95 | − | 782.282i | 1.37839 | − | 0.795811i | 0.386420 | − | 0.922323i | \(-0.373711\pi\) |
0.991965 | + | 0.126511i | \(0.0403781\pi\) | |||||||
\(984\) | −128.323 | − | 222.262i | −0.130410 | − | 0.225876i | ||||
\(985\) | −377.471 | − | 217.933i | −0.383219 | − | 0.221252i | ||||
\(986\) | − | 178.627i | − | 0.181163i | ||||||
\(987\) | 300.139 | − | 281.898i | 0.304092 | − | 0.285610i | ||||
\(988\) | 99.4184 | 0.100626 | ||||||||
\(989\) | −3.74186 | + | 6.48110i | −0.00378348 | + | 0.00655318i | ||||
\(990\) | 15.1075 | − | 8.72232i | 0.0152601 | − | 0.00881043i | ||||
\(991\) | −726.967 | − | 1259.14i | −0.733570 | − | 1.27058i | −0.955348 | − | 0.295483i | \(-0.904520\pi\) |
0.221779 | − | 0.975097i | \(-0.428814\pi\) | |||||||
\(992\) | −204.707 | − | 118.187i | −0.206358 | − | 0.119141i | ||||
\(993\) | − | 646.192i | − | 0.650747i | ||||||
\(994\) | 40.6191 | + | 173.114i | 0.0408643 | + | 0.174159i | ||||
\(995\) | −542.996 | −0.545724 | ||||||||
\(996\) | 267.976 | − | 464.148i | 0.269052 | − | 0.466012i | ||||
\(997\) | −701.023 | + | 404.736i | −0.703133 | + | 0.405954i | −0.808513 | − | 0.588478i | \(-0.799727\pi\) |
0.105380 | + | 0.994432i | \(0.466394\pi\) | |||||||
\(998\) | 310.394 | + | 537.618i | 0.311016 | + | 0.538695i | ||||
\(999\) | 32.7775 | + | 18.9241i | 0.0328103 | + | 0.0189430i |
(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 | 210.3.o.a.61.4 | yes | 8 | |
3.2 | odd | 2 | 630.3.v.b.271.1 | 8 | |||
5.2 | odd | 4 | 1050.3.q.c.649.6 | 16 | |||
5.3 | odd | 4 | 1050.3.q.c.649.3 | 16 | |||
5.4 | even | 2 | 1050.3.p.b.901.1 | 8 | |||
7.2 | even | 3 | 1470.3.f.a.391.3 | 8 | |||
7.3 | odd | 6 | inner | 210.3.o.a.31.4 | ✓ | 8 | |
7.5 | odd | 6 | 1470.3.f.a.391.2 | 8 | |||
21.17 | even | 6 | 630.3.v.b.451.1 | 8 | |||
35.3 | even | 12 | 1050.3.q.c.199.6 | 16 | |||
35.17 | even | 12 | 1050.3.q.c.199.3 | 16 | |||
35.24 | odd | 6 | 1050.3.p.b.451.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.o.a.31.4 | ✓ | 8 | 7.3 | odd | 6 | inner | |
210.3.o.a.61.4 | yes | 8 | 1.1 | even | 1 | trivial | |
630.3.v.b.271.1 | 8 | 3.2 | odd | 2 | |||
630.3.v.b.451.1 | 8 | 21.17 | even | 6 | |||
1050.3.p.b.451.1 | 8 | 35.24 | odd | 6 | |||
1050.3.p.b.901.1 | 8 | 5.4 | even | 2 | |||
1050.3.q.c.199.3 | 16 | 35.17 | even | 12 | |||
1050.3.q.c.199.6 | 16 | 35.3 | even | 12 | |||
1050.3.q.c.649.3 | 16 | 5.3 | odd | 4 | |||
1050.3.q.c.649.6 | 16 | 5.2 | odd | 4 | |||
1470.3.f.a.391.2 | 8 | 7.5 | odd | 6 | |||
1470.3.f.a.391.3 | 8 | 7.2 | even | 3 |