Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [175,4,Mod(29,175)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(175, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("175.29");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 175.n (of order \(10\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.3253342510\) |
Analytic rank: | \(0\) |
Dimension: | \(184\) |
Relative dimension: | \(46\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 29.12 | ||
Character | \(\chi\) | \(=\) | 175.29 |
Dual form | 175.4.n.a.169.12 |
$q$-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 \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{10}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.14628 | − | 1.02229i | −1.11238 | − | 0.361433i | −0.305524 | − | 0.952184i | \(-0.598832\pi\) |
−0.806854 | + | 0.590751i | \(0.798832\pi\) | |||||||
\(3\) | 5.97409 | − | 8.22263i | 1.14971 | − | 1.58245i | 0.406111 | − | 0.913824i | \(-0.366885\pi\) |
0.743603 | − | 0.668621i | \(-0.233115\pi\) | |||||||
\(4\) | 2.38186 | + | 1.73053i | 0.297733 | + | 0.216316i | ||||
\(5\) | 9.51619 | + | 5.86874i | 0.851154 | + | 0.524916i | ||||
\(6\) | −27.2020 | + | 19.7634i | −1.85086 | + | 1.34473i | ||||
\(7\) | 7.00000i | 0.377964i | ||||||||
\(8\) | 9.83115 | + | 13.5314i | 0.434479 | + | 0.598010i | ||||
\(9\) | −23.5784 | − | 72.5669i | −0.873274 | − | 2.68766i | ||||
\(10\) | −23.9411 | − | 28.1930i | −0.757083 | − | 0.891540i | ||||
\(11\) | 9.04891 | − | 27.8497i | 0.248032 | − | 0.763363i | −0.747091 | − | 0.664721i | \(-0.768550\pi\) |
0.995123 | − | 0.0986415i | \(-0.0314497\pi\) | |||||||
\(12\) | 28.4589 | − | 9.24687i | 0.684615 | − | 0.222445i | ||||
\(13\) | 63.2889 | − | 20.5638i | 1.35024 | − | 0.438721i | 0.457470 | − | 0.889225i | \(-0.348756\pi\) |
0.892774 | + | 0.450504i | \(0.148756\pi\) | |||||||
\(14\) | 7.15602 | − | 22.0240i | 0.136609 | − | 0.420439i | ||||
\(15\) | 105.107 | − | 43.1877i | 1.80923 | − | 0.743401i | ||||
\(16\) | −24.3769 | − | 75.0243i | −0.380888 | − | 1.17225i | ||||
\(17\) | −58.0070 | − | 79.8398i | −0.827575 | − | 1.13906i | −0.988370 | − | 0.152071i | \(-0.951406\pi\) |
0.160795 | − | 0.986988i | \(-0.448594\pi\) | |||||||
\(18\) | 252.420i | 3.30532i | ||||||||
\(19\) | −54.7786 | + | 39.7990i | −0.661425 | + | 0.480553i | −0.867144 | − | 0.498058i | \(-0.834047\pi\) |
0.205719 | + | 0.978611i | \(0.434047\pi\) | |||||||
\(20\) | 12.5103 | + | 30.4465i | 0.139869 | + | 0.340403i | ||||
\(21\) | 57.5584 | + | 41.8186i | 0.598108 | + | 0.434551i | ||||
\(22\) | −56.9408 | + | 78.3722i | −0.551810 | + | 0.759501i | ||||
\(23\) | 13.5376 | + | 4.39862i | 0.122729 | + | 0.0398772i | 0.369738 | − | 0.929136i | \(-0.379448\pi\) |
−0.247008 | + | 0.969013i | \(0.579448\pi\) | |||||||
\(24\) | 169.996 | 1.44584 | ||||||||
\(25\) | 56.1158 | + | 111.696i | 0.448926 | + | 0.893569i | ||||
\(26\) | −220.147 | −1.66055 | ||||||||
\(27\) | −476.560 | − | 154.844i | −3.39682 | − | 1.10369i | ||||
\(28\) | −12.1137 | + | 16.6730i | −0.0817596 | + | 0.112532i | ||||
\(29\) | 56.0150 | + | 40.6973i | 0.358680 | + | 0.260596i | 0.752501 | − | 0.658591i | \(-0.228847\pi\) |
−0.393821 | + | 0.919187i | \(0.628847\pi\) | |||||||
\(30\) | −374.846 | + | 28.4310i | −2.28124 | + | 0.173025i | ||||
\(31\) | 129.176 | − | 93.8515i | 0.748407 | − | 0.543749i | −0.146926 | − | 0.989148i | \(-0.546938\pi\) |
0.895333 | + | 0.445398i | \(0.146938\pi\) | |||||||
\(32\) | 127.161i | 0.702474i | ||||||||
\(33\) | −174.938 | − | 240.782i | −0.922814 | − | 1.27015i | ||||
\(34\) | 100.887 | + | 310.498i | 0.508882 | + | 1.56618i | ||||
\(35\) | −41.0812 | + | 66.6133i | −0.198400 | + | 0.321706i | ||||
\(36\) | 69.4182 | − | 213.647i | 0.321381 | − | 0.989108i | ||||
\(37\) | −189.138 | + | 61.4548i | −0.840382 | + | 0.273057i | −0.697412 | − | 0.716670i | \(-0.745665\pi\) |
−0.142970 | + | 0.989727i | \(0.545665\pi\) | |||||||
\(38\) | 213.035 | − | 69.2192i | 0.909443 | − | 0.295496i | ||||
\(39\) | 209.005 | − | 643.251i | 0.858142 | − | 2.64109i | ||||
\(40\) | 14.1427 | + | 186.464i | 0.0559041 | + | 0.737063i | ||||
\(41\) | 56.8400 | + | 174.936i | 0.216510 | + | 0.666350i | 0.999043 | + | 0.0437403i | \(0.0139274\pi\) |
−0.782533 | + | 0.622609i | \(0.786073\pi\) | |||||||
\(42\) | −138.344 | − | 190.414i | −0.508261 | − | 0.699561i | ||||
\(43\) | − | 231.141i | − | 0.819735i | −0.912145 | − | 0.409868i | \(-0.865575\pi\) | ||
0.912145 | − | 0.409868i | \(-0.134425\pi\) | |||||||
\(44\) | 69.7478 | − | 50.6748i | 0.238975 | − | 0.173625i | ||||
\(45\) | 201.499 | − | 828.936i | 0.667506 | − | 2.74601i | ||||
\(46\) | −38.0963 | − | 27.6786i | −0.122109 | − | 0.0887170i | ||||
\(47\) | 0.0431285 | − | 0.0593612i | 0.000133850 | − | 0.000184228i | −0.808950 | − | 0.587877i | \(-0.799964\pi\) |
0.809084 | + | 0.587693i | \(0.199964\pi\) | |||||||
\(48\) | −762.526 | − | 247.760i | −2.29294 | − | 0.745021i | ||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | −62.3704 | − | 408.794i | −0.176410 | − | 1.15624i | ||||
\(51\) | −1003.03 | −2.75397 | ||||||||
\(52\) | 186.332 | + | 60.5428i | 0.496914 | + | 0.161457i | ||||
\(53\) | −280.400 | + | 385.938i | −0.726715 | + | 1.00024i | 0.272559 | + | 0.962139i | \(0.412130\pi\) |
−0.999274 | + | 0.0380985i | \(0.987870\pi\) | |||||||
\(54\) | 1341.10 | + | 974.363i | 3.37963 | + | 2.45545i | ||||
\(55\) | 249.554 | − | 211.917i | 0.611814 | − | 0.519544i | ||||
\(56\) | −94.7199 | + | 68.8180i | −0.226026 | + | 0.164218i | ||||
\(57\) | 688.187i | 1.59917i | ||||||||
\(58\) | −134.635 | − | 185.308i | −0.304800 | − | 0.419521i | ||||
\(59\) | 156.640 | + | 482.089i | 0.345641 | + | 1.06377i | 0.961240 | + | 0.275714i | \(0.0889143\pi\) |
−0.615599 | + | 0.788060i | \(0.711086\pi\) | |||||||
\(60\) | 325.088 | + | 79.0231i | 0.699478 | + | 0.170031i | ||||
\(61\) | 161.899 | − | 498.273i | 0.339820 | − | 1.04586i | −0.624479 | − | 0.781042i | \(-0.714689\pi\) |
0.964299 | − | 0.264817i | \(-0.0853114\pi\) | |||||||
\(62\) | −502.366 | + | 163.228i | −1.02904 | + | 0.334355i | ||||
\(63\) | 507.968 | − | 165.049i | 1.01584 | − | 0.330067i | ||||
\(64\) | −65.0192 | + | 200.109i | −0.126991 | + | 0.390837i | ||||
\(65\) | 722.952 | + | 175.737i | 1.37956 | + | 0.335346i | ||||
\(66\) | 304.257 | + | 936.405i | 0.567445 | + | 1.74642i | ||||
\(67\) | −126.172 | − | 173.661i | −0.230066 | − | 0.316658i | 0.678340 | − | 0.734748i | \(-0.262700\pi\) |
−0.908406 | + | 0.418090i | \(0.862700\pi\) | |||||||
\(68\) | − | 290.550i | − | 0.518153i | ||||||
\(69\) | 117.043 | − | 85.0366i | 0.204207 | − | 0.148365i | ||||
\(70\) | 197.351 | − | 167.587i | 0.336971 | − | 0.286150i | ||||
\(71\) | 247.818 | + | 180.050i | 0.414234 | + | 0.300958i | 0.775314 | − | 0.631577i | \(-0.217592\pi\) |
−0.361080 | + | 0.932535i | \(0.617592\pi\) | |||||||
\(72\) | 750.129 | − | 1032.46i | 1.22783 | − | 1.68996i | ||||
\(73\) | 139.708 | + | 45.3939i | 0.223994 | + | 0.0727801i | 0.418864 | − | 0.908049i | \(-0.362428\pi\) |
−0.194870 | + | 0.980829i | \(0.562428\pi\) | |||||||
\(74\) | 657.906 | 1.03351 | ||||||||
\(75\) | 1253.68 | + | 205.863i | 1.93016 | + | 0.316947i | ||||
\(76\) | −199.348 | −0.300879 | ||||||||
\(77\) | 194.948 | + | 63.3423i | 0.288524 | + | 0.0937471i | ||||
\(78\) | −1315.17 | + | 1810.18i | −1.90916 | + | 2.62773i | ||||
\(79\) | 335.991 | + | 244.112i | 0.478506 | + | 0.347655i | 0.800747 | − | 0.599003i | \(-0.204436\pi\) |
−0.322241 | + | 0.946658i | \(0.604436\pi\) | |||||||
\(80\) | 208.323 | − | 857.007i | 0.291140 | − | 1.19770i | ||||
\(81\) | −2453.55 | + | 1782.61i | −3.36564 | + | 2.44528i | ||||
\(82\) | − | 608.503i | − | 0.819487i | ||||||
\(83\) | 410.942 | + | 565.613i | 0.543455 | + | 0.748001i | 0.989106 | − | 0.147206i | \(-0.0470279\pi\) |
−0.445651 | + | 0.895207i | \(0.647028\pi\) | |||||||
\(84\) | 64.7281 | + | 199.212i | 0.0840763 | + | 0.258760i | ||||
\(85\) | −83.4468 | − | 1100.20i | −0.106483 | − | 1.40392i | ||||
\(86\) | −236.292 | + | 727.233i | −0.296280 | + | 0.911855i | ||||
\(87\) | 669.277 | − | 217.461i | 0.824759 | − | 0.267980i | ||||
\(88\) | 465.806 | − | 151.350i | 0.564263 | − | 0.183340i | ||||
\(89\) | 126.174 | − | 388.322i | 0.150274 | − | 0.462495i | −0.847378 | − | 0.530991i | \(-0.821820\pi\) |
0.997651 | + | 0.0684955i | \(0.0218199\pi\) | |||||||
\(90\) | −1481.38 | + | 2402.07i | −1.73502 | + | 2.81334i | ||||
\(91\) | 143.947 | + | 443.022i | 0.165821 | + | 0.510344i | ||||
\(92\) | 24.6327 | + | 33.9040i | 0.0279145 | + | 0.0384211i | ||||
\(93\) | − | 1622.84i | − | 1.80947i | ||||||
\(94\) | −0.196378 | + | 0.142677i | −0.000215478 | + | 0.000156554i | ||||
\(95\) | −754.854 | + | 57.2534i | −0.815225 | + | 0.0618324i | ||||
\(96\) | 1045.60 | + | 759.674i | 1.11163 | + | 0.807645i | ||||
\(97\) | 945.961 | − | 1302.00i | 0.990183 | − | 1.36287i | 0.0590244 | − | 0.998257i | \(-0.481201\pi\) |
0.931159 | − | 0.364614i | \(-0.118799\pi\) | |||||||
\(98\) | 154.168 | + | 50.0921i | 0.158911 | + | 0.0516333i | ||||
\(99\) | −2234.32 | −2.26826 | ||||||||
\(100\) | −59.6328 | + | 363.155i | −0.0596328 | + | 0.363155i | ||||
\(101\) | 341.986 | 0.336920 | 0.168460 | − | 0.985709i | \(-0.446121\pi\) | ||||
0.168460 | + | 0.985709i | \(0.446121\pi\) | |||||||
\(102\) | 3155.82 | + | 1025.39i | 3.06346 | + | 0.995378i | ||||
\(103\) | 310.935 | − | 427.965i | 0.297450 | − | 0.409404i | −0.633966 | − | 0.773361i | \(-0.718574\pi\) |
0.931416 | + | 0.363956i | \(0.118574\pi\) | |||||||
\(104\) | 900.459 | + | 654.222i | 0.849013 | + | 0.616844i | ||||
\(105\) | 302.314 | + | 735.749i | 0.280979 | + | 0.683826i | ||||
\(106\) | 1276.76 | − | 927.618i | 1.16990 | − | 0.849983i | ||||
\(107\) | 1411.17i | 1.27498i | 0.770457 | + | 0.637492i | \(0.220028\pi\) | ||||
−0.770457 | + | 0.637492i | \(0.779972\pi\) | |||||||
\(108\) | −867.140 | − | 1193.52i | −0.772598 | − | 1.06339i | ||||
\(109\) | −365.196 | − | 1123.96i | −0.320912 | − | 0.987666i | −0.973252 | − | 0.229740i | \(-0.926213\pi\) |
0.652340 | − | 0.757926i | \(-0.273787\pi\) | |||||||
\(110\) | −1001.81 | + | 411.635i | −0.868349 | + | 0.356798i | ||||
\(111\) | −624.609 | + | 1922.35i | −0.534102 | + | 1.64380i | ||||
\(112\) | 525.170 | − | 170.638i | 0.443070 | − | 0.143962i | ||||
\(113\) | −1799.19 | + | 584.593i | −1.49782 | + | 0.486671i | −0.939381 | − | 0.342874i | \(-0.888600\pi\) |
−0.558439 | + | 0.829546i | \(0.688600\pi\) | |||||||
\(114\) | 703.525 | − | 2165.23i | 0.577993 | − | 1.77888i | ||||
\(115\) | 103.012 | + | 121.307i | 0.0835295 | + | 0.0983643i | ||||
\(116\) | 62.9924 | + | 193.871i | 0.0504198 | + | 0.155176i | ||||
\(117\) | −2984.50 | − | 4107.81i | −2.35827 | − | 3.24588i | ||||
\(118\) | − | 1676.92i | − | 1.30824i | ||||||
\(119\) | 558.879 | − | 406.049i | 0.430524 | − | 0.312794i | ||||
\(120\) | 1617.71 | + | 997.662i | 1.23064 | + | 0.758947i | ||||
\(121\) | 383.080 | + | 278.324i | 0.287814 | + | 0.209109i | ||||
\(122\) | −1018.76 | + | 1402.20i | −0.756016 | + | 1.04057i | ||||
\(123\) | 1778.00 | + | 577.706i | 1.30339 | + | 0.423496i | ||||
\(124\) | 470.091 | 0.340447 | ||||||||
\(125\) | −121.507 | + | 1392.25i | −0.0869431 | + | 0.996213i | ||||
\(126\) | −1766.94 | −1.24930 | ||||||||
\(127\) | 312.011 | + | 101.379i | 0.218004 | + | 0.0708339i | 0.415983 | − | 0.909372i | \(-0.363438\pi\) |
−0.197979 | + | 0.980206i | \(0.563438\pi\) | |||||||
\(128\) | 1007.09 | − | 1386.14i | 0.695427 | − | 0.957174i | ||||
\(129\) | −1900.58 | − | 1380.85i | −1.29719 | − | 0.942461i | ||||
\(130\) | −2094.96 | − | 1291.98i | −1.41338 | − | 0.871649i | ||||
\(131\) | 1988.57 | − | 1444.78i | 1.32627 | − | 0.963594i | 0.326442 | − | 0.945217i | \(-0.394150\pi\) |
0.999831 | − | 0.0183770i | \(-0.00584990\pi\) | |||||||
\(132\) | − | 876.246i | − | 0.577783i | ||||||
\(133\) | −278.593 | − | 383.450i | −0.181632 | − | 0.249995i | ||||
\(134\) | 219.441 | + | 675.371i | 0.141469 | + | 0.435397i | ||||
\(135\) | −3626.30 | − | 4270.33i | −2.31187 | − | 2.72246i | ||||
\(136\) | 510.070 | − | 1569.83i | 0.321604 | − | 0.989796i | ||||
\(137\) | −1848.52 | + | 600.621i | −1.15277 | + | 0.374558i | −0.822187 | − | 0.569218i | \(-0.807246\pi\) |
−0.330585 | + | 0.943776i | \(0.607246\pi\) | |||||||
\(138\) | −455.181 | + | 147.897i | −0.280780 | + | 0.0912308i | ||||
\(139\) | 216.178 | − | 665.327i | 0.131914 | − | 0.405988i | −0.863184 | − | 0.504890i | \(-0.831533\pi\) |
0.995097 | + | 0.0989020i | \(0.0315330\pi\) | |||||||
\(140\) | −213.126 | + | 87.5719i | −0.128660 | + | 0.0528655i | ||||
\(141\) | −0.230452 | − | 0.709258i | −0.000137642 | − | 0.000423619i | ||||
\(142\) | −595.641 | − | 819.830i | −0.352008 | − | 0.484497i | ||||
\(143\) | − | 1948.65i | − | 1.13954i | ||||||
\(144\) | −4869.51 | + | 3537.90i | −2.81800 | + | 2.04740i | ||||
\(145\) | 294.208 | + | 716.021i | 0.168501 | + | 0.410085i | ||||
\(146\) | −393.155 | − | 285.644i | −0.222861 | − | 0.161918i | ||||
\(147\) | −292.730 | + | 402.909i | −0.164245 | + | 0.226064i | ||||
\(148\) | −556.851 | − | 180.932i | −0.309276 | − | 0.100490i | ||||
\(149\) | 3079.53 | 1.69319 | 0.846594 | − | 0.532239i | \(-0.178649\pi\) | ||||
0.846594 | + | 0.532239i | \(0.178649\pi\) | |||||||
\(150\) | −3733.96 | − | 1929.32i | −2.03251 | − | 1.05019i | ||||
\(151\) | 2579.27 | 1.39005 | 0.695026 | − | 0.718985i | \(-0.255393\pi\) | ||||
0.695026 | + | 0.718985i | \(0.255393\pi\) | |||||||
\(152\) | −1077.07 | − | 349.962i | −0.574751 | − | 0.186748i | ||||
\(153\) | −4426.01 | + | 6091.88i | −2.33871 | + | 3.21895i | ||||
\(154\) | −548.606 | − | 398.585i | −0.287064 | − | 0.208564i | ||||
\(155\) | 1780.05 | − | 135.011i | 0.922432 | − | 0.0699637i | ||||
\(156\) | 1610.98 | − | 1170.45i | 0.826807 | − | 0.600710i | ||||
\(157\) | 2160.06i | 1.09804i | 0.835810 | + | 0.549018i | \(0.184998\pi\) | ||||
−0.835810 | + | 0.549018i | \(0.815002\pi\) | |||||||
\(158\) | −807.569 | − | 1111.52i | −0.406625 | − | 0.559671i | ||||
\(159\) | 1498.29 | + | 4611.25i | 0.747307 | + | 2.29997i | ||||
\(160\) | −746.277 | + | 1210.09i | −0.368740 | + | 0.597914i | ||||
\(161\) | −30.7903 | + | 94.7629i | −0.0150722 | + | 0.0463874i | ||||
\(162\) | 9541.89 | − | 3100.35i | 4.62767 | − | 1.50362i | ||||
\(163\) | 990.937 | − | 321.975i | 0.476173 | − | 0.154718i | −0.0610910 | − | 0.998132i | \(-0.519458\pi\) |
0.537264 | + | 0.843414i | \(0.319458\pi\) | |||||||
\(164\) | −167.345 | + | 515.036i | −0.0796797 | + | 0.245229i | ||||
\(165\) | −251.660 | − | 3318.00i | −0.118738 | − | 1.56549i | ||||
\(166\) | −714.718 | − | 2199.68i | −0.334174 | − | 1.02848i | ||||
\(167\) | 1367.96 | + | 1882.83i | 0.633866 | + | 0.872442i | 0.998270 | − | 0.0587992i | \(-0.0187272\pi\) |
−0.364404 | + | 0.931241i | \(0.618727\pi\) | |||||||
\(168\) | 1189.97i | 0.546478i | ||||||||
\(169\) | 1805.20 | − | 1311.55i | 0.821666 | − | 0.596975i | ||||
\(170\) | −862.174 | + | 3546.84i | −0.388975 | + | 1.60018i | ||||
\(171\) | 4179.68 | + | 3036.72i | 1.86917 | + | 1.35803i | ||||
\(172\) | 399.995 | − | 550.546i | 0.177322 | − | 0.244062i | ||||
\(173\) | −1631.08 | − | 529.969i | −0.716812 | − | 0.232906i | −0.0721713 | − | 0.997392i | \(-0.522993\pi\) |
−0.644640 | + | 0.764486i | \(0.722993\pi\) | |||||||
\(174\) | −2328.04 | −1.01430 | ||||||||
\(175\) | −781.873 | + | 392.811i | −0.337737 | + | 0.169678i | ||||
\(176\) | −2309.98 | −0.989327 | ||||||||
\(177\) | 4899.82 | + | 1592.05i | 2.08075 | + | 0.676077i | ||||
\(178\) | −793.955 | + | 1092.78i | −0.334323 | + | 0.460155i | ||||
\(179\) | 608.899 | + | 442.391i | 0.254253 | + | 0.184726i | 0.707610 | − | 0.706604i | \(-0.249774\pi\) |
−0.453357 | + | 0.891329i | \(0.649774\pi\) | |||||||
\(180\) | 1914.44 | − | 1625.71i | 0.792743 | − | 0.673186i | ||||
\(181\) | −3023.53 | + | 2196.73i | −1.24164 | + | 0.902107i | −0.997707 | − | 0.0676843i | \(-0.978439\pi\) |
−0.243937 | + | 0.969791i | \(0.578439\pi\) | |||||||
\(182\) | − | 1541.03i | − | 0.627629i | ||||||
\(183\) | −3129.92 | − | 4307.96i | −1.26432 | − | 1.74018i | ||||
\(184\) | 73.5702 | + | 226.426i | 0.0294765 | + | 0.0907192i | ||||
\(185\) | −2160.54 | − | 525.188i | −0.858627 | − | 0.208717i | ||||
\(186\) | −1659.01 | + | 5105.91i | −0.654003 | + | 2.01281i | ||||
\(187\) | −2748.41 | + | 893.014i | −1.07478 | + | 0.349217i | ||||
\(188\) | 0.205452 | − | 0.0667555i | 7.97029e−5 | − | 2.58970e-5i | ||||
\(189\) | 1083.91 | − | 3335.92i | 0.417157 | − | 1.28388i | ||||
\(190\) | 2433.51 | + | 591.543i | 0.929186 | + | 0.225869i | ||||
\(191\) | 1542.09 | + | 4746.06i | 0.584197 | + | 1.79797i | 0.602471 | + | 0.798140i | \(0.294183\pi\) |
−0.0182745 | + | 0.999833i | \(0.505817\pi\) | |||||||
\(192\) | 1256.99 | + | 1730.10i | 0.472475 | + | 0.650307i | ||||
\(193\) | 957.694i | 0.357183i | 0.983923 | + | 0.178592i | \(0.0571541\pi\) | ||||
−0.983923 | + | 0.178592i | \(0.942846\pi\) | |||||||
\(194\) | −4307.28 | + | 3129.42i | −1.59404 | + | 1.15814i | ||||
\(195\) | 5764.00 | − | 4894.70i | 2.11676 | − | 1.79752i | ||||
\(196\) | −116.711 | − | 84.7957i | −0.0425333 | − | 0.0309022i | ||||
\(197\) | 751.869 | − | 1034.86i | 0.271921 | − | 0.374267i | −0.651116 | − | 0.758978i | \(-0.725699\pi\) |
0.923037 | + | 0.384711i | \(0.125699\pi\) | |||||||
\(198\) | 7029.80 | + | 2284.12i | 2.52316 | + | 0.819825i | ||||
\(199\) | −947.559 | −0.337541 | −0.168771 | − | 0.985655i | \(-0.553980\pi\) | ||||
−0.168771 | + | 0.985655i | \(0.553980\pi\) | |||||||
\(200\) | −959.723 | + | 1857.43i | −0.339313 | + | 0.656699i | ||||
\(201\) | −2181.72 | −0.765604 | ||||||||
\(202\) | −1075.98 | − | 349.608i | −0.374782 | − | 0.121774i | ||||
\(203\) | −284.881 | + | 392.105i | −0.0984962 | + | 0.135568i | ||||
\(204\) | −2389.09 | − | 1735.77i | −0.819949 | − | 0.595728i | ||||
\(205\) | −485.751 | + | 1998.30i | −0.165494 | + | 0.680816i | ||||
\(206\) | −1415.79 | + | 1028.63i | −0.478849 | + | 0.347904i | ||||
\(207\) | − | 1086.09i | − | 0.364679i | ||||||
\(208\) | −3085.57 | − | 4246.92i | −1.02858 | − | 1.41573i | ||||
\(209\) | 612.702 | + | 1885.70i | 0.202782 | + | 0.624100i | ||||
\(210\) | −199.017 | − | 2623.92i | −0.0653975 | − | 0.862228i | ||||
\(211\) | −3.84433 | + | 11.8316i | −0.00125429 | + | 0.00386029i | −0.951682 | − | 0.307086i | \(-0.900646\pi\) |
0.950427 | + | 0.310947i | \(0.100646\pi\) | |||||||
\(212\) | −1335.75 | + | 434.011i | −0.432734 | + | 0.140604i | ||||
\(213\) | 2960.97 | − | 962.078i | 0.952500 | − | 0.309486i | ||||
\(214\) | 1442.63 | − | 4439.95i | 0.460822 | − | 1.41826i | ||||
\(215\) | 1356.50 | − | 2199.58i | 0.430292 | − | 0.697721i | ||||
\(216\) | −2589.88 | − | 7970.82i | −0.815828 | − | 2.51086i | ||||
\(217\) | 656.961 | + | 904.229i | 0.205518 | + | 0.282871i | ||||
\(218\) | 3909.62i | 1.21465i | ||||||||
\(219\) | 1207.88 | − | 877.579i | 0.372700 | − | 0.270782i | ||||
\(220\) | 961.130 | − | 72.8989i | 0.294543 | − | 0.0223402i | ||||
\(221\) | −5313.01 | − | 3860.13i | −1.61716 | − | 1.17493i | ||||
\(222\) | 3930.39 | − | 5409.72i | 1.18825 | − | 1.63548i | ||||
\(223\) | −851.215 | − | 276.577i | −0.255613 | − | 0.0830536i | 0.178408 | − | 0.983957i | \(-0.442905\pi\) |
−0.434020 | + | 0.900903i | \(0.642905\pi\) | |||||||
\(224\) | −890.130 | −0.265510 | ||||||||
\(225\) | 6782.31 | − | 6705.76i | 2.00957 | − | 1.98689i | ||||
\(226\) | 6258.38 | 1.84204 | ||||||||
\(227\) | −3007.91 | − | 977.328i | −0.879479 | − | 0.285760i | −0.165738 | − | 0.986170i | \(-0.553001\pi\) |
−0.713741 | + | 0.700410i | \(0.753001\pi\) | |||||||
\(228\) | −1190.92 | + | 1639.17i | −0.345925 | + | 0.476125i | ||||
\(229\) | 121.855 | + | 88.5328i | 0.0351633 | + | 0.0255476i | 0.605228 | − | 0.796052i | \(-0.293082\pi\) |
−0.570065 | + | 0.821600i | \(0.693082\pi\) | |||||||
\(230\) | −200.093 | − | 486.972i | −0.0573642 | − | 0.139609i | ||||
\(231\) | 1685.47 | − | 1224.57i | 0.480070 | − | 0.348791i | ||||
\(232\) | 1158.06i | 0.327718i | ||||||||
\(233\) | −1897.14 | − | 2611.19i | −0.533416 | − | 0.734184i | 0.454231 | − | 0.890884i | \(-0.349914\pi\) |
−0.987646 | + | 0.156701i | \(0.949914\pi\) | |||||||
\(234\) | 5190.70 | + | 15975.3i | 1.45012 | + | 4.46300i | ||||
\(235\) | 0.758794 | − | 0.311783i | 0.000210631 | − | 8.65468e-5i | ||||
\(236\) | −461.172 | + | 1419.34i | −0.127202 | + | 0.391488i | ||||
\(237\) | 4014.48 | − | 1304.38i | 1.10029 | − | 0.357506i | ||||
\(238\) | −2173.49 | + | 706.209i | −0.591959 | + | 0.192339i | ||||
\(239\) | −1329.15 | + | 4090.71i | −0.359731 | + | 1.10714i | 0.593484 | + | 0.804846i | \(0.297752\pi\) |
−0.953215 | + | 0.302292i | \(0.902248\pi\) | |||||||
\(240\) | −5802.31 | − | 6832.79i | −1.56057 | − | 1.83773i | ||||
\(241\) | −1543.37 | − | 4750.00i | −0.412519 | − | 1.26960i | −0.914451 | − | 0.404696i | \(-0.867377\pi\) |
0.501932 | − | 0.864907i | \(-0.332623\pi\) | |||||||
\(242\) | −920.750 | − | 1267.30i | −0.244579 | − | 0.336634i | ||||
\(243\) | 17294.8i | 4.56568i | ||||||||
\(244\) | 1247.90 | − | 906.649i | 0.327411 | − | 0.237878i | ||||
\(245\) | −466.293 | − | 287.568i | −0.121593 | − | 0.0749880i | ||||
\(246\) | −5003.49 | − | 3635.25i | −1.29679 | − | 0.942175i | ||||
\(247\) | −2648.46 | + | 3645.29i | −0.682256 | + | 0.939045i | ||||
\(248\) | 2539.89 | + | 825.260i | 0.650335 | + | 0.211307i | ||||
\(249\) | 7105.83 | 1.80849 | ||||||||
\(250\) | 1805.58 | − | 4256.19i | 0.456778 | − | 1.07674i | ||||
\(251\) | 6942.70 | 1.74589 | 0.872947 | − | 0.487816i | \(-0.162206\pi\) | ||||
0.872947 | + | 0.487816i | \(0.162206\pi\) | |||||||
\(252\) | 1495.53 | + | 485.928i | 0.373848 | + | 0.121471i | ||||
\(253\) | 245.000 | − | 337.214i | 0.0608816 | − | 0.0837963i | ||||
\(254\) | −878.037 | − | 637.931i | −0.216901 | − | 0.157588i | ||||
\(255\) | −9545.05 | − | 5886.54i | −2.34406 | − | 1.44560i | ||||
\(256\) | −3223.82 | + | 2342.25i | −0.787066 | + | 0.571837i | ||||
\(257\) | 5442.03i | 1.32087i | 0.750882 | + | 0.660436i | \(0.229629\pi\) | ||||
−0.750882 | + | 0.660436i | \(0.770371\pi\) | |||||||
\(258\) | 4568.14 | + | 6287.50i | 1.10232 | + | 1.51722i | ||||
\(259\) | −430.183 | − | 1323.97i | −0.103206 | − | 0.317635i | ||||
\(260\) | 1417.86 | + | 1669.67i | 0.338199 | + | 0.398263i | ||||
\(261\) | 1632.53 | − | 5024.41i | 0.387169 | − | 1.19158i | ||||
\(262\) | −7733.56 | + | 2512.79i | −1.82359 | + | 0.592521i | ||||
\(263\) | −1439.95 | + | 467.869i | −0.337609 | + | 0.109696i | −0.472915 | − | 0.881108i | \(-0.656798\pi\) |
0.135306 | + | 0.990804i | \(0.456798\pi\) | |||||||
\(264\) | 1538.28 | − | 4734.33i | 0.358615 | − | 1.10370i | ||||
\(265\) | −4933.31 | + | 2027.06i | −1.14359 | + | 0.469892i | ||||
\(266\) | 484.535 | + | 1491.24i | 0.111687 | + | 0.343737i | ||||
\(267\) | −2439.26 | − | 3357.35i | −0.559102 | − | 0.769537i | ||||
\(268\) | − | 631.982i | − | 0.144046i | ||||||
\(269\) | 2722.24 | − | 1977.83i | 0.617019 | − | 0.448290i | −0.234860 | − | 0.972029i | \(-0.575463\pi\) |
0.851879 | + | 0.523739i | \(0.175463\pi\) | |||||||
\(270\) | 7043.84 | + | 17142.8i | 1.58768 | + | 3.86399i | ||||
\(271\) | 4867.44 | + | 3536.40i | 1.09106 | + | 0.792698i | 0.979577 | − | 0.201069i | \(-0.0644415\pi\) |
0.111478 | + | 0.993767i | \(0.464441\pi\) | |||||||
\(272\) | −4575.90 | + | 6298.18i | −1.02005 | + | 1.40398i | ||||
\(273\) | 4502.75 | + | 1463.03i | 0.998238 | + | 0.324347i | ||||
\(274\) | 6429.97 | 1.41770 | ||||||||
\(275\) | 3618.49 | − | 552.079i | 0.793465 | − | 0.121060i | ||||
\(276\) | 425.938 | 0.0928929 | ||||||||
\(277\) | 3984.70 | + | 1294.71i | 0.864322 | + | 0.280835i | 0.707432 | − | 0.706781i | \(-0.249853\pi\) |
0.156889 | + | 0.987616i | \(0.449853\pi\) | |||||||
\(278\) | −1360.31 | + | 1872.31i | −0.293475 | + | 0.403934i | ||||
\(279\) | −9856.26 | − | 7160.99i | −2.11498 | − | 1.53662i | ||||
\(280\) | −1305.25 | + | 98.9991i | −0.278584 | + | 0.0211298i | ||||
\(281\) | −5323.49 | + | 3867.74i | −1.13015 | + | 0.821103i | −0.985717 | − | 0.168411i | \(-0.946136\pi\) |
−0.144435 | + | 0.989514i | \(0.546136\pi\) | |||||||
\(282\) | 2.46711i | 0.000520973i | ||||||||
\(283\) | −4022.26 | − | 5536.17i | −0.844872 | − | 1.16287i | −0.984969 | − | 0.172729i | \(-0.944742\pi\) |
0.140097 | − | 0.990138i | \(-0.455258\pi\) | |||||||
\(284\) | 278.687 | + | 857.711i | 0.0582290 | + | 0.179210i | ||||
\(285\) | −4038.79 | + | 6548.92i | −0.839429 | + | 1.36114i | ||||
\(286\) | −1992.09 | + | 6131.01i | −0.411869 | + | 1.26760i | ||||
\(287\) | −1224.55 | + | 397.880i | −0.251857 | + | 0.0818331i | ||||
\(288\) | 9227.71 | − | 2998.26i | 1.88801 | − | 0.613453i | ||||
\(289\) | −1491.38 | + | 4590.01i | −0.303559 | + | 0.934257i | ||||
\(290\) | −193.680 | − | 2553.57i | −0.0392183 | − | 0.517071i | ||||
\(291\) | −5054.63 | − | 15556.6i | −1.01824 | − | 3.13382i | ||||
\(292\) | 254.210 | + | 349.890i | 0.0509470 | + | 0.0701225i | ||||
\(293\) | − | 337.838i | − | 0.0673608i | −0.999433 | − | 0.0336804i | \(-0.989277\pi\) | ||
0.999433 | − | 0.0336804i | \(-0.0107228\pi\) | |||||||
\(294\) | 1332.90 | − | 968.409i | 0.264409 | − | 0.192105i | ||||
\(295\) | −1338.64 | + | 5506.93i | −0.264198 | + | 1.08687i | ||||
\(296\) | −2691.02 | − | 1955.14i | −0.528419 | − | 0.383919i | ||||
\(297\) | −8624.70 | + | 11870.9i | −1.68504 | + | 2.31925i | ||||
\(298\) | −9689.06 | − | 3148.17i | −1.88346 | − | 0.611975i | ||||
\(299\) | 947.229 | 0.183210 | ||||||||
\(300\) | 2629.83 | + | 2659.86i | 0.506112 | + | 0.511889i | ||||
\(301\) | 1617.98 | 0.309831 | ||||||||
\(302\) | −8115.09 | − | 2636.75i | −1.54626 | − | 0.502411i | ||||
\(303\) | 2043.05 | − | 2812.02i | 0.387361 | − | 0.533157i | ||||
\(304\) | 4321.22 | + | 3139.55i | 0.815260 | + | 0.592321i | ||||
\(305\) | 4464.90 | − | 3791.52i | 0.838227 | − | 0.711810i | ||||
\(306\) | 20153.1 | − | 14642.1i | 3.76496 | − | 2.73540i | ||||
\(307\) | 7605.20i | 1.41385i | 0.707289 | + | 0.706925i | \(0.249918\pi\) | ||||
−0.707289 | + | 0.706925i | \(0.750082\pi\) | |||||||
\(308\) | 354.723 | + | 488.235i | 0.0656241 | + | 0.0903239i | ||||
\(309\) | −1661.44 | − | 5113.40i | −0.305878 | − | 0.941395i | ||||
\(310\) | −5738.55 | − | 1394.94i | −1.05138 | − | 0.255572i | ||||
\(311\) | −1059.36 | + | 3260.37i | −0.193153 | + | 0.594464i | 0.806840 | + | 0.590770i | \(0.201176\pi\) |
−0.999993 | + | 0.00369440i | \(0.998824\pi\) | |||||||
\(312\) | 10758.8 | − | 3495.76i | 1.95224 | − | 0.634322i | ||||
\(313\) | 4679.86 | − | 1520.58i | 0.845117 | − | 0.274595i | 0.145717 | − | 0.989326i | \(-0.453451\pi\) |
0.699399 | + | 0.714731i | \(0.253451\pi\) | |||||||
\(314\) | 2208.21 | − | 6796.16i | 0.396867 | − | 1.22143i | ||||
\(315\) | 5802.55 | + | 1410.50i | 1.03789 | + | 0.252293i | ||||
\(316\) | 377.843 | + | 1162.88i | 0.0672638 | + | 0.207017i | ||||
\(317\) | −2987.86 | − | 4112.44i | −0.529385 | − | 0.728636i | 0.457652 | − | 0.889132i | \(-0.348691\pi\) |
−0.987036 | + | 0.160496i | \(0.948691\pi\) | |||||||
\(318\) | − | 16040.0i | − | 2.82854i | ||||||
\(319\) | 1640.28 | − | 1191.73i | 0.287894 | − | 0.209167i | ||||
\(320\) | −1793.12 | + | 1522.69i | −0.313245 | + | 0.266003i | ||||
\(321\) | 11603.6 | + | 8430.48i | 2.01759 | + | 1.46587i | ||||
\(322\) | 193.750 | − | 266.674i | 0.0335319 | − | 0.0461527i | ||||
\(323\) | 6355.09 | + | 2064.89i | 1.09476 | + | 0.355708i | ||||
\(324\) | −8928.87 | −1.53101 | ||||||||
\(325\) | 5848.40 | + | 5915.17i | 0.998187 | + | 1.00958i | ||||
\(326\) | −3446.92 | −0.585604 | ||||||||
\(327\) | −11423.6 | − | 3711.75i | −1.93188 | − | 0.627707i | ||||
\(328\) | −1808.32 | + | 2488.94i | −0.304414 | + | 0.418990i | ||||
\(329\) | 0.415529 | + | 0.301899i | 6.96317e−5 | + | 5.05904e-5i | ||||
\(330\) | −2600.16 | + | 10696.6i | −0.433739 | + | 1.78433i | ||||
\(331\) | 1607.87 | − | 1168.18i | 0.266998 | − | 0.193985i | −0.446229 | − | 0.894919i | \(-0.647233\pi\) |
0.713226 | + | 0.700934i | \(0.247233\pi\) | |||||||
\(332\) | 2058.36i | 0.340262i | ||||||||
\(333\) | 8919.16 | + | 12276.2i | 1.46777 | + | 2.02021i | ||||
\(334\) | −2379.18 | − | 7322.36i | −0.389769 | − | 1.19959i | ||||
\(335\) | −181.507 | − | 2393.07i | −0.0296023 | − | 0.390290i | ||||
\(336\) | 1734.32 | − | 5337.68i | 0.281592 | − | 0.866650i | ||||
\(337\) | 3532.10 | − | 1147.65i | 0.570936 | − | 0.185508i | −0.00929983 | − | 0.999957i | \(-0.502960\pi\) |
0.580236 | + | 0.814448i | \(0.302960\pi\) | |||||||
\(338\) | −7020.45 | + | 2281.08i | −1.12977 | + | 0.367084i | ||||
\(339\) | −5941.64 | + | 18286.5i | −0.951934 | + | 2.92975i | ||||
\(340\) | 1705.16 | − | 2764.93i | 0.271987 | − | 0.441028i | ||||
\(341\) | −1444.84 | − | 4446.75i | −0.229450 | − | 0.706173i | ||||
\(342\) | −10046.0 | − | 13827.2i | −1.58839 | − | 2.18622i | ||||
\(343\) | − | 343.000i | − | 0.0539949i | ||||||
\(344\) | 3127.66 | − | 2272.38i | 0.490210 | − | 0.356158i | ||||
\(345\) | 1612.86 | − | 122.331i | 0.251691 | − | 0.0190900i | ||||
\(346\) | 4590.04 | + | 3334.86i | 0.713185 | + | 0.518159i | ||||
\(347\) | −2225.24 | + | 3062.78i | −0.344257 | + | 0.473829i | −0.945679 | − | 0.325103i | \(-0.894601\pi\) |
0.601422 | + | 0.798932i | \(0.294601\pi\) | |||||||
\(348\) | 1970.45 | + | 640.238i | 0.303526 | + | 0.0986217i | ||||
\(349\) | −4753.20 | −0.729034 | −0.364517 | − | 0.931197i | \(-0.618766\pi\) | ||||
−0.364517 | + | 0.931197i | \(0.618766\pi\) | |||||||
\(350\) | 2861.56 | − | 436.592i | 0.437019 | − | 0.0666767i | ||||
\(351\) | −33345.1 | −5.07074 | ||||||||
\(352\) | 3541.40 | + | 1150.67i | 0.536243 | + | 0.174236i | ||||
\(353\) | 1110.94 | − | 1529.08i | 0.167506 | − | 0.230552i | −0.717009 | − | 0.697064i | \(-0.754489\pi\) |
0.884515 | + | 0.466512i | \(0.154489\pi\) | |||||||
\(354\) | −13788.7 | − | 10018.1i | −2.07023 | − | 1.50411i | ||||
\(355\) | 1301.61 | + | 3167.77i | 0.194599 | + | 0.473600i | ||||
\(356\) | 972.530 | − | 706.584i | 0.144786 | − | 0.105194i | ||||
\(357\) | − | 7021.23i | − | 1.04090i | ||||||
\(358\) | −1463.52 | − | 2014.36i | −0.216059 | − | 0.297380i | ||||
\(359\) | 47.0845 | + | 144.911i | 0.00692208 | + | 0.0213040i | 0.954458 | − | 0.298346i | \(-0.0964348\pi\) |
−0.947536 | + | 0.319650i | \(0.896435\pi\) | |||||||
\(360\) | 13197.6 | − | 5422.82i | 1.93216 | − | 0.793910i | ||||
\(361\) | −702.811 | + | 2163.03i | −0.102465 | + | 0.315356i | ||||
\(362\) | 11758.6 | − | 3820.59i | 1.70723 | − | 0.554712i | ||||
\(363\) | 4577.11 | − | 1487.19i | 0.661807 | − | 0.215034i | ||||
\(364\) | −423.800 | + | 1304.32i | −0.0610251 | + | 0.187816i | ||||
\(365\) | 1063.08 | + | 1251.89i | 0.152450 | + | 0.179525i | ||||
\(366\) | 5443.62 | + | 16753.7i | 0.777438 | + | 2.39271i | ||||
\(367\) | −3661.32 | − | 5039.38i | −0.520761 | − | 0.716767i | 0.464926 | − | 0.885350i | \(-0.346081\pi\) |
−0.985687 | + | 0.168583i | \(0.946081\pi\) | |||||||
\(368\) | − | 1122.87i | − | 0.159059i | ||||||
\(369\) | 11354.3 | − | 8249.40i | 1.60185 | − | 1.16381i | ||||
\(370\) | 6260.76 | + | 3861.08i | 0.879680 | + | 0.542508i | ||||
\(371\) | −2701.56 | − | 1962.80i | −0.378054 | − | 0.274673i | ||||
\(372\) | 2808.36 | − | 3865.38i | 0.391417 | − | 0.538739i | ||||
\(373\) | 4587.25 | + | 1490.49i | 0.636779 | + | 0.206902i | 0.609576 | − | 0.792728i | \(-0.291340\pi\) |
0.0272035 | + | 0.999630i | \(0.491340\pi\) | |||||||
\(374\) | 9560.19 | 1.32178 | ||||||||
\(375\) | 10722.1 | + | 9316.53i | 1.47649 | + | 1.28294i | ||||
\(376\) | 1.22724 | 0.000168325 | ||||||||
\(377\) | 4382.02 | + | 1423.80i | 0.598635 | + | 0.194508i | ||||
\(378\) | −6820.54 | + | 9387.67i | −0.928071 | + | 1.27738i | ||||
\(379\) | −837.146 | − | 608.222i | −0.113460 | − | 0.0824334i | 0.529608 | − | 0.848242i | \(-0.322339\pi\) |
−0.643068 | + | 0.765809i | \(0.722339\pi\) | |||||||
\(380\) | −1897.04 | − | 1169.92i | −0.256095 | − | 0.157936i | ||||
\(381\) | 2697.58 | − | 1959.91i | 0.362733 | − | 0.263541i | ||||
\(382\) | − | 16508.9i | − | 2.21117i | ||||||
\(383\) | −1209.32 | − | 1664.49i | −0.161341 | − | 0.222067i | 0.720691 | − | 0.693256i | \(-0.243825\pi\) |
−0.882032 | + | 0.471190i | \(0.843825\pi\) | |||||||
\(384\) | −5381.25 | − | 16561.8i | −0.715132 | − | 2.20095i | ||||
\(385\) | 1483.42 | + | 1746.87i | 0.196369 | + | 0.231244i | ||||
\(386\) | 979.039 | − | 3013.17i | 0.129098 | − | 0.397322i | ||||
\(387\) | −16773.2 | + | 5449.93i | −2.20317 | + | 0.715854i | ||||
\(388\) | 4506.30 | − | 1464.19i | 0.589620 | − | 0.191579i | ||||
\(389\) | 2297.28 | − | 7070.31i | 0.299426 | − | 0.921540i | −0.682272 | − | 0.731098i | \(-0.739008\pi\) |
0.981699 | − | 0.190441i | \(-0.0609919\pi\) | |||||||
\(390\) | −23138.9 | + | 9507.63i | −3.00432 | + | 1.23445i | ||||
\(391\) | −434.089 | − | 1335.99i | −0.0561453 | − | 0.172797i | ||||
\(392\) | −481.726 | − | 663.039i | −0.0620685 | − | 0.0854299i | ||||
\(393\) | − | 24982.5i | − | 3.20661i | ||||||
\(394\) | −3423.52 | + | 2487.33i | −0.437752 | + | 0.318045i | ||||
\(395\) | 1764.73 | + | 4294.86i | 0.224793 | + | 0.547083i | ||||
\(396\) | −5321.85 | − | 3866.55i | −0.675336 | − | 0.490660i | ||||
\(397\) | −5700.84 | + | 7846.53i | −0.720698 | + | 0.991955i | 0.278803 | + | 0.960348i | \(0.410062\pi\) |
−0.999500 | + | 0.0316069i | \(0.989938\pi\) | |||||||
\(398\) | 2981.29 | + | 968.679i | 0.375473 | + | 0.121999i | ||||
\(399\) | −4817.31 | −0.604429 | ||||||||
\(400\) | 7011.99 | − | 6932.85i | 0.876499 | − | 0.866606i | ||||
\(401\) | −4063.13 | −0.505993 | −0.252997 | − | 0.967467i | \(-0.581416\pi\) | ||||
−0.252997 | + | 0.967467i | \(0.581416\pi\) | |||||||
\(402\) | 6864.29 | + | 2230.34i | 0.851641 | + | 0.276715i | ||||
\(403\) | 6245.43 | − | 8596.10i | 0.771978 | − | 1.06254i | ||||
\(404\) | 814.564 | + | 591.815i | 0.100312 | + | 0.0728810i | ||||
\(405\) | −33810.1 | + | 2564.40i | −4.14824 | + | 0.314632i | ||||
\(406\) | 1297.16 | − | 942.442i | 0.158564 | − | 0.115203i | ||||
\(407\) | 5823.54i | 0.709243i | ||||||||
\(408\) | −9860.96 | − | 13572.4i | −1.19654 | − | 1.64690i | ||||
\(409\) | −1143.44 | − | 3519.14i | −0.138238 | − | 0.425453i | 0.857842 | − | 0.513914i | \(-0.171805\pi\) |
−0.996080 | + | 0.0884613i | \(0.971805\pi\) | |||||||
\(410\) | 3571.14 | − | 5790.63i | 0.430162 | − | 0.697509i | ||||
\(411\) | −6104.54 | + | 18787.8i | −0.732640 | + | 2.25483i | ||||
\(412\) | 1481.21 | − | 481.274i | 0.177121 | − | 0.0575501i | ||||
\(413\) | −3374.62 | + | 1096.48i | −0.402069 | + | 0.130640i | ||||
\(414\) | −1110.30 | + | 3417.14i | −0.131807 | + | 0.405661i | ||||
\(415\) | 591.166 | + | 7794.19i | 0.0699258 | + | 0.921932i | ||||
\(416\) | 2614.92 | + | 8047.90i | 0.308190 | + | 0.948512i | ||||
\(417\) | −4179.27 | − | 5752.28i | −0.490791 | − | 0.675516i | ||||
\(418\) | − | 6559.31i | − | 0.767527i | ||||||
\(419\) | −2319.99 | + | 1685.57i | −0.270498 | + | 0.196528i | −0.714762 | − | 0.699367i | \(-0.753465\pi\) |
0.444264 | + | 0.895896i | \(0.353465\pi\) | |||||||
\(420\) | −553.162 | + | 2275.62i | −0.0642655 | + | 0.264378i | ||||
\(421\) | 8139.25 | + | 5913.51i | 0.942239 | + | 0.684577i | 0.948959 | − | 0.315400i | \(-0.102139\pi\) |
−0.00671926 | + | 0.999977i | \(0.502139\pi\) | |||||||
\(422\) | 24.1906 | − | 33.2956i | 0.00279048 | − | 0.00384076i | ||||
\(423\) | −5.32456 | − | 1.73005i | −0.000612030 | − | 0.000198861i | ||||
\(424\) | −7978.93 | −0.913894 | ||||||||
\(425\) | 5662.69 | − | 10959.4i | 0.646308 | − | 1.25085i | ||||
\(426\) | −10299.6 | −1.17140 | ||||||||
\(427\) | 3487.91 | + | 1133.29i | 0.395297 | + | 0.128440i | ||||
\(428\) | −2442.07 | + | 3361.22i | −0.275799 | + | 0.379605i | ||||
\(429\) | −16023.1 | − | 11641.4i | −1.80326 | − | 1.31015i | ||||
\(430\) | −6516.55 | + | 5533.75i | −0.730827 | + | 0.620607i | ||||
\(431\) | 4173.63 | − | 3032.32i | 0.466442 | − | 0.338890i | −0.329611 | − | 0.944117i | \(-0.606918\pi\) |
0.796053 | + | 0.605227i | \(0.206918\pi\) | |||||||
\(432\) | 39528.2i | 4.40232i | ||||||||
\(433\) | 2086.64 | + | 2872.02i | 0.231588 | + | 0.318754i | 0.908957 | − | 0.416890i | \(-0.136880\pi\) |
−0.677369 | + | 0.735643i | \(0.736880\pi\) | |||||||
\(434\) | −1142.60 | − | 3516.56i | −0.126374 | − | 0.388941i | ||||
\(435\) | 7645.19 | + | 1858.41i | 0.842664 | + | 0.204837i | ||||
\(436\) | 1075.19 | − | 3309.09i | 0.118102 | − | 0.363479i | ||||
\(437\) | −916.630 | + | 297.831i | −0.100339 | + | 0.0326023i | ||||
\(438\) | −4697.48 | + | 1526.30i | −0.512453 | + | 0.166506i | ||||
\(439\) | 337.448 | − | 1038.56i | 0.0366868 | − | 0.112910i | −0.931036 | − | 0.364927i | \(-0.881094\pi\) |
0.967723 | + | 0.252017i | \(0.0810938\pi\) | |||||||
\(440\) | 5320.94 | + | 1293.42i | 0.576513 | + | 0.140140i | ||||
\(441\) | 1155.34 | + | 3555.78i | 0.124753 | + | 0.383952i | ||||
\(442\) | 12770.1 | + | 17576.5i | 1.37423 | + | 1.89146i | ||||
\(443\) | 13453.1i | 1.44284i | 0.692499 | + | 0.721419i | \(0.256510\pi\) | ||||
−0.692499 | + | 0.721419i | \(0.743490\pi\) | |||||||
\(444\) | −4814.41 | + | 3497.87i | −0.514598 | + | 0.373878i | ||||
\(445\) | 3479.65 | − | 2954.87i | 0.370677 | − | 0.314774i | ||||
\(446\) | 2395.42 | + | 1740.37i | 0.254319 | + | 0.184774i | ||||
\(447\) | 18397.4 | − | 25321.8i | 1.94668 | − | 2.67938i | ||||
\(448\) | −1400.76 | − | 455.135i | −0.147723 | − | 0.0479980i | ||||
\(449\) | −10445.2 | −1.09786 | −0.548928 | − | 0.835869i | \(-0.684964\pi\) | ||||
−0.548928 | + | 0.835869i | \(0.684964\pi\) | |||||||
\(450\) | −28194.3 | + | 14164.7i | −2.95354 | + | 1.48385i | ||||
\(451\) | 5386.24 | 0.562368 | ||||||||
\(452\) | −5297.08 | − | 1721.13i | −0.551225 | − | 0.179104i | ||||
\(453\) | 15408.8 | − | 21208.3i | 1.59816 | − | 2.19968i | ||||
\(454\) | 8464.60 | + | 6149.89i | 0.875030 | + | 0.635746i | ||||
\(455\) | −1230.16 | + | 5060.67i | −0.126749 | + | 0.521424i | ||||
\(456\) | −9312.14 | + | 6765.67i | −0.956318 | + | 0.694806i | ||||
\(457\) | − | 11092.0i | − | 1.13537i | −0.823246 | − | 0.567684i | \(-0.807839\pi\) | ||
0.823246 | − | 0.567684i | \(-0.192161\pi\) | |||||||
\(458\) | −292.884 | − | 403.120i | −0.0298811 | − | 0.0411278i | ||||
\(459\) | 15281.1 | + | 47030.5i | 1.55395 | + | 4.78256i | ||||
\(460\) | 35.4357 | + | 467.200i | 0.00359174 | + | 0.0473550i | ||||
\(461\) | −436.836 | + | 1344.44i | −0.0441333 | + | 0.135828i | −0.970695 | − | 0.240314i | \(-0.922750\pi\) |
0.926562 | + | 0.376142i | \(0.122750\pi\) | |||||||
\(462\) | −6554.84 | + | 2129.80i | −0.660084 | + | 0.214474i | ||||
\(463\) | 1743.68 | − | 566.555i | 0.175023 | − | 0.0568684i | −0.220195 | − | 0.975456i | \(-0.570669\pi\) |
0.395217 | + | 0.918588i | \(0.370669\pi\) | |||||||
\(464\) | 1687.81 | − | 5194.56i | 0.168868 | − | 0.519722i | ||||
\(465\) | 9524.02 | − | 15443.3i | 0.949819 | − | 1.54014i | ||||
\(466\) | 3299.55 | + | 10155.0i | 0.328001 | + | 1.00948i | ||||
\(467\) | −5204.43 | − | 7163.28i | −0.515701 | − | 0.709801i | 0.469167 | − | 0.883110i | \(-0.344554\pi\) |
−0.984868 | + | 0.173308i | \(0.944554\pi\) | |||||||
\(468\) | − | 14949.0i | − | 1.47653i | ||||||
\(469\) | 1215.63 | − | 883.206i | 0.119686 | − | 0.0869567i | ||||
\(470\) | −2.70611 | + | 0.205250i | −0.000265582 | + | 2.01436e-5i | ||||
\(471\) | 17761.4 | + | 12904.4i | 1.73758 | + | 1.26243i | ||||
\(472\) | −4983.39 | + | 6859.05i | −0.485973 | + | 0.668885i | ||||
\(473\) | −6437.19 | − | 2091.57i | −0.625756 | − | 0.203320i | ||||
\(474\) | −13964.1 | −1.35315 | ||||||||
\(475\) | −7519.34 | − | 3885.21i | −0.726339 | − | 0.375296i | ||||
\(476\) | 2033.85 | 0.195843 | ||||||||
\(477\) | 34617.7 | + | 11248.0i | 3.32292 | + | 1.07968i | ||||
\(478\) | 8363.77 | − | 11511.7i | 0.800313 | − | 1.10154i | ||||
\(479\) | 14121.4 | + | 10259.8i | 1.34702 | + | 0.978667i | 0.999154 | + | 0.0411219i | \(0.0130932\pi\) |
0.347865 | + | 0.937545i | \(0.386907\pi\) | |||||||
\(480\) | 5491.81 | + | 13365.6i | 0.522220 | + | 1.27094i | ||||
\(481\) | −10706.6 | + | 7778.80i | −1.01493 | + | 0.737386i | ||||
\(482\) | 16522.6i | 1.56138i | ||||||||
\(483\) | 595.256 | + | 819.300i | 0.0560768 | + | 0.0771831i | ||||
\(484\) | 430.798 | + | 1325.86i | 0.0404581 | + | 0.124517i | ||||
\(485\) | 16643.1 | − | 6838.52i | 1.55819 | − | 0.640249i | ||||
\(486\) | 17680.3 | − | 54414.2i | 1.65019 | − | 5.07877i | ||||
\(487\) | −14845.3 | + | 4823.53i | −1.38132 | + | 0.448819i | −0.903105 | − | 0.429421i | \(-0.858718\pi\) |
−0.478220 | + | 0.878240i | \(0.658718\pi\) | |||||||
\(488\) | 8333.99 | − | 2707.88i | 0.773078 | − | 0.251188i | ||||
\(489\) | 3272.46 | − | 10071.6i | 0.302630 | − | 0.931399i | ||||
\(490\) | 1173.11 | + | 1381.46i | 0.108155 | + | 0.127363i | ||||
\(491\) | −1717.72 | − | 5286.60i | −0.157881 | − | 0.485908i | 0.840560 | − | 0.541718i | \(-0.182226\pi\) |
−0.998441 | + | 0.0558101i | \(0.982226\pi\) | |||||||
\(492\) | 3235.21 | + | 4452.89i | 0.296452 | + | 0.408032i | ||||
\(493\) | − | 6832.96i | − | 0.624221i | ||||||
\(494\) | 12059.3 | − | 8761.61i | 1.09833 | − | 0.797983i | ||||
\(495\) | −21262.2 | − | 13112.7i | −1.93064 | − | 1.19065i | ||||
\(496\) | −10190.0 | − | 7403.49i | −0.922472 | − | 0.670215i | ||||
\(497\) | −1260.35 | + | 1734.73i | −0.113752 | + | 0.156566i | ||||
\(498\) | −22356.9 | − | 7264.20i | −2.01172 | − | 0.653648i | ||||
\(499\) | 9210.31 | 0.826273 | 0.413137 | − | 0.910669i | \(-0.364433\pi\) | ||||
0.413137 | + | 0.910669i | \(0.364433\pi\) | |||||||
\(500\) | −2698.74 | + | 3105.88i | −0.241382 | + | 0.277798i | ||||
\(501\) | 23654.1 | 2.10936 | ||||||||
\(502\) | −21843.7 | − | 7097.44i | −1.94209 | − | 0.631024i | ||||
\(503\) | −6386.80 | + | 8790.68i | −0.566150 | + | 0.779239i | −0.992092 | − | 0.125512i | \(-0.959943\pi\) |
0.425942 | + | 0.904750i | \(0.359943\pi\) | |||||||
\(504\) | 7227.25 | + | 5250.91i | 0.638745 | + | 0.464075i | ||||
\(505\) | 3254.40 | + | 2007.03i | 0.286770 | + | 0.176855i | ||||
\(506\) | −1115.57 | + | 810.508i | −0.0980100 | + | 0.0712085i | ||||
\(507\) | − | 22678.8i | − | 1.98659i | ||||||
\(508\) | 567.730 | + | 781.414i | 0.0495846 | + | 0.0682473i | ||||
\(509\) | 1407.72 | + | 4332.52i | 0.122586 | + | 0.377280i | 0.993454 | − | 0.114237i | \(-0.0364424\pi\) |
−0.870868 | + | 0.491518i | \(0.836442\pi\) | |||||||
\(510\) | 24013.7 | + | 28278.5i | 2.08498 | + | 2.45528i | ||||
\(511\) | −317.757 | + | 977.956i | −0.0275083 | + | 0.0846619i | ||||
\(512\) | −498.500 | + | 161.972i | −0.0430289 | + | 0.0139809i | ||||
\(513\) | 32267.9 | − | 10484.5i | 2.77712 | − | 0.902342i | ||||
\(514\) | 5563.32 | − | 17122.1i | 0.477407 | − | 1.46931i | ||||
\(515\) | 5470.53 | − | 2247.80i | 0.468078 | − | 0.192330i | ||||
\(516\) | −2137.33 | − | 6578.02i | −0.182346 | − | 0.561204i | ||||
\(517\) | −1.26293 | − | 1.73827i | −0.000107434 | − | 0.000147870i | ||||
\(518\) | 4605.34i | 0.390632i | ||||||||
\(519\) | −14101.9 | + | 10245.6i | −1.19269 | + | 0.866540i | ||||
\(520\) | 4729.48 | + | 11510.3i | 0.398849 | + | 0.970689i | ||||
\(521\) | −7234.47 | − | 5256.15i | −0.608345 | − | 0.441989i | 0.240486 | − | 0.970653i | \(-0.422693\pi\) |
−0.848831 | + | 0.528664i | \(0.822693\pi\) | |||||||
\(522\) | −10272.8 | + | 14139.3i | −0.861356 | + | 1.18555i | ||||
\(523\) | 3682.84 | + | 1196.63i | 0.307915 | + | 0.100048i | 0.458899 | − | 0.888489i | \(-0.348244\pi\) |
−0.150984 | + | 0.988536i | \(0.548244\pi\) | |||||||
\(524\) | 7236.72 | 0.603316 | ||||||||
\(525\) | −1441.04 | + | 8775.73i | −0.119795 | + | 0.729532i | ||||
\(526\) | 5008.79 | 0.415197 | ||||||||
\(527\) | −14986.2 | − | 4869.31i | −1.23873 | − | 0.402486i | ||||
\(528\) | −13800.1 | + | 18994.1i | −1.13744 | + | 1.56556i | ||||
\(529\) | −9679.39 | − | 7032.49i | −0.795545 | − | 0.577997i | ||||
\(530\) | 17593.8 | − | 1334.44i | 1.44194 | − | 0.109367i | ||||
\(531\) | 31290.4 | − | 22733.8i | 2.55723 | − | 1.85793i | ||||
\(532\) | − | 1395.44i | − | 0.113722i | ||||||
\(533\) | 7194.68 | + | 9902.62i | 0.584683 | + | 0.804747i | ||||
\(534\) | 4242.41 | + | 13056.8i | 0.343796 | + | 1.05809i | ||||
\(535\) | −8281.81 | + | 13429.0i | −0.669260 | + | 1.08521i | ||||
\(536\) | 1109.46 | − | 3414.58i | 0.0894059 | − | 0.275163i | ||||
\(537\) | 7275.24 | − | 2363.87i | 0.584636 | − | 0.189960i | ||||
\(538\) | −10586.8 | + | 3439.87i | −0.848385 | + | 0.275657i | ||||
\(539\) | −443.396 | + | 1364.63i | −0.0354331 | + | 0.109052i | ||||
\(540\) | −1247.44 | − | 16446.7i | −0.0994095 | − | 1.31066i | ||||
\(541\) | −2718.59 | − | 8366.97i | −0.216047 | − | 0.664924i | −0.999078 | − | 0.0429411i | \(-0.986327\pi\) |
0.783031 | − | 0.621983i | \(-0.213673\pi\) | |||||||
\(542\) | −11699.1 | − | 16102.4i | −0.927158 | − | 1.27612i | ||||
\(543\) | 37984.8i | 3.00200i | ||||||||
\(544\) | 10152.6 | − | 7376.26i | 0.800160 | − | 0.581350i | ||||
\(545\) | 3120.94 | − | 12839.0i | 0.245296 | − | 1.00911i | ||||
\(546\) | −12671.3 | − | 9206.22i | −0.993188 | − | 0.721593i | ||||
\(547\) | 5683.54 | − | 7822.72i | 0.444261 | − | 0.611472i | −0.526892 | − | 0.849932i | \(-0.676643\pi\) |
0.971152 | + | 0.238460i | \(0.0766427\pi\) | |||||||
\(548\) | −5442.31 | − | 1768.31i | −0.424241 | − | 0.137844i | ||||
\(549\) | −39975.4 | −3.10767 | ||||||||
\(550\) | −11949.1 | − | 1962.14i | −0.926388 | − | 0.152120i | ||||
\(551\) | −4688.14 | −0.362471 | ||||||||
\(552\) | 2301.33 | + | 747.747i | 0.177448 | + | 0.0576562i | ||||
\(553\) | −1708.78 | + | 2351.94i | −0.131401 | + | 0.180858i | ||||
\(554\) | −11213.4 | − | 8147.01i | −0.859949 | − | 0.624790i | ||||
\(555\) | −17225.7 | + | 14627.8i | −1.31746 | + | 1.11876i | ||||
\(556\) | 1666.27 | − | 1210.62i | 0.127097 | − | 0.0923411i | ||||
\(557\) | − | 4916.72i | − | 0.374018i | −0.982358 | − | 0.187009i | \(-0.940121\pi\) | ||
0.982358 | − | 0.187009i | \(-0.0598793\pi\) | |||||||
\(558\) | 23690.0 | + | 32606.4i | 1.79727 | + | 2.47373i | ||||
\(559\) | −4753.13 | − | 14628.6i | −0.359635 | − | 1.10684i | ||||
\(560\) | 5999.05 | + | 1458.26i | 0.452689 | + | 0.110041i | ||||
\(561\) | −9076.35 | + | 27934.1i | −0.683072 | + | 2.10228i | ||||
\(562\) | 20703.1 | − | 6726.85i | 1.55393 | − | 0.504902i | ||||
\(563\) | −12699.8 | + | 4126.40i | −0.950676 | + | 0.308893i | −0.742990 | − | 0.669302i | \(-0.766593\pi\) |
−0.207686 | + | 0.978196i | \(0.566593\pi\) | |||||||
\(564\) | 0.678484 | − | 2.08816i | 5.06549e−5 | − | 0.000155900i | ||||
\(565\) | −20552.3 | − | 4995.89i | −1.53034 | − | 0.371998i | ||||
\(566\) | 6995.60 | + | 21530.3i | 0.519518 | + | 1.59891i | ||||
\(567\) | −12478.3 | − | 17174.8i | −0.924229 | − | 1.27209i | ||||
\(568\) | 5123.43i | 0.378476i | ||||||||
\(569\) | 4658.63 | − | 3384.69i | 0.343233 | − | 0.249374i | −0.402792 | − | 0.915292i | \(-0.631960\pi\) |
0.746025 | + | 0.665918i | \(0.231960\pi\) | |||||||
\(570\) | 19402.0 | − | 16475.9i | 1.42572 | − | 1.21070i | ||||
\(571\) | −6551.42 | − | 4759.89i | −0.480155 | − | 0.348853i | 0.321231 | − | 0.947001i | \(-0.395903\pi\) |
−0.801386 | + | 0.598148i | \(0.795903\pi\) | |||||||
\(572\) | 3372.19 | − | 4641.43i | 0.246501 | − | 0.339279i | ||||
\(573\) | 48237.7 | + | 15673.4i | 3.51685 | + | 1.14270i | ||||
\(574\) | 4259.52 | 0.309737 | ||||||||
\(575\) | 268.362 | + | 1758.92i | 0.0194634 | + | 0.127569i | ||||
\(576\) | 16054.3 | 1.16134 | ||||||||
\(577\) | 13332.0 | + | 4331.84i | 0.961906 | + | 0.312542i | 0.747544 | − | 0.664212i | \(-0.231233\pi\) |
0.214362 | + | 0.976754i | \(0.431233\pi\) | |||||||
\(578\) | 9384.62 | − | 12916.8i | 0.675344 | − | 0.929531i | ||||
\(579\) | 7874.76 | + | 5721.35i | 0.565223 | + | 0.410658i | ||||
\(580\) | −538.329 | + | 2214.60i | −0.0385395 | + | 0.158545i | ||||
\(581\) | −3959.29 | + | 2876.59i | −0.282718 | + | 0.205406i | ||||
\(582\) | 54112.6i | 3.85402i | ||||||||
\(583\) | 8210.92 | + | 11301.4i | 0.583296 | + | 0.802838i | ||||
\(584\) | 759.246 | + | 2336.72i | 0.0537977 | + | 0.165572i | ||||
\(585\) | −4293.39 | − | 56606.0i | −0.303436 | − | 4.00063i | ||||
\(586\) | −345.368 | + | 1062.93i | −0.0243464 | + | 0.0749306i | ||||
\(587\) | −7166.64 | + | 2328.58i | −0.503916 | + | 0.163732i | −0.549934 | − | 0.835208i | \(-0.685347\pi\) |
0.0460174 | + | 0.998941i | \(0.485347\pi\) | |||||||
\(588\) | −1394.49 | + | 453.096i | −0.0978022 | + | 0.0317779i | ||||
\(589\) | −3340.86 | + | 10282.1i | −0.233714 | + | 0.719299i | ||||
\(590\) | 9841.40 | − | 15957.9i | 0.686719 | − | 1.11352i | ||||
\(591\) | −4017.53 | − | 12364.7i | −0.279626 | − | 0.860601i | ||||
\(592\) | 9221.19 | + | 12691.9i | 0.640184 | + | 0.881137i | ||||
\(593\) | 18970.6i | 1.31371i | 0.754017 | + | 0.656855i | \(0.228114\pi\) | ||||
−0.754017 | + | 0.656855i | \(0.771886\pi\) | |||||||
\(594\) | 39271.2 | − | 28532.2i | 2.71265 | − | 1.97086i | ||||
\(595\) | 7701.40 | − | 584.128i | 0.530633 | − | 0.0402469i | ||||
\(596\) | 7335.02 | + | 5329.21i | 0.504118 | + | 0.366263i | ||||
\(597\) | −5660.80 | + | 7791.43i | −0.388076 | + | 0.534141i | ||||
\(598\) | −2980.25 | − | 968.341i | −0.203798 | − | 0.0662181i | ||||
\(599\) | −27029.1 | −1.84371 | −0.921853 | − | 0.387540i | \(-0.873325\pi\) | ||||
−0.921853 | + | 0.387540i | \(0.873325\pi\) | |||||||
\(600\) | 9539.45 | + | 18987.9i | 0.649078 | + | 1.29196i | ||||
\(601\) | −15808.6 | −1.07296 | −0.536479 | − | 0.843913i | \(-0.680246\pi\) | ||||
−0.536479 | + | 0.843913i | \(0.680246\pi\) | |||||||
\(602\) | −5090.63 | − | 1654.05i | −0.344649 | − | 0.111983i | ||||
\(603\) | −9627.11 | + | 13250.6i | −0.650160 | + | 0.894868i | ||||
\(604\) | 6143.46 | + | 4463.49i | 0.413864 | + | 0.300690i | ||||
\(605\) | 2012.05 | + | 4896.78i | 0.135209 | + | 0.329062i | ||||
\(606\) | −9302.72 | + | 6758.82i | −0.623593 | + | 0.453066i | ||||
\(607\) | 1536.12i | 0.102717i | 0.998680 | + | 0.0513583i | \(0.0163551\pi\) | ||||
−0.998680 | + | 0.0513583i | \(0.983645\pi\) | |||||||
\(608\) | −5060.90 | − | 6965.73i | −0.337577 | − | 0.464634i | ||||
\(609\) | 1522.23 | + | 4684.94i | 0.101287 | + | 0.311730i | ||||
\(610\) | −17923.8 | + | 7364.78i | −1.18970 | + | 0.488838i | ||||
\(611\) | 1.50886 | − | 4.64379i | 9.99049e−5 | − | 0.000307476i | ||||
\(612\) | −21084.3 | + | 6850.71i | −1.39262 | + | 0.452490i | ||||
\(613\) | −21791.9 | + | 7080.60i | −1.43583 | + | 0.466530i | −0.920595 | − | 0.390518i | \(-0.872296\pi\) |
−0.515237 | + | 0.857048i | \(0.672296\pi\) | |||||||
\(614\) | 7774.71 | − | 23928.1i | 0.511012 | − | 1.57273i | ||||
\(615\) | 13529.3 | + | 15932.2i | 0.887083 | + | 1.04463i | ||||
\(616\) | 1059.45 | + | 3260.65i | 0.0692961 | + | 0.213271i | ||||
\(617\) | −4975.85 | − | 6848.68i | −0.324668 | − | 0.446868i | 0.615217 | − | 0.788358i | \(-0.289068\pi\) |
−0.939885 | + | 0.341490i | \(0.889068\pi\) | |||||||
\(618\) | 17786.7i | 1.15774i | ||||||||
\(619\) | −1894.56 | + | 1376.48i | −0.123019 | + | 0.0893785i | −0.647593 | − | 0.761986i | \(-0.724224\pi\) |
0.524574 | + | 0.851365i | \(0.324224\pi\) | |||||||
\(620\) | 4473.48 | + | 2758.84i | 0.289773 | + | 0.178706i | ||||
\(621\) | −5770.36 | − | 4192.41i | −0.372877 | − | 0.270911i | ||||
\(622\) | 6666.07 | − | 9175.06i | 0.429719 | − | 0.591457i | ||||
\(623\) | 2718.26 | + | 883.215i | 0.174807 | + | 0.0567982i | ||||
\(624\) | −53354.3 | −3.42289 | ||||||||
\(625\) | −9327.04 | + | 12535.8i | −0.596930 | + | 0.802293i | ||||
\(626\) | −16278.6 | −1.03934 | ||||||||
\(627\) | 19165.8 | + | 6227.34i | 1.22075 | + | 0.396644i | ||||
\(628\) | −3738.04 | + | 5144.97i | −0.237523 | + | 0.326922i | ||||
\(629\) | 15877.9 | + | 11536.0i | 1.00651 | + | 0.731270i | ||||
\(630\) | −16814.5 | − | 10369.7i | −1.06334 | − | 0.655775i | ||||
\(631\) | 3175.60 | − | 2307.21i | 0.200346 | − | 0.145560i | −0.483089 | − | 0.875571i | \(-0.660485\pi\) |
0.683435 | + | 0.730011i | \(0.260485\pi\) | |||||||
\(632\) | 6946.33i | 0.437200i | ||||||||
\(633\) | 74.3206 | + | 102.294i | 0.00466664 | + | 0.00642307i | ||||
\(634\) | 5196.55 | + | 15993.3i | 0.325522 | + | 1.00186i | ||||
\(635\) | 2374.20 | + | 2795.85i | 0.148373 | + | 0.174724i | ||||
\(636\) | −4411.17 | + | 13576.2i | −0.275022 | + | 0.846432i | ||||
\(637\) | −3101.15 | + | 1007.63i | −0.192892 | + | 0.0626744i | ||||
\(638\) | −6379.08 | + | 2072.69i | −0.395846 | + | 0.128618i | ||||
\(639\) | 7222.53 | − | 22228.7i | 0.447135 | − | 1.37614i | ||||
\(640\) | 17718.5 | − | 7280.40i | 1.09435 | − | 0.449661i | ||||
\(641\) | −7896.76 | − | 24303.7i | −0.486588 | − | 1.49757i | −0.829667 | − | 0.558258i | \(-0.811470\pi\) |
0.343079 | − | 0.939307i | \(-0.388530\pi\) | |||||||
\(642\) | −27889.7 | − | 38386.8i | −1.71451 | − | 2.35982i | ||||
\(643\) | − | 1843.46i | − | 0.113062i | −0.998401 | − | 0.0565311i | \(-0.981996\pi\) | ||
0.998401 | − | 0.0565311i | \(-0.0180040\pi\) | |||||||
\(644\) | −237.328 | + | 172.429i | −0.0145218 | + | 0.0105507i | ||||
\(645\) | −9982.44 | − | 24294.5i | −0.609393 | − | 1.48309i | ||||
\(646\) | −17884.0 | − | 12993.5i | −1.08922 | − | 0.791364i | ||||
\(647\) | 13198.2 | − | 18165.8i | 0.801970 | − | 1.10382i | −0.190543 | − | 0.981679i | \(-0.561025\pi\) |
0.992513 | − | 0.122138i | \(-0.0389750\pi\) | |||||||
\(648\) | −48242.4 | − | 15674.9i | −2.92460 | − | 0.950260i | ||||
\(649\) | 14843.4 | 0.897775 | ||||||||
\(650\) | −12353.7 | − | 24589.5i | −0.745464 | − | 1.48382i | ||||
\(651\) | 11359.9 | 0.683915 | ||||||||
\(652\) | 2917.46 | + | 947.941i | 0.175240 | + | 0.0569390i | ||||
\(653\) | 9978.84 | − | 13734.7i | 0.598013 | − | 0.823094i | −0.397512 | − | 0.917597i | \(-0.630126\pi\) |
0.995525 | + | 0.0945030i | \(0.0301262\pi\) | |||||||
\(654\) | 32147.3 | + | 23356.4i | 1.92211 | + | 1.39650i | ||||
\(655\) | 27402.6 | − | 2078.41i | 1.63467 | − | 0.123985i | ||||
\(656\) | 11738.8 | − | 8528.76i | 0.698665 | − | 0.507610i | ||||
\(657\) | − | 11208.5i | − | 0.665578i | ||||||
\(658\) | −0.998741 | − | 1.37465i | −5.91717e−5 | − | 8.14429e-5i | ||||
\(659\) | −3484.14 | − | 10723.1i | −0.205953 | − | 0.633857i | −0.999673 | − | 0.0255743i | \(-0.991859\pi\) |
0.793720 | − | 0.608283i | \(-0.208141\pi\) | |||||||
\(660\) | 5142.46 | − | 8338.52i | 0.303288 | − | 0.491783i | ||||
\(661\) | −5572.40 | + | 17150.1i | −0.327899 | + | 1.00917i | 0.642216 | + | 0.766524i | \(0.278015\pi\) |
−0.970115 | + | 0.242645i | \(0.921985\pi\) | |||||||
\(662\) | −6253.01 | + | 2031.73i | −0.367115 | + | 0.119283i | ||||
\(663\) | −63480.8 | + | 20626.2i | −3.71854 | + | 1.20823i | ||||
\(664\) | −3613.51 | + | 11121.2i | −0.211192 | + | 0.649982i | ||||
\(665\) | −400.774 | − | 5283.98i | −0.0233704 | − | 0.308126i | ||||
\(666\) | −15512.4 | − | 47742.2i | −0.902541 | − | 2.77774i | ||||
\(667\) | 579.295 | + | 797.331i | 0.0336288 | + | 0.0462860i | ||||
\(668\) | 6851.93i | 0.396870i | ||||||||
\(669\) | −7359.42 | + | 5346.93i | −0.425309 | + | 0.309005i | ||||
\(670\) | −1875.33 | + | 7714.81i | −0.108135 | + | 0.444849i | ||||
\(671\) | −12411.7 | − | 9017.66i | −0.714083 | − | 0.518812i | ||||
\(672\) | −5317.72 | + | 7319.21i | −0.305261 | + | 0.420156i | ||||
\(673\) | −14769.2 | − | 4798.80i | −0.845930 | − | 0.274859i | −0.146189 | − | 0.989257i | \(-0.546701\pi\) |
−0.699740 | + | 0.714397i | \(0.746701\pi\) | |||||||
\(674\) | −12286.2 | −0.702146 | ||||||||
\(675\) | −9447.10 | − | 61919.1i | −0.538695 | − | 3.53077i | ||||
\(676\) | 6569.42 | 0.373772 | ||||||||
\(677\) | −30517.0 | − | 9915.58i | −1.73244 | − | 0.562905i | −0.738645 | − | 0.674095i | \(-0.764534\pi\) |
−0.993799 | + | 0.111190i | \(0.964534\pi\) | |||||||
\(678\) | 37388.1 | − | 51460.3i | 2.11782 | − | 2.91493i | ||||
\(679\) | 9114.02 | + | 6621.73i | 0.515117 | + | 0.374254i | ||||
\(680\) | 14066.9 | − | 11945.4i | 0.793294 | − | 0.673653i | ||||
\(681\) | −26005.7 | + | 18894.2i | −1.46335 | + | 1.06319i | ||||
\(682\) | 15467.8i | 0.868462i | ||||||||
\(683\) | 5635.71 | + | 7756.90i | 0.315731 | + | 0.434567i | 0.937158 | − | 0.348905i | \(-0.113447\pi\) |
−0.621426 | + | 0.783472i | \(0.713447\pi\) | |||||||
\(684\) | 4700.32 | + | 14466.1i | 0.262750 | + | 0.808662i | ||||
\(685\) | −21115.8 | − | 5132.86i | −1.17780 | − | 0.286302i | ||||
\(686\) | −350.645 | + | 1079.17i | −0.0195156 | + | 0.0600627i | ||||
\(687\) | 1455.94 | − | 473.065i | 0.0808555 | − | 0.0262715i | ||||
\(688\) | −17341.2 | + | 5634.48i | −0.960938 | + | 0.312228i | ||||
\(689\) | −9809.86 | + | 30191.6i | −0.542418 | + | 1.66939i | ||||
\(690\) | −5199.56 | − | 1263.92i | −0.286875 | − | 0.0697342i | ||||
\(691\) | −3416.10 | − | 10513.7i | −0.188067 | − | 0.578812i | 0.811920 | − | 0.583768i | \(-0.198422\pi\) |
−0.999988 | + | 0.00495647i | \(0.998422\pi\) | |||||||
\(692\) | −2967.88 | − | 4084.93i | −0.163037 | − | 0.224401i | ||||
\(693\) | − | 15640.3i | − | 0.857322i | ||||||
\(694\) | 10132.3 | − | 7361.53i | 0.554202 | − | 0.402651i | ||||
\(695\) | 5961.82 | − | 5062.69i | 0.325388 | − | 0.276315i | ||||
\(696\) | 9522.32 | + | 6918.37i | 0.518596 | + | 0.376782i | ||||
\(697\) | 10669.7 | − | 14685.6i | 0.579833 | − | 0.798072i | ||||
\(698\) | 14954.9 | + | 4859.14i | 0.810962 | + | 0.263497i | ||||
\(699\) | −32804.5 | −1.77508 | ||||||||
\(700\) | −2542.08 | − | 417.429i | −0.137260 | − | 0.0225391i | ||||
\(701\) | 27227.8 | 1.46702 | 0.733508 | − | 0.679680i | \(-0.237882\pi\) | ||||
0.733508 | + | 0.679680i | \(0.237882\pi\) | |||||||
\(702\) | 104913. | + | 34088.3i | 5.64058 | + | 1.83274i | ||||
\(703\) | 7914.90 | − | 10893.9i | 0.424632 | − | 0.584455i | ||||
\(704\) | 4984.61 | + | 3621.53i | 0.266853 | + | 0.193880i | ||||
\(705\) | 1.96943 | − | 8.10190i | 0.000105210 | − | 0.000432816i | ||||
\(706\) | −5058.50 | + | 3675.22i | −0.269659 | + | 0.195919i | ||||
\(707\) | 2393.90i | 0.127344i | ||||||||
\(708\) | 8915.63 | + | 12271.3i | 0.473262 | + | 0.651390i | ||||
\(709\) | −6594.54 | − | 20295.9i | −0.349313 | − | 1.07508i | −0.959234 | − | 0.282613i | \(-0.908799\pi\) |
0.609921 | − | 0.792462i | \(-0.291201\pi\) | |||||||
\(710\) | −856.868 | − | 11297.3i | −0.0452925 | − | 0.597156i | ||||
\(711\) | 9792.30 | − | 30137.6i | 0.516512 | − | 1.58966i | ||||
\(712\) | 6494.98 | − | 2110.35i | 0.341868 | − | 0.111079i | ||||
\(713\) | 2161.54 | − | 702.327i | 0.113535 | − | 0.0368897i | ||||
\(714\) | −7177.72 | + | 22090.7i | −0.376217 | + | 1.15788i | ||||
\(715\) | 11436.1 | − | 18543.8i | 0.598164 | − | 0.969926i | ||||
\(716\) | 684.746 | + | 2107.43i | 0.0357405 | + | 0.109998i | ||||
\(717\) | 25695.9 | + | 35367.4i | 1.33840 | + | 1.84215i | ||||
\(718\) | − | 504.065i | − | 0.0261999i | ||||||
\(719\) | −7917.79 | + | 5752.61i | −0.410687 | + | 0.298382i | −0.773880 | − | 0.633332i | \(-0.781687\pi\) |
0.363193 | + | 0.931714i | \(0.381687\pi\) | |||||||
\(720\) | −67102.2 | + | 5089.50i | −3.47327 | + | 0.263437i | ||||
\(721\) | 2995.75 | + | 2176.54i | 0.154740 | + | 0.112425i | ||||
\(722\) | 4422.48 | − | 6087.02i | 0.227961 | − | 0.313761i | ||||
\(723\) | −48277.7 | − | 15686.4i | −2.48336 | − | 0.806892i | ||||
\(724\) | −11003.1 | −0.564818 | ||||||||
\(725\) | −1402.40 | + | 8540.42i | −0.0718398 | + | 0.437494i | ||||
\(726\) | −15921.2 | −0.813900 | ||||||||
\(727\) | −4529.59 | − | 1471.75i | −0.231077 | − | 0.0750816i | 0.191190 | − | 0.981553i | \(-0.438765\pi\) |
−0.422267 | + | 0.906472i | \(0.638765\pi\) | |||||||
\(728\) | −4579.55 | + | 6303.22i | −0.233145 | + | 0.320897i | ||||
\(729\) | 75962.7 | + | 55190.2i | 3.85931 | + | 2.80395i | ||||
\(730\) | −2064.97 | − | 5025.56i | −0.104696 | − | 0.254800i | ||||
\(731\) | −18454.2 | + | 13407.8i | −0.933727 | + | 0.678393i | ||||
\(732\) | − | 15677.4i | − | 0.791602i | ||||||
\(733\) | −10207.1 | − | 14048.9i | −0.514337 | − | 0.707924i | 0.470306 | − | 0.882503i | \(-0.344143\pi\) |
−0.984643 | + | 0.174579i | \(0.944143\pi\) | |||||||
\(734\) | 6367.85 | + | 19598.2i | 0.320220 | + | 0.985536i | ||||
\(735\) | −5150.24 | + | 2116.20i | −0.258462 | + | 0.106200i | ||||
\(736\) | −559.335 | + | 1721.46i | −0.0280127 | + | 0.0862143i | ||||
\(737\) | −5978.13 | + | 1942.41i | −0.298789 | + | 0.0970823i | ||||
\(738\) | −44157.1 | + | 14347.5i | −2.20250 | + | 0.715636i | ||||
\(739\) | 6797.66 | − | 20921.0i | 0.338371 | − | 1.04140i | −0.626667 | − | 0.779287i | \(-0.715581\pi\) |
0.965038 | − | 0.262111i | \(-0.0844186\pi\) | |||||||
\(740\) | −4237.26 | − | 4989.79i | −0.210493 | − | 0.247876i | ||||
\(741\) | 14151.7 | + | 43554.6i | 0.701588 | + | 2.15927i | ||||
\(742\) | 6493.32 | + | 8937.29i | 0.321263 | + | 0.442181i | ||||
\(743\) | − | 22487.6i | − | 1.11035i | −0.831733 | − | 0.555175i | \(-0.812651\pi\) | ||
0.831733 | − | 0.555175i | \(-0.187349\pi\) | |||||||
\(744\) | 21959.3 | − | 15954.4i | 1.08208 | − | 0.786177i | ||||
\(745\) | 29305.4 | + | 18073.0i | 1.44116 | + | 0.888781i | ||||
\(746\) | −12909.1 | − | 9378.98i | −0.633558 | − | 0.460307i | ||||
\(747\) | 31355.4 | − | 43157.0i | 1.53579 | − | 2.11383i | ||||
\(748\) | −8091.73 | − | 2629.16i | −0.395539 | − | 0.128518i | ||||
\(749\) | −9878.22 | −0.481899 | ||||||||
\(750\) | −24210.4 | − | 40273.4i | −1.17872 | − | 1.96077i | ||||
\(751\) | 25744.6 | 1.25091 | 0.625456 | − | 0.780260i | \(-0.284913\pi\) | ||||
0.625456 | + | 0.780260i | \(0.284913\pi\) | |||||||
\(752\) | −5.50487 | − | 1.78864i | −0.000266944 | − | 8.67354e-5i | ||||
\(753\) | 41476.3 | − | 57087.2i | 2.00728 | − | 2.76278i | ||||
\(754\) | −12331.5 | − | 8959.37i | −0.595606 | − | 0.432733i | ||||
\(755\) | 24544.8 | + | 15137.0i | 1.18315 | + | 0.729660i | ||||
\(756\) | 8354.61 | − | 6069.98i | 0.401924 | − | 0.292015i | ||||
\(757\) | − | 1972.69i | − | 0.0947144i | −0.998878 | − | 0.0473572i | \(-0.984920\pi\) | ||
0.998878 | − | 0.0473572i | \(-0.0150799\pi\) | |||||||
\(758\) | 2012.12 | + | 2769.44i | 0.0964160 | + | 0.132705i | ||||
\(759\) | −1309.13 | − | 4029.09i | −0.0626066 | − | 0.192683i | ||||
\(760\) | −8195.80 | − | 9651.37i | −0.391175 | − | 0.460647i | ||||
\(761\) | −9399.40 | + | 28928.4i | −0.447737 | + | 1.37799i | 0.431717 | + | 0.902009i | \(0.357908\pi\) |
−0.879454 | + | 0.475984i | \(0.842092\pi\) | |||||||
\(762\) | −10490.9 | + | 3408.71i | −0.498749 | + | 0.162053i | ||||
\(763\) | 7867.70 | − | 2556.37i | 0.373303 | − | 0.121293i | ||||
\(764\) | −4540.13 | + | 13973.1i | −0.214995 | + | 0.661687i | ||||
\(765\) | −77870.5 | + | 31996.4i | −3.68028 | + | 1.51220i | ||||
\(766\) | 2103.28 | + | 6473.23i | 0.0992097 | + | 0.305336i | ||||
\(767\) | 19827.2 | + | 27289.8i | 0.933400 | + | 1.28471i | ||||
\(768\) | 40501.1i | 1.90294i | ||||||||
\(769\) | −29090.9 | + | 21135.8i | −1.36417 | + | 0.991125i | −0.366000 | + | 0.930615i | \(0.619273\pi\) |
−0.998168 | + | 0.0605104i | \(0.980727\pi\) | |||||||
\(770\) | −2881.44 | − | 7012.64i | −0.134857 | − | 0.328205i | ||||
\(771\) | 44747.7 | + | 32511.1i | 2.09021 | + | 1.51863i | ||||
\(772\) | −1657.31 | + | 2281.10i | −0.0772643 | + | 0.106345i | ||||
\(773\) | 23003.0 | + | 7474.12i | 1.07032 | + | 0.347769i | 0.790613 | − | 0.612316i | \(-0.209762\pi\) |
0.279709 | + | 0.960085i | \(0.409762\pi\) | |||||||
\(774\) | 58344.4 | 2.70949 | ||||||||
\(775\) | 17731.6 | + | 9161.85i | 0.821857 | + | 0.424650i | ||||
\(776\) | 26917.8 | 1.24522 | ||||||||
\(777\) | −13456.4 | − | 4372.26i | −0.621296 | − | 0.201871i | ||||
\(778\) | −14455.8 | + | 19896.7i | −0.666151 | + | 0.916878i | ||||
\(779\) | −10075.9 | − | 7320.55i | −0.463422 | − | 0.336696i | ||||
\(780\) | 22199.5 | − | 1683.76i | 1.01906 | − | 0.0772928i | ||||
\(781\) | 7256.82 | − | 5272.39i | 0.332483 | − | 0.241563i | ||||
\(782\) | 4647.15i | 0.212509i | ||||||||
\(783\) | −20392.8 | − | 28068.3i | −0.930752 | − | 1.28107i | ||||
\(784\) | 1194.47 | + | 3676.19i | 0.0544126 | + | 0.167465i | ||||
\(785\) | −12676.8 | + | 20555.6i | −0.576377 | + | 0.934598i | ||||
\(786\) | −25539.3 | + | 78601.8i | −1.15898 | + | 3.56696i | ||||
\(787\) | −3595.95 | + | 1168.40i | −0.162874 | + | 0.0529210i | −0.389319 | − | 0.921103i | \(-0.627290\pi\) |
0.226445 | + | 0.974024i | \(0.427290\pi\) | |||||||
\(788\) | 3581.70 | − | 1163.77i | 0.161920 | − | 0.0526109i | ||||
\(789\) | −4755.29 | + | 14635.3i | −0.214566 | + | 0.660367i | ||||
\(790\) | −1161.74 | − | 15316.9i | −0.0523201 | − | 0.689811i | ||||
\(791\) | −4092.15 | − | 12594.3i | −0.183944 | − | 0.566123i | ||||
\(792\) | −21965.9 | − | 30233.5i | −0.985512 | − | 1.35644i | ||||
\(793\) | − | 34864.4i | − | 1.56125i | ||||||
\(794\) | 25957.9 | − | 18859.5i | 1.16021 | − | 0.842945i | ||||
\(795\) | −12804.2 | + | 52674.6i | −0.571220 | + | 2.34991i | ||||
\(796\) | −2256.96 | − | 1639.78i | −0.100497 | − | 0.0730155i | ||||
\(797\) | 9470.02 | − | 13034.4i | 0.420885 | − | 0.579299i | −0.544946 | − | 0.838471i | \(-0.683450\pi\) |
0.965831 | + | 0.259172i | \(0.0834498\pi\) | |||||||
\(798\) | 15156.6 | + | 4924.68i | 0.672353 | + | 0.218461i | ||||
\(799\) | −7.24115 | −0.000320617 | ||||||||
\(800\) | −14203.4 | + | 7135.77i | −0.627709 | + | 0.315359i | ||||
\(801\) | −31154.3 | −1.37426 | ||||||||
\(802\) | 12783.8 | + | 4153.69i | 0.562855 | + | 0.182883i | ||||
\(803\) | 2528.41 | − | 3480.05i | 0.111115 | − | 0.152937i | ||||
\(804\) | −5196.55 | − | 3775.52i | −0.227946 | − | 0.165612i | ||||
\(805\) | −849.146 | + | 721.082i | −0.0371782 | + | 0.0315712i | ||||
\(806\) | −28437.6 | + | 20661.1i | −1.24277 | + | 0.902923i | ||||
\(807\) | − | 34199.7i | − | 1.49180i | ||||||
\(808\) | 3362.11 | + | 4627.55i | 0.146385 | + | 0.201481i | ||||
\(809\) | −4487.80 | − | 13812.0i | −0.195034 | − | 0.600254i | −0.999976 | − | 0.00690012i | \(-0.997804\pi\) |
0.804942 | − | 0.593354i | \(-0.202196\pi\) | |||||||
\(810\) | 108998. | + | 26495.4i | 4.72813 | + | 1.14932i | ||||
\(811\) | 2851.31 | − | 8775.44i | 0.123456 | − | 0.379960i | −0.870160 | − | 0.492769i | \(-0.835985\pi\) |
0.993617 | + | 0.112809i | \(0.0359848\pi\) | |||||||
\(812\) | −1357.10 | + | 440.947i | −0.0586511 | + | 0.0190569i | ||||
\(813\) | 58157.0 | − | 18896.4i | 2.50880 | − | 0.815159i | ||||
\(814\) | 5953.33 | − | 18322.5i | 0.256344 | − | 0.788946i | ||||
\(815\) | 11319.5 | + | 2751.58i | 0.486510 | + | 0.118262i | ||||
\(816\) | 24450.8 | + | 75251.8i | 1.04896 | + | 3.22836i | ||||
\(817\) | 9199.17 | + | 12661.6i | 0.393927 | + | 0.542194i | ||||
\(818\) | 12241.1i | 0.523228i | ||||||||
\(819\) | 28754.7 | − | 20891.5i | 1.22683 | − | 0.891341i | ||||
\(820\) | −4615.10 | + | 3919.07i | −0.196544 | + | 0.166902i | ||||
\(821\) | −30901.9 | − | 22451.5i | −1.31362 | − | 0.954401i | −0.999988 | − | 0.00485661i | \(-0.998454\pi\) |
−0.313632 | − | 0.949545i | \(-0.601546\pi\) | |||||||
\(822\) | 38413.2 | − | 52871.2i | 1.62994 | − | 2.24343i | ||||
\(823\) | −38563.0 | − | 12529.9i | −1.63332 | − | 0.530697i | −0.658287 | − | 0.752767i | \(-0.728719\pi\) |
−0.975031 | + | 0.222070i | \(0.928719\pi\) | |||||||
\(824\) | 8847.81 | 0.374063 | ||||||||
\(825\) | 17077.6 | − | 33051.6i | 0.720686 | − | 1.39480i | ||||
\(826\) | 11738.4 | 0.494470 | ||||||||
\(827\) | 7636.81 | + | 2481.35i | 0.321110 | + | 0.104335i | 0.465137 | − | 0.885239i | \(-0.346005\pi\) |
−0.144027 | + | 0.989574i | \(0.546005\pi\) | |||||||
\(828\) | 1879.51 | − | 2586.92i | 0.0788857 | − | 0.108577i | ||||
\(829\) | −28319.0 | − | 20574.9i | −1.18644 | − | 0.861999i | −0.193556 | − | 0.981089i | \(-0.562002\pi\) |
−0.992883 | + | 0.119090i | \(0.962002\pi\) | |||||||
\(830\) | 6107.93 | − | 25127.0i | 0.255433 | − | 1.05081i | ||||
\(831\) | 34450.8 | − | 25030.0i | 1.43813 | − | 1.04486i | ||||
\(832\) | 14001.7i | 0.583439i | ||||||||
\(833\) | 2842.35 | + | 3912.15i | 0.118225 | + | 0.162723i | ||||
\(834\) | 7268.68 | + | 22370.7i | 0.301791 | + | 0.928817i | ||||
\(835\) | 1967.89 | + | 25945.6i | 0.0815590 | + | 1.07531i | ||||
\(836\) | −1803.88 | + | 5551.79i | −0.0746276 | + | 0.229680i | ||||
\(837\) | −76092.2 | + | 24723.9i | −3.14233 | + | 1.02101i | ||||
\(838\) | 9022.46 | − | 2931.58i | 0.371928 | − | 0.120847i | ||||
\(839\) | −2074.69 | + | 6385.23i | −0.0853708 | + | 0.262744i | −0.984625 | − | 0.174682i | \(-0.944110\pi\) |
0.899254 | + | 0.437427i | \(0.144110\pi\) | |||||||
\(840\) | −6983.63 | + | 11324.0i | −0.286855 | + | 0.465137i | ||||
\(841\) | −6055.20 | − | 18636.0i | −0.248276 | − | 0.764115i | ||||
\(842\) | −19563.0 | − | 26926.2i | −0.800697 | − | 1.10206i | ||||
\(843\) | 66879.3i | 2.73244i | ||||||||
\(844\) | −29.6316 | + | 21.5286i | −0.00120848 | + | 0.000878015i | ||||
\(845\) | 24875.8 | − | 1886.76i | 1.01273 | − | 0.0768123i | ||||
\(846\) | 14.9839 | + | 10.8865i | 0.000608934 | + | 0.000442417i | ||||
\(847\) | −1948.27 | + | 2681.56i | −0.0790358 | + | 0.108783i | ||||
\(848\) | 35789.9 | + | 11628.9i | 1.44933 | + | 0.470916i | ||||
\(849\) | −69551.2 | −2.81153 | ||||||||
\(850\) | −29020.1 | + | 28692.5i | −1.17104 | + | 1.15782i | ||||
\(851\) | −2830.79 | −0.114028 | ||||||||
\(852\) | 8717.53 | + | 2832.50i | 0.350537 | + | 0.113896i | ||||
\(853\) | −12983.3 | + | 17870.0i | −0.521150 | + | 0.717301i | −0.985750 | − | 0.168220i | \(-0.946198\pi\) |
0.464600 | + | 0.885521i | \(0.346198\pi\) | |||||||
\(854\) | −9815.40 | − | 7131.30i | −0.393297 | − | 0.285747i | ||||
\(855\) | 21952.9 | + | 53427.4i | 0.878099 | + | 2.13705i | ||||
\(856\) | −19095.2 | + | 13873.5i | −0.762453 | + | 0.553955i | ||||
\(857\) | − | 7913.89i | − | 0.315441i | −0.987484 | − | 0.157721i | \(-0.949585\pi\) | ||
0.987484 | − | 0.157721i | \(-0.0504146\pi\) | |||||||
\(858\) | 38512.1 | + | 53007.4i | 1.53238 | + | 2.10914i | ||||
\(859\) | 14101.7 | + | 43400.5i | 0.560120 | + | 1.72387i | 0.682023 | + | 0.731330i | \(0.261100\pi\) |
−0.121903 | + | 0.992542i | \(0.538900\pi\) | |||||||
\(860\) | 7037.44 | − | 2891.63i | 0.279040 | − | 0.114656i | ||||
\(861\) | −4043.94 | + | 12446.0i | −0.160066 | + | 0.492634i | ||||
\(862\) | −16231.3 | + | 5273.87i | −0.641346 | + | 0.208386i | ||||
\(863\) | 3629.40 | − | 1179.26i | 0.143159 | − | 0.0465152i | −0.236561 | − | 0.971617i | \(-0.576020\pi\) |
0.379720 | + | 0.925101i | \(0.376020\pi\) | |||||||
\(864\) | 19690.2 | − | 60600.1i | 0.775316 | − | 2.38618i | ||||
\(865\) | −12411.4 | − | 14615.6i | −0.487861 | − | 0.574505i | ||||
\(866\) | −3629.13 | − | 11169.3i | −0.142405 | − | 0.438278i | ||||
\(867\) | 28832.3 | + | 39684.2i | 1.12941 | + | 1.55449i | ||||
\(868\) | 3290.64i | 0.128677i | ||||||||
\(869\) | 9838.79 | − | 7148.30i | 0.384071 | − | 0.279044i | ||||
\(870\) | −22154.1 | − | 13662.7i | −0.863326 | − | 0.532423i | ||||
\(871\) | −11556.4 | − | 8396.24i | −0.449569 | − | 0.326631i | ||||
\(872\) | 11618.4 | − | 15991.4i | 0.451204 | − | 0.621029i | ||||
\(873\) | −116787. | − | 37946.2i | −4.52764 | − | 1.47112i | ||||
\(874\) | 3188.44 | 0.123399 | ||||||||
\(875\) | −9745.75 | − | 850.547i | −0.376533 | − | 0.0328614i | ||||
\(876\) | 4395.69 | 0.169539 | ||||||||
\(877\) | −3868.87 | − | 1257.07i | −0.148965 | − | 0.0484017i | 0.233585 | − | 0.972336i | \(-0.424954\pi\) |
−0.382550 | + | 0.923935i | \(0.624954\pi\) | |||||||
\(878\) | −2123.41 | + | 2922.63i | −0.0816192 | + | 0.112339i | ||||
\(879\) | −2777.91 | − | 2018.27i | −0.106595 | − | 0.0774456i | ||||
\(880\) | −21982.3 | − | 13556.7i | −0.842070 | − | 0.519314i | ||||
\(881\) | 32958.1 | − | 23945.5i | 1.26037 | − | 0.915714i | 0.261596 | − | 0.965177i | \(-0.415751\pi\) |
0.998776 | + | 0.0494636i | \(0.0157512\pi\) | |||||||
\(882\) | − | 12368.6i | − | 0.472189i | ||||||
\(883\) | −22512.5 | − | 30985.8i | −0.857991 | − | 1.18092i | −0.982045 | − | 0.188648i | \(-0.939589\pi\) |
0.124053 | − | 0.992276i | \(-0.460411\pi\) | |||||||
\(884\) | −5974.82 | − | 18388.6i | −0.227325 | − | 0.699633i | ||||
\(885\) | 37284.3 | + | 43906.0i | 1.41616 | + | 1.66767i | ||||
\(886\) | 13753.0 | − | 42327.3i | 0.521490 | − | 1.60498i | ||||
\(887\) | −16001.8 | + | 5199.30i | −0.605736 | + | 0.196816i | −0.595797 | − | 0.803135i | \(-0.703164\pi\) |
−0.00993895 | + | 0.999951i | \(0.503164\pi\) | |||||||
\(888\) | −32152.7 | + | 10447.1i | −1.21506 | + | 0.394798i | ||||
\(889\) | −709.651 | + | 2184.08i | −0.0267727 | + | 0.0823979i | ||||
\(890\) | −13968.7 | + | 5739.64i | −0.526103 | + | 0.216172i | ||||
\(891\) | 27443.1 | + | 84461.2i | 1.03185 | + | 3.17571i | ||||
\(892\) | −1548.86 | − | 2131.82i | −0.0581385 | − | 0.0800208i | ||||
\(893\) | 4.96820i | 0.000186175i | ||||||||
\(894\) | −83769.5 | + | 60862.1i | −3.13386 | + | 2.27688i | ||||
\(895\) | 3198.12 | + | 7783.35i | 0.119443 | + | 0.290691i | ||||
\(896\) | 9702.95 | + | 7049.60i | 0.361778 | + | 0.262847i | ||||
\(897\) | 5658.83 | − | 7788.71i | 0.210639 | − | 0.289919i | ||||
\(898\) | 32863.4 | + | 10678.0i | 1.22123 | + | 0.396802i | ||||
\(899\) | 11055.3 | 0.410138 | ||||||||
\(900\) | 27759.0 | − | 4235.24i | 1.02811 | − | 0.156861i | ||||
\(901\) | 47078.4 | 1.74074 | ||||||||
\(902\) | −16946.6 | − | 5506.28i | −0.625566 | − | 0.203259i | ||||
\(903\) | 9665.98 | − | 13304.1i | 0.356217 | − | 0.490290i | ||||
\(904\) | −25598.5 | − | 18598.4i | −0.941806 | − | 0.684262i | ||||
\(905\) | −41664.5 | + | 3160.13i | −1.53036 | + | 0.116073i | ||||
\(906\) | −70161.3 | + | 50975.2i | −2.57280 | + | 1.86925i | ||||
\(907\) | 22992.5i | 0.841735i | 0.907122 | + | 0.420868i | \(0.138274\pi\) | ||||
−0.907122 | + | 0.420868i | \(0.861726\pi\) | |||||||
\(908\) | −5473.13 | − | 7533.12i | −0.200036 | − | 0.275325i | ||||
\(909\) | −8063.48 | − | 24816.9i | −0.294223 | − | 0.905526i | ||||
\(910\) | 9043.88 | − | 14664.7i | 0.329452 | − | 0.534209i | ||||
\(911\) | 6565.50 | − | 20206.5i | 0.238776 | − | 0.734876i | −0.757822 | − | 0.652461i | \(-0.773737\pi\) |
0.996598 | − | 0.0824153i | \(-0.0262634\pi\) | |||||||
\(912\) | 51630.7 | − | 16775.8i | 1.87463 | − | 0.609105i | ||||
\(913\) | 19470.7 | − | 6326.42i | 0.705790 | − | 0.229325i | ||||
\(914\) | −11339.3 | + | 34898.6i | −0.410360 | + | 1.26296i | ||||
\(915\) | −4502.59 | − | 59364.1i | −0.162679 | − | 2.14483i | ||||
\(916\) | 137.034 | + | 421.746i | 0.00494292 | + | 0.0152127i | ||||
\(917\) | 10113.4 | + | 13920.0i | 0.364204 | + | 0.501284i | ||||
\(918\) | − | 163593.i | − | 5.88167i | ||||||
\(919\) | 28087.3 | − | 20406.6i | 1.00818 | − | 0.732482i | 0.0443497 | − | 0.999016i | \(-0.485878\pi\) |
0.963826 | + | 0.266534i | \(0.0858784\pi\) | |||||||
\(920\) | −628.726 | + | 2586.48i | −0.0225310 | + | 0.0926887i | ||||
\(921\) | 62534.7 | + | 45434.1i | 2.23734 | + | 1.62552i | ||||
\(922\) | 2748.81 | − | 3783.42i | 0.0981859 | − | 0.135141i | ||||
\(923\) | 19386.6 | + | 6299.10i | 0.691353 | + | 0.224634i | ||||
\(924\) | 6133.72 | 0.218382 | ||||||||
\(925\) | −17477.9 | − | 17677.4i | −0.621265 | − | 0.628357i | ||||
\(926\) | −6065.28 | −0.215246 | ||||||||
\(927\) | −38387.4 | − | 12472.8i | −1.36009 | − | 0.441922i | ||||
\(928\) | −5175.13 | + | 7122.95i | −0.183062 | + | 0.251964i | ||||
\(929\) | 16240.6 | + | 11799.5i | 0.573560 | + | 0.416716i | 0.836397 | − | 0.548125i | \(-0.184658\pi\) |
−0.262837 | + | 0.964840i | \(0.584658\pi\) | |||||||
\(930\) | −45752.7 | + | 38852.5i | −1.61321 | + | 1.36992i | ||||
\(931\) | 2684.15 | − | 1950.15i | 0.0944893 | − | 0.0686505i | ||||
\(932\) | − | 9502.55i | − | 0.333977i | ||||||
\(933\) | 20480.1 | + | 28188.4i | 0.718637 | + | 0.989118i | ||||
\(934\) | 9051.65 | + | 27858.1i | 0.317108 | + | 0.975959i | ||||
\(935\) | −31395.3 | − | 7631.63i | −1.09811 | − | 0.266932i | ||||
\(936\) | 26243.4 | − | 80769.0i | 0.916446 | − | 2.82053i | ||||
\(937\) | 24621.6 | − | 8000.03i | 0.858432 | − | 0.278922i | 0.153459 | − | 0.988155i | \(-0.450959\pi\) |
0.704974 | + | 0.709234i | \(0.250959\pi\) | |||||||
\(938\) | −4727.60 | + | 1536.09i | −0.164565 | + | 0.0534703i | ||||
\(939\) | 15454.8 | − | 47564.8i | 0.537111 | − | 1.65306i | ||||
\(940\) | 2.34689 | + | 0.570488i | 8.14332e−5 | + | 1.97950e-5i | ||||
\(941\) | −11851.8 | − | 36476.0i | −0.410581 | − | 1.26364i | −0.916144 | − | 0.400849i | \(-0.868715\pi\) |
0.505563 | − | 0.862790i | \(-0.331285\pi\) | |||||||
\(942\) | −42690.3 | − | 58758.1i | −1.47656 | − | 2.03232i | ||||
\(943\) | 2618.22i | 0.0904145i | ||||||||
\(944\) | 32350.0 | − | 23503.6i | 1.11536 | − | 0.810358i | ||||
\(945\) | 29892.3 | − | 25384.1i | 1.02899 | − | 0.873804i | ||||
\(946\) | 18115.0 | + | 13161.3i | 0.622590 | + | 0.452338i | ||||
\(947\) | −13503.2 | + | 18585.6i | −0.463353 | + | 0.637751i | −0.975200 | − | 0.221326i | \(-0.928961\pi\) |
0.511847 | + | 0.859077i | \(0.328961\pi\) | |||||||
\(948\) | 11819.2 | + | 3840.30i | 0.404926 | + | 0.131569i | ||||
\(949\) | 9775.43 | 0.334377 | ||||||||
\(950\) | 19686.1 | + | 19910.9i | 0.672319 | + | 0.679994i | ||||
\(951\) | −51664.8 | −1.76167 | ||||||||
\(952\) | 10988.8 | + | 3570.49i | 0.374108 | + | 0.121555i | ||||
\(953\) | −2440.00 | + | 3358.38i | −0.0829375 | + | 0.114154i | −0.848470 | − | 0.529244i | \(-0.822476\pi\) |
0.765532 | + | 0.643397i | \(0.222476\pi\) | |||||||
\(954\) | −97418.2 | − | 70778.4i | −3.30611 | − | 2.40203i | ||||
\(955\) | −13178.6 | + | 54214.5i | −0.446543 | + | 1.83701i | ||||
\(956\) | −10244.9 | + | 7443.38i | −0.346595 | + | 0.251816i | ||||
\(957\) | − | 20606.9i | − | 0.696058i | ||||||
\(958\) | −33941.3 | − | 46716.2i | −1.14467 | − | 1.57550i | ||||
\(959\) | −4204.34 | − | 12939.6i | −0.141570 | − | 0.435707i | ||||
\(960\) | 1808.26 | + | 23840.9i | 0.0607930 | + | 0.801521i | ||||
\(961\) | −1327.71 | + | 4086.28i | −0.0445676 | + | 0.137165i | ||||
\(962\) | 41638.1 | − | 13529.1i | 1.39550 | − | 0.453424i | ||||
\(963\) | 102404. | − | 33273.2i | 3.42673 | − | 1.11341i | ||||
\(964\) | 4543.90 | − | 13984.7i | 0.151815 | − | 0.467237i | ||||
\(965\) | −5620.46 | + | 9113.60i | −0.187491 | + | 0.304018i | ||||
\(966\) | −1035.28 | − | 3186.27i | −0.0344820 | − | 0.106125i | ||||
\(967\) | −11612.5 | − | 15983.2i | −0.386175 | − | 0.531525i | 0.571032 | − | 0.820928i | \(-0.306543\pi\) |
−0.957207 | + | 0.289403i | \(0.906543\pi\) | |||||||
\(968\) | 7919.86i | 0.262969i | ||||||||
\(969\) | 54944.7 | − | 39919.7i | 1.82155 | − | 1.32343i | ||||
\(970\) | −59354.7 | + | 4501.87i | −1.96470 | + | 0.149017i | ||||
\(971\) | −415.756 | − | 302.065i | −0.0137407 | − | 0.00998323i | 0.580894 | − | 0.813979i | \(-0.302703\pi\) |
−0.594634 | + | 0.803996i | \(0.702703\pi\) | |||||||
\(972\) | −29929.1 | + | 41193.8i | −0.987629 | + | 1.35935i | ||||
\(973\) | 4657.29 | + | 1513.25i | 0.153449 | + | 0.0498586i | ||||
\(974\) | 51638.5 | 1.69877 | ||||||||
\(975\) | 83577.1 | − | 12751.5i | 2.74524 | − | 0.418846i | ||||
\(976\) | −41329.2 | −1.35545 | ||||||||
\(977\) | 6400.56 | + | 2079.67i | 0.209593 | + | 0.0681008i | 0.411932 | − | 0.911215i | \(-0.364854\pi\) |
−0.202339 | + | 0.979316i | \(0.564854\pi\) | |||||||
\(978\) | −20592.2 | + | 28342.7i | −0.673277 | + | 0.926687i | ||||
\(979\) | −9672.91 | − | 7027.78i | −0.315779 | − | 0.229427i | ||||
\(980\) | −613.003 | − | 1491.88i | −0.0199813 | − | 0.0486290i | ||||
\(981\) | −72951.3 | + | 53002.2i | −2.37427 | + | 1.72501i | ||||
\(982\) | 18389.1i | 0.597576i | ||||||||
\(983\) | 7514.30 | + | 10342.5i | 0.243814 | + | 0.335581i | 0.913333 | − | 0.407214i | \(-0.133500\pi\) |
−0.669519 | + | 0.742795i | \(0.733500\pi\) | |||||||
\(984\) | 9662.57 | + | 29738.3i | 0.313040 | + | 0.963438i | ||||
\(985\) | 13228.3 | − | 5435.40i | 0.427906 | − | 0.175823i | ||||
\(986\) | −6985.25 | + | 21498.4i | −0.225614 | + | 0.694370i | ||||
\(987\) | 4.96481 | − | 1.61316i | 0.000160113 | − | 5.20239e-5i | ||||
\(988\) | −12616.5 | + | 4099.36i | −0.406260 | + | 0.132002i | ||||
\(989\) | 1016.70 | − | 3129.08i | 0.0326888 | − | 0.100606i | ||||
\(990\) | 53492.0 | + | 62992.2i | 1.71726 | + | 2.02225i | ||||
\(991\) | 13339.7 | + | 41055.3i | 0.427597 | + | 1.31601i | 0.900485 | + | 0.434887i | \(0.143212\pi\) |
−0.472888 | + | 0.881123i | \(0.656788\pi\) | |||||||
\(992\) | 11934.3 | + | 16426.2i | 0.381970 | + | 0.525737i | ||||
\(993\) | − | 20199.7i | − | 0.645537i | ||||||
\(994\) | 5738.81 | − | 4169.49i | 0.183123 | − | 0.133046i | ||||
\(995\) | −9017.16 | − | 5560.98i | −0.287300 | − | 0.177181i | ||||
\(996\) | 16925.1 | + | 12296.8i | 0.538446 | + | 0.391204i | ||||
\(997\) | −16198.5 | + | 22295.4i | −0.514556 | + | 0.708226i | −0.984679 | − | 0.174375i | \(-0.944210\pi\) |
0.470123 | + | 0.882601i | \(0.344210\pi\) | |||||||
\(998\) | −28978.2 | − | 9415.59i | −0.919128 | − | 0.298643i | ||||
\(999\) | 99651.7 | 3.15599 |
(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 | 175.4.n.a.29.12 | ✓ | 184 | |
25.19 | even | 10 | inner | 175.4.n.a.169.12 | yes | 184 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
175.4.n.a.29.12 | ✓ | 184 | 1.1 | even | 1 | trivial | |
175.4.n.a.169.12 | yes | 184 | 25.19 | even | 10 | inner |