Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,5,Mod(23,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.23");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.g (of order \(12\), 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: | \(7.64937726820\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 45.4 | ||
Character | \(\chi\) | \(=\) | 74.45 |
Dual form | 74.5.g.b.51.4 |
$q$-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 \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{12}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.73205 | + | 0.732051i | 0.683013 | + | 0.183013i | ||||
\(3\) | −0.984681 | − | 0.568506i | −0.109409 | − | 0.0631673i | 0.444297 | − | 0.895880i | \(-0.353454\pi\) |
−0.553706 | + | 0.832712i | \(0.686787\pi\) | |||||||
\(4\) | 6.92820 | + | 4.00000i | 0.433013 | + | 0.250000i | ||||
\(5\) | −27.3382 | + | 7.32524i | −1.09353 | + | 0.293010i | −0.760126 | − | 0.649775i | \(-0.774863\pi\) |
−0.333401 | + | 0.942785i | \(0.608196\pi\) | |||||||
\(6\) | −2.27402 | − | 2.27402i | −0.0631673 | − | 0.0631673i | ||||
\(7\) | −37.5434 | + | 65.0271i | −0.766192 | + | 1.32708i | 0.173422 | + | 0.984848i | \(0.444518\pi\) |
−0.939614 | + | 0.342236i | \(0.888816\pi\) | |||||||
\(8\) | 16.0000 | + | 16.0000i | 0.250000 | + | 0.250000i | ||||
\(9\) | −39.8536 | − | 69.0285i | −0.492020 | − | 0.852203i | ||||
\(10\) | −80.0517 | −0.800517 | ||||||||
\(11\) | 183.473i | 1.51630i | 0.652079 | + | 0.758151i | \(0.273897\pi\) | ||||
−0.652079 | + | 0.758151i | \(0.726103\pi\) | |||||||
\(12\) | −4.54805 | − | 7.87745i | −0.0315837 | − | 0.0547045i | ||||
\(13\) | 82.1869 | − | 22.0219i | 0.486313 | − | 0.130307i | −0.00732774 | − | 0.999973i | \(-0.502333\pi\) |
0.493641 | + | 0.869666i | \(0.335666\pi\) | |||||||
\(14\) | −150.174 | + | 150.174i | −0.766192 | + | 0.766192i | ||||
\(15\) | 31.0838 | + | 8.32889i | 0.138150 | + | 0.0370173i | ||||
\(16\) | 32.0000 | + | 55.4256i | 0.125000 | + | 0.216506i | ||||
\(17\) | 7.71214 | − | 28.7821i | 0.0266856 | − | 0.0995920i | −0.951299 | − | 0.308271i | \(-0.900250\pi\) |
0.977984 | + | 0.208679i | \(0.0669163\pi\) | |||||||
\(18\) | −58.3497 | − | 217.764i | −0.180092 | − | 0.672112i | ||||
\(19\) | −221.914 | + | 59.4616i | −0.614719 | + | 0.164713i | −0.552726 | − | 0.833363i | \(-0.686412\pi\) |
−0.0619931 | + | 0.998077i | \(0.519746\pi\) | |||||||
\(20\) | −218.705 | − | 58.6019i | −0.546764 | − | 0.146505i | ||||
\(21\) | 73.9366 | − | 42.6873i | 0.167657 | − | 0.0967966i | ||||
\(22\) | −134.311 | + | 501.256i | −0.277503 | + | 1.03565i | ||||
\(23\) | −7.30278 | − | 7.30278i | −0.0138049 | − | 0.0138049i | 0.700171 | − | 0.713976i | \(-0.253107\pi\) |
−0.713976 | + | 0.700171i | \(0.753107\pi\) | |||||||
\(24\) | −6.65880 | − | 24.8510i | −0.0115604 | − | 0.0431441i | ||||
\(25\) | 152.451 | − | 88.0176i | 0.243921 | − | 0.140828i | ||||
\(26\) | 240.660 | 0.356006 | ||||||||
\(27\) | 182.726i | 0.250653i | ||||||||
\(28\) | −520.217 | + | 300.347i | −0.663542 | + | 0.383096i | ||||
\(29\) | 251.882 | − | 251.882i | 0.299503 | − | 0.299503i | −0.541316 | − | 0.840819i | \(-0.682074\pi\) |
0.840819 | + | 0.541316i | \(0.182074\pi\) | |||||||
\(30\) | 78.8255 | + | 45.5099i | 0.0875838 | + | 0.0505666i | ||||
\(31\) | 581.602 | − | 581.602i | 0.605205 | − | 0.605205i | −0.336484 | − | 0.941689i | \(-0.609238\pi\) |
0.941689 | + | 0.336484i | \(0.109238\pi\) | |||||||
\(32\) | 46.8513 | + | 174.851i | 0.0457532 | + | 0.170753i | ||||
\(33\) | 104.305 | − | 180.662i | 0.0957808 | − | 0.165897i | ||||
\(34\) | 42.1399 | − | 72.9885i | 0.0364532 | − | 0.0631388i | ||||
\(35\) | 550.029 | − | 2052.74i | 0.449003 | − | 1.67570i | ||||
\(36\) | − | 637.658i | − | 0.492020i | ||||||
\(37\) | −873.668 | + | 1053.98i | −0.638180 | + | 0.769887i | ||||
\(38\) | −649.808 | −0.450006 | ||||||||
\(39\) | −93.4475 | − | 25.0392i | −0.0614382 | − | 0.0164623i | ||||
\(40\) | −554.615 | − | 320.207i | −0.346634 | − | 0.200129i | ||||
\(41\) | 2221.32 | + | 1282.48i | 1.32143 | + | 0.762928i | 0.983957 | − | 0.178408i | \(-0.0570946\pi\) |
0.337473 | + | 0.941335i | \(0.390428\pi\) | |||||||
\(42\) | 233.248 | − | 62.4986i | 0.132227 | − | 0.0354300i | ||||
\(43\) | 294.288 | + | 294.288i | 0.159161 | + | 0.159161i | 0.782195 | − | 0.623034i | \(-0.214100\pi\) |
−0.623034 | + | 0.782195i | \(0.714100\pi\) | |||||||
\(44\) | −733.890 | + | 1271.14i | −0.379076 | + | 0.656578i | ||||
\(45\) | 1595.18 | + | 1595.18i | 0.787741 | + | 0.787741i | ||||
\(46\) | −14.6056 | − | 25.2976i | −0.00690244 | − | 0.0119554i | ||||
\(47\) | 2453.54 | 1.11070 | 0.555352 | − | 0.831616i | \(-0.312584\pi\) | ||||
0.555352 | + | 0.831616i | \(0.312584\pi\) | |||||||
\(48\) | − | 72.7688i | − | 0.0315837i | ||||||
\(49\) | −1618.52 | − | 2803.35i | −0.674101 | − | 1.16758i | ||||
\(50\) | 480.937 | − | 128.867i | 0.192375 | − | 0.0515467i | ||||
\(51\) | −23.9568 | + | 23.9568i | −0.00921061 | + | 0.00921061i | ||||
\(52\) | 657.495 | + | 176.175i | 0.243156 | + | 0.0651536i | ||||
\(53\) | −1452.42 | − | 2515.67i | −0.517060 | − | 0.895574i | −0.999804 | − | 0.0198126i | \(-0.993693\pi\) |
0.482744 | − | 0.875762i | \(-0.339640\pi\) | |||||||
\(54\) | −133.765 | + | 499.217i | −0.0458727 | + | 0.171199i | ||||
\(55\) | −1343.98 | − | 5015.81i | −0.444291 | − | 1.65812i | ||||
\(56\) | −1641.13 | + | 439.739i | −0.523319 | + | 0.140223i | ||||
\(57\) | 252.318 | + | 67.6085i | 0.0776603 | + | 0.0208090i | ||||
\(58\) | 872.545 | − | 503.764i | 0.259377 | − | 0.149751i | ||||
\(59\) | −1058.12 | + | 3948.96i | −0.303971 | + | 1.13443i | 0.629857 | + | 0.776711i | \(0.283113\pi\) |
−0.933828 | + | 0.357723i | \(0.883553\pi\) | |||||||
\(60\) | 182.040 | + | 182.040i | 0.0505666 | + | 0.0505666i | ||||
\(61\) | −747.066 | − | 2788.09i | −0.200770 | − | 0.749284i | −0.990697 | − | 0.136084i | \(-0.956548\pi\) |
0.789927 | − | 0.613201i | \(-0.210118\pi\) | |||||||
\(62\) | 2014.73 | − | 1163.20i | 0.524123 | − | 0.302602i | ||||
\(63\) | 5984.96 | 1.50793 | ||||||||
\(64\) | 512.000i | 0.125000i | ||||||||
\(65\) | −2085.52 | + | 1204.08i | −0.493615 | + | 0.284989i | ||||
\(66\) | 417.221 | − | 417.221i | 0.0957808 | − | 0.0957808i | ||||
\(67\) | 3539.90 | + | 2043.76i | 0.788573 | + | 0.455283i | 0.839460 | − | 0.543422i | \(-0.182871\pi\) |
−0.0508869 | + | 0.998704i | \(0.516205\pi\) | |||||||
\(68\) | 168.560 | − | 168.560i | 0.0364532 | − | 0.0364532i | ||||
\(69\) | 3.03924 | + | 11.3426i | 0.000638361 | + | 0.00238240i | ||||
\(70\) | 3005.42 | − | 5205.53i | 0.613350 | − | 1.06235i | ||||
\(71\) | −1762.56 | + | 3052.84i | −0.349645 | + | 0.605603i | −0.986186 | − | 0.165640i | \(-0.947031\pi\) |
0.636541 | + | 0.771243i | \(0.280364\pi\) | |||||||
\(72\) | 466.798 | − | 1742.11i | 0.0900459 | − | 0.336056i | ||||
\(73\) | 8737.86i | 1.63968i | 0.572592 | + | 0.819841i | \(0.305938\pi\) | ||||
−0.572592 | + | 0.819841i | \(0.694062\pi\) | |||||||
\(74\) | −3158.47 | + | 2239.95i | −0.576784 | + | 0.409048i | ||||
\(75\) | −200.154 | −0.0355830 | ||||||||
\(76\) | −1775.31 | − | 475.692i | −0.307360 | − | 0.0823567i | ||||
\(77\) | −11930.7 | − | 6888.19i | −2.01226 | − | 1.16178i | ||||
\(78\) | −236.973 | − | 136.817i | −0.0389502 | − | 0.0224879i | ||||
\(79\) | −11115.1 | + | 2978.27i | −1.78097 | + | 0.477211i | −0.990761 | − | 0.135620i | \(-0.956697\pi\) |
−0.790214 | + | 0.612831i | \(0.790031\pi\) | |||||||
\(80\) | −1280.83 | − | 1280.83i | −0.200129 | − | 0.200129i | ||||
\(81\) | −3124.26 | + | 5411.38i | −0.476187 | + | 0.824780i | ||||
\(82\) | 5129.93 | + | 5129.93i | 0.762928 | + | 0.762928i | ||||
\(83\) | 3790.09 | + | 6564.64i | 0.550166 | + | 0.952916i | 0.998262 | + | 0.0589302i | \(0.0187689\pi\) |
−0.448096 | + | 0.893985i | \(0.647898\pi\) | |||||||
\(84\) | 682.997 | 0.0967966 | ||||||||
\(85\) | 843.343i | 0.116726i | ||||||||
\(86\) | 588.576 | + | 1019.44i | 0.0795803 | + | 0.137837i | ||||
\(87\) | −391.220 | + | 104.827i | −0.0516871 | + | 0.0138495i | ||||
\(88\) | −2935.56 | + | 2935.56i | −0.379076 | + | 0.379076i | ||||
\(89\) | −11588.2 | − | 3105.04i | −1.46297 | − | 0.392001i | −0.562454 | − | 0.826829i | \(-0.690143\pi\) |
−0.900514 | + | 0.434828i | \(0.856809\pi\) | |||||||
\(90\) | 3190.35 | + | 5525.85i | 0.393870 | + | 0.682204i | ||||
\(91\) | −1653.56 | + | 6171.15i | −0.199681 | + | 0.745218i | ||||
\(92\) | −21.3840 | − | 79.8063i | −0.00252647 | − | 0.00942891i | ||||
\(93\) | −903.336 | + | 242.048i | −0.104444 | + | 0.0279857i | ||||
\(94\) | 6703.21 | + | 1796.12i | 0.758624 | + | 0.203273i | ||||
\(95\) | 5631.14 | − | 3251.14i | 0.623949 | − | 0.360237i | ||||
\(96\) | 53.2704 | − | 198.808i | 0.00578021 | − | 0.0215720i | ||||
\(97\) | −3847.20 | − | 3847.20i | −0.408885 | − | 0.408885i | 0.472465 | − | 0.881350i | \(-0.343364\pi\) |
−0.881350 | + | 0.472465i | \(0.843364\pi\) | |||||||
\(98\) | −2369.67 | − | 8843.74i | −0.246738 | − | 0.920839i | ||||
\(99\) | 12664.8 | − | 7312.04i | 1.29220 | − | 0.746051i | ||||
\(100\) | 1408.28 | 0.140828 | ||||||||
\(101\) | 6065.92i | 0.594640i | 0.954778 | + | 0.297320i | \(0.0960928\pi\) | ||||
−0.954778 | + | 0.297320i | \(0.903907\pi\) | |||||||
\(102\) | −82.9888 | + | 47.9136i | −0.00797662 | + | 0.00460530i | ||||
\(103\) | 5359.94 | − | 5359.94i | 0.505226 | − | 0.505226i | −0.407831 | − | 0.913057i | \(-0.633715\pi\) |
0.913057 | + | 0.407831i | \(0.133715\pi\) | |||||||
\(104\) | 1667.34 | + | 962.639i | 0.154155 | + | 0.0890014i | ||||
\(105\) | −1708.60 | + | 1708.60i | −0.154975 | + | 0.154975i | ||||
\(106\) | −2126.49 | − | 7936.18i | −0.189257 | − | 0.706317i | ||||
\(107\) | −2950.54 | + | 5110.48i | −0.257711 | + | 0.446369i | −0.965628 | − | 0.259926i | \(-0.916302\pi\) |
0.707917 | + | 0.706296i | \(0.249635\pi\) | |||||||
\(108\) | −730.904 | + | 1265.96i | −0.0626632 | + | 0.108536i | ||||
\(109\) | 126.271 | − | 471.249i | 0.0106280 | − | 0.0396641i | −0.960408 | − | 0.278597i | \(-0.910131\pi\) |
0.971036 | + | 0.238932i | \(0.0767975\pi\) | |||||||
\(110\) | − | 14687.3i | − | 1.21383i | ||||||
\(111\) | 1459.48 | − | 541.144i | 0.118454 | − | 0.0439205i | ||||
\(112\) | −4805.56 | −0.383096 | ||||||||
\(113\) | 19324.1 | + | 5177.88i | 1.51336 | + | 0.405504i | 0.917550 | − | 0.397620i | \(-0.130164\pi\) |
0.595812 | + | 0.803124i | \(0.296830\pi\) | |||||||
\(114\) | 639.854 | + | 369.420i | 0.0492347 | + | 0.0284256i | ||||
\(115\) | 253.139 | + | 146.150i | 0.0191410 | + | 0.0110510i | ||||
\(116\) | 2752.62 | − | 737.561i | 0.204564 | − | 0.0548128i | ||||
\(117\) | −4795.58 | − | 4795.58i | −0.350324 | − | 0.350324i | ||||
\(118\) | −5781.69 | + | 10014.2i | −0.415232 | + | 0.719202i | ||||
\(119\) | 1582.08 | + | 1582.08i | 0.111721 | + | 0.111721i | ||||
\(120\) | 364.079 | + | 630.604i | 0.0252833 | + | 0.0437919i | ||||
\(121\) | −19021.2 | −1.29917 | ||||||||
\(122\) | − | 8164.09i | − | 0.548514i | ||||||
\(123\) | −1458.20 | − | 2525.67i | −0.0963842 | − | 0.166942i | ||||
\(124\) | 6355.86 | − | 1703.05i | 0.413363 | − | 0.110760i | ||||
\(125\) | 8985.10 | − | 8985.10i | 0.575047 | − | 0.575047i | ||||
\(126\) | 16351.2 | + | 4381.30i | 1.02993 | + | 0.275970i | ||||
\(127\) | −11833.7 | − | 20496.6i | −0.733691 | − | 1.27079i | −0.955295 | − | 0.295653i | \(-0.904463\pi\) |
0.221605 | − | 0.975137i | \(-0.428870\pi\) | |||||||
\(128\) | −374.810 | + | 1398.81i | −0.0228766 | + | 0.0853766i | ||||
\(129\) | −122.475 | − | 457.084i | −0.00735985 | − | 0.0274673i | ||||
\(130\) | −6579.20 | + | 1762.89i | −0.389302 | + | 0.104313i | ||||
\(131\) | 25835.6 | + | 6922.63i | 1.50548 | + | 0.403393i | 0.914932 | − | 0.403607i | \(-0.132244\pi\) |
0.590551 | + | 0.807000i | \(0.298910\pi\) | |||||||
\(132\) | 1445.30 | − | 834.442i | 0.0829486 | − | 0.0478904i | ||||
\(133\) | 4464.78 | − | 16662.8i | 0.252404 | − | 0.941986i | ||||
\(134\) | 8175.06 | + | 8175.06i | 0.455283 | + | 0.455283i | ||||
\(135\) | −1338.51 | − | 4995.40i | −0.0734438 | − | 0.274096i | ||||
\(136\) | 583.908 | − | 337.119i | 0.0315694 | − | 0.0182266i | ||||
\(137\) | 432.242 | 0.0230296 | 0.0115148 | − | 0.999934i | \(-0.496335\pi\) | ||||
0.0115148 | + | 0.999934i | \(0.496335\pi\) | |||||||
\(138\) | 33.2134i | 0.00174404i | ||||||||
\(139\) | 31541.9 | − | 18210.7i | 1.63252 | − | 0.942535i | 0.649205 | − | 0.760614i | \(-0.275102\pi\) |
0.983313 | − | 0.181921i | \(-0.0582314\pi\) | |||||||
\(140\) | 12021.7 | − | 12021.7i | 0.613350 | − | 0.613350i | ||||
\(141\) | −2415.96 | − | 1394.85i | −0.121521 | − | 0.0701602i | ||||
\(142\) | −7050.24 | + | 7050.24i | −0.349645 | + | 0.349645i | ||||
\(143\) | 4040.42 | + | 15079.0i | 0.197585 | + | 0.737397i | ||||
\(144\) | 2550.63 | − | 4417.82i | 0.123005 | − | 0.213051i | ||||
\(145\) | −5040.90 | + | 8731.09i | −0.239757 | + | 0.415272i | ||||
\(146\) | −6396.56 | + | 23872.3i | −0.300082 | + | 1.11992i | ||||
\(147\) | 3680.54i | 0.170325i | ||||||||
\(148\) | −10268.9 | + | 3807.48i | −0.468812 | + | 0.173826i | ||||
\(149\) | 28437.1 | 1.28089 | 0.640446 | − | 0.768003i | \(-0.278750\pi\) | ||||
0.640446 | + | 0.768003i | \(0.278750\pi\) | |||||||
\(150\) | −546.831 | − | 146.523i | −0.0243036 | − | 0.00651213i | ||||
\(151\) | −32341.8 | − | 18672.6i | −1.41844 | − | 0.818936i | −0.422277 | − | 0.906467i | \(-0.638769\pi\) |
−0.996162 | + | 0.0875308i | \(0.972102\pi\) | |||||||
\(152\) | −4502.00 | − | 2599.23i | −0.194858 | − | 0.112501i | ||||
\(153\) | −2294.14 | + | 614.713i | −0.0980025 | + | 0.0262597i | ||||
\(154\) | −27552.7 | − | 27552.7i | −1.16178 | − | 1.16178i | ||||
\(155\) | −11639.6 | + | 20160.3i | −0.484477 | + | 0.839139i | ||||
\(156\) | −547.266 | − | 547.266i | −0.0224879 | − | 0.0224879i | ||||
\(157\) | 5247.15 | + | 9088.34i | 0.212875 | + | 0.368710i | 0.952613 | − | 0.304185i | \(-0.0983840\pi\) |
−0.739738 | + | 0.672895i | \(0.765051\pi\) | |||||||
\(158\) | −32547.2 | −1.30376 | ||||||||
\(159\) | 3302.84i | 0.130645i | ||||||||
\(160\) | −2561.66 | − | 4436.92i | −0.100065 | − | 0.173317i | ||||
\(161\) | 749.050 | − | 200.707i | 0.0288974 | − | 0.00774304i | ||||
\(162\) | −12497.0 | + | 12497.0i | −0.476187 | + | 0.476187i | ||||
\(163\) | −7673.54 | − | 2056.12i | −0.288816 | − | 0.0773879i | 0.111503 | − | 0.993764i | \(-0.464434\pi\) |
−0.400318 | + | 0.916376i | \(0.631100\pi\) | |||||||
\(164\) | 10259.9 | + | 17770.6i | 0.381464 | + | 0.660715i | ||||
\(165\) | −1528.12 | + | 5703.03i | −0.0561294 | + | 0.209478i | ||||
\(166\) | 5549.08 | + | 20709.5i | 0.201375 | + | 0.751541i | ||||
\(167\) | 24119.3 | − | 6462.74i | 0.864831 | − | 0.231731i | 0.200979 | − | 0.979595i | \(-0.435588\pi\) |
0.663851 | + | 0.747865i | \(0.268921\pi\) | |||||||
\(168\) | 1865.98 | + | 499.989i | 0.0661133 | + | 0.0177150i | ||||
\(169\) | −18464.8 | + | 10660.7i | −0.646505 | + | 0.373260i | ||||
\(170\) | −617.370 | + | 2304.06i | −0.0213623 | + | 0.0797252i | ||||
\(171\) | 12948.6 | + | 12948.6i | 0.442823 | + | 0.442823i | ||||
\(172\) | 861.735 | + | 3216.04i | 0.0291284 | + | 0.108709i | ||||
\(173\) | −26470.6 | + | 15282.8i | −0.884447 | + | 0.510636i | −0.872122 | − | 0.489289i | \(-0.837257\pi\) |
−0.0123247 | + | 0.999924i | \(0.503923\pi\) | |||||||
\(174\) | −1145.57 | −0.0378376 | ||||||||
\(175\) | 13217.9i | 0.431606i | ||||||||
\(176\) | −10169.1 | + | 5871.12i | −0.328289 | + | 0.189538i | ||||
\(177\) | 3286.92 | − | 3286.92i | 0.104916 | − | 0.104916i | ||||
\(178\) | −29386.4 | − | 16966.3i | −0.927484 | − | 0.535483i | ||||
\(179\) | 32411.3 | − | 32411.3i | 1.01156 | − | 1.01156i | 0.0116234 | − | 0.999932i | \(-0.496300\pi\) |
0.999932 | − | 0.0116234i | \(-0.00369991\pi\) | |||||||
\(180\) | 4671.00 | + | 17432.4i | 0.144167 | + | 0.538037i | ||||
\(181\) | −24104.9 | + | 41750.9i | −0.735780 | + | 1.27441i | 0.218600 | + | 0.975815i | \(0.429851\pi\) |
−0.954380 | + | 0.298595i | \(0.903482\pi\) | |||||||
\(182\) | −9035.19 | + | 15649.4i | −0.272769 | + | 0.472449i | ||||
\(183\) | −849.423 | + | 3170.09i | −0.0253642 | + | 0.0946606i | ||||
\(184\) | − | 233.689i | − | 0.00690244i | ||||||
\(185\) | 16163.9 | − | 35213.6i | 0.472283 | − | 1.02889i | ||||
\(186\) | −2645.15 | −0.0764583 | ||||||||
\(187\) | 5280.73 | + | 1414.97i | 0.151012 | + | 0.0404634i | ||||
\(188\) | 16998.6 | + | 9814.17i | 0.480949 | + | 0.277676i | ||||
\(189\) | −11882.1 | − | 6860.16i | −0.332637 | − | 0.192048i | ||||
\(190\) | 17764.6 | − | 4760.00i | 0.492093 | − | 0.131856i | ||||
\(191\) | 20173.8 | + | 20173.8i | 0.552994 | + | 0.552994i | 0.927304 | − | 0.374310i | \(-0.122120\pi\) |
−0.374310 | + | 0.927304i | \(0.622120\pi\) | |||||||
\(192\) | 291.075 | − | 504.157i | 0.00789592 | − | 0.0136761i | ||||
\(193\) | −46724.9 | − | 46724.9i | −1.25439 | − | 1.25439i | −0.953731 | − | 0.300662i | \(-0.902793\pi\) |
−0.300662 | − | 0.953731i | \(-0.597207\pi\) | |||||||
\(194\) | −7694.39 | − | 13327.1i | −0.204442 | − | 0.354105i | ||||
\(195\) | 2738.10 | 0.0720079 | ||||||||
\(196\) | − | 25896.3i | − | 0.674101i | ||||||
\(197\) | 12888.2 | + | 22323.0i | 0.332093 | + | 0.575203i | 0.982922 | − | 0.184022i | \(-0.0589117\pi\) |
−0.650829 | + | 0.759225i | \(0.725578\pi\) | |||||||
\(198\) | 39953.7 | − | 10705.6i | 1.01912 | − | 0.273073i | ||||
\(199\) | −8277.28 | + | 8277.28i | −0.209017 | + | 0.209017i | −0.803850 | − | 0.594833i | \(-0.797218\pi\) |
0.594833 | + | 0.803850i | \(0.297218\pi\) | |||||||
\(200\) | 3847.50 | + | 1030.93i | 0.0961874 | + | 0.0257733i | ||||
\(201\) | −2323.78 | − | 4024.91i | −0.0575180 | − | 0.0996241i | ||||
\(202\) | −4440.56 | + | 16572.4i | −0.108827 | + | 0.406147i | ||||
\(203\) | 6922.64 | + | 25835.7i | 0.167989 | + | 0.626942i | ||||
\(204\) | −261.805 | + | 70.1504i | −0.00629096 | + | 0.00168566i | ||||
\(205\) | −70121.4 | − | 18789.0i | −1.66856 | − | 0.447090i | ||||
\(206\) | 18567.4 | − | 10719.9i | 0.437539 | − | 0.252613i | ||||
\(207\) | −213.058 | + | 795.142i | −0.00497229 | + | 0.0185568i | ||||
\(208\) | 3850.56 | + | 3850.56i | 0.0890014 | + | 0.0890014i | ||||
\(209\) | −10909.6 | − | 40715.1i | −0.249755 | − | 0.932100i | ||||
\(210\) | −5918.75 | + | 3417.19i | −0.134212 | + | 0.0774874i | ||||
\(211\) | −2791.01 | −0.0626898 | −0.0313449 | − | 0.999509i | \(-0.509979\pi\) | ||||
−0.0313449 | + | 0.999509i | \(0.509979\pi\) | |||||||
\(212\) | − | 23238.7i | − | 0.517060i | ||||||
\(213\) | 3471.12 | − | 2004.05i | 0.0765086 | − | 0.0441723i | ||||
\(214\) | −11802.1 | + | 11802.1i | −0.257711 | + | 0.257711i | ||||
\(215\) | −10201.0 | − | 5889.56i | −0.220682 | − | 0.127411i | ||||
\(216\) | −2923.62 | + | 2923.62i | −0.0626632 | + | 0.0626632i | ||||
\(217\) | 15984.6 | + | 59655.2i | 0.339454 | + | 1.26686i | ||||
\(218\) | 689.956 | − | 1195.04i | 0.0145181 | − | 0.0251460i | ||||
\(219\) | 4967.53 | − | 8604.01i | 0.103574 | − | 0.179396i | ||||
\(220\) | 10751.8 | − | 40126.4i | 0.222146 | − | 0.829059i | ||||
\(221\) | − | 2535.35i | − | 0.0519102i | ||||||
\(222\) | 4383.51 | − | 410.023i | 0.0889438 | − | 0.00831959i | ||||
\(223\) | 63283.7 | 1.27257 | 0.636286 | − | 0.771453i | \(-0.280470\pi\) | ||||
0.636286 | + | 0.771453i | \(0.280470\pi\) | |||||||
\(224\) | −13129.0 | − | 3517.91i | −0.261659 | − | 0.0701114i | ||||
\(225\) | −12151.4 | − | 7015.64i | −0.240028 | − | 0.138580i | ||||
\(226\) | 49004.0 | + | 28292.5i | 0.959433 | + | 0.553929i | ||||
\(227\) | 59461.2 | − | 15932.6i | 1.15394 | − | 0.309196i | 0.369395 | − | 0.929273i | \(-0.379565\pi\) |
0.784541 | + | 0.620076i | \(0.212898\pi\) | |||||||
\(228\) | 1477.68 | + | 1477.68i | 0.0284256 | + | 0.0284256i | ||||
\(229\) | −15363.4 | + | 26610.2i | −0.292966 | + | 0.507432i | −0.974510 | − | 0.224346i | \(-0.927976\pi\) |
0.681544 | + | 0.731777i | \(0.261309\pi\) | |||||||
\(230\) | 584.601 | + | 584.601i | 0.0110510 | + | 0.0110510i | ||||
\(231\) | 7831.95 | + | 13565.3i | 0.146773 | + | 0.254218i | ||||
\(232\) | 8060.22 | 0.149751 | ||||||||
\(233\) | − | 82692.5i | − | 1.52319i | −0.648053 | − | 0.761595i | \(-0.724417\pi\) | ||
0.648053 | − | 0.761595i | \(-0.275583\pi\) | |||||||
\(234\) | −9591.16 | − | 16612.4i | −0.175162 | − | 0.303389i | ||||
\(235\) | −67075.4 | + | 17972.8i | −1.21458 | + | 0.325447i | ||||
\(236\) | −23126.7 | + | 23126.7i | −0.415232 | + | 0.415232i | ||||
\(237\) | 12638.0 | + | 3386.33i | 0.224999 | + | 0.0602883i | ||||
\(238\) | 3164.15 | + | 5480.47i | 0.0558603 | + | 0.0967529i | ||||
\(239\) | −321.823 | + | 1201.06i | −0.00563406 | + | 0.0210266i | −0.968686 | − | 0.248290i | \(-0.920131\pi\) |
0.963052 | + | 0.269317i | \(0.0867979\pi\) | |||||||
\(240\) | 533.049 | + | 1989.37i | 0.00925432 | + | 0.0345376i | ||||
\(241\) | 47327.7 | − | 12681.4i | 0.814856 | − | 0.218340i | 0.172760 | − | 0.984964i | \(-0.444732\pi\) |
0.642096 | + | 0.766624i | \(0.278065\pi\) | |||||||
\(242\) | −51966.8 | − | 13924.5i | −0.887351 | − | 0.237765i | ||||
\(243\) | 18970.7 | − | 10952.7i | 0.321270 | − | 0.185485i | ||||
\(244\) | 5976.53 | − | 22304.7i | 0.100385 | − | 0.374642i | ||||
\(245\) | 64782.5 | + | 64782.5i | 1.07926 | + | 1.07926i | ||||
\(246\) | −2134.95 | − | 7967.73i | −0.0352791 | − | 0.131663i | ||||
\(247\) | −16928.9 | + | 9773.92i | −0.277482 | + | 0.160205i | ||||
\(248\) | 18611.3 | 0.302602 | ||||||||
\(249\) | − | 8618.76i | − | 0.139010i | ||||||
\(250\) | 31125.3 | − | 17970.2i | 0.498005 | − | 0.287523i | ||||
\(251\) | −76318.7 | + | 76318.7i | −1.21139 | + | 1.21139i | −0.240819 | + | 0.970570i | \(0.577416\pi\) |
−0.970570 | + | 0.240819i | \(0.922584\pi\) | |||||||
\(252\) | 41465.0 | + | 23939.8i | 0.652951 | + | 0.376982i | ||||
\(253\) | 1339.86 | − | 1339.86i | 0.0209324 | − | 0.0209324i | ||||
\(254\) | −17325.7 | − | 64660.5i | −0.268549 | − | 1.00224i | ||||
\(255\) | 479.446 | − | 830.424i | 0.00737325 | − | 0.0127708i | ||||
\(256\) | −2048.00 | + | 3547.24i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 14863.0 | − | 55469.3i | 0.225029 | − | 0.839821i | −0.757363 | − | 0.652994i | \(-0.773513\pi\) |
0.982393 | − | 0.186827i | \(-0.0598205\pi\) | |||||||
\(258\) | − | 1338.44i | − | 0.0201075i | ||||||
\(259\) | −35736.5 | − | 96382.0i | −0.532736 | − | 1.43680i | ||||
\(260\) | −19265.2 | −0.284989 | ||||||||
\(261\) | −27425.4 | − | 7348.62i | −0.402599 | − | 0.107876i | ||||
\(262\) | 65516.5 | + | 37825.9i | 0.954438 | + | 0.551045i | ||||
\(263\) | −19968.7 | − | 11528.9i | −0.288694 | − | 0.166678i | 0.348659 | − | 0.937250i | \(-0.386637\pi\) |
−0.637353 | + | 0.770572i | \(0.719971\pi\) | |||||||
\(264\) | 4559.48 | − | 1221.71i | 0.0654195 | − | 0.0175291i | ||||
\(265\) | 58134.4 | + | 58134.4i | 0.827831 | + | 0.827831i | ||||
\(266\) | 24396.0 | − | 42255.1i | 0.344791 | − | 0.597195i | ||||
\(267\) | 9645.42 | + | 9645.42i | 0.135300 | + | 0.135300i | ||||
\(268\) | 16350.1 | + | 28319.2i | 0.227641 | + | 0.394286i | ||||
\(269\) | 14533.4 | 0.200846 | 0.100423 | − | 0.994945i | \(-0.467980\pi\) | ||||
0.100423 | + | 0.994945i | \(0.467980\pi\) | |||||||
\(270\) | − | 14627.5i | − | 0.200652i | ||||||
\(271\) | −59263.2 | − | 102647.i | −0.806950 | − | 1.39768i | −0.914967 | − | 0.403529i | \(-0.867783\pi\) |
0.108017 | − | 0.994149i | \(-0.465550\pi\) | |||||||
\(272\) | 1842.05 | − | 493.577i | 0.0248980 | − | 0.00667140i | ||||
\(273\) | 5136.56 | − | 5136.56i | 0.0689203 | − | 0.0689203i | ||||
\(274\) | 1180.91 | + | 316.423i | 0.0157295 | + | 0.00421471i | ||||
\(275\) | 16148.8 | + | 27970.6i | 0.213538 | + | 0.369859i | ||||
\(276\) | −24.3139 | + | 90.7407i | −0.000319181 | + | 0.00119120i | ||||
\(277\) | 9263.78 | + | 34572.9i | 0.120734 | + | 0.450584i | 0.999652 | − | 0.0263884i | \(-0.00840067\pi\) |
−0.878918 | + | 0.476973i | \(0.841734\pi\) | |||||||
\(278\) | 99505.2 | − | 26662.3i | 1.28753 | − | 0.344992i | ||||
\(279\) | −63326.0 | − | 16968.2i | −0.813530 | − | 0.217985i | ||||
\(280\) | 41644.3 | − | 24043.3i | 0.531177 | − | 0.306675i | ||||
\(281\) | −30287.3 | + | 113034.i | −0.383573 | + | 1.43151i | 0.456831 | + | 0.889553i | \(0.348984\pi\) |
−0.840404 | + | 0.541960i | \(0.817682\pi\) | |||||||
\(282\) | −5579.42 | − | 5579.42i | −0.0701602 | − | 0.0701602i | ||||
\(283\) | −8409.83 | − | 31385.9i | −0.105006 | − | 0.391888i | 0.893340 | − | 0.449382i | \(-0.148356\pi\) |
−0.998346 | + | 0.0574939i | \(0.981689\pi\) | |||||||
\(284\) | −24422.7 | + | 14100.5i | −0.302801 | + | 0.174822i | ||||
\(285\) | −7393.17 | −0.0910209 | ||||||||
\(286\) | 44154.5i | 0.539812i | ||||||||
\(287\) | −166792. | + | 96297.5i | −2.02494 | + | 1.16910i | ||||
\(288\) | 10202.5 | − | 10202.5i | 0.123005 | − | 0.123005i | ||||
\(289\) | 71562.4 | + | 41316.6i | 0.856819 | + | 0.494685i | ||||
\(290\) | −20163.6 | + | 20163.6i | −0.239757 | + | 0.239757i | ||||
\(291\) | 1601.11 | + | 5975.42i | 0.0189075 | + | 0.0705638i | ||||
\(292\) | −34951.4 | + | 60537.7i | −0.409920 | + | 0.710003i | ||||
\(293\) | 36938.1 | − | 63978.7i | 0.430269 | − | 0.745247i | −0.566628 | − | 0.823974i | \(-0.691752\pi\) |
0.996896 | + | 0.0787268i | \(0.0250855\pi\) | |||||||
\(294\) | −2694.35 | + | 10055.4i | −0.0311716 | + | 0.116334i | ||||
\(295\) | − | 115709.i | − | 1.32960i | ||||||
\(296\) | −30842.3 | + | 2884.92i | −0.352017 | + | 0.0329268i | ||||
\(297\) | −33525.2 | −0.380066 | ||||||||
\(298\) | 77691.5 | + | 20817.4i | 0.874865 | + | 0.234419i | ||||
\(299\) | −761.014 | − | 439.372i | −0.00851237 | − | 0.00491462i | ||||
\(300\) | −1386.71 | − | 800.616i | −0.0154079 | − | 0.00889574i | ||||
\(301\) | −30185.3 | + | 8088.12i | −0.333167 | + | 0.0892718i | ||||
\(302\) | −74690.2 | − | 74690.2i | −0.818936 | − | 0.818936i | ||||
\(303\) | 3448.51 | − | 5973.00i | 0.0375618 | − | 0.0650590i | ||||
\(304\) | −10396.9 | − | 10396.9i | −0.112501 | − | 0.112501i | ||||
\(305\) | 40846.8 | + | 70748.8i | 0.439095 | + | 0.760535i | ||||
\(306\) | −6717.71 | −0.0717428 | ||||||||
\(307\) | − | 7991.40i | − | 0.0847903i | −0.999101 | − | 0.0423951i | \(-0.986501\pi\) | ||
0.999101 | − | 0.0423951i | \(-0.0134988\pi\) | |||||||
\(308\) | −55105.5 | − | 95445.5i | −0.580889 | − | 1.00613i | ||||
\(309\) | −8325.00 | + | 2230.68i | −0.0871901 | + | 0.0233625i | ||||
\(310\) | −46558.2 | + | 46558.2i | −0.484477 | + | 0.484477i | ||||
\(311\) | 144886. | + | 38822.0i | 1.49797 | + | 0.401381i | 0.912421 | − | 0.409253i | \(-0.134211\pi\) |
0.585553 | + | 0.810634i | \(0.300877\pi\) | |||||||
\(312\) | −1094.53 | − | 1895.79i | −0.0112440 | − | 0.0194751i | ||||
\(313\) | 23157.7 | − | 86425.7i | 0.236378 | − | 0.882174i | −0.741145 | − | 0.671345i | \(-0.765717\pi\) |
0.977523 | − | 0.210829i | \(-0.0676163\pi\) | |||||||
\(314\) | 7682.37 | + | 28671.0i | 0.0779176 | + | 0.290793i | ||||
\(315\) | −163618. | + | 43841.3i | −1.64896 | + | 0.441837i | ||||
\(316\) | −88920.5 | − | 23826.2i | −0.890487 | − | 0.238605i | ||||
\(317\) | 136205. | − | 78638.1i | 1.35542 | − | 0.782554i | 0.366421 | − | 0.930449i | \(-0.380583\pi\) |
0.989003 | + | 0.147895i | \(0.0472497\pi\) | |||||||
\(318\) | −2417.85 | + | 9023.53i | −0.0239097 | + | 0.0892323i | ||||
\(319\) | 46213.4 | + | 46213.4i | 0.454137 | + | 0.454137i | ||||
\(320\) | −3750.52 | − | 13997.1i | −0.0366262 | − | 0.136691i | ||||
\(321\) | 5810.68 | − | 3354.80i | 0.0563919 | − | 0.0325579i | ||||
\(322\) | 2193.37 | 0.0211544 | ||||||||
\(323\) | 6845.71i | 0.0656166i | ||||||||
\(324\) | −43291.0 | + | 24994.1i | −0.412390 | + | 0.238093i | ||||
\(325\) | 10591.1 | − | 10591.1i | 0.100271 | − | 0.100271i | ||||
\(326\) | −19459.3 | − | 11234.8i | −0.183102 | − | 0.105714i | ||||
\(327\) | −392.244 | + | 392.244i | −0.00366827 | + | 0.00366827i | ||||
\(328\) | 15021.5 | + | 56060.9i | 0.139625 | + | 0.521089i | ||||
\(329\) | −92114.4 | + | 159547.i | −0.851012 | + | 1.47400i | ||||
\(330\) | −8349.82 | + | 14462.3i | −0.0766742 | + | 0.132804i | ||||
\(331\) | −16540.0 | + | 61728.2i | −0.150966 | + | 0.563414i | 0.848451 | + | 0.529274i | \(0.177536\pi\) |
−0.999417 | + | 0.0341396i | \(0.989131\pi\) | |||||||
\(332\) | 60641.5i | 0.550166i | ||||||||
\(333\) | 107573. | + | 18303.3i | 0.970098 | + | 0.165059i | ||||
\(334\) | 70626.1 | 0.633100 | ||||||||
\(335\) | −111746. | − | 29942.1i | −0.995728 | − | 0.266805i | ||||
\(336\) | 4731.94 | + | 2731.99i | 0.0419142 | + | 0.0241992i | ||||
\(337\) | −1410.13 | − | 814.137i | −0.0124165 | − | 0.00716866i | 0.493779 | − | 0.869587i | \(-0.335615\pi\) |
−0.506195 | + | 0.862419i | \(0.668949\pi\) | |||||||
\(338\) | −58251.0 | + | 15608.3i | −0.509883 | + | 0.136623i | ||||
\(339\) | −16084.4 | − | 16084.4i | −0.139961 | − | 0.139961i | ||||
\(340\) | −3373.37 | + | 5842.85i | −0.0291814 | + | 0.0505437i | ||||
\(341\) | 106708. | + | 106708.i | 0.917673 | + | 0.917673i | ||||
\(342\) | 25897.2 | + | 44855.2i | 0.221412 | + | 0.383496i | ||||
\(343\) | 62775.0 | 0.533579 | ||||||||
\(344\) | 9417.21i | 0.0795803i | ||||||||
\(345\) | −166.174 | − | 287.823i | −0.00139613 | − | 0.00241817i | ||||
\(346\) | −83506.8 | + | 22375.6i | −0.697541 | + | 0.186906i | ||||
\(347\) | −85236.7 | + | 85236.7i | −0.707893 | + | 0.707893i | −0.966092 | − | 0.258199i | \(-0.916871\pi\) |
0.258199 | + | 0.966092i | \(0.416871\pi\) | |||||||
\(348\) | −3129.76 | − | 838.616i | −0.0258436 | − | 0.00692476i | ||||
\(349\) | −74341.0 | − | 128762.i | −0.610348 | − | 1.05715i | −0.991182 | − | 0.132510i | \(-0.957696\pi\) |
0.380834 | − | 0.924644i | \(-0.375637\pi\) | |||||||
\(350\) | −9676.19 | + | 36112.0i | −0.0789893 | + | 0.294792i | ||||
\(351\) | 4023.97 | + | 15017.7i | 0.0326619 | + | 0.121896i | ||||
\(352\) | −32080.4 | + | 8595.92i | −0.258913 | + | 0.0693756i | ||||
\(353\) | −37584.4 | − | 10070.7i | −0.301619 | − | 0.0808184i | 0.104836 | − | 0.994490i | \(-0.466568\pi\) |
−0.406454 | + | 0.913671i | \(0.633235\pi\) | |||||||
\(354\) | 11386.2 | − | 6573.85i | 0.0908602 | − | 0.0524582i | ||||
\(355\) | 25822.4 | − | 96370.4i | 0.204899 | − | 0.764692i | ||||
\(356\) | −67865.0 | − | 67865.0i | −0.535483 | − | 0.535483i | ||||
\(357\) | −658.421 | − | 2457.26i | −0.00516615 | − | 0.0192803i | ||||
\(358\) | 112276. | − | 64822.5i | 0.876033 | − | 0.505778i | ||||
\(359\) | −150005. | −1.16390 | −0.581952 | − | 0.813223i | \(-0.697711\pi\) | ||||
−0.581952 | + | 0.813223i | \(0.697711\pi\) | |||||||
\(360\) | 51045.6i | 0.393870i | ||||||||
\(361\) | −67151.3 | + | 38769.8i | −0.515276 | + | 0.297495i | ||||
\(362\) | −96419.6 | + | 96419.6i | −0.735780 | + | 0.735780i | ||||
\(363\) | 18729.8 | + | 10813.7i | 0.142141 | + | 0.0820653i | ||||
\(364\) | −36140.8 | + | 36140.8i | −0.272769 | + | 0.272769i | ||||
\(365\) | −64006.9 | − | 238877.i | −0.480442 | − | 1.79304i | ||||
\(366\) | −4641.33 | + | 8039.02i | −0.0346482 | + | 0.0600124i | ||||
\(367\) | −13237.0 | + | 22927.2i | −0.0982785 | + | 0.170223i | −0.910972 | − | 0.412468i | \(-0.864667\pi\) |
0.812694 | + | 0.582691i | \(0.198000\pi\) | |||||||
\(368\) | 171.072 | − | 638.450i | 0.00126323 | − | 0.00471446i | ||||
\(369\) | − | 204446.i | − | 1.50150i | ||||||
\(370\) | 69938.7 | − | 84372.6i | 0.510874 | − | 0.616308i | ||||
\(371\) | 218115. | 1.58467 | ||||||||
\(372\) | −7226.69 | − | 1936.39i | −0.0522220 | − | 0.0139928i | ||||
\(373\) | −44294.5 | − | 25573.5i | −0.318370 | − | 0.183811i | 0.332296 | − | 0.943175i | \(-0.392177\pi\) |
−0.650666 | + | 0.759364i | \(0.725510\pi\) | |||||||
\(374\) | 13391.4 | + | 7731.52i | 0.0957375 | + | 0.0552741i | ||||
\(375\) | −13955.5 | + | 3739.38i | −0.0992395 | + | 0.0265911i | ||||
\(376\) | 39256.7 | + | 39256.7i | 0.277676 | + | 0.277676i | ||||
\(377\) | 15154.5 | − | 26248.3i | 0.106625 | − | 0.184679i | ||||
\(378\) | −27440.6 | − | 27440.6i | −0.192048 | − | 0.192048i | ||||
\(379\) | 139759. | + | 242070.i | 0.972975 | + | 1.68524i | 0.686462 | + | 0.727166i | \(0.259163\pi\) |
0.286513 | + | 0.958076i | \(0.407504\pi\) | |||||||
\(380\) | 52018.3 | 0.360237 | ||||||||
\(381\) | 26910.1i | 0.185381i | ||||||||
\(382\) | 40347.5 | + | 69884.0i | 0.276497 | + | 0.478907i | ||||
\(383\) | −4219.03 | + | 1130.49i | −0.0287617 | + | 0.00770668i | −0.273171 | − | 0.961965i | \(-0.588073\pi\) |
0.244409 | + | 0.969672i | \(0.421406\pi\) | |||||||
\(384\) | 1164.30 | − | 1164.30i | 0.00789592 | − | 0.00789592i | ||||
\(385\) | 376621. | + | 100915.i | 2.54087 | + | 0.680825i | ||||
\(386\) | −93449.7 | − | 161860.i | −0.627196 | − | 1.08634i | ||||
\(387\) | 8585.81 | − | 32042.7i | 0.0573270 | − | 0.213947i | ||||
\(388\) | −11265.4 | − | 42043.0i | −0.0748311 | − | 0.279274i | ||||
\(389\) | 182556. | − | 48915.8i | 1.20642 | − | 0.323259i | 0.401062 | − | 0.916051i | \(-0.368641\pi\) |
0.805355 | + | 0.592792i | \(0.201974\pi\) | |||||||
\(390\) | 7480.63 | + | 2004.43i | 0.0491823 | + | 0.0131784i | ||||
\(391\) | −266.510 | + | 153.869i | −0.00174325 | + | 0.00100646i | ||||
\(392\) | 18957.4 | − | 70749.9i | 0.123369 | − | 0.460419i | ||||
\(393\) | −21504.3 | − | 21504.3i | −0.139232 | − | 0.139232i | ||||
\(394\) | 18869.7 | + | 70422.5i | 0.121555 | + | 0.453648i | ||||
\(395\) | 282049. | − | 162841.i | 1.80772 | − | 1.04369i | ||||
\(396\) | 116993. | 0.746051 | ||||||||
\(397\) | 68068.8i | 0.431884i | 0.976406 | + | 0.215942i | \(0.0692822\pi\) | ||||
−0.976406 | + | 0.215942i | \(0.930718\pi\) | |||||||
\(398\) | −28673.3 | + | 16554.6i | −0.181014 | + | 0.104508i | ||||
\(399\) | −13869.3 | + | 13869.3i | −0.0871180 | + | 0.0871180i | ||||
\(400\) | 9756.86 | + | 5633.13i | 0.0609804 | + | 0.0352070i | ||||
\(401\) | −160378. | + | 160378.i | −0.997368 | + | 0.997368i | −0.999997 | − | 0.00262810i | \(-0.999163\pi\) |
0.00262810 | + | 0.999997i | \(0.499163\pi\) | |||||||
\(402\) | −3402.26 | − | 12697.4i | −0.0210531 | − | 0.0785711i | ||||
\(403\) | 34992.0 | − | 60608.0i | 0.215456 | − | 0.373181i | ||||
\(404\) | −24263.7 | + | 42025.9i | −0.148660 | + | 0.257487i | ||||
\(405\) | 45771.9 | − | 170823.i | 0.279055 | − | 1.04145i | ||||
\(406\) | 75652.1i | 0.458954i | ||||||||
\(407\) | −193376. | − | 160294.i | −1.16738 | − | 0.967674i | ||||
\(408\) | −766.617 | −0.00460530 | ||||||||
\(409\) | 287544. | + | 77047.1i | 1.71893 | + | 0.460585i | 0.977585 | − | 0.210542i | \(-0.0675230\pi\) |
0.741342 | + | 0.671127i | \(0.234190\pi\) | |||||||
\(410\) | −177821. | − | 102665.i | −1.05783 | − | 0.610737i | ||||
\(411\) | −425.621 | − | 245.732i | −0.00251965 | − | 0.00145472i | ||||
\(412\) | 58574.6 | − | 15695.0i | 0.345076 | − | 0.0924628i | ||||
\(413\) | −217064. | − | 217064.i | −1.27259 | − | 1.27259i | ||||
\(414\) | −1164.17 | + | 2016.40i | −0.00679228 | + | 0.0117646i | ||||
\(415\) | −151702. | − | 151702.i | −0.880835 | − | 0.880835i | ||||
\(416\) | 7701.12 | + | 13338.7i | 0.0445007 | + | 0.0770775i | ||||
\(417\) | −41411.6 | −0.238150 | ||||||||
\(418\) | − | 119222.i | − | 0.682344i | ||||||
\(419\) | 6303.92 | + | 10918.7i | 0.0359073 | + | 0.0621932i | 0.883421 | − | 0.468581i | \(-0.155235\pi\) |
−0.847513 | + | 0.530774i | \(0.821901\pi\) | |||||||
\(420\) | −18671.9 | + | 5003.12i | −0.105850 | + | 0.0283624i | ||||
\(421\) | 15704.8 | − | 15704.8i | 0.0886069 | − | 0.0886069i | −0.661414 | − | 0.750021i | \(-0.730043\pi\) |
0.750021 | + | 0.661414i | \(0.230043\pi\) | |||||||
\(422\) | −7625.19 | − | 2043.16i | −0.0428179 | − | 0.0114730i | ||||
\(423\) | −97782.5 | − | 169364.i | −0.546488 | − | 0.946545i | ||||
\(424\) | 17011.9 | − | 63489.4i | 0.0946286 | − | 0.353159i | ||||
\(425\) | −1357.61 | − | 5066.66i | −0.00751617 | − | 0.0280507i | ||||
\(426\) | 10950.3 | − | 2934.14i | 0.0603404 | − | 0.0161682i | ||||
\(427\) | 209349. | + | 56094.8i | 1.14819 | + | 0.307657i | ||||
\(428\) | −40883.8 | + | 23604.3i | −0.223185 | + | 0.128856i | ||||
\(429\) | 4594.00 | − | 17145.0i | 0.0249618 | − | 0.0931588i | ||||
\(430\) | −23558.3 | − | 23558.3i | −0.127411 | − | 0.127411i | ||||
\(431\) | 45564.6 | + | 170049.i | 0.245286 | + | 0.915420i | 0.973239 | + | 0.229793i | \(0.0738050\pi\) |
−0.727954 | + | 0.685626i | \(0.759528\pi\) | |||||||
\(432\) | −10127.7 | + | 5847.23i | −0.0542680 | + | 0.0313316i | ||||
\(433\) | −16113.5 | −0.0859436 | −0.0429718 | − | 0.999076i | \(-0.513683\pi\) | ||||
−0.0429718 | + | 0.999076i | \(0.513683\pi\) | |||||||
\(434\) | 174683.i | 0.927406i | ||||||||
\(435\) | 9927.35 | − | 5731.56i | 0.0524632 | − | 0.0302897i | ||||
\(436\) | 2759.82 | − | 2759.82i | 0.0145181 | − | 0.0145181i | ||||
\(437\) | 2054.82 | + | 1186.35i | 0.0107600 | + | 0.00621227i | ||||
\(438\) | 19870.1 | − | 19870.1i | 0.103574 | − | 0.103574i | ||||
\(439\) | −18073.2 | − | 67450.1i | −0.0937791 | − | 0.349989i | 0.903052 | − | 0.429530i | \(-0.141321\pi\) |
−0.996832 | + | 0.0795419i | \(0.974654\pi\) | |||||||
\(440\) | 58749.2 | − | 101757.i | 0.303457 | − | 0.525602i | ||||
\(441\) | −129007. | + | 223447.i | −0.663342 | + | 1.14894i | ||||
\(442\) | 1856.00 | − | 6926.70i | 0.00950023 | − | 0.0354553i | ||||
\(443\) | − | 142626.i | − | 0.726762i | −0.931641 | − | 0.363381i | \(-0.881622\pi\) | ||
0.931641 | − | 0.363381i | \(-0.118378\pi\) | |||||||
\(444\) | 12276.1 | + | 2088.75i | 0.0622724 | + | 0.0105955i | ||||
\(445\) | 339545. | 1.71465 | ||||||||
\(446\) | 172894. | + | 46326.9i | 0.869183 | + | 0.232897i | ||||
\(447\) | −28001.4 | − | 16166.6i | −0.140141 | − | 0.0809105i | ||||
\(448\) | −33293.9 | − | 19222.2i | −0.165885 | − | 0.0957740i | ||||
\(449\) | −174251. | + | 46690.4i | −0.864335 | + | 0.231598i | −0.663637 | − | 0.748055i | \(-0.730988\pi\) |
−0.200699 | + | 0.979653i | \(0.564321\pi\) | |||||||
\(450\) | −28062.5 | − | 28062.5i | −0.138580 | − | 0.138580i | ||||
\(451\) | −235300. | + | 407552.i | −1.15683 | + | 2.00369i | ||||
\(452\) | 113170. | + | 113170.i | 0.553929 | + | 0.553929i | ||||
\(453\) | 21230.9 | + | 36773.0i | 0.103460 | + | 0.179198i | ||||
\(454\) | 174114. | 0.844740 | ||||||||
\(455\) | − | 180821.i | − | 0.873425i | ||||||
\(456\) | 2955.36 | + | 5118.83i | 0.0142128 | + | 0.0246173i | ||||
\(457\) | 229667. | − | 61539.1i | 1.09968 | − | 0.294658i | 0.337045 | − | 0.941488i | \(-0.390572\pi\) |
0.762634 | + | 0.646830i | \(0.223906\pi\) | |||||||
\(458\) | −61453.7 | + | 61453.7i | −0.292966 | + | 0.292966i | ||||
\(459\) | 5259.24 | + | 1409.21i | 0.0249630 | + | 0.00668883i | ||||
\(460\) | 1169.20 | + | 2025.12i | 0.00552552 | + | 0.00957049i | ||||
\(461\) | −48157.0 | + | 179725.i | −0.226599 | + | 0.845679i | 0.755159 | + | 0.655542i | \(0.227560\pi\) |
−0.981758 | + | 0.190137i | \(0.939107\pi\) | |||||||
\(462\) | 11466.8 | + | 42794.6i | 0.0537226 | + | 0.200496i | ||||
\(463\) | −304029. | + | 81464.4i | −1.41825 | + | 0.380020i | −0.884863 | − | 0.465851i | \(-0.845748\pi\) |
−0.533389 | + | 0.845870i | \(0.679082\pi\) | |||||||
\(464\) | 22020.9 | + | 5900.49i | 0.102282 | + | 0.0274064i | ||||
\(465\) | 22922.5 | − | 13234.3i | 0.106012 | − | 0.0612062i | ||||
\(466\) | 60535.1 | − | 225920.i | 0.278763 | − | 1.04036i | ||||
\(467\) | −55781.5 | − | 55781.5i | −0.255774 | − | 0.255774i | 0.567559 | − | 0.823333i | \(-0.307888\pi\) |
−0.823333 | + | 0.567559i | \(0.807888\pi\) | |||||||
\(468\) | −14042.4 | − | 52407.1i | −0.0641137 | − | 0.239276i | ||||
\(469\) | −265800. | + | 153460.i | −1.20840 | + | 0.697668i | ||||
\(470\) | −196410. | −0.889137 | ||||||||
\(471\) | − | 11932.2i | − | 0.0537870i | ||||||
\(472\) | −80113.4 | + | 46253.5i | −0.359601 | + | 0.207616i | ||||
\(473\) | −53993.7 | + | 53993.7i | −0.241335 | + | 0.241335i | ||||
\(474\) | 32048.6 | + | 18503.3i | 0.142644 | + | 0.0823553i | ||||
\(475\) | −28597.3 | + | 28597.3i | −0.126747 | + | 0.126747i | ||||
\(476\) | 4632.64 | + | 17289.3i | 0.0204463 | + | 0.0763066i | ||||
\(477\) | −115768. | + | 200517.i | −0.508808 | + | 0.881280i | ||||
\(478\) | −1758.48 | + | 3045.77i | −0.00769627 | + | 0.0133303i | ||||
\(479\) | 20346.1 | − | 75932.6i | 0.0886767 | − | 0.330946i | −0.907308 | − | 0.420466i | \(-0.861867\pi\) |
0.995985 | + | 0.0895199i | \(0.0285333\pi\) | |||||||
\(480\) | 5825.27i | 0.0252833i | ||||||||
\(481\) | −48593.5 | + | 105863.i | −0.210033 | + | 0.457565i | ||||
\(482\) | 138585. | 0.596516 | ||||||||
\(483\) | −851.679 | − | 228.207i | −0.00365075 | − | 0.000978215i | ||||
\(484\) | −131783. | − | 76084.7i | −0.562558 | − | 0.324793i | ||||
\(485\) | 133357. | + | 76993.7i | 0.566934 | + | 0.327319i | ||||
\(486\) | 59846.8 | − | 16035.9i | 0.253378 | − | 0.0678924i | ||||
\(487\) | 28889.3 | + | 28889.3i | 0.121809 | + | 0.121809i | 0.765383 | − | 0.643574i | \(-0.222549\pi\) |
−0.643574 | + | 0.765383i | \(0.722549\pi\) | |||||||
\(488\) | 32656.3 | − | 56562.4i | 0.137129 | − | 0.237514i | ||||
\(489\) | 6387.07 | + | 6387.07i | 0.0267106 | + | 0.0267106i | ||||
\(490\) | 129565. | + | 224413.i | 0.539629 | + | 0.934666i | ||||
\(491\) | −229188. | −0.950668 | −0.475334 | − | 0.879805i | \(-0.657673\pi\) | ||||
−0.475334 | + | 0.879805i | \(0.657673\pi\) | |||||||
\(492\) | − | 23331.1i | − | 0.0963842i | ||||||
\(493\) | −5307.14 | − | 9192.24i | −0.0218357 | − | 0.0378205i | ||||
\(494\) | −53405.7 | + | 14310.0i | −0.218843 | + | 0.0586389i | ||||
\(495\) | −292671. | + | 292671.i | −1.19445 | + | 1.19445i | ||||
\(496\) | 50846.9 | + | 13624.4i | 0.206681 | + | 0.0553801i | ||||
\(497\) | −132345. | − | 229228.i | −0.535790 | − | 0.928016i | ||||
\(498\) | 6309.37 | − | 23546.9i | 0.0254406 | − | 0.0949457i | ||||
\(499\) | 108805. | + | 406066.i | 0.436967 | + | 1.63078i | 0.736316 | + | 0.676638i | \(0.236564\pi\) |
−0.299350 | + | 0.954143i | \(0.596770\pi\) | |||||||
\(500\) | 98191.0 | − | 26310.2i | 0.392764 | − | 0.105241i | ||||
\(501\) | −27423.9 | − | 7348.21i | −0.109258 | − | 0.0292756i | ||||
\(502\) | −264376. | + | 152637.i | −1.04909 | + | 0.605695i | ||||
\(503\) | −41303.2 | + | 154146.i | −0.163248 | + | 0.609250i | 0.835009 | + | 0.550236i | \(0.185462\pi\) |
−0.998257 | + | 0.0590138i | \(0.981204\pi\) | |||||||
\(504\) | 95759.4 | + | 95759.4i | 0.376982 | + | 0.376982i | ||||
\(505\) | −44434.3 | − | 165831.i | −0.174235 | − | 0.650255i | ||||
\(506\) | 4641.41 | − | 2679.72i | 0.0181280 | − | 0.0104662i | ||||
\(507\) | 24242.6 | 0.0943113 | ||||||||
\(508\) | − | 189339.i | − | 0.733691i | ||||||
\(509\) | −306220. | + | 176796.i | −1.18195 | + | 0.682397i | −0.956464 | − | 0.291850i | \(-0.905729\pi\) |
−0.225483 | + | 0.974247i | \(0.572396\pi\) | |||||||
\(510\) | 1917.78 | − | 1917.78i | 0.00737325 | − | 0.00737325i | ||||
\(511\) | −568198. | − | 328049.i | −2.17599 | − | 1.25631i | ||||
\(512\) | −8192.00 | + | 8192.00i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | −10865.2 | − | 40549.4i | −0.0412859 | − | 0.154081i | ||||
\(514\) | 81212.8 | − | 140665.i | 0.307396 | − | 0.532425i | ||||
\(515\) | −107268. | + | 185794.i | −0.404442 | + | 0.700515i | ||||
\(516\) | 979.803 | − | 3656.67i | 0.00367993 | − | 0.0137337i | ||||
\(517\) | 450158.i | 1.68416i | ||||||||
\(518\) | −27077.4 | − | 289481.i | −0.100913 | − | 1.07885i | ||||
\(519\) | 34753.5 | 0.129022 | ||||||||
\(520\) | −52633.6 | − | 14103.1i | −0.194651 | − | 0.0521566i | ||||
\(521\) | 46957.8 | + | 27111.1i | 0.172994 | + | 0.0998784i | 0.583997 | − | 0.811756i | \(-0.301488\pi\) |
−0.411003 | + | 0.911634i | \(0.634821\pi\) | |||||||
\(522\) | −69548.1 | − | 40153.6i | −0.255237 | − | 0.147361i | ||||
\(523\) | 441399. | − | 118273.i | 1.61372 | − | 0.432395i | 0.664572 | − | 0.747225i | \(-0.268614\pi\) |
0.949148 | + | 0.314830i | \(0.101947\pi\) | |||||||
\(524\) | 151304. | + | 151304.i | 0.551045 | + | 0.551045i | ||||
\(525\) | 7514.47 | − | 13015.4i | 0.0272634 | − | 0.0472216i | ||||
\(526\) | −46115.7 | − | 46115.7i | −0.166678 | − | 0.166678i | ||||
\(527\) | −12254.3 | − | 21225.1i | −0.0441233 | − | 0.0764238i | ||||
\(528\) | 13351.1 | 0.0478904 | ||||||||
\(529\) | − | 279734.i | − | 0.999619i | ||||||
\(530\) | 116269. | + | 201384.i | 0.413916 | + | 0.716923i | ||||
\(531\) | 314761. | − | 84339.9i | 1.11633 | − | 0.299119i | ||||
\(532\) | 97584.0 | − | 97584.0i | 0.344791 | − | 0.344791i | ||||
\(533\) | 210806. | + | 56485.4i | 0.742043 | + | 0.198830i | ||||
\(534\) | 19290.8 | + | 33412.7i | 0.0676501 | + | 0.117173i | ||||
\(535\) | 43226.8 | − | 161325.i | 0.151024 | − | 0.563629i | ||||
\(536\) | 23938.2 | + | 89338.7i | 0.0833225 | + | 0.310964i | ||||
\(537\) | −50340.8 | + | 13488.8i | −0.174571 | + | 0.0467761i | ||||
\(538\) | 39706.0 | + | 10639.2i | 0.137180 | + | 0.0367574i | ||||
\(539\) | 514338. | − | 296953.i | 1.77040 | − | 1.02214i | ||||
\(540\) | 10708.1 | − | 39963.2i | 0.0367219 | − | 0.137048i | ||||
\(541\) | −250372. | − | 250372.i | −0.855444 | − | 0.855444i | 0.135354 | − | 0.990797i | \(-0.456783\pi\) |
−0.990797 | + | 0.135354i | \(0.956783\pi\) | |||||||
\(542\) | −86767.4 | − | 323820.i | −0.295364 | − | 1.10231i | ||||
\(543\) | 47471.3 | − | 27407.6i | 0.161002 | − | 0.0929546i | ||||
\(544\) | 5393.91 | 0.0182266 | ||||||||
\(545\) | 13808.0i | 0.0464878i | ||||||||
\(546\) | 17793.6 | − | 10273.1i | 0.0596867 | − | 0.0344602i | ||||
\(547\) | 16038.7 | − | 16038.7i | 0.0536035 | − | 0.0536035i | −0.679797 | − | 0.733400i | \(-0.737932\pi\) |
0.733400 | + | 0.679797i | \(0.237932\pi\) | |||||||
\(548\) | 2994.66 | + | 1728.97i | 0.00997211 | + | 0.00575740i | ||||
\(549\) | −162684. | + | 162684.i | −0.539760 | + | 0.539760i | ||||
\(550\) | 23643.5 | + | 88238.7i | 0.0781603 | + | 0.291698i | ||||
\(551\) | −40918.7 | + | 70873.3i | −0.134778 | + | 0.233442i | ||||
\(552\) | −132.854 | + | 230.109i | −0.000436009 | + | 0.000755189i | ||||
\(553\) | 223629. | − | 834595.i | 0.731270 | − | 2.72914i | ||||
\(554\) | 101236.i | 0.329851i | ||||||||
\(555\) | −35935.4 | + | 25484.9i | −0.116664 | + | 0.0827365i | ||||
\(556\) | 291371. | 0.942535 | ||||||||
\(557\) | 520115. | + | 139364.i | 1.67644 | + | 0.449201i | 0.966836 | − | 0.255397i | \(-0.0822062\pi\) |
0.709606 | + | 0.704599i | \(0.248873\pi\) | |||||||
\(558\) | −160588. | − | 92715.7i | −0.515757 | − | 0.297773i | ||||
\(559\) | 30667.4 | + | 17705.8i | 0.0981416 | + | 0.0566621i | ||||
\(560\) | 131375. | − | 35201.9i | 0.418926 | − | 0.112251i | ||||
\(561\) | −4395.41 | − | 4395.41i | −0.0139661 | − | 0.0139661i | ||||
\(562\) | −165493. | + | 286642.i | −0.523970 | + | 0.907543i | ||||
\(563\) | 430501. | + | 430501.i | 1.35818 | + | 1.35818i | 0.876159 | + | 0.482022i | \(0.160098\pi\) |
0.482022 | + | 0.876159i | \(0.339902\pi\) | |||||||
\(564\) | −11158.8 | − | 19327.7i | −0.0350801 | − | 0.0607605i | ||||
\(565\) | −566216. | −1.77372 | ||||||||
\(566\) | − | 91904.3i | − | 0.286882i | ||||||
\(567\) | −234591. | − | 406323.i | −0.729701 | − | 1.26388i | ||||
\(568\) | −77046.5 | + | 20644.5i | −0.238812 | + | 0.0639895i | ||||
\(569\) | 121421. | − | 121421.i | 0.375033 | − | 0.375033i | −0.494273 | − | 0.869306i | \(-0.664566\pi\) |
0.869306 | + | 0.494273i | \(0.164566\pi\) | |||||||
\(570\) | −20198.5 | − | 5412.18i | −0.0621684 | − | 0.0166580i | ||||
\(571\) | 137877. | + | 238810.i | 0.422883 | + | 0.732455i | 0.996220 | − | 0.0868645i | \(-0.0276847\pi\) |
−0.573337 | + | 0.819320i | \(0.694351\pi\) | |||||||
\(572\) | −32323.3 | + | 120632.i | −0.0987925 | + | 0.368699i | ||||
\(573\) | −8395.82 | − | 31333.6i | −0.0255714 | − | 0.0954337i | ||||
\(574\) | −526179. | + | 140989.i | −1.59702 | + | 0.427920i | ||||
\(575\) | −1756.09 | − | 470.543i | −0.00531142 | − | 0.00142319i | ||||
\(576\) | 35342.6 | − | 20405.0i | 0.106525 | − | 0.0615025i | ||||
\(577\) | 94277.9 | − | 351850.i | 0.283177 | − | 1.05683i | −0.666984 | − | 0.745072i | \(-0.732415\pi\) |
0.950161 | − | 0.311760i | \(-0.100918\pi\) | |||||||
\(578\) | 165266. | + | 165266.i | 0.494685 | + | 0.494685i | ||||
\(579\) | 19445.7 | + | 72572.5i | 0.0580052 | + | 0.216478i | ||||
\(580\) | −69848.7 | + | 40327.2i | −0.207636 | + | 0.119879i | ||||
\(581\) | −569172. | −1.68613 | ||||||||
\(582\) | 17497.2i | 0.0516563i | ||||||||
\(583\) | 461556. | − | 266480.i | 1.35796 | − | 0.784019i | ||||
\(584\) | −139806. | + | 139806.i | −0.409920 | + | 0.409920i | ||||
\(585\) | 166231. | + | 95973.7i | 0.485737 | + | 0.280440i | ||||
\(586\) | 147753. | − | 147753.i | 0.430269 | − | 0.430269i | ||||
\(587\) | 28541.9 | + | 106520.i | 0.0828337 | + | 0.309140i | 0.994895 | − | 0.100914i | \(-0.0321767\pi\) |
−0.912061 | + | 0.410054i | \(0.865510\pi\) | |||||||
\(588\) | −14722.2 | + | 25499.6i | −0.0425811 | + | 0.0737527i | ||||
\(589\) | −94482.4 | + | 163648.i | −0.272345 | + | 0.471716i | ||||
\(590\) | 84704.5 | − | 316122.i | 0.243334 | − | 0.908134i | ||||
\(591\) | − | 29308.1i | − | 0.0839098i | ||||||
\(592\) | −86374.6 | − | 14696.4i | −0.246458 | − | 0.0419341i | ||||
\(593\) | −357015. | −1.01526 | −0.507630 | − | 0.861575i | \(-0.669478\pi\) | ||||
−0.507630 | + | 0.861575i | \(0.669478\pi\) | |||||||
\(594\) | −91592.6 | − | 24542.2i | −0.259590 | − | 0.0695568i | ||||
\(595\) | −54840.2 | − | 31662.0i | −0.154905 | − | 0.0894343i | ||||
\(596\) | 197018. | + | 113748.i | 0.554642 | + | 0.320223i | ||||
\(597\) | 12856.2 | − | 3444.80i | 0.0360714 | − | 0.00966529i | ||||
\(598\) | −1757.49 | − | 1757.49i | −0.00491462 | − | 0.00491462i | ||||
\(599\) | −36147.8 | + | 62609.9i | −0.100746 | + | 0.174497i | −0.911992 | − | 0.410207i | \(-0.865456\pi\) |
0.811246 | + | 0.584705i | \(0.198790\pi\) | |||||||
\(600\) | −3202.47 | − | 3202.47i | −0.00889574 | − | 0.00889574i | ||||
\(601\) | 232362. | + | 402462.i | 0.643303 | + | 1.11423i | 0.984691 | + | 0.174311i | \(0.0557697\pi\) |
−0.341388 | + | 0.939922i | \(0.610897\pi\) | |||||||
\(602\) | −88388.6 | −0.243895 | ||||||||
\(603\) | − | 325806.i | − | 0.896033i | ||||||
\(604\) | −149380. | − | 258735.i | −0.409468 | − | 0.709219i | ||||
\(605\) | 520004. | − | 139335.i | 1.42068 | − | 0.380670i | ||||
\(606\) | 13794.0 | − | 13794.0i | 0.0375618 | − | 0.0375618i | ||||
\(607\) | 241107. | + | 64604.3i | 0.654383 | + | 0.175341i | 0.570710 | − | 0.821152i | \(-0.306668\pi\) |
0.0836730 | + | 0.996493i | \(0.473335\pi\) | |||||||
\(608\) | −20793.9 | − | 36016.0i | −0.0562507 | − | 0.0974291i | ||||
\(609\) | 7871.13 | − | 29375.5i | 0.0212228 | − | 0.0792045i | ||||
\(610\) | 59803.9 | + | 223191.i | 0.160720 | + | 0.599815i | ||||
\(611\) | 201649. | − | 54031.7i | 0.540149 | − | 0.144733i | ||||
\(612\) | −18353.1 | − | 4917.70i | −0.0490013 | − | 0.0131298i | ||||
\(613\) | 370621. | − | 213978.i | 0.986301 | − | 0.569441i | 0.0821345 | − | 0.996621i | \(-0.473826\pi\) |
0.904167 | + | 0.427180i | \(0.140493\pi\) | |||||||
\(614\) | 5850.11 | − | 21832.9i | 0.0155177 | − | 0.0579128i | ||||
\(615\) | 58365.6 | + | 58365.6i | 0.154314 | + | 0.154314i | ||||
\(616\) | −80680.0 | − | 301102.i | −0.212620 | − | 0.793510i | ||||
\(617\) | −381880. | + | 220478.i | −1.00313 | + | 0.579156i | −0.909172 | − | 0.416420i | \(-0.863285\pi\) |
−0.0939560 | + | 0.995576i | \(0.529951\pi\) | |||||||
\(618\) | −24377.3 | −0.0638276 | ||||||||
\(619\) | 518027.i | 1.35198i | 0.736910 | + | 0.675991i | \(0.236284\pi\) | ||||
−0.736910 | + | 0.675991i | \(0.763716\pi\) | |||||||
\(620\) | −161282. | + | 93116.5i | −0.419569 | + | 0.242238i | ||||
\(621\) | 1334.41 | − | 1334.41i | 0.00346024 | − | 0.00346024i | ||||
\(622\) | 367415. | + | 212127.i | 0.949678 | + | 0.548297i | ||||
\(623\) | 636971. | − | 636971.i | 1.64113 | − | 1.64113i | ||||
\(624\) | −1602.51 | − | 5980.64i | −0.00411558 | − | 0.0153595i | ||||
\(625\) | −234829. | + | 406736.i | −0.601163 | + | 1.04124i | ||||
\(626\) | 126536. | − | 219167.i | 0.322898 | − | 0.559276i | ||||
\(627\) | −12404.3 | + | 46293.5i | −0.0315528 | + | 0.117757i | ||||
\(628\) | 83954.5i | 0.212875i | ||||||||
\(629\) | 23597.8 | + | 33274.4i | 0.0596444 | + | 0.0841025i | ||||
\(630\) | −479107. | −1.20712 | ||||||||
\(631\) | −445382. | − | 119340.i | −1.11860 | − | 0.299727i | −0.348281 | − | 0.937390i | \(-0.613235\pi\) |
−0.770315 | + | 0.637663i | \(0.779901\pi\) | |||||||
\(632\) | −225493. | − | 130189.i | −0.564546 | − | 0.325941i | ||||
\(633\) | 2748.26 | + | 1586.71i | 0.00685883 | + | 0.00395995i | ||||
\(634\) | 429687. | − | 115134.i | 1.06899 | − | 0.286435i | ||||
\(635\) | 473654. | + | 473654.i | 1.17466 | + | 1.17466i | ||||
\(636\) | −13211.4 | + | 22882.8i | −0.0326613 | + | 0.0565710i | ||||
\(637\) | −194756. | − | 194756.i | −0.479967 | − | 0.479967i | ||||
\(638\) | 92426.8 | + | 160088.i | 0.227068 | + | 0.393294i | ||||
\(639\) | 280977. | 0.688129 | ||||||||
\(640\) | − | 40986.5i | − | 0.100065i | ||||||
\(641\) | −191271. | − | 331291.i | −0.465514 | − | 0.806294i | 0.533711 | − | 0.845667i | \(-0.320797\pi\) |
−0.999225 | + | 0.0393735i | \(0.987464\pi\) | |||||||
\(642\) | 18330.9 | − | 4911.76i | 0.0444749 | − | 0.0119170i | ||||
\(643\) | 60435.6 | − | 60435.6i | 0.146174 | − | 0.146174i | −0.630232 | − | 0.776407i | \(-0.717040\pi\) |
0.776407 | + | 0.630232i | \(0.217040\pi\) | |||||||
\(644\) | 5992.40 | + | 1605.66i | 0.0144487 | + | 0.00387152i | ||||
\(645\) | 6696.50 | + | 11598.7i | 0.0160964 | + | 0.0278798i | ||||
\(646\) | −5011.41 | + | 18702.8i | −0.0120087 | + | 0.0448170i | ||||
\(647\) | −44847.3 | − | 167372.i | −0.107134 | − | 0.399830i | 0.891444 | − | 0.453130i | \(-0.149693\pi\) |
−0.998579 | + | 0.0533000i | \(0.983026\pi\) | |||||||
\(648\) | −136570. | + | 36593.9i | −0.325242 | + | 0.0871482i | ||||
\(649\) | −724527. | − | 194136.i | −1.72014 | − | 0.460911i | ||||
\(650\) | 36688.8 | − | 21182.3i | 0.0868374 | − | 0.0501356i | ||||
\(651\) | 18174.6 | − | 67828.7i | 0.0428848 | − | 0.160048i | ||||
\(652\) | −44939.4 | − | 44939.4i | −0.105714 | − | 0.105714i | ||||
\(653\) | −117604. | − | 438903.i | −0.275800 | − | 1.02930i | −0.955303 | − | 0.295628i | \(-0.904471\pi\) |
0.679503 | − | 0.733673i | \(-0.262196\pi\) | |||||||
\(654\) | −1358.77 | + | 784.488i | −0.00317681 | + | 0.00183413i | ||||
\(655\) | −757008. | −1.76449 | ||||||||
\(656\) | 164158.i | 0.381464i | ||||||||
\(657\) | 603161. | − | 348235.i | 1.39734 | − | 0.806755i | ||||
\(658\) | −368458. | + | 368458.i | −0.851012 | + | 0.851012i | ||||
\(659\) | 63459.0 | + | 36638.1i | 0.146124 | + | 0.0843649i | 0.571280 | − | 0.820756i | \(-0.306447\pi\) |
−0.425155 | + | 0.905120i | \(0.639781\pi\) | |||||||
\(660\) | −33399.3 | + | 33399.3i | −0.0766742 | + | 0.0766742i | ||||
\(661\) | 38866.5 | + | 145052.i | 0.0889555 | + | 0.331987i | 0.996034 | − | 0.0889754i | \(-0.0283593\pi\) |
−0.907078 | + | 0.420962i | \(0.861693\pi\) | |||||||
\(662\) | −90376.3 | + | 156536.i | −0.206224 | + | 0.357190i | ||||
\(663\) | −1441.36 | + | 2496.51i | −0.00327903 | + | 0.00567945i | ||||
\(664\) | −44392.7 | + | 165676.i | −0.100687 | + | 0.375770i | ||||
\(665\) | 488236.i | 1.10404i | ||||||||
\(666\) | 280496. | + | 128754.i | 0.632381 | + | 0.290278i | ||||
\(667\) | −3678.88 | −0.00826920 | ||||||||
\(668\) | 192954. | + | 51701.9i | 0.432415 | + | 0.115865i | ||||
\(669\) | −62314.3 | − | 35977.2i | −0.139231 | − | 0.0803850i | ||||
\(670\) | −283375. | − | 163607.i | −0.631266 | − | 0.364462i | ||||
\(671\) | 511537. | − | 137066.i | 1.13614 | − | 0.304428i | ||||
\(672\) | 10928.0 | + | 10928.0i | 0.0241992 | + | 0.0241992i | ||||
\(673\) | −177884. | + | 308105.i | −0.392742 | + | 0.680250i | −0.992810 | − | 0.119699i | \(-0.961807\pi\) |
0.600068 | + | 0.799949i | \(0.295140\pi\) | |||||||
\(674\) | −3256.55 | − | 3256.55i | −0.00716866 | − | 0.00716866i | ||||
\(675\) | 16083.1 | + | 27856.8i | 0.0352990 | + | 0.0611396i | ||||
\(676\) | −170571. | −0.373260 | ||||||||
\(677\) | − | 547427.i | − | 1.19440i | −0.802093 | − | 0.597199i | \(-0.796280\pi\) | ||
0.802093 | − | 0.597199i | \(-0.203720\pi\) | |||||||
\(678\) | −32168.9 | − | 55718.2i | −0.0699805 | − | 0.121210i | ||||
\(679\) | 394609. | − | 105735.i | 0.855909 | − | 0.229340i | ||||
\(680\) | −13493.5 | + | 13493.5i | −0.0291814 | + | 0.0291814i | ||||
\(681\) | −67608.1 | − | 18115.5i | −0.145782 | − | 0.0390622i | ||||
\(682\) | 213416. | + | 369647.i | 0.458837 | + | 0.794728i | ||||
\(683\) | 6778.62 | − | 25298.2i | 0.0145312 | − | 0.0542310i | −0.958280 | − | 0.285833i | \(-0.907730\pi\) |
0.972811 | + | 0.231602i | \(0.0743966\pi\) | |||||||
\(684\) | 37916.1 | + | 141505.i | 0.0810423 | + | 0.302454i | ||||
\(685\) | −11816.7 | + | 3166.28i | −0.0251835 | + | 0.00674789i | ||||
\(686\) | 171504. | + | 45954.5i | 0.364441 | + | 0.0976517i | ||||
\(687\) | 30256.1 | − | 17468.4i | 0.0641062 | − | 0.0370117i | ||||
\(688\) | −6893.88 | + | 25728.3i | −0.0145642 | + | 0.0543543i | ||||
\(689\) | −174770. | − | 174770.i | −0.368153 | − | 0.368153i | ||||
\(690\) | −243.296 | − | 907.994i | −0.000511019 | − | 0.00190715i | ||||
\(691\) | −10608.0 | + | 6124.53i | −0.0222166 | + | 0.0128268i | −0.511067 | − | 0.859541i | \(-0.670750\pi\) |
0.488851 | + | 0.872368i | \(0.337416\pi\) | |||||||
\(692\) | −244525. | −0.510636 | ||||||||
\(693\) | 1.09808e6i | 2.28647i | ||||||||
\(694\) | −295268. | + | 170473.i | −0.613053 | + | 0.353946i | ||||
\(695\) | −728900. | + | 728900.i | −1.50903 | + | 1.50903i | ||||
\(696\) | −7936.75 | − | 4582.28i | −0.0163842 | − | 0.00945940i | ||||
\(697\) | 54043.7 | − | 54043.7i | 0.111245 | − | 0.111245i | ||||
\(698\) | −108843. | − | 406207.i | −0.223403 | − | 0.833751i | ||||
\(699\) | −47011.2 | + | 81425.7i | −0.0962158 | + | 0.166651i | ||||
\(700\) | −52871.7 | + | 91576.5i | −0.107901 | + | 0.186891i | ||||
\(701\) | 18563.3 | − | 69279.3i | 0.0377763 | − | 0.140983i | −0.944462 | − | 0.328620i | \(-0.893416\pi\) |
0.982238 | + | 0.187637i | \(0.0600830\pi\) | |||||||
\(702\) | 43974.8i | 0.0892339i | ||||||||
\(703\) | 131208. | − | 285841.i | 0.265491 | − | 0.578381i | ||||
\(704\) | −93938.0 | −0.189538 | ||||||||
\(705\) | 76265.5 | + | 20435.3i | 0.153444 | + | 0.0411152i | ||||
\(706\) | −95310.2 | − | 55027.4i | −0.191218 | − | 0.110400i | ||||
\(707\) | −394449. | − | 227735.i | −0.789137 | − | 0.455608i | ||||
\(708\) | 35920.2 | − | 9624.78i | 0.0716592 | − | 0.0192010i | ||||
\(709\) | 91287.1 | + | 91287.1i | 0.181601 | + | 0.181601i | 0.792053 | − | 0.610452i | \(-0.209012\pi\) |
−0.610452 | + | 0.792053i | \(0.709012\pi\) | |||||||
\(710\) | 141096. | − | 244385.i | 0.279897 | − | 0.484796i | ||||
\(711\) | 648561. | + | 648561.i | 1.28296 | + | 1.28296i | ||||
\(712\) | −135730. | − | 235091.i | −0.267742 | − | 0.463742i | ||||
\(713\) | −8494.62 | −0.0167096 | ||||||||
\(714\) | − | 7195.36i | − | 0.0141142i | ||||||
\(715\) | −220915. | − | 382636.i | −0.432129 | − | 0.748470i | ||||
\(716\) | 354197. | − | 94906.8i | 0.690905 | − | 0.185128i | ||||
\(717\) | 999.704 | − | 999.704i | 0.00194461 | − | 0.00194461i | ||||
\(718\) | −409822. | − | 109811.i | −0.794961 | − | 0.213009i | ||||
\(719\) | 76217.1 | + | 132012.i | 0.147433 | + | 0.255362i | 0.930278 | − | 0.366855i | \(-0.119566\pi\) |
−0.782845 | + | 0.622217i | \(0.786232\pi\) | |||||||
\(720\) | −37368.0 | + | 139459.i | −0.0720833 | + | 0.269018i | ||||
\(721\) | 147311. | + | 549772.i | 0.283377 | + | 1.05758i | ||||
\(722\) | −211842. | + | 56763.0i | −0.406386 | + | 0.108891i | ||||
\(723\) | −53812.1 | − | 14418.9i | −0.102945 | − | 0.0275839i | ||||
\(724\) | −334007. | + | 192839.i | −0.637205 | + | 0.367890i | ||||
\(725\) | 16229.6 | − | 60569.7i | 0.0308768 | − | 0.115234i | ||||
\(726\) | 43254.6 | + | 43254.6i | 0.0820653 | + | 0.0820653i | ||||
\(727\) | 28949.1 | + | 108039.i | 0.0547729 | + | 0.204415i | 0.987890 | − | 0.155158i | \(-0.0495888\pi\) |
−0.933117 | + | 0.359574i | \(0.882922\pi\) | |||||||
\(728\) | −125195. | + | 72281.5i | −0.236225 | + | 0.136384i | ||||
\(729\) | 481224. | 0.905507 | ||||||||
\(730\) | − | 699481.i | − | 1.31259i | ||||||
\(731\) | 10739.8 | − | 6200.63i | 0.0200984 | − | 0.0116038i | ||||
\(732\) | −18565.3 | + | 18565.3i | −0.0346482 | + | 0.0346482i | ||||
\(733\) | −577090. | − | 333183.i | −1.07408 | − | 0.620119i | −0.144785 | − | 0.989463i | \(-0.546249\pi\) |
−0.929293 | + | 0.369344i | \(0.879583\pi\) | |||||||
\(734\) | −52948.1 | + | 52948.1i | −0.0982785 | + | 0.0982785i | ||||
\(735\) | −26960.9 | − | 100619.i | −0.0499068 | − | 0.186255i | ||||
\(736\) | 934.756 | − | 1619.05i | 0.00172561 | − | 0.00298884i | ||||
\(737\) | −374975. | + | 649475.i | −0.690346 | + | 1.19571i | ||||
\(738\) | 149665. | − | 558557.i | 0.274794 | − | 1.02554i | ||||
\(739\) | 139826.i | 0.256035i | 0.991772 | + | 0.128018i | \(0.0408614\pi\) | ||||
−0.991772 | + | 0.128018i | \(0.959139\pi\) | |||||||
\(740\) | 252841. | − | 179312.i | 0.461726 | − | 0.327450i | ||||
\(741\) | 22226.1 | 0.0404788 | ||||||||
\(742\) | 595903. | + | 159672.i | 1.08235 | + | 0.290015i | ||||
\(743\) | −734489. | − | 424058.i | −1.33048 | − | 0.768152i | −0.345105 | − | 0.938564i | \(-0.612157\pi\) |
−0.985373 | + | 0.170412i | \(0.945490\pi\) | |||||||
\(744\) | −18326.2 | − | 10580.6i | −0.0331074 | − | 0.0191146i | ||||
\(745\) | −777418. | + | 208308.i | −1.40069 | + | 0.375314i | ||||
\(746\) | −102294. | − | 102294.i | −0.183811 | − | 0.183811i | ||||
\(747\) | 302098. | − | 523249.i | 0.541385 | − | 0.937707i | ||||
\(748\) | 30926.1 | + | 30926.1i | 0.0552741 | + | 0.0552741i | ||||
\(749\) | −221546. | − | 383730.i | −0.394913 | − | 0.684009i | ||||
\(750\) | −40864.7 | −0.0726483 | ||||||||
\(751\) | − | 184846.i | − | 0.327740i | −0.986482 | − | 0.163870i | \(-0.947602\pi\) | ||
0.986482 | − | 0.163870i | \(-0.0523977\pi\) | |||||||
\(752\) | 78513.4 | + | 135989.i | 0.138838 | + | 0.240474i | ||||
\(753\) | 118537. | − | 31762.0i | 0.209057 | − | 0.0560167i | ||||
\(754\) | 60617.9 | − | 60617.9i | 0.106625 | − | 0.106625i | ||||
\(755\) | 1.02095e6 | + | 273562.i | 1.79106 | + | 0.479912i | ||||
\(756\) | −54881.3 | − | 95057.1i | −0.0960242 | − | 0.166319i | ||||
\(757\) | 59199.5 | − | 220936.i | 0.103306 | − | 0.385544i | −0.894841 | − | 0.446384i | \(-0.852711\pi\) |
0.998148 | + | 0.0608404i | \(0.0193781\pi\) | |||||||
\(758\) | 204622. | + | 763658.i | 0.356134 | + | 1.32911i | ||||
\(759\) | −2081.05 | + | 557.617i | −0.00361243 | + | 0.000967949i | ||||
\(760\) | 142117. | + | 38080.0i | 0.246047 | + | 0.0659280i | ||||
\(761\) | 145275. | − | 83874.5i | 0.250854 | − | 0.144831i | −0.369301 | − | 0.929310i | \(-0.620403\pi\) |
0.620155 | + | 0.784479i | \(0.287070\pi\) | |||||||
\(762\) | −19699.6 | + | 73519.8i | −0.0339271 | + | 0.126618i | ||||
\(763\) | 25903.3 | + | 25903.3i | 0.0444945 | + | 0.0444945i | ||||
\(764\) | 59072.9 | + | 220463.i | 0.101205 | + | 0.377702i | ||||
\(765\) | 58214.7 | − | 33610.3i | 0.0994740 | − | 0.0574314i | ||||
\(766\) | −12354.2 | −0.0210550 | ||||||||
\(767\) | 347855.i | 0.591299i | ||||||||
\(768\) | 4033.25 | − | 2328.60i | 0.00683806 | − | 0.00394796i | ||||
\(769\) | −94379.3 | + | 94379.3i | −0.159597 | + | 0.159597i | −0.782388 | − | 0.622791i | \(-0.785999\pi\) |
0.622791 | + | 0.782388i | \(0.285999\pi\) | |||||||
\(770\) | 955072. | + | 551411.i | 1.61085 | + | 0.930024i | ||||
\(771\) | −46169.9 | + | 46169.9i | −0.0776695 | + | 0.0776695i | ||||
\(772\) | −136820. | − | 510619.i | −0.229570 | − | 0.856766i | ||||
\(773\) | −134471. | + | 232910.i | −0.225045 | + | 0.389789i | −0.956333 | − | 0.292280i | \(-0.905586\pi\) |
0.731288 | + | 0.682069i | \(0.238920\pi\) | |||||||
\(774\) | 46913.7 | − | 81257.0i | 0.0783101 | − | 0.135637i | ||||
\(775\) | 37474.5 | − | 139857.i | 0.0623926 | − | 0.232852i | ||||
\(776\) | − | 123110.i | − | 0.204442i | ||||||
\(777\) | −19604.7 | + | 115222.i | −0.0324726 | + | 0.190850i | ||||
\(778\) | 534562. | 0.883159 | ||||||||
\(779\) | −569200. | − | 152517.i | −0.937972 | − | 0.251329i | ||||
\(780\) | 18970.1 | + | 10952.4i | 0.0311803 | + | 0.0180020i | ||||
\(781\) | −560113. | − | 323381.i | −0.918277 | − | 0.530167i | ||||
\(782\) | −840.758 | + | 225.280i | −0.00137486 | + | 0.000368392i | ||||
\(783\) | 46025.4 | + | 46025.4i | 0.0750713 | + | 0.0750713i | ||||
\(784\) | 103585. | − | 179415.i | 0.168525 | − | 0.291894i | ||||
\(785\) | −210022. | − | 210022.i | −0.340820 | − | 0.340820i | ||||
\(786\) | −43008.6 | − | 74493.0i | −0.0696161 | − | 0.120579i | ||||
\(787\) | 286356. | 0.462335 | 0.231168 | − | 0.972914i | \(-0.425745\pi\) | ||||
0.231168 | + | 0.972914i | \(0.425745\pi\) | |||||||
\(788\) | 206211.i | 0.332093i | ||||||||
\(789\) | 13108.5 | + | 22704.6i | 0.0210572 | + | 0.0364721i | ||||
\(790\) | 889780. | − | 238416.i | 1.42570 | − | 0.382016i | ||||
\(791\) | −1.06220e6 | + | 1.06220e6i | −1.69766 | + | 1.69766i | ||||
\(792\) | 319630. | + | 85644.6i | 0.509562 | + | 0.136537i | ||||
\(793\) | −122798. | − | 212692.i | −0.195274 | − | 0.338225i | ||||
\(794\) | −49829.8 | + | 185967.i | −0.0790402 | + | 0.294982i | ||||
\(795\) | −24194.1 | − | 90293.7i | −0.0382803 | − | 0.142864i | ||||
\(796\) | −90455.8 | + | 24237.5i | −0.142761 | + | 0.0382527i | ||||
\(797\) | 686093. | + | 183838.i | 1.08011 | + | 0.289414i | 0.754639 | − | 0.656140i | \(-0.227812\pi\) |
0.325467 | + | 0.945553i | \(0.394479\pi\) | |||||||
\(798\) | −48044.6 | + | 27738.6i | −0.0754464 | + | 0.0435590i | ||||
\(799\) | 18922.1 | − | 70618.1i | 0.0296398 | − | 0.110617i | ||||
\(800\) | 22532.5 | + | 22532.5i | 0.0352070 | + | 0.0352070i | ||||
\(801\) | 247494. | + | 923660.i | 0.385745 | + | 1.43962i | ||||
\(802\) | −555565. | + | 320756.i | −0.863746 | + | 0.498684i | ||||
\(803\) | −1.60316e6 | −2.48625 | ||||||||
\(804\) | − | 37180.6i | − | 0.0575180i | ||||||
\(805\) | −19007.4 | + | 10973.9i | −0.0293313 | + | 0.0169345i | ||||
\(806\) | 139968. | − | 139968.i | 0.215456 | − | 0.215456i | ||||
\(807\) | −14310.8 | − | 8262.33i | −0.0219744 | − | 0.0126869i | ||||
\(808\) | −97054.7 | + | 97054.7i | −0.148660 | + | 0.148660i | ||||
\(809\) | −222489. | − | 830339.i | −0.339947 | − | 1.26870i | −0.898406 | − | 0.439166i | \(-0.855274\pi\) |
0.558459 | − | 0.829532i | \(-0.311393\pi\) | |||||||
\(810\) | 250103. | − | 433190.i | 0.381196 | − | 0.660250i | ||||
\(811\) | 223122. | − | 386459.i | 0.339236 | − | 0.587573i | −0.645054 | − | 0.764137i | \(-0.723165\pi\) |
0.984289 | + | 0.176564i | \(0.0564983\pi\) | |||||||
\(812\) | −55381.2 | + | 206685.i | −0.0839943 | + | 0.313471i | ||||
\(813\) | 134766.i | 0.203891i | ||||||||
\(814\) | −410968. | − | 579493.i | −0.620240 | − | 0.874579i | ||||
\(815\) | 224842. | 0.338503 | ||||||||
\(816\) | −2094.44 | − | 561.203i | −0.00314548 | − | 0.000842829i | ||||
\(817\) | −82805.3 | − | 47807.7i | −0.124055 | − | 0.0716231i | ||||
\(818\) | 729182. | + | 420993.i | 1.08976 | + | 0.629171i | ||||
\(819\) | 491885. | − | 131800.i | 0.733324 | − | 0.196494i | ||||
\(820\) | −410659. | − | 410659.i | −0.610737 | − | 0.610737i | ||||
\(821\) | 336463. | − | 582771.i | 0.499173 | − | 0.864593i | −0.500827 | − | 0.865548i | \(-0.666971\pi\) |
1.00000 | 0.000954793i | \(0.000303920\pi\) | ||||||||
\(822\) | −982.930 | − | 982.930i | −0.00145472 | − | 0.00145472i | ||||
\(823\) | 373480. | + | 646887.i | 0.551402 | + | 0.955056i | 0.998174 | + | 0.0604080i | \(0.0192402\pi\) |
−0.446772 | + | 0.894648i | \(0.647426\pi\) | |||||||
\(824\) | 171518. | 0.252613 | ||||||||
\(825\) | − | 36722.8i | − | 0.0539545i | ||||||
\(826\) | −434128. | − | 751933.i | −0.636294 | − | 1.10209i | ||||
\(827\) | 565485. | − | 151521.i | 0.826818 | − | 0.221545i | 0.179493 | − | 0.983759i | \(-0.442554\pi\) |
0.647325 | + | 0.762214i | \(0.275888\pi\) | |||||||
\(828\) | −4656.68 | + | 4656.68i | −0.00679228 | + | 0.00679228i | ||||
\(829\) | 953252. | + | 255423.i | 1.38707 | + | 0.371665i | 0.873685 | − | 0.486493i | \(-0.161724\pi\) |
0.513387 | + | 0.858157i | \(0.328391\pi\) | |||||||
\(830\) | −303404. | − | 525511.i | −0.440418 | − | 0.762826i | ||||
\(831\) | 10533.0 | − | 39309.8i | 0.0152529 | − | 0.0569244i | ||||
\(832\) | 11275.2 | + | 42079.7i | 0.0162884 | + | 0.0607891i | ||||
\(833\) | −93168.6 | + | 24964.4i | −0.134270 | + | 0.0359776i | ||||
\(834\) | −113139. | − | 30315.4i | −0.162659 | − | 0.0435844i | ||||
\(835\) | −612035. | + | 353359.i | −0.877816 | + | 0.506807i | ||||
\(836\) | 87276.5 | − | 325720.i | 0.124878 | − | 0.466050i | ||||
\(837\) | 106274. | + | 106274.i | 0.151696 | + | 0.151696i | ||||
\(838\) | 9229.58 | + | 34445.3i | 0.0131430 | + | 0.0490503i | ||||
\(839\) | 382799. | − | 221009.i | 0.543810 | − | 0.313969i | −0.202812 | − | 0.979218i | \(-0.565008\pi\) |
0.746622 | + | 0.665249i | \(0.231675\pi\) | |||||||
\(840\) | −54675.1 | −0.0774874 | ||||||||
\(841\) | 580392.i | 0.820596i | ||||||||
\(842\) | 54402.9 | − | 31409.5i | 0.0767358 | − | 0.0443034i | ||||
\(843\) | 94083.7 | − | 94083.7i | 0.132391 | − | 0.132391i | ||||
\(844\) | −19336.7 | − | 11164.1i | −0.0271455 | − | 0.0156725i | ||||
\(845\) | 426703. | − | 426703.i | 0.597602 | − | 0.597602i | ||||
\(846\) | −143164. | − | 534294.i | −0.200028 | − | 0.746516i | ||||
\(847\) | 714120. | − | 1.23689e6i | 0.995416 | − | 1.72411i | ||||
\(848\) | 92955.0 | − | 161003.i | 0.129265 | − | 0.223894i | ||||
\(849\) | −9562.07 | + | 35686.1i | −0.0132659 | + | 0.0495090i | ||||
\(850\) | − | 14836.2i | − | 0.0205346i | ||||||
\(851\) | 14077.2 | − | 1316.74i | 0.0194382 | − | 0.00181820i | ||||
\(852\) | 32064.8 | 0.0441723 | ||||||||
\(853\) | 883317. | + | 236684.i | 1.21400 | + | 0.325290i | 0.808330 | − | 0.588729i | \(-0.200372\pi\) |
0.405670 | + | 0.914020i | \(0.367038\pi\) | |||||||
\(854\) | 530887. | + | 306508.i | 0.727924 | + | 0.420267i | ||||
\(855\) | −448843. | − | 259139.i | −0.613991 | − | 0.354488i | ||||
\(856\) | −128976. | + | 34559.1i | −0.176020 | + | 0.0471644i | ||||
\(857\) | −108011. | − | 108011.i | −0.147064 | − | 0.147064i | 0.629741 | − | 0.776805i | \(-0.283161\pi\) |
−0.776805 | + | 0.629741i | \(0.783161\pi\) | |||||||
\(858\) | 25102.1 | − | 43478.1i | 0.0340985 | − | 0.0590603i | ||||
\(859\) | −334725. | − | 334725.i | −0.453630 | − | 0.453630i | 0.442927 | − | 0.896557i | \(-0.353940\pi\) |
−0.896557 | + | 0.442927i | \(0.853940\pi\) | |||||||
\(860\) | −47116.5 | − | 81608.2i | −0.0637054 | − | 0.110341i | ||||
\(861\) | 218983. | 0.295395 | ||||||||
\(862\) | 497939.i | 0.670134i | ||||||||
\(863\) | 344904. | + | 597391.i | 0.463102 | + | 0.802116i | 0.999114 | − | 0.0420944i | \(-0.0134030\pi\) |
−0.536012 | + | 0.844211i | \(0.680070\pi\) | |||||||
\(864\) | −31949.9 | + | 8560.94i | −0.0427998 | + | 0.0114682i | ||||
\(865\) | 611708. | − | 611708.i | 0.817545 | − | 0.817545i | ||||
\(866\) | −44022.9 | − | 11795.9i | −0.0587006 | − | 0.0157288i | ||||
\(867\) | −46977.4 | − | 81367.3i | −0.0624958 | − | 0.108246i | ||||
\(868\) | −127876. | + | 477242.i | −0.169727 | + | 0.633430i | ||||
\(869\) | −546431. | − | 2.03931e6i | −0.723596 | − | 2.70050i | ||||
\(870\) | 31317.8 | − | 8391.59i | 0.0413764 | − | 0.0110868i | ||||
\(871\) | 335941. | + | 90015.2i | 0.442820 | + | 0.118653i | ||||
\(872\) | 9560.31 | − | 5519.65i | 0.0125730 | − | 0.00725903i | ||||
\(873\) | −112241. | + | 418891.i | −0.147274 | + | 0.549632i | ||||
\(874\) | 4745.41 | + | 4745.41i | 0.00621227 | + | 0.00621227i | ||||
\(875\) | 246944. | + | 921607.i | 0.322539 | + | 1.20373i | ||||
\(876\) | 68832.1 | − | 39740.2i | 0.0896980 | − | 0.0517871i | ||||
\(877\) | −925043. | −1.20271 | −0.601357 | − | 0.798980i | \(-0.705373\pi\) | ||||
−0.601357 | + | 0.798980i | \(0.705373\pi\) | |||||||
\(878\) | − | 197508.i | − | 0.256209i | ||||||
\(879\) | −72744.6 | + | 41999.1i | −0.0941506 | + | 0.0543579i | ||||
\(880\) | 234997. | − | 234997.i | 0.303457 | − | 0.303457i | ||||
\(881\) | 446150. | + | 257585.i | 0.574816 | + | 0.331870i | 0.759071 | − | 0.651008i | \(-0.225654\pi\) |
−0.184255 | + | 0.982879i | \(0.558987\pi\) | |||||||
\(882\) | −516030. | + | 516030.i | −0.663342 | + | 0.663342i | ||||
\(883\) | 47073.4 | + | 175680.i | 0.0603746 | + | 0.225321i | 0.989521 | − | 0.144392i | \(-0.0461226\pi\) |
−0.929146 | + | 0.369713i | \(0.879456\pi\) | |||||||
\(884\) | 10141.4 | − | 17565.4i | 0.0129776 | − | 0.0224778i | ||||
\(885\) | −65781.0 | + | 113936.i | −0.0839873 | + | 0.145470i | ||||
\(886\) | 104410. | − | 389663.i | 0.133007 | − | 0.496388i | ||||
\(887\) | − | 314680.i | − | 0.399965i | −0.979800 | − | 0.199982i | \(-0.935912\pi\) | ||
0.979800 | − | 0.199982i | \(-0.0640885\pi\) | |||||||
\(888\) | 32009.9 | + | 14693.3i | 0.0405937 | + | 0.0186335i | ||||
\(889\) | 1.77711e6 | 2.24859 | ||||||||
\(890\) | 927653. | + | 248564.i | 1.17113 | + | 0.313804i | ||||
\(891\) | −992840. | − | 573216.i | −1.25062 | − | 0.722043i | ||||
\(892\) | 438442. | + | 253135.i | 0.551040 | + | 0.318143i | ||||
\(893\) | −544475. | + | 145892.i | −0.682770 | + | 0.182948i | ||||
\(894\) | −64666.6 | − | 64666.6i | −0.0809105 | − | 0.0809105i | ||||
\(895\) | −648644. | + | 1.12349e6i | −0.809768 | + | 1.40256i | ||||
\(896\) | −76888.9 | − | 76888.9i | −0.0957740 | − | 0.0957740i | ||||
\(897\) | 499.571 | + | 865.282i | 0.000620886 | + | 0.00107541i | ||||
\(898\) | −510242. | −0.632737 | ||||||||
\(899\) | − | 292990.i | − | 0.362521i | ||||||
\(900\) | −56125.1 | − | 97211.5i | −0.0692902 | − | 0.120014i | ||||
\(901\) | −83607.5 | + | 22402.6i | −0.102990 | + | 0.0275961i | ||||
\(902\) | −941201. | + | 941201.i | −1.15683 | + | 1.15683i | ||||
\(903\) | 34321.0 | + | 9196.28i | 0.0420905 | + | 0.0112781i | ||||
\(904\) | 226340. | + | 392032.i | 0.276965 | + | 0.479717i | ||||
\(905\) | 353149. | − | 1.31797e6i | 0.431182 | − | 1.60919i | ||||
\(906\) | 31084.2 | + | 116008.i | 0.0378690 | + | 0.141329i | ||||
\(907\) | 289631. | − | 77606.5i | 0.352071 | − | 0.0943373i | −0.0784489 | − | 0.996918i | \(-0.524997\pi\) |
0.430520 | + | 0.902581i | \(0.358330\pi\) | |||||||
\(908\) | 475689. | + | 127461.i | 0.576968 | + | 0.154598i | ||||
\(909\) | 418721. | − | 241749.i | 0.506754 | − | 0.292575i | ||||
\(910\) | 132370. | − | 494011.i | 0.159848 | − | 0.596560i | ||||
\(911\) | −674572. | − | 674572.i | −0.812815 | − | 0.812815i | 0.172240 | − | 0.985055i | \(-0.444900\pi\) |
−0.985055 | + | 0.172240i | \(0.944900\pi\) | |||||||
\(912\) | 4326.94 | + | 16148.4i | 0.00520225 | + | 0.0194151i | ||||
\(913\) | −1.20443e6 | + | 695378.i | −1.44491 | + | 0.834218i | ||||
\(914\) | 672512. | 0.805021 | ||||||||
\(915\) | − | 92886.7i | − | 0.110946i | ||||||
\(916\) | −212882. | + | 122907.i | −0.253716 | + | 0.146483i | ||||
\(917\) | −1.42012e6 | + | 1.42012e6i | −1.68883 | + | 1.68883i | ||||
\(918\) | 13336.9 | + | 7700.06i | 0.0158259 | + | 0.00913711i | ||||
\(919\) | −797613. | + | 797613.i | −0.944412 | + | 0.944412i | −0.998534 | − | 0.0541228i | \(-0.982764\pi\) |
0.0541228 | + | 0.998534i | \(0.482764\pi\) | |||||||
\(920\) | 1711.83 | + | 6388.63i | 0.00202248 | + | 0.00754801i | ||||
\(921\) | −4543.16 | + | 7868.98i | −0.00535598 | + | 0.00927682i | ||||
\(922\) | −263135. | + | 455763.i | −0.309540 | + | 0.536139i | ||||
\(923\) | −77629.9 | + | 289719.i | −0.0911224 | + | 0.340074i | ||||
\(924\) | 125311.i | 0.146773i | ||||||||
\(925\) | −40423.2 | + | 237578.i | −0.0472440 | + | 0.277666i | ||||
\(926\) | −890260. | −1.03823 | ||||||||
\(927\) | −583602. | − | 156376.i | −0.679137 | − | 0.181974i | ||||
\(928\) | 55842.9 | + | 32240.9i | 0.0648443 | + | 0.0374379i | ||||
\(929\) | −470393. | − | 271581.i | −0.545041 | − | 0.314680i | 0.202078 | − | 0.979369i | \(-0.435230\pi\) |
−0.747119 | + | 0.664690i | \(0.768564\pi\) | |||||||
\(930\) | 72313.7 | − | 19376.4i | 0.0836093 | − | 0.0224030i | ||||
\(931\) | 525862. | + | 525862.i | 0.606698 | + | 0.606698i | ||||
\(932\) | 330770. | − | 572910.i | 0.380797 | − | 0.659561i | ||||
\(933\) | −120596. | − | 120596.i | −0.138538 | − | 0.138538i | ||||
\(934\) | −111563. | − | 193233.i | −0.127887 | − | 0.221507i | ||||
\(935\) | −154730. | −0.176991 | ||||||||
\(936\) | − | 153459.i | − | 0.175162i | ||||||
\(937\) | 388513. | + | 672924.i | 0.442513 | + | 0.766456i | 0.997875 | − | 0.0651532i | \(-0.0207536\pi\) |
−0.555362 | + | 0.831609i | \(0.687420\pi\) | |||||||
\(938\) | −838520. | + | 224681.i | −0.953033 | + | 0.255364i | ||||
\(939\) | −71936.4 | + | 71936.4i | −0.0815864 | + | 0.0815864i | ||||
\(940\) | −536603. | − | 143782.i | −0.607292 | − | 0.162723i | ||||
\(941\) | −383643. | − | 664488.i | −0.433259 | − | 0.750427i | 0.563893 | − | 0.825848i | \(-0.309303\pi\) |
−0.997152 | + | 0.0754214i | \(0.975970\pi\) | |||||||
\(942\) | 8734.94 | − | 32599.2i | 0.00984370 | − | 0.0367372i | ||||
\(943\) | −6856.16 | − | 25587.5i | −0.00771005 | − | 0.0287743i | ||||
\(944\) | −252734. | + | 67719.8i | −0.283609 | + | 0.0759927i | ||||
\(945\) | 375088. | + | 100505.i | 0.420020 | + | 0.112544i | ||||
\(946\) | −187040. | + | 107987.i | −0.209003 | + | 0.120668i | ||||
\(947\) | 19274.0 | − | 71931.4i | 0.0214917 | − | 0.0802082i | −0.954347 | − | 0.298700i | \(-0.903447\pi\) |
0.975839 | + | 0.218492i | \(0.0701137\pi\) | |||||||
\(948\) | 74013.0 | + | 74013.0i | 0.0823553 | + | 0.0823553i | ||||
\(949\) | 192424. | + | 718137.i | 0.213662 | + | 0.797398i | ||||
\(950\) | −99063.8 | + | 57194.5i | −0.109766 | + | 0.0633734i | ||||
\(951\) | −178825. | −0.197728 | ||||||||
\(952\) | 50626.4i | 0.0558603i | ||||||||
\(953\) | −433172. | + | 250092.i | −0.476952 | + | 0.275368i | −0.719145 | − | 0.694860i | \(-0.755467\pi\) |
0.242193 | + | 0.970228i | \(0.422133\pi\) | |||||||
\(954\) | −463074. | + | 463074.i | −0.508808 | + | 0.508808i | ||||
\(955\) | −699292. | − | 403736.i | −0.766746 | − | 0.442681i | ||||
\(956\) | −7033.90 | + | 7033.90i | −0.00769627 | + | 0.00769627i | ||||
\(957\) | −19232.9 | − | 71778.1i | −0.0210001 | − | 0.0783733i | ||||
\(958\) | 111173. | − | 192557.i | 0.121135 | − | 0.209811i | ||||
\(959\) | −16227.9 | + | 28107.5i | −0.0176451 | + | 0.0305622i | ||||
\(960\) | −4264.39 | + | 15914.9i | −0.00462716 | + | 0.0172688i | ||||
\(961\) | 247000.i | 0.267454i | ||||||||
\(962\) | −210257. | + | 253650.i | −0.227196 | + | 0.274084i | ||||
\(963\) | 470358. | 0.507196 | ||||||||
\(964\) | 378621. | + | 101451.i | 0.407428 | + | 0.109170i | ||||
\(965\) | 1.61964e6 | + | 935102.i | 1.73926 | + | 1.00416i | ||||
\(966\) | −2159.77 | − | 1246.94i | −0.00231448 | − | 0.00133627i | ||||
\(967\) | −14506.5 | + | 3887.00i | −0.0155135 | + | 0.00415682i | −0.266567 | − | 0.963816i | \(-0.585890\pi\) |
0.251054 | + | 0.967973i | \(0.419223\pi\) | |||||||
\(968\) | −304339. | − | 304339.i | −0.324793 | − | 0.324793i | ||||
\(969\) | 3891.83 | − | 6740.85i | 0.00414483 | − | 0.00717905i | ||||
\(970\) | 307975. | + | 307975.i | 0.327319 | + | 0.327319i | ||||
\(971\) | 607691. | + | 1.05255e6i | 0.644532 | + | 1.11636i | 0.984409 | + | 0.175892i | \(0.0562810\pi\) |
−0.339878 | + | 0.940470i | \(0.610386\pi\) | |||||||
\(972\) | 175244. | 0.185485 | ||||||||
\(973\) | 2.73477e6i | 2.88865i | ||||||||
\(974\) | 57778.6 | + | 100076.i | 0.0609045 | + | 0.105490i | ||||
\(975\) | −16450.0 | + | 4407.77i | −0.0173044 | + | 0.00463671i | ||||
\(976\) | 130625. | − | 130625.i | 0.137129 | − | 0.137129i | ||||
\(977\) | 1.44776e6 | + | 387925.i | 1.51672 | + | 0.406405i | 0.918662 | − | 0.395045i | \(-0.129271\pi\) |
0.598062 | + | 0.801450i | \(0.295938\pi\) | |||||||
\(978\) | 12774.1 | + | 22125.5i | 0.0133553 | + | 0.0231321i | ||||
\(979\) | 569690. | − | 2.12611e6i | 0.594392 | − | 2.21830i | ||||
\(980\) | 189696. | + | 707956.i | 0.197518 | + | 0.737148i | ||||
\(981\) | −37561.9 | + | 10064.7i | −0.0390310 | + | 0.0104583i | ||||
\(982\) | −626154. | − | 167777.i | −0.649319 | − | 0.173984i | ||||
\(983\) | −374903. | + | 216451.i | −0.387983 | + | 0.224002i | −0.681286 | − | 0.732018i | \(-0.738579\pi\) |
0.293303 | + | 0.956020i | \(0.405246\pi\) | |||||||
\(984\) | 17079.6 | − | 63741.9i | 0.0176395 | − | 0.0658316i | ||||
\(985\) | −515862. | − | 515862.i | −0.531693 | − | 0.531693i | ||||
\(986\) | −7770.19 | − | 28998.8i | −0.00799242 | − | 0.0298281i | ||||
\(987\) | 181407. | − | 104735.i | 0.186217 | − | 0.107512i | ||||
\(988\) | −156383. | −0.160205 | ||||||||
\(989\) | − | 4298.24i | − | 0.00439439i | ||||||
\(990\) | −1.01384e6 | + | 585342.i | −1.03443 | + | 0.597227i | ||||
\(991\) | 1.17777e6 | − | 1.17777e6i | 1.19926 | − | 1.19926i | 0.224867 | − | 0.974390i | \(-0.427805\pi\) |
0.974390 | − | 0.224867i | \(-0.0721947\pi\) | |||||||
\(992\) | 128943. | + | 74445.0i | 0.131031 | + | 0.0756506i | ||||
\(993\) | 51379.5 | − | 51379.5i | 0.0521064 | − | 0.0521064i | ||||
\(994\) | −193767. | − | 723147.i | −0.196113 | − | 0.731903i | ||||
\(995\) | 165653. | − | 286919.i | 0.167322 | − | 0.289810i | ||||
\(996\) | 34475.1 | − | 59712.6i | 0.0347525 | − | 0.0601931i | ||||
\(997\) | 213346. | − | 796218.i | 0.214632 | − | 0.801017i | −0.771664 | − | 0.636030i | \(-0.780575\pi\) |
0.986296 | − | 0.164986i | \(-0.0527581\pi\) | |||||||
\(998\) | 1.18904e6i | 1.19381i | ||||||||
\(999\) | −192589. | − | 159642.i | −0.192975 | − | 0.159962i |
(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 | 74.5.g.b.45.4 | ✓ | 28 | |
37.14 | odd | 12 | inner | 74.5.g.b.51.4 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.5.g.b.45.4 | ✓ | 28 | 1.1 | even | 1 | trivial | |
74.5.g.b.51.4 | yes | 28 | 37.14 | odd | 12 | inner |