Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,3,Mod(2,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.2");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.n (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.71662566547\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 32.2 | ||
Character | \(\chi\) | \(=\) | 63.32 |
Dual form | 63.3.n.b.2.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.79169 | − | 1.61178i | −1.39584 | − | 0.805891i | −0.401890 | − | 0.915688i | \(-0.631647\pi\) |
−0.993954 | + | 0.109797i | \(0.964980\pi\) | |||||||
\(3\) | −0.476488 | + | 2.96192i | −0.158829 | + | 0.987306i | ||||
\(4\) | 3.19568 | + | 5.53509i | 0.798921 | + | 1.38377i | ||||
\(5\) | − | 5.53294i | − | 1.10659i | −0.832986 | − | 0.553294i | \(-0.813370\pi\) | ||
0.832986 | − | 0.553294i | \(-0.186630\pi\) | |||||||
\(6\) | 6.10417 | − | 7.50076i | 1.01736 | − | 1.25013i | ||||
\(7\) | 3.31972 | − | 6.16275i | 0.474246 | − | 0.880393i | ||||
\(8\) | − | 7.70873i | − | 0.963591i | ||||||
\(9\) | −8.54592 | − | 2.82264i | −0.949547 | − | 0.313626i | ||||
\(10\) | −8.91790 | + | 15.4463i | −0.891790 | + | 1.54463i | ||||
\(11\) | − | 17.6887i | − | 1.60806i | −0.594587 | − | 0.804032i | \(-0.702684\pi\) | ||
0.594587 | − | 0.804032i | \(-0.297316\pi\) | |||||||
\(12\) | −17.9172 | + | 6.82795i | −1.49310 | + | 0.568996i | ||||
\(13\) | 2.03775 | − | 3.52949i | 0.156750 | − | 0.271499i | −0.776945 | − | 0.629569i | \(-0.783232\pi\) |
0.933695 | + | 0.358070i | \(0.116565\pi\) | |||||||
\(14\) | −19.2006 | + | 11.8538i | −1.37147 | + | 0.846701i | ||||
\(15\) | 16.3881 | + | 2.63638i | 1.09254 | + | 0.175759i | ||||
\(16\) | 0.357941 | − | 0.619972i | 0.0223713 | − | 0.0387483i | ||||
\(17\) | 14.3348 | + | 8.27617i | 0.843221 | + | 0.486834i | 0.858358 | − | 0.513052i | \(-0.171485\pi\) |
−0.0151370 | + | 0.999885i | \(0.504818\pi\) | |||||||
\(18\) | 19.3081 | + | 21.6541i | 1.07267 | + | 1.20300i | ||||
\(19\) | −3.92096 | − | 6.79130i | −0.206366 | − | 0.357437i | 0.744201 | − | 0.667956i | \(-0.232830\pi\) |
−0.950567 | + | 0.310519i | \(0.899497\pi\) | |||||||
\(20\) | 30.6253 | − | 17.6815i | 1.53127 | − | 0.884077i | ||||
\(21\) | 16.6718 | + | 12.7692i | 0.793893 | + | 0.608058i | ||||
\(22\) | −28.5103 | + | 49.3813i | −1.29592 | + | 2.24461i | ||||
\(23\) | 10.0676i | 0.437720i | 0.975756 | + | 0.218860i | \(0.0702339\pi\) | ||||
−0.975756 | + | 0.218860i | \(0.929766\pi\) | |||||||
\(24\) | 22.8326 | + | 3.67312i | 0.951360 | + | 0.153047i | ||||
\(25\) | −5.61347 | −0.224539 | ||||||||
\(26\) | −11.3775 | + | 6.56882i | −0.437597 | + | 0.252647i | ||||
\(27\) | 12.4324 | − | 23.9674i | 0.460461 | − | 0.887680i | ||||
\(28\) | 44.7201 | − | 1.31926i | 1.59715 | − | 0.0471165i | ||||
\(29\) | −39.9040 | + | 23.0386i | −1.37600 | + | 0.794434i | −0.991675 | − | 0.128764i | \(-0.958899\pi\) |
−0.384324 | + | 0.923198i | \(0.625566\pi\) | |||||||
\(30\) | −41.5013 | − | 33.7740i | −1.38338 | − | 1.12580i | ||||
\(31\) | −14.8117 | − | 25.6547i | −0.477798 | − | 0.827570i | 0.521878 | − | 0.853020i | \(-0.325232\pi\) |
−0.999676 | + | 0.0254498i | \(0.991898\pi\) | |||||||
\(32\) | −28.7023 | + | 16.5713i | −0.896948 | + | 0.517853i | ||||
\(33\) | 52.3925 | + | 8.42845i | 1.58765 | + | 0.255408i | ||||
\(34\) | −26.6788 | − | 46.2090i | −0.784670 | − | 1.35909i | ||||
\(35\) | −34.0981 | − | 18.3678i | −0.974233 | − | 0.524795i | ||||
\(36\) | −11.6865 | − | 56.3227i | −0.324626 | − | 1.56452i | ||||
\(37\) | 15.5948 | + | 27.0110i | 0.421481 | + | 0.730026i | 0.996085 | − | 0.0884059i | \(-0.0281772\pi\) |
−0.574604 | + | 0.818432i | \(0.694844\pi\) | |||||||
\(38\) | 25.2789i | 0.665235i | ||||||||
\(39\) | 9.48309 | + | 7.71741i | 0.243156 | + | 0.197882i | ||||
\(40\) | −42.6520 | −1.06630 | ||||||||
\(41\) | 27.8184 | + | 16.0609i | 0.678497 | + | 0.391730i | 0.799288 | − | 0.600948i | \(-0.205210\pi\) |
−0.120792 | + | 0.992678i | \(0.538543\pi\) | |||||||
\(42\) | −25.9612 | − | 62.5189i | −0.618123 | − | 1.48855i | ||||
\(43\) | 3.35243 | + | 5.80658i | 0.0779635 | + | 0.135037i | 0.902371 | − | 0.430960i | \(-0.141825\pi\) |
−0.824408 | + | 0.565997i | \(0.808492\pi\) | |||||||
\(44\) | 97.9085 | − | 56.5275i | 2.22519 | − | 1.28472i | ||||
\(45\) | −15.6175 | + | 47.2841i | −0.347055 | + | 1.05076i | ||||
\(46\) | 16.2267 | − | 28.1055i | 0.352755 | − | 0.610990i | ||||
\(47\) | −14.2377 | − | 8.22012i | −0.302929 | − | 0.174896i | 0.340829 | − | 0.940125i | \(-0.389292\pi\) |
−0.643758 | + | 0.765229i | \(0.722626\pi\) | |||||||
\(48\) | 1.66575 | + | 1.35560i | 0.0347032 | + | 0.0282417i | ||||
\(49\) | −26.9589 | − | 40.9172i | −0.550182 | − | 0.835045i | ||||
\(50\) | 15.6711 | + | 9.04769i | 0.313421 | + | 0.180954i | ||||
\(51\) | −31.3437 | + | 38.5149i | −0.614582 | + | 0.755193i | ||||
\(52\) | 26.0480 | 0.500924 | ||||||||
\(53\) | 32.5897 | + | 18.8157i | 0.614900 | + | 0.355013i | 0.774881 | − | 0.632108i | \(-0.217810\pi\) |
−0.159981 | + | 0.987120i | \(0.551143\pi\) | |||||||
\(54\) | −73.3377 | + | 46.8710i | −1.35811 | + | 0.867982i | ||||
\(55\) | −97.8706 | −1.77946 | ||||||||
\(56\) | −47.5070 | − | 25.5908i | −0.848339 | − | 0.456979i | ||||
\(57\) | 21.9836 | − | 8.37759i | 0.385676 | − | 0.146975i | ||||
\(58\) | 148.533 | 2.56091 | ||||||||
\(59\) | 82.3206 | − | 47.5278i | 1.39527 | − | 0.805557i | 0.401373 | − | 0.915915i | \(-0.368533\pi\) |
0.993892 | + | 0.110358i | \(0.0351997\pi\) | |||||||
\(60\) | 37.7787 | + | 99.1348i | 0.629645 | + | 1.65225i | ||||
\(61\) | 36.8839 | − | 63.8848i | 0.604655 | − | 1.04729i | −0.387451 | − | 0.921890i | \(-0.626644\pi\) |
0.992106 | − | 0.125402i | \(-0.0400222\pi\) | |||||||
\(62\) | 95.4932i | 1.54021i | ||||||||
\(63\) | −45.7652 | + | 43.2960i | −0.726432 | + | 0.687238i | ||||
\(64\) | 103.974 | 1.62459 | ||||||||
\(65\) | −19.5285 | − | 11.2748i | −0.300438 | − | 0.173458i | ||||
\(66\) | −132.679 | − | 107.975i | −2.01028 | − | 1.63598i | ||||
\(67\) | 6.09545 | + | 10.5576i | 0.0909769 | + | 0.157577i | 0.907922 | − | 0.419138i | \(-0.137668\pi\) |
−0.816946 | + | 0.576715i | \(0.804334\pi\) | |||||||
\(68\) | 105.792i | 1.55577i | ||||||||
\(69\) | −29.8193 | − | 4.79707i | −0.432164 | − | 0.0695228i | ||||
\(70\) | 65.5865 | + | 106.236i | 0.936950 | + | 1.51766i | ||||
\(71\) | 20.0140i | 0.281887i | 0.990018 | + | 0.140944i | \(0.0450136\pi\) | ||||
−0.990018 | + | 0.140944i | \(0.954986\pi\) | |||||||
\(72\) | −21.7589 | + | 65.8782i | −0.302208 | + | 0.914975i | ||||
\(73\) | −11.4932 | + | 19.9068i | −0.157441 | + | 0.272696i | −0.933945 | − | 0.357416i | \(-0.883658\pi\) |
0.776504 | + | 0.630112i | \(0.216991\pi\) | |||||||
\(74\) | − | 100.542i | − | 1.35867i | ||||||
\(75\) | 2.67475 | − | 16.6266i | 0.0356633 | − | 0.221689i | ||||
\(76\) | 25.0603 | − | 43.4057i | 0.329741 | − | 0.571128i | ||||
\(77\) | −109.011 | − | 58.7215i | −1.41573 | − | 0.762617i | ||||
\(78\) | −14.0351 | − | 36.8293i | −0.179937 | − | 0.472170i | ||||
\(79\) | −69.4400 | + | 120.274i | −0.878988 | + | 1.52245i | −0.0265350 | + | 0.999648i | \(0.508447\pi\) |
−0.852453 | + | 0.522804i | \(0.824886\pi\) | |||||||
\(80\) | −3.43027 | − | 1.98047i | −0.0428784 | − | 0.0247559i | ||||
\(81\) | 65.0655 | + | 48.2440i | 0.803277 | + | 0.595605i | ||||
\(82\) | −51.7735 | − | 89.6743i | −0.631384 | − | 1.09359i | ||||
\(83\) | 13.6928 | − | 7.90552i | 0.164973 | − | 0.0952472i | −0.415240 | − | 0.909712i | \(-0.636303\pi\) |
0.580213 | + | 0.814465i | \(0.302969\pi\) | |||||||
\(84\) | −17.4010 | + | 133.086i | −0.207155 | + | 1.58436i | ||||
\(85\) | 45.7916 | − | 79.3134i | 0.538725 | − | 0.933099i | ||||
\(86\) | − | 21.6136i | − | 0.251320i | ||||||
\(87\) | −49.2246 | − | 129.170i | −0.565800 | − | 1.48471i | ||||
\(88\) | −136.357 | −1.54952 | ||||||||
\(89\) | 46.9444 | − | 27.1034i | 0.527466 | − | 0.304532i | −0.212518 | − | 0.977157i | \(-0.568166\pi\) |
0.739984 | + | 0.672625i | \(0.234833\pi\) | |||||||
\(90\) | 119.811 | − | 106.830i | 1.33123 | − | 1.18701i | ||||
\(91\) | −14.9866 | − | 24.2750i | −0.164688 | − | 0.266759i | ||||
\(92\) | −55.7249 | + | 32.1728i | −0.605705 | + | 0.349704i | ||||
\(93\) | 83.0447 | − | 31.6470i | 0.892953 | − | 0.340290i | ||||
\(94\) | 26.4981 | + | 45.8960i | 0.281894 | + | 0.488256i | ||||
\(95\) | −37.5759 | + | 21.6944i | −0.395536 | + | 0.228363i | ||||
\(96\) | −35.4065 | − | 92.9100i | −0.368818 | − | 0.967813i | ||||
\(97\) | 86.1189 | + | 149.162i | 0.887823 | + | 1.53776i | 0.842443 | + | 0.538785i | \(0.181117\pi\) |
0.0453802 | + | 0.998970i | \(0.485550\pi\) | |||||||
\(98\) | 9.31136 | + | 157.680i | 0.0950139 | + | 1.60898i | ||||
\(99\) | −49.9287 | + | 151.166i | −0.504331 | + | 1.52693i | ||||
\(100\) | −17.9389 | − | 31.0710i | −0.179389 | − | 0.310710i | ||||
\(101\) | 17.3176i | 0.171461i | 0.996318 | + | 0.0857307i | \(0.0273225\pi\) | ||||
−0.996318 | + | 0.0857307i | \(0.972678\pi\) | |||||||
\(102\) | 149.579 | − | 57.0023i | 1.46646 | − | 0.558846i | ||||
\(103\) | −27.5997 | −0.267958 | −0.133979 | − | 0.990984i | \(-0.542776\pi\) | ||||
−0.133979 | + | 0.990984i | \(0.542776\pi\) | |||||||
\(104\) | −27.2079 | − | 15.7085i | −0.261614 | − | 0.151043i | ||||
\(105\) | 70.6513 | − | 92.2439i | 0.672870 | − | 0.878513i | ||||
\(106\) | −60.6535 | − | 105.055i | −0.572203 | − | 0.991085i | ||||
\(107\) | 106.089 | − | 61.2506i | 0.991488 | − | 0.572436i | 0.0857691 | − | 0.996315i | \(-0.472665\pi\) |
0.905719 | + | 0.423879i | \(0.139332\pi\) | |||||||
\(108\) | 172.392 | − | 7.77745i | 1.59622 | − | 0.0720134i | ||||
\(109\) | −17.0725 | + | 29.5705i | −0.156629 | + | 0.271289i | −0.933651 | − | 0.358184i | \(-0.883396\pi\) |
0.777022 | + | 0.629473i | \(0.216729\pi\) | |||||||
\(110\) | 273.224 | + | 157.746i | 2.48386 | + | 1.43405i | ||||
\(111\) | −87.4350 | + | 33.3201i | −0.787702 | + | 0.300181i | ||||
\(112\) | −2.63247 | − | 4.26403i | −0.0235042 | − | 0.0380717i | ||||
\(113\) | 67.4250 | + | 38.9278i | 0.596681 | + | 0.344494i | 0.767735 | − | 0.640768i | \(-0.221384\pi\) |
−0.171054 | + | 0.985262i | \(0.554717\pi\) | |||||||
\(114\) | −74.8741 | − | 12.0451i | −0.656790 | − | 0.105659i | ||||
\(115\) | 55.7033 | 0.484377 | ||||||||
\(116\) | −255.041 | − | 147.248i | −2.19863 | − | 1.26938i | ||||
\(117\) | −27.3769 | + | 24.4109i | −0.233991 | + | 0.208640i | ||||
\(118\) | −306.418 | −2.59676 | ||||||||
\(119\) | 98.5913 | − | 60.8669i | 0.828498 | − | 0.511487i | ||||
\(120\) | 20.3231 | − | 126.332i | 0.169360 | − | 1.05276i | ||||
\(121\) | −191.890 | −1.58587 | ||||||||
\(122\) | −205.937 | + | 118.898i | −1.68801 | + | 0.974572i | ||||
\(123\) | −60.8263 | + | 74.7429i | −0.494523 | + | 0.607666i | ||||
\(124\) | 94.6673 | − | 163.968i | 0.763446 | − | 1.32233i | ||||
\(125\) | − | 107.265i | − | 0.858117i | ||||||
\(126\) | 197.546 | − | 47.1053i | 1.56783 | − | 0.373852i | ||||
\(127\) | 14.0742 | 0.110821 | 0.0554103 | − | 0.998464i | \(-0.482353\pi\) | ||||
0.0554103 | + | 0.998464i | \(0.482353\pi\) | |||||||
\(128\) | −175.453 | − | 101.298i | −1.37073 | − | 0.791390i | ||||
\(129\) | −18.7960 | + | 7.16286i | −0.145706 | + | 0.0555261i | ||||
\(130\) | 36.3449 | + | 62.9512i | 0.279576 | + | 0.484240i | ||||
\(131\) | 22.2699i | 0.169999i | 0.996381 | + | 0.0849995i | \(0.0270889\pi\) | ||||
−0.996381 | + | 0.0849995i | \(0.972911\pi\) | |||||||
\(132\) | 120.778 | + | 316.932i | 0.914982 | + | 2.40100i | ||||
\(133\) | −54.8695 | + | 1.61868i | −0.412553 | + | 0.0121705i | ||||
\(134\) | − | 39.2982i | − | 0.293270i | ||||||
\(135\) | −132.610 | − | 68.7880i | −0.982297 | − | 0.509541i | ||||
\(136\) | 63.7988 | − | 110.503i | 0.469109 | − | 0.812520i | ||||
\(137\) | − | 37.0861i | − | 0.270701i | −0.990798 | − | 0.135351i | \(-0.956784\pi\) | ||
0.990798 | − | 0.135351i | \(-0.0432161\pi\) | |||||||
\(138\) | 75.5144 | + | 61.4542i | 0.547206 | + | 0.445320i | ||||
\(139\) | 70.5358 | − | 122.172i | 0.507451 | − | 0.878932i | −0.492511 | − | 0.870306i | \(-0.663921\pi\) |
0.999963 | − | 0.00862568i | \(-0.00274567\pi\) | |||||||
\(140\) | −7.29941 | − | 247.434i | −0.0521386 | − | 1.76739i | ||||
\(141\) | 31.1314 | − | 38.2540i | 0.220790 | − | 0.271305i | ||||
\(142\) | 32.2582 | − | 55.8728i | 0.227170 | − | 0.393471i | ||||
\(143\) | −62.4320 | − | 36.0451i | −0.436587 | − | 0.252064i | ||||
\(144\) | −4.80889 | + | 4.28789i | −0.0333951 | + | 0.0297770i | ||||
\(145\) | 127.471 | + | 220.787i | 0.879111 | + | 1.52267i | ||||
\(146\) | 64.1710 | − | 37.0491i | 0.439527 | − | 0.253761i | ||||
\(147\) | 134.039 | − | 60.3536i | 0.911830 | − | 0.410569i | ||||
\(148\) | −99.6720 | + | 172.637i | −0.673459 | + | 1.16647i | ||||
\(149\) | 115.718i | 0.776631i | 0.921526 | + | 0.388315i | \(0.126943\pi\) | ||||
−0.921526 | + | 0.388315i | \(0.873057\pi\) | |||||||
\(150\) | −34.2656 | + | 42.1053i | −0.228437 | + | 0.280702i | ||||
\(151\) | −150.316 | −0.995469 | −0.497734 | − | 0.867330i | \(-0.665835\pi\) | ||||
−0.497734 | + | 0.867330i | \(0.665835\pi\) | |||||||
\(152\) | −52.3523 | + | 30.2256i | −0.344423 | + | 0.198853i | ||||
\(153\) | −99.1430 | − | 111.189i | −0.647993 | − | 0.726727i | ||||
\(154\) | 209.678 | + | 339.634i | 1.36155 | + | 2.20542i | ||||
\(155\) | −141.946 | + | 81.9525i | −0.915780 | + | 0.528726i | ||||
\(156\) | −12.4116 | + | 77.1521i | −0.0795613 | + | 0.494565i | ||||
\(157\) | 137.028 | + | 237.339i | 0.872788 | + | 1.51171i | 0.859100 | + | 0.511808i | \(0.171024\pi\) |
0.0136883 | + | 0.999906i | \(0.495643\pi\) | |||||||
\(158\) | 387.710 | − | 223.844i | 2.45386 | − | 1.41674i | ||||
\(159\) | −71.2591 | + | 87.5626i | −0.448170 | + | 0.550708i | ||||
\(160\) | 91.6881 | + | 158.808i | 0.573051 | + | 0.992553i | ||||
\(161\) | 62.0439 | + | 33.4215i | 0.385366 | + | 0.207587i | ||||
\(162\) | −103.884 | − | 239.554i | −0.641257 | − | 1.47873i | ||||
\(163\) | −111.326 | − | 192.822i | −0.682981 | − | 1.18296i | −0.974067 | − | 0.226261i | \(-0.927350\pi\) |
0.291085 | − | 0.956697i | \(-0.405984\pi\) | |||||||
\(164\) | 205.303i | 1.25185i | ||||||||
\(165\) | 46.6341 | − | 289.885i | 0.282631 | − | 1.75688i | ||||
\(166\) | −50.9679 | −0.307035 | ||||||||
\(167\) | 62.7878 | + | 36.2506i | 0.375975 | + | 0.217069i | 0.676066 | − | 0.736841i | \(-0.263684\pi\) |
−0.300091 | + | 0.953911i | \(0.597017\pi\) | |||||||
\(168\) | 98.4344 | − | 128.518i | 0.585919 | − | 0.764988i | ||||
\(169\) | 76.1951 | + | 131.974i | 0.450859 | + | 0.780910i | ||||
\(170\) | −255.672 | + | 147.612i | −1.50395 | + | 0.868307i | ||||
\(171\) | 14.3388 | + | 69.1053i | 0.0838528 | + | 0.404125i | ||||
\(172\) | −21.4266 | + | 37.1120i | −0.124573 | + | 0.215768i | ||||
\(173\) | −182.881 | − | 105.587i | −1.05712 | − | 0.610328i | −0.132485 | − | 0.991185i | \(-0.542296\pi\) |
−0.924634 | + | 0.380857i | \(0.875629\pi\) | |||||||
\(174\) | −70.7740 | + | 439.942i | −0.406747 | + | 2.52840i | ||||
\(175\) | −18.6351 | + | 34.5944i | −0.106487 | + | 0.197682i | ||||
\(176\) | −10.9665 | − | 6.33151i | −0.0623096 | − | 0.0359745i | ||||
\(177\) | 101.549 | + | 266.473i | 0.573722 | + | 1.50550i | ||||
\(178\) | −174.739 | −0.981680 | ||||||||
\(179\) | −69.5967 | − | 40.1817i | −0.388809 | − | 0.224479i | 0.292835 | − | 0.956163i | \(-0.405401\pi\) |
−0.681644 | + | 0.731684i | \(0.738735\pi\) | |||||||
\(180\) | −311.630 | + | 64.6609i | −1.73128 | + | 0.359227i | ||||
\(181\) | 122.944 | 0.679250 | 0.339625 | − | 0.940561i | \(-0.389700\pi\) | ||||
0.339625 | + | 0.940561i | \(0.389700\pi\) | |||||||
\(182\) | 2.71178 | + | 91.9235i | 0.0148999 | + | 0.505074i | ||||
\(183\) | 171.647 | + | 139.688i | 0.937961 | + | 0.763320i | ||||
\(184\) | 77.6082 | 0.421784 | ||||||||
\(185\) | 149.450 | − | 86.2850i | 0.807838 | − | 0.466406i | ||||
\(186\) | −282.843 | − | 45.5013i | −1.52066 | − | 0.244631i | ||||
\(187\) | 146.395 | − | 253.563i | 0.782859 | − | 1.35595i | ||||
\(188\) | − | 105.076i | − | 0.558913i | ||||||
\(189\) | −106.433 | − | 156.183i | −0.563135 | − | 0.826365i | ||||
\(190\) | 139.867 | 0.736141 | ||||||||
\(191\) | 307.863 | + | 177.745i | 1.61185 | + | 0.930602i | 0.988941 | + | 0.148308i | \(0.0473827\pi\) |
0.622909 | + | 0.782294i | \(0.285951\pi\) | |||||||
\(192\) | −49.5423 | + | 307.962i | −0.258033 | + | 1.60397i | ||||
\(193\) | 19.8296 | + | 34.3459i | 0.102744 | + | 0.177958i | 0.912814 | − | 0.408375i | \(-0.133904\pi\) |
−0.810070 | + | 0.586333i | \(0.800571\pi\) | |||||||
\(194\) | − | 555.219i | − | 2.86196i | ||||||
\(195\) | 42.7000 | − | 52.4694i | 0.218974 | − | 0.269074i | ||||
\(196\) | 140.328 | − | 279.978i | 0.715959 | − | 1.42846i | ||||
\(197\) | − | 130.634i | − | 0.663119i | −0.943434 | − | 0.331559i | \(-0.892425\pi\) | ||
0.943434 | − | 0.331559i | \(-0.107575\pi\) | |||||||
\(198\) | 383.032 | − | 341.535i | 1.93451 | − | 1.72492i | ||||
\(199\) | 108.521 | − | 187.964i | 0.545331 | − | 0.944540i | −0.453255 | − | 0.891381i | \(-0.649737\pi\) |
0.998586 | − | 0.0531596i | \(-0.0169292\pi\) | |||||||
\(200\) | 43.2727i | 0.216364i | ||||||||
\(201\) | −34.1753 | + | 13.0237i | −0.170026 | + | 0.0647943i | ||||
\(202\) | 27.9122 | − | 48.3454i | 0.138179 | − | 0.239333i | ||||
\(203\) | 9.51093 | + | 322.400i | 0.0468519 | + | 1.58818i | ||||
\(204\) | −313.348 | − | 50.4087i | −1.53602 | − | 0.247101i | ||||
\(205\) | 88.8643 | − | 153.917i | 0.433484 | − | 0.750817i | ||||
\(206\) | 77.0498 | + | 44.4847i | 0.374028 | + | 0.215945i | ||||
\(207\) | 28.4171 | − | 86.0366i | 0.137281 | − | 0.415636i | ||||
\(208\) | −1.45879 | − | 2.52670i | −0.00701341 | − | 0.0121476i | ||||
\(209\) | −120.129 | + | 69.3566i | −0.574781 | + | 0.331850i | ||||
\(210\) | −345.914 | + | 143.642i | −1.64721 | + | 0.684008i | ||||
\(211\) | 54.6113 | − | 94.5895i | 0.258821 | − | 0.448292i | −0.707105 | − | 0.707108i | \(-0.749999\pi\) |
0.965926 | + | 0.258817i | \(0.0833326\pi\) | |||||||
\(212\) | 240.516i | 1.13451i | ||||||||
\(213\) | −59.2798 | − | 9.53642i | −0.278309 | − | 0.0447719i | ||||
\(214\) | −394.891 | −1.84528 | ||||||||
\(215\) | 32.1275 | − | 18.5488i | 0.149430 | − | 0.0862736i | ||||
\(216\) | −184.758 | − | 95.8384i | −0.855361 | − | 0.443696i | ||||
\(217\) | −207.274 | + | 6.11468i | −0.955180 | + | 0.0281782i | ||||
\(218\) | 95.3224 | − | 55.0344i | 0.437259 | − | 0.252451i | ||||
\(219\) | −53.4860 | − | 43.5273i | −0.244228 | − | 0.198755i | ||||
\(220\) | −312.763 | − | 541.722i | −1.42165 | − | 2.46237i | ||||
\(221\) | 58.4213 | − | 33.7295i | 0.264350 | − | 0.152622i | ||||
\(222\) | 297.796 | + | 47.9068i | 1.34142 | + | 0.215797i | ||||
\(223\) | −93.3685 | − | 161.719i | −0.418693 | − | 0.725197i | 0.577115 | − | 0.816663i | \(-0.304178\pi\) |
−0.995808 | + | 0.0914653i | \(0.970845\pi\) | |||||||
\(224\) | 6.84107 | + | 231.897i | 0.0305405 | + | 1.03526i | ||||
\(225\) | 47.9723 | + | 15.8448i | 0.213210 | + | 0.0704213i | ||||
\(226\) | −125.486 | − | 217.349i | −0.555249 | − | 0.961720i | ||||
\(227\) | − | 202.548i | − | 0.892280i | −0.894963 | − | 0.446140i | \(-0.852798\pi\) | ||
0.894963 | − | 0.446140i | \(-0.147202\pi\) | |||||||
\(228\) | 116.623 | + | 94.9088i | 0.511505 | + | 0.416267i | ||||
\(229\) | −79.2731 | −0.346171 | −0.173085 | − | 0.984907i | \(-0.555374\pi\) | ||||
−0.173085 | + | 0.984907i | \(0.555374\pi\) | |||||||
\(230\) | −155.506 | − | 89.7816i | −0.676114 | − | 0.390355i | ||||
\(231\) | 225.871 | − | 294.901i | 0.977795 | − | 1.27663i | ||||
\(232\) | 177.598 | + | 307.609i | 0.765509 | + | 1.32590i | ||||
\(233\) | −282.430 | + | 163.061i | −1.21215 | + | 0.699833i | −0.963227 | − | 0.268690i | \(-0.913409\pi\) |
−0.248921 | + | 0.968524i | \(0.580076\pi\) | |||||||
\(234\) | 115.773 | − | 24.0220i | 0.494756 | − | 0.102658i | ||||
\(235\) | −45.4814 | + | 78.7762i | −0.193538 | + | 0.335218i | ||||
\(236\) | 526.142 | + | 303.768i | 2.22941 | + | 1.28715i | ||||
\(237\) | −323.154 | − | 262.985i | −1.36352 | − | 1.10964i | ||||
\(238\) | −373.340 | + | 11.0137i | −1.56866 | + | 0.0462761i | ||||
\(239\) | −210.918 | − | 121.774i | −0.882503 | − | 0.509514i | −0.0110203 | − | 0.999939i | \(-0.503508\pi\) |
−0.871483 | + | 0.490426i | \(0.836841\pi\) | |||||||
\(240\) | 7.50047 | − | 9.21651i | 0.0312519 | − | 0.0384021i | ||||
\(241\) | 28.3405 | 0.117595 | 0.0587976 | − | 0.998270i | \(-0.481273\pi\) | ||||
0.0587976 | + | 0.998270i | \(0.481273\pi\) | |||||||
\(242\) | 535.697 | + | 309.285i | 2.21362 | + | 1.27804i | ||||
\(243\) | −173.898 | + | 169.731i | −0.715629 | + | 0.698481i | ||||
\(244\) | 471.478 | 1.93229 | ||||||||
\(245\) | −226.392 | + | 149.162i | −0.924051 | + | 0.608826i | ||||
\(246\) | 290.277 | − | 110.620i | 1.17999 | − | 0.449675i | ||||
\(247\) | −31.9597 | −0.129392 | ||||||||
\(248\) | −197.765 | + | 114.180i | −0.797440 | + | 0.460402i | ||||
\(249\) | 16.8911 | + | 44.3237i | 0.0678356 | + | 0.178007i | ||||
\(250\) | −172.887 | + | 299.449i | −0.691549 | + | 1.19780i | ||||
\(251\) | 140.132i | 0.558294i | 0.960248 | + | 0.279147i | \(0.0900516\pi\) | ||||
−0.960248 | + | 0.279147i | \(0.909948\pi\) | |||||||
\(252\) | −385.898 | − | 114.954i | −1.53134 | − | 0.456168i | ||||
\(253\) | 178.082 | 0.703882 | ||||||||
\(254\) | −39.2909 | − | 22.6846i | −0.154688 | − | 0.0893094i | ||||
\(255\) | 213.101 | + | 173.423i | 0.835689 | + | 0.680090i | ||||
\(256\) | 118.593 | + | 205.409i | 0.463253 | + | 0.802378i | ||||
\(257\) | 110.672i | 0.430629i | 0.976545 | + | 0.215315i | \(0.0690777\pi\) | ||||
−0.976545 | + | 0.215315i | \(0.930922\pi\) | |||||||
\(258\) | 64.0176 | + | 10.2986i | 0.248130 | + | 0.0399171i | ||||
\(259\) | 218.232 | − | 6.43794i | 0.842595 | − | 0.0248569i | ||||
\(260\) | − | 144.122i | − | 0.554316i | ||||||
\(261\) | 406.046 | − | 84.2514i | 1.55573 | − | 0.322802i | ||||
\(262\) | 35.8942 | − | 62.1705i | 0.137001 | − | 0.237292i | ||||
\(263\) | 49.3684i | 0.187713i | 0.995586 | + | 0.0938563i | \(0.0299194\pi\) | ||||
−0.995586 | + | 0.0938563i | \(0.970081\pi\) | |||||||
\(264\) | 64.9726 | − | 403.879i | 0.246108 | − | 1.52985i | ||||
\(265\) | 104.106 | − | 180.317i | 0.392853 | − | 0.680441i | ||||
\(266\) | 155.788 | + | 83.9189i | 0.585668 | + | 0.315485i | ||||
\(267\) | 57.9095 | + | 151.960i | 0.216890 | + | 0.569139i | ||||
\(268\) | −38.9583 | + | 67.4777i | −0.145367 | + | 0.251783i | ||||
\(269\) | 162.040 | + | 93.5538i | 0.602379 | + | 0.347784i | 0.769977 | − | 0.638072i | \(-0.220268\pi\) |
−0.167598 | + | 0.985855i | \(0.553601\pi\) | |||||||
\(270\) | 259.335 | + | 405.773i | 0.960499 | + | 1.50286i | ||||
\(271\) | 108.146 | + | 187.315i | 0.399064 | + | 0.691199i | 0.993611 | − | 0.112862i | \(-0.0360018\pi\) |
−0.594547 | + | 0.804061i | \(0.702668\pi\) | |||||||
\(272\) | 10.2620 | − | 5.92476i | 0.0377279 | − | 0.0217822i | ||||
\(273\) | 79.0416 | − | 32.8223i | 0.289530 | − | 0.120228i | ||||
\(274\) | −59.7747 | + | 103.533i | −0.218156 | + | 0.377857i | ||||
\(275\) | 99.2950i | 0.361073i | ||||||||
\(276\) | −68.7409 | − | 180.382i | −0.249061 | − | 0.653560i | ||||
\(277\) | 78.1235 | 0.282034 | 0.141017 | − | 0.990007i | \(-0.454963\pi\) | ||||
0.141017 | + | 0.990007i | \(0.454963\pi\) | |||||||
\(278\) | −393.828 | + | 227.377i | −1.41665 | + | 0.817901i | ||||
\(279\) | 54.1661 | + | 261.051i | 0.194144 | + | 0.935666i | ||||
\(280\) | −141.593 | + | 262.853i | −0.505688 | + | 0.938762i | ||||
\(281\) | −385.051 | + | 222.309i | −1.37029 | + | 0.791135i | −0.990964 | − | 0.134129i | \(-0.957176\pi\) |
−0.379323 | + | 0.925264i | \(0.623843\pi\) | |||||||
\(282\) | −148.566 | + | 56.6162i | −0.526831 | + | 0.200767i | ||||
\(283\) | 64.2122 | + | 111.219i | 0.226898 | + | 0.392999i | 0.956887 | − | 0.290460i | \(-0.0938082\pi\) |
−0.729989 | + | 0.683459i | \(0.760475\pi\) | |||||||
\(284\) | −110.779 | + | 63.9584i | −0.390068 | + | 0.225206i | ||||
\(285\) | −46.3527 | − | 121.634i | −0.162641 | − | 0.426785i | ||||
\(286\) | 116.194 | + | 201.254i | 0.406272 | + | 0.703684i | ||||
\(287\) | 191.329 | − | 118.120i | 0.666650 | − | 0.411567i | ||||
\(288\) | 292.063 | − | 60.6008i | 1.01411 | − | 0.210419i | ||||
\(289\) | −7.50994 | − | 13.0076i | −0.0259859 | − | 0.0450090i | ||||
\(290\) | − | 821.823i | − | 2.83387i | ||||||
\(291\) | −482.841 | + | 184.003i | −1.65925 | + | 0.632313i | ||||
\(292\) | −146.915 | −0.503133 | ||||||||
\(293\) | −42.6510 | − | 24.6246i | −0.145567 | − | 0.0840429i | 0.425448 | − | 0.904983i | \(-0.360117\pi\) |
−0.571014 | + | 0.820940i | \(0.693450\pi\) | |||||||
\(294\) | −471.472 | − | 47.5531i | −1.60365 | − | 0.161745i | ||||
\(295\) | −262.969 | − | 455.475i | −0.891420 | − | 1.54398i | ||||
\(296\) | 208.220 | − | 120.216i | 0.703446 | − | 0.406135i | ||||
\(297\) | −423.951 | − | 219.914i | −1.42745 | − | 0.740450i | ||||
\(298\) | 186.512 | − | 323.049i | 0.625880 | − | 1.08406i | ||||
\(299\) | 35.5334 | + | 20.5152i | 0.118841 | + | 0.0686127i | ||||
\(300\) | 100.578 | − | 38.3285i | 0.335259 | − | 0.127762i | ||||
\(301\) | 46.9136 | − | 1.38397i | 0.155859 | − | 0.00459792i | ||||
\(302\) | 419.635 | + | 242.276i | 1.38952 | + | 0.802239i | ||||
\(303\) | −51.2933 | − | 8.25163i | −0.169285 | − | 0.0272331i | ||||
\(304\) | −5.61389 | −0.0184667 | ||||||||
\(305\) | −353.471 | − | 204.077i | −1.15892 | − | 0.669104i | ||||
\(306\) | 97.5635 | + | 470.203i | 0.318835 | + | 1.53661i | ||||
\(307\) | −387.296 | −1.26155 | −0.630776 | − | 0.775965i | \(-0.717263\pi\) | ||||
−0.630776 | + | 0.775965i | \(0.717263\pi\) | |||||||
\(308\) | −23.3360 | − | 791.041i | −0.0757664 | − | 2.56831i | ||||
\(309\) | 13.1509 | − | 81.7481i | 0.0425596 | − | 0.264557i | ||||
\(310\) | 528.358 | 1.70438 | ||||||||
\(311\) | −87.5525 | + | 50.5485i | −0.281519 | + | 0.162535i | −0.634111 | − | 0.773242i | \(-0.718634\pi\) |
0.352592 | + | 0.935777i | \(0.385300\pi\) | |||||||
\(312\) | 59.4914 | − | 73.1026i | 0.190678 | − | 0.234303i | ||||
\(313\) | −182.396 | + | 315.918i | −0.582733 | + | 1.00932i | 0.412420 | + | 0.910994i | \(0.364684\pi\) |
−0.995154 | + | 0.0983303i | \(0.968650\pi\) | |||||||
\(314\) | − | 883.436i | − | 2.81349i | ||||||
\(315\) | 239.554 | + | 253.217i | 0.760490 | + | 0.803862i | ||||
\(316\) | −887.634 | −2.80897 | ||||||||
\(317\) | 28.7096 | + | 16.5755i | 0.0905665 | + | 0.0522886i | 0.544599 | − | 0.838696i | \(-0.316682\pi\) |
−0.454033 | + | 0.890985i | \(0.650015\pi\) | |||||||
\(318\) | 340.065 | − | 129.593i | 1.06939 | − | 0.407526i | ||||
\(319\) | 407.522 | + | 705.849i | 1.27750 | + | 2.21269i | ||||
\(320\) | − | 575.281i | − | 1.79775i | ||||||
\(321\) | 130.869 | + | 343.413i | 0.407692 | + | 1.06982i | ||||
\(322\) | −119.339 | − | 193.304i | −0.370618 | − | 0.600322i | ||||
\(323\) | − | 129.802i | − | 0.401864i | ||||||
\(324\) | −59.1063 | + | 514.316i | −0.182427 | + | 1.58739i | ||||
\(325\) | −11.4388 | + | 19.8127i | −0.0351965 | + | 0.0609621i | ||||
\(326\) | 717.733i | 2.20163i | ||||||||
\(327\) | −79.4505 | − | 64.6574i | −0.242968 | − | 0.197729i | ||||
\(328\) | 123.809 | − | 214.444i | 0.377468 | − | 0.653794i | ||||
\(329\) | −97.9235 | + | 60.4546i | −0.297640 | + | 0.183753i | ||||
\(330\) | −597.419 | + | 734.103i | −1.81036 | + | 2.22456i | ||||
\(331\) | 45.2538 | − | 78.3820i | 0.136719 | − | 0.236804i | −0.789534 | − | 0.613707i | \(-0.789678\pi\) |
0.926253 | + | 0.376903i | \(0.123011\pi\) | |||||||
\(332\) | 87.5154 | + | 50.5271i | 0.263601 | + | 0.152190i | ||||
\(333\) | −57.0296 | − | 274.852i | −0.171260 | − | 0.825381i | ||||
\(334\) | −116.856 | − | 202.401i | −0.349869 | − | 0.605990i | ||||
\(335\) | 58.4148 | − | 33.7258i | 0.174373 | − | 0.100674i | ||||
\(336\) | 13.8841 | − | 5.76540i | 0.0413216 | − | 0.0171589i | ||||
\(337\) | 216.839 | − | 375.576i | 0.643438 | − | 1.11447i | −0.341221 | − | 0.939983i | \(-0.610841\pi\) |
0.984660 | − | 0.174485i | \(-0.0558261\pi\) | |||||||
\(338\) | − | 491.240i | − | 1.45337i | ||||||
\(339\) | −147.428 | + | 181.159i | −0.434891 | + | 0.534391i | ||||
\(340\) | 585.342 | 1.72159 | ||||||||
\(341\) | −453.798 | + | 262.000i | −1.33079 | + | 0.768329i | ||||
\(342\) | 71.3532 | − | 216.032i | 0.208635 | − | 0.631671i | ||||
\(343\) | −341.658 | + | 30.3076i | −0.996089 | + | 0.0883603i | ||||
\(344\) | 44.7614 | − | 25.8430i | 0.130120 | − | 0.0751250i | ||||
\(345\) | −26.5419 | + | 164.989i | −0.0769332 | + | 0.478228i | ||||
\(346\) | 340.365 | + | 589.530i | 0.983715 | + | 1.70384i | ||||
\(347\) | −10.1281 | + | 5.84745i | −0.0291876 | + | 0.0168514i | −0.514523 | − | 0.857477i | \(-0.672031\pi\) |
0.485335 | + | 0.874328i | \(0.338698\pi\) | |||||||
\(348\) | 557.661 | − | 685.249i | 1.60247 | − | 1.96911i | ||||
\(349\) | 91.7075 | + | 158.842i | 0.262772 | + | 0.455135i | 0.966978 | − | 0.254862i | \(-0.0820299\pi\) |
−0.704205 | + | 0.709996i | \(0.748697\pi\) | |||||||
\(350\) | 107.782 | − | 66.5410i | 0.307949 | − | 0.190117i | ||||
\(351\) | −59.2583 | − | 92.7196i | −0.168827 | − | 0.264159i | ||||
\(352\) | 293.125 | + | 507.707i | 0.832741 | + | 1.44235i | ||||
\(353\) | 68.0833i | 0.192871i | 0.995339 | + | 0.0964353i | \(0.0307441\pi\) | ||||
−0.995339 | + | 0.0964353i | \(0.969256\pi\) | |||||||
\(354\) | 146.005 | − | 907.585i | 0.412442 | − | 2.56380i | ||||
\(355\) | 110.736 | 0.311933 | ||||||||
\(356\) | 300.039 | + | 173.228i | 0.842807 | + | 0.486595i | ||||
\(357\) | 133.305 | + | 321.022i | 0.373404 | + | 0.899221i | ||||
\(358\) | 129.528 | + | 224.350i | 0.361811 | + | 0.626675i | ||||
\(359\) | 386.169 | − | 222.955i | 1.07568 | − | 0.621044i | 0.145952 | − | 0.989292i | \(-0.453375\pi\) |
0.929728 | + | 0.368247i | \(0.120042\pi\) | |||||||
\(360\) | 364.500 | + | 120.391i | 1.01250 | + | 0.334419i | ||||
\(361\) | 149.752 | − | 259.378i | 0.414826 | − | 0.718500i | ||||
\(362\) | −343.222 | − | 198.159i | −0.948127 | − | 0.547401i | ||||
\(363\) | 91.4332 | − | 568.362i | 0.251882 | − | 1.56574i | ||||
\(364\) | 86.4721 | − | 160.527i | 0.237561 | − | 0.441009i | ||||
\(365\) | 110.143 | + | 63.5913i | 0.301763 | + | 0.174223i | ||||
\(366\) | −254.039 | − | 666.622i | −0.694095 | − | 1.82137i | ||||
\(367\) | 126.685 | 0.345190 | 0.172595 | − | 0.984993i | \(-0.444785\pi\) | ||||
0.172595 | + | 0.984993i | \(0.444785\pi\) | |||||||
\(368\) | 6.24161 | + | 3.60360i | 0.0169609 | + | 0.00979238i | ||||
\(369\) | −192.399 | − | 215.777i | −0.521407 | − | 0.584760i | ||||
\(370\) | −556.291 | −1.50349 | ||||||||
\(371\) | 224.145 | − | 138.379i | 0.604164 | − | 0.372990i | ||||
\(372\) | 440.553 | + | 358.526i | 1.18428 | + | 0.963779i | ||||
\(373\) | −612.329 | −1.64163 | −0.820817 | − | 0.571192i | \(-0.806481\pi\) | ||||
−0.820817 | + | 0.571192i | \(0.806481\pi\) | |||||||
\(374\) | −817.377 | + | 471.913i | −2.18550 | + | 1.26180i | ||||
\(375\) | 317.709 | + | 51.1103i | 0.847224 | + | 0.136294i | ||||
\(376\) | −63.3667 | + | 109.754i | −0.168528 | + | 0.291900i | ||||
\(377\) | 187.787i | 0.498110i | ||||||||
\(378\) | 45.3938 | + | 607.560i | 0.120089 | + | 1.60730i | ||||
\(379\) | 410.847 | 1.08403 | 0.542015 | − | 0.840369i | \(-0.317662\pi\) | ||||
0.542015 | + | 0.840369i | \(0.317662\pi\) | |||||||
\(380\) | −240.161 | − | 138.657i | −0.632003 | − | 0.364887i | ||||
\(381\) | −6.70620 | + | 41.6867i | −0.0176016 | + | 0.109414i | ||||
\(382\) | −572.973 | − | 992.418i | −1.49993 | − | 2.59795i | ||||
\(383\) | 220.118i | 0.574720i | 0.957823 | + | 0.287360i | \(0.0927775\pi\) | ||||
−0.957823 | + | 0.287360i | \(0.907222\pi\) | |||||||
\(384\) | 383.638 | − | 471.411i | 0.999056 | − | 1.22763i | ||||
\(385\) | −324.903 | + | 603.152i | −0.843903 | + | 1.56663i | ||||
\(386\) | − | 127.844i | − | 0.331203i | ||||||
\(387\) | −12.2597 | − | 59.0853i | −0.0316789 | − | 0.152675i | ||||
\(388\) | −550.417 | + | 953.351i | −1.41860 | + | 2.45709i | ||||
\(389\) | − | 172.259i | − | 0.442824i | −0.975180 | − | 0.221412i | \(-0.928933\pi\) | ||
0.975180 | − | 0.221412i | \(-0.0710666\pi\) | |||||||
\(390\) | −203.774 | + | 77.6551i | −0.522498 | + | 0.199116i | ||||
\(391\) | −83.3209 | + | 144.316i | −0.213097 | + | 0.369095i | ||||
\(392\) | −315.420 | + | 207.819i | −0.804642 | + | 0.530151i | ||||
\(393\) | −65.9615 | − | 10.6113i | −0.167841 | − | 0.0270008i | ||||
\(394\) | −210.554 | + | 364.691i | −0.534402 | + | 0.925611i | ||||
\(395\) | 665.468 | + | 384.208i | 1.68473 | + | 0.972678i | ||||
\(396\) | −996.274 | + | 206.719i | −2.51584 | + | 0.522018i | ||||
\(397\) | −185.521 | − | 321.332i | −0.467308 | − | 0.809401i | 0.531995 | − | 0.846748i | \(-0.321443\pi\) |
−0.999302 | + | 0.0373470i | \(0.988109\pi\) | |||||||
\(398\) | −605.912 | + | 349.824i | −1.52239 | + | 0.878954i | ||||
\(399\) | 21.3503 | − | 163.290i | 0.0535095 | − | 0.409249i | ||||
\(400\) | −2.00929 | + | 3.48020i | −0.00502323 | + | 0.00870049i | ||||
\(401\) | − | 299.417i | − | 0.746675i | −0.927696 | − | 0.373338i | \(-0.878213\pi\) | ||
0.927696 | − | 0.373338i | \(-0.121787\pi\) | |||||||
\(402\) | 116.398 | + | 18.7251i | 0.289547 | + | 0.0465799i | ||||
\(403\) | −120.730 | −0.299579 | ||||||||
\(404\) | −95.8544 | + | 55.3416i | −0.237263 | + | 0.136984i | ||||
\(405\) | 266.932 | − | 360.004i | 0.659090 | − | 0.888898i | ||||
\(406\) | 493.087 | − | 915.370i | 1.21450 | − | 2.25460i | ||||
\(407\) | 477.788 | − | 275.851i | 1.17393 | − | 0.677767i | ||||
\(408\) | 296.901 | + | 241.620i | 0.727698 | + | 0.592206i | ||||
\(409\) | 187.201 | + | 324.241i | 0.457703 | + | 0.792766i | 0.998839 | − | 0.0481696i | \(-0.0153388\pi\) |
−0.541136 | + | 0.840935i | \(0.682005\pi\) | |||||||
\(410\) | −496.163 | + | 286.460i | −1.21015 | + | 0.698682i | ||||
\(411\) | 109.846 | + | 17.6711i | 0.267265 | + | 0.0429953i | ||||
\(412\) | −88.2000 | − | 152.767i | −0.214078 | − | 0.370793i | ||||
\(413\) | −19.6208 | − | 665.100i | −0.0475079 | − | 1.61041i | ||||
\(414\) | −218.004 | + | 194.385i | −0.526580 | + | 0.469530i | ||||
\(415\) | −43.7408 | − | 75.7613i | −0.105399 | − | 0.182557i | ||||
\(416\) | 135.073i | 0.324694i | ||||||||
\(417\) | 328.253 | + | 267.134i | 0.787176 | + | 0.640610i | ||||
\(418\) | 447.151 | 1.06974 | ||||||||
\(419\) | 350.317 | + | 202.256i | 0.836080 | + | 0.482711i | 0.855930 | − | 0.517092i | \(-0.172986\pi\) |
−0.0198501 | + | 0.999803i | \(0.506319\pi\) | |||||||
\(420\) | 736.357 | + | 96.2790i | 1.75323 | + | 0.229236i | ||||
\(421\) | −231.002 | − | 400.107i | −0.548698 | − | 0.950372i | −0.998364 | − | 0.0571757i | \(-0.981790\pi\) |
0.449666 | − | 0.893197i | \(-0.351543\pi\) | |||||||
\(422\) | −304.916 | + | 176.043i | −0.722549 | + | 0.417164i | ||||
\(423\) | 98.4715 | + | 110.436i | 0.232793 | + | 0.261078i | ||||
\(424\) | 145.045 | − | 251.225i | 0.342087 | − | 0.592512i | ||||
\(425\) | −80.4677 | − | 46.4580i | −0.189336 | − | 0.109313i | ||||
\(426\) | 150.120 | + | 122.169i | 0.352395 | + | 0.286781i | ||||
\(427\) | −271.262 | − | 439.386i | −0.635274 | − | 1.02901i | ||||
\(428\) | 678.055 | + | 391.475i | 1.58424 | + | 0.914662i | ||||
\(429\) | 136.511 | − | 167.743i | 0.318207 | − | 0.391010i | ||||
\(430\) | −119.587 | −0.278108 | ||||||||
\(431\) | −197.559 | − | 114.061i | −0.458374 | − | 0.264643i | 0.252986 | − | 0.967470i | \(-0.418587\pi\) |
−0.711360 | + | 0.702827i | \(0.751921\pi\) | |||||||
\(432\) | −10.4090 | − | 16.2867i | −0.0240949 | − | 0.0377006i | ||||
\(433\) | 777.626 | 1.79590 | 0.897951 | − | 0.440095i | \(-0.145055\pi\) | ||||
0.897951 | + | 0.440095i | \(0.145055\pi\) | |||||||
\(434\) | 588.500 | + | 317.010i | 1.35599 | + | 0.730439i | ||||
\(435\) | −714.690 | + | 272.357i | −1.64297 | + | 0.626108i | ||||
\(436\) | −218.234 | −0.500536 | ||||||||
\(437\) | 68.3719 | − | 39.4745i | 0.156457 | − | 0.0903307i | ||||
\(438\) | 79.1598 | + | 207.723i | 0.180730 | + | 0.474252i | ||||
\(439\) | −34.4006 | + | 59.5836i | −0.0783612 | + | 0.135726i | −0.902543 | − | 0.430600i | \(-0.858302\pi\) |
0.824182 | + | 0.566325i | \(0.191635\pi\) | |||||||
\(440\) | 754.458i | 1.71468i | ||||||||
\(441\) | 114.895 | + | 425.770i | 0.260532 | + | 0.965465i | ||||
\(442\) | −217.459 | −0.491988 | ||||||||
\(443\) | −180.419 | − | 104.165i | −0.407267 | − | 0.235136i | 0.282348 | − | 0.959312i | \(-0.408887\pi\) |
−0.689615 | + | 0.724176i | \(0.742220\pi\) | |||||||
\(444\) | −463.844 | − | 377.480i | −1.04469 | − | 0.850179i | ||||
\(445\) | −149.961 | − | 259.741i | −0.336992 | − | 0.583687i | ||||
\(446\) | 601.959i | 1.34968i | ||||||||
\(447\) | −342.747 | − | 55.1382i | −0.766772 | − | 0.123352i | ||||
\(448\) | 345.164 | − | 640.765i | 0.770455 | − | 1.43028i | ||||
\(449\) | 259.045i | 0.576937i | 0.957489 | + | 0.288469i | \(0.0931461\pi\) | ||||
−0.957489 | + | 0.288469i | \(0.906854\pi\) | |||||||
\(450\) | −108.385 | − | 121.555i | −0.240856 | − | 0.270121i | ||||
\(451\) | 284.097 | − | 492.071i | 0.629927 | − | 1.09107i | ||||
\(452\) | 497.604i | 1.10089i | ||||||||
\(453\) | 71.6236 | − | 445.223i | 0.158110 | − | 0.982832i | ||||
\(454\) | −326.463 | + | 565.450i | −0.719081 | + | 1.24548i | ||||
\(455\) | −134.312 | + | 82.9199i | −0.295192 | + | 0.182242i | ||||
\(456\) | −64.5806 | − | 169.465i | −0.141624 | − | 0.371635i | ||||
\(457\) | −79.7186 | + | 138.077i | −0.174439 | + | 0.302137i | −0.939967 | − | 0.341265i | \(-0.889144\pi\) |
0.765528 | + | 0.643403i | \(0.222478\pi\) | |||||||
\(458\) | 221.306 | + | 127.771i | 0.483201 | + | 0.278976i | ||||
\(459\) | 376.574 | − | 240.673i | 0.820423 | − | 0.524342i | ||||
\(460\) | 178.010 | + | 308.323i | 0.386979 | + | 0.670267i | ||||
\(461\) | −176.910 | + | 102.139i | −0.383752 | + | 0.221559i | −0.679449 | − | 0.733722i | \(-0.737781\pi\) |
0.295697 | + | 0.955282i | \(0.404448\pi\) | |||||||
\(462\) | −1105.88 | + | 459.219i | −2.39367 | + | 0.993980i | ||||
\(463\) | −381.105 | + | 660.092i | −0.823120 | + | 1.42569i | 0.0802276 | + | 0.996777i | \(0.474435\pi\) |
−0.903348 | + | 0.428909i | \(0.858898\pi\) | |||||||
\(464\) | 32.9858i | 0.0710901i | ||||||||
\(465\) | −175.101 | − | 459.481i | −0.376562 | − | 0.988132i | ||||
\(466\) | 1051.28 | 2.25596 | ||||||||
\(467\) | 462.046 | − | 266.762i | 0.989391 | − | 0.571225i | 0.0842988 | − | 0.996441i | \(-0.473135\pi\) |
0.905092 | + | 0.425215i | \(0.139802\pi\) | |||||||
\(468\) | −222.604 | − | 73.5241i | −0.475650 | − | 0.157103i | ||||
\(469\) | 85.2993 | − | 2.51636i | 0.181875 | − | 0.00536538i | ||||
\(470\) | 253.940 | − | 146.612i | 0.540298 | − | 0.311941i | ||||
\(471\) | −768.271 | + | 292.776i | −1.63115 | + | 0.621605i | ||||
\(472\) | −366.379 | − | 634.588i | −0.776227 | − | 1.34447i | ||||
\(473\) | 102.711 | − | 59.3001i | 0.217148 | − | 0.125370i | ||||
\(474\) | 478.270 | + | 1255.02i | 1.00901 | + | 2.64773i | ||||
\(475\) | 22.0102 | + | 38.1228i | 0.0463372 | + | 0.0802584i | ||||
\(476\) | 651.970 | + | 351.200i | 1.36969 | + | 0.737815i | ||||
\(477\) | −225.399 | − | 252.786i | −0.472535 | − | 0.529950i | ||||
\(478\) | 392.545 | + | 679.909i | 0.821225 | + | 1.42240i | ||||
\(479\) | − | 604.516i | − | 1.26204i | −0.775768 | − | 0.631019i | \(-0.782637\pi\) | ||
0.775768 | − | 0.631019i | \(-0.217363\pi\) | |||||||
\(480\) | −514.066 | + | 195.902i | −1.07097 | + | 0.408130i | ||||
\(481\) | 127.113 | 0.264268 | ||||||||
\(482\) | −79.1177 | − | 45.6787i | −0.164145 | − | 0.0947690i | ||||
\(483\) | −128.555 | + | 167.844i | −0.266159 | + | 0.347503i | ||||
\(484\) | −613.220 | − | 1062.13i | −1.26698 | − | 2.19448i | ||||
\(485\) | 825.306 | − | 476.491i | 1.70166 | − | 0.982455i | ||||
\(486\) | 759.038 | − | 193.550i | 1.56181 | − | 0.398252i | ||||
\(487\) | −78.1017 | + | 135.276i | −0.160373 | + | 0.277774i | −0.935002 | − | 0.354641i | \(-0.884603\pi\) |
0.774629 | + | 0.632415i | \(0.217936\pi\) | |||||||
\(488\) | −492.471 | − | 284.328i | −1.00916 | − | 0.582640i | ||||
\(489\) | 624.169 | − | 237.861i | 1.27642 | − | 0.486423i | ||||
\(490\) | 872.434 | − | 51.5192i | 1.78048 | − | 0.105141i | ||||
\(491\) | −346.903 | − | 200.285i | −0.706523 | − | 0.407911i | 0.103249 | − | 0.994656i | \(-0.467076\pi\) |
−0.809772 | + | 0.586744i | \(0.800409\pi\) | |||||||
\(492\) | −608.090 | − | 97.8243i | −1.23596 | − | 0.198830i | ||||
\(493\) | −762.685 | −1.54703 | ||||||||
\(494\) | 89.2216 | + | 51.5121i | 0.180611 | + | 0.104276i | ||||
\(495\) | 836.394 | + | 276.253i | 1.68968 | + | 0.558087i | ||||
\(496\) | −21.2069 | −0.0427559 | ||||||||
\(497\) | 123.341 | + | 66.4408i | 0.248171 | + | 0.133684i | ||||
\(498\) | 24.2856 | − | 150.963i | 0.0487662 | − | 0.303138i | ||||
\(499\) | −122.289 | −0.245068 | −0.122534 | − | 0.992464i | \(-0.539102\pi\) | ||||
−0.122534 | + | 0.992464i | \(0.539102\pi\) | |||||||
\(500\) | 593.719 | − | 342.784i | 1.18744 | − | 0.685567i | ||||
\(501\) | −137.289 | + | 168.700i | −0.274030 | + | 0.336726i | ||||
\(502\) | 225.862 | − | 391.204i | 0.449924 | − | 0.779291i | ||||
\(503\) | 786.814i | 1.56424i | 0.623126 | + | 0.782121i | \(0.285862\pi\) | ||||
−0.623126 | + | 0.782121i | \(0.714138\pi\) | |||||||
\(504\) | 333.757 | + | 352.792i | 0.662216 | + | 0.699984i | ||||
\(505\) | 95.8173 | 0.189737 | ||||||||
\(506\) | −497.150 | − | 287.030i | −0.982510 | − | 0.567252i | ||||
\(507\) | −427.202 | + | 162.800i | −0.842607 | + | 0.321104i | ||||
\(508\) | 44.9768 | + | 77.9021i | 0.0885370 | + | 0.153351i | ||||
\(509\) | − | 902.823i | − | 1.77372i | −0.462040 | − | 0.886859i | \(-0.652882\pi\) | ||
0.462040 | − | 0.886859i | \(-0.347118\pi\) | |||||||
\(510\) | −315.391 | − | 827.614i | −0.618413 | − | 1.62277i | ||||
\(511\) | 84.5265 | + | 136.915i | 0.165414 | + | 0.267935i | ||||
\(512\) | 45.8004i | 0.0894539i | ||||||||
\(513\) | −211.517 | + | 9.54258i | −0.412313 | + | 0.0186015i | ||||
\(514\) | 178.379 | − | 308.961i | 0.347040 | − | 0.601092i | ||||
\(515\) | 152.708i | 0.296520i | ||||||||
\(516\) | −99.7132 | − | 81.1473i | −0.193243 | − | 0.157262i | ||||
\(517\) | −145.403 | + | 251.846i | −0.281244 | + | 0.487129i | ||||
\(518\) | −619.612 | − | 333.770i | −1.19616 | − | 0.644343i | ||||
\(519\) | 399.880 | − | 491.369i | 0.770482 | − | 0.946762i | ||||
\(520\) | −86.9141 | + | 150.540i | −0.167142 | + | 0.289499i | ||||
\(521\) | −442.743 | − | 255.618i | −0.849795 | − | 0.490630i | 0.0107865 | − | 0.999942i | \(-0.496566\pi\) |
−0.860582 | + | 0.509312i | \(0.829900\pi\) | |||||||
\(522\) | −1269.35 | − | 419.254i | −2.43170 | − | 0.803168i | ||||
\(523\) | 489.654 | + | 848.105i | 0.936240 | + | 1.62162i | 0.772407 | + | 0.635128i | \(0.219053\pi\) |
0.163833 | + | 0.986488i | \(0.447614\pi\) | |||||||
\(524\) | −123.266 | + | 71.1675i | −0.235240 | + | 0.135816i | ||||
\(525\) | −93.5864 | − | 71.6796i | −0.178260 | − | 0.136533i | ||||
\(526\) | 79.5711 | − | 137.821i | 0.151276 | − | 0.262018i | ||||
\(527\) | − | 490.338i | − | 0.930432i | ||||||
\(528\) | 23.9788 | − | 29.4650i | 0.0454144 | − | 0.0558049i | ||||
\(529\) | 427.644 | 0.808401 | ||||||||
\(530\) | −581.263 | + | 335.592i | −1.09672 | + | 0.633193i | ||||
\(531\) | −837.659 | + | 173.808i | −1.57751 | + | 0.327322i | ||||
\(532\) | −184.305 | − | 298.535i | −0.346438 | − | 0.561156i | ||||
\(533\) | 113.374 | − | 65.4564i | 0.212709 | − | 0.122807i | ||||
\(534\) | 83.2610 | − | 517.563i | 0.155919 | − | 0.969218i | ||||
\(535\) | −338.896 | − | 586.986i | −0.633451 | − | 1.09717i | ||||
\(536\) | 81.3860 | − | 46.9882i | 0.151840 | − | 0.0876646i | ||||
\(537\) | 152.177 | − | 186.994i | 0.283383 | − | 0.348219i | ||||
\(538\) | −301.577 | − | 522.346i | −0.560552 | − | 0.970904i | ||||
\(539\) | −723.772 | + | 476.868i | −1.34280 | + | 0.884728i | ||||
\(540\) | −43.0322 | − | 953.833i | −0.0796893 | − | 1.76636i | ||||
\(541\) | 350.265 | + | 606.676i | 0.647439 | + | 1.12140i | 0.983732 | + | 0.179640i | \(0.0574934\pi\) |
−0.336293 | + | 0.941757i | \(0.609173\pi\) | |||||||
\(542\) | − | 697.234i | − | 1.28641i | ||||||
\(543\) | −58.5814 | + | 364.151i | −0.107885 | + | 0.670628i | ||||
\(544\) | −548.588 | −1.00843 | ||||||||
\(545\) | 163.612 | + | 94.4613i | 0.300205 | + | 0.173324i | ||||
\(546\) | −273.562 | − | 35.7683i | −0.501029 | − | 0.0655098i | ||||
\(547\) | 294.015 | + | 509.248i | 0.537504 | + | 0.930984i | 0.999038 | + | 0.0438616i | \(0.0139660\pi\) |
−0.461534 | + | 0.887123i | \(0.652701\pi\) | |||||||
\(548\) | 205.275 | − | 118.515i | 0.374589 | − | 0.216269i | ||||
\(549\) | −495.531 | + | 441.845i | −0.902606 | + | 0.804817i | ||||
\(550\) | 160.042 | − | 277.201i | 0.290985 | − | 0.504001i | ||||
\(551\) | 312.924 | + | 180.667i | 0.567920 | + | 0.327889i | ||||
\(552\) | −36.9794 | + | 229.869i | −0.0669916 | + | 0.416430i | ||||
\(553\) | 510.695 | + | 827.216i | 0.923499 | + | 1.49587i | ||||
\(554\) | −218.097 | − | 125.918i | −0.393676 | − | 0.227289i | ||||
\(555\) | 184.358 | + | 483.773i | 0.332177 | + | 0.871663i | ||||
\(556\) | 901.640 | 1.62165 | ||||||||
\(557\) | −347.042 | − | 200.365i | −0.623055 | − | 0.359721i | 0.155002 | − | 0.987914i | \(-0.450461\pi\) |
−0.778057 | + | 0.628193i | \(0.783795\pi\) | |||||||
\(558\) | 269.542 | − | 816.077i | 0.483051 | − | 1.46250i | ||||
\(559\) | 27.3257 | 0.0488831 | ||||||||
\(560\) | −23.5927 | + | 14.5653i | −0.0421298 | + | 0.0260095i | ||||
\(561\) | 681.278 | + | 554.429i | 1.21440 | + | 0.988287i | ||||
\(562\) | 1433.26 | 2.55028 | ||||||||
\(563\) | −78.9486 | + | 45.5810i | −0.140228 | + | 0.0809609i | −0.568473 | − | 0.822702i | \(-0.692466\pi\) |
0.428244 | + | 0.903663i | \(0.359132\pi\) | |||||||
\(564\) | 311.225 | + | 50.0672i | 0.551818 | + | 0.0887717i | ||||
\(565\) | 215.385 | − | 373.058i | 0.381213 | − | 0.660281i | ||||
\(566\) | − | 413.984i | − | 0.731421i | ||||||
\(567\) | 513.315 | − | 240.825i | 0.905317 | − | 0.424736i | ||||
\(568\) | 154.282 | 0.271624 | ||||||||
\(569\) | 255.596 | + | 147.568i | 0.449202 | + | 0.259347i | 0.707493 | − | 0.706720i | \(-0.249826\pi\) |
−0.258291 | + | 0.966067i | \(0.583159\pi\) | |||||||
\(570\) | −66.6449 | + | 414.274i | −0.116921 | + | 0.726797i | ||||
\(571\) | −457.407 | − | 792.252i | −0.801062 | − | 1.38748i | −0.918917 | − | 0.394450i | \(-0.870935\pi\) |
0.117855 | − | 0.993031i | \(-0.462398\pi\) | |||||||
\(572\) | − | 460.756i | − | 0.805517i | ||||||
\(573\) | −673.159 | + | 827.173i | −1.17480 | + | 1.44358i | ||||
\(574\) | −724.513 | + | 21.3735i | −1.26222 | + | 0.0372360i | ||||
\(575\) | − | 56.5140i | − | 0.0982852i | ||||||
\(576\) | −888.552 | − | 293.480i | −1.54262 | − | 0.509514i | ||||
\(577\) | −267.301 | + | 462.978i | −0.463259 | + | 0.802389i | −0.999121 | − | 0.0419171i | \(-0.986653\pi\) |
0.535862 | + | 0.844306i | \(0.319987\pi\) | |||||||
\(578\) | 48.4175i | 0.0837674i | ||||||||
\(579\) | −111.178 | + | 42.3683i | −0.192018 | + | 0.0731750i | ||||
\(580\) | −814.715 | + | 1411.13i | −1.40468 | + | 2.43298i | ||||
\(581\) | −3.26361 | − | 110.629i | −0.00561722 | − | 0.190412i | ||||
\(582\) | 1644.51 | + | 264.555i | 2.82563 | + | 0.454562i | ||||
\(583\) | 332.825 | − | 576.469i | 0.570883 | − | 0.988798i | ||||
\(584\) | 153.456 | + | 88.5981i | 0.262768 | + | 0.151709i | ||||
\(585\) | 135.064 | + | 151.475i | 0.230879 | + | 0.258931i | ||||
\(586\) | 79.3789 | + | 137.488i | 0.135459 | + | 0.234622i | ||||
\(587\) | 299.889 | − | 173.141i | 0.510884 | − | 0.294959i | −0.222313 | − | 0.974975i | \(-0.571361\pi\) |
0.733197 | + | 0.680016i | \(0.238027\pi\) | |||||||
\(588\) | 762.409 | + | 549.046i | 1.29661 | + | 0.933752i | ||||
\(589\) | −116.152 | + | 201.182i | −0.197203 | + | 0.341565i | ||||
\(590\) | 1695.39i | 2.87355i | ||||||||
\(591\) | 386.929 | + | 62.2457i | 0.654701 | + | 0.105323i | ||||
\(592\) | 22.3281 | 0.0377163 | ||||||||
\(593\) | −3.55214 | + | 2.05083i | −0.00599012 | + | 0.00345840i | −0.502992 | − | 0.864291i | \(-0.667768\pi\) |
0.497002 | + | 0.867749i | \(0.334434\pi\) | |||||||
\(594\) | 829.087 | + | 1297.25i | 1.39577 | + | 2.18392i | ||||
\(595\) | −336.773 | − | 545.500i | −0.566005 | − | 0.916807i | ||||
\(596\) | −640.509 | + | 369.798i | −1.07468 | + | 0.620467i | ||||
\(597\) | 505.024 | + | 410.992i | 0.845936 | + | 0.688429i | ||||
\(598\) | −66.1320 | − | 114.544i | −0.110589 | − | 0.191545i | ||||
\(599\) | 146.853 | − | 84.7858i | 0.245164 | − | 0.141546i | −0.372384 | − | 0.928079i | \(-0.621459\pi\) |
0.617548 | + | 0.786533i | \(0.288126\pi\) | |||||||
\(600\) | −128.170 | − | 20.6189i | −0.213617 | − | 0.0343649i | ||||
\(601\) | −312.975 | − | 542.089i | −0.520757 | − | 0.901978i | −0.999709 | − | 0.0241366i | \(-0.992316\pi\) |
0.478951 | − | 0.877841i | \(-0.341017\pi\) | |||||||
\(602\) | −133.199 | − | 71.7510i | −0.221261 | − | 0.119188i | ||||
\(603\) | −22.2909 | − | 107.430i | −0.0369667 | − | 0.178159i | ||||
\(604\) | −480.362 | − | 832.011i | −0.795301 | − | 1.37750i | ||||
\(605\) | 1061.72i | 1.75490i | ||||||||
\(606\) | 129.895 | + | 105.710i | 0.214348 | + | 0.174438i | ||||
\(607\) | −37.6117 | −0.0619633 | −0.0309817 | − | 0.999520i | \(-0.509863\pi\) | ||||
−0.0309817 | + | 0.999520i | \(0.509863\pi\) | |||||||
\(608\) | 225.081 | + | 129.951i | 0.370200 | + | 0.213735i | ||||
\(609\) | −959.454 | − | 125.449i | −1.57546 | − | 0.205992i | ||||
\(610\) | 657.855 | + | 1139.44i | 1.07845 | + | 1.86793i | ||||
\(611\) | −58.0256 | + | 33.5011i | −0.0949682 | + | 0.0548299i | ||||
\(612\) | 298.613 | − | 904.091i | 0.487929 | − | 1.47727i | ||||
\(613\) | −149.019 | + | 258.108i | −0.243098 | + | 0.421057i | −0.961595 | − | 0.274472i | \(-0.911497\pi\) |
0.718497 | + | 0.695530i | \(0.244830\pi\) | |||||||
\(614\) | 1081.21 | + | 624.238i | 1.76093 | + | 1.01667i | ||||
\(615\) | 413.548 | + | 336.549i | 0.672436 | + | 0.547233i | ||||
\(616\) | −452.668 | + | 840.336i | −0.734851 | + | 1.36418i | ||||
\(617\) | 818.560 | + | 472.596i | 1.32668 | + | 0.765957i | 0.984784 | − | 0.173782i | \(-0.0555987\pi\) |
0.341893 | + | 0.939739i | \(0.388932\pi\) | |||||||
\(618\) | −168.473 | + | 207.019i | −0.272611 | + | 0.334982i | ||||
\(619\) | −1193.60 | −1.92827 | −0.964133 | − | 0.265418i | \(-0.914490\pi\) | ||||
−0.964133 | + | 0.265418i | \(0.914490\pi\) | |||||||
\(620\) | −907.229 | − | 523.789i | −1.46327 | − | 0.844820i | ||||
\(621\) | 241.293 | + | 125.164i | 0.388556 | + | 0.201553i | ||||
\(622\) | 325.892 | 0.523943 | ||||||||
\(623\) | −11.1890 | − | 379.282i | −0.0179599 | − | 0.608800i | ||||
\(624\) | 8.17896 | − | 3.11687i | 0.0131073 | − | 0.00499499i | ||||
\(625\) | −733.826 | −1.17412 | ||||||||
\(626\) | 1018.38 | − | 587.964i | 1.62681 | − | 0.939239i | ||||
\(627\) | −148.189 | − | 388.860i | −0.236345 | − | 0.620192i | ||||
\(628\) | −875.795 | + | 1516.92i | −1.39458 | + | 2.41548i | ||||
\(629\) | 516.260i | 0.820764i | ||||||||
\(630\) | −260.631 | − | 1093.01i | −0.413700 | − | 1.73494i | ||||
\(631\) | −823.055 | −1.30437 | −0.652183 | − | 0.758062i | \(-0.726147\pi\) | ||||
−0.652183 | + | 0.758062i | \(0.726147\pi\) | |||||||
\(632\) | 927.158 | + | 535.295i | 1.46702 | + | 0.846985i | ||||
\(633\) | 254.145 | + | 206.825i | 0.401493 | + | 0.326738i | ||||
\(634\) | −53.4322 | − | 92.5472i | −0.0842779 | − | 0.145974i | ||||
\(635\) | − | 77.8719i | − | 0.122633i | ||||||
\(636\) | −712.388 | − | 114.603i | −1.12011 | − | 0.180193i | ||||
\(637\) | −199.352 | + | 11.7722i | −0.312955 | + | 0.0184807i | ||||
\(638\) | − | 2627.35i | − | 4.11810i | ||||||
\(639\) | 56.4922 | − | 171.038i | 0.0884072 | − | 0.267665i | ||||
\(640\) | −560.476 | + | 970.773i | −0.875744 | + | 1.51683i | ||||
\(641\) | 712.531i | 1.11159i | 0.831319 | + | 0.555796i | \(0.187587\pi\) | ||||
−0.831319 | + | 0.555796i | \(0.812413\pi\) | |||||||
\(642\) | 188.161 | − | 1169.63i | 0.293085 | − | 1.82186i | ||||
\(643\) | 534.902 | − | 926.478i | 0.831885 | − | 1.44087i | −0.0646564 | − | 0.997908i | \(-0.520595\pi\) |
0.896542 | − | 0.442960i | \(-0.146072\pi\) | |||||||
\(644\) | 13.2818 | + | 450.223i | 0.0206239 | + | 0.699104i | ||||
\(645\) | 39.6317 | + | 103.997i | 0.0614445 | + | 0.161236i | ||||
\(646\) | −209.213 | + | 362.367i | −0.323859 | + | 0.560940i | ||||
\(647\) | −973.422 | − | 562.006i | −1.50452 | − | 0.868633i | −0.999986 | − | 0.00523936i | \(-0.998332\pi\) |
−0.504531 | − | 0.863394i | \(-0.668334\pi\) | |||||||
\(648\) | 371.900 | − | 501.572i | 0.573920 | − | 0.774031i | ||||
\(649\) | −840.705 | − | 1456.14i | −1.29539 | − | 2.24367i | ||||
\(650\) | 63.8674 | − | 36.8739i | 0.0982576 | − | 0.0567290i | ||||
\(651\) | 80.6524 | − | 616.843i | 0.123890 | − | 0.947531i | ||||
\(652\) | 711.525 | − | 1232.40i | 1.09130 | − | 1.89018i | ||||
\(653\) | 48.4318i | 0.0741682i | 0.999312 | + | 0.0370841i | \(0.0118069\pi\) | ||||
−0.999312 | + | 0.0370841i | \(0.988193\pi\) | |||||||
\(654\) | 117.587 | + | 308.560i | 0.179797 | + | 0.471805i | ||||
\(655\) | 123.218 | 0.188119 | ||||||||
\(656\) | 19.9147 | − | 11.4977i | 0.0303577 | − | 0.0175270i | ||||
\(657\) | 154.410 | − | 137.681i | 0.235023 | − | 0.209560i | ||||
\(658\) | 370.812 | − | 10.9391i | 0.563544 | − | 0.0166248i | ||||
\(659\) | −818.128 | + | 472.346i | −1.24147 | + | 0.716762i | −0.969393 | − | 0.245514i | \(-0.921043\pi\) |
−0.272076 | + | 0.962276i | \(0.587710\pi\) | |||||||
\(660\) | 1753.56 | − | 668.256i | 2.65692 | − | 1.01251i | ||||
\(661\) | −140.597 | − | 243.521i | −0.212703 | − | 0.368413i | 0.739856 | − | 0.672765i | \(-0.234893\pi\) |
−0.952560 | + | 0.304352i | \(0.901560\pi\) | |||||||
\(662\) | −252.669 | + | 145.879i | −0.381676 | + | 0.220361i | ||||
\(663\) | 72.0671 | + | 189.111i | 0.108699 | + | 0.285235i | ||||
\(664\) | −60.9415 | − | 105.554i | −0.0917794 | − | 0.158967i | ||||
\(665\) | 8.95604 | + | 303.590i | 0.0134677 | + | 0.456526i | ||||
\(666\) | −283.792 | + | 859.220i | −0.426114 | + | 1.29012i | ||||
\(667\) | −231.942 | − | 401.736i | −0.347740 | − | 0.602303i | ||||
\(668\) | 463.382i | 0.693685i | ||||||||
\(669\) | 523.487 | − | 199.493i | 0.782492 | − | 0.298195i | ||||
\(670\) | −217.435 | −0.324529 | ||||||||
\(671\) | −1130.04 | − | 652.429i | −1.68411 | − | 0.972323i | ||||
\(672\) | −690.121 | − | 90.2336i | −1.02697 | − | 0.134276i | ||||
\(673\) | 246.892 | + | 427.630i | 0.366854 | + | 0.635409i | 0.989072 | − | 0.147435i | \(-0.0471017\pi\) |
−0.622218 | + | 0.782844i | \(0.713768\pi\) | |||||||
\(674\) | −1210.69 | + | 698.994i | −1.79628 | + | 1.03708i | ||||
\(675\) | −69.7892 | + | 134.540i | −0.103391 | + | 0.199319i | ||||
\(676\) | −486.991 | + | 843.494i | −0.720401 | + | 1.24777i | ||||
\(677\) | −611.085 | − | 352.810i | −0.902636 | − | 0.521137i | −0.0245816 | − | 0.999698i | \(-0.507825\pi\) |
−0.878055 | + | 0.478561i | \(0.841159\pi\) | |||||||
\(678\) | 703.562 | − | 268.116i | 1.03770 | − | 0.395452i | ||||
\(679\) | 1205.14 | − | 35.5521i | 1.77487 | − | 0.0523596i | ||||
\(680\) | −611.405 | − | 352.995i | −0.899126 | − | 0.519110i | ||||
\(681\) | 599.929 | + | 96.5114i | 0.880953 | + | 0.141720i | ||||
\(682\) | 1689.15 | 2.47676 | ||||||||
\(683\) | 1010.24 | + | 583.260i | 1.47912 | + | 0.853968i | 0.999721 | − | 0.0236320i | \(-0.00752300\pi\) |
0.479394 | + | 0.877600i | \(0.340856\pi\) | |||||||
\(684\) | −336.682 | + | 300.205i | −0.492225 | + | 0.438897i | ||||
\(685\) | −205.195 | −0.299555 | ||||||||
\(686\) | 1002.65 | + | 466.070i | 1.46159 | + | 0.679402i | ||||
\(687\) | 37.7727 | − | 234.800i | 0.0549821 | − | 0.341777i | ||||
\(688\) | 4.79989 | 0.00697659 | ||||||||
\(689\) | 132.819 | − | 76.6832i | 0.192771 | − | 0.111296i | ||||
\(690\) | 340.023 | − | 417.817i | 0.492786 | − | 0.605532i | ||||
\(691\) | −182.834 | + | 316.677i | −0.264593 | + | 0.458289i | −0.967457 | − | 0.253036i | \(-0.918571\pi\) |
0.702864 | + | 0.711324i | \(0.251904\pi\) | |||||||
\(692\) | − | 1349.69i | − | 1.95041i | ||||||
\(693\) | 765.849 | + | 809.527i | 1.10512 | + | 1.16815i | ||||
\(694\) | 37.6993 | 0.0543217 | ||||||||
\(695\) | −675.968 | − | 390.270i | −0.972616 | − | 0.561540i | ||||
\(696\) | −995.736 | + | 379.459i | −1.43066 | + | 0.545200i | ||||
\(697\) | 265.846 | + | 460.459i | 0.381415 | + | 0.660630i | ||||
\(698\) | − | 591.250i | − | 0.847063i | ||||||
\(699\) | −348.399 | − | 914.232i | −0.498425 | − | 1.30791i | ||||
\(700\) | −251.035 | + | 7.40564i | −0.358622 | + | 0.0105795i | ||||
\(701\) | 254.519i | 0.363080i | 0.983384 | + | 0.181540i | \(0.0581083\pi\) | ||||
−0.983384 | + | 0.181540i | \(0.941892\pi\) | |||||||
\(702\) | 15.9868 | + | 354.356i | 0.0227732 | + | 0.504780i | ||||
\(703\) | 122.293 | − | 211.818i | 0.173959 | − | 0.301305i | ||||
\(704\) | − | 1839.16i | − | 2.61245i | ||||||
\(705\) | −211.657 | − | 172.248i | −0.300223 | − | 0.244324i | ||||
\(706\) | 109.735 | − | 190.067i | 0.155433 | − | 0.269217i | ||||
\(707\) | 106.724 | + | 57.4896i | 0.150953 | + | 0.0813148i | ||||
\(708\) | −1150.44 | + | 1413.65i | −1.62491 | + | 1.99668i | ||||
\(709\) | 520.494 | − | 901.522i | 0.734124 | − | 1.27154i | −0.220982 | − | 0.975278i | \(-0.570926\pi\) |
0.955107 | − | 0.296263i | \(-0.0957403\pi\) | |||||||
\(710\) | −309.141 | − | 178.483i | −0.435410 | − | 0.251384i | ||||
\(711\) | 932.918 | − | 831.845i | 1.31212 | − | 1.16997i | ||||
\(712\) | −208.933 | − | 361.882i | −0.293445 | − | 0.508261i | ||||
\(713\) | 258.280 | − | 149.118i | 0.362244 | − | 0.209142i | ||||
\(714\) | 145.270 | − | 1111.05i | 0.203460 | − | 1.55609i | ||||
\(715\) | −199.436 | + | 345.433i | −0.278931 | + | 0.483123i | ||||
\(716\) | − | 513.632i | − | 0.717363i | ||||||
\(717\) | 461.184 | − | 566.699i | 0.643213 | − | 0.790375i | ||||
\(718\) | −1437.42 | −2.00198 | ||||||||
\(719\) | −653.543 | + | 377.323i | −0.908961 | + | 0.524789i | −0.880097 | − | 0.474795i | \(-0.842522\pi\) |
−0.0288642 | + | 0.999583i | \(0.509189\pi\) | |||||||
\(720\) | 23.7247 | + | 26.6073i | 0.0329509 | + | 0.0369546i | ||||
\(721\) | −91.6233 | + | 170.090i | −0.127078 | + | 0.235909i | ||||
\(722\) | −836.123 | + | 482.736i | −1.15807 | + | 0.668609i | ||||
\(723\) | −13.5039 | + | 83.9421i | −0.0186776 | + | 0.116103i | ||||
\(724\) | 392.891 | + | 680.507i | 0.542667 | + | 0.939927i | ||||
\(725\) | 224.000 | − | 129.326i | 0.308965 | − | 0.178381i | ||||
\(726\) | −1171.33 | + | 1439.32i | −1.61340 | + | 1.98253i | ||||
\(727\) | 698.773 | + | 1210.31i | 0.961174 | + | 1.66480i | 0.719561 | + | 0.694429i | \(0.244343\pi\) |
0.241612 | + | 0.970373i | \(0.422324\pi\) | |||||||
\(728\) | −187.130 | + | 115.528i | −0.257046 | + | 0.158692i | ||||
\(729\) | −419.869 | − | 595.946i | −0.575952 | − | 0.817484i | ||||
\(730\) | −204.991 | − | 355.054i | −0.280809 | − | 0.486376i | ||||
\(731\) | 110.981i | 0.151821i | ||||||||
\(732\) | −224.653 | + | 1396.48i | −0.306903 | + | 1.90776i | ||||
\(733\) | 1253.49 | 1.71008 | 0.855039 | − | 0.518564i | \(-0.173533\pi\) | ||||
0.855039 | + | 0.518564i | \(0.173533\pi\) | |||||||
\(734\) | −353.664 | − | 204.188i | −0.481832 | − | 0.278186i | ||||
\(735\) | −333.933 | − | 741.630i | −0.454331 | − | 1.00902i | ||||
\(736\) | −166.833 | − | 288.963i | −0.226675 | − | 0.392613i | ||||
\(737\) | 186.751 | − | 107.821i | 0.253393 | − | 0.146297i | ||||
\(738\) | 189.334 | + | 912.487i | 0.256550 | + | 1.23643i | ||||
\(739\) | −534.999 | + | 926.646i | −0.723950 | + | 1.25392i | 0.235454 | + | 0.971885i | \(0.424342\pi\) |
−0.959405 | + | 0.282033i | \(0.908991\pi\) | |||||||
\(740\) | 955.191 | + | 551.480i | 1.29080 | + | 0.745243i | ||||
\(741\) | 15.2284 | − | 94.6621i | 0.0205512 | − | 0.127749i | ||||
\(742\) | −848.780 | + | 25.0394i | −1.14391 | + | 0.0337458i | ||||
\(743\) | −620.266 | − | 358.111i | −0.834813 | − | 0.481980i | 0.0206847 | − | 0.999786i | \(-0.493415\pi\) |
−0.855498 | + | 0.517806i | \(0.826749\pi\) | |||||||
\(744\) | −243.958 | − | 640.169i | −0.327901 | − | 0.860442i | ||||
\(745\) | 640.261 | 0.859411 | ||||||||
\(746\) | 1709.43 | + | 986.941i | 2.29146 | + | 1.32298i | ||||
\(747\) | −139.332 | + | 28.9102i | −0.186522 | + | 0.0387018i | ||||
\(748\) | 1871.32 | 2.50177 | ||||||||
\(749\) | −25.2859 | − | 857.136i | −0.0337595 | − | 1.14437i | ||||
\(750\) | −804.566 | − | 654.762i | −1.07275 | − | 0.873015i | ||||
\(751\) | −120.642 | −0.160642 | −0.0803208 | − | 0.996769i | \(-0.525594\pi\) | ||||
−0.0803208 | + | 0.996769i | \(0.525594\pi\) | |||||||
\(752\) | −10.1925 | + | 5.88464i | −0.0135538 | + | 0.00782531i | ||||
\(753\) | −415.059 | − | 66.7711i | −0.551207 | − | 0.0886734i | ||||
\(754\) | 302.672 | − | 524.244i | 0.401422 | − | 0.695284i | ||||
\(755\) | 831.689i | 1.10157i | ||||||||
\(756\) | 524.361 | − | 1088.22i | 0.693599 | − | 1.43945i | ||||
\(757\) | −369.403 | −0.487983 | −0.243992 | − | 0.969777i | \(-0.578457\pi\) | ||||
−0.243992 | + | 0.969777i | \(0.578457\pi\) | |||||||
\(758\) | −1146.96 | − | 662.196i | −1.51314 | − | 0.873610i | ||||
\(759\) | −84.8540 | + | 527.465i | −0.111797 | + | 0.694947i | ||||
\(760\) | 167.237 | + | 289.662i | 0.220048 | + | 0.381135i | ||||
\(761\) | 1145.54i | 1.50531i | 0.658415 | + | 0.752655i | \(0.271227\pi\) | ||||
−0.658415 | + | 0.752655i | \(0.728773\pi\) | |||||||
\(762\) | 85.9115 | − | 105.567i | 0.112745 | − | 0.138540i | ||||
\(763\) | 125.559 | + | 203.379i | 0.164560 | + | 0.266552i | ||||
\(764\) | 2272.07i | 2.97391i | ||||||||
\(765\) | −615.204 | + | 548.553i | −0.804188 | + | 0.717062i | ||||
\(766\) | 354.782 | − | 614.500i | 0.463161 | − | 0.802219i | ||||
\(767\) | − | 387.399i | − | 0.505084i | ||||||
\(768\) | −664.912 | + | 253.387i | −0.865771 | + | 0.329932i | ||||
\(769\) | 319.295 | − | 553.035i | 0.415208 | − | 0.719162i | −0.580242 | − | 0.814444i | \(-0.697042\pi\) |
0.995450 | + | 0.0952822i | \(0.0303754\pi\) | |||||||
\(770\) | 1879.18 | − | 1160.14i | 2.44049 | − | 1.50667i | ||||
\(771\) | −327.801 | − | 52.7337i | −0.425163 | − | 0.0683966i | ||||
\(772\) | −126.738 | + | 219.517i | −0.164169 | + | 0.284349i | ||||
\(773\) | −169.438 | − | 97.8250i | −0.219195 | − | 0.126552i | 0.386382 | − | 0.922339i | \(-0.373725\pi\) |
−0.605578 | + | 0.795786i | \(0.707058\pi\) | |||||||
\(774\) | −61.0072 | + | 184.708i | −0.0788207 | + | 0.238641i | ||||
\(775\) | 83.1452 | + | 144.012i | 0.107284 | + | 0.185822i | ||||
\(776\) | 1149.85 | − | 663.867i | 1.48177 | − | 0.855499i | ||||
\(777\) | −84.9162 | + | 649.453i | −0.109287 | + | 0.835847i | ||||
\(778\) | −277.643 | + | 480.892i | −0.356868 | + | 0.618114i | ||||
\(779\) | − | 251.897i | − | 0.323360i | ||||||
\(780\) | 426.878 | + | 68.6725i | 0.547280 | + | 0.0880417i | ||||
\(781\) | 354.021 | 0.453292 | ||||||||
\(782\) | 465.212 | − | 268.590i | 0.594901 | − | 0.343466i | ||||
\(783\) | 56.0698 | + | 1242.82i | 0.0716090 | + | 1.58725i | ||||
\(784\) | −35.0172 | + | 2.06785i | −0.0446648 | + | 0.00263756i | ||||
\(785\) | 1313.18 | − | 758.167i | 1.67285 | − | 0.965818i | ||||
\(786\) | 167.041 | + | 135.939i | 0.212520 | + | 0.172951i | ||||
\(787\) | 8.68274 | + | 15.0389i | 0.0110327 | + | 0.0191092i | 0.871489 | − | 0.490415i | \(-0.163155\pi\) |
−0.860456 | + | 0.509524i | \(0.829821\pi\) | |||||||
\(788\) | 723.073 | − | 417.466i | 0.917605 | − | 0.529780i | ||||
\(789\) | −146.225 | − | 23.5235i | −0.185330 | − | 0.0298143i | ||||
\(790\) | −1238.52 | − | 2145.18i | −1.56775 | − | 2.71542i | ||||
\(791\) | 463.734 | − | 286.294i | 0.586263 | − | 0.361939i | ||||
\(792\) | 1165.30 | + | 384.887i | 1.47134 | + | 0.485969i | ||||
\(793\) | −150.320 | − | 260.363i | −0.189559 | − | 0.328326i | ||||
\(794\) | 1196.08i | 1.50640i | ||||||||
\(795\) | 484.479 | + | 394.272i | 0.609407 | + | 0.495940i | ||||
\(796\) | 1387.19 | 1.74270 | ||||||||
\(797\) | −871.920 | − | 503.403i | −1.09400 | − | 0.631622i | −0.159363 | − | 0.987220i | \(-0.550944\pi\) |
−0.934639 | + | 0.355598i | \(0.884277\pi\) | |||||||
\(798\) | −322.792 | + | 421.444i | −0.404501 | + | 0.528125i | ||||
\(799\) | −136.062 | − | 235.667i | −0.170291 | − | 0.294952i | ||||
\(800\) | 161.120 | − | 93.0225i | 0.201400 | − | 0.116278i | ||||
\(801\) | −477.686 | + | 99.1162i | −0.596362 | + | 0.123741i | ||||
\(802\) | −482.595 | + | 835.879i | −0.601739 | + | 1.04224i | ||||
\(803\) | 352.126 | + | 203.300i | 0.438513 | + | 0.253176i | ||||
\(804\) | −181.300 | − | 147.544i | −0.225498 | − | 0.183512i | ||||
\(805\) | 184.919 | − | 343.285i | 0.229713 | − | 0.426442i | ||||
\(806\) | 337.042 | + | 194.591i | 0.418166 | + | 0.241428i | ||||
\(807\) | −354.309 | + | 435.372i | −0.439045 | + | 0.539494i | ||||
\(808\) | 133.497 | 0.165219 | ||||||||
\(809\) | −364.210 | − | 210.277i | −0.450198 | − | 0.259922i | 0.257716 | − | 0.966221i | \(-0.417030\pi\) |
−0.707914 | + | 0.706299i | \(0.750364\pi\) | |||||||
\(810\) | −1325.44 | + | 574.782i | −1.63634 | + | 0.709608i | ||||
\(811\) | 1318.39 | 1.62564 | 0.812819 | − | 0.582517i | \(-0.197932\pi\) | ||||
0.812819 | + | 0.582517i | \(0.197932\pi\) | |||||||
\(812\) | −1754.12 | + | 1082.93i | −2.16024 | + | 1.33366i | ||||
\(813\) | −606.342 | + | 231.067i | −0.745808 | + | 0.284216i | ||||
\(814\) | −1778.45 | −2.18483 | ||||||||
\(815\) | −1066.87 | + | 615.960i | −1.30905 | + | 0.755780i | ||||
\(816\) | 12.6590 | + | 33.2183i | 0.0155134 | + | 0.0407087i | ||||
\(817\) | 26.2895 | − | 45.5347i | 0.0321781 | − | 0.0557341i | ||||
\(818\) | − | 1206.91i | − | 1.47544i | ||||||
\(819\) | 59.5545 | + | 249.754i | 0.0727161 | + | 0.304950i | ||||
\(820\) | 1135.93 | 1.38528 | ||||||||
\(821\) | 668.380 | + | 385.889i | 0.814104 | + | 0.470023i | 0.848379 | − | 0.529389i | \(-0.177579\pi\) |
−0.0342747 | + | 0.999412i | \(0.510912\pi\) | |||||||
\(822\) | −278.174 | − | 226.380i | −0.338411 | − | 0.275401i | ||||
\(823\) | −453.227 | − | 785.013i | −0.550702 | − | 0.953843i | −0.998224 | − | 0.0595705i | \(-0.981027\pi\) |
0.447522 | − | 0.894273i | \(-0.352306\pi\) | |||||||
\(824\) | 212.759i | 0.258202i | ||||||||
\(825\) | −294.104 | − | 47.3128i | −0.356489 | − | 0.0573489i | ||||
\(826\) | −1017.22 | + | 1888.38i | −1.23150 | + | 2.28617i | ||||
\(827\) | 509.463i | 0.616038i | 0.951380 | + | 0.308019i | \(0.0996660\pi\) | ||||
−0.951380 | + | 0.308019i | \(0.900334\pi\) | |||||||
\(828\) | 567.032 | − | 117.655i | 0.684822 | − | 0.142095i | ||||
\(829\) | 332.585 | − | 576.054i | 0.401188 | − | 0.694878i | −0.592682 | − | 0.805437i | \(-0.701931\pi\) |
0.993870 | + | 0.110559i | \(0.0352641\pi\) | |||||||
\(830\) | 282.002i | 0.339762i | ||||||||
\(831\) | −37.2249 | + | 231.396i | −0.0447953 | + | 0.278454i | ||||
\(832\) | 211.873 | − | 366.974i | 0.254655 | − | 0.441075i | ||||
\(833\) | −47.8119 | − | 809.654i | −0.0573973 | − | 0.971974i | ||||
\(834\) | −485.817 | − | 1274.83i | −0.582514 | − | 1.52857i | ||||
\(835\) | 200.572 | − | 347.402i | 0.240207 | − | 0.416050i | ||||
\(836\) | −767.790 | − | 443.284i | −0.918409 | − | 0.530244i | ||||
\(837\) | −799.021 | + | 36.0479i | −0.954625 | + | 0.0430679i | ||||
\(838\) | −651.985 | − | 1129.27i | −0.778025 | − | 1.34758i | ||||
\(839\) | 1237.78 | − | 714.635i | 1.47531 | − | 0.851770i | 0.475696 | − | 0.879610i | \(-0.342196\pi\) |
0.999612 | + | 0.0278396i | \(0.00886276\pi\) | |||||||
\(840\) | −711.083 | − | 544.632i | −0.846528 | − | 0.648372i | ||||
\(841\) | 641.052 | − | 1110.33i | 0.762250 | − | 1.32026i | ||||
\(842\) | 1489.30i | 1.76876i | ||||||||
\(843\) | −474.989 | − | 1246.42i | −0.563451 | − | 1.47855i | ||||
\(844\) | 698.082 | 0.827111 | ||||||||
\(845\) | 730.204 | − | 421.583i | 0.864147 | − | 0.498915i | ||||
\(846\) | −96.9027 | − | 467.018i | −0.114542 | − | 0.552031i | ||||
\(847\) | −637.020 | + | 1182.57i | −0.752090 | + | 1.39619i | ||||
\(848\) | 23.3304 | − | 13.4698i | 0.0275122 | − | 0.0158842i | ||||
\(849\) | −360.017 | + | 137.197i | −0.424048 | + | 0.161598i | ||||
\(850\) | 149.761 | + | 259.393i | 0.176189 | + | 0.305168i | ||||
\(851\) | −271.935 | + | 157.002i | −0.319547 | + | 0.184491i | ||||
\(852\) | −136.655 | − | 358.594i | −0.160393 | − | 0.420885i | ||||
\(853\) | 485.171 | + | 840.341i | 0.568782 | + | 0.985159i | 0.996687 | + | 0.0813353i | \(0.0259185\pi\) |
−0.427905 | + | 0.903824i | \(0.640748\pi\) | |||||||
\(854\) | 49.0841 | + | 1663.84i | 0.0574756 | + | 1.94830i | ||||
\(855\) | 382.356 | − | 79.3359i | 0.447200 | − | 0.0927905i | ||||
\(856\) | −472.165 | − | 817.813i | −0.551594 | − | 0.955389i | ||||
\(857\) | 1510.42i | 1.76245i | 0.472700 | + | 0.881223i | \(0.343279\pi\) | ||||
−0.472700 | + | 0.881223i | \(0.656721\pi\) | |||||||
\(858\) | −651.462 | + | 248.262i | −0.759279 | + | 0.289349i | ||||
\(859\) | −1228.38 | −1.43001 | −0.715007 | − | 0.699118i | \(-0.753576\pi\) | ||||
−0.715007 | + | 0.699118i | \(0.753576\pi\) | |||||||
\(860\) | 205.339 | + | 118.552i | 0.238766 | + | 0.137852i | ||||
\(861\) | 258.695 | + | 622.983i | 0.300459 | + | 0.723557i | ||||
\(862\) | 367.683 | + | 636.845i | 0.426546 | + | 0.738800i | ||||
\(863\) | −1292.69 | + | 746.335i | −1.49790 | + | 0.864815i | −0.999997 | − | 0.00241587i | \(-0.999231\pi\) |
−0.497906 | + | 0.867231i | \(0.665898\pi\) | |||||||
\(864\) | 40.3302 | + | 893.941i | 0.0466785 | + | 1.03465i | ||||
\(865\) | −584.205 | + | 1011.87i | −0.675382 | + | 1.16980i | ||||
\(866\) | −2170.89 | − | 1253.36i | −2.50680 | − | 1.44730i | ||||
\(867\) | 42.1058 | − | 16.0459i | 0.0485650 | − | 0.0185073i | ||||
\(868\) | −696.228 | − | 1127.74i | −0.802106 | − | 1.29924i | ||||
\(869\) | 2127.48 | + | 1228.30i | 2.44820 | + | 1.41347i | ||||
\(870\) | 2434.17 | + | 391.589i | 2.79790 | + | 0.450102i | ||||
\(871\) | 49.6841 | 0.0570425 | ||||||||
\(872\) | 227.951 | + | 131.608i | 0.261412 | + | 0.150926i | ||||
\(873\) | −314.934 | − | 1517.81i | −0.360749 | − | 1.73861i | ||||
\(874\) | −254.497 | −0.291187 | ||||||||
\(875\) | −661.045 | − | 356.088i | −0.755480 | − | 0.406958i | ||||
\(876\) | 70.0031 | − | 435.149i | 0.0799122 | − | 0.496746i | ||||
\(877\) | −346.948 | −0.395608 | −0.197804 | − | 0.980242i | \(-0.563381\pi\) | ||||
−0.197804 | + | 0.980242i | \(0.563381\pi\) | |||||||
\(878\) | 192.071 | − | 110.892i | 0.218760 | − | 0.126301i | ||||
\(879\) | 93.2586 | − | 114.595i | 0.106096 | − | 0.130370i | ||||
\(880\) | −35.0319 | + | 60.6770i | −0.0398090 | + | 0.0689512i | ||||
\(881\) | − | 738.403i | − | 0.838142i | −0.907953 | − | 0.419071i | \(-0.862356\pi\) | ||
0.907953 | − | 0.419071i | \(-0.137644\pi\) | |||||||
\(882\) | 365.499 | − | 1373.80i | 0.414398 | − | 1.55760i | ||||
\(883\) | 872.215 | 0.987786 | 0.493893 | − | 0.869523i | \(-0.335573\pi\) | ||||
0.493893 | + | 0.869523i | \(0.335573\pi\) | |||||||
\(884\) | 373.392 | + | 215.578i | 0.422389 | + | 0.243866i | ||||
\(885\) | 1474.38 | − | 561.864i | 1.66597 | − | 0.634874i | ||||
\(886\) | 335.783 | + | 581.593i | 0.378987 | + | 0.656426i | ||||
\(887\) | 633.281i | 0.713958i | 0.934112 | + | 0.356979i | \(0.116193\pi\) | ||||
−0.934112 | + | 0.356979i | \(0.883807\pi\) | |||||||
\(888\) | 256.855 | + | 674.013i | 0.289252 | + | 0.759023i | ||||
\(889\) | 46.7225 | − | 86.7359i | 0.0525562 | − | 0.0975657i | ||||
\(890\) | 966.821i | 1.08632i | ||||||||
\(891\) | 853.374 | − | 1150.92i | 0.957771 | − | 1.29172i | ||||
\(892\) | 596.753 | − | 1033.61i | 0.669005 | − | 1.15875i | ||||
\(893\) | 128.923i | 0.144371i | ||||||||
\(894\) | 867.973 | + | 706.363i | 0.970887 | + | 0.790115i | ||||
\(895\) | −222.323 | + | 385.075i | −0.248406 | + | 0.430251i | ||||
\(896\) | −1206.73 | + | 744.993i | −1.34680 | + | 0.831466i | ||||
\(897\) | −77.6955 | + | 95.4716i | −0.0866171 | + | 0.106434i | ||||
\(898\) | 417.524 | − | 723.172i | 0.464949 | − | 0.805314i | ||||
\(899\) | 1182.09 | + | 682.483i | 1.31490 | + | 0.759158i | ||||
\(900\) | 65.6019 | + | 316.166i | 0.0728910 | + | 0.351295i | ||||
\(901\) | 311.443 | + | 539.436i | 0.345664 | + | 0.598708i | ||||
\(902\) | −1586.22 | + | 915.805i | −1.75856 | + | 1.01531i | ||||
\(903\) | −18.2546 | + | 139.614i | −0.0202155 | + | 0.154611i | ||||
\(904\) | 300.084 | − | 519.761i | 0.331951 | − | 0.574957i | ||||
\(905\) | − | 680.244i | − | 0.751650i | ||||||
\(906\) | −917.553 | + | 1127.48i | −1.01275 | + | 1.24446i | ||||
\(907\) | 1121.71 | 1.23672 | 0.618361 | − | 0.785894i | \(-0.287797\pi\) | ||||
0.618361 | + | 0.785894i | \(0.287797\pi\) | |||||||
\(908\) | 1121.12 | − | 647.278i | 1.23471 | − | 0.712861i | ||||
\(909\) | 48.8813 | − | 147.995i | 0.0537748 | − | 0.162811i | ||||
\(910\) | 508.607 | − | 15.0041i | 0.558909 | − | 0.0164881i | ||||
\(911\) | −770.852 | + | 445.052i | −0.846160 | + | 0.488531i | −0.859353 | − | 0.511382i | \(-0.829134\pi\) |
0.0131931 | + | 0.999913i | \(0.495800\pi\) | |||||||
\(912\) | 2.67495 | − | 16.6279i | 0.00293306 | − | 0.0182323i | ||||
\(913\) | −139.838 | − | 242.207i | −0.153163 | − | 0.265287i | ||||
\(914\) | 445.099 | − | 256.978i | 0.486979 | − | 0.281158i | ||||
\(915\) | 772.883 | − | 949.713i | 0.844681 | − | 1.03794i | ||||
\(916\) | −253.332 | − | 438.784i | −0.276563 | − | 0.479021i | ||||
\(917\) | 137.244 | + | 73.9297i | 0.149666 | + | 0.0806213i | ||||
\(918\) | −1439.19 | + | 64.9291i | −1.56775 | + | 0.0707289i | ||||
\(919\) | 567.953 | + | 983.724i | 0.618012 | + | 1.07043i | 0.989848 | + | 0.142130i | \(0.0453952\pi\) |
−0.371836 | + | 0.928299i | \(0.621271\pi\) | |||||||
\(920\) | − | 429.402i | − | 0.466741i | ||||||
\(921\) | 184.542 | − | 1147.14i | 0.200371 | − | 1.24554i | ||||
\(922\) | 658.502 | 0.714211 | ||||||||
\(923\) | 70.6391 | + | 40.7835i | 0.0765321 | + | 0.0441858i | ||||
\(924\) | 2354.12 | + | 307.802i | 2.54775 | + | 0.333119i | ||||
\(925\) | −87.5408 | − | 151.625i | −0.0946387 | − | 0.163919i | ||||
\(926\) | 2127.85 | − | 1228.52i | 2.29790 | − | 1.32669i | ||||
\(927\) | 235.865 | + | 77.9040i | 0.254439 | + | 0.0840388i | ||||
\(928\) | 763.559 | − | 1322.52i | 0.822800 | − | 1.42513i | ||||
\(929\) | 622.843 | + | 359.598i | 0.670444 | + | 0.387081i | 0.796245 | − | 0.604974i | \(-0.206817\pi\) |
−0.125801 | + | 0.992056i | \(0.540150\pi\) | |||||||
\(930\) | −251.756 | + | 1564.95i | −0.270706 | + | 1.68275i | ||||
\(931\) | −172.176 | + | 343.521i | −0.184937 | + | 0.368980i | ||||
\(932\) | −1805.12 | − | 1042.18i | −1.93682 | − | 1.11822i | ||||
\(933\) | −108.003 | − | 283.409i | −0.115759 | − | 0.303761i | ||||
\(934\) | −1719.85 | −1.84138 | ||||||||
\(935\) | −1402.95 | − | 809.994i | −1.50048 | − | 0.866303i | ||||
\(936\) | 188.177 | + | 211.041i | 0.201044 | + | 0.225471i | ||||
\(937\) | −1522.34 | −1.62470 | −0.812348 | − | 0.583172i | \(-0.801811\pi\) | ||||
−0.812348 | + | 0.583172i | \(0.801811\pi\) | |||||||
\(938\) | −242.185 | − | 130.459i | −0.258193 | − | 0.139082i | ||||
\(939\) | −848.815 | − | 690.772i | −0.903957 | − | 0.735646i | ||||
\(940\) | −581.377 | −0.618487 | ||||||||
\(941\) | −886.384 | + | 511.754i | −0.941960 | + | 0.543841i | −0.890574 | − | 0.454838i | \(-0.849697\pi\) |
−0.0513858 | + | 0.998679i | \(0.516364\pi\) | |||||||
\(942\) | 2616.66 | + | 420.946i | 2.77778 | + | 0.446865i | ||||
\(943\) | −161.695 | + | 280.063i | −0.171468 | + | 0.296992i | ||||
\(944\) | − | 68.0487i | − | 0.0720855i | ||||||
\(945\) | −864.151 | + | 588.886i | −0.914446 | + | 0.623159i | ||||
\(946\) | −382.316 | −0.404139 | ||||||||
\(947\) | 1361.76 | + | 786.215i | 1.43798 | + | 0.830217i | 0.997709 | − | 0.0676499i | \(-0.0215501\pi\) |
0.440268 | + | 0.897866i | \(0.354883\pi\) | |||||||
\(948\) | 422.947 | − | 2629.10i | 0.446146 | − | 2.77331i | ||||
\(949\) | 46.8406 | + | 81.1303i | 0.0493578 | + | 0.0854903i | ||||
\(950\) | − | 141.902i | − | 0.149371i | ||||||
\(951\) | −62.7750 | + | 77.1374i | −0.0660095 | + | 0.0811119i | ||||
\(952\) | −469.207 | − | 760.014i | −0.492864 | − | 0.798334i | ||||
\(953\) | − | 1342.92i | − | 1.40915i | −0.709629 | − | 0.704576i | \(-0.751137\pi\) | ||
0.709629 | − | 0.704576i | \(-0.248863\pi\) | |||||||
\(954\) | 221.808 | + | 1068.99i | 0.232503 | + | 1.12054i | ||||
\(955\) | 983.453 | − | 1703.39i | 1.02979 | − | 1.78366i | ||||
\(956\) | − | 1556.60i | − | 1.62824i | ||||||
\(957\) | −2284.85 | + | 870.719i | −2.38751 | + | 0.909842i | ||||
\(958\) | −974.348 | + | 1687.62i | −1.01706 | + | 1.76161i | ||||
\(959\) | −228.552 | − | 123.115i | −0.238323 | − | 0.128379i | ||||
\(960\) | 1703.94 | + | 274.115i | 1.77493 | + | 0.285536i | ||||
\(961\) | 41.7250 | − | 72.2699i | 0.0434183 | − | 0.0752028i | ||||
\(962\) | −354.860 | − | 204.879i | −0.368877 | − | 0.212971i | ||||
\(963\) | −1079.52 | + | 223.992i | −1.12099 | + | 0.232598i | ||||
\(964\) | 90.5672 | + | 156.867i | 0.0939493 | + | 0.162725i | ||||
\(965\) | 190.034 | − | 109.716i | 0.196927 | − | 0.113696i | ||||
\(966\) | 629.413 | − | 261.366i | 0.651567 | − | 0.270565i | ||||
\(967\) | −867.804 | + | 1503.08i | −0.897418 | + | 1.55437i | −0.0666355 | + | 0.997777i | \(0.521226\pi\) |
−0.830783 | + | 0.556597i | \(0.812107\pi\) | |||||||
\(968\) | 1479.23i | 1.52813i | ||||||||
\(969\) | 384.463 | + | 61.8491i | 0.396763 | + | 0.0638278i | ||||
\(970\) | −3072.00 | −3.16701 | ||||||||
\(971\) | 43.8474 | − | 25.3153i | 0.0451569 | − | 0.0260714i | −0.477252 | − | 0.878767i | \(-0.658367\pi\) |
0.522409 | + | 0.852695i | \(0.325034\pi\) | |||||||
\(972\) | −1495.20 | − | 420.133i | −1.53827 | − | 0.432236i | ||||
\(973\) | −518.753 | − | 840.269i | −0.533148 | − | 0.863586i | ||||
\(974\) | 436.071 | − | 251.766i | 0.447712 | − | 0.258486i | ||||
\(975\) | −53.2330 | − | 43.3214i | −0.0545980 | − | 0.0444322i | ||||
\(976\) | −26.4045 | − | 45.7340i | −0.0270538 | − | 0.0468586i | ||||
\(977\) | 506.717 | − | 292.553i | 0.518646 | − | 0.299440i | −0.217734 | − | 0.976008i | \(-0.569867\pi\) |
0.736381 | + | 0.676568i | \(0.236533\pi\) | |||||||
\(978\) | −2125.87 | − | 341.991i | −2.17369 | − | 0.349684i | ||||
\(979\) | −479.423 | − | 830.386i | −0.489707 | − | 0.848198i | ||||
\(980\) | −1549.11 | − | 776.427i | −1.58072 | − | 0.792272i | ||||
\(981\) | 229.367 | − | 204.517i | 0.233810 | − | 0.208479i | ||||
\(982\) | 645.630 | + | 1118.26i | 0.657464 | + | 1.13876i | ||||
\(983\) | − | 968.896i | − | 0.985653i | −0.870128 | − | 0.492826i | \(-0.835964\pi\) | ||
0.870128 | − | 0.492826i | \(-0.164036\pi\) | |||||||
\(984\) | 576.173 | + | 468.894i | 0.585541 | + | 0.476518i | ||||
\(985\) | −722.793 | −0.733800 | ||||||||
\(986\) | 2129.18 | + | 1229.28i | 2.15941 | + | 1.24674i | ||||
\(987\) | −132.402 | − | 318.847i | −0.134146 | − | 0.323047i | ||||
\(988\) | −102.133 | − | 176.900i | −0.103374 | − | 0.179048i | ||||
\(989\) | −58.4582 | + | 33.7508i | −0.0591084 | + | 0.0341262i | ||||
\(990\) | −1889.69 | − | 2119.30i | −1.90878 | − | 2.14070i | ||||
\(991\) | −104.448 | + | 180.910i | −0.105397 | + | 0.182553i | −0.913900 | − | 0.405939i | \(-0.866945\pi\) |
0.808503 | + | 0.588492i | \(0.200278\pi\) | |||||||
\(992\) | 850.263 | + | 490.900i | 0.857120 | + | 0.494859i | ||||
\(993\) | 210.598 | + | 171.386i | 0.212083 | + | 0.172594i | ||||
\(994\) | −237.242 | − | 384.281i | −0.238674 | − | 0.386601i | ||||
\(995\) | −1039.99 | − | 600.439i | −1.04522 | − | 0.603457i | ||||
\(996\) | −191.357 | + | 235.138i | −0.192126 | + | 0.236082i | ||||
\(997\) | 152.170 | 0.152628 | 0.0763140 | − | 0.997084i | \(-0.475685\pi\) | ||||
0.0763140 | + | 0.997084i | \(0.475685\pi\) | |||||||
\(998\) | 341.392 | + | 197.103i | 0.342077 | + | 0.197498i | ||||
\(999\) | 841.262 | − | 37.9536i | 0.842105 | − | 0.0379916i |
(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 | 63.3.n.b.32.2 | yes | 22 | |
3.2 | odd | 2 | 189.3.n.b.179.10 | 22 | |||
7.2 | even | 3 | 63.3.j.b.23.10 | yes | 22 | ||
7.3 | odd | 6 | 441.3.r.f.50.10 | 22 | |||
7.4 | even | 3 | 441.3.r.g.50.10 | 22 | |||
7.5 | odd | 6 | 441.3.j.f.275.10 | 22 | |||
7.6 | odd | 2 | 441.3.n.f.410.2 | 22 | |||
9.2 | odd | 6 | 63.3.j.b.11.2 | ✓ | 22 | ||
9.7 | even | 3 | 189.3.j.b.116.10 | 22 | |||
21.2 | odd | 6 | 189.3.j.b.44.2 | 22 | |||
63.2 | odd | 6 | inner | 63.3.n.b.2.2 | yes | 22 | |
63.11 | odd | 6 | 441.3.r.g.344.10 | 22 | |||
63.16 | even | 3 | 189.3.n.b.170.10 | 22 | |||
63.20 | even | 6 | 441.3.j.f.263.2 | 22 | |||
63.38 | even | 6 | 441.3.r.f.344.10 | 22 | |||
63.47 | even | 6 | 441.3.n.f.128.2 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.3.j.b.11.2 | ✓ | 22 | 9.2 | odd | 6 | ||
63.3.j.b.23.10 | yes | 22 | 7.2 | even | 3 | ||
63.3.n.b.2.2 | yes | 22 | 63.2 | odd | 6 | inner | |
63.3.n.b.32.2 | yes | 22 | 1.1 | even | 1 | trivial | |
189.3.j.b.44.2 | 22 | 21.2 | odd | 6 | |||
189.3.j.b.116.10 | 22 | 9.7 | even | 3 | |||
189.3.n.b.170.10 | 22 | 63.16 | even | 3 | |||
189.3.n.b.179.10 | 22 | 3.2 | odd | 2 | |||
441.3.j.f.263.2 | 22 | 63.20 | even | 6 | |||
441.3.j.f.275.10 | 22 | 7.5 | odd | 6 | |||
441.3.n.f.128.2 | 22 | 63.47 | even | 6 | |||
441.3.n.f.410.2 | 22 | 7.6 | odd | 2 | |||
441.3.r.f.50.10 | 22 | 7.3 | odd | 6 | |||
441.3.r.f.344.10 | 22 | 63.38 | even | 6 | |||
441.3.r.g.50.10 | 22 | 7.4 | even | 3 | |||
441.3.r.g.344.10 | 22 | 63.11 | odd | 6 |