Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,4,Mod(22,63)]
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([2, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.22");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.f (of order \(3\), 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: | \(3.71712033036\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 58 x^{14} - 129 x^{13} + 2107 x^{12} - 4455 x^{11} + 42901 x^{10} - 76404 x^{9} + 599392 x^{8} - 1089732 x^{7} + 4808401 x^{6} - 7939134 x^{5} + \cdots + 21307456 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 43.1 | ||
Root | \(2.62188 - 4.54123i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 63.43 |
Dual form | 63.4.f.b.22.1 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.62188 | + | 4.54123i | −0.926974 | + | 1.60557i | −0.138618 | + | 0.990346i | \(0.544266\pi\) |
−0.788356 | + | 0.615220i | \(0.789067\pi\) | |||||||
\(3\) | −4.41799 | − | 2.73521i | −0.850242 | − | 0.526392i | ||||
\(4\) | −9.74848 | − | 16.8849i | −1.21856 | − | 2.11061i | ||||
\(5\) | 2.03009 | + | 3.51621i | 0.181576 | + | 0.314500i | 0.942418 | − | 0.334439i | \(-0.108547\pi\) |
−0.760841 | + | 0.648938i | \(0.775213\pi\) | |||||||
\(6\) | 24.0046 | − | 12.8917i | 1.63331 | − | 0.877168i | ||||
\(7\) | 3.50000 | − | 6.06218i | 0.188982 | − | 0.327327i | ||||
\(8\) | 60.2873 | 2.66435 | ||||||||
\(9\) | 12.0372 | + | 24.1683i | 0.445824 | + | 0.895121i | ||||
\(10\) | −21.2906 | −0.673266 | ||||||||
\(11\) | 7.57508 | − | 13.1204i | 0.207634 | − | 0.359633i | −0.743335 | − | 0.668920i | \(-0.766757\pi\) |
0.950969 | + | 0.309287i | \(0.100090\pi\) | |||||||
\(12\) | −3.11500 | + | 101.261i | −0.0749354 | + | 2.43597i | ||||
\(13\) | −24.2972 | − | 42.0840i | −0.518371 | − | 0.897846i | −0.999772 | − | 0.0213450i | \(-0.993205\pi\) |
0.481401 | − | 0.876501i | \(-0.340128\pi\) | |||||||
\(14\) | 18.3531 | + | 31.7886i | 0.350363 | + | 0.606847i | ||||
\(15\) | 0.648689 | − | 21.0873i | 0.0111660 | − | 0.362981i | ||||
\(16\) | −80.0780 | + | 138.699i | −1.25122 | + | 2.16717i | ||||
\(17\) | 107.332 | 1.53128 | 0.765641 | − | 0.643269i | \(-0.222422\pi\) | ||||
0.765641 | + | 0.643269i | \(0.222422\pi\) | |||||||
\(18\) | −141.314 | − | 8.70243i | −1.85044 | − | 0.113955i | ||||
\(19\) | 109.663 | 1.32413 | 0.662063 | − | 0.749448i | \(-0.269681\pi\) | ||||
0.662063 | + | 0.749448i | \(0.269681\pi\) | |||||||
\(20\) | 39.5805 | − | 68.5555i | 0.442524 | − | 0.766474i | ||||
\(21\) | −32.0443 | + | 17.2094i | −0.332983 | + | 0.178828i | ||||
\(22\) | 39.7219 | + | 68.8003i | 0.384942 | + | 0.666740i | ||||
\(23\) | −92.3377 | − | 159.934i | −0.837119 | − | 1.44993i | −0.892293 | − | 0.451456i | \(-0.850905\pi\) |
0.0551740 | − | 0.998477i | \(-0.482429\pi\) | |||||||
\(24\) | −266.348 | − | 164.898i | −2.26534 | − | 1.40249i | ||||
\(25\) | 54.2575 | − | 93.9767i | 0.434060 | − | 0.751814i | ||||
\(26\) | 254.817 | 1.92207 | ||||||||
\(27\) | 12.9250 | − | 139.699i | 0.0921262 | − | 0.995747i | ||||
\(28\) | −136.479 | −0.921145 | ||||||||
\(29\) | −47.0490 | + | 81.4912i | −0.301268 | + | 0.521812i | −0.976423 | − | 0.215864i | \(-0.930743\pi\) |
0.675155 | + | 0.737676i | \(0.264077\pi\) | |||||||
\(30\) | 94.0614 | + | 58.2342i | 0.572440 | + | 0.354402i | ||||
\(31\) | −67.6261 | − | 117.132i | −0.391806 | − | 0.678629i | 0.600881 | − | 0.799338i | \(-0.294816\pi\) |
−0.992688 | + | 0.120709i | \(0.961483\pi\) | |||||||
\(32\) | −178.760 | − | 309.622i | −0.987520 | − | 1.71043i | ||||
\(33\) | −69.3538 | + | 37.2464i | −0.365847 | + | 0.196478i | ||||
\(34\) | −281.411 | + | 487.418i | −1.41946 | + | 2.45857i | ||||
\(35\) | 28.4212 | 0.137259 | ||||||||
\(36\) | 290.733 | − | 438.851i | 1.34599 | − | 2.03172i | ||||
\(37\) | −149.833 | −0.665741 | −0.332870 | − | 0.942973i | \(-0.608017\pi\) | ||||
−0.332870 | + | 0.942973i | \(0.608017\pi\) | |||||||
\(38\) | −287.523 | + | 498.004i | −1.22743 | + | 2.12597i | ||||
\(39\) | −7.76386 | + | 252.384i | −0.0318772 | + | 1.03625i | ||||
\(40\) | 122.388 | + | 211.983i | 0.483783 | + | 0.837936i | ||||
\(41\) | 148.970 | + | 258.023i | 0.567443 | + | 0.982840i | 0.996818 | + | 0.0797135i | \(0.0254005\pi\) |
−0.429375 | + | 0.903126i | \(0.641266\pi\) | |||||||
\(42\) | 5.86451 | − | 190.641i | 0.0215456 | − | 0.700395i | ||||
\(43\) | 193.371 | − | 334.929i | 0.685787 | − | 1.18782i | −0.287401 | − | 0.957810i | \(-0.592791\pi\) |
0.973189 | − | 0.230008i | \(-0.0738753\pi\) | |||||||
\(44\) | −295.382 | −1.01206 | ||||||||
\(45\) | −60.5441 | + | 91.3892i | −0.200564 | + | 0.302744i | ||||
\(46\) | 968.393 | 3.10395 | ||||||||
\(47\) | 36.7525 | − | 63.6573i | 0.114062 | − | 0.197561i | −0.803342 | − | 0.595517i | \(-0.796947\pi\) |
0.917404 | + | 0.397956i | \(0.130280\pi\) | |||||||
\(48\) | 733.155 | − | 393.741i | 2.20462 | − | 1.18399i | ||||
\(49\) | −24.5000 | − | 42.4352i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 284.513 | + | 492.791i | 0.804724 | + | 1.39382i | ||||
\(51\) | −474.190 | − | 293.575i | −1.30196 | − | 0.806054i | ||||
\(52\) | −473.722 | + | 820.510i | −1.26333 | + | 2.18816i | ||||
\(53\) | −633.800 | −1.64262 | −0.821312 | − | 0.570479i | \(-0.806757\pi\) | ||||
−0.821312 | + | 0.570479i | \(0.806757\pi\) | |||||||
\(54\) | 600.519 | + | 424.970i | 1.51334 | + | 1.07095i | ||||
\(55\) | 61.5123 | 0.150806 | ||||||||
\(56\) | 211.005 | − | 365.472i | 0.503514 | − | 0.872112i | ||||
\(57\) | −484.490 | − | 299.951i | −1.12583 | − | 0.697009i | ||||
\(58\) | −246.713 | − | 427.320i | −0.558535 | − | 0.967412i | ||||
\(59\) | 162.787 | + | 281.955i | 0.359204 | + | 0.622160i | 0.987828 | − | 0.155550i | \(-0.0497149\pi\) |
−0.628624 | + | 0.777709i | \(0.716382\pi\) | |||||||
\(60\) | −362.380 | + | 194.616i | −0.779718 | + | 0.418747i | ||||
\(61\) | 34.7647 | − | 60.2142i | 0.0729699 | − | 0.126388i | −0.827232 | − | 0.561861i | \(-0.810086\pi\) |
0.900202 | + | 0.435473i | \(0.143419\pi\) | |||||||
\(62\) | 709.229 | 1.45278 | ||||||||
\(63\) | 188.643 | + | 11.6171i | 0.377250 | + | 0.0232319i | ||||
\(64\) | 593.502 | 1.15918 | ||||||||
\(65\) | 98.6508 | − | 170.868i | 0.188248 | − | 0.326055i | ||||
\(66\) | 12.6926 | − | 412.607i | 0.0236720 | − | 0.769521i | ||||
\(67\) | 139.762 | + | 242.074i | 0.254845 | + | 0.441404i | 0.964853 | − | 0.262789i | \(-0.0846423\pi\) |
−0.710009 | + | 0.704193i | \(0.751309\pi\) | |||||||
\(68\) | −1046.32 | − | 1812.28i | −1.86596 | − | 3.23193i | ||||
\(69\) | −29.5053 | + | 959.148i | −0.0514786 | + | 1.67345i | ||||
\(70\) | −74.5169 | + | 129.067i | −0.127235 | + | 0.220378i | ||||
\(71\) | 497.917 | 0.832280 | 0.416140 | − | 0.909301i | \(-0.363383\pi\) | ||||
0.416140 | + | 0.909301i | \(0.363383\pi\) | |||||||
\(72\) | 725.692 | + | 1457.04i | 1.18783 | + | 2.38491i | ||||
\(73\) | 457.155 | 0.732957 | 0.366479 | − | 0.930426i | \(-0.380563\pi\) | ||||
0.366479 | + | 0.930426i | \(0.380563\pi\) | |||||||
\(74\) | 392.844 | − | 680.426i | 0.617124 | − | 1.06889i | ||||
\(75\) | −496.755 | + | 266.782i | −0.764805 | + | 0.410738i | ||||
\(76\) | −1069.05 | − | 1851.64i | −1.61353 | − | 2.79471i | ||||
\(77\) | −53.0256 | − | 91.8430i | −0.0784783 | − | 0.135928i | ||||
\(78\) | −1125.78 | − | 696.979i | −1.63422 | − | 1.01176i | ||||
\(79\) | 548.381 | − | 949.824i | 0.780984 | − | 1.35270i | −0.150386 | − | 0.988627i | \(-0.548052\pi\) |
0.931369 | − | 0.364076i | \(-0.118615\pi\) | |||||||
\(80\) | −650.261 | −0.908767 | ||||||||
\(81\) | −439.210 | + | 581.838i | −0.602483 | + | 0.798132i | ||||
\(82\) | −1562.32 | −2.10402 | ||||||||
\(83\) | −39.3239 | + | 68.1109i | −0.0520043 | + | 0.0900740i | −0.890856 | − | 0.454286i | \(-0.849894\pi\) |
0.838851 | + | 0.544360i | \(0.183228\pi\) | |||||||
\(84\) | 602.962 | + | 373.298i | 0.783196 | + | 0.484883i | ||||
\(85\) | 217.893 | + | 377.401i | 0.278045 | + | 0.481587i | ||||
\(86\) | 1013.99 | + | 1756.29i | 1.27141 | + | 2.20215i | ||||
\(87\) | 430.758 | − | 231.338i | 0.530828 | − | 0.285081i | ||||
\(88\) | 456.681 | − | 790.995i | 0.553209 | − | 0.958186i | ||||
\(89\) | 292.702 | 0.348611 | 0.174305 | − | 0.984692i | \(-0.444232\pi\) | ||||
0.174305 | + | 0.984692i | \(0.444232\pi\) | |||||||
\(90\) | −256.279 | − | 514.556i | −0.300158 | − | 0.602655i | ||||
\(91\) | −340.161 | −0.391852 | ||||||||
\(92\) | −1800.31 | + | 3118.22i | −2.04016 | + | 3.53366i | ||||
\(93\) | −21.6091 | + | 702.458i | −0.0240941 | + | 0.783242i | ||||
\(94\) | 192.721 | + | 333.803i | 0.211465 | + | 0.366268i | ||||
\(95\) | 222.625 | + | 385.598i | 0.240430 | + | 0.416438i | ||||
\(96\) | −57.1206 | + | 1856.85i | −0.0607275 | + | 1.97411i | ||||
\(97\) | −82.2477 | + | 142.457i | −0.0860927 | + | 0.149117i | −0.905856 | − | 0.423585i | \(-0.860771\pi\) |
0.819764 | + | 0.572702i | \(0.194105\pi\) | |||||||
\(98\) | 256.944 | 0.264850 | ||||||||
\(99\) | 408.281 | + | 25.1429i | 0.414483 | + | 0.0255248i | ||||
\(100\) | −2115.71 | −2.11571 | ||||||||
\(101\) | −4.68272 | + | 8.11072i | −0.00461335 | + | 0.00799056i | −0.868323 | − | 0.495999i | \(-0.834802\pi\) |
0.863710 | + | 0.503990i | \(0.168135\pi\) | |||||||
\(102\) | 2576.46 | − | 1383.69i | 2.50105 | − | 1.34319i | ||||
\(103\) | −25.1731 | − | 43.6011i | −0.0240814 | − | 0.0417101i | 0.853734 | − | 0.520710i | \(-0.174333\pi\) |
−0.877815 | + | 0.479000i | \(0.840999\pi\) | |||||||
\(104\) | −1464.81 | − | 2537.13i | −1.38112 | − | 2.39217i | ||||
\(105\) | −125.565 | − | 77.7380i | −0.116703 | − | 0.0722520i | ||||
\(106\) | 1661.74 | − | 2878.23i | 1.52267 | − | 2.63734i | ||||
\(107\) | −618.870 | −0.559144 | −0.279572 | − | 0.960125i | \(-0.590193\pi\) | ||||
−0.279572 | + | 0.960125i | \(0.590193\pi\) | |||||||
\(108\) | −2484.81 | + | 1143.62i | −2.21389 | + | 1.01894i | ||||
\(109\) | −112.976 | −0.0992762 | −0.0496381 | − | 0.998767i | \(-0.515807\pi\) | ||||
−0.0496381 | + | 0.998767i | \(0.515807\pi\) | |||||||
\(110\) | −161.278 | + | 279.341i | −0.139793 | + | 0.242129i | ||||
\(111\) | 661.961 | + | 409.825i | 0.566041 | + | 0.350440i | ||||
\(112\) | 560.546 | + | 970.894i | 0.472916 | + | 0.819115i | ||||
\(113\) | −661.322 | − | 1145.44i | −0.550549 | − | 0.953578i | −0.998235 | − | 0.0593874i | \(-0.981085\pi\) |
0.447686 | − | 0.894191i | \(-0.352248\pi\) | |||||||
\(114\) | 2632.42 | − | 1413.74i | 2.16271 | − | 1.16148i | ||||
\(115\) | 374.907 | − | 649.358i | 0.304002 | − | 0.526547i | ||||
\(116\) | 1834.63 | 1.46845 | ||||||||
\(117\) | 724.625 | − | 1093.80i | 0.572578 | − | 0.864286i | ||||
\(118\) | −1707.23 | −1.33189 | ||||||||
\(119\) | 375.661 | − | 650.664i | 0.289385 | − | 0.501229i | ||||
\(120\) | 39.1077 | − | 1271.30i | 0.0297502 | − | 0.967108i | ||||
\(121\) | 550.736 | + | 953.903i | 0.413776 | + | 0.716682i | ||||
\(122\) | 182.298 | + | 315.749i | 0.135282 | + | 0.234316i | ||||
\(123\) | 47.6014 | − | 1547.41i | 0.0348949 | − | 1.13435i | ||||
\(124\) | −1318.50 | + | 2283.71i | −0.954880 | + | 1.65390i | ||||
\(125\) | 948.111 | 0.678413 | ||||||||
\(126\) | −547.354 | + | 826.210i | −0.387001 | + | 0.584164i | ||||
\(127\) | 644.235 | 0.450131 | 0.225065 | − | 0.974344i | \(-0.427740\pi\) | ||||
0.225065 | + | 0.974344i | \(0.427740\pi\) | |||||||
\(128\) | −126.008 | + | 218.252i | −0.0870125 | + | 0.150710i | ||||
\(129\) | −1770.41 | + | 950.801i | −1.20834 | + | 0.648941i | ||||
\(130\) | 517.301 | + | 895.991i | 0.349002 | + | 0.604489i | ||||
\(131\) | −810.755 | − | 1404.27i | −0.540733 | − | 0.936577i | −0.998862 | − | 0.0476914i | \(-0.984814\pi\) |
0.458129 | − | 0.888886i | \(-0.348520\pi\) | |||||||
\(132\) | 1305.00 | + | 807.933i | 0.860494 | + | 0.532739i | ||||
\(133\) | 383.820 | − | 664.796i | 0.250236 | − | 0.433422i | ||||
\(134\) | −1465.75 | −0.944938 | ||||||||
\(135\) | 517.452 | − | 238.155i | 0.329890 | − | 0.151831i | ||||
\(136\) | 6470.74 | 4.07986 | ||||||||
\(137\) | −781.158 | + | 1353.01i | −0.487145 | + | 0.843760i | −0.999891 | − | 0.0147805i | \(-0.995295\pi\) |
0.512746 | + | 0.858541i | \(0.328628\pi\) | |||||||
\(138\) | −4278.35 | − | 2648.76i | −2.63911 | − | 1.63389i | ||||
\(139\) | 1576.40 | + | 2730.40i | 0.961930 | + | 1.66611i | 0.717645 | + | 0.696409i | \(0.245220\pi\) |
0.244285 | + | 0.969703i | \(0.421447\pi\) | |||||||
\(140\) | −277.064 | − | 479.888i | −0.167258 | − | 0.289700i | ||||
\(141\) | −336.488 | + | 180.711i | −0.200975 | + | 0.107933i | ||||
\(142\) | −1305.48 | + | 2261.15i | −0.771501 | + | 1.33628i | ||||
\(143\) | −736.213 | −0.430526 | ||||||||
\(144\) | −4316.03 | − | 265.792i | −2.49771 | − | 0.153815i | ||||
\(145\) | −382.054 | −0.218813 | ||||||||
\(146\) | −1198.60 | + | 2076.04i | −0.679432 | + | 1.17681i | ||||
\(147\) | −7.82867 | + | 254.491i | −0.00439250 | + | 0.142790i | ||||
\(148\) | 1460.65 | + | 2529.91i | 0.811245 | + | 1.40512i | ||||
\(149\) | −1046.83 | − | 1813.17i | −0.575571 | − | 0.996918i | −0.995979 | − | 0.0895830i | \(-0.971447\pi\) |
0.420409 | − | 0.907335i | \(-0.361887\pi\) | |||||||
\(150\) | 90.9125 | − | 2955.35i | 0.0494865 | − | 1.60869i | ||||
\(151\) | −740.388 | + | 1282.39i | −0.399019 | + | 0.691122i | −0.993605 | − | 0.112910i | \(-0.963983\pi\) |
0.594586 | + | 0.804032i | \(0.297316\pi\) | |||||||
\(152\) | 6611.28 | 3.52793 | ||||||||
\(153\) | 1291.98 | + | 2594.02i | 0.682681 | + | 1.37068i | ||||
\(154\) | 556.106 | 0.290989 | ||||||||
\(155\) | 274.574 | − | 475.575i | 0.142286 | − | 0.246446i | ||||
\(156\) | 4337.16 | − | 2329.27i | 2.22597 | − | 1.19546i | ||||
\(157\) | −330.730 | − | 572.840i | −0.168122 | − | 0.291195i | 0.769638 | − | 0.638481i | \(-0.220437\pi\) |
−0.937759 | + | 0.347286i | \(0.887103\pi\) | |||||||
\(158\) | 2875.58 | + | 4980.64i | 1.44790 | + | 2.50784i | ||||
\(159\) | 2800.12 | + | 1733.58i | 1.39663 | + | 0.864664i | ||||
\(160\) | 725.798 | − | 1257.12i | 0.358621 | − | 0.621150i | ||||
\(161\) | −1292.73 | −0.632803 | ||||||||
\(162\) | −1490.70 | − | 3520.06i | −0.722967 | − | 1.70717i | ||||
\(163\) | −1257.65 | −0.604338 | −0.302169 | − | 0.953254i | \(-0.597711\pi\) | ||||
−0.302169 | + | 0.953254i | \(0.597711\pi\) | |||||||
\(164\) | 2904.46 | − | 5030.67i | 1.38293 | − | 2.39530i | ||||
\(165\) | −271.761 | − | 168.249i | −0.128221 | − | 0.0793829i | ||||
\(166\) | −206.205 | − | 357.157i | −0.0964132 | − | 0.166993i | ||||
\(167\) | −177.970 | − | 308.253i | −0.0824654 | − | 0.142834i | 0.821843 | − | 0.569714i | \(-0.192946\pi\) |
−0.904308 | + | 0.426880i | \(0.859613\pi\) | |||||||
\(168\) | −1931.86 | + | 1037.51i | −0.887182 | + | 0.476461i | ||||
\(169\) | −82.2071 | + | 142.387i | −0.0374179 | + | 0.0648097i | ||||
\(170\) | −2285.15 | −1.03096 | ||||||||
\(171\) | 1320.04 | + | 2650.36i | 0.590327 | + | 1.18525i | ||||
\(172\) | −7540.31 | −3.34269 | ||||||||
\(173\) | −816.664 | + | 1414.50i | −0.358901 | + | 0.621634i | −0.987777 | − | 0.155871i | \(-0.950182\pi\) |
0.628877 | + | 0.777505i | \(0.283515\pi\) | |||||||
\(174\) | −78.8341 | + | 2562.71i | −0.0343471 | + | 1.11654i | ||||
\(175\) | −379.802 | − | 657.837i | −0.164059 | − | 0.284159i | ||||
\(176\) | 1213.19 | + | 2101.31i | 0.519591 | + | 0.899958i | ||||
\(177\) | 52.0165 | − | 1690.93i | 0.0220893 | − | 0.718068i | ||||
\(178\) | −767.429 | + | 1329.23i | −0.323153 | + | 0.559717i | ||||
\(179\) | −2250.77 | −0.939836 | −0.469918 | − | 0.882710i | \(-0.655716\pi\) | ||||
−0.469918 | + | 0.882710i | \(0.655716\pi\) | |||||||
\(180\) | 2133.31 | + | 131.374i | 0.883374 | + | 0.0544003i | ||||
\(181\) | −1518.02 | −0.623388 | −0.311694 | − | 0.950183i | \(-0.600896\pi\) | ||||
−0.311694 | + | 0.950183i | \(0.600896\pi\) | |||||||
\(182\) | 891.860 | − | 1544.75i | 0.363236 | − | 0.629144i | ||||
\(183\) | −318.289 | + | 170.937i | −0.128571 | + | 0.0690493i | ||||
\(184\) | −5566.79 | − | 9641.96i | −2.23038 | − | 3.86312i | ||||
\(185\) | −304.174 | − | 526.845i | −0.120883 | − | 0.209375i | ||||
\(186\) | −3133.37 | − | 1939.89i | −1.23521 | − | 0.764730i | ||||
\(187\) | 813.047 | − | 1408.24i | 0.317946 | − | 0.550698i | ||||
\(188\) | −1433.13 | −0.555965 | ||||||||
\(189\) | −801.646 | − | 567.302i | −0.308525 | − | 0.218334i | ||||
\(190\) | −2334.79 | −0.891490 | ||||||||
\(191\) | −241.003 | + | 417.429i | −0.0913003 | + | 0.158137i | −0.908059 | − | 0.418843i | \(-0.862436\pi\) |
0.816758 | + | 0.576980i | \(0.195769\pi\) | |||||||
\(192\) | −2622.08 | − | 1623.35i | −0.985587 | − | 0.610185i | ||||
\(193\) | 2211.69 | + | 3830.75i | 0.824874 | + | 1.42872i | 0.902016 | + | 0.431703i | \(0.142087\pi\) |
−0.0771417 | + | 0.997020i | \(0.524579\pi\) | |||||||
\(194\) | −431.287 | − | 747.011i | −0.159611 | − | 0.276455i | ||||
\(195\) | −903.199 | + | 485.063i | −0.331689 | + | 0.178134i | ||||
\(196\) | −477.676 | + | 827.359i | −0.174080 | + | 0.301516i | ||||
\(197\) | 1477.59 | 0.534387 | 0.267193 | − | 0.963643i | \(-0.413904\pi\) | ||||
0.267193 | + | 0.963643i | \(0.413904\pi\) | |||||||
\(198\) | −1184.64 | + | 1788.17i | −0.425196 | + | 0.641818i | ||||
\(199\) | −1981.16 | −0.705731 | −0.352866 | − | 0.935674i | \(-0.614793\pi\) | ||||
−0.352866 | + | 0.935674i | \(0.614793\pi\) | |||||||
\(200\) | 3271.04 | − | 5665.60i | 1.15649 | − | 2.00309i | ||||
\(201\) | 44.6591 | − | 1451.76i | 0.0156717 | − | 0.509449i | ||||
\(202\) | −24.5551 | − | 42.5306i | −0.00855291 | − | 0.0148141i | ||||
\(203\) | 329.343 | + | 570.439i | 0.113869 | + | 0.197226i | ||||
\(204\) | −334.339 | + | 10868.6i | −0.114747 | + | 3.73015i | ||||
\(205\) | −604.843 | + | 1047.62i | −0.206069 | + | 0.356921i | ||||
\(206\) | 264.003 | 0.0892912 | ||||||||
\(207\) | 2753.83 | − | 4156.80i | 0.924658 | − | 1.39574i | ||||
\(208\) | 7782.68 | 2.59438 | ||||||||
\(209\) | 830.706 | − | 1438.83i | 0.274934 | − | 0.476199i | ||||
\(210\) | 682.241 | − | 366.397i | 0.224186 | − | 0.120399i | ||||
\(211\) | −1074.92 | − | 1861.82i | −0.350713 | − | 0.607454i | 0.635661 | − | 0.771968i | \(-0.280728\pi\) |
−0.986375 | + | 0.164515i | \(0.947394\pi\) | |||||||
\(212\) | 6178.58 | + | 10701.6i | 2.00164 | + | 3.46694i | ||||
\(213\) | −2199.79 | − | 1361.91i | −0.707639 | − | 0.438105i | ||||
\(214\) | 1622.60 | − | 2810.43i | 0.518312 | − | 0.897743i | ||||
\(215\) | 1570.24 | 0.498091 | ||||||||
\(216\) | 779.210 | − | 8422.10i | 0.245456 | − | 2.65302i | ||||
\(217\) | −946.765 | −0.296178 | ||||||||
\(218\) | 296.208 | − | 513.048i | 0.0920264 | − | 0.159394i | ||||
\(219\) | −2019.70 | − | 1250.41i | −0.623191 | − | 0.385823i | ||||
\(220\) | −599.652 | − | 1038.63i | −0.183766 | − | 0.318292i | ||||
\(221\) | −2607.86 | − | 4516.95i | −0.793772 | − | 1.37485i | ||||
\(222\) | −3596.69 | + | 1931.60i | −1.08736 | + | 0.583967i | ||||
\(223\) | 2663.41 | − | 4613.16i | 0.799798 | − | 1.38529i | −0.119949 | − | 0.992780i | \(-0.538273\pi\) |
0.919747 | − | 0.392512i | \(-0.128394\pi\) | |||||||
\(224\) | −2502.64 | −0.746495 | ||||||||
\(225\) | 2924.36 | + | 180.089i | 0.866478 | + | 0.0533598i | ||||
\(226\) | 6935.63 | 2.04138 | ||||||||
\(227\) | 478.162 | − | 828.200i | 0.139809 | − | 0.242157i | −0.787615 | − | 0.616168i | \(-0.788684\pi\) |
0.927424 | + | 0.374011i | \(0.122018\pi\) | |||||||
\(228\) | −341.601 | + | 11104.6i | −0.0992239 | + | 3.22553i | ||||
\(229\) | 2584.91 | + | 4477.19i | 0.745920 | + | 1.29197i | 0.949764 | + | 0.312967i | \(0.101323\pi\) |
−0.203844 | + | 0.979003i | \(0.565344\pi\) | |||||||
\(230\) | 1965.92 | + | 3405.08i | 0.563604 | + | 0.976191i | ||||
\(231\) | −16.9437 | + | 550.797i | −0.00482602 | + | 0.156882i | ||||
\(232\) | −2836.46 | + | 4912.88i | −0.802683 | + | 1.39029i | ||||
\(233\) | −85.9011 | −0.0241527 | −0.0120763 | − | 0.999927i | \(-0.503844\pi\) | ||||
−0.0120763 | + | 0.999927i | \(0.503844\pi\) | |||||||
\(234\) | 3067.29 | + | 6158.49i | 0.856903 | + | 1.72048i | ||||
\(235\) | 298.443 | 0.0828438 | ||||||||
\(236\) | 3173.85 | − | 5497.27i | 0.875424 | − | 1.51628i | ||||
\(237\) | −5020.71 | + | 2696.37i | −1.37608 | + | 0.739022i | ||||
\(238\) | 1969.88 | + | 3411.92i | 0.536504 | + | 0.929253i | ||||
\(239\) | 571.124 | + | 989.216i | 0.154573 | + | 0.267728i | 0.932903 | − | 0.360127i | \(-0.117266\pi\) |
−0.778330 | + | 0.627855i | \(0.783933\pi\) | |||||||
\(240\) | 2872.85 | + | 1778.60i | 0.772672 | + | 0.478368i | ||||
\(241\) | −2049.16 | + | 3549.26i | −0.547711 | + | 0.948663i | 0.450720 | + | 0.892665i | \(0.351167\pi\) |
−0.998431 | + | 0.0559975i | \(0.982166\pi\) | |||||||
\(242\) | −5775.85 | −1.53424 | ||||||||
\(243\) | 3531.87 | − | 1369.22i | 0.932386 | − | 0.361464i | ||||
\(244\) | −1355.61 | −0.355673 | ||||||||
\(245\) | 99.4743 | − | 172.294i | 0.0259395 | − | 0.0449285i | ||||
\(246\) | 6902.32 | + | 4273.28i | 1.78892 | + | 1.10754i | ||||
\(247\) | −2664.50 | − | 4615.05i | −0.686390 | − | 1.18886i | ||||
\(248\) | −4076.99 | − | 7061.56i | −1.04391 | − | 1.80810i | ||||
\(249\) | 360.030 | − | 193.354i | 0.0916305 | − | 0.0492101i | ||||
\(250\) | −2485.83 | + | 4305.59i | −0.628871 | + | 1.08924i | ||||
\(251\) | 553.608 | 0.139217 | 0.0696085 | − | 0.997574i | \(-0.477825\pi\) | ||||
0.0696085 | + | 0.997574i | \(0.477825\pi\) | |||||||
\(252\) | −1642.83 | − | 3298.45i | −0.410668 | − | 0.824536i | ||||
\(253\) | −2797.86 | −0.695258 | ||||||||
\(254\) | −1689.11 | + | 2925.62i | −0.417259 | + | 0.722715i | ||||
\(255\) | 69.6249 | − | 2263.34i | 0.0170984 | − | 0.555826i | ||||
\(256\) | 1713.25 | + | 2967.44i | 0.418275 | + | 0.724474i | ||||
\(257\) | −46.9236 | − | 81.2740i | −0.0113892 | − | 0.0197266i | 0.860275 | − | 0.509831i | \(-0.170292\pi\) |
−0.871664 | + | 0.490104i | \(0.836959\pi\) | |||||||
\(258\) | 324.008 | − | 10532.7i | 0.0781856 | − | 2.54162i | ||||
\(259\) | −524.416 | + | 908.315i | −0.125813 | + | 0.217915i | ||||
\(260\) | −3846.78 | −0.917567 | ||||||||
\(261\) | −2535.84 | − | 156.163i | −0.601397 | − | 0.0370355i | ||||
\(262\) | 8502.81 | 2.00498 | ||||||||
\(263\) | −1416.27 | + | 2453.06i | −0.332058 | + | 0.575141i | −0.982915 | − | 0.184059i | \(-0.941076\pi\) |
0.650857 | + | 0.759200i | \(0.274410\pi\) | |||||||
\(264\) | −4181.15 | + | 2245.49i | −0.974742 | + | 0.523485i | ||||
\(265\) | −1286.67 | − | 2228.57i | −0.298262 | − | 0.516605i | ||||
\(266\) | 2012.66 | + | 3486.03i | 0.463925 | + | 0.803542i | ||||
\(267\) | −1293.15 | − | 800.602i | −0.296404 | − | 0.183506i | ||||
\(268\) | 2724.93 | − | 4719.71i | 0.621088 | − | 1.07576i | ||||
\(269\) | 6088.87 | 1.38009 | 0.690046 | − | 0.723766i | \(-0.257590\pi\) | ||||
0.690046 | + | 0.723766i | \(0.257590\pi\) | |||||||
\(270\) | −275.179 | + | 2974.28i | −0.0620255 | + | 0.670403i | ||||
\(271\) | 6849.73 | 1.53539 | 0.767697 | − | 0.640813i | \(-0.221403\pi\) | ||||
0.767697 | + | 0.640813i | \(0.221403\pi\) | |||||||
\(272\) | −8594.91 | + | 14886.8i | −1.91597 | + | 3.31855i | ||||
\(273\) | 1502.83 | + | 930.411i | 0.333169 | + | 0.206268i | ||||
\(274\) | −4096.20 | − | 7094.83i | −0.903141 | − | 1.56429i | ||||
\(275\) | −822.010 | − | 1423.76i | −0.180251 | − | 0.312204i | ||||
\(276\) | 16482.7 | − | 8852.04i | 3.59472 | − | 1.93054i | ||||
\(277\) | 917.822 | − | 1589.71i | 0.199085 | − | 0.344826i | −0.749147 | − | 0.662404i | \(-0.769536\pi\) |
0.948232 | + | 0.317578i | \(0.102870\pi\) | |||||||
\(278\) | −16532.5 | −3.56674 | ||||||||
\(279\) | 2016.84 | − | 3044.35i | 0.432778 | − | 0.653263i | ||||
\(280\) | 1713.44 | 0.365705 | ||||||||
\(281\) | 1140.37 | − | 1975.19i | 0.242096 | − | 0.419323i | −0.719215 | − | 0.694788i | \(-0.755498\pi\) |
0.961311 | + | 0.275465i | \(0.0888317\pi\) | |||||||
\(282\) | 61.5817 | − | 2001.87i | 0.0130040 | − | 0.422729i | ||||
\(283\) | −2594.90 | − | 4494.50i | −0.545055 | − | 0.944064i | −0.998603 | − | 0.0528318i | \(-0.983175\pi\) |
0.453548 | − | 0.891232i | \(-0.350158\pi\) | |||||||
\(284\) | −4853.93 | − | 8407.26i | −1.01418 | − | 1.75662i | ||||
\(285\) | 71.1371 | − | 2312.50i | 0.0147853 | − | 0.480633i | ||||
\(286\) | 1930.26 | − | 3343.31i | 0.399086 | − | 0.691238i | ||||
\(287\) | 2085.58 | 0.428946 | ||||||||
\(288\) | 5331.24 | − | 8047.32i | 1.09079 | − | 1.64650i | ||||
\(289\) | 6607.11 | 1.34482 | ||||||||
\(290\) | 1001.70 | − | 1734.99i | 0.202834 | − | 0.351318i | ||||
\(291\) | 753.020 | − | 404.409i | 0.151694 | − | 0.0814670i | ||||
\(292\) | −4456.56 | − | 7718.99i | −0.893153 | − | 1.54699i | ||||
\(293\) | 2602.41 | + | 4507.50i | 0.518888 | + | 0.898740i | 0.999759 | + | 0.0219489i | \(0.00698712\pi\) |
−0.480871 | + | 0.876791i | \(0.659680\pi\) | |||||||
\(294\) | −1135.18 | − | 702.796i | −0.225186 | − | 0.139415i | ||||
\(295\) | −660.943 | + | 1144.79i | −0.130446 | + | 0.225939i | ||||
\(296\) | −9033.03 | −1.77376 | ||||||||
\(297\) | −1735.01 | − | 1227.82i | −0.338975 | − | 0.239883i | ||||
\(298\) | 10978.7 | 2.13416 | ||||||||
\(299\) | −4487.09 | + | 7771.87i | −0.867877 | + | 1.50321i | ||||
\(300\) | 9347.20 | + | 5786.92i | 1.79887 | + | 1.11369i | ||||
\(301\) | −1353.60 | − | 2344.50i | −0.259203 | − | 0.448953i | ||||
\(302\) | −3882.41 | − | 6724.54i | −0.739761 | − | 1.28130i | ||||
\(303\) | 42.8727 | − | 23.0248i | 0.00812863 | − | 0.00436548i | ||||
\(304\) | −8781.59 | + | 15210.2i | −1.65677 | + | 2.86961i | ||||
\(305\) | 282.301 | 0.0529985 | ||||||||
\(306\) | −15167.4 | − | 934.047i | −2.83355 | − | 0.174496i | ||||
\(307\) | −8924.71 | −1.65915 | −0.829576 | − | 0.558393i | \(-0.811418\pi\) | ||||
−0.829576 | + | 0.558393i | \(0.811418\pi\) | |||||||
\(308\) | −1033.84 | + | 1790.66i | −0.191261 | + | 0.331274i | ||||
\(309\) | −8.04375 | + | 261.483i | −0.00148088 | + | 0.0481400i | ||||
\(310\) | 1439.80 | + | 2493.80i | 0.263790 | + | 0.456898i | ||||
\(311\) | 3100.59 | + | 5370.38i | 0.565332 | + | 0.979184i | 0.997019 | + | 0.0771600i | \(0.0245852\pi\) |
−0.431687 | + | 0.902024i | \(0.642081\pi\) | |||||||
\(312\) | −468.062 | + | 15215.6i | −0.0849320 | + | 2.76094i | ||||
\(313\) | 3378.69 | − | 5852.06i | 0.610143 | − | 1.05680i | −0.381073 | − | 0.924545i | \(-0.624445\pi\) |
0.991216 | − | 0.132254i | \(-0.0422213\pi\) | |||||||
\(314\) | 3468.53 | 0.623377 | ||||||||
\(315\) | 342.113 | + | 686.891i | 0.0611933 | + | 0.122863i | ||||
\(316\) | −21383.5 | −3.80670 | ||||||||
\(317\) | −965.276 | + | 1671.91i | −0.171026 | + | 0.296226i | −0.938779 | − | 0.344520i | \(-0.888042\pi\) |
0.767753 | + | 0.640746i | \(0.221375\pi\) | |||||||
\(318\) | −15214.1 | + | 8170.75i | −2.68291 | + | 1.44086i | ||||
\(319\) | 712.800 | + | 1234.61i | 0.125107 | + | 0.216692i | ||||
\(320\) | 1204.86 | + | 2086.88i | 0.210480 | + | 0.364563i | ||||
\(321\) | 2734.16 | + | 1692.74i | 0.475408 | + | 0.294329i | ||||
\(322\) | 3389.37 | − | 5870.57i | 0.586591 | − | 1.01601i | ||||
\(323\) | 11770.3 | 2.02761 | ||||||||
\(324\) | 14105.9 | + | 1743.96i | 2.41871 | + | 0.299033i | ||||
\(325\) | −5273.22 | −0.900017 | ||||||||
\(326\) | 3297.41 | − | 5711.29i | 0.560205 | − | 0.970304i | ||||
\(327\) | 499.125 | + | 309.012i | 0.0844088 | + | 0.0522582i | ||||
\(328\) | 8980.98 | + | 15555.5i | 1.51186 | + | 2.61863i | ||||
\(329\) | −257.268 | − | 445.601i | −0.0431113 | − | 0.0746710i | ||||
\(330\) | 1476.58 | − | 792.997i | 0.246312 | − | 0.132282i | ||||
\(331\) | −3043.08 | + | 5270.77i | −0.505325 | + | 0.875249i | 0.494656 | + | 0.869089i | \(0.335294\pi\) |
−0.999981 | + | 0.00616017i | \(0.998039\pi\) | |||||||
\(332\) | 1533.39 | 0.253481 | ||||||||
\(333\) | −1803.58 | − | 3621.21i | −0.296803 | − | 0.595918i | ||||
\(334\) | 1866.46 | 0.305773 | ||||||||
\(335\) | −567.456 | + | 982.863i | −0.0925476 | + | 0.160297i | ||||
\(336\) | 179.115 | − | 5822.61i | 0.0290820 | − | 0.945385i | ||||
\(337\) | 3963.89 | + | 6865.67i | 0.640733 | + | 1.10978i | 0.985269 | + | 0.171009i | \(0.0547028\pi\) |
−0.344536 | + | 0.938773i | \(0.611964\pi\) | |||||||
\(338\) | −431.074 | − | 746.642i | −0.0693708 | − | 0.120154i | ||||
\(339\) | −211.317 | + | 6869.42i | −0.0338560 | + | 1.10058i | ||||
\(340\) | 4248.25 | − | 7358.18i | 0.677628 | − | 1.17369i | ||||
\(341\) | −2049.09 | −0.325409 | ||||||||
\(342\) | −15496.9 | − | 954.334i | −2.45022 | − | 0.150890i | ||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 11657.8 | − | 20192.0i | 1.82717 | − | 3.16476i | ||||
\(345\) | −3432.47 | + | 1843.41i | −0.535646 | + | 0.287669i | ||||
\(346\) | −4282.39 | − | 7417.31i | −0.665383 | − | 1.15248i | ||||
\(347\) | 56.0635 | + | 97.1048i | 0.00867333 | + | 0.0150227i | 0.870329 | − | 0.492470i | \(-0.163906\pi\) |
−0.861656 | + | 0.507493i | \(0.830572\pi\) | |||||||
\(348\) | −8105.35 | − | 5018.09i | −1.24854 | − | 0.772982i | ||||
\(349\) | −501.439 | + | 868.518i | −0.0769095 | + | 0.133211i | −0.901915 | − | 0.431913i | \(-0.857839\pi\) |
0.825006 | + | 0.565125i | \(0.191172\pi\) | |||||||
\(350\) | 3983.18 | 0.608314 | ||||||||
\(351\) | −6193.15 | + | 2850.37i | −0.941783 | + | 0.433452i | ||||
\(352\) | −5416.49 | −0.820171 | ||||||||
\(353\) | 702.900 | − | 1217.46i | 0.105982 | − | 0.183566i | −0.808157 | − | 0.588967i | \(-0.799535\pi\) |
0.914139 | + | 0.405401i | \(0.132868\pi\) | |||||||
\(354\) | 7542.51 | + | 4669.63i | 1.13243 | + | 0.701096i | ||||
\(355\) | 1010.81 | + | 1750.78i | 0.151122 | + | 0.261752i | ||||
\(356\) | −2853.40 | − | 4942.24i | −0.424803 | − | 0.735781i | ||||
\(357\) | −3439.37 | + | 1847.11i | −0.509890 | + | 0.273837i | ||||
\(358\) | 5901.25 | − | 10221.3i | 0.871203 | − | 1.50897i | ||||
\(359\) | −3444.33 | −0.506364 | −0.253182 | − | 0.967419i | \(-0.581477\pi\) | ||||
−0.253182 | + | 0.967419i | \(0.581477\pi\) | |||||||
\(360\) | −3650.04 | + | 5509.60i | −0.534372 | + | 0.806616i | ||||
\(361\) | 5166.97 | 0.753312 | ||||||||
\(362\) | 3980.05 | − | 6893.65i | 0.577864 | − | 1.00089i | ||||
\(363\) | 175.981 | − | 5720.71i | 0.0254452 | − | 0.827161i | ||||
\(364\) | 3316.05 | + | 5743.57i | 0.477495 | + | 0.827046i | ||||
\(365\) | 928.063 | + | 1607.45i | 0.133088 | + | 0.230515i | ||||
\(366\) | 58.2509 | − | 1893.60i | 0.00831919 | − | 0.270437i | ||||
\(367\) | 1179.28 | − | 2042.57i | 0.167733 | − | 0.290522i | −0.769890 | − | 0.638177i | \(-0.779689\pi\) |
0.937622 | + | 0.347656i | \(0.113022\pi\) | |||||||
\(368\) | 29576.9 | 4.18968 | ||||||||
\(369\) | −4442.79 | + | 6706.22i | −0.626781 | + | 0.946103i | ||||
\(370\) | 3190.03 | 0.448221 | ||||||||
\(371\) | −2218.30 | + | 3842.21i | −0.310427 | + | 0.537675i | ||||
\(372\) | 12071.6 | − | 6483.04i | 1.68248 | − | 0.903575i | ||||
\(373\) | 3771.74 | + | 6532.85i | 0.523575 | + | 0.906859i | 0.999623 | + | 0.0274397i | \(0.00873542\pi\) |
−0.476048 | + | 0.879419i | \(0.657931\pi\) | |||||||
\(374\) | 4263.42 | + | 7384.46i | 0.589455 | + | 1.02097i | ||||
\(375\) | −4188.74 | − | 2593.29i | −0.576816 | − | 0.357111i | ||||
\(376\) | 2215.71 | − | 3837.72i | 0.303900 | − | 0.526371i | ||||
\(377\) | 4572.63 | 0.624675 | ||||||||
\(378\) | 4678.06 | − | 2153.06i | 0.636544 | − | 0.292967i | ||||
\(379\) | −11587.7 | −1.57051 | −0.785253 | − | 0.619175i | \(-0.787467\pi\) | ||||
−0.785253 | + | 0.619175i | \(0.787467\pi\) | |||||||
\(380\) | 4340.52 | − | 7518.00i | 0.585958 | − | 1.01491i | ||||
\(381\) | −2846.22 | − | 1762.12i | −0.382720 | − | 0.236945i | ||||
\(382\) | −1263.76 | − | 2188.90i | −0.169266 | − | 0.293177i | ||||
\(383\) | 6403.54 | + | 11091.3i | 0.854322 | + | 1.47973i | 0.877272 | + | 0.479993i | \(0.159361\pi\) |
−0.0229501 | + | 0.999737i | \(0.507306\pi\) | |||||||
\(384\) | 1153.66 | − | 619.575i | 0.153314 | − | 0.0823374i | ||||
\(385\) | 215.293 | − | 372.899i | 0.0284996 | − | 0.0493628i | ||||
\(386\) | −23195.1 | −3.05855 | ||||||||
\(387\) | 10422.3 | + | 641.830i | 1.36898 | + | 0.0843051i | ||||
\(388\) | 3207.16 | 0.419637 | ||||||||
\(389\) | −4105.23 | + | 7110.46i | −0.535073 | + | 0.926773i | 0.464087 | + | 0.885790i | \(0.346382\pi\) |
−0.999160 | + | 0.0409836i | \(0.986951\pi\) | |||||||
\(390\) | 165.297 | − | 5373.40i | 0.0214619 | − | 0.697674i | ||||
\(391\) | −9910.77 | − | 17166.0i | −1.28186 | − | 2.22025i | ||||
\(392\) | −1477.04 | − | 2558.31i | −0.190310 | − | 0.329627i | ||||
\(393\) | −259.067 | + | 8421.63i | −0.0332524 | + | 1.08095i | ||||
\(394\) | −3874.07 | + | 6710.09i | −0.495363 | + | 0.857993i | ||||
\(395\) | 4453.05 | 0.567233 | ||||||||
\(396\) | −3555.59 | − | 7138.88i | −0.451199 | − | 0.905914i | ||||
\(397\) | −3076.35 | −0.388911 | −0.194455 | − | 0.980911i | \(-0.562294\pi\) | ||||
−0.194455 | + | 0.980911i | \(0.562294\pi\) | |||||||
\(398\) | 5194.35 | − | 8996.88i | 0.654194 | − | 1.13310i | ||||
\(399\) | −3514.07 | + | 1887.23i | −0.440911 | + | 0.236792i | ||||
\(400\) | 8689.66 | + | 15050.9i | 1.08621 | + | 1.88137i | ||||
\(401\) | 4381.71 | + | 7589.34i | 0.545666 | + | 0.945122i | 0.998565 | + | 0.0535595i | \(0.0170567\pi\) |
−0.452898 | + | 0.891562i | \(0.649610\pi\) | |||||||
\(402\) | 6475.67 | + | 4009.14i | 0.803426 | + | 0.497407i | ||||
\(403\) | −3286.25 | + | 5691.95i | −0.406203 | + | 0.703564i | ||||
\(404\) | 182.598 | 0.0224866 | ||||||||
\(405\) | −2937.50 | − | 363.174i | −0.360409 | − | 0.0445586i | ||||
\(406\) | −3453.99 | −0.422213 | ||||||||
\(407\) | −1135.00 | + | 1965.87i | −0.138230 | + | 0.239422i | ||||
\(408\) | −28587.7 | − | 17698.8i | −3.46887 | − | 2.14761i | ||||
\(409\) | −5187.79 | − | 8985.51i | −0.627187 | − | 1.08632i | −0.988114 | − | 0.153726i | \(-0.950873\pi\) |
0.360926 | − | 0.932594i | \(-0.382461\pi\) | |||||||
\(410\) | −3171.65 | − | 5493.45i | −0.382040 | − | 0.661713i | ||||
\(411\) | 7151.91 | − | 3840.93i | 0.858340 | − | 0.460971i | ||||
\(412\) | −490.799 | + | 850.089i | −0.0586892 | + | 0.101653i | ||||
\(413\) | 2279.02 | 0.271533 | ||||||||
\(414\) | 11656.8 | + | 23404.4i | 1.38381 | + | 2.77841i | ||||
\(415\) | −319.323 | −0.0377710 | ||||||||
\(416\) | −8686.74 | + | 15045.9i | −1.02380 | + | 1.77328i | ||||
\(417\) | 503.718 | − | 16374.7i | 0.0591539 | − | 1.92295i | ||||
\(418\) | 4356.02 | + | 7544.85i | 0.509713 | + | 0.882848i | ||||
\(419\) | −3764.22 | − | 6519.82i | −0.438888 | − | 0.760176i | 0.558716 | − | 0.829359i | \(-0.311294\pi\) |
−0.997604 | + | 0.0691827i | \(0.977961\pi\) | |||||||
\(420\) | −88.5322 | + | 2877.97i | −0.0102855 | + | 0.334358i | ||||
\(421\) | 1030.66 | − | 1785.16i | 0.119315 | − | 0.206659i | −0.800182 | − | 0.599758i | \(-0.795264\pi\) |
0.919496 | + | 0.393099i | \(0.128597\pi\) | |||||||
\(422\) | 11273.2 | 1.30041 | ||||||||
\(423\) | 1980.88 | + | 121.988i | 0.227692 | + | 0.0140218i | ||||
\(424\) | −38210.0 | −4.37652 | ||||||||
\(425\) | 5823.55 | − | 10086.7i | 0.664668 | − | 1.15124i | ||||
\(426\) | 11952.3 | − | 6418.99i | 1.35937 | − | 0.730049i | ||||
\(427\) | −243.353 | − | 421.499i | −0.0275800 | − | 0.0477700i | ||||
\(428\) | 6033.04 | + | 10449.5i | 0.681351 | + | 1.18013i | ||||
\(429\) | 3252.58 | + | 2013.70i | 0.366051 | + | 0.226625i | ||||
\(430\) | −4116.98 | + | 7130.82i | −0.461718 | + | 0.799718i | ||||
\(431\) | −12831.0 | −1.43398 | −0.716991 | − | 0.697082i | \(-0.754481\pi\) | ||||
−0.716991 | + | 0.697082i | \(0.754481\pi\) | |||||||
\(432\) | 18341.2 | + | 12979.5i | 2.04269 | + | 1.44555i | ||||
\(433\) | 17079.1 | 1.89554 | 0.947769 | − | 0.318958i | \(-0.103333\pi\) | ||||
0.947769 | + | 0.318958i | \(0.103333\pi\) | |||||||
\(434\) | 2482.30 | − | 4299.47i | 0.274549 | − | 0.475533i | ||||
\(435\) | 1687.91 | + | 1045.00i | 0.186044 | + | 0.115181i | ||||
\(436\) | 1101.34 | + | 1907.58i | 0.120974 | + | 0.209533i | ||||
\(437\) | −10126.0 | − | 17538.8i | −1.10845 | − | 1.91990i | ||||
\(438\) | 10973.8 | − | 5893.49i | 1.19715 | − | 0.642927i | ||||
\(439\) | −5991.87 | + | 10378.2i | −0.651427 | + | 1.12830i | 0.331350 | + | 0.943508i | \(0.392496\pi\) |
−0.982777 | + | 0.184797i | \(0.940837\pi\) | |||||||
\(440\) | 3708.41 | 0.401799 | ||||||||
\(441\) | 730.674 | − | 1102.93i | 0.0788979 | − | 0.119094i | ||||
\(442\) | 27350.0 | 2.94322 | ||||||||
\(443\) | −7338.91 | + | 12711.4i | −0.787093 | + | 1.36328i | 0.140648 | + | 0.990060i | \(0.455081\pi\) |
−0.927741 | + | 0.373225i | \(0.878252\pi\) | |||||||
\(444\) | 466.731 | − | 15172.3i | 0.0498875 | − | 1.62172i | ||||
\(445\) | 594.211 | + | 1029.20i | 0.0632995 | + | 0.109638i | ||||
\(446\) | 13966.3 | + | 24190.3i | 1.48278 | + | 2.56826i | ||||
\(447\) | −334.503 | + | 10873.9i | −0.0353947 | + | 1.15060i | ||||
\(448\) | 2077.26 | − | 3597.91i | 0.219065 | − | 0.379432i | ||||
\(449\) | 13056.6 | 1.37234 | 0.686170 | − | 0.727441i | \(-0.259290\pi\) | ||||
0.686170 | + | 0.727441i | \(0.259290\pi\) | |||||||
\(450\) | −8485.15 | + | 12808.0i | −0.888875 | + | 1.34172i | ||||
\(451\) | 4513.83 | 0.471282 | ||||||||
\(452\) | −12893.8 | + | 22332.7i | −1.34175 | + | 2.32398i | ||||
\(453\) | 6778.63 | − | 3640.46i | 0.703064 | − | 0.377580i | ||||
\(454\) | 2507.36 | + | 4342.88i | 0.259199 | + | 0.448946i | ||||
\(455\) | −690.556 | − | 1196.08i | −0.0711511 | − | 0.123237i | ||||
\(456\) | −29208.6 | − | 18083.3i | −2.99960 | − | 1.85707i | ||||
\(457\) | 2542.06 | − | 4402.98i | 0.260202 | − | 0.450684i | −0.706093 | − | 0.708119i | \(-0.749544\pi\) |
0.966296 | + | 0.257435i | \(0.0828773\pi\) | |||||||
\(458\) | −27109.3 | −2.76579 | ||||||||
\(459\) | 1387.26 | − | 14994.2i | 0.141071 | − | 1.52477i | ||||
\(460\) | −14619.1 | −1.48178 | ||||||||
\(461\) | 4505.66 | − | 7804.03i | 0.455205 | − | 0.788438i | −0.543495 | − | 0.839412i | \(-0.682899\pi\) |
0.998700 | + | 0.0509745i | \(0.0162327\pi\) | |||||||
\(462\) | −2456.87 | − | 1521.07i | −0.247411 | − | 0.153174i | ||||
\(463\) | 6282.84 | + | 10882.2i | 0.630644 | + | 1.09231i | 0.987420 | + | 0.158118i | \(0.0505425\pi\) |
−0.356776 | + | 0.934190i | \(0.616124\pi\) | |||||||
\(464\) | −7535.18 | − | 13051.3i | −0.753905 | − | 1.30580i | ||||
\(465\) | −2513.86 | + | 1350.07i | −0.250704 | + | 0.134641i | ||||
\(466\) | 225.222 | − | 390.096i | 0.0223889 | − | 0.0387787i | ||||
\(467\) | −12121.8 | −1.20113 | −0.600567 | − | 0.799575i | \(-0.705058\pi\) | ||||
−0.600567 | + | 0.799575i | \(0.705058\pi\) | |||||||
\(468\) | −25532.6 | − | 1572.36i | −2.52189 | − | 0.155304i | ||||
\(469\) | 1956.66 | 0.192645 | ||||||||
\(470\) | −782.482 | + | 1355.30i | −0.0767940 | + | 0.133011i | ||||
\(471\) | −105.680 | + | 3435.42i | −0.0103386 | + | 0.336084i | ||||
\(472\) | 9813.97 | + | 16998.3i | 0.957044 | + | 1.65765i | ||||
\(473\) | −2929.61 | − | 5074.23i | −0.284785 | − | 0.493263i | ||||
\(474\) | 918.854 | − | 29869.7i | 0.0890388 | − | 2.89444i | ||||
\(475\) | 5950.04 | − | 10305.8i | 0.574750 | − | 0.995497i | ||||
\(476\) | −14648.5 | −1.41053 | ||||||||
\(477\) | −7629.19 | − | 15317.8i | −0.732320 | − | 1.47035i | ||||
\(478\) | −5989.67 | −0.573140 | ||||||||
\(479\) | 16.2616 | − | 28.1659i | 0.00155117 | − | 0.00268671i | −0.865249 | − | 0.501343i | \(-0.832840\pi\) |
0.866800 | + | 0.498656i | \(0.166173\pi\) | |||||||
\(480\) | −6645.05 | + | 3568.72i | −0.631883 | + | 0.339352i | ||||
\(481\) | 3640.52 | + | 6305.57i | 0.345101 | + | 0.597732i | ||||
\(482\) | −10745.3 | − | 18611.4i | −1.01543 | − | 1.75877i | ||||
\(483\) | 5711.26 | + | 3535.88i | 0.538036 | + | 0.333102i | ||||
\(484\) | 10737.7 | − | 18598.2i | 1.00842 | − | 1.74664i | ||||
\(485\) | −667.880 | −0.0625296 | ||||||||
\(486\) | −3042.20 | + | 19629.0i | −0.283944 | + | 1.83207i | ||||
\(487\) | 2314.41 | 0.215351 | 0.107675 | − | 0.994186i | \(-0.465659\pi\) | ||||
0.107675 | + | 0.994186i | \(0.465659\pi\) | |||||||
\(488\) | 2095.87 | − | 3630.15i | 0.194417 | − | 0.336740i | ||||
\(489\) | 5556.30 | + | 3439.95i | 0.513833 | + | 0.318118i | ||||
\(490\) | 521.619 | + | 903.470i | 0.0480905 | + | 0.0832951i | ||||
\(491\) | 7131.80 | + | 12352.6i | 0.655507 | + | 1.13537i | 0.981767 | + | 0.190091i | \(0.0608782\pi\) |
−0.326260 | + | 0.945280i | \(0.605788\pi\) | |||||||
\(492\) | −26591.8 | + | 14281.1i | −2.43669 | + | 1.30862i | ||||
\(493\) | −5049.85 | + | 8746.60i | −0.461326 | + | 0.799041i | ||||
\(494\) | 27944.0 | 2.54506 | ||||||||
\(495\) | 740.438 | + | 1486.65i | 0.0672328 | + | 0.134989i | ||||
\(496\) | 21661.4 | 1.96094 | ||||||||
\(497\) | 1742.71 | − | 3018.46i | 0.157286 | − | 0.272427i | ||||
\(498\) | −65.8901 | + | 2141.93i | −0.00592893 | + | 0.192735i | ||||
\(499\) | −1537.92 | − | 2663.75i | −0.137969 | − | 0.238970i | 0.788759 | − | 0.614703i | \(-0.210724\pi\) |
−0.926728 | + | 0.375733i | \(0.877391\pi\) | |||||||
\(500\) | −9242.65 | − | 16008.7i | −0.826688 | − | 1.43186i | ||||
\(501\) | −56.8680 | + | 1848.64i | −0.00507121 | + | 0.164853i | ||||
\(502\) | −1451.49 | + | 2514.06i | −0.129050 | + | 0.223522i | ||||
\(503\) | 1297.38 | 0.115004 | 0.0575022 | − | 0.998345i | \(-0.481686\pi\) | ||||
0.0575022 | + | 0.998345i | \(0.481686\pi\) | |||||||
\(504\) | 11372.8 | + | 700.361i | 1.00512 | + | 0.0618979i | ||||
\(505\) | −38.0253 | −0.00335070 | ||||||||
\(506\) | 7335.65 | − | 12705.7i | 0.644485 | − | 1.11628i | ||||
\(507\) | 752.648 | − | 404.210i | 0.0659295 | − | 0.0354075i | ||||
\(508\) | −6280.32 | − | 10877.8i | −0.548512 | − | 0.950050i | ||||
\(509\) | −10654.5 | − | 18454.1i | −0.927800 | − | 1.60700i | −0.786995 | − | 0.616960i | \(-0.788364\pi\) |
−0.140805 | − | 0.990037i | \(-0.544969\pi\) | |||||||
\(510\) | 10095.8 | + | 6250.38i | 0.876566 | + | 0.542689i | ||||
\(511\) | 1600.04 | − | 2771.35i | 0.138516 | − | 0.239917i | ||||
\(512\) | −19983.9 | −1.72495 | ||||||||
\(513\) | 1417.39 | − | 15319.9i | 0.121987 | − | 1.31850i | ||||
\(514\) | 492.111 | 0.0422298 | ||||||||
\(515\) | 102.207 | − | 177.028i | 0.00874522 | − | 0.0151472i | ||||
\(516\) | 33313.0 | + | 20624.3i | 2.84210 | + | 1.75957i | ||||
\(517\) | −556.807 | − | 964.418i | −0.0473662 | − | 0.0820407i | ||||
\(518\) | −2749.91 | − | 4762.98i | −0.233251 | − | 0.404003i | ||||
\(519\) | 7476.98 | − | 4015.51i | 0.632376 | − | 0.339617i | ||||
\(520\) | 5947.39 | − | 10301.2i | 0.501558 | − | 0.868724i | ||||
\(521\) | 21484.7 | 1.80664 | 0.903322 | − | 0.428962i | \(-0.141121\pi\) | ||||
0.903322 | + | 0.428962i | \(0.141121\pi\) | |||||||
\(522\) | 7357.84 | − | 11106.4i | 0.616942 | − | 0.931252i | ||||
\(523\) | 275.174 | 0.0230067 | 0.0115034 | − | 0.999934i | \(-0.496338\pi\) | ||||
0.0115034 | + | 0.999934i | \(0.496338\pi\) | |||||||
\(524\) | −15807.3 | + | 27379.0i | −1.31783 | + | 2.28255i | ||||
\(525\) | −121.361 | + | 3945.16i | −0.0100888 | + | 0.327963i | ||||
\(526\) | −7426.59 | − | 12863.2i | −0.615618 | − | 1.06628i | ||||
\(527\) | −7258.43 | − | 12572.0i | −0.599966 | − | 1.03917i | ||||
\(528\) | 387.661 | − | 12601.9i | 0.0319522 | − | 1.03869i | ||||
\(529\) | −10969.0 | + | 18998.9i | −0.901537 | + | 1.56151i | ||||
\(530\) | 13493.9 | 1.10592 | ||||||||
\(531\) | −4854.86 | + | 7328.23i | −0.396766 | + | 0.598904i | ||||
\(532\) | −14966.7 | −1.21971 | ||||||||
\(533\) | 7239.09 | − | 12538.5i | 0.588292 | − | 1.01895i | ||||
\(534\) | 7026.21 | − | 3773.42i | 0.569389 | − | 0.305790i | ||||
\(535\) | −1256.36 | − | 2176.08i | −0.101527 | − | 0.175851i | ||||
\(536\) | 8425.85 | + | 14594.0i | 0.678995 | + | 1.17605i | ||||
\(537\) | 9943.88 | + | 6156.34i | 0.799088 | + | 0.494722i | ||||
\(538\) | −15964.3 | + | 27650.9i | −1.27931 | + | 2.21583i | ||||
\(539\) | −742.358 | −0.0593240 | ||||||||
\(540\) | −9065.59 | − | 6415.46i | −0.722446 | − | 0.511254i | ||||
\(541\) | −4249.84 | −0.337735 | −0.168868 | − | 0.985639i | \(-0.554011\pi\) | ||||
−0.168868 | + | 0.985639i | \(0.554011\pi\) | |||||||
\(542\) | −17959.2 | + | 31106.2i | −1.42327 | + | 2.46518i | ||||
\(543\) | 6706.57 | + | 4152.09i | 0.530031 | + | 0.328146i | ||||
\(544\) | −19186.7 | − | 33232.3i | −1.51217 | − | 2.61916i | ||||
\(545\) | −229.350 | − | 397.247i | −0.0180262 | − | 0.0312223i | ||||
\(546\) | −8165.43 | + | 4385.25i | −0.640015 | + | 0.343720i | ||||
\(547\) | −1636.36 | + | 2834.25i | −0.127908 | + | 0.221543i | −0.922866 | − | 0.385122i | \(-0.874159\pi\) |
0.794958 | + | 0.606664i | \(0.207493\pi\) | |||||||
\(548\) | 30460.4 | 2.37446 | ||||||||
\(549\) | 1873.74 | + | 115.390i | 0.145664 | + | 0.00897032i | ||||
\(550\) | 8620.84 | 0.668352 | ||||||||
\(551\) | −5159.53 | + | 8936.57i | −0.398917 | + | 0.690945i | ||||
\(552\) | −1778.80 | + | 57824.4i | −0.137157 | + | 4.45864i | ||||
\(553\) | −3838.67 | − | 6648.77i | −0.295184 | − | 0.511274i | ||||
\(554\) | 4812.84 | + | 8336.07i | 0.369093 | + | 0.639289i | ||||
\(555\) | −97.1950 | + | 3159.58i | −0.00743369 | + | 0.241651i | ||||
\(556\) | 30735.0 | − | 53234.5i | 2.34434 | − | 4.06052i | ||||
\(557\) | −12118.1 | −0.921831 | −0.460915 | − | 0.887444i | \(-0.652479\pi\) | ||||
−0.460915 | + | 0.887444i | \(0.652479\pi\) | |||||||
\(558\) | 8537.16 | + | 17140.8i | 0.647682 | + | 1.30041i | ||||
\(559\) | −18793.5 | −1.42197 | ||||||||
\(560\) | −2275.91 | + | 3942.00i | −0.171741 | + | 0.297464i | ||||
\(561\) | −7443.86 | + | 3997.73i | −0.560214 | + | 0.300863i | ||||
\(562\) | 5979.84 | + | 10357.4i | 0.448834 | + | 0.777403i | ||||
\(563\) | 732.714 | + | 1269.10i | 0.0548494 | + | 0.0950020i | 0.892146 | − | 0.451746i | \(-0.149199\pi\) |
−0.837297 | + | 0.546748i | \(0.815865\pi\) | |||||||
\(564\) | 6331.53 | + | 3919.90i | 0.472705 | + | 0.292655i | ||||
\(565\) | 2685.08 | − | 4650.70i | 0.199933 | − | 0.346295i | ||||
\(566\) | 27214.0 | 2.02101 | ||||||||
\(567\) | 1989.97 | + | 4699.00i | 0.147391 | + | 0.348042i | ||||
\(568\) | 30018.0 | 2.21748 | ||||||||
\(569\) | 1680.55 | − | 2910.80i | 0.123818 | − | 0.214459i | −0.797452 | − | 0.603382i | \(-0.793819\pi\) |
0.921270 | + | 0.388923i | \(0.127153\pi\) | |||||||
\(570\) | 10315.1 | + | 6386.13i | 0.757983 | + | 0.469273i | ||||
\(571\) | −1816.88 | − | 3146.93i | −0.133160 | − | 0.230639i | 0.791733 | − | 0.610867i | \(-0.209179\pi\) |
−0.924893 | + | 0.380228i | \(0.875846\pi\) | |||||||
\(572\) | 7176.96 | + | 12430.9i | 0.524622 | + | 0.908672i | ||||
\(573\) | 2206.50 | − | 1185.00i | 0.160869 | − | 0.0863948i | ||||
\(574\) | −5468.12 | + | 9471.07i | −0.397622 | + | 0.688702i | ||||
\(575\) | −20040.1 | −1.45344 | ||||||||
\(576\) | 7144.12 | + | 14343.9i | 0.516791 | + | 1.03761i | ||||
\(577\) | 18168.7 | 1.31087 | 0.655437 | − | 0.755250i | \(-0.272484\pi\) | ||||
0.655437 | + | 0.755250i | \(0.272484\pi\) | |||||||
\(578\) | −17323.0 | + | 30004.4i | −1.24661 | + | 2.15920i | ||||
\(579\) | 706.716 | − | 22973.7i | 0.0507256 | − | 1.64897i | ||||
\(580\) | 3724.45 | + | 6450.93i | 0.266637 | + | 0.461828i | ||||
\(581\) | 275.267 | + | 476.776i | 0.0196558 | + | 0.0340448i | ||||
\(582\) | −137.812 | + | 4479.95i | −0.00981530 | + | 0.319072i | ||||
\(583\) | −4801.08 | + | 8315.72i | −0.341064 | + | 0.590741i | ||||
\(584\) | 27560.6 | 1.95285 | ||||||||
\(585\) | 5317.07 | + | 327.438i | 0.375784 | + | 0.0231417i | ||||
\(586\) | −27292.8 | −1.92398 | ||||||||
\(587\) | 5458.16 | − | 9453.81i | 0.383786 | − | 0.664736i | −0.607814 | − | 0.794079i | \(-0.707953\pi\) |
0.991600 | + | 0.129343i | \(0.0412868\pi\) | |||||||
\(588\) | 4373.37 | − | 2348.72i | 0.306725 | − | 0.164727i | ||||
\(589\) | −7416.08 | − | 12845.0i | −0.518802 | − | 0.898591i | ||||
\(590\) | −3465.82 | − | 6002.98i | −0.241840 | − | 0.418879i | ||||
\(591\) | −6527.99 | − | 4041.53i | −0.454358 | − | 0.281297i | ||||
\(592\) | 11998.3 | − | 20781.7i | 0.832987 | − | 1.44278i | ||||
\(593\) | −6098.18 | −0.422298 | −0.211149 | − | 0.977454i | \(-0.567720\pi\) | ||||
−0.211149 | + | 0.977454i | \(0.567720\pi\) | |||||||
\(594\) | 10124.8 | − | 4659.89i | 0.699368 | − | 0.321881i | ||||
\(595\) | 3050.50 | 0.210182 | ||||||||
\(596\) | −20410.1 | + | 35351.3i | −1.40274 | + | 2.42961i | ||||
\(597\) | 8752.73 | + | 5418.88i | 0.600042 | + | 0.371491i | ||||
\(598\) | −23529.2 | − | 40753.8i | −1.60900 | − | 2.78687i | ||||
\(599\) | 2249.19 | + | 3895.71i | 0.153421 | + | 0.265733i | 0.932483 | − | 0.361214i | \(-0.117638\pi\) |
−0.779062 | + | 0.626947i | \(0.784304\pi\) | |||||||
\(600\) | −29948.0 | + | 16083.6i | −2.03770 | + | 1.09435i | ||||
\(601\) | −4664.46 | + | 8079.09i | −0.316585 | + | 0.548341i | −0.979773 | − | 0.200112i | \(-0.935869\pi\) |
0.663188 | + | 0.748452i | \(0.269203\pi\) | |||||||
\(602\) | 14195.9 | 0.961098 | ||||||||
\(603\) | −4168.17 | + | 6291.70i | −0.281494 | + | 0.424905i | ||||
\(604\) | 28870.6 | 1.94492 | ||||||||
\(605\) | −2236.08 | + | 3873.01i | −0.150264 | + | 0.260265i | ||||
\(606\) | −7.84626 | + | 255.063i | −0.000525961 | + | 0.0170977i | ||||
\(607\) | −3658.99 | − | 6337.56i | −0.244669 | − | 0.423779i | 0.717370 | − | 0.696693i | \(-0.245346\pi\) |
−0.962038 | + | 0.272914i | \(0.912013\pi\) | |||||||
\(608\) | −19603.4 | − | 33954.0i | −1.30760 | − | 2.26483i | ||||
\(609\) | 105.237 | − | 3421.01i | 0.00700235 | − | 0.227630i | ||||
\(610\) | −740.160 | + | 1281.99i | −0.0491282 | + | 0.0850925i | ||||
\(611\) | −3571.93 | −0.236506 | ||||||||
\(612\) | 31204.9 | − | 47102.7i | 2.06108 | − | 3.11113i | ||||
\(613\) | 25150.6 | 1.65713 | 0.828566 | − | 0.559891i | \(-0.189157\pi\) | ||||
0.828566 | + | 0.559891i | \(0.189157\pi\) | |||||||
\(614\) | 23399.5 | − | 40529.1i | 1.53799 | − | 2.66388i | ||||
\(615\) | 5537.65 | − | 2973.99i | 0.363089 | − | 0.194997i | ||||
\(616\) | −3196.77 | − | 5536.96i | −0.209093 | − | 0.362160i | ||||
\(617\) | −7064.74 | − | 12236.5i | −0.460966 | − | 0.798416i | 0.538044 | − | 0.842917i | \(-0.319164\pi\) |
−0.999009 | + | 0.0445011i | \(0.985830\pi\) | |||||||
\(618\) | −1166.36 | − | 722.105i | −0.0759191 | − | 0.0470021i | ||||
\(619\) | −8932.53 | + | 15471.6i | −0.580014 | + | 1.00461i | 0.415463 | + | 0.909610i | \(0.363620\pi\) |
−0.995477 | + | 0.0950038i | \(0.969714\pi\) | |||||||
\(620\) | −10706.7 | −0.693535 | ||||||||
\(621\) | −23536.1 | + | 10832.4i | −1.52089 | + | 0.699982i | ||||
\(622\) | −32517.4 | −2.09619 | ||||||||
\(623\) | 1024.46 | − | 1774.41i | 0.0658812 | − | 0.114110i | ||||
\(624\) | −34383.8 | − | 21287.3i | −2.20585 | − | 1.36566i | ||||
\(625\) | −4857.44 | − | 8413.33i | −0.310876 | − | 0.538453i | ||||
\(626\) | 17717.0 | + | 30686.8i | 1.13117 | + | 1.95925i | ||||
\(627\) | −7605.54 | + | 4084.56i | −0.484428 | + | 0.260162i | ||||
\(628\) | −6448.22 | + | 11168.7i | −0.409733 | + | 0.709678i | ||||
\(629\) | −16081.8 | −1.01944 | ||||||||
\(630\) | −4016.31 | − | 247.334i | −0.253990 | − | 0.0156413i | ||||
\(631\) | 8812.01 | 0.555944 | 0.277972 | − | 0.960589i | \(-0.410338\pi\) | ||||
0.277972 | + | 0.960589i | \(0.410338\pi\) | |||||||
\(632\) | 33060.4 | − | 57262.3i | 2.08081 | − | 3.60407i | ||||
\(633\) | −343.477 | + | 11165.6i | −0.0215671 | + | 0.701095i | ||||
\(634\) | −5061.67 | − | 8767.07i | −0.317074 | − | 0.549188i | ||||
\(635\) | 1307.85 | + | 2265.27i | 0.0817332 | + | 0.141566i | ||||
\(636\) | 1974.29 | − | 64179.4i | 0.123091 | − | 4.00138i | ||||
\(637\) | −1190.56 | + | 2062.11i | −0.0740531 | + | 0.128264i | ||||
\(638\) | −7475.50 | −0.463884 | ||||||||
\(639\) | 5993.54 | + | 12033.8i | 0.371050 | + | 0.744991i | ||||
\(640\) | −1023.23 | −0.0631977 | ||||||||
\(641\) | 4393.35 | − | 7609.51i | 0.270713 | − | 0.468888i | −0.698332 | − | 0.715774i | \(-0.746074\pi\) |
0.969045 | + | 0.246886i | \(0.0794073\pi\) | |||||||
\(642\) | −14855.8 | + | 7978.28i | −0.913255 | + | 0.490464i | ||||
\(643\) | 2332.78 | + | 4040.49i | 0.143073 | + | 0.247809i | 0.928652 | − | 0.370951i | \(-0.120968\pi\) |
−0.785580 | + | 0.618761i | \(0.787635\pi\) | |||||||
\(644\) | 12602.1 | + | 21827.5i | 0.771108 | + | 1.33560i | ||||
\(645\) | −6937.31 | − | 4294.94i | −0.423498 | − | 0.262191i | ||||
\(646\) | −30860.3 | + | 53451.7i | −1.87954 | + | 3.25546i | ||||
\(647\) | −6140.64 | −0.373127 | −0.186564 | − | 0.982443i | \(-0.559735\pi\) | ||||
−0.186564 | + | 0.982443i | \(0.559735\pi\) | |||||||
\(648\) | −26478.8 | + | 35077.4i | −1.60522 | + | 2.12650i | ||||
\(649\) | 4932.49 | 0.298332 | ||||||||
\(650\) | 13825.7 | − | 23946.9i | 0.834292 | − | 1.44504i | ||||
\(651\) | 4182.80 | + | 2589.60i | 0.251823 | + | 0.155906i | ||||
\(652\) | 12260.2 | + | 21235.3i | 0.736422 | + | 1.27552i | ||||
\(653\) | −13049.0 | − | 22601.5i | −0.782000 | − | 1.35446i | −0.930775 | − | 0.365593i | \(-0.880866\pi\) |
0.148775 | − | 0.988871i | \(-0.452467\pi\) | |||||||
\(654\) | −2711.94 | + | 1456.45i | −0.162149 | + | 0.0870819i | ||||
\(655\) | 3291.81 | − | 5701.58i | 0.196369 | − | 0.340121i | ||||
\(656\) | −47716.8 | −2.83998 | ||||||||
\(657\) | 5502.88 | + | 11048.6i | 0.326770 | + | 0.656085i | ||||
\(658\) | 2698.10 | 0.159852 | ||||||||
\(659\) | 1487.51 | − | 2576.45i | 0.0879292 | − | 0.152298i | −0.818706 | − | 0.574212i | \(-0.805308\pi\) |
0.906636 | + | 0.421914i | \(0.138642\pi\) | |||||||
\(660\) | −191.611 | + | 6228.82i | −0.0113007 | + | 0.367358i | ||||
\(661\) | 9670.56 | + | 16749.9i | 0.569048 | + | 0.985621i | 0.996660 | + | 0.0816584i | \(0.0260217\pi\) |
−0.427612 | + | 0.903962i | \(0.640645\pi\) | |||||||
\(662\) | −15957.2 | − | 27638.6i | −0.936847 | − | 1.62267i | ||||
\(663\) | −833.309 | + | 27088.9i | −0.0488130 | + | 1.58679i | ||||
\(664\) | −2370.73 | + | 4106.22i | −0.138557 | + | 0.239988i | ||||
\(665\) | 3116.75 | 0.181748 | ||||||||
\(666\) | 21173.5 | + | 1303.91i | 1.23191 | + | 0.0758642i | ||||
\(667\) | 17377.6 | 1.00879 | ||||||||
\(668\) | −3469.87 | + | 6009.99i | −0.200978 | + | 0.348104i | ||||
\(669\) | −24384.9 | + | 13095.9i | −1.40923 | + | 0.756826i | ||||
\(670\) | −2975.60 | − | 5153.90i | −0.171578 | − | 0.297183i | ||||
\(671\) | −526.691 | − | 912.255i | −0.0303020 | − | 0.0524847i | ||||
\(672\) | 11056.6 | + | 6845.26i | 0.634702 | + | 0.392949i | ||||
\(673\) | −9283.70 | + | 16079.8i | −0.531739 | + | 0.920999i | 0.467574 | + | 0.883954i | \(0.345128\pi\) |
−0.999314 | + | 0.0370455i | \(0.988205\pi\) | |||||||
\(674\) | −41571.4 | −2.37577 | ||||||||
\(675\) | −12427.2 | − | 8794.39i | −0.708628 | − | 0.501476i | ||||
\(676\) | 3205.58 | 0.182384 | ||||||||
\(677\) | −9936.68 | + | 17210.8i | −0.564103 | + | 0.977055i | 0.433030 | + | 0.901380i | \(0.357445\pi\) |
−0.997133 | + | 0.0756752i | \(0.975889\pi\) | |||||||
\(678\) | −30641.5 | − | 18970.4i | −1.73566 | − | 1.07456i | ||||
\(679\) | 575.734 | + | 997.201i | 0.0325400 | + | 0.0563609i | ||||
\(680\) | 13136.2 | + | 22752.5i | 0.740807 | + | 1.28312i | ||||
\(681\) | −4377.82 | + | 2351.11i | −0.246341 | + | 0.132297i | ||||
\(682\) | 5372.47 | − | 9305.39i | 0.301646 | − | 0.522466i | ||||
\(683\) | 11761.6 | 0.658923 | 0.329461 | − | 0.944169i | \(-0.393133\pi\) | ||||
0.329461 | + | 0.944169i | \(0.393133\pi\) | |||||||
\(684\) | 31882.7 | − | 48125.7i | 1.78226 | − | 2.69025i | ||||
\(685\) | −6343.28 | −0.353816 | ||||||||
\(686\) | 899.304 | − | 1557.64i | 0.0500519 | − | 0.0866924i | ||||
\(687\) | 825.975 | − | 26850.5i | 0.0458703 | − | 1.49113i | ||||
\(688\) | 30969.6 | + | 53640.9i | 1.71614 | + | 2.97244i | ||||
\(689\) | 15399.5 | + | 26672.8i | 0.851489 | + | 1.47482i | ||||
\(690\) | 628.185 | − | 20420.8i | 0.0346588 | − | 1.12668i | ||||
\(691\) | 10838.2 | − | 18772.2i | 0.596676 | − | 1.03347i | −0.396632 | − | 0.917978i | \(-0.629821\pi\) |
0.993308 | − | 0.115495i | \(-0.0368455\pi\) | |||||||
\(692\) | 31845.0 | 1.74937 | ||||||||
\(693\) | 1581.40 | − | 2387.07i | 0.0866848 | − | 0.130848i | ||||
\(694\) | −587.966 | −0.0321598 | ||||||||
\(695\) | −6400.45 | + | 11085.9i | −0.349328 | + | 0.605054i | ||||
\(696\) | 25969.2 | − | 13946.8i | 1.41431 | − | 0.759555i | ||||
\(697\) | 15989.2 | + | 27694.1i | 0.868914 | + | 1.50500i | ||||
\(698\) | −2629.42 | − | 4554.29i | −0.142586 | − | 0.246966i | ||||
\(699\) | 379.510 | + | 234.958i | 0.0205356 | + | 0.0127138i | ||||
\(700\) | −7405.00 | + | 12825.8i | −0.399832 | + | 0.692530i | ||||
\(701\) | 29579.8 | 1.59374 | 0.796870 | − | 0.604151i | \(-0.206488\pi\) | ||||
0.796870 | + | 0.604151i | \(0.206488\pi\) | |||||||
\(702\) | 3293.50 | − | 35597.8i | 0.177073 | − | 1.91389i | ||||
\(703\) | −16431.1 | −0.881525 | ||||||||
\(704\) | 4495.83 | − | 7787.00i | 0.240686 | − | 0.416880i | ||||
\(705\) | −1318.52 | − | 816.306i | −0.0704373 | − | 0.0436083i | ||||
\(706\) | 3685.84 | + | 6384.06i | 0.196485 | + | 0.340322i | ||||
\(707\) | 32.7791 | + | 56.7750i | 0.00174368 | + | 0.00302015i | ||||
\(708\) | −29058.2 | + | 15605.7i | −1.54248 | + | 0.828388i | ||||
\(709\) | 10976.9 | − | 19012.6i | 0.581448 | − | 1.00710i | −0.413860 | − | 0.910340i | \(-0.635820\pi\) |
0.995308 | − | 0.0967567i | \(-0.0308469\pi\) | |||||||
\(710\) | −10600.9 | −0.560346 | ||||||||
\(711\) | 29556.6 | + | 1820.16i | 1.55901 | + | 0.0960077i | ||||
\(712\) | 17646.2 | 0.928820 | ||||||||
\(713\) | −12488.9 | + | 21631.4i | −0.655978 | + | 1.13619i | ||||
\(714\) | 629.449 | − | 20461.9i | 0.0329923 | − | 1.07250i | ||||
\(715\) | −1494.58 | − | 2588.68i | −0.0781734 | − | 0.135400i | ||||
\(716\) | 21941.6 | + | 38004.0i | 1.14525 | + | 1.98363i | ||||
\(717\) | 182.495 | − | 5932.49i | 0.00950547 | − | 0.309000i | ||||
\(718\) | 9030.61 | − | 15641.5i | 0.469386 | − | 0.813001i | ||||
\(719\) | −16886.2 | −0.875869 | −0.437935 | − | 0.899007i | \(-0.644290\pi\) | ||||
−0.437935 | + | 0.899007i | \(0.644290\pi\) | |||||||
\(720\) | −7827.35 | − | 15715.7i | −0.405150 | − | 0.813457i | ||||
\(721\) | −352.424 | −0.0182038 | ||||||||
\(722\) | −13547.2 | + | 23464.4i | −0.698301 | + | 1.20949i | ||||
\(723\) | 18761.2 | − | 10075.7i | 0.965055 | − | 0.518283i | ||||
\(724\) | 14798.3 | + | 25631.5i | 0.759636 | + | 1.31573i | ||||
\(725\) | 5105.52 | + | 8843.02i | 0.261537 | + | 0.452995i | ||||
\(726\) | 25517.6 | + | 15798.2i | 1.30447 | + | 0.807611i | ||||
\(727\) | 17261.7 | − | 29898.2i | 0.880609 | − | 1.52526i | 0.0299429 | − | 0.999552i | \(-0.490467\pi\) |
0.850666 | − | 0.525707i | \(-0.176199\pi\) | |||||||
\(728\) | −20507.4 | −1.04403 | ||||||||
\(729\) | −19348.9 | − | 3611.22i | −0.983026 | − | 0.183469i | ||||
\(730\) | −9733.07 | −0.493476 | ||||||||
\(731\) | 20754.9 | − | 35948.5i | 1.05013 | − | 1.81888i | ||||
\(732\) | 5989.08 | + | 3707.89i | 0.302408 | + | 0.187223i | ||||
\(733\) | −4744.05 | − | 8216.93i | −0.239052 | − | 0.414051i | 0.721390 | − | 0.692529i | \(-0.243503\pi\) |
−0.960443 | + | 0.278478i | \(0.910170\pi\) | |||||||
\(734\) | 6183.85 | + | 10710.7i | 0.310968 | + | 0.538612i | ||||
\(735\) | −910.738 | + | 489.112i | −0.0457049 | + | 0.0245458i | ||||
\(736\) | −33012.6 | + | 57179.5i | −1.65334 | + | 2.86368i | ||||
\(737\) | 4234.82 | 0.211658 | ||||||||
\(738\) | −18806.0 | − | 37758.6i | −0.938021 | − | 1.88335i | ||||
\(739\) | 19240.5 | 0.957742 | 0.478871 | − | 0.877885i | \(-0.341046\pi\) | ||||
0.478871 | + | 0.877885i | \(0.341046\pi\) | |||||||
\(740\) | −5930.47 | + | 10271.9i | −0.294606 | + | 0.510273i | ||||
\(741\) | −851.408 | + | 27677.2i | −0.0422095 | + | 1.37213i | ||||
\(742\) | −11632.2 | − | 20147.6i | −0.575515 | − | 0.996821i | ||||
\(743\) | 7798.16 | + | 13506.8i | 0.385043 | + | 0.666914i | 0.991775 | − | 0.127992i | \(-0.0408533\pi\) |
−0.606732 | + | 0.794906i | \(0.707520\pi\) | |||||||
\(744\) | −1302.75 | + | 42349.3i | −0.0641951 | + | 2.08683i | ||||
\(745\) | 4250.33 | − | 7361.79i | 0.209020 | − | 0.362034i | ||||
\(746\) | −39556.2 | −1.94136 | ||||||||
\(747\) | −2119.47 | − | 130.522i | −0.103812 | − | 0.00639298i | ||||
\(748\) | −31703.9 | −1.54975 | ||||||||
\(749\) | −2166.05 | + | 3751.70i | −0.105668 | + | 0.183023i | ||||
\(750\) | 22759.1 | − | 12222.8i | 1.10806 | − | 0.595083i | ||||
\(751\) | −6986.43 | − | 12100.9i | −0.339466 | − | 0.587972i | 0.644867 | − | 0.764295i | \(-0.276913\pi\) |
−0.984332 | + | 0.176323i | \(0.943580\pi\) | |||||||
\(752\) | 5886.14 | + | 10195.1i | 0.285433 | + | 0.494384i | ||||
\(753\) | −2445.84 | − | 1514.24i | −0.118368 | − | 0.0732827i | ||||
\(754\) | −11988.9 | + | 20765.4i | −0.579058 | + | 1.00296i | ||||
\(755\) | −6012.21 | −0.289810 | ||||||||
\(756\) | −1763.98 | + | 19066.0i | −0.0848616 | + | 0.917228i | ||||
\(757\) | −6110.89 | −0.293400 | −0.146700 | − | 0.989181i | \(-0.546865\pi\) | ||||
−0.146700 | + | 0.989181i | \(0.546865\pi\) | |||||||
\(758\) | 30381.6 | − | 52622.5i | 1.45582 | − | 2.52155i | ||||
\(759\) | 12360.9 | + | 7652.75i | 0.591137 | + | 0.365978i | ||||
\(760\) | 13421.5 | + | 23246.7i | 0.640590 | + | 1.10953i | ||||
\(761\) | −16491.7 | − | 28564.5i | −0.785576 | − | 1.36066i | −0.928654 | − | 0.370946i | \(-0.879033\pi\) |
0.143078 | − | 0.989711i | \(-0.454300\pi\) | |||||||
\(762\) | 15464.6 | − | 8305.28i | 0.735203 | − | 0.394841i | ||||
\(763\) | −395.415 | + | 684.879i | −0.0187614 | + | 0.0324958i | ||||
\(764\) | 9397.65 | 0.445020 | ||||||||
\(765\) | −6498.31 | + | 9808.96i | −0.307120 | + | 0.463587i | ||||
\(766\) | −67157.2 | −3.16774 | ||||||||
\(767\) | 7910.53 | − | 13701.4i | 0.372402 | − | 0.645020i | ||||
\(768\) | 547.449 | − | 17796.2i | 0.0257218 | − | 0.836155i | ||||
\(769\) | 8782.08 | + | 15211.0i | 0.411820 | + | 0.713294i | 0.995089 | − | 0.0989858i | \(-0.0315598\pi\) |
−0.583269 | + | 0.812279i | \(0.698226\pi\) | |||||||
\(770\) | 1128.94 | + | 1955.39i | 0.0528368 | + | 0.0915160i | ||||
\(771\) | −14.9938 | + | 487.413i | −0.000700376 | + | 0.0227675i | ||||
\(772\) | 43121.2 | − | 74688.1i | 2.01032 | − | 3.48197i | ||||
\(773\) | −9666.74 | −0.449791 | −0.224896 | − | 0.974383i | \(-0.572204\pi\) | ||||
−0.224896 | + | 0.974383i | \(0.572204\pi\) | |||||||
\(774\) | −30240.7 | + | 45647.2i | −1.40437 | + | 2.11984i | ||||
\(775\) | −14676.9 | −0.680270 | ||||||||
\(776\) | −4958.49 | + | 8588.36i | −0.229381 | + | 0.397299i | ||||
\(777\) | 4801.30 | − | 2578.54i | 0.221680 | − | 0.119053i | ||||
\(778\) | −21526.8 | − | 37285.5i | −0.991997 | − | 1.71819i | ||||
\(779\) | 16336.5 | + | 28295.6i | 0.751366 | + | 1.30140i | ||||
\(780\) | 16995.0 | + | 10521.8i | 0.780154 | + | 0.483000i | ||||
\(781\) | 3771.76 | − | 6532.88i | 0.172809 | − | 0.299315i | ||||
\(782\) | 103939. | 4.75302 | ||||||||
\(783\) | 10776.2 | + | 7625.99i | 0.491838 | + | 0.348060i | ||||
\(784\) | 7847.64 | 0.357491 | ||||||||
\(785\) | 1342.82 | − | 2325.83i | 0.0610539 | − | 0.105748i | ||||
\(786\) | −37565.3 | − | 23257.0i | −1.70472 | − | 1.05541i | ||||
\(787\) | −691.575 | − | 1197.84i | −0.0313240 | − | 0.0542547i | 0.849938 | − | 0.526882i | \(-0.176639\pi\) |
−0.881262 | + | 0.472627i | \(0.843306\pi\) | |||||||
\(788\) | −14404.3 | − | 24949.0i | −0.651183 | − | 1.12788i | ||||
\(789\) | 12966.7 | − | 6963.77i | 0.585079 | − | 0.314217i | ||||
\(790\) | −11675.3 | + | 20222.3i | −0.525810 | + | 0.910730i | ||||
\(791\) | −9258.51 | −0.416176 | ||||||||
\(792\) | 24614.2 | + | 1515.80i | 1.10433 | + | 0.0680070i | ||||
\(793\) | −3378.74 | −0.151302 | ||||||||
\(794\) | 8065.82 | − | 13970.4i | 0.360510 | − | 0.624422i | ||||
\(795\) | −411.139 | + | 13365.1i | −0.0183416 | + | 0.596242i | ||||
\(796\) | 19313.3 | + | 33451.6i | 0.859976 | + | 1.48952i | ||||
\(797\) | 20428.3 | + | 35382.9i | 0.907914 | + | 1.57255i | 0.816957 | + | 0.576698i | \(0.195659\pi\) |
0.0909570 | + | 0.995855i | \(0.471007\pi\) | |||||||
\(798\) | 643.120 | − | 20906.3i | 0.0285291 | − | 0.927412i | ||||
\(799\) | 3944.71 | − | 6832.45i | 0.174661 | − | 0.302521i | ||||
\(800\) | −38796.3 | −1.71457 | ||||||||
\(801\) | 3523.32 | + | 7074.10i | 0.155419 | + | 0.312049i | ||||
\(802\) | −45953.2 | −2.02327 | ||||||||
\(803\) | 3462.98 | − | 5998.06i | 0.152187 | − | 0.263595i | ||||
\(804\) | −24948.1 | + | 13398.4i | −1.09434 | + | 0.587717i | ||||
\(805\) | −2624.35 | − | 4545.51i | −0.114902 | − | 0.199016i | ||||
\(806\) | −17232.3 | − | 29847.2i | −0.753078 | − | 1.30437i | ||||
\(807\) | −26900.5 | − | 16654.3i | −1.17341 | − | 0.726469i | ||||
\(808\) | −282.309 | + | 488.973i | −0.0122916 | + | 0.0212896i | ||||
\(809\) | 9088.42 | 0.394971 | 0.197486 | − | 0.980306i | \(-0.436722\pi\) | ||||
0.197486 | + | 0.980306i | \(0.436722\pi\) | |||||||
\(810\) | 9351.02 | − | 12387.7i | 0.405631 | − | 0.537355i | ||||
\(811\) | 22851.8 | 0.989439 | 0.494720 | − | 0.869053i | \(-0.335271\pi\) | ||||
0.494720 | + | 0.869053i | \(0.335271\pi\) | |||||||
\(812\) | 6421.19 | − | 11121.8i | 0.277512 | − | 0.480664i | ||||
\(813\) | −30262.0 | − | 18735.5i | −1.30546 | − | 0.808219i | ||||
\(814\) | −5951.65 | − | 10308.6i | −0.256272 | − | 0.443876i | ||||
\(815\) | −2553.15 | − | 4422.18i | −0.109734 | − | 0.190064i | ||||
\(816\) | 78690.8 | − | 42260.9i | 3.37589 | − | 1.81302i | ||||
\(817\) | 21205.7 | − | 36729.3i | 0.908069 | − | 1.57282i | ||||
\(818\) | 54407.0 | 2.32554 | ||||||||
\(819\) | −4094.59 | − | 8221.09i | −0.174697 | − | 0.350755i | ||||
\(820\) | 23585.2 | 1.00443 | ||||||||
\(821\) | 5655.11 | − | 9794.94i | 0.240396 | − | 0.416377i | −0.720431 | − | 0.693526i | \(-0.756056\pi\) |
0.960827 | + | 0.277149i | \(0.0893895\pi\) | |||||||
\(822\) | −1308.89 | + | 42548.9i | −0.0555387 | + | 1.80543i | ||||
\(823\) | −16777.1 | − | 29058.8i | −0.710586 | − | 1.23077i | −0.964637 | − | 0.263580i | \(-0.915097\pi\) |
0.254051 | − | 0.967191i | \(-0.418237\pi\) | |||||||
\(824\) | −1517.62 | − | 2628.59i | −0.0641611 | − | 0.111130i | ||||
\(825\) | −262.663 | + | 8538.54i | −0.0110845 | + | 0.360332i | ||||
\(826\) | −5975.30 | + | 10349.5i | −0.251704 | + | 0.435964i | ||||
\(827\) | −881.951 | −0.0370840 | −0.0185420 | − | 0.999828i | \(-0.505902\pi\) | ||||
−0.0185420 | + | 0.999828i | \(0.505902\pi\) | |||||||
\(828\) | −97032.7 | − | 5975.50i | −4.07261 | − | 0.250801i | ||||
\(829\) | 8149.05 | 0.341409 | 0.170705 | − | 0.985322i | \(-0.445396\pi\) | ||||
0.170705 | + | 0.985322i | \(0.445396\pi\) | |||||||
\(830\) | 837.227 | − | 1450.12i | 0.0350127 | − | 0.0606438i | ||||
\(831\) | −8403.13 | + | 4512.90i | −0.350784 | + | 0.188389i | ||||
\(832\) | −14420.4 | − | 24976.9i | −0.600888 | − | 1.04077i | ||||
\(833\) | −2629.63 | − | 4554.65i | −0.109377 | − | 0.189447i | ||||
\(834\) | 73040.3 | + | 45219.9i | 3.03259 | + | 1.87750i | ||||
\(835\) | 722.588 | − | 1251.56i | 0.0299476 | − | 0.0518707i | ||||
\(836\) | −32392.5 | −1.34009 | ||||||||
\(837\) | −17237.3 | + | 7933.40i | −0.711838 | + | 0.327621i | ||||
\(838\) | 39477.3 | 1.62735 | ||||||||
\(839\) | −12769.7 | + | 22117.8i | −0.525457 | + | 0.910119i | 0.474103 | + | 0.880469i | \(0.342772\pi\) |
−0.999560 | + | 0.0296495i | \(0.990561\pi\) | |||||||
\(840\) | −7569.95 | − | 4686.61i | −0.310938 | − | 0.192504i | ||||
\(841\) | 7767.29 | + | 13453.3i | 0.318475 | + | 0.551615i | ||||
\(842\) | 5404.54 | + | 9360.94i | 0.221203 | + | 0.383134i | ||||
\(843\) | −10440.7 | + | 5607.18i | −0.426568 | + | 0.229089i | ||||
\(844\) | −20957.7 | + | 36299.8i | −0.854731 | + | 1.48044i | ||||
\(845\) | −667.550 | −0.0271768 | ||||||||
\(846\) | −5747.61 | + | 8675.81i | −0.233578 | + | 0.352577i | ||||
\(847\) | 7710.31 | 0.312785 | ||||||||
\(848\) | 50753.4 | − | 87907.5i | 2.05528 | − | 3.55985i | ||||
\(849\) | −829.167 | + | 26954.2i | −0.0335182 | + | 1.08960i | ||||
\(850\) | 30537.3 | + | 52892.1i | 1.23226 | + | 2.13434i | ||||
\(851\) | 13835.2 | + | 23963.3i | 0.557304 | + | 0.965279i | ||||
\(852\) | −1551.01 | + | 50419.7i | −0.0623672 | + | 2.02741i | ||||
\(853\) | −14430.5 | + | 24994.4i | −0.579240 | + | 1.00327i | 0.416326 | + | 0.909215i | \(0.363317\pi\) |
−0.995567 | + | 0.0940584i | \(0.970016\pi\) | |||||||
\(854\) | 2552.17 | 0.102264 | ||||||||
\(855\) | −6639.45 | + | 10022.0i | −0.265572 | + | 0.400872i | ||||
\(856\) | −37310.0 | −1.48975 | ||||||||
\(857\) | −18499.0 | + | 32041.2i | −0.737355 | + | 1.27714i | 0.216328 | + | 0.976321i | \(0.430592\pi\) |
−0.953682 | + | 0.300815i | \(0.902741\pi\) | |||||||
\(858\) | −17672.5 | + | 9491.03i | −0.703182 | + | 0.377644i | ||||
\(859\) | 13948.0 | + | 24158.6i | 0.554015 | + | 0.959582i | 0.997979 | + | 0.0635378i | \(0.0202383\pi\) |
−0.443964 | + | 0.896044i | \(0.646428\pi\) | |||||||
\(860\) | −15307.5 | − | 26513.3i | −0.606954 | − | 1.05128i | ||||
\(861\) | −9214.05 | − | 5704.49i | −0.364708 | − | 0.225794i | ||||
\(862\) | 33641.3 | − | 58268.4i | 1.32926 | − | 2.30235i | ||||
\(863\) | 37973.3 | 1.49783 | 0.748915 | − | 0.662666i | \(-0.230575\pi\) | ||||
0.748915 | + | 0.662666i | \(0.230575\pi\) | |||||||
\(864\) | −45564.5 | + | 20970.9i | −1.79414 | + | 0.825745i | ||||
\(865\) | −6631.60 | −0.260672 | ||||||||
\(866\) | −44779.2 | + | 77559.9i | −1.75711 | + | 3.04341i | ||||
\(867\) | −29190.1 | − | 18071.8i | −1.14342 | − | 0.707903i | ||||
\(868\) | 9229.52 | + | 15986.0i | 0.360911 | + | 0.625116i | ||||
\(869\) | −8308.07 | − | 14390.0i | −0.324317 | − | 0.561734i | ||||
\(870\) | −9171.07 | + | 4925.32i | −0.357389 | + | 0.191936i | ||||
\(871\) | 6791.63 | − | 11763.4i | 0.264209 | − | 0.457623i | ||||
\(872\) | −6811.00 | −0.264506 | ||||||||
\(873\) | −4432.98 | − | 272.993i | −0.171860 | − | 0.0105835i | ||||
\(874\) | 106197. | 4.11002 | ||||||||
\(875\) | 3318.39 | − | 5747.62i | 0.128208 | − | 0.222063i | ||||
\(876\) | −1424.04 | + | 46292.1i | −0.0549244 | + | 1.78546i | ||||
\(877\) | −5889.76 | − | 10201.4i | −0.226777 | − | 0.392789i | 0.730074 | − | 0.683368i | \(-0.239485\pi\) |
−0.956851 | + | 0.290579i | \(0.906152\pi\) | |||||||
\(878\) | −31419.9 | − | 54420.9i | −1.20771 | − | 2.09182i | ||||
\(879\) | 831.566 | − | 27032.2i | 0.0319090 | − | 1.03729i | ||||
\(880\) | −4925.78 | + | 8531.70i | −0.188691 | + | 0.326822i | ||||
\(881\) | 5297.92 | 0.202601 | 0.101301 | − | 0.994856i | \(-0.467700\pi\) | ||||
0.101301 | + | 0.994856i | \(0.467700\pi\) | |||||||
\(882\) | 3092.90 | + | 6209.89i | 0.118076 | + | 0.237072i | ||||
\(883\) | −31565.0 | −1.20300 | −0.601498 | − | 0.798874i | \(-0.705429\pi\) | ||||
−0.601498 | + | 0.798874i | \(0.705429\pi\) | |||||||
\(884\) | −50845.4 | + | 88066.8i | −1.93452 | + | 3.35069i | ||||
\(885\) | 6051.27 | − | 3249.83i | 0.229843 | − | 0.123437i | ||||
\(886\) | −38483.4 | − | 66655.3i | −1.45923 | − | 2.52746i | ||||
\(887\) | −8032.19 | − | 13912.2i | −0.304053 | − | 0.526634i | 0.672997 | − | 0.739645i | \(-0.265007\pi\) |
−0.977050 | + | 0.213010i | \(0.931673\pi\) | |||||||
\(888\) | 39907.8 | + | 24707.2i | 1.50813 | + | 0.933695i | ||||
\(889\) | 2254.82 | − | 3905.47i | 0.0850667 | − | 0.147340i | ||||
\(890\) | −6231.79 | −0.234708 | ||||||||
\(891\) | 4306.91 | + | 10170.1i | 0.161938 | + | 0.382392i | ||||
\(892\) | −103857. | −3.89841 | ||||||||
\(893\) | 4030.39 | − | 6980.84i | 0.151032 | − | 0.261596i | ||||
\(894\) | −48503.7 | − | 30029.0i | −1.81455 | − | 1.12340i | ||||
\(895\) | −4569.26 | − | 7914.19i | −0.170652 | − | 0.295578i | ||||
\(896\) | 882.053 | + | 1527.76i | 0.0328876 | + | 0.0569631i | ||||
\(897\) | 41081.6 | − | 22062.9i | 1.52918 | − | 0.821247i | ||||
\(898\) | −34232.9 | + | 59293.2i | −1.27212 | + | 2.20338i | ||||
\(899\) | 12727.0 | 0.472155 | ||||||||
\(900\) | −25467.3 | − | 51133.1i | −0.943235 | − | 1.89382i | ||||
\(901\) | −68026.8 | −2.51532 | ||||||||
\(902\) | −11834.7 | + | 20498.3i | −0.436866 | + | 0.756673i | ||||
\(903\) | −432.526 | + | 14060.4i | −0.0159397 | + | 0.518161i | ||||
\(904\) | −39869.3 | − | 69055.7i | −1.46685 | − | 2.54066i | ||||
\(905\) | −3081.70 | − | 5337.67i | −0.113193 | − | 0.196055i | ||||
\(906\) | −1240.58 | + | 40328.2i | −0.0454916 | + | 1.47882i | ||||
\(907\) | −23932.5 | + | 41452.4i | −0.876149 | + | 1.51753i | −0.0206152 | + | 0.999787i | \(0.506563\pi\) |
−0.855534 | + | 0.517747i | \(0.826771\pi\) | |||||||
\(908\) | −18645.4 | −0.681464 | ||||||||
\(909\) | −252.389 | − | 15.5427i | −0.00920926 | − | 0.000567128i | ||||
\(910\) | 7242.21 | 0.263821 | ||||||||
\(911\) | 19636.1 | − | 34010.7i | 0.714131 | − | 1.23691i | −0.249163 | − | 0.968462i | \(-0.580155\pi\) |
0.963294 | − | 0.268450i | \(-0.0865113\pi\) | |||||||
\(912\) | 80400.0 | − | 43178.8i | 2.91920 | − | 1.56776i | ||||
\(913\) | 595.763 | + | 1031.89i | 0.0215957 | + | 0.0374049i | ||||
\(914\) | 13329.9 | + | 23088.1i | 0.482402 | + | 0.835544i | ||||
\(915\) | −1247.20 | − | 772.154i | −0.0450615 | − | 0.0278979i | ||||
\(916\) | 50397.9 | − | 87291.7i | 1.81790 | − | 3.14869i | ||||
\(917\) | −11350.6 | −0.408756 | ||||||||
\(918\) | 64454.8 | + | 45612.8i | 2.31735 | + | 1.63992i | ||||
\(919\) | 31919.9 | 1.14574 | 0.572872 | − | 0.819645i | \(-0.305829\pi\) | ||||
0.572872 | + | 0.819645i | \(0.305829\pi\) | |||||||
\(920\) | 22602.1 | − | 39148.0i | 0.809968 | − | 1.40290i | ||||
\(921\) | 39429.2 | + | 24411.0i | 1.41068 | + | 0.873364i | ||||
\(922\) | 23626.6 | + | 40922.4i | 0.843926 | + | 1.46172i | ||||
\(923\) | −12098.0 | − | 20954.3i | −0.431430 | − | 0.747259i | ||||
\(924\) | 9465.32 | − | 5083.35i | 0.336998 | − | 0.180985i | ||||
\(925\) | −8129.57 | + | 14080.8i | −0.288971 | + | 0.500513i | ||||
\(926\) | −65891.3 | −2.33836 | ||||||||
\(927\) | 750.748 | − | 1133.23i | 0.0265996 | − | 0.0401511i | ||||
\(928\) | 33642.0 | 1.19003 | ||||||||
\(929\) | −5050.59 | + | 8747.88i | −0.178369 | + | 0.308944i | −0.941322 | − | 0.337510i | \(-0.890415\pi\) |
0.762953 | + | 0.646454i | \(0.223749\pi\) | |||||||
\(930\) | 460.069 | − | 14955.7i | 0.0162218 | − | 0.527331i | ||||
\(931\) | −2686.74 | − | 4653.58i | −0.0945805 | − | 0.163818i | ||||
\(932\) | 837.405 | + | 1450.43i | 0.0294315 | + | 0.0509768i | ||||
\(933\) | 990.754 | − | 32207.0i | 0.0347651 | − | 1.13013i | ||||
\(934\) | 31781.8 | − | 55047.8i | 1.11342 | − | 1.92850i | ||||
\(935\) | 6602.22 | 0.230926 | ||||||||
\(936\) | 43685.7 | − | 65942.0i | 1.52555 | − | 2.30276i | ||||
\(937\) | −21792.5 | −0.759798 | −0.379899 | − | 0.925028i | \(-0.624041\pi\) | ||||
−0.379899 | + | 0.925028i | \(0.624041\pi\) | |||||||
\(938\) | −5130.13 | + | 8885.65i | −0.178576 | + | 0.309303i | ||||
\(939\) | −30933.6 | + | 16612.9i | −1.07506 | + | 0.577361i | ||||
\(940\) | −2909.37 | − | 5039.18i | −0.100950 | − | 0.174851i | ||||
\(941\) | −6708.04 | − | 11618.7i | −0.232387 | − | 0.402505i | 0.726123 | − | 0.687564i | \(-0.241320\pi\) |
−0.958510 | + | 0.285059i | \(0.907987\pi\) | |||||||
\(942\) | −15323.9 | − | 9487.16i | −0.530022 | − | 0.328141i | ||||
\(943\) | 27511.0 | − | 47650.5i | 0.950035 | − | 1.64551i | ||||
\(944\) | −52142.6 | −1.79777 | ||||||||
\(945\) | 367.343 | − | 3970.43i | 0.0126451 | − | 0.136675i | ||||
\(946\) | 30724.3 | 1.05595 | ||||||||
\(947\) | 4211.34 | − | 7294.25i | 0.144509 | − | 0.250297i | −0.784681 | − | 0.619900i | \(-0.787173\pi\) |
0.929190 | + | 0.369603i | \(0.120506\pi\) | |||||||
\(948\) | 94472.2 | + | 58488.5i | 3.23662 | + | 2.00382i | ||||
\(949\) | −11107.6 | − | 19238.9i | −0.379944 | − | 0.658083i | ||||
\(950\) | 31200.5 | + | 54040.9i | 1.06556 | + | 1.84560i | ||||
\(951\) | 8837.60 | − | 4746.23i | 0.301345 | − | 0.161837i | ||||
\(952\) | 22647.6 | − | 39226.8i | 0.771022 | − | 1.33545i | ||||
\(953\) | −22257.1 | −0.756536 | −0.378268 | − | 0.925696i | \(-0.623480\pi\) | ||||
−0.378268 | + | 0.925696i | \(0.623480\pi\) | |||||||
\(954\) | 89564.5 | + | 5515.60i | 3.03958 | + | 0.187185i | ||||
\(955\) | −1957.03 | −0.0663119 | ||||||||
\(956\) | 11135.2 | − | 19286.7i | 0.376713 | − | 0.652486i | ||||
\(957\) | 227.766 | − | 7404.13i | 0.00769346 | − | 0.250096i | ||||
\(958\) | 85.2718 | + | 147.695i | 0.00287579 | + | 0.00498102i | ||||
\(959\) | 5468.11 | + | 9471.04i | 0.184124 | + | 0.318911i | ||||
\(960\) | 384.998 | − | 12515.4i | 0.0129435 | − | 0.420762i | ||||
\(961\) | 5748.93 | − | 9957.44i | 0.192975 | − | 0.334243i | ||||
\(962\) | −38180.0 | −1.27960 | ||||||||
\(963\) | −7449.49 | − | 14957.0i | −0.249280 | − | 0.500502i | ||||
\(964\) | 79905.0 | 2.66967 | ||||||||
\(965\) | −8979.83 | + | 15553.5i | −0.299555 | + | 0.518845i | ||||
\(966\) | −31031.5 | + | 16665.4i | −1.03356 | + | 0.555074i | ||||
\(967\) | 26277.9 | + | 45514.7i | 0.873878 | + | 1.51360i | 0.857953 | + | 0.513728i | \(0.171736\pi\) |
0.0159255 | + | 0.999873i | \(0.494931\pi\) | |||||||
\(968\) | 33202.4 | + | 57508.2i | 1.10244 | + | 1.90949i | ||||
\(969\) | −52001.1 | − | 32194.3i | −1.72396 | − | 1.06732i | ||||
\(970\) | 1751.10 | − | 3032.99i | 0.0579633 | − | 0.100395i | ||||
\(971\) | 26276.1 | 0.868425 | 0.434213 | − | 0.900810i | \(-0.357027\pi\) | ||||
0.434213 | + | 0.900810i | \(0.357027\pi\) | |||||||
\(972\) | −57549.6 | − | 46287.4i | −1.89908 | − | 1.52744i | ||||
\(973\) | 22069.6 | 0.727151 | ||||||||
\(974\) | −6068.09 | + | 10510.2i | −0.199624 | + | 0.345759i | ||||
\(975\) | 23297.0 | + | 14423.4i | 0.765233 | + | 0.473762i | ||||
\(976\) | 5567.77 | + | 9643.67i | 0.182603 | + | 0.316277i | ||||
\(977\) | 20578.0 | + | 35642.2i | 0.673848 | + | 1.16714i | 0.976804 | + | 0.214134i | \(0.0686930\pi\) |
−0.302957 | + | 0.953004i | \(0.597974\pi\) | |||||||
\(978\) | −30189.5 | + | 16213.3i | −0.987070 | + | 0.530106i | ||||
\(979\) | 2217.24 | − | 3840.38i | 0.0723834 | − | 0.125372i | ||||
\(980\) | −3878.89 | −0.126435 | ||||||||
\(981\) | −1359.91 | − | 2730.43i | −0.0442597 | − | 0.0888642i | ||||
\(982\) | −74794.8 | −2.43055 | ||||||||
\(983\) | −9791.61 | + | 16959.6i | −0.317705 | + | 0.550281i | −0.980009 | − | 0.198954i | \(-0.936245\pi\) |
0.662304 | + | 0.749235i | \(0.269579\pi\) | |||||||
\(984\) | 2869.76 | − | 93288.9i | 0.0929721 | − | 3.02230i | ||||
\(985\) | 2999.64 | + | 5195.54i | 0.0970321 | + | 0.168064i | ||||
\(986\) | −26480.2 | − | 45865.0i | −0.855275 | − | 1.48138i | ||||
\(987\) | −82.2067 | + | 2672.34i | −0.00265113 | + | 0.0861819i | ||||
\(988\) | −51949.7 | + | 89979.5i | −1.67281 | + | 2.89740i | ||||
\(989\) | −71421.9 | −2.29634 | ||||||||
\(990\) | −8692.53 | − | 535.306i | −0.279057 | − | 0.0171850i | ||||
\(991\) | −40167.0 | −1.28753 | −0.643767 | − | 0.765222i | \(-0.722629\pi\) | ||||
−0.643767 | + | 0.765222i | \(0.722629\pi\) | |||||||
\(992\) | −24177.7 | + | 41877.0i | −0.773834 | + | 1.34032i | ||||
\(993\) | 27860.9 | − | 14962.7i | 0.890373 | − | 0.478175i | ||||
\(994\) | 9138.34 | + | 15828.1i | 0.291600 | + | 0.505066i | ||||
\(995\) | −4021.92 | − | 6966.17i | −0.128144 | − | 0.221952i | ||||
\(996\) | −6774.51 | − | 4194.15i | −0.215521 | − | 0.133431i | ||||
\(997\) | −10470.6 | + | 18135.6i | −0.332605 | + | 0.576090i | −0.983022 | − | 0.183488i | \(-0.941261\pi\) |
0.650416 | + | 0.759578i | \(0.274594\pi\) | |||||||
\(998\) | 16128.9 | 0.511575 | ||||||||
\(999\) | −1936.59 | + | 20931.6i | −0.0613322 | + | 0.662910i |
(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 | 63.4.f.b.43.1 | yes | 16 | |
3.2 | odd | 2 | 189.4.f.b.127.8 | 16 | |||
9.2 | odd | 6 | 567.4.a.g.1.1 | 8 | |||
9.4 | even | 3 | inner | 63.4.f.b.22.1 | ✓ | 16 | |
9.5 | odd | 6 | 189.4.f.b.64.8 | 16 | |||
9.7 | even | 3 | 567.4.a.i.1.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.f.b.22.1 | ✓ | 16 | 9.4 | even | 3 | inner | |
63.4.f.b.43.1 | yes | 16 | 1.1 | even | 1 | trivial | |
189.4.f.b.64.8 | 16 | 9.5 | odd | 6 | |||
189.4.f.b.127.8 | 16 | 3.2 | odd | 2 | |||
567.4.a.g.1.1 | 8 | 9.2 | odd | 6 | |||
567.4.a.i.1.8 | 8 | 9.7 | even | 3 |