Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [18,5,Mod(5,18)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(18, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("18.5");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 18 = 2 \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 18.d (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: | \(1.86065933551\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.221456830464.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 38x^{6} - 100x^{5} + 449x^{4} - 736x^{3} + 1900x^{2} - 1548x + 2307 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 5.4 | ||
Root | \(0.500000 - 3.61825i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 18.5 |
Dual form | 18.5.d.a.11.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/18\mathbb{Z}\right)^\times\).
\(n\) | \(11\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.44949 | − | 1.41421i | 0.612372 | − | 0.353553i | ||||
\(3\) | 5.62909 | + | 7.02235i | 0.625454 | + | 0.780261i | ||||
\(4\) | 4.00000 | − | 6.92820i | 0.250000 | − | 0.433013i | ||||
\(5\) | −1.91371 | − | 1.10488i | −0.0765485 | − | 0.0441953i | 0.461237 | − | 0.887277i | \(-0.347406\pi\) |
−0.537786 | + | 0.843082i | \(0.680739\pi\) | |||||||
\(6\) | 23.7195 | + | 9.24044i | 0.658875 | + | 0.256679i | ||||
\(7\) | −21.9913 | − | 38.0900i | −0.448802 | − | 0.777348i | 0.549507 | − | 0.835489i | \(-0.314816\pi\) |
−0.998308 | + | 0.0581419i | \(0.981482\pi\) | |||||||
\(8\) | − | 22.6274i | − | 0.353553i | ||||||
\(9\) | −17.6268 | + | 79.0588i | −0.217615 | + | 0.976035i | ||||
\(10\) | −6.25016 | −0.0625016 | ||||||||
\(11\) | −183.766 | + | 106.097i | −1.51873 | + | 0.876838i | −0.518971 | + | 0.854792i | \(0.673685\pi\) |
−0.999757 | + | 0.0220466i | \(0.992982\pi\) | |||||||
\(12\) | 71.1686 | − | 10.9101i | 0.494226 | − | 0.0757643i | ||||
\(13\) | 88.7063 | − | 153.644i | 0.524889 | − | 0.909135i | −0.474691 | − | 0.880153i | \(-0.657440\pi\) |
0.999580 | − | 0.0289822i | \(-0.00922662\pi\) | |||||||
\(14\) | −107.735 | − | 62.2008i | −0.549668 | − | 0.317351i | ||||
\(15\) | −3.01358 | − | 19.6582i | −0.0133937 | − | 0.0873699i | ||||
\(16\) | −32.0000 | − | 55.4256i | −0.125000 | − | 0.216506i | ||||
\(17\) | 43.3642i | 0.150049i | 0.997182 | + | 0.0750246i | \(0.0239035\pi\) | ||||
−0.997182 | + | 0.0750246i | \(0.976096\pi\) | |||||||
\(18\) | 68.6294 | + | 218.582i | 0.211819 | + | 0.674635i | ||||
\(19\) | 528.015 | 1.46265 | 0.731323 | − | 0.682031i | \(-0.238903\pi\) | ||||
0.731323 | + | 0.682031i | \(0.238903\pi\) | |||||||
\(20\) | −15.3097 | + | 8.83905i | −0.0382742 | + | 0.0220976i | ||||
\(21\) | 143.691 | − | 368.843i | 0.325829 | − | 0.836378i | ||||
\(22\) | −300.089 | + | 519.769i | −0.620018 | + | 1.07390i | ||||
\(23\) | 517.028 | + | 298.506i | 0.977369 | + | 0.564284i | 0.901475 | − | 0.432832i | \(-0.142486\pi\) |
0.0758941 | + | 0.997116i | \(0.475819\pi\) | |||||||
\(24\) | 158.898 | − | 127.372i | 0.275864 | − | 0.221131i | ||||
\(25\) | −310.058 | − | 537.037i | −0.496094 | − | 0.859259i | ||||
\(26\) | − | 501.799i | − | 0.742306i | ||||||
\(27\) | −654.401 | + | 321.247i | −0.897670 | + | 0.440669i | ||||
\(28\) | −351.861 | −0.448802 | ||||||||
\(29\) | 380.563 | − | 219.718i | 0.452513 | − | 0.261258i | −0.256378 | − | 0.966577i | \(-0.582529\pi\) |
0.708891 | + | 0.705318i | \(0.249196\pi\) | |||||||
\(30\) | −35.1827 | − | 43.8908i | −0.0390918 | − | 0.0487675i | ||||
\(31\) | −756.471 | + | 1310.25i | −0.787170 | + | 1.36342i | 0.140523 | + | 0.990077i | \(0.455121\pi\) |
−0.927694 | + | 0.373342i | \(0.878212\pi\) | |||||||
\(32\) | −156.767 | − | 90.5097i | −0.153093 | − | 0.0883883i | ||||
\(33\) | −1779.49 | − | 693.238i | −1.63406 | − | 0.636583i | ||||
\(34\) | 61.3263 | + | 106.220i | 0.0530504 | + | 0.0918860i | ||||
\(35\) | 97.1911i | 0.0793397i | ||||||||
\(36\) | 477.228 | + | 438.357i | 0.368232 | + | 0.338239i | ||||
\(37\) | 702.206 | 0.512933 | 0.256467 | − | 0.966553i | \(-0.417442\pi\) | ||||
0.256467 | + | 0.966553i | \(0.417442\pi\) | |||||||
\(38\) | 1293.37 | − | 746.726i | 0.895684 | − | 0.517123i | ||||
\(39\) | 1578.28 | − | 241.948i | 1.03766 | − | 0.159071i | ||||
\(40\) | −25.0006 | + | 43.3023i | −0.0156254 | + | 0.0270640i | ||||
\(41\) | 517.534 | + | 298.798i | 0.307873 | + | 0.177750i | 0.645974 | − | 0.763359i | \(-0.276451\pi\) |
−0.338101 | + | 0.941110i | \(0.609785\pi\) | |||||||
\(42\) | −169.653 | − | 1106.69i | −0.0961754 | − | 0.627373i | ||||
\(43\) | 46.1125 | + | 79.8692i | 0.0249392 | + | 0.0431959i | 0.878226 | − | 0.478247i | \(-0.158727\pi\) |
−0.853286 | + | 0.521442i | \(0.825394\pi\) | |||||||
\(44\) | 1697.56i | 0.876838i | ||||||||
\(45\) | 121.083 | − | 131.820i | 0.0597942 | − | 0.0650964i | ||||
\(46\) | 1688.61 | 0.798018 | ||||||||
\(47\) | −1490.34 | + | 860.449i | −0.674668 | + | 0.389520i | −0.797843 | − | 0.602865i | \(-0.794026\pi\) |
0.123175 | + | 0.992385i | \(0.460692\pi\) | |||||||
\(48\) | 209.087 | − | 536.711i | 0.0907497 | − | 0.232947i | ||||
\(49\) | 233.266 | − | 404.029i | 0.0971538 | − | 0.168275i | ||||
\(50\) | −1518.97 | − | 876.978i | −0.607588 | − | 0.350791i | ||||
\(51\) | −304.519 | + | 244.101i | −0.117078 | + | 0.0938489i | ||||
\(52\) | −709.650 | − | 1229.15i | −0.262445 | − | 0.454567i | ||||
\(53\) | − | 1311.69i | − | 0.466958i | −0.972362 | − | 0.233479i | \(-0.924989\pi\) | ||
0.972362 | − | 0.233479i | \(-0.0750111\pi\) | |||||||
\(54\) | −1148.64 | + | 1712.36i | −0.393908 | + | 0.587228i | ||||
\(55\) | 468.900 | 0.155008 | ||||||||
\(56\) | −861.879 | + | 497.606i | −0.274834 | + | 0.158675i | ||||
\(57\) | 2972.24 | + | 3707.91i | 0.914818 | + | 1.14125i | ||||
\(58\) | 621.457 | − | 1076.40i | 0.184738 | − | 0.319975i | ||||
\(59\) | −3418.31 | − | 1973.56i | −0.981990 | − | 0.566952i | −0.0791193 | − | 0.996865i | \(-0.525211\pi\) |
−0.902870 | + | 0.429913i | \(0.858544\pi\) | |||||||
\(60\) | −148.250 | − | 57.7542i | −0.0411807 | − | 0.0160428i | ||||
\(61\) | −2112.34 | − | 3658.68i | −0.567681 | − | 0.983253i | −0.996795 | − | 0.0800020i | \(-0.974507\pi\) |
0.429114 | − | 0.903251i | \(-0.358826\pi\) | |||||||
\(62\) | 4279.24i | 1.11323i | ||||||||
\(63\) | 3398.99 | − | 1067.20i | 0.856384 | − | 0.268884i | ||||
\(64\) | −512.000 | −0.125000 | ||||||||
\(65\) | −339.516 | + | 196.020i | −0.0803589 | + | 0.0463953i | ||||
\(66\) | −5339.23 | + | 818.496i | −1.22572 | + | 0.187901i | ||||
\(67\) | −322.592 | + | 558.746i | −0.0718628 | + | 0.124470i | −0.899718 | − | 0.436472i | \(-0.856228\pi\) |
0.827855 | + | 0.560942i | \(0.189561\pi\) | |||||||
\(68\) | 300.436 | + | 173.457i | 0.0649732 | + | 0.0375123i | ||||
\(69\) | 814.180 | + | 5311.07i | 0.171010 | + | 1.11554i | ||||
\(70\) | 137.449 | + | 238.069i | 0.0280508 | + | 0.0485854i | ||||
\(71\) | − | 6397.63i | − | 1.26912i | −0.772874 | − | 0.634560i | \(-0.781181\pi\) | ||
0.772874 | − | 0.634560i | \(-0.218819\pi\) | |||||||
\(72\) | 1788.90 | + | 398.849i | 0.345080 | + | 0.0769384i | ||||
\(73\) | −3196.15 | −0.599766 | −0.299883 | − | 0.953976i | \(-0.596948\pi\) | ||||
−0.299883 | + | 0.953976i | \(0.596948\pi\) | |||||||
\(74\) | 1720.05 | − | 993.069i | 0.314106 | − | 0.181349i | ||||
\(75\) | 2025.92 | − | 5200.37i | 0.360163 | − | 0.924510i | ||||
\(76\) | 2112.06 | − | 3658.20i | 0.365662 | − | 0.633344i | ||||
\(77\) | 8082.51 | + | 4666.44i | 1.36322 | + | 0.787053i | ||||
\(78\) | 3523.80 | − | 2824.67i | 0.579192 | − | 0.464278i | ||||
\(79\) | 4782.69 | + | 8283.86i | 0.766334 | + | 1.32733i | 0.939538 | + | 0.342444i | \(0.111255\pi\) |
−0.173204 | + | 0.984886i | \(0.555412\pi\) | |||||||
\(80\) | 141.425i | 0.0220976i | ||||||||
\(81\) | −5939.59 | − | 2787.10i | −0.905288 | − | 0.424799i | ||||
\(82\) | 1690.26 | 0.251377 | ||||||||
\(83\) | −3074.70 | + | 1775.18i | −0.446321 | + | 0.257683i | −0.706275 | − | 0.707938i | \(-0.749626\pi\) |
0.259954 | + | 0.965621i | \(0.416292\pi\) | |||||||
\(84\) | −1980.65 | − | 2470.89i | −0.280705 | − | 0.350183i | ||||
\(85\) | 47.9123 | − | 82.9866i | 0.00663146 | − | 0.0114860i | ||||
\(86\) | 225.904 | + | 130.426i | 0.0305441 | + | 0.0176346i | ||||
\(87\) | 3685.16 | + | 1435.64i | 0.486876 | + | 0.189673i | ||||
\(88\) | 2400.71 | + | 4158.15i | 0.310009 | + | 0.536952i | ||||
\(89\) | 502.000i | 0.0633759i | 0.999498 | + | 0.0316879i | \(0.0100883\pi\) | ||||
−0.999498 | + | 0.0316879i | \(0.989912\pi\) | |||||||
\(90\) | 110.170 | − | 494.130i | 0.0136012 | − | 0.0610037i | ||||
\(91\) | −7803.06 | −0.942285 | ||||||||
\(92\) | 4136.22 | − | 2388.05i | 0.488684 | − | 0.282142i | ||||
\(93\) | −13459.2 | + | 2063.28i | −1.55616 | + | 0.238558i | ||||
\(94\) | −2433.72 | + | 4215.32i | −0.275432 | + | 0.477062i | ||||
\(95\) | −1010.47 | − | 583.394i | −0.111963 | − | 0.0646420i | ||||
\(96\) | −246.866 | − | 1610.36i | −0.0267867 | − | 0.174735i | ||||
\(97\) | 3714.42 | + | 6433.56i | 0.394773 | + | 0.683767i | 0.993072 | − | 0.117506i | \(-0.0374899\pi\) |
−0.598299 | + | 0.801273i | \(0.704157\pi\) | |||||||
\(98\) | − | 1319.55i | − | 0.137396i | ||||||
\(99\) | −5148.73 | − | 16398.5i | −0.525327 | − | 1.67314i | ||||
\(100\) | −4960.94 | −0.496094 | ||||||||
\(101\) | −793.864 | + | 458.338i | −0.0778222 | + | 0.0449307i | −0.538406 | − | 0.842685i | \(-0.680973\pi\) |
0.460584 | + | 0.887616i | \(0.347640\pi\) | |||||||
\(102\) | −400.705 | + | 1028.58i | −0.0385145 | + | 0.0988636i | ||||
\(103\) | 1777.12 | − | 3078.07i | 0.167511 | − | 0.290137i | −0.770033 | − | 0.638004i | \(-0.779760\pi\) |
0.937544 | + | 0.347866i | \(0.113094\pi\) | |||||||
\(104\) | −3476.56 | − | 2007.19i | −0.321428 | − | 0.185576i | ||||
\(105\) | −682.510 | + | 547.097i | −0.0619057 | + | 0.0496233i | ||||
\(106\) | −1855.00 | − | 3212.96i | −0.165095 | − | 0.285952i | ||||
\(107\) | − | 550.477i | − | 0.0480808i | −0.999711 | − | 0.0240404i | \(-0.992347\pi\) | ||
0.999711 | − | 0.0240404i | \(-0.00765304\pi\) | |||||||
\(108\) | −391.937 | + | 5818.82i | −0.0336023 | + | 0.498870i | ||||
\(109\) | −2561.93 | −0.215633 | −0.107816 | − | 0.994171i | \(-0.534386\pi\) | ||||
−0.107816 | + | 0.994171i | \(0.534386\pi\) | |||||||
\(110\) | 1148.57 | − | 663.125i | 0.0949229 | − | 0.0548037i | ||||
\(111\) | 3952.78 | + | 4931.14i | 0.320816 | + | 0.400222i | ||||
\(112\) | −1407.44 | + | 2437.76i | −0.112200 | + | 0.194337i | ||||
\(113\) | 17598.8 | + | 10160.7i | 1.37825 | + | 0.795731i | 0.991948 | − | 0.126642i | \(-0.0404200\pi\) |
0.386299 | + | 0.922374i | \(0.373753\pi\) | |||||||
\(114\) | 12524.3 | + | 4879.09i | 0.963701 | + | 0.375430i | ||||
\(115\) | −659.628 | − | 1142.51i | −0.0498774 | − | 0.0863902i | ||||
\(116\) | − | 3515.49i | − | 0.261258i | ||||||
\(117\) | 10583.3 | + | 9721.26i | 0.773124 | + | 0.710151i | ||||
\(118\) | −11164.1 | −0.801791 | ||||||||
\(119\) | 1651.74 | − | 953.635i | 0.116640 | − | 0.0673424i | ||||
\(120\) | −444.815 | + | 68.1895i | −0.0308899 | + | 0.00473538i | ||||
\(121\) | 15192.8 | − | 26314.7i | 1.03769 | − | 1.79733i | ||||
\(122\) | −10348.3 | − | 5974.60i | −0.695265 | − | 0.401411i | ||||
\(123\) | 814.977 | + | 5316.27i | 0.0538685 | + | 0.351396i | ||||
\(124\) | 6051.77 | + | 10482.0i | 0.393585 | + | 0.681710i | ||||
\(125\) | 2751.41i | 0.176090i | ||||||||
\(126\) | 6816.54 | − | 7420.99i | 0.429361 | − | 0.467435i | ||||
\(127\) | 21354.6 | 1.32399 | 0.661995 | − | 0.749508i | \(-0.269710\pi\) | ||||
0.661995 | + | 0.749508i | \(0.269710\pi\) | |||||||
\(128\) | −1254.14 | + | 724.077i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | −301.298 | + | 773.409i | −0.0181058 | + | 0.0464761i | ||||
\(130\) | −554.428 | + | 960.298i | −0.0328064 | + | 0.0568223i | ||||
\(131\) | −26706.4 | − | 15419.0i | −1.55623 | − | 0.898489i | −0.997612 | − | 0.0690626i | \(-0.977999\pi\) |
−0.558616 | − | 0.829426i | \(-0.688667\pi\) | |||||||
\(132\) | −11920.9 | + | 9555.70i | −0.684163 | + | 0.548422i | ||||
\(133\) | −11611.7 | − | 20112.1i | −0.656438 | − | 1.13698i | ||||
\(134\) | 1824.86i | 0.101629i | ||||||||
\(135\) | 1607.28 | + | 108.261i | 0.0881907 | + | 0.00594025i | ||||
\(136\) | 981.220 | 0.0530504 | ||||||||
\(137\) | −9523.95 | + | 5498.66i | −0.507430 | + | 0.292965i | −0.731777 | − | 0.681545i | \(-0.761309\pi\) |
0.224347 | + | 0.974509i | \(0.427975\pi\) | |||||||
\(138\) | 9505.31 | + | 11858.0i | 0.499124 | + | 0.622663i | ||||
\(139\) | −8472.63 | + | 14675.0i | −0.438519 | + | 0.759537i | −0.997576 | − | 0.0695923i | \(-0.977830\pi\) |
0.559056 | + | 0.829130i | \(0.311163\pi\) | |||||||
\(140\) | 673.360 | + | 388.764i | 0.0343551 | + | 0.0198349i | ||||
\(141\) | −14431.6 | − | 5622.16i | −0.725901 | − | 0.282790i | ||||
\(142\) | −9047.62 | − | 15670.9i | −0.448701 | − | 0.777174i | ||||
\(143\) | 37646.0i | 1.84097i | ||||||||
\(144\) | 4945.94 | − | 1552.91i | 0.238520 | − | 0.0748894i | ||||
\(145\) | −971.051 | −0.0461856 | ||||||||
\(146\) | −7828.95 | + | 4520.04i | −0.367280 | + | 0.212049i | ||||
\(147\) | 4150.31 | − | 636.237i | 0.192064 | − | 0.0294432i | ||||
\(148\) | 2808.82 | − | 4865.03i | 0.128233 | − | 0.222107i | ||||
\(149\) | −14383.7 | − | 8304.42i | −0.647885 | − | 0.374056i | 0.139761 | − | 0.990185i | \(-0.455367\pi\) |
−0.787645 | + | 0.616129i | \(0.788700\pi\) | |||||||
\(150\) | −2391.97 | − | 15603.3i | −0.106310 | − | 0.693481i | ||||
\(151\) | 5515.31 | + | 9552.80i | 0.241889 | + | 0.418964i | 0.961252 | − | 0.275670i | \(-0.0888996\pi\) |
−0.719363 | + | 0.694634i | \(0.755566\pi\) | |||||||
\(152\) | − | 11947.6i | − | 0.517123i | ||||||
\(153\) | −3428.32 | − | 764.371i | −0.146453 | − | 0.0326529i | ||||
\(154\) | 26397.4 | 1.11306 | ||||||||
\(155\) | 2895.33 | − | 1671.62i | 0.120513 | − | 0.0695784i | ||||
\(156\) | 4636.84 | − | 11902.4i | 0.190534 | − | 0.489086i | ||||
\(157\) | −9967.29 | + | 17263.9i | −0.404369 | + | 0.700388i | −0.994248 | − | 0.107104i | \(-0.965842\pi\) |
0.589879 | + | 0.807492i | \(0.299176\pi\) | |||||||
\(158\) | 23430.3 | + | 13527.5i | 0.938564 | + | 0.541880i | ||||
\(159\) | 9211.12 | − | 7383.59i | 0.364349 | − | 0.292061i | ||||
\(160\) | 200.005 | + | 346.419i | 0.00781269 | + | 0.0135320i | ||||
\(161\) | − | 26258.2i | − | 1.01301i | ||||||
\(162\) | −18490.5 | + | 1572.87i | −0.704562 | + | 0.0599325i | ||||
\(163\) | −7936.22 | −0.298702 | −0.149351 | − | 0.988784i | \(-0.547718\pi\) | ||||
−0.149351 | + | 0.988784i | \(0.547718\pi\) | |||||||
\(164\) | 4140.27 | − | 2390.39i | 0.153936 | − | 0.0888752i | ||||
\(165\) | 2639.48 | + | 3292.78i | 0.0969506 | + | 0.120947i | ||||
\(166\) | −5020.97 | + | 8696.57i | −0.182210 | + | 0.315596i | ||||
\(167\) | 16616.5 | + | 9593.52i | 0.595807 | + | 0.343989i | 0.767390 | − | 0.641180i | \(-0.221555\pi\) |
−0.171583 | + | 0.985170i | \(0.554888\pi\) | |||||||
\(168\) | −8345.95 | − | 3251.35i | −0.295704 | − | 0.115198i | ||||
\(169\) | −1457.11 | − | 2523.79i | −0.0510176 | − | 0.0883650i | ||||
\(170\) | − | 271.033i | − | 0.00937831i | ||||||
\(171\) | −9307.21 | + | 41744.3i | −0.318293 | + | 1.42759i | ||||
\(172\) | 737.800 | 0.0249392 | ||||||||
\(173\) | 45196.2 | − | 26094.1i | 1.51011 | − | 0.871865i | 0.510184 | − | 0.860065i | \(-0.329577\pi\) |
0.999930 | − | 0.0118002i | \(-0.00375621\pi\) | |||||||
\(174\) | 11057.1 | − | 1695.03i | 0.365209 | − | 0.0559861i | ||||
\(175\) | −13637.2 | + | 23620.3i | −0.445295 | + | 0.771274i | ||||
\(176\) | 11761.0 | + | 6790.24i | 0.379682 | + | 0.219210i | ||||
\(177\) | −5382.91 | − | 35113.9i | −0.171819 | − | 1.12081i | ||||
\(178\) | 709.936 | + | 1229.64i | 0.0224068 | + | 0.0388096i | ||||
\(179\) | − | 12197.1i | − | 0.380672i | −0.981719 | − | 0.190336i | \(-0.939042\pi\) | ||
0.981719 | − | 0.190336i | \(-0.0609578\pi\) | |||||||
\(180\) | −428.945 | − | 1366.17i | −0.0132390 | − | 0.0421657i | ||||
\(181\) | 6870.48 | 0.209715 | 0.104858 | − | 0.994487i | \(-0.466561\pi\) | ||||
0.104858 | + | 0.994487i | \(0.466561\pi\) | |||||||
\(182\) | −19113.5 | + | 11035.2i | −0.577029 | + | 0.333148i | ||||
\(183\) | 13802.0 | − | 35428.6i | 0.412135 | − | 1.05792i | ||||
\(184\) | 6754.43 | − | 11699.0i | 0.199505 | − | 0.345552i | ||||
\(185\) | −1343.82 | − | 775.855i | −0.0392643 | − | 0.0226692i | ||||
\(186\) | −30050.4 | + | 24088.2i | −0.868608 | + | 0.696272i | ||||
\(187\) | −4600.83 | − | 7968.87i | −0.131569 | − | 0.227884i | ||||
\(188\) | 13767.2i | 0.389520i | ||||||||
\(189\) | 26627.5 | + | 17861.5i | 0.745429 | + | 0.500029i | ||||
\(190\) | −3300.18 | −0.0914176 | ||||||||
\(191\) | 35951.4 | − | 20756.5i | 0.985482 | − | 0.568968i | 0.0815609 | − | 0.996668i | \(-0.474009\pi\) |
0.903921 | + | 0.427700i | \(0.140676\pi\) | |||||||
\(192\) | −2882.09 | − | 3595.44i | −0.0781818 | − | 0.0975326i | ||||
\(193\) | −29868.0 | + | 51732.9i | −0.801847 | + | 1.38884i | 0.116553 | + | 0.993184i | \(0.462816\pi\) |
−0.918399 | + | 0.395654i | \(0.870518\pi\) | |||||||
\(194\) | 18196.9 | + | 10506.0i | 0.483496 | + | 0.279147i | ||||
\(195\) | −3287.69 | − | 1280.79i | −0.0864612 | − | 0.0336828i | ||||
\(196\) | −1866.13 | − | 3232.23i | −0.0485769 | − | 0.0841377i | ||||
\(197\) | − | 12371.6i | − | 0.318783i | −0.987215 | − | 0.159391i | \(-0.949047\pi\) | ||
0.987215 | − | 0.159391i | \(-0.0509532\pi\) | |||||||
\(198\) | −35802.7 | − | 32886.5i | −0.913242 | − | 0.838856i | ||||
\(199\) | −16836.3 | −0.425149 | −0.212575 | − | 0.977145i | \(-0.568185\pi\) | ||||
−0.212575 | + | 0.977145i | \(0.568185\pi\) | |||||||
\(200\) | −12151.8 | + | 7015.82i | −0.303794 | + | 0.175396i | ||||
\(201\) | −5739.61 | + | 879.875i | −0.142066 | + | 0.0217785i | ||||
\(202\) | −1296.37 | + | 2245.39i | −0.0317708 | + | 0.0550286i | ||||
\(203\) | −16738.2 | − | 9663.78i | −0.406177 | − | 0.234507i | ||||
\(204\) | 473.106 | + | 3086.17i | 0.0113684 | + | 0.0741583i | ||||
\(205\) | −660.274 | − | 1143.63i | −0.0157114 | − | 0.0272130i | ||||
\(206\) | − | 10052.9i | − | 0.236896i | ||||||
\(207\) | −32713.1 | + | 35613.9i | −0.763451 | + | 0.831150i | ||||
\(208\) | −11354.4 | −0.262445 | ||||||||
\(209\) | −97031.3 | + | 56021.1i | −2.22136 | + | 1.28250i | ||||
\(210\) | −898.089 | + | 2305.32i | −0.0203648 | + | 0.0522749i | ||||
\(211\) | 22606.7 | − | 39155.9i | 0.507776 | − | 0.879493i | −0.492184 | − | 0.870491i | \(-0.663801\pi\) |
0.999959 | − | 0.00900203i | \(-0.00286547\pi\) | |||||||
\(212\) | −9087.63 | − | 5246.74i | −0.202199 | − | 0.116740i | ||||
\(213\) | 44926.4 | − | 36012.8i | 0.990244 | − | 0.793776i | ||||
\(214\) | −778.493 | − | 1348.39i | −0.0169991 | − | 0.0294434i | ||||
\(215\) | − | 203.795i | − | 0.00440877i | ||||||
\(216\) | 7269.00 | + | 14807.4i | 0.155800 | + | 0.317374i | ||||
\(217\) | 66543.1 | 1.41313 | ||||||||
\(218\) | −6275.43 | + | 3623.12i | −0.132048 | + | 0.0762377i | ||||
\(219\) | −17991.4 | − | 22444.5i | −0.375126 | − | 0.467974i | ||||
\(220\) | 1875.60 | − | 3248.64i | 0.0387521 | − | 0.0671206i | ||||
\(221\) | 6662.64 | + | 3846.68i | 0.136415 | + | 0.0787592i | ||||
\(222\) | 16656.0 | + | 6488.69i | 0.337959 | + | 0.131659i | ||||
\(223\) | −25333.0 | − | 43878.0i | −0.509420 | − | 0.882341i | −0.999940 | − | 0.0109118i | \(-0.996527\pi\) |
0.490520 | − | 0.871430i | \(-0.336807\pi\) | |||||||
\(224\) | 7961.70i | 0.158675i | ||||||||
\(225\) | 47922.8 | − | 15046.6i | 0.946624 | − | 0.297217i | ||||
\(226\) | 57477.6 | 1.12533 | ||||||||
\(227\) | 34671.8 | − | 20017.8i | 0.672860 | − | 0.388476i | −0.124299 | − | 0.992245i | \(-0.539668\pi\) |
0.797159 | + | 0.603769i | \(0.206335\pi\) | |||||||
\(228\) | 37578.1 | − | 5760.68i | 0.722878 | − | 0.110816i | ||||
\(229\) | 13383.7 | − | 23181.3i | 0.255215 | − | 0.442045i | −0.709739 | − | 0.704465i | \(-0.751187\pi\) |
0.964954 | + | 0.262419i | \(0.0845204\pi\) | |||||||
\(230\) | −3231.51 | − | 1865.71i | −0.0610871 | − | 0.0352686i | ||||
\(231\) | 12727.8 | + | 83026.0i | 0.238522 | + | 1.55593i | ||||
\(232\) | −4971.66 | − | 8611.17i | −0.0923688 | − | 0.159987i | ||||
\(233\) | 39898.5i | 0.734927i | 0.930038 | + | 0.367464i | \(0.119774\pi\) | ||||
−0.930038 | + | 0.367464i | \(0.880226\pi\) | |||||||
\(234\) | 39671.6 | + | 8845.09i | 0.724516 | + | 0.161537i | ||||
\(235\) | 3802.78 | 0.0688597 | ||||||||
\(236\) | −27346.4 | + | 15788.5i | −0.490995 | + | 0.283476i | ||||
\(237\) | −31250.0 | + | 80216.3i | −0.556357 | + | 1.42812i | ||||
\(238\) | 2697.29 | − | 4671.84i | 0.0476182 | − | 0.0824772i | ||||
\(239\) | −43509.3 | − | 25120.1i | −0.761704 | − | 0.439770i | 0.0682035 | − | 0.997671i | \(-0.478273\pi\) |
−0.829907 | + | 0.557902i | \(0.811607\pi\) | |||||||
\(240\) | −993.135 | + | 796.093i | −0.0172419 | + | 0.0138211i | ||||
\(241\) | 34630.4 | + | 59981.6i | 0.596243 | + | 1.03272i | 0.993370 | + | 0.114960i | \(0.0366740\pi\) |
−0.397127 | + | 0.917764i | \(0.629993\pi\) | |||||||
\(242\) | − | 85943.6i | − | 1.46752i | ||||||
\(243\) | −13862.5 | − | 57398.8i | −0.234762 | − | 0.972053i | ||||
\(244\) | −33797.5 | −0.567681 | ||||||||
\(245\) | −892.809 | + | 515.464i | −0.0148740 | + | 0.00858748i | ||||
\(246\) | 9514.61 | + | 11869.6i | 0.157225 | + | 0.196140i | ||||
\(247\) | 46838.3 | − | 81126.3i | 0.767727 | − | 1.32974i | ||||
\(248\) | 29647.5 | + | 17117.0i | 0.482041 | + | 0.278307i | ||||
\(249\) | −29773.7 | − | 11599.0i | −0.480213 | − | 0.187077i | ||||
\(250\) | 3891.09 | + | 6739.56i | 0.0622574 | + | 0.107833i | ||||
\(251\) | 117510.i | 1.86521i | 0.360904 | + | 0.932603i | \(0.382468\pi\) | ||||
−0.360904 | + | 0.932603i | \(0.617532\pi\) | |||||||
\(252\) | 6202.17 | − | 27817.7i | 0.0976658 | − | 0.438046i | ||||
\(253\) | −126683. | −1.97914 | ||||||||
\(254\) | 52308.0 | − | 30200.0i | 0.810775 | − | 0.468101i | ||||
\(255\) | 852.463 | − | 130.682i | 0.0131098 | − | 0.00200971i | ||||
\(256\) | −2048.00 | + | 3547.24i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −53336.3 | − | 30793.7i | −0.807526 | − | 0.466225i | 0.0385699 | − | 0.999256i | \(-0.487720\pi\) |
−0.846096 | + | 0.533030i | \(0.821053\pi\) | |||||||
\(258\) | 355.738 | + | 2320.56i | 0.00534430 | + | 0.0348620i | ||||
\(259\) | −15442.4 | − | 26747.0i | −0.230205 | − | 0.398728i | ||||
\(260\) | 3136.32i | 0.0463953i | ||||||||
\(261\) | 10662.6 | + | 33959.8i | 0.156524 | + | 0.498522i | ||||
\(262\) | −87222.9 | −1.27066 | ||||||||
\(263\) | 22201.4 | − | 12818.0i | 0.320974 | − | 0.185314i | −0.330853 | − | 0.943682i | \(-0.607336\pi\) |
0.651827 | + | 0.758368i | \(0.274003\pi\) | |||||||
\(264\) | −15686.2 | + | 40265.2i | −0.225066 | + | 0.577727i | ||||
\(265\) | −1449.26 | + | 2510.19i | −0.0206374 | + | 0.0357449i | ||||
\(266\) | −56885.7 | − | 32842.9i | −0.803969 | − | 0.464172i | ||||
\(267\) | −3525.22 | + | 2825.80i | −0.0494497 | + | 0.0396387i | ||||
\(268\) | 2580.74 | + | 4469.97i | 0.0359314 | + | 0.0622350i | ||||
\(269\) | − | 70454.4i | − | 0.973652i | −0.873499 | − | 0.486826i | \(-0.838155\pi\) | ||
0.873499 | − | 0.486826i | \(-0.161845\pi\) | |||||||
\(270\) | 4090.11 | − | 2007.85i | 0.0561058 | − | 0.0275425i | ||||
\(271\) | −677.821 | −0.00922946 | −0.00461473 | − | 0.999989i | \(-0.501469\pi\) | ||||
−0.00461473 | + | 0.999989i | \(0.501469\pi\) | |||||||
\(272\) | 2403.49 | − | 1387.65i | 0.0324866 | − | 0.0187561i | ||||
\(273\) | −43924.1 | − | 54795.8i | −0.589356 | − | 0.735228i | ||||
\(274\) | −15552.6 | + | 26937.8i | −0.207157 | + | 0.358807i | ||||
\(275\) | 113956. | + | 65792.8i | 1.50686 | + | 0.869988i | ||||
\(276\) | 40052.9 | + | 15603.5i | 0.525794 | + | 0.204835i | ||||
\(277\) | 52964.2 | + | 91736.6i | 0.690276 | + | 1.19559i | 0.971747 | + | 0.236023i | \(0.0758441\pi\) |
−0.281472 | + | 0.959570i | \(0.590823\pi\) | |||||||
\(278\) | 47928.4i | 0.620160i | ||||||||
\(279\) | −90252.3 | − | 82901.1i | −1.15944 | − | 1.06501i | ||||
\(280\) | 2199.18 | 0.0280508 | ||||||||
\(281\) | −626.791 | + | 361.878i | −0.00793798 | + | 0.00458300i | −0.503964 | − | 0.863725i | \(-0.668125\pi\) |
0.496026 | + | 0.868308i | \(0.334792\pi\) | |||||||
\(282\) | −43301.1 | + | 6638.00i | −0.544503 | + | 0.0834716i | ||||
\(283\) | 10787.6 | − | 18684.6i | 0.134695 | − | 0.233299i | −0.790786 | − | 0.612093i | \(-0.790328\pi\) |
0.925481 | + | 0.378794i | \(0.123661\pi\) | |||||||
\(284\) | −44324.1 | − | 25590.5i | −0.549545 | − | 0.317280i | ||||
\(285\) | −1591.22 | − | 10379.8i | −0.0195902 | − | 0.127791i | ||||
\(286\) | 53239.5 | + | 92213.6i | 0.650882 | + | 1.12736i | ||||
\(287\) | − | 26283.8i | − | 0.319099i | ||||||
\(288\) | 9918.89 | − | 10798.4i | 0.119585 | − | 0.130190i | ||||
\(289\) | 81640.5 | 0.977485 | ||||||||
\(290\) | −2378.58 | + | 1373.27i | −0.0282828 | + | 0.0163291i | ||||
\(291\) | −24269.9 | + | 62299.0i | −0.286604 | + | 0.735691i | ||||
\(292\) | −12784.6 | + | 22143.6i | −0.149942 | + | 0.259706i | ||||
\(293\) | 90289.5 | + | 52128.7i | 1.05172 | + | 0.607213i | 0.923132 | − | 0.384484i | \(-0.125621\pi\) |
0.128593 | + | 0.991697i | \(0.458954\pi\) | |||||||
\(294\) | 9266.37 | − | 7427.88i | 0.107205 | − | 0.0859351i | ||||
\(295\) | 4361.10 | + | 7553.65i | 0.0501132 | + | 0.0867986i | ||||
\(296\) | − | 15889.1i | − | 0.181349i | ||||||
\(297\) | 86173.3 | − | 128465.i | 0.976921 | − | 1.45637i | ||||
\(298\) | −46976.9 | −0.528996 | ||||||||
\(299\) | 91727.3 | − | 52958.8i | 1.02602 | − | 0.592373i | ||||
\(300\) | −27925.5 | − | 34837.4i | −0.310284 | − | 0.387082i | ||||
\(301\) | 2028.15 | − | 3512.85i | 0.0223855 | − | 0.0387728i | ||||
\(302\) | 27019.4 | + | 15599.7i | 0.296252 | + | 0.171041i | ||||
\(303\) | −7687.34 | − | 2994.77i | −0.0837319 | − | 0.0326196i | ||||
\(304\) | −16896.5 | − | 29265.6i | −0.182831 | − | 0.316672i | ||||
\(305\) | 9335.55i | 0.100355i | ||||||||
\(306\) | −9478.63 | + | 2976.06i | −0.101228 | + | 0.0317833i | ||||
\(307\) | 3762.72 | 0.0399232 | 0.0199616 | − | 0.999801i | \(-0.493646\pi\) | ||||
0.0199616 | + | 0.999801i | \(0.493646\pi\) | |||||||
\(308\) | 64660.1 | − | 37331.5i | 0.681608 | − | 0.393527i | ||||
\(309\) | 31618.8 | − | 4847.13i | 0.331153 | − | 0.0507654i | ||||
\(310\) | 4728.06 | − | 8189.24i | 0.0491994 | − | 0.0852158i | ||||
\(311\) | −72658.7 | − | 41949.5i | −0.751220 | − | 0.433717i | 0.0749146 | − | 0.997190i | \(-0.476132\pi\) |
−0.826135 | + | 0.563473i | \(0.809465\pi\) | |||||||
\(312\) | −5474.65 | − | 35712.3i | −0.0562402 | − | 0.366867i | ||||
\(313\) | 17717.5 | + | 30687.5i | 0.180848 | + | 0.313237i | 0.942169 | − | 0.335137i | \(-0.108783\pi\) |
−0.761322 | + | 0.648374i | \(0.775449\pi\) | |||||||
\(314\) | 56383.5i | 0.571864i | ||||||||
\(315\) | −7683.81 | − | 1713.17i | −0.0774383 | − | 0.0172655i | ||||
\(316\) | 76523.1 | 0.766334 | ||||||||
\(317\) | −132069. | + | 76250.1i | −1.31426 | + | 0.758791i | −0.982799 | − | 0.184677i | \(-0.940876\pi\) |
−0.331465 | + | 0.943468i | \(0.607543\pi\) | |||||||
\(318\) | 12120.6 | − | 31112.5i | 0.119858 | − | 0.307667i | ||||
\(319\) | −46623.1 | + | 80753.6i | −0.458163 | + | 0.793561i | ||||
\(320\) | 979.820 | + | 565.699i | 0.00956856 | + | 0.00552441i | ||||
\(321\) | 3865.64 | − | 3098.68i | 0.0375156 | − | 0.0300723i | ||||
\(322\) | −37134.6 | − | 64319.1i | −0.358152 | − | 0.620338i | ||||
\(323\) | 22897.0i | 0.219469i | ||||||||
\(324\) | −43068.0 | + | 30002.3i | −0.410265 | + | 0.285801i | ||||
\(325\) | −110017. | −1.04158 | ||||||||
\(326\) | −19439.7 | + | 11223.5i | −0.182917 | + | 0.105607i | ||||
\(327\) | −14421.3 | − | 17990.8i | −0.134868 | − | 0.168250i | ||||
\(328\) | 6761.03 | − | 11710.5i | 0.0628442 | − | 0.108849i | ||||
\(329\) | 65549.1 | + | 37844.8i | 0.605584 | + | 0.349634i | ||||
\(330\) | 11122.1 | + | 4332.85i | 0.102131 | + | 0.0397874i | ||||
\(331\) | 18573.5 | + | 32170.2i | 0.169526 | + | 0.293628i | 0.938253 | − | 0.345949i | \(-0.112443\pi\) |
−0.768727 | + | 0.639577i | \(0.779110\pi\) | |||||||
\(332\) | 28402.9i | 0.257683i | ||||||||
\(333\) | −12377.6 | + | 55515.6i | −0.111622 | + | 0.500641i | ||||
\(334\) | 54269.1 | 0.486474 | ||||||||
\(335\) | 1234.70 | − | 712.853i | 0.0110020 | − | 0.00635199i | ||||
\(336\) | −25041.4 | + | 3838.82i | −0.221810 | + | 0.0340031i | ||||
\(337\) | 21032.6 | − | 36429.5i | 0.185197 | − | 0.320770i | −0.758446 | − | 0.651736i | \(-0.774041\pi\) |
0.943643 | + | 0.330966i | \(0.107374\pi\) | |||||||
\(338\) | −7138.36 | − | 4121.34i | −0.0624835 | − | 0.0360749i | ||||
\(339\) | 27713.4 | + | 180781.i | 0.241152 | + | 1.57309i | ||||
\(340\) | −383.299 | − | 663.893i | −0.00331573 | − | 0.00574302i | ||||
\(341\) | − | 321038.i | − | 2.76088i | ||||||
\(342\) | 36237.4 | + | 115415.i | 0.309817 | + | 0.986752i | ||||
\(343\) | −126121. | −1.07201 | ||||||||
\(344\) | 1807.23 | − | 1043.41i | 0.0152721 | − | 0.00881732i | ||||
\(345\) | 4310.00 | − | 11063.4i | 0.0362109 | − | 0.0929504i | ||||
\(346\) | 73805.1 | − | 127834.i | 0.616502 | − | 1.06781i | ||||
\(347\) | −92575.6 | − | 53448.5i | −0.768843 | − | 0.443892i | 0.0636189 | − | 0.997974i | \(-0.479736\pi\) |
−0.832462 | + | 0.554083i | \(0.813069\pi\) | |||||||
\(348\) | 24687.0 | − | 19789.0i | 0.203850 | − | 0.163405i | ||||
\(349\) | −94844.8 | − | 164276.i | −0.778686 | − | 1.34872i | −0.932699 | − | 0.360655i | \(-0.882553\pi\) |
0.154013 | − | 0.988069i | \(-0.450780\pi\) | |||||||
\(350\) | 77143.5i | 0.629743i | ||||||||
\(351\) | −8691.83 | + | 129041.i | −0.0705500 | + | 1.04741i | ||||
\(352\) | 38411.4 | 0.310009 | ||||||||
\(353\) | −186532. | + | 107694.i | −1.49694 | + | 0.864257i | −0.999994 | − | 0.00352519i | \(-0.998878\pi\) |
−0.496944 | + | 0.867783i | \(0.665545\pi\) | |||||||
\(354\) | −62843.9 | − | 78398.5i | −0.501483 | − | 0.625606i | ||||
\(355\) | −7068.63 | + | 12243.2i | −0.0560891 | + | 0.0971491i | ||||
\(356\) | 3477.96 | + | 2008.00i | 0.0274426 | + | 0.0158440i | ||||
\(357\) | 15994.6 | + | 6231.03i | 0.125498 | + | 0.0488904i | ||||
\(358\) | −17249.3 | − | 29876.7i | −0.134588 | − | 0.233113i | ||||
\(359\) | 116777.i | 0.906085i | 0.891489 | + | 0.453043i | \(0.149661\pi\) | ||||
−0.891489 | + | 0.453043i | \(0.850339\pi\) | |||||||
\(360\) | −2982.75 | − | 2739.80i | −0.0230151 | − | 0.0211404i | ||||
\(361\) | 148479. | 1.13933 | ||||||||
\(362\) | 16829.2 | − | 9716.33i | 0.128424 | − | 0.0741455i | ||||
\(363\) | 270313. | − | 41438.6i | 2.05142 | − | 0.314479i | ||||
\(364\) | −31212.3 | + | 54061.2i | −0.235571 | + | 0.408021i | ||||
\(365\) | 6116.52 | + | 3531.37i | 0.0459112 | + | 0.0265068i | ||||
\(366\) | −16295.8 | − | 106301.i | −0.121650 | − | 0.793552i | ||||
\(367\) | −63101.8 | − | 109295.i | −0.468500 | − | 0.811465i | 0.530852 | − | 0.847464i | \(-0.321872\pi\) |
−0.999352 | + | 0.0359992i | \(0.988539\pi\) | |||||||
\(368\) | − | 38208.8i | − | 0.282142i | ||||||
\(369\) | −32745.1 | + | 35648.8i | −0.240488 | + | 0.261813i | ||||
\(370\) | −4388.90 | −0.0320591 | ||||||||
\(371\) | −49962.2 | + | 28845.7i | −0.362989 | + | 0.209572i | ||||
\(372\) | −39542.1 | + | 101502.i | −0.285742 | + | 0.733477i | ||||
\(373\) | −55732.4 | + | 96531.3i | −0.400581 | + | 0.693826i | −0.993796 | − | 0.111218i | \(-0.964525\pi\) |
0.593215 | + | 0.805044i | \(0.297858\pi\) | |||||||
\(374\) | −22539.4 | − | 13013.1i | −0.161138 | − | 0.0930332i | ||||
\(375\) | −19321.4 | + | 15487.9i | −0.137397 | + | 0.110137i | ||||
\(376\) | 19469.7 | + | 33722.6i | 0.137716 | + | 0.238531i | ||||
\(377\) | − | 77961.6i | − | 0.548527i | ||||||
\(378\) | 90483.7 | + | 6094.70i | 0.633267 | + | 0.0426549i | ||||
\(379\) | 200558. | 1.39624 | 0.698121 | − | 0.715980i | \(-0.254020\pi\) | ||||
0.698121 | + | 0.715980i | \(0.254020\pi\) | |||||||
\(380\) | −8083.75 | + | 4667.16i | −0.0559816 | + | 0.0323210i | ||||
\(381\) | 120207. | + | 149960.i | 0.828095 | + | 1.03306i | ||||
\(382\) | 58708.3 | − | 101686.i | 0.402321 | − | 0.696841i | ||||
\(383\) | 65495.5 | + | 37813.8i | 0.446492 | + | 0.257782i | 0.706347 | − | 0.707865i | \(-0.250342\pi\) |
−0.259856 | + | 0.965648i | \(0.583675\pi\) | |||||||
\(384\) | −12144.4 | − | 4731.11i | −0.0823593 | − | 0.0320849i | ||||
\(385\) | −10311.7 | − | 17860.4i | −0.0695681 | − | 0.120495i | ||||
\(386\) | 168959.i | 1.13398i | ||||||||
\(387\) | −7127.18 | + | 2237.76i | −0.0475878 | + | 0.0149414i | ||||
\(388\) | 59430.7 | 0.394773 | ||||||||
\(389\) | 237715. | − | 137245.i | 1.57093 | − | 0.906977i | 0.574874 | − | 0.818242i | \(-0.305051\pi\) |
0.996055 | − | 0.0887346i | \(-0.0282823\pi\) | |||||||
\(390\) | −9864.47 | + | 1512.21i | −0.0648552 | + | 0.00994221i | ||||
\(391\) | −12944.5 | + | 22420.5i | −0.0846704 | + | 0.146653i | ||||
\(392\) | −9142.14 | − | 5278.22i | −0.0594943 | − | 0.0343491i | ||||
\(393\) | −42055.4 | − | 274337.i | −0.272293 | − | 1.77623i | ||||
\(394\) | −17496.1 | − | 30304.2i | −0.112707 | − | 0.195214i | ||||
\(395\) | − | 21137.2i | − | 0.135473i | ||||||
\(396\) | −134207. | − | 29922.5i | −0.855825 | − | 0.190813i | ||||
\(397\) | 3509.10 | 0.0222646 | 0.0111323 | − | 0.999938i | \(-0.496456\pi\) | ||||
0.0111323 | + | 0.999938i | \(0.496456\pi\) | |||||||
\(398\) | −41240.4 | + | 23810.2i | −0.260350 | + | 0.150313i | ||||
\(399\) | 75870.8 | − | 194754.i | 0.476573 | − | 1.22332i | ||||
\(400\) | −19843.7 | + | 34370.4i | −0.124023 | + | 0.214815i | ||||
\(401\) | −14126.3 | − | 8155.82i | −0.0878496 | − | 0.0507200i | 0.455432 | − | 0.890271i | \(-0.349485\pi\) |
−0.543281 | + | 0.839551i | \(0.682818\pi\) | |||||||
\(402\) | −12814.8 | + | 10272.3i | −0.0792975 | + | 0.0635645i | ||||
\(403\) | 134207. | + | 232454.i | 0.826355 | + | 1.43129i | ||||
\(404\) | 7333.40i | 0.0449307i | ||||||||
\(405\) | 8287.25 | + | 11896.3i | 0.0505243 | + | 0.0725271i | ||||
\(406\) | −54666.6 | −0.331642 | ||||||||
\(407\) | −129042. | + | 74502.2i | −0.779007 | + | 0.449760i | ||||
\(408\) | 5523.37 | + | 6890.47i | 0.0331806 | + | 0.0413932i | ||||
\(409\) | 3742.95 | − | 6482.97i | 0.0223752 | − | 0.0387550i | −0.854621 | − | 0.519252i | \(-0.826210\pi\) |
0.876996 | + | 0.480497i | \(0.159544\pi\) | |||||||
\(410\) | −3234.67 | − | 1867.54i | −0.0192425 | − | 0.0111097i | ||||
\(411\) | −92224.6 | − | 35928.1i | −0.545963 | − | 0.212692i | ||||
\(412\) | −14217.0 | − | 24624.5i | −0.0837554 | − | 0.145069i | ||||
\(413\) | 173604.i | 1.01780i | ||||||||
\(414\) | −29764.7 | + | 133499.i | −0.173660 | + | 0.778894i | ||||
\(415\) | 7845.46 | 0.0455535 | ||||||||
\(416\) | −27812.5 | + | 16057.6i | −0.160714 | + | 0.0927882i | ||||
\(417\) | −150746. | + | 23109.2i | −0.866911 | + | 0.132896i | ||||
\(418\) | −158451. | + | 274446.i | −0.906867 | + | 1.57074i | ||||
\(419\) | −94399.3 | − | 54501.5i | −0.537701 | − | 0.310442i | 0.206446 | − | 0.978458i | \(-0.433810\pi\) |
−0.744147 | + | 0.668016i | \(0.767144\pi\) | |||||||
\(420\) | 1060.36 | + | 6916.96i | 0.00601111 | + | 0.0392118i | ||||
\(421\) | −165636. | − | 286890.i | −0.934525 | − | 1.61865i | −0.775478 | − | 0.631374i | \(-0.782491\pi\) |
−0.159047 | − | 0.987271i | \(-0.550842\pi\) | |||||||
\(422\) | − | 127883.i | − | 0.718103i | ||||||
\(423\) | −41756.2 | − | 132992.i | −0.233367 | − | 0.743264i | ||||
\(424\) | −29680.1 | −0.165095 | ||||||||
\(425\) | 23288.2 | − | 13445.4i | 0.128931 | − | 0.0744384i | ||||
\(426\) | 59116.9 | − | 151749.i | 0.325756 | − | 0.836191i | ||||
\(427\) | −92906.2 | + | 160918.i | −0.509553 | + | 0.882571i | ||||
\(428\) | −3813.82 | − | 2201.91i | −0.0208196 | − | 0.0120202i | ||||
\(429\) | −264364. | + | 211913.i | −1.43644 | + | 1.15144i | ||||
\(430\) | −288.210 | − | 499.195i | −0.00155874 | − | 0.00269981i | ||||
\(431\) | − | 270347.i | − | 1.45535i | −0.685922 | − | 0.727675i | \(-0.740601\pi\) | ||
0.685922 | − | 0.727675i | \(-0.259399\pi\) | |||||||
\(432\) | 38746.2 | + | 25990.7i | 0.207616 | + | 0.139268i | ||||
\(433\) | −7609.14 | −0.0405845 | −0.0202922 | − | 0.999794i | \(-0.506460\pi\) | ||||
−0.0202922 | + | 0.999794i | \(0.506460\pi\) | |||||||
\(434\) | 162997. | − | 94106.1i | 0.865364 | − | 0.499618i | ||||
\(435\) | −5466.13 | − | 6819.06i | −0.0288869 | − | 0.0360368i | ||||
\(436\) | −10247.7 | + | 17749.6i | −0.0539082 | + | 0.0933717i | ||||
\(437\) | 272999. | + | 157616.i | 1.42954 | + | 0.825348i | ||||
\(438\) | −75811.1 | − | 29533.9i | −0.395171 | − | 0.153947i | ||||
\(439\) | 49775.5 | + | 86213.8i | 0.258278 | + | 0.447350i | 0.965781 | − | 0.259360i | \(-0.0835117\pi\) |
−0.707503 | + | 0.706710i | \(0.750178\pi\) | |||||||
\(440\) | − | 10610.0i | − | 0.0548037i | ||||||
\(441\) | 27830.3 | + | 25563.5i | 0.143101 | + | 0.131445i | ||||
\(442\) | 21760.1 | 0.111382 | ||||||||
\(443\) | 192291. | − | 111019.i | 0.979830 | − | 0.565705i | 0.0776111 | − | 0.996984i | \(-0.475271\pi\) |
0.902219 | + | 0.431279i | \(0.141937\pi\) | |||||||
\(444\) | 49975.0 | − | 7661.11i | 0.253505 | − | 0.0388620i | ||||
\(445\) | 554.651 | − | 960.684i | 0.00280091 | − | 0.00485133i | ||||
\(446\) | −124106. | − | 71652.4i | −0.623910 | − | 0.360214i | ||||
\(447\) | −22650.4 | − | 147754.i | −0.113360 | − | 0.739474i | ||||
\(448\) | 11259.5 | + | 19502.1i | 0.0561002 | + | 0.0971684i | ||||
\(449\) | 353910.i | 1.75550i | 0.479122 | + | 0.877749i | \(0.340955\pi\) | ||||
−0.479122 | + | 0.877749i | \(0.659045\pi\) | |||||||
\(450\) | 96107.4 | − | 104630.i | 0.474604 | − | 0.516690i | ||||
\(451\) | −126807. | −0.623433 | ||||||||
\(452\) | 140791. | − | 81285.6i | 0.689124 | − | 0.397866i | ||||
\(453\) | −36036.9 | + | 92504.0i | −0.175611 | + | 0.450780i | ||||
\(454\) | 56618.8 | − | 98066.7i | 0.274694 | − | 0.475784i | ||||
\(455\) | 14932.8 | + | 8621.46i | 0.0721305 | + | 0.0416445i | ||||
\(456\) | 83900.4 | − | 67254.2i | 0.403491 | − | 0.323437i | ||||
\(457\) | 128991. | + | 223419.i | 0.617629 | + | 1.06976i | 0.989917 | + | 0.141647i | \(0.0452399\pi\) |
−0.372288 | + | 0.928117i | \(0.621427\pi\) | |||||||
\(458\) | − | 75709.8i | − | 0.360929i | ||||||
\(459\) | −13930.6 | − | 28377.6i | −0.0661220 | − | 0.134695i | ||||
\(460\) | −10554.1 | −0.0498774 | ||||||||
\(461\) | 183775. | − | 106103.i | 0.864738 | − | 0.499257i | −0.000858089 | − | 1.00000i | \(-0.500273\pi\) |
0.865596 | + | 0.500743i | \(0.166940\pi\) | |||||||
\(462\) | 148593. | + | 185371.i | 0.696169 | + | 0.868478i | ||||
\(463\) | 34545.2 | − | 59834.0i | 0.161148 | − | 0.279117i | −0.774133 | − | 0.633024i | \(-0.781814\pi\) |
0.935281 | + | 0.353907i | \(0.115147\pi\) | |||||||
\(464\) | −24356.1 | − | 14062.0i | −0.113128 | − | 0.0653146i | ||||
\(465\) | 28036.8 | + | 10922.3i | 0.129665 | + | 0.0505138i | ||||
\(466\) | 56425.0 | + | 97730.9i | 0.259836 | + | 0.450049i | ||||
\(467\) | 126113.i | 0.578264i | 0.957289 | + | 0.289132i | \(0.0933667\pi\) | ||||
−0.957289 | + | 0.289132i | \(0.906633\pi\) | |||||||
\(468\) | 109684. | − | 34438.2i | 0.500785 | − | 0.157235i | ||||
\(469\) | 28376.9 | 0.129009 | ||||||||
\(470\) | 9314.86 | − | 5377.94i | 0.0421678 | − | 0.0243456i | ||||
\(471\) | −177340. | + | 27185.9i | −0.799400 | + | 0.122547i | ||||
\(472\) | −44656.6 | + | 77347.4i | −0.200448 | + | 0.347186i | ||||
\(473\) | −16947.8 | − | 9784.84i | −0.0757516 | − | 0.0437352i | ||||
\(474\) | 36896.4 | + | 240683.i | 0.164221 | + | 1.07125i | ||||
\(475\) | −163716. | − | 283564.i | −0.725609 | − | 1.25679i | ||||
\(476\) | − | 15258.2i | − | 0.0673424i | ||||||
\(477\) | 103700. | + | 23120.8i | 0.455768 | + | 0.101617i | ||||
\(478\) | −142101. | −0.621928 | ||||||||
\(479\) | −248690. | + | 143582.i | −1.08390 | + | 0.625788i | −0.931945 | − | 0.362599i | \(-0.881889\pi\) |
−0.151952 | + | 0.988388i | \(0.548556\pi\) | |||||||
\(480\) | −1306.83 | + | 3354.53i | −0.00567200 | + | 0.0145596i | ||||
\(481\) | 62290.1 | − | 107890.i | 0.269233 | − | 0.466326i | ||||
\(482\) | 169654. | + | 97949.6i | 0.730246 | + | 0.421608i | ||||
\(483\) | 184394. | − | 147809.i | 0.790410 | − | 0.633589i | ||||
\(484\) | −121543. | − | 210518.i | −0.518845 | − | 0.898666i | ||||
\(485\) | − | 16416.0i | − | 0.0697884i | ||||||
\(486\) | −115130. | − | 120993.i | −0.487434 | − | 0.512258i | ||||
\(487\) | 274661. | 1.15808 | 0.579040 | − | 0.815299i | \(-0.303427\pi\) | ||||
0.579040 | + | 0.815299i | \(0.303427\pi\) | |||||||
\(488\) | −82786.5 | + | 47796.8i | −0.347632 | + | 0.200706i | ||||
\(489\) | −44673.7 | − | 55730.9i | −0.186825 | − | 0.233066i | ||||
\(490\) | −1457.95 | + | 2525.25i | −0.00607227 | + | 0.0105175i | ||||
\(491\) | −274978. | − | 158759.i | −1.14060 | − | 0.658528i | −0.194024 | − | 0.980997i | \(-0.562154\pi\) |
−0.946580 | + | 0.322469i | \(0.895487\pi\) | |||||||
\(492\) | 40092.1 | + | 15618.7i | 0.165626 | + | 0.0645232i | ||||
\(493\) | 9527.92 | + | 16502.8i | 0.0392016 | + | 0.0678992i | ||||
\(494\) | − | 264957.i | − | 1.08573i | ||||||
\(495\) | −8265.20 | + | 37070.7i | −0.0337321 | + | 0.151294i | ||||
\(496\) | 96828.3 | 0.393585 | ||||||||
\(497\) | −243686. | + | 140692.i | −0.986547 | + | 0.569583i | ||||
\(498\) | −89333.8 | + | 13694.8i | −0.360211 | + | 0.0552199i | ||||
\(499\) | 97561.4 | − | 168981.i | 0.391811 | − | 0.678637i | −0.600877 | − | 0.799341i | \(-0.705182\pi\) |
0.992688 | + | 0.120704i | \(0.0385153\pi\) | |||||||
\(500\) | 19062.4 | + | 11005.7i | 0.0762494 | + | 0.0440226i | ||||
\(501\) | 26166.5 | + | 170689.i | 0.104248 | + | 0.680034i | ||||
\(502\) | 166184. | + | 287839.i | 0.659450 | + | 1.14220i | ||||
\(503\) | 21373.6i | 0.0844777i | 0.999108 | + | 0.0422388i | \(0.0134490\pi\) | ||||
−0.999108 | + | 0.0422388i | \(0.986551\pi\) | |||||||
\(504\) | −24148.0 | − | 76910.3i | −0.0950649 | − | 0.302777i | ||||
\(505\) | 2025.64 | 0.00794289 | ||||||||
\(506\) | −310309. | + | 179157.i | −1.21197 | + | 0.699733i | ||||
\(507\) | 9520.74 | − | 24439.0i | 0.0370386 | − | 0.0950752i | ||||
\(508\) | 85418.6 | − | 147949.i | 0.330998 | − | 0.573305i | ||||
\(509\) | −69165.6 | − | 39932.8i | −0.266965 | − | 0.154132i | 0.360543 | − | 0.932743i | \(-0.382592\pi\) |
−0.627508 | + | 0.778610i | \(0.715925\pi\) | |||||||
\(510\) | 1903.29 | − | 1525.67i | 0.00731753 | − | 0.00586570i | ||||
\(511\) | 70287.5 | + | 121742.i | 0.269176 | + | 0.466227i | ||||
\(512\) | 11585.2i | 0.0441942i | ||||||||
\(513\) | −345534. | + | 169624.i | −1.31297 | + | 0.644542i | ||||
\(514\) | −174196. | −0.659342 | ||||||||
\(515\) | −6801.80 | + | 3927.02i | −0.0256454 | + | 0.0148064i | ||||
\(516\) | 4153.14 | + | 5181.09i | 0.0155983 | + | 0.0194591i | ||||
\(517\) | 182583. | − | 316243.i | 0.683091 | − | 1.18315i | ||||
\(518\) | −75652.1 | − | 43677.7i | −0.281943 | − | 0.162780i | ||||
\(519\) | 437655. | + | 170498.i | 1.62479 | + | 0.632972i | ||||
\(520\) | 4435.42 | + | 7682.38i | 0.0164032 | + | 0.0284112i | ||||
\(521\) | 142732.i | 0.525830i | 0.964819 | + | 0.262915i | \(0.0846839\pi\) | ||||
−0.964819 | + | 0.262915i | \(0.915316\pi\) | |||||||
\(522\) | 74144.3 | + | 68105.1i | 0.272105 | + | 0.249942i | ||||
\(523\) | −232027. | −0.848271 | −0.424136 | − | 0.905599i | \(-0.639422\pi\) | ||||
−0.424136 | + | 0.905599i | \(0.639422\pi\) | |||||||
\(524\) | −213651. | + | 123352.i | −0.778114 | + | 0.449244i | ||||
\(525\) | −242635. | + | 37195.6i | −0.880307 | + | 0.134950i | ||||
\(526\) | 36254.8 | − | 62795.1i | 0.131037 | − | 0.226963i | ||||
\(527\) | −56817.8 | − | 32803.8i | −0.204580 | − | 0.118114i | ||||
\(528\) | 18520.5 | + | 120813.i | 0.0664330 | + | 0.433357i | ||||
\(529\) | 38291.5 | + | 66322.9i | 0.136833 | + | 0.237002i | ||||
\(530\) | 8198.24i | 0.0291856i | ||||||||
\(531\) | 216281. | − | 235460.i | 0.767060 | − | 0.835079i | ||||
\(532\) | −185788. | −0.656438 | ||||||||
\(533\) | 91817.0 | − | 53010.6i | 0.323198 | − | 0.186599i | ||||
\(534\) | −4638.71 | + | 11907.2i | −0.0162673 | + | 0.0417568i | ||||
\(535\) | −608.213 | + | 1053.45i | −0.00212495 | + | 0.00368051i | ||||
\(536\) | 12643.0 | + | 7299.43i | 0.0440068 | + | 0.0254073i | ||||
\(537\) | 85652.4 | − | 68658.6i | 0.297024 | − | 0.238093i | ||||
\(538\) | −99637.6 | − | 172577.i | −0.344238 | − | 0.596238i | ||||
\(539\) | 98995.8i | 0.340753i | ||||||||
\(540\) | 7179.16 | − | 10702.5i | 0.0246199 | − | 0.0367026i | ||||
\(541\) | −376322. | −1.28577 | −0.642887 | − | 0.765961i | \(-0.722264\pi\) | ||||
−0.642887 | + | 0.765961i | \(0.722264\pi\) | |||||||
\(542\) | −1660.32 | + | 958.583i | −0.00565187 | + | 0.00326311i | ||||
\(543\) | 38674.5 | + | 48246.9i | 0.131167 | + | 0.163633i | ||||
\(544\) | 3924.88 | − | 6798.09i | 0.0132626 | − | 0.0229715i | ||||
\(545\) | 4902.80 | + | 2830.63i | 0.0165064 | + | 0.00952995i | ||||
\(546\) | −185085. | − | 72103.8i | −0.620848 | − | 0.241865i | ||||
\(547\) | 137517. | + | 238187.i | 0.459602 | + | 0.796054i | 0.998940 | − | 0.0460355i | \(-0.0146587\pi\) |
−0.539338 | + | 0.842090i | \(0.681325\pi\) | |||||||
\(548\) | 87978.5i | 0.292965i | ||||||||
\(549\) | 326485. | − | 102508.i | 1.08322 | − | 0.340106i | ||||
\(550\) | 372180. | 1.23035 | ||||||||
\(551\) | 200943. | − | 116015.i | 0.661866 | − | 0.382129i | ||||
\(552\) | 120176. | − | 18422.8i | 0.394402 | − | 0.0604613i | ||||
\(553\) | 210355. | − | 364346.i | 0.687864 | − | 1.19142i | ||||
\(554\) | 259470. | + | 149805.i | 0.845412 | + | 0.488099i | ||||
\(555\) | −2116.15 | − | 13804.1i | −0.00687007 | − | 0.0448149i | ||||
\(556\) | 67781.0 | + | 117400.i | 0.219260 | + | 0.379769i | ||||
\(557\) | − | 318602.i | − | 1.02692i | −0.858112 | − | 0.513462i | \(-0.828363\pi\) | ||
0.858112 | − | 0.513462i | \(-0.171637\pi\) | |||||||
\(558\) | −338312. | − | 75429.3i | −1.08655 | − | 0.242254i | ||||
\(559\) | 16361.9 | 0.0523612 | ||||||||
\(560\) | 5386.88 | − | 3110.12i | 0.0171775 | − | 0.00991746i | ||||
\(561\) | 30061.7 | − | 77166.1i | 0.0955187 | − | 0.245189i | ||||
\(562\) | −1023.55 | + | 1772.83i | −0.00324067 | + | 0.00561300i | ||||
\(563\) | −41192.5 | − | 23782.5i | −0.129958 | − | 0.0750311i | 0.433612 | − | 0.901100i | \(-0.357239\pi\) |
−0.563569 | + | 0.826069i | \(0.690572\pi\) | |||||||
\(564\) | −96678.0 | + | 77496.7i | −0.303927 | + | 0.243627i | ||||
\(565\) | −22452.7 | − | 38889.3i | −0.0703351 | − | 0.121824i | ||||
\(566\) | − | 61023.8i | − | 0.190487i | ||||||
\(567\) | 24458.4 | + | 287531.i | 0.0760785 | + | 0.894374i | ||||
\(568\) | −144762. | −0.448701 | ||||||||
\(569\) | 271738. | − | 156888.i | 0.839318 | − | 0.484580i | −0.0177144 | − | 0.999843i | \(-0.505639\pi\) |
0.857032 | + | 0.515263i | \(0.172306\pi\) | |||||||
\(570\) | −18577.0 | − | 23175.0i | −0.0571775 | − | 0.0713296i | ||||
\(571\) | −162047. | + | 280674.i | −0.497015 | + | 0.860856i | −0.999994 | − | 0.00344295i | \(-0.998904\pi\) |
0.502979 | + | 0.864299i | \(0.332237\pi\) | |||||||
\(572\) | 260819. | + | 150584.i | 0.797164 | + | 0.460243i | ||||
\(573\) | 348133. | + | 135623.i | 1.06032 | + | 0.413070i | ||||
\(574\) | −37171.0 | − | 64382.0i | −0.112818 | − | 0.195407i | ||||
\(575\) | − | 370218.i | − | 1.11975i | ||||||
\(576\) | 9024.91 | − | 40478.1i | 0.0272018 | − | 0.122004i | ||||
\(577\) | −292524. | −0.878636 | −0.439318 | − | 0.898332i | \(-0.644780\pi\) | ||||
−0.439318 | + | 0.898332i | \(0.644780\pi\) | |||||||
\(578\) | 199978. | − | 115457.i | 0.598585 | − | 0.345593i | ||||
\(579\) | −531416. | + | 81465.3i | −1.58518 | + | 0.243005i | ||||
\(580\) | −3884.21 | + | 6727.64i | −0.0115464 | + | 0.0199989i | ||||
\(581\) | 135233. | + | 78077.0i | 0.400619 | + | 0.231297i | ||||
\(582\) | 28655.2 | + | 186924.i | 0.0845974 | + | 0.551847i | ||||
\(583\) | 139167. | + | 241043.i | 0.409447 | + | 0.709183i | ||||
\(584\) | 72320.7i | 0.212049i | ||||||||
\(585\) | −9512.52 | − | 30297.0i | −0.0277961 | − | 0.0885294i | ||||
\(586\) | 294884. | 0.858729 | ||||||||
\(587\) | −32013.0 | + | 18482.7i | −0.0929073 | + | 0.0536400i | −0.545734 | − | 0.837959i | \(-0.683749\pi\) |
0.452827 | + | 0.891599i | \(0.350416\pi\) | |||||||
\(588\) | 12193.3 | − | 31299.1i | 0.0352667 | − | 0.0905269i | ||||
\(589\) | −399428. | + | 691830.i | −1.15135 | + | 1.99420i | ||||
\(590\) | 21364.9 | + | 12335.1i | 0.0613759 | + | 0.0354354i | ||||
\(591\) | 86877.9 | − | 69641.0i | 0.248734 | − | 0.199384i | ||||
\(592\) | −22470.6 | − | 38920.2i | −0.0641167 | − | 0.111053i | ||||
\(593\) | − | 5939.58i | − | 0.0168906i | −0.999964 | − | 0.00844532i | \(-0.997312\pi\) | ||
0.999964 | − | 0.00844532i | \(-0.00268826\pi\) | |||||||
\(594\) | 29404.0 | − | 436540.i | 0.0833362 | − | 1.23723i | ||||
\(595\) | −4214.62 | −0.0119049 | ||||||||
\(596\) | −115069. | + | 66435.4i | −0.323942 | + | 0.187028i | ||||
\(597\) | −94773.1 | − | 118231.i | −0.265911 | − | 0.331727i | ||||
\(598\) | 149790. | − | 259444.i | 0.418871 | − | 0.725506i | ||||
\(599\) | 135382. | + | 78162.8i | 0.377318 | + | 0.217845i | 0.676651 | − | 0.736304i | \(-0.263431\pi\) |
−0.299333 | + | 0.954149i | \(0.596764\pi\) | |||||||
\(600\) | −117671. | − | 45841.2i | −0.326864 | − | 0.127337i | ||||
\(601\) | −70819.1 | − | 122662.i | −0.196066 | − | 0.339596i | 0.751184 | − | 0.660093i | \(-0.229483\pi\) |
−0.947249 | + | 0.320498i | \(0.896150\pi\) | |||||||
\(602\) | − | 11472.9i | − | 0.0316578i | ||||||
\(603\) | −38487.5 | − | 35352.7i | −0.105849 | − | 0.0972271i | ||||
\(604\) | 88245.0 | 0.241889 | ||||||||
\(605\) | −58149.4 | + | 33572.6i | −0.158867 | + | 0.0917220i | ||||
\(606\) | −23065.3 | + | 3535.88i | −0.0628078 | + | 0.00962836i | ||||
\(607\) | −133819. | + | 231782.i | −0.363196 | + | 0.629074i | −0.988485 | − | 0.151320i | \(-0.951648\pi\) |
0.625289 | + | 0.780393i | \(0.284981\pi\) | |||||||
\(608\) | −82775.5 | − | 47790.5i | −0.223921 | − | 0.129281i | ||||
\(609\) | −26358.1 | − | 171939.i | −0.0710689 | − | 0.463597i | ||||
\(610\) | 13202.5 | + | 22867.3i | 0.0354809 | + | 0.0614548i | ||||
\(611\) | 305309.i | 0.817819i | ||||||||
\(612\) | −19009.0 | + | 20694.6i | −0.0507524 | + | 0.0552529i | ||||
\(613\) | 191952. | 0.510825 | 0.255413 | − | 0.966832i | \(-0.417789\pi\) | ||||
0.255413 | + | 0.966832i | \(0.417789\pi\) | |||||||
\(614\) | 9216.74 | − | 5321.29i | 0.0244479 | − | 0.0141150i | ||||
\(615\) | 4314.21 | − | 11074.3i | 0.0114065 | − | 0.0292795i | ||||
\(616\) | 105589. | − | 182886.i | 0.278265 | − | 0.481970i | ||||
\(617\) | −332409. | − | 191917.i | −0.873178 | − | 0.504130i | −0.00477496 | − | 0.999989i | \(-0.501520\pi\) |
−0.868403 | + | 0.495859i | \(0.834853\pi\) | |||||||
\(618\) | 70595.2 | − | 56588.8i | 0.184841 | − | 0.148168i | ||||
\(619\) | −60619.2 | − | 104996.i | −0.158208 | − | 0.274025i | 0.776014 | − | 0.630715i | \(-0.217238\pi\) |
−0.934223 | + | 0.356691i | \(0.883905\pi\) | |||||||
\(620\) | − | 26745.9i | − | 0.0695784i | ||||||
\(621\) | −434238. | − | 29248.9i | −1.12602 | − | 0.0758450i | ||||
\(622\) | −237302. | −0.613368 | ||||||||
\(623\) | 19121.2 | − | 11039.6i | 0.0492651 | − | 0.0284432i | ||||
\(624\) | −63914.9 | − | 79734.6i | −0.164147 | − | 0.204775i | ||||
\(625\) | −190747. | + | 330383.i | −0.488311 | + | 0.845780i | ||||
\(626\) | 86797.5 | + | 50112.5i | 0.221492 | + | 0.127879i | ||||
\(627\) | −939597. | − | 366040.i | −2.39005 | − | 0.931095i | ||||
\(628\) | 79738.4 | + | 138111.i | 0.202185 | + | 0.350194i | ||||
\(629\) | 30450.6i | 0.0769653i | ||||||||
\(630\) | −21244.2 | + | 6670.17i | −0.0535253 | + | 0.0168057i | ||||
\(631\) | −455676. | −1.14445 | −0.572226 | − | 0.820096i | \(-0.693920\pi\) | ||||
−0.572226 | + | 0.820096i | \(0.693920\pi\) | |||||||
\(632\) | 187442. | − | 108220.i | 0.469282 | − | 0.270940i | ||||
\(633\) | 402222. | − | 61660.0i | 1.00382 | − | 0.153885i | ||||
\(634\) | −215668. | + | 373548.i | −0.536546 | + | 0.929325i | ||||
\(635\) | −40866.6 | − | 23594.4i | −0.101349 | − | 0.0585141i | ||||
\(636\) | −14310.6 | − | 93350.9i | −0.0353788 | − | 0.230783i | ||||
\(637\) | −41384.4 | − | 71679.9i | −0.101990 | − | 0.176652i | ||||
\(638\) | 263740.i | 0.647940i | ||||||||
\(639\) | 505789. | + | 112770.i | 1.23870 | + | 0.276179i | ||||
\(640\) | 3200.08 | 0.00781269 | ||||||||
\(641\) | 496152. | − | 286453.i | 1.20753 | − | 0.697168i | 0.245312 | − | 0.969444i | \(-0.421110\pi\) |
0.962219 | + | 0.272276i | \(0.0877763\pi\) | |||||||
\(642\) | 5086.66 | − | 13057.0i | 0.0123413 | − | 0.0316792i | ||||
\(643\) | 224632. | − | 389074.i | 0.543313 | − | 0.941046i | −0.455398 | − | 0.890288i | \(-0.650503\pi\) |
0.998711 | − | 0.0507578i | \(-0.0161637\pi\) | |||||||
\(644\) | −181922. | − | 105033.i | −0.438645 | − | 0.253252i | ||||
\(645\) | 1431.12 | − | 1147.18i | 0.00343999 | − | 0.00275748i | ||||
\(646\) | 32381.2 | + | 56085.9i | 0.0775940 | + | 0.134397i | ||||
\(647\) | 502638.i | 1.20073i | 0.799725 | + | 0.600366i | \(0.204979\pi\) | ||||
−0.799725 | + | 0.600366i | \(0.795021\pi\) | |||||||
\(648\) | −63065.0 | + | 134398.i | −0.150189 | + | 0.320068i | ||||
\(649\) | 837558. | 1.98850 | ||||||||
\(650\) | −269484. | + | 155587.i | −0.637833 | + | 0.368253i | ||||
\(651\) | 374577. | + | 467289.i | 0.883850 | + | 1.10261i | ||||
\(652\) | −31744.9 | + | 54983.8i | −0.0746756 | + | 0.129342i | ||||
\(653\) | −595663. | − | 343906.i | −1.39693 | − | 0.806517i | −0.402859 | − | 0.915262i | \(-0.631983\pi\) |
−0.994070 | + | 0.108745i | \(0.965317\pi\) | |||||||
\(654\) | −60767.7 | − | 23673.4i | −0.142075 | − | 0.0553484i | ||||
\(655\) | 34072.3 | + | 59014.9i | 0.0794179 | + | 0.137556i | ||||
\(656\) | − | 38246.2i | − | 0.0888752i | ||||||
\(657\) | 56337.9 | − | 252684.i | 0.130518 | − | 0.585393i | ||||
\(658\) | 214082. | 0.494458 | ||||||||
\(659\) | −233033. | + | 134542.i | −0.536595 | + | 0.309803i | −0.743698 | − | 0.668516i | \(-0.766930\pi\) |
0.207103 | + | 0.978319i | \(0.433597\pi\) | |||||||
\(660\) | 33371.0 | − | 5115.73i | 0.0766093 | − | 0.0117441i | ||||
\(661\) | 200626. | − | 347494.i | 0.459181 | − | 0.795324i | −0.539737 | − | 0.841834i | \(-0.681476\pi\) |
0.998918 | + | 0.0465092i | \(0.0148097\pi\) | |||||||
\(662\) | 90991.0 | + | 52533.7i | 0.207626 | + | 0.119873i | ||||
\(663\) | 10491.9 | + | 68440.7i | 0.0238685 | + | 0.155700i | ||||
\(664\) | 40167.7 | + | 69572.6i | 0.0911048 | + | 0.157798i | ||||
\(665\) | 51318.4i | 0.116046i | ||||||||
\(666\) | 48192.0 | + | 153489.i | 0.108649 | + | 0.346043i | ||||
\(667\) | 262349. | 0.589696 | ||||||||
\(668\) | 132932. | − | 76748.1i | 0.297903 | − | 0.171995i | ||||
\(669\) | 165525. | − | 424890.i | 0.369838 | − | 0.949345i | ||||
\(670\) | 2016.25 | − | 3492.25i | 0.00449154 | − | 0.00777957i | ||||
\(671\) | 776354. | + | 448228.i | 1.72431 | + | 0.995529i | ||||
\(672\) | −55909.8 | + | 44817.1i | −0.123808 | + | 0.0992442i | ||||
\(673\) | 54368.5 | + | 94169.0i | 0.120038 | + | 0.207911i | 0.919782 | − | 0.392429i | \(-0.128365\pi\) |
−0.799745 | + | 0.600340i | \(0.795032\pi\) | |||||||
\(674\) | − | 118978.i | − | 0.261907i | ||||||
\(675\) | 375424. | + | 251832.i | 0.823977 | + | 0.552718i | ||||
\(676\) | −23313.8 | −0.0510176 | ||||||||
\(677\) | −82318.9 | + | 47526.9i | −0.179607 | + | 0.103696i | −0.587108 | − | 0.809509i | \(-0.699734\pi\) |
0.407501 | + | 0.913205i | \(0.366400\pi\) | |||||||
\(678\) | 323546. | + | 403628.i | 0.703845 | + | 0.878054i | ||||
\(679\) | 163370. | − | 282965.i | 0.354350 | − | 0.613752i | ||||
\(680\) | −1877.77 | − | 1084.13i | −0.00406093 | − | 0.00234458i | ||||
\(681\) | 335742. | + | 130796.i | 0.723956 | + | 0.282033i | ||||
\(682\) | −454017. | − | 786380.i | −0.976120 | − | 1.69069i | ||||
\(683\) | − | 704385.i | − | 1.50997i | −0.655741 | − | 0.754986i | \(-0.727644\pi\) | ||
0.655741 | − | 0.754986i | \(-0.272356\pi\) | |||||||
\(684\) | 251984. | + | 231459.i | 0.538593 | + | 0.494723i | ||||
\(685\) | 24301.5 | 0.0517906 | ||||||||
\(686\) | −308933. | + | 178363.i | −0.656472 | + | 0.379015i | ||||
\(687\) | 238125. | − | 36504.3i | 0.504536 | − | 0.0773447i | ||||
\(688\) | 2951.20 | − | 5111.63i | 0.00623479 | − | 0.0107990i | ||||
\(689\) | −201532. | − | 116355.i | −0.424528 | − | 0.245101i | ||||
\(690\) | −5088.75 | − | 33195.0i | −0.0106884 | − | 0.0697228i | ||||
\(691\) | −441540. | − | 764770.i | −0.924729 | − | 1.60168i | −0.791997 | − | 0.610525i | \(-0.790959\pi\) |
−0.132731 | − | 0.991152i | \(-0.542375\pi\) | |||||||
\(692\) | − | 417505.i | − | 0.871865i | ||||||
\(693\) | −511392. | + | 556739.i | −1.06485 | + | 1.15927i | ||||
\(694\) | −302351. | −0.627757 | ||||||||
\(695\) | 32428.3 | − | 18722.5i | 0.0671359 | − | 0.0387609i | ||||
\(696\) | 32484.7 | − | 83385.7i | 0.0670596 | − | 0.172137i | ||||
\(697\) | −12957.2 | + | 22442.5i | −0.0266713 | + | 0.0461960i | ||||
\(698\) | −464643. | − | 268262.i | −0.953692 | − | 0.550614i | ||||
\(699\) | −280181. | + | 224592.i | −0.573435 | + | 0.459663i | ||||
\(700\) | 109097. | + | 188962.i | 0.222648 | + | 0.385637i | ||||
\(701\) | 713342.i | 1.45165i | 0.687879 | + | 0.725825i | \(0.258542\pi\) | ||||
−0.687879 | + | 0.725825i | \(0.741458\pi\) | |||||||
\(702\) | 161202. | + | 328378.i | 0.327111 | + | 0.666345i | ||||
\(703\) | 370775. | 0.750240 | ||||||||
\(704\) | 94088.3 | − | 54321.9i | 0.189841 | − | 0.109605i | ||||
\(705\) | 21406.2 | + | 26704.4i | 0.0430686 | + | 0.0537286i | ||||
\(706\) | −304605. | + | 527592.i | −0.611122 | + | 1.05849i | ||||
\(707\) | 34916.2 | + | 20158.9i | 0.0698535 | + | 0.0403299i | ||||
\(708\) | −264808. | − | 103162.i | −0.528280 | − | 0.205803i | ||||
\(709\) | −39245.0 | − | 67974.3i | −0.0780713 | − | 0.135223i | 0.824346 | − | 0.566086i | \(-0.191543\pi\) |
−0.902418 | + | 0.430862i | \(0.858210\pi\) | |||||||
\(710\) | 39986.2i | 0.0793219i | ||||||||
\(711\) | −739216. | + | 232096.i | −1.46229 | + | 0.459122i | ||||
\(712\) | 11359.0 | 0.0224068 | ||||||||
\(713\) | −782233. | + | 451623.i | −1.53871 | + | 0.888376i | ||||
\(714\) | 47990.5 | − | 7356.89i | 0.0941368 | − | 0.0144310i | ||||
\(715\) | 41594.4 | − | 72043.6i | 0.0813623 | − | 0.140924i | ||||
\(716\) | −84504.1 | − | 48788.5i | −0.164836 | − | 0.0951681i | ||||
\(717\) | −68515.4 | − | 446940.i | −0.133275 | − | 0.869383i | ||||
\(718\) | 165148. | + | 286044.i | 0.320349 | + | 0.554862i | ||||
\(719\) | − | 146207.i | − | 0.282820i | −0.989951 | − | 0.141410i | \(-0.954836\pi\) | ||
0.989951 | − | 0.141410i | \(-0.0451636\pi\) | |||||||
\(720\) | −11180.9 | − | 2492.87i | −0.0215681 | − | 0.00480877i | ||||
\(721\) | −156325. | −0.300717 | ||||||||
\(722\) | 363698. | − | 209981.i | 0.697696 | − | 0.402815i | ||||
\(723\) | −226274. | + | 580829.i | −0.432871 | + | 1.11115i | ||||
\(724\) | 27481.9 | − | 47600.1i | 0.0524288 | − | 0.0908094i | ||||
\(725\) | −235994. | − | 136251.i | −0.448978 | − | 0.259217i | ||||
\(726\) | 603526. | − | 483784.i | 1.14505 | − | 0.917864i | ||||
\(727\) | −352617. | − | 610750.i | −0.667166 | − | 1.15557i | −0.978693 | − | 0.205328i | \(-0.934174\pi\) |
0.311527 | − | 0.950237i | \(-0.399159\pi\) | |||||||
\(728\) | 176563.i | 0.333148i | ||||||||
\(729\) | 325041. | − | 420450.i | 0.611622 | − | 0.791150i | ||||
\(730\) | 19976.5 | 0.0374863 | ||||||||
\(731\) | −3463.47 | + | 1999.63i | −0.00648151 | + | 0.00374210i | ||||
\(732\) | −190249. | − | 237338.i | −0.355058 | − | 0.442939i | ||||
\(733\) | −65548.2 | + | 113533.i | −0.121998 | + | 0.211307i | −0.920555 | − | 0.390612i | \(-0.872263\pi\) |
0.798558 | + | 0.601919i | \(0.205597\pi\) | |||||||
\(734\) | −309134. | − | 178479.i | −0.573793 | − | 0.331279i | ||||
\(735\) | −8645.46 | − | 3368.03i | −0.0160035 | − | 0.00623449i | ||||
\(736\) | −54035.4 | − | 93592.1i | −0.0997523 | − | 0.172776i | ||||
\(737\) | − | 136905.i | − | 0.252048i | ||||||
\(738\) | −29793.8 | + | 133630.i | −0.0547033 | + | 0.245353i | ||||
\(739\) | 82938.7 | 0.151869 | 0.0759344 | − | 0.997113i | \(-0.475806\pi\) | ||||
0.0759344 | + | 0.997113i | \(0.475806\pi\) | |||||||
\(740\) | −10750.6 | + | 6206.84i | −0.0196321 | + | 0.0113346i | ||||
\(741\) | 833354. | − | 127752.i | 1.51772 | − | 0.232665i | ||||
\(742\) | −81587.9 | + | 141314.i | −0.148190 | + | 0.256672i | ||||
\(743\) | 726053. | + | 419187.i | 1.31520 | + | 0.759329i | 0.982952 | − | 0.183865i | \(-0.0588608\pi\) |
0.332244 | + | 0.943193i | \(0.392194\pi\) | |||||||
\(744\) | 46686.8 | + | 304548.i | 0.0843428 | + | 0.550186i | ||||
\(745\) | 18350.8 | + | 31784.5i | 0.0330630 | + | 0.0572669i | ||||
\(746\) | 315270.i | 0.566507i | ||||||||
\(747\) | −86146.5 | − | 274373.i | −0.154382 | − | 0.491700i | ||||
\(748\) | −73613.3 | −0.131569 | ||||||||
\(749\) | −20967.7 | + | 12105.7i | −0.0373755 | + | 0.0215788i | ||||
\(750\) | −25424.3 | + | 65262.1i | −0.0451987 | + | 0.116022i | ||||
\(751\) | −154122. | + | 266948.i | −0.273266 | + | 0.473311i | −0.969696 | − | 0.244314i | \(-0.921437\pi\) |
0.696430 | + | 0.717625i | \(0.254771\pi\) | |||||||
\(752\) | 95381.8 | + | 55068.7i | 0.168667 | + | 0.0973799i | ||||
\(753\) | −825195. | + | 661473.i | −1.45535 | + | 1.16660i | ||||
\(754\) | −110254. | − | 190966.i | −0.193934 | − | 0.335903i | ||||
\(755\) | − | 24375.1i | − | 0.0427614i | ||||||
\(756\) | 230258. | − | 113034.i | 0.402876 | − | 0.197773i | ||||
\(757\) | 298072. | 0.520151 | 0.260075 | − | 0.965588i | \(-0.416253\pi\) | ||||
0.260075 | + | 0.965588i | \(0.416253\pi\) | |||||||
\(758\) | 491264. | − | 283631.i | 0.855020 | − | 0.493646i | ||||
\(759\) | −713110. | − | 889612.i | −1.23786 | − | 1.54425i | ||||
\(760\) | −13200.7 | + | 22864.3i | −0.0228544 | + | 0.0395850i | ||||
\(761\) | 205714. | + | 118769.i | 0.355218 | + | 0.205085i | 0.666981 | − | 0.745075i | \(-0.267586\pi\) |
−0.311763 | + | 0.950160i | \(0.600920\pi\) | |||||||
\(762\) | 506521. | + | 197326.i | 0.872344 | + | 0.339840i | ||||
\(763\) | 56340.2 | + | 97584.1i | 0.0967764 | + | 0.167622i | ||||
\(764\) | − | 332104.i | − | 0.568968i | ||||||
\(765\) | 5716.28 | + | 5250.68i | 0.00976767 | + | 0.00897207i | ||||
\(766\) | 213907. | 0.364559 | ||||||||
\(767\) | −606450. | + | 350134.i | −1.03087 | + | 0.595174i | ||||
\(768\) | −36438.3 | + | 5585.95i | −0.0617783 | + | 0.00947053i | ||||
\(769\) | −346986. | + | 600997.i | −0.586758 | + | 1.01629i | 0.407896 | + | 0.913029i | \(0.366263\pi\) |
−0.994654 | + | 0.103266i | \(0.967071\pi\) | |||||||
\(770\) | −50516.9 | − | 29166.0i | −0.0852031 | − | 0.0491920i | ||||
\(771\) | −83990.3 | − | 547887.i | −0.141293 | − | 0.921684i | ||||
\(772\) | 238944. | + | 413863.i | 0.400923 | + | 0.694419i | ||||
\(773\) | 106414.i | 0.178091i | 0.996028 | + | 0.0890454i | \(0.0283816\pi\) | ||||
−0.996028 | + | 0.0890454i | \(0.971618\pi\) | |||||||
\(774\) | −14293.3 | + | 15560.7i | −0.0238589 | + | 0.0259746i | ||||
\(775\) | 938201. | 1.56204 | ||||||||
\(776\) | 145575. | − | 84047.7i | 0.241748 | − | 0.139573i | ||||
\(777\) | 100900. | − | 259003.i | 0.167129 | − | 0.429006i | ||||
\(778\) | 388186. | − | 672358.i | 0.641329 | − | 1.11081i | ||||
\(779\) | 273266. | + | 157770.i | 0.450309 | + | 0.259986i | ||||
\(780\) | −22024.3 | + | 17654.6i | −0.0362004 | + | 0.0290181i | ||||
\(781\) | 678772. | + | 1.17567e6i | 1.11281 | + | 1.92745i | ||||
\(782\) | 73225.1i | 0.119742i | ||||||||
\(783\) | −178457. | + | 266039.i | −0.291079 | + | 0.433932i | ||||
\(784\) | −29858.1 | −0.0485769 | ||||||||
\(785\) | 38149.1 | − | 22025.4i | 0.0619077 | − | 0.0357424i | ||||
\(786\) | −490985. | − | 612509.i | −0.794736 | − | 0.991443i | ||||
\(787\) | −48361.5 | + | 83764.7i | −0.0780820 | + | 0.135242i | −0.902422 | − | 0.430853i | \(-0.858213\pi\) |
0.824340 | + | 0.566094i | \(0.191546\pi\) | |||||||
\(788\) | −85713.2 | − | 49486.5i | −0.138037 | − | 0.0796957i | ||||
\(789\) | 214986. | + | 83752.6i | 0.345348 | + | 0.134538i | ||||
\(790\) | −29892.6 | − | 51775.4i | −0.0478971 | − | 0.0829602i | ||||
\(791\) | − | 893787.i | − | 1.42850i | ||||||
\(792\) | −371055. | + | 116502.i | −0.591546 | + | 0.185731i | ||||
\(793\) | −749512. | −1.19188 | ||||||||
\(794\) | 8595.51 | − | 4962.62i | 0.0136342 | − | 0.00787173i | ||||
\(795\) | −25785.4 | + | 3952.87i | −0.0407981 | + | 0.00625430i | ||||
\(796\) | −67345.3 | + | 116646.i | −0.106287 | + | 0.184095i | ||||
\(797\) | 473218. | + | 273213.i | 0.744980 | + | 0.430115i | 0.823877 | − | 0.566768i | \(-0.191806\pi\) |
−0.0788969 | + | 0.996883i | \(0.525140\pi\) | |||||||
\(798\) | −89579.6 | − | 584347.i | −0.140671 | − | 0.917624i | ||||
\(799\) | −37312.7 | − | 64627.5i | −0.0584471 | − | 0.101233i | ||||
\(800\) | 112253.i | 0.175396i | ||||||||
\(801\) | −39687.6 | − | 8848.65i | −0.0618571 | − | 0.0137915i | ||||
\(802\) | −46136.3 | −0.0717289 | ||||||||
\(803\) | 587345. | − | 339104.i | 0.910882 | − | 0.525898i | ||||
\(804\) | −16862.5 | + | 43284.7i | −0.0260861 | + | 0.0669610i | ||||
\(805\) | −29012.2 | + | 50250.5i | −0.0447701 | + | 0.0775441i | ||||
\(806\) | 657479. | + | 379596.i | 1.01207 | + | 0.584321i | ||||
\(807\) | 494756. | − | 396594.i | 0.759703 | − | 0.608974i | ||||
\(808\) | 10371.0 | + | 17963.1i | 0.0158854 | + | 0.0275143i | ||||
\(809\) | − | 467941.i | − | 0.714981i | −0.933917 | − | 0.357490i | \(-0.883633\pi\) | ||
0.933917 | − | 0.357490i | \(-0.116367\pi\) | |||||||
\(810\) | 37123.4 | + | 17419.8i | 0.0565819 | + | 0.0265506i | ||||
\(811\) | −1.15071e6 | −1.74954 | −0.874771 | − | 0.484537i | \(-0.838988\pi\) | ||||
−0.874771 | + | 0.484537i | \(0.838988\pi\) | |||||||
\(812\) | −133905. | + | 77310.2i | −0.203089 | + | 0.117253i | ||||
\(813\) | −3815.51 | − | 4759.89i | −0.00577260 | − | 0.00720139i | ||||
\(814\) | −210724. | + | 364985.i | −0.318028 | + | 0.550841i | ||||
\(815\) | 15187.6 | + | 8768.59i | 0.0228652 | + | 0.0132012i | ||||
\(816\) | 23274.0 | + | 9066.91i | 0.0349536 | + | 0.0136169i | ||||
\(817\) | 24348.1 | + | 42172.2i | 0.0364772 | + | 0.0631803i | ||||
\(818\) | − | 21173.3i | − | 0.0316433i | ||||||
\(819\) | 137543. | − | 616901.i | 0.205055 | − | 0.919703i | ||||
\(820\) | −10564.4 | −0.0157114 | ||||||||
\(821\) | 411132. | − | 237367.i | 0.609952 | − | 0.352156i | −0.162995 | − | 0.986627i | \(-0.552115\pi\) |
0.772947 | + | 0.634471i | \(0.218782\pi\) | |||||||
\(822\) | −276713. | + | 42419.8i | −0.409531 | + | 0.0627805i | ||||
\(823\) | 599334. | − | 1.03808e6i | 0.884849 | − | 1.53260i | 0.0389627 | − | 0.999241i | \(-0.487595\pi\) |
0.845886 | − | 0.533363i | \(-0.179072\pi\) | |||||||
\(824\) | −69648.7 | − | 40211.7i | −0.102579 | − | 0.0592240i | ||||
\(825\) | 179451. | + | 1.17060e6i | 0.263656 | + | 1.71988i | ||||
\(826\) | 245514. | + | 425242.i | 0.359845 | + | 0.623270i | ||||
\(827\) | 227743.i | 0.332993i | 0.986042 | + | 0.166496i | \(0.0532454\pi\) | ||||
−0.986042 | + | 0.166496i | \(0.946755\pi\) | |||||||
\(828\) | 115888. | + | 369099.i | 0.169036 | + | 0.538371i | ||||
\(829\) | 17171.5 | 0.0249862 | 0.0124931 | − | 0.999922i | \(-0.496023\pi\) | ||||
0.0124931 | + | 0.999922i | \(0.496023\pi\) | |||||||
\(830\) | 19217.4 | − | 11095.2i | 0.0278957 | − | 0.0161056i | ||||
\(831\) | −346067. | + | 888326.i | −0.501139 | + | 1.28638i | ||||
\(832\) | −45417.6 | + | 78665.6i | −0.0656112 | + | 0.113642i | ||||
\(833\) | 17520.4 | + | 10115.4i | 0.0252496 | + | 0.0145779i | ||||
\(834\) | −336570. | + | 269793.i | −0.483886 | + | 0.387881i | ||||
\(835\) | −21199.4 | − | 36718.4i | −0.0304054 | − | 0.0526637i | ||||
\(836\) | 896337.i | 1.28250i | ||||||||
\(837\) | 74122.3 | − | 1.10044e6i | 0.105803 | − | 1.57078i | ||||
\(838\) | −308307. | −0.439031 | ||||||||
\(839\) | −655294. | + | 378334.i | −0.930920 | + | 0.537467i | −0.887102 | − | 0.461573i | \(-0.847285\pi\) |
−0.0438177 | + | 0.999040i | \(0.513952\pi\) | |||||||
\(840\) | 12379.4 | + | 15443.4i | 0.0175445 | + | 0.0218870i | ||||
\(841\) | −257088. | + | 445290.i | −0.363488 | + | 0.629580i | ||||
\(842\) | −811448. | − | 468490.i | −1.14456 | − | 0.660809i | ||||
\(843\) | −6069.49 | − | 2364.50i | −0.00854078 | − | 0.00332725i | ||||
\(844\) | −180853. | − | 313247.i | −0.253888 | − | 0.439747i | ||||
\(845\) | 6439.75i | 0.00901894i | ||||||||
\(846\) | −290360. | − | 266709.i | −0.405691 | − | 0.372647i | ||||
\(847\) | −1.33644e6 | −1.86287 | ||||||||
\(848\) | −72701.0 | + | 41974.0i | −0.101099 | + | 0.0583698i | ||||
\(849\) | 191934. | − | 29423.3i | 0.266279 | − | 0.0408203i | ||||
\(850\) | 38029.5 | − | 65868.9i | 0.0526359 | − | 0.0911681i | ||||
\(851\) | 363060. | + | 209613.i | 0.501325 | + | 0.289440i | ||||
\(852\) | −69798.5 | − | 455311.i | −0.0961539 | − | 0.627232i | ||||
\(853\) | 281438. | + | 487465.i | 0.386798 | + | 0.669954i | 0.992017 | − | 0.126105i | \(-0.0402477\pi\) |
−0.605219 | + | 0.796059i | \(0.706914\pi\) | |||||||
\(854\) | 525557.i | 0.720616i | ||||||||
\(855\) | 63933.8 | − | 69603.1i | 0.0874577 | − | 0.0952130i | ||||
\(856\) | −12455.9 | −0.0169991 | ||||||||
\(857\) | 753246. | − | 434887.i | 1.02559 | − | 0.592127i | 0.109874 | − | 0.993945i | \(-0.464955\pi\) |
0.915719 | + | 0.401819i | \(0.131622\pi\) | |||||||
\(858\) | −347866. | + | 892945.i | −0.472539 | + | 1.21297i | ||||
\(859\) | −211385. | + | 366130.i | −0.286476 | + | 0.496191i | −0.972966 | − | 0.230948i | \(-0.925817\pi\) |
0.686490 | + | 0.727139i | \(0.259151\pi\) | |||||||
\(860\) | −1411.94 | − | 815.182i | −0.00190905 | − | 0.00110219i | ||||
\(861\) | 184574. | − | 147954.i | 0.248980 | − | 0.199582i | ||||
\(862\) | −382329. | − | 662213.i | −0.514544 | − | 0.891217i | ||||
\(863\) | − | 1.33087e6i | − | 1.78696i | −0.449100 | − | 0.893482i | \(-0.648255\pi\) | ||
0.449100 | − | 0.893482i | \(-0.351745\pi\) | |||||||
\(864\) | 131665. | + | 8868.53i | 0.176377 | + | 0.0118802i | ||||
\(865\) | −115323. | −0.154129 | ||||||||
\(866\) | −18638.5 | + | 10761.0i | −0.0248528 | + | 0.0143488i | ||||
\(867\) | 459562. | + | 573308.i | 0.611372 | + | 0.762694i | ||||
\(868\) | 266172. | − | 461024.i | 0.353284 | − | 0.611905i | ||||
\(869\) | −1.75779e6 | − | 1.01486e6i | −2.32771 | − | 1.34390i | ||||
\(870\) | −23032.8 | − | 8972.94i | −0.0304305 | − | 0.0118549i | ||||
\(871\) | 57231.9 | + | 99128.6i | 0.0754401 | + | 0.130666i | ||||
\(872\) | 57969.9i | 0.0762377i | ||||||||
\(873\) | −574103. | + | 180255.i | −0.753289 | + | 0.236515i | ||||
\(874\) | 891610. | 1.16722 | ||||||||
\(875\) | 104801. | − | 60507.1i | 0.136884 | − | 0.0790297i | ||||
\(876\) | −227466. | + | 34870.2i | −0.296420 | + | 0.0454408i | ||||
\(877\) | 638412. | − | 1.10576e6i | 0.830045 | − | 1.43768i | −0.0679561 | − | 0.997688i | \(-0.521648\pi\) |
0.898001 | − | 0.439992i | \(-0.145019\pi\) | |||||||
\(878\) | 243849. | + | 140787.i | 0.316324 | + | 0.182630i | ||||
\(879\) | 142182. | + | 927481.i | 0.184020 | + | 1.20040i | ||||
\(880\) | −15004.8 | − | 25989.1i | −0.0193761 | − | 0.0335603i | ||||
\(881\) | 404060.i | 0.520588i | 0.965529 | + | 0.260294i | \(0.0838194\pi\) | ||||
−0.965529 | + | 0.260294i | \(0.916181\pi\) | |||||||
\(882\) | 104322. | + | 23259.5i | 0.134104 | + | 0.0298994i | ||||
\(883\) | 728109. | 0.933845 | 0.466923 | − | 0.884298i | \(-0.345363\pi\) | ||||
0.466923 | + | 0.884298i | \(0.345363\pi\) | |||||||
\(884\) | 53301.1 | − | 30773.4i | 0.0682075 | − | 0.0393796i | ||||
\(885\) | −28495.3 | + | 73145.3i | −0.0363821 | + | 0.0933899i | ||||
\(886\) | 314009. | − | 543880.i | 0.400014 | − | 0.692844i | ||||
\(887\) | 94847.0 | + | 54759.9i | 0.120552 | + | 0.0696010i | 0.559064 | − | 0.829125i | \(-0.311161\pi\) |
−0.438511 | + | 0.898726i | \(0.644494\pi\) | |||||||
\(888\) | 111579. | − | 89441.1i | 0.141500 | − | 0.113426i | ||||
\(889\) | −469616. | − | 813399.i | −0.594209 | − | 1.02920i | ||||
\(890\) | − | 3137.58i | − | 0.00396109i | ||||||
\(891\) | 1.38720e6 | − | 118000.i | 1.74737 | − | 0.148637i | ||||
\(892\) | −405327. | −0.509420 | ||||||||
\(893\) | −786923. | + | 454330.i | −0.986800 | + | 0.569729i | ||||
\(894\) | −264437. | − | 329888.i | −0.330862 | − | 0.412755i | ||||
\(895\) | −13476.4 | + | 23341.8i | −0.0168239 | + | 0.0291399i | ||||
\(896\) | 55160.3 | + | 31846.8i | 0.0687085 | + | 0.0396689i | ||||
\(897\) | 888236. | + | 346032.i | 1.10393 | + | 0.430062i | ||||
\(898\) | 500504. | + | 866899.i | 0.620662 | + | 1.07502i | ||||
\(899\) | 664842.i | 0.822620i | ||||||||
\(900\) | 87445.3 | − | 392206.i | 0.107957 | − | 0.484205i | ||||
\(901\) | 56880.2 | 0.0700667 | ||||||||
\(902\) | −310612. | + | 179332.i | −0.381773 | + | 0.220417i | ||||
\(903\) | 36085.1 | − | 5531.80i | 0.0442540 | − | 0.00678408i | ||||
\(904\) | 229910. | − | 398216.i | 0.281334 | − | 0.487284i | ||||
\(905\) | −13148.1 | − | 7591.07i | −0.0160534 | − | 0.00926842i | ||||
\(906\) | 42548.3 | + | 277552.i | 0.0518353 | + | 0.338133i | ||||
\(907\) | 714661. | + | 1.23783e6i | 0.868731 | + | 1.50469i | 0.863294 | + | 0.504702i | \(0.168397\pi\) |
0.00543754 | + | 0.999985i | \(0.498269\pi\) | |||||||
\(908\) | − | 320284.i | − | 0.388476i | ||||||
\(909\) | −22242.4 | − | 70841.0i | −0.0269186 | − | 0.0857347i | ||||
\(910\) | 48770.4 | 0.0588943 | ||||||||
\(911\) | −487451. | + | 281430.i | −0.587347 | + | 0.339105i | −0.764048 | − | 0.645160i | \(-0.776791\pi\) |
0.176701 | + | 0.984265i | \(0.443457\pi\) | |||||||
\(912\) | 110401. | − | 283391.i | 0.132735 | − | 0.340720i | ||||
\(913\) | 376684. | − | 652436.i | 0.451893 | − | 0.782702i | ||||
\(914\) | 631925. | + | 364842.i | 0.756438 | + | 0.436730i | ||||
\(915\) | −65557.5 | + | 52550.6i | −0.0783033 | + | 0.0627676i | ||||
\(916\) | −107070. | − | 185450.i | −0.127608 | − | 0.221023i | ||||
\(917\) | 1.35633e6i | 1.61297i | ||||||||
\(918\) | −74255.0 | − | 49809.7i | −0.0881130 | − | 0.0591056i | ||||
\(919\) | 290385. | 0.343829 | 0.171915 | − | 0.985112i | \(-0.445005\pi\) | ||||
0.171915 | + | 0.985112i | \(0.445005\pi\) | |||||||
\(920\) | −25852.0 | + | 14925.7i | −0.0305435 | + | 0.0176343i | ||||
\(921\) | 21180.7 | + | 26423.1i | 0.0249701 | + | 0.0311505i | ||||
\(922\) | 300103. | − | 519794.i | 0.353028 | − | 0.611462i | ||||
\(923\) | −982956. | − | 567510.i | −1.15380 | − | 0.666147i | ||||
\(924\) | 626132. | + | 243923.i | 0.733368 | + | 0.285699i | ||||
\(925\) | −217725. | − | 377111.i | −0.254463 | − | 0.440743i | ||||
\(926\) | − | 195417.i | − | 0.227898i | ||||||
\(927\) | 212023. | + | 194754.i | 0.246731 | + | 0.226635i | ||||
\(928\) | −79546.6 | −0.0923688 | ||||||||
\(929\) | 280640. | − | 162027.i | 0.325176 | − | 0.187740i | −0.328522 | − | 0.944496i | \(-0.606550\pi\) |
0.653697 | + | 0.756756i | \(0.273217\pi\) | |||||||
\(930\) | 84122.4 | − | 12895.8i | 0.0972625 | − | 0.0149102i | ||||
\(931\) | 123168. | − | 213334.i | 0.142102 | − | 0.246127i | ||||
\(932\) | 276425. | + | 159594.i | 0.318233 | + | 0.183732i | ||||
\(933\) | −114418. | − | 746373.i | −0.131441 | − | 0.857418i | ||||
\(934\) | 178351. | + | 308913.i | 0.204447 | + | 0.354113i | ||||
\(935\) | 20333.5i | 0.0232589i | ||||||||
\(936\) | 219967. | − | 239473.i | 0.251076 | − | 0.273341i | ||||
\(937\) | −672276. | −0.765717 | −0.382859 | − | 0.923807i | \(-0.625060\pi\) | ||||
−0.382859 | + | 0.923807i | \(0.625060\pi\) | |||||||
\(938\) | 69508.9 | − | 40131.0i | 0.0790014 | − | 0.0456115i | ||||
\(939\) | −115765. | + | 297161.i | −0.131295 | + | 0.337024i | ||||
\(940\) | 15211.1 | − | 26346.4i | 0.0172149 | − | 0.0298171i | ||||
\(941\) | 47102.5 | + | 27194.6i | 0.0531942 | + | 0.0307117i | 0.526361 | − | 0.850261i | \(-0.323556\pi\) |
−0.473167 | + | 0.880973i | \(0.656889\pi\) | |||||||
\(942\) | −395945. | + | 317388.i | −0.446203 | + | 0.357675i | ||||
\(943\) | 178386. | + | 308974.i | 0.200603 | + | 0.347455i | ||||
\(944\) | 252616.i | 0.283476i | ||||||||
\(945\) | −31222.4 | − | 63602.0i | −0.0349625 | − | 0.0712208i | ||||
\(946\) | −55351.4 | −0.0618509 | ||||||||
\(947\) | 290380. | − | 167651.i | 0.323793 | − | 0.186942i | −0.329289 | − | 0.944229i | \(-0.606809\pi\) |
0.653082 | + | 0.757287i | \(0.273476\pi\) | |||||||
\(948\) | 430755. | + | 537372.i | 0.479307 | + | 0.597941i | ||||
\(949\) | −283519. | + | 491069.i | −0.314811 | + | 0.545268i | ||||
\(950\) | −802039. | − | 463058.i | −0.888686 | − | 0.513083i | ||||
\(951\) | −1.27888e6 | − | 498217.i | −1.41407 | − | 0.550880i | ||||
\(952\) | −21578.3 | − | 37374.7i | −0.0238091 | − | 0.0412386i | ||||
\(953\) | − | 1.29405e6i | − | 1.42484i | −0.701753 | − | 0.712421i | \(-0.747599\pi\) | ||
0.701753 | − | 0.712421i | \(-0.252401\pi\) | |||||||
\(954\) | 286711. | − | 90020.3i | 0.315027 | − | 0.0989108i | ||||
\(955\) | −91734.0 | −0.100583 | ||||||||
\(956\) | −348074. | + | 200961.i | −0.380852 | + | 0.219885i | ||||
\(957\) | −829525. | + | 127165.i | −0.905745 | + | 0.138849i | ||||
\(958\) | −406110. | + | 703403.i | −0.442499 | + | 0.766431i | ||||
\(959\) | 418888. | + | 241845.i | 0.455471 | + | 0.262966i | ||||
\(960\) | 1542.95 | + | 10065.0i | 0.00167421 | + | 0.0109212i | ||||
\(961\) | −682735. | − | 1.18253e6i | −0.739274 | − | 1.28046i | ||||
\(962\) | − | 352366.i | − | 0.380753i | ||||||
\(963\) | 43520.1 | + | 9703.14i | 0.0469286 | + | 0.0104631i | ||||
\(964\) | 554087. | 0.596243 | ||||||||
\(965\) | 114317. | − | 66001.2i | 0.122760 | − | 0.0708757i | ||||
\(966\) | 242637. | − | 622830.i | 0.260018 | − | 0.667445i | ||||
\(967\) | −495246. | + | 857790.i | −0.529624 | + | 0.917336i | 0.469779 | + | 0.882784i | \(0.344334\pi\) |
−0.999403 | + | 0.0345516i | \(0.989000\pi\) | |||||||
\(968\) | −595435. | − | 343774.i | −0.635453 | − | 0.366879i | ||||
\(969\) | −160790. | + | 128889.i | −0.171243 | + | 0.137268i | ||||
\(970\) | −23215.7 | − | 40210.8i | −0.0246739 | − | 0.0427365i | ||||
\(971\) | 1.17055e6i | 1.24152i | 0.784002 | + | 0.620758i | \(0.213175\pi\) | ||||
−0.784002 | + | 0.620758i | \(0.786825\pi\) | |||||||
\(972\) | −453120. | − | 133553.i | −0.479602 | − | 0.141358i | ||||
\(973\) | 745296. | 0.787233 | ||||||||
\(974\) | 672779. | − | 388429.i | 0.709176 | − | 0.409443i | ||||
\(975\) | −619293. | − | 772575.i | −0.651458 | − | 0.812702i | ||||
\(976\) | −135190. | + | 234156.i | −0.141920 | + | 0.245813i | ||||
\(977\) | 454795. | + | 262576.i | 0.476460 | + | 0.275084i | 0.718940 | − | 0.695072i | \(-0.244628\pi\) |
−0.242480 | + | 0.970156i | \(0.577961\pi\) | |||||||
\(978\) | −188243. | − | 73334.2i | −0.196807 | − | 0.0766706i | ||||
\(979\) | −53260.9 | − | 92250.7i | −0.0555704 | − | 0.0962507i | ||||
\(980\) | 8247.42i | 0.00858748i | ||||||||
\(981\) | 45158.6 | − | 202543.i | 0.0469248 | − | 0.210465i | ||||
\(982\) | −898075. | −0.931300 | ||||||||
\(983\) | −1.31637e6 | + | 760008.i | −1.36230 | + | 0.786522i | −0.989929 | − | 0.141563i | \(-0.954787\pi\) |
−0.372367 | + | 0.928086i | \(0.621454\pi\) | |||||||
\(984\) | 120293. | − | 18440.8i | 0.124237 | − | 0.0190454i | ||||
\(985\) | −13669.2 | + | 23675.7i | −0.0140887 | + | 0.0244023i | ||||
\(986\) | 46677.1 | + | 26949.0i | 0.0480120 | + | 0.0277197i | ||||
\(987\) | 103222. | + | 673340.i | 0.105959 | + | 0.691194i | ||||
\(988\) | −374706. | − | 649010.i | −0.383864 | − | 0.664871i | ||||
\(989\) | 55059.5i | 0.0562911i | ||||||||
\(990\) | 32180.4 | + | 102493.i | 0.0328338 | + | 0.104574i | ||||
\(991\) | −1.13839e6 | −1.15916 | −0.579580 | − | 0.814915i | \(-0.696783\pi\) | ||||
−0.579580 | + | 0.814915i | \(0.696783\pi\) | |||||||
\(992\) | 237180. | − | 136936.i | 0.241021 | − | 0.139153i | ||||
\(993\) | −121359. | + | 311518.i | −0.123076 | + | 0.315925i | ||||
\(994\) | −397938. | + | 689248.i | −0.402756 | + | 0.697594i | ||||
\(995\) | 32219.9 | + | 18602.2i | 0.0325445 | + | 0.0187896i | ||||
\(996\) | −199455. | + | 159882.i | −0.201060 | + | 0.161169i | ||||
\(997\) | 396715. | + | 687130.i | 0.399106 | + | 0.691272i | 0.993616 | − | 0.112817i | \(-0.0359872\pi\) |
−0.594510 | + | 0.804088i | \(0.702654\pi\) | |||||||
\(998\) | − | 551890.i | − | 0.554105i | ||||||
\(999\) | −459524. | + | 225582.i | −0.460445 | + | 0.226034i |
(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 | 18.5.d.a.5.4 | ✓ | 8 | |
3.2 | odd | 2 | 54.5.d.a.17.2 | 8 | |||
4.3 | odd | 2 | 144.5.q.b.113.2 | 8 | |||
9.2 | odd | 6 | inner | 18.5.d.a.11.4 | yes | 8 | |
9.4 | even | 3 | 162.5.b.c.161.7 | 8 | |||
9.5 | odd | 6 | 162.5.b.c.161.2 | 8 | |||
9.7 | even | 3 | 54.5.d.a.35.2 | 8 | |||
12.11 | even | 2 | 432.5.q.b.17.3 | 8 | |||
36.7 | odd | 6 | 432.5.q.b.305.3 | 8 | |||
36.11 | even | 6 | 144.5.q.b.65.2 | 8 | |||
36.23 | even | 6 | 1296.5.e.e.161.4 | 8 | |||
36.31 | odd | 6 | 1296.5.e.e.161.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
18.5.d.a.5.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
18.5.d.a.11.4 | yes | 8 | 9.2 | odd | 6 | inner | |
54.5.d.a.17.2 | 8 | 3.2 | odd | 2 | |||
54.5.d.a.35.2 | 8 | 9.7 | even | 3 | |||
144.5.q.b.65.2 | 8 | 36.11 | even | 6 | |||
144.5.q.b.113.2 | 8 | 4.3 | odd | 2 | |||
162.5.b.c.161.2 | 8 | 9.5 | odd | 6 | |||
162.5.b.c.161.7 | 8 | 9.4 | even | 3 | |||
432.5.q.b.17.3 | 8 | 12.11 | even | 2 | |||
432.5.q.b.305.3 | 8 | 36.7 | odd | 6 | |||
1296.5.e.e.161.4 | 8 | 36.23 | even | 6 | |||
1296.5.e.e.161.5 | 8 | 36.31 | odd | 6 |