Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,5,Mod(23,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.23");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.g (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.64937726820\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 51.6 | ||
Character | \(\chi\) | \(=\) | 74.51 |
Dual form | 74.5.g.a.45.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{11}{12}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.73205 | + | 0.732051i | −0.683013 | + | 0.183013i | ||||
\(3\) | 8.28780 | − | 4.78497i | 0.920867 | − | 0.531663i | 0.0369555 | − | 0.999317i | \(-0.488234\pi\) |
0.883912 | + | 0.467654i | \(0.154901\pi\) | |||||||
\(4\) | 6.92820 | − | 4.00000i | 0.433013 | − | 0.250000i | ||||
\(5\) | −17.4826 | − | 4.68445i | −0.699305 | − | 0.187378i | −0.108386 | − | 0.994109i | \(-0.534568\pi\) |
−0.590919 | + | 0.806731i | \(0.701235\pi\) | |||||||
\(6\) | −19.1399 | + | 19.1399i | −0.531663 | + | 0.531663i | ||||
\(7\) | −36.2925 | − | 62.8605i | −0.740664 | − | 1.28287i | −0.952193 | − | 0.305496i | \(-0.901178\pi\) |
0.211529 | − | 0.977372i | \(-0.432156\pi\) | |||||||
\(8\) | −16.0000 | + | 16.0000i | −0.250000 | + | 0.250000i | ||||
\(9\) | 5.29180 | − | 9.16567i | 0.0653309 | − | 0.113156i | ||||
\(10\) | 51.1927 | 0.511927 | ||||||||
\(11\) | 102.318i | 0.845605i | 0.906222 | + | 0.422802i | \(0.138954\pi\) | ||||
−0.906222 | + | 0.422802i | \(0.861046\pi\) | |||||||
\(12\) | 38.2797 | − | 66.3024i | 0.265831 | − | 0.460434i | ||||
\(13\) | −128.387 | − | 34.4011i | −0.759683 | − | 0.203557i | −0.141874 | − | 0.989885i | \(-0.545313\pi\) |
−0.617809 | + | 0.786328i | \(0.711980\pi\) | |||||||
\(14\) | 145.170 | + | 145.170i | 0.740664 | + | 0.740664i | ||||
\(15\) | −167.307 | + | 44.8299i | −0.743589 | + | 0.199244i | ||||
\(16\) | 32.0000 | − | 55.4256i | 0.125000 | − | 0.216506i | ||||
\(17\) | −36.3083 | − | 135.504i | −0.125634 | − | 0.468873i | 0.874227 | − | 0.485517i | \(-0.161369\pi\) |
−0.999861 | + | 0.0166439i | \(0.994702\pi\) | |||||||
\(18\) | −7.74773 | + | 28.9149i | −0.0239128 | + | 0.0892436i | ||||
\(19\) | −527.582 | − | 141.365i | −1.46145 | − | 0.391594i | −0.561458 | − | 0.827505i | \(-0.689759\pi\) |
−0.899989 | + | 0.435912i | \(0.856426\pi\) | |||||||
\(20\) | −139.861 | + | 37.4756i | −0.349652 | + | 0.0936891i | ||||
\(21\) | −601.571 | − | 347.317i | −1.36411 | − | 0.787567i | ||||
\(22\) | −74.9021 | − | 279.538i | −0.154756 | − | 0.577559i | ||||
\(23\) | 686.570 | − | 686.570i | 1.29786 | − | 1.29786i | 0.368062 | − | 0.929801i | \(-0.380021\pi\) |
0.929801 | − | 0.368062i | \(-0.119979\pi\) | |||||||
\(24\) | −56.0454 | + | 209.164i | −0.0973011 | + | 0.363133i | ||||
\(25\) | −257.568 | − | 148.707i | −0.412109 | − | 0.237931i | ||||
\(26\) | 375.942 | 0.556127 | ||||||||
\(27\) | 673.880i | 0.924390i | ||||||||
\(28\) | −502.884 | − | 290.340i | −0.641434 | − | 0.370332i | ||||
\(29\) | −892.638 | − | 892.638i | −1.06140 | − | 1.06140i | −0.997987 | − | 0.0634133i | \(-0.979801\pi\) |
−0.0634133 | − | 0.997987i | \(-0.520199\pi\) | |||||||
\(30\) | 424.275 | − | 244.955i | 0.471416 | − | 0.272172i | ||||
\(31\) | 439.389 | + | 439.389i | 0.457220 | + | 0.457220i | 0.897742 | − | 0.440522i | \(-0.145206\pi\) |
−0.440522 | + | 0.897742i | \(0.645206\pi\) | |||||||
\(32\) | −46.8513 | + | 174.851i | −0.0457532 | + | 0.170753i | ||||
\(33\) | 489.589 | + | 847.993i | 0.449577 | + | 0.778689i | ||||
\(34\) | 198.392 | + | 343.625i | 0.171619 | + | 0.297253i | ||||
\(35\) | 340.021 | + | 1268.98i | 0.277569 | + | 1.03590i | ||||
\(36\) | − | 84.6688i | − | 0.0653309i | ||||||
\(37\) | 664.189 | + | 1197.09i | 0.485164 | + | 0.874423i | ||||
\(38\) | 1544.87 | 1.06985 | ||||||||
\(39\) | −1228.65 | + | 329.216i | −0.807791 | + | 0.216447i | ||||
\(40\) | 354.673 | − | 204.771i | 0.221671 | − | 0.127982i | ||||
\(41\) | 876.607 | − | 506.109i | 0.521480 | − | 0.301076i | −0.216060 | − | 0.976380i | \(-0.569321\pi\) |
0.737540 | + | 0.675304i | \(0.235987\pi\) | |||||||
\(42\) | 1897.78 | + | 508.508i | 1.07584 | + | 0.288270i | ||||
\(43\) | 1235.74 | − | 1235.74i | 0.668330 | − | 0.668330i | −0.288999 | − | 0.957329i | \(-0.593323\pi\) |
0.957329 | + | 0.288999i | \(0.0933226\pi\) | |||||||
\(44\) | 409.273 | + | 708.881i | 0.211401 | + | 0.366158i | ||||
\(45\) | −135.451 | + | 135.451i | −0.0668892 | + | 0.0668892i | ||||
\(46\) | −1373.14 | + | 2378.35i | −0.648932 | + | 1.12398i | ||||
\(47\) | 2111.90 | 0.956043 | 0.478021 | − | 0.878348i | \(-0.341354\pi\) | ||||
0.478021 | + | 0.878348i | \(0.341354\pi\) | |||||||
\(48\) | − | 612.476i | − | 0.265831i | ||||||
\(49\) | −1433.80 | + | 2483.41i | −0.597167 | + | 1.03432i | ||||
\(50\) | 812.550 | + | 217.722i | 0.325020 | + | 0.0870889i | ||||
\(51\) | −949.299 | − | 949.299i | −0.364975 | − | 0.364975i | ||||
\(52\) | −1027.09 | + | 275.208i | −0.379842 | + | 0.101778i | ||||
\(53\) | 995.706 | − | 1724.61i | 0.354470 | − | 0.613960i | −0.632557 | − | 0.774514i | \(-0.717995\pi\) |
0.987027 | + | 0.160554i | \(0.0513280\pi\) | |||||||
\(54\) | −493.315 | − | 1841.07i | −0.169175 | − | 0.631370i | ||||
\(55\) | 479.305 | − | 1788.79i | 0.158448 | − | 0.591335i | ||||
\(56\) | 1586.45 | + | 425.088i | 0.505883 | + | 0.135551i | ||||
\(57\) | −5048.93 | + | 1352.86i | −1.55399 | + | 0.416392i | ||||
\(58\) | 3092.19 | + | 1785.28i | 0.919200 | + | 0.530700i | ||||
\(59\) | −392.361 | − | 1464.31i | −0.112715 | − | 0.420658i | 0.886391 | − | 0.462937i | \(-0.153205\pi\) |
−0.999106 | + | 0.0422798i | \(0.986538\pi\) | |||||||
\(60\) | −979.821 | + | 979.821i | −0.272172 | + | 0.272172i | ||||
\(61\) | 341.515 | − | 1274.55i | 0.0917805 | − | 0.342529i | −0.904731 | − | 0.425983i | \(-0.859928\pi\) |
0.996512 | + | 0.0834535i | \(0.0265950\pi\) | |||||||
\(62\) | −1522.09 | − | 878.778i | −0.395964 | − | 0.228610i | ||||
\(63\) | −768.212 | −0.193553 | ||||||||
\(64\) | − | 512.000i | − | 0.125000i | ||||||
\(65\) | 2083.38 | + | 1202.84i | 0.493108 | + | 0.284696i | ||||
\(66\) | −1958.36 | − | 1958.36i | −0.449577 | − | 0.449577i | ||||
\(67\) | −3494.20 | + | 2017.38i | −0.778392 | + | 0.449405i | −0.835860 | − | 0.548942i | \(-0.815031\pi\) |
0.0574681 | + | 0.998347i | \(0.481697\pi\) | |||||||
\(68\) | −793.568 | − | 793.568i | −0.171619 | − | 0.171619i | ||||
\(69\) | 2404.94 | − | 8975.37i | 0.505134 | − | 1.88519i | ||||
\(70\) | −1857.91 | − | 3218.00i | −0.379166 | − | 0.656734i | ||||
\(71\) | 1686.23 | + | 2920.63i | 0.334503 | + | 0.579376i | 0.983389 | − | 0.181509i | \(-0.0580983\pi\) |
−0.648886 | + | 0.760885i | \(0.724765\pi\) | |||||||
\(72\) | 61.9819 | + | 231.320i | 0.0119564 | + | 0.0446218i | ||||
\(73\) | 1548.71i | 0.290620i | 0.989386 | + | 0.145310i | \(0.0464179\pi\) | ||||
−0.989386 | + | 0.145310i | \(0.953582\pi\) | |||||||
\(74\) | −2690.93 | − | 2784.28i | −0.491404 | − | 0.508451i | ||||
\(75\) | −2846.23 | −0.505997 | ||||||||
\(76\) | −4220.66 | + | 1130.92i | −0.730724 | + | 0.195797i | ||||
\(77\) | 6431.77 | − | 3713.39i | 1.08480 | − | 0.626309i | ||||
\(78\) | 3115.73 | − | 1798.87i | 0.512119 | − | 0.295672i | ||||
\(79\) | −2387.54 | − | 639.741i | −0.382558 | − | 0.102506i | 0.0624146 | − | 0.998050i | \(-0.480120\pi\) |
−0.444973 | + | 0.895544i | \(0.646787\pi\) | |||||||
\(80\) | −819.083 | + | 819.083i | −0.127982 | + | 0.127982i | ||||
\(81\) | 3653.13 | + | 6327.41i | 0.556795 | + | 0.964397i | ||||
\(82\) | −2024.44 | + | 2024.44i | −0.301076 | + | 0.301076i | ||||
\(83\) | −3359.95 | + | 5819.61i | −0.487727 | + | 0.844769i | −0.999900 | − | 0.0141137i | \(-0.995507\pi\) |
0.512173 | + | 0.858882i | \(0.328841\pi\) | |||||||
\(84\) | −5557.07 | −0.787567 | ||||||||
\(85\) | 2539.05i | 0.351426i | ||||||||
\(86\) | −2471.48 | + | 4280.74i | −0.334165 | + | 0.578791i | ||||
\(87\) | −11669.3 | − | 3126.77i | −1.54172 | − | 0.413102i | ||||
\(88\) | −1637.09 | − | 1637.09i | −0.211401 | − | 0.211401i | ||||
\(89\) | 5076.65 | − | 1360.29i | 0.640911 | − | 0.171731i | 0.0762948 | − | 0.997085i | \(-0.475691\pi\) |
0.564616 | + | 0.825354i | \(0.309024\pi\) | |||||||
\(90\) | 270.901 | − | 469.215i | 0.0334446 | − | 0.0579278i | ||||
\(91\) | 2497.00 | + | 9318.94i | 0.301534 | + | 1.12534i | ||||
\(92\) | 2010.42 | − | 7502.97i | 0.237525 | − | 0.886457i | ||||
\(93\) | 5744.03 | + | 1539.11i | 0.664126 | + | 0.177952i | ||||
\(94\) | −5769.81 | + | 1546.02i | −0.652989 | + | 0.174968i | ||||
\(95\) | 8561.30 | + | 4942.87i | 0.948621 | + | 0.547686i | ||||
\(96\) | 448.363 | + | 1673.31i | 0.0486505 | + | 0.181566i | ||||
\(97\) | 11036.0 | − | 11036.0i | 1.17292 | − | 1.17292i | 0.191409 | − | 0.981510i | \(-0.438694\pi\) |
0.981510 | − | 0.191409i | \(-0.0613058\pi\) | |||||||
\(98\) | 2099.22 | − | 7834.41i | 0.218578 | − | 0.815745i | ||||
\(99\) | 937.814 | + | 541.447i | 0.0956856 | + | 0.0552441i | ||||
\(100\) | −2379.31 | −0.237931 | ||||||||
\(101\) | − | 5598.79i | − | 0.548847i | −0.961609 | − | 0.274423i | \(-0.911513\pi\) | ||
0.961609 | − | 0.274423i | \(-0.0884870\pi\) | |||||||
\(102\) | 3288.47 | + | 1898.60i | 0.316077 | + | 0.182487i | ||||
\(103\) | −13301.9 | − | 13301.9i | −1.25383 | − | 1.25383i | −0.953990 | − | 0.299840i | \(-0.903067\pi\) |
−0.299840 | − | 0.953990i | \(-0.596933\pi\) | |||||||
\(104\) | 2604.60 | − | 1503.77i | 0.240810 | − | 0.139032i | ||||
\(105\) | 8890.04 | + | 8890.04i | 0.806353 | + | 0.806353i | ||||
\(106\) | −1457.81 | + | 5440.64i | −0.129745 | + | 0.484215i | ||||
\(107\) | −2824.37 | − | 4891.96i | −0.246692 | − | 0.427283i | 0.715914 | − | 0.698188i | \(-0.246010\pi\) |
−0.962606 | + | 0.270906i | \(0.912677\pi\) | |||||||
\(108\) | 2695.52 | + | 4668.78i | 0.231097 | + | 0.400273i | ||||
\(109\) | −2273.27 | − | 8483.95i | −0.191336 | − | 0.714077i | −0.993185 | − | 0.116550i | \(-0.962817\pi\) |
0.801848 | − | 0.597527i | \(-0.203850\pi\) | |||||||
\(110\) | 5237.94i | 0.432887i | ||||||||
\(111\) | 11232.7 | + | 6743.09i | 0.911670 | + | 0.547284i | ||||
\(112\) | −4645.45 | −0.370332 | ||||||||
\(113\) | −15027.4 | + | 4026.58i | −1.17687 | + | 0.315340i | −0.793683 | − | 0.608332i | \(-0.791839\pi\) |
−0.383184 | + | 0.923672i | \(0.625172\pi\) | |||||||
\(114\) | 12803.6 | − | 7392.14i | 0.985193 | − | 0.568801i | ||||
\(115\) | −15219.2 | + | 8786.83i | −1.15079 | + | 0.664411i | ||||
\(116\) | −9754.93 | − | 2613.83i | −0.724950 | − | 0.194250i | ||||
\(117\) | −994.705 | + | 994.705i | −0.0726645 | + | 0.0726645i | ||||
\(118\) | 2143.90 | + | 3713.34i | 0.153971 | + | 0.266686i | ||||
\(119\) | −7200.15 | + | 7200.15i | −0.508449 | + | 0.508449i | ||||
\(120\) | 1959.64 | − | 3394.20i | 0.136086 | − | 0.235708i | ||||
\(121\) | 4172.00 | 0.284953 | ||||||||
\(122\) | 3732.15i | 0.250749i | ||||||||
\(123\) | 4843.43 | − | 8389.07i | 0.320142 | − | 0.554503i | ||||
\(124\) | 4801.73 | + | 1286.62i | 0.312287 | + | 0.0836771i | ||||
\(125\) | 11805.2 | + | 11805.2i | 0.755533 | + | 0.755533i | ||||
\(126\) | 2098.79 | − | 562.370i | 0.132199 | − | 0.0354226i | ||||
\(127\) | 5145.77 | − | 8912.73i | 0.319038 | − | 0.552590i | −0.661249 | − | 0.750166i | \(-0.729974\pi\) |
0.980288 | + | 0.197576i | \(0.0633069\pi\) | |||||||
\(128\) | 374.810 | + | 1398.81i | 0.0228766 | + | 0.0853766i | ||||
\(129\) | 4328.60 | − | 16154.6i | 0.260117 | − | 0.970769i | ||||
\(130\) | −6572.45 | − | 1761.08i | −0.388902 | − | 0.104206i | ||||
\(131\) | 7233.90 | − | 1938.32i | 0.421531 | − | 0.112949i | −0.0418169 | − | 0.999125i | \(-0.513315\pi\) |
0.463348 | + | 0.886176i | \(0.346648\pi\) | |||||||
\(132\) | 6783.94 | + | 3916.71i | 0.389345 | + | 0.224788i | ||||
\(133\) | 10261.0 | + | 38294.6i | 0.580079 | + | 2.16488i | ||||
\(134\) | 8069.51 | − | 8069.51i | 0.449405 | − | 0.449405i | ||||
\(135\) | 3156.76 | − | 11781.2i | 0.173210 | − | 0.646430i | ||||
\(136\) | 2749.00 | + | 1587.14i | 0.148627 | + | 0.0858097i | ||||
\(137\) | −1833.19 | −0.0976713 | −0.0488356 | − | 0.998807i | \(-0.515551\pi\) | ||||
−0.0488356 | + | 0.998807i | \(0.515551\pi\) | |||||||
\(138\) | 26281.7i | 1.38005i | ||||||||
\(139\) | −27223.5 | − | 15717.5i | −1.40901 | − | 0.813492i | −0.413717 | − | 0.910406i | \(-0.635770\pi\) |
−0.995293 | + | 0.0969134i | \(0.969103\pi\) | |||||||
\(140\) | 7431.65 | + | 7431.65i | 0.379166 | + | 0.379166i | ||||
\(141\) | 17503.0 | − | 10105.4i | 0.880389 | − | 0.508293i | ||||
\(142\) | −6744.92 | − | 6744.92i | −0.334503 | − | 0.334503i | ||||
\(143\) | 3519.85 | − | 13136.3i | 0.172128 | − | 0.642392i | ||||
\(144\) | −338.675 | − | 586.603i | −0.0163327 | − | 0.0282891i | ||||
\(145\) | 11424.1 | + | 19787.2i | 0.543359 | + | 0.941126i | ||||
\(146\) | −1133.74 | − | 4231.16i | −0.0531871 | − | 0.198497i | ||||
\(147\) | 27442.7i | 1.26997i | ||||||||
\(148\) | 9389.98 | + | 5636.89i | 0.428688 | + | 0.257345i | ||||
\(149\) | 41948.9 | 1.88951 | 0.944753 | − | 0.327783i | \(-0.106302\pi\) | ||||
0.944753 | + | 0.327783i | \(0.106302\pi\) | |||||||
\(150\) | 7776.05 | − | 2083.59i | 0.345602 | − | 0.0926038i | ||||
\(151\) | −34676.4 | + | 20020.4i | −1.52083 | + | 0.878050i | −0.521130 | + | 0.853478i | \(0.674489\pi\) |
−0.999698 | + | 0.0245728i | \(0.992177\pi\) | |||||||
\(152\) | 10703.2 | − | 6179.47i | 0.463260 | − | 0.267463i | ||||
\(153\) | −1434.12 | − | 384.272i | −0.0612637 | − | 0.0164156i | ||||
\(154\) | −14853.5 | + | 14853.5i | −0.626309 | + | 0.626309i | ||||
\(155\) | −5623.37 | − | 9739.96i | −0.234063 | − | 0.405409i | ||||
\(156\) | −7195.47 | + | 7195.47i | −0.295672 | + | 0.295672i | ||||
\(157\) | −3586.44 | + | 6211.89i | −0.145500 | + | 0.252014i | −0.929559 | − | 0.368672i | \(-0.879813\pi\) |
0.784059 | + | 0.620686i | \(0.213146\pi\) | |||||||
\(158\) | 6991.22 | 0.280052 | ||||||||
\(159\) | − | 19057.7i | − | 0.753834i | ||||||
\(160\) | 1638.17 | − | 2837.39i | 0.0639908 | − | 0.110835i | ||||
\(161\) | −68075.5 | − | 18240.8i | −2.62627 | − | 0.703706i | ||||
\(162\) | −14612.5 | − | 14612.5i | −0.556795 | − | 0.556795i | ||||
\(163\) | −34496.1 | + | 9243.21i | −1.29836 | + | 0.347894i | −0.840830 | − | 0.541300i | \(-0.817932\pi\) |
−0.457530 | + | 0.889194i | \(0.651266\pi\) | |||||||
\(164\) | 4048.88 | − | 7012.86i | 0.150538 | − | 0.260740i | ||||
\(165\) | −4586.91 | − | 17118.6i | −0.168482 | − | 0.628782i | ||||
\(166\) | 4919.31 | − | 18359.1i | 0.178521 | − | 0.666248i | ||||
\(167\) | 29103.0 | + | 7798.12i | 1.04353 | + | 0.279613i | 0.739575 | − | 0.673074i | \(-0.235026\pi\) |
0.303954 | + | 0.952687i | \(0.401693\pi\) | |||||||
\(168\) | 15182.2 | − | 4068.06i | 0.537918 | − | 0.144135i | ||||
\(169\) | −9434.89 | − | 5447.24i | −0.330342 | − | 0.190723i | ||||
\(170\) | −1858.72 | − | 6936.82i | −0.0643154 | − | 0.240028i | ||||
\(171\) | −4087.57 | + | 4087.57i | −0.139789 | + | 0.139789i | ||||
\(172\) | 3618.50 | − | 13504.4i | 0.122313 | − | 0.456478i | ||||
\(173\) | −3054.33 | − | 1763.42i | −0.102053 | − | 0.0589201i | 0.448105 | − | 0.893981i | \(-0.352099\pi\) |
−0.550158 | + | 0.835061i | \(0.685432\pi\) | |||||||
\(174\) | 34169.9 | 1.12861 | ||||||||
\(175\) | 21587.8i | 0.704908i | ||||||||
\(176\) | 5671.05 | + | 3274.18i | 0.183079 | + | 0.105701i | ||||
\(177\) | −10258.5 | − | 10258.5i | −0.327444 | − | 0.327444i | ||||
\(178\) | −12873.9 | + | 7432.74i | −0.406321 | + | 0.234590i | ||||
\(179\) | −20194.0 | − | 20194.0i | −0.630256 | − | 0.630256i | 0.317876 | − | 0.948132i | \(-0.397030\pi\) |
−0.948132 | + | 0.317876i | \(0.897030\pi\) | |||||||
\(180\) | −396.627 | + | 1480.23i | −0.0122416 | + | 0.0456862i | ||||
\(181\) | −4460.18 | − | 7725.25i | −0.136143 | − | 0.235806i | 0.789891 | − | 0.613248i | \(-0.210137\pi\) |
−0.926033 | + | 0.377441i | \(0.876804\pi\) | |||||||
\(182\) | −13643.9 | − | 23631.9i | −0.411903 | − | 0.713437i | ||||
\(183\) | −3268.28 | − | 12197.4i | −0.0975926 | − | 0.364220i | ||||
\(184\) | 21970.2i | 0.648932i | ||||||||
\(185\) | −6004.08 | − | 24039.6i | −0.175430 | − | 0.702397i | ||||
\(186\) | −16819.7 | −0.486174 | ||||||||
\(187\) | 13864.5 | − | 3714.99i | 0.396481 | − | 0.106237i | ||||
\(188\) | 14631.7 | − | 8447.60i | 0.413979 | − | 0.239011i | ||||
\(189\) | 42360.5 | − | 24456.8i | 1.18587 | − | 0.684662i | ||||
\(190\) | −27008.3 | − | 7236.86i | −0.748154 | − | 0.200467i | ||||
\(191\) | −17638.2 | + | 17638.2i | −0.483489 | + | 0.483489i | −0.906244 | − | 0.422755i | \(-0.861063\pi\) |
0.422755 | + | 0.906244i | \(0.361063\pi\) | |||||||
\(192\) | −2449.90 | − | 4243.36i | −0.0664579 | − | 0.115108i | ||||
\(193\) | −7874.79 | + | 7874.79i | −0.211410 | + | 0.211410i | −0.804866 | − | 0.593457i | \(-0.797763\pi\) |
0.593457 | + | 0.804866i | \(0.297763\pi\) | |||||||
\(194\) | −22072.0 | + | 38229.8i | −0.586460 | + | 1.01578i | ||||
\(195\) | 23022.2 | 0.605449 | ||||||||
\(196\) | 22940.8i | 0.597167i | ||||||||
\(197\) | 5605.45 | − | 9708.92i | 0.144437 | − | 0.250172i | −0.784726 | − | 0.619843i | \(-0.787196\pi\) |
0.929163 | + | 0.369671i | \(0.120530\pi\) | |||||||
\(198\) | −2958.52 | − | 792.734i | −0.0754648 | − | 0.0202207i | ||||
\(199\) | −46663.6 | − | 46663.6i | −1.17834 | − | 1.17834i | −0.980166 | − | 0.198179i | \(-0.936497\pi\) |
−0.198179 | − | 0.980166i | \(-0.563503\pi\) | |||||||
\(200\) | 6500.40 | − | 1741.78i | 0.162510 | − | 0.0435444i | ||||
\(201\) | −19306.2 | + | 33439.3i | −0.477864 | + | 0.827684i | ||||
\(202\) | 4098.60 | + | 15296.2i | 0.100446 | + | 0.374869i | ||||
\(203\) | −23715.6 | + | 88507.8i | −0.575495 | + | 2.14778i | ||||
\(204\) | −10374.1 | − | 2779.74i | −0.249282 | − | 0.0667950i | ||||
\(205\) | −17696.2 | + | 4741.69i | −0.421088 | + | 0.112830i | ||||
\(206\) | 46079.1 | + | 26603.8i | 1.08585 | + | 0.626915i | ||||
\(207\) | −2659.68 | − | 9926.06i | −0.0620710 | − | 0.231652i | ||||
\(208\) | −6015.07 | + | 6015.07i | −0.139032 | + | 0.139032i | ||||
\(209\) | 14464.2 | − | 53981.3i | 0.331133 | − | 1.23581i | ||||
\(210\) | −30796.0 | − | 17780.1i | −0.698322 | − | 0.403177i | ||||
\(211\) | 62358.8 | 1.40066 | 0.700330 | − | 0.713819i | \(-0.253036\pi\) | ||||
0.700330 | + | 0.713819i | \(0.253036\pi\) | |||||||
\(212\) | − | 15931.3i | − | 0.354470i | ||||||
\(213\) | 27950.3 | + | 16137.1i | 0.616065 | + | 0.355686i | ||||
\(214\) | 11297.5 | + | 11297.5i | 0.246692 | + | 0.246692i | ||||
\(215\) | −27392.8 | + | 15815.2i | −0.592597 | + | 0.342136i | ||||
\(216\) | −10782.1 | − | 10782.1i | −0.231097 | − | 0.231097i | ||||
\(217\) | 11673.7 | − | 43566.7i | 0.247907 | − | 0.925200i | ||||
\(218\) | 12421.4 | + | 21514.4i | 0.261370 | + | 0.452707i | ||||
\(219\) | 7410.53 | + | 12835.4i | 0.154512 | + | 0.267622i | ||||
\(220\) | −3834.44 | − | 14310.3i | −0.0792239 | − | 0.295668i | ||||
\(221\) | 18646.0i | 0.381769i | ||||||||
\(222\) | −35624.5 | − | 10199.6i | −0.722842 | − | 0.206955i | ||||
\(223\) | 78249.7 | 1.57352 | 0.786761 | − | 0.617257i | \(-0.211756\pi\) | ||||
0.786761 | + | 0.617257i | \(0.211756\pi\) | |||||||
\(224\) | 12691.6 | − | 3400.70i | 0.252942 | − | 0.0677755i | ||||
\(225\) | −2726.00 | + | 1573.86i | −0.0538469 | + | 0.0310885i | ||||
\(226\) | 38108.0 | − | 22001.7i | 0.746103 | − | 0.430763i | ||||
\(227\) | −77094.5 | − | 20657.4i | −1.49614 | − | 0.400889i | −0.584334 | − | 0.811513i | \(-0.698644\pi\) |
−0.911805 | + | 0.410624i | \(0.865311\pi\) | |||||||
\(228\) | −29568.6 | + | 29568.6i | −0.568801 | + | 0.568801i | ||||
\(229\) | −17268.4 | − | 29909.7i | −0.329291 | − | 0.570349i | 0.653080 | − | 0.757289i | \(-0.273477\pi\) |
−0.982371 | + | 0.186939i | \(0.940143\pi\) | |||||||
\(230\) | 35147.3 | − | 35147.3i | 0.664411 | − | 0.664411i | ||||
\(231\) | 35536.8 | − | 61551.6i | 0.665970 | − | 1.15349i | ||||
\(232\) | 28564.4 | 0.530700 | ||||||||
\(233\) | 20726.5i | 0.381780i | 0.981611 | + | 0.190890i | \(0.0611374\pi\) | ||||
−0.981611 | + | 0.190890i | \(0.938863\pi\) | |||||||
\(234\) | 1989.41 | − | 3445.76i | 0.0363323 | − | 0.0629293i | ||||
\(235\) | −36921.5 | − | 9893.09i | −0.668565 | − | 0.179142i | ||||
\(236\) | −8575.59 | − | 8575.59i | −0.153971 | − | 0.153971i | ||||
\(237\) | −22848.6 | + | 6122.27i | −0.406784 | + | 0.108997i | ||||
\(238\) | 14400.3 | − | 24942.0i | 0.254225 | − | 0.440330i | ||||
\(239\) | 27364.6 | + | 102126.i | 0.479064 | + | 1.78789i | 0.605418 | + | 0.795908i | \(0.293006\pi\) |
−0.126354 | + | 0.991985i | \(0.540327\pi\) | |||||||
\(240\) | −2869.11 | + | 10707.7i | −0.0498110 | + | 0.185897i | ||||
\(241\) | 10794.3 | + | 2892.33i | 0.185850 | + | 0.0497983i | 0.350543 | − | 0.936546i | \(-0.385997\pi\) |
−0.164694 | + | 0.986345i | \(0.552664\pi\) | |||||||
\(242\) | −11398.1 | + | 3054.11i | −0.194626 | + | 0.0521500i | ||||
\(243\) | 13281.5 | + | 7668.06i | 0.224923 | + | 0.129859i | ||||
\(244\) | −2732.12 | − | 10196.4i | −0.0458902 | − | 0.171265i | ||||
\(245\) | 36699.9 | − | 36699.9i | 0.611411 | − | 0.611411i | ||||
\(246\) | −7091.28 | + | 26465.0i | −0.117180 | + | 0.437323i | ||||
\(247\) | 62871.3 | + | 36298.8i | 1.03053 | + | 0.594974i | ||||
\(248\) | −14060.4 | −0.228610 | ||||||||
\(249\) | 64309.1i | 1.03723i | ||||||||
\(250\) | −40894.4 | − | 23610.4i | −0.654311 | − | 0.377767i | ||||
\(251\) | 74907.1 | + | 74907.1i | 1.18898 | + | 1.18898i | 0.977349 | + | 0.211634i | \(0.0678785\pi\) |
0.211634 | + | 0.977349i | \(0.432122\pi\) | |||||||
\(252\) | −5322.33 | + | 3072.85i | −0.0838109 | + | 0.0483882i | ||||
\(253\) | 70248.5 | + | 70248.5i | 1.09748 | + | 1.09748i | ||||
\(254\) | −7533.92 | + | 28117.0i | −0.116776 | + | 0.435814i | ||||
\(255\) | 12149.3 | + | 21043.2i | 0.186840 | + | 0.323617i | ||||
\(256\) | −2048.00 | − | 3547.24i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 14066.2 | + | 52495.9i | 0.212967 | + | 0.794802i | 0.986872 | + | 0.161502i | \(0.0516337\pi\) |
−0.773906 | + | 0.633301i | \(0.781700\pi\) | |||||||
\(258\) | 47303.9i | 0.710652i | ||||||||
\(259\) | 51144.3 | − | 85196.6i | 0.762426 | − | 1.27006i | ||||
\(260\) | 19245.5 | 0.284696 | ||||||||
\(261\) | −12905.3 | + | 3457.96i | −0.189447 | + | 0.0507620i | ||||
\(262\) | −18344.4 | + | 10591.2i | −0.267240 | + | 0.154291i | ||||
\(263\) | 72524.7 | − | 41872.2i | 1.04852 | − | 0.605361i | 0.126282 | − | 0.991994i | \(-0.459696\pi\) |
0.922233 | + | 0.386634i | \(0.126362\pi\) | |||||||
\(264\) | −21401.3 | − | 5734.46i | −0.307067 | − | 0.0822782i | ||||
\(265\) | −25486.4 | + | 25486.4i | −0.362925 | + | 0.362925i | ||||
\(266\) | −56067.2 | − | 97111.2i | −0.792402 | − | 1.37248i | ||||
\(267\) | 35565.4 | − | 35565.4i | 0.498890 | − | 0.498890i | ||||
\(268\) | −16139.0 | + | 27953.6i | −0.224702 | + | 0.389196i | ||||
\(269\) | −115991. | −1.60295 | −0.801474 | − | 0.598030i | \(-0.795951\pi\) | ||||
−0.801474 | + | 0.598030i | \(0.795951\pi\) | |||||||
\(270\) | 34497.7i | 0.473220i | ||||||||
\(271\) | 24093.1 | − | 41730.5i | 0.328061 | − | 0.568218i | −0.654066 | − | 0.756437i | \(-0.726938\pi\) |
0.982127 | + | 0.188219i | \(0.0602716\pi\) | |||||||
\(272\) | −8672.27 | − | 2323.73i | −0.117218 | − | 0.0314085i | ||||
\(273\) | 65285.5 | + | 65285.5i | 0.875975 | + | 0.875975i | ||||
\(274\) | 5008.37 | − | 1341.99i | 0.0667107 | − | 0.0178751i | ||||
\(275\) | 15215.4 | − | 26353.9i | 0.201196 | − | 0.348481i | ||||
\(276\) | −19239.5 | − | 71802.9i | −0.252567 | − | 0.942593i | ||||
\(277\) | −16993.5 | + | 63420.5i | −0.221474 | + | 0.826552i | 0.762313 | + | 0.647209i | \(0.224064\pi\) |
−0.983787 | + | 0.179343i | \(0.942603\pi\) | |||||||
\(278\) | 85881.9 | + | 23012.0i | 1.11125 | + | 0.297759i | ||||
\(279\) | 6352.45 | − | 1702.13i | 0.0816080 | − | 0.0218668i | ||||
\(280\) | −25744.0 | − | 14863.3i | −0.328367 | − | 0.189583i | ||||
\(281\) | −16981.3 | − | 63375.1i | −0.215059 | − | 0.802613i | −0.986146 | − | 0.165882i | \(-0.946953\pi\) |
0.771086 | − | 0.636731i | \(-0.219714\pi\) | |||||||
\(282\) | −40421.5 | + | 40421.5i | −0.508293 | + | 0.508293i | ||||
\(283\) | −36002.6 | + | 134364.i | −0.449533 | + | 1.67768i | 0.254149 | + | 0.967165i | \(0.418205\pi\) |
−0.703682 | + | 0.710515i | \(0.748462\pi\) | |||||||
\(284\) | 23365.1 | + | 13489.8i | 0.289688 | + | 0.167251i | ||||
\(285\) | 94605.9 | 1.16474 | ||||||||
\(286\) | 38465.7i | 0.470263i | ||||||||
\(287\) | −63628.6 | − | 36736.0i | −0.772482 | − | 0.445993i | ||||
\(288\) | 1354.70 | + | 1354.70i | 0.0163327 | + | 0.0163327i | ||||
\(289\) | 55288.2 | − | 31920.7i | 0.661968 | − | 0.382187i | ||||
\(290\) | −45696.5 | − | 45696.5i | −0.543359 | − | 0.543359i | ||||
\(291\) | 38657.3 | − | 144271.i | 0.456505 | − | 1.70370i | ||||
\(292\) | 6194.85 | + | 10729.8i | 0.0726549 | + | 0.125842i | ||||
\(293\) | 10973.3 | + | 19006.3i | 0.127821 | + | 0.221392i | 0.922832 | − | 0.385202i | \(-0.125868\pi\) |
−0.795011 | + | 0.606595i | \(0.792535\pi\) | |||||||
\(294\) | −20089.4 | − | 74974.8i | −0.232420 | − | 0.867403i | ||||
\(295\) | 27438.0i | 0.315288i | ||||||||
\(296\) | −29780.4 | − | 8526.34i | −0.339897 | − | 0.0973149i | ||||
\(297\) | −68950.2 | −0.781668 | ||||||||
\(298\) | −114607. | + | 30708.7i | −1.29056 | + | 0.345804i | ||||
\(299\) | −111765. | + | 64527.6i | −1.25015 | + | 0.721777i | ||||
\(300\) | −19719.3 | + | 11384.9i | −0.219103 | + | 0.126499i | ||||
\(301\) | −122528. | − | 32831.2i | −1.35239 | − | 0.362371i | ||||
\(302\) | 80081.7 | − | 80081.7i | 0.878050 | − | 0.878050i | ||||
\(303\) | −26790.0 | − | 46401.6i | −0.291801 | − | 0.505415i | ||||
\(304\) | −24717.9 | + | 24717.9i | −0.267463 | + | 0.267463i | ||||
\(305\) | −11941.2 | + | 20682.7i | −0.128365 | + | 0.222335i | ||||
\(306\) | 4199.40 | 0.0448482 | ||||||||
\(307\) | − | 103669.i | − | 1.09995i | −0.835180 | − | 0.549976i | \(-0.814637\pi\) | ||
0.835180 | − | 0.549976i | \(-0.185363\pi\) | |||||||
\(308\) | 29707.1 | − | 51454.2i | 0.313154 | − | 0.542399i | ||||
\(309\) | −173892. | − | 46594.3i | −1.82122 | − | 0.487996i | ||||
\(310\) | 22493.5 | + | 22493.5i | 0.234063 | + | 0.234063i | ||||
\(311\) | −81554.8 | + | 21852.6i | −0.843197 | + | 0.225934i | −0.654463 | − | 0.756094i | \(-0.727105\pi\) |
−0.188734 | + | 0.982028i | \(0.560438\pi\) | |||||||
\(312\) | 14390.9 | − | 24925.9i | 0.147836 | − | 0.256059i | ||||
\(313\) | −25227.5 | − | 94150.2i | −0.257505 | − | 0.961020i | −0.966680 | − | 0.255988i | \(-0.917599\pi\) |
0.709175 | − | 0.705032i | \(-0.249067\pi\) | |||||||
\(314\) | 5250.91 | − | 19596.7i | 0.0532568 | − | 0.198757i | ||||
\(315\) | 13430.4 | + | 3598.65i | 0.135352 | + | 0.0362676i | ||||
\(316\) | −19100.4 | + | 5117.92i | −0.191279 | + | 0.0512531i | ||||
\(317\) | −4675.51 | − | 2699.40i | −0.0465275 | − | 0.0268627i | 0.476556 | − | 0.879144i | \(-0.341885\pi\) |
−0.523083 | + | 0.852282i | \(0.675218\pi\) | |||||||
\(318\) | 13951.2 | + | 52066.5i | 0.137961 | + | 0.514878i | ||||
\(319\) | 91333.1 | − | 91333.1i | 0.897525 | − | 0.897525i | ||||
\(320\) | −2398.44 | + | 8951.10i | −0.0234223 | + | 0.0874131i | ||||
\(321\) | −46815.7 | − | 27029.1i | −0.454341 | − | 0.262314i | ||||
\(322\) | 199339. | 1.92256 | ||||||||
\(323\) | 76622.4i | 0.734430i | ||||||||
\(324\) | 50619.2 | + | 29225.0i | 0.482198 | + | 0.278397i | ||||
\(325\) | 27952.6 | + | 27952.6i | 0.264640 | + | 0.264640i | ||||
\(326\) | 87478.6 | − | 50505.8i | 0.823127 | − | 0.475233i | ||||
\(327\) | −59435.8 | − | 59435.8i | −0.555844 | − | 0.555844i | ||||
\(328\) | −5927.96 | + | 22123.5i | −0.0551008 | + | 0.205639i | ||||
\(329\) | −76646.2 | − | 132755.i | −0.708107 | − | 1.22648i | ||||
\(330\) | 25063.4 | + | 43411.0i | 0.230150 | + | 0.398632i | ||||
\(331\) | −24537.4 | − | 91574.7i | −0.223961 | − | 0.835833i | −0.982818 | − | 0.184576i | \(-0.940909\pi\) |
0.758857 | − | 0.651257i | \(-0.225758\pi\) | |||||||
\(332\) | 53759.3i | 0.487727i | ||||||||
\(333\) | 14486.8 | + | 246.999i | 0.130643 | + | 0.00222745i | ||||
\(334\) | −85219.5 | −0.763917 | ||||||||
\(335\) | 70538.1 | − | 18900.6i | 0.628542 | − | 0.168417i | ||||
\(336\) | −38500.5 | + | 22228.3i | −0.341027 | + | 0.196892i | ||||
\(337\) | −56879.5 | + | 32839.4i | −0.500836 | + | 0.289158i | −0.729059 | − | 0.684451i | \(-0.760042\pi\) |
0.228223 | + | 0.973609i | \(0.426709\pi\) | |||||||
\(338\) | 29764.3 | + | 7975.31i | 0.260532 | + | 0.0698094i | ||||
\(339\) | −105277. | + | 105277.i | −0.916083 | + | 0.916083i | ||||
\(340\) | 10156.2 | + | 17591.1i | 0.0878565 | + | 0.152172i | ||||
\(341\) | −44957.4 | + | 44957.4i | −0.386628 | + | 0.386628i | ||||
\(342\) | 8175.14 | − | 14159.8i | 0.0698945 | − | 0.121061i | ||||
\(343\) | 33867.8 | 0.287871 | ||||||||
\(344\) | 39543.7i | 0.334165i | ||||||||
\(345\) | −84089.4 | + | 145647.i | −0.706485 | + | 1.22367i | ||||
\(346\) | 9635.51 | + | 2581.83i | 0.0804864 | + | 0.0215663i | ||||
\(347\) | 73825.0 | + | 73825.0i | 0.613119 | + | 0.613119i | 0.943757 | − | 0.330639i | \(-0.107264\pi\) |
−0.330639 | + | 0.943757i | \(0.607264\pi\) | |||||||
\(348\) | −93354.0 | + | 25014.1i | −0.770858 | + | 0.206551i | ||||
\(349\) | 37900.0 | − | 65644.7i | 0.311163 | − | 0.538950i | −0.667451 | − | 0.744653i | \(-0.732615\pi\) |
0.978614 | + | 0.205703i | \(0.0659482\pi\) | |||||||
\(350\) | −15803.4 | − | 58979.0i | −0.129007 | − | 0.481461i | ||||
\(351\) | 23182.2 | − | 86517.1i | 0.188166 | − | 0.702244i | ||||
\(352\) | −17890.5 | − | 4793.73i | −0.144390 | − | 0.0386891i | ||||
\(353\) | 34893.5 | − | 9349.67i | 0.280024 | − | 0.0750321i | −0.116074 | − | 0.993241i | \(-0.537031\pi\) |
0.396097 | + | 0.918208i | \(0.370364\pi\) | |||||||
\(354\) | 35536.4 | + | 20517.0i | 0.283574 | + | 0.163722i | ||||
\(355\) | −15798.1 | − | 58959.4i | −0.125357 | − | 0.467839i | ||||
\(356\) | 29730.9 | − | 29730.9i | 0.234590 | − | 0.234590i | ||||
\(357\) | −25221.0 | + | 94125.9i | −0.197891 | + | 0.738538i | ||||
\(358\) | 69954.1 | + | 40388.0i | 0.545817 | + | 0.315128i | ||||
\(359\) | −83839.2 | −0.650516 | −0.325258 | − | 0.945625i | \(-0.605451\pi\) | ||||
−0.325258 | + | 0.945625i | \(0.605451\pi\) | |||||||
\(360\) | − | 4334.42i | − | 0.0334446i | ||||||
\(361\) | 145498. | + | 84003.2i | 1.11646 | + | 0.644587i | ||||
\(362\) | 17840.7 | + | 17840.7i | 0.136143 | + | 0.136143i | ||||
\(363\) | 34576.7 | − | 19962.9i | 0.262404 | − | 0.151499i | ||||
\(364\) | 54575.5 | + | 54575.5i | 0.411903 | + | 0.411903i | ||||
\(365\) | 7254.87 | − | 27075.5i | 0.0544558 | − | 0.203232i | ||||
\(366\) | 17858.2 | + | 30931.3i | 0.133314 | + | 0.230906i | ||||
\(367\) | 62813.0 | + | 108795.i | 0.466356 | + | 0.807752i | 0.999262 | − | 0.0384227i | \(-0.0122333\pi\) |
−0.532906 | + | 0.846175i | \(0.678900\pi\) | |||||||
\(368\) | −16083.3 | − | 60023.8i | −0.118763 | − | 0.443229i | ||||
\(369\) | − | 10712.9i | − | 0.0786783i | ||||||
\(370\) | 34001.6 | + | 61282.0i | 0.248368 | + | 0.447641i | ||||
\(371\) | −144547. | −1.05017 | ||||||||
\(372\) | 45952.2 | − | 12312.9i | 0.332063 | − | 0.0889761i | ||||
\(373\) | 147987. | − | 85440.3i | 1.06367 | − | 0.614109i | 0.137223 | − | 0.990540i | \(-0.456182\pi\) |
0.926444 | + | 0.376432i | \(0.122849\pi\) | |||||||
\(374\) | −35159.1 | + | 20299.1i | −0.251359 | + | 0.145122i | ||||
\(375\) | 154327. | + | 41351.7i | 1.09743 | + | 0.294057i | ||||
\(376\) | −33790.4 | + | 33790.4i | −0.239011 | + | 0.239011i | ||||
\(377\) | 83895.0 | + | 145310.i | 0.590273 | + | 1.02238i | ||||
\(378\) | −97827.3 | + | 97827.3i | −0.684662 | + | 0.684662i | ||||
\(379\) | −84059.3 | + | 145595.i | −0.585204 | + | 1.01360i | 0.409646 | + | 0.912245i | \(0.365652\pi\) |
−0.994850 | + | 0.101359i | \(0.967681\pi\) | |||||||
\(380\) | 79085.9 | 0.547686 | ||||||||
\(381\) | − | 98489.3i | − | 0.678483i | ||||||
\(382\) | 35276.3 | − | 61100.4i | 0.241744 | − | 0.418714i | ||||
\(383\) | −17421.5 | − | 4668.07i | −0.118765 | − | 0.0318229i | 0.198947 | − | 0.980010i | \(-0.436248\pi\) |
−0.317712 | + | 0.948187i | \(0.602914\pi\) | |||||||
\(384\) | 9799.61 | + | 9799.61i | 0.0664579 | + | 0.0664579i | ||||
\(385\) | −129839. | + | 34790.4i | −0.875962 | + | 0.234713i | ||||
\(386\) | 15749.6 | − | 27279.1i | 0.105705 | − | 0.183086i | ||||
\(387\) | −4787.10 | − | 17865.7i | −0.0319632 | − | 0.119288i | ||||
\(388\) | 32315.7 | − | 120604.i | 0.214659 | − | 0.801119i | ||||
\(389\) | 175773. | + | 47098.1i | 1.16159 | + | 0.311246i | 0.787600 | − | 0.616187i | \(-0.211324\pi\) |
0.373988 | + | 0.927434i | \(0.377990\pi\) | |||||||
\(390\) | −62897.9 | + | 16853.4i | −0.413530 | + | 0.110805i | ||||
\(391\) | −117961. | − | 68105.0i | −0.771589 | − | 0.445477i | ||||
\(392\) | −16793.8 | − | 62675.3i | −0.109289 | − | 0.407872i | ||||
\(393\) | 50678.4 | − | 50678.4i | 0.328124 | − | 0.328124i | ||||
\(394\) | −8206.94 | + | 30628.7i | −0.0528675 | + | 0.197304i | ||||
\(395\) | 38743.7 | + | 22368.7i | 0.248317 | + | 0.143366i | ||||
\(396\) | 8663.16 | 0.0552441 | ||||||||
\(397\) | − | 161561.i | − | 1.02507i | −0.858666 | − | 0.512536i | \(-0.828706\pi\) | ||
0.858666 | − | 0.512536i | \(-0.171294\pi\) | |||||||
\(398\) | 161648. | + | 93327.2i | 1.02048 | + | 0.589172i | ||||
\(399\) | 268280. | + | 268280.i | 1.68516 | + | 1.68516i | ||||
\(400\) | −16484.4 | + | 9517.25i | −0.103027 | + | 0.0594828i | ||||
\(401\) | 73656.6 | + | 73656.6i | 0.458061 | + | 0.458061i | 0.898018 | − | 0.439958i | \(-0.145007\pi\) |
−0.439958 | + | 0.898018i | \(0.645007\pi\) | |||||||
\(402\) | 28266.2 | − | 105491.i | 0.174910 | − | 0.652774i | ||||
\(403\) | −41296.1 | − | 71527.0i | −0.254273 | − | 0.440413i | ||||
\(404\) | −22395.1 | − | 38789.5i | −0.137212 | − | 0.237658i | ||||
\(405\) | −34225.8 | − | 127733.i | −0.208662 | − | 0.778738i | ||||
\(406\) | − | 259169.i | − | 1.57228i | ||||||
\(407\) | −122484. | + | 67958.6i | −0.739416 | + | 0.410257i | ||||
\(408\) | 30377.6 | 0.182487 | ||||||||
\(409\) | 22432.7 | − | 6010.81i | 0.134102 | − | 0.0359324i | −0.191144 | − | 0.981562i | \(-0.561220\pi\) |
0.325246 | + | 0.945630i | \(0.394553\pi\) | |||||||
\(410\) | 44875.9 | − | 25909.1i | 0.266959 | − | 0.154129i | ||||
\(411\) | −15193.1 | + | 8771.76i | −0.0899423 | + | 0.0519282i | ||||
\(412\) | −145366. | − | 38950.6i | −0.856381 | − | 0.229467i | ||||
\(413\) | −77807.5 | + | 77807.5i | −0.456164 | + | 0.456164i | ||||
\(414\) | 14532.8 | + | 25171.5i | 0.0847905 | + | 0.146862i | ||||
\(415\) | 86002.5 | − | 86002.5i | 0.499361 | − | 0.499361i | ||||
\(416\) | 12030.1 | − | 20836.8i | 0.0695159 | − | 0.120405i | ||||
\(417\) | −300830. | −1.73001 | ||||||||
\(418\) | 158068.i | 0.904673i | ||||||||
\(419\) | 59939.4 | − | 103818.i | 0.341417 | − | 0.591351i | −0.643279 | − | 0.765631i | \(-0.722427\pi\) |
0.984696 | + | 0.174281i | \(0.0557600\pi\) | |||||||
\(420\) | 97152.2 | + | 26031.9i | 0.550750 | + | 0.147573i | ||||
\(421\) | −119336. | − | 119336.i | −0.673299 | − | 0.673299i | 0.285176 | − | 0.958475i | \(-0.407948\pi\) |
−0.958475 | + | 0.285176i | \(0.907948\pi\) | |||||||
\(422\) | −170367. | + | 45649.8i | −0.956669 | + | 0.256339i | ||||
\(423\) | 11175.7 | − | 19357.0i | 0.0624591 | − | 0.108182i | ||||
\(424\) | 11662.5 | + | 43525.1i | 0.0648725 | + | 0.242107i | ||||
\(425\) | −10798.6 | + | 40300.9i | −0.0597845 | + | 0.223119i | ||||
\(426\) | −88174.7 | − | 23626.3i | −0.485875 | − | 0.130190i | ||||
\(427\) | −92513.5 | + | 24788.9i | −0.507399 | + | 0.135957i | ||||
\(428\) | −39135.7 | − | 22595.0i | −0.213641 | − | 0.123346i | ||||
\(429\) | −33684.8 | − | 125713.i | −0.183029 | − | 0.683072i | ||||
\(430\) | 63260.9 | − | 63260.9i | 0.342136 | − | 0.342136i | ||||
\(431\) | 44293.1 | − | 165304.i | 0.238441 | − | 0.889876i | −0.738126 | − | 0.674663i | \(-0.764289\pi\) |
0.976567 | − | 0.215213i | \(-0.0690444\pi\) | |||||||
\(432\) | 37350.2 | + | 21564.2i | 0.200136 | + | 0.115549i | ||||
\(433\) | 265556. | 1.41638 | 0.708192 | − | 0.706020i | \(-0.249511\pi\) | ||||
0.708192 | + | 0.706020i | \(0.249511\pi\) | |||||||
\(434\) | 127572.i | 0.677293i | ||||||||
\(435\) | 189362. | + | 109328.i | 1.00072 | + | 0.577768i | ||||
\(436\) | −49685.5 | − | 49685.5i | −0.261370 | − | 0.261370i | ||||
\(437\) | −459279. | + | 265165.i | −2.40499 | + | 1.38852i | ||||
\(438\) | −29642.1 | − | 29642.1i | −0.154512 | − | 0.154512i | ||||
\(439\) | 37654.4 | − | 140528.i | 0.195383 | − | 0.729180i | −0.796784 | − | 0.604264i | \(-0.793467\pi\) |
0.992167 | − | 0.124916i | \(-0.0398661\pi\) | |||||||
\(440\) | 20951.8 | + | 36289.5i | 0.108222 | + | 0.187446i | ||||
\(441\) | 15174.7 | + | 26283.4i | 0.0780268 | + | 0.135146i | ||||
\(442\) | −13649.8 | − | 50941.7i | −0.0698685 | − | 0.260753i | ||||
\(443\) | 291905.i | 1.48742i | 0.668501 | + | 0.743711i | \(0.266936\pi\) | ||||
−0.668501 | + | 0.743711i | \(0.733064\pi\) | |||||||
\(444\) | 104795. | + | 1786.74i | 0.531586 | + | 0.00906348i | ||||
\(445\) | −95125.4 | −0.480371 | ||||||||
\(446\) | −213782. | + | 57282.8i | −1.07474 | + | 0.287975i | ||||
\(447\) | 347664. | − | 200724.i | 1.73998 | − | 1.00458i | ||||
\(448\) | −32184.6 | + | 18581.8i | −0.160358 | + | 0.0925830i | ||||
\(449\) | 236386. | + | 63339.5i | 1.17254 | + | 0.314182i | 0.791965 | − | 0.610566i | \(-0.209058\pi\) |
0.380579 | + | 0.924748i | \(0.375725\pi\) | |||||||
\(450\) | 6295.42 | − | 6295.42i | 0.0310885 | − | 0.0310885i | ||||
\(451\) | 51784.2 | + | 89692.8i | 0.254592 | + | 0.440966i | ||||
\(452\) | −88006.6 | + | 88006.6i | −0.430763 | + | 0.430763i | ||||
\(453\) | −191594. | + | 331851.i | −0.933654 | + | 1.61714i | ||||
\(454\) | 225748. | 1.09525 | ||||||||
\(455\) | − | 174617.i | − | 0.843457i | ||||||
\(456\) | 59137.1 | − | 102429.i | 0.284401 | − | 0.492596i | ||||
\(457\) | 44335.2 | + | 11879.6i | 0.212284 | + | 0.0568812i | 0.363394 | − | 0.931636i | \(-0.381618\pi\) |
−0.151110 | + | 0.988517i | \(0.548285\pi\) | |||||||
\(458\) | 69073.5 | + | 69073.5i | 0.329291 | + | 0.329291i | ||||
\(459\) | 91313.6 | − | 24467.4i | 0.433421 | − | 0.116135i | ||||
\(460\) | −70294.7 | + | 121754.i | −0.332205 | + | 0.575397i | ||||
\(461\) | −93701.0 | − | 349697.i | −0.440902 | − | 1.64547i | −0.726535 | − | 0.687130i | \(-0.758870\pi\) |
0.285632 | − | 0.958339i | \(-0.407796\pi\) | |||||||
\(462\) | −52029.6 | + | 194177.i | −0.243762 | + | 0.909733i | ||||
\(463\) | 236666. | + | 63414.3i | 1.10401 | + | 0.295819i | 0.764397 | − | 0.644746i | \(-0.223037\pi\) |
0.339614 | + | 0.940565i | \(0.389704\pi\) | |||||||
\(464\) | −78039.4 | + | 20910.6i | −0.362475 | + | 0.0971249i | ||||
\(465\) | −93210.8 | − | 53815.3i | −0.431082 | − | 0.248886i | ||||
\(466\) | −15172.8 | − | 56625.8i | −0.0698706 | − | 0.260761i | ||||
\(467\) | 154729. | − | 154729.i | 0.709477 | − | 0.709477i | −0.256948 | − | 0.966425i | \(-0.582717\pi\) |
0.966425 | + | 0.256948i | \(0.0827170\pi\) | |||||||
\(468\) | −2912.70 | + | 10870.3i | −0.0132985 | + | 0.0496308i | ||||
\(469\) | 253627. | + | 146432.i | 1.15305 | + | 0.665716i | ||||
\(470\) | 108114. | 0.489424 | ||||||||
\(471\) | 68643.9i | 0.309428i | ||||||||
\(472\) | 29706.7 | + | 17151.2i | 0.133343 | + | 0.0769857i | ||||
\(473\) | 126439. | + | 126439.i | 0.565143 | + | 0.565143i | ||||
\(474\) | 57941.8 | − | 33452.7i | 0.257891 | − | 0.148893i | ||||
\(475\) | 114866. | + | 114866.i | 0.509103 | + | 0.509103i | ||||
\(476\) | −21083.5 | + | 78684.7i | −0.0930527 | + | 0.347277i | ||||
\(477\) | −10538.2 | − | 18252.6i | −0.0463157 | − | 0.0802211i | ||||
\(478\) | −149523. | − | 258982.i | −0.654414 | − | 1.13348i | ||||
\(479\) | −86636.4 | − | 323332.i | −0.377598 | − | 1.40921i | −0.849512 | − | 0.527570i | \(-0.823103\pi\) |
0.471914 | − | 0.881645i | \(-0.343563\pi\) | |||||||
\(480\) | − | 31354.3i | − | 0.136086i | ||||||
\(481\) | −44091.9 | − | 176538.i | −0.190576 | − | 0.763043i | ||||
\(482\) | −31608.0 | −0.136051 | ||||||||
\(483\) | −651478. | + | 174563.i | −2.79258 | + | 0.748269i | ||||
\(484\) | 28904.4 | − | 16688.0i | 0.123388 | − | 0.0712382i | ||||
\(485\) | −244636. | + | 141241.i | −1.04001 | + | 0.600449i | ||||
\(486\) | −41899.0 | − | 11226.8i | −0.177391 | − | 0.0475318i | ||||
\(487\) | 248817. | − | 248817.i | 1.04911 | − | 1.04911i | 0.0503816 | − | 0.998730i | \(-0.483956\pi\) |
0.998730 | − | 0.0503816i | \(-0.0160438\pi\) | |||||||
\(488\) | 14928.6 | + | 25857.1i | 0.0626872 | + | 0.108577i | ||||
\(489\) | −241669. | + | 241669.i | −1.01065 | + | 1.01065i | ||||
\(490\) | −73399.9 | + | 127132.i | −0.305706 | + | 0.529497i | ||||
\(491\) | −281769. | −1.16877 | −0.584386 | − | 0.811476i | \(-0.698665\pi\) | ||||
−0.584386 | + | 0.811476i | \(0.698665\pi\) | |||||||
\(492\) | − | 77494.9i | − | 0.320142i | ||||||
\(493\) | −88546.1 | + | 153366.i | −0.364314 | + | 0.631010i | ||||
\(494\) | −198340. | − | 53145.1i | −0.812750 | − | 0.217776i | ||||
\(495\) | −13859.1 | − | 13859.1i | −0.0565618 | − | 0.0565618i | ||||
\(496\) | 38413.8 | − | 10293.0i | 0.156144 | − | 0.0418386i | ||||
\(497\) | 122395. | − | 211994.i | 0.495509 | − | 0.858246i | ||||
\(498\) | −47077.5 | − | 175696.i | −0.189826 | − | 0.708439i | ||||
\(499\) | −105760. | + | 394700.i | −0.424735 | + | 1.58513i | 0.339765 | + | 0.940510i | \(0.389652\pi\) |
−0.764500 | + | 0.644623i | \(0.777014\pi\) | |||||||
\(500\) | 129010. | + | 34568.0i | 0.516039 | + | 0.138272i | ||||
\(501\) | 278514. | − | 74627.5i | 1.10961 | − | 0.297320i | ||||
\(502\) | −259486. | − | 149814.i | −1.02969 | − | 0.594491i | ||||
\(503\) | −86561.1 | − | 323050.i | −0.342126 | − | 1.27683i | −0.895933 | − | 0.444188i | \(-0.853492\pi\) |
0.553807 | − | 0.832645i | \(-0.313175\pi\) | |||||||
\(504\) | 12291.4 | − | 12291.4i | 0.0483882 | − | 0.0483882i | ||||
\(505\) | −26227.3 | + | 97881.4i | −0.102842 | + | 0.383811i | ||||
\(506\) | −243348. | − | 140497.i | −0.950445 | − | 0.548740i | ||||
\(507\) | −104259. | −0.405601 | ||||||||
\(508\) | − | 82332.3i | − | 0.319038i | ||||||
\(509\) | −280589. | − | 161998.i | −1.08302 | − | 0.625280i | −0.151309 | − | 0.988487i | \(-0.548349\pi\) |
−0.931709 | + | 0.363206i | \(0.881682\pi\) | |||||||
\(510\) | −48597.1 | − | 48597.1i | −0.186840 | − | 0.186840i | ||||
\(511\) | 97352.9 | − | 56206.7i | 0.372827 | − | 0.215252i | ||||
\(512\) | 8192.00 | + | 8192.00i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 95263.3 | − | 355527.i | 0.361985 | − | 1.35095i | ||||
\(514\) | −76859.3 | − | 133124.i | −0.290918 | − | 0.503884i | ||||
\(515\) | 170240. | + | 294864.i | 0.641869 | + | 1.11175i | ||||
\(516\) | −34628.8 | − | 129237.i | −0.130058 | − | 0.485385i | ||||
\(517\) | 216086.i | 0.808434i | ||||||||
\(518\) | −77360.6 | + | 270202.i | −0.288310 | + | 1.00700i | ||||
\(519\) | −33751.6 | −0.125303 | ||||||||
\(520\) | −52579.6 | + | 14088.7i | −0.194451 | + | 0.0521030i | ||||
\(521\) | 459470. | − | 265275.i | 1.69271 | − | 0.977285i | 0.740388 | − | 0.672180i | \(-0.234642\pi\) |
0.952319 | − | 0.305105i | \(-0.0986916\pi\) | |||||||
\(522\) | 32726.5 | − | 18894.6i | 0.120104 | − | 0.0693422i | ||||
\(523\) | 258320. | + | 69216.7i | 0.944398 | + | 0.253051i | 0.697984 | − | 0.716114i | \(-0.254081\pi\) |
0.246415 | + | 0.969165i | \(0.420748\pi\) | |||||||
\(524\) | 42364.6 | − | 42364.6i | 0.154291 | − | 0.154291i | ||||
\(525\) | 103297. | + | 178916.i | 0.374774 | + | 0.649127i | ||||
\(526\) | −167489. | + | 167489.i | −0.605361 | + | 0.605361i | ||||
\(527\) | 43585.6 | − | 75492.5i | 0.156936 | − | 0.271821i | ||||
\(528\) | 62667.4 | 0.224788 | ||||||||
\(529\) | − | 662915.i | − | 2.36890i | ||||||
\(530\) | 50972.8 | − | 88287.5i | 0.181463 | − | 0.314302i | ||||
\(531\) | −15497.7 | − | 4152.59i | −0.0549639 | − | 0.0147275i | ||||
\(532\) | 224269. | + | 224269.i | 0.792402 | + | 0.792402i | ||||
\(533\) | −129955. | + | 34821.4i | −0.457445 | + | 0.122572i | ||||
\(534\) | −71130.8 | + | 123202.i | −0.249445 | + | 0.432052i | ||||
\(535\) | 26461.3 | + | 98754.9i | 0.0924493 | + | 0.345025i | ||||
\(536\) | 23629.2 | − | 88185.3i | 0.0822468 | − | 0.306949i | ||||
\(537\) | −263992. | − | 70736.4i | −0.915465 | − | 0.245298i | ||||
\(538\) | 316893. | − | 84911.3i | 1.09483 | − | 0.293360i | ||||
\(539\) | −254098. | − | 146703.i | −0.874628 | − | 0.504967i | ||||
\(540\) | −25254.1 | − | 94249.5i | −0.0866052 | − | 0.323215i | ||||
\(541\) | −165201. | + | 165201.i | −0.564440 | + | 0.564440i | −0.930566 | − | 0.366125i | \(-0.880684\pi\) |
0.366125 | + | 0.930566i | \(0.380684\pi\) | |||||||
\(542\) | −35274.8 | + | 131647.i | −0.120079 | + | 0.448139i | ||||
\(543\) | −73930.1 | − | 42683.6i | −0.250739 | − | 0.144764i | ||||
\(544\) | 25394.2 | 0.0858097 | ||||||||
\(545\) | 158971.i | 0.535210i | ||||||||
\(546\) | −226156. | − | 130571.i | −0.758616 | − | 0.437987i | ||||
\(547\) | −3798.88 | − | 3798.88i | −0.0126964 | − | 0.0126964i | 0.700730 | − | 0.713426i | \(-0.252858\pi\) |
−0.713426 | + | 0.700730i | \(0.752858\pi\) | |||||||
\(548\) | −12700.7 | + | 7332.77i | −0.0422929 | + | 0.0244178i | ||||
\(549\) | −9874.89 | − | 9874.89i | −0.0327633 | − | 0.0327633i | ||||
\(550\) | −22276.9 | + | 83138.6i | −0.0736427 | + | 0.274838i | ||||
\(551\) | 344752. | + | 597128.i | 1.13554 | + | 1.96682i | ||||
\(552\) | 105127. | + | 182085.i | 0.345013 | + | 0.597580i | ||||
\(553\) | 46435.6 | + | 173300.i | 0.151845 | + | 0.566694i | ||||
\(554\) | − | 185708.i | − | 0.605078i | ||||||
\(555\) | −164789. | − | 170506.i | −0.534986 | − | 0.553545i | ||||
\(556\) | −251480. | −0.813492 | ||||||||
\(557\) | 456838. | − | 122409.i | 1.47249 | − | 0.394552i | 0.568704 | − | 0.822542i | \(-0.307445\pi\) |
0.903783 | + | 0.427990i | \(0.140778\pi\) | |||||||
\(558\) | −16109.2 | + | 9300.63i | −0.0517374 | + | 0.0298706i | ||||
\(559\) | −201163. | + | 116142.i | −0.643762 | + | 0.371676i | ||||
\(560\) | 81214.5 | + | 21761.4i | 0.258975 | + | 0.0693921i | ||||
\(561\) | 97130.5 | − | 97130.5i | 0.308624 | − | 0.308624i | ||||
\(562\) | 92787.6 | + | 160713.i | 0.293777 | + | 0.508836i | ||||
\(563\) | −104456. | + | 104456.i | −0.329547 | + | 0.329547i | −0.852414 | − | 0.522867i | \(-0.824862\pi\) |
0.522867 | + | 0.852414i | \(0.324862\pi\) | |||||||
\(564\) | 80842.9 | − | 140024.i | 0.254146 | − | 0.440194i | ||||
\(565\) | 281581. | 0.882076 | ||||||||
\(566\) | − | 393444.i | − | 1.22815i | ||||||
\(567\) | 265163. | − | 459275.i | 0.824796 | − | 1.42859i | ||||
\(568\) | −73709.8 | − | 19750.5i | −0.228470 | − | 0.0612183i | ||||
\(569\) | 306476. | + | 306476.i | 0.946612 | + | 0.946612i | 0.998645 | − | 0.0520335i | \(-0.0165703\pi\) |
−0.0520335 | + | 0.998645i | \(0.516570\pi\) | |||||||
\(570\) | −258468. | + | 69256.3i | −0.795531 | + | 0.213162i | ||||
\(571\) | −147284. | + | 255103.i | −0.451735 | + | 0.782427i | −0.998494 | − | 0.0548627i | \(-0.982528\pi\) |
0.546759 | + | 0.837290i | \(0.315861\pi\) | |||||||
\(572\) | −28158.8 | − | 105090.i | −0.0860642 | − | 0.321196i | ||||
\(573\) | −61783.6 | + | 230580.i | −0.188176 | + | 0.702282i | ||||
\(574\) | 200729. | + | 53785.2i | 0.609238 | + | 0.163245i | ||||
\(575\) | −278936. | + | 74740.7i | −0.843663 | + | 0.226059i | ||||
\(576\) | −4692.82 | − | 2709.40i | −0.0141445 | − | 0.00816636i | ||||
\(577\) | −54992.2 | − | 205234.i | −0.165177 | − | 0.616448i | −0.998018 | − | 0.0629357i | \(-0.979954\pi\) |
0.832841 | − | 0.553513i | \(-0.186713\pi\) | |||||||
\(578\) | −127683. | + | 127683.i | −0.382187 | + | 0.382187i | ||||
\(579\) | −27584.1 | + | 102945.i | −0.0822815 | + | 0.307079i | ||||
\(580\) | 158297. | + | 91393.0i | 0.470563 | + | 0.271680i | ||||
\(581\) | 487765. | 1.44497 | ||||||||
\(582\) | 422455.i | 1.24720i | ||||||||
\(583\) | 176459. | + | 101879.i | 0.519167 | + | 0.299741i | ||||
\(584\) | −24779.4 | − | 24779.4i | −0.0726549 | − | 0.0726549i | ||||
\(585\) | 22049.7 | − | 12730.4i | 0.0644304 | − | 0.0371989i | ||||
\(586\) | −43893.2 | − | 43893.2i | −0.127821 | − | 0.127821i | ||||
\(587\) | −83728.0 | + | 312477.i | −0.242994 | + | 0.906864i | 0.731388 | + | 0.681962i | \(0.238873\pi\) |
−0.974381 | + | 0.224902i | \(0.927794\pi\) | |||||||
\(588\) | 109771. | + | 190128.i | 0.317491 | + | 0.549911i | ||||
\(589\) | −169699. | − | 293928.i | −0.489159 | − | 0.847248i | ||||
\(590\) | −20086.0 | − | 74961.9i | −0.0577017 | − | 0.215346i | ||||
\(591\) | − | 107287.i | − | 0.307167i | ||||||
\(592\) | 87603.3 | + | 1493.63i | 0.249964 | + | 0.00426185i | ||||
\(593\) | −328329. | −0.933683 | −0.466841 | − | 0.884341i | \(-0.654608\pi\) | ||||
−0.466841 | + | 0.884341i | \(0.654608\pi\) | |||||||
\(594\) | 188375. | − | 50475.0i | 0.533889 | − | 0.143055i | ||||
\(595\) | 159606. | − | 92148.7i | 0.450833 | − | 0.260289i | ||||
\(596\) | 290631. | − | 167796.i | 0.818180 | − | 0.472376i | ||||
\(597\) | −610023. | − | 163455.i | −1.71158 | − | 0.458617i | ||||
\(598\) | 258110. | − | 258110.i | 0.721777 | − | 0.721777i | ||||
\(599\) | 187920. | + | 325486.i | 0.523743 | + | 0.907150i | 0.999618 | + | 0.0276368i | \(0.00879820\pi\) |
−0.475875 | + | 0.879513i | \(0.657868\pi\) | |||||||
\(600\) | 45539.7 | − | 45539.7i | 0.126499 | − | 0.126499i | ||||
\(601\) | 117824. | − | 204077.i | 0.326200 | − | 0.564994i | −0.655555 | − | 0.755148i | \(-0.727565\pi\) |
0.981754 | + | 0.190153i | \(0.0608985\pi\) | |||||||
\(602\) | 358786. | 0.990016 | ||||||||
\(603\) | 42702.3i | 0.117440i | ||||||||
\(604\) | −160163. | + | 277411.i | −0.439025 | + | 0.760414i | ||||
\(605\) | −72937.4 | − | 19543.5i | −0.199269 | − | 0.0533940i | ||||
\(606\) | 107160. | + | 107160.i | 0.291801 | + | 0.291801i | ||||
\(607\) | 47042.2 | − | 12604.9i | 0.127676 | − | 0.0342108i | −0.194415 | − | 0.980919i | \(-0.562281\pi\) |
0.322091 | + | 0.946709i | \(0.395614\pi\) | |||||||
\(608\) | 49435.8 | − | 85625.3i | 0.133732 | − | 0.231630i | ||||
\(609\) | 226957. | + | 847014.i | 0.611939 | + | 2.28379i | ||||
\(610\) | 17483.1 | − | 65247.7i | 0.0469849 | − | 0.175350i | ||||
\(611\) | −271139. | − | 72651.6i | −0.726290 | − | 0.194609i | ||||
\(612\) | −11473.0 | + | 3074.18i | −0.0306319 | + | 0.00820778i | ||||
\(613\) | 205696. | + | 118759.i | 0.547401 | + | 0.316042i | 0.748073 | − | 0.663616i | \(-0.230979\pi\) |
−0.200672 | + | 0.979658i | \(0.564313\pi\) | |||||||
\(614\) | 75891.3 | + | 283230.i | 0.201305 | + | 0.751281i | ||||
\(615\) | −123974. | + | 123974.i | −0.327779 | + | 0.327779i | ||||
\(616\) | −43494.2 | + | 162323.i | −0.114622 | + | 0.427777i | ||||
\(617\) | 87837.3 | + | 50712.9i | 0.230732 | + | 0.133213i | 0.610910 | − | 0.791700i | \(-0.290804\pi\) |
−0.380177 | + | 0.924914i | \(0.624137\pi\) | |||||||
\(618\) | 509192. | 1.33323 | ||||||||
\(619\) | − | 66828.7i | − | 0.174414i | −0.996190 | − | 0.0872071i | \(-0.972206\pi\) | ||
0.996190 | − | 0.0872071i | \(-0.0277942\pi\) | |||||||
\(620\) | −77919.7 | − | 44987.0i | −0.202705 | − | 0.117032i | ||||
\(621\) | 462666. | + | 462666.i | 1.19973 | + | 1.19973i | ||||
\(622\) | 206815. | − | 119405.i | 0.534565 | − | 0.308631i | ||||
\(623\) | −269753. | − | 269753.i | −0.695008 | − | 0.695008i | ||||
\(624\) | −21069.8 | + | 78633.6i | −0.0541117 | + | 0.201948i | ||||
\(625\) | −58143.1 | − | 100707.i | −0.148846 | − | 0.257809i | ||||
\(626\) | 137845. | + | 238755.i | 0.351758 | + | 0.609262i | ||||
\(627\) | −138422. | − | 516597.i | −0.352103 | − | 1.31406i | ||||
\(628\) | 57383.0i | 0.145500i | ||||||||
\(629\) | 138095. | − | 133465.i | 0.349040 | − | 0.337337i | ||||
\(630\) | −39326.8 | −0.0990849 | ||||||||
\(631\) | −509606. | + | 136549.i | −1.27990 | + | 0.342948i | −0.833816 | − | 0.552043i | \(-0.813849\pi\) |
−0.446084 | + | 0.894991i | \(0.647182\pi\) | |||||||
\(632\) | 48436.6 | − | 27964.9i | 0.121266 | − | 0.0700130i | ||||
\(633\) | 516818. | − | 298385.i | 1.28982 | − | 0.744679i | ||||
\(634\) | 14749.8 | + | 3952.20i | 0.0366951 | + | 0.00983243i | ||||
\(635\) | −131713. | + | 131713.i | −0.326648 | + | 0.326648i | ||||
\(636\) | −76230.7 | − | 132035.i | −0.188458 | − | 0.326420i | ||||
\(637\) | 269512. | − | 269512.i | 0.664201 | − | 0.664201i | ||||
\(638\) | −182666. | + | 316387.i | −0.448763 | + | 0.777280i | ||||
\(639\) | 35692.8 | 0.0874135 | ||||||||
\(640\) | − | 26210.6i | − | 0.0639908i | ||||||
\(641\) | 186200. | − | 322508.i | 0.453173 | − | 0.784919i | −0.545408 | − | 0.838171i | \(-0.683625\pi\) |
0.998581 | + | 0.0532520i | \(0.0169587\pi\) | |||||||
\(642\) | 147690. | + | 39573.3i | 0.358327 | + | 0.0960135i | ||||
\(643\) | −298628. | − | 298628.i | −0.722285 | − | 0.722285i | 0.246785 | − | 0.969070i | \(-0.420626\pi\) |
−0.969070 | + | 0.246785i | \(0.920626\pi\) | |||||||
\(644\) | −544604. | + | 145926.i | −1.31313 | + | 0.351853i | ||||
\(645\) | −151351. | + | 262147.i | −0.363802 | + | 0.630123i | ||||
\(646\) | −56091.5 | − | 209336.i | −0.134410 | − | 0.501625i | ||||
\(647\) | −49301.6 | + | 183996.i | −0.117775 | + | 0.439541i | −0.999480 | − | 0.0322603i | \(-0.989729\pi\) |
0.881705 | + | 0.471801i | \(0.156396\pi\) | |||||||
\(648\) | −159689. | − | 42788.4i | −0.380298 | − | 0.101900i | ||||
\(649\) | 149825. | − | 40145.6i | 0.355710 | − | 0.0953122i | ||||
\(650\) | −96830.6 | − | 55905.2i | −0.229185 | − | 0.132320i | ||||
\(651\) | −111716. | − | 416931.i | −0.263605 | − | 0.983789i | ||||
\(652\) | −202023. | + | 202023.i | −0.475233 | + | 0.475233i | ||||
\(653\) | 33910.6 | − | 126556.i | 0.0795261 | − | 0.296795i | −0.914695 | − | 0.404144i | \(-0.867569\pi\) |
0.994221 | + | 0.107349i | \(0.0342361\pi\) | |||||||
\(654\) | 205892. | + | 118872.i | 0.481375 | + | 0.277922i | ||||
\(655\) | −135547. | −0.315943 | ||||||||
\(656\) | − | 64782.0i | − | 0.150538i | ||||||
\(657\) | 14195.0 | + | 8195.48i | 0.0328855 | + | 0.0189864i | ||||
\(658\) | 306585. | + | 306585.i | 0.708107 | + | 0.708107i | ||||
\(659\) | −241916. | + | 139670.i | −0.557048 | + | 0.321612i | −0.751960 | − | 0.659209i | \(-0.770891\pi\) |
0.194912 | + | 0.980821i | \(0.437558\pi\) | |||||||
\(660\) | −100253. | − | 100253.i | −0.230150 | − | 0.230150i | ||||
\(661\) | −145356. | + | 542475.i | −0.332682 | + | 1.24159i | 0.573678 | + | 0.819081i | \(0.305516\pi\) |
−0.906360 | + | 0.422506i | \(0.861151\pi\) | |||||||
\(662\) | 134075. | + | 232224.i | 0.305936 | + | 0.529897i | ||||
\(663\) | 89220.3 | + | 154534.i | 0.202972 | + | 0.351558i | ||||
\(664\) | −39354.5 | − | 146873.i | −0.0892603 | − | 0.333124i | ||||
\(665\) | − | 717557.i | − | 1.62261i | ||||||
\(666\) | −39759.6 | + | 9930.29i | −0.0896383 | + | 0.0223879i | ||||
\(667\) | −1.22572e6 | −2.75511 | ||||||||
\(668\) | 232824. | − | 62385.0i | 0.521765 | − | 0.139806i | ||||
\(669\) | 648518. | − | 374422.i | 1.44901 | − | 0.836584i | ||||
\(670\) | −178877. | + | 103275.i | −0.398480 | + | 0.230062i | ||||
\(671\) | 130410. | + | 34943.2i | 0.289644 | + | 0.0776100i | ||||
\(672\) | 88913.2 | − | 88913.2i | 0.196892 | − | 0.196892i | ||||
\(673\) | 158202. | + | 274013.i | 0.349286 | + | 0.604981i | 0.986123 | − | 0.166018i | \(-0.0530908\pi\) |
−0.636837 | + | 0.770999i | \(0.719758\pi\) | |||||||
\(674\) | 131357. | − | 131357.i | 0.289158 | − | 0.289158i | ||||
\(675\) | 100211. | − | 173570.i | 0.219941 | − | 0.380949i | ||||
\(676\) | −87155.8 | −0.190723 | ||||||||
\(677\) | − | 796725.i | − | 1.73833i | −0.494526 | − | 0.869163i | \(-0.664658\pi\) | ||
0.494526 | − | 0.869163i | \(-0.335342\pi\) | |||||||
\(678\) | 210554. | − | 364691.i | 0.458041 | − | 0.793351i | ||||
\(679\) | −1.09425e6 | − | 293204.i | −2.37344 | − | 0.635961i | ||||
\(680\) | −40624.8 | − | 40624.8i | −0.0878565 | − | 0.0878565i | ||||
\(681\) | −737789. | + | 197690.i | −1.59088 | + | 0.426276i | ||||
\(682\) | 89914.9 | − | 155737.i | 0.193314 | − | 0.334829i | ||||
\(683\) | 19115.5 | + | 71339.9i | 0.0409773 | + | 0.152929i | 0.983383 | − | 0.181542i | \(-0.0581089\pi\) |
−0.942406 | + | 0.334472i | \(0.891442\pi\) | |||||||
\(684\) | −11969.2 | + | 44669.8i | −0.0255832 | + | 0.0954776i | ||||
\(685\) | 32049.0 | + | 8587.50i | 0.0683020 | + | 0.0183015i | ||||
\(686\) | −92528.5 | + | 24792.9i | −0.196620 | + | 0.0526841i | ||||
\(687\) | −286234. | − | 165257.i | −0.606467 | − | 0.350144i | ||||
\(688\) | −28948.0 | − | 108036.i | −0.0611564 | − | 0.228239i | ||||
\(689\) | −187164. | + | 187164.i | −0.394260 | + | 0.394260i | ||||
\(690\) | 123115. | − | 459473.i | 0.258591 | − | 0.965077i | ||||
\(691\) | 410049. | + | 236742.i | 0.858775 | + | 0.495814i | 0.863602 | − | 0.504175i | \(-0.168203\pi\) |
−0.00482708 | + | 0.999988i | \(0.501537\pi\) | |||||||
\(692\) | −28214.7 | −0.0589201 | ||||||||
\(693\) | − | 78602.0i | − | 0.163669i | ||||||
\(694\) | −255737. | − | 147650.i | −0.530977 | − | 0.306559i | ||||
\(695\) | 402310. | + | 402310.i | 0.832897 | + | 0.832897i | ||||
\(696\) | 236736. | − | 136680.i | 0.488705 | − | 0.282154i | ||||
\(697\) | −100408. | − | 100408.i | −0.206682 | − | 0.206682i | ||||
\(698\) | −55489.4 | + | 207089.i | −0.113894 | + | 0.425056i | ||||
\(699\) | 99175.5 | + | 171777.i | 0.202978 | + | 0.351569i | ||||
\(700\) | 86351.3 | + | 149565.i | 0.176227 | + | 0.305234i | ||||
\(701\) | −114518. | − | 427386.i | −0.233044 | − | 0.869730i | −0.979021 | − | 0.203759i | \(-0.934684\pi\) |
0.745977 | − | 0.665971i | \(-0.231983\pi\) | |||||||
\(702\) | 253340.i | 0.514078i | ||||||||
\(703\) | −181188. | − | 725455.i | −0.366623 | − | 1.46791i | ||||
\(704\) | 52386.9 | 0.105701 | ||||||||
\(705\) | −353336. | + | 94676.2i | −0.710903 | + | 0.190486i | ||||
\(706\) | −88486.3 | + | 51087.6i | −0.177528 | + | 0.102496i | ||||
\(707\) | −351943. | + | 203194.i | −0.704098 | + | 0.406511i | ||||
\(708\) | −112107. | − | 30038.9i | −0.223648 | − | 0.0599263i | ||||
\(709\) | −303158. | + | 303158.i | −0.603082 | + | 0.603082i | −0.941129 | − | 0.338047i | \(-0.890234\pi\) |
0.338047 | + | 0.941129i | \(0.390234\pi\) | |||||||
\(710\) | 86322.5 | + | 149515.i | 0.171241 | + | 0.296598i | ||||
\(711\) | −18498.1 | + | 18498.1i | −0.0365921 | + | 0.0365921i | ||||
\(712\) | −59461.9 | + | 102991.i | −0.117295 | + | 0.203161i | ||||
\(713\) | 603342. | 1.18682 | ||||||||
\(714\) | − | 275620.i | − | 0.540647i | ||||||
\(715\) | −123072. | + | 213168.i | −0.240740 | + | 0.416975i | ||||
\(716\) | −220684. | − | 59132.2i | −0.430473 | − | 0.115345i | ||||
\(717\) | 715463. | + | 715463.i | 1.39171 | + | 1.39171i | ||||
\(718\) | 229053. | − | 61374.5i | 0.444311 | − | 0.119053i | ||||
\(719\) | 391419. | − | 677958.i | 0.757154 | − | 1.31143i | −0.187142 | − | 0.982333i | \(-0.559923\pi\) |
0.944296 | − | 0.329096i | \(-0.106744\pi\) | |||||||
\(720\) | 3173.02 | + | 11841.9i | 0.00612079 | + | 0.0228431i | ||||
\(721\) | −353404. | + | 1.31892e6i | −0.679831 | + | 2.53716i | ||||
\(722\) | −459002. | − | 122989.i | −0.880522 | − | 0.235935i | ||||
\(723\) | 103301. | − | 27679.4i | 0.197619 | − | 0.0529518i | ||||
\(724\) | −61802.0 | − | 35681.4i | −0.117903 | − | 0.0680714i | ||||
\(725\) | 97173.5 | + | 362657.i | 0.184872 | + | 0.689953i | ||||
\(726\) | −79851.4 | + | 79851.4i | −0.151499 | + | 0.151499i | ||||
\(727\) | 264520. | − | 987201.i | 0.500483 | − | 1.86783i | 0.00362734 | − | 0.999993i | \(-0.498845\pi\) |
0.496855 | − | 0.867833i | \(-0.334488\pi\) | |||||||
\(728\) | −189055. | − | 109151.i | −0.356719 | − | 0.205952i | ||||
\(729\) | −445041. | −0.837424 | ||||||||
\(730\) | 79282.7i | 0.148776i | ||||||||
\(731\) | −212316. | − | 122581.i | −0.397327 | − | 0.229397i | ||||
\(732\) | −71432.8 | − | 71432.8i | −0.133314 | − | 0.133314i | ||||
\(733\) | −246276. | + | 142188.i | −0.458368 | + | 0.264639i | −0.711358 | − | 0.702830i | \(-0.751919\pi\) |
0.252990 | + | 0.967469i | \(0.418586\pi\) | |||||||
\(734\) | −251252. | − | 251252.i | −0.466356 | − | 0.466356i | ||||
\(735\) | 128554. | − | 479770.i | 0.237964 | − | 0.888093i | ||||
\(736\) | 87880.9 | + | 152214.i | 0.162233 | + | 0.280996i | ||||
\(737\) | −206414. | − | 357520.i | −0.380019 | − | 0.658212i | ||||
\(738\) | 7842.40 | + | 29268.2i | 0.0143991 | + | 0.0537383i | ||||
\(739\) | 590831.i | 1.08187i | 0.841065 | + | 0.540934i | \(0.181929\pi\) | ||||
−0.841065 | + | 0.540934i | \(0.818071\pi\) | |||||||
\(740\) | −137756. | − | 142535.i | −0.251563 | − | 0.260290i | ||||
\(741\) | 694754. | 1.26530 | ||||||||
\(742\) | 394909. | − | 105816.i | 0.717281 | − | 0.192195i | ||||
\(743\) | −48940.7 | + | 28255.9i | −0.0886529 | + | 0.0511838i | −0.543671 | − | 0.839298i | \(-0.682966\pi\) |
0.455018 | + | 0.890482i | \(0.349633\pi\) | |||||||
\(744\) | −116530. | + | 67278.7i | −0.210520 | + | 0.121544i | ||||
\(745\) | −733377. | − | 196508.i | −1.32134 | − | 0.354052i | ||||
\(746\) | −341761. | + | 341761.i | −0.614109 | + | 0.614109i | ||||
\(747\) | 35560.4 | + | 61592.4i | 0.0637273 | + | 0.110379i | ||||
\(748\) | 81196.4 | − | 81196.4i | 0.145122 | − | 0.145122i | ||||
\(749\) | −205007. | + | 355083.i | −0.365431 | + | 0.632946i | ||||
\(750\) | −451900. | −0.803378 | ||||||||
\(751\) | 625070.i | 1.10828i | 0.832424 | + | 0.554139i | \(0.186953\pi\) | ||||
−0.832424 | + | 0.554139i | \(0.813047\pi\) | |||||||
\(752\) | 67580.8 | − | 117053.i | 0.119505 | − | 0.206989i | ||||
\(753\) | 979244. | + | 262388.i | 1.72703 | + | 0.462757i | ||||
\(754\) | −335580. | − | 335580.i | −0.590273 | − | 0.590273i | ||||
\(755\) | 700019. | − | 187569.i | 1.22805 | − | 0.329055i | ||||
\(756\) | 195655. | − | 338884.i | 0.342331 | − | 0.592935i | ||||
\(757\) | −234907. | − | 876684.i | −0.409924 | − | 1.52986i | −0.794789 | − | 0.606885i | \(-0.792419\pi\) |
0.384865 | − | 0.922973i | \(-0.374248\pi\) | |||||||
\(758\) | 123071. | − | 459309.i | 0.214200 | − | 0.799404i | ||||
\(759\) | 918343. | + | 246069.i | 1.59412 | + | 0.427144i | ||||
\(760\) | −216067. | + | 57894.9i | −0.374077 | + | 0.100234i | ||||
\(761\) | 100001. | + | 57735.5i | 0.172677 | + | 0.0996951i | 0.583848 | − | 0.811863i | \(-0.301547\pi\) |
−0.411171 | + | 0.911558i | \(0.634880\pi\) | |||||||
\(762\) | 72099.1 | + | 269078.i | 0.124171 | + | 0.463412i | ||||
\(763\) | −450803. | + | 450803.i | −0.774351 | + | 0.774351i | ||||
\(764\) | −51648.1 | + | 192753.i | −0.0884846 | + | 0.330229i | ||||
\(765\) | 23272.1 | + | 13436.2i | 0.0397661 | + | 0.0229590i | ||||
\(766\) | 51013.7 | 0.0869419 | ||||||||
\(767\) | 201495.i | 0.342511i | ||||||||
\(768\) | −33946.8 | − | 19599.2i | −0.0575542 | − | 0.0332289i | ||||
\(769\) | −41224.0 | − | 41224.0i | −0.0697105 | − | 0.0697105i | 0.671392 | − | 0.741102i | \(-0.265697\pi\) |
−0.741102 | + | 0.671392i | \(0.765697\pi\) | |||||||
\(770\) | 329260. | − | 190098.i | 0.555337 | − | 0.320624i | ||||
\(771\) | 367769. | + | 367769.i | 0.618681 | + | 0.618681i | ||||
\(772\) | −23059.0 | + | 86057.3i | −0.0386906 | + | 0.144395i | ||||
\(773\) | −114279. | − | 197938.i | −0.191253 | − | 0.331260i | 0.754413 | − | 0.656401i | \(-0.227922\pi\) |
−0.945666 | + | 0.325140i | \(0.894589\pi\) | |||||||
\(774\) | 26157.2 | + | 45305.6i | 0.0436626 | + | 0.0756258i | ||||
\(775\) | −47832.3 | − | 178513.i | −0.0796376 | − | 0.297212i | ||||
\(776\) | 353152.i | 0.586460i | ||||||||
\(777\) | 16211.3 | − | 950816.i | 0.0268520 | − | 1.57491i | ||||
\(778\) | −514698. | −0.850341 | ||||||||
\(779\) | −534029. | + | 143093.i | −0.880014 | + | 0.235799i | ||||
\(780\) | 159503. | − | 92088.9i | 0.262167 | − | 0.151362i | ||||
\(781\) | −298834. | + | 172532.i | −0.489923 | + | 0.282857i | ||||
\(782\) | 372132. | + | 99712.6i | 0.608533 | + | 0.163056i | ||||
\(783\) | 601531. | − | 601531.i | 0.981148 | − | 0.981148i | ||||
\(784\) | 91763.0 | + | 158938.i | 0.149292 | + | 0.258581i | ||||
\(785\) | 91799.6 | − | 91799.6i | 0.148971 | − | 0.148971i | ||||
\(786\) | −101357. | + | 175555.i | −0.164062 | + | 0.284163i | ||||
\(787\) | 923559. | 1.49113 | 0.745564 | − | 0.666434i | \(-0.232180\pi\) | ||||
0.745564 | + | 0.666434i | \(0.232180\pi\) | |||||||
\(788\) | − | 89687.1i | − | 0.144437i | ||||||
\(789\) | 400714. | − | 694057.i | 0.643695 | − | 1.11491i | ||||
\(790\) | −122225. | − | 32750.0i | −0.195842 | − | 0.0524756i | ||||
\(791\) | 798496. | + | 798496.i | 1.27620 | + | 1.27620i | ||||
\(792\) | −23668.2 | + | 6341.87i | −0.0377324 | + | 0.0101104i | ||||
\(793\) | −87691.9 | + | 151887.i | −0.139448 | + | 0.241531i | ||||
\(794\) | 118271. | + | 441392.i | 0.187601 | + | 0.700138i | ||||
\(795\) | −89274.8 | + | 333178.i | −0.141252 | + | 0.527160i | ||||
\(796\) | −509950. | − | 136641.i | −0.804824 | − | 0.215652i | ||||
\(797\) | 655934. | − | 175757.i | 1.03263 | − | 0.276692i | 0.297572 | − | 0.954699i | \(-0.403823\pi\) |
0.735055 | + | 0.678008i | \(0.237156\pi\) | |||||||
\(798\) | −929348. | − | 536559.i | −1.45939 | − | 0.842582i | ||||
\(799\) | −76679.4 | − | 286171.i | −0.120112 | − | 0.448263i | ||||
\(800\) | 38069.0 | − | 38069.0i | 0.0594828 | − | 0.0594828i | ||||
\(801\) | 14396.7 | − | 53729.3i | 0.0224387 | − | 0.0837425i | ||||
\(802\) | −255154. | − | 147313.i | −0.396692 | − | 0.229030i | ||||
\(803\) | −158461. | −0.245749 | ||||||||
\(804\) | 308899.i | 0.477864i | ||||||||
\(805\) | 1.10469e6 | + | 637793.i | 1.70470 | + | 0.984210i | ||||
\(806\) | 165185. | + | 165185.i | 0.254273 | + | 0.254273i | ||||
\(807\) | −961310. | + | 555013.i | −1.47610 | + | 0.852228i | ||||
\(808\) | 89580.6 | + | 89580.6i | 0.137212 | + | 0.137212i | ||||
\(809\) | 129613. | − | 483722.i | 0.198039 | − | 0.739093i | −0.793420 | − | 0.608675i | \(-0.791701\pi\) |
0.991459 | − | 0.130418i | \(-0.0416319\pi\) | |||||||
\(810\) | 187013. | + | 323917.i | 0.285038 | + | 0.493700i | ||||
\(811\) | 348012. | + | 602774.i | 0.529118 | + | 0.916459i | 0.999423 | + | 0.0339550i | \(0.0108103\pi\) |
−0.470306 | + | 0.882504i | \(0.655856\pi\) | |||||||
\(812\) | 189725. | + | 708062.i | 0.287748 | + | 1.07389i | ||||
\(813\) | − | 461139.i | − | 0.697671i | ||||||
\(814\) | 284882. | − | 275331.i | 0.429949 | − | 0.415533i | ||||
\(815\) | 646382. | 0.973137 | ||||||||
\(816\) | −82993.0 | + | 22237.9i | −0.124641 | + | 0.0333975i | ||||
\(817\) | −826647. | + | 477265.i | −1.23844 | + | 0.715015i | ||||
\(818\) | −56887.0 | + | 32843.7i | −0.0850171 | + | 0.0490846i | ||||
\(819\) | 98628.0 | + | 26427.3i | 0.147039 | + | 0.0393990i | ||||
\(820\) | −103636. | + | 103636.i | −0.154129 | + | 0.154129i | ||||
\(821\) | −587541. | − | 1.01765e6i | −0.871670 | − | 1.50978i | −0.860269 | − | 0.509841i | \(-0.829704\pi\) |
−0.0114010 | − | 0.999935i | \(-0.503629\pi\) | |||||||
\(822\) | 35087.0 | − | 35087.0i | 0.0519282 | − | 0.0519282i | ||||
\(823\) | −626063. | + | 1.08437e6i | −0.924312 | + | 1.60096i | −0.131648 | + | 0.991297i | \(0.542027\pi\) |
−0.792664 | + | 0.609658i | \(0.791307\pi\) | |||||||
\(824\) | 425660. | 0.626915 | ||||||||
\(825\) | − | 291221.i | − | 0.427873i | ||||||
\(826\) | 155615. | − | 269533.i | 0.228082 | − | 0.395050i | ||||
\(827\) | 267880. | + | 71778.1i | 0.391678 | + | 0.104950i | 0.449282 | − | 0.893390i | \(-0.351680\pi\) |
−0.0576049 | + | 0.998339i | \(0.518346\pi\) | |||||||
\(828\) | −58131.0 | − | 58131.0i | −0.0847905 | − | 0.0847905i | ||||
\(829\) | −34920.7 | + | 9356.98i | −0.0508129 | + | 0.0136153i | −0.284136 | − | 0.958784i | \(-0.591707\pi\) |
0.233323 | + | 0.972399i | \(0.425040\pi\) | |||||||
\(830\) | −172005. | + | 297921.i | −0.249681 | + | 0.432459i | ||||
\(831\) | 162626. | + | 606930.i | 0.235499 | + | 0.878894i | ||||
\(832\) | −17613.3 | + | 65733.9i | −0.0254446 | + | 0.0949604i | ||||
\(833\) | 388571. | + | 104117.i | 0.559990 | + | 0.150049i | ||||
\(834\) | 821884. | − | 220223.i | 1.18162 | − | 0.316615i | ||||
\(835\) | −472267. | − | 272663.i | −0.677352 | − | 0.391069i | ||||
\(836\) | −115714. | − | 431850.i | −0.165567 | − | 0.617903i | ||||
\(837\) | −296095. | + | 296095.i | −0.422650 | + | 0.422650i | ||||
\(838\) | −87757.4 | + | 327515.i | −0.124967 | + | 0.466384i | ||||
\(839\) | −153305. | − | 88510.5i | −0.217787 | − | 0.125739i | 0.387138 | − | 0.922022i | \(-0.373464\pi\) |
−0.604925 | + | 0.796282i | \(0.706797\pi\) | |||||||
\(840\) | −284481. | −0.403177 | ||||||||
\(841\) | 886324.i | 1.25314i | ||||||||
\(842\) | 413393. | + | 238672.i | 0.583094 | + | 0.336649i | ||||
\(843\) | −443986. | − | 443986.i | −0.624761 | − | 0.624761i | ||||
\(844\) | 432035. | − | 249435.i | 0.606504 | − | 0.350165i | ||||
\(845\) | 139429. | + | 139429.i | 0.195272 | + | 0.195272i | ||||
\(846\) | −16362.4 | + | 61065.4i | −0.0228616 | + | 0.0853207i | ||||
\(847\) | −151412. | − | 262254.i | −0.211054 | − | 0.365557i | ||||
\(848\) | −63725.2 | − | 110375.i | −0.0886175 | − | 0.153490i | ||||
\(849\) | 344543. | + | 1.28585e6i | 0.478000 | + | 1.78392i | ||||
\(850\) | − | 118009.i | − | 0.163334i | ||||||
\(851\) | 1.27789e6 | + | 365870.i | 1.76456 | + | 0.505205i | ||||
\(852\) | 258194. | 0.355686 | ||||||||
\(853\) | −194483. | + | 52111.5i | −0.267290 | + | 0.0716202i | −0.389975 | − | 0.920825i | \(-0.627516\pi\) |
0.122685 | + | 0.992446i | \(0.460850\pi\) | |||||||
\(854\) | 234605. | − | 135449.i | 0.321678 | − | 0.185721i | ||||
\(855\) | 90609.4 | − | 52313.4i | 0.123948 | − | 0.0715617i | ||||
\(856\) | 123461. | + | 33081.4i | 0.168494 | + | 0.0451477i | ||||
\(857\) | −50015.9 | + | 50015.9i | −0.0680999 | + | 0.0680999i | −0.740336 | − | 0.672237i | \(-0.765334\pi\) |
0.672237 | + | 0.740336i | \(0.265334\pi\) | |||||||
\(858\) | 184057. | + | 318796.i | 0.250022 | + | 0.433050i | ||||
\(859\) | 263501. | − | 263501.i | 0.357105 | − | 0.357105i | −0.505640 | − | 0.862745i | \(-0.668744\pi\) |
0.862745 | + | 0.505640i | \(0.168744\pi\) | |||||||
\(860\) | −126522. | + | 219142.i | −0.171068 | + | 0.296298i | ||||
\(861\) | −703122. | −0.948472 | ||||||||
\(862\) | 484044.i | 0.651434i | ||||||||
\(863\) | 301192. | − | 521680.i | 0.404410 | − | 0.700458i | −0.589843 | − | 0.807518i | \(-0.700810\pi\) |
0.994253 | + | 0.107060i | \(0.0341436\pi\) | |||||||
\(864\) | −117829. | − | 31572.1i | −0.157842 | − | 0.0422938i | ||||
\(865\) | 45137.1 | + | 45137.1i | 0.0603256 | + | 0.0603256i | ||||
\(866\) | −725513. | + | 194401.i | −0.967408 | + | 0.259216i | ||||
\(867\) | 305479. | − | 529104.i | 0.406390 | − | 0.703887i | ||||
\(868\) | −93389.4 | − | 348534.i | −0.123953 | − | 0.462600i | ||||
\(869\) | 65457.1 | − | 244289.i | 0.0866796 | − | 0.323493i | ||||
\(870\) | −597380. | − | 160067.i | −0.789246 | − | 0.211478i | ||||
\(871\) | 518008. | − | 138800.i | 0.682811 | − | 0.182959i | ||||
\(872\) | 172116. | + | 99370.9i | 0.226353 | + | 0.130685i | ||||
\(873\) | −42752.0 | − | 159553.i | −0.0560955 | − | 0.209351i | ||||
\(874\) | 1.06066e6 | − | 1.06066e6i | 1.38852 | − | 1.38852i | ||||
\(875\) | 313641. | − | 1.17052e6i | 0.409653 | − | 1.52885i | ||||
\(876\) | 102683. | + | 59284.3i | 0.133811 | + | 0.0772558i | ||||
\(877\) | 418158. | 0.543677 | 0.271839 | − | 0.962343i | \(-0.412368\pi\) | ||||
0.271839 | + | 0.962343i | \(0.412368\pi\) | |||||||
\(878\) | 411495.i | 0.533797i | ||||||||
\(879\) | 181889. | + | 105014.i | 0.235412 | + | 0.135915i | ||||
\(880\) | −83807.0 | − | 83807.0i | −0.108222 | − | 0.108222i | ||||
\(881\) | 252820. | − | 145966.i | 0.325731 | − | 0.188061i | −0.328213 | − | 0.944604i | \(-0.606446\pi\) |
0.653944 | + | 0.756543i | \(0.273113\pi\) | |||||||
\(882\) | −60699.0 | − | 60699.0i | −0.0780268 | − | 0.0780268i | ||||
\(883\) | 130671. | − | 487671.i | 0.167594 | − | 0.625469i | −0.830101 | − | 0.557613i | \(-0.811717\pi\) |
0.997695 | − | 0.0678564i | \(-0.0216160\pi\) | |||||||
\(884\) | 74583.8 | + | 129183.i | 0.0954421 | + | 0.165311i | ||||
\(885\) | 131290. | + | 227400.i | 0.167627 | + | 0.290339i | ||||
\(886\) | −213689. | − | 797500.i | −0.272217 | − | 1.01593i | ||||
\(887\) | 302503.i | 0.384488i | 0.981347 | + | 0.192244i | \(0.0615764\pi\) | ||||
−0.981347 | + | 0.192244i | \(0.938424\pi\) | |||||||
\(888\) | −287612. | + | 71833.6i | −0.364738 | + | 0.0910965i | ||||
\(889\) | −747012. | −0.945200 | ||||||||
\(890\) | 259887. | − | 69636.6i | 0.328099 | − | 0.0879139i | ||||
\(891\) | −647408. | + | 373781.i | −0.815498 | + | 0.470828i | ||||
\(892\) | 542130. | − | 312999.i | 0.681355 | − | 0.393381i | ||||
\(893\) | −1.11420e6 | − | 298549.i | −1.39721 | − | 0.374380i | ||||
\(894\) | −802897. | + | 802897.i | −1.00458 | + | 1.00458i | ||||
\(895\) | 258446. | + | 447642.i | 0.322645 | + | 0.558837i | ||||
\(896\) | 74327.1 | − | 74327.1i | 0.0925830 | − | 0.0925830i | ||||
\(897\) | −617524. | + | 1.06958e6i | −0.767484 | + | 1.32932i | ||||
\(898\) | −692186. | −0.858362 | ||||||||
\(899\) | − | 784430.i | − | 0.970588i | ||||||
\(900\) | −12590.8 | + | 21808.0i | −0.0155443 | + | 0.0269234i | ||||
\(901\) | −269845. | − | 72304.7i | −0.332403 | − | 0.0890670i | ||||
\(902\) | −207137. | − | 207137.i | −0.254592 | − | 0.254592i | ||||
\(903\) | −1.17258e6 | + | 314192.i | −1.43803 | + | 0.385318i | ||||
\(904\) | 176013. | − | 304864.i | 0.215382 | − | 0.373052i | ||||
\(905\) | 41787.0 | + | 155951.i | 0.0510204 | + | 0.190411i | ||||
\(906\) | 280513. | − | 1.04689e6i | 0.341741 | − | 1.27539i | ||||
\(907\) | 330404. | + | 88531.4i | 0.401634 | + | 0.107617i | 0.453981 | − | 0.891012i | \(-0.350003\pi\) |
−0.0523469 | + | 0.998629i | \(0.516670\pi\) | |||||||
\(908\) | −616756. | + | 165259.i | −0.748069 | + | 0.200445i | ||||
\(909\) | −51316.6 | − | 29627.7i | −0.0621055 | − | 0.0358566i | ||||
\(910\) | 127828. | + | 477062.i | 0.154363 | + | 0.576092i | ||||
\(911\) | 262310. | − | 262310.i | 0.316066 | − | 0.316066i | −0.531188 | − | 0.847254i | \(-0.678254\pi\) |
0.847254 | + | 0.531188i | \(0.178254\pi\) | |||||||
\(912\) | −86582.8 | + | 323131.i | −0.104098 | + | 0.388499i | ||||
\(913\) | −595452. | − | 343784.i | −0.714340 | − | 0.412424i | ||||
\(914\) | −129823. | −0.155402 | ||||||||
\(915\) | 228552.i | 0.272988i | ||||||||
\(916\) | −239278. | − | 138147.i | −0.285175 | − | 0.164646i | ||||
\(917\) | −384380. | − | 384380.i | −0.457112 | − | 0.457112i | ||||
\(918\) | −231562. | + | 133692.i | −0.274778 | + | 0.158643i | ||||
\(919\) | 383862. | + | 383862.i | 0.454511 | + | 0.454511i | 0.896849 | − | 0.442337i | \(-0.145851\pi\) |
−0.442337 | + | 0.896849i | \(0.645851\pi\) | |||||||
\(920\) | 102919. | − | 384097.i | 0.121596 | − | 0.453801i | ||||
\(921\) | −496054. | − | 859192.i | −0.584804 | − | 1.01291i | ||||
\(922\) | 511992. | + | 886795.i | 0.602284 | + | 1.04319i | ||||
\(923\) | −116016. | − | 432978.i | −0.136181 | − | 0.508233i | ||||
\(924\) | − | 568590.i | − | 0.665970i | ||||||
\(925\) | 6941.02 | − | 407101.i | 0.00811222 | − | 0.475793i | ||||
\(926\) | −693005. | −0.808192 | ||||||||
\(927\) | −192311. | + | 51529.7i | −0.223793 | + | 0.0599650i | ||||
\(928\) | 197900. | − | 114258.i | 0.229800 | − | 0.132675i | ||||
\(929\) | −108139. | + | 62433.9i | −0.125300 | + | 0.0723418i | −0.561340 | − | 0.827585i | \(-0.689714\pi\) |
0.436040 | + | 0.899927i | \(0.356381\pi\) | |||||||
\(930\) | 294052. | + | 78791.0i | 0.339984 | + | 0.0910984i | ||||
\(931\) | 1.10751e6 | − | 1.10751e6i | 1.27776 | − | 1.27776i | ||||
\(932\) | 82905.9 | + | 143597.i | 0.0954451 | + | 0.165316i | ||||
\(933\) | −571347. | + | 571347.i | −0.656352 | + | 0.656352i | ||||
\(934\) | −309458. | + | 535997.i | −0.354738 | + | 0.614425i | ||||
\(935\) | −259791. | −0.297167 | ||||||||
\(936\) | − | 31830.5i | − | 0.0363323i | ||||||
\(937\) | 173846. | − | 301111.i | 0.198010 | − | 0.342963i | −0.749873 | − | 0.661582i | \(-0.769886\pi\) |
0.947883 | + | 0.318618i | \(0.103219\pi\) | |||||||
\(938\) | −800117. | − | 214391.i | −0.909385 | − | 0.243669i | ||||
\(939\) | −659586. | − | 659586.i | −0.748066 | − | 0.748066i | ||||
\(940\) | −295372. | + | 79144.7i | −0.334283 | + | 0.0895708i | ||||
\(941\) | −244739. | + | 423900.i | −0.276391 | + | 0.478723i | −0.970485 | − | 0.241161i | \(-0.922472\pi\) |
0.694094 | + | 0.719884i | \(0.255805\pi\) | |||||||
\(942\) | −50250.8 | − | 187539.i | −0.0566293 | − | 0.211344i | ||||
\(943\) | 254373. | − | 949331.i | 0.286053 | − | 1.06757i | ||||
\(944\) | −93715.8 | − | 25111.1i | −0.105164 | − | 0.0281787i | ||||
\(945\) | −855139. | + | 229134.i | −0.957575 | + | 0.256582i | ||||
\(946\) | −437997. | − | 252878.i | −0.489428 | − | 0.282571i | ||||
\(947\) | 247142. | + | 922348.i | 0.275580 | + | 1.02848i | 0.955452 | + | 0.295147i | \(0.0953686\pi\) |
−0.679872 | + | 0.733331i | \(0.737965\pi\) | |||||||
\(948\) | −133811. | + | 133811.i | −0.148893 | + | 0.148893i | ||||
\(949\) | 53277.3 | − | 198834.i | 0.0591575 | − | 0.220779i | ||||
\(950\) | −397909. | − | 229733.i | −0.440896 | − | 0.254552i | ||||
\(951\) | −51666.2 | −0.0571276 | ||||||||
\(952\) | − | 230405.i | − | 0.254225i | ||||||
\(953\) | 1.43087e6 | + | 826116.i | 1.57549 | + | 0.909610i | 0.995477 | + | 0.0950031i | \(0.0302861\pi\) |
0.580014 | + | 0.814607i | \(0.303047\pi\) | |||||||
\(954\) | 42152.6 | + | 42152.6i | 0.0463157 | + | 0.0463157i | ||||
\(955\) | 390986. | − | 225736.i | 0.428701 | − | 0.247511i | ||||
\(956\) | 598093. | + | 598093.i | 0.654414 | + | 0.654414i | ||||
\(957\) | 319925. | − | 1.19398e6i | 0.349321 | − | 1.30368i | ||||
\(958\) | 473390. | + | 819936.i | 0.515808 | + | 0.893406i | ||||
\(959\) | 66531.2 | + | 115235.i | 0.0723416 | + | 0.125299i | ||||
\(960\) | 22952.9 | + | 85661.4i | 0.0249055 | + | 0.0929486i | ||||
\(961\) | − | 537396.i | − | 0.581899i | ||||||
\(962\) | 249697. | + | 450034.i | 0.269813 | + | 0.486290i | ||||
\(963\) | −59784.1 | −0.0644664 | ||||||||
\(964\) | 86354.7 | − | 23138.7i | 0.0929249 | − | 0.0248991i | ||||
\(965\) | 174561. | − | 100783.i | 0.187453 | − | 0.108226i | ||||
\(966\) | 1.65208e6 | − | 953830.i | 1.77042 | − | 1.02215i | ||||
\(967\) | −999074. | − | 267701.i | −1.06843 | − | 0.286284i | −0.318580 | − | 0.947896i | \(-0.603206\pi\) |
−0.749847 | + | 0.661612i | \(0.769873\pi\) | |||||||
\(968\) | −66751.9 | + | 66751.9i | −0.0712382 | + | 0.0712382i | ||||
\(969\) | 366635. | + | 635031.i | 0.390469 | + | 0.676313i | ||||
\(970\) | 564962. | − | 564962.i | 0.600449 | − | 0.600449i | ||||
\(971\) | −203757. | + | 352918.i | −0.216110 | + | 0.374314i | −0.953615 | − | 0.301028i | \(-0.902670\pi\) |
0.737505 | + | 0.675341i | \(0.236004\pi\) | |||||||
\(972\) | 122689. | 0.129859 | ||||||||
\(973\) | 2.28171e6i | 2.41010i | ||||||||
\(974\) | −497634. | + | 861927.i | −0.524556 | + | 0.908557i | ||||
\(975\) | 365418. | + | 97913.4i | 0.384397 | + | 0.102999i | ||||
\(976\) | −59714.4 | − | 59714.4i | −0.0626872 | − | 0.0626872i | ||||
\(977\) | −775552. | + | 207809.i | −0.812497 | + | 0.217708i | −0.641064 | − | 0.767488i | \(-0.721507\pi\) |
−0.171434 | + | 0.985196i | \(0.554840\pi\) | |||||||
\(978\) | 483337. | − | 837165.i | 0.505327 | − | 0.875252i | ||||
\(979\) | 139182. | + | 519434.i | 0.145217 | + | 0.541957i | ||||
\(980\) | 107465. | − | 401064.i | 0.111896 | − | 0.417601i | ||||
\(981\) | −89790.8 | − | 24059.4i | −0.0933026 | − | 0.0250004i | ||||
\(982\) | 769807. | − | 206269.i | 0.798287 | − | 0.213900i | ||||
\(983\) | 757657. | + | 437434.i | 0.784090 | + | 0.452694i | 0.837878 | − | 0.545858i | \(-0.183796\pi\) |
−0.0537881 | + | 0.998552i | \(0.517130\pi\) | |||||||
\(984\) | 56730.2 | + | 211720.i | 0.0585901 | + | 0.218661i | ||||
\(985\) | −143479. | + | 143479.i | −0.147882 | + | 0.147882i | ||||
\(986\) | 129640. | − | 483825.i | 0.133348 | − | 0.497662i | ||||
\(987\) | −1.27046e6 | − | 733499.i | −1.30414 | − | 0.752948i | ||||
\(988\) | 580781. | 0.594974 | ||||||||
\(989\) | − | 1.69685e6i | − | 1.73480i | ||||||
\(990\) | 48009.2 | + | 27718.1i | 0.0489840 | + | 0.0282809i | ||||
\(991\) | −390656. | − | 390656.i | −0.397784 | − | 0.397784i | 0.479667 | − | 0.877451i | \(-0.340758\pi\) |
−0.877451 | + | 0.479667i | \(0.840758\pi\) | |||||||
\(992\) | −97413.6 | + | 56241.8i | −0.0989911 | + | 0.0571525i | ||||
\(993\) | −641543. | − | 641543.i | −0.650619 | − | 0.650619i | ||||
\(994\) | −179199. | + | 668779.i | −0.181369 | + | 0.676877i | ||||
\(995\) | 597209. | + | 1.03440e6i | 0.603226 | + | 1.04482i | ||||
\(996\) | 257236. | + | 445546.i | 0.259307 | + | 0.449132i | ||||
\(997\) | 8899.16 | + | 33212.1i | 0.00895280 | + | 0.0334123i | 0.970258 | − | 0.242074i | \(-0.0778277\pi\) |
−0.961305 | + | 0.275486i | \(0.911161\pi\) | |||||||
\(998\) | − | 1.15576e6i | − | 1.16040i | ||||||
\(999\) | −806692. | + | 447584.i | −0.808308 | + | 0.448481i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 74.5.g.a.51.6 | yes | 28 | |
37.8 | odd | 12 | inner | 74.5.g.a.45.6 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.5.g.a.45.6 | ✓ | 28 | 37.8 | odd | 12 | inner | |
74.5.g.a.51.6 | yes | 28 | 1.1 | even | 1 | trivial |