Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [354,4,Mod(1,354)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(354, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("354.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 354 = 2 \cdot 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 354.a (trivial) |
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: | yes |
Analytic conductor: | \(20.8866761420\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{51}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 51 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-7.14143\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 354.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 5.85857 | 0.524007 | 0.262003 | − | 0.965067i | \(-0.415617\pi\) | ||||
0.262003 | + | 0.965067i | \(0.415617\pi\) | |||||||
\(6\) | −6.00000 | −0.408248 | ||||||||
\(7\) | 28.5657 | 1.54240 | 0.771202 | − | 0.636591i | \(-0.219656\pi\) | ||||
0.771202 | + | 0.636591i | \(0.219656\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −11.7171 | −0.370529 | ||||||||
\(11\) | −2.56571 | −0.0703265 | −0.0351633 | − | 0.999382i | \(-0.511195\pi\) | ||||
−0.0351633 | + | 0.999382i | \(0.511195\pi\) | |||||||
\(12\) | 12.0000 | 0.288675 | ||||||||
\(13\) | 82.9900 | 1.77056 | 0.885280 | − | 0.465058i | \(-0.153967\pi\) | ||||
0.885280 | + | 0.465058i | \(0.153967\pi\) | |||||||
\(14\) | −57.1314 | −1.09064 | ||||||||
\(15\) | 17.5757 | 0.302535 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −74.8486 | −1.06785 | −0.533925 | − | 0.845532i | \(-0.679283\pi\) | ||||
−0.533925 | + | 0.845532i | \(0.679283\pi\) | |||||||
\(18\) | −18.0000 | −0.235702 | ||||||||
\(19\) | 34.0000 | 0.410533 | 0.205267 | − | 0.978706i | \(-0.434194\pi\) | ||||
0.205267 | + | 0.978706i | \(0.434194\pi\) | |||||||
\(20\) | 23.4343 | 0.262003 | ||||||||
\(21\) | 85.6971 | 0.890507 | ||||||||
\(22\) | 5.13143 | 0.0497284 | ||||||||
\(23\) | 15.1514 | 0.137360 | 0.0686802 | − | 0.997639i | \(-0.478121\pi\) | ||||
0.0686802 | + | 0.997639i | \(0.478121\pi\) | |||||||
\(24\) | −24.0000 | −0.204124 | ||||||||
\(25\) | −90.6771 | −0.725417 | ||||||||
\(26\) | −165.980 | −1.25198 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 114.263 | 0.771202 | ||||||||
\(29\) | 239.273 | 1.53213 | 0.766066 | − | 0.642761i | \(-0.222211\pi\) | ||||
0.766066 | + | 0.642761i | \(0.222211\pi\) | |||||||
\(30\) | −35.1514 | −0.213925 | ||||||||
\(31\) | −242.404 | −1.40442 | −0.702211 | − | 0.711969i | \(-0.747804\pi\) | ||||
−0.702211 | + | 0.711969i | \(0.747804\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | −7.69714 | −0.0406030 | ||||||||
\(34\) | 149.697 | 0.755084 | ||||||||
\(35\) | 167.354 | 0.808230 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | −269.010 | −1.19527 | −0.597635 | − | 0.801768i | \(-0.703893\pi\) | ||||
−0.597635 | + | 0.801768i | \(0.703893\pi\) | |||||||
\(38\) | −68.0000 | −0.290291 | ||||||||
\(39\) | 248.970 | 1.02223 | ||||||||
\(40\) | −46.8686 | −0.185264 | ||||||||
\(41\) | −179.454 | −0.683562 | −0.341781 | − | 0.939780i | \(-0.611030\pi\) | ||||
−0.341781 | + | 0.939780i | \(0.611030\pi\) | |||||||
\(42\) | −171.394 | −0.629684 | ||||||||
\(43\) | 441.131 | 1.56446 | 0.782232 | − | 0.622988i | \(-0.214081\pi\) | ||||
0.782232 | + | 0.622988i | \(0.214081\pi\) | |||||||
\(44\) | −10.2629 | −0.0351633 | ||||||||
\(45\) | 52.7271 | 0.174669 | ||||||||
\(46\) | −30.3029 | −0.0971285 | ||||||||
\(47\) | −249.374 | −0.773936 | −0.386968 | − | 0.922093i | \(-0.626478\pi\) | ||||
−0.386968 | + | 0.922093i | \(0.626478\pi\) | |||||||
\(48\) | 48.0000 | 0.144338 | ||||||||
\(49\) | 473.000 | 1.37901 | ||||||||
\(50\) | 181.354 | 0.512947 | ||||||||
\(51\) | −224.546 | −0.616523 | ||||||||
\(52\) | 331.960 | 0.885280 | ||||||||
\(53\) | −19.2729 | −0.0499496 | −0.0249748 | − | 0.999688i | \(-0.507951\pi\) | ||||
−0.0249748 | + | 0.999688i | \(0.507951\pi\) | |||||||
\(54\) | −54.0000 | −0.136083 | ||||||||
\(55\) | −15.0314 | −0.0368516 | ||||||||
\(56\) | −228.526 | −0.545322 | ||||||||
\(57\) | 102.000 | 0.237022 | ||||||||
\(58\) | −478.546 | −1.08338 | ||||||||
\(59\) | 59.0000 | 0.130189 | ||||||||
\(60\) | 70.3029 | 0.151268 | ||||||||
\(61\) | 789.253 | 1.65661 | 0.828307 | − | 0.560274i | \(-0.189304\pi\) | ||||
0.828307 | + | 0.560274i | \(0.189304\pi\) | |||||||
\(62\) | 484.809 | 0.993077 | ||||||||
\(63\) | 257.091 | 0.514135 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 486.203 | 0.927785 | ||||||||
\(66\) | 15.3943 | 0.0287107 | ||||||||
\(67\) | 829.980 | 1.51341 | 0.756703 | − | 0.653759i | \(-0.226809\pi\) | ||||
0.756703 | + | 0.653759i | \(0.226809\pi\) | |||||||
\(68\) | −299.394 | −0.533925 | ||||||||
\(69\) | 45.4543 | 0.0793051 | ||||||||
\(70\) | −334.709 | −0.571505 | ||||||||
\(71\) | −825.961 | −1.38061 | −0.690307 | − | 0.723517i | \(-0.742525\pi\) | ||||
−0.690307 | + | 0.723517i | \(0.742525\pi\) | |||||||
\(72\) | −72.0000 | −0.117851 | ||||||||
\(73\) | 913.274 | 1.46426 | 0.732128 | − | 0.681167i | \(-0.238527\pi\) | ||||
0.732128 | + | 0.681167i | \(0.238527\pi\) | |||||||
\(74\) | 538.020 | 0.845183 | ||||||||
\(75\) | −272.031 | −0.418820 | ||||||||
\(76\) | 136.000 | 0.205267 | ||||||||
\(77\) | −73.2914 | −0.108472 | ||||||||
\(78\) | −497.940 | −0.722828 | ||||||||
\(79\) | −1227.23 | −1.74778 | −0.873890 | − | 0.486123i | \(-0.838411\pi\) | ||||
−0.873890 | + | 0.486123i | \(0.838411\pi\) | |||||||
\(80\) | 93.7371 | 0.131002 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 358.909 | 0.483351 | ||||||||
\(83\) | 873.577 | 1.15527 | 0.577636 | − | 0.816295i | \(-0.303975\pi\) | ||||
0.577636 | + | 0.816295i | \(0.303975\pi\) | |||||||
\(84\) | 342.789 | 0.445254 | ||||||||
\(85\) | −438.506 | −0.559560 | ||||||||
\(86\) | −882.263 | −1.10624 | ||||||||
\(87\) | 717.819 | 0.884577 | ||||||||
\(88\) | 20.5257 | 0.0248642 | ||||||||
\(89\) | −888.729 | −1.05848 | −0.529242 | − | 0.848471i | \(-0.677524\pi\) | ||||
−0.529242 | + | 0.848471i | \(0.677524\pi\) | |||||||
\(90\) | −105.454 | −0.123510 | ||||||||
\(91\) | 2370.67 | 2.73092 | ||||||||
\(92\) | 60.6057 | 0.0686802 | ||||||||
\(93\) | −727.213 | −0.810844 | ||||||||
\(94\) | 498.749 | 0.547255 | ||||||||
\(95\) | 199.191 | 0.215122 | ||||||||
\(96\) | −96.0000 | −0.102062 | ||||||||
\(97\) | 384.386 | 0.402355 | 0.201178 | − | 0.979555i | \(-0.435523\pi\) | ||||
0.201178 | + | 0.979555i | \(0.435523\pi\) | |||||||
\(98\) | −946.000 | −0.975106 | ||||||||
\(99\) | −23.0914 | −0.0234422 | ||||||||
\(100\) | −362.709 | −0.362709 | ||||||||
\(101\) | 1745.03 | 1.71918 | 0.859590 | − | 0.510985i | \(-0.170719\pi\) | ||||
0.859590 | + | 0.510985i | \(0.170719\pi\) | |||||||
\(102\) | 449.091 | 0.435948 | ||||||||
\(103\) | 500.221 | 0.478527 | 0.239264 | − | 0.970955i | \(-0.423094\pi\) | ||||
0.239264 | + | 0.970955i | \(0.423094\pi\) | |||||||
\(104\) | −663.920 | −0.625988 | ||||||||
\(105\) | 502.063 | 0.466632 | ||||||||
\(106\) | 38.5457 | 0.0353197 | ||||||||
\(107\) | 1124.57 | 1.01604 | 0.508019 | − | 0.861346i | \(-0.330378\pi\) | ||||
0.508019 | + | 0.861346i | \(0.330378\pi\) | |||||||
\(108\) | 108.000 | 0.0962250 | ||||||||
\(109\) | −42.2614 | −0.0371368 | −0.0185684 | − | 0.999828i | \(-0.505911\pi\) | ||||
−0.0185684 | + | 0.999828i | \(0.505911\pi\) | |||||||
\(110\) | 30.0628 | 0.0260580 | ||||||||
\(111\) | −807.030 | −0.690089 | ||||||||
\(112\) | 457.051 | 0.385601 | ||||||||
\(113\) | 1156.63 | 0.962889 | 0.481445 | − | 0.876477i | \(-0.340112\pi\) | ||||
0.481445 | + | 0.876477i | \(0.340112\pi\) | |||||||
\(114\) | −204.000 | −0.167600 | ||||||||
\(115\) | 88.7657 | 0.0719778 | ||||||||
\(116\) | 957.091 | 0.766066 | ||||||||
\(117\) | 746.910 | 0.590187 | ||||||||
\(118\) | −118.000 | −0.0920575 | ||||||||
\(119\) | −2138.10 | −1.64706 | ||||||||
\(120\) | −140.606 | −0.106962 | ||||||||
\(121\) | −1324.42 | −0.995054 | ||||||||
\(122\) | −1578.51 | −1.17140 | ||||||||
\(123\) | −538.363 | −0.394655 | ||||||||
\(124\) | −969.617 | −0.702211 | ||||||||
\(125\) | −1263.56 | −0.904130 | ||||||||
\(126\) | −514.183 | −0.363548 | ||||||||
\(127\) | −933.900 | −0.652521 | −0.326261 | − | 0.945280i | \(-0.605789\pi\) | ||||
−0.326261 | + | 0.945280i | \(0.605789\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 1323.39 | 0.903243 | ||||||||
\(130\) | −972.406 | −0.656043 | ||||||||
\(131\) | −2424.02 | −1.61670 | −0.808351 | − | 0.588701i | \(-0.799639\pi\) | ||||
−0.808351 | + | 0.588701i | \(0.799639\pi\) | |||||||
\(132\) | −30.7886 | −0.0203015 | ||||||||
\(133\) | 971.234 | 0.633208 | ||||||||
\(134\) | −1659.96 | −1.07014 | ||||||||
\(135\) | 158.181 | 0.100845 | ||||||||
\(136\) | 598.789 | 0.377542 | ||||||||
\(137\) | −2958.20 | −1.84479 | −0.922395 | − | 0.386247i | \(-0.873771\pi\) | ||||
−0.922395 | + | 0.386247i | \(0.873771\pi\) | |||||||
\(138\) | −90.9086 | −0.0560772 | ||||||||
\(139\) | −498.080 | −0.303932 | −0.151966 | − | 0.988386i | \(-0.548560\pi\) | ||||
−0.151966 | + | 0.988386i | \(0.548560\pi\) | |||||||
\(140\) | 669.417 | 0.404115 | ||||||||
\(141\) | −748.123 | −0.446832 | ||||||||
\(142\) | 1651.92 | 0.976241 | ||||||||
\(143\) | −212.929 | −0.124517 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | 1401.80 | 0.802848 | ||||||||
\(146\) | −1826.55 | −1.03539 | ||||||||
\(147\) | 1419.00 | 0.796171 | ||||||||
\(148\) | −1076.04 | −0.597635 | ||||||||
\(149\) | −2904.35 | −1.59687 | −0.798435 | − | 0.602082i | \(-0.794338\pi\) | ||||
−0.798435 | + | 0.602082i | \(0.794338\pi\) | |||||||
\(150\) | 544.063 | 0.296150 | ||||||||
\(151\) | 536.064 | 0.288903 | 0.144451 | − | 0.989512i | \(-0.453858\pi\) | ||||
0.144451 | + | 0.989512i | \(0.453858\pi\) | |||||||
\(152\) | −272.000 | −0.145145 | ||||||||
\(153\) | −673.637 | −0.355950 | ||||||||
\(154\) | 146.583 | 0.0767012 | ||||||||
\(155\) | −1420.14 | −0.735927 | ||||||||
\(156\) | 995.880 | 0.511117 | ||||||||
\(157\) | −1996.04 | −1.01466 | −0.507330 | − | 0.861752i | \(-0.669368\pi\) | ||||
−0.507330 | + | 0.861752i | \(0.669368\pi\) | |||||||
\(158\) | 2454.47 | 1.23587 | ||||||||
\(159\) | −57.8186 | −0.0288384 | ||||||||
\(160\) | −187.474 | −0.0926322 | ||||||||
\(161\) | 432.811 | 0.211865 | ||||||||
\(162\) | −162.000 | −0.0785674 | ||||||||
\(163\) | −2393.15 | −1.14998 | −0.574989 | − | 0.818161i | \(-0.694994\pi\) | ||||
−0.574989 | + | 0.818161i | \(0.694994\pi\) | |||||||
\(164\) | −717.817 | −0.341781 | ||||||||
\(165\) | −45.0943 | −0.0212763 | ||||||||
\(166\) | −1747.15 | −0.816900 | ||||||||
\(167\) | 61.2729 | 0.0283918 | 0.0141959 | − | 0.999899i | \(-0.495481\pi\) | ||||
0.0141959 | + | 0.999899i | \(0.495481\pi\) | |||||||
\(168\) | −685.577 | −0.314842 | ||||||||
\(169\) | 4690.34 | 2.13488 | ||||||||
\(170\) | 877.011 | 0.395669 | ||||||||
\(171\) | 306.000 | 0.136844 | ||||||||
\(172\) | 1764.53 | 0.782232 | ||||||||
\(173\) | −3133.08 | −1.37690 | −0.688449 | − | 0.725285i | \(-0.741708\pi\) | ||||
−0.688449 | + | 0.725285i | \(0.741708\pi\) | |||||||
\(174\) | −1435.64 | −0.625491 | ||||||||
\(175\) | −2590.26 | −1.11889 | ||||||||
\(176\) | −41.0514 | −0.0175816 | ||||||||
\(177\) | 177.000 | 0.0751646 | ||||||||
\(178\) | 1777.46 | 0.748461 | ||||||||
\(179\) | −85.9428 | −0.0358864 | −0.0179432 | − | 0.999839i | \(-0.505712\pi\) | ||||
−0.0179432 | + | 0.999839i | \(0.505712\pi\) | |||||||
\(180\) | 210.909 | 0.0873344 | ||||||||
\(181\) | −4292.06 | −1.76258 | −0.881289 | − | 0.472578i | \(-0.843323\pi\) | ||||
−0.881289 | + | 0.472578i | \(0.843323\pi\) | |||||||
\(182\) | −4741.34 | −1.93105 | ||||||||
\(183\) | 2367.76 | 0.956447 | ||||||||
\(184\) | −121.211 | −0.0485643 | ||||||||
\(185\) | −1576.01 | −0.626329 | ||||||||
\(186\) | 1454.43 | 0.573353 | ||||||||
\(187\) | 192.040 | 0.0750982 | ||||||||
\(188\) | −997.497 | −0.386968 | ||||||||
\(189\) | 771.274 | 0.296836 | ||||||||
\(190\) | −398.383 | −0.152114 | ||||||||
\(191\) | 2606.47 | 0.987422 | 0.493711 | − | 0.869626i | \(-0.335640\pi\) | ||||
0.493711 | + | 0.869626i | \(0.335640\pi\) | |||||||
\(192\) | 192.000 | 0.0721688 | ||||||||
\(193\) | −2118.45 | −0.790099 | −0.395049 | − | 0.918660i | \(-0.629273\pi\) | ||||
−0.395049 | + | 0.918660i | \(0.629273\pi\) | |||||||
\(194\) | −768.771 | −0.284508 | ||||||||
\(195\) | 1458.61 | 0.535657 | ||||||||
\(196\) | 1892.00 | 0.689504 | ||||||||
\(197\) | 3831.92 | 1.38585 | 0.692927 | − | 0.721008i | \(-0.256321\pi\) | ||||
0.692927 | + | 0.721008i | \(0.256321\pi\) | |||||||
\(198\) | 46.1828 | 0.0165761 | ||||||||
\(199\) | 415.837 | 0.148130 | 0.0740651 | − | 0.997253i | \(-0.476403\pi\) | ||||
0.0740651 | + | 0.997253i | \(0.476403\pi\) | |||||||
\(200\) | 725.417 | 0.256474 | ||||||||
\(201\) | 2489.94 | 0.873765 | ||||||||
\(202\) | −3490.06 | −1.21564 | ||||||||
\(203\) | 6835.00 | 2.36317 | ||||||||
\(204\) | −898.183 | −0.308262 | ||||||||
\(205\) | −1051.35 | −0.358191 | ||||||||
\(206\) | −1000.44 | −0.338370 | ||||||||
\(207\) | 136.363 | 0.0457868 | ||||||||
\(208\) | 1327.84 | 0.442640 | ||||||||
\(209\) | −87.2343 | −0.0288714 | ||||||||
\(210\) | −1004.13 | −0.329958 | ||||||||
\(211\) | 710.026 | 0.231660 | 0.115830 | − | 0.993269i | \(-0.463047\pi\) | ||||
0.115830 | + | 0.993269i | \(0.463047\pi\) | |||||||
\(212\) | −77.0914 | −0.0249748 | ||||||||
\(213\) | −2477.88 | −0.797098 | ||||||||
\(214\) | −2249.14 | −0.718448 | ||||||||
\(215\) | 2584.40 | 0.819789 | ||||||||
\(216\) | −216.000 | −0.0680414 | ||||||||
\(217\) | −6924.45 | −2.16619 | ||||||||
\(218\) | 84.5229 | 0.0262597 | ||||||||
\(219\) | 2739.82 | 0.845388 | ||||||||
\(220\) | −60.1257 | −0.0184258 | ||||||||
\(221\) | −6211.68 | −1.89069 | ||||||||
\(222\) | 1614.06 | 0.487967 | ||||||||
\(223\) | 2339.69 | 0.702587 | 0.351294 | − | 0.936265i | \(-0.385742\pi\) | ||||
0.351294 | + | 0.936265i | \(0.385742\pi\) | |||||||
\(224\) | −914.103 | −0.272661 | ||||||||
\(225\) | −816.094 | −0.241806 | ||||||||
\(226\) | −2313.26 | −0.680865 | ||||||||
\(227\) | −405.617 | −0.118598 | −0.0592990 | − | 0.998240i | \(-0.518887\pi\) | ||||
−0.0592990 | + | 0.998240i | \(0.518887\pi\) | |||||||
\(228\) | 408.000 | 0.118511 | ||||||||
\(229\) | 2445.74 | 0.705760 | 0.352880 | − | 0.935669i | \(-0.385202\pi\) | ||||
0.352880 | + | 0.935669i | \(0.385202\pi\) | |||||||
\(230\) | −177.531 | −0.0508960 | ||||||||
\(231\) | −219.874 | −0.0626263 | ||||||||
\(232\) | −1914.18 | −0.541691 | ||||||||
\(233\) | −1010.14 | −0.284019 | −0.142010 | − | 0.989865i | \(-0.545356\pi\) | ||||
−0.142010 | + | 0.989865i | \(0.545356\pi\) | |||||||
\(234\) | −1493.82 | −0.417325 | ||||||||
\(235\) | −1460.98 | −0.405547 | ||||||||
\(236\) | 236.000 | 0.0650945 | ||||||||
\(237\) | −3681.70 | −1.00908 | ||||||||
\(238\) | 4276.21 | 1.16464 | ||||||||
\(239\) | 4185.81 | 1.13288 | 0.566438 | − | 0.824104i | \(-0.308321\pi\) | ||||
0.566438 | + | 0.824104i | \(0.308321\pi\) | |||||||
\(240\) | 281.211 | 0.0756338 | ||||||||
\(241\) | 2986.14 | 0.798150 | 0.399075 | − | 0.916918i | \(-0.369331\pi\) | ||||
0.399075 | + | 0.916918i | \(0.369331\pi\) | |||||||
\(242\) | 2648.83 | 0.703610 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 3157.01 | 0.828307 | ||||||||
\(245\) | 2771.10 | 0.722610 | ||||||||
\(246\) | 1076.73 | 0.279063 | ||||||||
\(247\) | 2821.66 | 0.726874 | ||||||||
\(248\) | 1939.23 | 0.496538 | ||||||||
\(249\) | 2620.73 | 0.666996 | ||||||||
\(250\) | 2527.12 | 0.639316 | ||||||||
\(251\) | −2092.89 | −0.526303 | −0.263152 | − | 0.964754i | \(-0.584762\pi\) | ||||
−0.263152 | + | 0.964754i | \(0.584762\pi\) | |||||||
\(252\) | 1028.37 | 0.257067 | ||||||||
\(253\) | −38.8742 | −0.00966009 | ||||||||
\(254\) | 1867.80 | 0.461402 | ||||||||
\(255\) | −1315.52 | −0.323062 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −1619.57 | −0.393098 | −0.196549 | − | 0.980494i | \(-0.562973\pi\) | ||||
−0.196549 | + | 0.980494i | \(0.562973\pi\) | |||||||
\(258\) | −2646.79 | −0.638689 | ||||||||
\(259\) | −7684.46 | −1.84359 | ||||||||
\(260\) | 1944.81 | 0.463893 | ||||||||
\(261\) | 2153.46 | 0.510711 | ||||||||
\(262\) | 4848.05 | 1.14318 | ||||||||
\(263\) | 5558.30 | 1.30319 | 0.651595 | − | 0.758567i | \(-0.274100\pi\) | ||||
0.651595 | + | 0.758567i | \(0.274100\pi\) | |||||||
\(264\) | 61.5771 | 0.0143553 | ||||||||
\(265\) | −112.911 | −0.0261739 | ||||||||
\(266\) | −1942.47 | −0.447746 | ||||||||
\(267\) | −2666.19 | −0.611116 | ||||||||
\(268\) | 3319.92 | 0.756703 | ||||||||
\(269\) | 297.389 | 0.0674056 | 0.0337028 | − | 0.999432i | \(-0.489270\pi\) | ||||
0.0337028 | + | 0.999432i | \(0.489270\pi\) | |||||||
\(270\) | −316.363 | −0.0713083 | ||||||||
\(271\) | −2734.07 | −0.612852 | −0.306426 | − | 0.951895i | \(-0.599133\pi\) | ||||
−0.306426 | + | 0.951895i | \(0.599133\pi\) | |||||||
\(272\) | −1197.58 | −0.266962 | ||||||||
\(273\) | 7112.01 | 1.57670 | ||||||||
\(274\) | 5916.41 | 1.30446 | ||||||||
\(275\) | 232.652 | 0.0510161 | ||||||||
\(276\) | 181.817 | 0.0396526 | ||||||||
\(277\) | 760.174 | 0.164890 | 0.0824449 | − | 0.996596i | \(-0.473727\pi\) | ||||
0.0824449 | + | 0.996596i | \(0.473727\pi\) | |||||||
\(278\) | 996.160 | 0.214913 | ||||||||
\(279\) | −2181.64 | −0.468141 | ||||||||
\(280\) | −1338.83 | −0.285752 | ||||||||
\(281\) | −2050.65 | −0.435343 | −0.217671 | − | 0.976022i | \(-0.569846\pi\) | ||||
−0.217671 | + | 0.976022i | \(0.569846\pi\) | |||||||
\(282\) | 1496.25 | 0.315958 | ||||||||
\(283\) | −4818.39 | −1.01210 | −0.506049 | − | 0.862505i | \(-0.668894\pi\) | ||||
−0.506049 | + | 0.862505i | \(0.668894\pi\) | |||||||
\(284\) | −3303.85 | −0.690307 | ||||||||
\(285\) | 597.574 | 0.124201 | ||||||||
\(286\) | 425.857 | 0.0880471 | ||||||||
\(287\) | −5126.24 | −1.05433 | ||||||||
\(288\) | −288.000 | −0.0589256 | ||||||||
\(289\) | 689.309 | 0.140303 | ||||||||
\(290\) | −2803.59 | −0.567699 | ||||||||
\(291\) | 1153.16 | 0.232300 | ||||||||
\(292\) | 3653.10 | 0.732128 | ||||||||
\(293\) | 1876.25 | 0.374102 | 0.187051 | − | 0.982350i | \(-0.440107\pi\) | ||||
0.187051 | + | 0.982350i | \(0.440107\pi\) | |||||||
\(294\) | −2838.00 | −0.562978 | ||||||||
\(295\) | 345.656 | 0.0682198 | ||||||||
\(296\) | 2152.08 | 0.422592 | ||||||||
\(297\) | −69.2743 | −0.0135343 | ||||||||
\(298\) | 5808.70 | 1.12916 | ||||||||
\(299\) | 1257.42 | 0.243205 | ||||||||
\(300\) | −1088.13 | −0.209410 | ||||||||
\(301\) | 12601.2 | 2.41303 | ||||||||
\(302\) | −1072.13 | −0.204285 | ||||||||
\(303\) | 5235.09 | 0.992569 | ||||||||
\(304\) | 544.000 | 0.102633 | ||||||||
\(305\) | 4623.89 | 0.868077 | ||||||||
\(306\) | 1347.27 | 0.251695 | ||||||||
\(307\) | 556.954 | 0.103541 | 0.0517705 | − | 0.998659i | \(-0.483514\pi\) | ||||
0.0517705 | + | 0.998659i | \(0.483514\pi\) | |||||||
\(308\) | −293.166 | −0.0542359 | ||||||||
\(309\) | 1500.66 | 0.276278 | ||||||||
\(310\) | 2840.29 | 0.520379 | ||||||||
\(311\) | 3023.63 | 0.551300 | 0.275650 | − | 0.961258i | \(-0.411107\pi\) | ||||
0.275650 | + | 0.961258i | \(0.411107\pi\) | |||||||
\(312\) | −1991.76 | −0.361414 | ||||||||
\(313\) | −467.129 | −0.0843568 | −0.0421784 | − | 0.999110i | \(-0.513430\pi\) | ||||
−0.0421784 | + | 0.999110i | \(0.513430\pi\) | |||||||
\(314\) | 3992.09 | 0.717473 | ||||||||
\(315\) | 1506.19 | 0.269410 | ||||||||
\(316\) | −4908.94 | −0.873890 | ||||||||
\(317\) | −5033.09 | −0.891756 | −0.445878 | − | 0.895094i | \(-0.647108\pi\) | ||||
−0.445878 | + | 0.895094i | \(0.647108\pi\) | |||||||
\(318\) | 115.637 | 0.0203919 | ||||||||
\(319\) | −613.906 | −0.107750 | ||||||||
\(320\) | 374.949 | 0.0655008 | ||||||||
\(321\) | 3373.71 | 0.586610 | ||||||||
\(322\) | −865.623 | −0.149811 | ||||||||
\(323\) | −2544.85 | −0.438388 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | −7525.30 | −1.28439 | ||||||||
\(326\) | 4786.31 | 0.813157 | ||||||||
\(327\) | −126.784 | −0.0214409 | ||||||||
\(328\) | 1435.63 | 0.241676 | ||||||||
\(329\) | −7123.55 | −1.19372 | ||||||||
\(330\) | 90.1885 | 0.0150446 | ||||||||
\(331\) | 5335.14 | 0.885939 | 0.442970 | − | 0.896537i | \(-0.353925\pi\) | ||||
0.442970 | + | 0.896537i | \(0.353925\pi\) | |||||||
\(332\) | 3494.31 | 0.577636 | ||||||||
\(333\) | −2421.09 | −0.398423 | ||||||||
\(334\) | −122.546 | −0.0200761 | ||||||||
\(335\) | 4862.50 | 0.793035 | ||||||||
\(336\) | 1371.15 | 0.222627 | ||||||||
\(337\) | −10352.7 | −1.67343 | −0.836715 | − | 0.547639i | \(-0.815527\pi\) | ||||
−0.836715 | + | 0.547639i | \(0.815527\pi\) | |||||||
\(338\) | −9380.68 | −1.50959 | ||||||||
\(339\) | 3469.89 | 0.555924 | ||||||||
\(340\) | −1754.02 | −0.279780 | ||||||||
\(341\) | 621.940 | 0.0987681 | ||||||||
\(342\) | −612.000 | −0.0967637 | ||||||||
\(343\) | 3713.54 | 0.584584 | ||||||||
\(344\) | −3529.05 | −0.553121 | ||||||||
\(345\) | 266.297 | 0.0415564 | ||||||||
\(346\) | 6266.15 | 0.973614 | ||||||||
\(347\) | 7113.77 | 1.10054 | 0.550269 | − | 0.834987i | \(-0.314525\pi\) | ||||
0.550269 | + | 0.834987i | \(0.314525\pi\) | |||||||
\(348\) | 2871.27 | 0.442289 | ||||||||
\(349\) | 3342.31 | 0.512635 | 0.256318 | − | 0.966593i | \(-0.417491\pi\) | ||||
0.256318 | + | 0.966593i | \(0.417491\pi\) | |||||||
\(350\) | 5180.51 | 0.791172 | ||||||||
\(351\) | 2240.73 | 0.340744 | ||||||||
\(352\) | 82.1028 | 0.0124321 | ||||||||
\(353\) | −12792.3 | −1.92880 | −0.964400 | − | 0.264447i | \(-0.914810\pi\) | ||||
−0.964400 | + | 0.264447i | \(0.914810\pi\) | |||||||
\(354\) | −354.000 | −0.0531494 | ||||||||
\(355\) | −4838.95 | −0.723451 | ||||||||
\(356\) | −3554.91 | −0.529242 | ||||||||
\(357\) | −6414.31 | −0.950928 | ||||||||
\(358\) | 171.886 | 0.0253755 | ||||||||
\(359\) | −5664.03 | −0.832691 | −0.416345 | − | 0.909207i | \(-0.636689\pi\) | ||||
−0.416345 | + | 0.909207i | \(0.636689\pi\) | |||||||
\(360\) | −421.817 | −0.0617548 | ||||||||
\(361\) | −5703.00 | −0.831462 | ||||||||
\(362\) | 8584.13 | 1.24633 | ||||||||
\(363\) | −3973.25 | −0.574495 | ||||||||
\(364\) | 9482.67 | 1.36546 | ||||||||
\(365\) | 5350.48 | 0.767280 | ||||||||
\(366\) | −4735.52 | −0.676310 | ||||||||
\(367\) | −7565.11 | −1.07601 | −0.538005 | − | 0.842942i | \(-0.680822\pi\) | ||||
−0.538005 | + | 0.842942i | \(0.680822\pi\) | |||||||
\(368\) | 242.423 | 0.0343401 | ||||||||
\(369\) | −1615.09 | −0.227854 | ||||||||
\(370\) | 3152.03 | 0.442882 | ||||||||
\(371\) | −550.543 | −0.0770425 | ||||||||
\(372\) | −2908.85 | −0.405422 | ||||||||
\(373\) | −4152.32 | −0.576405 | −0.288202 | − | 0.957570i | \(-0.593058\pi\) | ||||
−0.288202 | + | 0.957570i | \(0.593058\pi\) | |||||||
\(374\) | −384.080 | −0.0531024 | ||||||||
\(375\) | −3790.68 | −0.522000 | ||||||||
\(376\) | 1994.99 | 0.273628 | ||||||||
\(377\) | 19857.3 | 2.71273 | ||||||||
\(378\) | −1542.55 | −0.209895 | ||||||||
\(379\) | 2639.87 | 0.357787 | 0.178893 | − | 0.983868i | \(-0.442748\pi\) | ||||
0.178893 | + | 0.983868i | \(0.442748\pi\) | |||||||
\(380\) | 796.766 | 0.107561 | ||||||||
\(381\) | −2801.70 | −0.376733 | ||||||||
\(382\) | −5212.94 | −0.698213 | ||||||||
\(383\) | −7683.83 | −1.02513 | −0.512566 | − | 0.858648i | \(-0.671305\pi\) | ||||
−0.512566 | + | 0.858648i | \(0.671305\pi\) | |||||||
\(384\) | −384.000 | −0.0510310 | ||||||||
\(385\) | −429.383 | −0.0568400 | ||||||||
\(386\) | 4236.89 | 0.558684 | ||||||||
\(387\) | 3970.18 | 0.521488 | ||||||||
\(388\) | 1537.54 | 0.201178 | ||||||||
\(389\) | 206.350 | 0.0268955 | 0.0134478 | − | 0.999910i | \(-0.495719\pi\) | ||||
0.0134478 | + | 0.999910i | \(0.495719\pi\) | |||||||
\(390\) | −2917.22 | −0.378767 | ||||||||
\(391\) | −1134.06 | −0.146680 | ||||||||
\(392\) | −3784.00 | −0.487553 | ||||||||
\(393\) | −7272.07 | −0.933403 | ||||||||
\(394\) | −7663.85 | −0.979947 | ||||||||
\(395\) | −7189.84 | −0.915848 | ||||||||
\(396\) | −92.3657 | −0.0117211 | ||||||||
\(397\) | −5677.30 | −0.717722 | −0.358861 | − | 0.933391i | \(-0.616835\pi\) | ||||
−0.358861 | + | 0.933391i | \(0.616835\pi\) | |||||||
\(398\) | −831.674 | −0.104744 | ||||||||
\(399\) | 2913.70 | 0.365583 | ||||||||
\(400\) | −1450.83 | −0.181354 | ||||||||
\(401\) | −2969.25 | −0.369769 | −0.184884 | − | 0.982760i | \(-0.559191\pi\) | ||||
−0.184884 | + | 0.982760i | \(0.559191\pi\) | |||||||
\(402\) | −4979.88 | −0.617845 | ||||||||
\(403\) | −20117.1 | −2.48661 | ||||||||
\(404\) | 6980.13 | 0.859590 | ||||||||
\(405\) | 474.544 | 0.0582230 | ||||||||
\(406\) | −13670.0 | −1.67101 | ||||||||
\(407\) | 690.203 | 0.0840592 | ||||||||
\(408\) | 1796.37 | 0.217974 | ||||||||
\(409\) | 1198.04 | 0.144839 | 0.0724195 | − | 0.997374i | \(-0.476928\pi\) | ||||
0.0724195 | + | 0.997374i | \(0.476928\pi\) | |||||||
\(410\) | 2102.69 | 0.253279 | ||||||||
\(411\) | −8874.61 | −1.06509 | ||||||||
\(412\) | 2000.89 | 0.239264 | ||||||||
\(413\) | 1685.38 | 0.200804 | ||||||||
\(414\) | −272.726 | −0.0323762 | ||||||||
\(415\) | 5117.91 | 0.605370 | ||||||||
\(416\) | −2655.68 | −0.312994 | ||||||||
\(417\) | −1494.24 | −0.175475 | ||||||||
\(418\) | 174.469 | 0.0204152 | ||||||||
\(419\) | 11776.3 | 1.37305 | 0.686526 | − | 0.727105i | \(-0.259135\pi\) | ||||
0.686526 | + | 0.727105i | \(0.259135\pi\) | |||||||
\(420\) | 2008.25 | 0.233316 | ||||||||
\(421\) | −10303.0 | −1.19272 | −0.596362 | − | 0.802715i | \(-0.703388\pi\) | ||||
−0.596362 | + | 0.802715i | \(0.703388\pi\) | |||||||
\(422\) | −1420.05 | −0.163808 | ||||||||
\(423\) | −2244.37 | −0.257979 | ||||||||
\(424\) | 154.183 | 0.0176599 | ||||||||
\(425\) | 6787.05 | 0.774636 | ||||||||
\(426\) | 4955.77 | 0.563633 | ||||||||
\(427\) | 22545.6 | 2.55517 | ||||||||
\(428\) | 4498.27 | 0.508019 | ||||||||
\(429\) | −638.786 | −0.0718901 | ||||||||
\(430\) | −5168.80 | −0.579678 | ||||||||
\(431\) | 14017.8 | 1.56662 | 0.783310 | − | 0.621631i | \(-0.213530\pi\) | ||||
0.783310 | + | 0.621631i | \(0.213530\pi\) | |||||||
\(432\) | 432.000 | 0.0481125 | ||||||||
\(433\) | −6668.16 | −0.740072 | −0.370036 | − | 0.929017i | \(-0.620655\pi\) | ||||
−0.370036 | + | 0.929017i | \(0.620655\pi\) | |||||||
\(434\) | 13848.9 | 1.53172 | ||||||||
\(435\) | 4205.39 | 0.463524 | ||||||||
\(436\) | −169.046 | −0.0185684 | ||||||||
\(437\) | 515.149 | 0.0563911 | ||||||||
\(438\) | −5479.65 | −0.597780 | ||||||||
\(439\) | 11331.8 | 1.23198 | 0.615988 | − | 0.787756i | \(-0.288757\pi\) | ||||
0.615988 | + | 0.787756i | \(0.288757\pi\) | |||||||
\(440\) | 120.251 | 0.0130290 | ||||||||
\(441\) | 4257.00 | 0.459670 | ||||||||
\(442\) | 12423.4 | 1.33692 | ||||||||
\(443\) | 1013.77 | 0.108726 | 0.0543628 | − | 0.998521i | \(-0.482687\pi\) | ||||
0.0543628 | + | 0.998521i | \(0.482687\pi\) | |||||||
\(444\) | −3228.12 | −0.345045 | ||||||||
\(445\) | −5206.68 | −0.554652 | ||||||||
\(446\) | −4679.37 | −0.496804 | ||||||||
\(447\) | −8713.05 | −0.921953 | ||||||||
\(448\) | 1828.21 | 0.192800 | ||||||||
\(449\) | 15549.2 | 1.63433 | 0.817163 | − | 0.576407i | \(-0.195546\pi\) | ||||
0.817163 | + | 0.576407i | \(0.195546\pi\) | |||||||
\(450\) | 1632.19 | 0.170982 | ||||||||
\(451\) | 460.428 | 0.0480726 | ||||||||
\(452\) | 4626.51 | 0.481445 | ||||||||
\(453\) | 1608.19 | 0.166798 | ||||||||
\(454\) | 811.234 | 0.0838615 | ||||||||
\(455\) | 13888.7 | 1.43102 | ||||||||
\(456\) | −816.000 | −0.0837998 | ||||||||
\(457\) | −7003.64 | −0.716885 | −0.358442 | − | 0.933552i | \(-0.616692\pi\) | ||||
−0.358442 | + | 0.933552i | \(0.616692\pi\) | |||||||
\(458\) | −4891.48 | −0.499047 | ||||||||
\(459\) | −2020.91 | −0.205508 | ||||||||
\(460\) | 355.063 | 0.0359889 | ||||||||
\(461\) | −7990.32 | −0.807258 | −0.403629 | − | 0.914923i | \(-0.632251\pi\) | ||||
−0.403629 | + | 0.914923i | \(0.632251\pi\) | |||||||
\(462\) | 439.749 | 0.0442835 | ||||||||
\(463\) | −2385.84 | −0.239480 | −0.119740 | − | 0.992805i | \(-0.538206\pi\) | ||||
−0.119740 | + | 0.992805i | \(0.538206\pi\) | |||||||
\(464\) | 3828.37 | 0.383033 | ||||||||
\(465\) | −4260.43 | −0.424887 | ||||||||
\(466\) | 2020.28 | 0.200832 | ||||||||
\(467\) | 5687.82 | 0.563599 | 0.281800 | − | 0.959473i | \(-0.409069\pi\) | ||||
0.281800 | + | 0.959473i | \(0.409069\pi\) | |||||||
\(468\) | 2987.64 | 0.295093 | ||||||||
\(469\) | 23709.0 | 2.33428 | ||||||||
\(470\) | 2921.95 | 0.286765 | ||||||||
\(471\) | −5988.13 | −0.585814 | ||||||||
\(472\) | −472.000 | −0.0460287 | ||||||||
\(473\) | −1131.82 | −0.110023 | ||||||||
\(474\) | 7363.41 | 0.713528 | ||||||||
\(475\) | −3083.02 | −0.297808 | ||||||||
\(476\) | −8552.41 | −0.823528 | ||||||||
\(477\) | −173.456 | −0.0166499 | ||||||||
\(478\) | −8371.61 | −0.801064 | ||||||||
\(479\) | −13880.1 | −1.32400 | −0.662000 | − | 0.749504i | \(-0.730292\pi\) | ||||
−0.662000 | + | 0.749504i | \(0.730292\pi\) | |||||||
\(480\) | −562.423 | −0.0534812 | ||||||||
\(481\) | −22325.1 | −2.11630 | ||||||||
\(482\) | −5972.28 | −0.564377 | ||||||||
\(483\) | 1298.43 | 0.122320 | ||||||||
\(484\) | −5297.67 | −0.497527 | ||||||||
\(485\) | 2251.95 | 0.210837 | ||||||||
\(486\) | −486.000 | −0.0453609 | ||||||||
\(487\) | 11256.2 | 1.04736 | 0.523681 | − | 0.851914i | \(-0.324558\pi\) | ||||
0.523681 | + | 0.851914i | \(0.324558\pi\) | |||||||
\(488\) | −6314.02 | −0.585702 | ||||||||
\(489\) | −7179.46 | −0.663940 | ||||||||
\(490\) | −5542.21 | −0.510962 | ||||||||
\(491\) | −1621.08 | −0.148999 | −0.0744994 | − | 0.997221i | \(-0.523736\pi\) | ||||
−0.0744994 | + | 0.997221i | \(0.523736\pi\) | |||||||
\(492\) | −2153.45 | −0.197327 | ||||||||
\(493\) | −17909.2 | −1.63609 | ||||||||
\(494\) | −5643.32 | −0.513978 | ||||||||
\(495\) | −135.283 | −0.0122839 | ||||||||
\(496\) | −3878.47 | −0.351106 | ||||||||
\(497\) | −23594.2 | −2.12946 | ||||||||
\(498\) | −5241.46 | −0.471638 | ||||||||
\(499\) | 17760.9 | 1.59337 | 0.796683 | − | 0.604398i | \(-0.206586\pi\) | ||||
0.796683 | + | 0.604398i | \(0.206586\pi\) | |||||||
\(500\) | −5054.24 | −0.452065 | ||||||||
\(501\) | 183.819 | 0.0163920 | ||||||||
\(502\) | 4185.78 | 0.372153 | ||||||||
\(503\) | −19375.0 | −1.71747 | −0.858737 | − | 0.512416i | \(-0.828751\pi\) | ||||
−0.858737 | + | 0.512416i | \(0.828751\pi\) | |||||||
\(504\) | −2056.73 | −0.181774 | ||||||||
\(505\) | 10223.4 | 0.900861 | ||||||||
\(506\) | 77.7485 | 0.00683071 | ||||||||
\(507\) | 14071.0 | 1.23258 | ||||||||
\(508\) | −3735.60 | −0.326261 | ||||||||
\(509\) | −7180.52 | −0.625287 | −0.312643 | − | 0.949871i | \(-0.601215\pi\) | ||||
−0.312643 | + | 0.949871i | \(0.601215\pi\) | |||||||
\(510\) | 2631.03 | 0.228440 | ||||||||
\(511\) | 26088.3 | 2.25847 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 918.000 | 0.0790072 | ||||||||
\(514\) | 3239.14 | 0.277962 | ||||||||
\(515\) | 2930.58 | 0.250751 | ||||||||
\(516\) | 5293.58 | 0.451622 | ||||||||
\(517\) | 639.823 | 0.0544282 | ||||||||
\(518\) | 15368.9 | 1.30361 | ||||||||
\(519\) | −9399.23 | −0.794953 | ||||||||
\(520\) | −3889.62 | −0.328022 | ||||||||
\(521\) | 8578.05 | 0.721327 | 0.360664 | − | 0.932696i | \(-0.382550\pi\) | ||||
0.360664 | + | 0.932696i | \(0.382550\pi\) | |||||||
\(522\) | −4306.91 | −0.361127 | ||||||||
\(523\) | −5665.17 | −0.473653 | −0.236826 | − | 0.971552i | \(-0.576107\pi\) | ||||
−0.236826 | + | 0.971552i | \(0.576107\pi\) | |||||||
\(524\) | −9696.09 | −0.808351 | ||||||||
\(525\) | −7770.77 | −0.645989 | ||||||||
\(526\) | −11116.6 | −0.921495 | ||||||||
\(527\) | 18143.6 | 1.49971 | ||||||||
\(528\) | −123.154 | −0.0101508 | ||||||||
\(529\) | −11937.4 | −0.981132 | ||||||||
\(530\) | 225.823 | 0.0185078 | ||||||||
\(531\) | 531.000 | 0.0433963 | ||||||||
\(532\) | 3884.94 | 0.316604 | ||||||||
\(533\) | −14892.9 | −1.21029 | ||||||||
\(534\) | 5332.37 | 0.432124 | ||||||||
\(535\) | 6588.37 | 0.532411 | ||||||||
\(536\) | −6639.84 | −0.535070 | ||||||||
\(537\) | −257.828 | −0.0207190 | ||||||||
\(538\) | −594.777 | −0.0476630 | ||||||||
\(539\) | −1213.58 | −0.0969809 | ||||||||
\(540\) | 632.726 | 0.0504226 | ||||||||
\(541\) | −15726.2 | −1.24976 | −0.624881 | − | 0.780720i | \(-0.714852\pi\) | ||||
−0.624881 | + | 0.780720i | \(0.714852\pi\) | |||||||
\(542\) | 5468.14 | 0.433352 | ||||||||
\(543\) | −12876.2 | −1.01762 | ||||||||
\(544\) | 2395.15 | 0.188771 | ||||||||
\(545\) | −247.592 | −0.0194599 | ||||||||
\(546\) | −14224.0 | −1.11489 | ||||||||
\(547\) | −12232.3 | −0.956153 | −0.478077 | − | 0.878318i | \(-0.658666\pi\) | ||||
−0.478077 | + | 0.878318i | \(0.658666\pi\) | |||||||
\(548\) | −11832.8 | −0.922395 | ||||||||
\(549\) | 7103.28 | 0.552205 | ||||||||
\(550\) | −465.303 | −0.0360738 | ||||||||
\(551\) | 8135.28 | 0.628992 | ||||||||
\(552\) | −363.634 | −0.0280386 | ||||||||
\(553\) | −35056.8 | −2.69578 | ||||||||
\(554\) | −1520.35 | −0.116595 | ||||||||
\(555\) | −4728.04 | −0.361611 | ||||||||
\(556\) | −1992.32 | −0.151966 | ||||||||
\(557\) | 350.487 | 0.0266618 | 0.0133309 | − | 0.999911i | \(-0.495757\pi\) | ||||
0.0133309 | + | 0.999911i | \(0.495757\pi\) | |||||||
\(558\) | 4363.28 | 0.331026 | ||||||||
\(559\) | 36609.5 | 2.76998 | ||||||||
\(560\) | 2677.67 | 0.202057 | ||||||||
\(561\) | 576.120 | 0.0433579 | ||||||||
\(562\) | 4101.29 | 0.307834 | ||||||||
\(563\) | −2402.60 | −0.179853 | −0.0899267 | − | 0.995948i | \(-0.528663\pi\) | ||||
−0.0899267 | + | 0.995948i | \(0.528663\pi\) | |||||||
\(564\) | −2992.49 | −0.223416 | ||||||||
\(565\) | 6776.19 | 0.504560 | ||||||||
\(566\) | 9636.78 | 0.715661 | ||||||||
\(567\) | 2313.82 | 0.171378 | ||||||||
\(568\) | 6607.69 | 0.488121 | ||||||||
\(569\) | −61.7656 | −0.00455070 | −0.00227535 | − | 0.999997i | \(-0.500724\pi\) | ||||
−0.00227535 | + | 0.999997i | \(0.500724\pi\) | |||||||
\(570\) | −1195.15 | −0.0878233 | ||||||||
\(571\) | 22744.5 | 1.66695 | 0.833473 | − | 0.552561i | \(-0.186349\pi\) | ||||
0.833473 | + | 0.552561i | \(0.186349\pi\) | |||||||
\(572\) | −851.714 | −0.0622587 | ||||||||
\(573\) | 7819.41 | 0.570088 | ||||||||
\(574\) | 10252.5 | 0.745523 | ||||||||
\(575\) | −1373.89 | −0.0996437 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | −23704.2 | −1.71026 | −0.855130 | − | 0.518413i | \(-0.826523\pi\) | ||||
−0.855130 | + | 0.518413i | \(0.826523\pi\) | |||||||
\(578\) | −1378.62 | −0.0992092 | ||||||||
\(579\) | −6355.34 | −0.456164 | ||||||||
\(580\) | 5607.19 | 0.401424 | ||||||||
\(581\) | 24954.4 | 1.78190 | ||||||||
\(582\) | −2306.31 | −0.164261 | ||||||||
\(583\) | 49.4486 | 0.00351278 | ||||||||
\(584\) | −7306.19 | −0.517693 | ||||||||
\(585\) | 4375.83 | 0.309262 | ||||||||
\(586\) | −3752.51 | −0.264530 | ||||||||
\(587\) | 26918.0 | 1.89271 | 0.946357 | − | 0.323122i | \(-0.104733\pi\) | ||||
0.946357 | + | 0.323122i | \(0.104733\pi\) | |||||||
\(588\) | 5676.00 | 0.398086 | ||||||||
\(589\) | −8241.75 | −0.576562 | ||||||||
\(590\) | −691.311 | −0.0482387 | ||||||||
\(591\) | 11495.8 | 0.800123 | ||||||||
\(592\) | −4304.16 | −0.298817 | ||||||||
\(593\) | 16937.8 | 1.17294 | 0.586468 | − | 0.809973i | \(-0.300518\pi\) | ||||
0.586468 | + | 0.809973i | \(0.300518\pi\) | |||||||
\(594\) | 138.549 | 0.00957023 | ||||||||
\(595\) | −12526.2 | −0.863068 | ||||||||
\(596\) | −11617.4 | −0.798435 | ||||||||
\(597\) | 1247.51 | 0.0855230 | ||||||||
\(598\) | −2514.83 | −0.171972 | ||||||||
\(599\) | 4012.73 | 0.273716 | 0.136858 | − | 0.990591i | \(-0.456300\pi\) | ||||
0.136858 | + | 0.990591i | \(0.456300\pi\) | |||||||
\(600\) | 2176.25 | 0.148075 | ||||||||
\(601\) | −18843.7 | −1.27895 | −0.639477 | − | 0.768810i | \(-0.720849\pi\) | ||||
−0.639477 | + | 0.768810i | \(0.720849\pi\) | |||||||
\(602\) | −25202.5 | −1.70627 | ||||||||
\(603\) | 7469.82 | 0.504469 | ||||||||
\(604\) | 2144.26 | 0.144451 | ||||||||
\(605\) | −7759.19 | −0.521415 | ||||||||
\(606\) | −10470.2 | −0.701852 | ||||||||
\(607\) | 22926.5 | 1.53305 | 0.766523 | − | 0.642217i | \(-0.221985\pi\) | ||||
0.766523 | + | 0.642217i | \(0.221985\pi\) | |||||||
\(608\) | −1088.00 | −0.0725727 | ||||||||
\(609\) | 20505.0 | 1.36438 | ||||||||
\(610\) | −9247.79 | −0.613823 | ||||||||
\(611\) | −20695.6 | −1.37030 | ||||||||
\(612\) | −2694.55 | −0.177975 | ||||||||
\(613\) | 4307.74 | 0.283830 | 0.141915 | − | 0.989879i | \(-0.454674\pi\) | ||||
0.141915 | + | 0.989879i | \(0.454674\pi\) | |||||||
\(614\) | −1113.91 | −0.0732145 | ||||||||
\(615\) | −3154.04 | −0.206802 | ||||||||
\(616\) | 586.332 | 0.0383506 | ||||||||
\(617\) | −2484.00 | −0.162078 | −0.0810390 | − | 0.996711i | \(-0.525824\pi\) | ||||
−0.0810390 | + | 0.996711i | \(0.525824\pi\) | |||||||
\(618\) | −3001.33 | −0.195358 | ||||||||
\(619\) | −6644.09 | −0.431419 | −0.215709 | − | 0.976458i | \(-0.569206\pi\) | ||||
−0.215709 | + | 0.976458i | \(0.569206\pi\) | |||||||
\(620\) | −5680.57 | −0.367963 | ||||||||
\(621\) | 409.089 | 0.0264350 | ||||||||
\(622\) | −6047.25 | −0.389828 | ||||||||
\(623\) | −25387.2 | −1.63261 | ||||||||
\(624\) | 3983.52 | 0.255558 | ||||||||
\(625\) | 3931.99 | 0.251647 | ||||||||
\(626\) | 934.257 | 0.0596492 | ||||||||
\(627\) | −261.703 | −0.0166689 | ||||||||
\(628\) | −7984.18 | −0.507330 | ||||||||
\(629\) | 20135.0 | 1.27637 | ||||||||
\(630\) | −3012.38 | −0.190502 | ||||||||
\(631\) | 4264.63 | 0.269053 | 0.134526 | − | 0.990910i | \(-0.457049\pi\) | ||||
0.134526 | + | 0.990910i | \(0.457049\pi\) | |||||||
\(632\) | 9817.87 | 0.617934 | ||||||||
\(633\) | 2130.08 | 0.133749 | ||||||||
\(634\) | 10066.2 | 0.630566 | ||||||||
\(635\) | −5471.32 | −0.341926 | ||||||||
\(636\) | −231.274 | −0.0144192 | ||||||||
\(637\) | 39254.3 | 2.44162 | ||||||||
\(638\) | 1227.81 | 0.0761905 | ||||||||
\(639\) | −7433.65 | −0.460205 | ||||||||
\(640\) | −749.897 | −0.0463161 | ||||||||
\(641\) | −11537.6 | −0.710931 | −0.355466 | − | 0.934689i | \(-0.615678\pi\) | ||||
−0.355466 | + | 0.934689i | \(0.615678\pi\) | |||||||
\(642\) | −6747.41 | −0.414796 | ||||||||
\(643\) | 10699.0 | 0.656188 | 0.328094 | − | 0.944645i | \(-0.393594\pi\) | ||||
0.328094 | + | 0.944645i | \(0.393594\pi\) | |||||||
\(644\) | 1731.25 | 0.105933 | ||||||||
\(645\) | 7753.20 | 0.473305 | ||||||||
\(646\) | 5089.70 | 0.309987 | ||||||||
\(647\) | 1499.52 | 0.0911163 | 0.0455582 | − | 0.998962i | \(-0.485493\pi\) | ||||
0.0455582 | + | 0.998962i | \(0.485493\pi\) | |||||||
\(648\) | −648.000 | −0.0392837 | ||||||||
\(649\) | −151.377 | −0.00915573 | ||||||||
\(650\) | 15050.6 | 0.908204 | ||||||||
\(651\) | −20773.4 | −1.25065 | ||||||||
\(652\) | −9572.62 | −0.574989 | ||||||||
\(653\) | 26399.4 | 1.58207 | 0.791033 | − | 0.611774i | \(-0.209544\pi\) | ||||
0.791033 | + | 0.611774i | \(0.209544\pi\) | |||||||
\(654\) | 253.569 | 0.0151610 | ||||||||
\(655\) | −14201.3 | −0.847162 | ||||||||
\(656\) | −2871.27 | −0.170891 | ||||||||
\(657\) | 8219.47 | 0.488085 | ||||||||
\(658\) | 14247.1 | 0.844088 | ||||||||
\(659\) | −9799.08 | −0.579238 | −0.289619 | − | 0.957142i | \(-0.593529\pi\) | ||||
−0.289619 | + | 0.957142i | \(0.593529\pi\) | |||||||
\(660\) | −180.377 | −0.0106381 | ||||||||
\(661\) | −17044.3 | −1.00294 | −0.501471 | − | 0.865174i | \(-0.667208\pi\) | ||||
−0.501471 | + | 0.865174i | \(0.667208\pi\) | |||||||
\(662\) | −10670.3 | −0.626454 | ||||||||
\(663\) | −18635.0 | −1.09159 | ||||||||
\(664\) | −6988.62 | −0.408450 | ||||||||
\(665\) | 5690.05 | 0.331805 | ||||||||
\(666\) | 4842.18 | 0.281728 | ||||||||
\(667\) | 3625.33 | 0.210455 | ||||||||
\(668\) | 245.091 | 0.0141959 | ||||||||
\(669\) | 7019.06 | 0.405639 | ||||||||
\(670\) | −9724.99 | −0.560760 | ||||||||
\(671\) | −2025.00 | −0.116504 | ||||||||
\(672\) | −2742.31 | −0.157421 | ||||||||
\(673\) | −3868.05 | −0.221549 | −0.110775 | − | 0.993846i | \(-0.535333\pi\) | ||||
−0.110775 | + | 0.993846i | \(0.535333\pi\) | |||||||
\(674\) | 20705.3 | 1.18329 | ||||||||
\(675\) | −2448.28 | −0.139607 | ||||||||
\(676\) | 18761.4 | 1.06744 | ||||||||
\(677\) | 20146.7 | 1.14372 | 0.571861 | − | 0.820351i | \(-0.306222\pi\) | ||||
0.571861 | + | 0.820351i | \(0.306222\pi\) | |||||||
\(678\) | −6939.77 | −0.393098 | ||||||||
\(679\) | 10980.3 | 0.620594 | ||||||||
\(680\) | 3508.05 | 0.197834 | ||||||||
\(681\) | −1216.85 | −0.0684726 | ||||||||
\(682\) | −1243.88 | −0.0698396 | ||||||||
\(683\) | 20028.9 | 1.12209 | 0.561044 | − | 0.827786i | \(-0.310400\pi\) | ||||
0.561044 | + | 0.827786i | \(0.310400\pi\) | |||||||
\(684\) | 1224.00 | 0.0684222 | ||||||||
\(685\) | −17330.8 | −0.966682 | ||||||||
\(686\) | −7427.09 | −0.413364 | ||||||||
\(687\) | 7337.22 | 0.407471 | ||||||||
\(688\) | 7058.10 | 0.391116 | ||||||||
\(689\) | −1599.45 | −0.0884388 | ||||||||
\(690\) | −532.594 | −0.0293848 | ||||||||
\(691\) | −24354.1 | −1.34077 | −0.670385 | − | 0.742013i | \(-0.733871\pi\) | ||||
−0.670385 | + | 0.742013i | \(0.733871\pi\) | |||||||
\(692\) | −12532.3 | −0.688449 | ||||||||
\(693\) | −659.623 | −0.0361573 | ||||||||
\(694\) | −14227.5 | −0.778198 | ||||||||
\(695\) | −2918.04 | −0.159263 | ||||||||
\(696\) | −5742.55 | −0.312745 | ||||||||
\(697\) | 13431.9 | 0.729942 | ||||||||
\(698\) | −6684.62 | −0.362488 | ||||||||
\(699\) | −3030.42 | −0.163979 | ||||||||
\(700\) | −10361.0 | −0.559443 | ||||||||
\(701\) | −12776.4 | −0.688386 | −0.344193 | − | 0.938899i | \(-0.611847\pi\) | ||||
−0.344193 | + | 0.938899i | \(0.611847\pi\) | |||||||
\(702\) | −4481.46 | −0.240943 | ||||||||
\(703\) | −9146.34 | −0.490698 | ||||||||
\(704\) | −164.206 | −0.00879082 | ||||||||
\(705\) | −4382.93 | −0.234143 | ||||||||
\(706\) | 25584.6 | 1.36387 | ||||||||
\(707\) | 49848.1 | 2.65167 | ||||||||
\(708\) | 708.000 | 0.0375823 | ||||||||
\(709\) | −26252.7 | −1.39061 | −0.695305 | − | 0.718715i | \(-0.744731\pi\) | ||||
−0.695305 | + | 0.718715i | \(0.744731\pi\) | |||||||
\(710\) | 9677.91 | 0.511557 | ||||||||
\(711\) | −11045.1 | −0.582593 | ||||||||
\(712\) | 7109.83 | 0.374230 | ||||||||
\(713\) | −3672.77 | −0.192912 | ||||||||
\(714\) | 12828.6 | 0.672407 | ||||||||
\(715\) | −1247.46 | −0.0652479 | ||||||||
\(716\) | −343.771 | −0.0179432 | ||||||||
\(717\) | 12557.4 | 0.654066 | ||||||||
\(718\) | 11328.1 | 0.588801 | ||||||||
\(719\) | −2432.80 | −0.126187 | −0.0630934 | − | 0.998008i | \(-0.520097\pi\) | ||||
−0.0630934 | + | 0.998008i | \(0.520097\pi\) | |||||||
\(720\) | 843.634 | 0.0436672 | ||||||||
\(721\) | 14289.2 | 0.738082 | ||||||||
\(722\) | 11406.0 | 0.587933 | ||||||||
\(723\) | 8958.42 | 0.460812 | ||||||||
\(724\) | −17168.3 | −0.881289 | ||||||||
\(725\) | −21696.6 | −1.11144 | ||||||||
\(726\) | 7946.50 | 0.406229 | ||||||||
\(727\) | −28792.5 | −1.46885 | −0.734426 | − | 0.678689i | \(-0.762548\pi\) | ||||
−0.734426 | + | 0.678689i | \(0.762548\pi\) | |||||||
\(728\) | −18965.3 | −0.965526 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −10701.0 | −0.542549 | ||||||||
\(731\) | −33018.1 | −1.67061 | ||||||||
\(732\) | 9471.03 | 0.478223 | ||||||||
\(733\) | −2585.38 | −0.130277 | −0.0651386 | − | 0.997876i | \(-0.520749\pi\) | ||||
−0.0651386 | + | 0.997876i | \(0.520749\pi\) | |||||||
\(734\) | 15130.2 | 0.760854 | ||||||||
\(735\) | 8313.31 | 0.417199 | ||||||||
\(736\) | −484.846 | −0.0242821 | ||||||||
\(737\) | −2129.49 | −0.106433 | ||||||||
\(738\) | 3230.18 | 0.161117 | ||||||||
\(739\) | 20270.7 | 1.00902 | 0.504511 | − | 0.863405i | \(-0.331673\pi\) | ||||
0.504511 | + | 0.863405i | \(0.331673\pi\) | |||||||
\(740\) | −6304.06 | −0.313165 | ||||||||
\(741\) | 8464.98 | 0.419661 | ||||||||
\(742\) | 1101.09 | 0.0544773 | ||||||||
\(743\) | −16354.8 | −0.807538 | −0.403769 | − | 0.914861i | \(-0.632300\pi\) | ||||
−0.403769 | + | 0.914861i | \(0.632300\pi\) | |||||||
\(744\) | 5817.70 | 0.286677 | ||||||||
\(745\) | −17015.3 | −0.836770 | ||||||||
\(746\) | 8304.64 | 0.407580 | ||||||||
\(747\) | 7862.19 | 0.385091 | ||||||||
\(748\) | 768.160 | 0.0375491 | ||||||||
\(749\) | 32124.1 | 1.56714 | ||||||||
\(750\) | 7581.36 | 0.369109 | ||||||||
\(751\) | 15766.0 | 0.766059 | 0.383030 | − | 0.923736i | \(-0.374881\pi\) | ||||
0.383030 | + | 0.923736i | \(0.374881\pi\) | |||||||
\(752\) | −3989.99 | −0.193484 | ||||||||
\(753\) | −6278.67 | −0.303861 | ||||||||
\(754\) | −39714.5 | −1.91819 | ||||||||
\(755\) | 3140.57 | 0.151387 | ||||||||
\(756\) | 3085.10 | 0.148418 | ||||||||
\(757\) | −3767.14 | −0.180871 | −0.0904354 | − | 0.995902i | \(-0.528826\pi\) | ||||
−0.0904354 | + | 0.995902i | \(0.528826\pi\) | |||||||
\(758\) | −5279.75 | −0.252994 | ||||||||
\(759\) | −116.623 | −0.00557725 | ||||||||
\(760\) | −1593.53 | −0.0760572 | ||||||||
\(761\) | −24685.2 | −1.17587 | −0.587936 | − | 0.808907i | \(-0.700059\pi\) | ||||
−0.587936 | + | 0.808907i | \(0.700059\pi\) | |||||||
\(762\) | 5603.40 | 0.266391 | ||||||||
\(763\) | −1207.23 | −0.0572799 | ||||||||
\(764\) | 10425.9 | 0.493711 | ||||||||
\(765\) | −3946.55 | −0.186520 | ||||||||
\(766\) | 15367.7 | 0.724878 | ||||||||
\(767\) | 4896.41 | 0.230507 | ||||||||
\(768\) | 768.000 | 0.0360844 | ||||||||
\(769\) | 36694.2 | 1.72071 | 0.860356 | − | 0.509694i | \(-0.170241\pi\) | ||||
0.860356 | + | 0.509694i | \(0.170241\pi\) | |||||||
\(770\) | 858.766 | 0.0401919 | ||||||||
\(771\) | −4858.71 | −0.226955 | ||||||||
\(772\) | −8473.78 | −0.395049 | ||||||||
\(773\) | 14539.4 | 0.676514 | 0.338257 | − | 0.941054i | \(-0.390163\pi\) | ||||
0.338257 | + | 0.941054i | \(0.390163\pi\) | |||||||
\(774\) | −7940.37 | −0.368747 | ||||||||
\(775\) | 21980.5 | 1.01879 | ||||||||
\(776\) | −3075.09 | −0.142254 | ||||||||
\(777\) | −23053.4 | −1.06440 | ||||||||
\(778\) | −412.700 | −0.0190180 | ||||||||
\(779\) | −6101.45 | −0.280625 | ||||||||
\(780\) | 5834.43 | 0.267829 | ||||||||
\(781\) | 2119.18 | 0.0970938 | ||||||||
\(782\) | 2268.13 | 0.103719 | ||||||||
\(783\) | 6460.37 | 0.294859 | ||||||||
\(784\) | 7568.00 | 0.344752 | ||||||||
\(785\) | −11694.0 | −0.531689 | ||||||||
\(786\) | 14544.1 | 0.660016 | ||||||||
\(787\) | −21340.0 | −0.966567 | −0.483283 | − | 0.875464i | \(-0.660556\pi\) | ||||
−0.483283 | + | 0.875464i | \(0.660556\pi\) | |||||||
\(788\) | 15327.7 | 0.692927 | ||||||||
\(789\) | 16674.9 | 0.752398 | ||||||||
\(790\) | 14379.7 | 0.647603 | ||||||||
\(791\) | 33039.9 | 1.48516 | ||||||||
\(792\) | 184.731 | 0.00828806 | ||||||||
\(793\) | 65500.1 | 2.93314 | ||||||||
\(794\) | 11354.6 | 0.507506 | ||||||||
\(795\) | −338.734 | −0.0151115 | ||||||||
\(796\) | 1663.35 | 0.0740651 | ||||||||
\(797\) | 20967.1 | 0.931861 | 0.465930 | − | 0.884821i | \(-0.345720\pi\) | ||||
0.465930 | + | 0.884821i | \(0.345720\pi\) | |||||||
\(798\) | −5827.41 | −0.258506 | ||||||||
\(799\) | 18665.3 | 0.826447 | ||||||||
\(800\) | 2901.67 | 0.128237 | ||||||||
\(801\) | −7998.56 | −0.352828 | ||||||||
\(802\) | 5938.50 | 0.261466 | ||||||||
\(803\) | −2343.20 | −0.102976 | ||||||||
\(804\) | 9959.76 | 0.436883 | ||||||||
\(805\) | 2535.66 | 0.111019 | ||||||||
\(806\) | 40234.3 | 1.75830 | ||||||||
\(807\) | 892.166 | 0.0389166 | ||||||||
\(808\) | −13960.3 | −0.607822 | ||||||||
\(809\) | −4118.53 | −0.178986 | −0.0894931 | − | 0.995987i | \(-0.528525\pi\) | ||||
−0.0894931 | + | 0.995987i | \(0.528525\pi\) | |||||||
\(810\) | −949.089 | −0.0411698 | ||||||||
\(811\) | 11302.8 | 0.489389 | 0.244695 | − | 0.969600i | \(-0.421312\pi\) | ||||
0.244695 | + | 0.969600i | \(0.421312\pi\) | |||||||
\(812\) | 27340.0 | 1.18158 | ||||||||
\(813\) | −8202.21 | −0.353830 | ||||||||
\(814\) | −1380.41 | −0.0594388 | ||||||||
\(815\) | −14020.5 | −0.602596 | ||||||||
\(816\) | −3592.73 | −0.154131 | ||||||||
\(817\) | 14998.5 | 0.642264 | ||||||||
\(818\) | −2396.07 | −0.102417 | ||||||||
\(819\) | 21336.0 | 0.910306 | ||||||||
\(820\) | −4205.38 | −0.179096 | ||||||||
\(821\) | 34915.8 | 1.48425 | 0.742125 | − | 0.670261i | \(-0.233818\pi\) | ||||
0.742125 | + | 0.670261i | \(0.233818\pi\) | |||||||
\(822\) | 17749.2 | 0.753133 | ||||||||
\(823\) | −4155.81 | −0.176018 | −0.0880088 | − | 0.996120i | \(-0.528050\pi\) | ||||
−0.0880088 | + | 0.996120i | \(0.528050\pi\) | |||||||
\(824\) | −4001.77 | −0.169185 | ||||||||
\(825\) | 697.955 | 0.0294541 | ||||||||
\(826\) | −3370.75 | −0.141990 | ||||||||
\(827\) | 29006.5 | 1.21965 | 0.609827 | − | 0.792535i | \(-0.291239\pi\) | ||||
0.609827 | + | 0.792535i | \(0.291239\pi\) | |||||||
\(828\) | 545.451 | 0.0228934 | ||||||||
\(829\) | 23464.3 | 0.983052 | 0.491526 | − | 0.870863i | \(-0.336439\pi\) | ||||
0.491526 | + | 0.870863i | \(0.336439\pi\) | |||||||
\(830\) | −10235.8 | −0.428061 | ||||||||
\(831\) | 2280.52 | 0.0951991 | ||||||||
\(832\) | 5311.36 | 0.221320 | ||||||||
\(833\) | −35403.4 | −1.47257 | ||||||||
\(834\) | 2988.48 | 0.124080 | ||||||||
\(835\) | 358.971 | 0.0148775 | ||||||||
\(836\) | −348.937 | −0.0144357 | ||||||||
\(837\) | −6544.92 | −0.270281 | ||||||||
\(838\) | −23552.6 | −0.970895 | ||||||||
\(839\) | 24537.3 | 1.00968 | 0.504840 | − | 0.863213i | \(-0.331552\pi\) | ||||
0.504840 | + | 0.863213i | \(0.331552\pi\) | |||||||
\(840\) | −4016.50 | −0.164979 | ||||||||
\(841\) | 32862.5 | 1.34743 | ||||||||
\(842\) | 20606.0 | 0.843384 | ||||||||
\(843\) | −6151.94 | −0.251345 | ||||||||
\(844\) | 2840.10 | 0.115830 | ||||||||
\(845\) | 27478.7 | 1.11869 | ||||||||
\(846\) | 4488.74 | 0.182418 | ||||||||
\(847\) | −37832.9 | −1.53478 | ||||||||
\(848\) | −308.366 | −0.0124874 | ||||||||
\(849\) | −14455.2 | −0.584335 | ||||||||
\(850\) | −13574.1 | −0.547751 | ||||||||
\(851\) | −4075.89 | −0.164183 | ||||||||
\(852\) | −9911.54 | −0.398549 | ||||||||
\(853\) | −19684.4 | −0.790130 | −0.395065 | − | 0.918653i | \(-0.629278\pi\) | ||||
−0.395065 | + | 0.918653i | \(0.629278\pi\) | |||||||
\(854\) | −45091.1 | −1.80678 | ||||||||
\(855\) | 1792.72 | 0.0717074 | ||||||||
\(856\) | −8996.55 | −0.359224 | ||||||||
\(857\) | −33312.2 | −1.32780 | −0.663898 | − | 0.747823i | \(-0.731099\pi\) | ||||
−0.663898 | + | 0.747823i | \(0.731099\pi\) | |||||||
\(858\) | 1277.57 | 0.0508340 | ||||||||
\(859\) | −11928.6 | −0.473805 | −0.236902 | − | 0.971533i | \(-0.576132\pi\) | ||||
−0.236902 | + | 0.971533i | \(0.576132\pi\) | |||||||
\(860\) | 10337.6 | 0.409894 | ||||||||
\(861\) | −15378.7 | −0.608717 | ||||||||
\(862\) | −28035.6 | −1.10777 | ||||||||
\(863\) | −42805.1 | −1.68842 | −0.844208 | − | 0.536015i | \(-0.819929\pi\) | ||||
−0.844208 | + | 0.536015i | \(0.819929\pi\) | |||||||
\(864\) | −864.000 | −0.0340207 | ||||||||
\(865\) | −18355.4 | −0.721504 | ||||||||
\(866\) | 13336.3 | 0.523310 | ||||||||
\(867\) | 2067.93 | 0.0810040 | ||||||||
\(868\) | −27697.8 | −1.08309 | ||||||||
\(869\) | 3148.73 | 0.122915 | ||||||||
\(870\) | −8410.78 | −0.327761 | ||||||||
\(871\) | 68880.0 | 2.67958 | ||||||||
\(872\) | 338.092 | 0.0131298 | ||||||||
\(873\) | 3459.47 | 0.134118 | ||||||||
\(874\) | −1030.30 | −0.0398745 | ||||||||
\(875\) | −36094.5 | −1.39453 | ||||||||
\(876\) | 10959.3 | 0.422694 | ||||||||
\(877\) | 11297.7 | 0.435002 | 0.217501 | − | 0.976060i | \(-0.430209\pi\) | ||||
0.217501 | + | 0.976060i | \(0.430209\pi\) | |||||||
\(878\) | −22663.6 | −0.871139 | ||||||||
\(879\) | 5628.76 | 0.215988 | ||||||||
\(880\) | −240.503 | −0.00921289 | ||||||||
\(881\) | 44382.1 | 1.69724 | 0.848622 | − | 0.529000i | \(-0.177433\pi\) | ||||
0.848622 | + | 0.529000i | \(0.177433\pi\) | |||||||
\(882\) | −8514.00 | −0.325035 | ||||||||
\(883\) | −16656.6 | −0.634813 | −0.317407 | − | 0.948290i | \(-0.602812\pi\) | ||||
−0.317407 | + | 0.948290i | \(0.602812\pi\) | |||||||
\(884\) | −24846.7 | −0.945346 | ||||||||
\(885\) | 1036.97 | 0.0393867 | ||||||||
\(886\) | −2027.53 | −0.0768807 | ||||||||
\(887\) | 15233.9 | 0.576669 | 0.288334 | − | 0.957530i | \(-0.406899\pi\) | ||||
0.288334 | + | 0.957530i | \(0.406899\pi\) | |||||||
\(888\) | 6456.24 | 0.243983 | ||||||||
\(889\) | −26677.5 | −1.00645 | ||||||||
\(890\) | 10413.4 | 0.392198 | ||||||||
\(891\) | −207.823 | −0.00781406 | ||||||||
\(892\) | 9358.74 | 0.351294 | ||||||||
\(893\) | −8478.73 | −0.317726 | ||||||||
\(894\) | 17426.1 | 0.651919 | ||||||||
\(895\) | −503.502 | −0.0188047 | ||||||||
\(896\) | −3656.41 | −0.136331 | ||||||||
\(897\) | 3772.25 | 0.140414 | ||||||||
\(898\) | −31098.4 | −1.15564 | ||||||||
\(899\) | −58000.8 | −2.15176 | ||||||||
\(900\) | −3264.38 | −0.120903 | ||||||||
\(901\) | 1442.55 | 0.0533387 | ||||||||
\(902\) | −920.857 | −0.0339924 | ||||||||
\(903\) | 37803.7 | 1.39317 | ||||||||
\(904\) | −9253.03 | −0.340433 | ||||||||
\(905\) | −25145.4 | −0.923602 | ||||||||
\(906\) | −3216.39 | −0.117944 | ||||||||
\(907\) | 7813.26 | 0.286037 | 0.143018 | − | 0.989720i | \(-0.454319\pi\) | ||||
0.143018 | + | 0.989720i | \(0.454319\pi\) | |||||||
\(908\) | −1622.47 | −0.0592990 | ||||||||
\(909\) | 15705.3 | 0.573060 | ||||||||
\(910\) | −27777.5 | −1.01188 | ||||||||
\(911\) | −10661.5 | −0.387739 | −0.193869 | − | 0.981027i | \(-0.562104\pi\) | ||||
−0.193869 | + | 0.981027i | \(0.562104\pi\) | |||||||
\(912\) | 1632.00 | 0.0592554 | ||||||||
\(913\) | −2241.35 | −0.0812462 | ||||||||
\(914\) | 14007.3 | 0.506914 | ||||||||
\(915\) | 13871.7 | 0.501184 | ||||||||
\(916\) | 9782.95 | 0.352880 | ||||||||
\(917\) | −69243.9 | −2.49361 | ||||||||
\(918\) | 4041.82 | 0.145316 | ||||||||
\(919\) | −30469.0 | −1.09367 | −0.546834 | − | 0.837241i | \(-0.684167\pi\) | ||||
−0.546834 | + | 0.837241i | \(0.684167\pi\) | |||||||
\(920\) | −710.126 | −0.0254480 | ||||||||
\(921\) | 1670.86 | 0.0597794 | ||||||||
\(922\) | 15980.6 | 0.570818 | ||||||||
\(923\) | −68546.5 | −2.44446 | ||||||||
\(924\) | −879.497 | −0.0313131 | ||||||||
\(925\) | 24393.1 | 0.867069 | ||||||||
\(926\) | 4771.68 | 0.169338 | ||||||||
\(927\) | 4501.99 | 0.159509 | ||||||||
\(928\) | −7656.73 | −0.270845 | ||||||||
\(929\) | −4514.41 | −0.159433 | −0.0797164 | − | 0.996818i | \(-0.525401\pi\) | ||||
−0.0797164 | + | 0.996818i | \(0.525401\pi\) | |||||||
\(930\) | 8520.86 | 0.300441 | ||||||||
\(931\) | 16082.0 | 0.566129 | ||||||||
\(932\) | −4040.56 | −0.142010 | ||||||||
\(933\) | 9070.88 | 0.318293 | ||||||||
\(934\) | −11375.6 | −0.398525 | ||||||||
\(935\) | 1125.08 | 0.0393519 | ||||||||
\(936\) | −5975.28 | −0.208663 | ||||||||
\(937\) | −20904.5 | −0.728837 | −0.364418 | − | 0.931235i | \(-0.618732\pi\) | ||||
−0.364418 | + | 0.931235i | \(0.618732\pi\) | |||||||
\(938\) | −47417.9 | −1.65059 | ||||||||
\(939\) | −1401.39 | −0.0487034 | ||||||||
\(940\) | −5843.91 | −0.202774 | ||||||||
\(941\) | 22393.3 | 0.775771 | 0.387886 | − | 0.921708i | \(-0.373206\pi\) | ||||
0.387886 | + | 0.921708i | \(0.373206\pi\) | |||||||
\(942\) | 11976.3 | 0.414233 | ||||||||
\(943\) | −2718.99 | −0.0938944 | ||||||||
\(944\) | 944.000 | 0.0325472 | ||||||||
\(945\) | 4518.57 | 0.155544 | ||||||||
\(946\) | 2263.63 | 0.0777982 | ||||||||
\(947\) | −52752.3 | −1.81016 | −0.905079 | − | 0.425243i | \(-0.860189\pi\) | ||||
−0.905079 | + | 0.425243i | \(0.860189\pi\) | |||||||
\(948\) | −14726.8 | −0.504541 | ||||||||
\(949\) | 75792.6 | 2.59255 | ||||||||
\(950\) | 6166.05 | 0.210582 | ||||||||
\(951\) | −15099.3 | −0.514855 | ||||||||
\(952\) | 17104.8 | 0.582322 | ||||||||
\(953\) | 19837.4 | 0.674287 | 0.337144 | − | 0.941453i | \(-0.390539\pi\) | ||||
0.337144 | + | 0.941453i | \(0.390539\pi\) | |||||||
\(954\) | 346.911 | 0.0117732 | ||||||||
\(955\) | 15270.2 | 0.517416 | ||||||||
\(956\) | 16743.2 | 0.566438 | ||||||||
\(957\) | −1841.72 | −0.0622093 | ||||||||
\(958\) | 27760.1 | 0.936210 | ||||||||
\(959\) | −84503.2 | −2.84541 | ||||||||
\(960\) | 1124.85 | 0.0378169 | ||||||||
\(961\) | 28968.8 | 0.972402 | ||||||||
\(962\) | 44650.3 | 1.49645 | ||||||||
\(963\) | 10121.1 | 0.338680 | ||||||||
\(964\) | 11944.6 | 0.399075 | ||||||||
\(965\) | −12411.1 | −0.414017 | ||||||||
\(966\) | −2596.87 | −0.0864937 | ||||||||
\(967\) | 35535.4 | 1.18174 | 0.590870 | − | 0.806767i | \(-0.298785\pi\) | ||||
0.590870 | + | 0.806767i | \(0.298785\pi\) | |||||||
\(968\) | 10595.3 | 0.351805 | ||||||||
\(969\) | −7634.55 | −0.253103 | ||||||||
\(970\) | −4503.90 | −0.149084 | ||||||||
\(971\) | −6393.93 | −0.211319 | −0.105660 | − | 0.994402i | \(-0.533695\pi\) | ||||
−0.105660 | + | 0.994402i | \(0.533695\pi\) | |||||||
\(972\) | 972.000 | 0.0320750 | ||||||||
\(973\) | −14228.0 | −0.468786 | ||||||||
\(974\) | −22512.3 | −0.740597 | ||||||||
\(975\) | −22575.9 | −0.741546 | ||||||||
\(976\) | 12628.0 | 0.414154 | ||||||||
\(977\) | 900.777 | 0.0294968 | 0.0147484 | − | 0.999891i | \(-0.495305\pi\) | ||||
0.0147484 | + | 0.999891i | \(0.495305\pi\) | |||||||
\(978\) | 14358.9 | 0.469476 | ||||||||
\(979\) | 2280.22 | 0.0744395 | ||||||||
\(980\) | 11084.4 | 0.361305 | ||||||||
\(981\) | −380.353 | −0.0123789 | ||||||||
\(982\) | 3242.17 | 0.105358 | ||||||||
\(983\) | −56145.1 | −1.82172 | −0.910860 | − | 0.412716i | \(-0.864580\pi\) | ||||
−0.910860 | + | 0.412716i | \(0.864580\pi\) | |||||||
\(984\) | 4306.90 | 0.139532 | ||||||||
\(985\) | 22449.6 | 0.726197 | ||||||||
\(986\) | 35818.5 | 1.15689 | ||||||||
\(987\) | −21370.7 | −0.689195 | ||||||||
\(988\) | 11286.6 | 0.363437 | ||||||||
\(989\) | 6683.77 | 0.214895 | ||||||||
\(990\) | 270.566 | 0.00868600 | ||||||||
\(991\) | 4295.90 | 0.137703 | 0.0688515 | − | 0.997627i | \(-0.478067\pi\) | ||||
0.0688515 | + | 0.997627i | \(0.478067\pi\) | |||||||
\(992\) | 7756.94 | 0.248269 | ||||||||
\(993\) | 16005.4 | 0.511497 | ||||||||
\(994\) | 47188.4 | 1.50576 | ||||||||
\(995\) | 2436.21 | 0.0776212 | ||||||||
\(996\) | 10482.9 | 0.333498 | ||||||||
\(997\) | −36710.7 | −1.16614 | −0.583070 | − | 0.812422i | \(-0.698149\pi\) | ||||
−0.583070 | + | 0.812422i | \(0.698149\pi\) | |||||||
\(998\) | −35521.9 | −1.12668 | ||||||||
\(999\) | −7263.27 | −0.230030 |
(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 | 354.4.a.b.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 1062.4.a.g.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
354.4.a.b.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1062.4.a.g.1.2 | 2 | 3.2 | odd | 2 |