Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1815,4,Mod(1,1815)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1815, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1815.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1815 = 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1815.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: | \(107.088466660\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1815.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.46410 | −1.22474 | −0.612372 | − | 0.790569i | \(-0.709785\pi\) | ||||
−0.612372 | + | 0.790569i | \(0.709785\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | −10.3923 | −0.707107 | ||||||||
\(7\) | −27.7128 | −1.49635 | −0.748176 | − | 0.663501i | \(-0.769070\pi\) | ||||
−0.748176 | + | 0.663501i | \(0.769070\pi\) | |||||||
\(8\) | 13.8564 | 0.612372 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 17.3205 | 0.547723 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 12.0000 | 0.288675 | ||||||||
\(13\) | 58.8897 | 1.25639 | 0.628195 | − | 0.778056i | \(-0.283794\pi\) | ||||
0.628195 | + | 0.778056i | \(0.283794\pi\) | |||||||
\(14\) | 96.0000 | 1.83265 | ||||||||
\(15\) | −15.0000 | −0.258199 | ||||||||
\(16\) | −80.0000 | −1.25000 | ||||||||
\(17\) | −19.0526 | −0.271819 | −0.135910 | − | 0.990721i | \(-0.543396\pi\) | ||||
−0.135910 | + | 0.990721i | \(0.543396\pi\) | |||||||
\(18\) | −31.1769 | −0.408248 | ||||||||
\(19\) | 45.0333 | 0.543755 | 0.271878 | − | 0.962332i | \(-0.412355\pi\) | ||||
0.271878 | + | 0.962332i | \(0.412355\pi\) | |||||||
\(20\) | −20.0000 | −0.223607 | ||||||||
\(21\) | −83.1384 | −0.863919 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −75.0000 | −0.679938 | −0.339969 | − | 0.940437i | \(-0.610417\pi\) | ||||
−0.339969 | + | 0.940437i | \(0.610417\pi\) | |||||||
\(24\) | 41.5692 | 0.353553 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −204.000 | −1.53876 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −110.851 | −0.748176 | ||||||||
\(29\) | 128.172 | 0.820721 | 0.410360 | − | 0.911923i | \(-0.365403\pi\) | ||||
0.410360 | + | 0.911923i | \(0.365403\pi\) | |||||||
\(30\) | 51.9615 | 0.316228 | ||||||||
\(31\) | −263.000 | −1.52375 | −0.761874 | − | 0.647725i | \(-0.775721\pi\) | ||||
−0.761874 | + | 0.647725i | \(0.775721\pi\) | |||||||
\(32\) | 166.277 | 0.918559 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 66.0000 | 0.332909 | ||||||||
\(35\) | 138.564 | 0.669189 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | −308.000 | −1.36851 | −0.684255 | − | 0.729243i | \(-0.739873\pi\) | ||||
−0.684255 | + | 0.729243i | \(0.739873\pi\) | |||||||
\(38\) | −156.000 | −0.665962 | ||||||||
\(39\) | 176.669 | 0.725377 | ||||||||
\(40\) | −69.2820 | −0.273861 | ||||||||
\(41\) | −162.813 | −0.620173 | −0.310086 | − | 0.950708i | \(-0.600358\pi\) | ||||
−0.310086 | + | 0.950708i | \(0.600358\pi\) | |||||||
\(42\) | 288.000 | 1.05808 | ||||||||
\(43\) | 38.1051 | 0.135139 | 0.0675695 | − | 0.997715i | \(-0.478476\pi\) | ||||
0.0675695 | + | 0.997715i | \(0.478476\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −45.0000 | −0.149071 | ||||||||
\(46\) | 259.808 | 0.832751 | ||||||||
\(47\) | 93.0000 | 0.288626 | 0.144313 | − | 0.989532i | \(-0.453903\pi\) | ||||
0.144313 | + | 0.989532i | \(0.453903\pi\) | |||||||
\(48\) | −240.000 | −0.721688 | ||||||||
\(49\) | 425.000 | 1.23907 | ||||||||
\(50\) | −86.6025 | −0.244949 | ||||||||
\(51\) | −57.1577 | −0.156935 | ||||||||
\(52\) | 235.559 | 0.628195 | ||||||||
\(53\) | 525.000 | 1.36065 | 0.680324 | − | 0.732912i | \(-0.261839\pi\) | ||||
0.680324 | + | 0.732912i | \(0.261839\pi\) | |||||||
\(54\) | −93.5307 | −0.235702 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −384.000 | −0.916324 | ||||||||
\(57\) | 135.100 | 0.313937 | ||||||||
\(58\) | −444.000 | −1.00517 | ||||||||
\(59\) | 498.000 | 1.09888 | 0.549441 | − | 0.835532i | \(-0.314841\pi\) | ||||
0.549441 | + | 0.835532i | \(0.314841\pi\) | |||||||
\(60\) | −60.0000 | −0.129099 | ||||||||
\(61\) | 441.673 | 0.927056 | 0.463528 | − | 0.886082i | \(-0.346583\pi\) | ||||
0.463528 | + | 0.886082i | \(0.346583\pi\) | |||||||
\(62\) | 911.059 | 1.86620 | ||||||||
\(63\) | −249.415 | −0.498784 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −294.449 | −0.561875 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 316.000 | 0.576202 | 0.288101 | − | 0.957600i | \(-0.406976\pi\) | ||||
0.288101 | + | 0.957600i | \(0.406976\pi\) | |||||||
\(68\) | −76.2102 | −0.135910 | ||||||||
\(69\) | −225.000 | −0.392563 | ||||||||
\(70\) | −480.000 | −0.819585 | ||||||||
\(71\) | −288.000 | −0.481399 | −0.240699 | − | 0.970600i | \(-0.577377\pi\) | ||||
−0.240699 | + | 0.970600i | \(0.577377\pi\) | |||||||
\(72\) | 124.708 | 0.204124 | ||||||||
\(73\) | 928.379 | 1.48847 | 0.744237 | − | 0.667916i | \(-0.232813\pi\) | ||||
0.744237 | + | 0.667916i | \(0.232813\pi\) | |||||||
\(74\) | 1066.94 | 1.67608 | ||||||||
\(75\) | 75.0000 | 0.115470 | ||||||||
\(76\) | 180.133 | 0.271878 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −612.000 | −0.888402 | ||||||||
\(79\) | 1137.96 | 1.62064 | 0.810318 | − | 0.585991i | \(-0.199294\pi\) | ||||
0.810318 | + | 0.585991i | \(0.199294\pi\) | |||||||
\(80\) | 400.000 | 0.559017 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 564.000 | 0.759553 | ||||||||
\(83\) | −571.577 | −0.755888 | −0.377944 | − | 0.925828i | \(-0.623369\pi\) | ||||
−0.377944 | + | 0.925828i | \(0.623369\pi\) | |||||||
\(84\) | −332.554 | −0.431959 | ||||||||
\(85\) | 95.2628 | 0.121561 | ||||||||
\(86\) | −132.000 | −0.165511 | ||||||||
\(87\) | 384.515 | 0.473843 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −180.000 | −0.214382 | −0.107191 | − | 0.994238i | \(-0.534186\pi\) | ||||
−0.107191 | + | 0.994238i | \(0.534186\pi\) | |||||||
\(90\) | 155.885 | 0.182574 | ||||||||
\(91\) | −1632.00 | −1.88000 | ||||||||
\(92\) | −300.000 | −0.339969 | ||||||||
\(93\) | −789.000 | −0.879736 | ||||||||
\(94\) | −322.161 | −0.353494 | ||||||||
\(95\) | −225.167 | −0.243175 | ||||||||
\(96\) | 498.831 | 0.530330 | ||||||||
\(97\) | −904.000 | −0.946261 | −0.473130 | − | 0.880992i | \(-0.656876\pi\) | ||||
−0.473130 | + | 0.880992i | \(0.656876\pi\) | |||||||
\(98\) | −1472.24 | −1.51754 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 100.000 | 0.100000 | ||||||||
\(101\) | 1046.16 | 1.03066 | 0.515330 | − | 0.856992i | \(-0.327669\pi\) | ||||
0.515330 | + | 0.856992i | \(0.327669\pi\) | |||||||
\(102\) | 198.000 | 0.192205 | ||||||||
\(103\) | 1352.00 | 1.29336 | 0.646682 | − | 0.762760i | \(-0.276156\pi\) | ||||
0.646682 | + | 0.762760i | \(0.276156\pi\) | |||||||
\(104\) | 816.000 | 0.769379 | ||||||||
\(105\) | 415.692 | 0.386356 | ||||||||
\(106\) | −1818.65 | −1.66645 | ||||||||
\(107\) | 1047.89 | 0.946761 | 0.473380 | − | 0.880858i | \(-0.343034\pi\) | ||||
0.473380 | + | 0.880858i | \(0.343034\pi\) | |||||||
\(108\) | 108.000 | 0.0962250 | ||||||||
\(109\) | −1870.61 | −1.64378 | −0.821892 | − | 0.569644i | \(-0.807081\pi\) | ||||
−0.821892 | + | 0.569644i | \(0.807081\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −924.000 | −0.790110 | ||||||||
\(112\) | 2217.03 | 1.87044 | ||||||||
\(113\) | −1971.00 | −1.64085 | −0.820425 | − | 0.571754i | \(-0.806263\pi\) | ||||
−0.820425 | + | 0.571754i | \(0.806263\pi\) | |||||||
\(114\) | −468.000 | −0.384493 | ||||||||
\(115\) | 375.000 | 0.304078 | ||||||||
\(116\) | 512.687 | 0.410360 | ||||||||
\(117\) | 530.008 | 0.418797 | ||||||||
\(118\) | −1725.12 | −1.34585 | ||||||||
\(119\) | 528.000 | 0.406737 | ||||||||
\(120\) | −207.846 | −0.158114 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1530.00 | −1.13541 | ||||||||
\(123\) | −488.438 | −0.358057 | ||||||||
\(124\) | −1052.00 | −0.761874 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 864.000 | 0.610883 | ||||||||
\(127\) | −945.700 | −0.660766 | −0.330383 | − | 0.943847i | \(-0.607178\pi\) | ||||
−0.330383 | + | 0.943847i | \(0.607178\pi\) | |||||||
\(128\) | −1551.92 | −1.07165 | ||||||||
\(129\) | 114.315 | 0.0780225 | ||||||||
\(130\) | 1020.00 | 0.688153 | ||||||||
\(131\) | 980.341 | 0.653838 | 0.326919 | − | 0.945052i | \(-0.393990\pi\) | ||||
0.326919 | + | 0.945052i | \(0.393990\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1248.00 | −0.813649 | ||||||||
\(134\) | −1094.66 | −0.705701 | ||||||||
\(135\) | −135.000 | −0.0860663 | ||||||||
\(136\) | −264.000 | −0.166455 | ||||||||
\(137\) | −2169.00 | −1.35263 | −0.676315 | − | 0.736613i | \(-0.736424\pi\) | ||||
−0.676315 | + | 0.736613i | \(0.736424\pi\) | |||||||
\(138\) | 779.423 | 0.480789 | ||||||||
\(139\) | −1002.86 | −0.611951 | −0.305976 | − | 0.952039i | \(-0.598983\pi\) | ||||
−0.305976 | + | 0.952039i | \(0.598983\pi\) | |||||||
\(140\) | 554.256 | 0.334594 | ||||||||
\(141\) | 279.000 | 0.166639 | ||||||||
\(142\) | 997.661 | 0.589591 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −720.000 | −0.416667 | ||||||||
\(145\) | −640.859 | −0.367037 | ||||||||
\(146\) | −3216.00 | −1.82300 | ||||||||
\(147\) | 1275.00 | 0.715376 | ||||||||
\(148\) | −1232.00 | −0.684255 | ||||||||
\(149\) | −536.936 | −0.295218 | −0.147609 | − | 0.989046i | \(-0.547158\pi\) | ||||
−0.147609 | + | 0.989046i | \(0.547158\pi\) | |||||||
\(150\) | −259.808 | −0.141421 | ||||||||
\(151\) | −226.899 | −0.122283 | −0.0611416 | − | 0.998129i | \(-0.519474\pi\) | ||||
−0.0611416 | + | 0.998129i | \(0.519474\pi\) | |||||||
\(152\) | 624.000 | 0.332981 | ||||||||
\(153\) | −171.473 | −0.0906064 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1315.00 | 0.681441 | ||||||||
\(156\) | 706.677 | 0.362689 | ||||||||
\(157\) | −2576.00 | −1.30947 | −0.654736 | − | 0.755857i | \(-0.727220\pi\) | ||||
−0.654736 | + | 0.755857i | \(0.727220\pi\) | |||||||
\(158\) | −3942.00 | −1.98487 | ||||||||
\(159\) | 1575.00 | 0.785570 | ||||||||
\(160\) | −831.384 | −0.410792 | ||||||||
\(161\) | 2078.46 | 1.01743 | ||||||||
\(162\) | −280.592 | −0.136083 | ||||||||
\(163\) | 1694.00 | 0.814014 | 0.407007 | − | 0.913425i | \(-0.366572\pi\) | ||||
0.407007 | + | 0.913425i | \(0.366572\pi\) | |||||||
\(164\) | −651.251 | −0.310086 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1980.00 | 0.925770 | ||||||||
\(167\) | 874.686 | 0.405301 | 0.202650 | − | 0.979251i | \(-0.435045\pi\) | ||||
0.202650 | + | 0.979251i | \(0.435045\pi\) | |||||||
\(168\) | −1152.00 | −0.529040 | ||||||||
\(169\) | 1271.00 | 0.578516 | ||||||||
\(170\) | −330.000 | −0.148881 | ||||||||
\(171\) | 405.300 | 0.181252 | ||||||||
\(172\) | 152.420 | 0.0675695 | ||||||||
\(173\) | 2868.28 | 1.26053 | 0.630263 | − | 0.776382i | \(-0.282947\pi\) | ||||
0.630263 | + | 0.776382i | \(0.282947\pi\) | |||||||
\(174\) | −1332.00 | −0.580337 | ||||||||
\(175\) | −692.820 | −0.299270 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1494.00 | 0.634440 | ||||||||
\(178\) | 623.538 | 0.262563 | ||||||||
\(179\) | −4416.00 | −1.84395 | −0.921976 | − | 0.387247i | \(-0.873426\pi\) | ||||
−0.921976 | + | 0.387247i | \(0.873426\pi\) | |||||||
\(180\) | −180.000 | −0.0745356 | ||||||||
\(181\) | 4430.00 | 1.81922 | 0.909611 | − | 0.415460i | \(-0.136379\pi\) | ||||
0.909611 | + | 0.415460i | \(0.136379\pi\) | |||||||
\(182\) | 5653.41 | 2.30252 | ||||||||
\(183\) | 1325.02 | 0.535236 | ||||||||
\(184\) | −1039.23 | −0.416375 | ||||||||
\(185\) | 1540.00 | 0.612016 | ||||||||
\(186\) | 2733.18 | 1.07745 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 372.000 | 0.144313 | ||||||||
\(189\) | −748.246 | −0.287973 | ||||||||
\(190\) | 780.000 | 0.297827 | ||||||||
\(191\) | −4632.00 | −1.75476 | −0.877382 | − | 0.479793i | \(-0.840712\pi\) | ||||
−0.877382 | + | 0.479793i | \(0.840712\pi\) | |||||||
\(192\) | 192.000 | 0.0721688 | ||||||||
\(193\) | −3076.12 | −1.14728 | −0.573638 | − | 0.819109i | \(-0.694468\pi\) | ||||
−0.573638 | + | 0.819109i | \(0.694468\pi\) | |||||||
\(194\) | 3131.55 | 1.15893 | ||||||||
\(195\) | −883.346 | −0.324399 | ||||||||
\(196\) | 1700.00 | 0.619534 | ||||||||
\(197\) | −1406.43 | −0.508648 | −0.254324 | − | 0.967119i | \(-0.581853\pi\) | ||||
−0.254324 | + | 0.967119i | \(0.581853\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4753.00 | 1.69312 | 0.846561 | − | 0.532292i | \(-0.178669\pi\) | ||||
0.846561 | + | 0.532292i | \(0.178669\pi\) | |||||||
\(200\) | 346.410 | 0.122474 | ||||||||
\(201\) | 948.000 | 0.332670 | ||||||||
\(202\) | −3624.00 | −1.26230 | ||||||||
\(203\) | −3552.00 | −1.22809 | ||||||||
\(204\) | −228.631 | −0.0784674 | ||||||||
\(205\) | 814.064 | 0.277350 | ||||||||
\(206\) | −4683.47 | −1.58404 | ||||||||
\(207\) | −675.000 | −0.226646 | ||||||||
\(208\) | −4711.18 | −1.57049 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1440.00 | −0.473188 | ||||||||
\(211\) | 3670.22 | 1.19748 | 0.598739 | − | 0.800944i | \(-0.295668\pi\) | ||||
0.598739 | + | 0.800944i | \(0.295668\pi\) | |||||||
\(212\) | 2100.00 | 0.680324 | ||||||||
\(213\) | −864.000 | −0.277936 | ||||||||
\(214\) | −3630.00 | −1.15954 | ||||||||
\(215\) | −190.526 | −0.0604360 | ||||||||
\(216\) | 374.123 | 0.117851 | ||||||||
\(217\) | 7288.47 | 2.28006 | ||||||||
\(218\) | 6480.00 | 2.01322 | ||||||||
\(219\) | 2785.14 | 0.859371 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1122.00 | −0.341511 | ||||||||
\(222\) | 3200.83 | 0.967683 | ||||||||
\(223\) | −1606.00 | −0.482268 | −0.241134 | − | 0.970492i | \(-0.577519\pi\) | ||||
−0.241134 | + | 0.970492i | \(0.577519\pi\) | |||||||
\(224\) | −4608.00 | −1.37449 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 6827.74 | 2.00962 | ||||||||
\(227\) | −4581.27 | −1.33951 | −0.669757 | − | 0.742580i | \(-0.733602\pi\) | ||||
−0.669757 | + | 0.742580i | \(0.733602\pi\) | |||||||
\(228\) | 540.400 | 0.156969 | ||||||||
\(229\) | 4021.00 | 1.16033 | 0.580164 | − | 0.814500i | \(-0.302988\pi\) | ||||
0.580164 | + | 0.814500i | \(0.302988\pi\) | |||||||
\(230\) | −1299.04 | −0.372418 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1776.00 | 0.502587 | ||||||||
\(233\) | −1498.22 | −0.421253 | −0.210626 | − | 0.977567i | \(-0.567550\pi\) | ||||
−0.210626 | + | 0.977567i | \(0.567550\pi\) | |||||||
\(234\) | −1836.00 | −0.512919 | ||||||||
\(235\) | −465.000 | −0.129078 | ||||||||
\(236\) | 1992.00 | 0.549441 | ||||||||
\(237\) | 3413.87 | 0.935674 | ||||||||
\(238\) | −1829.05 | −0.498149 | ||||||||
\(239\) | 543.864 | 0.147195 | 0.0735976 | − | 0.997288i | \(-0.476552\pi\) | ||||
0.0735976 | + | 0.997288i | \(0.476552\pi\) | |||||||
\(240\) | 1200.00 | 0.322749 | ||||||||
\(241\) | 2270.72 | 0.606929 | 0.303464 | − | 0.952843i | \(-0.401857\pi\) | ||||
0.303464 | + | 0.952843i | \(0.401857\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 1766.69 | 0.463528 | ||||||||
\(245\) | −2125.00 | −0.554128 | ||||||||
\(246\) | 1692.00 | 0.438528 | ||||||||
\(247\) | 2652.00 | 0.683169 | ||||||||
\(248\) | −3644.23 | −0.933101 | ||||||||
\(249\) | −1714.73 | −0.436412 | ||||||||
\(250\) | 433.013 | 0.109545 | ||||||||
\(251\) | −4746.00 | −1.19349 | −0.596743 | − | 0.802433i | \(-0.703539\pi\) | ||||
−0.596743 | + | 0.802433i | \(0.703539\pi\) | |||||||
\(252\) | −997.661 | −0.249392 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 3276.00 | 0.809270 | ||||||||
\(255\) | 285.788 | 0.0701834 | ||||||||
\(256\) | 4864.00 | 1.18750 | ||||||||
\(257\) | −2691.00 | −0.653152 | −0.326576 | − | 0.945171i | \(-0.605895\pi\) | ||||
−0.326576 | + | 0.945171i | \(0.605895\pi\) | |||||||
\(258\) | −396.000 | −0.0955577 | ||||||||
\(259\) | 8535.55 | 2.04777 | ||||||||
\(260\) | −1177.79 | −0.280937 | ||||||||
\(261\) | 1153.55 | 0.273574 | ||||||||
\(262\) | −3396.00 | −0.800785 | ||||||||
\(263\) | −3909.24 | −0.916555 | −0.458278 | − | 0.888809i | \(-0.651533\pi\) | ||||
−0.458278 | + | 0.888809i | \(0.651533\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2625.00 | −0.608500 | ||||||||
\(266\) | 4323.20 | 0.996513 | ||||||||
\(267\) | −540.000 | −0.123773 | ||||||||
\(268\) | 1264.00 | 0.288101 | ||||||||
\(269\) | −7848.00 | −1.77881 | −0.889407 | − | 0.457116i | \(-0.848882\pi\) | ||||
−0.889407 | + | 0.457116i | \(0.848882\pi\) | |||||||
\(270\) | 467.654 | 0.105409 | ||||||||
\(271\) | −4823.76 | −1.08126 | −0.540632 | − | 0.841259i | \(-0.681815\pi\) | ||||
−0.540632 | + | 0.841259i | \(0.681815\pi\) | |||||||
\(272\) | 1524.20 | 0.339774 | ||||||||
\(273\) | −4896.00 | −1.08542 | ||||||||
\(274\) | 7513.64 | 1.65663 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −900.000 | −0.196281 | ||||||||
\(277\) | −4842.81 | −1.05046 | −0.525228 | − | 0.850961i | \(-0.676020\pi\) | ||||
−0.525228 | + | 0.850961i | \(0.676020\pi\) | |||||||
\(278\) | 3474.00 | 0.749484 | ||||||||
\(279\) | −2367.00 | −0.507916 | ||||||||
\(280\) | 1920.00 | 0.409793 | ||||||||
\(281\) | −7676.45 | −1.62967 | −0.814837 | − | 0.579690i | \(-0.803174\pi\) | ||||
−0.814837 | + | 0.579690i | \(0.803174\pi\) | |||||||
\(282\) | −966.484 | −0.204090 | ||||||||
\(283\) | 7430.50 | 1.56077 | 0.780384 | − | 0.625301i | \(-0.215024\pi\) | ||||
0.780384 | + | 0.625301i | \(0.215024\pi\) | |||||||
\(284\) | −1152.00 | −0.240699 | ||||||||
\(285\) | −675.500 | −0.140397 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4512.00 | 0.927996 | ||||||||
\(288\) | 1496.49 | 0.306186 | ||||||||
\(289\) | −4550.00 | −0.926114 | ||||||||
\(290\) | 2220.00 | 0.449527 | ||||||||
\(291\) | −2712.00 | −0.546324 | ||||||||
\(292\) | 3713.52 | 0.744237 | ||||||||
\(293\) | −4460.03 | −0.889276 | −0.444638 | − | 0.895710i | \(-0.646668\pi\) | ||||
−0.444638 | + | 0.895710i | \(0.646668\pi\) | |||||||
\(294\) | −4416.73 | −0.876153 | ||||||||
\(295\) | −2490.00 | −0.491435 | ||||||||
\(296\) | −4267.77 | −0.838038 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1860.00 | 0.361567 | ||||||||
\(299\) | −4416.73 | −0.854268 | ||||||||
\(300\) | 300.000 | 0.0577350 | ||||||||
\(301\) | −1056.00 | −0.202215 | ||||||||
\(302\) | 786.000 | 0.149766 | ||||||||
\(303\) | 3138.48 | 0.595052 | ||||||||
\(304\) | −3602.67 | −0.679694 | ||||||||
\(305\) | −2208.36 | −0.414592 | ||||||||
\(306\) | 594.000 | 0.110970 | ||||||||
\(307\) | 827.920 | 0.153915 | 0.0769575 | − | 0.997034i | \(-0.475479\pi\) | ||||
0.0769575 | + | 0.997034i | \(0.475479\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4056.00 | 0.746724 | ||||||||
\(310\) | −4555.29 | −0.834591 | ||||||||
\(311\) | 6300.00 | 1.14868 | 0.574341 | − | 0.818616i | \(-0.305258\pi\) | ||||
0.574341 | + | 0.818616i | \(0.305258\pi\) | |||||||
\(312\) | 2448.00 | 0.444201 | ||||||||
\(313\) | −2318.00 | −0.418598 | −0.209299 | − | 0.977852i | \(-0.567118\pi\) | ||||
−0.209299 | + | 0.977852i | \(0.567118\pi\) | |||||||
\(314\) | 8923.53 | 1.60377 | ||||||||
\(315\) | 1247.08 | 0.223063 | ||||||||
\(316\) | 4551.83 | 0.810318 | ||||||||
\(317\) | 1767.00 | 0.313074 | 0.156537 | − | 0.987672i | \(-0.449967\pi\) | ||||
0.156537 | + | 0.987672i | \(0.449967\pi\) | |||||||
\(318\) | −5455.96 | −0.962123 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −320.000 | −0.0559017 | ||||||||
\(321\) | 3143.67 | 0.546613 | ||||||||
\(322\) | −7200.00 | −1.24609 | ||||||||
\(323\) | −858.000 | −0.147803 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | 1472.24 | 0.251278 | ||||||||
\(326\) | −5868.19 | −0.996960 | ||||||||
\(327\) | −5611.84 | −0.949039 | ||||||||
\(328\) | −2256.00 | −0.379777 | ||||||||
\(329\) | −2577.29 | −0.431887 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1309.00 | −0.217369 | −0.108685 | − | 0.994076i | \(-0.534664\pi\) | ||||
−0.108685 | + | 0.994076i | \(0.534664\pi\) | |||||||
\(332\) | −2286.31 | −0.377944 | ||||||||
\(333\) | −2772.00 | −0.456170 | ||||||||
\(334\) | −3030.00 | −0.496390 | ||||||||
\(335\) | −1580.00 | −0.257685 | ||||||||
\(336\) | 6651.08 | 1.07990 | ||||||||
\(337\) | −7278.08 | −1.17645 | −0.588223 | − | 0.808699i | \(-0.700172\pi\) | ||||
−0.588223 | + | 0.808699i | \(0.700172\pi\) | |||||||
\(338\) | −4402.87 | −0.708535 | ||||||||
\(339\) | −5913.00 | −0.947345 | ||||||||
\(340\) | 381.051 | 0.0607806 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −1404.00 | −0.221987 | ||||||||
\(343\) | −2272.45 | −0.357728 | ||||||||
\(344\) | 528.000 | 0.0827554 | ||||||||
\(345\) | 1125.00 | 0.175559 | ||||||||
\(346\) | −9936.00 | −1.54382 | ||||||||
\(347\) | −1536.33 | −0.237679 | −0.118839 | − | 0.992914i | \(-0.537917\pi\) | ||||
−0.118839 | + | 0.992914i | \(0.537917\pi\) | |||||||
\(348\) | 1538.06 | 0.236922 | ||||||||
\(349\) | −10806.3 | −1.65744 | −0.828719 | − | 0.559664i | \(-0.810930\pi\) | ||||
−0.828719 | + | 0.559664i | \(0.810930\pi\) | |||||||
\(350\) | 2400.00 | 0.366530 | ||||||||
\(351\) | 1590.02 | 0.241792 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8319.00 | −1.25432 | −0.627161 | − | 0.778890i | \(-0.715783\pi\) | ||||
−0.627161 | + | 0.778890i | \(0.715783\pi\) | |||||||
\(354\) | −5175.37 | −0.777027 | ||||||||
\(355\) | 1440.00 | 0.215288 | ||||||||
\(356\) | −720.000 | −0.107191 | ||||||||
\(357\) | 1584.00 | 0.234830 | ||||||||
\(358\) | 15297.5 | 2.25837 | ||||||||
\(359\) | 10142.9 | 1.49115 | 0.745573 | − | 0.666424i | \(-0.232176\pi\) | ||||
0.745573 | + | 0.666424i | \(0.232176\pi\) | |||||||
\(360\) | −623.538 | −0.0912871 | ||||||||
\(361\) | −4831.00 | −0.704330 | ||||||||
\(362\) | −15346.0 | −2.22808 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6528.00 | −0.940000 | ||||||||
\(365\) | −4641.90 | −0.665666 | ||||||||
\(366\) | −4590.00 | −0.655528 | ||||||||
\(367\) | 1136.00 | 0.161577 | 0.0807884 | − | 0.996731i | \(-0.474256\pi\) | ||||
0.0807884 | + | 0.996731i | \(0.474256\pi\) | |||||||
\(368\) | 6000.00 | 0.849923 | ||||||||
\(369\) | −1465.31 | −0.206724 | ||||||||
\(370\) | −5334.72 | −0.749564 | ||||||||
\(371\) | −14549.2 | −2.03601 | ||||||||
\(372\) | −3156.00 | −0.439868 | ||||||||
\(373\) | −9976.61 | −1.38490 | −0.692452 | − | 0.721464i | \(-0.743470\pi\) | ||||
−0.692452 | + | 0.721464i | \(0.743470\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −375.000 | −0.0516398 | ||||||||
\(376\) | 1288.65 | 0.176747 | ||||||||
\(377\) | 7548.00 | 1.03115 | ||||||||
\(378\) | 2592.00 | 0.352693 | ||||||||
\(379\) | 12929.0 | 1.75229 | 0.876145 | − | 0.482047i | \(-0.160107\pi\) | ||||
0.876145 | + | 0.482047i | \(0.160107\pi\) | |||||||
\(380\) | −900.666 | −0.121587 | ||||||||
\(381\) | −2837.10 | −0.381493 | ||||||||
\(382\) | 16045.7 | 2.14914 | ||||||||
\(383\) | 360.000 | 0.0480291 | 0.0240145 | − | 0.999712i | \(-0.492355\pi\) | ||||
0.0240145 | + | 0.999712i | \(0.492355\pi\) | |||||||
\(384\) | −4655.75 | −0.618718 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10656.0 | 1.40512 | ||||||||
\(387\) | 342.946 | 0.0450463 | ||||||||
\(388\) | −3616.00 | −0.473130 | ||||||||
\(389\) | −3918.00 | −0.510670 | −0.255335 | − | 0.966853i | \(-0.582186\pi\) | ||||
−0.255335 | + | 0.966853i | \(0.582186\pi\) | |||||||
\(390\) | 3060.00 | 0.397305 | ||||||||
\(391\) | 1428.94 | 0.184820 | ||||||||
\(392\) | 5888.97 | 0.758771 | ||||||||
\(393\) | 2941.02 | 0.377494 | ||||||||
\(394\) | 4872.00 | 0.622964 | ||||||||
\(395\) | −5689.79 | −0.724770 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5546.00 | 0.701123 | 0.350561 | − | 0.936540i | \(-0.385991\pi\) | ||||
0.350561 | + | 0.936540i | \(0.385991\pi\) | |||||||
\(398\) | −16464.9 | −2.07364 | ||||||||
\(399\) | −3744.00 | −0.469761 | ||||||||
\(400\) | −2000.00 | −0.250000 | ||||||||
\(401\) | −672.000 | −0.0836860 | −0.0418430 | − | 0.999124i | \(-0.513323\pi\) | ||||
−0.0418430 | + | 0.999124i | \(0.513323\pi\) | |||||||
\(402\) | −3283.97 | −0.407436 | ||||||||
\(403\) | −15488.0 | −1.91442 | ||||||||
\(404\) | 4184.63 | 0.515330 | ||||||||
\(405\) | −405.000 | −0.0496904 | ||||||||
\(406\) | 12304.5 | 1.50409 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −792.000 | −0.0961026 | ||||||||
\(409\) | 226.899 | 0.0274313 | 0.0137157 | − | 0.999906i | \(-0.495634\pi\) | ||||
0.0137157 | + | 0.999906i | \(0.495634\pi\) | |||||||
\(410\) | −2820.00 | −0.339683 | ||||||||
\(411\) | −6507.00 | −0.780941 | ||||||||
\(412\) | 5408.00 | 0.646682 | ||||||||
\(413\) | −13801.0 | −1.64431 | ||||||||
\(414\) | 2338.27 | 0.277584 | ||||||||
\(415\) | 2857.88 | 0.338043 | ||||||||
\(416\) | 9792.00 | 1.15407 | ||||||||
\(417\) | −3008.57 | −0.353310 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4470.00 | 0.521178 | 0.260589 | − | 0.965450i | \(-0.416083\pi\) | ||||
0.260589 | + | 0.965450i | \(0.416083\pi\) | |||||||
\(420\) | 1662.77 | 0.193178 | ||||||||
\(421\) | 5539.00 | 0.641222 | 0.320611 | − | 0.947211i | \(-0.396112\pi\) | ||||
0.320611 | + | 0.947211i | \(0.396112\pi\) | |||||||
\(422\) | −12714.0 | −1.46661 | ||||||||
\(423\) | 837.000 | 0.0962088 | ||||||||
\(424\) | 7274.61 | 0.833223 | ||||||||
\(425\) | −476.314 | −0.0543638 | ||||||||
\(426\) | 2992.98 | 0.340400 | ||||||||
\(427\) | −12240.0 | −1.38720 | ||||||||
\(428\) | 4191.56 | 0.473380 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 660.000 | 0.0740187 | ||||||||
\(431\) | 9980.08 | 1.11537 | 0.557684 | − | 0.830054i | \(-0.311690\pi\) | ||||
0.557684 | + | 0.830054i | \(0.311690\pi\) | |||||||
\(432\) | −2160.00 | −0.240563 | ||||||||
\(433\) | 13526.0 | 1.50120 | 0.750598 | − | 0.660759i | \(-0.229765\pi\) | ||||
0.750598 | + | 0.660759i | \(0.229765\pi\) | |||||||
\(434\) | −25248.0 | −2.79249 | ||||||||
\(435\) | −1922.58 | −0.211909 | ||||||||
\(436\) | −7482.46 | −0.821892 | ||||||||
\(437\) | −3377.50 | −0.369720 | ||||||||
\(438\) | −9648.00 | −1.05251 | ||||||||
\(439\) | 11869.7 | 1.29046 | 0.645230 | − | 0.763988i | \(-0.276762\pi\) | ||||
0.645230 | + | 0.763988i | \(0.276762\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3825.00 | 0.413022 | ||||||||
\(442\) | 3886.72 | 0.418264 | ||||||||
\(443\) | −12108.0 | −1.29857 | −0.649287 | − | 0.760543i | \(-0.724933\pi\) | ||||
−0.649287 | + | 0.760543i | \(0.724933\pi\) | |||||||
\(444\) | −3696.00 | −0.395055 | ||||||||
\(445\) | 900.000 | 0.0958744 | ||||||||
\(446\) | 5563.35 | 0.590655 | ||||||||
\(447\) | −1610.81 | −0.170444 | ||||||||
\(448\) | −1773.62 | −0.187044 | ||||||||
\(449\) | −5586.00 | −0.587126 | −0.293563 | − | 0.955940i | \(-0.594841\pi\) | ||||
−0.293563 | + | 0.955940i | \(0.594841\pi\) | |||||||
\(450\) | −779.423 | −0.0816497 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −7884.00 | −0.820425 | ||||||||
\(453\) | −680.696 | −0.0706002 | ||||||||
\(454\) | 15870.0 | 1.64056 | ||||||||
\(455\) | 8160.00 | 0.840762 | ||||||||
\(456\) | 1872.00 | 0.192247 | ||||||||
\(457\) | −17767.4 | −1.81865 | −0.909325 | − | 0.416087i | \(-0.863401\pi\) | ||||
−0.909325 | + | 0.416087i | \(0.863401\pi\) | |||||||
\(458\) | −13929.2 | −1.42111 | ||||||||
\(459\) | −514.419 | −0.0523116 | ||||||||
\(460\) | 1500.00 | 0.152039 | ||||||||
\(461\) | −17594.2 | −1.77753 | −0.888766 | − | 0.458361i | \(-0.848437\pi\) | ||||
−0.888766 | + | 0.458361i | \(0.848437\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −622.000 | −0.0624337 | −0.0312168 | − | 0.999513i | \(-0.509938\pi\) | ||||
−0.0312168 | + | 0.999513i | \(0.509938\pi\) | |||||||
\(464\) | −10253.7 | −1.02590 | ||||||||
\(465\) | 3945.00 | 0.393430 | ||||||||
\(466\) | 5190.00 | 0.515927 | ||||||||
\(467\) | −14019.0 | −1.38913 | −0.694563 | − | 0.719432i | \(-0.744402\pi\) | ||||
−0.694563 | + | 0.719432i | \(0.744402\pi\) | |||||||
\(468\) | 2120.03 | 0.209398 | ||||||||
\(469\) | −8757.25 | −0.862201 | ||||||||
\(470\) | 1610.81 | 0.158087 | ||||||||
\(471\) | −7728.00 | −0.756024 | ||||||||
\(472\) | 6900.49 | 0.672925 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −11826.0 | −1.14596 | ||||||||
\(475\) | 1125.83 | 0.108751 | ||||||||
\(476\) | 2112.00 | 0.203368 | ||||||||
\(477\) | 4725.00 | 0.453549 | ||||||||
\(478\) | −1884.00 | −0.180276 | ||||||||
\(479\) | −13735.2 | −1.31018 | −0.655089 | − | 0.755551i | \(-0.727369\pi\) | ||||
−0.655089 | + | 0.755551i | \(0.727369\pi\) | |||||||
\(480\) | −2494.15 | −0.237171 | ||||||||
\(481\) | −18138.0 | −1.71938 | ||||||||
\(482\) | −7866.00 | −0.743333 | ||||||||
\(483\) | 6235.38 | 0.587411 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4520.00 | 0.423181 | ||||||||
\(486\) | −841.777 | −0.0785674 | ||||||||
\(487\) | 6982.00 | 0.649660 | 0.324830 | − | 0.945772i | \(-0.394693\pi\) | ||||
0.324830 | + | 0.945772i | \(0.394693\pi\) | |||||||
\(488\) | 6120.00 | 0.567704 | ||||||||
\(489\) | 5082.00 | 0.469971 | ||||||||
\(490\) | 7361.22 | 0.678665 | ||||||||
\(491\) | 6609.51 | 0.607501 | 0.303750 | − | 0.952752i | \(-0.401761\pi\) | ||||
0.303750 | + | 0.952752i | \(0.401761\pi\) | |||||||
\(492\) | −1953.75 | −0.179028 | ||||||||
\(493\) | −2442.00 | −0.223088 | ||||||||
\(494\) | −9186.80 | −0.836708 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 21040.0 | 1.90469 | ||||||||
\(497\) | 7981.29 | 0.720342 | ||||||||
\(498\) | 5940.00 | 0.534494 | ||||||||
\(499\) | −6104.00 | −0.547600 | −0.273800 | − | 0.961787i | \(-0.588281\pi\) | ||||
−0.273800 | + | 0.961787i | \(0.588281\pi\) | |||||||
\(500\) | −500.000 | −0.0447214 | ||||||||
\(501\) | 2624.06 | 0.234000 | ||||||||
\(502\) | 16440.6 | 1.46172 | ||||||||
\(503\) | −12496.7 | −1.10776 | −0.553879 | − | 0.832597i | \(-0.686853\pi\) | ||||
−0.553879 | + | 0.832597i | \(0.686853\pi\) | |||||||
\(504\) | −3456.00 | −0.305441 | ||||||||
\(505\) | −5230.79 | −0.460925 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3813.00 | 0.334006 | ||||||||
\(508\) | −3782.80 | −0.330383 | ||||||||
\(509\) | 5904.00 | 0.514126 | 0.257063 | − | 0.966395i | \(-0.417245\pi\) | ||||
0.257063 | + | 0.966395i | \(0.417245\pi\) | |||||||
\(510\) | −990.000 | −0.0859567 | ||||||||
\(511\) | −25728.0 | −2.22728 | ||||||||
\(512\) | −4434.05 | −0.382733 | ||||||||
\(513\) | 1215.90 | 0.104646 | ||||||||
\(514\) | 9321.90 | 0.799944 | ||||||||
\(515\) | −6760.00 | −0.578410 | ||||||||
\(516\) | 457.261 | 0.0390113 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −29568.0 | −2.50800 | ||||||||
\(519\) | 8604.83 | 0.727765 | ||||||||
\(520\) | −4080.00 | −0.344077 | ||||||||
\(521\) | −22878.0 | −1.92381 | −0.961903 | − | 0.273389i | \(-0.911855\pi\) | ||||
−0.961903 | + | 0.273389i | \(0.911855\pi\) | |||||||
\(522\) | −3996.00 | −0.335058 | ||||||||
\(523\) | −6858.92 | −0.573460 | −0.286730 | − | 0.958011i | \(-0.592568\pi\) | ||||
−0.286730 | + | 0.958011i | \(0.592568\pi\) | |||||||
\(524\) | 3921.36 | 0.326919 | ||||||||
\(525\) | −2078.46 | −0.172784 | ||||||||
\(526\) | 13542.0 | 1.12255 | ||||||||
\(527\) | 5010.82 | 0.414184 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6542.00 | −0.537684 | ||||||||
\(530\) | 9093.27 | 0.745257 | ||||||||
\(531\) | 4482.00 | 0.366294 | ||||||||
\(532\) | −4992.00 | −0.406825 | ||||||||
\(533\) | −9588.00 | −0.779179 | ||||||||
\(534\) | 1870.61 | 0.151591 | ||||||||
\(535\) | −5239.45 | −0.423404 | ||||||||
\(536\) | 4378.62 | 0.352850 | ||||||||
\(537\) | −13248.0 | −1.06461 | ||||||||
\(538\) | 27186.3 | 2.17859 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −540.000 | −0.0430331 | ||||||||
\(541\) | 4240.06 | 0.336958 | 0.168479 | − | 0.985705i | \(-0.446114\pi\) | ||||
0.168479 | + | 0.985705i | \(0.446114\pi\) | |||||||
\(542\) | 16710.0 | 1.32427 | ||||||||
\(543\) | 13290.0 | 1.05033 | ||||||||
\(544\) | −3168.00 | −0.249682 | ||||||||
\(545\) | 9353.07 | 0.735122 | ||||||||
\(546\) | 16960.2 | 1.32936 | ||||||||
\(547\) | −11261.8 | −0.880292 | −0.440146 | − | 0.897926i | \(-0.645073\pi\) | ||||
−0.440146 | + | 0.897926i | \(0.645073\pi\) | |||||||
\(548\) | −8676.00 | −0.676315 | ||||||||
\(549\) | 3975.06 | 0.309019 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5772.00 | 0.446271 | ||||||||
\(552\) | −3117.69 | −0.240394 | ||||||||
\(553\) | −31536.0 | −2.42504 | ||||||||
\(554\) | 16776.0 | 1.28654 | ||||||||
\(555\) | 4620.00 | 0.353348 | ||||||||
\(556\) | −4011.43 | −0.305976 | ||||||||
\(557\) | −14138.7 | −1.07554 | −0.537771 | − | 0.843091i | \(-0.680734\pi\) | ||||
−0.537771 | + | 0.843091i | \(0.680734\pi\) | |||||||
\(558\) | 8199.53 | 0.622068 | ||||||||
\(559\) | 2244.00 | 0.169787 | ||||||||
\(560\) | −11085.1 | −0.836486 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 26592.0 | 1.99594 | ||||||||
\(563\) | 6460.55 | 0.483623 | 0.241811 | − | 0.970323i | \(-0.422258\pi\) | ||||
0.241811 | + | 0.970323i | \(0.422258\pi\) | |||||||
\(564\) | 1116.00 | 0.0833193 | ||||||||
\(565\) | 9855.00 | 0.733811 | ||||||||
\(566\) | −25740.0 | −1.91154 | ||||||||
\(567\) | −2244.74 | −0.166261 | ||||||||
\(568\) | −3990.65 | −0.294795 | ||||||||
\(569\) | 12037.8 | 0.886905 | 0.443452 | − | 0.896298i | \(-0.353754\pi\) | ||||
0.443452 | + | 0.896298i | \(0.353754\pi\) | |||||||
\(570\) | 2340.00 | 0.171951 | ||||||||
\(571\) | 17013.9 | 1.24695 | 0.623477 | − | 0.781841i | \(-0.285719\pi\) | ||||
0.623477 | + | 0.781841i | \(0.285719\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13896.0 | −1.01311 | ||||||||
\(574\) | −15630.0 | −1.13656 | ||||||||
\(575\) | −1875.00 | −0.135988 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | −9788.00 | −0.706204 | −0.353102 | − | 0.935585i | \(-0.614873\pi\) | ||||
−0.353102 | + | 0.935585i | \(0.614873\pi\) | |||||||
\(578\) | 15761.7 | 1.13425 | ||||||||
\(579\) | −9228.37 | −0.662380 | ||||||||
\(580\) | −2563.44 | −0.183519 | ||||||||
\(581\) | 15840.0 | 1.13107 | ||||||||
\(582\) | 9394.64 | 0.669107 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 12864.0 | 0.911500 | ||||||||
\(585\) | −2650.04 | −0.187292 | ||||||||
\(586\) | 15450.0 | 1.08914 | ||||||||
\(587\) | −27633.0 | −1.94299 | −0.971496 | − | 0.237057i | \(-0.923817\pi\) | ||||
−0.971496 | + | 0.237057i | \(0.923817\pi\) | |||||||
\(588\) | 5100.00 | 0.357688 | ||||||||
\(589\) | −11843.8 | −0.828546 | ||||||||
\(590\) | 8625.61 | 0.601883 | ||||||||
\(591\) | −4219.28 | −0.293668 | ||||||||
\(592\) | 24640.0 | 1.71064 | ||||||||
\(593\) | −1960.68 | −0.135777 | −0.0678883 | − | 0.997693i | \(-0.521626\pi\) | ||||
−0.0678883 | + | 0.997693i | \(0.521626\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2640.00 | −0.181898 | ||||||||
\(596\) | −2147.74 | −0.147609 | ||||||||
\(597\) | 14259.0 | 0.977524 | ||||||||
\(598\) | 15300.0 | 1.04626 | ||||||||
\(599\) | 20496.0 | 1.39807 | 0.699035 | − | 0.715088i | \(-0.253613\pi\) | ||||
0.699035 | + | 0.715088i | \(0.253613\pi\) | |||||||
\(600\) | 1039.23 | 0.0707107 | ||||||||
\(601\) | 10399.2 | 0.705813 | 0.352906 | − | 0.935659i | \(-0.385193\pi\) | ||||
0.352906 | + | 0.935659i | \(0.385193\pi\) | |||||||
\(602\) | 3658.09 | 0.247662 | ||||||||
\(603\) | 2844.00 | 0.192067 | ||||||||
\(604\) | −907.595 | −0.0611416 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −10872.0 | −0.728787 | ||||||||
\(607\) | 1953.75 | 0.130643 | 0.0653216 | − | 0.997864i | \(-0.479193\pi\) | ||||
0.0653216 | + | 0.997864i | \(0.479193\pi\) | |||||||
\(608\) | 7488.00 | 0.499471 | ||||||||
\(609\) | −10656.0 | −0.709036 | ||||||||
\(610\) | 7650.00 | 0.507770 | ||||||||
\(611\) | 5476.74 | 0.362627 | ||||||||
\(612\) | −685.892 | −0.0453032 | ||||||||
\(613\) | 5203.08 | 0.342823 | 0.171411 | − | 0.985200i | \(-0.445167\pi\) | ||||
0.171411 | + | 0.985200i | \(0.445167\pi\) | |||||||
\(614\) | −2868.00 | −0.188507 | ||||||||
\(615\) | 2442.19 | 0.160128 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23046.0 | 1.50372 | 0.751861 | − | 0.659321i | \(-0.229156\pi\) | ||||
0.751861 | + | 0.659321i | \(0.229156\pi\) | |||||||
\(618\) | −14050.4 | −0.914547 | ||||||||
\(619\) | −17584.0 | −1.14178 | −0.570889 | − | 0.821027i | \(-0.693401\pi\) | ||||
−0.570889 | + | 0.821027i | \(0.693401\pi\) | |||||||
\(620\) | 5260.00 | 0.340720 | ||||||||
\(621\) | −2025.00 | −0.130854 | ||||||||
\(622\) | −21823.8 | −1.40684 | ||||||||
\(623\) | 4988.31 | 0.320790 | ||||||||
\(624\) | −14133.5 | −0.906721 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 8029.79 | 0.512675 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10304.0 | −0.654736 | ||||||||
\(629\) | 5868.19 | 0.371987 | ||||||||
\(630\) | −4320.00 | −0.273195 | ||||||||
\(631\) | 6925.00 | 0.436894 | 0.218447 | − | 0.975849i | \(-0.429901\pi\) | ||||
0.218447 | + | 0.975849i | \(0.429901\pi\) | |||||||
\(632\) | 15768.0 | 0.992433 | ||||||||
\(633\) | 11010.6 | 0.691365 | ||||||||
\(634\) | −6121.07 | −0.383436 | ||||||||
\(635\) | 4728.50 | 0.295504 | ||||||||
\(636\) | 6300.00 | 0.392785 | ||||||||
\(637\) | 25028.1 | 1.55675 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2592.00 | −0.160466 | ||||||||
\(640\) | 7759.59 | 0.479257 | ||||||||
\(641\) | 5388.00 | 0.332002 | 0.166001 | − | 0.986126i | \(-0.446915\pi\) | ||||
0.166001 | + | 0.986126i | \(0.446915\pi\) | |||||||
\(642\) | −10890.0 | −0.669461 | ||||||||
\(643\) | 17882.0 | 1.09673 | 0.548365 | − | 0.836239i | \(-0.315251\pi\) | ||||
0.548365 | + | 0.836239i | \(0.315251\pi\) | |||||||
\(644\) | 8313.84 | 0.508713 | ||||||||
\(645\) | −571.577 | −0.0348927 | ||||||||
\(646\) | 2972.20 | 0.181021 | ||||||||
\(647\) | 4989.00 | 0.303150 | 0.151575 | − | 0.988446i | \(-0.451566\pi\) | ||||
0.151575 | + | 0.988446i | \(0.451566\pi\) | |||||||
\(648\) | 1122.37 | 0.0680414 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −5100.00 | −0.307751 | ||||||||
\(651\) | 21865.4 | 1.31639 | ||||||||
\(652\) | 6776.00 | 0.407007 | ||||||||
\(653\) | 9258.00 | 0.554814 | 0.277407 | − | 0.960752i | \(-0.410525\pi\) | ||||
0.277407 | + | 0.960752i | \(0.410525\pi\) | |||||||
\(654\) | 19440.0 | 1.16233 | ||||||||
\(655\) | −4901.70 | −0.292405 | ||||||||
\(656\) | 13025.0 | 0.775216 | ||||||||
\(657\) | 8355.41 | 0.496158 | ||||||||
\(658\) | 8928.00 | 0.528951 | ||||||||
\(659\) | 595.825 | 0.0352201 | 0.0176101 | − | 0.999845i | \(-0.494394\pi\) | ||||
0.0176101 | + | 0.999845i | \(0.494394\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11410.0 | 0.671403 | 0.335702 | − | 0.941968i | \(-0.391027\pi\) | ||||
0.335702 | + | 0.941968i | \(0.391027\pi\) | |||||||
\(662\) | 4534.51 | 0.266222 | ||||||||
\(663\) | −3366.00 | −0.197171 | ||||||||
\(664\) | −7920.00 | −0.462885 | ||||||||
\(665\) | 6240.00 | 0.363875 | ||||||||
\(666\) | 9602.49 | 0.558692 | ||||||||
\(667\) | −9612.88 | −0.558039 | ||||||||
\(668\) | 3498.74 | 0.202650 | ||||||||
\(669\) | −4818.00 | −0.278437 | ||||||||
\(670\) | 5473.28 | 0.315599 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −13824.0 | −0.793560 | ||||||||
\(673\) | −24858.4 | −1.42380 | −0.711902 | − | 0.702278i | \(-0.752166\pi\) | ||||
−0.711902 | + | 0.702278i | \(0.752166\pi\) | |||||||
\(674\) | 25212.0 | 1.44085 | ||||||||
\(675\) | 675.000 | 0.0384900 | ||||||||
\(676\) | 5084.00 | 0.289258 | ||||||||
\(677\) | −17805.5 | −1.01081 | −0.505406 | − | 0.862881i | \(-0.668657\pi\) | ||||
−0.505406 | + | 0.862881i | \(0.668657\pi\) | |||||||
\(678\) | 20483.2 | 1.16026 | ||||||||
\(679\) | 25052.4 | 1.41594 | ||||||||
\(680\) | 1320.00 | 0.0744407 | ||||||||
\(681\) | −13743.8 | −0.773369 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25164.0 | −1.40977 | −0.704886 | − | 0.709321i | \(-0.749002\pi\) | ||||
−0.704886 | + | 0.709321i | \(0.749002\pi\) | |||||||
\(684\) | 1621.20 | 0.0906259 | ||||||||
\(685\) | 10845.0 | 0.604914 | ||||||||
\(686\) | 7872.00 | 0.438126 | ||||||||
\(687\) | 12063.0 | 0.669916 | ||||||||
\(688\) | −3048.41 | −0.168924 | ||||||||
\(689\) | 30917.1 | 1.70950 | ||||||||
\(690\) | −3897.11 | −0.215015 | ||||||||
\(691\) | −2707.00 | −0.149029 | −0.0745146 | − | 0.997220i | \(-0.523741\pi\) | ||||
−0.0745146 | + | 0.997220i | \(0.523741\pi\) | |||||||
\(692\) | 11473.1 | 0.630263 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5322.00 | 0.291096 | ||||||||
\(695\) | 5014.29 | 0.273673 | ||||||||
\(696\) | 5328.00 | 0.290169 | ||||||||
\(697\) | 3102.00 | 0.168575 | ||||||||
\(698\) | 37434.0 | 2.02994 | ||||||||
\(699\) | −4494.67 | −0.243210 | ||||||||
\(700\) | −2771.28 | −0.149635 | ||||||||
\(701\) | −3775.87 | −0.203442 | −0.101721 | − | 0.994813i | \(-0.532435\pi\) | ||||
−0.101721 | + | 0.994813i | \(0.532435\pi\) | |||||||
\(702\) | −5508.00 | −0.296134 | ||||||||
\(703\) | −13870.3 | −0.744135 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1395.00 | −0.0745230 | ||||||||
\(706\) | 28817.9 | 1.53622 | ||||||||
\(707\) | −28992.0 | −1.54223 | ||||||||
\(708\) | 5976.00 | 0.317220 | ||||||||
\(709\) | 8119.00 | 0.430064 | 0.215032 | − | 0.976607i | \(-0.431014\pi\) | ||||
0.215032 | + | 0.976607i | \(0.431014\pi\) | |||||||
\(710\) | −4988.31 | −0.263673 | ||||||||
\(711\) | 10241.6 | 0.540212 | ||||||||
\(712\) | −2494.15 | −0.131281 | ||||||||
\(713\) | 19725.0 | 1.03605 | ||||||||
\(714\) | −5487.14 | −0.287606 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −17664.0 | −0.921976 | ||||||||
\(717\) | 1631.59 | 0.0849831 | ||||||||
\(718\) | −35136.0 | −1.82627 | ||||||||
\(719\) | 27042.0 | 1.40264 | 0.701319 | − | 0.712848i | \(-0.252595\pi\) | ||||
0.701319 | + | 0.712848i | \(0.252595\pi\) | |||||||
\(720\) | 3600.00 | 0.186339 | ||||||||
\(721\) | −37467.7 | −1.93533 | ||||||||
\(722\) | 16735.1 | 0.862625 | ||||||||
\(723\) | 6812.16 | 0.350411 | ||||||||
\(724\) | 17720.0 | 0.909611 | ||||||||
\(725\) | 3204.29 | 0.164144 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12290.0 | −0.626975 | −0.313488 | − | 0.949592i | \(-0.601497\pi\) | ||||
−0.313488 | + | 0.949592i | \(0.601497\pi\) | |||||||
\(728\) | −22613.7 | −1.15126 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 16080.0 | 0.815271 | ||||||||
\(731\) | −726.000 | −0.0367334 | ||||||||
\(732\) | 5300.08 | 0.267618 | ||||||||
\(733\) | 1326.75 | 0.0668549 | 0.0334275 | − | 0.999441i | \(-0.489358\pi\) | ||||
0.0334275 | + | 0.999441i | \(0.489358\pi\) | |||||||
\(734\) | −3935.22 | −0.197890 | ||||||||
\(735\) | −6375.00 | −0.319926 | ||||||||
\(736\) | −12470.8 | −0.624563 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 5076.00 | 0.253184 | ||||||||
\(739\) | −4830.69 | −0.240460 | −0.120230 | − | 0.992746i | \(-0.538363\pi\) | ||||
−0.120230 | + | 0.992746i | \(0.538363\pi\) | |||||||
\(740\) | 6160.00 | 0.306008 | ||||||||
\(741\) | 7956.00 | 0.394428 | ||||||||
\(742\) | 50400.0 | 2.49359 | ||||||||
\(743\) | 743.050 | 0.0366889 | 0.0183445 | − | 0.999832i | \(-0.494160\pi\) | ||||
0.0183445 | + | 0.999832i | \(0.494160\pi\) | |||||||
\(744\) | −10932.7 | −0.538726 | ||||||||
\(745\) | 2684.68 | 0.132026 | ||||||||
\(746\) | 34560.0 | 1.69615 | ||||||||
\(747\) | −5144.19 | −0.251963 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −29040.0 | −1.41669 | ||||||||
\(750\) | 1299.04 | 0.0632456 | ||||||||
\(751\) | −10835.0 | −0.526464 | −0.263232 | − | 0.964733i | \(-0.584789\pi\) | ||||
−0.263232 | + | 0.964733i | \(0.584789\pi\) | |||||||
\(752\) | −7440.00 | −0.360783 | ||||||||
\(753\) | −14238.0 | −0.689059 | ||||||||
\(754\) | −26147.0 | −1.26289 | ||||||||
\(755\) | 1134.49 | 0.0546867 | ||||||||
\(756\) | −2992.98 | −0.143986 | ||||||||
\(757\) | −21050.0 | −1.01067 | −0.505334 | − | 0.862924i | \(-0.668631\pi\) | ||||
−0.505334 | + | 0.862924i | \(0.668631\pi\) | |||||||
\(758\) | −44787.4 | −2.14611 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3120.00 | −0.148914 | ||||||||
\(761\) | 26621.6 | 1.26811 | 0.634056 | − | 0.773287i | \(-0.281389\pi\) | ||||
0.634056 | + | 0.773287i | \(0.281389\pi\) | |||||||
\(762\) | 9828.00 | 0.467232 | ||||||||
\(763\) | 51840.0 | 2.45968 | ||||||||
\(764\) | −18528.0 | −0.877382 | ||||||||
\(765\) | 857.365 | 0.0405204 | ||||||||
\(766\) | −1247.08 | −0.0588234 | ||||||||
\(767\) | 29327.1 | 1.38063 | ||||||||
\(768\) | 14592.0 | 0.685603 | ||||||||
\(769\) | 20654.7 | 0.968567 | 0.484283 | − | 0.874911i | \(-0.339080\pi\) | ||||
0.484283 | + | 0.874911i | \(0.339080\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8073.00 | −0.377097 | ||||||||
\(772\) | −12304.5 | −0.573638 | ||||||||
\(773\) | 15435.0 | 0.718187 | 0.359093 | − | 0.933302i | \(-0.383086\pi\) | ||||
0.359093 | + | 0.933302i | \(0.383086\pi\) | |||||||
\(774\) | −1188.00 | −0.0551703 | ||||||||
\(775\) | −6575.00 | −0.304750 | ||||||||
\(776\) | −12526.2 | −0.579464 | ||||||||
\(777\) | 25606.6 | 1.18228 | ||||||||
\(778\) | 13572.4 | 0.625440 | ||||||||
\(779\) | −7332.00 | −0.337222 | ||||||||
\(780\) | −3533.38 | −0.162199 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −4950.00 | −0.226358 | ||||||||
\(783\) | 3460.64 | 0.157948 | ||||||||
\(784\) | −34000.0 | −1.54883 | ||||||||
\(785\) | 12880.0 | 0.585614 | ||||||||
\(786\) | −10188.0 | −0.462333 | ||||||||
\(787\) | 10149.8 | 0.459723 | 0.229861 | − | 0.973223i | \(-0.426173\pi\) | ||||
0.229861 | + | 0.973223i | \(0.426173\pi\) | |||||||
\(788\) | −5625.70 | −0.254324 | ||||||||
\(789\) | −11727.7 | −0.529173 | ||||||||
\(790\) | 19710.0 | 0.887659 | ||||||||
\(791\) | 54622.0 | 2.45529 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26010.0 | 1.16474 | ||||||||
\(794\) | −19211.9 | −0.858697 | ||||||||
\(795\) | −7875.00 | −0.351318 | ||||||||
\(796\) | 19012.0 | 0.846561 | ||||||||
\(797\) | −954.000 | −0.0423995 | −0.0211998 | − | 0.999775i | \(-0.506749\pi\) | ||||
−0.0211998 | + | 0.999775i | \(0.506749\pi\) | |||||||
\(798\) | 12969.6 | 0.575337 | ||||||||
\(799\) | −1771.89 | −0.0784542 | ||||||||
\(800\) | 4156.92 | 0.183712 | ||||||||
\(801\) | −1620.00 | −0.0714605 | ||||||||
\(802\) | 2327.88 | 0.102494 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 3792.00 | 0.166335 | ||||||||
\(805\) | −10392.3 | −0.455007 | ||||||||
\(806\) | 53652.0 | 2.34468 | ||||||||
\(807\) | −23544.0 | −1.02700 | ||||||||
\(808\) | 14496.0 | 0.631148 | ||||||||
\(809\) | −33421.7 | −1.45246 | −0.726232 | − | 0.687450i | \(-0.758730\pi\) | ||||
−0.726232 | + | 0.687450i | \(0.758730\pi\) | |||||||
\(810\) | 1402.96 | 0.0608581 | ||||||||
\(811\) | −3386.16 | −0.146614 | −0.0733071 | − | 0.997309i | \(-0.523355\pi\) | ||||
−0.0733071 | + | 0.997309i | \(0.523355\pi\) | |||||||
\(812\) | −14208.0 | −0.614043 | ||||||||
\(813\) | −14471.3 | −0.624268 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8470.00 | −0.364038 | ||||||||
\(816\) | 4572.61 | 0.196169 | ||||||||
\(817\) | 1716.00 | 0.0734825 | ||||||||
\(818\) | −786.000 | −0.0335964 | ||||||||
\(819\) | −14688.0 | −0.626667 | ||||||||
\(820\) | 3256.26 | 0.138675 | ||||||||
\(821\) | 35462.0 | 1.50747 | 0.753735 | − | 0.657179i | \(-0.228250\pi\) | ||||
0.753735 | + | 0.657179i | \(0.228250\pi\) | |||||||
\(822\) | 22540.9 | 0.956453 | ||||||||
\(823\) | −5668.00 | −0.240066 | −0.120033 | − | 0.992770i | \(-0.538300\pi\) | ||||
−0.120033 | + | 0.992770i | \(0.538300\pi\) | |||||||
\(824\) | 18733.9 | 0.792021 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 47808.0 | 2.01387 | ||||||||
\(827\) | −24397.7 | −1.02586 | −0.512932 | − | 0.858429i | \(-0.671441\pi\) | ||||
−0.512932 | + | 0.858429i | \(0.671441\pi\) | |||||||
\(828\) | −2700.00 | −0.113323 | ||||||||
\(829\) | −27889.0 | −1.16843 | −0.584213 | − | 0.811600i | \(-0.698597\pi\) | ||||
−0.584213 | + | 0.811600i | \(0.698597\pi\) | |||||||
\(830\) | −9900.00 | −0.414017 | ||||||||
\(831\) | −14528.4 | −0.606481 | ||||||||
\(832\) | 3768.94 | 0.157049 | ||||||||
\(833\) | −8097.34 | −0.336802 | ||||||||
\(834\) | 10422.0 | 0.432715 | ||||||||
\(835\) | −4373.43 | −0.181256 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7101.00 | −0.293245 | ||||||||
\(838\) | −15484.5 | −0.638311 | ||||||||
\(839\) | −38220.0 | −1.57271 | −0.786353 | − | 0.617777i | \(-0.788033\pi\) | ||||
−0.786353 | + | 0.617777i | \(0.788033\pi\) | |||||||
\(840\) | 5760.00 | 0.236594 | ||||||||
\(841\) | −7961.00 | −0.326418 | ||||||||
\(842\) | −19187.7 | −0.785333 | ||||||||
\(843\) | −23029.3 | −0.940893 | ||||||||
\(844\) | 14680.9 | 0.598739 | ||||||||
\(845\) | −6355.00 | −0.258720 | ||||||||
\(846\) | −2899.45 | −0.117831 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −42000.0 | −1.70081 | ||||||||
\(849\) | 22291.5 | 0.901110 | ||||||||
\(850\) | 1650.00 | 0.0665818 | ||||||||
\(851\) | 23100.0 | 0.930503 | ||||||||
\(852\) | −3456.00 | −0.138968 | ||||||||
\(853\) | −45459.4 | −1.82474 | −0.912368 | − | 0.409370i | \(-0.865748\pi\) | ||||
−0.912368 | + | 0.409370i | \(0.865748\pi\) | |||||||
\(854\) | 42400.6 | 1.69897 | ||||||||
\(855\) | −2026.50 | −0.0810583 | ||||||||
\(856\) | 14520.0 | 0.579770 | ||||||||
\(857\) | −24728.5 | −0.985658 | −0.492829 | − | 0.870126i | \(-0.664037\pi\) | ||||
−0.492829 | + | 0.870126i | \(0.664037\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18556.0 | −0.737046 | −0.368523 | − | 0.929619i | \(-0.620136\pi\) | ||||
−0.368523 | + | 0.929619i | \(0.620136\pi\) | |||||||
\(860\) | −762.102 | −0.0302180 | ||||||||
\(861\) | 13536.0 | 0.535779 | ||||||||
\(862\) | −34572.0 | −1.36604 | ||||||||
\(863\) | 41088.0 | 1.62069 | 0.810343 | − | 0.585956i | \(-0.199281\pi\) | ||||
0.810343 | + | 0.585956i | \(0.199281\pi\) | |||||||
\(864\) | 4489.48 | 0.176777 | ||||||||
\(865\) | −14341.4 | −0.563724 | ||||||||
\(866\) | −46855.4 | −1.83858 | ||||||||
\(867\) | −13650.0 | −0.534692 | ||||||||
\(868\) | 29153.9 | 1.14003 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 6660.00 | 0.259535 | ||||||||
\(871\) | 18609.2 | 0.723935 | ||||||||
\(872\) | −25920.0 | −1.00661 | ||||||||
\(873\) | −8136.00 | −0.315420 | ||||||||
\(874\) | 11700.0 | 0.452813 | ||||||||
\(875\) | 3464.10 | 0.133838 | ||||||||
\(876\) | 11140.6 | 0.429685 | ||||||||
\(877\) | −7520.56 | −0.289568 | −0.144784 | − | 0.989463i | \(-0.546249\pi\) | ||||
−0.144784 | + | 0.989463i | \(0.546249\pi\) | |||||||
\(878\) | −41118.0 | −1.58048 | ||||||||
\(879\) | −13380.1 | −0.513424 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19320.0 | 0.738828 | 0.369414 | − | 0.929265i | \(-0.379558\pi\) | ||||
0.369414 | + | 0.929265i | \(0.379558\pi\) | |||||||
\(882\) | −13250.2 | −0.505847 | ||||||||
\(883\) | 5818.00 | 0.221734 | 0.110867 | − | 0.993835i | \(-0.464637\pi\) | ||||
0.110867 | + | 0.993835i | \(0.464637\pi\) | |||||||
\(884\) | −4488.00 | −0.170755 | ||||||||
\(885\) | −7470.00 | −0.283730 | ||||||||
\(886\) | 41943.3 | 1.59042 | ||||||||
\(887\) | 30667.7 | 1.16090 | 0.580451 | − | 0.814295i | \(-0.302876\pi\) | ||||
0.580451 | + | 0.814295i | \(0.302876\pi\) | |||||||
\(888\) | −12803.3 | −0.483842 | ||||||||
\(889\) | 26208.0 | 0.988738 | ||||||||
\(890\) | −3117.69 | −0.117422 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6424.00 | −0.241134 | ||||||||
\(893\) | 4188.10 | 0.156942 | ||||||||
\(894\) | 5580.00 | 0.208751 | ||||||||
\(895\) | 22080.0 | 0.824640 | ||||||||
\(896\) | 43008.0 | 1.60357 | ||||||||
\(897\) | −13250.2 | −0.493212 | ||||||||
\(898\) | 19350.5 | 0.719080 | ||||||||
\(899\) | −33709.2 | −1.25057 | ||||||||
\(900\) | 900.000 | 0.0333333 | ||||||||
\(901\) | −10002.6 | −0.369850 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3168.00 | −0.116749 | ||||||||
\(904\) | −27311.0 | −1.00481 | ||||||||
\(905\) | −22150.0 | −0.813581 | ||||||||
\(906\) | 2358.00 | 0.0864672 | ||||||||
\(907\) | −31474.0 | −1.15223 | −0.576117 | − | 0.817367i | \(-0.695433\pi\) | ||||
−0.576117 | + | 0.817367i | \(0.695433\pi\) | |||||||
\(908\) | −18325.1 | −0.669757 | ||||||||
\(909\) | 9415.43 | 0.343553 | ||||||||
\(910\) | −28267.1 | −1.02972 | ||||||||
\(911\) | 16560.0 | 0.602258 | 0.301129 | − | 0.953583i | \(-0.402636\pi\) | ||||
0.301129 | + | 0.953583i | \(0.402636\pi\) | |||||||
\(912\) | −10808.0 | −0.392422 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 61548.0 | 2.22738 | ||||||||
\(915\) | −6625.09 | −0.239365 | ||||||||
\(916\) | 16084.0 | 0.580164 | ||||||||
\(917\) | −27168.0 | −0.978371 | ||||||||
\(918\) | 1782.00 | 0.0640684 | ||||||||
\(919\) | 13617.4 | 0.488788 | 0.244394 | − | 0.969676i | \(-0.421411\pi\) | ||||
0.244394 | + | 0.969676i | \(0.421411\pi\) | |||||||
\(920\) | 5196.15 | 0.186209 | ||||||||
\(921\) | 2483.76 | 0.0888629 | ||||||||
\(922\) | 60948.0 | 2.17702 | ||||||||
\(923\) | −16960.2 | −0.604825 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7700.00 | −0.273702 | ||||||||
\(926\) | 2154.67 | 0.0764653 | ||||||||
\(927\) | 12168.0 | 0.431121 | ||||||||
\(928\) | 21312.0 | 0.753880 | ||||||||
\(929\) | −2634.00 | −0.0930234 | −0.0465117 | − | 0.998918i | \(-0.514810\pi\) | ||||
−0.0465117 | + | 0.998918i | \(0.514810\pi\) | |||||||
\(930\) | −13665.9 | −0.481851 | ||||||||
\(931\) | 19139.2 | 0.673749 | ||||||||
\(932\) | −5992.90 | −0.210626 | ||||||||
\(933\) | 18900.0 | 0.663192 | ||||||||
\(934\) | 48563.2 | 1.70133 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7344.00 | 0.256460 | ||||||||
\(937\) | 48455.9 | 1.68942 | 0.844709 | − | 0.535227i | \(-0.179774\pi\) | ||||
0.844709 | + | 0.535227i | \(0.179774\pi\) | |||||||
\(938\) | 30336.0 | 1.05598 | ||||||||
\(939\) | −6954.00 | −0.241678 | ||||||||
\(940\) | −1860.00 | −0.0645388 | ||||||||
\(941\) | 33861.6 | 1.17307 | 0.586534 | − | 0.809925i | \(-0.300492\pi\) | ||||
0.586534 | + | 0.809925i | \(0.300492\pi\) | |||||||
\(942\) | 26770.6 | 0.925937 | ||||||||
\(943\) | 12211.0 | 0.421679 | ||||||||
\(944\) | −39840.0 | −1.37360 | ||||||||
\(945\) | 3741.23 | 0.128785 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4557.00 | −0.156370 | −0.0781851 | − | 0.996939i | \(-0.524913\pi\) | ||||
−0.0781851 | + | 0.996939i | \(0.524913\pi\) | |||||||
\(948\) | 13655.5 | 0.467837 | ||||||||
\(949\) | 54672.0 | 1.87010 | ||||||||
\(950\) | −3900.00 | −0.133192 | ||||||||
\(951\) | 5301.00 | 0.180754 | ||||||||
\(952\) | 7316.18 | 0.249074 | ||||||||
\(953\) | 36601.7 | 1.24412 | 0.622059 | − | 0.782970i | \(-0.286296\pi\) | ||||
0.622059 | + | 0.782970i | \(0.286296\pi\) | |||||||
\(954\) | −16367.9 | −0.555482 | ||||||||
\(955\) | 23160.0 | 0.784754 | ||||||||
\(956\) | 2175.46 | 0.0735976 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 47580.0 | 1.60463 | ||||||||
\(959\) | 60109.1 | 2.02401 | ||||||||
\(960\) | −960.000 | −0.0322749 | ||||||||
\(961\) | 39378.0 | 1.32181 | ||||||||
\(962\) | 62832.0 | 2.10581 | ||||||||
\(963\) | 9431.02 | 0.315587 | ||||||||
\(964\) | 9082.87 | 0.303464 | ||||||||
\(965\) | 15380.6 | 0.513077 | ||||||||
\(966\) | −21600.0 | −0.719429 | ||||||||
\(967\) | 12242.1 | 0.407115 | 0.203558 | − | 0.979063i | \(-0.434750\pi\) | ||||
0.203558 | + | 0.979063i | \(0.434750\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2574.00 | −0.0853342 | ||||||||
\(970\) | −15657.7 | −0.518288 | ||||||||
\(971\) | 31398.0 | 1.03770 | 0.518852 | − | 0.854864i | \(-0.326360\pi\) | ||||
0.518852 | + | 0.854864i | \(0.326360\pi\) | |||||||
\(972\) | 972.000 | 0.0320750 | ||||||||
\(973\) | 27792.0 | 0.915694 | ||||||||
\(974\) | −24186.4 | −0.795668 | ||||||||
\(975\) | 4416.73 | 0.145075 | ||||||||
\(976\) | −35333.8 | −1.15882 | ||||||||
\(977\) | −54783.0 | −1.79392 | −0.896962 | − | 0.442108i | \(-0.854231\pi\) | ||||
−0.896962 | + | 0.442108i | \(0.854231\pi\) | |||||||
\(978\) | −17604.6 | −0.575595 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −8500.00 | −0.277064 | ||||||||
\(981\) | −16835.5 | −0.547928 | ||||||||
\(982\) | −22896.0 | −0.744033 | ||||||||
\(983\) | −14325.0 | −0.464798 | −0.232399 | − | 0.972621i | \(-0.574658\pi\) | ||||
−0.232399 | + | 0.972621i | \(0.574658\pi\) | |||||||
\(984\) | −6768.00 | −0.219264 | ||||||||
\(985\) | 7032.13 | 0.227474 | ||||||||
\(986\) | 8459.34 | 0.273225 | ||||||||
\(987\) | −7731.87 | −0.249350 | ||||||||
\(988\) | 10608.0 | 0.341584 | ||||||||
\(989\) | −2857.88 | −0.0918862 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17017.0 | 0.545472 | 0.272736 | − | 0.962089i | \(-0.412071\pi\) | ||||
0.272736 | + | 0.962089i | \(0.412071\pi\) | |||||||
\(992\) | −43730.8 | −1.39965 | ||||||||
\(993\) | −3927.00 | −0.125498 | ||||||||
\(994\) | −27648.0 | −0.882235 | ||||||||
\(995\) | −23765.0 | −0.757187 | ||||||||
\(996\) | −6858.92 | −0.218206 | ||||||||
\(997\) | 4964.06 | 0.157686 | 0.0788432 | − | 0.996887i | \(-0.474877\pi\) | ||||
0.0788432 | + | 0.996887i | \(0.474877\pi\) | |||||||
\(998\) | 21144.9 | 0.670671 | ||||||||
\(999\) | −8316.00 | −0.263370 |
(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 | 1815.4.a.k.1.1 | ✓ | 2 | |
11.10 | odd | 2 | inner | 1815.4.a.k.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1815.4.a.k.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1815.4.a.k.1.2 | yes | 2 | 11.10 | odd | 2 | inner |