Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,4,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.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: | \(17.0515519917\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{12} - 72 x^{10} - 17 x^{9} + 1872 x^{8} + 627 x^{7} - 20922 x^{6} - 5163 x^{5} + 93255 x^{4} - 4607 x^{3} - 117822 x^{2} + 21960 x + 29352 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3}\cdot 17^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-0.447590\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.447590 | 0.158247 | 0.0791235 | − | 0.996865i | \(-0.474788\pi\) | ||||
0.0791235 | + | 0.996865i | \(0.474788\pi\) | |||||||
\(3\) | −9.51519 | −1.83120 | −0.915599 | − | 0.402092i | \(-0.868283\pi\) | ||||
−0.915599 | + | 0.402092i | \(0.868283\pi\) | |||||||
\(4\) | −7.79966 | −0.974958 | ||||||||
\(5\) | 11.7425 | 1.05028 | 0.525142 | − | 0.851015i | \(-0.324012\pi\) | ||||
0.525142 | + | 0.851015i | \(0.324012\pi\) | |||||||
\(6\) | −4.25890 | −0.289782 | ||||||||
\(7\) | −2.27797 | −0.122999 | −0.0614994 | − | 0.998107i | \(-0.519588\pi\) | ||||
−0.0614994 | + | 0.998107i | \(0.519588\pi\) | |||||||
\(8\) | −7.07177 | −0.312531 | ||||||||
\(9\) | 63.5388 | 2.35329 | ||||||||
\(10\) | 5.25584 | 0.166204 | ||||||||
\(11\) | −22.6868 | −0.621848 | −0.310924 | − | 0.950435i | \(-0.600638\pi\) | ||||
−0.310924 | + | 0.950435i | \(0.600638\pi\) | |||||||
\(12\) | 74.2152 | 1.78534 | ||||||||
\(13\) | 67.4022 | 1.43800 | 0.719001 | − | 0.695009i | \(-0.244600\pi\) | ||||
0.719001 | + | 0.695009i | \(0.244600\pi\) | |||||||
\(14\) | −1.01960 | −0.0194642 | ||||||||
\(15\) | −111.732 | −1.92328 | ||||||||
\(16\) | 59.2321 | 0.925501 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 28.4393 | 0.372400 | ||||||||
\(19\) | 42.9965 | 0.519161 | 0.259581 | − | 0.965721i | \(-0.416416\pi\) | ||||
0.259581 | + | 0.965721i | \(0.416416\pi\) | |||||||
\(20\) | −91.5878 | −1.02398 | ||||||||
\(21\) | 21.6753 | 0.225235 | ||||||||
\(22\) | −10.1544 | −0.0984055 | ||||||||
\(23\) | −117.444 | −1.06473 | −0.532364 | − | 0.846516i | \(-0.678696\pi\) | ||||
−0.532364 | + | 0.846516i | \(0.678696\pi\) | |||||||
\(24\) | 67.2892 | 0.572306 | ||||||||
\(25\) | 12.8870 | 0.103096 | ||||||||
\(26\) | 30.1686 | 0.227559 | ||||||||
\(27\) | −347.673 | −2.47814 | ||||||||
\(28\) | 17.7674 | 0.119919 | ||||||||
\(29\) | −226.336 | −1.44930 | −0.724648 | − | 0.689120i | \(-0.757997\pi\) | ||||
−0.724648 | + | 0.689120i | \(0.757997\pi\) | |||||||
\(30\) | −50.0103 | −0.304353 | ||||||||
\(31\) | 0.673139 | 0.00389998 | 0.00194999 | − | 0.999998i | \(-0.499379\pi\) | ||||
0.00194999 | + | 0.999998i | \(0.499379\pi\) | |||||||
\(32\) | 83.0858 | 0.458989 | ||||||||
\(33\) | 215.869 | 1.13873 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −26.7491 | −0.129184 | ||||||||
\(36\) | −495.581 | −2.29436 | ||||||||
\(37\) | 99.9003 | 0.443878 | 0.221939 | − | 0.975060i | \(-0.428761\pi\) | ||||
0.221939 | + | 0.975060i | \(0.428761\pi\) | |||||||
\(38\) | 19.2448 | 0.0821557 | ||||||||
\(39\) | −641.345 | −2.63327 | ||||||||
\(40\) | −83.0405 | −0.328246 | ||||||||
\(41\) | 154.092 | 0.586956 | 0.293478 | − | 0.955966i | \(-0.405187\pi\) | ||||
0.293478 | + | 0.955966i | \(0.405187\pi\) | |||||||
\(42\) | 9.70165 | 0.0356428 | ||||||||
\(43\) | −321.792 | −1.14123 | −0.570615 | − | 0.821218i | \(-0.693295\pi\) | ||||
−0.570615 | + | 0.821218i | \(0.693295\pi\) | |||||||
\(44\) | 176.949 | 0.606275 | ||||||||
\(45\) | 746.106 | 2.47162 | ||||||||
\(46\) | −52.5667 | −0.168490 | ||||||||
\(47\) | −30.4214 | −0.0944132 | −0.0472066 | − | 0.998885i | \(-0.515032\pi\) | ||||
−0.0472066 | + | 0.998885i | \(0.515032\pi\) | |||||||
\(48\) | −563.604 | −1.69478 | ||||||||
\(49\) | −337.811 | −0.984871 | ||||||||
\(50\) | 5.76808 | 0.0163146 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −525.715 | −1.40199 | ||||||||
\(53\) | −361.595 | −0.937148 | −0.468574 | − | 0.883424i | \(-0.655232\pi\) | ||||
−0.468574 | + | 0.883424i | \(0.655232\pi\) | |||||||
\(54\) | −155.615 | −0.392158 | ||||||||
\(55\) | −266.400 | −0.653116 | ||||||||
\(56\) | 16.1093 | 0.0384410 | ||||||||
\(57\) | −409.119 | −0.950687 | ||||||||
\(58\) | −101.306 | −0.229347 | ||||||||
\(59\) | 147.417 | 0.325289 | 0.162645 | − | 0.986685i | \(-0.447998\pi\) | ||||
0.162645 | + | 0.986685i | \(0.447998\pi\) | |||||||
\(60\) | 871.475 | 1.87511 | ||||||||
\(61\) | −321.075 | −0.673925 | −0.336963 | − | 0.941518i | \(-0.609400\pi\) | ||||
−0.336963 | + | 0.941518i | \(0.609400\pi\) | |||||||
\(62\) | 0.301290 | 0.000617160 0 | ||||||||
\(63\) | −144.739 | −0.289452 | ||||||||
\(64\) | −436.668 | −0.852867 | ||||||||
\(65\) | 791.473 | 1.51031 | ||||||||
\(66\) | 96.6208 | 0.180200 | ||||||||
\(67\) | 612.509 | 1.11686 | 0.558432 | − | 0.829550i | \(-0.311403\pi\) | ||||
0.558432 | + | 0.829550i | \(0.311403\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1117.50 | 1.94973 | ||||||||
\(70\) | −11.9726 | −0.0204429 | ||||||||
\(71\) | −248.823 | −0.415913 | −0.207956 | − | 0.978138i | \(-0.566681\pi\) | ||||
−0.207956 | + | 0.978138i | \(0.566681\pi\) | |||||||
\(72\) | −449.331 | −0.735475 | ||||||||
\(73\) | 701.031 | 1.12397 | 0.561983 | − | 0.827149i | \(-0.310039\pi\) | ||||
0.561983 | + | 0.827149i | \(0.310039\pi\) | |||||||
\(74\) | 44.7144 | 0.0702424 | ||||||||
\(75\) | −122.622 | −0.188789 | ||||||||
\(76\) | −335.358 | −0.506160 | ||||||||
\(77\) | 51.6798 | 0.0764865 | ||||||||
\(78\) | −287.059 | −0.416706 | ||||||||
\(79\) | −773.040 | −1.10093 | −0.550467 | − | 0.834857i | \(-0.685550\pi\) | ||||
−0.550467 | + | 0.834857i | \(0.685550\pi\) | |||||||
\(80\) | 695.534 | 0.972038 | ||||||||
\(81\) | 1592.63 | 2.18467 | ||||||||
\(82\) | 68.9702 | 0.0928840 | ||||||||
\(83\) | −1005.91 | −1.33028 | −0.665139 | − | 0.746720i | \(-0.731628\pi\) | ||||
−0.665139 | + | 0.746720i | \(0.731628\pi\) | |||||||
\(84\) | −169.060 | −0.219595 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −144.031 | −0.180596 | ||||||||
\(87\) | 2153.63 | 2.65395 | ||||||||
\(88\) | 160.436 | 0.194347 | ||||||||
\(89\) | 1641.08 | 1.95454 | 0.977271 | − | 0.211994i | \(-0.0679958\pi\) | ||||
0.977271 | + | 0.211994i | \(0.0679958\pi\) | |||||||
\(90\) | 333.949 | 0.391126 | ||||||||
\(91\) | −153.540 | −0.176872 | ||||||||
\(92\) | 916.023 | 1.03806 | ||||||||
\(93\) | −6.40505 | −0.00714164 | ||||||||
\(94\) | −13.6163 | −0.0149406 | ||||||||
\(95\) | 504.887 | 0.545267 | ||||||||
\(96\) | −790.577 | −0.840499 | ||||||||
\(97\) | 479.663 | 0.502087 | 0.251043 | − | 0.967976i | \(-0.419226\pi\) | ||||
0.251043 | + | 0.967976i | \(0.419226\pi\) | |||||||
\(98\) | −151.201 | −0.155853 | ||||||||
\(99\) | −1441.49 | −1.46339 | ||||||||
\(100\) | −100.514 | −0.100514 | ||||||||
\(101\) | −814.043 | −0.801984 | −0.400992 | − | 0.916082i | \(-0.631334\pi\) | ||||
−0.400992 | + | 0.916082i | \(0.631334\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −543.806 | −0.520222 | −0.260111 | − | 0.965579i | \(-0.583759\pi\) | ||||
−0.260111 | + | 0.965579i | \(0.583759\pi\) | |||||||
\(104\) | −476.653 | −0.449420 | ||||||||
\(105\) | 254.523 | 0.236561 | ||||||||
\(106\) | −161.846 | −0.148301 | ||||||||
\(107\) | 171.706 | 0.155135 | 0.0775673 | − | 0.996987i | \(-0.475285\pi\) | ||||
0.0775673 | + | 0.996987i | \(0.475285\pi\) | |||||||
\(108\) | 2711.73 | 2.41608 | ||||||||
\(109\) | −1310.16 | −1.15129 | −0.575644 | − | 0.817700i | \(-0.695249\pi\) | ||||
−0.575644 | + | 0.817700i | \(0.695249\pi\) | |||||||
\(110\) | −119.238 | −0.103354 | ||||||||
\(111\) | −950.570 | −0.812830 | ||||||||
\(112\) | −134.929 | −0.113836 | ||||||||
\(113\) | −879.939 | −0.732546 | −0.366273 | − | 0.930507i | \(-0.619366\pi\) | ||||
−0.366273 | + | 0.930507i | \(0.619366\pi\) | |||||||
\(114\) | −183.118 | −0.150443 | ||||||||
\(115\) | −1379.09 | −1.11827 | ||||||||
\(116\) | 1765.35 | 1.41300 | ||||||||
\(117\) | 4282.65 | 3.38403 | ||||||||
\(118\) | 65.9824 | 0.0514760 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 790.145 | 0.601084 | ||||||||
\(121\) | −816.310 | −0.613306 | ||||||||
\(122\) | −143.710 | −0.106647 | ||||||||
\(123\) | −1466.22 | −1.07483 | ||||||||
\(124\) | −5.25026 | −0.00380232 | ||||||||
\(125\) | −1316.49 | −0.942004 | ||||||||
\(126\) | −64.7839 | −0.0458048 | ||||||||
\(127\) | −1303.39 | −0.910684 | −0.455342 | − | 0.890317i | \(-0.650483\pi\) | ||||
−0.455342 | + | 0.890317i | \(0.650483\pi\) | |||||||
\(128\) | −860.135 | −0.593952 | ||||||||
\(129\) | 3061.91 | 2.08982 | ||||||||
\(130\) | 354.255 | 0.239002 | ||||||||
\(131\) | −1523.87 | −1.01634 | −0.508171 | − | 0.861256i | \(-0.669678\pi\) | ||||
−0.508171 | + | 0.861256i | \(0.669678\pi\) | |||||||
\(132\) | −1683.71 | −1.11021 | ||||||||
\(133\) | −97.9447 | −0.0638562 | ||||||||
\(134\) | 274.153 | 0.176740 | ||||||||
\(135\) | −4082.56 | −2.60275 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2617.59 | −1.63238 | −0.816189 | − | 0.577785i | \(-0.803917\pi\) | ||||
−0.816189 | + | 0.577785i | \(0.803917\pi\) | |||||||
\(138\) | 500.182 | 0.308538 | ||||||||
\(139\) | 232.950 | 0.142148 | 0.0710741 | − | 0.997471i | \(-0.477357\pi\) | ||||
0.0710741 | + | 0.997471i | \(0.477357\pi\) | |||||||
\(140\) | 208.634 | 0.125949 | ||||||||
\(141\) | 289.466 | 0.172889 | ||||||||
\(142\) | −111.370 | −0.0658169 | ||||||||
\(143\) | −1529.14 | −0.894218 | ||||||||
\(144\) | 3763.53 | 2.17797 | ||||||||
\(145\) | −2657.76 | −1.52217 | ||||||||
\(146\) | 313.774 | 0.177864 | ||||||||
\(147\) | 3214.33 | 1.80349 | ||||||||
\(148\) | −779.189 | −0.432763 | ||||||||
\(149\) | 429.754 | 0.236287 | 0.118144 | − | 0.992997i | \(-0.462306\pi\) | ||||
0.118144 | + | 0.992997i | \(0.462306\pi\) | |||||||
\(150\) | −54.8844 | −0.0298753 | ||||||||
\(151\) | −1373.00 | −0.739953 | −0.369976 | − | 0.929041i | \(-0.620634\pi\) | ||||
−0.369976 | + | 0.929041i | \(0.620634\pi\) | |||||||
\(152\) | −304.061 | −0.162254 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 23.1314 | 0.0121038 | ||||||||
\(155\) | 7.90436 | 0.00409609 | ||||||||
\(156\) | 5002.27 | 2.56732 | ||||||||
\(157\) | 616.059 | 0.313165 | 0.156582 | − | 0.987665i | \(-0.449952\pi\) | ||||
0.156582 | + | 0.987665i | \(0.449952\pi\) | |||||||
\(158\) | −346.005 | −0.174220 | ||||||||
\(159\) | 3440.64 | 1.71610 | ||||||||
\(160\) | 975.638 | 0.482068 | ||||||||
\(161\) | 267.534 | 0.130960 | ||||||||
\(162\) | 712.844 | 0.345718 | ||||||||
\(163\) | 3460.81 | 1.66301 | 0.831507 | − | 0.555515i | \(-0.187479\pi\) | ||||
0.831507 | + | 0.555515i | \(0.187479\pi\) | |||||||
\(164\) | −1201.87 | −0.572257 | ||||||||
\(165\) | 2534.85 | 1.19599 | ||||||||
\(166\) | −450.235 | −0.210512 | ||||||||
\(167\) | 2424.76 | 1.12355 | 0.561777 | − | 0.827288i | \(-0.310118\pi\) | ||||
0.561777 | + | 0.827288i | \(0.310118\pi\) | |||||||
\(168\) | −153.283 | −0.0703930 | ||||||||
\(169\) | 2346.06 | 1.06785 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2731.94 | 1.22174 | ||||||||
\(172\) | 2509.87 | 1.11265 | ||||||||
\(173\) | −2853.14 | −1.25388 | −0.626938 | − | 0.779069i | \(-0.715692\pi\) | ||||
−0.626938 | + | 0.779069i | \(0.715692\pi\) | |||||||
\(174\) | 963.943 | 0.419979 | ||||||||
\(175\) | −29.3562 | −0.0126807 | ||||||||
\(176\) | −1343.79 | −0.575521 | ||||||||
\(177\) | −1402.70 | −0.595669 | ||||||||
\(178\) | 734.531 | 0.309300 | ||||||||
\(179\) | 1195.13 | 0.499040 | 0.249520 | − | 0.968370i | \(-0.419727\pi\) | ||||
0.249520 | + | 0.968370i | \(0.419727\pi\) | |||||||
\(180\) | −5819.37 | −2.40972 | ||||||||
\(181\) | −2669.80 | −1.09638 | −0.548190 | − | 0.836354i | \(-0.684683\pi\) | ||||
−0.548190 | + | 0.836354i | \(0.684683\pi\) | |||||||
\(182\) | −68.7231 | −0.0279895 | ||||||||
\(183\) | 3055.09 | 1.23409 | ||||||||
\(184\) | 830.536 | 0.332760 | ||||||||
\(185\) | 1173.08 | 0.466198 | ||||||||
\(186\) | −2.86683 | −0.00113014 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 237.277 | 0.0920489 | ||||||||
\(189\) | 791.989 | 0.304808 | ||||||||
\(190\) | 225.982 | 0.0862868 | ||||||||
\(191\) | −3394.56 | −1.28598 | −0.642988 | − | 0.765876i | \(-0.722306\pi\) | ||||
−0.642988 | + | 0.765876i | \(0.722306\pi\) | |||||||
\(192\) | 4154.98 | 1.56177 | ||||||||
\(193\) | −3003.88 | −1.12033 | −0.560165 | − | 0.828381i | \(-0.689262\pi\) | ||||
−0.560165 | + | 0.828381i | \(0.689262\pi\) | |||||||
\(194\) | 214.692 | 0.0794537 | ||||||||
\(195\) | −7531.01 | −2.76568 | ||||||||
\(196\) | 2634.81 | 0.960208 | ||||||||
\(197\) | −1636.63 | −0.591902 | −0.295951 | − | 0.955203i | \(-0.595637\pi\) | ||||
−0.295951 | + | 0.955203i | \(0.595637\pi\) | |||||||
\(198\) | −645.197 | −0.231576 | ||||||||
\(199\) | −1600.54 | −0.570146 | −0.285073 | − | 0.958506i | \(-0.592018\pi\) | ||||
−0.285073 | + | 0.958506i | \(0.592018\pi\) | |||||||
\(200\) | −91.1337 | −0.0322206 | ||||||||
\(201\) | −5828.14 | −2.04520 | ||||||||
\(202\) | −364.358 | −0.126911 | ||||||||
\(203\) | 515.587 | 0.178262 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1809.44 | 0.616470 | ||||||||
\(206\) | −243.402 | −0.0823235 | ||||||||
\(207\) | −7462.24 | −2.50561 | ||||||||
\(208\) | 3992.37 | 1.33087 | ||||||||
\(209\) | −975.452 | −0.322839 | ||||||||
\(210\) | 113.922 | 0.0374350 | ||||||||
\(211\) | 4282.36 | 1.39720 | 0.698602 | − | 0.715510i | \(-0.253806\pi\) | ||||
0.698602 | + | 0.715510i | \(0.253806\pi\) | |||||||
\(212\) | 2820.32 | 0.913680 | ||||||||
\(213\) | 2367.59 | 0.761619 | ||||||||
\(214\) | 76.8537 | 0.0245496 | ||||||||
\(215\) | −3778.65 | −1.19861 | ||||||||
\(216\) | 2458.66 | 0.774495 | ||||||||
\(217\) | −1.53339 | −0.000479693 0 | ||||||||
\(218\) | −586.414 | −0.182188 | ||||||||
\(219\) | −6670.44 | −2.05820 | ||||||||
\(220\) | 2077.83 | 0.636761 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −425.465 | −0.128628 | ||||||||
\(223\) | −1396.84 | −0.419460 | −0.209730 | − | 0.977759i | \(-0.567258\pi\) | ||||
−0.209730 | + | 0.977759i | \(0.567258\pi\) | |||||||
\(224\) | −189.267 | −0.0564551 | ||||||||
\(225\) | 818.822 | 0.242614 | ||||||||
\(226\) | −393.852 | −0.115923 | ||||||||
\(227\) | 1612.43 | 0.471458 | 0.235729 | − | 0.971819i | \(-0.424252\pi\) | ||||
0.235729 | + | 0.971819i | \(0.424252\pi\) | |||||||
\(228\) | 3190.99 | 0.926880 | ||||||||
\(229\) | −2530.45 | −0.730204 | −0.365102 | − | 0.930968i | \(-0.618966\pi\) | ||||
−0.365102 | + | 0.930968i | \(0.618966\pi\) | |||||||
\(230\) | −617.266 | −0.176962 | ||||||||
\(231\) | −491.743 | −0.140062 | ||||||||
\(232\) | 1600.60 | 0.452950 | ||||||||
\(233\) | 4689.59 | 1.31856 | 0.659282 | − | 0.751896i | \(-0.270860\pi\) | ||||
0.659282 | + | 0.751896i | \(0.270860\pi\) | |||||||
\(234\) | 1916.87 | 0.535512 | ||||||||
\(235\) | −357.225 | −0.0991607 | ||||||||
\(236\) | −1149.80 | −0.317143 | ||||||||
\(237\) | 7355.62 | 2.01603 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6332.33 | −1.71383 | −0.856913 | − | 0.515462i | \(-0.827620\pi\) | ||||
−0.856913 | + | 0.515462i | \(0.827620\pi\) | |||||||
\(240\) | −6618.14 | −1.78000 | ||||||||
\(241\) | 4438.39 | 1.18631 | 0.593157 | − | 0.805087i | \(-0.297881\pi\) | ||||
0.593157 | + | 0.805087i | \(0.297881\pi\) | |||||||
\(242\) | −365.372 | −0.0970537 | ||||||||
\(243\) | −5766.97 | −1.52243 | ||||||||
\(244\) | 2504.28 | 0.657049 | ||||||||
\(245\) | −3966.75 | −1.03439 | ||||||||
\(246\) | −656.265 | −0.170089 | ||||||||
\(247\) | 2898.06 | 0.746555 | ||||||||
\(248\) | −4.76029 | −0.00121886 | ||||||||
\(249\) | 9571.43 | 2.43600 | ||||||||
\(250\) | −589.248 | −0.149069 | ||||||||
\(251\) | 2085.26 | 0.524385 | 0.262193 | − | 0.965016i | \(-0.415554\pi\) | ||||
0.262193 | + | 0.965016i | \(0.415554\pi\) | |||||||
\(252\) | 1128.92 | 0.282203 | ||||||||
\(253\) | 2664.42 | 0.662098 | ||||||||
\(254\) | −583.383 | −0.144113 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3108.36 | 0.758876 | ||||||||
\(257\) | −537.124 | −0.130369 | −0.0651846 | − | 0.997873i | \(-0.520764\pi\) | ||||
−0.0651846 | + | 0.997873i | \(0.520764\pi\) | |||||||
\(258\) | 1370.48 | 0.330707 | ||||||||
\(259\) | −227.570 | −0.0545965 | ||||||||
\(260\) | −6173.22 | −1.47249 | ||||||||
\(261\) | −14381.1 | −3.41061 | ||||||||
\(262\) | −682.068 | −0.160833 | ||||||||
\(263\) | 6617.18 | 1.55146 | 0.775728 | − | 0.631068i | \(-0.217383\pi\) | ||||
0.775728 | + | 0.631068i | \(0.217383\pi\) | |||||||
\(264\) | −1526.58 | −0.355887 | ||||||||
\(265\) | −4246.03 | −0.984271 | ||||||||
\(266\) | −43.8390 | −0.0101051 | ||||||||
\(267\) | −15615.2 | −3.57915 | ||||||||
\(268\) | −4777.36 | −1.08890 | ||||||||
\(269\) | 617.429 | 0.139945 | 0.0699726 | − | 0.997549i | \(-0.477709\pi\) | ||||
0.0699726 | + | 0.997549i | \(0.477709\pi\) | |||||||
\(270\) | −1827.31 | −0.411877 | ||||||||
\(271\) | −5332.00 | −1.19519 | −0.597594 | − | 0.801799i | \(-0.703877\pi\) | ||||
−0.597594 | + | 0.801799i | \(0.703877\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1460.96 | 0.323889 | ||||||||
\(274\) | −1171.61 | −0.258319 | ||||||||
\(275\) | −292.364 | −0.0641099 | ||||||||
\(276\) | −8716.12 | −1.90090 | ||||||||
\(277\) | 2486.63 | 0.539376 | 0.269688 | − | 0.962948i | \(-0.413079\pi\) | ||||
0.269688 | + | 0.962948i | \(0.413079\pi\) | |||||||
\(278\) | 104.266 | 0.0224945 | ||||||||
\(279\) | 42.7704 | 0.00917777 | ||||||||
\(280\) | 189.164 | 0.0403739 | ||||||||
\(281\) | −4951.96 | −1.05128 | −0.525639 | − | 0.850708i | \(-0.676174\pi\) | ||||
−0.525639 | + | 0.850708i | \(0.676174\pi\) | |||||||
\(282\) | 129.562 | 0.0273592 | ||||||||
\(283\) | 8216.86 | 1.72594 | 0.862971 | − | 0.505253i | \(-0.168601\pi\) | ||||
0.862971 | + | 0.505253i | \(0.168601\pi\) | |||||||
\(284\) | 1940.73 | 0.405498 | ||||||||
\(285\) | −4804.10 | −0.998491 | ||||||||
\(286\) | −684.428 | −0.141507 | ||||||||
\(287\) | −351.018 | −0.0721949 | ||||||||
\(288\) | 5279.17 | 1.08013 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −1189.59 | −0.240879 | ||||||||
\(291\) | −4564.08 | −0.919420 | ||||||||
\(292\) | −5467.81 | −1.09582 | ||||||||
\(293\) | −737.775 | −0.147103 | −0.0735516 | − | 0.997291i | \(-0.523433\pi\) | ||||
−0.0735516 | + | 0.997291i | \(0.523433\pi\) | |||||||
\(294\) | 1438.70 | 0.285397 | ||||||||
\(295\) | 1731.05 | 0.341646 | ||||||||
\(296\) | −706.472 | −0.138726 | ||||||||
\(297\) | 7887.59 | 1.54102 | ||||||||
\(298\) | 192.354 | 0.0373917 | ||||||||
\(299\) | −7915.98 | −1.53108 | ||||||||
\(300\) | 956.410 | 0.184061 | ||||||||
\(301\) | 733.033 | 0.140370 | ||||||||
\(302\) | −614.539 | −0.117095 | ||||||||
\(303\) | 7745.77 | 1.46859 | ||||||||
\(304\) | 2546.77 | 0.480484 | ||||||||
\(305\) | −3770.23 | −0.707813 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5994.47 | 1.11441 | 0.557203 | − | 0.830377i | \(-0.311875\pi\) | ||||
0.557203 | + | 0.830377i | \(0.311875\pi\) | |||||||
\(308\) | −403.085 | −0.0745712 | ||||||||
\(309\) | 5174.42 | 0.952629 | ||||||||
\(310\) | 3.53791 | 0.000648193 0 | ||||||||
\(311\) | −9460.76 | −1.72498 | −0.862492 | − | 0.506070i | \(-0.831098\pi\) | ||||
−0.862492 | + | 0.506070i | \(0.831098\pi\) | |||||||
\(312\) | 4535.44 | 0.822977 | ||||||||
\(313\) | 4674.92 | 0.844225 | 0.422112 | − | 0.906544i | \(-0.361289\pi\) | ||||
0.422112 | + | 0.906544i | \(0.361289\pi\) | |||||||
\(314\) | 275.742 | 0.0495574 | ||||||||
\(315\) | −1699.61 | −0.304006 | ||||||||
\(316\) | 6029.45 | 1.07336 | ||||||||
\(317\) | −692.929 | −0.122772 | −0.0613861 | − | 0.998114i | \(-0.519552\pi\) | ||||
−0.0613861 | + | 0.998114i | \(0.519552\pi\) | |||||||
\(318\) | 1540.00 | 0.271568 | ||||||||
\(319\) | 5134.84 | 0.901241 | ||||||||
\(320\) | −5127.59 | −0.895753 | ||||||||
\(321\) | −1633.81 | −0.284082 | ||||||||
\(322\) | 119.745 | 0.0207241 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −12422.0 | −2.12997 | ||||||||
\(325\) | 868.611 | 0.148252 | ||||||||
\(326\) | 1549.02 | 0.263167 | ||||||||
\(327\) | 12466.4 | 2.10824 | ||||||||
\(328\) | −1089.71 | −0.183442 | ||||||||
\(329\) | 69.2991 | 0.0116127 | ||||||||
\(330\) | 1134.57 | 0.189261 | ||||||||
\(331\) | −7067.34 | −1.17358 | −0.586792 | − | 0.809738i | \(-0.699609\pi\) | ||||
−0.586792 | + | 0.809738i | \(0.699609\pi\) | |||||||
\(332\) | 7845.76 | 1.29696 | ||||||||
\(333\) | 6347.54 | 1.04457 | ||||||||
\(334\) | 1085.30 | 0.177799 | ||||||||
\(335\) | 7192.40 | 1.17302 | ||||||||
\(336\) | 1283.87 | 0.208455 | ||||||||
\(337\) | −5897.11 | −0.953223 | −0.476611 | − | 0.879114i | \(-0.658135\pi\) | ||||
−0.476611 | + | 0.879114i | \(0.658135\pi\) | |||||||
\(338\) | 1050.07 | 0.168984 | ||||||||
\(339\) | 8372.78 | 1.34144 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.2714 | −0.00242519 | ||||||||
\(342\) | 1222.79 | 0.193336 | ||||||||
\(343\) | 1550.87 | 0.244137 | ||||||||
\(344\) | 2275.64 | 0.356669 | ||||||||
\(345\) | 13122.3 | 2.04777 | ||||||||
\(346\) | −1277.04 | −0.198422 | ||||||||
\(347\) | −9529.27 | −1.47423 | −0.737115 | − | 0.675767i | \(-0.763812\pi\) | ||||
−0.737115 | + | 0.675767i | \(0.763812\pi\) | |||||||
\(348\) | −16797.6 | −2.58749 | ||||||||
\(349\) | −2516.87 | −0.386031 | −0.193016 | − | 0.981196i | \(-0.561827\pi\) | ||||
−0.193016 | + | 0.981196i | \(0.561827\pi\) | |||||||
\(350\) | −13.1395 | −0.00200668 | ||||||||
\(351\) | −23433.9 | −3.56356 | ||||||||
\(352\) | −1884.95 | −0.285421 | ||||||||
\(353\) | 9296.21 | 1.40166 | 0.700832 | − | 0.713327i | \(-0.252812\pi\) | ||||
0.700832 | + | 0.713327i | \(0.252812\pi\) | |||||||
\(354\) | −627.834 | −0.0942628 | ||||||||
\(355\) | −2921.81 | −0.436826 | ||||||||
\(356\) | −12799.9 | −1.90560 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 534.928 | 0.0789716 | ||||||||
\(359\) | 10477.8 | 1.54038 | 0.770192 | − | 0.637812i | \(-0.220160\pi\) | ||||
0.770192 | + | 0.637812i | \(0.220160\pi\) | |||||||
\(360\) | −5276.29 | −0.772458 | ||||||||
\(361\) | −5010.30 | −0.730472 | ||||||||
\(362\) | −1194.98 | −0.173499 | ||||||||
\(363\) | 7767.34 | 1.12308 | ||||||||
\(364\) | 1197.56 | 0.172443 | ||||||||
\(365\) | 8231.88 | 1.18048 | ||||||||
\(366\) | 1367.43 | 0.195291 | ||||||||
\(367\) | −2779.47 | −0.395332 | −0.197666 | − | 0.980269i | \(-0.563336\pi\) | ||||
−0.197666 | + | 0.980269i | \(0.563336\pi\) | |||||||
\(368\) | −6956.44 | −0.985406 | ||||||||
\(369\) | 9790.84 | 1.38128 | ||||||||
\(370\) | 525.060 | 0.0737745 | ||||||||
\(371\) | 823.702 | 0.115268 | ||||||||
\(372\) | 49.9572 | 0.00696280 | ||||||||
\(373\) | 2548.58 | 0.353782 | 0.176891 | − | 0.984230i | \(-0.443396\pi\) | ||||
0.176891 | + | 0.984230i | \(0.443396\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12526.7 | 1.72500 | ||||||||
\(376\) | 215.133 | 0.0295071 | ||||||||
\(377\) | −15255.6 | −2.08409 | ||||||||
\(378\) | 354.486 | 0.0482349 | ||||||||
\(379\) | 11378.4 | 1.54213 | 0.771067 | − | 0.636754i | \(-0.219723\pi\) | ||||
0.771067 | + | 0.636754i | \(0.219723\pi\) | |||||||
\(380\) | −3937.95 | −0.531612 | ||||||||
\(381\) | 12402.0 | 1.66764 | ||||||||
\(382\) | −1519.37 | −0.203502 | ||||||||
\(383\) | −633.266 | −0.0844867 | −0.0422433 | − | 0.999107i | \(-0.513450\pi\) | ||||
−0.0422433 | + | 0.999107i | \(0.513450\pi\) | |||||||
\(384\) | 8184.34 | 1.08764 | ||||||||
\(385\) | 606.852 | 0.0803326 | ||||||||
\(386\) | −1344.50 | −0.177289 | ||||||||
\(387\) | −20446.3 | −2.68564 | ||||||||
\(388\) | −3741.21 | −0.489513 | ||||||||
\(389\) | 12163.4 | 1.58537 | 0.792685 | − | 0.609632i | \(-0.208683\pi\) | ||||
0.792685 | + | 0.609632i | \(0.208683\pi\) | |||||||
\(390\) | −3370.80 | −0.437660 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 2388.92 | 0.307803 | ||||||||
\(393\) | 14499.9 | 1.86113 | ||||||||
\(394\) | −732.537 | −0.0936667 | ||||||||
\(395\) | −9077.45 | −1.15629 | ||||||||
\(396\) | 11243.1 | 1.42674 | ||||||||
\(397\) | 11911.8 | 1.50589 | 0.752944 | − | 0.658084i | \(-0.228633\pi\) | ||||
0.752944 | + | 0.658084i | \(0.228633\pi\) | |||||||
\(398\) | −716.384 | −0.0902239 | ||||||||
\(399\) | 931.962 | 0.116933 | ||||||||
\(400\) | 763.322 | 0.0954153 | ||||||||
\(401\) | −7875.79 | −0.980793 | −0.490396 | − | 0.871499i | \(-0.663148\pi\) | ||||
−0.490396 | + | 0.871499i | \(0.663148\pi\) | |||||||
\(402\) | −2608.62 | −0.323647 | ||||||||
\(403\) | 45.3711 | 0.00560818 | ||||||||
\(404\) | 6349.26 | 0.781900 | ||||||||
\(405\) | 18701.5 | 2.29453 | ||||||||
\(406\) | 230.772 | 0.0282094 | ||||||||
\(407\) | −2266.42 | −0.276025 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4351.34 | −0.526064 | −0.263032 | − | 0.964787i | \(-0.584722\pi\) | ||||
−0.263032 | + | 0.964787i | \(0.584722\pi\) | |||||||
\(410\) | 809.885 | 0.0975545 | ||||||||
\(411\) | 24906.9 | 2.98921 | ||||||||
\(412\) | 4241.51 | 0.507194 | ||||||||
\(413\) | −335.812 | −0.0400102 | ||||||||
\(414\) | −3340.02 | −0.396505 | ||||||||
\(415\) | −11811.9 | −1.39717 | ||||||||
\(416\) | 5600.17 | 0.660026 | ||||||||
\(417\) | −2216.57 | −0.260301 | ||||||||
\(418\) | −436.602 | −0.0510883 | ||||||||
\(419\) | 2066.20 | 0.240908 | 0.120454 | − | 0.992719i | \(-0.461565\pi\) | ||||
0.120454 | + | 0.992719i | \(0.461565\pi\) | |||||||
\(420\) | −1985.19 | −0.230637 | ||||||||
\(421\) | 10563.5 | 1.22289 | 0.611443 | − | 0.791289i | \(-0.290589\pi\) | ||||
0.611443 | + | 0.791289i | \(0.290589\pi\) | |||||||
\(422\) | 1916.74 | 0.221103 | ||||||||
\(423\) | −1932.94 | −0.222181 | ||||||||
\(424\) | 2557.11 | 0.292888 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1059.71 | 0.120524 | ||||||||
\(427\) | 731.399 | 0.0828920 | ||||||||
\(428\) | −1339.25 | −0.151250 | ||||||||
\(429\) | 14550.1 | 1.63749 | ||||||||
\(430\) | −1691.29 | −0.189677 | ||||||||
\(431\) | 4347.98 | 0.485928 | 0.242964 | − | 0.970035i | \(-0.421880\pi\) | ||||
0.242964 | + | 0.970035i | \(0.421880\pi\) | |||||||
\(432\) | −20593.4 | −2.29352 | ||||||||
\(433\) | 949.003 | 0.105326 | 0.0526630 | − | 0.998612i | \(-0.483229\pi\) | ||||
0.0526630 | + | 0.998612i | \(0.483229\pi\) | |||||||
\(434\) | −0.686331 | −7.59100e−5 0 | ||||||||
\(435\) | 25289.1 | 2.78740 | ||||||||
\(436\) | 10218.8 | 1.12246 | ||||||||
\(437\) | −5049.67 | −0.552765 | ||||||||
\(438\) | −2985.62 | −0.325704 | ||||||||
\(439\) | −7256.78 | −0.788946 | −0.394473 | − | 0.918908i | \(-0.629073\pi\) | ||||
−0.394473 | + | 0.918908i | \(0.629073\pi\) | |||||||
\(440\) | 1883.92 | 0.204119 | ||||||||
\(441\) | −21464.1 | −2.31769 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3674.08 | −0.394043 | −0.197021 | − | 0.980399i | \(-0.563127\pi\) | ||||
−0.197021 | + | 0.980399i | \(0.563127\pi\) | |||||||
\(444\) | 7414.12 | 0.792475 | ||||||||
\(445\) | 19270.4 | 2.05282 | ||||||||
\(446\) | −625.213 | −0.0663782 | ||||||||
\(447\) | −4089.19 | −0.432689 | ||||||||
\(448\) | 994.717 | 0.104902 | ||||||||
\(449\) | 13012.3 | 1.36769 | 0.683843 | − | 0.729630i | \(-0.260307\pi\) | ||||
0.683843 | + | 0.729630i | \(0.260307\pi\) | |||||||
\(450\) | 366.497 | 0.0383929 | ||||||||
\(451\) | −3495.86 | −0.364997 | ||||||||
\(452\) | 6863.23 | 0.714201 | ||||||||
\(453\) | 13064.3 | 1.35500 | ||||||||
\(454\) | 721.708 | 0.0746067 | ||||||||
\(455\) | −1802.95 | −0.185766 | ||||||||
\(456\) | 2893.20 | 0.297119 | ||||||||
\(457\) | −13.1283 | −0.00134380 | −0.000671900 | − | 1.00000i | \(-0.500214\pi\) | ||||
−0.000671900 | 1.00000i | \(0.500214\pi\) | ||||||||
\(458\) | −1132.60 | −0.115553 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 10756.4 | 1.09026 | ||||||||
\(461\) | −14382.6 | −1.45307 | −0.726537 | − | 0.687128i | \(-0.758871\pi\) | ||||
−0.726537 | + | 0.687128i | \(0.758871\pi\) | |||||||
\(462\) | −220.099 | −0.0221644 | ||||||||
\(463\) | −13264.3 | −1.33141 | −0.665705 | − | 0.746215i | \(-0.731869\pi\) | ||||
−0.665705 | + | 0.746215i | \(0.731869\pi\) | |||||||
\(464\) | −13406.4 | −1.34132 | ||||||||
\(465\) | −75.2114 | −0.00750075 | ||||||||
\(466\) | 2099.01 | 0.208659 | ||||||||
\(467\) | 12992.0 | 1.28736 | 0.643681 | − | 0.765294i | \(-0.277406\pi\) | ||||
0.643681 | + | 0.765294i | \(0.277406\pi\) | |||||||
\(468\) | −33403.3 | −3.29929 | ||||||||
\(469\) | −1395.28 | −0.137373 | ||||||||
\(470\) | −159.890 | −0.0156919 | ||||||||
\(471\) | −5861.92 | −0.573467 | ||||||||
\(472\) | −1042.50 | −0.101663 | ||||||||
\(473\) | 7300.43 | 0.709671 | ||||||||
\(474\) | 3292.30 | 0.319030 | ||||||||
\(475\) | 554.094 | 0.0535234 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −22975.3 | −2.20538 | ||||||||
\(478\) | −2834.29 | −0.271208 | ||||||||
\(479\) | −8697.74 | −0.829665 | −0.414833 | − | 0.909898i | \(-0.636160\pi\) | ||||
−0.414833 | + | 0.909898i | \(0.636160\pi\) | |||||||
\(480\) | −9283.37 | −0.882763 | ||||||||
\(481\) | 6733.50 | 0.638298 | ||||||||
\(482\) | 1986.58 | 0.187730 | ||||||||
\(483\) | −2545.63 | −0.239814 | ||||||||
\(484\) | 6366.94 | 0.597947 | ||||||||
\(485\) | 5632.46 | 0.527333 | ||||||||
\(486\) | −2581.24 | −0.240920 | ||||||||
\(487\) | −1219.66 | −0.113487 | −0.0567435 | − | 0.998389i | \(-0.518072\pi\) | ||||
−0.0567435 | + | 0.998389i | \(0.518072\pi\) | |||||||
\(488\) | 2270.57 | 0.210623 | ||||||||
\(489\) | −32930.2 | −3.04531 | ||||||||
\(490\) | −1775.48 | −0.163690 | ||||||||
\(491\) | 11340.1 | 1.04231 | 0.521154 | − | 0.853463i | \(-0.325502\pi\) | ||||
0.521154 | + | 0.853463i | \(0.325502\pi\) | |||||||
\(492\) | 11436.0 | 1.04792 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 1297.14 | 0.118140 | ||||||||
\(495\) | −16926.7 | −1.53697 | ||||||||
\(496\) | 39.8714 | 0.00360944 | ||||||||
\(497\) | 566.811 | 0.0511568 | ||||||||
\(498\) | 4284.07 | 0.385490 | ||||||||
\(499\) | 7357.73 | 0.660074 | 0.330037 | − | 0.943968i | \(-0.392939\pi\) | ||||
0.330037 | + | 0.943968i | \(0.392939\pi\) | |||||||
\(500\) | 10268.2 | 0.918414 | ||||||||
\(501\) | −23072.1 | −2.05745 | ||||||||
\(502\) | 933.343 | 0.0829824 | ||||||||
\(503\) | −4549.92 | −0.403321 | −0.201661 | − | 0.979455i | \(-0.564634\pi\) | ||||
−0.201661 | + | 0.979455i | \(0.564634\pi\) | |||||||
\(504\) | 1023.56 | 0.0904626 | ||||||||
\(505\) | −9558.93 | −0.842310 | ||||||||
\(506\) | 1192.57 | 0.104775 | ||||||||
\(507\) | −22323.2 | −1.95544 | ||||||||
\(508\) | 10166.0 | 0.887879 | ||||||||
\(509\) | −13630.1 | −1.18692 | −0.593461 | − | 0.804863i | \(-0.702239\pi\) | ||||
−0.593461 | + | 0.804863i | \(0.702239\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1596.93 | −0.138246 | ||||||||
\(512\) | 8272.35 | 0.714042 | ||||||||
\(513\) | −14948.7 | −1.28655 | ||||||||
\(514\) | −240.411 | −0.0206305 | ||||||||
\(515\) | −6385.66 | −0.546380 | ||||||||
\(516\) | −23881.9 | −2.03748 | ||||||||
\(517\) | 690.165 | 0.0587106 | ||||||||
\(518\) | −101.858 | −0.00863974 | ||||||||
\(519\) | 27148.2 | 2.29609 | ||||||||
\(520\) | −5597.11 | −0.472018 | ||||||||
\(521\) | −14004.2 | −1.17761 | −0.588805 | − | 0.808275i | \(-0.700402\pi\) | ||||
−0.588805 | + | 0.808275i | \(0.700402\pi\) | |||||||
\(522\) | −6436.84 | −0.539718 | ||||||||
\(523\) | −5652.21 | −0.472570 | −0.236285 | − | 0.971684i | \(-0.575930\pi\) | ||||
−0.236285 | + | 0.971684i | \(0.575930\pi\) | |||||||
\(524\) | 11885.7 | 0.990891 | ||||||||
\(525\) | 279.329 | 0.0232208 | ||||||||
\(526\) | 2961.78 | 0.245513 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 12786.4 | 1.05389 | ||||||||
\(529\) | 1626.06 | 0.133645 | ||||||||
\(530\) | −1900.48 | −0.155758 | ||||||||
\(531\) | 9366.69 | 0.765499 | ||||||||
\(532\) | 763.935 | 0.0622571 | ||||||||
\(533\) | 10386.2 | 0.844044 | ||||||||
\(534\) | −6989.20 | −0.566390 | ||||||||
\(535\) | 2016.26 | 0.162935 | ||||||||
\(536\) | −4331.52 | −0.349055 | ||||||||
\(537\) | −11371.9 | −0.913842 | ||||||||
\(538\) | 276.355 | 0.0221459 | ||||||||
\(539\) | 7663.84 | 0.612440 | ||||||||
\(540\) | 31842.6 | 2.53757 | ||||||||
\(541\) | −8809.75 | −0.700112 | −0.350056 | − | 0.936729i | \(-0.613837\pi\) | ||||
−0.350056 | + | 0.936729i | \(0.613837\pi\) | |||||||
\(542\) | −2386.55 | −0.189135 | ||||||||
\(543\) | 25403.7 | 2.00769 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15384.6 | −1.20918 | ||||||||
\(546\) | 653.913 | 0.0512544 | ||||||||
\(547\) | −2198.83 | −0.171874 | −0.0859372 | − | 0.996301i | \(-0.527388\pi\) | ||||
−0.0859372 | + | 0.996301i | \(0.527388\pi\) | |||||||
\(548\) | 20416.3 | 1.59150 | ||||||||
\(549\) | −20400.7 | −1.58594 | ||||||||
\(550\) | −130.859 | −0.0101452 | ||||||||
\(551\) | −9731.65 | −0.752418 | ||||||||
\(552\) | −7902.70 | −0.609350 | ||||||||
\(553\) | 1760.96 | 0.135414 | ||||||||
\(554\) | 1112.99 | 0.0853546 | ||||||||
\(555\) | −11162.1 | −0.853702 | ||||||||
\(556\) | −1816.93 | −0.138588 | ||||||||
\(557\) | 19799.3 | 1.50614 | 0.753072 | − | 0.657938i | \(-0.228571\pi\) | ||||
0.753072 | + | 0.657938i | \(0.228571\pi\) | |||||||
\(558\) | 19.1436 | 0.00145235 | ||||||||
\(559\) | −21689.5 | −1.64109 | ||||||||
\(560\) | −1584.41 | −0.119560 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2216.45 | −0.166362 | ||||||||
\(563\) | −20671.9 | −1.54745 | −0.773726 | − | 0.633521i | \(-0.781609\pi\) | ||||
−0.773726 | + | 0.633521i | \(0.781609\pi\) | |||||||
\(564\) | −2257.73 | −0.168560 | ||||||||
\(565\) | −10332.7 | −0.769381 | ||||||||
\(566\) | 3677.78 | 0.273125 | ||||||||
\(567\) | −3627.96 | −0.268712 | ||||||||
\(568\) | 1759.62 | 0.129986 | ||||||||
\(569\) | −10735.1 | −0.790928 | −0.395464 | − | 0.918481i | \(-0.629416\pi\) | ||||
−0.395464 | + | 0.918481i | \(0.629416\pi\) | |||||||
\(570\) | −2150.26 | −0.158008 | ||||||||
\(571\) | −1413.36 | −0.103586 | −0.0517929 | − | 0.998658i | \(-0.516494\pi\) | ||||
−0.0517929 | + | 0.998658i | \(0.516494\pi\) | |||||||
\(572\) | 11926.8 | 0.871825 | ||||||||
\(573\) | 32299.8 | 2.35488 | ||||||||
\(574\) | −157.112 | −0.0114246 | ||||||||
\(575\) | −1513.50 | −0.109769 | ||||||||
\(576\) | −27745.3 | −2.00704 | ||||||||
\(577\) | 13903.6 | 1.00314 | 0.501572 | − | 0.865116i | \(-0.332755\pi\) | ||||
0.501572 | + | 0.865116i | \(0.332755\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 28582.4 | 2.05155 | ||||||||
\(580\) | 20729.6 | 1.48405 | ||||||||
\(581\) | 2291.43 | 0.163623 | ||||||||
\(582\) | −2042.84 | −0.145495 | ||||||||
\(583\) | 8203.42 | 0.582763 | ||||||||
\(584\) | −4957.53 | −0.351274 | ||||||||
\(585\) | 50289.2 | 3.55419 | ||||||||
\(586\) | −330.220 | −0.0232786 | ||||||||
\(587\) | 7153.64 | 0.503002 | 0.251501 | − | 0.967857i | \(-0.419076\pi\) | ||||
0.251501 | + | 0.967857i | \(0.419076\pi\) | |||||||
\(588\) | −25070.7 | −1.75833 | ||||||||
\(589\) | 28.9426 | 0.00202472 | ||||||||
\(590\) | 774.800 | 0.0540644 | ||||||||
\(591\) | 15572.8 | 1.08389 | ||||||||
\(592\) | 5917.30 | 0.410810 | ||||||||
\(593\) | −22686.9 | −1.57106 | −0.785530 | − | 0.618824i | \(-0.787610\pi\) | ||||
−0.785530 | + | 0.618824i | \(0.787610\pi\) | |||||||
\(594\) | 3530.40 | 0.243862 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3351.94 | −0.230370 | ||||||||
\(597\) | 15229.4 | 1.04405 | ||||||||
\(598\) | −3543.11 | −0.242289 | ||||||||
\(599\) | 9190.22 | 0.626882 | 0.313441 | − | 0.949608i | \(-0.398518\pi\) | ||||
0.313441 | + | 0.949608i | \(0.398518\pi\) | |||||||
\(600\) | 867.154 | 0.0590024 | ||||||||
\(601\) | −12350.7 | −0.838260 | −0.419130 | − | 0.907926i | \(-0.637665\pi\) | ||||
−0.419130 | + | 0.907926i | \(0.637665\pi\) | |||||||
\(602\) | 328.098 | 0.0222131 | ||||||||
\(603\) | 38918.1 | 2.62830 | ||||||||
\(604\) | 10708.9 | 0.721423 | ||||||||
\(605\) | −9585.54 | −0.644145 | ||||||||
\(606\) | 3466.93 | 0.232400 | ||||||||
\(607\) | 22662.6 | 1.51540 | 0.757698 | − | 0.652606i | \(-0.226324\pi\) | ||||
0.757698 | + | 0.652606i | \(0.226324\pi\) | |||||||
\(608\) | 3572.40 | 0.238289 | ||||||||
\(609\) | −4905.91 | −0.326432 | ||||||||
\(610\) | −1687.52 | −0.112009 | ||||||||
\(611\) | −2050.47 | −0.135766 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5314.94 | 0.350193 | 0.175097 | − | 0.984551i | \(-0.443976\pi\) | ||||
0.175097 | + | 0.984551i | \(0.443976\pi\) | |||||||
\(614\) | 2683.06 | 0.176351 | ||||||||
\(615\) | −17217.1 | −1.12888 | ||||||||
\(616\) | −365.468 | −0.0239044 | ||||||||
\(617\) | 7956.05 | 0.519122 | 0.259561 | − | 0.965727i | \(-0.416422\pi\) | ||||
0.259561 | + | 0.965727i | \(0.416422\pi\) | |||||||
\(618\) | 2316.02 | 0.150751 | ||||||||
\(619\) | −13874.9 | −0.900933 | −0.450467 | − | 0.892793i | \(-0.648742\pi\) | ||||
−0.450467 | + | 0.892793i | \(0.648742\pi\) | |||||||
\(620\) | −61.6513 | −0.00399351 | ||||||||
\(621\) | 40832.1 | 2.63854 | ||||||||
\(622\) | −4234.54 | −0.272974 | ||||||||
\(623\) | −3738.33 | −0.240406 | ||||||||
\(624\) | −37988.2 | −2.43709 | ||||||||
\(625\) | −17069.8 | −1.09247 | ||||||||
\(626\) | 2092.45 | 0.133596 | ||||||||
\(627\) | 9281.60 | 0.591183 | ||||||||
\(628\) | −4805.06 | −0.305323 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −760.727 | −0.0481081 | ||||||||
\(631\) | −23668.0 | −1.49320 | −0.746598 | − | 0.665276i | \(-0.768314\pi\) | ||||
−0.746598 | + | 0.665276i | \(0.768314\pi\) | |||||||
\(632\) | 5466.76 | 0.344076 | ||||||||
\(633\) | −40747.5 | −2.55856 | ||||||||
\(634\) | −310.148 | −0.0194283 | ||||||||
\(635\) | −15305.1 | −0.956477 | ||||||||
\(636\) | −26835.8 | −1.67313 | ||||||||
\(637\) | −22769.2 | −1.41625 | ||||||||
\(638\) | 2298.30 | 0.142619 | ||||||||
\(639\) | −15809.9 | −0.978762 | ||||||||
\(640\) | −10100.2 | −0.623818 | ||||||||
\(641\) | −18274.3 | −1.12604 | −0.563021 | − | 0.826442i | \(-0.690361\pi\) | ||||
−0.563021 | + | 0.826442i | \(0.690361\pi\) | |||||||
\(642\) | −731.277 | −0.0449552 | ||||||||
\(643\) | 19527.2 | 1.19763 | 0.598815 | − | 0.800887i | \(-0.295639\pi\) | ||||
0.598815 | + | 0.800887i | \(0.295639\pi\) | |||||||
\(644\) | −2086.67 | −0.127681 | ||||||||
\(645\) | 35954.6 | 2.19490 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4471.27 | −0.271690 | −0.135845 | − | 0.990730i | \(-0.543375\pi\) | ||||
−0.135845 | + | 0.990730i | \(0.543375\pi\) | |||||||
\(648\) | −11262.7 | −0.682778 | ||||||||
\(649\) | −3344.42 | −0.202280 | ||||||||
\(650\) | 388.781 | 0.0234604 | ||||||||
\(651\) | 14.5905 | 0.000878413 0 | ||||||||
\(652\) | −26993.1 | −1.62137 | ||||||||
\(653\) | −10869.7 | −0.651399 | −0.325699 | − | 0.945473i | \(-0.605600\pi\) | ||||
−0.325699 | + | 0.945473i | \(0.605600\pi\) | |||||||
\(654\) | 5579.84 | 0.333622 | ||||||||
\(655\) | −17894.1 | −1.06745 | ||||||||
\(656\) | 9127.21 | 0.543228 | ||||||||
\(657\) | 44542.6 | 2.64501 | ||||||||
\(658\) | 31.0176 | 0.00183768 | ||||||||
\(659\) | −3827.54 | −0.226252 | −0.113126 | − | 0.993581i | \(-0.536086\pi\) | ||||
−0.113126 | + | 0.993581i | \(0.536086\pi\) | |||||||
\(660\) | −19771.0 | −1.16604 | ||||||||
\(661\) | 15347.3 | 0.903087 | 0.451543 | − | 0.892249i | \(-0.350874\pi\) | ||||
0.451543 | + | 0.892249i | \(0.350874\pi\) | |||||||
\(662\) | −3163.27 | −0.185716 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7113.57 | 0.415753 | ||||||||
\(665\) | −1150.12 | −0.0670672 | ||||||||
\(666\) | 2841.09 | 0.165301 | ||||||||
\(667\) | 26581.8 | 1.54310 | ||||||||
\(668\) | −18912.3 | −1.09542 | ||||||||
\(669\) | 13291.2 | 0.768114 | ||||||||
\(670\) | 3219.25 | 0.185627 | ||||||||
\(671\) | 7284.16 | 0.419079 | ||||||||
\(672\) | 1800.91 | 0.103380 | ||||||||
\(673\) | 26133.5 | 1.49684 | 0.748418 | − | 0.663227i | \(-0.230814\pi\) | ||||
0.748418 | + | 0.663227i | \(0.230814\pi\) | |||||||
\(674\) | −2639.49 | −0.150845 | ||||||||
\(675\) | −4480.45 | −0.255486 | ||||||||
\(676\) | −18298.5 | −1.04111 | ||||||||
\(677\) | 19539.0 | 1.10922 | 0.554612 | − | 0.832109i | \(-0.312867\pi\) | ||||
0.554612 | + | 0.832109i | \(0.312867\pi\) | |||||||
\(678\) | 3747.57 | 0.212278 | ||||||||
\(679\) | −1092.66 | −0.0617561 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15342.6 | −0.863332 | ||||||||
\(682\) | −6.83531 | −0.000383779 0 | ||||||||
\(683\) | −16057.8 | −0.899612 | −0.449806 | − | 0.893126i | \(-0.648507\pi\) | ||||
−0.449806 | + | 0.893126i | \(0.648507\pi\) | |||||||
\(684\) | −21308.2 | −1.19114 | ||||||||
\(685\) | −30737.1 | −1.71446 | ||||||||
\(686\) | 694.152 | 0.0386339 | ||||||||
\(687\) | 24077.7 | 1.33715 | ||||||||
\(688\) | −19060.4 | −1.05621 | ||||||||
\(689\) | −24372.3 | −1.34762 | ||||||||
\(690\) | 5873.40 | 0.324053 | ||||||||
\(691\) | 14698.6 | 0.809206 | 0.404603 | − | 0.914493i | \(-0.367410\pi\) | ||||
0.404603 | + | 0.914493i | \(0.367410\pi\) | |||||||
\(692\) | 22253.6 | 1.22248 | ||||||||
\(693\) | 3283.67 | 0.179995 | ||||||||
\(694\) | −4265.20 | −0.233292 | ||||||||
\(695\) | 2735.43 | 0.149296 | ||||||||
\(696\) | −15230.0 | −0.829441 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −1126.53 | −0.0610883 | ||||||||
\(699\) | −44622.3 | −2.41455 | ||||||||
\(700\) | 228.968 | 0.0123631 | ||||||||
\(701\) | −7042.75 | −0.379459 | −0.189730 | − | 0.981836i | \(-0.560761\pi\) | ||||
−0.189730 | + | 0.981836i | \(0.560761\pi\) | |||||||
\(702\) | −10488.8 | −0.563923 | ||||||||
\(703\) | 4295.36 | 0.230445 | ||||||||
\(704\) | 9906.60 | 0.530354 | ||||||||
\(705\) | 3399.06 | 0.181583 | ||||||||
\(706\) | 4160.89 | 0.221809 | ||||||||
\(707\) | 1854.37 | 0.0986431 | ||||||||
\(708\) | 10940.6 | 0.580752 | ||||||||
\(709\) | −5951.66 | −0.315260 | −0.157630 | − | 0.987498i | \(-0.550385\pi\) | ||||
−0.157630 | + | 0.987498i | \(0.550385\pi\) | |||||||
\(710\) | −1307.77 | −0.0691265 | ||||||||
\(711\) | −49118.0 | −2.59082 | ||||||||
\(712\) | −11605.3 | −0.610855 | ||||||||
\(713\) | −79.0561 | −0.00415242 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17956.0 | −0.939182 | ||||||||
\(716\) | −9321.61 | −0.486543 | ||||||||
\(717\) | 60253.3 | 3.13835 | ||||||||
\(718\) | 4689.76 | 0.243761 | ||||||||
\(719\) | 34823.3 | 1.80625 | 0.903123 | − | 0.429381i | \(-0.141268\pi\) | ||||
0.903123 | + | 0.429381i | \(0.141268\pi\) | |||||||
\(720\) | 44193.4 | 2.28749 | ||||||||
\(721\) | 1238.77 | 0.0639866 | ||||||||
\(722\) | −2242.56 | −0.115595 | ||||||||
\(723\) | −42232.1 | −2.17238 | ||||||||
\(724\) | 20823.6 | 1.06892 | ||||||||
\(725\) | −2916.79 | −0.149416 | ||||||||
\(726\) | 3476.58 | 0.177725 | ||||||||
\(727\) | −3241.15 | −0.165348 | −0.0826738 | − | 0.996577i | \(-0.526346\pi\) | ||||
−0.0826738 | + | 0.996577i | \(0.526346\pi\) | |||||||
\(728\) | 1085.80 | 0.0552781 | ||||||||
\(729\) | 11872.9 | 0.603204 | ||||||||
\(730\) | 3684.51 | 0.186808 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −23828.7 | −1.20319 | ||||||||
\(733\) | 18578.8 | 0.936185 | 0.468093 | − | 0.883679i | \(-0.344941\pi\) | ||||
0.468093 | + | 0.883679i | \(0.344941\pi\) | |||||||
\(734\) | −1244.06 | −0.0625601 | ||||||||
\(735\) | 37744.4 | 1.89418 | ||||||||
\(736\) | −9757.92 | −0.488698 | ||||||||
\(737\) | −13895.9 | −0.694519 | ||||||||
\(738\) | 4382.28 | 0.218583 | ||||||||
\(739\) | 30393.0 | 1.51289 | 0.756444 | − | 0.654058i | \(-0.226935\pi\) | ||||
0.756444 | + | 0.654058i | \(0.226935\pi\) | |||||||
\(740\) | −9149.64 | −0.454524 | ||||||||
\(741\) | −27575.6 | −1.36709 | ||||||||
\(742\) | 368.681 | 0.0182408 | ||||||||
\(743\) | −37449.0 | −1.84908 | −0.924542 | − | 0.381081i | \(-0.875552\pi\) | ||||
−0.924542 | + | 0.381081i | \(0.875552\pi\) | |||||||
\(744\) | 45.2950 | 0.00223198 | ||||||||
\(745\) | 5046.40 | 0.248169 | ||||||||
\(746\) | 1140.72 | 0.0559849 | ||||||||
\(747\) | −63914.3 | −3.13052 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −391.140 | −0.0190814 | ||||||||
\(750\) | 5606.80 | 0.272975 | ||||||||
\(751\) | 5541.28 | 0.269247 | 0.134623 | − | 0.990897i | \(-0.457018\pi\) | ||||
0.134623 | + | 0.990897i | \(0.457018\pi\) | |||||||
\(752\) | −1801.92 | −0.0873795 | ||||||||
\(753\) | −19841.7 | −0.960253 | ||||||||
\(754\) | −6828.23 | −0.329801 | ||||||||
\(755\) | −16122.5 | −0.777160 | ||||||||
\(756\) | −6177.25 | −0.297175 | ||||||||
\(757\) | 13531.4 | 0.649680 | 0.324840 | − | 0.945769i | \(-0.394690\pi\) | ||||
0.324840 | + | 0.945769i | \(0.394690\pi\) | |||||||
\(758\) | 5092.85 | 0.244038 | ||||||||
\(759\) | −25352.5 | −1.21243 | ||||||||
\(760\) | −3570.45 | −0.170413 | ||||||||
\(761\) | −37110.8 | −1.76776 | −0.883879 | − | 0.467715i | \(-0.845077\pi\) | ||||
−0.883879 | + | 0.467715i | \(0.845077\pi\) | |||||||
\(762\) | 5551.00 | 0.263899 | ||||||||
\(763\) | 2984.50 | 0.141607 | ||||||||
\(764\) | 26476.4 | 1.25377 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −283.444 | −0.0133698 | ||||||||
\(767\) | 9936.24 | 0.467766 | ||||||||
\(768\) | −29576.6 | −1.38965 | ||||||||
\(769\) | −820.351 | −0.0384689 | −0.0192345 | − | 0.999815i | \(-0.506123\pi\) | ||||
−0.0192345 | + | 0.999815i | \(0.506123\pi\) | |||||||
\(770\) | 271.621 | 0.0127124 | ||||||||
\(771\) | 5110.84 | 0.238732 | ||||||||
\(772\) | 23429.2 | 1.09227 | ||||||||
\(773\) | −25113.2 | −1.16851 | −0.584255 | − | 0.811570i | \(-0.698613\pi\) | ||||
−0.584255 | + | 0.811570i | \(0.698613\pi\) | |||||||
\(774\) | −9151.55 | −0.424994 | ||||||||
\(775\) | 8.67473 | 0.000402072 0 | ||||||||
\(776\) | −3392.07 | −0.156918 | ||||||||
\(777\) | 2165.37 | 0.0999771 | ||||||||
\(778\) | 5444.21 | 0.250880 | ||||||||
\(779\) | 6625.43 | 0.304725 | ||||||||
\(780\) | 58739.3 | 2.69642 | ||||||||
\(781\) | 5644.99 | 0.258634 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 78691.0 | 3.59155 | ||||||||
\(784\) | −20009.2 | −0.911499 | ||||||||
\(785\) | 7234.10 | 0.328912 | ||||||||
\(786\) | 6490.00 | 0.294517 | ||||||||
\(787\) | 20784.0 | 0.941384 | 0.470692 | − | 0.882298i | \(-0.344004\pi\) | ||||
0.470692 | + | 0.882298i | \(0.344004\pi\) | |||||||
\(788\) | 12765.1 | 0.577080 | ||||||||
\(789\) | −62963.7 | −2.84102 | ||||||||
\(790\) | −4062.97 | −0.182980 | ||||||||
\(791\) | 2004.47 | 0.0901023 | ||||||||
\(792\) | 10193.9 | 0.457354 | ||||||||
\(793\) | −21641.2 | −0.969105 | ||||||||
\(794\) | 5331.62 | 0.238302 | ||||||||
\(795\) | 40401.8 | 1.80240 | ||||||||
\(796\) | 12483.7 | 0.555868 | ||||||||
\(797\) | 4974.23 | 0.221074 | 0.110537 | − | 0.993872i | \(-0.464743\pi\) | ||||
0.110537 | + | 0.993872i | \(0.464743\pi\) | |||||||
\(798\) | 417.137 | 0.0185044 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 1070.73 | 0.0473198 | ||||||||
\(801\) | 104272. | 4.59960 | ||||||||
\(802\) | −3525.12 | −0.155207 | ||||||||
\(803\) | −15904.1 | −0.698935 | ||||||||
\(804\) | 45457.5 | 1.99398 | ||||||||
\(805\) | 3141.52 | 0.137545 | ||||||||
\(806\) | 20.3076 | 0.000887477 0 | ||||||||
\(807\) | −5874.95 | −0.256268 | ||||||||
\(808\) | 5756.73 | 0.250645 | ||||||||
\(809\) | −27460.1 | −1.19338 | −0.596692 | − | 0.802471i | \(-0.703519\pi\) | ||||
−0.596692 | + | 0.802471i | \(0.703519\pi\) | |||||||
\(810\) | 8370.59 | 0.363102 | ||||||||
\(811\) | −14356.6 | −0.621612 | −0.310806 | − | 0.950473i | \(-0.600599\pi\) | ||||
−0.310806 | + | 0.950473i | \(0.600599\pi\) | |||||||
\(812\) | −4021.40 | −0.173798 | ||||||||
\(813\) | 50735.0 | 2.18863 | ||||||||
\(814\) | −1014.43 | −0.0436801 | ||||||||
\(815\) | 40638.6 | 1.74664 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13835.9 | −0.592482 | ||||||||
\(818\) | −1947.62 | −0.0832480 | ||||||||
\(819\) | −9755.76 | −0.416232 | ||||||||
\(820\) | −14113.0 | −0.601033 | ||||||||
\(821\) | 15953.0 | 0.678155 | 0.339077 | − | 0.940758i | \(-0.389885\pi\) | ||||
0.339077 | + | 0.940758i | \(0.389885\pi\) | |||||||
\(822\) | 11148.1 | 0.473033 | ||||||||
\(823\) | 17581.1 | 0.744641 | 0.372321 | − | 0.928104i | \(-0.378562\pi\) | ||||
0.372321 | + | 0.928104i | \(0.378562\pi\) | |||||||
\(824\) | 3845.67 | 0.162585 | ||||||||
\(825\) | 2781.90 | 0.117398 | ||||||||
\(826\) | −150.306 | −0.00633149 | ||||||||
\(827\) | −39492.2 | −1.66056 | −0.830278 | − | 0.557349i | \(-0.811818\pi\) | ||||
−0.830278 | + | 0.557349i | \(0.811818\pi\) | |||||||
\(828\) | 58202.9 | 2.44286 | ||||||||
\(829\) | 15789.1 | 0.661494 | 0.330747 | − | 0.943720i | \(-0.392699\pi\) | ||||
0.330747 | + | 0.943720i | \(0.392699\pi\) | |||||||
\(830\) | −5286.90 | −0.221098 | ||||||||
\(831\) | −23660.7 | −0.987704 | ||||||||
\(832\) | −29432.4 | −1.22642 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −992.112 | −0.0411919 | ||||||||
\(835\) | 28472.8 | 1.18005 | ||||||||
\(836\) | 7608.19 | 0.314755 | ||||||||
\(837\) | −234.032 | −0.00966469 | ||||||||
\(838\) | 924.812 | 0.0381230 | ||||||||
\(839\) | −9439.37 | −0.388419 | −0.194209 | − | 0.980960i | \(-0.562214\pi\) | ||||
−0.194209 | + | 0.980960i | \(0.562214\pi\) | |||||||
\(840\) | −1799.93 | −0.0739326 | ||||||||
\(841\) | 26839.0 | 1.10046 | ||||||||
\(842\) | 4728.13 | 0.193518 | ||||||||
\(843\) | 47118.8 | 1.92510 | ||||||||
\(844\) | −33401.0 | −1.36222 | ||||||||
\(845\) | 27548.7 | 1.12154 | ||||||||
\(846\) | −865.164 | −0.0351595 | ||||||||
\(847\) | 1859.53 | 0.0754359 | ||||||||
\(848\) | −21418.0 | −0.867331 | ||||||||
\(849\) | −78185.0 | −3.16054 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11732.7 | −0.472610 | ||||||||
\(852\) | −18466.4 | −0.742546 | ||||||||
\(853\) | −2324.12 | −0.0932898 | −0.0466449 | − | 0.998912i | \(-0.514853\pi\) | ||||
−0.0466449 | + | 0.998912i | \(0.514853\pi\) | |||||||
\(854\) | 327.367 | 0.0131174 | ||||||||
\(855\) | 32079.9 | 1.28317 | ||||||||
\(856\) | −1214.26 | −0.0484844 | ||||||||
\(857\) | 22464.0 | 0.895399 | 0.447699 | − | 0.894184i | \(-0.352244\pi\) | ||||
0.447699 | + | 0.894184i | \(0.352244\pi\) | |||||||
\(858\) | 6512.46 | 0.259128 | ||||||||
\(859\) | −1314.36 | −0.0522064 | −0.0261032 | − | 0.999659i | \(-0.508310\pi\) | ||||
−0.0261032 | + | 0.999659i | \(0.508310\pi\) | |||||||
\(860\) | 29472.2 | 1.16860 | ||||||||
\(861\) | 3340.00 | 0.132203 | ||||||||
\(862\) | 1946.11 | 0.0768966 | ||||||||
\(863\) | −15380.5 | −0.606674 | −0.303337 | − | 0.952883i | \(-0.598101\pi\) | ||||
−0.303337 | + | 0.952883i | \(0.598101\pi\) | |||||||
\(864\) | −28886.7 | −1.13744 | ||||||||
\(865\) | −33503.1 | −1.31693 | ||||||||
\(866\) | 424.764 | 0.0166675 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 11.9599 | 0.000467681 0 | ||||||||
\(869\) | 17537.8 | 0.684614 | ||||||||
\(870\) | 11319.1 | 0.441097 | ||||||||
\(871\) | 41284.5 | 1.60605 | ||||||||
\(872\) | 9265.14 | 0.359813 | ||||||||
\(873\) | 30477.2 | 1.18155 | ||||||||
\(874\) | −2260.18 | −0.0874734 | ||||||||
\(875\) | 2998.93 | 0.115865 | ||||||||
\(876\) | 52027.2 | 2.00666 | ||||||||
\(877\) | 14688.9 | 0.565574 | 0.282787 | − | 0.959183i | \(-0.408741\pi\) | ||||
0.282787 | + | 0.959183i | \(0.408741\pi\) | |||||||
\(878\) | −3248.06 | −0.124848 | ||||||||
\(879\) | 7020.06 | 0.269375 | ||||||||
\(880\) | −15779.4 | −0.604460 | ||||||||
\(881\) | −9512.25 | −0.363764 | −0.181882 | − | 0.983320i | \(-0.558219\pi\) | ||||
−0.181882 | + | 0.983320i | \(0.558219\pi\) | |||||||
\(882\) | −9607.11 | −0.366767 | ||||||||
\(883\) | 14662.1 | 0.558798 | 0.279399 | − | 0.960175i | \(-0.409865\pi\) | ||||
0.279399 | + | 0.960175i | \(0.409865\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16471.2 | −0.625621 | ||||||||
\(886\) | −1644.48 | −0.0623561 | ||||||||
\(887\) | 27847.1 | 1.05413 | 0.527065 | − | 0.849825i | \(-0.323292\pi\) | ||||
0.527065 | + | 0.849825i | \(0.323292\pi\) | |||||||
\(888\) | 6722.21 | 0.254034 | ||||||||
\(889\) | 2969.08 | 0.112013 | ||||||||
\(890\) | 8625.25 | 0.324853 | ||||||||
\(891\) | −36131.6 | −1.35853 | ||||||||
\(892\) | 10894.9 | 0.408956 | ||||||||
\(893\) | −1308.01 | −0.0490157 | ||||||||
\(894\) | −1830.28 | −0.0684717 | ||||||||
\(895\) | 14033.8 | 0.524134 | ||||||||
\(896\) | 1959.36 | 0.0730554 | ||||||||
\(897\) | 75322.0 | 2.80371 | ||||||||
\(898\) | 5824.20 | 0.216432 | ||||||||
\(899\) | −152.356 | −0.00565222 | ||||||||
\(900\) | −6386.54 | −0.236538 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −1564.71 | −0.0577597 | ||||||||
\(903\) | −6974.95 | −0.257045 | ||||||||
\(904\) | 6222.72 | 0.228943 | ||||||||
\(905\) | −31350.2 | −1.15151 | ||||||||
\(906\) | 5847.46 | 0.214425 | ||||||||
\(907\) | 141.986 | 0.00519799 | 0.00259899 | − | 0.999997i | \(-0.499173\pi\) | ||||
0.00259899 | + | 0.999997i | \(0.499173\pi\) | |||||||
\(908\) | −12576.4 | −0.459651 | ||||||||
\(909\) | −51723.3 | −1.88730 | ||||||||
\(910\) | −806.983 | −0.0293969 | ||||||||
\(911\) | 32439.3 | 1.17976 | 0.589881 | − | 0.807490i | \(-0.299175\pi\) | ||||
0.589881 | + | 0.807490i | \(0.299175\pi\) | |||||||
\(912\) | −24233.0 | −0.879862 | ||||||||
\(913\) | 22820.9 | 0.827230 | ||||||||
\(914\) | −5.87610 | −0.000212652 0 | ||||||||
\(915\) | 35874.5 | 1.29615 | ||||||||
\(916\) | 19736.6 | 0.711918 | ||||||||
\(917\) | 3471.32 | 0.125009 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11802.3 | 0.423638 | 0.211819 | − | 0.977309i | \(-0.432061\pi\) | ||||
0.211819 | + | 0.977309i | \(0.432061\pi\) | |||||||
\(920\) | 9752.59 | 0.349493 | ||||||||
\(921\) | −57038.5 | −2.04070 | ||||||||
\(922\) | −6437.53 | −0.229944 | ||||||||
\(923\) | −16771.2 | −0.598083 | ||||||||
\(924\) | 3835.43 | 0.136555 | ||||||||
\(925\) | 1287.41 | 0.0457620 | ||||||||
\(926\) | −5936.95 | −0.210691 | ||||||||
\(927\) | −34552.8 | −1.22423 | ||||||||
\(928\) | −18805.3 | −0.665210 | ||||||||
\(929\) | 30089.9 | 1.06267 | 0.531334 | − | 0.847163i | \(-0.321691\pi\) | ||||
0.531334 | + | 0.847163i | \(0.321691\pi\) | |||||||
\(930\) | −33.6639 | −0.00118697 | ||||||||
\(931\) | −14524.7 | −0.511307 | ||||||||
\(932\) | −36577.2 | −1.28554 | ||||||||
\(933\) | 90020.9 | 3.15879 | ||||||||
\(934\) | 5815.09 | 0.203721 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −30285.9 | −1.05761 | ||||||||
\(937\) | −34961.5 | −1.21894 | −0.609468 | − | 0.792810i | \(-0.708617\pi\) | ||||
−0.609468 | + | 0.792810i | \(0.708617\pi\) | |||||||
\(938\) | −624.512 | −0.0217389 | ||||||||
\(939\) | −44482.8 | −1.54594 | ||||||||
\(940\) | 2786.23 | 0.0966775 | ||||||||
\(941\) | −8933.80 | −0.309494 | −0.154747 | − | 0.987954i | \(-0.549456\pi\) | ||||
−0.154747 | + | 0.987954i | \(0.549456\pi\) | |||||||
\(942\) | −2623.74 | −0.0907494 | ||||||||
\(943\) | −18097.2 | −0.624948 | ||||||||
\(944\) | 8731.81 | 0.301055 | ||||||||
\(945\) | 9299.95 | 0.320135 | ||||||||
\(946\) | 3267.60 | 0.112303 | ||||||||
\(947\) | −17816.2 | −0.611350 | −0.305675 | − | 0.952136i | \(-0.598882\pi\) | ||||
−0.305675 | + | 0.952136i | \(0.598882\pi\) | |||||||
\(948\) | −57371.4 | −1.96554 | ||||||||
\(949\) | 47251.1 | 1.61626 | ||||||||
\(950\) | 248.007 | 0.00846991 | ||||||||
\(951\) | 6593.35 | 0.224820 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36249.3 | 1.23214 | 0.616070 | − | 0.787691i | \(-0.288724\pi\) | ||||
0.616070 | + | 0.787691i | \(0.288724\pi\) | |||||||
\(954\) | −10283.5 | −0.348994 | ||||||||
\(955\) | −39860.7 | −1.35064 | ||||||||
\(956\) | 49390.0 | 1.67091 | ||||||||
\(957\) | −48858.9 | −1.65035 | ||||||||
\(958\) | −3893.02 | −0.131292 | ||||||||
\(959\) | 5962.79 | 0.200781 | ||||||||
\(960\) | 48789.9 | 1.64030 | ||||||||
\(961\) | −29790.5 | −0.999985 | ||||||||
\(962\) | 3013.85 | 0.101009 | ||||||||
\(963\) | 10910.0 | 0.365076 | ||||||||
\(964\) | −34617.9 | −1.15661 | ||||||||
\(965\) | −35273.1 | −1.17666 | ||||||||
\(966\) | −1139.40 | −0.0379499 | ||||||||
\(967\) | 10020.3 | 0.333227 | 0.166613 | − | 0.986022i | \(-0.446717\pi\) | ||||
0.166613 | + | 0.986022i | \(0.446717\pi\) | |||||||
\(968\) | 5772.75 | 0.191677 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2521.03 | 0.0834489 | ||||||||
\(971\) | 24562.5 | 0.811789 | 0.405894 | − | 0.913920i | \(-0.366960\pi\) | ||||
0.405894 | + | 0.913920i | \(0.366960\pi\) | |||||||
\(972\) | 44980.4 | 1.48431 | ||||||||
\(973\) | −530.654 | −0.0174841 | ||||||||
\(974\) | −545.908 | −0.0179590 | ||||||||
\(975\) | −8264.99 | −0.271479 | ||||||||
\(976\) | −19017.9 | −0.623718 | ||||||||
\(977\) | −17102.8 | −0.560048 | −0.280024 | − | 0.959993i | \(-0.590342\pi\) | ||||
−0.280024 | + | 0.959993i | \(0.590342\pi\) | |||||||
\(978\) | −14739.2 | −0.481911 | ||||||||
\(979\) | −37230.9 | −1.21543 | ||||||||
\(980\) | 30939.3 | 1.00849 | ||||||||
\(981\) | −83245.8 | −2.70931 | ||||||||
\(982\) | 5075.73 | 0.164942 | ||||||||
\(983\) | −51204.2 | −1.66140 | −0.830702 | − | 0.556718i | \(-0.812061\pi\) | ||||
−0.830702 | + | 0.556718i | \(0.812061\pi\) | |||||||
\(984\) | 10368.8 | 0.335919 | ||||||||
\(985\) | −19218.1 | −0.621665 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −659.394 | −0.0212652 | ||||||||
\(988\) | −22603.9 | −0.727859 | ||||||||
\(989\) | 37792.5 | 1.21510 | ||||||||
\(990\) | −7576.24 | −0.243221 | ||||||||
\(991\) | −19176.3 | −0.614686 | −0.307343 | − | 0.951599i | \(-0.599440\pi\) | ||||
−0.307343 | + | 0.951599i | \(0.599440\pi\) | |||||||
\(992\) | 55.9283 | 0.00179005 | ||||||||
\(993\) | 67247.0 | 2.14906 | ||||||||
\(994\) | 253.699 | 0.00809541 | ||||||||
\(995\) | −18794.4 | −0.598815 | ||||||||
\(996\) | −74653.9 | −2.37500 | ||||||||
\(997\) | −18251.7 | −0.579775 | −0.289888 | − | 0.957061i | \(-0.593618\pi\) | ||||
−0.289888 | + | 0.957061i | \(0.593618\pi\) | |||||||
\(998\) | 3293.24 | 0.104455 | ||||||||
\(999\) | −34732.6 | −1.09999 |
(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 | 289.4.a.h.1.7 | ✓ | 12 | |
17.4 | even | 4 | 289.4.b.f.288.11 | 24 | |||
17.13 | even | 4 | 289.4.b.f.288.12 | 24 | |||
17.16 | even | 2 | 289.4.a.i.1.7 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.4.a.h.1.7 | ✓ | 12 | 1.1 | even | 1 | trivial | |
289.4.a.i.1.7 | yes | 12 | 17.16 | even | 2 | ||
289.4.b.f.288.11 | 24 | 17.4 | even | 4 | |||
289.4.b.f.288.12 | 24 | 17.13 | even | 4 |